TSTP Solution File: SCT105+1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SCT105+1 : TPTP v8.1.2. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n027.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 14:55:54 EDT 2024
% Result : Theorem 7.99s 1.57s
% Output : Refutation 7.99s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 1420
% Syntax : Number of formulae : 4664 ( 948 unt; 0 def)
% Number of atoms : 13285 (1481 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 14275 (5654 ~;5737 |; 790 &)
% (1136 <=>; 955 =>; 0 <=; 3 <~>)
% Maximal formula depth : 19 ( 6 avg)
% Maximal term depth : 9 ( 1 avg)
% Number of predicates : 967 ( 965 usr; 925 prp; 0-7 aty)
% Number of functors : 138 ( 138 usr; 19 con; 0-7 aty)
% Number of variables : 12385 (12052 !; 333 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f24916,plain,
$false,
inference(avatar_sat_refutation,[],[f2885,f2890,f2895,f2900,f2905,f2910,f2915,f2920,f2925,f2930,f2935,f2940,f2945,f2950,f2955,f2960,f2965,f2970,f2975,f2980,f2985,f2990,f2994,f2998,f3002,f3006,f3011,f3016,f3020,f3024,f3028,f3032,f3036,f3040,f3044,f3048,f3053,f3057,f3061,f3065,f3069,f3073,f3077,f3081,f3085,f3089,f3093,f3097,f3101,f3105,f3109,f3113,f3117,f3121,f3125,f3129,f3133,f3144,f3149,f3154,f3159,f3163,f3167,f3171,f3176,f3180,f3184,f3188,f3192,f3196,f3200,f3204,f3209,f3214,f3218,f3223,f3228,f3232,f3236,f3240,f3244,f3248,f3252,f3256,f3260,f3264,f3268,f3272,f3276,f3280,f3284,f3288,f3292,f3296,f3300,f3304,f3308,f3312,f3340,f3344,f3348,f3352,f3357,f3361,f3365,f3369,f3373,f3377,f3381,f3385,f3389,f3393,f3398,f3411,f3418,f3422,f3426,f3430,f3434,f3438,f3442,f3446,f3451,f3455,f3459,f3463,f3467,f3471,f3475,f3479,f3483,f3487,f3491,f3495,f3549,f3550,f3554,f3558,f3562,f3568,f3572,f3576,f3580,f3584,f3588,f3592,f3596,f3600,f3604,f3608,f3612,f3616,f3620,f3624,f3628,f3632,f3636,f3640,f3644,f3648,f3652,f3656,f3660,f3664,f3668,f3672,f3676,f3680,f3684,f3688,f3692,f3696,f3700,f3840,f3845,f3850,f3855,f3860,f3865,f3869,f3873,f3877,f3881,f3885,f3889,f3893,f3897,f3901,f3905,f3911,f3915,f3919,f4013,f4026,f4030,f4034,f4038,f4042,f4046,f4050,f4054,f4058,f4062,f4066,f4070,f4074,f4078,f4082,f4086,f4090,f4094,f4098,f4102,f4106,f4110,f4114,f4118,f4122,f4126,f4130,f4134,f4138,f4142,f4146,f4150,f4154,f4158,f4162,f4166,f4170,f4174,f4178,f4182,f4306,f4554,f4605,f4609,f4613,f4617,f4621,f4625,f4629,f4633,f4637,f4641,f4645,f4649,f4655,f4659,f4663,f4667,f4671,f4675,f4679,f4683,f4687,f4691,f4701,f4705,f4709,f4713,f4717,f4721,f4725,f4729,f4733,f4737,f4754,f4758,f4762,f4766,f4770,f4774,f4778,f4782,f4786,f4790,f4808,f4812,f4816,f4820,f4824,f4948,f5293,f5387,f5393,f5397,f5401,f5405,f5409,f5413,f5417,f5421,f5425,f5429,f5433,f5437,f5441,f5445,f5449,f5453,f5457,f5461,f5479,f5483,f5487,f5491,f5560,f5712,f5716,f5720,f5724,f5728,f5729,f5733,f5737,f5741,f5745,f5749,f5753,f5757,f5854,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,f6142,f6252,f6411,f6443,f6447,f6451,f6455,f6459,f6463,f6467,f6471,f6475,f6479,f6483,f6487,f6491,f6495,f6499,f6503,f6507,f6511,f6515,f6519,f6523,f6527,f6531,f6535,f6539,f6649,f6834,f7004,f7008,f7012,f7016,f7020,f7024,f7028,f7032,f7036,f7040,f7044,f7048,f7052,f7056,f7060,f7064,f7068,f7072,f7076,f7080,f7084,f7088,f7092,f7096,f7100,f7104,f7108,f7112,f7295,f7549,f7553,f7557,f7562,f7566,f7570,f7574,f7578,f7582,f7586,f7590,f7594,f7598,f7602,f7612,f7616,f7620,f8008,f8018,f8079,f8083,f8087,f8091,f8095,f8099,f8103,f8107,f8288,f8292,f8296,f8300,f8304,f8308,f8312,f8316,f8320,f8324,f8328,f8619,f8623,f8629,f8633,f8637,f8641,f8645,f8649,f8653,f8657,f8661,f8686,f9243,f9247,f9293,f9304,f9314,f9318,f9322,f9326,f9339,f9343,f9347,f9351,f9356,f9382,f9387,f9447,f9705,f9709,f9713,f9717,f9722,f9824,f9828,f9832,f9836,f9840,f9844,f9848,f9852,f9856,f9860,f9864,f9868,f10164,f10168,f10172,f10203,f10207,f10211,f10215,f10219,f10223,f10229,f10233,f10302,f10640,f10644,f10649,f10653,f10657,f10661,f10665,f10955,f10959,f11015,f11019,f11023,f11027,f11031,f11035,f11173,f11177,f11181,f11185,f11189,f11193,f11197,f11201,f11536,f11540,f11544,f11548,f11552,f11556,f11560,f11628,f11878,f11882,f11886,f11890,f11898,f11964,f11968,f11972,f11976,f12127,f12132,f12136,f12140,f12144,f12148,f12152,f12399,f12403,f12407,f12411,f12415,f12419,f12423,f12427,f12431,f12435,f12439,f12443,f12447,f12451,f13302,f13306,f13452,f13456,f13460,f13554,f13558,f13562,f13769,f13773,f13777,f13781,f13838,f13843,f13847,f13993,f13997,f14001,f14013,f14017,f14175,f14179,f14183,f14189,f14193,f14441,f14445,f14516,f14586,f14590,f14596,f14772,f14776,f14780,f14955,f14959,f14963,f15126,f15342,f15562,f15568,f15704,f15708,f15712,f15716,f15927,f15934,f15940,f15945,f15950,f16190,f16194,f16198,f16202,f16511,f16515,f16526,f16530,f16534,f16653,f16764,f16768,f16772,f16776,f16780,f16784,f16788,f16792,f16796,f17198,f17291,f17321,f17325,f17383,f17387,f17455,f17538,f17542,f17546,f17550,f17554,f17558,f17562,f17566,f17571,f17576,f17580,f17588,f17592,f17596,f17600,f17604,f17608,f17619,f17632,f17636,f17640,f17644,f17648,f17652,f17656,f17661,f17666,f17726,f18074,f18078,f18082,f18086,f18090,f18094,f18098,f18102,f18106,f18133,f18137,f18146,f18150,f18154,f18158,f18168,f18338,f18360,f18364,f18368,f18372,f18376,f18380,f18384,f18388,f18408,f18412,f18429,f18433,f18437,f18441,f18445,f18449,f18453,f18457,f18461,f18465,f18469,f18473,f18499,f18503,f18507,f18511,f18515,f18519,f18523,f18527,f18531,f18535,f18539,f18552,f18556,f18565,f18573,f18582,f18586,f18590,f18594,f19291,f19439,f19446,f19451,f19458,f19462,f19466,f19470,f19474,f19502,f19532,f19536,f19540,f19544,f19548,f19552,f19556,f19560,f19564,f19568,f19573,f19577,f19581,f19585,f19589,f19593,f19597,f19601,f19606,f19610,f19614,f19618,f19622,f19626,f19630,f19634,f19638,f19642,f19646,f19650,f19654,f19659,f19663,f19667,f19671,f19675,f19679,f19683,f19687,f19691,f19695,f19699,f19704,f19708,f19712,f19716,f19720,f19724,f19728,f19732,f19736,f19740,f19744,f19749,f19753,f20096,f21099,f21103,f21107,f21111,f21115,f21119,f21123,f21139,f21143,f21147,f21151,f21155,f21190,f21197,f21201,f21205,f21209,f21241,f21245,f21249,f21253,f21286,f21290,f21323,f21327,f21331,f21335,f21339,f21343,f21347,f21351,f21355,f21359,f21363,f21367,f21371,f21375,f21379,f21383,f21387,f21391,f21426,f21463,f21480,f21484,f21488,f21492,f21496,f21531,f21535,f21539,f21543,f21551,f21555,f21581,f21585,f21589,f21593,f21597,f21601,f21605,f21609,f21613,f21617,f21621,f21625,f21629,f21633,f21637,f21641,f21645,f21649,f21653,f21657,f21661,f21665,f21669,f21673,f21705,f21709,f21713,f21717,f21721,f21725,f21729,f21733,f21737,f21741,f21788,f21792,f21796,f21797,f21828,f21831,f21835,f21868,f21873,f21886,f21899,f21904,f21916,f21920,f21921,f21930,f21935,f21942,f21951,f21959,f21963,f21968,f22051,f22056,f22219,f22670,f23871,f24785,f24823,f24860,f24865,f24889,f24893,f24894,f24895,f24915]) ).
fof(f24915,plain,
( ~ spl104_1
| spl104_469 ),
inference(avatar_split_clause,[],[f1860,f9245,f2878]) ).
fof(f2878,plain,
( spl104_1
<=> sP0 ),
introduced(avatar_definition,[new_symbols(naming,[spl104_1])]) ).
fof(f9245,plain,
( spl104_469
<=> ! [X4,X3] :
( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X4,X3),v_L)
| X3 = X4
| c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X3,X4),v_L) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_469])]) ).
fof(f1860,plain,
! [X3,X4] :
( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X3,X4),v_L)
| c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X4,X3),v_L)
| X3 = X4
| ~ sP0 ),
inference(cnf_transformation,[],[f1558]) ).
fof(f1558,plain,
( ( sP0
| ( ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,sK15,sK16),v_L)
& ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,sK16,sK15),v_L)
& sK15 != sK16 )
| c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,sK17,sK17),v_L)
| ~ c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,v_L) )
& ( ( ! [X3,X4] :
( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X3,X4),v_L)
| c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X4,X3),v_L)
| X3 = X4 )
& ! [X5] : ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X5,X5),v_L)
& c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,v_L) )
| ~ sP0 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK15,sK16,sK17])],[f1555,f1557,f1556]) ).
fof(f1556,plain,
( ? [X0,X1] :
( ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,X1),v_L)
& ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X1,X0),v_L)
& X0 != X1 )
=> ( ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,sK15,sK16),v_L)
& ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,sK16,sK15),v_L)
& sK15 != sK16 ) ),
introduced(choice_axiom,[]) ).
fof(f1557,plain,
( ? [X2] : c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X2,X2),v_L)
=> c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,sK17,sK17),v_L) ),
introduced(choice_axiom,[]) ).
fof(f1555,plain,
( ( sP0
| ? [X0,X1] :
( ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,X1),v_L)
& ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X1,X0),v_L)
& X0 != X1 )
| ? [X2] : c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X2,X2),v_L)
| ~ c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,v_L) )
& ( ( ! [X3,X4] :
( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X3,X4),v_L)
| c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X4,X3),v_L)
| X3 = X4 )
& ! [X5] : ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X5,X5),v_L)
& c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,v_L) )
| ~ sP0 ) ),
inference(rectify,[],[f1554]) ).
fof(f1554,plain,
( ( sP0
| ? [X0,X1] :
( ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,X1),v_L)
& ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X1,X0),v_L)
& X0 != X1 )
| ? [X2] : c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X2,X2),v_L)
| ~ c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,v_L) )
& ( ( ! [X0,X1] :
( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,X1),v_L)
| c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X1,X0),v_L)
| X0 = X1 )
& ! [X2] : ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X2,X2),v_L)
& c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,v_L) )
| ~ sP0 ) ),
inference(flattening,[],[f1553]) ).
fof(f1553,plain,
( ( sP0
| ? [X0,X1] :
( ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,X1),v_L)
& ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X1,X0),v_L)
& X0 != X1 )
| ? [X2] : c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X2,X2),v_L)
| ~ c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,v_L) )
& ( ( ! [X0,X1] :
( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,X1),v_L)
| c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X1,X0),v_L)
| X0 = X1 )
& ! [X2] : ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X2,X2),v_L)
& c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,v_L) )
| ~ sP0 ) ),
inference(nnf_transformation,[],[f1526]) ).
fof(f1526,plain,
( sP0
<=> ( ! [X0,X1] :
( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,X1),v_L)
| c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X1,X0),v_L)
| X0 = X1 )
& ! [X2] : ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X2,X2),v_L)
& c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,v_L) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f24895,plain,
( ~ spl104_1
| spl104_23 ),
inference(avatar_split_clause,[],[f1858,f2987,f2878]) ).
fof(f2987,plain,
( spl104_23
<=> c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,v_L) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_23])]) ).
fof(f1858,plain,
( c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,v_L)
| ~ sP0 ),
inference(cnf_transformation,[],[f1558]) ).
fof(f24894,plain,
( spl104_23
| ~ spl104_33
| ~ spl104_124 ),
inference(avatar_split_clause,[],[f3564,f3448,f3030,f2987]) ).
fof(f3030,plain,
( spl104_33
<=> ! [X0,X1] : c_Relation_Otrans(X1,c_Transitive__Closure_Otrancl(X1,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_33])]) ).
fof(f3448,plain,
( spl104_124
<=> v_L = c_Transitive__Closure_Otrancl(tc_Arrow__Order__Mirabelle_Oalt,v_L) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_124])]) ).
fof(f3564,plain,
( c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,v_L)
| ~ spl104_33
| ~ spl104_124 ),
inference(superposition,[],[f3031,f3450]) ).
fof(f3450,plain,
( v_L = c_Transitive__Closure_Otrancl(tc_Arrow__Order__Mirabelle_Oalt,v_L)
| ~ spl104_124 ),
inference(avatar_component_clause,[],[f3448]) ).
fof(f3031,plain,
( ! [X0,X1] : c_Relation_Otrans(X1,c_Transitive__Closure_Otrancl(X1,X0))
| ~ spl104_33 ),
inference(avatar_component_clause,[],[f3030]) ).
fof(f24893,plain,
( spl104_922
| ~ spl104_386
| ~ spl104_900 ),
inference(avatar_split_clause,[],[f24828,f21883,f6537,f24891]) ).
fof(f24891,plain,
( spl104_922
<=> ! [X0] :
( c_member(tc_Arrow__Order__Mirabelle_Oalt,sK13,X0)
| ~ c_Relation_Orefl__on(tc_Arrow__Order__Mirabelle_Oalt,X0,v_L) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_922])]) ).
fof(f6537,plain,
( spl104_386
<=> ! [X4,X0,X3,X2,X1] :
( c_member(X4,X1,X3)
| ~ c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X1,X0),X2)
| ~ c_Relation_Orefl__on(X4,X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_386])]) ).
fof(f21883,plain,
( spl104_900
<=> c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,sK13,sK12),v_L) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_900])]) ).
fof(f24828,plain,
( ! [X0] :
( c_member(tc_Arrow__Order__Mirabelle_Oalt,sK13,X0)
| ~ c_Relation_Orefl__on(tc_Arrow__Order__Mirabelle_Oalt,X0,v_L) )
| ~ spl104_386
| ~ spl104_900 ),
inference(resolution,[],[f21884,f6538]) ).
fof(f6538,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X1,X0),X2)
| c_member(X4,X1,X3)
| ~ c_Relation_Orefl__on(X4,X3,X2) )
| ~ spl104_386 ),
inference(avatar_component_clause,[],[f6537]) ).
fof(f21884,plain,
( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,sK13,sK12),v_L)
| ~ spl104_900 ),
inference(avatar_component_clause,[],[f21883]) ).
fof(f24889,plain,
( spl104_921
| ~ spl104_385
| ~ spl104_900 ),
inference(avatar_split_clause,[],[f24827,f21883,f6533,f24887]) ).
fof(f24887,plain,
( spl104_921
<=> ! [X0] :
( c_member(tc_Arrow__Order__Mirabelle_Oalt,sK12,X0)
| ~ c_Relation_Orefl__on(tc_Arrow__Order__Mirabelle_Oalt,X0,v_L) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_921])]) ).
fof(f6533,plain,
( spl104_385
<=> ! [X4,X0,X3,X2,X1] :
( c_member(X4,X0,X3)
| ~ c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X1,X0),X2)
| ~ c_Relation_Orefl__on(X4,X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_385])]) ).
fof(f24827,plain,
( ! [X0] :
( c_member(tc_Arrow__Order__Mirabelle_Oalt,sK12,X0)
| ~ c_Relation_Orefl__on(tc_Arrow__Order__Mirabelle_Oalt,X0,v_L) )
| ~ spl104_385
| ~ spl104_900 ),
inference(resolution,[],[f21884,f6534]) ).
fof(f6534,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X1,X0),X2)
| c_member(X4,X0,X3)
| ~ c_Relation_Orefl__on(X4,X3,X2) )
| ~ spl104_385 ),
inference(avatar_component_clause,[],[f6533]) ).
fof(f24865,plain,
( spl104_920
| ~ spl104_354
| ~ spl104_900 ),
inference(avatar_split_clause,[],[f24842,f21883,f5973,f24862]) ).
fof(f24862,plain,
( spl104_920
<=> c_member(tc_Arrow__Order__Mirabelle_Oalt,sK12,c_Relation_ORange(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_L)) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_920])]) ).
fof(f5973,plain,
( spl104_354
<=> ! [X4,X0,X3,X2,X1] :
( c_member(X3,X2,c_Relation_ORange(X1,X3,X0))
| ~ c_member(tc_prod(X1,X3),c_Product__Type_OPair(X1,X3,X4,X2),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_354])]) ).
fof(f24842,plain,
( c_member(tc_Arrow__Order__Mirabelle_Oalt,sK12,c_Relation_ORange(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_L))
| ~ spl104_354
| ~ spl104_900 ),
inference(resolution,[],[f21884,f5974]) ).
fof(f5974,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ c_member(tc_prod(X1,X3),c_Product__Type_OPair(X1,X3,X4,X2),X0)
| c_member(X3,X2,c_Relation_ORange(X1,X3,X0)) )
| ~ spl104_354 ),
inference(avatar_component_clause,[],[f5973]) ).
fof(f24860,plain,
( spl104_919
| ~ spl104_355
| ~ spl104_900 ),
inference(avatar_split_clause,[],[f24841,f21883,f5977,f24857]) ).
fof(f24857,plain,
( spl104_919
<=> c_member(tc_Arrow__Order__Mirabelle_Oalt,sK13,c_Relation_ODomain(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_L)) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_919])]) ).
fof(f5977,plain,
( spl104_355
<=> ! [X4,X0,X3,X2,X1] :
( c_member(X3,X2,c_Relation_ODomain(X3,X1,X0))
| ~ c_member(tc_prod(X3,X1),c_Product__Type_OPair(X3,X1,X2,X4),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_355])]) ).
fof(f24841,plain,
( c_member(tc_Arrow__Order__Mirabelle_Oalt,sK13,c_Relation_ODomain(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_L))
| ~ spl104_355
| ~ spl104_900 ),
inference(resolution,[],[f21884,f5978]) ).
fof(f5978,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ c_member(tc_prod(X3,X1),c_Product__Type_OPair(X3,X1,X2,X4),X0)
| c_member(X3,X2,c_Relation_ODomain(X3,X1,X0)) )
| ~ spl104_355 ),
inference(avatar_component_clause,[],[f5977]) ).
fof(f24823,plain,
( ~ spl104_136
| ~ spl104_897 ),
inference(avatar_contradiction_clause,[],[f24790]) ).
fof(f24790,plain,
( $false
| ~ spl104_136
| ~ spl104_897 ),
inference(resolution,[],[f21863,f3548]) ).
fof(f3548,plain,
( ! [X5] : ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X5,X5),v_L)
| ~ spl104_136 ),
inference(avatar_component_clause,[],[f3547]) ).
fof(f3547,plain,
( spl104_136
<=> ! [X5] : ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X5,X5),v_L) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_136])]) ).
fof(f21863,plain,
( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,sK14,sK14),v_L)
| ~ spl104_897 ),
inference(avatar_component_clause,[],[f21861]) ).
fof(f21861,plain,
( spl104_897
<=> c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,sK14,sK14),v_L) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_897])]) ).
fof(f24785,plain,
( spl104_898
| spl104_899
| ~ spl104_469
| spl104_900 ),
inference(avatar_split_clause,[],[f21887,f21883,f9245,f21870,f21865]) ).
fof(f21865,plain,
( spl104_898
<=> sK12 = sK13 ),
introduced(avatar_definition,[new_symbols(naming,[spl104_898])]) ).
fof(f21870,plain,
( spl104_899
<=> c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,sK12,sK13),v_L) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_899])]) ).
fof(f21887,plain,
( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,sK12,sK13),v_L)
| sK12 = sK13
| ~ spl104_469
| spl104_900 ),
inference(resolution,[],[f21885,f9246]) ).
fof(f9246,plain,
( ! [X3,X4] :
( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X4,X3),v_L)
| c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X3,X4),v_L)
| X3 = X4 )
| ~ spl104_469 ),
inference(avatar_component_clause,[],[f9245]) ).
fof(f21885,plain,
( ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,sK13,sK12),v_L)
| spl104_900 ),
inference(avatar_component_clause,[],[f21883]) ).
fof(f23871,plain,
( ~ spl104_918
| ~ spl104_535
| ~ spl104_855 ),
inference(avatar_split_clause,[],[f23432,f21537,f11199,f23868]) ).
fof(f23868,plain,
( spl104_918
<=> c_Wellfounded_Oacyclic(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),c_FunDef_Omin__weak) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_918])]) ).
fof(f11199,plain,
( spl104_535
<=> ! [X0] : c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),X0,c_Relation_OId__on(tc_Nat_Onat,c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))),c_FunDef_Omin__weak) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_535])]) ).
fof(f21537,plain,
( spl104_855
<=> ! [X2,X0,X1] :
( ~ c_Wellfounded_Oacyclic(X0,X1)
| ~ c_member(tc_prod(X0,X0),c_Product__Type_OPair(X0,X0,X2,X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_855])]) ).
fof(f23432,plain,
( ~ c_Wellfounded_Oacyclic(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),c_FunDef_Omin__weak)
| ~ spl104_535
| ~ spl104_855 ),
inference(resolution,[],[f21538,f11200]) ).
fof(f11200,plain,
( ! [X0] : c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),X0,c_Relation_OId__on(tc_Nat_Onat,c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))),c_FunDef_Omin__weak)
| ~ spl104_535 ),
inference(avatar_component_clause,[],[f11199]) ).
fof(f21538,plain,
( ! [X2,X0,X1] :
( ~ c_member(tc_prod(X0,X0),c_Product__Type_OPair(X0,X0,X2,X2),X1)
| ~ c_Wellfounded_Oacyclic(X0,X1) )
| ~ spl104_855 ),
inference(avatar_component_clause,[],[f21537]) ).
fof(f22670,plain,
( ~ spl104_917
| ~ spl104_131
| ~ spl104_677 ),
inference(avatar_split_clause,[],[f21925,f17663,f3477,f22667]) ).
fof(f22667,plain,
( spl104_917
<=> sP3(sK16,sK15,c_FunDef_Oin__rel(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_L)) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_917])]) ).
fof(f3477,plain,
( spl104_131
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(X2,X1),X0))
| ~ sP3(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_131])]) ).
fof(f17663,plain,
( spl104_677
<=> hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_L),sK15),sK16)) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_677])]) ).
fof(f21925,plain,
( ~ sP3(sK16,sK15,c_FunDef_Oin__rel(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_L))
| ~ spl104_131
| ~ spl104_677 ),
inference(resolution,[],[f17664,f3478]) ).
fof(f3478,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(X2,X1),X0))
| ~ sP3(X0,X1,X2) )
| ~ spl104_131 ),
inference(avatar_component_clause,[],[f3477]) ).
fof(f17664,plain,
( hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_L),sK15),sK16))
| ~ spl104_677 ),
inference(avatar_component_clause,[],[f17663]) ).
fof(f22219,plain,
( spl104_916
| ~ spl104_95
| ~ spl104_902 ),
inference(avatar_split_clause,[],[f21912,f21901,f3294,f22216]) ).
fof(f22216,plain,
( spl104_916
<=> hBOOL(hAPP(c_Relation_ORange(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_L),sK16)) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_916])]) ).
fof(f3294,plain,
( spl104_95
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(X0,X1))
| ~ c_member(X2,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_95])]) ).
fof(f21901,plain,
( spl104_902
<=> c_member(tc_Arrow__Order__Mirabelle_Oalt,sK16,c_Relation_ORange(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_L)) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_902])]) ).
fof(f21912,plain,
( hBOOL(hAPP(c_Relation_ORange(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_L),sK16))
| ~ spl104_95
| ~ spl104_902 ),
inference(resolution,[],[f21903,f3295]) ).
fof(f3295,plain,
( ! [X2,X0,X1] :
( ~ c_member(X2,X1,X0)
| hBOOL(hAPP(X0,X1)) )
| ~ spl104_95 ),
inference(avatar_component_clause,[],[f3294]) ).
fof(f21903,plain,
( c_member(tc_Arrow__Order__Mirabelle_Oalt,sK16,c_Relation_ORange(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_L))
| ~ spl104_902 ),
inference(avatar_component_clause,[],[f21901]) ).
fof(f22056,plain,
( ~ spl104_915
| spl104_914
| spl104_914
| ~ spl104_196
| ~ spl104_550 ),
inference(avatar_split_clause,[],[f12002,f11966,f4032,f22049,f22049,f22053]) ).
fof(f22053,plain,
( spl104_915
<=> c_Relation_Oirrefl(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__leq) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_915])]) ).
fof(f22049,plain,
( spl104_914
<=> ! [X1] : ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_914])]) ).
fof(f4032,plain,
( spl104_196
<=> ! [X2,X0,X1] :
( ~ c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,X2,X2),X0)
| ~ c_Relation_Oirrefl(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_196])]) ).
fof(f11966,plain,
( spl104_550
<=> ! [X0,X3,X2,X1] :
( c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat,X3,X1),c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat,X2,X0)),c_FunDef_Opair__leq)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_550])]) ).
fof(f12002,plain,
( ! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X1)
| ~ c_Relation_Oirrefl(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__leq) )
| ~ spl104_196
| ~ spl104_550 ),
inference(resolution,[],[f11967,f4033]) ).
fof(f4033,plain,
( ! [X2,X0,X1] :
( ~ c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,X2,X2),X0)
| ~ c_Relation_Oirrefl(X1,X0) )
| ~ spl104_196 ),
inference(avatar_component_clause,[],[f4032]) ).
fof(f11967,plain,
( ! [X2,X3,X0,X1] :
( c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat,X3,X1),c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat,X2,X0)),c_FunDef_Opair__leq)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X2) )
| ~ spl104_550 ),
inference(avatar_component_clause,[],[f11966]) ).
fof(f22051,plain,
( ~ spl104_913
| spl104_914
| spl104_914
| ~ spl104_206
| ~ spl104_550 ),
inference(avatar_split_clause,[],[f12001,f11966,f4072,f22049,f22049,f22045]) ).
fof(f22045,plain,
( spl104_913
<=> c_Wellfounded_Owf(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__leq) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_913])]) ).
fof(f4072,plain,
( spl104_206
<=> ! [X2,X0,X1] :
( ~ c_member(tc_prod(X2,X2),c_Product__Type_OPair(X2,X2,X0,X0),X1)
| ~ c_Wellfounded_Owf(X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_206])]) ).
fof(f12001,plain,
( ! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X1)
| ~ c_Wellfounded_Owf(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__leq) )
| ~ spl104_206
| ~ spl104_550 ),
inference(resolution,[],[f11967,f4073]) ).
fof(f4073,plain,
( ! [X2,X0,X1] :
( ~ c_member(tc_prod(X2,X2),c_Product__Type_OPair(X2,X2,X0,X0),X1)
| ~ c_Wellfounded_Owf(X2,X1) )
| ~ spl104_206 ),
inference(avatar_component_clause,[],[f4072]) ).
fof(f21968,plain,
( spl104_912
| ~ spl104_130
| ~ spl104_471 ),
inference(avatar_split_clause,[],[f21856,f9301,f3473,f21965]) ).
fof(f21965,plain,
( spl104_912
<=> v_L = c_Set_Oinsert(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,sK15,sK16),v_L) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_912])]) ).
fof(f3473,plain,
( spl104_130
<=> ! [X2,X0,X1] :
( c_Set_Oinsert(X2,X1,X0) = X0
| ~ c_member(X2,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_130])]) ).
fof(f9301,plain,
( spl104_471
<=> c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,sK15,sK16),v_L) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_471])]) ).
fof(f21856,plain,
( v_L = c_Set_Oinsert(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,sK15,sK16),v_L)
| ~ spl104_130
| ~ spl104_471 ),
inference(resolution,[],[f9302,f3474]) ).
fof(f3474,plain,
( ! [X2,X0,X1] :
( ~ c_member(X2,X1,X0)
| c_Set_Oinsert(X2,X1,X0) = X0 )
| ~ spl104_130 ),
inference(avatar_component_clause,[],[f3473]) ).
fof(f9302,plain,
( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,sK15,sK16),v_L)
| ~ spl104_471 ),
inference(avatar_component_clause,[],[f9301]) ).
fof(f21963,plain,
( spl104_911
| ~ spl104_453
| ~ spl104_471 ),
inference(avatar_split_clause,[],[f21849,f9301,f8318,f21961]) ).
fof(f21961,plain,
( spl104_911
<=> ! [X0] :
( c_member(tc_Arrow__Order__Mirabelle_Oalt,sK16,c_Relation_OImage(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_L,X0))
| ~ c_member(tc_Arrow__Order__Mirabelle_Oalt,sK15,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_911])]) ).
fof(f8318,plain,
( spl104_453
<=> ! [X2,X4,X0,X3,X5,X1] :
( c_member(X4,X3,c_Relation_OImage(X2,X4,X1,X0))
| ~ c_member(tc_prod(X2,X4),c_Product__Type_OPair(X2,X4,X5,X3),X1)
| ~ c_member(X2,X5,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_453])]) ).
fof(f21849,plain,
( ! [X0] :
( c_member(tc_Arrow__Order__Mirabelle_Oalt,sK16,c_Relation_OImage(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_L,X0))
| ~ c_member(tc_Arrow__Order__Mirabelle_Oalt,sK15,X0) )
| ~ spl104_453
| ~ spl104_471 ),
inference(resolution,[],[f9302,f8319]) ).
fof(f8319,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ c_member(tc_prod(X2,X4),c_Product__Type_OPair(X2,X4,X5,X3),X1)
| c_member(X4,X3,c_Relation_OImage(X2,X4,X1,X0))
| ~ c_member(X2,X5,X0) )
| ~ spl104_453 ),
inference(avatar_component_clause,[],[f8318]) ).
fof(f21959,plain,
( spl104_910
| ~ spl104_454
| ~ spl104_471 ),
inference(avatar_split_clause,[],[f21840,f9301,f8322,f21957]) ).
fof(f21957,plain,
( spl104_910
<=> ! [X0,X1] : hAPP(X0,sK15) = hAPP(c_Recdef_Ocut(tc_Arrow__Order__Mirabelle_Oalt,X1,X0,v_L,sK16),sK15) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_910])]) ).
fof(f8322,plain,
( spl104_454
<=> ! [X5,X4,X0,X3,X2,X1] :
( hAPP(X0,X4) = hAPP(c_Recdef_Ocut(X5,X1,X0,X2,X3),X4)
| ~ c_member(tc_prod(X5,X5),c_Product__Type_OPair(X5,X5,X4,X3),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_454])]) ).
fof(f21840,plain,
( ! [X0,X1] : hAPP(X0,sK15) = hAPP(c_Recdef_Ocut(tc_Arrow__Order__Mirabelle_Oalt,X1,X0,v_L,sK16),sK15)
| ~ spl104_454
| ~ spl104_471 ),
inference(resolution,[],[f9302,f8323]) ).
fof(f8323,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ c_member(tc_prod(X5,X5),c_Product__Type_OPair(X5,X5,X4,X3),X2)
| hAPP(X0,X4) = hAPP(c_Recdef_Ocut(X5,X1,X0,X2,X3),X4) )
| ~ spl104_454 ),
inference(avatar_component_clause,[],[f8322]) ).
fof(f21951,plain,
( ~ spl104_908
| spl104_909
| ~ spl104_449
| ~ spl104_471 ),
inference(avatar_split_clause,[],[f21839,f9301,f8302,f21948,f21944]) ).
fof(f21944,plain,
( spl104_908
<=> c_member(tc_Arrow__Order__Mirabelle_Oalt,sK16,c_Wellfounded_Oacc(tc_Arrow__Order__Mirabelle_Oalt,v_L)) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_908])]) ).
fof(f21948,plain,
( spl104_909
<=> c_member(tc_Arrow__Order__Mirabelle_Oalt,sK15,c_Wellfounded_Oacc(tc_Arrow__Order__Mirabelle_Oalt,v_L)) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_909])]) ).
fof(f8302,plain,
( spl104_449
<=> ! [X4,X0,X2,X1] :
( c_member(X2,X4,c_Wellfounded_Oacc(X2,X0))
| ~ c_member(tc_prod(X2,X2),c_Product__Type_OPair(X2,X2,X4,X1),X0)
| ~ c_member(X2,X1,c_Wellfounded_Oacc(X2,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_449])]) ).
fof(f21839,plain,
( c_member(tc_Arrow__Order__Mirabelle_Oalt,sK15,c_Wellfounded_Oacc(tc_Arrow__Order__Mirabelle_Oalt,v_L))
| ~ c_member(tc_Arrow__Order__Mirabelle_Oalt,sK16,c_Wellfounded_Oacc(tc_Arrow__Order__Mirabelle_Oalt,v_L))
| ~ spl104_449
| ~ spl104_471 ),
inference(resolution,[],[f9302,f8303]) ).
fof(f8303,plain,
( ! [X2,X0,X1,X4] :
( ~ c_member(tc_prod(X2,X2),c_Product__Type_OPair(X2,X2,X4,X1),X0)
| c_member(X2,X4,c_Wellfounded_Oacc(X2,X0))
| ~ c_member(X2,X1,c_Wellfounded_Oacc(X2,X0)) )
| ~ spl104_449 ),
inference(avatar_component_clause,[],[f8302]) ).
fof(f21942,plain,
( spl104_907
| ~ spl104_95
| ~ spl104_901 ),
inference(avatar_split_clause,[],[f21908,f21896,f3294,f21939]) ).
fof(f21939,plain,
( spl104_907
<=> hBOOL(hAPP(c_Relation_ODomain(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_L),sK15)) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_907])]) ).
fof(f21896,plain,
( spl104_901
<=> c_member(tc_Arrow__Order__Mirabelle_Oalt,sK15,c_Relation_ODomain(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_L)) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_901])]) ).
fof(f21908,plain,
( hBOOL(hAPP(c_Relation_ODomain(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_L),sK15))
| ~ spl104_95
| ~ spl104_901 ),
inference(resolution,[],[f21898,f3295]) ).
fof(f21898,plain,
( c_member(tc_Arrow__Order__Mirabelle_Oalt,sK15,c_Relation_ODomain(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_L))
| ~ spl104_901 ),
inference(avatar_component_clause,[],[f21896]) ).
fof(f21935,plain,
( ~ spl104_906
| ~ spl104_411
| spl104_900 ),
inference(avatar_split_clause,[],[f21891,f21883,f7090,f21932]) ).
fof(f21932,plain,
( spl104_906
<=> hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_L),sK13),sK12)) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_906])]) ).
fof(f7090,plain,
( spl104_411
<=> ! [X4,X0,X3,X2,X1] :
( c_member(tc_prod(X4,X3),c_Product__Type_OPair(X4,X3,X1,X0),X2)
| ~ hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(X4,X3,X2),X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_411])]) ).
fof(f21891,plain,
( ~ hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_L),sK13),sK12))
| ~ spl104_411
| spl104_900 ),
inference(resolution,[],[f21885,f7091]) ).
fof(f7091,plain,
( ! [X2,X3,X0,X1,X4] :
( c_member(tc_prod(X4,X3),c_Product__Type_OPair(X4,X3,X1,X0),X2)
| ~ hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(X4,X3,X2),X1),X0)) )
| ~ spl104_411 ),
inference(avatar_component_clause,[],[f7090]) ).
fof(f21930,plain,
( ~ spl104_905
| ~ spl104_411
| spl104_899 ),
inference(avatar_split_clause,[],[f21878,f21870,f7090,f21927]) ).
fof(f21927,plain,
( spl104_905
<=> hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_L),sK12),sK13)) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_905])]) ).
fof(f21878,plain,
( ~ hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_L),sK12),sK13))
| ~ spl104_411
| spl104_899 ),
inference(resolution,[],[f21872,f7091]) ).
fof(f21872,plain,
( ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,sK12,sK13),v_L)
| spl104_899 ),
inference(avatar_component_clause,[],[f21870]) ).
fof(f21921,plain,
( spl104_677
| ~ spl104_412
| ~ spl104_471 ),
inference(avatar_split_clause,[],[f21850,f9301,f7094,f17663]) ).
fof(f7094,plain,
( spl104_412
<=> ! [X4,X0,X3,X2,X1] :
( hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(X4,X3,X2),X1),X0))
| ~ c_member(tc_prod(X4,X3),c_Product__Type_OPair(X4,X3,X1,X0),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_412])]) ).
fof(f21850,plain,
( hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_L),sK15),sK16))
| ~ spl104_412
| ~ spl104_471 ),
inference(resolution,[],[f9302,f7095]) ).
fof(f7095,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ c_member(tc_prod(X4,X3),c_Product__Type_OPair(X4,X3,X1,X0),X2)
| hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(X4,X3,X2),X1),X0)) )
| ~ spl104_412 ),
inference(avatar_component_clause,[],[f7094]) ).
fof(f21920,plain,
( spl104_904
| ~ spl104_386
| ~ spl104_471 ),
inference(avatar_split_clause,[],[f21838,f9301,f6537,f21918]) ).
fof(f21918,plain,
( spl104_904
<=> ! [X0] :
( c_member(tc_Arrow__Order__Mirabelle_Oalt,sK15,X0)
| ~ c_Relation_Orefl__on(tc_Arrow__Order__Mirabelle_Oalt,X0,v_L) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_904])]) ).
fof(f21838,plain,
( ! [X0] :
( c_member(tc_Arrow__Order__Mirabelle_Oalt,sK15,X0)
| ~ c_Relation_Orefl__on(tc_Arrow__Order__Mirabelle_Oalt,X0,v_L) )
| ~ spl104_386
| ~ spl104_471 ),
inference(resolution,[],[f9302,f6538]) ).
fof(f21916,plain,
( spl104_903
| ~ spl104_385
| ~ spl104_471 ),
inference(avatar_split_clause,[],[f21837,f9301,f6533,f21914]) ).
fof(f21914,plain,
( spl104_903
<=> ! [X0] :
( c_member(tc_Arrow__Order__Mirabelle_Oalt,sK16,X0)
| ~ c_Relation_Orefl__on(tc_Arrow__Order__Mirabelle_Oalt,X0,v_L) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_903])]) ).
fof(f21837,plain,
( ! [X0] :
( c_member(tc_Arrow__Order__Mirabelle_Oalt,sK16,X0)
| ~ c_Relation_Orefl__on(tc_Arrow__Order__Mirabelle_Oalt,X0,v_L) )
| ~ spl104_385
| ~ spl104_471 ),
inference(resolution,[],[f9302,f6534]) ).
fof(f21904,plain,
( spl104_902
| ~ spl104_354
| ~ spl104_471 ),
inference(avatar_split_clause,[],[f21852,f9301,f5973,f21901]) ).
fof(f21852,plain,
( c_member(tc_Arrow__Order__Mirabelle_Oalt,sK16,c_Relation_ORange(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_L))
| ~ spl104_354
| ~ spl104_471 ),
inference(resolution,[],[f9302,f5974]) ).
fof(f21899,plain,
( spl104_901
| ~ spl104_355
| ~ spl104_471 ),
inference(avatar_split_clause,[],[f21851,f9301,f5977,f21896]) ).
fof(f21851,plain,
( c_member(tc_Arrow__Order__Mirabelle_Oalt,sK15,c_Relation_ODomain(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_L))
| ~ spl104_355
| ~ spl104_471 ),
inference(resolution,[],[f9302,f5978]) ).
fof(f21886,plain,
( ~ spl104_23
| spl104_897
| ~ spl104_900
| spl104_2 ),
inference(avatar_split_clause,[],[f1857,f2882,f21883,f21861,f2987]) ).
fof(f2882,plain,
( spl104_2
<=> sP1 ),
introduced(avatar_definition,[new_symbols(naming,[spl104_2])]) ).
fof(f1857,plain,
( sP1
| ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,sK13,sK12),v_L)
| c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,sK14,sK14),v_L)
| ~ c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,v_L) ),
inference(cnf_transformation,[],[f1552]) ).
fof(f1552,plain,
( ( sP1
| ( ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,sK13,sK12),v_L)
& ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,sK12,sK13),v_L)
& sK12 != sK13 )
| c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,sK14,sK14),v_L)
| ~ c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,v_L) )
& ( ( ! [X3,X4] :
( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X4,X3),v_L)
| c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X3,X4),v_L)
| X3 = X4 )
& ! [X5] : ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X5,X5),v_L)
& c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,v_L) )
| ~ sP1 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK12,sK13,sK14])],[f1549,f1551,f1550]) ).
fof(f1550,plain,
( ? [X0,X1] :
( ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X1,X0),v_L)
& ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,X1),v_L)
& X0 != X1 )
=> ( ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,sK13,sK12),v_L)
& ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,sK12,sK13),v_L)
& sK12 != sK13 ) ),
introduced(choice_axiom,[]) ).
fof(f1551,plain,
( ? [X2] : c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X2,X2),v_L)
=> c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,sK14,sK14),v_L) ),
introduced(choice_axiom,[]) ).
fof(f1549,plain,
( ( sP1
| ? [X0,X1] :
( ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X1,X0),v_L)
& ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,X1),v_L)
& X0 != X1 )
| ? [X2] : c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X2,X2),v_L)
| ~ c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,v_L) )
& ( ( ! [X3,X4] :
( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X4,X3),v_L)
| c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X3,X4),v_L)
| X3 = X4 )
& ! [X5] : ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X5,X5),v_L)
& c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,v_L) )
| ~ sP1 ) ),
inference(rectify,[],[f1548]) ).
fof(f1548,plain,
( ( sP1
| ? [X3,X4] :
( ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X4,X3),v_L)
& ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X3,X4),v_L)
& X3 != X4 )
| ? [X5] : c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X5,X5),v_L)
| ~ c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,v_L) )
& ( ( ! [X3,X4] :
( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X4,X3),v_L)
| c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X3,X4),v_L)
| X3 = X4 )
& ! [X5] : ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X5,X5),v_L)
& c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,v_L) )
| ~ sP1 ) ),
inference(flattening,[],[f1547]) ).
fof(f1547,plain,
( ( sP1
| ? [X3,X4] :
( ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X4,X3),v_L)
& ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X3,X4),v_L)
& X3 != X4 )
| ? [X5] : c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X5,X5),v_L)
| ~ c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,v_L) )
& ( ( ! [X3,X4] :
( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X4,X3),v_L)
| c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X3,X4),v_L)
| X3 = X4 )
& ! [X5] : ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X5,X5),v_L)
& c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,v_L) )
| ~ sP1 ) ),
inference(nnf_transformation,[],[f1527]) ).
fof(f1527,plain,
( sP1
<=> ( ! [X3,X4] :
( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X4,X3),v_L)
| c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X3,X4),v_L)
| X3 = X4 )
& ! [X5] : ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X5,X5),v_L)
& c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,v_L) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).
fof(f21873,plain,
( ~ spl104_23
| spl104_897
| ~ spl104_899
| spl104_2 ),
inference(avatar_split_clause,[],[f1856,f2882,f21870,f21861,f2987]) ).
fof(f1856,plain,
( sP1
| ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,sK12,sK13),v_L)
| c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,sK14,sK14),v_L)
| ~ c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,v_L) ),
inference(cnf_transformation,[],[f1552]) ).
fof(f21868,plain,
( ~ spl104_23
| spl104_897
| ~ spl104_898
| spl104_2 ),
inference(avatar_split_clause,[],[f1855,f2882,f21865,f21861,f2987]) ).
fof(f1855,plain,
( sP1
| sK12 != sK13
| c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,sK14,sK14),v_L)
| ~ c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,v_L) ),
inference(cnf_transformation,[],[f1552]) ).
fof(f21835,plain,
( spl104_896
| ~ spl104_96
| ~ spl104_809 ),
inference(avatar_split_clause,[],[f21193,f21113,f3298,f21833]) ).
fof(f21833,plain,
( spl104_896
<=> ! [X2,X0,X1] : c_member(X0,X1,c_Transitive__Closure_Otrancl(X2,c_fequal(X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_896])]) ).
fof(f3298,plain,
( spl104_96
<=> ! [X2,X0,X1] :
( c_member(X2,X1,X0)
| ~ hBOOL(hAPP(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_96])]) ).
fof(f21113,plain,
( spl104_809
<=> ! [X0,X1] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(X0,c_fequal(X1)),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_809])]) ).
fof(f21193,plain,
( ! [X2,X0,X1] : c_member(X0,X1,c_Transitive__Closure_Otrancl(X2,c_fequal(X1)))
| ~ spl104_96
| ~ spl104_809 ),
inference(resolution,[],[f21114,f3299]) ).
fof(f3299,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(X0,X1))
| c_member(X2,X1,X0) )
| ~ spl104_96 ),
inference(avatar_component_clause,[],[f3298]) ).
fof(f21114,plain,
( ! [X0,X1] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(X0,c_fequal(X1)),X1))
| ~ spl104_809 ),
inference(avatar_component_clause,[],[f21113]) ).
fof(f21831,plain,
( ~ spl104_1
| ~ spl104_2 ),
inference(avatar_split_clause,[],[f1865,f2882,f2878]) ).
fof(f1865,plain,
( ~ sP1
| ~ sP0 ),
inference(cnf_transformation,[],[f1559]) ).
fof(f1559,plain,
( ( ~ sP1
| ~ sP0 )
& ( sP1
| sP0 ) ),
inference(nnf_transformation,[],[f1528]) ).
fof(f1528,plain,
( sP0
<~> sP1 ),
inference(definition_folding,[],[f1026,f1527,f1526]) ).
fof(f1026,plain,
( ( ! [X0,X1] :
( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,X1),v_L)
| c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X1,X0),v_L)
| X0 = X1 )
& ! [X2] : ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X2,X2),v_L)
& c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,v_L) )
<~> ( ! [X3,X4] :
( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X4,X3),v_L)
| c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X3,X4),v_L)
| X3 = X4 )
& ! [X5] : ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X5,X5),v_L)
& c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,v_L) ) ),
inference(flattening,[],[f1025]) ).
fof(f1025,plain,
( ( ! [X0,X1] :
( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,X1),v_L)
| c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X1,X0),v_L)
| X0 = X1 )
& ! [X2] : ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X2,X2),v_L)
& c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,v_L) )
<~> ( ! [X3,X4] :
( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X4,X3),v_L)
| c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X3,X4),v_L)
| X3 = X4 )
& ! [X5] : ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X5,X5),v_L)
& c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,v_L) ) ),
inference(ennf_transformation,[],[f525]) ).
fof(f525,plain,
~ ( ( ! [X0,X1] :
( X0 != X1
=> ( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,X1),v_L)
| c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X1,X0),v_L) ) )
& ! [X2] : ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X2,X2),v_L)
& c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,v_L) )
<=> ( ! [X3,X4] :
( X3 != X4
=> ( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X4,X3),v_L)
| c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X3,X4),v_L) ) )
& ! [X5] : ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X5,X5),v_L)
& c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,v_L) ) ),
inference(rectify,[],[f524]) ).
fof(f524,negated_conjecture,
~ ( ( ! [X2,X5] :
( X2 != X5
=> ( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X2,X5),v_L)
| c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X5,X2),v_L) ) )
& ! [X2] : ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X2,X2),v_L)
& c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,v_L) )
<=> ( ! [X2,X5] :
( X2 != X5
=> ( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X5,X2),v_L)
| c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X2,X5),v_L) ) )
& ! [X2] : ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X2,X2),v_L)
& c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,v_L) ) ),
inference(negated_conjecture,[],[f523]) ).
fof(f523,conjecture,
( ( ! [X2,X5] :
( X2 != X5
=> ( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X2,X5),v_L)
| c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X5,X2),v_L) ) )
& ! [X2] : ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X2,X2),v_L)
& c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,v_L) )
<=> ( ! [X2,X5] :
( X2 != X5
=> ( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X5,X2),v_L)
| c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X2,X5),v_L) ) )
& ! [X2] : ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X2,X2),v_L)
& c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,v_L) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
fof(f21828,plain,
( ~ spl104_136
| ~ spl104_323 ),
inference(avatar_contradiction_clause,[],[f21802]) ).
fof(f21802,plain,
( $false
| ~ spl104_136
| ~ spl104_323 ),
inference(resolution,[],[f5849,f3548]) ).
fof(f5849,plain,
( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,sK17,sK17),v_L)
| ~ spl104_323 ),
inference(avatar_component_clause,[],[f5847]) ).
fof(f5847,plain,
( spl104_323
<=> c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,sK17,sK17),v_L) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_323])]) ).
fof(f21797,plain,
( spl104_324
| spl104_471
| ~ spl104_469
| spl104_470 ),
inference(avatar_split_clause,[],[f9294,f9290,f9245,f9301,f5851]) ).
fof(f5851,plain,
( spl104_324
<=> sK15 = sK16 ),
introduced(avatar_definition,[new_symbols(naming,[spl104_324])]) ).
fof(f9290,plain,
( spl104_470
<=> c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,sK16,sK15),v_L) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_470])]) ).
fof(f9294,plain,
( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,sK15,sK16),v_L)
| sK15 = sK16
| ~ spl104_469
| spl104_470 ),
inference(resolution,[],[f9292,f9246]) ).
fof(f9292,plain,
( ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,sK16,sK15),v_L)
| spl104_470 ),
inference(avatar_component_clause,[],[f9290]) ).
fof(f21796,plain,
( spl104_895
| ~ spl104_81
| ~ spl104_259
| ~ spl104_463 ),
inference(avatar_split_clause,[],[f9142,f8647,f4703,f3238,f21794]) ).
fof(f21794,plain,
( spl104_895
<=> ! [X2,X0,X1] :
( ~ c_member(X0,X1,X2)
| sK85(X2,c_Relation_OId(X0),X0,X1,X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_895])]) ).
fof(f3238,plain,
( spl104_81
<=> ! [X0,X1] : c_Relation_OImage(X1,X1,c_Relation_OId(X1),X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl104_81])]) ).
fof(f4703,plain,
( spl104_259
<=> ! [X2,X0,X1] :
( X0 = X1
| ~ c_member(tc_prod(X2,X2),c_Product__Type_OPair(X2,X2,X1,X0),c_Relation_OId(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_259])]) ).
fof(f8647,plain,
( spl104_463
<=> ! [X4,X0,X3,X2,X1] :
( c_member(tc_prod(X2,X4),c_Product__Type_OPair(X2,X4,sK85(X0,X1,X2,X3,X4),X3),X1)
| ~ c_member(X4,X3,c_Relation_OImage(X2,X4,X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_463])]) ).
fof(f9142,plain,
( ! [X2,X0,X1] :
( ~ c_member(X0,X1,X2)
| sK85(X2,c_Relation_OId(X0),X0,X1,X0) = X1 )
| ~ spl104_81
| ~ spl104_259
| ~ spl104_463 ),
inference(forward_demodulation,[],[f9122,f3239]) ).
fof(f3239,plain,
( ! [X0,X1] : c_Relation_OImage(X1,X1,c_Relation_OId(X1),X0) = X0
| ~ spl104_81 ),
inference(avatar_component_clause,[],[f3238]) ).
fof(f9122,plain,
( ! [X2,X0,X1] :
( ~ c_member(X0,X1,c_Relation_OImage(X0,X0,c_Relation_OId(X0),X2))
| sK85(X2,c_Relation_OId(X0),X0,X1,X0) = X1 )
| ~ spl104_259
| ~ spl104_463 ),
inference(resolution,[],[f8648,f4704]) ).
fof(f4704,plain,
( ! [X2,X0,X1] :
( ~ c_member(tc_prod(X2,X2),c_Product__Type_OPair(X2,X2,X1,X0),c_Relation_OId(X2))
| X0 = X1 )
| ~ spl104_259 ),
inference(avatar_component_clause,[],[f4703]) ).
fof(f8648,plain,
( ! [X2,X3,X0,X1,X4] :
( c_member(tc_prod(X2,X4),c_Product__Type_OPair(X2,X4,sK85(X0,X1,X2,X3,X4),X3),X1)
| ~ c_member(X4,X3,c_Relation_OImage(X2,X4,X1,X0)) )
| ~ spl104_463 ),
inference(avatar_component_clause,[],[f8647]) ).
fof(f21792,plain,
( spl104_894
| ~ spl104_81
| ~ spl104_259
| ~ spl104_462 ),
inference(avatar_split_clause,[],[f9109,f8643,f4703,f3238,f21790]) ).
fof(f21790,plain,
( spl104_894
<=> ! [X2,X0,X1] :
( ~ c_member(X0,X1,X2)
| sK76(X2,c_Relation_OId(X0),X0,X1,X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_894])]) ).
fof(f8643,plain,
( spl104_462
<=> ! [X4,X0,X3,X2,X1] :
( c_member(tc_prod(X2,X4),c_Product__Type_OPair(X2,X4,sK76(X0,X1,X2,X3,X4),X3),X1)
| ~ c_member(X4,X3,c_Relation_OImage(X2,X4,X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_462])]) ).
fof(f9109,plain,
( ! [X2,X0,X1] :
( ~ c_member(X0,X1,X2)
| sK76(X2,c_Relation_OId(X0),X0,X1,X0) = X1 )
| ~ spl104_81
| ~ spl104_259
| ~ spl104_462 ),
inference(forward_demodulation,[],[f9089,f3239]) ).
fof(f9089,plain,
( ! [X2,X0,X1] :
( ~ c_member(X0,X1,c_Relation_OImage(X0,X0,c_Relation_OId(X0),X2))
| sK76(X2,c_Relation_OId(X0),X0,X1,X0) = X1 )
| ~ spl104_259
| ~ spl104_462 ),
inference(resolution,[],[f8644,f4704]) ).
fof(f8644,plain,
( ! [X2,X3,X0,X1,X4] :
( c_member(tc_prod(X2,X4),c_Product__Type_OPair(X2,X4,sK76(X0,X1,X2,X3,X4),X3),X1)
| ~ c_member(X4,X3,c_Relation_OImage(X2,X4,X1,X0)) )
| ~ spl104_462 ),
inference(avatar_component_clause,[],[f8643]) ).
fof(f21788,plain,
( spl104_893
| ~ spl104_63
| ~ spl104_462 ),
inference(avatar_split_clause,[],[f9106,f8643,f3161,f21786]) ).
fof(f21786,plain,
( spl104_893
<=> ! [X0,X3,X2,X1] : ~ c_member(X0,X1,c_Relation_OImage(X2,X0,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X0),tc_HOL_Obool)),X3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_893])]) ).
fof(f3161,plain,
( spl104_63
<=> ! [X0,X1] : ~ c_member(X1,X0,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_63])]) ).
fof(f9106,plain,
( ! [X2,X3,X0,X1] : ~ c_member(X0,X1,c_Relation_OImage(X2,X0,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X0),tc_HOL_Obool)),X3))
| ~ spl104_63
| ~ spl104_462 ),
inference(resolution,[],[f8644,f3162]) ).
fof(f3162,plain,
( ! [X0,X1] : ~ c_member(X1,X0,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))
| ~ spl104_63 ),
inference(avatar_component_clause,[],[f3161]) ).
fof(f21741,plain,
( spl104_892
| ~ spl104_145
| ~ spl104_454 ),
inference(avatar_split_clause,[],[f8551,f8322,f3586,f21739]) ).
fof(f21739,plain,
( spl104_892
<=> ! [X0,X3,X2,X1] : hAPP(X0,X1) = hAPP(c_Recdef_Ocut(X2,X3,X0,c_Relation_OId(X2),X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_892])]) ).
fof(f3586,plain,
( spl104_145
<=> ! [X0,X1] : c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,X0,X0),c_Relation_OId(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_145])]) ).
fof(f8551,plain,
( ! [X2,X3,X0,X1] : hAPP(X0,X1) = hAPP(c_Recdef_Ocut(X2,X3,X0,c_Relation_OId(X2),X1),X1)
| ~ spl104_145
| ~ spl104_454 ),
inference(resolution,[],[f8323,f3587]) ).
fof(f3587,plain,
( ! [X0,X1] : c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,X0,X0),c_Relation_OId(X1))
| ~ spl104_145 ),
inference(avatar_component_clause,[],[f3586]) ).
fof(f21737,plain,
( spl104_891
| ~ spl104_80
| ~ spl104_308
| ~ spl104_441 ),
inference(avatar_split_clause,[],[f8264,f8093,f5489,f3234,f21735]) ).
fof(f21735,plain,
( spl104_891
<=> ! [X2,X0,X1] :
( ~ c_member(X0,X1,X2)
| sK69(c_Relation_OId__on(X0,X2),X0,X1,X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_891])]) ).
fof(f3234,plain,
( spl104_80
<=> ! [X0,X1] : c_Relation_ODomain(X1,X1,c_Relation_OId__on(X1,X0)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl104_80])]) ).
fof(f5489,plain,
( spl104_308
<=> ! [X0,X3,X2,X1] :
( X1 = X2
| ~ c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X2,X1),c_Relation_OId__on(X3,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_308])]) ).
fof(f8093,plain,
( spl104_441
<=> ! [X0,X3,X2,X1] :
( c_member(tc_prod(X3,X1),c_Product__Type_OPair(X3,X1,X2,sK69(X0,X1,X2,X3)),X0)
| ~ c_member(X3,X2,c_Relation_ODomain(X3,X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_441])]) ).
fof(f8264,plain,
( ! [X2,X0,X1] :
( ~ c_member(X0,X1,X2)
| sK69(c_Relation_OId__on(X0,X2),X0,X1,X0) = X1 )
| ~ spl104_80
| ~ spl104_308
| ~ spl104_441 ),
inference(forward_demodulation,[],[f8242,f3235]) ).
fof(f3235,plain,
( ! [X0,X1] : c_Relation_ODomain(X1,X1,c_Relation_OId__on(X1,X0)) = X0
| ~ spl104_80 ),
inference(avatar_component_clause,[],[f3234]) ).
fof(f8242,plain,
( ! [X2,X0,X1] :
( ~ c_member(X0,X1,c_Relation_ODomain(X0,X0,c_Relation_OId__on(X0,X2)))
| sK69(c_Relation_OId__on(X0,X2),X0,X1,X0) = X1 )
| ~ spl104_308
| ~ spl104_441 ),
inference(resolution,[],[f8094,f5490]) ).
fof(f5490,plain,
( ! [X2,X3,X0,X1] :
( ~ c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X2,X1),c_Relation_OId__on(X3,X0))
| X1 = X2 )
| ~ spl104_308 ),
inference(avatar_component_clause,[],[f5489]) ).
fof(f8094,plain,
( ! [X2,X3,X0,X1] :
( c_member(tc_prod(X3,X1),c_Product__Type_OPair(X3,X1,X2,sK69(X0,X1,X2,X3)),X0)
| ~ c_member(X3,X2,c_Relation_ODomain(X3,X1,X0)) )
| ~ spl104_441 ),
inference(avatar_component_clause,[],[f8093]) ).
fof(f21733,plain,
( spl104_890
| ~ spl104_79
| ~ spl104_308
| ~ spl104_440 ),
inference(avatar_split_clause,[],[f8231,f8089,f5489,f3230,f21731]) ).
fof(f21731,plain,
( spl104_890
<=> ! [X2,X0,X1] :
( ~ c_member(X0,X1,X2)
| sK68(c_Relation_OId__on(X0,X2),X0,X1,X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_890])]) ).
fof(f3230,plain,
( spl104_79
<=> ! [X0,X1] : c_Relation_ORange(X1,X1,c_Relation_OId__on(X1,X0)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl104_79])]) ).
fof(f8089,plain,
( spl104_440
<=> ! [X0,X3,X2,X1] :
( c_member(tc_prod(X1,X3),c_Product__Type_OPair(X1,X3,sK68(X0,X1,X2,X3),X2),X0)
| ~ c_member(X3,X2,c_Relation_ORange(X1,X3,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_440])]) ).
fof(f8231,plain,
( ! [X2,X0,X1] :
( ~ c_member(X0,X1,X2)
| sK68(c_Relation_OId__on(X0,X2),X0,X1,X0) = X1 )
| ~ spl104_79
| ~ spl104_308
| ~ spl104_440 ),
inference(forward_demodulation,[],[f8209,f3231]) ).
fof(f3231,plain,
( ! [X0,X1] : c_Relation_ORange(X1,X1,c_Relation_OId__on(X1,X0)) = X0
| ~ spl104_79 ),
inference(avatar_component_clause,[],[f3230]) ).
fof(f8209,plain,
( ! [X2,X0,X1] :
( ~ c_member(X0,X1,c_Relation_ORange(X0,X0,c_Relation_OId__on(X0,X2)))
| sK68(c_Relation_OId__on(X0,X2),X0,X1,X0) = X1 )
| ~ spl104_308
| ~ spl104_440 ),
inference(resolution,[],[f8090,f5490]) ).
fof(f8090,plain,
( ! [X2,X3,X0,X1] :
( c_member(tc_prod(X1,X3),c_Product__Type_OPair(X1,X3,sK68(X0,X1,X2,X3),X2),X0)
| ~ c_member(X3,X2,c_Relation_ORange(X1,X3,X0)) )
| ~ spl104_440 ),
inference(avatar_component_clause,[],[f8089]) ).
fof(f21729,plain,
( spl104_889
| ~ spl104_80
| ~ spl104_308
| ~ spl104_439 ),
inference(avatar_split_clause,[],[f8198,f8085,f5489,f3234,f21727]) ).
fof(f21727,plain,
( spl104_889
<=> ! [X2,X0,X1] :
( ~ c_member(X0,X1,X2)
| sK59(c_Relation_OId__on(X0,X2),X0,X1,X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_889])]) ).
fof(f8085,plain,
( spl104_439
<=> ! [X0,X3,X2,X1] :
( c_member(tc_prod(X3,X1),c_Product__Type_OPair(X3,X1,X2,sK59(X0,X1,X2,X3)),X0)
| ~ c_member(X3,X2,c_Relation_ODomain(X3,X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_439])]) ).
fof(f8198,plain,
( ! [X2,X0,X1] :
( ~ c_member(X0,X1,X2)
| sK59(c_Relation_OId__on(X0,X2),X0,X1,X0) = X1 )
| ~ spl104_80
| ~ spl104_308
| ~ spl104_439 ),
inference(forward_demodulation,[],[f8176,f3235]) ).
