TSTP Solution File: SWV345-1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SWV345-1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n032.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Apr 30 16:45:14 EDT 2024
% Result : Unsatisfiable 10.60s 1.93s
% Output : Refutation 10.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 4752
% Syntax : Number of formulae : 8415 (3051 unt; 0 def)
% Number of atoms : 18551 (3428 equ)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 17504 (7368 ~;7604 |; 0 &)
% (2532 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 4 avg)
% Maximal term depth : 10 ( 1 avg)
% Number of predicates : 2602 (2600 usr;2533 prp; 0-3 aty)
% Number of functors : 277 ( 277 usr; 66 con; 0-18 aty)
% Number of variables : 12318 (12318 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f32552,plain,
$false,
inference(avatar_sat_refutation,[],[f3415,f3420,f3425,f3430,f3435,f3440,f3445,f3450,f3455,f3460,f3465,f3470,f3475,f3480,f3485,f3490,f3495,f3500,f3505,f3510,f3515,f3520,f3525,f3530,f3535,f3540,f3545,f3550,f3555,f3560,f3565,f3570,f3575,f3580,f3585,f3590,f3595,f3600,f3605,f3610,f3615,f3620,f3625,f3630,f3635,f3640,f3645,f3650,f3655,f3660,f3665,f3670,f3675,f3680,f3685,f3690,f3695,f3700,f3705,f3710,f3715,f3720,f3725,f3730,f3735,f3740,f3745,f3750,f3755,f3760,f3765,f3770,f3775,f3780,f3785,f3790,f3795,f3800,f3805,f3810,f3815,f3820,f3825,f3830,f3835,f3840,f3845,f3850,f3855,f3860,f3865,f3870,f3875,f3880,f3885,f3890,f3895,f3899,f3904,f3909,f3913,f3917,f3922,f3927,f3931,f3935,f3940,f3945,f3950,f3955,f3960,f3965,f3970,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,f6104,f6109,f6114,f6118,f6122,f6126,f6131,f6135,f6140,f6144,f6148,f6152,f6157,f6162,f6167,f6172,f6177,f6182,f6187,f6191,f6196,f6963,f6968,f6972,f6976,f6980,f6984,f6988,f6992,f6996,f7000,f7004,f7008,f7013,f7018,f7023,f7027,f7031,f7035,f7040,f7044,f7048,f7052,f7056,f7060,f7064,f7068,f7073,f7078,f7083,f7088,f7093,f7098,f7103,f7108,f7113,f7118,f7123,f7128,f7133,f7138,f7143,f7148,f7152,f7156,f7160,f7164,f7168,f7172,f7177,f7182,f7187,f7191,f7195,f7199,f7203,f7207,f7211,f7216,f7221,f7225,f7230,f7235,f7239,f7243,f7247,f7251,f7255,f7259,f7263,f7267,f7272,f7277,f7281,f7286,f7291,f7295,f7300,f7304,f7309,f7316,f7325,f7332,f7337,f7341,f7345,f7349,f7353,f7357,f7361,f7365,f7369,f7373,f7377,f7382,f7386,f7390,f7394,f7398,f7402,f7406,f7410,f7414,f7418,f7422,f7426,f7430,f7434,f7438,f7442,f7446,f7450,f7454,f7458,f7462,f7466,f7470,f7474,f7478,f7482,f7486,f7490,f7494,f7498,f7502,f7506,f7510,f7514,f7518,f7522,f7526,f7531,f7535,f7539,f7543,f7547,f7551,f7555,f7559,f7563,f7567,f7571,f7575,f7579,f7583,f7587,f7591,f7595,f7599,f7603,f7607,f7611,f7615,f7619,f7623,f7627,f7631,f7635,f7639,f7643,f7647,f7651,f7655,f7659,f7663,f7667,f7672,f7676,f7681,f7685,f7690,f7694,f7708,f7712,f7716,f7720,f7724,f7728,f7732,f7736,f7740,f7744,f7748,f7752,f7756,f7760,f7764,f7768,f7772,f7776,f7780,f7784,f7788,f7792,f7796,f7800,f7804,f7808,f7812,f7816,f7820,f7824,f7828,f7832,f7836,f7840,f7844,f7848,f7852,f7856,f7860,f7864,f7868,f7872,f7876,f7880,f7884,f7888,f7892,f7896,f7900,f7904,f7908,f7912,f7916,f7920,f7924,f7928,f7932,f7936,f7940,f7944,f7948,f7952,f7956,f7960,f7964,f7968,f7972,f7976,f7980,f7984,f7989,f7993,f7998,f8002,f8006,f8010,f8026,f8056,f8077,f8089,f8095,f8101,f8110,f8114,f8118,f8122,f8127,f8131,f8135,f8139,f8143,f8147,f8151,f8155,f8159,f8163,f8167,f8172,f8176,f8180,f8184,f8188,f8192,f8196,f8200,f8204,f8208,f8217,f8221,f8225,f8229,f8233,f8237,f8241,f8245,f8249,f8253,f8257,f8261,f8265,f8269,f8273,f8277,f8281,f8285,f8289,f8293,f8297,f8301,f8305,f8309,f8313,f8317,f8321,f8325,f8329,f8333,f8337,f8342,f8346,f8350,f8354,f8358,f8362,f8366,f8370,f8374,f8378,f8383,f8387,f8391,f8395,f8399,f8403,f8407,f8411,f8415,f8419,f8424,f8429,f8433,f8437,f8441,f8445,f8449,f8453,f8457,f8461,f8465,f8469,f8474,f8478,f8482,f8486,f8490,f8494,f8498,f8502,f8506,f8510,f8514,f8518,f8522,f8526,f8631,f8660,f8668,f8672,f8676,f8680,f8684,f8688,f8692,f8696,f8700,f8704,f8708,f8712,f8717,f8721,f8725,f8729,f8733,f8737,f8741,f8745,f8749,f8753,f8757,f8761,f8765,f8769,f8773,f8777,f8781,f8785,f8789,f8793,f8797,f8801,f8805,f8809,f8813,f8817,f8821,f8825,f8829,f8833,f8837,f8841,f8845,f8849,f8853,f8857,f8861,f8865,f8869,f8873,f8877,f8881,f8885,f8889,f8893,f8897,f8901,f8905,f8909,f8913,f8917,f8921,f8925,f8929,f8933,f8937,f8941,f8945,f8949,f8953,f8957,f8961,f8965,f8969,f8973,f8977,f8981,f8985,f8989,f8993,f8997,f9001,f9005,f9009,f9013,f9017,f9021,f9025,f9029,f9033,f9037,f9041,f9045,f9049,f9053,f9057,f9061,f9065,f9069,f9073,f9077,f9098,f9151,f9184,f9203,f9251,f9275,f9291,f9326,f9330,f9334,f9338,f9342,f9346,f9350,f9354,f9358,f9362,f9366,f9370,f9375,f9379,f9383,f9387,f9391,f9395,f9399,f9403,f9407,f9411,f9415,f9419,f9423,f9427,f9431,f9435,f9439,f9443,f9447,f9451,f9456,f9460,f9464,f9468,f9472,f9476,f9480,f9484,f9488,f9492,f9496,f9500,f9504,f9508,f9512,f9516,f9520,f9524,f9528,f9532,f9536,f9540,f9544,f9548,f9552,f9556,f9560,f9564,f9568,f9572,f9576,f9580,f9584,f9588,f9592,f9596,f9600,f9604,f9608,f9612,f9616,f9620,f9624,f9628,f9632,f9636,f9640,f9644,f9648,f9652,f9656,f9660,f9664,f9668,f9672,f9677,f9681,f9685,f9690,f9697,f9701,f9705,f9709,f9713,f9717,f9722,f9726,f9779,f9835,f9860,f9900,f9926,f9934,f9964,f9983,f9987,f9991,f9995,f9999,f10003,f10007,f10011,f10016,f10020,f10024,f10028,f10032,f10036,f10040,f10044,f10048,f10052,f10056,f10060,f10064,f10068,f10072,f10076,f10080,f10084,f10088,f10092,f10096,f10100,f10104,f10108,f10112,f10117,f10121,f10125,f10129,f10133,f10137,f10141,f10145,f10149,f10153,f10157,f10162,f10166,f10170,f10174,f10178,f10182,f10186,f10190,f10194,f10198,f10202,f10211,f10215,f10219,f10223,f10227,f10231,f10235,f10239,f10243,f10247,f10257,f10261,f10265,f10269,f10273,f10277,f10281,f10285,f10290,f10304,f10308,f10312,f10316,f10320,f10324,f10328,f10362,f10637,f10722,f10726,f10730,f10734,f10738,f10742,f10746,f10750,f10754,f10758,f10762,f10766,f10770,f10774,f10778,f10782,f10786,f10790,f10794,f10802,f10806,f10810,f10814,f10818,f10822,f10826,f10830,f10834,f10838,f10846,f10850,f10855,f10860,f10864,f10868,f10872,f10876,f10880,f10884,f10888,f10892,f10896,f10900,f10904,f10908,f10912,f10916,f10920,f10924,f10929,f10933,f10937,f10941,f10945,f10949,f10953,f10957,f10961,f10965,f10969,f10974,f10978,f10982,f10986,f10990,f10994,f10998,f11002,f11006,f11010,f11017,f11021,f11025,f11029,f11033,f11037,f11041,f11045,f11049,f11053,f11063,f11067,f11071,f11075,f11079,f11083,f11087,f11091,f11095,f11099,f11116,f11120,f11124,f11128,f11132,f11136,f11140,f11144,f11148,f11152,f11162,f11166,f11170,f11174,f11178,f11182,f11186,f11190,f11194,f11198,f11215,f11219,f11223,f11227,f11231,f11235,f11239,f11243,f11247,f11251,f11255,f11259,f11263,f11267,f11271,f11275,f11279,f11283,f11287,f11291,f11295,f11299,f11303,f11307,f11311,f11315,f11319,f11323,f11327,f11331,f11335,f11339,f11403,f11591,f11801,f11898,f12359,f12363,f12367,f12371,f12375,f12390,f12394,f12398,f12402,f12406,f12410,f12414,f12418,f12422,f12426,f12431,f12435,f12439,f12443,f12447,f12451,f12455,f12459,f12463,f12467,f12471,f12481,f12485,f12489,f12493,f12497,f12501,f12505,f12509,f12513,f12517,f12526,f12530,f12534,f12538,f12542,f12546,f12550,f12554,f12558,f12562,f12570,f12574,f12578,f12582,f12586,f12590,f12594,f12598,f12602,f12606,f12615,f12619,f12623,f12627,f12631,f12635,f12639,f12643,f12647,f12651,f12659,f12663,f12667,f12671,f12675,f12679,f12683,f12687,f12691,f12695,f12699,f12703,f12707,f12711,f12715,f12719,f12723,f12727,f12731,f12735,f12739,f12746,f12750,f12754,f12758,f12762,f12766,f12770,f12774,f12778,f12782,f12790,f12794,f12798,f12802,f12806,f12810,f12814,f12819,f12826,f12830,f12834,f12838,f12843,f12851,f12855,f12860,f12891,f12895,f12905,f12909,f12913,f12917,f12921,f13156,f13499,f13604,f13787,f13906,f14073,f14217,f14221,f14225,f14229,f14233,f14237,f14241,f14245,f14249,f14253,f14257,f14261,f14265,f14269,f14273,f14277,f14281,f14285,f14289,f14293,f14297,f14301,f14305,f14309,f14313,f14317,f14321,f14325,f14329,f14333,f14337,f14341,f14345,f14349,f14353,f14357,f14361,f14365,f14369,f14373,f14377,f14381,f14385,f14389,f14393,f14397,f14401,f14406,f14410,f14414,f14418,f14422,f14426,f14430,f14434,f14438,f14442,f14446,f14450,f14454,f14458,f14462,f14466,f14470,f14474,f14478,f14482,f14486,f14490,f14516,f14520,f14524,f14528,f14532,f14536,f14540,f14544,f14548,f14552,f14577,f14582,f14591,f14595,f14599,f14603,f15086,f15572,f15625,f15629,f15633,f15637,f15641,f15645,f15649,f15653,f15657,f15661,f15665,f15669,f15673,f15677,f15681,f15685,f15689,f15693,f15697,f15701,f15705,f15709,f15713,f15717,f15721,f15725,f15729,f15733,f15737,f15741,f15745,f15749,f15753,f15757,f15761,f15765,f15769,f15773,f15777,f15781,f15785,f15789,f15793,f15797,f15801,f15805,f15809,f15813,f15817,f15821,f15825,f15829,f15833,f15837,f15841,f15845,f15849,f15853,f15857,f15861,f15865,f15869,f15873,f15878,f15902,f15907,f15925,f15930,f15954,f15958,f15962,f15966,f15970,f15974,f15978,f15982,f15986,f15990,f15994,f15998,f16113,f16310,f16594,f16888,f16956,f16960,f16969,f16973,f16977,f16981,f16985,f16989,f16993,f16997,f17001,f17005,f17009,f17013,f17017,f17021,f17025,f17029,f17033,f17037,f17041,f17045,f17050,f17107,f17111,f17115,f17119,f17123,f17127,f17131,f17135,f17139,f17143,f17162,f17166,f17170,f17174,f17178,f17182,f17186,f17190,f17194,f17198,f17202,f17206,f17210,f17214,f17218,f17222,f17226,f17230,f17234,f17238,f17242,f17247,f17251,f17255,f17259,f17263,f17267,f17271,f17275,f17279,f17283,f17287,f17292,f17296,f17324,f17329,f17387,f17392,f17487,f17492,f17496,f17595,f17600,f17632,f17637,f17655,f17660,f17668,f17672,f17677,f17685,f17689,f17695,f17701,f17705,f17709,f17715,f17721,f17725,f17729,f17733,f17737,f17741,f17747,f17780,f17784,f17795,f17803,f17967,f18077,f18352,f18864,f19074,f19078,f19082,f19086,f19090,f19094,f19098,f19102,f19106,f19110,f19114,f19127,f19131,f19135,f19139,f19143,f19147,f19151,f19155,f19159,f19163,f19176,f19180,f19184,f19188,f19192,f19196,f19200,f19204,f19208,f19212,f19217,f19221,f19225,f19229,f19233,f19237,f19241,f19245,f19249,f19253,f19257,f19274,f19278,f19282,f19286,f19290,f19294,f19298,f19302,f19306,f19310,f19315,f19319,f19323,f19327,f19331,f19337,f19363,f19369,f19454,f19470,f19495,f19499,f19503,f19508,f19513,f19518,f19524,f19528,f19533,f19538,f19542,f19546,f19550,f19555,f19577,f19589,f19593,f19597,f19602,f19607,f19612,f19618,f19623,f19627,f19633,f19638,f19651,f19655,f19660,f19669,f19673,f19677,f19681,f19685,f19689,f20013,f20177,f20450,f20734,f20738,f20742,f20746,f20750,f20754,f20758,f20764,f20770,f20774,f20778,f20782,f20786,f20790,f20794,f20798,f20802,f20806,f20810,f20814,f20818,f20822,f20826,f20830,f20834,f20838,f20842,f20846,f20850,f20854,f20858,f20862,f20866,f20870,f20874,f20878,f20882,f20886,f20890,f20894,f20898,f20902,f20919,f20923,f20927,f20931,f20935,f20941,f21277,f21281,f21507,f22000,f22197,f22241,f22245,f22249,f22253,f22257,f22262,f22266,f22293,f22298,f22302,f22306,f22310,f22314,f22318,f22322,f22326,f22330,f22357,f22361,f22365,f22369,f22427,f22439,f22465,f22721,f22859,f22863,f22867,f22871,f22875,f22879,f22883,f22887,f22891,f22895,f22899,f22903,f22907,f22911,f22915,f22919,f22923,f22927,f22931,f22935,f22939,f22944,f22949,f22955,f22987,f22992,f23005,f23009,f23013,f23018,f23039,f23044,f23078,f23082,f23086,f23091,f23212,f23417,f23421,f23533,f23537,f23541,f23545,f23549,f23553,f23557,f23561,f23578,f23582,f23586,f23590,f23594,f23598,f23602,f23606,f23610,f23614,f23618,f23622,f23626,f23630,f23634,f23638,f23642,f23646,f23650,f23654,f23658,f23669,f23673,f23677,f23681,f23685,f23689,f23693,f23697,f23701,f23705,f23709,f23713,f23717,f23721,f23725,f23729,f23733,f23737,f23741,f23745,f23749,f23753,f23757,f23761,f23765,f23769,f23773,f23777,f23781,f23785,f23789,f23793,f23809,f23813,f23820,f23840,f23847,f23870,f23874,f23878,f23894,f23900,f23962,f23966,f23970,f23974,f23978,f23982,f23986,f23995,f23999,f24004,f24031,f24037,f24380,f24422,f24430,f24892,f25019,f25023,f25027,f25031,f25035,f25070,f25074,f25078,f25082,f25086,f25090,f25094,f25098,f25102,f25106,f25110,f25114,f25118,f25122,f25126,f25130,f25134,f25138,f25142,f25146,f25150,f25162,f25166,f25170,f25174,f25178,f25332,f25777,f25899,f25903,f25907,f25911,f25915,f25926,f25930,f25934,f25938,f25942,f25946,f25950,f25954,f25958,f25962,f25967,f25971,f25975,f25979,f25983,f25987,f25991,f25995,f26000,f26025,f26048,f26098,f26102,f26106,f26111,f26243,f26907,f26911,f26915,f26919,f26923,f26927,f26931,f26935,f26940,f26945,f26949,f26959,f26963,f26967,f26971,f26975,f26979,f26985,f26991,f27073,f27077,f27081,f27085,f27089,f27094,f27104,f27108,f27198,f27202,f27421,f27629,f27689,f27693,f27697,f27701,f27705,f27709,f27713,f27910,f27914,f27918,f27922,f27926,f27930,f27934,f27938,f27942,f27946,f27950,f27954,f27958,f27962,f27966,f27970,f28261,f28326,f28330,f28334,f28338,f28342,f28347,f28493,f28497,f28501,f28505,f28509,f28513,f28517,f28521,f28525,f28529,f28533,f28537,f28541,f28545,f28549,f28553,f28564,f28568,f28572,f28576,f28580,f28584,f28588,f28592,f28596,f28600,f28607,f28611,f28619,f28625,f28633,f28639,f28655,f28661,f28732,f28738,f28751,f28756,f28900,f29467,f29471,f29475,f29487,f29491,f29495,f29499,f29503,f29508,f29594,f29598,f29602,f29606,f29610,f29614,f29618,f29622,f29912,f29930,f29934,f30032,f30036,f30040,f30044,f30048,f30053,f30057,f30061,f30067,f30087,f30233,f30237,f30241,f30245,f30383,f30387,f30391,f30395,f30400,f30405,f30410,f30415,f30438,f30442,f30446,f30450,f30454,f30493,f30497,f30501,f30509,f30513,f30517,f30521,f30653,f30673,f30678,f30682,f30710,f30714,f30718,f30722,f30728,f30733,f30738,f30743,f30823,f30827,f30835,f30839,f30859,f30863,f30867,f30873,f30878,f30905,f30940,f30947,f30986,f30992,f31012,f31051,f31057,f31073,f31077,f31081,f31086,f31125,f31129,f31133,f31137,f31291,f31298,f31342,f31346,f31350,f31354,f31394,f31410,f31414,f31430,f31451,f31474,f31478,f31482,f31524,f31547,f31560,f31569,f31620,f31628,f31659,f31664,f31728,f31733,f31737,f31741,f31745,f31749,f31753,f31757,f31761,f31768,f31773,f32031,f32092,f32096,f32201,f32206,f32216,f32221,f32231,f32236,f32246,f32256,f32262,f32266,f32271,f32275,f32287,f32291,f32295,f32299,f32303,f32307,f32312,f32316,f32325,f32330,f32335,f32339,f32343,f32347,f32351,f32355,f32382,f32386,f32390,f32406,f32413,f32423,f32454,f32472,f32476,f32486,f32490,f32494,f32499,f32503,f32508,f32512,f32516,f32520,f32524,f32528,f32532,f32536,f32541,f32546,f32550,f32551]) ).
fof(f32551,plain,
( spl0_3
| ~ spl0_749
| ~ spl0_2484 ),
inference(avatar_split_clause,[],[f32247,f32244,f7334,f3422]) ).
fof(f3422,plain,
( spl0_3
<=> c_Message_Omsg_ONonce(v_NB) = v_nb ),
introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).
fof(f7334,plain,
( spl0_749
<=> c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_Aa,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_ONonce(v_NB))))),v_X)),c_List_Oset(v_evso,tc_Event_Oevent),tc_Event_Oevent) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_749])]) ).
fof(f32244,plain,
( spl0_2484
<=> ! [X4,X0,X3,X2,X1] :
( ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,X0,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(X0),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(X1),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K),c_Message_Omsg_OMPair(X2,X3)))),X4)),c_List_Oset(v_evso,tc_Event_Oevent),tc_Event_Oevent)
| v_nb = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2484])]) ).
fof(f32247,plain,
( c_Message_Omsg_ONonce(v_NB) = v_nb
| ~ spl0_749
| ~ spl0_2484 ),
inference(resolution,[],[f32245,f7336]) ).
fof(f7336,plain,
( c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_Aa,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_ONonce(v_NB))))),v_X)),c_List_Oset(v_evso,tc_Event_Oevent),tc_Event_Oevent)
| ~ spl0_749 ),
inference(avatar_component_clause,[],[f7334]) ).
fof(f32245,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,X0,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(X0),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(X1),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K),c_Message_Omsg_OMPair(X2,X3)))),X4)),c_List_Oset(v_evso,tc_Event_Oevent),tc_Event_Oevent)
| v_nb = X3 )
| ~ spl0_2484 ),
inference(avatar_component_clause,[],[f32244]) ).
fof(f32550,plain,
( spl0_2532
| ~ spl0_1025
| ~ spl0_1537 ),
inference(avatar_split_clause,[],[f13716,f12649,f8666,f32548]) ).
fof(f32548,plain,
( spl0_2532
<=> ! [X0] : c_Divides_Oop_Advd(c_GCD_Ogcd(X0),c_Main_Osurj__pair__1(X0,tc_nat,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2532])]) ).
fof(f8666,plain,
( spl0_1025
<=> ! [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_1025])]) ).
fof(f12649,plain,
( spl0_1537
<=> ! [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_1537])]) ).
fof(f13716,plain,
( ! [X0] : c_Divides_Oop_Advd(c_GCD_Ogcd(X0),c_Main_Osurj__pair__1(X0,tc_nat,tc_nat),tc_nat)
| ~ spl0_1025
| ~ spl0_1537 ),
inference(superposition,[],[f8667,f12650]) ).
fof(f12650,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_1537 ),
inference(avatar_component_clause,[],[f12649]) ).
fof(f8667,plain,
( ! [X21,X15] : c_Divides_Oop_Advd(c_GCD_Ogcd(c_Pair(X15,X21,tc_nat,tc_nat)),X15,tc_nat)
| ~ spl0_1025 ),
inference(avatar_component_clause,[],[f8666]) ).
fof(f32546,plain,
( spl0_2531
| ~ spl0_1026
| ~ spl0_1537 ),
inference(avatar_split_clause,[],[f13715,f12649,f8670,f32544]) ).
fof(f32544,plain,
( spl0_2531
<=> ! [X0] : c_Divides_Oop_Advd(c_GCD_Ogcd(X0),c_Main_Osurj__pair__2(X0,tc_nat,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2531])]) ).
fof(f8670,plain,
( spl0_1026
<=> ! [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_1026])]) ).
fof(f13715,plain,
( ! [X0] : c_Divides_Oop_Advd(c_GCD_Ogcd(X0),c_Main_Osurj__pair__2(X0,tc_nat,tc_nat),tc_nat)
| ~ spl0_1026
| ~ spl0_1537 ),
inference(superposition,[],[f8671,f12650]) ).
fof(f8671,plain,
( ! [X21,X15] : c_Divides_Oop_Advd(c_GCD_Ogcd(c_Pair(X15,X21,tc_nat,tc_nat)),X21,tc_nat)
| ~ spl0_1026 ),
inference(avatar_component_clause,[],[f8670]) ).
fof(f32541,plain,
( spl0_2530
| ~ spl0_1025
| ~ spl0_1536 ),
inference(avatar_split_clause,[],[f13710,f12645,f8666,f32539]) ).
fof(f32539,plain,
( spl0_2530
<=> ! [X0] : c_Divides_Oop_Advd(c_GCD_Ogcd(X0),c_fst(X0,tc_nat,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2530])]) ).
fof(f12645,plain,
( spl0_1536
<=> ! [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_1536])]) ).
fof(f13710,plain,
( ! [X0] : c_Divides_Oop_Advd(c_GCD_Ogcd(X0),c_fst(X0,tc_nat,tc_nat),tc_nat)
| ~ spl0_1025
| ~ spl0_1536 ),
inference(superposition,[],[f8667,f12646]) ).
fof(f12646,plain,
( ! [X2,X3,X1] : c_Pair(c_fst(X3,X1,X2),c_snd(X3,X1,X2),X1,X2) = X3
| ~ spl0_1536 ),
inference(avatar_component_clause,[],[f12645]) ).
fof(f32536,plain,
( spl0_2529
| ~ spl0_1026
| ~ spl0_1536 ),
inference(avatar_split_clause,[],[f13709,f12645,f8670,f32534]) ).
fof(f32534,plain,
( spl0_2529
<=> ! [X0] : c_Divides_Oop_Advd(c_GCD_Ogcd(X0),c_snd(X0,tc_nat,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2529])]) ).
fof(f13709,plain,
( ! [X0] : c_Divides_Oop_Advd(c_GCD_Ogcd(X0),c_snd(X0,tc_nat,tc_nat),tc_nat)
| ~ spl0_1026
| ~ spl0_1536 ),
inference(superposition,[],[f8671,f12646]) ).
fof(f32532,plain,
( spl0_2528
| ~ spl0_816
| ~ spl0_1501 ),
inference(avatar_split_clause,[],[f13197,f12491,f7605,f32530]) ).
fof(f32530,plain,
( spl0_2528
<=> ! [X2,X0,X1] : c_emptyset != c_List_Oset(c_List_Olist_OCons(X0,X1,X2),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2528])]) ).
fof(f7605,plain,
( spl0_816
<=> ! [X12,X1,X18] : c_emptyset != c_insert(X18,X12,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_816])]) ).
fof(f12491,plain,
( spl0_1501
<=> ! [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_1501])]) ).
fof(f13197,plain,
( ! [X2,X0,X1] : c_emptyset != c_List_Oset(c_List_Olist_OCons(X0,X1,X2),X2)
| ~ spl0_816
| ~ spl0_1501 ),
inference(superposition,[],[f7606,f12492]) ).
fof(f12492,plain,
( ! [X41,X0,X23] : c_List_Oset(c_List_Olist_OCons(X0,X23,X41),X41) = c_insert(X0,c_List_Oset(X23,X41),X41)
| ~ spl0_1501 ),
inference(avatar_component_clause,[],[f12491]) ).
fof(f7606,plain,
( ! [X18,X1,X12] : c_emptyset != c_insert(X18,X12,X1)
| ~ spl0_816 ),
inference(avatar_component_clause,[],[f7605]) ).
fof(f32528,plain,
( spl0_2527
| ~ spl0_785
| ~ spl0_1494 ),
inference(avatar_split_clause,[],[f13131,f12457,f7480,f32526]) ).
fof(f32526,plain,
( spl0_2527
<=> ! [X0,X1] :
( c_List_Otl(X0,X1) != X0
| c_List_Olist_ONil = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2527])]) ).
fof(f7480,plain,
( spl0_785
<=> ! [X0,X81,X1] : c_List_Olist_OCons(X0,X81,X1) != X81 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_785])]) ).
fof(f12457,plain,
( spl0_1494
<=> ! [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_1494])]) ).
fof(f13131,plain,
( ! [X0,X1] :
( c_List_Otl(X0,X1) != X0
| c_List_Olist_ONil = X0 )
| ~ spl0_785
| ~ spl0_1494 ),
inference(superposition,[],[f7481,f12458]) ).
fof(f12458,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_1494 ),
inference(avatar_component_clause,[],[f12457]) ).
fof(f7481,plain,
( ! [X0,X1,X81] : c_List_Olist_OCons(X0,X81,X1) != X81
| ~ spl0_785 ),
inference(avatar_component_clause,[],[f7480]) ).
fof(f32524,plain,
( spl0_2526
| ~ spl0_1020
| ~ spl0_1486 ),
inference(avatar_split_clause,[],[f13073,f12424,f8516,f32522]) ).
fof(f32522,plain,
( spl0_2526
<=> ! [X0,X1] :
( ~ c_Divides_Oop_Advd(X1,c_1,tc_nat)
| c_Divides_Oop_Advd(X1,X0,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2526])]) ).
fof(f8516,plain,
( spl0_1020
<=> ! [X15] : c_1 = c_GCD_Ogcd(c_Pair(X15,c_1,tc_nat,tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1020])]) ).
fof(f12424,plain,
( spl0_1486
<=> ! [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_1486])]) ).
fof(f13073,plain,
( ! [X0,X1] :
( ~ c_Divides_Oop_Advd(X1,c_1,tc_nat)
| c_Divides_Oop_Advd(X1,X0,tc_nat) )
| ~ spl0_1020
| ~ spl0_1486 ),
inference(superposition,[],[f12425,f8517]) ).
fof(f8517,plain,
( ! [X15] : c_1 = c_GCD_Ogcd(c_Pair(X15,c_1,tc_nat,tc_nat))
| ~ spl0_1020 ),
inference(avatar_component_clause,[],[f8516]) ).
fof(f12425,plain,
( ! [X21,X16,X15] :
( ~ c_Divides_Oop_Advd(X16,c_GCD_Ogcd(c_Pair(X15,X21,tc_nat,tc_nat)),tc_nat)
| c_Divides_Oop_Advd(X16,X15,tc_nat) )
| ~ spl0_1486 ),
inference(avatar_component_clause,[],[f12424]) ).
fof(f32520,plain,
( spl0_2525
| ~ spl0_735
| ~ spl0_1477 ),
inference(avatar_split_clause,[],[f12968,f12388,f7261,f32518]) ).
fof(f32518,plain,
( spl0_2525
<=> ! [X0,X1] :
( ~ c_lessequals(c_UNIV,X0,tc_set(X1))
| c_UNIV = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2525])]) ).
fof(f7261,plain,
( spl0_735
<=> ! [X12,X1] : c_lessequals(X12,c_UNIV,tc_set(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_735])]) ).
fof(f12388,plain,
( spl0_1477
<=> ! [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_1477])]) ).
fof(f12968,plain,
( ! [X0,X1] :
( ~ c_lessequals(c_UNIV,X0,tc_set(X1))
| c_UNIV = X0 )
| ~ spl0_735
| ~ spl0_1477 ),
inference(resolution,[],[f12389,f7262]) ).
fof(f7262,plain,
( ! [X1,X12] : c_lessequals(X12,c_UNIV,tc_set(X1))
| ~ spl0_735 ),
inference(avatar_component_clause,[],[f7261]) ).
fof(f12389,plain,
( ! [X1,X12,X13] :
( ~ c_lessequals(X13,X12,tc_set(X1))
| ~ c_lessequals(X12,X13,tc_set(X1))
| X12 = X13 )
| ~ spl0_1477 ),
inference(avatar_component_clause,[],[f12388]) ).
fof(f32516,plain,
( spl0_2524
| ~ spl0_671
| ~ spl0_1475 ),
inference(avatar_split_clause,[],[f12936,f12369,f6978,f32514]) ).
fof(f32514,plain,
( spl0_2524
<=> ! [X0,X1] :
( c_emptyset = X0
| c_less(c_emptyset,X0,tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2524])]) ).
fof(f6978,plain,
( spl0_671
<=> ! [X12,X1] : c_lessequals(c_emptyset,X12,tc_set(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_671])]) ).
fof(f12369,plain,
( spl0_1475
<=> ! [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_1475])]) ).
fof(f12936,plain,
( ! [X0,X1] :
( c_emptyset = X0
| c_less(c_emptyset,X0,tc_set(X1)) )
| ~ spl0_671
| ~ spl0_1475 ),
inference(resolution,[],[f12370,f6979]) ).
fof(f6979,plain,
( ! [X1,X12] : c_lessequals(c_emptyset,X12,tc_set(X1))
| ~ spl0_671 ),
inference(avatar_component_clause,[],[f6978]) ).
fof(f12370,plain,
( ! [X1,X12,X13] :
( ~ c_lessequals(X12,X13,tc_set(X1))
| X12 = X13
| c_less(X12,X13,tc_set(X1)) )
| ~ spl0_1475 ),
inference(avatar_component_clause,[],[f12369]) ).
fof(f32512,plain,
( spl0_2523
| ~ spl0_735
| ~ spl0_1475 ),
inference(avatar_split_clause,[],[f12927,f12369,f7261,f32510]) ).
fof(f32510,plain,
( spl0_2523
<=> ! [X0,X1] :
( c_UNIV = X0
| c_less(X0,c_UNIV,tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2523])]) ).
fof(f12927,plain,
( ! [X0,X1] :
( c_UNIV = X0
| c_less(X0,c_UNIV,tc_set(X1)) )
| ~ spl0_735
| ~ spl0_1475 ),
inference(resolution,[],[f12370,f7262]) ).
fof(f32508,plain,
( spl0_2522
| ~ spl0_749
| ~ spl0_2483 ),
inference(avatar_split_clause,[],[f32237,f32234,f7334,f32505]) ).
fof(f32505,plain,
( spl0_2522
<=> c_Message_Omsg_ONonce(v_NA) = v_na ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2522])]) ).
fof(f32234,plain,
( spl0_2483
<=> ! [X4,X0,X3,X2,X1] :
( ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,X0,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(X0),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(X1),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K),c_Message_Omsg_OMPair(X2,X3)))),X4)),c_List_Oset(v_evso,tc_Event_Oevent),tc_Event_Oevent)
| v_na = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2483])]) ).
fof(f32237,plain,
( c_Message_Omsg_ONonce(v_NA) = v_na
| ~ spl0_749
| ~ spl0_2483 ),
inference(resolution,[],[f32235,f7336]) ).
fof(f32235,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,X0,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(X0),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(X1),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K),c_Message_Omsg_OMPair(X2,X3)))),X4)),c_List_Oset(v_evso,tc_Event_Oevent),tc_Event_Oevent)
| v_na = X2 )
| ~ spl0_2483 ),
inference(avatar_component_clause,[],[f32234]) ).
fof(f32503,plain,
( spl0_2521
| ~ spl0_786
| ~ spl0_869
| ~ spl0_1586 ),
inference(avatar_split_clause,[],[f12881,f12858,f7830,f7484,f32501]) ).
fof(f32501,plain,
( spl0_2521
<=> ! [X0] :
( c_List_Olist_ONil = c_List_Oupt(X0,c_1)
| c_0 = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2521])]) ).
fof(f7484,plain,
( spl0_786
<=> ! [X3] : c_plus(X3,c_0,tc_nat) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_786])]) ).
fof(f7830,plain,
( spl0_869
<=> ! [X43] :
( c_0 = X43
| ~ c_lessequals(X43,c_0,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_869])]) ).
fof(f12858,plain,
( spl0_1586
<=> ! [X59,X43] :
( c_List_Olist_ONil = c_List_Oupt(X43,c_plus(c_1,X59,tc_nat))
| c_lessequals(X43,X59,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1586])]) ).
fof(f12881,plain,
( ! [X0] :
( c_List_Olist_ONil = c_List_Oupt(X0,c_1)
| c_0 = X0 )
| ~ spl0_786
| ~ spl0_869
| ~ spl0_1586 ),
inference(forward_demodulation,[],[f12868,f7485]) ).
fof(f7485,plain,
( ! [X3] : c_plus(X3,c_0,tc_nat) = X3
| ~ spl0_786 ),
inference(avatar_component_clause,[],[f7484]) ).
fof(f12868,plain,
( ! [X0] :
( c_List_Olist_ONil = c_List_Oupt(X0,c_plus(c_1,c_0,tc_nat))
| c_0 = X0 )
| ~ spl0_869
| ~ spl0_1586 ),
inference(resolution,[],[f12859,f7831]) ).
fof(f7831,plain,
( ! [X43] :
( ~ c_lessequals(X43,c_0,tc_nat)
| c_0 = X43 )
| ~ spl0_869 ),
inference(avatar_component_clause,[],[f7830]) ).
fof(f12859,plain,
( ! [X59,X43] :
( c_lessequals(X43,X59,tc_nat)
| c_List_Olist_ONil = c_List_Oupt(X43,c_plus(c_1,X59,tc_nat)) )
| ~ spl0_1586 ),
inference(avatar_component_clause,[],[f12858]) ).
fof(f32499,plain,
( spl0_2520
| ~ spl0_786
| ~ spl0_997
| ~ spl0_1583 ),
inference(avatar_split_clause,[],[f12847,f12841,f8421,f7484,f32496]) ).
fof(f32496,plain,
( spl0_2520
<=> c_SetInterval_OatMost(c_0,tc_nat) = c_SetInterval_OatLeastLessThan(c_0,c_1,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2520])]) ).
fof(f8421,plain,
( spl0_997
<=> c_SetInterval_OatMost(c_0,tc_nat) = c_insert(c_0,c_emptyset,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_997])]) ).
fof(f12841,plain,
( spl0_1583
<=> ! [X15] : c_insert(X15,c_emptyset,tc_nat) = c_SetInterval_OatLeastLessThan(X15,c_plus(c_1,X15,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1583])]) ).
fof(f12847,plain,
( c_SetInterval_OatMost(c_0,tc_nat) = c_SetInterval_OatLeastLessThan(c_0,c_1,tc_nat)
| ~ spl0_786
| ~ spl0_997
| ~ spl0_1583 ),
inference(forward_demodulation,[],[f12844,f8423]) ).
fof(f8423,plain,
( c_SetInterval_OatMost(c_0,tc_nat) = c_insert(c_0,c_emptyset,tc_nat)
| ~ spl0_997 ),
inference(avatar_component_clause,[],[f8421]) ).
fof(f12844,plain,
( c_insert(c_0,c_emptyset,tc_nat) = c_SetInterval_OatLeastLessThan(c_0,c_1,tc_nat)
| ~ spl0_786
| ~ spl0_1583 ),
inference(superposition,[],[f12842,f7485]) ).
fof(f12842,plain,
( ! [X15] : c_insert(X15,c_emptyset,tc_nat) = c_SetInterval_OatLeastLessThan(X15,c_plus(c_1,X15,tc_nat),tc_nat)
| ~ spl0_1583 ),
inference(avatar_component_clause,[],[f12841]) ).
fof(f32494,plain,
( spl0_2519
| ~ spl0_925
| ~ spl0_1583 ),
inference(avatar_split_clause,[],[f12846,f12841,f8129,f32492]) ).
fof(f32492,plain,
( spl0_2519
<=> ! [X0] : c_in(c_insert(X0,c_emptyset,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2519])]) ).
fof(f8129,plain,
( spl0_925
<=> ! [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_925])]) ).
fof(f12846,plain,
( ! [X0] : c_in(c_insert(X0,c_emptyset,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat))
| ~ spl0_925
| ~ spl0_1583 ),
inference(superposition,[],[f8130,f12842]) ).
fof(f8130,plain,
( ! [X26,X14] : c_in(c_SetInterval_OatLeastLessThan(X26,X14,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat))
| ~ spl0_925 ),
inference(avatar_component_clause,[],[f8129]) ).
fof(f32490,plain,
( spl0_2518
| ~ spl0_891
| ~ spl0_1424 ),
inference(avatar_split_clause,[],[f11966,f11146,f7918,f32488]) ).
fof(f32488,plain,
( spl0_2518
<=> ! [X0,X1] :
( c_emptyset != X0
| c_lessequals(X0,c_emptyset,tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2518])]) ).
fof(f7918,plain,
( spl0_891
<=> ! [X1,X3] : c_minus(X3,c_emptyset,tc_set(X1)) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_891])]) ).
fof(f11146,plain,
( spl0_1424
<=> ! [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_1424])]) ).
fof(f11966,plain,
( ! [X0,X1] :
( c_emptyset != X0
| c_lessequals(X0,c_emptyset,tc_set(X1)) )
| ~ spl0_891
| ~ spl0_1424 ),
inference(superposition,[],[f11147,f7919]) ).
fof(f7919,plain,
( ! [X3,X1] : c_minus(X3,c_emptyset,tc_set(X1)) = X3
| ~ spl0_891 ),
inference(avatar_component_clause,[],[f7918]) ).
fof(f11147,plain,
( ! [X1,X12,X13] :
( c_emptyset != c_minus(X12,X13,tc_set(X1))
| c_lessequals(X12,X13,tc_set(X1)) )
| ~ spl0_1424 ),
inference(avatar_component_clause,[],[f11146]) ).
fof(f32486,plain,
( spl0_2517
| ~ spl0_750
| ~ spl0_1416 ),
inference(avatar_split_clause,[],[f11938,f11114,f7339,f32484]) ).
fof(f32484,plain,
( spl0_2517
<=> ! [X0,X1] :
( ~ class_Orderings_Oorder(X0)
| c_emptyset = c_SetInterval_OgreaterThanAtMost(X1,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2517])]) ).
fof(f7339,plain,
( spl0_750
<=> ! [X0,X1] :
( ~ class_Orderings_Oorder(X1)
| c_lessequals(X0,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_750])]) ).
fof(f11114,plain,
( spl0_1416
<=> ! [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_1416])]) ).
fof(f11938,plain,
( ! [X0,X1] :
( ~ class_Orderings_Oorder(X0)
| c_emptyset = c_SetInterval_OgreaterThanAtMost(X1,X1,X0) )
| ~ spl0_750
| ~ spl0_1416 ),
inference(duplicate_literal_removal,[],[f11905]) ).
fof(f11905,plain,
( ! [X0,X1] :
( ~ class_Orderings_Oorder(X0)
| c_emptyset = c_SetInterval_OgreaterThanAtMost(X1,X1,X0)
| ~ class_Orderings_Oorder(X0) )
| ~ spl0_750
| ~ spl0_1416 ),
inference(resolution,[],[f11115,f7340]) ).
fof(f7340,plain,
( ! [X0,X1] :
( c_lessequals(X0,X0,X1)
| ~ class_Orderings_Oorder(X1) )
| ~ spl0_750 ),
inference(avatar_component_clause,[],[f7339]) ).
fof(f11115,plain,
( ! [X1,X26,X16] :
( ~ c_lessequals(X26,X16,X1)
| ~ class_Orderings_Oorder(X1)
| c_emptyset = c_SetInterval_OgreaterThanAtMost(X16,X26,X1) )
| ~ spl0_1416 ),
inference(avatar_component_clause,[],[f11114]) ).
fof(f32476,plain,
( spl0_2516
| ~ spl0_76
| ~ spl0_118
| ~ spl0_1416 ),
inference(avatar_split_clause,[],[f11911,f11114,f3989,f3787,f32474]) ).
fof(f32474,plain,
( spl0_2516
<=> ! [X0] : c_emptyset = c_SetInterval_OgreaterThanAtMost(X0,c_0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2516])]) ).
fof(f3787,plain,
( spl0_76
<=> class_Orderings_Oorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_76])]) ).
fof(f3989,plain,
( spl0_118
<=> ! [X21] : c_lessequals(c_0,X21,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_118])]) ).
fof(f11911,plain,
( ! [X0] :
( ~ class_Orderings_Oorder(tc_nat)
| c_emptyset = c_SetInterval_OgreaterThanAtMost(X0,c_0,tc_nat) )
| ~ spl0_118
| ~ spl0_1416 ),
inference(resolution,[],[f11115,f3990]) ).
fof(f3990,plain,
( ! [X21] : c_lessequals(c_0,X21,tc_nat)
| ~ spl0_118 ),
inference(avatar_component_clause,[],[f3989]) ).
fof(f32472,plain,
( spl0_2515
| ~ spl0_750
| ~ spl0_1407 ),
inference(avatar_split_clause,[],[f11883,f11065,f7339,f32470]) ).
fof(f32470,plain,
( spl0_2515
<=> ! [X0,X1] :
( ~ class_Orderings_Oorder(X0)
| c_emptyset = c_SetInterval_OatLeastLessThan(X1,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2515])]) ).
fof(f11065,plain,
( spl0_1407
<=> ! [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_1407])]) ).
fof(f11883,plain,
( ! [X0,X1] :
( ~ class_Orderings_Oorder(X0)
| c_emptyset = c_SetInterval_OatLeastLessThan(X1,X1,X0) )
| ~ spl0_750
| ~ spl0_1407 ),
inference(duplicate_literal_removal,[],[f11850]) ).
fof(f11850,plain,
( ! [X0,X1] :
( ~ class_Orderings_Oorder(X0)
| c_emptyset = c_SetInterval_OatLeastLessThan(X1,X1,X0)
| ~ class_Orderings_Oorder(X0) )
| ~ spl0_750
| ~ spl0_1407 ),
inference(resolution,[],[f11066,f7340]) ).
fof(f11066,plain,
( ! [X21,X1,X15] :
( ~ c_lessequals(X21,X15,X1)
| ~ class_Orderings_Oorder(X1)
| c_emptyset = c_SetInterval_OatLeastLessThan(X15,X21,X1) )
| ~ spl0_1407 ),
inference(avatar_component_clause,[],[f11065]) ).
fof(f32454,plain,
( spl0_2514
| ~ spl0_76
| ~ spl0_118
| ~ spl0_1407 ),
inference(avatar_split_clause,[],[f11856,f11065,f3989,f3787,f32452]) ).
fof(f32452,plain,
( spl0_2514
<=> ! [X0] : c_emptyset = c_SetInterval_OatLeastLessThan(X0,c_0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2514])]) ).
fof(f11856,plain,
( ! [X0] :
( ~ class_Orderings_Oorder(tc_nat)
| c_emptyset = c_SetInterval_OatLeastLessThan(X0,c_0,tc_nat) )
| ~ spl0_118
| ~ spl0_1407 ),
inference(resolution,[],[f11066,f3990]) ).
fof(f32423,plain,
( spl0_2513
| ~ spl0_28
| ~ spl0_666
| ~ spl0_1406 ),
inference(avatar_split_clause,[],[f11831,f11061,f6193,f3547,f32420]) ).
fof(f32420,plain,
( spl0_2513
<=> c_emptyset = c_SetInterval_OatLeastAtMost(c_1,c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2513])]) ).
fof(f3547,plain,
( spl0_28
<=> class_Orderings_Oorder(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_28])]) ).
fof(f6193,plain,
( spl0_666
<=> c_less(c_0,c_1,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_666])]) ).
fof(f11061,plain,
( spl0_1406
<=> ! [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_1406])]) ).
fof(f11831,plain,
( ~ class_Orderings_Oorder(tc_IntDef_Oint)
| c_emptyset = c_SetInterval_OatLeastAtMost(c_1,c_0,tc_IntDef_Oint)
| ~ spl0_666
| ~ spl0_1406 ),
inference(resolution,[],[f11062,f6195]) ).
fof(f6195,plain,
( c_less(c_0,c_1,tc_IntDef_Oint)
| ~ spl0_666 ),
inference(avatar_component_clause,[],[f6193]) ).
fof(f11062,plain,
( ! [X21,X1,X15] :
( ~ c_less(X21,X15,X1)
| ~ class_Orderings_Oorder(X1)
| c_emptyset = c_SetInterval_OatLeastAtMost(X15,X21,X1) )
| ~ spl0_1406 ),
inference(avatar_component_clause,[],[f11061]) ).
fof(f32413,plain,
( spl0_2512
| ~ spl0_76
| ~ spl0_652
| ~ spl0_1406 ),
inference(avatar_split_clause,[],[f11830,f11061,f6128,f3787,f32410]) ).
fof(f32410,plain,
( spl0_2512
<=> c_emptyset = c_SetInterval_OatLeastAtMost(c_1,c_0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2512])]) ).
fof(f6128,plain,
( spl0_652
<=> c_less(c_0,c_1,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_652])]) ).
fof(f11830,plain,
( ~ class_Orderings_Oorder(tc_nat)
| c_emptyset = c_SetInterval_OatLeastAtMost(c_1,c_0,tc_nat)
| ~ spl0_652
| ~ spl0_1406 ),
inference(resolution,[],[f11062,f6130]) ).
fof(f6130,plain,
( c_less(c_0,c_1,tc_nat)
| ~ spl0_652 ),
inference(avatar_component_clause,[],[f6128]) ).
fof(f32406,plain,
( spl0_2510
| ~ spl0_2511
| ~ spl0_794
| ~ spl0_1320 ),
inference(avatar_split_clause,[],[f10714,f10322,f7516,f32403,f32400]) ).
fof(f32400,plain,
( spl0_2510
<=> ! [X0] : c_lessequals(c_1,X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2510])]) ).
fof(f32403,plain,
( spl0_2511
<=> c_lessequals(c_1,c_0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2511])]) ).
fof(f7516,plain,
( spl0_794
<=> ! [X21] : c_0 = c_times(c_0,X21,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_794])]) ).
fof(f10322,plain,
( spl0_1320
<=> ! [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_1320])]) ).
fof(f10714,plain,
( ! [X0] :
( ~ c_lessequals(c_1,c_0,tc_nat)
| c_lessequals(c_1,X0,tc_nat) )
| ~ spl0_794
| ~ spl0_1320 ),
inference(superposition,[],[f10323,f7517]) ).
fof(f7517,plain,
( ! [X21] : c_0 = c_times(c_0,X21,tc_nat)
| ~ spl0_794 ),
inference(avatar_component_clause,[],[f7516]) ).
fof(f10323,plain,
( ! [X21,X15] :
( ~ c_lessequals(c_1,c_times(X15,X21,tc_nat),tc_nat)
| c_lessequals(c_1,X21,tc_nat) )
| ~ spl0_1320 ),
inference(avatar_component_clause,[],[f10322]) ).
fof(f32390,plain,
( spl0_2509
| ~ spl0_45
| ~ spl0_688
| ~ spl0_1291 ),
inference(avatar_split_clause,[],[f10544,f10184,f7050,f3632,f32388]) ).
fof(f32388,plain,
( spl0_2509
<=> ! [X0] : c_0 = c_OrderedGroup_Onprt(c_IntDef_Oint(X0),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2509])]) ).
fof(f3632,plain,
( spl0_45
<=> class_OrderedGroup_Olordered__ab__group(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_45])]) ).
fof(f7050,plain,
( spl0_688
<=> ! [X21] : c_lessequals(c_0,c_IntDef_Oint(X21),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_688])]) ).
fof(f10184,plain,
( spl0_1291
<=> ! [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_1291])]) ).
fof(f10544,plain,
( ! [X0] :
( ~ class_OrderedGroup_Olordered__ab__group(tc_IntDef_Oint)
| c_0 = c_OrderedGroup_Onprt(c_IntDef_Oint(X0),tc_IntDef_Oint) )
| ~ spl0_688
| ~ spl0_1291 ),
inference(resolution,[],[f10185,f7051]) ).
fof(f7051,plain,
( ! [X21] : c_lessequals(c_0,c_IntDef_Oint(X21),tc_IntDef_Oint)
| ~ spl0_688 ),
inference(avatar_component_clause,[],[f7050]) ).
fof(f10185,plain,
( ! [X0,X1] :
( ~ c_lessequals(c_0,X0,X1)
| ~ class_OrderedGroup_Olordered__ab__group(X1)
| c_0 = c_OrderedGroup_Onprt(X0,X1) )
| ~ spl0_1291 ),
inference(avatar_component_clause,[],[f10184]) ).
fof(f32386,plain,
( spl0_2508
| ~ spl0_14
| ~ spl0_1189 ),
inference(avatar_split_clause,[],[f9909,f9542,f3477,f32384]) ).
fof(f32384,plain,
( spl0_2508
<=> ! [X0] : c_0 = c_plus(X0,c_uminus(X0,tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2508])]) ).
fof(f3477,plain,
( spl0_14
<=> class_OrderedGroup_Oab__group__add(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).
fof(f9542,plain,
( spl0_1189
<=> ! [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_1189])]) ).
fof(f9909,plain,
( ! [X0] : c_0 = c_plus(X0,c_uminus(X0,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_14
| ~ spl0_1189 ),
inference(resolution,[],[f9543,f3479]) ).
fof(f3479,plain,
( class_OrderedGroup_Oab__group__add(tc_IntDef_Oint)
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f3477]) ).
fof(f9543,plain,
( ! [X1,X18] :
( ~ class_OrderedGroup_Oab__group__add(X1)
| c_0 = c_plus(X18,c_uminus(X18,X1),X1) )
| ~ spl0_1189 ),
inference(avatar_component_clause,[],[f9542]) ).
fof(f32382,plain,
( spl0_2507
| ~ spl0_14
| ~ spl0_1185 ),
inference(avatar_split_clause,[],[f9894,f9526,f3477,f32380]) ).
fof(f32380,plain,
( spl0_2507
<=> ! [X0] : c_uminus(X0,tc_IntDef_Oint) = c_minus(c_0,X0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2507])]) ).
fof(f9526,plain,
( spl0_1185
<=> ! [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_1185])]) ).
fof(f9894,plain,
( ! [X0] : c_uminus(X0,tc_IntDef_Oint) = c_minus(c_0,X0,tc_IntDef_Oint)
| ~ spl0_14
| ~ spl0_1185 ),
inference(resolution,[],[f9527,f3479]) ).
fof(f9527,plain,
( ! [X1,X18] :
( ~ class_OrderedGroup_Oab__group__add(X1)
| c_uminus(X18,X1) = c_minus(c_0,X18,X1) )
| ~ spl0_1185 ),
inference(avatar_component_clause,[],[f9526]) ).
fof(f32355,plain,
( spl0_2506
| ~ spl0_14
| ~ spl0_1183 ),
inference(avatar_split_clause,[],[f9890,f9518,f3477,f32353]) ).
fof(f32353,plain,
( spl0_2506
<=> ! [X0] : c_0 = c_plus(c_uminus(X0,tc_IntDef_Oint),X0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2506])]) ).
fof(f9518,plain,
( spl0_1183
<=> ! [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_1183])]) ).
fof(f9890,plain,
( ! [X0] : c_0 = c_plus(c_uminus(X0,tc_IntDef_Oint),X0,tc_IntDef_Oint)
| ~ spl0_14
| ~ spl0_1183 ),
inference(resolution,[],[f9519,f3479]) ).
fof(f9519,plain,
( ! [X1,X18] :
( ~ class_OrderedGroup_Oab__group__add(X1)
| c_0 = c_plus(c_uminus(X18,X1),X18,X1) )
| ~ spl0_1183 ),
inference(avatar_component_clause,[],[f9518]) ).
fof(f32351,plain,
( spl0_2505
| ~ spl0_27
| ~ spl0_1156 ),
inference(avatar_split_clause,[],[f9785,f9409,f3542,f32349]) ).
fof(f32349,plain,
( spl0_2505
<=> ! [X0] : c_NatArith_Oof__nat(X0,tc_IntDef_Oint) = c_IntDef_Oof__int(c_IntDef_Oint(X0),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2505])]) ).
fof(f3542,plain,
( spl0_27
<=> class_Ring__and__Field_Ocomm__ring__1(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_27])]) ).
fof(f9409,plain,
( spl0_1156
<=> ! [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_1156])]) ).
fof(f9785,plain,
( ! [X0] : c_NatArith_Oof__nat(X0,tc_IntDef_Oint) = c_IntDef_Oof__int(c_IntDef_Oint(X0),tc_IntDef_Oint)
| ~ spl0_27
| ~ spl0_1156 ),
inference(resolution,[],[f9410,f3544]) ).
fof(f3544,plain,
( class_Ring__and__Field_Ocomm__ring__1(tc_IntDef_Oint)
| ~ spl0_27 ),
inference(avatar_component_clause,[],[f3542]) ).
fof(f9410,plain,
( ! [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) )
| ~ spl0_1156 ),
inference(avatar_component_clause,[],[f9409]) ).
fof(f32347,plain,
( spl0_2504
| ~ spl0_96
| ~ spl0_1151 ),
inference(avatar_split_clause,[],[f9771,f9389,f3887,f32345]) ).
fof(f32345,plain,
( spl0_2504
<=> ! [X0] : c_Finite__Set_OMin(c_insert(X0,c_emptyset,tc_nat),tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2504])]) ).
fof(f3887,plain,
( spl0_96
<=> class_Orderings_Olinorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_96])]) ).
fof(f9389,plain,
( spl0_1151
<=> ! [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_1151])]) ).
fof(f9771,plain,
( ! [X0] : c_Finite__Set_OMin(c_insert(X0,c_emptyset,tc_nat),tc_nat) = X0
| ~ spl0_96
| ~ spl0_1151 ),
inference(resolution,[],[f9390,f3889]) ).
fof(f3889,plain,
( class_Orderings_Olinorder(tc_nat)
| ~ spl0_96 ),
inference(avatar_component_clause,[],[f3887]) ).
fof(f9390,plain,
( ! [X3,X1] :
( ~ class_Orderings_Olinorder(X1)
| c_Finite__Set_OMin(c_insert(X3,c_emptyset,X1),X1) = X3 )
| ~ spl0_1151 ),
inference(avatar_component_clause,[],[f9389]) ).
fof(f32343,plain,
( spl0_2503
| ~ spl0_32
| ~ spl0_1151 ),
inference(avatar_split_clause,[],[f9770,f9389,f3567,f32341]) ).
fof(f32341,plain,
( spl0_2503
<=> ! [X0] : c_Finite__Set_OMin(c_insert(X0,c_emptyset,tc_IntDef_Oint),tc_IntDef_Oint) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2503])]) ).
fof(f3567,plain,
( spl0_32
<=> class_Orderings_Olinorder(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_32])]) ).
fof(f9770,plain,
( ! [X0] : c_Finite__Set_OMin(c_insert(X0,c_emptyset,tc_IntDef_Oint),tc_IntDef_Oint) = X0
| ~ spl0_32
| ~ spl0_1151 ),
inference(resolution,[],[f9390,f3569]) ).
fof(f3569,plain,
( class_Orderings_Olinorder(tc_IntDef_Oint)
| ~ spl0_32 ),
inference(avatar_component_clause,[],[f3567]) ).
fof(f32339,plain,
( spl0_2502
| ~ spl0_96
| ~ spl0_1150 ),
inference(avatar_split_clause,[],[f9769,f9385,f3887,f32337]) ).
fof(f32337,plain,
( spl0_2502
<=> ! [X0] : c_Finite__Set_OMax(c_insert(X0,c_emptyset,tc_nat),tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2502])]) ).
fof(f9385,plain,
( spl0_1150
<=> ! [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_1150])]) ).
fof(f9769,plain,
( ! [X0] : c_Finite__Set_OMax(c_insert(X0,c_emptyset,tc_nat),tc_nat) = X0
| ~ spl0_96
| ~ spl0_1150 ),
inference(resolution,[],[f9386,f3889]) ).
fof(f9386,plain,
( ! [X3,X1] :
( ~ class_Orderings_Olinorder(X1)
| c_Finite__Set_OMax(c_insert(X3,c_emptyset,X1),X1) = X3 )
| ~ spl0_1150 ),
inference(avatar_component_clause,[],[f9385]) ).
fof(f32335,plain,
( spl0_2501
| ~ spl0_32
| ~ spl0_1150 ),
inference(avatar_split_clause,[],[f9768,f9385,f3567,f32333]) ).
fof(f32333,plain,
( spl0_2501
<=> ! [X0] : c_Finite__Set_OMax(c_insert(X0,c_emptyset,tc_IntDef_Oint),tc_IntDef_Oint) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2501])]) ).
fof(f9768,plain,
( ! [X0] : c_Finite__Set_OMax(c_insert(X0,c_emptyset,tc_IntDef_Oint),tc_IntDef_Oint) = X0
| ~ spl0_32
| ~ spl0_1150 ),
inference(resolution,[],[f9386,f3569]) ).
fof(f32330,plain,
( spl0_2500
| ~ spl0_646
| ~ spl0_1225 ),
inference(avatar_split_clause,[],[f9691,f9688,f6101,f32327]) ).
fof(f32327,plain,
( spl0_2500
<=> c_IntDef_Oneg(c_uminus(c_plus(c_1,c_1,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2500])]) ).
fof(f6101,plain,
( spl0_646
<=> c_1 = c_IntDef_Oint(c_1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_646])]) ).
fof(f9688,plain,
( spl0_1225
<=> ! [X21] : c_IntDef_Oneg(c_uminus(c_plus(c_1,c_IntDef_Oint(X21),tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1225])]) ).
fof(f9691,plain,
( c_IntDef_Oneg(c_uminus(c_plus(c_1,c_1,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_646
| ~ spl0_1225 ),
inference(superposition,[],[f9689,f6103]) ).
fof(f6103,plain,
( c_1 = c_IntDef_Oint(c_1)
| ~ spl0_646 ),
inference(avatar_component_clause,[],[f6101]) ).
fof(f9689,plain,
( ! [X21] : c_IntDef_Oneg(c_uminus(c_plus(c_1,c_IntDef_Oint(X21),tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_1225 ),
inference(avatar_component_clause,[],[f9688]) ).
fof(f32325,plain,
( ~ spl0_2498
| spl0_2499
| ~ spl0_663
| ~ spl0_1126 ),
inference(avatar_split_clause,[],[f9315,f9071,f6179,f32322,f32318]) ).
fof(f32318,plain,
( spl0_2498
<=> c_less(c_1,c_1,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2498])]) ).
fof(f32322,plain,
( spl0_2499
<=> c_less(c_1,c_1,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2499])]) ).
fof(f6179,plain,
( spl0_663
<=> c_1 = c_IntDef_Onat(c_1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_663])]) ).
fof(f9071,plain,
( spl0_1126
<=> ! [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_1126])]) ).
fof(f9315,plain,
( c_less(c_1,c_1,tc_nat)
| ~ c_less(c_1,c_1,tc_IntDef_Oint)
| ~ spl0_663
| ~ spl0_1126 ),
inference(superposition,[],[f9072,f6181]) ).
fof(f6181,plain,
( c_1 = c_IntDef_Onat(c_1)
| ~ spl0_663 ),
inference(avatar_component_clause,[],[f6179]) ).
fof(f9072,plain,
( ! [X48] :
( c_less(c_1,c_IntDef_Onat(X48),tc_nat)
| ~ c_less(c_1,X48,tc_IntDef_Oint) )
| ~ spl0_1126 ),
inference(avatar_component_clause,[],[f9071]) ).
fof(f32316,plain,
( spl0_2497
| ~ spl0_999
| ~ spl0_1089 ),
inference(avatar_split_clause,[],[f9253,f8923,f8431,f32314]) ).
fof(f32314,plain,
( spl0_2497
<=> ! [X0] : c_emptyset = c_Set_Ocontents(c_Pow(c_emptyset,X0),tc_set(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2497])]) ).
fof(f8431,plain,
( spl0_999
<=> ! [X1,X3] : c_Set_Ocontents(c_insert(X3,c_emptyset,X1),X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_999])]) ).
fof(f8923,plain,
( spl0_1089
<=> ! [X1] : c_Pow(c_emptyset,X1) = c_insert(c_emptyset,c_emptyset,tc_set(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1089])]) ).
fof(f9253,plain,
( ! [X0] : c_emptyset = c_Set_Ocontents(c_Pow(c_emptyset,X0),tc_set(X0))
| ~ spl0_999
| ~ spl0_1089 ),
inference(superposition,[],[f8432,f8924]) ).
fof(f8924,plain,
( ! [X1] : c_Pow(c_emptyset,X1) = c_insert(c_emptyset,c_emptyset,tc_set(X1))
| ~ spl0_1089 ),
inference(avatar_component_clause,[],[f8923]) ).
fof(f8432,plain,
( ! [X3,X1] : c_Set_Ocontents(c_insert(X3,c_emptyset,X1),X1) = X3
| ~ spl0_999 ),
inference(avatar_component_clause,[],[f8431]) ).
fof(f32312,plain,
( spl0_2496
| ~ spl0_920
| ~ spl0_2481 ),
inference(avatar_split_clause,[],[f32223,f32219,f8107,f32309]) ).
fof(f32309,plain,
( spl0_2496
<=> v_B = v_Ba ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2496])]) ).
fof(f8107,plain,
( spl0_920
<=> c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_A,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K),c_Message_Omsg_OMPair(v_na,v_nb)))),c_Message_Omsg_OCrypt(c_Public_OshrK(v_B),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OKey(v_K))))),c_List_Oset(v_evso,tc_Event_Oevent),tc_Event_Oevent) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_920])]) ).
fof(f32219,plain,
( spl0_2481
<=> ! [X4,X0,X3,X2,X1] :
( ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,X0,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(X0),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(X1),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K),c_Message_Omsg_OMPair(X2,X3)))),X4)),c_List_Oset(v_evso,tc_Event_Oevent),tc_Event_Oevent)
| v_Ba = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2481])]) ).
fof(f32223,plain,
( v_B = v_Ba
| ~ spl0_920
| ~ spl0_2481 ),
inference(resolution,[],[f32220,f8109]) ).
fof(f8109,plain,
( c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_A,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K),c_Message_Omsg_OMPair(v_na,v_nb)))),c_Message_Omsg_OCrypt(c_Public_OshrK(v_B),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OKey(v_K))))),c_List_Oset(v_evso,tc_Event_Oevent),tc_Event_Oevent)
| ~ spl0_920 ),
inference(avatar_component_clause,[],[f8107]) ).
fof(f32220,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,X0,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(X0),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(X1),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K),c_Message_Omsg_OMPair(X2,X3)))),X4)),c_List_Oset(v_evso,tc_Event_Oevent),tc_Event_Oevent)
| v_Ba = X1 )
| ~ spl0_2481 ),
inference(avatar_component_clause,[],[f32219]) ).
fof(f32307,plain,
( spl0_2495
| ~ spl0_868
| ~ spl0_1072 ),
inference(avatar_split_clause,[],[f9224,f8855,f7826,f32305]) ).
fof(f32305,plain,
( spl0_2495
<=> ! [X0,X1] : c_List_Olist_ONil = c_List_Oupt(X0,c_minus(X0,X1,tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2495])]) ).
fof(f7826,plain,
( spl0_868
<=> ! [X21,X15] : c_lessequals(c_minus(X15,X21,tc_nat),X15,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_868])]) ).
fof(f8855,plain,
( spl0_1072
<=> ! [X43,X59] :
( ~ c_lessequals(X59,X43,tc_nat)
| c_List_Olist_ONil = c_List_Oupt(X43,X59) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1072])]) ).
fof(f9224,plain,
( ! [X0,X1] : c_List_Olist_ONil = c_List_Oupt(X0,c_minus(X0,X1,tc_nat))
| ~ spl0_868
| ~ spl0_1072 ),
inference(resolution,[],[f8856,f7827]) ).
fof(f7827,plain,
( ! [X21,X15] : c_lessequals(c_minus(X15,X21,tc_nat),X15,tc_nat)
| ~ spl0_868 ),
inference(avatar_component_clause,[],[f7826]) ).
fof(f8856,plain,
( ! [X59,X43] :
( ~ c_lessequals(X59,X43,tc_nat)
| c_List_Olist_ONil = c_List_Oupt(X43,X59) )
| ~ spl0_1072 ),
inference(avatar_component_clause,[],[f8855]) ).
fof(f32303,plain,
( spl0_2494
| ~ spl0_848
| ~ spl0_1072 ),
inference(avatar_split_clause,[],[f9223,f8855,f7746,f32301]) ).
fof(f32301,plain,
( spl0_2494
<=> ! [X0,X1] : c_List_Olist_ONil = c_List_Oupt(X0,c_div(X0,X1,tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2494])]) ).
fof(f7746,plain,
( spl0_848
<=> ! [X21,X15] : c_lessequals(c_div(X15,X21,tc_nat),X15,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_848])]) ).
fof(f9223,plain,
( ! [X0,X1] : c_List_Olist_ONil = c_List_Oupt(X0,c_div(X0,X1,tc_nat))
| ~ spl0_848
| ~ spl0_1072 ),
inference(resolution,[],[f8856,f7747]) ).
fof(f7747,plain,
( ! [X21,X15] : c_lessequals(c_div(X15,X21,tc_nat),X15,tc_nat)
| ~ spl0_848 ),
inference(avatar_component_clause,[],[f7746]) ).
fof(f32299,plain,
( spl0_2493
| ~ spl0_999
| ~ spl0_1062 ),
inference(avatar_split_clause,[],[f9196,f8815,f8431,f32297]) ).
fof(f32297,plain,
( spl0_2493
<=> ! [X0] : c_List_Olist_ONil = c_Set_Ocontents(c_List_Olistset(c_List_Olist_ONil,X0),tc_List_Olist(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2493])]) ).
fof(f8815,plain,
( spl0_1062
<=> ! [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_1062])]) ).
fof(f9196,plain,
( ! [X0] : c_List_Olist_ONil = c_Set_Ocontents(c_List_Olistset(c_List_Olist_ONil,X0),tc_List_Olist(X0))
| ~ spl0_999
| ~ spl0_1062 ),
inference(superposition,[],[f8432,f8816]) ).
fof(f8816,plain,
( ! [X41] : c_List_Olistset(c_List_Olist_ONil,X41) = c_insert(c_List_Olist_ONil,c_emptyset,tc_List_Olist(X41))
| ~ spl0_1062 ),
inference(avatar_component_clause,[],[f8815]) ).
fof(f32295,plain,
( spl0_2492
| ~ spl0_854
| ~ spl0_1045 ),
inference(avatar_split_clause,[],[f9162,f8747,f7770,f32293]) ).
fof(f32293,plain,
( spl0_2492
<=> ! [X0,X1] : c_lessequals(c_0,c_Nat_Opower(c_IntDef_Oint(X0),X1,tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2492])]) ).
fof(f7770,plain,
( spl0_854
<=> ! [X15] : c_IntDef_Oint(X15) = c_HOL_Oabs(c_IntDef_Oint(X15),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_854])]) ).
fof(f8747,plain,
( spl0_1045
<=> ! [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_1045])]) ).
fof(f9162,plain,
( ! [X0,X1] : c_lessequals(c_0,c_Nat_Opower(c_IntDef_Oint(X0),X1,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_854
| ~ spl0_1045 ),
inference(superposition,[],[f8748,f7771]) ).
fof(f7771,plain,
( ! [X15] : c_IntDef_Oint(X15) = c_HOL_Oabs(c_IntDef_Oint(X15),tc_IntDef_Oint)
| ~ spl0_854 ),
inference(avatar_component_clause,[],[f7770]) ).
fof(f8748,plain,
( ! [X21,X0] : c_lessequals(c_0,c_Nat_Opower(c_HOL_Oabs(X0,tc_IntDef_Oint),X21,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_1045 ),
inference(avatar_component_clause,[],[f8747]) ).
fof(f32291,plain,
( spl0_2491
| ~ spl0_873
| ~ spl0_1041 ),
inference(avatar_split_clause,[],[f9136,f8731,f7846,f32289]) ).
fof(f32289,plain,
( spl0_2491
<=> ! [X0] :
( c_less(c_0,X0,tc_IntDef_Oint)
| c_0 = c_IntDef_Onat(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2491])]) ).
fof(f7846,plain,
( spl0_873
<=> ! [X21] :
( c_0 = X21
| c_less(c_0,X21,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_873])]) ).
fof(f8731,plain,
( spl0_1041
<=> ! [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_1041])]) ).
fof(f9136,plain,
( ! [X0] :
( c_less(c_0,X0,tc_IntDef_Oint)
| c_0 = c_IntDef_Onat(X0) )
| ~ spl0_873
| ~ spl0_1041 ),
inference(resolution,[],[f8732,f7847]) ).
fof(f7847,plain,
( ! [X21] :
( c_less(c_0,X21,tc_nat)
| c_0 = X21 )
| ~ spl0_873 ),
inference(avatar_component_clause,[],[f7846]) ).
fof(f8732,plain,
( ! [X48] :
( ~ c_less(c_0,c_IntDef_Onat(X48),tc_nat)
| c_less(c_0,X48,tc_IntDef_Oint) )
| ~ spl0_1041 ),
inference(avatar_component_clause,[],[f8731]) ).
fof(f32287,plain,
( spl0_2490
| ~ spl0_739
| ~ spl0_1002 ),
inference(avatar_split_clause,[],[f8645,f8443,f7279,f32285]) ).
fof(f32285,plain,
( spl0_2490
<=> ! [X0,X1] :
( c_Message_OinvKey(X1) != X0
| c_Message_OinvKey(X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2490])]) ).
fof(f7279,plain,
( spl0_739
<=> ! [X3] : c_Message_OinvKey(c_Message_OinvKey(X3)) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_739])]) ).
fof(f8443,plain,
( spl0_1002
<=> ! [X92,X91] :
( X91 = X92
| c_Message_OinvKey(X91) != c_Message_OinvKey(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1002])]) ).
fof(f8645,plain,
( ! [X0,X1] :
( c_Message_OinvKey(X1) != X0
| c_Message_OinvKey(X0) = X1 )
| ~ spl0_739
| ~ spl0_1002 ),
inference(superposition,[],[f8444,f7280]) ).
fof(f7280,plain,
( ! [X3] : c_Message_OinvKey(c_Message_OinvKey(X3)) = X3
| ~ spl0_739 ),
inference(avatar_component_clause,[],[f7279]) ).
fof(f8444,plain,
( ! [X91,X92] :
( c_Message_OinvKey(X91) != c_Message_OinvKey(X92)
| X91 = X92 )
| ~ spl0_1002 ),
inference(avatar_component_clause,[],[f8443]) ).
fof(f32275,plain,
( spl0_2489
| ~ spl0_45
| ~ spl0_942
| ~ spl0_976 ),
inference(avatar_split_clause,[],[f8605,f8335,f8198,f3632,f32273]) ).
fof(f32273,plain,
( spl0_2489
<=> ! [X0] : c_0 = c_IntDef_Onat(c_OrderedGroup_Onprt(X0,tc_IntDef_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2489])]) ).
fof(f8198,plain,
( spl0_942
<=> ! [X48] :
( ~ c_lessequals(X48,c_0,tc_IntDef_Oint)
| c_0 = c_IntDef_Onat(X48) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_942])]) ).
fof(f8335,plain,
( spl0_976
<=> ! [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_976])]) ).
fof(f8605,plain,
( ! [X0] :
( ~ class_OrderedGroup_Olordered__ab__group(tc_IntDef_Oint)
| c_0 = c_IntDef_Onat(c_OrderedGroup_Onprt(X0,tc_IntDef_Oint)) )
| ~ spl0_942
| ~ spl0_976 ),
inference(resolution,[],[f8336,f8199]) ).
fof(f8199,plain,
( ! [X48] :
( ~ c_lessequals(X48,c_0,tc_IntDef_Oint)
| c_0 = c_IntDef_Onat(X48) )
| ~ spl0_942 ),
inference(avatar_component_clause,[],[f8198]) ).
fof(f8336,plain,
( ! [X18,X1] :
( c_lessequals(c_OrderedGroup_Onprt(X18,X1),c_0,X1)
| ~ class_OrderedGroup_Olordered__ab__group(X1) )
| ~ spl0_976 ),
inference(avatar_component_clause,[],[f8335]) ).
fof(f32271,plain,
( spl0_2488
| ~ spl0_863
| ~ spl0_958 ),
inference(avatar_split_clause,[],[f8564,f8263,f7806,f32269]) ).
fof(f32269,plain,
( spl0_2488
<=> ! [X0,X1] :
( c_List_Olist_ONil != X0
| c_List_Olist_ONil = c_List_Orev(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2488])]) ).
fof(f7806,plain,
( spl0_863
<=> ! [X1,X3] : c_List_Orev(c_List_Orev(X3,X1),X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_863])]) ).
fof(f8263,plain,
( spl0_958
<=> ! [X1,X23] :
( c_List_Olist_ONil = X23
| c_List_Olist_ONil != c_List_Orev(X23,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_958])]) ).
fof(f8564,plain,
( ! [X0,X1] :
( c_List_Olist_ONil != X0
| c_List_Olist_ONil = c_List_Orev(X0,X1) )
| ~ spl0_863
| ~ spl0_958 ),
inference(superposition,[],[f8264,f7807]) ).
fof(f7807,plain,
( ! [X3,X1] : c_List_Orev(c_List_Orev(X3,X1),X1) = X3
| ~ spl0_863 ),
inference(avatar_component_clause,[],[f7806]) ).
fof(f8264,plain,
( ! [X1,X23] :
( c_List_Olist_ONil != c_List_Orev(X23,X1)
| c_List_Olist_ONil = X23 )
| ~ spl0_958 ),
inference(avatar_component_clause,[],[f8263]) ).
fof(f32266,plain,
( spl0_2487
| ~ spl0_4
| ~ spl0_749
| ~ spl0_2446 ),
inference(avatar_split_clause,[],[f31395,f31352,f7334,f3427,f32264]) ).
fof(f32264,plain,
( spl0_2487
<=> ! [X4,X0,X3,X2,X1] :
( ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,X0,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(X0),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(X1),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K),c_Message_Omsg_OMPair(X2,X3)))),X4)),c_List_Oset(v_evso,tc_Event_Oevent),tc_Event_Oevent)
| c_Message_Omsg_ONonce(v_NB) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2487])]) ).
fof(f3427,plain,
( spl0_4
<=> c_in(v_evso,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).
fof(f31352,plain,
( spl0_2446
<=> ! [X116,X113,X112,X12,X91,X86,X115,X107,X111,X114,X102,X13] :
( X114 = X116
| ~ c_in(X102,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
| ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,X12,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(X12),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(X13),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(X91),c_Message_Omsg_OMPair(X115,X116)))),X86)),c_List_Oset(X102,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,X111,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(X111),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(X112),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(X91),c_Message_Omsg_OMPair(X113,X114)))),X107)),c_List_Oset(X102,tc_Event_Oevent),tc_Event_Oevent) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2446])]) ).
fof(f31395,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ c_in(v_evso,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
| ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,X0,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(X0),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(X1),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K),c_Message_Omsg_OMPair(X2,X3)))),X4)),c_List_Oset(v_evso,tc_Event_Oevent),tc_Event_Oevent)
| c_Message_Omsg_ONonce(v_NB) = X3 )
| ~ spl0_749
| ~ spl0_2446 ),
inference(resolution,[],[f31353,f7336]) ).
fof(f31353,plain,
( ! [X113,X111,X91,X116,X86,X107,X114,X102,X12,X112,X13,X115] :
( ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,X111,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(X111),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(X112),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(X91),c_Message_Omsg_OMPair(X113,X114)))),X107)),c_List_Oset(X102,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(X102,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
| ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,X12,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(X12),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(X13),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(X91),c_Message_Omsg_OMPair(X115,X116)))),X86)),c_List_Oset(X102,tc_Event_Oevent),tc_Event_Oevent)
| X114 = X116 )
| ~ spl0_2446 ),
inference(avatar_component_clause,[],[f31352]) ).
fof(f32262,plain,
( spl0_2486
| ~ spl0_920
| ~ spl0_2478 ),
inference(avatar_split_clause,[],[f32208,f32199,f8107,f32259]) ).
fof(f32259,plain,
( spl0_2486
<=> v_A = v_Aa ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2486])]) ).
fof(f32199,plain,
( spl0_2478
<=> ! [X4,X0,X3,X2,X1] :
( ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,X0,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(X0),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(X1),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K),c_Message_Omsg_OMPair(X2,X3)))),X4)),c_List_Oset(v_evso,tc_Event_Oevent),tc_Event_Oevent)
| v_Aa = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2478])]) ).
fof(f32208,plain,
( v_A = v_Aa
| ~ spl0_920
| ~ spl0_2478 ),
inference(resolution,[],[f32200,f8109]) ).
fof(f32200,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,X0,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(X0),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(X1),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K),c_Message_Omsg_OMPair(X2,X3)))),X4)),c_List_Oset(v_evso,tc_Event_Oevent),tc_Event_Oevent)
| v_Aa = X0 )
| ~ spl0_2478 ),
inference(avatar_component_clause,[],[f32199]) ).
fof(f32256,plain,
( spl0_2485
| ~ spl0_4
| ~ spl0_749
| ~ spl0_2445 ),
inference(avatar_split_clause,[],[f31379,f31348,f7334,f3427,f32254]) ).
fof(f32254,plain,
( spl0_2485
<=> ! [X4,X0,X3,X2,X1] :
( ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,X0,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(X0),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(X1),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K),c_Message_Omsg_OMPair(X2,X3)))),X4)),c_List_Oset(v_evso,tc_Event_Oevent),tc_Event_Oevent)
| c_Message_Omsg_ONonce(v_NA) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2485])]) ).
fof(f31348,plain,
( spl0_2445
<=> ! [X116,X113,X112,X12,X91,X86,X115,X107,X111,X114,X102,X13] :
( X113 = X115
| ~ c_in(X102,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
| ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,X12,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(X12),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(X13),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(X91),c_Message_Omsg_OMPair(X115,X116)))),X86)),c_List_Oset(X102,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,X111,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(X111),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(X112),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(X91),c_Message_Omsg_OMPair(X113,X114)))),X107)),c_List_Oset(X102,tc_Event_Oevent),tc_Event_Oevent) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2445])]) ).
fof(f31379,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ c_in(v_evso,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
| ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,X0,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(X0),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(X1),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K),c_Message_Omsg_OMPair(X2,X3)))),X4)),c_List_Oset(v_evso,tc_Event_Oevent),tc_Event_Oevent)
| c_Message_Omsg_ONonce(v_NA) = X2 )
| ~ spl0_749
| ~ spl0_2445 ),
inference(resolution,[],[f31349,f7336]) ).
fof(f31349,plain,
( ! [X113,X111,X91,X116,X86,X107,X114,X102,X12,X112,X13,X115] :
( ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,X111,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(X111),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(X112),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(X91),c_Message_Omsg_OMPair(X113,X114)))),X107)),c_List_Oset(X102,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(X102,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
| ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,X12,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(X12),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(X13),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(X91),c_Message_Omsg_OMPair(X115,X116)))),X86)),c_List_Oset(X102,tc_Event_Oevent),tc_Event_Oevent)
| X113 = X115 )
| ~ spl0_2445 ),
inference(avatar_component_clause,[],[f31348]) ).
fof(f32246,plain,
( spl0_2484
| ~ spl0_4
| ~ spl0_920
| ~ spl0_2446 ),
inference(avatar_split_clause,[],[f31396,f31352,f8107,f3427,f32244]) ).
fof(f31396,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ c_in(v_evso,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
| ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,X0,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(X0),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(X1),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K),c_Message_Omsg_OMPair(X2,X3)))),X4)),c_List_Oset(v_evso,tc_Event_Oevent),tc_Event_Oevent)
| v_nb = X3 )
| ~ spl0_920
| ~ spl0_2446 ),
inference(resolution,[],[f31353,f8109]) ).
fof(f32236,plain,
( spl0_2483
| ~ spl0_4
| ~ spl0_920
| ~ spl0_2445 ),
inference(avatar_split_clause,[],[f31380,f31348,f8107,f3427,f32234]) ).
fof(f31380,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ c_in(v_evso,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
| ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,X0,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(X0),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(X1),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K),c_Message_Omsg_OMPair(X2,X3)))),X4)),c_List_Oset(v_evso,tc_Event_Oevent),tc_Event_Oevent)
| v_na = X2 )
| ~ spl0_920
| ~ spl0_2445 ),
inference(resolution,[],[f31349,f8109]) ).
fof(f32231,plain,
( spl0_2482
| ~ spl0_4
| ~ spl0_920
| ~ spl0_2444 ),
inference(avatar_split_clause,[],[f31368,f31344,f8107,f3427,f32229]) ).
fof(f32229,plain,
( spl0_2482
<=> ! [X4,X0,X3,X2,X1] :
( ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,X0,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(X0),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(X1),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K),c_Message_Omsg_OMPair(X2,X3)))),X4)),c_List_Oset(v_evso,tc_Event_Oevent),tc_Event_Oevent)
| v_B = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2482])]) ).
fof(f31344,plain,
( spl0_2444
<=> ! [X116,X113,X111,X12,X91,X13,X86,X115,X107,X114,X102,X112] :
( X13 = X112
| ~ c_in(X102,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
| ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,X12,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(X12),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(X13),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(X91),c_Message_Omsg_OMPair(X115,X116)))),X86)),c_List_Oset(X102,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,X111,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(X111),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(X112),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(X91),c_Message_Omsg_OMPair(X113,X114)))),X107)),c_List_Oset(X102,tc_Event_Oevent),tc_Event_Oevent) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2444])]) ).
fof(f31368,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ c_in(v_evso,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
| ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,X0,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(X0),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(X1),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K),c_Message_Omsg_OMPair(X2,X3)))),X4)),c_List_Oset(v_evso,tc_Event_Oevent),tc_Event_Oevent)
| v_B = X1 )
| ~ spl0_920
| ~ spl0_2444 ),
inference(resolution,[],[f31345,f8109]) ).
fof(f31345,plain,
( ! [X113,X111,X91,X116,X86,X107,X114,X102,X12,X112,X13,X115] :
( ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,X111,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(X111),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(X112),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(X91),c_Message_Omsg_OMPair(X113,X114)))),X107)),c_List_Oset(X102,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(X102,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
| ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,X12,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(X12),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(X13),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(X91),c_Message_Omsg_OMPair(X115,X116)))),X86)),c_List_Oset(X102,tc_Event_Oevent),tc_Event_Oevent)
| X13 = X112 )
| ~ spl0_2444 ),
inference(avatar_component_clause,[],[f31344]) ).
fof(f32221,plain,
( spl0_2481
| ~ spl0_4
| ~ spl0_749
| ~ spl0_2444 ),
inference(avatar_split_clause,[],[f31367,f31344,f7334,f3427,f32219]) ).
fof(f31367,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ c_in(v_evso,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
| ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,X0,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(X0),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(X1),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K),c_Message_Omsg_OMPair(X2,X3)))),X4)),c_List_Oset(v_evso,tc_Event_Oevent),tc_Event_Oevent)
| v_Ba = X1 )
| ~ spl0_749
| ~ spl0_2444 ),
inference(resolution,[],[f31345,f7336]) ).
fof(f32216,plain,
( spl0_2480
| ~ spl0_4
| ~ spl0_920
| ~ spl0_2443 ),
inference(avatar_split_clause,[],[f31356,f31340,f8107,f3427,f32214]) ).
fof(f32214,plain,
( spl0_2480
<=> ! [X4,X0,X3,X2,X1] :
( ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,X0,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(X0),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(X1),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K),c_Message_Omsg_OMPair(X2,X3)))),X4)),c_List_Oset(v_evso,tc_Event_Oevent),tc_Event_Oevent)
| v_A = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2480])]) ).
fof(f31340,plain,
( spl0_2443
<=> ! [X116,X113,X111,X12,X91,X86,X115,X107,X112,X114,X102,X13] :
( X12 = X111
| ~ c_in(X102,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
| ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,X12,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(X12),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(X13),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(X91),c_Message_Omsg_OMPair(X115,X116)))),X86)),c_List_Oset(X102,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,X111,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(X111),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(X112),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(X91),c_Message_Omsg_OMPair(X113,X114)))),X107)),c_List_Oset(X102,tc_Event_Oevent),tc_Event_Oevent) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2443])]) ).
fof(f31356,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ c_in(v_evso,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
| ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,X0,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(X0),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(X1),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K),c_Message_Omsg_OMPair(X2,X3)))),X4)),c_List_Oset(v_evso,tc_Event_Oevent),tc_Event_Oevent)
| v_A = X0 )
| ~ spl0_920
| ~ spl0_2443 ),
inference(resolution,[],[f31341,f8109]) ).
fof(f31341,plain,
( ! [X113,X111,X91,X116,X86,X107,X114,X102,X12,X112,X13,X115] :
( ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,X111,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(X111),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(X112),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(X91),c_Message_Omsg_OMPair(X113,X114)))),X107)),c_List_Oset(X102,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(X102,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
| ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,X12,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(X12),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(X13),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(X91),c_Message_Omsg_OMPair(X115,X116)))),X86)),c_List_Oset(X102,tc_Event_Oevent),tc_Event_Oevent)
| X12 = X111 )
| ~ spl0_2443 ),
inference(avatar_component_clause,[],[f31340]) ).
fof(f32206,plain,
( spl0_2479
| ~ spl0_1444
| ~ spl0_2475 ),
inference(avatar_split_clause,[],[f32103,f32028,f11245,f32203]) ).
fof(f32203,plain,
( spl0_2479
<=> c_in(v_X,c_Event_Oused(v_evso),tc_Message_Omsg) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2479])]) ).
fof(f11245,plain,
( spl0_1444
<=> ! [X102,X4] :
( c_in(X4,c_Event_Oused(X102),tc_Message_Omsg)
| ~ c_in(X4,c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,X102)),tc_Message_Omsg) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1444])]) ).
fof(f32028,plain,
( spl0_2475
<=> c_in(v_X,c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evso)),tc_Message_Omsg) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2475])]) ).
fof(f32103,plain,
( c_in(v_X,c_Event_Oused(v_evso),tc_Message_Omsg)
| ~ spl0_1444
| ~ spl0_2475 ),
inference(resolution,[],[f32030,f11246]) ).
fof(f11246,plain,
( ! [X4,X102] :
( ~ c_in(X4,c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,X102)),tc_Message_Omsg)
| c_in(X4,c_Event_Oused(X102),tc_Message_Omsg) )
| ~ spl0_1444 ),
inference(avatar_component_clause,[],[f11245]) ).
fof(f32030,plain,
( c_in(v_X,c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evso)),tc_Message_Omsg)
| ~ spl0_2475 ),
inference(avatar_component_clause,[],[f32028]) ).
fof(f32201,plain,
( spl0_2478
| ~ spl0_4
| ~ spl0_749
| ~ spl0_2443 ),
inference(avatar_split_clause,[],[f31355,f31340,f7334,f3427,f32199]) ).
fof(f31355,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ c_in(v_evso,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
| ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,X0,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(X0),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(X1),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K),c_Message_Omsg_OMPair(X2,X3)))),X4)),c_List_Oset(v_evso,tc_Event_Oevent),tc_Event_Oevent)
| v_Aa = X0 )
| ~ spl0_749
| ~ spl0_2443 ),
inference(resolution,[],[f31341,f7336]) ).
fof(f32096,plain,
( spl0_2477
| ~ spl0_120
| ~ spl0_1885 ),
inference(avatar_split_clause,[],[f19764,f19096,f3997,f32094]) ).
fof(f32094,plain,
( spl0_2477
<=> ! [X2,X0,X1] : c_in(X0,c_Relation_ORange(c_UNIV,X1,X2),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2477])]) ).
fof(f3997,plain,
( spl0_120
<=> ! [X0,X1] : c_in(X0,c_UNIV,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_120])]) ).
fof(f19096,plain,
( spl0_1885
<=> ! [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_1885])]) ).
fof(f19764,plain,
( ! [X2,X0,X1] : c_in(X0,c_Relation_ORange(c_UNIV,X1,X2),X2)
| ~ spl0_120
| ~ spl0_1885 ),
inference(resolution,[],[f19097,f3998]) ).
fof(f3998,plain,
( ! [X0,X1] : c_in(X0,c_UNIV,X1)
| ~ spl0_120 ),
inference(avatar_component_clause,[],[f3997]) ).
fof(f19097,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_1885 ),
inference(avatar_component_clause,[],[f19096]) ).
fof(f32092,plain,
( spl0_2476
| ~ spl0_120
| ~ spl0_1882 ),
inference(avatar_split_clause,[],[f19711,f19084,f3997,f32090]) ).
fof(f32090,plain,
( spl0_2476
<=> ! [X2,X0,X1] : c_in(X0,c_Relation_ODomain(c_UNIV,X1,X2),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2476])]) ).
fof(f19084,plain,
( spl0_1882
<=> ! [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_1882])]) ).
fof(f19711,plain,
( ! [X2,X0,X1] : c_in(X0,c_Relation_ODomain(c_UNIV,X1,X2),X1)
| ~ spl0_120
| ~ spl0_1882 ),
inference(resolution,[],[f19085,f3998]) ).
fof(f19085,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_1882 ),
inference(avatar_component_clause,[],[f19084]) ).
fof(f32031,plain,
( spl0_2475
| ~ spl0_1215
| ~ spl0_2464 ),
inference(avatar_split_clause,[],[f31774,f31730,f9646,f32028]) ).
fof(f9646,plain,
( spl0_1215
<=> ! [X86,X88] :
( ~ c_in(X86,c_Message_Oanalz(X88),tc_Message_Omsg)
| c_in(X86,c_Message_Oparts(X88),tc_Message_Omsg) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1215])]) ).
fof(f31730,plain,
( spl0_2464
<=> c_in(v_X,c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evso)),tc_Message_Omsg) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2464])]) ).
fof(f31774,plain,
( c_in(v_X,c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evso)),tc_Message_Omsg)
| ~ spl0_1215
| ~ spl0_2464 ),
inference(resolution,[],[f31732,f9647]) ).
fof(f9647,plain,
( ! [X88,X86] :
( ~ c_in(X86,c_Message_Oanalz(X88),tc_Message_Omsg)
| c_in(X86,c_Message_Oparts(X88),tc_Message_Omsg) )
| ~ spl0_1215 ),
inference(avatar_component_clause,[],[f9646]) ).
fof(f31732,plain,
( c_in(v_X,c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evso)),tc_Message_Omsg)
| ~ spl0_2464 ),
inference(avatar_component_clause,[],[f31730]) ).
fof(f31773,plain,
( spl0_2474
| ~ spl0_652
| ~ spl0_788
| ~ spl0_1617 ),
inference(avatar_split_clause,[],[f14836,f14283,f7492,f6128,f31770]) ).
fof(f31770,plain,
( spl0_2474
<=> c_0 = c_List_Olast(c_List_Oupt(c_0,c_1),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2474])]) ).
fof(f7492,plain,
( spl0_788
<=> ! [X15] : c_0 = c_minus(X15,X15,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_788])]) ).
fof(f14283,plain,
( spl0_1617
<=> ! [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_1617])]) ).
fof(f14836,plain,
( c_0 = c_List_Olast(c_List_Oupt(c_0,c_1),tc_nat)
| ~ spl0_652
| ~ spl0_788
| ~ spl0_1617 ),
inference(forward_demodulation,[],[f14818,f7493]) ).
fof(f7493,plain,
( ! [X15] : c_0 = c_minus(X15,X15,tc_nat)
| ~ spl0_788 ),
inference(avatar_component_clause,[],[f7492]) ).
fof(f14818,plain,
( c_minus(c_1,c_1,tc_nat) = c_List_Olast(c_List_Oupt(c_0,c_1),tc_nat)
| ~ spl0_652
| ~ spl0_1617 ),
inference(resolution,[],[f14284,f6130]) ).
fof(f14284,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_1617 ),
inference(avatar_component_clause,[],[f14283]) ).
fof(f31768,plain,
( spl0_2472
| spl0_2473
| ~ spl0_672
| ~ spl0_1609 ),
inference(avatar_split_clause,[],[f14725,f14251,f6982,f31766,f31763]) ).
fof(f31763,plain,
( spl0_2472
<=> ! [X1] : ~ class_Ring__and__Field_Oordered__idom(tc_set(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2472])]) ).
fof(f31766,plain,
( spl0_2473
<=> ! [X0] : c_lessequals(X0,X0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2473])]) ).
fof(f6982,plain,
( spl0_672
<=> ! [X12,X1] : c_lessequals(X12,X12,tc_set(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_672])]) ).
fof(f14251,plain,
( spl0_1609
<=> ! [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_1609])]) ).
fof(f14725,plain,
( ! [X0,X1] :
( c_lessequals(X0,X0,tc_IntDef_Oint)
| ~ class_Ring__and__Field_Oordered__idom(tc_set(X1)) )
| ~ spl0_672
| ~ spl0_1609 ),
inference(resolution,[],[f14252,f6983]) ).
fof(f6983,plain,
( ! [X1,X12] : c_lessequals(X12,X12,tc_set(X1))
| ~ spl0_672 ),
inference(avatar_component_clause,[],[f6982]) ).
fof(f14252,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_1609 ),
inference(avatar_component_clause,[],[f14251]) ).
fof(f31761,plain,
( spl0_2471
| ~ spl0_848
| ~ spl0_1591 ),
inference(avatar_split_clause,[],[f14199,f12911,f7746,f31759]) ).
fof(f31759,plain,
( spl0_2471
<=> ! [X0] : c_lessequals(X0,c_plus(X0,X0,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2471])]) ).
fof(f12911,plain,
( spl0_1591
<=> ! [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_1591])]) ).
fof(f14199,plain,
( ! [X0] : c_lessequals(X0,c_plus(X0,X0,tc_nat),tc_nat)
| ~ spl0_848
| ~ spl0_1591 ),
inference(superposition,[],[f7747,f12912]) ).
fof(f12912,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_1591 ),
inference(avatar_component_clause,[],[f12911]) ).
fof(f31757,plain,
( spl0_2470
| ~ spl0_1243
| ~ spl0_1536 ),
inference(avatar_split_clause,[],[f13706,f12645,f9989,f31755]) ).
fof(f31755,plain,
( spl0_2470
<=> ! [X2,X0,X1] : c_0 = c_Nat_Osize(X0,tc_prod(X1,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2470])]) ).
fof(f9989,plain,
( spl0_1243
<=> ! [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_1243])]) ).
fof(f13706,plain,
( ! [X2,X0,X1] : c_0 = c_Nat_Osize(X0,tc_prod(X1,X2))
| ~ spl0_1243
| ~ spl0_1536 ),
inference(superposition,[],[f9990,f12646]) ).
fof(f9990,plain,
( ! [X2,X18,X1,X27] : c_0 = c_Nat_Osize(c_Pair(X18,X27,X1,X2),tc_prod(X1,X2))
| ~ spl0_1243 ),
inference(avatar_component_clause,[],[f9989]) ).
fof(f31753,plain,
( spl0_2469
| ~ spl0_795
| ~ spl0_819
| ~ spl0_1318 ),
inference(avatar_split_clause,[],[f10709,f10314,f7617,f7520,f31751]) ).
fof(f31751,plain,
( spl0_2469
<=> ! [X0] : c_1 = c_Nat_Osize(c_Message_Omsg_OHash(c_Message_Omsg_ONumber(X0)),tc_Message_Omsg) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2469])]) ).
fof(f7520,plain,
( spl0_795
<=> ! [X3] : c_plus(c_0,X3,tc_nat) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_795])]) ).
fof(f7617,plain,
( spl0_819
<=> ! [X90] : c_0 = c_Nat_Osize(c_Message_Omsg_ONumber(X90),tc_Message_Omsg) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_819])]) ).
fof(f10314,plain,
( spl0_1318
<=> ! [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_1318])]) ).
fof(f10709,plain,
( ! [X0] : c_1 = c_Nat_Osize(c_Message_Omsg_OHash(c_Message_Omsg_ONumber(X0)),tc_Message_Omsg)
| ~ spl0_795
| ~ spl0_819
| ~ spl0_1318 ),
inference(forward_demodulation,[],[f10698,f7521]) ).
fof(f7521,plain,
( ! [X3] : c_plus(c_0,X3,tc_nat) = X3
| ~ spl0_795 ),
inference(avatar_component_clause,[],[f7520]) ).
fof(f10698,plain,
( ! [X0] : c_plus(c_0,c_1,tc_nat) = c_Nat_Osize(c_Message_Omsg_OHash(c_Message_Omsg_ONumber(X0)),tc_Message_Omsg)
| ~ spl0_819
| ~ spl0_1318 ),
inference(superposition,[],[f10315,f7618]) ).
fof(f7618,plain,
( ! [X90] : c_0 = c_Nat_Osize(c_Message_Omsg_ONumber(X90),tc_Message_Omsg)
| ~ spl0_819 ),
inference(avatar_component_clause,[],[f7617]) ).
fof(f10315,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_1318 ),
inference(avatar_component_clause,[],[f10314]) ).
fof(f31749,plain,
( spl0_2468
| ~ spl0_795
| ~ spl0_820
| ~ spl0_1318 ),
inference(avatar_split_clause,[],[f10708,f10314,f7621,f7520,f31747]) ).
fof(f31747,plain,
( spl0_2468
<=> ! [X0] : c_1 = c_Nat_Osize(c_Message_Omsg_OHash(c_Message_Omsg_ONonce(X0)),tc_Message_Omsg) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2468])]) ).
fof(f7621,plain,
( spl0_820
<=> ! [X90] : c_0 = c_Nat_Osize(c_Message_Omsg_ONonce(X90),tc_Message_Omsg) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_820])]) ).
fof(f10708,plain,
( ! [X0] : c_1 = c_Nat_Osize(c_Message_Omsg_OHash(c_Message_Omsg_ONonce(X0)),tc_Message_Omsg)
| ~ spl0_795
| ~ spl0_820
| ~ spl0_1318 ),
inference(forward_demodulation,[],[f10697,f7521]) ).
fof(f10697,plain,
( ! [X0] : c_plus(c_0,c_1,tc_nat) = c_Nat_Osize(c_Message_Omsg_OHash(c_Message_Omsg_ONonce(X0)),tc_Message_Omsg)
| ~ spl0_820
| ~ spl0_1318 ),
inference(superposition,[],[f10315,f7622]) ).
fof(f7622,plain,
( ! [X90] : c_0 = c_Nat_Osize(c_Message_Omsg_ONonce(X90),tc_Message_Omsg)
| ~ spl0_820 ),
inference(avatar_component_clause,[],[f7621]) ).
fof(f31745,plain,
( spl0_2467
| ~ spl0_795
| ~ spl0_821
| ~ spl0_1318 ),
inference(avatar_split_clause,[],[f10707,f10314,f7625,f7520,f31743]) ).
fof(f31743,plain,
( spl0_2467
<=> ! [X0] : c_1 = c_Nat_Osize(c_Message_Omsg_OHash(c_Message_Omsg_OKey(X0)),tc_Message_Omsg) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2467])]) ).
fof(f7625,plain,
( spl0_821
<=> ! [X90] : c_0 = c_Nat_Osize(c_Message_Omsg_OKey(X90),tc_Message_Omsg) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_821])]) ).
fof(f10707,plain,
( ! [X0] : c_1 = c_Nat_Osize(c_Message_Omsg_OHash(c_Message_Omsg_OKey(X0)),tc_Message_Omsg)
| ~ spl0_795
| ~ spl0_821
| ~ spl0_1318 ),
inference(forward_demodulation,[],[f10696,f7521]) ).
fof(f10696,plain,
( ! [X0] : c_plus(c_0,c_1,tc_nat) = c_Nat_Osize(c_Message_Omsg_OHash(c_Message_Omsg_OKey(X0)),tc_Message_Omsg)
| ~ spl0_821
| ~ spl0_1318 ),
inference(superposition,[],[f10315,f7626]) ).
fof(f7626,plain,
( ! [X90] : c_0 = c_Nat_Osize(c_Message_Omsg_OKey(X90),tc_Message_Omsg)
| ~ spl0_821 ),
inference(avatar_component_clause,[],[f7625]) ).
fof(f31741,plain,
( spl0_2466
| ~ spl0_795
| ~ spl0_818
| ~ spl0_1318 ),
inference(avatar_split_clause,[],[f10705,f10314,f7613,f7520,f31739]) ).
fof(f31739,plain,
( spl0_2466
<=> ! [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_2466])]) ).
fof(f7613,plain,
( spl0_818
<=> ! [X94] : c_0 = c_Nat_Osize(c_Message_Omsg_OAgent(X94),tc_Message_Omsg) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_818])]) ).
fof(f10705,plain,
( ! [X0] : c_1 = c_Nat_Osize(c_Message_Omsg_OHash(c_Message_Omsg_OAgent(X0)),tc_Message_Omsg)
| ~ spl0_795
| ~ spl0_818
| ~ spl0_1318 ),
inference(forward_demodulation,[],[f10694,f7521]) ).
fof(f10694,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_818
| ~ spl0_1318 ),
inference(superposition,[],[f10315,f7614]) ).
fof(f7614,plain,
( ! [X94] : c_0 = c_Nat_Osize(c_Message_Omsg_OAgent(X94),tc_Message_Omsg)
| ~ spl0_818 ),
inference(avatar_component_clause,[],[f7613]) ).
fof(f31737,plain,
( spl0_2465
| ~ spl0_872
| ~ spl0_1318 ),
inference(avatar_split_clause,[],[f10703,f10314,f7842,f31735]) ).
fof(f31735,plain,
( spl0_2465
<=> ! [X0] : ~ c_less(c_Nat_Osize(c_Message_Omsg_OHash(X0),tc_Message_Omsg),c_1,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2465])]) ).
fof(f7842,plain,
( spl0_872
<=> ! [X43,X59] : ~ c_less(c_plus(X59,X43,tc_nat),X43,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_872])]) ).
fof(f10703,plain,
( ! [X0] : ~ c_less(c_Nat_Osize(c_Message_Omsg_OHash(X0),tc_Message_Omsg),c_1,tc_nat)
| ~ spl0_872
| ~ spl0_1318 ),
inference(superposition,[],[f7843,f10315]) ).
fof(f7843,plain,
( ! [X59,X43] : ~ c_less(c_plus(X59,X43,tc_nat),X43,tc_nat)
| ~ spl0_872 ),
inference(avatar_component_clause,[],[f7842]) ).
fof(f31733,plain,
( spl0_2464
| ~ spl0_1451
| ~ spl0_2459 ),
inference(avatar_split_clause,[],[f31622,f31617,f11273,f31730]) ).
fof(f11273,plain,
( spl0_1451
<=> ! [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_1451])]) ).
fof(f31617,plain,
( spl0_2459
<=> c_in(c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_ONonce(v_NB))))),v_X),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evso)),tc_Message_Omsg) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2459])]) ).
fof(f31622,plain,
( c_in(v_X,c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evso)),tc_Message_Omsg)
| ~ spl0_1451
| ~ spl0_2459 ),
inference(resolution,[],[f31619,f11274]) ).
fof(f11274,plain,
( ! [X88,X86,X87] :
( ~ c_in(c_Message_Omsg_OMPair(X86,X87),c_Message_Oanalz(X88),tc_Message_Omsg)
| c_in(X87,c_Message_Oanalz(X88),tc_Message_Omsg) )
| ~ spl0_1451 ),
inference(avatar_component_clause,[],[f11273]) ).
fof(f31619,plain,
( c_in(c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_ONonce(v_NB))))),v_X),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evso)),tc_Message_Omsg)
| ~ spl0_2459 ),
inference(avatar_component_clause,[],[f31617]) ).
fof(f31728,plain,
( spl0_2463
| ~ spl0_647
| ~ spl0_1129
| ~ spl0_1317 ),
inference(avatar_split_clause,[],[f10693,f10310,f9149,f6106,f31726]) ).
fof(f31726,plain,
( spl0_2463
<=> ! [X0] : c_less(c_uminus(c_1,tc_IntDef_Oint),c_IntDef_Oint(X0),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2463])]) ).
fof(f6106,plain,
( spl0_647
<=> c_0 = c_IntDef_Oint(c_0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_647])]) ).
fof(f9149,plain,
( spl0_1129
<=> ! [X0] : c_plus(X0,c_0,tc_IntDef_Oint) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1129])]) ).
fof(f10310,plain,
( spl0_1317
<=> ! [X21,X15] : c_less(c_uminus(c_plus(c_1,c_IntDef_Oint(X21),tc_IntDef_Oint),tc_IntDef_Oint),c_IntDef_Oint(X15),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1317])]) ).
fof(f10693,plain,
( ! [X0] : c_less(c_uminus(c_1,tc_IntDef_Oint),c_IntDef_Oint(X0),tc_IntDef_Oint)
| ~ spl0_647
| ~ spl0_1129
| ~ spl0_1317 ),
inference(forward_demodulation,[],[f10690,f9150]) ).
fof(f9150,plain,
( ! [X0] : c_plus(X0,c_0,tc_IntDef_Oint) = X0
| ~ spl0_1129 ),
inference(avatar_component_clause,[],[f9149]) ).
fof(f10690,plain,
( ! [X0] : c_less(c_uminus(c_plus(c_1,c_0,tc_IntDef_Oint),tc_IntDef_Oint),c_IntDef_Oint(X0),tc_IntDef_Oint)
| ~ spl0_647
| ~ spl0_1317 ),
inference(superposition,[],[f10311,f6108]) ).
fof(f6108,plain,
( c_0 = c_IntDef_Oint(c_0)
| ~ spl0_647 ),
inference(avatar_component_clause,[],[f6106]) ).
fof(f10311,plain,
( ! [X21,X15] : c_less(c_uminus(c_plus(c_1,c_IntDef_Oint(X21),tc_IntDef_Oint),tc_IntDef_Oint),c_IntDef_Oint(X15),tc_IntDef_Oint)
| ~ spl0_1317 ),
inference(avatar_component_clause,[],[f10310]) ).
fof(f31664,plain,
( spl0_2462
| spl0_114
| ~ spl0_2038 ),
inference(avatar_split_clause,[],[f22440,f22264,f3972,f31661]) ).
fof(f31661,plain,
( spl0_2462
<=> c_List_Oremdups(c_List_Olist_OCons(c_Event_Oevent_ONotes(c_Message_Oagent_OSpy,c_Message_Omsg_OMPair(v_na,c_Message_Omsg_OMPair(v_nb,c_Message_Omsg_OKey(v_K)))),v_evso,tc_Event_Oevent),tc_Event_Oevent) = c_List_Olist_OCons(c_Event_Oevent_ONotes(c_Message_Oagent_OSpy,c_Message_Omsg_OMPair(v_na,c_Message_Omsg_OMPair(v_nb,c_Message_Omsg_OKey(v_K)))),c_List_Oremdups(v_evso,tc_Event_Oevent),tc_Event_Oevent) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2462])]) ).
fof(f3972,plain,
( spl0_114
<=> c_in(c_Event_Oevent_ONotes(c_Message_Oagent_OSpy,c_Message_Omsg_OMPair(v_na,c_Message_Omsg_OMPair(v_nb,c_Message_Omsg_OKey(v_K)))),c_List_Oset(v_evso,tc_Event_Oevent),tc_Event_Oevent) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_114])]) ).
fof(f22264,plain,
( spl0_2038
<=> ! [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_2038])]) ).
fof(f22440,plain,
( c_List_Oremdups(c_List_Olist_OCons(c_Event_Oevent_ONotes(c_Message_Oagent_OSpy,c_Message_Omsg_OMPair(v_na,c_Message_Omsg_OMPair(v_nb,c_Message_Omsg_OKey(v_K)))),v_evso,tc_Event_Oevent),tc_Event_Oevent) = c_List_Olist_OCons(c_Event_Oevent_ONotes(c_Message_Oagent_OSpy,c_Message_Omsg_OMPair(v_na,c_Message_Omsg_OMPair(v_nb,c_Message_Omsg_OKey(v_K)))),c_List_Oremdups(v_evso,tc_Event_Oevent),tc_Event_Oevent)
| spl0_114
| ~ spl0_2038 ),
inference(resolution,[],[f22265,f3974]) ).
fof(f3974,plain,
( ~ c_in(c_Event_Oevent_ONotes(c_Message_Oagent_OSpy,c_Message_Omsg_OMPair(v_na,c_Message_Omsg_OMPair(v_nb,c_Message_Omsg_OKey(v_K)))),c_List_Oset(v_evso,tc_Event_Oevent),tc_Event_Oevent)
| spl0_114 ),
inference(avatar_component_clause,[],[f3972]) ).
fof(f22265,plain,
( ! [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) )
| ~ spl0_2038 ),
inference(avatar_component_clause,[],[f22264]) ).
fof(f31659,plain,
( spl0_2461
| ~ spl0_920
| ~ spl0_1835 ),
inference(avatar_split_clause,[],[f18904,f17277,f8107,f31656]) ).
fof(f31656,plain,
( spl0_2461
<=> c_in(c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K),c_Message_Omsg_OMPair(v_na,v_nb)))),c_Message_Omsg_OCrypt(c_Public_OshrK(v_B),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OKey(v_K)))),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evso)),tc_Message_Omsg) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2461])]) ).
fof(f17277,plain,
( spl0_1835
<=> ! [X102,X86,X12,X13] :
( c_in(X86,c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,X102)),tc_Message_Omsg)
| ~ c_in(c_Event_Oevent_OSays(X12,X13,X86),c_List_Oset(X102,tc_Event_Oevent),tc_Event_Oevent) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1835])]) ).
fof(f18904,plain,
( c_in(c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K),c_Message_Omsg_OMPair(v_na,v_nb)))),c_Message_Omsg_OCrypt(c_Public_OshrK(v_B),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OKey(v_K)))),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evso)),tc_Message_Omsg)
| ~ spl0_920
| ~ spl0_1835 ),
inference(resolution,[],[f17278,f8109]) ).
fof(f17278,plain,
( ! [X86,X12,X102,X13] :
( ~ c_in(c_Event_Oevent_OSays(X12,X13,X86),c_List_Oset(X102,tc_Event_Oevent),tc_Event_Oevent)
| c_in(X86,c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,X102)),tc_Message_Omsg) )
| ~ spl0_1835 ),
inference(avatar_component_clause,[],[f17277]) ).
fof(f31628,plain,
( spl0_2460
| spl0_114
| ~ spl0_2004 ),
inference(avatar_split_clause,[],[f21697,f20836,f3972,f31626]) ).
fof(f31626,plain,
( spl0_2460
<=> ! [X0] : c_minus(c_List_Oset(v_evso,tc_Event_Oevent),X0,tc_set(tc_Event_Oevent)) = c_minus(c_List_Oset(v_evso,tc_Event_Oevent),c_insert(c_Event_Oevent_ONotes(c_Message_Oagent_OSpy,c_Message_Omsg_OMPair(v_na,c_Message_Omsg_OMPair(v_nb,c_Message_Omsg_OKey(v_K)))),X0,tc_Event_Oevent),tc_set(tc_Event_Oevent)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2460])]) ).
fof(f20836,plain,
( spl0_2004
<=> ! [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_2004])]) ).
fof(f21697,plain,
( ! [X0] : c_minus(c_List_Oset(v_evso,tc_Event_Oevent),X0,tc_set(tc_Event_Oevent)) = c_minus(c_List_Oset(v_evso,tc_Event_Oevent),c_insert(c_Event_Oevent_ONotes(c_Message_Oagent_OSpy,c_Message_Omsg_OMPair(v_na,c_Message_Omsg_OMPair(v_nb,c_Message_Omsg_OKey(v_K)))),X0,tc_Event_Oevent),tc_set(tc_Event_Oevent))
| spl0_114
| ~ spl0_2004 ),
inference(resolution,[],[f20837,f3974]) ).
fof(f20837,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_2004 ),
inference(avatar_component_clause,[],[f20836]) ).
fof(f31620,plain,
( spl0_2459
| ~ spl0_749
| ~ spl0_1835 ),
inference(avatar_split_clause,[],[f18903,f17277,f7334,f31617]) ).
fof(f18903,plain,
( c_in(c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_ONonce(v_NB))))),v_X),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evso)),tc_Message_Omsg)
| ~ spl0_749
| ~ spl0_1835 ),
inference(resolution,[],[f17278,f7336]) ).
fof(f31569,plain,
( spl0_2458
| spl0_5
| ~ spl0_2004 ),
inference(avatar_split_clause,[],[f21760,f20836,f3432,f31567]) ).
fof(f31567,plain,
( spl0_2458
<=> ! [X0] : c_minus(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evso)),X0,tc_set(tc_Message_Omsg)) = c_minus(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evso)),c_insert(c_Message_Omsg_OKey(v_K),X0,tc_Message_Omsg),tc_set(tc_Message_Omsg)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2458])]) ).
fof(f3432,plain,
( spl0_5
<=> c_in(c_Message_Omsg_OKey(v_K),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evso)),tc_Message_Omsg) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).
fof(f21760,plain,
( ! [X0] : c_minus(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evso)),X0,tc_set(tc_Message_Omsg)) = c_minus(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evso)),c_insert(c_Message_Omsg_OKey(v_K),X0,tc_Message_Omsg),tc_set(tc_Message_Omsg))
| spl0_5
| ~ spl0_2004 ),
inference(resolution,[],[f20837,f3434]) ).
fof(f3434,plain,
( ~ c_in(c_Message_Omsg_OKey(v_K),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evso)),tc_Message_Omsg)
| spl0_5 ),
inference(avatar_component_clause,[],[f3432]) ).
fof(f31560,plain,
( spl0_2457
| spl0_114
| ~ spl0_1988 ),
inference(avatar_split_clause,[],[f21379,f20772,f3972,f31558]) ).
fof(f31558,plain,
( spl0_2457
<=> ! [X0] : c_List_Olist__inter(c_List_Olist_OCons(c_Event_Oevent_ONotes(c_Message_Oagent_OSpy,c_Message_Omsg_OMPair(v_na,c_Message_Omsg_OMPair(v_nb,c_Message_Omsg_OKey(v_K)))),X0,tc_Event_Oevent),v_evso,tc_Event_Oevent) = c_List_Olist__inter(X0,v_evso,tc_Event_Oevent) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2457])]) ).
fof(f20772,plain,
( spl0_1988
<=> ! [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_1988])]) ).
fof(f21379,plain,
( ! [X0] : c_List_Olist__inter(c_List_Olist_OCons(c_Event_Oevent_ONotes(c_Message_Oagent_OSpy,c_Message_Omsg_OMPair(v_na,c_Message_Omsg_OMPair(v_nb,c_Message_Omsg_OKey(v_K)))),X0,tc_Event_Oevent),v_evso,tc_Event_Oevent) = c_List_Olist__inter(X0,v_evso,tc_Event_Oevent)
| spl0_114
| ~ spl0_1988 ),
inference(resolution,[],[f20773,f3974]) ).
fof(f20773,plain,
( ! [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) )
| ~ spl0_1988 ),
inference(avatar_component_clause,[],[f20772]) ).
fof(f31547,plain,
spl0_2456,
inference(avatar_split_clause,[],[f6,f31545]) ).
fof(f31545,plain,
( spl0_2456
<=> ! [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_2456])]) ).
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/benchmark/theBenchmark.p',cls_Datatype__Universe_OdprodI_0) ).
fof(f31524,plain,
spl0_2455,
inference(avatar_split_clause,[],[f10,f31522]) ).
fof(f31522,plain,
( spl0_2455
<=> ! [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_2455])]) ).
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/benchmark/theBenchmark.p',cls_Datatype__Universe_OdsumE_3) ).
fof(f31482,plain,
spl0_2454,
inference(avatar_split_clause,[],[f9,f31480]) ).
fof(f31480,plain,
( spl0_2454
<=> ! [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_2454])]) ).
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/benchmark/theBenchmark.p',cls_Datatype__Universe_OdsumE_2) ).
fof(f31478,plain,
( spl0_2453
| ~ spl0_1552
| ~ spl0_2436 ),
inference(avatar_split_clause,[],[f31286,f31084,f12709,f31476]) ).
fof(f31476,plain,
( spl0_2453
<=> ! [X0] : c_union(c_Yahalom_Oyahalom,c_insert(v_evso,X0,tc_List_Olist(tc_Event_Oevent)),tc_List_Olist(tc_Event_Oevent)) = c_union(c_Yahalom_Oyahalom,X0,tc_List_Olist(tc_Event_Oevent)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2453])]) ).
fof(f12709,plain,
( spl0_1552
<=> ! [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_1552])]) ).
fof(f31084,plain,
( spl0_2436
<=> ! [X0] : c_minus(X0,c_Yahalom_Oyahalom,tc_set(tc_List_Olist(tc_Event_Oevent))) = c_minus(c_insert(v_evso,X0,tc_List_Olist(tc_Event_Oevent)),c_Yahalom_Oyahalom,tc_set(tc_List_Olist(tc_Event_Oevent))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2436])]) ).
fof(f31286,plain,
( ! [X0] : c_union(c_Yahalom_Oyahalom,c_insert(v_evso,X0,tc_List_Olist(tc_Event_Oevent)),tc_List_Olist(tc_Event_Oevent)) = c_union(c_Yahalom_Oyahalom,X0,tc_List_Olist(tc_Event_Oevent))
| ~ spl0_1552
| ~ spl0_2436 ),
inference(forward_demodulation,[],[f31272,f12710]) ).
fof(f12710,plain,
( ! [X1,X12,X13] : c_union(X12,X13,X1) = c_union(X12,c_minus(X13,X12,tc_set(X1)),X1)
| ~ spl0_1552 ),
inference(avatar_component_clause,[],[f12709]) ).
fof(f31272,plain,
( ! [X0] : c_union(c_Yahalom_Oyahalom,c_insert(v_evso,X0,tc_List_Olist(tc_Event_Oevent)),tc_List_Olist(tc_Event_Oevent)) = c_union(c_Yahalom_Oyahalom,c_minus(X0,c_Yahalom_Oyahalom,tc_set(tc_List_Olist(tc_Event_Oevent))),tc_List_Olist(tc_Event_Oevent))
| ~ spl0_1552
| ~ spl0_2436 ),
inference(superposition,[],[f12710,f31085]) ).
fof(f31085,plain,
( ! [X0] : c_minus(X0,c_Yahalom_Oyahalom,tc_set(tc_List_Olist(tc_Event_Oevent))) = c_minus(c_insert(v_evso,X0,tc_List_Olist(tc_Event_Oevent)),c_Yahalom_Oyahalom,tc_set(tc_List_Olist(tc_Event_Oevent)))
| ~ spl0_2436 ),
inference(avatar_component_clause,[],[f31084]) ).
fof(f31474,plain,
spl0_2452,
inference(avatar_split_clause,[],[f8,f31472]) ).
fof(f31472,plain,
( spl0_2452
<=> ! [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_2452])]) ).
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/benchmark/theBenchmark.p',cls_Datatype__Universe_OdsumE_1) ).
fof(f31451,plain,
spl0_2451,
inference(avatar_split_clause,[],[f7,f31449]) ).
fof(f31449,plain,
( spl0_2451
<=> ! [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_2451])]) ).
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/benchmark/theBenchmark.p',cls_Datatype__Universe_OdsumE_0) ).
fof(f31430,plain,
spl0_2450,
inference(avatar_split_clause,[],[f3,f31428]) ).
fof(f31428,plain,
( spl0_2450
<=> ! [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_2450])]) ).
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/benchmark/theBenchmark.p',cls_Datatype__Universe_OdprodE_0) ).
fof(f31414,plain,
spl0_2449,
inference(avatar_split_clause,[],[f12,f31412]) ).
fof(f31412,plain,
( spl0_2449
<=> ! [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_2449])]) ).
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/benchmark/theBenchmark.p',cls_Datatype__Universe_Odsum__In1I_0) ).
fof(f31410,plain,
spl0_2448,
inference(avatar_split_clause,[],[f11,f31408]) ).
fof(f31408,plain,
( spl0_2448
<=> ! [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_2448])]) ).
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/benchmark/theBenchmark.p',cls_Datatype__Universe_Odsum__In0I_0) ).
fof(f31394,plain,
( spl0_2447
| ~ spl0_1551
| ~ spl0_2436 ),
inference(avatar_split_clause,[],[f31285,f31084,f12705,f31392]) ).
fof(f31392,plain,
( spl0_2447
<=> ! [X0] : c_union(c_insert(v_evso,X0,tc_List_Olist(tc_Event_Oevent)),c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent)) = c_union(X0,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2447])]) ).
fof(f12705,plain,
( spl0_1551
<=> ! [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_1551])]) ).
fof(f31285,plain,
( ! [X0] : c_union(c_insert(v_evso,X0,tc_List_Olist(tc_Event_Oevent)),c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent)) = c_union(X0,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
| ~ spl0_1551
| ~ spl0_2436 ),
inference(forward_demodulation,[],[f31271,f12706]) ).
fof(f12706,plain,
( ! [X1,X12,X13] : c_union(c_minus(X13,X12,tc_set(X1)),X12,X1) = c_union(X13,X12,X1)
| ~ spl0_1551 ),
inference(avatar_component_clause,[],[f12705]) ).
fof(f31271,plain,
( ! [X0] : c_union(c_insert(v_evso,X0,tc_List_Olist(tc_Event_Oevent)),c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent)) = c_union(c_minus(X0,c_Yahalom_Oyahalom,tc_set(tc_List_Olist(tc_Event_Oevent))),c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
| ~ spl0_1551
| ~ spl0_2436 ),
inference(superposition,[],[f12706,f31085]) ).
fof(f31354,plain,
spl0_2446,
inference(avatar_split_clause,[],[f2945,f31352]) ).
fof(f2945,axiom,
! [X113,X111,X116,X91,X86,X107,X114,X102,X12,X13,X115,X112] :
( X114 = X116
| ~ c_in(X102,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
| ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,X12,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(X12),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(X13),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(X91),c_Message_Omsg_OMPair(X115,X116)))),X86)),c_List_Oset(X102,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,X111,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(X111),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(X112),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(X91),c_Message_Omsg_OMPair(X113,X114)))),X107)),c_List_Oset(X102,tc_Event_Oevent),tc_Event_Oevent) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Yahalom_Ounique__session__keys__dest_3) ).
fof(f31350,plain,
spl0_2445,
inference(avatar_split_clause,[],[f2944,f31348]) ).
fof(f2944,axiom,
! [X113,X111,X91,X116,X86,X107,X114,X115,X102,X12,X13,X112] :
( X113 = X115
| ~ c_in(X102,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
| ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,X12,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(X12),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(X13),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(X91),c_Message_Omsg_OMPair(X115,X116)))),X86)),c_List_Oset(X102,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,X111,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(X111),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(X112),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(X91),c_Message_Omsg_OMPair(X113,X114)))),X107)),c_List_Oset(X102,tc_Event_Oevent),tc_Event_Oevent) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Yahalom_Ounique__session__keys__dest_2) ).
fof(f31346,plain,
spl0_2444,
inference(avatar_split_clause,[],[f2943,f31344]) ).
fof(f2943,axiom,
! [X113,X111,X91,X116,X86,X107,X114,X102,X12,X13,X112,X115] :
( X13 = X112
| ~ c_in(X102,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
| ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,X12,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(X12),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(X13),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(X91),c_Message_Omsg_OMPair(X115,X116)))),X86)),c_List_Oset(X102,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,X111,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(X111),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(X112),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(X91),c_Message_Omsg_OMPair(X113,X114)))),X107)),c_List_Oset(X102,tc_Event_Oevent),tc_Event_Oevent) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Yahalom_Ounique__session__keys__dest_1) ).
fof(f31342,plain,
spl0_2443,
inference(avatar_split_clause,[],[f2942,f31340]) ).
fof(f2942,axiom,
! [X113,X111,X91,X116,X86,X107,X114,X12,X102,X13,X115,X112] :
( X12 = X111
| ~ c_in(X102,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
| ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,X12,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(X12),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(X13),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(X91),c_Message_Omsg_OMPair(X115,X116)))),X86)),c_List_Oset(X102,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,X111,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(X111),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(X112),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(X91),c_Message_Omsg_OMPair(X113,X114)))),X107)),c_List_Oset(X102,tc_Event_Oevent),tc_Event_Oevent) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Yahalom_Ounique__session__keys__dest_0) ).
fof(f31298,plain,
( spl0_2442
| ~ spl0_57
| ~ spl0_797
| ~ spl0_1078
| ~ spl0_1283
| ~ spl0_1658
| ~ spl0_1806
| ~ spl0_1807
| ~ spl0_2441 ),
inference(avatar_split_clause,[],[f31294,f31289,f17164,f17160,f14448,f10151,f8879,f7528,f3692,f31296]) ).
fof(f31296,plain,
( spl0_2442
<=> ! [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_OBit(X47,c_Numeral_Obit_OB0),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_2442])]) ).
fof(f3692,plain,
( spl0_57
<=> class_Numeral_Onumber__ring(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_57])]) ).
fof(f7528,plain,
( spl0_797
<=> c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1) = c_Numeral_Obin__succ(c_Numeral_OPls) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_797])]) ).
fof(f8879,plain,
( spl0_1078
<=> ! [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_1078])]) ).
fof(f10151,plain,
( spl0_1283
<=> ! [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_1283])]) ).
fof(f14448,plain,
( spl0_1658
<=> ! [X0] : c_Numeral_Obin__mult(c_Numeral_Obin__succ(c_Numeral_OPls),X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1658])]) ).
fof(f17160,plain,
( spl0_1806
<=> ! [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_1806])]) ).
fof(f17164,plain,
( spl0_1807
<=> ! [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_1807])]) ).
fof(f31289,plain,
( spl0_2441
<=> ! [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_2441])]) ).
fof(f31294,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_OBit(X47,c_Numeral_Obit_OB0),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_57
| ~ spl0_797
| ~ spl0_1078
| ~ spl0_1283
| ~ spl0_1658
| ~ spl0_1806
| ~ spl0_1807
| ~ spl0_2441 ),
inference(forward_demodulation,[],[f31293,f18302]) ).
fof(f18302,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_57
| ~ spl0_1806 ),
inference(resolution,[],[f17161,f3694]) ).
fof(f3694,plain,
( class_Numeral_Onumber__ring(tc_IntDef_Oint)
| ~ spl0_57 ),
inference(avatar_component_clause,[],[f3692]) ).
fof(f17161,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_1806 ),
inference(avatar_component_clause,[],[f17160]) ).
fof(f31293,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_OBit(X47,c_Numeral_Obit_OB0),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_57
| ~ spl0_797
| ~ spl0_1078
| ~ spl0_1283
| ~ spl0_1658
| ~ spl0_1807
| ~ spl0_2441 ),
inference(forward_demodulation,[],[f31292,f14933]) ).
fof(f14933,plain,
( ! [X0] : c_Numeral_OBit(X0,c_Numeral_Obit_OB0) = c_Numeral_Obin__mult(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),X0)
| ~ spl0_797
| ~ spl0_1078
| ~ spl0_1283
| ~ spl0_1658 ),
inference(forward_demodulation,[],[f14932,f7530]) ).
fof(f7530,plain,
( c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1) = c_Numeral_Obin__succ(c_Numeral_OPls)
| ~ spl0_797 ),
inference(avatar_component_clause,[],[f7528]) ).
fof(f14932,plain,
( ! [X0] : c_Numeral_OBit(X0,c_Numeral_Obit_OB0) = c_Numeral_Obin__mult(c_Numeral_Obin__succ(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1)),X0)
| ~ spl0_1078
| ~ spl0_1283
| ~ spl0_1658 ),
inference(forward_demodulation,[],[f14931,f8880]) ).
fof(f8880,plain,
( ! [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)
| ~ spl0_1078 ),
inference(avatar_component_clause,[],[f8879]) ).
fof(f14931,plain,
( ! [X0] : c_Numeral_OBit(X0,c_Numeral_Obit_OB0) = c_Numeral_Obin__mult(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB0),X0)
| ~ spl0_1283
| ~ spl0_1658 ),
inference(superposition,[],[f10152,f14449]) ).
fof(f14449,plain,
( ! [X0] : c_Numeral_Obin__mult(c_Numeral_Obin__succ(c_Numeral_OPls),X0) = X0
| ~ spl0_1658 ),
inference(avatar_component_clause,[],[f14448]) ).
fof(f10152,plain,
( ! [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)
| ~ spl0_1283 ),
inference(avatar_component_clause,[],[f10151]) ).
fof(f31292,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_57
| ~ spl0_1807
| ~ spl0_2441 ),
inference(forward_demodulation,[],[f31290,f18303]) ).
fof(f18303,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_57
| ~ spl0_1807 ),
inference(resolution,[],[f17165,f3694]) ).
fof(f17165,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_1807 ),
inference(avatar_component_clause,[],[f17164]) ).
fof(f31290,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_2441 ),
inference(avatar_component_clause,[],[f31289]) ).
fof(f31291,plain,
spl0_2441,
inference(avatar_split_clause,[],[f3388,f31289]) ).
fof(f3388,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,[],[f3387,f2156]) ).
fof(f2156,axiom,
c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1) = c_Numeral_Obin__succ(c_Numeral_OPls),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obin__succ__Pls_0) ).
fof(f3387,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,[],[f3386,f2154]) ).
fof(f2154,axiom,
! [X11] : c_Numeral_Obin__succ(c_Numeral_OBit(X11,c_Numeral_Obit_OB1)) = c_Numeral_OBit(c_Numeral_Obin__succ(X11),c_Numeral_Obit_OB0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obin__succ__1_0) ).
fof(f3386,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/benchmark/theBenchmark.p',cls_IntDiv_OnegDivAlg__eqn__number__of_1) ).
fof(f31137,plain,
spl0_2440,
inference(avatar_split_clause,[],[f1620,f31135]) ).
fof(f31135,plain,
( spl0_2440
<=> ! [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_2440])]) ).
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/benchmark/theBenchmark.p',cls_List_Olexord__cons__cons_1) ).
fof(f31133,plain,
spl0_2439,
inference(avatar_split_clause,[],[f1501,f31131]) ).
fof(f31131,plain,
( spl0_2439
<=> ! [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_2439])]) ).
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/benchmark/theBenchmark.p',cls_List_OCons__in__lex_1) ).
fof(f31129,plain,
spl0_2438,
inference(avatar_split_clause,[],[f5,f31127]) ).
fof(f31127,plain,
( spl0_2438
<=> ! [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_2438])]) ).
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/benchmark/theBenchmark.p',cls_Datatype__Universe_OdprodE_2) ).
fof(f31125,plain,
spl0_2437,
inference(avatar_split_clause,[],[f4,f31123]) ).
fof(f31123,plain,
( spl0_2437
<=> ! [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_2437])]) ).
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/benchmark/theBenchmark.p',cls_Datatype__Universe_OdprodE_1) ).
fof(f31086,plain,
( spl0_2436
| ~ spl0_4
| ~ spl0_2006 ),
inference(avatar_split_clause,[],[f21916,f20844,f3427,f31084]) ).
fof(f20844,plain,
( spl0_2006
<=> ! [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_2006])]) ).
fof(f21916,plain,
( ! [X0] : c_minus(X0,c_Yahalom_Oyahalom,tc_set(tc_List_Olist(tc_Event_Oevent))) = c_minus(c_insert(v_evso,X0,tc_List_Olist(tc_Event_Oevent)),c_Yahalom_Oyahalom,tc_set(tc_List_Olist(tc_Event_Oevent)))
| ~ spl0_4
| ~ spl0_2006 ),
inference(resolution,[],[f20845,f3429]) ).
fof(f3429,plain,
( c_in(v_evso,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f3427]) ).
fof(f20845,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_2006 ),
inference(avatar_component_clause,[],[f20844]) ).
fof(f31081,plain,
spl0_2435,
inference(avatar_split_clause,[],[f1503,f31079]) ).
fof(f31079,plain,
( spl0_2435
<=> ! [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_2435])]) ).
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/benchmark/theBenchmark.p',cls_List_OCons__in__lex_3) ).
fof(f31077,plain,
spl0_2434,
inference(avatar_split_clause,[],[f1369,f31075]) ).
fof(f31075,plain,
( spl0_2434
<=> ! [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_2434])]) ).
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/benchmark/theBenchmark.p',cls_IntDef_Oequiv__intrel__iff_1) ).
fof(f31073,plain,
spl0_2433,
inference(avatar_split_clause,[],[f1368,f31071]) ).
fof(f31071,plain,
( spl0_2433
<=> ! [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_2433])]) ).
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/benchmark/theBenchmark.p',cls_IntDef_Oequiv__intrel__iff_0) ).
fof(f31057,plain,
( spl0_2432
| ~ spl0_57
| ~ spl0_797
| ~ spl0_1078
| ~ spl0_1283
| ~ spl0_1658
| ~ spl0_1807
| ~ spl0_2431 ),
inference(avatar_split_clause,[],[f31053,f31049,f17164,f14448,f10151,f8879,f7528,f3692,f31055]) ).
fof(f31055,plain,
( spl0_2432
<=> ! [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_OBit(X47,c_Numeral_Obit_OB0),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_2432])]) ).
fof(f31049,plain,
( spl0_2431
<=> ! [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_2431])]) ).
fof(f31053,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_OBit(X47,c_Numeral_Obit_OB0),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_57
| ~ spl0_797
| ~ spl0_1078
| ~ spl0_1283
| ~ spl0_1658
| ~ spl0_1807
| ~ spl0_2431 ),
inference(forward_demodulation,[],[f31052,f14933]) ).
fof(f31052,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_57
| ~ spl0_1807
| ~ spl0_2431 ),
inference(forward_demodulation,[],[f31050,f18303]) ).
fof(f31050,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_2431 ),
inference(avatar_component_clause,[],[f31049]) ).
fof(f31051,plain,
spl0_2431,
inference(avatar_split_clause,[],[f3382,f31049]) ).
fof(f3382,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,[],[f3381,f2156]) ).
fof(f3381,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,[],[f3380,f2154]) ).
fof(f3380,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/benchmark/theBenchmark.p',cls_IntDiv_OposDivAlg__eqn__number__of_1) ).
fof(f31012,plain,
spl0_2430,
inference(avatar_split_clause,[],[f1791,f31010]) ).
fof(f31010,plain,
( spl0_2430
<=> ! [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_2430])]) ).
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/benchmark/theBenchmark.p',cls_List_Ozip__append_0) ).
fof(f30992,plain,
( spl0_2429
| ~ spl0_57
| ~ spl0_797
| ~ spl0_1078
| ~ spl0_1283
| ~ spl0_1658
| ~ spl0_1807
| ~ spl0_2428 ),
inference(avatar_split_clause,[],[f30988,f30984,f17164,f14448,f10151,f8879,f7528,f3692,f30990]) ).
fof(f30990,plain,
( spl0_2429
<=> ! [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_OBit(X11,c_Numeral_Obit_OB0),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_2429])]) ).
fof(f30984,plain,
( spl0_2428
<=> ! [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_2428])]) ).
fof(f30988,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_OBit(X11,c_Numeral_Obit_OB0),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_57
| ~ spl0_797
| ~ spl0_1078
| ~ spl0_1283
| ~ spl0_1658
| ~ spl0_1807
| ~ spl0_2428 ),
inference(forward_demodulation,[],[f30987,f14933]) ).
fof(f30987,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_57
| ~ spl0_1807
| ~ spl0_2428 ),
inference(forward_demodulation,[],[f30985,f18303]) ).
fof(f30985,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_2428 ),
inference(avatar_component_clause,[],[f30984]) ).
fof(f30986,plain,
spl0_2428,
inference(avatar_split_clause,[],[f3385,f30984]) ).
fof(f3385,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,[],[f3384,f2156]) ).
fof(f3384,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,[],[f3383,f2154]) ).
fof(f3383,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/benchmark/theBenchmark.p',cls_IntDiv_OnegDivAlg__eqn__1__number__of_1) ).
fof(f30947,plain,
( spl0_2427
| ~ spl0_57
| ~ spl0_1806
| ~ spl0_1827
| ~ spl0_2426 ),
inference(avatar_split_clause,[],[f30943,f30938,f17244,f17160,f3692,f30945]) ).
fof(f30945,plain,
( spl0_2427
<=> ! [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_2427])]) ).
fof(f17244,plain,
( spl0_1827
<=> c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint) = c_uminus(c_1,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1827])]) ).
fof(f30938,plain,
( spl0_2426
<=> ! [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_2426])]) ).
fof(f30943,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_57
| ~ spl0_1806
| ~ spl0_1827
| ~ spl0_2426 ),
inference(forward_demodulation,[],[f30942,f17246]) ).
fof(f17246,plain,
( c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint) = c_uminus(c_1,tc_IntDef_Oint)
| ~ spl0_1827 ),
inference(avatar_component_clause,[],[f17244]) ).
fof(f30942,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_57
| ~ spl0_1806
| ~ spl0_2426 ),
inference(forward_demodulation,[],[f30941,f18302]) ).
fof(f30941,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_57
| ~ spl0_1806
| ~ spl0_2426 ),
inference(forward_demodulation,[],[f30939,f18302]) ).
fof(f30939,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_2426 ),
inference(avatar_component_clause,[],[f30938]) ).
fof(f30940,plain,
spl0_2426,
inference(avatar_split_clause,[],[f1451,f30938]) ).
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/benchmark/theBenchmark.p',cls_IntDiv_OnegDivAlg__eqn__number__of_0) ).
fof(f30905,plain,
spl0_2425,
inference(avatar_split_clause,[],[f1504,f30903]) ).
fof(f30903,plain,
( spl0_2425
<=> ! [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_2425])]) ).
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/benchmark/theBenchmark.p',cls_List_OCons__in__lex_4) ).
fof(f30878,plain,
( ~ spl0_2424
| ~ spl0_786
| ~ spl0_2394 ),
inference(avatar_split_clause,[],[f30829,f30444,f7484,f30875]) ).
fof(f30875,plain,
( spl0_2424
<=> c_in(v_B,c_Inter(c_List_Oset(c_List_Oreplicate(c_1,c_Event_Obad,tc_set(tc_Message_Oagent)),tc_set(tc_Message_Oagent)),tc_Message_Oagent),tc_Message_Oagent) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2424])]) ).
fof(f30444,plain,
( spl0_2394
<=> ! [X0] : ~ c_in(v_B,c_Inter(c_List_Oset(c_List_Oreplicate(c_plus(c_1,X0,tc_nat),c_Event_Obad,tc_set(tc_Message_Oagent)),tc_set(tc_Message_Oagent)),tc_Message_Oagent),tc_Message_Oagent) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2394])]) ).
fof(f30829,plain,
( ~ c_in(v_B,c_Inter(c_List_Oset(c_List_Oreplicate(c_1,c_Event_Obad,tc_set(tc_Message_Oagent)),tc_set(tc_Message_Oagent)),tc_Message_Oagent),tc_Message_Oagent)
| ~ spl0_786
| ~ spl0_2394 ),
inference(superposition,[],[f30445,f7485]) ).
fof(f30445,plain,
( ! [X0] : ~ c_in(v_B,c_Inter(c_List_Oset(c_List_Oreplicate(c_plus(c_1,X0,tc_nat),c_Event_Obad,tc_set(tc_Message_Oagent)),tc_set(tc_Message_Oagent)),tc_Message_Oagent),tc_Message_Oagent)
| ~ spl0_2394 ),
inference(avatar_component_clause,[],[f30444]) ).
fof(f30873,plain,
( spl0_2423
| ~ spl0_57
| ~ spl0_797
| ~ spl0_1078
| ~ spl0_1283
| ~ spl0_1658
| ~ spl0_1807
| ~ spl0_2422 ),
inference(avatar_split_clause,[],[f30869,f30865,f17164,f14448,f10151,f8879,f7528,f3692,f30871]) ).
fof(f30871,plain,
( spl0_2423
<=> ! [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_OBit(X11,c_Numeral_Obit_OB0),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_2423])]) ).
fof(f30865,plain,
( spl0_2422
<=> ! [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_2422])]) ).
fof(f30869,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_OBit(X11,c_Numeral_Obit_OB0),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_57
| ~ spl0_797
| ~ spl0_1078
| ~ spl0_1283
| ~ spl0_1658
| ~ spl0_1807
| ~ spl0_2422 ),
inference(forward_demodulation,[],[f30868,f14933]) ).
fof(f30868,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_57
| ~ spl0_1807
| ~ spl0_2422 ),
inference(forward_demodulation,[],[f30866,f18303]) ).
fof(f30866,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_2422 ),
inference(avatar_component_clause,[],[f30865]) ).
fof(f30867,plain,
spl0_2422,
inference(avatar_split_clause,[],[f3379,f30865]) ).
fof(f3379,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,[],[f3378,f2156]) ).
fof(f3378,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,[],[f3377,f2154]) ).
fof(f3377,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/benchmark/theBenchmark.p',cls_IntDiv_OposDivAlg__eqn__1__number__of_1) ).
fof(f30863,plain,
spl0_2421,
inference(avatar_split_clause,[],[f54,f30861]) ).
fof(f30861,plain,
( spl0_2421
<=> ! [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_2421])]) ).
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/benchmark/theBenchmark.p',cls_List_Olistrel__Cons2_1) ).
fof(f30859,plain,
spl0_2420,
inference(avatar_split_clause,[],[f51,f30857]) ).
fof(f30857,plain,
( spl0_2420
<=> ! [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_2420])]) ).
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/benchmark/theBenchmark.p',cls_List_Olistrel__Cons1_1) ).
fof(f30839,plain,
( spl0_2419
| ~ spl0_1196
| ~ spl0_1537
| ~ spl0_2415 ),
inference(avatar_split_clause,[],[f30744,f30741,f12649,f9570,f30837]) ).
fof(f30837,plain,
( spl0_2419
<=> ! [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) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2419])]) ).
fof(f9570,plain,
( spl0_1196
<=> ! [X2,X18,X1,X3] : c_snd(c_Pair(X18,X3,X2,X1),X2,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1196])]) ).
fof(f30741,plain,
( spl0_2415
<=> ! [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_2415])]) ).
fof(f30744,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_1196
| ~ spl0_1537
| ~ spl0_2415 ),
inference(forward_demodulation,[],[f30742,f13711]) ).
fof(f13711,plain,
( ! [X2,X0,X1] : c_Main_Osurj__pair__2(X0,X1,X2) = c_snd(X0,X1,X2)
| ~ spl0_1196
| ~ spl0_1537 ),
inference(superposition,[],[f9571,f12650]) ).
fof(f9571,plain,
( ! [X2,X3,X18,X1] : c_snd(c_Pair(X18,X3,X2,X1),X2,X1) = X3
| ~ spl0_1196 ),
inference(avatar_component_clause,[],[f9570]) ).
fof(f30742,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_2415 ),
inference(avatar_component_clause,[],[f30741]) ).
fof(f30835,plain,
( spl0_2418
| ~ spl0_1195
| ~ spl0_1537
| ~ spl0_2414 ),
inference(avatar_split_clause,[],[f30739,f30736,f12649,f9566,f30833]) ).
fof(f30833,plain,
( spl0_2418
<=> ! [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) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2418])]) ).
fof(f9566,plain,
( spl0_1195
<=> ! [X3,X27,X2,X1] : c_fst(c_Pair(X3,X27,X1,X2),X1,X2) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1195])]) ).
fof(f30736,plain,
( spl0_2414
<=> ! [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_2414])]) ).
fof(f30739,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_1195
| ~ spl0_1537
| ~ spl0_2414 ),
inference(forward_demodulation,[],[f30737,f13712]) ).
fof(f13712,plain,
( ! [X2,X0,X1] : c_Main_Osurj__pair__1(X0,X1,X2) = c_fst(X0,X1,X2)
| ~ spl0_1195
| ~ spl0_1537 ),
inference(superposition,[],[f9567,f12650]) ).
fof(f9567,plain,
( ! [X2,X3,X1,X27] : c_fst(c_Pair(X3,X27,X1,X2),X1,X2) = X3
| ~ spl0_1195 ),
inference(avatar_component_clause,[],[f9566]) ).
fof(f30737,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_2414 ),
inference(avatar_component_clause,[],[f30736]) ).
fof(f30827,plain,
( spl0_2417
| ~ spl0_1196
| ~ spl0_1537
| ~ spl0_2413 ),
inference(avatar_split_clause,[],[f30734,f30731,f12649,f9570,f30825]) ).
fof(f30825,plain,
( spl0_2417
<=> ! [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) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2417])]) ).
fof(f30731,plain,
( spl0_2413
<=> ! [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_2413])]) ).
fof(f30734,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_1196
| ~ spl0_1537
| ~ spl0_2413 ),
inference(forward_demodulation,[],[f30732,f13711]) ).
fof(f30732,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_2413 ),
inference(avatar_component_clause,[],[f30731]) ).
fof(f30823,plain,
( spl0_2416
| ~ spl0_1195
| ~ spl0_1537
| ~ spl0_2412 ),
inference(avatar_split_clause,[],[f30729,f30726,f12649,f9566,f30821]) ).
fof(f30821,plain,
( spl0_2416
<=> ! [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) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2416])]) ).
fof(f30726,plain,
( spl0_2412
<=> ! [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_2412])]) ).
fof(f30729,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_1195
| ~ spl0_1537
| ~ spl0_2412 ),
inference(forward_demodulation,[],[f30727,f13712]) ).
fof(f30727,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_2412 ),
inference(avatar_component_clause,[],[f30726]) ).
fof(f30743,plain,
spl0_2415,
inference(avatar_split_clause,[],[f3376,f30741]) ).
fof(f3376,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/benchmark/theBenchmark.p',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/benchmark/theBenchmark.p',cls_IntDiv_Omod__pos__neg__number__of_0) ).
fof(f30738,plain,
spl0_2414,
inference(avatar_split_clause,[],[f3375,f30736]) ).
fof(f3375,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/benchmark/theBenchmark.p',cls_IntDiv_Odiv__pos__neg__number__of_0) ).
fof(f30733,plain,
spl0_2413,
inference(avatar_split_clause,[],[f3374,f30731]) ).
fof(f3374,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/benchmark/theBenchmark.p',cls_IntDiv_Omod__neg__neg__number__of_0) ).
fof(f30728,plain,
spl0_2412,
inference(avatar_split_clause,[],[f3373,f30726]) ).
fof(f3373,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/benchmark/theBenchmark.p',cls_IntDiv_Odiv__neg__neg__number__of_0) ).
fof(f30722,plain,
spl0_2411,
inference(avatar_split_clause,[],[f1622,f30720]) ).
fof(f30720,plain,
( spl0_2411
<=> ! [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_2411])]) ).
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/benchmark/theBenchmark.p',cls_List_Olexord__cons__cons_3) ).
fof(f30718,plain,
spl0_2410,
inference(avatar_split_clause,[],[f1505,f30716]) ).
fof(f30716,plain,
( spl0_2410
<=> ! [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_2410])]) ).
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/benchmark/theBenchmark.p',cls_List_OCons__in__lex_5) ).
fof(f30714,plain,
spl0_2409,
inference(avatar_split_clause,[],[f1188,f30712]) ).
fof(f30712,plain,
( spl0_2409
<=> ! [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_2409])]) ).
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/benchmark/theBenchmark.p',cls_Datatype__Universe_ODomain__dsum_0) ).
fof(f30710,plain,
spl0_2408,
inference(avatar_split_clause,[],[f1187,f30708]) ).
fof(f30708,plain,
( spl0_2408
<=> ! [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_2408])]) ).
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/benchmark/theBenchmark.p',cls_Datatype__Universe_ODomain__dprod_0) ).
fof(f30682,plain,
( spl0_2407
| ~ spl0_1827
| ~ spl0_2405 ),
inference(avatar_split_clause,[],[f30674,f30671,f17244,f30680]) ).
fof(f30680,plain,
( spl0_2407
<=> ! [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_2407])]) ).
fof(f30671,plain,
( spl0_2405
<=> ! [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_2405])]) ).
fof(f30674,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_1827
| ~ spl0_2405 ),
inference(forward_demodulation,[],[f30672,f17246]) ).
fof(f30672,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_2405 ),
inference(avatar_component_clause,[],[f30671]) ).
fof(f30678,plain,
spl0_2406,
inference(avatar_split_clause,[],[f1705,f30676]) ).
fof(f30676,plain,
( spl0_2406
<=> ! [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_2406])]) ).
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/benchmark/theBenchmark.p',cls_List_Onth__zip_0) ).
fof(f30673,plain,
spl0_2405,
inference(avatar_split_clause,[],[f1449,f30671]) ).
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/benchmark/theBenchmark.p',cls_IntDiv_OnegDivAlg__eqn__1__number__of_0) ).
fof(f30653,plain,
( ~ spl0_2404
| ~ spl0_786
| ~ spl0_2385 ),
inference(avatar_split_clause,[],[f30503,f30385,f7484,f30650]) ).
fof(f30650,plain,
( spl0_2404
<=> c_in(v_A,c_Inter(c_List_Oset(c_List_Oreplicate(c_1,c_Event_Obad,tc_set(tc_Message_Oagent)),tc_set(tc_Message_Oagent)),tc_Message_Oagent),tc_Message_Oagent) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2404])]) ).
fof(f30385,plain,
( spl0_2385
<=> ! [X0] : ~ c_in(v_A,c_Inter(c_List_Oset(c_List_Oreplicate(c_plus(c_1,X0,tc_nat),c_Event_Obad,tc_set(tc_Message_Oagent)),tc_set(tc_Message_Oagent)),tc_Message_Oagent),tc_Message_Oagent) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2385])]) ).
fof(f30503,plain,
( ~ c_in(v_A,c_Inter(c_List_Oset(c_List_Oreplicate(c_1,c_Event_Obad,tc_set(tc_Message_Oagent)),tc_set(tc_Message_Oagent)),tc_Message_Oagent),tc_Message_Oagent)
| ~ spl0_786
| ~ spl0_2385 ),
inference(superposition,[],[f30386,f7485]) ).
fof(f30386,plain,
( ! [X0] : ~ c_in(v_A,c_Inter(c_List_Oset(c_List_Oreplicate(c_plus(c_1,X0,tc_nat),c_Event_Obad,tc_set(tc_Message_Oagent)),tc_set(tc_Message_Oagent)),tc_Message_Oagent),tc_Message_Oagent)
| ~ spl0_2385 ),
inference(avatar_component_clause,[],[f30385]) ).
fof(f30521,plain,
spl0_2403,
inference(avatar_split_clause,[],[f1619,f30519]) ).
fof(f30519,plain,
( spl0_2403
<=> ! [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_2403])]) ).
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/benchmark/theBenchmark.p',cls_List_Olexord__cons__cons_0) ).
fof(f30517,plain,
spl0_2402,
inference(avatar_split_clause,[],[f1500,f30515]) ).
fof(f30515,plain,
( spl0_2402
<=> ! [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_2402])]) ).
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/benchmark/theBenchmark.p',cls_List_OCons__in__lex_0) ).
fof(f30513,plain,
spl0_2401,
inference(avatar_split_clause,[],[f1383,f30511]) ).
fof(f30511,plain,
( spl0_2401
<=> ! [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_2401])]) ).
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/benchmark/theBenchmark.p',cls_IntDef_Ointrel__iff_1) ).
fof(f30509,plain,
spl0_2400,
inference(avatar_split_clause,[],[f1382,f30507]) ).
fof(f30507,plain,
( spl0_2400
<=> ! [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_2400])]) ).
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/benchmark/theBenchmark.p',cls_IntDef_Ointrel__iff_0) ).
fof(f30501,plain,
spl0_2399,
inference(avatar_split_clause,[],[f85,f30499]) ).
fof(f30499,plain,
( spl0_2399
<=> ! [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_2399])]) ).
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/benchmark/theBenchmark.p',cls_Relation_Orel__compI_0) ).
fof(f30497,plain,
spl0_2398,
inference(avatar_split_clause,[],[f53,f30495]) ).
fof(f30495,plain,
( spl0_2398
<=> ! [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_2398])]) ).
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/benchmark/theBenchmark.p',cls_List_Olistrel__Cons2_0) ).
fof(f30493,plain,
spl0_2397,
inference(avatar_split_clause,[],[f50,f30491]) ).
fof(f30491,plain,
( spl0_2397
<=> ! [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_2397])]) ).
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/benchmark/theBenchmark.p',cls_List_Olistrel__Cons1_0) ).
fof(f30454,plain,
( spl0_2396
| ~ spl0_1196
| ~ spl0_1537
| ~ spl0_2390 ),
inference(avatar_split_clause,[],[f30411,f30408,f12649,f9570,f30452]) ).
fof(f30452,plain,
( spl0_2396
<=> ! [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_2396])]) ).
fof(f30408,plain,
( spl0_2390
<=> ! [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_2390])]) ).
fof(f30411,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_1196
| ~ spl0_1537
| ~ spl0_2390 ),
inference(forward_demodulation,[],[f30409,f13711]) ).
fof(f30409,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_2390 ),
inference(avatar_component_clause,[],[f30408]) ).
fof(f30450,plain,
( spl0_2395
| ~ spl0_1196
| ~ spl0_1537
| ~ spl0_2389 ),
inference(avatar_split_clause,[],[f30406,f30403,f12649,f9570,f30448]) ).
fof(f30448,plain,
( spl0_2395
<=> ! [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_2395])]) ).
fof(f30403,plain,
( spl0_2389
<=> ! [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_2389])]) ).
fof(f30406,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_1196
| ~ spl0_1537
| ~ spl0_2389 ),
inference(forward_demodulation,[],[f30404,f13711]) ).
fof(f30404,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_2389 ),
inference(avatar_component_clause,[],[f30403]) ).
fof(f30446,plain,
( spl0_2394
| ~ spl0_1848
| ~ spl0_2350 ),
inference(avatar_split_clause,[],[f29513,f29465,f17598,f30444]) ).
fof(f17598,plain,
( spl0_1848
<=> ! [X41,X0,X21] : c_List_Olist_OCons(X0,c_List_Oreplicate(X21,X0,X41),X41) = c_List_Oreplicate(c_plus(c_1,X21,tc_nat),X0,X41) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1848])]) ).
fof(f29465,plain,
( spl0_2350
<=> ! [X0] : ~ c_in(v_B,c_Inter(c_List_Oset(c_List_Olist_OCons(c_Event_Obad,X0,tc_set(tc_Message_Oagent)),tc_set(tc_Message_Oagent)),tc_Message_Oagent),tc_Message_Oagent) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2350])]) ).
fof(f29513,plain,
( ! [X0] : ~ c_in(v_B,c_Inter(c_List_Oset(c_List_Oreplicate(c_plus(c_1,X0,tc_nat),c_Event_Obad,tc_set(tc_Message_Oagent)),tc_set(tc_Message_Oagent)),tc_Message_Oagent),tc_Message_Oagent)
| ~ spl0_1848
| ~ spl0_2350 ),
inference(superposition,[],[f29466,f17599]) ).
fof(f17599,plain,
( ! [X21,X41,X0] : c_List_Olist_OCons(X0,c_List_Oreplicate(X21,X0,X41),X41) = c_List_Oreplicate(c_plus(c_1,X21,tc_nat),X0,X41)
| ~ spl0_1848 ),
inference(avatar_component_clause,[],[f17598]) ).
fof(f29466,plain,
( ! [X0] : ~ c_in(v_B,c_Inter(c_List_Oset(c_List_Olist_OCons(c_Event_Obad,X0,tc_set(tc_Message_Oagent)),tc_set(tc_Message_Oagent)),tc_Message_Oagent),tc_Message_Oagent)
| ~ spl0_2350 ),
inference(avatar_component_clause,[],[f29465]) ).
fof(f30442,plain,
( spl0_2393
| ~ spl0_1195
| ~ spl0_1537
| ~ spl0_2388 ),
inference(avatar_split_clause,[],[f30401,f30398,f12649,f9566,f30440]) ).
fof(f30440,plain,
( spl0_2393
<=> ! [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_2393])]) ).
fof(f30398,plain,
( spl0_2388
<=> ! [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_2388])]) ).
fof(f30401,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_1195
| ~ spl0_1537
| ~ spl0_2388 ),
inference(forward_demodulation,[],[f30399,f13712]) ).
fof(f30399,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_2388 ),
inference(avatar_component_clause,[],[f30398]) ).
fof(f30438,plain,
( spl0_2392
| ~ spl0_1195
| ~ spl0_1537
| ~ spl0_2387 ),
inference(avatar_split_clause,[],[f30396,f30393,f12649,f9566,f30436]) ).
fof(f30436,plain,
( spl0_2392
<=> ! [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_2392])]) ).
fof(f30393,plain,
( spl0_2387
<=> ! [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_2387])]) ).
fof(f30396,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_1195
| ~ spl0_1537
| ~ spl0_2387 ),
inference(forward_demodulation,[],[f30394,f13712]) ).
fof(f30394,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_2387 ),
inference(avatar_component_clause,[],[f30393]) ).
fof(f30415,plain,
spl0_2391,
inference(avatar_split_clause,[],[f1502,f30413]) ).
fof(f30413,plain,
( spl0_2391
<=> ! [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_2391])]) ).