fof(f8176,plain,
( ! [X2,X0,X1] :
( ~ c_member(X0,X1,c_Relation_ODomain(X0,X0,c_Relation_OId__on(X0,X2)))
| sK59(c_Relation_OId__on(X0,X2),X0,X1,X0) = X1 )
| ~ spl104_308
| ~ spl104_439 ),
inference(resolution,[],[f8086,f5490]) ).
fof(f8086,plain,
( ! [X2,X3,X0,X1] :
( c_member(tc_prod(X3,X1),c_Product__Type_OPair(X3,X1,X2,sK59(X0,X1,X2,X3)),X0)
| ~ c_member(X3,X2,c_Relation_ODomain(X3,X1,X0)) )
| ~ spl104_439 ),
inference(avatar_component_clause,[],[f8085]) ).
fof(f21725,plain,
( spl104_888
| ~ spl104_79
| ~ spl104_308
| ~ spl104_438 ),
inference(avatar_split_clause,[],[f8165,f8081,f5489,f3230,f21723]) ).
fof(f21723,plain,
( spl104_888
<=> ! [X2,X0,X1] :
( ~ c_member(X0,X1,X2)
| sK58(c_Relation_OId__on(X0,X2),X0,X1,X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_888])]) ).
fof(f8081,plain,
( spl104_438
<=> ! [X0,X3,X2,X1] :
( c_member(tc_prod(X1,X3),c_Product__Type_OPair(X1,X3,sK58(X0,X1,X2,X3),X2),X0)
| ~ c_member(X3,X2,c_Relation_ORange(X1,X3,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_438])]) ).
fof(f8165,plain,
( ! [X2,X0,X1] :
( ~ c_member(X0,X1,X2)
| sK58(c_Relation_OId__on(X0,X2),X0,X1,X0) = X1 )
| ~ spl104_79
| ~ spl104_308
| ~ spl104_438 ),
inference(forward_demodulation,[],[f8143,f3231]) ).
fof(f8143,plain,
( ! [X2,X0,X1] :
( ~ c_member(X0,X1,c_Relation_ORange(X0,X0,c_Relation_OId__on(X0,X2)))
| sK58(c_Relation_OId__on(X0,X2),X0,X1,X0) = X1 )
| ~ spl104_308
| ~ spl104_438 ),
inference(resolution,[],[f8082,f5490]) ).
fof(f8082,plain,
( ! [X2,X3,X0,X1] :
( c_member(tc_prod(X1,X3),c_Product__Type_OPair(X1,X3,sK58(X0,X1,X2,X3),X2),X0)
| ~ c_member(X3,X2,c_Relation_ORange(X1,X3,X0)) )
| ~ spl104_438 ),
inference(avatar_component_clause,[],[f8081]) ).
fof(f21721,plain,
( spl104_887
| ~ spl104_196
| ~ spl104_434 ),
inference(avatar_split_clause,[],[f7983,f7618,f4032,f21719]) ).
fof(f21719,plain,
( spl104_887
<=> ! [X0,X1] : ~ c_Relation_Oirrefl(X0,c_Transitive__Closure_Otrancl(X0,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X0,X0),tc_HOL_Obool),X1,c_Relation_OId(X0)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_887])]) ).
fof(f7618,plain,
( spl104_434
<=> ! [X2,X0,X1] : c_member(tc_prod(X2,X2),c_Product__Type_OPair(X2,X2,X1,X1),c_Transitive__Closure_Otrancl(X2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),X0,c_Relation_OId(X2)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_434])]) ).
fof(f7983,plain,
( ! [X0,X1] : ~ c_Relation_Oirrefl(X0,c_Transitive__Closure_Otrancl(X0,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X0,X0),tc_HOL_Obool),X1,c_Relation_OId(X0))))
| ~ spl104_196
| ~ spl104_434 ),
inference(resolution,[],[f7619,f4033]) ).
fof(f7619,plain,
( ! [X2,X0,X1] : c_member(tc_prod(X2,X2),c_Product__Type_OPair(X2,X2,X1,X1),c_Transitive__Closure_Otrancl(X2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),X0,c_Relation_OId(X2))))
| ~ spl104_434 ),
inference(avatar_component_clause,[],[f7618]) ).
fof(f21717,plain,
( spl104_886
| ~ spl104_206
| ~ spl104_434 ),
inference(avatar_split_clause,[],[f7982,f7618,f4072,f21715]) ).
fof(f21715,plain,
( spl104_886
<=> ! [X0,X1] : ~ c_Wellfounded_Owf(X0,c_Transitive__Closure_Otrancl(X0,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X0,X0),tc_HOL_Obool),X1,c_Relation_OId(X0)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_886])]) ).
fof(f7982,plain,
( ! [X0,X1] : ~ c_Wellfounded_Owf(X0,c_Transitive__Closure_Otrancl(X0,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X0,X0),tc_HOL_Obool),X1,c_Relation_OId(X0))))
| ~ spl104_206
| ~ spl104_434 ),
inference(resolution,[],[f7619,f4073]) ).
fof(f21713,plain,
( spl104_885
| ~ spl104_106
| ~ spl104_423 ),
inference(avatar_split_clause,[],[f7707,f7568,f3363,f21711]) ).
fof(f21711,plain,
( spl104_885
<=> ! [X2,X0,X1] :
( c_Relation_Ototal__on(X0,X1,c_Wellfounded_Oacc(tc_prod(X0,X0),X2))
| ~ c_Wellfounded_Owf(tc_prod(X0,X0),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_885])]) ).
fof(f3363,plain,
( spl104_106
<=> ! [X0,X1,X3] :
( c_member(X1,X3,c_Wellfounded_Oacc(X1,X0))
| ~ c_Wellfounded_Owf(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_106])]) ).
fof(f7568,plain,
( spl104_423
<=> ! [X2,X0,X1] :
( c_Relation_Ototal__on(X2,X1,X0)
| ~ c_member(tc_prod(X2,X2),c_Product__Type_OPair(X2,X2,sK46(X0,X1,X2),sK47(X0,X1,X2)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_423])]) ).
fof(f7707,plain,
( ! [X2,X0,X1] :
( c_Relation_Ototal__on(X0,X1,c_Wellfounded_Oacc(tc_prod(X0,X0),X2))
| ~ c_Wellfounded_Owf(tc_prod(X0,X0),X2) )
| ~ spl104_106
| ~ spl104_423 ),
inference(resolution,[],[f7569,f3364]) ).
fof(f3364,plain,
( ! [X3,X0,X1] :
( c_member(X1,X3,c_Wellfounded_Oacc(X1,X0))
| ~ c_Wellfounded_Owf(X1,X0) )
| ~ spl104_106 ),
inference(avatar_component_clause,[],[f3363]) ).
fof(f7569,plain,
( ! [X2,X0,X1] :
( ~ c_member(tc_prod(X2,X2),c_Product__Type_OPair(X2,X2,sK46(X0,X1,X2),sK47(X0,X1,X2)),X0)
| c_Relation_Ototal__on(X2,X1,X0) )
| ~ spl104_423 ),
inference(avatar_component_clause,[],[f7568]) ).
fof(f21709,plain,
( spl104_884
| ~ spl104_243
| ~ spl104_412 ),
inference(avatar_split_clause,[],[f7506,f7094,f4631,f21707]) ).
fof(f21707,plain,
( spl104_884
<=> ! [X0,X1] :
( hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(tc_Nat_Onat,tc_Nat_Onat,c_Wellfounded_Oless__than),X0),X1))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_884])]) ).
fof(f4631,plain,
( spl104_243
<=> ! [X0,X1] :
( c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat,X1,X0),c_Wellfounded_Oless__than)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_243])]) ).
fof(f7506,plain,
( ! [X0,X1] :
( hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(tc_Nat_Onat,tc_Nat_Onat,c_Wellfounded_Oless__than),X0),X1))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1) )
| ~ spl104_243
| ~ spl104_412 ),
inference(resolution,[],[f7095,f4632]) ).
fof(f4632,plain,
( ! [X0,X1] :
( c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat,X1,X0),c_Wellfounded_Oless__than)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) )
| ~ spl104_243 ),
inference(avatar_component_clause,[],[f4631]) ).
fof(f21705,plain,
( spl104_883
| ~ spl104_242
| ~ spl104_411 ),
inference(avatar_split_clause,[],[f7487,f7090,f4627,f21703]) ).
fof(f21703,plain,
( spl104_883
<=> ! [X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(tc_Nat_Onat,tc_Nat_Onat,c_Wellfounded_Oless__than),X0),X1))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_883])]) ).
fof(f4627,plain,
( spl104_242
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| ~ c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat,X1,X0),c_Wellfounded_Oless__than) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_242])]) ).
fof(f7487,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(tc_Nat_Onat,tc_Nat_Onat,c_Wellfounded_Oless__than),X0),X1))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1) )
| ~ spl104_242
| ~ spl104_411 ),
inference(resolution,[],[f7091,f4628]) ).
fof(f4628,plain,
( ! [X0,X1] :
( ~ c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat,X1,X0),c_Wellfounded_Oless__than)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) )
| ~ spl104_242 ),
inference(avatar_component_clause,[],[f4627]) ).
fof(f21673,plain,
( spl104_882
| ~ spl104_259
| ~ spl104_411 ),
inference(avatar_split_clause,[],[f7486,f7090,f4703,f21671]) ).
fof(f21671,plain,
( spl104_882
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(X0,X0,c_Relation_OId(X0)),X1),X2))
| X1 = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_882])]) ).
fof(f7486,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(X0,X0,c_Relation_OId(X0)),X1),X2))
| X1 = X2 )
| ~ spl104_259
| ~ spl104_411 ),
inference(resolution,[],[f7091,f4704]) ).
fof(f21669,plain,
( spl104_881
| ~ spl104_242
| ~ spl104_395 ),
inference(avatar_split_clause,[],[f7215,f7026,f4627,f21667]) ).
fof(f21667,plain,
( spl104_881
<=> ! [X0] :
( c_member(tc_Nat_Onat,X0,c_Wellfounded_Oacc(tc_Nat_Onat,c_Wellfounded_Oless__than))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,sK51(c_Wellfounded_Oless__than,X0,tc_Nat_Onat),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_881])]) ).
fof(f7026,plain,
( spl104_395
<=> ! [X2,X0,X1] :
( c_member(X2,X1,c_Wellfounded_Oacc(X2,X0))
| c_member(tc_prod(X2,X2),c_Product__Type_OPair(X2,X2,sK51(X0,X1,X2),X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_395])]) ).
fof(f7215,plain,
( ! [X0] :
( c_member(tc_Nat_Onat,X0,c_Wellfounded_Oacc(tc_Nat_Onat,c_Wellfounded_Oless__than))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,sK51(c_Wellfounded_Oless__than,X0,tc_Nat_Onat),X0) )
| ~ spl104_242
| ~ spl104_395 ),
inference(resolution,[],[f7027,f4628]) ).
fof(f7027,plain,
( ! [X2,X0,X1] :
( c_member(tc_prod(X2,X2),c_Product__Type_OPair(X2,X2,sK51(X0,X1,X2),X1),X0)
| c_member(X2,X1,c_Wellfounded_Oacc(X2,X0)) )
| ~ spl104_395 ),
inference(avatar_component_clause,[],[f7026]) ).
fof(f21665,plain,
( spl104_880
| ~ spl104_242
| ~ spl104_394 ),
inference(avatar_split_clause,[],[f7188,f7022,f4627,f21663]) ).
fof(f21663,plain,
( spl104_880
<=> ! [X0] :
( c_member(tc_Nat_Onat,X0,c_Wellfounded_Oacc(tc_Nat_Onat,c_Wellfounded_Oless__than))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,sK42(c_Wellfounded_Oless__than,X0,tc_Nat_Onat),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_880])]) ).
fof(f7022,plain,
( spl104_394
<=> ! [X2,X0,X1] :
( c_member(X2,X1,c_Wellfounded_Oacc(X2,X0))
| c_member(tc_prod(X2,X2),c_Product__Type_OPair(X2,X2,sK42(X0,X1,X2),X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_394])]) ).
fof(f7188,plain,
( ! [X0] :
( c_member(tc_Nat_Onat,X0,c_Wellfounded_Oacc(tc_Nat_Onat,c_Wellfounded_Oless__than))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,sK42(c_Wellfounded_Oless__than,X0,tc_Nat_Onat),X0) )
| ~ spl104_242
| ~ spl104_394 ),
inference(resolution,[],[f7023,f4628]) ).
fof(f7023,plain,
( ! [X2,X0,X1] :
( c_member(tc_prod(X2,X2),c_Product__Type_OPair(X2,X2,sK42(X0,X1,X2),X1),X0)
| c_member(X2,X1,c_Wellfounded_Oacc(X2,X0)) )
| ~ spl104_394 ),
inference(avatar_component_clause,[],[f7022]) ).
fof(f21661,plain,
( spl104_879
| ~ spl104_242
| ~ spl104_393 ),
inference(avatar_split_clause,[],[f7161,f7018,f4627,f21659]) ).
fof(f21659,plain,
( spl104_879
<=> ! [X0] :
( c_member(tc_Nat_Onat,X0,c_Wellfounded_Oacc(tc_Nat_Onat,c_Wellfounded_Oless__than))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,sK40(c_Wellfounded_Oless__than,X0,tc_Nat_Onat),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_879])]) ).
fof(f7018,plain,
( spl104_393
<=> ! [X2,X0,X1] :
( c_member(tc_prod(X2,X2),c_Product__Type_OPair(X2,X2,sK40(X0,X1,X2),X1),X0)
| c_member(X2,X1,c_Wellfounded_Oacc(X2,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_393])]) ).
fof(f7161,plain,
( ! [X0] :
( c_member(tc_Nat_Onat,X0,c_Wellfounded_Oacc(tc_Nat_Onat,c_Wellfounded_Oless__than))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,sK40(c_Wellfounded_Oless__than,X0,tc_Nat_Onat),X0) )
| ~ spl104_242
| ~ spl104_393 ),
inference(resolution,[],[f7019,f4628]) ).
fof(f7019,plain,
( ! [X2,X0,X1] :
( c_member(tc_prod(X2,X2),c_Product__Type_OPair(X2,X2,sK40(X0,X1,X2),X1),X0)
| c_member(X2,X1,c_Wellfounded_Oacc(X2,X0)) )
| ~ spl104_393 ),
inference(avatar_component_clause,[],[f7018]) ).
fof(f21657,plain,
( spl104_878
| ~ spl104_354
| ~ spl104_393 ),
inference(avatar_split_clause,[],[f7157,f7018,f5973,f21655]) ).
fof(f21655,plain,
( spl104_878
<=> ! [X2,X0,X1] :
( c_member(X0,X1,c_Wellfounded_Oacc(X0,X2))
| c_member(X0,X1,c_Relation_ORange(X0,X0,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_878])]) ).
fof(f7157,plain,
( ! [X2,X0,X1] :
( c_member(X0,X1,c_Wellfounded_Oacc(X0,X2))
| c_member(X0,X1,c_Relation_ORange(X0,X0,X2)) )
| ~ spl104_354
| ~ spl104_393 ),
inference(resolution,[],[f7019,f5974]) ).
fof(f21653,plain,
( spl104_877
| ~ spl104_35
| ~ spl104_386 ),
inference(avatar_split_clause,[],[f6999,f6537,f3038,f21651]) ).
fof(f21651,plain,
( spl104_877
<=> ! [X0,X3,X2,X1] :
( c_member(X0,X1,X2)
| ~ c_Relation_Orefl__on(X0,X2,c_fequal(c_Product__Type_OPair(X0,X0,X1,X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_877])]) ).
fof(f3038,plain,
( spl104_35
<=> ! [X2,X1] : c_member(X2,X1,c_fequal(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_35])]) ).
fof(f6999,plain,
( ! [X2,X3,X0,X1] :
( c_member(X0,X1,X2)
| ~ c_Relation_Orefl__on(X0,X2,c_fequal(c_Product__Type_OPair(X0,X0,X1,X3))) )
| ~ spl104_35
| ~ spl104_386 ),
inference(resolution,[],[f6538,f3039]) ).
fof(f3039,plain,
( ! [X2,X1] : c_member(X2,X1,c_fequal(X1))
| ~ spl104_35 ),
inference(avatar_component_clause,[],[f3038]) ).
fof(f21649,plain,
( spl104_876
| ~ spl104_334
| ~ spl104_386 ),
inference(avatar_split_clause,[],[f6991,f6537,f5893,f21647]) ).
fof(f21647,plain,
( spl104_876
<=> ! [X2,X0,X1] :
( c_member(X0,sK30(X1,X0),X2)
| ~ c_Relation_Orefl__on(X0,X2,X1)
| c_Relation_Otrans(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_876])]) ).
fof(f5893,plain,
( spl104_334
<=> ! [X0,X1] :
( c_Relation_Otrans(X1,X0)
| c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,sK30(X0,X1),sK31(X0,X1)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_334])]) ).
fof(f6991,plain,
( ! [X2,X0,X1] :
( c_member(X0,sK30(X1,X0),X2)
| ~ c_Relation_Orefl__on(X0,X2,X1)
| c_Relation_Otrans(X0,X1) )
| ~ spl104_334
| ~ spl104_386 ),
inference(resolution,[],[f6538,f5894]) ).
fof(f5894,plain,
( ! [X0,X1] :
( c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,sK30(X0,X1),sK31(X0,X1)),X0)
| c_Relation_Otrans(X1,X0) )
| ~ spl104_334 ),
inference(avatar_component_clause,[],[f5893]) ).
fof(f21645,plain,
( spl104_875
| ~ spl104_329
| ~ spl104_386 ),
inference(avatar_split_clause,[],[f6987,f6537,f5873,f21643]) ).
fof(f21643,plain,
( spl104_875
<=> ! [X2,X0,X1] :
( c_member(X0,sK24(X1,X0),X2)
| ~ c_Relation_Orefl__on(X0,X2,X1)
| c_Relation_Otrans(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_875])]) ).
fof(f5873,plain,
( spl104_329
<=> ! [X0,X1] :
( c_Relation_Otrans(X1,X0)
| c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,sK24(X0,X1),sK25(X0,X1)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_329])]) ).
fof(f6987,plain,
( ! [X2,X0,X1] :
( c_member(X0,sK24(X1,X0),X2)
| ~ c_Relation_Orefl__on(X0,X2,X1)
| c_Relation_Otrans(X0,X1) )
| ~ spl104_329
| ~ spl104_386 ),
inference(resolution,[],[f6538,f5874]) ).
fof(f5874,plain,
( ! [X0,X1] :
( c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,sK24(X0,X1),sK25(X0,X1)),X0)
| c_Relation_Otrans(X1,X0) )
| ~ spl104_329 ),
inference(avatar_component_clause,[],[f5873]) ).
fof(f21641,plain,
( spl104_874
| ~ spl104_35
| ~ spl104_385 ),
inference(avatar_split_clause,[],[f6980,f6533,f3038,f21639]) ).
fof(f21639,plain,
( spl104_874
<=> ! [X0,X3,X2,X1] :
( c_member(X0,X1,X2)
| ~ c_Relation_Orefl__on(X0,X2,c_fequal(c_Product__Type_OPair(X0,X0,X3,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_874])]) ).
fof(f6980,plain,
( ! [X2,X3,X0,X1] :
( c_member(X0,X1,X2)
| ~ c_Relation_Orefl__on(X0,X2,c_fequal(c_Product__Type_OPair(X0,X0,X3,X1))) )
| ~ spl104_35
| ~ spl104_385 ),
inference(resolution,[],[f6534,f3039]) ).
fof(f21637,plain,
( spl104_873
| ~ spl104_336
| ~ spl104_385 ),
inference(avatar_split_clause,[],[f6973,f6533,f5901,f21635]) ).
fof(f21635,plain,
( spl104_873
<=> ! [X2,X0,X1] :
( c_member(X0,sK32(X1,X0),X2)
| ~ c_Relation_Orefl__on(X0,X2,X1)
| c_Relation_Otrans(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_873])]) ).
fof(f5901,plain,
( spl104_336
<=> ! [X0,X1] :
( c_Relation_Otrans(X1,X0)
| c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,sK31(X0,X1),sK32(X0,X1)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_336])]) ).
fof(f6973,plain,
( ! [X2,X0,X1] :
( c_member(X0,sK32(X1,X0),X2)
| ~ c_Relation_Orefl__on(X0,X2,X1)
| c_Relation_Otrans(X0,X1) )
| ~ spl104_336
| ~ spl104_385 ),
inference(resolution,[],[f6534,f5902]) ).
fof(f5902,plain,
( ! [X0,X1] :
( c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,sK31(X0,X1),sK32(X0,X1)),X0)
| c_Relation_Otrans(X1,X0) )
| ~ spl104_336 ),
inference(avatar_component_clause,[],[f5901]) ).
fof(f21633,plain,
( spl104_872
| ~ spl104_718
| ~ spl104_821 ),
inference(avatar_split_clause,[],[f21233,f21207,f18471,f21631]) ).
fof(f21631,plain,
( spl104_872
<=> ! [X0] : c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat,X0,c_Orderings_Obot__class_Obot(tc_Nat_Onat)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl104_872])]) ).
fof(f18471,plain,
( spl104_718
<=> ! [X0,X1] : c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl104_718])]) ).
fof(f21207,plain,
( spl104_821
<=> ! [X0] : c_Orderings_Obot__class_Obot(tc_Nat_Onat) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,c_Orderings_Obot__class_Obot(tc_Nat_Onat))) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_821])]) ).
fof(f21233,plain,
( ! [X0] : c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat,X0,c_Orderings_Obot__class_Obot(tc_Nat_Onat)) = X0
| ~ spl104_718
| ~ spl104_821 ),
inference(superposition,[],[f18472,f21208]) ).
fof(f21208,plain,
( ! [X0] : c_Orderings_Obot__class_Obot(tc_Nat_Onat) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,c_Orderings_Obot__class_Obot(tc_Nat_Onat)))
| ~ spl104_821 ),
inference(avatar_component_clause,[],[f21207]) ).
fof(f18472,plain,
( ! [X0,X1] : c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1)) = X0
| ~ spl104_718 ),
inference(avatar_component_clause,[],[f18471]) ).
fof(f21629,plain,
( spl104_871
| ~ spl104_334
| ~ spl104_385 ),
inference(avatar_split_clause,[],[f6972,f6533,f5893,f21627]) ).
fof(f21627,plain,
( spl104_871
<=> ! [X2,X0,X1] :
( c_member(X0,sK31(X1,X0),X2)
| ~ c_Relation_Orefl__on(X0,X2,X1)
| c_Relation_Otrans(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_871])]) ).
fof(f6972,plain,
( ! [X2,X0,X1] :
( c_member(X0,sK31(X1,X0),X2)
| ~ c_Relation_Orefl__on(X0,X2,X1)
| c_Relation_Otrans(X0,X1) )
| ~ spl104_334
| ~ spl104_385 ),
inference(resolution,[],[f6534,f5894]) ).
fof(f21625,plain,
( spl104_870
| ~ spl104_332
| ~ spl104_385 ),
inference(avatar_split_clause,[],[f6971,f6533,f5885,f21623]) ).
fof(f21623,plain,
( spl104_870
<=> ! [X2,X0,X1] :
( c_member(X0,sK29(X1,X0),X2)
| ~ c_Relation_Orefl__on(X0,X2,X1)
| c_Relation_Oantisym(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_870])]) ).
fof(f5885,plain,
( spl104_332
<=> ! [X0,X1] :
( c_Relation_Oantisym(X1,X0)
| c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,sK28(X0,X1),sK29(X0,X1)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_332])]) ).
fof(f6971,plain,
( ! [X2,X0,X1] :
( c_member(X0,sK29(X1,X0),X2)
| ~ c_Relation_Orefl__on(X0,X2,X1)
| c_Relation_Oantisym(X0,X1) )
| ~ spl104_332
| ~ spl104_385 ),
inference(resolution,[],[f6534,f5886]) ).
fof(f5886,plain,
( ! [X0,X1] :
( c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,sK28(X0,X1),sK29(X0,X1)),X0)
| c_Relation_Oantisym(X1,X0) )
| ~ spl104_332 ),
inference(avatar_component_clause,[],[f5885]) ).
fof(f21621,plain,
( spl104_869
| ~ spl104_333
| ~ spl104_385 ),
inference(avatar_split_clause,[],[f6970,f6533,f5889,f21619]) ).
fof(f21619,plain,
( spl104_869
<=> ! [X2,X0,X1] :
( c_member(X0,sK28(X1,X0),X2)
| ~ c_Relation_Orefl__on(X0,X2,X1)
| c_Relation_Oantisym(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_869])]) ).
fof(f5889,plain,
( spl104_333
<=> ! [X0,X1] :
( c_Relation_Oantisym(X1,X0)
| c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,sK29(X0,X1),sK28(X0,X1)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_333])]) ).
fof(f6970,plain,
( ! [X2,X0,X1] :
( c_member(X0,sK28(X1,X0),X2)
| ~ c_Relation_Orefl__on(X0,X2,X1)
| c_Relation_Oantisym(X0,X1) )
| ~ spl104_333
| ~ spl104_385 ),
inference(resolution,[],[f6534,f5890]) ).
fof(f5890,plain,
( ! [X0,X1] :
( c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,sK29(X0,X1),sK28(X0,X1)),X0)
| c_Relation_Oantisym(X1,X0) )
| ~ spl104_333 ),
inference(avatar_component_clause,[],[f5889]) ).
fof(f21617,plain,
( spl104_868
| ~ spl104_330
| ~ spl104_385 ),
inference(avatar_split_clause,[],[f6969,f6533,f5877,f21615]) ).
fof(f21615,plain,
( spl104_868
<=> ! [X2,X0,X1] :
( c_member(X0,sK26(X1,X0),X2)
| ~ c_Relation_Orefl__on(X0,X2,X1)
| c_Relation_Otrans(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_868])]) ).
fof(f5877,plain,
( spl104_330
<=> ! [X0,X1] :
( c_Relation_Otrans(X1,X0)
| c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,sK25(X0,X1),sK26(X0,X1)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_330])]) ).
fof(f6969,plain,
( ! [X2,X0,X1] :
( c_member(X0,sK26(X1,X0),X2)
| ~ c_Relation_Orefl__on(X0,X2,X1)
| c_Relation_Otrans(X0,X1) )
| ~ spl104_330
| ~ spl104_385 ),
inference(resolution,[],[f6534,f5878]) ).
fof(f5878,plain,
( ! [X0,X1] :
( c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,sK25(X0,X1),sK26(X0,X1)),X0)
| c_Relation_Otrans(X1,X0) )
| ~ spl104_330 ),
inference(avatar_component_clause,[],[f5877]) ).
fof(f21613,plain,
( spl104_867
| ~ spl104_329
| ~ spl104_385 ),
inference(avatar_split_clause,[],[f6968,f6533,f5873,f21611]) ).
fof(f21611,plain,
( spl104_867
<=> ! [X2,X0,X1] :
( c_member(X0,sK25(X1,X0),X2)
| ~ c_Relation_Orefl__on(X0,X2,X1)
| c_Relation_Otrans(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_867])]) ).
fof(f6968,plain,
( ! [X2,X0,X1] :
( c_member(X0,sK25(X1,X0),X2)
| ~ c_Relation_Orefl__on(X0,X2,X1)
| c_Relation_Otrans(X0,X1) )
| ~ spl104_329
| ~ spl104_385 ),
inference(resolution,[],[f6534,f5874]) ).
fof(f21609,plain,
( spl104_866
| ~ spl104_327
| ~ spl104_385 ),
inference(avatar_split_clause,[],[f6967,f6533,f5865,f21607]) ).
fof(f21607,plain,
( spl104_866
<=> ! [X2,X0,X1] :
( c_member(X0,sK23(X1,X0),X2)
| ~ c_Relation_Orefl__on(X0,X2,X1)
| c_Relation_Oantisym(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_866])]) ).
fof(f5865,plain,
( spl104_327
<=> ! [X0,X1] :
( c_Relation_Oantisym(X1,X0)
| c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,sK22(X0,X1),sK23(X0,X1)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_327])]) ).
fof(f6967,plain,
( ! [X2,X0,X1] :
( c_member(X0,sK23(X1,X0),X2)
| ~ c_Relation_Orefl__on(X0,X2,X1)
| c_Relation_Oantisym(X0,X1) )
| ~ spl104_327
| ~ spl104_385 ),
inference(resolution,[],[f6534,f5866]) ).
fof(f5866,plain,
( ! [X0,X1] :
( c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,sK22(X0,X1),sK23(X0,X1)),X0)
| c_Relation_Oantisym(X1,X0) )
| ~ spl104_327 ),
inference(avatar_component_clause,[],[f5865]) ).
fof(f21605,plain,
( spl104_865
| ~ spl104_328
| ~ spl104_385 ),
inference(avatar_split_clause,[],[f6966,f6533,f5869,f21603]) ).
fof(f21603,plain,
( spl104_865
<=> ! [X2,X0,X1] :
( c_member(X0,sK22(X1,X0),X2)
| ~ c_Relation_Orefl__on(X0,X2,X1)
| c_Relation_Oantisym(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_865])]) ).
fof(f5869,plain,
( spl104_328
<=> ! [X0,X1] :
( c_Relation_Oantisym(X1,X0)
| c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,sK23(X0,X1),sK22(X0,X1)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_328])]) ).
fof(f6966,plain,
( ! [X2,X0,X1] :
( c_member(X0,sK22(X1,X0),X2)
| ~ c_Relation_Orefl__on(X0,X2,X1)
| c_Relation_Oantisym(X0,X1) )
| ~ spl104_328
| ~ spl104_385 ),
inference(resolution,[],[f6534,f5870]) ).
fof(f5870,plain,
( ! [X0,X1] :
( c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,sK23(X0,X1),sK22(X0,X1)),X0)
| c_Relation_Oantisym(X1,X0) )
| ~ spl104_328 ),
inference(avatar_component_clause,[],[f5869]) ).
fof(f21601,plain,
( spl104_864
| ~ spl104_222
| ~ spl104_384 ),
inference(avatar_split_clause,[],[f6938,f6529,f4136,f21599]) ).
fof(f21599,plain,
( spl104_864
<=> ! [X2,X4,X0,X3,X1] :
( ~ hBOOL(hAPP(X0,X1))
| sP8(X0,X2,X3,X4)
| ~ c_member(X4,X1,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_864])]) ).
fof(f4136,plain,
( spl104_222
<=> ! [X0,X3,X2,X1] :
( c_member(X3,X2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),X1,X0))
| ~ c_member(X3,X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_222])]) ).
fof(f6529,plain,
( spl104_384
<=> ! [X4,X0,X3,X2,X1] :
( sP8(X0,X1,X2,X3)
| ~ hBOOL(hAPP(X0,X4))
| ~ c_member(X3,X4,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),X2,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_384])]) ).
fof(f6938,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ hBOOL(hAPP(X0,X1))
| sP8(X0,X2,X3,X4)
| ~ c_member(X4,X1,X3) )
| ~ spl104_222
| ~ spl104_384 ),
inference(resolution,[],[f6530,f4137]) ).
fof(f4137,plain,
( ! [X2,X3,X0,X1] :
( c_member(X3,X2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),X1,X0))
| ~ c_member(X3,X2,X1) )
| ~ spl104_222 ),
inference(avatar_component_clause,[],[f4136]) ).
fof(f6530,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ c_member(X3,X4,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),X2,X1))
| ~ hBOOL(hAPP(X0,X4))
| sP8(X0,X1,X2,X3) )
| ~ spl104_384 ),
inference(avatar_component_clause,[],[f6529]) ).
fof(f21597,plain,
( spl104_863
| ~ spl104_223
| ~ spl104_384 ),
inference(avatar_split_clause,[],[f6937,f6529,f4140,f21595]) ).
fof(f21595,plain,
( spl104_863
<=> ! [X2,X4,X0,X3,X1] :
( ~ hBOOL(hAPP(X0,X1))
| sP8(X0,X2,X3,X4)
| ~ c_member(X4,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_863])]) ).
fof(f4140,plain,
( spl104_223
<=> ! [X0,X3,X2,X1] :
( c_member(X3,X2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),X0,X1))
| ~ c_member(X3,X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_223])]) ).
fof(f6937,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ hBOOL(hAPP(X0,X1))
| sP8(X0,X2,X3,X4)
| ~ c_member(X4,X1,X2) )
| ~ spl104_223
| ~ spl104_384 ),
inference(resolution,[],[f6530,f4141]) ).
fof(f4141,plain,
( ! [X2,X3,X0,X1] :
( c_member(X3,X2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),X0,X1))
| ~ c_member(X3,X2,X1) )
| ~ spl104_223 ),
inference(avatar_component_clause,[],[f4140]) ).
fof(f21593,plain,
( spl104_862
| ~ spl104_78
| ~ spl104_383 ),
inference(avatar_split_clause,[],[f6927,f6525,f3226,f21591]) ).
fof(f21591,plain,
( spl104_862
<=> ! [X2,X0,X1] :
( c_member(X0,sK75(X2,X1,X1,X0),X1)
| ~ sP8(X2,X1,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_862])]) ).
fof(f3226,plain,
( spl104_78
<=> ! [X0,X1] : c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool),X0,X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl104_78])]) ).
fof(f6525,plain,
( spl104_383
<=> ! [X0,X3,X2,X1] :
( c_member(X3,sK75(X0,X1,X2,X3),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),X2,X1))
| ~ sP8(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_383])]) ).
fof(f6927,plain,
( ! [X2,X0,X1] :
( c_member(X0,sK75(X2,X1,X1,X0),X1)
| ~ sP8(X2,X1,X1,X0) )
| ~ spl104_78
| ~ spl104_383 ),
inference(superposition,[],[f6526,f3227]) ).
fof(f3227,plain,
( ! [X0,X1] : c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool),X0,X0) = X0
| ~ spl104_78 ),
inference(avatar_component_clause,[],[f3226]) ).
fof(f6526,plain,
( ! [X2,X3,X0,X1] :
( c_member(X3,sK75(X0,X1,X2,X3),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),X2,X1))
| ~ sP8(X0,X1,X2,X3) )
| ~ spl104_383 ),
inference(avatar_component_clause,[],[f6525]) ).
fof(f21589,plain,
( spl104_861
| ~ spl104_27
| ~ spl104_816 ),
inference(avatar_split_clause,[],[f21156,f21153,f3004,f21587]) ).
fof(f21587,plain,
( spl104_861
<=> ! [X0,X1] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat,X1,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_861])]) ).
fof(f3004,plain,
( spl104_27
<=> ! [X0] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_27])]) ).
fof(f21153,plain,
( spl104_816
<=> ! [X2,X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat,X0,X1),X2)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_816])]) ).
fof(f21156,plain,
( ! [X0,X1] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat,X1,X0))
| ~ spl104_27
| ~ spl104_816 ),
inference(resolution,[],[f21154,f3005]) ).
fof(f3005,plain,
( ! [X0] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X0)
| ~ spl104_27 ),
inference(avatar_component_clause,[],[f3004]) ).
fof(f21154,plain,
( ! [X2,X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat,X0,X1),X2)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) )
| ~ spl104_816 ),
inference(avatar_component_clause,[],[f21153]) ).
fof(f21585,plain,
( spl104_860
| ~ spl104_78
| ~ spl104_380 ),
inference(avatar_split_clause,[],[f6887,f6513,f3226,f21583]) ).
fof(f21583,plain,
( spl104_860
<=> ! [X2,X0,X1] :
( c_member(X0,sK72(X2,X1,X1,X0),X1)
| sP7(X2,X1,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_860])]) ).
fof(f6513,plain,
( spl104_380
<=> ! [X0,X3,X2,X1] :
( sP7(X0,X1,X3,X2)
| c_member(X3,sK72(X0,X1,X2,X3),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),X2,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_380])]) ).
fof(f6887,plain,
( ! [X2,X0,X1] :
( c_member(X0,sK72(X2,X1,X1,X0),X1)
| sP7(X2,X1,X0,X1) )
| ~ spl104_78
| ~ spl104_380 ),
inference(superposition,[],[f6514,f3227]) ).
fof(f6514,plain,
( ! [X2,X3,X0,X1] :
( c_member(X3,sK72(X0,X1,X2,X3),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),X2,X1))
| sP7(X0,X1,X3,X2) )
| ~ spl104_380 ),
inference(avatar_component_clause,[],[f6513]) ).
fof(f21581,plain,
( spl104_859
| ~ spl104_108
| ~ spl104_315 ),
inference(avatar_split_clause,[],[f5801,f5726,f3371,f21579]) ).
fof(f21579,plain,
( spl104_859
<=> ! [X0,X3,X2,X1] :
( ~ c_Relation_Osingle__valued(X0,X1,c_Set_Oinsert(tc_prod(X0,X1),X2,X3))
| c_Relation_Osingle__valued(X0,X1,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_859])]) ).
fof(f3371,plain,
( spl104_108
<=> ! [X2,X0,X1] : c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool),X1,c_Set_Oinsert(X2,X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_108])]) ).
fof(f5726,plain,
( spl104_315
<=> ! [X0,X3,X2,X1] :
( c_Relation_Osingle__valued(X3,X2,X1)
| ~ c_Relation_Osingle__valued(X3,X2,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X3,X2),tc_HOL_Obool),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_315])]) ).
fof(f5801,plain,
( ! [X2,X3,X0,X1] :
( ~ c_Relation_Osingle__valued(X0,X1,c_Set_Oinsert(tc_prod(X0,X1),X2,X3))
| c_Relation_Osingle__valued(X0,X1,X3) )
| ~ spl104_108
| ~ spl104_315 ),
inference(resolution,[],[f5727,f3372]) ).
fof(f3372,plain,
( ! [X2,X0,X1] : c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool),X1,c_Set_Oinsert(X2,X0,X1))
| ~ spl104_108 ),
inference(avatar_component_clause,[],[f3371]) ).
fof(f5727,plain,
( ! [X2,X3,X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X3,X2),tc_HOL_Obool),X1,X0)
| ~ c_Relation_Osingle__valued(X3,X2,X0)
| c_Relation_Osingle__valued(X3,X2,X1) )
| ~ spl104_315 ),
inference(avatar_component_clause,[],[f5726]) ).
fof(f21555,plain,
( ~ spl104_12
| spl104_858
| ~ spl104_108
| ~ spl104_314 ),
inference(avatar_split_clause,[],[f5779,f5722,f3371,f21553,f2932]) ).
fof(f2932,plain,
( spl104_12
<=> class_Orderings_Oord(tc_HOL_Obool) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_12])]) ).
fof(f21553,plain,
( spl104_858
<=> ! [X0,X3,X2,X1] : c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,hAPP(X0,X1),hAPP(c_Set_Oinsert(X2,X3,X0),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_858])]) ).
fof(f5722,plain,
( spl104_314
<=> ! [X2,X3,X0,X5,X1] :
( c_Orderings_Oord__class_Oless__eq(X3,hAPP(X1,X5),hAPP(X0,X5))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X2,X3),X1,X0)
| ~ class_Orderings_Oord(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_314])]) ).
fof(f5779,plain,
( ! [X2,X3,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,hAPP(X0,X1),hAPP(c_Set_Oinsert(X2,X3,X0),X1))
| ~ class_Orderings_Oord(tc_HOL_Obool) )
| ~ spl104_108
| ~ spl104_314 ),
inference(resolution,[],[f5723,f3372]) ).
fof(f5723,plain,
( ! [X2,X3,X0,X1,X5] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X2,X3),X1,X0)
| c_Orderings_Oord__class_Oless__eq(X3,hAPP(X1,X5),hAPP(X0,X5))
| ~ class_Orderings_Oord(X3) )
| ~ spl104_314 ),
inference(avatar_component_clause,[],[f5722]) ).
fof(f21551,plain,
( spl104_857
| ~ spl104_65
| ~ spl104_289 ),
inference(avatar_split_clause,[],[f5512,f5399,f3169,f21549]) ).
fof(f21549,plain,
( spl104_857
<=> ! [X2,X0,X1] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X2),X1),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_857])]) ).
fof(f3169,plain,
( spl104_65
<=> ! [X0,X1] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_65])]) ).
fof(f5399,plain,
( spl104_289
<=> ! [X2,X0,X1] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),X0) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X0),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_289])]) ).
fof(f5512,plain,
( ! [X2,X0,X1] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X2),X1),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1))
| ~ spl104_65
| ~ spl104_289 ),
inference(superposition,[],[f3170,f5400]) ).
fof(f5400,plain,
( ! [X2,X0,X1] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),X0) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X0),X1)
| ~ spl104_289 ),
inference(avatar_component_clause,[],[f5399]) ).
fof(f3170,plain,
( ! [X0,X1] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0),X1)
| ~ spl104_65 ),
inference(avatar_component_clause,[],[f3169]) ).
fof(f21543,plain,
( ~ spl104_59
| spl104_856
| ~ spl104_28
| ~ spl104_287 ),
inference(avatar_split_clause,[],[f5493,f5391,f3008,f21541,f3141]) ).
fof(f3141,plain,
( spl104_59
<=> c_Wellfounded_Oacyclic(tc_Nat_Onat,c_Wellfounded_Opred__nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_59])]) ).
fof(f21541,plain,
( spl104_856
<=> ! [X0] : ~ c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat,X0,X0),c_Wellfounded_Oless__than) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_856])]) ).
fof(f3008,plain,
( spl104_28
<=> c_Wellfounded_Oless__than = c_Transitive__Closure_Otrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_28])]) ).
fof(f5391,plain,
( spl104_287
<=> ! [X0,X1,X3] :
( ~ c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,X3,X3),c_Transitive__Closure_Otrancl(X1,X0))
| ~ c_Wellfounded_Oacyclic(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_287])]) ).
fof(f5493,plain,
( ! [X0] :
( ~ c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat,X0,X0),c_Wellfounded_Oless__than)
| ~ c_Wellfounded_Oacyclic(tc_Nat_Onat,c_Wellfounded_Opred__nat) )
| ~ spl104_28
| ~ spl104_287 ),
inference(superposition,[],[f5392,f3010]) ).
fof(f3010,plain,
( c_Wellfounded_Oless__than = c_Transitive__Closure_Otrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat)
| ~ spl104_28 ),
inference(avatar_component_clause,[],[f3008]) ).
fof(f5392,plain,
( ! [X3,X0,X1] :
( ~ c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,X3,X3),c_Transitive__Closure_Otrancl(X1,X0))
| ~ c_Wellfounded_Oacyclic(X1,X0) )
| ~ spl104_287 ),
inference(avatar_component_clause,[],[f5391]) ).
fof(f21539,plain,
( spl104_855
| ~ spl104_256
| ~ spl104_287 ),
inference(avatar_split_clause,[],[f5492,f5391,f4685,f21537]) ).
fof(f4685,plain,
( spl104_256
<=> ! [X2,X0,X1] :
( c_member(tc_prod(X2,X2),X1,c_Transitive__Closure_Otrancl(X2,X0))
| ~ c_member(tc_prod(X2,X2),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_256])]) ).
fof(f5492,plain,
( ! [X2,X0,X1] :
( ~ c_Wellfounded_Oacyclic(X0,X1)
| ~ c_member(tc_prod(X0,X0),c_Product__Type_OPair(X0,X0,X2,X2),X1) )
| ~ spl104_256
| ~ spl104_287 ),
inference(resolution,[],[f5392,f4686]) ).
fof(f4686,plain,
( ! [X2,X0,X1] :
( c_member(tc_prod(X2,X2),X1,c_Transitive__Closure_Otrancl(X2,X0))
| ~ c_member(tc_prod(X2,X2),X1,X0) )
| ~ spl104_256 ),
inference(avatar_component_clause,[],[f4685]) ).
fof(f21535,plain,
( spl104_854
| ~ spl104_155
| ~ spl104_279 ),
inference(avatar_split_clause,[],[f5346,f4810,f3626,f21533]) ).
fof(f21533,plain,
( spl104_854
<=> ! [X0,X3,X2,X1] : sP6(X0,c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool),c_Set_Oinsert(X1,X2,X0),X3),X1,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_854])]) ).
fof(f3626,plain,
( spl104_155
<=> ! [X2,X0,X1] : c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool),c_Groups_Ominus__class_Ominus(tc_fun(X2,tc_HOL_Obool),X1,X0),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_155])]) ).
fof(f4810,plain,
( spl104_279
<=> ! [X0,X3,X2,X1] :
( sP6(X0,X2,X3,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X2,c_Set_Oinsert(X3,X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_279])]) ).
fof(f5346,plain,
( ! [X2,X3,X0,X1] : sP6(X0,c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool),c_Set_Oinsert(X1,X2,X0),X3),X1,X2)
| ~ spl104_155
| ~ spl104_279 ),
inference(resolution,[],[f4811,f3627]) ).
fof(f3627,plain,
( ! [X2,X0,X1] : c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool),c_Groups_Ominus__class_Ominus(tc_fun(X2,tc_HOL_Obool),X1,X0),X1)
| ~ spl104_155 ),
inference(avatar_component_clause,[],[f3626]) ).
fof(f4811,plain,
( ! [X2,X3,X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X2,c_Set_Oinsert(X3,X1,X0))
| sP6(X0,X2,X3,X1) )
| ~ spl104_279 ),
inference(avatar_component_clause,[],[f4810]) ).
fof(f21531,plain,
( spl104_853
| ~ spl104_155
| ~ spl104_270 ),
inference(avatar_split_clause,[],[f5271,f4760,f3626,f21529]) ).
fof(f21529,plain,
( spl104_853
<=> ! [X2,X0,X1,X3] :
( hBOOL(hAPP(X0,X1))
| ~ hBOOL(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X2,tc_HOL_Obool),X0,X3),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_853])]) ).
fof(f4760,plain,
( spl104_270
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP(X0,X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X3,X0)
| ~ hBOOL(hAPP(X3,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_270])]) ).
fof(f5271,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(hAPP(X0,X1))
| ~ hBOOL(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X2,tc_HOL_Obool),X0,X3),X1)) )
| ~ spl104_155
| ~ spl104_270 ),
inference(resolution,[],[f4761,f3627]) ).
fof(f4761,plain,
( ! [X2,X3,X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X3,X0)
| hBOOL(hAPP(X0,X2))
| ~ hBOOL(hAPP(X3,X2)) )
| ~ spl104_270 ),
inference(avatar_component_clause,[],[f4760]) ).
fof(f21496,plain,
( ~ spl104_17
| spl104_852
| ~ spl104_65
| ~ spl104_269 ),
inference(avatar_split_clause,[],[f5263,f4756,f3169,f21494,f2957]) ).
fof(f2957,plain,
( spl104_17
<=> class_Orderings_Oorder(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_17])]) ).
fof(f21494,plain,
( spl104_852
<=> ! [X2,X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_852])]) ).
fof(f4756,plain,
( spl104_269
<=> ! [X0,X3,X2,X1] :
( c_Orderings_Oord__class_Oless__eq(X3,X0,X1)
| ~ c_Orderings_Oord__class_Oless__eq(X3,X0,X2)
| ~ c_Orderings_Oord__class_Oless__eq(X3,X2,X1)
| ~ class_Orderings_Oorder(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_269])]) ).
fof(f5263,plain,
( ! [X2,X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1)
| ~ class_Orderings_Oorder(tc_Nat_Onat) )
| ~ spl104_65
| ~ spl104_269 ),
inference(resolution,[],[f4757,f3170]) ).
fof(f4757,plain,
( ! [X2,X3,X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(X3,X2,X1)
| ~ c_Orderings_Oord__class_Oless__eq(X3,X0,X2)
| c_Orderings_Oord__class_Oless__eq(X3,X0,X1)
| ~ class_Orderings_Oorder(X3) )
| ~ spl104_269 ),
inference(avatar_component_clause,[],[f4756]) ).
fof(f21492,plain,
( spl104_851
| ~ spl104_67
| ~ spl104_269 ),
inference(avatar_split_clause,[],[f5245,f4756,f3178,f21490]) ).
fof(f21490,plain,
( spl104_851
<=> ! [X2,X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(X0,X1,c_Orderings_Obot__class_Obot(X0))
| c_Orderings_Oord__class_Oless__eq(X0,X1,X2)
| ~ class_Orderings_Oorder(X0)
| ~ class_Orderings_Obot(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_851])]) ).
fof(f3178,plain,
( spl104_67
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X1,c_Orderings_Obot__class_Obot(X1),X0)
| ~ class_Orderings_Obot(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_67])]) ).
fof(f5245,plain,
( ! [X2,X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(X0,X1,c_Orderings_Obot__class_Obot(X0))
| c_Orderings_Oord__class_Oless__eq(X0,X1,X2)
| ~ class_Orderings_Oorder(X0)
| ~ class_Orderings_Obot(X0) )
| ~ spl104_67
| ~ spl104_269 ),
inference(resolution,[],[f4757,f3179]) ).
fof(f3179,plain,
( ! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X1,c_Orderings_Obot__class_Obot(X1),X0)
| ~ class_Orderings_Obot(X1) )
| ~ spl104_67 ),
inference(avatar_component_clause,[],[f3178]) ).
fof(f21488,plain,
( spl104_850
| ~ spl104_67
| ~ spl104_268 ),
inference(avatar_split_clause,[],[f5218,f4752,f3178,f21486]) ).
fof(f21486,plain,
( spl104_850
<=> ! [X2,X0,X1] :
( ~ c_Orderings_Oord__class_Oless(X0,X1,c_Orderings_Obot__class_Obot(X0))
| c_Orderings_Oord__class_Oless(X0,X1,X2)
| ~ class_Orderings_Oorder(X0)
| ~ class_Orderings_Obot(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_850])]) ).
fof(f4752,plain,
( spl104_268
<=> ! [X0,X3,X2,X1] :
( c_Orderings_Oord__class_Oless(X3,X0,X1)
| ~ c_Orderings_Oord__class_Oless(X3,X0,X2)
| ~ c_Orderings_Oord__class_Oless__eq(X3,X2,X1)
| ~ class_Orderings_Oorder(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_268])]) ).
fof(f5218,plain,
( ! [X2,X0,X1] :
( ~ c_Orderings_Oord__class_Oless(X0,X1,c_Orderings_Obot__class_Obot(X0))
| c_Orderings_Oord__class_Oless(X0,X1,X2)
| ~ class_Orderings_Oorder(X0)
| ~ class_Orderings_Obot(X0) )
| ~ spl104_67
| ~ spl104_268 ),
inference(resolution,[],[f4753,f3179]) ).
fof(f4753,plain,
( ! [X2,X3,X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(X3,X2,X1)
| ~ c_Orderings_Oord__class_Oless(X3,X0,X2)
| c_Orderings_Oord__class_Oless(X3,X0,X1)
| ~ class_Orderings_Oorder(X3) )
| ~ spl104_268 ),
inference(avatar_component_clause,[],[f4752]) ).
fof(f21484,plain,
( spl104_849
| ~ spl104_67
| ~ spl104_267 ),
inference(avatar_split_clause,[],[f5191,f4735,f3178,f21482]) ).
fof(f21482,plain,
( spl104_849
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless(X0,c_Orderings_Obot__class_Obot(X0),X1)
| ~ c_Orderings_Oord__class_Oless(X0,X2,X1)
| ~ class_Orderings_Oorder(X0)
| ~ class_Orderings_Obot(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_849])]) ).
fof(f4735,plain,
( spl104_267
<=> ! [X0,X3,X2,X1] :
( c_Orderings_Oord__class_Oless(X3,X0,X1)
| ~ c_Orderings_Oord__class_Oless__eq(X3,X0,X2)
| ~ c_Orderings_Oord__class_Oless(X3,X2,X1)
| ~ class_Orderings_Oorder(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_267])]) ).
fof(f5191,plain,
( ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless(X0,c_Orderings_Obot__class_Obot(X0),X1)
| ~ c_Orderings_Oord__class_Oless(X0,X2,X1)
| ~ class_Orderings_Oorder(X0)
| ~ class_Orderings_Obot(X0) )
| ~ spl104_67
| ~ spl104_267 ),
inference(resolution,[],[f4736,f3179]) ).
fof(f4736,plain,
( ! [X2,X3,X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(X3,X0,X2)
| c_Orderings_Oord__class_Oless(X3,X0,X1)
| ~ c_Orderings_Oord__class_Oless(X3,X2,X1)
| ~ class_Orderings_Oorder(X3) )
| ~ spl104_267 ),
inference(avatar_component_clause,[],[f4735]) ).
fof(f21480,plain,
( spl104_848
| ~ spl104_67
| ~ spl104_264 ),
inference(avatar_split_clause,[],[f5130,f4723,f3178,f21478]) ).
fof(f21478,plain,
( spl104_848
<=> ! [X2,X0,X1] :
( ~ c_Orderings_Oord__class_Oless(X0,X1,X2)
| c_Orderings_Oord__class_Oless(X0,c_Orderings_Obot__class_Obot(X0),X2)
| ~ class_Orderings_Opreorder(X0)
| ~ class_Orderings_Obot(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_848])]) ).
fof(f4723,plain,
( spl104_264
<=> ! [X0,X3,X2,X1] :
( c_Orderings_Oord__class_Oless(X3,X2,X0)
| ~ c_Orderings_Oord__class_Oless(X3,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(X3,X2,X1)
| ~ class_Orderings_Opreorder(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_264])]) ).
fof(f5130,plain,
( ! [X2,X0,X1] :
( ~ c_Orderings_Oord__class_Oless(X0,X1,X2)
| c_Orderings_Oord__class_Oless(X0,c_Orderings_Obot__class_Obot(X0),X2)
| ~ class_Orderings_Opreorder(X0)
| ~ class_Orderings_Obot(X0) )
| ~ spl104_67
| ~ spl104_264 ),
inference(resolution,[],[f4724,f3179]) ).
fof(f4724,plain,
( ! [X2,X3,X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(X3,X2,X1)
| ~ c_Orderings_Oord__class_Oless(X3,X1,X0)
| c_Orderings_Oord__class_Oless(X3,X2,X0)
| ~ class_Orderings_Opreorder(X3) )
| ~ spl104_264 ),
inference(avatar_component_clause,[],[f4723]) ).
fof(f21463,plain,
( ~ spl104_14
| spl104_847
| ~ spl104_65
| ~ spl104_263 ),
inference(avatar_split_clause,[],[f5121,f4719,f3169,f21461,f2942]) ).
fof(f2942,plain,
( spl104_14
<=> class_Orderings_Opreorder(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_14])]) ).
fof(f21461,plain,
( spl104_847
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_847])]) ).
fof(f4719,plain,
( spl104_263
<=> ! [X0,X3,X2,X1] :
( c_Orderings_Oord__class_Oless(X3,X2,X0)
| ~ c_Orderings_Oord__class_Oless__eq(X3,X1,X0)
| ~ c_Orderings_Oord__class_Oless(X3,X2,X1)
| ~ class_Orderings_Opreorder(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_263])]) ).
fof(f5121,plain,
( ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2))
| ~ class_Orderings_Opreorder(tc_Nat_Onat) )
| ~ spl104_65
| ~ spl104_263 ),
inference(resolution,[],[f4720,f3170]) ).
fof(f4720,plain,
( ! [X2,X3,X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(X3,X1,X0)
| c_Orderings_Oord__class_Oless(X3,X2,X0)
| ~ c_Orderings_Oord__class_Oless(X3,X2,X1)
| ~ class_Orderings_Opreorder(X3) )
| ~ spl104_263 ),
inference(avatar_component_clause,[],[f4719]) ).
fof(f21426,plain,
( ~ spl104_12
| spl104_846
| ~ spl104_153
| ~ spl104_261 ),
inference(avatar_split_clause,[],[f5078,f4711,f3618,f21424,f2932]) ).
fof(f21424,plain,
( spl104_846
<=> ! [X2,X0,X1] : ~ c_Orderings_Oord__class_Oless(tc_fun(X0,tc_HOL_Obool),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X0,tc_HOL_Obool),X1,X2),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_846])]) ).
fof(f3618,plain,
( spl104_153
<=> ! [X2,X0,X1] : c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool),X1,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool),X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_153])]) ).
fof(f4711,plain,
( spl104_261
<=> ! [X0,X3,X2,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X2,X3),X0,X1)
| ~ c_Orderings_Oord__class_Oless(tc_fun(X2,X3),X1,X0)
| ~ class_Orderings_Oord(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_261])]) ).
fof(f5078,plain,
( ! [X2,X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_fun(X0,tc_HOL_Obool),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X0,tc_HOL_Obool),X1,X2),X2)
| ~ class_Orderings_Oord(tc_HOL_Obool) )
| ~ spl104_153
| ~ spl104_261 ),
inference(resolution,[],[f4712,f3619]) ).
fof(f3619,plain,
( ! [X2,X0,X1] : c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool),X1,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool),X0,X1))
| ~ spl104_153 ),
inference(avatar_component_clause,[],[f3618]) ).
fof(f4712,plain,
( ! [X2,X3,X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X2,X3),X0,X1)
| ~ c_Orderings_Oord__class_Oless(tc_fun(X2,X3),X1,X0)
| ~ class_Orderings_Oord(X3) )
| ~ spl104_261 ),
inference(avatar_component_clause,[],[f4711]) ).
fof(f21391,plain,
( ~ spl104_12
| spl104_845
| ~ spl104_155
| ~ spl104_261 ),
inference(avatar_split_clause,[],[f5076,f4711,f3626,f21389,f2932]) ).
fof(f21389,plain,
( spl104_845
<=> ! [X2,X0,X1] : ~ c_Orderings_Oord__class_Oless(tc_fun(X0,tc_HOL_Obool),X1,c_Groups_Ominus__class_Ominus(tc_fun(X0,tc_HOL_Obool),X1,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_845])]) ).
fof(f5076,plain,
( ! [X2,X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_fun(X0,tc_HOL_Obool),X1,c_Groups_Ominus__class_Ominus(tc_fun(X0,tc_HOL_Obool),X1,X2))
| ~ class_Orderings_Oord(tc_HOL_Obool) )
| ~ spl104_155
| ~ spl104_261 ),
inference(resolution,[],[f4712,f3627]) ).
fof(f21387,plain,
( spl104_844
| ~ spl104_154
| ~ spl104_257 ),
inference(avatar_split_clause,[],[f5046,f4689,f3622,f21385]) ).
fof(f21385,plain,
( spl104_844
<=> ! [X2,X0,X1] :
( ~ c_Relation_Oantisym(X0,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X0,X0),tc_HOL_Obool),X1,X2))
| c_Relation_Oantisym(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_844])]) ).
fof(f3622,plain,
( spl104_154
<=> ! [X2,X0,X1] : c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool),X1,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool),X1,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_154])]) ).
fof(f4689,plain,
( spl104_257
<=> ! [X2,X0,X1] :
( c_Relation_Oantisym(X2,X1)
| ~ c_Relation_Oantisym(X2,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_257])]) ).
fof(f5046,plain,
( ! [X2,X0,X1] :
( ~ c_Relation_Oantisym(X0,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X0,X0),tc_HOL_Obool),X1,X2))
| c_Relation_Oantisym(X0,X1) )
| ~ spl104_154
| ~ spl104_257 ),
inference(resolution,[],[f4690,f3623]) ).
fof(f3623,plain,
( ! [X2,X0,X1] : c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool),X1,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool),X1,X0))
| ~ spl104_154 ),
inference(avatar_component_clause,[],[f3622]) ).
fof(f4690,plain,
( ! [X2,X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),X1,X0)
| ~ c_Relation_Oantisym(X2,X0)
| c_Relation_Oantisym(X2,X1) )
| ~ spl104_257 ),
inference(avatar_component_clause,[],[f4689]) ).
fof(f21383,plain,
( spl104_843
| ~ spl104_153
| ~ spl104_257 ),
inference(avatar_split_clause,[],[f5045,f4689,f3618,f21381]) ).
fof(f21381,plain,
( spl104_843
<=> ! [X2,X0,X1] :
( ~ c_Relation_Oantisym(X0,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X0,X0),tc_HOL_Obool),X1,X2))
| c_Relation_Oantisym(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_843])]) ).
fof(f5045,plain,
( ! [X2,X0,X1] :
( ~ c_Relation_Oantisym(X0,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X0,X0),tc_HOL_Obool),X1,X2))
| c_Relation_Oantisym(X0,X2) )
| ~ spl104_153
| ~ spl104_257 ),
inference(resolution,[],[f4690,f3619]) ).
fof(f21379,plain,
( spl104_842
| ~ spl104_155
| ~ spl104_257 ),
inference(avatar_split_clause,[],[f5043,f4689,f3626,f21377]) ).
fof(f21377,plain,
( spl104_842
<=> ! [X2,X0,X1] :
( ~ c_Relation_Oantisym(X0,X1)
| c_Relation_Oantisym(X0,c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X0,X0),tc_HOL_Obool),X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_842])]) ).
fof(f5043,plain,
( ! [X2,X0,X1] :
( ~ c_Relation_Oantisym(X0,X1)
| c_Relation_Oantisym(X0,c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X0,X0),tc_HOL_Obool),X1,X2)) )
| ~ spl104_155
| ~ spl104_257 ),
inference(resolution,[],[f4690,f3627]) ).
fof(f21375,plain,
( spl104_841
| ~ spl104_155
| ~ spl104_255 ),
inference(avatar_split_clause,[],[f5015,f4681,f3626,f21373]) ).
fof(f21373,plain,
( spl104_841
<=> ! [X2,X0,X1] : c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X0,tc_HOL_Obool),X1,c_Groups_Ominus__class_Ominus(tc_fun(X0,tc_HOL_Obool),X1,X2)) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl104_841])]) ).
fof(f4681,plain,
( spl104_255
<=> ! [X2,X0,X1] :
( c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool),X0,X1) = X0
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_255])]) ).
fof(f5015,plain,
( ! [X2,X0,X1] : c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X0,tc_HOL_Obool),X1,c_Groups_Ominus__class_Ominus(tc_fun(X0,tc_HOL_Obool),X1,X2)) = X1
| ~ spl104_155
| ~ spl104_255 ),
inference(resolution,[],[f4682,f3627]) ).
fof(f4682,plain,
( ! [X2,X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool),X1,X0)
| c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool),X0,X1) = X0 )
| ~ spl104_255 ),
inference(avatar_component_clause,[],[f4681]) ).
fof(f21371,plain,
( spl104_840
| ~ spl104_155
| ~ spl104_254 ),
inference(avatar_split_clause,[],[f4996,f4677,f3626,f21369]) ).
fof(f21369,plain,
( spl104_840
<=> ! [X2,X0,X1] : c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X0,tc_HOL_Obool),c_Groups_Ominus__class_Ominus(tc_fun(X0,tc_HOL_Obool),X1,X2),X1) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl104_840])]) ).
fof(f4677,plain,
( spl104_254
<=> ! [X2,X0,X1] :
( c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool),X1,X0) = X0
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_254])]) ).
fof(f4996,plain,
( ! [X2,X0,X1] : c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X0,tc_HOL_Obool),c_Groups_Ominus__class_Ominus(tc_fun(X0,tc_HOL_Obool),X1,X2),X1) = X1
| ~ spl104_155
| ~ spl104_254 ),
inference(resolution,[],[f4678,f3627]) ).
fof(f4678,plain,
( ! [X2,X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool),X1,X0)
| c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool),X1,X0) = X0 )
| ~ spl104_254 ),
inference(avatar_component_clause,[],[f4677]) ).
fof(f21367,plain,
( spl104_839
| ~ spl104_154
| ~ spl104_251 ),
inference(avatar_split_clause,[],[f4954,f4665,f3622,f21365]) ).
fof(f21365,plain,
( spl104_839
<=> ! [X2,X0,X1] :
( c_Wellfounded_Owf(X0,X1)
| ~ c_Wellfounded_Owf(X0,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X0,X0),tc_HOL_Obool),X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_839])]) ).
fof(f4665,plain,
( spl104_251
<=> ! [X2,X0,X1] :
( c_Wellfounded_Owf(X2,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),X0,X1)
| ~ c_Wellfounded_Owf(X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_251])]) ).