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/benchmark/theBenchmark.p',cls_List_OCons__in__lex_2) ).
fof(f30410,plain,
spl0_2390,
inference(avatar_split_clause,[],[f1448,f30408]) ).
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/benchmark/theBenchmark.p',cls_IntDiv_Omod__pos__pos__number__of_0) ).
fof(f30405,plain,
spl0_2389,
inference(avatar_split_clause,[],[f1444,f30403]) ).
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/benchmark/theBenchmark.p',cls_IntDiv_Omod__neg__pos__number__of_0) ).
fof(f30400,plain,
spl0_2388,
inference(avatar_split_clause,[],[f1438,f30398]) ).
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/benchmark/theBenchmark.p',cls_IntDiv_Odiv__pos__pos__number__of_0) ).
fof(f30395,plain,
spl0_2387,
inference(avatar_split_clause,[],[f1434,f30393]) ).
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/benchmark/theBenchmark.p',cls_IntDiv_Odiv__neg__pos__number__of_0) ).
fof(f30391,plain,
spl0_2386,
inference(avatar_split_clause,[],[f55,f30389]) ).
fof(f30389,plain,
( spl0_2386
<=> ! [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_2386])]) ).
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/benchmark/theBenchmark.p',cls_List_Olistrel__Cons2_2) ).
fof(f30387,plain,
( spl0_2385
| ~ spl0_1848
| ~ spl0_2250 ),
inference(avatar_split_clause,[],[f26954,f26905,f17598,f30385]) ).
fof(f26905,plain,
( spl0_2250
<=> ! [X0] : ~ c_in(v_A,c_Inter(c_List_Oset(c_List_Olist_OCons(c_Event_Obad,X0,tc_set(tc_Message_Oagent)),tc_set(tc_Message_Oagent)),tc_Message_Oagent),tc_Message_Oagent) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2250])]) ).
fof(f26954,plain,
( ! [X0] : ~ c_in(v_A,c_Inter(c_List_Oset(c_List_Oreplicate(c_plus(c_1,X0,tc_nat),c_Event_Obad,tc_set(tc_Message_Oagent)),tc_set(tc_Message_Oagent)),tc_Message_Oagent),tc_Message_Oagent)
| ~ spl0_1848
| ~ spl0_2250 ),
inference(superposition,[],[f26906,f17599]) ).
fof(f26906,plain,
( ! [X0] : ~ c_in(v_A,c_Inter(c_List_Oset(c_List_Olist_OCons(c_Event_Obad,X0,tc_set(tc_Message_Oagent)),tc_set(tc_Message_Oagent)),tc_Message_Oagent),tc_Message_Oagent)
| ~ spl0_2250 ),
inference(avatar_component_clause,[],[f26905]) ).
fof(f30383,plain,
spl0_2384,
inference(avatar_split_clause,[],[f52,f30381]) ).
fof(f30381,plain,
( spl0_2384
<=> ! [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_2384])]) ).
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/benchmark/theBenchmark.p',cls_List_Olistrel__Cons1_2) ).
fof(f30245,plain,
spl0_2383,
inference(avatar_split_clause,[],[f1470,f30243]) ).
fof(f30243,plain,
( spl0_2383
<=> ! [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_2383])]) ).
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/benchmark/theBenchmark.p',cls_IntDiv_Ozdiv__number__of__BIT_2) ).
fof(f30241,plain,
spl0_2382,
inference(avatar_split_clause,[],[f83,f30239]) ).
fof(f30239,plain,
( spl0_2382
<=> ! [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_2382])]) ).
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/benchmark/theBenchmark.p',cls_Relation_Orel__compE_1) ).
fof(f30237,plain,
spl0_2381,
inference(avatar_split_clause,[],[f82,f30235]) ).
fof(f30235,plain,
( spl0_2381
<=> ! [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_2381])]) ).
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/benchmark/theBenchmark.p',cls_Relation_Orel__compE_0) ).
fof(f30233,plain,
spl0_2380,
inference(avatar_split_clause,[],[f20,f30231]) ).
fof(f30231,plain,
( spl0_2380
<=> ! [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_2380])]) ).
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/benchmark/theBenchmark.p',cls_Datatype__Universe_OusumE_3) ).
fof(f30087,plain,
spl0_2379,
inference(avatar_split_clause,[],[f3280,f30085]) ).
fof(f30085,plain,
( spl0_2379
<=> ! [X15,X47] : c_Divides_Oop_Amod(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_plus(X15,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),tc_nat),tc_nat),c_Numeral_Onumber__of(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_2379])]) ).
fof(f3280,plain,
! [X47,X15] : c_Divides_Oop_Amod(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_plus(X15,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),tc_nat),tc_nat),c_Numeral_Onumber__of(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,[],[f3279,f2156]) ).
fof(f3279,plain,
! [X47,X15] : 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) = c_Divides_Oop_Amod(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_plus(X15,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),tc_nat),tc_nat),c_Numeral_Onumber__of(X47,tc_nat),tc_nat),
inference(forward_demodulation,[],[f3278,f3024]) ).
fof(f3024,plain,
! [X21,X15] : c_Finite__Set_Ocard(c_SetInterval_OatMost(c_plus(X15,X21,tc_nat),tc_nat),tc_nat) = c_plus(c_Finite__Set_Ocard(c_SetInterval_OatMost(X15,tc_nat),tc_nat),X21,tc_nat),
inference(definition_unfolding,[],[f2101,f2544,f2544]) ).
fof(f2544,axiom,
! [X14] : c_Suc(X14) = c_Finite__Set_Ocard(c_SetInterval_OatMost(X14,tc_nat),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ocard__atMost_0) ).
fof(f2101,axiom,
! [X21,X15] : c_Suc(c_plus(X15,X21,tc_nat)) = c_plus(c_Suc(X15),X21,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oop_A_L_Oadd__Suc_0) ).
fof(f3278,plain,
! [X47,X15] : 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) = c_Divides_Oop_Amod(c_plus(c_Finite__Set_Ocard(c_SetInterval_OatMost(X15,tc_nat),tc_nat),c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),c_Numeral_Onumber__of(X47,tc_nat),tc_nat),
inference(forward_demodulation,[],[f3079,f3242]) ).
fof(f3242,plain,
! [X21] : c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),tc_nat),tc_nat) = 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,[],[f3241,f2156]) ).
fof(f3241,plain,
! [X21] : c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),tc_nat),tc_nat) = 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,[],[f3240,f2154]) ).
fof(f3240,plain,
! [X21] : c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),tc_nat),tc_nat) = 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,[],[f3045,f2156]) ).
fof(f3045,plain,
! [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) = c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),tc_nat),tc_nat),
inference(definition_unfolding,[],[f1882,f2544,f2544]) ).
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/benchmark/theBenchmark.p',cls_NatSimprocs_Oadd__2__eq__Suc_H_0) ).
fof(f3079,plain,
! [X47,X15] : 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) = c_Divides_Oop_Amod(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Finite__Set_Ocard(c_SetInterval_OatMost(X15,tc_nat),tc_nat),tc_nat),tc_nat),tc_nat),tc_nat),c_Numeral_Onumber__of(X47,tc_nat),tc_nat),
inference(definition_unfolding,[],[f1880,f2544,f2544,f2544]) ).
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/benchmark/theBenchmark.p',cls_NatSimprocs_OSuc__mod__eq__add3__mod__number__of_0) ).
fof(f30067,plain,
( spl0_2378
| ~ spl0_646
| ~ spl0_687
| ~ spl0_1372
| ~ spl0_1461
| ~ spl0_2026
| ~ spl0_2377 ),
inference(avatar_split_clause,[],[f30063,f30059,f20939,f11313,f10914,f7046,f6101,f30065]) ).
fof(f30065,plain,
( spl0_2378
<=> ! [X15,X47] : 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) = c_div(c_plus(c_1,c_plus(c_1,c_plus(c_1,X15,tc_nat),tc_nat),tc_nat),c_Numeral_Onumber__of(X47,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2378])]) ).
fof(f7046,plain,
( spl0_687
<=> ! [X3] : c_IntDef_Onat(c_IntDef_Oint(X3)) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_687])]) ).
fof(f10914,plain,
( spl0_1372
<=> ! [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_1372])]) ).
fof(f11313,plain,
( spl0_1461
<=> ! [X15] : c_plus(c_1,c_IntDef_Oint(X15),tc_IntDef_Oint) = c_IntDef_Oint(c_Finite__Set_Ocard(c_SetInterval_OatMost(X15,tc_nat),tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1461])]) ).
fof(f20939,plain,
( spl0_2026
<=> ! [X21] : c_plus(X21,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat) = c_plus(c_1,c_plus(c_1,X21,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2026])]) ).
fof(f30059,plain,
( spl0_2377
<=> ! [X15,X47] : c_div(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_plus(X15,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),tc_nat),tc_nat),c_Numeral_Onumber__of(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_2377])]) ).
fof(f30063,plain,
( ! [X47,X15] : 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) = c_div(c_plus(c_1,c_plus(c_1,c_plus(c_1,X15,tc_nat),tc_nat),tc_nat),c_Numeral_Onumber__of(X47,tc_nat),tc_nat)
| ~ spl0_646
| ~ spl0_687
| ~ spl0_1372
| ~ spl0_1461
| ~ spl0_2026
| ~ spl0_2377 ),
inference(forward_demodulation,[],[f30062,f20940]) ).
fof(f20940,plain,
( ! [X21] : c_plus(X21,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat) = c_plus(c_1,c_plus(c_1,X21,tc_nat),tc_nat)
| ~ spl0_2026 ),
inference(avatar_component_clause,[],[f20939]) ).
fof(f30062,plain,
( ! [X47,X15] : 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) = c_div(c_plus(c_1,c_plus(X15,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),tc_nat),c_Numeral_Onumber__of(X47,tc_nat),tc_nat)
| ~ spl0_646
| ~ spl0_687
| ~ spl0_1372
| ~ spl0_1461
| ~ spl0_2377 ),
inference(forward_demodulation,[],[f30060,f12280]) ).
fof(f12280,plain,
( ! [X0] : c_Finite__Set_Ocard(c_SetInterval_OatMost(X0,tc_nat),tc_nat) = c_plus(c_1,X0,tc_nat)
| ~ spl0_646
| ~ spl0_687
| ~ spl0_1372
| ~ spl0_1461 ),
inference(forward_demodulation,[],[f12279,f7047]) ).
fof(f7047,plain,
( ! [X3] : c_IntDef_Onat(c_IntDef_Oint(X3)) = X3
| ~ spl0_687 ),
inference(avatar_component_clause,[],[f7046]) ).
fof(f12279,plain,
( ! [X0] : c_Finite__Set_Ocard(c_SetInterval_OatMost(X0,tc_nat),tc_nat) = c_IntDef_Onat(c_IntDef_Oint(c_plus(c_1,X0,tc_nat)))
| ~ spl0_646
| ~ spl0_687
| ~ spl0_1372
| ~ spl0_1461 ),
inference(forward_demodulation,[],[f12241,f11614]) ).
fof(f11614,plain,
( ! [X0] : c_plus(c_1,c_IntDef_Oint(X0),tc_IntDef_Oint) = c_IntDef_Oint(c_plus(c_1,X0,tc_nat))
| ~ spl0_646
| ~ spl0_1372 ),
inference(superposition,[],[f10915,f6103]) ).
fof(f10915,plain,
( ! [X21,X15] : c_IntDef_Oint(c_plus(X15,X21,tc_nat)) = c_plus(c_IntDef_Oint(X15),c_IntDef_Oint(X21),tc_IntDef_Oint)
| ~ spl0_1372 ),
inference(avatar_component_clause,[],[f10914]) ).
fof(f12241,plain,
( ! [X0] : c_Finite__Set_Ocard(c_SetInterval_OatMost(X0,tc_nat),tc_nat) = c_IntDef_Onat(c_plus(c_1,c_IntDef_Oint(X0),tc_IntDef_Oint))
| ~ spl0_687
| ~ spl0_1461 ),
inference(superposition,[],[f7047,f11314]) ).
fof(f11314,plain,
( ! [X15] : c_plus(c_1,c_IntDef_Oint(X15),tc_IntDef_Oint) = c_IntDef_Oint(c_Finite__Set_Ocard(c_SetInterval_OatMost(X15,tc_nat),tc_nat))
| ~ spl0_1461 ),
inference(avatar_component_clause,[],[f11313]) ).
fof(f30060,plain,
( ! [X47,X15] : c_div(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_plus(X15,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),tc_nat),tc_nat),c_Numeral_Onumber__of(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)
| ~ spl0_2377 ),
inference(avatar_component_clause,[],[f30059]) ).
fof(f30061,plain,
spl0_2377,
inference(avatar_split_clause,[],[f3277,f30059]) ).
fof(f3277,plain,
! [X47,X15] : c_div(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_plus(X15,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),tc_nat),tc_nat),c_Numeral_Onumber__of(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,[],[f3276,f2156]) ).
fof(f3276,plain,
! [X47,X15] : 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) = c_div(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_plus(X15,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),tc_nat),tc_nat),c_Numeral_Onumber__of(X47,tc_nat),tc_nat),
inference(forward_demodulation,[],[f3275,f3024]) ).
fof(f3275,plain,
! [X47,X15] : 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) = c_div(c_plus(c_Finite__Set_Ocard(c_SetInterval_OatMost(X15,tc_nat),tc_nat),c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),c_Numeral_Onumber__of(X47,tc_nat),tc_nat),
inference(forward_demodulation,[],[f3078,f3242]) ).
fof(f3078,plain,
! [X47,X15] : 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) = c_div(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Finite__Set_Ocard(c_SetInterval_OatMost(X15,tc_nat),tc_nat),tc_nat),tc_nat),tc_nat),tc_nat),c_Numeral_Onumber__of(X47,tc_nat),tc_nat),
inference(definition_unfolding,[],[f1879,f2544,f2544,f2544]) ).
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/benchmark/theBenchmark.p',cls_NatSimprocs_OSuc__div__eq__add3__div__number__of_0) ).
fof(f30057,plain,
spl0_2376,
inference(avatar_split_clause,[],[f3162,f30055]) ).
fof(f30055,plain,
( spl0_2376
<=> ! [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_Otrancl(c_union(X5,c_Relation_OId,tc_prod(X1,X1)),X1),tc_prod(X1,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2376])]) ).
fof(f3162,plain,
! [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_Otrancl(c_union(X5,c_Relation_OId,tc_prod(X1,X1)),X1),tc_prod(X1,X1)) ),
inference(definition_unfolding,[],[f2724,f2716]) ).
fof(f2716,axiom,
! [X1,X5] : c_Transitive__Closure_Ortrancl(X5,X1) = c_Transitive__Closure_Otrancl(c_union(X5,c_Relation_OId,tc_prod(X1,X1)),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Transitive__Closure_Otrancl__reflcl_0) ).
fof(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/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Owf__insert_2) ).
fof(f30053,plain,
( spl0_2375
| ~ spl0_810
| ~ spl0_2163
| ~ spl0_2337 ),
inference(avatar_split_clause,[],[f28682,f28604,f23872,f7581,f30050]) ).
fof(f30050,plain,
( spl0_2375
<=> c_UNIV = c_union(c_uminus(c_insert(v_B,c_emptyset,tc_Message_Oagent),tc_set(tc_Message_Oagent)),c_uminus(c_Event_Obad,tc_set(tc_Message_Oagent)),tc_Message_Oagent) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2375])]) ).
fof(f7581,plain,
( spl0_810
<=> ! [X1] : c_UNIV = c_uminus(c_emptyset,tc_set(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_810])]) ).
fof(f23872,plain,
( spl0_2163
<=> ! [X13,X12,X1] : c_union(c_uminus(X12,tc_set(X1)),c_uminus(X13,tc_set(X1)),X1) = c_uminus(c_Relation_OImage(c_Relation_Odiag(X12,X1),X13,X1,X1),tc_set(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2163])]) ).
fof(f28604,plain,
( spl0_2337
<=> c_emptyset = c_Relation_OImage(c_Relation_Odiag(c_insert(v_B,c_emptyset,tc_Message_Oagent),tc_Message_Oagent),c_Event_Obad,tc_Message_Oagent,tc_Message_Oagent) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2337])]) ).
fof(f28682,plain,
( c_UNIV = c_union(c_uminus(c_insert(v_B,c_emptyset,tc_Message_Oagent),tc_set(tc_Message_Oagent)),c_uminus(c_Event_Obad,tc_set(tc_Message_Oagent)),tc_Message_Oagent)
| ~ spl0_810
| ~ spl0_2163
| ~ spl0_2337 ),
inference(forward_demodulation,[],[f28671,f7582]) ).
fof(f7582,plain,
( ! [X1] : c_UNIV = c_uminus(c_emptyset,tc_set(X1))
| ~ spl0_810 ),
inference(avatar_component_clause,[],[f7581]) ).
fof(f28671,plain,
( c_uminus(c_emptyset,tc_set(tc_Message_Oagent)) = c_union(c_uminus(c_insert(v_B,c_emptyset,tc_Message_Oagent),tc_set(tc_Message_Oagent)),c_uminus(c_Event_Obad,tc_set(tc_Message_Oagent)),tc_Message_Oagent)
| ~ spl0_2163
| ~ spl0_2337 ),
inference(superposition,[],[f23873,f28606]) ).
fof(f28606,plain,
( c_emptyset = c_Relation_OImage(c_Relation_Odiag(c_insert(v_B,c_emptyset,tc_Message_Oagent),tc_Message_Oagent),c_Event_Obad,tc_Message_Oagent,tc_Message_Oagent)
| ~ spl0_2337 ),
inference(avatar_component_clause,[],[f28604]) ).
fof(f23873,plain,
( ! [X1,X12,X13] : c_union(c_uminus(X12,tc_set(X1)),c_uminus(X13,tc_set(X1)),X1) = c_uminus(c_Relation_OImage(c_Relation_Odiag(X12,X1),X13,X1,X1),tc_set(X1))
| ~ spl0_2163 ),
inference(avatar_component_clause,[],[f23872]) ).
fof(f30048,plain,
spl0_2374,
inference(avatar_split_clause,[],[f3161,f30046]) ).
fof(f30046,plain,
( spl0_2374
<=> ! [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_Otrancl(c_union(X5,c_Relation_OId,tc_prod(X1,X1)),X1),tc_prod(X1,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2374])]) ).
fof(f3161,plain,
! [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_Otrancl(c_union(X5,c_Relation_OId,tc_prod(X1,X1)),X1),tc_prod(X1,X1)) ),
inference(definition_unfolding,[],[f2721,f2716]) ).
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/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Oacyclic__insert_2) ).
fof(f30044,plain,
spl0_2373,
inference(avatar_split_clause,[],[f1621,f30042]) ).
fof(f30042,plain,
( spl0_2373
<=> ! [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_2373])]) ).
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/benchmark/theBenchmark.p',cls_List_Olexord__cons__cons_2) ).
fof(f30040,plain,
spl0_2372,
inference(avatar_split_clause,[],[f1460,f30038]) ).
fof(f30038,plain,
( spl0_2372
<=> ! [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_2372])]) ).
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/benchmark/theBenchmark.p',cls_IntDiv_OposDivAlg__eqn__number__of_0) ).
fof(f30036,plain,
spl0_2371,
inference(avatar_split_clause,[],[f19,f30034]) ).
fof(f30034,plain,
( spl0_2371
<=> ! [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_2371])]) ).
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/benchmark/theBenchmark.p',cls_Datatype__Universe_OusumE_2) ).
fof(f30032,plain,
spl0_2370,
inference(avatar_split_clause,[],[f18,f30030]) ).
fof(f30030,plain,
( spl0_2370
<=> ! [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_2370])]) ).
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/benchmark/theBenchmark.p',cls_Datatype__Universe_OusumE_1) ).
fof(f29934,plain,
spl0_2369,
inference(avatar_split_clause,[],[f3206,f29932]) ).
fof(f29932,plain,
( spl0_2369
<=> ! [X87,X86,X88] :
( ~ c_in(X87,c_Message_Osynth(c_Message_Oanalz(X88)),tc_Message_Omsg)
| c_in(X86,c_Message_Osynth(c_Message_Oanalz(X88)),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OHash(c_Message_Omsg_OMPair(X86,X87)),c_Message_Oanalz(X88),tc_Message_Omsg)
| c_in(c_Message_Omsg_OMPair(c_Message_Omsg_OHash(c_Message_Omsg_OMPair(X86,X87)),X87),c_Message_Osynth(c_Message_Oanalz(X88)),tc_Message_Omsg) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2369])]) ).
fof(f3206,plain,
! [X88,X86,X87] :
( ~ c_in(X87,c_Message_Osynth(c_Message_Oanalz(X88)),tc_Message_Omsg)
| c_in(X86,c_Message_Osynth(c_Message_Oanalz(X88)),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OHash(c_Message_Omsg_OMPair(X86,X87)),c_Message_Oanalz(X88),tc_Message_Omsg)
| c_in(c_Message_Omsg_OMPair(c_Message_Omsg_OHash(c_Message_Omsg_OMPair(X86,X87)),X87),c_Message_Osynth(c_Message_Oanalz(X88)),tc_Message_Omsg) ),
inference(definition_unfolding,[],[f2821,f2837]) ).
fof(f2837,axiom,
! [X0,X86] : c_Message_OHPair(X86,X0) = c_Message_Omsg_OMPair(c_Message_Omsg_OHash(c_Message_Omsg_OMPair(X86,X0)),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OMPair__eq__HPair_2) ).
fof(f2821,axiom,
! [X88,X86,X87] :
( ~ c_in(X87,c_Message_Osynth(c_Message_Oanalz(X88)),tc_Message_Omsg)
| c_in(X86,c_Message_Osynth(c_Message_Oanalz(X88)),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OHash(c_Message_Omsg_OMPair(X86,X87)),c_Message_Oanalz(X88),tc_Message_Omsg)
| c_in(c_Message_OHPair(X86,X87),c_Message_Osynth(c_Message_Oanalz(X88)),tc_Message_Omsg) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OHPair__synth__analz_2) ).
fof(f29930,plain,
spl0_2368,
inference(avatar_split_clause,[],[f3131,f29928]) ).
fof(f29928,plain,
( spl0_2368
<=> ! [X47,X0,X23,X1] :
( c_0 = c_Numeral_Onumber__of(X47,tc_nat)
| c_List_Osublist(c_List_Olist_OCons(X0,X23,X1),c_SetInterval_OlessThan(c_Numeral_Onumber__of(X47,tc_nat),tc_nat),X1) = c_List_Olist_OCons(X0,c_List_Osublist(X23,c_SetInterval_OlessThan(c_minus(c_Numeral_Onumber__of(X47,tc_nat),c_1,tc_nat),tc_nat),X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2368])]) ).
fof(f3131,plain,
! [X0,X47,X1,X23] :
( c_0 = c_Numeral_Onumber__of(X47,tc_nat)
| c_List_Osublist(c_List_Olist_OCons(X0,X23,X1),c_SetInterval_OlessThan(c_Numeral_Onumber__of(X47,tc_nat),tc_nat),X1) = c_List_Olist_OCons(X0,c_List_Osublist(X23,c_SetInterval_OlessThan(c_minus(c_Numeral_Onumber__of(X47,tc_nat),c_1,tc_nat),tc_nat),X1),X1) ),
inference(definition_unfolding,[],[f1768,f1766,f1766]) ).
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/benchmark/theBenchmark.p',cls_List_Osublist__upt__eq__take_0) ).
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/benchmark/theBenchmark.p',cls_List_Otake__Cons__number__of_1) ).
fof(f29912,plain,
spl0_2367,
inference(avatar_split_clause,[],[f17,f29910]) ).
fof(f29910,plain,
( spl0_2367
<=> ! [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_2367])]) ).
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/benchmark/theBenchmark.p',cls_Datatype__Universe_OusumE_0) ).
fof(f29622,plain,
spl0_2366,
inference(avatar_split_clause,[],[f3075,f29620]) ).
fof(f29620,plain,
( spl0_2366
<=> ! [X21,X23,X25,X1] : c_List_Osublist(c_append(X23,X25,X1),c_SetInterval_OlessThan(X21,tc_nat),X1) = c_append(c_List_Osublist(X23,c_SetInterval_OlessThan(X21,tc_nat),X1),c_List_Osublist(X25,c_SetInterval_OlessThan(c_minus(X21,c_Nat_Osize(X23,tc_List_Olist(X1)),tc_nat),tc_nat),X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2366])]) ).
fof(f3075,plain,
! [X21,X1,X25,X23] : c_List_Osublist(c_append(X23,X25,X1),c_SetInterval_OlessThan(X21,tc_nat),X1) = c_append(c_List_Osublist(X23,c_SetInterval_OlessThan(X21,tc_nat),X1),c_List_Osublist(X25,c_SetInterval_OlessThan(c_minus(X21,c_Nat_Osize(X23,tc_List_Olist(X1)),tc_nat),tc_nat),X1),X1),
inference(definition_unfolding,[],[f1771,f1766,f1766,f1766]) ).
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/benchmark/theBenchmark.p',cls_List_Otake__append_0) ).
fof(f29618,plain,
spl0_2365,
inference(avatar_split_clause,[],[f1998,f29616]) ).
fof(f29616,plain,
( spl0_2365
<=> ! [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_2365])]) ).
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/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__less__cancel__right__number__of_2) ).
fof(f29614,plain,
( spl0_2364
| ~ spl0_1744
| ~ spl0_2316 ),
inference(avatar_split_clause,[],[f28559,f28511,f15851,f29612]) ).
fof(f29612,plain,
( spl0_2364
<=> ! [X0,X1] : ~ c_in(v_B,c_Inter(c_union(X0,c_insert(c_Event_Obad,X1,tc_set(tc_Message_Oagent)),tc_set(tc_Message_Oagent)),tc_Message_Oagent),tc_Message_Oagent) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2364])]) ).
fof(f15851,plain,
( spl0_1744
<=> ! [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_1744])]) ).
fof(f28511,plain,
( spl0_2316
<=> ! [X0] : ~ c_in(v_B,c_Inter(c_insert(c_Event_Obad,X0,tc_set(tc_Message_Oagent)),tc_Message_Oagent),tc_Message_Oagent) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2316])]) ).
fof(f28559,plain,
( ! [X0,X1] : ~ c_in(v_B,c_Inter(c_union(X0,c_insert(c_Event_Obad,X1,tc_set(tc_Message_Oagent)),tc_set(tc_Message_Oagent)),tc_Message_Oagent),tc_Message_Oagent)
| ~ spl0_1744
| ~ spl0_2316 ),
inference(superposition,[],[f28512,f15852]) ).
fof(f15852,plain,
( ! [X18,X1,X12,X13] : c_union(X12,c_insert(X18,X13,X1),X1) = c_insert(X18,c_union(X12,X13,X1),X1)
| ~ spl0_1744 ),
inference(avatar_component_clause,[],[f15851]) ).
fof(f28512,plain,
( ! [X0] : ~ c_in(v_B,c_Inter(c_insert(c_Event_Obad,X0,tc_set(tc_Message_Oagent)),tc_Message_Oagent),tc_Message_Oagent)
| ~ spl0_2316 ),
inference(avatar_component_clause,[],[f28511]) ).
fof(f29610,plain,
spl0_2363,
inference(avatar_split_clause,[],[f1992,f29608]) ).
fof(f29608,plain,
( spl0_2363
<=> ! [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_2363])]) ).
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/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__less__cancel__left__number__of_2) ).
fof(f29606,plain,
spl0_2362,
inference(avatar_split_clause,[],[f1986,f29604]) ).
fof(f29604,plain,
( spl0_2362
<=> ! [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_2362])]) ).
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/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__le__cancel__right__number__of_2) ).
fof(f29602,plain,
spl0_2361,
inference(avatar_split_clause,[],[f1980,f29600]) ).
fof(f29600,plain,
( spl0_2361
<=> ! [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_2361])]) ).
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/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__le__cancel__left__number__of_2) ).
fof(f29598,plain,
spl0_2360,
inference(avatar_split_clause,[],[f115,f29596]) ).
fof(f29596,plain,
( spl0_2360
<=> ! [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_2360])]) ).
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/benchmark/theBenchmark.p',cls_Sum__Type_OPlusE_0) ).
fof(f29594,plain,
spl0_2359,
inference(avatar_split_clause,[],[f84,f29592]) ).
fof(f29592,plain,
( spl0_2359
<=> ! [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_2359])]) ).
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/benchmark/theBenchmark.p',cls_Relation_Orel__compE_2) ).
fof(f29508,plain,
( spl0_2358
| ~ spl0_786
| ~ spl0_795
| ~ spl0_2026
| ~ spl0_2357 ),
inference(avatar_split_clause,[],[f29504,f29501,f20939,f7520,f7484,f29506]) ).
fof(f29506,plain,
( spl0_2358
<=> ! [X18,X21,X1] :
( c_Nat_Opower(c_uminus(X18,X1),c_times(c_plus(c_1,c_1,tc_nat),X21,tc_nat),X1) = c_Nat_Opower(X18,c_times(c_plus(c_1,c_1,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_2358])]) ).
fof(f29501,plain,
( spl0_2357
<=> ! [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_2357])]) ).
fof(f29504,plain,
( ! [X21,X18,X1] :
( c_Nat_Opower(c_uminus(X18,X1),c_times(c_plus(c_1,c_1,tc_nat),X21,tc_nat),X1) = c_Nat_Opower(X18,c_times(c_plus(c_1,c_1,tc_nat),X21,tc_nat),X1)
| ~ class_Power_Orecpower(X1)
| ~ class_Ring__and__Field_Ocomm__ring__1(X1) )
| ~ spl0_786
| ~ spl0_795
| ~ spl0_2026
| ~ spl0_2357 ),
inference(forward_demodulation,[],[f29502,f21022]) ).
fof(f21022,plain,
( c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat) = c_plus(c_1,c_1,tc_nat)
| ~ spl0_786
| ~ spl0_795
| ~ spl0_2026 ),
inference(forward_demodulation,[],[f20943,f7485]) ).
fof(f20943,plain,
( c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat) = c_plus(c_1,c_plus(c_1,c_0,tc_nat),tc_nat)
| ~ spl0_795
| ~ spl0_2026 ),
inference(superposition,[],[f20940,f7521]) ).
fof(f29502,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_2357 ),
inference(avatar_component_clause,[],[f29501]) ).
fof(f29503,plain,
spl0_2357,
inference(avatar_split_clause,[],[f3370,f29501]) ).
fof(f3370,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,[],[f3369,f2156]) ).
fof(f3369,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,[],[f3368,f2154]) ).
fof(f3368,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/benchmark/theBenchmark.p',cls_NatBin_Opower__minus__even_0) ).
fof(f29499,plain,
spl0_2356,
inference(avatar_split_clause,[],[f3149,f29497]) ).
fof(f29497,plain,
( spl0_2356
<=> ! [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_Otrancl(c_union(X5,c_Relation_OId,tc_prod(X1,X1)),X1),tc_prod(X1,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2356])]) ).
fof(f3149,plain,
! [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_Otrancl(c_union(X5,c_Relation_OId,tc_prod(X1,X1)),X1),tc_prod(X1,X1)) ),
inference(definition_unfolding,[],[f2723,f2716]) ).
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/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Owf__insert_1) ).
fof(f29495,plain,
spl0_2355,
inference(avatar_split_clause,[],[f3148,f29493]) ).
fof(f29493,plain,
( spl0_2355
<=> ! [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_Otrancl(c_union(X5,c_Relation_OId,tc_prod(X1,X1)),X1),tc_prod(X1,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2355])]) ).
fof(f3148,plain,
! [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_Otrancl(c_union(X5,c_Relation_OId,tc_prod(X1,X1)),X1),tc_prod(X1,X1)) ),
inference(definition_unfolding,[],[f2720,f2716]) ).
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/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Oacyclic__insert_1) ).
fof(f29491,plain,
spl0_2354,
inference(avatar_split_clause,[],[f3046,f29489]) ).
fof(f29489,plain,
( spl0_2354
<=> ! [X85,X1] : c_Transitive__Closure_Otrancl(c_union(X85,c_Relation_OId,tc_prod(X1,X1)),X1) = c_Relation_Orel__comp(c_Transitive__Closure_Otrancl(c_union(X85,c_Relation_OId,tc_prod(X1,X1)),X1),c_Transitive__Closure_Otrancl(c_union(X85,c_Relation_OId,tc_prod(X1,X1)),X1),X1,X1,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2354])]) ).
fof(f3046,plain,
! [X1,X85] : c_Transitive__Closure_Otrancl(c_union(X85,c_Relation_OId,tc_prod(X1,X1)),X1) = c_Relation_Orel__comp(c_Transitive__Closure_Otrancl(c_union(X85,c_Relation_OId,tc_prod(X1,X1)),X1),c_Transitive__Closure_Otrancl(c_union(X85,c_Relation_OId,tc_prod(X1,X1)),X1),X1,X1,X1),
inference(definition_unfolding,[],[f2711,f2716,f2716,f2716]) ).
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/benchmark/theBenchmark.p',cls_Transitive__Closure_Ortrancl__idemp__self__comp_0) ).
fof(f29487,plain,
spl0_2353,
inference(avatar_split_clause,[],[f16,f29485]) ).
fof(f29485,plain,
( spl0_2353
<=> ! [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_2353])]) ).
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/benchmark/theBenchmark.p',cls_Datatype__Universe_OuprodI_0) ).
fof(f29475,plain,
( spl0_2352
| ~ spl0_1196
| ~ spl0_1537
| ~ spl0_2348 ),
inference(avatar_split_clause,[],[f28757,f28754,f12649,f9570,f29473]) ).
fof(f29473,plain,
( spl0_2352
<=> ! [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_2352])]) ).
fof(f28754,plain,
( spl0_2348
<=> ! [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_2348])]) ).
fof(f28757,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_1196
| ~ spl0_1537
| ~ spl0_2348 ),
inference(forward_demodulation,[],[f28755,f13711]) ).
fof(f28755,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_2348 ),
inference(avatar_component_clause,[],[f28754]) ).
fof(f29471,plain,
( spl0_2351
| ~ spl0_1195
| ~ spl0_1537
| ~ spl0_2347 ),
inference(avatar_split_clause,[],[f28752,f28749,f12649,f9566,f29469]) ).
fof(f29469,plain,
( spl0_2351
<=> ! [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_2351])]) ).
fof(f28749,plain,
( spl0_2347
<=> ! [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_2347])]) ).
fof(f28752,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_1195
| ~ spl0_1537
| ~ spl0_2347 ),
inference(forward_demodulation,[],[f28750,f13712]) ).
fof(f28750,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_2347 ),
inference(avatar_component_clause,[],[f28749]) ).
fof(f29467,plain,
( spl0_2350
| ~ spl0_1501
| ~ spl0_2316 ),
inference(avatar_split_clause,[],[f28556,f28511,f12491,f29465]) ).
fof(f28556,plain,
( ! [X0] : ~ c_in(v_B,c_Inter(c_List_Oset(c_List_Olist_OCons(c_Event_Obad,X0,tc_set(tc_Message_Oagent)),tc_set(tc_Message_Oagent)),tc_Message_Oagent),tc_Message_Oagent)
| ~ spl0_1501
| ~ spl0_2316 ),
inference(superposition,[],[f28512,f12492]) ).
fof(f28900,plain,
( spl0_2349
| ~ spl0_2152
| ~ spl0_2304 ),
inference(avatar_split_clause,[],[f28349,f28259,f23775,f28898]) ).
fof(f28898,plain,
( spl0_2349
<=> ! [X0] : ~ c_in(c_Pair(X0,v_B,tc_Message_Oagent,tc_Message_Oagent),c_Relation_Odiag(c_Event_Obad,tc_Message_Oagent),tc_prod(tc_Message_Oagent,tc_Message_Oagent)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2349])]) ).
fof(f23775,plain,
( spl0_2152
<=> ! [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_2152])]) ).
fof(f28259,plain,
( spl0_2304
<=> ! [X0] : ~ c_in(v_B,c_Relation_OImage(c_Relation_Odiag(c_Event_Obad,tc_Message_Oagent),X0,tc_Message_Oagent,tc_Message_Oagent),tc_Message_Oagent) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2304])]) ).
fof(f28349,plain,
( ! [X0] : ~ c_in(c_Pair(X0,v_B,tc_Message_Oagent,tc_Message_Oagent),c_Relation_Odiag(c_Event_Obad,tc_Message_Oagent),tc_prod(tc_Message_Oagent,tc_Message_Oagent))
| ~ spl0_2152
| ~ spl0_2304 ),
inference(resolution,[],[f28260,f23776]) ).
fof(f23776,plain,
( ! [X2,X18,X1,X27,X5] :
( c_in(X27,c_Relation_OImage(X5,c_insert(X18,c_emptyset,X2),X2,X1),X1)
| ~ c_in(c_Pair(X18,X27,X2,X1),X5,tc_prod(X2,X1)) )
| ~ spl0_2152 ),
inference(avatar_component_clause,[],[f23775]) ).
fof(f28260,plain,
( ! [X0] : ~ c_in(v_B,c_Relation_OImage(c_Relation_Odiag(c_Event_Obad,tc_Message_Oagent),X0,tc_Message_Oagent,tc_Message_Oagent),tc_Message_Oagent)
| ~ spl0_2304 ),
inference(avatar_component_clause,[],[f28259]) ).
fof(f28756,plain,
spl0_2348,
inference(avatar_split_clause,[],[f3327,f28754]) ).
fof(f3327,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/benchmark/theBenchmark.p',cls_IntDiv_Omod__pos__neg__1__number__of_0) ).
fof(f28751,plain,
spl0_2347,
inference(avatar_split_clause,[],[f3326,f28749]) ).
fof(f3326,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/benchmark/theBenchmark.p',cls_IntDiv_Odiv__pos__neg__1__number__of_0) ).
fof(f28738,plain,
( spl0_2346
| ~ spl0_646
| ~ spl0_687
| ~ spl0_786
| ~ spl0_795
| ~ spl0_1372
| ~ spl0_1461
| ~ spl0_2026
| ~ spl0_2345 ),
inference(avatar_split_clause,[],[f28734,f28730,f20939,f11313,f10914,f7520,f7484,f7046,f6101,f28736]) ).
fof(f28736,plain,
( spl0_2346
<=> ! [X15] : c_div(c_plus(X15,c_plus(c_1,c_1,tc_nat),tc_nat),c_plus(c_1,c_1,tc_nat),tc_nat) = c_plus(c_1,c_div(X15,c_plus(c_1,c_1,tc_nat),tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2346])]) ).
fof(f28730,plain,
( spl0_2345
<=> ! [X15] : c_Finite__Set_Ocard(c_SetInterval_OatMost(c_div(X15,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),tc_nat),tc_nat) = c_div(c_plus(X15,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2345])]) ).
fof(f28734,plain,
( ! [X15] : c_div(c_plus(X15,c_plus(c_1,c_1,tc_nat),tc_nat),c_plus(c_1,c_1,tc_nat),tc_nat) = c_plus(c_1,c_div(X15,c_plus(c_1,c_1,tc_nat),tc_nat),tc_nat)
| ~ spl0_646
| ~ spl0_687
| ~ spl0_786
| ~ spl0_795
| ~ spl0_1372
| ~ spl0_1461
| ~ spl0_2026
| ~ spl0_2345 ),
inference(forward_demodulation,[],[f28733,f12280]) ).
fof(f28733,plain,
( ! [X15] : c_Finite__Set_Ocard(c_SetInterval_OatMost(c_div(X15,c_plus(c_1,c_1,tc_nat),tc_nat),tc_nat),tc_nat) = c_div(c_plus(X15,c_plus(c_1,c_1,tc_nat),tc_nat),c_plus(c_1,c_1,tc_nat),tc_nat)
| ~ spl0_786
| ~ spl0_795
| ~ spl0_2026
| ~ spl0_2345 ),
inference(forward_demodulation,[],[f28731,f21022]) ).
fof(f28731,plain,
( ! [X15] : c_Finite__Set_Ocard(c_SetInterval_OatMost(c_div(X15,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),tc_nat),tc_nat) = c_div(c_plus(X15,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat)
| ~ spl0_2345 ),
inference(avatar_component_clause,[],[f28730]) ).
fof(f28732,plain,
spl0_2345,
inference(avatar_split_clause,[],[f3274,f28730]) ).
fof(f3274,plain,
! [X15] : c_Finite__Set_Ocard(c_SetInterval_OatMost(c_div(X15,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),tc_nat),tc_nat) = c_div(c_plus(X15,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),
inference(forward_demodulation,[],[f3273,f3242]) ).
fof(f3273,plain,
! [X15] : c_div(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Finite__Set_Ocard(c_SetInterval_OatMost(X15,tc_nat),tc_nat),tc_nat),tc_nat),c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat) = c_Finite__Set_Ocard(c_SetInterval_OatMost(c_div(X15,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),tc_nat),tc_nat),
inference(forward_demodulation,[],[f3272,f2156]) ).
fof(f3272,plain,
! [X15] : c_div(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Finite__Set_Ocard(c_SetInterval_OatMost(X15,tc_nat),tc_nat),tc_nat),tc_nat),c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1)),tc_nat),tc_nat) = c_Finite__Set_Ocard(c_SetInterval_OatMost(c_div(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),tc_nat),
inference(forward_demodulation,[],[f3271,f2154]) ).
fof(f3271,plain,
! [X15] : c_div(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Finite__Set_Ocard(c_SetInterval_OatMost(X15,tc_nat),tc_nat),tc_nat),tc_nat),c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB0),tc_nat),tc_nat) = c_Finite__Set_Ocard(c_SetInterval_OatMost(c_div(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),tc_nat),
inference(forward_demodulation,[],[f3077,f2156]) ).
fof(f3077,plain,
! [X15] : c_div(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Finite__Set_Ocard(c_SetInterval_OatMost(X15,tc_nat),tc_nat),tc_nat),tc_nat),c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),tc_nat) = c_Finite__Set_Ocard(c_SetInterval_OatMost(c_div(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),tc_nat),
inference(definition_unfolding,[],[f1884,f2544,f2544,f2544]) ).
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/benchmark/theBenchmark.p',cls_NatSimprocs_Odiv2__Suc__Suc_0) ).
fof(f28661,plain,
( spl0_2344
| ~ spl0_646
| ~ spl0_687
| ~ spl0_1372
| ~ spl0_1461
| ~ spl0_2026
| ~ spl0_2343 ),
inference(avatar_split_clause,[],[f28657,f28653,f20939,f11313,f10914,f7046,f6101,f28659]) ).
fof(f28659,plain,
( spl0_2344
<=> ! [X21,X15] : 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) = c_Divides_Oop_Amod(X15,c_plus(c_1,c_plus(c_1,c_plus(c_1,X21,tc_nat),tc_nat),tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2344])]) ).
fof(f28653,plain,
( spl0_2343
<=> ! [X21,X15] : c_Divides_Oop_Amod(X15,c_Finite__Set_Ocard(c_SetInterval_OatMost(c_plus(X21,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),tc_nat),tc_nat),tc_nat) = c_Divides_Oop_Amod(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_2343])]) ).
fof(f28657,plain,
( ! [X21,X15] : 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) = c_Divides_Oop_Amod(X15,c_plus(c_1,c_plus(c_1,c_plus(c_1,X21,tc_nat),tc_nat),tc_nat),tc_nat)
| ~ spl0_646
| ~ spl0_687
| ~ spl0_1372
| ~ spl0_1461
| ~ spl0_2026
| ~ spl0_2343 ),
inference(forward_demodulation,[],[f28656,f20940]) ).
fof(f28656,plain,
( ! [X21,X15] : 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) = c_Divides_Oop_Amod(X15,c_plus(c_1,c_plus(X21,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),tc_nat),tc_nat)
| ~ spl0_646
| ~ spl0_687
| ~ spl0_1372
| ~ spl0_1461
| ~ spl0_2343 ),
inference(forward_demodulation,[],[f28654,f12280]) ).
fof(f28654,plain,
( ! [X21,X15] : c_Divides_Oop_Amod(X15,c_Finite__Set_Ocard(c_SetInterval_OatMost(c_plus(X21,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),tc_nat),tc_nat),tc_nat) = c_Divides_Oop_Amod(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)
| ~ spl0_2343 ),
inference(avatar_component_clause,[],[f28653]) ).
fof(f28655,plain,
spl0_2343,
inference(avatar_split_clause,[],[f3264,f28653]) ).
fof(f3264,plain,
! [X21,X15] : c_Divides_Oop_Amod(X15,c_Finite__Set_Ocard(c_SetInterval_OatMost(c_plus(X21,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),tc_nat),tc_nat),tc_nat) = c_Divides_Oop_Amod(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,[],[f3263,f2156]) ).
fof(f3263,plain,
! [X21,X15] : 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) = c_Divides_Oop_Amod(X15,c_Finite__Set_Ocard(c_SetInterval_OatMost(c_plus(X21,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),tc_nat),tc_nat),tc_nat),
inference(forward_demodulation,[],[f3262,f3024]) ).
fof(f3262,plain,
! [X21,X15] : 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) = c_Divides_Oop_Amod(X15,c_plus(c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),tc_nat),
inference(forward_demodulation,[],[f3070,f3242]) ).
fof(f3070,plain,
! [X21,X15] : 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) = c_Divides_Oop_Amod(X15,c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),tc_nat),tc_nat),tc_nat),tc_nat),tc_nat),
inference(definition_unfolding,[],[f1977,f2544,f2544,f2544]) ).
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/benchmark/theBenchmark.p',cls_NatSimprocs_Omod__Suc__eq__mod__add3_0) ).
fof(f28639,plain,
( spl0_2342
| ~ spl0_646
| ~ spl0_687
| ~ spl0_1372
| ~ spl0_1461
| ~ spl0_2026
| ~ spl0_2341 ),
inference(avatar_split_clause,[],[f28635,f28631,f20939,f11313,f10914,f7046,f6101,f28637]) ).
fof(f28637,plain,
( spl0_2342
<=> ! [X21,X15] : 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) = c_div(X15,c_plus(c_1,c_plus(c_1,c_plus(c_1,X21,tc_nat),tc_nat),tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2342])]) ).
fof(f28631,plain,
( spl0_2341
<=> ! [X21,X15] : c_div(X15,c_Finite__Set_Ocard(c_SetInterval_OatMost(c_plus(X21,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),tc_nat),tc_nat),tc_nat) = c_div(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_2341])]) ).
fof(f28635,plain,
( ! [X21,X15] : 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) = c_div(X15,c_plus(c_1,c_plus(c_1,c_plus(c_1,X21,tc_nat),tc_nat),tc_nat),tc_nat)
| ~ spl0_646
| ~ spl0_687
| ~ spl0_1372
| ~ spl0_1461
| ~ spl0_2026
| ~ spl0_2341 ),
inference(forward_demodulation,[],[f28634,f20940]) ).
fof(f28634,plain,
( ! [X21,X15] : 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) = c_div(X15,c_plus(c_1,c_plus(X21,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),tc_nat),tc_nat)
| ~ spl0_646
| ~ spl0_687
| ~ spl0_1372
| ~ spl0_1461
| ~ spl0_2341 ),
inference(forward_demodulation,[],[f28632,f12280]) ).
fof(f28632,plain,
( ! [X21,X15] : c_div(X15,c_Finite__Set_Ocard(c_SetInterval_OatMost(c_plus(X21,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),tc_nat),tc_nat),tc_nat) = c_div(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)
| ~ spl0_2341 ),
inference(avatar_component_clause,[],[f28631]) ).
fof(f28633,plain,
spl0_2341,
inference(avatar_split_clause,[],[f3261,f28631]) ).
fof(f3261,plain,
! [X21,X15] : c_div(X15,c_Finite__Set_Ocard(c_SetInterval_OatMost(c_plus(X21,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),tc_nat),tc_nat),tc_nat) = c_div(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,[],[f3260,f2156]) ).
fof(f3260,plain,
! [X21,X15] : 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) = c_div(X15,c_Finite__Set_Ocard(c_SetInterval_OatMost(c_plus(X21,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),tc_nat),tc_nat),tc_nat),
inference(forward_demodulation,[],[f3259,f3024]) ).
fof(f3259,plain,
! [X21,X15] : 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) = c_div(X15,c_plus(c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),tc_nat),
inference(forward_demodulation,[],[f3069,f3242]) ).
fof(f3069,plain,
! [X21,X15] : 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) = c_div(X15,c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),tc_nat),tc_nat),tc_nat),tc_nat),tc_nat),
inference(definition_unfolding,[],[f1885,f2544,f2544,f2544]) ).
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/benchmark/theBenchmark.p',cls_NatSimprocs_Odiv__Suc__eq__div__add3_0) ).
fof(f28625,plain,
( spl0_2340
| ~ spl0_646
| ~ spl0_687
| ~ spl0_1372
| ~ spl0_1461
| ~ spl0_2026
| ~ spl0_2339 ),
inference(avatar_split_clause,[],[f28621,f28617,f20939,f11313,f10914,f7046,f6101,f28623]) ).
fof(f28623,plain,
( spl0_2340
<=> ! [X9,X16,X2,X1] : c_Datatype__Universe_Ontrunc(c_plus(c_1,c_plus(c_1,X16,tc_nat),tc_nat),c_Datatype__Universe_OIn0(X9,X1,X2),X1,X2) = c_Datatype__Universe_OIn0(c_Datatype__Universe_Ontrunc(c_plus(c_1,X16,tc_nat),X9,X1,X2),X1,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2340])]) ).
fof(f28617,plain,
( spl0_2339
<=> ! [X9,X16,X2,X1] : c_Datatype__Universe_OIn0(c_Datatype__Universe_Ontrunc(c_Finite__Set_Ocard(c_SetInterval_OatMost(X16,tc_nat),tc_nat),X9,X1,X2),X1,X2) = c_Datatype__Universe_Ontrunc(c_plus(X16,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),c_Datatype__Universe_OIn0(X9,X1,X2),X1,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2339])]) ).
fof(f28621,plain,
( ! [X2,X1,X9,X16] : c_Datatype__Universe_Ontrunc(c_plus(c_1,c_plus(c_1,X16,tc_nat),tc_nat),c_Datatype__Universe_OIn0(X9,X1,X2),X1,X2) = c_Datatype__Universe_OIn0(c_Datatype__Universe_Ontrunc(c_plus(c_1,X16,tc_nat),X9,X1,X2),X1,X2)
| ~ spl0_646
| ~ spl0_687
| ~ spl0_1372
| ~ spl0_1461
| ~ spl0_2026
| ~ spl0_2339 ),
inference(forward_demodulation,[],[f28620,f12280]) ).
fof(f28620,plain,
( ! [X2,X1,X9,X16] : c_Datatype__Universe_OIn0(c_Datatype__Universe_Ontrunc(c_Finite__Set_Ocard(c_SetInterval_OatMost(X16,tc_nat),tc_nat),X9,X1,X2),X1,X2) = c_Datatype__Universe_Ontrunc(c_plus(c_1,c_plus(c_1,X16,tc_nat),tc_nat),c_Datatype__Universe_OIn0(X9,X1,X2),X1,X2)
| ~ spl0_2026
| ~ spl0_2339 ),
inference(forward_demodulation,[],[f28618,f20940]) ).
fof(f28618,plain,
( ! [X2,X1,X9,X16] : c_Datatype__Universe_OIn0(c_Datatype__Universe_Ontrunc(c_Finite__Set_Ocard(c_SetInterval_OatMost(X16,tc_nat),tc_nat),X9,X1,X2),X1,X2) = c_Datatype__Universe_Ontrunc(c_plus(X16,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),c_Datatype__Universe_OIn0(X9,X1,X2),X1,X2)
| ~ spl0_2339 ),
inference(avatar_component_clause,[],[f28617]) ).
fof(f28619,plain,
spl0_2339,
inference(avatar_split_clause,[],[f3258,f28617]) ).
fof(f3258,plain,
! [X2,X1,X9,X16] : c_Datatype__Universe_OIn0(c_Datatype__Universe_Ontrunc(c_Finite__Set_Ocard(c_SetInterval_OatMost(X16,tc_nat),tc_nat),X9,X1,X2),X1,X2) = c_Datatype__Universe_Ontrunc(c_plus(X16,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),c_Datatype__Universe_OIn0(X9,X1,X2),X1,X2),
inference(forward_demodulation,[],[f3068,f3242]) ).
fof(f3068,plain,
! [X2,X1,X9,X16] : c_Datatype__Universe_Ontrunc(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Finite__Set_Ocard(c_SetInterval_OatMost(X16,tc_nat),tc_nat),tc_nat),tc_nat),c_Datatype__Universe_OIn0(X9,X1,X2),X1,X2) = c_Datatype__Universe_OIn0(c_Datatype__Universe_Ontrunc(c_Finite__Set_Ocard(c_SetInterval_OatMost(X16,tc_nat),tc_nat),X9,X1,X2),X1,X2),
inference(definition_unfolding,[],[f1204,f2544,f2544,f2544]) ).
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/benchmark/theBenchmark.p',cls_Datatype__Universe_Ontrunc__In0_0) ).
fof(f28611,plain,
( spl0_2338
| ~ spl0_646
| ~ spl0_687
| ~ spl0_1372
| ~ spl0_1461
| ~ spl0_2026
| ~ spl0_2336 ),
inference(avatar_split_clause,[],[f28602,f28598,f20939,f11313,f10914,f7046,f6101,f28609]) ).
fof(f28609,plain,
( spl0_2338
<=> ! [X9,X16,X2,X1] : c_Datatype__Universe_Ontrunc(c_plus(c_1,c_plus(c_1,X16,tc_nat),tc_nat),c_Datatype__Universe_OIn1(X9,X1,X2),X1,X2) = c_Datatype__Universe_OIn1(c_Datatype__Universe_Ontrunc(c_plus(c_1,X16,tc_nat),X9,X1,X2),X1,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2338])]) ).
fof(f28598,plain,
( spl0_2336
<=> ! [X9,X16,X2,X1] : c_Datatype__Universe_OIn1(c_Datatype__Universe_Ontrunc(c_Finite__Set_Ocard(c_SetInterval_OatMost(X16,tc_nat),tc_nat),X9,X1,X2),X1,X2) = c_Datatype__Universe_Ontrunc(c_plus(X16,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),c_Datatype__Universe_OIn1(X9,X1,X2),X1,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2336])]) ).
fof(f28602,plain,
( ! [X2,X1,X9,X16] : c_Datatype__Universe_Ontrunc(c_plus(c_1,c_plus(c_1,X16,tc_nat),tc_nat),c_Datatype__Universe_OIn1(X9,X1,X2),X1,X2) = c_Datatype__Universe_OIn1(c_Datatype__Universe_Ontrunc(c_plus(c_1,X16,tc_nat),X9,X1,X2),X1,X2)
| ~ spl0_646
| ~ spl0_687
| ~ spl0_1372
| ~ spl0_1461
| ~ spl0_2026
| ~ spl0_2336 ),
inference(forward_demodulation,[],[f28601,f12280]) ).
fof(f28601,plain,
( ! [X2,X1,X9,X16] : c_Datatype__Universe_OIn1(c_Datatype__Universe_Ontrunc(c_Finite__Set_Ocard(c_SetInterval_OatMost(X16,tc_nat),tc_nat),X9,X1,X2),X1,X2) = c_Datatype__Universe_Ontrunc(c_plus(c_1,c_plus(c_1,X16,tc_nat),tc_nat),c_Datatype__Universe_OIn1(X9,X1,X2),X1,X2)
| ~ spl0_2026
| ~ spl0_2336 ),
inference(forward_demodulation,[],[f28599,f20940]) ).
fof(f28599,plain,
( ! [X2,X1,X9,X16] : c_Datatype__Universe_OIn1(c_Datatype__Universe_Ontrunc(c_Finite__Set_Ocard(c_SetInterval_OatMost(X16,tc_nat),tc_nat),X9,X1,X2),X1,X2) = c_Datatype__Universe_Ontrunc(c_plus(X16,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),c_Datatype__Universe_OIn1(X9,X1,X2),X1,X2)
| ~ spl0_2336 ),
inference(avatar_component_clause,[],[f28598]) ).
fof(f28607,plain,
( spl0_2337
| ~ spl0_891
| ~ spl0_2185 ),
inference(avatar_split_clause,[],[f27798,f24890,f7918,f28604]) ).
fof(f24890,plain,
( spl0_2185
<=> ! [X0] : c_emptyset = c_Relation_OImage(c_Relation_Odiag(c_insert(v_B,X0,tc_Message_Oagent),tc_Message_Oagent),c_minus(c_Event_Obad,X0,tc_set(tc_Message_Oagent)),tc_Message_Oagent,tc_Message_Oagent) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2185])]) ).
fof(f27798,plain,
( c_emptyset = c_Relation_OImage(c_Relation_Odiag(c_insert(v_B,c_emptyset,tc_Message_Oagent),tc_Message_Oagent),c_Event_Obad,tc_Message_Oagent,tc_Message_Oagent)
| ~ spl0_891
| ~ spl0_2185 ),
inference(superposition,[],[f24891,f7919]) ).
fof(f24891,plain,
( ! [X0] : c_emptyset = c_Relation_OImage(c_Relation_Odiag(c_insert(v_B,X0,tc_Message_Oagent),tc_Message_Oagent),c_minus(c_Event_Obad,X0,tc_set(tc_Message_Oagent)),tc_Message_Oagent,tc_Message_Oagent)
| ~ spl0_2185 ),
inference(avatar_component_clause,[],[f24890]) ).
fof(f28600,plain,
spl0_2336,
inference(avatar_split_clause,[],[f3257,f28598]) ).
fof(f3257,plain,
! [X2,X1,X9,X16] : c_Datatype__Universe_OIn1(c_Datatype__Universe_Ontrunc(c_Finite__Set_Ocard(c_SetInterval_OatMost(X16,tc_nat),tc_nat),X9,X1,X2),X1,X2) = c_Datatype__Universe_Ontrunc(c_plus(X16,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),c_Datatype__Universe_OIn1(X9,X1,X2),X1,X2),
inference(forward_demodulation,[],[f3067,f3242]) ).
fof(f3067,plain,
! [X2,X1,X9,X16] : c_Datatype__Universe_Ontrunc(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Finite__Set_Ocard(c_SetInterval_OatMost(X16,tc_nat),tc_nat),tc_nat),tc_nat),c_Datatype__Universe_OIn1(X9,X1,X2),X1,X2) = c_Datatype__Universe_OIn1(c_Datatype__Universe_Ontrunc(c_Finite__Set_Ocard(c_SetInterval_OatMost(X16,tc_nat),tc_nat),X9,X1,X2),X1,X2),
inference(definition_unfolding,[],[f1205,f2544,f2544,f2544]) ).
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/benchmark/theBenchmark.p',cls_Datatype__Universe_Ontrunc__In1_0) ).
fof(f28596,plain,
spl0_2335,
inference(avatar_split_clause,[],[f2003,f28594]) ).
fof(f28594,plain,
( spl0_2335
<=> ! [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_2335])]) ).
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/benchmark/theBenchmark.p',cls_NatSimprocs_Oright__distrib__number__of_0) ).
fof(f28592,plain,
spl0_2334,
inference(avatar_split_clause,[],[f2002,f28590]) ).
fof(f28590,plain,
( spl0_2334
<=> ! [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_2334])]) ).
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/benchmark/theBenchmark.p',cls_NatSimprocs_Oright__diff__distrib__number__of_0) ).
fof(f28588,plain,
spl0_2333,
inference(avatar_split_clause,[],[f2000,f28586]) ).
fof(f28586,plain,
( spl0_2333
<=> ! [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_2333])]) ).
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/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__less__cancel__right__number__of_4) ).
fof(f28584,plain,
spl0_2332,
inference(avatar_split_clause,[],[f1999,f28582]) ).
fof(f28582,plain,
( spl0_2332
<=> ! [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_2332])]) ).
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/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__less__cancel__right__number__of_3) ).
fof(f28580,plain,
spl0_2331,
inference(avatar_split_clause,[],[f1997,f28578]) ).
fof(f28578,plain,
( spl0_2331
<=> ! [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_2331])]) ).
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/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__less__cancel__right__number__of_1) ).
fof(f28576,plain,
spl0_2330,
inference(avatar_split_clause,[],[f1996,f28574]) ).
fof(f28574,plain,
( spl0_2330
<=> ! [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_2330])]) ).
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/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__less__cancel__right__number__of_0) ).
fof(f28572,plain,
spl0_2329,
inference(avatar_split_clause,[],[f1994,f28570]) ).
fof(f28570,plain,
( spl0_2329
<=> ! [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_2329])]) ).
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/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__less__cancel__left__number__of_4) ).
fof(f28568,plain,
spl0_2328,
inference(avatar_split_clause,[],[f1993,f28566]) ).
fof(f28566,plain,
( spl0_2328
<=> ! [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_2328])]) ).
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/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__less__cancel__left__number__of_3) ).
fof(f28564,plain,
spl0_2327,
inference(avatar_split_clause,[],[f1991,f28562]) ).
fof(f28562,plain,
( spl0_2327
<=> ! [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_2327])]) ).
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/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__less__cancel__left__number__of_1) ).
fof(f28553,plain,
spl0_2326,
inference(avatar_split_clause,[],[f1990,f28551]) ).
fof(f28551,plain,
( spl0_2326
<=> ! [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_2326])]) ).
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/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__less__cancel__left__number__of_0) ).
fof(f28549,plain,
spl0_2325,
inference(avatar_split_clause,[],[f1988,f28547]) ).
fof(f28547,plain,
( spl0_2325
<=> ! [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_2325])]) ).
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/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__le__cancel__right__number__of_4) ).
fof(f28545,plain,
spl0_2324,
inference(avatar_split_clause,[],[f1987,f28543]) ).
fof(f28543,plain,
( spl0_2324
<=> ! [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_2324])]) ).
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/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__le__cancel__right__number__of_3) ).
fof(f28541,plain,
spl0_2323,
inference(avatar_split_clause,[],[f1985,f28539]) ).
fof(f28539,plain,
( spl0_2323
<=> ! [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_2323])]) ).
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/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__le__cancel__right__number__of_1) ).
fof(f28537,plain,
spl0_2322,
inference(avatar_split_clause,[],[f1984,f28535]) ).
fof(f28535,plain,
( spl0_2322
<=> ! [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_2322])]) ).
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/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__le__cancel__right__number__of_0) ).
fof(f28533,plain,
spl0_2321,
inference(avatar_split_clause,[],[f1982,f28531]) ).
fof(f28531,plain,
( spl0_2321
<=> ! [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_2321])]) ).
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/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__le__cancel__left__number__of_4) ).
fof(f28529,plain,
spl0_2320,
inference(avatar_split_clause,[],[f1981,f28527]) ).
fof(f28527,plain,
( spl0_2320
<=> ! [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_2320])]) ).
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/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__le__cancel__left__number__of_3) ).
fof(f28525,plain,
spl0_2319,
inference(avatar_split_clause,[],[f1979,f28523]) ).
fof(f28523,plain,
( spl0_2319
<=> ! [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_2319])]) ).
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/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__le__cancel__left__number__of_1) ).
fof(f28521,plain,
spl0_2318,
inference(avatar_split_clause,[],[f1978,f28519]) ).
fof(f28519,plain,
( spl0_2318
<=> ! [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_2318])]) ).
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/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__le__cancel__left__number__of_0) ).
fof(f28517,plain,
spl0_2317,
inference(avatar_split_clause,[],[f1948,f28515]) ).
fof(f28515,plain,
( spl0_2317
<=> ! [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_2317])]) ).
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/benchmark/theBenchmark.p',cls_NatSimprocs_Oleft__distrib__number__of_0) ).
fof(f28513,plain,
( spl0_2316
| ~ spl0_1950
| ~ spl0_2304 ),
inference(avatar_split_clause,[],[f28353,f28259,f19536,f28511]) ).
fof(f19536,plain,
( spl0_1950
<=> ! [X13,X18,X1] : c_Inter(c_insert(X18,X13,tc_set(X1)),X1) = c_Relation_OImage(c_Relation_Odiag(X18,X1),c_Inter(X13,X1),X1,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1950])]) ).
fof(f28353,plain,
( ! [X0] : ~ c_in(v_B,c_Inter(c_insert(c_Event_Obad,X0,tc_set(tc_Message_Oagent)),tc_Message_Oagent),tc_Message_Oagent)
| ~ spl0_1950
| ~ spl0_2304 ),
inference(superposition,[],[f28260,f19537]) ).
fof(f19537,plain,
( ! [X18,X1,X13] : c_Inter(c_insert(X18,X13,tc_set(X1)),X1) = c_Relation_OImage(c_Relation_Odiag(X18,X1),c_Inter(X13,X1),X1,X1)
| ~ spl0_1950 ),
inference(avatar_component_clause,[],[f19536]) ).
fof(f28509,plain,
spl0_2315,
inference(avatar_split_clause,[],[f1947,f28507]) ).
fof(f28507,plain,
( spl0_2315
<=> ! [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_2315])]) ).
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/benchmark/theBenchmark.p',cls_NatSimprocs_Oleft__diff__distrib__number__of_0) ).
fof(f28505,plain,
spl0_2314,
inference(avatar_split_clause,[],[f1862,f28503]) ).
fof(f28503,plain,
( spl0_2314
<=> ! [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_2314])]) ).
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/benchmark/theBenchmark.p',cls_NatBin_Omod__nat__number__of_2) ).
fof(f28501,plain,
spl0_2313,
inference(avatar_split_clause,[],[f117,f28499]) ).
fof(f28499,plain,
( spl0_2313
<=> ! [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_2313])]) ).
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/benchmark/theBenchmark.p',cls_Sum__Type_OPlusE_2) ).
fof(f28497,plain,
spl0_2312,
inference(avatar_split_clause,[],[f116,f28495]) ).
fof(f28495,plain,
( spl0_2312
<=> ! [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_2312])]) ).
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/benchmark/theBenchmark.p',cls_Sum__Type_OPlusE_1) ).
fof(f28493,plain,
spl0_2311,
inference(avatar_split_clause,[],[f13,f28491]) ).
fof(f28491,plain,
( spl0_2311
<=> ! [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_2311])]) ).
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/benchmark/theBenchmark.p',cls_Datatype__Universe_OuprodE_0) ).
fof(f28347,plain,
( spl0_2310
| ~ spl0_646
| ~ spl0_687
| ~ spl0_1372
| ~ spl0_1461
| ~ spl0_2309 ),
inference(avatar_split_clause,[],[f28343,f28340,f11313,f10914,f7046,f6101,f28345]) ).
fof(f28345,plain,
( spl0_2310
<=> ! [X16,X7,X9,X2,X1] : c_Datatype__Universe_OScons(c_Datatype__Universe_Ontrunc(X16,X9,X1,X2),c_Datatype__Universe_Ontrunc(X16,X7,X1,X2),X1,X2) = c_Datatype__Universe_Ontrunc(c_plus(c_1,X16,tc_nat),c_Datatype__Universe_OScons(X9,X7,X1,X2),X1,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2310])]) ).
fof(f28340,plain,
( spl0_2309
<=> ! [X16,X7,X9,X2,X1] : c_Datatype__Universe_OScons(c_Datatype__Universe_Ontrunc(X16,X9,X1,X2),c_Datatype__Universe_Ontrunc(X16,X7,X1,X2),X1,X2) = c_Datatype__Universe_Ontrunc(c_Finite__Set_Ocard(c_SetInterval_OatMost(X16,tc_nat),tc_nat),c_Datatype__Universe_OScons(X9,X7,X1,X2),X1,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2309])]) ).
fof(f28343,plain,
( ! [X2,X1,X9,X16,X7] : c_Datatype__Universe_OScons(c_Datatype__Universe_Ontrunc(X16,X9,X1,X2),c_Datatype__Universe_Ontrunc(X16,X7,X1,X2),X1,X2) = c_Datatype__Universe_Ontrunc(c_plus(c_1,X16,tc_nat),c_Datatype__Universe_OScons(X9,X7,X1,X2),X1,X2)
| ~ spl0_646
| ~ spl0_687
| ~ spl0_1372
| ~ spl0_1461
| ~ spl0_2309 ),
inference(forward_demodulation,[],[f28341,f12280]) ).
fof(f28341,plain,
( ! [X2,X1,X9,X16,X7] : c_Datatype__Universe_OScons(c_Datatype__Universe_Ontrunc(X16,X9,X1,X2),c_Datatype__Universe_Ontrunc(X16,X7,X1,X2),X1,X2) = c_Datatype__Universe_Ontrunc(c_Finite__Set_Ocard(c_SetInterval_OatMost(X16,tc_nat),tc_nat),c_Datatype__Universe_OScons(X9,X7,X1,X2),X1,X2)
| ~ spl0_2309 ),
inference(avatar_component_clause,[],[f28340]) ).
fof(f28342,plain,
spl0_2309,
inference(avatar_split_clause,[],[f3076,f28340]) ).
fof(f3076,plain,
! [X2,X1,X9,X16,X7] : c_Datatype__Universe_OScons(c_Datatype__Universe_Ontrunc(X16,X9,X1,X2),c_Datatype__Universe_Ontrunc(X16,X7,X1,X2),X1,X2) = c_Datatype__Universe_Ontrunc(c_Finite__Set_Ocard(c_SetInterval_OatMost(X16,tc_nat),tc_nat),c_Datatype__Universe_OScons(X9,X7,X1,X2),X1,X2),
inference(definition_unfolding,[],[f1208,f2544]) ).
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/benchmark/theBenchmark.p',cls_Datatype__Universe_Ontrunc__Scons_0) ).
fof(f28338,plain,
spl0_2308,
inference(avatar_split_clause,[],[f2331,f28336]) ).
fof(f28336,plain,
( spl0_2308
<=> ! [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_2308])]) ).
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/benchmark/theBenchmark.p',cls_Parity_Ozero__less__power__eq__number__of_0) ).
fof(f28334,plain,
spl0_2307,
inference(avatar_split_clause,[],[f2321,f28332]) ).
fof(f28332,plain,
( spl0_2307
<=> ! [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_2307])]) ).
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/benchmark/theBenchmark.p',cls_Parity_Opower__le__zero__eq__number__of_4) ).
fof(f28330,plain,
spl0_2306,
inference(avatar_split_clause,[],[f1469,f28328]) ).
fof(f28328,plain,
( spl0_2306
<=> ! [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_2306])]) ).
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/benchmark/theBenchmark.p',cls_IntDiv_Ozdiv__number__of__BIT_1) ).
fof(f28326,plain,
spl0_2305,
inference(avatar_split_clause,[],[f77,f28324]) ).
fof(f28324,plain,
( spl0_2305
<=> ! [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_2305])]) ).
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/benchmark/theBenchmark.p',cls_Relation_OconverseE_0) ).
fof(f28261,plain,
( spl0_2304
| ~ spl0_1836
| ~ spl0_2294 ),
inference(avatar_split_clause,[],[f27990,f27932,f17281,f28259]) ).
fof(f17281,plain,
( spl0_1836
<=> ! [X13,X12,X1] : c_Relation_OImage(c_Relation_Odiag(X12,X1),X13,X1,X1) = c_minus(X12,c_uminus(X13,tc_set(X1)),tc_set(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1836])]) ).
fof(f27932,plain,
( spl0_2294
<=> ! [X0] : ~ c_in(v_B,c_minus(c_Event_Obad,X0,tc_set(tc_Message_Oagent)),tc_Message_Oagent) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2294])]) ).
fof(f27990,plain,
( ! [X0] : ~ c_in(v_B,c_Relation_OImage(c_Relation_Odiag(c_Event_Obad,tc_Message_Oagent),X0,tc_Message_Oagent,tc_Message_Oagent),tc_Message_Oagent)
| ~ spl0_1836
| ~ spl0_2294 ),
inference(superposition,[],[f27933,f17282]) ).
fof(f17282,plain,
( ! [X1,X12,X13] : c_Relation_OImage(c_Relation_Odiag(X12,X1),X13,X1,X1) = c_minus(X12,c_uminus(X13,tc_set(X1)),tc_set(X1))
| ~ spl0_1836 ),
inference(avatar_component_clause,[],[f17281]) ).
fof(f27933,plain,
( ! [X0] : ~ c_in(v_B,c_minus(c_Event_Obad,X0,tc_set(tc_Message_Oagent)),tc_Message_Oagent)
| ~ spl0_2294 ),
inference(avatar_component_clause,[],[f27932]) ).
fof(f27970,plain,
spl0_2303,
inference(avatar_split_clause,[],[f3205,f27968]) ).
fof(f27968,plain,
( spl0_2303
<=> ! [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__mult(c_Numeral_OMin,X83)),tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2303])]) ).
fof(f3205,plain,
! [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__mult(c_Numeral_OMin,X83)),tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(definition_unfolding,[],[f1840,f2129]) ).
fof(f2129,axiom,
! [X11] : c_Numeral_Obin__minus(X11) = c_Numeral_Obin__mult(c_Numeral_OMin,X11),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obin__mult__Min_0) ).
fof(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/benchmark/theBenchmark.p',cls_NatBin_Oeq__nat__number__of_3) ).
fof(f27966,plain,
spl0_2302,
inference(avatar_split_clause,[],[f3204,f27964]) ).
fof(f27964,plain,
( spl0_2302
<=> ! [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__mult(c_Numeral_OMin,X83)),tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2302])]) ).
fof(f3204,plain,
! [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__mult(c_Numeral_OMin,X83)),tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(definition_unfolding,[],[f1839,f2129]) ).
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/benchmark/theBenchmark.p',cls_NatBin_Oeq__nat__number__of_2) ).
fof(f27962,plain,
spl0_2301,
inference(avatar_split_clause,[],[f3203,f27960]) ).
fof(f27960,plain,
( spl0_2301
<=> ! [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__mult(c_Numeral_OMin,X83)),tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2301])]) ).
fof(f3203,plain,
! [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__mult(c_Numeral_OMin,X83)),tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(definition_unfolding,[],[f1844,f2129]) ).
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/benchmark/theBenchmark.p',cls_NatBin_Oeq__nat__number__of_7) ).
fof(f27958,plain,
spl0_2300,
inference(avatar_split_clause,[],[f3202,f27956]) ).
fof(f27956,plain,
( spl0_2300
<=> ! [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__mult(c_Numeral_OMin,X83)),tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2300])]) ).
fof(f3202,plain,
! [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__mult(c_Numeral_OMin,X83)),tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(definition_unfolding,[],[f1842,f2129]) ).
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/benchmark/theBenchmark.p',cls_NatBin_Oeq__nat__number__of_5) ).
fof(f27954,plain,
spl0_2299,
inference(avatar_split_clause,[],[f3200,f27952]) ).
fof(f27952,plain,
( spl0_2299
<=> ! [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__mult(c_Numeral_OMin,X83)),tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2299])]) ).
fof(f3200,plain,
! [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__mult(c_Numeral_OMin,X83)),tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(definition_unfolding,[],[f1846,f2129]) ).
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/benchmark/theBenchmark.p',cls_NatBin_Oeq__nat__number__of_9) ).
fof(f27950,plain,
spl0_2298,
inference(avatar_split_clause,[],[f2001,f27948]) ).
fof(f27948,plain,
( spl0_2298
<=> ! [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_2298])]) ).
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/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__less__cancel__right__number__of_5) ).
fof(f27946,plain,
spl0_2297,
inference(avatar_split_clause,[],[f1995,f27944]) ).
fof(f27944,plain,
( spl0_2297
<=> ! [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_2297])]) ).
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/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__less__cancel__left__number__of_5) ).
fof(f27942,plain,
spl0_2296,
inference(avatar_split_clause,[],[f1989,f27940]) ).
fof(f27940,plain,
( spl0_2296
<=> ! [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_2296])]) ).
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/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__le__cancel__right__number__of_5) ).
fof(f27938,plain,
spl0_2295,
inference(avatar_split_clause,[],[f1983,f27936]) ).
fof(f27936,plain,
( spl0_2295
<=> ! [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_2295])]) ).
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/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__le__cancel__left__number__of_5) ).
fof(f27934,plain,
( spl0_2294
| ~ spl0_1860
| ~ spl0_2185 ),
inference(avatar_split_clause,[],[f27814,f24890,f17703,f27932]) ).
fof(f17703,plain,
( spl0_1860
<=> ! [X18,X13,X12,X1] :
( ~ c_in(X18,X13,X1)
| c_emptyset != c_Relation_OImage(c_Relation_Odiag(c_insert(X18,X12,X1),X1),X13,X1,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1860])]) ).
fof(f27814,plain,
( ! [X0] : ~ c_in(v_B,c_minus(c_Event_Obad,X0,tc_set(tc_Message_Oagent)),tc_Message_Oagent)
| ~ spl0_1860
| ~ spl0_2185 ),
inference(trivial_inequality_removal,[],[f27812]) ).
fof(f27812,plain,
( ! [X0] :
( c_emptyset != c_emptyset
| ~ c_in(v_B,c_minus(c_Event_Obad,X0,tc_set(tc_Message_Oagent)),tc_Message_Oagent) )
| ~ spl0_1860
| ~ spl0_2185 ),
inference(superposition,[],[f17704,f24891]) ).
fof(f17704,plain,
( ! [X18,X1,X12,X13] :
( c_emptyset != c_Relation_OImage(c_Relation_Odiag(c_insert(X18,X12,X1),X1),X13,X1,X1)
| ~ c_in(X18,X13,X1) )
| ~ spl0_1860 ),
inference(avatar_component_clause,[],[f17703]) ).
fof(f27930,plain,
spl0_2293,
inference(avatar_split_clause,[],[f1794,f27928]) ).
fof(f27928,plain,
( spl0_2293
<=> ! [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_2293])]) ).
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/benchmark/theBenchmark.p',cls_Map_Omap__of__zip__is__None_1) ).
fof(f27926,plain,
spl0_2292,
inference(avatar_split_clause,[],[f1793,f27924]) ).
fof(f27924,plain,
( spl0_2292
<=> ! [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_2292])]) ).
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/benchmark/theBenchmark.p',cls_Map_Omap__of__zip__is__None_0) ).
fof(f27922,plain,
spl0_2291,
inference(avatar_split_clause,[],[f1789,f27920]) ).
fof(f27920,plain,
( spl0_2291
<=> ! [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_2291])]) ).
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/benchmark/theBenchmark.p',cls_List_Ozip__Cons__Cons_0) ).
fof(f27918,plain,
spl0_2290,
inference(avatar_split_clause,[],[f1616,f27916]) ).
fof(f27916,plain,
( spl0_2290
<=> ! [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_2290])]) ).
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/benchmark/theBenchmark.p',cls_List_Olexord__Nil__left_0) ).
fof(f27914,plain,
spl0_2289,
inference(avatar_split_clause,[],[f1458,f27912]) ).
fof(f27912,plain,
( spl0_2289
<=> ! [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_2289])]) ).
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/benchmark/theBenchmark.p',cls_IntDiv_OposDivAlg__eqn__1__number__of_0) ).
fof(f27910,plain,
spl0_2288,
inference(avatar_split_clause,[],[f118,f27908]) ).
fof(f27908,plain,
( spl0_2288
<=> ! [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_2288])]) ).
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/benchmark/theBenchmark.p',cls_Sum__Type_OPlusE_3) ).
fof(f27713,plain,
spl0_2287,
inference(avatar_split_clause,[],[f3199,f27711]) ).
fof(f27711,plain,
( spl0_2287
<=> ! [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_Relation_OImage(c_Relation_Odiag(c_List_Oset(X23,X1),X1),c_List_Oset(X25,X1),X1,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2287])]) ).
fof(f3199,plain,
! [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_Relation_OImage(c_Relation_Odiag(c_List_Oset(X23,X1),X1),c_List_Oset(X25,X1),X1,X1) ),
inference(definition_unfolding,[],[f1558,f2373]) ).
fof(f2373,axiom,
! [X1,X12,X13] : c_inter(X12,X13,X1) = c_Relation_OImage(c_Relation_Odiag(X12,X1),X13,X1,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_OImage__diag_0) ).
fof(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/benchmark/theBenchmark.p',cls_List_Odistinct__append_3) ).
fof(f27709,plain,
spl0_2286,
inference(avatar_split_clause,[],[f3178,f27707]) ).
fof(f27707,plain,
( spl0_2286
<=> ! [X86,X87,X88] :
( c_in(X86,c_Message_Osynth(c_Message_Oanalz(X88)),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OMPair(c_Message_Omsg_OHash(c_Message_Omsg_OMPair(X86,X87)),X87),c_Message_Osynth(c_Message_Oanalz(X88)),tc_Message_Omsg)
| c_in(c_Message_Omsg_OHash(c_Message_Omsg_OMPair(X86,X87)),c_Message_Oanalz(X88),tc_Message_Omsg) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2286])]) ).
fof(f3178,plain,
! [X88,X86,X87] :
( c_in(X86,c_Message_Osynth(c_Message_Oanalz(X88)),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OMPair(c_Message_Omsg_OHash(c_Message_Omsg_OMPair(X86,X87)),X87),c_Message_Osynth(c_Message_Oanalz(X88)),tc_Message_Omsg)
| c_in(c_Message_Omsg_OHash(c_Message_Omsg_OMPair(X86,X87)),c_Message_Oanalz(X88),tc_Message_Omsg) ),
inference(definition_unfolding,[],[f2819,f2837]) ).
fof(f2819,axiom,
! [X88,X86,X87] :
( c_in(X86,c_Message_Osynth(c_Message_Oanalz(X88)),tc_Message_Omsg)
| ~ c_in(c_Message_OHPair(X86,X87),c_Message_Osynth(c_Message_Oanalz(X88)),tc_Message_Omsg)
| c_in(c_Message_Omsg_OHash(c_Message_Omsg_OMPair(X86,X87)),c_Message_Oanalz(X88),tc_Message_Omsg) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OHPair__synth__analz_0) ).
fof(f27705,plain,
spl0_2285,
inference(avatar_split_clause,[],[f3169,f27703]) ).
fof(f27703,plain,
( spl0_2285
<=> ! [X18,X13,X12,X1] :
( c_in(X18,X13,X1)
| c_emptyset != c_Relation_OImage(c_Relation_Odiag(X12,X1),X13,X1,X1)
| c_emptyset = c_Relation_OImage(c_Relation_Odiag(c_insert(X18,X12,X1),X1),X13,X1,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2285])]) ).
fof(f3169,plain,
! [X18,X1,X12,X13] :
( c_in(X18,X13,X1)
| c_emptyset != c_Relation_OImage(c_Relation_Odiag(X12,X1),X13,X1,X1)
| c_emptyset = c_Relation_OImage(c_Relation_Odiag(c_insert(X18,X12,X1),X1),X13,X1,X1) ),
inference(definition_unfolding,[],[f2679,f2373,f2373]) ).
fof(f2679,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/benchmark/theBenchmark.p',cls_Set_Oinsert__disjoint__1_2) ).
fof(f27701,plain,
spl0_2284,
inference(avatar_split_clause,[],[f3167,f27699]) ).
fof(f27699,plain,
( spl0_2284
<=> ! [X18,X13,X12,X1] :
( c_in(X18,X13,X1)
| c_emptyset != c_Relation_OImage(c_Relation_Odiag(X13,X1),X12,X1,X1)
| c_emptyset = c_Relation_OImage(c_Relation_Odiag(X13,X1),c_insert(X18,X12,X1),X1,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2284])]) ).
fof(f3167,plain,
! [X18,X1,X12,X13] :
( c_in(X18,X13,X1)
| c_emptyset != c_Relation_OImage(c_Relation_Odiag(X13,X1),X12,X1,X1)
| c_emptyset = c_Relation_OImage(c_Relation_Odiag(X13,X1),c_insert(X18,X12,X1),X1,X1) ),
inference(definition_unfolding,[],[f2663,f2373,f2373]) ).
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/benchmark/theBenchmark.p',cls_Set_Odisjoint__insert__1_2) ).
fof(f27697,plain,
spl0_2283,
inference(avatar_split_clause,[],[f2848,f27695]) ).
fof(f27695,plain,
( spl0_2283
<=> ! [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_2283])]) ).
fof(f2848,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/benchmark/theBenchmark.p',cls_Message_Oanalz__Crypt__if_0) ).
fof(f27693,plain,
spl0_2282,
inference(avatar_split_clause,[],[f1792,f27691]) ).
fof(f27691,plain,
( spl0_2282
<=> ! [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_2282])]) ).
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/benchmark/theBenchmark.p',cls_List_Ozip__replicate_0) ).
fof(f27689,plain,
spl0_2281,
inference(avatar_split_clause,[],[f1698,f27687]) ).
fof(f27687,plain,
( spl0_2281
<=> ! [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_2281])]) ).
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/benchmark/theBenchmark.p',cls_List_Onth__drop_0) ).
fof(f27629,plain,
( spl0_2280
| ~ spl0_57
| ~ spl0_1584
| ~ spl0_2276 ),
inference(avatar_split_clause,[],[f27109,f27106,f12849,f3692,f27627]) ).
fof(f27627,plain,
( spl0_2280
<=> ! [X83,X47] :
( ~ c_IntDef_Oneg(c_uminus(c_Numeral_Onumber__of(X83,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X47,c_Numeral_Obin__mult(c_Numeral_OMin,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_2280])]) ).
fof(f12849,plain,
( spl0_1584
<=> ! [X11,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| c_uminus(c_Numeral_Onumber__of(X11,X1),X1) = c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X11),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1584])]) ).
fof(f27106,plain,
( spl0_2276
<=> ! [X83,X47] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X83),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X47,c_Numeral_Obin__mult(c_Numeral_OMin,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_2276])]) ).
fof(f27109,plain,
( ! [X83,X47] :
( ~ c_IntDef_Oneg(c_uminus(c_Numeral_Onumber__of(X83,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X47,c_Numeral_Obin__mult(c_Numeral_OMin,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) )
| ~ spl0_57
| ~ spl0_1584
| ~ spl0_2276 ),
inference(forward_demodulation,[],[f27107,f14151]) ).
fof(f14151,plain,
( ! [X0] : c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X0),tc_IntDef_Oint) = c_uminus(c_Numeral_Onumber__of(X0,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_57
| ~ spl0_1584 ),
inference(resolution,[],[f12850,f3694]) ).
fof(f12850,plain,
( ! [X11,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| c_uminus(c_Numeral_Onumber__of(X11,X1),X1) = c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X11),X1) )
| ~ spl0_1584 ),
inference(avatar_component_clause,[],[f12849]) ).
fof(f27107,plain,
( ! [X83,X47] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X83),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X47,c_Numeral_Obin__mult(c_Numeral_OMin,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) )
| ~ spl0_2276 ),
inference(avatar_component_clause,[],[f27106]) ).
fof(f27421,plain,
( spl0_2279
| ~ spl0_810
| ~ spl0_2163
| ~ spl0_2234 ),
inference(avatar_split_clause,[],[f26043,f25964,f23872,f7581,f27418]) ).
fof(f27418,plain,
( spl0_2279
<=> c_UNIV = c_union(c_uminus(c_insert(v_A,c_emptyset,tc_Message_Oagent),tc_set(tc_Message_Oagent)),c_uminus(c_Event_Obad,tc_set(tc_Message_Oagent)),tc_Message_Oagent) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2279])]) ).
fof(f25964,plain,
( spl0_2234
<=> c_emptyset = c_Relation_OImage(c_Relation_Odiag(c_insert(v_A,c_emptyset,tc_Message_Oagent),tc_Message_Oagent),c_Event_Obad,tc_Message_Oagent,tc_Message_Oagent) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2234])]) ).
fof(f26043,plain,
( c_UNIV = c_union(c_uminus(c_insert(v_A,c_emptyset,tc_Message_Oagent),tc_set(tc_Message_Oagent)),c_uminus(c_Event_Obad,tc_set(tc_Message_Oagent)),tc_Message_Oagent)
| ~ spl0_810
| ~ spl0_2163
| ~ spl0_2234 ),
inference(forward_demodulation,[],[f26036,f7582]) ).
fof(f26036,plain,
( c_uminus(c_emptyset,tc_set(tc_Message_Oagent)) = c_union(c_uminus(c_insert(v_A,c_emptyset,tc_Message_Oagent),tc_set(tc_Message_Oagent)),c_uminus(c_Event_Obad,tc_set(tc_Message_Oagent)),tc_Message_Oagent)
| ~ spl0_2163
| ~ spl0_2234 ),
inference(superposition,[],[f23873,f25966]) ).
fof(f25966,plain,
( c_emptyset = c_Relation_OImage(c_Relation_Odiag(c_insert(v_A,c_emptyset,tc_Message_Oagent),tc_Message_Oagent),c_Event_Obad,tc_Message_Oagent,tc_Message_Oagent)
| ~ spl0_2234 ),
inference(avatar_component_clause,[],[f25964]) ).
fof(f27202,plain,
( spl0_2278
| ~ spl0_1196
| ~ spl0_1537
| ~ spl0_2258 ),
inference(avatar_split_clause,[],[f26941,f26938,f12649,f9570,f27200]) ).
fof(f27200,plain,
( spl0_2278
<=> ! [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_2278])]) ).
fof(f26938,plain,
( spl0_2258
<=> ! [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_2258])]) ).
fof(f26941,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_1196
| ~ spl0_1537
| ~ spl0_2258 ),
inference(forward_demodulation,[],[f26939,f13711]) ).
fof(f26939,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_2258 ),
inference(avatar_component_clause,[],[f26938]) ).
fof(f27198,plain,
( spl0_2277
| ~ spl0_1195
| ~ spl0_1537
| ~ spl0_2257 ),
inference(avatar_split_clause,[],[f26936,f26933,f12649,f9566,f27196]) ).
fof(f27196,plain,
( spl0_2277
<=> ! [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_2277])]) ).
fof(f26933,plain,
( spl0_2257
<=> ! [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_2257])]) ).
fof(f26936,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_1195
| ~ spl0_1537
| ~ spl0_2257 ),
inference(forward_demodulation,[],[f26934,f13712]) ).
fof(f26934,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_2257 ),
inference(avatar_component_clause,[],[f26933]) ).
fof(f27108,plain,
spl0_2276,
inference(avatar_split_clause,[],[f3176,f27106]) ).
fof(f3176,plain,
! [X83,X47] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X83),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X47,c_Numeral_Obin__mult(c_Numeral_OMin,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) ),
inference(definition_unfolding,[],[f1859,f2129,f2129]) ).
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/benchmark/theBenchmark.p',cls_NatBin_Oless__nat__number__of_4) ).
fof(f27104,plain,
spl0_2275,
inference(avatar_split_clause,[],[f3085,f27102]) ).
fof(f27102,plain,
( spl0_2275
<=> ! [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__mult(c_Numeral_OMin,X11)),X1),X4,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2275])]) ).
fof(f3085,plain,
! [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__mult(c_Numeral_OMin,X11)),X1),X4,X1) ),
inference(definition_unfolding,[],[f2107,f2129]) ).
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/benchmark/theBenchmark.p',cls_Numeral_Oadd__number__of__diff2_0) ).
fof(f27094,plain,
( spl0_2274
| ~ spl0_646
| ~ spl0_687
| ~ spl0_1372
| ~ spl0_1461
| ~ spl0_2273 ),
inference(avatar_split_clause,[],[f27090,f27087,f11313,f10914,f7046,f6101,f27092]) ).
fof(f27092,plain,
( spl0_2274
<=> ! [X41,X21,X85] : c_Relation_Orel__comp(X85,c_Nat_Opower(X85,X21,tc_set(tc_prod(X41,X41))),X41,X41,X41) = c_Nat_Opower(X85,c_plus(c_1,X21,tc_nat),tc_set(tc_prod(X41,X41))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2274])]) ).
fof(f27087,plain,
( spl0_2273
<=> ! [X41,X21,X85] : c_Relation_Orel__comp(X85,c_Nat_Opower(X85,X21,tc_set(tc_prod(X41,X41))),X41,X41,X41) = c_Nat_Opower(X85,c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),tc_set(tc_prod(X41,X41))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2273])]) ).
fof(f27090,plain,
( ! [X21,X41,X85] : c_Relation_Orel__comp(X85,c_Nat_Opower(X85,X21,tc_set(tc_prod(X41,X41))),X41,X41,X41) = c_Nat_Opower(X85,c_plus(c_1,X21,tc_nat),tc_set(tc_prod(X41,X41)))
| ~ spl0_646
| ~ spl0_687
| ~ spl0_1372
| ~ spl0_1461
| ~ spl0_2273 ),
inference(forward_demodulation,[],[f27088,f12280]) ).
fof(f27088,plain,
( ! [X21,X41,X85] : c_Relation_Orel__comp(X85,c_Nat_Opower(X85,X21,tc_set(tc_prod(X41,X41))),X41,X41,X41) = c_Nat_Opower(X85,c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),tc_set(tc_prod(X41,X41)))
| ~ spl0_2273 ),
inference(avatar_component_clause,[],[f27087]) ).
fof(f27089,plain,
spl0_2273,
inference(avatar_split_clause,[],[f3071,f27087]) ).
fof(f3071,plain,
! [X21,X41,X85] : c_Relation_Orel__comp(X85,c_Nat_Opower(X85,X21,tc_set(tc_prod(X41,X41))),X41,X41,X41) = c_Nat_Opower(X85,c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),tc_set(tc_prod(X41,X41))),
inference(definition_unfolding,[],[f2391,f2544]) ).
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/benchmark/theBenchmark.p',cls_Relation__Power_Orelpow_Osimps__2_0) ).
fof(f27085,plain,
spl0_2272,
inference(avatar_split_clause,[],[f3066,f27083]) ).
fof(f27083,plain,
( spl0_2272
<=> ! [X18,X13,X12,X1] : c_Relation_OImage(c_Relation_Odiag(c_insert(X18,X12,X1),X1),c_insert(X18,X13,X1),X1,X1) = c_insert(X18,c_Relation_OImage(c_Relation_Odiag(X12,X1),X13,X1,X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2272])]) ).
fof(f3066,plain,
! [X18,X1,X12,X13] : c_Relation_OImage(c_Relation_Odiag(c_insert(X18,X12,X1),X1),c_insert(X18,X13,X1),X1,X1) = c_insert(X18,c_Relation_OImage(c_Relation_Odiag(X12,X1),X13,X1,X1),X1),
inference(definition_unfolding,[],[f2686,f2373,f2373]) ).
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/benchmark/theBenchmark.p',cls_Set_Oinsert__inter__insert_0) ).
fof(f27081,plain,
spl0_2271,
inference(avatar_split_clause,[],[f3059,f27079]) ).
fof(f27079,plain,
( spl0_2271
<=> ! [X13,X12,X1] : c_List_Olists(c_Relation_OImage(c_Relation_Odiag(X12,X1),X13,X1,X1),X1) = c_Relation_OImage(c_Relation_Odiag(c_List_Olists(X12,X1),tc_List_Olist(X1)),c_List_Olists(X13,X1),tc_List_Olist(X1),tc_List_Olist(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2271])]) ).
fof(f3059,plain,
! [X1,X12,X13] : c_List_Olists(c_Relation_OImage(c_Relation_Odiag(X12,X1),X13,X1,X1),X1) = c_Relation_OImage(c_Relation_Odiag(c_List_Olists(X12,X1),tc_List_Olist(X1)),c_List_Olists(X13,X1),tc_List_Olist(X1),tc_List_Olist(X1)),
inference(definition_unfolding,[],[f1637,f2373,f2373]) ).
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/benchmark/theBenchmark.p',cls_List_Olists__Int__eq_0) ).
fof(f27077,plain,
( spl0_2270
| ~ spl0_1744
| ~ spl0_2218 ),
inference(avatar_split_clause,[],[f25921,f25775,f15851,f27075]) ).
fof(f27075,plain,
( spl0_2270
<=> ! [X0,X1] : ~ c_in(v_A,c_Inter(c_union(X0,c_insert(c_Event_Obad,X1,tc_set(tc_Message_Oagent)),tc_set(tc_Message_Oagent)),tc_Message_Oagent),tc_Message_Oagent) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2270])]) ).
fof(f25775,plain,
( spl0_2218
<=> ! [X0] : ~ c_in(v_A,c_Inter(c_insert(c_Event_Obad,X0,tc_set(tc_Message_Oagent)),tc_Message_Oagent),tc_Message_Oagent) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2218])]) ).
fof(f25921,plain,
( ! [X0,X1] : ~ c_in(v_A,c_Inter(c_union(X0,c_insert(c_Event_Obad,X1,tc_set(tc_Message_Oagent)),tc_set(tc_Message_Oagent)),tc_Message_Oagent),tc_Message_Oagent)
| ~ spl0_1744
| ~ spl0_2218 ),
inference(superposition,[],[f25776,f15852]) ).
fof(f25776,plain,
( ! [X0] : ~ c_in(v_A,c_Inter(c_insert(c_Event_Obad,X0,tc_set(tc_Message_Oagent)),tc_Message_Oagent),tc_Message_Oagent)
| ~ spl0_2218 ),
inference(avatar_component_clause,[],[f25775]) ).
fof(f27073,plain,
spl0_2269,
inference(avatar_split_clause,[],[f3058,f27071]) ).
fof(f27071,plain,
( spl0_2269
<=> ! [X13,X12,X1] : c_Pow(c_Relation_OImage(c_Relation_Odiag(X12,X1),X13,X1,X1),X1) = c_Relation_OImage(c_Relation_Odiag(c_Pow(X12,X1),tc_set(X1)),c_Pow(X13,X1),tc_set(X1),tc_set(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2269])]) ).
fof(f3058,plain,
! [X1,X12,X13] : c_Pow(c_Relation_OImage(c_Relation_Odiag(X12,X1),X13,X1,X1),X1) = c_Relation_OImage(c_Relation_Odiag(c_Pow(X12,X1),tc_set(X1)),c_Pow(X13,X1),tc_set(X1),tc_set(X1)),
inference(definition_unfolding,[],[f2624,f2373,f2373]) ).
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/benchmark/theBenchmark.p',cls_Set_OPow__Int__eq_0) ).
fof(f26991,plain,
( spl0_2268
| ~ spl0_646
| ~ spl0_687
| ~ spl0_1372
| ~ spl0_1461
| ~ spl0_2267 ),
inference(avatar_split_clause,[],[f26987,f26983,f11313,f10914,f7046,f6101,f26989]) ).
fof(f26989,plain,
( spl0_2268
<=> ! [X16,X21] : c_plus(c_Binomial_Obinomial(X21,X16),c_Binomial_Obinomial(X21,c_plus(c_1,X16,tc_nat)),tc_nat) = c_Binomial_Obinomial(c_plus(c_1,X21,tc_nat),c_plus(c_1,X16,tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2268])]) ).
fof(f26983,plain,
( spl0_2267
<=> ! [X16,X21] : c_Binomial_Obinomial(c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X16,tc_nat),tc_nat)) = c_plus(c_Binomial_Obinomial(X21,X16),c_Binomial_Obinomial(X21,c_Finite__Set_Ocard(c_SetInterval_OatMost(X16,tc_nat),tc_nat)),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2267])]) ).
fof(f26987,plain,
( ! [X21,X16] : c_plus(c_Binomial_Obinomial(X21,X16),c_Binomial_Obinomial(X21,c_plus(c_1,X16,tc_nat)),tc_nat) = c_Binomial_Obinomial(c_plus(c_1,X21,tc_nat),c_plus(c_1,X16,tc_nat))
| ~ spl0_646
| ~ spl0_687
| ~ spl0_1372
| ~ spl0_1461
| ~ spl0_2267 ),
inference(forward_demodulation,[],[f26986,f12280]) ).
fof(f26986,plain,
( ! [X21,X16] : c_Binomial_Obinomial(c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),c_plus(c_1,X16,tc_nat)) = c_plus(c_Binomial_Obinomial(X21,X16),c_Binomial_Obinomial(X21,c_plus(c_1,X16,tc_nat)),tc_nat)
| ~ spl0_646
| ~ spl0_687
| ~ spl0_1372
| ~ spl0_1461
| ~ spl0_2267 ),
inference(forward_demodulation,[],[f26984,f12280]) ).
fof(f26984,plain,
( ! [X21,X16] : c_Binomial_Obinomial(c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X16,tc_nat),tc_nat)) = c_plus(c_Binomial_Obinomial(X21,X16),c_Binomial_Obinomial(X21,c_Finite__Set_Ocard(c_SetInterval_OatMost(X16,tc_nat),tc_nat)),tc_nat)
| ~ spl0_2267 ),
inference(avatar_component_clause,[],[f26983]) ).
fof(f26985,plain,
spl0_2267,
inference(avatar_split_clause,[],[f3052,f26983]) ).
fof(f3052,plain,
! [X21,X16] : c_Binomial_Obinomial(c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X16,tc_nat),tc_nat)) = c_plus(c_Binomial_Obinomial(X21,X16),c_Binomial_Obinomial(X21,c_Finite__Set_Ocard(c_SetInterval_OatMost(X16,tc_nat),tc_nat)),tc_nat),
inference(definition_unfolding,[],[f1162,f2544,f2544,f2544]) ).
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/benchmark/theBenchmark.p',cls_Binomial_Obinomial__Suc__Suc_0) ).
fof(f26979,plain,
spl0_2266,
inference(avatar_split_clause,[],[f3011,f26977]) ).
fof(f26977,plain,
( spl0_2266
<=> ! [X5,X1] : c_Transitive__Closure_Otrancl(c_union(X5,c_Relation_OId,tc_prod(X1,X1)),X1) = c_Transitive__Closure_Otrancl(c_union(c_Transitive__Closure_Otrancl(c_union(X5,c_Relation_OId,tc_prod(X1,X1)),X1),c_Relation_OId,tc_prod(X1,X1)),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2266])]) ).
fof(f3011,plain,
! [X1,X5] : c_Transitive__Closure_Otrancl(c_union(X5,c_Relation_OId,tc_prod(X1,X1)),X1) = c_Transitive__Closure_Otrancl(c_union(c_Transitive__Closure_Otrancl(c_union(X5,c_Relation_OId,tc_prod(X1,X1)),X1),c_Relation_OId,tc_prod(X1,X1)),X1),
inference(definition_unfolding,[],[f2710,f2716,f2716,f2716]) ).
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/benchmark/theBenchmark.p',cls_Transitive__Closure_Ortrancl__idemp_0) ).
fof(f26975,plain,
spl0_2265,
inference(avatar_split_clause,[],[f2934,f26973]) ).
fof(f26973,plain,
( spl0_2265
<=> ! [X86,X109,X88] :
( ~ c_in(X86,c_Message_Osynth(c_Message_Oanalz(X88)),tc_Message_Omsg)
| ~ c_in(X109,c_Message_Oparts(c_insert(X86,X88,tc_Message_Omsg)),tc_Message_Omsg)
| c_in(X109,c_union(c_Message_Osynth(c_Message_Oanalz(X88)),c_Message_Oparts(X88),tc_Message_Omsg),tc_Message_Omsg) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2265])]) ).
fof(f2934,axiom,
! [X109,X88,X86] :
( ~ c_in(X86,c_Message_Osynth(c_Message_Oanalz(X88)),tc_Message_Omsg)
| ~ c_in(X109,c_Message_Oparts(c_insert(X86,X88,tc_Message_Omsg)),tc_Message_Omsg)
| c_in(X109,c_union(c_Message_Osynth(c_Message_Oanalz(X88)),c_Message_Oparts(X88),tc_Message_Omsg),tc_Message_Omsg) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OFake__parts__insert__in__Un__dest_0) ).
fof(f26971,plain,
spl0_2264,
inference(avatar_split_clause,[],[f2316,f26969]) ).
fof(f26969,plain,
( spl0_2264
<=> ! [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_2264])]) ).
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/benchmark/theBenchmark.p',cls_Parity_Opower__even__abs__number__of_0) ).
fof(f26967,plain,
spl0_2263,
inference(avatar_split_clause,[],[f1826,f26965]) ).
fof(f26965,plain,
( spl0_2263
<=> ! [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_2263])]) ).
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/benchmark/theBenchmark.p',cls_NatBin_Oadd__nat__number__of_2) ).
fof(f26963,plain,
spl0_2262,
inference(avatar_split_clause,[],[f1695,f26961]) ).
fof(f26961,plain,
( spl0_2262
<=> ! [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_2262])]) ).
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/benchmark/theBenchmark.p',cls_List_Onth__Cons__number__of_1) ).
fof(f26959,plain,
spl0_2261,
inference(avatar_split_clause,[],[f1573,f26957]) ).
fof(f26957,plain,
( spl0_2261
<=> ! [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_2261])]) ).
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/benchmark/theBenchmark.p',cls_List_Odrop__append_0) ).
fof(f26949,plain,
spl0_2260,
inference(avatar_split_clause,[],[f1571,f26947]) ).
fof(f26947,plain,
( spl0_2260
<=> ! [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_2260])]) ).
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/benchmark/theBenchmark.p',cls_List_Odrop__Cons__number__of_1) ).
fof(f26945,plain,
spl0_2259,
inference(avatar_split_clause,[],[f1526,f26943]) ).
fof(f26943,plain,
( spl0_2259
<=> ! [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_2259])]) ).
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/benchmark/theBenchmark.p',cls_List_Oappend__in__lists__conv_2) ).
fof(f26940,plain,
spl0_2258,
inference(avatar_split_clause,[],[f1447,f26938]) ).
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/benchmark/theBenchmark.p',cls_IntDiv_Omod__pos__pos__1__number__of_0) ).
fof(f26935,plain,
spl0_2257,
inference(avatar_split_clause,[],[f1437,f26933]) ).
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/benchmark/theBenchmark.p',cls_IntDiv_Odiv__pos__pos__1__number__of_0) ).
fof(f26931,plain,
spl0_2256,
inference(avatar_split_clause,[],[f1381,f26929]) ).
fof(f26929,plain,
( spl0_2256
<=> ! [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_2256])]) ).
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/benchmark/theBenchmark.p',cls_IntDef_Ointrel_A_96_96_A_123_Ix1_M_Ay1_J_125_A_58_AInteg_A_61_61_ATrue_0) ).
fof(f26927,plain,
spl0_2255,
inference(avatar_split_clause,[],[f1269,f26925]) ).
fof(f26925,plain,
( spl0_2255
<=> ! [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_2255])]) ).
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/benchmark/theBenchmark.p',cls_Finite__Set_OMin__gr__iff_0) ).
fof(f26923,plain,
spl0_2254,
inference(avatar_split_clause,[],[f1266,f26921]) ).
fof(f26921,plain,
( spl0_2254
<=> ! [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_2254])]) ).
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/benchmark/theBenchmark.p',cls_Finite__Set_OMin__ge__iff_0) ).
fof(f26919,plain,
spl0_2253,
inference(avatar_split_clause,[],[f1262,f26917]) ).
fof(f26917,plain,
( spl0_2253
<=> ! [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_2253])]) ).
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/benchmark/theBenchmark.p',cls_Finite__Set_OMax__less__iff_0) ).
fof(f26915,plain,
spl0_2252,
inference(avatar_split_clause,[],[f1259,f26913]) ).
fof(f26913,plain,
( spl0_2252
<=> ! [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_2252])]) ).
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/benchmark/theBenchmark.p',cls_Finite__Set_OMax__le__iff_0) ).
fof(f26911,plain,
spl0_2251,
inference(avatar_split_clause,[],[f78,f26909]) ).
fof(f26909,plain,
( spl0_2251
<=> ! [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_2251])]) ).
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/benchmark/theBenchmark.p',cls_Relation_OconverseE_1) ).
fof(f26907,plain,
( spl0_2250
| ~ spl0_1501
| ~ spl0_2218 ),
inference(avatar_split_clause,[],[f25918,f25775,f12491,f26905]) ).
fof(f25918,plain,
( ! [X0] : ~ c_in(v_A,c_Inter(c_List_Oset(c_List_Olist_OCons(c_Event_Obad,X0,tc_set(tc_Message_Oagent)),tc_set(tc_Message_Oagent)),tc_Message_Oagent),tc_Message_Oagent)
| ~ spl0_1501
| ~ spl0_2218 ),
inference(superposition,[],[f25776,f12492]) ).
fof(f26243,plain,
( spl0_2249
| ~ spl0_2152
| ~ spl0_2217 ),
inference(avatar_split_clause,[],[f25480,f25330,f23775,f26241]) ).
fof(f26241,plain,
( spl0_2249
<=> ! [X0] : ~ c_in(c_Pair(X0,v_A,tc_Message_Oagent,tc_Message_Oagent),c_Relation_Odiag(c_Event_Obad,tc_Message_Oagent),tc_prod(tc_Message_Oagent,tc_Message_Oagent)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2249])]) ).
fof(f25330,plain,
( spl0_2217
<=> ! [X0] : ~ c_in(v_A,c_Relation_OImage(c_Relation_Odiag(c_Event_Obad,tc_Message_Oagent),X0,tc_Message_Oagent,tc_Message_Oagent),tc_Message_Oagent) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2217])]) ).
fof(f25480,plain,
( ! [X0] : ~ c_in(c_Pair(X0,v_A,tc_Message_Oagent,tc_Message_Oagent),c_Relation_Odiag(c_Event_Obad,tc_Message_Oagent),tc_prod(tc_Message_Oagent,tc_Message_Oagent))
| ~ spl0_2152
| ~ spl0_2217 ),
inference(resolution,[],[f25331,f23776]) ).
fof(f25331,plain,
( ! [X0] : ~ c_in(v_A,c_Relation_OImage(c_Relation_Odiag(c_Event_Obad,tc_Message_Oagent),X0,tc_Message_Oagent,tc_Message_Oagent),tc_Message_Oagent)
| ~ spl0_2217 ),
inference(avatar_component_clause,[],[f25330]) ).
fof(f26111,plain,
( spl0_2248
| ~ spl0_786
| ~ spl0_795
| ~ spl0_2026
| ~ spl0_2247 ),
inference(avatar_split_clause,[],[f26107,f26104,f20939,f7520,f7484,f26109]) ).
fof(f26109,plain,
( spl0_2248
<=> ! [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_plus(c_1,c_1,tc_nat),X2)
| ~ class_Power_Orecpower(X2)
| ~ class_Numeral_Onumber(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2248])]) ).
fof(f26104,plain,
( spl0_2247
<=> ! [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_2247])]) ).
fof(f26107,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_plus(c_1,c_1,tc_nat),X2)
| ~ class_Power_Orecpower(X2)
| ~ class_Numeral_Onumber(X2) )
| ~ spl0_786
| ~ spl0_795
| ~ spl0_2026
| ~ spl0_2247 ),
inference(forward_demodulation,[],[f26105,f21022]) ).
fof(f26105,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_2247 ),
inference(avatar_component_clause,[],[f26104]) ).
fof(f26106,plain,
spl0_2247,
inference(avatar_split_clause,[],[f3367,f26104]) ).
fof(f3367,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,[],[f3366,f2156]) ).
fof(f3366,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,[],[f3365,f2154]) ).
fof(f3365,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/benchmark/theBenchmark.p',cls_NatBin_Opower2__eq__square__number__of_0) ).
fof(f26102,plain,
spl0_2246,
inference(avatar_split_clause,[],[f3304,f26100]) ).
fof(f26100,plain,
( spl0_2246
<=> ! [X16,X59,X15] :
( c_Finite__Set_Ocard(c_SetInterval_OatLeastAtMost(c_plus(X16,X15,tc_nat),X59,tc_nat),tc_nat) = c_Finite__Set_Ocard(c_SetInterval_OatLeastAtMost(X15,c_minus(X59,X16,tc_nat),tc_nat),tc_nat)
| ~ c_lessequals(X16,X59,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2246])]) ).
fof(f3304,plain,
! [X59,X16,X15] :
( c_Finite__Set_Ocard(c_SetInterval_OatLeastAtMost(c_plus(X16,X15,tc_nat),X59,tc_nat),tc_nat) = c_Finite__Set_Ocard(c_SetInterval_OatLeastAtMost(X15,c_minus(X59,X16,tc_nat),tc_nat),tc_nat)
| ~ c_lessequals(X16,X59,tc_nat) ),
inference(forward_demodulation,[],[f3303,f3031]) ).
fof(f3031,plain,
! [X26,X14] : c_Finite__Set_Ocard(c_SetInterval_OatLeastAtMost(X26,X14,tc_nat),tc_nat) = c_minus(c_Finite__Set_Ocard(c_SetInterval_OatMost(X14,tc_nat),tc_nat),X26,tc_nat),
inference(definition_unfolding,[],[f2540,f2544]) ).
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/benchmark/theBenchmark.p',cls_SetInterval_Ocard__atLeastAtMost_0) ).
fof(f3303,plain,
! [X59,X16,X15] :
( c_minus(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_minus(X59,X16,tc_nat),tc_nat),tc_nat),X15,tc_nat) = c_Finite__Set_Ocard(c_SetInterval_OatLeastAtMost(c_plus(X16,X15,tc_nat),X59,tc_nat),tc_nat)
| ~ c_lessequals(X16,X59,tc_nat) ),
inference(forward_demodulation,[],[f3112,f3031]) ).
fof(f3112,plain,
! [X59,X16,X15] :
( ~ c_lessequals(X16,X59,tc_nat)
| c_minus(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_minus(X59,X16,tc_nat),tc_nat),tc_nat),X15,tc_nat) = c_minus(c_Finite__Set_Ocard(c_SetInterval_OatMost(X59,tc_nat),tc_nat),c_plus(X16,X15,tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f1798,f2544,f2544]) ).
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/benchmark/theBenchmark.p',cls_NatArith_Odiff__Suc__diff__eq2_0) ).
fof(f26098,plain,
spl0_2245,
inference(avatar_split_clause,[],[f3302,f26096]) ).
fof(f26096,plain,
( spl0_2245
<=> ! [X16,X59,X15] :
( c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(X59,c_plus(X15,X16,tc_nat),tc_nat),tc_nat) = c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(c_minus(X59,X16,tc_nat),X15,tc_nat),tc_nat)
| ~ c_lessequals(X16,X59,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2245])]) ).
fof(f3302,plain,
! [X59,X16,X15] :
( c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(X59,c_plus(X15,X16,tc_nat),tc_nat),tc_nat) = c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(c_minus(X59,X16,tc_nat),X15,tc_nat),tc_nat)
| ~ c_lessequals(X16,X59,tc_nat) ),
inference(forward_demodulation,[],[f3301,f3030]) ).
fof(f3030,plain,
! [X26,X14] : c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(X26,X14,tc_nat),tc_nat) = c_minus(X14,c_Finite__Set_Ocard(c_SetInterval_OatMost(X26,tc_nat),tc_nat),tc_nat),
inference(definition_unfolding,[],[f2547,f2544]) ).
fof(f2547,axiom,
! [X26,X14] : c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(X26,X14,tc_nat),tc_nat) = c_minus(X14,c_Suc(X26),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ocard__greaterThanLessThan_0) ).
fof(f3301,plain,
! [X59,X16,X15] :
( c_minus(X15,c_Finite__Set_Ocard(c_SetInterval_OatMost(c_minus(X59,X16,tc_nat),tc_nat),tc_nat),tc_nat) = c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(X59,c_plus(X15,X16,tc_nat),tc_nat),tc_nat)
| ~ c_lessequals(X16,X59,tc_nat) ),
inference(forward_demodulation,[],[f3111,f3030]) ).
fof(f3111,plain,
! [X59,X16,X15] :
( ~ c_lessequals(X16,X59,tc_nat)
| c_minus(X15,c_Finite__Set_Ocard(c_SetInterval_OatMost(c_minus(X59,X16,tc_nat),tc_nat),tc_nat),tc_nat) = c_minus(c_plus(X15,X16,tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X59,tc_nat),tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f1797,f2544,f2544]) ).
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/benchmark/theBenchmark.p',cls_NatArith_Odiff__Suc__diff__eq1_0) ).
fof(f26048,plain,
( spl0_2244
| ~ spl0_646
| ~ spl0_687
| ~ spl0_1372
| ~ spl0_1461
| ~ spl0_2243 ),
inference(avatar_split_clause,[],[f26026,f26023,f11313,f10914,f7046,f6101,f26046]) ).
fof(f26046,plain,
( spl0_2244
<=> ! [X12,X0,X1] :
( c_Finite__Set_Ocard(c_insert(X0,X12,X1),X1) = c_plus(c_1,c_Finite__Set_Ocard(X12,X1),tc_nat)
| c_in(X0,X12,X1)
| ~ c_in(X12,c_Finite__Set_OFinites,tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2244])]) ).
fof(f26023,plain,
( spl0_2243
<=> ! [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_Finite__Set_Ocard(c_SetInterval_OatMost(c_Finite__Set_Ocard(X12,X1),tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2243])]) ).
fof(f26026,plain,
( ! [X0,X1,X12] :
( c_Finite__Set_Ocard(c_insert(X0,X12,X1),X1) = c_plus(c_1,c_Finite__Set_Ocard(X12,X1),tc_nat)
| c_in(X0,X12,X1)
| ~ c_in(X12,c_Finite__Set_OFinites,tc_set(X1)) )
| ~ spl0_646
| ~ spl0_687
| ~ spl0_1372
| ~ spl0_1461
| ~ spl0_2243 ),
inference(forward_demodulation,[],[f26024,f12280]) ).
fof(f26024,plain,
( ! [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_Finite__Set_Ocard(c_SetInterval_OatMost(c_Finite__Set_Ocard(X12,X1),tc_nat),tc_nat) )
| ~ spl0_2243 ),
inference(avatar_component_clause,[],[f26023]) ).
fof(f26025,plain,
spl0_2243,
inference(avatar_split_clause,[],[f3166,f26023]) ).
fof(f3166,plain,
! [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_Finite__Set_Ocard(c_SetInterval_OatMost(c_Finite__Set_Ocard(X12,X1),tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f1280,f2544]) ).
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/benchmark/theBenchmark.p',cls_Finite__Set_Ocard__insert__disjoint_0) ).
fof(f26000,plain,
( spl0_2242
| ~ spl0_646
| ~ spl0_687
| ~ spl0_1372
| ~ spl0_1461
| ~ spl0_2241 ),
inference(avatar_split_clause,[],[f25996,f25993,f11313,f10914,f7046,f6101,f25998]) ).
fof(f25998,plain,
( spl0_2242
<=> ! [X0,X23,X21,X1] : c_List_Olist_OCons(X0,c_List_Osublist(X23,c_SetInterval_OlessThan(X21,tc_nat),X1),X1) = c_List_Osublist(c_List_Olist_OCons(X0,X23,X1),c_SetInterval_OlessThan(c_plus(c_1,X21,tc_nat),tc_nat),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2242])]) ).
fof(f25993,plain,
( spl0_2241
<=> ! [X0,X23,X21,X1] : c_List_Osublist(c_List_Olist_OCons(X0,X23,X1),c_SetInterval_OlessThan(c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),tc_nat),X1) = c_List_Olist_OCons(X0,c_List_Osublist(X23,c_SetInterval_OlessThan(X21,tc_nat),X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2241])]) ).
fof(f25996,plain,
( ! [X21,X0,X1,X23] : c_List_Olist_OCons(X0,c_List_Osublist(X23,c_SetInterval_OlessThan(X21,tc_nat),X1),X1) = c_List_Osublist(c_List_Olist_OCons(X0,X23,X1),c_SetInterval_OlessThan(c_plus(c_1,X21,tc_nat),tc_nat),X1)
| ~ spl0_646
| ~ spl0_687
| ~ spl0_1372
| ~ spl0_1461
| ~ spl0_2241 ),
inference(forward_demodulation,[],[f25994,f12280]) ).
fof(f25994,plain,
( ! [X21,X0,X1,X23] : c_List_Osublist(c_List_Olist_OCons(X0,X23,X1),c_SetInterval_OlessThan(c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),tc_nat),X1) = c_List_Olist_OCons(X0,c_List_Osublist(X23,c_SetInterval_OlessThan(X21,tc_nat),X1),X1)
| ~ spl0_2241 ),
inference(avatar_component_clause,[],[f25993]) ).
fof(f25995,plain,
spl0_2241,
inference(avatar_split_clause,[],[f3061,f25993]) ).
fof(f3061,plain,
! [X21,X0,X1,X23] : c_List_Osublist(c_List_Olist_OCons(X0,X23,X1),c_SetInterval_OlessThan(c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),tc_nat),X1) = c_List_Olist_OCons(X0,c_List_Osublist(X23,c_SetInterval_OlessThan(X21,tc_nat),X1),X1),
inference(definition_unfolding,[],[f1769,f1766,f2544,f1766]) ).
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/benchmark/theBenchmark.p',cls_List_Otake__Suc__Cons_0) ).
fof(f25991,plain,
spl0_2240,
inference(avatar_split_clause,[],[f2941,f25989]) ).
fof(f25989,plain,
( spl0_2240
<=> ! [X102,X91] :
( ~ c_in(X91,c_Message_OsymKeys,tc_nat)
| ~ c_in(X102,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
| c_in(c_Message_Omsg_OKey(X91),c_Event_Oused(X102),tc_Message_Omsg)
| ~ c_in(X91,c_Message_OkeysFor(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,X102))),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2240])]) ).
fof(f2941,axiom,
! [X91,X102] :
( ~ c_in(X91,c_Message_OsymKeys,tc_nat)
| ~ c_in(X102,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
| c_in(c_Message_Omsg_OKey(X91),c_Event_Oused(X102),tc_Message_Omsg)
| ~ c_in(X91,c_Message_OkeysFor(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,X102))),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Yahalom_Onew__keys__not__used_0) ).
fof(f25987,plain,
spl0_2239,
inference(avatar_split_clause,[],[f2829,f25985]) ).
fof(f25985,plain,
( spl0_2239
<=> ! [X86,X87,X88] :
( c_in(X86,c_Message_Osynth(c_Message_Oanalz(X88)),tc_Message_Omsg)
| c_in(c_Message_Omsg_OHash(c_Message_Omsg_OMPair(X86,X87)),c_Message_Oanalz(X88),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OHash(c_Message_Omsg_OMPair(X86,X87)),c_Message_Osynth(c_Message_Oanalz(X88)),tc_Message_Omsg) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2239])]) ).
fof(f2829,axiom,
! [X88,X86,X87] :
( c_in(X86,c_Message_Osynth(c_Message_Oanalz(X88)),tc_Message_Omsg)
| c_in(c_Message_Omsg_OHash(c_Message_Omsg_OMPair(X86,X87)),c_Message_Oanalz(X88),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OHash(c_Message_Omsg_OMPair(X86,X87)),c_Message_Osynth(c_Message_Oanalz(X88)),tc_Message_Omsg) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OHash__synth__analz_0) ).
fof(f25983,plain,
spl0_2238,
inference(avatar_split_clause,[],[f2385,f25981]) ).
fof(f25981,plain,
( spl0_2238
<=> ! [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_2238])]) ).
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/benchmark/theBenchmark.p',cls_Relation_Oconverse__iff_1) ).
fof(f25979,plain,
spl0_2237,
inference(avatar_split_clause,[],[f2384,f25977]) ).
fof(f25977,plain,
( spl0_2237
<=> ! [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_2237])]) ).
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/benchmark/theBenchmark.p',cls_Relation_Oconverse__iff_0) ).
fof(f25975,plain,
spl0_2236,
inference(avatar_split_clause,[],[f2332,f25973]) ).
fof(f25973,plain,
( spl0_2236
<=> ! [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_2236])]) ).
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/benchmark/theBenchmark.p',cls_Parity_Ozero__less__power__eq__number__of_1) ).
fof(f25971,plain,
spl0_2235,
inference(avatar_split_clause,[],[f2322,f25969]) ).
fof(f25969,plain,
( spl0_2235
<=> ! [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_2235])]) ).
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/benchmark/theBenchmark.p',cls_Parity_Opower__le__zero__eq__number__of_5) ).
fof(f25967,plain,
( spl0_2234
| ~ spl0_891
| ~ spl0_2182 ),
inference(avatar_split_clause,[],[f25045,f24420,f7918,f25964]) ).
fof(f24420,plain,
( spl0_2182
<=> ! [X0] : c_emptyset = c_Relation_OImage(c_Relation_Odiag(c_insert(v_A,X0,tc_Message_Oagent),tc_Message_Oagent),c_minus(c_Event_Obad,X0,tc_set(tc_Message_Oagent)),tc_Message_Oagent,tc_Message_Oagent) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2182])]) ).
fof(f25045,plain,
( c_emptyset = c_Relation_OImage(c_Relation_Odiag(c_insert(v_A,c_emptyset,tc_Message_Oagent),tc_Message_Oagent),c_Event_Obad,tc_Message_Oagent,tc_Message_Oagent)
| ~ spl0_891
| ~ spl0_2182 ),
inference(superposition,[],[f24421,f7919]) ).
fof(f24421,plain,
( ! [X0] : c_emptyset = c_Relation_OImage(c_Relation_Odiag(c_insert(v_A,X0,tc_Message_Oagent),tc_Message_Oagent),c_minus(c_Event_Obad,X0,tc_set(tc_Message_Oagent)),tc_Message_Oagent,tc_Message_Oagent)
| ~ spl0_2182 ),
inference(avatar_component_clause,[],[f24420]) ).
fof(f25962,plain,
spl0_2233,
inference(avatar_split_clause,[],[f1877,f25960]) ).
fof(f25960,plain,
( spl0_2233
<=> ! [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_2233])]) ).
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/benchmark/theBenchmark.p',cls_NatBin_Opower__nat__number__of__number__of_1) ).
fof(f25958,plain,
spl0_2232,
inference(avatar_split_clause,[],[f1828,f25956]) ).
fof(f25956,plain,
( spl0_2232
<=> ! [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_2232])]) ).
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/benchmark/theBenchmark.p',cls_NatBin_Odiv__nat__number__of_1) ).
fof(f25954,plain,
spl0_2231,
inference(avatar_split_clause,[],[f1273,f25952]) ).
fof(f25952,plain,
( spl0_2231
<=> ! [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_2231])]) ).
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/benchmark/theBenchmark.p',cls_Finite__Set_OMin__insert_0) ).
fof(f25950,plain,
spl0_2230,
inference(avatar_split_clause,[],[f1271,f25948]) ).
fof(f25948,plain,
( spl0_2230
<=> ! [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_2230])]) ).
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/benchmark/theBenchmark.p',cls_Finite__Set_OMin__gr__iff_2) ).
fof(f25946,plain,
spl0_2229,
inference(avatar_split_clause,[],[f1270,f25944]) ).
fof(f25944,plain,
( spl0_2229
<=> ! [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_2229])]) ).
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/benchmark/theBenchmark.p',cls_Finite__Set_OMin__gr__iff_1) ).
fof(f25942,plain,
spl0_2228,
inference(avatar_split_clause,[],[f1268,f25940]) ).
fof(f25940,plain,
( spl0_2228
<=> ! [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_2228])]) ).
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/benchmark/theBenchmark.p',cls_Finite__Set_OMin__ge__iff_2) ).
fof(f25938,plain,
spl0_2227,
inference(avatar_split_clause,[],[f1267,f25936]) ).
fof(f25936,plain,
( spl0_2227
<=> ! [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_2227])]) ).
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/benchmark/theBenchmark.p',cls_Finite__Set_OMin__ge__iff_1) ).
fof(f25934,plain,
spl0_2226,
inference(avatar_split_clause,[],[f1264,f25932]) ).
fof(f25932,plain,
( spl0_2226
<=> ! [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_2226])]) ).
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/benchmark/theBenchmark.p',cls_Finite__Set_OMax__less__iff_2) ).
fof(f25930,plain,
spl0_2225,
inference(avatar_split_clause,[],[f1263,f25928]) ).
fof(f25928,plain,
( spl0_2225
<=> ! [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_2225])]) ).
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/benchmark/theBenchmark.p',cls_Finite__Set_OMax__less__iff_1) ).
fof(f25926,plain,
spl0_2224,
inference(avatar_split_clause,[],[f1261,f25924]) ).
fof(f25924,plain,
( spl0_2224
<=> ! [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_2224])]) ).
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/benchmark/theBenchmark.p',cls_Finite__Set_OMax__le__iff_2) ).
fof(f25915,plain,
spl0_2223,
inference(avatar_split_clause,[],[f1260,f25913]) ).
fof(f25913,plain,
( spl0_2223
<=> ! [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_2223])]) ).
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/benchmark/theBenchmark.p',cls_Finite__Set_OMax__le__iff_1) ).
fof(f25911,plain,
spl0_2222,
inference(avatar_split_clause,[],[f1258,f25909]) ).
fof(f25909,plain,
( spl0_2222
<=> ! [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_2222])]) ).
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/benchmark/theBenchmark.p',cls_Finite__Set_OMax__insert_0) ).
fof(f25907,plain,
spl0_2221,
inference(avatar_split_clause,[],[f73,f25905]) ).
fof(f25905,plain,
( spl0_2221
<=> ! [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_2221])]) ).
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/benchmark/theBenchmark.p',cls_Relation_OImageE_1) ).
fof(f25903,plain,
spl0_2220,
inference(avatar_split_clause,[],[f15,f25901]) ).
fof(f25901,plain,
( spl0_2220
<=> ! [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_2220])]) ).
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/benchmark/theBenchmark.p',cls_Datatype__Universe_OuprodE_2) ).
fof(f25899,plain,
spl0_2219,
inference(avatar_split_clause,[],[f14,f25897]) ).
fof(f25897,plain,
( spl0_2219
<=> ! [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_2219])]) ).
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/benchmark/theBenchmark.p',cls_Datatype__Universe_OuprodE_1) ).
fof(f25777,plain,
( spl0_2218
| ~ spl0_1950
| ~ spl0_2217 ),
inference(avatar_split_clause,[],[f25484,f25330,f19536,f25775]) ).
fof(f25484,plain,
( ! [X0] : ~ c_in(v_A,c_Inter(c_insert(c_Event_Obad,X0,tc_set(tc_Message_Oagent)),tc_Message_Oagent),tc_Message_Oagent)
| ~ spl0_1950
| ~ spl0_2217 ),
inference(superposition,[],[f25331,f19537]) ).
fof(f25332,plain,
( spl0_2217
| ~ spl0_1836
| ~ spl0_2201 ),
inference(avatar_split_clause,[],[f25158,f25108,f17281,f25330]) ).
fof(f25108,plain,
( spl0_2201
<=> ! [X0] : ~ c_in(v_A,c_minus(c_Event_Obad,X0,tc_set(tc_Message_Oagent)),tc_Message_Oagent) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2201])]) ).
fof(f25158,plain,
( ! [X0] : ~ c_in(v_A,c_Relation_OImage(c_Relation_Odiag(c_Event_Obad,tc_Message_Oagent),X0,tc_Message_Oagent,tc_Message_Oagent),tc_Message_Oagent)
| ~ spl0_1836
| ~ spl0_2201 ),
inference(superposition,[],[f25109,f17282]) ).
fof(f25109,plain,
( ! [X0] : ~ c_in(v_A,c_minus(c_Event_Obad,X0,tc_set(tc_Message_Oagent)),tc_Message_Oagent)
| ~ spl0_2201 ),
inference(avatar_component_clause,[],[f25108]) ).
fof(f25178,plain,
spl0_2216,
inference(avatar_split_clause,[],[f3175,f25176]) ).
fof(f25176,plain,
( spl0_2216
<=> ! [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__mult(c_Numeral_OMin,X83)),tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2216])]) ).
fof(f3175,plain,
! [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__mult(c_Numeral_OMin,X83)),tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(definition_unfolding,[],[f1856,f2129]) ).
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/benchmark/theBenchmark.p',cls_NatBin_Oless__nat__number__of_1) ).
fof(f25174,plain,
spl0_2215,
inference(avatar_split_clause,[],[f3174,f25172]) ).
fof(f25172,plain,
( spl0_2215
<=> ! [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__mult(c_Numeral_OMin,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_2215])]) ).
fof(f3174,plain,
! [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__mult(c_Numeral_OMin,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) ),
inference(definition_unfolding,[],[f1857,f2129]) ).
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/benchmark/theBenchmark.p',cls_NatBin_Oless__nat__number__of_2) ).
fof(f25170,plain,
spl0_2214,
inference(avatar_split_clause,[],[f3147,f25168]) ).
fof(f25168,plain,
( spl0_2214
<=> ! [X21,X43,X15] :
( ~ c_lessequals(c_plus(X43,X15,tc_nat),X21,tc_nat)
| c_List_Oupt(X43,c_plus(X43,X15,tc_nat)) = c_List_Osublist(c_List_Oupt(X43,X21),c_SetInterval_OlessThan(X15,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2214])]) ).
fof(f3147,plain,
! [X21,X15,X43] :
( ~ c_lessequals(c_plus(X43,X15,tc_nat),X21,tc_nat)
| c_List_Oupt(X43,c_plus(X43,X15,tc_nat)) = c_List_Osublist(c_List_Oupt(X43,X21),c_SetInterval_OlessThan(X15,tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f1777,f1766]) ).
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/benchmark/theBenchmark.p',cls_List_Otake__upt_0) ).
fof(f25166,plain,
spl0_2213,
inference(avatar_split_clause,[],[f3026,f25164]) ).
fof(f25164,plain,
( spl0_2213
<=> ! [X85,X1] : c_Transitive__Closure_Otrancl(c_union(X85,c_Relation_OId,tc_prod(X1,X1)),X1) = c_Transitive__Closure_Otrancl(c_union(c_union(X85,c_Relation_OId,tc_prod(X1,X1)),c_Relation_OId,tc_prod(X1,X1)),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2213])]) ).
fof(f3026,plain,
! [X1,X85] : c_Transitive__Closure_Otrancl(c_union(X85,c_Relation_OId,tc_prod(X1,X1)),X1) = c_Transitive__Closure_Otrancl(c_union(c_union(X85,c_Relation_OId,tc_prod(X1,X1)),c_Relation_OId,tc_prod(X1,X1)),X1),
inference(definition_unfolding,[],[f2712,f2716,f2716]) ).
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/benchmark/theBenchmark.p',cls_Transitive__Closure_Ortrancl__reflcl_0) ).
fof(f25162,plain,
spl0_2212,
inference(avatar_split_clause,[],[f2849,f25160]) ).
fof(f25160,plain,
( spl0_2212
<=> ! [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_2212])]) ).
fof(f2849,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/benchmark/theBenchmark.p',cls_Message_Oanalz__Crypt__if_1) ).
fof(f25150,plain,
spl0_2211,
inference(avatar_split_clause,[],[f2562,f25148]) ).
fof(f25148,plain,
( spl0_2211
<=> ! [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_2211])]) ).
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/benchmark/theBenchmark.p',cls_SetInterval_Oivl__diff_0) ).
fof(f25146,plain,
spl0_2210,
inference(avatar_split_clause,[],[f2356,f25144]) ).
fof(f25144,plain,
( spl0_2210
<=> ! [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_2210])]) ).
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/benchmark/theBenchmark.p',cls_Power_Opower__strict__increasing__iff_1) ).
fof(f25142,plain,
spl0_2209,
inference(avatar_split_clause,[],[f2355,f25140]) ).
fof(f25140,plain,
( spl0_2209
<=> ! [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_2209])]) ).
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/benchmark/theBenchmark.p',cls_Power_Opower__strict__increasing__iff_0) ).
fof(f25138,plain,
spl0_2208,
inference(avatar_split_clause,[],[f2351,f25136]) ).
fof(f25136,plain,
( spl0_2208
<=> ! [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_2208])]) ).
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/benchmark/theBenchmark.p',cls_Power_Opower__increasing__iff_1) ).
fof(f25134,plain,
spl0_2207,
inference(avatar_split_clause,[],[f2350,f25132]) ).
fof(f25132,plain,
( spl0_2207
<=> ! [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_2207])]) ).
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/benchmark/theBenchmark.p',cls_Power_Opower__increasing__iff_0) ).
fof(f25130,plain,
spl0_2206,
inference(avatar_split_clause,[],[f2336,f25128]) ).
fof(f25128,plain,
( spl0_2206
<=> ! [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_2206])]) ).
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/benchmark/theBenchmark.p',cls_Parity_Ozero__less__power__eq__number__of_5) ).
fof(f25126,plain,
spl0_2205,
inference(avatar_split_clause,[],[f2333,f25124]) ).
fof(f25124,plain,
( spl0_2205
<=> ! [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_2205])]) ).
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/benchmark/theBenchmark.p',cls_Parity_Ozero__less__power__eq__number__of_2) ).
fof(f25122,plain,
spl0_2204,
inference(avatar_split_clause,[],[f2330,f25120]) ).
fof(f25120,plain,
( spl0_2204
<=> ! [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_2204])]) ).
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/benchmark/theBenchmark.p',cls_Parity_Ozero__le__power__eq__number__of_2) ).
fof(f25118,plain,
spl0_2203,
inference(avatar_split_clause,[],[f2328,f25116]) ).
fof(f25116,plain,
( spl0_2203
<=> ! [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_2203])]) ).
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/benchmark/theBenchmark.p',cls_Parity_Ozero__le__power__eq__number__of_0) ).
fof(f25114,plain,
spl0_2202,
inference(avatar_split_clause,[],[f2325,f25112]) ).
fof(f25112,plain,
( spl0_2202
<=> ! [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_2202])]) ).
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/benchmark/theBenchmark.p',cls_Parity_Opower__less__zero__eq__number__of_2) ).
fof(f25110,plain,
( spl0_2201
| ~ spl0_1860
| ~ spl0_2182 ),
inference(avatar_split_clause,[],[f25061,f24420,f17703,f25108]) ).
fof(f25061,plain,
( ! [X0] : ~ c_in(v_A,c_minus(c_Event_Obad,X0,tc_set(tc_Message_Oagent)),tc_Message_Oagent)
| ~ spl0_1860
| ~ spl0_2182 ),
inference(trivial_inequality_removal,[],[f25059]) ).
fof(f25059,plain,
( ! [X0] :
( c_emptyset != c_emptyset
| ~ c_in(v_A,c_minus(c_Event_Obad,X0,tc_set(tc_Message_Oagent)),tc_Message_Oagent) )
| ~ spl0_1860
| ~ spl0_2182 ),
inference(superposition,[],[f17704,f24421]) ).
fof(f25106,plain,
spl0_2200,
inference(avatar_split_clause,[],[f2319,f25104]) ).
fof(f25104,plain,
( spl0_2200
<=> ! [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_2200])]) ).
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/benchmark/theBenchmark.p',cls_Parity_Opower__le__zero__eq__number__of_2) ).
fof(f25102,plain,
spl0_2199,
inference(avatar_split_clause,[],[f2168,f25100]) ).
fof(f25100,plain,
( spl0_2199
<=> ! [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_2199])]) ).
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/benchmark/theBenchmark.p',cls_Numeral_Omult__number__of__left_0) ).
fof(f25098,plain,
spl0_2198,
inference(avatar_split_clause,[],[f2108,f25096]) ).
fof(f25096,plain,
( spl0_2198
<=> ! [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_2198])]) ).
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/benchmark/theBenchmark.p',cls_Numeral_Oadd__number__of__left_0) ).
fof(f25094,plain,
spl0_2197,
inference(avatar_split_clause,[],[f1861,f25092]) ).
fof(f25092,plain,
( spl0_2197
<=> ! [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_2197])]) ).
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/benchmark/theBenchmark.p',cls_NatBin_Omod__nat__number__of_1) ).
fof(f25090,plain,
spl0_2196,
inference(avatar_split_clause,[],[f1835,f25088]) ).
fof(f25088,plain,
( spl0_2196
<=> ! [X83,X47] :
( ~ c_IntDef_Oneg(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_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_2196])]) ).
fof(f1835,axiom,
! [X83,X47] :
( ~ c_IntDef_Oneg(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_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/benchmark/theBenchmark.p',cls_NatBin_Oeq__nat__number__of_1) ).
fof(f25086,plain,
spl0_2195,
inference(avatar_split_clause,[],[f1825,f25084]) ).
fof(f25084,plain,
( spl0_2195
<=> ! [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_2195])]) ).
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/benchmark/theBenchmark.p',cls_NatBin_Oadd__nat__number__of_1) ).
fof(f25082,plain,
spl0_2194,
inference(avatar_split_clause,[],[f1635,f25080]) ).
fof(f25080,plain,
( spl0_2194
<=> ! [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_2194])]) ).
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/benchmark/theBenchmark.p',cls_List_Olist__update__overwrite_0) ).
fof(f25078,plain,
spl0_2193,
inference(avatar_split_clause,[],[f1634,f25076]) ).
fof(f25076,plain,
( spl0_2193
<=> ! [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_2193])]) ).
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/benchmark/theBenchmark.p',cls_List_Olist__update__length_0) ).
fof(f25074,plain,
spl0_2192,
inference(avatar_split_clause,[],[f1355,f25072]) ).
fof(f25072,plain,
( spl0_2192
<=> ! [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_2192])]) ).
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/benchmark/theBenchmark.p',cls_IntDef_OInteg_OAbs__Integ__inject_0) ).
fof(f25070,plain,
spl0_2191,
inference(avatar_split_clause,[],[f1294,f25068]) ).
fof(f25068,plain,
( spl0_2191
<=> ! [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_2191])]) ).
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/benchmark/theBenchmark.p',cls_Finite__Set_Omin__max_Obelow__inf__sup__Inf__Sup_Osup__Inf__absorb_0) ).
fof(f25035,plain,
spl0_2190,
inference(avatar_split_clause,[],[f1293,f25033]) ).
fof(f25033,plain,
( spl0_2190
<=> ! [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_2190])]) ).
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/benchmark/theBenchmark.p',cls_Finite__Set_Omin__max_Obelow__inf__sup__Inf__Sup_Oinf__Sup__absorb_0) ).
fof(f25031,plain,
spl0_2189,
inference(avatar_split_clause,[],[f1222,f25029]) ).
fof(f25029,plain,
( spl0_2189
<=> ! [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_2189])]) ).
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/benchmark/theBenchmark.p',cls_Divides_Odiv__mult__self2_0) ).
fof(f25027,plain,
spl0_2188,
inference(avatar_split_clause,[],[f1220,f25025]) ).
fof(f25025,plain,
( spl0_2188
<=> ! [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_2188])]) ).
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/benchmark/theBenchmark.p',cls_Divides_Odiv__mult__self1_0) ).
fof(f25023,plain,
spl0_2187,
inference(avatar_split_clause,[],[f121,f25021]) ).
fof(f25021,plain,
( spl0_2187
<=> ! [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_2187])]) ).
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/benchmark/theBenchmark.p',cls_Transitive__Closure_Otrancl_Or__into__trancl_0) ).
fof(f25019,plain,
spl0_2186,
inference(avatar_split_clause,[],[f74,f25017]) ).
fof(f25017,plain,
( spl0_2186
<=> ! [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_2186])]) ).
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/benchmark/theBenchmark.p',cls_Relation_OImageI_0) ).
fof(f24892,plain,
( spl0_2185
| ~ spl0_1581
| ~ spl0_2031 ),
inference(avatar_split_clause,[],[f22340,f22195,f12832,f24890]) ).
fof(f12832,plain,
( spl0_1581
<=> ! [X13,X12,X1] : c_emptyset = c_Relation_OImage(c_Relation_Odiag(X12,X1),c_minus(X13,X12,tc_set(X1)),X1,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1581])]) ).
fof(f22195,plain,
( spl0_2031
<=> ! [X0] : c_minus(c_Event_Obad,X0,tc_set(tc_Message_Oagent)) = c_minus(c_Event_Obad,c_insert(v_B,X0,tc_Message_Oagent),tc_set(tc_Message_Oagent)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2031])]) ).
fof(f22340,plain,
( ! [X0] : c_emptyset = c_Relation_OImage(c_Relation_Odiag(c_insert(v_B,X0,tc_Message_Oagent),tc_Message_Oagent),c_minus(c_Event_Obad,X0,tc_set(tc_Message_Oagent)),tc_Message_Oagent,tc_Message_Oagent)
| ~ spl0_1581
| ~ spl0_2031 ),
inference(superposition,[],[f12833,f22196]) ).
fof(f22196,plain,
( ! [X0] : c_minus(c_Event_Obad,X0,tc_set(tc_Message_Oagent)) = c_minus(c_Event_Obad,c_insert(v_B,X0,tc_Message_Oagent),tc_set(tc_Message_Oagent))
| ~ spl0_2031 ),
inference(avatar_component_clause,[],[f22195]) ).
fof(f12833,plain,
( ! [X1,X12,X13] : c_emptyset = c_Relation_OImage(c_Relation_Odiag(X12,X1),c_minus(X13,X12,tc_set(X1)),X1,X1)
| ~ spl0_1581 ),
inference(avatar_component_clause,[],[f12832]) ).
fof(f24430,plain,
( ~ spl0_2183
| spl0_2184
| ~ spl0_1290
| ~ spl0_2030 ),
inference(avatar_split_clause,[],[f22286,f21998,f10180,f24428,f24424]) ).
fof(f24424,plain,
( spl0_2183
<=> class_OrderedGroup_Oab__group__add(tc_set(tc_Message_Oagent)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2183])]) ).
fof(f24428,plain,
( spl0_2184
<=> ! [X0] :
( c_0 != c_minus(c_Event_Obad,X0,tc_set(tc_Message_Oagent))
| c_Event_Obad = c_insert(v_A,X0,tc_Message_Oagent) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2184])]) ).
fof(f10180,plain,
( spl0_1290
<=> ! [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_1290])]) ).
fof(f21998,plain,
( spl0_2030
<=> ! [X0] : c_minus(c_Event_Obad,X0,tc_set(tc_Message_Oagent)) = c_minus(c_Event_Obad,c_insert(v_A,X0,tc_Message_Oagent),tc_set(tc_Message_Oagent)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2030])]) ).
fof(f22286,plain,
( ! [X0] :
( c_0 != c_minus(c_Event_Obad,X0,tc_set(tc_Message_Oagent))
| c_Event_Obad = c_insert(v_A,X0,tc_Message_Oagent)
| ~ class_OrderedGroup_Oab__group__add(tc_set(tc_Message_Oagent)) )
| ~ spl0_1290
| ~ spl0_2030 ),
inference(superposition,[],[f10181,f21999]) ).
fof(f21999,plain,
( ! [X0] : c_minus(c_Event_Obad,X0,tc_set(tc_Message_Oagent)) = c_minus(c_Event_Obad,c_insert(v_A,X0,tc_Message_Oagent),tc_set(tc_Message_Oagent))
| ~ spl0_2030 ),
inference(avatar_component_clause,[],[f21998]) ).
fof(f10181,plain,
( ! [X18,X1,X27] :
( c_0 != c_minus(X18,X27,X1)
| X18 = X27
| ~ class_OrderedGroup_Oab__group__add(X1) )
| ~ spl0_1290 ),
inference(avatar_component_clause,[],[f10180]) ).
fof(f24422,plain,
( spl0_2182
| ~ spl0_1581
| ~ spl0_2030 ),
inference(avatar_split_clause,[],[f22276,f21998,f12832,f24420]) ).
fof(f22276,plain,
( ! [X0] : c_emptyset = c_Relation_OImage(c_Relation_Odiag(c_insert(v_A,X0,tc_Message_Oagent),tc_Message_Oagent),c_minus(c_Event_Obad,X0,tc_set(tc_Message_Oagent)),tc_Message_Oagent,tc_Message_Oagent)
| ~ spl0_1581
| ~ spl0_2030 ),
inference(superposition,[],[f12833,f21999]) ).
fof(f24380,plain,
( spl0_2180
| ~ spl0_2181
| ~ spl0_1093
| ~ spl0_2114 ),
inference(avatar_split_clause,[],[f23665,f23616,f8939,f24377,f24373]) ).
fof(f24373,plain,
( spl0_2180
<=> c_emptyset = c_insert(v_B,c_emptyset,tc_Message_Oagent) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2180])]) ).
fof(f24377,plain,
( spl0_2181
<=> c_in(c_Main_Oall__not__in__conv__1(c_insert(v_B,c_emptyset,tc_Message_Oagent),tc_Message_Oagent),c_Event_Obad,tc_Message_Oagent) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2181])]) ).
fof(f8939,plain,
( spl0_1093
<=> ! [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_1093])]) ).
fof(f23616,plain,
( spl0_2114
<=> ! [X0] :
( ~ c_in(X0,c_Event_Obad,tc_Message_Oagent)
| ~ c_in(X0,c_insert(v_B,c_emptyset,tc_Message_Oagent),tc_Message_Oagent) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2114])]) ).
fof(f23665,plain,
( ~ c_in(c_Main_Oall__not__in__conv__1(c_insert(v_B,c_emptyset,tc_Message_Oagent),tc_Message_Oagent),c_Event_Obad,tc_Message_Oagent)
| c_emptyset = c_insert(v_B,c_emptyset,tc_Message_Oagent)
| ~ spl0_1093
| ~ spl0_2114 ),
inference(resolution,[],[f23617,f8940]) ).
fof(f8940,plain,
( ! [X1,X12] :
( c_in(c_Main_Oall__not__in__conv__1(X12,X1),X12,X1)
| c_emptyset = X12 )
| ~ spl0_1093 ),
inference(avatar_component_clause,[],[f8939]) ).
fof(f23617,plain,
( ! [X0] :
( ~ c_in(X0,c_insert(v_B,c_emptyset,tc_Message_Oagent),tc_Message_Oagent)
| ~ c_in(X0,c_Event_Obad,tc_Message_Oagent) )
| ~ spl0_2114 ),
inference(avatar_component_clause,[],[f23616]) ).
fof(f24037,plain,
( spl0_2179
| ~ spl0_786
| ~ spl0_795
| ~ spl0_2026
| ~ spl0_2178 ),
inference(avatar_split_clause,[],[f24033,f24029,f20939,f7520,f7484,f24035]) ).
fof(f24035,plain,
( spl0_2179
<=> ! [X15] :
( c_1 = c_Divides_Oop_Amod(X15,c_plus(c_1,c_1,tc_nat),tc_nat)
| ~ c_less(c_0,c_Divides_Oop_Amod(X15,c_plus(c_1,c_1,tc_nat),tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2179])]) ).
fof(f24029,plain,
( spl0_2178
<=> ! [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_2178])]) ).
fof(f24033,plain,
( ! [X15] :
( c_1 = c_Divides_Oop_Amod(X15,c_plus(c_1,c_1,tc_nat),tc_nat)
| ~ c_less(c_0,c_Divides_Oop_Amod(X15,c_plus(c_1,c_1,tc_nat),tc_nat),tc_nat) )
| ~ spl0_786
| ~ spl0_795
| ~ spl0_2026
| ~ spl0_2178 ),
inference(forward_demodulation,[],[f24032,f21022]) ).
fof(f24032,plain,
( ! [X15] :
( ~ c_less(c_0,c_Divides_Oop_Amod(X15,c_plus(c_1,c_1,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_786
| ~ spl0_795
| ~ spl0_2026
| ~ spl0_2178 ),
inference(forward_demodulation,[],[f24030,f21022]) ).
fof(f24030,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_2178 ),
inference(avatar_component_clause,[],[f24029]) ).
fof(f24031,plain,
spl0_2178,
inference(avatar_split_clause,[],[f3353,f24029]) ).
fof(f3353,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,[],[f3352,f2156]) ).
fof(f3352,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,[],[f3351,f2154]) ).
fof(f3351,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,[],[f3350,f2156]) ).
fof(f3350,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,[],[f3349,f2156]) ).
fof(f3349,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,[],[f3348,f2154]) ).
fof(f3348,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/benchmark/theBenchmark.p',cls_NatSimprocs_Omod2__gr__0_0) ).
fof(f24004,plain,
( spl0_2177
| ~ spl0_646
| ~ spl0_687
| ~ spl0_1372
| ~ spl0_1461
| ~ spl0_2176 ),
inference(avatar_split_clause,[],[f24000,f23997,f11313,f10914,f7046,f6101,f24002]) ).
fof(f24002,plain,
( spl0_2177
<=> ! [X16,X21,X15] : c_minus(X15,c_plus(X21,X16,tc_nat),tc_nat) = c_minus(c_Finite__Set_Ocard(c_SetInterval_OatLeastAtMost(X21,X15,tc_nat),tc_nat),c_plus(c_1,X16,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2177])]) ).
fof(f23997,plain,
( spl0_2176
<=> ! [X16,X21,X15] : c_minus(c_Finite__Set_Ocard(c_SetInterval_OatLeastAtMost(X21,X15,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X16,tc_nat),tc_nat),tc_nat) = c_minus(X15,c_plus(X21,X16,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2176])]) ).
fof(f24000,plain,
( ! [X21,X16,X15] : c_minus(X15,c_plus(X21,X16,tc_nat),tc_nat) = c_minus(c_Finite__Set_Ocard(c_SetInterval_OatLeastAtMost(X21,X15,tc_nat),tc_nat),c_plus(c_1,X16,tc_nat),tc_nat)
| ~ spl0_646
| ~ spl0_687
| ~ spl0_1372
| ~ spl0_1461
| ~ spl0_2176 ),
inference(forward_demodulation,[],[f23998,f12280]) ).
fof(f23998,plain,
( ! [X21,X16,X15] : c_minus(c_Finite__Set_Ocard(c_SetInterval_OatLeastAtMost(X21,X15,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X16,tc_nat),tc_nat),tc_nat) = c_minus(X15,c_plus(X21,X16,tc_nat),tc_nat)
| ~ spl0_2176 ),
inference(avatar_component_clause,[],[f23997]) ).
fof(f23999,plain,
spl0_2176,
inference(avatar_split_clause,[],[f3254,f23997]) ).
fof(f3254,plain,
! [X21,X16,X15] : c_minus(c_Finite__Set_Ocard(c_SetInterval_OatLeastAtMost(X21,X15,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X16,tc_nat),tc_nat),tc_nat) = c_minus(X15,c_plus(X21,X16,tc_nat),tc_nat),
inference(forward_demodulation,[],[f3253,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/benchmark/theBenchmark.p',cls_Nat_Odiff__diff__left_0) ).
fof(f3253,plain,
! [X21,X16,X15] : c_minus(c_minus(X15,X21,tc_nat),X16,tc_nat) = c_minus(c_Finite__Set_Ocard(c_SetInterval_OatLeastAtMost(X21,X15,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X16,tc_nat),tc_nat),tc_nat),
inference(forward_demodulation,[],[f3062,f3031]) ).
fof(f3062,plain,
! [X21,X16,X15] : c_minus(c_minus(X15,X21,tc_nat),X16,tc_nat) = c_minus(c_minus(c_Finite__Set_Ocard(c_SetInterval_OatMost(X15,tc_nat),tc_nat),X21,tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X16,tc_nat),tc_nat),tc_nat),
inference(definition_unfolding,[],[f2018,f2544,f2544]) ).
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/benchmark/theBenchmark.p',cls_Nat_OSuc__diff__diff_0) ).
fof(f23995,plain,
( spl0_2174
| ~ spl0_2175
| ~ spl0_1093
| ~ spl0_2093 ),
inference(avatar_split_clause,[],[f23377,f23210,f8939,f23992,f23988]) ).
fof(f23988,plain,
( spl0_2174
<=> c_emptyset = c_insert(v_A,c_emptyset,tc_Message_Oagent) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2174])]) ).
fof(f23992,plain,
( spl0_2175
<=> c_in(c_Main_Oall__not__in__conv__1(c_insert(v_A,c_emptyset,tc_Message_Oagent),tc_Message_Oagent),c_Event_Obad,tc_Message_Oagent) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2175])]) ).
fof(f23210,plain,
( spl0_2093
<=> ! [X0] :
( ~ c_in(X0,c_Event_Obad,tc_Message_Oagent)
| ~ c_in(X0,c_insert(v_A,c_emptyset,tc_Message_Oagent),tc_Message_Oagent) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2093])]) ).
fof(f23377,plain,
( ~ c_in(c_Main_Oall__not__in__conv__1(c_insert(v_A,c_emptyset,tc_Message_Oagent),tc_Message_Oagent),c_Event_Obad,tc_Message_Oagent)
| c_emptyset = c_insert(v_A,c_emptyset,tc_Message_Oagent)
| ~ spl0_1093
| ~ spl0_2093 ),
inference(resolution,[],[f23211,f8940]) ).
fof(f23211,plain,
( ! [X0] :
( ~ c_in(X0,c_insert(v_A,c_emptyset,tc_Message_Oagent),tc_Message_Oagent)
| ~ c_in(X0,c_Event_Obad,tc_Message_Oagent) )
| ~ spl0_2093 ),
inference(avatar_component_clause,[],[f23210]) ).
fof(f23986,plain,
spl0_2173,
inference(avatar_split_clause,[],[f3198,f23984]) ).
fof(f23984,plain,
( spl0_2173
<=> ! [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__mult(c_Numeral_OMin,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_2173])]) ).
fof(f3198,plain,
! [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__mult(c_Numeral_OMin,X0)),X1),X1)
| c_lessequals(c_Numeral_Onumber__of(X0,X1),c_Numeral_Onumber__of(X3,X1),X1) ),
inference(definition_unfolding,[],[f2140,f2129]) ).
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/benchmark/theBenchmark.p',cls_Numeral_Obin__rel__simps__13_1) ).
fof(f23982,plain,
spl0_2172,
inference(avatar_split_clause,[],[f3197,f23980]) ).
fof(f23980,plain,
( spl0_2172
<=> ! [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__mult(c_Numeral_OMin,X3)),X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2172])]) ).
fof(f3197,plain,
! [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__mult(c_Numeral_OMin,X3)),X1),X1) ),
inference(definition_unfolding,[],[f2148,f2129]) ).
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/benchmark/theBenchmark.p',cls_Numeral_Obin__rel__simps__6_0) ).
fof(f23978,plain,
spl0_2171,
inference(avatar_split_clause,[],[f3196,f23976]) ).
fof(f23976,plain,
( spl0_2171
<=> ! [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__mult(c_Numeral_OMin,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_2171])]) ).
fof(f3196,plain,
! [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__mult(c_Numeral_OMin,X3)),X1),X1)
| c_less(c_Numeral_Onumber__of(X0,X1),c_Numeral_Onumber__of(X3,X1),X1) ),
inference(definition_unfolding,[],[f2149,f2129]) ).
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/benchmark/theBenchmark.p',cls_Numeral_Obin__rel__simps__6_1) ).
fof(f23974,plain,
spl0_2170,
inference(avatar_split_clause,[],[f3195,f23972]) ).
fof(f23972,plain,
( spl0_2170
<=> ! [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__mult(c_Numeral_OMin,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_2170])]) ).
fof(f3195,plain,
! [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__mult(c_Numeral_OMin,X0)),X1),X1)
| ~ c_lessequals(c_Numeral_Onumber__of(X0,X1),c_Numeral_Onumber__of(X3,X1),X1) ),
inference(definition_unfolding,[],[f2139,f2129]) ).
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/benchmark/theBenchmark.p',cls_Numeral_Obin__rel__simps__13_0) ).
fof(f23970,plain,
spl0_2169,
inference(avatar_split_clause,[],[f3173,f23968]) ).
fof(f23968,plain,
( spl0_2169
<=> ! [X13,X12,X32,X1] :
( ~ c_lessequals(X32,X13,tc_set(X1))
| ~ c_lessequals(X32,X12,tc_set(X1))
| c_lessequals(X32,c_Relation_OImage(c_Relation_Odiag(X12,X1),X13,X1,X1),tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2169])]) ).
fof(f3173,plain,
! [X1,X12,X32,X13] :
( ~ c_lessequals(X32,X13,tc_set(X1))
| ~ c_lessequals(X32,X12,tc_set(X1))
| c_lessequals(X32,c_Relation_OImage(c_Relation_Odiag(X12,X1),X13,X1,X1),tc_set(X1)) ),
inference(definition_unfolding,[],[f2611,f2373]) ).