fof(f4954,plain,
( ! [X2,X0,X1] :
( c_Wellfounded_Owf(X0,X1)
| ~ c_Wellfounded_Owf(X0,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X0,X0),tc_HOL_Obool),X1,X2)) )
| ~ spl104_154
| ~ spl104_251 ),
inference(resolution,[],[f4666,f3623]) ).
fof(f4666,plain,
( ! [X2,X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),X0,X1)
| c_Wellfounded_Owf(X2,X0)
| ~ c_Wellfounded_Owf(X2,X1) )
| ~ spl104_251 ),
inference(avatar_component_clause,[],[f4665]) ).
fof(f21363,plain,
( spl104_838
| ~ spl104_153
| ~ spl104_251 ),
inference(avatar_split_clause,[],[f4953,f4665,f3618,f21361]) ).
fof(f21361,plain,
( spl104_838
<=> ! [X2,X0,X1] :
( c_Wellfounded_Owf(X0,X1)
| ~ c_Wellfounded_Owf(X0,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X0,X0),tc_HOL_Obool),X2,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_838])]) ).
fof(f4953,plain,
( ! [X2,X0,X1] :
( c_Wellfounded_Owf(X0,X1)
| ~ c_Wellfounded_Owf(X0,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X0,X0),tc_HOL_Obool),X2,X1)) )
| ~ spl104_153
| ~ spl104_251 ),
inference(resolution,[],[f4666,f3619]) ).
fof(f21359,plain,
( spl104_837
| ~ spl104_155
| ~ spl104_251 ),
inference(avatar_split_clause,[],[f4951,f4665,f3626,f21357]) ).
fof(f21357,plain,
( spl104_837
<=> ! [X2,X0,X1] :
( c_Wellfounded_Owf(X0,c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X0,X0),tc_HOL_Obool),X1,X2))
| ~ c_Wellfounded_Owf(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_837])]) ).
fof(f4951,plain,
( ! [X2,X0,X1] :
( c_Wellfounded_Owf(X0,c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X0,X0),tc_HOL_Obool),X1,X2))
| ~ c_Wellfounded_Owf(X0,X1) )
| ~ spl104_155
| ~ spl104_251 ),
inference(resolution,[],[f4666,f3627]) ).
fof(f21355,plain,
( spl104_836
| ~ spl104_231
| ~ spl104_821 ),
inference(avatar_split_clause,[],[f21215,f21207,f4172,f21353]) ).
fof(f21353,plain,
( spl104_836
<=> ! [X0] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Orderings_Obot__class_Obot(tc_Nat_Onat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_836])]) ).
fof(f4172,plain,
( spl104_231
<=> ! [X0,X1] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_231])]) ).
fof(f21215,plain,
( ! [X0] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Orderings_Obot__class_Obot(tc_Nat_Onat))
| ~ spl104_231
| ~ spl104_821 ),
inference(superposition,[],[f4173,f21208]) ).
fof(f4173,plain,
( ! [X0,X1] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1))
| ~ spl104_231 ),
inference(avatar_component_clause,[],[f4172]) ).
fof(f21351,plain,
( spl104_835
| ~ spl104_154
| ~ spl104_250 ),
inference(avatar_split_clause,[],[f4925,f4661,f3622,f21349]) ).
fof(f21349,plain,
( spl104_835
<=> ! [X2,X0,X1] :
( c_Wellfounded_Oacyclic(X0,X1)
| ~ c_Wellfounded_Oacyclic(X0,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X0,X0),tc_HOL_Obool),X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_835])]) ).
fof(f4661,plain,
( spl104_250
<=> ! [X2,X0,X1] :
( c_Wellfounded_Oacyclic(X2,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),X0,X1)
| ~ c_Wellfounded_Oacyclic(X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_250])]) ).
fof(f4925,plain,
( ! [X2,X0,X1] :
( c_Wellfounded_Oacyclic(X0,X1)
| ~ c_Wellfounded_Oacyclic(X0,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X0,X0),tc_HOL_Obool),X1,X2)) )
| ~ spl104_154
| ~ spl104_250 ),
inference(resolution,[],[f4662,f3623]) ).
fof(f4662,plain,
( ! [X2,X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),X0,X1)
| c_Wellfounded_Oacyclic(X2,X0)
| ~ c_Wellfounded_Oacyclic(X2,X1) )
| ~ spl104_250 ),
inference(avatar_component_clause,[],[f4661]) ).
fof(f21347,plain,
( spl104_834
| ~ spl104_153
| ~ spl104_250 ),
inference(avatar_split_clause,[],[f4924,f4661,f3618,f21345]) ).
fof(f21345,plain,
( spl104_834
<=> ! [X2,X0,X1] :
( c_Wellfounded_Oacyclic(X0,X1)
| ~ c_Wellfounded_Oacyclic(X0,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X0,X0),tc_HOL_Obool),X2,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_834])]) ).
fof(f4924,plain,
( ! [X2,X0,X1] :
( c_Wellfounded_Oacyclic(X0,X1)
| ~ c_Wellfounded_Oacyclic(X0,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X0,X0),tc_HOL_Obool),X2,X1)) )
| ~ spl104_153
| ~ spl104_250 ),
inference(resolution,[],[f4662,f3619]) ).
fof(f21343,plain,
( spl104_833
| ~ spl104_155
| ~ spl104_250 ),
inference(avatar_split_clause,[],[f4922,f4661,f3626,f21341]) ).
fof(f21341,plain,
( spl104_833
<=> ! [X2,X0,X1] :
( c_Wellfounded_Oacyclic(X0,c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X0,X0),tc_HOL_Obool),X1,X2))
| ~ c_Wellfounded_Oacyclic(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_833])]) ).
fof(f4922,plain,
( ! [X2,X0,X1] :
( c_Wellfounded_Oacyclic(X0,c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X0,X0),tc_HOL_Obool),X1,X2))
| ~ c_Wellfounded_Oacyclic(X0,X1) )
| ~ spl104_155
| ~ spl104_250 ),
inference(resolution,[],[f4662,f3627]) ).
fof(f21339,plain,
( spl104_832
| ~ spl104_96
| ~ spl104_233 ),
inference(avatar_split_clause,[],[f4600,f4180,f3298,f21337]) ).
fof(f21337,plain,
( spl104_832
<=> ! [X4,X0,X3,X2,X1] :
( ~ sP8(X0,X1,X2,X3)
| c_member(X4,sK75(X0,X1,X2,X3),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_832])]) ).
fof(f4180,plain,
( spl104_233
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP(X0,sK75(X0,X1,X2,X3)))
| ~ sP8(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_233])]) ).
fof(f4600,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ sP8(X0,X1,X2,X3)
| c_member(X4,sK75(X0,X1,X2,X3),X0) )
| ~ spl104_96
| ~ spl104_233 ),
inference(resolution,[],[f4181,f3299]) ).
fof(f4181,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(hAPP(X0,sK75(X0,X1,X2,X3)))
| ~ sP8(X0,X1,X2,X3) )
| ~ spl104_233 ),
inference(avatar_component_clause,[],[f4180]) ).
fof(f21335,plain,
( spl104_831
| ~ spl104_95
| ~ spl104_223 ),
inference(avatar_split_clause,[],[f4537,f4140,f3294,f21333]) ).
fof(f21333,plain,
( spl104_831
<=> ! [X0,X3,X2,X1] :
( ~ c_member(X0,X1,X2)
| hBOOL(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X0,tc_HOL_Obool),X3,X2),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_831])]) ).
fof(f4537,plain,
( ! [X2,X3,X0,X1] :
( ~ c_member(X0,X1,X2)
| hBOOL(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X0,tc_HOL_Obool),X3,X2),X1)) )
| ~ spl104_95
| ~ spl104_223 ),
inference(resolution,[],[f4141,f3295]) ).
fof(f21331,plain,
( spl104_830
| ~ spl104_95
| ~ spl104_222 ),
inference(avatar_split_clause,[],[f4528,f4136,f3294,f21329]) ).
fof(f21329,plain,
( spl104_830
<=> ! [X0,X3,X2,X1] :
( ~ c_member(X0,X1,X2)
| hBOOL(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X0,tc_HOL_Obool),X2,X3),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_830])]) ).
fof(f4528,plain,
( ! [X2,X3,X0,X1] :
( ~ c_member(X0,X1,X2)
| hBOOL(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X0,tc_HOL_Obool),X2,X3),X1)) )
| ~ spl104_95
| ~ spl104_222 ),
inference(resolution,[],[f4137,f3295]) ).
fof(f21327,plain,
( spl104_829
| ~ spl104_96
| ~ spl104_221 ),
inference(avatar_split_clause,[],[f4519,f4132,f3298,f21325]) ).
fof(f21325,plain,
( spl104_829
<=> ! [X2,X4,X0,X3,X1] :
( ~ hBOOL(hAPP(X0,X1))
| c_member(X2,X1,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),X4,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_829])]) ).
fof(f4132,plain,
( spl104_221
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool),X0,X3),X2))
| ~ hBOOL(hAPP(X3,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_221])]) ).
fof(f4519,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ hBOOL(hAPP(X0,X1))
| c_member(X2,X1,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),X4,X0)) )
| ~ spl104_96
| ~ spl104_221 ),
inference(resolution,[],[f4133,f3299]) ).
fof(f4133,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool),X0,X3),X2))
| ~ hBOOL(hAPP(X3,X2)) )
| ~ spl104_221 ),
inference(avatar_component_clause,[],[f4132]) ).
fof(f21323,plain,
( spl104_828
| ~ spl104_96
| ~ spl104_219 ),
inference(avatar_split_clause,[],[f4511,f4124,f3298,f21321]) ).
fof(f21321,plain,
( spl104_828
<=> ! [X2,X4,X0,X3,X1] :
( ~ hBOOL(hAPP(X0,X1))
| c_member(X2,X1,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),X0,X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_828])]) ).
fof(f4124,plain,
( spl104_219
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool),X3,X0),X2))
| ~ hBOOL(hAPP(X3,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_219])]) ).
fof(f4511,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ hBOOL(hAPP(X0,X1))
| c_member(X2,X1,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),X0,X4)) )
| ~ spl104_96
| ~ spl104_219 ),
inference(resolution,[],[f4125,f3299]) ).
fof(f4125,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool),X3,X0),X2))
| ~ hBOOL(hAPP(X3,X2)) )
| ~ spl104_219 ),
inference(avatar_component_clause,[],[f4124]) ).
fof(f21290,plain,
( ~ spl104_16
| spl104_827
| ~ spl104_82
| ~ spl104_217 ),
inference(avatar_split_clause,[],[f4467,f4116,f3242,f21288,f2952]) ).
fof(f2952,plain,
( spl104_16
<=> class_Lattices_Osemilattice__sup(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_16])]) ).
fof(f21288,plain,
( spl104_827
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat,X0,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_827])]) ).
fof(f3242,plain,
( spl104_82
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_82])]) ).
fof(f4116,plain,
( spl104_217
<=> ! [X0,X3,X2,X1] :
( c_Orderings_Oord__class_Oless__eq(X3,X2,X0)
| ~ c_Orderings_Oord__class_Oless__eq(X3,c_Lattices_Osemilattice__sup__class_Osup(X3,X2,X1),X0)
| ~ class_Lattices_Osemilattice__sup(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_217])]) ).
fof(f4467,plain,
( ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1)
| ~ class_Lattices_Osemilattice__sup(tc_Nat_Onat)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat,X0,X2)) )
| ~ spl104_82
| ~ spl104_217 ),
inference(resolution,[],[f4117,f3243]) ).
fof(f3243,plain,
( ! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) )
| ~ spl104_82 ),
inference(avatar_component_clause,[],[f3242]) ).
fof(f4117,plain,
( ! [X2,X3,X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(X3,c_Lattices_Osemilattice__sup__class_Osup(X3,X2,X1),X0)
| c_Orderings_Oord__class_Oless__eq(X3,X2,X0)
| ~ class_Lattices_Osemilattice__sup(X3) )
| ~ spl104_217 ),
inference(avatar_component_clause,[],[f4116]) ).
fof(f21286,plain,
( spl104_826
| ~ spl104_65
| ~ spl104_821 ),
inference(avatar_split_clause,[],[f21213,f21207,f3169,f21284]) ).
fof(f21284,plain,
( spl104_826
<=> ! [X0] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Orderings_Obot__class_Obot(tc_Nat_Onat),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_826])]) ).
fof(f21213,plain,
( ! [X0] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Orderings_Obot__class_Obot(tc_Nat_Onat),X0)
| ~ spl104_65
| ~ spl104_821 ),
inference(superposition,[],[f3170,f21208]) ).
fof(f21253,plain,
( ~ spl104_16
| spl104_825
| ~ spl104_87
| ~ spl104_213 ),
inference(avatar_split_clause,[],[f4372,f4100,f3262,f21251,f2952]) ).
fof(f21251,plain,
( spl104_825
<=> ! [X2,X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat,X2,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_825])]) ).
fof(f3262,plain,
( spl104_87
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_87])]) ).
fof(f4100,plain,
( spl104_213
<=> ! [X0,X3,X2,X1] :
( c_Orderings_Oord__class_Oless(X3,X2,c_Lattices_Osemilattice__sup__class_Osup(X3,X0,X1))
| ~ c_Orderings_Oord__class_Oless(X3,X2,X1)
| ~ class_Lattices_Osemilattice__sup(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_213])]) ).
fof(f4372,plain,
( ! [X2,X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1)
| ~ class_Lattices_Osemilattice__sup(tc_Nat_Onat)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat,X2,X1)) )
| ~ spl104_87
| ~ spl104_213 ),
inference(resolution,[],[f4101,f3263]) ).
fof(f3263,plain,
( ! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) )
| ~ spl104_87 ),
inference(avatar_component_clause,[],[f3262]) ).
fof(f4101,plain,
( ! [X2,X3,X0,X1] :
( c_Orderings_Oord__class_Oless(X3,X2,c_Lattices_Osemilattice__sup__class_Osup(X3,X0,X1))
| ~ c_Orderings_Oord__class_Oless(X3,X2,X1)
| ~ class_Lattices_Osemilattice__sup(X3) )
| ~ spl104_213 ),
inference(avatar_component_clause,[],[f4100]) ).
fof(f21249,plain,
( spl104_824
| ~ spl104_67
| ~ spl104_205 ),
inference(avatar_split_clause,[],[f4340,f4068,f3178,f21247]) ).
fof(f21247,plain,
( spl104_824
<=> ! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(X0,X1,c_Orderings_Obot__class_Obot(X0))
| c_Orderings_Obot__class_Obot(X0) = X1
| ~ class_Orderings_Oorder(X0)
| ~ class_Orderings_Obot(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_824])]) ).
fof(f4068,plain,
( spl104_205
<=> ! [X2,X0,X1] :
( X0 = X1
| ~ c_Orderings_Oord__class_Oless__eq(X2,X0,X1)
| ~ c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
| ~ class_Orderings_Oorder(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_205])]) ).
fof(f4340,plain,
( ! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(X0,X1,c_Orderings_Obot__class_Obot(X0))
| c_Orderings_Obot__class_Obot(X0) = X1
| ~ class_Orderings_Oorder(X0)
| ~ class_Orderings_Obot(X0) )
| ~ spl104_67
| ~ spl104_205 ),
inference(resolution,[],[f4069,f3179]) ).
fof(f4069,plain,
( ! [X2,X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(X2,X0,X1)
| X0 = X1
| ~ class_Orderings_Oorder(X2) )
| ~ spl104_205 ),
inference(avatar_component_clause,[],[f4068]) ).
fof(f21245,plain,
( spl104_823
| ~ spl104_67
| ~ spl104_204 ),
inference(avatar_split_clause,[],[f4317,f4064,f3178,f21243]) ).
fof(f21243,plain,
( spl104_823
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless(X0,c_Orderings_Obot__class_Obot(X0),X1)
| c_Orderings_Obot__class_Obot(X0) = X1
| ~ class_Orderings_Oorder(X0)
| ~ class_Orderings_Obot(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_823])]) ).
fof(f4064,plain,
( spl104_204
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless(X2,X0,X1)
| ~ c_Orderings_Oord__class_Oless__eq(X2,X0,X1)
| X0 = X1
| ~ class_Orderings_Oorder(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_204])]) ).
fof(f4317,plain,
( ! [X0,X1] :
( c_Orderings_Oord__class_Oless(X0,c_Orderings_Obot__class_Obot(X0),X1)
| c_Orderings_Obot__class_Obot(X0) = X1
| ~ class_Orderings_Oorder(X0)
| ~ class_Orderings_Obot(X0) )
| ~ spl104_67
| ~ spl104_204 ),
inference(resolution,[],[f4065,f3179]) ).
fof(f4065,plain,
( ! [X2,X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(X2,X0,X1)
| c_Orderings_Oord__class_Oless(X2,X0,X1)
| X0 = X1
| ~ class_Orderings_Oorder(X2) )
| ~ spl104_204 ),
inference(avatar_component_clause,[],[f4064]) ).
fof(f21241,plain,
( spl104_822
| ~ spl104_67
| ~ spl104_201 ),
inference(avatar_split_clause,[],[f4273,f4052,f3178,f21239]) ).
fof(f21239,plain,
( spl104_822
<=> ! [X0,X1] :
( c_Orderings_Obot__class_Obot(X1) = X0
| c_Orderings_Oord__class_Oless(X1,c_Orderings_Obot__class_Obot(X1),X0)
| ~ class_Orderings_Olinorder(X1)
| ~ class_Orderings_Obot(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_822])]) ).
fof(f4052,plain,
( spl104_201
<=> ! [X2,X0,X1] :
( X0 = X1
| ~ c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
| c_Orderings_Oord__class_Oless(X2,X1,X0)
| ~ class_Orderings_Olinorder(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_201])]) ).
fof(f4273,plain,
( ! [X0,X1] :
( c_Orderings_Obot__class_Obot(X1) = X0
| c_Orderings_Oord__class_Oless(X1,c_Orderings_Obot__class_Obot(X1),X0)
| ~ class_Orderings_Olinorder(X1)
| ~ class_Orderings_Obot(X1) )
| ~ spl104_67
| ~ spl104_201 ),
inference(resolution,[],[f4053,f3179]) ).
fof(f4053,plain,
( ! [X2,X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
| X0 = X1
| c_Orderings_Oord__class_Oless(X2,X1,X0)
| ~ class_Orderings_Olinorder(X2) )
| ~ spl104_201 ),
inference(avatar_component_clause,[],[f4052]) ).
fof(f21209,plain,
( ~ spl104_8
| spl104_821
| ~ spl104_67
| ~ spl104_195 ),
inference(avatar_split_clause,[],[f4206,f4028,f3178,f21207,f2912]) ).
fof(f2912,plain,
( spl104_8
<=> class_Orderings_Obot(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_8])]) ).
fof(f4028,plain,
( spl104_195
<=> ! [X0,X1] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1)) = X1
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_195])]) ).
fof(f4206,plain,
( ! [X0] :
( c_Orderings_Obot__class_Obot(tc_Nat_Onat) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,c_Orderings_Obot__class_Obot(tc_Nat_Onat)))
| ~ class_Orderings_Obot(tc_Nat_Onat) )
| ~ spl104_67
| ~ spl104_195 ),
inference(resolution,[],[f4029,f3179]) ).
fof(f4029,plain,
( ! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1)) = X1 )
| ~ spl104_195 ),
inference(avatar_component_clause,[],[f4028]) ).
fof(f21205,plain,
( spl104_820
| ~ spl104_82
| ~ spl104_195 ),
inference(avatar_split_clause,[],[f4201,f4028,f3242,f21203]) ).
fof(f21203,plain,
( spl104_820
<=> ! [X0,X1] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1)) = X1
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_820])]) ).
fof(f4201,plain,
( ! [X0,X1] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1)) = X1
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1) )
| ~ spl104_82
| ~ spl104_195 ),
inference(resolution,[],[f4029,f3243]) ).
fof(f21201,plain,
( spl104_819
| ~ spl104_107
| ~ spl104_194 ),
inference(avatar_split_clause,[],[f4188,f4024,f3367,f21199]) ).
fof(f21199,plain,
( spl104_819
<=> ! [X2,X0,X1] : c_Relation_OId__on(X0,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool))) != c_Set_Oinsert(tc_prod(X0,X0),X1,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_819])]) ).
fof(f3367,plain,
( spl104_107
<=> ! [X2,X0,X1] : c_Set_Oinsert(X2,X1,X0) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_107])]) ).
fof(f4024,plain,
( spl104_194
<=> ! [X0] : c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X0,X0),tc_HOL_Obool)) = c_Relation_OId__on(X0,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool))) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_194])]) ).
fof(f4188,plain,
( ! [X2,X0,X1] : c_Relation_OId__on(X0,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool))) != c_Set_Oinsert(tc_prod(X0,X0),X1,X2)
| ~ spl104_107
| ~ spl104_194 ),
inference(superposition,[],[f3368,f4025]) ).
fof(f4025,plain,
( ! [X0] : c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X0,X0),tc_HOL_Obool)) = c_Relation_OId__on(X0,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)))
| ~ spl104_194 ),
inference(avatar_component_clause,[],[f4024]) ).
fof(f3368,plain,
( ! [X2,X0,X1] : c_Set_Oinsert(X2,X1,X0) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
| ~ spl104_107 ),
inference(avatar_component_clause,[],[f3367]) ).
fof(f21197,plain,
( spl104_818
| ~ spl104_101
| ~ spl104_194 ),
inference(avatar_split_clause,[],[f4187,f4024,f3342,f21195]) ).
fof(f21195,plain,
( spl104_818
<=> ! [X0,X1] : c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X0,X0),tc_HOL_Obool),c_Relation_OId__on(X0,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool))),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_818])]) ).
fof(f3342,plain,
( spl104_101
<=> ! [X0,X1] : c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_101])]) ).
fof(f4187,plain,
( ! [X0,X1] : c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X0,X0),tc_HOL_Obool),c_Relation_OId__on(X0,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool))),X1)
| ~ spl104_101
| ~ spl104_194 ),
inference(superposition,[],[f3343,f4025]) ).
fof(f3343,plain,
( ! [X0,X1] : c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),X0)
| ~ spl104_101 ),
inference(avatar_component_clause,[],[f3342]) ).
fof(f21190,plain,
( spl104_817
| ~ spl104_100
| ~ spl104_194 ),
inference(avatar_split_clause,[],[f4186,f4024,f3338,f21188]) ).
fof(f21188,plain,
( spl104_817
<=> ! [X0,X1] : ~ c_Orderings_Oord__class_Oless(tc_fun(tc_prod(X0,X0),tc_HOL_Obool),X1,c_Relation_OId__on(X0,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_817])]) ).
fof(f3338,plain,
( spl104_100
<=> ! [X0,X1] : ~ c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool),X0,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_100])]) ).
fof(f4186,plain,
( ! [X0,X1] : ~ c_Orderings_Oord__class_Oless(tc_fun(tc_prod(X0,X0),tc_HOL_Obool),X1,c_Relation_OId__on(X0,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool))))
| ~ spl104_100
| ~ spl104_194 ),
inference(superposition,[],[f3339,f4025]) ).
fof(f3339,plain,
( ! [X0,X1] : ~ c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool),X0,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))
| ~ spl104_100 ),
inference(avatar_component_clause,[],[f3338]) ).
fof(f21155,plain,
( ~ spl104_10
| spl104_816
| ~ spl104_109
| ~ spl104_186 ),
inference(avatar_split_clause,[],[f4004,f3891,f3375,f21153,f2922]) ).
fof(f2922,plain,
( spl104_10
<=> class_Lattices_Olattice(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_10])]) ).
fof(f3375,plain,
( spl104_109
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X2,X1,c_Lattices_Osemilattice__sup__class_Osup(X2,X0,X1))
| ~ class_Lattices_Olattice(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_109])]) ).
fof(f3891,plain,
( spl104_186
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_186])]) ).
fof(f4004,plain,
( ! [X2,X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat,X0,X1),X2)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| ~ class_Lattices_Olattice(tc_Nat_Onat) )
| ~ spl104_109
| ~ spl104_186 ),
inference(resolution,[],[f3892,f3376]) ).
fof(f3376,plain,
( ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X2,X1,c_Lattices_Osemilattice__sup__class_Osup(X2,X0,X1))
| ~ class_Lattices_Olattice(X2) )
| ~ spl104_109 ),
inference(avatar_component_clause,[],[f3375]) ).
fof(f3892,plain,
( ! [X2,X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X0) )
| ~ spl104_186 ),
inference(avatar_component_clause,[],[f3891]) ).
fof(f21151,plain,
( spl104_815
| ~ spl104_97
| ~ spl104_181 ),
inference(avatar_split_clause,[],[f3927,f3871,f3302,f21149]) ).
fof(f21149,plain,
( spl104_815
<=> ! [X0,X1] :
( c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)) = c_fequal(X1)
| sK39(c_fequal(X1),X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_815])]) ).
fof(f3302,plain,
( spl104_97
<=> ! [X2,X0,X1] :
( X0 = X1
| ~ c_member(X2,X1,c_fequal(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_97])]) ).
fof(f3871,plain,
( spl104_181
<=> ! [X0,X1] :
( c_member(X1,sK39(X0,X1),X0)
| c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_181])]) ).
fof(f3927,plain,
( ! [X0,X1] :
( c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)) = c_fequal(X1)
| sK39(c_fequal(X1),X0) = X1 )
| ~ spl104_97
| ~ spl104_181 ),
inference(resolution,[],[f3872,f3303]) ).
fof(f3303,plain,
( ! [X2,X0,X1] :
( ~ c_member(X2,X1,c_fequal(X0))
| X0 = X1 )
| ~ spl104_97 ),
inference(avatar_component_clause,[],[f3302]) ).
fof(f3872,plain,
( ! [X0,X1] :
( c_member(X1,sK39(X0,X1),X0)
| c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) = X0 )
| ~ spl104_181 ),
inference(avatar_component_clause,[],[f3871]) ).
fof(f21147,plain,
( spl104_814
| ~ spl104_97
| ~ spl104_180 ),
inference(avatar_split_clause,[],[f3923,f3867,f3302,f21145]) ).
fof(f21145,plain,
( spl104_814
<=> ! [X0,X1] :
( c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)) = c_fequal(X1)
| sK38(c_fequal(X1),X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_814])]) ).
fof(f3867,plain,
( spl104_180
<=> ! [X0,X1] :
( c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) = X0
| c_member(X1,sK38(X0,X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_180])]) ).
fof(f3923,plain,
( ! [X0,X1] :
( c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)) = c_fequal(X1)
| sK38(c_fequal(X1),X0) = X1 )
| ~ spl104_97
| ~ spl104_180 ),
inference(resolution,[],[f3868,f3303]) ).
fof(f3868,plain,
( ! [X0,X1] :
( c_member(X1,sK38(X0,X1),X0)
| c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) = X0 )
| ~ spl104_180 ),
inference(avatar_component_clause,[],[f3867]) ).
fof(f21143,plain,
( spl104_813
| ~ spl104_130
| ~ spl104_162 ),
inference(avatar_split_clause,[],[f3814,f3654,f3473,f21141]) ).
fof(f21141,plain,
( spl104_813
<=> ! [X2,X0,X1] :
( c_Relation_Ototal__on(X0,X1,X2)
| c_Set_Oinsert(X0,sK47(X2,X1,X0),X1) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_813])]) ).
fof(f3654,plain,
( spl104_162
<=> ! [X2,X0,X1] :
( c_Relation_Ototal__on(X2,X1,X0)
| c_member(X2,sK47(X0,X1,X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_162])]) ).
fof(f3814,plain,
( ! [X2,X0,X1] :
( c_Relation_Ototal__on(X0,X1,X2)
| c_Set_Oinsert(X0,sK47(X2,X1,X0),X1) = X1 )
| ~ spl104_130
| ~ spl104_162 ),
inference(resolution,[],[f3655,f3474]) ).
fof(f3655,plain,
( ! [X2,X0,X1] :
( c_member(X2,sK47(X0,X1,X2),X1)
| c_Relation_Ototal__on(X2,X1,X0) )
| ~ spl104_162 ),
inference(avatar_component_clause,[],[f3654]) ).
fof(f21139,plain,
( spl104_812
| ~ spl104_130
| ~ spl104_160 ),
inference(avatar_split_clause,[],[f3810,f3646,f3473,f21137]) ).
fof(f21137,plain,
( spl104_812
<=> ! [X2,X0,X1] :
( c_Relation_Ototal__on(X0,X1,X2)
| c_Set_Oinsert(X0,sK46(X2,X1,X0),X1) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_812])]) ).
fof(f3646,plain,
( spl104_160
<=> ! [X2,X0,X1] :
( c_Relation_Ototal__on(X2,X1,X0)
| c_member(X2,sK46(X0,X1,X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_160])]) ).
fof(f3810,plain,
( ! [X2,X0,X1] :
( c_Relation_Ototal__on(X0,X1,X2)
| c_Set_Oinsert(X0,sK46(X2,X1,X0),X1) = X1 )
| ~ spl104_130
| ~ spl104_160 ),
inference(resolution,[],[f3647,f3474]) ).
fof(f3647,plain,
( ! [X2,X0,X1] :
( c_member(X2,sK46(X0,X1,X2),X1)
| c_Relation_Ototal__on(X2,X1,X0) )
| ~ spl104_160 ),
inference(avatar_component_clause,[],[f3646]) ).
fof(f21123,plain,
( ~ spl104_17
| spl104_811
| ~ spl104_128
| ~ spl104_159 ),
inference(avatar_split_clause,[],[f3805,f3642,f3465,f21121,f2957]) ).
fof(f21121,plain,
( spl104_811
<=> ! [X2,X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_811])]) ).
fof(f3465,plain,
( spl104_128
<=> ! [X2,X0,X1] :
( ~ c_Orderings_Oord__class_Oless(X2,X0,X1)
| ~ c_Orderings_Oord__class_Oless(X2,X1,X0)
| ~ class_Orderings_Oorder(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_128])]) ).
fof(f3642,plain,
( spl104_159
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X0),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_159])]) ).
fof(f3805,plain,
( ! [X2,X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X2))
| ~ class_Orderings_Oorder(tc_Nat_Onat) )
| ~ spl104_128
| ~ spl104_159 ),
inference(resolution,[],[f3643,f3466]) ).
fof(f3466,plain,
( ! [X2,X0,X1] :
( ~ c_Orderings_Oord__class_Oless(X2,X1,X0)
| ~ c_Orderings_Oord__class_Oless(X2,X0,X1)
| ~ class_Orderings_Oorder(X2) )
| ~ spl104_128 ),
inference(avatar_component_clause,[],[f3465]) ).
fof(f3643,plain,
( ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X0),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1) )
| ~ spl104_159 ),
inference(avatar_component_clause,[],[f3642]) ).
fof(f21119,plain,
( spl104_810
| ~ spl104_65
| ~ spl104_148 ),
inference(avatar_split_clause,[],[f3755,f3598,f3169,f21117]) ).
fof(f21117,plain,
( spl104_810
<=> ! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1))
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_810])]) ).
fof(f3598,plain,
( spl104_148
<=> ! [X0,X1] :
( X0 = X1
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_148])]) ).
fof(f3755,plain,
( ! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1))
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1) = X0 )
| ~ spl104_65
| ~ spl104_148 ),
inference(resolution,[],[f3599,f3170]) ).
fof(f3599,plain,
( ! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1)
| X0 = X1 )
| ~ spl104_148 ),
inference(avatar_component_clause,[],[f3598]) ).
fof(f21115,plain,
( spl104_809
| ~ spl104_35
| ~ spl104_763 ),
inference(avatar_split_clause,[],[f20560,f19587,f3038,f21113]) ).
fof(f19587,plain,
( spl104_763
<=> ! [X2,X0,X1] :
( ~ c_member(tc_prod(X0,X0),X1,X2)
| hBOOL(hAPP(c_Transitive__Closure_Otrancl(X0,X2),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_763])]) ).
fof(f20560,plain,
( ! [X0,X1] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(X0,c_fequal(X1)),X1))
| ~ spl104_35
| ~ spl104_763 ),
inference(resolution,[],[f19588,f3039]) ).
fof(f19588,plain,
( ! [X2,X0,X1] :
( ~ c_member(tc_prod(X0,X0),X1,X2)
| hBOOL(hAPP(c_Transitive__Closure_Otrancl(X0,X2),X1)) )
| ~ spl104_763 ),
inference(avatar_component_clause,[],[f19587]) ).
fof(f21111,plain,
( spl104_808
| ~ spl104_65
| ~ spl104_147 ),
inference(avatar_split_clause,[],[f3741,f3594,f3169,f21109]) ).
fof(f21109,plain,
( spl104_808
<=> ! [X0,X1] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1) = X0
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_808])]) ).
fof(f3594,plain,
( spl104_147
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| X0 = X1
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_147])]) ).
fof(f3741,plain,
( ! [X0,X1] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1) = X0
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1),X0) )
| ~ spl104_65
| ~ spl104_147 ),
inference(resolution,[],[f3595,f3170]) ).
fof(f3595,plain,
( ! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| X0 = X1
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) )
| ~ spl104_147 ),
inference(avatar_component_clause,[],[f3594]) ).
fof(f21107,plain,
( spl104_807
| ~ spl104_106
| ~ spl104_130 ),
inference(avatar_split_clause,[],[f3543,f3473,f3363,f21105]) ).
fof(f21105,plain,
( spl104_807
<=> ! [X2,X0,X1] :
( c_Wellfounded_Oacc(X0,X2) = c_Set_Oinsert(X0,X1,c_Wellfounded_Oacc(X0,X2))
| ~ c_Wellfounded_Owf(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_807])]) ).
fof(f3543,plain,
( ! [X2,X0,X1] :
( c_Wellfounded_Oacc(X0,X2) = c_Set_Oinsert(X0,X1,c_Wellfounded_Oacc(X0,X2))
| ~ c_Wellfounded_Owf(X0,X2) )
| ~ spl104_106
| ~ spl104_130 ),
inference(resolution,[],[f3474,f3364]) ).
fof(f21103,plain,
( spl104_806
| ~ spl104_42
| ~ spl104_103 ),
inference(avatar_split_clause,[],[f3402,f3350,f3067,f21101]) ).
fof(f21101,plain,
( spl104_806
<=> ! [X2,X0,X1] :
( c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X0,X1),c_Orderings_Obot__class_Obot(tc_fun(X0,X1)),X2) = X2
| ~ class_Lattices_Obounded__lattice(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_806])]) ).
fof(f3067,plain,
( spl104_42
<=> ! [X0,X1] :
( class_Lattices_Obounded__lattice__bot(tc_fun(X0,X1))
| ~ class_Lattices_Obounded__lattice(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_42])]) ).
fof(f3350,plain,
( spl104_103
<=> ! [X0,X1] :
( c_Lattices_Osemilattice__sup__class_Osup(X1,c_Orderings_Obot__class_Obot(X1),X0) = X0
| ~ class_Lattices_Obounded__lattice__bot(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_103])]) ).
fof(f3402,plain,
( ! [X2,X0,X1] :
( c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X0,X1),c_Orderings_Obot__class_Obot(tc_fun(X0,X1)),X2) = X2
| ~ class_Lattices_Obounded__lattice(X1) )
| ~ spl104_42
| ~ spl104_103 ),
inference(resolution,[],[f3351,f3068]) ).
fof(f3068,plain,
( ! [X0,X1] :
( class_Lattices_Obounded__lattice__bot(tc_fun(X0,X1))
| ~ class_Lattices_Obounded__lattice(X1) )
| ~ spl104_42 ),
inference(avatar_component_clause,[],[f3067]) ).
fof(f3351,plain,
( ! [X0,X1] :
( ~ class_Lattices_Obounded__lattice__bot(X1)
| c_Lattices_Osemilattice__sup__class_Osup(X1,c_Orderings_Obot__class_Obot(X1),X0) = X0 )
| ~ spl104_103 ),
inference(avatar_component_clause,[],[f3350]) ).
fof(f21099,plain,
( spl104_805
| ~ spl104_42
| ~ spl104_102 ),
inference(avatar_split_clause,[],[f3400,f3346,f3067,f21097]) ).
fof(f21097,plain,
( spl104_805
<=> ! [X2,X0,X1] :
( c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X0,X1),X2,c_Orderings_Obot__class_Obot(tc_fun(X0,X1))) = X2
| ~ class_Lattices_Obounded__lattice(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_805])]) ).
fof(f3346,plain,
( spl104_102
<=> ! [X0,X1] :
( c_Lattices_Osemilattice__sup__class_Osup(X1,X0,c_Orderings_Obot__class_Obot(X1)) = X0
| ~ class_Lattices_Obounded__lattice__bot(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_102])]) ).
fof(f3400,plain,
( ! [X2,X0,X1] :
( c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X0,X1),X2,c_Orderings_Obot__class_Obot(tc_fun(X0,X1))) = X2
| ~ class_Lattices_Obounded__lattice(X1) )
| ~ spl104_42
| ~ spl104_102 ),
inference(resolution,[],[f3347,f3068]) ).
fof(f3347,plain,
( ! [X0,X1] :
( ~ class_Lattices_Obounded__lattice__bot(X1)
| c_Lattices_Osemilattice__sup__class_Osup(X1,X0,c_Orderings_Obot__class_Obot(X1)) = X0 )
| ~ spl104_102 ),
inference(avatar_component_clause,[],[f3346]) ).
fof(f20096,plain,
( spl104_804
| ~ spl104_52
| ~ spl104_742 ),
inference(avatar_split_clause,[],[f19454,f19448,f3107,f20093]) ).
fof(f20093,plain,
( spl104_804
<=> c_Wellfounded_Oacyclic(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),c_FunDef_Omax__strict) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_804])]) ).
fof(f3107,plain,
( spl104_52
<=> ! [X0,X1] :
( c_Wellfounded_Oacyclic(X1,X0)
| ~ c_Wellfounded_Owf(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_52])]) ).
fof(f19448,plain,
( spl104_742
<=> c_Wellfounded_Owf(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),c_FunDef_Omax__strict) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_742])]) ).
fof(f19454,plain,
( c_Wellfounded_Oacyclic(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),c_FunDef_Omax__strict)
| ~ spl104_52
| ~ spl104_742 ),
inference(resolution,[],[f19450,f3108]) ).
fof(f3108,plain,
( ! [X0,X1] :
( ~ c_Wellfounded_Owf(X1,X0)
| c_Wellfounded_Oacyclic(X1,X0) )
| ~ spl104_52 ),
inference(avatar_component_clause,[],[f3107]) ).
fof(f19450,plain,
( c_Wellfounded_Owf(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),c_FunDef_Omax__strict)
| ~ spl104_742 ),
inference(avatar_component_clause,[],[f19448]) ).
fof(f19753,plain,
( spl104_803
| ~ spl104_219
| ~ spl104_623 ),
inference(avatar_split_clause,[],[f16110,f15947,f4124,f19751]) ).
fof(f19751,plain,
( spl104_803
<=> ! [X0] :
( hBOOL(hAPP(c_FunDef_Omin__weak,X0))
| ~ hBOOL(hAPP(c_Wellfounded_Omin__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__leq),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_803])]) ).
fof(f15947,plain,
( spl104_623
<=> c_FunDef_Omin__weak = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool),c_Wellfounded_Omin__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__leq),c_Set_Oinsert(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),c_Relation_OId__on(tc_Nat_Onat,c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),c_Relation_OId__on(tc_Nat_Onat,c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))),c_Relation_OId__on(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_HOL_Obool))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_623])]) ).
fof(f16110,plain,
( ! [X0] :
( hBOOL(hAPP(c_FunDef_Omin__weak,X0))
| ~ hBOOL(hAPP(c_Wellfounded_Omin__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__leq),X0)) )
| ~ spl104_219
| ~ spl104_623 ),
inference(superposition,[],[f4125,f15949]) ).
fof(f15949,plain,
( c_FunDef_Omin__weak = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool),c_Wellfounded_Omin__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__leq),c_Set_Oinsert(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),c_Relation_OId__on(tc_Nat_Onat,c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),c_Relation_OId__on(tc_Nat_Onat,c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))),c_Relation_OId__on(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_HOL_Obool)))))
| ~ spl104_623 ),
inference(avatar_component_clause,[],[f15947]) ).
fof(f19749,plain,
( spl104_802
| ~ spl104_53
| ~ spl104_742 ),
inference(avatar_split_clause,[],[f19453,f19448,f3111,f19746]) ).
fof(f19746,plain,
( spl104_802
<=> sP2(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),c_FunDef_Omax__strict) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_802])]) ).
fof(f3111,plain,
( spl104_53
<=> ! [X0,X1] :
( sP2(X1,X0)
| ~ c_Wellfounded_Owf(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_53])]) ).
fof(f19453,plain,
( sP2(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),c_FunDef_Omax__strict)
| ~ spl104_53
| ~ spl104_742 ),
inference(resolution,[],[f19450,f3112]) ).
fof(f3112,plain,
( ! [X0,X1] :
( ~ c_Wellfounded_Owf(X1,X0)
| sP2(X1,X0) )
| ~ spl104_53 ),
inference(avatar_component_clause,[],[f3111]) ).
fof(f19744,plain,
( spl104_801
| ~ spl104_219
| ~ spl104_622 ),
inference(avatar_split_clause,[],[f16033,f15942,f4124,f19742]) ).
fof(f19742,plain,
( spl104_801
<=> ! [X0] :
( hBOOL(hAPP(c_FunDef_Omax__weak,X0))
| ~ hBOOL(hAPP(c_Wellfounded_Omax__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__leq),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_801])]) ).
fof(f15942,plain,
( spl104_622
<=> c_FunDef_Omax__weak = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool),c_Wellfounded_Omax__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__leq),c_Set_Oinsert(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),c_Relation_OId__on(tc_Nat_Onat,c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),c_Relation_OId__on(tc_Nat_Onat,c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))),c_Relation_OId__on(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_HOL_Obool))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_622])]) ).
fof(f16033,plain,
( ! [X0] :
( hBOOL(hAPP(c_FunDef_Omax__weak,X0))
| ~ hBOOL(hAPP(c_Wellfounded_Omax__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__leq),X0)) )
| ~ spl104_219
| ~ spl104_622 ),
inference(superposition,[],[f4125,f15944]) ).
fof(f15944,plain,
( c_FunDef_Omax__weak = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool),c_Wellfounded_Omax__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__leq),c_Set_Oinsert(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),c_Relation_OId__on(tc_Nat_Onat,c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),c_Relation_OId__on(tc_Nat_Onat,c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))),c_Relation_OId__on(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_HOL_Obool)))))
| ~ spl104_622 ),
inference(avatar_component_clause,[],[f15942]) ).
fof(f19740,plain,
( spl104_800
| ~ spl104_434
| ~ spl104_540 ),
inference(avatar_split_clause,[],[f11749,f11550,f7618,f19738]) ).
fof(f19738,plain,
( spl104_800
<=> ! [X2,X0,X1] : ~ c_Wellfounded_Oacyclic(X0,c_Set_Oinsert(tc_prod(X0,X0),c_Product__Type_OPair(X0,X0,X1,X1),X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_800])]) ).
fof(f11550,plain,
( spl104_540
<=> ! [X0,X3,X2,X1] :
( ~ c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X1,X2),c_Transitive__Closure_Otrancl(X3,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X3,X3),tc_HOL_Obool),X0,c_Relation_OId(X3))))
| ~ c_Wellfounded_Oacyclic(X3,c_Set_Oinsert(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X2,X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_540])]) ).
fof(f11749,plain,
( ! [X2,X0,X1] : ~ c_Wellfounded_Oacyclic(X0,c_Set_Oinsert(tc_prod(X0,X0),c_Product__Type_OPair(X0,X0,X1,X1),X2))
| ~ spl104_434
| ~ spl104_540 ),
inference(resolution,[],[f11551,f7619]) ).
fof(f11551,plain,
( ! [X2,X3,X0,X1] :
( ~ c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X1,X2),c_Transitive__Closure_Otrancl(X3,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X3,X3),tc_HOL_Obool),X0,c_Relation_OId(X3))))
| ~ c_Wellfounded_Oacyclic(X3,c_Set_Oinsert(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X2,X1),X0)) )
| ~ spl104_540 ),
inference(avatar_component_clause,[],[f11550]) ).
fof(f19736,plain,
( spl104_799
| ~ spl104_100
| ~ spl104_492 ),
inference(avatar_split_clause,[],[f10018,f9834,f3338,f19734]) ).
fof(f19734,plain,
( spl104_799
<=> ! [X2,X0,X1] :
( ~ c_member(X0,X1,X2)
| ~ sP4(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)),X2,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_799])]) ).
fof(f9834,plain,
( spl104_492
<=> ! [X0,X3,X2,X1] :
( c_Orderings_Oord__class_Oless(tc_fun(X2,tc_HOL_Obool),c_Groups_Ominus__class_Ominus(tc_fun(X2,tc_HOL_Obool),X1,c_Set_Oinsert(X2,X3,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)))),X0)
| ~ c_member(X2,X3,X1)
| ~ sP4(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_492])]) ).
fof(f10018,plain,
( ! [X2,X0,X1] :
( ~ c_member(X0,X1,X2)
| ~ sP4(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)),X2,X0,X1) )
| ~ spl104_100
| ~ spl104_492 ),
inference(resolution,[],[f9835,f3339]) ).
fof(f9835,plain,
( ! [X2,X3,X0,X1] :
( c_Orderings_Oord__class_Oless(tc_fun(X2,tc_HOL_Obool),c_Groups_Ominus__class_Ominus(tc_fun(X2,tc_HOL_Obool),X1,c_Set_Oinsert(X2,X3,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)))),X0)
| ~ c_member(X2,X3,X1)
| ~ sP4(X0,X1,X2,X3) )
| ~ spl104_492 ),
inference(avatar_component_clause,[],[f9834]) ).
fof(f19732,plain,
( spl104_798
| ~ spl104_38
| ~ spl104_450 ),
inference(avatar_split_clause,[],[f8438,f8306,f3051,f19730]) ).
fof(f19730,plain,
( spl104_798
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X0,tc_fun(X1,tc_HOL_Obool)),X2,X2)
| ~ class_Orderings_Oord(tc_fun(X1,tc_HOL_Obool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_798])]) ).
fof(f3051,plain,
( spl104_38
<=> ! [X0,X1] : c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_38])]) ).
fof(f8306,plain,
( spl104_450
<=> ! [X0,X3,X2,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X2,X3),X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(X3,hAPP(X1,sK55(X0,X1,X3)),hAPP(X0,sK55(X0,X1,X3)))
| ~ class_Orderings_Oord(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_450])]) ).
fof(f8438,plain,
( ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X0,tc_fun(X1,tc_HOL_Obool)),X2,X2)
| ~ class_Orderings_Oord(tc_fun(X1,tc_HOL_Obool)) )
| ~ spl104_38
| ~ spl104_450 ),
inference(resolution,[],[f8307,f3052]) ).
fof(f3052,plain,
( ! [X0,X1] : c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X0,X0)
| ~ spl104_38 ),
inference(avatar_component_clause,[],[f3051]) ).
fof(f8307,plain,
( ! [X2,X3,X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(X3,hAPP(X1,sK55(X0,X1,X3)),hAPP(X0,sK55(X0,X1,X3)))
| c_Orderings_Oord__class_Oless__eq(tc_fun(X2,X3),X1,X0)
| ~ class_Orderings_Oord(X3) )
| ~ spl104_450 ),
inference(avatar_component_clause,[],[f8306]) ).
fof(f19728,plain,
( spl104_797
| ~ spl104_196
| ~ spl104_411 ),
inference(avatar_split_clause,[],[f7478,f7090,f4032,f19726]) ).
fof(f19726,plain,
( spl104_797
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(X0,X0,X1),X2),X2))
| ~ c_Relation_Oirrefl(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_797])]) ).
fof(f7478,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(X0,X0,X1),X2),X2))
| ~ c_Relation_Oirrefl(X0,X1) )
| ~ spl104_196
| ~ spl104_411 ),
inference(resolution,[],[f7091,f4033]) ).
fof(f19724,plain,
( spl104_796
| ~ spl104_206
| ~ spl104_411 ),
inference(avatar_split_clause,[],[f7477,f7090,f4072,f19722]) ).
fof(f19722,plain,
( spl104_796
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(X0,X0,X1),X2),X2))
| ~ c_Wellfounded_Owf(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_796])]) ).
fof(f7477,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(X0,X0,X1),X2),X2))
| ~ c_Wellfounded_Owf(X0,X1) )
| ~ spl104_206
| ~ spl104_411 ),
inference(resolution,[],[f7091,f4073]) ).
fof(f19720,plain,
( spl104_795
| ~ spl104_138
| ~ spl104_354
| ~ spl104_390 ),
inference(avatar_split_clause,[],[f7145,f7006,f5973,f3556,f19718]) ).
fof(f19718,plain,
( spl104_795
<=> ! [X0,X1] :
( c_member(X0,sK27(X1,X0),c_Relation_ORange(X0,X0,X1))
| c_Wellfounded_Oacyclic(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_795])]) ).
fof(f3556,plain,
( spl104_138
<=> ! [X0,X1] : c_Relation_ORange(X1,X1,c_Transitive__Closure_Otrancl(X1,X0)) = c_Relation_ORange(X1,X1,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_138])]) ).
fof(f7006,plain,
( spl104_390
<=> ! [X0,X1] :
( c_Wellfounded_Oacyclic(X1,X0)
| c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,sK27(X0,X1),sK27(X0,X1)),c_Transitive__Closure_Otrancl(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_390])]) ).
fof(f7145,plain,
( ! [X0,X1] :
( c_member(X0,sK27(X1,X0),c_Relation_ORange(X0,X0,X1))
| c_Wellfounded_Oacyclic(X0,X1) )
| ~ spl104_138
| ~ spl104_354
| ~ spl104_390 ),
inference(forward_demodulation,[],[f7136,f3557]) ).
fof(f3557,plain,
( ! [X0,X1] : c_Relation_ORange(X1,X1,c_Transitive__Closure_Otrancl(X1,X0)) = c_Relation_ORange(X1,X1,X0)
| ~ spl104_138 ),
inference(avatar_component_clause,[],[f3556]) ).
fof(f7136,plain,
( ! [X0,X1] :
( c_Wellfounded_Oacyclic(X0,X1)
| c_member(X0,sK27(X1,X0),c_Relation_ORange(X0,X0,c_Transitive__Closure_Otrancl(X0,X1))) )
| ~ spl104_354
| ~ spl104_390 ),
inference(resolution,[],[f7007,f5974]) ).
fof(f7007,plain,
( ! [X0,X1] :
( c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,sK27(X0,X1),sK27(X0,X1)),c_Transitive__Closure_Otrancl(X1,X0))
| c_Wellfounded_Oacyclic(X1,X0) )
| ~ spl104_390 ),
inference(avatar_component_clause,[],[f7006]) ).
fof(f19716,plain,
( spl104_794
| ~ spl104_139
| ~ spl104_355
| ~ spl104_390 ),
inference(avatar_split_clause,[],[f7144,f7006,f5977,f3560,f19714]) ).
fof(f19714,plain,
( spl104_794
<=> ! [X0,X1] :
( c_member(X0,sK27(X1,X0),c_Relation_ODomain(X0,X0,X1))
| c_Wellfounded_Oacyclic(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_794])]) ).
fof(f3560,plain,
( spl104_139
<=> ! [X0,X1] : c_Relation_ODomain(X1,X1,c_Transitive__Closure_Otrancl(X1,X0)) = c_Relation_ODomain(X1,X1,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_139])]) ).
fof(f7144,plain,
( ! [X0,X1] :
( c_member(X0,sK27(X1,X0),c_Relation_ODomain(X0,X0,X1))
| c_Wellfounded_Oacyclic(X0,X1) )
| ~ spl104_139
| ~ spl104_355
| ~ spl104_390 ),
inference(forward_demodulation,[],[f7135,f3561]) ).
fof(f3561,plain,
( ! [X0,X1] : c_Relation_ODomain(X1,X1,c_Transitive__Closure_Otrancl(X1,X0)) = c_Relation_ODomain(X1,X1,X0)
| ~ spl104_139 ),
inference(avatar_component_clause,[],[f3560]) ).
fof(f7135,plain,
( ! [X0,X1] :
( c_Wellfounded_Oacyclic(X0,X1)
| c_member(X0,sK27(X1,X0),c_Relation_ODomain(X0,X0,c_Transitive__Closure_Otrancl(X0,X1))) )
| ~ spl104_355
| ~ spl104_390 ),
inference(resolution,[],[f7007,f5978]) ).
fof(f19712,plain,
( spl104_793
| ~ spl104_138
| ~ spl104_354
| ~ spl104_389 ),
inference(avatar_split_clause,[],[f7129,f7002,f5973,f3556,f19710]) ).
fof(f19710,plain,
( spl104_793
<=> ! [X0,X1] :
( c_member(X0,sK21(X1,X0),c_Relation_ORange(X0,X0,X1))
| c_Wellfounded_Oacyclic(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_793])]) ).
fof(f7002,plain,
( spl104_389
<=> ! [X0,X1] :
( c_Wellfounded_Oacyclic(X1,X0)
| c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,sK21(X0,X1),sK21(X0,X1)),c_Transitive__Closure_Otrancl(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_389])]) ).
fof(f7129,plain,
( ! [X0,X1] :
( c_member(X0,sK21(X1,X0),c_Relation_ORange(X0,X0,X1))
| c_Wellfounded_Oacyclic(X0,X1) )
| ~ spl104_138
| ~ spl104_354
| ~ spl104_389 ),
inference(forward_demodulation,[],[f7120,f3557]) ).
fof(f7120,plain,
( ! [X0,X1] :
( c_Wellfounded_Oacyclic(X0,X1)
| c_member(X0,sK21(X1,X0),c_Relation_ORange(X0,X0,c_Transitive__Closure_Otrancl(X0,X1))) )
| ~ spl104_354
| ~ spl104_389 ),
inference(resolution,[],[f7003,f5974]) ).
fof(f7003,plain,
( ! [X0,X1] :
( c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,sK21(X0,X1),sK21(X0,X1)),c_Transitive__Closure_Otrancl(X1,X0))
| c_Wellfounded_Oacyclic(X1,X0) )
| ~ spl104_389 ),
inference(avatar_component_clause,[],[f7002]) ).
fof(f19708,plain,
( spl104_792
| ~ spl104_139
| ~ spl104_355
| ~ spl104_389 ),
inference(avatar_split_clause,[],[f7128,f7002,f5977,f3560,f19706]) ).
fof(f19706,plain,
( spl104_792
<=> ! [X0,X1] :
( c_member(X0,sK21(X1,X0),c_Relation_ODomain(X0,X0,X1))
| c_Wellfounded_Oacyclic(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_792])]) ).
fof(f7128,plain,
( ! [X0,X1] :
( c_member(X0,sK21(X1,X0),c_Relation_ODomain(X0,X0,X1))
| c_Wellfounded_Oacyclic(X0,X1) )
| ~ spl104_139
| ~ spl104_355
| ~ spl104_389 ),
inference(forward_demodulation,[],[f7119,f3561]) ).
fof(f7119,plain,
( ! [X0,X1] :
( c_Wellfounded_Oacyclic(X0,X1)
| c_member(X0,sK21(X1,X0),c_Relation_ODomain(X0,X0,c_Transitive__Closure_Otrancl(X0,X1))) )
| ~ spl104_355
| ~ spl104_389 ),
inference(resolution,[],[f7003,f5978]) ).
fof(f19704,plain,
( spl104_791
| ~ spl104_52
| ~ spl104_740 ),
inference(avatar_split_clause,[],[f19442,f19436,f3107,f19701]) ).
fof(f19701,plain,
( spl104_791
<=> c_Wellfounded_Oacyclic(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),c_FunDef_Omin__strict) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_791])]) ).
fof(f19436,plain,
( spl104_740
<=> c_Wellfounded_Owf(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),c_FunDef_Omin__strict) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_740])]) ).
fof(f19442,plain,
( c_Wellfounded_Oacyclic(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),c_FunDef_Omin__strict)
| ~ spl104_52
| ~ spl104_740 ),
inference(resolution,[],[f19438,f3108]) ).
fof(f19438,plain,
( c_Wellfounded_Owf(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),c_FunDef_Omin__strict)
| ~ spl104_740 ),
inference(avatar_component_clause,[],[f19436]) ).
fof(f19699,plain,
( spl104_790
| ~ spl104_243
| ~ spl104_386 ),
inference(avatar_split_clause,[],[f6983,f6537,f4631,f19697]) ).
fof(f19697,plain,
( spl104_790
<=> ! [X2,X0,X1] :
( c_member(tc_Nat_Onat,X0,X1)
| ~ c_Relation_Orefl__on(tc_Nat_Onat,X1,c_Wellfounded_Oless__than)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_790])]) ).
fof(f6983,plain,
( ! [X2,X0,X1] :
( c_member(tc_Nat_Onat,X0,X1)
| ~ c_Relation_Orefl__on(tc_Nat_Onat,X1,c_Wellfounded_Oless__than)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X2) )
| ~ spl104_243
| ~ spl104_386 ),
inference(resolution,[],[f6538,f4632]) ).
fof(f19695,plain,
( spl104_789
| ~ spl104_243
| ~ spl104_385 ),
inference(avatar_split_clause,[],[f6964,f6533,f4631,f19693]) ).
fof(f19693,plain,
( spl104_789
<=> ! [X2,X0,X1] :
( c_member(tc_Nat_Onat,X0,X1)
| ~ c_Relation_Orefl__on(tc_Nat_Onat,X1,c_Wellfounded_Oless__than)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_789])]) ).
fof(f6964,plain,
( ! [X2,X0,X1] :
( c_member(tc_Nat_Onat,X0,X1)
| ~ c_Relation_Orefl__on(tc_Nat_Onat,X1,c_Wellfounded_Oless__than)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X0) )
| ~ spl104_243
| ~ spl104_385 ),
inference(resolution,[],[f6534,f4632]) ).
fof(f19691,plain,
( spl104_788
| ~ spl104_35
| ~ spl104_355 ),
inference(avatar_split_clause,[],[f6403,f5977,f3038,f19689]) ).
fof(f19689,plain,
( spl104_788
<=> ! [X0,X3,X2,X1] : c_member(X0,X1,c_Relation_ODomain(X0,X2,c_fequal(c_Product__Type_OPair(X0,X2,X1,X3)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_788])]) ).
fof(f6403,plain,
( ! [X2,X3,X0,X1] : c_member(X0,X1,c_Relation_ODomain(X0,X2,c_fequal(c_Product__Type_OPair(X0,X2,X1,X3))))
| ~ spl104_35
| ~ spl104_355 ),
inference(resolution,[],[f5978,f3039]) ).
fof(f19687,plain,
( spl104_787
| ~ spl104_336
| ~ spl104_355 ),
inference(avatar_split_clause,[],[f6396,f5977,f5901,f19685]) ).
fof(f19685,plain,
( spl104_787
<=> ! [X0,X1] :
( c_member(X0,sK31(X1,X0),c_Relation_ODomain(X0,X0,X1))
| c_Relation_Otrans(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_787])]) ).
fof(f6396,plain,
( ! [X0,X1] :
( c_member(X0,sK31(X1,X0),c_Relation_ODomain(X0,X0,X1))
| c_Relation_Otrans(X0,X1) )
| ~ spl104_336
| ~ spl104_355 ),
inference(resolution,[],[f5978,f5902]) ).
fof(f19683,plain,
( spl104_786
| ~ spl104_334
| ~ spl104_355 ),
inference(avatar_split_clause,[],[f6395,f5977,f5893,f19681]) ).
fof(f19681,plain,
( spl104_786
<=> ! [X0,X1] :
( c_member(X0,sK30(X1,X0),c_Relation_ODomain(X0,X0,X1))
| c_Relation_Otrans(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_786])]) ).
fof(f6395,plain,
( ! [X0,X1] :
( c_member(X0,sK30(X1,X0),c_Relation_ODomain(X0,X0,X1))
| c_Relation_Otrans(X0,X1) )
| ~ spl104_334
| ~ spl104_355 ),
inference(resolution,[],[f5978,f5894]) ).
fof(f19679,plain,
( spl104_785
| ~ spl104_332
| ~ spl104_355 ),
inference(avatar_split_clause,[],[f6394,f5977,f5885,f19677]) ).
fof(f19677,plain,
( spl104_785
<=> ! [X0,X1] :
( c_member(X0,sK28(X1,X0),c_Relation_ODomain(X0,X0,X1))
| c_Relation_Oantisym(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_785])]) ).
fof(f6394,plain,
( ! [X0,X1] :
( c_member(X0,sK28(X1,X0),c_Relation_ODomain(X0,X0,X1))
| c_Relation_Oantisym(X0,X1) )
| ~ spl104_332
| ~ spl104_355 ),
inference(resolution,[],[f5978,f5886]) ).
fof(f19675,plain,
( spl104_784
| ~ spl104_333
| ~ spl104_355 ),
inference(avatar_split_clause,[],[f6393,f5977,f5889,f19673]) ).
fof(f19673,plain,
( spl104_784
<=> ! [X0,X1] :
( c_member(X0,sK29(X1,X0),c_Relation_ODomain(X0,X0,X1))
| c_Relation_Oantisym(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_784])]) ).
fof(f6393,plain,
( ! [X0,X1] :
( c_member(X0,sK29(X1,X0),c_Relation_ODomain(X0,X0,X1))
| c_Relation_Oantisym(X0,X1) )
| ~ spl104_333
| ~ spl104_355 ),
inference(resolution,[],[f5978,f5890]) ).
fof(f19671,plain,
( spl104_783
| ~ spl104_330
| ~ spl104_355 ),
inference(avatar_split_clause,[],[f6392,f5977,f5877,f19669]) ).
fof(f19669,plain,
( spl104_783
<=> ! [X0,X1] :
( c_member(X0,sK25(X1,X0),c_Relation_ODomain(X0,X0,X1))
| c_Relation_Otrans(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_783])]) ).
fof(f6392,plain,
( ! [X0,X1] :
( c_member(X0,sK25(X1,X0),c_Relation_ODomain(X0,X0,X1))
| c_Relation_Otrans(X0,X1) )
| ~ spl104_330
| ~ spl104_355 ),
inference(resolution,[],[f5978,f5878]) ).
fof(f19667,plain,
( spl104_782
| ~ spl104_329
| ~ spl104_355 ),
inference(avatar_split_clause,[],[f6391,f5977,f5873,f19665]) ).
fof(f19665,plain,
( spl104_782
<=> ! [X0,X1] :
( c_member(X0,sK24(X1,X0),c_Relation_ODomain(X0,X0,X1))
| c_Relation_Otrans(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_782])]) ).
fof(f6391,plain,
( ! [X0,X1] :
( c_member(X0,sK24(X1,X0),c_Relation_ODomain(X0,X0,X1))
| c_Relation_Otrans(X0,X1) )
| ~ spl104_329
| ~ spl104_355 ),
inference(resolution,[],[f5978,f5874]) ).
fof(f19663,plain,
( spl104_781
| ~ spl104_327
| ~ spl104_355 ),
inference(avatar_split_clause,[],[f6390,f5977,f5865,f19661]) ).
fof(f19661,plain,
( spl104_781
<=> ! [X0,X1] :
( c_member(X0,sK22(X1,X0),c_Relation_ODomain(X0,X0,X1))
| c_Relation_Oantisym(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_781])]) ).
fof(f6390,plain,
( ! [X0,X1] :
( c_member(X0,sK22(X1,X0),c_Relation_ODomain(X0,X0,X1))
| c_Relation_Oantisym(X0,X1) )
| ~ spl104_327
| ~ spl104_355 ),
inference(resolution,[],[f5978,f5866]) ).
fof(f19659,plain,
( spl104_780
| ~ spl104_53
| ~ spl104_740 ),
inference(avatar_split_clause,[],[f19441,f19436,f3111,f19656]) ).
fof(f19656,plain,
( spl104_780
<=> sP2(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),c_FunDef_Omin__strict) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_780])]) ).
fof(f19441,plain,
( sP2(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),c_FunDef_Omin__strict)
| ~ spl104_53
| ~ spl104_740 ),
inference(resolution,[],[f19438,f3112]) ).
fof(f19654,plain,
( spl104_779
| ~ spl104_328
| ~ spl104_355 ),
inference(avatar_split_clause,[],[f6389,f5977,f5869,f19652]) ).
fof(f19652,plain,
( spl104_779
<=> ! [X0,X1] :
( c_member(X0,sK23(X1,X0),c_Relation_ODomain(X0,X0,X1))
| c_Relation_Oantisym(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_779])]) ).
fof(f6389,plain,
( ! [X0,X1] :
( c_member(X0,sK23(X1,X0),c_Relation_ODomain(X0,X0,X1))
| c_Relation_Oantisym(X0,X1) )
| ~ spl104_328
| ~ spl104_355 ),
inference(resolution,[],[f5978,f5870]) ).
fof(f19650,plain,
( spl104_778
| ~ spl104_35
| ~ spl104_354 ),
inference(avatar_split_clause,[],[f6381,f5973,f3038,f19648]) ).
fof(f19648,plain,
( spl104_778
<=> ! [X0,X3,X2,X1] : c_member(X0,X1,c_Relation_ORange(X2,X0,c_fequal(c_Product__Type_OPair(X2,X0,X3,X1)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_778])]) ).
fof(f6381,plain,
( ! [X2,X3,X0,X1] : c_member(X0,X1,c_Relation_ORange(X2,X0,c_fequal(c_Product__Type_OPair(X2,X0,X3,X1))))
| ~ spl104_35
| ~ spl104_354 ),
inference(resolution,[],[f5974,f3039]) ).
fof(f19646,plain,
( spl104_777
| ~ spl104_336
| ~ spl104_354 ),
inference(avatar_split_clause,[],[f6374,f5973,f5901,f19644]) ).
fof(f19644,plain,
( spl104_777
<=> ! [X0,X1] :
( c_member(X0,sK32(X1,X0),c_Relation_ORange(X0,X0,X1))
| c_Relation_Otrans(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_777])]) ).
fof(f6374,plain,
( ! [X0,X1] :
( c_member(X0,sK32(X1,X0),c_Relation_ORange(X0,X0,X1))
| c_Relation_Otrans(X0,X1) )
| ~ spl104_336
| ~ spl104_354 ),
inference(resolution,[],[f5974,f5902]) ).
fof(f19642,plain,
( spl104_776
| ~ spl104_334
| ~ spl104_354 ),
inference(avatar_split_clause,[],[f6373,f5973,f5893,f19640]) ).
fof(f19640,plain,
( spl104_776
<=> ! [X0,X1] :
( c_member(X0,sK31(X1,X0),c_Relation_ORange(X0,X0,X1))
| c_Relation_Otrans(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_776])]) ).
fof(f6373,plain,
( ! [X0,X1] :
( c_member(X0,sK31(X1,X0),c_Relation_ORange(X0,X0,X1))
| c_Relation_Otrans(X0,X1) )
| ~ spl104_334
| ~ spl104_354 ),
inference(resolution,[],[f5974,f5894]) ).
fof(f19638,plain,
( spl104_775
| ~ spl104_332
| ~ spl104_354 ),
inference(avatar_split_clause,[],[f6372,f5973,f5885,f19636]) ).
fof(f19636,plain,
( spl104_775
<=> ! [X0,X1] :
( c_member(X0,sK29(X1,X0),c_Relation_ORange(X0,X0,X1))
| c_Relation_Oantisym(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_775])]) ).
fof(f6372,plain,
( ! [X0,X1] :
( c_member(X0,sK29(X1,X0),c_Relation_ORange(X0,X0,X1))
| c_Relation_Oantisym(X0,X1) )
| ~ spl104_332
| ~ spl104_354 ),
inference(resolution,[],[f5974,f5886]) ).
fof(f19634,plain,
( spl104_774
| ~ spl104_333
| ~ spl104_354 ),
inference(avatar_split_clause,[],[f6371,f5973,f5889,f19632]) ).
fof(f19632,plain,
( spl104_774
<=> ! [X0,X1] :
( c_member(X0,sK28(X1,X0),c_Relation_ORange(X0,X0,X1))
| c_Relation_Oantisym(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_774])]) ).
fof(f6371,plain,
( ! [X0,X1] :
( c_member(X0,sK28(X1,X0),c_Relation_ORange(X0,X0,X1))
| c_Relation_Oantisym(X0,X1) )
| ~ spl104_333
| ~ spl104_354 ),
inference(resolution,[],[f5974,f5890]) ).
fof(f19630,plain,
( spl104_773
| ~ spl104_330
| ~ spl104_354 ),
inference(avatar_split_clause,[],[f6370,f5973,f5877,f19628]) ).
fof(f19628,plain,
( spl104_773
<=> ! [X0,X1] :
( c_member(X0,sK26(X1,X0),c_Relation_ORange(X0,X0,X1))
| c_Relation_Otrans(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_773])]) ).
fof(f6370,plain,
( ! [X0,X1] :
( c_member(X0,sK26(X1,X0),c_Relation_ORange(X0,X0,X1))
| c_Relation_Otrans(X0,X1) )
| ~ spl104_330
| ~ spl104_354 ),
inference(resolution,[],[f5974,f5878]) ).
fof(f19626,plain,
( spl104_772
| ~ spl104_329
| ~ spl104_354 ),
inference(avatar_split_clause,[],[f6369,f5973,f5873,f19624]) ).
fof(f19624,plain,
( spl104_772
<=> ! [X0,X1] :
( c_member(X0,sK25(X1,X0),c_Relation_ORange(X0,X0,X1))
| c_Relation_Otrans(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_772])]) ).
fof(f6369,plain,
( ! [X0,X1] :
( c_member(X0,sK25(X1,X0),c_Relation_ORange(X0,X0,X1))
| c_Relation_Otrans(X0,X1) )
| ~ spl104_329
| ~ spl104_354 ),
inference(resolution,[],[f5974,f5874]) ).
fof(f19622,plain,
( spl104_771
| ~ spl104_327
| ~ spl104_354 ),
inference(avatar_split_clause,[],[f6368,f5973,f5865,f19620]) ).
fof(f19620,plain,
( spl104_771
<=> ! [X0,X1] :
( c_member(X0,sK23(X1,X0),c_Relation_ORange(X0,X0,X1))
| c_Relation_Oantisym(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_771])]) ).
fof(f6368,plain,
( ! [X0,X1] :
( c_member(X0,sK23(X1,X0),c_Relation_ORange(X0,X0,X1))
| c_Relation_Oantisym(X0,X1) )
| ~ spl104_327
| ~ spl104_354 ),
inference(resolution,[],[f5974,f5866]) ).
fof(f19618,plain,
( spl104_770
| ~ spl104_328
| ~ spl104_354 ),
inference(avatar_split_clause,[],[f6367,f5973,f5869,f19616]) ).
fof(f19616,plain,
( spl104_770
<=> ! [X0,X1] :
( c_member(X0,sK22(X1,X0),c_Relation_ORange(X0,X0,X1))
| c_Relation_Oantisym(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_770])]) ).
fof(f6367,plain,
( ! [X0,X1] :
( c_member(X0,sK22(X1,X0),c_Relation_ORange(X0,X0,X1))
| c_Relation_Oantisym(X0,X1) )
| ~ spl104_328
| ~ spl104_354 ),
inference(resolution,[],[f5974,f5870]) ).
fof(f19614,plain,
( spl104_769
| ~ spl104_98
| ~ spl104_353 ),
inference(avatar_split_clause,[],[f6362,f5969,f3306,f19612]) ).
fof(f19612,plain,
( spl104_769
<=> ! [X2,X0,X1] : c_Wellfounded_Owf(tc_prod(X0,X1),c_Recdef_Osame__fst(X0,X1,X2,c_Relation_Oinv__image(tc_Nat_Onat,X1,c_Wellfounded_Oless__than))) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_769])]) ).
fof(f3306,plain,
( spl104_98
<=> ! [X0,X1] : c_Wellfounded_Owf(X1,hAPP(c_Relation_Oinv__image(tc_Nat_Onat,X1,c_Wellfounded_Oless__than),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_98])]) ).
fof(f5969,plain,
( spl104_353
<=> ! [X0,X3,X2,X1] :
( c_Wellfounded_Owf(tc_prod(X0,X2),c_Recdef_Osame__fst(X0,X2,X3,X1))
| ~ c_Wellfounded_Owf(X2,hAPP(X1,sK67(X1,X2,X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_353])]) ).
fof(f6362,plain,
( ! [X2,X0,X1] : c_Wellfounded_Owf(tc_prod(X0,X1),c_Recdef_Osame__fst(X0,X1,X2,c_Relation_Oinv__image(tc_Nat_Onat,X1,c_Wellfounded_Oless__than)))
| ~ spl104_98
| ~ spl104_353 ),
inference(resolution,[],[f5970,f3307]) ).
fof(f3307,plain,
( ! [X0,X1] : c_Wellfounded_Owf(X1,hAPP(c_Relation_Oinv__image(tc_Nat_Onat,X1,c_Wellfounded_Oless__than),X0))
| ~ spl104_98 ),
inference(avatar_component_clause,[],[f3306]) ).
fof(f5970,plain,
( ! [X2,X3,X0,X1] :
( ~ c_Wellfounded_Owf(X2,hAPP(X1,sK67(X1,X2,X3)))
| c_Wellfounded_Owf(tc_prod(X0,X2),c_Recdef_Osame__fst(X0,X2,X3,X1)) )
| ~ spl104_353 ),
inference(avatar_component_clause,[],[f5969]) ).
fof(f19610,plain,
( spl104_768
| ~ spl104_106
| ~ spl104_331 ),
inference(avatar_split_clause,[],[f6101,f5881,f3363,f19608]) ).
fof(f19608,plain,
( spl104_768
<=> ! [X0,X1] :
( c_Relation_Otrans(X0,c_Wellfounded_Oacc(tc_prod(X0,X0),X1))
| ~ c_Wellfounded_Owf(tc_prod(X0,X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_768])]) ).
fof(f5881,plain,
( spl104_331
<=> ! [X0,X1] :
( c_Relation_Otrans(X1,X0)
| ~ c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,sK24(X0,X1),sK26(X0,X1)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_331])]) ).
fof(f6101,plain,
( ! [X0,X1] :
( c_Relation_Otrans(X0,c_Wellfounded_Oacc(tc_prod(X0,X0),X1))
| ~ c_Wellfounded_Owf(tc_prod(X0,X0),X1) )
| ~ spl104_106
| ~ spl104_331 ),
inference(resolution,[],[f5882,f3364]) ).
fof(f5882,plain,
( ! [X0,X1] :
( ~ c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,sK24(X0,X1),sK26(X0,X1)),X0)
| c_Relation_Otrans(X1,X0) )
| ~ spl104_331 ),
inference(avatar_component_clause,[],[f5881]) ).
fof(f19606,plain,
( spl104_767
| ~ spl104_154
| ~ spl104_325 ),
inference(avatar_split_clause,[],[f5996,f5856,f3622,f19603]) ).
fof(f19603,plain,
( spl104_767
<=> c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),tc_HOL_Obool),c_FunDef_Opair__less,c_FunDef_Opair__leq) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_767])]) ).
fof(f5856,plain,
( spl104_325
<=> c_FunDef_Opair__leq = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),tc_HOL_Obool),c_FunDef_Opair__less,c_Relation_OId(tc_prod(tc_Nat_Onat,tc_Nat_Onat))) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_325])]) ).
fof(f5996,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),tc_HOL_Obool),c_FunDef_Opair__less,c_FunDef_Opair__leq)
| ~ spl104_154
| ~ spl104_325 ),
inference(superposition,[],[f3623,f5858]) ).
fof(f5858,plain,
( c_FunDef_Opair__leq = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),tc_HOL_Obool),c_FunDef_Opair__less,c_Relation_OId(tc_prod(tc_Nat_Onat,tc_Nat_Onat)))
| ~ spl104_325 ),
inference(avatar_component_clause,[],[f5856]) ).
fof(f19601,plain,
( spl104_766
| ~ spl104_108
| ~ spl104_307 ),
inference(avatar_split_clause,[],[f5684,f5485,f3371,f19599]) ).
fof(f19599,plain,
( spl104_766
<=> ! [X0,X3,X2,X1] : c_Orderings_Oord__class_Oless__eq(tc_fun(X0,tc_HOL_Obool),X1,c_Set_Oinsert(X0,X2,c_Set_Oinsert(X0,X3,X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_766])]) ).
fof(f5485,plain,
( spl104_307
<=> ! [X0,X3,X2,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),c_Set_Oinsert(X3,X2,X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_307])]) ).
fof(f5684,plain,
( ! [X2,X3,X0,X1] : c_Orderings_Oord__class_Oless__eq(tc_fun(X0,tc_HOL_Obool),X1,c_Set_Oinsert(X0,X2,c_Set_Oinsert(X0,X3,X1)))
| ~ spl104_108
| ~ spl104_307 ),
inference(resolution,[],[f5486,f3372]) ).
fof(f5486,plain,
( ! [X2,X3,X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),c_Set_Oinsert(X3,X2,X1),X0)
| c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X1,X0) )
| ~ spl104_307 ),
inference(avatar_component_clause,[],[f5485]) ).
fof(f19597,plain,
( spl104_765
| ~ spl104_108
| ~ spl104_304 ),
inference(avatar_split_clause,[],[f5664,f5459,f3371,f19595]) ).
fof(f19595,plain,
( spl104_765
<=> ! [X0,X3,X2,X1] :
( sP4(c_Set_Oinsert(X0,X1,X2),X2,X0,X3)
| c_member(X0,X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_765])]) ).
fof(f5459,plain,
( spl104_304
<=> ! [X0,X3,X2,X1] :
( sP4(X0,X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool),X1,X0)
| c_member(X2,X3,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_304])]) ).
fof(f5664,plain,
( ! [X2,X3,X0,X1] :
( sP4(c_Set_Oinsert(X0,X1,X2),X2,X0,X3)
| c_member(X0,X3,X2) )
| ~ spl104_108
| ~ spl104_304 ),
inference(resolution,[],[f5460,f3372]) ).
fof(f5460,plain,
( ! [X2,X3,X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool),X1,X0)
| sP4(X0,X1,X2,X3)
| c_member(X2,X3,X1) )
| ~ spl104_304 ),
inference(avatar_component_clause,[],[f5459]) ).
fof(f19593,plain,
( spl104_764
| ~ spl104_28
| ~ spl104_256 ),
inference(avatar_split_clause,[],[f5037,f4685,f3008,f19591]) ).
fof(f19591,plain,
( spl104_764
<=> ! [X0] :
( c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat),X0,c_Wellfounded_Oless__than)
| ~ c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat),X0,c_Wellfounded_Opred__nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_764])]) ).
fof(f5037,plain,
( ! [X0] :
( c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat),X0,c_Wellfounded_Oless__than)
| ~ c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat),X0,c_Wellfounded_Opred__nat) )
| ~ spl104_28
| ~ spl104_256 ),
inference(superposition,[],[f4686,f3010]) ).
fof(f19589,plain,
( spl104_763
| ~ spl104_95
| ~ spl104_256 ),
inference(avatar_split_clause,[],[f5036,f4685,f3294,f19587]) ).
fof(f5036,plain,
( ! [X2,X0,X1] :
( ~ c_member(tc_prod(X0,X0),X1,X2)
| hBOOL(hAPP(c_Transitive__Closure_Otrancl(X0,X2),X1)) )
| ~ spl104_95
| ~ spl104_256 ),
inference(resolution,[],[f4686,f3295]) ).
fof(f19585,plain,
( spl104_762
| ~ spl104_13
| ~ spl104_246 ),
inference(avatar_split_clause,[],[f4873,f4643,f2937,f19583]) ).
fof(f19583,plain,
( spl104_762
<=> ! [X0,X1] : c_Lattices_Osemilattice__sup__class_Osup(tc_HOL_Obool,X0,X1) = c_Lattices_Osemilattice__sup__class_Osup(tc_HOL_Obool,X0,c_Lattices_Osemilattice__sup__class_Osup(tc_HOL_Obool,X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_762])]) ).
fof(f2937,plain,
( spl104_13
<=> class_Lattices_Olattice(tc_HOL_Obool) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_13])]) ).
fof(f4643,plain,
( spl104_246
<=> ! [X2,X0,X1] :
( c_Lattices_Osemilattice__sup__class_Osup(X2,X1,X0) = c_Lattices_Osemilattice__sup__class_Osup(X2,X1,c_Lattices_Osemilattice__sup__class_Osup(X2,X1,X0))
| ~ class_Lattices_Olattice(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_246])]) ).
fof(f4873,plain,
( ! [X0,X1] : c_Lattices_Osemilattice__sup__class_Osup(tc_HOL_Obool,X0,X1) = c_Lattices_Osemilattice__sup__class_Osup(tc_HOL_Obool,X0,c_Lattices_Osemilattice__sup__class_Osup(tc_HOL_Obool,X0,X1))
| ~ spl104_13
| ~ spl104_246 ),
inference(resolution,[],[f4644,f2939]) ).
fof(f2939,plain,
( class_Lattices_Olattice(tc_HOL_Obool)
| ~ spl104_13 ),
inference(avatar_component_clause,[],[f2937]) ).
fof(f4644,plain,
( ! [X2,X0,X1] :
( ~ class_Lattices_Olattice(X2)
| c_Lattices_Osemilattice__sup__class_Osup(X2,X1,X0) = c_Lattices_Osemilattice__sup__class_Osup(X2,X1,c_Lattices_Osemilattice__sup__class_Osup(X2,X1,X0)) )
| ~ spl104_246 ),
inference(avatar_component_clause,[],[f4643]) ).
fof(f19581,plain,
( spl104_761
| ~ spl104_10
| ~ spl104_246 ),
inference(avatar_split_clause,[],[f4872,f4643,f2922,f19579]) ).
fof(f19579,plain,
( spl104_761
<=> ! [X0,X1] : c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat,X0,X1) = c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat,X0,c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat,X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_761])]) ).
fof(f4872,plain,
( ! [X0,X1] : c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat,X0,X1) = c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat,X0,c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat,X0,X1))
| ~ spl104_10
| ~ spl104_246 ),
inference(resolution,[],[f4644,f2924]) ).
fof(f2924,plain,
( class_Lattices_Olattice(tc_Nat_Onat)
| ~ spl104_10 ),
inference(avatar_component_clause,[],[f2922]) ).
fof(f19577,plain,
( spl104_760
| ~ spl104_95
| ~ spl104_243 ),
inference(avatar_split_clause,[],[f4861,f4631,f3294,f19575]) ).
fof(f19575,plain,
( spl104_760
<=> ! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1)
| hBOOL(hAPP(c_Wellfounded_Oless__than,c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat,X0,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_760])]) ).
fof(f4861,plain,
( ! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1)
| hBOOL(hAPP(c_Wellfounded_Oless__than,c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat,X0,X1))) )
| ~ spl104_95
| ~ spl104_243 ),
inference(resolution,[],[f4632,f3295]) ).
fof(f19573,plain,
( ~ spl104_759
| ~ spl104_325
| ~ spl104_738 ),
inference(avatar_split_clause,[],[f19424,f18592,f5856,f19570]) ).
fof(f19570,plain,
( spl104_759
<=> c_Wellfounded_Oacyclic(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__leq) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_759])]) ).
fof(f18592,plain,
( spl104_738
<=> ! [X0,X1] : ~ c_Wellfounded_Oacyclic(X0,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X0,X0),tc_HOL_Obool),X1,c_Relation_OId(X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_738])]) ).
fof(f19424,plain,
( ~ c_Wellfounded_Oacyclic(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__leq)
| ~ spl104_325
| ~ spl104_738 ),
inference(superposition,[],[f18593,f5858]) ).
fof(f18593,plain,
( ! [X0,X1] : ~ c_Wellfounded_Oacyclic(X0,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X0,X0),tc_HOL_Obool),X1,c_Relation_OId(X0)))
| ~ spl104_738 ),
inference(avatar_component_clause,[],[f18592]) ).
fof(f19568,plain,
( spl104_758
| ~ spl104_35
| ~ spl104_241 ),
inference(avatar_split_clause,[],[f4849,f4623,f3038,f19566]) ).
fof(f19566,plain,
( spl104_758
<=> ! [X2,X0,X1] :
( c_member(X0,sK37(X0,X1,c_fequal(X2)),c_fequal(X2))
| ~ sP2(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_758])]) ).
fof(f4623,plain,
( spl104_241
<=> ! [X9,X0,X6,X1] :
( c_member(X0,sK37(X0,X1,X6),X6)
| ~ c_member(X0,X9,X6)
| ~ sP2(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_241])]) ).
fof(f4849,plain,
( ! [X2,X0,X1] :
( c_member(X0,sK37(X0,X1,c_fequal(X2)),c_fequal(X2))
| ~ sP2(X0,X1) )
| ~ spl104_35
| ~ spl104_241 ),
inference(resolution,[],[f4624,f3039]) ).
fof(f4624,plain,
( ! [X0,X1,X6,X9] :
( ~ c_member(X0,X9,X6)
| c_member(X0,sK37(X0,X1,X6),X6)
| ~ sP2(X0,X1) )
| ~ spl104_241 ),
inference(avatar_component_clause,[],[f4623]) ).
fof(f19564,plain,
( spl104_757
| ~ spl104_73
| ~ spl104_232 ),
inference(avatar_split_clause,[],[f4593,f4176,f3202,f19562]) ).
fof(f19562,plain,
( spl104_757
<=> ! [X3,X4,X0,X5,X2,X1] :
( sP9(c_Set_Oinsert(X0,X1,X2),X3,X4,X5)
| ~ c_member(X4,X1,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_757])]) ).
fof(f3202,plain,
( spl104_73
<=> ! [X2,X1,X3] : hBOOL(hAPP(c_Set_Oinsert(X3,X2,X1),X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_73])]) ).
fof(f4176,plain,
( spl104_232
<=> ! [X4,X0,X3,X2,X1] :
( sP9(X0,X1,X2,X3)
| ~ hBOOL(hAPP(X0,X4))
| ~ c_member(X2,X4,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_232])]) ).
fof(f4593,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( sP9(c_Set_Oinsert(X0,X1,X2),X3,X4,X5)
| ~ c_member(X4,X1,X3) )
| ~ spl104_73
| ~ spl104_232 ),
inference(resolution,[],[f4177,f3203]) ).
fof(f3203,plain,
( ! [X2,X3,X1] : hBOOL(hAPP(c_Set_Oinsert(X3,X2,X1),X2))
| ~ spl104_73 ),
inference(avatar_component_clause,[],[f3202]) ).
fof(f4177,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ hBOOL(hAPP(X0,X4))
| sP9(X0,X1,X2,X3)
| ~ c_member(X2,X4,X1) )
| ~ spl104_232 ),
inference(avatar_component_clause,[],[f4176]) ).
fof(f19560,plain,
( spl104_756
| ~ spl104_73
| ~ spl104_230 ),
inference(avatar_split_clause,[],[f4588,f4168,f3202,f19558]) ).
fof(f19558,plain,
( spl104_756
<=> ! [X3,X4,X0,X5,X2,X1] :
( sP9(c_Set_Oinsert(X0,X1,X2),X3,X4,X5)
| ~ c_member(X4,X1,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_756])]) ).
fof(f4168,plain,
( spl104_230
<=> ! [X5,X0,X3,X2,X1] :
( sP9(X0,X1,X2,X3)
| ~ hBOOL(hAPP(X0,X5))
| ~ c_member(X2,X5,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_230])]) ).
fof(f4588,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( sP9(c_Set_Oinsert(X0,X1,X2),X3,X4,X5)
| ~ c_member(X4,X1,X5) )
| ~ spl104_73
| ~ spl104_230 ),
inference(resolution,[],[f4169,f3203]) ).
fof(f4169,plain,
( ! [X2,X3,X0,X1,X5] :
( ~ hBOOL(hAPP(X0,X5))
| sP9(X0,X1,X2,X3)
| ~ c_member(X2,X5,X3) )
| ~ spl104_230 ),
inference(avatar_component_clause,[],[f4168]) ).
fof(f19556,plain,
( spl104_755
| ~ spl104_111
| ~ spl104_218 ),
inference(avatar_split_clause,[],[f4510,f4120,f3383,f19554]) ).
fof(f19554,plain,
( spl104_755
<=> ! [X0,X3,X2,X1] :
( c_Orderings_Oord__class_Oless__eq(X0,X1,c_Lattices_Osemilattice__sup__class_Osup(X0,X2,c_Lattices_Osemilattice__sup__class_Osup(X0,X3,X1)))
| ~ class_Lattices_Osemilattice__sup(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_755])]) ).
fof(f3383,plain,
( spl104_111
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X2,X1,c_Lattices_Osemilattice__sup__class_Osup(X2,X0,X1))
| ~ class_Lattices_Osemilattice__sup(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_111])]) ).
fof(f4120,plain,
( spl104_218
<=> ! [X0,X3,X2,X1] :
( c_Orderings_Oord__class_Oless__eq(X3,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(X3,c_Lattices_Osemilattice__sup__class_Osup(X3,X2,X1),X0)
| ~ class_Lattices_Osemilattice__sup(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_218])]) ).
fof(f4510,plain,
( ! [X2,X3,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X0,X1,c_Lattices_Osemilattice__sup__class_Osup(X0,X2,c_Lattices_Osemilattice__sup__class_Osup(X0,X3,X1)))
| ~ class_Lattices_Osemilattice__sup(X0) )
| ~ spl104_111
| ~ spl104_218 ),
inference(duplicate_literal_removal,[],[f4483]) ).
fof(f4483,plain,
( ! [X2,X3,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X0,X1,c_Lattices_Osemilattice__sup__class_Osup(X0,X2,c_Lattices_Osemilattice__sup__class_Osup(X0,X3,X1)))
| ~ class_Lattices_Osemilattice__sup(X0)
| ~ class_Lattices_Osemilattice__sup(X0) )
| ~ spl104_111
| ~ spl104_218 ),
inference(resolution,[],[f4121,f3384]) ).
fof(f3384,plain,
( ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X2,X1,c_Lattices_Osemilattice__sup__class_Osup(X2,X0,X1))
| ~ class_Lattices_Osemilattice__sup(X2) )
| ~ spl104_111 ),
inference(avatar_component_clause,[],[f3383]) ).
fof(f4121,plain,
( ! [X2,X3,X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(X3,c_Lattices_Osemilattice__sup__class_Osup(X3,X2,X1),X0)
| c_Orderings_Oord__class_Oless__eq(X3,X1,X0)
| ~ class_Lattices_Osemilattice__sup(X3) )
| ~ spl104_218 ),
inference(avatar_component_clause,[],[f4120]) ).
fof(f19552,plain,
( spl104_754
| ~ spl104_112
| ~ spl104_218 ),
inference(avatar_split_clause,[],[f4507,f4120,f3387,f19550]) ).
fof(f19550,plain,
( spl104_754
<=> ! [X0,X3,X2,X1] :
( c_Orderings_Oord__class_Oless__eq(X0,X1,c_Lattices_Osemilattice__sup__class_Osup(X0,c_Lattices_Osemilattice__sup__class_Osup(X0,X2,X1),X3))
| ~ class_Lattices_Osemilattice__sup(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_754])]) ).
fof(f3387,plain,
( spl104_112
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X2,X1,c_Lattices_Osemilattice__sup__class_Osup(X2,X1,X0))
| ~ class_Lattices_Osemilattice__sup(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_112])]) ).
fof(f4507,plain,
( ! [X2,X3,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X0,X1,c_Lattices_Osemilattice__sup__class_Osup(X0,c_Lattices_Osemilattice__sup__class_Osup(X0,X2,X1),X3))
| ~ class_Lattices_Osemilattice__sup(X0) )
| ~ spl104_112
| ~ spl104_218 ),
inference(duplicate_literal_removal,[],[f4487]) ).
fof(f4487,plain,
( ! [X2,X3,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X0,X1,c_Lattices_Osemilattice__sup__class_Osup(X0,c_Lattices_Osemilattice__sup__class_Osup(X0,X2,X1),X3))
| ~ class_Lattices_Osemilattice__sup(X0)
| ~ class_Lattices_Osemilattice__sup(X0) )
| ~ spl104_112
| ~ spl104_218 ),
inference(resolution,[],[f4121,f3388]) ).
fof(f3388,plain,
( ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X2,X1,c_Lattices_Osemilattice__sup__class_Osup(X2,X1,X0))
| ~ class_Lattices_Osemilattice__sup(X2) )
| ~ spl104_112 ),
inference(avatar_component_clause,[],[f3387]) ).
fof(f19548,plain,
( spl104_753
| ~ spl104_111
| ~ spl104_217 ),
inference(avatar_split_clause,[],[f4479,f4116,f3383,f19546]) ).
fof(f19546,plain,
( spl104_753
<=> ! [X0,X3,X2,X1] :
( c_Orderings_Oord__class_Oless__eq(X0,X1,c_Lattices_Osemilattice__sup__class_Osup(X0,X2,c_Lattices_Osemilattice__sup__class_Osup(X0,X1,X3)))
| ~ class_Lattices_Osemilattice__sup(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_753])]) ).
fof(f4479,plain,
( ! [X2,X3,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X0,X1,c_Lattices_Osemilattice__sup__class_Osup(X0,X2,c_Lattices_Osemilattice__sup__class_Osup(X0,X1,X3)))
| ~ class_Lattices_Osemilattice__sup(X0) )
| ~ spl104_111
| ~ spl104_217 ),
inference(duplicate_literal_removal,[],[f4452]) ).
fof(f4452,plain,
( ! [X2,X3,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X0,X1,c_Lattices_Osemilattice__sup__class_Osup(X0,X2,c_Lattices_Osemilattice__sup__class_Osup(X0,X1,X3)))
| ~ class_Lattices_Osemilattice__sup(X0)
| ~ class_Lattices_Osemilattice__sup(X0) )
| ~ spl104_111
| ~ spl104_217 ),
inference(resolution,[],[f4117,f3384]) ).
fof(f19544,plain,
( spl104_752
| ~ spl104_112
| ~ spl104_217 ),
inference(avatar_split_clause,[],[f4476,f4116,f3387,f19542]) ).
fof(f19542,plain,
( spl104_752
<=> ! [X0,X3,X2,X1] :
( c_Orderings_Oord__class_Oless__eq(X0,X1,c_Lattices_Osemilattice__sup__class_Osup(X0,c_Lattices_Osemilattice__sup__class_Osup(X0,X1,X2),X3))
| ~ class_Lattices_Osemilattice__sup(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_752])]) ).
fof(f4476,plain,
( ! [X2,X3,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X0,X1,c_Lattices_Osemilattice__sup__class_Osup(X0,c_Lattices_Osemilattice__sup__class_Osup(X0,X1,X2),X3))
| ~ class_Lattices_Osemilattice__sup(X0) )
| ~ spl104_112
| ~ spl104_217 ),
inference(duplicate_literal_removal,[],[f4456]) ).
fof(f4456,plain,
( ! [X2,X3,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X0,X1,c_Lattices_Osemilattice__sup__class_Osup(X0,c_Lattices_Osemilattice__sup__class_Osup(X0,X1,X2),X3))
| ~ class_Lattices_Osemilattice__sup(X0)
| ~ class_Lattices_Osemilattice__sup(X0) )
| ~ spl104_112
| ~ spl104_217 ),
inference(resolution,[],[f4117,f3388]) ).
fof(f19540,plain,
( spl104_751
| ~ spl104_106
| ~ spl104_206 ),
inference(avatar_split_clause,[],[f4362,f4072,f3363,f19538]) ).
fof(f19538,plain,
( spl104_751
<=> ! [X0,X1] :
( ~ c_Wellfounded_Owf(X0,c_Wellfounded_Oacc(tc_prod(X0,X0),X1))
| ~ c_Wellfounded_Owf(tc_prod(X0,X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_751])]) ).
fof(f4362,plain,
( ! [X0,X1] :
( ~ c_Wellfounded_Owf(X0,c_Wellfounded_Oacc(tc_prod(X0,X0),X1))
| ~ c_Wellfounded_Owf(tc_prod(X0,X0),X1) )
| ~ spl104_106
| ~ spl104_206 ),
inference(resolution,[],[f4073,f3364]) ).
fof(f19536,plain,
( spl104_750
| ~ spl104_106
| ~ spl104_196 ),
inference(avatar_split_clause,[],[f4216,f4032,f3363,f19534]) ).
fof(f19534,plain,
( spl104_750
<=> ! [X0,X1] :
( ~ c_Relation_Oirrefl(X0,c_Wellfounded_Oacc(tc_prod(X0,X0),X1))
| ~ c_Wellfounded_Owf(tc_prod(X0,X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_750])]) ).
fof(f4216,plain,
( ! [X0,X1] :
( ~ c_Relation_Oirrefl(X0,c_Wellfounded_Oacc(tc_prod(X0,X0),X1))
| ~ c_Wellfounded_Owf(tc_prod(X0,X0),X1) )
| ~ spl104_106
| ~ spl104_196 ),
inference(resolution,[],[f4033,f3364]) ).
fof(f19532,plain,
( spl104_749
| ~ spl104_82
| ~ spl104_186 ),
inference(avatar_split_clause,[],[f3997,f3891,f3242,f19530]) ).
fof(f19530,plain,
( spl104_749
<=> ! [X2,X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_749])]) ).
fof(f3997,plain,
( ! [X2,X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X2) )
| ~ spl104_82
| ~ spl104_186 ),
inference(resolution,[],[f3892,f3243]) ).
fof(f19502,plain,
( ~ spl104_16
| spl104_748
| ~ spl104_82
| ~ spl104_184 ),
inference(avatar_split_clause,[],[f3981,f3883,f3242,f19500,f2952]) ).
fof(f19500,plain,
( spl104_748
<=> ! [X0,X1] :
( c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat,X0,X1) = X0
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_748])]) ).
fof(f3883,plain,
( spl104_184
<=> ! [X2,X0,X1] :
( c_Lattices_Osemilattice__sup__class_Osup(X2,X0,X1) = X0
| ~ c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
| ~ class_Lattices_Osemilattice__sup(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_184])]) ).
fof(f3981,plain,
( ! [X0,X1] :
( c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat,X0,X1) = X0
| ~ class_Lattices_Osemilattice__sup(tc_Nat_Onat)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1) )
| ~ spl104_82
| ~ spl104_184 ),
inference(resolution,[],[f3884,f3243]) ).
fof(f3884,plain,
( ! [X2,X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
| c_Lattices_Osemilattice__sup__class_Osup(X2,X0,X1) = X0
| ~ class_Lattices_Osemilattice__sup(X2) )
| ~ spl104_184 ),
inference(avatar_component_clause,[],[f3883]) ).
fof(f19474,plain,
( ~ spl104_16
| spl104_747
| ~ spl104_82
| ~ spl104_183 ),
inference(avatar_split_clause,[],[f3954,f3879,f3242,f19472,f2952]) ).
fof(f19472,plain,
( spl104_747
<=> ! [X0,X1] :
( c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat,X0,X1) = X1
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_747])]) ).
fof(f3879,plain,
( spl104_183
<=> ! [X2,X0,X1] :
( c_Lattices_Osemilattice__sup__class_Osup(X2,X1,X0) = X0
| ~ c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
| ~ class_Lattices_Osemilattice__sup(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_183])]) ).
fof(f3954,plain,
( ! [X0,X1] :
( c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat,X0,X1) = X1
| ~ class_Lattices_Osemilattice__sup(tc_Nat_Onat)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) )
| ~ spl104_82
| ~ spl104_183 ),
inference(resolution,[],[f3880,f3243]) ).
fof(f3880,plain,
( ! [X2,X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
| c_Lattices_Osemilattice__sup__class_Osup(X2,X1,X0) = X0
| ~ class_Lattices_Osemilattice__sup(X2) )
| ~ spl104_183 ),
inference(avatar_component_clause,[],[f3879]) ).
fof(f19470,plain,
( spl104_746
| ~ spl104_95
| ~ spl104_181 ),
inference(avatar_split_clause,[],[f3926,f3871,f3294,f19468]) ).
fof(f19468,plain,
( spl104_746
<=> ! [X0,X1] :
( c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)) = X1
| hBOOL(hAPP(X1,sK39(X1,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_746])]) ).
fof(f3926,plain,
( ! [X0,X1] :
( c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)) = X1
| hBOOL(hAPP(X1,sK39(X1,X0))) )
| ~ spl104_95
| ~ spl104_181 ),
inference(resolution,[],[f3872,f3295]) ).
fof(f19466,plain,
( spl104_745
| ~ spl104_95
| ~ spl104_180 ),
inference(avatar_split_clause,[],[f3922,f3867,f3294,f19464]) ).
fof(f19464,plain,
( spl104_745
<=> ! [X0,X1] :
( c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)) = X1
| hBOOL(hAPP(X1,sK38(X1,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_745])]) ).
fof(f3922,plain,
( ! [X0,X1] :
( c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)) = X1
| hBOOL(hAPP(X1,sK38(X1,X0))) )
| ~ spl104_95
| ~ spl104_180 ),
inference(resolution,[],[f3868,f3295]) ).
fof(f19462,plain,
( spl104_744
| ~ spl104_97
| ~ spl104_162 ),
inference(avatar_split_clause,[],[f3816,f3654,f3302,f19460]) ).
fof(f19460,plain,
( spl104_744
<=> ! [X2,X0,X1] :
( c_Relation_Ototal__on(X0,c_fequal(X1),X2)
| sK47(X2,c_fequal(X1),X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_744])]) ).
fof(f3816,plain,
( ! [X2,X0,X1] :
( c_Relation_Ototal__on(X0,c_fequal(X1),X2)
| sK47(X2,c_fequal(X1),X0) = X1 )
| ~ spl104_97
| ~ spl104_162 ),
inference(resolution,[],[f3655,f3303]) ).
fof(f19458,plain,
( spl104_743
| ~ spl104_97
| ~ spl104_160 ),
inference(avatar_split_clause,[],[f3812,f3646,f3302,f19456]) ).
fof(f19456,plain,
( spl104_743
<=> ! [X2,X0,X1] :
( c_Relation_Ototal__on(X0,c_fequal(X1),X2)
| sK46(X2,c_fequal(X1),X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_743])]) ).
fof(f3812,plain,
( ! [X2,X0,X1] :
( c_Relation_Ototal__on(X0,c_fequal(X1),X2)
| sK46(X2,c_fequal(X1),X0) = X1 )
| ~ spl104_97
| ~ spl104_160 ),
inference(resolution,[],[f3647,f3303]) ).
fof(f19451,plain,
( ~ spl104_29
| spl104_742
| ~ spl104_60
| ~ spl104_117 ),
inference(avatar_split_clause,[],[f3501,f3420,f3146,f19448,f3013]) ).
fof(f3013,plain,
( spl104_29
<=> c_Wellfounded_Owf(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_29])]) ).
fof(f3146,plain,
( spl104_60
<=> c_FunDef_Omax__strict = c_Wellfounded_Omax__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_60])]) ).
fof(f3420,plain,
( spl104_117
<=> ! [X0,X1] :
( c_Wellfounded_Owf(tc_fun(X1,tc_HOL_Obool),c_Wellfounded_Omax__ext(X1,X0))
| ~ c_Wellfounded_Owf(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_117])]) ).
fof(f3501,plain,
( c_Wellfounded_Owf(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),c_FunDef_Omax__strict)
| ~ c_Wellfounded_Owf(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less)
| ~ spl104_60
| ~ spl104_117 ),
inference(superposition,[],[f3421,f3148]) ).
fof(f3148,plain,
( c_FunDef_Omax__strict = c_Wellfounded_Omax__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less)
| ~ spl104_60 ),
inference(avatar_component_clause,[],[f3146]) ).
fof(f3421,plain,
( ! [X0,X1] :
( c_Wellfounded_Owf(tc_fun(X1,tc_HOL_Obool),c_Wellfounded_Omax__ext(X1,X0))
| ~ c_Wellfounded_Owf(X1,X0) )
| ~ spl104_117 ),
inference(avatar_component_clause,[],[f3420]) ).
fof(f19446,plain,
( spl104_741
| ~ spl104_78
| ~ spl104_738 ),
inference(avatar_split_clause,[],[f19427,f18592,f3226,f19444]) ).
fof(f19444,plain,
( spl104_741
<=> ! [X0] : ~ c_Wellfounded_Oacyclic(X0,c_Relation_OId(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_741])]) ).
fof(f19427,plain,
( ! [X0] : ~ c_Wellfounded_Oacyclic(X0,c_Relation_OId(X0))
| ~ spl104_78
| ~ spl104_738 ),
inference(superposition,[],[f18593,f3227]) ).
fof(f19439,plain,
( ~ spl104_29
| spl104_740
| ~ spl104_61
| ~ spl104_116 ),
inference(avatar_split_clause,[],[f3498,f3416,f3151,f19436,f3013]) ).
fof(f3151,plain,
( spl104_61
<=> c_FunDef_Omin__strict = c_Wellfounded_Omin__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_61])]) ).
fof(f3416,plain,
( spl104_116
<=> ! [X0,X1] :
( c_Wellfounded_Owf(tc_fun(X1,tc_HOL_Obool),c_Wellfounded_Omin__ext(X1,X0))
| ~ c_Wellfounded_Owf(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_116])]) ).
fof(f3498,plain,
( c_Wellfounded_Owf(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),c_FunDef_Omin__strict)
| ~ c_Wellfounded_Owf(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less)
| ~ spl104_61
| ~ spl104_116 ),
inference(superposition,[],[f3417,f3153]) ).
fof(f3153,plain,
( c_FunDef_Omin__strict = c_Wellfounded_Omin__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less)
| ~ spl104_61 ),
inference(avatar_component_clause,[],[f3151]) ).
fof(f3417,plain,
( ! [X0,X1] :
( c_Wellfounded_Owf(tc_fun(X1,tc_HOL_Obool),c_Wellfounded_Omin__ext(X1,X0))
| ~ c_Wellfounded_Owf(X1,X0) )
| ~ spl104_116 ),
inference(avatar_component_clause,[],[f3416]) ).
fof(f19291,plain,
( spl104_739
| ~ spl104_96
| ~ spl104_678 ),
inference(avatar_split_clause,[],[f18064,f17724,f3298,f19289]) ).
fof(f19289,plain,
( spl104_739
<=> ! [X2,X0,X1] : c_member(X0,X1,c_Relation_ODomain(X2,X2,c_Relation_OId(X2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_739])]) ).
fof(f17724,plain,
( spl104_678
<=> ! [X0,X1] : hBOOL(hAPP(c_Relation_ODomain(X0,X0,c_Relation_OId(X0)),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_678])]) ).
fof(f18064,plain,
( ! [X2,X0,X1] : c_member(X0,X1,c_Relation_ODomain(X2,X2,c_Relation_OId(X2)))
| ~ spl104_96
| ~ spl104_678 ),
inference(resolution,[],[f17725,f3299]) ).
fof(f17725,plain,
( ! [X0,X1] : hBOOL(hAPP(c_Relation_ODomain(X0,X0,c_Relation_OId(X0)),X1))
| ~ spl104_678 ),
inference(avatar_component_clause,[],[f17724]) ).
fof(f18594,plain,
( spl104_738
| ~ spl104_287
| ~ spl104_434 ),
inference(avatar_split_clause,[],[f7981,f7618,f5391,f18592]) ).
fof(f7981,plain,
( ! [X0,X1] : ~ c_Wellfounded_Oacyclic(X0,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X0,X0),tc_HOL_Obool),X1,c_Relation_OId(X0)))
| ~ spl104_287
| ~ spl104_434 ),
inference(resolution,[],[f7619,f5392]) ).
fof(f18590,plain,
( spl104_737
| ~ spl104_63
| ~ spl104_414 ),
inference(avatar_split_clause,[],[f7541,f7102,f3161,f18588]) ).
fof(f18588,plain,
( spl104_737
<=> ! [X3,X4,X0,X5,X2,X1] : ~ sP11(X0,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)),X1,X2,X3,X4,X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_737])]) ).
fof(f7102,plain,
( spl104_414
<=> ! [X5,X3,X4,X2,X0,X6,X1] :
( c_member(X0,sK94(X0,X1,X2,X3,X4,X5,X6),X1)
| ~ sP11(X0,X1,X2,X3,X4,X5,X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_414])]) ).
fof(f7541,plain,
( ! [X2,X3,X0,X1,X4,X5] : ~ sP11(X0,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)),X1,X2,X3,X4,X5)
| ~ spl104_63
| ~ spl104_414 ),
inference(resolution,[],[f7103,f3162]) ).
fof(f7103,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] :
( c_member(X0,sK94(X0,X1,X2,X3,X4,X5,X6),X1)
| ~ sP11(X0,X1,X2,X3,X4,X5,X6) )
| ~ spl104_414 ),
inference(avatar_component_clause,[],[f7102]) ).
fof(f18586,plain,
( spl104_736
| ~ spl104_63
| ~ spl104_194
| ~ spl104_393 ),
inference(avatar_split_clause,[],[f7180,f7018,f4024,f3161,f18584]) ).
fof(f18584,plain,
( spl104_736
<=> ! [X0,X1] : c_member(X0,X1,c_Wellfounded_Oacc(X0,c_Relation_OId__on(X0,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_736])]) ).
fof(f7180,plain,
( ! [X0,X1] : c_member(X0,X1,c_Wellfounded_Oacc(X0,c_Relation_OId__on(X0,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)))))
| ~ spl104_63
| ~ spl104_194
| ~ spl104_393 ),
inference(forward_demodulation,[],[f7175,f4025]) ).
fof(f7175,plain,
( ! [X0,X1] : c_member(X0,X1,c_Wellfounded_Oacc(X0,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X0,X0),tc_HOL_Obool))))
| ~ spl104_63
| ~ spl104_393 ),
inference(resolution,[],[f7019,f3162]) ).
fof(f18582,plain,
( spl104_735
| ~ spl104_28
| ~ spl104_139
| ~ spl104_243
| ~ spl104_355 ),
inference(avatar_split_clause,[],[f6405,f5977,f4631,f3560,f3008,f18580]) ).
fof(f18580,plain,
( spl104_735
<=> ! [X0,X1] :
( c_member(tc_Nat_Onat,X0,c_Relation_ODomain(tc_Nat_Onat,tc_Nat_Onat,c_Wellfounded_Opred__nat))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_735])]) ).
fof(f6405,plain,
( ! [X0,X1] :
( c_member(tc_Nat_Onat,X0,c_Relation_ODomain(tc_Nat_Onat,tc_Nat_Onat,c_Wellfounded_Opred__nat))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1) )
| ~ spl104_28
| ~ spl104_139
| ~ spl104_243
| ~ spl104_355 ),
inference(forward_demodulation,[],[f6387,f3702]) ).
fof(f3702,plain,
( c_Relation_ODomain(tc_Nat_Onat,tc_Nat_Onat,c_Wellfounded_Opred__nat) = c_Relation_ODomain(tc_Nat_Onat,tc_Nat_Onat,c_Wellfounded_Oless__than)
| ~ spl104_28
| ~ spl104_139 ),
inference(superposition,[],[f3561,f3010]) ).
fof(f6387,plain,
( ! [X0,X1] :
( c_member(tc_Nat_Onat,X0,c_Relation_ODomain(tc_Nat_Onat,tc_Nat_Onat,c_Wellfounded_Oless__than))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1) )
| ~ spl104_243
| ~ spl104_355 ),
inference(resolution,[],[f5978,f4632]) ).
fof(f18573,plain,
( spl104_734
| ~ spl104_28
| ~ spl104_138
| ~ spl104_243
| ~ spl104_354 ),
inference(avatar_split_clause,[],[f6383,f5973,f4631,f3556,f3008,f18571]) ).
fof(f18571,plain,
( spl104_734
<=> ! [X0,X1] :
( c_member(tc_Nat_Onat,X0,c_Relation_ORange(tc_Nat_Onat,tc_Nat_Onat,c_Wellfounded_Opred__nat))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_734])]) ).
fof(f6383,plain,
( ! [X0,X1] :
( c_member(tc_Nat_Onat,X0,c_Relation_ORange(tc_Nat_Onat,tc_Nat_Onat,c_Wellfounded_Opred__nat))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) )
| ~ spl104_28
| ~ spl104_138
| ~ spl104_243
| ~ spl104_354 ),
inference(forward_demodulation,[],[f6365,f3701]) ).
fof(f3701,plain,
( c_Relation_ORange(tc_Nat_Onat,tc_Nat_Onat,c_Wellfounded_Opred__nat) = c_Relation_ORange(tc_Nat_Onat,tc_Nat_Onat,c_Wellfounded_Oless__than)
| ~ spl104_28
| ~ spl104_138 ),
inference(superposition,[],[f3557,f3010]) ).
fof(f6365,plain,
( ! [X0,X1] :
( c_member(tc_Nat_Onat,X0,c_Relation_ORange(tc_Nat_Onat,tc_Nat_Onat,c_Wellfounded_Oless__than))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) )
| ~ spl104_243
| ~ spl104_354 ),
inference(resolution,[],[f5974,f4632]) ).
fof(f18565,plain,
( spl104_732
| spl104_733
| ~ spl104_242
| ~ spl104_327 ),
inference(avatar_split_clause,[],[f6034,f5865,f4627,f18562,f18558]) ).
fof(f18558,plain,
( spl104_732
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,sK22(c_Wellfounded_Oless__than,tc_Nat_Onat),sK23(c_Wellfounded_Oless__than,tc_Nat_Onat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_732])]) ).
fof(f18562,plain,
( spl104_733
<=> c_Relation_Oantisym(tc_Nat_Onat,c_Wellfounded_Oless__than) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_733])]) ).
fof(f6034,plain,
( c_Relation_Oantisym(tc_Nat_Onat,c_Wellfounded_Oless__than)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,sK22(c_Wellfounded_Oless__than,tc_Nat_Onat),sK23(c_Wellfounded_Oless__than,tc_Nat_Onat))
| ~ spl104_242
| ~ spl104_327 ),
inference(resolution,[],[f5866,f4628]) ).
fof(f18556,plain,
( spl104_731
| ~ spl104_221
| ~ spl104_325 ),
inference(avatar_split_clause,[],[f5998,f5856,f4132,f18554]) ).
fof(f18554,plain,
( spl104_731
<=> ! [X0] :
( hBOOL(hAPP(c_FunDef_Opair__leq,X0))
| ~ hBOOL(hAPP(c_Relation_OId(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_731])]) ).
fof(f5998,plain,
( ! [X0] :
( hBOOL(hAPP(c_FunDef_Opair__leq,X0))
| ~ hBOOL(hAPP(c_Relation_OId(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X0)) )
| ~ spl104_221
| ~ spl104_325 ),
inference(superposition,[],[f4133,f5858]) ).
fof(f18552,plain,
( spl104_730
| ~ spl104_279
| ~ spl104_300 ),
inference(avatar_split_clause,[],[f5623,f5443,f4810,f18550]) ).
fof(f18550,plain,
( spl104_730
<=> ! [X0,X3,X2,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X0,tc_HOL_Obool),X1,X2)
| sP6(X2,X1,X0,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_730])]) ).
fof(f5443,plain,
( spl104_300
<=> ! [X0,X3,X2,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X2,c_Set_Oinsert(X3,X0,X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_300])]) ).
fof(f5623,plain,
( ! [X2,X3,X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X0,tc_HOL_Obool),X1,X2)
| sP6(X2,X1,X0,X3) )
| ~ spl104_279
| ~ spl104_300 ),
inference(resolution,[],[f5444,f4811]) ).
fof(f5444,plain,
( ! [X2,X3,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X2,c_Set_Oinsert(X3,X0,X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X2,X1) )
| ~ spl104_300 ),
inference(avatar_component_clause,[],[f5443]) ).
fof(f18539,plain,
( ~ spl104_12
| spl104_729
| ~ spl104_108
| ~ spl104_261 ),
inference(avatar_split_clause,[],[f5077,f4711,f3371,f18537,f2932]) ).
fof(f18537,plain,
( spl104_729
<=> ! [X2,X0,X1] : ~ c_Orderings_Oord__class_Oless(tc_fun(X0,tc_HOL_Obool),c_Set_Oinsert(X0,X1,X2),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_729])]) ).
fof(f5077,plain,
( ! [X2,X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_fun(X0,tc_HOL_Obool),c_Set_Oinsert(X0,X1,X2),X2)
| ~ class_Orderings_Oord(tc_HOL_Obool) )
| ~ spl104_108
| ~ spl104_261 ),
inference(resolution,[],[f4712,f3372]) ).
fof(f18535,plain,
( spl104_728
| ~ spl104_108
| ~ spl104_257 ),
inference(avatar_split_clause,[],[f5044,f4689,f3371,f18533]) ).
fof(f18533,plain,
( spl104_728
<=> ! [X2,X0,X1] :
( ~ c_Relation_Oantisym(X0,c_Set_Oinsert(tc_prod(X0,X0),X1,X2))
| c_Relation_Oantisym(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_728])]) ).
fof(f5044,plain,
( ! [X2,X0,X1] :
( ~ c_Relation_Oantisym(X0,c_Set_Oinsert(tc_prod(X0,X0),X1,X2))
| c_Relation_Oantisym(X0,X2) )
| ~ spl104_108
| ~ spl104_257 ),
inference(resolution,[],[f4690,f3372]) ).
fof(f18531,plain,
( spl104_727
| ~ spl104_108
| ~ spl104_251 ),
inference(avatar_split_clause,[],[f4952,f4665,f3371,f18529]) ).
fof(f18529,plain,
( spl104_727
<=> ! [X2,X0,X1] :
( c_Wellfounded_Owf(X0,X1)
| ~ c_Wellfounded_Owf(X0,c_Set_Oinsert(tc_prod(X0,X0),X2,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_727])]) ).
fof(f4952,plain,
( ! [X2,X0,X1] :
( c_Wellfounded_Owf(X0,X1)
| ~ c_Wellfounded_Owf(X0,c_Set_Oinsert(tc_prod(X0,X0),X2,X1)) )
| ~ spl104_108
| ~ spl104_251 ),
inference(resolution,[],[f4666,f3372]) ).
fof(f18527,plain,
( spl104_726
| ~ spl104_231
| ~ spl104_704 ),
inference(avatar_split_clause,[],[f18391,f18386,f4172,f18525]) ).
fof(f18525,plain,
( spl104_726
<=> ! [X0] : c_Orderings_Obot__class_Obot(tc_Nat_Onat) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Orderings_Obot__class_Obot(tc_Nat_Onat),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_726])]) ).
fof(f18386,plain,
( spl104_704
<=> ! [X0] :
( c_Orderings_Obot__class_Obot(tc_Nat_Onat) = X0
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Orderings_Obot__class_Obot(tc_Nat_Onat),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_704])]) ).
fof(f18391,plain,
( ! [X0] : c_Orderings_Obot__class_Obot(tc_Nat_Onat) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Orderings_Obot__class_Obot(tc_Nat_Onat),X0)
| ~ spl104_231
| ~ spl104_704 ),
inference(resolution,[],[f18387,f4173]) ).
fof(f18387,plain,
( ! [X0] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Orderings_Obot__class_Obot(tc_Nat_Onat),X0)
| c_Orderings_Obot__class_Obot(tc_Nat_Onat) = X0 )
| ~ spl104_704 ),
inference(avatar_component_clause,[],[f18386]) ).
fof(f18523,plain,
( spl104_725
| ~ spl104_108
| ~ spl104_250 ),
inference(avatar_split_clause,[],[f4923,f4661,f3371,f18521]) ).
fof(f18521,plain,
( spl104_725
<=> ! [X2,X0,X1] :
( c_Wellfounded_Oacyclic(X0,X1)
| ~ c_Wellfounded_Oacyclic(X0,c_Set_Oinsert(tc_prod(X0,X0),X2,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_725])]) ).
fof(f4923,plain,
( ! [X2,X0,X1] :
( c_Wellfounded_Oacyclic(X0,X1)
| ~ c_Wellfounded_Oacyclic(X0,c_Set_Oinsert(tc_prod(X0,X0),X2,X1)) )
| ~ spl104_108
| ~ spl104_250 ),
inference(resolution,[],[f4662,f3372]) ).
fof(f18519,plain,
( spl104_724
| ~ spl104_56
| ~ spl104_214 ),
inference(avatar_split_clause,[],[f4392,f4104,f3123,f18517]) ).
fof(f18517,plain,
( spl104_724
<=> ! [X2,X0,X1] :
( ~ c_Orderings_Oord__class_Oless(X0,c_Lattices_Osemilattice__sup__class_Osup(X0,X1,X2),X1)
| ~ class_Lattices_Osemilattice__sup(X0)
| ~ class_Orderings_Oorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_724])]) ).
fof(f3123,plain,
( spl104_56
<=> ! [X2,X1] :
( ~ c_Orderings_Oord__class_Oless(X2,X1,X1)
| ~ class_Orderings_Oorder(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_56])]) ).
fof(f4104,plain,
( spl104_214
<=> ! [X0,X3,X2,X1] :
( c_Orderings_Oord__class_Oless(X3,X2,c_Lattices_Osemilattice__sup__class_Osup(X3,X1,X0))
| ~ c_Orderings_Oord__class_Oless(X3,X2,X1)
| ~ class_Lattices_Osemilattice__sup(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_214])]) ).
fof(f4392,plain,
( ! [X2,X0,X1] :
( ~ c_Orderings_Oord__class_Oless(X0,c_Lattices_Osemilattice__sup__class_Osup(X0,X1,X2),X1)
| ~ class_Lattices_Osemilattice__sup(X0)
| ~ class_Orderings_Oorder(X0) )
| ~ spl104_56
| ~ spl104_214 ),
inference(resolution,[],[f4105,f3124]) ).
fof(f3124,plain,
( ! [X2,X1] :
( ~ c_Orderings_Oord__class_Oless(X2,X1,X1)
| ~ class_Orderings_Oorder(X2) )
| ~ spl104_56 ),
inference(avatar_component_clause,[],[f3123]) ).
fof(f4105,plain,
( ! [X2,X3,X0,X1] :
( c_Orderings_Oord__class_Oless(X3,X2,c_Lattices_Osemilattice__sup__class_Osup(X3,X1,X0))
| ~ c_Orderings_Oord__class_Oless(X3,X2,X1)
| ~ class_Lattices_Osemilattice__sup(X3) )
| ~ spl104_214 ),
inference(avatar_component_clause,[],[f4104]) ).
fof(f18515,plain,
( spl104_723
| ~ spl104_56
| ~ spl104_213 ),
inference(avatar_split_clause,[],[f4373,f4100,f3123,f18513]) ).
fof(f18513,plain,
( spl104_723
<=> ! [X2,X0,X1] :
( ~ c_Orderings_Oord__class_Oless(X0,c_Lattices_Osemilattice__sup__class_Osup(X0,X1,X2),X2)
| ~ class_Lattices_Osemilattice__sup(X0)
| ~ class_Orderings_Oorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_723])]) ).
fof(f4373,plain,
( ! [X2,X0,X1] :
( ~ c_Orderings_Oord__class_Oless(X0,c_Lattices_Osemilattice__sup__class_Osup(X0,X1,X2),X2)
| ~ class_Lattices_Osemilattice__sup(X0)
| ~ class_Orderings_Oorder(X0) )
| ~ spl104_56
| ~ spl104_213 ),
inference(resolution,[],[f4101,f3124]) ).
fof(f18511,plain,
( spl104_722
| ~ spl104_64
| ~ spl104_194 ),
inference(avatar_split_clause,[],[f4184,f4024,f3165,f18509]) ).
fof(f18509,plain,
( spl104_722
<=> ! [X0,X1] : c_Relation_Ototal__on(tc_prod(X0,X0),c_Relation_OId__on(X0,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool))),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_722])]) ).
fof(f3165,plain,
( spl104_64
<=> ! [X0,X1] : c_Relation_Ototal__on(X1,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_64])]) ).
fof(f4184,plain,
( ! [X0,X1] : c_Relation_Ototal__on(tc_prod(X0,X0),c_Relation_OId__on(X0,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool))),X1)
| ~ spl104_64
| ~ spl104_194 ),
inference(superposition,[],[f3166,f4025]) ).
fof(f3166,plain,
( ! [X0,X1] : c_Relation_Ototal__on(X1,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),X0)
| ~ spl104_64 ),
inference(avatar_component_clause,[],[f3165]) ).
fof(f18507,plain,
( spl104_721
| ~ spl104_63
| ~ spl104_194 ),
inference(avatar_split_clause,[],[f4183,f4024,f3161,f18505]) ).
fof(f18505,plain,
( spl104_721
<=> ! [X0,X1] : ~ c_member(tc_prod(X0,X0),X1,c_Relation_OId__on(X0,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_721])]) ).
fof(f4183,plain,
( ! [X0,X1] : ~ c_member(tc_prod(X0,X0),X1,c_Relation_OId__on(X0,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool))))
| ~ spl104_63
| ~ spl104_194 ),
inference(superposition,[],[f3162,f4025]) ).
fof(f18503,plain,
( spl104_720
| ~ spl104_65
| ~ spl104_186 ),
inference(avatar_split_clause,[],[f3996,f3891,f3169,f18501]) ).
fof(f18501,plain,
( spl104_720
<=> ! [X2,X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_720])]) ).
fof(f3996,plain,
( ! [X2,X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X2),X1) )
| ~ spl104_65
| ~ spl104_186 ),
inference(resolution,[],[f3892,f3170]) ).
fof(f18499,plain,
( spl104_719
| ~ spl104_67
| ~ spl104_184 ),
inference(avatar_split_clause,[],[f3964,f3883,f3178,f18497]) ).
fof(f18497,plain,
( spl104_719
<=> ! [X0,X1] :
( c_Lattices_Osemilattice__sup__class_Osup(X0,X1,c_Orderings_Obot__class_Obot(X0)) = X1
| ~ class_Lattices_Osemilattice__sup(X0)
| ~ class_Orderings_Obot(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_719])]) ).
fof(f3964,plain,
( ! [X0,X1] :
( c_Lattices_Osemilattice__sup__class_Osup(X0,X1,c_Orderings_Obot__class_Obot(X0)) = X1
| ~ class_Lattices_Osemilattice__sup(X0)
| ~ class_Orderings_Obot(X0) )
| ~ spl104_67
| ~ spl104_184 ),
inference(resolution,[],[f3884,f3179]) ).
fof(f18473,plain,
( ~ spl104_16
| spl104_718
| ~ spl104_10
| ~ spl104_65
| ~ spl104_157
| ~ spl104_183 ),
inference(avatar_split_clause,[],[f3960,f3879,f3634,f3169,f2922,f18471,f2952]) ).
fof(f3634,plain,
( spl104_157
<=> ! [X2,X0,X1] :
( c_Lattices_Osemilattice__sup__class_Osup(X2,X1,X0) = c_Lattices_Osemilattice__sup__class_Osup(X2,X0,X1)
| ~ class_Lattices_Olattice(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_157])]) ).
fof(f3960,plain,
( ! [X0,X1] :
( c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1)) = X0
| ~ class_Lattices_Osemilattice__sup(tc_Nat_Onat) )
| ~ spl104_10
| ~ spl104_65
| ~ spl104_157
| ~ spl104_183 ),
inference(forward_demodulation,[],[f3953,f3793]) ).