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/benchmark/theBenchmark.p',cls_Set_OInt__subset__iff_2) ).
fof(f23966,plain,
spl0_2168,
inference(avatar_split_clause,[],[f3142,f23964]) ).
fof(f23964,plain,
( spl0_2168
<=> ! [X13,X12,X1,X18] :
( c_emptyset = c_Relation_OImage(c_Relation_Odiag(X12,X1),X13,X1,X1)
| c_emptyset != c_Relation_OImage(c_Relation_Odiag(c_insert(X18,X12,X1),X1),X13,X1,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2168])]) ).
fof(f3142,plain,
! [X1,X18,X12,X13] :
( c_emptyset = c_Relation_OImage(c_Relation_Odiag(X12,X1),X13,X1,X1)
| c_emptyset != c_Relation_OImage(c_Relation_Odiag(c_insert(X18,X12,X1),X1),X13,X1,X1) ),
inference(definition_unfolding,[],[f2678,f2373,f2373]) ).
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/benchmark/theBenchmark.p',cls_Set_Oinsert__disjoint__1_1) ).
fof(f23962,plain,
spl0_2167,
inference(avatar_split_clause,[],[f3140,f23960]) ).
fof(f23960,plain,
( spl0_2167
<=> ! [X18,X13,X12,X1] :
( c_emptyset = c_Relation_OImage(c_Relation_Odiag(X13,X1),X12,X1,X1)
| c_emptyset != c_Relation_OImage(c_Relation_Odiag(X13,X1),c_insert(X18,X12,X1),X1,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2167])]) ).
fof(f3140,plain,
! [X1,X18,X12,X13] :
( c_emptyset = c_Relation_OImage(c_Relation_Odiag(X13,X1),X12,X1,X1)
| c_emptyset != c_Relation_OImage(c_Relation_Odiag(X13,X1),c_insert(X18,X12,X1),X1,X1) ),
inference(definition_unfolding,[],[f2662,f2373,f2373]) ).
fof(f2662,axiom,
! [X1,X18,X12,X13] :
( c_emptyset = c_inter(X13,X12,X1)
| c_emptyset != c_inter(X13,c_insert(X18,X12,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Odisjoint__insert__1_1) ).
fof(f23900,plain,
( spl0_2166
| ~ spl0_646
| ~ spl0_687
| ~ spl0_781
| ~ spl0_786
| ~ spl0_1372
| ~ spl0_1461
| ~ spl0_1848
| ~ spl0_2165 ),
inference(avatar_split_clause,[],[f23896,f23892,f17598,f11313,f10914,f7484,f7464,f7046,f6101,f23898]) ).
fof(f23898,plain,
( spl0_2166
<=> ! [X59,X43] :
( c_List_Oupt(X43,c_plus(c_1,X59,tc_nat)) = 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_2166])]) ).
fof(f7464,plain,
( spl0_781
<=> ! [X41,X0] : c_List_Olist_ONil = c_List_Oreplicate(c_0,X0,X41) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_781])]) ).
fof(f23892,plain,
( spl0_2165
<=> ! [X59,X43] :
( ~ c_lessequals(X43,X59,tc_nat)
| c_append(c_List_Oupt(X43,X59),c_List_Olist_OCons(X59,c_List_Olist_ONil,tc_nat),tc_nat) = c_List_Oupt(X43,c_Finite__Set_Ocard(c_SetInterval_OatMost(X59,tc_nat),tc_nat)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2165])]) ).
fof(f23896,plain,
( ! [X59,X43] :
( c_List_Oupt(X43,c_plus(c_1,X59,tc_nat)) = c_append(c_List_Oupt(X43,X59),c_List_Oreplicate(c_1,X59,tc_nat),tc_nat)
| ~ c_lessequals(X43,X59,tc_nat) )
| ~ spl0_646
| ~ spl0_687
| ~ spl0_781
| ~ spl0_786
| ~ spl0_1372
| ~ spl0_1461
| ~ spl0_1848
| ~ spl0_2165 ),
inference(forward_demodulation,[],[f23895,f17626]) ).
fof(f17626,plain,
( ! [X0,X1] : c_List_Olist_OCons(X0,c_List_Olist_ONil,X1) = c_List_Oreplicate(c_1,X0,X1)
| ~ spl0_781
| ~ spl0_786
| ~ spl0_1848 ),
inference(forward_demodulation,[],[f17601,f7485]) ).
fof(f17601,plain,
( ! [X0,X1] : c_List_Olist_OCons(X0,c_List_Olist_ONil,X1) = c_List_Oreplicate(c_plus(c_1,c_0,tc_nat),X0,X1)
| ~ spl0_781
| ~ spl0_1848 ),
inference(superposition,[],[f17599,f7465]) ).
fof(f7465,plain,
( ! [X41,X0] : c_List_Olist_ONil = c_List_Oreplicate(c_0,X0,X41)
| ~ spl0_781 ),
inference(avatar_component_clause,[],[f7464]) ).
fof(f23895,plain,
( ! [X59,X43] :
( c_append(c_List_Oupt(X43,X59),c_List_Olist_OCons(X59,c_List_Olist_ONil,tc_nat),tc_nat) = c_List_Oupt(X43,c_plus(c_1,X59,tc_nat))
| ~ c_lessequals(X43,X59,tc_nat) )
| ~ spl0_646
| ~ spl0_687
| ~ spl0_1372
| ~ spl0_1461
| ~ spl0_2165 ),
inference(forward_demodulation,[],[f23893,f12280]) ).
fof(f23893,plain,
( ! [X59,X43] :
( ~ c_lessequals(X43,X59,tc_nat)
| c_append(c_List_Oupt(X43,X59),c_List_Olist_OCons(X59,c_List_Olist_ONil,tc_nat),tc_nat) = c_List_Oupt(X43,c_Finite__Set_Ocard(c_SetInterval_OatMost(X59,tc_nat),tc_nat)) )
| ~ spl0_2165 ),
inference(avatar_component_clause,[],[f23892]) ).
fof(f23894,plain,
spl0_2165,
inference(avatar_split_clause,[],[f3110,f23892]) ).
fof(f3110,plain,
! [X59,X43] :
( ~ c_lessequals(X43,X59,tc_nat)
| c_append(c_List_Oupt(X43,X59),c_List_Olist_OCons(X59,c_List_Olist_ONil,tc_nat),tc_nat) = c_List_Oupt(X43,c_Finite__Set_Ocard(c_SetInterval_OatMost(X59,tc_nat),tc_nat)) ),
inference(definition_unfolding,[],[f1782,f2544]) ).
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/benchmark/theBenchmark.p',cls_List_Oupt_Oupt__Suc_0) ).
fof(f23878,plain,
spl0_2164,
inference(avatar_split_clause,[],[f3065,f23876]) ).
fof(f23876,plain,
( spl0_2164
<=> ! [X13,X12,X1] : c_uminus(c_union(X12,X13,X1),tc_set(X1)) = c_Relation_OImage(c_Relation_Odiag(c_uminus(X12,tc_set(X1)),X1),c_uminus(X13,tc_set(X1)),X1,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2164])]) ).
fof(f3065,plain,
! [X1,X12,X13] : c_uminus(c_union(X12,X13,X1),tc_set(X1)) = c_Relation_OImage(c_Relation_Odiag(c_uminus(X12,tc_set(X1)),X1),c_uminus(X13,tc_set(X1)),X1,X1),
inference(definition_unfolding,[],[f2577,f2373]) ).
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/benchmark/theBenchmark.p',cls_Set_OCompl__Un_0) ).
fof(f23874,plain,
spl0_2163,
inference(avatar_split_clause,[],[f3064,f23872]) ).
fof(f3064,plain,
! [X1,X12,X13] : c_union(c_uminus(X12,tc_set(X1)),c_uminus(X13,tc_set(X1)),X1) = c_uminus(c_Relation_OImage(c_Relation_Odiag(X12,X1),X13,X1,X1),tc_set(X1)),
inference(definition_unfolding,[],[f2575,f2373]) ).
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/benchmark/theBenchmark.p',cls_Set_OCompl__Int_0) ).
fof(f23870,plain,
spl0_2162,
inference(avatar_split_clause,[],[f3057,f23868]) ).
fof(f23868,plain,
( spl0_2162
<=> ! [X15,X23,X21,X1] : c_List_Osublist(c_List_Osublist(X23,c_SetInterval_OlessThan(X15,tc_nat),X1),c_SetInterval_OlessThan(X21,tc_nat),X1) = c_List_Osublist(X23,c_SetInterval_OlessThan(c_Orderings_Omin(X21,X15,tc_nat),tc_nat),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2162])]) ).
fof(f3057,plain,
! [X21,X1,X15,X23] : c_List_Osublist(c_List_Osublist(X23,c_SetInterval_OlessThan(X15,tc_nat),X1),c_SetInterval_OlessThan(X21,tc_nat),X1) = c_List_Osublist(X23,c_SetInterval_OlessThan(c_Orderings_Omin(X21,X15,tc_nat),tc_nat),X1),
inference(definition_unfolding,[],[f1776,f1766,f1766,f1766]) ).
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/benchmark/theBenchmark.p',cls_List_Otake__take_0) ).
fof(f23847,plain,
( spl0_2161
| ~ spl0_646
| ~ spl0_687
| ~ spl0_1372
| ~ spl0_1461
| ~ spl0_2160 ),
inference(avatar_split_clause,[],[f23843,f23838,f11313,f10914,f7046,f6101,f23845]) ).
fof(f23845,plain,
( spl0_2161
<=> ! [X21,X15] : c_plus(c_1,c_Orderings_Omin(X15,X21,tc_nat),tc_nat) = c_Orderings_Omin(c_plus(c_1,X15,tc_nat),c_plus(c_1,X21,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2161])]) ).
fof(f23838,plain,
( spl0_2160
<=> ! [X21,X15] : c_Orderings_Omin(c_Finite__Set_Ocard(c_SetInterval_OatMost(X15,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),tc_nat) = c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Orderings_Omin(X15,X21,tc_nat),tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2160])]) ).
fof(f23843,plain,
( ! [X21,X15] : c_plus(c_1,c_Orderings_Omin(X15,X21,tc_nat),tc_nat) = c_Orderings_Omin(c_plus(c_1,X15,tc_nat),c_plus(c_1,X21,tc_nat),tc_nat)
| ~ spl0_646
| ~ spl0_687
| ~ spl0_1372
| ~ spl0_1461
| ~ spl0_2160 ),
inference(forward_demodulation,[],[f23842,f12280]) ).
fof(f23842,plain,
( ! [X21,X15] : c_plus(c_1,c_Orderings_Omin(X15,X21,tc_nat),tc_nat) = c_Orderings_Omin(c_Finite__Set_Ocard(c_SetInterval_OatMost(X15,tc_nat),tc_nat),c_plus(c_1,X21,tc_nat),tc_nat)
| ~ spl0_646
| ~ spl0_687
| ~ spl0_1372
| ~ spl0_1461
| ~ spl0_2160 ),
inference(forward_demodulation,[],[f23841,f12280]) ).
fof(f23841,plain,
( ! [X21,X15] : c_Orderings_Omin(c_Finite__Set_Ocard(c_SetInterval_OatMost(X15,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),tc_nat) = c_plus(c_1,c_Orderings_Omin(X15,X21,tc_nat),tc_nat)
| ~ spl0_646
| ~ spl0_687
| ~ spl0_1372
| ~ spl0_1461
| ~ spl0_2160 ),
inference(forward_demodulation,[],[f23839,f12280]) ).
fof(f23839,plain,
( ! [X21,X15] : c_Orderings_Omin(c_Finite__Set_Ocard(c_SetInterval_OatMost(X15,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),tc_nat) = c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Orderings_Omin(X15,X21,tc_nat),tc_nat),tc_nat)
| ~ spl0_2160 ),
inference(avatar_component_clause,[],[f23838]) ).
fof(f23840,plain,
spl0_2160,
inference(avatar_split_clause,[],[f3033,f23838]) ).
fof(f3033,plain,
! [X21,X15] : c_Orderings_Omin(c_Finite__Set_Ocard(c_SetInterval_OatMost(X15,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),tc_nat) = c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Orderings_Omin(X15,X21,tc_nat),tc_nat),tc_nat),
inference(definition_unfolding,[],[f2055,f2544,f2544,f2544]) ).
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/benchmark/theBenchmark.p',cls_Nat_Omin__Suc__Suc_0) ).
fof(f23820,plain,
( spl0_2159
| ~ spl0_646
| ~ spl0_687
| ~ spl0_1372
| ~ spl0_1461
| ~ spl0_2158 ),
inference(avatar_split_clause,[],[f23816,f23811,f11313,f10914,f7046,f6101,f23818]) ).
fof(f23818,plain,
( spl0_2159
<=> ! [X21,X15] : c_plus(c_1,c_Orderings_Omax(X15,X21,tc_nat),tc_nat) = c_Orderings_Omax(c_plus(c_1,X15,tc_nat),c_plus(c_1,X21,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2159])]) ).
fof(f23811,plain,
( spl0_2158
<=> ! [X21,X15] : c_Orderings_Omax(c_Finite__Set_Ocard(c_SetInterval_OatMost(X15,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),tc_nat) = c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Orderings_Omax(X15,X21,tc_nat),tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2158])]) ).
fof(f23816,plain,
( ! [X21,X15] : c_plus(c_1,c_Orderings_Omax(X15,X21,tc_nat),tc_nat) = c_Orderings_Omax(c_plus(c_1,X15,tc_nat),c_plus(c_1,X21,tc_nat),tc_nat)
| ~ spl0_646
| ~ spl0_687
| ~ spl0_1372
| ~ spl0_1461
| ~ spl0_2158 ),
inference(forward_demodulation,[],[f23815,f12280]) ).
fof(f23815,plain,
( ! [X21,X15] : c_plus(c_1,c_Orderings_Omax(X15,X21,tc_nat),tc_nat) = c_Orderings_Omax(c_Finite__Set_Ocard(c_SetInterval_OatMost(X15,tc_nat),tc_nat),c_plus(c_1,X21,tc_nat),tc_nat)
| ~ spl0_646
| ~ spl0_687
| ~ spl0_1372
| ~ spl0_1461
| ~ spl0_2158 ),
inference(forward_demodulation,[],[f23814,f12280]) ).
fof(f23814,plain,
( ! [X21,X15] : c_Orderings_Omax(c_Finite__Set_Ocard(c_SetInterval_OatMost(X15,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),tc_nat) = c_plus(c_1,c_Orderings_Omax(X15,X21,tc_nat),tc_nat)
| ~ spl0_646
| ~ spl0_687
| ~ spl0_1372
| ~ spl0_1461
| ~ spl0_2158 ),
inference(forward_demodulation,[],[f23812,f12280]) ).
fof(f23812,plain,
( ! [X21,X15] : c_Orderings_Omax(c_Finite__Set_Ocard(c_SetInterval_OatMost(X15,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),tc_nat) = c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Orderings_Omax(X15,X21,tc_nat),tc_nat),tc_nat)
| ~ spl0_2158 ),
inference(avatar_component_clause,[],[f23811]) ).
fof(f23813,plain,
spl0_2158,
inference(avatar_split_clause,[],[f3032,f23811]) ).
fof(f3032,plain,
! [X21,X15] : c_Orderings_Omax(c_Finite__Set_Ocard(c_SetInterval_OatMost(X15,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),tc_nat) = c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Orderings_Omax(X15,X21,tc_nat),tc_nat),tc_nat),
inference(definition_unfolding,[],[f2052,f2544,f2544,f2544]) ).
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/benchmark/theBenchmark.p',cls_Nat_Omax__Suc__Suc_0) ).
fof(f23809,plain,
spl0_2157,
inference(avatar_split_clause,[],[f2877,f23807]) ).
fof(f23807,plain,
( spl0_2157
<=> ! [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_2157])]) ).
fof(f2877,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/benchmark/theBenchmark.p',cls_Message_Oparts__insert__MPair_0) ).
fof(f23793,plain,
spl0_2156,
inference(avatar_split_clause,[],[f2859,f23791]) ).
fof(f23791,plain,
( spl0_2156
<=> ! [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_2156])]) ).
fof(f2859,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/benchmark/theBenchmark.p',cls_Message_Oanalz__insert__MPair_0) ).
fof(f23789,plain,
spl0_2155,
inference(avatar_split_clause,[],[f2566,f23787]) ).
fof(f23787,plain,
( spl0_2155
<=> ! [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_2155])]) ).
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/benchmark/theBenchmark.p',cls_SetInterval_Oivl__subset_3) ).
fof(f23785,plain,
spl0_2154,
inference(avatar_split_clause,[],[f2564,f23783]) ).
fof(f23783,plain,
( spl0_2154
<=> ! [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_2154])]) ).
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/benchmark/theBenchmark.p',cls_SetInterval_Oivl__subset_1) ).
fof(f23781,plain,
spl0_2153,
inference(avatar_split_clause,[],[f2563,f23779]) ).
fof(f23779,plain,
( spl0_2153
<=> ! [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_2153])]) ).
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/benchmark/theBenchmark.p',cls_SetInterval_Oivl__subset_0) ).
fof(f23777,plain,
spl0_2152,
inference(avatar_split_clause,[],[f2376,f23775]) ).
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/benchmark/theBenchmark.p',cls_Relation_OImage__singleton__iff_1) ).
fof(f23773,plain,
spl0_2151,
inference(avatar_split_clause,[],[f2375,f23771]) ).
fof(f23771,plain,
( spl0_2151
<=> ! [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_2151])]) ).
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/benchmark/theBenchmark.p',cls_Relation_OImage__singleton__iff_0) ).
fof(f23769,plain,
spl0_2150,
inference(avatar_split_clause,[],[f2335,f23767]) ).
fof(f23767,plain,
( spl0_2150
<=> ! [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_2150])]) ).
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/benchmark/theBenchmark.p',cls_Parity_Ozero__less__power__eq__number__of_4) ).
fof(f23765,plain,
spl0_2149,
inference(avatar_split_clause,[],[f2318,f23763]) ).
fof(f23763,plain,
( spl0_2149
<=> ! [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_2149])]) ).
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/benchmark/theBenchmark.p',cls_Parity_Opower__le__zero__eq__number__of_1) ).
fof(f23761,plain,
spl0_2148,
inference(avatar_split_clause,[],[f2174,f23759]) ).
fof(f23759,plain,
( spl0_2148
<=> ! [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_2148])]) ).
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/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__add__abs_0) ).
fof(f23757,plain,
spl0_2147,
inference(avatar_split_clause,[],[f2121,f23755]) ).
fof(f23755,plain,
( spl0_2147
<=> ! [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_2147])]) ).
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/benchmark/theBenchmark.p',cls_Numeral_Obin__arith__extra__simps__6_0) ).
fof(f23753,plain,
( spl0_2146
| ~ spl0_1826
| ~ spl0_2071 ),
inference(avatar_split_clause,[],[f23562,f22913,f17240,f23751]) ).
fof(f23751,plain,
( spl0_2146
<=> ! [X0,X1] :
( ~ c_in(X0,c_insert(v_B,X1,tc_Message_Oagent),tc_Message_Oagent)
| c_in(X0,X1,tc_Message_Oagent)
| ~ c_in(X0,c_Event_Obad,tc_Message_Oagent) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2146])]) ).
fof(f17240,plain,
( spl0_1826
<=> ! [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_1826])]) ).
fof(f22913,plain,
( spl0_2071
<=> ! [X0,X1] :
( ~ c_in(X1,c_minus(c_Event_Obad,X0,tc_set(tc_Message_Oagent)),tc_Message_Oagent)
| ~ c_in(X1,c_insert(v_B,X0,tc_Message_Oagent),tc_Message_Oagent) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2071])]) ).
fof(f23562,plain,
( ! [X0,X1] :
( ~ c_in(X0,c_insert(v_B,X1,tc_Message_Oagent),tc_Message_Oagent)
| c_in(X0,X1,tc_Message_Oagent)
| ~ c_in(X0,c_Event_Obad,tc_Message_Oagent) )
| ~ spl0_1826
| ~ spl0_2071 ),
inference(resolution,[],[f22914,f17241]) ).
fof(f17241,plain,
( ! [X1,X4,X12,X13] :
( c_in(X4,c_minus(X12,X13,tc_set(X1)),X1)
| c_in(X4,X13,X1)
| ~ c_in(X4,X12,X1) )
| ~ spl0_1826 ),
inference(avatar_component_clause,[],[f17240]) ).
fof(f22914,plain,
( ! [X0,X1] :
( ~ c_in(X1,c_minus(c_Event_Obad,X0,tc_set(tc_Message_Oagent)),tc_Message_Oagent)
| ~ c_in(X1,c_insert(v_B,X0,tc_Message_Oagent),tc_Message_Oagent) )
| ~ spl0_2071 ),
inference(avatar_component_clause,[],[f22913]) ).
fof(f23749,plain,
spl0_2145,
inference(avatar_split_clause,[],[f1810,f23747]) ).
fof(f23747,plain,
( spl0_2145
<=> ! [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_2145])]) ).
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/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__diff_0) ).
fof(f23745,plain,
spl0_2144,
inference(avatar_split_clause,[],[f1672,f23743]) ).
fof(f23743,plain,
( spl0_2144
<=> ! [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_2144])]) ).
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/benchmark/theBenchmark.p',cls_List_Onibble_Orecs__9_0) ).
fof(f23741,plain,
spl0_2143,
inference(avatar_split_clause,[],[f1671,f23739]) ).
fof(f23739,plain,
( spl0_2143
<=> ! [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_2143])]) ).
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/benchmark/theBenchmark.p',cls_List_Onibble_Orecs__8_0) ).
fof(f23737,plain,
spl0_2142,
inference(avatar_split_clause,[],[f1670,f23735]) ).
fof(f23735,plain,
( spl0_2142
<=> ! [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_2142])]) ).
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/benchmark/theBenchmark.p',cls_List_Onibble_Orecs__7_0) ).
fof(f23733,plain,
spl0_2141,
inference(avatar_split_clause,[],[f1669,f23731]) ).
fof(f23731,plain,
( spl0_2141
<=> ! [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_2141])]) ).
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/benchmark/theBenchmark.p',cls_List_Onibble_Orecs__6_0) ).
fof(f23729,plain,
spl0_2140,
inference(avatar_split_clause,[],[f1668,f23727]) ).
fof(f23727,plain,
( spl0_2140
<=> ! [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_2140])]) ).
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/benchmark/theBenchmark.p',cls_List_Onibble_Orecs__5_0) ).
fof(f23725,plain,
spl0_2139,
inference(avatar_split_clause,[],[f1667,f23723]) ).
fof(f23723,plain,
( spl0_2139
<=> ! [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_2139])]) ).
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/benchmark/theBenchmark.p',cls_List_Onibble_Orecs__4_0) ).
fof(f23721,plain,
spl0_2138,
inference(avatar_split_clause,[],[f1666,f23719]) ).
fof(f23719,plain,
( spl0_2138
<=> ! [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_2138])]) ).
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/benchmark/theBenchmark.p',cls_List_Onibble_Orecs__3_0) ).
fof(f23717,plain,
spl0_2137,
inference(avatar_split_clause,[],[f1665,f23715]) ).
fof(f23715,plain,
( spl0_2137
<=> ! [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_2137])]) ).
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/benchmark/theBenchmark.p',cls_List_Onibble_Orecs__2_0) ).
fof(f23713,plain,
spl0_2136,
inference(avatar_split_clause,[],[f1664,f23711]) ).
fof(f23711,plain,
( spl0_2136
<=> ! [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_2136])]) ).
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/benchmark/theBenchmark.p',cls_List_Onibble_Orecs__1_0) ).
fof(f23709,plain,
( spl0_2135
| ~ spl0_1826
| ~ spl0_2056 ),
inference(avatar_split_clause,[],[f23045,f22719,f17240,f23707]) ).
fof(f23707,plain,
( spl0_2135
<=> ! [X0,X1] :
( ~ c_in(X0,c_insert(v_A,X1,tc_Message_Oagent),tc_Message_Oagent)
| c_in(X0,X1,tc_Message_Oagent)
| ~ c_in(X0,c_Event_Obad,tc_Message_Oagent) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2135])]) ).
fof(f22719,plain,
( spl0_2056
<=> ! [X0,X1] :
( ~ c_in(X1,c_minus(c_Event_Obad,X0,tc_set(tc_Message_Oagent)),tc_Message_Oagent)
| ~ c_in(X1,c_insert(v_A,X0,tc_Message_Oagent),tc_Message_Oagent) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2056])]) ).
fof(f23045,plain,
( ! [X0,X1] :
( ~ c_in(X0,c_insert(v_A,X1,tc_Message_Oagent),tc_Message_Oagent)
| c_in(X0,X1,tc_Message_Oagent)
| ~ c_in(X0,c_Event_Obad,tc_Message_Oagent) )
| ~ spl0_1826
| ~ spl0_2056 ),
inference(resolution,[],[f22720,f17241]) ).
fof(f22720,plain,
( ! [X0,X1] :
( ~ c_in(X1,c_minus(c_Event_Obad,X0,tc_set(tc_Message_Oagent)),tc_Message_Oagent)
| ~ c_in(X1,c_insert(v_A,X0,tc_Message_Oagent),tc_Message_Oagent) )
| ~ spl0_2056 ),
inference(avatar_component_clause,[],[f22719]) ).
fof(f23705,plain,
spl0_2134,
inference(avatar_split_clause,[],[f1663,f23703]) ).
fof(f23703,plain,
( spl0_2134
<=> ! [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_2134])]) ).
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/benchmark/theBenchmark.p',cls_List_Onibble_Orecs__16_0) ).
fof(f23701,plain,
spl0_2133,
inference(avatar_split_clause,[],[f1662,f23699]) ).
fof(f23699,plain,
( spl0_2133
<=> ! [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_2133])]) ).
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/benchmark/theBenchmark.p',cls_List_Onibble_Orecs__15_0) ).
fof(f23697,plain,
spl0_2132,
inference(avatar_split_clause,[],[f1661,f23695]) ).
fof(f23695,plain,
( spl0_2132
<=> ! [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_2132])]) ).
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/benchmark/theBenchmark.p',cls_List_Onibble_Orecs__14_0) ).
fof(f23693,plain,
spl0_2131,
inference(avatar_split_clause,[],[f1660,f23691]) ).
fof(f23691,plain,
( spl0_2131
<=> ! [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_2131])]) ).
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/benchmark/theBenchmark.p',cls_List_Onibble_Orecs__13_0) ).
fof(f23689,plain,
spl0_2130,
inference(avatar_split_clause,[],[f1659,f23687]) ).
fof(f23687,plain,
( spl0_2130
<=> ! [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_2130])]) ).
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/benchmark/theBenchmark.p',cls_List_Onibble_Orecs__12_0) ).
fof(f23685,plain,
spl0_2129,
inference(avatar_split_clause,[],[f1658,f23683]) ).
fof(f23683,plain,
( spl0_2129
<=> ! [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_2129])]) ).
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/benchmark/theBenchmark.p',cls_List_Onibble_Orecs__11_0) ).
fof(f23681,plain,
spl0_2128,
inference(avatar_split_clause,[],[f1657,f23679]) ).
fof(f23679,plain,
( spl0_2128
<=> ! [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_2128])]) ).
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/benchmark/theBenchmark.p',cls_List_Onibble_Orecs__10_0) ).
fof(f23677,plain,
spl0_2127,
inference(avatar_split_clause,[],[f1656,f23675]) ).
fof(f23675,plain,
( spl0_2127
<=> ! [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_2127])]) ).
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/benchmark/theBenchmark.p',cls_List_Onibble_Ocases__9_0) ).
fof(f23673,plain,
spl0_2126,
inference(avatar_split_clause,[],[f1655,f23671]) ).
fof(f23671,plain,
( spl0_2126
<=> ! [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_2126])]) ).
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/benchmark/theBenchmark.p',cls_List_Onibble_Ocases__8_0) ).
fof(f23669,plain,
spl0_2125,
inference(avatar_split_clause,[],[f1654,f23667]) ).
fof(f23667,plain,
( spl0_2125
<=> ! [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_2125])]) ).
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/benchmark/theBenchmark.p',cls_List_Onibble_Ocases__7_0) ).
fof(f23658,plain,
spl0_2124,
inference(avatar_split_clause,[],[f1653,f23656]) ).
fof(f23656,plain,
( spl0_2124
<=> ! [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_2124])]) ).
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/benchmark/theBenchmark.p',cls_List_Onibble_Ocases__6_0) ).
fof(f23654,plain,
spl0_2123,
inference(avatar_split_clause,[],[f1652,f23652]) ).
fof(f23652,plain,
( spl0_2123
<=> ! [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_2123])]) ).
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/benchmark/theBenchmark.p',cls_List_Onibble_Ocases__5_0) ).
fof(f23650,plain,
spl0_2122,
inference(avatar_split_clause,[],[f1651,f23648]) ).
fof(f23648,plain,
( spl0_2122
<=> ! [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_2122])]) ).
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/benchmark/theBenchmark.p',cls_List_Onibble_Ocases__4_0) ).
fof(f23646,plain,
spl0_2121,
inference(avatar_split_clause,[],[f1650,f23644]) ).
fof(f23644,plain,
( spl0_2121
<=> ! [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_2121])]) ).
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/benchmark/theBenchmark.p',cls_List_Onibble_Ocases__3_0) ).
fof(f23642,plain,
spl0_2120,
inference(avatar_split_clause,[],[f1649,f23640]) ).
fof(f23640,plain,
( spl0_2120
<=> ! [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_2120])]) ).
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/benchmark/theBenchmark.p',cls_List_Onibble_Ocases__2_0) ).
fof(f23638,plain,
spl0_2119,
inference(avatar_split_clause,[],[f1648,f23636]) ).
fof(f23636,plain,
( spl0_2119
<=> ! [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_2119])]) ).
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/benchmark/theBenchmark.p',cls_List_Onibble_Ocases__1_0) ).
fof(f23634,plain,
spl0_2118,
inference(avatar_split_clause,[],[f1647,f23632]) ).
fof(f23632,plain,
( spl0_2118
<=> ! [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_2118])]) ).
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/benchmark/theBenchmark.p',cls_List_Onibble_Ocases__16_0) ).
fof(f23630,plain,
spl0_2117,
inference(avatar_split_clause,[],[f1646,f23628]) ).
fof(f23628,plain,
( spl0_2117
<=> ! [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_2117])]) ).
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/benchmark/theBenchmark.p',cls_List_Onibble_Ocases__15_0) ).
fof(f23626,plain,
spl0_2116,
inference(avatar_split_clause,[],[f1645,f23624]) ).
fof(f23624,plain,
( spl0_2116
<=> ! [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_2116])]) ).
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/benchmark/theBenchmark.p',cls_List_Onibble_Ocases__14_0) ).
fof(f23622,plain,
spl0_2115,
inference(avatar_split_clause,[],[f1644,f23620]) ).
fof(f23620,plain,
( spl0_2115
<=> ! [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_2115])]) ).
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/benchmark/theBenchmark.p',cls_List_Onibble_Ocases__13_0) ).
fof(f23618,plain,
( spl0_2114
| ~ spl0_891
| ~ spl0_2071 ),
inference(avatar_split_clause,[],[f23572,f22913,f7918,f23616]) ).
fof(f23572,plain,
( ! [X0] :
( ~ c_in(X0,c_Event_Obad,tc_Message_Oagent)
| ~ c_in(X0,c_insert(v_B,c_emptyset,tc_Message_Oagent),tc_Message_Oagent) )
| ~ spl0_891
| ~ spl0_2071 ),
inference(superposition,[],[f22914,f7919]) ).
fof(f23614,plain,
spl0_2113,
inference(avatar_split_clause,[],[f1643,f23612]) ).
fof(f23612,plain,
( spl0_2113
<=> ! [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_2113])]) ).
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/benchmark/theBenchmark.p',cls_List_Onibble_Ocases__12_0) ).
fof(f23610,plain,
spl0_2112,
inference(avatar_split_clause,[],[f1642,f23608]) ).
fof(f23608,plain,
( spl0_2112
<=> ! [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_2112])]) ).
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/benchmark/theBenchmark.p',cls_List_Onibble_Ocases__11_0) ).
fof(f23606,plain,
spl0_2111,
inference(avatar_split_clause,[],[f1641,f23604]) ).
fof(f23604,plain,
( spl0_2111
<=> ! [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_2111])]) ).
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/benchmark/theBenchmark.p',cls_List_Onibble_Ocases__10_0) ).
fof(f23602,plain,
spl0_2110,
inference(avatar_split_clause,[],[f1629,f23600]) ).
fof(f23600,plain,
( spl0_2110
<=> ! [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_2110])]) ).
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/benchmark/theBenchmark.p',cls_List_Olist__inter_Osimps__2_0) ).
fof(f23598,plain,
spl0_2109,
inference(avatar_split_clause,[],[f1614,f23596]) ).
fof(f23596,plain,
( spl0_2109
<=> ! [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_2109])]) ).
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/benchmark/theBenchmark.p',cls_List_Olength__zip_0) ).
fof(f23594,plain,
spl0_2108,
inference(avatar_split_clause,[],[f1523,f23592]) ).
fof(f23592,plain,
( spl0_2108
<=> ! [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_2108])]) ).
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/benchmark/theBenchmark.p',cls_List_Oappend__eq__append__conv_3) ).
fof(f23590,plain,
spl0_2107,
inference(avatar_split_clause,[],[f1522,f23588]) ).
fof(f23588,plain,
( spl0_2107
<=> ! [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_2107])]) ).
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/benchmark/theBenchmark.p',cls_List_Oappend__eq__append__conv_2) ).
fof(f23586,plain,
spl0_2106,
inference(avatar_split_clause,[],[f1521,f23584]) ).
fof(f23584,plain,
( spl0_2106
<=> ! [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_2106])]) ).
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/benchmark/theBenchmark.p',cls_List_Oappend__eq__append__conv_1) ).
fof(f23582,plain,
spl0_2105,
inference(avatar_split_clause,[],[f1520,f23580]) ).
fof(f23580,plain,
( spl0_2105
<=> ! [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_2105])]) ).
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/benchmark/theBenchmark.p',cls_List_Oappend__eq__append__conv_0) ).
fof(f23578,plain,
spl0_2104,
inference(avatar_split_clause,[],[f1468,f23576]) ).
fof(f23576,plain,
( spl0_2104
<=> ! [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_2104])]) ).
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/benchmark/theBenchmark.p',cls_IntDiv_Ozdiv__number__of__BIT_0) ).
fof(f23561,plain,
spl0_2103,
inference(avatar_split_clause,[],[f1283,f23559]) ).
fof(f23559,plain,
( spl0_2103
<=> ! [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_2103])]) ).
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/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Diff__insert_1) ).
fof(f23557,plain,
spl0_2102,
inference(avatar_split_clause,[],[f1282,f23555]) ).
fof(f23555,plain,
( spl0_2102
<=> ! [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_2102])]) ).
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/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Diff__insert_0) ).
fof(f23553,plain,
spl0_2101,
inference(avatar_split_clause,[],[f79,f23551]) ).
fof(f23551,plain,
( spl0_2101
<=> ! [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_2101])]) ).
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/benchmark/theBenchmark.p',cls_Relation_OdiagE_0) ).
fof(f23549,plain,
spl0_2100,
inference(avatar_split_clause,[],[f75,f23547]) ).
fof(f23547,plain,
( spl0_2100
<=> ! [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_2100])]) ).
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/benchmark/theBenchmark.p',cls_Relation_ORangeE_0) ).
fof(f23545,plain,
spl0_2099,
inference(avatar_split_clause,[],[f69,f23543]) ).
fof(f23543,plain,
( spl0_2099
<=> ! [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_2099])]) ).
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/benchmark/theBenchmark.p',cls_Relation_ODomainE_0) ).
fof(f23541,plain,
spl0_2098,
inference(avatar_split_clause,[],[f60,f23539]) ).
fof(f23539,plain,
( spl0_2098
<=> ! [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_2098])]) ).
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/benchmark/theBenchmark.p',cls_List_Olists_OCons_0) ).
fof(f23537,plain,
spl0_2097,
inference(avatar_split_clause,[],[f22,f23535]) ).
fof(f23535,plain,
( spl0_2097
<=> ! [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_2097])]) ).
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/benchmark/theBenchmark.p',cls_Datatype__Universe_Ousum__In1I_0) ).
fof(f23533,plain,
spl0_2096,
inference(avatar_split_clause,[],[f21,f23531]) ).
fof(f23531,plain,
( spl0_2096
<=> ! [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_2096])]) ).
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/benchmark/theBenchmark.p',cls_Datatype__Universe_Ousum__In0I_0) ).
fof(f23421,plain,
( spl0_2095
| ~ spl0_57
| ~ spl0_1584
| ~ spl0_2078 ),
inference(avatar_split_clause,[],[f22945,f22942,f12849,f3692,f23419]) ).
fof(f23419,plain,
( spl0_2095
<=> ! [X83,X47] :
( c_IntDef_Oneg(c_uminus(c_Numeral_Onumber__of(X83,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ 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) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2095])]) ).
fof(f22942,plain,
( spl0_2078
<=> ! [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__mult(c_Numeral_OMin,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_2078])]) ).
fof(f22945,plain,
( ! [X83,X47] :
( c_IntDef_Oneg(c_uminus(c_Numeral_Onumber__of(X83,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ 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) )
| ~ spl0_57
| ~ spl0_1584
| ~ spl0_2078 ),
inference(forward_demodulation,[],[f22943,f14151]) ).
fof(f22943,plain,
( ! [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__mult(c_Numeral_OMin,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) )
| ~ spl0_2078 ),
inference(avatar_component_clause,[],[f22942]) ).
fof(f23417,plain,
( spl0_2094
| ~ spl0_57
| ~ spl0_1584
| ~ spl0_2077 ),
inference(avatar_split_clause,[],[f22940,f22937,f12849,f3692,f23415]) ).
fof(f23415,plain,
( spl0_2094
<=> ! [X83,X47] :
( ~ c_IntDef_Oneg(c_uminus(c_Numeral_Onumber__of(X83,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ 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) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2094])]) ).
fof(f22937,plain,
( spl0_2077
<=> ! [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__mult(c_Numeral_OMin,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_2077])]) ).
fof(f22940,plain,
( ! [X83,X47] :
( ~ c_IntDef_Oneg(c_uminus(c_Numeral_Onumber__of(X83,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ 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) )
| ~ spl0_57
| ~ spl0_1584
| ~ spl0_2077 ),
inference(forward_demodulation,[],[f22938,f14151]) ).
fof(f22938,plain,
( ! [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__mult(c_Numeral_OMin,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) )
| ~ spl0_2077 ),
inference(avatar_component_clause,[],[f22937]) ).
fof(f23212,plain,
( spl0_2093
| ~ spl0_891
| ~ spl0_2056 ),
inference(avatar_split_clause,[],[f23055,f22719,f7918,f23210]) ).
fof(f23055,plain,
( ! [X0] :
( ~ c_in(X0,c_Event_Obad,tc_Message_Oagent)
| ~ c_in(X0,c_insert(v_A,c_emptyset,tc_Message_Oagent),tc_Message_Oagent) )
| ~ spl0_891
| ~ spl0_2056 ),
inference(superposition,[],[f22720,f7919]) ).
fof(f23091,plain,
( spl0_2092
| ~ spl0_1647
| ~ spl0_2091 ),
inference(avatar_split_clause,[],[f23087,f23084,f14403,f23089]) ).
fof(f23089,plain,
( spl0_2092
<=> ! [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) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2092])]) ).
fof(f14403,plain,
( spl0_1647
<=> c_Numeral_OMin = c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_Obin__succ(c_Numeral_OPls)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1647])]) ).
fof(f23084,plain,
( spl0_2091
<=> ! [X0,X1] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X0,c_Numeral_Obin__mult(c_Numeral_OMin,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_2091])]) ).
fof(f23087,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_1647
| ~ spl0_2091 ),
inference(forward_demodulation,[],[f23085,f14405]) ).
fof(f14405,plain,
( c_Numeral_OMin = c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_Obin__succ(c_Numeral_OPls))
| ~ spl0_1647 ),
inference(avatar_component_clause,[],[f14403]) ).
fof(f23085,plain,
( ! [X0,X1] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X0,c_Numeral_Obin__mult(c_Numeral_OMin,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_2091 ),
inference(avatar_component_clause,[],[f23084]) ).
fof(f23086,plain,
spl0_2091,
inference(avatar_split_clause,[],[f3406,f23084]) ).
fof(f3406,plain,
! [X0,X1] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X0,c_Numeral_Obin__mult(c_Numeral_OMin,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,[],[f3193,f2156]) ).
fof(f3193,plain,
! [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__mult(c_Numeral_OMin,c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),X1),X1) ),
inference(definition_unfolding,[],[f1319,f2129]) ).
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/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__13_1) ).
fof(f23082,plain,
spl0_2090,
inference(avatar_split_clause,[],[f3404,f23080]) ).
fof(f23080,plain,
( spl0_2090
<=> ! [X1,X3] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obin__mult(c_Numeral_OMin,X3)),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_2090])]) ).
fof(f3404,plain,
! [X3,X1] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obin__mult(c_Numeral_OMin,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,[],[f3191,f2156]) ).
fof(f3191,plain,
! [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__mult(c_Numeral_OMin,X3)),X1),X1) ),
inference(definition_unfolding,[],[f1315,f2129]) ).
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/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__11_1) ).
fof(f23078,plain,
spl0_2089,
inference(avatar_split_clause,[],[f3402,f23076]) ).
fof(f23076,plain,
( spl0_2089
<=> ! [X0,X1] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obin__mult(c_Numeral_OMin,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_2089])]) ).
fof(f3402,plain,
! [X0,X1] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obin__mult(c_Numeral_OMin,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,[],[f3189,f2156]) ).
fof(f3189,plain,
! [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__mult(c_Numeral_OMin,X0)),X1),X1) ),
inference(definition_unfolding,[],[f1327,f2129]) ).
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/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__17_1) ).
fof(f23044,plain,
( spl0_2088
| ~ spl0_1647
| ~ spl0_2087 ),
inference(avatar_split_clause,[],[f23040,f23037,f14403,f23042]) ).
fof(f23042,plain,
( spl0_2088
<=> ! [X1,X3] :
( 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) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2088])]) ).
fof(f23037,plain,
( spl0_2087
<=> ! [X1,X3] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X3,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_Obin__succ(c_Numeral_OPls))),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_2087])]) ).
fof(f23040,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_1647
| ~ spl0_2087 ),
inference(forward_demodulation,[],[f23038,f14405]) ).
fof(f23038,plain,
( ! [X3,X1] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X3,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_Obin__succ(c_Numeral_OPls))),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_2087 ),
inference(avatar_component_clause,[],[f23037]) ).
fof(f23039,plain,
spl0_2087,
inference(avatar_split_clause,[],[f3399,f23037]) ).
fof(f3399,plain,
! [X3,X1] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X3,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_Obin__succ(c_Numeral_OPls))),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,[],[f3187,f2156]) ).
fof(f3187,plain,
! [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__mult(c_Numeral_OMin,c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),X1),X1) ),
inference(definition_unfolding,[],[f1323,f2129]) ).
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/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__15_1) ).
fof(f23018,plain,
( spl0_2086
| ~ spl0_1647
| ~ spl0_2085 ),
inference(avatar_split_clause,[],[f23014,f23011,f14403,f23016]) ).
fof(f23016,plain,
( spl0_2086
<=> ! [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) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2086])]) ).
fof(f23011,plain,
( spl0_2085
<=> ! [X0,X1] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X0,c_Numeral_Obin__mult(c_Numeral_OMin,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_2085])]) ).
fof(f23014,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_1647
| ~ spl0_2085 ),
inference(forward_demodulation,[],[f23012,f14405]) ).
fof(f23012,plain,
( ! [X0,X1] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X0,c_Numeral_Obin__mult(c_Numeral_OMin,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_2085 ),
inference(avatar_component_clause,[],[f23011]) ).
fof(f23013,plain,
spl0_2085,
inference(avatar_split_clause,[],[f3396,f23011]) ).
fof(f3396,plain,
! [X0,X1] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X0,c_Numeral_Obin__mult(c_Numeral_OMin,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,[],[f3185,f2156]) ).
fof(f3185,plain,
! [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__mult(c_Numeral_OMin,c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),X1),X1) ),
inference(definition_unfolding,[],[f1318,f2129]) ).
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/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__13_0) ).
fof(f23009,plain,
spl0_2084,
inference(avatar_split_clause,[],[f3394,f23007]) ).
fof(f23007,plain,
( spl0_2084
<=> ! [X1,X3] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obin__mult(c_Numeral_OMin,X3)),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_2084])]) ).
fof(f3394,plain,
! [X3,X1] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obin__mult(c_Numeral_OMin,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,[],[f3183,f2156]) ).
fof(f3183,plain,
! [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__mult(c_Numeral_OMin,X3)),X1),X1) ),
inference(definition_unfolding,[],[f1314,f2129]) ).
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/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__11_0) ).
fof(f23005,plain,
spl0_2083,
inference(avatar_split_clause,[],[f3392,f23003]) ).
fof(f23003,plain,
( spl0_2083
<=> ! [X0,X1] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obin__mult(c_Numeral_OMin,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_2083])]) ).
fof(f3392,plain,
! [X0,X1] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obin__mult(c_Numeral_OMin,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,[],[f3181,f2156]) ).
fof(f3181,plain,
! [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__mult(c_Numeral_OMin,X0)),X1),X1) ),
inference(definition_unfolding,[],[f1326,f2129]) ).
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/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__17_0) ).
fof(f22992,plain,
( spl0_2082
| ~ spl0_1647
| ~ spl0_2081 ),
inference(avatar_split_clause,[],[f22988,f22985,f14403,f22990]) ).
fof(f22990,plain,
( spl0_2082
<=> ! [X1,X3] :
( ~ 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) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2082])]) ).
fof(f22985,plain,
( spl0_2081
<=> ! [X1,X3] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X3,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_Obin__succ(c_Numeral_OPls))),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_2081])]) ).
fof(f22988,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_1647
| ~ spl0_2081 ),
inference(forward_demodulation,[],[f22986,f14405]) ).
fof(f22986,plain,
( ! [X3,X1] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X3,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_Obin__succ(c_Numeral_OPls))),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_2081 ),
inference(avatar_component_clause,[],[f22985]) ).
fof(f22987,plain,
spl0_2081,
inference(avatar_split_clause,[],[f3389,f22985]) ).
fof(f3389,plain,
! [X3,X1] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X3,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_Obin__succ(c_Numeral_OPls))),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,[],[f3179,f2156]) ).
fof(f3179,plain,
! [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__mult(c_Numeral_OMin,c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),X1),X1) ),
inference(definition_unfolding,[],[f1322,f2129]) ).
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/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__15_0) ).
fof(f22955,plain,
( spl0_2080
| ~ spl0_57
| ~ spl0_1465
| ~ spl0_2079 ),
inference(avatar_split_clause,[],[f22951,f22947,f11329,f3692,f22953]) ).
fof(f22953,plain,
( spl0_2080
<=> ! [X0] :
( c_1 = c_Divides_Oop_Amod(X0,c_plus(c_1,c_1,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 = c_Divides_Oop_Amod(X0,c_plus(c_1,c_1,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2080])]) ).
fof(f11329,plain,
( spl0_1465
<=> ! [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_1465])]) ).
fof(f22947,plain,
( spl0_2079
<=> ! [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_2079])]) ).
fof(f22951,plain,
( ! [X0] :
( c_1 = c_Divides_Oop_Amod(X0,c_plus(c_1,c_1,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 = c_Divides_Oop_Amod(X0,c_plus(c_1,c_1,tc_IntDef_Oint),tc_IntDef_Oint) )
| ~ spl0_57
| ~ spl0_1465
| ~ spl0_2079 ),
inference(forward_demodulation,[],[f22950,f12348]) ).
fof(f12348,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_57
| ~ spl0_1465 ),
inference(resolution,[],[f11330,f3694]) ).
fof(f11330,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_1465 ),
inference(avatar_component_clause,[],[f11329]) ).
fof(f22950,plain,
( ! [X0] :
( c_0 = c_Divides_Oop_Amod(X0,c_plus(c_1,c_1,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_57
| ~ spl0_1465
| ~ spl0_2079 ),
inference(forward_demodulation,[],[f22948,f12348]) ).
fof(f22948,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_2079 ),
inference(avatar_component_clause,[],[f22947]) ).
fof(f22949,plain,
spl0_2079,
inference(avatar_split_clause,[],[f3347,f22947]) ).
fof(f3347,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,[],[f3346,f2156]) ).
fof(f3346,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,[],[f3345,f2154]) ).
fof(f3345,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,[],[f3344,f2156]) ).
fof(f3344,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,[],[f3343,f2156]) ).
fof(f3343,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,[],[f3342,f2154]) ).
fof(f3342,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/benchmark/theBenchmark.p',cls_Parity_Oneq__one__mod__two_0) ).
fof(f22944,plain,
spl0_2078,
inference(avatar_split_clause,[],[f3172,f22942]) ).
fof(f3172,plain,
! [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__mult(c_Numeral_OMin,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) ),
inference(definition_unfolding,[],[f1855,f2129]) ).
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/benchmark/theBenchmark.p',cls_NatBin_Oless__nat__number__of_0) ).
fof(f22939,plain,
spl0_2077,
inference(avatar_split_clause,[],[f3171,f22937]) ).
fof(f3171,plain,
! [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__mult(c_Numeral_OMin,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) ),
inference(definition_unfolding,[],[f1858,f2129]) ).
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/benchmark/theBenchmark.p',cls_NatBin_Oless__nat__number__of_3) ).
fof(f22935,plain,
spl0_2076,
inference(avatar_split_clause,[],[f2936,f22933]) ).
fof(f22933,plain,
( spl0_2076
<=> ! [X102,X86,X13] :
( ~ c_in(X102,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
| c_in(X86,c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,X102)),tc_Message_Omsg)
| ~ c_in(c_Event_Oevent_OGets(X13,X86),c_List_Oset(X102,tc_Event_Oevent),tc_Event_Oevent) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2076])]) ).
fof(f2936,axiom,
! [X86,X102,X13] :
( ~ c_in(X102,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
| c_in(X86,c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,X102)),tc_Message_Omsg)
| ~ c_in(c_Event_Oevent_OGets(X13,X86),c_List_Oset(X102,tc_Event_Oevent),tc_Event_Oevent) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Yahalom_OGets__imp__analz__Spy__dest_0) ).
fof(f22931,plain,
spl0_2075,
inference(avatar_split_clause,[],[f2352,f22929]) ).
fof(f22929,plain,
( spl0_2075
<=> ! [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_2075])]) ).
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/benchmark/theBenchmark.p',cls_Power_Opower__inject__exp_0) ).
fof(f22927,plain,
spl0_2074,
inference(avatar_split_clause,[],[f2327,f22925]) ).
fof(f22925,plain,
( spl0_2074
<=> ! [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_2074])]) ).
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/benchmark/theBenchmark.p',cls_Parity_Opower__minus__odd_0) ).
fof(f22923,plain,
spl0_2073,
inference(avatar_split_clause,[],[f2320,f22921]) ).
fof(f22921,plain,
( spl0_2073
<=> ! [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_2073])]) ).
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/benchmark/theBenchmark.p',cls_Parity_Opower__le__zero__eq__number__of_3) ).
fof(f22919,plain,
spl0_2072,
inference(avatar_split_clause,[],[f1973,f22917]) ).
fof(f22917,plain,
( spl0_2072
<=> ! [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_2072])]) ).
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/benchmark/theBenchmark.p',cls_NatSimprocs_Ominus__less__iff__number__of_1) ).
fof(f22915,plain,
( spl0_2071
| ~ spl0_1427
| ~ spl0_2031 ),
inference(avatar_split_clause,[],[f22337,f22195,f11164,f22913]) ).
fof(f11164,plain,
( spl0_1427
<=> ! [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_1427])]) ).
fof(f22337,plain,
( ! [X0,X1] :
( ~ c_in(X1,c_minus(c_Event_Obad,X0,tc_set(tc_Message_Oagent)),tc_Message_Oagent)
| ~ c_in(X1,c_insert(v_B,X0,tc_Message_Oagent),tc_Message_Oagent) )
| ~ spl0_1427
| ~ spl0_2031 ),
inference(superposition,[],[f11165,f22196]) ).
fof(f11165,plain,
( ! [X1,X4,X12,X13] :
( ~ c_in(X4,c_minus(X12,X13,tc_set(X1)),X1)
| ~ c_in(X4,X13,X1) )
| ~ spl0_1427 ),
inference(avatar_component_clause,[],[f11164]) ).
fof(f22911,plain,
spl0_2070,
inference(avatar_split_clause,[],[f1972,f22909]) ).
fof(f22909,plain,
( spl0_2070
<=> ! [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_2070])]) ).
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/benchmark/theBenchmark.p',cls_NatSimprocs_Ominus__less__iff__number__of_0) ).
fof(f22907,plain,
spl0_2069,
inference(avatar_split_clause,[],[f1969,f22905]) ).
fof(f22905,plain,
( spl0_2069
<=> ! [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_2069])]) ).
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/benchmark/theBenchmark.p',cls_NatSimprocs_Ominus__le__iff__number__of_1) ).
fof(f22903,plain,
spl0_2068,
inference(avatar_split_clause,[],[f1968,f22901]) ).
fof(f22901,plain,
( spl0_2068
<=> ! [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_2068])]) ).
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/benchmark/theBenchmark.p',cls_NatSimprocs_Ominus__le__iff__number__of_0) ).
fof(f22899,plain,
spl0_2067,
inference(avatar_split_clause,[],[f1962,f22897]) ).
fof(f22897,plain,
( spl0_2067
<=> ! [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_2067])]) ).
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/benchmark/theBenchmark.p',cls_NatSimprocs_Oless__minus__iff__number__of_1) ).
fof(f22895,plain,
spl0_2066,
inference(avatar_split_clause,[],[f1961,f22893]) ).
fof(f22893,plain,
( spl0_2066
<=> ! [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_2066])]) ).
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/benchmark/theBenchmark.p',cls_NatSimprocs_Oless__minus__iff__number__of_0) ).
fof(f22891,plain,
spl0_2065,
inference(avatar_split_clause,[],[f1946,f22889]) ).
fof(f22889,plain,
( spl0_2065
<=> ! [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_2065])]) ).
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/benchmark/theBenchmark.p',cls_NatSimprocs_Ole__minus__iff__number__of_1) ).
fof(f22887,plain,
spl0_2064,
inference(avatar_split_clause,[],[f1945,f22885]) ).
fof(f22885,plain,
( spl0_2064
<=> ! [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_2064])]) ).
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/benchmark/theBenchmark.p',cls_NatSimprocs_Ole__minus__iff__number__of_0) ).
fof(f22883,plain,
spl0_2063,
inference(avatar_split_clause,[],[f1876,f22881]) ).
fof(f22881,plain,
( spl0_2063
<=> ! [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_2063])]) ).
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/benchmark/theBenchmark.p',cls_NatBin_Opower__nat__number__of__number__of_0) ).
fof(f22879,plain,
spl0_2062,
inference(avatar_split_clause,[],[f1755,f22877]) ).
fof(f22877,plain,
( spl0_2062
<=> ! [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_2062])]) ).
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/benchmark/theBenchmark.p',cls_List_Oset__remove1__eq_0) ).
fof(f22875,plain,
spl0_2061,
inference(avatar_split_clause,[],[f1274,f22873]) ).
fof(f22873,plain,
( spl0_2061
<=> ! [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_2061])]) ).
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/benchmark/theBenchmark.p',cls_Finite__Set_OMin__le_0) ).
fof(f22871,plain,
( spl0_2060
| ~ spl0_1424
| ~ spl0_2031 ),
inference(avatar_split_clause,[],[f22335,f22195,f11146,f22869]) ).
fof(f22869,plain,
( spl0_2060
<=> ! [X0] :
( c_emptyset != c_minus(c_Event_Obad,X0,tc_set(tc_Message_Oagent))
| c_lessequals(c_Event_Obad,c_insert(v_B,X0,tc_Message_Oagent),tc_set(tc_Message_Oagent)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2060])]) ).
fof(f22335,plain,
( ! [X0] :
( c_emptyset != c_minus(c_Event_Obad,X0,tc_set(tc_Message_Oagent))
| c_lessequals(c_Event_Obad,c_insert(v_B,X0,tc_Message_Oagent),tc_set(tc_Message_Oagent)) )
| ~ spl0_1424
| ~ spl0_2031 ),
inference(superposition,[],[f11147,f22196]) ).
fof(f22867,plain,
spl0_2059,
inference(avatar_split_clause,[],[f1256,f22865]) ).
fof(f22865,plain,
( spl0_2059
<=> ! [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_2059])]) ).
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/benchmark/theBenchmark.p',cls_Finite__Set_OMax__ge_0) ).
fof(f22863,plain,
spl0_2058,
inference(avatar_split_clause,[],[f33,f22861]) ).
fof(f22861,plain,
( spl0_2058
<=> ! [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_2058])]) ).
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/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Union_1) ).
fof(f22859,plain,
spl0_2057,
inference(avatar_split_clause,[],[f32,f22857]) ).
fof(f22857,plain,
( spl0_2057
<=> ! [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_2057])]) ).
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/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Union_0) ).
fof(f22721,plain,
( spl0_2056
| ~ spl0_1427
| ~ spl0_2030 ),
inference(avatar_split_clause,[],[f22273,f21998,f11164,f22719]) ).
fof(f22273,plain,
( ! [X0,X1] :
( ~ c_in(X1,c_minus(c_Event_Obad,X0,tc_set(tc_Message_Oagent)),tc_Message_Oagent)
| ~ c_in(X1,c_insert(v_A,X0,tc_Message_Oagent),tc_Message_Oagent) )
| ~ spl0_1427
| ~ spl0_2030 ),
inference(superposition,[],[f11165,f21999]) ).
fof(f22465,plain,
( spl0_2055
| ~ spl0_781
| ~ spl0_786
| ~ spl0_1848
| ~ spl0_2039 ),
inference(avatar_split_clause,[],[f22294,f22291,f17598,f7484,f7464,f22463]) ).
fof(f22463,plain,
( spl0_2055
<=> ! [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_2055])]) ).
fof(f22291,plain,
( spl0_2039
<=> ! [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_2039])]) ).
fof(f22294,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_781
| ~ spl0_786
| ~ spl0_1848
| ~ spl0_2039 ),
inference(forward_demodulation,[],[f22292,f17626]) ).
fof(f22292,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_2039 ),
inference(avatar_component_clause,[],[f22291]) ).
fof(f22439,plain,
( spl0_2054
| ~ spl0_1424
| ~ spl0_2030 ),
inference(avatar_split_clause,[],[f22271,f21998,f11146,f22437]) ).
fof(f22437,plain,
( spl0_2054
<=> ! [X0] :
( c_emptyset != c_minus(c_Event_Obad,X0,tc_set(tc_Message_Oagent))
| c_lessequals(c_Event_Obad,c_insert(v_A,X0,tc_Message_Oagent),tc_set(tc_Message_Oagent)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2054])]) ).
fof(f22271,plain,
( ! [X0] :
( c_emptyset != c_minus(c_Event_Obad,X0,tc_set(tc_Message_Oagent))
| c_lessequals(c_Event_Obad,c_insert(v_A,X0,tc_Message_Oagent),tc_set(tc_Message_Oagent)) )
| ~ spl0_1424
| ~ spl0_2030 ),
inference(superposition,[],[f11147,f21999]) ).
fof(f22427,plain,
( spl0_2053
| ~ spl0_1827
| ~ spl0_2036 ),
inference(avatar_split_clause,[],[f22258,f22255,f17244,f22425]) ).
fof(f22425,plain,
( spl0_2053
<=> ! [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_2053])]) ).
fof(f22255,plain,
( spl0_2036
<=> ! [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_2036])]) ).
fof(f22258,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_1827
| ~ spl0_2036 ),
inference(forward_demodulation,[],[f22256,f17246]) ).
fof(f22256,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_2036 ),
inference(avatar_component_clause,[],[f22255]) ).
fof(f22369,plain,
spl0_2052,
inference(avatar_split_clause,[],[f3320,f22367]) ).
fof(f22367,plain,
( spl0_2052
<=> ! [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_2052])]) ).
fof(f3320,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,[],[f3133,f2958]) ).
fof(f2958,plain,
c_1 = c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),
inference(definition_unfolding,[],[f2016,f2544]) ).
fof(f2016,axiom,
c_Suc(c_0) = c_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_OOne__nat__def_0) ).
fof(f3133,plain,
! [X83] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X83,tc_IntDef_Oint),tc_IntDef_Oint)
| 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_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),c_Numeral_Onumber__of(X83,tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f1872,f2544]) ).
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/benchmark/theBenchmark.p',cls_NatBin_Oone__mod__nat__number__of_1) ).
fof(f22365,plain,
spl0_2051,
inference(avatar_split_clause,[],[f3139,f22363]) ).
fof(f22363,plain,
( spl0_2051
<=> ! [X5,X1,X28] :
( ~ c_in(X28,X5,tc_prod(X1,X1))
| c_in(X28,c_Transitive__Closure_Otrancl(c_union(X5,c_Relation_OId,tc_prod(X1,X1)),X1),tc_prod(X1,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2051])]) ).
fof(f3139,plain,
! [X28,X1,X5] :
( ~ c_in(X28,X5,tc_prod(X1,X1))
| c_in(X28,c_Transitive__Closure_Otrancl(c_union(X5,c_Relation_OId,tc_prod(X1,X1)),X1),tc_prod(X1,X1)) ),
inference(definition_unfolding,[],[f119,f2716]) ).
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/benchmark/theBenchmark.p',cls_Transitive__Closure_Or__into__rtrancl_0) ).
fof(f22361,plain,
spl0_2050,
inference(avatar_split_clause,[],[f3137,f22359]) ).
fof(f22359,plain,
( spl0_2050
<=> ! [X25,X1,X23] :
( ~ c_List_Odistinct(c_append(X23,X25,X1),X1)
| c_emptyset = c_Relation_OImage(c_Relation_Odiag(c_List_Oset(X23,X1),X1),c_List_Oset(X25,X1),X1,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2050])]) ).
fof(f3137,plain,
! [X1,X25,X23] :
( ~ c_List_Odistinct(c_append(X23,X25,X1),X1)
| c_emptyset = c_Relation_OImage(c_Relation_Odiag(c_List_Oset(X23,X1),X1),c_List_Oset(X25,X1),X1,X1) ),
inference(definition_unfolding,[],[f1557,f2373]) ).
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/benchmark/theBenchmark.p',cls_List_Odistinct__append_2) ).
fof(f22357,plain,
spl0_2049,
inference(avatar_split_clause,[],[f3084,f22355]) ).
fof(f22355,plain,
( spl0_2049
<=> ! [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__mult(c_Numeral_OMin,X11),X1),X48,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2049])]) ).
fof(f3084,plain,
! [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__mult(c_Numeral_OMin,X11),X1),X48,X1) ),
inference(definition_unfolding,[],[f2165,f2129]) ).
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/benchmark/theBenchmark.p',cls_Numeral_Ominus__number__of__mult_0) ).
fof(f22330,plain,
spl0_2048,
inference(avatar_split_clause,[],[f3055,f22328]) ).
fof(f22328,plain,
( spl0_2048
<=> ! [X41,X0,X23,X25] : c_append(c_List_Orev(c_List_Olist_OCons(X0,X23,X41),X41),X25,X41) = c_append(c_List_Orev(X23,X41),c_List_Olist_OCons(X0,X25,X41),X41) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2048])]) ).
fof(f3055,plain,
! [X41,X0,X25,X23] : c_append(c_List_Orev(c_List_Olist_OCons(X0,X23,X41),X41),X25,X41) = c_append(c_List_Orev(X23,X41),c_List_Olist_OCons(X0,X25,X41),X41),
inference(definition_unfolding,[],[f1587,f1585,f1585]) ).
fof(f1585,axiom,
! [X0,X1,X23] : c_List_Oitrev(X23,X0,X1) = c_append(c_List_Orev(X23,X1),X0,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oitrev_0) ).
fof(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/benchmark/theBenchmark.p',cls_List_Oitrev_Osimps__2_0) ).
fof(f22326,plain,
spl0_2047,
inference(avatar_split_clause,[],[f2858,f22324]) ).
fof(f22324,plain,
( spl0_2047
<=> ! [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_2047])]) ).
fof(f2858,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/benchmark/theBenchmark.p',cls_Message_Oanalz__insert__Key_0) ).
fof(f22322,plain,
spl0_2046,
inference(avatar_split_clause,[],[f2846,f22320]) ).
fof(f22320,plain,
( spl0_2046
<=> ! [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_2046])]) ).
fof(f2846,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/benchmark/theBenchmark.p',cls_Message_Oanalz_ODecrypt__dest_0) ).
fof(f22318,plain,
spl0_2045,
inference(avatar_split_clause,[],[f2797,f22316]) ).
fof(f22316,plain,
( spl0_2045
<=> ! [X102,X86,X12] :
( ~ c_in(X12,c_Event_Obad,tc_Message_Oagent)
| c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Olist_OCons(c_Event_Oevent_ONotes(X12,X86),X102,tc_Event_Oevent)) = c_insert(X86,c_Event_Oknows(c_Message_Oagent_OSpy,X102),tc_Message_Omsg) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2045])]) ).
fof(f2797,axiom,
! [X86,X12,X102] :
( ~ c_in(X12,c_Event_Obad,tc_Message_Oagent)
| c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Olist_OCons(c_Event_Oevent_ONotes(X12,X86),X102,tc_Event_Oevent)) = c_insert(X86,c_Event_Oknows(c_Message_Oagent_OSpy,X102),tc_Message_Omsg) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Event_Oknows__Spy__Notes_0) ).
fof(f22314,plain,
spl0_2044,
inference(avatar_split_clause,[],[f2122,f22312]) ).
fof(f22312,plain,
( spl0_2044
<=> ! [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_2044])]) ).
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/benchmark/theBenchmark.p',cls_Numeral_Obin__arith__extra__simps__6_1) ).
fof(f22310,plain,
spl0_2043,
inference(avatar_split_clause,[],[f1864,f22308]) ).
fof(f22308,plain,
( spl0_2043
<=> ! [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_2043])]) ).
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/benchmark/theBenchmark.p',cls_NatBin_Omult__nat__number__of_1) ).
fof(f22306,plain,
spl0_2042,
inference(avatar_split_clause,[],[f1800,f22304]) ).
fof(f22304,plain,
( spl0_2042
<=> ! [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_2042])]) ).
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/benchmark/theBenchmark.p',cls_NatArith_Odiff__diff__right_0) ).
fof(f22302,plain,
spl0_2041,
inference(avatar_split_clause,[],[f1796,f22300]) ).
fof(f22300,plain,
( spl0_2041
<=> ! [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_2041])]) ).
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/benchmark/theBenchmark.p',cls_NatArith_Oadd__diff__assoc_0) ).
fof(f22298,plain,
spl0_2040,
inference(avatar_split_clause,[],[f1795,f22296]) ).
fof(f22296,plain,
( spl0_2040
<=> ! [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_2040])]) ).
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/benchmark/theBenchmark.p',cls_NatArith_Oadd__diff__assoc2_0) ).
fof(f22293,plain,
spl0_2039,
inference(avatar_split_clause,[],[f1726,f22291]) ).
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/benchmark/theBenchmark.p',cls_List_Orev__eq__Cons__iff_0) ).
fof(f22266,plain,
spl0_2038,
inference(avatar_split_clause,[],[f1714,f22264]) ).
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/benchmark/theBenchmark.p',cls_List_Oremdups_Osimps__2_1) ).
fof(f22262,plain,
spl0_2037,
inference(avatar_split_clause,[],[f1617,f22260]) ).
fof(f22260,plain,
( spl0_2037
<=> ! [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_2037])]) ).
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/benchmark/theBenchmark.p',cls_List_Olexord__Nil__left_1) ).
fof(f22257,plain,
spl0_2036,
inference(avatar_split_clause,[],[f1453,f22255]) ).
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/benchmark/theBenchmark.p',cls_IntDiv_OnegDivAlg__minus1_0) ).
fof(f22253,plain,
spl0_2035,
inference(avatar_split_clause,[],[f1219,f22251]) ).
fof(f22251,plain,
( spl0_2035
<=> ! [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_2035])]) ).
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/benchmark/theBenchmark.p',cls_Divides_Odiv__mult__mult2_0) ).
fof(f22249,plain,
spl0_2034,
inference(avatar_split_clause,[],[f1218,f22247]) ).
fof(f22247,plain,
( spl0_2034
<=> ! [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_2034])]) ).
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/benchmark/theBenchmark.p',cls_Divides_Odiv__mult__mult1_0) ).
fof(f22245,plain,
spl0_2033,
inference(avatar_split_clause,[],[f57,f22243]) ).
fof(f22243,plain,
( spl0_2033
<=> ! [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_2033])]) ).
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/benchmark/theBenchmark.p',cls_List_Olistrel__Nil2_0) ).
fof(f22241,plain,
spl0_2032,
inference(avatar_split_clause,[],[f56,f22239]) ).
fof(f22239,plain,
( spl0_2032
<=> ! [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_2032])]) ).
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/benchmark/theBenchmark.p',cls_List_Olistrel__Nil1_0) ).
fof(f22197,plain,
( spl0_2031
| spl0_2
| ~ spl0_2004 ),
inference(avatar_split_clause,[],[f21746,f20836,f3417,f22195]) ).
fof(f3417,plain,
( spl0_2
<=> c_in(v_B,c_Event_Obad,tc_Message_Oagent) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).
fof(f21746,plain,
( ! [X0] : c_minus(c_Event_Obad,X0,tc_set(tc_Message_Oagent)) = c_minus(c_Event_Obad,c_insert(v_B,X0,tc_Message_Oagent),tc_set(tc_Message_Oagent))
| spl0_2
| ~ spl0_2004 ),
inference(resolution,[],[f20837,f3419]) ).
fof(f3419,plain,
( ~ c_in(v_B,c_Event_Obad,tc_Message_Oagent)
| spl0_2 ),
inference(avatar_component_clause,[],[f3417]) ).
fof(f22000,plain,
( spl0_2030
| spl0_1
| ~ spl0_2004 ),
inference(avatar_split_clause,[],[f21745,f20836,f3412,f21998]) ).
fof(f3412,plain,
( spl0_1
<=> c_in(v_A,c_Event_Obad,tc_Message_Oagent) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).
fof(f21745,plain,
( ! [X0] : c_minus(c_Event_Obad,X0,tc_set(tc_Message_Oagent)) = c_minus(c_Event_Obad,c_insert(v_A,X0,tc_Message_Oagent),tc_set(tc_Message_Oagent))
| spl0_1
| ~ spl0_2004 ),
inference(resolution,[],[f20837,f3414]) ).
fof(f3414,plain,
( ~ c_in(v_A,c_Event_Obad,tc_Message_Oagent)
| spl0_1 ),
inference(avatar_component_clause,[],[f3412]) ).
fof(f21507,plain,
( spl0_2029
| ~ spl0_1757
| ~ spl0_1910 ),
inference(avatar_split_clause,[],[f19265,f19214,f15956,f21504]) ).
fof(f21504,plain,
( spl0_2029
<=> c_List_Oremdups(v_evso,tc_Event_Oevent) = c_List_Osublist(c_List_Oremdups(v_evso,tc_Event_Oevent),c_SetInterval_OlessThan(c_plus(c_1,c_Nat_Osize(v_evso,tc_List_Olist(tc_Event_Oevent)),tc_nat),tc_nat),tc_Event_Oevent) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2029])]) ).
fof(f15956,plain,
( spl0_1757
<=> ! [X21,X1,X3] :
( c_List_Osublist(X3,c_SetInterval_OlessThan(X21,tc_nat),X1) = X3
| ~ c_lessequals(c_Nat_Osize(X3,tc_List_Olist(X1)),X21,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1757])]) ).
fof(f19214,plain,
( spl0_1910
<=> c_lessequals(c_Nat_Osize(c_List_Oremdups(v_evso,tc_Event_Oevent),tc_List_Olist(tc_Event_Oevent)),c_plus(c_1,c_Nat_Osize(v_evso,tc_List_Olist(tc_Event_Oevent)),tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1910])]) ).
fof(f19265,plain,
( c_List_Oremdups(v_evso,tc_Event_Oevent) = c_List_Osublist(c_List_Oremdups(v_evso,tc_Event_Oevent),c_SetInterval_OlessThan(c_plus(c_1,c_Nat_Osize(v_evso,tc_List_Olist(tc_Event_Oevent)),tc_nat),tc_nat),tc_Event_Oevent)
| ~ spl0_1757
| ~ spl0_1910 ),
inference(resolution,[],[f19216,f15957]) ).
fof(f15957,plain,
( ! [X21,X3,X1] :
( ~ c_lessequals(c_Nat_Osize(X3,tc_List_Olist(X1)),X21,tc_nat)
| c_List_Osublist(X3,c_SetInterval_OlessThan(X21,tc_nat),X1) = X3 )
| ~ spl0_1757 ),
inference(avatar_component_clause,[],[f15956]) ).
fof(f19216,plain,
( c_lessequals(c_Nat_Osize(c_List_Oremdups(v_evso,tc_Event_Oevent),tc_List_Olist(tc_Event_Oevent)),c_plus(c_1,c_Nat_Osize(v_evso,tc_List_Olist(tc_Event_Oevent)),tc_nat),tc_nat)
| ~ spl0_1910 ),
inference(avatar_component_clause,[],[f19214]) ).
fof(f21281,plain,
( spl0_2028
| ~ spl0_781
| ~ spl0_786
| ~ spl0_1848
| ~ spl0_1986 ),
inference(avatar_split_clause,[],[f20766,f20762,f17598,f7484,f7464,f21279]) ).
fof(f21279,plain,
( spl0_2028
<=> ! [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_2028])]) ).
fof(f20762,plain,
( spl0_1986
<=> ! [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_1986])]) ).
fof(f20766,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_781
| ~ spl0_786
| ~ spl0_1848
| ~ spl0_1986 ),
inference(forward_demodulation,[],[f20765,f17626]) ).
fof(f20765,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_781
| ~ spl0_786
| ~ spl0_1848
| ~ spl0_1986 ),
inference(forward_demodulation,[],[f20763,f17626]) ).
fof(f20763,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_1986 ),
inference(avatar_component_clause,[],[f20762]) ).
fof(f21277,plain,
( spl0_2027
| ~ spl0_781
| ~ spl0_786
| ~ spl0_1848
| ~ spl0_1985 ),
inference(avatar_split_clause,[],[f20760,f20756,f17598,f7484,f7464,f21275]) ).
fof(f21275,plain,
( spl0_2027
<=> ! [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_2027])]) ).
fof(f20756,plain,
( spl0_1985
<=> ! [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_1985])]) ).
fof(f20760,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_781
| ~ spl0_786
| ~ spl0_1848
| ~ spl0_1985 ),
inference(forward_demodulation,[],[f20759,f17626]) ).
fof(f20759,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_781
| ~ spl0_786
| ~ spl0_1848
| ~ spl0_1985 ),
inference(forward_demodulation,[],[f20757,f17626]) ).
fof(f20757,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_1985 ),
inference(avatar_component_clause,[],[f20756]) ).
fof(f20941,plain,
( spl0_2026
| ~ spl0_646
| ~ spl0_687
| ~ spl0_1372
| ~ spl0_1461
| ~ spl0_2025 ),
inference(avatar_split_clause,[],[f20937,f20933,f11313,f10914,f7046,f6101,f20939]) ).
fof(f20933,plain,
( spl0_2025
<=> ! [X21] : c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),tc_nat),tc_nat) = 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_2025])]) ).
fof(f20937,plain,
( ! [X21] : c_plus(X21,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat) = c_plus(c_1,c_plus(c_1,X21,tc_nat),tc_nat)
| ~ spl0_646
| ~ spl0_687
| ~ spl0_1372
| ~ spl0_1461
| ~ spl0_2025 ),
inference(forward_demodulation,[],[f20936,f12280]) ).
fof(f20936,plain,
( ! [X21] : c_plus(X21,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat) = c_Finite__Set_Ocard(c_SetInterval_OatMost(c_plus(c_1,X21,tc_nat),tc_nat),tc_nat)
| ~ spl0_646
| ~ spl0_687
| ~ spl0_1372
| ~ spl0_1461
| ~ spl0_2025 ),
inference(forward_demodulation,[],[f20934,f12280]) ).
fof(f20934,plain,
( ! [X21] : c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),tc_nat),tc_nat) = c_plus(X21,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat)
| ~ spl0_2025 ),
inference(avatar_component_clause,[],[f20933]) ).
fof(f20935,plain,
spl0_2025,
inference(avatar_split_clause,[],[f3242,f20933]) ).
fof(f20931,plain,
spl0_2024,
inference(avatar_split_clause,[],[f3165,f20929]) ).
fof(f20929,plain,
( spl0_2024
<=> ! [X4,X13,X12,X1] :
( ~ c_in(X4,X13,X1)
| ~ c_in(X4,X12,X1)
| c_in(X4,c_Relation_OImage(c_Relation_Odiag(X12,X1),X13,X1,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2024])]) ).
fof(f3165,plain,
! [X1,X4,X12,X13] :
( ~ c_in(X4,X13,X1)
| ~ c_in(X4,X12,X1)
| c_in(X4,c_Relation_OImage(c_Relation_Odiag(X12,X1),X13,X1,X1),X1) ),
inference(definition_unfolding,[],[f2608,f2373]) ).
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/benchmark/theBenchmark.p',cls_Set_OInt__iff_2) ).
fof(f20927,plain,
spl0_2023,
inference(avatar_split_clause,[],[f3160,f20925]) ).
fof(f20925,plain,
( spl0_2023
<=> ! [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__mult(c_Numeral_OMin,X3)),X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2023])]) ).
fof(f3160,plain,
! [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__mult(c_Numeral_OMin,X3)),X1),X1) ),
inference(definition_unfolding,[],[f2142,f2129]) ).
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/benchmark/theBenchmark.p',cls_Numeral_Obin__rel__simps__1_1) ).
fof(f20923,plain,
spl0_2022,
inference(avatar_split_clause,[],[f3159,f20921]) ).
fof(f20921,plain,
( spl0_2022
<=> ! [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__mult(c_Numeral_OMin,X3)),X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2022])]) ).
fof(f3159,plain,
! [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__mult(c_Numeral_OMin,X3)),X1),X1) ),
inference(definition_unfolding,[],[f2141,f2129]) ).
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/benchmark/theBenchmark.p',cls_Numeral_Obin__rel__simps__1_0) ).
fof(f20919,plain,
spl0_2021,
inference(avatar_split_clause,[],[f3105,f20917]) ).
fof(f20917,plain,
( spl0_2021
<=> ! [X43,X23,X21,X1] :
( ~ c_less(X43,X21,tc_nat)
| c_List_Onth(X23,X43,X1) = c_List_Onth(c_List_Osublist(X23,c_SetInterval_OlessThan(X21,tc_nat),X1),X43,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2021])]) ).
fof(f3105,plain,
! [X21,X1,X23,X43] :
( ~ c_less(X43,X21,tc_nat)
| c_List_Onth(X23,X43,X1) = c_List_Onth(c_List_Osublist(X23,c_SetInterval_OlessThan(X21,tc_nat),X1),X43,X1) ),
inference(definition_unfolding,[],[f1703,f1766]) ).
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/benchmark/theBenchmark.p',cls_List_Onth__take_0) ).
fof(f20902,plain,
spl0_2020,
inference(avatar_split_clause,[],[f3081,f20900]) ).
fof(f20900,plain,
( spl0_2020
<=> ! [X11,X1,X47] :
( ~ class_Numeral_Onumber__ring(X1)
| c_minus(c_Numeral_Onumber__of(X47,X1),c_Numeral_Onumber__of(X11,X1),X1) = c_Numeral_Onumber__of(c_Numeral_Obin__add(X47,c_Numeral_Obin__mult(c_Numeral_OMin,X11)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2020])]) ).
fof(f3081,plain,
! [X11,X1,X47] :
( ~ class_Numeral_Onumber__ring(X1)
| c_minus(c_Numeral_Onumber__of(X47,X1),c_Numeral_Onumber__of(X11,X1),X1) = c_Numeral_Onumber__of(c_Numeral_Obin__add(X47,c_Numeral_Obin__mult(c_Numeral_OMin,X11)),X1) ),
inference(definition_unfolding,[],[f2120,f2129]) ).
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/benchmark/theBenchmark.p',cls_Numeral_Obin__arith__extra__simps__5_0) ).
fof(f20898,plain,
spl0_2019,
inference(avatar_split_clause,[],[f2940,f20896]) ).
fof(f20896,plain,
( spl0_2019
<=> ! [X102,X12] :
( ~ c_in(X12,c_Event_Obad,tc_Message_Oagent)
| ~ c_in(X102,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
| c_in(c_Message_Omsg_OKey(c_Public_OshrK(X12)),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,X102)),tc_Message_Omsg) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2019])]) ).
fof(f2940,axiom,
! [X12,X102] :
( ~ c_in(X12,c_Event_Obad,tc_Message_Oagent)
| ~ c_in(X102,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
| c_in(c_Message_Omsg_OKey(c_Public_OshrK(X12)),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,X102)),tc_Message_Omsg) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Yahalom_OSpy__see__shrK_1) ).
fof(f20894,plain,
spl0_2018,
inference(avatar_split_clause,[],[f2939,f20892]) ).
fof(f20892,plain,
( spl0_2018
<=> ! [X102,X12] :
( c_in(X12,c_Event_Obad,tc_Message_Oagent)
| ~ c_in(X102,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
| ~ c_in(c_Message_Omsg_OKey(c_Public_OshrK(X12)),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,X102)),tc_Message_Omsg) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2018])]) ).
fof(f2939,axiom,
! [X12,X102] :
( c_in(X12,c_Event_Obad,tc_Message_Oagent)
| ~ c_in(X102,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
| ~ c_in(c_Message_Omsg_OKey(c_Public_OshrK(X12)),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,X102)),tc_Message_Omsg) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Yahalom_OSpy__see__shrK_0) ).
fof(f20890,plain,
spl0_2017,
inference(avatar_split_clause,[],[f2938,f20888]) ).
fof(f20888,plain,
( spl0_2017
<=> ! [X102,X12] :
( ~ c_in(X12,c_Event_Obad,tc_Message_Oagent)
| ~ c_in(X102,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
| c_in(c_Message_Omsg_OKey(c_Public_OshrK(X12)),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,X102)),tc_Message_Omsg) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2017])]) ).
fof(f2938,axiom,
! [X12,X102] :
( ~ c_in(X12,c_Event_Obad,tc_Message_Oagent)
| ~ c_in(X102,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
| c_in(c_Message_Omsg_OKey(c_Public_OshrK(X12)),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,X102)),tc_Message_Omsg) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Yahalom_OSpy__analz__shrK_1) ).
fof(f20886,plain,
spl0_2016,
inference(avatar_split_clause,[],[f2937,f20884]) ).
fof(f20884,plain,
( spl0_2016
<=> ! [X102,X12] :
( c_in(X12,c_Event_Obad,tc_Message_Oagent)
| ~ c_in(X102,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
| ~ c_in(c_Message_Omsg_OKey(c_Public_OshrK(X12)),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,X102)),tc_Message_Omsg) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2016])]) ).
fof(f2937,axiom,
! [X12,X102] :
( c_in(X12,c_Event_Obad,tc_Message_Oagent)
| ~ c_in(X102,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
| ~ c_in(c_Message_Omsg_OKey(c_Public_OshrK(X12)),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,X102)),tc_Message_Omsg) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Yahalom_OSpy__analz__shrK_0) ).
fof(f20882,plain,
spl0_2015,
inference(avatar_split_clause,[],[f2873,f20880]) ).
fof(f20880,plain,
( spl0_2015
<=> ! [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_2015])]) ).
fof(f2873,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/benchmark/theBenchmark.p',cls_Message_Oparts__insert__Crypt_0) ).
fof(f20878,plain,
spl0_2014,
inference(avatar_split_clause,[],[f2867,f20876]) ).
fof(f20876,plain,
( spl0_2014
<=> ! [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_2014])]) ).
fof(f2867,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/benchmark/theBenchmark.p',cls_Message_Oin__parts__UnE_0) ).
fof(f20874,plain,
spl0_2013,
inference(avatar_split_clause,[],[f2839,f20872]) ).
fof(f20872,plain,
( spl0_2013
<=> ! [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_2013])]) ).
fof(f2839,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/benchmark/theBenchmark.p',cls_Message_OMPair__synth_1) ).
fof(f20870,plain,
spl0_2012,
inference(avatar_split_clause,[],[f2838,f20868]) ).
fof(f20868,plain,
( spl0_2012
<=> ! [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_2012])]) ).
fof(f2838,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/benchmark/theBenchmark.p',cls_Message_OMPair__synth_0) ).
fof(f20866,plain,
spl0_2011,
inference(avatar_split_clause,[],[f2805,f20864]) ).
fof(f20864,plain,
( spl0_2011
<=> ! [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_2011])]) ).
fof(f2805,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/benchmark/theBenchmark.p',cls_Message_OCrypt__synth__eq_0) ).
fof(f20862,plain,
( spl0_2010
| ~ spl0_1706
| ~ spl0_1879 ),
inference(avatar_split_clause,[],[f19164,f19072,f15699,f20860]) ).
fof(f20860,plain,
( spl0_2010
<=> ! [X2,X0,X1] : c_Event_Oknows(c_Message_Oagent_OSpy,c_append(X1,X2,tc_Event_Oevent)) = c_Event_Oknows(c_Message_Oagent_OSpy,c_append(c_List_Olist_OCons(c_Event_Oevent_ONotes(v_B,X0),X1,tc_Event_Oevent),X2,tc_Event_Oevent)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2010])]) ).
fof(f15699,plain,
( spl0_1706
<=> ! [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_1706])]) ).
fof(f19072,plain,
( spl0_1879
<=> ! [X0,X1] : c_Event_Oknows(c_Message_Oagent_OSpy,X0) = c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Olist_OCons(c_Event_Oevent_ONotes(v_B,X1),X0,tc_Event_Oevent)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1879])]) ).
fof(f19164,plain,
( ! [X2,X0,X1] : c_Event_Oknows(c_Message_Oagent_OSpy,c_append(X1,X2,tc_Event_Oevent)) = c_Event_Oknows(c_Message_Oagent_OSpy,c_append(c_List_Olist_OCons(c_Event_Oevent_ONotes(v_B,X0),X1,tc_Event_Oevent),X2,tc_Event_Oevent))
| ~ spl0_1706
| ~ spl0_1879 ),
inference(superposition,[],[f19073,f15700]) ).
fof(f15700,plain,
( ! [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)
| ~ spl0_1706 ),
inference(avatar_component_clause,[],[f15699]) ).
fof(f19073,plain,
( ! [X0,X1] : c_Event_Oknows(c_Message_Oagent_OSpy,X0) = c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Olist_OCons(c_Event_Oevent_ONotes(v_B,X1),X0,tc_Event_Oevent))
| ~ spl0_1879 ),
inference(avatar_component_clause,[],[f19072]) ).
fof(f20858,plain,
spl0_2009,
inference(avatar_split_clause,[],[f2804,f20856]) ).
fof(f20856,plain,
( spl0_2009
<=> ! [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_2009])]) ).
fof(f2804,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/benchmark/theBenchmark.p',cls_Message_OCrypt__synth_1) ).
fof(f20854,plain,
spl0_2008,
inference(avatar_split_clause,[],[f2802,f20852]) ).
fof(f20852,plain,
( spl0_2008
<=> ! [X102,X13,X12,X86] : c_union(c_Message_Oparts(c_insert(X86,c_emptyset,tc_Message_Omsg)),c_Event_Oused(X102),tc_Message_Omsg) = c_Event_Oused(c_List_Olist_OCons(c_Event_Oevent_OSays(X12,X13,X86),X102,tc_Event_Oevent)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2008])]) ).
fof(f2802,axiom,
! [X86,X102,X12,X13] : c_union(c_Message_Oparts(c_insert(X86,c_emptyset,tc_Message_Omsg)),c_Event_Oused(X102),tc_Message_Omsg) = c_Event_Oused(c_List_Olist_OCons(c_Event_Oevent_OSays(X12,X13,X86),X102,tc_Event_Oevent)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Event_Oused__Says_0) ).
fof(f20850,plain,
spl0_2007,
inference(avatar_split_clause,[],[f2791,f20848]) ).
fof(f20848,plain,
( spl0_2007
<=> ! [X91,X88] :
( c_in(X91,c_Message_OkeysFor(X88),tc_nat)
| ~ c_in(X91,c_Message_OkeysFor(c_Message_Osynth(X88)),tc_nat)
| c_in(c_Message_Omsg_OKey(v_sko__uhi(X88,X91)),X88,tc_Message_Omsg) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2007])]) ).
fof(f2791,axiom,
! [X91,X88] :
( c_in(X91,c_Message_OkeysFor(X88),tc_nat)
| ~ c_in(X91,c_Message_OkeysFor(c_Message_Osynth(X88)),tc_nat)
| c_in(c_Message_Omsg_OKey(v_sko__uhi(X88,X91)),X88,tc_Message_Omsg) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Event_OkeysFor__synth_H_0) ).
fof(f20846,plain,
spl0_2006,
inference(avatar_split_clause,[],[f2674,f20844]) ).
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/benchmark/theBenchmark.p',cls_Set_Oinsert__Diff1_0) ).
fof(f20842,plain,
spl0_2005,
inference(avatar_split_clause,[],[f2647,f20840]) ).
fof(f20840,plain,
( spl0_2005
<=> ! [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_2005])]) ).
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/benchmark/theBenchmark.p',cls_Set_OUn__subset__iff_2) ).
fof(f20838,plain,
spl0_2004,
inference(avatar_split_clause,[],[f2597,f20836]) ).
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/benchmark/theBenchmark.p',cls_Set_ODiff__insert0_0) ).
fof(f20834,plain,
spl0_2003,
inference(avatar_split_clause,[],[f2337,f20832]) ).
fof(f20832,plain,
( spl0_2003
<=> ! [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_2003])]) ).
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/benchmark/theBenchmark.p',cls_Parity_Ozero__less__power__nat__eq__number__of_0) ).
fof(f20830,plain,
spl0_2002,
inference(avatar_split_clause,[],[f2329,f20828]) ).
fof(f20828,plain,
( spl0_2002
<=> ! [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_2002])]) ).
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/benchmark/theBenchmark.p',cls_Parity_Ozero__le__power__eq__number__of_1) ).
fof(f20826,plain,
spl0_2001,
inference(avatar_split_clause,[],[f2326,f20824]) ).
fof(f20824,plain,
( spl0_2001
<=> ! [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_2001])]) ).
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/benchmark/theBenchmark.p',cls_Parity_Opower__minus__even_0) ).
fof(f20822,plain,
spl0_2000,
inference(avatar_split_clause,[],[f2323,f20820]) ).
fof(f20820,plain,
( spl0_2000
<=> ! [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_2000])]) ).
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/benchmark/theBenchmark.p',cls_Parity_Opower__less__zero__eq__number__of_0) ).
fof(f20818,plain,
( spl0_1999
| ~ spl0_1706
| ~ spl0_1878 ),
inference(avatar_split_clause,[],[f19115,f18862,f15699,f20816]) ).
fof(f20816,plain,
( spl0_1999
<=> ! [X2,X0,X1] : c_Event_Oknows(c_Message_Oagent_OSpy,c_append(X1,X2,tc_Event_Oevent)) = c_Event_Oknows(c_Message_Oagent_OSpy,c_append(c_List_Olist_OCons(c_Event_Oevent_ONotes(v_A,X0),X1,tc_Event_Oevent),X2,tc_Event_Oevent)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1999])]) ).
fof(f18862,plain,
( spl0_1878
<=> ! [X0,X1] : c_Event_Oknows(c_Message_Oagent_OSpy,X0) = c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Olist_OCons(c_Event_Oevent_ONotes(v_A,X1),X0,tc_Event_Oevent)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1878])]) ).
fof(f19115,plain,
( ! [X2,X0,X1] : c_Event_Oknows(c_Message_Oagent_OSpy,c_append(X1,X2,tc_Event_Oevent)) = c_Event_Oknows(c_Message_Oagent_OSpy,c_append(c_List_Olist_OCons(c_Event_Oevent_ONotes(v_A,X0),X1,tc_Event_Oevent),X2,tc_Event_Oevent))
| ~ spl0_1706
| ~ spl0_1878 ),
inference(superposition,[],[f18863,f15700]) ).
fof(f18863,plain,
( ! [X0,X1] : c_Event_Oknows(c_Message_Oagent_OSpy,X0) = c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Olist_OCons(c_Event_Oevent_ONotes(v_A,X1),X0,tc_Event_Oevent))
| ~ spl0_1878 ),
inference(avatar_component_clause,[],[f18862]) ).
fof(f20814,plain,
spl0_1998,
inference(avatar_split_clause,[],[f2077,f20812]) ).
fof(f20812,plain,
( spl0_1998
<=> ! [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_1998])]) ).
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/benchmark/theBenchmark.p',cls_Nat_Omult__less__cancel2_2) ).
fof(f20810,plain,
spl0_1997,
inference(avatar_split_clause,[],[f2074,f20808]) ).
fof(f20808,plain,
( spl0_1997
<=> ! [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_1997])]) ).
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/benchmark/theBenchmark.p',cls_Nat_Omult__less__cancel1_2) ).
fof(f20806,plain,
spl0_1996,
inference(avatar_split_clause,[],[f2069,f20804]) ).
fof(f20804,plain,
( spl0_1996
<=> ! [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_1996])]) ).
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/benchmark/theBenchmark.p',cls_Nat_Omult__le__cancel2_0) ).
fof(f20802,plain,
spl0_1995,
inference(avatar_split_clause,[],[f2066,f20800]) ).
fof(f20800,plain,
( spl0_1995
<=> ! [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_1995])]) ).
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/benchmark/theBenchmark.p',cls_Nat_Omult__le__cancel1_0) ).
fof(f20798,plain,
spl0_1994,
inference(avatar_split_clause,[],[f1929,f20796]) ).
fof(f20796,plain,
( spl0_1994
<=> ! [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_1994])]) ).
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/benchmark/theBenchmark.p',cls_NatSimprocs_Oequation__minus__iff__number__of_0) ).
fof(f20794,plain,
spl0_1993,
inference(avatar_split_clause,[],[f1830,f20792]) ).
fof(f20792,plain,
( spl0_1993
<=> ! [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_1993])]) ).
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/benchmark/theBenchmark.p',cls_NatBin_Odvd__eq__mod__eq__0__number__of_1) ).
fof(f20790,plain,
spl0_1992,
inference(avatar_split_clause,[],[f1829,f20788]) ).
fof(f20788,plain,
( spl0_1992
<=> ! [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_1992])]) ).
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/benchmark/theBenchmark.p',cls_NatBin_Odvd__eq__mod__eq__0__number__of_0) ).
fof(f20786,plain,
spl0_1991,
inference(avatar_split_clause,[],[f1721,f20784]) ).
fof(f20784,plain,
( spl0_1991
<=> ! [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_1991])]) ).
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/benchmark/theBenchmark.p',cls_List_Oremove1_Osimps__2_1) ).
fof(f20782,plain,
spl0_1990,
inference(avatar_split_clause,[],[f1704,f20780]) ).
fof(f20780,plain,
( spl0_1990
<=> ! [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_1990])]) ).
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/benchmark/theBenchmark.p',cls_List_Onth__upt_0) ).
fof(f20778,plain,
spl0_1989,
inference(avatar_split_clause,[],[f1697,f20776]) ).
fof(f20776,plain,
( spl0_1989
<=> ! [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_1989])]) ).
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/benchmark/theBenchmark.p',cls_List_Onth__append__length__plus_0) ).
fof(f20774,plain,
spl0_1988,
inference(avatar_split_clause,[],[f1630,f20772]) ).
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/benchmark/theBenchmark.p',cls_List_Olist__inter_Osimps__2_1) ).
fof(f20770,plain,
spl0_1987,
inference(avatar_split_clause,[],[f1599,f20768]) ).
fof(f20768,plain,
( spl0_1987
<=> ! [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_1987])]) ).
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/benchmark/theBenchmark.p',cls_List_Olength__append_0) ).
fof(f20764,plain,
spl0_1986,
inference(avatar_split_clause,[],[f1517,f20762]) ).
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/benchmark/theBenchmark.p',cls_List_Oappend1__eq__conv_1) ).
fof(f20758,plain,
spl0_1985,
inference(avatar_split_clause,[],[f1516,f20756]) ).
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/benchmark/theBenchmark.p',cls_List_Oappend1__eq__conv_0) ).
fof(f20754,plain,
spl0_1984,
inference(avatar_split_clause,[],[f1481,f20752]) ).
fof(f20752,plain,
( spl0_1984
<=> ! [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_1984])]) ).
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/benchmark/theBenchmark.p',cls_IntDiv_Ozdvd__iff__zmod__eq__0__number__of_1) ).
fof(f20750,plain,
spl0_1983,
inference(avatar_split_clause,[],[f1480,f20748]) ).
fof(f20748,plain,
( spl0_1983
<=> ! [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_1983])]) ).
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/benchmark/theBenchmark.p',cls_IntDiv_Ozdvd__iff__zmod__eq__0__number__of_0) ).
fof(f20746,plain,
spl0_1982,
inference(avatar_split_clause,[],[f1473,f20744]) ).
fof(f20744,plain,
( spl0_1982
<=> ! [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_1982])]) ).
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/benchmark/theBenchmark.p',cls_IntDiv_Ozdiv__zadd__self2_0) ).
fof(f20742,plain,
spl0_1981,
inference(avatar_split_clause,[],[f1472,f20740]) ).
fof(f20740,plain,
( spl0_1981
<=> ! [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_1981])]) ).
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/benchmark/theBenchmark.p',cls_IntDiv_Ozdiv__zadd__self1_0) ).
fof(f20738,plain,
spl0_1980,
inference(avatar_split_clause,[],[f1292,f20736]) ).
fof(f20736,plain,
( spl0_1980
<=> ! [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_1980])]) ).
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/benchmark/theBenchmark.p',cls_Finite__Set_Omin__max_Obelow__inf__sup__Inf__Sup_OInf__le__Sup_0) ).
fof(f20734,plain,
spl0_1979,
inference(avatar_split_clause,[],[f1288,f20732]) ).
fof(f20732,plain,
( spl0_1979
<=> ! [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_1979])]) ).
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/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Un_2) ).
fof(f20450,plain,
( spl0_1978
| ~ spl0_1752
| ~ spl0_1976 ),
inference(avatar_split_clause,[],[f20279,f20010,f15905,f20447]) ).
fof(f20447,plain,
( spl0_1978
<=> c_0 = c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(c_Nat_Osize(v_evso,tc_List_Olist(tc_Event_Oevent)),c_Nat_Osize(c_List_Oremdups(v_evso,tc_Event_Oevent),tc_List_Olist(tc_Event_Oevent)),tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1978])]) ).
fof(f15905,plain,
( spl0_1752
<=> ! [X14,X26] : c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(X26,X14,tc_nat),tc_nat) = c_minus(X14,c_plus(c_1,X26,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1752])]) ).
fof(f20010,plain,
( spl0_1976
<=> c_0 = c_minus(c_Nat_Osize(c_List_Oremdups(v_evso,tc_Event_Oevent),tc_List_Olist(tc_Event_Oevent)),c_plus(c_1,c_Nat_Osize(v_evso,tc_List_Olist(tc_Event_Oevent)),tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1976])]) ).
fof(f20279,plain,
( c_0 = c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(c_Nat_Osize(v_evso,tc_List_Olist(tc_Event_Oevent)),c_Nat_Osize(c_List_Oremdups(v_evso,tc_Event_Oevent),tc_List_Olist(tc_Event_Oevent)),tc_nat),tc_nat)
| ~ spl0_1752
| ~ spl0_1976 ),
inference(superposition,[],[f20012,f15906]) ).
fof(f15906,plain,
( ! [X26,X14] : c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(X26,X14,tc_nat),tc_nat) = c_minus(X14,c_plus(c_1,X26,tc_nat),tc_nat)
| ~ spl0_1752 ),
inference(avatar_component_clause,[],[f15905]) ).
fof(f20012,plain,
( c_0 = c_minus(c_Nat_Osize(c_List_Oremdups(v_evso,tc_Event_Oevent),tc_List_Olist(tc_Event_Oevent)),c_plus(c_1,c_Nat_Osize(v_evso,tc_List_Olist(tc_Event_Oevent)),tc_nat),tc_nat)
| ~ spl0_1976 ),
inference(avatar_component_clause,[],[f20010]) ).
fof(f20177,plain,
( spl0_1977
| ~ spl0_1620
| ~ spl0_1910 ),
inference(avatar_split_clause,[],[f19266,f19214,f14295,f20175]) ).
fof(f20175,plain,
( spl0_1977
<=> ! [X0] : c_List_Oremdups(v_evso,tc_Event_Oevent) = c_List_Olist__update(c_List_Oremdups(v_evso,tc_Event_Oevent),c_plus(c_1,c_Nat_Osize(v_evso,tc_List_Olist(tc_Event_Oevent)),tc_nat),X0,tc_Event_Oevent) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1977])]) ).
fof(f14295,plain,
( spl0_1620
<=> ! [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_1620])]) ).
fof(f19266,plain,
( ! [X0] : c_List_Oremdups(v_evso,tc_Event_Oevent) = c_List_Olist__update(c_List_Oremdups(v_evso,tc_Event_Oevent),c_plus(c_1,c_Nat_Osize(v_evso,tc_List_Olist(tc_Event_Oevent)),tc_nat),X0,tc_Event_Oevent)
| ~ spl0_1620
| ~ spl0_1910 ),
inference(resolution,[],[f19216,f14296]) ).
fof(f14296,plain,
( ! [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 )
| ~ spl0_1620 ),
inference(avatar_component_clause,[],[f14295]) ).
fof(f20013,plain,
( spl0_1976
| ~ spl0_1182
| ~ spl0_1910 ),
inference(avatar_split_clause,[],[f19261,f19214,f9514,f20010]) ).
fof(f9514,plain,
( spl0_1182
<=> ! [X21,X15] :
( ~ c_lessequals(X15,X21,tc_nat)
| c_0 = c_minus(X15,X21,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1182])]) ).
fof(f19261,plain,
( c_0 = c_minus(c_Nat_Osize(c_List_Oremdups(v_evso,tc_Event_Oevent),tc_List_Olist(tc_Event_Oevent)),c_plus(c_1,c_Nat_Osize(v_evso,tc_List_Olist(tc_Event_Oevent)),tc_nat),tc_nat)
| ~ spl0_1182
| ~ spl0_1910 ),
inference(resolution,[],[f19216,f9515]) ).
fof(f9515,plain,
( ! [X21,X15] :
( ~ c_lessequals(X15,X21,tc_nat)
| c_0 = c_minus(X15,X21,tc_nat) )
| ~ spl0_1182 ),
inference(avatar_component_clause,[],[f9514]) ).
fof(f19689,plain,
spl0_1975,
inference(avatar_split_clause,[],[f3405,f19687]) ).
fof(f19687,plain,
( spl0_1975
<=> ! [X1,X3] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,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_1975])]) ).
fof(f3405,plain,
! [X3,X1] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,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,[],[f3192,f2114]) ).
fof(f2114,axiom,
! [X3] : c_Numeral_Obin__add(c_Numeral_OPls,X3) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obin__add__Pls_0) ).
fof(f3192,plain,
! [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__mult(c_Numeral_OMin,X3)),X1),X1) ),
inference(definition_unfolding,[],[f1313,f2129]) ).
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/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__10_1) ).
fof(f19685,plain,
spl0_1974,
inference(avatar_split_clause,[],[f3403,f19683]) ).
fof(f19683,plain,
( spl0_1974
<=> ! [X0,X1] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,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_1974])]) ).
fof(f3403,plain,
! [X0,X1] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,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,[],[f3190,f2114]) ).
fof(f3190,plain,
! [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__mult(c_Numeral_OMin,X0)),X1),X1) ),
inference(definition_unfolding,[],[f1325,f2129]) ).
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/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__16_1) ).
fof(f19681,plain,
spl0_1973,
inference(avatar_split_clause,[],[f3395,f19679]) ).
fof(f19679,plain,
( spl0_1973
<=> ! [X1,X3] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,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_1973])]) ).
fof(f3395,plain,
! [X3,X1] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,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,[],[f3184,f2114]) ).
fof(f3184,plain,
! [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__mult(c_Numeral_OMin,X3)),X1),X1) ),
inference(definition_unfolding,[],[f1312,f2129]) ).
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/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__10_0) ).
fof(f19677,plain,
( spl0_1972
| ~ spl0_1444
| ~ spl0_1879 ),
inference(avatar_split_clause,[],[f19169,f19072,f11245,f19675]) ).
fof(f19675,plain,
( spl0_1972
<=> ! [X2,X0,X1] :
( ~ c_in(X2,c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,X1)),tc_Message_Omsg)
| c_in(X2,c_Event_Oused(c_List_Olist_OCons(c_Event_Oevent_ONotes(v_B,X0),X1,tc_Event_Oevent)),tc_Message_Omsg) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1972])]) ).
fof(f19169,plain,
( ! [X2,X0,X1] :
( ~ c_in(X2,c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,X1)),tc_Message_Omsg)
| c_in(X2,c_Event_Oused(c_List_Olist_OCons(c_Event_Oevent_ONotes(v_B,X0),X1,tc_Event_Oevent)),tc_Message_Omsg) )
| ~ spl0_1444
| ~ spl0_1879 ),
inference(superposition,[],[f11246,f19073]) ).
fof(f19673,plain,
spl0_1971,
inference(avatar_split_clause,[],[f3393,f19671]) ).
fof(f19671,plain,
( spl0_1971
<=> ! [X0,X1] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,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_1971])]) ).
fof(f3393,plain,
! [X0,X1] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,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,[],[f3182,f2114]) ).
fof(f3182,plain,
! [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__mult(c_Numeral_OMin,X0)),X1),X1) ),
inference(definition_unfolding,[],[f1324,f2129]) ).
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/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__16_0) ).
fof(f19669,plain,
spl0_1970,
inference(avatar_split_clause,[],[f3361,f19667]) ).
fof(f19667,plain,
( spl0_1970
<=> ! [X1,X3] :
( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obin__mult(c_Numeral_OMin,X3)),X1),X1)
| ~ class_Numeral_Onumber__ring(X1)
| c_1 = c_Numeral_Onumber__of(X3,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1970])]) ).
fof(f3361,plain,
! [X3,X1] :
( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obin__mult(c_Numeral_OMin,X3)),X1),X1)
| ~ class_Numeral_Onumber__ring(X1)
| c_1 = c_Numeral_Onumber__of(X3,X1) ),
inference(forward_demodulation,[],[f3156,f2156]) ).
fof(f3156,plain,
! [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__mult(c_Numeral_OMin,X3)),X1),X1) ),
inference(definition_unfolding,[],[f1336,f2129]) ).
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/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__7_1) ).
fof(f19660,plain,
( spl0_1969
| ~ spl0_1647
| ~ spl0_1968 ),
inference(avatar_split_clause,[],[f19656,f19653,f14403,f19658]) ).
fof(f19658,plain,
( spl0_1969
<=> ! [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) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1969])]) ).
fof(f19653,plain,
( spl0_1968
<=> ! [X0,X1] :
( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X0,c_Numeral_Obin__mult(c_Numeral_OMin,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_1968])]) ).
fof(f19656,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_1647
| ~ spl0_1968 ),
inference(forward_demodulation,[],[f19654,f14405]) ).
fof(f19654,plain,
( ! [X0,X1] :
( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X0,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_Obin__succ(c_Numeral_OPls))),X1),X1)
| ~ class_Numeral_Onumber__ring(X1)
| c_1 = c_Numeral_Onumber__of(X0,X1) )
| ~ spl0_1968 ),
inference(avatar_component_clause,[],[f19653]) ).
fof(f19655,plain,
spl0_1968,
inference(avatar_split_clause,[],[f3360,f19653]) ).
fof(f3360,plain,
! [X0,X1] :
( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X0,c_Numeral_Obin__mult(c_Numeral_OMin,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,[],[f3155,f2156]) ).
fof(f3155,plain,
! [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__mult(c_Numeral_OMin,c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),X1),X1) ),
inference(definition_unfolding,[],[f1340,f2129]) ).
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/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__9_1) ).
fof(f19651,plain,
spl0_1967,
inference(avatar_split_clause,[],[f3355,f19649]) ).
fof(f19649,plain,
( spl0_1967
<=> ! [X1,X3] :
( c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obin__mult(c_Numeral_OMin,X3)),X1),X1)
| ~ class_Numeral_Onumber__ring(X1)
| c_1 != c_Numeral_Onumber__of(X3,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1967])]) ).
fof(f3355,plain,
! [X3,X1] :
( c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obin__mult(c_Numeral_OMin,X3)),X1),X1)
| ~ class_Numeral_Onumber__ring(X1)
| c_1 != c_Numeral_Onumber__of(X3,X1) ),
inference(forward_demodulation,[],[f3152,f2156]) ).
fof(f3152,plain,
! [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__mult(c_Numeral_OMin,X3)),X1),X1) ),
inference(definition_unfolding,[],[f1335,f2129]) ).
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/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__7_0) ).
fof(f19638,plain,
( spl0_1966
| ~ spl0_1647
| ~ spl0_1965 ),
inference(avatar_split_clause,[],[f19634,f19631,f14403,f19636]) ).
fof(f19636,plain,
( spl0_1966
<=> ! [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) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1966])]) ).
fof(f19631,plain,
( spl0_1965
<=> ! [X0,X1] :
( c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X0,c_Numeral_Obin__mult(c_Numeral_OMin,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_1965])]) ).
fof(f19634,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_1647
| ~ spl0_1965 ),
inference(forward_demodulation,[],[f19632,f14405]) ).
fof(f19632,plain,
( ! [X0,X1] :
( c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X0,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_Obin__succ(c_Numeral_OPls))),X1),X1)
| ~ class_Numeral_Onumber__ring(X1)
| c_1 != c_Numeral_Onumber__of(X0,X1) )
| ~ spl0_1965 ),
inference(avatar_component_clause,[],[f19631]) ).
fof(f19633,plain,
spl0_1965,
inference(avatar_split_clause,[],[f3354,f19631]) ).
fof(f3354,plain,
! [X0,X1] :
( c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X0,c_Numeral_Obin__mult(c_Numeral_OMin,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,[],[f3151,f2156]) ).
fof(f3151,plain,
! [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__mult(c_Numeral_OMin,c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),X1),X1) ),
inference(definition_unfolding,[],[f1339,f2129]) ).
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/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__9_0) ).
fof(f19627,plain,
( spl0_1964
| ~ spl0_1444
| ~ spl0_1878 ),
inference(avatar_split_clause,[],[f19120,f18862,f11245,f19625]) ).
fof(f19625,plain,
( spl0_1964
<=> ! [X2,X0,X1] :
( ~ c_in(X2,c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,X1)),tc_Message_Omsg)
| c_in(X2,c_Event_Oused(c_List_Olist_OCons(c_Event_Oevent_ONotes(v_A,X0),X1,tc_Event_Oevent)),tc_Message_Omsg) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1964])]) ).
fof(f19120,plain,
( ! [X2,X0,X1] :
( ~ c_in(X2,c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,X1)),tc_Message_Omsg)
| c_in(X2,c_Event_Oused(c_List_Olist_OCons(c_Event_Oevent_ONotes(v_A,X0),X1,tc_Event_Oevent)),tc_Message_Omsg) )
| ~ spl0_1444
| ~ spl0_1878 ),
inference(superposition,[],[f11246,f18863]) ).
fof(f19623,plain,
( spl0_1963
| ~ spl0_57
| ~ spl0_1465
| ~ spl0_1962 ),
inference(avatar_split_clause,[],[f19619,f19616,f11329,f3692,f19621]) ).
fof(f19621,plain,
( spl0_1963
<=> ! [X47] :
( c_0 != c_Divides_Oop_Amod(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_plus(c_1,c_1,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_1963])]) ).
fof(f19616,plain,
( spl0_1962
<=> ! [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_1962])]) ).
fof(f19619,plain,
( ! [X47] :
( c_0 != c_Divides_Oop_Amod(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_plus(c_1,c_1,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Parity_Oeven(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint) )
| ~ spl0_57
| ~ spl0_1465
| ~ spl0_1962 ),
inference(forward_demodulation,[],[f19617,f12348]) ).
fof(f19617,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_1962 ),
inference(avatar_component_clause,[],[f19616]) ).
fof(f19618,plain,
spl0_1962,
inference(avatar_split_clause,[],[f3323,f19616]) ).
fof(f3323,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,[],[f3322,f2156]) ).
fof(f3322,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,[],[f3321,f2154]) ).
fof(f3321,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/benchmark/theBenchmark.p',cls_Parity_Oeven_A_Inumber__of_Av_J_A_61_61_Anumber__of_Av_Amod_A2_A_61_A0_1) ).
fof(f19612,plain,
( spl0_1961
| ~ spl0_57
| ~ spl0_1465
| ~ spl0_1960 ),
inference(avatar_split_clause,[],[f19608,f19605,f11329,f3692,f19610]) ).
fof(f19610,plain,
( spl0_1961
<=> ! [X47] :
( c_0 = c_Divides_Oop_Amod(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_plus(c_1,c_1,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_1961])]) ).
fof(f19605,plain,
( spl0_1960
<=> ! [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_1960])]) ).
fof(f19608,plain,
( ! [X47] :
( c_0 = c_Divides_Oop_Amod(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_plus(c_1,c_1,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_Parity_Oeven(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint) )
| ~ spl0_57
| ~ spl0_1465
| ~ spl0_1960 ),
inference(forward_demodulation,[],[f19606,f12348]) ).
fof(f19606,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_1960 ),
inference(avatar_component_clause,[],[f19605]) ).
fof(f19607,plain,
spl0_1960,
inference(avatar_split_clause,[],[f3319,f19605]) ).
fof(f3319,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,[],[f3318,f2156]) ).
fof(f3318,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,[],[f3317,f2154]) ).
fof(f3317,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/benchmark/theBenchmark.p',cls_Parity_Oeven_A_Inumber__of_Av_J_A_61_61_Anumber__of_Av_Amod_A2_A_61_A0_0) ).
fof(f19602,plain,
( spl0_1959
| ~ spl0_1647
| ~ spl0_1958 ),
inference(avatar_split_clause,[],[f19598,f19595,f14403,f19600]) ).
fof(f19600,plain,
( spl0_1959
<=> ! [X1,X47] :
( 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) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1959])]) ).
fof(f19595,plain,
( spl0_1958
<=> ! [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__mult(c_Numeral_OMin,c_Numeral_Obin__succ(c_Numeral_OPls))),X1)
| ~ class_Numeral_Onumber__ring(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1958])]) ).
fof(f19598,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_1647
| ~ spl0_1958 ),
inference(forward_demodulation,[],[f19596,f14405]) ).
fof(f19596,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__mult(c_Numeral_OMin,c_Numeral_Obin__succ(c_Numeral_OPls))),X1)
| ~ class_Numeral_Onumber__ring(X1) )
| ~ spl0_1958 ),
inference(avatar_component_clause,[],[f19595]) ).
fof(f19597,plain,
spl0_1958,
inference(avatar_split_clause,[],[f3288,f19595]) ).
fof(f3288,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__mult(c_Numeral_OMin,c_Numeral_Obin__succ(c_Numeral_OPls))),X1)
| ~ class_Numeral_Onumber__ring(X1) ),
inference(forward_demodulation,[],[f3083,f2156]) ).
fof(f3083,plain,
! [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__mult(c_Numeral_OMin,c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),X1) ),
inference(definition_unfolding,[],[f1332,f2129]) ).
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/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__5_0) ).
fof(f19593,plain,
spl0_1957,
inference(avatar_split_clause,[],[f3287,f19591]) ).
fof(f19591,plain,
( spl0_1957
<=> ! [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__mult(c_Numeral_OMin,X11)),X1)
| ~ class_Numeral_Onumber__ring(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1957])]) ).
fof(f3287,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__mult(c_Numeral_OMin,X11)),X1)
| ~ class_Numeral_Onumber__ring(X1) ),
inference(forward_demodulation,[],[f3082,f2156]) ).
fof(f3082,plain,
! [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__mult(c_Numeral_OMin,X11)),X1) ),
inference(definition_unfolding,[],[f1331,f2129]) ).
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/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__4_0) ).
fof(f19589,plain,
spl0_1956,
inference(avatar_split_clause,[],[f3255,f19587]) ).
fof(f19587,plain,
( spl0_1956
<=> ! [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_1956])]) ).
fof(f3255,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,[],[f3063,f2958]) ).
fof(f3063,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_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),tc_nat),
inference(definition_unfolding,[],[f2765,f2544]) ).
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/benchmark/theBenchmark.p',cls_Message_Omsg_Osize__6_0) ).
fof(f19577,plain,
spl0_1955,
inference(avatar_split_clause,[],[f3246,f19575]) ).
fof(f19575,plain,
( spl0_1955
<=> ! [X21] : c_plus(X21,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat) = c_plus(c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),X21,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1955])]) ).
fof(f3246,plain,
! [X21] : c_plus(X21,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat) = c_plus(c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),X21,tc_nat),
inference(forward_demodulation,[],[f3245,f2156]) ).
fof(f3245,plain,
! [X21] : c_plus(X21,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat) = c_plus(c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1)),tc_nat),X21,tc_nat),
inference(forward_demodulation,[],[f3244,f2154]) ).
fof(f3244,plain,
! [X21] : c_plus(X21,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat) = c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB0),tc_nat),X21,tc_nat),
inference(forward_demodulation,[],[f3243,f2156]) ).
fof(f3243,plain,
! [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_plus(X21,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),
inference(forward_demodulation,[],[f3051,f3242]) ).
fof(f3051,plain,
! [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_Finite__Set_Ocard(c_SetInterval_OatMost(c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),tc_nat),tc_nat),
inference(definition_unfolding,[],[f1881,f2544,f2544]) ).
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/benchmark/theBenchmark.p',cls_NatSimprocs_Oadd__2__eq__Suc_0) ).
fof(f19555,plain,
( spl0_1954
| ~ spl0_646
| ~ spl0_687
| ~ spl0_1372
| ~ spl0_1461
| ~ spl0_1953 ),
inference(avatar_split_clause,[],[f19551,f19548,f11313,f10914,f7046,f6101,f19553]) ).
fof(f19553,plain,
( spl0_1954
<=> ! [X47] :
( c_Numeral_Onumber__of(c_Numeral_Obin__succ(X47),tc_nat) = c_plus(c_1,c_Numeral_Onumber__of(X47,tc_nat),tc_nat)
| c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1954])]) ).
fof(f19548,plain,
( spl0_1953
<=> ! [X47] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(c_Numeral_Obin__succ(X47),tc_nat) = c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Numeral_Onumber__of(X47,tc_nat),tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1953])]) ).
fof(f19551,plain,
( ! [X47] :
( c_Numeral_Onumber__of(c_Numeral_Obin__succ(X47),tc_nat) = c_plus(c_1,c_Numeral_Onumber__of(X47,tc_nat),tc_nat)
| c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint) )
| ~ spl0_646
| ~ spl0_687
| ~ spl0_1372
| ~ spl0_1461
| ~ spl0_1953 ),
inference(forward_demodulation,[],[f19549,f12280]) ).
fof(f19549,plain,
( ! [X47] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(c_Numeral_Obin__succ(X47),tc_nat) = c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Numeral_Onumber__of(X47,tc_nat),tc_nat),tc_nat) )
| ~ spl0_1953 ),
inference(avatar_component_clause,[],[f19548]) ).
fof(f19550,plain,
spl0_1953,
inference(avatar_split_clause,[],[f3132,f19548]) ).
fof(f3132,plain,
! [X47] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(c_Numeral_Obin__succ(X47),tc_nat) = c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Numeral_Onumber__of(X47,tc_nat),tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f1823,f2544]) ).
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/benchmark/theBenchmark.p',cls_NatBin_OSuc__nat__number__of_1) ).
fof(f19546,plain,
spl0_1952,
inference(avatar_split_clause,[],[f3056,f19544]) ).
fof(f19544,plain,
( spl0_1952
<=> ! [X43,X0,X16,X1] : c_List_Oreplicate(c_Orderings_Omin(X43,X16,tc_nat),X0,X1) = c_List_Osublist(c_List_Oreplicate(X16,X0,X1),c_SetInterval_OlessThan(X43,tc_nat),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1952])]) ).
fof(f3056,plain,
! [X0,X1,X16,X43] : c_List_Oreplicate(c_Orderings_Omin(X43,X16,tc_nat),X0,X1) = c_List_Osublist(c_List_Oreplicate(X16,X0,X1),c_SetInterval_OlessThan(X43,tc_nat),X1),
inference(definition_unfolding,[],[f1775,f1766]) ).
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/benchmark/theBenchmark.p',cls_List_Otake__replicate_0) ).
fof(f19542,plain,
spl0_1951,
inference(avatar_split_clause,[],[f3054,f19540]) ).
fof(f19540,plain,
( spl0_1951
<=> ! [X21,X1,X23] : c_Orderings_Omin(c_Nat_Osize(X23,tc_List_Olist(X1)),X21,tc_nat) = c_Nat_Osize(c_List_Osublist(X23,c_SetInterval_OlessThan(X21,tc_nat),X1),tc_List_Olist(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1951])]) ).
fof(f3054,plain,
! [X21,X1,X23] : c_Orderings_Omin(c_Nat_Osize(X23,tc_List_Olist(X1)),X21,tc_nat) = c_Nat_Osize(c_List_Osublist(X23,c_SetInterval_OlessThan(X21,tc_nat),X1),tc_List_Olist(X1)),
inference(definition_unfolding,[],[f1611,f1766]) ).
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/benchmark/theBenchmark.p',cls_List_Olength__take_0) ).
fof(f19538,plain,
spl0_1950,
inference(avatar_split_clause,[],[f3050,f19536]) ).
fof(f3050,plain,
! [X18,X1,X13] : c_Inter(c_insert(X18,X13,tc_set(X1)),X1) = c_Relation_OImage(c_Relation_Odiag(X18,X1),c_Inter(X13,X1),X1,X1),
inference(definition_unfolding,[],[f2623,f2373]) ).
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/benchmark/theBenchmark.p',cls_Set_OInter__insert_0) ).
fof(f19533,plain,
( spl0_1949
| ~ spl0_646
| ~ spl0_687
| ~ spl0_1372
| ~ spl0_1461
| ~ spl0_1948 ),
inference(avatar_split_clause,[],[f19529,f19526,f11313,f10914,f7046,f6101,f19531]) ).
fof(f19531,plain,
( spl0_1949
<=> ! [X18,X16,X2,X1] : c_Datatype__Universe_OLeaf(X18,X1,X2) = c_Datatype__Universe_Ontrunc(c_plus(c_1,X16,tc_nat),c_Datatype__Universe_OLeaf(X18,X1,X2),X1,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1949])]) ).
fof(f19526,plain,
( spl0_1948
<=> ! [X18,X16,X2,X1] : c_Datatype__Universe_OLeaf(X18,X1,X2) = c_Datatype__Universe_Ontrunc(c_Finite__Set_Ocard(c_SetInterval_OatMost(X16,tc_nat),tc_nat),c_Datatype__Universe_OLeaf(X18,X1,X2),X1,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1948])]) ).
fof(f19529,plain,
( ! [X2,X18,X1,X16] : c_Datatype__Universe_OLeaf(X18,X1,X2) = c_Datatype__Universe_Ontrunc(c_plus(c_1,X16,tc_nat),c_Datatype__Universe_OLeaf(X18,X1,X2),X1,X2)
| ~ spl0_646
| ~ spl0_687
| ~ spl0_1372
| ~ spl0_1461
| ~ spl0_1948 ),
inference(forward_demodulation,[],[f19527,f12280]) ).
fof(f19527,plain,
( ! [X2,X18,X1,X16] : c_Datatype__Universe_OLeaf(X18,X1,X2) = c_Datatype__Universe_Ontrunc(c_Finite__Set_Ocard(c_SetInterval_OatMost(X16,tc_nat),tc_nat),c_Datatype__Universe_OLeaf(X18,X1,X2),X1,X2)
| ~ spl0_1948 ),
inference(avatar_component_clause,[],[f19526]) ).
fof(f19528,plain,
spl0_1948,
inference(avatar_split_clause,[],[f3049,f19526]) ).
fof(f3049,plain,
! [X2,X18,X1,X16] : c_Datatype__Universe_OLeaf(X18,X1,X2) = c_Datatype__Universe_Ontrunc(c_Finite__Set_Ocard(c_SetInterval_OatMost(X16,tc_nat),tc_nat),c_Datatype__Universe_OLeaf(X18,X1,X2),X1,X2),
inference(definition_unfolding,[],[f1206,f2544]) ).
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/benchmark/theBenchmark.p',cls_Datatype__Universe_Ontrunc__Leaf_0) ).
fof(f19524,plain,
( spl0_1947
| ~ spl0_1072
| ~ spl0_1910 ),
inference(avatar_split_clause,[],[f19262,f19214,f8855,f19521]) ).
fof(f19521,plain,
( spl0_1947
<=> c_List_Olist_ONil = c_List_Oupt(c_plus(c_1,c_Nat_Osize(v_evso,tc_List_Olist(tc_Event_Oevent)),tc_nat),c_Nat_Osize(c_List_Oremdups(v_evso,tc_Event_Oevent),tc_List_Olist(tc_Event_Oevent))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1947])]) ).
fof(f19262,plain,
( c_List_Olist_ONil = c_List_Oupt(c_plus(c_1,c_Nat_Osize(v_evso,tc_List_Olist(tc_Event_Oevent)),tc_nat),c_Nat_Osize(c_List_Oremdups(v_evso,tc_Event_Oevent),tc_List_Olist(tc_Event_Oevent)))
| ~ spl0_1072
| ~ spl0_1910 ),
inference(resolution,[],[f19216,f8856]) ).
fof(f19518,plain,
( spl0_1946
| ~ spl0_646
| ~ spl0_687
| ~ spl0_1372
| ~ spl0_1461
| ~ spl0_1945 ),
inference(avatar_split_clause,[],[f19514,f19511,f11313,f10914,f7046,f6101,f19516]) ).
fof(f19516,plain,
( spl0_1946
<=> ! [X43,X16,X2,X1] : c_Datatype__Universe_ONumb(X43,X1,X2) = c_Datatype__Universe_Ontrunc(c_plus(c_1,X16,tc_nat),c_Datatype__Universe_ONumb(X43,X1,X2),X1,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1946])]) ).
fof(f19511,plain,
( spl0_1945
<=> ! [X43,X16,X2,X1] : c_Datatype__Universe_ONumb(X43,X1,X2) = c_Datatype__Universe_Ontrunc(c_Finite__Set_Ocard(c_SetInterval_OatMost(X16,tc_nat),tc_nat),c_Datatype__Universe_ONumb(X43,X1,X2),X1,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1945])]) ).
fof(f19514,plain,
( ! [X2,X1,X16,X43] : c_Datatype__Universe_ONumb(X43,X1,X2) = c_Datatype__Universe_Ontrunc(c_plus(c_1,X16,tc_nat),c_Datatype__Universe_ONumb(X43,X1,X2),X1,X2)
| ~ spl0_646
| ~ spl0_687
| ~ spl0_1372
| ~ spl0_1461
| ~ spl0_1945 ),
inference(forward_demodulation,[],[f19512,f12280]) ).
fof(f19512,plain,
( ! [X2,X1,X16,X43] : c_Datatype__Universe_ONumb(X43,X1,X2) = c_Datatype__Universe_Ontrunc(c_Finite__Set_Ocard(c_SetInterval_OatMost(X16,tc_nat),tc_nat),c_Datatype__Universe_ONumb(X43,X1,X2),X1,X2)
| ~ spl0_1945 ),
inference(avatar_component_clause,[],[f19511]) ).
fof(f19513,plain,
spl0_1945,
inference(avatar_split_clause,[],[f3048,f19511]) ).
fof(f3048,plain,
! [X2,X1,X16,X43] : c_Datatype__Universe_ONumb(X43,X1,X2) = c_Datatype__Universe_Ontrunc(c_Finite__Set_Ocard(c_SetInterval_OatMost(X16,tc_nat),tc_nat),c_Datatype__Universe_ONumb(X43,X1,X2),X1,X2),
inference(definition_unfolding,[],[f1207,f2544]) ).
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/benchmark/theBenchmark.p',cls_Datatype__Universe_Ontrunc__Numb_0) ).
fof(f19508,plain,
( spl0_1944
| ~ spl0_646
| ~ spl0_687
| ~ spl0_1372
| ~ spl0_1461
| ~ spl0_1943 ),
inference(avatar_split_clause,[],[f19504,f19501,f11313,f10914,f7046,f6101,f19506]) ).
fof(f19506,plain,
( spl0_1944
<=> ! [X18,X16,X2,X1] : c_Datatype__Universe_OAtom(X18,X1,X2) = c_Datatype__Universe_Ontrunc(c_plus(c_1,X16,tc_nat),c_Datatype__Universe_OAtom(X18,X1,X2),X1,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1944])]) ).
fof(f19501,plain,
( spl0_1943
<=> ! [X18,X16,X2,X1] : c_Datatype__Universe_OAtom(X18,X1,X2) = c_Datatype__Universe_Ontrunc(c_Finite__Set_Ocard(c_SetInterval_OatMost(X16,tc_nat),tc_nat),c_Datatype__Universe_OAtom(X18,X1,X2),X1,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1943])]) ).
fof(f19504,plain,
( ! [X2,X18,X1,X16] : c_Datatype__Universe_OAtom(X18,X1,X2) = c_Datatype__Universe_Ontrunc(c_plus(c_1,X16,tc_nat),c_Datatype__Universe_OAtom(X18,X1,X2),X1,X2)
| ~ spl0_646
| ~ spl0_687
| ~ spl0_1372
| ~ spl0_1461
| ~ spl0_1943 ),
inference(forward_demodulation,[],[f19502,f12280]) ).
fof(f19502,plain,
( ! [X2,X18,X1,X16] : c_Datatype__Universe_OAtom(X18,X1,X2) = c_Datatype__Universe_Ontrunc(c_Finite__Set_Ocard(c_SetInterval_OatMost(X16,tc_nat),tc_nat),c_Datatype__Universe_OAtom(X18,X1,X2),X1,X2)
| ~ spl0_1943 ),
inference(avatar_component_clause,[],[f19501]) ).
fof(f19503,plain,
spl0_1943,
inference(avatar_split_clause,[],[f3047,f19501]) ).
fof(f3047,plain,
! [X2,X18,X1,X16] : c_Datatype__Universe_OAtom(X18,X1,X2) = c_Datatype__Universe_Ontrunc(c_Finite__Set_Ocard(c_SetInterval_OatMost(X16,tc_nat),tc_nat),c_Datatype__Universe_OAtom(X18,X1,X2),X1,X2),
inference(definition_unfolding,[],[f1203,f2544]) ).
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/benchmark/theBenchmark.p',cls_Datatype__Universe_Ontrunc__Atom_0) ).
fof(f19499,plain,
spl0_1942,
inference(avatar_split_clause,[],[f3035,f19497]) ).
fof(f19497,plain,
( spl0_1942
<=> ! [X18,X5,X1] : c_in(c_Pair(X18,X18,X1,X1),c_Transitive__Closure_Otrancl(c_union(X5,c_Relation_OId,tc_prod(X1,X1)),X1),tc_prod(X1,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1942])]) ).
fof(f3035,plain,
! [X18,X1,X5] : c_in(c_Pair(X18,X18,X1,X1),c_Transitive__Closure_Otrancl(c_union(X5,c_Relation_OId,tc_prod(X1,X1)),X1),tc_prod(X1,X1)),
inference(definition_unfolding,[],[f120,f2716]) ).
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/benchmark/theBenchmark.p',cls_Transitive__Closure_Ortrancl_Ortrancl__refl_0) ).
fof(f19495,plain,
spl0_1941,
inference(avatar_split_clause,[],[f3027,f19493]) ).
fof(f19493,plain,
( spl0_1941
<=> ! [X5,X1] : c_union(c_Transitive__Closure_Otrancl(X5,X1),c_Relation_OId,tc_prod(X1,X1)) = c_Transitive__Closure_Otrancl(c_union(X5,c_Relation_OId,tc_prod(X1,X1)),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1941])]) ).
fof(f3027,plain,
! [X1,X5] : c_union(c_Transitive__Closure_Otrancl(X5,X1),c_Relation_OId,tc_prod(X1,X1)) = c_Transitive__Closure_Otrancl(c_union(X5,c_Relation_OId,tc_prod(X1,X1)),X1),
inference(definition_unfolding,[],[f2708,f2716]) ).
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/benchmark/theBenchmark.p',cls_Transitive__Closure_Oreflcl__trancl_0) ).
fof(f19470,plain,
( spl0_1940
| ~ spl0_646
| ~ spl0_687
| ~ spl0_1372
| ~ spl0_1461
| ~ spl0_1939 ),
inference(avatar_split_clause,[],[f19455,f19452,f11313,f10914,f7046,f6101,f19468]) ).
fof(f19468,plain,
( spl0_1940
<=> ! [X21,X15] : c_Finite__Set_Ocard(c_SetInterval_OatMost(c_plus(X15,X21,tc_nat),tc_nat),tc_nat) = c_plus(X15,c_plus(c_1,X21,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1940])]) ).
fof(f19452,plain,
( spl0_1939
<=> ! [X21,X15] : c_Finite__Set_Ocard(c_SetInterval_OatMost(c_plus(X15,X21,tc_nat),tc_nat),tc_nat) = c_plus(X15,c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1939])]) ).
fof(f19455,plain,
( ! [X21,X15] : c_Finite__Set_Ocard(c_SetInterval_OatMost(c_plus(X15,X21,tc_nat),tc_nat),tc_nat) = c_plus(X15,c_plus(c_1,X21,tc_nat),tc_nat)
| ~ spl0_646
| ~ spl0_687
| ~ spl0_1372
| ~ spl0_1461
| ~ spl0_1939 ),
inference(forward_demodulation,[],[f19453,f12280]) ).
fof(f19453,plain,
( ! [X21,X15] : c_Finite__Set_Ocard(c_SetInterval_OatMost(c_plus(X15,X21,tc_nat),tc_nat),tc_nat) = c_plus(X15,c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),tc_nat)
| ~ spl0_1939 ),
inference(avatar_component_clause,[],[f19452]) ).
fof(f19454,plain,
spl0_1939,
inference(avatar_split_clause,[],[f3025,f19452]) ).
fof(f3025,plain,
! [X21,X15] : c_Finite__Set_Ocard(c_SetInterval_OatMost(c_plus(X15,X21,tc_nat),tc_nat),tc_nat) = c_plus(X15,c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),tc_nat),
inference(definition_unfolding,[],[f2027,f2544,f2544]) ).
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/benchmark/theBenchmark.p',cls_Nat_Oadd__Suc__right_0) ).
fof(f19369,plain,
( spl0_1938
| ~ spl0_646
| ~ spl0_687
| ~ spl0_1372
| ~ spl0_1461
| ~ spl0_1937 ),
inference(avatar_split_clause,[],[f19365,f19361,f11313,f10914,f7046,f6101,f19367]) ).
fof(f19367,plain,
( spl0_1938
<=> ! [X21,X15] : c_plus(c_plus(c_1,X15,tc_nat),X21,tc_nat) = c_plus(c_1,c_plus(X15,X21,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1938])]) ).
fof(f19361,plain,
( spl0_1937
<=> ! [X21,X15] : c_Finite__Set_Ocard(c_SetInterval_OatMost(c_plus(X15,X21,tc_nat),tc_nat),tc_nat) = c_plus(c_Finite__Set_Ocard(c_SetInterval_OatMost(X15,tc_nat),tc_nat),X21,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1937])]) ).
fof(f19365,plain,
( ! [X21,X15] : c_plus(c_plus(c_1,X15,tc_nat),X21,tc_nat) = c_plus(c_1,c_plus(X15,X21,tc_nat),tc_nat)
| ~ spl0_646
| ~ spl0_687
| ~ spl0_1372
| ~ spl0_1461
| ~ spl0_1937 ),
inference(forward_demodulation,[],[f19364,f12280]) ).
fof(f19364,plain,
( ! [X21,X15] : c_Finite__Set_Ocard(c_SetInterval_OatMost(c_plus(X15,X21,tc_nat),tc_nat),tc_nat) = c_plus(c_plus(c_1,X15,tc_nat),X21,tc_nat)
| ~ spl0_646
| ~ spl0_687
| ~ spl0_1372
| ~ spl0_1461
| ~ spl0_1937 ),
inference(forward_demodulation,[],[f19362,f12280]) ).
fof(f19362,plain,
( ! [X21,X15] : c_Finite__Set_Ocard(c_SetInterval_OatMost(c_plus(X15,X21,tc_nat),tc_nat),tc_nat) = c_plus(c_Finite__Set_Ocard(c_SetInterval_OatMost(X15,tc_nat),tc_nat),X21,tc_nat)
| ~ spl0_1937 ),
inference(avatar_component_clause,[],[f19361]) ).
fof(f19363,plain,
spl0_1937,
inference(avatar_split_clause,[],[f3024,f19361]) ).
fof(f19337,plain,
( spl0_1936
| ~ spl0_646
| ~ spl0_687
| ~ spl0_1372
| ~ spl0_1461
| ~ spl0_1935 ),
inference(avatar_split_clause,[],[f19333,f19329,f11313,f10914,f7046,f6101,f19335]) ).
fof(f19335,plain,
( spl0_1936
<=> ! [X21,X15] : c_minus(X15,X21,tc_nat) = c_minus(c_plus(c_1,X15,tc_nat),c_plus(c_1,X21,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1936])]) ).
fof(f19329,plain,
( spl0_1935
<=> ! [X21,X15] : c_minus(X15,X21,tc_nat) = c_minus(c_Finite__Set_Ocard(c_SetInterval_OatMost(X15,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1935])]) ).
fof(f19333,plain,
( ! [X21,X15] : c_minus(X15,X21,tc_nat) = c_minus(c_plus(c_1,X15,tc_nat),c_plus(c_1,X21,tc_nat),tc_nat)
| ~ spl0_646
| ~ spl0_687
| ~ spl0_1372
| ~ spl0_1461
| ~ spl0_1935 ),
inference(forward_demodulation,[],[f19332,f12280]) ).
fof(f19332,plain,
( ! [X21,X15] : c_minus(X15,X21,tc_nat) = c_minus(c_Finite__Set_Ocard(c_SetInterval_OatMost(X15,tc_nat),tc_nat),c_plus(c_1,X21,tc_nat),tc_nat)
| ~ spl0_646
| ~ spl0_687
| ~ spl0_1372
| ~ spl0_1461
| ~ spl0_1935 ),
inference(forward_demodulation,[],[f19330,f12280]) ).
fof(f19330,plain,
( ! [X21,X15] : c_minus(X15,X21,tc_nat) = c_minus(c_Finite__Set_Ocard(c_SetInterval_OatMost(X15,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),tc_nat)
| ~ spl0_1935 ),
inference(avatar_component_clause,[],[f19329]) ).
fof(f19331,plain,
spl0_1935,
inference(avatar_split_clause,[],[f3023,f19329]) ).
fof(f3023,plain,
! [X21,X15] : c_minus(X15,X21,tc_nat) = c_minus(c_Finite__Set_Ocard(c_SetInterval_OatMost(X15,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),tc_nat),
inference(definition_unfolding,[],[f2035,f2544,f2544]) ).
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/benchmark/theBenchmark.p',cls_Nat_Odiff__Suc__Suc_0) ).
fof(f19327,plain,
spl0_1934,
inference(avatar_split_clause,[],[f2887,f19325]) ).
fof(f19325,plain,
( spl0_1934
<=> ! [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_1934])]) ).
fof(f2887,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/benchmark/theBenchmark.p',cls_Message_Osynth_OMPair_0) ).
fof(f19323,plain,
spl0_1933,
inference(avatar_split_clause,[],[f2884,f19321]) ).
fof(f19321,plain,
( spl0_1933
<=> ! [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_1933])]) ).
fof(f2884,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/benchmark/theBenchmark.p',cls_Message_Osynth_OCrypt_0) ).
fof(f19319,plain,
spl0_1932,
inference(avatar_split_clause,[],[f2801,f19317]) ).
fof(f19317,plain,
( spl0_1932
<=> ! [X102,X86,X12] : c_Event_Oused(c_List_Olist_OCons(c_Event_Oevent_ONotes(X12,X86),X102,tc_Event_Oevent)) = c_union(c_Message_Oparts(c_insert(X86,c_emptyset,tc_Message_Omsg)),c_Event_Oused(X102),tc_Message_Omsg) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1932])]) ).
fof(f2801,axiom,
! [X86,X12,X102] : c_Event_Oused(c_List_Olist_OCons(c_Event_Oevent_ONotes(X12,X86),X102,tc_Event_Oevent)) = c_union(c_Message_Oparts(c_insert(X86,c_emptyset,tc_Message_Omsg)),c_Event_Oused(X102),tc_Message_Omsg),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Event_Oused__Notes_0) ).
fof(f19315,plain,
( spl0_1931
| ~ spl0_1492
| ~ spl0_1910 ),
inference(avatar_split_clause,[],[f19267,f19214,f12449,f19312]) ).
fof(f19312,plain,
( spl0_1931
<=> c_List_Olist_ONil = c_List_Odrop(c_plus(c_1,c_Nat_Osize(v_evso,tc_List_Olist(tc_Event_Oevent)),tc_nat),c_List_Oremdups(v_evso,tc_Event_Oevent),tc_Event_Oevent) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1931])]) ).
fof(f12449,plain,
( spl0_1492
<=> ! [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_1492])]) ).
fof(f19267,plain,
( c_List_Olist_ONil = c_List_Odrop(c_plus(c_1,c_Nat_Osize(v_evso,tc_List_Olist(tc_Event_Oevent)),tc_nat),c_List_Oremdups(v_evso,tc_Event_Oevent),tc_Event_Oevent)
| ~ spl0_1492
| ~ spl0_1910 ),
inference(resolution,[],[f19216,f12450]) ).
fof(f12450,plain,
( ! [X21,X1,X23] :
( ~ c_lessequals(c_Nat_Osize(X23,tc_List_Olist(X1)),X21,tc_nat)
| c_List_Olist_ONil = c_List_Odrop(X21,X23,X1) )
| ~ spl0_1492 ),
inference(avatar_component_clause,[],[f12449]) ).
fof(f19310,plain,
spl0_1930,
inference(avatar_split_clause,[],[f2792,f19308]) ).
fof(f19308,plain,
( spl0_1930
<=> ! [X91,X88] :
( c_in(X91,c_Message_OkeysFor(X88),tc_nat)
| ~ c_in(X91,c_Message_OkeysFor(c_Message_Osynth(X88)),tc_nat)
| c_Message_OinvKey(v_sko__uhi(X88,X91)) = X91 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1930])]) ).
fof(f2792,axiom,
! [X91,X88] :
( c_in(X91,c_Message_OkeysFor(X88),tc_nat)
| ~ c_in(X91,c_Message_OkeysFor(c_Message_Osynth(X88)),tc_nat)
| c_Message_OinvKey(v_sko__uhi(X88,X91)) = X91 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Event_OkeysFor__synth_H_1) ).
fof(f19306,plain,
spl0_1929,
inference(avatar_split_clause,[],[f2697,f19304]) ).
fof(f19304,plain,
( spl0_1929
<=> ! [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_1929])]) ).
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/benchmark/theBenchmark.p',cls_Set_Osingleton__insert__inj__eq_H_2) ).
fof(f19302,plain,
spl0_1928,
inference(avatar_split_clause,[],[f2696,f19300]) ).
fof(f19300,plain,
( spl0_1928
<=> ! [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_1928])]) ).
fof(f2696,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/benchmark/theBenchmark.p',cls_Set_Osingleton__insert__inj__eq_H_1) ).
fof(f19298,plain,
spl0_1927,
inference(avatar_split_clause,[],[f2690,f19296]) ).
fof(f19296,plain,
( spl0_1927
<=> ! [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_1927])]) ).
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/benchmark/theBenchmark.p',cls_Set_Oinsert__subset_2) ).
fof(f19294,plain,
spl0_1926,
inference(avatar_split_clause,[],[f2573,f19292]) ).
fof(f19292,plain,
( spl0_1926
<=> ! [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_1926])]) ).
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/benchmark/theBenchmark.p',cls_SetInterval_Osingle__Diff__lessThan_0) ).
fof(f19290,plain,
spl0_1925,
inference(avatar_split_clause,[],[f2565,f19288]) ).
fof(f19288,plain,
( spl0_1925
<=> ! [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_1925])]) ).
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/benchmark/theBenchmark.p',cls_SetInterval_Oivl__subset_2) ).
fof(f19286,plain,
spl0_1924,
inference(avatar_split_clause,[],[f2556,f19284]) ).
fof(f19284,plain,
( spl0_1924
<=> ! [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_1924])]) ).
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/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThanLessThan__iff_2) ).
fof(f19282,plain,
spl0_1923,
inference(avatar_split_clause,[],[f2553,f19280]) ).
fof(f19280,plain,
( spl0_1923
<=> ! [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_1923])]) ).
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/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThanAtMost__iff_2) ).
fof(f19278,plain,
spl0_1922,
inference(avatar_split_clause,[],[f2526,f19276]) ).
fof(f19276,plain,
( spl0_1922
<=> ! [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_1922])]) ).
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/benchmark/theBenchmark.p',cls_SetInterval_OatLeastLessThan__iff_2) ).
fof(f19274,plain,
spl0_1921,
inference(avatar_split_clause,[],[f2521,f19272]) ).
fof(f19272,plain,
( spl0_1921
<=> ! [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_1921])]) ).
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/benchmark/theBenchmark.p',cls_SetInterval_OatLeastAtMost__iff_2) ).
fof(f19257,plain,
spl0_1920,
inference(avatar_split_clause,[],[f2324,f19255]) ).
fof(f19255,plain,
( spl0_1920
<=> ! [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_1920])]) ).
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/benchmark/theBenchmark.p',cls_Parity_Opower__less__zero__eq__number__of_1) ).
fof(f19253,plain,
spl0_1919,
inference(avatar_split_clause,[],[f2307,f19251]) ).
fof(f19251,plain,
( spl0_1919
<=> ! [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_1919])]) ).
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/benchmark/theBenchmark.p',cls_Parity_Oneg__one__odd__power_0) ).
fof(f19249,plain,
spl0_1918,
inference(avatar_split_clause,[],[f2305,f19247]) ).
fof(f19247,plain,
( spl0_1918
<=> ! [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_1918])]) ).
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/benchmark/theBenchmark.p',cls_Parity_Ominus__one__odd__power_0) ).
fof(f19245,plain,
spl0_1917,
inference(avatar_split_clause,[],[f2266,f19243]) ).
fof(f19243,plain,
( spl0_1917
<=> ! [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_1917])]) ).
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/benchmark/theBenchmark.p',cls_Orderings_Omin__max_Obelow__sup_Oabove__sup__conv_2) ).
fof(f19241,plain,
spl0_1916,
inference(avatar_split_clause,[],[f2261,f19239]) ).
fof(f19239,plain,
( spl0_1916
<=> ! [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_1916])]) ).
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/benchmark/theBenchmark.p',cls_Orderings_Omin__max_Obelow__inf_Obelow__inf__conv_2) ).
fof(f19237,plain,
spl0_1915,
inference(avatar_split_clause,[],[f2258,f19235]) ).
fof(f19235,plain,
( spl0_1915
<=> ! [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_1915])]) ).
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/benchmark/theBenchmark.p',cls_Orderings_Omin__less__iff__conj_2) ).
fof(f19233,plain,
spl0_1914,
inference(avatar_split_clause,[],[f2255,f19231]) ).
fof(f19231,plain,
( spl0_1914
<=> ! [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_1914])]) ).
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/benchmark/theBenchmark.p',cls_Orderings_Omax__less__iff__conj_2) ).
fof(f19229,plain,
spl0_1913,
inference(avatar_split_clause,[],[f2237,f19227]) ).
fof(f19227,plain,
( spl0_1913
<=> ! [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_1913])]) ).
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/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__meet__eq__join_0) ).
fof(f19225,plain,
spl0_1912,
inference(avatar_split_clause,[],[f2228,f19223]) ).
fof(f19223,plain,
( spl0_1912
<=> ! [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_1912])]) ).
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/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__join__eq__meet_0) ).
fof(f19221,plain,
spl0_1911,
inference(avatar_split_clause,[],[f2214,f19219]) ).
fof(f19219,plain,
( spl0_1911
<=> ! [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_1911])]) ).
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/benchmark/theBenchmark.p',cls_OrderedGroup_Ominus__add__distrib_0) ).
fof(f19217,plain,
( spl0_1910
| ~ spl0_1061
| ~ spl0_1327
| ~ spl0_1759
| ~ spl0_1848
| ~ spl0_1877 ),
inference(avatar_split_clause,[],[f18680,f18349,f17598,f15964,f10728,f8811,f19214]) ).
fof(f8811,plain,
( spl0_1061
<=> ! [X0,X1,X3] : c_Nat_Osize(c_List_Oreplicate(X3,X0,X1),tc_List_Olist(X1)) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1061])]) ).
fof(f10728,plain,
( spl0_1327
<=> ! [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_1327])]) ).
fof(f15964,plain,
( spl0_1759
<=> ! [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_1759])]) ).
fof(f18349,plain,
( spl0_1877
<=> c_List_Oremdups(c_List_Olist_OCons(c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_Aa,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_ONonce(v_NB))))),v_X)),v_evso,tc_Event_Oevent),tc_Event_Oevent) = c_List_Oremdups(v_evso,tc_Event_Oevent) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1877])]) ).
fof(f18680,plain,
( c_lessequals(c_Nat_Osize(c_List_Oremdups(v_evso,tc_Event_Oevent),tc_List_Olist(tc_Event_Oevent)),c_plus(c_1,c_Nat_Osize(v_evso,tc_List_Olist(tc_Event_Oevent)),tc_nat),tc_nat)
| ~ spl0_1061
| ~ spl0_1327
| ~ spl0_1759
| ~ spl0_1848
| ~ spl0_1877 ),
inference(forward_demodulation,[],[f18679,f17628]) ).
fof(f17628,plain,
( ! [X1] : c_plus(X1,c_1,tc_nat) = c_plus(c_1,X1,tc_nat)
| ~ spl0_1061
| ~ spl0_1759
| ~ spl0_1848 ),
inference(forward_demodulation,[],[f17627,f8812]) ).
fof(f8812,plain,
( ! [X3,X0,X1] : c_Nat_Osize(c_List_Oreplicate(X3,X0,X1),tc_List_Olist(X1)) = X3
| ~ spl0_1061 ),
inference(avatar_component_clause,[],[f8811]) ).
fof(f17627,plain,
( ! [X2,X0,X1] : c_plus(c_1,X1,tc_nat) = c_plus(c_Nat_Osize(c_List_Oreplicate(X1,X0,X2),tc_List_Olist(X2)),c_1,tc_nat)
| ~ spl0_1061
| ~ spl0_1759
| ~ spl0_1848 ),
inference(forward_demodulation,[],[f17621,f8812]) ).
fof(f17621,plain,
( ! [X2,X0,X1] : c_plus(c_Nat_Osize(c_List_Oreplicate(X1,X0,X2),tc_List_Olist(X2)),c_1,tc_nat) = c_Nat_Osize(c_List_Oreplicate(c_plus(c_1,X1,tc_nat),X0,X2),tc_List_Olist(X2))
| ~ spl0_1759
| ~ spl0_1848 ),
inference(superposition,[],[f15965,f17599]) ).
fof(f15965,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_1759 ),
inference(avatar_component_clause,[],[f15964]) ).
fof(f18679,plain,
( c_lessequals(c_Nat_Osize(c_List_Oremdups(v_evso,tc_Event_Oevent),tc_List_Olist(tc_Event_Oevent)),c_plus(c_Nat_Osize(v_evso,tc_List_Olist(tc_Event_Oevent)),c_1,tc_nat),tc_nat)
| ~ spl0_1327
| ~ spl0_1759
| ~ spl0_1877 ),
inference(forward_demodulation,[],[f18675,f15965]) ).
fof(f18675,plain,
( c_lessequals(c_Nat_Osize(c_List_Oremdups(v_evso,tc_Event_Oevent),tc_List_Olist(tc_Event_Oevent)),c_Nat_Osize(c_List_Olist_OCons(c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_Aa,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_ONonce(v_NB))))),v_X)),v_evso,tc_Event_Oevent),tc_List_Olist(tc_Event_Oevent)),tc_nat)
| ~ spl0_1327
| ~ spl0_1877 ),
inference(superposition,[],[f10729,f18351]) ).
fof(f18351,plain,
( c_List_Oremdups(c_List_Olist_OCons(c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_Aa,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_ONonce(v_NB))))),v_X)),v_evso,tc_Event_Oevent),tc_Event_Oevent) = c_List_Oremdups(v_evso,tc_Event_Oevent)
| ~ spl0_1877 ),
inference(avatar_component_clause,[],[f18349]) ).
fof(f10729,plain,
( ! [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)
| ~ spl0_1327 ),
inference(avatar_component_clause,[],[f10728]) ).
fof(f19212,plain,
spl0_1909,
inference(avatar_split_clause,[],[f1843,f19210]) ).
fof(f19210,plain,
( spl0_1909
<=> ! [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_1909])]) ).
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/benchmark/theBenchmark.p',cls_NatBin_Oeq__nat__number__of_6) ).
fof(f19208,plain,
spl0_1908,
inference(avatar_split_clause,[],[f1836,f19206]) ).
fof(f19206,plain,
( spl0_1908
<=> ! [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_1908])]) ).
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/benchmark/theBenchmark.p',cls_NatBin_Oeq__nat__number__of_10) ).
fof(f19204,plain,
spl0_1907,
inference(avatar_split_clause,[],[f1824,f19202]) ).
fof(f19202,plain,
( spl0_1907
<=> ! [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_1907])]) ).
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/benchmark/theBenchmark.p',cls_NatBin_Oadd__nat__number__of_0) ).
fof(f19200,plain,
spl0_1906,
inference(avatar_split_clause,[],[f1821,f19198]) ).
fof(f19198,plain,
( spl0_1906
<=> ! [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_1906])]) ).
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/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__mult_0) ).
fof(f19196,plain,
spl0_1905,
inference(avatar_split_clause,[],[f1809,f19194]) ).
fof(f19194,plain,
( spl0_1905
<=> ! [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_1905])]) ).
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/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__add_0) ).
fof(f19192,plain,
spl0_1904,
inference(avatar_split_clause,[],[f1781,f19190]) ).
fof(f19190,plain,
( spl0_1904
<=> ! [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_1904])]) ).
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/benchmark/theBenchmark.p',cls_List_Otl__replicate_0) ).
fof(f19188,plain,
spl0_1903,
inference(avatar_split_clause,[],[f1699,f19186]) ).
fof(f19186,plain,
( spl0_1903
<=> ! [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_1903])]) ).
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/benchmark/theBenchmark.p',cls_List_Onth__list__update__eq_0) ).
fof(f19184,plain,
spl0_1902,
inference(avatar_split_clause,[],[f1633,f19182]) ).
fof(f19182,plain,
( spl0_1902
<=> ! [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_1902])]) ).
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/benchmark/theBenchmark.p',cls_List_Olist__update__id_0) ).
fof(f19180,plain,
spl0_1901,
inference(avatar_split_clause,[],[f1592,f19178]) ).
fof(f19178,plain,
( spl0_1901
<=> ! [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_1901])]) ).
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/benchmark/theBenchmark.p',cls_List_Olast__drop_0) ).
fof(f19176,plain,
spl0_1900,
inference(avatar_split_clause,[],[f1525,f19174]) ).
fof(f19174,plain,
( spl0_1900
<=> ! [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_1900])]) ).
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/benchmark/theBenchmark.p',cls_List_Oappend__in__lists__conv_1) ).
fof(f19163,plain,
spl0_1899,
inference(avatar_split_clause,[],[f1524,f19161]) ).
fof(f19161,plain,
( spl0_1899
<=> ! [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_1899])]) ).
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/benchmark/theBenchmark.p',cls_List_Oappend__in__lists__conv_0) ).
fof(f19159,plain,
spl0_1898,
inference(avatar_split_clause,[],[f1417,f19157]) ).
fof(f19157,plain,
( spl0_1898
<=> ! [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_1898])]) ).
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/benchmark/theBenchmark.p',cls_IntDef_Oof__int__mult_0) ).
fof(f19155,plain,
spl0_1897,
inference(avatar_split_clause,[],[f1403,f19153]) ).
fof(f19153,plain,
( spl0_1897
<=> ! [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_1897])]) ).
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/benchmark/theBenchmark.p',cls_IntDef_Oof__int__diff_0) ).
fof(f19151,plain,
spl0_1896,
inference(avatar_split_clause,[],[f1402,f19149]) ).
fof(f19149,plain,
( spl0_1896
<=> ! [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_1896])]) ).
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/benchmark/theBenchmark.p',cls_IntDef_Oof__int__add_0) ).
fof(f19147,plain,
spl0_1895,
inference(avatar_split_clause,[],[f1366,f19145]) ).
fof(f19145,plain,
( spl0_1895
<=> ! [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_1895])]) ).
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/benchmark/theBenchmark.p',cls_IntDef_ONats__mult_0) ).
fof(f19143,plain,
spl0_1894,
inference(avatar_split_clause,[],[f1365,f19141]) ).
fof(f19141,plain,
( spl0_1894
<=> ! [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_1894])]) ).
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/benchmark/theBenchmark.p',cls_IntDef_ONats__add_0) ).
fof(f19139,plain,
spl0_1893,
inference(avatar_split_clause,[],[f1362,f19137]) ).
fof(f19137,plain,
( spl0_1893
<=> ! [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_1893])]) ).
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/benchmark/theBenchmark.p',cls_IntDef_OInts__mult_0) ).
fof(f19135,plain,
spl0_1892,
inference(avatar_split_clause,[],[f1360,f19133]) ).
fof(f19133,plain,
( spl0_1892
<=> ! [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_1892])]) ).
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/benchmark/theBenchmark.p',cls_IntDef_OInts__diff_0) ).
fof(f19131,plain,
spl0_1891,
inference(avatar_split_clause,[],[f1359,f19129]) ).
fof(f19129,plain,
( spl0_1891
<=> ! [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_1891])]) ).
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/benchmark/theBenchmark.p',cls_IntDef_OInts__add_0) ).
fof(f19127,plain,
spl0_1890,
inference(avatar_split_clause,[],[f1306,f19125]) ).
fof(f19125,plain,
( spl0_1890
<=> ! [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_1890])]) ).