fof(f3793,plain,
( ! [X0,X1] : c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat,X0,X1) = c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat,X1,X0)
| ~ spl104_10
| ~ spl104_157 ),
inference(resolution,[],[f3635,f2924]) ).
fof(f3635,plain,
( ! [X2,X0,X1] :
( ~ class_Lattices_Olattice(X2)
| c_Lattices_Osemilattice__sup__class_Osup(X2,X1,X0) = c_Lattices_Osemilattice__sup__class_Osup(X2,X0,X1) )
| ~ spl104_157 ),
inference(avatar_component_clause,[],[f3634]) ).
fof(f3953,plain,
( ! [X0,X1] :
( c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1),X0) = X0
| ~ class_Lattices_Osemilattice__sup(tc_Nat_Onat) )
| ~ spl104_65
| ~ spl104_183 ),
inference(resolution,[],[f3880,f3170]) ).
fof(f18469,plain,
( spl104_717
| ~ spl104_67
| ~ spl104_183 ),
inference(avatar_split_clause,[],[f3937,f3879,f3178,f18467]) ).
fof(f18467,plain,
( spl104_717
<=> ! [X0,X1] :
( c_Lattices_Osemilattice__sup__class_Osup(X0,c_Orderings_Obot__class_Obot(X0),X1) = X1
| ~ class_Lattices_Osemilattice__sup(X0)
| ~ class_Orderings_Obot(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_717])]) ).
fof(f3937,plain,
( ! [X0,X1] :
( c_Lattices_Osemilattice__sup__class_Osup(X0,c_Orderings_Obot__class_Obot(X0),X1) = X1
| ~ class_Lattices_Osemilattice__sup(X0)
| ~ class_Orderings_Obot(X0) )
| ~ spl104_67
| ~ spl104_183 ),
inference(resolution,[],[f3880,f3179]) ).
fof(f18465,plain,
( spl104_716
| ~ spl104_131
| ~ spl104_692 ),
inference(avatar_split_clause,[],[f18208,f18148,f3477,f18463]) ).
fof(f18463,plain,
( spl104_716
<=> ! [X0,X1] : ~ sP3(X0,X0,c_FunDef_Oin__rel(X1,X1,c_Relation_OId(X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_716])]) ).
fof(f18148,plain,
( spl104_692
<=> ! [X0,X1] : hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(X0,X0,c_Relation_OId(X0)),X1),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_692])]) ).
fof(f18208,plain,
( ! [X0,X1] : ~ sP3(X0,X0,c_FunDef_Oin__rel(X1,X1,c_Relation_OId(X1)))
| ~ spl104_131
| ~ spl104_692 ),
inference(resolution,[],[f18149,f3478]) ).
fof(f18149,plain,
( ! [X0,X1] : hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(X0,X0,c_Relation_OId(X0)),X1),X1))
| ~ spl104_692 ),
inference(avatar_component_clause,[],[f18148]) ).
fof(f18461,plain,
( spl104_715
| ~ spl104_96
| ~ spl104_168 ),
inference(avatar_split_clause,[],[f3828,f3678,f3298,f18459]) ).
fof(f18459,plain,
( spl104_715
<=> ! [X2,X4,X0,X3,X1] :
( ~ hBOOL(hAPP(X0,X1))
| c_member(X2,X1,c_Set_Oinsert(X3,X4,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_715])]) ).
fof(f3678,plain,
( spl104_168
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP(c_Set_Oinsert(X3,X2,X1),X0))
| ~ hBOOL(hAPP(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_168])]) ).
fof(f3828,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ hBOOL(hAPP(X0,X1))
| c_member(X2,X1,c_Set_Oinsert(X3,X4,X0)) )
| ~ spl104_96
| ~ spl104_168 ),
inference(resolution,[],[f3679,f3299]) ).
fof(f3679,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(hAPP(c_Set_Oinsert(X3,X2,X1),X0))
| ~ hBOOL(hAPP(X1,X0)) )
| ~ spl104_168 ),
inference(avatar_component_clause,[],[f3678]) ).
fof(f18457,plain,
( spl104_714
| ~ spl104_95
| ~ spl104_167 ),
inference(avatar_split_clause,[],[f3822,f3674,f3294,f18455]) ).
fof(f18455,plain,
( spl104_714
<=> ! [X0,X3,X2,X1] :
( ~ c_member(X0,X1,X2)
| hBOOL(hAPP(c_Set_Oinsert(X0,X3,X2),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_714])]) ).
fof(f3674,plain,
( spl104_167
<=> ! [X0,X3,X2,X1] :
( c_member(X3,X2,c_Set_Oinsert(X3,X0,X1))
| ~ c_member(X3,X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_167])]) ).
fof(f3822,plain,
( ! [X2,X3,X0,X1] :
( ~ c_member(X0,X1,X2)
| hBOOL(hAPP(c_Set_Oinsert(X0,X3,X2),X1)) )
| ~ spl104_95
| ~ spl104_167 ),
inference(resolution,[],[f3675,f3295]) ).
fof(f3675,plain,
( ! [X2,X3,X0,X1] :
( c_member(X3,X2,c_Set_Oinsert(X3,X0,X1))
| ~ c_member(X3,X2,X1) )
| ~ spl104_167 ),
inference(avatar_component_clause,[],[f3674]) ).
fof(f18453,plain,
( spl104_713
| ~ spl104_52
| ~ spl104_166 ),
inference(avatar_split_clause,[],[f3820,f3670,f3107,f18451]) ).
fof(f18451,plain,
( spl104_713
<=> ! [X0,X3,X2,X1] :
( ~ c_Wellfounded_Owf(X0,X1)
| c_Wellfounded_Oacyclic(X2,hAPP(c_Relation_Oinv__image(X0,X2,X1),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_713])]) ).
fof(f3670,plain,
( spl104_166
<=> ! [X0,X3,X2,X1] :
( c_Wellfounded_Owf(X1,hAPP(c_Relation_Oinv__image(X3,X1,X2),X0))
| ~ c_Wellfounded_Owf(X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_166])]) ).
fof(f3820,plain,
( ! [X2,X3,X0,X1] :
( ~ c_Wellfounded_Owf(X0,X1)
| c_Wellfounded_Oacyclic(X2,hAPP(c_Relation_Oinv__image(X0,X2,X1),X3)) )
| ~ spl104_52
| ~ spl104_166 ),
inference(resolution,[],[f3671,f3108]) ).
fof(f3671,plain,
( ! [X2,X3,X0,X1] :
( c_Wellfounded_Owf(X1,hAPP(c_Relation_Oinv__image(X3,X1,X2),X0))
| ~ c_Wellfounded_Owf(X3,X2) )
| ~ spl104_166 ),
inference(avatar_component_clause,[],[f3670]) ).
fof(f18449,plain,
( spl104_712
| ~ spl104_53
| ~ spl104_166 ),
inference(avatar_split_clause,[],[f3819,f3670,f3111,f18447]) ).
fof(f18447,plain,
( spl104_712
<=> ! [X0,X3,X2,X1] :
( ~ c_Wellfounded_Owf(X0,X1)
| sP2(X2,hAPP(c_Relation_Oinv__image(X0,X2,X1),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_712])]) ).
fof(f3819,plain,
( ! [X2,X3,X0,X1] :
( ~ c_Wellfounded_Owf(X0,X1)
| sP2(X2,hAPP(c_Relation_Oinv__image(X0,X2,X1),X3)) )
| ~ spl104_53
| ~ spl104_166 ),
inference(resolution,[],[f3671,f3112]) ).
fof(f18445,plain,
( spl104_711
| ~ spl104_39
| ~ spl104_164 ),
inference(avatar_split_clause,[],[f3817,f3662,f3055,f18443]) ).
fof(f18443,plain,
( spl104_711
<=> ! [X0,X1] :
( ~ c_Relation_Otrans(X0,c_Relation_OId__on(X0,X1))
| c_Order__Relation_Opreorder__on(X0,X1,c_Relation_OId__on(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_711])]) ).
fof(f3055,plain,
( spl104_39
<=> ! [X0,X1] : c_Relation_Orefl__on(X1,X0,c_Relation_OId__on(X1,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_39])]) ).
fof(f3662,plain,
( spl104_164
<=> ! [X2,X0,X1] :
( c_Order__Relation_Opreorder__on(X2,X1,X0)
| ~ c_Relation_Otrans(X2,X0)
| ~ c_Relation_Orefl__on(X2,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_164])]) ).
fof(f3817,plain,
( ! [X0,X1] :
( ~ c_Relation_Otrans(X0,c_Relation_OId__on(X0,X1))
| c_Order__Relation_Opreorder__on(X0,X1,c_Relation_OId__on(X0,X1)) )
| ~ spl104_39
| ~ spl104_164 ),
inference(resolution,[],[f3663,f3056]) ).
fof(f3056,plain,
( ! [X0,X1] : c_Relation_Orefl__on(X1,X0,c_Relation_OId__on(X1,X0))
| ~ spl104_39 ),
inference(avatar_component_clause,[],[f3055]) ).
fof(f3663,plain,
( ! [X2,X0,X1] :
( ~ c_Relation_Orefl__on(X2,X1,X0)
| ~ c_Relation_Otrans(X2,X0)
| c_Order__Relation_Opreorder__on(X2,X1,X0) )
| ~ spl104_164 ),
inference(avatar_component_clause,[],[f3662]) ).
fof(f18441,plain,
( spl104_710
| ~ spl104_95
| ~ spl104_162 ),
inference(avatar_split_clause,[],[f3815,f3654,f3294,f18439]) ).
fof(f18439,plain,
( spl104_710
<=> ! [X2,X0,X1] :
( c_Relation_Ototal__on(X0,X1,X2)
| hBOOL(hAPP(X1,sK47(X2,X1,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_710])]) ).
fof(f3815,plain,
( ! [X2,X0,X1] :
( c_Relation_Ototal__on(X0,X1,X2)
| hBOOL(hAPP(X1,sK47(X2,X1,X0))) )
| ~ spl104_95
| ~ spl104_162 ),
inference(resolution,[],[f3655,f3295]) ).
fof(f18437,plain,
( spl104_709
| ~ spl104_95
| ~ spl104_160 ),
inference(avatar_split_clause,[],[f3811,f3646,f3294,f18435]) ).
fof(f18435,plain,
( spl104_709
<=> ! [X2,X0,X1] :
( c_Relation_Ototal__on(X0,X1,X2)
| hBOOL(hAPP(X1,sK46(X2,X1,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_709])]) ).
fof(f3811,plain,
( ! [X2,X0,X1] :
( c_Relation_Ototal__on(X0,X1,X2)
| hBOOL(hAPP(X1,sK46(X2,X1,X0))) )
| ~ spl104_95
| ~ spl104_160 ),
inference(resolution,[],[f3647,f3295]) ).
fof(f18433,plain,
( spl104_708
| ~ spl104_87
| ~ spl104_159 ),
inference(avatar_split_clause,[],[f3800,f3642,f3262,f18431]) ).
fof(f18431,plain,
( spl104_708
<=> ! [X2,X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_708])]) ).
fof(f3800,plain,
( ! [X2,X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X2),X1) )
| ~ spl104_87
| ~ spl104_159 ),
inference(resolution,[],[f3643,f3263]) ).
fof(f18429,plain,
( spl104_707
| ~ spl104_95
| ~ spl104_152 ),
inference(avatar_split_clause,[],[f3771,f3614,f3294,f18427]) ).
fof(f18427,plain,
( spl104_707
<=> ! [X0,X1] :
( sP2(X0,X1)
| hBOOL(hAPP(sK34(X0,X1),sK36(X0,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_707])]) ).
fof(f3614,plain,
( spl104_152
<=> ! [X0,X1] :
( sP2(X0,X1)
| c_member(X0,sK36(X0,X1),sK34(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_152])]) ).
fof(f3771,plain,
( ! [X0,X1] :
( sP2(X0,X1)
| hBOOL(hAPP(sK34(X0,X1),sK36(X0,X1))) )
| ~ spl104_95
| ~ spl104_152 ),
inference(resolution,[],[f3615,f3295]) ).
fof(f3615,plain,
( ! [X0,X1] :
( c_member(X0,sK36(X0,X1),sK34(X0,X1))
| sP2(X0,X1) )
| ~ spl104_152 ),
inference(avatar_component_clause,[],[f3614]) ).
fof(f18412,plain,
( spl104_706
| ~ spl104_370
| ~ spl104_689 ),
inference(avatar_split_clause,[],[f18202,f18135,f6473,f18410]) ).
fof(f18410,plain,
( spl104_706
<=> ! [X2,X0,X1] : hBOOL(hAPP(c_Set_Oinsert(X0,X2,c_fequal(X1)),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_706])]) ).
fof(f6473,plain,
( spl104_370
<=> ! [X0,X1] : c_fequal(X1) = c_Set_Oinsert(X0,X1,c_fequal(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_370])]) ).
fof(f18135,plain,
( spl104_689
<=> ! [X0,X3,X2,X1] : hBOOL(hAPP(c_Set_Oinsert(X0,X2,c_Set_Oinsert(X0,X1,X3)),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_689])]) ).
fof(f18202,plain,
( ! [X2,X0,X1] : hBOOL(hAPP(c_Set_Oinsert(X0,X2,c_fequal(X1)),X1))
| ~ spl104_370
| ~ spl104_689 ),
inference(superposition,[],[f18136,f6474]) ).
fof(f6474,plain,
( ! [X0,X1] : c_fequal(X1) = c_Set_Oinsert(X0,X1,c_fequal(X1))
| ~ spl104_370 ),
inference(avatar_component_clause,[],[f6473]) ).
fof(f18136,plain,
( ! [X2,X3,X0,X1] : hBOOL(hAPP(c_Set_Oinsert(X0,X2,c_Set_Oinsert(X0,X1,X3)),X1))
| ~ spl104_689 ),
inference(avatar_component_clause,[],[f18135]) ).
fof(f18408,plain,
( ~ spl104_8
| spl104_705
| ~ spl104_67
| ~ spl104_148 ),
inference(avatar_split_clause,[],[f3760,f3598,f3178,f18406,f2912]) ).
fof(f18406,plain,
( spl104_705
<=> ! [X0] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Orderings_Obot__class_Obot(tc_Nat_Onat))
| c_Orderings_Obot__class_Obot(tc_Nat_Onat) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_705])]) ).
fof(f3760,plain,
( ! [X0] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Orderings_Obot__class_Obot(tc_Nat_Onat))
| c_Orderings_Obot__class_Obot(tc_Nat_Onat) = X0
| ~ class_Orderings_Obot(tc_Nat_Onat) )
| ~ spl104_67
| ~ spl104_148 ),
inference(resolution,[],[f3599,f3179]) ).
fof(f18388,plain,
( ~ spl104_8
| spl104_704
| ~ spl104_67
| ~ spl104_147 ),
inference(avatar_split_clause,[],[f3746,f3594,f3178,f18386,f2912]) ).
fof(f3746,plain,
( ! [X0] :
( c_Orderings_Obot__class_Obot(tc_Nat_Onat) = X0
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Orderings_Obot__class_Obot(tc_Nat_Onat),X0)
| ~ class_Orderings_Obot(tc_Nat_Onat) )
| ~ spl104_67
| ~ spl104_147 ),
inference(resolution,[],[f3595,f3179]) ).
fof(f18384,plain,
( spl104_703
| ~ spl104_110
| ~ spl104_127 ),
inference(avatar_split_clause,[],[f3537,f3461,f3379,f18382]) ).
fof(f18382,plain,
( spl104_703
<=> ! [X2,X0,X1] :
( ~ c_Orderings_Oord__class_Oless(X0,c_Lattices_Osemilattice__sup__class_Osup(X0,X1,X2),X1)
| ~ class_Orderings_Opreorder(X0)
| ~ class_Lattices_Olattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_703])]) ).
fof(f3379,plain,
( spl104_110
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X2,X1,c_Lattices_Osemilattice__sup__class_Osup(X2,X1,X0))
| ~ class_Lattices_Olattice(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_110])]) ).
fof(f3461,plain,
( spl104_127
<=> ! [X2,X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(X2,X0,X1)
| ~ c_Orderings_Oord__class_Oless(X2,X1,X0)
| ~ class_Orderings_Opreorder(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_127])]) ).
fof(f3537,plain,
( ! [X2,X0,X1] :
( ~ c_Orderings_Oord__class_Oless(X0,c_Lattices_Osemilattice__sup__class_Osup(X0,X1,X2),X1)
| ~ class_Orderings_Opreorder(X0)
| ~ class_Lattices_Olattice(X0) )
| ~ spl104_110
| ~ spl104_127 ),
inference(resolution,[],[f3462,f3380]) ).
fof(f3380,plain,
( ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X2,X1,c_Lattices_Osemilattice__sup__class_Osup(X2,X1,X0))
| ~ class_Lattices_Olattice(X2) )
| ~ spl104_110 ),
inference(avatar_component_clause,[],[f3379]) ).
fof(f3462,plain,
( ! [X2,X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(X2,X0,X1)
| ~ c_Orderings_Oord__class_Oless(X2,X1,X0)
| ~ class_Orderings_Opreorder(X2) )
| ~ spl104_127 ),
inference(avatar_component_clause,[],[f3461]) ).
fof(f18380,plain,
( spl104_702
| ~ spl104_112
| ~ spl104_127 ),
inference(avatar_split_clause,[],[f3536,f3461,f3387,f18378]) ).
fof(f18378,plain,
( spl104_702
<=> ! [X2,X0,X1] :
( ~ c_Orderings_Oord__class_Oless(X0,c_Lattices_Osemilattice__sup__class_Osup(X0,X1,X2),X1)
| ~ class_Orderings_Opreorder(X0)
| ~ class_Lattices_Osemilattice__sup(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_702])]) ).
fof(f3536,plain,
( ! [X2,X0,X1] :
( ~ c_Orderings_Oord__class_Oless(X0,c_Lattices_Osemilattice__sup__class_Osup(X0,X1,X2),X1)
| ~ class_Orderings_Opreorder(X0)
| ~ class_Lattices_Osemilattice__sup(X0) )
| ~ spl104_112
| ~ spl104_127 ),
inference(resolution,[],[f3462,f3388]) ).
fof(f18376,plain,
( spl104_701
| ~ spl104_109
| ~ spl104_127 ),
inference(avatar_split_clause,[],[f3535,f3461,f3375,f18374]) ).
fof(f18374,plain,
( spl104_701
<=> ! [X2,X0,X1] :
( ~ c_Orderings_Oord__class_Oless(X0,c_Lattices_Osemilattice__sup__class_Osup(X0,X1,X2),X2)
| ~ class_Orderings_Opreorder(X0)
| ~ class_Lattices_Olattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_701])]) ).
fof(f3535,plain,
( ! [X2,X0,X1] :
( ~ c_Orderings_Oord__class_Oless(X0,c_Lattices_Osemilattice__sup__class_Osup(X0,X1,X2),X2)
| ~ class_Orderings_Opreorder(X0)
| ~ class_Lattices_Olattice(X0) )
| ~ spl104_109
| ~ spl104_127 ),
inference(resolution,[],[f3462,f3376]) ).
fof(f18372,plain,
( spl104_700
| ~ spl104_111
| ~ spl104_127 ),
inference(avatar_split_clause,[],[f3534,f3461,f3383,f18370]) ).
fof(f18370,plain,
( spl104_700
<=> ! [X2,X0,X1] :
( ~ c_Orderings_Oord__class_Oless(X0,c_Lattices_Osemilattice__sup__class_Osup(X0,X1,X2),X2)
| ~ class_Orderings_Opreorder(X0)
| ~ class_Lattices_Osemilattice__sup(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_700])]) ).
fof(f3534,plain,
( ! [X2,X0,X1] :
( ~ c_Orderings_Oord__class_Oless(X0,c_Lattices_Osemilattice__sup__class_Osup(X0,X1,X2),X2)
| ~ class_Orderings_Opreorder(X0)
| ~ class_Lattices_Osemilattice__sup(X0) )
| ~ spl104_111
| ~ spl104_127 ),
inference(resolution,[],[f3462,f3384]) ).
fof(f18368,plain,
( spl104_699
| ~ spl104_110
| ~ spl104_122 ),
inference(avatar_split_clause,[],[f3516,f3440,f3379,f18366]) ).
fof(f18366,plain,
( spl104_699
<=> ! [X2,X0,X1] :
( ~ c_Orderings_Oord__class_Oless(X0,c_Lattices_Osemilattice__sup__class_Osup(X0,X1,X2),X1)
| ~ class_Orderings_Olinorder(X0)
| ~ class_Lattices_Olattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_699])]) ).
fof(f3440,plain,
( spl104_122
<=> ! [X2,X0,X1] :
( ~ c_Orderings_Oord__class_Oless(X2,X0,X1)
| ~ c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
| ~ class_Orderings_Olinorder(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_122])]) ).
fof(f3516,plain,
( ! [X2,X0,X1] :
( ~ c_Orderings_Oord__class_Oless(X0,c_Lattices_Osemilattice__sup__class_Osup(X0,X1,X2),X1)
| ~ class_Orderings_Olinorder(X0)
| ~ class_Lattices_Olattice(X0) )
| ~ spl104_110
| ~ spl104_122 ),
inference(resolution,[],[f3441,f3380]) ).
fof(f3441,plain,
( ! [X2,X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
| ~ c_Orderings_Oord__class_Oless(X2,X0,X1)
| ~ class_Orderings_Olinorder(X2) )
| ~ spl104_122 ),
inference(avatar_component_clause,[],[f3440]) ).
fof(f18364,plain,
( spl104_698
| ~ spl104_112
| ~ spl104_122 ),
inference(avatar_split_clause,[],[f3515,f3440,f3387,f18362]) ).
fof(f18362,plain,
( spl104_698
<=> ! [X2,X0,X1] :
( ~ c_Orderings_Oord__class_Oless(X0,c_Lattices_Osemilattice__sup__class_Osup(X0,X1,X2),X1)
| ~ class_Orderings_Olinorder(X0)
| ~ class_Lattices_Osemilattice__sup(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_698])]) ).
fof(f3515,plain,
( ! [X2,X0,X1] :
( ~ c_Orderings_Oord__class_Oless(X0,c_Lattices_Osemilattice__sup__class_Osup(X0,X1,X2),X1)
| ~ class_Orderings_Olinorder(X0)
| ~ class_Lattices_Osemilattice__sup(X0) )
| ~ spl104_112
| ~ spl104_122 ),
inference(resolution,[],[f3441,f3388]) ).
fof(f18360,plain,
( spl104_697
| ~ spl104_109
| ~ spl104_122 ),
inference(avatar_split_clause,[],[f3514,f3440,f3375,f18358]) ).
fof(f18358,plain,
( spl104_697
<=> ! [X2,X0,X1] :
( ~ c_Orderings_Oord__class_Oless(X0,c_Lattices_Osemilattice__sup__class_Osup(X0,X1,X2),X2)
| ~ class_Orderings_Olinorder(X0)
| ~ class_Lattices_Olattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_697])]) ).
fof(f3514,plain,
( ! [X2,X0,X1] :
( ~ c_Orderings_Oord__class_Oless(X0,c_Lattices_Osemilattice__sup__class_Osup(X0,X1,X2),X2)
| ~ class_Orderings_Olinorder(X0)
| ~ class_Lattices_Olattice(X0) )
| ~ spl104_109
| ~ spl104_122 ),
inference(resolution,[],[f3441,f3376]) ).
fof(f18338,plain,
( spl104_696
| ~ spl104_111
| ~ spl104_122 ),
inference(avatar_split_clause,[],[f3513,f3440,f3383,f18336]) ).
fof(f18336,plain,
( spl104_696
<=> ! [X2,X0,X1] :
( ~ c_Orderings_Oord__class_Oless(X0,c_Lattices_Osemilattice__sup__class_Osup(X0,X1,X2),X2)
| ~ class_Orderings_Olinorder(X0)
| ~ class_Lattices_Osemilattice__sup(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_696])]) ).
fof(f3513,plain,
( ! [X2,X0,X1] :
( ~ c_Orderings_Oord__class_Oless(X0,c_Lattices_Osemilattice__sup__class_Osup(X0,X1,X2),X2)
| ~ class_Orderings_Olinorder(X0)
| ~ class_Lattices_Osemilattice__sup(X0) )
| ~ spl104_111
| ~ spl104_122 ),
inference(resolution,[],[f3441,f3384]) ).
fof(f18168,plain,
( spl104_695
| ~ spl104_10
| ~ spl104_679 ),
inference(avatar_split_clause,[],[f18159,f18072,f2922,f18166]) ).
fof(f18166,plain,
( spl104_695
<=> ! [X0,X1] : c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X0,tc_Nat_Onat),X1,X1) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl104_695])]) ).
fof(f18072,plain,
( spl104_679
<=> ! [X2,X0,X1] :
( c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X0,X1),X2,X2) = X2
| ~ class_Lattices_Olattice(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_679])]) ).
fof(f18159,plain,
( ! [X0,X1] : c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X0,tc_Nat_Onat),X1,X1) = X1
| ~ spl104_10
| ~ spl104_679 ),
inference(resolution,[],[f18073,f2924]) ).
fof(f18073,plain,
( ! [X2,X0,X1] :
( ~ class_Lattices_Olattice(X1)
| c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X0,X1),X2,X2) = X2 )
| ~ spl104_679 ),
inference(avatar_component_clause,[],[f18072]) ).
fof(f18158,plain,
( spl104_694
| ~ spl104_50
| ~ spl104_450 ),
inference(avatar_split_clause,[],[f8433,f8306,f3099,f18156]) ).
fof(f18156,plain,
( spl104_694
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X0,X1),X2,X2)
| ~ class_Orderings_Oord(X1)
| ~ class_Orderings_Opreorder(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_694])]) ).
fof(f3099,plain,
( spl104_50
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X1,X0,X0)
| ~ class_Orderings_Opreorder(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_50])]) ).
fof(f8433,plain,
( ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X0,X1),X2,X2)
| ~ class_Orderings_Oord(X1)
| ~ class_Orderings_Opreorder(X1) )
| ~ spl104_50
| ~ spl104_450 ),
inference(resolution,[],[f8307,f3100]) ).
fof(f3100,plain,
( ! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X1,X0,X0)
| ~ class_Orderings_Opreorder(X1) )
| ~ spl104_50 ),
inference(avatar_component_clause,[],[f3099]) ).
fof(f18154,plain,
( spl104_693
| ~ spl104_57
| ~ spl104_450 ),
inference(avatar_split_clause,[],[f8432,f8306,f3127,f18152]) ).
fof(f18152,plain,
( spl104_693
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X0,X1),X2,X2)
| ~ class_Orderings_Oord(X1)
| ~ class_Orderings_Oorder(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_693])]) ).
fof(f3127,plain,
( spl104_57
<=> ! [X2,X1] :
( c_Orderings_Oord__class_Oless__eq(X2,X1,X1)
| ~ class_Orderings_Oorder(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_57])]) ).
fof(f8432,plain,
( ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X0,X1),X2,X2)
| ~ class_Orderings_Oord(X1)
| ~ class_Orderings_Oorder(X1) )
| ~ spl104_57
| ~ spl104_450 ),
inference(resolution,[],[f8307,f3128]) ).
fof(f3128,plain,
( ! [X2,X1] :
( c_Orderings_Oord__class_Oless__eq(X2,X1,X1)
| ~ class_Orderings_Oorder(X2) )
| ~ spl104_57 ),
inference(avatar_component_clause,[],[f3127]) ).
fof(f18150,plain,
( spl104_692
| ~ spl104_145
| ~ spl104_412 ),
inference(avatar_split_clause,[],[f7505,f7094,f3586,f18148]) ).
fof(f7505,plain,
( ! [X0,X1] : hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(X0,X0,c_Relation_OId(X0)),X1),X1))
| ~ spl104_145
| ~ spl104_412 ),
inference(resolution,[],[f7095,f3587]) ).
fof(f18146,plain,
( ~ spl104_690
| spl104_691
| ~ spl104_245
| ~ spl104_325 ),
inference(avatar_split_clause,[],[f5993,f5856,f4639,f18143,f18139]) ).
fof(f18139,plain,
( spl104_690
<=> c_Relation_Oantisym(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_690])]) ).
fof(f18143,plain,
( spl104_691
<=> c_Relation_Oantisym(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__leq) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_691])]) ).
fof(f4639,plain,
( spl104_245
<=> ! [X0,X1] :
( c_Relation_Oantisym(X1,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),X0,c_Relation_OId(X1)))
| ~ c_Relation_Oantisym(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_245])]) ).
fof(f5993,plain,
( c_Relation_Oantisym(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__leq)
| ~ c_Relation_Oantisym(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less)
| ~ spl104_245
| ~ spl104_325 ),
inference(superposition,[],[f4640,f5858]) ).
fof(f4640,plain,
( ! [X0,X1] :
( c_Relation_Oantisym(X1,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),X0,c_Relation_OId(X1)))
| ~ c_Relation_Oantisym(X1,X0) )
| ~ spl104_245 ),
inference(avatar_component_clause,[],[f4639]) ).
fof(f18137,plain,
( spl104_689
| ~ spl104_73
| ~ spl104_297 ),
inference(avatar_split_clause,[],[f5589,f5431,f3202,f18135]) ).
fof(f5431,plain,
( spl104_297
<=> ! [X0,X3,X2,X1] : c_Set_Oinsert(X3,X2,c_Set_Oinsert(X3,X1,X0)) = c_Set_Oinsert(X3,X1,c_Set_Oinsert(X3,X2,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_297])]) ).
fof(f5589,plain,
( ! [X2,X3,X0,X1] : hBOOL(hAPP(c_Set_Oinsert(X0,X2,c_Set_Oinsert(X0,X1,X3)),X1))
| ~ spl104_73
| ~ spl104_297 ),
inference(superposition,[],[f3203,f5432]) ).
fof(f5432,plain,
( ! [X2,X3,X0,X1] : c_Set_Oinsert(X3,X2,c_Set_Oinsert(X3,X1,X0)) = c_Set_Oinsert(X3,X1,c_Set_Oinsert(X3,X2,X0))
| ~ spl104_297 ),
inference(avatar_component_clause,[],[f5431]) ).
fof(f18133,plain,
( spl104_688
| ~ spl104_96
| ~ spl104_670 ),
inference(avatar_split_clause,[],[f17986,f17634,f3298,f18131]) ).
fof(f18131,plain,
( spl104_688
<=> ! [X2,X0,X1] : c_member(X0,X1,c_Relation_ORange(X2,X2,c_Relation_OId(X2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_688])]) ).
fof(f17634,plain,
( spl104_670
<=> ! [X0,X1] : hBOOL(hAPP(c_Relation_ORange(X0,X0,c_Relation_OId(X0)),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_670])]) ).
fof(f17986,plain,
( ! [X2,X0,X1] : c_member(X0,X1,c_Relation_ORange(X2,X2,c_Relation_OId(X2)))
| ~ spl104_96
| ~ spl104_670 ),
inference(resolution,[],[f17635,f3299]) ).
fof(f17635,plain,
( ! [X0,X1] : hBOOL(hAPP(c_Relation_ORange(X0,X0,c_Relation_OId(X0)),X1))
| ~ spl104_670 ),
inference(avatar_component_clause,[],[f17634]) ).
fof(f18106,plain,
( ~ spl104_14
| spl104_687
| ~ spl104_82
| ~ spl104_247 ),
inference(avatar_split_clause,[],[f4900,f4647,f3242,f18104,f2942]) ).
fof(f18104,plain,
( spl104_687
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_687])]) ).
fof(f4647,plain,
( spl104_247
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless(X2,X1,X0)
| c_Orderings_Oord__class_Oless__eq(X2,X0,X1)
| ~ c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
| ~ class_Orderings_Opreorder(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_247])]) ).
fof(f4900,plain,
( ! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| ~ class_Orderings_Opreorder(tc_Nat_Onat) )
| ~ spl104_82
| ~ spl104_247 ),
inference(duplicate_literal_removal,[],[f4897]) ).
fof(f4897,plain,
( ! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| ~ class_Orderings_Opreorder(tc_Nat_Onat)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1) )
| ~ spl104_82
| ~ spl104_247 ),
inference(resolution,[],[f4648,f3243]) ).
fof(f4648,plain,
( ! [X2,X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
| c_Orderings_Oord__class_Oless__eq(X2,X0,X1)
| c_Orderings_Oord__class_Oless(X2,X1,X0)
| ~ class_Orderings_Opreorder(X2) )
| ~ spl104_247 ),
inference(avatar_component_clause,[],[f4647]) ).
fof(f18102,plain,
( spl104_686
| ~ spl104_34
| ~ spl104_232 ),
inference(avatar_split_clause,[],[f4592,f4176,f3034,f18100]) ).
fof(f18100,plain,
( spl104_686
<=> ! [X0,X3,X2,X1] :
( sP9(c_fequal(X0),X1,X2,X3)
| ~ c_member(X2,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_686])]) ).
fof(f3034,plain,
( spl104_34
<=> ! [X1] : hBOOL(hAPP(c_fequal(X1),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_34])]) ).
fof(f4592,plain,
( ! [X2,X3,X0,X1] :
( sP9(c_fequal(X0),X1,X2,X3)
| ~ c_member(X2,X0,X1) )
| ~ spl104_34
| ~ spl104_232 ),
inference(resolution,[],[f4177,f3035]) ).
fof(f3035,plain,
( ! [X1] : hBOOL(hAPP(c_fequal(X1),X1))
| ~ spl104_34 ),
inference(avatar_component_clause,[],[f3034]) ).
fof(f18098,plain,
( spl104_685
| ~ spl104_34
| ~ spl104_230 ),
inference(avatar_split_clause,[],[f4587,f4168,f3034,f18096]) ).
fof(f18096,plain,
( spl104_685
<=> ! [X0,X3,X2,X1] :
( sP9(c_fequal(X0),X1,X2,X3)
| ~ c_member(X2,X0,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_685])]) ).
fof(f4587,plain,
( ! [X2,X3,X0,X1] :
( sP9(c_fequal(X0),X1,X2,X3)
| ~ c_member(X2,X0,X3) )
| ~ spl104_34
| ~ spl104_230 ),
inference(resolution,[],[f4169,f3035]) ).
fof(f18094,plain,
( spl104_684
| ~ spl104_121
| ~ spl104_122 ),
inference(avatar_split_clause,[],[f3522,f3440,f3436,f18092]) ).
fof(f18092,plain,
( spl104_684
<=> ! [X2,X0,X1] :
( ~ c_Orderings_Oord__class_Oless(X0,X1,X2)
| ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Oless__eq(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_684])]) ).
fof(f3436,plain,
( spl104_121
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X2,X0,X1)
| c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
| ~ class_Orderings_Olinorder(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_121])]) ).
fof(f3522,plain,
( ! [X2,X0,X1] :
( ~ c_Orderings_Oord__class_Oless(X0,X1,X2)
| ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Oless__eq(X0,X1,X2) )
| ~ spl104_121
| ~ spl104_122 ),
inference(duplicate_literal_removal,[],[f3517]) ).
fof(f3517,plain,
( ! [X2,X0,X1] :
( ~ c_Orderings_Oord__class_Oless(X0,X1,X2)
| ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Oless__eq(X0,X1,X2)
| ~ class_Orderings_Olinorder(X0) )
| ~ spl104_121
| ~ spl104_122 ),
inference(resolution,[],[f3441,f3437]) ).
fof(f3437,plain,
( ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
| c_Orderings_Oord__class_Oless__eq(X2,X0,X1)
| ~ class_Orderings_Olinorder(X2) )
| ~ spl104_121 ),
inference(avatar_component_clause,[],[f3436]) ).
fof(f18090,plain,
( spl104_683
| ~ spl104_52
| ~ spl104_117 ),
inference(avatar_split_clause,[],[f3500,f3420,f3107,f18088]) ).
fof(f18088,plain,
( spl104_683
<=> ! [X0,X1] :
( ~ c_Wellfounded_Owf(X0,X1)
| c_Wellfounded_Oacyclic(tc_fun(X0,tc_HOL_Obool),c_Wellfounded_Omax__ext(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_683])]) ).
fof(f3500,plain,
( ! [X0,X1] :
( ~ c_Wellfounded_Owf(X0,X1)
| c_Wellfounded_Oacyclic(tc_fun(X0,tc_HOL_Obool),c_Wellfounded_Omax__ext(X0,X1)) )
| ~ spl104_52
| ~ spl104_117 ),
inference(resolution,[],[f3421,f3108]) ).
fof(f18086,plain,
( spl104_682
| ~ spl104_53
| ~ spl104_117 ),
inference(avatar_split_clause,[],[f3499,f3420,f3111,f18084]) ).
fof(f18084,plain,
( spl104_682
<=> ! [X0,X1] :
( ~ c_Wellfounded_Owf(X0,X1)
| sP2(tc_fun(X0,tc_HOL_Obool),c_Wellfounded_Omax__ext(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_682])]) ).
fof(f3499,plain,
( ! [X0,X1] :
( ~ c_Wellfounded_Owf(X0,X1)
| sP2(tc_fun(X0,tc_HOL_Obool),c_Wellfounded_Omax__ext(X0,X1)) )
| ~ spl104_53
| ~ spl104_117 ),
inference(resolution,[],[f3421,f3112]) ).
fof(f18082,plain,
( spl104_681
| ~ spl104_52
| ~ spl104_116 ),
inference(avatar_split_clause,[],[f3497,f3416,f3107,f18080]) ).
fof(f18080,plain,
( spl104_681
<=> ! [X0,X1] :
( ~ c_Wellfounded_Owf(X0,X1)
| c_Wellfounded_Oacyclic(tc_fun(X0,tc_HOL_Obool),c_Wellfounded_Omin__ext(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_681])]) ).
fof(f3497,plain,
( ! [X0,X1] :
( ~ c_Wellfounded_Owf(X0,X1)
| c_Wellfounded_Oacyclic(tc_fun(X0,tc_HOL_Obool),c_Wellfounded_Omin__ext(X0,X1)) )
| ~ spl104_52
| ~ spl104_116 ),
inference(resolution,[],[f3417,f3108]) ).
fof(f18078,plain,
( spl104_680
| ~ spl104_53
| ~ spl104_116 ),
inference(avatar_split_clause,[],[f3496,f3416,f3111,f18076]) ).
fof(f18076,plain,
( spl104_680
<=> ! [X0,X1] :
( ~ c_Wellfounded_Owf(X0,X1)
| sP2(tc_fun(X0,tc_HOL_Obool),c_Wellfounded_Omin__ext(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_680])]) ).
fof(f3496,plain,
( ! [X0,X1] :
( ~ c_Wellfounded_Owf(X0,X1)
| sP2(tc_fun(X0,tc_HOL_Obool),c_Wellfounded_Omin__ext(X0,X1)) )
| ~ spl104_53
| ~ spl104_116 ),
inference(resolution,[],[f3417,f3112]) ).
fof(f18074,plain,
( spl104_679
| ~ spl104_47
| ~ spl104_84 ),
inference(avatar_split_clause,[],[f3318,f3250,f3087,f18072]) ).
fof(f3087,plain,
( spl104_47
<=> ! [X0,X1] :
( class_Lattices_Osemilattice__sup(tc_fun(X0,X1))
| ~ class_Lattices_Olattice(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_47])]) ).
fof(f3250,plain,
( spl104_84
<=> ! [X0,X1] :
( c_Lattices_Osemilattice__sup__class_Osup(X1,X0,X0) = X0
| ~ class_Lattices_Osemilattice__sup(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_84])]) ).
fof(f3318,plain,
( ! [X2,X0,X1] :
( c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X0,X1),X2,X2) = X2
| ~ class_Lattices_Olattice(X1) )
| ~ spl104_47
| ~ spl104_84 ),
inference(resolution,[],[f3251,f3088]) ).
fof(f3088,plain,
( ! [X0,X1] :
( class_Lattices_Osemilattice__sup(tc_fun(X0,X1))
| ~ class_Lattices_Olattice(X1) )
| ~ spl104_47 ),
inference(avatar_component_clause,[],[f3087]) ).
fof(f3251,plain,
( ! [X0,X1] :
( ~ class_Lattices_Osemilattice__sup(X1)
| c_Lattices_Osemilattice__sup__class_Osup(X1,X0,X0) = X0 )
| ~ spl104_84 ),
inference(avatar_component_clause,[],[f3250]) ).
fof(f17726,plain,
( spl104_678
| ~ spl104_95
| ~ spl104_494 ),
inference(avatar_split_clause,[],[f15720,f9842,f3294,f17724]) ).
fof(f9842,plain,
( spl104_494
<=> ! [X0,X1] : c_member(X0,X1,c_Relation_ODomain(X0,X0,c_Relation_OId(X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_494])]) ).
fof(f15720,plain,
( ! [X0,X1] : hBOOL(hAPP(c_Relation_ODomain(X0,X0,c_Relation_OId(X0)),X1))
| ~ spl104_95
| ~ spl104_494 ),
inference(resolution,[],[f9843,f3295]) ).
fof(f9843,plain,
( ! [X0,X1] : c_member(X0,X1,c_Relation_ODomain(X0,X0,c_Relation_OId(X0)))
| ~ spl104_494 ),
inference(avatar_component_clause,[],[f9842]) ).
fof(f17666,plain,
( ~ spl104_677
| ~ spl104_411
| spl104_471 ),
inference(avatar_split_clause,[],[f9307,f9301,f7090,f17663]) ).
fof(f9307,plain,
( ~ hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_L),sK15),sK16))
| ~ spl104_411
| spl104_471 ),
inference(resolution,[],[f9303,f7091]) ).
fof(f9303,plain,
( ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,sK15,sK16),v_L)
| spl104_471 ),
inference(avatar_component_clause,[],[f9301]) ).
fof(f17661,plain,
( ~ spl104_676
| ~ spl104_411
| spl104_470 ),
inference(avatar_split_clause,[],[f9296,f9290,f7090,f17658]) ).
fof(f17658,plain,
( spl104_676
<=> hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_L),sK16),sK15)) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_676])]) ).
fof(f9296,plain,
( ~ hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_L),sK16),sK15))
| ~ spl104_411
| spl104_470 ),
inference(resolution,[],[f9292,f7091]) ).
fof(f17656,plain,
( spl104_675
| ~ spl104_63
| ~ spl104_420 ),
inference(avatar_split_clause,[],[f7676,f7555,f3161,f17654]) ).
fof(f17654,plain,
( spl104_675
<=> ! [X0,X1] : c_Relation_Osingle__valued(X0,X1,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X0,X1),tc_HOL_Obool))) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_675])]) ).
fof(f7555,plain,
( spl104_420
<=> ! [X2,X0,X1] :
( c_Relation_Osingle__valued(X2,X1,X0)
| c_member(tc_prod(X2,X1),c_Product__Type_OPair(X2,X1,sK43(X0,X1,X2),sK44(X0,X1,X2)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_420])]) ).
fof(f7676,plain,
( ! [X0,X1] : c_Relation_Osingle__valued(X0,X1,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X0,X1),tc_HOL_Obool)))
| ~ spl104_63
| ~ spl104_420 ),
inference(resolution,[],[f7556,f3162]) ).
fof(f7556,plain,
( ! [X2,X0,X1] :
( c_member(tc_prod(X2,X1),c_Product__Type_OPair(X2,X1,sK43(X0,X1,X2),sK44(X0,X1,X2)),X0)
| c_Relation_Osingle__valued(X2,X1,X0) )
| ~ spl104_420 ),
inference(avatar_component_clause,[],[f7555]) ).
fof(f17652,plain,
( spl104_674
| ~ spl104_136
| ~ spl104_411 ),
inference(avatar_split_clause,[],[f7488,f7090,f3547,f17650]) ).
fof(f17650,plain,
( spl104_674
<=> ! [X0] : ~ hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_L),X0),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_674])]) ).
fof(f7488,plain,
( ! [X0] : ~ hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_L),X0),X0))
| ~ spl104_136
| ~ spl104_411 ),
inference(resolution,[],[f7091,f3548]) ).
fof(f17648,plain,
( spl104_673
| ~ spl104_145
| ~ spl104_385 ),
inference(avatar_split_clause,[],[f6963,f6533,f3586,f17646]) ).
fof(f17646,plain,
( spl104_673
<=> ! [X2,X0,X1] :
( c_member(X0,X1,X2)
| ~ c_Relation_Orefl__on(X0,X2,c_Relation_OId(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_673])]) ).
fof(f6963,plain,
( ! [X2,X0,X1] :
( c_member(X0,X1,X2)
| ~ c_Relation_Orefl__on(X0,X2,c_Relation_OId(X0)) )
| ~ spl104_145
| ~ spl104_385 ),
inference(resolution,[],[f6534,f3587]) ).
fof(f17644,plain,
( spl104_672
| ~ spl104_196
| ~ spl104_322 ),
inference(avatar_split_clause,[],[f5841,f5755,f4032,f17642]) ).
fof(f17642,plain,
( spl104_672
<=> ! [X2,X0,X1] :
( ~ c_member(X0,X1,X2)
| ~ c_Relation_Oirrefl(X0,c_Relation_OId__on(X0,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_672])]) ).
fof(f5755,plain,
( spl104_322
<=> ! [X0,X1,X3] :
( c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,X3,X3),c_Relation_OId__on(X1,X0))
| ~ c_member(X1,X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_322])]) ).
fof(f5841,plain,
( ! [X2,X0,X1] :
( ~ c_member(X0,X1,X2)
| ~ c_Relation_Oirrefl(X0,c_Relation_OId__on(X0,X2)) )
| ~ spl104_196
| ~ spl104_322 ),
inference(resolution,[],[f5756,f4033]) ).
fof(f5756,plain,
( ! [X3,X0,X1] :
( c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,X3,X3),c_Relation_OId__on(X1,X0))
| ~ c_member(X1,X3,X0) )
| ~ spl104_322 ),
inference(avatar_component_clause,[],[f5755]) ).
fof(f17640,plain,
( spl104_671
| ~ spl104_206
| ~ spl104_322 ),
inference(avatar_split_clause,[],[f5840,f5755,f4072,f17638]) ).
fof(f17638,plain,
( spl104_671
<=> ! [X2,X0,X1] :
( ~ c_member(X0,X1,X2)
| ~ c_Wellfounded_Owf(X0,c_Relation_OId__on(X0,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_671])]) ).
fof(f5840,plain,
( ! [X2,X0,X1] :
( ~ c_member(X0,X1,X2)
| ~ c_Wellfounded_Owf(X0,c_Relation_OId__on(X0,X2)) )
| ~ spl104_206
| ~ spl104_322 ),
inference(resolution,[],[f5756,f4073]) ).
fof(f17636,plain,
( spl104_670
| ~ spl104_95
| ~ spl104_467 ),
inference(avatar_split_clause,[],[f15346,f8684,f3294,f17634]) ).
fof(f8684,plain,
( spl104_467
<=> ! [X0,X1] : c_member(X0,X1,c_Relation_ORange(X0,X0,c_Relation_OId(X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_467])]) ).
fof(f15346,plain,
( ! [X0,X1] : hBOOL(hAPP(c_Relation_ORange(X0,X0,c_Relation_OId(X0)),X1))
| ~ spl104_95
| ~ spl104_467 ),
inference(resolution,[],[f8685,f3295]) ).
fof(f8685,plain,
( ! [X0,X1] : c_member(X0,X1,c_Relation_ORange(X0,X0,c_Relation_OId(X0)))
| ~ spl104_467 ),
inference(avatar_component_clause,[],[f8684]) ).
fof(f17632,plain,
( spl104_669
| ~ spl104_38
| ~ spl104_304 ),
inference(avatar_split_clause,[],[f5661,f5459,f3051,f17630]) ).
fof(f17630,plain,
( spl104_669
<=> ! [X2,X0,X1] :
( sP4(X0,X0,X1,X2)
| c_member(X1,X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_669])]) ).
fof(f5661,plain,
( ! [X2,X0,X1] :
( sP4(X0,X0,X1,X2)
| c_member(X1,X2,X0) )
| ~ spl104_38
| ~ spl104_304 ),
inference(resolution,[],[f5460,f3052]) ).
fof(f17619,plain,
( ~ spl104_16
| spl104_668
| ~ spl104_24
| ~ spl104_214 ),
inference(avatar_split_clause,[],[f4390,f4104,f2992,f17617,f2952]) ).
fof(f17617,plain,
( spl104_668
<=> ! [X0,X1] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat,X0,X1),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_668])]) ).
fof(f2992,plain,
( spl104_24
<=> ! [X0] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_24])]) ).
fof(f4390,plain,
( ! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat,X0,X1),X0)
| ~ class_Lattices_Osemilattice__sup(tc_Nat_Onat) )
| ~ spl104_24
| ~ spl104_214 ),
inference(resolution,[],[f4105,f2993]) ).
fof(f2993,plain,
( ! [X0] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X0)
| ~ spl104_24 ),
inference(avatar_component_clause,[],[f2992]) ).
fof(f17608,plain,
( ~ spl104_16
| spl104_667
| ~ spl104_24
| ~ spl104_213 ),
inference(avatar_split_clause,[],[f4371,f4100,f2992,f17606,f2952]) ).
fof(f17606,plain,
( spl104_667
<=> ! [X0,X1] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat,X0,X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_667])]) ).
fof(f4371,plain,
( ! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat,X0,X1),X1)
| ~ class_Lattices_Osemilattice__sup(tc_Nat_Onat) )
| ~ spl104_24
| ~ spl104_213 ),
inference(resolution,[],[f4101,f2993]) ).
fof(f17604,plain,
( spl104_666
| ~ spl104_27
| ~ spl104_195 ),
inference(avatar_split_clause,[],[f4199,f4028,f3004,f17602]) ).
fof(f17602,plain,
( spl104_666
<=> ! [X0] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X0)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl104_666])]) ).
fof(f4199,plain,
( ! [X0] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X0)) = X0
| ~ spl104_27
| ~ spl104_195 ),
inference(resolution,[],[f4029,f3005]) ).
fof(f17600,plain,
( spl104_665
| ~ spl104_13
| ~ spl104_157 ),
inference(avatar_split_clause,[],[f3794,f3634,f2937,f17598]) ).
fof(f17598,plain,
( spl104_665
<=> ! [X0,X1] : c_Lattices_Osemilattice__sup__class_Osup(tc_HOL_Obool,X0,X1) = c_Lattices_Osemilattice__sup__class_Osup(tc_HOL_Obool,X1,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_665])]) ).
fof(f3794,plain,
( ! [X0,X1] : c_Lattices_Osemilattice__sup__class_Osup(tc_HOL_Obool,X0,X1) = c_Lattices_Osemilattice__sup__class_Osup(tc_HOL_Obool,X1,X0)
| ~ spl104_13
| ~ spl104_157 ),
inference(resolution,[],[f3635,f2939]) ).
fof(f17596,plain,
( spl104_664
| ~ spl104_10
| ~ spl104_157 ),
inference(avatar_split_clause,[],[f3793,f3634,f2922,f17594]) ).
fof(f17594,plain,
( spl104_664
<=> ! [X0,X1] : c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat,X0,X1) = c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat,X1,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_664])]) ).
fof(f17592,plain,
( spl104_663
| ~ spl104_9
| ~ spl104_156 ),
inference(avatar_split_clause,[],[f3787,f3630,f2917,f17590]) ).
fof(f17590,plain,
( spl104_663
<=> ! [X0,X1] : c_Orderings_Obot__class_Obot(tc_HOL_Obool) = hAPP(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_663])]) ).
fof(f2917,plain,
( spl104_9
<=> class_Orderings_Obot(tc_HOL_Obool) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_9])]) ).
fof(f3630,plain,
( spl104_156
<=> ! [X2,X0,X1] :
( c_Orderings_Obot__class_Obot(X2) = hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,X2)),X0)
| ~ class_Orderings_Obot(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_156])]) ).
fof(f3787,plain,
( ! [X0,X1] : c_Orderings_Obot__class_Obot(tc_HOL_Obool) = hAPP(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)),X1)
| ~ spl104_9
| ~ spl104_156 ),
inference(resolution,[],[f3631,f2919]) ).
fof(f2919,plain,
( class_Orderings_Obot(tc_HOL_Obool)
| ~ spl104_9 ),
inference(avatar_component_clause,[],[f2917]) ).
fof(f3631,plain,
( ! [X2,X0,X1] :
( ~ class_Orderings_Obot(X2)
| c_Orderings_Obot__class_Obot(X2) = hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,X2)),X0) )
| ~ spl104_156 ),
inference(avatar_component_clause,[],[f3630]) ).
fof(f17588,plain,
( spl104_662
| ~ spl104_8
| ~ spl104_156 ),
inference(avatar_split_clause,[],[f3786,f3630,f2912,f17586]) ).
fof(f17586,plain,
( spl104_662
<=> ! [X0,X1] : c_Orderings_Obot__class_Obot(tc_Nat_Onat) = hAPP(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_Nat_Onat)),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_662])]) ).
fof(f3786,plain,
( ! [X0,X1] : c_Orderings_Obot__class_Obot(tc_Nat_Onat) = hAPP(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_Nat_Onat)),X1)
| ~ spl104_8
| ~ spl104_156 ),
inference(resolution,[],[f3631,f2914]) ).
fof(f2914,plain,
( class_Orderings_Obot(tc_Nat_Onat)
| ~ spl104_8 ),
inference(avatar_component_clause,[],[f2912]) ).
fof(f17580,plain,
( spl104_661
| ~ spl104_95
| ~ spl104_145 ),
inference(avatar_split_clause,[],[f3714,f3586,f3294,f17578]) ).
fof(f17578,plain,
( spl104_661
<=> ! [X0,X1] : hBOOL(hAPP(c_Relation_OId(X0),c_Product__Type_OPair(X0,X0,X1,X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_661])]) ).
fof(f3714,plain,
( ! [X0,X1] : hBOOL(hAPP(c_Relation_OId(X0),c_Product__Type_OPair(X0,X0,X1,X1)))
| ~ spl104_95
| ~ spl104_145 ),
inference(resolution,[],[f3587,f3295]) ).
fof(f17576,plain,
( spl104_660
| ~ spl104_28
| ~ spl104_139 ),
inference(avatar_split_clause,[],[f3702,f3560,f3008,f17573]) ).
fof(f17573,plain,
( spl104_660
<=> c_Relation_ODomain(tc_Nat_Onat,tc_Nat_Onat,c_Wellfounded_Opred__nat) = c_Relation_ODomain(tc_Nat_Onat,tc_Nat_Onat,c_Wellfounded_Oless__than) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_660])]) ).
fof(f17571,plain,
( spl104_659
| ~ spl104_28
| ~ spl104_138 ),
inference(avatar_split_clause,[],[f3701,f3556,f3008,f17568]) ).
fof(f17568,plain,
( spl104_659
<=> c_Relation_ORange(tc_Nat_Onat,tc_Nat_Onat,c_Wellfounded_Opred__nat) = c_Relation_ORange(tc_Nat_Onat,tc_Nat_Onat,c_Wellfounded_Oless__than) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_659])]) ).
fof(f17566,plain,
( spl104_658
| ~ spl104_67
| ~ spl104_127 ),
inference(avatar_split_clause,[],[f3533,f3461,f3178,f17564]) ).
fof(f17564,plain,
( spl104_658
<=> ! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless(X0,X1,c_Orderings_Obot__class_Obot(X0))
| ~ class_Orderings_Opreorder(X0)
| ~ class_Orderings_Obot(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_658])]) ).
fof(f3533,plain,
( ! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless(X0,X1,c_Orderings_Obot__class_Obot(X0))
| ~ class_Orderings_Opreorder(X0)
| ~ class_Orderings_Obot(X0) )
| ~ spl104_67
| ~ spl104_127 ),
inference(resolution,[],[f3462,f3179]) ).
fof(f17562,plain,
( spl104_657
| ~ spl104_67
| ~ spl104_122 ),
inference(avatar_split_clause,[],[f3512,f3440,f3178,f17560]) ).
fof(f17560,plain,
( spl104_657
<=> ! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless(X0,X1,c_Orderings_Obot__class_Obot(X0))
| ~ class_Orderings_Olinorder(X0)
| ~ class_Orderings_Obot(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_657])]) ).
fof(f3512,plain,
( ! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless(X0,X1,c_Orderings_Obot__class_Obot(X0))
| ~ class_Orderings_Olinorder(X0)
| ~ class_Orderings_Obot(X0) )
| ~ spl104_67
| ~ spl104_122 ),
inference(resolution,[],[f3441,f3179]) ).
fof(f17558,plain,
( spl104_656
| ~ spl104_52
| ~ spl104_113 ),
inference(avatar_split_clause,[],[f3414,f3391,f3107,f17556]) ).
fof(f17556,plain,
( spl104_656
<=> ! [X2,X0,X1] :
( ~ c_Wellfounded_Owf(X0,X1)
| c_Wellfounded_Oacyclic(X0,c_Wellfounded_Omlex__prod(X0,X2,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_656])]) ).
fof(f3391,plain,
( spl104_113
<=> ! [X2,X0,X1] :
( c_Wellfounded_Owf(X2,c_Wellfounded_Omlex__prod(X2,X0,X1))
| ~ c_Wellfounded_Owf(X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_113])]) ).
fof(f3414,plain,
( ! [X2,X0,X1] :
( ~ c_Wellfounded_Owf(X0,X1)
| c_Wellfounded_Oacyclic(X0,c_Wellfounded_Omlex__prod(X0,X2,X1)) )
| ~ spl104_52
| ~ spl104_113 ),
inference(resolution,[],[f3392,f3108]) ).
fof(f3392,plain,
( ! [X2,X0,X1] :
( c_Wellfounded_Owf(X2,c_Wellfounded_Omlex__prod(X2,X0,X1))
| ~ c_Wellfounded_Owf(X2,X1) )
| ~ spl104_113 ),
inference(avatar_component_clause,[],[f3391]) ).
fof(f17554,plain,
( spl104_655
| ~ spl104_53
| ~ spl104_113 ),
inference(avatar_split_clause,[],[f3413,f3391,f3111,f17552]) ).
fof(f17552,plain,
( spl104_655
<=> ! [X2,X0,X1] :
( ~ c_Wellfounded_Owf(X0,X1)
| sP2(X0,c_Wellfounded_Omlex__prod(X0,X2,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_655])]) ).
fof(f3413,plain,
( ! [X2,X0,X1] :
( ~ c_Wellfounded_Owf(X0,X1)
| sP2(X0,c_Wellfounded_Omlex__prod(X0,X2,X1)) )
| ~ spl104_53
| ~ spl104_113 ),
inference(resolution,[],[f3392,f3112]) ).
fof(f17550,plain,
( spl104_654
| ~ spl104_95
| ~ spl104_106 ),
inference(avatar_split_clause,[],[f3403,f3363,f3294,f17548]) ).
fof(f17548,plain,
( spl104_654
<=> ! [X2,X0,X1] :
( ~ c_Wellfounded_Owf(X0,X1)
| hBOOL(hAPP(c_Wellfounded_Oacc(X0,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_654])]) ).
fof(f3403,plain,
( ! [X2,X0,X1] :
( ~ c_Wellfounded_Owf(X0,X1)
| hBOOL(hAPP(c_Wellfounded_Oacc(X0,X1),X2)) )
| ~ spl104_95
| ~ spl104_106 ),
inference(resolution,[],[f3364,f3295]) ).
fof(f17546,plain,
( spl104_653
| ~ spl104_33
| ~ spl104_85 ),
inference(avatar_split_clause,[],[f3323,f3254,f3030,f17544]) ).
fof(f17544,plain,
( spl104_653
<=> ! [X0,X1] : c_Transitive__Closure_Otrancl(X0,X1) = c_Transitive__Closure_Otrancl(X0,c_Transitive__Closure_Otrancl(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_653])]) ).
fof(f3254,plain,
( spl104_85
<=> ! [X0,X1] :
( c_Transitive__Closure_Otrancl(X1,X0) = X0
| ~ c_Relation_Otrans(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_85])]) ).
fof(f3323,plain,
( ! [X0,X1] : c_Transitive__Closure_Otrancl(X0,X1) = c_Transitive__Closure_Otrancl(X0,c_Transitive__Closure_Otrancl(X0,X1))
| ~ spl104_33
| ~ spl104_85 ),
inference(resolution,[],[f3255,f3031]) ).
fof(f3255,plain,
( ! [X0,X1] :
( ~ c_Relation_Otrans(X1,X0)
| c_Transitive__Closure_Otrancl(X1,X0) = X0 )
| ~ spl104_85 ),
inference(avatar_component_clause,[],[f3254]) ).
fof(f17542,plain,
( spl104_652
| ~ spl104_32
| ~ spl104_85 ),
inference(avatar_split_clause,[],[f3322,f3254,f3026,f17540]) ).
fof(f17540,plain,
( spl104_652
<=> ! [X0,X1] : c_Relation_OId__on(X0,X1) = c_Transitive__Closure_Otrancl(X0,c_Relation_OId__on(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_652])]) ).
fof(f3026,plain,
( spl104_32
<=> ! [X0,X1] : c_Relation_Otrans(X1,c_Relation_OId__on(X1,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_32])]) ).
fof(f3322,plain,
( ! [X0,X1] : c_Relation_OId__on(X0,X1) = c_Transitive__Closure_Otrancl(X0,c_Relation_OId__on(X0,X1))
| ~ spl104_32
| ~ spl104_85 ),
inference(resolution,[],[f3255,f3027]) ).
fof(f3027,plain,
( ! [X0,X1] : c_Relation_Otrans(X1,c_Relation_OId__on(X1,X0))
| ~ spl104_32 ),
inference(avatar_component_clause,[],[f3026]) ).
fof(f17538,plain,
( ~ spl104_11
| spl104_651
| ~ spl104_261
| ~ spl104_601 ),
inference(avatar_split_clause,[],[f14790,f14514,f4711,f17536,f2927]) ).
fof(f2927,plain,
( spl104_11
<=> class_Orderings_Oord(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_11])]) ).
fof(f17536,plain,
( spl104_651
<=> ! [X0,X1] : ~ c_Orderings_Oord__class_Oless(tc_fun(X0,tc_Nat_Onat),X1,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_651])]) ).
fof(f14514,plain,
( spl104_601
<=> ! [X0,X1] : c_Orderings_Oord__class_Oless__eq(tc_fun(X0,tc_Nat_Onat),X1,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_601])]) ).
fof(f14790,plain,
( ! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_fun(X0,tc_Nat_Onat),X1,X1)
| ~ class_Orderings_Oord(tc_Nat_Onat) )
| ~ spl104_261
| ~ spl104_601 ),
inference(resolution,[],[f14515,f4712]) ).
fof(f14515,plain,
( ! [X0,X1] : c_Orderings_Oord__class_Oless__eq(tc_fun(X0,tc_Nat_Onat),X1,X1)
| ~ spl104_601 ),
inference(avatar_component_clause,[],[f14514]) ).
fof(f17455,plain,
spl104_650,
inference(avatar_split_clause,[],[f2719,f17453]) ).
fof(f17453,plain,
( spl104_650
<=> ! [X5,X3,X2,X0,X4,X6,X1] :
( c_member(tc_prod(tc_prod(X6,X5),tc_prod(X6,X5)),c_Product__Type_OPair(tc_prod(X6,X5),tc_prod(X6,X5),c_Product__Type_OPair(X6,X5,sK92(X0,X1,X2,X3,X4,X5,X6),sK93(X0,X1,X2,X3,X4,X5,X6)),c_Product__Type_OPair(X6,X5,X2,X1)),c_Transitive__Closure_Otrancl(tc_prod(X6,X5),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_prod(X6,X5),tc_prod(X6,X5)),tc_HOL_Obool),X0,c_Relation_OId(tc_prod(X6,X5)))))
| c_Product__Type_OPair(X6,X5,X4,X3) = c_Product__Type_OPair(X6,X5,X2,X1)
| ~ c_member(tc_prod(tc_prod(X6,X5),tc_prod(X6,X5)),c_Product__Type_OPair(tc_prod(X6,X5),tc_prod(X6,X5),c_Product__Type_OPair(X6,X5,X4,X3),c_Product__Type_OPair(X6,X5,X2,X1)),c_Transitive__Closure_Otrancl(tc_prod(X6,X5),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_prod(X6,X5),tc_prod(X6,X5)),tc_HOL_Obool),X0,c_Relation_OId(tc_prod(X6,X5))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_650])]) ).
fof(f2719,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( c_member(tc_prod(tc_prod(X6,X5),tc_prod(X6,X5)),c_Product__Type_OPair(tc_prod(X6,X5),tc_prod(X6,X5),c_Product__Type_OPair(X6,X5,sK92(X0,X1,X2,X3,X4,X5,X6),sK93(X0,X1,X2,X3,X4,X5,X6)),c_Product__Type_OPair(X6,X5,X2,X1)),c_Transitive__Closure_Otrancl(tc_prod(X6,X5),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_prod(X6,X5),tc_prod(X6,X5)),tc_HOL_Obool),X0,c_Relation_OId(tc_prod(X6,X5)))))
| c_Product__Type_OPair(X6,X5,X4,X3) = c_Product__Type_OPair(X6,X5,X2,X1)
| ~ c_member(tc_prod(tc_prod(X6,X5),tc_prod(X6,X5)),c_Product__Type_OPair(tc_prod(X6,X5),tc_prod(X6,X5),c_Product__Type_OPair(X6,X5,X4,X3),c_Product__Type_OPair(X6,X5,X2,X1)),c_Transitive__Closure_Otrancl(tc_prod(X6,X5),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_prod(X6,X5),tc_prod(X6,X5)),tc_HOL_Obool),X0,c_Relation_OId(tc_prod(X6,X5))))) ),
inference(definition_unfolding,[],[f2611,f1949,f1949]) ).
fof(f1949,plain,
! [X0,X1] : c_Transitive__Closure_Ortrancl(X1,X0) = c_Transitive__Closure_Otrancl(X1,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),X0,c_Relation_OId(X1))),
inference(cnf_transformation,[],[f579]) ).
fof(f579,plain,
! [X0,X1] : c_Transitive__Closure_Ortrancl(X1,X0) = c_Transitive__Closure_Otrancl(X1,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),X0,c_Relation_OId(X1))),
inference(rectify,[],[f113]) ).
fof(f113,axiom,
! [X3,X4] : c_Transitive__Closure_Ortrancl(X4,X3) = c_Transitive__Closure_Otrancl(X4,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),X3,c_Relation_OId(X4))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trancl__reflcl) ).
fof(f2611,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( c_member(tc_prod(tc_prod(X6,X5),tc_prod(X6,X5)),c_Product__Type_OPair(tc_prod(X6,X5),tc_prod(X6,X5),c_Product__Type_OPair(X6,X5,sK92(X0,X1,X2,X3,X4,X5,X6),sK93(X0,X1,X2,X3,X4,X5,X6)),c_Product__Type_OPair(X6,X5,X2,X1)),c_Transitive__Closure_Ortrancl(tc_prod(X6,X5),X0))
| c_Product__Type_OPair(X6,X5,X4,X3) = c_Product__Type_OPair(X6,X5,X2,X1)
| ~ c_member(tc_prod(tc_prod(X6,X5),tc_prod(X6,X5)),c_Product__Type_OPair(tc_prod(X6,X5),tc_prod(X6,X5),c_Product__Type_OPair(X6,X5,X4,X3),c_Product__Type_OPair(X6,X5,X2,X1)),c_Transitive__Closure_Ortrancl(tc_prod(X6,X5),X0)) ),
inference(cnf_transformation,[],[f1838]) ).
fof(f1838,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ( c_member(tc_prod(tc_prod(X6,X5),tc_prod(X6,X5)),c_Product__Type_OPair(tc_prod(X6,X5),tc_prod(X6,X5),c_Product__Type_OPair(X6,X5,sK92(X0,X1,X2,X3,X4,X5,X6),sK93(X0,X1,X2,X3,X4,X5,X6)),c_Product__Type_OPair(X6,X5,X2,X1)),c_Transitive__Closure_Ortrancl(tc_prod(X6,X5),X0))
& c_member(tc_prod(tc_prod(X6,X5),tc_prod(X6,X5)),c_Product__Type_OPair(tc_prod(X6,X5),tc_prod(X6,X5),c_Product__Type_OPair(X6,X5,X4,X3),c_Product__Type_OPair(X6,X5,sK92(X0,X1,X2,X3,X4,X5,X6),sK93(X0,X1,X2,X3,X4,X5,X6))),X0) )
| c_Product__Type_OPair(X6,X5,X4,X3) = c_Product__Type_OPair(X6,X5,X2,X1)
| ~ c_member(tc_prod(tc_prod(X6,X5),tc_prod(X6,X5)),c_Product__Type_OPair(tc_prod(X6,X5),tc_prod(X6,X5),c_Product__Type_OPair(X6,X5,X4,X3),c_Product__Type_OPair(X6,X5,X2,X1)),c_Transitive__Closure_Ortrancl(tc_prod(X6,X5),X0)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK92,sK93])],[f1519,f1837]) ).
fof(f1837,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ? [X7,X8] :
( c_member(tc_prod(tc_prod(X6,X5),tc_prod(X6,X5)),c_Product__Type_OPair(tc_prod(X6,X5),tc_prod(X6,X5),c_Product__Type_OPair(X6,X5,X7,X8),c_Product__Type_OPair(X6,X5,X2,X1)),c_Transitive__Closure_Ortrancl(tc_prod(X6,X5),X0))
& c_member(tc_prod(tc_prod(X6,X5),tc_prod(X6,X5)),c_Product__Type_OPair(tc_prod(X6,X5),tc_prod(X6,X5),c_Product__Type_OPair(X6,X5,X4,X3),c_Product__Type_OPair(X6,X5,X7,X8)),X0) )
=> ( c_member(tc_prod(tc_prod(X6,X5),tc_prod(X6,X5)),c_Product__Type_OPair(tc_prod(X6,X5),tc_prod(X6,X5),c_Product__Type_OPair(X6,X5,sK92(X0,X1,X2,X3,X4,X5,X6),sK93(X0,X1,X2,X3,X4,X5,X6)),c_Product__Type_OPair(X6,X5,X2,X1)),c_Transitive__Closure_Ortrancl(tc_prod(X6,X5),X0))
& c_member(tc_prod(tc_prod(X6,X5),tc_prod(X6,X5)),c_Product__Type_OPair(tc_prod(X6,X5),tc_prod(X6,X5),c_Product__Type_OPair(X6,X5,X4,X3),c_Product__Type_OPair(X6,X5,sK92(X0,X1,X2,X3,X4,X5,X6),sK93(X0,X1,X2,X3,X4,X5,X6))),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f1519,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ? [X7,X8] :
( c_member(tc_prod(tc_prod(X6,X5),tc_prod(X6,X5)),c_Product__Type_OPair(tc_prod(X6,X5),tc_prod(X6,X5),c_Product__Type_OPair(X6,X5,X7,X8),c_Product__Type_OPair(X6,X5,X2,X1)),c_Transitive__Closure_Ortrancl(tc_prod(X6,X5),X0))
& c_member(tc_prod(tc_prod(X6,X5),tc_prod(X6,X5)),c_Product__Type_OPair(tc_prod(X6,X5),tc_prod(X6,X5),c_Product__Type_OPair(X6,X5,X4,X3),c_Product__Type_OPair(X6,X5,X7,X8)),X0) )
| c_Product__Type_OPair(X6,X5,X4,X3) = c_Product__Type_OPair(X6,X5,X2,X1)
| ~ c_member(tc_prod(tc_prod(X6,X5),tc_prod(X6,X5)),c_Product__Type_OPair(tc_prod(X6,X5),tc_prod(X6,X5),c_Product__Type_OPair(X6,X5,X4,X3),c_Product__Type_OPair(X6,X5,X2,X1)),c_Transitive__Closure_Ortrancl(tc_prod(X6,X5),X0)) ),
inference(flattening,[],[f1518]) ).
fof(f1518,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ? [X7,X8] :
( c_member(tc_prod(tc_prod(X6,X5),tc_prod(X6,X5)),c_Product__Type_OPair(tc_prod(X6,X5),tc_prod(X6,X5),c_Product__Type_OPair(X6,X5,X7,X8),c_Product__Type_OPair(X6,X5,X2,X1)),c_Transitive__Closure_Ortrancl(tc_prod(X6,X5),X0))
& c_member(tc_prod(tc_prod(X6,X5),tc_prod(X6,X5)),c_Product__Type_OPair(tc_prod(X6,X5),tc_prod(X6,X5),c_Product__Type_OPair(X6,X5,X4,X3),c_Product__Type_OPair(X6,X5,X7,X8)),X0) )
| c_Product__Type_OPair(X6,X5,X4,X3) = c_Product__Type_OPair(X6,X5,X2,X1)
| ~ c_member(tc_prod(tc_prod(X6,X5),tc_prod(X6,X5)),c_Product__Type_OPair(tc_prod(X6,X5),tc_prod(X6,X5),c_Product__Type_OPair(X6,X5,X4,X3),c_Product__Type_OPair(X6,X5,X2,X1)),c_Transitive__Closure_Ortrancl(tc_prod(X6,X5),X0)) ),
inference(ennf_transformation,[],[f1011]) ).
fof(f1011,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( c_member(tc_prod(tc_prod(X6,X5),tc_prod(X6,X5)),c_Product__Type_OPair(tc_prod(X6,X5),tc_prod(X6,X5),c_Product__Type_OPair(X6,X5,X4,X3),c_Product__Type_OPair(X6,X5,X2,X1)),c_Transitive__Closure_Ortrancl(tc_prod(X6,X5),X0))
=> ( c_Product__Type_OPair(X6,X5,X4,X3) != c_Product__Type_OPair(X6,X5,X2,X1)
=> ~ ! [X7,X8] :
( c_member(tc_prod(tc_prod(X6,X5),tc_prod(X6,X5)),c_Product__Type_OPair(tc_prod(X6,X5),tc_prod(X6,X5),c_Product__Type_OPair(X6,X5,X4,X3),c_Product__Type_OPair(X6,X5,X7,X8)),X0)
=> ~ c_member(tc_prod(tc_prod(X6,X5),tc_prod(X6,X5)),c_Product__Type_OPair(tc_prod(X6,X5),tc_prod(X6,X5),c_Product__Type_OPair(X6,X5,X7,X8),c_Product__Type_OPair(X6,X5,X2,X1)),c_Transitive__Closure_Ortrancl(tc_prod(X6,X5),X0)) ) ) ),
inference(rectify,[],[f71]) ).
fof(f71,axiom,
! [X3,X46,X47,X48,X49,X15,X4] :
( c_member(tc_prod(tc_prod(X4,X15),tc_prod(X4,X15)),c_Product__Type_OPair(tc_prod(X4,X15),tc_prod(X4,X15),c_Product__Type_OPair(X4,X15,X49,X48),c_Product__Type_OPair(X4,X15,X47,X46)),c_Transitive__Closure_Ortrancl(tc_prod(X4,X15),X3))
=> ( c_Product__Type_OPair(X4,X15,X49,X48) != c_Product__Type_OPair(X4,X15,X47,X46)
=> ~ ! [X20,X21] :
( c_member(tc_prod(tc_prod(X4,X15),tc_prod(X4,X15)),c_Product__Type_OPair(tc_prod(X4,X15),tc_prod(X4,X15),c_Product__Type_OPair(X4,X15,X49,X48),c_Product__Type_OPair(X4,X15,X20,X21)),X3)
=> ~ c_member(tc_prod(tc_prod(X4,X15),tc_prod(X4,X15)),c_Product__Type_OPair(tc_prod(X4,X15),tc_prod(X4,X15),c_Product__Type_OPair(X4,X15,X20,X21),c_Product__Type_OPair(X4,X15,X47,X46)),c_Transitive__Closure_Ortrancl(tc_prod(X4,X15),X3)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_converse__rtranclE2) ).
fof(f17387,plain,
spl104_649,
inference(avatar_split_clause,[],[f2727,f17385]) ).
fof(f17385,plain,
( spl104_649
<=> ! [X5,X3,X4,X2,X0,X6,X1,X7] :
( hBOOL(hAPP(hAPP(X0,X5),X4))
| c_member(tc_prod(tc_prod(X7,X6),tc_prod(X7,X6)),c_Product__Type_OPair(tc_prod(X7,X6),tc_prod(X7,X6),c_Product__Type_OPair(X7,X6,sK102(X0,X1,X2,X3,X6,X7),sK103(X0,X1,X2,X3,X6,X7)),c_Product__Type_OPair(X7,X6,X3,X2)),c_Transitive__Closure_Otrancl(tc_prod(X7,X6),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_prod(X7,X6),tc_prod(X7,X6)),tc_HOL_Obool),X1,c_Relation_OId(tc_prod(X7,X6)))))
| ~ hBOOL(hAPP(hAPP(X0,X3),X2))
| ~ c_member(tc_prod(tc_prod(X7,X6),tc_prod(X7,X6)),c_Product__Type_OPair(tc_prod(X7,X6),tc_prod(X7,X6),c_Product__Type_OPair(X7,X6,X5,X4),c_Product__Type_OPair(X7,X6,X3,X2)),c_Transitive__Closure_Otrancl(tc_prod(X7,X6),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_prod(X7,X6),tc_prod(X7,X6)),tc_HOL_Obool),X1,c_Relation_OId(tc_prod(X7,X6))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_649])]) ).
fof(f2727,plain,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( hBOOL(hAPP(hAPP(X0,X5),X4))
| c_member(tc_prod(tc_prod(X7,X6),tc_prod(X7,X6)),c_Product__Type_OPair(tc_prod(X7,X6),tc_prod(X7,X6),c_Product__Type_OPair(X7,X6,sK102(X0,X1,X2,X3,X6,X7),sK103(X0,X1,X2,X3,X6,X7)),c_Product__Type_OPair(X7,X6,X3,X2)),c_Transitive__Closure_Otrancl(tc_prod(X7,X6),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_prod(X7,X6),tc_prod(X7,X6)),tc_HOL_Obool),X1,c_Relation_OId(tc_prod(X7,X6)))))
| ~ hBOOL(hAPP(hAPP(X0,X3),X2))
| ~ c_member(tc_prod(tc_prod(X7,X6),tc_prod(X7,X6)),c_Product__Type_OPair(tc_prod(X7,X6),tc_prod(X7,X6),c_Product__Type_OPair(X7,X6,X5,X4),c_Product__Type_OPair(X7,X6,X3,X2)),c_Transitive__Closure_Otrancl(tc_prod(X7,X6),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_prod(X7,X6),tc_prod(X7,X6)),tc_HOL_Obool),X1,c_Relation_OId(tc_prod(X7,X6))))) ),
inference(definition_unfolding,[],[f2626,f1949,f1949]) ).
fof(f2626,plain,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( hBOOL(hAPP(hAPP(X0,X5),X4))
| c_member(tc_prod(tc_prod(X7,X6),tc_prod(X7,X6)),c_Product__Type_OPair(tc_prod(X7,X6),tc_prod(X7,X6),c_Product__Type_OPair(X7,X6,sK102(X0,X1,X2,X3,X6,X7),sK103(X0,X1,X2,X3,X6,X7)),c_Product__Type_OPair(X7,X6,X3,X2)),c_Transitive__Closure_Ortrancl(tc_prod(X7,X6),X1))
| ~ hBOOL(hAPP(hAPP(X0,X3),X2))
| ~ c_member(tc_prod(tc_prod(X7,X6),tc_prod(X7,X6)),c_Product__Type_OPair(tc_prod(X7,X6),tc_prod(X7,X6),c_Product__Type_OPair(X7,X6,X5,X4),c_Product__Type_OPair(X7,X6,X3,X2)),c_Transitive__Closure_Ortrancl(tc_prod(X7,X6),X1)) ),
inference(cnf_transformation,[],[f1849]) ).
fof(f1849,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( hBOOL(hAPP(hAPP(X0,X5),X4))
| ( ~ hBOOL(hAPP(hAPP(X0,sK100(X0,X1,X2,X3,X6,X7)),sK101(X0,X1,X2,X3,X6,X7)))
& hBOOL(hAPP(hAPP(X0,sK102(X0,X1,X2,X3,X6,X7)),sK103(X0,X1,X2,X3,X6,X7)))
& c_member(tc_prod(tc_prod(X7,X6),tc_prod(X7,X6)),c_Product__Type_OPair(tc_prod(X7,X6),tc_prod(X7,X6),c_Product__Type_OPair(X7,X6,sK102(X0,X1,X2,X3,X6,X7),sK103(X0,X1,X2,X3,X6,X7)),c_Product__Type_OPair(X7,X6,X3,X2)),c_Transitive__Closure_Ortrancl(tc_prod(X7,X6),X1))
& c_member(tc_prod(tc_prod(X7,X6),tc_prod(X7,X6)),c_Product__Type_OPair(tc_prod(X7,X6),tc_prod(X7,X6),c_Product__Type_OPair(X7,X6,sK100(X0,X1,X2,X3,X6,X7),sK101(X0,X1,X2,X3,X6,X7)),c_Product__Type_OPair(X7,X6,sK102(X0,X1,X2,X3,X6,X7),sK103(X0,X1,X2,X3,X6,X7))),X1) )
| ~ hBOOL(hAPP(hAPP(X0,X3),X2))
| ~ c_member(tc_prod(tc_prod(X7,X6),tc_prod(X7,X6)),c_Product__Type_OPair(tc_prod(X7,X6),tc_prod(X7,X6),c_Product__Type_OPair(X7,X6,X5,X4),c_Product__Type_OPair(X7,X6,X3,X2)),c_Transitive__Closure_Ortrancl(tc_prod(X7,X6),X1)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK100,sK101,sK102,sK103])],[f1525,f1848]) ).
fof(f1848,plain,
! [X0,X1,X2,X3,X6,X7] :
( ? [X8,X9,X10,X11] :
( ~ hBOOL(hAPP(hAPP(X0,X8),X9))
& hBOOL(hAPP(hAPP(X0,X10),X11))
& c_member(tc_prod(tc_prod(X7,X6),tc_prod(X7,X6)),c_Product__Type_OPair(tc_prod(X7,X6),tc_prod(X7,X6),c_Product__Type_OPair(X7,X6,X10,X11),c_Product__Type_OPair(X7,X6,X3,X2)),c_Transitive__Closure_Ortrancl(tc_prod(X7,X6),X1))
& c_member(tc_prod(tc_prod(X7,X6),tc_prod(X7,X6)),c_Product__Type_OPair(tc_prod(X7,X6),tc_prod(X7,X6),c_Product__Type_OPair(X7,X6,X8,X9),c_Product__Type_OPair(X7,X6,X10,X11)),X1) )
=> ( ~ hBOOL(hAPP(hAPP(X0,sK100(X0,X1,X2,X3,X6,X7)),sK101(X0,X1,X2,X3,X6,X7)))
& hBOOL(hAPP(hAPP(X0,sK102(X0,X1,X2,X3,X6,X7)),sK103(X0,X1,X2,X3,X6,X7)))
& c_member(tc_prod(tc_prod(X7,X6),tc_prod(X7,X6)),c_Product__Type_OPair(tc_prod(X7,X6),tc_prod(X7,X6),c_Product__Type_OPair(X7,X6,sK102(X0,X1,X2,X3,X6,X7),sK103(X0,X1,X2,X3,X6,X7)),c_Product__Type_OPair(X7,X6,X3,X2)),c_Transitive__Closure_Ortrancl(tc_prod(X7,X6),X1))
& c_member(tc_prod(tc_prod(X7,X6),tc_prod(X7,X6)),c_Product__Type_OPair(tc_prod(X7,X6),tc_prod(X7,X6),c_Product__Type_OPair(X7,X6,sK100(X0,X1,X2,X3,X6,X7),sK101(X0,X1,X2,X3,X6,X7)),c_Product__Type_OPair(X7,X6,sK102(X0,X1,X2,X3,X6,X7),sK103(X0,X1,X2,X3,X6,X7))),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f1525,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( hBOOL(hAPP(hAPP(X0,X5),X4))
| ? [X8,X9,X10,X11] :
( ~ hBOOL(hAPP(hAPP(X0,X8),X9))
& hBOOL(hAPP(hAPP(X0,X10),X11))
& c_member(tc_prod(tc_prod(X7,X6),tc_prod(X7,X6)),c_Product__Type_OPair(tc_prod(X7,X6),tc_prod(X7,X6),c_Product__Type_OPair(X7,X6,X10,X11),c_Product__Type_OPair(X7,X6,X3,X2)),c_Transitive__Closure_Ortrancl(tc_prod(X7,X6),X1))
& c_member(tc_prod(tc_prod(X7,X6),tc_prod(X7,X6)),c_Product__Type_OPair(tc_prod(X7,X6),tc_prod(X7,X6),c_Product__Type_OPair(X7,X6,X8,X9),c_Product__Type_OPair(X7,X6,X10,X11)),X1) )
| ~ hBOOL(hAPP(hAPP(X0,X3),X2))
| ~ c_member(tc_prod(tc_prod(X7,X6),tc_prod(X7,X6)),c_Product__Type_OPair(tc_prod(X7,X6),tc_prod(X7,X6),c_Product__Type_OPair(X7,X6,X5,X4),c_Product__Type_OPair(X7,X6,X3,X2)),c_Transitive__Closure_Ortrancl(tc_prod(X7,X6),X1)) ),
inference(flattening,[],[f1524]) ).
fof(f1524,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( hBOOL(hAPP(hAPP(X0,X5),X4))
| ? [X8,X9,X10,X11] :
( ~ hBOOL(hAPP(hAPP(X0,X8),X9))
& hBOOL(hAPP(hAPP(X0,X10),X11))
& c_member(tc_prod(tc_prod(X7,X6),tc_prod(X7,X6)),c_Product__Type_OPair(tc_prod(X7,X6),tc_prod(X7,X6),c_Product__Type_OPair(X7,X6,X10,X11),c_Product__Type_OPair(X7,X6,X3,X2)),c_Transitive__Closure_Ortrancl(tc_prod(X7,X6),X1))
& c_member(tc_prod(tc_prod(X7,X6),tc_prod(X7,X6)),c_Product__Type_OPair(tc_prod(X7,X6),tc_prod(X7,X6),c_Product__Type_OPair(X7,X6,X8,X9),c_Product__Type_OPair(X7,X6,X10,X11)),X1) )
| ~ hBOOL(hAPP(hAPP(X0,X3),X2))
| ~ c_member(tc_prod(tc_prod(X7,X6),tc_prod(X7,X6)),c_Product__Type_OPair(tc_prod(X7,X6),tc_prod(X7,X6),c_Product__Type_OPair(X7,X6,X5,X4),c_Product__Type_OPair(X7,X6,X3,X2)),c_Transitive__Closure_Ortrancl(tc_prod(X7,X6),X1)) ),
inference(ennf_transformation,[],[f1015]) ).
fof(f1015,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( c_member(tc_prod(tc_prod(X7,X6),tc_prod(X7,X6)),c_Product__Type_OPair(tc_prod(X7,X6),tc_prod(X7,X6),c_Product__Type_OPair(X7,X6,X5,X4),c_Product__Type_OPair(X7,X6,X3,X2)),c_Transitive__Closure_Ortrancl(tc_prod(X7,X6),X1))
=> ( hBOOL(hAPP(hAPP(X0,X3),X2))
=> ( ! [X8,X9,X10,X11] :
( c_member(tc_prod(tc_prod(X7,X6),tc_prod(X7,X6)),c_Product__Type_OPair(tc_prod(X7,X6),tc_prod(X7,X6),c_Product__Type_OPair(X7,X6,X8,X9),c_Product__Type_OPair(X7,X6,X10,X11)),X1)
=> ( c_member(tc_prod(tc_prod(X7,X6),tc_prod(X7,X6)),c_Product__Type_OPair(tc_prod(X7,X6),tc_prod(X7,X6),c_Product__Type_OPair(X7,X6,X10,X11),c_Product__Type_OPair(X7,X6,X3,X2)),c_Transitive__Closure_Ortrancl(tc_prod(X7,X6),X1))
=> ( hBOOL(hAPP(hAPP(X0,X10),X11))
=> hBOOL(hAPP(hAPP(X0,X8),X9)) ) ) )
=> hBOOL(hAPP(hAPP(X0,X5),X4)) ) ) ),
inference(rectify,[],[f70]) ).
fof(f70,axiom,
! [X17,X3,X40,X41,X42,X43,X15,X4] :
( c_member(tc_prod(tc_prod(X4,X15),tc_prod(X4,X15)),c_Product__Type_OPair(tc_prod(X4,X15),tc_prod(X4,X15),c_Product__Type_OPair(X4,X15,X43,X42),c_Product__Type_OPair(X4,X15,X41,X40)),c_Transitive__Closure_Ortrancl(tc_prod(X4,X15),X3))
=> ( hBOOL(hAPP(hAPP(X17,X41),X40))
=> ( ! [X20,X21,X44,X45] :
( c_member(tc_prod(tc_prod(X4,X15),tc_prod(X4,X15)),c_Product__Type_OPair(tc_prod(X4,X15),tc_prod(X4,X15),c_Product__Type_OPair(X4,X15,X20,X21),c_Product__Type_OPair(X4,X15,X44,X45)),X3)
=> ( c_member(tc_prod(tc_prod(X4,X15),tc_prod(X4,X15)),c_Product__Type_OPair(tc_prod(X4,X15),tc_prod(X4,X15),c_Product__Type_OPair(X4,X15,X44,X45),c_Product__Type_OPair(X4,X15,X41,X40)),c_Transitive__Closure_Ortrancl(tc_prod(X4,X15),X3))
=> ( hBOOL(hAPP(hAPP(X17,X44),X45))
=> hBOOL(hAPP(hAPP(X17,X20),X21)) ) ) )
=> hBOOL(hAPP(hAPP(X17,X43),X42)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_converse__rtrancl__induct2) ).
fof(f17383,plain,
spl104_648,
inference(avatar_split_clause,[],[f2724,f17381]) ).
fof(f17381,plain,
( spl104_648
<=> ! [X1,X3,X4,X0,X6,X5,X2,X7] :
( hBOOL(hAPP(hAPP(X0,X3),X2))
| c_member(tc_prod(tc_prod(X7,X6),tc_prod(X7,X6)),c_Product__Type_OPair(tc_prod(X7,X6),tc_prod(X7,X6),c_Product__Type_OPair(X7,X6,X5,X4),c_Product__Type_OPair(X7,X6,sK96(X0,X1,X4,X5,X6,X7),sK97(X0,X1,X4,X5,X6,X7))),c_Transitive__Closure_Otrancl(tc_prod(X7,X6),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_prod(X7,X6),tc_prod(X7,X6)),tc_HOL_Obool),X1,c_Relation_OId(tc_prod(X7,X6)))))
| ~ hBOOL(hAPP(hAPP(X0,X5),X4))
| ~ c_member(tc_prod(tc_prod(X7,X6),tc_prod(X7,X6)),c_Product__Type_OPair(tc_prod(X7,X6),tc_prod(X7,X6),c_Product__Type_OPair(X7,X6,X5,X4),c_Product__Type_OPair(X7,X6,X3,X2)),c_Transitive__Closure_Otrancl(tc_prod(X7,X6),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_prod(X7,X6),tc_prod(X7,X6)),tc_HOL_Obool),X1,c_Relation_OId(tc_prod(X7,X6))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_648])]) ).
fof(f2724,plain,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( hBOOL(hAPP(hAPP(X0,X3),X2))
| c_member(tc_prod(tc_prod(X7,X6),tc_prod(X7,X6)),c_Product__Type_OPair(tc_prod(X7,X6),tc_prod(X7,X6),c_Product__Type_OPair(X7,X6,X5,X4),c_Product__Type_OPair(X7,X6,sK96(X0,X1,X4,X5,X6,X7),sK97(X0,X1,X4,X5,X6,X7))),c_Transitive__Closure_Otrancl(tc_prod(X7,X6),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_prod(X7,X6),tc_prod(X7,X6)),tc_HOL_Obool),X1,c_Relation_OId(tc_prod(X7,X6)))))
| ~ hBOOL(hAPP(hAPP(X0,X5),X4))
| ~ c_member(tc_prod(tc_prod(X7,X6),tc_prod(X7,X6)),c_Product__Type_OPair(tc_prod(X7,X6),tc_prod(X7,X6),c_Product__Type_OPair(X7,X6,X5,X4),c_Product__Type_OPair(X7,X6,X3,X2)),c_Transitive__Closure_Otrancl(tc_prod(X7,X6),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_prod(X7,X6),tc_prod(X7,X6)),tc_HOL_Obool),X1,c_Relation_OId(tc_prod(X7,X6))))) ),
inference(definition_unfolding,[],[f2621,f1949,f1949]) ).
fof(f2621,plain,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( hBOOL(hAPP(hAPP(X0,X3),X2))
| c_member(tc_prod(tc_prod(X7,X6),tc_prod(X7,X6)),c_Product__Type_OPair(tc_prod(X7,X6),tc_prod(X7,X6),c_Product__Type_OPair(X7,X6,X5,X4),c_Product__Type_OPair(X7,X6,sK96(X0,X1,X4,X5,X6,X7),sK97(X0,X1,X4,X5,X6,X7))),c_Transitive__Closure_Ortrancl(tc_prod(X7,X6),X1))
| ~ hBOOL(hAPP(hAPP(X0,X5),X4))
| ~ c_member(tc_prod(tc_prod(X7,X6),tc_prod(X7,X6)),c_Product__Type_OPair(tc_prod(X7,X6),tc_prod(X7,X6),c_Product__Type_OPair(X7,X6,X5,X4),c_Product__Type_OPair(X7,X6,X3,X2)),c_Transitive__Closure_Ortrancl(tc_prod(X7,X6),X1)) ),
inference(cnf_transformation,[],[f1847]) ).
fof(f1847,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( hBOOL(hAPP(hAPP(X0,X3),X2))
| ( ~ hBOOL(hAPP(hAPP(X0,sK98(X0,X1,X4,X5,X6,X7)),sK99(X0,X1,X4,X5,X6,X7)))
& hBOOL(hAPP(hAPP(X0,sK96(X0,X1,X4,X5,X6,X7)),sK97(X0,X1,X4,X5,X6,X7)))
& c_member(tc_prod(tc_prod(X7,X6),tc_prod(X7,X6)),c_Product__Type_OPair(tc_prod(X7,X6),tc_prod(X7,X6),c_Product__Type_OPair(X7,X6,sK96(X0,X1,X4,X5,X6,X7),sK97(X0,X1,X4,X5,X6,X7)),c_Product__Type_OPair(X7,X6,sK98(X0,X1,X4,X5,X6,X7),sK99(X0,X1,X4,X5,X6,X7))),X1)
& c_member(tc_prod(tc_prod(X7,X6),tc_prod(X7,X6)),c_Product__Type_OPair(tc_prod(X7,X6),tc_prod(X7,X6),c_Product__Type_OPair(X7,X6,X5,X4),c_Product__Type_OPair(X7,X6,sK96(X0,X1,X4,X5,X6,X7),sK97(X0,X1,X4,X5,X6,X7))),c_Transitive__Closure_Ortrancl(tc_prod(X7,X6),X1)) )
| ~ hBOOL(hAPP(hAPP(X0,X5),X4))
| ~ c_member(tc_prod(tc_prod(X7,X6),tc_prod(X7,X6)),c_Product__Type_OPair(tc_prod(X7,X6),tc_prod(X7,X6),c_Product__Type_OPair(X7,X6,X5,X4),c_Product__Type_OPair(X7,X6,X3,X2)),c_Transitive__Closure_Ortrancl(tc_prod(X7,X6),X1)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK96,sK97,sK98,sK99])],[f1523,f1846,f1845]) ).
fof(f1845,plain,
! [X0,X1,X4,X5,X6,X7] :
( ? [X8,X9] :
( ? [X10,X11] :
( ~ hBOOL(hAPP(hAPP(X0,X10),X11))
& hBOOL(hAPP(hAPP(X0,X8),X9))
& c_member(tc_prod(tc_prod(X7,X6),tc_prod(X7,X6)),c_Product__Type_OPair(tc_prod(X7,X6),tc_prod(X7,X6),c_Product__Type_OPair(X7,X6,X8,X9),c_Product__Type_OPair(X7,X6,X10,X11)),X1) )
& c_member(tc_prod(tc_prod(X7,X6),tc_prod(X7,X6)),c_Product__Type_OPair(tc_prod(X7,X6),tc_prod(X7,X6),c_Product__Type_OPair(X7,X6,X5,X4),c_Product__Type_OPair(X7,X6,X8,X9)),c_Transitive__Closure_Ortrancl(tc_prod(X7,X6),X1)) )
=> ( ? [X11,X10] :
( ~ hBOOL(hAPP(hAPP(X0,X10),X11))
& hBOOL(hAPP(hAPP(X0,sK96(X0,X1,X4,X5,X6,X7)),sK97(X0,X1,X4,X5,X6,X7)))
& c_member(tc_prod(tc_prod(X7,X6),tc_prod(X7,X6)),c_Product__Type_OPair(tc_prod(X7,X6),tc_prod(X7,X6),c_Product__Type_OPair(X7,X6,sK96(X0,X1,X4,X5,X6,X7),sK97(X0,X1,X4,X5,X6,X7)),c_Product__Type_OPair(X7,X6,X10,X11)),X1) )
& c_member(tc_prod(tc_prod(X7,X6),tc_prod(X7,X6)),c_Product__Type_OPair(tc_prod(X7,X6),tc_prod(X7,X6),c_Product__Type_OPair(X7,X6,X5,X4),c_Product__Type_OPair(X7,X6,sK96(X0,X1,X4,X5,X6,X7),sK97(X0,X1,X4,X5,X6,X7))),c_Transitive__Closure_Ortrancl(tc_prod(X7,X6),X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f1846,plain,
! [X0,X1,X4,X5,X6,X7] :
( ? [X11,X10] :
( ~ hBOOL(hAPP(hAPP(X0,X10),X11))
& hBOOL(hAPP(hAPP(X0,sK96(X0,X1,X4,X5,X6,X7)),sK97(X0,X1,X4,X5,X6,X7)))
& c_member(tc_prod(tc_prod(X7,X6),tc_prod(X7,X6)),c_Product__Type_OPair(tc_prod(X7,X6),tc_prod(X7,X6),c_Product__Type_OPair(X7,X6,sK96(X0,X1,X4,X5,X6,X7),sK97(X0,X1,X4,X5,X6,X7)),c_Product__Type_OPair(X7,X6,X10,X11)),X1) )
=> ( ~ hBOOL(hAPP(hAPP(X0,sK98(X0,X1,X4,X5,X6,X7)),sK99(X0,X1,X4,X5,X6,X7)))
& hBOOL(hAPP(hAPP(X0,sK96(X0,X1,X4,X5,X6,X7)),sK97(X0,X1,X4,X5,X6,X7)))
& c_member(tc_prod(tc_prod(X7,X6),tc_prod(X7,X6)),c_Product__Type_OPair(tc_prod(X7,X6),tc_prod(X7,X6),c_Product__Type_OPair(X7,X6,sK96(X0,X1,X4,X5,X6,X7),sK97(X0,X1,X4,X5,X6,X7)),c_Product__Type_OPair(X7,X6,sK98(X0,X1,X4,X5,X6,X7),sK99(X0,X1,X4,X5,X6,X7))),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f1523,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( hBOOL(hAPP(hAPP(X0,X3),X2))
| ? [X8,X9] :
( ? [X10,X11] :
( ~ hBOOL(hAPP(hAPP(X0,X10),X11))
& hBOOL(hAPP(hAPP(X0,X8),X9))
& c_member(tc_prod(tc_prod(X7,X6),tc_prod(X7,X6)),c_Product__Type_OPair(tc_prod(X7,X6),tc_prod(X7,X6),c_Product__Type_OPair(X7,X6,X8,X9),c_Product__Type_OPair(X7,X6,X10,X11)),X1) )
& c_member(tc_prod(tc_prod(X7,X6),tc_prod(X7,X6)),c_Product__Type_OPair(tc_prod(X7,X6),tc_prod(X7,X6),c_Product__Type_OPair(X7,X6,X5,X4),c_Product__Type_OPair(X7,X6,X8,X9)),c_Transitive__Closure_Ortrancl(tc_prod(X7,X6),X1)) )
| ~ hBOOL(hAPP(hAPP(X0,X5),X4))
| ~ c_member(tc_prod(tc_prod(X7,X6),tc_prod(X7,X6)),c_Product__Type_OPair(tc_prod(X7,X6),tc_prod(X7,X6),c_Product__Type_OPair(X7,X6,X5,X4),c_Product__Type_OPair(X7,X6,X3,X2)),c_Transitive__Closure_Ortrancl(tc_prod(X7,X6),X1)) ),
inference(flattening,[],[f1522]) ).
fof(f1522,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( hBOOL(hAPP(hAPP(X0,X3),X2))
| ? [X8,X9] :
( ? [X10,X11] :
( ~ hBOOL(hAPP(hAPP(X0,X10),X11))
& hBOOL(hAPP(hAPP(X0,X8),X9))
& c_member(tc_prod(tc_prod(X7,X6),tc_prod(X7,X6)),c_Product__Type_OPair(tc_prod(X7,X6),tc_prod(X7,X6),c_Product__Type_OPair(X7,X6,X8,X9),c_Product__Type_OPair(X7,X6,X10,X11)),X1) )
& c_member(tc_prod(tc_prod(X7,X6),tc_prod(X7,X6)),c_Product__Type_OPair(tc_prod(X7,X6),tc_prod(X7,X6),c_Product__Type_OPair(X7,X6,X5,X4),c_Product__Type_OPair(X7,X6,X8,X9)),c_Transitive__Closure_Ortrancl(tc_prod(X7,X6),X1)) )
| ~ hBOOL(hAPP(hAPP(X0,X5),X4))
| ~ c_member(tc_prod(tc_prod(X7,X6),tc_prod(X7,X6)),c_Product__Type_OPair(tc_prod(X7,X6),tc_prod(X7,X6),c_Product__Type_OPair(X7,X6,X5,X4),c_Product__Type_OPair(X7,X6,X3,X2)),c_Transitive__Closure_Ortrancl(tc_prod(X7,X6),X1)) ),
inference(ennf_transformation,[],[f1014]) ).
fof(f1014,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( c_member(tc_prod(tc_prod(X7,X6),tc_prod(X7,X6)),c_Product__Type_OPair(tc_prod(X7,X6),tc_prod(X7,X6),c_Product__Type_OPair(X7,X6,X5,X4),c_Product__Type_OPair(X7,X6,X3,X2)),c_Transitive__Closure_Ortrancl(tc_prod(X7,X6),X1))
=> ( hBOOL(hAPP(hAPP(X0,X5),X4))
=> ( ! [X8,X9] :
( c_member(tc_prod(tc_prod(X7,X6),tc_prod(X7,X6)),c_Product__Type_OPair(tc_prod(X7,X6),tc_prod(X7,X6),c_Product__Type_OPair(X7,X6,X5,X4),c_Product__Type_OPair(X7,X6,X8,X9)),c_Transitive__Closure_Ortrancl(tc_prod(X7,X6),X1))
=> ! [X10,X11] :
( c_member(tc_prod(tc_prod(X7,X6),tc_prod(X7,X6)),c_Product__Type_OPair(tc_prod(X7,X6),tc_prod(X7,X6),c_Product__Type_OPair(X7,X6,X8,X9),c_Product__Type_OPair(X7,X6,X10,X11)),X1)
=> ( hBOOL(hAPP(hAPP(X0,X8),X9))
=> hBOOL(hAPP(hAPP(X0,X10),X11)) ) ) )
=> hBOOL(hAPP(hAPP(X0,X3),X2)) ) ) ),
inference(rectify,[],[f69]) ).
fof(f69,axiom,
! [X17,X3,X40,X41,X42,X43,X15,X4] :
( c_member(tc_prod(tc_prod(X4,X15),tc_prod(X4,X15)),c_Product__Type_OPair(tc_prod(X4,X15),tc_prod(X4,X15),c_Product__Type_OPair(X4,X15,X43,X42),c_Product__Type_OPair(X4,X15,X41,X40)),c_Transitive__Closure_Ortrancl(tc_prod(X4,X15),X3))
=> ( hBOOL(hAPP(hAPP(X17,X43),X42))
=> ( ! [X20,X21] :
( c_member(tc_prod(tc_prod(X4,X15),tc_prod(X4,X15)),c_Product__Type_OPair(tc_prod(X4,X15),tc_prod(X4,X15),c_Product__Type_OPair(X4,X15,X43,X42),c_Product__Type_OPair(X4,X15,X20,X21)),c_Transitive__Closure_Ortrancl(tc_prod(X4,X15),X3))
=> ! [X44,X45] :
( c_member(tc_prod(tc_prod(X4,X15),tc_prod(X4,X15)),c_Product__Type_OPair(tc_prod(X4,X15),tc_prod(X4,X15),c_Product__Type_OPair(X4,X15,X20,X21),c_Product__Type_OPair(X4,X15,X44,X45)),X3)
=> ( hBOOL(hAPP(hAPP(X17,X20),X21))
=> hBOOL(hAPP(hAPP(X17,X44),X45)) ) ) )
=> hBOOL(hAPP(hAPP(X17,X41),X40)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__induct2) ).
fof(f17325,plain,
spl104_647,
inference(avatar_split_clause,[],[f2728,f17323]) ).
fof(f17323,plain,
( spl104_647
<=> ! [X2,X6,X4,X3,X0,X5,X1,X7] :
( hBOOL(hAPP(hAPP(X0,X5),X4))
| c_member(tc_prod(tc_prod(X7,X6),tc_prod(X7,X6)),c_Product__Type_OPair(tc_prod(X7,X6),tc_prod(X7,X6),c_Product__Type_OPair(X7,X6,sK100(X0,X1,X2,X3,X6,X7),sK101(X0,X1,X2,X3,X6,X7)),c_Product__Type_OPair(X7,X6,sK102(X0,X1,X2,X3,X6,X7),sK103(X0,X1,X2,X3,X6,X7))),X1)
| ~ hBOOL(hAPP(hAPP(X0,X3),X2))
| ~ c_member(tc_prod(tc_prod(X7,X6),tc_prod(X7,X6)),c_Product__Type_OPair(tc_prod(X7,X6),tc_prod(X7,X6),c_Product__Type_OPair(X7,X6,X5,X4),c_Product__Type_OPair(X7,X6,X3,X2)),c_Transitive__Closure_Otrancl(tc_prod(X7,X6),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_prod(X7,X6),tc_prod(X7,X6)),tc_HOL_Obool),X1,c_Relation_OId(tc_prod(X7,X6))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_647])]) ).
fof(f2728,plain,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( hBOOL(hAPP(hAPP(X0,X5),X4))
| c_member(tc_prod(tc_prod(X7,X6),tc_prod(X7,X6)),c_Product__Type_OPair(tc_prod(X7,X6),tc_prod(X7,X6),c_Product__Type_OPair(X7,X6,sK100(X0,X1,X2,X3,X6,X7),sK101(X0,X1,X2,X3,X6,X7)),c_Product__Type_OPair(X7,X6,sK102(X0,X1,X2,X3,X6,X7),sK103(X0,X1,X2,X3,X6,X7))),X1)
| ~ hBOOL(hAPP(hAPP(X0,X3),X2))
| ~ c_member(tc_prod(tc_prod(X7,X6),tc_prod(X7,X6)),c_Product__Type_OPair(tc_prod(X7,X6),tc_prod(X7,X6),c_Product__Type_OPair(X7,X6,X5,X4),c_Product__Type_OPair(X7,X6,X3,X2)),c_Transitive__Closure_Otrancl(tc_prod(X7,X6),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_prod(X7,X6),tc_prod(X7,X6)),tc_HOL_Obool),X1,c_Relation_OId(tc_prod(X7,X6))))) ),
inference(definition_unfolding,[],[f2625,f1949]) ).
fof(f2625,plain,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( hBOOL(hAPP(hAPP(X0,X5),X4))
| c_member(tc_prod(tc_prod(X7,X6),tc_prod(X7,X6)),c_Product__Type_OPair(tc_prod(X7,X6),tc_prod(X7,X6),c_Product__Type_OPair(X7,X6,sK100(X0,X1,X2,X3,X6,X7),sK101(X0,X1,X2,X3,X6,X7)),c_Product__Type_OPair(X7,X6,sK102(X0,X1,X2,X3,X6,X7),sK103(X0,X1,X2,X3,X6,X7))),X1)
| ~ hBOOL(hAPP(hAPP(X0,X3),X2))
| ~ c_member(tc_prod(tc_prod(X7,X6),tc_prod(X7,X6)),c_Product__Type_OPair(tc_prod(X7,X6),tc_prod(X7,X6),c_Product__Type_OPair(X7,X6,X5,X4),c_Product__Type_OPair(X7,X6,X3,X2)),c_Transitive__Closure_Ortrancl(tc_prod(X7,X6),X1)) ),
inference(cnf_transformation,[],[f1849]) ).
fof(f17321,plain,
spl104_646,
inference(avatar_split_clause,[],[f2723,f17319]) ).
fof(f17319,plain,
( spl104_646
<=> ! [X5,X6,X4,X0,X7,X3,X2,X1] :
( hBOOL(hAPP(hAPP(X0,X3),X2))
| c_member(tc_prod(tc_prod(X7,X6),tc_prod(X7,X6)),c_Product__Type_OPair(tc_prod(X7,X6),tc_prod(X7,X6),c_Product__Type_OPair(X7,X6,sK96(X0,X1,X4,X5,X6,X7),sK97(X0,X1,X4,X5,X6,X7)),c_Product__Type_OPair(X7,X6,sK98(X0,X1,X4,X5,X6,X7),sK99(X0,X1,X4,X5,X6,X7))),X1)
| ~ hBOOL(hAPP(hAPP(X0,X5),X4))
| ~ c_member(tc_prod(tc_prod(X7,X6),tc_prod(X7,X6)),c_Product__Type_OPair(tc_prod(X7,X6),tc_prod(X7,X6),c_Product__Type_OPair(X7,X6,X5,X4),c_Product__Type_OPair(X7,X6,X3,X2)),c_Transitive__Closure_Otrancl(tc_prod(X7,X6),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_prod(X7,X6),tc_prod(X7,X6)),tc_HOL_Obool),X1,c_Relation_OId(tc_prod(X7,X6))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_646])]) ).
fof(f2723,plain,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( hBOOL(hAPP(hAPP(X0,X3),X2))
| c_member(tc_prod(tc_prod(X7,X6),tc_prod(X7,X6)),c_Product__Type_OPair(tc_prod(X7,X6),tc_prod(X7,X6),c_Product__Type_OPair(X7,X6,sK96(X0,X1,X4,X5,X6,X7),sK97(X0,X1,X4,X5,X6,X7)),c_Product__Type_OPair(X7,X6,sK98(X0,X1,X4,X5,X6,X7),sK99(X0,X1,X4,X5,X6,X7))),X1)
| ~ hBOOL(hAPP(hAPP(X0,X5),X4))
| ~ c_member(tc_prod(tc_prod(X7,X6),tc_prod(X7,X6)),c_Product__Type_OPair(tc_prod(X7,X6),tc_prod(X7,X6),c_Product__Type_OPair(X7,X6,X5,X4),c_Product__Type_OPair(X7,X6,X3,X2)),c_Transitive__Closure_Otrancl(tc_prod(X7,X6),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_prod(X7,X6),tc_prod(X7,X6)),tc_HOL_Obool),X1,c_Relation_OId(tc_prod(X7,X6))))) ),
inference(definition_unfolding,[],[f2622,f1949]) ).
fof(f2622,plain,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( hBOOL(hAPP(hAPP(X0,X3),X2))
| c_member(tc_prod(tc_prod(X7,X6),tc_prod(X7,X6)),c_Product__Type_OPair(tc_prod(X7,X6),tc_prod(X7,X6),c_Product__Type_OPair(X7,X6,sK96(X0,X1,X4,X5,X6,X7),sK97(X0,X1,X4,X5,X6,X7)),c_Product__Type_OPair(X7,X6,sK98(X0,X1,X4,X5,X6,X7),sK99(X0,X1,X4,X5,X6,X7))),X1)
| ~ hBOOL(hAPP(hAPP(X0,X5),X4))
| ~ c_member(tc_prod(tc_prod(X7,X6),tc_prod(X7,X6)),c_Product__Type_OPair(tc_prod(X7,X6),tc_prod(X7,X6),c_Product__Type_OPair(X7,X6,X5,X4),c_Product__Type_OPair(X7,X6,X3,X2)),c_Transitive__Closure_Ortrancl(tc_prod(X7,X6),X1)) ),
inference(cnf_transformation,[],[f1847]) ).
fof(f17291,plain,
spl104_645,
inference(avatar_split_clause,[],[f2720,f17289]) ).
fof(f17289,plain,
( spl104_645
<=> ! [X5,X4,X2,X0,X6,X3,X1] :
( c_member(tc_prod(tc_prod(X6,X5),tc_prod(X6,X5)),c_Product__Type_OPair(tc_prod(X6,X5),tc_prod(X6,X5),c_Product__Type_OPair(X6,X5,X4,X3),c_Product__Type_OPair(X6,X5,sK92(X0,X1,X2,X3,X4,X5,X6),sK93(X0,X1,X2,X3,X4,X5,X6))),X0)
| c_Product__Type_OPair(X6,X5,X4,X3) = c_Product__Type_OPair(X6,X5,X2,X1)
| ~ c_member(tc_prod(tc_prod(X6,X5),tc_prod(X6,X5)),c_Product__Type_OPair(tc_prod(X6,X5),tc_prod(X6,X5),c_Product__Type_OPair(X6,X5,X4,X3),c_Product__Type_OPair(X6,X5,X2,X1)),c_Transitive__Closure_Otrancl(tc_prod(X6,X5),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_prod(X6,X5),tc_prod(X6,X5)),tc_HOL_Obool),X0,c_Relation_OId(tc_prod(X6,X5))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_645])]) ).
fof(f2720,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( c_member(tc_prod(tc_prod(X6,X5),tc_prod(X6,X5)),c_Product__Type_OPair(tc_prod(X6,X5),tc_prod(X6,X5),c_Product__Type_OPair(X6,X5,X4,X3),c_Product__Type_OPair(X6,X5,sK92(X0,X1,X2,X3,X4,X5,X6),sK93(X0,X1,X2,X3,X4,X5,X6))),X0)
| c_Product__Type_OPair(X6,X5,X4,X3) = c_Product__Type_OPair(X6,X5,X2,X1)
| ~ c_member(tc_prod(tc_prod(X6,X5),tc_prod(X6,X5)),c_Product__Type_OPair(tc_prod(X6,X5),tc_prod(X6,X5),c_Product__Type_OPair(X6,X5,X4,X3),c_Product__Type_OPair(X6,X5,X2,X1)),c_Transitive__Closure_Otrancl(tc_prod(X6,X5),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_prod(X6,X5),tc_prod(X6,X5)),tc_HOL_Obool),X0,c_Relation_OId(tc_prod(X6,X5))))) ),
inference(definition_unfolding,[],[f2610,f1949]) ).
fof(f2610,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( c_member(tc_prod(tc_prod(X6,X5),tc_prod(X6,X5)),c_Product__Type_OPair(tc_prod(X6,X5),tc_prod(X6,X5),c_Product__Type_OPair(X6,X5,X4,X3),c_Product__Type_OPair(X6,X5,sK92(X0,X1,X2,X3,X4,X5,X6),sK93(X0,X1,X2,X3,X4,X5,X6))),X0)
| c_Product__Type_OPair(X6,X5,X4,X3) = c_Product__Type_OPair(X6,X5,X2,X1)
| ~ c_member(tc_prod(tc_prod(X6,X5),tc_prod(X6,X5)),c_Product__Type_OPair(tc_prod(X6,X5),tc_prod(X6,X5),c_Product__Type_OPair(X6,X5,X4,X3),c_Product__Type_OPair(X6,X5,X2,X1)),c_Transitive__Closure_Ortrancl(tc_prod(X6,X5),X0)) ),
inference(cnf_transformation,[],[f1838]) ).
fof(f17198,plain,
spl104_644,
inference(avatar_split_clause,[],[f2694,f17196]) ).
fof(f17196,plain,
( spl104_644
<=> ! [X2,X4,X0,X3,X1] :
( c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X0,X1),c_Transitive__Closure_Otrancl(X4,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),X3,c_Relation_OId(X4))))
| c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X1,X0),c_Transitive__Closure_Otrancl(X4,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),X3,c_Relation_OId(X4))))
| ~ c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X2,X0),c_Transitive__Closure_Otrancl(X4,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),X3,c_Relation_OId(X4))))
| ~ c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X2,X1),c_Transitive__Closure_Otrancl(X4,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),X3,c_Relation_OId(X4))))
| ~ c_Relation_Osingle__valued(X4,X4,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_644])]) ).
fof(f2694,plain,
! [X2,X3,X0,X1,X4] :
( c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X0,X1),c_Transitive__Closure_Otrancl(X4,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),X3,c_Relation_OId(X4))))
| c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X1,X0),c_Transitive__Closure_Otrancl(X4,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),X3,c_Relation_OId(X4))))
| ~ c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X2,X0),c_Transitive__Closure_Otrancl(X4,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),X3,c_Relation_OId(X4))))
| ~ c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X2,X1),c_Transitive__Closure_Otrancl(X4,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),X3,c_Relation_OId(X4))))
| ~ c_Relation_Osingle__valued(X4,X4,X3) ),
inference(definition_unfolding,[],[f2524,f1949,f1949,f1949,f1949]) ).
fof(f2524,plain,
! [X2,X3,X0,X1,X4] :
( c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X0,X1),c_Transitive__Closure_Ortrancl(X4,X3))
| c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X1,X0),c_Transitive__Closure_Ortrancl(X4,X3))
| ~ c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X2,X0),c_Transitive__Closure_Ortrancl(X4,X3))
| ~ c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X2,X1),c_Transitive__Closure_Ortrancl(X4,X3))
| ~ c_Relation_Osingle__valued(X4,X4,X3) ),
inference(cnf_transformation,[],[f1449]) ).
fof(f1449,plain,
! [X0,X1,X2,X3,X4] :
( c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X0,X1),c_Transitive__Closure_Ortrancl(X4,X3))
| c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X1,X0),c_Transitive__Closure_Ortrancl(X4,X3))
| ~ c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X2,X0),c_Transitive__Closure_Ortrancl(X4,X3))
| ~ c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X2,X1),c_Transitive__Closure_Ortrancl(X4,X3))
| ~ c_Relation_Osingle__valued(X4,X4,X3) ),
inference(flattening,[],[f1448]) ).
fof(f1448,plain,
! [X0,X1,X2,X3,X4] :
( c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X0,X1),c_Transitive__Closure_Ortrancl(X4,X3))
| c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X1,X0),c_Transitive__Closure_Ortrancl(X4,X3))
| ~ c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X2,X0),c_Transitive__Closure_Ortrancl(X4,X3))
| ~ c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X2,X1),c_Transitive__Closure_Ortrancl(X4,X3))
| ~ c_Relation_Osingle__valued(X4,X4,X3) ),
inference(ennf_transformation,[],[f960]) ).
fof(f960,plain,
! [X0,X1,X2,X3,X4] :
( c_Relation_Osingle__valued(X4,X4,X3)
=> ( c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X2,X1),c_Transitive__Closure_Ortrancl(X4,X3))
=> ( c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X2,X0),c_Transitive__Closure_Ortrancl(X4,X3))
=> ( c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X0,X1),c_Transitive__Closure_Ortrancl(X4,X3))
| c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X1,X0),c_Transitive__Closure_Ortrancl(X4,X3)) ) ) ) ),
inference(rectify,[],[f62]) ).
fof(f62,axiom,
! [X38,X12,X13,X3,X4] :
( c_Relation_Osingle__valued(X4,X4,X3)
=> ( c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X13,X12),c_Transitive__Closure_Ortrancl(X4,X3))
=> ( c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X13,X38),c_Transitive__Closure_Ortrancl(X4,X3))
=> ( c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X38,X12),c_Transitive__Closure_Ortrancl(X4,X3))
| c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X12,X38),c_Transitive__Closure_Ortrancl(X4,X3)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_single__valued__confluent) ).
fof(f16796,plain,
spl104_643,
inference(avatar_split_clause,[],[f2859,f16794]) ).
fof(f16794,plain,
( spl104_643
<=> ! [X6,X0,X3,X2,X1] :
( ~ c_Order__Relation_Opreorder__on(X3,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),c_Relation_ORange(X3,X3,X2),c_Relation_ODomain(X3,X3,X2)),X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X1,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),c_Relation_ORange(X3,X3,X2),c_Relation_ODomain(X3,X3,X2)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X0,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),c_Relation_ORange(X3,X3,X2),c_Relation_ODomain(X3,X3,X2)))
| c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,sK57(X0,X2,X3,X6),X6),X2)
| ~ c_member(X3,X6,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),c_Relation_OImage(X3,X3,X2,X1),c_Relation_OImage(X3,X3,X2,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_643])]) ).
fof(f2859,plain,
! [X2,X3,X0,X1,X6] :
( ~ c_Order__Relation_Opreorder__on(X3,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),c_Relation_ORange(X3,X3,X2),c_Relation_ODomain(X3,X3,X2)),X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X1,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),c_Relation_ORange(X3,X3,X2),c_Relation_ODomain(X3,X3,X2)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X0,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),c_Relation_ORange(X3,X3,X2),c_Relation_ODomain(X3,X3,X2)))
| c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,sK57(X0,X2,X3,X6),X6),X2)
| ~ c_member(X3,X6,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),c_Relation_OImage(X3,X3,X2,X1),c_Relation_OImage(X3,X3,X2,X0)) ),
inference(forward_demodulation,[],[f2858,f2058]) ).
fof(f2058,plain,
! [X2,X0,X1] : c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool),X0,X1) = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool),X1,X0),
inference(cnf_transformation,[],[f656]) ).
fof(f656,plain,
! [X0,X1,X2] : c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool),X0,X1) = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool),X1,X0),
inference(rectify,[],[f122]) ).
fof(f122,axiom,
! [X10,X11,X4] : c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool),X11,X10) = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool),X10,X11),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__commute) ).
fof(f2858,plain,
! [X2,X3,X0,X1,X6] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X1,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),c_Relation_ORange(X3,X3,X2),c_Relation_ODomain(X3,X3,X2)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X0,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),c_Relation_ORange(X3,X3,X2),c_Relation_ODomain(X3,X3,X2)))
| c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,sK57(X0,X2,X3,X6),X6),X2)
| ~ c_member(X3,X6,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),c_Relation_OImage(X3,X3,X2,X1),c_Relation_OImage(X3,X3,X2,X0))
| ~ c_Order__Relation_Opreorder__on(X3,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),c_Relation_ODomain(X3,X3,X2),c_Relation_ORange(X3,X3,X2)),X2) ),
inference(forward_demodulation,[],[f2857,f2058]) ).
fof(f2857,plain,
! [X2,X3,X0,X1,X6] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X0,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),c_Relation_ORange(X3,X3,X2),c_Relation_ODomain(X3,X3,X2)))
| c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,sK57(X0,X2,X3,X6),X6),X2)
| ~ c_member(X3,X6,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),c_Relation_OImage(X3,X3,X2,X1),c_Relation_OImage(X3,X3,X2,X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X1,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),c_Relation_ODomain(X3,X3,X2),c_Relation_ORange(X3,X3,X2)))
| ~ c_Order__Relation_Opreorder__on(X3,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),c_Relation_ODomain(X3,X3,X2),c_Relation_ORange(X3,X3,X2)),X2) ),
inference(forward_demodulation,[],[f2665,f2058]) ).
fof(f2665,plain,
! [X2,X3,X0,X1,X6] :
( c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,sK57(X0,X2,X3,X6),X6),X2)
| ~ c_member(X3,X6,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),c_Relation_OImage(X3,X3,X2,X1),c_Relation_OImage(X3,X3,X2,X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X0,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),c_Relation_ODomain(X3,X3,X2),c_Relation_ORange(X3,X3,X2)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X1,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),c_Relation_ODomain(X3,X3,X2),c_Relation_ORange(X3,X3,X2)))
| ~ c_Order__Relation_Opreorder__on(X3,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),c_Relation_ODomain(X3,X3,X2),c_Relation_ORange(X3,X3,X2)),X2) ),
inference(definition_unfolding,[],[f2380,f1954,f1954,f1954]) ).
fof(f1954,plain,
! [X0,X1] : c_Relation_OField(X1,X0) = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool),c_Relation_ODomain(X1,X1,X0),c_Relation_ORange(X1,X1,X0)),
inference(cnf_transformation,[],[f584]) ).
fof(f584,plain,
! [X0,X1] : c_Relation_OField(X1,X0) = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool),c_Relation_ODomain(X1,X1,X0),c_Relation_ORange(X1,X1,X0)),
inference(rectify,[],[f216]) ).
fof(f216,axiom,
! [X3,X4] : c_Relation_OField(X4,X3) = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool),c_Relation_ODomain(X4,X4,X3),c_Relation_ORange(X4,X4,X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Field__def) ).
fof(f2380,plain,
! [X2,X3,X0,X1,X6] :
( c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,sK57(X0,X2,X3,X6),X6),X2)
| ~ c_member(X3,X6,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),c_Relation_OImage(X3,X3,X2,X1),c_Relation_OImage(X3,X3,X2,X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X0,c_Relation_OField(X3,X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X1,c_Relation_OField(X3,X2))
| ~ c_Order__Relation_Opreorder__on(X3,c_Relation_OField(X3,X2),X2) ),
inference(cnf_transformation,[],[f1712]) ).
fof(f1712,plain,
! [X0,X1,X2,X3] :
( ( ( c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),c_Relation_OImage(X3,X3,X2,X1),c_Relation_OImage(X3,X3,X2,X0))
| ( ! [X5] :
( ~ c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X5,sK56(X0,X1,X2,X3)),X2)
| ~ c_member(X3,X5,X0) )
& c_member(X3,sK56(X0,X1,X2,X3),X1) ) )
& ( ! [X6] :
( ( c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,sK57(X0,X2,X3,X6),X6),X2)
& c_member(X3,sK57(X0,X2,X3,X6),X0) )
| ~ c_member(X3,X6,X1) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),c_Relation_OImage(X3,X3,X2,X1),c_Relation_OImage(X3,X3,X2,X0)) ) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X0,c_Relation_OField(X3,X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X1,c_Relation_OField(X3,X2))
| ~ c_Order__Relation_Opreorder__on(X3,c_Relation_OField(X3,X2),X2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK56,sK57])],[f1709,f1711,f1710]) ).
fof(f1710,plain,
! [X0,X1,X2,X3] :
( ? [X4] :
( ! [X5] :
( ~ c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X5,X4),X2)
| ~ c_member(X3,X5,X0) )
& c_member(X3,X4,X1) )
=> ( ! [X5] :
( ~ c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X5,sK56(X0,X1,X2,X3)),X2)
| ~ c_member(X3,X5,X0) )
& c_member(X3,sK56(X0,X1,X2,X3),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f1711,plain,
! [X0,X2,X3,X6] :
( ? [X7] :
( c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X7,X6),X2)
& c_member(X3,X7,X0) )
=> ( c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,sK57(X0,X2,X3,X6),X6),X2)
& c_member(X3,sK57(X0,X2,X3,X6),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f1709,plain,
! [X0,X1,X2,X3] :
( ( ( c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),c_Relation_OImage(X3,X3,X2,X1),c_Relation_OImage(X3,X3,X2,X0))
| ? [X4] :
( ! [X5] :
( ~ c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X5,X4),X2)
| ~ c_member(X3,X5,X0) )
& c_member(X3,X4,X1) ) )
& ( ! [X6] :
( ? [X7] :
( c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X7,X6),X2)
& c_member(X3,X7,X0) )
| ~ c_member(X3,X6,X1) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),c_Relation_OImage(X3,X3,X2,X1),c_Relation_OImage(X3,X3,X2,X0)) ) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X0,c_Relation_OField(X3,X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X1,c_Relation_OField(X3,X2))
| ~ c_Order__Relation_Opreorder__on(X3,c_Relation_OField(X3,X2),X2) ),
inference(rectify,[],[f1708]) ).