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/benchmark/theBenchmark.p',cls_GCD_Ogcd__greatest__iff_2) ).
fof(f19114,plain,
spl0_1889,
inference(avatar_split_clause,[],[f1290,f19112]) ).
fof(f19112,plain,
( spl0_1889
<=> ! [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_1889])]) ).
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/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__converse_1) ).
fof(f19110,plain,
spl0_1888,
inference(avatar_split_clause,[],[f1289,f19108]) ).
fof(f19108,plain,
( spl0_1888
<=> ! [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_1888])]) ).
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/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__converse_0) ).
fof(f19106,plain,
spl0_1887,
inference(avatar_split_clause,[],[f114,f19104]) ).
fof(f19104,plain,
( spl0_1887
<=> ! [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_1887])]) ).
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/benchmark/theBenchmark.p',cls_Sum__Type_OInrI_0) ).
fof(f19102,plain,
spl0_1886,
inference(avatar_split_clause,[],[f113,f19100]) ).
fof(f19100,plain,
( spl0_1886
<=> ! [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_1886])]) ).
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/benchmark/theBenchmark.p',cls_Sum__Type_OInlI_0) ).
fof(f19098,plain,
spl0_1885,
inference(avatar_split_clause,[],[f76,f19096]) ).
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/benchmark/theBenchmark.p',cls_Relation_ORangeI_0) ).
fof(f19094,plain,
spl0_1884,
inference(avatar_split_clause,[],[f72,f19092]) ).
fof(f19092,plain,
( spl0_1884
<=> ! [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_1884])]) ).
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/benchmark/theBenchmark.p',cls_Relation_OImageE_0) ).
fof(f19090,plain,
spl0_1883,
inference(avatar_split_clause,[],[f71,f19088]) ).
fof(f19088,plain,
( spl0_1883
<=> ! [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_1883])]) ).
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/benchmark/theBenchmark.p',cls_Relation_OIdE_0) ).
fof(f19086,plain,
spl0_1882,
inference(avatar_split_clause,[],[f70,f19084]) ).
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/benchmark/theBenchmark.p',cls_Relation_ODomainI_0) ).
fof(f19082,plain,
spl0_1881,
inference(avatar_split_clause,[],[f58,f19080]) ).
fof(f19080,plain,
( spl0_1881
<=> ! [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_1881])]) ).
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/benchmark/theBenchmark.p',cls_List_OlistsE_0) ).
fof(f19078,plain,
spl0_1880,
inference(avatar_split_clause,[],[f46,f19076]) ).
fof(f19076,plain,
( spl0_1880
<=> ! [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_1880])]) ).
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/benchmark/theBenchmark.p',cls_List_Oin__listsD__dest_0) ).
fof(f19074,plain,
( spl0_1879
| spl0_2
| ~ spl0_1830 ),
inference(avatar_split_clause,[],[f18831,f17257,f3417,f19072]) ).
fof(f17257,plain,
( spl0_1830
<=> ! [X102,X86,X12] :
( c_in(X12,c_Event_Obad,tc_Message_Oagent)
| c_Event_Oknows(c_Message_Oagent_OSpy,X102) = c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Olist_OCons(c_Event_Oevent_ONotes(X12,X86),X102,tc_Event_Oevent)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1830])]) ).
fof(f18831,plain,
( ! [X0,X1] : c_Event_Oknows(c_Message_Oagent_OSpy,X0) = c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Olist_OCons(c_Event_Oevent_ONotes(v_B,X1),X0,tc_Event_Oevent))
| spl0_2
| ~ spl0_1830 ),
inference(resolution,[],[f17258,f3419]) ).
fof(f17258,plain,
( ! [X86,X12,X102] :
( c_in(X12,c_Event_Obad,tc_Message_Oagent)
| c_Event_Oknows(c_Message_Oagent_OSpy,X102) = c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Olist_OCons(c_Event_Oevent_ONotes(X12,X86),X102,tc_Event_Oevent)) )
| ~ spl0_1830 ),
inference(avatar_component_clause,[],[f17257]) ).
fof(f18864,plain,
( spl0_1878
| spl0_1
| ~ spl0_1830 ),
inference(avatar_split_clause,[],[f18830,f17257,f3412,f18862]) ).
fof(f18830,plain,
( ! [X0,X1] : c_Event_Oknows(c_Message_Oagent_OSpy,X0) = c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Olist_OCons(c_Event_Oevent_ONotes(v_A,X1),X0,tc_Event_Oevent))
| spl0_1
| ~ spl0_1830 ),
inference(resolution,[],[f17258,f3414]) ).
fof(f18352,plain,
( spl0_1877
| ~ spl0_749
| ~ spl0_1792 ),
inference(avatar_split_clause,[],[f18117,f17035,f7334,f18349]) ).
fof(f17035,plain,
( spl0_1792
<=> ! [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_1792])]) ).
fof(f18117,plain,
( c_List_Oremdups(c_List_Olist_OCons(c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_Aa,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_ONonce(v_NB))))),v_X)),v_evso,tc_Event_Oevent),tc_Event_Oevent) = c_List_Oremdups(v_evso,tc_Event_Oevent)
| ~ spl0_749
| ~ spl0_1792 ),
inference(resolution,[],[f17036,f7336]) ).
fof(f17036,plain,
( ! [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) )
| ~ spl0_1792 ),
inference(avatar_component_clause,[],[f17035]) ).
fof(f18077,plain,
( spl0_1875
| ~ spl0_1876
| ~ spl0_118
| ~ spl0_1289 ),
inference(avatar_split_clause,[],[f10515,f10176,f3989,f18074,f18071]) ).
fof(f18071,plain,
( spl0_1875
<=> ! [X0] : c_HOL_Oabs(X0,tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1875])]) ).
fof(f18074,plain,
( spl0_1876
<=> class_OrderedGroup_Olordered__ab__group__abs(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1876])]) ).
fof(f10176,plain,
( spl0_1289
<=> ! [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_1289])]) ).
fof(f10515,plain,
( ! [X0] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(tc_nat)
| c_HOL_Oabs(X0,tc_nat) = X0 )
| ~ spl0_118
| ~ spl0_1289 ),
inference(resolution,[],[f10177,f3990]) ).
fof(f10177,plain,
( ! [X3,X1] :
( ~ c_lessequals(c_0,X3,X1)
| ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
| c_HOL_Oabs(X3,X1) = X3 )
| ~ spl0_1289 ),
inference(avatar_component_clause,[],[f10176]) ).
fof(f17967,plain,
( spl0_1874
| ~ spl0_717
| ~ spl0_743
| ~ spl0_910
| ~ spl0_1283 ),
inference(avatar_split_clause,[],[f10499,f10151,f7995,f7297,f7184,f17964]) ).
fof(f17964,plain,
( spl0_1874
<=> c_Numeral_OPls = c_Numeral_Obin__mult(c_Numeral_Obin__add(c_Numeral_OMin,c_Numeral_OMin),c_Numeral_OPls) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1874])]) ).
fof(f7184,plain,
( spl0_717
<=> c_Numeral_OPls = c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_717])]) ).
fof(f7297,plain,
( spl0_743
<=> c_Numeral_OPls = c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OPls) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_743])]) ).
fof(f7995,plain,
( spl0_910
<=> c_Numeral_OBit(c_Numeral_OMin,c_Numeral_Obit_OB0) = c_Numeral_Obin__add(c_Numeral_OMin,c_Numeral_OMin) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_910])]) ).
fof(f10499,plain,
( c_Numeral_OPls = c_Numeral_Obin__mult(c_Numeral_Obin__add(c_Numeral_OMin,c_Numeral_OMin),c_Numeral_OPls)
| ~ spl0_717
| ~ spl0_743
| ~ spl0_910
| ~ spl0_1283 ),
inference(forward_demodulation,[],[f10498,f7186]) ).
fof(f7186,plain,
( c_Numeral_OPls = c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB0)
| ~ spl0_717 ),
inference(avatar_component_clause,[],[f7184]) ).
fof(f10498,plain,
( c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB0) = c_Numeral_Obin__mult(c_Numeral_Obin__add(c_Numeral_OMin,c_Numeral_OMin),c_Numeral_OPls)
| ~ spl0_743
| ~ spl0_910
| ~ spl0_1283 ),
inference(forward_demodulation,[],[f10494,f7997]) ).
fof(f7997,plain,
( c_Numeral_OBit(c_Numeral_OMin,c_Numeral_Obit_OB0) = c_Numeral_Obin__add(c_Numeral_OMin,c_Numeral_OMin)
| ~ spl0_910 ),
inference(avatar_component_clause,[],[f7995]) ).
fof(f10494,plain,
( c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB0) = c_Numeral_Obin__mult(c_Numeral_OBit(c_Numeral_OMin,c_Numeral_Obit_OB0),c_Numeral_OPls)
| ~ spl0_743
| ~ spl0_1283 ),
inference(superposition,[],[f10152,f7299]) ).
fof(f7299,plain,
( c_Numeral_OPls = c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OPls)
| ~ spl0_743 ),
inference(avatar_component_clause,[],[f7297]) ).
fof(f17803,plain,
( spl0_1870
| spl0_1873 ),
inference(avatar_split_clause,[],[f3410,f17801,f17775]) ).
fof(f17775,plain,
( spl0_1870
<=> ! [X11] : c_0 != c_Numeral_Onumber__of(X11,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1870])]) ).
fof(f17801,plain,
( spl0_1873
<=> ! [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_1873])]) ).
fof(f3410,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/benchmark/theBenchmark.p',cls_Parity_Ozero__less__power__eq__number__of_3) ).
fof(f17795,plain,
( spl0_1872
| ~ spl0_652
| ~ spl0_1264 ),
inference(avatar_split_clause,[],[f10414,f10074,f6128,f17792]) ).
fof(f17792,plain,
( spl0_1872
<=> c_0 = c_List_Ohd(c_List_Oupt(c_0,c_1),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1872])]) ).
fof(f10074,plain,
( spl0_1264
<=> ! [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_1264])]) ).
fof(f10414,plain,
( c_0 = c_List_Ohd(c_List_Oupt(c_0,c_1),tc_nat)
| ~ spl0_652
| ~ spl0_1264 ),
inference(resolution,[],[f10075,f6130]) ).
fof(f10075,plain,
( ! [X3,X59] :
( ~ c_less(X3,X59,tc_nat)
| c_List_Ohd(c_List_Oupt(X3,X59),tc_nat) = X3 )
| ~ spl0_1264 ),
inference(avatar_component_clause,[],[f10074]) ).
fof(f17784,plain,
( ~ spl0_715
| ~ spl0_1870 ),
inference(avatar_contradiction_clause,[],[f17783]) ).
fof(f17783,plain,
( $false
| ~ spl0_715
| ~ spl0_1870 ),
inference(trivial_inequality_removal,[],[f17781]) ).
fof(f17781,plain,
( c_0 != c_0
| ~ spl0_715
| ~ spl0_1870 ),
inference(superposition,[],[f17776,f7176]) ).
fof(f7176,plain,
( c_0 = c_Numeral_Onumber__of(c_Numeral_OPls,tc_nat)
| ~ spl0_715 ),
inference(avatar_component_clause,[],[f7174]) ).
fof(f7174,plain,
( spl0_715
<=> c_0 = c_Numeral_Onumber__of(c_Numeral_OPls,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_715])]) ).
fof(f17776,plain,
( ! [X11] : c_0 != c_Numeral_Onumber__of(X11,tc_nat)
| ~ spl0_1870 ),
inference(avatar_component_clause,[],[f17775]) ).
fof(f17780,plain,
( spl0_1870
| spl0_1871 ),
inference(avatar_split_clause,[],[f3409,f17778,f17775]) ).
fof(f17778,plain,
( spl0_1871
<=> ! [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_1871])]) ).
fof(f3409,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/benchmark/theBenchmark.p',cls_Parity_Opower__le__zero__eq__number__of_0) ).
fof(f17747,plain,
( spl0_1869
| ~ spl0_646
| ~ spl0_687
| ~ spl0_786
| ~ spl0_1372
| ~ spl0_1461
| ~ spl0_1752
| ~ spl0_1868 ),
inference(avatar_split_clause,[],[f17743,f17739,f15905,f11313,f10914,f7484,f7046,f6101,f17745]) ).
fof(f17745,plain,
( spl0_1869
<=> ! [X3] :
( c_plus(c_1,c_minus(X3,c_1,tc_nat),tc_nat) = X3
| ~ c_less(c_0,X3,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1869])]) ).
fof(f17739,plain,
( spl0_1868
<=> ! [X3] :
( c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(c_0,X3,tc_nat),tc_nat),tc_nat),tc_nat) = X3
| ~ c_less(c_0,X3,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1868])]) ).
fof(f17743,plain,
( ! [X3] :
( c_plus(c_1,c_minus(X3,c_1,tc_nat),tc_nat) = X3
| ~ c_less(c_0,X3,tc_nat) )
| ~ spl0_646
| ~ spl0_687
| ~ spl0_786
| ~ spl0_1372
| ~ spl0_1461
| ~ spl0_1752
| ~ spl0_1868 ),
inference(forward_demodulation,[],[f17742,f15908]) ).
fof(f15908,plain,
( ! [X0] : c_minus(X0,c_1,tc_nat) = c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(c_0,X0,tc_nat),tc_nat)
| ~ spl0_786
| ~ spl0_1752 ),
inference(superposition,[],[f15906,f7485]) ).
fof(f17742,plain,
( ! [X3] :
( c_plus(c_1,c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(c_0,X3,tc_nat),tc_nat),tc_nat) = X3
| ~ c_less(c_0,X3,tc_nat) )
| ~ spl0_646
| ~ spl0_687
| ~ spl0_1372
| ~ spl0_1461
| ~ spl0_1868 ),
inference(forward_demodulation,[],[f17740,f12280]) ).
fof(f17740,plain,
( ! [X3] :
( c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(c_0,X3,tc_nat),tc_nat),tc_nat),tc_nat) = X3
| ~ c_less(c_0,X3,tc_nat) )
| ~ spl0_1868 ),
inference(avatar_component_clause,[],[f17739]) ).
fof(f17741,plain,
spl0_1868,
inference(avatar_split_clause,[],[f3299,f17739]) ).
fof(f3299,plain,
! [X3] :
( c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(c_0,X3,tc_nat),tc_nat),tc_nat),tc_nat) = X3
| ~ c_less(c_0,X3,tc_nat) ),
inference(forward_demodulation,[],[f3107,f3030]) ).
fof(f3107,plain,
! [X3] :
( ~ c_less(c_0,X3,tc_nat)
| c_Finite__Set_Ocard(c_SetInterval_OatMost(c_minus(X3,c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),tc_nat),tc_nat),tc_nat) = X3 ),
inference(definition_unfolding,[],[f2024,f2544,f2544]) ).
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/benchmark/theBenchmark.p',cls_Nat_OSuc__pred_0) ).
fof(f17737,plain,
spl0_1867,
inference(avatar_split_clause,[],[f3135,f17735]) ).
fof(f17735,plain,
( spl0_1867
<=> ! [X13,X12,X32,X1] :
( c_lessequals(X32,X13,tc_set(X1))
| ~ c_lessequals(X32,c_Relation_OImage(c_Relation_Odiag(X12,X1),X13,X1,X1),tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1867])]) ).
fof(f3135,plain,
! [X1,X12,X32,X13] :
( c_lessequals(X32,X13,tc_set(X1))
| ~ c_lessequals(X32,c_Relation_OImage(c_Relation_Odiag(X12,X1),X13,X1,X1),tc_set(X1)) ),
inference(definition_unfolding,[],[f2610,f2373]) ).
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/benchmark/theBenchmark.p',cls_Set_OInt__subset__iff_1) ).
fof(f17733,plain,
spl0_1866,
inference(avatar_split_clause,[],[f3134,f17731]) ).
fof(f17731,plain,
( spl0_1866
<=> ! [X13,X12,X32,X1] :
( c_lessequals(X32,X12,tc_set(X1))
| ~ c_lessequals(X32,c_Relation_OImage(c_Relation_Odiag(X12,X1),X13,X1,X1),tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1866])]) ).
fof(f3134,plain,
! [X1,X12,X32,X13] :
( c_lessequals(X32,X12,tc_set(X1))
| ~ c_lessequals(X32,c_Relation_OImage(c_Relation_Odiag(X12,X1),X13,X1,X1),tc_set(X1)) ),
inference(definition_unfolding,[],[f2609,f2373]) ).
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/benchmark/theBenchmark.p',cls_Set_OInt__subset__iff_0) ).
fof(f17729,plain,
spl0_1865,
inference(avatar_split_clause,[],[f3130,f17727]) ).
fof(f17727,plain,
( spl0_1865
<=> ! [X20,X1,X19] :
( ~ c_in(X19,c_Finite__Set_OFinites,tc_set(X1))
| c_in(c_Relation_OImage(c_Relation_Odiag(X19,X1),X20,X1,X1),c_Finite__Set_OFinites,tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1865])]) ).
fof(f3130,plain,
! [X1,X19,X20] :
( ~ c_in(X19,c_Finite__Set_OFinites,tc_set(X1))
| c_in(c_Relation_OImage(c_Relation_Odiag(X19,X1),X20,X1,X1),c_Finite__Set_OFinites,tc_set(X1)) ),
inference(definition_unfolding,[],[f30,f2373]) ).
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/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Int_0) ).
fof(f17725,plain,
spl0_1864,
inference(avatar_split_clause,[],[f3129,f17723]) ).
fof(f17723,plain,
( spl0_1864
<=> ! [X20,X1,X19] :
( ~ c_in(X20,c_Finite__Set_OFinites,tc_set(X1))
| c_in(c_Relation_OImage(c_Relation_Odiag(X19,X1),X20,X1,X1),c_Finite__Set_OFinites,tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1864])]) ).
fof(f3129,plain,
! [X1,X19,X20] :
( ~ c_in(X20,c_Finite__Set_OFinites,tc_set(X1))
| c_in(c_Relation_OImage(c_Relation_Odiag(X19,X1),X20,X1,X1),c_Finite__Set_OFinites,tc_set(X1)) ),
inference(definition_unfolding,[],[f31,f2373]) ).
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/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Int_1) ).
fof(f17721,plain,
( spl0_1863
| ~ spl0_796
| ~ spl0_1181 ),
inference(avatar_split_clause,[],[f9872,f9510,f7524,f17719]) ).
fof(f17719,plain,
( spl0_1863
<=> ! [X0] :
( c_0 != X0
| c_lessequals(X0,c_0,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1863])]) ).
fof(f7524,plain,
( spl0_796
<=> ! [X3] : c_minus(X3,c_0,tc_nat) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_796])]) ).
fof(f9510,plain,
( spl0_1181
<=> ! [X21,X15] :
( c_lessequals(X15,X21,tc_nat)
| c_0 != c_minus(X15,X21,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1181])]) ).
fof(f9872,plain,
( ! [X0] :
( c_0 != X0
| c_lessequals(X0,c_0,tc_nat) )
| ~ spl0_796
| ~ spl0_1181 ),
inference(superposition,[],[f9511,f7525]) ).
fof(f7525,plain,
( ! [X3] : c_minus(X3,c_0,tc_nat) = X3
| ~ spl0_796 ),
inference(avatar_component_clause,[],[f7524]) ).
fof(f9511,plain,
( ! [X21,X15] :
( c_0 != c_minus(X15,X21,tc_nat)
| c_lessequals(X15,X21,tc_nat) )
| ~ spl0_1181 ),
inference(avatar_component_clause,[],[f9510]) ).
fof(f17715,plain,
spl0_1862,
inference(avatar_split_clause,[],[f3122,f17713]) ).
fof(f17713,plain,
( spl0_1862
<=> ! [X21,X15] :
( c_lessequals(X21,X15,tc_nat)
| ~ c_lessequals(c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X15,tc_nat),tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1862])]) ).
fof(f3122,plain,
! [X21,X15] :
( c_lessequals(X21,X15,tc_nat)
| ~ c_lessequals(c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X15,tc_nat),tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f2019,f2544,f2544]) ).
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/benchmark/theBenchmark.p',cls_Nat_OSuc__le__mono_0) ).
fof(f17709,plain,
spl0_1861,
inference(avatar_split_clause,[],[f3120,f17707]) ).
fof(f17707,plain,
( spl0_1861
<=> ! [X21,X15] :
( c_less(X15,X21,tc_nat)
| ~ c_less(c_Finite__Set_Ocard(c_SetInterval_OatMost(X15,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1861])]) ).
fof(f3120,plain,
! [X21,X15] :
( c_less(X15,X21,tc_nat)
| ~ c_less(c_Finite__Set_Ocard(c_SetInterval_OatMost(X15,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f2021,f2544,f2544]) ).
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/benchmark/theBenchmark.p',cls_Nat_OSuc__less__eq_0) ).
fof(f17705,plain,
spl0_1860,
inference(avatar_split_clause,[],[f3115,f17703]) ).
fof(f3115,plain,
! [X18,X1,X12,X13] :
( ~ c_in(X18,X13,X1)
| c_emptyset != c_Relation_OImage(c_Relation_Odiag(c_insert(X18,X12,X1),X1),X13,X1,X1) ),
inference(definition_unfolding,[],[f2677,f2373]) ).
fof(f2677,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/benchmark/theBenchmark.p',cls_Set_Oinsert__disjoint__1_0) ).
fof(f17701,plain,
spl0_1859,
inference(avatar_split_clause,[],[f3113,f17699]) ).
fof(f17699,plain,
( spl0_1859
<=> ! [X18,X13,X12,X1] :
( ~ c_in(X18,X13,X1)
| c_emptyset != c_Relation_OImage(c_Relation_Odiag(X13,X1),c_insert(X18,X12,X1),X1,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1859])]) ).
fof(f3113,plain,
! [X18,X1,X12,X13] :
( ~ c_in(X18,X13,X1)
| c_emptyset != c_Relation_OImage(c_Relation_Odiag(X13,X1),c_insert(X18,X12,X1),X1,X1) ),
inference(definition_unfolding,[],[f2661,f2373]) ).
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/benchmark/theBenchmark.p',cls_Set_Odisjoint__insert__1_0) ).
fof(f17695,plain,
spl0_1858,
inference(avatar_split_clause,[],[f3109,f17693]) ).
fof(f17693,plain,
( spl0_1858
<=> ! [X21,X15] :
( ~ c_lessequals(X21,X15,tc_nat)
| c_lessequals(c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X15,tc_nat),tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1858])]) ).
fof(f3109,plain,
! [X21,X15] :
( ~ c_lessequals(X21,X15,tc_nat)
| c_lessequals(c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X15,tc_nat),tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f2020,f2544,f2544]) ).
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/benchmark/theBenchmark.p',cls_Nat_OSuc__le__mono_1) ).
fof(f17689,plain,
spl0_1857,
inference(avatar_split_clause,[],[f3104,f17687]) ).
fof(f17687,plain,
( spl0_1857
<=> ! [X21,X15] :
( ~ c_less(X15,X21,tc_nat)
| c_less(c_Finite__Set_Ocard(c_SetInterval_OatMost(X15,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1857])]) ).
fof(f3104,plain,
! [X21,X15] :
( ~ c_less(X15,X21,tc_nat)
| c_less(c_Finite__Set_Ocard(c_SetInterval_OatMost(X15,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f2022,f2544,f2544]) ).
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/benchmark/theBenchmark.p',cls_Nat_OSuc__less__eq_1) ).
fof(f17685,plain,
spl0_1856,
inference(avatar_split_clause,[],[f3091,f17683]) ).
fof(f17683,plain,
( spl0_1856
<=> ! [X107,X108,X87,X86] :
( X86 = X107
| c_Message_Omsg_OMPair(c_Message_Omsg_OHash(c_Message_Omsg_OMPair(X86,X87)),X87) != c_Message_Omsg_OMPair(c_Message_Omsg_OHash(c_Message_Omsg_OMPair(X107,X108)),X108) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1856])]) ).
fof(f3091,plain,
! [X108,X86,X87,X107] :
( X86 = X107
| c_Message_Omsg_OMPair(c_Message_Omsg_OHash(c_Message_Omsg_OMPair(X86,X87)),X87) != c_Message_Omsg_OMPair(c_Message_Omsg_OHash(c_Message_Omsg_OMPair(X107,X108)),X108) ),
inference(definition_unfolding,[],[f2808,f2837,f2837]) ).
fof(f2808,axiom,
! [X108,X86,X87,X107] :
( X86 = X107
| c_Message_OHPair(X107,X108) != c_Message_OHPair(X86,X87) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OHPair__eq_0) ).
fof(f17677,plain,
( spl0_1855
| ~ spl0_646
| ~ spl0_687
| ~ spl0_1372
| ~ spl0_1461
| ~ spl0_1854 ),
inference(avatar_split_clause,[],[f17673,f17670,f11313,f10914,f7046,f6101,f17675]) ).
fof(f17675,plain,
( spl0_1855
<=> ! [X41,X15] :
( c_plus(c_NatArith_Oof__nat(X15,X41),c_1,X41) = c_NatArith_Oof__nat(c_plus(c_1,X15,tc_nat),X41)
| ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X41) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1855])]) ).
fof(f17670,plain,
( spl0_1854
<=> ! [X41,X15] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X41)
| c_plus(c_NatArith_Oof__nat(X15,X41),c_1,X41) = c_NatArith_Oof__nat(c_Finite__Set_Ocard(c_SetInterval_OatMost(X15,tc_nat),tc_nat),X41) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1854])]) ).
fof(f17673,plain,
( ! [X41,X15] :
( c_plus(c_NatArith_Oof__nat(X15,X41),c_1,X41) = c_NatArith_Oof__nat(c_plus(c_1,X15,tc_nat),X41)
| ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X41) )
| ~ spl0_646
| ~ spl0_687
| ~ spl0_1372
| ~ spl0_1461
| ~ spl0_1854 ),
inference(forward_demodulation,[],[f17671,f12280]) ).
fof(f17671,plain,
( ! [X41,X15] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X41)
| c_plus(c_NatArith_Oof__nat(X15,X41),c_1,X41) = c_NatArith_Oof__nat(c_Finite__Set_Ocard(c_SetInterval_OatMost(X15,tc_nat),tc_nat),X41) )
| ~ spl0_1854 ),
inference(avatar_component_clause,[],[f17670]) ).
fof(f17672,plain,
spl0_1854,
inference(avatar_split_clause,[],[f3087,f17670]) ).
fof(f3087,plain,
! [X41,X15] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X41)
| c_plus(c_NatArith_Oof__nat(X15,X41),c_1,X41) = c_NatArith_Oof__nat(c_Finite__Set_Ocard(c_SetInterval_OatMost(X15,tc_nat),tc_nat),X41) ),
inference(definition_unfolding,[],[f1802,f2544]) ).
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/benchmark/theBenchmark.p',cls_NatArith_Oof__nat_Oof__nat__Suc_0) ).
fof(f17668,plain,
( spl0_1853
| ~ spl0_1019
| ~ spl0_1104 ),
inference(avatar_split_clause,[],[f9279,f8983,f8512,f17666]) ).
fof(f17666,plain,
( spl0_1853
<=> ! [X0,X1] : ~ c_in(c_Message_Omsg_ONonce(X0),c_Event_Oknows(X1,c_List_Olist_ONil),tc_Message_Omsg) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1853])]) ).
fof(f8512,plain,
( spl0_1019
<=> ! [X13,X7] : ~ c_in(c_Message_Omsg_ONonce(X7),c_Message_Oparts(c_Event_Oknows(X13,c_List_Olist_ONil)),tc_Message_Omsg) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1019])]) ).
fof(f8983,plain,
( spl0_1104
<=> ! [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_1104])]) ).
fof(f9279,plain,
( ! [X0,X1] : ~ c_in(c_Message_Omsg_ONonce(X0),c_Event_Oknows(X1,c_List_Olist_ONil),tc_Message_Omsg)
| ~ spl0_1019
| ~ spl0_1104 ),
inference(resolution,[],[f8984,f8513]) ).
fof(f8513,plain,
( ! [X7,X13] : ~ c_in(c_Message_Omsg_ONonce(X7),c_Message_Oparts(c_Event_Oknows(X13,c_List_Olist_ONil)),tc_Message_Omsg)
| ~ spl0_1019 ),
inference(avatar_component_clause,[],[f8512]) ).
fof(f8984,plain,
( ! [X88,X86] :
( c_in(X86,c_Message_Oparts(X88),tc_Message_Omsg)
| ~ c_in(X86,X88,tc_Message_Omsg) )
| ~ spl0_1104 ),
inference(avatar_component_clause,[],[f8983]) ).
fof(f17660,plain,
( spl0_1852
| ~ spl0_646
| ~ spl0_687
| ~ spl0_1372
| ~ spl0_1461
| ~ spl0_1851 ),
inference(avatar_split_clause,[],[f17656,f17653,f11313,f10914,f7046,f6101,f17658]) ).
fof(f17658,plain,
( spl0_1852
<=> ! [X0,X23,X21,X1] : c_List_Onth(X23,X21,X1) = c_List_Onth(c_List_Olist_OCons(X0,X23,X1),c_plus(c_1,X21,tc_nat),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1852])]) ).
fof(f17653,plain,
( spl0_1851
<=> ! [X0,X23,X21,X1] : c_List_Onth(X23,X21,X1) = c_List_Onth(c_List_Olist_OCons(X0,X23,X1),c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1851])]) ).
fof(f17656,plain,
( ! [X21,X0,X1,X23] : c_List_Onth(X23,X21,X1) = c_List_Onth(c_List_Olist_OCons(X0,X23,X1),c_plus(c_1,X21,tc_nat),X1)
| ~ spl0_646
| ~ spl0_687
| ~ spl0_1372
| ~ spl0_1461
| ~ spl0_1851 ),
inference(forward_demodulation,[],[f17654,f12280]) ).
fof(f17654,plain,
( ! [X21,X0,X1,X23] : c_List_Onth(X23,X21,X1) = c_List_Onth(c_List_Olist_OCons(X0,X23,X1),c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),X1)
| ~ spl0_1851 ),
inference(avatar_component_clause,[],[f17653]) ).
fof(f17655,plain,
spl0_1851,
inference(avatar_split_clause,[],[f3044,f17653]) ).
fof(f3044,plain,
! [X21,X0,X1,X23] : c_List_Onth(X23,X21,X1) = c_List_Onth(c_List_Olist_OCons(X0,X23,X1),c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),X1),
inference(definition_unfolding,[],[f1693,f2544]) ).
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/benchmark/theBenchmark.p',cls_List_Onth__Cons__Suc_0) ).
fof(f17637,plain,
( spl0_1850
| ~ spl0_646
| ~ spl0_687
| ~ spl0_1372
| ~ spl0_1461
| ~ spl0_1849 ),
inference(avatar_split_clause,[],[f17633,f17630,f11313,f10914,f7046,f6101,f17635]) ).
fof(f17635,plain,
( spl0_1850
<=> ! [X0,X21,X23,X1] : c_List_Odrop(X21,X23,X1) = c_List_Odrop(c_plus(c_1,X21,tc_nat),c_List_Olist_OCons(X0,X23,X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1850])]) ).
fof(f17630,plain,
( spl0_1849
<=> ! [X0,X21,X23,X1] : c_List_Odrop(X21,X23,X1) = c_List_Odrop(c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),c_List_Olist_OCons(X0,X23,X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1849])]) ).
fof(f17633,plain,
( ! [X21,X0,X1,X23] : c_List_Odrop(X21,X23,X1) = c_List_Odrop(c_plus(c_1,X21,tc_nat),c_List_Olist_OCons(X0,X23,X1),X1)
| ~ spl0_646
| ~ spl0_687
| ~ spl0_1372
| ~ spl0_1461
| ~ spl0_1849 ),
inference(forward_demodulation,[],[f17631,f12280]) ).
fof(f17631,plain,
( ! [X21,X0,X1,X23] : c_List_Odrop(X21,X23,X1) = c_List_Odrop(c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),c_List_Olist_OCons(X0,X23,X1),X1)
| ~ spl0_1849 ),
inference(avatar_component_clause,[],[f17630]) ).
fof(f17632,plain,
spl0_1849,
inference(avatar_split_clause,[],[f3043,f17630]) ).
fof(f3043,plain,
! [X21,X0,X1,X23] : c_List_Odrop(X21,X23,X1) = c_List_Odrop(c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),c_List_Olist_OCons(X0,X23,X1),X1),
inference(definition_unfolding,[],[f1572,f2544]) ).
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/benchmark/theBenchmark.p',cls_List_Odrop__Suc__Cons_0) ).
fof(f17600,plain,
( spl0_1848
| ~ spl0_646
| ~ spl0_687
| ~ spl0_1372
| ~ spl0_1461
| ~ spl0_1847 ),
inference(avatar_split_clause,[],[f17596,f17593,f11313,f10914,f7046,f6101,f17598]) ).
fof(f17593,plain,
( spl0_1847
<=> ! [X41,X0,X21] : c_List_Olist_OCons(X0,c_List_Oreplicate(X21,X0,X41),X41) = c_List_Oreplicate(c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),X0,X41) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1847])]) ).
fof(f17596,plain,
( ! [X21,X41,X0] : c_List_Olist_OCons(X0,c_List_Oreplicate(X21,X0,X41),X41) = c_List_Oreplicate(c_plus(c_1,X21,tc_nat),X0,X41)
| ~ spl0_646
| ~ spl0_687
| ~ spl0_1372
| ~ spl0_1461
| ~ spl0_1847 ),
inference(forward_demodulation,[],[f17594,f12280]) ).
fof(f17594,plain,
( ! [X21,X41,X0] : c_List_Olist_OCons(X0,c_List_Oreplicate(X21,X0,X41),X41) = c_List_Oreplicate(c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),X0,X41)
| ~ spl0_1847 ),
inference(avatar_component_clause,[],[f17593]) ).
fof(f17595,plain,
spl0_1847,
inference(avatar_split_clause,[],[f3041,f17593]) ).
fof(f3041,plain,
! [X21,X41,X0] : c_List_Olist_OCons(X0,c_List_Oreplicate(X21,X0,X41),X41) = c_List_Oreplicate(c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),X0,X41),
inference(definition_unfolding,[],[f1723,f2544]) ).
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/benchmark/theBenchmark.p',cls_List_Oreplicate_Oreplicate__Suc_0) ).
fof(f17496,plain,
( spl0_1846
| ~ spl0_894
| ~ spl0_1089 ),
inference(avatar_split_clause,[],[f9254,f8923,f7930,f17494]) ).
fof(f17494,plain,
( spl0_1846
<=> ! [X0] : c_in(c_emptyset,c_Pow(c_emptyset,X0),tc_set(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1846])]) ).
fof(f7930,plain,
( spl0_894
<=> ! [X12,X0,X1] : c_in(X0,c_insert(X0,X12,X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_894])]) ).
fof(f9254,plain,
( ! [X0] : c_in(c_emptyset,c_Pow(c_emptyset,X0),tc_set(X0))
| ~ spl0_894
| ~ spl0_1089 ),
inference(superposition,[],[f7931,f8924]) ).
fof(f7931,plain,
( ! [X0,X1,X12] : c_in(X0,c_insert(X0,X12,X1),X1)
| ~ spl0_894 ),
inference(avatar_component_clause,[],[f7930]) ).
fof(f17492,plain,
( spl0_1845
| ~ spl0_646
| ~ spl0_687
| ~ spl0_1372
| ~ spl0_1461
| ~ spl0_1844 ),
inference(avatar_split_clause,[],[f17488,f17485,f11313,f10914,f7046,f6101,f17490]) ).
fof(f17490,plain,
( spl0_1845
<=> ! [X21,X15] : c_plus(X21,c_times(X15,X21,tc_nat),tc_nat) = c_times(c_plus(c_1,X15,tc_nat),X21,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1845])]) ).
fof(f17485,plain,
( spl0_1844
<=> ! [X21,X15] : c_plus(X21,c_times(X15,X21,tc_nat),tc_nat) = c_times(c_Finite__Set_Ocard(c_SetInterval_OatMost(X15,tc_nat),tc_nat),X21,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1844])]) ).
fof(f17488,plain,
( ! [X21,X15] : c_plus(X21,c_times(X15,X21,tc_nat),tc_nat) = c_times(c_plus(c_1,X15,tc_nat),X21,tc_nat)
| ~ spl0_646
| ~ spl0_687
| ~ spl0_1372
| ~ spl0_1461
| ~ spl0_1844 ),
inference(forward_demodulation,[],[f17486,f12280]) ).
fof(f17486,plain,
( ! [X21,X15] : c_plus(X21,c_times(X15,X21,tc_nat),tc_nat) = c_times(c_Finite__Set_Ocard(c_SetInterval_OatMost(X15,tc_nat),tc_nat),X21,tc_nat)
| ~ spl0_1844 ),
inference(avatar_component_clause,[],[f17485]) ).
fof(f17487,plain,
spl0_1844,
inference(avatar_split_clause,[],[f3040,f17485]) ).
fof(f3040,plain,
! [X21,X15] : c_plus(X21,c_times(X15,X21,tc_nat),tc_nat) = c_times(c_Finite__Set_Ocard(c_SetInterval_OatMost(X15,tc_nat),tc_nat),X21,tc_nat),
inference(definition_unfolding,[],[f2099,f2544]) ).
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/benchmark/theBenchmark.p',cls_Nat_Oop_A_K_Omult__Suc_0) ).
fof(f17392,plain,
( spl0_1843
| ~ spl0_646
| ~ spl0_687
| ~ spl0_1372
| ~ spl0_1461
| ~ spl0_1842 ),
inference(avatar_split_clause,[],[f17388,f17385,f11313,f10914,f7046,f6101,f17390]) ).
fof(f17390,plain,
( spl0_1843
<=> ! [X21,X15] : c_plus(X15,c_times(X15,X21,tc_nat),tc_nat) = c_times(X15,c_plus(c_1,X21,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1843])]) ).
fof(f17385,plain,
( spl0_1842
<=> ! [X21,X15] : c_plus(X15,c_times(X15,X21,tc_nat),tc_nat) = c_times(X15,c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1842])]) ).
fof(f17388,plain,
( ! [X21,X15] : c_plus(X15,c_times(X15,X21,tc_nat),tc_nat) = c_times(X15,c_plus(c_1,X21,tc_nat),tc_nat)
| ~ spl0_646
| ~ spl0_687
| ~ spl0_1372
| ~ spl0_1461
| ~ spl0_1842 ),
inference(forward_demodulation,[],[f17386,f12280]) ).
fof(f17386,plain,
( ! [X21,X15] : c_plus(X15,c_times(X15,X21,tc_nat),tc_nat) = c_times(X15,c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),tc_nat)
| ~ spl0_1842 ),
inference(avatar_component_clause,[],[f17385]) ).
fof(f17387,plain,
spl0_1842,
inference(avatar_split_clause,[],[f3039,f17385]) ).
fof(f3039,plain,
! [X21,X15] : c_plus(X15,c_times(X15,X21,tc_nat),tc_nat) = c_times(X15,c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),tc_nat),
inference(definition_unfolding,[],[f2057,f2544]) ).
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/benchmark/theBenchmark.p',cls_Nat_Omult__Suc__right_0) ).
fof(f17329,plain,
( spl0_1841
| ~ spl0_646
| ~ spl0_687
| ~ spl0_1372
| ~ spl0_1461
| ~ spl0_1840 ),
inference(avatar_split_clause,[],[f17325,f17322,f11313,f10914,f7046,f6101,f17327]) ).
fof(f17327,plain,
( spl0_1841
<=> ! [X21,X28] : c_times(X28,c_Nat_Opower(X28,X21,tc_nat),tc_nat) = c_Nat_Opower(X28,c_plus(c_1,X21,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1841])]) ).
fof(f17322,plain,
( spl0_1840
<=> ! [X21,X28] : c_times(X28,c_Nat_Opower(X28,X21,tc_nat),tc_nat) = c_Nat_Opower(X28,c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1840])]) ).
fof(f17325,plain,
( ! [X21,X28] : c_times(X28,c_Nat_Opower(X28,X21,tc_nat),tc_nat) = c_Nat_Opower(X28,c_plus(c_1,X21,tc_nat),tc_nat)
| ~ spl0_646
| ~ spl0_687
| ~ spl0_1372
| ~ spl0_1461
| ~ spl0_1840 ),
inference(forward_demodulation,[],[f17323,f12280]) ).
fof(f17323,plain,
( ! [X21,X28] : c_times(X28,c_Nat_Opower(X28,X21,tc_nat),tc_nat) = c_Nat_Opower(X28,c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),tc_nat)
| ~ spl0_1840 ),
inference(avatar_component_clause,[],[f17322]) ).
fof(f17324,plain,
spl0_1840,
inference(avatar_split_clause,[],[f3038,f17322]) ).
fof(f3038,plain,
! [X21,X28] : c_times(X28,c_Nat_Opower(X28,X21,tc_nat),tc_nat) = c_Nat_Opower(X28,c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),tc_nat),
inference(definition_unfolding,[],[f2345,f2544]) ).
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/benchmark/theBenchmark.p',cls_Power_Opower_Osimps__2_0) ).
fof(f17296,plain,
( spl0_1839
| ~ spl0_646
| ~ spl0_687
| ~ spl0_1372
| ~ spl0_1461
| ~ spl0_1837 ),
inference(avatar_split_clause,[],[f17288,f17285,f11313,f10914,f7046,f6101,f17294]) ).
fof(f17294,plain,
( spl0_1839
<=> ! [X21,X28] : c_times(X28,c_Nat_Opower(X28,X21,tc_IntDef_Oint),tc_IntDef_Oint) = c_Nat_Opower(X28,c_plus(c_1,X21,tc_nat),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1839])]) ).
fof(f17285,plain,
( spl0_1837
<=> ! [X21,X28] : c_times(X28,c_Nat_Opower(X28,X21,tc_IntDef_Oint),tc_IntDef_Oint) = c_Nat_Opower(X28,c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1837])]) ).
fof(f17288,plain,
( ! [X21,X28] : c_times(X28,c_Nat_Opower(X28,X21,tc_IntDef_Oint),tc_IntDef_Oint) = c_Nat_Opower(X28,c_plus(c_1,X21,tc_nat),tc_IntDef_Oint)
| ~ spl0_646
| ~ spl0_687
| ~ spl0_1372
| ~ spl0_1461
| ~ spl0_1837 ),
inference(forward_demodulation,[],[f17286,f12280]) ).
fof(f17286,plain,
( ! [X21,X28] : c_times(X28,c_Nat_Opower(X28,X21,tc_IntDef_Oint),tc_IntDef_Oint) = c_Nat_Opower(X28,c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),tc_IntDef_Oint)
| ~ spl0_1837 ),
inference(avatar_component_clause,[],[f17285]) ).
fof(f17292,plain,
( spl0_1838
| ~ spl0_14
| ~ spl0_1079 ),
inference(avatar_split_clause,[],[f9241,f8883,f3477,f17290]) ).
fof(f17290,plain,
( spl0_1838
<=> ! [X0] : c_uminus(c_uminus(X0,tc_IntDef_Oint),tc_IntDef_Oint) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1838])]) ).
fof(f8883,plain,
( spl0_1079
<=> ! [X1,X3] :
( ~ class_OrderedGroup_Oab__group__add(X1)
| c_uminus(c_uminus(X3,X1),X1) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1079])]) ).
fof(f9241,plain,
( ! [X0] : c_uminus(c_uminus(X0,tc_IntDef_Oint),tc_IntDef_Oint) = X0
| ~ spl0_14
| ~ spl0_1079 ),
inference(resolution,[],[f8884,f3479]) ).
fof(f8884,plain,
( ! [X3,X1] :
( ~ class_OrderedGroup_Oab__group__add(X1)
| c_uminus(c_uminus(X3,X1),X1) = X3 )
| ~ spl0_1079 ),
inference(avatar_component_clause,[],[f8883]) ).
fof(f17287,plain,
spl0_1837,
inference(avatar_split_clause,[],[f3037,f17285]) ).
fof(f3037,plain,
! [X21,X28] : c_times(X28,c_Nat_Opower(X28,X21,tc_IntDef_Oint),tc_IntDef_Oint) = c_Nat_Opower(X28,c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),tc_IntDef_Oint),
inference(definition_unfolding,[],[f1465,f2544]) ).
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/benchmark/theBenchmark.p',cls_IntDiv_Opower_Osimps__2_0) ).
fof(f17283,plain,
spl0_1836,
inference(avatar_split_clause,[],[f3036,f17281]) ).
fof(f3036,plain,
! [X1,X12,X13] : c_Relation_OImage(c_Relation_Odiag(X12,X1),X13,X1,X1) = c_minus(X12,c_uminus(X13,tc_set(X1)),tc_set(X1)),
inference(definition_unfolding,[],[f2586,f2373]) ).
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/benchmark/theBenchmark.p',cls_Set_ODiff__Compl_0) ).
fof(f17279,plain,
spl0_1835,
inference(avatar_split_clause,[],[f2933,f17277]) ).
fof(f2933,axiom,
! [X86,X102,X12,X13] :
( c_in(X86,c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,X102)),tc_Message_Omsg)
| ~ c_in(c_Event_Oevent_OSays(X12,X13,X86),c_List_Oset(X102,tc_Event_Oevent),tc_Event_Oevent) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Event_OSays__imp__analz__Spy__dest_0) ).
fof(f17275,plain,
spl0_1834,
inference(avatar_split_clause,[],[f2866,f17273]) ).
fof(f17273,plain,
( spl0_1834
<=> ! [X20,X88] : c_Message_Oanalz(c_union(c_Message_Osynth(X20),X88,tc_Message_Omsg)) = c_union(c_Message_Oanalz(c_union(X20,X88,tc_Message_Omsg)),c_Message_Osynth(X20),tc_Message_Omsg) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1834])]) ).
fof(f2866,axiom,
! [X88,X20] : c_Message_Oanalz(c_union(c_Message_Osynth(X20),X88,tc_Message_Omsg)) = c_union(c_Message_Oanalz(c_union(X20,X88,tc_Message_Omsg)),c_Message_Osynth(X20),tc_Message_Omsg),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oanalz__synth__Un_0) ).
fof(f17271,plain,
spl0_1833,
inference(avatar_split_clause,[],[f2828,f17269]) ).
fof(f17269,plain,
( spl0_1833
<=> ! [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_1833])]) ).
fof(f2828,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/benchmark/theBenchmark.p',cls_Message_OHash__synth_0) ).
fof(f17267,plain,
spl0_1832,
inference(avatar_split_clause,[],[f2807,f17265]) ).
fof(f17265,plain,
( spl0_1832
<=> ! [X86,X88] :
( ~ c_in(X86,c_Message_Osynth(c_Message_Oanalz(X88)),tc_Message_Omsg)
| c_Message_Osynth(c_Message_Oanalz(X88)) = c_Message_Osynth(c_Message_Oanalz(c_insert(X86,X88,tc_Message_Omsg))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1832])]) ).
fof(f2807,axiom,
! [X88,X86] :
( ~ c_in(X86,c_Message_Osynth(c_Message_Oanalz(X88)),tc_Message_Omsg)
| c_Message_Osynth(c_Message_Oanalz(X88)) = c_Message_Osynth(c_Message_Oanalz(c_insert(X86,X88,tc_Message_Omsg))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OFake__analz__eq_0) ).
fof(f17263,plain,
spl0_1831,
inference(avatar_split_clause,[],[f2799,f17261]) ).
fof(f17261,plain,
( spl0_1831
<=> ! [X102,X13,X12,X86] : c_insert(X86,c_Event_Oknows(c_Message_Oagent_OSpy,X102),tc_Message_Omsg) = c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Olist_OCons(c_Event_Oevent_OSays(X12,X13,X86),X102,tc_Event_Oevent)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1831])]) ).
fof(f2799,axiom,
! [X86,X102,X12,X13] : c_insert(X86,c_Event_Oknows(c_Message_Oagent_OSpy,X102),tc_Message_Omsg) = c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Olist_OCons(c_Event_Oevent_OSays(X12,X13,X86),X102,tc_Event_Oevent)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Event_Oknows__Spy__Says_0) ).
fof(f17259,plain,
spl0_1830,
inference(avatar_split_clause,[],[f2798,f17257]) ).
fof(f2798,axiom,
! [X86,X12,X102] :
( c_in(X12,c_Event_Obad,tc_Message_Oagent)
| c_Event_Oknows(c_Message_Oagent_OSpy,X102) = c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Olist_OCons(c_Event_Oevent_ONotes(X12,X86),X102,tc_Event_Oevent)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Event_Oknows__Spy__Notes_1) ).
fof(f17255,plain,
spl0_1829,
inference(avatar_split_clause,[],[f2675,f17253]) ).
fof(f17253,plain,
( spl0_1829
<=> ! [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_1829])]) ).
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/benchmark/theBenchmark.p',cls_Set_Oinsert__Diff__single_0) ).
fof(f17251,plain,
spl0_1828,
inference(avatar_split_clause,[],[f2650,f17249]) ).
fof(f17249,plain,
( spl0_1828
<=> ! [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_1828])]) ).
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/benchmark/theBenchmark.p',cls_Set_OUnion__Un__distrib_0) ).
fof(f17247,plain,
( spl0_1827
| ~ spl0_57
| ~ spl0_1075 ),
inference(avatar_split_clause,[],[f9233,f8867,f3692,f17244]) ).
fof(f8867,plain,
( spl0_1075
<=> ! [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_1075])]) ).
fof(f9233,plain,
( c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint) = c_uminus(c_1,tc_IntDef_Oint)
| ~ spl0_57
| ~ spl0_1075 ),
inference(resolution,[],[f8868,f3694]) ).
fof(f8868,plain,
( ! [X1] :
( ~ class_Numeral_Onumber__ring(X1)
| c_Numeral_Onumber__of(c_Numeral_OMin,X1) = c_uminus(c_1,X1) )
| ~ spl0_1075 ),
inference(avatar_component_clause,[],[f8867]) ).
fof(f17242,plain,
spl0_1826,
inference(avatar_split_clause,[],[f2596,f17240]) ).
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/benchmark/theBenchmark.p',cls_Set_ODiff__iff_2) ).
fof(f17238,plain,
spl0_1825,
inference(avatar_split_clause,[],[f2585,f17236]) ).
fof(f17236,plain,
( spl0_1825
<=> ! [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_1825])]) ).
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/benchmark/theBenchmark.p',cls_Set_OCompl__subset__Compl__iff_1) ).
fof(f17234,plain,
spl0_1824,
inference(avatar_split_clause,[],[f2584,f17232]) ).
fof(f17232,plain,
( spl0_1824
<=> ! [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_1824])]) ).
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/benchmark/theBenchmark.p',cls_Set_OCompl__subset__Compl__iff_0) ).
fof(f17230,plain,
spl0_1823,
inference(avatar_split_clause,[],[f2574,f17228]) ).
fof(f17228,plain,
( spl0_1823
<=> ! [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_1823])]) ).
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/benchmark/theBenchmark.p',cls_Set_OCompl__Diff__eq_0) ).
fof(f17226,plain,
spl0_1822,
inference(avatar_split_clause,[],[f2360,f17224]) ).
fof(f17224,plain,
( spl0_1822
<=> ! [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_1822])]) ).
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/benchmark/theBenchmark.p',cls_Power_Ozero__less__power__abs__iff_1) ).
fof(f17222,plain,
spl0_1821,
inference(avatar_split_clause,[],[f2359,f17220]) ).
fof(f17220,plain,
( spl0_1821
<=> ! [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_1821])]) ).
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/benchmark/theBenchmark.p',cls_Power_Ozero__less__power__abs__iff_0) ).
fof(f17218,plain,
spl0_1820,
inference(avatar_split_clause,[],[f2194,f17216]) ).
fof(f17216,plain,
( spl0_1820
<=> ! [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_1820])]) ).
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/benchmark/theBenchmark.p',cls_OrderedGroup_Oadd__less__cancel__right_1) ).
fof(f17214,plain,
spl0_1819,
inference(avatar_split_clause,[],[f2193,f17212]) ).
fof(f17212,plain,
( spl0_1819
<=> ! [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_1819])]) ).
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/benchmark/theBenchmark.p',cls_OrderedGroup_Oadd__less__cancel__right_0) ).
fof(f17210,plain,
spl0_1818,
inference(avatar_split_clause,[],[f2192,f17208]) ).
fof(f17208,plain,
( spl0_1818
<=> ! [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_1818])]) ).
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/benchmark/theBenchmark.p',cls_OrderedGroup_Oadd__less__cancel__left_1) ).
fof(f17206,plain,
spl0_1817,
inference(avatar_split_clause,[],[f2191,f17204]) ).
fof(f17204,plain,
( spl0_1817
<=> ! [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_1817])]) ).
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/benchmark/theBenchmark.p',cls_OrderedGroup_Oadd__less__cancel__left_0) ).
fof(f17202,plain,
( spl0_1816
| ~ spl0_894
| ~ spl0_1062 ),
inference(avatar_split_clause,[],[f9197,f8815,f7930,f17200]) ).
fof(f17200,plain,
( spl0_1816
<=> ! [X0] : c_in(c_List_Olist_ONil,c_List_Olistset(c_List_Olist_ONil,X0),tc_List_Olist(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1816])]) ).
fof(f9197,plain,
( ! [X0] : c_in(c_List_Olist_ONil,c_List_Olistset(c_List_Olist_ONil,X0),tc_List_Olist(X0))
| ~ spl0_894
| ~ spl0_1062 ),
inference(superposition,[],[f7931,f8816]) ).
fof(f17198,plain,
spl0_1815,
inference(avatar_split_clause,[],[f2189,f17196]) ).
fof(f17196,plain,
( spl0_1815
<=> ! [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_1815])]) ).
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/benchmark/theBenchmark.p',cls_OrderedGroup_Oadd__le__cancel__right_1) ).
fof(f17194,plain,
spl0_1814,
inference(avatar_split_clause,[],[f2188,f17192]) ).
fof(f17192,plain,
( spl0_1814
<=> ! [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_1814])]) ).
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/benchmark/theBenchmark.p',cls_OrderedGroup_Oadd__le__cancel__right_0) ).
fof(f17190,plain,
spl0_1813,
inference(avatar_split_clause,[],[f2187,f17188]) ).
fof(f17188,plain,
( spl0_1813
<=> ! [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_1813])]) ).
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/benchmark/theBenchmark.p',cls_OrderedGroup_Oadd__le__cancel__left_1) ).
fof(f17186,plain,
spl0_1812,
inference(avatar_split_clause,[],[f2186,f17184]) ).
fof(f17184,plain,
( spl0_1812
<=> ! [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_1812])]) ).
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/benchmark/theBenchmark.p',cls_OrderedGroup_Oadd__le__cancel__left_0) ).
fof(f17182,plain,
spl0_1811,
inference(avatar_split_clause,[],[f2146,f17180]) ).
fof(f17180,plain,
( spl0_1811
<=> ! [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_1811])]) ).
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/benchmark/theBenchmark.p',cls_Numeral_Obin__rel__simps__4_1) ).
fof(f17178,plain,
spl0_1810,
inference(avatar_split_clause,[],[f2145,f17176]) ).
fof(f17176,plain,
( spl0_1810
<=> ! [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_1810])]) ).
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/benchmark/theBenchmark.p',cls_Numeral_Obin__rel__simps__4_0) ).
fof(f17174,plain,
spl0_1809,
inference(avatar_split_clause,[],[f2138,f17172]) ).
fof(f17172,plain,
( spl0_1809
<=> ! [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_1809])]) ).
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/benchmark/theBenchmark.p',cls_Numeral_Obin__rel__simps__12_1) ).
fof(f17170,plain,
spl0_1808,
inference(avatar_split_clause,[],[f2137,f17168]) ).
fof(f17168,plain,
( spl0_1808
<=> ! [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_1808])]) ).
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/benchmark/theBenchmark.p',cls_Numeral_Obin__rel__simps__12_0) ).
fof(f17166,plain,
spl0_1807,
inference(avatar_split_clause,[],[f2119,f17164]) ).
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/benchmark/theBenchmark.p',cls_Numeral_Obin__arith__extra__simps__4_0) ).
fof(f17162,plain,
spl0_1806,
inference(avatar_split_clause,[],[f2116,f17160]) ).
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/benchmark/theBenchmark.p',cls_Numeral_Obin__arith__extra__simps__1_0) ).
fof(f17143,plain,
spl0_1805,
inference(avatar_split_clause,[],[f1971,f17141]) ).
fof(f17141,plain,
( spl0_1805
<=> ! [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_1805])]) ).
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/benchmark/theBenchmark.p',cls_NatSimprocs_Ominus__less__iff__1_1) ).
fof(f17139,plain,
spl0_1804,
inference(avatar_split_clause,[],[f1970,f17137]) ).
fof(f17137,plain,
( spl0_1804
<=> ! [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_1804])]) ).
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/benchmark/theBenchmark.p',cls_NatSimprocs_Ominus__less__iff__1_0) ).
fof(f17135,plain,
spl0_1803,
inference(avatar_split_clause,[],[f1967,f17133]) ).
fof(f17133,plain,
( spl0_1803
<=> ! [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_1803])]) ).
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/benchmark/theBenchmark.p',cls_NatSimprocs_Ominus__le__iff__1_1) ).
fof(f17131,plain,
spl0_1802,
inference(avatar_split_clause,[],[f1966,f17129]) ).
fof(f17129,plain,
( spl0_1802
<=> ! [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_1802])]) ).
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/benchmark/theBenchmark.p',cls_NatSimprocs_Ominus__le__iff__1_0) ).
fof(f17127,plain,
spl0_1801,
inference(avatar_split_clause,[],[f1960,f17125]) ).
fof(f17125,plain,
( spl0_1801
<=> ! [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_1801])]) ).
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/benchmark/theBenchmark.p',cls_NatSimprocs_Oless__minus__iff__1_1) ).
fof(f17123,plain,
spl0_1800,
inference(avatar_split_clause,[],[f1959,f17121]) ).
fof(f17121,plain,
( spl0_1800
<=> ! [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_1800])]) ).
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/benchmark/theBenchmark.p',cls_NatSimprocs_Oless__minus__iff__1_0) ).
fof(f17119,plain,
spl0_1799,
inference(avatar_split_clause,[],[f1944,f17117]) ).
fof(f17117,plain,
( spl0_1799
<=> ! [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_1799])]) ).
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/benchmark/theBenchmark.p',cls_NatSimprocs_Ole__minus__iff__1_1) ).
fof(f17115,plain,
spl0_1798,
inference(avatar_split_clause,[],[f1943,f17113]) ).
fof(f17113,plain,
( spl0_1798
<=> ! [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_1798])]) ).
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/benchmark/theBenchmark.p',cls_NatSimprocs_Ole__minus__iff__1_0) ).
fof(f17111,plain,
spl0_1797,
inference(avatar_split_clause,[],[f1869,f17109]) ).
fof(f17109,plain,
( spl0_1797
<=> ! [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_1797])]) ).
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/benchmark/theBenchmark.p',cls_NatBin_Oof__nat__number__of__eq_1) ).
fof(f17107,plain,
spl0_1796,
inference(avatar_split_clause,[],[f1780,f17105]) ).
fof(f17105,plain,
( spl0_1796
<=> ! [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_1796])]) ).
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/benchmark/theBenchmark.p',cls_List_Otl__append2_0) ).
fof(f17050,plain,
spl0_1795,
inference(avatar_split_clause,[],[f1764,f17048]) ).
fof(f17048,plain,
( spl0_1795
<=> ! [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_1795])]) ).
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/benchmark/theBenchmark.p',cls_List_Osublist__singleton_0) ).
fof(f17045,plain,
spl0_1794,
inference(avatar_split_clause,[],[f1727,f17043]) ).
fof(f17043,plain,
( spl0_1794
<=> ! [X25,X1,X3] : 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) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1794])]) ).
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/benchmark/theBenchmark.p',cls_List_Orev__eq__Cons__iff_1) ).
fof(f17041,plain,
spl0_1793,
inference(avatar_split_clause,[],[f1724,f17039]) ).
fof(f17039,plain,
( spl0_1793
<=> ! [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_1793])]) ).
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/benchmark/theBenchmark.p',cls_List_Orev_Osimps__2_0) ).
fof(f17037,plain,
spl0_1792,
inference(avatar_split_clause,[],[f1713,f17035]) ).
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/benchmark/theBenchmark.p',cls_List_Oremdups_Osimps__2_0) ).
fof(f17033,plain,
spl0_1791,
inference(avatar_split_clause,[],[f1701,f17031]) ).
fof(f17031,plain,
( spl0_1791
<=> ! [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_1791])]) ).
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/benchmark/theBenchmark.p',cls_List_Onth__mem_0) ).
fof(f17029,plain,
spl0_1790,
inference(avatar_split_clause,[],[f1700,f17027]) ).
fof(f17027,plain,
( spl0_1790
<=> ! [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_1790])]) ).
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/benchmark/theBenchmark.p',cls_List_Onth__list__update__neq_0) ).
fof(f17025,plain,
spl0_1789,
inference(avatar_split_clause,[],[f1618,f17023]) ).
fof(f17023,plain,
( spl0_1789
<=> ! [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_1789])]) ).
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/benchmark/theBenchmark.p',cls_List_Olexord__Nil__right_0) ).
fof(f17021,plain,
spl0_1788,
inference(avatar_split_clause,[],[f1605,f17019]) ).
fof(f17019,plain,
( spl0_1788
<=> ! [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_1788])]) ).
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/benchmark/theBenchmark.p',cls_List_Olength__remdups__eq_0) ).
fof(f17017,plain,
spl0_1787,
inference(avatar_split_clause,[],[f1546,f17015]) ).
fof(f17015,plain,
( spl0_1787
<=> ! [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_1787])]) ).
fof(f1546,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/benchmark/theBenchmark.p',cls_List_Oconcat__eq__Nil__conv_0) ).
fof(f17013,plain,
spl0_1786,
inference(avatar_split_clause,[],[f1545,f17011]) ).
fof(f17011,plain,
( spl0_1786
<=> ! [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_1786])]) ).
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/benchmark/theBenchmark.p',cls_List_Oconcat__append_0) ).
fof(f17009,plain,
( spl0_1785
| ~ spl0_811
| ~ spl0_1744 ),
inference(avatar_split_clause,[],[f16689,f15851,f7585,f17007]) ).
fof(f17007,plain,
( spl0_1785
<=> ! [X2,X1] : c_UNIV = c_insert(X2,c_UNIV,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1785])]) ).
fof(f7585,plain,
( spl0_811
<=> ! [X13,X1] : c_UNIV = c_union(c_UNIV,X13,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_811])]) ).
fof(f16689,plain,
( ! [X2,X1] : c_UNIV = c_insert(X2,c_UNIV,X1)
| ~ spl0_811
| ~ spl0_1744 ),
inference(forward_demodulation,[],[f16659,f7586]) ).
fof(f7586,plain,
( ! [X1,X13] : c_UNIV = c_union(c_UNIV,X13,X1)
| ~ spl0_811 ),
inference(avatar_component_clause,[],[f7585]) ).
fof(f16659,plain,
( ! [X2,X0,X1] : c_insert(X2,c_UNIV,X1) = c_union(c_UNIV,c_insert(X2,X0,X1),X1)
| ~ spl0_811
| ~ spl0_1744 ),
inference(superposition,[],[f15852,f7586]) ).
fof(f17005,plain,
spl0_1784,
inference(avatar_split_clause,[],[f1538,f17003]) ).
fof(f17003,plain,
( spl0_1784
<=> ! [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_1784])]) ).
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/benchmark/theBenchmark.p',cls_List_Obutlast_Osimps__2_1) ).
fof(f17001,plain,
spl0_1783,
inference(avatar_split_clause,[],[f1519,f16999]) ).
fof(f16999,plain,
( spl0_1783
<=> ! [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_1783])]) ).
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/benchmark/theBenchmark.p',cls_List_Oappend__butlast__last__id_0) ).
fof(f16997,plain,
spl0_1782,
inference(avatar_split_clause,[],[f1515,f16995]) ).
fof(f16995,plain,
( spl0_1782
<=> ! [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_1782])]) ).
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/benchmark/theBenchmark.p',cls_List_ONil__notin__lex_0) ).
fof(f16993,plain,
spl0_1781,
inference(avatar_split_clause,[],[f1506,f16991]) ).
fof(f16991,plain,
( spl0_1781
<=> ! [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_1781])]) ).
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/benchmark/theBenchmark.p',cls_List_ONil2__notin__lex_0) ).
fof(f16989,plain,
spl0_1780,
inference(avatar_split_clause,[],[f1311,f16987]) ).
fof(f16987,plain,
( spl0_1780
<=> ! [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_1780])]) ).
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/benchmark/theBenchmark.p',cls_IntArith_Oabs__power__minus__one_0) ).
fof(f16985,plain,
spl0_1779,
inference(avatar_split_clause,[],[f1303,f16983]) ).
fof(f16983,plain,
( spl0_1779
<=> ! [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_1779])]) ).
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/benchmark/theBenchmark.p',cls_GCD_Ogcd__add2_H_0) ).
fof(f16981,plain,
spl0_1778,
inference(avatar_split_clause,[],[f1302,f16979]) ).
fof(f16979,plain,
( spl0_1778
<=> ! [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_1778])]) ).
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/benchmark/theBenchmark.p',cls_GCD_Ogcd__add2_0) ).
fof(f16977,plain,
spl0_1777,
inference(avatar_split_clause,[],[f1301,f16975]) ).
fof(f16975,plain,
( spl0_1777
<=> ! [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_1777])]) ).
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/benchmark/theBenchmark.p',cls_GCD_Ogcd__add1_0) ).
fof(f16973,plain,
spl0_1776,
inference(avatar_split_clause,[],[f1272,f16971]) ).
fof(f16971,plain,
( spl0_1776
<=> ! [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_1776])]) ).
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/benchmark/theBenchmark.p',cls_Finite__Set_OMin__in_0) ).
fof(f16969,plain,
spl0_1775,
inference(avatar_split_clause,[],[f1257,f16967]) ).
fof(f16967,plain,
( spl0_1775
<=> ! [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_1775])]) ).
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/benchmark/theBenchmark.p',cls_Finite__Set_OMax__in_0) ).
fof(f16960,plain,
spl0_1774,
inference(avatar_split_clause,[],[f81,f16958]) ).
fof(f16958,plain,
( spl0_1774
<=> ! [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_1774])]) ).
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/benchmark/theBenchmark.p',cls_Relation_OdiagI_0) ).
fof(f16956,plain,
spl0_1773,
inference(avatar_split_clause,[],[f47,f16954]) ).
fof(f16954,plain,
( spl0_1773
<=> ! [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_1773])]) ).
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/benchmark/theBenchmark.p',cls_List_Oin__listsI_0) ).
fof(f16888,plain,
( spl0_1772
| ~ spl0_672
| ~ spl0_1737 ),
inference(avatar_split_clause,[],[f16567,f15823,f6982,f16886]) ).
fof(f16886,plain,
( spl0_1772
<=> ! [X0,X1] :
( c_lessequals(X0,X0,X1)
| ~ class_Orderings_Olinorder(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1772])]) ).
fof(f15823,plain,
( spl0_1737
<=> ! [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_1737])]) ).
fof(f16567,plain,
( ! [X0,X1] :
( c_lessequals(X0,X0,X1)
| ~ class_Orderings_Olinorder(X1) )
| ~ spl0_672
| ~ spl0_1737 ),
inference(resolution,[],[f15824,f6983]) ).
fof(f15824,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_1737 ),
inference(avatar_component_clause,[],[f15823]) ).
fof(f16594,plain,
( spl0_1771
| ~ spl0_757
| ~ spl0_1708 ),
inference(avatar_split_clause,[],[f16332,f15707,f7367,f16592]) ).
fof(f16592,plain,
( spl0_1771
<=> ! [X0,X1] : c_List_Orotate(c_0,X0,X1) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1771])]) ).
fof(f7367,plain,
( spl0_757
<=> ! [X15] : c_0 = c_Divides_Oop_Amod(c_0,X15,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_757])]) ).
fof(f15707,plain,
( spl0_1708
<=> ! [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_1708])]) ).
fof(f16332,plain,
( ! [X0,X1] : c_List_Orotate(c_0,X0,X1) = X0
| ~ spl0_757
| ~ spl0_1708 ),
inference(trivial_inequality_removal,[],[f16322]) ).
fof(f16322,plain,
( ! [X0,X1] :
( c_0 != c_0
| c_List_Orotate(c_0,X0,X1) = X0 )
| ~ spl0_757
| ~ spl0_1708 ),
inference(superposition,[],[f15708,f7368]) ).
fof(f7368,plain,
( ! [X15] : c_0 = c_Divides_Oop_Amod(c_0,X15,tc_nat)
| ~ spl0_757 ),
inference(avatar_component_clause,[],[f7367]) ).
fof(f15708,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_1708 ),
inference(avatar_component_clause,[],[f15707]) ).
fof(f16310,plain,
( ~ spl0_1769
| spl0_1770
| spl0_114
| ~ spl0_1698 ),
inference(avatar_split_clause,[],[f16120,f15667,f3972,f16307,f16303]) ).
fof(f16303,plain,
( spl0_1769
<=> c_List_Odistinct(v_evso,tc_Event_Oevent) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1769])]) ).
fof(f16307,plain,
( spl0_1770
<=> c_List_Odistinct(c_List_Olist_OCons(c_Event_Oevent_ONotes(c_Message_Oagent_OSpy,c_Message_Omsg_OMPair(v_na,c_Message_Omsg_OMPair(v_nb,c_Message_Omsg_OKey(v_K)))),v_evso,tc_Event_Oevent),tc_Event_Oevent) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1770])]) ).
fof(f15667,plain,
( spl0_1698
<=> ! [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_1698])]) ).
fof(f16120,plain,
( c_List_Odistinct(c_List_Olist_OCons(c_Event_Oevent_ONotes(c_Message_Oagent_OSpy,c_Message_Omsg_OMPair(v_na,c_Message_Omsg_OMPair(v_nb,c_Message_Omsg_OKey(v_K)))),v_evso,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_List_Odistinct(v_evso,tc_Event_Oevent)
| spl0_114
| ~ spl0_1698 ),
inference(resolution,[],[f15668,f3974]) ).
fof(f15668,plain,
( ! [X41,X0,X23] :
( c_in(X0,c_List_Oset(X23,X41),X41)
| c_List_Odistinct(c_List_Olist_OCons(X0,X23,X41),X41)
| ~ c_List_Odistinct(X23,X41) )
| ~ spl0_1698 ),
inference(avatar_component_clause,[],[f15667]) ).
fof(f16113,plain,
( spl0_1768
| ~ spl0_997
| ~ spl0_999 ),
inference(avatar_split_clause,[],[f8640,f8431,f8421,f16110]) ).
fof(f16110,plain,
( spl0_1768
<=> c_0 = c_Set_Ocontents(c_SetInterval_OatMost(c_0,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1768])]) ).
fof(f8640,plain,
( c_0 = c_Set_Ocontents(c_SetInterval_OatMost(c_0,tc_nat),tc_nat)
| ~ spl0_997
| ~ spl0_999 ),
inference(superposition,[],[f8432,f8423]) ).
fof(f15998,plain,
spl0_1767,
inference(avatar_split_clause,[],[f3408,f15996]) ).
fof(f15996,plain,
( spl0_1767
<=> ! [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_1767])]) ).
fof(f3408,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,[],[f3407,f2115]) ).
fof(f2115,axiom,
! [X3] : c_Numeral_Obin__add(X3,c_Numeral_OPls) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obin__add__Pls__right_0) ).
fof(f3407,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,[],[f3194,f2957]) ).
fof(f2957,plain,
c_Numeral_OPls = c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OPls),
inference(definition_unfolding,[],[f2126,f2129]) ).
fof(f2126,axiom,
c_Numeral_OPls = c_Numeral_Obin__minus(c_Numeral_OPls),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obin__minus__Pls_0) ).
fof(f3194,plain,
! [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__mult(c_Numeral_OMin,c_Numeral_OPls)),X1),X1) ),
inference(definition_unfolding,[],[f1317,f2129]) ).
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/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__12_1) ).
fof(f15994,plain,
spl0_1766,
inference(avatar_split_clause,[],[f3401,f15992]) ).
fof(f15992,plain,
( spl0_1766
<=> ! [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_1766])]) ).
fof(f3401,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,[],[f3400,f2115]) ).
fof(f3400,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,[],[f3188,f2957]) ).
fof(f3188,plain,
! [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__mult(c_Numeral_OMin,c_Numeral_OPls)),X1),X1) ),
inference(definition_unfolding,[],[f1321,f2129]) ).
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/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__14_1) ).
fof(f15990,plain,
spl0_1765,
inference(avatar_split_clause,[],[f3398,f15988]) ).
fof(f15988,plain,
( spl0_1765
<=> ! [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_1765])]) ).
fof(f3398,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,[],[f3397,f2115]) ).
fof(f3397,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,[],[f3186,f2957]) ).
fof(f3186,plain,
! [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__mult(c_Numeral_OMin,c_Numeral_OPls)),X1),X1) ),
inference(definition_unfolding,[],[f1316,f2129]) ).
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/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__12_0) ).
fof(f15986,plain,
spl0_1764,
inference(avatar_split_clause,[],[f3391,f15984]) ).
fof(f15984,plain,
( spl0_1764
<=> ! [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_1764])]) ).
fof(f3391,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,[],[f3390,f2115]) ).
fof(f3390,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,[],[f3180,f2957]) ).
fof(f3180,plain,
! [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__mult(c_Numeral_OMin,c_Numeral_OPls)),X1),X1) ),
inference(definition_unfolding,[],[f1320,f2129]) ).
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/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__14_0) ).
fof(f15982,plain,
spl0_1763,
inference(avatar_split_clause,[],[f3372,f15980]) ).
fof(f15980,plain,
( spl0_1763
<=> ! [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_1763])]) ).
fof(f3372,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,[],[f3164,f2958]) ).
fof(f3164,plain,
! [X21,X15] :
( ~ c_lessequals(c_1,X21,tc_nat)
| ~ c_lessequals(c_1,X15,tc_nat)
| c_lessequals(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),c_times(X15,X21,tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f2097,f2544]) ).
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/benchmark/theBenchmark.p',cls_Nat_Oone__le__mult__iff_2) ).
fof(f15978,plain,
spl0_1762,
inference(avatar_split_clause,[],[f3286,f15976]) ).
fof(f15976,plain,
( spl0_1762
<=> ! [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_1762])]) ).
fof(f3286,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/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__3_0) ).
fof(f15974,plain,
spl0_1761,
inference(avatar_split_clause,[],[f3285,f15972]) ).
fof(f15972,plain,
( spl0_1761
<=> ! [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_1761])]) ).
fof(f3285,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/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__2_0) ).
fof(f15970,plain,
spl0_1760,
inference(avatar_split_clause,[],[f3256,f15968]) ).
fof(f15968,plain,
( spl0_1760
<=> ! [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_1760])]) ).
fof(f3256,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/benchmark/theBenchmark.p',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/benchmark/theBenchmark.p',cls_List_Olistrel__Nil_0) ).
fof(f15966,plain,
spl0_1759,
inference(avatar_split_clause,[],[f3252,f15964]) ).
fof(f3252,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,[],[f3060,f2958]) ).
fof(f3060,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_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),tc_nat),
inference(definition_unfolding,[],[f1627,f2544]) ).
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/benchmark/theBenchmark.p',cls_List_Olist_Osize__2_0) ).
fof(f15962,plain,
spl0_1758,
inference(avatar_split_clause,[],[f3248,f15960]) ).
fof(f15960,plain,
( spl0_1758
<=> ! [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_1758])]) ).
fof(f3248,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/benchmark/theBenchmark.p',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/benchmark/theBenchmark.p',cls_Set_OUn__insert__left_0) ).
fof(f15958,plain,
spl0_1757,
inference(avatar_split_clause,[],[f3146,f15956]) ).
fof(f3146,plain,
! [X21,X3,X1] :
( c_List_Osublist(X3,c_SetInterval_OlessThan(X21,tc_nat),X1) = X3
| ~ c_lessequals(c_Nat_Osize(X3,tc_List_Olist(X1)),X21,tc_nat) ),
inference(definition_unfolding,[],[f1770,f1766]) ).
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/benchmark/theBenchmark.p',cls_List_Otake__all_0) ).
fof(f15954,plain,
( spl0_1755
| ~ spl0_1756
| ~ spl0_869
| ~ spl0_976 ),
inference(avatar_split_clause,[],[f8604,f8335,f7830,f15951,f15948]) ).
fof(f15948,plain,
( spl0_1755
<=> ! [X0] : c_0 = c_OrderedGroup_Onprt(X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1755])]) ).
fof(f15951,plain,
( spl0_1756
<=> class_OrderedGroup_Olordered__ab__group(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1756])]) ).
fof(f8604,plain,
( ! [X0] :
( ~ class_OrderedGroup_Olordered__ab__group(tc_nat)
| c_0 = c_OrderedGroup_Onprt(X0,tc_nat) )
| ~ spl0_869
| ~ spl0_976 ),
inference(resolution,[],[f8336,f7831]) ).
fof(f15930,plain,
( spl0_1754
| ~ spl0_646
| ~ spl0_687
| ~ spl0_1372
| ~ spl0_1461
| ~ spl0_1753 ),
inference(avatar_split_clause,[],[f15926,f15923,f11313,f10914,f7046,f6101,f15928]) ).
fof(f15928,plain,
( spl0_1754
<=> ! [X14,X26] : c_Finite__Set_Ocard(c_SetInterval_OatLeastAtMost(X26,X14,tc_nat),tc_nat) = c_minus(c_plus(c_1,X14,tc_nat),X26,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1754])]) ).
fof(f15923,plain,
( spl0_1753
<=> ! [X14,X26] : c_Finite__Set_Ocard(c_SetInterval_OatLeastAtMost(X26,X14,tc_nat),tc_nat) = c_minus(c_Finite__Set_Ocard(c_SetInterval_OatMost(X14,tc_nat),tc_nat),X26,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1753])]) ).
fof(f15926,plain,
( ! [X26,X14] : c_Finite__Set_Ocard(c_SetInterval_OatLeastAtMost(X26,X14,tc_nat),tc_nat) = c_minus(c_plus(c_1,X14,tc_nat),X26,tc_nat)
| ~ spl0_646
| ~ spl0_687
| ~ spl0_1372
| ~ spl0_1461
| ~ spl0_1753 ),
inference(forward_demodulation,[],[f15924,f12280]) ).
fof(f15924,plain,
( ! [X26,X14] : c_Finite__Set_Ocard(c_SetInterval_OatLeastAtMost(X26,X14,tc_nat),tc_nat) = c_minus(c_Finite__Set_Ocard(c_SetInterval_OatMost(X14,tc_nat),tc_nat),X26,tc_nat)
| ~ spl0_1753 ),
inference(avatar_component_clause,[],[f15923]) ).
fof(f15925,plain,
spl0_1753,
inference(avatar_split_clause,[],[f3031,f15923]) ).
fof(f15907,plain,
( spl0_1752
| ~ spl0_646
| ~ spl0_687
| ~ spl0_1372
| ~ spl0_1461
| ~ spl0_1751 ),
inference(avatar_split_clause,[],[f15903,f15900,f11313,f10914,f7046,f6101,f15905]) ).
fof(f15900,plain,
( spl0_1751
<=> ! [X14,X26] : c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(X26,X14,tc_nat),tc_nat) = c_minus(X14,c_Finite__Set_Ocard(c_SetInterval_OatMost(X26,tc_nat),tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1751])]) ).
fof(f15903,plain,
( ! [X26,X14] : c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(X26,X14,tc_nat),tc_nat) = c_minus(X14,c_plus(c_1,X26,tc_nat),tc_nat)
| ~ spl0_646
| ~ spl0_687
| ~ spl0_1372
| ~ spl0_1461
| ~ spl0_1751 ),
inference(forward_demodulation,[],[f15901,f12280]) ).
fof(f15901,plain,
( ! [X26,X14] : c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(X26,X14,tc_nat),tc_nat) = c_minus(X14,c_Finite__Set_Ocard(c_SetInterval_OatMost(X26,tc_nat),tc_nat),tc_nat)
| ~ spl0_1751 ),
inference(avatar_component_clause,[],[f15900]) ).
fof(f15902,plain,
spl0_1751,
inference(avatar_split_clause,[],[f3030,f15900]) ).
fof(f15878,plain,
( spl0_1750
| ~ spl0_646
| ~ spl0_687
| ~ spl0_1372
| ~ spl0_1461
| ~ spl0_1749 ),
inference(avatar_split_clause,[],[f15874,f15871,f11313,f10914,f7046,f6101,f15876]) ).
fof(f15876,plain,
( spl0_1750
<=> ! [X21,X1,X23] : c_List_Orotate1(c_List_Orotate(X21,X23,X1),X1) = c_List_Orotate(c_plus(c_1,X21,tc_nat),X23,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1750])]) ).
fof(f15871,plain,
( spl0_1749
<=> ! [X21,X1,X23] : c_List_Orotate1(c_List_Orotate(X21,X23,X1),X1) = c_List_Orotate(c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),X23,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1749])]) ).
fof(f15874,plain,
( ! [X21,X1,X23] : c_List_Orotate1(c_List_Orotate(X21,X23,X1),X1) = c_List_Orotate(c_plus(c_1,X21,tc_nat),X23,X1)
| ~ spl0_646
| ~ spl0_687
| ~ spl0_1372
| ~ spl0_1461
| ~ spl0_1749 ),
inference(forward_demodulation,[],[f15872,f12280]) ).
fof(f15872,plain,
( ! [X21,X1,X23] : c_List_Orotate1(c_List_Orotate(X21,X23,X1),X1) = c_List_Orotate(c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),X23,X1)
| ~ spl0_1749 ),
inference(avatar_component_clause,[],[f15871]) ).
fof(f15873,plain,
spl0_1749,
inference(avatar_split_clause,[],[f3029,f15871]) ).
fof(f3029,plain,
! [X21,X1,X23] : c_List_Orotate1(c_List_Orotate(X21,X23,X1),X1) = c_List_Orotate(c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),X23,X1),
inference(definition_unfolding,[],[f1738,f2544]) ).
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/benchmark/theBenchmark.p',cls_List_Orotate__Suc_0) ).
fof(f15869,plain,
spl0_1748,
inference(avatar_split_clause,[],[f2722,f15867]) ).
fof(f15867,plain,
( spl0_1748
<=> ! [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_1748])]) ).
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/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Owf__insert_0) ).
fof(f15865,plain,
( spl0_1747
| ~ spl0_646
| ~ spl0_943 ),
inference(avatar_split_clause,[],[f8544,f8202,f6101,f15863]) ).
fof(f15863,plain,
( spl0_1747
<=> ! [X0] : ~ c_less(c_IntDef_Oint(X0),c_uminus(c_1,tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1747])]) ).
fof(f8202,plain,
( spl0_943
<=> ! [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_943])]) ).
fof(f8544,plain,
( ! [X0] : ~ c_less(c_IntDef_Oint(X0),c_uminus(c_1,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_646
| ~ spl0_943 ),
inference(superposition,[],[f8203,f6103]) ).
fof(f8203,plain,
( ! [X21,X15] : ~ c_less(c_IntDef_Oint(X21),c_uminus(c_IntDef_Oint(X15),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_943 ),
inference(avatar_component_clause,[],[f8202]) ).
fof(f15861,plain,
spl0_1746,
inference(avatar_split_clause,[],[f2719,f15859]) ).
fof(f15859,plain,
( spl0_1746
<=> ! [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_1746])]) ).
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/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Oacyclic__insert_0) ).
fof(f15857,plain,
spl0_1745,
inference(avatar_split_clause,[],[f2657,f15855]) ).
fof(f15855,plain,
( spl0_1745
<=> ! [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_1745])]) ).
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/benchmark/theBenchmark.p',cls_Set_OUnion__iff_2) ).
fof(f15853,plain,
spl0_1744,
inference(avatar_split_clause,[],[f2644,f15851]) ).
fof(f15849,plain,
spl0_1743,
inference(avatar_split_clause,[],[f2640,f15847]) ).
fof(f15847,plain,
( spl0_1743
<=> ! [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_1743])]) ).
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/benchmark/theBenchmark.p',cls_Set_OUn__iff_0) ).
fof(f15845,plain,
spl0_1742,
inference(avatar_split_clause,[],[f2620,f15843]) ).
fof(f15843,plain,
( spl0_1742
<=> ! [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_1742])]) ).
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/benchmark/theBenchmark.p',cls_Set_OInter__iff_0) ).
fof(f15841,plain,
spl0_1741,
inference(avatar_split_clause,[],[f2593,f15839]) ).
fof(f15839,plain,
( spl0_1741
<=> ! [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_1741])]) ).
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/benchmark/theBenchmark.p',cls_Set_ODiff__idemp_0) ).
fof(f15837,plain,
spl0_1740,
inference(avatar_split_clause,[],[f2572,f15835]) ).
fof(f15835,plain,
( spl0_1740
<=> ! [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_1740])]) ).
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/benchmark/theBenchmark.p',cls_SetInterval_OlessThan__subset__iff_1) ).
fof(f15833,plain,
spl0_1739,
inference(avatar_split_clause,[],[f2571,f15831]) ).
fof(f15831,plain,
( spl0_1739
<=> ! [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_1739])]) ).
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/benchmark/theBenchmark.p',cls_SetInterval_OlessThan__subset__iff_0) ).
fof(f15829,plain,
spl0_1738,
inference(avatar_split_clause,[],[f2561,f15827]) ).
fof(f15827,plain,
( spl0_1738
<=> ! [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_1738])]) ).
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/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThan__subset__iff_1) ).
fof(f15825,plain,
spl0_1737,
inference(avatar_split_clause,[],[f2560,f15823]) ).
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/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThan__subset__iff_0) ).
fof(f15821,plain,
( spl0_1736
| ~ spl0_647
| ~ spl0_943 ),
inference(avatar_split_clause,[],[f8543,f8202,f6106,f15819]) ).
fof(f15819,plain,
( spl0_1736
<=> ! [X0] : ~ c_less(c_0,c_uminus(c_IntDef_Oint(X0),tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1736])]) ).
fof(f8543,plain,
( ! [X0] : ~ c_less(c_0,c_uminus(c_IntDef_Oint(X0),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_647
| ~ spl0_943 ),
inference(superposition,[],[f8203,f6108]) ).
fof(f15817,plain,
spl0_1735,
inference(avatar_split_clause,[],[f2548,f15815]) ).
fof(f15815,plain,
( spl0_1735
<=> ! [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_1735])]) ).
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/benchmark/theBenchmark.p',cls_SetInterval_Ocard__greaterThanLessThan__int_0) ).
fof(f15813,plain,
spl0_1734,
inference(avatar_split_clause,[],[f2541,f15811]) ).
fof(f15811,plain,
( spl0_1734
<=> ! [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_1734])]) ).
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/benchmark/theBenchmark.p',cls_SetInterval_Ocard__atLeastAtMost__int_0) ).
fof(f15809,plain,
spl0_1733,
inference(avatar_split_clause,[],[f2539,f15807]) ).
fof(f15807,plain,
( spl0_1733
<=> ! [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_1733])]) ).
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/benchmark/theBenchmark.p',cls_SetInterval_OatMost__subset__iff_1) ).
fof(f15805,plain,
spl0_1732,
inference(avatar_split_clause,[],[f2538,f15803]) ).
fof(f15803,plain,
( spl0_1732
<=> ! [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_1732])]) ).
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/benchmark/theBenchmark.p',cls_SetInterval_OatMost__subset__iff_0) ).
fof(f15801,plain,
spl0_1731,
inference(avatar_split_clause,[],[f2533,f15799]) ).
fof(f15799,plain,
( spl0_1731
<=> ! [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_1731])]) ).
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/benchmark/theBenchmark.p',cls_SetInterval_OatLeast__subset__iff_1) ).
fof(f15797,plain,
spl0_1730,
inference(avatar_split_clause,[],[f2532,f15795]) ).
fof(f15795,plain,
( spl0_1730
<=> ! [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_1730])]) ).
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/benchmark/theBenchmark.p',cls_SetInterval_OatLeast__subset__iff_0) ).
fof(f15793,plain,
spl0_1729,
inference(avatar_split_clause,[],[f2490,f15791]) ).
fof(f15791,plain,
( spl0_1729
<=> ! [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_1729])]) ).
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/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__minus__right_0) ).
fof(f15789,plain,
spl0_1728,
inference(avatar_split_clause,[],[f2489,f15787]) ).
fof(f15787,plain,
( spl0_1728
<=> ! [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_1728])]) ).
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/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__minus__left_0) ).
fof(f15785,plain,
spl0_1727,
inference(avatar_split_clause,[],[f2467,f15783]) ).
fof(f15783,plain,
( spl0_1727
<=> ! [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_1727])]) ).
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/benchmark/theBenchmark.p',cls_Ring__and__Field_Ominus__mult__minus_0) ).
fof(f15781,plain,
spl0_1726,
inference(avatar_split_clause,[],[f2312,f15779]) ).
fof(f15779,plain,
( spl0_1726
<=> ! [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_1726])]) ).
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/benchmark/theBenchmark.p',cls_Parity_Opower__0__left__number__of_1) ).
fof(f15777,plain,
( spl0_1725
| ~ spl0_646
| ~ spl0_943 ),
inference(avatar_split_clause,[],[f8542,f8202,f6101,f15775]) ).
fof(f15775,plain,
( spl0_1725
<=> ! [X0] : ~ c_less(c_1,c_uminus(c_IntDef_Oint(X0),tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1725])]) ).
fof(f8542,plain,
( ! [X0] : ~ c_less(c_1,c_uminus(c_IntDef_Oint(X0),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_646
| ~ spl0_943 ),
inference(superposition,[],[f8203,f6103]) ).
fof(f15773,plain,
spl0_1724,
inference(avatar_split_clause,[],[f2306,f15771]) ).
fof(f15771,plain,
( spl0_1724
<=> ! [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_1724])]) ).
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/benchmark/theBenchmark.p',cls_Parity_Oneg__one__even__power_0) ).
fof(f15769,plain,
spl0_1723,
inference(avatar_split_clause,[],[f2304,f15767]) ).
fof(f15767,plain,
( spl0_1723
<=> ! [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_1723])]) ).
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/benchmark/theBenchmark.p',cls_Parity_Ominus__one__even__power_0) ).
fof(f15765,plain,
spl0_1722,
inference(avatar_split_clause,[],[f2209,f15763]) ).
fof(f15763,plain,
( spl0_1722
<=> ! [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_1722])]) ).
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/benchmark/theBenchmark.p',cls_OrderedGroup_Odouble__add__less__zero__iff__single__less__zero_1) ).
fof(f15761,plain,
spl0_1721,
inference(avatar_split_clause,[],[f2208,f15759]) ).
fof(f15759,plain,
( spl0_1721
<=> ! [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_1721])]) ).
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/benchmark/theBenchmark.p',cls_OrderedGroup_Odouble__add__less__zero__iff__single__less__zero_0) ).
fof(f15757,plain,
spl0_1720,
inference(avatar_split_clause,[],[f2080,f15755]) ).
fof(f15755,plain,
( spl0_1720
<=> ! [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_1720])]) ).
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/benchmark/theBenchmark.p',cls_Nat_Onat__0__less__mult__iff_2) ).
fof(f15753,plain,
spl0_1719,
inference(avatar_split_clause,[],[f2060,f15751]) ).
fof(f15751,plain,
( spl0_1719
<=> ! [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_1719])]) ).
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/benchmark/theBenchmark.p',cls_Nat_Omult__cancel2_0) ).
fof(f15749,plain,
spl0_1718,
inference(avatar_split_clause,[],[f2058,f15747]) ).
fof(f15747,plain,
( spl0_1718
<=> ! [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_1718])]) ).
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/benchmark/theBenchmark.p',cls_Nat_Omult__cancel1_0) ).
fof(f15745,plain,
spl0_1717,
inference(avatar_split_clause,[],[f2037,f15743]) ).
fof(f15743,plain,
( spl0_1717
<=> ! [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_1717])]) ).
fof(f15741,plain,
spl0_1716,
inference(avatar_split_clause,[],[f2028,f15739]) ).
fof(f15739,plain,
( spl0_1716
<=> ! [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_1716])]) ).
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/benchmark/theBenchmark.p',cls_Nat_Oadd__gr__0_0) ).
fof(f15737,plain,
spl0_1715,
inference(avatar_split_clause,[],[f1863,f15735]) ).
fof(f15735,plain,
( spl0_1715
<=> ! [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_1715])]) ).
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/benchmark/theBenchmark.p',cls_NatBin_Omult__nat__number__of_0) ).
fof(f15733,plain,
( spl0_1714
| ~ spl0_646
| ~ spl0_940 ),
inference(avatar_split_clause,[],[f8533,f8190,f6101,f15731]) ).
fof(f15731,plain,
( spl0_1714
<=> ! [X0] :
( c_1 != c_IntDef_Oint(X0)
| c_1 = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1714])]) ).
fof(f8190,plain,
( spl0_940
<=> ! [X21,X15] :
( X15 = X21
| c_IntDef_Oint(X21) != c_IntDef_Oint(X15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_940])]) ).
fof(f8533,plain,
( ! [X0] :
( c_1 != c_IntDef_Oint(X0)
| c_1 = X0 )
| ~ spl0_646
| ~ spl0_940 ),
inference(superposition,[],[f8191,f6103]) ).
fof(f8191,plain,
( ! [X21,X15] :
( c_IntDef_Oint(X21) != c_IntDef_Oint(X15)
| X15 = X21 )
| ~ spl0_940 ),
inference(avatar_component_clause,[],[f8190]) ).
fof(f15729,plain,
spl0_1713,
inference(avatar_split_clause,[],[f1860,f15727]) ).
fof(f15727,plain,
( spl0_1713
<=> ! [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_1713])]) ).
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/benchmark/theBenchmark.p',cls_NatBin_Omod__nat__number__of_0) ).
fof(f15725,plain,
spl0_1712,
inference(avatar_split_clause,[],[f1847,f15723]) ).
fof(f15723,plain,
( spl0_1712
<=> ! [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_1712])]) ).
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/benchmark/theBenchmark.p',cls_NatBin_Oeq__number__of__0_0) ).
fof(f15721,plain,
spl0_1711,
inference(avatar_split_clause,[],[f1827,f15719]) ).
fof(f15719,plain,
( spl0_1711
<=> ! [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_1711])]) ).
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/benchmark/theBenchmark.p',cls_NatBin_Odiv__nat__number__of_0) ).
fof(f15717,plain,
spl0_1710,
inference(avatar_split_clause,[],[f1801,f15715]) ).
fof(f15715,plain,
( spl0_1710
<=> ! [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_1710])]) ).
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/benchmark/theBenchmark.p',cls_NatArith_Odiff__less_0) ).
fof(f15713,plain,
spl0_1709,
inference(avatar_split_clause,[],[f1749,f15711]) ).
fof(f15711,plain,
( spl0_1709
<=> ! [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_1709])]) ).
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/benchmark/theBenchmark.p',cls_List_Oset__append_0) ).
fof(f15709,plain,
spl0_1708,
inference(avatar_split_clause,[],[f1739,f15707]) ).
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/benchmark/theBenchmark.p',cls_List_Orotate__id_0) ).
fof(f15705,plain,
spl0_1707,
inference(avatar_split_clause,[],[f1725,f15703]) ).
fof(f15703,plain,
( spl0_1707
<=> ! [X25,X1,X23] : c_List_Orev(c_append(X23,X25,X1),X1) = c_append(c_List_Orev(X25,X1),c_List_Orev(X23,X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1707])]) ).
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/benchmark/theBenchmark.p',cls_List_Orev__append_0) ).
fof(f15701,plain,
spl0_1706,
inference(avatar_split_clause,[],[f1708,f15699]) ).
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/benchmark/theBenchmark.p',cls_List_Oop_A_64_Oappend__Cons_0) ).
fof(f15697,plain,
spl0_1705,
inference(avatar_split_clause,[],[f1696,f15695]) ).
fof(f15695,plain,
( spl0_1705
<=> ! [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_1705])]) ).
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/benchmark/theBenchmark.p',cls_List_Onth__append__length_0) ).
fof(f15693,plain,
spl0_1704,
inference(avatar_split_clause,[],[f1691,f15691]) ).
fof(f15691,plain,
( spl0_1704
<=> ! [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_1704])]) ).
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/benchmark/theBenchmark.p',cls_List_Onotin__set__sublistI_0) ).
fof(f15689,plain,
( spl0_1703
| ~ spl0_647
| ~ spl0_921 ),
inference(avatar_split_clause,[],[f8530,f8112,f6106,f15687]) ).
fof(f15687,plain,
( spl0_1703
<=> ! [X0] : c_lessequals(c_uminus(c_IntDef_Oint(X0),tc_IntDef_Oint),c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1703])]) ).
fof(f8112,plain,
( spl0_921
<=> ! [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_921])]) ).
fof(f8530,plain,
( ! [X0] : c_lessequals(c_uminus(c_IntDef_Oint(X0),tc_IntDef_Oint),c_0,tc_IntDef_Oint)
| ~ spl0_647
| ~ spl0_921 ),
inference(superposition,[],[f8113,f6108]) ).
fof(f8113,plain,
( ! [X21,X15] : c_lessequals(c_uminus(c_IntDef_Oint(X21),tc_IntDef_Oint),c_IntDef_Oint(X15),tc_IntDef_Oint)
| ~ spl0_921 ),
inference(avatar_component_clause,[],[f8112]) ).
fof(f15685,plain,
spl0_1702,
inference(avatar_split_clause,[],[f1690,f15683]) ).
fof(f15683,plain,
( spl0_1702
<=> ! [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_1702])]) ).
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/benchmark/theBenchmark.p',cls_List_Onotin__set__remove1_0) ).
fof(f15681,plain,
spl0_1701,
inference(avatar_split_clause,[],[f1601,f15679]) ).
fof(f15679,plain,
( spl0_1701
<=> ! [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_1701])]) ).
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/benchmark/theBenchmark.p',cls_List_Olength__drop_0) ).
fof(f15677,plain,
spl0_1700,
inference(avatar_split_clause,[],[f1577,f15675]) ).
fof(f15675,plain,
( spl0_1700
<=> ! [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_1700])]) ).
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/benchmark/theBenchmark.p',cls_List_Odrop__replicate_0) ).
fof(f15673,plain,
spl0_1699,
inference(avatar_split_clause,[],[f1574,f15671]) ).
fof(f15671,plain,
( spl0_1699
<=> ! [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_1699])]) ).
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/benchmark/theBenchmark.p',cls_List_Odrop__drop_0) ).
fof(f15669,plain,
spl0_1698,
inference(avatar_split_clause,[],[f1554,f15667]) ).
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/benchmark/theBenchmark.p',cls_List_Odistinct_Osimps__2_2) ).
fof(f15665,plain,
spl0_1697,
inference(avatar_split_clause,[],[f1547,f15663]) ).
fof(f15663,plain,
( spl0_1697
<=> ! [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_1697])]) ).
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/benchmark/theBenchmark.p',cls_List_Oconcat__eq__Nil__conv_1) ).
fof(f15661,plain,
spl0_1696,
inference(avatar_split_clause,[],[f1518,f15659]) ).
fof(f15659,plain,
( spl0_1696
<=> ! [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_1696])]) ).
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/benchmark/theBenchmark.p',cls_List_Oappend__assoc_0) ).
fof(f15657,plain,
spl0_1695,
inference(avatar_split_clause,[],[f1508,f15655]) ).
fof(f15655,plain,
( spl0_1695
<=> ! [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_1695])]) ).
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/benchmark/theBenchmark.p',cls_List_ONil__eq__concat__conv_1) ).
fof(f15653,plain,
spl0_1694,
inference(avatar_split_clause,[],[f1495,f15651]) ).
fof(f15651,plain,
( spl0_1694
<=> ! [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_1694])]) ).
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/benchmark/theBenchmark.p',cls_IntDiv_Ozmod__zminus__zminus_0) ).
fof(f15649,plain,
spl0_1693,
inference(avatar_split_clause,[],[f1239,f15647]) ).
fof(f15647,plain,
( spl0_1693
<=> ! [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_1693])]) ).
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/benchmark/theBenchmark.p',cls_Divides_Omod__mult__self2_0) ).
fof(f15645,plain,
( spl0_1692
| ~ spl0_646
| ~ spl0_921 ),
inference(avatar_split_clause,[],[f8529,f8112,f6101,f15643]) ).
fof(f15643,plain,
( spl0_1692
<=> ! [X0] : c_lessequals(c_uminus(c_IntDef_Oint(X0),tc_IntDef_Oint),c_1,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1692])]) ).
fof(f8529,plain,
( ! [X0] : c_lessequals(c_uminus(c_IntDef_Oint(X0),tc_IntDef_Oint),c_1,tc_IntDef_Oint)
| ~ spl0_646
| ~ spl0_921 ),
inference(superposition,[],[f8113,f6103]) ).
fof(f15641,plain,
spl0_1691,
inference(avatar_split_clause,[],[f1237,f15639]) ).
fof(f15639,plain,
( spl0_1691
<=> ! [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_1691])]) ).
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/benchmark/theBenchmark.p',cls_Divides_Omod__mult__self1_0) ).
fof(f15637,plain,
spl0_1690,
inference(avatar_split_clause,[],[f1217,f15635]) ).
fof(f15635,plain,
( spl0_1690
<=> ! [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_1690])]) ).
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/benchmark/theBenchmark.p',cls_Divides_Odiv__less__dividend_0) ).
fof(f15633,plain,
spl0_1689,
inference(avatar_split_clause,[],[f127,f15631]) ).
fof(f15631,plain,
( spl0_1689
<=> ! [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_1689])]) ).
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/benchmark/theBenchmark.p',cls_Wellfounded__Relations_Owf__lex__prod_0) ).
fof(f15629,plain,
spl0_1688,
inference(avatar_split_clause,[],[f125,f15627]) ).
fof(f15627,plain,
( spl0_1688
<=> ! [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_1688])]) ).
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/benchmark/theBenchmark.p',cls_Wellfounded__Relations_Otrans__lex__prod_0) ).
fof(f15625,plain,
spl0_1687,
inference(avatar_split_clause,[],[f80,f15623]) ).
fof(f15623,plain,
( spl0_1687
<=> ! [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_1687])]) ).
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/benchmark/theBenchmark.p',cls_Relation_OdiagE_1) ).
fof(f15572,plain,
( spl0_1686
| ~ spl0_646
| ~ spl0_921 ),
inference(avatar_split_clause,[],[f8527,f8112,f6101,f15570]) ).
fof(f15570,plain,
( spl0_1686
<=> ! [X0] : c_lessequals(c_uminus(c_1,tc_IntDef_Oint),c_IntDef_Oint(X0),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1686])]) ).
fof(f8527,plain,
( ! [X0] : c_lessequals(c_uminus(c_1,tc_IntDef_Oint),c_IntDef_Oint(X0),tc_IntDef_Oint)
| ~ spl0_646
| ~ spl0_921 ),
inference(superposition,[],[f8113,f6103]) ).
fof(f15086,plain,
( ~ spl0_44
| ~ spl0_1685
| ~ spl0_1380
| spl0_1487 ),
inference(avatar_split_clause,[],[f13076,f12428,f10947,f15083,f3627]) ).
fof(f3627,plain,
( spl0_44
<=> class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_44])]) ).
fof(f15083,plain,
( spl0_1685
<=> c_lessequals(c_1,c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1685])]) ).
fof(f10947,plain,
( spl0_1380
<=> ! [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_1380])]) ).
fof(f12428,plain,
( spl0_1487
<=> c_lessequals(c_0,c_uminus(c_1,tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1487])]) ).
fof(f13076,plain,
( ~ c_lessequals(c_1,c_0,tc_IntDef_Oint)
| ~ class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint)
| ~ spl0_1380
| spl0_1487 ),
inference(resolution,[],[f12430,f10948]) ).
fof(f10948,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_1380 ),
inference(avatar_component_clause,[],[f10947]) ).
fof(f12430,plain,
( ~ c_lessequals(c_0,c_uminus(c_1,tc_IntDef_Oint),tc_IntDef_Oint)
| spl0_1487 ),
inference(avatar_component_clause,[],[f12428]) ).
fof(f14603,plain,
spl0_1684,
inference(avatar_split_clause,[],[f3364,f14601]) ).
fof(f14601,plain,
( spl0_1684
<=> ! [X1,X3] :
( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X3),X1),X1)
| ~ class_Numeral_Onumber__ring(X1)
| c_0 = c_Numeral_Onumber__of(X3,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1684])]) ).
fof(f3364,plain,
! [X3,X1] :
( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X3),X1),X1)
| ~ class_Numeral_Onumber__ring(X1)
| c_0 = c_Numeral_Onumber__of(X3,X1) ),
inference(forward_demodulation,[],[f3158,f2114]) ).
fof(f3158,plain,
! [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__mult(c_Numeral_OMin,X3)),X1),X1) ),
inference(definition_unfolding,[],[f1334,f2129]) ).
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/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__6_1) ).
fof(f14599,plain,
spl0_1683,
inference(avatar_split_clause,[],[f3359,f14597]) ).
fof(f14597,plain,
( spl0_1683
<=> ! [X1,X3] :
( c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X3),X1),X1)
| ~ class_Numeral_Onumber__ring(X1)
| c_0 != c_Numeral_Onumber__of(X3,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1683])]) ).
fof(f3359,plain,
! [X3,X1] :
( c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X3),X1),X1)
| ~ class_Numeral_Onumber__ring(X1)
| c_0 != c_Numeral_Onumber__of(X3,X1) ),
inference(forward_demodulation,[],[f3154,f2114]) ).
fof(f3154,plain,
! [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__mult(c_Numeral_OMin,X3)),X1),X1) ),
inference(definition_unfolding,[],[f1333,f2129]) ).
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/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__6_0) ).
fof(f14595,plain,
spl0_1682,
inference(avatar_split_clause,[],[f3247,f14593]) ).
fof(f14593,plain,
( spl0_1682
<=> ! [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_1682])]) ).
fof(f3247,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,[],[f3053,f2958]) ).
fof(f3053,plain,
! [X83] : c_IntDef_Onat(c_div(c_1,c_Numeral_Onumber__of(X83,tc_IntDef_Oint),tc_IntDef_Oint)) = c_div(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),c_Numeral_Onumber__of(X83,tc_nat),tc_nat),
inference(definition_unfolding,[],[f1870,f2544]) ).
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/benchmark/theBenchmark.p',cls_NatBin_Oone__div__nat__number__of_0) ).
fof(f14591,plain,
spl0_1681,
inference(avatar_split_clause,[],[f3163,f14589]) ).
fof(f14589,plain,
( spl0_1681
<=> ! [X21,X1,X23] :
( c_List_Olist_ONil = X23
| c_0 = X21
| c_List_Olist_ONil != c_List_Osublist(X23,c_SetInterval_OlessThan(X21,tc_nat),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1681])]) ).
fof(f3163,plain,
! [X21,X1,X23] :
( c_List_Olist_ONil = X23
| c_0 = X21
| c_List_Olist_ONil != c_List_Osublist(X23,c_SetInterval_OlessThan(X21,tc_nat),X1) ),
inference(definition_unfolding,[],[f1772,f1766]) ).
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/benchmark/theBenchmark.p',cls_List_Otake__eq__Nil_0) ).
fof(f14582,plain,
( spl0_1680
| ~ spl0_646
| ~ spl0_687
| ~ spl0_1372
| ~ spl0_1461
| ~ spl0_1679 ),
inference(avatar_split_clause,[],[f14578,f14575,f11313,f10914,f7046,f6101,f14580]) ).
fof(f14580,plain,
( spl0_1680
<=> ! [X47] :
( c_1 = c_plus(c_1,c_Numeral_Onumber__of(X47,tc_nat),tc_nat)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1680])]) ).
fof(f14575,plain,
( spl0_1679
<=> ! [X47] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_1 = c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Numeral_Onumber__of(X47,tc_nat),tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1679])]) ).
fof(f14578,plain,
( ! [X47] :
( c_1 = c_plus(c_1,c_Numeral_Onumber__of(X47,tc_nat),tc_nat)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint) )
| ~ spl0_646
| ~ spl0_687
| ~ spl0_1372
| ~ spl0_1461
| ~ spl0_1679 ),
inference(forward_demodulation,[],[f14576,f12280]) ).
fof(f14576,plain,
( ! [X47] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_1 = c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Numeral_Onumber__of(X47,tc_nat),tc_nat),tc_nat) )
| ~ spl0_1679 ),
inference(avatar_component_clause,[],[f14575]) ).
fof(f14577,plain,
spl0_1679,
inference(avatar_split_clause,[],[f3127,f14575]) ).
fof(f3127,plain,
! [X47] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_1 = c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Numeral_Onumber__of(X47,tc_nat),tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f1822,f2544]) ).
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/benchmark/theBenchmark.p',cls_NatBin_OSuc__nat__number__of_0) ).
fof(f14552,plain,
spl0_1678,
inference(avatar_split_clause,[],[f3125,f14550]) ).
fof(f14550,plain,
( spl0_1678
<=> ! [X4,X13,X12,X1] :
( c_in(X4,X12,X1)
| ~ c_in(X4,c_Relation_OImage(c_Relation_Odiag(X12,X1),X13,X1,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1678])]) ).
fof(f3125,plain,
! [X1,X4,X12,X13] :
( c_in(X4,X12,X1)
| ~ c_in(X4,c_Relation_OImage(c_Relation_Odiag(X12,X1),X13,X1,X1),X1) ),
inference(definition_unfolding,[],[f2606,f2373]) ).
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/benchmark/theBenchmark.p',cls_Set_OInt__iff_0) ).
fof(f14548,plain,
spl0_1677,
inference(avatar_split_clause,[],[f3124,f14546]) ).
fof(f14546,plain,
( spl0_1677
<=> ! [X4,X13,X12,X1] :
( c_in(X4,X13,X1)
| ~ c_in(X4,c_Relation_OImage(c_Relation_Odiag(X12,X1),X13,X1,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1677])]) ).
fof(f3124,plain,
! [X1,X4,X12,X13] :
( c_in(X4,X13,X1)
| ~ c_in(X4,c_Relation_OImage(c_Relation_Odiag(X12,X1),X13,X1,X1),X1) ),
inference(definition_unfolding,[],[f2607,f2373]) ).
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/benchmark/theBenchmark.p',cls_Set_OInt__iff_1) ).
fof(f14544,plain,
spl0_1676,
inference(avatar_split_clause,[],[f3090,f14542]) ).
fof(f14542,plain,
( spl0_1676
<=> ! [X21,X15] :
( X15 = X21
| c_Finite__Set_Ocard(c_SetInterval_OatMost(X15,tc_nat),tc_nat) != c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1676])]) ).
fof(f3090,plain,
! [X21,X15] :
( X15 = X21
| c_Finite__Set_Ocard(c_SetInterval_OatMost(X15,tc_nat),tc_nat) != c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f2017,f2544,f2544]) ).
fof(f2017,axiom,
! [X21,X15] :
( X15 = X21
| c_Suc(X21) != c_Suc(X15) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_OSuc__Suc__eq_0) ).
fof(f14540,plain,
spl0_1675,
inference(avatar_split_clause,[],[f3034,f14538]) ).
fof(f14538,plain,
( spl0_1675
<=> ! [X21,X1,X3] : c_append(c_List_Osublist(X3,c_SetInterval_OlessThan(X21,tc_nat),X1),c_List_Odrop(X21,X3,X1),X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1675])]) ).
fof(f3034,plain,
! [X21,X3,X1] : c_append(c_List_Osublist(X3,c_SetInterval_OlessThan(X21,tc_nat),X1),c_List_Odrop(X21,X3,X1),X1) = X3,
inference(definition_unfolding,[],[f1535,f1766]) ).
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/benchmark/theBenchmark.p',cls_List_Oappend__take__drop__id_0) ).
fof(f14536,plain,
spl0_1674,
inference(avatar_split_clause,[],[f2896,f14534]) ).
fof(f14534,plain,
( spl0_1674
<=> ! [X102,X27,X12] :
( ~ c_in(X12,c_Event_Obad,tc_Message_Oagent)
| c_in(c_Message_Omsg_OKey(c_Message_OinvKey(c_Public_OpublicKey(X27,X12))),c_Event_Oknows(c_Message_Oagent_OSpy,X102),tc_Message_Omsg) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1674])]) ).
fof(f2896,axiom,
! [X27,X12,X102] :
( ~ c_in(X12,c_Event_Obad,tc_Message_Oagent)
| c_in(c_Message_Omsg_OKey(c_Message_OinvKey(c_Public_OpublicKey(X27,X12))),c_Event_Oknows(c_Message_Oagent_OSpy,X102),tc_Message_Omsg) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Public_OSpy__spies__bad__privateKey_0) ).
fof(f14532,plain,
spl0_1673,
inference(avatar_split_clause,[],[f2841,f14530]) ).
fof(f14530,plain,
( spl0_1673
<=> ! [X87,X86,X88] :
( c_in(X87,c_Message_Osynth(c_Message_Oanalz(X88)),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OMPair(X86,X87),c_Message_Osynth(c_Message_Oanalz(X88)),tc_Message_Omsg) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1673])]) ).
fof(f2841,axiom,
! [X88,X86,X87] :
( c_in(X87,c_Message_Osynth(c_Message_Oanalz(X88)),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OMPair(X86,X87),c_Message_Osynth(c_Message_Oanalz(X88)),tc_Message_Omsg) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OMPair__synth__analz_1) ).
fof(f14528,plain,
spl0_1672,
inference(avatar_split_clause,[],[f2840,f14526]) ).
fof(f14526,plain,
( spl0_1672
<=> ! [X86,X87,X88] :
( c_in(X86,c_Message_Osynth(c_Message_Oanalz(X88)),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OMPair(X86,X87),c_Message_Osynth(c_Message_Oanalz(X88)),tc_Message_Omsg) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1672])]) ).
fof(f2840,axiom,
! [X88,X86,X87] :
( c_in(X86,c_Message_Osynth(c_Message_Oanalz(X88)),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OMPair(X86,X87),c_Message_Osynth(c_Message_Oanalz(X88)),tc_Message_Omsg) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OMPair__synth__analz_0) ).
fof(f14524,plain,
spl0_1671,
inference(avatar_split_clause,[],[f2745,f14522]) ).
fof(f14522,plain,
( spl0_1671
<=> ! [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_1671])]) ).
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/benchmark/theBenchmark.p',cls_Message_OkeysFor__insert__Crypt_0) ).
fof(f14520,plain,
spl0_1670,
inference(avatar_split_clause,[],[f2727,f14518]) ).
fof(f14518,plain,
( spl0_1670
<=> ! [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_1670])]) ).
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/benchmark/theBenchmark.p',cls_Wellfounded__Relations_Oless__than__iff_1) ).
fof(f14516,plain,
spl0_1669,
inference(avatar_split_clause,[],[f2726,f14514]) ).
fof(f14514,plain,
( spl0_1669
<=> ! [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_1669])]) ).
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/benchmark/theBenchmark.p',cls_Wellfounded__Relations_Oless__than__iff_0) ).
fof(f14490,plain,
spl0_1668,
inference(avatar_split_clause,[],[f2683,f14488]) ).
fof(f14488,plain,
( spl0_1668
<=> ! [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_1668])]) ).
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/benchmark/theBenchmark.p',cls_Set_Oinsert__iff_0) ).
fof(f14486,plain,
spl0_1667,
inference(avatar_split_clause,[],[f2658,f14484]) ).
fof(f14484,plain,
( spl0_1667
<=> ! [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_1667])]) ).
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/benchmark/theBenchmark.p',cls_Set_OUnion__insert_0) ).
fof(f14482,plain,
spl0_1666,
inference(avatar_split_clause,[],[f2655,f14480]) ).
fof(f14480,plain,
( spl0_1666
<=> ! [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_1666])]) ).
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/benchmark/theBenchmark.p',cls_Set_OUnion__iff_0) ).
fof(f14478,plain,
spl0_1665,
inference(avatar_split_clause,[],[f2621,f14476]) ).
fof(f14476,plain,
( spl0_1665
<=> ! [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_1665])]) ).
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/benchmark/theBenchmark.p',cls_Set_OInter__iff_1) ).
fof(f14474,plain,
spl0_1664,
inference(avatar_split_clause,[],[f2488,f14472]) ).
fof(f14472,plain,
( spl0_1664
<=> ! [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_1664])]) ).
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/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__eq__0__iff_0) ).
fof(f14470,plain,
spl0_1663,
inference(avatar_split_clause,[],[f2475,f14468]) ).
fof(f14468,plain,
( spl0_1663
<=> ! [X18,X1,X4] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| c_1 = X18
| c_0 = X4
| c_times(X18,X4,X1) != X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1663])]) ).
fof(f2475,axiom,
! [X1,X18,X4] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| c_1 = X18
| c_0 = X4
| c_times(X18,X4,X1) != X4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__cancel__right2_0) ).
fof(f14466,plain,
spl0_1662,
inference(avatar_split_clause,[],[f2471,f14464]) ).
fof(f14464,plain,
( spl0_1662
<=> ! [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_1662])]) ).
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/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__cancel__left2_0) ).
fof(f14462,plain,
spl0_1661,
inference(avatar_split_clause,[],[f2363,f14460]) ).
fof(f14460,plain,
( spl0_1661
<=> ! [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_1661])]) ).
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/benchmark/theBenchmark.p',cls_Product__Type_OPair__eq_1) ).
fof(f14458,plain,
spl0_1660,
inference(avatar_split_clause,[],[f2362,f14456]) ).
fof(f14456,plain,
( spl0_1660
<=> ! [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_1660])]) ).
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/benchmark/theBenchmark.p',cls_Product__Type_OPair__eq_0) ).
fof(f14454,plain,
spl0_1659,
inference(avatar_split_clause,[],[f2349,f14452]) ).
fof(f14452,plain,
( spl0_1659
<=> ! [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_1659])]) ).
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/benchmark/theBenchmark.p',cls_Power_Opower__eq__0__iff_2) ).
fof(f14450,plain,
( spl0_1658
| ~ spl0_717
| ~ spl0_718
| ~ spl0_720
| ~ spl0_797
| ~ spl0_1590 ),
inference(avatar_split_clause,[],[f14194,f12907,f7528,f7197,f7189,f7184,f14448]) ).
fof(f7189,plain,
( spl0_718
<=> ! [X3] : c_Numeral_Obin__add(c_Numeral_OPls,X3) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_718])]) ).
fof(f7197,plain,
( spl0_720
<=> ! [X11] : c_Numeral_OPls = c_Numeral_Obin__mult(c_Numeral_OPls,X11) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_720])]) ).
fof(f12907,plain,
( spl0_1590
<=> ! [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_1590])]) ).
fof(f14194,plain,
( ! [X0] : c_Numeral_Obin__mult(c_Numeral_Obin__succ(c_Numeral_OPls),X0) = X0
| ~ spl0_717
| ~ spl0_718
| ~ spl0_720
| ~ spl0_797
| ~ spl0_1590 ),
inference(forward_demodulation,[],[f14193,f7190]) ).
fof(f7190,plain,
( ! [X3] : c_Numeral_Obin__add(c_Numeral_OPls,X3) = X3
| ~ spl0_718 ),
inference(avatar_component_clause,[],[f7189]) ).
fof(f14193,plain,
( ! [X0] : c_Numeral_Obin__add(c_Numeral_OPls,X0) = c_Numeral_Obin__mult(c_Numeral_Obin__succ(c_Numeral_OPls),X0)
| ~ spl0_717
| ~ spl0_720
| ~ spl0_797
| ~ spl0_1590 ),
inference(forward_demodulation,[],[f14192,f7530]) ).
fof(f14192,plain,
( ! [X0] : c_Numeral_Obin__add(c_Numeral_OPls,X0) = c_Numeral_Obin__mult(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),X0)
| ~ spl0_717
| ~ spl0_720
| ~ spl0_1590 ),
inference(forward_demodulation,[],[f14181,f7198]) ).
fof(f7198,plain,
( ! [X11] : c_Numeral_OPls = c_Numeral_Obin__mult(c_Numeral_OPls,X11)
| ~ spl0_720 ),
inference(avatar_component_clause,[],[f7197]) ).
fof(f14181,plain,
( ! [X0] : c_Numeral_Obin__mult(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),X0) = c_Numeral_Obin__add(c_Numeral_Obin__mult(c_Numeral_OPls,X0),X0)
| ~ spl0_717
| ~ spl0_1590 ),
inference(superposition,[],[f12908,f7186]) ).
fof(f12908,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_1590 ),
inference(avatar_component_clause,[],[f12907]) ).
fof(f14446,plain,
spl0_1657,
inference(avatar_split_clause,[],[f2348,f14444]) ).
fof(f14444,plain,
( spl0_1657
<=> ! [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_1657])]) ).
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/benchmark/theBenchmark.p',cls_Power_Opower__eq__0__iff_1) ).
fof(f14442,plain,
spl0_1656,
inference(avatar_split_clause,[],[f2268,f14440]) ).
fof(f14440,plain,
( spl0_1656
<=> ! [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_1656])]) ).
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/benchmark/theBenchmark.p',cls_Orderings_Omin__max_Obelow__sup_Osup__left__idem_0) ).
fof(f14438,plain,
spl0_1655,
inference(avatar_split_clause,[],[f2263,f14436]) ).
fof(f14436,plain,
( spl0_1655
<=> ! [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_1655])]) ).
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/benchmark/theBenchmark.p',cls_Orderings_Omin__max_Obelow__inf_Oinf__left__idem_0) ).
fof(f14434,plain,
spl0_1654,
inference(avatar_split_clause,[],[f2246,f14432]) ).
fof(f14432,plain,
( spl0_1654
<=> ! [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_1654])]) ).
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/benchmark/theBenchmark.p',cls_OrderedGroup_Opprt__mono_0) ).
fof(f14430,plain,
spl0_1653,
inference(avatar_split_clause,[],[f2242,f14428]) ).
fof(f14428,plain,
( spl0_1653
<=> ! [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_1653])]) ).
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/benchmark/theBenchmark.p',cls_OrderedGroup_Onprt__mono_0) ).
fof(f14426,plain,
spl0_1652,
inference(avatar_split_clause,[],[f2236,f14424]) ).
fof(f14424,plain,
( spl0_1652
<=> ! [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_1652])]) ).
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/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__less__iff__less_1) ).
fof(f14422,plain,
spl0_1651,
inference(avatar_split_clause,[],[f2235,f14420]) ).
fof(f14420,plain,
( spl0_1651
<=> ! [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_1651])]) ).
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/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__less__iff__less_0) ).
fof(f14418,plain,
spl0_1650,
inference(avatar_split_clause,[],[f2232,f14416]) ).
fof(f14416,plain,
( spl0_1650
<=> ! [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_1650])]) ).
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/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__le__iff__le_1) ).
fof(f14414,plain,
spl0_1649,
inference(avatar_split_clause,[],[f2231,f14412]) ).
fof(f14412,plain,
( spl0_1649
<=> ! [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_1649])]) ).
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/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__le__iff__le_0) ).
fof(f14410,plain,
spl0_1648,
inference(avatar_split_clause,[],[f2195,f14408]) ).
fof(f14408,plain,
( spl0_1648
<=> ! [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_1648])]) ).
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/benchmark/theBenchmark.p',cls_OrderedGroup_Oadd__right__cancel_0) ).
fof(f14406,plain,
( spl0_1647
| ~ spl0_716
| ~ spl0_718
| ~ spl0_743
| ~ spl0_797
| ~ spl0_911
| ~ spl0_1589 ),
inference(avatar_split_clause,[],[f14175,f12903,f8000,f7528,f7297,f7189,f7179,f14403]) ).
fof(f7179,plain,
( spl0_716
<=> c_Numeral_OMin = c_Numeral_OBit(c_Numeral_OMin,c_Numeral_Obit_OB1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_716])]) ).
fof(f8000,plain,
( spl0_911
<=> ! [X11] : c_Numeral_Obin__add(c_Numeral_OMin,X11) = c_Numeral_Obin__add(X11,c_Numeral_OMin) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_911])]) ).
fof(f12903,plain,
( spl0_1589
<=> ! [X11] : c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OBit(X11,c_Numeral_Obit_OB1)) = c_Numeral_OBit(c_Numeral_Obin__add(c_Numeral_OMin,c_Numeral_Obin__mult(c_Numeral_OMin,X11)),c_Numeral_Obit_OB1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1589])]) ).
fof(f14175,plain,
( c_Numeral_OMin = c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_Obin__succ(c_Numeral_OPls))
| ~ spl0_716
| ~ spl0_718
| ~ spl0_743
| ~ spl0_797
| ~ spl0_911
| ~ spl0_1589 ),
inference(forward_demodulation,[],[f14174,f7181]) ).
fof(f7181,plain,
( c_Numeral_OMin = c_Numeral_OBit(c_Numeral_OMin,c_Numeral_Obit_OB1)
| ~ spl0_716 ),
inference(avatar_component_clause,[],[f7179]) ).
fof(f14174,plain,
( c_Numeral_OBit(c_Numeral_OMin,c_Numeral_Obit_OB1) = c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_Obin__succ(c_Numeral_OPls))
| ~ spl0_718
| ~ spl0_743
| ~ spl0_797
| ~ spl0_911
| ~ spl0_1589 ),
inference(forward_demodulation,[],[f14173,f7530]) ).
fof(f14173,plain,
( c_Numeral_OBit(c_Numeral_OMin,c_Numeral_Obit_OB1) = c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))
| ~ spl0_718
| ~ spl0_743
| ~ spl0_911
| ~ spl0_1589 ),
inference(forward_demodulation,[],[f14172,f7190]) ).
fof(f14172,plain,
( c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1)) = c_Numeral_OBit(c_Numeral_Obin__add(c_Numeral_OPls,c_Numeral_OMin),c_Numeral_Obit_OB1)
| ~ spl0_743
| ~ spl0_911
| ~ spl0_1589 ),
inference(forward_demodulation,[],[f14166,f8001]) ).
fof(f8001,plain,
( ! [X11] : c_Numeral_Obin__add(c_Numeral_OMin,X11) = c_Numeral_Obin__add(X11,c_Numeral_OMin)
| ~ spl0_911 ),
inference(avatar_component_clause,[],[f8000]) ).
fof(f14166,plain,
( c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1)) = c_Numeral_OBit(c_Numeral_Obin__add(c_Numeral_OMin,c_Numeral_OPls),c_Numeral_Obit_OB1)
| ~ spl0_743
| ~ spl0_1589 ),
inference(superposition,[],[f12904,f7299]) ).
fof(f12904,plain,
( ! [X11] : c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OBit(X11,c_Numeral_Obit_OB1)) = c_Numeral_OBit(c_Numeral_Obin__add(c_Numeral_OMin,c_Numeral_Obin__mult(c_Numeral_OMin,X11)),c_Numeral_Obit_OB1)
| ~ spl0_1589 ),
inference(avatar_component_clause,[],[f12903]) ).
fof(f14401,plain,
spl0_1646,
inference(avatar_split_clause,[],[f2190,f14399]) ).
fof(f14399,plain,
( spl0_1646
<=> ! [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_1646])]) ).
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/benchmark/theBenchmark.p',cls_OrderedGroup_Oadd__left__cancel_0) ).
fof(f14397,plain,
spl0_1645,
inference(avatar_split_clause,[],[f2111,f14395]) ).
fof(f14395,plain,
( spl0_1645
<=> ! [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_1645])]) ).
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/benchmark/theBenchmark.p',cls_Numeral_Obin__add__BIT__11_0) ).
fof(f14393,plain,
spl0_1644,
inference(avatar_split_clause,[],[f2085,f14391]) ).
fof(f14391,plain,
( spl0_1644
<=> ! [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_1644])]) ).
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/benchmark/theBenchmark.p',cls_Nat_Onat__add__left__cancel__less_1) ).
fof(f14389,plain,
spl0_1643,
inference(avatar_split_clause,[],[f2084,f14387]) ).
fof(f14387,plain,
( spl0_1643
<=> ! [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_1643])]) ).
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/benchmark/theBenchmark.p',cls_Nat_Onat__add__left__cancel__less_0) ).
fof(f14385,plain,
spl0_1642,
inference(avatar_split_clause,[],[f2083,f14383]) ).
fof(f14383,plain,
( spl0_1642
<=> ! [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_1642])]) ).
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/benchmark/theBenchmark.p',cls_Nat_Onat__add__left__cancel__le_1) ).
fof(f14381,plain,
spl0_1641,
inference(avatar_split_clause,[],[f2082,f14379]) ).
fof(f14379,plain,
( spl0_1641
<=> ! [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_1641])]) ).
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/benchmark/theBenchmark.p',cls_Nat_Onat__add__left__cancel__le_0) ).
fof(f14377,plain,
spl0_1640,
inference(avatar_split_clause,[],[f2076,f14375]) ).
fof(f14375,plain,
( spl0_1640
<=> ! [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_1640])]) ).
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/benchmark/theBenchmark.p',cls_Nat_Omult__less__cancel2_1) ).
fof(f14373,plain,
spl0_1639,
inference(avatar_split_clause,[],[f2075,f14371]) ).
fof(f14371,plain,
( spl0_1639
<=> ! [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_1639])]) ).
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/benchmark/theBenchmark.p',cls_Nat_Omult__less__cancel2_0) ).
fof(f14369,plain,
spl0_1638,
inference(avatar_split_clause,[],[f2073,f14367]) ).
fof(f14367,plain,
( spl0_1638
<=> ! [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_1638])]) ).
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/benchmark/theBenchmark.p',cls_Nat_Omult__less__cancel1_1) ).
fof(f14365,plain,
spl0_1637,
inference(avatar_split_clause,[],[f2072,f14363]) ).
fof(f14363,plain,
( spl0_1637
<=> ! [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_1637])]) ).
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/benchmark/theBenchmark.p',cls_Nat_Omult__less__cancel1_0) ).
fof(f14361,plain,
( spl0_1636
| ~ spl0_672
| ~ spl0_1575 ),
inference(avatar_split_clause,[],[f14116,f12804,f6982,f14359]) ).
fof(f14359,plain,
( spl0_1636
<=> ! [X0] : c_lessequals(X0,c_Message_Osynth(X0),tc_set(tc_Message_Omsg)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1636])]) ).
fof(f12804,plain,
( spl0_1575
<=> ! [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_1575])]) ).
fof(f14116,plain,
( ! [X0] : c_lessequals(X0,c_Message_Osynth(X0),tc_set(tc_Message_Omsg))
| ~ spl0_672
| ~ spl0_1575 ),
inference(resolution,[],[f12805,f6983]) ).
fof(f12805,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_1575 ),
inference(avatar_component_clause,[],[f12804]) ).
fof(f14357,plain,
spl0_1635,
inference(avatar_split_clause,[],[f2071,f14355]) ).
fof(f14355,plain,
( spl0_1635
<=> ! [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_1635])]) ).
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/benchmark/theBenchmark.p',cls_Nat_Omult__le__cancel2_2) ).
fof(f14353,plain,
spl0_1634,
inference(avatar_split_clause,[],[f2070,f14351]) ).
fof(f14351,plain,
( spl0_1634
<=> ! [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_1634])]) ).
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/benchmark/theBenchmark.p',cls_Nat_Omult__le__cancel2_1) ).
fof(f14349,plain,
spl0_1633,
inference(avatar_split_clause,[],[f2068,f14347]) ).
fof(f14347,plain,
( spl0_1633
<=> ! [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_1633])]) ).
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/benchmark/theBenchmark.p',cls_Nat_Omult__le__cancel1_2) ).
fof(f14345,plain,
spl0_1632,
inference(avatar_split_clause,[],[f2067,f14343]) ).
fof(f14343,plain,
( spl0_1632
<=> ! [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_1632])]) ).
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/benchmark/theBenchmark.p',cls_Nat_Omult__le__cancel1_1) ).
fof(f14341,plain,
spl0_1631,
inference(avatar_split_clause,[],[f1927,f14339]) ).
fof(f14339,plain,
( spl0_1631
<=> ! [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_1631])]) ).
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/benchmark/theBenchmark.p',cls_NatSimprocs_Oequation__minus__iff__1_0) ).
fof(f14337,plain,
spl0_1630,
inference(avatar_split_clause,[],[f1868,f14335]) ).
fof(f14335,plain,
( spl0_1630
<=> ! [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_1630])]) ).
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/benchmark/theBenchmark.p',cls_NatBin_Oof__nat__number__of__eq_0) ).
fof(f14333,plain,
spl0_1629,
inference(avatar_split_clause,[],[f1820,f14331]) ).
fof(f14331,plain,
( spl0_1629
<=> ! [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_1629])]) ).
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/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__less__iff_1) ).
fof(f14329,plain,
spl0_1628,
inference(avatar_split_clause,[],[f1819,f14327]) ).
fof(f14327,plain,
( spl0_1628
<=> ! [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_1628])]) ).
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/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__less__iff_0) ).
fof(f14325,plain,
spl0_1627,
inference(avatar_split_clause,[],[f1817,f14323]) ).
fof(f14323,plain,
( spl0_1627
<=> ! [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_1627])]) ).
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/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__le__iff_1) ).
fof(f14321,plain,
spl0_1626,
inference(avatar_split_clause,[],[f1816,f14319]) ).
fof(f14319,plain,
( spl0_1626
<=> ! [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_1626])]) ).
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/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__le__iff_0) ).
fof(f14317,plain,
( spl0_1625
| ~ spl0_672
| ~ spl0_1573 ),
inference(avatar_split_clause,[],[f14091,f12796,f6982,f14315]) ).
fof(f14315,plain,
( spl0_1625
<=> ! [X0] : c_lessequals(X0,c_Message_Oparts(X0),tc_set(tc_Message_Omsg)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1625])]) ).
fof(f12796,plain,
( spl0_1573
<=> ! [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_1573])]) ).
fof(f14091,plain,
( ! [X0] : c_lessequals(X0,c_Message_Oparts(X0),tc_set(tc_Message_Omsg))
| ~ spl0_672
| ~ spl0_1573 ),
inference(resolution,[],[f12797,f6983]) ).
fof(f12797,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_1573 ),
inference(avatar_component_clause,[],[f12796]) ).
fof(f14313,plain,
spl0_1624,
inference(avatar_split_clause,[],[f1756,f14311]) ).
fof(f14311,plain,
( spl0_1624
<=> ! [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_1624])]) ).
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/benchmark/theBenchmark.p',cls_List_Oset__replicate_0) ).
fof(f14309,plain,
spl0_1623,
inference(avatar_split_clause,[],[f1733,f14307]) ).
fof(f14307,plain,
( spl0_1623
<=> ! [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_1623])]) ).
fof(f1733,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/benchmark/theBenchmark.p',cls_List_Orev__singleton__conv_0) ).
fof(f14305,plain,
spl0_1622,
inference(avatar_split_clause,[],[f1710,f14303]) ).
fof(f14303,plain,
( spl0_1622
<=> ! [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_1622])]) ).
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/benchmark/theBenchmark.p',cls_List_Oop_Amem_Osimps__2_0) ).
fof(f14301,plain,
spl0_1621,
inference(avatar_split_clause,[],[f1640,f14299]) ).
fof(f14299,plain,
( spl0_1621
<=> ! [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_1621])]) ).
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/benchmark/theBenchmark.p',cls_List_Olistset_Osimps__2_0) ).
fof(f14297,plain,
spl0_1620,
inference(avatar_split_clause,[],[f1632,f14295]) ).
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/benchmark/theBenchmark.p',cls_List_Olist__update__beyond_0) ).
fof(f14293,plain,
spl0_1619,
inference(avatar_split_clause,[],[f1612,f14291]) ).
fof(f14291,plain,
( spl0_1619
<=> ! [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_1619])]) ).
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/benchmark/theBenchmark.p',cls_List_Olength__tl_0) ).
fof(f14289,plain,
spl0_1618,
inference(avatar_split_clause,[],[f1600,f14287]) ).
fof(f14287,plain,
( spl0_1618
<=> ! [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_1618])]) ).
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/benchmark/theBenchmark.p',cls_List_Olength__butlast_0) ).
fof(f14285,plain,
spl0_1617,
inference(avatar_split_clause,[],[f1596,f14283]) ).
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/benchmark/theBenchmark.p',cls_List_Olast__upt_0) ).
fof(f14281,plain,
spl0_1616,
inference(avatar_split_clause,[],[f1544,f14279]) ).
fof(f14279,plain,
( spl0_1616
<=> ! [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_1616])]) ).
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/benchmark/theBenchmark.p',cls_List_Oconcat_Osimps__2_0) ).
fof(f14277,plain,
spl0_1615,
inference(avatar_split_clause,[],[f1456,f14275]) ).
fof(f14275,plain,
( spl0_1615
<=> ! [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_1615])]) ).
fof(f14273,plain,
( spl0_1614
| ~ spl0_672
| ~ spl0_1563 ),
inference(avatar_split_clause,[],[f13967,f12756,f6982,f14271]) ).
fof(f14271,plain,
( spl0_1614
<=> ! [X0] : c_lessequals(X0,c_Message_Oanalz(X0),tc_set(tc_Message_Omsg)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1614])]) ).
fof(f12756,plain,
( spl0_1563
<=> ! [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_1563])]) ).
fof(f13967,plain,
( ! [X0] : c_lessequals(X0,c_Message_Oanalz(X0),tc_set(tc_Message_Omsg))
| ~ spl0_672
| ~ spl0_1563 ),
inference(resolution,[],[f12757,f6983]) ).
fof(f12757,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_1563 ),
inference(avatar_component_clause,[],[f12756]) ).
fof(f14269,plain,
spl0_1613,
inference(avatar_split_clause,[],[f1431,f14267]) ).
fof(f14267,plain,
( spl0_1613
<=> ! [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_1613])]) ).
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/benchmark/theBenchmark.p',cls_IntDef_Ozless__nat__conj_2) ).
fof(f14265,plain,
spl0_1612,
inference(avatar_split_clause,[],[f1415,f14263]) ).
fof(f14263,plain,
( spl0_1612
<=> ! [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_1612])]) ).
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/benchmark/theBenchmark.p',cls_IntDef_Oof__int__less__iff_1) ).
fof(f14261,plain,
spl0_1611,
inference(avatar_split_clause,[],[f1414,f14259]) ).
fof(f14259,plain,
( spl0_1611
<=> ! [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_1611])]) ).
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/benchmark/theBenchmark.p',cls_IntDef_Oof__int__less__iff_0) ).
fof(f14257,plain,
spl0_1610,
inference(avatar_split_clause,[],[f1411,f14255]) ).
fof(f14255,plain,
( spl0_1610
<=> ! [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_1610])]) ).
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/benchmark/theBenchmark.p',cls_IntDef_Oof__int__le__iff_1) ).
fof(f14253,plain,
spl0_1609,
inference(avatar_split_clause,[],[f1410,f14251]) ).
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/benchmark/theBenchmark.p',cls_IntDef_Oof__int__le__iff_0) ).
fof(f14249,plain,
spl0_1608,
inference(avatar_split_clause,[],[f1281,f14247]) ).
fof(f14247,plain,
( spl0_1608
<=> ! [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_1608])]) ).
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/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Diff_0) ).
fof(f14245,plain,
spl0_1607,
inference(avatar_split_clause,[],[f1198,f14243]) ).
fof(f14243,plain,
( spl0_1607
<=> ! [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_1607])]) ).
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/benchmark/theBenchmark.p',cls_Datatype__Universe_OScons__Scons__eq_1) ).
fof(f14241,plain,
spl0_1606,
inference(avatar_split_clause,[],[f1197,f14239]) ).
fof(f14239,plain,
( spl0_1606
<=> ! [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_1606])]) ).
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/benchmark/theBenchmark.p',cls_Datatype__Universe_OScons__Scons__eq_0) ).
fof(f14237,plain,
spl0_1605,
inference(avatar_split_clause,[],[f99,f14235]) ).
fof(f14235,plain,
( spl0_1605
<=> ! [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_1605])]) ).
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/benchmark/theBenchmark.p',cls_Set_OUnionE_0) ).
fof(f14233,plain,
spl0_1604,
inference(avatar_split_clause,[],[f96,f14231]) ).
fof(f14231,plain,
( spl0_1604
<=> ! [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_1604])]) ).
fof(f96,axiom,
! [X1,X12,X32] :
( c_in(X12,c_Inter(X32,X1),X1)
| c_in(c_Main_OInterI__1(X12,X32,X1),X32,tc_set(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OInterI_0) ).
fof(f14229,plain,
spl0_1603,
inference(avatar_split_clause,[],[f59,f14227]) ).
fof(f14227,plain,
( spl0_1603
<=> ! [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_1603])]) ).
fof(f59,axiom,
! [X0,X1,X26,X12] :
( c_in(X0,X12,X1)
| ~ c_in(c_List_Olist_OCons(X0,X26,X1),c_List_Olists(X12,X1),tc_List_Olist(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_OlistsE_1) ).
fof(f14225,plain,
spl0_1602,
inference(avatar_split_clause,[],[f48,f14223]) ).
fof(f14223,plain,
( spl0_1602
<=> ! [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_1602])]) ).
fof(f48,axiom,
! [X1,X12,X23] :
( ~ c_in(c_Main_Oin__listsI__1(X12,X23,X1),X12,X1)
| c_in(X23,c_List_Olists(X12,X1),tc_List_Olist(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oin__listsI_1) ).
fof(f14221,plain,
spl0_1601,
inference(avatar_split_clause,[],[f43,f14219]) ).
fof(f14219,plain,
( spl0_1601
<=> ! [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_1601])]) ).
fof(f43,axiom,
! [X17,X15] :
( c_0 != c_Divides_Oop_Amod(X15,X17,tc_IntDef_Oint)
| c_times(X17,c_Main_Ozmod__eq__0D__dest__1(X17,X15),tc_IntDef_Oint) = X15 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozmod__eq__0D__dest_0) ).
fof(f14217,plain,
spl0_1600,
inference(avatar_split_clause,[],[f27,f14215]) ).
fof(f14215,plain,
( spl0_1600
<=> ! [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_1600])]) ).
fof(f27,axiom,
! [X17,X15] :
( c_0 != c_Divides_Oop_Amod(X15,X17,tc_nat)
| c_times(X17,c_Main_Omod__eq__0D__dest__1(X17,X15),tc_nat) = X15 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Omod__eq__0D__dest_0) ).
fof(f14073,plain,
( spl0_1599
| ~ spl0_120
| ~ spl0_1558 ),
inference(avatar_split_clause,[],[f13876,f12733,f3997,f14071]) ).
fof(f14071,plain,
( spl0_1599
<=> ! [X0] : ~ c_Wellfounded__Recursion_Owf(c_UNIV,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1599])]) ).
fof(f12733,plain,
( spl0_1558
<=> ! [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_1558])]) ).
fof(f13876,plain,
( ! [X0] : ~ c_Wellfounded__Recursion_Owf(c_UNIV,X0)
| ~ spl0_120
| ~ spl0_1558 ),
inference(resolution,[],[f12734,f3998]) ).
fof(f12734,plain,
( ! [X18,X1,X5] :
( ~ c_in(c_Pair(X18,X18,X1,X1),X5,tc_prod(X1,X1))
| ~ c_Wellfounded__Recursion_Owf(X5,X1) )
| ~ spl0_1558 ),
inference(avatar_component_clause,[],[f12733]) ).
fof(f13906,plain,
( spl0_1598
| ~ spl0_1198
| ~ spl0_1558 ),
inference(avatar_split_clause,[],[f13870,f12733,f9578,f13904]) ).
fof(f13904,plain,
( spl0_1598
<=> ! [X0] : ~ c_Wellfounded__Recursion_Owf(c_Relation_OId,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1598])]) ).
fof(f9578,plain,
( spl0_1198
<=> ! [X0,X1] : c_in(c_Pair(X0,X0,X1,X1),c_Relation_OId,tc_prod(X1,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1198])]) ).
fof(f13870,plain,
( ! [X0] : ~ c_Wellfounded__Recursion_Owf(c_Relation_OId,X0)
| ~ spl0_1198
| ~ spl0_1558 ),
inference(resolution,[],[f12734,f9579]) ).
fof(f9579,plain,
( ! [X0,X1] : c_in(c_Pair(X0,X0,X1,X1),c_Relation_OId,tc_prod(X1,X1))
| ~ spl0_1198 ),
inference(avatar_component_clause,[],[f9578]) ).
fof(f13787,plain,
( spl0_1597
| ~ spl0_911
| ~ spl0_1375 ),
inference(avatar_split_clause,[],[f12518,f10926,f8000,f13784]) ).
fof(f13784,plain,
( spl0_1597
<=> c_Numeral_OPls = c_Numeral_Obin__add(c_Numeral_OMin,c_Numeral_Obin__succ(c_Numeral_OPls)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1597])]) ).
fof(f10926,plain,
( spl0_1375
<=> c_Numeral_OPls = c_Numeral_Obin__add(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_OMin) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1375])]) ).
fof(f12518,plain,
( c_Numeral_OPls = c_Numeral_Obin__add(c_Numeral_OMin,c_Numeral_Obin__succ(c_Numeral_OPls))
| ~ spl0_911
| ~ spl0_1375 ),
inference(superposition,[],[f10928,f8001]) ).
fof(f10928,plain,
( c_Numeral_OPls = c_Numeral_Obin__add(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_OMin)
| ~ spl0_1375 ),
inference(avatar_component_clause,[],[f10926]) ).
fof(f13604,plain,
( ~ spl0_1596
| spl0_104
| ~ spl0_834
| ~ spl0_1180
| ~ spl0_1285 ),
inference(avatar_split_clause,[],[f12385,f10159,f9506,f7678,f3924,f13601]) ).
fof(f13601,plain,
( spl0_1596
<=> c_IntDef_Oiszero(c_1,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1596])]) ).
fof(f3924,plain,
( spl0_104
<=> c_0 = c_1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_104])]) ).
fof(f7678,plain,
( spl0_834
<=> c_1 = c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OPls),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_834])]) ).
fof(f9506,plain,
( spl0_1180
<=> ! [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_1180])]) ).
fof(f10159,plain,
( spl0_1285
<=> c_1 = c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OPls),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1285])]) ).
fof(f12385,plain,
( c_0 = c_1
| ~ c_IntDef_Oiszero(c_1,tc_IntDef_Oint)
| ~ spl0_834
| ~ spl0_1180
| ~ spl0_1285 ),
inference(forward_demodulation,[],[f12379,f7680]) ).
fof(f7680,plain,
( c_1 = c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OPls),tc_nat)
| ~ spl0_834 ),
inference(avatar_component_clause,[],[f7678]) ).
fof(f12379,plain,
( ~ c_IntDef_Oiszero(c_1,tc_IntDef_Oint)
| c_0 = c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OPls),tc_nat)
| ~ spl0_1180
| ~ spl0_1285 ),
inference(superposition,[],[f9507,f10161]) ).
fof(f10161,plain,
( c_1 = c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OPls),tc_IntDef_Oint)
| ~ spl0_1285 ),
inference(avatar_component_clause,[],[f10159]) ).
fof(f9507,plain,
( ! [X47] :
( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 = c_Numeral_Onumber__of(X47,tc_nat) )
| ~ spl0_1180 ),
inference(avatar_component_clause,[],[f9506]) ).
fof(f13499,plain,
( spl0_1595
| ~ spl0_1045
| ~ spl0_1252 ),
inference(avatar_split_clause,[],[f12096,f10026,f8747,f13497]) ).
fof(f13497,plain,
( spl0_1595
<=> ! [X0] : c_lessequals(c_0,c_HOL_Oabs(X0,tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1595])]) ).
fof(f10026,plain,
( spl0_1252
<=> ! [X0] : c_Nat_Opower(X0,c_1,tc_IntDef_Oint) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1252])]) ).
fof(f12096,plain,
( ! [X0] : c_lessequals(c_0,c_HOL_Oabs(X0,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_1045
| ~ spl0_1252 ),
inference(superposition,[],[f8748,f10027]) ).
fof(f10027,plain,
( ! [X0] : c_Nat_Opower(X0,c_1,tc_IntDef_Oint) = X0
| ~ spl0_1252 ),
inference(avatar_component_clause,[],[f10026]) ).
fof(f13156,plain,
( spl0_1594
| ~ spl0_779
| ~ spl0_1494 ),
inference(avatar_split_clause,[],[f13130,f12457,f7456,f13154]) ).
fof(f13154,plain,
( spl0_1594
<=> ! [X0,X1] :
( ~ c_List_Onull(X0,X1)
| c_List_Olist_ONil = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1594])]) ).
fof(f7456,plain,
( spl0_779
<=> ! [X41,X0,X23] : ~ c_List_Onull(c_List_Olist_OCons(X0,X23,X41),X41) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_779])]) ).
fof(f13130,plain,
( ! [X0,X1] :
( ~ c_List_Onull(X0,X1)
| c_List_Olist_ONil = X0 )
| ~ spl0_779
| ~ spl0_1494 ),
inference(superposition,[],[f7457,f12458]) ).
fof(f7457,plain,
( ! [X41,X0,X23] : ~ c_List_Onull(c_List_Olist_OCons(X0,X23,X41),X41)
| ~ spl0_779 ),
inference(avatar_component_clause,[],[f7456]) ).
fof(f12921,plain,
spl0_1593,
inference(avatar_split_clause,[],[f3316,f12919]) ).
fof(f12919,plain,
( spl0_1593
<=> ! [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_1593])]) ).
fof(f3316,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,[],[f3128,f2958]) ).
fof(f3128,plain,
! [X83] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X83,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat) = c_Divides_Oop_Amod(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),c_Numeral_Onumber__of(X83,tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f1871,f2544,f2544]) ).
fof(f1871,axiom,
! [X83] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X83,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Suc(c_0) = c_Divides_Oop_Amod(c_Suc(c_0),c_Numeral_Onumber__of(X83,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatBin_Oone__mod__nat__number__of_0) ).
fof(f12917,plain,
spl0_1592,
inference(avatar_split_clause,[],[f3300,f12915]) ).
fof(f12915,plain,
( spl0_1592
<=> ! [X21,X43] :
( c_less(c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(X43,X21,tc_nat),tc_nat),X21,tc_nat)
| ~ c_less(c_0,X21,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1592])]) ).
fof(f3300,plain,
! [X21,X43] :
( c_less(c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(X43,X21,tc_nat),tc_nat),X21,tc_nat)
| ~ c_less(c_0,X21,tc_nat) ),
inference(forward_demodulation,[],[f3108,f3030]) ).
fof(f3108,plain,
! [X21,X43] :
( ~ c_less(c_0,X21,tc_nat)
| c_less(c_minus(X21,c_Finite__Set_Ocard(c_SetInterval_OatMost(X43,tc_nat),tc_nat),tc_nat),X21,tc_nat) ),
inference(definition_unfolding,[],[f2036,f2544]) ).
fof(f2036,axiom,
! [X21,X43] :
( ~ c_less(c_0,X21,tc_nat)
| c_less(c_minus(X21,c_Suc(X43),tc_nat),X21,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Odiff__Suc__less_0) ).
fof(f12913,plain,
spl0_1591,
inference(avatar_split_clause,[],[f3251,f12911]) ).
fof(f3251,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,[],[f3250,f2156]) ).
fof(f3250,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,[],[f3249,f2154]) ).
fof(f3249,plain,
! [X3] : c_div(c_plus(X3,X3,tc_nat),c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB0),tc_nat),tc_nat) = X3,
inference(forward_demodulation,[],[f1883,f2156]) ).
fof(f1883,axiom,
! [X3] : c_div(c_plus(X3,X3,tc_nat),c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),tc_nat) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Oadd__self__div__2_0) ).
fof(f12909,plain,
spl0_1590,
inference(avatar_split_clause,[],[f3237,f12907]) ).
fof(f3237,plain,
! [X11,X47] : c_Numeral_Obin__mult(c_Numeral_OBit(X47,c_Numeral_Obit_OB1),X11) = c_Numeral_Obin__add(c_Numeral_Obin__mult(c_Numeral_OBit(X47,c_Numeral_Obit_OB0),X11),X11),
inference(forward_demodulation,[],[f2128,f2127]) ).
fof(f2127,axiom,
! [X11,X47] : c_Numeral_Obin__mult(c_Numeral_OBit(X47,c_Numeral_Obit_OB0),X11) = c_Numeral_OBit(c_Numeral_Obin__mult(X47,X11),c_Numeral_Obit_OB0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obin__mult__0_0) ).
fof(f2128,axiom,
! [X11,X47] : c_Numeral_Obin__mult(c_Numeral_OBit(X47,c_Numeral_Obit_OB1),X11) = c_Numeral_Obin__add(c_Numeral_OBit(c_Numeral_Obin__mult(X47,X11),c_Numeral_Obit_OB0),X11),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obin__mult__1_0) ).
fof(f12905,plain,
spl0_1589,
inference(avatar_split_clause,[],[f3233,f12903]) ).
fof(f3233,plain,
! [X11] : c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OBit(X11,c_Numeral_Obit_OB1)) = c_Numeral_OBit(c_Numeral_Obin__add(c_Numeral_OMin,c_Numeral_Obin__mult(c_Numeral_OMin,X11)),c_Numeral_Obit_OB1),
inference(forward_demodulation,[],[f3019,f2984]) ).
fof(f2984,plain,
! [X11] : c_Numeral_Obin__add(c_Numeral_OMin,X11) = c_Numeral_Obin__add(X11,c_Numeral_OMin),
inference(definition_unfolding,[],[f2112,f2113]) ).
fof(f2113,axiom,
! [X11] : c_Numeral_Obin__pred(X11) = c_Numeral_Obin__add(X11,c_Numeral_OMin),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obin__add__Min__right_0) ).
fof(f2112,axiom,
! [X11] : c_Numeral_Obin__add(c_Numeral_OMin,X11) = c_Numeral_Obin__pred(X11),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obin__add__Min_0) ).
fof(f3019,plain,
! [X11] : c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OBit(X11,c_Numeral_Obit_OB1)) = c_Numeral_OBit(c_Numeral_Obin__add(c_Numeral_Obin__mult(c_Numeral_OMin,X11),c_Numeral_OMin),c_Numeral_Obit_OB1),
inference(definition_unfolding,[],[f2124,f2129,f2113,f2129]) ).
fof(f2124,axiom,
! [X11] : c_Numeral_Obin__minus(c_Numeral_OBit(X11,c_Numeral_Obit_OB1)) = c_Numeral_OBit(c_Numeral_Obin__pred(c_Numeral_Obin__minus(X11)),c_Numeral_Obit_OB1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obin__minus__1_0) ).
fof(f12895,plain,
spl0_1588,
inference(avatar_split_clause,[],[f3138,f12893]) ).
fof(f12893,plain,
( spl0_1588
<=> ! [X47] :
( ~ c_less(c_0,c_Numeral_Onumber__of(X47,tc_nat),tc_nat)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X47),tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1588])]) ).
fof(f3138,plain,
! [X47] :
( ~ c_less(c_0,c_Numeral_Onumber__of(X47,tc_nat),tc_nat)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X47),tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(definition_unfolding,[],[f1853,f2129]) ).
fof(f1853,axiom,
! [X47] :
( ~ c_less(c_0,c_Numeral_Onumber__of(X47,tc_nat),tc_nat)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__minus(X47),tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatBin_Oless__0__number__of_0) ).
fof(f12891,plain,
spl0_1587,
inference(avatar_split_clause,[],[f3136,f12889]) ).
fof(f12889,plain,
( spl0_1587
<=> ! [X47] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X47),tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(c_0,c_Numeral_Onumber__of(X47,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1587])]) ).
fof(f3136,plain,
! [X47] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X47),tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(c_0,c_Numeral_Onumber__of(X47,tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f1854,f2129]) ).
fof(f1854,axiom,
! [X47] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__minus(X47),tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(c_0,c_Numeral_Onumber__of(X47,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatBin_Oless__0__number__of_1) ).
fof(f12860,plain,
( spl0_1586
| ~ spl0_646
| ~ spl0_687
| ~ spl0_1372
| ~ spl0_1461
| ~ spl0_1585 ),
inference(avatar_split_clause,[],[f12856,f12853,f11313,f10914,f7046,f6101,f12858]) ).
fof(f12853,plain,
( spl0_1585
<=> ! [X59,X43] :
( c_lessequals(X43,X59,tc_nat)
| c_List_Olist_ONil = c_List_Oupt(X43,c_Finite__Set_Ocard(c_SetInterval_OatMost(X59,tc_nat),tc_nat)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1585])]) ).
fof(f12856,plain,
( ! [X59,X43] :
( c_List_Olist_ONil = c_List_Oupt(X43,c_plus(c_1,X59,tc_nat))
| c_lessequals(X43,X59,tc_nat) )
| ~ spl0_646
| ~ spl0_687
| ~ spl0_1372
| ~ spl0_1461
| ~ spl0_1585 ),
inference(forward_demodulation,[],[f12854,f12280]) ).
fof(f12854,plain,
( ! [X59,X43] :
( c_lessequals(X43,X59,tc_nat)
| c_List_Olist_ONil = c_List_Oupt(X43,c_Finite__Set_Ocard(c_SetInterval_OatMost(X59,tc_nat),tc_nat)) )
| ~ spl0_1585 ),
inference(avatar_component_clause,[],[f12853]) ).
fof(f12855,plain,
spl0_1585,
inference(avatar_split_clause,[],[f3123,f12853]) ).
fof(f3123,plain,
! [X59,X43] :
( c_lessequals(X43,X59,tc_nat)
| c_List_Olist_ONil = c_List_Oupt(X43,c_Finite__Set_Ocard(c_SetInterval_OatMost(X59,tc_nat),tc_nat)) ),
inference(definition_unfolding,[],[f1783,f2544]) ).
fof(f1783,axiom,
! [X59,X43] :
( c_lessequals(X43,X59,tc_nat)
| c_List_Olist_ONil = c_List_Oupt(X43,c_Suc(X59)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oupt_Oupt__Suc_1) ).
fof(f12851,plain,
spl0_1584,
inference(avatar_split_clause,[],[f3080,f12849]) ).
fof(f3080,plain,
! [X11,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| c_uminus(c_Numeral_Onumber__of(X11,X1),X1) = c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X11),X1) ),
inference(definition_unfolding,[],[f2117,f2129]) ).
fof(f2117,axiom,
! [X11,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| c_uminus(c_Numeral_Onumber__of(X11,X1),X1) = c_Numeral_Onumber__of(c_Numeral_Obin__minus(X11),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obin__arith__extra__simps__2_0) ).
fof(f12843,plain,
( spl0_1583
| ~ spl0_646
| ~ spl0_687
| ~ spl0_1372
| ~ spl0_1461
| ~ spl0_1582 ),
inference(avatar_split_clause,[],[f12839,f12836,f11313,f10914,f7046,f6101,f12841]) ).
fof(f12836,plain,
( spl0_1582
<=> ! [X15] : c_insert(X15,c_emptyset,tc_nat) = c_SetInterval_OatLeastLessThan(X15,c_Finite__Set_Ocard(c_SetInterval_OatMost(X15,tc_nat),tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1582])]) ).
fof(f12839,plain,
( ! [X15] : c_insert(X15,c_emptyset,tc_nat) = c_SetInterval_OatLeastLessThan(X15,c_plus(c_1,X15,tc_nat),tc_nat)
| ~ spl0_646
| ~ spl0_687
| ~ spl0_1372
| ~ spl0_1461
| ~ spl0_1582 ),
inference(forward_demodulation,[],[f12837,f12280]) ).
fof(f12837,plain,
( ! [X15] : c_insert(X15,c_emptyset,tc_nat) = c_SetInterval_OatLeastLessThan(X15,c_Finite__Set_Ocard(c_SetInterval_OatMost(X15,tc_nat),tc_nat),tc_nat)
| ~ spl0_1582 ),
inference(avatar_component_clause,[],[f12836]) ).
fof(f12838,plain,
spl0_1582,
inference(avatar_split_clause,[],[f3020,f12836]) ).
fof(f3020,plain,
! [X15] : c_insert(X15,c_emptyset,tc_nat) = c_SetInterval_OatLeastLessThan(X15,c_Finite__Set_Ocard(c_SetInterval_OatMost(X15,tc_nat),tc_nat),tc_nat),
inference(definition_unfolding,[],[f2527,f2544]) ).
fof(f2527,axiom,
! [X15] : c_SetInterval_OatLeastLessThan(X15,c_Suc(X15),tc_nat) = c_insert(X15,c_emptyset,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatLeastLessThan__singleton_0) ).
fof(f12834,plain,
spl0_1581,
inference(avatar_split_clause,[],[f3016,f12832]) ).
fof(f3016,plain,
! [X1,X12,X13] : c_emptyset = c_Relation_OImage(c_Relation_Odiag(X12,X1),c_minus(X13,X12,tc_set(X1)),X1,X1),
inference(definition_unfolding,[],[f2589,f2373]) ).
fof(f2589,axiom,
! [X1,X12,X13] : c_emptyset = c_inter(X12,c_minus(X13,X12,tc_set(X1)),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_ODiff__disjoint_0) ).
fof(f12830,plain,
spl0_1580,
inference(avatar_split_clause,[],[f3003,f12828]) ).
fof(f12828,plain,
( spl0_1580
<=> ! [X85,X1] : c_UNIV = c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_union(X85,c_Relation_OId,tc_prod(X1,X1)),X1),X1,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1580])]) ).
fof(f3003,plain,
! [X1,X85] : c_UNIV = c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_union(X85,c_Relation_OId,tc_prod(X1,X1)),X1),X1,X1),
inference(definition_unfolding,[],[f2706,f2716]) ).
fof(f2706,axiom,
! [X1,X85] : c_UNIV = c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X85,X1),X1,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Transitive__Closure_ODomain__rtrancl_0) ).
fof(f12826,plain,
spl0_1579,
inference(avatar_split_clause,[],[f3002,f12824]) ).
fof(f12824,plain,
( spl0_1579
<=> ! [X85,X1] : c_UNIV = c_Relation_ORange(c_Transitive__Closure_Otrancl(c_union(X85,c_Relation_OId,tc_prod(X1,X1)),X1),X1,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1579])]) ).
fof(f3002,plain,
! [X1,X85] : c_UNIV = c_Relation_ORange(c_Transitive__Closure_Otrancl(c_union(X85,c_Relation_OId,tc_prod(X1,X1)),X1),X1,X1),
inference(definition_unfolding,[],[f2707,f2716]) ).
fof(f2707,axiom,
! [X1,X85] : c_UNIV = c_Relation_ORange(c_Transitive__Closure_Ortrancl(X85,X1),X1,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Transitive__Closure_ORange__rtrancl_0) ).
fof(f12819,plain,
( spl0_1578
| ~ spl0_646
| ~ spl0_687
| ~ spl0_1372
| ~ spl0_1461
| ~ spl0_1577 ),
inference(avatar_split_clause,[],[f12815,f12812,f11313,f10914,f7046,f6101,f12817]) ).
fof(f12817,plain,
( spl0_1578
<=> ! [X21] : c_plus(c_1,X21,tc_nat) = c_Binomial_Obinomial(c_plus(c_1,X21,tc_nat),X21) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1578])]) ).
fof(f12812,plain,
( spl0_1577
<=> ! [X21] : c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat) = c_Binomial_Obinomial(c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),X21) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1577])]) ).
fof(f12815,plain,
( ! [X21] : c_plus(c_1,X21,tc_nat) = c_Binomial_Obinomial(c_plus(c_1,X21,tc_nat),X21)
| ~ spl0_646
| ~ spl0_687
| ~ spl0_1372
| ~ spl0_1461
| ~ spl0_1577 ),
inference(forward_demodulation,[],[f12813,f12280]) ).
fof(f12813,plain,
( ! [X21] : c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat) = c_Binomial_Obinomial(c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),X21)
| ~ spl0_1577 ),
inference(avatar_component_clause,[],[f12812]) ).
fof(f12814,plain,
spl0_1577,
inference(avatar_split_clause,[],[f2997,f12812]) ).
fof(f2997,plain,
! [X21] : c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat) = c_Binomial_Obinomial(c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),X21),
inference(definition_unfolding,[],[f1163,f2544,f2544]) ).
fof(f1163,axiom,
! [X21] : c_Suc(X21) = c_Binomial_Obinomial(c_Suc(X21),X21),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Binomial_Obinomial__Suc__n_0) ).
fof(f12810,plain,
spl0_1576,
inference(avatar_split_clause,[],[f2889,f12808]) ).
fof(f12808,plain,
( spl0_1576
<=> ! [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_1576])]) ).
fof(f2889,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/benchmark/theBenchmark.p',cls_Message_Osynth__subset__iff_1) ).
fof(f12806,plain,
spl0_1575,
inference(avatar_split_clause,[],[f2888,f12804]) ).
fof(f2888,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/benchmark/theBenchmark.p',cls_Message_Osynth__subset__iff_0) ).
fof(f12802,plain,
spl0_1574,
inference(avatar_split_clause,[],[f2882,f12800]) ).
fof(f12800,plain,
( spl0_1574
<=> ! [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_1574])]) ).
fof(f2882,axiom,
! [X88,X20] :
( ~ c_lessequals(X20,c_Message_Oparts(X88),tc_set(tc_Message_Omsg))
| c_lessequals(c_Message_Oparts(X20),c_Message_Oparts(X88),tc_set(tc_Message_Omsg)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oparts__subset__iff_1) ).
fof(f12798,plain,
spl0_1573,
inference(avatar_split_clause,[],[f2881,f12796]) ).
fof(f2881,axiom,
! [X88,X20] :
( c_lessequals(X20,c_Message_Oparts(X88),tc_set(tc_Message_Omsg))
| ~ c_lessequals(c_Message_Oparts(X20),c_Message_Oparts(X88),tc_set(tc_Message_Omsg)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oparts__subset__iff_0) ).
fof(f12794,plain,
spl0_1572,
inference(avatar_split_clause,[],[f2879,f12792]) ).
fof(f12792,plain,
( spl0_1572
<=> ! [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_1572])]) ).
fof(f2879,axiom,
! [X88,X7] : c_Message_Oparts(c_insert(c_Message_Omsg_ONumber(X7),X88,tc_Message_Omsg)) = c_insert(c_Message_Omsg_ONumber(X7),c_Message_Oparts(X88),tc_Message_Omsg),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oparts__insert__Number_0) ).
fof(f12790,plain,
( ~ spl0_1570
| spl0_1571
| ~ spl0_118
| ~ spl0_1379 ),
inference(avatar_split_clause,[],[f11644,f10943,f3989,f12788,f12784]) ).
fof(f12784,plain,
( spl0_1570
<=> class_OrderedGroup_Opordered__ab__group__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1570])]) ).
fof(f12788,plain,
( spl0_1571
<=> ! [X0] : c_lessequals(X0,c_0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1571])]) ).
fof(f10943,plain,
( spl0_1379
<=> ! [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_1379])]) ).
fof(f11644,plain,
( ! [X0] :
( c_lessequals(X0,c_0,tc_nat)
| ~ class_OrderedGroup_Opordered__ab__group__add(tc_nat) )
| ~ spl0_118
| ~ spl0_1379 ),
inference(resolution,[],[f10944,f3990]) ).
fof(f10944,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_1379 ),
inference(avatar_component_clause,[],[f10943]) ).
fof(f12782,plain,
spl0_1569,
inference(avatar_split_clause,[],[f2878,f12780]) ).
fof(f12780,plain,
( spl0_1569
<=> ! [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_1569])]) ).
fof(f2878,axiom,
! [X88,X7] : c_Message_Oparts(c_insert(c_Message_Omsg_ONonce(X7),X88,tc_Message_Omsg)) = c_insert(c_Message_Omsg_ONonce(X7),c_Message_Oparts(X88),tc_Message_Omsg),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oparts__insert__Nonce_0) ).
fof(f12778,plain,
spl0_1568,
inference(avatar_split_clause,[],[f2876,f12776]) ).
fof(f12776,plain,
( spl0_1568
<=> ! [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_1568])]) ).
fof(f2876,axiom,
! [X91,X88] : c_Message_Oparts(c_insert(c_Message_Omsg_OKey(X91),X88,tc_Message_Omsg)) = c_insert(c_Message_Omsg_OKey(X91),c_Message_Oparts(X88),tc_Message_Omsg),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oparts__insert__Key_0) ).
fof(f12774,plain,
spl0_1567,
inference(avatar_split_clause,[],[f2875,f12772]) ).
fof(f12772,plain,
( spl0_1567
<=> ! [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_1567])]) ).
fof(f2875,axiom,
! [X88,X86] : c_Message_Oparts(c_insert(c_Message_Omsg_OHash(X86),X88,tc_Message_Omsg)) = c_insert(c_Message_Omsg_OHash(X86),c_Message_Oparts(X88),tc_Message_Omsg),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oparts__insert__Hash_0) ).
fof(f12770,plain,
spl0_1566,
inference(avatar_split_clause,[],[f2872,f12768]) ).
fof(f12768,plain,
( spl0_1566
<=> ! [X88,X110] : c_Message_Oparts(c_insert(c_Message_Omsg_OAgent(X110),X88,tc_Message_Omsg)) = c_insert(c_Message_Omsg_OAgent(X110),c_Message_Oparts(X88),tc_Message_Omsg) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1566])]) ).
fof(f2872,axiom,
! [X88,X110] : c_Message_Oparts(c_insert(c_Message_Omsg_OAgent(X110),X88,tc_Message_Omsg)) = c_insert(c_Message_Omsg_OAgent(X110),c_Message_Oparts(X88),tc_Message_Omsg),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oparts__insert__Agent_0) ).
fof(f12766,plain,
spl0_1565,
inference(avatar_split_clause,[],[f2870,f12764]) ).
fof(f12764,plain,
( spl0_1565
<=> ! [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_1565])]) ).
fof(f2870,axiom,
! [X88,X86] :
( ~ c_in(X86,c_Message_Oparts(X88),tc_Message_Omsg)
| c_Message_Oparts(X88) = c_Message_Oparts(c_insert(X86,X88,tc_Message_Omsg)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oparts__cut__eq_0) ).
fof(f12762,plain,
spl0_1564,
inference(avatar_split_clause,[],[f2864,f12760]) ).
fof(f12760,plain,
( spl0_1564
<=> ! [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_1564])]) ).
fof(f2864,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/benchmark/theBenchmark.p',cls_Message_Oanalz__subset__iff_1) ).
fof(f12758,plain,
spl0_1563,
inference(avatar_split_clause,[],[f2863,f12756]) ).
fof(f2863,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/benchmark/theBenchmark.p',cls_Message_Oanalz__subset__iff_0) ).
fof(f12754,plain,
spl0_1562,
inference(avatar_split_clause,[],[f2861,f12752]) ).
fof(f12752,plain,
( spl0_1562
<=> ! [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_1562])]) ).
fof(f2861,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/benchmark/theBenchmark.p',cls_Message_Oanalz__insert__Number_0) ).
fof(f12750,plain,
spl0_1561,
inference(avatar_split_clause,[],[f2860,f12748]) ).
fof(f12748,plain,
( spl0_1561
<=> ! [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_1561])]) ).
fof(f2860,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/benchmark/theBenchmark.p',cls_Message_Oanalz__insert__Nonce_0) ).
fof(f12746,plain,
spl0_1560,
inference(avatar_split_clause,[],[f2857,f12744]) ).
fof(f12744,plain,
( spl0_1560
<=> ! [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_1560])]) ).
fof(f2857,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/benchmark/theBenchmark.p',cls_Message_Oanalz__insert__Hash_0) ).
fof(f12739,plain,
spl0_1559,
inference(avatar_split_clause,[],[f2855,f12737]) ).
fof(f12737,plain,
( spl0_1559
<=> ! [X88,X110] : c_Message_Oanalz(c_insert(c_Message_Omsg_OAgent(X110),X88,tc_Message_Omsg)) = c_insert(c_Message_Omsg_OAgent(X110),c_Message_Oanalz(X88),tc_Message_Omsg) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1559])]) ).
fof(f2855,axiom,
! [X88,X110] : c_Message_Oanalz(c_insert(c_Message_Omsg_OAgent(X110),X88,tc_Message_Omsg)) = c_insert(c_Message_Omsg_OAgent(X110),c_Message_Oanalz(X88),tc_Message_Omsg),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oanalz__insert__Agent_0) ).
fof(f12735,plain,
spl0_1558,
inference(avatar_split_clause,[],[f2725,f12733]) ).
fof(f2725,axiom,
! [X1,X18,X5] :
( ~ c_Wellfounded__Recursion_Owf(X5,X1)
| ~ c_in(c_Pair(X18,X18,X1,X1),X5,tc_prod(X1,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Owf__not__refl_0) ).
fof(f12731,plain,
spl0_1557,
inference(avatar_split_clause,[],[f2689,f12729]) ).
fof(f12729,plain,
( spl0_1557
<=> ! [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_1557])]) ).
fof(f2689,axiom,
! [X0,X1,X12,X13] :
( c_lessequals(X12,X13,tc_set(X1))
| ~ c_lessequals(c_insert(X0,X12,X1),X13,tc_set(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Oinsert__subset_1) ).
fof(f12727,plain,
spl0_1556,
inference(avatar_split_clause,[],[f2656,f12725]) ).
fof(f12725,plain,
( spl0_1556
<=> ! [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_1556])]) ).
fof(f2656,axiom,
! [X1,X12,X32] :
( ~ c_in(X12,c_Union(X32,X1),X1)
| c_in(X12,c_Main_OUnion__iff__1(X12,X32,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUnion__iff_1) ).
fof(f12723,plain,
spl0_1555,
inference(avatar_split_clause,[],[f2652,f12721]) ).
fof(f12721,plain,
( spl0_1555
<=> ! [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_1555])]) ).
fof(f2652,axiom,
! [X1,X24,X12] :
( c_emptyset = X24
| c_emptyset != c_Union(X12,X1)
| ~ c_in(X24,X12,tc_set(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUnion__empty__conv_0) ).
fof(f12719,plain,
spl0_1554,
inference(avatar_split_clause,[],[f2646,f12717]) ).
fof(f12717,plain,
( spl0_1554
<=> ! [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_1554])]) ).
fof(f2646,axiom,
! [X1,X12,X32,X13] :
( c_lessequals(X13,X32,tc_set(X1))
| ~ c_lessequals(c_union(X12,X13,X1),X32,tc_set(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUn__subset__iff_1) ).
fof(f12715,plain,
spl0_1553,
inference(avatar_split_clause,[],[f2645,f12713]) ).
fof(f12713,plain,
( spl0_1553
<=> ! [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_1553])]) ).
fof(f2645,axiom,
! [X1,X12,X32,X13] :
( c_lessequals(X12,X32,tc_set(X1))
| ~ c_lessequals(c_union(X12,X13,X1),X32,tc_set(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUn__subset__iff_0) ).
fof(f12711,plain,
spl0_1552,
inference(avatar_split_clause,[],[f2631,f12709]) ).
fof(f2631,axiom,
! [X1,X12,X13] : c_union(X12,X13,X1) = c_union(X12,c_minus(X13,X12,tc_set(X1)),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUn__Diff__cancel_0) ).
fof(f12707,plain,
spl0_1551,
inference(avatar_split_clause,[],[f2630,f12705]) ).
fof(f2630,axiom,
! [X1,X12,X13] : c_union(c_minus(X13,X12,tc_set(X1)),X12,X1) = c_union(X13,X12,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUn__Diff__cancel2_0) ).
fof(f12703,plain,
spl0_1550,
inference(avatar_split_clause,[],[f2622,f12701]) ).
fof(f12701,plain,
( spl0_1550
<=> ! [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_1550])]) ).
fof(f2622,axiom,
! [X1,X12,X32] :
( c_in(X12,c_Inter(X32,X1),X1)
| ~ c_in(X12,c_Main_OInter__iff__1(X12,X32,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OInter__iff_2) ).
fof(f12699,plain,
spl0_1549,
inference(avatar_split_clause,[],[f2616,f12697]) ).
fof(f12697,plain,
( spl0_1549
<=> ! [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_1549])]) ).
fof(f2616,axiom,
! [X1,X24,X12] :
( c_UNIV = X24
| c_UNIV != c_Inter(X12,X1)
| ~ c_in(X24,X12,tc_set(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OInter__UNIV__conv__2_0) ).
fof(f12695,plain,
spl0_1548,
inference(avatar_split_clause,[],[f2555,f12693]) ).
fof(f12693,plain,
( spl0_1548
<=> ! [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_1548])]) ).
fof(f2555,axiom,
! [X1,X26,X14,X43] :
( ~ class_Orderings_Oord(X1)
| c_less(X43,X14,X1)
| ~ c_in(X43,c_SetInterval_OgreaterThanLessThan(X26,X14,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThanLessThan__iff_1) ).
fof(f12691,plain,
spl0_1547,
inference(avatar_split_clause,[],[f2554,f12689]) ).
fof(f12689,plain,
( spl0_1547
<=> ! [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_1547])]) ).
fof(f2554,axiom,
! [X1,X26,X14,X43] :
( ~ class_Orderings_Oord(X1)
| c_less(X26,X43,X1)
| ~ c_in(X43,c_SetInterval_OgreaterThanLessThan(X26,X14,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThanLessThan__iff_0) ).
fof(f12687,plain,
spl0_1546,
inference(avatar_split_clause,[],[f2552,f12685]) ).
fof(f12685,plain,
( spl0_1546
<=> ! [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_1546])]) ).
fof(f2552,axiom,
! [X1,X26,X14,X43] :
( ~ class_Orderings_Oord(X1)
| c_lessequals(X43,X14,X1)
| ~ c_in(X43,c_SetInterval_OgreaterThanAtMost(X26,X14,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThanAtMost__iff_1) ).
fof(f12683,plain,
spl0_1545,
inference(avatar_split_clause,[],[f2551,f12681]) ).
fof(f12681,plain,
( spl0_1545
<=> ! [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_1545])]) ).
fof(f2551,axiom,
! [X1,X26,X14,X43] :
( ~ class_Orderings_Oord(X1)
| c_less(X26,X43,X1)
| ~ c_in(X43,c_SetInterval_OgreaterThanAtMost(X26,X14,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThanAtMost__iff_0) ).
fof(f12679,plain,
spl0_1544,
inference(avatar_split_clause,[],[f2525,f12677]) ).
fof(f12677,plain,
( spl0_1544
<=> ! [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_1544])]) ).
fof(f2525,axiom,
! [X1,X26,X14,X43] :
( ~ class_Orderings_Oord(X1)
| c_less(X43,X14,X1)
| ~ c_in(X43,c_SetInterval_OatLeastLessThan(X26,X14,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatLeastLessThan__iff_1) ).
fof(f12675,plain,
spl0_1543,
inference(avatar_split_clause,[],[f2524,f12673]) ).
fof(f12673,plain,
( spl0_1543
<=> ! [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_1543])]) ).
fof(f2524,axiom,
! [X1,X26,X14,X43] :
( ~ class_Orderings_Oord(X1)
| c_lessequals(X26,X43,X1)
| ~ c_in(X43,c_SetInterval_OatLeastLessThan(X26,X14,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatLeastLessThan__iff_0) ).
fof(f12671,plain,
spl0_1542,
inference(avatar_split_clause,[],[f2520,f12669]) ).
fof(f12669,plain,
( spl0_1542
<=> ! [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_1542])]) ).
fof(f2520,axiom,
! [X1,X26,X14,X43] :
( ~ class_Orderings_Oord(X1)
| c_lessequals(X43,X14,X1)
| ~ c_in(X43,c_SetInterval_OatLeastAtMost(X26,X14,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatLeastAtMost__iff_1) ).
fof(f12667,plain,
spl0_1541,
inference(avatar_split_clause,[],[f2519,f12665]) ).
fof(f12665,plain,
( spl0_1541
<=> ! [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_1541])]) ).
fof(f2519,axiom,
! [X1,X26,X14,X43] :
( ~ class_Orderings_Oord(X1)
| c_lessequals(X26,X43,X1)
| ~ c_in(X43,c_SetInterval_OatLeastAtMost(X26,X14,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatLeastAtMost__iff_0) ).
fof(f12663,plain,
spl0_1540,
inference(avatar_split_clause,[],[f2387,f12661]) ).
fof(f12661,plain,
( spl0_1540
<=> ! [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_1540])]) ).
fof(f2387,axiom,
! [X18,X1,X27] :
( X18 = X27
| ~ c_in(c_Pair(X18,X27,X1,X1),c_Relation_OId,tc_prod(X1,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_Opair__in__Id__conv_0) ).
fof(f12659,plain,
( ~ spl0_1538
| spl0_1539
| ~ spl0_118
| ~ spl0_1341 ),
inference(avatar_split_clause,[],[f11427,f10784,f3989,f12657,f12653]) ).
fof(f12653,plain,
( spl0_1538
<=> class_Ring__and__Field_Oordered__idom(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1538])]) ).
fof(f12657,plain,
( spl0_1539
<=> ! [X0] : c_lessequals(c_0,X0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1539])]) ).
fof(f10784,plain,
( spl0_1341
<=> ! [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_1341])]) ).
fof(f11427,plain,
( ! [X0] :
( c_lessequals(c_0,X0,tc_IntDef_Oint)
| ~ class_Ring__and__Field_Oordered__idom(tc_nat) )
| ~ spl0_118
| ~ spl0_1341 ),
inference(resolution,[],[f10785,f3990]) ).
fof(f10785,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_1341 ),
inference(avatar_component_clause,[],[f10784]) ).
fof(f12651,plain,
spl0_1537,
inference(avatar_split_clause,[],[f2367,f12649]) ).
fof(f2367,axiom,
! [X2,X48,X1] : c_Pair(c_Main_Osurj__pair__1(X48,X1,X2),c_Main_Osurj__pair__2(X48,X1,X2),X1,X2) = X48,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Product__Type_Osurj__pair_0) ).
fof(f12647,plain,
spl0_1536,
inference(avatar_split_clause,[],[f2365,f12645]) ).
fof(f2365,axiom,
! [X2,X3,X1] : c_Pair(c_fst(X3,X1,X2),c_snd(X3,X1,X2),X1,X2) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Product__Type_Opair__collapse_0) ).
fof(f12643,plain,
spl0_1535,
inference(avatar_split_clause,[],[f2361,f12641]) ).
fof(f12641,plain,
( spl0_1535
<=> ! [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_1535])]) ).
fof(f2361,axiom,
! [X1,X18] :
( ~ class_Power_Orecpower(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_less(c_0,c_Nat_Opower(c_HOL_Oabs(X18,X1),c_0,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Power_Ozero__less__power__abs__iff_2) ).
fof(f12639,plain,
spl0_1534,
inference(avatar_split_clause,[],[f2358,f12637]) ).
fof(f12637,plain,
( spl0_1534
<=> ! [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_1534])]) ).
fof(f2358,axiom,
! [X21,X1,X18] :
( ~ class_Power_Orecpower(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_lessequals(c_0,c_Nat_Opower(c_HOL_Oabs(X18,X1),X21,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Power_Ozero__le__power__abs_0) ).
fof(f12635,plain,
spl0_1533,
inference(avatar_split_clause,[],[f2347,f12633]) ).
fof(f12633,plain,
( spl0_1533
<=> ! [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_1533])]) ).
fof(f2347,axiom,
! [X21,X1,X18] :
( ~ class_Power_Orecpower(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_0 = X18
| c_0 != c_Nat_Opower(X18,X21,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Power_Opower__eq__0__iff_0) ).
fof(f12631,plain,
spl0_1532,
inference(avatar_split_clause,[],[f2339,f12629]) ).
fof(f12629,plain,
( spl0_1532
<=> ! [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_1532])]) ).
fof(f2339,axiom,
! [X0,X11] :
( ~ c_less(c_0,X0,tc_nat)
| c_less(c_0,c_Nat_Opower(X0,c_Numeral_Onumber__of(X11,tc_nat),tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Ozero__less__power__nat__eq__number__of_2) ).
fof(f12627,plain,
spl0_1531,
inference(avatar_split_clause,[],[f2295,f12625]) ).
fof(f12625,plain,
( spl0_1531
<=> ! [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_1531])]) ).
fof(f2295,axiom,
! [X21,X0] :
( ~ c_Parity_Oeven(X0,tc_IntDef_Oint)
| ~ c_less(c_0,X21,tc_nat)
| c_Parity_Oeven(c_Nat_Opower(X0,X21,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__power_2) ).
fof(f12623,plain,
spl0_1530,
inference(avatar_split_clause,[],[f2282,f12621]) ).
fof(f12621,plain,
( spl0_1530
<=> ! [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_1530])]) ).
fof(f2282,axiom,
! [X3,X0] :
( ~ c_Parity_Oeven(X0,tc_nat)
| ~ c_less(c_0,X3,tc_nat)
| c_Parity_Oeven(c_Nat_Opower(X0,X3,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__nat__power_2) ).
fof(f12619,plain,
spl0_1529,
inference(avatar_split_clause,[],[f2265,f12617]) ).
fof(f12617,plain,
( spl0_1529
<=> ! [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_1529])]) ).
fof(f2265,axiom,
! [X2,X3,X48,X0] :
( ~ class_Orderings_Olinorder(X2)
| c_lessequals(X3,X48,X2)
| ~ c_lessequals(c_Orderings_Omax(X0,X3,X2),X48,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Orderings_Omin__max_Obelow__sup_Oabove__sup__conv_1) ).
fof(f12615,plain,
spl0_1528,
inference(avatar_split_clause,[],[f2264,f12613]) ).
fof(f12613,plain,
( spl0_1528
<=> ! [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_1528])]) ).
fof(f2264,axiom,
! [X2,X3,X48,X0] :
( ~ class_Orderings_Olinorder(X2)
| c_lessequals(X0,X48,X2)
| ~ c_lessequals(c_Orderings_Omax(X0,X3,X2),X48,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Orderings_Omin__max_Obelow__sup_Oabove__sup__conv_0) ).
fof(f12606,plain,
spl0_1527,
inference(avatar_split_clause,[],[f2260,f12604]) ).
fof(f12604,plain,
( spl0_1527
<=> ! [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_1527])]) ).
fof(f2260,axiom,
! [X2,X3,X48,X0] :
( ~ class_Orderings_Olinorder(X2)
| c_lessequals(X0,X48,X2)
| ~ c_lessequals(X0,c_Orderings_Omin(X3,X48,X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Orderings_Omin__max_Obelow__inf_Obelow__inf__conv_1) ).
fof(f12602,plain,
spl0_1526,
inference(avatar_split_clause,[],[f2259,f12600]) ).
fof(f12600,plain,
( spl0_1526
<=> ! [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_1526])]) ).
fof(f2259,axiom,
! [X2,X3,X48,X0] :
( ~ class_Orderings_Olinorder(X2)
| c_lessequals(X0,X3,X2)
| ~ c_lessequals(X0,c_Orderings_Omin(X3,X48,X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Orderings_Omin__max_Obelow__inf_Obelow__inf__conv_0) ).
fof(f12598,plain,
spl0_1525,
inference(avatar_split_clause,[],[f2257,f12596]) ).
fof(f12596,plain,
( spl0_1525
<=> ! [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_1525])]) ).
fof(f2257,axiom,
! [X3,X48,X0,X1] :
( ~ class_Orderings_Olinorder(X1)
| c_less(X48,X3,X1)
| ~ c_less(X48,c_Orderings_Omin(X0,X3,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Orderings_Omin__less__iff__conj_1) ).
fof(f12594,plain,
spl0_1524,
inference(avatar_split_clause,[],[f2256,f12592]) ).
fof(f12592,plain,
( spl0_1524
<=> ! [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_1524])]) ).
fof(f2256,axiom,
! [X3,X48,X0,X1] :
( ~ class_Orderings_Olinorder(X1)
| c_less(X48,X0,X1)
| ~ c_less(X48,c_Orderings_Omin(X0,X3,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Orderings_Omin__less__iff__conj_0) ).
fof(f12590,plain,
spl0_1523,
inference(avatar_split_clause,[],[f2254,f12588]) ).
fof(f12588,plain,
( spl0_1523
<=> ! [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_1523])]) ).
fof(f2254,axiom,
! [X3,X48,X0,X1] :
( ~ class_Orderings_Olinorder(X1)
| c_less(X3,X48,X1)
| ~ c_less(c_Orderings_Omax(X0,X3,X1),X48,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Orderings_Omax__less__iff__conj_1) ).
fof(f12586,plain,
spl0_1522,
inference(avatar_split_clause,[],[f2253,f12584]) ).
fof(f12584,plain,
( spl0_1522
<=> ! [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_1522])]) ).
fof(f2253,axiom,
! [X3,X48,X0,X1] :
( ~ class_Orderings_Olinorder(X1)
| c_less(X0,X48,X1)
| ~ c_less(c_Orderings_Omax(X0,X3,X1),X48,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Orderings_Omax__less__iff__conj_0) ).
fof(f12582,plain,
spl0_1521,
inference(avatar_split_clause,[],[f2249,f12580]) ).
fof(f12580,plain,
( spl0_1521
<=> ! [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_1521])]) ).
fof(f2249,axiom,
! [X1,X18] :
( ~ class_OrderedGroup_Olordered__ab__group(X1)
| ~ c_lessequals(c_0,X18,X1)
| c_lessequals(c_0,c_plus(X18,X18,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Ozero__le__double__add__iff__zero__le__single__add_1) ).
fof(f12578,plain,
spl0_1520,
inference(avatar_split_clause,[],[f2248,f12576]) ).
fof(f12576,plain,
( spl0_1520
<=> ! [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_1520])]) ).
fof(f2248,axiom,
! [X1,X18] :
( ~ class_OrderedGroup_Olordered__ab__group(X1)
| c_lessequals(c_0,X18,X1)
| ~ c_lessequals(c_0,c_plus(X18,X18,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Ozero__le__double__add__iff__zero__le__single__add_0) ).
fof(f12574,plain,
spl0_1519,
inference(avatar_split_clause,[],[f2215,f12572]) ).
fof(f12572,plain,
( spl0_1519
<=> ! [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_1519])]) ).
fof(f2215,axiom,
! [X1,X18,X27] :
( ~ class_OrderedGroup_Oab__group__add(X1)
| c_uminus(c_minus(X18,X27,X1),X1) = c_minus(X27,X18,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Ominus__diff__eq_0) ).
fof(f12570,plain,
spl0_1518,
inference(avatar_split_clause,[],[f2212,f12568]) ).
fof(f12568,plain,
( spl0_1518
<=> ! [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_1518])]) ).
fof(f2212,axiom,
! [X1,X18] :
( ~ class_OrderedGroup_Olordered__ab__group(X1)
| c_0 = X18
| c_0 != c_LOrder_Omeet(X18,c_uminus(X18,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Omeet__0__eq__0_0) ).
fof(f12562,plain,
spl0_1517,
inference(avatar_split_clause,[],[f2210,f12560]) ).
fof(f12560,plain,
( spl0_1517
<=> ! [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_1517])]) ).
fof(f2210,axiom,
! [X1,X18] :
( ~ class_OrderedGroup_Olordered__ab__group(X1)
| c_0 = X18
| c_0 != c_LOrder_Ojoin(X18,c_uminus(X18,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Ojoin__0__eq__0_0) ).
fof(f12558,plain,
spl0_1516,
inference(avatar_split_clause,[],[f2207,f12556]) ).
fof(f12556,plain,
( spl0_1516
<=> ! [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_1516])]) ).
fof(f2207,axiom,
! [X1,X18] :
( ~ class_OrderedGroup_Olordered__ab__group(X1)
| ~ c_lessequals(X18,c_0,X1)
| c_lessequals(c_plus(X18,X18,X1),c_0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Odouble__add__le__zero__iff__single__add__le__zero_1) ).
fof(f12554,plain,
spl0_1515,
inference(avatar_split_clause,[],[f2206,f12552]) ).
fof(f12552,plain,
( spl0_1515
<=> ! [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_1515])]) ).
fof(f2206,axiom,
! [X1,X18] :
( ~ class_OrderedGroup_Olordered__ab__group(X1)
| c_lessequals(X18,c_0,X1)
| ~ c_lessequals(c_plus(X18,X18,X1),c_0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Odouble__add__le__zero__iff__single__add__le__zero_0) ).
fof(f12550,plain,
spl0_1514,
inference(avatar_split_clause,[],[f2204,f12548]) ).
fof(f12548,plain,
( spl0_1514
<=> ! [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_1514])]) ).
fof(f2204,axiom,
! [X1,X18,X27] :
( ~ class_OrderedGroup_Oab__group__add(X1)
| c_plus(X18,X27,X1) = c_minus(X18,c_uminus(X27,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Odiff__minus__eq__add_0) ).
fof(f12546,plain,
spl0_1513,
inference(avatar_split_clause,[],[f2203,f12544]) ).
fof(f12544,plain,
( spl0_1513
<=> ! [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_1513])]) ).
fof(f2203,axiom,
! [X1,X18,X27] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_less(X18,X27,X1)
| c_less(c_minus(X18,X27,X1),c_0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Odiff__less__0__iff__less_1) ).
fof(f12542,plain,
spl0_1512,
inference(avatar_split_clause,[],[f2202,f12540]) ).
fof(f12540,plain,
( spl0_1512
<=> ! [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_1512])]) ).
fof(f2202,axiom,
! [X1,X18,X27] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| c_less(X18,X27,X1)
| ~ c_less(c_minus(X18,X27,X1),c_0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Odiff__less__0__iff__less_0) ).
fof(f12538,plain,
spl0_1511,
inference(avatar_split_clause,[],[f2201,f12536]) ).
fof(f12536,plain,
( spl0_1511
<=> ! [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_1511])]) ).
fof(f2201,axiom,
! [X1,X18,X27] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_lessequals(X18,X27,X1)
| c_lessequals(c_minus(X18,X27,X1),c_0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Odiff__le__0__iff__le_1) ).
fof(f12534,plain,
spl0_1510,
inference(avatar_split_clause,[],[f2200,f12532]) ).
fof(f12532,plain,
( spl0_1510
<=> ! [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_1510])]) ).
fof(f2200,axiom,
! [X1,X18,X27] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| c_lessequals(X18,X27,X1)
| ~ c_lessequals(c_minus(X18,X27,X1),c_0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Odiff__le__0__iff__le_0) ).
fof(f12530,plain,
spl0_1509,
inference(avatar_split_clause,[],[f2184,f12528]) ).
fof(f12528,plain,
( spl0_1509
<=> ! [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_1509])]) ).
fof(f2184,axiom,
! [X1,X18] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
| ~ c_lessequals(X18,c_0,X1)
| c_uminus(X18,X1) = c_HOL_Oabs(X18,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__of__nonpos_0) ).
fof(f12526,plain,
spl0_1508,
inference(avatar_split_clause,[],[f2110,f12524]) ).
fof(f12524,plain,
( spl0_1508
<=> ! [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_1508])]) ).
fof(f2110,axiom,
! [X11,X47] : c_Numeral_Obin__add(c_Numeral_OBit(X47,c_Numeral_Obit_OB1),c_Numeral_OBit(X11,c_Numeral_Obit_OB0)) = c_Numeral_OBit(c_Numeral_Obin__add(X47,X11),c_Numeral_Obit_OB1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obin__add__BIT__10_0) ).
fof(f12517,plain,
spl0_1507,
inference(avatar_split_clause,[],[f2109,f12515]) ).
fof(f12515,plain,
( spl0_1507
<=> ! [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_1507])]) ).
fof(f2109,axiom,
! [X3,X11,X47] : c_Numeral_Obin__add(c_Numeral_OBit(X47,c_Numeral_Obit_OB0),c_Numeral_OBit(X11,X3)) = c_Numeral_OBit(c_Numeral_Obin__add(X47,X11),X3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obin__add__BIT__0_0) ).
fof(f12513,plain,
spl0_1506,
inference(avatar_split_clause,[],[f2045,f12511]) ).
fof(f12511,plain,
( spl0_1506
<=> ! [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_1506])]) ).
fof(f2045,axiom,
! [X21,X3] :
( ~ c_lessequals(X21,X3,tc_nat)
| c_plus(X21,c_minus(X3,X21,tc_nat),tc_nat) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Ole__add__diff__inverse_0) ).
fof(f12509,plain,
spl0_1505,
inference(avatar_split_clause,[],[f2044,f12507]) ).
fof(f12507,plain,
( spl0_1505
<=> ! [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_1505])]) ).
fof(f2044,axiom,
! [X21,X3] :
( ~ c_lessequals(X21,X3,tc_nat)
| c_plus(c_minus(X3,X21,tc_nat),X21,tc_nat) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Ole__add__diff__inverse2_0) ).
fof(f12505,plain,
spl0_1504,
inference(avatar_split_clause,[],[f1852,f12503]) ).
fof(f12503,plain,
( spl0_1504
<=> ! [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_1504])]) ).
fof(f1852,axiom,
! [X47] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(X47,tc_IntDef_Oint) = c_IntDef_Oint(c_Numeral_Onumber__of(X47,tc_nat)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatBin_Oint__nat__number__of_1) ).
fof(f12501,plain,
spl0_1503,
inference(avatar_split_clause,[],[f1799,f12499]) ).
fof(f12499,plain,
( spl0_1503
<=> ! [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_1503])]) ).
fof(f1799,axiom,
! [X21,X3] :
( ~ c_lessequals(X3,X21,tc_nat)
| c_minus(X21,c_minus(X21,X3,tc_nat),tc_nat) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatArith_Odiff__diff__cancel_0) ).
fof(f12497,plain,
spl0_1502,
inference(avatar_split_clause,[],[f1765,f12495]) ).
fof(f12495,plain,
( spl0_1502
<=> ! [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_1502])]) ).
fof(f1765,axiom,
! [X0,X1,X12] :
( c_in(c_0,X12,tc_nat)
| c_List_Olist_ONil = c_List_Osublist(c_List_Olist_OCons(X0,c_List_Olist_ONil,X1),X12,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Osublist__singleton_1) ).
fof(f12493,plain,
spl0_1501,
inference(avatar_split_clause,[],[f1748,f12491]) ).
fof(f1748,axiom,
! [X41,X0,X23] : c_List_Oset(c_List_Olist_OCons(X0,X23,X41),X41) = c_insert(X0,c_List_Oset(X23,X41),X41),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oset_Osimps__2_0) ).
fof(f12489,plain,
spl0_1500,
inference(avatar_split_clause,[],[f1742,f12487]) ).
fof(f12487,plain,
( spl0_1500
<=> ! [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_1500])]) ).
fof(f1742,axiom,
! [X21,X3,X1] :
( c_List_Orotate(X21,X3,X1) = X3
| ~ c_lessequals(c_Nat_Osize(X3,tc_List_Olist(X1)),c_1,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Orotate__length01_0) ).
fof(f12485,plain,
spl0_1499,
inference(avatar_split_clause,[],[f1702,f12483]) ).
fof(f12483,plain,
( spl0_1499
<=> ! [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_1499])]) ).
fof(f1702,axiom,
! [X21,X3,X1,X43] :
( ~ c_less(X43,X21,tc_nat)
| c_List_Onth(c_List_Oreplicate(X21,X3,X1),X43,X1) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Onth__replicate_0) ).
fof(f12481,plain,
spl0_1498,
inference(avatar_split_clause,[],[f1604,f12479]) ).
fof(f12479,plain,
( spl0_1498
<=> ! [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_1498])]) ).
fof(f1604,axiom,
! [X0,X1,X23,X43] : c_Nat_Osize(X23,tc_List_Olist(X1)) = c_Nat_Osize(c_List_Olist__update(X23,X43,X0,X1),tc_List_Olist(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olength__list__update_0) ).
fof(f12471,plain,
spl0_1497,
inference(avatar_split_clause,[],[f1591,f12469]) ).
fof(f12469,plain,
( spl0_1497
<=> ! [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_1497])]) ).
fof(f1591,axiom,
! [X1,X25,X23] :
( c_List_Olist_ONil = X25
| c_List_Olast(c_append(X23,X25,X1),X1) = c_List_Olast(X25,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olast__appendR_0) ).
fof(f12467,plain,
spl0_1496,
inference(avatar_split_clause,[],[f1589,f12465]) ).
fof(f12465,plain,
( spl0_1496
<=> ! [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_1496])]) ).
fof(f1589,axiom,
! [X0,X1,X23] :
( c_List_Olist_ONil = X23
| c_List_Olast(c_List_Olist_OCons(X0,X23,X1),X1) = c_List_Olast(X23,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olast_Osimps_1) ).
fof(f12463,plain,
spl0_1495,
inference(avatar_split_clause,[],[f1581,f12461]) ).
fof(f12461,plain,
( spl0_1495
<=> ! [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_1495])]) ).
fof(f1581,axiom,
! [X1,X25,X23] :
( c_List_Olist_ONil = X23
| c_List_Ohd(c_append(X23,X25,X1),X1) = c_List_Ohd(X23,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Ohd__append2_0) ).
fof(f12459,plain,
spl0_1494,
inference(avatar_split_clause,[],[f1580,f12457]) ).
fof(f1580,axiom,
! [X3,X1] :
( c_List_Olist_ONil = X3
| c_List_Olist_OCons(c_List_Ohd(X3,X1),c_List_Otl(X3,X1),X1) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Ohd__Cons__tl_0) ).
fof(f12455,plain,
spl0_1493,
inference(avatar_split_clause,[],[f1578,f12453]) ).
fof(f12453,plain,
( spl0_1493
<=> ! [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_1493])]) ).
fof(f1578,axiom,
! [X59,X15,X43] : c_List_Odrop(X15,c_List_Oupt(X43,X59),tc_nat) = c_List_Oupt(c_plus(X43,X15,tc_nat),X59),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Odrop__upt_0) ).
fof(f12451,plain,
spl0_1492,
inference(avatar_split_clause,[],[f1576,f12449]) ).
fof(f1576,axiom,
! [X21,X1,X23] :
( c_List_Olist_ONil = c_List_Odrop(X21,X23,X1)
| ~ c_lessequals(c_Nat_Osize(X23,tc_List_Olist(X1)),X21,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Odrop__eq__Nil_1) ).
fof(f12447,plain,
spl0_1491,
inference(avatar_split_clause,[],[f1575,f12445]) ).
fof(f12445,plain,
( spl0_1491
<=> ! [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_1491])]) ).
fof(f1575,axiom,
! [X21,X1,X23] :
( c_List_Olist_ONil != c_List_Odrop(X21,X23,X1)
| c_lessequals(c_Nat_Osize(X23,tc_List_Olist(X1)),X21,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Odrop__eq__Nil_0) ).
fof(f12443,plain,
spl0_1490,
inference(avatar_split_clause,[],[f1475,f12441]) ).
fof(f12441,plain,
( spl0_1490
<=> ! [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_1490])]) ).
fof(f1475,axiom,
! [X18,X27] : c_div(c_uminus(X18,tc_IntDef_Oint),c_uminus(X27,tc_IntDef_Oint),tc_IntDef_Oint) = c_div(X18,X27,tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozdiv__zminus__zminus_0) ).
fof(f12439,plain,
spl0_1489,
inference(avatar_split_clause,[],[f1416,f12437]) ).
fof(f12437,plain,
( spl0_1489
<=> ! [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_1489])]) ).
fof(f1416,axiom,
! [X48,X1] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X1)
| c_IntDef_Oof__int(c_uminus(X48,tc_IntDef_Oint),X1) = c_uminus(c_IntDef_Oof__int(X48,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oof__int__minus_0) ).
fof(f12435,plain,
spl0_1488,
inference(avatar_split_clause,[],[f1305,f12433]) ).
fof(f12433,plain,
( spl0_1488
<=> ! [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_1488])]) ).
fof(f1305,axiom,
! [X21,X16,X15] :
( c_Divides_Oop_Advd(X16,X21,tc_nat)
| ~ c_Divides_Oop_Advd(X16,c_GCD_Ogcd(c_Pair(X15,X21,tc_nat,tc_nat)),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_GCD_Ogcd__greatest__iff_1) ).
fof(f12431,plain,
( ~ spl0_1487
| ~ spl0_647
| ~ spl0_1129
| ~ spl0_1314 ),
inference(avatar_split_clause,[],[f10294,f10288,f9149,f6106,f12428]) ).
fof(f10288,plain,
( spl0_1314
<=> ! [X21] : ~ c_lessequals(c_0,c_uminus(c_plus(c_1,c_IntDef_Oint(X21),tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1314])]) ).
fof(f10294,plain,
( ~ c_lessequals(c_0,c_uminus(c_1,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_647
| ~ spl0_1129
| ~ spl0_1314 ),
inference(forward_demodulation,[],[f10293,f9150]) ).
fof(f10293,plain,
( ~ c_lessequals(c_0,c_uminus(c_plus(c_1,c_0,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_647
| ~ spl0_1314 ),
inference(superposition,[],[f10289,f6108]) ).
fof(f10289,plain,
( ! [X21] : ~ c_lessequals(c_0,c_uminus(c_plus(c_1,c_IntDef_Oint(X21),tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_1314 ),
inference(avatar_component_clause,[],[f10288]) ).
fof(f12426,plain,
spl0_1486,
inference(avatar_split_clause,[],[f1304,f12424]) ).
fof(f1304,axiom,
! [X21,X16,X15] :
( c_Divides_Oop_Advd(X16,X15,tc_nat)
| ~ c_Divides_Oop_Advd(X16,c_GCD_Ogcd(c_Pair(X15,X21,tc_nat,tc_nat)),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_GCD_Ogcd__greatest__iff_0) ).
fof(f12422,plain,
spl0_1485,
inference(avatar_split_clause,[],[f1291,f12420]) ).
fof(f12420,plain,
( spl0_1485
<=> ! [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_1485])]) ).
fof(f1291,axiom,
! [X1,X18,X12] :
( c_in(X12,c_Finite__Set_OFinites,tc_set(X1))
| ~ c_in(c_insert(X18,X12,X1),c_Finite__Set_OFinites,tc_set(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__insert_0) ).
fof(f12418,plain,
spl0_1484,
inference(avatar_split_clause,[],[f1287,f12416]) ).
fof(f12416,plain,
( spl0_1484
<=> ! [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_1484])]) ).
fof(f1287,axiom,
! [X1,X19,X20] :
( c_in(X20,c_Finite__Set_OFinites,tc_set(X1))
| ~ c_in(c_union(X19,X20,X1),c_Finite__Set_OFinites,tc_set(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Un_1) ).
fof(f12414,plain,
spl0_1483,
inference(avatar_split_clause,[],[f1286,f12412]) ).
fof(f12412,plain,
( spl0_1483
<=> ! [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_1483])]) ).
fof(f1286,axiom,
! [X1,X19,X20] :
( c_in(X19,c_Finite__Set_OFinites,tc_set(X1))
| ~ c_in(c_union(X19,X20,X1),c_Finite__Set_OFinites,tc_set(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Un_0) ).
fof(f12410,plain,
spl0_1482,
inference(avatar_split_clause,[],[f1285,f12408]) ).
fof(f12408,plain,
( spl0_1482
<=> ! [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_1482])]) ).
fof(f1285,axiom,
! [X1,X12] :
( ~ c_in(X12,c_Finite__Set_OFinites,tc_set(X1))
| c_in(c_Pow(X12,X1),c_Finite__Set_OFinites,tc_set(tc_set(X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Pow__iff_1) ).
fof(f12406,plain,
spl0_1481,
inference(avatar_split_clause,[],[f1284,f12404]) ).
fof(f12404,plain,
( spl0_1481
<=> ! [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_1481])]) ).
fof(f1284,axiom,
! [X1,X12] :
( c_in(X12,c_Finite__Set_OFinites,tc_set(X1))
| ~ c_in(c_Pow(X12,X1),c_Finite__Set_OFinites,tc_set(tc_set(X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Pow__iff_0) ).
fof(f12402,plain,
spl0_1480,
inference(avatar_split_clause,[],[f1276,f12400]) ).
fof(f12400,plain,
( spl0_1480
<=> ! [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_1480])]) ).
fof(f1276,axiom,
! [X1,X12] :
( c_emptyset = X12
| c_0 != c_Finite__Set_Ocard(X12,X1)
| ~ c_in(X12,c_Finite__Set_OFinites,tc_set(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ocard__0__eq_0) ).
fof(f12398,plain,
spl0_1479,
inference(avatar_split_clause,[],[f1223,f12396]) ).
fof(f12396,plain,
( spl0_1479
<=> ! [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_1479])]) ).
fof(f1223,axiom,
! [X21,X3] :
( ~ c_less(c_0,X21,tc_nat)
| c_div(c_times(X3,X21,tc_nat),X21,tc_nat) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Odiv__mult__self__is__m_0) ).
fof(f12394,plain,
spl0_1478,
inference(avatar_split_clause,[],[f1221,f12392]) ).
fof(f12392,plain,
( spl0_1478
<=> ! [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_1478])]) ).
fof(f1221,axiom,
! [X21,X3] :
( ~ c_less(c_0,X21,tc_nat)
| c_div(c_times(X21,X3,tc_nat),X21,tc_nat) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Odiv__mult__self1__is__m_0) ).
fof(f12390,plain,
spl0_1477,
inference(avatar_split_clause,[],[f111,f12388]) ).
fof(f111,axiom,
! [X1,X12,X13] :
( X12 = X13
| ~ c_lessequals(X12,X13,tc_set(X1))
| ~ c_lessequals(X13,X12,tc_set(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osubset__antisym_0) ).
fof(f12375,plain,
spl0_1476,
inference(avatar_split_clause,[],[f108,f12373]) ).
fof(f12373,plain,
( spl0_1476
<=> ! [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_1476])]) ).
fof(f108,axiom,
! [X1,X4,X12,X13] :
( ~ c_in(X4,X12,X1)
| c_in(X4,X13,X1)
| ~ c_lessequals(X12,X13,tc_set(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OsubsetD_0) ).
fof(f12371,plain,
spl0_1475,
inference(avatar_split_clause,[],[f104,f12369]) ).
fof(f104,axiom,
! [X1,X12,X13] :
( X12 = X13
| ~ c_lessequals(X12,X13,tc_set(X1))
| c_less(X12,X13,tc_set(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OpsubsetI_0) ).
fof(f12367,plain,
spl0_1474,
inference(avatar_split_clause,[],[f100,f12365]) ).
fof(f12365,plain,
( spl0_1474
<=> ! [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_1474])]) ).
fof(f100,axiom,
! [X1,X12,X32] :
( ~ c_in(X12,c_Union(X32,X1),X1)
| c_in(X12,c_Main_OUnionE__1(X12,X32,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUnionE_1) ).
fof(f12363,plain,
spl0_1473,
inference(avatar_split_clause,[],[f97,f12361]) ).
fof(f12361,plain,
( spl0_1473
<=> ! [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_1473])]) ).
fof(f97,axiom,
! [X1,X12,X32] :
( c_in(X12,c_Inter(X32,X1),X1)
| ~ c_in(X12,c_Main_OInterI__1(X12,X32,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OInterI_1) ).
fof(f12359,plain,
spl0_1472,
inference(avatar_split_clause,[],[f29,f12357]) ).
fof(f12357,plain,
( spl0_1472
<=> ! [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_1472])]) ).
fof(f29,axiom,
! [X1,X18,X12] :
( ~ c_in(X12,c_Finite__Set_OFinites,tc_set(X1))
| c_in(c_insert(X18,X12,X1),c_Finite__Set_OFinites,tc_set(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_OFinites_OinsertI_0) ).
fof(f11898,plain,
( spl0_1471
| ~ spl0_659
| ~ spl0_814
| ~ spl0_1217 ),
inference(avatar_split_clause,[],[f9958,f9654,f7597,f6159,f11895]) ).
fof(f11895,plain,
( spl0_1471
<=> c_Message_Osynth(c_emptyset) = c_Message_Oparts(c_Message_Osynth(c_emptyset)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1471])]) ).
fof(f6159,plain,
( spl0_659
<=> c_emptyset = c_Message_Oparts(c_emptyset) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_659])]) ).
fof(f7597,plain,
( spl0_814
<=> ! [X1,X3] : c_union(c_emptyset,X3,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_814])]) ).
fof(f9654,plain,
( spl0_1217
<=> ! [X88] : c_Message_Oparts(c_Message_Osynth(X88)) = c_union(c_Message_Oparts(X88),c_Message_Osynth(X88),tc_Message_Omsg) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1217])]) ).
fof(f9958,plain,
( c_Message_Osynth(c_emptyset) = c_Message_Oparts(c_Message_Osynth(c_emptyset))
| ~ spl0_659
| ~ spl0_814
| ~ spl0_1217 ),
inference(forward_demodulation,[],[f9953,f7598]) ).
fof(f7598,plain,
( ! [X3,X1] : c_union(c_emptyset,X3,X1) = X3
| ~ spl0_814 ),
inference(avatar_component_clause,[],[f7597]) ).
fof(f9953,plain,
( c_union(c_emptyset,c_Message_Osynth(c_emptyset),tc_Message_Omsg) = c_Message_Oparts(c_Message_Osynth(c_emptyset))
| ~ spl0_659
| ~ spl0_1217 ),
inference(superposition,[],[f9655,f6161]) ).
fof(f6161,plain,
( c_emptyset = c_Message_Oparts(c_emptyset)
| ~ spl0_659 ),
inference(avatar_component_clause,[],[f6159]) ).
fof(f9655,plain,
( ! [X88] : c_Message_Oparts(c_Message_Osynth(X88)) = c_union(c_Message_Oparts(X88),c_Message_Osynth(X88),tc_Message_Omsg)
| ~ spl0_1217 ),
inference(avatar_component_clause,[],[f9654]) ).
fof(f11801,plain,
( spl0_1470
| ~ spl0_662
| ~ spl0_814
| ~ spl0_1216 ),
inference(avatar_split_clause,[],[f9952,f9650,f7597,f6174,f11798]) ).
fof(f11798,plain,
( spl0_1470
<=> c_Message_Osynth(c_emptyset) = c_Message_Oanalz(c_Message_Osynth(c_emptyset)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1470])]) ).
fof(f6174,plain,
( spl0_662
<=> c_emptyset = c_Message_Oanalz(c_emptyset) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_662])]) ).
fof(f9650,plain,
( spl0_1216
<=> ! [X88] : c_Message_Oanalz(c_Message_Osynth(X88)) = c_union(c_Message_Oanalz(X88),c_Message_Osynth(X88),tc_Message_Omsg) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1216])]) ).
fof(f9952,plain,
( c_Message_Osynth(c_emptyset) = c_Message_Oanalz(c_Message_Osynth(c_emptyset))
| ~ spl0_662
| ~ spl0_814
| ~ spl0_1216 ),
inference(forward_demodulation,[],[f9947,f7598]) ).
fof(f9947,plain,
( c_Message_Oanalz(c_Message_Osynth(c_emptyset)) = c_union(c_emptyset,c_Message_Osynth(c_emptyset),tc_Message_Omsg)
| ~ spl0_662
| ~ spl0_1216 ),
inference(superposition,[],[f9651,f6176]) ).
fof(f6176,plain,
( c_emptyset = c_Message_Oanalz(c_emptyset)
| ~ spl0_662 ),
inference(avatar_component_clause,[],[f6174]) ).
fof(f9651,plain,
( ! [X88] : c_Message_Oanalz(c_Message_Osynth(X88)) = c_union(c_Message_Oanalz(X88),c_Message_Osynth(X88),tc_Message_Omsg)
| ~ spl0_1216 ),
inference(avatar_component_clause,[],[f9650]) ).
fof(f11591,plain,
( spl0_1469
| ~ spl0_726
| ~ spl0_1197 ),
inference(avatar_split_clause,[],[f9919,f9574,f7223,f11589]) ).
fof(f11589,plain,
( spl0_1469
<=> ! [X0] : c_emptyset = c_Relation_Oconverse(c_emptyset,X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1469])]) ).
fof(f7223,plain,
( spl0_726
<=> ! [X1] : c_emptyset = c_Relation_Odiag(c_emptyset,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_726])]) ).
fof(f9574,plain,
( spl0_1197
<=> ! [X12,X1] : c_Relation_Odiag(X12,X1) = c_Relation_Oconverse(c_Relation_Odiag(X12,X1),X1,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1197])]) ).
fof(f9919,plain,
( ! [X0] : c_emptyset = c_Relation_Oconverse(c_emptyset,X0,X0)
| ~ spl0_726
| ~ spl0_1197 ),
inference(superposition,[],[f9575,f7224]) ).
fof(f7224,plain,
( ! [X1] : c_emptyset = c_Relation_Odiag(c_emptyset,X1)
| ~ spl0_726 ),
inference(avatar_component_clause,[],[f7223]) ).
fof(f9575,plain,
( ! [X1,X12] : c_Relation_Odiag(X12,X1) = c_Relation_Oconverse(c_Relation_Odiag(X12,X1),X1,X1)
| ~ spl0_1197 ),
inference(avatar_component_clause,[],[f9574]) ).
fof(f11403,plain,
( spl0_1468
| ~ spl0_1070
| ~ spl0_1329 ),
inference(avatar_split_clause,[],[f11366,f10736,f8847,f11401]) ).
fof(f11401,plain,
( spl0_1468
<=> ! [X0] : c_lessequals(X0,c_IntDef_ONats,tc_set(tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1468])]) ).
fof(f8847,plain,
( spl0_1070
<=> ! [X0] : c_in(X0,c_IntDef_ONats,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1070])]) ).
fof(f10736,plain,
( spl0_1329
<=> ! [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_1329])]) ).
fof(f11366,plain,
( ! [X0] : c_lessequals(X0,c_IntDef_ONats,tc_set(tc_nat))
| ~ spl0_1070
| ~ spl0_1329 ),
inference(resolution,[],[f10737,f8848]) ).
fof(f8848,plain,
( ! [X0] : c_in(X0,c_IntDef_ONats,tc_nat)
| ~ spl0_1070 ),
inference(avatar_component_clause,[],[f8847]) ).
fof(f10737,plain,
( ! [X1,X12,X13] :
( ~ c_in(c_Main_OsubsetI__1(X12,X13,X1),X13,X1)
| c_lessequals(X12,X13,tc_set(X1)) )
| ~ spl0_1329 ),
inference(avatar_component_clause,[],[f10736]) ).
fof(f11339,plain,
spl0_1467,
inference(avatar_split_clause,[],[f3363,f11337]) ).
fof(f11337,plain,
( spl0_1467
<=> ! [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_1467])]) ).
fof(f3363,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,[],[f3362,f2115]) ).
fof(f3362,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,[],[f3157,f2957]) ).
fof(f3157,plain,
! [X0,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| c_0 = c_Numeral_Onumber__of(X0,X1)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X0,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OPls)),X1),X1) ),
inference(definition_unfolding,[],[f1338,f2129]) ).
fof(f1338,axiom,
! [X0,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| c_0 = c_Numeral_Onumber__of(X0,X1)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X0,c_Numeral_Obin__minus(c_Numeral_OPls)),X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__8_1) ).
fof(f11335,plain,
spl0_1466,
inference(avatar_split_clause,[],[f3291,f11333]) ).
fof(f11333,plain,
( spl0_1466
<=> ! [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_1466])]) ).
fof(f3291,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,[],[f3290,f2156]) ).
fof(f3290,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,[],[f3289,f2154]) ).
fof(f3289,plain,
! [X1] :
( c_0 = c_Nat_Opower(c_0,c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB0),tc_nat),X1)
| ~ class_Power_Orecpower(X1) ),
inference(forward_demodulation,[],[f1878,f2156]) ).
fof(f1878,axiom,
! [X1] :
( ~ class_Power_Orecpower(X1)
| c_0 = c_Nat_Opower(c_0,c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatBin_Ozero__power2_0) ).
fof(f11331,plain,
spl0_1465,
inference(avatar_split_clause,[],[f3284,f11329]) ).
fof(f3284,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,[],[f3283,f2156]) ).
fof(f3283,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,[],[f3282,f2154]) ).
fof(f3282,plain,
! [X1] :
( c_plus(c_1,c_1,X1) = c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB0),X1)
| ~ class_Numeral_Onumber__ring(X1) ),
inference(forward_demodulation,[],[f1328,f2156]) ).
fof(f1328,axiom,
! [X1] :
( ~ class_Numeral_Onumber__ring(X1)
| c_plus(c_1,c_1,X1) = c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__1_0) ).
fof(f11327,plain,
spl0_1464,
inference(avatar_split_clause,[],[f3096,f11325]) ).
fof(f11325,plain,
( spl0_1464
<=> ! [X13,X12,X1] :
( c_UNIV = X13
| c_UNIV != c_Relation_OImage(c_Relation_Odiag(X12,X1),X13,X1,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1464])]) ).
fof(f3096,plain,
! [X1,X12,X13] :
( c_UNIV = X13
| c_UNIV != c_Relation_OImage(c_Relation_Odiag(X12,X1),X13,X1,X1) ),
inference(definition_unfolding,[],[f2599,f2373]) ).
fof(f2599,axiom,
! [X1,X12,X13] :
( c_UNIV = X13
| c_UNIV != c_inter(X12,X13,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OInt__UNIV_1) ).
fof(f11323,plain,
spl0_1463,
inference(avatar_split_clause,[],[f3095,f11321]) ).
fof(f11321,plain,
( spl0_1463
<=> ! [X13,X12,X1] :
( c_UNIV = X12
| c_UNIV != c_Relation_OImage(c_Relation_Odiag(X12,X1),X13,X1,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1463])]) ).
fof(f3095,plain,
! [X1,X12,X13] :
( c_UNIV = X12
| c_UNIV != c_Relation_OImage(c_Relation_Odiag(X12,X1),X13,X1,X1) ),
inference(definition_unfolding,[],[f2598,f2373]) ).
fof(f2598,axiom,
! [X1,X12,X13] :
( c_UNIV = X12
| c_UNIV != c_inter(X12,X13,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OInt__UNIV_0) ).
fof(f11319,plain,
spl0_1462,
inference(avatar_split_clause,[],[f3086,f11317]) ).
fof(f11317,plain,
( spl0_1462
<=> ! [X21,X1] :
( ~ class_Power_Orecpower(X1)
| c_0 = c_Nat_Opower(c_0,c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1462])]) ).
fof(f3086,plain,
! [X21,X1] :
( ~ class_Power_Orecpower(X1)
| c_0 = c_Nat_Opower(c_0,c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),X1) ),
inference(definition_unfolding,[],[f2346,f2544]) ).
fof(f2346,axiom,
! [X21,X1] :
( ~ class_Power_Orecpower(X1)
| c_0 = c_Nat_Opower(c_0,c_Suc(X21),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Power_Opower__0__Suc_0) ).
fof(f11315,plain,
spl0_1461,
inference(avatar_split_clause,[],[f3010,f11313]) ).
fof(f3010,plain,
! [X15] : c_plus(c_1,c_IntDef_Oint(X15),tc_IntDef_Oint) = c_IntDef_Oint(c_Finite__Set_Ocard(c_SetInterval_OatMost(X15,tc_nat),tc_nat)),
inference(definition_unfolding,[],[f1372,f2544]) ).
fof(f1372,axiom,
! [X15] : c_IntDef_Oint(c_Suc(X15)) = c_plus(c_1,c_IntDef_Oint(X15),tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oint__Suc_0) ).
fof(f11311,plain,
spl0_1460,
inference(avatar_split_clause,[],[f3007,f11309]) ).
fof(f11309,plain,
( spl0_1460
<=> ! [X12,X1] : c_emptyset = c_Relation_OImage(c_Relation_Odiag(c_uminus(X12,tc_set(X1)),X1),X12,X1,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1460])]) ).
fof(f3007,plain,
! [X1,X12] : c_emptyset = c_Relation_OImage(c_Relation_Odiag(c_uminus(X12,tc_set(X1)),X1),X12,X1,X1),
inference(definition_unfolding,[],[f2578,f2373]) ).
fof(f2578,axiom,
! [X1,X12] : c_emptyset = c_inter(c_uminus(X12,tc_set(X1)),X12,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OCompl__disjoint2_0) ).
fof(f11307,plain,
spl0_1459,
inference(avatar_split_clause,[],[f3006,f11305]) ).
fof(f11305,plain,
( spl0_1459
<=> ! [X12,X1] : c_emptyset = c_Relation_OImage(c_Relation_Odiag(X12,X1),c_uminus(X12,tc_set(X1)),X1,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1459])]) ).
fof(f3006,plain,
! [X1,X12] : c_emptyset = c_Relation_OImage(c_Relation_Odiag(X12,X1),c_uminus(X12,tc_set(X1)),X1,X1),
inference(definition_unfolding,[],[f2579,f2373]) ).
fof(f2579,axiom,
! [X1,X12] : c_emptyset = c_inter(X12,c_uminus(X12,tc_set(X1)),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OCompl__disjoint_0) ).
fof(f11303,plain,
spl0_1458,
inference(avatar_split_clause,[],[f2935,f11301]) ).
fof(f11301,plain,
( spl0_1458
<=> ! [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_1458])]) ).
fof(f2935,axiom,
! [X91,X88,X86] :
( c_in(X86,c_Message_Oparts(X88),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(X91,X86),c_Message_Oparts(X88),tc_Message_Omsg) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oparts_OBody__dest_0) ).
fof(f11299,plain,
( spl0_1457
| ~ spl0_650
| ~ spl0_1167 ),
inference(avatar_split_clause,[],[f9836,f9454,f6120,f11297]) ).
fof(f11297,plain,
( spl0_1457
<=> ! [X0] : c_Divides_Oop_Advd(X0,c_uminus(X0,tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1457])]) ).
fof(f6120,plain,
( spl0_650
<=> ! [X15] : c_Divides_Oop_Advd(X15,X15,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_650])]) ).
fof(f9454,plain,
( spl0_1167
<=> ! [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_1167])]) ).
fof(f9836,plain,
( ! [X0] : c_Divides_Oop_Advd(X0,c_uminus(X0,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_650
| ~ spl0_1167 ),
inference(resolution,[],[f9455,f6121]) ).
fof(f6121,plain,
( ! [X15] : c_Divides_Oop_Advd(X15,X15,tc_IntDef_Oint)
| ~ spl0_650 ),
inference(avatar_component_clause,[],[f6120]) ).
fof(f9455,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_1167 ),
inference(avatar_component_clause,[],[f9454]) ).
fof(f11295,plain,
spl0_1456,
inference(avatar_split_clause,[],[f2897,f11293]) ).
fof(f11293,plain,
( spl0_1456
<=> ! [X102,X12] :
( ~ c_in(X12,c_Event_Obad,tc_Message_Oagent)
| c_in(c_Message_Omsg_OKey(c_Public_OshrK(X12)),c_Event_Oknows(c_Message_Oagent_OSpy,X102),tc_Message_Omsg) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1456])]) ).
fof(f2897,axiom,
! [X12,X102] :
( ~ c_in(X12,c_Event_Obad,tc_Message_Oagent)
| c_in(c_Message_Omsg_OKey(c_Public_OshrK(X12)),c_Event_Oknows(c_Message_Oagent_OSpy,X102),tc_Message_Omsg) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Public_OSpy__spies__bad__shrK_0) ).
fof(f11291,plain,
spl0_1455,
inference(avatar_split_clause,[],[f2893,f11289]) ).
fof(f11289,plain,
( spl0_1455
<=> ! [X86,X87,X88] :
( c_in(X86,c_Event_Oused(X88),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OMPair(X86,X87),c_Event_Oused(X88),tc_Message_Omsg) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1455])]) ).
fof(f2893,axiom,
! [X88,X86,X87] :
( c_in(X86,c_Event_Oused(X88),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OMPair(X86,X87),c_Event_Oused(X88),tc_Message_Omsg) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Public_OMPair__used_1) ).
fof(f11287,plain,
spl0_1454,
inference(avatar_split_clause,[],[f2892,f11285]) ).
fof(f11285,plain,
( spl0_1454
<=> ! [X87,X86,X88] :
( c_in(X87,c_Event_Oused(X88),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OMPair(X86,X87),c_Event_Oused(X88),tc_Message_Omsg) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1454])]) ).
fof(f2892,axiom,
! [X88,X86,X87] :
( c_in(X87,c_Event_Oused(X88),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OMPair(X86,X87),c_Event_Oused(X88),tc_Message_Omsg) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Public_OMPair__used_0) ).
fof(f11283,plain,
spl0_1453,
inference(avatar_split_clause,[],[f2851,f11281]) ).
fof(f11281,plain,
( spl0_1453
<=> ! [X20,X88] : c_Message_Oanalz(c_union(c_Message_Oanalz(X20),X88,tc_Message_Omsg)) = c_Message_Oanalz(c_union(X20,X88,tc_Message_Omsg)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1453])]) ).
fof(f2851,axiom,
! [X88,X20] : c_Message_Oanalz(c_union(c_Message_Oanalz(X20),X88,tc_Message_Omsg)) = c_Message_Oanalz(c_union(X20,X88,tc_Message_Omsg)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oanalz__analz__Un_0) ).
fof(f11279,plain,
spl0_1452,
inference(avatar_split_clause,[],[f2834,f11277]) ).
fof(f11277,plain,
( spl0_1452
<=> ! [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_1452])]) ).
fof(f2834,axiom,
! [X88,X86,X87] :
( c_in(X86,c_Message_Oanalz(X88),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OMPair(X86,X87),c_Message_Oanalz(X88),tc_Message_Omsg) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OMPair__analz_1) ).
fof(f11275,plain,
spl0_1451,
inference(avatar_split_clause,[],[f2833,f11273]) ).
fof(f2833,axiom,
! [X88,X86,X87] :
( c_in(X87,c_Message_Oanalz(X88),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OMPair(X86,X87),c_Message_Oanalz(X88),tc_Message_Omsg) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OMPair__analz_0) ).
fof(f11271,plain,
spl0_1450,
inference(avatar_split_clause,[],[f2796,f11269]) ).
fof(f11269,plain,
( spl0_1450
<=> ! [X102,X86,X12] : c_Event_Oknows(c_Message_Oagent_OSpy,X102) = c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Olist_OCons(c_Event_Oevent_OGets(X12,X86),X102,tc_Event_Oevent)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1450])]) ).
fof(f2796,axiom,
! [X86,X102,X12] : c_Event_Oknows(c_Message_Oagent_OSpy,X102) = c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Olist_OCons(c_Event_Oevent_OGets(X12,X86),X102,tc_Event_Oevent)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Event_Oknows__Spy__Gets_0) ).
fof(f11267,plain,
spl0_1449,
inference(avatar_split_clause,[],[f2794,f11265]) ).
fof(f11265,plain,
( spl0_1449
<=> ! [X24,X88] :
( ~ c_in(c_Message_Omsg_OKey(X24),X88,tc_Message_Omsg)
| c_in(c_Message_OinvKey(X24),c_Message_OkeysFor(c_Message_Osynth(X88)),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1449])]) ).
fof(f2794,axiom,
! [X88,X24] :
( ~ c_in(c_Message_Omsg_OKey(X24),X88,tc_Message_Omsg)
| c_in(c_Message_OinvKey(X24),c_Message_OkeysFor(c_Message_Osynth(X88)),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Event_OkeysFor__synth_H_3) ).
fof(f11263,plain,
spl0_1448,
inference(avatar_split_clause,[],[f2783,f11261]) ).
fof(f11261,plain,
( spl0_1448
<=> ! [X105,X106,X97,X104,X103,X96] :
( X96 = X97
| c_Event_Oevent_OSays(X103,X104,X96) != c_Event_Oevent_OSays(X105,X106,X97) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1448])]) ).
fof(f2783,axiom,
! [X106,X96,X97,X104,X105,X103] :
( X96 = X97
| c_Event_Oevent_OSays(X103,X104,X96) != c_Event_Oevent_OSays(X105,X106,X97) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Event_Oevent_Oinject__1_2) ).
fof(f11259,plain,
spl0_1447,
inference(avatar_split_clause,[],[f2782,f11257]) ).
fof(f11257,plain,
( spl0_1447
<=> ! [X105,X106,X97,X104,X103,X96] :
( X104 = X106
| c_Event_Oevent_OSays(X103,X104,X96) != c_Event_Oevent_OSays(X105,X106,X97) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1447])]) ).
fof(f2782,axiom,
! [X106,X96,X97,X104,X105,X103] :
( X104 = X106
| c_Event_Oevent_OSays(X103,X104,X96) != c_Event_Oevent_OSays(X105,X106,X97) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Event_Oevent_Oinject__1_1) ).
fof(f11255,plain,
( spl0_1446
| ~ spl0_650
| ~ spl0_1164 ),
inference(avatar_split_clause,[],[f9826,f9441,f6120,f11253]) ).
fof(f11253,plain,
( spl0_1446
<=> ! [X0] : c_Divides_Oop_Advd(c_uminus(X0,tc_IntDef_Oint),X0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1446])]) ).
fof(f9441,plain,
( spl0_1164
<=> ! [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_1164])]) ).
fof(f9826,plain,
( ! [X0] : c_Divides_Oop_Advd(c_uminus(X0,tc_IntDef_Oint),X0,tc_IntDef_Oint)
| ~ spl0_650
| ~ spl0_1164 ),
inference(resolution,[],[f9442,f6121]) ).
fof(f9442,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_1164 ),
inference(avatar_component_clause,[],[f9441]) ).
fof(f11251,plain,
spl0_1445,
inference(avatar_split_clause,[],[f2781,f11249]) ).
fof(f11249,plain,
( spl0_1445
<=> ! [X105,X106,X97,X104,X96,X103] :
( X103 = X105
| c_Event_Oevent_OSays(X103,X104,X96) != c_Event_Oevent_OSays(X105,X106,X97) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1445])]) ).
fof(f2781,axiom,
! [X106,X96,X97,X104,X105,X103] :
( X103 = X105
| c_Event_Oevent_OSays(X103,X104,X96) != c_Event_Oevent_OSays(X105,X106,X97) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Event_Oevent_Oinject__1_0) ).
fof(f11247,plain,
spl0_1444,
inference(avatar_split_clause,[],[f2774,f11245]) ).
fof(f2774,axiom,
! [X4,X102] :
( c_in(X4,c_Event_Oused(X102),tc_Message_Omsg)
| ~ c_in(X4,c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,X102)),tc_Message_Omsg) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Event_Oc_A_58_Aparts_A_Iknows_ASpy_Aevs1_J_A_61_61_62_Ac_A_58_Aused_Aevs1_0) ).
fof(f11243,plain,
spl0_1443,
inference(avatar_split_clause,[],[f2771,f11241]) ).
fof(f11241,plain,
( spl0_1443
<=> ! [X13,X12,X1] : c_union(X13,X12,X1) = c_union(X12,c_union(X13,X12,X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1443])]) ).
fof(f2771,axiom,
! [X1,X12,X13] : c_union(X13,X12,X1) = c_union(X12,c_union(X13,X12,X1),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Ostrange__Un__eq_0) ).
fof(f11239,plain,
spl0_1442,
inference(avatar_split_clause,[],[f2768,f11237]) ).
fof(f11237,plain,
( spl0_1442
<=> ! [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_1442])]) ).
fof(f2768,axiom,
! [X88,X20] : c_Message_Oparts(c_union(X20,X88,tc_Message_Omsg)) = c_union(c_Message_Oparts(X20),c_Message_Oparts(X88),tc_Message_Omsg),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oparts__Un_0) ).
fof(f11235,plain,
spl0_1441,
inference(avatar_split_clause,[],[f2742,f11233]) ).
fof(f11233,plain,
( spl0_1441
<=> ! [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_1441])]) ).
fof(f2742,axiom,
! [X88,X93] : c_Message_OkeysFor(c_union(X88,X93,tc_Message_Omsg)) = c_union(c_Message_OkeysFor(X88),c_Message_OkeysFor(X93),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OkeysFor__Un_0) ).
fof(f11231,plain,
spl0_1440,
inference(avatar_split_clause,[],[f2729,f11229]) ).
fof(f11229,plain,
( spl0_1440
<=> ! [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_1440])]) ).
fof(f2729,axiom,
! [X88,X86,X87] :
( c_in(X86,c_Message_Oparts(X88),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OMPair(X86,X87),c_Message_Oparts(X88),tc_Message_Omsg) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OMPair__parts_1) ).
fof(f11227,plain,
spl0_1439,
inference(avatar_split_clause,[],[f2728,f11225]) ).
fof(f11225,plain,
( spl0_1439
<=> ! [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_1439])]) ).
fof(f2728,axiom,
! [X88,X86,X87] :
( c_in(X87,c_Message_Oparts(X88),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OMPair(X86,X87),c_Message_Oparts(X88),tc_Message_Omsg) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OMPair__parts_0) ).
fof(f11223,plain,
spl0_1438,
inference(avatar_split_clause,[],[f2703,f11221]) ).
fof(f11221,plain,
( spl0_1438
<=> ! [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_1438])]) ).
fof(f2703,axiom,
! [X2,X3,X0,X1] :
( X0 = X3
| c_Sum__Type_OInr(X0,X2,X1) != c_Sum__Type_OInr(X3,X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sum__Type_OInr__eq_0) ).
fof(f11219,plain,
spl0_1437,
inference(avatar_split_clause,[],[f2701,f11217]) ).
fof(f11217,plain,
( spl0_1437
<=> ! [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_1437])]) ).
fof(f2701,axiom,
! [X2,X3,X0,X1] :
( X0 = X3
| c_Sum__Type_OInl(X0,X1,X2) != c_Sum__Type_OInl(X3,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sum__Type_OInl__eq_0) ).
fof(f11215,plain,
spl0_1436,
inference(avatar_split_clause,[],[f2692,f11213]) ).
fof(f11213,plain,
( spl0_1436
<=> ! [X18,X12,X27,X1] :
( X18 = X27
| c_insert(X18,X12,X1) != c_insert(X27,c_emptyset,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1436])]) ).
fof(f2692,axiom,
! [X18,X1,X27,X12] :
( X18 = X27
| c_insert(X18,X12,X1) != c_insert(X27,c_emptyset,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osingleton__insert__inj__eq_0) ).
fof(f11198,plain,
spl0_1435,
inference(avatar_split_clause,[],[f2688,f11196]) ).
fof(f11196,plain,
( spl0_1435
<=> ! [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_1435])]) ).
fof(f2688,axiom,
! [X0,X1,X12,X13] :
( c_in(X0,X13,X1)
| ~ c_lessequals(c_insert(X0,X12,X1),X13,tc_set(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Oinsert__subset_0) ).
fof(f11194,plain,
spl0_1434,
inference(avatar_split_clause,[],[f2676,f11192]) ).
fof(f11192,plain,
( spl0_1434
<=> ! [X12,X0,X1] : c_insert(X0,X12,X1) = c_insert(X0,c_insert(X0,X12,X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1434])]) ).
fof(f2676,axiom,
! [X0,X1,X12] : c_insert(X0,X12,X1) = c_insert(X0,c_insert(X0,X12,X1),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Oinsert__absorb2_0) ).
fof(f11190,plain,
spl0_1433,
inference(avatar_split_clause,[],[f2670,f11188]) ).
fof(f11188,plain,
( spl0_1433
<=> ! [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_1433])]) ).
fof(f2670,axiom,
! [X1,X12] :
( c_emptyset = c_Union(X12,X1)
| c_in(c_Main_Oempty__Union__conv__1(X12,X1),X12,tc_set(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Oempty__Union__conv_1) ).
fof(f11186,plain,
spl0_1432,
inference(avatar_split_clause,[],[f2653,f11184]) ).
fof(f11184,plain,
( spl0_1432
<=> ! [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_1432])]) ).
fof(f2653,axiom,
! [X1,X12] :
( c_emptyset = c_Union(X12,X1)
| c_in(c_Main_OUnion__empty__conv__1(X12,X1),X12,tc_set(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUnion__empty__conv_1) ).
fof(f11182,plain,
spl0_1431,
inference(avatar_split_clause,[],[f2628,f11180]) ).
fof(f11180,plain,
( spl0_1431
<=> ! [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_1431])]) ).
fof(f2628,axiom,
! [X1,X12,X13] :
( ~ c_lessequals(X12,X13,tc_set(X1))
| c_in(X12,c_Pow(X13,X1),tc_set(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OPow__iff_1) ).
fof(f11178,plain,
spl0_1430,
inference(avatar_split_clause,[],[f2627,f11176]) ).
fof(f11176,plain,
( spl0_1430
<=> ! [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_1430])]) ).
fof(f2627,axiom,
! [X1,X12,X13] :
( c_lessequals(X12,X13,tc_set(X1))
| ~ c_in(X12,c_Pow(X13,X1),tc_set(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OPow__iff_0) ).
fof(f11174,plain,
spl0_1429,
inference(avatar_split_clause,[],[f2617,f11172]) ).
fof(f11172,plain,
( spl0_1429
<=> ! [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_1429])]) ).
fof(f2617,axiom,
! [X1,X12] :
( c_UNIV = c_Inter(X12,X1)
| c_in(c_Main_OInter__UNIV__conv__2__1(X12,X1),X12,tc_set(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OInter__UNIV__conv__2_1) ).
fof(f11170,plain,
spl0_1428,
inference(avatar_split_clause,[],[f2614,f11168]) ).
fof(f11168,plain,
( spl0_1428
<=> ! [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_1428])]) ).
fof(f2614,axiom,
! [X1,X12] :
( c_UNIV = c_Inter(X12,X1)
| c_in(c_Main_OInter__UNIV__conv__1__1(X12,X1),X12,tc_set(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OInter__UNIV__conv__1_1) ).
fof(f11166,plain,
spl0_1427,
inference(avatar_split_clause,[],[f2595,f11164]) ).
fof(f2595,axiom,
! [X1,X4,X12,X13] :
( ~ c_in(X4,X13,X1)
| ~ c_in(X4,c_minus(X12,X13,tc_set(X1)),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_ODiff__iff_1) ).
fof(f11162,plain,
spl0_1426,
inference(avatar_split_clause,[],[f2594,f11160]) ).
fof(f11160,plain,
( spl0_1426
<=> ! [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_1426])]) ).
fof(f2594,axiom,
! [X1,X4,X12,X13] :
( c_in(X4,X12,X1)
| ~ c_in(X4,c_minus(X12,X13,tc_set(X1)),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_ODiff__iff_0) ).
fof(f11152,plain,
spl0_1425,
inference(avatar_split_clause,[],[f2592,f11150]) ).
fof(f11150,plain,
( spl0_1425
<=> ! [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_1425])]) ).
fof(f2592,axiom,
! [X1,X12,X13] :
( ~ c_lessequals(X12,X13,tc_set(X1))
| c_emptyset = c_minus(X12,X13,tc_set(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_ODiff__eq__empty__iff_1) ).
fof(f11148,plain,
spl0_1424,
inference(avatar_split_clause,[],[f2591,f11146]) ).
fof(f2591,axiom,
! [X1,X12,X13] :
( c_lessequals(X12,X13,tc_set(X1))
| c_emptyset != c_minus(X12,X13,tc_set(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_ODiff__eq__empty__iff_0) ).
fof(f11144,plain,
spl0_1423,
inference(avatar_split_clause,[],[f2581,f11142]) ).
fof(f11142,plain,
( spl0_1423
<=> ! [X13,X12,X1] :
( X12 = X13
| c_uminus(X12,tc_set(X1)) != c_uminus(X13,tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1423])]) ).
fof(f2581,axiom,
! [X1,X12,X13] :
( X12 = X13
| c_uminus(X12,tc_set(X1)) != c_uminus(X13,tc_set(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OCompl__eq__Compl__iff_0) ).
fof(f11140,plain,
spl0_1422,
inference(avatar_split_clause,[],[f2570,f11138]) ).
fof(f11138,plain,
( spl0_1422
<=> ! [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_1422])]) ).
fof(f2570,axiom,
! [X1,X16,X43] :
( ~ class_Orderings_Oord(X1)
| ~ c_less(X43,X16,X1)
| c_in(X43,c_SetInterval_OlessThan(X16,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OlessThan__iff_1) ).
fof(f11136,plain,
spl0_1421,
inference(avatar_split_clause,[],[f2569,f11134]) ).
fof(f11134,plain,
( spl0_1421
<=> ! [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_1421])]) ).
fof(f2569,axiom,
! [X1,X16,X43] :
( ~ class_Orderings_Oord(X1)
| c_less(X43,X16,X1)
| ~ c_in(X43,c_SetInterval_OlessThan(X16,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OlessThan__iff_0) ).
fof(f11132,plain,
spl0_1420,
inference(avatar_split_clause,[],[f2568,f11130]) ).
fof(f11130,plain,
( spl0_1420
<=> ! [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_1420])]) ).
fof(f2568,axiom,
! [X3,X0,X1] :
( ~ class_Orderings_Olinorder(X1)
| X0 = X3
| c_SetInterval_OlessThan(X0,X1) != c_SetInterval_OlessThan(X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OlessThan__eq__iff_0) ).
fof(f11128,plain,
spl0_1419,
inference(avatar_split_clause,[],[f2559,f11126]) ).
fof(f11126,plain,
( spl0_1419
<=> ! [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_1419])]) ).
fof(f2559,axiom,
! [X1,X16,X43] :
( ~ class_Orderings_Oord(X1)
| ~ c_less(X16,X43,X1)
| c_in(X43,c_SetInterval_OgreaterThan(X16,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThan__iff_1) ).
fof(f11124,plain,
spl0_1418,
inference(avatar_split_clause,[],[f2558,f11122]) ).
fof(f11122,plain,
( spl0_1418
<=> ! [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_1418])]) ).
fof(f2558,axiom,
! [X1,X16,X43] :
( ~ class_Orderings_Oord(X1)
| c_less(X16,X43,X1)
| ~ c_in(X43,c_SetInterval_OgreaterThan(X16,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThan__iff_0) ).
fof(f11120,plain,
spl0_1417,
inference(avatar_split_clause,[],[f2557,f11118]) ).
fof(f11118,plain,
( spl0_1417
<=> ! [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_1417])]) ).
fof(f2557,axiom,
! [X3,X0,X1] :
( ~ class_Orderings_Olinorder(X1)
| X0 = X3
| c_SetInterval_OgreaterThan(X0,X1) != c_SetInterval_OgreaterThan(X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThan__eq__iff_0) ).
fof(f11116,plain,
spl0_1416,
inference(avatar_split_clause,[],[f2550,f11114]) ).
fof(f2550,axiom,
! [X1,X26,X16] :
( ~ class_Orderings_Oorder(X1)
| ~ c_lessequals(X26,X16,X1)
| c_emptyset = c_SetInterval_OgreaterThanAtMost(X16,X26,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThanAtMost__empty_0) ).
fof(f11099,plain,
spl0_1415,
inference(avatar_split_clause,[],[f2546,f11097]) ).
fof(f11097,plain,
( spl0_1415
<=> ! [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_1415])]) ).
fof(f2546,axiom,
! [X26,X14] : c_IntDef_Onat(c_minus(X14,X26,tc_IntDef_Oint)) = c_Finite__Set_Ocard(c_SetInterval_OgreaterThanAtMost(X26,X14,tc_IntDef_Oint),tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ocard__greaterThanAtMost__int_0) ).
fof(f11095,plain,
spl0_1414,
inference(avatar_split_clause,[],[f2543,f11093]) ).
fof(f11093,plain,
( spl0_1414
<=> ! [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_1414])]) ).
fof(f2543,axiom,
! [X26,X14] : c_Finite__Set_Ocard(c_SetInterval_OatLeastLessThan(X26,X14,tc_IntDef_Oint),tc_IntDef_Oint) = c_IntDef_Onat(c_minus(X14,X26,tc_IntDef_Oint)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ocard__atLeastLessThan__int_0) ).
fof(f11091,plain,
spl0_1413,
inference(avatar_split_clause,[],[f2537,f11089]) ).
fof(f11089,plain,
( spl0_1413
<=> ! [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_1413])]) ).
fof(f2537,axiom,
! [X1,X16,X43] :
( ~ class_Orderings_Oord(X1)
| ~ c_lessequals(X43,X16,X1)
| c_in(X43,c_SetInterval_OatMost(X16,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatMost__iff_1) ).
fof(f11087,plain,
spl0_1412,
inference(avatar_split_clause,[],[f2536,f11085]) ).
fof(f11085,plain,
( spl0_1412
<=> ! [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_1412])]) ).
fof(f2536,axiom,
! [X1,X16,X43] :
( ~ class_Orderings_Oord(X1)
| c_lessequals(X43,X16,X1)
| ~ c_in(X43,c_SetInterval_OatMost(X16,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatMost__iff_0) ).
fof(f11083,plain,
spl0_1411,
inference(avatar_split_clause,[],[f2535,f11081]) ).
fof(f11081,plain,
( spl0_1411
<=> ! [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_1411])]) ).
fof(f2535,axiom,
! [X3,X0,X1] :
( ~ class_Orderings_Olinorder(X1)
| X0 = X3
| c_SetInterval_OatMost(X0,X1) != c_SetInterval_OatMost(X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatMost__eq__iff_0) ).
fof(f11079,plain,
spl0_1410,
inference(avatar_split_clause,[],[f2531,f11077]) ).
fof(f11077,plain,
( spl0_1410
<=> ! [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_1410])]) ).
fof(f2531,axiom,
! [X1,X16,X43] :
( ~ class_Orderings_Oord(X1)
| ~ c_lessequals(X16,X43,X1)
| c_in(X43,c_SetInterval_OatLeast(X16,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatLeast__iff_1) ).
fof(f11075,plain,
spl0_1409,
inference(avatar_split_clause,[],[f2530,f11073]) ).
fof(f11073,plain,
( spl0_1409
<=> ! [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_1409])]) ).
fof(f2530,axiom,
! [X1,X16,X43] :
( ~ class_Orderings_Oord(X1)
| c_lessequals(X16,X43,X1)
| ~ c_in(X43,c_SetInterval_OatLeast(X16,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatLeast__iff_0) ).
fof(f11071,plain,
spl0_1408,
inference(avatar_split_clause,[],[f2529,f11069]) ).
fof(f11069,plain,
( spl0_1408
<=> ! [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_1408])]) ).
fof(f2529,axiom,
! [X3,X0,X1] :
( ~ class_Orderings_Olinorder(X1)
| X0 = X3
| c_SetInterval_OatLeast(X0,X1) != c_SetInterval_OatLeast(X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatLeast__eq__iff_0) ).
fof(f11067,plain,
spl0_1407,
inference(avatar_split_clause,[],[f2523,f11065]) ).
fof(f2523,axiom,
! [X21,X1,X15] :
( ~ class_Orderings_Oorder(X1)
| ~ c_lessequals(X21,X15,X1)
| c_emptyset = c_SetInterval_OatLeastLessThan(X15,X21,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatLeastLessThan__empty_0) ).
fof(f11063,plain,
spl0_1406,
inference(avatar_split_clause,[],[f2518,f11061]) ).
fof(f2518,axiom,
! [X21,X1,X15] :
( ~ class_Orderings_Oorder(X1)
| ~ c_less(X21,X15,X1)
| c_emptyset = c_SetInterval_OatLeastAtMost(X15,X21,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatLeastAtMost__empty_0) ).
fof(f11053,plain,
spl0_1405,
inference(avatar_split_clause,[],[f2517,f11051]) ).
fof(f11051,plain,
( spl0_1405
<=> ! [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_1405])]) ).
fof(f2517,axiom,
! [X1,X16] :
( ~ class_Orderings_Olinorder(X1)
| c_SetInterval_OatLeast(X16,X1) = c_uminus(c_SetInterval_OlessThan(X16,X1),tc_set(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OCompl__lessThan_0) ).
fof(f11049,plain,
spl0_1404,
inference(avatar_split_clause,[],[f2516,f11047]) ).
fof(f11047,plain,
( spl0_1404
<=> ! [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_1404])]) ).
fof(f2516,axiom,
! [X1,X16] :
( ~ class_Orderings_Olinorder(X1)
| c_SetInterval_OatMost(X16,X1) = c_uminus(c_SetInterval_OgreaterThan(X16,X1),tc_set(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OCompl__greaterThan_0) ).
fof(f11045,plain,
spl0_1403,
inference(avatar_split_clause,[],[f2515,f11043]) ).
fof(f11043,plain,
( spl0_1403
<=> ! [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_1403])]) ).
fof(f2515,axiom,
! [X1,X16] :
( ~ class_Orderings_Olinorder(X1)
| c_uminus(c_SetInterval_OatMost(X16,X1),tc_set(X1)) = c_SetInterval_OgreaterThan(X16,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OCompl__atMost_0) ).
fof(f11041,plain,
spl0_1402,
inference(avatar_split_clause,[],[f2514,f11039]) ).
fof(f11039,plain,
( spl0_1402
<=> ! [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_1402])]) ).
fof(f2514,axiom,
! [X1,X16] :
( ~ class_Orderings_Olinorder(X1)
| c_uminus(c_SetInterval_OatLeast(X16,X1),tc_set(X1)) = c_SetInterval_OlessThan(X16,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OCompl__atLeast_0) ).
fof(f11037,plain,
spl0_1401,
inference(avatar_split_clause,[],[f2302,f11035]) ).
fof(f11035,plain,
( spl0_1401
<=> ! [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_1401])]) ).
fof(f2302,axiom,
! [X3,X0] :
( c_Parity_Oeven(X3,tc_IntDef_Oint)
| c_Parity_Oeven(X0,tc_IntDef_Oint)
| c_Parity_Oeven(c_plus(X0,X3,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__sum_3) ).
fof(f11033,plain,
spl0_1400,
inference(avatar_split_clause,[],[f2301,f11031]) ).
fof(f11031,plain,
( spl0_1400
<=> ! [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_1400])]) ).
fof(f2301,axiom,
! [X3,X0] :
( ~ c_Parity_Oeven(X3,tc_IntDef_Oint)
| ~ c_Parity_Oeven(X0,tc_IntDef_Oint)
| c_Parity_Oeven(c_plus(X0,X3,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__sum_2) ).
fof(f11029,plain,
spl0_1399,
inference(avatar_split_clause,[],[f2300,f11027]) ).
fof(f11027,plain,
( spl0_1399
<=> ! [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_1399])]) ).
fof(f2300,axiom,
! [X3,X0] :
( ~ c_Parity_Oeven(X0,tc_IntDef_Oint)
| c_Parity_Oeven(X3,tc_IntDef_Oint)
| ~ c_Parity_Oeven(c_plus(X0,X3,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__sum_1) ).
fof(f11025,plain,
spl0_1398,
inference(avatar_split_clause,[],[f2299,f11023]) ).
fof(f11023,plain,
( spl0_1398
<=> ! [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_1398])]) ).
fof(f2299,axiom,
! [X3,X0] :
( ~ c_Parity_Oeven(X3,tc_IntDef_Oint)
| c_Parity_Oeven(X0,tc_IntDef_Oint)
| ~ c_Parity_Oeven(c_plus(X0,X3,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__sum_0) ).
fof(f11021,plain,
spl0_1397,
inference(avatar_split_clause,[],[f2296,f11019]) ).
fof(f11019,plain,
( spl0_1397
<=> ! [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_1397])]) ).
fof(f2296,axiom,
! [X3,X0] :
( c_Parity_Oeven(X0,tc_IntDef_Oint)
| c_Parity_Oeven(X3,tc_IntDef_Oint)
| ~ c_Parity_Oeven(c_times(X0,X3,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__product_0) ).
fof(f11017,plain,
spl0_1396,
inference(avatar_split_clause,[],[f2289,f11015]) ).
fof(f11015,plain,
( spl0_1396
<=> ! [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_1396])]) ).
fof(f2289,axiom,
! [X3,X0] :
( c_Parity_Oeven(X3,tc_nat)
| c_Parity_Oeven(X0,tc_nat)
| c_Parity_Oeven(c_plus(X0,X3,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__nat__sum_3) ).
fof(f11010,plain,
spl0_1395,
inference(avatar_split_clause,[],[f2288,f11008]) ).
fof(f11008,plain,
( spl0_1395
<=> ! [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_1395])]) ).
fof(f2288,axiom,
! [X3,X0] :
( ~ c_Parity_Oeven(X3,tc_nat)
| ~ c_Parity_Oeven(X0,tc_nat)
| c_Parity_Oeven(c_plus(X0,X3,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__nat__sum_2) ).
fof(f11006,plain,
spl0_1394,
inference(avatar_split_clause,[],[f2287,f11004]) ).
fof(f11004,plain,
( spl0_1394
<=> ! [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_1394])]) ).
fof(f2287,axiom,
! [X3,X0] :
( ~ c_Parity_Oeven(X0,tc_nat)
| c_Parity_Oeven(X3,tc_nat)
| ~ c_Parity_Oeven(c_plus(X0,X3,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__nat__sum_1) ).
fof(f11002,plain,
spl0_1393,
inference(avatar_split_clause,[],[f2286,f11000]) ).
fof(f11000,plain,
( spl0_1393
<=> ! [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_1393])]) ).
fof(f2286,axiom,
! [X3,X0] :
( ~ c_Parity_Oeven(X3,tc_nat)
| c_Parity_Oeven(X0,tc_nat)
| ~ c_Parity_Oeven(c_plus(X0,X3,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__nat__sum_0) ).
fof(f10998,plain,
spl0_1392,
inference(avatar_split_clause,[],[f2283,f10996]) ).
fof(f10996,plain,
( spl0_1392
<=> ! [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_1392])]) ).
fof(f2283,axiom,
! [X3,X0] :
( c_Parity_Oeven(X0,tc_nat)
| c_Parity_Oeven(X3,tc_nat)
| ~ c_Parity_Oeven(c_times(X0,X3,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__nat__product_0) ).
fof(f10994,plain,
spl0_1391,
inference(avatar_split_clause,[],[f2277,f10992]) ).
fof(f10992,plain,
( spl0_1391
<=> ! [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_1391])]) ).
fof(f2277,axiom,
! [X3,X0] :
( c_Parity_Oeven(X3,tc_IntDef_Oint)
| c_Parity_Oeven(X0,tc_IntDef_Oint)
| c_Parity_Oeven(c_minus(X0,X3,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__difference_3) ).
fof(f10990,plain,
spl0_1390,
inference(avatar_split_clause,[],[f2276,f10988]) ).
fof(f10988,plain,
( spl0_1390
<=> ! [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_1390])]) ).
fof(f2276,axiom,
! [X3,X0] :
( ~ c_Parity_Oeven(X3,tc_IntDef_Oint)
| ~ c_Parity_Oeven(X0,tc_IntDef_Oint)
| c_Parity_Oeven(c_minus(X0,X3,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__difference_2) ).
fof(f10986,plain,
spl0_1389,
inference(avatar_split_clause,[],[f2275,f10984]) ).
fof(f10984,plain,
( spl0_1389
<=> ! [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_1389])]) ).
fof(f2275,axiom,
! [X3,X0] :
( ~ c_Parity_Oeven(X0,tc_IntDef_Oint)
| c_Parity_Oeven(X3,tc_IntDef_Oint)
| ~ c_Parity_Oeven(c_minus(X0,X3,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__difference_1) ).
fof(f10982,plain,
spl0_1388,
inference(avatar_split_clause,[],[f2274,f10980]) ).
fof(f10980,plain,
( spl0_1388
<=> ! [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_1388])]) ).
fof(f2274,axiom,
! [X3,X0] :
( ~ c_Parity_Oeven(X3,tc_IntDef_Oint)
| c_Parity_Oeven(X0,tc_IntDef_Oint)
| ~ c_Parity_Oeven(c_minus(X0,X3,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__difference_0) ).
fof(f10978,plain,
spl0_1387,
inference(avatar_split_clause,[],[f2234,f10976]) ).
fof(f10976,plain,
( spl0_1387
<=> ! [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_1387])]) ).
fof(f2234,axiom,
! [X1,X18] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_less(c_0,X18,X1)
| c_less(c_uminus(X18,X1),c_0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__less__0__iff__less_1) ).
fof(f10974,plain,
spl0_1386,
inference(avatar_split_clause,[],[f2233,f10972]) ).
fof(f10972,plain,
( spl0_1386
<=> ! [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_1386])]) ).
fof(f2233,axiom,
! [X1,X18] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| c_less(c_0,X18,X1)
| ~ c_less(c_uminus(X18,X1),c_0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__less__0__iff__less_0) ).
fof(f10969,plain,
spl0_1385,
inference(avatar_split_clause,[],[f2230,f10967]) ).
fof(f10967,plain,
( spl0_1385
<=> ! [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_1385])]) ).
fof(f2230,axiom,
! [X1,X18] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_lessequals(c_0,X18,X1)
| c_lessequals(c_uminus(X18,X1),c_0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__le__0__iff__le_1) ).
fof(f10965,plain,
spl0_1384,
inference(avatar_split_clause,[],[f2229,f10963]) ).
fof(f10963,plain,
( spl0_1384
<=> ! [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_1384])]) ).
fof(f2229,axiom,
! [X1,X18] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| c_lessequals(c_0,X18,X1)
| ~ c_lessequals(c_uminus(X18,X1),c_0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__le__0__iff__le_0) ).
fof(f10961,plain,
spl0_1383,
inference(avatar_split_clause,[],[f2227,f10959]) ).
fof(f10959,plain,
( spl0_1383
<=> ! [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_1383])]) ).
fof(f2227,axiom,
! [X1,X18,X27] :
( ~ class_OrderedGroup_Oab__group__add(X1)
| X18 = X27
| c_uminus(X18,X1) != c_uminus(X27,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__equal__iff__equal_0) ).
fof(f10957,plain,
spl0_1382,
inference(avatar_split_clause,[],[f2224,f10955]) ).
fof(f10955,plain,
( spl0_1382
<=> ! [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_1382])]) ).
fof(f2224,axiom,
! [X1,X18] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_less(X18,c_0,X1)
| c_less(c_0,c_uminus(X18,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__0__less__iff__less_1) ).
fof(f10953,plain,
spl0_1381,
inference(avatar_split_clause,[],[f2223,f10951]) ).
fof(f10951,plain,
( spl0_1381
<=> ! [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_1381])]) ).
fof(f2223,axiom,
! [X1,X18] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| c_less(X18,c_0,X1)
| ~ c_less(c_0,c_uminus(X18,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__0__less__iff__less_0) ).
fof(f10949,plain,
spl0_1380,
inference(avatar_split_clause,[],[f2222,f10947]) ).
fof(f2222,axiom,
! [X1,X18] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_lessequals(X18,c_0,X1)
| c_lessequals(c_0,c_uminus(X18,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__0__le__iff__le_1) ).
fof(f10945,plain,
spl0_1379,
inference(avatar_split_clause,[],[f2221,f10943]) ).
fof(f2221,axiom,
! [X1,X18] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| c_lessequals(X18,c_0,X1)
| ~ c_lessequals(c_0,c_uminus(X18,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__0__le__iff__le_0) ).
fof(f10941,plain,
spl0_1378,
inference(avatar_split_clause,[],[f2167,f10939]) ).
fof(f10939,plain,
( spl0_1378
<=> ! [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_1378])]) ).
fof(f2167,axiom,
! [X48,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| c_uminus(X48,X1) = c_times(X48,c_Numeral_Onumber__of(c_Numeral_OMin,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Omult__minus1__right_0) ).
fof(f10937,plain,
spl0_1377,
inference(avatar_split_clause,[],[f2166,f10935]) ).
fof(f10935,plain,
( spl0_1377
<=> ! [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_1377])]) ).
fof(f2166,axiom,
! [X48,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| c_times(c_Numeral_Onumber__of(c_Numeral_OMin,X1),X48,X1) = c_uminus(X48,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Omult__minus1_0) ).
fof(f10933,plain,
spl0_1376,
inference(avatar_split_clause,[],[f2086,f10931]) ).
fof(f10931,plain,
( spl0_1376
<=> ! [X21,X16,X15] :
( X15 = X21
| c_plus(X15,X16,tc_nat) != c_plus(X21,X16,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1376])]) ).
fof(f2086,axiom,
! [X21,X16,X15] :
( X15 = X21
| c_plus(X15,X16,tc_nat) != c_plus(X21,X16,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Onat__add__right__cancel_0) ).
fof(f10929,plain,
( spl0_1375
| ~ spl0_717
| ~ spl0_797
| ~ spl0_1121 ),
inference(avatar_split_clause,[],[f9307,f9051,f7528,f7184,f10926]) ).
fof(f9051,plain,
( spl0_1121
<=> ! [X11] : c_Numeral_OBit(X11,c_Numeral_Obit_OB0) = c_Numeral_Obin__add(c_Numeral_OBit(X11,c_Numeral_Obit_OB1),c_Numeral_OMin) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1121])]) ).
fof(f9307,plain,
( c_Numeral_OPls = c_Numeral_Obin__add(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_OMin)
| ~ spl0_717
| ~ spl0_797
| ~ spl0_1121 ),
inference(forward_demodulation,[],[f9304,f7186]) ).
fof(f9304,plain,
( c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB0) = c_Numeral_Obin__add(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_OMin)
| ~ spl0_797
| ~ spl0_1121 ),
inference(superposition,[],[f9052,f7530]) ).
fof(f9052,plain,
( ! [X11] : c_Numeral_OBit(X11,c_Numeral_Obit_OB0) = c_Numeral_Obin__add(c_Numeral_OBit(X11,c_Numeral_Obit_OB1),c_Numeral_OMin)
| ~ spl0_1121 ),
inference(avatar_component_clause,[],[f9051]) ).
fof(f10924,plain,
spl0_1374,
inference(avatar_split_clause,[],[f2081,f10922]) ).
fof(f10922,plain,
( spl0_1374
<=> ! [X21,X16,X15] :
( X15 = X21
| c_plus(X16,X15,tc_nat) != c_plus(X16,X21,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1374])]) ).
fof(f2081,axiom,
! [X21,X16,X15] :
( X15 = X21
| c_plus(X16,X15,tc_nat) != c_plus(X16,X21,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Onat__add__left__cancel_0) ).
fof(f10920,plain,
spl0_1373,
inference(avatar_split_clause,[],[f2065,f10918]) ).
fof(f10918,plain,
( spl0_1373
<=> ! [X21,X15] :
( c_0 = X15
| c_0 = X21
| c_0 != c_times(X15,X21,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1373])]) ).
fof(f2065,axiom,
! [X21,X15] :
( c_0 = X15
| c_0 = X21
| c_0 != c_times(X15,X21,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Omult__is__0_0) ).
fof(f10916,plain,
spl0_1372,
inference(avatar_split_clause,[],[f1850,f10914]) ).
fof(f1850,axiom,
! [X21,X15] : c_IntDef_Oint(c_plus(X15,X21,tc_nat)) = c_plus(c_IntDef_Oint(X15),c_IntDef_Oint(X21),tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatBin_Oint_A_Im2_A_L_An2_J_A_61_61_Aint_Am2_A_L_Aint_An2_0) ).
fof(f10912,plain,
spl0_1371,
inference(avatar_split_clause,[],[f1813,f10910]) ).
fof(f10910,plain,
( spl0_1371
<=> ! [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_1371])]) ).
fof(f1813,axiom,
! [X21,X1,X15] :
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| X15 = X21
| c_NatArith_Oof__nat(X21,X1) != c_NatArith_Oof__nat(X15,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__eq__iff_0) ).
fof(f10908,plain,
spl0_1370,
inference(avatar_split_clause,[],[f1807,f10906]) ).
fof(f10906,plain,
( spl0_1370
<=> ! [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_1370])]) ).
fof(f1807,axiom,
! [X21,X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_less(c_0,X21,tc_nat)
| c_less(c_0,c_NatArith_Oof__nat(X21,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__0__less__iff_1) ).
fof(f10904,plain,
spl0_1369,
inference(avatar_split_clause,[],[f1806,f10902]) ).
fof(f10902,plain,
( spl0_1369
<=> ! [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_1369])]) ).
fof(f1806,axiom,
! [X21,X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| c_less(c_0,X21,tc_nat)
| ~ c_less(c_0,c_NatArith_Oof__nat(X21,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__0__less__iff_0) ).
fof(f10900,plain,
spl0_1368,
inference(avatar_split_clause,[],[f1784,f10898]) ).
fof(f10898,plain,
( spl0_1368
<=> ! [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_1368])]) ).
fof(f1784,axiom,
! [X59,X43] :
( c_0 = X59
| c_lessequals(X59,X43,tc_nat)
| c_List_Olist_ONil != c_List_Oupt(X43,X59) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oupt__eq__Nil__conv_0) ).
fof(f10896,plain,
spl0_1367,
inference(avatar_split_clause,[],[f1743,f10894]) ).
fof(f10894,plain,
( spl0_1367
<=> ! [X51,X23,X25,X1] :
( X25 = X51
| c_append(X23,X25,X1) != c_append(X23,X51,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1367])]) ).
fof(f1743,axiom,
! [X51,X1,X25,X23] :
( X25 = X51
| c_append(X23,X25,X1) != c_append(X23,X51,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Osame__append__eq_0) ).
fof(f10892,plain,
spl0_1366,
inference(avatar_split_clause,[],[f1737,f10890]) ).
fof(f10890,plain,
( spl0_1366
<=> ! [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_1366])]) ).
fof(f1737,axiom,
! [X3,X1] :
( c_List_Orotate1(X3,X1) = X3
| ~ c_lessequals(c_Nat_Osize(X3,tc_List_Olist(X1)),c_1,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Orotate1__length01_0) ).
fof(f10888,plain,
spl0_1365,
inference(avatar_split_clause,[],[f1626,f10886]) ).
fof(f10886,plain,
( spl0_1365
<=> ! [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_1365])]) ).
fof(f1626,axiom,
! [X1,X18,X63,X42,X64] :
( X63 = X64
| c_List_Olist_OCons(X42,X63,X1) != c_List_Olist_OCons(X18,X64,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olist_Oinject_1) ).
fof(f10884,plain,
spl0_1364,
inference(avatar_split_clause,[],[f1625,f10882]) ).
fof(f10882,plain,
( spl0_1364
<=> ! [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_1364])]) ).
fof(f1625,axiom,
! [X18,X1,X63,X42,X64] :
( X18 = X42
| c_List_Olist_OCons(X42,X63,X1) != c_List_Olist_OCons(X18,X64,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olist_Oinject_0) ).
fof(f10880,plain,
spl0_1363,
inference(avatar_split_clause,[],[f1610,f10878]) ).
fof(f10878,plain,
( spl0_1363
<=> ! [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_1363])]) ).
fof(f1610,axiom,
! [X21,X1,X23] : c_Nat_Osize(X23,tc_List_Olist(X1)) = c_Nat_Osize(c_List_Orotate(X21,X23,X1),tc_List_Olist(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olength__rotate_0) ).
fof(f10876,plain,
spl0_1362,
inference(avatar_split_clause,[],[f1552,f10874]) ).
fof(f10874,plain,
( spl0_1362
<=> ! [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_1362])]) ).
fof(f1552,axiom,
! [X41,X0,X23] :
( ~ c_List_Odistinct(c_List_Olist_OCons(X0,X23,X41),X41)
| ~ c_in(X0,c_List_Oset(X23,X41),X41) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Odistinct_Osimps__2_0) ).
fof(f10872,plain,
spl0_1361,
inference(avatar_split_clause,[],[f1530,f10870]) ).
fof(f10870,plain,
( spl0_1361
<=> ! [X51,X23,X25,X1] :
( X25 = X51
| c_append(X25,X23,X1) != c_append(X51,X23,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1361])]) ).
fof(f1530,axiom,
! [X51,X1,X25,X23] :
( X25 = X51
| c_append(X25,X23,X1) != c_append(X51,X23,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oappend__same__eq_0) ).
fof(f10868,plain,
spl0_1360,
inference(avatar_split_clause,[],[f1493,f10866]) ).
fof(f10866,plain,
( spl0_1360
<=> ! [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_1360])]) ).
fof(f1493,axiom,
! [X18,X27] : c_Divides_Oop_Amod(X27,X18,tc_IntDef_Oint) = c_Divides_Oop_Amod(c_plus(X27,X18,tc_IntDef_Oint),X18,tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozmod__zadd__self2_0) ).
fof(f10864,plain,
spl0_1359,
inference(avatar_split_clause,[],[f1492,f10862]) ).
fof(f10862,plain,
( spl0_1359
<=> ! [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_1359])]) ).
fof(f1492,axiom,
! [X18,X27] : c_Divides_Oop_Amod(c_plus(X18,X27,tc_IntDef_Oint),X18,tc_IntDef_Oint) = c_Divides_Oop_Amod(X27,X18,tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozmod__zadd__self1_0) ).
fof(f10860,plain,
spl0_1358,
inference(avatar_split_clause,[],[f1485,f10858]) ).
fof(f10858,plain,
( spl0_1358
<=> ! [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_1358])]) ).
fof(f1485,axiom,
! [X21,X0] :
( c_0 = X0
| c_less(c_0,c_Nat_Opower(c_HOL_Oabs(X0,tc_IntDef_Oint),X21,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozero__less__zpower__abs__iff_1) ).
fof(f10855,plain,
( spl0_1357
| ~ spl0_916
| ~ spl0_1356 ),
inference(avatar_split_clause,[],[f10851,f10848,f8074,f10853]) ).
fof(f10853,plain,
( spl0_1357
<=> ! [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_1357])]) ).
fof(f8074,plain,
( spl0_916
<=> c_0 = c_HOL_Oabs(c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_916])]) ).
fof(f10848,plain,
( spl0_1356
<=> ! [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_1356])]) ).
fof(f10851,plain,
( ! [X21] :
( ~ c_less(c_0,c_Nat_Opower(c_0,X21,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 = X21 )
| ~ spl0_916
| ~ spl0_1356 ),
inference(forward_demodulation,[],[f10849,f8076]) ).
fof(f8076,plain,
( c_0 = c_HOL_Oabs(c_0,tc_IntDef_Oint)
| ~ spl0_916 ),
inference(avatar_component_clause,[],[f8074]) ).
fof(f10849,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_1356 ),
inference(avatar_component_clause,[],[f10848]) ).
fof(f10850,plain,
spl0_1356,
inference(avatar_split_clause,[],[f1484,f10848]) ).
fof(f1484,axiom,
! [X21] :
( c_0 = X21
| ~ c_less(c_0,c_Nat_Opower(c_HOL_Oabs(c_0,tc_IntDef_Oint),X21,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozero__less__zpower__abs__iff_0) ).
fof(f10846,plain,
( spl0_1354
| ~ spl0_1355
| ~ spl0_799
| ~ spl0_1080 ),
inference(avatar_split_clause,[],[f9242,f8887,f7537,f10843,f10840]) ).
fof(f10840,plain,
( spl0_1354
<=> ! [X0] : c_Parity_Oeven(X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1354])]) ).
fof(f10843,plain,
( spl0_1355
<=> c_Parity_Oeven(c_1,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1355])]) ).
fof(f7537,plain,
( spl0_799
<=> ! [X28] : c_1 = c_Nat_Opower(X28,c_0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_799])]) ).
fof(f8887,plain,
( spl0_1080
<=> ! [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_1080])]) ).
fof(f9242,plain,
( ! [X0] :
( ~ c_Parity_Oeven(c_1,tc_nat)
| c_Parity_Oeven(X0,tc_nat) )
| ~ spl0_799
| ~ spl0_1080 ),
inference(superposition,[],[f8888,f7538]) ).
fof(f7538,plain,
( ! [X28] : c_1 = c_Nat_Opower(X28,c_0,tc_nat)
| ~ spl0_799 ),
inference(avatar_component_clause,[],[f7537]) ).
fof(f8888,plain,
( ! [X3,X0] :
( ~ c_Parity_Oeven(c_Nat_Opower(X0,X3,tc_nat),tc_nat)
| c_Parity_Oeven(X0,tc_nat) )
| ~ spl0_1080 ),
inference(avatar_component_clause,[],[f8887]) ).
fof(f10838,plain,
spl0_1353,
inference(avatar_split_clause,[],[f1477,f10836]) ).
fof(f10836,plain,
( spl0_1353
<=> ! [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_1353])]) ).
fof(f1477,axiom,
! [X3,X27] :
( c_0 = X27
| c_div(c_times(X27,X3,tc_IntDef_Oint),X27,tc_IntDef_Oint) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozdiv__zmult__self2_0) ).
fof(f10834,plain,
spl0_1352,
inference(avatar_split_clause,[],[f1476,f10832]) ).
fof(f10832,plain,
( spl0_1352
<=> ! [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_1352])]) ).
fof(f1476,axiom,
! [X3,X27] :
( c_0 = X27
| c_div(c_times(X3,X27,tc_IntDef_Oint),X27,tc_IntDef_Oint) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozdiv__zmult__self1_0) ).
fof(f10830,plain,
spl0_1351,
inference(avatar_split_clause,[],[f1457,f10828]) ).
fof(f10828,plain,
( spl0_1351
<=> ! [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_1351])]) ).
fof(f1457,axiom,
! [X27] : c_IntDiv_OposDivAlg(c_Pair(c_0,X27,tc_IntDef_Oint,tc_IntDef_Oint)) = c_Pair(c_0,c_0,tc_IntDef_Oint,tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_OposDivAlg__0_0) ).
fof(f10826,plain,
spl0_1350,
inference(avatar_split_clause,[],[f1442,f10824]) ).
fof(f10824,plain,
( spl0_1350
<=> ! [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_1350])]) ).
fof(f1442,axiom,
! [X18,X27] : c_Divides_Oop_Amod(X18,X27,tc_IntDef_Oint) = c_Divides_Oop_Amod(c_Divides_Oop_Amod(X18,X27,tc_IntDef_Oint),X27,tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Omod__mod__trivial_0) ).
fof(f10822,plain,
spl0_1349,
inference(avatar_split_clause,[],[f1413,f10820]) ).
fof(f10820,plain,
( spl0_1349
<=> ! [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_1349])]) ).
fof(f1413,axiom,
! [X11,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_less(X11,c_0,tc_IntDef_Oint)
| c_less(c_IntDef_Oof__int(X11,X1),c_0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oof__int__less__0__iff_1) ).
fof(f10818,plain,
spl0_1348,
inference(avatar_split_clause,[],[f1412,f10816]) ).
fof(f10816,plain,
( spl0_1348
<=> ! [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_1348])]) ).
fof(f1412,axiom,
! [X11,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| c_less(X11,c_0,tc_IntDef_Oint)
| ~ c_less(c_IntDef_Oof__int(X11,X1),c_0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oof__int__less__0__iff_0) ).
fof(f10814,plain,
spl0_1347,
inference(avatar_split_clause,[],[f1409,f10812]) ).
fof(f10812,plain,
( spl0_1347
<=> ! [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_1347])]) ).
fof(f1409,axiom,
! [X11,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_lessequals(X11,c_0,tc_IntDef_Oint)
| c_lessequals(c_IntDef_Oof__int(X11,X1),c_0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oof__int__le__0__iff_1) ).
fof(f10810,plain,
spl0_1346,
inference(avatar_split_clause,[],[f1408,f10808]) ).
fof(f10808,plain,
( spl0_1346
<=> ! [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_1346])]) ).
fof(f1408,axiom,
! [X11,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| c_lessequals(X11,c_0,tc_IntDef_Oint)
| ~ c_lessequals(c_IntDef_Oof__int(X11,X1),c_0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oof__int__le__0__iff_0) ).
fof(f10806,plain,
spl0_1345,
inference(avatar_split_clause,[],[f1406,f10804]) ).
fof(f10804,plain,
( spl0_1345
<=> ! [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_1345])]) ).
fof(f1406,axiom,
! [X48,X11,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| X11 = X48
| c_IntDef_Oof__int(X48,X1) != c_IntDef_Oof__int(X11,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oof__int__eq__iff_0) ).
fof(f10802,plain,
spl0_1344,
inference(avatar_split_clause,[],[f1400,f10800]) ).
fof(f10800,plain,
( spl0_1344
<=> ! [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_1344])]) ).
fof(f1400,axiom,
! [X48,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_less(c_0,X48,tc_IntDef_Oint)
| c_less(c_0,c_IntDef_Oof__int(X48,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oof__int__0__less__iff_1) ).
fof(f10794,plain,
spl0_1343,
inference(avatar_split_clause,[],[f1399,f10792]) ).
fof(f10792,plain,
( spl0_1343
<=> ! [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_1343])]) ).
fof(f1399,axiom,
! [X48,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| c_less(c_0,X48,tc_IntDef_Oint)
| ~ c_less(c_0,c_IntDef_Oof__int(X48,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oof__int__0__less__iff_0) ).
fof(f10790,plain,
spl0_1342,
inference(avatar_split_clause,[],[f1398,f10788]) ).
fof(f10788,plain,
( spl0_1342
<=> ! [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_1342])]) ).
fof(f1398,axiom,
! [X48,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_lessequals(c_0,X48,tc_IntDef_Oint)
| c_lessequals(c_0,c_IntDef_Oof__int(X48,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oof__int__0__le__iff_1) ).
fof(f10786,plain,
spl0_1341,
inference(avatar_split_clause,[],[f1397,f10784]) ).
fof(f1397,axiom,
! [X48,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| c_lessequals(c_0,X48,tc_IntDef_Oint)
| ~ c_lessequals(c_0,c_IntDef_Oof__int(X48,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oof__int__0__le__iff_0) ).
fof(f10782,plain,
spl0_1340,
inference(avatar_split_clause,[],[f1361,f10780]) ).
fof(f10780,plain,
( spl0_1340
<=> ! [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_1340])]) ).
fof(f1361,axiom,
! [X1,X18] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X1)
| ~ c_in(X18,c_IntDef_OInts,X1)
| c_in(c_uminus(X18,X1),c_IntDef_OInts,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_OInts__minus_0) ).
fof(f10778,plain,
spl0_1339,
inference(avatar_split_clause,[],[f1356,f10776]) ).
fof(f10776,plain,
( spl0_1339
<=> ! [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_1339])]) ).
fof(f1356,axiom,
! [X3] :
( c_IntDef_ORep__Integ(c_IntDef_OAbs__Integ(X3)) = X3
| ~ c_in(X3,c_IntDef_OInteg,tc_set(tc_prod(tc_nat,tc_nat))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_OInteg_OAbs__Integ__inverse_0) ).
fof(f10774,plain,
spl0_1338,
inference(avatar_split_clause,[],[f1342,f10772]) ).
fof(f10772,plain,
( spl0_1338
<=> ! [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_1338])]) ).
fof(f1342,axiom,
! [X47,X15] :
( c_IntDef_Oint(X15) != c_Numeral_Onumber__of(X47,tc_IntDef_Oint)
| c_lessequals(c_0,c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntArith_Oint__eq__iff__number__of_1) ).
fof(f10770,plain,
spl0_1337,
inference(avatar_split_clause,[],[f1341,f10768]) ).
fof(f10768,plain,
( spl0_1337
<=> ! [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_1337])]) ).
fof(f1341,axiom,
! [X47,X15] :
( c_IntDef_Oint(X15) != c_Numeral_Onumber__of(X47,tc_IntDef_Oint)
| c_IntDef_Onat(c_Numeral_Onumber__of(X47,tc_IntDef_Oint)) = X15 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntArith_Oint__eq__iff__number__of_0) ).
fof(f10766,plain,
spl0_1336,
inference(avatar_split_clause,[],[f1243,f10764]) ).
fof(f10764,plain,
( spl0_1336
<=> ! [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_1336])]) ).
fof(f1243,axiom,
! [X21,X15] : c_Divides_Oop_Amod(X15,X21,tc_nat) = c_Divides_Oop_Amod(c_Divides_Oop_Amod(X15,X21,tc_nat),X21,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Onat__mod__mod__trivial_0) ).
fof(f10762,plain,
spl0_1335,
inference(avatar_split_clause,[],[f1233,f10760]) ).
fof(f10760,plain,
( spl0_1335
<=> ! [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_1335])]) ).
fof(f1233,axiom,
! [X21,X15] : c_Divides_Oop_Amod(X15,X21,tc_nat) = c_Divides_Oop_Amod(c_plus(X15,X21,tc_nat),X21,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Omod__add__self2_0) ).
fof(f10758,plain,
spl0_1334,
inference(avatar_split_clause,[],[f1232,f10756]) ).
fof(f10756,plain,
( spl0_1334
<=> ! [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_1334])]) ).
fof(f1232,axiom,
! [X21,X15] : c_Divides_Oop_Amod(c_plus(X21,X15,tc_nat),X21,tc_nat) = c_Divides_Oop_Amod(X15,X21,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Omod__add__self1_0) ).
fof(f10754,plain,
( spl0_1333
| ~ spl0_765
| ~ spl0_1043 ),
inference(avatar_split_clause,[],[f9153,f8739,f7400,f10752]) ).
fof(f10752,plain,
( spl0_1333
<=> ! [X0] : c_0 = c_div(X0,c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1333])]) ).
fof(f7400,plain,
( spl0_765
<=> ! [X3] : c_Divides_Oop_Amod(X3,c_0,tc_IntDef_Oint) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_765])]) ).
fof(f8739,plain,
( spl0_1043
<=> ! [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_1043])]) ).
fof(f9153,plain,
( ! [X0] : c_0 = c_div(X0,c_0,tc_IntDef_Oint)
| ~ spl0_765
| ~ spl0_1043 ),
inference(superposition,[],[f8740,f7401]) ).
fof(f7401,plain,
( ! [X3] : c_Divides_Oop_Amod(X3,c_0,tc_IntDef_Oint) = X3
| ~ spl0_765 ),
inference(avatar_component_clause,[],[f7400]) ).
fof(f8740,plain,
( ! [X18,X27] : c_0 = c_div(c_Divides_Oop_Amod(X18,X27,tc_IntDef_Oint),X27,tc_IntDef_Oint)
| ~ spl0_1043 ),
inference(avatar_component_clause,[],[f8739]) ).
fof(f10750,plain,
spl0_1332,
inference(avatar_split_clause,[],[f1191,f10748]) ).
fof(f10748,plain,
( spl0_1332
<=> ! [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_1332])]) ).
fof(f1191,axiom,
! [X2,X1,X9,X7] :
( X7 = X9
| c_Datatype__Universe_OIn1(X7,X1,X2) != c_Datatype__Universe_OIn1(X9,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OIn1__eq_0) ).
fof(f10746,plain,
spl0_1331,
inference(avatar_split_clause,[],[f1189,f10744]) ).
fof(f10744,plain,
( spl0_1331
<=> ! [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_1331])]) ).
fof(f1189,axiom,
! [X2,X1,X9,X7] :
( X7 = X9
| c_Datatype__Universe_OIn0(X9,X1,X2) != c_Datatype__Universe_OIn0(X7,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OIn0__eq_0) ).
fof(f10742,plain,
spl0_1330,
inference(avatar_split_clause,[],[f1185,f10740]) ).
fof(f10740,plain,
( spl0_1330
<=> ! [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_1330])]) ).
fof(f1185,axiom,
! [X2,X18,X1,X27] :
( X18 = X27
| c_Datatype__Universe_OAtom(X18,X1,X2) != c_Datatype__Universe_OAtom(X27,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OAtom__Atom__eq_0) ).
fof(f10738,plain,
spl0_1329,
inference(avatar_split_clause,[],[f110,f10736]) ).
fof(f110,axiom,
! [X1,X12,X13] :
( c_lessequals(X12,X13,tc_set(X1))
| ~ c_in(c_Main_OsubsetI__1(X12,X13,X1),X13,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OsubsetI_1) ).
fof(f10734,plain,
spl0_1328,
inference(avatar_split_clause,[],[f109,f10732]) ).
fof(f10732,plain,
( spl0_1328
<=> ! [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_1328])]) ).
fof(f109,axiom,
! [X1,X12,X13] :
( c_lessequals(X12,X13,tc_set(X1))
| c_in(c_Main_OsubsetI__1(X12,X13,X1),X12,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OsubsetI_0) ).
fof(f10730,plain,
spl0_1327,
inference(avatar_split_clause,[],[f49,f10728]) ).
fof(f49,axiom,
! [X1,X23] : c_lessequals(c_Nat_Osize(c_List_Oremdups(X23,X1),tc_List_Olist(X1)),c_Nat_Osize(X23,tc_List_Olist(X1)),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olength__remdups__leq_0) ).
fof(f10726,plain,
spl0_1326,
inference(avatar_split_clause,[],[f2,f10724]) ).
fof(f10724,plain,
( spl0_1326
<=> ! [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_1326])]) ).
fof(f2,axiom,
! [X2,X3,X0,X1] :
( X0 = X3
| c_Datatype__Universe_ONumb(X0,X1,X2) != c_Datatype__Universe_ONumb(X3,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_ONumb__inject__dest_0) ).
fof(f10722,plain,
spl0_1325,
inference(avatar_split_clause,[],[f1,f10720]) ).
fof(f10720,plain,
( spl0_1325
<=> ! [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_1325])]) ).
fof(f1,axiom,
! [X2,X3,X0,X1] :
( X0 = X3
| c_Datatype__Universe_OLeaf(X0,X1,X2) != c_Datatype__Universe_OLeaf(X3,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OLeaf__inject__dest_0) ).
fof(f10637,plain,
( ~ spl0_1323
| spl0_1324
| ~ spl0_787
| ~ spl0_1290 ),
inference(avatar_split_clause,[],[f10539,f10180,f7488,f10635,f10631]) ).
fof(f10631,plain,
( spl0_1323
<=> class_OrderedGroup_Oab__group__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1323])]) ).
fof(f10635,plain,
( spl0_1324
<=> ! [X0] : c_0 = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1324])]) ).
fof(f7488,plain,
( spl0_787
<=> ! [X21] : c_0 = c_minus(c_0,X21,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_787])]) ).
fof(f10539,plain,
( ! [X0] :
( c_0 = X0
| ~ class_OrderedGroup_Oab__group__add(tc_nat) )
| ~ spl0_787
| ~ spl0_1290 ),
inference(trivial_inequality_removal,[],[f10532]) ).
fof(f10532,plain,
( ! [X0] :
( c_0 != c_0
| c_0 = X0
| ~ class_OrderedGroup_Oab__group__add(tc_nat) )
| ~ spl0_787
| ~ spl0_1290 ),
inference(superposition,[],[f10181,f7489]) ).
fof(f7489,plain,
( ! [X21] : c_0 = c_minus(c_0,X21,tc_nat)
| ~ spl0_787 ),
inference(avatar_component_clause,[],[f7488]) ).
fof(f10362,plain,
( spl0_1322
| ~ spl0_57
| ~ spl0_1075
| ~ spl0_1248 ),
inference(avatar_split_clause,[],[f10012,f10009,f8867,f3692,f10360]) ).
fof(f10360,plain,
( spl0_1322
<=> ! [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_1322])]) ).
fof(f10009,plain,
( spl0_1248
<=> ! [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_1248])]) ).
fof(f10012,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_57
| ~ spl0_1075
| ~ spl0_1248 ),
inference(forward_demodulation,[],[f10010,f9233]) ).
fof(f10010,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_1248 ),
inference(avatar_component_clause,[],[f10009]) ).
fof(f10328,plain,
spl0_1321,
inference(avatar_split_clause,[],[f3308,f10326]) ).
fof(f10326,plain,
( spl0_1321
<=> ! [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_1321])]) ).
fof(f3308,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,[],[f3119,f2958]) ).
fof(f3119,plain,
! [X21,X15] :
( c_lessequals(c_1,X15,tc_nat)
| ~ c_lessequals(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),c_times(X15,X21,tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f2095,f2544]) ).
fof(f2095,axiom,
! [X21,X15] :
( c_lessequals(c_1,X15,tc_nat)
| ~ c_lessequals(c_Suc(c_0),c_times(X15,X21,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oone__le__mult__iff_0) ).
fof(f10324,plain,
spl0_1320,
inference(avatar_split_clause,[],[f3307,f10322]) ).
fof(f3307,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,[],[f3118,f2958]) ).
fof(f3118,plain,
! [X21,X15] :
( c_lessequals(c_1,X21,tc_nat)
| ~ c_lessequals(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),c_times(X15,X21,tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f2096,f2544]) ).
fof(f2096,axiom,
! [X21,X15] :
( c_lessequals(c_1,X21,tc_nat)
| ~ c_lessequals(c_Suc(c_0),c_times(X15,X21,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oone__le__mult__iff_1) ).
fof(f10320,plain,
spl0_1319,
inference(avatar_split_clause,[],[f3297,f10318]) ).
fof(f10318,plain,
( spl0_1319
<=> ! [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_1319])]) ).
fof(f3297,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,[],[f3103,f2958]) ).
fof(f3103,plain,
! [X21,X43] :
( ~ c_lessequals(c_1,X43,tc_nat)
| c_lessequals(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),c_Nat_Opower(X43,X21,tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f2340,f2544]) ).
fof(f2340,axiom,
! [X21,X43] :
( ~ c_lessequals(c_1,X43,tc_nat)
| c_lessequals(c_Suc(c_0),c_Nat_Opower(X43,X21,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Power_Onat__one__le__power_0) ).
fof(f10316,plain,
spl0_1318,
inference(avatar_split_clause,[],[f3236,f10314]) ).
fof(f3236,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,[],[f3028,f2958]) ).
fof(f3028,plain,
! [X96] : c_Nat_Osize(c_Message_Omsg_OHash(X96),tc_Message_Omsg) = c_plus(c_Nat_Osize(X96,tc_Message_Omsg),c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),tc_nat),
inference(definition_unfolding,[],[f2764,f2544]) ).
fof(f2764,axiom,
! [X96] : c_Nat_Osize(c_Message_Omsg_OHash(X96),tc_Message_Omsg) = c_plus(c_Nat_Osize(X96,tc_Message_Omsg),c_Suc(c_0),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Omsg_Osize__5_0) ).
fof(f10312,plain,
spl0_1317,
inference(avatar_split_clause,[],[f3232,f10310]) ).
fof(f3232,plain,
! [X21,X15] : c_less(c_uminus(c_plus(c_1,c_IntDef_Oint(X21),tc_IntDef_Oint),tc_IntDef_Oint),c_IntDef_Oint(X15),tc_IntDef_Oint),
inference(forward_demodulation,[],[f3014,f3010]) ).
fof(f3014,plain,
! [X21,X15] : c_less(c_uminus(c_IntDef_Oint(c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat)),tc_IntDef_Oint),c_IntDef_Oint(X15),tc_IntDef_Oint),
inference(definition_unfolding,[],[f38,f2544]) ).
fof(f38,axiom,
! [X21,X15] : c_less(c_uminus(c_IntDef_Oint(c_Suc(X21)),tc_IntDef_Oint),c_IntDef_Oint(X15),tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Onegative__zless_0) ).
fof(f10308,plain,
spl0_1316,
inference(avatar_split_clause,[],[f3228,f10306]) ).
fof(f10306,plain,
( spl0_1316
<=> ! [X11] : c_Numeral_OBit(c_Numeral_Obin__add(X11,c_Numeral_OMin),c_Numeral_Obit_OB1) = c_Numeral_Obin__add(c_Numeral_OMin,c_Numeral_OBit(X11,c_Numeral_Obit_OB0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1316])]) ).
fof(f3228,plain,
! [X11] : c_Numeral_OBit(c_Numeral_Obin__add(X11,c_Numeral_OMin),c_Numeral_Obit_OB1) = c_Numeral_Obin__add(c_Numeral_OMin,c_Numeral_OBit(X11,c_Numeral_Obit_OB0)),
inference(forward_demodulation,[],[f3012,f2984]) ).
fof(f3012,plain,
! [X11] : c_Numeral_Obin__add(c_Numeral_OBit(X11,c_Numeral_Obit_OB0),c_Numeral_OMin) = c_Numeral_OBit(c_Numeral_Obin__add(X11,c_Numeral_OMin),c_Numeral_Obit_OB1),
inference(definition_unfolding,[],[f2131,f2113,f2113]) ).
fof(f2131,axiom,
! [X11] : c_Numeral_Obin__pred(c_Numeral_OBit(X11,c_Numeral_Obit_OB0)) = c_Numeral_OBit(c_Numeral_Obin__pred(X11),c_Numeral_Obit_OB1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obin__pred__0_0) ).
fof(f10304,plain,
spl0_1315,
inference(avatar_split_clause,[],[f3013,f10302]) ).
fof(f10302,plain,
( spl0_1315
<=> ! [X11] : c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OBit(X11,c_Numeral_Obit_OB0)) = c_Numeral_OBit(c_Numeral_Obin__mult(c_Numeral_OMin,X11),c_Numeral_Obit_OB0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1315])]) ).
fof(f3013,plain,
! [X11] : c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OBit(X11,c_Numeral_Obit_OB0)) = c_Numeral_OBit(c_Numeral_Obin__mult(c_Numeral_OMin,X11),c_Numeral_Obit_OB0),
inference(definition_unfolding,[],[f2123,f2129,f2129]) ).
fof(f2123,axiom,
! [X11] : c_Numeral_Obin__minus(c_Numeral_OBit(X11,c_Numeral_Obit_OB0)) = c_Numeral_OBit(c_Numeral_Obin__minus(X11),c_Numeral_Obit_OB0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obin__minus__0_0) ).
fof(f10290,plain,
( spl0_1314
| ~ spl0_1313 ),
inference(avatar_split_clause,[],[f10286,f10283,f10288]) ).
fof(f10283,plain,
( spl0_1313
<=> ! [X21] : ~ c_lessequals(c_0,c_uminus(c_IntDef_Oint(c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat)),tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1313])]) ).
fof(f10286,plain,
( ! [X21] : ~ c_lessequals(c_0,c_uminus(c_plus(c_1,c_IntDef_Oint(X21),tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_1313 ),
inference(forward_demodulation,[],[f10284,f3010]) ).
fof(f10284,plain,
( ! [X21] : ~ c_lessequals(c_0,c_uminus(c_IntDef_Oint(c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat)),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_1313 ),
inference(avatar_component_clause,[],[f10283]) ).
fof(f10285,plain,
spl0_1313,
inference(avatar_split_clause,[],[f3001,f10283]) ).
fof(f3001,plain,
! [X21] : ~ c_lessequals(c_0,c_uminus(c_IntDef_Oint(c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat)),tc_IntDef_Oint),tc_IntDef_Oint),
inference(definition_unfolding,[],[f1394,f2544]) ).
fof(f1394,axiom,
! [X21] : ~ c_lessequals(c_0,c_uminus(c_IntDef_Oint(c_Suc(X21)),tc_IntDef_Oint),tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Onot__zle__0__negative_0) ).
fof(f10281,plain,
spl0_1312,
inference(avatar_split_clause,[],[f2890,f10279]) ).
fof(f10279,plain,
( spl0_1312
<=> ! [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_1312])]) ).
fof(f2890,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/benchmark/theBenchmark.p',cls_Message_Osynth__synthD__dest_0) ).
fof(f10277,plain,
spl0_1311,
inference(avatar_split_clause,[],[f2885,f10275]) ).
fof(f10275,plain,
( spl0_1311
<=> ! [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_1311])]) ).
fof(f2885,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/benchmark/theBenchmark.p',cls_Message_Osynth_OHash_0) ).
fof(f10273,plain,
spl0_1310,
inference(avatar_split_clause,[],[f2843,f10271]) ).
fof(f10271,plain,
( spl0_1310
<=> ! [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_1310])]) ).
fof(f2843,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/benchmark/theBenchmark.p',cls_Message_ONonce__synth__eq_0) ).
fof(f10269,plain,
spl0_1309,
inference(avatar_split_clause,[],[f2831,f10267]) ).
fof(f10267,plain,
( spl0_1309
<=> ! [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_1309])]) ).
fof(f2831,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/benchmark/theBenchmark.p',cls_Message_OKey__synth__eq_0) ).
fof(f10265,plain,
spl0_1308,
inference(avatar_split_clause,[],[f2793,f10263]) ).
fof(f10263,plain,
( spl0_1308
<=> ! [X91,X88] :
( ~ c_in(X91,c_Message_OkeysFor(X88),tc_nat)
| c_in(X91,c_Message_OkeysFor(c_Message_Osynth(X88)),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1308])]) ).
fof(f2793,axiom,
! [X91,X88] :
( ~ c_in(X91,c_Message_OkeysFor(X88),tc_nat)
| c_in(X91,c_Message_OkeysFor(c_Message_Osynth(X88)),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Event_OkeysFor__synth_H_2) ).
fof(f10261,plain,
spl0_1307,
inference(avatar_split_clause,[],[f2715,f10259]) ).
fof(f10259,plain,
( spl0_1307
<=> ! [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_1307])]) ).
fof(f2715,axiom,
! [X1,X5] : c_Relation_ORange(c_Transitive__Closure_Otrancl(X5,X1),X1,X1) = c_Relation_ORange(X5,X1,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Transitive__Closure_Otrancl__range_0) ).
fof(f10257,plain,
spl0_1306,
inference(avatar_split_clause,[],[f2713,f10255]) ).
fof(f10255,plain,
( spl0_1306
<=> ! [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_1306])]) ).
fof(f2713,axiom,
! [X1,X5] : c_Relation_ODomain(c_Transitive__Closure_Otrancl(X5,X1),X1,X1) = c_Relation_ODomain(X5,X1,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Transitive__Closure_Otrancl__domain_0) ).
fof(f10247,plain,
spl0_1305,
inference(avatar_split_clause,[],[f2685,f10245]) ).
fof(f10245,plain,
( spl0_1305
<=> ! [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_1305])]) ).
fof(f2685,axiom,
! [X18,X1,X27,X12] :
( ~ c_in(X18,X12,X1)
| c_in(X18,c_insert(X27,X12,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Oinsert__iff_2) ).
fof(f10243,plain,
spl0_1304,
inference(avatar_split_clause,[],[f2642,f10241]) ).
fof(f10241,plain,
( spl0_1304
<=> ! [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_1304])]) ).
fof(f2642,axiom,
! [X1,X4,X12,X13] :
( ~ c_in(X4,X13,X1)
| c_in(X4,c_union(X12,X13,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUn__iff_2) ).
fof(f10239,plain,
spl0_1303,
inference(avatar_split_clause,[],[f2641,f10237]) ).
fof(f10237,plain,
( spl0_1303
<=> ! [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_1303])]) ).
fof(f2641,axiom,
! [X1,X4,X12,X13] :
( ~ c_in(X4,X12,X1)
| c_in(X4,c_union(X12,X13,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUn__iff_1) ).
fof(f10235,plain,
spl0_1302,
inference(avatar_split_clause,[],[f2583,f10233]) ).
fof(f10233,plain,
( spl0_1302
<=> ! [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_1302])]) ).
fof(f2583,axiom,
! [X1,X4,X12] :
( c_in(X4,X12,X1)
| c_in(X4,c_uminus(X12,tc_set(X1)),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OCompl__iff_1) ).
fof(f10231,plain,
spl0_1301,
inference(avatar_split_clause,[],[f2582,f10229]) ).
fof(f10229,plain,
( spl0_1301
<=> ! [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_1301])]) ).
fof(f2582,axiom,
! [X1,X4,X12] :
( ~ c_in(X4,X12,X1)
| ~ c_in(X4,c_uminus(X12,tc_set(X1)),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OCompl__iff_0) ).
fof(f10227,plain,
spl0_1300,
inference(avatar_split_clause,[],[f2545,f10225]) ).
fof(f10225,plain,
( spl0_1300
<=> ! [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_1300])]) ).
fof(f2545,axiom,
! [X26,X14] : c_minus(X14,X26,tc_nat) = c_Finite__Set_Ocard(c_SetInterval_OgreaterThanAtMost(X26,X14,tc_nat),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ocard__greaterThanAtMost_0) ).
fof(f10223,plain,
spl0_1299,
inference(avatar_split_clause,[],[f2542,f10221]) ).
fof(f10221,plain,
( spl0_1299
<=> ! [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_1299])]) ).
fof(f2542,axiom,
! [X26,X14] : c_Finite__Set_Ocard(c_SetInterval_OatLeastLessThan(X26,X14,tc_nat),tc_nat) = c_minus(X14,X26,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ocard__atLeastLessThan_0) ).
fof(f10219,plain,
spl0_1298,
inference(avatar_split_clause,[],[f2522,f10217]) ).
fof(f10217,plain,
( spl0_1298
<=> ! [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_1298])]) ).
fof(f2522,axiom,
! [X1,X18] :
( ~ class_Orderings_Oorder(X1)
| c_insert(X18,c_emptyset,X1) = c_SetInterval_OatLeastAtMost(X18,X18,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatLeastAtMost__singleton_0) ).
fof(f10215,plain,
spl0_1297,
inference(avatar_split_clause,[],[f2271,f10213]) ).
fof(f10213,plain,
( spl0_1297
<=> ! [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_1297])]) ).
fof(f2271,axiom,
! [X47] :
( c_Parity_Oeven(c_Numeral_Onumber__of(X47,tc_nat),tc_nat)
| ~ c_Parity_Oeven(c_IntDef_Oint(c_Numeral_Onumber__of(X47,tc_nat)),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven_A_Inumber__of_Av_J_A_61_61_Aeven_A_Iint_A_Inumber__of_Av_J_J_1) ).
fof(f10211,plain,
spl0_1296,
inference(avatar_split_clause,[],[f2270,f10209]) ).
fof(f10209,plain,
( spl0_1296
<=> ! [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_1296])]) ).
fof(f2270,axiom,
! [X47] :
( ~ c_Parity_Oeven(c_Numeral_Onumber__of(X47,tc_nat),tc_nat)
| c_Parity_Oeven(c_IntDef_Oint(c_Numeral_Onumber__of(X47,tc_nat)),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven_A_Inumber__of_Av_J_A_61_61_Aeven_A_Iint_A_Inumber__of_Av_J_J_0) ).
fof(f10202,plain,
spl0_1295,
inference(avatar_split_clause,[],[f2252,f10200]) ).
fof(f10200,plain,
( spl0_1295
<=> ! [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_1295])]) ).
fof(f2252,axiom,
! [X1,X18] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
| c_0 = X18
| c_less(c_0,c_HOL_Oabs(X18,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Ozero__less__abs__iff_1) ).
fof(f10198,plain,
spl0_1294,
inference(avatar_split_clause,[],[f2245,f10196]) ).
fof(f10196,plain,
( spl0_1294
<=> ! [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_1294])]) ).
fof(f2245,axiom,
! [X3,X1] :
( ~ class_OrderedGroup_Olordered__ab__group(X1)
| ~ c_lessequals(c_0,X3,X1)
| c_OrderedGroup_Opprt(X3,X1) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Opprt__eq__id_0) ).
fof(f10194,plain,
spl0_1293,
inference(avatar_split_clause,[],[f2244,f10192]) ).
fof(f10192,plain,
( spl0_1293
<=> ! [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_1293])]) ).
fof(f2244,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group(X1)
| ~ c_lessequals(X0,c_0,X1)
| c_0 = c_OrderedGroup_Opprt(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Opprt__eq__0_0) ).
fof(f10190,plain,
spl0_1292,
inference(avatar_split_clause,[],[f2240,f10188]) ).
fof(f10188,plain,
( spl0_1292
<=> ! [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_1292])]) ).
fof(f2240,axiom,
! [X3,X1] :
( ~ class_OrderedGroup_Olordered__ab__group(X1)
| ~ c_lessequals(X3,c_0,X1)
| c_OrderedGroup_Onprt(X3,X1) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Onprt__eq__id_0) ).
fof(f10186,plain,
spl0_1291,
inference(avatar_split_clause,[],[f2239,f10184]) ).
fof(f2239,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group(X1)
| ~ c_lessequals(c_0,X0,X1)
| c_0 = c_OrderedGroup_Onprt(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Onprt__eq__0_0) ).
fof(f10182,plain,
spl0_1290,
inference(avatar_split_clause,[],[f2199,f10180]) ).
fof(f2199,axiom,
! [X1,X18,X27] :
( ~ class_OrderedGroup_Oab__group__add(X1)
| X18 = X27
| c_0 != c_minus(X18,X27,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Odiff__eq__0__iff__eq_0) ).
fof(f10178,plain,
spl0_1289,
inference(avatar_split_clause,[],[f2183,f10176]) ).
fof(f2183,axiom,
! [X3,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
| ~ c_lessequals(c_0,X3,X1)
| c_HOL_Oabs(X3,X1) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__of__nonneg_0) ).
fof(f10174,plain,
spl0_1288,
inference(avatar_split_clause,[],[f2181,f10172]) ).
fof(f10172,plain,
( spl0_1288
<=> ! [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_1288])]) ).
fof(f2181,axiom,
! [X1,X18] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
| c_HOL_Oabs(X18,X1) = c_HOL_Oabs(c_uminus(X18,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__minus__cancel_0) ).
fof(f10170,plain,
spl0_1287,
inference(avatar_split_clause,[],[f2179,f10168]) ).
fof(f10168,plain,
( spl0_1287
<=> ! [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_1287])]) ).
fof(f2179,axiom,
! [X1,X18] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
| c_0 = X18
| ~ c_lessequals(c_HOL_Oabs(X18,X1),c_0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__le__zero__iff_0) ).
fof(f10166,plain,
spl0_1286,
inference(avatar_split_clause,[],[f2178,f10164]) ).
fof(f10164,plain,
( spl0_1286
<=> ! [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_1286])]) ).
fof(f2178,axiom,
! [X1,X18] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
| c_HOL_Oabs(X18,X1) = c_HOL_Oabs(c_HOL_Oabs(X18,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__idempotent_0) ).
fof(f10162,plain,
( spl0_1285
| ~ spl0_57
| ~ spl0_1022 ),
inference(avatar_split_clause,[],[f8664,f8524,f3692,f10159]) ).
fof(f8524,plain,
( spl0_1022
<=> ! [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_1022])]) ).
fof(f8664,plain,
( c_1 = c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OPls),tc_IntDef_Oint)
| ~ spl0_57
| ~ spl0_1022 ),
inference(resolution,[],[f8525,f3694]) ).
fof(f8525,plain,
( ! [X1] :
( ~ class_Numeral_Onumber__ring(X1)
| c_1 = c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OPls),X1) )
| ~ spl0_1022 ),
inference(avatar_component_clause,[],[f8524]) ).
fof(f10157,plain,
spl0_1284,
inference(avatar_split_clause,[],[f2147,f10155]) ).
fof(f10155,plain,
( spl0_1284
<=> ! [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_1284])]) ).
fof(f2147,axiom,
! [X11,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_OBit(X11,c_Numeral_Obit_OB1),X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obin__rel__simps__5_0) ).
fof(f10153,plain,
spl0_1283,
inference(avatar_split_clause,[],[f2127,f10151]) ).
fof(f10149,plain,
spl0_1282,
inference(avatar_split_clause,[],[f2104,f10147]) ).
fof(f10147,plain,
( spl0_1282
<=> ! [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_1282])]) ).
fof(f2104,axiom,
! [X21,X15] :
( ~ c_less(X15,X21,tc_nat)
| c_less(c_0,c_minus(X21,X15,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Ozero__less__diff_1) ).
fof(f10145,plain,
spl0_1281,
inference(avatar_split_clause,[],[f2103,f10143]) ).
fof(f10143,plain,
( spl0_1281
<=> ! [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_1281])]) ).
fof(f2103,axiom,
! [X21,X15] :
( c_less(X15,X21,tc_nat)
| ~ c_less(c_0,c_minus(X21,X15,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Ozero__less__diff_0) ).
fof(f10141,plain,
spl0_1280,
inference(avatar_split_clause,[],[f2079,f10139]) ).
fof(f10139,plain,
( spl0_1280
<=> ! [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_1280])]) ).
fof(f2079,axiom,
! [X21,X15] :
( c_less(c_0,X21,tc_nat)
| ~ c_less(c_0,c_times(X15,X21,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Onat__0__less__mult__iff_1) ).
fof(f10137,plain,
spl0_1279,
inference(avatar_split_clause,[],[f2078,f10135]) ).
fof(f10135,plain,
( spl0_1279
<=> ! [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_1279])]) ).
fof(f2078,axiom,
! [X21,X15] :
( c_less(c_0,X15,tc_nat)
| ~ c_less(c_0,c_times(X15,X21,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Onat__0__less__mult__iff_0) ).
fof(f10133,plain,
spl0_1278,
inference(avatar_split_clause,[],[f2030,f10131]) ).
fof(f10131,plain,
( spl0_1278
<=> ! [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_1278])]) ).
fof(f2030,axiom,
! [X21,X15] :
( ~ c_less(c_0,X21,tc_nat)
| c_less(c_0,c_plus(X15,X21,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oadd__gr__0_2) ).
fof(f10129,plain,
spl0_1277,
inference(avatar_split_clause,[],[f2029,f10127]) ).
fof(f10127,plain,
( spl0_1277
<=> ! [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_1277])]) ).
fof(f2029,axiom,
! [X21,X15] :
( ~ c_less(c_0,X15,tc_nat)
| c_less(c_0,c_plus(X15,X21,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oadd__gr__0_1) ).
fof(f10125,plain,
spl0_1276,
inference(avatar_split_clause,[],[f1851,f10123]) ).
fof(f10123,plain,
( spl0_1276
<=> ! [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_1276])]) ).
fof(f1851,axiom,
! [X47] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 = c_IntDef_Oint(c_Numeral_Onumber__of(X47,tc_nat)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatBin_Oint__nat__number__of_0) ).
fof(f10121,plain,
spl0_1275,
inference(avatar_split_clause,[],[f1814,f10119]) ).
fof(f10119,plain,
( spl0_1275
<=> ! [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_1275])]) ).
fof(f1814,axiom,
! [X1,X15] :
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| c_0 = X15
| ~ c_lessequals(c_NatArith_Oof__nat(X15,X1),c_0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__le__0__iff_0) ).
fof(f10117,plain,
( spl0_1274
| ~ spl0_894
| ~ spl0_997 ),
inference(avatar_split_clause,[],[f8638,f8421,f7930,f10114]) ).
fof(f10114,plain,
( spl0_1274
<=> c_in(c_0,c_SetInterval_OatMost(c_0,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1274])]) ).
fof(f8638,plain,
( c_in(c_0,c_SetInterval_OatMost(c_0,tc_nat),tc_nat)
| ~ spl0_894
| ~ spl0_997 ),
inference(superposition,[],[f7931,f8423]) ).
fof(f10112,plain,
spl0_1273,
inference(avatar_split_clause,[],[f1734,f10110]) ).
fof(f10110,plain,
( spl0_1273
<=> ! [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_1273])]) ).
fof(f1734,axiom,
! [X0,X1] : c_List_Olist_OCons(X0,c_List_Olist_ONil,X1) = c_List_Orev(c_List_Olist_OCons(X0,c_List_Olist_ONil,X1),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Orev__singleton__conv_1) ).
fof(f10108,plain,
spl0_1272,
inference(avatar_split_clause,[],[f1731,f10106]) ).
fof(f10106,plain,
( spl0_1272
<=> ! [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_1272])]) ).
fof(f1731,axiom,
! [X21,X0,X1] : c_List_Oreplicate(X21,X0,X1) = c_List_Orev(c_List_Oreplicate(X21,X0,X1),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Orev__replicate_0) ).
fof(f10104,plain,
spl0_1271,
inference(avatar_split_clause,[],[f1712,f10102]) ).
fof(f10102,plain,
( spl0_1271
<=> ! [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_1271])]) ).
fof(f1712,axiom,
! [X41,X3,X0,X25] :
( ~ c_List_Oop_Amem(X0,X25,X41)
| c_List_Oop_Amem(X0,c_List_Olist_OCons(X3,X25,X41),X41) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oop_Amem_Osimps__2_2) ).
fof(f10100,plain,
spl0_1270,
inference(avatar_split_clause,[],[f1613,f10098]) ).
fof(f10098,plain,
( spl0_1270
<=> ! [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_1270])]) ).
fof(f1613,axiom,
! [X59,X43] : c_Nat_Osize(c_List_Oupt(X43,X59),tc_List_Olist(tc_nat)) = c_minus(X59,X43,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olength__upt_0) ).
fof(f10096,plain,
spl0_1269,
inference(avatar_split_clause,[],[f1609,f10094]) ).
fof(f10094,plain,
( spl0_1269
<=> ! [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_1269])]) ).
fof(f1609,axiom,
! [X1,X23] : c_Nat_Osize(X23,tc_List_Olist(X1)) = c_Nat_Osize(c_List_Orotate1(X23,X1),tc_List_Olist(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olength__rotate1_0) ).
fof(f10092,plain,
spl0_1268,
inference(avatar_split_clause,[],[f1608,f10090]) ).
fof(f10090,plain,
( spl0_1268
<=> ! [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_1268])]) ).
fof(f1608,axiom,
! [X1,X23] : c_Nat_Osize(X23,tc_List_Olist(X1)) = c_Nat_Osize(c_List_Orev(X23,X1),tc_List_Olist(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olength__rev_0) ).
fof(f10088,plain,
spl0_1267,
inference(avatar_split_clause,[],[f1595,f10086]) ).
fof(f10086,plain,
( spl0_1267
<=> ! [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_1267])]) ).
fof(f1595,axiom,
! [X3,X1,X23] : c_List_Olast(c_append(X23,c_List_Olist_OCons(X3,c_List_Olist_ONil,X1),X1),X1) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olast__snoc_0) ).
fof(f10084,plain,
spl0_1266,
inference(avatar_split_clause,[],[f1594,f10082]) ).
fof(f10082,plain,
( spl0_1266
<=> ! [X21,X1,X3] :
( c_0 = X21
| c_List_Olast(c_List_Oreplicate(X21,X3,X1),X1) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1266])]) ).
fof(f1594,axiom,
! [X21,X3,X1] :
( c_0 = X21
| c_List_Olast(c_List_Oreplicate(X21,X3,X1),X1) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olast__replicate_0) ).
fof(f10080,plain,
spl0_1265,
inference(avatar_split_clause,[],[f1593,f10078]) ).
fof(f10078,plain,
( spl0_1265
<=> ! [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_1265])]) ).
fof(f1593,axiom,
! [X1,X60] :
( c_List_Olist_ONil = X60
| c_in(c_List_Olast(X60,X1),c_List_Oset(X60,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olast__in__set_0) ).
fof(f10076,plain,
spl0_1264,
inference(avatar_split_clause,[],[f1584,f10074]) ).
fof(f1584,axiom,
! [X3,X59] :
( ~ c_less(X3,X59,tc_nat)
| c_List_Ohd(c_List_Oupt(X3,X59),tc_nat) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Ohd__upt_0) ).
fof(f10072,plain,
( spl0_1263
| ~ spl0_92
| ~ spl0_984 ),
inference(avatar_split_clause,[],[f8620,f8368,f3867,f10070]) ).
fof(f10070,plain,
( spl0_1263
<=> ! [X0] : c_Nat_Opower(X0,c_1,tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1263])]) ).
fof(f3867,plain,
( spl0_92
<=> class_Power_Orecpower(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_92])]) ).
fof(f8368,plain,
( spl0_984
<=> ! [X1,X3] :
( ~ class_Power_Orecpower(X1)
| c_Nat_Opower(X3,c_1,X1) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_984])]) ).
fof(f8620,plain,
( ! [X0] : c_Nat_Opower(X0,c_1,tc_nat) = X0
| ~ spl0_92
| ~ spl0_984 ),
inference(resolution,[],[f8369,f3869]) ).