fof(f1708,plain,
! [X0,X1,X2,X3] :
( ( ( c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),c_Relation_OImage(X3,X3,X2,X1),c_Relation_OImage(X3,X3,X2,X0))
| ? [X4] :
( ! [X5] :
( ~ c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X5,X4),X2)
| ~ c_member(X3,X5,X0) )
& c_member(X3,X4,X1) ) )
& ( ! [X4] :
( ? [X5] :
( c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X5,X4),X2)
& c_member(X3,X5,X0) )
| ~ c_member(X3,X4,X1) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),c_Relation_OImage(X3,X3,X2,X1),c_Relation_OImage(X3,X3,X2,X0)) ) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X0,c_Relation_OField(X3,X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X1,c_Relation_OField(X3,X2))
| ~ c_Order__Relation_Opreorder__on(X3,c_Relation_OField(X3,X2),X2) ),
inference(nnf_transformation,[],[f1377]) ).
fof(f1377,plain,
! [X0,X1,X2,X3] :
( ( c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),c_Relation_OImage(X3,X3,X2,X1),c_Relation_OImage(X3,X3,X2,X0))
<=> ! [X4] :
( ? [X5] :
( c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X5,X4),X2)
& c_member(X3,X5,X0) )
| ~ c_member(X3,X4,X1) ) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X0,c_Relation_OField(X3,X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X1,c_Relation_OField(X3,X2))
| ~ c_Order__Relation_Opreorder__on(X3,c_Relation_OField(X3,X2),X2) ),
inference(flattening,[],[f1376]) ).
fof(f1376,plain,
! [X0,X1,X2,X3] :
( ( c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),c_Relation_OImage(X3,X3,X2,X1),c_Relation_OImage(X3,X3,X2,X0))
<=> ! [X4] :
( ? [X5] :
( c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X5,X4),X2)
& c_member(X3,X5,X0) )
| ~ c_member(X3,X4,X1) ) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X0,c_Relation_OField(X3,X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X1,c_Relation_OField(X3,X2))
| ~ c_Order__Relation_Opreorder__on(X3,c_Relation_OField(X3,X2),X2) ),
inference(ennf_transformation,[],[f890]) ).
fof(f890,plain,
! [X0,X1,X2,X3] :
( c_Order__Relation_Opreorder__on(X3,c_Relation_OField(X3,X2),X2)
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X1,c_Relation_OField(X3,X2))
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X0,c_Relation_OField(X3,X2))
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),c_Relation_OImage(X3,X3,X2,X1),c_Relation_OImage(X3,X3,X2,X0))
<=> ! [X4] :
( c_member(X3,X4,X1)
=> ? [X5] :
( c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X5,X4),X2)
& c_member(X3,X5,X0) ) ) ) ) ) ),
inference(rectify,[],[f485]) ).
fof(f485,axiom,
! [X10,X11,X3,X4] :
( c_Order__Relation_Opreorder__on(X4,c_Relation_OField(X4,X3),X3)
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool),X11,c_Relation_OField(X4,X3))
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool),X10,c_Relation_OField(X4,X3))
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool),c_Relation_OImage(X4,X4,X3,X11),c_Relation_OImage(X4,X4,X3,X10))
<=> ! [X2] :
( c_member(X4,X2,X11)
=> ? [X31] :
( c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X31,X2),X3)
& c_member(X4,X31,X10) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__Image__Image__iff) ).
fof(f16792,plain,
spl104_642,
inference(avatar_split_clause,[],[f2853,f16790]) ).
fof(f16790,plain,
( spl104_642
<=> ! [X5,X0,X3,X2,X1] :
( ~ c_Order__Relation_Opreorder__on(X3,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),c_Relation_ORange(X3,X3,X2),c_Relation_ODomain(X3,X3,X2)),X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X1,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),c_Relation_ORange(X3,X3,X2),c_Relation_ODomain(X3,X3,X2)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X0,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),c_Relation_ORange(X3,X3,X2),c_Relation_ODomain(X3,X3,X2)))
| c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),c_Relation_OImage(X3,X3,X2,X1),c_Relation_OImage(X3,X3,X2,X0))
| ~ c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X5,sK56(X0,X1,X2,X3)),X2)
| ~ c_member(X3,X5,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_642])]) ).
fof(f2853,plain,
! [X2,X3,X0,X1,X5] :
( ~ c_Order__Relation_Opreorder__on(X3,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),c_Relation_ORange(X3,X3,X2),c_Relation_ODomain(X3,X3,X2)),X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X1,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),c_Relation_ORange(X3,X3,X2),c_Relation_ODomain(X3,X3,X2)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X0,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),c_Relation_ORange(X3,X3,X2),c_Relation_ODomain(X3,X3,X2)))
| c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),c_Relation_OImage(X3,X3,X2,X1),c_Relation_OImage(X3,X3,X2,X0))
| ~ c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X5,sK56(X0,X1,X2,X3)),X2)
| ~ c_member(X3,X5,X0) ),
inference(forward_demodulation,[],[f2852,f2058]) ).
fof(f2852,plain,
! [X2,X3,X0,X1,X5] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X1,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),c_Relation_ORange(X3,X3,X2),c_Relation_ODomain(X3,X3,X2)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X0,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),c_Relation_ORange(X3,X3,X2),c_Relation_ODomain(X3,X3,X2)))
| c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),c_Relation_OImage(X3,X3,X2,X1),c_Relation_OImage(X3,X3,X2,X0))
| ~ c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X5,sK56(X0,X1,X2,X3)),X2)
| ~ c_member(X3,X5,X0)
| ~ c_Order__Relation_Opreorder__on(X3,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),c_Relation_ODomain(X3,X3,X2),c_Relation_ORange(X3,X3,X2)),X2) ),
inference(forward_demodulation,[],[f2851,f2058]) ).
fof(f2851,plain,
! [X2,X3,X0,X1,X5] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X0,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),c_Relation_ORange(X3,X3,X2),c_Relation_ODomain(X3,X3,X2)))
| c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),c_Relation_OImage(X3,X3,X2,X1),c_Relation_OImage(X3,X3,X2,X0))
| ~ c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X5,sK56(X0,X1,X2,X3)),X2)
| ~ c_member(X3,X5,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X1,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),c_Relation_ODomain(X3,X3,X2),c_Relation_ORange(X3,X3,X2)))
| ~ c_Order__Relation_Opreorder__on(X3,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),c_Relation_ODomain(X3,X3,X2),c_Relation_ORange(X3,X3,X2)),X2) ),
inference(forward_demodulation,[],[f2663,f2058]) ).
fof(f2663,plain,
! [X2,X3,X0,X1,X5] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),c_Relation_OImage(X3,X3,X2,X1),c_Relation_OImage(X3,X3,X2,X0))
| ~ c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X5,sK56(X0,X1,X2,X3)),X2)
| ~ c_member(X3,X5,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X0,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),c_Relation_ODomain(X3,X3,X2),c_Relation_ORange(X3,X3,X2)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X1,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),c_Relation_ODomain(X3,X3,X2),c_Relation_ORange(X3,X3,X2)))
| ~ c_Order__Relation_Opreorder__on(X3,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),c_Relation_ODomain(X3,X3,X2),c_Relation_ORange(X3,X3,X2)),X2) ),
inference(definition_unfolding,[],[f2382,f1954,f1954,f1954]) ).
fof(f2382,plain,
! [X2,X3,X0,X1,X5] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),c_Relation_OImage(X3,X3,X2,X1),c_Relation_OImage(X3,X3,X2,X0))
| ~ c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X5,sK56(X0,X1,X2,X3)),X2)
| ~ c_member(X3,X5,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X0,c_Relation_OField(X3,X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X1,c_Relation_OField(X3,X2))
| ~ c_Order__Relation_Opreorder__on(X3,c_Relation_OField(X3,X2),X2) ),
inference(cnf_transformation,[],[f1712]) ).
fof(f16788,plain,
spl104_641,
inference(avatar_split_clause,[],[f2850,f16786]) ).
fof(f16786,plain,
( spl104_641
<=> ! [X0,X3,X2,X1] :
( ~ c_Order__Relation_Opreorder__on(X3,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),c_Relation_ORange(X3,X3,X2),c_Relation_ODomain(X3,X3,X2)),X2)
| ~ c_member(X3,X1,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),c_Relation_ORange(X3,X3,X2),c_Relation_ODomain(X3,X3,X2)))
| ~ c_member(X3,X0,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),c_Relation_ORange(X3,X3,X2),c_Relation_ODomain(X3,X3,X2)))
| c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X0,X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),c_Relation_OImage(X3,X3,X2,c_Set_Oinsert(X3,X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)))),c_Relation_OImage(X3,X3,X2,c_Set_Oinsert(X3,X0,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_641])]) ).
fof(f2850,plain,
! [X2,X3,X0,X1] :
( ~ c_Order__Relation_Opreorder__on(X3,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),c_Relation_ORange(X3,X3,X2),c_Relation_ODomain(X3,X3,X2)),X2)
| ~ c_member(X3,X1,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),c_Relation_ORange(X3,X3,X2),c_Relation_ODomain(X3,X3,X2)))
| ~ c_member(X3,X0,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),c_Relation_ORange(X3,X3,X2),c_Relation_ODomain(X3,X3,X2)))
| c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X0,X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),c_Relation_OImage(X3,X3,X2,c_Set_Oinsert(X3,X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)))),c_Relation_OImage(X3,X3,X2,c_Set_Oinsert(X3,X0,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))))) ),
inference(forward_demodulation,[],[f2849,f2058]) ).
fof(f2849,plain,
! [X2,X3,X0,X1] :
( ~ c_member(X3,X1,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),c_Relation_ORange(X3,X3,X2),c_Relation_ODomain(X3,X3,X2)))
| ~ c_member(X3,X0,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),c_Relation_ORange(X3,X3,X2),c_Relation_ODomain(X3,X3,X2)))
| c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X0,X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),c_Relation_OImage(X3,X3,X2,c_Set_Oinsert(X3,X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)))),c_Relation_OImage(X3,X3,X2,c_Set_Oinsert(X3,X0,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)))))
| ~ c_Order__Relation_Opreorder__on(X3,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),c_Relation_ODomain(X3,X3,X2),c_Relation_ORange(X3,X3,X2)),X2) ),
inference(forward_demodulation,[],[f2848,f2058]) ).
fof(f2848,plain,
! [X2,X3,X0,X1] :
( ~ c_member(X3,X0,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),c_Relation_ORange(X3,X3,X2),c_Relation_ODomain(X3,X3,X2)))
| c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X0,X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),c_Relation_OImage(X3,X3,X2,c_Set_Oinsert(X3,X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)))),c_Relation_OImage(X3,X3,X2,c_Set_Oinsert(X3,X0,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)))))
| ~ c_member(X3,X1,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),c_Relation_ODomain(X3,X3,X2),c_Relation_ORange(X3,X3,X2)))
| ~ c_Order__Relation_Opreorder__on(X3,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),c_Relation_ODomain(X3,X3,X2),c_Relation_ORange(X3,X3,X2)),X2) ),
inference(forward_demodulation,[],[f2662,f2058]) ).
fof(f2662,plain,
! [X2,X3,X0,X1] :
( c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X0,X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),c_Relation_OImage(X3,X3,X2,c_Set_Oinsert(X3,X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)))),c_Relation_OImage(X3,X3,X2,c_Set_Oinsert(X3,X0,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)))))
| ~ c_member(X3,X0,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),c_Relation_ODomain(X3,X3,X2),c_Relation_ORange(X3,X3,X2)))
| ~ c_member(X3,X1,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),c_Relation_ODomain(X3,X3,X2),c_Relation_ORange(X3,X3,X2)))
| ~ c_Order__Relation_Opreorder__on(X3,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),c_Relation_ODomain(X3,X3,X2),c_Relation_ORange(X3,X3,X2)),X2) ),
inference(definition_unfolding,[],[f2377,f1954,f1954,f1954]) ).
fof(f2377,plain,
! [X2,X3,X0,X1] :
( c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X0,X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),c_Relation_OImage(X3,X3,X2,c_Set_Oinsert(X3,X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)))),c_Relation_OImage(X3,X3,X2,c_Set_Oinsert(X3,X0,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)))))
| ~ c_member(X3,X0,c_Relation_OField(X3,X2))
| ~ c_member(X3,X1,c_Relation_OField(X3,X2))
| ~ c_Order__Relation_Opreorder__on(X3,c_Relation_OField(X3,X2),X2) ),
inference(cnf_transformation,[],[f1707]) ).
fof(f1707,plain,
! [X0,X1,X2,X3] :
( ( ( c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),c_Relation_OImage(X3,X3,X2,c_Set_Oinsert(X3,X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)))),c_Relation_OImage(X3,X3,X2,c_Set_Oinsert(X3,X0,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)))))
| ~ c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X0,X1),X2) )
& ( c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X0,X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),c_Relation_OImage(X3,X3,X2,c_Set_Oinsert(X3,X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)))),c_Relation_OImage(X3,X3,X2,c_Set_Oinsert(X3,X0,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))))) ) )
| ~ c_member(X3,X0,c_Relation_OField(X3,X2))
| ~ c_member(X3,X1,c_Relation_OField(X3,X2))
| ~ c_Order__Relation_Opreorder__on(X3,c_Relation_OField(X3,X2),X2) ),
inference(nnf_transformation,[],[f1375]) ).
fof(f1375,plain,
! [X0,X1,X2,X3] :
( ( c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),c_Relation_OImage(X3,X3,X2,c_Set_Oinsert(X3,X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)))),c_Relation_OImage(X3,X3,X2,c_Set_Oinsert(X3,X0,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)))))
<=> c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X0,X1),X2) )
| ~ c_member(X3,X0,c_Relation_OField(X3,X2))
| ~ c_member(X3,X1,c_Relation_OField(X3,X2))
| ~ c_Order__Relation_Opreorder__on(X3,c_Relation_OField(X3,X2),X2) ),
inference(flattening,[],[f1374]) ).
fof(f1374,plain,
! [X0,X1,X2,X3] :
( ( c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),c_Relation_OImage(X3,X3,X2,c_Set_Oinsert(X3,X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)))),c_Relation_OImage(X3,X3,X2,c_Set_Oinsert(X3,X0,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)))))
<=> c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X0,X1),X2) )
| ~ c_member(X3,X0,c_Relation_OField(X3,X2))
| ~ c_member(X3,X1,c_Relation_OField(X3,X2))
| ~ c_Order__Relation_Opreorder__on(X3,c_Relation_OField(X3,X2),X2) ),
inference(ennf_transformation,[],[f889]) ).
fof(f889,plain,
! [X0,X1,X2,X3] :
( c_Order__Relation_Opreorder__on(X3,c_Relation_OField(X3,X2),X2)
=> ( c_member(X3,X1,c_Relation_OField(X3,X2))
=> ( c_member(X3,X0,c_Relation_OField(X3,X2))
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),c_Relation_OImage(X3,X3,X2,c_Set_Oinsert(X3,X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)))),c_Relation_OImage(X3,X3,X2,c_Set_Oinsert(X3,X0,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)))))
<=> c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X0,X1),X2) ) ) ) ),
inference(rectify,[],[f470]) ).
fof(f470,axiom,
! [X8,X9,X3,X4] :
( c_Order__Relation_Opreorder__on(X4,c_Relation_OField(X4,X3),X3)
=> ( c_member(X4,X9,c_Relation_OField(X4,X3))
=> ( c_member(X4,X8,c_Relation_OField(X4,X3))
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool),c_Relation_OImage(X4,X4,X3,c_Set_Oinsert(X4,X9,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))),c_Relation_OImage(X4,X4,X3,c_Set_Oinsert(X4,X8,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))))
<=> c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X8,X9),X3) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__Image1__Image1__iff) ).
fof(f16784,plain,
spl104_640,
inference(avatar_split_clause,[],[f2847,f16782]) ).
fof(f16782,plain,
( spl104_640
<=> ! [X0,X3,X2,X1] :
( ~ c_Order__Relation_Opreorder__on(X3,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),c_Relation_ORange(X3,X3,X2),c_Relation_ODomain(X3,X3,X2)),X2)
| ~ c_member(X3,X1,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),c_Relation_ORange(X3,X3,X2),c_Relation_ODomain(X3,X3,X2)))
| ~ c_member(X3,X0,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),c_Relation_ORange(X3,X3,X2),c_Relation_ODomain(X3,X3,X2)))
| c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),c_Relation_OImage(X3,X3,X2,c_Set_Oinsert(X3,X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)))),c_Relation_OImage(X3,X3,X2,c_Set_Oinsert(X3,X0,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)))))
| ~ c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_640])]) ).
fof(f2847,plain,
! [X2,X3,X0,X1] :
( ~ c_Order__Relation_Opreorder__on(X3,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),c_Relation_ORange(X3,X3,X2),c_Relation_ODomain(X3,X3,X2)),X2)
| ~ c_member(X3,X1,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),c_Relation_ORange(X3,X3,X2),c_Relation_ODomain(X3,X3,X2)))
| ~ c_member(X3,X0,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),c_Relation_ORange(X3,X3,X2),c_Relation_ODomain(X3,X3,X2)))
| c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),c_Relation_OImage(X3,X3,X2,c_Set_Oinsert(X3,X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)))),c_Relation_OImage(X3,X3,X2,c_Set_Oinsert(X3,X0,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)))))
| ~ c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X0,X1),X2) ),
inference(forward_demodulation,[],[f2846,f2058]) ).
fof(f2846,plain,
! [X2,X3,X0,X1] :
( ~ c_member(X3,X1,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),c_Relation_ORange(X3,X3,X2),c_Relation_ODomain(X3,X3,X2)))
| ~ c_member(X3,X0,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),c_Relation_ORange(X3,X3,X2),c_Relation_ODomain(X3,X3,X2)))
| c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),c_Relation_OImage(X3,X3,X2,c_Set_Oinsert(X3,X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)))),c_Relation_OImage(X3,X3,X2,c_Set_Oinsert(X3,X0,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)))))
| ~ c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X0,X1),X2)
| ~ c_Order__Relation_Opreorder__on(X3,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),c_Relation_ODomain(X3,X3,X2),c_Relation_ORange(X3,X3,X2)),X2) ),
inference(forward_demodulation,[],[f2845,f2058]) ).
fof(f2845,plain,
! [X2,X3,X0,X1] :
( ~ c_member(X3,X0,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),c_Relation_ORange(X3,X3,X2),c_Relation_ODomain(X3,X3,X2)))
| c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),c_Relation_OImage(X3,X3,X2,c_Set_Oinsert(X3,X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)))),c_Relation_OImage(X3,X3,X2,c_Set_Oinsert(X3,X0,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)))))
| ~ c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X0,X1),X2)
| ~ c_member(X3,X1,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),c_Relation_ODomain(X3,X3,X2),c_Relation_ORange(X3,X3,X2)))
| ~ c_Order__Relation_Opreorder__on(X3,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),c_Relation_ODomain(X3,X3,X2),c_Relation_ORange(X3,X3,X2)),X2) ),
inference(forward_demodulation,[],[f2661,f2058]) ).
fof(f2661,plain,
! [X2,X3,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),c_Relation_OImage(X3,X3,X2,c_Set_Oinsert(X3,X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)))),c_Relation_OImage(X3,X3,X2,c_Set_Oinsert(X3,X0,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)))))
| ~ c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X0,X1),X2)
| ~ c_member(X3,X0,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),c_Relation_ODomain(X3,X3,X2),c_Relation_ORange(X3,X3,X2)))
| ~ c_member(X3,X1,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),c_Relation_ODomain(X3,X3,X2),c_Relation_ORange(X3,X3,X2)))
| ~ c_Order__Relation_Opreorder__on(X3,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),c_Relation_ODomain(X3,X3,X2),c_Relation_ORange(X3,X3,X2)),X2) ),
inference(definition_unfolding,[],[f2378,f1954,f1954,f1954]) ).
fof(f2378,plain,
! [X2,X3,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),c_Relation_OImage(X3,X3,X2,c_Set_Oinsert(X3,X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)))),c_Relation_OImage(X3,X3,X2,c_Set_Oinsert(X3,X0,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)))))
| ~ c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X0,X1),X2)
| ~ c_member(X3,X0,c_Relation_OField(X3,X2))
| ~ c_member(X3,X1,c_Relation_OField(X3,X2))
| ~ c_Order__Relation_Opreorder__on(X3,c_Relation_OField(X3,X2),X2) ),
inference(cnf_transformation,[],[f1707]) ).
fof(f16780,plain,
spl104_639,
inference(avatar_split_clause,[],[f2361,f16778]) ).
fof(f16778,plain,
( spl104_639
<=> ! [X0,X3,X2,X1] :
( c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),X2,c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat),X1,X0)),c_FunDef_Omin__strict)
| ~ c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),X2,X0),c_FunDef_Omin__strict)
| ~ c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),X3,X1),c_FunDef_Opair__less)
| ~ c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat),X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_639])]) ).
fof(f2361,plain,
! [X2,X3,X0,X1] :
( c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),X2,c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat),X1,X0)),c_FunDef_Omin__strict)
| ~ c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),X2,X0),c_FunDef_Omin__strict)
| ~ c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),X3,X1),c_FunDef_Opair__less)
| ~ c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat),X3,X2) ),
inference(cnf_transformation,[],[f1347]) ).
fof(f1347,plain,
! [X0,X1,X2,X3] :
( c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),X2,c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat),X1,X0)),c_FunDef_Omin__strict)
| ~ c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),X2,X0),c_FunDef_Omin__strict)
| ~ c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),X3,X1),c_FunDef_Opair__less)
| ~ c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat),X3,X2) ),
inference(flattening,[],[f1346]) ).
fof(f1346,plain,
! [X0,X1,X2,X3] :
( c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),X2,c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat),X1,X0)),c_FunDef_Omin__strict)
| ~ c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),X2,X0),c_FunDef_Omin__strict)
| ~ c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),X3,X1),c_FunDef_Opair__less)
| ~ c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat),X3,X2) ),
inference(ennf_transformation,[],[f874]) ).
fof(f874,plain,
! [X0,X1,X2,X3] :
( c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat),X3,X2)
=> ( c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),X3,X1),c_FunDef_Opair__less)
=> ( c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),X2,X0),c_FunDef_Omin__strict)
=> c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),X2,c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat),X1,X0)),c_FunDef_Omin__strict) ) ) ),
inference(rectify,[],[f451]) ).
fof(f451,axiom,
! [X82,X12,X83,X13] :
( c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat),X13,X83)
=> ( c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),X13,X12),c_FunDef_Opair__less)
=> ( c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),X83,X82),c_FunDef_Omin__strict)
=> c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),X83,c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat),X12,X82)),c_FunDef_Omin__strict) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_smin__insertI) ).
fof(f16776,plain,
spl104_638,
inference(avatar_split_clause,[],[f2360,f16774]) ).
fof(f16774,plain,
( spl104_638
<=> ! [X0,X3,X2,X1] :
( c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat),X1,X0),X2),c_FunDef_Omax__strict)
| ~ c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),X0,X2),c_FunDef_Omax__strict)
| ~ c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),X1,X3),c_FunDef_Opair__less)
| ~ c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat),X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_638])]) ).
fof(f2360,plain,
! [X2,X3,X0,X1] :
( c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat),X1,X0),X2),c_FunDef_Omax__strict)
| ~ c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),X0,X2),c_FunDef_Omax__strict)
| ~ c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),X1,X3),c_FunDef_Opair__less)
| ~ c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat),X3,X2) ),
inference(cnf_transformation,[],[f1345]) ).
fof(f1345,plain,
! [X0,X1,X2,X3] :
( c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat),X1,X0),X2),c_FunDef_Omax__strict)
| ~ c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),X0,X2),c_FunDef_Omax__strict)
| ~ c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),X1,X3),c_FunDef_Opair__less)
| ~ c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat),X3,X2) ),
inference(flattening,[],[f1344]) ).
fof(f1344,plain,
! [X0,X1,X2,X3] :
( c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat),X1,X0),X2),c_FunDef_Omax__strict)
| ~ c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),X0,X2),c_FunDef_Omax__strict)
| ~ c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),X1,X3),c_FunDef_Opair__less)
| ~ c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat),X3,X2) ),
inference(ennf_transformation,[],[f873]) ).
fof(f873,plain,
! [X0,X1,X2,X3] :
( c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat),X3,X2)
=> ( c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),X1,X3),c_FunDef_Opair__less)
=> ( c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),X0,X2),c_FunDef_Omax__strict)
=> c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat),X1,X0),X2),c_FunDef_Omax__strict) ) ) ),
inference(rectify,[],[f450]) ).
fof(f450,axiom,
! [X80,X13,X81,X12] :
( c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat),X12,X81)
=> ( c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),X13,X12),c_FunDef_Opair__less)
=> ( c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),X80,X81),c_FunDef_Omax__strict)
=> c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat),X13,X80),X81),c_FunDef_Omax__strict) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_smax__insertI) ).
fof(f16772,plain,
spl104_637,
inference(avatar_split_clause,[],[f2359,f16770]) ).
fof(f16770,plain,
( spl104_637
<=> ! [X0,X3,X2,X1] :
( c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),X2,c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat),X1,X0)),c_FunDef_Omin__weak)
| ~ c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),X2,X0),c_FunDef_Omin__weak)
| ~ c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),X3,X1),c_FunDef_Opair__leq)
| ~ c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat),X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_637])]) ).
fof(f2359,plain,
! [X2,X3,X0,X1] :
( c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),X2,c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat),X1,X0)),c_FunDef_Omin__weak)
| ~ c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),X2,X0),c_FunDef_Omin__weak)
| ~ c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),X3,X1),c_FunDef_Opair__leq)
| ~ c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat),X3,X2) ),
inference(cnf_transformation,[],[f1343]) ).
fof(f1343,plain,
! [X0,X1,X2,X3] :
( c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),X2,c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat),X1,X0)),c_FunDef_Omin__weak)
| ~ c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),X2,X0),c_FunDef_Omin__weak)
| ~ c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),X3,X1),c_FunDef_Opair__leq)
| ~ c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat),X3,X2) ),
inference(flattening,[],[f1342]) ).
fof(f1342,plain,
! [X0,X1,X2,X3] :
( c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),X2,c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat),X1,X0)),c_FunDef_Omin__weak)
| ~ c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),X2,X0),c_FunDef_Omin__weak)
| ~ c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),X3,X1),c_FunDef_Opair__leq)
| ~ c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat),X3,X2) ),
inference(ennf_transformation,[],[f872]) ).
fof(f872,plain,
! [X0,X1,X2,X3] :
( c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat),X3,X2)
=> ( c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),X3,X1),c_FunDef_Opair__leq)
=> ( c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),X2,X0),c_FunDef_Omin__weak)
=> c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),X2,c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat),X1,X0)),c_FunDef_Omin__weak) ) ) ),
inference(rectify,[],[f457]) ).
fof(f457,axiom,
! [X82,X12,X83,X13] :
( c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat),X13,X83)
=> ( c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),X13,X12),c_FunDef_Opair__leq)
=> ( c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),X83,X82),c_FunDef_Omin__weak)
=> c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),X83,c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat),X12,X82)),c_FunDef_Omin__weak) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wmin__insertI) ).
fof(f16768,plain,
spl104_636,
inference(avatar_split_clause,[],[f2358,f16766]) ).
fof(f16766,plain,
( spl104_636
<=> ! [X0,X3,X2,X1] :
( c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat),X1,X0),X2),c_FunDef_Omax__weak)
| ~ c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),X0,X2),c_FunDef_Omax__weak)
| ~ c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),X1,X3),c_FunDef_Opair__leq)
| ~ c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat),X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_636])]) ).
fof(f2358,plain,
! [X2,X3,X0,X1] :
( c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat),X1,X0),X2),c_FunDef_Omax__weak)
| ~ c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),X0,X2),c_FunDef_Omax__weak)
| ~ c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),X1,X3),c_FunDef_Opair__leq)
| ~ c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat),X3,X2) ),
inference(cnf_transformation,[],[f1341]) ).
fof(f1341,plain,
! [X0,X1,X2,X3] :
( c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat),X1,X0),X2),c_FunDef_Omax__weak)
| ~ c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),X0,X2),c_FunDef_Omax__weak)
| ~ c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),X1,X3),c_FunDef_Opair__leq)
| ~ c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat),X3,X2) ),
inference(flattening,[],[f1340]) ).
fof(f1340,plain,
! [X0,X1,X2,X3] :
( c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat),X1,X0),X2),c_FunDef_Omax__weak)
| ~ c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),X0,X2),c_FunDef_Omax__weak)
| ~ c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),X1,X3),c_FunDef_Opair__leq)
| ~ c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat),X3,X2) ),
inference(ennf_transformation,[],[f871]) ).
fof(f871,plain,
! [X0,X1,X2,X3] :
( c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat),X3,X2)
=> ( c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),X1,X3),c_FunDef_Opair__leq)
=> ( c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),X0,X2),c_FunDef_Omax__weak)
=> c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat),X1,X0),X2),c_FunDef_Omax__weak) ) ) ),
inference(rectify,[],[f456]) ).
fof(f456,axiom,
! [X83,X13,X82,X12] :
( c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat),X12,X82)
=> ( c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),X13,X12),c_FunDef_Opair__leq)
=> ( c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),X83,X82),c_FunDef_Omax__weak)
=> c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat),X13,X83),X82),c_FunDef_Omax__weak) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wmax__insertI) ).
fof(f16764,plain,
( spl104_634
| ~ spl104_635
| ~ spl104_124
| ~ spl104_590 ),
inference(avatar_split_clause,[],[f16520,f13995,f3448,f16761,f16757]) ).
fof(f16757,plain,
( spl104_634
<=> c_Wellfounded_Oacyclic(tc_Arrow__Order__Mirabelle_Oalt,v_L) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_634])]) ).
fof(f16761,plain,
( spl104_635
<=> c_Relation_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,v_L) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_635])]) ).
fof(f13995,plain,
( spl104_590
<=> ! [X0,X1] :
( c_Wellfounded_Oacyclic(X0,X1)
| ~ c_Relation_Oirrefl(X0,c_Transitive__Closure_Otrancl(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_590])]) ).
fof(f16520,plain,
( ~ c_Relation_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,v_L)
| c_Wellfounded_Oacyclic(tc_Arrow__Order__Mirabelle_Oalt,v_L)
| ~ spl104_124
| ~ spl104_590 ),
inference(superposition,[],[f13996,f3450]) ).
fof(f13996,plain,
( ! [X0,X1] :
( ~ c_Relation_Oirrefl(X0,c_Transitive__Closure_Otrancl(X0,X1))
| c_Wellfounded_Oacyclic(X0,X1) )
| ~ spl104_590 ),
inference(avatar_component_clause,[],[f13995]) ).
fof(f16653,plain,
spl104_633,
inference(avatar_split_clause,[],[f2862,f16651]) ).
fof(f16651,plain,
( spl104_633
<=> ! [X6,X0,X3,X2,X1] :
( ~ c_Order__Relation_Opreorder__on(X3,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),c_Relation_ORange(X3,X3,X2),c_Relation_ODomain(X3,X3,X2)),X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X1,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),c_Relation_ORange(X3,X3,X2),c_Relation_ODomain(X3,X3,X2)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X0,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),c_Relation_ORange(X3,X3,X2),c_Relation_ODomain(X3,X3,X2)))
| c_member(X3,sK57(X0,X2,X3,X6),X0)
| ~ c_member(X3,X6,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),c_Relation_OImage(X3,X3,X2,X1),c_Relation_OImage(X3,X3,X2,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_633])]) ).
fof(f2862,plain,
! [X2,X3,X0,X1,X6] :
( ~ c_Order__Relation_Opreorder__on(X3,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),c_Relation_ORange(X3,X3,X2),c_Relation_ODomain(X3,X3,X2)),X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X1,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),c_Relation_ORange(X3,X3,X2),c_Relation_ODomain(X3,X3,X2)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X0,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),c_Relation_ORange(X3,X3,X2),c_Relation_ODomain(X3,X3,X2)))
| c_member(X3,sK57(X0,X2,X3,X6),X0)
| ~ c_member(X3,X6,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),c_Relation_OImage(X3,X3,X2,X1),c_Relation_OImage(X3,X3,X2,X0)) ),
inference(forward_demodulation,[],[f2861,f2058]) ).
fof(f2861,plain,
! [X2,X3,X0,X1,X6] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X1,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),c_Relation_ORange(X3,X3,X2),c_Relation_ODomain(X3,X3,X2)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X0,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),c_Relation_ORange(X3,X3,X2),c_Relation_ODomain(X3,X3,X2)))
| c_member(X3,sK57(X0,X2,X3,X6),X0)
| ~ c_member(X3,X6,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),c_Relation_OImage(X3,X3,X2,X1),c_Relation_OImage(X3,X3,X2,X0))
| ~ c_Order__Relation_Opreorder__on(X3,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),c_Relation_ODomain(X3,X3,X2),c_Relation_ORange(X3,X3,X2)),X2) ),
inference(forward_demodulation,[],[f2860,f2058]) ).
fof(f2860,plain,
! [X2,X3,X0,X1,X6] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X0,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),c_Relation_ORange(X3,X3,X2),c_Relation_ODomain(X3,X3,X2)))
| c_member(X3,sK57(X0,X2,X3,X6),X0)
| ~ c_member(X3,X6,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),c_Relation_OImage(X3,X3,X2,X1),c_Relation_OImage(X3,X3,X2,X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X1,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),c_Relation_ODomain(X3,X3,X2),c_Relation_ORange(X3,X3,X2)))
| ~ c_Order__Relation_Opreorder__on(X3,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),c_Relation_ODomain(X3,X3,X2),c_Relation_ORange(X3,X3,X2)),X2) ),
inference(forward_demodulation,[],[f2666,f2058]) ).
fof(f2666,plain,
! [X2,X3,X0,X1,X6] :
( c_member(X3,sK57(X0,X2,X3,X6),X0)
| ~ c_member(X3,X6,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),c_Relation_OImage(X3,X3,X2,X1),c_Relation_OImage(X3,X3,X2,X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X0,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),c_Relation_ODomain(X3,X3,X2),c_Relation_ORange(X3,X3,X2)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X1,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),c_Relation_ODomain(X3,X3,X2),c_Relation_ORange(X3,X3,X2)))
| ~ c_Order__Relation_Opreorder__on(X3,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),c_Relation_ODomain(X3,X3,X2),c_Relation_ORange(X3,X3,X2)),X2) ),
inference(definition_unfolding,[],[f2379,f1954,f1954,f1954]) ).
fof(f2379,plain,
! [X2,X3,X0,X1,X6] :
( c_member(X3,sK57(X0,X2,X3,X6),X0)
| ~ c_member(X3,X6,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),c_Relation_OImage(X3,X3,X2,X1),c_Relation_OImage(X3,X3,X2,X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X0,c_Relation_OField(X3,X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X1,c_Relation_OField(X3,X2))
| ~ c_Order__Relation_Opreorder__on(X3,c_Relation_OField(X3,X2),X2) ),
inference(cnf_transformation,[],[f1712]) ).
fof(f16534,plain,
spl104_632,
inference(avatar_split_clause,[],[f2865,f16532]) ).
fof(f16532,plain,
( spl104_632
<=> ! [X0,X3,X2,X1] :
( ~ c_Relation_Orefl__on(X3,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),c_Relation_ORange(X3,X3,X2),c_Relation_ODomain(X3,X3,X2)),X2)
| ~ c_member(X3,X1,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),c_Relation_ORange(X3,X3,X2),c_Relation_ODomain(X3,X3,X2)))
| ~ c_member(X3,X0,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),c_Relation_ORange(X3,X3,X2),c_Relation_ODomain(X3,X3,X2)))
| X0 = X1
| c_Relation_OImage(X3,X3,X2,c_Set_Oinsert(X3,X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)))) != c_Relation_OImage(X3,X3,X2,c_Set_Oinsert(X3,X0,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))))
| ~ c_Relation_Oantisym(X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_632])]) ).
fof(f2865,plain,
! [X2,X3,X0,X1] :
( ~ c_Relation_Orefl__on(X3,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),c_Relation_ORange(X3,X3,X2),c_Relation_ODomain(X3,X3,X2)),X2)
| ~ c_member(X3,X1,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),c_Relation_ORange(X3,X3,X2),c_Relation_ODomain(X3,X3,X2)))
| ~ c_member(X3,X0,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),c_Relation_ORange(X3,X3,X2),c_Relation_ODomain(X3,X3,X2)))
| X0 = X1
| c_Relation_OImage(X3,X3,X2,c_Set_Oinsert(X3,X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)))) != c_Relation_OImage(X3,X3,X2,c_Set_Oinsert(X3,X0,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))))
| ~ c_Relation_Oantisym(X3,X2) ),
inference(forward_demodulation,[],[f2864,f2058]) ).
fof(f2864,plain,
! [X2,X3,X0,X1] :
( ~ c_member(X3,X1,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),c_Relation_ORange(X3,X3,X2),c_Relation_ODomain(X3,X3,X2)))
| ~ c_member(X3,X0,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),c_Relation_ORange(X3,X3,X2),c_Relation_ODomain(X3,X3,X2)))
| X0 = X1
| c_Relation_OImage(X3,X3,X2,c_Set_Oinsert(X3,X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)))) != c_Relation_OImage(X3,X3,X2,c_Set_Oinsert(X3,X0,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))))
| ~ c_Relation_Oantisym(X3,X2)
| ~ c_Relation_Orefl__on(X3,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),c_Relation_ODomain(X3,X3,X2),c_Relation_ORange(X3,X3,X2)),X2) ),
inference(forward_demodulation,[],[f2863,f2058]) ).
fof(f2863,plain,
! [X2,X3,X0,X1] :
( ~ c_member(X3,X0,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),c_Relation_ORange(X3,X3,X2),c_Relation_ODomain(X3,X3,X2)))
| X0 = X1
| c_Relation_OImage(X3,X3,X2,c_Set_Oinsert(X3,X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)))) != c_Relation_OImage(X3,X3,X2,c_Set_Oinsert(X3,X0,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))))
| ~ c_member(X3,X1,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),c_Relation_ODomain(X3,X3,X2),c_Relation_ORange(X3,X3,X2)))
| ~ c_Relation_Oantisym(X3,X2)
| ~ c_Relation_Orefl__on(X3,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),c_Relation_ODomain(X3,X3,X2),c_Relation_ORange(X3,X3,X2)),X2) ),
inference(forward_demodulation,[],[f2668,f2058]) ).
fof(f2668,plain,
! [X2,X3,X0,X1] :
( X0 = X1
| c_Relation_OImage(X3,X3,X2,c_Set_Oinsert(X3,X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)))) != c_Relation_OImage(X3,X3,X2,c_Set_Oinsert(X3,X0,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))))
| ~ c_member(X3,X0,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),c_Relation_ODomain(X3,X3,X2),c_Relation_ORange(X3,X3,X2)))
| ~ c_member(X3,X1,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),c_Relation_ODomain(X3,X3,X2),c_Relation_ORange(X3,X3,X2)))
| ~ c_Relation_Oantisym(X3,X2)
| ~ c_Relation_Orefl__on(X3,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),c_Relation_ODomain(X3,X3,X2),c_Relation_ORange(X3,X3,X2)),X2) ),
inference(definition_unfolding,[],[f2383,f1954,f1954,f1954]) ).
fof(f2383,plain,
! [X2,X3,X0,X1] :
( X0 = X1
| c_Relation_OImage(X3,X3,X2,c_Set_Oinsert(X3,X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)))) != c_Relation_OImage(X3,X3,X2,c_Set_Oinsert(X3,X0,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))))
| ~ c_member(X3,X0,c_Relation_OField(X3,X2))
| ~ c_member(X3,X1,c_Relation_OField(X3,X2))
| ~ c_Relation_Oantisym(X3,X2)
| ~ c_Relation_Orefl__on(X3,c_Relation_OField(X3,X2),X2) ),
inference(cnf_transformation,[],[f1713]) ).
fof(f1713,plain,
! [X0,X1,X2,X3] :
( ( ( c_Relation_OImage(X3,X3,X2,c_Set_Oinsert(X3,X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)))) = c_Relation_OImage(X3,X3,X2,c_Set_Oinsert(X3,X0,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))))
| X0 != X1 )
& ( X0 = X1
| c_Relation_OImage(X3,X3,X2,c_Set_Oinsert(X3,X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)))) != c_Relation_OImage(X3,X3,X2,c_Set_Oinsert(X3,X0,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)))) ) )
| ~ c_member(X3,X0,c_Relation_OField(X3,X2))
| ~ c_member(X3,X1,c_Relation_OField(X3,X2))
| ~ c_Relation_Oantisym(X3,X2)
| ~ c_Relation_Orefl__on(X3,c_Relation_OField(X3,X2),X2) ),
inference(nnf_transformation,[],[f1379]) ).
fof(f1379,plain,
! [X0,X1,X2,X3] :
( ( c_Relation_OImage(X3,X3,X2,c_Set_Oinsert(X3,X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)))) = c_Relation_OImage(X3,X3,X2,c_Set_Oinsert(X3,X0,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))))
<=> X0 = X1 )
| ~ c_member(X3,X0,c_Relation_OField(X3,X2))
| ~ c_member(X3,X1,c_Relation_OField(X3,X2))
| ~ c_Relation_Oantisym(X3,X2)
| ~ c_Relation_Orefl__on(X3,c_Relation_OField(X3,X2),X2) ),
inference(flattening,[],[f1378]) ).
fof(f1378,plain,
! [X0,X1,X2,X3] :
( ( c_Relation_OImage(X3,X3,X2,c_Set_Oinsert(X3,X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)))) = c_Relation_OImage(X3,X3,X2,c_Set_Oinsert(X3,X0,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))))
<=> X0 = X1 )
| ~ c_member(X3,X0,c_Relation_OField(X3,X2))
| ~ c_member(X3,X1,c_Relation_OField(X3,X2))
| ~ c_Relation_Oantisym(X3,X2)
| ~ c_Relation_Orefl__on(X3,c_Relation_OField(X3,X2),X2) ),
inference(ennf_transformation,[],[f891]) ).
fof(f891,plain,
! [X0,X1,X2,X3] :
( c_Relation_Orefl__on(X3,c_Relation_OField(X3,X2),X2)
=> ( c_Relation_Oantisym(X3,X2)
=> ( c_member(X3,X1,c_Relation_OField(X3,X2))
=> ( c_member(X3,X0,c_Relation_OField(X3,X2))
=> ( c_Relation_OImage(X3,X3,X2,c_Set_Oinsert(X3,X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)))) = c_Relation_OImage(X3,X3,X2,c_Set_Oinsert(X3,X0,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))))
<=> X0 = X1 ) ) ) ) ),
inference(rectify,[],[f483]) ).
fof(f483,axiom,
! [X8,X9,X3,X4] :
( c_Relation_Orefl__on(X4,c_Relation_OField(X4,X3),X3)
=> ( c_Relation_Oantisym(X4,X3)
=> ( c_member(X4,X9,c_Relation_OField(X4,X3))
=> ( c_member(X4,X8,c_Relation_OField(X4,X3))
=> ( c_Relation_OImage(X4,X4,X3,c_Set_Oinsert(X4,X9,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))) = c_Relation_OImage(X4,X4,X3,c_Set_Oinsert(X4,X8,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))
<=> X8 = X9 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Refl__antisym__eq__Image1__Image1__iff) ).
fof(f16530,plain,
spl104_631,
inference(avatar_split_clause,[],[f2726,f16528]) ).
fof(f16528,plain,
( spl104_631
<=> ! [X2,X6,X4,X1,X0,X5,X3,X7] :
( hBOOL(hAPP(hAPP(X0,X5),X4))
| hBOOL(hAPP(hAPP(X0,sK102(X0,X1,X2,X3,X6,X7)),sK103(X0,X1,X2,X3,X6,X7)))
| ~ hBOOL(hAPP(hAPP(X0,X3),X2))
| ~ c_member(tc_prod(tc_prod(X7,X6),tc_prod(X7,X6)),c_Product__Type_OPair(tc_prod(X7,X6),tc_prod(X7,X6),c_Product__Type_OPair(X7,X6,X5,X4),c_Product__Type_OPair(X7,X6,X3,X2)),c_Transitive__Closure_Otrancl(tc_prod(X7,X6),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_prod(X7,X6),tc_prod(X7,X6)),tc_HOL_Obool),X1,c_Relation_OId(tc_prod(X7,X6))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_631])]) ).
fof(f2726,plain,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( hBOOL(hAPP(hAPP(X0,X5),X4))
| hBOOL(hAPP(hAPP(X0,sK102(X0,X1,X2,X3,X6,X7)),sK103(X0,X1,X2,X3,X6,X7)))
| ~ hBOOL(hAPP(hAPP(X0,X3),X2))
| ~ c_member(tc_prod(tc_prod(X7,X6),tc_prod(X7,X6)),c_Product__Type_OPair(tc_prod(X7,X6),tc_prod(X7,X6),c_Product__Type_OPair(X7,X6,X5,X4),c_Product__Type_OPair(X7,X6,X3,X2)),c_Transitive__Closure_Otrancl(tc_prod(X7,X6),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_prod(X7,X6),tc_prod(X7,X6)),tc_HOL_Obool),X1,c_Relation_OId(tc_prod(X7,X6))))) ),
inference(definition_unfolding,[],[f2627,f1949]) ).
fof(f2627,plain,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( hBOOL(hAPP(hAPP(X0,X5),X4))
| hBOOL(hAPP(hAPP(X0,sK102(X0,X1,X2,X3,X6,X7)),sK103(X0,X1,X2,X3,X6,X7)))
| ~ hBOOL(hAPP(hAPP(X0,X3),X2))
| ~ c_member(tc_prod(tc_prod(X7,X6),tc_prod(X7,X6)),c_Product__Type_OPair(tc_prod(X7,X6),tc_prod(X7,X6),c_Product__Type_OPair(X7,X6,X5,X4),c_Product__Type_OPair(X7,X6,X3,X2)),c_Transitive__Closure_Ortrancl(tc_prod(X7,X6),X1)) ),
inference(cnf_transformation,[],[f1849]) ).
fof(f16526,plain,
spl104_630,
inference(avatar_split_clause,[],[f2725,f16524]) ).
fof(f16524,plain,
( spl104_630
<=> ! [X2,X6,X4,X1,X0,X5,X3,X7] :
( hBOOL(hAPP(hAPP(X0,X5),X4))
| ~ hBOOL(hAPP(hAPP(X0,sK100(X0,X1,X2,X3,X6,X7)),sK101(X0,X1,X2,X3,X6,X7)))
| ~ hBOOL(hAPP(hAPP(X0,X3),X2))
| ~ c_member(tc_prod(tc_prod(X7,X6),tc_prod(X7,X6)),c_Product__Type_OPair(tc_prod(X7,X6),tc_prod(X7,X6),c_Product__Type_OPair(X7,X6,X5,X4),c_Product__Type_OPair(X7,X6,X3,X2)),c_Transitive__Closure_Otrancl(tc_prod(X7,X6),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_prod(X7,X6),tc_prod(X7,X6)),tc_HOL_Obool),X1,c_Relation_OId(tc_prod(X7,X6))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_630])]) ).
fof(f2725,plain,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( hBOOL(hAPP(hAPP(X0,X5),X4))
| ~ hBOOL(hAPP(hAPP(X0,sK100(X0,X1,X2,X3,X6,X7)),sK101(X0,X1,X2,X3,X6,X7)))
| ~ hBOOL(hAPP(hAPP(X0,X3),X2))
| ~ c_member(tc_prod(tc_prod(X7,X6),tc_prod(X7,X6)),c_Product__Type_OPair(tc_prod(X7,X6),tc_prod(X7,X6),c_Product__Type_OPair(X7,X6,X5,X4),c_Product__Type_OPair(X7,X6,X3,X2)),c_Transitive__Closure_Otrancl(tc_prod(X7,X6),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_prod(X7,X6),tc_prod(X7,X6)),tc_HOL_Obool),X1,c_Relation_OId(tc_prod(X7,X6))))) ),
inference(definition_unfolding,[],[f2628,f1949]) ).
fof(f2628,plain,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( hBOOL(hAPP(hAPP(X0,X5),X4))
| ~ hBOOL(hAPP(hAPP(X0,sK100(X0,X1,X2,X3,X6,X7)),sK101(X0,X1,X2,X3,X6,X7)))
| ~ hBOOL(hAPP(hAPP(X0,X3),X2))
| ~ c_member(tc_prod(tc_prod(X7,X6),tc_prod(X7,X6)),c_Product__Type_OPair(tc_prod(X7,X6),tc_prod(X7,X6),c_Product__Type_OPair(X7,X6,X5,X4),c_Product__Type_OPair(X7,X6,X3,X2)),c_Transitive__Closure_Ortrancl(tc_prod(X7,X6),X1)) ),
inference(cnf_transformation,[],[f1849]) ).
fof(f16515,plain,
spl104_629,
inference(avatar_split_clause,[],[f2722,f16513]) ).
fof(f16513,plain,
( spl104_629
<=> ! [X5,X6,X4,X1,X0,X3,X2,X7] :
( hBOOL(hAPP(hAPP(X0,X3),X2))
| hBOOL(hAPP(hAPP(X0,sK96(X0,X1,X4,X5,X6,X7)),sK97(X0,X1,X4,X5,X6,X7)))
| ~ hBOOL(hAPP(hAPP(X0,X5),X4))
| ~ c_member(tc_prod(tc_prod(X7,X6),tc_prod(X7,X6)),c_Product__Type_OPair(tc_prod(X7,X6),tc_prod(X7,X6),c_Product__Type_OPair(X7,X6,X5,X4),c_Product__Type_OPair(X7,X6,X3,X2)),c_Transitive__Closure_Otrancl(tc_prod(X7,X6),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_prod(X7,X6),tc_prod(X7,X6)),tc_HOL_Obool),X1,c_Relation_OId(tc_prod(X7,X6))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_629])]) ).
fof(f2722,plain,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( hBOOL(hAPP(hAPP(X0,X3),X2))
| hBOOL(hAPP(hAPP(X0,sK96(X0,X1,X4,X5,X6,X7)),sK97(X0,X1,X4,X5,X6,X7)))
| ~ hBOOL(hAPP(hAPP(X0,X5),X4))
| ~ c_member(tc_prod(tc_prod(X7,X6),tc_prod(X7,X6)),c_Product__Type_OPair(tc_prod(X7,X6),tc_prod(X7,X6),c_Product__Type_OPair(X7,X6,X5,X4),c_Product__Type_OPair(X7,X6,X3,X2)),c_Transitive__Closure_Otrancl(tc_prod(X7,X6),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_prod(X7,X6),tc_prod(X7,X6)),tc_HOL_Obool),X1,c_Relation_OId(tc_prod(X7,X6))))) ),
inference(definition_unfolding,[],[f2623,f1949]) ).
fof(f2623,plain,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( hBOOL(hAPP(hAPP(X0,X3),X2))
| hBOOL(hAPP(hAPP(X0,sK96(X0,X1,X4,X5,X6,X7)),sK97(X0,X1,X4,X5,X6,X7)))
| ~ hBOOL(hAPP(hAPP(X0,X5),X4))
| ~ c_member(tc_prod(tc_prod(X7,X6),tc_prod(X7,X6)),c_Product__Type_OPair(tc_prod(X7,X6),tc_prod(X7,X6),c_Product__Type_OPair(X7,X6,X5,X4),c_Product__Type_OPair(X7,X6,X3,X2)),c_Transitive__Closure_Ortrancl(tc_prod(X7,X6),X1)) ),
inference(cnf_transformation,[],[f1847]) ).
fof(f16511,plain,
spl104_628,
inference(avatar_split_clause,[],[f2721,f16509]) ).
fof(f16509,plain,
( spl104_628
<=> ! [X5,X6,X4,X1,X0,X3,X2,X7] :
( hBOOL(hAPP(hAPP(X0,X3),X2))
| ~ hBOOL(hAPP(hAPP(X0,sK98(X0,X1,X4,X5,X6,X7)),sK99(X0,X1,X4,X5,X6,X7)))
| ~ hBOOL(hAPP(hAPP(X0,X5),X4))
| ~ c_member(tc_prod(tc_prod(X7,X6),tc_prod(X7,X6)),c_Product__Type_OPair(tc_prod(X7,X6),tc_prod(X7,X6),c_Product__Type_OPair(X7,X6,X5,X4),c_Product__Type_OPair(X7,X6,X3,X2)),c_Transitive__Closure_Otrancl(tc_prod(X7,X6),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_prod(X7,X6),tc_prod(X7,X6)),tc_HOL_Obool),X1,c_Relation_OId(tc_prod(X7,X6))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_628])]) ).
fof(f2721,plain,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( hBOOL(hAPP(hAPP(X0,X3),X2))
| ~ hBOOL(hAPP(hAPP(X0,sK98(X0,X1,X4,X5,X6,X7)),sK99(X0,X1,X4,X5,X6,X7)))
| ~ hBOOL(hAPP(hAPP(X0,X5),X4))
| ~ c_member(tc_prod(tc_prod(X7,X6),tc_prod(X7,X6)),c_Product__Type_OPair(tc_prod(X7,X6),tc_prod(X7,X6),c_Product__Type_OPair(X7,X6,X5,X4),c_Product__Type_OPair(X7,X6,X3,X2)),c_Transitive__Closure_Otrancl(tc_prod(X7,X6),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_prod(X7,X6),tc_prod(X7,X6)),tc_HOL_Obool),X1,c_Relation_OId(tc_prod(X7,X6))))) ),
inference(definition_unfolding,[],[f2624,f1949]) ).
fof(f2624,plain,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( hBOOL(hAPP(hAPP(X0,X3),X2))
| ~ hBOOL(hAPP(hAPP(X0,sK98(X0,X1,X4,X5,X6,X7)),sK99(X0,X1,X4,X5,X6,X7)))
| ~ hBOOL(hAPP(hAPP(X0,X5),X4))
| ~ c_member(tc_prod(tc_prod(X7,X6),tc_prod(X7,X6)),c_Product__Type_OPair(tc_prod(X7,X6),tc_prod(X7,X6),c_Product__Type_OPair(X7,X6,X5,X4),c_Product__Type_OPair(X7,X6,X3,X2)),c_Transitive__Closure_Ortrancl(tc_prod(X7,X6),X1)) ),
inference(cnf_transformation,[],[f1847]) ).
fof(f16202,plain,
spl104_627,
inference(avatar_split_clause,[],[f2876,f16200]) ).
fof(f16200,plain,
( spl104_627
<=> ! [X2,X4,X0,X3,X1] :
( ~ c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,X2),c_Transitive__Closure_Otrancl(X4,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),X1,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),X0,c_Relation_OId(X4)))))
| c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,X2),c_Transitive__Closure_Otrancl(X4,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),X1,c_Relation_OId(X4))))
| c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,sK83(X0,X1,X3,X4)),c_Transitive__Closure_Otrancl(X4,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),X1,c_Relation_OId(X4)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_627])]) ).
fof(f2876,plain,
! [X2,X3,X0,X1,X4] :
( ~ c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,X2),c_Transitive__Closure_Otrancl(X4,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),X1,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),X0,c_Relation_OId(X4)))))
| c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,X2),c_Transitive__Closure_Otrancl(X4,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),X1,c_Relation_OId(X4))))
| c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,sK83(X0,X1,X3,X4)),c_Transitive__Closure_Otrancl(X4,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),X1,c_Relation_OId(X4)))) ),
inference(forward_demodulation,[],[f2718,f2272]) ).
fof(f2272,plain,
! [X2,X3,X0,X1] : c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),X2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),X1,X0)) = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),X2,X1),X0),
inference(cnf_transformation,[],[f798]) ).
fof(f798,plain,
! [X0,X1,X2,X3] : c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),X2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),X1,X0)) = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),X2,X1),X0),
inference(rectify,[],[f129]) ).
fof(f129,axiom,
! [X53,X10,X11,X4] : c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool),X11,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool),X10,X53)) = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool),X11,X10),X53),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__assoc) ).
fof(f2718,plain,
! [X2,X3,X0,X1,X4] :
( c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,X2),c_Transitive__Closure_Otrancl(X4,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),X1,c_Relation_OId(X4))))
| c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,sK83(X0,X1,X3,X4)),c_Transitive__Closure_Otrancl(X4,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),X1,c_Relation_OId(X4))))
| ~ c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,X2),c_Transitive__Closure_Otrancl(X4,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),X1,X0),c_Relation_OId(X4)))) ),
inference(definition_unfolding,[],[f2558,f1949,f1949,f1949]) ).
fof(f2558,plain,
! [X2,X3,X0,X1,X4] :
( c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,X2),c_Transitive__Closure_Ortrancl(X4,X1))
| c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,sK83(X0,X1,X3,X4)),c_Transitive__Closure_Ortrancl(X4,X1))
| ~ c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,X2),c_Transitive__Closure_Ortrancl(X4,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),X1,X0))) ),
inference(cnf_transformation,[],[f1807]) ).
fof(f1807,plain,
! [X0,X1,X2,X3,X4] :
( c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,X2),c_Transitive__Closure_Ortrancl(X4,X1))
| ( sK83(X0,X1,X3,X4) != sK84(X0,X1,X3,X4)
& c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,sK83(X0,X1,X3,X4),sK84(X0,X1,X3,X4)),X0)
& c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,sK83(X0,X1,X3,X4)),c_Transitive__Closure_Ortrancl(X4,X1)) )
| ~ c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,X2),c_Transitive__Closure_Ortrancl(X4,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),X1,X0))) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK83,sK84])],[f1492,f1806,f1805]) ).
fof(f1805,plain,
! [X0,X1,X3,X4] :
( ? [X5] :
( ? [X6] :
( X5 != X6
& c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X5,X6),X0) )
& c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,X5),c_Transitive__Closure_Ortrancl(X4,X1)) )
=> ( ? [X6] :
( sK83(X0,X1,X3,X4) != X6
& c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,sK83(X0,X1,X3,X4),X6),X0) )
& c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,sK83(X0,X1,X3,X4)),c_Transitive__Closure_Ortrancl(X4,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f1806,plain,
! [X0,X1,X3,X4] :
( ? [X6] :
( sK83(X0,X1,X3,X4) != X6
& c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,sK83(X0,X1,X3,X4),X6),X0) )
=> ( sK83(X0,X1,X3,X4) != sK84(X0,X1,X3,X4)
& c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,sK83(X0,X1,X3,X4),sK84(X0,X1,X3,X4)),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f1492,plain,
! [X0,X1,X2,X3,X4] :
( c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,X2),c_Transitive__Closure_Ortrancl(X4,X1))
| ? [X5] :
( ? [X6] :
( X5 != X6
& c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X5,X6),X0) )
& c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,X5),c_Transitive__Closure_Ortrancl(X4,X1)) )
| ~ c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,X2),c_Transitive__Closure_Ortrancl(X4,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),X1,X0))) ),
inference(flattening,[],[f1491]) ).
fof(f1491,plain,
! [X0,X1,X2,X3,X4] :
( c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,X2),c_Transitive__Closure_Ortrancl(X4,X1))
| ? [X5] :
( ? [X6] :
( X5 != X6
& c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X5,X6),X0) )
& c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,X5),c_Transitive__Closure_Ortrancl(X4,X1)) )
| ~ c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,X2),c_Transitive__Closure_Ortrancl(X4,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),X1,X0))) ),
inference(ennf_transformation,[],[f985]) ).
fof(f985,plain,
! [X0,X1,X2,X3,X4] :
( c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,X2),c_Transitive__Closure_Ortrancl(X4,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),X1,X0)))
=> ( ! [X5] :
( c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,X5),c_Transitive__Closure_Ortrancl(X4,X1))
=> ! [X6] :
( c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X5,X6),X0)
=> X5 = X6 ) )
=> c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,X2),c_Transitive__Closure_Ortrancl(X4,X1)) ) ),
inference(rectify,[],[f159]) ).
fof(f159,axiom,
! [X55,X17,X8,X9,X4] :
( c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X9,X8),c_Transitive__Closure_Ortrancl(X4,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),X17,X55)))
=> ( ! [X2] :
( c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X9,X2),c_Transitive__Closure_Ortrancl(X4,X17))
=> ! [X5] :
( c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X2,X5),X55)
=> X2 = X5 ) )
=> c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X9,X8),c_Transitive__Closure_Ortrancl(X4,X17)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__Un__separatorE) ).
fof(f16198,plain,
spl104_626,
inference(avatar_split_clause,[],[f2873,f16196]) ).
fof(f16196,plain,
( spl104_626
<=> ! [X2,X4,X0,X3,X1] :
( ~ c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,X2),c_Transitive__Closure_Otrancl(X4,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),X1,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),X0,c_Relation_OId(X4)))))
| c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,X2),c_Transitive__Closure_Otrancl(X4,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),X1,c_Relation_OId(X4))))
| c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,sK81(X0,X1,X2,X4),X2),c_Transitive__Closure_Otrancl(X4,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),X1,c_Relation_OId(X4)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_626])]) ).
fof(f2873,plain,
! [X2,X3,X0,X1,X4] :
( ~ c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,X2),c_Transitive__Closure_Otrancl(X4,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),X1,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),X0,c_Relation_OId(X4)))))
| c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,X2),c_Transitive__Closure_Otrancl(X4,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),X1,c_Relation_OId(X4))))
| c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,sK81(X0,X1,X2,X4),X2),c_Transitive__Closure_Otrancl(X4,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),X1,c_Relation_OId(X4)))) ),
inference(forward_demodulation,[],[f2715,f2272]) ).
fof(f2715,plain,
! [X2,X3,X0,X1,X4] :
( c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,X2),c_Transitive__Closure_Otrancl(X4,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),X1,c_Relation_OId(X4))))
| c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,sK81(X0,X1,X2,X4),X2),c_Transitive__Closure_Otrancl(X4,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),X1,c_Relation_OId(X4))))
| ~ c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,X2),c_Transitive__Closure_Otrancl(X4,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),X1,X0),c_Relation_OId(X4)))) ),
inference(definition_unfolding,[],[f2555,f1949,f1949,f1949]) ).
fof(f2555,plain,
! [X2,X3,X0,X1,X4] :
( c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,X2),c_Transitive__Closure_Ortrancl(X4,X1))
| c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,sK81(X0,X1,X2,X4),X2),c_Transitive__Closure_Ortrancl(X4,X1))
| ~ c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,X2),c_Transitive__Closure_Ortrancl(X4,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),X1,X0))) ),
inference(cnf_transformation,[],[f1804]) ).
fof(f1804,plain,
! [X0,X1,X2,X3,X4] :
( c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,X2),c_Transitive__Closure_Ortrancl(X4,X1))
| ( sK81(X0,X1,X2,X4) != sK82(X0,X1,X2,X4)
& c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,sK82(X0,X1,X2,X4),sK81(X0,X1,X2,X4)),X0)
& c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,sK81(X0,X1,X2,X4),X2),c_Transitive__Closure_Ortrancl(X4,X1)) )
| ~ c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,X2),c_Transitive__Closure_Ortrancl(X4,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),X1,X0))) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK81,sK82])],[f1490,f1803,f1802]) ).