fof(f3869,plain,
( class_Power_Orecpower(tc_nat)
| ~ spl0_92 ),
inference(avatar_component_clause,[],[f3867]) ).
fof(f8369,plain,
( ! [X3,X1] :
( ~ class_Power_Orecpower(X1)
| c_Nat_Opower(X3,c_1,X1) = X3 )
| ~ spl0_984 ),
inference(avatar_component_clause,[],[f8368]) ).
fof(f10068,plain,
spl0_1262,
inference(avatar_split_clause,[],[f1583,f10066]) ).
fof(f10066,plain,
( spl0_1262
<=> ! [X21,X1,X3] :
( c_0 = X21
| c_List_Ohd(c_List_Oreplicate(X21,X3,X1),X1) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1262])]) ).
fof(f1583,axiom,
! [X21,X3,X1] :
( c_0 = X21
| c_List_Ohd(c_List_Oreplicate(X21,X3,X1),X1) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Ohd__replicate_0) ).
fof(f10064,plain,
spl0_1261,
inference(avatar_split_clause,[],[f1582,f10062]) ).
fof(f10062,plain,
( spl0_1261
<=> ! [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_1261])]) ).
fof(f1582,axiom,
! [X1,X23] :
( c_List_Olist_ONil = X23
| c_in(c_List_Ohd(X23,X1),c_List_Oset(X23,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Ohd__in__set_0) ).
fof(f10060,plain,
spl0_1260,
inference(avatar_split_clause,[],[f1539,f10058]) ).
fof(f10058,plain,
( spl0_1260
<=> ! [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_1260])]) ).
fof(f1539,axiom,
! [X3,X0,X1] : c_List_Obutlast(c_append(X3,c_List_Olist_OCons(X0,c_List_Olist_ONil,X1),X1),X1) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Obutlast__snoc_0) ).
fof(f10056,plain,
spl0_1259,
inference(avatar_split_clause,[],[f1463,f10054]) ).
fof(f10054,plain,
( spl0_1259
<=> ! [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_1259])]) ).
fof(f1463,axiom,
! [X18,X27] :
( ~ c_less(c_0,X27,tc_IntDef_Oint)
| c_lessequals(c_0,c_Divides_Oop_Amod(X18,X27,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Opos__mod__sign_0) ).
fof(f10052,plain,
spl0_1258,
inference(avatar_split_clause,[],[f1462,f10050]) ).
fof(f10050,plain,
( spl0_1258
<=> ! [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_1258])]) ).
fof(f1462,axiom,
! [X18,X27] :
( ~ c_less(c_0,X27,tc_IntDef_Oint)
| c_less(c_Divides_Oop_Amod(X18,X27,tc_IntDef_Oint),X27,tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Opos__mod__bound_0) ).
fof(f10048,plain,
spl0_1257,
inference(avatar_split_clause,[],[f1455,f10046]) ).
fof(f10046,plain,
( spl0_1257
<=> ! [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_1257])]) ).
fof(f1455,axiom,
! [X18,X27] :
( ~ c_less(X27,c_0,tc_IntDef_Oint)
| c_lessequals(c_Divides_Oop_Amod(X18,X27,tc_IntDef_Oint),c_0,tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Oneg__mod__sign_0) ).
fof(f10044,plain,
spl0_1256,
inference(avatar_split_clause,[],[f1454,f10042]) ).
fof(f10042,plain,
( spl0_1256
<=> ! [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_1256])]) ).
fof(f1454,axiom,
! [X18,X27] :
( ~ c_less(X27,c_0,tc_IntDef_Oint)
| c_less(X27,c_Divides_Oop_Amod(X18,X27,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Oneg__mod__bound_0) ).
fof(f10040,plain,
spl0_1255,
inference(avatar_split_clause,[],[f1418,f10038]) ).
fof(f10038,plain,
( spl0_1255
<=> ! [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_1255])]) ).
fof(f1418,axiom,
! [X21,X1] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X1)
| c_NatArith_Oof__nat(X21,X1) = c_IntDef_Oof__int(c_NatArith_Oof__nat(X21,tc_IntDef_Oint),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oof__int__of__nat__eq_0) ).
fof(f10036,plain,
spl0_1254,
inference(avatar_split_clause,[],[f1354,f10034]) ).
fof(f10034,plain,
( spl0_1254
<=> ! [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_1254])]) ).
fof(f1354,axiom,
! [X48,X11] :
( ~ c_less(X11,X48,tc_IntDef_Oint)
| c_lessequals(X11,c_minus(X48,c_1,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntArith_Ozle__diff1__eq_1) ).
fof(f10032,plain,
spl0_1253,
inference(avatar_split_clause,[],[f1353,f10030]) ).
fof(f10030,plain,
( spl0_1253
<=> ! [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_1253])]) ).
fof(f1353,axiom,
! [X48,X11] :
( c_less(X11,X48,tc_IntDef_Oint)
| ~ c_lessequals(X11,c_minus(X48,c_1,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntArith_Ozle__diff1__eq_0) ).
fof(f10028,plain,
( spl0_1252
| ~ spl0_58
| ~ spl0_984 ),
inference(avatar_split_clause,[],[f8619,f8368,f3697,f10026]) ).
fof(f3697,plain,
( spl0_58
<=> class_Power_Orecpower(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_58])]) ).
fof(f8619,plain,
( ! [X0] : c_Nat_Opower(X0,c_1,tc_IntDef_Oint) = X0
| ~ spl0_58
| ~ spl0_984 ),
inference(resolution,[],[f8369,f3699]) ).
fof(f3699,plain,
( class_Power_Orecpower(tc_IntDef_Oint)
| ~ spl0_58 ),
inference(avatar_component_clause,[],[f3697]) ).
fof(f10024,plain,
spl0_1251,
inference(avatar_split_clause,[],[f1352,f10022]) ).
fof(f10022,plain,
( spl0_1251
<=> ! [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_1251])]) ).
fof(f1352,axiom,
! [X48,X11] :
( ~ c_lessequals(X11,X48,tc_IntDef_Oint)
| c_less(X11,c_plus(X48,c_1,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntArith_Ozle__add1__eq__le_1) ).
fof(f10020,plain,
spl0_1250,
inference(avatar_split_clause,[],[f1351,f10018]) ).
fof(f10018,plain,
( spl0_1250
<=> ! [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_1250])]) ).
fof(f1351,axiom,
! [X48,X11] :
( c_lessequals(X11,X48,tc_IntDef_Oint)
| ~ c_less(X11,c_plus(X48,c_1,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntArith_Ozle__add1__eq__le_0) ).
fof(f10016,plain,
spl0_1249,
inference(avatar_split_clause,[],[f1348,f10014]) ).
fof(f10014,plain,
( spl0_1249
<=> ! [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_1249])]) ).
fof(f1348,axiom,
! [X48,X11] : c_plus(X48,c_uminus(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_minus(X48,X11,tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntArith_Oz1_A_L_A_N_Aw1_A_61_61_Az1_A_N_Aw1_0) ).
fof(f10011,plain,
spl0_1248,
inference(avatar_split_clause,[],[f1345,f10009]) ).
fof(f1345,axiom,
! [X1] :
( ~ class_Numeral_Onumber__ring(X1)
| c_Numeral_Onumber__of(c_Numeral_OMin,X1) = c_IntDef_Oof__int(c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntArith_Oof__int__m1_0) ).
fof(f10007,plain,
spl0_1247,
inference(avatar_split_clause,[],[f1310,f10005]) ).
fof(f10005,plain,
( spl0_1247
<=> ! [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_1247])]) ).
fof(f1310,axiom,
! [X1] :
( ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_1 = c_HOL_Oabs(c_Numeral_Onumber__of(c_Numeral_OMin,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntArith_Oabs__minus__one_0) ).
fof(f10003,plain,
spl0_1246,
inference(avatar_split_clause,[],[f1307,f10001]) ).
fof(f10001,plain,
( spl0_1246
<=> ! [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_1246])]) ).
fof(f1307,axiom,
! [X21,X3] : c_GCD_Ogcd(c_Pair(X3,c_times(X3,X21,tc_nat),tc_nat,tc_nat)) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_GCD_Ogcd__mult_0) ).
fof(f9999,plain,
spl0_1245,
inference(avatar_split_clause,[],[f1236,f9997]) ).
fof(f9997,plain,
( spl0_1245
<=> ! [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_1245])]) ).
fof(f1236,axiom,
! [X21,X15] :
( ~ c_less(c_0,X21,tc_nat)
| c_less(c_Divides_Oop_Amod(X15,X21,tc_nat),X21,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Omod__less__divisor_0) ).
fof(f9995,plain,
spl0_1244,
inference(avatar_split_clause,[],[f1234,f9993]) ).
fof(f9993,plain,
( spl0_1244
<=> ! [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_1244])]) ).
fof(f1234,axiom,
! [X21,X15] :
( ~ c_less(c_0,X21,tc_nat)
| c_lessequals(c_Divides_Oop_Amod(X15,X21,tc_nat),X21,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Omod__le__divisor_0) ).
fof(f9991,plain,
spl0_1243,
inference(avatar_split_clause,[],[f1178,f9989]) ).
fof(f1178,axiom,
! [X2,X18,X1,X27] : c_0 = c_Nat_Osize(c_Pair(X18,X27,X1,X2),tc_prod(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype_Oprod_Osize_0) ).
fof(f9987,plain,
spl0_1242,
inference(avatar_split_clause,[],[f1166,f9985]) ).
fof(f9985,plain,
( spl0_1242
<=> ! [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_1242])]) ).
fof(f1166,axiom,
! [X40,X0,X1] :
( c_Datatype_Ooption_OSome(X0,X1) = X40
| ~ c_in(X0,c_Datatype_Oo2s(X40,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype_Oelem__o2s_0) ).
fof(f9983,plain,
( spl0_1241
| ~ spl0_92
| ~ spl0_983 ),
inference(avatar_split_clause,[],[f8618,f8364,f3867,f9981]) ).
fof(f9981,plain,
( spl0_1241
<=> ! [X0] : c_1 = c_Nat_Opower(c_1,X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1241])]) ).
fof(f8364,plain,
( spl0_983
<=> ! [X21,X1] :
( ~ class_Power_Orecpower(X1)
| c_1 = c_Nat_Opower(c_1,X21,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_983])]) ).
fof(f8618,plain,
( ! [X0] : c_1 = c_Nat_Opower(c_1,X0,tc_nat)
| ~ spl0_92
| ~ spl0_983 ),
inference(resolution,[],[f8365,f3869]) ).
fof(f8365,plain,
( ! [X21,X1] :
( ~ class_Power_Orecpower(X1)
| c_1 = c_Nat_Opower(c_1,X21,X1) )
| ~ spl0_983 ),
inference(avatar_component_clause,[],[f8364]) ).
fof(f9964,plain,
( spl0_1240
| ~ spl0_58
| ~ spl0_983 ),
inference(avatar_split_clause,[],[f8617,f8364,f3697,f9962]) ).
fof(f9962,plain,
( spl0_1240
<=> ! [X0] : c_1 = c_Nat_Opower(c_1,X0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1240])]) ).
fof(f8617,plain,
( ! [X0] : c_1 = c_Nat_Opower(c_1,X0,tc_IntDef_Oint)
| ~ spl0_58
| ~ spl0_983 ),
inference(resolution,[],[f8365,f3699]) ).
fof(f9934,plain,
( spl0_1239
| ~ spl0_96
| ~ spl0_980 ),
inference(avatar_split_clause,[],[f8612,f8352,f3887,f9932]) ).
fof(f9932,plain,
( spl0_1239
<=> ! [X0] : c_Orderings_Omax(X0,X0,tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1239])]) ).
fof(f8352,plain,
( spl0_980
<=> ! [X2,X3] :
( ~ class_Orderings_Olinorder(X2)
| c_Orderings_Omax(X3,X3,X2) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_980])]) ).
fof(f8612,plain,
( ! [X0] : c_Orderings_Omax(X0,X0,tc_nat) = X0
| ~ spl0_96
| ~ spl0_980 ),
inference(resolution,[],[f8353,f3889]) ).
fof(f8353,plain,
( ! [X2,X3] :
( ~ class_Orderings_Olinorder(X2)
| c_Orderings_Omax(X3,X3,X2) = X3 )
| ~ spl0_980 ),
inference(avatar_component_clause,[],[f8352]) ).
fof(f9926,plain,
( spl0_1238
| ~ spl0_32
| ~ spl0_980 ),
inference(avatar_split_clause,[],[f8611,f8352,f3567,f9924]) ).
fof(f9924,plain,
( spl0_1238
<=> ! [X0] : c_Orderings_Omax(X0,X0,tc_IntDef_Oint) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1238])]) ).
fof(f8611,plain,
( ! [X0] : c_Orderings_Omax(X0,X0,tc_IntDef_Oint) = X0
| ~ spl0_32
| ~ spl0_980 ),
inference(resolution,[],[f8353,f3569]) ).
fof(f9900,plain,
( spl0_1237
| ~ spl0_96
| ~ spl0_979 ),
inference(avatar_split_clause,[],[f8610,f8348,f3887,f9898]) ).
fof(f9898,plain,
( spl0_1237
<=> ! [X0] : c_Orderings_Omin(X0,X0,tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1237])]) ).
fof(f8348,plain,
( spl0_979
<=> ! [X2,X3] :
( ~ class_Orderings_Olinorder(X2)
| c_Orderings_Omin(X3,X3,X2) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_979])]) ).
fof(f8610,plain,
( ! [X0] : c_Orderings_Omin(X0,X0,tc_nat) = X0
| ~ spl0_96
| ~ spl0_979 ),
inference(resolution,[],[f8349,f3889]) ).
fof(f8349,plain,
( ! [X2,X3] :
( ~ class_Orderings_Olinorder(X2)
| c_Orderings_Omin(X3,X3,X2) = X3 )
| ~ spl0_979 ),
inference(avatar_component_clause,[],[f8348]) ).
fof(f9860,plain,
( spl0_1236
| ~ spl0_32
| ~ spl0_979 ),
inference(avatar_split_clause,[],[f8609,f8348,f3567,f9858]) ).
fof(f9858,plain,
( spl0_1236
<=> ! [X0] : c_Orderings_Omin(X0,X0,tc_IntDef_Oint) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1236])]) ).
fof(f8609,plain,
( ! [X0] : c_Orderings_Omin(X0,X0,tc_IntDef_Oint) = X0
| ~ spl0_32
| ~ spl0_979 ),
inference(resolution,[],[f8349,f3569]) ).
fof(f9835,plain,
( spl0_1235
| ~ spl0_57
| ~ spl0_1075
| ~ spl0_1166 ),
inference(avatar_split_clause,[],[f9452,f9449,f8867,f3692,f9833]) ).
fof(f9833,plain,
( spl0_1235
<=> ! [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_1235])]) ).
fof(f9449,plain,
( spl0_1166
<=> ! [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_1166])]) ).
fof(f9452,plain,
( ! [X18] : c_uminus(X18,tc_IntDef_Oint) = c_div(X18,c_uminus(c_1,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_57
| ~ spl0_1075
| ~ spl0_1166 ),
inference(forward_demodulation,[],[f9450,f9233]) ).
fof(f9450,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_1166 ),
inference(avatar_component_clause,[],[f9449]) ).
fof(f9779,plain,
( spl0_1234
| spl0_685
| ~ spl0_1152 ),
inference(avatar_split_clause,[],[f9772,f9393,f7037,f9776]) ).
fof(f9776,plain,
( spl0_1234
<=> c_0 = c_Finite__Set_Ocard(c_UNIV,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1234])]) ).
fof(f7037,plain,
( spl0_685
<=> c_in(c_UNIV,c_Finite__Set_OFinites,tc_set(tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_685])]) ).
fof(f9393,plain,
( spl0_1152
<=> ! [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_1152])]) ).
fof(f9772,plain,
( c_0 = c_Finite__Set_Ocard(c_UNIV,tc_nat)
| spl0_685
| ~ spl0_1152 ),
inference(resolution,[],[f9394,f7039]) ).
fof(f7039,plain,
( ~ c_in(c_UNIV,c_Finite__Set_OFinites,tc_set(tc_nat))
| spl0_685 ),
inference(avatar_component_clause,[],[f7037]) ).
fof(f9394,plain,
( ! [X1,X12] :
( c_in(X12,c_Finite__Set_OFinites,tc_set(X1))
| c_0 = c_Finite__Set_Ocard(X12,X1) )
| ~ spl0_1152 ),
inference(avatar_component_clause,[],[f9393]) ).
fof(f9726,plain,
spl0_1233,
inference(avatar_split_clause,[],[f3358,f9724]) ).
fof(f9724,plain,
( spl0_1233
<=> ! [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_1233])]) ).
fof(f3358,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,[],[f3357]) ).
fof(f3357,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,[],[f3356,f2115]) ).
fof(f3356,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,[],[f3153,f2957]) ).
fof(f3153,plain,
! [X0,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| c_0 != c_Numeral_Onumber__of(X0,X1)
| c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X0,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OPls)),X1),X1) ),
inference(definition_unfolding,[],[f1337,f2129]) ).
fof(f1337,axiom,
! [X0,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| c_0 != c_Numeral_Onumber__of(X0,X1)
| c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X0,c_Numeral_Obin__minus(c_Numeral_OPls)),X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__8_0) ).
fof(f9722,plain,
( spl0_1232
| ~ spl0_647
| ~ spl0_1129
| ~ spl0_1225 ),
inference(avatar_split_clause,[],[f9693,f9688,f9149,f6106,f9719]) ).
fof(f9719,plain,
( spl0_1232
<=> c_IntDef_Oneg(c_uminus(c_1,tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1232])]) ).
fof(f9693,plain,
( c_IntDef_Oneg(c_uminus(c_1,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_647
| ~ spl0_1129
| ~ spl0_1225 ),
inference(forward_demodulation,[],[f9692,f9150]) ).
fof(f9692,plain,
( c_IntDef_Oneg(c_uminus(c_plus(c_1,c_0,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_647
| ~ spl0_1225 ),
inference(superposition,[],[f9689,f6108]) ).
fof(f9717,plain,
spl0_1231,
inference(avatar_split_clause,[],[f3239,f9715]) ).
fof(f9715,plain,
( spl0_1231
<=> ! [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_1231])]) ).
fof(f3239,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,[],[f3238,f3236]) ).
fof(f3238,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,[],[f3042,f2958]) ).
fof(f3042,plain,
! [X90,X96] : c_Nat_Osize(c_Message_Omsg_OCrypt(X90,X96),tc_Message_Omsg) = c_plus(c_Nat_Osize(X96,tc_Message_Omsg),c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),tc_nat),
inference(definition_unfolding,[],[f2766,f2544]) ).
fof(f2766,axiom,
! [X90,X96] : c_plus(c_Nat_Osize(X96,tc_Message_Omsg),c_Suc(c_0),tc_nat) = c_Nat_Osize(c_Message_Omsg_OCrypt(X90,X96),tc_Message_Omsg),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Omsg_Osize__7_0) ).
fof(f9713,plain,
spl0_1230,
inference(avatar_split_clause,[],[f3235,f9711]) ).
fof(f9711,plain,
( spl0_1230
<=> ! [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_1230])]) ).
fof(f3235,plain,
! [X2,X1,X9] : c_emptyset = c_Datatype__Universe_Ontrunc(c_1,c_Datatype__Universe_OIn0(X9,X1,X2),X1,X2),
inference(forward_demodulation,[],[f3022,f2958]) ).
fof(f3022,plain,
! [X2,X1,X9] : c_emptyset = c_Datatype__Universe_Ontrunc(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),c_Datatype__Universe_OIn0(X9,X1,X2),X1,X2),
inference(definition_unfolding,[],[f1209,f2544]) ).
fof(f1209,axiom,
! [X2,X1,X9] : c_emptyset = c_Datatype__Universe_Ontrunc(c_Suc(c_0),c_Datatype__Universe_OIn0(X9,X1,X2),X1,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_Ontrunc__one__In0_0) ).
fof(f9709,plain,
spl0_1229,
inference(avatar_split_clause,[],[f3234,f9707]) ).
fof(f9707,plain,
( spl0_1229
<=> ! [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_1229])]) ).
fof(f3234,plain,
! [X2,X1,X9] : c_emptyset = c_Datatype__Universe_Ontrunc(c_1,c_Datatype__Universe_OIn1(X9,X1,X2),X1,X2),
inference(forward_demodulation,[],[f3021,f2958]) ).
fof(f3021,plain,
! [X2,X1,X9] : c_emptyset = c_Datatype__Universe_Ontrunc(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),c_Datatype__Universe_OIn1(X9,X1,X2),X1,X2),
inference(definition_unfolding,[],[f1210,f2544]) ).
fof(f1210,axiom,
! [X2,X1,X9] : c_emptyset = c_Datatype__Universe_Ontrunc(c_Suc(c_0),c_Datatype__Universe_OIn1(X9,X1,X2),X1,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_Ontrunc__one__In1_0) ).
fof(f9705,plain,
spl0_1228,
inference(avatar_split_clause,[],[f3102,f9703]) ).
fof(f9703,plain,
( spl0_1228
<=> ! [X0] :
( c_Parity_Oeven(X0,tc_nat)
| c_Parity_Oeven(c_Finite__Set_Ocard(c_SetInterval_OatMost(X0,tc_nat),tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1228])]) ).
fof(f3102,plain,
! [X0] :
( c_Parity_Oeven(X0,tc_nat)
| c_Parity_Oeven(c_Finite__Set_Ocard(c_SetInterval_OatMost(X0,tc_nat),tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f2279,f2544]) ).
fof(f2279,axiom,
! [X0] :
( c_Parity_Oeven(X0,tc_nat)
| c_Parity_Oeven(c_Suc(X0),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__nat__Suc_1) ).
fof(f9701,plain,
spl0_1227,
inference(avatar_split_clause,[],[f3088,f9699]) ).
fof(f9699,plain,
( spl0_1227
<=> ! [X0] :
( ~ c_Parity_Oeven(X0,tc_nat)
| ~ c_Parity_Oeven(c_Finite__Set_Ocard(c_SetInterval_OatMost(X0,tc_nat),tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1227])]) ).
fof(f3088,plain,
! [X0] :
( ~ c_Parity_Oeven(X0,tc_nat)
| ~ c_Parity_Oeven(c_Finite__Set_Ocard(c_SetInterval_OatMost(X0,tc_nat),tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f2278,f2544]) ).
fof(f2278,axiom,
! [X0] :
( ~ c_Parity_Oeven(X0,tc_nat)
| ~ c_Parity_Oeven(c_Suc(X0),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__nat__Suc_0) ).
fof(f9697,plain,
spl0_1226,
inference(avatar_split_clause,[],[f3015,f9695]) ).
fof(f9695,plain,
( spl0_1226
<=> ! [X27,X12] : c_in(c_Message_Omsg_OKey(c_Message_OinvKey(c_Public_OpublicKey(X27,X12))),c_Event_Oknows(X12,c_List_Olist_ONil),tc_Message_Omsg) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1226])]) ).
fof(f3015,plain,
! [X27,X12] : c_in(c_Message_Omsg_OKey(c_Message_OinvKey(c_Public_OpublicKey(X27,X12))),c_Event_Oknows(X12,c_List_Olist_ONil),tc_Message_Omsg),
inference(definition_unfolding,[],[f2913,f2795]) ).
fof(f2795,axiom,
! [X12] : c_Event_Oknows(X12,c_List_Olist_ONil) = c_Event_OinitState(X12),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Event_Oknows_Oknows__Nil_0) ).
fof(f2913,axiom,
! [X27,X12] : c_in(c_Message_Omsg_OKey(c_Message_OinvKey(c_Public_OpublicKey(X27,X12))),c_Event_OinitState(X12),tc_Message_Omsg),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Public_OpriK__in__initState_0) ).
fof(f9690,plain,
( spl0_1225
| ~ spl0_1224 ),
inference(avatar_split_clause,[],[f9686,f9683,f9688]) ).
fof(f9683,plain,
( spl0_1224
<=> ! [X21] : c_IntDef_Oneg(c_uminus(c_IntDef_Oint(c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat)),tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1224])]) ).
fof(f9686,plain,
( ! [X21] : c_IntDef_Oneg(c_uminus(c_plus(c_1,c_IntDef_Oint(X21),tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_1224 ),
inference(forward_demodulation,[],[f9684,f3010]) ).
fof(f9684,plain,
( ! [X21] : c_IntDef_Oneg(c_uminus(c_IntDef_Oint(c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat)),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_1224 ),
inference(avatar_component_clause,[],[f9683]) ).
fof(f9685,plain,
spl0_1224,
inference(avatar_split_clause,[],[f2999,f9683]) ).
fof(f2999,plain,
! [X21] : c_IntDef_Oneg(c_uminus(c_IntDef_Oint(c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat)),tc_IntDef_Oint),tc_IntDef_Oint),
inference(definition_unfolding,[],[f1388,f2544]) ).
fof(f1388,axiom,
! [X21] : c_IntDef_Oneg(c_uminus(c_IntDef_Oint(c_Suc(X21)),tc_IntDef_Oint),tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oneg__zminus__int_0) ).
fof(f9681,plain,
spl0_1223,
inference(avatar_split_clause,[],[f2991,f9679]) ).
fof(f9679,plain,
( spl0_1223
<=> ! [X86,X107,X87,X91] : c_Message_Omsg_OCrypt(X91,X107) != c_Message_Omsg_OMPair(c_Message_Omsg_OHash(c_Message_Omsg_OMPair(X86,X87)),X87) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1223])]) ).
fof(f2991,plain,
! [X91,X86,X87,X107] : c_Message_Omsg_OCrypt(X91,X107) != c_Message_Omsg_OMPair(c_Message_Omsg_OHash(c_Message_Omsg_OMPair(X86,X87)),X87),
inference(definition_unfolding,[],[f2818,f2837]) ).
fof(f2818,axiom,
! [X91,X86,X87,X107] : c_Message_OHPair(X86,X87) != c_Message_Omsg_OCrypt(X91,X107),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OHPair__neqs__6_0) ).
fof(f9677,plain,
( spl0_1222
| ~ spl0_814
| ~ spl0_1221 ),
inference(avatar_split_clause,[],[f9673,f9670,f7597,f9675]) ).
fof(f9675,plain,
( spl0_1222
<=> ! [X1] : c_Relation_OId = c_Transitive__Closure_Otrancl(c_Relation_OId,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1222])]) ).
fof(f9670,plain,
( spl0_1221
<=> ! [X1] : c_Relation_OId = c_Transitive__Closure_Otrancl(c_union(c_emptyset,c_Relation_OId,tc_prod(X1,X1)),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1221])]) ).
fof(f9673,plain,
( ! [X1] : c_Relation_OId = c_Transitive__Closure_Otrancl(c_Relation_OId,X1)
| ~ spl0_814
| ~ spl0_1221 ),
inference(forward_demodulation,[],[f9671,f7598]) ).
fof(f9671,plain,
( ! [X1] : c_Relation_OId = c_Transitive__Closure_Otrancl(c_union(c_emptyset,c_Relation_OId,tc_prod(X1,X1)),X1)
| ~ spl0_1221 ),
inference(avatar_component_clause,[],[f9670]) ).
fof(f9672,plain,
spl0_1221,
inference(avatar_split_clause,[],[f2959,f9670]) ).
fof(f2959,plain,
! [X1] : c_Relation_OId = c_Transitive__Closure_Otrancl(c_union(c_emptyset,c_Relation_OId,tc_prod(X1,X1)),X1),
inference(definition_unfolding,[],[f2709,f2716]) ).
fof(f2709,axiom,
! [X1] : c_Relation_OId = c_Transitive__Closure_Ortrancl(c_emptyset,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Transitive__Closure_Ortrancl__empty_0) ).
fof(f9668,plain,
spl0_1220,
inference(avatar_split_clause,[],[f2920,f9666]) ).
fof(f9666,plain,
( spl0_1220
<=> ! [X4,X27,X12,X111] :
( X12 = X111
| c_Public_OpublicKey(X27,X12) != c_Public_OpublicKey(X4,X111) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1220])]) ).
fof(f2920,axiom,
! [X111,X27,X4,X12] :
( X12 = X111
| c_Public_OpublicKey(X27,X12) != c_Public_OpublicKey(X4,X111) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Public_OpublicKey__inject_1) ).
fof(f9664,plain,
spl0_1219,
inference(avatar_split_clause,[],[f2919,f9662]) ).
fof(f9662,plain,
( spl0_1219
<=> ! [X4,X111,X12,X27] :
( X4 = X27
| c_Public_OpublicKey(X27,X12) != c_Public_OpublicKey(X4,X111) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1219])]) ).
fof(f2919,axiom,
! [X111,X27,X4,X12] :
( X4 = X27
| c_Public_OpublicKey(X27,X12) != c_Public_OpublicKey(X4,X111) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Public_OpublicKey__inject_0) ).
fof(f9660,plain,
spl0_1218,
inference(avatar_split_clause,[],[f2898,f9658]) ).
fof(f9658,plain,
( spl0_1218
<=> ! [X102,X27,X12] : c_in(c_Message_Omsg_OKey(c_Public_OpublicKey(X27,X12)),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,X102)),tc_Message_Omsg) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1218])]) ).
fof(f2898,axiom,
! [X27,X12,X102] : c_in(c_Message_Omsg_OKey(c_Public_OpublicKey(X27,X12)),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,X102)),tc_Message_Omsg),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Public_Oanalz__spies__pubK_0) ).
fof(f9656,plain,
spl0_1217,
inference(avatar_split_clause,[],[f2883,f9654]) ).
fof(f2883,axiom,
! [X88] : c_Message_Oparts(c_Message_Osynth(X88)) = c_union(c_Message_Oparts(X88),c_Message_Osynth(X88),tc_Message_Omsg),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oparts__synth_0) ).
fof(f9652,plain,
spl0_1216,
inference(avatar_split_clause,[],[f2865,f9650]) ).
fof(f2865,axiom,
! [X88] : c_Message_Oanalz(c_Message_Osynth(X88)) = c_union(c_Message_Oanalz(X88),c_Message_Osynth(X88),tc_Message_Omsg),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oanalz__synth_0) ).
fof(f9648,plain,
spl0_1215,
inference(avatar_split_clause,[],[f2852,f9646]) ).
fof(f2852,axiom,
! [X88,X86] :
( ~ c_in(X86,c_Message_Oanalz(X88),tc_Message_Omsg)
| c_in(X86,c_Message_Oparts(X88),tc_Message_Omsg) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oanalz__conj__parts_0) ).
fof(f9644,plain,
spl0_1214,
inference(avatar_split_clause,[],[f2800,f9642]) ).
fof(f9642,plain,
( spl0_1214
<=> ! [X102,X86,X12] : c_Event_Oused(X102) = c_Event_Oused(c_List_Olist_OCons(c_Event_Oevent_OGets(X12,X86),X102,tc_Event_Oevent)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1214])]) ).
fof(f2800,axiom,
! [X86,X102,X12] : c_Event_Oused(X102) = c_Event_Oused(c_List_Olist_OCons(c_Event_Oevent_OGets(X12,X86),X102,tc_Event_Oevent)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Event_Oused__Gets_0) ).
fof(f9640,plain,
spl0_1213,
inference(avatar_split_clause,[],[f2787,f9638]) ).
fof(f9638,plain,
( spl0_1213
<=> ! [X96,X97,X94,X95] :
( X96 = X97
| c_Event_Oevent_ONotes(X95,X97) != c_Event_Oevent_ONotes(X94,X96) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1213])]) ).
fof(f2787,axiom,
! [X96,X94,X97,X95] :
( X96 = X97
| c_Event_Oevent_ONotes(X95,X97) != c_Event_Oevent_ONotes(X94,X96) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Event_Oevent_Oinject__3_1) ).
fof(f9636,plain,
( spl0_1212
| ~ spl0_69
| ~ spl0_975 ),
inference(avatar_split_clause,[],[f8603,f8331,f3752,f9634]) ).
fof(f9634,plain,
( spl0_1212
<=> ! [X0] : c_times(X0,c_1,tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1212])]) ).
fof(f3752,plain,
( spl0_69
<=> class_OrderedGroup_Omonoid__mult(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_69])]) ).
fof(f8331,plain,
( spl0_975
<=> ! [X1,X3] :
( ~ class_OrderedGroup_Omonoid__mult(X1)
| c_times(X3,c_1,X1) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_975])]) ).
fof(f8603,plain,
( ! [X0] : c_times(X0,c_1,tc_nat) = X0
| ~ spl0_69
| ~ spl0_975 ),
inference(resolution,[],[f8332,f3754]) ).
fof(f3754,plain,
( class_OrderedGroup_Omonoid__mult(tc_nat)
| ~ spl0_69 ),
inference(avatar_component_clause,[],[f3752]) ).
fof(f8332,plain,
( ! [X3,X1] :
( ~ class_OrderedGroup_Omonoid__mult(X1)
| c_times(X3,c_1,X1) = X3 )
| ~ spl0_975 ),
inference(avatar_component_clause,[],[f8331]) ).
fof(f9632,plain,
spl0_1211,
inference(avatar_split_clause,[],[f2786,f9630]) ).
fof(f9630,plain,
( spl0_1211
<=> ! [X95,X97,X94,X96] :
( X94 = X95
| c_Event_Oevent_ONotes(X95,X97) != c_Event_Oevent_ONotes(X94,X96) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1211])]) ).
fof(f2786,axiom,
! [X96,X94,X97,X95] :
( X94 = X95
| c_Event_Oevent_ONotes(X95,X97) != c_Event_Oevent_ONotes(X94,X96) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Event_Oevent_Oinject__3_0) ).
fof(f9628,plain,
spl0_1210,
inference(avatar_split_clause,[],[f2785,f9626]) ).
fof(f9626,plain,
( spl0_1210
<=> ! [X96,X97,X94,X95] :
( X96 = X97
| c_Event_Oevent_OGets(X95,X97) != c_Event_Oevent_OGets(X94,X96) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1210])]) ).
fof(f2785,axiom,
! [X96,X94,X97,X95] :
( X96 = X97
| c_Event_Oevent_OGets(X95,X97) != c_Event_Oevent_OGets(X94,X96) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Event_Oevent_Oinject__2_1) ).
fof(f9624,plain,
spl0_1209,
inference(avatar_split_clause,[],[f2784,f9622]) ).
fof(f9622,plain,
( spl0_1209
<=> ! [X95,X97,X94,X96] :
( X94 = X95
| c_Event_Oevent_OGets(X95,X97) != c_Event_Oevent_OGets(X94,X96) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1209])]) ).
fof(f2784,axiom,
! [X96,X94,X97,X95] :
( X94 = X95
| c_Event_Oevent_OGets(X95,X97) != c_Event_Oevent_OGets(X94,X96) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Event_Oevent_Oinject__2_0) ).
fof(f9620,plain,
spl0_1208,
inference(avatar_split_clause,[],[f2759,f9618]) ).
fof(f9618,plain,
( spl0_1208
<=> ! [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_1208])]) ).
fof(f2759,axiom,
! [X90,X89,X96,X97] :
( X96 = X97
| c_Message_Omsg_OCrypt(X90,X96) != c_Message_Omsg_OCrypt(X89,X97) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Omsg_Oinject__7_1) ).
fof(f9616,plain,
spl0_1207,
inference(avatar_split_clause,[],[f2758,f9614]) ).
fof(f9614,plain,
( spl0_1207
<=> ! [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_1207])]) ).
fof(f2758,axiom,
! [X90,X89,X96,X97] :
( X89 = X90
| c_Message_Omsg_OCrypt(X90,X96) != c_Message_Omsg_OCrypt(X89,X97) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Omsg_Oinject__7_0) ).
fof(f9612,plain,
spl0_1206,
inference(avatar_split_clause,[],[f2757,f9610]) ).
fof(f9610,plain,
( spl0_1206
<=> ! [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_1206])]) ).
fof(f2757,axiom,
! [X101,X98,X99,X100] :
( X99 = X101
| c_Message_Omsg_OMPair(X98,X99) != c_Message_Omsg_OMPair(X100,X101) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Omsg_Oinject__6_1) ).
fof(f9608,plain,
spl0_1205,
inference(avatar_split_clause,[],[f2756,f9606]) ).
fof(f9606,plain,
( spl0_1205
<=> ! [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_1205])]) ).
fof(f2756,axiom,
! [X101,X98,X99,X100] :
( X98 = X100
| c_Message_Omsg_OMPair(X98,X99) != c_Message_Omsg_OMPair(X100,X101) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Omsg_Oinject__6_0) ).
fof(f9604,plain,
spl0_1204,
inference(avatar_split_clause,[],[f2748,f9602]) ).
fof(f9602,plain,
( spl0_1204
<=> ! [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_1204])]) ).
fof(f2748,axiom,
! [X88,X86,X87] : c_Message_OkeysFor(X88) = c_Message_OkeysFor(c_insert(c_Message_Omsg_OMPair(X86,X87),X88,tc_Message_Omsg)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OkeysFor__insert__MPair_0) ).
fof(f9600,plain,
spl0_1203,
inference(avatar_split_clause,[],[f2671,f9598]) ).
fof(f9598,plain,
( spl0_1203
<=> ! [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_1203])]) ).
fof(f2671,axiom,
! [X1,X12] :
( c_emptyset != c_Main_Oempty__Union__conv__1(X12,X1)
| c_emptyset = c_Union(X12,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Oempty__Union__conv_2) ).
fof(f9596,plain,
spl0_1202,
inference(avatar_split_clause,[],[f2654,f9594]) ).
fof(f9594,plain,
( spl0_1202
<=> ! [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_1202])]) ).
fof(f2654,axiom,
! [X1,X12] :
( c_emptyset != c_Main_OUnion__empty__conv__1(X12,X1)
| c_emptyset = c_Union(X12,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUnion__empty__conv_2) ).
fof(f9592,plain,
( spl0_1201
| ~ spl0_20
| ~ spl0_975 ),
inference(avatar_split_clause,[],[f8602,f8331,f3507,f9590]) ).
fof(f9590,plain,
( spl0_1201
<=> ! [X0] : c_times(X0,c_1,tc_IntDef_Oint) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1201])]) ).
fof(f3507,plain,
( spl0_20
<=> class_OrderedGroup_Omonoid__mult(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_20])]) ).
fof(f8602,plain,
( ! [X0] : c_times(X0,c_1,tc_IntDef_Oint) = X0
| ~ spl0_20
| ~ spl0_975 ),
inference(resolution,[],[f8332,f3509]) ).
fof(f3509,plain,
( class_OrderedGroup_Omonoid__mult(tc_IntDef_Oint)
| ~ spl0_20 ),
inference(avatar_component_clause,[],[f3507]) ).
fof(f9588,plain,
spl0_1200,
inference(avatar_split_clause,[],[f2618,f9586]) ).
fof(f9586,plain,
( spl0_1200
<=> ! [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_1200])]) ).
fof(f2618,axiom,
! [X1,X12] :
( c_UNIV != c_Main_OInter__UNIV__conv__2__1(X12,X1)
| c_UNIV = c_Inter(X12,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OInter__UNIV__conv__2_2) ).
fof(f9584,plain,
spl0_1199,
inference(avatar_split_clause,[],[f2615,f9582]) ).
fof(f9582,plain,
( spl0_1199
<=> ! [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_1199])]) ).
fof(f2615,axiom,
! [X1,X12] :
( c_UNIV != c_Main_OInter__UNIV__conv__1__1(X12,X1)
| c_UNIV = c_Inter(X12,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OInter__UNIV__conv__1_2) ).
fof(f9580,plain,
spl0_1198,
inference(avatar_split_clause,[],[f2388,f9578]) ).
fof(f2388,axiom,
! [X0,X1] : c_in(c_Pair(X0,X0,X1,X1),c_Relation_OId,tc_prod(X1,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_Opair__in__Id__conv_1) ).
fof(f9576,plain,
spl0_1197,
inference(avatar_split_clause,[],[f2383,f9574]) ).
fof(f2383,axiom,
! [X1,X12] : c_Relation_Odiag(X12,X1) = c_Relation_Oconverse(c_Relation_Odiag(X12,X1),X1,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_Oconverse__diag_0) ).
fof(f9572,plain,
spl0_1196,
inference(avatar_split_clause,[],[f2366,f9570]) ).
fof(f2366,axiom,
! [X2,X3,X18,X1] : c_snd(c_Pair(X18,X3,X2,X1),X2,X1) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Product__Type_Osnd__conv_0) ).
fof(f9568,plain,
spl0_1195,
inference(avatar_split_clause,[],[f2364,f9566]) ).
fof(f2364,axiom,
! [X2,X3,X1,X27] : c_fst(c_Pair(X3,X27,X1,X2),X1,X2) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Product__Type_Ofst__conv_0) ).
fof(f9564,plain,
spl0_1194,
inference(avatar_split_clause,[],[f2342,f9562]) ).
fof(f9562,plain,
( spl0_1194
<=> ! [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_1194])]) ).
fof(f2342,axiom,
! [X21,X0] :
( c_0 = X0
| c_less(c_0,c_Nat_Opower(X0,X21,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Power_Onat__zero__less__power__iff_1) ).
fof(f9560,plain,
spl0_1193,
inference(avatar_split_clause,[],[f2341,f9558]) ).
fof(f9558,plain,
( spl0_1193
<=> ! [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_1193])]) ).
fof(f2341,axiom,
! [X21] :
( c_0 = X21
| ~ c_less(c_0,c_Nat_Opower(c_0,X21,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Power_Onat__zero__less__power__iff_0) ).
fof(f9556,plain,
spl0_1192,
inference(avatar_split_clause,[],[f2294,f9554]) ).
fof(f9554,plain,
( spl0_1192
<=> ! [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_1192])]) ).
fof(f2294,axiom,
! [X21,X0] :
( c_less(c_0,X21,tc_nat)
| ~ c_Parity_Oeven(c_Nat_Opower(X0,X21,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__power_1) ).
fof(f9552,plain,
spl0_1191,
inference(avatar_split_clause,[],[f2281,f9550]) ).
fof(f9550,plain,
( spl0_1191
<=> ! [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_1191])]) ).
fof(f2281,axiom,
! [X3,X0] :
( c_less(c_0,X3,tc_nat)
| ~ c_Parity_Oeven(c_Nat_Opower(X0,X3,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__nat__power_1) ).
fof(f9548,plain,
( spl0_1190
| ~ spl0_69
| ~ spl0_974 ),
inference(avatar_split_clause,[],[f8601,f8327,f3752,f9546]) ).
fof(f9546,plain,
( spl0_1190
<=> ! [X0] : c_times(c_1,X0,tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1190])]) ).
fof(f8327,plain,
( spl0_974
<=> ! [X1,X3] :
( ~ class_OrderedGroup_Omonoid__mult(X1)
| c_times(c_1,X3,X1) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_974])]) ).
fof(f8601,plain,
( ! [X0] : c_times(c_1,X0,tc_nat) = X0
| ~ spl0_69
| ~ spl0_974 ),
inference(resolution,[],[f8328,f3754]) ).
fof(f8328,plain,
( ! [X3,X1] :
( ~ class_OrderedGroup_Omonoid__mult(X1)
| c_times(c_1,X3,X1) = X3 )
| ~ spl0_974 ),
inference(avatar_component_clause,[],[f8327]) ).
fof(f9544,plain,
spl0_1189,
inference(avatar_split_clause,[],[f2247,f9542]) ).
fof(f2247,axiom,
! [X1,X18] :
( ~ class_OrderedGroup_Oab__group__add(X1)
| c_0 = c_plus(X18,c_uminus(X18,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oright__minus_0) ).
fof(f9540,plain,
spl0_1188,
inference(avatar_split_clause,[],[f2219,f9538]) ).
fof(f9538,plain,
( spl0_1188
<=> ! [X18,X1] :
( ~ class_OrderedGroup_Oab__group__add(X1)
| c_0 = X18
| c_0 != c_uminus(X18,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1188])]) ).
fof(f2219,axiom,
! [X1,X18] :
( ~ class_OrderedGroup_Oab__group__add(X1)
| c_0 = X18
| c_0 != c_uminus(X18,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__0__equal__iff__equal_0) ).
fof(f9536,plain,
spl0_1187,
inference(avatar_split_clause,[],[f2213,f9534]) ).
fof(f9534,plain,
( spl0_1187
<=> ! [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_1187])]) ).
fof(f2213,axiom,
! [X1] :
( ~ class_OrderedGroup_Olordered__ab__group(X1)
| c_0 = c_LOrder_Omeet(c_0,c_uminus(c_0,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Omeet__0__eq__0_1) ).
fof(f9532,plain,
spl0_1186,
inference(avatar_split_clause,[],[f2211,f9530]) ).
fof(f9530,plain,
( spl0_1186
<=> ! [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_1186])]) ).
fof(f2211,axiom,
! [X1] :
( ~ class_OrderedGroup_Olordered__ab__group(X1)
| c_0 = c_LOrder_Ojoin(c_0,c_uminus(c_0,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Ojoin__0__eq__0_1) ).
fof(f9528,plain,
spl0_1185,
inference(avatar_split_clause,[],[f2197,f9526]) ).
fof(f2197,axiom,
! [X1,X18] :
( ~ class_OrderedGroup_Oab__group__add(X1)
| c_uminus(X18,X1) = c_minus(c_0,X18,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Odiff__0_0) ).
fof(f9524,plain,
spl0_1184,
inference(avatar_split_clause,[],[f2175,f9522]) ).
fof(f9522,plain,
( spl0_1184
<=> ! [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_1184])]) ).
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/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__eq__0_0) ).
fof(f9520,plain,
spl0_1183,
inference(avatar_split_clause,[],[f2171,f9518]) ).
fof(f2171,axiom,
! [X1,X18] :
( ~ class_OrderedGroup_Oab__group__add(X1)
| c_0 = c_plus(c_uminus(X18,X1),X18,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oab__group__add__class_Oaxioms__1_0) ).
fof(f9516,plain,
spl0_1182,
inference(avatar_split_clause,[],[f2039,f9514]) ).
fof(f2039,axiom,
! [X21,X15] :
( ~ c_lessequals(X15,X21,tc_nat)
| c_0 = c_minus(X15,X21,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Odiff__is__0__eq_H_0) ).
fof(f9512,plain,
spl0_1181,
inference(avatar_split_clause,[],[f2038,f9510]) ).
fof(f2038,axiom,
! [X21,X15] :
( c_lessequals(X15,X21,tc_nat)
| c_0 != c_minus(X15,X21,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Odiff__is__0__eq_0) ).
fof(f9508,plain,
spl0_1180,
inference(avatar_split_clause,[],[f1849,f9506]) ).
fof(f1849,axiom,
! [X47] :
( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 = c_Numeral_Onumber__of(X47,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatBin_Oeq__number__of__0_2) ).
fof(f9504,plain,
( spl0_1179
| ~ spl0_20
| ~ spl0_974 ),
inference(avatar_split_clause,[],[f8600,f8327,f3507,f9502]) ).
fof(f9502,plain,
( spl0_1179
<=> ! [X0] : c_times(c_1,X0,tc_IntDef_Oint) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1179])]) ).
fof(f8600,plain,
( ! [X0] : c_times(c_1,X0,tc_IntDef_Oint) = X0
| ~ spl0_20
| ~ spl0_974 ),
inference(resolution,[],[f8328,f3509]) ).
fof(f9500,plain,
spl0_1178,
inference(avatar_split_clause,[],[f1832,f9498]) ).
fof(f9498,plain,
( spl0_1178
<=> ! [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_1178])]) ).
fof(f1832,axiom,
! [X47] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 = c_Numeral_Onumber__of(X47,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatBin_Oeq__0__number__of_1) ).
fof(f9496,plain,
spl0_1177,
inference(avatar_split_clause,[],[f1803,f9494]) ).
fof(f9494,plain,
( spl0_1177
<=> ! [X21,X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| c_0 = X21
| c_0 != c_NatArith_Oof__nat(X21,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1177])]) ).
fof(f1803,axiom,
! [X21,X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| c_0 = X21
| c_0 != c_NatArith_Oof__nat(X21,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__0__eq__iff_0) ).
fof(f9492,plain,
spl0_1176,
inference(avatar_split_clause,[],[f1759,f9490]) ).
fof(f9490,plain,
( spl0_1176
<=> ! [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_1176])]) ).
fof(f1759,axiom,
! [X21,X1,X23] : c_List_Oset(X23,X1) = c_List_Oset(c_List_Orotate(X21,X23,X1),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oset__rotate_0) ).
fof(f9488,plain,
spl0_1175,
inference(avatar_split_clause,[],[f1730,f9486]) ).
fof(f9486,plain,
( spl0_1175
<=> ! [X25,X1,X23] :
( X23 = X25
| c_List_Orev(X23,X1) != c_List_Orev(X25,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1175])]) ).
fof(f1730,axiom,
! [X1,X25,X23] :
( X23 = X25
| c_List_Orev(X23,X1) != c_List_Orev(X25,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Orev__is__rev__conv_0) ).
fof(f9484,plain,
spl0_1174,
inference(avatar_split_clause,[],[f1603,f9482]) ).
fof(f9482,plain,
( spl0_1174
<=> ! [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_1174])]) ).
fof(f1603,axiom,
! [X1,X23] :
( c_List_Olist_ONil = X23
| c_less(c_0,c_Nat_Osize(X23,tc_List_Olist(X1)),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olength__greater__0__conv_1) ).
fof(f9480,plain,
spl0_1173,
inference(avatar_split_clause,[],[f1548,f9478]) ).
fof(f9478,plain,
( spl0_1173
<=> ! [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_1173])]) ).
fof(f1548,axiom,
! [X50,X1] :
( c_List_Olist_ONil != c_Main_Oconcat__eq__Nil__conv__1(X50,X1)
| c_List_Olist_ONil = c_List_Oconcat(X50,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oconcat__eq__Nil__conv_2) ).
fof(f9476,plain,
spl0_1172,
inference(avatar_split_clause,[],[f1541,f9474]) ).
fof(f9474,plain,
( spl0_1172
<=> ! [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_1172])]) ).
fof(f1541,axiom,
! [X56,X54,X57,X55] :
( X55 = X57
| c_List_Ochar_OChar(X54,X55) != c_List_Ochar_OChar(X56,X57) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Ochar_Oinject_1) ).
fof(f9472,plain,
spl0_1171,
inference(avatar_split_clause,[],[f1540,f9470]) ).
fof(f9470,plain,
( spl0_1171
<=> ! [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_1171])]) ).
fof(f1540,axiom,
! [X56,X54,X57,X55] :
( X54 = X56
| c_List_Ochar_OChar(X54,X55) != c_List_Ochar_OChar(X56,X57) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Ochar_Oinject_0) ).
fof(f9468,plain,
spl0_1170,
inference(avatar_split_clause,[],[f1509,f9466]) ).
fof(f9466,plain,
( spl0_1170
<=> ! [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_1170])]) ).
fof(f1509,axiom,
! [X50,X1] :
( c_List_Olist_ONil != c_Main_ONil__eq__concat__conv__1(X50,X1)
| c_List_Olist_ONil = c_List_Oconcat(X50,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_ONil__eq__concat__conv_2) ).
fof(f9464,plain,
spl0_1169,
inference(avatar_split_clause,[],[f1488,f9462]) ).
fof(f9462,plain,
( spl0_1169
<=> ! [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_1169])]) ).
fof(f1488,axiom,
! [X48,X11] :
( ~ c_Divides_Oop_Advd(X48,X11,tc_IntDef_Oint)
| c_Divides_Oop_Advd(c_uminus(X48,tc_IntDef_Oint),X11,tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozminus__dvd__iff_1) ).
fof(f9460,plain,
( spl0_1168
| ~ spl0_14
| ~ spl0_973 ),
inference(avatar_split_clause,[],[f8599,f8323,f3477,f9458]) ).
fof(f9458,plain,
( spl0_1168
<=> ! [X0] : c_0 = c_minus(X0,X0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1168])]) ).
fof(f8323,plain,
( spl0_973
<=> ! [X18,X1] :
( ~ class_OrderedGroup_Oab__group__add(X1)
| c_0 = c_minus(X18,X18,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_973])]) ).
fof(f8599,plain,
( ! [X0] : c_0 = c_minus(X0,X0,tc_IntDef_Oint)
| ~ spl0_14
| ~ spl0_973 ),
inference(resolution,[],[f8324,f3479]) ).
fof(f8324,plain,
( ! [X1,X18] :
( ~ class_OrderedGroup_Oab__group__add(X1)
| c_0 = c_minus(X18,X18,X1) )
| ~ spl0_973 ),
inference(avatar_component_clause,[],[f8323]) ).
fof(f9456,plain,
spl0_1167,
inference(avatar_split_clause,[],[f1487,f9454]) ).
fof(f1487,axiom,
! [X48,X11] :
( c_Divides_Oop_Advd(X48,X11,tc_IntDef_Oint)
| ~ c_Divides_Oop_Advd(c_uminus(X48,tc_IntDef_Oint),X11,tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozminus__dvd__iff_0) ).
fof(f9451,plain,
spl0_1166,
inference(avatar_split_clause,[],[f1467,f9449]) ).
fof(f1467,axiom,
! [X18] : c_div(X18,c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),tc_IntDef_Oint) = c_uminus(X18,tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozdiv__minus1__right_0) ).
fof(f9447,plain,
spl0_1165,
inference(avatar_split_clause,[],[f1440,f9445]) ).
fof(f9445,plain,
( spl0_1165
<=> ! [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_1165])]) ).
fof(f1440,axiom,
! [X48,X11] :
( ~ c_Divides_Oop_Advd(X48,X11,tc_IntDef_Oint)
| c_Divides_Oop_Advd(X48,c_uminus(X11,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Odvd__zminus__iff_1) ).
fof(f9443,plain,
spl0_1164,
inference(avatar_split_clause,[],[f1439,f9441]) ).
fof(f1439,axiom,
! [X48,X11] :
( c_Divides_Oop_Advd(X48,X11,tc_IntDef_Oint)
| ~ c_Divides_Oop_Advd(X48,c_uminus(X11,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Odvd__zminus__iff_0) ).
fof(f9439,plain,
spl0_1163,
inference(avatar_split_clause,[],[f1430,f9437]) ).
fof(f9437,plain,
( spl0_1163
<=> ! [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_1163])]) ).
fof(f1430,axiom,
! [X48,X11] :
( c_less(X11,X48,tc_IntDef_Oint)
| ~ c_less(c_IntDef_Onat(X11),c_IntDef_Onat(X48),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Ozless__nat__conj_1) ).
fof(f9435,plain,
spl0_1162,
inference(avatar_split_clause,[],[f1429,f9433]) ).
fof(f9433,plain,
( spl0_1162
<=> ! [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_1162])]) ).
fof(f1429,axiom,
! [X48,X11] :
( c_less(c_0,X48,tc_IntDef_Oint)
| ~ c_less(c_IntDef_Onat(X11),c_IntDef_Onat(X48),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Ozless__nat__conj_0) ).
fof(f9431,plain,
spl0_1161,
inference(avatar_split_clause,[],[f1428,f9429]) ).
fof(f9429,plain,
( spl0_1161
<=> ! [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_1161])]) ).
fof(f1428,axiom,
! [X21,X15] :
( ~ c_less(X15,X21,tc_nat)
| c_less(c_IntDef_Oint(X15),c_IntDef_Oint(X21),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Ozless__int_1) ).
fof(f9427,plain,
spl0_1160,
inference(avatar_split_clause,[],[f1427,f9425]) ).
fof(f9425,plain,
( spl0_1160
<=> ! [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_1160])]) ).
fof(f1427,axiom,
! [X21,X15] :
( c_less(X15,X21,tc_nat)
| ~ c_less(c_IntDef_Oint(X15),c_IntDef_Oint(X21),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Ozless__int_0) ).
fof(f9423,plain,
spl0_1159,
inference(avatar_split_clause,[],[f1426,f9421]) ).
fof(f9421,plain,
( spl0_1159
<=> ! [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_1159])]) ).
fof(f1426,axiom,
! [X21,X15] :
( ~ c_lessequals(X15,X21,tc_nat)
| c_lessequals(c_IntDef_Oint(X15),c_IntDef_Oint(X21),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Ozle__int_1) ).
fof(f9419,plain,
spl0_1158,
inference(avatar_split_clause,[],[f1425,f9417]) ).
fof(f9417,plain,
( spl0_1158
<=> ! [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_1158])]) ).
fof(f1425,axiom,
! [X21,X15] :
( c_lessequals(X15,X21,tc_nat)
| ~ c_lessequals(c_IntDef_Oint(X15),c_IntDef_Oint(X21),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Ozle__int_0) ).
fof(f9415,plain,
( spl0_1157
| ~ spl0_14
| ~ spl0_972 ),
inference(avatar_split_clause,[],[f8598,f8319,f3477,f9413]) ).
fof(f9413,plain,
( spl0_1157
<=> ! [X0] : c_minus(X0,c_0,tc_IntDef_Oint) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1157])]) ).
fof(f8319,plain,
( spl0_972
<=> ! [X1,X3] :
( ~ class_OrderedGroup_Oab__group__add(X1)
| c_minus(X3,c_0,X1) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_972])]) ).
fof(f8598,plain,
( ! [X0] : c_minus(X0,c_0,tc_IntDef_Oint) = X0
| ~ spl0_14
| ~ spl0_972 ),
inference(resolution,[],[f8320,f3479]) ).
fof(f8320,plain,
( ! [X3,X1] :
( ~ class_OrderedGroup_Oab__group__add(X1)
| c_minus(X3,c_0,X1) = X3 )
| ~ spl0_972 ),
inference(avatar_component_clause,[],[f8319]) ).
fof(f9411,plain,
spl0_1156,
inference(avatar_split_clause,[],[f1407,f9409]) ).
fof(f1407,axiom,
! [X21,X1] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X1)
| c_IntDef_Oof__int(c_IntDef_Oint(X21),X1) = c_NatArith_Oof__nat(X21,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oof__int__int__eq_0) ).
fof(f9407,plain,
spl0_1155,
inference(avatar_split_clause,[],[f1404,f9405]) ).
fof(f9405,plain,
( spl0_1155
<=> ! [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_1155])]) ).
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/benchmark/theBenchmark.p',cls_IntDef_Oof__int__eq__0__iff_0) ).
fof(f9403,plain,
spl0_1154,
inference(avatar_split_clause,[],[f1390,f9401]) ).
fof(f9401,plain,
( spl0_1154
<=> ! [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_1154])]) ).
fof(f1390,axiom,
! [X21,X15] :
( c_0 = X15
| c_uminus(c_IntDef_Oint(X21),tc_IntDef_Oint) != c_IntDef_Oint(X15) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Onegative__eq__positive_1) ).
fof(f9399,plain,
spl0_1153,
inference(avatar_split_clause,[],[f1389,f9397]) ).
fof(f9397,plain,
( spl0_1153
<=> ! [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_1153])]) ).
fof(f1389,axiom,
! [X21,X15] :
( c_0 = X21
| c_uminus(c_IntDef_Oint(X21),tc_IntDef_Oint) != c_IntDef_Oint(X15) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Onegative__eq__positive_0) ).
fof(f9395,plain,
spl0_1152,
inference(avatar_split_clause,[],[f1279,f9393]) ).
fof(f1279,axiom,
! [X1,X12] :
( c_0 = c_Finite__Set_Ocard(X12,X1)
| c_in(X12,c_Finite__Set_OFinites,tc_set(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ocard__infinite_0) ).
fof(f9391,plain,
spl0_1151,
inference(avatar_split_clause,[],[f1275,f9389]) ).
fof(f1275,axiom,
! [X3,X1] :
( ~ class_Orderings_Olinorder(X1)
| c_Finite__Set_OMin(c_insert(X3,c_emptyset,X1),X1) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_OMin__singleton_0) ).
fof(f9387,plain,
spl0_1150,
inference(avatar_split_clause,[],[f1265,f9385]) ).
fof(f1265,axiom,
! [X3,X1] :
( ~ class_Orderings_Olinorder(X1)
| c_Finite__Set_OMax(c_insert(X3,c_emptyset,X1),X1) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_OMax__singleton_0) ).
fof(f9383,plain,
spl0_1149,
inference(avatar_split_clause,[],[f1235,f9381]) ).
fof(f9381,plain,
( spl0_1149
<=> ! [X21,X3] :
( ~ c_less(X3,X21,tc_nat)
| c_Divides_Oop_Amod(X3,X21,tc_nat) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1149])]) ).
fof(f1235,axiom,
! [X21,X3] :
( ~ c_less(X3,X21,tc_nat)
| c_Divides_Oop_Amod(X3,X21,tc_nat) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Omod__less_0) ).
fof(f9379,plain,
spl0_1148,
inference(avatar_split_clause,[],[f1224,f9377]) ).
fof(f9377,plain,
( spl0_1148
<=> ! [X21] :
( ~ c_less(c_0,X21,tc_nat)
| c_1 = c_div(X21,X21,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1148])]) ).
fof(f1224,axiom,
! [X21] :
( ~ c_less(c_0,X21,tc_nat)
| c_1 = c_div(X21,X21,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Odiv__self_0) ).
fof(f9375,plain,
spl0_1147,
inference(avatar_split_clause,[],[f1216,f9373]) ).
fof(f9373,plain,
( spl0_1147
<=> ! [X21,X15] :
( ~ c_less(X15,X21,tc_nat)
| c_0 = c_div(X15,X21,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1147])]) ).
fof(f1216,axiom,
! [X21,X15] :
( ~ c_less(X15,X21,tc_nat)
| c_0 = c_div(X15,X21,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Odiv__less_0) ).
fof(f9370,plain,
spl0_1146,
inference(avatar_split_clause,[],[f1200,f9368]) ).
fof(f9368,plain,
( spl0_1146
<=> ! [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_1146])]) ).
fof(f1200,axiom,
! [X2,X1,X18,X9,X7] : c_Datatype__Universe_OScons(X9,X7,X1,X2) != c_Datatype__Universe_OLeaf(X18,X1,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OScons__not__Leaf_0) ).
fof(f9366,plain,
spl0_1145,
inference(avatar_split_clause,[],[f1199,f9364]) ).
fof(f9364,plain,
( spl0_1145
<=> ! [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_1145])]) ).
fof(f1199,axiom,
! [X2,X1,X18,X9,X7] : c_Datatype__Universe_OScons(X9,X7,X1,X2) != c_Datatype__Universe_OAtom(X18,X1,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OScons__not__Atom_0) ).
fof(f9362,plain,
spl0_1144,
inference(avatar_split_clause,[],[f1196,f9360]) ).
fof(f9360,plain,
( spl0_1144
<=> ! [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_1144])]) ).
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/benchmark/theBenchmark.p',cls_Datatype__Universe_ONumb__not__Scons_0) ).
fof(f9358,plain,
spl0_1143,
inference(avatar_split_clause,[],[f1180,f9356]) ).
fof(f9356,plain,
( spl0_1143
<=> ! [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_1143])]) ).
fof(f1180,axiom,
! [X2,X1,X27] : c_0 = c_Nat_Osize(c_Sum__Type_OInr(X27,X2,X1),tc_sum(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype_Osum_Osize__2_0) ).
fof(f9354,plain,
spl0_1142,
inference(avatar_split_clause,[],[f1179,f9352]) ).
fof(f9352,plain,
( spl0_1142
<=> ! [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_1142])]) ).
fof(f1179,axiom,
! [X2,X18,X1] : c_0 = c_Nat_Osize(c_Sum__Type_OInl(X18,X1,X2),tc_sum(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype_Osum_Osize__1_0) ).
fof(f9350,plain,
spl0_1141,
inference(avatar_split_clause,[],[f1175,f9348]) ).
fof(f9348,plain,
( spl0_1141
<=> ! [X18,X1,X42] :
( X18 = X42
| c_Datatype_Ooption_OSome(X42,X1) != c_Datatype_Ooption_OSome(X18,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1141])]) ).
fof(f1175,axiom,
! [X18,X1,X42] :
( X18 = X42
| c_Datatype_Ooption_OSome(X42,X1) != c_Datatype_Ooption_OSome(X18,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype_Ooption_Oinject_0) ).
fof(f9346,plain,
spl0_1140,
inference(avatar_split_clause,[],[f1170,f9344]) ).
fof(f9344,plain,
( spl0_1140
<=> ! [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_1140])]) ).
fof(f1170,axiom,
! [X41,X0] : c_Datatype_Oo2s(c_Datatype_Ooption_OSome(X0,X41),X41) = c_insert(X0,c_emptyset,X41),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype_Oo2s_Osimps__2_0) ).
fof(f9342,plain,
spl0_1139,
inference(avatar_split_clause,[],[f1169,f9340]) ).
fof(f9340,plain,
( spl0_1139
<=> ! [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_1139])]) ).
fof(f1169,axiom,
! [X0,X1] :
( c_Datatype_Ooption_ONone = X0
| c_Datatype_Ooption_OSome(c_Main_Onot__Some__eq__1(X0,X1),X1) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype_Onot__Some__eq_0) ).
fof(f9338,plain,
spl0_1138,
inference(avatar_split_clause,[],[f1168,f9336]) ).
fof(f9336,plain,
( spl0_1138
<=> ! [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_1138])]) ).
fof(f1168,axiom,
! [X0,X1] :
( c_Datatype_Ooption_ONone = X0
| c_Datatype_Ooption_OSome(c_Main_Onot__None__eq__1(X0,X1),X1) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype_Onot__None__eq_0) ).
fof(f9334,plain,
spl0_1137,
inference(avatar_split_clause,[],[f105,f9332]) ).
fof(f9332,plain,
( spl0_1137
<=> ! [X18,X27,X1] :
( X18 = X27
| ~ c_in(X27,c_insert(X18,c_emptyset,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1137])]) ).
fof(f105,axiom,
! [X18,X1,X27] :
( X18 = X27
| ~ c_in(X27,c_insert(X18,c_emptyset,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OsingletonD__dest_0) ).
fof(f9330,plain,
spl0_1136,
inference(avatar_split_clause,[],[f103,f9328]) ).
fof(f9328,plain,
( spl0_1136
<=> ! [X13,X12,X1] :
( ~ c_less(X12,X13,tc_set(X1))
| c_lessequals(X12,X13,tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1136])]) ).
fof(f103,axiom,
! [X1,X12,X13] :
( ~ c_less(X12,X13,tc_set(X1))
| c_lessequals(X12,X13,tc_set(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OpsubsetE_1) ).
fof(f9326,plain,
spl0_1135,
inference(avatar_split_clause,[],[f102,f9324]) ).
fof(f9324,plain,
( spl0_1135
<=> ! [X13,X12,X1] :
( ~ c_lessequals(X13,X12,tc_set(X1))
| ~ c_less(X12,X13,tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1135])]) ).
fof(f102,axiom,
! [X1,X12,X13] :
( ~ c_lessequals(X13,X12,tc_set(X1))
| ~ c_less(X12,X13,tc_set(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OpsubsetE_0) ).
fof(f9291,plain,
( ~ spl0_1134
| spl0_5
| ~ spl0_1105 ),
inference(avatar_split_clause,[],[f9283,f8987,f3432,f9288]) ).
fof(f9288,plain,
( spl0_1134
<=> c_in(c_Message_Omsg_OKey(v_K),c_Event_Oknows(c_Message_Oagent_OSpy,v_evso),tc_Message_Omsg) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1134])]) ).
fof(f8987,plain,
( spl0_1105
<=> ! [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_1105])]) ).
fof(f9283,plain,
( ~ c_in(c_Message_Omsg_OKey(v_K),c_Event_Oknows(c_Message_Oagent_OSpy,v_evso),tc_Message_Omsg)
| spl0_5
| ~ spl0_1105 ),
inference(resolution,[],[f8988,f3434]) ).
fof(f8988,plain,
( ! [X88,X86] :
( c_in(X86,c_Message_Oanalz(X88),tc_Message_Omsg)
| ~ c_in(X86,X88,tc_Message_Omsg) )
| ~ spl0_1105 ),
inference(avatar_component_clause,[],[f8987]) ).
fof(f9275,plain,
( spl0_1133
| ~ spl0_816
| ~ spl0_1089 ),
inference(avatar_split_clause,[],[f9255,f8923,f7605,f9273]) ).
fof(f9273,plain,
( spl0_1133
<=> ! [X0] : c_emptyset != c_Pow(c_emptyset,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1133])]) ).
fof(f9255,plain,
( ! [X0] : c_emptyset != c_Pow(c_emptyset,X0)
| ~ spl0_816
| ~ spl0_1089 ),
inference(superposition,[],[f7606,f8924]) ).
fof(f9251,plain,
( spl0_1132
| ~ spl0_914
| ~ spl0_1072 ),
inference(avatar_split_clause,[],[f9216,f8855,f8024,f9249]) ).
fof(f9249,plain,
( spl0_1132
<=> ! [X0] : c_List_Olist_ONil = c_List_Oupt(X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1132])]) ).
fof(f8024,plain,
( spl0_914
<=> ! [X0] : c_lessequals(X0,X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_914])]) ).
fof(f9216,plain,
( ! [X0] : c_List_Olist_ONil = c_List_Oupt(X0,X0)
| ~ spl0_914
| ~ spl0_1072 ),
inference(resolution,[],[f8856,f8025]) ).
fof(f8025,plain,
( ! [X0] : c_lessequals(X0,X0,tc_nat)
| ~ spl0_914 ),
inference(avatar_component_clause,[],[f8024]) ).
fof(f9203,plain,
( spl0_1131
| ~ spl0_816
| ~ spl0_1062 ),
inference(avatar_split_clause,[],[f9198,f8815,f7605,f9201]) ).
fof(f9201,plain,
( spl0_1131
<=> ! [X0] : c_emptyset != c_List_Olistset(c_List_Olist_ONil,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1131])]) ).
fof(f9198,plain,
( ! [X0] : c_emptyset != c_List_Olistset(c_List_Olist_ONil,X0)
| ~ spl0_816
| ~ spl0_1062 ),
inference(superposition,[],[f7606,f8816]) ).
fof(f9184,plain,
( spl0_1130
| ~ spl0_9
| ~ spl0_971 ),
inference(avatar_split_clause,[],[f8596,f8315,f3452,f9182]) ).
fof(f9182,plain,
( spl0_1130
<=> ! [X0] : c_plus(c_0,X0,tc_IntDef_Oint) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1130])]) ).
fof(f3452,plain,
( spl0_9
<=> class_OrderedGroup_Ocomm__monoid__add(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).
fof(f8315,plain,
( spl0_971
<=> ! [X1,X3] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| c_plus(c_0,X3,X1) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_971])]) ).
fof(f8596,plain,
( ! [X0] : c_plus(c_0,X0,tc_IntDef_Oint) = X0
| ~ spl0_9
| ~ spl0_971 ),
inference(resolution,[],[f8316,f3454]) ).
fof(f3454,plain,
( class_OrderedGroup_Ocomm__monoid__add(tc_IntDef_Oint)
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f3452]) ).
fof(f8316,plain,
( ! [X3,X1] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| c_plus(c_0,X3,X1) = X3 )
| ~ spl0_971 ),
inference(avatar_component_clause,[],[f8315]) ).
fof(f9151,plain,
( spl0_1129
| ~ spl0_9
| ~ spl0_970 ),
inference(avatar_split_clause,[],[f8594,f8311,f3452,f9149]) ).
fof(f8311,plain,
( spl0_970
<=> ! [X1,X3] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| c_plus(X3,c_0,X1) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_970])]) ).
fof(f8594,plain,
( ! [X0] : c_plus(X0,c_0,tc_IntDef_Oint) = X0
| ~ spl0_9
| ~ spl0_970 ),
inference(resolution,[],[f8312,f3454]) ).
fof(f8312,plain,
( ! [X3,X1] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| c_plus(X3,c_0,X1) = X3 )
| ~ spl0_970 ),
inference(avatar_component_clause,[],[f8311]) ).
fof(f9098,plain,
( spl0_1128
| ~ spl0_716
| ~ spl0_910
| ~ spl0_966 ),
inference(avatar_split_clause,[],[f8583,f8295,f7995,f7179,f9095]) ).
fof(f9095,plain,
( spl0_1128
<=> c_Numeral_OMin = c_Numeral_Obin__succ(c_Numeral_Obin__add(c_Numeral_OMin,c_Numeral_OMin)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1128])]) ).
fof(f8295,plain,
( spl0_966
<=> ! [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_966])]) ).
fof(f8583,plain,
( c_Numeral_OMin = c_Numeral_Obin__succ(c_Numeral_Obin__add(c_Numeral_OMin,c_Numeral_OMin))
| ~ spl0_716
| ~ spl0_910
| ~ spl0_966 ),
inference(forward_demodulation,[],[f8581,f7181]) ).
fof(f8581,plain,
( c_Numeral_OBit(c_Numeral_OMin,c_Numeral_Obit_OB1) = c_Numeral_Obin__succ(c_Numeral_Obin__add(c_Numeral_OMin,c_Numeral_OMin))
| ~ spl0_910
| ~ spl0_966 ),
inference(superposition,[],[f8296,f7997]) ).
fof(f8296,plain,
( ! [X11] : c_Numeral_OBit(X11,c_Numeral_Obit_OB1) = c_Numeral_Obin__succ(c_Numeral_OBit(X11,c_Numeral_Obit_OB0))
| ~ spl0_966 ),
inference(avatar_component_clause,[],[f8295]) ).
fof(f9077,plain,
spl0_1127,
inference(avatar_split_clause,[],[f3309,f9075]) ).
fof(f9075,plain,
( spl0_1127
<=> ! [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_1127])]) ).
fof(f3309,plain,
! [X48] :
( ~ c_less(c_1,c_IntDef_Onat(X48),tc_nat)
| c_less(c_1,X48,tc_IntDef_Oint) ),
inference(forward_demodulation,[],[f3121,f2958]) ).
fof(f3121,plain,
! [X48] :
( c_less(c_1,X48,tc_IntDef_Oint)
| ~ c_less(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),c_IntDef_Onat(X48),tc_nat) ),
inference(definition_unfolding,[],[f1346,f2544]) ).
fof(f1346,axiom,
! [X48] :
( c_less(c_1,X48,tc_IntDef_Oint)
| ~ c_less(c_Suc(c_0),c_IntDef_Onat(X48),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntArith_Oone__less__nat__eq_0) ).
fof(f9073,plain,
spl0_1126,
inference(avatar_split_clause,[],[f3298,f9071]) ).
fof(f3298,plain,
! [X48] :
( c_less(c_1,c_IntDef_Onat(X48),tc_nat)
| ~ c_less(c_1,X48,tc_IntDef_Oint) ),
inference(forward_demodulation,[],[f3106,f2958]) ).
fof(f3106,plain,
! [X48] :
( ~ c_less(c_1,X48,tc_IntDef_Oint)
| c_less(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),c_IntDef_Onat(X48),tc_nat) ),
inference(definition_unfolding,[],[f1347,f2544]) ).
fof(f1347,axiom,
! [X48] :
( ~ c_less(c_1,X48,tc_IntDef_Oint)
| c_less(c_Suc(c_0),c_IntDef_Onat(X48),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntArith_Oone__less__nat__eq_1) ).
fof(f9069,plain,
spl0_1125,
inference(avatar_split_clause,[],[f3293,f9067]) ).
fof(f9067,plain,
( spl0_1125
<=> ! [X21,X15] :
( c_1 != c_times(X15,X21,tc_nat)
| c_1 = X15 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1125])]) ).
fof(f3293,plain,
! [X21,X15] :
( c_1 != c_times(X15,X21,tc_nat)
| c_1 = X15 ),
inference(forward_demodulation,[],[f3098,f2958]) ).
fof(f3098,plain,
! [X21,X15] :
( c_1 = X15
| c_times(X15,X21,tc_nat) != c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f2092,f2544]) ).
fof(f2092,axiom,
! [X21,X15] :
( c_1 = X15
| c_Suc(c_0) != c_times(X15,X21,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oone__eq__mult__iff_0) ).
fof(f9065,plain,
( spl0_1124
| ~ spl0_87
| ~ spl0_949 ),
inference(avatar_split_clause,[],[f8552,f8227,f3842,f9063]) ).
fof(f9063,plain,
( spl0_1124
<=> ! [X0] : c_LOrder_Omeet(X0,X0,tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1124])]) ).
fof(f3842,plain,
( spl0_87
<=> class_LOrder_Omeet__semilorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_87])]) ).
fof(f8227,plain,
( spl0_949
<=> ! [X1,X3] :
( ~ class_LOrder_Omeet__semilorder(X1)
| c_LOrder_Omeet(X3,X3,X1) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_949])]) ).
fof(f8552,plain,
( ! [X0] : c_LOrder_Omeet(X0,X0,tc_nat) = X0
| ~ spl0_87
| ~ spl0_949 ),
inference(resolution,[],[f8228,f3844]) ).
fof(f3844,plain,
( class_LOrder_Omeet__semilorder(tc_nat)
| ~ spl0_87 ),
inference(avatar_component_clause,[],[f3842]) ).
fof(f8228,plain,
( ! [X3,X1] :
( ~ class_LOrder_Omeet__semilorder(X1)
| c_LOrder_Omeet(X3,X3,X1) = X3 )
| ~ spl0_949 ),
inference(avatar_component_clause,[],[f8227]) ).
fof(f9061,plain,
spl0_1123,
inference(avatar_split_clause,[],[f3292,f9059]) ).
fof(f9059,plain,
( spl0_1123
<=> ! [X21,X15] :
( c_1 != c_times(X15,X21,tc_nat)
| c_1 = X21 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1123])]) ).
fof(f3292,plain,
! [X21,X15] :
( c_1 != c_times(X15,X21,tc_nat)
| c_1 = X21 ),
inference(forward_demodulation,[],[f3097,f2958]) ).
fof(f3097,plain,
! [X21,X15] :
( c_1 = X21
| c_times(X15,X21,tc_nat) != c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f2093,f2544]) ).
fof(f2093,axiom,
! [X21,X15] :
( c_1 = X21
| c_Suc(c_0) != c_times(X15,X21,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oone__eq__mult__iff_1) ).
fof(f9057,plain,
spl0_1122,
inference(avatar_split_clause,[],[f3005,f9055]) ).
fof(f9055,plain,
( spl0_1122
<=> ! [X13,X27,X12] : c_in(c_Message_Omsg_OKey(c_Public_OpublicKey(X27,X12)),c_Event_Oknows(X13,c_List_Olist_ONil),tc_Message_Omsg) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1122])]) ).
fof(f3005,plain,
! [X27,X12,X13] : c_in(c_Message_Omsg_OKey(c_Public_OpublicKey(X27,X12)),c_Event_Oknows(X13,c_List_Olist_ONil),tc_Message_Omsg),
inference(definition_unfolding,[],[f2918,f2795]) ).
fof(f2918,axiom,
! [X27,X12,X13] : c_in(c_Message_Omsg_OKey(c_Public_OpublicKey(X27,X12)),c_Event_OinitState(X13),tc_Message_Omsg),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Public_OpublicKey__in__initState_0) ).
fof(f9053,plain,
spl0_1121,
inference(avatar_split_clause,[],[f3004,f9051]) ).
fof(f3004,plain,
! [X11] : c_Numeral_OBit(X11,c_Numeral_Obit_OB0) = c_Numeral_Obin__add(c_Numeral_OBit(X11,c_Numeral_Obit_OB1),c_Numeral_OMin),
inference(definition_unfolding,[],[f2132,f2113]) ).
fof(f2132,axiom,
! [X11] : c_Numeral_OBit(X11,c_Numeral_Obit_OB0) = c_Numeral_Obin__pred(c_Numeral_OBit(X11,c_Numeral_Obit_OB1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obin__pred__1_0) ).
fof(f9049,plain,
spl0_1120,
inference(avatar_split_clause,[],[f2989,f9047]) ).
fof(f9047,plain,
( spl0_1120
<=> ! [X1,X3] : c_Relation_OImage(c_Relation_Odiag(X3,X1),X3,X1,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1120])]) ).
fof(f2989,plain,
! [X3,X1] : c_Relation_OImage(c_Relation_Odiag(X3,X1),X3,X1,X1) = X3,
inference(definition_unfolding,[],[f2603,f2373]) ).
fof(f2603,axiom,
! [X3,X1] : c_inter(X3,X3,X1) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OInt__absorb_0) ).
fof(f9045,plain,
spl0_1119,
inference(avatar_split_clause,[],[f2988,f9043]) ).
fof(f9043,plain,
( spl0_1119
<=> ! [X1,X3] : c_Relation_OImage(c_Relation_Odiag(c_UNIV,X1),X3,X1,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1119])]) ).
fof(f2988,plain,
! [X3,X1] : c_Relation_OImage(c_Relation_Odiag(c_UNIV,X1),X3,X1,X1) = X3,
inference(definition_unfolding,[],[f2601,f2373]) ).
fof(f2601,axiom,
! [X3,X1] : c_inter(c_UNIV,X3,X1) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OInt__UNIV__left_0) ).
fof(f9041,plain,
spl0_1118,
inference(avatar_split_clause,[],[f2987,f9039]) ).
fof(f9039,plain,
( spl0_1118
<=> ! [X1,X3] : c_Relation_OImage(c_Relation_Odiag(X3,X1),c_UNIV,X1,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1118])]) ).
fof(f2987,plain,
! [X3,X1] : c_Relation_OImage(c_Relation_Odiag(X3,X1),c_UNIV,X1,X1) = X3,
inference(definition_unfolding,[],[f2602,f2373]) ).
fof(f2602,axiom,
! [X3,X1] : c_inter(X3,c_UNIV,X1) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OInt__UNIV__right_0) ).
fof(f9037,plain,
spl0_1117,
inference(avatar_split_clause,[],[f2981,f9035]) ).
fof(f9035,plain,
( spl0_1117
<=> ! [X16] : c_0 = c_Binomial_Obinomial(c_0,c_Finite__Set_Ocard(c_SetInterval_OatMost(X16,tc_nat),tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1117])]) ).
fof(f2981,plain,
! [X16] : c_0 = c_Binomial_Obinomial(c_0,c_Finite__Set_Ocard(c_SetInterval_OatMost(X16,tc_nat),tc_nat)),
inference(definition_unfolding,[],[f1160,f2544]) ).
fof(f1160,axiom,
! [X16] : c_0 = c_Binomial_Obinomial(c_0,c_Suc(X16)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Binomial_Obinomial__0__Suc_0) ).
fof(f9033,plain,
spl0_1116,
inference(avatar_split_clause,[],[f2973,f9031]) ).
fof(f9031,plain,
( spl0_1116
<=> ! [X86,X109,X87] : c_Message_Omsg_OHash(X109) != c_Message_Omsg_OMPair(c_Message_Omsg_OHash(c_Message_Omsg_OMPair(X86,X87)),X87) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1116])]) ).
fof(f2973,plain,
! [X109,X86,X87] : c_Message_Omsg_OHash(X109) != c_Message_Omsg_OMPair(c_Message_Omsg_OHash(c_Message_Omsg_OMPair(X86,X87)),X87),
inference(definition_unfolding,[],[f2817,f2837]) ).
fof(f2817,axiom,
! [X109,X86,X87] : c_Message_OHPair(X86,X87) != c_Message_Omsg_OHash(X109),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OHPair__neqs__5_0) ).
fof(f9029,plain,
spl0_1115,
inference(avatar_split_clause,[],[f2971,f9027]) ).
fof(f9027,plain,
( spl0_1115
<=> ! [X86,X91,X87] : c_Message_Omsg_OKey(X91) != c_Message_Omsg_OMPair(c_Message_Omsg_OHash(c_Message_Omsg_OMPair(X86,X87)),X87) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1115])]) ).
fof(f2971,plain,
! [X91,X86,X87] : c_Message_Omsg_OKey(X91) != c_Message_Omsg_OMPair(c_Message_Omsg_OHash(c_Message_Omsg_OMPair(X86,X87)),X87),
inference(definition_unfolding,[],[f2816,f2837]) ).
fof(f2816,axiom,
! [X91,X86,X87] : c_Message_Omsg_OKey(X91) != c_Message_OHPair(X86,X87),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OHPair__neqs__4_0) ).
fof(f9025,plain,
spl0_1114,
inference(avatar_split_clause,[],[f2969,f9023]) ).
fof(f9023,plain,
( spl0_1114
<=> ! [X86,X12,X87] : c_Message_Omsg_OAgent(X12) != c_Message_Omsg_OMPair(c_Message_Omsg_OHash(c_Message_Omsg_OMPair(X86,X87)),X87) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1114])]) ).
fof(f2969,plain,
! [X86,X87,X12] : c_Message_Omsg_OAgent(X12) != c_Message_Omsg_OMPair(c_Message_Omsg_OHash(c_Message_Omsg_OMPair(X86,X87)),X87),
inference(definition_unfolding,[],[f2822,f2837]) ).
fof(f2822,axiom,
! [X86,X87,X12] : c_Message_Omsg_OAgent(X12) != c_Message_OHPair(X86,X87),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OHash_91X2_93_AY2_A_61_AAgent_AA2_A_61_61_AFalse_0) ).
fof(f9021,plain,
( spl0_1113
| ~ spl0_29
| ~ spl0_949 ),
inference(avatar_split_clause,[],[f8551,f8227,f3552,f9019]) ).
fof(f9019,plain,
( spl0_1113
<=> ! [X0] : c_LOrder_Omeet(X0,X0,tc_IntDef_Oint) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1113])]) ).
fof(f3552,plain,
( spl0_29
<=> class_LOrder_Omeet__semilorder(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_29])]) ).
fof(f8551,plain,
( ! [X0] : c_LOrder_Omeet(X0,X0,tc_IntDef_Oint) = X0
| ~ spl0_29
| ~ spl0_949 ),
inference(resolution,[],[f8228,f3554]) ).
fof(f3554,plain,
( class_LOrder_Omeet__semilorder(tc_IntDef_Oint)
| ~ spl0_29 ),
inference(avatar_component_clause,[],[f3552]) ).
fof(f9017,plain,
spl0_1112,
inference(avatar_split_clause,[],[f2967,f9015]) ).
fof(f9015,plain,
( spl0_1112
<=> ! [X86,X87,X7] : c_Message_Omsg_ONonce(X7) != c_Message_Omsg_OMPair(c_Message_Omsg_OHash(c_Message_Omsg_OMPair(X86,X87)),X87) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1112])]) ).
fof(f2967,plain,
! [X86,X7,X87] : c_Message_Omsg_ONonce(X7) != c_Message_Omsg_OMPair(c_Message_Omsg_OHash(c_Message_Omsg_OMPair(X86,X87)),X87),
inference(definition_unfolding,[],[f2814,f2837]) ).
fof(f2814,axiom,
! [X86,X7,X87] : c_Message_Omsg_ONonce(X7) != c_Message_OHPair(X86,X87),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OHPair__neqs__2_0) ).
fof(f9013,plain,
spl0_1111,
inference(avatar_split_clause,[],[f2965,f9011]) ).
fof(f9011,plain,
( spl0_1111
<=> ! [X86,X87,X7] : c_Message_Omsg_ONumber(X7) != c_Message_Omsg_OMPair(c_Message_Omsg_OHash(c_Message_Omsg_OMPair(X86,X87)),X87) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1111])]) ).
fof(f2965,plain,
! [X86,X7,X87] : c_Message_Omsg_ONumber(X7) != c_Message_Omsg_OMPair(c_Message_Omsg_OHash(c_Message_Omsg_OMPair(X86,X87)),X87),
inference(definition_unfolding,[],[f2815,f2837]) ).
fof(f2815,axiom,
! [X86,X7,X87] : c_Message_Omsg_ONumber(X7) != c_Message_OHPair(X86,X87),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OHPair__neqs__3_0) ).
fof(f9009,plain,
spl0_1110,
inference(avatar_split_clause,[],[f2932,f9007]) ).
fof(f9007,plain,
( spl0_1110
<=> ! [X91] :
( ~ c_in(X91,c_Message_OsymKeys,tc_nat)
| c_in(c_Message_OinvKey(X91),c_Message_OsymKeys,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1110])]) ).
fof(f2932,axiom,
! [X91] :
( ~ c_in(X91,c_Message_OsymKeys,tc_nat)
| c_in(c_Message_OinvKey(X91),c_Message_OsymKeys,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Public_OsymKeys__invKey__iff_1) ).
fof(f9005,plain,
spl0_1109,
inference(avatar_split_clause,[],[f2931,f9003]) ).
fof(f9003,plain,
( spl0_1109
<=> ! [X91] :
( c_in(X91,c_Message_OsymKeys,tc_nat)
| ~ c_in(c_Message_OinvKey(X91),c_Message_OsymKeys,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1109])]) ).
fof(f2931,axiom,
! [X91] :
( c_in(X91,c_Message_OsymKeys,tc_nat)
| ~ c_in(c_Message_OinvKey(X91),c_Message_OsymKeys,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Public_OsymKeys__invKey__iff_0) ).
fof(f9001,plain,
spl0_1108,
inference(avatar_split_clause,[],[f2930,f8999]) ).
fof(f8999,plain,
( spl0_1108
<=> ! [X102,X27,X12] : c_in(c_Message_Omsg_OKey(c_Public_OpublicKey(X27,X12)),c_Event_Oknows(c_Message_Oagent_OSpy,X102),tc_Message_Omsg) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1108])]) ).
fof(f2930,axiom,
! [X27,X12,X102] : c_in(c_Message_Omsg_OKey(c_Public_OpublicKey(X27,X12)),c_Event_Oknows(c_Message_Oagent_OSpy,X102),tc_Message_Omsg),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Public_Ospies__pubK_0) ).
fof(f8997,plain,
spl0_1107,
inference(avatar_split_clause,[],[f2916,f8995]) ).
fof(f8995,plain,
( spl0_1107
<=> ! [X102,X27,X12] : c_in(c_Message_Omsg_OKey(c_Message_OinvKey(c_Public_OpublicKey(X27,X12))),c_Event_Oused(X102),tc_Message_Omsg) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1107])]) ).
fof(f2916,axiom,
! [X27,X12,X102] : c_in(c_Message_Omsg_OKey(c_Message_OinvKey(c_Public_OpublicKey(X27,X12))),c_Event_Oused(X102),tc_Message_Omsg),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Public_OprivateKey__into__used_0) ).
fof(f8993,plain,
spl0_1106,
inference(avatar_split_clause,[],[f2886,f8991]) ).
fof(f8991,plain,
( spl0_1106
<=> ! [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_1106])]) ).
fof(f2886,axiom,
! [X88,X86] :
( ~ c_in(X86,X88,tc_Message_Omsg)
| c_in(X86,c_Message_Osynth(X88),tc_Message_Omsg) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Osynth_OInj_0) ).
fof(f8989,plain,
spl0_1105,
inference(avatar_split_clause,[],[f2847,f8987]) ).
fof(f2847,axiom,
! [X88,X86] :
( ~ c_in(X86,X88,tc_Message_Omsg)
| c_in(X86,c_Message_Oanalz(X88),tc_Message_Omsg) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oanalz_OInj_0) ).
fof(f8985,plain,
spl0_1104,
inference(avatar_split_clause,[],[f2767,f8983]) ).
fof(f2767,axiom,
! [X88,X86] :
( ~ c_in(X86,X88,tc_Message_Omsg)
| c_in(X86,c_Message_Oparts(X88),tc_Message_Omsg) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oparts_OInj_0) ).
fof(f8981,plain,
spl0_1103,
inference(avatar_split_clause,[],[f2750,f8979]) ).
fof(f8979,plain,
( spl0_1103
<=> ! [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_1103])]) ).
fof(f2750,axiom,
! [X88,X7] : c_Message_OkeysFor(X88) = c_Message_OkeysFor(c_insert(c_Message_Omsg_ONumber(X7),X88,tc_Message_Omsg)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OkeysFor__insert__Number_0) ).
fof(f8977,plain,
( spl0_1102
| ~ spl0_94
| ~ spl0_948 ),
inference(avatar_split_clause,[],[f8550,f8223,f3877,f8975]) ).
fof(f8975,plain,
( spl0_1102
<=> ! [X0] : c_LOrder_Ojoin(X0,X0,tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1102])]) ).
fof(f3877,plain,
( spl0_94
<=> class_LOrder_Ojoin__semilorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_94])]) ).
fof(f8223,plain,
( spl0_948
<=> ! [X1,X3] :
( ~ class_LOrder_Ojoin__semilorder(X1)
| c_LOrder_Ojoin(X3,X3,X1) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_948])]) ).
fof(f8550,plain,
( ! [X0] : c_LOrder_Ojoin(X0,X0,tc_nat) = X0
| ~ spl0_94
| ~ spl0_948 ),
inference(resolution,[],[f8224,f3879]) ).
fof(f3879,plain,
( class_LOrder_Ojoin__semilorder(tc_nat)
| ~ spl0_94 ),
inference(avatar_component_clause,[],[f3877]) ).
fof(f8224,plain,
( ! [X3,X1] :
( ~ class_LOrder_Ojoin__semilorder(X1)
| c_LOrder_Ojoin(X3,X3,X1) = X3 )
| ~ spl0_948 ),
inference(avatar_component_clause,[],[f8223]) ).
fof(f8973,plain,
spl0_1101,
inference(avatar_split_clause,[],[f2749,f8971]) ).
fof(f8971,plain,
( spl0_1101
<=> ! [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_1101])]) ).
fof(f2749,axiom,
! [X88,X7] : c_Message_OkeysFor(X88) = c_Message_OkeysFor(c_insert(c_Message_Omsg_ONonce(X7),X88,tc_Message_Omsg)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OkeysFor__insert__Nonce_0) ).
fof(f8969,plain,
spl0_1100,
inference(avatar_split_clause,[],[f2747,f8967]) ).
fof(f8967,plain,
( spl0_1100
<=> ! [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_1100])]) ).
fof(f2747,axiom,
! [X91,X88] : c_Message_OkeysFor(X88) = c_Message_OkeysFor(c_insert(c_Message_Omsg_OKey(X91),X88,tc_Message_Omsg)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OkeysFor__insert__Key_0) ).
fof(f8965,plain,
spl0_1099,
inference(avatar_split_clause,[],[f2746,f8963]) ).
fof(f8963,plain,
( spl0_1099
<=> ! [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_1099])]) ).
fof(f2746,axiom,
! [X88,X86] : c_Message_OkeysFor(X88) = c_Message_OkeysFor(c_insert(c_Message_Omsg_OHash(X86),X88,tc_Message_Omsg)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OkeysFor__insert__Hash_0) ).
fof(f8961,plain,
spl0_1098,
inference(avatar_split_clause,[],[f2744,f8959]) ).
fof(f8959,plain,
( spl0_1098
<=> ! [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_1098])]) ).
fof(f2744,axiom,
! [X88,X12] : c_Message_OkeysFor(X88) = c_Message_OkeysFor(c_insert(c_Message_Omsg_OAgent(X12),X88,tc_Message_Omsg)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OkeysFor__insert__Agent_0) ).
fof(f8957,plain,
spl0_1097,
inference(avatar_split_clause,[],[f2718,f8955]) ).
fof(f8955,plain,
( spl0_1097
<=> ! [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_1097])]) ).
fof(f2718,axiom,
! [X1,X5] :
( ~ c_Wellfounded__Recursion_Oacyclic(X5,X1)
| c_Wellfounded__Recursion_Oacyclic(c_Relation_Oconverse(X5,X1,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Oacyclic__converse_1) ).
fof(f8953,plain,
spl0_1096,
inference(avatar_split_clause,[],[f2717,f8951]) ).
fof(f8951,plain,
( spl0_1096
<=> ! [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_1096])]) ).
fof(f2717,axiom,
! [X1,X5] :
( c_Wellfounded__Recursion_Oacyclic(X5,X1)
| ~ c_Wellfounded__Recursion_Oacyclic(c_Relation_Oconverse(X5,X1,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Oacyclic__converse_0) ).
fof(f8949,plain,
spl0_1095,
inference(avatar_split_clause,[],[f2704,f8947]) ).
fof(f8947,plain,
( spl0_1095
<=> ! [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_1095])]) ).
fof(f2704,axiom,
! [X2,X18,X1,X27] : c_Sum__Type_OInl(X18,X1,X2) != c_Sum__Type_OInr(X27,X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sum__Type_OInr__not__Inl_0) ).
fof(f8945,plain,
spl0_1094,
inference(avatar_split_clause,[],[f2667,f8943]) ).
fof(f8943,plain,
( spl0_1094
<=> ! [X1,X3] : c_uminus(c_uminus(X3,tc_set(X1)),tc_set(X1)) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1094])]) ).
fof(f2667,axiom,
! [X3,X1] : c_uminus(c_uminus(X3,tc_set(X1)),tc_set(X1)) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Odouble__complement_0) ).
fof(f8941,plain,
spl0_1093,
inference(avatar_split_clause,[],[f2659,f8939]) ).
fof(f2659,axiom,
! [X1,X12] :
( c_emptyset = X12
| c_in(c_Main_Oall__not__in__conv__1(X12,X1),X12,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Oall__not__in__conv_0) ).
fof(f8937,plain,
spl0_1092,
inference(avatar_split_clause,[],[f2636,f8935]) ).
fof(f8935,plain,
( spl0_1092
<=> ! [X13,X12,X1] :
( c_emptyset = X13
| c_emptyset != c_union(X12,X13,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1092])]) ).
fof(f2636,axiom,
! [X1,X12,X13] :
( c_emptyset = X13
| c_emptyset != c_union(X12,X13,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUn__empty_1) ).
fof(f8933,plain,
( spl0_1091
| ~ spl0_30
| ~ spl0_948 ),
inference(avatar_split_clause,[],[f8549,f8223,f3557,f8931]) ).
fof(f8931,plain,
( spl0_1091
<=> ! [X0] : c_LOrder_Ojoin(X0,X0,tc_IntDef_Oint) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1091])]) ).
fof(f3557,plain,
( spl0_30
<=> class_LOrder_Ojoin__semilorder(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_30])]) ).
fof(f8549,plain,
( ! [X0] : c_LOrder_Ojoin(X0,X0,tc_IntDef_Oint) = X0
| ~ spl0_30
| ~ spl0_948 ),
inference(resolution,[],[f8224,f3559]) ).
fof(f3559,plain,
( class_LOrder_Ojoin__semilorder(tc_IntDef_Oint)
| ~ spl0_30 ),
inference(avatar_component_clause,[],[f3557]) ).
fof(f8929,plain,
spl0_1090,
inference(avatar_split_clause,[],[f2635,f8927]) ).
fof(f8927,plain,
( spl0_1090
<=> ! [X13,X12,X1] :
( c_emptyset = X12
| c_emptyset != c_union(X12,X13,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1090])]) ).
fof(f2635,axiom,
! [X1,X12,X13] :
( c_emptyset = X12
| c_emptyset != c_union(X12,X13,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUn__empty_0) ).
fof(f8925,plain,
spl0_1089,
inference(avatar_split_clause,[],[f2626,f8923]) ).
fof(f2626,axiom,
! [X1] : c_Pow(c_emptyset,X1) = c_insert(c_emptyset,c_emptyset,tc_set(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OPow__empty_0) ).
fof(f8921,plain,
spl0_1088,
inference(avatar_split_clause,[],[f2390,f8919]) ).
fof(f8919,plain,
( spl0_1088
<=> ! [X41,X85] : c_Relation_OId = c_Nat_Opower(X85,c_0,tc_set(tc_prod(X41,X41))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1088])]) ).
fof(f2390,axiom,
! [X41,X85] : c_Relation_OId = c_Nat_Opower(X85,c_0,tc_set(tc_prod(X41,X41))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation__Power_Orelpow_Osimps__1_0) ).
fof(f8917,plain,
spl0_1087,
inference(avatar_split_clause,[],[f2389,f8915]) ).
fof(f8915,plain,
( spl0_1087
<=> ! [X1,X3] : c_Nat_Opower(X3,c_1,tc_set(tc_prod(X1,X1))) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1087])]) ).
fof(f2389,axiom,
! [X3,X1] : c_Nat_Opower(X3,c_1,tc_set(tc_prod(X1,X1))) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation__Power_Orel__pow__1_0) ).
fof(f8913,plain,
spl0_1086,
inference(avatar_split_clause,[],[f2382,f8911]) ).
fof(f8911,plain,
( spl0_1086
<=> ! [X2,X1,X3] : c_Relation_Oconverse(c_Relation_Oconverse(X3,X1,X2),X2,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1086])]) ).
fof(f2382,axiom,
! [X2,X3,X1] : c_Relation_Oconverse(c_Relation_Oconverse(X3,X1,X2),X2,X1) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_Oconverse__converse_0) ).
fof(f8909,plain,
spl0_1085,
inference(avatar_split_clause,[],[f2298,f8907]) ).
fof(f8907,plain,
( spl0_1085
<=> ! [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_1085])]) ).
fof(f2298,axiom,
! [X3,X0] :
( ~ c_Parity_Oeven(X3,tc_IntDef_Oint)
| c_Parity_Oeven(c_times(X0,X3,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__product_2) ).
fof(f8905,plain,
spl0_1084,
inference(avatar_split_clause,[],[f2297,f8903]) ).
fof(f8903,plain,
( spl0_1084
<=> ! [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_1084])]) ).
fof(f2297,axiom,
! [X3,X0] :
( ~ c_Parity_Oeven(X0,tc_IntDef_Oint)
| c_Parity_Oeven(c_times(X0,X3,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__product_1) ).
fof(f8901,plain,
spl0_1083,
inference(avatar_split_clause,[],[f2293,f8899]) ).
fof(f8899,plain,
( spl0_1083
<=> ! [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_1083])]) ).
fof(f2293,axiom,
! [X21,X0] :
( c_Parity_Oeven(X0,tc_IntDef_Oint)
| ~ c_Parity_Oeven(c_Nat_Opower(X0,X21,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__power_0) ).
fof(f8897,plain,
spl0_1082,
inference(avatar_split_clause,[],[f2285,f8895]) ).
fof(f8895,plain,
( spl0_1082
<=> ! [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_1082])]) ).
fof(f2285,axiom,
! [X3,X0] :
( ~ c_Parity_Oeven(X3,tc_nat)
| c_Parity_Oeven(c_times(X0,X3,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__nat__product_2) ).
fof(f8893,plain,
spl0_1081,
inference(avatar_split_clause,[],[f2284,f8891]) ).
fof(f8891,plain,
( spl0_1081
<=> ! [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_1081])]) ).
fof(f2284,axiom,
! [X3,X0] :
( ~ c_Parity_Oeven(X0,tc_nat)
| c_Parity_Oeven(c_times(X0,X3,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__nat__product_1) ).
fof(f8889,plain,
spl0_1080,
inference(avatar_split_clause,[],[f2280,f8887]) ).
fof(f2280,axiom,
! [X3,X0] :
( c_Parity_Oeven(X0,tc_nat)
| ~ c_Parity_Oeven(c_Nat_Opower(X0,X3,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__nat__power_0) ).
fof(f8885,plain,
spl0_1079,
inference(avatar_split_clause,[],[f2216,f8883]) ).
fof(f2216,axiom,
! [X3,X1] :
( ~ class_OrderedGroup_Oab__group__add(X1)
| c_uminus(c_uminus(X3,X1),X1) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Ominus__minus_0) ).
fof(f8881,plain,
spl0_1078,
inference(avatar_split_clause,[],[f2154,f8879]) ).
fof(f8877,plain,
spl0_1077,
inference(avatar_split_clause,[],[f2150,f8875]) ).
fof(f8875,plain,
( spl0_1077
<=> ! [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_1077])]) ).
fof(f2150,axiom,
! [X1] :
( ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_OPls,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obin__rel__simps__7_0) ).
fof(f8873,plain,
spl0_1076,
inference(avatar_split_clause,[],[f2136,f8871]) ).
fof(f8871,plain,
( spl0_1076
<=> ! [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_1076])]) ).
fof(f2136,axiom,
! [X1] :
( ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_OMin,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obin__rel__simps__11_0) ).
fof(f8869,plain,
spl0_1075,
inference(avatar_split_clause,[],[f2118,f8867]) ).
fof(f2118,axiom,
! [X1] :
( ~ class_Numeral_Onumber__ring(X1)
| c_Numeral_Onumber__of(c_Numeral_OMin,X1) = c_uminus(c_1,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obin__arith__extra__simps__3_0) ).
fof(f8865,plain,
spl0_1074,
inference(avatar_split_clause,[],[f2032,f8863]) ).
fof(f8863,plain,
( spl0_1074
<=> ! [X21,X15] :
( c_0 = X21
| c_0 != c_plus(X15,X21,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1074])]) ).
fof(f2032,axiom,
! [X21,X15] :
( c_0 = X21
| c_0 != c_plus(X15,X21,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oadd__is__0_1) ).
fof(f8861,plain,
spl0_1073,
inference(avatar_split_clause,[],[f2031,f8859]) ).
fof(f8859,plain,
( spl0_1073
<=> ! [X21,X15] :
( c_0 = X15
| c_0 != c_plus(X15,X21,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1073])]) ).
fof(f2031,axiom,
! [X21,X15] :
( c_0 = X15
| c_0 != c_plus(X15,X21,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oadd__is__0_0) ).
fof(f8857,plain,
spl0_1072,
inference(avatar_split_clause,[],[f1786,f8855]) ).
fof(f1786,axiom,
! [X59,X43] :
( ~ c_lessequals(X59,X43,tc_nat)
| c_List_Olist_ONil = c_List_Oupt(X43,X59) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oupt__eq__Nil__conv_2) ).
fof(f8853,plain,
spl0_1071,
inference(avatar_split_clause,[],[f1758,f8851]) ).
fof(f8851,plain,
( spl0_1071
<=> ! [X1,X23] : c_List_Oset(X23,X1) = c_List_Oset(c_List_Orotate1(X23,X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1071])]) ).
fof(f1758,axiom,
! [X1,X23] : c_List_Oset(X23,X1) = c_List_Oset(c_List_Orotate1(X23,X1),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oset__rotate1_0) ).
fof(f8849,plain,
( ~ spl0_79
| spl0_1070
| ~ spl0_683
| ~ spl0_944 ),
inference(avatar_split_clause,[],[f8547,f8206,f7029,f8847,f3802]) ).
fof(f3802,plain,
( spl0_79
<=> class_Ring__and__Field_Ocomm__semiring__1__cancel(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_79])]) ).
fof(f7029,plain,
( spl0_683
<=> ! [X3] : c_NatArith_Oof__nat(X3,tc_nat) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_683])]) ).
fof(f8206,plain,
( spl0_944
<=> ! [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_944])]) ).
fof(f8547,plain,
( ! [X0] :
( c_in(X0,c_IntDef_ONats,tc_nat)
| ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(tc_nat) )
| ~ spl0_683
| ~ spl0_944 ),
inference(superposition,[],[f8207,f7030]) ).
fof(f7030,plain,
( ! [X3] : c_NatArith_Oof__nat(X3,tc_nat) = X3
| ~ spl0_683 ),
inference(avatar_component_clause,[],[f7029]) ).
fof(f8207,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_944 ),
inference(avatar_component_clause,[],[f8206]) ).
fof(f8845,plain,
spl0_1069,
inference(avatar_split_clause,[],[f1757,f8843]) ).
fof(f8843,plain,
( spl0_1069
<=> ! [X1,X23] : c_List_Oset(X23,X1) = c_List_Oset(c_List_Orev(X23,X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1069])]) ).
fof(f1757,axiom,
! [X1,X23] : c_List_Oset(X23,X1) = c_List_Oset(c_List_Orev(X23,X1),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oset__rev_0) ).
fof(f8841,plain,
spl0_1068,
inference(avatar_split_clause,[],[f1754,f8839]) ).
fof(f8839,plain,
( spl0_1068
<=> ! [X1,X23] : c_List_Oset(X23,X1) = c_List_Oset(c_List_Oremdups(X23,X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1068])]) ).
fof(f1754,axiom,
! [X1,X23] : c_List_Oset(X23,X1) = c_List_Oset(c_List_Oremdups(X23,X1),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oset__remdups_0) ).
fof(f8837,plain,
spl0_1067,
inference(avatar_split_clause,[],[f1746,f8835]) ).
fof(f8835,plain,
( spl0_1067
<=> ! [X25,X1,X23] :
( c_List_Olist_ONil = X25
| c_append(X23,X25,X1) != X23 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1067])]) ).
fof(f1746,axiom,
! [X1,X25,X23] :
( c_List_Olist_ONil = X25
| c_append(X23,X25,X1) != X23 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oself__append__conv_0) ).
fof(f8833,plain,
spl0_1066,
inference(avatar_split_clause,[],[f1744,f8831]) ).
fof(f8831,plain,
( spl0_1066
<=> ! [X25,X1,X23] :
( c_List_Olist_ONil = X23
| c_append(X23,X25,X1) != X25 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1066])]) ).
fof(f1744,axiom,
! [X1,X25,X23] :
( c_List_Olist_ONil = X23
| c_append(X23,X25,X1) != X25 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oself__append__conv2_0) ).
fof(f8829,plain,
spl0_1065,
inference(avatar_split_clause,[],[f1740,f8827]) ).
fof(f8827,plain,
( spl0_1065
<=> ! [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_1065])]) ).
fof(f1740,axiom,
! [X21,X1,X23] :
( c_List_Olist_ONil = X23
| c_List_Olist_ONil != c_List_Orotate(X21,X23,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Orotate__is__Nil__conv_0) ).
fof(f8825,plain,
spl0_1064,
inference(avatar_split_clause,[],[f1720,f8823]) ).
fof(f8823,plain,
( spl0_1064
<=> ! [X0,X1,X23] : c_List_Oremove1(X0,c_List_Olist_OCons(X0,X23,X1),X1) = X23 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1064])]) ).
fof(f1720,axiom,
! [X0,X1,X23] : c_List_Oremove1(X0,c_List_Olist_OCons(X0,X23,X1),X1) = X23,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oremove1_Osimps__2_0) ).
fof(f8821,plain,
spl0_1063,
inference(avatar_split_clause,[],[f1692,f8819]) ).
fof(f8819,plain,
( spl0_1063
<=> ! [X1,X23,X3] : c_List_Onth(c_List_Olist_OCons(X3,X23,X1),c_0,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1063])]) ).
fof(f1692,axiom,
! [X3,X1,X23] : c_List_Onth(c_List_Olist_OCons(X3,X23,X1),c_0,X1) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Onth__Cons__0_0) ).
fof(f8817,plain,
spl0_1062,
inference(avatar_split_clause,[],[f1639,f8815]) ).
fof(f8813,plain,
spl0_1061,
inference(avatar_split_clause,[],[f1607,f8811]) ).
fof(f1607,axiom,
! [X3,X0,X1] : c_Nat_Osize(c_List_Oreplicate(X3,X0,X1),tc_List_Olist(X1)) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olength__replicate_0) ).
fof(f8809,plain,
spl0_1060,
inference(avatar_split_clause,[],[f1597,f8807]) ).
fof(f8807,plain,
( spl0_1060
<=> ! [X1,X23] :
( c_List_Olist_ONil = X23
| c_0 != c_Nat_Osize(X23,tc_List_Olist(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1060])]) ).
fof(f1597,axiom,
! [X1,X23] :
( c_List_Olist_ONil = X23
| c_0 != c_Nat_Osize(X23,tc_List_Olist(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olength__0__conv_0) ).
fof(f8805,plain,
( spl0_1059
| ~ spl0_841
| ~ spl0_859 ),
inference(avatar_split_clause,[],[f8043,f7790,f7718,f8803]) ).
fof(f8803,plain,
( spl0_1059
<=> ! [X0] : c_0 = c_times(X0,c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1059])]) ).
fof(f7718,plain,
( spl0_841
<=> ! [X16,X15] : c_Divides_Oop_Advd(X16,c_times(X15,X16,tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_841])]) ).
fof(f7790,plain,
( spl0_859
<=> ! [X15] :
( c_0 = X15
| ~ c_Divides_Oop_Advd(c_0,X15,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_859])]) ).
fof(f8043,plain,
( ! [X0] : c_0 = c_times(X0,c_0,tc_IntDef_Oint)
| ~ spl0_841
| ~ spl0_859 ),
inference(resolution,[],[f7791,f7719]) ).
fof(f7719,plain,
( ! [X16,X15] : c_Divides_Oop_Advd(X16,c_times(X15,X16,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_841 ),
inference(avatar_component_clause,[],[f7718]) ).
fof(f7791,plain,
( ! [X15] :
( ~ c_Divides_Oop_Advd(c_0,X15,tc_IntDef_Oint)
| c_0 = X15 )
| ~ spl0_859 ),
inference(avatar_component_clause,[],[f7790]) ).
fof(f8801,plain,
spl0_1058,
inference(avatar_split_clause,[],[f1565,f8799]) ).
fof(f8799,plain,
( spl0_1058
<=> ! [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_1058])]) ).
fof(f1565,axiom,
! [X58,X1,X23] :
( ~ c_List_Odistinct(X23,X1)
| c_List_Odistinct(c_List_Osublist(X23,X58,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Odistinct__sublistI_0) ).
fof(f8797,plain,
spl0_1057,
inference(avatar_split_clause,[],[f1564,f8795]) ).
fof(f8795,plain,
( spl0_1057
<=> ! [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_1057])]) ).
fof(f1564,axiom,
! [X21,X1,X23] :
( ~ c_List_Odistinct(X23,X1)
| c_List_Odistinct(c_List_Orotate(X21,X23,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Odistinct__rotate_1) ).
fof(f8793,plain,
spl0_1056,
inference(avatar_split_clause,[],[f1563,f8791]) ).
fof(f8791,plain,
( spl0_1056
<=> ! [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_1056])]) ).
fof(f1563,axiom,
! [X21,X1,X23] :
( c_List_Odistinct(X23,X1)
| ~ c_List_Odistinct(c_List_Orotate(X21,X23,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Odistinct__rotate_0) ).
fof(f8789,plain,
spl0_1055,
inference(avatar_split_clause,[],[f1560,f8787]) ).
fof(f8787,plain,
( spl0_1055
<=> ! [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_1055])]) ).
fof(f1560,axiom,
! [X0,X1,X23] :
( ~ c_List_Odistinct(X23,X1)
| c_List_Odistinct(c_List_Oremove1(X0,X23,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Odistinct__remove1_0) ).
fof(f8785,plain,
spl0_1054,
inference(avatar_split_clause,[],[f1559,f8783]) ).
fof(f8783,plain,
( spl0_1054
<=> ! [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_1054])]) ).
fof(f1559,axiom,
! [X1,X23,X43] :
( ~ c_List_Odistinct(X23,X1)
| c_List_Odistinct(c_List_Odrop(X43,X23,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Odistinct__drop_0) ).
fof(f8781,plain,
spl0_1053,
inference(avatar_split_clause,[],[f1556,f8779]) ).
fof(f8779,plain,
( spl0_1053
<=> ! [X25,X1,X23] :
( c_List_Odistinct(X25,X1)
| ~ c_List_Odistinct(c_append(X23,X25,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1053])]) ).
fof(f1556,axiom,
! [X1,X25,X23] :
( c_List_Odistinct(X25,X1)
| ~ c_List_Odistinct(c_append(X23,X25,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Odistinct__append_1) ).
fof(f8777,plain,
spl0_1052,
inference(avatar_split_clause,[],[f1555,f8775]) ).
fof(f8775,plain,
( spl0_1052
<=> ! [X25,X1,X23] :
( c_List_Odistinct(X23,X1)
| ~ c_List_Odistinct(c_append(X23,X25,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1052])]) ).
fof(f1555,axiom,
! [X1,X25,X23] :
( c_List_Odistinct(X23,X1)
| ~ c_List_Odistinct(c_append(X23,X25,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Odistinct__append_0) ).
fof(f8773,plain,
spl0_1051,
inference(avatar_split_clause,[],[f1553,f8771]) ).
fof(f8771,plain,
( spl0_1051
<=> ! [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_1051])]) ).
fof(f1553,axiom,
! [X41,X0,X23] :
( c_List_Odistinct(X23,X41)
| ~ c_List_Odistinct(c_List_Olist_OCons(X0,X23,X41),X41) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Odistinct_Osimps__2_1) ).
fof(f8769,plain,
spl0_1050,
inference(avatar_split_clause,[],[f1527,f8767]) ).
fof(f8767,plain,
( spl0_1050
<=> ! [X25,X1,X23] :
( c_List_Olist_ONil = X23
| c_List_Olist_ONil != c_append(X23,X25,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1050])]) ).
fof(f1527,axiom,
! [X1,X25,X23] :
( c_List_Olist_ONil = X23
| c_List_Olist_ONil != c_append(X23,X25,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oappend__is__Nil__conv_0) ).
fof(f8765,plain,
spl0_1049,
inference(avatar_split_clause,[],[f1511,f8763]) ).
fof(f8763,plain,
( spl0_1049
<=> ! [X25,X1,X23] :
( c_List_Olist_ONil = X25
| c_List_Olist_ONil != c_append(X23,X25,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1049])]) ).
fof(f1511,axiom,
! [X1,X25,X23] :
( c_List_Olist_ONil = X25
| c_List_Olist_ONil != c_append(X23,X25,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_ONil__is__append__conv_1) ).
fof(f8761,plain,
( spl0_1048
| ~ spl0_840
| ~ spl0_859 ),
inference(avatar_split_clause,[],[f8042,f7790,f7714,f8759]) ).
fof(f8759,plain,
( spl0_1048
<=> ! [X0] : c_0 = c_times(c_0,X0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1048])]) ).
fof(f7714,plain,
( spl0_840
<=> ! [X16,X15] : c_Divides_Oop_Advd(X16,c_times(X16,X15,tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_840])]) ).
fof(f8042,plain,
( ! [X0] : c_0 = c_times(c_0,X0,tc_IntDef_Oint)
| ~ spl0_840
| ~ spl0_859 ),
inference(resolution,[],[f7791,f7715]) ).
fof(f7715,plain,
( ! [X16,X15] : c_Divides_Oop_Advd(X16,c_times(X16,X15,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_840 ),
inference(avatar_component_clause,[],[f7714]) ).
fof(f8757,plain,
spl0_1047,
inference(avatar_split_clause,[],[f1497,f8755]) ).
fof(f8755,plain,
( spl0_1047
<=> ! [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_1047])]) ).
fof(f1497,axiom,
! [X18,X27] : c_0 = c_Divides_Oop_Amod(c_times(X27,X18,tc_IntDef_Oint),X27,tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozmod__zmult__self2_0) ).
fof(f8753,plain,
spl0_1046,
inference(avatar_split_clause,[],[f1496,f8751]) ).
fof(f8751,plain,
( spl0_1046
<=> ! [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_1046])]) ).
fof(f1496,axiom,
! [X18,X27] : c_0 = c_Divides_Oop_Amod(c_times(X18,X27,tc_IntDef_Oint),X27,tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozmod__zmult__self1_0) ).
fof(f8749,plain,
spl0_1045,
inference(avatar_split_clause,[],[f1483,f8747]) ).
fof(f1483,axiom,
! [X21,X0] : c_lessequals(c_0,c_Nat_Opower(c_HOL_Oabs(X0,tc_IntDef_Oint),X21,tc_IntDef_Oint),tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozero__le__zpower__abs_0) ).
fof(f8745,plain,
spl0_1044,
inference(avatar_split_clause,[],[f1471,f8743]) ).
fof(f8743,plain,
( spl0_1044
<=> ! [X18] :
( c_0 = X18
| c_1 = c_div(X18,X18,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1044])]) ).
fof(f1471,axiom,
! [X18] :
( c_0 = X18
| c_1 = c_div(X18,X18,tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozdiv__self_0) ).
fof(f8741,plain,
spl0_1043,
inference(avatar_split_clause,[],[f1441,f8739]) ).
fof(f1441,axiom,
! [X18,X27] : c_0 = c_div(c_Divides_Oop_Amod(X18,X27,tc_IntDef_Oint),X27,tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Omod__div__trivial_0) ).
fof(f8737,plain,
spl0_1042,
inference(avatar_split_clause,[],[f1423,f8735]) ).
fof(f8735,plain,
( spl0_1042
<=> ! [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_1042])]) ).
fof(f1423,axiom,
! [X48] :
( ~ c_less(c_0,X48,tc_IntDef_Oint)
| c_less(c_0,c_IntDef_Onat(X48),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Ozero__less__nat__eq_1) ).
fof(f8733,plain,
spl0_1041,
inference(avatar_split_clause,[],[f1422,f8731]) ).
fof(f1422,axiom,
! [X48] :
( c_less(c_0,X48,tc_IntDef_Oint)
| ~ c_less(c_0,c_IntDef_Onat(X48),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Ozero__less__nat__eq_0) ).
fof(f8729,plain,
spl0_1040,
inference(avatar_split_clause,[],[f1421,f8727]) ).
fof(f8727,plain,
( spl0_1040
<=> ! [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_1040])]) ).
fof(f1421,axiom,
! [X21] :
( ~ c_less(c_0,X21,tc_nat)
| c_less(c_0,c_IntDef_Oint(X21),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Ozero__less__int__conv_1) ).
fof(f8725,plain,
spl0_1039,
inference(avatar_split_clause,[],[f1420,f8723]) ).
fof(f8723,plain,
( spl0_1039
<=> ! [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_1039])]) ).
fof(f1420,axiom,
! [X21] :
( c_less(c_0,X21,tc_nat)
| ~ c_less(c_0,c_IntDef_Oint(X21),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Ozero__less__int__conv_0) ).
fof(f8721,plain,
spl0_1038,
inference(avatar_split_clause,[],[f1380,f8719]) ).
fof(f8719,plain,
( spl0_1038
<=> ! [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_1038])]) ).
fof(f1380,axiom,
! [X48] :
( c_lessequals(c_0,X48,tc_IntDef_Oint)
| c_0 = c_IntDef_Oint(c_IntDef_Onat(X48)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oint__nat__eq_1) ).
fof(f8717,plain,
( spl0_1037
| ~ spl0_646
| ~ spl0_856 ),
inference(avatar_split_clause,[],[f8035,f7778,f6101,f8714]) ).
fof(f8714,plain,
( spl0_1037
<=> c_0 = c_IntDef_Onat(c_uminus(c_1,tc_IntDef_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1037])]) ).
fof(f7778,plain,
( spl0_856
<=> ! [X21] : c_0 = c_IntDef_Onat(c_uminus(c_IntDef_Oint(X21),tc_IntDef_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_856])]) ).
fof(f8035,plain,
( c_0 = c_IntDef_Onat(c_uminus(c_1,tc_IntDef_Oint))
| ~ spl0_646
| ~ spl0_856 ),
inference(superposition,[],[f7779,f6103]) ).
fof(f7779,plain,
( ! [X21] : c_0 = c_IntDef_Onat(c_uminus(c_IntDef_Oint(X21),tc_IntDef_Oint))
| ~ spl0_856 ),
inference(avatar_component_clause,[],[f7778]) ).
fof(f8712,plain,
spl0_1036,
inference(avatar_split_clause,[],[f1379,f8710]) ).
fof(f8710,plain,
( spl0_1036
<=> ! [X48] :
( ~ c_lessequals(c_0,X48,tc_IntDef_Oint)
| c_IntDef_Oint(c_IntDef_Onat(X48)) = X48 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1036])]) ).
fof(f1379,axiom,
! [X48] :
( ~ c_lessequals(c_0,X48,tc_IntDef_Oint)
| c_IntDef_Oint(c_IntDef_Onat(X48)) = X48 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oint__nat__eq_0) ).
fof(f8708,plain,
spl0_1035,
inference(avatar_split_clause,[],[f1349,f8706]) ).
fof(f8706,plain,
( spl0_1035
<=> ! [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_1035])]) ).
fof(f1349,axiom,
! [X48] :
( c_0 = X48
| ~ c_less(c_HOL_Oabs(X48,tc_IntDef_Oint),c_1,tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntArith_Ozabs__less__one__iff_0) ).
fof(f8704,plain,
spl0_1034,
inference(avatar_split_clause,[],[f1246,f8702]) ).
fof(f8702,plain,
( spl0_1034
<=> ! [X5,X12,X1] :
( c_emptyset = X12
| c_emptyset != c_Equiv__Relations_Oquotient(X12,X5,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1034])]) ).
fof(f1246,axiom,
! [X1,X5,X12] :
( c_emptyset = X12
| c_emptyset != c_Equiv__Relations_Oquotient(X12,X5,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Equiv__Relations_Oquotient__is__empty_0) ).
fof(f8700,plain,
spl0_1033,
inference(avatar_split_clause,[],[f1242,f8698]) ).
fof(f8698,plain,
( spl0_1033
<=> ! [X21,X15] : c_0 = c_div(c_Divides_Oop_Amod(X15,X21,tc_nat),X21,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1033])]) ).
fof(f1242,axiom,
! [X21,X15] : c_0 = c_div(c_Divides_Oop_Amod(X15,X21,tc_nat),X21,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Onat__mod__div__trivial_0) ).
fof(f8696,plain,
spl0_1032,
inference(avatar_split_clause,[],[f1240,f8694]) ).
fof(f8694,plain,
( spl0_1032
<=> ! [X21,X15] : c_0 = c_Divides_Oop_Amod(c_times(X15,X21,tc_nat),X21,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1032])]) ).
fof(f1240,axiom,
! [X21,X15] : c_0 = c_Divides_Oop_Amod(c_times(X15,X21,tc_nat),X21,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Omod__mult__self__is__0_0) ).
fof(f8692,plain,
spl0_1031,
inference(avatar_split_clause,[],[f1238,f8690]) ).
fof(f8690,plain,
( spl0_1031
<=> ! [X21,X15] : c_0 = c_Divides_Oop_Amod(c_times(X21,X15,tc_nat),X21,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1031])]) ).
fof(f1238,axiom,
! [X21,X15] : c_0 = c_Divides_Oop_Amod(c_times(X21,X15,tc_nat),X21,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Omod__mult__self1__is__0_0) ).
fof(f8688,plain,
spl0_1030,
inference(avatar_split_clause,[],[f1195,f8686]) ).
fof(f8686,plain,
( spl0_1030
<=> ! [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_1030])]) ).
fof(f1195,axiom,
! [X2,X18,X1,X16] : c_Datatype__Universe_OLeaf(X18,X1,X2) != c_Datatype__Universe_ONumb(X16,X1,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_ONumb__not__Leaf_0) ).
fof(f8684,plain,
spl0_1029,
inference(avatar_split_clause,[],[f1190,f8682]) ).
fof(f8682,plain,
( spl0_1029
<=> ! [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_1029])]) ).
fof(f1190,axiom,
! [X2,X1,X9,X7] : c_Datatype__Universe_OIn0(X9,X1,X2) != c_Datatype__Universe_OIn1(X7,X1,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OIn0__not__In1_0) ).
fof(f8680,plain,
spl0_1028,
inference(avatar_split_clause,[],[f63,f8678]) ).
fof(f8678,plain,
( spl0_1028
<=> ! [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_1028])]) ).
fof(f63,axiom,
! [X1,X5] :
( ~ c_Wellfounded__Recursion_Owf(X5,X1)
| c_Wellfounded__Recursion_Owf(c_List_Olex(X5,X1),tc_List_Olist(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Owf__lex_0) ).
fof(f8676,plain,
spl0_1027,
inference(avatar_split_clause,[],[f62,f8674]) ).
fof(f8674,plain,
( spl0_1027
<=> ! [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_1027])]) ).
fof(f62,axiom,
! [X1,X5] :
( ~ c_Wellfounded__Recursion_Owf(X5,X1)
| c_Wellfounded__Recursion_Owf(c_List_Olenlex(X5,X1),tc_List_Olist(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Owf__lenlex_0) ).
fof(f8672,plain,
spl0_1026,
inference(avatar_split_clause,[],[f35,f8670]) ).
fof(f35,axiom,
! [X21,X15] : c_Divides_Oop_Advd(c_GCD_Ogcd(c_Pair(X15,X21,tc_nat,tc_nat)),X21,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_GCD_Ogcd__dvd2_0) ).
fof(f8668,plain,
spl0_1025,
inference(avatar_split_clause,[],[f34,f8666]) ).
fof(f34,axiom,
! [X21,X15] : c_Divides_Oop_Advd(c_GCD_Ogcd(c_Pair(X15,X21,tc_nat,tc_nat)),X15,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_GCD_Ogcd__dvd1_0) ).
fof(f8660,plain,
( ~ spl0_1024
| ~ spl0_816
| ~ spl0_997 ),
inference(avatar_split_clause,[],[f8639,f8421,f7605,f8657]) ).
fof(f8657,plain,
( spl0_1024
<=> c_emptyset = c_SetInterval_OatMost(c_0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1024])]) ).
fof(f8639,plain,
( c_emptyset != c_SetInterval_OatMost(c_0,tc_nat)
| ~ spl0_816
| ~ spl0_997 ),
inference(superposition,[],[f7606,f8423]) ).
fof(f8631,plain,
( ~ spl0_57
| spl0_1023
| ~ spl0_874
| ~ spl0_987 ),
inference(avatar_split_clause,[],[f8567,f8380,f7850,f8628,f3692]) ).
fof(f8628,plain,
( spl0_1023
<=> c_IntDef_Oiszero(c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1023])]) ).
fof(f7850,plain,
( spl0_874
<=> ! [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_874])]) ).
fof(f8380,plain,
( spl0_987
<=> c_0 = c_Numeral_Onumber__of(c_Numeral_OPls,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_987])]) ).
fof(f8567,plain,
( c_IntDef_Oiszero(c_0,tc_IntDef_Oint)
| ~ class_Numeral_Onumber__ring(tc_IntDef_Oint)
| ~ spl0_874
| ~ spl0_987 ),
inference(superposition,[],[f7851,f8382]) ).
fof(f8382,plain,
( c_0 = c_Numeral_Onumber__of(c_Numeral_OPls,tc_IntDef_Oint)
| ~ spl0_987 ),
inference(avatar_component_clause,[],[f8380]) ).
fof(f7851,plain,
( ! [X1] :
( c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_OPls,X1),X1)
| ~ class_Numeral_Onumber__ring(X1) )
| ~ spl0_874 ),
inference(avatar_component_clause,[],[f7850]) ).
fof(f8526,plain,
spl0_1022,
inference(avatar_split_clause,[],[f3281,f8524]) ).
fof(f3281,plain,
! [X1] :
( c_1 = c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OPls),X1)
| ~ class_Numeral_Onumber__ring(X1) ),
inference(forward_demodulation,[],[f2170,f2156]) ).
fof(f2170,axiom,
! [X1] :
( ~ class_Numeral_Onumber__ring(X1)
| c_1 = c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Onumeral__1__eq__1_0) ).
fof(f8522,plain,
spl0_1021,
inference(avatar_split_clause,[],[f3227,f8520]) ).
fof(f8520,plain,
( spl0_1021
<=> ! [X15] : c_1 = c_GCD_Ogcd(c_Pair(c_1,X15,tc_nat,tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1021])]) ).
fof(f3227,plain,
! [X15] : c_1 = c_GCD_Ogcd(c_Pair(c_1,X15,tc_nat,tc_nat)),
inference(forward_demodulation,[],[f3009,f2958]) ).
fof(f3009,plain,
! [X15] : c_1 = c_GCD_Ogcd(c_Pair(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),X15,tc_nat,tc_nat)),
inference(definition_unfolding,[],[f1300,f2544]) ).
fof(f1300,axiom,
! [X15] : c_1 = c_GCD_Ogcd(c_Pair(c_Suc(c_0),X15,tc_nat,tc_nat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_GCD_Ogcd__1__left_0) ).
fof(f8518,plain,
spl0_1020,
inference(avatar_split_clause,[],[f3226,f8516]) ).
fof(f3226,plain,
! [X15] : c_1 = c_GCD_Ogcd(c_Pair(X15,c_1,tc_nat,tc_nat)),
inference(forward_demodulation,[],[f3008,f2958]) ).
fof(f3008,plain,
! [X15] : c_1 = c_GCD_Ogcd(c_Pair(X15,c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),tc_nat,tc_nat)),
inference(definition_unfolding,[],[f1299,f2544]) ).
fof(f1299,axiom,
! [X15] : c_1 = c_GCD_Ogcd(c_Pair(X15,c_Suc(c_0),tc_nat,tc_nat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_GCD_Ogcd__1_0) ).
fof(f8514,plain,
spl0_1019,
inference(avatar_split_clause,[],[f2993,f8512]) ).
fof(f2993,plain,
! [X7,X13] : ~ c_in(c_Message_Omsg_ONonce(X7),c_Message_Oparts(c_Event_Oknows(X13,c_List_Olist_ONil)),tc_Message_Omsg),
inference(definition_unfolding,[],[f2894,f2795]) ).
fof(f2894,axiom,
! [X7,X13] : ~ c_in(c_Message_Omsg_ONonce(X7),c_Message_Oparts(c_Event_OinitState(X13)),tc_Message_Omsg),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Public_ONonce__notin__initState_0) ).
fof(f8510,plain,
spl0_1018,
inference(avatar_split_clause,[],[f2964,f8508]) ).
fof(f8508,plain,
( spl0_1018
<=> ! [X21] : c_less(X21,c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1018])]) ).
fof(f2964,plain,
! [X21] : c_less(X21,c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),tc_nat),
inference(definition_unfolding,[],[f65,f2544]) ).
fof(f65,axiom,
! [X21] : c_less(X21,c_Suc(X21),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_OlessI_0) ).
fof(f8506,plain,
spl0_1017,
inference(avatar_split_clause,[],[f2963,f8504]) ).
fof(f8504,plain,
( spl0_1017
<=> ! [X21] : c_less(c_0,c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1017])]) ).
fof(f2963,plain,
! [X21] : c_less(c_0,c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),tc_nat),
inference(definition_unfolding,[],[f67,f2544]) ).
fof(f67,axiom,
! [X21] : c_less(c_0,c_Suc(X21),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Ozero__less__Suc_0) ).
fof(f8502,plain,
spl0_1016,
inference(avatar_split_clause,[],[f2927,f8500]) ).
fof(f8500,plain,
( spl0_1016
<=> ! [X0,X3] :
( X0 = X3
| c_Public_OshrK(X0) != c_Public_OshrK(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1016])]) ).
fof(f2927,axiom,
! [X3,X0] :
( X0 = X3
| c_Public_OshrK(X0) != c_Public_OshrK(X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Public_OshrK__injective_0) ).
fof(f8498,plain,
spl0_1015,
inference(avatar_split_clause,[],[f2925,f8496]) ).
fof(f8496,plain,
( spl0_1015
<=> ! [X102,X12] : c_in(c_Message_Omsg_OKey(c_Public_OshrK(X12)),c_Event_Oknows(X12,X102),tc_Message_Omsg) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1015])]) ).
fof(f2925,axiom,
! [X12,X102] : c_in(c_Message_Omsg_OKey(c_Public_OshrK(X12)),c_Event_Oknows(X12,X102),tc_Message_Omsg),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Public_OshrK__in__knows_0) ).
fof(f8494,plain,
spl0_1014,
inference(avatar_split_clause,[],[f2921,f8492]) ).
fof(f8492,plain,
( spl0_1014
<=> ! [X102,X27,X12] : c_in(c_Message_Omsg_OKey(c_Public_OpublicKey(X27,X12)),c_Event_Oused(X102),tc_Message_Omsg) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1014])]) ).
fof(f2921,axiom,
! [X27,X12,X102] : c_in(c_Message_Omsg_OKey(c_Public_OpublicKey(X27,X12)),c_Event_Oused(X102),tc_Message_Omsg),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Public_OpublicKey__into__used_0) ).
fof(f8490,plain,
spl0_1013,
inference(avatar_split_clause,[],[f2915,f8488]) ).
fof(f8488,plain,
( spl0_1013
<=> ! [X4,X27,X12,X111] : c_Message_OinvKey(c_Public_OpublicKey(X27,X12)) != c_Public_OpublicKey(X4,X111) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1013])]) ).
fof(f2915,axiom,
! [X111,X27,X4,X12] : c_Message_OinvKey(c_Public_OpublicKey(X27,X12)) != c_Public_OpublicKey(X4,X111),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Public_OprivateKey_Ab1_AA1_A_61_ApublicKey_Ac1_AA_H1_A_61_61_AFalse_0) ).
fof(f8486,plain,
spl0_1012,
inference(avatar_split_clause,[],[f2899,f8484]) ).
fof(f8484,plain,
( spl0_1012
<=> ! [X3] :
( ~ c_in(X3,c_Message_OsymKeys,tc_nat)
| c_Message_OinvKey(X3) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1012])]) ).
fof(f2899,axiom,
! [X3] :
( ~ c_in(X3,c_Message_OsymKeys,tc_nat)
| c_Message_OinvKey(X3) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Public_OinvKey__K_0) ).
fof(f8482,plain,
spl0_1011,
inference(avatar_split_clause,[],[f2788,f8480]) ).
fof(f8480,plain,
( spl0_1011
<=> ! [X103,X96,X104] : c_0 = c_Nat_Osize(c_Event_Oevent_OSays(X103,X104,X96),tc_Event_Oevent) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1011])]) ).
fof(f2788,axiom,
! [X96,X104,X103] : c_0 = c_Nat_Osize(c_Event_Oevent_OSays(X103,X104,X96),tc_Event_Oevent),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Event_Oevent_Osize__1_0) ).
fof(f8478,plain,
spl0_1010,
inference(avatar_split_clause,[],[f2778,f8476]) ).
fof(f8476,plain,
( spl0_1010
<=> ! [X95,X97,X104,X103,X96] : c_Event_Oevent_OSays(X103,X104,X96) != c_Event_Oevent_ONotes(X95,X97) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1010])]) ).
fof(f2778,axiom,
! [X96,X97,X104,X95,X103] : c_Event_Oevent_OSays(X103,X104,X96) != c_Event_Oevent_ONotes(X95,X97),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Event_Oevent_Odistinct__4_0) ).
fof(f8474,plain,
( spl0_1009
| ~ spl0_45
| ~ spl0_884 ),
inference(avatar_split_clause,[],[f8082,f7890,f3632,f8471]) ).
fof(f8471,plain,
( spl0_1009
<=> c_0 = c_OrderedGroup_Opprt(c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1009])]) ).
fof(f7890,plain,
( spl0_884
<=> ! [X1] :
( ~ class_OrderedGroup_Olordered__ab__group(X1)
| c_0 = c_OrderedGroup_Opprt(c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_884])]) ).
fof(f8082,plain,
( c_0 = c_OrderedGroup_Opprt(c_0,tc_IntDef_Oint)
| ~ spl0_45
| ~ spl0_884 ),
inference(resolution,[],[f7891,f3634]) ).
fof(f3634,plain,
( class_OrderedGroup_Olordered__ab__group(tc_IntDef_Oint)
| ~ spl0_45 ),
inference(avatar_component_clause,[],[f3632]) ).
fof(f7891,plain,
( ! [X1] :
( ~ class_OrderedGroup_Olordered__ab__group(X1)
| c_0 = c_OrderedGroup_Opprt(c_0,X1) )
| ~ spl0_884 ),
inference(avatar_component_clause,[],[f7890]) ).
fof(f8469,plain,
spl0_1008,
inference(avatar_split_clause,[],[f2775,f8467]) ).
fof(f8467,plain,
( spl0_1008
<=> ! [X95,X97,X104,X103,X96] : c_Event_Oevent_OSays(X103,X104,X96) != c_Event_Oevent_OGets(X95,X97) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1008])]) ).
fof(f2775,axiom,
! [X96,X97,X104,X95,X103] : c_Event_Oevent_OSays(X103,X104,X96) != c_Event_Oevent_OGets(X95,X97),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Event_Oevent_Odistinct__1_0) ).
fof(f8465,plain,
spl0_1007,
inference(avatar_split_clause,[],[f2755,f8463]) ).
fof(f8463,plain,
( spl0_1007
<=> ! [X96,X97] :
( X96 = X97
| c_Message_Omsg_OHash(X96) != c_Message_Omsg_OHash(X97) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1007])]) ).
fof(f2755,axiom,
! [X96,X97] :
( X96 = X97
| c_Message_Omsg_OHash(X96) != c_Message_Omsg_OHash(X97) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Omsg_Oinject__5_0) ).
fof(f8461,plain,
spl0_1006,
inference(avatar_split_clause,[],[f2754,f8459]) ).
fof(f8459,plain,
( spl0_1006
<=> ! [X89,X90] :
( X89 = X90
| c_Message_Omsg_OKey(X90) != c_Message_Omsg_OKey(X89) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1006])]) ).
fof(f2754,axiom,
! [X90,X89] :
( X89 = X90
| c_Message_Omsg_OKey(X90) != c_Message_Omsg_OKey(X89) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Omsg_Oinject__4_0) ).
fof(f8457,plain,
spl0_1005,
inference(avatar_split_clause,[],[f2753,f8455]) ).
fof(f8455,plain,
( spl0_1005
<=> ! [X89,X90] :
( X89 = X90
| c_Message_Omsg_ONonce(X90) != c_Message_Omsg_ONonce(X89) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1005])]) ).
fof(f2753,axiom,
! [X90,X89] :
( X89 = X90
| c_Message_Omsg_ONonce(X90) != c_Message_Omsg_ONonce(X89) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Omsg_Oinject__3_0) ).
fof(f8453,plain,
spl0_1004,
inference(avatar_split_clause,[],[f2752,f8451]) ).
fof(f8451,plain,
( spl0_1004
<=> ! [X89,X90] :
( X89 = X90
| c_Message_Omsg_ONumber(X90) != c_Message_Omsg_ONumber(X89) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1004])]) ).
fof(f2752,axiom,
! [X90,X89] :
( X89 = X90
| c_Message_Omsg_ONumber(X90) != c_Message_Omsg_ONumber(X89) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Omsg_Oinject__2_0) ).
fof(f8449,plain,
spl0_1003,
inference(avatar_split_clause,[],[f2751,f8447]) ).
fof(f8447,plain,
( spl0_1003
<=> ! [X94,X95] :
( X94 = X95
| c_Message_Omsg_OAgent(X94) != c_Message_Omsg_OAgent(X95) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1003])]) ).
fof(f2751,axiom,
! [X94,X95] :
( X94 = X95
| c_Message_Omsg_OAgent(X94) != c_Message_Omsg_OAgent(X95) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Omsg_Oinject__1_0) ).
fof(f8445,plain,
spl0_1002,
inference(avatar_split_clause,[],[f2741,f8443]) ).
fof(f2741,axiom,
! [X91,X92] :
( X91 = X92
| c_Message_OinvKey(X91) != c_Message_OinvKey(X92) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OinvKey__eq_0) ).
fof(f8441,plain,
spl0_1001,
inference(avatar_split_clause,[],[f2736,f8439]) ).
fof(f8439,plain,
( spl0_1001
<=> ! [X89,X90] :
( X89 = X90
| c_Message_Oagent_OFriend(X89) != c_Message_Oagent_OFriend(X90) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1001])]) ).
fof(f2736,axiom,
! [X90,X89] :
( X89 = X90
| c_Message_Oagent_OFriend(X89) != c_Message_Oagent_OFriend(X90) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oagent_Oinject_0) ).
fof(f8437,plain,
spl0_1000,
inference(avatar_split_clause,[],[f2699,f8435]) ).
fof(f8435,plain,
( spl0_1000
<=> ! [X12,X1] :
( c_emptyset = X12
| ~ c_lessequals(X12,c_emptyset,tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1000])]) ).
fof(f2699,axiom,
! [X1,X12] :
( c_emptyset = X12
| ~ c_lessequals(X12,c_emptyset,tc_set(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osubset__empty_0) ).
fof(f8433,plain,
spl0_999,
inference(avatar_split_clause,[],[f2660,f8431]) ).
fof(f2660,axiom,
! [X3,X1] : c_Set_Ocontents(c_insert(X3,c_emptyset,X1),X1) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Ocontents__eq_0) ).
fof(f8429,plain,
( spl0_998
| ~ spl0_45
| ~ spl0_883 ),
inference(avatar_split_clause,[],[f8081,f7886,f3632,f8426]) ).
fof(f8426,plain,
( spl0_998
<=> c_0 = c_OrderedGroup_Onprt(c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_998])]) ).
fof(f7886,plain,
( spl0_883
<=> ! [X1] :
( ~ class_OrderedGroup_Olordered__ab__group(X1)
| c_0 = c_OrderedGroup_Onprt(c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_883])]) ).
fof(f8081,plain,
( c_0 = c_OrderedGroup_Onprt(c_0,tc_IntDef_Oint)
| ~ spl0_45
| ~ spl0_883 ),
inference(resolution,[],[f7887,f3634]) ).
fof(f7887,plain,
( ! [X1] :
( ~ class_OrderedGroup_Olordered__ab__group(X1)
| c_0 = c_OrderedGroup_Onprt(c_0,X1) )
| ~ spl0_883 ),
inference(avatar_component_clause,[],[f7886]) ).
fof(f8424,plain,
spl0_997,
inference(avatar_split_clause,[],[f2534,f8421]) ).
fof(f2534,axiom,
c_SetInterval_OatMost(c_0,tc_nat) = c_insert(c_0,c_emptyset,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatMost__0_0) ).
fof(f8419,plain,
spl0_996,
inference(avatar_split_clause,[],[f2492,f8417]) ).
fof(f8417,plain,
( spl0_996
<=> ! [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_996])]) ).
fof(f2492,axiom,
! [X1,X18] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X1)
| c_0 = c_times(X18,c_0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__zero__right_0) ).
fof(f8415,plain,
spl0_995,
inference(avatar_split_clause,[],[f2491,f8413]) ).
fof(f8413,plain,
( spl0_995
<=> ! [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_995])]) ).
fof(f2491,axiom,
! [X1,X18] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X1)
| c_0 = c_times(c_0,X18,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__zero__left_0) ).
fof(f8411,plain,
spl0_994,
inference(avatar_split_clause,[],[f2474,f8409]) ).
fof(f8409,plain,
( spl0_994
<=> ! [X4,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| c_times(c_1,X4,X1) = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_994])]) ).
fof(f2474,axiom,
! [X1,X4] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| c_times(c_1,X4,X1) = X4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__cancel__right1_2) ).
fof(f8407,plain,
spl0_993,
inference(avatar_split_clause,[],[f2473,f8405]) ).
fof(f8405,plain,
( spl0_993
<=> ! [X27,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| c_0 = c_times(X27,c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_993])]) ).
fof(f2473,axiom,
! [X1,X27] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| c_0 = c_times(X27,c_0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__cancel__right1_1) ).
fof(f8403,plain,
spl0_992,
inference(avatar_split_clause,[],[f2470,f8401]) ).
fof(f8401,plain,
( spl0_992
<=> ! [X4,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| c_times(X4,c_1,X1) = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_992])]) ).
fof(f2470,axiom,
! [X1,X4] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| c_times(X4,c_1,X1) = X4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__cancel__left1_2) ).
fof(f8399,plain,
spl0_991,
inference(avatar_split_clause,[],[f2469,f8397]) ).
fof(f8397,plain,
( spl0_991
<=> ! [X27,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| c_0 = c_times(c_0,X27,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_991])]) ).
fof(f2469,axiom,
! [X1,X27] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| c_0 = c_times(c_0,X27,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__cancel__left1_1) ).
fof(f8395,plain,
spl0_990,
inference(avatar_split_clause,[],[f2379,f8393]) ).
fof(f8393,plain,
( spl0_990
<=> ! [X1,X3] : c_Relation_ORange(c_Relation_Odiag(X3,X1),X1,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_990])]) ).
fof(f2379,axiom,
! [X3,X1] : c_Relation_ORange(c_Relation_Odiag(X3,X1),X1,X1) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_ORange__diag_0) ).
fof(f8391,plain,
spl0_989,
inference(avatar_split_clause,[],[f2377,f8389]) ).
fof(f8389,plain,
( spl0_989
<=> ! [X2,X1,X3] : c_Relation_Orel__comp(X3,c_Relation_OId,X1,X2,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_989])]) ).
fof(f2377,axiom,
! [X2,X3,X1] : c_Relation_Orel__comp(X3,c_Relation_OId,X1,X2,X1) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_OR__O__Id_0) ).
fof(f8387,plain,
spl0_988,
inference(avatar_split_clause,[],[f2371,f8385]) ).
fof(f8385,plain,
( spl0_988
<=> ! [X2,X1,X3] : c_Relation_Orel__comp(c_Relation_OId,X3,X2,X2,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_988])]) ).
fof(f2371,axiom,
! [X2,X3,X1] : c_Relation_Orel__comp(c_Relation_OId,X3,X2,X2,X1) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_OId__O__R_0) ).
fof(f8383,plain,
( spl0_987
| ~ spl0_57
| ~ spl0_880 ),
inference(avatar_split_clause,[],[f8078,f7874,f3692,f8380]) ).
fof(f7874,plain,
( spl0_880
<=> ! [X1] :
( ~ class_Numeral_Onumber__ring(X1)
| c_0 = c_Numeral_Onumber__of(c_Numeral_OPls,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_880])]) ).
fof(f8078,plain,
( c_0 = c_Numeral_Onumber__of(c_Numeral_OPls,tc_IntDef_Oint)
| ~ spl0_57
| ~ spl0_880 ),
inference(resolution,[],[f7875,f3694]) ).
fof(f7875,plain,
( ! [X1] :
( ~ class_Numeral_Onumber__ring(X1)
| c_0 = c_Numeral_Onumber__of(c_Numeral_OPls,X1) )
| ~ spl0_880 ),
inference(avatar_component_clause,[],[f7874]) ).
fof(f8378,plain,
spl0_986,
inference(avatar_split_clause,[],[f2369,f8376]) ).
fof(f8376,plain,
( spl0_986
<=> ! [X1,X3] : c_Relation_ODomain(c_Relation_Odiag(X3,X1),X1,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_986])]) ).
fof(f2369,axiom,
! [X3,X1] : c_Relation_ODomain(c_Relation_Odiag(X3,X1),X1,X1) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_ODomain__diag_0) ).
fof(f8374,plain,
spl0_985,
inference(avatar_split_clause,[],[f2357,f8372]) ).
fof(f8372,plain,
( spl0_985
<=> ! [X18,X1] :
( ~ class_Power_Orecpower(X1)
| c_1 = c_Nat_Opower(X18,c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_985])]) ).
fof(f2357,axiom,
! [X1,X18] :
( ~ class_Power_Orecpower(X1)
| c_1 = c_Nat_Opower(X18,c_0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Power_Orecpower__class_Oaxioms__1_0) ).
fof(f8370,plain,
spl0_984,
inference(avatar_split_clause,[],[f2354,f8368]) ).
fof(f2354,axiom,
! [X3,X1] :
( ~ class_Power_Orecpower(X1)
| c_Nat_Opower(X3,c_1,X1) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Power_Opower__one__right_0) ).
fof(f8366,plain,
spl0_983,
inference(avatar_split_clause,[],[f2353,f8364]) ).
fof(f2353,axiom,
! [X21,X1] :
( ~ class_Power_Orecpower(X1)
| c_1 = c_Nat_Opower(c_1,X21,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Power_Opower__one_0) ).
fof(f8362,plain,
spl0_982,
inference(avatar_split_clause,[],[f2292,f8360]) ).
fof(f8360,plain,
( spl0_982
<=> ! [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_982])]) ).
fof(f2292,axiom,
! [X0] :
( ~ c_Parity_Oeven(X0,tc_IntDef_Oint)
| c_Parity_Oeven(c_uminus(X0,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__neg_1) ).
fof(f8358,plain,
spl0_981,
inference(avatar_split_clause,[],[f2291,f8356]) ).
fof(f8356,plain,
( spl0_981
<=> ! [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_981])]) ).
fof(f2291,axiom,
! [X0] :
( c_Parity_Oeven(X0,tc_IntDef_Oint)
| ~ c_Parity_Oeven(c_uminus(X0,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__neg_0) ).
fof(f8354,plain,
spl0_980,
inference(avatar_split_clause,[],[f2267,f8352]) ).
fof(f2267,axiom,
! [X2,X3] :
( ~ class_Orderings_Olinorder(X2)
| c_Orderings_Omax(X3,X3,X2) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Orderings_Omin__max_Obelow__sup_Osup__idem_0) ).
fof(f8350,plain,
spl0_979,
inference(avatar_split_clause,[],[f2262,f8348]) ).
fof(f2262,axiom,
! [X2,X3] :
( ~ class_Orderings_Olinorder(X2)
| c_Orderings_Omin(X3,X3,X2) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Orderings_Omin__max_Obelow__inf_Oinf__idem_0) ).
fof(f8346,plain,
spl0_978,
inference(avatar_split_clause,[],[f2251,f8344]) ).
fof(f8344,plain,
( spl0_978
<=> ! [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_978])]) ).
fof(f2251,axiom,
! [X1] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
| ~ c_less(c_0,c_HOL_Oabs(c_0,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Ozero__less__abs__iff_0) ).
fof(f8342,plain,
spl0_977,
inference(avatar_split_clause,[],[f2250,f8340]) ).
fof(f8340,plain,
( spl0_977
<=> ! [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_977])]) ).
fof(f2250,axiom,
! [X1,X18] :
( ~ class_OrderedGroup_Olordered__ab__group(X1)
| c_lessequals(c_0,c_OrderedGroup_Opprt(X18,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Ozero__le__pprt_0) ).
fof(f8337,plain,
spl0_976,
inference(avatar_split_clause,[],[f2241,f8335]) ).
fof(f2241,axiom,
! [X1,X18] :
( ~ class_OrderedGroup_Olordered__ab__group(X1)
| c_lessequals(c_OrderedGroup_Onprt(X18,X1),c_0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Onprt__le__zero_0) ).
fof(f8333,plain,
spl0_975,
inference(avatar_split_clause,[],[f2218,f8331]) ).
fof(f2218,axiom,
! [X3,X1] :
( ~ class_OrderedGroup_Omonoid__mult(X1)
| c_times(X3,c_1,X1) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Omonoid__mult__class_Oaxioms__2_0) ).
fof(f8329,plain,
spl0_974,
inference(avatar_split_clause,[],[f2217,f8327]) ).
fof(f2217,axiom,
! [X3,X1] :
( ~ class_OrderedGroup_Omonoid__mult(X1)
| c_times(c_1,X3,X1) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Omonoid__mult__class_Oaxioms__1_0) ).
fof(f8325,plain,
spl0_973,
inference(avatar_split_clause,[],[f2205,f8323]) ).
fof(f2205,axiom,
! [X1,X18] :
( ~ class_OrderedGroup_Oab__group__add(X1)
| c_0 = c_minus(X18,X18,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Odiff__self_0) ).
fof(f8321,plain,
spl0_972,
inference(avatar_split_clause,[],[f2198,f8319]) ).
fof(f2198,axiom,
! [X3,X1] :
( ~ class_OrderedGroup_Oab__group__add(X1)
| c_minus(X3,c_0,X1) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Odiff__0__right_0) ).
fof(f8317,plain,
spl0_971,
inference(avatar_split_clause,[],[f2196,f8315]) ).
fof(f2196,axiom,
! [X3,X1] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| c_plus(c_0,X3,X1) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Ocomm__monoid__add__class_Oaxioms_0) ).
fof(f8313,plain,
spl0_970,
inference(avatar_split_clause,[],[f2185,f8311]) ).
fof(f2185,axiom,
! [X3,X1] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| c_plus(X3,c_0,X1) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oadd__0__right_0) ).
fof(f8309,plain,
spl0_969,
inference(avatar_split_clause,[],[f2182,f8307]) ).
fof(f8307,plain,
( spl0_969
<=> ! [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_969])]) ).
fof(f2182,axiom,
! [X1,X18] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
| ~ c_less(c_HOL_Oabs(X18,X1),c_0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__not__less__zero_0) ).
fof(f8305,plain,
spl0_968,
inference(avatar_split_clause,[],[f2180,f8303]) ).
fof(f8303,plain,
( spl0_968
<=> ! [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_968])]) ).
fof(f2180,axiom,
! [X1] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
| c_lessequals(c_HOL_Oabs(c_0,X1),c_0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__le__zero__iff_1) ).
fof(f8301,plain,
spl0_967,
inference(avatar_split_clause,[],[f2177,f8299]) ).
fof(f8299,plain,
( spl0_967
<=> ! [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_967])]) ).
fof(f2177,axiom,
! [X1,X18] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
| c_lessequals(c_0,c_HOL_Oabs(X18,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__ge__zero_0) ).
fof(f8297,plain,
spl0_966,
inference(avatar_split_clause,[],[f2153,f8295]) ).
fof(f2153,axiom,
! [X11] : c_Numeral_OBit(X11,c_Numeral_Obit_OB1) = c_Numeral_Obin__succ(c_Numeral_OBit(X11,c_Numeral_Obit_OB0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obin__succ__0_0) ).
fof(f8293,plain,
spl0_965,
inference(avatar_split_clause,[],[f1865,f8291]) ).
fof(f8291,plain,
( spl0_965
<=> ! [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_965])]) ).
fof(f1865,axiom,
! [X11] : c_IntDef_Onat(c_Numeral_Onumber__of(X11,tc_IntDef_Oint)) = c_Numeral_Onumber__of(X11,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatBin_Onat__number__of_0) ).
fof(f8289,plain,
spl0_964,
inference(avatar_split_clause,[],[f1818,f8287]) ).
fof(f8287,plain,
( spl0_964
<=> ! [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_964])]) ).
fof(f1818,axiom,
! [X1,X15] :
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_less(c_NatArith_Oof__nat(X15,X1),c_0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__less__0__iff_0) ).
fof(f8285,plain,
spl0_963,
inference(avatar_split_clause,[],[f1815,f8283]) ).
fof(f8283,plain,
( spl0_963
<=> ! [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_963])]) ).
fof(f1815,axiom,
! [X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| c_lessequals(c_NatArith_Oof__nat(c_0,X1),c_0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__le__0__iff_1) ).
fof(f8281,plain,
spl0_962,
inference(avatar_split_clause,[],[f1805,f8279]) ).
fof(f8279,plain,
( spl0_962
<=> ! [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_962])]) ).
fof(f1805,axiom,
! [X21,X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| c_lessequals(c_0,c_NatArith_Oof__nat(X21,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__0__le__iff_0) ).
fof(f8277,plain,
spl0_961,
inference(avatar_split_clause,[],[f1779,f8275]) ).
fof(f8275,plain,
( spl0_961
<=> ! [X41,X0,X3] : c_List_Otl(c_List_Olist_OCons(X0,X3,X41),X41) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_961])]) ).
fof(f1779,axiom,
! [X3,X41,X0] : c_List_Otl(c_List_Olist_OCons(X0,X3,X41),X41) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Otl_Osimps__2_0) ).
fof(f8273,plain,
spl0_960,
inference(avatar_split_clause,[],[f1752,f8271]) ).
fof(f8271,plain,
( spl0_960
<=> ! [X1,X23] :
( c_List_Olist_ONil = X23
| c_emptyset != c_List_Oset(X23,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_960])]) ).
fof(f1752,axiom,
! [X1,X23] :
( c_List_Olist_ONil = X23
| c_emptyset != c_List_Oset(X23,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oset__empty_0) ).
fof(f8269,plain,
spl0_959,
inference(avatar_split_clause,[],[f1735,f8267]) ).
fof(f8267,plain,
( spl0_959
<=> ! [X1,X23] :
( c_List_Olist_ONil = X23
| c_List_Olist_ONil != c_List_Orotate1(X23,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_959])]) ).
fof(f1735,axiom,
! [X1,X23] :
( c_List_Olist_ONil = X23
| c_List_Olist_ONil != c_List_Orotate1(X23,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Orotate1__is__Nil__conv_0) ).
fof(f8265,plain,
spl0_958,
inference(avatar_split_clause,[],[f1728,f8263]) ).
fof(f1728,axiom,
! [X1,X23] :
( c_List_Olist_ONil = X23
| c_List_Olist_ONil != c_List_Orev(X23,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Orev__is__Nil__conv_0) ).
fof(f8261,plain,
spl0_957,
inference(avatar_split_clause,[],[f1715,f8259]) ).
fof(f8259,plain,
( spl0_957
<=> ! [X0,X1] :
( c_List_Olist_ONil = X0
| c_List_Olist_ONil != c_List_Oremdups(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_957])]) ).
fof(f1715,axiom,
! [X0,X1] :
( c_List_Olist_ONil = X0
| c_List_Olist_ONil != c_List_Oremdups(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oremdups__eq__nil__iff_0) ).
fof(f8257,plain,
spl0_956,
inference(avatar_split_clause,[],[f1588,f8255]) ).
fof(f8255,plain,
( spl0_956
<=> ! [X0,X1] : c_List_Olast(c_List_Olist_OCons(X0,c_List_Olist_ONil,X1),X1) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_956])]) ).
fof(f1588,axiom,
! [X0,X1] : c_List_Olast(c_List_Olist_OCons(X0,c_List_Olist_ONil,X1),X1) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olast_Osimps_0) ).
fof(f8253,plain,
spl0_955,
inference(avatar_split_clause,[],[f1579,f8251]) ).
fof(f8251,plain,
( spl0_955
<=> ! [X1,X23,X3] : c_List_Ohd(c_List_Olist_OCons(X3,X23,X1),X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_955])]) ).
fof(f1579,axiom,
! [X3,X1,X23] : c_List_Ohd(c_List_Olist_OCons(X3,X23,X1),X1) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Ohd_Osimps_0) ).
fof(f8249,plain,
spl0_954,
inference(avatar_split_clause,[],[f1562,f8247]) ).
fof(f8247,plain,
( spl0_954
<=> ! [X1,X23] :
( ~ c_List_Odistinct(X23,X1)
| c_List_Odistinct(c_List_Orev(X23,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_954])]) ).
fof(f1562,axiom,
! [X1,X23] :
( ~ c_List_Odistinct(X23,X1)
| c_List_Odistinct(c_List_Orev(X23,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Odistinct__rev_1) ).
fof(f8245,plain,
spl0_953,
inference(avatar_split_clause,[],[f1561,f8243]) ).
fof(f8243,plain,
( spl0_953
<=> ! [X1,X23] :
( c_List_Odistinct(X23,X1)
| ~ c_List_Odistinct(c_List_Orev(X23,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_953])]) ).
fof(f1561,axiom,
! [X1,X23] :
( c_List_Odistinct(X23,X1)
| ~ c_List_Odistinct(c_List_Orev(X23,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Odistinct__rev_0) ).
fof(f8241,plain,
spl0_952,
inference(avatar_split_clause,[],[f1550,f8239]) ).
fof(f8239,plain,
( spl0_952
<=> ! [X1,X23] :
( ~ c_List_Odistinct(X23,X1)
| c_List_Odistinct(c_List_Orotate1(X23,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_952])]) ).
fof(f1550,axiom,
! [X1,X23] :
( ~ c_List_Odistinct(X23,X1)
| c_List_Odistinct(c_List_Orotate1(X23,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Odistinct1__rotate_1) ).
fof(f8237,plain,
spl0_951,
inference(avatar_split_clause,[],[f1549,f8235]) ).
fof(f8235,plain,
( spl0_951
<=> ! [X1,X23] :
( c_List_Odistinct(X23,X1)
| ~ c_List_Odistinct(c_List_Orotate1(X23,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_951])]) ).
fof(f1549,axiom,
! [X1,X23] :
( c_List_Odistinct(X23,X1)
| ~ c_List_Odistinct(c_List_Orotate1(X23,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Odistinct1__rotate_0) ).
fof(f8233,plain,
spl0_950,
inference(avatar_split_clause,[],[f1537,f8231]) ).
fof(f8231,plain,
( spl0_950
<=> ! [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_950])]) ).
fof(f1537,axiom,
! [X41,X0] : c_List_Olist_ONil = c_List_Obutlast(c_List_Olist_OCons(X0,c_List_Olist_ONil,X41),X41),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Obutlast_Osimps__2_0) ).
fof(f8229,plain,
spl0_949,
inference(avatar_split_clause,[],[f1499,f8227]) ).
fof(f1499,axiom,
! [X3,X1] :
( ~ class_LOrder_Omeet__semilorder(X1)
| c_LOrder_Omeet(X3,X3,X1) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_LOrder_Omeet__idempotent_0) ).
fof(f8225,plain,
spl0_948,
inference(avatar_split_clause,[],[f1498,f8223]) ).
fof(f1498,axiom,
! [X3,X1] :
( ~ class_LOrder_Ojoin__semilorder(X1)
| c_LOrder_Ojoin(X3,X3,X1) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_LOrder_Ojoin__idempotent_0) ).
fof(f8221,plain,
spl0_947,
inference(avatar_split_clause,[],[f1490,f8219]) ).
fof(f8219,plain,
( spl0_947
<=> ! [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_947])]) ).
fof(f1490,axiom,
! [X18] : c_0 = c_Divides_Oop_Amod(X18,c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozmod__minus1__right_0) ).
fof(f8217,plain,
( ~ spl0_945
| spl0_946
| ~ spl0_715
| ~ spl0_874 ),
inference(avatar_split_clause,[],[f8072,f7850,f7174,f8214,f8210]) ).
fof(f8210,plain,
( spl0_945
<=> class_Numeral_Onumber__ring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_945])]) ).
fof(f8214,plain,
( spl0_946
<=> c_IntDef_Oiszero(c_0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_946])]) ).
fof(f8072,plain,
( c_IntDef_Oiszero(c_0,tc_nat)
| ~ class_Numeral_Onumber__ring(tc_nat)
| ~ spl0_715
| ~ spl0_874 ),
inference(superposition,[],[f7851,f7176]) ).
fof(f8208,plain,
spl0_944,
inference(avatar_split_clause,[],[f1419,f8206]) ).
fof(f1419,axiom,
! [X21,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1)
| c_in(c_NatArith_Oof__nat(X21,X1),c_IntDef_ONats,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oof__nat__in__Nats_0) ).
fof(f8204,plain,
spl0_943,
inference(avatar_split_clause,[],[f1392,f8202]) ).
fof(f1392,axiom,
! [X21,X15] : ~ c_less(c_IntDef_Oint(X21),c_uminus(c_IntDef_Oint(X15),tc_IntDef_Oint),tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Onot__int__zless__negative_0) ).
fof(f8200,plain,
spl0_942,
inference(avatar_split_clause,[],[f1385,f8198]) ).
fof(f1385,axiom,
! [X48] :
( ~ c_lessequals(X48,c_0,tc_IntDef_Oint)
| c_0 = c_IntDef_Onat(X48) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Onat__le__0_0) ).
fof(f8196,plain,
spl0_941,
inference(avatar_split_clause,[],[f1376,f8194]) ).
fof(f8194,plain,
( spl0_941
<=> ! [X21] :
( c_0 = X21
| ~ c_lessequals(c_IntDef_Oint(X21),c_0,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_941])]) ).
fof(f1376,axiom,
! [X21] :
( c_0 = X21
| ~ c_lessequals(c_IntDef_Oint(X21),c_0,tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oint__le__0__conv_0) ).
fof(f8192,plain,
spl0_940,
inference(avatar_split_clause,[],[f1375,f8190]) ).
fof(f1375,axiom,
! [X21,X15] :
( X15 = X21
| c_IntDef_Oint(X21) != c_IntDef_Oint(X15) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oint__int__eq_0) ).
fof(f8188,plain,
spl0_939,
inference(avatar_split_clause,[],[f1308,f8186]) ).
fof(f8186,plain,
( spl0_939
<=> ! [X3] : c_GCD_Ogcd(c_Pair(X3,X3,tc_nat,tc_nat)) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_939])]) ).
fof(f1308,axiom,
! [X3] : c_GCD_Ogcd(c_Pair(X3,X3,tc_nat,tc_nat)) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_GCD_Ogcd__self_0) ).
fof(f8184,plain,
spl0_938,
inference(avatar_split_clause,[],[f1298,f8182]) ).
fof(f8182,plain,
( spl0_938
<=> ! [X3] : c_GCD_Ogcd(c_Pair(c_0,X3,tc_nat,tc_nat)) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_938])]) ).
fof(f1298,axiom,
! [X3] : c_GCD_Ogcd(c_Pair(c_0,X3,tc_nat,tc_nat)) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_GCD_Ogcd__0__left_0) ).
fof(f8180,plain,
spl0_937,
inference(avatar_split_clause,[],[f1297,f8178]) ).
fof(f8178,plain,
( spl0_937
<=> ! [X3] : c_GCD_Ogcd(c_Pair(X3,c_0,tc_nat,tc_nat)) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_937])]) ).
fof(f1297,axiom,
! [X3] : c_GCD_Ogcd(c_Pair(X3,c_0,tc_nat,tc_nat)) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_GCD_Ogcd__0_0) ).
fof(f8176,plain,
spl0_936,
inference(avatar_split_clause,[],[f1177,f8174]) ).
fof(f8174,plain,
( spl0_936
<=> ! [X18,X1] : c_0 = c_Nat_Osize(c_Datatype_Ooption_OSome(X18,X1),tc_Datatype_Ooption(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_936])]) ).
fof(f1177,axiom,
! [X18,X1] : c_0 = c_Nat_Osize(c_Datatype_Ooption_OSome(X18,X1),tc_Datatype_Ooption(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype_Ooption_Osize__2_0) ).
fof(f8172,plain,
spl0_935,
inference(avatar_split_clause,[],[f1171,f8170]) ).
fof(f8170,plain,
( spl0_935
<=> ! [X1,X40] :
( c_Datatype_Ooption_ONone = X40
| c_emptyset != c_Datatype_Oo2s(X40,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_935])]) ).
fof(f1171,axiom,
! [X40,X1] :
( c_Datatype_Ooption_ONone = X40
| c_emptyset != c_Datatype_Oo2s(X40,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype_Oo2s__empty__eq_0) ).
fof(f8167,plain,
spl0_934,
inference(avatar_split_clause,[],[f1167,f8165]) ).
fof(f8165,plain,
( spl0_934
<=> ! [X0,X1] : c_in(X0,c_Datatype_Oo2s(c_Datatype_Ooption_OSome(X0,X1),X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_934])]) ).
fof(f1167,axiom,
! [X0,X1] : c_in(X0,c_Datatype_Oo2s(c_Datatype_Ooption_OSome(X0,X1),X1),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype_Oelem__o2s_1) ).
fof(f8163,plain,
spl0_933,
inference(avatar_split_clause,[],[f252,f8161]) ).
fof(f8161,plain,
( spl0_933
<=> ! [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_933])]) ).
fof(f252,axiom,
! [X38,X37] :
( ~ class_Finite__Set_Ofinite(X38)
| ~ class_Finite__Set_Ofinite(X37)
| class_Finite__Set_Ofinite(tc_sum(X38,X37)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_sum_0) ).
fof(f8159,plain,
spl0_932,
inference(avatar_split_clause,[],[f246,f8157]) ).
fof(f8157,plain,
( spl0_932
<=> ! [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_932])]) ).
fof(f246,axiom,
! [X38,X37] :
( ~ class_Finite__Set_Ofinite(X38)
| ~ class_Finite__Set_Ofinite(X37)
| class_Finite__Set_Ofinite(tc_prod(X38,X37)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_prod_0) ).
fof(f8155,plain,
spl0_931,
inference(avatar_split_clause,[],[f196,f8153]) ).
fof(f8153,plain,
( spl0_931
<=> ! [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_931])]) ).
fof(f196,axiom,
! [X38,X37] :
( ~ class_Finite__Set_Ofinite(X38)
| ~ class_Finite__Set_Ofinite(X37)
| class_Finite__Set_Ofinite(tc_fun(X38,X37)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun_0) ).
fof(f8151,plain,
spl0_930,
inference(avatar_split_clause,[],[f94,f8149]) ).
fof(f8149,plain,
( spl0_930
<=> ! [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_930])]) ).
fof(f94,axiom,
! [X26,X14] : c_in(c_SetInterval_OgreaterThanLessThan(X26,X14,tc_IntDef_Oint),c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__greaterThanLessThan__int_0) ).
fof(f8147,plain,
spl0_929,
inference(avatar_split_clause,[],[f93,f8145]) ).
fof(f8145,plain,
( spl0_929
<=> ! [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_929])]) ).
fof(f93,axiom,
! [X26,X14] : c_in(c_SetInterval_OgreaterThanLessThan(X26,X14,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__greaterThanLessThan_0) ).
fof(f8143,plain,
spl0_928,
inference(avatar_split_clause,[],[f92,f8141]) ).
fof(f8141,plain,
( spl0_928
<=> ! [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_928])]) ).
fof(f92,axiom,
! [X26,X14] : c_in(c_SetInterval_OgreaterThanAtMost(X26,X14,tc_IntDef_Oint),c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__greaterThanAtMost__int_0) ).
fof(f8139,plain,
spl0_927,
inference(avatar_split_clause,[],[f91,f8137]) ).
fof(f8137,plain,
( spl0_927
<=> ! [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_927])]) ).
fof(f91,axiom,
! [X26,X14] : c_in(c_SetInterval_OgreaterThanAtMost(X26,X14,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__greaterThanAtMost_0) ).
fof(f8135,plain,
spl0_926,
inference(avatar_split_clause,[],[f89,f8133]) ).
fof(f8133,plain,
( spl0_926
<=> ! [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_926])]) ).
fof(f89,axiom,
! [X26,X14] : c_in(c_SetInterval_OatLeastLessThan(X26,X14,tc_IntDef_Oint),c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__atLeastLessThan__int_0) ).
fof(f8131,plain,
spl0_925,
inference(avatar_split_clause,[],[f88,f8129]) ).
fof(f88,axiom,
! [X26,X14] : c_in(c_SetInterval_OatLeastLessThan(X26,X14,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__atLeastLessThan_0) ).
fof(f8127,plain,
( spl0_924
| ~ spl0_53
| ~ spl0_867 ),
inference(avatar_split_clause,[],[f8047,f7822,f3672,f8124]) ).
fof(f8124,plain,
( spl0_924
<=> c_0 = c_NatArith_Oof__nat(c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_924])]) ).
fof(f3672,plain,
( spl0_53
<=> class_Ring__and__Field_Oordered__semidom(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_53])]) ).
fof(f7822,plain,
( spl0_867
<=> ! [X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| c_0 = c_NatArith_Oof__nat(c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_867])]) ).
fof(f8047,plain,
( c_0 = c_NatArith_Oof__nat(c_0,tc_IntDef_Oint)
| ~ spl0_53
| ~ spl0_867 ),
inference(resolution,[],[f7823,f3674]) ).
fof(f3674,plain,
( class_Ring__and__Field_Oordered__semidom(tc_IntDef_Oint)
| ~ spl0_53 ),
inference(avatar_component_clause,[],[f3672]) ).
fof(f7823,plain,
( ! [X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| c_0 = c_NatArith_Oof__nat(c_0,X1) )
| ~ spl0_867 ),
inference(avatar_component_clause,[],[f7822]) ).
fof(f8122,plain,
spl0_923,
inference(avatar_split_clause,[],[f87,f8120]) ).
fof(f8120,plain,
( spl0_923
<=> ! [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_923])]) ).
fof(f87,axiom,
! [X26,X14] : c_in(c_SetInterval_OatLeastAtMost(X26,X14,tc_IntDef_Oint),c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__atLeastAtMost__int_0) ).
fof(f8118,plain,
spl0_922,
inference(avatar_split_clause,[],[f86,f8116]) ).
fof(f8116,plain,
( spl0_922
<=> ! [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_922])]) ).
fof(f86,axiom,
! [X26,X14] : c_in(c_SetInterval_OatLeastAtMost(X26,X14,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__atLeastAtMost_0) ).
fof(f8114,plain,
spl0_921,
inference(avatar_split_clause,[],[f37,f8112]) ).
fof(f37,axiom,
! [X21,X15] : c_lessequals(c_uminus(c_IntDef_Oint(X21),tc_IntDef_Oint),c_IntDef_Oint(X15),tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Onegative__zle_0) ).
fof(f8110,plain,
spl0_920,
inference(avatar_split_clause,[],[f2950,f8107]) ).
fof(f2950,axiom,
c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_A,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K),c_Message_Omsg_OMPair(v_na,v_nb)))),c_Message_Omsg_OCrypt(c_Public_OshrK(v_B),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OKey(v_K))))),c_List_Oset(v_evso,tc_Event_Oevent),tc_Event_Oevent),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_4) ).
fof(f8101,plain,
( spl0_919
| ~ spl0_26
| ~ spl0_866 ),
inference(avatar_split_clause,[],[f8045,f7818,f3537,f8098]) ).
fof(f8098,plain,
( spl0_919
<=> c_1 = c_NatArith_Oof__nat(c_1,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_919])]) ).
fof(f3537,plain,
( spl0_26
<=> class_Ring__and__Field_Ocomm__semiring__1__cancel(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_26])]) ).
fof(f7818,plain,
( spl0_866
<=> ! [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_866])]) ).
fof(f8045,plain,
( c_1 = c_NatArith_Oof__nat(c_1,tc_IntDef_Oint)
| ~ spl0_26
| ~ spl0_866 ),
inference(resolution,[],[f7819,f3539]) ).
fof(f3539,plain,
( class_Ring__and__Field_Ocomm__semiring__1__cancel(tc_IntDef_Oint)
| ~ spl0_26 ),
inference(avatar_component_clause,[],[f3537]) ).
fof(f7819,plain,
( ! [X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1)
| c_1 = c_NatArith_Oof__nat(c_1,X1) )
| ~ spl0_866 ),
inference(avatar_component_clause,[],[f7818]) ).
fof(f8095,plain,
( spl0_918
| ~ spl0_27
| ~ spl0_858 ),
inference(avatar_split_clause,[],[f8039,f7786,f3542,f8092]) ).
fof(f8092,plain,
( spl0_918
<=> c_1 = c_IntDef_Oof__int(c_1,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_918])]) ).
fof(f7786,plain,
( spl0_858
<=> ! [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_858])]) ).
fof(f8039,plain,
( c_1 = c_IntDef_Oof__int(c_1,tc_IntDef_Oint)
| ~ spl0_27
| ~ spl0_858 ),
inference(resolution,[],[f7787,f3544]) ).
fof(f7787,plain,
( ! [X1] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X1)
| c_1 = c_IntDef_Oof__int(c_1,X1) )
| ~ spl0_858 ),
inference(avatar_component_clause,[],[f7786]) ).
fof(f8089,plain,
( spl0_917
| ~ spl0_55
| ~ spl0_857 ),
inference(avatar_split_clause,[],[f8038,f7782,f3682,f8086]) ).
fof(f8086,plain,
( spl0_917
<=> c_0 = c_IntDef_Oof__int(c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_917])]) ).
fof(f3682,plain,
( spl0_55
<=> class_Ring__and__Field_Oordered__idom(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_55])]) ).
fof(f7782,plain,
( spl0_857
<=> ! [X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| c_0 = c_IntDef_Oof__int(c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_857])]) ).
fof(f8038,plain,
( c_0 = c_IntDef_Oof__int(c_0,tc_IntDef_Oint)
| ~ spl0_55
| ~ spl0_857 ),
inference(resolution,[],[f7783,f3684]) ).
fof(f3684,plain,
( class_Ring__and__Field_Oordered__idom(tc_IntDef_Oint)
| ~ spl0_55 ),
inference(avatar_component_clause,[],[f3682]) ).
fof(f7783,plain,
( ! [X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| c_0 = c_IntDef_Oof__int(c_0,X1) )
| ~ spl0_857 ),
inference(avatar_component_clause,[],[f7782]) ).
fof(f8077,plain,
( spl0_916
| ~ spl0_647
| ~ spl0_854 ),
inference(avatar_split_clause,[],[f8032,f7770,f6106,f8074]) ).
fof(f8032,plain,
( c_0 = c_HOL_Oabs(c_0,tc_IntDef_Oint)
| ~ spl0_647
| ~ spl0_854 ),
inference(superposition,[],[f7771,f6108]) ).
fof(f8056,plain,
( spl0_915
| ~ spl0_646
| ~ spl0_854 ),
inference(avatar_split_clause,[],[f8031,f7770,f6101,f8053]) ).
fof(f8053,plain,
( spl0_915
<=> c_1 = c_HOL_Oabs(c_1,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_915])]) ).
fof(f8031,plain,
( c_1 = c_HOL_Oabs(c_1,tc_IntDef_Oint)
| ~ spl0_646
| ~ spl0_854 ),
inference(superposition,[],[f7771,f6103]) ).
fof(f8026,plain,
( spl0_914
| ~ spl0_837
| ~ spl0_848 ),
inference(avatar_split_clause,[],[f8021,f7746,f7692,f8024]) ).
fof(f7692,plain,
( spl0_837
<=> ! [X3] : c_div(X3,c_1,tc_nat) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_837])]) ).
fof(f8021,plain,
( ! [X0] : c_lessequals(X0,X0,tc_nat)
| ~ spl0_837
| ~ spl0_848 ),
inference(superposition,[],[f7747,f7693]) ).
fof(f7693,plain,
( ! [X3] : c_div(X3,c_1,tc_nat) = X3
| ~ spl0_837 ),
inference(avatar_component_clause,[],[f7692]) ).
fof(f8010,plain,
spl0_913,
inference(avatar_split_clause,[],[f3306,f8008]) ).
fof(f8008,plain,
( spl0_913
<=> ! [X15] :
( ~ c_Divides_Oop_Advd(X15,c_1,tc_nat)
| c_1 = X15 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_913])]) ).
fof(f3306,plain,
! [X15] :
( ~ c_Divides_Oop_Advd(X15,c_1,tc_nat)
| c_1 = X15 ),
inference(forward_demodulation,[],[f3305,f2958]) ).
fof(f3305,plain,
! [X15] :
( c_1 = X15
| ~ c_Divides_Oop_Advd(X15,c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),tc_nat) ),
inference(forward_demodulation,[],[f3117,f2958]) ).
fof(f3117,plain,
! [X15] :
( c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat) = X15
| ~ c_Divides_Oop_Advd(X15,c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f1227,f2544,f2544]) ).
fof(f1227,axiom,
! [X15] :
( c_Suc(c_0) = X15
| ~ c_Divides_Oop_Advd(X15,c_Suc(c_0),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Odvd__1__iff__1_0) ).
fof(f8006,plain,
spl0_912,
inference(avatar_split_clause,[],[f3214,f8004]) ).
fof(f8004,plain,
( spl0_912
<=> ! [X13,X1] : c_emptyset = c_Relation_OImage(c_emptyset,X13,X1,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_912])]) ).
fof(f3214,plain,
! [X1,X13] : c_emptyset = c_Relation_OImage(c_emptyset,X13,X1,X1),
inference(forward_demodulation,[],[f2980,f2386]) ).
fof(f2386,axiom,
! [X1] : c_emptyset = c_Relation_Odiag(c_emptyset,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_Odiag__empty_0) ).
fof(f2980,plain,
! [X1,X13] : c_emptyset = c_Relation_OImage(c_Relation_Odiag(c_emptyset,X1),X13,X1,X1),
inference(definition_unfolding,[],[f2604,f2373]) ).
fof(f2604,axiom,
! [X1,X13] : c_emptyset = c_inter(c_emptyset,X13,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OInt__empty__left_0) ).
fof(f8002,plain,
spl0_911,
inference(avatar_split_clause,[],[f2984,f8000]) ).
fof(f7998,plain,
spl0_910,
inference(avatar_split_clause,[],[f2982,f7995]) ).
fof(f2982,plain,
c_Numeral_OBit(c_Numeral_OMin,c_Numeral_Obit_OB0) = c_Numeral_Obin__add(c_Numeral_OMin,c_Numeral_OMin),
inference(definition_unfolding,[],[f2133,f2113]) ).
fof(f2133,axiom,
c_Numeral_Obin__pred(c_Numeral_OMin) = c_Numeral_OBit(c_Numeral_OMin,c_Numeral_Obit_OB0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obin__pred__Min_0) ).
fof(f7993,plain,
spl0_909,
inference(avatar_split_clause,[],[f2978,f7991]) ).
fof(f7991,plain,
( spl0_909
<=> ! [X32] : c_emptyset = c_Message_OkeysFor(c_Message_Oparts(c_Event_Oknows(X32,c_List_Olist_ONil))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_909])]) ).
fof(f2978,plain,
! [X32] : c_emptyset = c_Message_OkeysFor(c_Message_Oparts(c_Event_Oknows(X32,c_List_Olist_ONil))),
inference(definition_unfolding,[],[f2909,f2795]) ).
fof(f2909,axiom,
! [X32] : c_emptyset = c_Message_OkeysFor(c_Message_Oparts(c_Event_OinitState(X32))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Public_OkeysFor__parts__initState_0) ).
fof(f7989,plain,
spl0_908,
inference(avatar_split_clause,[],[f2958,f7986]) ).
fof(f7986,plain,
( spl0_908
<=> c_1 = c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_908])]) ).
fof(f7984,plain,
spl0_907,
inference(avatar_split_clause,[],[f2954,f7982]) ).
fof(f7982,plain,
( spl0_907
<=> ! [X15] : c_0 != c_Finite__Set_Ocard(c_SetInterval_OatMost(X15,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_907])]) ).
fof(f2954,plain,
! [X15] : c_0 != c_Finite__Set_Ocard(c_SetInterval_OatMost(X15,tc_nat),tc_nat),
inference(definition_unfolding,[],[f2023,f2544]) ).
fof(f2023,axiom,
! [X15] : c_0 != c_Suc(X15),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_OSuc__not__Zero_0) ).
fof(f7980,plain,
spl0_906,
inference(avatar_split_clause,[],[f2926,f7978]) ).
fof(f7978,plain,
( spl0_906
<=> ! [X102,X12] : c_in(c_Message_Omsg_OKey(c_Public_OshrK(X12)),c_Event_Oused(X102),tc_Message_Omsg) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_906])]) ).
fof(f2926,axiom,
! [X12,X102] : c_in(c_Message_Omsg_OKey(c_Public_OshrK(X12)),c_Event_Oused(X102),tc_Message_Omsg),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Public_OshrK__in__used_0) ).
fof(f7976,plain,
spl0_905,
inference(avatar_split_clause,[],[f2914,f7974]) ).
fof(f7974,plain,
( spl0_905
<=> ! [X12,X32,X27] : c_Public_OshrK(X12) != c_Message_OinvKey(c_Public_OpublicKey(X27,X32)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_905])]) ).
fof(f2914,axiom,
! [X27,X12,X32] : c_Public_OshrK(X12) != c_Message_OinvKey(c_Public_OpublicKey(X27,X32)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Public_OpriK__neq__shrK_0) ).
fof(f7972,plain,
spl0_904,
inference(avatar_split_clause,[],[f2910,f7970]) ).
fof(f7970,plain,
( spl0_904
<=> ! [X27,X12] : ~ c_in(c_Message_OinvKey(c_Public_OpublicKey(X27,X12)),c_Message_OsymKeys,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_904])]) ).
fof(f2910,axiom,
! [X27,X12] : ~ c_in(c_Message_OinvKey(c_Public_OpublicKey(X27,X12)),c_Message_OsymKeys,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Public_Onot__symKeys__priK_0) ).
fof(f7968,plain,
spl0_903,
inference(avatar_split_clause,[],[f2906,f7966]) ).
fof(f7966,plain,
( spl0_903
<=> ! [X45,X1,X3] : c_Public_Okeymode_Okeymode__rec(X45,X3,c_Public_Okeymode_OEncryption,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_903])]) ).
fof(f2906,axiom,
! [X3,X1,X45] : c_Public_Okeymode_Okeymode__rec(X45,X3,c_Public_Okeymode_OEncryption,X1) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Public_Okeymode_Orecs__2_0) ).
fof(f7964,plain,
spl0_902,
inference(avatar_split_clause,[],[f2905,f7962]) ).
fof(f7962,plain,
( spl0_902
<=> ! [X44,X1,X3] : c_Public_Okeymode_Okeymode__rec(X3,X44,c_Public_Okeymode_OSignature,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_902])]) ).
fof(f2905,axiom,
! [X3,X1,X44] : c_Public_Okeymode_Okeymode__rec(X3,X44,c_Public_Okeymode_OSignature,X1) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Public_Okeymode_Orecs__1_0) ).
fof(f7960,plain,
spl0_901,
inference(avatar_split_clause,[],[f2902,f7958]) ).
fof(f7958,plain,
( spl0_901
<=> ! [X45,X1,X3] : c_Public_Okeymode_Okeymode__case(X45,X3,c_Public_Okeymode_OEncryption,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_901])]) ).
fof(f2902,axiom,
! [X3,X1,X45] : c_Public_Okeymode_Okeymode__case(X45,X3,c_Public_Okeymode_OEncryption,X1) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Public_Okeymode_Ocases__2_0) ).
fof(f7956,plain,
spl0_900,
inference(avatar_split_clause,[],[f2901,f7954]) ).
fof(f7954,plain,
( spl0_900
<=> ! [X44,X1,X3] : c_Public_Okeymode_Okeymode__case(X3,X44,c_Public_Okeymode_OSignature,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_900])]) ).
fof(f2901,axiom,
! [X3,X1,X44] : c_Public_Okeymode_Okeymode__case(X3,X44,c_Public_Okeymode_OSignature,X1) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Public_Okeymode_Ocases__1_0) ).
fof(f7952,plain,
spl0_899,
inference(avatar_split_clause,[],[f2891,f7950]) ).
fof(f7950,plain,
( spl0_899
<=> ! [X86,X91] : ~ c_in(c_Message_Omsg_OCrypt(X91,X86),c_Event_Oused(c_List_Olist_ONil),tc_Message_Omsg) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_899])]) ).
fof(f2891,axiom,
! [X91,X86] : ~ c_in(c_Message_Omsg_OCrypt(X91,X86),c_Event_Oused(c_List_Olist_ONil),tc_Message_Omsg),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Public_OCrypt__notin__used__empty_0) ).
fof(f7948,plain,
spl0_898,
inference(avatar_split_clause,[],[f2790,f7946]) ).
fof(f7946,plain,
( spl0_898
<=> ! [X96,X94] : c_0 = c_Nat_Osize(c_Event_Oevent_ONotes(X94,X96),tc_Event_Oevent) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_898])]) ).
fof(f2790,axiom,
! [X96,X94] : c_0 = c_Nat_Osize(c_Event_Oevent_ONotes(X94,X96),tc_Event_Oevent),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Event_Oevent_Osize__3_0) ).
fof(f7944,plain,
spl0_897,
inference(avatar_split_clause,[],[f2789,f7942]) ).
fof(f7942,plain,
( spl0_897
<=> ! [X96,X94] : c_0 = c_Nat_Osize(c_Event_Oevent_OGets(X94,X96),tc_Event_Oevent) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_897])]) ).
fof(f2789,axiom,
! [X96,X94] : c_0 = c_Nat_Osize(c_Event_Oevent_OGets(X94,X96),tc_Event_Oevent),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Event_Oevent_Osize__2_0) ).
fof(f7940,plain,
spl0_896,
inference(avatar_split_clause,[],[f2779,f7938]) ).
fof(f7938,plain,
( spl0_896
<=> ! [X96,X97,X94,X95] : c_Event_Oevent_ONotes(X95,X97) != c_Event_Oevent_OGets(X94,X96) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_896])]) ).
fof(f2779,axiom,
! [X96,X94,X97,X95] : c_Event_Oevent_ONotes(X95,X97) != c_Event_Oevent_OGets(X94,X96),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Event_Oevent_Odistinct__5_0) ).
fof(f7936,plain,
spl0_895,
inference(avatar_split_clause,[],[f2705,f7934]) ).
fof(f7934,plain,
( spl0_895
<=> ! [X2,X1] : c_UNIV = c_Sum__Type_OPlus(c_UNIV,c_UNIV,X1,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_895])]) ).
fof(f2705,axiom,
! [X2,X1] : c_UNIV = c_Sum__Type_OPlus(c_UNIV,c_UNIV,X1,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sum__Type_OUNIV__Plus__UNIV_0) ).
fof(f7932,plain,
spl0_894,
inference(avatar_split_clause,[],[f2684,f7930]) ).
fof(f2684,axiom,
! [X0,X1,X12] : c_in(X0,c_insert(X0,X12,X1),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Oinsert__iff_1) ).
fof(f7928,plain,
spl0_893,
inference(avatar_split_clause,[],[f2668,f7926]) ).
fof(f7926,plain,
( spl0_893
<=> ! [X12,X1] : c_emptyset = c_minus(c_emptyset,X12,tc_set(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_893])]) ).
fof(f2668,axiom,
! [X1,X12] : c_emptyset = c_minus(c_emptyset,X12,tc_set(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Oempty__Diff_0) ).
fof(f7924,plain,
spl0_892,
inference(avatar_split_clause,[],[f2648,f7922]) ).
fof(f7922,plain,
( spl0_892
<=> ! [X1,X3] : c_Union(c_Pow(X3,X1),X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_892])]) ).
fof(f2648,axiom,
! [X3,X1] : c_Union(c_Pow(X3,X1),X1) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUnion__Pow__eq_0) ).
fof(f7920,plain,
spl0_891,
inference(avatar_split_clause,[],[f2590,f7918]) ).
fof(f2590,axiom,
! [X3,X1] : c_minus(X3,c_emptyset,tc_set(X1)) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_ODiff__empty_0) ).
fof(f7916,plain,
spl0_890,
inference(avatar_split_clause,[],[f2588,f7914]) ).
fof(f7914,plain,
( spl0_890
<=> ! [X12,X1] : c_emptyset = c_minus(X12,X12,tc_set(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_890])]) ).
fof(f2588,axiom,
! [X1,X12] : c_emptyset = c_minus(X12,X12,tc_set(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_ODiff__cancel_0) ).
fof(f7912,plain,
spl0_889,
inference(avatar_split_clause,[],[f2587,f7910]) ).
fof(f7910,plain,
( spl0_889
<=> ! [X12,X1] : c_emptyset = c_minus(X12,c_UNIV,tc_set(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_889])]) ).
fof(f2587,axiom,
! [X1,X12] : c_emptyset = c_minus(X12,c_UNIV,tc_set(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_ODiff__UNIV_0) ).
fof(f7908,plain,
spl0_888,
inference(avatar_split_clause,[],[f2549,f7906]) ).
fof(f7906,plain,
( spl0_888
<=> ! [X3] : c_Finite__Set_Ocard(c_SetInterval_OlessThan(X3,tc_nat),tc_nat) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_888])]) ).
fof(f2549,axiom,
! [X3] : c_Finite__Set_Ocard(c_SetInterval_OlessThan(X3,tc_nat),tc_nat) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ocard__lessThan_0) ).
fof(f7904,plain,
spl0_887,
inference(avatar_split_clause,[],[f2394,f7902]) ).
fof(f7902,plain,
( spl0_887
<=> ! [X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| c_1 = c_HOL_Oabs(c_1,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_887])]) ).
fof(f2394,axiom,
! [X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| c_1 = c_HOL_Oabs(c_1,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Oabs__one_0) ).
fof(f7900,plain,
spl0_886,
inference(avatar_split_clause,[],[f2374,f7898]) ).
fof(f7898,plain,
( spl0_886
<=> ! [X2,X85,X1] : c_emptyset = c_Relation_OImage(X85,c_emptyset,X2,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_886])]) ).
fof(f2374,axiom,
! [X2,X1,X85] : c_emptyset = c_Relation_OImage(X85,c_emptyset,X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_OImage__empty_0) ).
fof(f7896,plain,
spl0_885,
inference(avatar_split_clause,[],[f2372,f7894]) ).
fof(f7894,plain,
( spl0_885
<=> ! [X1,X3] : c_Relation_OImage(c_Relation_OId,X3,X1,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_885])]) ).
fof(f2372,axiom,
! [X3,X1] : c_Relation_OImage(c_Relation_OId,X3,X1,X1) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_OImage__Id_0) ).
fof(f7892,plain,
spl0_884,
inference(avatar_split_clause,[],[f2243,f7890]) ).
fof(f2243,axiom,
! [X1] :
( ~ class_OrderedGroup_Olordered__ab__group(X1)
| c_0 = c_OrderedGroup_Opprt(c_0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Opprt__0_0) ).
fof(f7888,plain,
spl0_883,
inference(avatar_split_clause,[],[f2238,f7886]) ).
fof(f2238,axiom,
! [X1] :
( ~ class_OrderedGroup_Olordered__ab__group(X1)
| c_0 = c_OrderedGroup_Onprt(c_0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Onprt__0_0) ).
fof(f7884,plain,
spl0_882,
inference(avatar_split_clause,[],[f2226,f7882]) ).
fof(f7882,plain,
( spl0_882
<=> ! [X1] :
( ~ class_OrderedGroup_Oab__group__add(X1)
| c_0 = c_uminus(c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_882])]) ).
fof(f2226,axiom,
! [X1] :
( ~ class_OrderedGroup_Oab__group__add(X1)
| c_0 = c_uminus(c_0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__equal__0__iff__equal_1) ).
fof(f7880,plain,
spl0_881,
inference(avatar_split_clause,[],[f2176,f7878]) ).
fof(f7878,plain,
( spl0_881
<=> ! [X1] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
| c_0 = c_HOL_Oabs(c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_881])]) ).
fof(f2176,axiom,
! [X1] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
| c_0 = c_HOL_Oabs(c_0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__eq__0_1) ).
fof(f7876,plain,
spl0_880,
inference(avatar_split_clause,[],[f2169,f7874]) ).
fof(f2169,axiom,
! [X1] :
( ~ class_Numeral_Onumber__ring(X1)
| c_0 = c_Numeral_Onumber__of(c_Numeral_OPls,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Onumeral__0__eq__0_0) ).
fof(f7872,plain,
spl0_879,
inference(avatar_split_clause,[],[f2162,f7870]) ).
fof(f7870,plain,
( spl0_879
<=> ! [X45,X1,X3] : c_Numeral_Obit_Obit__rec(X45,X3,c_Numeral_Obit_OB1,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_879])]) ).
fof(f2162,axiom,
! [X3,X1,X45] : c_Numeral_Obit_Obit__rec(X45,X3,c_Numeral_Obit_OB1,X1) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obit_Orecs__2_0) ).
fof(f7868,plain,
spl0_878,
inference(avatar_split_clause,[],[f2161,f7866]) ).
fof(f7866,plain,
( spl0_878
<=> ! [X44,X1,X3] : c_Numeral_Obit_Obit__rec(X3,X44,c_Numeral_Obit_OB0,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_878])]) ).
fof(f2161,axiom,
! [X3,X1,X44] : c_Numeral_Obit_Obit__rec(X3,X44,c_Numeral_Obit_OB0,X1) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obit_Orecs__1_0) ).
fof(f7864,plain,
spl0_877,
inference(avatar_split_clause,[],[f2158,f7862]) ).
fof(f7862,plain,
( spl0_877
<=> ! [X45,X1,X3] : c_Numeral_Obit_Obit__case(X45,X3,c_Numeral_Obit_OB1,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_877])]) ).
fof(f2158,axiom,
! [X3,X1,X45] : c_Numeral_Obit_Obit__case(X45,X3,c_Numeral_Obit_OB1,X1) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obit_Ocases__2_0) ).
fof(f7860,plain,
spl0_876,
inference(avatar_split_clause,[],[f2157,f7858]) ).
fof(f7858,plain,
( spl0_876
<=> ! [X44,X1,X3] : c_Numeral_Obit_Obit__case(X3,X44,c_Numeral_Obit_OB0,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_876])]) ).
fof(f2157,axiom,
! [X3,X1,X44] : c_Numeral_Obit_Obit__case(X3,X44,c_Numeral_Obit_OB0,X1) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obit_Ocases__1_0) ).
fof(f7856,plain,
spl0_875,
inference(avatar_split_clause,[],[f2144,f7854]) ).
fof(f7854,plain,
( spl0_875
<=> ! [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_875])]) ).
fof(f2144,axiom,
! [X1] :
( ~ class_Numeral_Onumber__ring(X1)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_OMin,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obin__rel__simps__3_0) ).
fof(f7852,plain,
spl0_874,
inference(avatar_split_clause,[],[f2143,f7850]) ).
fof(f2143,axiom,
! [X1] :
( ~ class_Numeral_Onumber__ring(X1)
| c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_OPls,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obin__rel__simps__2_0) ).
fof(f7848,plain,
spl0_873,
inference(avatar_split_clause,[],[f2089,f7846]) ).
fof(f2089,axiom,
! [X21] :
( c_0 = X21
| c_less(c_0,X21,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Onot__gr0_0) ).
fof(f7844,plain,
spl0_872,
inference(avatar_split_clause,[],[f2088,f7842]) ).
fof(f2088,axiom,
! [X59,X43] : ~ c_less(c_plus(X59,X43,tc_nat),X43,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Onot__add__less2_0) ).
fof(f7840,plain,
spl0_871,
inference(avatar_split_clause,[],[f2087,f7838]) ).
fof(f7838,plain,
( spl0_871
<=> ! [X43,X59] : ~ c_less(c_plus(X43,X59,tc_nat),X43,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_871])]) ).
fof(f2087,axiom,
! [X59,X43] : ~ c_less(c_plus(X43,X59,tc_nat),X43,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Onot__add__less1_0) ).
fof(f7836,plain,
spl0_870,
inference(avatar_split_clause,[],[f2048,f7834]) ).
fof(f7834,plain,
( spl0_870
<=> ! [X21] :
( c_0 = X21
| ~ c_less(X21,c_1,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_870])]) ).
fof(f2048,axiom,
! [X21] :
( c_0 = X21
| ~ c_less(X21,c_1,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oless__one_0) ).
fof(f7832,plain,
spl0_869,
inference(avatar_split_clause,[],[f2042,f7830]) ).
fof(f2042,axiom,
! [X43] :
( c_0 = X43
| ~ c_lessequals(X43,c_0,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Ole__0__eq_0) ).
fof(f7828,plain,
spl0_868,
inference(avatar_split_clause,[],[f2040,f7826]) ).
fof(f2040,axiom,
! [X21,X15] : c_lessequals(c_minus(X15,X21,tc_nat),X15,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Odiff__le__self_0) ).
fof(f7824,plain,
spl0_867,
inference(avatar_split_clause,[],[f1812,f7822]) ).
fof(f1812,axiom,
! [X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| c_0 = c_NatArith_Oof__nat(c_0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__eq__0__iff_1) ).
fof(f7820,plain,
spl0_866,
inference(avatar_split_clause,[],[f1808,f7818]) ).
fof(f1808,axiom,
! [X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1)
| c_1 = c_NatArith_Oof__nat(c_1,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__1_0) ).
fof(f7816,plain,
spl0_865,
inference(avatar_split_clause,[],[f1790,f7814]) ).
fof(f7814,plain,
( spl0_865
<=> ! [X2,X1,X25] : c_List_Olist_ONil = c_List_Ozip(c_List_Olist_ONil,X25,X1,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_865])]) ).
fof(f1790,axiom,
! [X2,X1,X25] : c_List_Olist_ONil = c_List_Ozip(c_List_Olist_ONil,X25,X1,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Ozip__Nil_0) ).
fof(f7812,plain,
spl0_864,
inference(avatar_split_clause,[],[f1788,f7810]) ).
fof(f7810,plain,
( spl0_864
<=> ! [X41,X82,X23] : c_List_Olist_ONil = c_List_Ozip(X23,c_List_Olist_ONil,X41,X82) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_864])]) ).
fof(f1788,axiom,
! [X82,X41,X23] : c_List_Olist_ONil = c_List_Ozip(X23,c_List_Olist_ONil,X41,X82),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Ozip_Osimps__1_0) ).
fof(f7808,plain,
spl0_863,
inference(avatar_split_clause,[],[f1732,f7806]) ).
fof(f1732,axiom,
! [X3,X1] : c_List_Orev(c_List_Orev(X3,X1),X1) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Orev__rev__ident_0) ).
fof(f7804,plain,
spl0_862,
inference(avatar_split_clause,[],[f1711,f7802]) ).
fof(f7802,plain,
( spl0_862
<=> ! [X25,X0,X1] : c_List_Oop_Amem(X0,c_List_Olist_OCons(X0,X25,X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_862])]) ).
fof(f1711,axiom,
! [X0,X1,X25] : c_List_Oop_Amem(X0,c_List_Olist_OCons(X0,X25,X1),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oop_Amem_Osimps__2_1) ).
fof(f7800,plain,
spl0_861,
inference(avatar_split_clause,[],[f1631,f7798]) ).
fof(f7798,plain,
( spl0_861
<=> ! [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_861])]) ).
fof(f1631,axiom,
! [X41,X47,X43] : c_List_Olist_ONil = c_List_Olist__update(c_List_Olist_ONil,X43,X47,X41),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olist__update_Osimps__1_0) ).
fof(f7796,plain,
spl0_860,
inference(avatar_split_clause,[],[f1542,f7794]) ).
fof(f7794,plain,
( spl0_860
<=> ! [X54,X55] : c_0 = c_Nat_Osize(c_List_Ochar_OChar(X54,X55),tc_List_Ochar) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_860])]) ).
fof(f1542,axiom,
! [X54,X55] : c_0 = c_Nat_Osize(c_List_Ochar_OChar(X54,X55),tc_List_Ochar),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Ochar_Osize_0) ).
fof(f7792,plain,
spl0_859,
inference(avatar_split_clause,[],[f1478,f7790]) ).
fof(f1478,axiom,
! [X15] :
( c_0 = X15
| ~ c_Divides_Oop_Advd(c_0,X15,tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozdvd__0__left_0) ).
fof(f7788,plain,
spl0_858,
inference(avatar_split_clause,[],[f1401,f7786]) ).
fof(f1401,axiom,
! [X1] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X1)
| c_1 = c_IntDef_Oof__int(c_1,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oof__int__1_0) ).
fof(f7784,plain,
spl0_857,
inference(avatar_split_clause,[],[f1396,f7782]) ).
fof(f1396,axiom,
! [X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| c_0 = c_IntDef_Oof__int(c_0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oof__int__0__eq__iff_1) ).
fof(f7780,plain,
spl0_856,
inference(avatar_split_clause,[],[f1387,f7778]) ).
fof(f1387,axiom,
! [X21] : c_0 = c_IntDef_Onat(c_uminus(c_IntDef_Oint(X21),tc_IntDef_Oint)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Onat__zminus__int_0) ).
fof(f7776,plain,
spl0_855,
inference(avatar_split_clause,[],[f1373,f7774]) ).
fof(f7774,plain,
( spl0_855
<=> ! [X21] :
( c_0 = X21
| c_0 != c_IntDef_Oint(X21) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_855])]) ).
fof(f1373,axiom,
! [X21] :
( c_0 = X21
| c_0 != c_IntDef_Oint(X21) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oint__eq__0__conv_0) ).
fof(f7772,plain,
spl0_854,
inference(avatar_split_clause,[],[f1367,f7770]) ).
fof(f1367,axiom,
! [X15] : c_IntDef_Oint(X15) = c_HOL_Oabs(c_IntDef_Oint(X15),tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oabs__int__eq_0) ).
fof(f7768,plain,
spl0_853,
inference(avatar_split_clause,[],[f1253,f7766]) ).
fof(f7766,plain,
( spl0_853
<=> ! [X45,X1,X3] : c_Extraction_Osumbool_Osumbool__rec(X45,X3,c_Extraction_Osumbool_ORight,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_853])]) ).
fof(f1253,axiom,
! [X3,X1,X45] : c_Extraction_Osumbool_Osumbool__rec(X45,X3,c_Extraction_Osumbool_ORight,X1) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Extraction_Osumbool_Orecs__2_0) ).
fof(f7764,plain,
spl0_852,
inference(avatar_split_clause,[],[f1252,f7762]) ).
fof(f7762,plain,
( spl0_852
<=> ! [X44,X1,X3] : c_Extraction_Osumbool_Osumbool__rec(X3,X44,c_Extraction_Osumbool_OLeft,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_852])]) ).
fof(f1252,axiom,
! [X3,X1,X44] : c_Extraction_Osumbool_Osumbool__rec(X3,X44,c_Extraction_Osumbool_OLeft,X1) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Extraction_Osumbool_Orecs__1_0) ).
fof(f7760,plain,
spl0_851,
inference(avatar_split_clause,[],[f1249,f7758]) ).
fof(f7758,plain,
( spl0_851
<=> ! [X45,X1,X3] : c_Extraction_Osumbool_Osumbool__case(X45,X3,c_Extraction_Osumbool_ORight,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_851])]) ).
fof(f1249,axiom,
! [X3,X1,X45] : c_Extraction_Osumbool_Osumbool__case(X45,X3,c_Extraction_Osumbool_ORight,X1) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Extraction_Osumbool_Ocases__2_0) ).
fof(f7756,plain,
spl0_850,
inference(avatar_split_clause,[],[f1248,f7754]) ).
fof(f7754,plain,
( spl0_850
<=> ! [X44,X1,X3] : c_Extraction_Osumbool_Osumbool__case(X3,X44,c_Extraction_Osumbool_OLeft,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_850])]) ).
fof(f1248,axiom,
! [X3,X1,X44] : c_Extraction_Osumbool_Osumbool__case(X3,X44,c_Extraction_Osumbool_OLeft,X1) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Extraction_Osumbool_Ocases__1_0) ).
fof(f7752,plain,
spl0_849,
inference(avatar_split_clause,[],[f1225,f7750]) ).
fof(f7750,plain,
( spl0_849
<=> ! [X15] :
( c_0 = X15
| ~ c_Divides_Oop_Advd(c_0,X15,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_849])]) ).
fof(f1225,axiom,
! [X15] :
( c_0 = X15
| ~ c_Divides_Oop_Advd(c_0,X15,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Odvd__0__left__iff_0) ).
fof(f7748,plain,
spl0_848,
inference(avatar_split_clause,[],[f1215,f7746]) ).
fof(f1215,axiom,
! [X21,X15] : c_lessequals(c_div(X15,X21,tc_nat),X15,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Odiv__le__dividend_0) ).
fof(f7744,plain,
spl0_847,
inference(avatar_split_clause,[],[f1202,f7742]) ).
fof(f7742,plain,
( spl0_847
<=> ! [X2,X1,X9] : c_emptyset = c_Datatype__Universe_Ontrunc(c_0,X9,X1,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_847])]) ).
fof(f1202,axiom,
! [X2,X1,X9] : c_emptyset = c_Datatype__Universe_Ontrunc(c_0,X9,X1,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_Ontrunc__0_0) ).
fof(f7740,plain,
spl0_846,
inference(avatar_split_clause,[],[f1181,f7738]) ).
fof(f7738,plain,
( spl0_846
<=> ! [X1,X3] : c_Datatype_Othe(c_Datatype_Ooption_OSome(X3,X1),X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_846])]) ).
fof(f1181,axiom,
! [X3,X1] : c_Datatype_Othe(c_Datatype_Ooption_OSome(X3,X1),X1) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype_Othe_Osimps_0) ).
fof(f7736,plain,
spl0_845,
inference(avatar_split_clause,[],[f95,f7734]) ).
fof(f7734,plain,
( spl0_845
<=> ! [X16] : c_in(c_SetInterval_OlessThan(X16,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_845])]) ).
fof(f95,axiom,
! [X16] : c_in(c_SetInterval_OlessThan(X16,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__lessThan_0) ).
fof(f7732,plain,
spl0_844,
inference(avatar_split_clause,[],[f90,f7730]) ).
fof(f7730,plain,
( spl0_844
<=> ! [X16] : c_in(c_SetInterval_OatMost(X16,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_844])]) ).
fof(f90,axiom,
! [X16] : c_in(c_SetInterval_OatMost(X16,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__atMost_0) ).
fof(f7728,plain,
spl0_843,
inference(avatar_split_clause,[],[f61,f7726]) ).
fof(f7726,plain,
( spl0_843
<=> ! [X12,X1] : c_in(c_List_Olist_ONil,c_List_Olists(X12,X1),tc_List_Olist(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_843])]) ).
fof(f61,axiom,
! [X1,X12] : c_in(c_List_Olist_ONil,c_List_Olists(X12,X1),tc_List_Olist(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olists_ONil_0) ).
fof(f7724,plain,
spl0_842,
inference(avatar_split_clause,[],[f45,f7722]) ).
fof(f7722,plain,
( spl0_842
<=> ! [X1,X23] : c_in(c_List_Oset(X23,X1),c_Finite__Set_OFinites,tc_set(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_842])]) ).
fof(f45,axiom,
! [X1,X23] : c_in(c_List_Oset(X23,X1),c_Finite__Set_OFinites,tc_set(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Ofinite__set_0) ).
fof(f7720,plain,
spl0_841,
inference(avatar_split_clause,[],[f42,f7718]) ).
fof(f42,axiom,
! [X16,X15] : c_Divides_Oop_Advd(X16,c_times(X15,X16,tc_IntDef_Oint),tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozdvd__triv__right_0) ).
fof(f7716,plain,
spl0_840,
inference(avatar_split_clause,[],[f41,f7714]) ).
fof(f41,axiom,
! [X16,X15] : c_Divides_Oop_Advd(X16,c_times(X16,X15,tc_IntDef_Oint),tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozdvd__triv__left_0) ).
fof(f7712,plain,
spl0_839,
inference(avatar_split_clause,[],[f26,f7710]) ).
fof(f7710,plain,
( spl0_839
<=> ! [X16,X15] : c_Divides_Oop_Advd(X16,c_times(X15,X16,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_839])]) ).
fof(f26,axiom,
! [X16,X15] : c_Divides_Oop_Advd(X16,c_times(X15,X16,tc_nat),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Odvd__triv__right_0) ).
fof(f7708,plain,
spl0_838,
inference(avatar_split_clause,[],[f25,f7706]) ).
fof(f7706,plain,
( spl0_838
<=> ! [X16,X15] : c_Divides_Oop_Advd(X16,c_times(X16,X15,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_838])]) ).
fof(f25,axiom,
! [X16,X15] : c_Divides_Oop_Advd(X16,c_times(X16,X15,tc_nat),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Odvd__triv__left_0) ).
fof(f7694,plain,
spl0_837,
inference(avatar_split_clause,[],[f3224,f7692]) ).
fof(f3224,plain,
! [X3] : c_div(X3,c_1,tc_nat) = X3,
inference(forward_demodulation,[],[f2998,f2958]) ).
fof(f2998,plain,
! [X3] : c_div(X3,c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),tc_nat) = X3,
inference(definition_unfolding,[],[f1214,f2544]) ).
fof(f1214,axiom,
! [X3] : c_div(X3,c_Suc(c_0),tc_nat) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Odiv__1_0) ).
fof(f7690,plain,
spl0_836,
inference(avatar_split_clause,[],[f3222,f7687]) ).
fof(f7687,plain,
( spl0_836
<=> c_1 = c_times(c_1,c_1,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_836])]) ).
fof(f3222,plain,
c_1 = c_times(c_1,c_1,tc_nat),
inference(forward_demodulation,[],[f2995,f2958]) ).
fof(f2995,plain,
c_times(c_1,c_1,tc_nat) = c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),
inference(definition_unfolding,[],[f2094,f2544]) ).
fof(f2094,axiom,
c_Suc(c_0) = c_times(c_1,c_1,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oone__eq__mult__iff_2) ).
fof(f7685,plain,
spl0_835,
inference(avatar_split_clause,[],[f3220,f7683]) ).
fof(f7683,plain,
( spl0_835
<=> ! [X15] : c_0 = c_Divides_Oop_Amod(X15,c_1,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_835])]) ).
fof(f3220,plain,
! [X15] : c_0 = c_Divides_Oop_Amod(X15,c_1,tc_nat),
inference(forward_demodulation,[],[f2994,f2958]) ).
fof(f2994,plain,
! [X15] : c_0 = c_Divides_Oop_Amod(X15,c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),tc_nat),
inference(definition_unfolding,[],[f1231,f2544]) ).
fof(f1231,axiom,
! [X15] : c_0 = c_Divides_Oop_Amod(X15,c_Suc(c_0),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Omod__1_0) ).
fof(f7681,plain,
spl0_834,
inference(avatar_split_clause,[],[f3219,f7678]) ).
fof(f3219,plain,
c_1 = c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OPls),tc_nat),
inference(forward_demodulation,[],[f1867,f2156]) ).
fof(f1867,axiom,
c_1 = c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatBin_Onat__numeral__1__eq__1_0) ).
fof(f7676,plain,
spl0_833,
inference(avatar_split_clause,[],[f3217,f7674]) ).
fof(f7674,plain,
( spl0_833
<=> ! [X41,X3] : c_append(c_List_Olist_ONil,X3,X41) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_833])]) ).
fof(f3217,plain,
! [X3,X41] : c_append(c_List_Olist_ONil,X3,X41) = X3,
inference(forward_demodulation,[],[f2986,f1729]) ).
fof(f1729,axiom,
! [X1] : c_List_Olist_ONil = c_List_Orev(c_List_Olist_ONil,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Orev__is__Nil__conv_1) ).
fof(f2986,plain,
! [X41,X3] : c_append(c_List_Orev(c_List_Olist_ONil,X41),X3,X41) = X3,
inference(definition_unfolding,[],[f1586,f1585]) ).
fof(f1586,axiom,
! [X3,X41] : c_List_Oitrev(c_List_Olist_ONil,X3,X41) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oitrev_Osimps__1_0) ).
fof(f7672,plain,
spl0_832,
inference(avatar_split_clause,[],[f3215,f7669]) ).
fof(f7669,plain,
( spl0_832
<=> c_Numeral_Obin__succ(c_Numeral_OPls) = c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OMin) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_832])]) ).
fof(f3215,plain,
c_Numeral_Obin__succ(c_Numeral_OPls) = c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OMin),
inference(forward_demodulation,[],[f2983,f2156]) ).
fof(f2983,plain,
c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1) = c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OMin),
inference(definition_unfolding,[],[f2125,f2129]) ).
fof(f2125,axiom,
c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1) = c_Numeral_Obin__minus(c_Numeral_OMin),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obin__minus__Min_0) ).
fof(f7667,plain,
spl0_831,
inference(avatar_split_clause,[],[f2917,f7665]) ).
fof(f7665,plain,
( spl0_831
<=> ! [X12,X32,X27] : c_Public_OshrK(X12) != c_Public_OpublicKey(X27,X32) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_831])]) ).
fof(f2917,axiom,
! [X27,X12,X32] : c_Public_OshrK(X12) != c_Public_OpublicKey(X27,X32),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Public_OpubK__neq__shrK_0) ).
fof(f7663,plain,
spl0_830,
inference(avatar_split_clause,[],[f2911,f7661]) ).
fof(f7661,plain,
( spl0_830
<=> ! [X27,X12] : ~ c_in(c_Public_OpublicKey(X27,X12),c_Message_OsymKeys,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_830])]) ).
fof(f2911,axiom,
! [X27,X12] : ~ c_in(c_Public_OpublicKey(X27,X12),c_Message_OsymKeys,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Public_Onot__symKeys__pubK_0) ).
fof(f7659,plain,
spl0_829,
inference(avatar_split_clause,[],[f2900,f7657]) ).
fof(f7657,plain,
( spl0_829
<=> ! [X12] : c_Public_OshrK(X12) = c_Message_OinvKey(c_Public_OshrK(X12)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_829])]) ).
fof(f2900,axiom,
! [X12] : c_Public_OshrK(X12) = c_Message_OinvKey(c_Public_OshrK(X12)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Public_OinvKey__shrK_0) ).
fof(f7655,plain,
spl0_828,
inference(avatar_split_clause,[],[f2895,f7653]) ).
fof(f7653,plain,
( spl0_828
<=> ! [X7] : ~ c_in(c_Message_Omsg_ONonce(X7),c_Event_Oused(c_List_Olist_ONil),tc_Message_Omsg) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_828])]) ).
fof(f2895,axiom,
! [X7] : ~ c_in(c_Message_Omsg_ONonce(X7),c_Event_Oused(c_List_Olist_ONil),tc_Message_Omsg),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Public_ONonce__notin__used__empty_0) ).
fof(f7651,plain,
spl0_827,
inference(avatar_split_clause,[],[f2871,f7649]) ).
fof(f7649,plain,
( spl0_827
<=> ! [X88] : c_Message_Oparts(X88) = c_Message_Oparts(c_Message_Oparts(X88)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_827])]) ).
fof(f2871,axiom,
! [X88] : c_Message_Oparts(X88) = c_Message_Oparts(c_Message_Oparts(X88)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oparts__idem_0) ).
fof(f7647,plain,
spl0_826,
inference(avatar_split_clause,[],[f2869,f7645]) ).
fof(f7645,plain,
( spl0_826
<=> ! [X88] : c_Message_Oparts(X88) = c_Message_Oparts(c_Message_Oanalz(X88)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_826])]) ).
fof(f2869,axiom,
! [X88] : c_Message_Oparts(X88) = c_Message_Oparts(c_Message_Oanalz(X88)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oparts__analz_0) ).
fof(f7643,plain,
spl0_825,
inference(avatar_split_clause,[],[f2862,f7641]) ).
fof(f7641,plain,
( spl0_825
<=> ! [X88] : c_Message_Oparts(X88) = c_Message_Oanalz(c_Message_Oparts(X88)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_825])]) ).
fof(f2862,axiom,
! [X88] : c_Message_Oparts(X88) = c_Message_Oanalz(c_Message_Oparts(X88)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oanalz__parts_0) ).
fof(f7639,plain,
spl0_824,
inference(avatar_split_clause,[],[f2854,f7637]) ).
fof(f7637,plain,
( spl0_824
<=> ! [X88] : c_Message_Oanalz(X88) = c_Message_Oanalz(c_Message_Oanalz(X88)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_824])]) ).
fof(f2854,axiom,
! [X88] : c_Message_Oanalz(X88) = c_Message_Oanalz(c_Message_Oanalz(X88)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oanalz__idem_0) ).
fof(f7635,plain,
spl0_823,
inference(avatar_split_clause,[],[f2845,f7633]) ).
fof(f7633,plain,
( spl0_823
<=> ! [X21,X88] : c_in(c_Message_Omsg_ONumber(X21),c_Message_Osynth(X88),tc_Message_Omsg) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_823])]) ).
fof(f2845,axiom,
! [X21,X88] : c_in(c_Message_Omsg_ONumber(X21),c_Message_Osynth(X88),tc_Message_Omsg),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_ONumber__synth_0) ).
fof(f7631,plain,
spl0_822,
inference(avatar_split_clause,[],[f2803,f7629]) ).
fof(f7629,plain,
( spl0_822
<=> ! [X12,X88] : c_in(c_Message_Omsg_OAgent(X12),c_Message_Osynth(X88),tc_Message_Omsg) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_822])]) ).
fof(f2803,axiom,
! [X88,X12] : c_in(c_Message_Omsg_OAgent(X12),c_Message_Osynth(X88),tc_Message_Omsg),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OAgent__synth_0) ).
fof(f7627,plain,
spl0_821,
inference(avatar_split_clause,[],[f2763,f7625]) ).
fof(f2763,axiom,
! [X90] : c_0 = c_Nat_Osize(c_Message_Omsg_OKey(X90),tc_Message_Omsg),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Omsg_Osize__4_0) ).
fof(f7623,plain,
spl0_820,
inference(avatar_split_clause,[],[f2762,f7621]) ).
fof(f2762,axiom,
! [X90] : c_0 = c_Nat_Osize(c_Message_Omsg_ONonce(X90),tc_Message_Omsg),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Omsg_Osize__3_0) ).
fof(f7619,plain,
spl0_819,
inference(avatar_split_clause,[],[f2761,f7617]) ).
fof(f2761,axiom,
! [X90] : c_0 = c_Nat_Osize(c_Message_Omsg_ONumber(X90),tc_Message_Omsg),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Omsg_Osize__2_0) ).
fof(f7615,plain,
spl0_818,
inference(avatar_split_clause,[],[f2760,f7613]) ).
fof(f2760,axiom,
! [X94] : c_0 = c_Nat_Osize(c_Message_Omsg_OAgent(X94),tc_Message_Omsg),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Omsg_Osize__1_0) ).
fof(f7611,plain,
spl0_817,
inference(avatar_split_clause,[],[f2738,f7609]) ).
fof(f7609,plain,
( spl0_817
<=> ! [X90] : c_0 = c_Nat_Osize(c_Message_Oagent_OFriend(X90),tc_Message_Oagent) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_817])]) ).
fof(f2738,axiom,
! [X90] : c_0 = c_Nat_Osize(c_Message_Oagent_OFriend(X90),tc_Message_Oagent),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oagent_Osize__2_0) ).
fof(f7607,plain,
spl0_816,
inference(avatar_split_clause,[],[f2687,f7605]) ).
fof(f2687,axiom,
! [X18,X1,X12] : c_emptyset != c_insert(X18,X12,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Oinsert__not__empty_0) ).
fof(f7603,plain,
spl0_815,
inference(avatar_split_clause,[],[f2639,f7601]) ).
fof(f7601,plain,
( spl0_815
<=> ! [X1,X3] : c_union(X3,c_emptyset,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_815])]) ).
fof(f2639,axiom,
! [X3,X1] : c_union(X3,c_emptyset,X1) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUn__empty__right_0) ).
fof(f7599,plain,
spl0_814,
inference(avatar_split_clause,[],[f2638,f7597]) ).
fof(f2638,axiom,
! [X3,X1] : c_union(c_emptyset,X3,X1) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUn__empty__left_0) ).
fof(f7595,plain,
spl0_813,
inference(avatar_split_clause,[],[f2634,f7593]) ).
fof(f7593,plain,
( spl0_813
<=> ! [X1,X3] : c_union(X3,X3,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_813])]) ).
fof(f2634,axiom,
! [X3,X1] : c_union(X3,X3,X1) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUn__absorb_0) ).
fof(f7591,plain,
spl0_812,
inference(avatar_split_clause,[],[f2633,f7589]) ).
fof(f7589,plain,
( spl0_812
<=> ! [X12,X1] : c_UNIV = c_union(X12,c_UNIV,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_812])]) ).
fof(f2633,axiom,
! [X1,X12] : c_UNIV = c_union(X12,c_UNIV,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUn__UNIV__right_0) ).
fof(f7587,plain,
spl0_811,
inference(avatar_split_clause,[],[f2632,f7585]) ).
fof(f2632,axiom,
! [X1,X13] : c_UNIV = c_union(c_UNIV,X13,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUn__UNIV__left_0) ).
fof(f7583,plain,
spl0_810,
inference(avatar_split_clause,[],[f2580,f7581]) ).
fof(f2580,axiom,
! [X1] : c_UNIV = c_uminus(c_emptyset,tc_set(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OCompl__empty__eq_0) ).
fof(f7579,plain,
spl0_809,
inference(avatar_split_clause,[],[f2576,f7577]) ).
fof(f7577,plain,
( spl0_809
<=> ! [X1] : c_emptyset = c_uminus(c_UNIV,tc_set(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_809])]) ).
fof(f2576,axiom,
! [X1] : c_emptyset = c_uminus(c_UNIV,tc_set(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OCompl__UNIV__eq_0) ).
fof(f7575,plain,
spl0_808,
inference(avatar_split_clause,[],[f2511,f7573]) ).
fof(f7573,plain,
( spl0_808
<=> ! [X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| c_lessequals(c_0,c_1,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_808])]) ).
fof(f2511,axiom,
! [X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| c_lessequals(c_0,c_1,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Ozero__le__one_0) ).
fof(f7571,plain,
spl0_807,
inference(avatar_split_clause,[],[f2499,f7569]) ).
fof(f7569,plain,
( spl0_807
<=> ! [X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| c_less(c_0,c_1,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_807])]) ).
fof(f2499,axiom,
! [X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| c_less(c_0,c_1,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Oordered__semidom__class_Oaxioms_0) ).
fof(f7567,plain,
spl0_806,
inference(avatar_split_clause,[],[f2494,f7565]) ).
fof(f7565,plain,
( spl0_806
<=> ! [X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_less(c_1,c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_806])]) ).
fof(f2494,axiom,
! [X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_less(c_1,c_0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Onot__one__less__zero_0) ).
fof(f7563,plain,
spl0_805,
inference(avatar_split_clause,[],[f2493,f7561]) ).
fof(f7561,plain,
( spl0_805
<=> ! [X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_lessequals(c_1,c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_805])]) ).
fof(f2493,axiom,
! [X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_lessequals(c_1,c_0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Onot__one__le__zero_0) ).
fof(f7559,plain,
spl0_804,
inference(avatar_split_clause,[],[f2381,f7557]) ).
fof(f7557,plain,
( spl0_804
<=> ! [X1] : c_Relation_OId = c_Relation_Oconverse(c_Relation_OId,X1,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_804])]) ).
fof(f2381,axiom,
! [X1] : c_Relation_OId = c_Relation_Oconverse(c_Relation_OId,X1,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_Oconverse__Id_0) ).
fof(f7555,plain,
spl0_803,
inference(avatar_split_clause,[],[f2380,f7553]) ).
fof(f7553,plain,
( spl0_803
<=> ! [X2,X1] : c_emptyset = c_Relation_ORange(c_emptyset,X2,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_803])]) ).
fof(f2380,axiom,
! [X2,X1] : c_emptyset = c_Relation_ORange(c_emptyset,X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_ORange__empty_0) ).
fof(f7551,plain,
spl0_802,
inference(avatar_split_clause,[],[f2378,f7549]) ).
fof(f7549,plain,
( spl0_802
<=> ! [X1] : c_UNIV = c_Relation_ORange(c_Relation_OId,X1,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_802])]) ).
fof(f2378,axiom,
! [X1] : c_UNIV = c_Relation_ORange(c_Relation_OId,X1,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_ORange__Id_0) ).
fof(f7547,plain,
spl0_801,
inference(avatar_split_clause,[],[f2370,f7545]) ).
fof(f7545,plain,
( spl0_801
<=> ! [X2,X1] : c_emptyset = c_Relation_ODomain(c_emptyset,X1,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_801])]) ).
fof(f2370,axiom,
! [X2,X1] : c_emptyset = c_Relation_ODomain(c_emptyset,X1,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_ODomain__empty_0) ).
fof(f7543,plain,
spl0_800,
inference(avatar_split_clause,[],[f2368,f7541]) ).
fof(f7541,plain,
( spl0_800
<=> ! [X1] : c_UNIV = c_Relation_ODomain(c_Relation_OId,X1,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_800])]) ).
fof(f2368,axiom,
! [X1] : c_UNIV = c_Relation_ODomain(c_Relation_OId,X1,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_ODomain__Id_0) ).
fof(f7539,plain,
spl0_799,
inference(avatar_split_clause,[],[f2344,f7537]) ).
fof(f2344,axiom,
! [X28] : c_1 = c_Nat_Opower(X28,c_0,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Power_Opower_Osimps__1_0) ).
fof(f7535,plain,
spl0_798,
inference(avatar_split_clause,[],[f2269,f7533]) ).
fof(f7533,plain,
( spl0_798
<=> ! [X0,X1] :
( ~ class_Orderings_Oorder(X1)
| ~ c_less(X0,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_798])]) ).
fof(f2269,axiom,
! [X0,X1] :
( ~ class_Orderings_Oorder(X1)
| ~ c_less(X0,X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Orderings_Oorder__less__irrefl_0) ).
fof(f7531,plain,
spl0_797,
inference(avatar_split_clause,[],[f2156,f7528]) ).
fof(f7526,plain,
spl0_796,
inference(avatar_split_clause,[],[f2102,f7524]) ).
fof(f2102,axiom,
! [X3] : c_minus(X3,c_0,tc_nat) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oop_A_N_Odiff__0_0) ).
fof(f7522,plain,
spl0_795,
inference(avatar_split_clause,[],[f2100,f7520]) ).
fof(f2100,axiom,
! [X3] : c_plus(c_0,X3,tc_nat) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oop_A_L_Oadd__0_0) ).
fof(f7518,plain,
spl0_794,
inference(avatar_split_clause,[],[f2098,f7516]) ).
fof(f2098,axiom,
! [X21] : c_0 = c_times(c_0,X21,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oop_A_K_Omult__0_0) ).
fof(f7514,plain,
spl0_793,
inference(avatar_split_clause,[],[f2056,f7512]) ).
fof(f7512,plain,
( spl0_793
<=> ! [X15] : c_0 = c_times(X15,c_0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_793])]) ).
fof(f2056,axiom,
! [X15] : c_0 = c_times(X15,c_0,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Omult__0__right_0) ).
fof(f7510,plain,
spl0_792,
inference(avatar_split_clause,[],[f2054,f7508]) ).
fof(f7508,plain,
( spl0_792
<=> ! [X21] : c_0 = c_Orderings_Omin(X21,c_0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_792])]) ).
fof(f2054,axiom,
! [X21] : c_0 = c_Orderings_Omin(X21,c_0,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Omin__0R_0) ).
fof(f7506,plain,
spl0_791,
inference(avatar_split_clause,[],[f2053,f7504]) ).
fof(f7504,plain,
( spl0_791
<=> ! [X21] : c_0 = c_Orderings_Omin(c_0,X21,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_791])]) ).
fof(f2053,axiom,
! [X21] : c_0 = c_Orderings_Omin(c_0,X21,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Omin__0L_0) ).
fof(f7502,plain,
spl0_790,
inference(avatar_split_clause,[],[f2051,f7500]) ).
fof(f7500,plain,
( spl0_790
<=> ! [X3] : c_Orderings_Omax(X3,c_0,tc_nat) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_790])]) ).
fof(f2051,axiom,
! [X3] : c_Orderings_Omax(X3,c_0,tc_nat) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Omax__0R_0) ).
fof(f7498,plain,
spl0_789,
inference(avatar_split_clause,[],[f2050,f7496]) ).
fof(f7496,plain,
( spl0_789
<=> ! [X3] : c_Orderings_Omax(c_0,X3,tc_nat) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_789])]) ).
fof(f2050,axiom,
! [X3] : c_Orderings_Omax(c_0,X3,tc_nat) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Omax__0L_0) ).
fof(f7494,plain,
spl0_788,
inference(avatar_split_clause,[],[f2041,f7492]) ).
fof(f2041,axiom,
! [X15] : c_0 = c_minus(X15,X15,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Odiff__self__eq__0_0) ).
fof(f7490,plain,
spl0_787,
inference(avatar_split_clause,[],[f2034,f7488]) ).
fof(f2034,axiom,
! [X21] : c_0 = c_minus(c_0,X21,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Odiff__0__eq__0_0) ).
fof(f7486,plain,
spl0_786,
inference(avatar_split_clause,[],[f2026,f7484]) ).
fof(f2026,axiom,
! [X3] : c_plus(X3,c_0,tc_nat) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oadd__0__right_0) ).
fof(f7482,plain,
spl0_785,
inference(avatar_split_clause,[],[f1787,f7480]) ).
fof(f1787,axiom,
! [X0,X1,X81] : c_List_Olist_OCons(X0,X81,X1) != X81,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Ox2_A_D_At1_A_61_At1_A_61_61_AFalse_0) ).
fof(f7478,plain,
spl0_784,
inference(avatar_split_clause,[],[f1763,f7476]) ).
fof(f7476,plain,
( spl0_784
<=> ! [X12,X1] : c_List_Olist_ONil = c_List_Osublist(c_List_Olist_ONil,X12,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_784])]) ).
fof(f1763,axiom,
! [X1,X12] : c_List_Olist_ONil = c_List_Osublist(c_List_Olist_ONil,X12,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Osublist__nil_0) ).
fof(f7474,plain,
spl0_783,
inference(avatar_split_clause,[],[f1762,f7472]) ).
fof(f7472,plain,
( spl0_783
<=> ! [X1,X23] : c_List_Olist_ONil = c_List_Osublist(X23,c_emptyset,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_783])]) ).
fof(f1762,axiom,
! [X1,X23] : c_List_Olist_ONil = c_List_Osublist(X23,c_emptyset,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Osublist__empty_0) ).
fof(f7470,plain,
spl0_782,
inference(avatar_split_clause,[],[f1741,f7468]) ).
fof(f7468,plain,
( spl0_782
<=> ! [X21,X1] : c_List_Olist_ONil = c_List_Orotate(X21,c_List_Olist_ONil,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_782])]) ).
fof(f1741,axiom,
! [X21,X1] : c_List_Olist_ONil = c_List_Orotate(X21,c_List_Olist_ONil,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Orotate__is__Nil__conv_1) ).
fof(f7466,plain,
spl0_781,
inference(avatar_split_clause,[],[f1722,f7464]) ).
fof(f1722,axiom,
! [X41,X0] : c_List_Olist_ONil = c_List_Oreplicate(c_0,X0,X41),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oreplicate_Oreplicate__0_0) ).
fof(f7462,plain,
spl0_780,
inference(avatar_split_clause,[],[f1719,f7460]) ).
fof(f7460,plain,
( spl0_780
<=> ! [X41,X0] : c_List_Olist_ONil = c_List_Oremove1(X0,c_List_Olist_ONil,X41) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_780])]) ).
fof(f1719,axiom,
! [X41,X0] : c_List_Olist_ONil = c_List_Oremove1(X0,c_List_Olist_ONil,X41),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oremove1_Osimps__1_0) ).
fof(f7458,plain,
spl0_779,
inference(avatar_split_clause,[],[f1707,f7456]) ).
fof(f1707,axiom,
! [X41,X0,X23] : ~ c_List_Onull(c_List_Olist_OCons(X0,X23,X41),X41),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Onull_Osimps__2_0) ).
fof(f7454,plain,
spl0_778,
inference(avatar_split_clause,[],[f1628,f7452]) ).
fof(f7452,plain,
( spl0_778
<=> ! [X41,X65] : c_List_Olist_ONil = c_List_Olist__inter(c_List_Olist_ONil,X65,X41) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_778])]) ).
fof(f1628,axiom,
! [X65,X41] : c_List_Olist_ONil = c_List_Olist__inter(c_List_Olist_ONil,X65,X41),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olist__inter_Osimps__1_0) ).
fof(f7450,plain,
spl0_777,
inference(avatar_split_clause,[],[f1624,f7448]) ).
fof(f7448,plain,
( spl0_777
<=> ! [X42,X1,X63] : c_List_Olist_ONil != c_List_Olist_OCons(X42,X63,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_777])]) ).
fof(f1624,axiom,
! [X1,X63,X42] : c_List_Olist_ONil != c_List_Olist_OCons(X42,X63,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olist_Odistinct__2_0) ).
fof(f7446,plain,
spl0_776,
inference(avatar_split_clause,[],[f1615,f7444]) ).
fof(f7444,plain,
( spl0_776
<=> ! [X41,X5] : c_emptyset = c_List_Olexn(X5,c_0,X41) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_776])]) ).
fof(f1615,axiom,
! [X41,X5] : c_emptyset = c_List_Olexn(X5,c_0,X41),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olexn_Osimps__1_0) ).
fof(f7442,plain,
spl0_775,
inference(avatar_split_clause,[],[f1598,f7440]) ).
fof(f7440,plain,
( spl0_775
<=> ! [X1] : c_0 = c_Nat_Osize(c_List_Olist_ONil,tc_List_Olist(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_775])]) ).
fof(f1598,axiom,
! [X1] : c_0 = c_Nat_Osize(c_List_Olist_ONil,tc_List_Olist(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olength__0__conv_1) ).
fof(f7438,plain,
spl0_774,
inference(avatar_split_clause,[],[f1569,f7436]) ).
fof(f7436,plain,
( spl0_774
<=> ! [X1,X3] : c_List_Odrop(c_0,X3,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_774])]) ).
fof(f1569,axiom,
! [X3,X1] : c_List_Odrop(c_0,X3,X1) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Odrop__0_0) ).
fof(f7434,plain,
spl0_773,
inference(avatar_split_clause,[],[f1568,f7432]) ).
fof(f7432,plain,
( spl0_773
<=> ! [X41,X21] : c_List_Olist_ONil = c_List_Odrop(X21,c_List_Olist_ONil,X41) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_773])]) ).
fof(f1568,axiom,
! [X21,X41] : c_List_Olist_ONil = c_List_Odrop(X21,c_List_Olist_ONil,X41),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Odrop_Odrop__Nil_0) ).
fof(f7430,plain,
spl0_772,
inference(avatar_split_clause,[],[f1534,f7428]) ).
fof(f7428,plain,
( spl0_772
<=> ! [X1,X23] : c_append(X23,c_List_Olist_ONil,X1) = X23 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_772])]) ).
fof(f1534,axiom,
! [X1,X23] : c_append(X23,c_List_Olist_ONil,X1) = X23,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oappend__self__conv_1) ).
fof(f7426,plain,
spl0_771,
inference(avatar_split_clause,[],[f1494,f7424]) ).
fof(f7424,plain,
( spl0_771
<=> ! [X27] : c_0 = c_Divides_Oop_Amod(c_0,X27,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_771])]) ).
fof(f1494,axiom,
! [X27] : c_0 = c_Divides_Oop_Amod(c_0,X27,tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozmod__zero_0) ).
fof(f7422,plain,
spl0_770,
inference(avatar_split_clause,[],[f1491,f7420]) ).
fof(f7420,plain,
( spl0_770
<=> ! [X18] : c_0 = c_Divides_Oop_Amod(X18,X18,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_770])]) ).
fof(f1491,axiom,
! [X18] : c_0 = c_Divides_Oop_Amod(X18,X18,tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozmod__self_0) ).
fof(f7418,plain,
spl0_769,
inference(avatar_split_clause,[],[f1489,f7416]) ).
fof(f7416,plain,
( spl0_769
<=> ! [X18] : c_0 = c_Divides_Oop_Amod(X18,c_1,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_769])]) ).
fof(f1489,axiom,
! [X18] : c_0 = c_Divides_Oop_Amod(X18,c_1,tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozmod__1_0) ).
fof(f7414,plain,
spl0_768,
inference(avatar_split_clause,[],[f1474,f7412]) ).
fof(f7412,plain,
( spl0_768
<=> ! [X27] : c_0 = c_div(c_0,X27,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_768])]) ).
fof(f1474,axiom,
! [X27] : c_0 = c_div(c_0,X27,tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozdiv__zero_0) ).
fof(f7410,plain,
spl0_767,
inference(avatar_split_clause,[],[f1466,f7408]) ).
fof(f7408,plain,
( spl0_767
<=> ! [X3] : c_div(X3,c_1,tc_IntDef_Oint) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_767])]) ).
fof(f1466,axiom,
! [X3] : c_div(X3,c_1,tc_IntDef_Oint) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozdiv__1_0) ).
fof(f7406,plain,
spl0_766,
inference(avatar_split_clause,[],[f1464,f7404]) ).
fof(f7404,plain,
( spl0_766
<=> ! [X28] : c_1 = c_Nat_Opower(X28,c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_766])]) ).
fof(f1464,axiom,
! [X28] : c_1 = c_Nat_Opower(X28,c_0,tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Opower_Osimps__1_0) ).
fof(f7402,plain,
spl0_765,
inference(avatar_split_clause,[],[f1432,f7400]) ).
fof(f1432,axiom,
! [X3] : c_Divides_Oop_Amod(X3,c_0,tc_IntDef_Oint) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_ODIVISION__BY__ZERO_0) ).
fof(f7398,plain,
spl0_764,
inference(avatar_split_clause,[],[f1364,f7396]) ).
fof(f7396,plain,
( spl0_764
<=> ! [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_764])]) ).
fof(f1364,axiom,
! [X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1)
| c_in(c_1,c_IntDef_ONats,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_ONats__1_0) ).
fof(f7394,plain,
spl0_763,
inference(avatar_split_clause,[],[f1363,f7392]) ).
fof(f7392,plain,
( spl0_763
<=> ! [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_763])]) ).
fof(f1363,axiom,
! [X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1)
| c_in(c_0,c_IntDef_ONats,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_ONats__0_0) ).
fof(f7390,plain,
spl0_762,
inference(avatar_split_clause,[],[f1358,f7388]) ).
fof(f7388,plain,
( spl0_762
<=> ! [X1] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X1)
| c_in(c_1,c_IntDef_OInts,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_762])]) ).
fof(f1358,axiom,
! [X1] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X1)
| c_in(c_1,c_IntDef_OInts,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_OInts__1_0) ).
fof(f7386,plain,
spl0_761,
inference(avatar_split_clause,[],[f1357,f7384]) ).
fof(f7384,plain,
( spl0_761
<=> ! [X1] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X1)
| c_in(c_0,c_IntDef_OInts,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_761])]) ).
fof(f1357,axiom,
! [X1] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X1)
| c_in(c_0,c_IntDef_OInts,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_OInts__0_0) ).
fof(f7382,plain,
spl0_760,
inference(avatar_split_clause,[],[f1350,f7379]) ).
fof(f7379,plain,
( spl0_760
<=> c_less(c_HOL_Oabs(c_0,tc_IntDef_Oint),c_1,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_760])]) ).
fof(f1350,axiom,
c_less(c_HOL_Oabs(c_0,tc_IntDef_Oint),c_1,tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntArith_Ozabs__less__one__iff_1) ).
fof(f7377,plain,
spl0_759,
inference(avatar_split_clause,[],[f1247,f7375]) ).
fof(f7375,plain,
( spl0_759
<=> ! [X5,X1] : c_emptyset = c_Equiv__Relations_Oquotient(c_emptyset,X5,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_759])]) ).
fof(f1247,axiom,
! [X1,X5] : c_emptyset = c_Equiv__Relations_Oquotient(c_emptyset,X5,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Equiv__Relations_Oquotient__is__empty_1) ).
fof(f7373,plain,
spl0_758,
inference(avatar_split_clause,[],[f1241,f7371]) ).
fof(f7371,plain,
( spl0_758
<=> ! [X21] : c_0 = c_Divides_Oop_Amod(X21,X21,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_758])]) ).
fof(f1241,axiom,
! [X21] : c_0 = c_Divides_Oop_Amod(X21,X21,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Omod__self_0) ).
fof(f7369,plain,
spl0_757,
inference(avatar_split_clause,[],[f1230,f7367]) ).
fof(f1230,axiom,
! [X15] : c_0 = c_Divides_Oop_Amod(c_0,X15,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Omod__0_0) ).
fof(f7365,plain,
spl0_756,
inference(avatar_split_clause,[],[f1213,f7363]) ).
fof(f7363,plain,
( spl0_756
<=> ! [X15] : c_0 = c_div(c_0,X15,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_756])]) ).
fof(f1213,axiom,
! [X15] : c_0 = c_div(c_0,X15,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Odiv__0_0) ).
fof(f7361,plain,
spl0_755,
inference(avatar_split_clause,[],[f1212,f7359]) ).
fof(f7359,plain,
( spl0_755
<=> ! [X3] : c_Divides_Oop_Amod(X3,c_0,tc_nat) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_755])]) ).
fof(f1212,axiom,
! [X3] : c_Divides_Oop_Amod(X3,c_0,tc_nat) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_ODIVISION__BY__ZERO__MOD_0) ).
fof(f7357,plain,
spl0_754,
inference(avatar_split_clause,[],[f1211,f7355]) ).
fof(f7355,plain,
( spl0_754
<=> ! [X18] : c_0 = c_div(X18,c_0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_754])]) ).
fof(f1211,axiom,
! [X18] : c_0 = c_div(X18,c_0,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_ODIVISION__BY__ZERO__DIV_0) ).
fof(f7353,plain,
spl0_753,
inference(avatar_split_clause,[],[f1183,f7351]) ).
fof(f7351,plain,
( spl0_753
<=> ! [X1,X3] : c_Datatype_Ounit_Ounit__rec(X3,c_Product__Type_OUnity,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_753])]) ).
fof(f1183,axiom,
! [X3,X1] : c_Datatype_Ounit_Ounit__rec(X3,c_Product__Type_OUnity,X1) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype_Ounit_Orecs_0) ).
fof(f7349,plain,
spl0_752,
inference(avatar_split_clause,[],[f1182,f7347]) ).
fof(f7347,plain,
( spl0_752
<=> ! [X1,X3] : c_Datatype_Ounit_Ounit__case(X3,c_Product__Type_OUnity,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_752])]) ).
fof(f1182,axiom,
! [X3,X1] : c_Datatype_Ounit_Ounit__case(X3,c_Product__Type_OUnity,X1) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype_Ounit_Ocases_0) ).
fof(f7345,plain,
spl0_751,
inference(avatar_split_clause,[],[f1176,f7343]) ).
fof(f7343,plain,
( spl0_751
<=> ! [X1] : c_0 = c_Nat_Osize(c_Datatype_Ooption_ONone,tc_Datatype_Ooption(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_751])]) ).
fof(f1176,axiom,
! [X1] : c_0 = c_Nat_Osize(c_Datatype_Ooption_ONone,tc_Datatype_Ooption(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype_Ooption_Osize__1_0) ).
fof(f7341,plain,
spl0_750,
inference(avatar_split_clause,[],[f68,f7339]) ).
fof(f68,axiom,
! [X0,X1] :
( ~ class_Orderings_Oorder(X1)
| c_lessequals(X0,X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Orderings_Oorder__class_Oaxioms__1_0) ).
fof(f7337,plain,
spl0_749,
inference(avatar_split_clause,[],[f2949,f7334]) ).
fof(f2949,axiom,
c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_Aa,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_ONonce(v_NB))))),v_X)),c_List_Oset(v_evso,tc_Event_Oevent),tc_Event_Oevent),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_3) ).
fof(f7332,plain,
( spl0_748
| ~ spl0_646
| ~ spl0_688 ),
inference(avatar_split_clause,[],[f7319,f7050,f6101,f7329]) ).
fof(f7329,plain,
( spl0_748
<=> c_lessequals(c_0,c_1,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_748])]) ).
fof(f7319,plain,
( c_lessequals(c_0,c_1,tc_IntDef_Oint)
| ~ spl0_646
| ~ spl0_688 ),
inference(superposition,[],[f7051,f6103]) ).
fof(f7325,plain,
( ~ spl0_747
| ~ spl0_647
| ~ spl0_686 ),
inference(avatar_split_clause,[],[f7311,f7042,f6106,f7322]) ).
fof(f7322,plain,
( spl0_747
<=> c_less(c_0,c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_747])]) ).
fof(f7042,plain,
( spl0_686
<=> ! [X16] : ~ c_less(c_IntDef_Oint(X16),c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_686])]) ).
fof(f7311,plain,
( ~ c_less(c_0,c_0,tc_IntDef_Oint)
| ~ spl0_647
| ~ spl0_686 ),
inference(superposition,[],[f7043,f6108]) ).
fof(f7043,plain,
( ! [X16] : ~ c_less(c_IntDef_Oint(X16),c_0,tc_IntDef_Oint)
| ~ spl0_686 ),
inference(avatar_component_clause,[],[f7042]) ).
fof(f7316,plain,
( ~ spl0_746
| ~ spl0_646
| ~ spl0_686 ),
inference(avatar_split_clause,[],[f7310,f7042,f6101,f7313]) ).
fof(f7313,plain,
( spl0_746
<=> c_less(c_1,c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_746])]) ).
fof(f7310,plain,
( ~ c_less(c_1,c_0,tc_IntDef_Oint)
| ~ spl0_646
| ~ spl0_686 ),
inference(superposition,[],[f7043,f6103]) ).
fof(f7309,plain,
spl0_745,
inference(avatar_split_clause,[],[f3221,f7306]) ).
fof(f7306,plain,
( spl0_745
<=> c_0 = c_uminus(c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_745])]) ).
fof(f3221,plain,
c_0 = c_uminus(c_0,tc_IntDef_Oint),
inference(forward_demodulation,[],[f1391,f1374]) ).
fof(f1374,axiom,
c_0 = c_IntDef_Oint(c_0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oint__eq__0__conv_1) ).
fof(f1391,axiom,
c_IntDef_Oint(c_0) = c_uminus(c_IntDef_Oint(c_0),tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Onegative__eq__positive_2) ).
fof(f7304,plain,
spl0_744,
inference(avatar_split_clause,[],[f3216,f7302]) ).
fof(f7302,plain,
( spl0_744
<=> ! [X3] : c_Binomial_Obinomial(X3,c_1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_744])]) ).
fof(f3216,plain,
! [X3] : c_Binomial_Obinomial(X3,c_1) = X3,
inference(forward_demodulation,[],[f2985,f2958]) ).
fof(f2985,plain,
! [X3] : c_Binomial_Obinomial(X3,c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat)) = X3,
inference(definition_unfolding,[],[f1161,f2544]) ).
fof(f1161,axiom,
! [X3] : c_Binomial_Obinomial(X3,c_Suc(c_0)) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Binomial_Obinomial__1_0) ).
fof(f7300,plain,
spl0_743,
inference(avatar_split_clause,[],[f2957,f7297]) ).
fof(f7295,plain,
spl0_742,
inference(avatar_split_clause,[],[f2923,f7293]) ).
fof(f7293,plain,
( spl0_742
<=> ! [X86] : c_in(c_Public_OshrK(X86),c_Message_OsymKeys,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_742])]) ).
fof(f2923,axiom,
! [X86] : c_in(c_Public_OshrK(X86),c_Message_OsymKeys,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Public_OshrK_AX1_A_58_AsymKeys_A_61_61_ATrue_0) ).
fof(f7291,plain,
spl0_741,
inference(avatar_split_clause,[],[f2908,f7288]) ).
fof(f7288,plain,
( spl0_741
<=> c_0 = c_Nat_Osize(c_Public_Okeymode_OEncryption,tc_Public_Okeymode) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_741])]) ).
fof(f2908,axiom,
c_0 = c_Nat_Osize(c_Public_Okeymode_OEncryption,tc_Public_Okeymode),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Public_Okeymode_Osize__2_0) ).
fof(f7286,plain,
spl0_740,
inference(avatar_split_clause,[],[f2907,f7283]) ).
fof(f7283,plain,
( spl0_740
<=> c_0 = c_Nat_Osize(c_Public_Okeymode_OSignature,tc_Public_Okeymode) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_740])]) ).
fof(f2907,axiom,
c_0 = c_Nat_Osize(c_Public_Okeymode_OSignature,tc_Public_Okeymode),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Public_Okeymode_Osize__1_0) ).
fof(f7281,plain,
spl0_739,
inference(avatar_split_clause,[],[f2740,f7279]) ).
fof(f2740,axiom,
! [X3] : c_Message_OinvKey(c_Message_OinvKey(X3)) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OinvKey_A_IinvKey_Ay_J_A_61_61_Ay_0) ).
fof(f7277,plain,
spl0_738,
inference(avatar_split_clause,[],[f2739,f7274]) ).
fof(f7274,plain,
( spl0_738
<=> c_0 = c_Nat_Osize(c_Message_Oagent_OSpy,tc_Message_Oagent) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_738])]) ).
fof(f2739,axiom,
c_0 = c_Nat_Osize(c_Message_Oagent_OSpy,tc_Message_Oagent),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oagent_Osize__3_0) ).
fof(f7272,plain,
spl0_737,
inference(avatar_split_clause,[],[f2737,f7269]) ).
fof(f7269,plain,
( spl0_737
<=> c_0 = c_Nat_Osize(c_Message_Oagent_OServer,tc_Message_Oagent) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_737])]) ).
fof(f2737,axiom,
c_0 = c_Nat_Osize(c_Message_Oagent_OServer,tc_Message_Oagent),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oagent_Osize__1_0) ).
fof(f7267,plain,
spl0_736,
inference(avatar_split_clause,[],[f2714,f7265]) ).
fof(f7265,plain,
( spl0_736
<=> ! [X1] : c_emptyset = c_Transitive__Closure_Otrancl(c_emptyset,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_736])]) ).
fof(f2714,axiom,
! [X1] : c_emptyset = c_Transitive__Closure_Otrancl(c_emptyset,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Transitive__Closure_Otrancl__empty_0) ).
fof(f7263,plain,
spl0_735,
inference(avatar_split_clause,[],[f2698,f7261]) ).
fof(f2698,axiom,
! [X1,X12] : c_lessequals(X12,c_UNIV,tc_set(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osubset__UNIV_0) ).
fof(f7259,plain,
spl0_734,
inference(avatar_split_clause,[],[f2691,f7257]) ).
fof(f7257,plain,
( spl0_734
<=> ! [X12,X1] : ~ c_less(X12,c_emptyset,tc_set(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_734])]) ).
fof(f2691,axiom,
! [X1,X12] : ~ c_less(X12,c_emptyset,tc_set(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Onot__psubset__empty_0) ).
fof(f7255,plain,
spl0_733,
inference(avatar_split_clause,[],[f2651,f7253]) ).
fof(f7253,plain,
( spl0_733
<=> ! [X1] : c_emptyset = c_Union(c_emptyset,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_733])]) ).
fof(f2651,axiom,
! [X1] : c_emptyset = c_Union(c_emptyset,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUnion__empty_0) ).
fof(f7251,plain,
spl0_732,
inference(avatar_split_clause,[],[f2649,f7249]) ).
fof(f7249,plain,
( spl0_732
<=> ! [X1] : c_UNIV = c_Union(c_UNIV,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_732])]) ).
fof(f2649,axiom,
! [X1] : c_UNIV = c_Union(c_UNIV,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUnion__UNIV_0) ).
fof(f7247,plain,
spl0_731,
inference(avatar_split_clause,[],[f2625,f7245]) ).
fof(f7245,plain,
( spl0_731
<=> ! [X1] : c_UNIV = c_Pow(c_UNIV,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_731])]) ).
fof(f2625,axiom,
! [X1] : c_UNIV = c_Pow(c_UNIV,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OPow__UNIV_0) ).
fof(f7243,plain,
spl0_730,
inference(avatar_split_clause,[],[f2619,f7241]) ).
fof(f7241,plain,
( spl0_730
<=> ! [X1] : c_UNIV = c_Inter(c_emptyset,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_730])]) ).
fof(f2619,axiom,
! [X1] : c_UNIV = c_Inter(c_emptyset,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OInter__empty_0) ).
fof(f7239,plain,
spl0_729,
inference(avatar_split_clause,[],[f2612,f7237]) ).
fof(f7237,plain,
( spl0_729
<=> ! [X1] : c_emptyset = c_Inter(c_UNIV,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_729])]) ).
fof(f2612,axiom,
! [X1] : c_emptyset = c_Inter(c_UNIV,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OInter__UNIV_0) ).
fof(f7235,plain,
spl0_728,
inference(avatar_split_clause,[],[f2567,f7232]) ).
fof(f7232,plain,
( spl0_728
<=> c_emptyset = c_SetInterval_OlessThan(c_0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_728])]) ).
fof(f2567,axiom,
c_emptyset = c_SetInterval_OlessThan(c_0,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OlessThan__0_0) ).
fof(f7230,plain,
spl0_727,
inference(avatar_split_clause,[],[f2528,f7227]) ).
fof(f7227,plain,
( spl0_727
<=> c_UNIV = c_SetInterval_OatLeast(c_0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_727])]) ).
fof(f2528,axiom,
c_UNIV = c_SetInterval_OatLeast(c_0,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatLeast__0_0) ).
fof(f7225,plain,
spl0_726,
inference(avatar_split_clause,[],[f2386,f7223]) ).
fof(f7221,plain,
spl0_725,
inference(avatar_split_clause,[],[f2164,f7218]) ).
fof(f7218,plain,
( spl0_725
<=> c_0 = c_Nat_Osize(c_Numeral_Obit_OB1,tc_Numeral_Obit) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_725])]) ).
fof(f2164,axiom,
c_0 = c_Nat_Osize(c_Numeral_Obit_OB1,tc_Numeral_Obit),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obit_Osize__2_0) ).
fof(f7216,plain,
spl0_724,
inference(avatar_split_clause,[],[f2163,f7213]) ).
fof(f7213,plain,
( spl0_724
<=> c_0 = c_Nat_Osize(c_Numeral_Obit_OB0,tc_Numeral_Obit) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_724])]) ).
fof(f2163,axiom,
c_0 = c_Nat_Osize(c_Numeral_Obit_OB0,tc_Numeral_Obit),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obit_Osize__1_0) ).
fof(f7211,plain,
spl0_723,
inference(avatar_split_clause,[],[f2152,f7209]) ).
fof(f7209,plain,
( spl0_723
<=> ! [X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_IntDef_Oneg(c_1,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_723])]) ).
fof(f2152,axiom,
! [X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_IntDef_Oneg(c_1,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obin__rel__simps__9_0) ).
fof(f7207,plain,
spl0_722,
inference(avatar_split_clause,[],[f2151,f7205]) ).
fof(f7205,plain,
( spl0_722
<=> ! [X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_IntDef_Oneg(c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_722])]) ).
fof(f2151,axiom,
! [X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_IntDef_Oneg(c_0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obin__rel__simps__8_0) ).
fof(f7203,plain,
spl0_721,
inference(avatar_split_clause,[],[f2135,f7201]) ).
fof(f7201,plain,
( spl0_721
<=> ! [X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1)
| ~ c_IntDef_Oiszero(c_1,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_721])]) ).
fof(f2135,axiom,
! [X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1)
| ~ c_IntDef_Oiszero(c_1,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obin__rel__simps__10_0) ).
fof(f7199,plain,
spl0_720,
inference(avatar_split_clause,[],[f2130,f7197]) ).
fof(f2130,axiom,
! [X11] : c_Numeral_OPls = c_Numeral_Obin__mult(c_Numeral_OPls,X11),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obin__mult__Pls_0) ).
fof(f7195,plain,
spl0_719,
inference(avatar_split_clause,[],[f2115,f7193]) ).
fof(f7193,plain,
( spl0_719
<=> ! [X3] : c_Numeral_Obin__add(X3,c_Numeral_OPls) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_719])]) ).
fof(f7191,plain,
spl0_718,
inference(avatar_split_clause,[],[f2114,f7189]) ).
fof(f7187,plain,
spl0_717,
inference(avatar_split_clause,[],[f2106,f7184]) ).
fof(f2106,axiom,
c_Numeral_OPls = c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_OPls__0__eq_0) ).
fof(f7182,plain,
spl0_716,
inference(avatar_split_clause,[],[f2105,f7179]) ).
fof(f2105,axiom,
c_Numeral_OMin = c_Numeral_OBit(c_Numeral_OMin,c_Numeral_Obit_OB1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_OMin__1__eq_0) ).
fof(f7177,plain,
spl0_715,
inference(avatar_split_clause,[],[f1866,f7174]) ).
fof(f1866,axiom,
c_0 = c_Numeral_Onumber__of(c_Numeral_OPls,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatBin_Onat__numeral__0__eq__0_0) ).
fof(f7172,plain,
spl0_714,
inference(avatar_split_clause,[],[f1785,f7170]) ).
fof(f7170,plain,
( spl0_714
<=> ! [X43] : c_List_Olist_ONil = c_List_Oupt(X43,c_0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_714])]) ).
fof(f1785,axiom,
! [X43] : c_List_Olist_ONil = c_List_Oupt(X43,c_0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oupt__eq__Nil__conv_1) ).
fof(f7168,plain,
spl0_713,
inference(avatar_split_clause,[],[f1778,f7166]) ).
fof(f7166,plain,
( spl0_713
<=> ! [X41] : c_List_Olist_ONil = c_List_Otl(c_List_Olist_ONil,X41) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_713])]) ).
fof(f1778,axiom,
! [X41] : c_List_Olist_ONil = c_List_Otl(c_List_Olist_ONil,X41),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Otl_Osimps__1_0) ).
fof(f7164,plain,
spl0_712,
inference(avatar_split_clause,[],[f1753,f7162]) ).
fof(f7162,plain,
( spl0_712
<=> ! [X1] : c_emptyset = c_List_Oset(c_List_Olist_ONil,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_712])]) ).
fof(f1753,axiom,
! [X1] : c_emptyset = c_List_Oset(c_List_Olist_ONil,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oset__empty_1) ).
fof(f7160,plain,
spl0_711,
inference(avatar_split_clause,[],[f1736,f7158]) ).
fof(f7158,plain,
( spl0_711
<=> ! [X1] : c_List_Olist_ONil = c_List_Orotate1(c_List_Olist_ONil,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_711])]) ).
fof(f1736,axiom,
! [X1] : c_List_Olist_ONil = c_List_Orotate1(c_List_Olist_ONil,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Orotate1__is__Nil__conv_1) ).
fof(f7156,plain,
spl0_710,
inference(avatar_split_clause,[],[f1729,f7154]) ).
fof(f7154,plain,
( spl0_710
<=> ! [X1] : c_List_Olist_ONil = c_List_Orev(c_List_Olist_ONil,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_710])]) ).
fof(f7152,plain,
spl0_709,
inference(avatar_split_clause,[],[f1716,f7150]) ).
fof(f7150,plain,
( spl0_709
<=> ! [X1] : c_List_Olist_ONil = c_List_Oremdups(c_List_Olist_ONil,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_709])]) ).
fof(f1716,axiom,
! [X1] : c_List_Olist_ONil = c_List_Oremdups(c_List_Olist_ONil,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oremdups__eq__nil__iff_1) ).
fof(f7148,plain,
spl0_708,
inference(avatar_split_clause,[],[f1688,f7145]) ).
fof(f7145,plain,
( spl0_708
<=> c_0 = c_Nat_Osize(c_List_Onibble_ONibble8,tc_List_Onibble) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_708])]) ).
fof(f1688,axiom,
c_0 = c_Nat_Osize(c_List_Onibble_ONibble8,tc_List_Onibble),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Onibble_Osize__9_0) ).
fof(f7143,plain,
spl0_707,
inference(avatar_split_clause,[],[f1687,f7140]) ).
fof(f7140,plain,
( spl0_707
<=> c_0 = c_Nat_Osize(c_List_Onibble_ONibble7,tc_List_Onibble) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_707])]) ).
fof(f1687,axiom,
c_0 = c_Nat_Osize(c_List_Onibble_ONibble7,tc_List_Onibble),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Onibble_Osize__8_0) ).
fof(f7138,plain,
spl0_706,
inference(avatar_split_clause,[],[f1686,f7135]) ).
fof(f7135,plain,
( spl0_706
<=> c_0 = c_Nat_Osize(c_List_Onibble_ONibble6,tc_List_Onibble) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_706])]) ).
fof(f1686,axiom,
c_0 = c_Nat_Osize(c_List_Onibble_ONibble6,tc_List_Onibble),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Onibble_Osize__7_0) ).
fof(f7133,plain,
spl0_705,
inference(avatar_split_clause,[],[f1685,f7130]) ).
fof(f7130,plain,
( spl0_705
<=> c_0 = c_Nat_Osize(c_List_Onibble_ONibble5,tc_List_Onibble) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_705])]) ).
fof(f1685,axiom,
c_0 = c_Nat_Osize(c_List_Onibble_ONibble5,tc_List_Onibble),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Onibble_Osize__6_0) ).
fof(f7128,plain,
spl0_704,
inference(avatar_split_clause,[],[f1684,f7125]) ).
fof(f7125,plain,
( spl0_704
<=> c_0 = c_Nat_Osize(c_List_Onibble_ONibble4,tc_List_Onibble) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_704])]) ).
fof(f1684,axiom,
c_0 = c_Nat_Osize(c_List_Onibble_ONibble4,tc_List_Onibble),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Onibble_Osize__5_0) ).
fof(f7123,plain,
spl0_703,
inference(avatar_split_clause,[],[f1683,f7120]) ).
fof(f7120,plain,
( spl0_703
<=> c_0 = c_Nat_Osize(c_List_Onibble_ONibble3,tc_List_Onibble) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_703])]) ).
fof(f1683,axiom,
c_0 = c_Nat_Osize(c_List_Onibble_ONibble3,tc_List_Onibble),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Onibble_Osize__4_0) ).
fof(f7118,plain,
spl0_702,
inference(avatar_split_clause,[],[f1682,f7115]) ).
fof(f7115,plain,
( spl0_702
<=> c_0 = c_Nat_Osize(c_List_Onibble_ONibble2,tc_List_Onibble) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_702])]) ).
fof(f1682,axiom,
c_0 = c_Nat_Osize(c_List_Onibble_ONibble2,tc_List_Onibble),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Onibble_Osize__3_0) ).
fof(f7113,plain,
spl0_701,
inference(avatar_split_clause,[],[f1681,f7110]) ).
fof(f7110,plain,
( spl0_701
<=> c_0 = c_Nat_Osize(c_List_Onibble_ONibble1,tc_List_Onibble) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_701])]) ).
fof(f1681,axiom,
c_0 = c_Nat_Osize(c_List_Onibble_ONibble1,tc_List_Onibble),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Onibble_Osize__2_0) ).
fof(f7108,plain,
spl0_700,
inference(avatar_split_clause,[],[f1680,f7105]) ).
fof(f7105,plain,
( spl0_700
<=> c_0 = c_Nat_Osize(c_List_Onibble_ONibble0,tc_List_Onibble) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_700])]) ).
fof(f1680,axiom,
c_0 = c_Nat_Osize(c_List_Onibble_ONibble0,tc_List_Onibble),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Onibble_Osize__1_0) ).
fof(f7103,plain,
spl0_699,
inference(avatar_split_clause,[],[f1679,f7100]) ).
fof(f7100,plain,
( spl0_699
<=> c_0 = c_Nat_Osize(c_List_Onibble_ONibbleF,tc_List_Onibble) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_699])]) ).
fof(f1679,axiom,
c_0 = c_Nat_Osize(c_List_Onibble_ONibbleF,tc_List_Onibble),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Onibble_Osize__16_0) ).
fof(f7098,plain,
spl0_698,
inference(avatar_split_clause,[],[f1678,f7095]) ).
fof(f7095,plain,
( spl0_698
<=> c_0 = c_Nat_Osize(c_List_Onibble_ONibbleE,tc_List_Onibble) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_698])]) ).
fof(f1678,axiom,
c_0 = c_Nat_Osize(c_List_Onibble_ONibbleE,tc_List_Onibble),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Onibble_Osize__15_0) ).
fof(f7093,plain,
spl0_697,
inference(avatar_split_clause,[],[f1677,f7090]) ).
fof(f7090,plain,
( spl0_697
<=> c_0 = c_Nat_Osize(c_List_Onibble_ONibbleD,tc_List_Onibble) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_697])]) ).
fof(f1677,axiom,
c_0 = c_Nat_Osize(c_List_Onibble_ONibbleD,tc_List_Onibble),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Onibble_Osize__14_0) ).
fof(f7088,plain,
spl0_696,
inference(avatar_split_clause,[],[f1676,f7085]) ).
fof(f7085,plain,
( spl0_696
<=> c_0 = c_Nat_Osize(c_List_Onibble_ONibbleC,tc_List_Onibble) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_696])]) ).
fof(f1676,axiom,
c_0 = c_Nat_Osize(c_List_Onibble_ONibbleC,tc_List_Onibble),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Onibble_Osize__13_0) ).
fof(f7083,plain,
spl0_695,
inference(avatar_split_clause,[],[f1675,f7080]) ).
fof(f7080,plain,
( spl0_695
<=> c_0 = c_Nat_Osize(c_List_Onibble_ONibbleB,tc_List_Onibble) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_695])]) ).
fof(f1675,axiom,
c_0 = c_Nat_Osize(c_List_Onibble_ONibbleB,tc_List_Onibble),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Onibble_Osize__12_0) ).
fof(f7078,plain,
spl0_694,
inference(avatar_split_clause,[],[f1674,f7075]) ).
fof(f7075,plain,
( spl0_694
<=> c_0 = c_Nat_Osize(c_List_Onibble_ONibbleA,tc_List_Onibble) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_694])]) ).
fof(f1674,axiom,
c_0 = c_Nat_Osize(c_List_Onibble_ONibbleA,tc_List_Onibble),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Onibble_Osize__11_0) ).
fof(f7073,plain,
spl0_693,
inference(avatar_split_clause,[],[f1673,f7070]) ).
fof(f7070,plain,
( spl0_693
<=> c_0 = c_Nat_Osize(c_List_Onibble_ONibble9,tc_List_Onibble) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_693])]) ).
fof(f1673,axiom,
c_0 = c_Nat_Osize(c_List_Onibble_ONibble9,tc_List_Onibble),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Onibble_Osize__10_0) ).
fof(f7068,plain,
spl0_692,
inference(avatar_split_clause,[],[f1638,f7066]) ).
fof(f7066,plain,
( spl0_692
<=> ! [X1] : c_UNIV = c_List_Olists(c_UNIV,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_692])]) ).
fof(f1638,axiom,
! [X1] : c_UNIV = c_List_Olists(c_UNIV,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olists__UNIV_0) ).
fof(f7064,plain,
spl0_691,
inference(avatar_split_clause,[],[f1567,f7062]) ).
fof(f7062,plain,
( spl0_691
<=> ! [X59,X43] : c_List_Odistinct(c_List_Oupt(X43,X59),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_691])]) ).
fof(f1567,axiom,
! [X59,X43] : c_List_Odistinct(c_List_Oupt(X43,X59),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Odistinct__upt_0) ).
fof(f7060,plain,
spl0_690,
inference(avatar_split_clause,[],[f1543,f7058]) ).
fof(f7058,plain,
( spl0_690
<=> ! [X41] : c_List_Olist_ONil = c_List_Oconcat(c_List_Olist_ONil,X41) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_690])]) ).
fof(f1543,axiom,
! [X41] : c_List_Olist_ONil = c_List_Oconcat(c_List_Olist_ONil,X41),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oconcat_Osimps__1_0) ).
fof(f7056,plain,
spl0_689,
inference(avatar_split_clause,[],[f1536,f7054]) ).
fof(f7054,plain,
( spl0_689
<=> ! [X41] : c_List_Olist_ONil = c_List_Obutlast(c_List_Olist_ONil,X41) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_689])]) ).
fof(f1536,axiom,
! [X41] : c_List_Olist_ONil = c_List_Obutlast(c_List_Olist_ONil,X41),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Obutlast_Osimps__1_0) ).
fof(f7052,plain,
spl0_688,
inference(avatar_split_clause,[],[f1424,f7050]) ).
fof(f1424,axiom,
! [X21] : c_lessequals(c_0,c_IntDef_Oint(X21),tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Ozero__zle__int_0) ).
fof(f7048,plain,
spl0_687,
inference(avatar_split_clause,[],[f1384,f7046]) ).
fof(f1384,axiom,
! [X3] : c_IntDef_Onat(c_IntDef_Oint(X3)) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Onat__int_0) ).
fof(f7044,plain,
spl0_686,
inference(avatar_split_clause,[],[f1378,f7042]) ).
fof(f1378,axiom,
! [X16] : ~ c_less(c_IntDef_Oint(X16),c_0,tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oint__less__0__conv_0) ).
fof(f7040,plain,
~ spl0_685,
inference(avatar_split_clause,[],[f1309,f7037]) ).
fof(f1309,axiom,
~ c_in(c_UNIV,c_Finite__Set_OFinites,tc_set(tc_nat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Infinite__Set_Onat__infinite_0) ).
fof(f7035,plain,
spl0_684,
inference(avatar_split_clause,[],[f1296,f7033]) ).
fof(f7033,plain,
( spl0_684
<=> ! [X1,X3] : c_Fun_Oid(X3,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_684])]) ).
fof(f1296,axiom,
! [X3,X1] : c_Fun_Oid(X3,X1) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Fun_Oid__apply_0) ).
fof(f7031,plain,
spl0_683,
inference(avatar_split_clause,[],[f1295,f7029]) ).
fof(f1295,axiom,
! [X3] : c_NatArith_Oof__nat(X3,tc_nat) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Oof__nat__id_0) ).
fof(f7027,plain,
spl0_682,
inference(avatar_split_clause,[],[f1278,f7025]) ).
fof(f7025,plain,
( spl0_682
<=> ! [X1] : c_0 = c_Finite__Set_Ocard(c_emptyset,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_682])]) ).
fof(f1278,axiom,
! [X1] : c_0 = c_Finite__Set_Ocard(c_emptyset,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ocard__empty_0) ).
fof(f7023,plain,
spl0_681,
inference(avatar_split_clause,[],[f1255,f7020]) ).
fof(f7020,plain,
( spl0_681
<=> c_0 = c_Nat_Osize(c_Extraction_Osumbool_ORight,tc_Extraction_Osumbool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_681])]) ).
fof(f1255,axiom,
c_0 = c_Nat_Osize(c_Extraction_Osumbool_ORight,tc_Extraction_Osumbool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Extraction_Osumbool_Osize__2_0) ).
fof(f7018,plain,
spl0_680,
inference(avatar_split_clause,[],[f1254,f7015]) ).
fof(f7015,plain,
( spl0_680
<=> c_0 = c_Nat_Osize(c_Extraction_Osumbool_OLeft,tc_Extraction_Osumbool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_680])]) ).
fof(f1254,axiom,
c_0 = c_Nat_Osize(c_Extraction_Osumbool_OLeft,tc_Extraction_Osumbool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Extraction_Osumbool_Osize__1_0) ).
fof(f7013,plain,
spl0_679,
inference(avatar_split_clause,[],[f1184,f7010]) ).
fof(f7010,plain,
( spl0_679
<=> c_0 = c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_679])]) ).
fof(f1184,axiom,
c_0 = c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype_Ounit_Osize_0) ).
fof(f7008,plain,
spl0_678,
inference(avatar_split_clause,[],[f1173,f7006]) ).
fof(f7006,plain,
( spl0_678
<=> ! [X1,X42] : c_Datatype_Ooption_ONone != c_Datatype_Ooption_OSome(X42,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_678])]) ).
fof(f1173,axiom,
! [X1,X42] : c_Datatype_Ooption_ONone != c_Datatype_Ooption_OSome(X42,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype_Ooption_Odistinct__1_0) ).
fof(f7004,plain,
spl0_677,
inference(avatar_split_clause,[],[f1172,f7002]) ).
fof(f7002,plain,
( spl0_677
<=> ! [X1] : c_emptyset = c_Datatype_Oo2s(c_Datatype_Ooption_ONone,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_677])]) ).
fof(f1172,axiom,
! [X1] : c_emptyset = c_Datatype_Oo2s(c_Datatype_Ooption_ONone,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype_Oo2s__empty__eq_1) ).
fof(f7000,plain,
spl0_676,
inference(avatar_split_clause,[],[f1165,f6998]) ).
fof(f6998,plain,
( spl0_676
<=> ! [X21] : c_1 = c_Binomial_Obinomial(X21,X21) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_676])]) ).
fof(f1165,axiom,
! [X21] : c_1 = c_Binomial_Obinomial(X21,X21),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Binomial_Obinomial__n__n_0) ).
fof(f6996,plain,
spl0_675,
inference(avatar_split_clause,[],[f1164,f6994]) ).
fof(f6994,plain,
( spl0_675
<=> ! [X21] : c_1 = c_Binomial_Obinomial(X21,c_0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_675])]) ).
fof(f1164,axiom,
! [X21] : c_1 = c_Binomial_Obinomial(X21,c_0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Binomial_Obinomial__n__0_0) ).
fof(f6992,plain,
spl0_674,
inference(avatar_split_clause,[],[f250,f6990]) ).
fof(f6990,plain,
( spl0_674
<=> ! [X37] :
( ~ class_Finite__Set_Ofinite(X37)
| class_Finite__Set_Ofinite(tc_set(X37)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_674])]) ).
fof(f250,axiom,
! [X37] :
( ~ class_Finite__Set_Ofinite(X37)
| class_Finite__Set_Ofinite(tc_set(X37)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_set_3) ).
fof(f6988,plain,
spl0_673,
inference(avatar_split_clause,[],[f128,f6986]) ).
fof(f6986,plain,
( spl0_673
<=> ! [X37] :
( ~ class_Finite__Set_Ofinite(X37)
| class_Finite__Set_Ofinite(tc_Datatype_Ooption(X37)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_673])]) ).
fof(f128,axiom,
! [X37] :
( ~ class_Finite__Set_Ofinite(X37)
| class_Finite__Set_Ofinite(tc_Datatype_Ooption(X37)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Datatype__Ooption_0) ).
fof(f6984,plain,
spl0_672,
inference(avatar_split_clause,[],[f112,f6982]) ).
fof(f112,axiom,
! [X1,X12] : c_lessequals(X12,X12,tc_set(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osubset__refl_0) ).
fof(f6980,plain,
spl0_671,
inference(avatar_split_clause,[],[f101,f6978]) ).
fof(f101,axiom,
! [X1,X12] : c_lessequals(c_emptyset,X12,tc_set(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Oempty__subsetI_0) ).
fof(f6976,plain,
spl0_670,
inference(avatar_split_clause,[],[f44,f6974]) ).
fof(f6974,plain,
( spl0_670
<=> ! [X1,X23] : c_List_Odistinct(c_List_Oremdups(X23,X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_670])]) ).
fof(f44,axiom,
! [X1,X23] : c_List_Odistinct(c_List_Oremdups(X23,X1),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Odistinct__remdups_0) ).
fof(f6972,plain,
spl0_669,
inference(avatar_split_clause,[],[f28,f6970]) ).
fof(f6970,plain,
( spl0_669
<=> ! [X1] : c_in(c_emptyset,c_Finite__Set_OFinites,tc_set(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_669])]) ).
fof(f28,axiom,
! [X1] : c_in(c_emptyset,c_Finite__Set_OFinites,tc_set(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_OFinites_OemptyI_0) ).
fof(f6968,plain,
( ~ spl0_668
| ~ spl0_647
| ~ spl0_649 ),
inference(avatar_split_clause,[],[f6958,f6116,f6106,f6965]) ).
fof(f6965,plain,
( spl0_668
<=> c_IntDef_Oneg(c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_668])]) ).
fof(f6116,plain,
( spl0_649
<=> ! [X21] : ~ c_IntDef_Oneg(c_IntDef_Oint(X21),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_649])]) ).
fof(f6958,plain,
( ~ c_IntDef_Oneg(c_0,tc_IntDef_Oint)
| ~ spl0_647
| ~ spl0_649 ),
inference(superposition,[],[f6117,f6108]) ).
fof(f6117,plain,
( ! [X21] : ~ c_IntDef_Oneg(c_IntDef_Oint(X21),tc_IntDef_Oint)
| ~ spl0_649 ),
inference(avatar_component_clause,[],[f6116]) ).
fof(f6963,plain,
( ~ spl0_667
| ~ spl0_646
| ~ spl0_649 ),
inference(avatar_split_clause,[],[f6957,f6116,f6101,f6960]) ).
fof(f6960,plain,
( spl0_667
<=> c_IntDef_Oneg(c_1,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_667])]) ).
fof(f6957,plain,
( ~ c_IntDef_Oneg(c_1,tc_IntDef_Oint)
| ~ spl0_646
| ~ spl0_649 ),
inference(superposition,[],[f6117,f6103]) ).
fof(f6196,plain,
spl0_666,
inference(avatar_split_clause,[],[f3231,f6193]) ).
fof(f3231,plain,
c_less(c_0,c_1,tc_IntDef_Oint),
inference(forward_demodulation,[],[f1486,f1464]) ).
fof(f1486,axiom,
! [X0] : c_less(c_0,c_Nat_Opower(c_HOL_Oabs(X0,tc_IntDef_Oint),c_0,tc_IntDef_Oint),tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozero__less__zpower__abs__iff_2) ).
fof(f6191,plain,
spl0_665,
inference(avatar_split_clause,[],[f3212,f6189]) ).
fof(f6189,plain,
( spl0_665
<=> ! [X16] : c_Divides_Oop_Advd(c_1,X16,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_665])]) ).
fof(f3212,plain,
! [X16] : c_Divides_Oop_Advd(c_1,X16,tc_nat),
inference(forward_demodulation,[],[f2962,f2958]) ).
fof(f2962,plain,
! [X16] : c_Divides_Oop_Advd(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),X16,tc_nat),
inference(definition_unfolding,[],[f24,f2544]) ).
fof(f24,axiom,
! [X16] : c_Divides_Oop_Advd(c_Suc(c_0),X16,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Odvd__1__left_0) ).
fof(f6187,plain,
spl0_664,
inference(avatar_split_clause,[],[f3210,f6184]) ).
fof(f6184,plain,
( spl0_664
<=> c_lessequals(c_0,c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_664])]) ).
fof(f3210,plain,
c_lessequals(c_0,c_0,tc_IntDef_Oint),
inference(forward_demodulation,[],[f1377,f1374]) ).
fof(f1377,axiom,
c_lessequals(c_IntDef_Oint(c_0),c_0,tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oint__le__0__conv_1) ).
fof(f6182,plain,
spl0_663,
inference(avatar_split_clause,[],[f3209,f6179]) ).
fof(f3209,plain,
c_1 = c_IntDef_Onat(c_1),
inference(forward_demodulation,[],[f2960,f2958]) ).
fof(f2960,plain,
c_IntDef_Onat(c_1) = c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),
inference(definition_unfolding,[],[f1344,f2544]) ).
fof(f1344,axiom,
c_Suc(c_0) = c_IntDef_Onat(c_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntArith_Onat__1_0) ).
fof(f6177,plain,
spl0_662,
inference(avatar_split_clause,[],[f2853,f6174]) ).
fof(f2853,axiom,
c_emptyset = c_Message_Oanalz(c_emptyset),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oanalz__empty_0) ).
fof(f6172,plain,
spl0_661,
inference(avatar_split_clause,[],[f2773,f6169]) ).
fof(f6169,plain,
( spl0_661
<=> c_in(c_Message_Oagent_OSpy,c_Event_Obad,tc_Message_Oagent) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_661])]) ).
fof(f2773,axiom,
c_in(c_Message_Oagent_OSpy,c_Event_Obad,tc_Message_Oagent),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Event_OSpy_A_58_Abad_A_61_61_ATrue_0) ).
fof(f6167,plain,
~ spl0_660,
inference(avatar_split_clause,[],[f2772,f6164]) ).
fof(f6164,plain,
( spl0_660
<=> c_in(c_Message_Oagent_OServer,c_Event_Obad,tc_Message_Oagent) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_660])]) ).
fof(f2772,axiom,
~ c_in(c_Message_Oagent_OServer,c_Event_Obad,tc_Message_Oagent),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Event_OServer_A_58_Abad_A_61_61_AFalse_0) ).
fof(f6162,plain,
spl0_659,
inference(avatar_split_clause,[],[f2770,f6159]) ).
fof(f2770,axiom,
c_emptyset = c_Message_Oparts(c_emptyset),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oparts__empty_0) ).
fof(f6157,plain,
spl0_658,
inference(avatar_split_clause,[],[f2743,f6154]) ).
fof(f6154,plain,
( spl0_658
<=> c_emptyset = c_Message_OkeysFor(c_emptyset) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_658])]) ).
fof(f2743,axiom,
c_emptyset = c_Message_OkeysFor(c_emptyset),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OkeysFor__empty_0) ).
fof(f6152,plain,
spl0_657,
inference(avatar_split_clause,[],[f2735,f6150]) ).
fof(f6150,plain,
( spl0_657
<=> ! [X90] : c_Message_Oagent_OSpy != c_Message_Oagent_OFriend(X90) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_657])]) ).
fof(f2735,axiom,
! [X90] : c_Message_Oagent_OSpy != c_Message_Oagent_OFriend(X90),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oagent_Odistinct__6_0) ).
fof(f6148,plain,
spl0_656,
inference(avatar_split_clause,[],[f2731,f6146]) ).
fof(f6146,plain,
( spl0_656
<=> ! [X89] : c_Message_Oagent_OServer != c_Message_Oagent_OFriend(X89) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_656])]) ).
fof(f2731,axiom,
! [X89] : c_Message_Oagent_OServer != c_Message_Oagent_OFriend(X89),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oagent_Odistinct__2_0) ).
fof(f6144,plain,
spl0_655,
inference(avatar_split_clause,[],[f2672,f6142]) ).
fof(f6142,plain,
( spl0_655
<=> ! [X4,X1] : ~ c_in(X4,c_emptyset,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_655])]) ).
fof(f2672,axiom,
! [X1,X4] : ~ c_in(X4,c_emptyset,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Oempty__iff_0) ).
fof(f6140,plain,
spl0_654,
inference(avatar_split_clause,[],[f2155,f6137]) ).
fof(f6137,plain,
( spl0_654
<=> c_Numeral_OPls = c_Numeral_Obin__succ(c_Numeral_OMin) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_654])]) ).
fof(f2155,axiom,
c_Numeral_OPls = c_Numeral_Obin__succ(c_Numeral_OMin),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obin__succ__Min_0) ).
fof(f6135,plain,
spl0_653,
inference(avatar_split_clause,[],[f2091,f6133]) ).
fof(f6133,plain,
( spl0_653
<=> ! [X21] : ~ c_less(X21,c_0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_653])]) ).
fof(f2091,axiom,
! [X21] : ~ c_less(X21,c_0,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Onot__less0_0) ).
fof(f6131,plain,
spl0_652,
inference(avatar_split_clause,[],[f2049,f6128]) ).
fof(f2049,axiom,
c_less(c_0,c_1,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oless__one_1) ).
fof(f6126,plain,
spl0_651,
inference(avatar_split_clause,[],[f1709,f6124]) ).
fof(f6124,plain,
( spl0_651
<=> ! [X41,X0] : ~ c_List_Oop_Amem(X0,c_List_Olist_ONil,X41) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_651])]) ).
fof(f1709,axiom,
! [X41,X0] : ~ c_List_Oop_Amem(X0,c_List_Olist_ONil,X41),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oop_Amem_Osimps__1_0) ).
fof(f6122,plain,
spl0_650,
inference(avatar_split_clause,[],[f1482,f6120]) ).
fof(f1482,axiom,
! [X15] : c_Divides_Oop_Advd(X15,X15,tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozdvd__refl_0) ).
fof(f6118,plain,
spl0_649,
inference(avatar_split_clause,[],[f1393,f6116]) ).
fof(f1393,axiom,
! [X21] : ~ c_IntDef_Oneg(c_IntDef_Oint(X21),tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Onot__neg__int_0) ).
fof(f6114,plain,
spl0_648,
inference(avatar_split_clause,[],[f1386,f6111]) ).
fof(f6111,plain,
( spl0_648
<=> c_0 = c_IntDef_Onat(c_0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_648])]) ).
fof(f1386,axiom,
c_0 = c_IntDef_Onat(c_0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Onat__zero_0) ).
fof(f6109,plain,
spl0_647,
inference(avatar_split_clause,[],[f1374,f6106]) ).
fof(f6104,plain,
spl0_646,
inference(avatar_split_clause,[],[f1371,f6101]) ).
fof(f1371,axiom,
c_1 = c_IntDef_Oint(c_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oint__1_0) ).
fof(f6099,plain,
spl0_645,
inference(avatar_split_clause,[],[f1229,f6097]) ).
fof(f6097,plain,
( spl0_645
<=> ! [X15] : c_Divides_Oop_Advd(X15,X15,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_645])]) ).
fof(f1229,axiom,
! [X15] : c_Divides_Oop_Advd(X15,X15,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Odvd__refl_0) ).
fof(f6095,plain,
spl0_644,
inference(avatar_split_clause,[],[f1159,f6093]) ).
fof(f6093,plain,
( spl0_644
<=> ! [X39] :
( ~ class_Wellfounded__Recursion_Owellorder(X39)
| class_Orderings_Olinorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_644])]) ).
fof(f1159,axiom,
! [X39] :
( ~ class_Wellfounded__Recursion_Owellorder(X39)
| class_Orderings_Olinorder(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Wellfounded__Recursion_Owellorder_5) ).
fof(f6091,plain,
spl0_643,
inference(avatar_split_clause,[],[f1158,f6089]) ).
fof(f6089,plain,
( spl0_643
<=> ! [X39] :
( ~ class_Wellfounded__Recursion_Owellorder(X39)
| class_LOrder_Olorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_643])]) ).
fof(f1158,axiom,
! [X39] :
( ~ class_Wellfounded__Recursion_Owellorder(X39)
| class_LOrder_Olorder(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Wellfounded__Recursion_Owellorder_4) ).
fof(f6087,plain,
spl0_642,
inference(avatar_split_clause,[],[f1157,f6085]) ).
fof(f6085,plain,
( spl0_642
<=> ! [X39] :
( ~ class_Wellfounded__Recursion_Owellorder(X39)
| class_LOrder_Ojoin__semilorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_642])]) ).
fof(f1157,axiom,
! [X39] :
( ~ class_Wellfounded__Recursion_Owellorder(X39)
| class_LOrder_Ojoin__semilorder(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Wellfounded__Recursion_Owellorder_3) ).
fof(f6083,plain,
spl0_641,
inference(avatar_split_clause,[],[f1156,f6081]) ).
fof(f6081,plain,
( spl0_641
<=> ! [X39] :
( ~ class_Wellfounded__Recursion_Owellorder(X39)
| class_LOrder_Omeet__semilorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_641])]) ).
fof(f1156,axiom,
! [X39] :
( ~ class_Wellfounded__Recursion_Owellorder(X39)
| class_LOrder_Omeet__semilorder(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Wellfounded__Recursion_Owellorder_2) ).
fof(f6079,plain,
spl0_640,
inference(avatar_split_clause,[],[f1155,f6077]) ).
fof(f6077,plain,
( spl0_640
<=> ! [X39] :
( ~ class_Wellfounded__Recursion_Owellorder(X39)
| class_Orderings_Oorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_640])]) ).
fof(f1155,axiom,
! [X39] :
( ~ class_Wellfounded__Recursion_Owellorder(X39)
| class_Orderings_Oorder(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Wellfounded__Recursion_Owellorder_1) ).
fof(f6075,plain,
spl0_639,
inference(avatar_split_clause,[],[f1154,f6073]) ).
fof(f6073,plain,
( spl0_639
<=> ! [X39] :
( ~ class_Wellfounded__Recursion_Owellorder(X39)
| class_Orderings_Oord(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_639])]) ).
fof(f1154,axiom,
! [X39] :
( ~ class_Wellfounded__Recursion_Owellorder(X39)
| class_Orderings_Oord(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Wellfounded__Recursion_Owellorder_0) ).
fof(f6071,plain,
spl0_638,
inference(avatar_split_clause,[],[f1153,f6069]) ).
fof(f6069,plain,
( spl0_638
<=> ! [X39] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X39)
| class_OrderedGroup_Omonoid__mult(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_638])]) ).
fof(f1153,axiom,
! [X39] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X39)
| class_OrderedGroup_Omonoid__mult(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_9) ).
fof(f6067,plain,
spl0_637,
inference(avatar_split_clause,[],[f1148,f6065]) ).
fof(f6065,plain,
( spl0_637
<=> ! [X39] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_637])]) ).
fof(f1148,axiom,
! [X39] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_4) ).
fof(f6063,plain,
spl0_636,
inference(avatar_split_clause,[],[f1147,f6061]) ).
fof(f6061,plain,
( spl0_636
<=> ! [X39] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X39)
| class_Ring__and__Field_Osemiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_636])]) ).
fof(f1147,axiom,
! [X39] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X39)
| class_Ring__and__Field_Osemiring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_3) ).
fof(f6059,plain,
spl0_635,
inference(avatar_split_clause,[],[f1146,f6057]) ).
fof(f6057,plain,
( spl0_635
<=> ! [X39] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X39)
| class_Ring__and__Field_Osemiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_635])]) ).
fof(f1146,axiom,
! [X39] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X39)
| class_Ring__and__Field_Osemiring__0(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_2) ).
fof(f6055,plain,
spl0_634,
inference(avatar_split_clause,[],[f1145,f6053]) ).
fof(f6053,plain,
( spl0_634
<=> ! [X39] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_634])]) ).
fof(f1145,axiom,
! [X39] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_15) ).
fof(f6051,plain,
spl0_633,
inference(avatar_split_clause,[],[f1144,f6049]) ).
fof(f6049,plain,
( spl0_633
<=> ! [X39] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_633])]) ).
fof(f1144,axiom,
! [X39] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_14) ).
fof(f6047,plain,
spl0_632,
inference(avatar_split_clause,[],[f1143,f6045]) ).
fof(f6045,plain,
( spl0_632
<=> ! [X39] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_632])]) ).
fof(f1143,axiom,
! [X39] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_13) ).
fof(f6043,plain,
spl0_631,
inference(avatar_split_clause,[],[f1140,f6041]) ).
fof(f6041,plain,
( spl0_631
<=> ! [X39] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X39)
| class_HOL_Oone(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_631])]) ).
fof(f1140,axiom,
! [X39] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X39)
| class_HOL_Oone(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_10) ).
fof(f6039,plain,
spl0_630,
inference(avatar_split_clause,[],[f1139,f6037]) ).
fof(f6037,plain,
( spl0_630
<=> ! [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_630])]) ).
fof(f1139,axiom,
! [X39] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X39)
| class_Ring__and__Field_Oaxclass__0__neq__1(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_1) ).
fof(f6035,plain,
spl0_629,
inference(avatar_split_clause,[],[f1138,f6033]) ).
fof(f6033,plain,
( spl0_629
<=> ! [X39] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X39)
| class_Ring__and__Field_Osemiring__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_629])]) ).
fof(f1138,axiom,
! [X39] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X39)
| class_Ring__and__Field_Osemiring__1(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_0) ).
fof(f6031,plain,
spl0_628,
inference(avatar_split_clause,[],[f1135,f6029]) ).
fof(f6029,plain,
( spl0_628
<=> ! [X39] :
( ~ class_Ring__and__Field_Osemiring__1(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_628])]) ).
fof(f1135,axiom,
! [X39] :
( ~ class_Ring__and__Field_Osemiring__1(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1_7) ).
fof(f6027,plain,
spl0_627,
inference(avatar_split_clause,[],[f1132,f6025]) ).
fof(f6025,plain,
( spl0_627
<=> ! [X39] :
( ~ class_Ring__and__Field_Osemiring__1(X39)
| class_Ring__and__Field_Osemiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_627])]) ).
fof(f1132,axiom,
! [X39] :
( ~ class_Ring__and__Field_Osemiring__1(X39)
| class_Ring__and__Field_Osemiring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1_4) ).
fof(f6023,plain,
spl0_626,
inference(avatar_split_clause,[],[f1131,f6021]) ).
fof(f6021,plain,
( spl0_626
<=> ! [X39] :
( ~ class_Ring__and__Field_Osemiring__1(X39)
| class_Ring__and__Field_Osemiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_626])]) ).
fof(f1131,axiom,
! [X39] :
( ~ class_Ring__and__Field_Osemiring__1(X39)
| class_Ring__and__Field_Osemiring__0(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1_3) ).
fof(f6019,plain,
spl0_625,
inference(avatar_split_clause,[],[f1130,f6017]) ).
fof(f6017,plain,
( spl0_625
<=> ! [X39] :
( ~ class_Ring__and__Field_Osemiring__1(X39)
| class_HOL_Oone(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_625])]) ).
fof(f1130,axiom,
! [X39] :
( ~ class_Ring__and__Field_Osemiring__1(X39)
| class_HOL_Oone(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1_2) ).
fof(f6015,plain,
spl0_624,
inference(avatar_split_clause,[],[f1129,f6013]) ).
fof(f6013,plain,
( spl0_624
<=> ! [X39] :
( ~ class_Ring__and__Field_Osemiring__1(X39)
| class_OrderedGroup_Omonoid__mult(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_624])]) ).
fof(f1129,axiom,
! [X39] :
( ~ class_Ring__and__Field_Osemiring__1(X39)
| class_OrderedGroup_Omonoid__mult(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1_11) ).
fof(f6011,plain,
spl0_623,
inference(avatar_split_clause,[],[f1126,f6009]) ).
fof(f6009,plain,
( spl0_623
<=> ! [X39] :
( ~ class_Ring__and__Field_Osemiring__1(X39)
| class_Ring__and__Field_Oaxclass__0__neq__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_623])]) ).
fof(f1126,axiom,
! [X39] :
( ~ class_Ring__and__Field_Osemiring__1(X39)
| class_Ring__and__Field_Oaxclass__0__neq__1(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1_0) ).
fof(f6007,plain,
spl0_622,
inference(avatar_split_clause,[],[f1125,f6005]) ).
fof(f6005,plain,
( spl0_622
<=> ! [X39] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_622])]) ).
fof(f1125,axiom,
! [X39] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0__cancel_9) ).
fof(f6003,plain,
spl0_621,
inference(avatar_split_clause,[],[f1120,f6001]) ).
fof(f6001,plain,
( spl0_621
<=> ! [X39] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_621])]) ).
fof(f1120,axiom,
! [X39] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0__cancel_4) ).
fof(f5999,plain,
spl0_620,
inference(avatar_split_clause,[],[f1117,f5997]) ).
fof(f5997,plain,
( spl0_620
<=> ! [X39] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_620])]) ).
fof(f1117,axiom,
! [X39] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0__cancel_10) ).
fof(f5995,plain,
spl0_619,
inference(avatar_split_clause,[],[f1116,f5993]) ).
fof(f5993,plain,
( spl0_619
<=> ! [X39] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X39)
| class_Ring__and__Field_Osemiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_619])]) ).
fof(f1116,axiom,
! [X39] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X39)
| class_Ring__and__Field_Osemiring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0__cancel_1) ).
fof(f5991,plain,
spl0_618,
inference(avatar_split_clause,[],[f1115,f5989]) ).
fof(f5989,plain,
( spl0_618
<=> ! [X39] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X39)
| class_Ring__and__Field_Osemiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_618])]) ).
fof(f1115,axiom,
! [X39] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X39)
| class_Ring__and__Field_Osemiring__0(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0__cancel_0) ).
fof(f5987,plain,
spl0_617,
inference(avatar_split_clause,[],[f1113,f5985]) ).
fof(f5985,plain,
( spl0_617
<=> ! [X39] :
( ~ class_Ring__and__Field_Osemiring__0(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_617])]) ).
fof(f1113,axiom,
! [X39] :
( ~ class_Ring__and__Field_Osemiring__0(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0_6) ).
fof(f5983,plain,
spl0_616,
inference(avatar_split_clause,[],[f1107,f5981]) ).
fof(f5981,plain,
( spl0_616
<=> ! [X39] :
( ~ class_Ring__and__Field_Osemiring__0(X39)
| class_Ring__and__Field_Osemiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_616])]) ).
fof(f1107,axiom,
! [X39] :
( ~ class_Ring__and__Field_Osemiring__0(X39)
| class_Ring__and__Field_Osemiring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0_0) ).
fof(f5979,plain,
spl0_615,
inference(avatar_split_clause,[],[f1099,f5977]) ).
fof(f5977,plain,
( spl0_615
<=> ! [X39] :
( ~ class_Ring__and__Field_Oring__1(X39)
| class_Ring__and__Field_Osemiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_615])]) ).
fof(f1099,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oring__1(X39)
| class_Ring__and__Field_Osemiring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_7) ).
fof(f5975,plain,
spl0_614,
inference(avatar_split_clause,[],[f1098,f5973]) ).
fof(f5973,plain,
( spl0_614
<=> ! [X39] :
( ~ class_Ring__and__Field_Oring__1(X39)
| class_Ring__and__Field_Osemiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_614])]) ).
fof(f1098,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oring__1(X39)
| class_Ring__and__Field_Osemiring__0(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_6) ).
fof(f5971,plain,
spl0_613,
inference(avatar_split_clause,[],[f1097,f5969]) ).
fof(f5969,plain,
( spl0_613
<=> ! [X39] :
( ~ class_Ring__and__Field_Oring__1(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_613])]) ).
fof(f1097,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oring__1(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_5) ).
fof(f5967,plain,
spl0_612,
inference(avatar_split_clause,[],[f1096,f5965]) ).
fof(f5965,plain,
( spl0_612
<=> ! [X39] :
( ~ class_Ring__and__Field_Oring__1(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_612])]) ).
fof(f1096,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oring__1(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_4) ).
fof(f5963,plain,
spl0_611,
inference(avatar_split_clause,[],[f1095,f5961]) ).
fof(f5961,plain,
( spl0_611
<=> ! [X39] :
( ~ class_Ring__and__Field_Oring__1(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_611])]) ).
fof(f1095,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oring__1(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_3) ).
fof(f5959,plain,
spl0_610,
inference(avatar_split_clause,[],[f1093,f5957]) ).
fof(f5957,plain,
( spl0_610
<=> ! [X39] :
( ~ class_Ring__and__Field_Oring__1(X39)
| class_Ring__and__Field_Osemiring__1__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_610])]) ).
fof(f1093,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oring__1(X39)
| class_Ring__and__Field_Osemiring__1__cancel(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_19) ).
fof(f5955,plain,
spl0_609,
inference(avatar_split_clause,[],[f1092,f5953]) ).
fof(f5953,plain,
( spl0_609
<=> ! [X39] :
( ~ class_Ring__and__Field_Oring__1(X39)
| class_HOL_Oone(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_609])]) ).
fof(f1092,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oring__1(X39)
| class_HOL_Oone(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_18) ).
fof(f5951,plain,
spl0_608,
inference(avatar_split_clause,[],[f1091,f5949]) ).
fof(f5949,plain,
( spl0_608
<=> ! [X39] :
( ~ class_Ring__and__Field_Oring__1(X39)
| class_OrderedGroup_Omonoid__mult(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_608])]) ).
fof(f1091,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oring__1(X39)
| class_OrderedGroup_Omonoid__mult(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_17) ).
fof(f5947,plain,
spl0_607,
inference(avatar_split_clause,[],[f1090,f5945]) ).
fof(f5945,plain,
( spl0_607
<=> ! [X39] :
( ~ class_Ring__and__Field_Oring__1(X39)
| class_Ring__and__Field_Oaxclass__0__neq__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_607])]) ).
fof(f1090,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oring__1(X39)
| class_Ring__and__Field_Oaxclass__0__neq__1(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_16) ).
fof(f5943,plain,
spl0_606,
inference(avatar_split_clause,[],[f1089,f5941]) ).
fof(f5941,plain,
( spl0_606
<=> ! [X39] :
( ~ class_Ring__and__Field_Oring__1(X39)
| class_Ring__and__Field_Osemiring__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_606])]) ).
fof(f1089,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oring__1(X39)
| class_Ring__and__Field_Osemiring__1(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_15) ).
fof(f5939,plain,
spl0_605,
inference(avatar_split_clause,[],[f1084,f5937]) ).
fof(f5937,plain,
( spl0_605
<=> ! [X39] :
( ~ class_Ring__and__Field_Oring__1(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_605])]) ).
fof(f1084,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oring__1(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_10) ).
fof(f5935,plain,
spl0_604,
inference(avatar_split_clause,[],[f1083,f5933]) ).
fof(f5933,plain,
( spl0_604
<=> ! [X39] :
( ~ class_Ring__and__Field_Oring__1(X39)
| class_OrderedGroup_Oab__group__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_604])]) ).
fof(f1083,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oring__1(X39)
| class_OrderedGroup_Oab__group__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_1) ).
fof(f5931,plain,
spl0_603,
inference(avatar_split_clause,[],[f1082,f5929]) ).
fof(f5929,plain,
( spl0_603
<=> ! [X39] :
( ~ class_Ring__and__Field_Oring__1(X39)
| class_Ring__and__Field_Oring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_603])]) ).
fof(f1082,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oring__1(X39)
| class_Ring__and__Field_Oring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_0) ).
fof(f5927,plain,
spl0_602,
inference(avatar_split_clause,[],[f1080,f5925]) ).
fof(f5925,plain,
( spl0_602
<=> ! [X39] :
( ~ class_Ring__and__Field_Oring(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_602])]) ).
fof(f1080,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oring(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring_8) ).
fof(f5923,plain,
spl0_601,
inference(avatar_split_clause,[],[f1078,f5921]) ).
fof(f5921,plain,
( spl0_601
<=> ! [X39] :
( ~ class_Ring__and__Field_Oring(X39)
| class_OrderedGroup_Oab__group__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_601])]) ).
fof(f1078,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oring(X39)
| class_OrderedGroup_Oab__group__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring_6) ).
fof(f5919,plain,
spl0_600,
inference(avatar_split_clause,[],[f1073,f5917]) ).
fof(f5917,plain,
( spl0_600
<=> ! [X39] :
( ~ class_Ring__and__Field_Oring(X39)
| class_Ring__and__Field_Osemiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_600])]) ).
fof(f1073,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oring(X39)
| class_Ring__and__Field_Osemiring__0(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring_13) ).
fof(f5915,plain,
spl0_599,
inference(avatar_split_clause,[],[f1072,f5913]) ).
fof(f5913,plain,
( spl0_599
<=> ! [X39] :
( ~ class_Ring__and__Field_Oring(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_599])]) ).
fof(f1072,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oring(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring_12) ).
fof(f5911,plain,
spl0_598,
inference(avatar_split_clause,[],[f1071,f5909]) ).
fof(f5909,plain,
( spl0_598
<=> ! [X39] :
( ~ class_Ring__and__Field_Oring(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_598])]) ).
fof(f1071,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oring(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring_11) ).
fof(f5907,plain,
spl0_597,
inference(avatar_split_clause,[],[f1070,f5905]) ).
fof(f5905,plain,
( spl0_597
<=> ! [X39] :
( ~ class_Ring__and__Field_Oring(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_597])]) ).
fof(f1070,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oring(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring_10) ).
fof(f5903,plain,
spl0_596,
inference(avatar_split_clause,[],[f1068,f5901]) ).
fof(f5901,plain,
( spl0_596
<=> ! [X39] :
( ~ class_Ring__and__Field_Oring(X39)
| class_Ring__and__Field_Osemiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_596])]) ).
fof(f1068,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oring(X39)
| class_Ring__and__Field_Osemiring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring_0) ).
fof(f5899,plain,
spl0_595,
inference(avatar_split_clause,[],[f1067,f5897]) ).
fof(f5897,plain,
( spl0_595
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__semiring(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_595])]) ).
fof(f1067,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__semiring(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__semiring_9) ).
fof(f5895,plain,
spl0_594,
inference(avatar_split_clause,[],[f1062,f5893]) ).
fof(f5893,plain,
( spl0_594
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__semiring(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_594])]) ).
fof(f1062,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__semiring(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__semiring_4) ).
fof(f5891,plain,
spl0_593,
inference(avatar_split_clause,[],[f1059,f5889]) ).
fof(f5889,plain,
( spl0_593
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__semiring(X39)
| class_Orderings_Oord(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_593])]) ).
fof(f1059,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__semiring(X39)
| class_Orderings_Oord(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__semiring_11) ).
fof(f5887,plain,
spl0_592,
inference(avatar_split_clause,[],[f1058,f5885]) ).
fof(f5885,plain,
( spl0_592
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__semiring(X39)
| class_Orderings_Oorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_592])]) ).
fof(f1058,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__semiring(X39)
| class_Orderings_Oorder(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__semiring_10) ).
fof(f5883,plain,
spl0_591,
inference(avatar_split_clause,[],[f1057,f5881]) ).
fof(f5881,plain,
( spl0_591
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__semiring(X39)
| class_Ring__and__Field_Osemiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_591])]) ).
fof(f1057,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__semiring(X39)
| class_Ring__and__Field_Osemiring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__semiring_1) ).
fof(f5879,plain,
spl0_590,
inference(avatar_split_clause,[],[f1056,f5877]) ).
fof(f5877,plain,
( spl0_590
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__semiring(X39)
| class_Ring__and__Field_Osemiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_590])]) ).
fof(f1056,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__semiring(X39)
| class_Ring__and__Field_Osemiring__0(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__semiring_0) ).
fof(f5875,plain,
spl0_589,
inference(avatar_split_clause,[],[f1053,f5873]) ).
fof(f5873,plain,
( spl0_589
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__ring(X39)
| class_Ring__and__Field_Osemiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_589])]) ).
fof(f1053,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__ring(X39)
| class_Ring__and__Field_Osemiring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_7) ).
fof(f5871,plain,
spl0_588,
inference(avatar_split_clause,[],[f1052,f5869]) ).
fof(f5869,plain,
( spl0_588
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__ring(X39)
| class_Ring__and__Field_Osemiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_588])]) ).
fof(f1052,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__ring(X39)
| class_Ring__and__Field_Osemiring__0(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_6) ).
fof(f5867,plain,
spl0_587,
inference(avatar_split_clause,[],[f1051,f5865]) ).
fof(f5865,plain,
( spl0_587
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__ring(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_587])]) ).
fof(f1051,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__ring(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_5) ).
fof(f5863,plain,
spl0_586,
inference(avatar_split_clause,[],[f1050,f5861]) ).
fof(f5861,plain,
( spl0_586
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__ring(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_586])]) ).
fof(f1050,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__ring(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_4) ).
fof(f5859,plain,
spl0_585,
inference(avatar_split_clause,[],[f1049,f5857]) ).
fof(f5857,plain,
( spl0_585
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__ring(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_585])]) ).
fof(f1049,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__ring(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_3) ).
fof(f5855,plain,
spl0_584,
inference(avatar_split_clause,[],[f1048,f5853]) ).
fof(f5853,plain,
( spl0_584
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__ring(X39)
| class_Ring__and__Field_Opordered__cancel__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_584])]) ).
fof(f1048,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__ring(X39)
| class_Ring__and__Field_Opordered__cancel__semiring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_22) ).
fof(f5851,plain,
spl0_583,
inference(avatar_split_clause,[],[f1047,f5849]) ).
fof(f5849,plain,
( spl0_583
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__ring(X39)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_583])]) ).
fof(f1047,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__ring(X39)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_21) ).
fof(f5847,plain,
spl0_582,
inference(avatar_split_clause,[],[f1046,f5845]) ).
fof(f5845,plain,
( spl0_582
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__ring(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_582])]) ).
fof(f1046,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__ring(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_20) ).
fof(f5843,plain,
spl0_581,
inference(avatar_split_clause,[],[f1044,f5841]) ).
fof(f5841,plain,
( spl0_581
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__ring(X39)
| class_OrderedGroup_Opordered__ab__group__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_581])]) ).
fof(f1044,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__ring(X39)
| class_OrderedGroup_Opordered__ab__group__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_19) ).
fof(f5839,plain,
spl0_580,
inference(avatar_split_clause,[],[f1043,f5837]) ).
fof(f5837,plain,
( spl0_580
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__ring(X39)
| class_Orderings_Oord(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_580])]) ).
fof(f1043,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__ring(X39)
| class_Orderings_Oord(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_18) ).
fof(f5835,plain,
spl0_579,
inference(avatar_split_clause,[],[f1042,f5833]) ).
fof(f5833,plain,
( spl0_579
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__ring(X39)
| class_Orderings_Oorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_579])]) ).
fof(f1042,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__ring(X39)
| class_Orderings_Oorder(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_17) ).
fof(f5831,plain,
spl0_578,
inference(avatar_split_clause,[],[f1041,f5829]) ).
fof(f5829,plain,
( spl0_578
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__ring(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_578])]) ).
fof(f1041,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__ring(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_16) ).
fof(f5827,plain,
spl0_577,
inference(avatar_split_clause,[],[f1040,f5825]) ).
fof(f5825,plain,
( spl0_577
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__ring(X39)
| class_Ring__and__Field_Opordered__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_577])]) ).
fof(f1040,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__ring(X39)
| class_Ring__and__Field_Opordered__semiring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_15) ).
fof(f5823,plain,
spl0_576,
inference(avatar_split_clause,[],[f1035,f5821]) ).
fof(f5821,plain,
( spl0_576
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__ring(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_576])]) ).
fof(f1035,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__ring(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_10) ).
fof(f5819,plain,
spl0_575,
inference(avatar_split_clause,[],[f1034,f5817]) ).
fof(f5817,plain,
( spl0_575
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__ring(X39)
| class_OrderedGroup_Oab__group__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_575])]) ).
fof(f1034,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__ring(X39)
| class_OrderedGroup_Oab__group__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_1) ).
fof(f5815,plain,
spl0_574,
inference(avatar_split_clause,[],[f1033,f5813]) ).
fof(f5813,plain,
( spl0_574
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__ring(X39)
| class_Ring__and__Field_Oring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_574])]) ).
fof(f1033,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__ring(X39)
| class_Ring__and__Field_Oring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_0) ).
fof(f5811,plain,
spl0_573,
inference(avatar_split_clause,[],[f1030,f5809]) ).
fof(f5809,plain,
( spl0_573
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_573])]) ).
fof(f1030,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_7) ).
fof(f5807,plain,
spl0_572,
inference(avatar_split_clause,[],[f1027,f5805]) ).
fof(f5805,plain,
( spl0_572
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X39)
| class_Ring__and__Field_Osemiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_572])]) ).
fof(f1027,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X39)
| class_Ring__and__Field_Osemiring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_4) ).
fof(f5803,plain,
spl0_571,
inference(avatar_split_clause,[],[f1026,f5801]) ).
fof(f5801,plain,
( spl0_571
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X39)
| class_Ring__and__Field_Osemiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_571])]) ).
fof(f1026,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X39)
| class_Ring__and__Field_Osemiring__0(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_3) ).
fof(f5799,plain,
spl0_570,
inference(avatar_split_clause,[],[f1024,f5797]) ).
fof(f5797,plain,
( spl0_570
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X39)
| class_Ring__and__Field_Opordered__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_570])]) ).
fof(f1024,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X39)
| class_Ring__and__Field_Opordered__semiring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_15) ).
fof(f5795,plain,
spl0_569,
inference(avatar_split_clause,[],[f1023,f5793]) ).
fof(f5793,plain,
( spl0_569
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X39)
| class_Orderings_Oord(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_569])]) ).
fof(f1023,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X39)
| class_Orderings_Oord(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_14) ).
fof(f5791,plain,
spl0_568,
inference(avatar_split_clause,[],[f1022,f5789]) ).
fof(f5789,plain,
( spl0_568
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X39)
| class_Orderings_Oorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_568])]) ).
fof(f1022,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X39)
| class_Orderings_Oorder(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_13) ).
fof(f5787,plain,
spl0_567,
inference(avatar_split_clause,[],[f1021,f5785]) ).
fof(f5785,plain,
( spl0_567
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_567])]) ).
fof(f1021,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_12) ).
fof(f5783,plain,
spl0_566,
inference(avatar_split_clause,[],[f1018,f5781]) ).
fof(f5781,plain,
( spl0_566
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X39)
| class_Ring__and__Field_Ocomm__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_566])]) ).
fof(f1018,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X39)
| class_Ring__and__Field_Ocomm__semiring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_1) ).
fof(f5779,plain,
spl0_565,
inference(avatar_split_clause,[],[f1017,f5777]) ).
fof(f5777,plain,
( spl0_565
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X39)
| class_Ring__and__Field_Ocomm__semiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_565])]) ).
fof(f1017,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X39)
| class_Ring__and__Field_Ocomm__semiring__0(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_0) ).
fof(f5775,plain,
spl0_564,
inference(avatar_split_clause,[],[f989,f5773]) ).
fof(f5773,plain,
( spl0_564
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_564])]) ).
fof(f989,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_7) ).
fof(f5771,plain,
spl0_563,
inference(avatar_split_clause,[],[f987,f5769]) ).
fof(f5769,plain,
( spl0_563
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_563])]) ).
fof(f987,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_5) ).
fof(f5767,plain,
spl0_562,
inference(avatar_split_clause,[],[f984,f5765]) ).
fof(f5765,plain,
( spl0_562
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X39)
| class_Ring__and__Field_Osemiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_562])]) ).
fof(f984,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X39)
| class_Ring__and__Field_Osemiring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_2) ).
fof(f5763,plain,
spl0_561,
inference(avatar_split_clause,[],[f983,f5761]) ).
fof(f5761,plain,
( spl0_561
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_561])]) ).
fof(f983,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_15) ).
fof(f5759,plain,
spl0_560,
inference(avatar_split_clause,[],[f982,f5757]) ).
fof(f5757,plain,
( spl0_560
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_560])]) ).
fof(f982,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_14) ).
fof(f5755,plain,
spl0_559,
inference(avatar_split_clause,[],[f981,f5753]) ).
fof(f5753,plain,
( spl0_559
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_559])]) ).
fof(f981,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_13) ).
fof(f5751,plain,
spl0_558,
inference(avatar_split_clause,[],[f980,f5749]) ).
fof(f5749,plain,
( spl0_558
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X39)
| class_Orderings_Oord(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_558])]) ).
fof(f980,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X39)
| class_Orderings_Oord(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_12) ).
fof(f5747,plain,
spl0_557,
inference(avatar_split_clause,[],[f979,f5745]) ).
fof(f5745,plain,
( spl0_557
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X39)
| class_Orderings_Oorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_557])]) ).
fof(f979,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X39)
| class_Orderings_Oorder(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_11) ).
fof(f5743,plain,
spl0_556,
inference(avatar_split_clause,[],[f977,f5741]) ).
fof(f5741,plain,
( spl0_556
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X39)
| class_Ring__and__Field_Osemiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_556])]) ).
fof(f977,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X39)
| class_Ring__and__Field_Osemiring__0(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_1) ).
fof(f5739,plain,
spl0_555,
inference(avatar_split_clause,[],[f976,f5737]) ).
fof(f5737,plain,
( spl0_555
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X39)
| class_Ring__and__Field_Opordered__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_555])]) ).
fof(f976,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X39)
| class_Ring__and__Field_Opordered__semiring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_0) ).
fof(f5735,plain,
spl0_554,
inference(avatar_split_clause,[],[f974,f5733]) ).
fof(f5733,plain,
( spl0_554
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_554])]) ).
fof(f974,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_8) ).
fof(f5731,plain,
spl0_553,
inference(avatar_split_clause,[],[f971,f5729]) ).
fof(f5729,plain,
( spl0_553
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X39)
| class_Ring__and__Field_Osemiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_553])]) ).
fof(f971,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X39)
| class_Ring__and__Field_Osemiring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_5) ).
fof(f5727,plain,
spl0_552,
inference(avatar_split_clause,[],[f970,f5725]) ).
fof(f5725,plain,
( spl0_552
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X39)
| class_Ring__and__Field_Osemiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_552])]) ).
fof(f970,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X39)
| class_Ring__and__Field_Osemiring__0(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_4) ).
fof(f5723,plain,
spl0_551,
inference(avatar_split_clause,[],[f968,f5721]) ).
fof(f5721,plain,
( spl0_551
<=> ! [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_551])]) ).
fof(f968,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_20) ).
fof(f5719,plain,
spl0_550,
inference(avatar_split_clause,[],[f967,f5717]) ).
fof(f5717,plain,
( spl0_550
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X39)
| class_Ring__and__Field_Ocomm__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_550])]) ).
fof(f967,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X39)
| class_Ring__and__Field_Ocomm__semiring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_2) ).
fof(f5715,plain,
spl0_549,
inference(avatar_split_clause,[],[f966,f5713]) ).
fof(f5713,plain,
( spl0_549
<=> ! [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_549])]) ).
fof(f966,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X39)
| class_Ring__and__Field_Opordered__cancel__semiring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_19) ).
fof(f5711,plain,
spl0_548,
inference(avatar_split_clause,[],[f965,f5709]) ).
fof(f5709,plain,
( spl0_548
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X39)
| class_Ring__and__Field_Opordered__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_548])]) ).
fof(f965,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X39)
| class_Ring__and__Field_Opordered__semiring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_18) ).
fof(f5707,plain,
spl0_547,
inference(avatar_split_clause,[],[f964,f5705]) ).
fof(f5705,plain,
( spl0_547
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_547])]) ).
fof(f964,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_17) ).
fof(f5703,plain,
spl0_546,
inference(avatar_split_clause,[],[f963,f5701]) ).
fof(f5701,plain,
( spl0_546
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_546])]) ).
fof(f963,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_16) ).
fof(f5699,plain,
spl0_545,
inference(avatar_split_clause,[],[f962,f5697]) ).
fof(f5697,plain,
( spl0_545
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X39)
| class_Orderings_Oord(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_545])]) ).
fof(f962,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X39)
| class_Orderings_Oord(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_15) ).
fof(f5695,plain,
spl0_544,
inference(avatar_split_clause,[],[f961,f5693]) ).
fof(f5693,plain,
( spl0_544
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X39)
| class_Orderings_Oorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_544])]) ).
fof(f961,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X39)
| class_Orderings_Oorder(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_14) ).
fof(f5691,plain,
spl0_543,
inference(avatar_split_clause,[],[f957,f5689]) ).
fof(f5689,plain,
( spl0_543
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_543])]) ).
fof(f957,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_10) ).
fof(f5687,plain,
spl0_542,
inference(avatar_split_clause,[],[f956,f5685]) ).
fof(f5685,plain,
( spl0_542
<=> ! [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_542])]) ).
fof(f956,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X39)
| class_Ring__and__Field_Ocomm__semiring__0(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_1) ).
fof(f5683,plain,
spl0_541,
inference(avatar_split_clause,[],[f955,f5681]) ).
fof(f5681,plain,
( spl0_541
<=> ! [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_541])]) ).
fof(f955,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X39)
| class_Ring__and__Field_Opordered__comm__semiring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_0) ).
fof(f5679,plain,
spl0_540,
inference(avatar_split_clause,[],[f954,f5677]) ).
fof(f5677,plain,
( spl0_540
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_540])]) ).
fof(f954,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_9) ).
fof(f5675,plain,
spl0_539,
inference(avatar_split_clause,[],[f949,f5673]) ).
fof(f5673,plain,
( spl0_539
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_539])]) ).
fof(f949,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_4) ).
fof(f5671,plain,
spl0_538,
inference(avatar_split_clause,[],[f947,f5669]) ).
fof(f5669,plain,
( spl0_538
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_Ring__and__Field_Opordered__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_538])]) ).
fof(f947,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_Ring__and__Field_Opordered__semiring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_23) ).
fof(f5667,plain,
spl0_537,
inference(avatar_split_clause,[],[f946,f5665]) ).
fof(f5665,plain,
( spl0_537
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_Ring__and__Field_Opordered__cancel__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_537])]) ).
fof(f946,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_Ring__and__Field_Opordered__cancel__semiring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_22) ).
fof(f5663,plain,
spl0_536,
inference(avatar_split_clause,[],[f945,f5661]) ).
fof(f5661,plain,
( spl0_536
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_536])]) ).
fof(f945,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_21) ).
fof(f5659,plain,
spl0_535,
inference(avatar_split_clause,[],[f944,f5657]) ).
fof(f5657,plain,
( spl0_535
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_535])]) ).
fof(f944,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_20) ).
fof(f5655,plain,
spl0_534,
inference(avatar_split_clause,[],[f942,f5653]) ).
fof(f5653,plain,
( spl0_534
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_534])]) ).
fof(f942,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_19) ).
fof(f5651,plain,
spl0_533,
inference(avatar_split_clause,[],[f941,f5649]) ).
fof(f5649,plain,
( spl0_533
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_Orderings_Oord(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_533])]) ).
fof(f941,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_Orderings_Oord(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_18) ).
fof(f5647,plain,
spl0_532,
inference(avatar_split_clause,[],[f940,f5645]) ).
fof(f5645,plain,
( spl0_532
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_Orderings_Oorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_532])]) ).
fof(f940,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_Orderings_Oorder(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_17) ).
fof(f5643,plain,
spl0_531,
inference(avatar_split_clause,[],[f939,f5641]) ).
fof(f5641,plain,
( spl0_531
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_531])]) ).
fof(f939,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_16) ).
fof(f5639,plain,
spl0_530,
inference(avatar_split_clause,[],[f938,f5637]) ).
fof(f5637,plain,
( spl0_530
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_530])]) ).
fof(f938,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_15) ).
fof(f5635,plain,
spl0_529,
inference(avatar_split_clause,[],[f937,f5633]) ).
fof(f5633,plain,
( spl0_529
<=> ! [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_529])]) ).
fof(f937,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_14) ).
fof(f5631,plain,
spl0_528,
inference(avatar_split_clause,[],[f936,f5629]) ).
fof(f5629,plain,
( spl0_528
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_LOrder_Omeet__semilorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_528])]) ).
fof(f936,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_LOrder_Omeet__semilorder(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_13) ).
fof(f5627,plain,
spl0_527,
inference(avatar_split_clause,[],[f935,f5625]) ).
fof(f5625,plain,
( spl0_527
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_LOrder_Ojoin__semilorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_527])]) ).
fof(f935,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_LOrder_Ojoin__semilorder(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_12) ).
fof(f5623,plain,
spl0_526,
inference(avatar_split_clause,[],[f934,f5621]) ).
fof(f5621,plain,
( spl0_526
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_LOrder_Olorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_526])]) ).
fof(f934,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_LOrder_Olorder(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_11) ).
fof(f5619,plain,
spl0_525,
inference(avatar_split_clause,[],[f933,f5617]) ).
fof(f5617,plain,
( spl0_525
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_Orderings_Olinorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_525])]) ).
fof(f933,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_Orderings_Olinorder(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_10) ).
fof(f5615,plain,
spl0_524,
inference(avatar_split_clause,[],[f932,f5613]) ).
fof(f5613,plain,
( spl0_524
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_Ring__and__Field_Osemiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_524])]) ).
fof(f932,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_Ring__and__Field_Osemiring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_1) ).
fof(f5611,plain,
spl0_523,
inference(avatar_split_clause,[],[f931,f5609]) ).
fof(f5609,plain,
( spl0_523
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_Ring__and__Field_Osemiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_523])]) ).
fof(f931,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_Ring__and__Field_Osemiring__0(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_0) ).
fof(f5607,plain,
spl0_522,
inference(avatar_split_clause,[],[f930,f5605]) ).
fof(f5605,plain,
( spl0_522
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Ring__and__Field_Ocomm__semiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_522])]) ).
fof(f930,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Ring__and__Field_Ocomm__semiring__0(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_9) ).
fof(f5603,plain,
spl0_521,
inference(avatar_split_clause,[],[f929,f5601]) ).
fof(f5601,plain,
( spl0_521
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_521])]) ).
fof(f929,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_8) ).
fof(f5599,plain,
spl0_520,
inference(avatar_split_clause,[],[f928,f5597]) ).
fof(f5597,plain,
( spl0_520
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_HOL_Oone(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_520])]) ).
fof(f928,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_HOL_Oone(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_7) ).
fof(f5595,plain,
spl0_519,
inference(avatar_split_clause,[],[f927,f5593]) ).
fof(f5593,plain,
( spl0_519
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_OrderedGroup_Omonoid__mult(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_519])]) ).
fof(f927,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_OrderedGroup_Omonoid__mult(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_6) ).
fof(f5591,plain,
spl0_518,
inference(avatar_split_clause,[],[f926,f5589]) ).
fof(f5589,plain,
( spl0_518
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Ring__and__Field_Oaxclass__0__neq__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_518])]) ).
fof(f926,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Ring__and__Field_Oaxclass__0__neq__1(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_5) ).
fof(f5587,plain,
spl0_517,
inference(avatar_split_clause,[],[f925,f5585]) ).
fof(f5585,plain,
( spl0_517
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Ring__and__Field_Osemiring__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_517])]) ).
fof(f925,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Ring__and__Field_Osemiring__1(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_4) ).
fof(f5583,plain,
spl0_516,
inference(avatar_split_clause,[],[f924,f5581]) ).
fof(f5581,plain,
( spl0_516
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Orderings_Oord(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_516])]) ).
fof(f924,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Orderings_Oord(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_39) ).
fof(f5579,plain,
spl0_515,
inference(avatar_split_clause,[],[f923,f5577]) ).
fof(f5577,plain,
( spl0_515
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Orderings_Oorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_515])]) ).
fof(f923,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Orderings_Oorder(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_38) ).
fof(f5575,plain,
spl0_514,
inference(avatar_split_clause,[],[f922,f5573]) ).
fof(f5573,plain,
( spl0_514
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_514])]) ).
fof(f922,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_37) ).
fof(f5571,plain,
spl0_513,
inference(avatar_split_clause,[],[f921,f5569]) ).
fof(f5569,plain,
( spl0_513
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Ring__and__Field_Opordered__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_513])]) ).
fof(f921,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Ring__and__Field_Opordered__semiring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_36) ).
fof(f5567,plain,
spl0_512,
inference(avatar_split_clause,[],[f920,f5565]) ).
fof(f5565,plain,
( spl0_512
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Ring__and__Field_Opordered__comm__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_512])]) ).
fof(f920,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Ring__and__Field_Opordered__comm__semiring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_35) ).
fof(f5563,plain,
spl0_511,
inference(avatar_split_clause,[],[f919,f5561]) ).
fof(f5561,plain,
( spl0_511
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Ring__and__Field_Opordered__cancel__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_511])]) ).
fof(f919,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Ring__and__Field_Opordered__cancel__semiring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_34) ).
fof(f5559,plain,
spl0_510,
inference(avatar_split_clause,[],[f918,f5557]) ).
fof(f5557,plain,
( spl0_510
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Ring__and__Field_Opordered__cancel__comm__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_510])]) ).
fof(f918,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Ring__and__Field_Opordered__cancel__comm__semiring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_33) ).
fof(f5555,plain,
spl0_509,
inference(avatar_split_clause,[],[f917,f5553]) ).
fof(f5553,plain,
( spl0_509
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_509])]) ).
fof(f917,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_32) ).
fof(f5551,plain,
spl0_508,
inference(avatar_split_clause,[],[f916,f5549]) ).
fof(f5549,plain,
( spl0_508
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_508])]) ).
fof(f916,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_31) ).
fof(f5547,plain,
spl0_507,
inference(avatar_split_clause,[],[f915,f5545]) ).
fof(f5545,plain,
( spl0_507
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_LOrder_Omeet__semilorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_507])]) ).
fof(f915,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_LOrder_Omeet__semilorder(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_30) ).
fof(f5543,plain,
spl0_506,
inference(avatar_split_clause,[],[f914,f5541]) ).
fof(f5541,plain,
( spl0_506
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Ring__and__Field_Osemiring__1__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_506])]) ).
fof(f914,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Ring__and__Field_Osemiring__1__cancel(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_3) ).
fof(f5539,plain,
spl0_505,
inference(avatar_split_clause,[],[f913,f5537]) ).
fof(f5537,plain,
( spl0_505
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_LOrder_Ojoin__semilorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_505])]) ).
fof(f913,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_LOrder_Ojoin__semilorder(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_29) ).
fof(f5535,plain,
spl0_504,
inference(avatar_split_clause,[],[f912,f5533]) ).
fof(f5533,plain,
( spl0_504
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_LOrder_Olorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_504])]) ).
fof(f912,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_LOrder_Olorder(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_28) ).
fof(f5531,plain,
spl0_503,
inference(avatar_split_clause,[],[f911,f5529]) ).
fof(f5529,plain,
( spl0_503
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Orderings_Olinorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_503])]) ).
fof(f911,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Orderings_Olinorder(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_27) ).
fof(f5527,plain,
spl0_502,
inference(avatar_split_clause,[],[f910,f5525]) ).
fof(f5525,plain,
( spl0_502
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_502])]) ).
fof(f910,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_26) ).
fof(f5523,plain,
spl0_501,
inference(avatar_split_clause,[],[f909,f5521]) ).
fof(f5521,plain,
( spl0_501
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Ring__and__Field_Oordered__semiring__strict(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_501])]) ).
fof(f909,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Ring__and__Field_Oordered__semiring__strict(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_25) ).
fof(f5519,plain,
spl0_500,
inference(avatar_split_clause,[],[f908,f5517]) ).
fof(f5517,plain,
( spl0_500
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Ring__and__Field_Oordered__comm__semiring__strict(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_500])]) ).
fof(f908,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Ring__and__Field_Oordered__comm__semiring__strict(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_24) ).
fof(f5515,plain,
spl0_499,
inference(avatar_split_clause,[],[f905,f5513]) ).
fof(f5513,plain,
( spl0_499
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_499])]) ).
fof(f905,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_21) ).
fof(f5511,plain,
spl0_498,
inference(avatar_split_clause,[],[f903,f5509]) ).
fof(f5509,plain,
( spl0_498
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_OrderedGroup_Ocomm__monoid__mult(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_498])]) ).
fof(f903,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_OrderedGroup_Ocomm__monoid__mult(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_2) ).
fof(f5507,plain,
spl0_497,
inference(avatar_split_clause,[],[f902,f5505]) ).
fof(f5505,plain,
( spl0_497
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_497])]) ).
fof(f902,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_19) ).
fof(f5503,plain,
spl0_496,
inference(avatar_split_clause,[],[f900,f5501]) ).
fof(f5501,plain,
( spl0_496
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_496])]) ).
fof(f900,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_17) ).
fof(f5499,plain,
spl0_495,
inference(avatar_split_clause,[],[f897,f5497]) ).
fof(f5497,plain,
( spl0_495
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Ring__and__Field_Osemiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_495])]) ).
fof(f897,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Ring__and__Field_Osemiring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_14) ).
fof(f5495,plain,
spl0_494,
inference(avatar_split_clause,[],[f896,f5493]) ).
fof(f5493,plain,
( spl0_494
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Ring__and__Field_Osemiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_494])]) ).
fof(f896,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Ring__and__Field_Osemiring__0(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_13) ).
fof(f5491,plain,
spl0_493,
inference(avatar_split_clause,[],[f895,f5489]) ).
fof(f5489,plain,
( spl0_493
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_493])]) ).
fof(f895,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_12) ).
fof(f5487,plain,
spl0_492,
inference(avatar_split_clause,[],[f893,f5485]) ).
fof(f5485,plain,
( spl0_492
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Ring__and__Field_Ocomm__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_492])]) ).
fof(f893,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Ring__and__Field_Ocomm__semiring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_10) ).
fof(f5483,plain,
spl0_491,
inference(avatar_split_clause,[],[f892,f5481]) ).
fof(f5481,plain,
( spl0_491
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Ring__and__Field_Ocomm__semiring__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_491])]) ).
fof(f892,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Ring__and__Field_Ocomm__semiring__1(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_1) ).
fof(f5479,plain,
spl0_490,
inference(avatar_split_clause,[],[f891,f5477]) ).
fof(f5477,plain,
( spl0_490
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Ring__and__Field_Ocomm__semiring__1__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_490])]) ).
fof(f891,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Ring__and__Field_Ocomm__semiring__1__cancel(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_0) ).
fof(f5475,plain,
spl0_489,
inference(avatar_split_clause,[],[f888,f5473]) ).
fof(f5473,plain,
( spl0_489
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_Ring__and__Field_Osemiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_489])]) ).
fof(f888,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_Ring__and__Field_Osemiring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_7) ).
fof(f5471,plain,
spl0_488,
inference(avatar_split_clause,[],[f887,f5469]) ).
fof(f5469,plain,
( spl0_488
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_Ring__and__Field_Osemiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_488])]) ).
fof(f887,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_Ring__and__Field_Osemiring__0(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_6) ).
fof(f5467,plain,
spl0_487,
inference(avatar_split_clause,[],[f886,f5465]) ).
fof(f5465,plain,
( spl0_487
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_487])]) ).
fof(f886,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_5) ).
fof(f5463,plain,
spl0_486,
inference(avatar_split_clause,[],[f885,f5461]) ).
fof(f5461,plain,
( spl0_486
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_486])]) ).
fof(f885,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_4) ).
fof(f5459,plain,
spl0_485,
inference(avatar_split_clause,[],[f883,f5457]) ).
fof(f5457,plain,
( spl0_485
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_OrderedGroup_Olordered__ab__group__join(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_485])]) ).
fof(f883,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_OrderedGroup_Olordered__ab__group__join(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_35) ).
fof(f5455,plain,
spl0_484,
inference(avatar_split_clause,[],[f882,f5453]) ).
fof(f5453,plain,
( spl0_484
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_OrderedGroup_Olordered__ab__group__meet(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_484])]) ).
fof(f882,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_OrderedGroup_Olordered__ab__group__meet(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_34) ).
fof(f5451,plain,
spl0_483,
inference(avatar_split_clause,[],[f881,f5449]) ).
fof(f5449,plain,
( spl0_483
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_OrderedGroup_Olordered__ab__group__abs(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_483])]) ).
fof(f881,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_OrderedGroup_Olordered__ab__group__abs(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_33) ).
fof(f5447,plain,
spl0_482,
inference(avatar_split_clause,[],[f880,f5445]) ).
fof(f5445,plain,
( spl0_482
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_Ring__and__Field_Opordered__ring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_482])]) ).
fof(f880,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_Ring__and__Field_Opordered__ring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_32) ).
fof(f5443,plain,
spl0_481,
inference(avatar_split_clause,[],[f879,f5441]) ).
fof(f5441,plain,
( spl0_481
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_Ring__and__Field_Olordered__ring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_481])]) ).
fof(f879,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_Ring__and__Field_Olordered__ring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_31) ).
fof(f5439,plain,
spl0_480,
inference(avatar_split_clause,[],[f878,f5437]) ).
fof(f5437,plain,
( spl0_480
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_OrderedGroup_Opordered__ab__group__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_480])]) ).
fof(f878,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_OrderedGroup_Opordered__ab__group__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_30) ).
fof(f5435,plain,
spl0_479,
inference(avatar_split_clause,[],[f877,f5433]) ).
fof(f5433,plain,
( spl0_479
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_479])]) ).
fof(f877,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_3) ).
fof(f5431,plain,
spl0_478,
inference(avatar_split_clause,[],[f876,f5429]) ).
fof(f5429,plain,
( spl0_478
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_OrderedGroup_Olordered__ab__group(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_478])]) ).
fof(f876,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_OrderedGroup_Olordered__ab__group(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_29) ).
fof(f5427,plain,
spl0_477,
inference(avatar_split_clause,[],[f875,f5425]) ).
fof(f5425,plain,
( spl0_477
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_Ring__and__Field_Oaxclass__abs__if(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_477])]) ).
fof(f875,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_Ring__and__Field_Oaxclass__abs__if(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_28) ).
fof(f5423,plain,
spl0_476,
inference(avatar_split_clause,[],[f874,f5421]) ).
fof(f5421,plain,
( spl0_476
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_Orderings_Oord(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_476])]) ).
fof(f874,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_Orderings_Oord(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_27) ).
fof(f5419,plain,
spl0_475,
inference(avatar_split_clause,[],[f873,f5417]) ).
fof(f5417,plain,
( spl0_475
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_Orderings_Oorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_475])]) ).
fof(f873,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_Orderings_Oorder(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_26) ).
fof(f5415,plain,
spl0_474,
inference(avatar_split_clause,[],[f872,f5413]) ).
fof(f5413,plain,
( spl0_474
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_474])]) ).
fof(f872,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_25) ).
fof(f5411,plain,
spl0_473,
inference(avatar_split_clause,[],[f871,f5409]) ).
fof(f5409,plain,
( spl0_473
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_Ring__and__Field_Opordered__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_473])]) ).
fof(f871,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_Ring__and__Field_Opordered__semiring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_24) ).
fof(f5407,plain,
spl0_472,
inference(avatar_split_clause,[],[f870,f5405]) ).
fof(f5405,plain,
( spl0_472
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_Ring__and__Field_Opordered__cancel__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_472])]) ).
fof(f870,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_Ring__and__Field_Opordered__cancel__semiring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_23) ).
fof(f5403,plain,
spl0_471,
inference(avatar_split_clause,[],[f869,f5401]) ).
fof(f5401,plain,
( spl0_471
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_471])]) ).
fof(f869,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_22) ).
fof(f5399,plain,
spl0_470,
inference(avatar_split_clause,[],[f868,f5397]) ).
fof(f5397,plain,
( spl0_470
<=> ! [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_470])]) ).
fof(f868,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_21) ).
fof(f5395,plain,
spl0_469,
inference(avatar_split_clause,[],[f867,f5393]) ).
fof(f5393,plain,
( spl0_469
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_LOrder_Omeet__semilorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_469])]) ).
fof(f867,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_LOrder_Omeet__semilorder(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_20) ).
fof(f5391,plain,
spl0_468,
inference(avatar_split_clause,[],[f865,f5389]) ).
fof(f5389,plain,
( spl0_468
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_LOrder_Ojoin__semilorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_468])]) ).
fof(f865,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_LOrder_Ojoin__semilorder(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_19) ).
fof(f5387,plain,
spl0_467,
inference(avatar_split_clause,[],[f864,f5385]) ).
fof(f5385,plain,
( spl0_467
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_LOrder_Olorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_467])]) ).
fof(f864,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_LOrder_Olorder(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_18) ).
fof(f5383,plain,
spl0_466,
inference(avatar_split_clause,[],[f863,f5381]) ).
fof(f5381,plain,
( spl0_466
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_Orderings_Olinorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_466])]) ).
fof(f863,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_Orderings_Olinorder(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_17) ).
fof(f5379,plain,
spl0_465,
inference(avatar_split_clause,[],[f862,f5377]) ).
fof(f5377,plain,
( spl0_465
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_465])]) ).
fof(f862,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_16) ).
fof(f5375,plain,
spl0_464,
inference(avatar_split_clause,[],[f861,f5373]) ).
fof(f5373,plain,
( spl0_464
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_Ring__and__Field_Oordered__semiring__strict(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_464])]) ).
fof(f861,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_Ring__and__Field_Oordered__semiring__strict(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_15) ).
fof(f5371,plain,
spl0_463,
inference(avatar_split_clause,[],[f856,f5369]) ).
fof(f5369,plain,
( spl0_463
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_463])]) ).
fof(f856,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_10) ).
fof(f5367,plain,
spl0_462,
inference(avatar_split_clause,[],[f855,f5365]) ).
fof(f5365,plain,
( spl0_462
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_OrderedGroup_Oab__group__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_462])]) ).
fof(f855,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_OrderedGroup_Oab__group__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_1) ).
fof(f5363,plain,
spl0_461,
inference(avatar_split_clause,[],[f854,f5361]) ).
fof(f5361,plain,
( spl0_461
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_Ring__and__Field_Oring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_461])]) ).
fof(f854,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_Ring__and__Field_Oring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_0) ).
fof(f5359,plain,
spl0_460,
inference(avatar_split_clause,[],[f853,f5357]) ).
fof(f5357,plain,
( spl0_460
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Osemiring__1__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_460])]) ).
fof(f853,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Osemiring__1__cancel(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_9) ).
fof(f5355,plain,
spl0_459,
inference(avatar_split_clause,[],[f852,f5353]) ).
fof(f5353,plain,
( spl0_459
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_OrderedGroup_Ocomm__monoid__mult(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_459])]) ).
fof(f852,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_OrderedGroup_Ocomm__monoid__mult(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_8) ).
fof(f5351,plain,
spl0_458,
inference(avatar_split_clause,[],[f851,f5349]) ).
fof(f5349,plain,
( spl0_458
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Ocomm__semiring__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_458])]) ).
fof(f851,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Ocomm__semiring__1(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_7) ).
fof(f5347,plain,
spl0_457,
inference(avatar_split_clause,[],[f850,f5345]) ).
fof(f5345,plain,
( spl0_457
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Ocomm__semiring__1__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_457])]) ).
fof(f850,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Ocomm__semiring__1__cancel(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_6) ).
fof(f5343,plain,
spl0_456,
inference(avatar_split_clause,[],[f849,f5341]) ).
fof(f5341,plain,
( spl0_456
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Oidom(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_456])]) ).
fof(f849,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Oidom(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_57) ).
fof(f5339,plain,
spl0_455,
inference(avatar_split_clause,[],[f847,f5337]) ).
fof(f5337,plain,
( spl0_455
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Oordered__semidom(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_455])]) ).
fof(f847,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Oordered__semidom(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_55) ).
fof(f5335,plain,
spl0_454,
inference(avatar_split_clause,[],[f846,f5333]) ).
fof(f5333,plain,
( spl0_454
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_OrderedGroup_Opordered__ab__group__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_454])]) ).
fof(f846,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_OrderedGroup_Opordered__ab__group__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_54) ).
fof(f5331,plain,
spl0_453,
inference(avatar_split_clause,[],[f845,f5329]) ).
fof(f5329,plain,
( spl0_453
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_OrderedGroup_Olordered__ab__group(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_453])]) ).
fof(f845,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_OrderedGroup_Olordered__ab__group(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_53) ).
fof(f5327,plain,
spl0_452,
inference(avatar_split_clause,[],[f844,f5325]) ).
fof(f5325,plain,
( spl0_452
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_OrderedGroup_Olordered__ab__group__join(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_452])]) ).
fof(f844,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_OrderedGroup_Olordered__ab__group__join(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_52) ).
fof(f5323,plain,
spl0_451,
inference(avatar_split_clause,[],[f843,f5321]) ).
fof(f5321,plain,
( spl0_451
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_OrderedGroup_Olordered__ab__group__meet(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_451])]) ).
fof(f843,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_OrderedGroup_Olordered__ab__group__meet(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_51) ).
fof(f5319,plain,
spl0_450,
inference(avatar_split_clause,[],[f842,f5317]) ).
fof(f5317,plain,
( spl0_450
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_OrderedGroup_Olordered__ab__group__abs(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_450])]) ).
fof(f842,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_OrderedGroup_Olordered__ab__group__abs(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_50) ).
fof(f5315,plain,
spl0_449,
inference(avatar_split_clause,[],[f840,f5313]) ).
fof(f5313,plain,
( spl0_449
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Opordered__ring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_449])]) ).
fof(f840,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Opordered__ring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_49) ).
fof(f5311,plain,
spl0_448,
inference(avatar_split_clause,[],[f839,f5309]) ).
fof(f5309,plain,
( spl0_448
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Olordered__ring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_448])]) ).
fof(f839,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Olordered__ring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_48) ).
fof(f5307,plain,
spl0_447,
inference(avatar_split_clause,[],[f838,f5305]) ).
fof(f5305,plain,
( spl0_447
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Oordered__ring__strict(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_447])]) ).
fof(f838,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Oordered__ring__strict(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_47) ).
fof(f5303,plain,
spl0_446,
inference(avatar_split_clause,[],[f837,f5301]) ).
fof(f5301,plain,
( spl0_446
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Oaxclass__abs__if(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_446])]) ).
fof(f837,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Oaxclass__abs__if(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_46) ).
fof(f5299,plain,
spl0_445,
inference(avatar_split_clause,[],[f836,f5297]) ).
fof(f5297,plain,
( spl0_445
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Orderings_Oord(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_445])]) ).
fof(f836,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Orderings_Oord(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_45) ).
fof(f5295,plain,
spl0_444,
inference(avatar_split_clause,[],[f835,f5293]) ).
fof(f5293,plain,
( spl0_444
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Orderings_Oorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_444])]) ).
fof(f835,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Orderings_Oorder(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_44) ).
fof(f5291,plain,
spl0_443,
inference(avatar_split_clause,[],[f834,f5289]) ).
fof(f5289,plain,
( spl0_443
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_443])]) ).
fof(f834,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_43) ).
fof(f5287,plain,
spl0_442,
inference(avatar_split_clause,[],[f833,f5285]) ).
fof(f5285,plain,
( spl0_442
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Opordered__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_442])]) ).
fof(f833,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Opordered__semiring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_42) ).
fof(f5283,plain,
spl0_441,
inference(avatar_split_clause,[],[f832,f5281]) ).
fof(f5281,plain,
( spl0_441
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Opordered__comm__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_441])]) ).
fof(f832,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Opordered__comm__semiring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_41) ).
fof(f5279,plain,
spl0_440,
inference(avatar_split_clause,[],[f831,f5277]) ).
fof(f5277,plain,
( spl0_440
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Opordered__cancel__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_440])]) ).
fof(f831,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Opordered__cancel__semiring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_40) ).
fof(f5275,plain,
spl0_439,
inference(avatar_split_clause,[],[f830,f5273]) ).
fof(f5273,plain,
( spl0_439
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_OrderedGroup_Oab__group__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_439])]) ).
fof(f830,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_OrderedGroup_Oab__group__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_4) ).
fof(f5271,plain,
spl0_438,
inference(avatar_split_clause,[],[f829,f5269]) ).
fof(f5269,plain,
( spl0_438
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Opordered__cancel__comm__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_438])]) ).
fof(f829,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Opordered__cancel__comm__semiring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_39) ).
fof(f5267,plain,
spl0_437,
inference(avatar_split_clause,[],[f828,f5265]) ).
fof(f5265,plain,
( spl0_437
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_437])]) ).
fof(f828,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_38) ).
fof(f5263,plain,
spl0_436,
inference(avatar_split_clause,[],[f827,f5261]) ).
fof(f5261,plain,
( spl0_436
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_436])]) ).
fof(f827,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_37) ).
fof(f5259,plain,
spl0_435,
inference(avatar_split_clause,[],[f826,f5257]) ).
fof(f5257,plain,
( spl0_435
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_LOrder_Omeet__semilorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_435])]) ).
fof(f826,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_LOrder_Omeet__semilorder(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_36) ).
fof(f5255,plain,
spl0_434,
inference(avatar_split_clause,[],[f825,f5253]) ).
fof(f5253,plain,
( spl0_434
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_LOrder_Ojoin__semilorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_434])]) ).
fof(f825,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_LOrder_Ojoin__semilorder(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_35) ).
fof(f5251,plain,
spl0_433,
inference(avatar_split_clause,[],[f824,f5249]) ).
fof(f5249,plain,
( spl0_433
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_LOrder_Olorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_433])]) ).
fof(f824,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_LOrder_Olorder(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_34) ).
fof(f5247,plain,
spl0_432,
inference(avatar_split_clause,[],[f823,f5245]) ).
fof(f5245,plain,
( spl0_432
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Orderings_Olinorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_432])]) ).
fof(f823,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Orderings_Olinorder(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_33) ).
fof(f5243,plain,
spl0_431,
inference(avatar_split_clause,[],[f822,f5241]) ).
fof(f5241,plain,
( spl0_431
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_431])]) ).
fof(f822,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_32) ).
fof(f5239,plain,
spl0_430,
inference(avatar_split_clause,[],[f821,f5237]) ).
fof(f5237,plain,
( spl0_430
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Oordered__semiring__strict(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_430])]) ).
fof(f821,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Oordered__semiring__strict(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_31) ).
fof(f5235,plain,
spl0_429,
inference(avatar_split_clause,[],[f820,f5233]) ).
fof(f5233,plain,
( spl0_429
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Oordered__comm__semiring__strict(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_429])]) ).
fof(f820,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Oordered__comm__semiring__strict(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_30) ).
fof(f5231,plain,
spl0_428,
inference(avatar_split_clause,[],[f819,f5229]) ).
fof(f5229,plain,
( spl0_428
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Oring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_428])]) ).
fof(f819,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Oring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_3) ).
fof(f5227,plain,
spl0_427,
inference(avatar_split_clause,[],[f816,f5225]) ).
fof(f5225,plain,
( spl0_427
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_427])]) ).
fof(f816,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_27) ).
fof(f5223,plain,
spl0_426,
inference(avatar_split_clause,[],[f814,f5221]) ).
fof(f5221,plain,
( spl0_426
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_426])]) ).
fof(f814,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_25) ).
fof(f5219,plain,
spl0_425,
inference(avatar_split_clause,[],[f812,f5217]) ).
fof(f5217,plain,
( spl0_425
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_425])]) ).
fof(f812,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_23) ).
fof(f5215,plain,
spl0_424,
inference(avatar_split_clause,[],[f809,f5213]) ).
fof(f5213,plain,
( spl0_424
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Osemiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_424])]) ).
fof(f809,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Osemiring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_20) ).
fof(f5211,plain,
spl0_423,
inference(avatar_split_clause,[],[f808,f5209]) ).
fof(f5209,plain,
( spl0_423
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Oring__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_423])]) ).
fof(f808,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Oring__1(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_2) ).
fof(f5207,plain,
spl0_422,
inference(avatar_split_clause,[],[f807,f5205]) ).
fof(f5205,plain,
( spl0_422
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Osemiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_422])]) ).
fof(f807,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Osemiring__0(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_19) ).
fof(f5203,plain,
spl0_421,
inference(avatar_split_clause,[],[f806,f5201]) ).
fof(f5201,plain,
( spl0_421
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_421])]) ).
fof(f806,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_18) ).
fof(f5199,plain,
spl0_420,
inference(avatar_split_clause,[],[f804,f5197]) ).
fof(f5197,plain,
( spl0_420
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Ocomm__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_420])]) ).
fof(f804,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Ocomm__semiring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_16) ).
fof(f5195,plain,
spl0_419,
inference(avatar_split_clause,[],[f803,f5193]) ).
fof(f5193,plain,
( spl0_419
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Ocomm__semiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_419])]) ).
fof(f803,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Ocomm__semiring__0(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_15) ).
fof(f5191,plain,
spl0_418,
inference(avatar_split_clause,[],[f802,f5189]) ).
fof(f5189,plain,
( spl0_418
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_418])]) ).
fof(f802,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_14) ).
fof(f5187,plain,
spl0_417,
inference(avatar_split_clause,[],[f801,f5185]) ).
fof(f5185,plain,
( spl0_417
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_HOL_Oone(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_417])]) ).
fof(f801,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_HOL_Oone(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_13) ).
fof(f5183,plain,
spl0_416,
inference(avatar_split_clause,[],[f800,f5181]) ).
fof(f5181,plain,
( spl0_416
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_OrderedGroup_Omonoid__mult(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_416])]) ).
fof(f800,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_OrderedGroup_Omonoid__mult(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_12) ).
fof(f5179,plain,
spl0_415,
inference(avatar_split_clause,[],[f799,f5177]) ).
fof(f5177,plain,
( spl0_415
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Oaxclass__0__neq__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_415])]) ).
fof(f799,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Oaxclass__0__neq__1(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_11) ).
fof(f5175,plain,
spl0_414,
inference(avatar_split_clause,[],[f798,f5173]) ).
fof(f5173,plain,
( spl0_414
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Osemiring__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_414])]) ).
fof(f798,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Osemiring__1(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_10) ).
fof(f5171,plain,
spl0_413,
inference(avatar_split_clause,[],[f797,f5169]) ).
fof(f5169,plain,
( spl0_413
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Ocomm__ring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_413])]) ).
fof(f797,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Ocomm__ring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_1) ).
fof(f5167,plain,
spl0_412,
inference(avatar_split_clause,[],[f796,f5165]) ).
fof(f5165,plain,
( spl0_412
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Ocomm__ring__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_412])]) ).
fof(f796,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Ocomm__ring__1(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_0) ).
fof(f5163,plain,
spl0_411,
inference(avatar_split_clause,[],[f732,f5161]) ).
fof(f5161,plain,
( spl0_411
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_411])]) ).
fof(f732,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_7) ).
fof(f5159,plain,
spl0_410,
inference(avatar_split_clause,[],[f729,f5157]) ).
fof(f5157,plain,
( spl0_410
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_Ring__and__Field_Osemiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_410])]) ).
fof(f729,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_Ring__and__Field_Osemiring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_4) ).
fof(f5155,plain,
spl0_409,
inference(avatar_split_clause,[],[f728,f5153]) ).
fof(f5153,plain,
( spl0_409
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_Ring__and__Field_Osemiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_409])]) ).
fof(f728,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_Ring__and__Field_Osemiring__0(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_3) ).
fof(f5151,plain,
spl0_408,
inference(avatar_split_clause,[],[f727,f5149]) ).
fof(f5149,plain,
( spl0_408
<=> ! [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_408])]) ).
fof(f727,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_Ring__and__Field_Opordered__comm__semiring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_29) ).
fof(f5147,plain,
spl0_407,
inference(avatar_split_clause,[],[f726,f5145]) ).
fof(f5145,plain,
( spl0_407
<=> ! [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_407])]) ).
fof(f726,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_Ring__and__Field_Opordered__cancel__comm__semiring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_28) ).
fof(f5143,plain,
spl0_406,
inference(avatar_split_clause,[],[f725,f5141]) ).
fof(f5141,plain,
( spl0_406
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_Ring__and__Field_Opordered__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_406])]) ).
fof(f725,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_Ring__and__Field_Opordered__semiring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_27) ).
fof(f5139,plain,
spl0_405,
inference(avatar_split_clause,[],[f724,f5137]) ).
fof(f5137,plain,
( spl0_405
<=> ! [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_405])]) ).
fof(f724,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_26) ).
fof(f5135,plain,
spl0_404,
inference(avatar_split_clause,[],[f723,f5133]) ).
fof(f5133,plain,
( spl0_404
<=> ! [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_404])]) ).
fof(f723,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_Ring__and__Field_Opordered__cancel__semiring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_25) ).
fof(f5131,plain,
spl0_403,
inference(avatar_split_clause,[],[f722,f5129]) ).
fof(f5129,plain,
( spl0_403
<=> ! [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_403])]) ).
fof(f722,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_Ring__and__Field_Oordered__semiring__strict(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_24) ).
fof(f5127,plain,
spl0_402,
inference(avatar_split_clause,[],[f721,f5125]) ).
fof(f5125,plain,
( spl0_402
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_402])]) ).
fof(f721,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_23) ).
fof(f5123,plain,
spl0_401,
inference(avatar_split_clause,[],[f720,f5121]) ).
fof(f5121,plain,
( spl0_401
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_401])]) ).
fof(f720,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_22) ).
fof(f5119,plain,
spl0_400,
inference(avatar_split_clause,[],[f719,f5117]) ).
fof(f5117,plain,
( spl0_400
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_Orderings_Oord(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_400])]) ).
fof(f719,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_Orderings_Oord(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_21) ).
fof(f5115,plain,
spl0_399,
inference(avatar_split_clause,[],[f718,f5113]) ).
fof(f5113,plain,
( spl0_399
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_Orderings_Oorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_399])]) ).
fof(f718,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_Orderings_Oorder(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_20) ).
fof(f5111,plain,
spl0_398,
inference(avatar_split_clause,[],[f716,f5109]) ).
fof(f5109,plain,
( spl0_398
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_398])]) ).
fof(f716,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_19) ).
fof(f5107,plain,
spl0_397,
inference(avatar_split_clause,[],[f715,f5105]) ).
fof(f5105,plain,
( spl0_397
<=> ! [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_397])]) ).
fof(f715,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_18) ).
fof(f5103,plain,
spl0_396,
inference(avatar_split_clause,[],[f714,f5101]) ).
fof(f5101,plain,
( spl0_396
<=> ! [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_396])]) ).
fof(f714,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_17) ).
fof(f5099,plain,
spl0_395,
inference(avatar_split_clause,[],[f713,f5097]) ).
fof(f5097,plain,
( spl0_395
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_LOrder_Omeet__semilorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_395])]) ).
fof(f713,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_LOrder_Omeet__semilorder(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_16) ).
fof(f5095,plain,
spl0_394,
inference(avatar_split_clause,[],[f712,f5093]) ).
fof(f5093,plain,
( spl0_394
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_LOrder_Ojoin__semilorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_394])]) ).
fof(f712,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_LOrder_Ojoin__semilorder(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_15) ).
fof(f5091,plain,
spl0_393,
inference(avatar_split_clause,[],[f711,f5089]) ).
fof(f5089,plain,
( spl0_393
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_LOrder_Olorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_393])]) ).
fof(f711,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_LOrder_Olorder(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_14) ).
fof(f5087,plain,
spl0_392,
inference(avatar_split_clause,[],[f710,f5085]) ).
fof(f5085,plain,
( spl0_392
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_Orderings_Olinorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_392])]) ).
fof(f710,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_Orderings_Olinorder(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_13) ).
fof(f5083,plain,
spl0_391,
inference(avatar_split_clause,[],[f709,f5081]) ).
fof(f5081,plain,
( spl0_391
<=> ! [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_391])]) ).
fof(f709,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_12) ).
fof(f5079,plain,
spl0_390,
inference(avatar_split_clause,[],[f706,f5077]) ).
fof(f5077,plain,
( spl0_390
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_Ring__and__Field_Ocomm__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_390])]) ).
fof(f706,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_Ring__and__Field_Ocomm__semiring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_1) ).
fof(f5075,plain,
spl0_389,
inference(avatar_split_clause,[],[f705,f5073]) ).
fof(f5073,plain,
( spl0_389
<=> ! [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_389])]) ).
fof(f705,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_Ring__and__Field_Ocomm__semiring__0(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_0) ).
fof(f5071,plain,
spl0_388,
inference(avatar_split_clause,[],[f704,f5069]) ).
fof(f5069,plain,
( spl0_388
<=> ! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_388])]) ).
fof(f704,axiom,
! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_9) ).
fof(f5067,plain,
spl0_387,
inference(avatar_split_clause,[],[f703,f5065]) ).
fof(f5065,plain,
( spl0_387
<=> ! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_Ring__and__Field_Opordered__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_387])]) ).
fof(f703,axiom,
! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_Ring__and__Field_Opordered__semiring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_8) ).
fof(f5063,plain,
spl0_386,
inference(avatar_split_clause,[],[f702,f5061]) ).
fof(f5061,plain,
( spl0_386
<=> ! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_Ring__and__Field_Opordered__cancel__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_386])]) ).
fof(f702,axiom,
! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_Ring__and__Field_Opordered__cancel__semiring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_7) ).
fof(f5059,plain,
spl0_385,
inference(avatar_split_clause,[],[f701,f5057]) ).
fof(f5057,plain,
( spl0_385
<=> ! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_385])]) ).
fof(f701,axiom,
! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_6) ).
fof(f5055,plain,
spl0_384,
inference(avatar_split_clause,[],[f700,f5053]) ).
fof(f5053,plain,
( spl0_384
<=> ! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_384])]) ).
fof(f700,axiom,
! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_5) ).
fof(f5051,plain,
spl0_383,
inference(avatar_split_clause,[],[f698,f5049]) ).
fof(f5049,plain,
( spl0_383
<=> ! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_OrderedGroup_Olordered__ab__group__join(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_383])]) ).
fof(f698,axiom,
! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_OrderedGroup_Olordered__ab__group__join(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_30) ).
fof(f5047,plain,
spl0_382,
inference(avatar_split_clause,[],[f697,f5045]) ).
fof(f5045,plain,
( spl0_382
<=> ! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_OrderedGroup_Oab__group__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_382])]) ).
fof(f697,axiom,
! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_OrderedGroup_Oab__group__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_3) ).
fof(f5043,plain,
spl0_381,
inference(avatar_split_clause,[],[f696,f5041]) ).
fof(f5041,plain,
( spl0_381
<=> ! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_OrderedGroup_Olordered__ab__group__meet(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_381])]) ).
fof(f696,axiom,
! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_OrderedGroup_Olordered__ab__group__meet(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_29) ).
fof(f5039,plain,
spl0_380,
inference(avatar_split_clause,[],[f695,f5037]) ).
fof(f5037,plain,
( spl0_380
<=> ! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_LOrder_Omeet__semilorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_380])]) ).
fof(f695,axiom,
! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_LOrder_Omeet__semilorder(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_28) ).
fof(f5035,plain,
spl0_379,
inference(avatar_split_clause,[],[f694,f5033]) ).
fof(f5033,plain,
( spl0_379
<=> ! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_LOrder_Ojoin__semilorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_379])]) ).
fof(f694,axiom,
! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_LOrder_Ojoin__semilorder(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_27) ).
fof(f5031,plain,
spl0_378,
inference(avatar_split_clause,[],[f693,f5029]) ).
fof(f5029,plain,
( spl0_378
<=> ! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_LOrder_Olorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_378])]) ).
fof(f693,axiom,
! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_LOrder_Olorder(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_26) ).
fof(f5027,plain,
spl0_377,
inference(avatar_split_clause,[],[f692,f5025]) ).
fof(f5025,plain,
( spl0_377
<=> ! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_OrderedGroup_Olordered__ab__group(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_377])]) ).
fof(f692,axiom,
! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_OrderedGroup_Olordered__ab__group(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_25) ).
fof(f5023,plain,
spl0_376,
inference(avatar_split_clause,[],[f691,f5021]) ).
fof(f5021,plain,
( spl0_376
<=> ! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_OrderedGroup_Olordered__ab__group__abs(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_376])]) ).
fof(f691,axiom,
! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_OrderedGroup_Olordered__ab__group__abs(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_24) ).
fof(f5019,plain,
spl0_375,
inference(avatar_split_clause,[],[f688,f5017]) ).
fof(f5017,plain,
( spl0_375
<=> ! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_375])]) ).
fof(f688,axiom,
! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_21) ).
fof(f5015,plain,
spl0_374,
inference(avatar_split_clause,[],[f686,f5013]) ).
fof(f5013,plain,
( spl0_374
<=> ! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_OrderedGroup_Opordered__ab__group__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_374])]) ).
fof(f686,axiom,
! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_OrderedGroup_Opordered__ab__group__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_2) ).
fof(f5011,plain,
spl0_373,
inference(avatar_split_clause,[],[f685,f5009]) ).
fof(f5009,plain,
( spl0_373
<=> ! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_373])]) ).
fof(f685,axiom,
! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_19) ).
fof(f5007,plain,
spl0_372,
inference(avatar_split_clause,[],[f683,f5005]) ).
fof(f5005,plain,
( spl0_372
<=> ! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_372])]) ).
fof(f683,axiom,
! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_17) ).
fof(f5003,plain,
spl0_371,
inference(avatar_split_clause,[],[f680,f5001]) ).
fof(f5001,plain,
( spl0_371
<=> ! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_Ring__and__Field_Osemiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_371])]) ).
fof(f680,axiom,
! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_Ring__and__Field_Osemiring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_14) ).
fof(f4999,plain,
spl0_370,
inference(avatar_split_clause,[],[f679,f4997]) ).
fof(f4997,plain,
( spl0_370
<=> ! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_Ring__and__Field_Osemiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_370])]) ).
fof(f679,axiom,
! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_Ring__and__Field_Osemiring__0(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_13) ).
fof(f4995,plain,
spl0_369,
inference(avatar_split_clause,[],[f678,f4993]) ).
fof(f4993,plain,
( spl0_369
<=> ! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_369])]) ).
fof(f678,axiom,
! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_12) ).
fof(f4991,plain,
spl0_368,
inference(avatar_split_clause,[],[f677,f4989]) ).
fof(f4989,plain,
( spl0_368
<=> ! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_Orderings_Oord(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_368])]) ).
fof(f677,axiom,
! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_Orderings_Oord(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_11) ).
fof(f4987,plain,
spl0_367,
inference(avatar_split_clause,[],[f676,f4985]) ).
fof(f4985,plain,
( spl0_367
<=> ! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_Orderings_Oorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_367])]) ).
fof(f676,axiom,
! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_Orderings_Oorder(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_10) ).
fof(f4983,plain,
spl0_366,
inference(avatar_split_clause,[],[f675,f4981]) ).
fof(f4981,plain,
( spl0_366
<=> ! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_Ring__and__Field_Oring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_366])]) ).
fof(f675,axiom,
! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_Ring__and__Field_Oring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_1) ).
fof(f4979,plain,
spl0_365,
inference(avatar_split_clause,[],[f674,f4977]) ).
fof(f4977,plain,
( spl0_365
<=> ! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_Ring__and__Field_Opordered__ring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_365])]) ).
fof(f674,axiom,
! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_Ring__and__Field_Opordered__ring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_0) ).
fof(f4975,plain,
spl0_364,
inference(avatar_split_clause,[],[f673,f4973]) ).
fof(f4973,plain,
( spl0_364
<=> ! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_Ring__and__Field_Osemiring__1__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_364])]) ).
fof(f673,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_Ring__and__Field_Osemiring__1__cancel(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_9) ).
fof(f4971,plain,
spl0_363,
inference(avatar_split_clause,[],[f672,f4969]) ).
fof(f4969,plain,
( spl0_363
<=> ! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_OrderedGroup_Ocomm__monoid__mult(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_363])]) ).
fof(f672,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_OrderedGroup_Ocomm__monoid__mult(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_8) ).
fof(f4967,plain,
spl0_362,
inference(avatar_split_clause,[],[f671,f4965]) ).
fof(f4965,plain,
( spl0_362
<=> ! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_Ring__and__Field_Ocomm__semiring__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_362])]) ).
fof(f671,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_Ring__and__Field_Ocomm__semiring__1(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_7) ).
fof(f4963,plain,
spl0_361,
inference(avatar_split_clause,[],[f670,f4961]) ).
fof(f4961,plain,
( spl0_361
<=> ! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_Ring__and__Field_Ocomm__semiring__1__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_361])]) ).
fof(f670,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_Ring__and__Field_Ocomm__semiring__1__cancel(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_6) ).
fof(f4959,plain,
spl0_360,
inference(avatar_split_clause,[],[f668,f4957]) ).
fof(f4957,plain,
( spl0_360
<=> ! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_OrderedGroup_Oab__group__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_360])]) ).
fof(f668,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_OrderedGroup_Oab__group__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_4) ).
fof(f4955,plain,
spl0_359,
inference(avatar_split_clause,[],[f666,f4953]) ).
fof(f4953,plain,
( spl0_359
<=> ! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_Ring__and__Field_Oring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_359])]) ).
fof(f666,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_Ring__and__Field_Oring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_3) ).
fof(f4951,plain,
spl0_358,
inference(avatar_split_clause,[],[f663,f4949]) ).
fof(f4949,plain,
( spl0_358
<=> ! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_358])]) ).
fof(f663,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_27) ).
fof(f4947,plain,
spl0_357,
inference(avatar_split_clause,[],[f661,f4945]) ).
fof(f4945,plain,
( spl0_357
<=> ! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_357])]) ).
fof(f661,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_25) ).
fof(f4943,plain,
spl0_356,
inference(avatar_split_clause,[],[f659,f4941]) ).
fof(f4941,plain,
( spl0_356
<=> ! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_356])]) ).
fof(f659,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_23) ).
fof(f4939,plain,
spl0_355,
inference(avatar_split_clause,[],[f656,f4937]) ).
fof(f4937,plain,
( spl0_355
<=> ! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_Ring__and__Field_Osemiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_355])]) ).
fof(f656,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_Ring__and__Field_Osemiring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_20) ).
fof(f4935,plain,
spl0_354,
inference(avatar_split_clause,[],[f655,f4933]) ).
fof(f4933,plain,
( spl0_354
<=> ! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_Ring__and__Field_Oring__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_354])]) ).
fof(f655,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_Ring__and__Field_Oring__1(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_2) ).
fof(f4931,plain,
spl0_353,
inference(avatar_split_clause,[],[f654,f4929]) ).
fof(f4929,plain,
( spl0_353
<=> ! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_Ring__and__Field_Osemiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_353])]) ).
fof(f654,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_Ring__and__Field_Osemiring__0(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_19) ).
fof(f4927,plain,
spl0_352,
inference(avatar_split_clause,[],[f653,f4925]) ).
fof(f4925,plain,
( spl0_352
<=> ! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_352])]) ).
fof(f653,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_18) ).
fof(f4923,plain,
spl0_351,
inference(avatar_split_clause,[],[f651,f4921]) ).
fof(f4921,plain,
( spl0_351
<=> ! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_Ring__and__Field_Ocomm__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_351])]) ).
fof(f651,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_Ring__and__Field_Ocomm__semiring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_16) ).
fof(f4919,plain,
spl0_350,
inference(avatar_split_clause,[],[f650,f4917]) ).
fof(f4917,plain,
( spl0_350
<=> ! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_Ring__and__Field_Ocomm__semiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_350])]) ).
fof(f650,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_Ring__and__Field_Ocomm__semiring__0(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_15) ).
fof(f4915,plain,
spl0_349,
inference(avatar_split_clause,[],[f649,f4913]) ).
fof(f4913,plain,
( spl0_349
<=> ! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_349])]) ).
fof(f649,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_14) ).
fof(f4911,plain,
spl0_348,
inference(avatar_split_clause,[],[f648,f4909]) ).
fof(f4909,plain,
( spl0_348
<=> ! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_HOL_Oone(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_348])]) ).
fof(f648,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_HOL_Oone(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_13) ).
fof(f4907,plain,
spl0_347,
inference(avatar_split_clause,[],[f647,f4905]) ).
fof(f4905,plain,
( spl0_347
<=> ! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_OrderedGroup_Omonoid__mult(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_347])]) ).
fof(f647,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_OrderedGroup_Omonoid__mult(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_12) ).
fof(f4903,plain,
spl0_346,
inference(avatar_split_clause,[],[f646,f4901]) ).
fof(f4901,plain,
( spl0_346
<=> ! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_Ring__and__Field_Oaxclass__0__neq__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_346])]) ).
fof(f646,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_Ring__and__Field_Oaxclass__0__neq__1(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_11) ).
fof(f4899,plain,
spl0_345,
inference(avatar_split_clause,[],[f645,f4897]) ).
fof(f4897,plain,
( spl0_345
<=> ! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_Ring__and__Field_Osemiring__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_345])]) ).
fof(f645,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_Ring__and__Field_Osemiring__1(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_10) ).
fof(f4895,plain,
spl0_344,
inference(avatar_split_clause,[],[f644,f4893]) ).
fof(f4893,plain,
( spl0_344
<=> ! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_Ring__and__Field_Ocomm__ring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_344])]) ).
fof(f644,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_Ring__and__Field_Ocomm__ring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_1) ).
fof(f4891,plain,
spl0_343,
inference(avatar_split_clause,[],[f643,f4889]) ).
fof(f4889,plain,
( spl0_343
<=> ! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_Ring__and__Field_Ocomm__ring__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_343])]) ).
fof(f643,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_Ring__and__Field_Ocomm__ring__1(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_0) ).
fof(f4887,plain,
spl0_342,
inference(avatar_split_clause,[],[f607,f4885]) ).
fof(f4885,plain,
( spl0_342
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_342])]) ).
fof(f607,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_9) ).
fof(f4883,plain,
spl0_341,
inference(avatar_split_clause,[],[f606,f4881]) ).
fof(f4881,plain,
( spl0_341
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X39)
| class_Ring__and__Field_Osemiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_341])]) ).
fof(f606,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X39)
| class_Ring__and__Field_Osemiring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_8) ).
fof(f4879,plain,
spl0_340,
inference(avatar_split_clause,[],[f605,f4877]) ).
fof(f4877,plain,
( spl0_340
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X39)
| class_Ring__and__Field_Osemiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_340])]) ).
fof(f605,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X39)
| class_Ring__and__Field_Osemiring__0(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_7) ).
fof(f4875,plain,
spl0_339,
inference(avatar_split_clause,[],[f604,f4873]) ).
fof(f4873,plain,
( spl0_339
<=> ! [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_339])]) ).
fof(f604,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X39)
| class_Ring__and__Field_Oaxclass__0__neq__1(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_6) ).
fof(f4871,plain,
spl0_338,
inference(avatar_split_clause,[],[f603,f4869]) ).
fof(f4869,plain,
( spl0_338
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X39)
| class_Ring__and__Field_Osemiring__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_338])]) ).
fof(f603,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X39)
| class_Ring__and__Field_Osemiring__1(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_5) ).
fof(f4867,plain,
spl0_337,
inference(avatar_split_clause,[],[f601,f4865]) ).
fof(f4865,plain,
( spl0_337
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X39)
| class_OrderedGroup_Ocomm__monoid__mult(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_337])]) ).
fof(f601,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X39)
| class_OrderedGroup_Ocomm__monoid__mult(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_3) ).
fof(f4863,plain,
spl0_336,
inference(avatar_split_clause,[],[f600,f4861]) ).
fof(f4861,plain,
( spl0_336
<=> ! [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_336])]) ).
fof(f600,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X39)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_22) ).
fof(f4859,plain,
spl0_335,
inference(avatar_split_clause,[],[f599,f4857]) ).
fof(f4857,plain,
( spl0_335
<=> ! [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_335])]) ).
fof(f599,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_21) ).
fof(f4855,plain,
spl0_334,
inference(avatar_split_clause,[],[f598,f4853]) ).
fof(f4853,plain,
( spl0_334
<=> ! [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_334])]) ).
fof(f598,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X39)
| class_Ring__and__Field_Osemiring__1__cancel(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_20) ).
fof(f4851,plain,
spl0_333,
inference(avatar_split_clause,[],[f597,f4849]) ).
fof(f4849,plain,
( spl0_333
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X39)
| class_Ring__and__Field_Ocomm__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_333])]) ).
fof(f597,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X39)
| class_Ring__and__Field_Ocomm__semiring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_2) ).
fof(f4847,plain,
spl0_332,
inference(avatar_split_clause,[],[f596,f4845]) ).
fof(f4845,plain,
( spl0_332
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_332])]) ).
fof(f596,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_19) ).
fof(f4843,plain,
spl0_331,
inference(avatar_split_clause,[],[f595,f4841]) ).
fof(f4841,plain,
( spl0_331
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_331])]) ).
fof(f595,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_18) ).
fof(f4839,plain,
spl0_330,
inference(avatar_split_clause,[],[f592,f4837]) ).
fof(f4837,plain,
( spl0_330
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X39)
| class_HOL_Oone(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_330])]) ).
fof(f592,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X39)
| class_HOL_Oone(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_15) ).
fof(f4835,plain,
spl0_329,
inference(avatar_split_clause,[],[f591,f4833]) ).
fof(f4833,plain,
( spl0_329
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X39)
| class_OrderedGroup_Omonoid__mult(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_329])]) ).
fof(f591,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X39)
| class_OrderedGroup_Omonoid__mult(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_14) ).
fof(f4831,plain,
spl0_328,
inference(avatar_split_clause,[],[f586,f4829]) ).
fof(f4829,plain,
( spl0_328
<=> ! [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_328])]) ).
fof(f586,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X39)
| class_Ring__and__Field_Ocomm__semiring__0(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_1) ).
fof(f4827,plain,
spl0_327,
inference(avatar_split_clause,[],[f585,f4825]) ).
fof(f4825,plain,
( spl0_327
<=> ! [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_327])]) ).
fof(f585,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X39)
| class_Ring__and__Field_Ocomm__semiring__1(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_0) ).
fof(f4823,plain,
spl0_326,
inference(avatar_split_clause,[],[f582,f4821]) ).
fof(f4821,plain,
( spl0_326
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X39)
| class_Ring__and__Field_Osemiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_326])]) ).
fof(f582,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X39)
| class_Ring__and__Field_Osemiring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_7) ).
fof(f4819,plain,
spl0_325,
inference(avatar_split_clause,[],[f581,f4817]) ).
fof(f4817,plain,
( spl0_325
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X39)
| class_Ring__and__Field_Osemiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_325])]) ).
fof(f581,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X39)
| class_Ring__and__Field_Osemiring__0(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_6) ).
fof(f4815,plain,
spl0_324,
inference(avatar_split_clause,[],[f579,f4813]) ).
fof(f4813,plain,
( spl0_324
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X39)
| class_Ring__and__Field_Ocomm__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_324])]) ).
fof(f579,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X39)
| class_Ring__and__Field_Ocomm__semiring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_4) ).
fof(f4811,plain,
spl0_323,
inference(avatar_split_clause,[],[f578,f4809]) ).
fof(f4809,plain,
( spl0_323
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X39)
| class_Ring__and__Field_Ocomm__semiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_323])]) ).
fof(f578,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X39)
| class_Ring__and__Field_Ocomm__semiring__0(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_3) ).
fof(f4807,plain,
spl0_322,
inference(avatar_split_clause,[],[f577,f4805]) ).
fof(f4805,plain,
( spl0_322
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X39)
| class_HOL_Oone(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_322])]) ).
fof(f577,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X39)
| class_HOL_Oone(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_2) ).
fof(f4803,plain,
spl0_321,
inference(avatar_split_clause,[],[f576,f4801]) ).
fof(f4801,plain,
( spl0_321
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X39)
| class_Ring__and__Field_Osemiring__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_321])]) ).
fof(f576,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X39)
| class_Ring__and__Field_Osemiring__1(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_16) ).
fof(f4799,plain,
spl0_320,
inference(avatar_split_clause,[],[f575,f4797]) ).
fof(f4797,plain,
( spl0_320
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X39)
| class_OrderedGroup_Omonoid__mult(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_320])]) ).
fof(f575,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X39)
| class_OrderedGroup_Omonoid__mult(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_15) ).
fof(f4795,plain,
spl0_319,
inference(avatar_split_clause,[],[f574,f4793]) ).
fof(f4793,plain,
( spl0_319
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X39)
| class_OrderedGroup_Ocomm__monoid__mult(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_319])]) ).
fof(f574,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X39)
| class_OrderedGroup_Ocomm__monoid__mult(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_14) ).
fof(f4791,plain,
spl0_318,
inference(avatar_split_clause,[],[f570,f4789]) ).
fof(f4789,plain,
( spl0_318
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_318])]) ).
fof(f570,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_10) ).
fof(f4787,plain,
spl0_317,
inference(avatar_split_clause,[],[f568,f4785]) ).
fof(f4785,plain,
( spl0_317
<=> ! [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_317])]) ).
fof(f568,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X39)
| class_Ring__and__Field_Oaxclass__0__neq__1(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_0) ).
fof(f4783,plain,
spl0_316,
inference(avatar_split_clause,[],[f565,f4781]) ).
fof(f4781,plain,
( spl0_316
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_316])]) ).
fof(f565,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_7) ).
fof(f4779,plain,
spl0_315,
inference(avatar_split_clause,[],[f562,f4777]) ).
fof(f4777,plain,
( spl0_315
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X39)
| class_Ring__and__Field_Osemiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_315])]) ).
fof(f562,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X39)
| class_Ring__and__Field_Osemiring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_4) ).
fof(f4775,plain,
spl0_314,
inference(avatar_split_clause,[],[f561,f4773]) ).
fof(f4773,plain,
( spl0_314
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X39)
| class_Ring__and__Field_Osemiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_314])]) ).
fof(f561,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X39)
| class_Ring__and__Field_Osemiring__0(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_3) ).
fof(f4771,plain,
spl0_313,
inference(avatar_split_clause,[],[f559,f4769]) ).
fof(f4769,plain,
( spl0_313
<=> ! [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_313])]) ).
fof(f559,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_14) ).
fof(f4767,plain,
spl0_312,
inference(avatar_split_clause,[],[f558,f4765]) ).
fof(f4765,plain,
( spl0_312
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_312])]) ).
fof(f558,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_13) ).
fof(f4763,plain,
spl0_311,
inference(avatar_split_clause,[],[f557,f4761]) ).
fof(f4761,plain,
( spl0_311
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_311])]) ).
fof(f557,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_12) ).
fof(f4759,plain,
spl0_310,
inference(avatar_split_clause,[],[f554,f4757]) ).
fof(f4757,plain,
( spl0_310
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X39)
| class_Ring__and__Field_Ocomm__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_310])]) ).
fof(f554,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X39)
| class_Ring__and__Field_Ocomm__semiring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_1) ).
fof(f4755,plain,
spl0_309,
inference(avatar_split_clause,[],[f553,f4753]) ).
fof(f4753,plain,
( spl0_309
<=> ! [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_309])]) ).
fof(f553,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X39)
| class_Ring__and__Field_Ocomm__semiring__0(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_0) ).
fof(f4751,plain,
spl0_308,
inference(avatar_split_clause,[],[f551,f4749]) ).
fof(f4749,plain,
( spl0_308
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_308])]) ).
fof(f551,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0_8) ).
fof(f4747,plain,
spl0_307,
inference(avatar_split_clause,[],[f545,f4745]) ).
fof(f4745,plain,
( spl0_307
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X39)
| class_Ring__and__Field_Osemiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_307])]) ).
fof(f545,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X39)
| class_Ring__and__Field_Osemiring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0_2) ).
fof(f4743,plain,
spl0_306,
inference(avatar_split_clause,[],[f544,f4741]) ).
fof(f4741,plain,
( spl0_306
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X39)
| class_Ring__and__Field_Osemiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_306])]) ).
fof(f544,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X39)
| class_Ring__and__Field_Osemiring__0(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0_10) ).
fof(f4739,plain,
spl0_305,
inference(avatar_split_clause,[],[f542,f4737]) ).
fof(f4737,plain,
( spl0_305
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X39)
| class_Ring__and__Field_Ocomm__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_305])]) ).
fof(f542,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X39)
| class_Ring__and__Field_Ocomm__semiring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0_0) ).
fof(f4735,plain,
spl0_304,
inference(avatar_split_clause,[],[f541,f4733]) ).
fof(f4733,plain,
( spl0_304
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring(X39)
| class_Ring__and__Field_Osemiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_304])]) ).
fof(f541,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring(X39)
| class_Ring__and__Field_Osemiring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring_6) ).
fof(f4731,plain,
spl0_303,
inference(avatar_split_clause,[],[f534,f4729]) ).
fof(f4729,plain,
( spl0_303
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_Ring__and__Field_Osemiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_303])]) ).
fof(f534,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_Ring__and__Field_Osemiring__0(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_9) ).
fof(f4727,plain,
spl0_302,
inference(avatar_split_clause,[],[f533,f4725]) ).
fof(f4725,plain,
( spl0_302
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_302])]) ).
fof(f533,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_8) ).
fof(f4723,plain,
spl0_301,
inference(avatar_split_clause,[],[f531,f4721]) ).
fof(f4721,plain,
( spl0_301
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_Ring__and__Field_Ocomm__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_301])]) ).
fof(f531,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_Ring__and__Field_Ocomm__semiring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_6) ).
fof(f4719,plain,
spl0_300,
inference(avatar_split_clause,[],[f530,f4717]) ).
fof(f4717,plain,
( spl0_300
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_Ring__and__Field_Ocomm__semiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_300])]) ).
fof(f530,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_Ring__and__Field_Ocomm__semiring__0(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_5) ).
fof(f4715,plain,
spl0_299,
inference(avatar_split_clause,[],[f529,f4713]) ).
fof(f4713,plain,
( spl0_299
<=> ! [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_299])]) ).
fof(f529,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_4) ).
fof(f4711,plain,
spl0_298,
inference(avatar_split_clause,[],[f527,f4709]) ).
fof(f4709,plain,
( spl0_298
<=> ! [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_298])]) ).
fof(f527,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_Ring__and__Field_Ocomm__semiring__1__cancel(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_28) ).
fof(f4707,plain,
spl0_297,
inference(avatar_split_clause,[],[f526,f4705]) ).
fof(f4705,plain,
( spl0_297
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_Ring__and__Field_Osemiring__1__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_297])]) ).
fof(f526,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_Ring__and__Field_Osemiring__1__cancel(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_27) ).
fof(f4703,plain,
spl0_296,
inference(avatar_split_clause,[],[f525,f4701]) ).
fof(f4701,plain,
( spl0_296
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_Ring__and__Field_Oring__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_296])]) ).
fof(f525,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_Ring__and__Field_Oring__1(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_26) ).
fof(f4699,plain,
spl0_295,
inference(avatar_split_clause,[],[f524,f4697]) ).
fof(f4697,plain,
( spl0_295
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_HOL_Oone(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_295])]) ).
fof(f524,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_HOL_Oone(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_25) ).
fof(f4695,plain,
spl0_294,
inference(avatar_split_clause,[],[f523,f4693]) ).
fof(f4693,plain,
( spl0_294
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_OrderedGroup_Omonoid__mult(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_294])]) ).
fof(f523,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_OrderedGroup_Omonoid__mult(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_24) ).
fof(f4691,plain,
spl0_293,
inference(avatar_split_clause,[],[f522,f4689]) ).
fof(f4689,plain,
( spl0_293
<=> ! [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_293])]) ).
fof(f522,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_Ring__and__Field_Oaxclass__0__neq__1(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_23) ).
fof(f4687,plain,
spl0_292,
inference(avatar_split_clause,[],[f521,f4685]) ).
fof(f4685,plain,
( spl0_292
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_Ring__and__Field_Osemiring__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_292])]) ).
fof(f521,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_Ring__and__Field_Osemiring__1(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_22) ).
fof(f4683,plain,
spl0_291,
inference(avatar_split_clause,[],[f520,f4681]) ).
fof(f4681,plain,
( spl0_291
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_OrderedGroup_Ocomm__monoid__mult(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_291])]) ).
fof(f520,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_OrderedGroup_Ocomm__monoid__mult(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_21) ).
fof(f4679,plain,
spl0_290,
inference(avatar_split_clause,[],[f519,f4677]) ).
fof(f4677,plain,
( spl0_290
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_Ring__and__Field_Ocomm__semiring__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_290])]) ).
fof(f519,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_Ring__and__Field_Ocomm__semiring__1(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_20) ).
fof(f4675,plain,
spl0_289,
inference(avatar_split_clause,[],[f518,f4673]) ).
fof(f4673,plain,
( spl0_289
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_OrderedGroup_Oab__group__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_289])]) ).
fof(f518,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_OrderedGroup_Oab__group__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_2) ).
fof(f4671,plain,
spl0_288,
inference(avatar_split_clause,[],[f515,f4669]) ).
fof(f4669,plain,
( spl0_288
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_288])]) ).
fof(f515,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_17) ).
fof(f4667,plain,
spl0_287,
inference(avatar_split_clause,[],[f513,f4665]) ).
fof(f4665,plain,
( spl0_287
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_287])]) ).
fof(f513,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_15) ).
fof(f4663,plain,
spl0_286,
inference(avatar_split_clause,[],[f511,f4661]) ).
fof(f4661,plain,
( spl0_286
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_286])]) ).
fof(f511,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_13) ).
fof(f4659,plain,
spl0_285,
inference(avatar_split_clause,[],[f508,f4657]) ).
fof(f4657,plain,
( spl0_285
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_Ring__and__Field_Osemiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_285])]) ).
fof(f508,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_Ring__and__Field_Osemiring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_10) ).
fof(f4655,plain,
spl0_284,
inference(avatar_split_clause,[],[f507,f4653]) ).
fof(f4653,plain,
( spl0_284
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_Ring__and__Field_Oring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_284])]) ).
fof(f507,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_Ring__and__Field_Oring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_1) ).
fof(f4651,plain,
spl0_283,
inference(avatar_split_clause,[],[f506,f4649]) ).
fof(f4649,plain,
( spl0_283
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_Ring__and__Field_Ocomm__ring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_283])]) ).
fof(f506,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_Ring__and__Field_Ocomm__ring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_0) ).
fof(f4647,plain,
spl0_282,
inference(avatar_split_clause,[],[f503,f4645]) ).
fof(f4645,plain,
( spl0_282
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_282])]) ).
fof(f503,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_7) ).
fof(f4643,plain,
spl0_281,
inference(avatar_split_clause,[],[f500,f4641]) ).
fof(f4641,plain,
( spl0_281
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring(X39)
| class_Ring__and__Field_Osemiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_281])]) ).
fof(f500,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring(X39)
| class_Ring__and__Field_Osemiring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_4) ).
fof(f4639,plain,
spl0_280,
inference(avatar_split_clause,[],[f499,f4637]) ).
fof(f4637,plain,
( spl0_280
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring(X39)
| class_Ring__and__Field_Osemiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_280])]) ).
fof(f499,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring(X39)
| class_Ring__and__Field_Osemiring__0(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_3) ).
fof(f4635,plain,
spl0_279,
inference(avatar_split_clause,[],[f497,f4633]) ).
fof(f4633,plain,
( spl0_279
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring(X39)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_279])]) ).
fof(f497,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring(X39)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_18) ).
fof(f4631,plain,
spl0_278,
inference(avatar_split_clause,[],[f496,f4629]) ).
fof(f4629,plain,
( spl0_278
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_278])]) ).
fof(f496,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_17) ).
fof(f4627,plain,
spl0_277,
inference(avatar_split_clause,[],[f495,f4625]) ).
fof(f4625,plain,
( spl0_277
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring(X39)
| class_Ring__and__Field_Oring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_277])]) ).
fof(f495,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring(X39)
| class_Ring__and__Field_Oring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_16) ).
fof(f4623,plain,
spl0_276,
inference(avatar_split_clause,[],[f494,f4621]) ).
fof(f4621,plain,
( spl0_276
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_276])]) ).
fof(f494,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_15) ).
fof(f4619,plain,
spl0_275,
inference(avatar_split_clause,[],[f493,f4617]) ).
fof(f4617,plain,
( spl0_275
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_275])]) ).
fof(f493,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_14) ).
fof(f4615,plain,
spl0_274,
inference(avatar_split_clause,[],[f491,f4613]) ).
fof(f4613,plain,
( spl0_274
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring(X39)
| class_OrderedGroup_Oab__group__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_274])]) ).
fof(f491,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring(X39)
| class_OrderedGroup_Oab__group__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_12) ).
fof(f4611,plain,
spl0_273,
inference(avatar_split_clause,[],[f488,f4609]) ).
fof(f4609,plain,
( spl0_273
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring(X39)
| class_Ring__and__Field_Ocomm__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_273])]) ).
fof(f488,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring(X39)
| class_Ring__and__Field_Ocomm__semiring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_1) ).
fof(f4607,plain,
spl0_272,
inference(avatar_split_clause,[],[f487,f4605]) ).
fof(f4605,plain,
( spl0_272
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring(X39)
| class_Ring__and__Field_Ocomm__semiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_272])]) ).
fof(f487,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring(X39)
| class_Ring__and__Field_Ocomm__semiring__0(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_0) ).
fof(f4603,plain,
spl0_271,
inference(avatar_split_clause,[],[f483,f4601]) ).
fof(f4601,plain,
( spl0_271
<=> ! [X39] :
( ~ class_Ring__and__Field_Oaxclass__abs__if(X39)
| class_Orderings_Oord(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_271])]) ).
fof(f483,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oaxclass__abs__if(X39)
| class_Orderings_Oord(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oaxclass__abs__if_1) ).
fof(f4599,plain,
spl0_270,
inference(avatar_split_clause,[],[f481,f4597]) ).
fof(f4597,plain,
( spl0_270
<=> ! [X39] :
( ~ class_Ring__and__Field_Oaxclass__0__neq__1(X39)
| class_HOL_Oone(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_270])]) ).
fof(f481,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oaxclass__0__neq__1(X39)
| class_HOL_Oone(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oaxclass__0__neq__1_1) ).
fof(f4595,plain,
spl0_269,
inference(avatar_split_clause,[],[f473,f4593]) ).
fof(f4593,plain,
( spl0_269
<=> ! [X39] :
( ~ class_Power_Orecpower(X39)
| class_Ring__and__Field_Oaxclass__0__neq__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_269])]) ).
fof(f473,axiom,
! [X39] :
( ~ class_Power_Orecpower(X39)
| class_Ring__and__Field_Oaxclass__0__neq__1(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_3) ).
fof(f4591,plain,
spl0_268,
inference(avatar_split_clause,[],[f472,f4589]) ).
fof(f4589,plain,
( spl0_268
<=> ! [X39] :
( ~ class_Power_Orecpower(X39)
| class_Ring__and__Field_Ocomm__semiring__1__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_268])]) ).
fof(f472,axiom,
! [X39] :
( ~ class_Power_Orecpower(X39)
| class_Ring__and__Field_Ocomm__semiring__1__cancel(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_24) ).
fof(f4587,plain,
spl0_267,
inference(avatar_split_clause,[],[f471,f4585]) ).
fof(f4585,plain,
( spl0_267
<=> ! [X39] :
( ~ class_Power_Orecpower(X39)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_267])]) ).
fof(f471,axiom,
! [X39] :
( ~ class_Power_Orecpower(X39)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_23) ).
fof(f4583,plain,
spl0_266,
inference(avatar_split_clause,[],[f470,f4581]) ).
fof(f4581,plain,
( spl0_266
<=> ! [X39] :
( ~ class_Power_Orecpower(X39)
| class_Ring__and__Field_Osemiring__1__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_266])]) ).
fof(f470,axiom,
! [X39] :
( ~ class_Power_Orecpower(X39)
| class_Ring__and__Field_Osemiring__1__cancel(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_22) ).
fof(f4579,plain,
spl0_265,
inference(avatar_split_clause,[],[f469,f4577]) ).
fof(f4577,plain,
( spl0_265
<=> ! [X39] :
( ~ class_Power_Orecpower(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_265])]) ).
fof(f469,axiom,
! [X39] :
( ~ class_Power_Orecpower(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_21) ).
fof(f4575,plain,
spl0_264,
inference(avatar_split_clause,[],[f468,f4573]) ).
fof(f4573,plain,
( spl0_264
<=> ! [X39] :
( ~ class_Power_Orecpower(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_264])]) ).
fof(f468,axiom,
! [X39] :
( ~ class_Power_Orecpower(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_20) ).
fof(f4571,plain,
spl0_263,
inference(avatar_split_clause,[],[f467,f4569]) ).
fof(f4569,plain,
( spl0_263
<=> ! [X39] :
( ~ class_Power_Orecpower(X39)
| class_HOL_Oone(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_263])]) ).
fof(f467,axiom,
! [X39] :
( ~ class_Power_Orecpower(X39)
| class_HOL_Oone(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_2) ).
fof(f4567,plain,
spl0_262,
inference(avatar_split_clause,[],[f466,f4565]) ).
fof(f4565,plain,
( spl0_262
<=> ! [X39] :
( ~ class_Power_Orecpower(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_262])]) ).
fof(f466,axiom,
! [X39] :
( ~ class_Power_Orecpower(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_19) ).
fof(f4563,plain,
spl0_261,
inference(avatar_split_clause,[],[f465,f4561]) ).
fof(f4561,plain,
( spl0_261
<=> ! [X39] :
( ~ class_Power_Orecpower(X39)
| class_Ring__and__Field_Ocomm__semiring__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_261])]) ).
fof(f465,axiom,
! [X39] :
( ~ class_Power_Orecpower(X39)
| class_Ring__and__Field_Ocomm__semiring__1(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_18) ).
fof(f4559,plain,
spl0_260,
inference(avatar_split_clause,[],[f464,f4557]) ).
fof(f4557,plain,
( spl0_260
<=> ! [X39] :
( ~ class_Power_Orecpower(X39)
| class_Ring__and__Field_Osemiring__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_260])]) ).
fof(f464,axiom,
! [X39] :
( ~ class_Power_Orecpower(X39)
| class_Ring__and__Field_Osemiring__1(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_17) ).
fof(f4555,plain,
spl0_259,
inference(avatar_split_clause,[],[f463,f4553]) ).
fof(f4553,plain,
( spl0_259
<=> ! [X39] :
( ~ class_Power_Orecpower(X39)
| class_OrderedGroup_Ocomm__monoid__mult(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_259])]) ).
fof(f463,axiom,
! [X39] :
( ~ class_Power_Orecpower(X39)
| class_OrderedGroup_Ocomm__monoid__mult(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_16) ).
fof(f4551,plain,
spl0_258,
inference(avatar_split_clause,[],[f462,f4549]) ).
fof(f4549,plain,
( spl0_258
<=> ! [X39] :
( ~ class_Power_Orecpower(X39)
| class_OrderedGroup_Omonoid__mult(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_258])]) ).
fof(f462,axiom,
! [X39] :
( ~ class_Power_Orecpower(X39)
| class_OrderedGroup_Omonoid__mult(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_15) ).
fof(f4547,plain,
spl0_257,
inference(avatar_split_clause,[],[f461,f4545]) ).
fof(f4545,plain,
( spl0_257
<=> ! [X39] :
( ~ class_Power_Orecpower(X39)
| class_Ring__and__Field_Ocomm__semiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_257])]) ).
fof(f461,axiom,
! [X39] :
( ~ class_Power_Orecpower(X39)
| class_Ring__and__Field_Ocomm__semiring__0(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_14) ).
fof(f4543,plain,
spl0_256,
inference(avatar_split_clause,[],[f460,f4541]) ).
fof(f4541,plain,
( spl0_256
<=> ! [X39] :
( ~ class_Power_Orecpower(X39)
| class_Ring__and__Field_Osemiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_256])]) ).
fof(f460,axiom,
! [X39] :
( ~ class_Power_Orecpower(X39)
| class_Ring__and__Field_Osemiring__0(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_13) ).
fof(f4539,plain,
spl0_255,
inference(avatar_split_clause,[],[f459,f4537]) ).
fof(f4537,plain,
( spl0_255
<=> ! [X39] :
( ~ class_Power_Orecpower(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_255])]) ).
fof(f459,axiom,
! [X39] :
( ~ class_Power_Orecpower(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_12) ).
fof(f4535,plain,
spl0_254,
inference(avatar_split_clause,[],[f458,f4533]) ).
fof(f4533,plain,
( spl0_254
<=> ! [X39] :
( ~ class_Power_Orecpower(X39)
| class_Ring__and__Field_Ocomm__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_254])]) ).
fof(f458,axiom,
! [X39] :
( ~ class_Power_Orecpower(X39)
| class_Ring__and__Field_Ocomm__semiring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_11) ).
fof(f4531,plain,
spl0_253,
inference(avatar_split_clause,[],[f457,f4529]) ).
fof(f4529,plain,
( spl0_253
<=> ! [X39] :
( ~ class_Power_Orecpower(X39)
| class_Ring__and__Field_Osemiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_253])]) ).
fof(f457,axiom,
! [X39] :
( ~ class_Power_Orecpower(X39)
| class_Ring__and__Field_Osemiring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_10) ).
fof(f4527,plain,
spl0_252,
inference(avatar_split_clause,[],[f454,f4525]) ).
fof(f4525,plain,
( spl0_252
<=> ! [X39] :
( ~ class_Orderings_Oorder(X39)
| class_Orderings_Oord(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_252])]) ).
fof(f454,axiom,
! [X39] :
( ~ class_Orderings_Oorder(X39)
| class_Orderings_Oord(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Orderings_Oorder_0) ).
fof(f4523,plain,
spl0_251,
inference(avatar_split_clause,[],[f453,f4521]) ).
fof(f4521,plain,
( spl0_251
<=> ! [X39] :
( ~ class_Orderings_Olinorder(X39)
| class_Orderings_Oorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_251])]) ).
fof(f453,axiom,
! [X39] :
( ~ class_Orderings_Olinorder(X39)
| class_Orderings_Oorder(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Orderings_Olinorder_4) ).
fof(f4519,plain,
spl0_250,
inference(avatar_split_clause,[],[f452,f4517]) ).
fof(f4517,plain,
( spl0_250
<=> ! [X39] :
( ~ class_Orderings_Olinorder(X39)
| class_Orderings_Oord(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_250])]) ).
fof(f452,axiom,
! [X39] :
( ~ class_Orderings_Olinorder(X39)
| class_Orderings_Oord(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Orderings_Olinorder_3) ).
fof(f4515,plain,
spl0_249,
inference(avatar_split_clause,[],[f451,f4513]) ).
fof(f4513,plain,
( spl0_249
<=> ! [X39] :
( ~ class_Orderings_Olinorder(X39)
| class_LOrder_Omeet__semilorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_249])]) ).
fof(f451,axiom,
! [X39] :
( ~ class_Orderings_Olinorder(X39)
| class_LOrder_Omeet__semilorder(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Orderings_Olinorder_2) ).
fof(f4511,plain,
spl0_248,
inference(avatar_split_clause,[],[f450,f4509]) ).
fof(f4509,plain,
( spl0_248
<=> ! [X39] :
( ~ class_Orderings_Olinorder(X39)
| class_LOrder_Ojoin__semilorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_248])]) ).
fof(f450,axiom,
! [X39] :
( ~ class_Orderings_Olinorder(X39)
| class_LOrder_Ojoin__semilorder(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Orderings_Olinorder_1) ).
fof(f4507,plain,
spl0_247,
inference(avatar_split_clause,[],[f449,f4505]) ).
fof(f4505,plain,
( spl0_247
<=> ! [X39] :
( ~ class_Orderings_Olinorder(X39)
| class_LOrder_Olorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_247])]) ).
fof(f449,axiom,
! [X39] :
( ~ class_Orderings_Olinorder(X39)
| class_LOrder_Olorder(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Orderings_Olinorder_0) ).
fof(f4503,plain,
spl0_246,
inference(avatar_split_clause,[],[f446,f4501]) ).
fof(f4501,plain,
( spl0_246
<=> ! [X39] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_246])]) ).
fof(f446,axiom,
! [X39] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_7) ).
fof(f4499,plain,
spl0_245,
inference(avatar_split_clause,[],[f445,f4497]) ).
fof(f4497,plain,
( spl0_245
<=> ! [X39] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_245])]) ).
fof(f445,axiom,
! [X39] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_6) ).
fof(f4495,plain,
spl0_244,
inference(avatar_split_clause,[],[f441,f4493]) ).
fof(f4493,plain,
( spl0_244
<=> ! [X39] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39)
| class_Orderings_Oord(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_244])]) ).
fof(f441,axiom,
! [X39] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39)
| class_Orderings_Oord(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_2) ).
fof(f4491,plain,
spl0_243,
inference(avatar_split_clause,[],[f440,f4489]) ).
fof(f4489,plain,
( spl0_243
<=> ! [X39] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39)
| class_Orderings_Oorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_243])]) ).
fof(f440,axiom,
! [X39] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39)
| class_Orderings_Oorder(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_1) ).
fof(f4487,plain,
spl0_242,
inference(avatar_split_clause,[],[f439,f4485]) ).
fof(f4485,plain,
( spl0_242
<=> ! [X39] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_242])]) ).
fof(f439,axiom,
! [X39] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_0) ).
fof(f4483,plain,
spl0_241,
inference(avatar_split_clause,[],[f436,f4481]) ).
fof(f4481,plain,
( spl0_241
<=> ! [X39] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_241])]) ).
fof(f436,axiom,
! [X39] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_6) ).
fof(f4479,plain,
spl0_240,
inference(avatar_split_clause,[],[f434,f4477]) ).
fof(f4477,plain,
( spl0_240
<=> ! [X39] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_240])]) ).
fof(f434,axiom,
! [X39] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_4) ).
fof(f4475,plain,
spl0_239,
inference(avatar_split_clause,[],[f433,f4473]) ).
fof(f4473,plain,
( spl0_239
<=> ! [X39] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39)
| class_Orderings_Oord(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_239])]) ).
fof(f433,axiom,
! [X39] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39)
| class_Orderings_Oord(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_3) ).
fof(f4471,plain,
spl0_238,
inference(avatar_split_clause,[],[f432,f4469]) ).
fof(f4469,plain,
( spl0_238
<=> ! [X39] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39)
| class_Orderings_Oorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_238])]) ).
fof(f432,axiom,
! [X39] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39)
| class_Orderings_Oorder(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_2) ).
fof(f4467,plain,
spl0_237,
inference(avatar_split_clause,[],[f431,f4465]) ).
fof(f4465,plain,
( spl0_237
<=> ! [X39] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_237])]) ).
fof(f431,axiom,
! [X39] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_1) ).
fof(f4463,plain,
spl0_236,
inference(avatar_split_clause,[],[f430,f4461]) ).
fof(f4461,plain,
( spl0_236
<=> ! [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_236])]) ).
fof(f430,axiom,
! [X39] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_0) ).
fof(f4459,plain,
spl0_235,
inference(avatar_split_clause,[],[f426,f4457]) ).
fof(f4457,plain,
( spl0_235
<=> ! [X39] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X39)
| class_Orderings_Oord(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_235])]) ).
fof(f426,axiom,
! [X39] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X39)
| class_Orderings_Oord(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add_1) ).
fof(f4455,plain,
spl0_234,
inference(avatar_split_clause,[],[f425,f4453]) ).
fof(f4453,plain,
( spl0_234
<=> ! [X39] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X39)
| class_Orderings_Oorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_234])]) ).
fof(f425,axiom,
! [X39] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X39)
| class_Orderings_Oorder(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add_0) ).
fof(f4451,plain,
spl0_233,
inference(avatar_split_clause,[],[f424,f4449]) ).
fof(f4449,plain,
( spl0_233
<=> ! [X39] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_233])]) ).
fof(f424,axiom,
! [X39] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_9) ).
fof(f4447,plain,
spl0_232,
inference(avatar_split_clause,[],[f421,f4445]) ).
fof(f4445,plain,
( spl0_232
<=> ! [X39] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_232])]) ).
fof(f421,axiom,
! [X39] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_6) ).
fof(f4443,plain,
spl0_231,
inference(avatar_split_clause,[],[f419,f4441]) ).
fof(f4441,plain,
( spl0_231
<=> ! [X39] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_231])]) ).
fof(f419,axiom,
! [X39] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_4) ).
fof(f4439,plain,
spl0_230,
inference(avatar_split_clause,[],[f417,f4437]) ).
fof(f4437,plain,
( spl0_230
<=> ! [X39] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_230])]) ).
fof(f417,axiom,
! [X39] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_2) ).
fof(f4435,plain,
spl0_229,
inference(avatar_split_clause,[],[f416,f4433]) ).
fof(f4433,plain,
( spl0_229
<=> ! [X39] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X39)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_229])]) ).
fof(f416,axiom,
! [X39] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X39)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_13) ).
fof(f4431,plain,
spl0_228,
inference(avatar_split_clause,[],[f415,f4429]) ).
fof(f4429,plain,
( spl0_228
<=> ! [X39] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_228])]) ).
fof(f415,axiom,
! [X39] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_12) ).
fof(f4427,plain,
spl0_227,
inference(avatar_split_clause,[],[f414,f4425]) ).
fof(f4425,plain,
( spl0_227
<=> ! [X39] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X39)
| class_Orderings_Oord(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_227])]) ).
fof(f414,axiom,
! [X39] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X39)
| class_Orderings_Oord(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_11) ).
fof(f4423,plain,
spl0_226,
inference(avatar_split_clause,[],[f413,f4421]) ).
fof(f4421,plain,
( spl0_226
<=> ! [X39] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X39)
| class_Orderings_Oorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_226])]) ).
fof(f413,axiom,
! [X39] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X39)
| class_Orderings_Oorder(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_10) ).
fof(f4419,plain,
spl0_225,
inference(avatar_split_clause,[],[f411,f4417]) ).
fof(f4417,plain,
( spl0_225
<=> ! [X39] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X39)
| class_OrderedGroup_Oab__group__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_225])]) ).
fof(f411,axiom,
! [X39] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X39)
| class_OrderedGroup_Oab__group__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_0) ).
fof(f4415,plain,
spl0_224,
inference(avatar_split_clause,[],[f410,f4413]) ).
fof(f4413,plain,
( spl0_224
<=> ! [X39] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39)
| class_Orderings_Olinorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_224])]) ).
fof(f410,axiom,
! [X39] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39)
| class_Orderings_Olinorder(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_9) ).
fof(f4411,plain,
spl0_223,
inference(avatar_split_clause,[],[f407,f4409]) ).
fof(f4409,plain,
( spl0_223
<=> ! [X39] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_223])]) ).
fof(f407,axiom,
! [X39] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_6) ).
fof(f4407,plain,
spl0_222,
inference(avatar_split_clause,[],[f405,f4405]) ).
fof(f4405,plain,
( spl0_222
<=> ! [X39] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_222])]) ).
fof(f405,axiom,
! [X39] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_4) ).
fof(f4403,plain,
spl0_221,
inference(avatar_split_clause,[],[f404,f4401]) ).
fof(f4401,plain,
( spl0_221
<=> ! [X39] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39)
| class_Orderings_Oord(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_221])]) ).
fof(f404,axiom,
! [X39] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39)
| class_Orderings_Oord(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_3) ).
fof(f4399,plain,
spl0_220,
inference(avatar_split_clause,[],[f403,f4397]) ).
fof(f4397,plain,
( spl0_220
<=> ! [X39] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39)
| class_Orderings_Oorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_220])]) ).
fof(f403,axiom,
! [X39] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39)
| class_Orderings_Oorder(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_2) ).
fof(f4395,plain,
spl0_219,
inference(avatar_split_clause,[],[f402,f4393]) ).
fof(f4393,plain,
( spl0_219
<=> ! [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_219])]) ).
fof(f402,axiom,
! [X39] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_13) ).
fof(f4391,plain,
spl0_218,
inference(avatar_split_clause,[],[f401,f4389]) ).
fof(f4389,plain,
( spl0_218
<=> ! [X39] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39)
| class_LOrder_Omeet__semilorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_218])]) ).
fof(f401,axiom,
! [X39] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39)
| class_LOrder_Omeet__semilorder(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_12) ).
fof(f4387,plain,
spl0_217,
inference(avatar_split_clause,[],[f400,f4385]) ).
fof(f4385,plain,
( spl0_217
<=> ! [X39] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39)
| class_LOrder_Ojoin__semilorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_217])]) ).
fof(f400,axiom,
! [X39] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39)
| class_LOrder_Ojoin__semilorder(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_11) ).
fof(f4383,plain,
spl0_216,
inference(avatar_split_clause,[],[f399,f4381]) ).
fof(f4381,plain,
( spl0_216
<=> ! [X39] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39)
| class_LOrder_Olorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_216])]) ).
fof(f399,axiom,
! [X39] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39)
| class_LOrder_Olorder(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_10) ).
fof(f4379,plain,
spl0_215,
inference(avatar_split_clause,[],[f398,f4377]) ).
fof(f4377,plain,
( spl0_215
<=> ! [X39] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_215])]) ).
fof(f398,axiom,
! [X39] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_1) ).
fof(f4375,plain,
spl0_214,
inference(avatar_split_clause,[],[f397,f4373]) ).
fof(f4373,plain,
( spl0_214
<=> ! [X39] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_214])]) ).
fof(f397,axiom,
! [X39] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_0) ).
fof(f4371,plain,
spl0_213,
inference(avatar_split_clause,[],[f394,f4369]) ).
fof(f4369,plain,
( spl0_213
<=> ! [X39] :
( ~ class_OrderedGroup_Omonoid__mult(X39)
| class_HOL_Oone(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_213])]) ).
fof(f394,axiom,
! [X39] :
( ~ class_OrderedGroup_Omonoid__mult(X39)
| class_HOL_Oone(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Omonoid__mult_0) ).
fof(f4367,plain,
spl0_212,
inference(avatar_split_clause,[],[f393,f4365]) ).
fof(f4365,plain,
( spl0_212
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
| class_Orderings_Oord(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_212])]) ).
fof(f393,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
| class_Orderings_Oord(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_9) ).
fof(f4363,plain,
spl0_211,
inference(avatar_split_clause,[],[f392,f4361]) ).
fof(f4361,plain,
( spl0_211
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
| class_Orderings_Oorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_211])]) ).
fof(f392,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
| class_Orderings_Oorder(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_8) ).
fof(f4359,plain,
spl0_210,
inference(avatar_split_clause,[],[f391,f4357]) ).
fof(f4357,plain,
( spl0_210
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_210])]) ).
fof(f391,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_7) ).
fof(f4355,plain,
spl0_209,
inference(avatar_split_clause,[],[f390,f4353]) ).
fof(f4353,plain,
( spl0_209
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_209])]) ).
fof(f390,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_6) ).
fof(f4351,plain,
spl0_208,
inference(avatar_split_clause,[],[f389,f4349]) ).
fof(f4349,plain,
( spl0_208
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_208])]) ).
fof(f389,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_5) ).
fof(f4347,plain,
spl0_207,
inference(avatar_split_clause,[],[f387,f4345]) ).
fof(f4345,plain,
( spl0_207
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_207])]) ).
fof(f387,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_3) ).
fof(f4343,plain,
spl0_206,
inference(avatar_split_clause,[],[f385,f4341]) ).
fof(f4341,plain,
( spl0_206
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
| class_LOrder_Ojoin__semilorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_206])]) ).
fof(f385,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
| class_LOrder_Ojoin__semilorder(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_18) ).
fof(f4339,plain,
spl0_205,
inference(avatar_split_clause,[],[f384,f4337]) ).
fof(f4337,plain,
( spl0_205
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
| class_LOrder_Olorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_205])]) ).
fof(f384,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
| class_LOrder_Olorder(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_17) ).
fof(f4335,plain,
spl0_204,
inference(avatar_split_clause,[],[f383,f4333]) ).
fof(f4333,plain,
( spl0_204
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
| class_OrderedGroup_Olordered__ab__group(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_204])]) ).
fof(f383,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
| class_OrderedGroup_Olordered__ab__group(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_16) ).
fof(f4331,plain,
spl0_203,
inference(avatar_split_clause,[],[f382,f4329]) ).
fof(f4329,plain,
( spl0_203
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
| class_LOrder_Omeet__semilorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_203])]) ).
fof(f382,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
| class_LOrder_Omeet__semilorder(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_15) ).
fof(f4327,plain,
spl0_202,
inference(avatar_split_clause,[],[f379,f4325]) ).
fof(f4325,plain,
( spl0_202
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_202])]) ).
fof(f379,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_12) ).
fof(f4323,plain,
spl0_201,
inference(avatar_split_clause,[],[f377,f4321]) ).
fof(f4321,plain,
( spl0_201
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_201])]) ).
fof(f377,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_10) ).
fof(f4319,plain,
spl0_200,
inference(avatar_split_clause,[],[f376,f4317]) ).
fof(f4317,plain,
( spl0_200
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
| class_OrderedGroup_Oab__group__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_200])]) ).
fof(f376,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
| class_OrderedGroup_Oab__group__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_1) ).
fof(f4315,plain,
spl0_199,
inference(avatar_split_clause,[],[f375,f4313]) ).
fof(f4313,plain,
( spl0_199
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
| class_OrderedGroup_Opordered__ab__group__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_199])]) ).
fof(f375,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
| class_OrderedGroup_Opordered__ab__group__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_0) ).
fof(f4311,plain,
spl0_198,
inference(avatar_split_clause,[],[f374,f4309]) ).
fof(f4309,plain,
( spl0_198
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
| class_Orderings_Oord(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_198])]) ).
fof(f374,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
| class_Orderings_Oord(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_9) ).
fof(f4307,plain,
spl0_197,
inference(avatar_split_clause,[],[f373,f4305]) ).
fof(f4305,plain,
( spl0_197
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
| class_Orderings_Oorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_197])]) ).
fof(f373,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
| class_Orderings_Oorder(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_8) ).
fof(f4303,plain,
spl0_196,
inference(avatar_split_clause,[],[f372,f4301]) ).
fof(f4301,plain,
( spl0_196
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_196])]) ).
fof(f372,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_7) ).
fof(f4299,plain,
spl0_195,
inference(avatar_split_clause,[],[f371,f4297]) ).
fof(f4297,plain,
( spl0_195
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_195])]) ).
fof(f371,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_6) ).
fof(f4295,plain,
spl0_194,
inference(avatar_split_clause,[],[f370,f4293]) ).
fof(f4293,plain,
( spl0_194
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_194])]) ).
fof(f370,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_5) ).
fof(f4291,plain,
spl0_193,
inference(avatar_split_clause,[],[f368,f4289]) ).
fof(f4289,plain,
( spl0_193
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_193])]) ).
fof(f368,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_3) ).
fof(f4287,plain,
spl0_192,
inference(avatar_split_clause,[],[f366,f4285]) ).
fof(f4285,plain,
( spl0_192
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
| class_LOrder_Omeet__semilorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_192])]) ).
fof(f366,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
| class_LOrder_Omeet__semilorder(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_18) ).
fof(f4283,plain,
spl0_191,
inference(avatar_split_clause,[],[f365,f4281]) ).
fof(f4281,plain,
( spl0_191
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
| class_LOrder_Olorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_191])]) ).
fof(f365,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
| class_LOrder_Olorder(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_17) ).
fof(f4279,plain,
spl0_190,
inference(avatar_split_clause,[],[f364,f4277]) ).
fof(f4277,plain,
( spl0_190
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
| class_OrderedGroup_Olordered__ab__group(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_190])]) ).
fof(f364,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
| class_OrderedGroup_Olordered__ab__group(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_16) ).
fof(f4275,plain,
spl0_189,
inference(avatar_split_clause,[],[f363,f4273]) ).
fof(f4273,plain,
( spl0_189
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
| class_LOrder_Ojoin__semilorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_189])]) ).
fof(f363,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
| class_LOrder_Ojoin__semilorder(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_15) ).
fof(f4271,plain,
spl0_188,
inference(avatar_split_clause,[],[f360,f4269]) ).
fof(f4269,plain,
( spl0_188
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_188])]) ).
fof(f360,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_12) ).
fof(f4267,plain,
spl0_187,
inference(avatar_split_clause,[],[f358,f4265]) ).
fof(f4265,plain,
( spl0_187
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_187])]) ).
fof(f358,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_10) ).
fof(f4263,plain,
spl0_186,
inference(avatar_split_clause,[],[f357,f4261]) ).
fof(f4261,plain,
( spl0_186
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
| class_OrderedGroup_Oab__group__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_186])]) ).
fof(f357,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
| class_OrderedGroup_Oab__group__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_1) ).
fof(f4259,plain,
spl0_185,
inference(avatar_split_clause,[],[f356,f4257]) ).
fof(f4257,plain,
( spl0_185
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
| class_OrderedGroup_Opordered__ab__group__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_185])]) ).
fof(f356,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
| class_OrderedGroup_Opordered__ab__group__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_0) ).
fof(f4255,plain,
spl0_184,
inference(avatar_split_clause,[],[f355,f4253]) ).
fof(f4253,plain,
( spl0_184
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_184])]) ).
fof(f355,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_9) ).
fof(f4251,plain,
spl0_183,
inference(avatar_split_clause,[],[f354,f4249]) ).
fof(f4249,plain,
( spl0_183
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_183])]) ).
fof(f354,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_8) ).
fof(f4247,plain,
spl0_182,
inference(avatar_split_clause,[],[f353,f4245]) ).
fof(f4245,plain,
( spl0_182
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_182])]) ).
fof(f353,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_7) ).
fof(f4243,plain,
spl0_181,
inference(avatar_split_clause,[],[f352,f4241]) ).
fof(f4241,plain,
( spl0_181
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_181])]) ).
fof(f352,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_6) ).
fof(f4239,plain,
spl0_180,
inference(avatar_split_clause,[],[f350,f4237]) ).
fof(f4237,plain,
( spl0_180
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_180])]) ).
fof(f350,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_4) ).
fof(f4235,plain,
spl0_179,
inference(avatar_split_clause,[],[f348,f4233]) ).
fof(f4233,plain,
( spl0_179
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
| class_OrderedGroup_Oab__group__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_179])]) ).
fof(f348,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
| class_OrderedGroup_Oab__group__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_2) ).
fof(f4231,plain,
spl0_178,
inference(avatar_split_clause,[],[f347,f4229]) ).
fof(f4229,plain,
( spl0_178
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
| class_Orderings_Oord(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_178])]) ).
fof(f347,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
| class_Orderings_Oord(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_18) ).
fof(f4227,plain,
spl0_177,
inference(avatar_split_clause,[],[f346,f4225]) ).
fof(f4225,plain,
( spl0_177
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
| class_Orderings_Oorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_177])]) ).
fof(f346,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
| class_Orderings_Oorder(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_17) ).
fof(f4223,plain,
spl0_176,
inference(avatar_split_clause,[],[f345,f4221]) ).
fof(f4221,plain,
( spl0_176
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
| class_LOrder_Omeet__semilorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_176])]) ).
fof(f345,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
| class_LOrder_Omeet__semilorder(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_16) ).
fof(f4219,plain,
spl0_175,
inference(avatar_split_clause,[],[f344,f4217]) ).
fof(f4217,plain,
( spl0_175
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
| class_LOrder_Ojoin__semilorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_175])]) ).
fof(f344,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
| class_LOrder_Ojoin__semilorder(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_15) ).
fof(f4215,plain,
spl0_174,
inference(avatar_split_clause,[],[f343,f4213]) ).
fof(f4213,plain,
( spl0_174
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
| class_LOrder_Olorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_174])]) ).
fof(f343,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
| class_LOrder_Olorder(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_14) ).
fof(f4211,plain,
spl0_173,
inference(avatar_split_clause,[],[f340,f4209]) ).
fof(f4209,plain,
( spl0_173
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_173])]) ).
fof(f340,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_11) ).
fof(f4207,plain,
spl0_172,
inference(avatar_split_clause,[],[f338,f4205]) ).
fof(f4205,plain,
( spl0_172
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
| class_OrderedGroup_Opordered__ab__group__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_172])]) ).
fof(f338,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
| class_OrderedGroup_Opordered__ab__group__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_1) ).
fof(f4203,plain,
spl0_171,
inference(avatar_split_clause,[],[f337,f4201]) ).
fof(f4201,plain,
( spl0_171
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
| class_OrderedGroup_Olordered__ab__group(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_171])]) ).
fof(f337,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
| class_OrderedGroup_Olordered__ab__group(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_0) ).
fof(f4199,plain,
spl0_170,
inference(avatar_split_clause,[],[f336,f4197]) ).
fof(f4197,plain,
( spl0_170
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group(X39)
| class_Orderings_Oord(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_170])]) ).
fof(f336,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group(X39)
| class_Orderings_Oord(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_9) ).
fof(f4195,plain,
spl0_169,
inference(avatar_split_clause,[],[f335,f4193]) ).
fof(f4193,plain,
( spl0_169
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group(X39)
| class_Orderings_Oorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_169])]) ).
fof(f335,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group(X39)
| class_Orderings_Oorder(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_8) ).
fof(f4191,plain,
spl0_168,
inference(avatar_split_clause,[],[f334,f4189]) ).
fof(f4189,plain,
( spl0_168
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_168])]) ).
fof(f334,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_7) ).
fof(f4187,plain,
spl0_167,
inference(avatar_split_clause,[],[f333,f4185]) ).
fof(f4185,plain,
( spl0_167
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group(X39)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_167])]) ).
fof(f333,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group(X39)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_6) ).
fof(f4183,plain,
spl0_166,
inference(avatar_split_clause,[],[f332,f4181]) ).
fof(f4181,plain,
( spl0_166
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_166])]) ).
fof(f332,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_5) ).
fof(f4179,plain,
spl0_165,
inference(avatar_split_clause,[],[f330,f4177]) ).
fof(f4177,plain,
( spl0_165
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_165])]) ).
fof(f330,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_3) ).
fof(f4175,plain,
spl0_164,
inference(avatar_split_clause,[],[f328,f4173]) ).
fof(f4173,plain,
( spl0_164
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group(X39)
| class_LOrder_Omeet__semilorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_164])]) ).
fof(f328,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group(X39)
| class_LOrder_Omeet__semilorder(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_17) ).
fof(f4171,plain,
spl0_163,
inference(avatar_split_clause,[],[f327,f4169]) ).
fof(f4169,plain,
( spl0_163
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group(X39)
| class_LOrder_Ojoin__semilorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_163])]) ).
fof(f327,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group(X39)
| class_LOrder_Ojoin__semilorder(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_16) ).
fof(f4167,plain,
spl0_162,
inference(avatar_split_clause,[],[f326,f4165]) ).
fof(f4165,plain,
( spl0_162
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group(X39)
| class_LOrder_Olorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_162])]) ).
fof(f326,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group(X39)
| class_LOrder_Olorder(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_15) ).
fof(f4163,plain,
spl0_161,
inference(avatar_split_clause,[],[f323,f4161]) ).
fof(f4161,plain,
( spl0_161
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_161])]) ).
fof(f323,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_12) ).
fof(f4159,plain,
spl0_160,
inference(avatar_split_clause,[],[f321,f4157]) ).
fof(f4157,plain,
( spl0_160
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_160])]) ).
fof(f321,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_10) ).
fof(f4155,plain,
spl0_159,
inference(avatar_split_clause,[],[f320,f4153]) ).
fof(f4153,plain,
( spl0_159
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group(X39)
| class_OrderedGroup_Oab__group__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_159])]) ).
fof(f320,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group(X39)
| class_OrderedGroup_Oab__group__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_1) ).
fof(f4151,plain,
spl0_158,
inference(avatar_split_clause,[],[f319,f4149]) ).
fof(f4149,plain,
( spl0_158
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group(X39)
| class_OrderedGroup_Opordered__ab__group__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_158])]) ).
fof(f319,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group(X39)
| class_OrderedGroup_Opordered__ab__group__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_0) ).
fof(f4147,plain,
spl0_157,
inference(avatar_split_clause,[],[f318,f4145]) ).
fof(f4145,plain,
( spl0_157
<=> ! [X39] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X39)
| class_OrderedGroup_Omonoid__mult(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_157])]) ).
fof(f318,axiom,
! [X39] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X39)
| class_OrderedGroup_Omonoid__mult(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocomm__monoid__mult_4) ).
fof(f4143,plain,
spl0_156,
inference(avatar_split_clause,[],[f314,f4141]) ).
fof(f4141,plain,
( spl0_156
<=> ! [X39] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X39)
| class_HOL_Oone(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_156])]) ).
fof(f314,axiom,
! [X39] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X39)
| class_HOL_Oone(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocomm__monoid__mult_0) ).
fof(f4139,plain,
spl0_155,
inference(avatar_split_clause,[],[f307,f4137]) ).
fof(f4137,plain,
( spl0_155
<=> ! [X39] :
( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_155])]) ).
fof(f307,axiom,
! [X39] :
( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocancel__ab__semigroup__add_3) ).
fof(f4135,plain,
spl0_154,
inference(avatar_split_clause,[],[f299,f4133]) ).
fof(f4133,plain,
( spl0_154
<=> ! [X39] :
( ~ class_OrderedGroup_Oab__group__add(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_154])]) ).
fof(f299,axiom,
! [X39] :
( ~ class_OrderedGroup_Oab__group__add(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oab__group__add_7) ).
fof(f4131,plain,
spl0_153,
inference(avatar_split_clause,[],[f298,f4129]) ).
fof(f4129,plain,
( spl0_153
<=> ! [X39] :
( ~ class_OrderedGroup_Oab__group__add(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_153])]) ).
fof(f298,axiom,
! [X39] :
( ~ class_OrderedGroup_Oab__group__add(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oab__group__add_6) ).
fof(f4127,plain,
spl0_152,
inference(avatar_split_clause,[],[f293,f4125]) ).
fof(f4125,plain,
( spl0_152
<=> ! [X39] :
( ~ class_OrderedGroup_Oab__group__add(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_152])]) ).
fof(f293,axiom,
! [X39] :
( ~ class_OrderedGroup_Oab__group__add(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oab__group__add_1) ).
fof(f4123,plain,
spl0_151,
inference(avatar_split_clause,[],[f291,f4121]) ).
fof(f4121,plain,
( spl0_151
<=> ! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_151])]) ).
fof(f291,axiom,
! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_9) ).
fof(f4119,plain,
spl0_150,
inference(avatar_split_clause,[],[f289,f4117]) ).
fof(f4117,plain,
( spl0_150
<=> ! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_Ring__and__Field_Ocomm__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_150])]) ).
fof(f289,axiom,
! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_Ring__and__Field_Ocomm__semiring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_7) ).
fof(f4115,plain,
spl0_149,
inference(avatar_split_clause,[],[f288,f4113]) ).
fof(f4113,plain,
( spl0_149
<=> ! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_Ring__and__Field_Osemiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_149])]) ).
fof(f288,axiom,
! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_Ring__and__Field_Osemiring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_6) ).
fof(f4111,plain,
spl0_148,
inference(avatar_split_clause,[],[f285,f4109]) ).
fof(f4109,plain,
( spl0_148
<=> ! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_Numeral_Onumber(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_148])]) ).
fof(f285,axiom,
! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_Numeral_Onumber(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_30) ).
fof(f4107,plain,
spl0_147,
inference(avatar_split_clause,[],[f283,f4105]) ).
fof(f4105,plain,
( spl0_147
<=> ! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_Ring__and__Field_Ocomm__ring__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_147])]) ).
fof(f283,axiom,
! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_Ring__and__Field_Ocomm__ring__1(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_29) ).
fof(f4103,plain,
spl0_146,
inference(avatar_split_clause,[],[f282,f4101]) ).
fof(f4101,plain,
( spl0_146
<=> ! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_Ring__and__Field_Ocomm__semiring__1__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_146])]) ).
fof(f282,axiom,
! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_Ring__and__Field_Ocomm__semiring__1__cancel(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_28) ).
fof(f4099,plain,
spl0_145,
inference(avatar_split_clause,[],[f281,f4097]) ).
fof(f4097,plain,
( spl0_145
<=> ! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_Ring__and__Field_Oring__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_145])]) ).
fof(f281,axiom,
! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_Ring__and__Field_Oring__1(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_27) ).
fof(f4095,plain,
spl0_144,
inference(avatar_split_clause,[],[f280,f4093]) ).
fof(f4093,plain,
( spl0_144
<=> ! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_Ring__and__Field_Osemiring__1__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_144])]) ).
fof(f280,axiom,
! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_Ring__and__Field_Osemiring__1__cancel(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_26) ).
fof(f4091,plain,
spl0_143,
inference(avatar_split_clause,[],[f279,f4089]) ).
fof(f4089,plain,
( spl0_143
<=> ! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_Ring__and__Field_Ocomm__semiring__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_143])]) ).
fof(f279,axiom,
! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_Ring__and__Field_Ocomm__semiring__1(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_25) ).
fof(f4087,plain,
spl0_142,
inference(avatar_split_clause,[],[f278,f4085]) ).
fof(f4085,plain,
( spl0_142
<=> ! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_Ring__and__Field_Osemiring__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_142])]) ).
fof(f278,axiom,
! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_Ring__and__Field_Osemiring__1(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_24) ).
fof(f4083,plain,
spl0_141,
inference(avatar_split_clause,[],[f277,f4081]) ).
fof(f4081,plain,
( spl0_141
<=> ! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_OrderedGroup_Ocomm__monoid__mult(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_141])]) ).
fof(f277,axiom,
! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_OrderedGroup_Ocomm__monoid__mult(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_23) ).
fof(f4079,plain,
spl0_140,
inference(avatar_split_clause,[],[f276,f4077]) ).
fof(f4077,plain,
( spl0_140
<=> ! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_OrderedGroup_Omonoid__mult(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_140])]) ).
fof(f276,axiom,
! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_OrderedGroup_Omonoid__mult(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_22) ).
fof(f4075,plain,
spl0_139,
inference(avatar_split_clause,[],[f275,f4073]) ).
fof(f4073,plain,
( spl0_139
<=> ! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_Ring__and__Field_Oaxclass__0__neq__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_139])]) ).
fof(f275,axiom,
! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_Ring__and__Field_Oaxclass__0__neq__1(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_21) ).
fof(f4071,plain,
spl0_138,
inference(avatar_split_clause,[],[f274,f4069]) ).
fof(f4069,plain,
( spl0_138
<=> ! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_HOL_Oone(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_138])]) ).
fof(f274,axiom,
! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_HOL_Oone(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_20) ).
fof(f4067,plain,
spl0_137,
inference(avatar_split_clause,[],[f272,f4065]) ).
fof(f4065,plain,
( spl0_137
<=> ! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_Ring__and__Field_Ocomm__ring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_137])]) ).
fof(f272,axiom,
! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_Ring__and__Field_Ocomm__ring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_19) ).
fof(f4063,plain,
spl0_136,
inference(avatar_split_clause,[],[f271,f4061]) ).
fof(f4061,plain,
( spl0_136
<=> ! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_136])]) ).
fof(f271,axiom,
! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_18) ).
fof(f4059,plain,
spl0_135,
inference(avatar_split_clause,[],[f270,f4057]) ).
fof(f4057,plain,
( spl0_135
<=> ! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_Ring__and__Field_Oring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_135])]) ).
fof(f270,axiom,
! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_Ring__and__Field_Oring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_17) ).
fof(f4055,plain,
spl0_134,
inference(avatar_split_clause,[],[f269,f4053]) ).
fof(f4053,plain,
( spl0_134
<=> ! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_134])]) ).
fof(f269,axiom,
! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_16) ).
fof(f4051,plain,
spl0_133,
inference(avatar_split_clause,[],[f268,f4049]) ).
fof(f4049,plain,
( spl0_133
<=> ! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_OrderedGroup_Oab__group__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_133])]) ).
fof(f268,axiom,
! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_OrderedGroup_Oab__group__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_15) ).
fof(f4047,plain,
spl0_132,
inference(avatar_split_clause,[],[f267,f4045]) ).
fof(f4045,plain,
( spl0_132
<=> ! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_132])]) ).
fof(f267,axiom,
! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_14) ).
fof(f4043,plain,
spl0_131,
inference(avatar_split_clause,[],[f266,f4041]) ).
fof(f4041,plain,
( spl0_131
<=> ! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_131])]) ).
fof(f266,axiom,
! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_13) ).
fof(f4039,plain,
spl0_130,
inference(avatar_split_clause,[],[f264,f4037]) ).
fof(f4037,plain,
( spl0_130
<=> ! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_Ring__and__Field_Ocomm__semiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_130])]) ).
fof(f264,axiom,
! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_Ring__and__Field_Ocomm__semiring__0(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_11) ).
fof(f4035,plain,
spl0_129,
inference(avatar_split_clause,[],[f263,f4033]) ).
fof(f4033,plain,
( spl0_129
<=> ! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_Ring__and__Field_Osemiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_129])]) ).
fof(f263,axiom,
! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_Ring__and__Field_Osemiring__0(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_10) ).
fof(f4031,plain,
spl0_128,
inference(avatar_split_clause,[],[f260,f4029]) ).
fof(f4029,plain,
( spl0_128
<=> ! [X39] :
( ~ class_LOrder_Omeet__semilorder(X39)
| class_Orderings_Oorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_128])]) ).
fof(f260,axiom,
! [X39] :
( ~ class_LOrder_Omeet__semilorder(X39)
| class_Orderings_Oorder(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_LOrder_Omeet__semilorder_1) ).
fof(f4027,plain,
spl0_127,
inference(avatar_split_clause,[],[f259,f4025]) ).
fof(f4025,plain,
( spl0_127
<=> ! [X39] :
( ~ class_LOrder_Omeet__semilorder(X39)
| class_Orderings_Oord(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_127])]) ).
fof(f259,axiom,
! [X39] :
( ~ class_LOrder_Omeet__semilorder(X39)
| class_Orderings_Oord(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_LOrder_Omeet__semilorder_0) ).
fof(f4023,plain,
spl0_126,
inference(avatar_split_clause,[],[f258,f4021]) ).
fof(f4021,plain,
( spl0_126
<=> ! [X39] :
( ~ class_LOrder_Olorder(X39)
| class_LOrder_Ojoin__semilorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_126])]) ).
fof(f258,axiom,
! [X39] :
( ~ class_LOrder_Olorder(X39)
| class_LOrder_Ojoin__semilorder(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_LOrder_Olorder_3) ).
fof(f4019,plain,
spl0_125,
inference(avatar_split_clause,[],[f257,f4017]) ).
fof(f4017,plain,
( spl0_125
<=> ! [X39] :
( ~ class_LOrder_Olorder(X39)
| class_Orderings_Oorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_125])]) ).
fof(f257,axiom,
! [X39] :
( ~ class_LOrder_Olorder(X39)
| class_Orderings_Oorder(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_LOrder_Olorder_2) ).
fof(f4015,plain,
spl0_124,
inference(avatar_split_clause,[],[f256,f4013]) ).
fof(f4013,plain,
( spl0_124
<=> ! [X39] :
( ~ class_LOrder_Olorder(X39)
| class_Orderings_Oord(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_124])]) ).
fof(f256,axiom,
! [X39] :
( ~ class_LOrder_Olorder(X39)
| class_Orderings_Oord(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_LOrder_Olorder_1) ).
fof(f4011,plain,
spl0_123,
inference(avatar_split_clause,[],[f255,f4009]) ).
fof(f4009,plain,
( spl0_123
<=> ! [X39] :
( ~ class_LOrder_Olorder(X39)
| class_LOrder_Omeet__semilorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_123])]) ).
fof(f255,axiom,
! [X39] :
( ~ class_LOrder_Olorder(X39)
| class_LOrder_Omeet__semilorder(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_LOrder_Olorder_0) ).
fof(f4007,plain,
spl0_122,
inference(avatar_split_clause,[],[f254,f4005]) ).
fof(f4005,plain,
( spl0_122
<=> ! [X39] :
( ~ class_LOrder_Ojoin__semilorder(X39)
| class_Orderings_Oorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_122])]) ).
fof(f254,axiom,
! [X39] :
( ~ class_LOrder_Ojoin__semilorder(X39)
| class_Orderings_Oorder(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_LOrder_Ojoin__semilorder_1) ).
fof(f4003,plain,
spl0_121,
inference(avatar_split_clause,[],[f253,f4001]) ).
fof(f4001,plain,
( spl0_121
<=> ! [X39] :
( ~ class_LOrder_Ojoin__semilorder(X39)
| class_Orderings_Oord(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_121])]) ).
fof(f253,axiom,
! [X39] :
( ~ class_LOrder_Ojoin__semilorder(X39)
| class_Orderings_Oord(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_LOrder_Ojoin__semilorder_0) ).
fof(f3999,plain,
spl0_120,
inference(avatar_split_clause,[],[f98,f3997]) ).
fof(f98,axiom,
! [X0,X1] : c_in(X0,c_UNIV,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUNIV__I_0) ).
fof(f3995,plain,
spl0_119,
inference(avatar_split_clause,[],[f66,f3993]) ).
fof(f3993,plain,
( spl0_119
<=> ! [X21] : ~ c_less(X21,X21,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_119])]) ).
fof(f66,axiom,
! [X21] : ~ c_less(X21,X21,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oless__irrefl_0) ).
fof(f3991,plain,
spl0_118,
inference(avatar_split_clause,[],[f64,f3989]) ).
fof(f64,axiom,
! [X21] : c_lessequals(c_0,X21,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Ole0_0) ).
fof(f3987,plain,
spl0_117,
inference(avatar_split_clause,[],[f40,f3985]) ).
fof(f3985,plain,
( spl0_117
<=> ! [X15] : c_Divides_Oop_Advd(c_1,X15,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_117])]) ).
fof(f40,axiom,
! [X15] : c_Divides_Oop_Advd(c_1,X15,tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozdvd__1__left_0) ).
fof(f3983,plain,
spl0_116,
inference(avatar_split_clause,[],[f39,f3981]) ).
fof(f3981,plain,
( spl0_116
<=> ! [X15] : c_Divides_Oop_Advd(X15,c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_116])]) ).
fof(f39,axiom,
! [X15] : c_Divides_Oop_Advd(X15,c_0,tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozdvd__0__right_0) ).
fof(f3979,plain,
spl0_115,
inference(avatar_split_clause,[],[f23,f3977]) ).
fof(f3977,plain,
( spl0_115
<=> ! [X15] : c_Divides_Oop_Advd(X15,c_0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_115])]) ).
fof(f23,axiom,
! [X15] : c_Divides_Oop_Advd(X15,c_0,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Odvd__0__right_0) ).
fof(f3975,plain,
~ spl0_114,
inference(avatar_split_clause,[],[f2951,f3972]) ).
fof(f2951,axiom,
~ c_in(c_Event_Oevent_ONotes(c_Message_Oagent_OSpy,c_Message_Omsg_OMPair(v_na,c_Message_Omsg_OMPair(v_nb,c_Message_Omsg_OKey(v_K)))),c_List_Oset(v_evso,tc_Event_Oevent),tc_Event_Oevent),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_5) ).
fof(f3970,plain,
~ spl0_113,
inference(avatar_split_clause,[],[f2904,f3967]) ).
fof(f3967,plain,
( spl0_113
<=> c_Public_Okeymode_OSignature = c_Public_Okeymode_OEncryption ),
introduced(avatar_definition,[new_symbols(naming,[spl0_113])]) ).
fof(f2904,axiom,
c_Public_Okeymode_OSignature != c_Public_Okeymode_OEncryption,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Public_Okeymode_Odistinct__2_0) ).
fof(f3965,plain,
~ spl0_112,
inference(avatar_split_clause,[],[f2732,f3962]) ).
fof(f3962,plain,
( spl0_112
<=> c_Message_Oagent_OServer = c_Message_Oagent_OSpy ),
introduced(avatar_definition,[new_symbols(naming,[spl0_112])]) ).
fof(f2732,axiom,
c_Message_Oagent_OServer != c_Message_Oagent_OSpy,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oagent_Odistinct__3_0) ).
fof(f3960,plain,
~ spl0_111,
inference(avatar_split_clause,[],[f2629,f3957]) ).
fof(f3957,plain,
( spl0_111
<=> c_emptyset = c_UNIV ),
introduced(avatar_definition,[new_symbols(naming,[spl0_111])]) ).
fof(f2629,axiom,
c_emptyset != c_UNIV,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUNIV__not__empty_0) ).
fof(f3955,plain,
~ spl0_110,
inference(avatar_split_clause,[],[f2310,f3952]) ).
fof(f3952,plain,
( spl0_110
<=> c_Parity_Oeven(c_1,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_110])]) ).
fof(f2310,axiom,
~ c_Parity_Oeven(c_1,tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oodd__one_0) ).
fof(f3950,plain,
spl0_109,
inference(avatar_split_clause,[],[f2303,f3947]) ).
fof(f3947,plain,
( spl0_109
<=> c_Parity_Oeven(c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_109])]) ).
fof(f2303,axiom,
c_Parity_Oeven(c_0,tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__zero_0) ).
fof(f3945,plain,
spl0_108,
inference(avatar_split_clause,[],[f2290,f3942]) ).
fof(f3942,plain,
( spl0_108
<=> c_Parity_Oeven(c_0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_108])]) ).
fof(f2290,axiom,
c_Parity_Oeven(c_0,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__nat__zero_0) ).
fof(f3940,plain,
~ spl0_107,
inference(avatar_split_clause,[],[f2159,f3937]) ).
fof(f3937,plain,
( spl0_107
<=> c_Numeral_Obit_OB1 = c_Numeral_Obit_OB0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_107])]) ).
fof(f2159,axiom,
c_Numeral_Obit_OB1 != c_Numeral_Obit_OB0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obit_Odistinct__1_0) ).
fof(f3935,plain,
spl0_106,
inference(avatar_split_clause,[],[f1706,f3933]) ).
fof(f3933,plain,
( spl0_106
<=> ! [X41] : c_List_Onull(c_List_Olist_ONil,X41) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_106])]) ).
fof(f1706,axiom,
! [X41] : c_List_Onull(c_List_Olist_ONil,X41),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Onull_Osimps__1_0) ).
fof(f3931,plain,
spl0_105,
inference(avatar_split_clause,[],[f1551,f3929]) ).
fof(f3929,plain,
( spl0_105
<=> ! [X41] : c_List_Odistinct(c_List_Olist_ONil,X41) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_105])]) ).
fof(f1551,axiom,
! [X41] : c_List_Odistinct(c_List_Olist_ONil,X41),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Odistinct_Osimps__1_0) ).
fof(f3927,plain,
~ spl0_104,
inference(avatar_split_clause,[],[f1370,f3924]) ).
fof(f1370,axiom,
c_0 != c_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oint__0__neq__1_0) ).
fof(f3922,plain,
~ spl0_103,
inference(avatar_split_clause,[],[f1251,f3919]) ).
fof(f3919,plain,
( spl0_103
<=> c_Extraction_Osumbool_OLeft = c_Extraction_Osumbool_ORight ),
introduced(avatar_definition,[new_symbols(naming,[spl0_103])]) ).
fof(f1251,axiom,
c_Extraction_Osumbool_OLeft != c_Extraction_Osumbool_ORight,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Extraction_Osumbool_Odistinct__2_0) ).
fof(f3917,plain,
spl0_102,
inference(avatar_split_clause,[],[f249,f3915]) ).
fof(f3915,plain,
( spl0_102
<=> ! [X37] : class_Orderings_Oorder(tc_set(X37)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_102])]) ).
fof(f249,axiom,
! [X37] : class_Orderings_Oorder(tc_set(X37)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_set_2) ).
fof(f3913,plain,
spl0_101,
inference(avatar_split_clause,[],[f248,f3911]) ).
fof(f3911,plain,
( spl0_101
<=> ! [X37] : class_Orderings_Oord(tc_set(X37)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_101])]) ).
fof(f248,axiom,
! [X37] : class_Orderings_Oord(tc_set(X37)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_set_1) ).
fof(f3909,plain,
spl0_100,
inference(avatar_split_clause,[],[f126,f3906]) ).
fof(f3906,plain,
( spl0_100
<=> c_Wellfounded__Recursion_Owf(c_Wellfounded__Relations_Oless__than,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_100])]) ).
fof(f126,axiom,
c_Wellfounded__Recursion_Owf(c_Wellfounded__Relations_Oless__than,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Relations_Owf__less__than_0) ).
fof(f3904,plain,
spl0_99,
inference(avatar_split_clause,[],[f124,f3901]) ).
fof(f3901,plain,
( spl0_99
<=> c_Relation_Otrans(c_Wellfounded__Relations_Oless__than,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_99])]) ).
fof(f124,axiom,
c_Relation_Otrans(c_Wellfounded__Relations_Oless__than,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Relations_Otrans__less__than_0) ).
fof(f3899,plain,
spl0_98,
inference(avatar_split_clause,[],[f123,f3897]) ).
fof(f3897,plain,
( spl0_98
<=> ! [X1] : c_Wellfounded__Recursion_Owf(c_emptyset,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_98])]) ).
fof(f123,axiom,
! [X1] : c_Wellfounded__Recursion_Owf(c_emptyset,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Owf__empty_0) ).
fof(f3895,plain,
spl0_97,
inference(avatar_split_clause,[],[f244,f3892]) ).
fof(f3892,plain,
( spl0_97
<=> class_Wellfounded__Recursion_Owellorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_97])]) ).
fof(f244,axiom,
class_Wellfounded__Recursion_Owellorder(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_8) ).
fof(f3890,plain,
spl0_96,
inference(avatar_split_clause,[],[f243,f3887]) ).
fof(f243,axiom,
class_Orderings_Olinorder(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_7) ).
fof(f3885,plain,
spl0_95,
inference(avatar_split_clause,[],[f242,f3882]) ).
fof(f3882,plain,
( spl0_95
<=> class_LOrder_Olorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_95])]) ).
fof(f242,axiom,
class_LOrder_Olorder(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_6) ).
fof(f3880,plain,
spl0_94,
inference(avatar_split_clause,[],[f241,f3877]) ).
fof(f241,axiom,
class_LOrder_Ojoin__semilorder(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_5) ).
fof(f3875,plain,
spl0_93,
inference(avatar_split_clause,[],[f239,f3872]) ).
fof(f3872,plain,
( spl0_93
<=> class_Numeral_Onumber(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_93])]) ).
fof(f239,axiom,
class_Numeral_Onumber(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_46) ).
fof(f3870,plain,
spl0_92,
inference(avatar_split_clause,[],[f238,f3867]) ).
fof(f238,axiom,
class_Power_Orecpower(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_45) ).
fof(f3865,plain,
spl0_91,
inference(avatar_split_clause,[],[f236,f3862]) ).
fof(f3862,plain,
( spl0_91
<=> class_Ring__and__Field_Oordered__semidom(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_91])]) ).
fof(f236,axiom,
class_Ring__and__Field_Oordered__semidom(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_43) ).
fof(f3860,plain,
spl0_90,
inference(avatar_split_clause,[],[f235,f3857]) ).
fof(f3857,plain,
( spl0_90
<=> class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_90])]) ).
fof(f235,axiom,
class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_42) ).
fof(f3855,plain,
spl0_89,
inference(avatar_split_clause,[],[f234,f3852]) ).
fof(f3852,plain,
( spl0_89
<=> class_Ring__and__Field_Opordered__cancel__comm__semiring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_89])]) ).
fof(f234,axiom,
class_Ring__and__Field_Opordered__cancel__comm__semiring(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_41) ).
fof(f3850,plain,
spl0_88,
inference(avatar_split_clause,[],[f233,f3847]) ).
fof(f3847,plain,
( spl0_88
<=> class_Ring__and__Field_Opordered__comm__semiring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_88])]) ).
fof(f233,axiom,
class_Ring__and__Field_Opordered__comm__semiring(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_40) ).
fof(f3845,plain,
spl0_87,
inference(avatar_split_clause,[],[f232,f3842]) ).
fof(f232,axiom,
class_LOrder_Omeet__semilorder(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_4) ).
fof(f3840,plain,
spl0_86,
inference(avatar_split_clause,[],[f231,f3837]) ).
fof(f3837,plain,
( spl0_86
<=> class_Ring__and__Field_Oordered__semiring__strict(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_86])]) ).
fof(f231,axiom,
class_Ring__and__Field_Oordered__semiring__strict(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_39) ).
fof(f3835,plain,
spl0_85,
inference(avatar_split_clause,[],[f230,f3832]) ).
fof(f3832,plain,
( spl0_85
<=> class_Ring__and__Field_Opordered__cancel__semiring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_85])]) ).
fof(f230,axiom,
class_Ring__and__Field_Opordered__cancel__semiring(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_38) ).
fof(f3830,plain,
spl0_84,
inference(avatar_split_clause,[],[f229,f3827]) ).
fof(f3827,plain,
( spl0_84
<=> class_Ring__and__Field_Opordered__semiring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_84])]) ).
fof(f229,axiom,
class_Ring__and__Field_Opordered__semiring(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_37) ).
fof(f3825,plain,
spl0_83,
inference(avatar_split_clause,[],[f228,f3822]) ).
fof(f3822,plain,
( spl0_83
<=> class_OrderedGroup_Oordered__cancel__ab__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_83])]) ).
fof(f228,axiom,
class_OrderedGroup_Oordered__cancel__ab__semigroup__add(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_36) ).
fof(f3820,plain,
spl0_82,
inference(avatar_split_clause,[],[f227,f3817]) ).
fof(f3817,plain,
( spl0_82
<=> class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_82])]) ).
fof(f227,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_35) ).
fof(f3815,plain,
spl0_81,
inference(avatar_split_clause,[],[f226,f3812]) ).
fof(f3812,plain,
( spl0_81
<=> class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_81])]) ).
fof(f226,axiom,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_34) ).
fof(f3810,plain,
spl0_80,
inference(avatar_split_clause,[],[f225,f3807]) ).
fof(f3807,plain,
( spl0_80
<=> class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_80])]) ).
fof(f225,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_33) ).
fof(f3805,plain,
spl0_79,
inference(avatar_split_clause,[],[f224,f3802]) ).
fof(f224,axiom,
class_Ring__and__Field_Ocomm__semiring__1__cancel(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_32) ).
fof(f3800,plain,
spl0_78,
inference(avatar_split_clause,[],[f223,f3797]) ).
fof(f3797,plain,
( spl0_78
<=> class_Ring__and__Field_Ocomm__semiring__0__cancel(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_78])]) ).
fof(f223,axiom,
class_Ring__and__Field_Ocomm__semiring__0__cancel(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_31) ).
fof(f3795,plain,
spl0_77,
inference(avatar_split_clause,[],[f222,f3792]) ).
fof(f3792,plain,
( spl0_77
<=> class_Ring__and__Field_Osemiring__1__cancel(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_77])]) ).
fof(f222,axiom,
class_Ring__and__Field_Osemiring__1__cancel(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_30) ).
fof(f3790,plain,
spl0_76,
inference(avatar_split_clause,[],[f221,f3787]) ).
fof(f221,axiom,
class_Orderings_Oorder(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_3) ).
fof(f3785,plain,
spl0_75,
inference(avatar_split_clause,[],[f220,f3782]) ).
fof(f3782,plain,
( spl0_75
<=> class_Ring__and__Field_Osemiring__0__cancel(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_75])]) ).
fof(f220,axiom,
class_Ring__and__Field_Osemiring__0__cancel(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_29) ).
fof(f3780,plain,
spl0_74,
inference(avatar_split_clause,[],[f219,f3777]) ).
fof(f3777,plain,
( spl0_74
<=> class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_74])]) ).
fof(f219,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_28) ).
fof(f3775,plain,
spl0_73,
inference(avatar_split_clause,[],[f218,f3772]) ).
fof(f3772,plain,
( spl0_73
<=> class_OrderedGroup_Ocancel__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_73])]) ).
fof(f218,axiom,
class_OrderedGroup_Ocancel__semigroup__add(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_27) ).
fof(f3770,plain,
spl0_72,
inference(avatar_split_clause,[],[f217,f3767]) ).
fof(f3767,plain,
( spl0_72
<=> class_Ring__and__Field_Ocomm__semiring__1(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_72])]) ).
fof(f217,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_26) ).
fof(f3765,plain,
spl0_71,
inference(avatar_split_clause,[],[f216,f3762]) ).
fof(f3762,plain,
( spl0_71
<=> class_Ring__and__Field_Osemiring__1(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_71])]) ).
fof(f216,axiom,
class_Ring__and__Field_Osemiring__1(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_25) ).
fof(f3760,plain,
spl0_70,
inference(avatar_split_clause,[],[f215,f3757]) ).
fof(f3757,plain,
( spl0_70
<=> class_OrderedGroup_Ocomm__monoid__mult(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_70])]) ).
fof(f215,axiom,
class_OrderedGroup_Ocomm__monoid__mult(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_24) ).
fof(f3755,plain,
spl0_69,
inference(avatar_split_clause,[],[f214,f3752]) ).
fof(f214,axiom,
class_OrderedGroup_Omonoid__mult(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_23) ).
fof(f3750,plain,
spl0_68,
inference(avatar_split_clause,[],[f213,f3747]) ).
fof(f3747,plain,
( spl0_68
<=> class_Ring__and__Field_Ocomm__semiring__0(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_68])]) ).
fof(f213,axiom,
class_Ring__and__Field_Ocomm__semiring__0(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_22) ).
fof(f3745,plain,
spl0_67,
inference(avatar_split_clause,[],[f212,f3742]) ).
fof(f3742,plain,
( spl0_67
<=> class_Ring__and__Field_Osemiring__0(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_67])]) ).
fof(f212,axiom,
class_Ring__and__Field_Osemiring__0(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_21) ).
fof(f3740,plain,
spl0_66,
inference(avatar_split_clause,[],[f211,f3737]) ).
fof(f3737,plain,
( spl0_66
<=> class_OrderedGroup_Ocomm__monoid__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_66])]) ).
fof(f211,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_20) ).
fof(f3735,plain,
spl0_65,
inference(avatar_split_clause,[],[f210,f3732]) ).
fof(f3732,plain,
( spl0_65
<=> class_Orderings_Oord(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_65])]) ).
fof(f210,axiom,
class_Orderings_Oord(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_2) ).
fof(f3730,plain,
spl0_64,
inference(avatar_split_clause,[],[f209,f3727]) ).
fof(f3727,plain,
( spl0_64
<=> class_Ring__and__Field_Ocomm__semiring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_64])]) ).
fof(f209,axiom,
class_Ring__and__Field_Ocomm__semiring(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_19) ).
fof(f3725,plain,
spl0_63,
inference(avatar_split_clause,[],[f208,f3722]) ).
fof(f3722,plain,
( spl0_63
<=> class_Ring__and__Field_Osemiring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_63])]) ).
fof(f208,axiom,
class_Ring__and__Field_Osemiring(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_18) ).
fof(f3720,plain,
spl0_62,
inference(avatar_split_clause,[],[f203,f3717]) ).
fof(f3717,plain,
( spl0_62
<=> class_Ring__and__Field_Oaxclass__0__neq__1(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_62])]) ).
fof(f203,axiom,
class_Ring__and__Field_Oaxclass__0__neq__1(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_13) ).
fof(f3715,plain,
spl0_61,
inference(avatar_split_clause,[],[f198,f3712]) ).
fof(f3712,plain,
( spl0_61
<=> class_HOL_Oone(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_61])]) ).
fof(f198,axiom,
class_HOL_Oone(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_0) ).
fof(f3710,plain,
spl0_60,
inference(avatar_split_clause,[],[f195,f3707]) ).
fof(f3707,plain,
( spl0_60
<=> class_Finite__Set_Ofinite(tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_60])]) ).
fof(f195,axiom,
class_Finite__Set_Ofinite(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool_0) ).
fof(f3705,plain,
spl0_59,
inference(avatar_split_clause,[],[f194,f3702]) ).
fof(f3702,plain,
( spl0_59
<=> class_Finite__Set_Ofinite(tc_Product__Type_Ounit) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_59])]) ).
fof(f194,axiom,
class_Finite__Set_Ofinite(tc_Product__Type_Ounit),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Product____Type__Ounit_0) ).
fof(f3700,plain,
spl0_58,
inference(avatar_split_clause,[],[f189,f3697]) ).
fof(f189,axiom,
class_Power_Orecpower(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_63) ).
fof(f3695,plain,
spl0_57,
inference(avatar_split_clause,[],[f186,f3692]) ).
fof(f186,axiom,
class_Numeral_Onumber__ring(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_60) ).
fof(f3690,plain,
spl0_56,
inference(avatar_split_clause,[],[f184,f3687]) ).
fof(f3687,plain,
( spl0_56
<=> class_Numeral_Onumber(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_56])]) ).
fof(f184,axiom,
class_Numeral_Onumber(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_59) ).
fof(f3685,plain,
spl0_55,
inference(avatar_split_clause,[],[f183,f3682]) ).
fof(f183,axiom,
class_Ring__and__Field_Oordered__idom(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_58) ).
fof(f3680,plain,
spl0_54,
inference(avatar_split_clause,[],[f182,f3677]) ).
fof(f3677,plain,
( spl0_54
<=> class_Ring__and__Field_Oidom(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_54])]) ).
fof(f182,axiom,
class_Ring__and__Field_Oidom(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_57) ).
fof(f3675,plain,
spl0_53,
inference(avatar_split_clause,[],[f181,f3672]) ).
fof(f181,axiom,
class_Ring__and__Field_Oordered__semidom(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_56) ).
fof(f3670,plain,
spl0_52,
inference(avatar_split_clause,[],[f180,f3667]) ).
fof(f3667,plain,
( spl0_52
<=> class_Ring__and__Field_Oordered__ring__strict(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_52])]) ).
fof(f180,axiom,
class_Ring__and__Field_Oordered__ring__strict(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_55) ).
fof(f3665,plain,
spl0_51,
inference(avatar_split_clause,[],[f178,f3662]) ).
fof(f3662,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/benchmark/theBenchmark.p',clsarity_IntDef__Oint_53) ).
fof(f3660,plain,
spl0_50,
inference(avatar_split_clause,[],[f177,f3657]) ).
fof(f3657,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/benchmark/theBenchmark.p',clsarity_IntDef__Oint_52) ).
fof(f3655,plain,
spl0_49,
inference(avatar_split_clause,[],[f176,f3652]) ).
fof(f3652,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/benchmark/theBenchmark.p',clsarity_IntDef__Oint_51) ).
fof(f3650,plain,
spl0_48,
inference(avatar_split_clause,[],[f175,f3647]) ).
fof(f3647,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/benchmark/theBenchmark.p',clsarity_IntDef__Oint_50) ).
fof(f3645,plain,
spl0_47,
inference(avatar_split_clause,[],[f174,f3642]) ).
fof(f3642,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/benchmark/theBenchmark.p',clsarity_IntDef__Oint_5) ).
fof(f3640,plain,
spl0_46,
inference(avatar_split_clause,[],[f173,f3637]) ).
fof(f3637,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/benchmark/theBenchmark.p',clsarity_IntDef__Oint_49) ).
fof(f3635,plain,
spl0_45,
inference(avatar_split_clause,[],[f172,f3632]) ).
fof(f172,axiom,
class_OrderedGroup_Olordered__ab__group(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_48) ).
fof(f3630,plain,
spl0_44,
inference(avatar_split_clause,[],[f171,f3627]) ).
fof(f171,axiom,
class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_47) ).
fof(f3625,plain,
spl0_43,
inference(avatar_split_clause,[],[f170,f3622]) ).
fof(f3622,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/benchmark/theBenchmark.p',clsarity_IntDef__Oint_46) ).
fof(f3620,plain,
spl0_42,
inference(avatar_split_clause,[],[f169,f3617]) ).
fof(f3617,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/benchmark/theBenchmark.p',clsarity_IntDef__Oint_45) ).
fof(f3615,plain,
spl0_41,
inference(avatar_split_clause,[],[f168,f3612]) ).
fof(f3612,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/benchmark/theBenchmark.p',clsarity_IntDef__Oint_44) ).
fof(f3610,plain,
spl0_40,
inference(avatar_split_clause,[],[f167,f3607]) ).
fof(f3607,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/benchmark/theBenchmark.p',clsarity_IntDef__Oint_43) ).
fof(f3605,plain,
spl0_39,
inference(avatar_split_clause,[],[f166,f3602]) ).
fof(f3602,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/benchmark/theBenchmark.p',clsarity_IntDef__Oint_42) ).
fof(f3600,plain,
spl0_38,
inference(avatar_split_clause,[],[f165,f3597]) ).
fof(f3597,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/benchmark/theBenchmark.p',clsarity_IntDef__Oint_41) ).
fof(f3595,plain,
spl0_37,
inference(avatar_split_clause,[],[f164,f3592]) ).
fof(f3592,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/benchmark/theBenchmark.p',clsarity_IntDef__Oint_40) ).
fof(f3590,plain,
spl0_36,
inference(avatar_split_clause,[],[f162,f3587]) ).
fof(f3587,plain,
( spl0_36
<=> class_OrderedGroup_Oordered__cancel__ab__semigroup__add(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_36])]) ).
fof(f162,axiom,
class_OrderedGroup_Oordered__cancel__ab__semigroup__add(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_39) ).
fof(f3585,plain,
spl0_35,
inference(avatar_split_clause,[],[f161,f3582]) ).
fof(f3582,plain,
( spl0_35
<=> class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_35])]) ).
fof(f161,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_38) ).
fof(f3580,plain,
spl0_34,
inference(avatar_split_clause,[],[f160,f3577]) ).
fof(f3577,plain,
( spl0_34
<=> class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_34])]) ).
fof(f160,axiom,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_37) ).
fof(f3575,plain,
spl0_33,
inference(avatar_split_clause,[],[f159,f3572]) ).
fof(f3572,plain,
( spl0_33
<=> class_OrderedGroup_Opordered__ab__semigroup__add(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_33])]) ).
fof(f159,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_36) ).
fof(f3570,plain,
spl0_32,
inference(avatar_split_clause,[],[f158,f3567]) ).
fof(f158,axiom,
class_Orderings_Olinorder(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_35) ).
fof(f3565,plain,
spl0_31,
inference(avatar_split_clause,[],[f157,f3562]) ).
fof(f3562,plain,
( spl0_31
<=> class_LOrder_Olorder(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_31])]) ).
fof(f157,axiom,
class_LOrder_Olorder(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_34) ).
fof(f3560,plain,
spl0_30,
inference(avatar_split_clause,[],[f156,f3557]) ).
fof(f156,axiom,
class_LOrder_Ojoin__semilorder(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_33) ).
fof(f3555,plain,
spl0_29,
inference(avatar_split_clause,[],[f155,f3552]) ).
fof(f155,axiom,
class_LOrder_Omeet__semilorder(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_32) ).
fof(f3550,plain,
spl0_28,
inference(avatar_split_clause,[],[f154,f3547]) ).
fof(f154,axiom,
class_Orderings_Oorder(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_31) ).
fof(f3545,plain,
spl0_27,
inference(avatar_split_clause,[],[f153,f3542]) ).
fof(f153,axiom,
class_Ring__and__Field_Ocomm__ring__1(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_30) ).
fof(f3540,plain,
spl0_26,
inference(avatar_split_clause,[],[f151,f3537]) ).
fof(f151,axiom,
class_Ring__and__Field_Ocomm__semiring__1__cancel(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_29) ).
fof(f3535,plain,
spl0_25,
inference(avatar_split_clause,[],[f150,f3532]) ).
fof(f3532,plain,
( spl0_25
<=> class_Ring__and__Field_Oring__1(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_25])]) ).
fof(f150,axiom,
class_Ring__and__Field_Oring__1(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_28) ).
fof(f3530,plain,
spl0_24,
inference(avatar_split_clause,[],[f149,f3527]) ).
fof(f3527,plain,
( spl0_24
<=> class_Ring__and__Field_Osemiring__1__cancel(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_24])]) ).
fof(f149,axiom,
class_Ring__and__Field_Osemiring__1__cancel(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_27) ).
fof(f3525,plain,
spl0_23,
inference(avatar_split_clause,[],[f148,f3522]) ).
fof(f3522,plain,
( spl0_23
<=> class_Ring__and__Field_Ocomm__semiring__1(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_23])]) ).
fof(f148,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_26) ).
fof(f3520,plain,
spl0_22,
inference(avatar_split_clause,[],[f147,f3517]) ).
fof(f3517,plain,
( spl0_22
<=> class_Ring__and__Field_Osemiring__1(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_22])]) ).
fof(f147,axiom,
class_Ring__and__Field_Osemiring__1(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_25) ).
fof(f3515,plain,
spl0_21,
inference(avatar_split_clause,[],[f146,f3512]) ).
fof(f3512,plain,
( spl0_21
<=> class_OrderedGroup_Ocomm__monoid__mult(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_21])]) ).
fof(f146,axiom,
class_OrderedGroup_Ocomm__monoid__mult(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_24) ).
fof(f3510,plain,
spl0_20,
inference(avatar_split_clause,[],[f145,f3507]) ).
fof(f145,axiom,
class_OrderedGroup_Omonoid__mult(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_23) ).
fof(f3505,plain,
spl0_19,
inference(avatar_split_clause,[],[f144,f3502]) ).
fof(f3502,plain,
( spl0_19
<=> class_Ring__and__Field_Oaxclass__0__neq__1(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_19])]) ).
fof(f144,axiom,
class_Ring__and__Field_Oaxclass__0__neq__1(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_22) ).
fof(f3500,plain,
spl0_18,
inference(avatar_split_clause,[],[f143,f3497]) ).
fof(f3497,plain,
( spl0_18
<=> class_Ring__and__Field_Ocomm__ring(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_18])]) ).
fof(f143,axiom,
class_Ring__and__Field_Ocomm__ring(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_21) ).
fof(f3495,plain,
spl0_17,
inference(avatar_split_clause,[],[f142,f3492]) ).
fof(f3492,plain,
( spl0_17
<=> class_Ring__and__Field_Ocomm__semiring__0__cancel(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_17])]) ).
fof(f142,axiom,
class_Ring__and__Field_Ocomm__semiring__0__cancel(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_20) ).
fof(f3490,plain,
spl0_16,
inference(avatar_split_clause,[],[f140,f3487]) ).
fof(f3487,plain,
( spl0_16
<=> class_Ring__and__Field_Oring(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_16])]) ).
fof(f140,axiom,
class_Ring__and__Field_Oring(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_19) ).
fof(f3485,plain,
spl0_15,
inference(avatar_split_clause,[],[f139,f3482]) ).
fof(f3482,plain,
( spl0_15
<=> class_Ring__and__Field_Osemiring__0__cancel(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_15])]) ).
fof(f139,axiom,
class_Ring__and__Field_Osemiring__0__cancel(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_18) ).
fof(f3480,plain,
spl0_14,
inference(avatar_split_clause,[],[f138,f3477]) ).
fof(f138,axiom,
class_OrderedGroup_Oab__group__add(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_17) ).
fof(f3475,plain,
spl0_13,
inference(avatar_split_clause,[],[f137,f3472]) ).
fof(f3472,plain,
( spl0_13
<=> class_OrderedGroup_Ocancel__ab__semigroup__add(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).
fof(f137,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_16) ).
fof(f3470,plain,
spl0_12,
inference(avatar_split_clause,[],[f136,f3467]) ).
fof(f3467,plain,
( spl0_12
<=> class_OrderedGroup_Ocancel__semigroup__add(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_12])]) ).
fof(f136,axiom,
class_OrderedGroup_Ocancel__semigroup__add(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_15) ).
fof(f3465,plain,
spl0_11,
inference(avatar_split_clause,[],[f135,f3462]) ).
fof(f3462,plain,
( spl0_11
<=> class_Ring__and__Field_Ocomm__semiring__0(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).
fof(f135,axiom,
class_Ring__and__Field_Ocomm__semiring__0(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_14) ).
fof(f3460,plain,
spl0_10,
inference(avatar_split_clause,[],[f134,f3457]) ).
fof(f3457,plain,
( spl0_10
<=> class_Ring__and__Field_Osemiring__0(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).
fof(f134,axiom,
class_Ring__and__Field_Osemiring__0(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_13) ).
fof(f3455,plain,
spl0_9,
inference(avatar_split_clause,[],[f133,f3452]) ).
fof(f133,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_12) ).
fof(f3450,plain,
spl0_8,
inference(avatar_split_clause,[],[f132,f3447]) ).
fof(f3447,plain,
( spl0_8
<=> class_Ring__and__Field_Ocomm__semiring(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).
fof(f132,axiom,
class_Ring__and__Field_Ocomm__semiring(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_11) ).
fof(f3445,plain,
spl0_7,
inference(avatar_split_clause,[],[f131,f3442]) ).
fof(f3442,plain,
( spl0_7
<=> class_Ring__and__Field_Osemiring(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).
fof(f131,axiom,
class_Ring__and__Field_Osemiring(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_10) ).
fof(f3440,plain,
spl0_6,
inference(avatar_split_clause,[],[f130,f3437]) ).
fof(f3437,plain,
( spl0_6
<=> class_HOL_Oone(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).
fof(f130,axiom,
class_HOL_Oone(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_1) ).
fof(f3435,plain,
~ spl0_5,
inference(avatar_split_clause,[],[f2952,f3432]) ).
fof(f2952,axiom,
~ c_in(c_Message_Omsg_OKey(v_K),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evso)),tc_Message_Omsg),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_6) ).
fof(f3430,plain,
spl0_4,
inference(avatar_split_clause,[],[f2948,f3427]) ).
fof(f2948,axiom,
c_in(v_evso,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
fof(f3425,plain,
~ spl0_3,
inference(avatar_split_clause,[],[f2953,f3422]) ).
fof(f2953,axiom,
c_Message_Omsg_ONonce(v_NB) != v_nb,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_7) ).
fof(f3420,plain,
~ spl0_2,
inference(avatar_split_clause,[],[f2947,f3417]) ).
fof(f2947,axiom,
~ c_in(v_B,c_Event_Obad,tc_Message_Oagent),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
fof(f3415,plain,
~ spl0_1,
inference(avatar_split_clause,[],[f2946,f3412]) ).
fof(f2946,axiom,
~ c_in(v_A,c_Event_Obad,tc_Message_Oagent),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.10 % Problem : SWV345-1 : TPTP v8.1.2. Released v3.2.0.
% 0.10/0.12 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.11/0.32 % Computer : n032.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Tue Apr 30 05:03:21 EDT 2024
% 0.11/0.32 % CPUTime :
% 0.11/0.32 % (852)Running in auto input_syntax mode. Trying TPTP
% 0.16/0.44 % (855)WARNING: value z3 for option sas not known
% 0.16/0.44 % (857)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.16/0.44 % (856)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.16/0.44 % (859)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.16/0.44 % (858)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.16/0.44 % (854)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.16/0.44 % (855)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.16/0.44 % (853)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 2.24/0.76 TRYING [1]
% 5.81/1.25 TRYING [2]
% 8.94/1.69 TRYING [1]
% 9.80/1.81 % (857)First to succeed.
% 9.80/1.82 TRYING [1]
% 10.60/1.93 % (857)Refutation found. Thanks to Tanya!
% 10.60/1.93 % SZS status Unsatisfiable for theBenchmark
% 10.60/1.93 % SZS output start Proof for theBenchmark
% See solution above
% 10.78/2.01 % (857)------------------------------
% 10.78/2.01 % (857)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 10.78/2.01 % (857)Termination reason: Refutation
% 10.78/2.01
% 10.78/2.01 % (857)Memory used [KB]: 20517
% 10.78/2.01 % (857)Time elapsed: 1.490 s
% 10.78/2.01 % (857)Instructions burned: 2588 (million)
% 10.78/2.01 % (857)------------------------------
% 10.78/2.01 % (857)------------------------------
% 10.78/2.01 % (852)Success in time 1.654 s
%------------------------------------------------------------------------------