fof(f1802,plain,
! [X0,X1,X2,X4] :
( ? [X5] :
( ? [X6] :
( X5 != X6
& c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X6,X5),X0) )
& c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X5,X2),c_Transitive__Closure_Ortrancl(X4,X1)) )
=> ( ? [X6] :
( sK81(X0,X1,X2,X4) != X6
& c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X6,sK81(X0,X1,X2,X4)),X0) )
& c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,sK81(X0,X1,X2,X4),X2),c_Transitive__Closure_Ortrancl(X4,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f1803,plain,
! [X0,X1,X2,X4] :
( ? [X6] :
( sK81(X0,X1,X2,X4) != X6
& c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X6,sK81(X0,X1,X2,X4)),X0) )
=> ( sK81(X0,X1,X2,X4) != sK82(X0,X1,X2,X4)
& c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,sK82(X0,X1,X2,X4),sK81(X0,X1,X2,X4)),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f1490,plain,
! [X0,X1,X2,X3,X4] :
( c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,X2),c_Transitive__Closure_Ortrancl(X4,X1))
| ? [X5] :
( ? [X6] :
( X5 != X6
& c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X6,X5),X0) )
& c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X5,X2),c_Transitive__Closure_Ortrancl(X4,X1)) )
| ~ c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,X2),c_Transitive__Closure_Ortrancl(X4,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),X1,X0))) ),
inference(flattening,[],[f1489]) ).
fof(f1489,plain,
! [X0,X1,X2,X3,X4] :
( c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,X2),c_Transitive__Closure_Ortrancl(X4,X1))
| ? [X5] :
( ? [X6] :
( X5 != X6
& c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X6,X5),X0) )
& c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X5,X2),c_Transitive__Closure_Ortrancl(X4,X1)) )
| ~ c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,X2),c_Transitive__Closure_Ortrancl(X4,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),X1,X0))) ),
inference(ennf_transformation,[],[f984]) ).
fof(f984,plain,
! [X0,X1,X2,X3,X4] :
( c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,X2),c_Transitive__Closure_Ortrancl(X4,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),X1,X0)))
=> ( ! [X5] :
( c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X5,X2),c_Transitive__Closure_Ortrancl(X4,X1))
=> ! [X6] :
( c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X6,X5),X0)
=> X5 = X6 ) )
=> c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,X2),c_Transitive__Closure_Ortrancl(X4,X1)) ) ),
inference(rectify,[],[f158]) ).
fof(f158,axiom,
! [X55,X17,X8,X9,X4] :
( c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X9,X8),c_Transitive__Closure_Ortrancl(X4,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),X17,X55)))
=> ( ! [X2] :
( c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X2,X8),c_Transitive__Closure_Ortrancl(X4,X17))
=> ! [X5] :
( c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X5,X2),X55)
=> X2 = X5 ) )
=> c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X9,X8),c_Transitive__Closure_Ortrancl(X4,X17)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__Un__separator__converseE) ).
fof(f16194,plain,
spl104_625,
inference(avatar_split_clause,[],[f2856,f16192]) ).
fof(f16192,plain,
( spl104_625
<=> ! [X0,X3,X2,X1] :
( ~ c_Order__Relation_Opreorder__on(X3,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),c_Relation_ORange(X3,X3,X2),c_Relation_ODomain(X3,X3,X2)),X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X1,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),c_Relation_ORange(X3,X3,X2),c_Relation_ODomain(X3,X3,X2)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X0,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),c_Relation_ORange(X3,X3,X2),c_Relation_ODomain(X3,X3,X2)))
| c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),c_Relation_OImage(X3,X3,X2,X1),c_Relation_OImage(X3,X3,X2,X0))
| c_member(X3,sK56(X0,X1,X2,X3),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_625])]) ).
fof(f2856,plain,
! [X2,X3,X0,X1] :
( ~ c_Order__Relation_Opreorder__on(X3,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),c_Relation_ORange(X3,X3,X2),c_Relation_ODomain(X3,X3,X2)),X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X1,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),c_Relation_ORange(X3,X3,X2),c_Relation_ODomain(X3,X3,X2)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X0,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),c_Relation_ORange(X3,X3,X2),c_Relation_ODomain(X3,X3,X2)))
| c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),c_Relation_OImage(X3,X3,X2,X1),c_Relation_OImage(X3,X3,X2,X0))
| c_member(X3,sK56(X0,X1,X2,X3),X1) ),
inference(forward_demodulation,[],[f2855,f2058]) ).
fof(f2855,plain,
! [X2,X3,X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X1,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),c_Relation_ORange(X3,X3,X2),c_Relation_ODomain(X3,X3,X2)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X0,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),c_Relation_ORange(X3,X3,X2),c_Relation_ODomain(X3,X3,X2)))
| c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),c_Relation_OImage(X3,X3,X2,X1),c_Relation_OImage(X3,X3,X2,X0))
| c_member(X3,sK56(X0,X1,X2,X3),X1)
| ~ c_Order__Relation_Opreorder__on(X3,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),c_Relation_ODomain(X3,X3,X2),c_Relation_ORange(X3,X3,X2)),X2) ),
inference(forward_demodulation,[],[f2854,f2058]) ).
fof(f2854,plain,
! [X2,X3,X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X0,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),c_Relation_ORange(X3,X3,X2),c_Relation_ODomain(X3,X3,X2)))
| c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),c_Relation_OImage(X3,X3,X2,X1),c_Relation_OImage(X3,X3,X2,X0))
| c_member(X3,sK56(X0,X1,X2,X3),X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X1,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),c_Relation_ODomain(X3,X3,X2),c_Relation_ORange(X3,X3,X2)))
| ~ c_Order__Relation_Opreorder__on(X3,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),c_Relation_ODomain(X3,X3,X2),c_Relation_ORange(X3,X3,X2)),X2) ),
inference(forward_demodulation,[],[f2664,f2058]) ).
fof(f2664,plain,
! [X2,X3,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),c_Relation_OImage(X3,X3,X2,X1),c_Relation_OImage(X3,X3,X2,X0))
| c_member(X3,sK56(X0,X1,X2,X3),X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X0,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),c_Relation_ODomain(X3,X3,X2),c_Relation_ORange(X3,X3,X2)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X1,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),c_Relation_ODomain(X3,X3,X2),c_Relation_ORange(X3,X3,X2)))
| ~ c_Order__Relation_Opreorder__on(X3,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),c_Relation_ODomain(X3,X3,X2),c_Relation_ORange(X3,X3,X2)),X2) ),
inference(definition_unfolding,[],[f2381,f1954,f1954,f1954]) ).
fof(f2381,plain,
! [X2,X3,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),c_Relation_OImage(X3,X3,X2,X1),c_Relation_OImage(X3,X3,X2,X0))
| c_member(X3,sK56(X0,X1,X2,X3),X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X0,c_Relation_OField(X3,X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X1,c_Relation_OField(X3,X2))
| ~ c_Order__Relation_Opreorder__on(X3,c_Relation_OField(X3,X2),X2) ),
inference(cnf_transformation,[],[f1712]) ).
fof(f16190,plain,
spl104_624,
inference(avatar_split_clause,[],[f2844,f16188]) ).
fof(f16188,plain,
( spl104_624
<=> ! [X0,X3,X2,X1] :
( ~ c_Order__Relation_Opartial__order__on(X3,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),c_Relation_ORange(X3,X3,X2),c_Relation_ODomain(X3,X3,X2)),X2)
| ~ c_member(X3,X1,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),c_Relation_ORange(X3,X3,X2),c_Relation_ODomain(X3,X3,X2)))
| ~ c_member(X3,X0,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),c_Relation_ORange(X3,X3,X2),c_Relation_ODomain(X3,X3,X2)))
| X0 = X1
| c_Relation_OImage(X3,X3,X2,c_Set_Oinsert(X3,X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)))) != c_Relation_OImage(X3,X3,X2,c_Set_Oinsert(X3,X0,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_624])]) ).
fof(f2844,plain,
! [X2,X3,X0,X1] :
( ~ c_Order__Relation_Opartial__order__on(X3,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),c_Relation_ORange(X3,X3,X2),c_Relation_ODomain(X3,X3,X2)),X2)
| ~ c_member(X3,X1,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),c_Relation_ORange(X3,X3,X2),c_Relation_ODomain(X3,X3,X2)))
| ~ c_member(X3,X0,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),c_Relation_ORange(X3,X3,X2),c_Relation_ODomain(X3,X3,X2)))
| X0 = X1
| c_Relation_OImage(X3,X3,X2,c_Set_Oinsert(X3,X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)))) != c_Relation_OImage(X3,X3,X2,c_Set_Oinsert(X3,X0,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)))) ),
inference(forward_demodulation,[],[f2843,f2058]) ).
fof(f2843,plain,
! [X2,X3,X0,X1] :
( ~ c_member(X3,X1,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),c_Relation_ORange(X3,X3,X2),c_Relation_ODomain(X3,X3,X2)))
| ~ c_member(X3,X0,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),c_Relation_ORange(X3,X3,X2),c_Relation_ODomain(X3,X3,X2)))
| X0 = X1
| c_Relation_OImage(X3,X3,X2,c_Set_Oinsert(X3,X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)))) != c_Relation_OImage(X3,X3,X2,c_Set_Oinsert(X3,X0,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))))
| ~ c_Order__Relation_Opartial__order__on(X3,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),c_Relation_ODomain(X3,X3,X2),c_Relation_ORange(X3,X3,X2)),X2) ),
inference(forward_demodulation,[],[f2842,f2058]) ).
fof(f2842,plain,
! [X2,X3,X0,X1] :
( ~ c_member(X3,X0,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),c_Relation_ORange(X3,X3,X2),c_Relation_ODomain(X3,X3,X2)))
| X0 = X1
| c_Relation_OImage(X3,X3,X2,c_Set_Oinsert(X3,X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)))) != c_Relation_OImage(X3,X3,X2,c_Set_Oinsert(X3,X0,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))))
| ~ c_member(X3,X1,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),c_Relation_ODomain(X3,X3,X2),c_Relation_ORange(X3,X3,X2)))
| ~ c_Order__Relation_Opartial__order__on(X3,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),c_Relation_ODomain(X3,X3,X2),c_Relation_ORange(X3,X3,X2)),X2) ),
inference(forward_demodulation,[],[f2660,f2058]) ).
fof(f2660,plain,
! [X2,X3,X0,X1] :
( X0 = X1
| c_Relation_OImage(X3,X3,X2,c_Set_Oinsert(X3,X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)))) != c_Relation_OImage(X3,X3,X2,c_Set_Oinsert(X3,X0,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))))
| ~ c_member(X3,X0,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),c_Relation_ODomain(X3,X3,X2),c_Relation_ORange(X3,X3,X2)))
| ~ c_member(X3,X1,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),c_Relation_ODomain(X3,X3,X2),c_Relation_ORange(X3,X3,X2)))
| ~ c_Order__Relation_Opartial__order__on(X3,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),c_Relation_ODomain(X3,X3,X2),c_Relation_ORange(X3,X3,X2)),X2) ),
inference(definition_unfolding,[],[f2375,f1954,f1954,f1954]) ).
fof(f2375,plain,
! [X2,X3,X0,X1] :
( X0 = X1
| c_Relation_OImage(X3,X3,X2,c_Set_Oinsert(X3,X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)))) != c_Relation_OImage(X3,X3,X2,c_Set_Oinsert(X3,X0,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))))
| ~ c_member(X3,X0,c_Relation_OField(X3,X2))
| ~ c_member(X3,X1,c_Relation_OField(X3,X2))
| ~ c_Order__Relation_Opartial__order__on(X3,c_Relation_OField(X3,X2),X2) ),
inference(cnf_transformation,[],[f1706]) ).
fof(f1706,plain,
! [X0,X1,X2,X3] :
( ( ( c_Relation_OImage(X3,X3,X2,c_Set_Oinsert(X3,X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)))) = c_Relation_OImage(X3,X3,X2,c_Set_Oinsert(X3,X0,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))))
| X0 != X1 )
& ( X0 = X1
| c_Relation_OImage(X3,X3,X2,c_Set_Oinsert(X3,X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)))) != c_Relation_OImage(X3,X3,X2,c_Set_Oinsert(X3,X0,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)))) ) )
| ~ c_member(X3,X0,c_Relation_OField(X3,X2))
| ~ c_member(X3,X1,c_Relation_OField(X3,X2))
| ~ c_Order__Relation_Opartial__order__on(X3,c_Relation_OField(X3,X2),X2) ),
inference(nnf_transformation,[],[f1373]) ).
fof(f1373,plain,
! [X0,X1,X2,X3] :
( ( c_Relation_OImage(X3,X3,X2,c_Set_Oinsert(X3,X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)))) = c_Relation_OImage(X3,X3,X2,c_Set_Oinsert(X3,X0,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))))
<=> X0 = X1 )
| ~ c_member(X3,X0,c_Relation_OField(X3,X2))
| ~ c_member(X3,X1,c_Relation_OField(X3,X2))
| ~ c_Order__Relation_Opartial__order__on(X3,c_Relation_OField(X3,X2),X2) ),
inference(flattening,[],[f1372]) ).
fof(f1372,plain,
! [X0,X1,X2,X3] :
( ( c_Relation_OImage(X3,X3,X2,c_Set_Oinsert(X3,X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)))) = c_Relation_OImage(X3,X3,X2,c_Set_Oinsert(X3,X0,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))))
<=> X0 = X1 )
| ~ c_member(X3,X0,c_Relation_OField(X3,X2))
| ~ c_member(X3,X1,c_Relation_OField(X3,X2))
| ~ c_Order__Relation_Opartial__order__on(X3,c_Relation_OField(X3,X2),X2) ),
inference(ennf_transformation,[],[f888]) ).
fof(f888,plain,
! [X0,X1,X2,X3] :
( c_Order__Relation_Opartial__order__on(X3,c_Relation_OField(X3,X2),X2)
=> ( c_member(X3,X1,c_Relation_OField(X3,X2))
=> ( c_member(X3,X0,c_Relation_OField(X3,X2))
=> ( c_Relation_OImage(X3,X3,X2,c_Set_Oinsert(X3,X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)))) = c_Relation_OImage(X3,X3,X2,c_Set_Oinsert(X3,X0,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))))
<=> X0 = X1 ) ) ) ),
inference(rectify,[],[f482]) ).
fof(f482,axiom,
! [X8,X9,X3,X4] :
( c_Order__Relation_Opartial__order__on(X4,c_Relation_OField(X4,X3),X3)
=> ( c_member(X4,X9,c_Relation_OField(X4,X3))
=> ( c_member(X4,X8,c_Relation_OField(X4,X3))
=> ( c_Relation_OImage(X4,X4,X3,c_Set_Oinsert(X4,X9,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))) = c_Relation_OImage(X4,X4,X3,c_Set_Oinsert(X4,X8,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))
<=> X8 = X9 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Partial__order__eq__Image1__Image1__iff) ).
fof(f15950,plain,
( spl104_623
| ~ spl104_194
| ~ spl104_620 ),
inference(avatar_split_clause,[],[f15936,f15931,f4024,f15947]) ).
fof(f15931,plain,
( spl104_620
<=> c_FunDef_Omin__weak = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool),c_Wellfounded_Omin__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__leq),c_Set_Oinsert(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_620])]) ).
fof(f15936,plain,
( c_FunDef_Omin__weak = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool),c_Wellfounded_Omin__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__leq),c_Set_Oinsert(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),c_Relation_OId__on(tc_Nat_Onat,c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),c_Relation_OId__on(tc_Nat_Onat,c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))),c_Relation_OId__on(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_HOL_Obool)))))
| ~ spl104_194
| ~ spl104_620 ),
inference(forward_demodulation,[],[f15935,f4025]) ).
fof(f15935,plain,
( c_FunDef_Omin__weak = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool),c_Wellfounded_Omin__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__leq),c_Set_Oinsert(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),c_Relation_OId__on(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_HOL_Obool)))))
| ~ spl104_194
| ~ spl104_620 ),
inference(forward_demodulation,[],[f15933,f4025]) ).
fof(f15933,plain,
( c_FunDef_Omin__weak = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool),c_Wellfounded_Omin__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__leq),c_Set_Oinsert(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool))))
| ~ spl104_620 ),
inference(avatar_component_clause,[],[f15931]) ).
fof(f15945,plain,
( spl104_622
| ~ spl104_194
| ~ spl104_619 ),
inference(avatar_split_clause,[],[f15929,f15924,f4024,f15942]) ).
fof(f15924,plain,
( spl104_619
<=> c_FunDef_Omax__weak = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool),c_Wellfounded_Omax__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__leq),c_Set_Oinsert(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_619])]) ).
fof(f15929,plain,
( c_FunDef_Omax__weak = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool),c_Wellfounded_Omax__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__leq),c_Set_Oinsert(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),c_Relation_OId__on(tc_Nat_Onat,c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),c_Relation_OId__on(tc_Nat_Onat,c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))),c_Relation_OId__on(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_HOL_Obool)))))
| ~ spl104_194
| ~ spl104_619 ),
inference(forward_demodulation,[],[f15928,f4025]) ).
fof(f15928,plain,
( c_FunDef_Omax__weak = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool),c_Wellfounded_Omax__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__leq),c_Set_Oinsert(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),c_Relation_OId__on(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_HOL_Obool)))))
| ~ spl104_194
| ~ spl104_619 ),
inference(forward_demodulation,[],[f15926,f4025]) ).
fof(f15926,plain,
( c_FunDef_Omax__weak = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool),c_Wellfounded_Omax__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__leq),c_Set_Oinsert(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool))))
| ~ spl104_619 ),
inference(avatar_component_clause,[],[f15924]) ).
fof(f15940,plain,
spl104_621,
inference(avatar_split_clause,[],[f2589,f15938]) ).
fof(f15938,plain,
( spl104_621
<=> ! [X3,X4,X0,X5,X2,X1] :
( c_member(tc_prod(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),c_Product__Type_OPair(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool),X4,X1),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool),X3,X0)),c_Wellfounded_Omax__ext(X5,X2))
| ~ c_member(tc_prod(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),c_Product__Type_OPair(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool),X1,X0),c_Wellfounded_Omax__ext(X5,X2))
| ~ c_member(tc_prod(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),c_Product__Type_OPair(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool),X4,X3),c_Wellfounded_Omax__ext(X5,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_621])]) ).
fof(f2589,plain,
! [X2,X3,X0,X1,X4,X5] :
( c_member(tc_prod(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),c_Product__Type_OPair(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool),X4,X1),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool),X3,X0)),c_Wellfounded_Omax__ext(X5,X2))
| ~ c_member(tc_prod(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),c_Product__Type_OPair(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool),X1,X0),c_Wellfounded_Omax__ext(X5,X2))
| ~ c_member(tc_prod(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),c_Product__Type_OPair(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool),X4,X3),c_Wellfounded_Omax__ext(X5,X2)) ),
inference(cnf_transformation,[],[f1509]) ).
fof(f1509,plain,
! [X0,X1,X2,X3,X4,X5] :
( c_member(tc_prod(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),c_Product__Type_OPair(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool),X4,X1),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool),X3,X0)),c_Wellfounded_Omax__ext(X5,X2))
| ~ c_member(tc_prod(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),c_Product__Type_OPair(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool),X1,X0),c_Wellfounded_Omax__ext(X5,X2))
| ~ c_member(tc_prod(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),c_Product__Type_OPair(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool),X4,X3),c_Wellfounded_Omax__ext(X5,X2)) ),
inference(flattening,[],[f1508]) ).
fof(f1508,plain,
! [X0,X1,X2,X3,X4,X5] :
( c_member(tc_prod(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),c_Product__Type_OPair(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool),X4,X1),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool),X3,X0)),c_Wellfounded_Omax__ext(X5,X2))
| ~ c_member(tc_prod(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),c_Product__Type_OPair(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool),X1,X0),c_Wellfounded_Omax__ext(X5,X2))
| ~ c_member(tc_prod(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),c_Product__Type_OPair(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool),X4,X3),c_Wellfounded_Omax__ext(X5,X2)) ),
inference(ennf_transformation,[],[f1002]) ).
fof(f1002,plain,
! [X0,X1,X2,X3,X4,X5] :
( c_member(tc_prod(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),c_Product__Type_OPair(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool),X4,X3),c_Wellfounded_Omax__ext(X5,X2))
=> ( c_member(tc_prod(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),c_Product__Type_OPair(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool),X1,X0),c_Wellfounded_Omax__ext(X5,X2))
=> c_member(tc_prod(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),c_Product__Type_OPair(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool),X4,X1),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool),X3,X0)),c_Wellfounded_Omax__ext(X5,X2)) ) ),
inference(rectify,[],[f464]) ).
fof(f464,axiom,
! [X65,X53,X14,X10,X11,X4] :
( c_member(tc_prod(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),c_Product__Type_OPair(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool),X11,X10),c_Wellfounded_Omax__ext(X4,X14))
=> ( c_member(tc_prod(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),c_Product__Type_OPair(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool),X53,X65),c_Wellfounded_Omax__ext(X4,X14))
=> c_member(tc_prod(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),c_Product__Type_OPair(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool),X11,X53),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool),X10,X65)),c_Wellfounded_Omax__ext(X4,X14)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_max__ext__additive) ).
fof(f15934,plain,
spl104_620,
inference(avatar_split_clause,[],[f1895,f15931]) ).
fof(f1895,plain,
c_FunDef_Omin__weak = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool),c_Wellfounded_Omin__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__leq),c_Set_Oinsert(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool)))),
inference(cnf_transformation,[],[f459]) ).
fof(f459,axiom,
c_FunDef_Omin__weak = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool),c_Wellfounded_Omin__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__leq),c_Set_Oinsert(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__weak__def) ).
fof(f15927,plain,
spl104_619,
inference(avatar_split_clause,[],[f1894,f15924]) ).
fof(f1894,plain,
c_FunDef_Omax__weak = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool),c_Wellfounded_Omax__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__leq),c_Set_Oinsert(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool)))),
inference(cnf_transformation,[],[f460]) ).
fof(f460,axiom,
c_FunDef_Omax__weak = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool),c_Wellfounded_Omax__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__leq),c_Set_Oinsert(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_max__weak__def) ).
fof(f15716,plain,
spl104_618,
inference(avatar_split_clause,[],[f2875,f15714]) ).
fof(f15714,plain,
( spl104_618
<=> ! [X2,X4,X0,X3,X1] :
( ~ c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,X2),c_Transitive__Closure_Otrancl(X4,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),X1,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),X0,c_Relation_OId(X4)))))
| c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,X2),c_Transitive__Closure_Otrancl(X4,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),X1,c_Relation_OId(X4))))
| c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,sK83(X0,X1,X3,X4),sK84(X0,X1,X3,X4)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_618])]) ).
fof(f2875,plain,
! [X2,X3,X0,X1,X4] :
( ~ c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,X2),c_Transitive__Closure_Otrancl(X4,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),X1,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),X0,c_Relation_OId(X4)))))
| c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,X2),c_Transitive__Closure_Otrancl(X4,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),X1,c_Relation_OId(X4))))
| c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,sK83(X0,X1,X3,X4),sK84(X0,X1,X3,X4)),X0) ),
inference(forward_demodulation,[],[f2717,f2272]) ).
fof(f2717,plain,
! [X2,X3,X0,X1,X4] :
( c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,X2),c_Transitive__Closure_Otrancl(X4,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),X1,c_Relation_OId(X4))))
| c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,sK83(X0,X1,X3,X4),sK84(X0,X1,X3,X4)),X0)
| ~ c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,X2),c_Transitive__Closure_Otrancl(X4,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),X1,X0),c_Relation_OId(X4)))) ),
inference(definition_unfolding,[],[f2559,f1949,f1949]) ).
fof(f2559,plain,
! [X2,X3,X0,X1,X4] :
( c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,X2),c_Transitive__Closure_Ortrancl(X4,X1))
| c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,sK83(X0,X1,X3,X4),sK84(X0,X1,X3,X4)),X0)
| ~ c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,X2),c_Transitive__Closure_Ortrancl(X4,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),X1,X0))) ),
inference(cnf_transformation,[],[f1807]) ).
fof(f15712,plain,
spl104_617,
inference(avatar_split_clause,[],[f2872,f15710]) ).
fof(f15710,plain,
( spl104_617
<=> ! [X2,X4,X0,X3,X1] :
( ~ c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,X2),c_Transitive__Closure_Otrancl(X4,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),X1,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),X0,c_Relation_OId(X4)))))
| c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,X2),c_Transitive__Closure_Otrancl(X4,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),X1,c_Relation_OId(X4))))
| c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,sK82(X0,X1,X2,X4),sK81(X0,X1,X2,X4)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_617])]) ).
fof(f2872,plain,
! [X2,X3,X0,X1,X4] :
( ~ c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,X2),c_Transitive__Closure_Otrancl(X4,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),X1,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),X0,c_Relation_OId(X4)))))
| c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,X2),c_Transitive__Closure_Otrancl(X4,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),X1,c_Relation_OId(X4))))
| c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,sK82(X0,X1,X2,X4),sK81(X0,X1,X2,X4)),X0) ),
inference(forward_demodulation,[],[f2714,f2272]) ).
fof(f2714,plain,
! [X2,X3,X0,X1,X4] :
( c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,X2),c_Transitive__Closure_Otrancl(X4,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),X1,c_Relation_OId(X4))))
| c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,sK82(X0,X1,X2,X4),sK81(X0,X1,X2,X4)),X0)
| ~ c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,X2),c_Transitive__Closure_Otrancl(X4,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),X1,X0),c_Relation_OId(X4)))) ),
inference(definition_unfolding,[],[f2556,f1949,f1949]) ).
fof(f2556,plain,
! [X2,X3,X0,X1,X4] :
( c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,X2),c_Transitive__Closure_Ortrancl(X4,X1))
| c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,sK82(X0,X1,X2,X4),sK81(X0,X1,X2,X4)),X0)
| ~ c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,X2),c_Transitive__Closure_Ortrancl(X4,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),X1,X0))) ),
inference(cnf_transformation,[],[f1804]) ).
fof(f15708,plain,
spl104_616,
inference(avatar_split_clause,[],[f2874,f15706]) ).
fof(f15706,plain,
( spl104_616
<=> ! [X2,X4,X0,X3,X1] :
( ~ c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,X2),c_Transitive__Closure_Otrancl(X4,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),X1,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),X0,c_Relation_OId(X4)))))
| c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,X2),c_Transitive__Closure_Otrancl(X4,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),X1,c_Relation_OId(X4))))
| sK83(X0,X1,X3,X4) != sK84(X0,X1,X3,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_616])]) ).
fof(f2874,plain,
! [X2,X3,X0,X1,X4] :
( ~ c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,X2),c_Transitive__Closure_Otrancl(X4,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),X1,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),X0,c_Relation_OId(X4)))))
| c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,X2),c_Transitive__Closure_Otrancl(X4,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),X1,c_Relation_OId(X4))))
| sK83(X0,X1,X3,X4) != sK84(X0,X1,X3,X4) ),
inference(forward_demodulation,[],[f2716,f2272]) ).
fof(f2716,plain,
! [X2,X3,X0,X1,X4] :
( c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,X2),c_Transitive__Closure_Otrancl(X4,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),X1,c_Relation_OId(X4))))
| sK83(X0,X1,X3,X4) != sK84(X0,X1,X3,X4)
| ~ c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,X2),c_Transitive__Closure_Otrancl(X4,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),X1,X0),c_Relation_OId(X4)))) ),
inference(definition_unfolding,[],[f2560,f1949,f1949]) ).
fof(f2560,plain,
! [X2,X3,X0,X1,X4] :
( c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,X2),c_Transitive__Closure_Ortrancl(X4,X1))
| sK83(X0,X1,X3,X4) != sK84(X0,X1,X3,X4)
| ~ c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,X2),c_Transitive__Closure_Ortrancl(X4,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),X1,X0))) ),
inference(cnf_transformation,[],[f1807]) ).
fof(f15704,plain,
spl104_615,
inference(avatar_split_clause,[],[f2871,f15702]) ).
fof(f15702,plain,
( spl104_615
<=> ! [X2,X4,X0,X3,X1] :
( ~ c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,X2),c_Transitive__Closure_Otrancl(X4,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),X1,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),X0,c_Relation_OId(X4)))))
| c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,X2),c_Transitive__Closure_Otrancl(X4,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),X1,c_Relation_OId(X4))))
| sK81(X0,X1,X2,X4) != sK82(X0,X1,X2,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_615])]) ).
fof(f2871,plain,
! [X2,X3,X0,X1,X4] :
( ~ c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,X2),c_Transitive__Closure_Otrancl(X4,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),X1,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),X0,c_Relation_OId(X4)))))
| c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,X2),c_Transitive__Closure_Otrancl(X4,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),X1,c_Relation_OId(X4))))
| sK81(X0,X1,X2,X4) != sK82(X0,X1,X2,X4) ),
inference(forward_demodulation,[],[f2713,f2272]) ).
fof(f2713,plain,
! [X2,X3,X0,X1,X4] :
( c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,X2),c_Transitive__Closure_Otrancl(X4,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),X1,c_Relation_OId(X4))))
| sK81(X0,X1,X2,X4) != sK82(X0,X1,X2,X4)
| ~ c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,X2),c_Transitive__Closure_Otrancl(X4,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),X1,X0),c_Relation_OId(X4)))) ),
inference(definition_unfolding,[],[f2557,f1949,f1949]) ).
fof(f2557,plain,
! [X2,X3,X0,X1,X4] :
( c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,X2),c_Transitive__Closure_Ortrancl(X4,X1))
| sK81(X0,X1,X2,X4) != sK82(X0,X1,X2,X4)
| ~ c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,X2),c_Transitive__Closure_Ortrancl(X4,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),X1,X0))) ),
inference(cnf_transformation,[],[f1804]) ).
fof(f15568,plain,
( spl104_614
| ~ spl104_366
| ~ spl104_457
| ~ spl104_458
| ~ spl104_464
| ~ spl104_613 ),
inference(avatar_split_clause,[],[f15564,f15560,f8651,f8627,f8621,f6457,f15566]) ).
fof(f15566,plain,
( spl104_614
<=> ! [X2,X0,X1] : c_Transitive__Closure_Otrancl(X2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),c_Relation_OId(X2),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),X1,X0))) = c_Transitive__Closure_Otrancl(X2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),c_Relation_OId(X2),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),c_Transitive__Closure_Otrancl(X2,X1),c_Transitive__Closure_Otrancl(X2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),X0,c_Relation_OId(X2)))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_614])]) ).
fof(f6457,plain,
( spl104_366
<=> ! [X2,X0,X1] : c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool),X1,X0) = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool),X1,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool),X1,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_366])]) ).
fof(f8621,plain,
( spl104_457
<=> ! [X0,X3,X2,X1] : c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),X2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),X1,X0)) = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),X1,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),X2,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_457])]) ).
fof(f8627,plain,
( spl104_458
<=> ! [X0,X3,X2,X1] : c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),X2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),X1,X0)) = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),X2,X1),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_458])]) ).
fof(f8651,plain,
( spl104_464
<=> ! [X0,X1] : c_Transitive__Closure_Otrancl(X1,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),X0,c_Relation_OId(X1))) = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),c_Transitive__Closure_Otrancl(X1,X0),c_Relation_OId(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_464])]) ).
fof(f15560,plain,
( spl104_613
<=> ! [X2,X0,X1] : c_Transitive__Closure_Otrancl(X2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),c_Relation_OId(X2),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),X1,X0))) = c_Transitive__Closure_Otrancl(X2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),c_Relation_OId(X2),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),c_Transitive__Closure_Otrancl(X2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),X1,c_Relation_OId(X2))),c_Transitive__Closure_Otrancl(X2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),X0,c_Relation_OId(X2)))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_613])]) ).
fof(f15564,plain,
( ! [X2,X0,X1] : c_Transitive__Closure_Otrancl(X2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),c_Relation_OId(X2),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),X1,X0))) = c_Transitive__Closure_Otrancl(X2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),c_Relation_OId(X2),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),c_Transitive__Closure_Otrancl(X2,X1),c_Transitive__Closure_Otrancl(X2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),X0,c_Relation_OId(X2))))))
| ~ spl104_366
| ~ spl104_457
| ~ spl104_458
| ~ spl104_464
| ~ spl104_613 ),
inference(forward_demodulation,[],[f15563,f6458]) ).
fof(f6458,plain,
( ! [X2,X0,X1] : c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool),X1,X0) = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool),X1,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool),X1,X0))
| ~ spl104_366 ),
inference(avatar_component_clause,[],[f6457]) ).
fof(f15563,plain,
( ! [X2,X0,X1] : c_Transitive__Closure_Otrancl(X2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),c_Relation_OId(X2),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),X1,X0))) = c_Transitive__Closure_Otrancl(X2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),c_Relation_OId(X2),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),c_Relation_OId(X2),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),c_Transitive__Closure_Otrancl(X2,X1),c_Transitive__Closure_Otrancl(X2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),X0,c_Relation_OId(X2)))))))
| ~ spl104_457
| ~ spl104_458
| ~ spl104_464
| ~ spl104_613 ),
inference(forward_demodulation,[],[f15561,f9204]) ).
fof(f9204,plain,
( ! [X2,X0,X1] : c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X0,X0),tc_HOL_Obool),c_Transitive__Closure_Otrancl(X0,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X0,X0),tc_HOL_Obool),X1,c_Relation_OId(X0))),X2) = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X0,X0),tc_HOL_Obool),c_Relation_OId(X0),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X0,X0),tc_HOL_Obool),c_Transitive__Closure_Otrancl(X0,X1),X2))
| ~ spl104_457
| ~ spl104_458
| ~ spl104_464 ),
inference(forward_demodulation,[],[f9177,f8622]) ).
fof(f8622,plain,
( ! [X2,X3,X0,X1] : c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),X2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),X1,X0)) = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),X1,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),X2,X0))
| ~ spl104_457 ),
inference(avatar_component_clause,[],[f8621]) ).
fof(f9177,plain,
( ! [X2,X0,X1] : c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X0,X0),tc_HOL_Obool),c_Transitive__Closure_Otrancl(X0,X1),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X0,X0),tc_HOL_Obool),c_Relation_OId(X0),X2)) = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X0,X0),tc_HOL_Obool),c_Transitive__Closure_Otrancl(X0,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X0,X0),tc_HOL_Obool),X1,c_Relation_OId(X0))),X2)
| ~ spl104_458
| ~ spl104_464 ),
inference(superposition,[],[f8628,f8652]) ).
fof(f8652,plain,
( ! [X0,X1] : c_Transitive__Closure_Otrancl(X1,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),X0,c_Relation_OId(X1))) = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),c_Transitive__Closure_Otrancl(X1,X0),c_Relation_OId(X1))
| ~ spl104_464 ),
inference(avatar_component_clause,[],[f8651]) ).
fof(f8628,plain,
( ! [X2,X3,X0,X1] : c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),X2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),X1,X0)) = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),X2,X1),X0)
| ~ spl104_458 ),
inference(avatar_component_clause,[],[f8627]) ).
fof(f15561,plain,
( ! [X2,X0,X1] : c_Transitive__Closure_Otrancl(X2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),c_Relation_OId(X2),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),X1,X0))) = c_Transitive__Closure_Otrancl(X2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),c_Relation_OId(X2),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),c_Transitive__Closure_Otrancl(X2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),X1,c_Relation_OId(X2))),c_Transitive__Closure_Otrancl(X2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),X0,c_Relation_OId(X2))))))
| ~ spl104_613 ),
inference(avatar_component_clause,[],[f15560]) ).
fof(f15562,plain,
spl104_613,
inference(avatar_split_clause,[],[f2833,f15560]) ).
fof(f2833,plain,
! [X2,X0,X1] : c_Transitive__Closure_Otrancl(X2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),c_Relation_OId(X2),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),X1,X0))) = c_Transitive__Closure_Otrancl(X2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),c_Relation_OId(X2),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),c_Transitive__Closure_Otrancl(X2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),X1,c_Relation_OId(X2))),c_Transitive__Closure_Otrancl(X2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),X0,c_Relation_OId(X2)))))),
inference(forward_demodulation,[],[f2832,f2058]) ).
fof(f2832,plain,
! [X2,X0,X1] : c_Transitive__Closure_Otrancl(X2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),c_Transitive__Closure_Otrancl(X2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),X1,c_Relation_OId(X2))),c_Transitive__Closure_Otrancl(X2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),X0,c_Relation_OId(X2)))),c_Relation_OId(X2))) = c_Transitive__Closure_Otrancl(X2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),c_Relation_OId(X2),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),X1,X0))),
inference(forward_demodulation,[],[f2650,f2058]) ).
fof(f2650,plain,
! [X2,X0,X1] : c_Transitive__Closure_Otrancl(X2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),c_Transitive__Closure_Otrancl(X2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),X1,c_Relation_OId(X2))),c_Transitive__Closure_Otrancl(X2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),X0,c_Relation_OId(X2)))),c_Relation_OId(X2))) = c_Transitive__Closure_Otrancl(X2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),X1,X0),c_Relation_OId(X2))),
inference(definition_unfolding,[],[f2067,f1949,f1949,f1949,f1949]) ).
fof(f2067,plain,
! [X2,X0,X1] : c_Transitive__Closure_Ortrancl(X2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),c_Transitive__Closure_Ortrancl(X2,X1),c_Transitive__Closure_Ortrancl(X2,X0))) = c_Transitive__Closure_Ortrancl(X2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),X1,X0)),
inference(cnf_transformation,[],[f665]) ).
fof(f665,plain,
! [X0,X1,X2] : c_Transitive__Closure_Ortrancl(X2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),c_Transitive__Closure_Ortrancl(X2,X1),c_Transitive__Closure_Ortrancl(X2,X0))) = c_Transitive__Closure_Ortrancl(X2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),X1,X0)),
inference(rectify,[],[f146]) ).
fof(f146,axiom,
! [X54,X14,X4] : c_Transitive__Closure_Ortrancl(X4,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),c_Transitive__Closure_Ortrancl(X4,X14),c_Transitive__Closure_Ortrancl(X4,X54))) = c_Transitive__Closure_Ortrancl(X4,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),X14,X54)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__Un__rtrancl) ).
fof(f15342,plain,
spl104_612,
inference(avatar_split_clause,[],[f2831,f15340]) ).
fof(f15340,plain,
( spl104_612
<=> ! [X2,X0,X1] : c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool),c_Relation_ORange(X2,X2,X1),c_Relation_ODomain(X2,X2,X1)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool),c_Relation_ORange(X2,X2,X0),c_Relation_ODomain(X2,X2,X0))) = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool),c_Relation_ORange(X2,X2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),X1,X0)),c_Relation_ODomain(X2,X2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),X1,X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_612])]) ).
fof(f2831,plain,
! [X2,X0,X1] : c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool),c_Relation_ORange(X2,X2,X1),c_Relation_ODomain(X2,X2,X1)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool),c_Relation_ORange(X2,X2,X0),c_Relation_ODomain(X2,X2,X0))) = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool),c_Relation_ORange(X2,X2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),X1,X0)),c_Relation_ODomain(X2,X2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),X1,X0))),
inference(forward_demodulation,[],[f2830,f2058]) ).
fof(f2830,plain,
! [X2,X0,X1] : c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool),c_Relation_ODomain(X2,X2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),X1,X0)),c_Relation_ORange(X2,X2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),X1,X0))) = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool),c_Relation_ORange(X2,X2,X1),c_Relation_ODomain(X2,X2,X1)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool),c_Relation_ORange(X2,X2,X0),c_Relation_ODomain(X2,X2,X0))),
inference(forward_demodulation,[],[f2829,f2058]) ).
fof(f2829,plain,
! [X2,X0,X1] : c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool),c_Relation_ODomain(X2,X2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),X1,X0)),c_Relation_ORange(X2,X2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),X1,X0))) = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool),c_Relation_ODomain(X2,X2,X1),c_Relation_ORange(X2,X2,X1)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool),c_Relation_ORange(X2,X2,X0),c_Relation_ODomain(X2,X2,X0))),
inference(forward_demodulation,[],[f2649,f2058]) ).
fof(f2649,plain,
! [X2,X0,X1] : c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool),c_Relation_ODomain(X2,X2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),X1,X0)),c_Relation_ORange(X2,X2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),X1,X0))) = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool),c_Relation_ODomain(X2,X2,X1),c_Relation_ORange(X2,X2,X1)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool),c_Relation_ODomain(X2,X2,X0),c_Relation_ORange(X2,X2,X0))),
inference(definition_unfolding,[],[f2066,f1954,f1954,f1954]) ).
fof(f2066,plain,
! [X2,X0,X1] : c_Relation_OField(X2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),X1,X0)) = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool),c_Relation_OField(X2,X1),c_Relation_OField(X2,X0)),
inference(cnf_transformation,[],[f664]) ).
fof(f664,plain,
! [X0,X1,X2] : c_Relation_OField(X2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),X1,X0)) = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool),c_Relation_OField(X2,X1),c_Relation_OField(X2,X0)),
inference(rectify,[],[f281]) ).
fof(f281,axiom,
! [X30,X3,X4] : c_Relation_OField(X4,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),X3,X30)) = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool),c_Relation_OField(X4,X3),c_Relation_OField(X4,X30)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Field__Un) ).
fof(f15126,plain,
( spl104_611
| ~ spl104_457
| ~ spl104_458
| ~ spl104_464
| ~ spl104_610 ),
inference(avatar_split_clause,[],[f14964,f14961,f8651,f8627,f8621,f15124]) ).
fof(f15124,plain,
( spl104_611
<=> ! [X2,X0,X1] : c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),c_Relation_OId(X2),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),c_Transitive__Closure_Otrancl(X2,X1),c_Transitive__Closure_Otrancl(X2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),X0,c_Relation_OId(X2))))),c_Transitive__Closure_Otrancl(X2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),c_Relation_OId(X2),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),X1,X0)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_611])]) ).
fof(f14961,plain,
( spl104_610
<=> ! [X2,X0,X1] : c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),c_Transitive__Closure_Otrancl(X2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),X1,c_Relation_OId(X2))),c_Transitive__Closure_Otrancl(X2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),X0,c_Relation_OId(X2)))),c_Transitive__Closure_Otrancl(X2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),c_Relation_OId(X2),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),X1,X0)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_610])]) ).
fof(f14964,plain,
( ! [X2,X0,X1] : c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),c_Relation_OId(X2),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),c_Transitive__Closure_Otrancl(X2,X1),c_Transitive__Closure_Otrancl(X2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),X0,c_Relation_OId(X2))))),c_Transitive__Closure_Otrancl(X2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),c_Relation_OId(X2),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),X1,X0))))
| ~ spl104_457
| ~ spl104_458
| ~ spl104_464
| ~ spl104_610 ),
inference(forward_demodulation,[],[f14962,f9204]) ).
fof(f14962,plain,
( ! [X2,X0,X1] : c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),c_Transitive__Closure_Otrancl(X2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),X1,c_Relation_OId(X2))),c_Transitive__Closure_Otrancl(X2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),X0,c_Relation_OId(X2)))),c_Transitive__Closure_Otrancl(X2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),c_Relation_OId(X2),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),X1,X0))))
| ~ spl104_610 ),
inference(avatar_component_clause,[],[f14961]) ).
fof(f14963,plain,
spl104_610,
inference(avatar_split_clause,[],[f2834,f14961]) ).
fof(f2834,plain,
! [X2,X0,X1] : c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),c_Transitive__Closure_Otrancl(X2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),X1,c_Relation_OId(X2))),c_Transitive__Closure_Otrancl(X2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),X0,c_Relation_OId(X2)))),c_Transitive__Closure_Otrancl(X2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),c_Relation_OId(X2),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),X1,X0)))),
inference(forward_demodulation,[],[f2651,f2058]) ).
fof(f2651,plain,
! [X2,X0,X1] : c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),c_Transitive__Closure_Otrancl(X2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),X1,c_Relation_OId(X2))),c_Transitive__Closure_Otrancl(X2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),X0,c_Relation_OId(X2)))),c_Transitive__Closure_Otrancl(X2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),X1,X0),c_Relation_OId(X2)))),
inference(definition_unfolding,[],[f2068,f1949,f1949,f1949]) ).
fof(f2068,plain,
! [X2,X0,X1] : c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),c_Transitive__Closure_Ortrancl(X2,X1),c_Transitive__Closure_Ortrancl(X2,X0)),c_Transitive__Closure_Ortrancl(X2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),X1,X0))),
inference(cnf_transformation,[],[f666]) ).
fof(f666,plain,
! [X0,X1,X2] : c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),c_Transitive__Closure_Ortrancl(X2,X1),c_Transitive__Closure_Ortrancl(X2,X0)),c_Transitive__Closure_Ortrancl(X2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),X1,X0))),
inference(rectify,[],[f280]) ).
fof(f280,axiom,
! [X54,X14,X4] : c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),c_Transitive__Closure_Ortrancl(X4,X14),c_Transitive__Closure_Ortrancl(X4,X54)),c_Transitive__Closure_Ortrancl(X4,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),X14,X54))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__Un__subset) ).
fof(f14959,plain,
spl104_609,
inference(avatar_split_clause,[],[f2707,f14957]) ).
fof(f14957,plain,
( spl104_609
<=> ! [X2,X4,X0,X3,X1] :
( hBOOL(hAPP(X0,X3))
| c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,sK80(X0,X1,X2,X4),X2),c_Transitive__Closure_Otrancl(X4,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),X1,c_Relation_OId(X4))))
| ~ hBOOL(hAPP(X0,X2))
| ~ c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,X2),c_Transitive__Closure_Otrancl(X4,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),X1,c_Relation_OId(X4)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_609])]) ).
fof(f2707,plain,
! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(X0,X3))
| c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,sK80(X0,X1,X2,X4),X2),c_Transitive__Closure_Otrancl(X4,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),X1,c_Relation_OId(X4))))
| ~ hBOOL(hAPP(X0,X2))
| ~ c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,X2),c_Transitive__Closure_Otrancl(X4,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),X1,c_Relation_OId(X4)))) ),
inference(definition_unfolding,[],[f2548,f1949,f1949]) ).
fof(f2548,plain,
! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(X0,X3))
| c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,sK80(X0,X1,X2,X4),X2),c_Transitive__Closure_Ortrancl(X4,X1))
| ~ hBOOL(hAPP(X0,X2))
| ~ c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,X2),c_Transitive__Closure_Ortrancl(X4,X1)) ),
inference(cnf_transformation,[],[f1801]) ).
fof(f1801,plain,
! [X0,X1,X2,X3,X4] :
( hBOOL(hAPP(X0,X3))
| ( ~ hBOOL(hAPP(X0,sK79(X0,X1,X2,X4)))
& hBOOL(hAPP(X0,sK80(X0,X1,X2,X4)))
& c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,sK80(X0,X1,X2,X4),X2),c_Transitive__Closure_Ortrancl(X4,X1))
& c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,sK79(X0,X1,X2,X4),sK80(X0,X1,X2,X4)),X1) )
| ~ hBOOL(hAPP(X0,X2))
| ~ c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,X2),c_Transitive__Closure_Ortrancl(X4,X1)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK79,sK80])],[f1480,f1800]) ).
fof(f1800,plain,
! [X0,X1,X2,X4] :
( ? [X5,X6] :
( ~ hBOOL(hAPP(X0,X5))
& hBOOL(hAPP(X0,X6))
& c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X6,X2),c_Transitive__Closure_Ortrancl(X4,X1))
& c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X5,X6),X1) )
=> ( ~ hBOOL(hAPP(X0,sK79(X0,X1,X2,X4)))
& hBOOL(hAPP(X0,sK80(X0,X1,X2,X4)))
& c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,sK80(X0,X1,X2,X4),X2),c_Transitive__Closure_Ortrancl(X4,X1))
& c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,sK79(X0,X1,X2,X4),sK80(X0,X1,X2,X4)),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f1480,plain,
! [X0,X1,X2,X3,X4] :
( hBOOL(hAPP(X0,X3))
| ? [X5,X6] :
( ~ hBOOL(hAPP(X0,X5))
& hBOOL(hAPP(X0,X6))
& c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X6,X2),c_Transitive__Closure_Ortrancl(X4,X1))
& c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X5,X6),X1) )
| ~ hBOOL(hAPP(X0,X2))
| ~ c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,X2),c_Transitive__Closure_Ortrancl(X4,X1)) ),
inference(flattening,[],[f1479]) ).
fof(f1479,plain,
! [X0,X1,X2,X3,X4] :
( hBOOL(hAPP(X0,X3))
| ? [X5,X6] :
( ~ hBOOL(hAPP(X0,X5))
& hBOOL(hAPP(X0,X6))
& c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X6,X2),c_Transitive__Closure_Ortrancl(X4,X1))
& c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X5,X6),X1) )
| ~ hBOOL(hAPP(X0,X2))
| ~ c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,X2),c_Transitive__Closure_Ortrancl(X4,X1)) ),
inference(ennf_transformation,[],[f979]) ).
fof(f979,plain,
! [X0,X1,X2,X3,X4] :
( c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,X2),c_Transitive__Closure_Ortrancl(X4,X1))
=> ( hBOOL(hAPP(X0,X2))
=> ( ! [X5,X6] :
( c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X5,X6),X1)
=> ( c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X6,X2),c_Transitive__Closure_Ortrancl(X4,X1))
=> ( hBOOL(hAPP(X0,X6))
=> hBOOL(hAPP(X0,X5)) ) ) )
=> hBOOL(hAPP(X0,X3)) ) ) ),
inference(rectify,[],[f74]) ).
fof(f74,axiom,
! [X17,X3,X8,X9,X4] :
( c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X9,X8),c_Transitive__Closure_Ortrancl(X4,X3))
=> ( hBOOL(hAPP(X17,X8))
=> ( ! [X5,X6] :
( c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X5,X6),X3)
=> ( c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X6,X8),c_Transitive__Closure_Ortrancl(X4,X3))
=> ( hBOOL(hAPP(X17,X6))
=> hBOOL(hAPP(X17,X5)) ) ) )
=> hBOOL(hAPP(X17,X9)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_converse__rtrancl__induct) ).
fof(f14955,plain,
spl104_608,
inference(avatar_split_clause,[],[f2704,f14953]) ).
fof(f14953,plain,
( spl104_608
<=> ! [X4,X0,X3,X2,X1] :
( hBOOL(hAPP(X0,X2))
| c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,sK77(X0,X1,X3,X4)),c_Transitive__Closure_Otrancl(X4,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),X1,c_Relation_OId(X4))))
| ~ hBOOL(hAPP(X0,X3))
| ~ c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,X2),c_Transitive__Closure_Otrancl(X4,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),X1,c_Relation_OId(X4)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_608])]) ).
fof(f2704,plain,
! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(X0,X2))
| c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,sK77(X0,X1,X3,X4)),c_Transitive__Closure_Otrancl(X4,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),X1,c_Relation_OId(X4))))
| ~ hBOOL(hAPP(X0,X3))
| ~ c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,X2),c_Transitive__Closure_Otrancl(X4,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),X1,c_Relation_OId(X4)))) ),
inference(definition_unfolding,[],[f2543,f1949,f1949]) ).
fof(f2543,plain,
! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(X0,X2))
| c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,sK77(X0,X1,X3,X4)),c_Transitive__Closure_Ortrancl(X4,X1))
| ~ hBOOL(hAPP(X0,X3))
| ~ c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,X2),c_Transitive__Closure_Ortrancl(X4,X1)) ),
inference(cnf_transformation,[],[f1799]) ).
fof(f1799,plain,
! [X0,X1,X2,X3,X4] :
( hBOOL(hAPP(X0,X2))
| ( ~ hBOOL(hAPP(X0,sK78(X0,X1,X3,X4)))
& hBOOL(hAPP(X0,sK77(X0,X1,X3,X4)))
& c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,sK77(X0,X1,X3,X4),sK78(X0,X1,X3,X4)),X1)
& c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,sK77(X0,X1,X3,X4)),c_Transitive__Closure_Ortrancl(X4,X1)) )
| ~ hBOOL(hAPP(X0,X3))
| ~ c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,X2),c_Transitive__Closure_Ortrancl(X4,X1)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK77,sK78])],[f1478,f1798,f1797]) ).
fof(f1797,plain,
! [X0,X1,X3,X4] :
( ? [X5] :
( ? [X6] :
( ~ hBOOL(hAPP(X0,X6))
& hBOOL(hAPP(X0,X5))
& c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X5,X6),X1) )
& c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,X5),c_Transitive__Closure_Ortrancl(X4,X1)) )
=> ( ? [X6] :
( ~ hBOOL(hAPP(X0,X6))
& hBOOL(hAPP(X0,sK77(X0,X1,X3,X4)))
& c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,sK77(X0,X1,X3,X4),X6),X1) )
& c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,sK77(X0,X1,X3,X4)),c_Transitive__Closure_Ortrancl(X4,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f1798,plain,
! [X0,X1,X3,X4] :
( ? [X6] :
( ~ hBOOL(hAPP(X0,X6))
& hBOOL(hAPP(X0,sK77(X0,X1,X3,X4)))
& c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,sK77(X0,X1,X3,X4),X6),X1) )
=> ( ~ hBOOL(hAPP(X0,sK78(X0,X1,X3,X4)))
& hBOOL(hAPP(X0,sK77(X0,X1,X3,X4)))
& c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,sK77(X0,X1,X3,X4),sK78(X0,X1,X3,X4)),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f1478,plain,
! [X0,X1,X2,X3,X4] :
( hBOOL(hAPP(X0,X2))
| ? [X5] :
( ? [X6] :
( ~ hBOOL(hAPP(X0,X6))
& hBOOL(hAPP(X0,X5))
& c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X5,X6),X1) )
& c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,X5),c_Transitive__Closure_Ortrancl(X4,X1)) )
| ~ hBOOL(hAPP(X0,X3))
| ~ c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,X2),c_Transitive__Closure_Ortrancl(X4,X1)) ),
inference(flattening,[],[f1477]) ).
fof(f1477,plain,
! [X0,X1,X2,X3,X4] :
( hBOOL(hAPP(X0,X2))
| ? [X5] :
( ? [X6] :
( ~ hBOOL(hAPP(X0,X6))
& hBOOL(hAPP(X0,X5))
& c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X5,X6),X1) )
& c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,X5),c_Transitive__Closure_Ortrancl(X4,X1)) )
| ~ hBOOL(hAPP(X0,X3))
| ~ c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,X2),c_Transitive__Closure_Ortrancl(X4,X1)) ),
inference(ennf_transformation,[],[f978]) ).
fof(f978,plain,
! [X0,X1,X2,X3,X4] :
( c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,X2),c_Transitive__Closure_Ortrancl(X4,X1))
=> ( hBOOL(hAPP(X0,X3))
=> ( ! [X5] :
( c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,X5),c_Transitive__Closure_Ortrancl(X4,X1))
=> ! [X6] :
( c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X5,X6),X1)
=> ( hBOOL(hAPP(X0,X5))
=> hBOOL(hAPP(X0,X6)) ) ) )
=> hBOOL(hAPP(X0,X2)) ) ) ),
inference(rectify,[],[f75]) ).
fof(f75,axiom,
! [X17,X3,X8,X9,X4] :
( c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X9,X8),c_Transitive__Closure_Ortrancl(X4,X3))
=> ( hBOOL(hAPP(X17,X9))
=> ( ! [X5] :
( c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X9,X5),c_Transitive__Closure_Ortrancl(X4,X3))
=> ! [X6] :
( c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X5,X6),X3)
=> ( hBOOL(hAPP(X17,X5))
=> hBOOL(hAPP(X17,X6)) ) ) )
=> hBOOL(hAPP(X17,X8)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__induct) ).
fof(f14780,plain,
spl104_607,
inference(avatar_split_clause,[],[f2710,f14778]) ).
fof(f14778,plain,
( spl104_607
<=> ! [X2,X4,X0,X3,X1] :
( c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,X0),c_Transitive__Closure_Otrancl(X4,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),X1,c_Relation_OId(X4))))
| ~ c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X2,X0),X1)
| ~ c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,X2),c_Transitive__Closure_Otrancl(X4,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),X1,c_Relation_OId(X4)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_607])]) ).
fof(f2710,plain,
! [X2,X3,X0,X1,X4] :
( c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,X0),c_Transitive__Closure_Otrancl(X4,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),X1,c_Relation_OId(X4))))
| ~ c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X2,X0),X1)
| ~ c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,X2),c_Transitive__Closure_Otrancl(X4,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),X1,c_Relation_OId(X4)))) ),
inference(definition_unfolding,[],[f2552,f1949,f1949]) ).
fof(f2552,plain,
! [X2,X3,X0,X1,X4] :
( c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,X0),c_Transitive__Closure_Ortrancl(X4,X1))
| ~ c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X2,X0),X1)
| ~ c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,X2),c_Transitive__Closure_Ortrancl(X4,X1)) ),
inference(cnf_transformation,[],[f1484]) ).
fof(f1484,plain,
! [X0,X1,X2,X3,X4] :
( c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,X0),c_Transitive__Closure_Ortrancl(X4,X1))
| ~ c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X2,X0),X1)
| ~ c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,X2),c_Transitive__Closure_Ortrancl(X4,X1)) ),
inference(flattening,[],[f1483]) ).
fof(f1483,plain,
! [X0,X1,X2,X3,X4] :
( c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,X0),c_Transitive__Closure_Ortrancl(X4,X1))
| ~ c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X2,X0),X1)
| ~ c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,X2),c_Transitive__Closure_Ortrancl(X4,X1)) ),
inference(ennf_transformation,[],[f981]) ).
fof(f981,plain,
! [X0,X1,X2,X3,X4] :
( c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,X2),c_Transitive__Closure_Ortrancl(X4,X1))
=> ( c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X2,X0),X1)
=> c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,X0),c_Transitive__Closure_Ortrancl(X4,X1)) ) ),
inference(rectify,[],[f64]) ).
fof(f64,axiom,
! [X7,X3,X8,X9,X4] :
( c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X9,X8),c_Transitive__Closure_Ortrancl(X4,X3))
=> ( c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X8,X7),X3)
=> c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X9,X7),c_Transitive__Closure_Ortrancl(X4,X3)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl_Ortrancl__into__rtrancl) ).
fof(f14776,plain,
spl104_606,
inference(avatar_split_clause,[],[f2699,f14774]) ).
fof(f14774,plain,
( spl104_606
<=> ! [X2,X4,X0,X3,X1] :
( c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,X0),c_Transitive__Closure_Otrancl(X4,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),X1,c_Relation_OId(X4))))
| ~ c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X2,X0),c_Transitive__Closure_Otrancl(X4,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),X1,c_Relation_OId(X4))))
| ~ c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_606])]) ).
fof(f2699,plain,
! [X2,X3,X0,X1,X4] :
( c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,X0),c_Transitive__Closure_Otrancl(X4,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),X1,c_Relation_OId(X4))))
| ~ c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X2,X0),c_Transitive__Closure_Otrancl(X4,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),X1,c_Relation_OId(X4))))
| ~ c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,X2),X1) ),
inference(definition_unfolding,[],[f2539,f1949,f1949]) ).
fof(f2539,plain,
! [X2,X3,X0,X1,X4] :
( c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,X0),c_Transitive__Closure_Ortrancl(X4,X1))
| ~ c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X2,X0),c_Transitive__Closure_Ortrancl(X4,X1))
| ~ c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,X2),X1) ),
inference(cnf_transformation,[],[f1470]) ).
fof(f1470,plain,
! [X0,X1,X2,X3,X4] :
( c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,X0),c_Transitive__Closure_Ortrancl(X4,X1))
| ~ c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X2,X0),c_Transitive__Closure_Ortrancl(X4,X1))
| ~ c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,X2),X1) ),
inference(flattening,[],[f1469]) ).
fof(f1469,plain,
! [X0,X1,X2,X3,X4] :
( c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,X0),c_Transitive__Closure_Ortrancl(X4,X1))
| ~ c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X2,X0),c_Transitive__Closure_Ortrancl(X4,X1))
| ~ c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,X2),X1) ),
inference(ennf_transformation,[],[f974]) ).
fof(f974,plain,
! [X0,X1,X2,X3,X4] :
( c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,X2),X1)
=> ( c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X2,X0),c_Transitive__Closure_Ortrancl(X4,X1))
=> c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,X0),c_Transitive__Closure_Ortrancl(X4,X1)) ) ),
inference(rectify,[],[f63]) ).
fof(f63,axiom,
! [X7,X3,X8,X9,X4] :
( c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X9,X8),X3)
=> ( c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X8,X7),c_Transitive__Closure_Ortrancl(X4,X3))
=> c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X9,X7),c_Transitive__Closure_Ortrancl(X4,X3)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_converse__rtrancl__into__rtrancl) ).
fof(f14772,plain,
spl104_605,
inference(avatar_split_clause,[],[f2630,f14770]) ).
fof(f14770,plain,
( spl104_605
<=> ! [X5,X3,X4,X0,X7,X6,X2,X1] :
( c_member(tc_prod(X6,X6),c_Product__Type_OPair(X6,X6,X4,X2),X0)
| c_member(tc_prod(X7,X7),c_Product__Type_OPair(X7,X7,X5,X3),X1)
| ~ c_member(tc_prod(tc_prod(X7,X6),tc_prod(X7,X6)),c_Product__Type_OPair(tc_prod(X7,X6),tc_prod(X7,X6),c_Product__Type_OPair(X7,X6,X5,X4),c_Product__Type_OPair(X7,X6,X3,X2)),c_Wellfounded_Olex__prod(X7,X6,X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_605])]) ).
fof(f2630,plain,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( c_member(tc_prod(X6,X6),c_Product__Type_OPair(X6,X6,X4,X2),X0)
| c_member(tc_prod(X7,X7),c_Product__Type_OPair(X7,X7,X5,X3),X1)
| ~ c_member(tc_prod(tc_prod(X7,X6),tc_prod(X7,X6)),c_Product__Type_OPair(tc_prod(X7,X6),tc_prod(X7,X6),c_Product__Type_OPair(X7,X6,X5,X4),c_Product__Type_OPair(X7,X6,X3,X2)),c_Wellfounded_Olex__prod(X7,X6,X1,X0)) ),
inference(cnf_transformation,[],[f1851]) ).
fof(f1851,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( ( c_member(tc_prod(tc_prod(X7,X6),tc_prod(X7,X6)),c_Product__Type_OPair(tc_prod(X7,X6),tc_prod(X7,X6),c_Product__Type_OPair(X7,X6,X5,X4),c_Product__Type_OPair(X7,X6,X3,X2)),c_Wellfounded_Olex__prod(X7,X6,X1,X0))
| ( ( ~ c_member(tc_prod(X6,X6),c_Product__Type_OPair(X6,X6,X4,X2),X0)
| X3 != X5 )
& ~ c_member(tc_prod(X7,X7),c_Product__Type_OPair(X7,X7,X5,X3),X1) ) )
& ( ( c_member(tc_prod(X6,X6),c_Product__Type_OPair(X6,X6,X4,X2),X0)
& X3 = X5 )
| c_member(tc_prod(X7,X7),c_Product__Type_OPair(X7,X7,X5,X3),X1)
| ~ c_member(tc_prod(tc_prod(X7,X6),tc_prod(X7,X6)),c_Product__Type_OPair(tc_prod(X7,X6),tc_prod(X7,X6),c_Product__Type_OPair(X7,X6,X5,X4),c_Product__Type_OPair(X7,X6,X3,X2)),c_Wellfounded_Olex__prod(X7,X6,X1,X0)) ) ),
inference(flattening,[],[f1850]) ).
fof(f1850,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( ( c_member(tc_prod(tc_prod(X7,X6),tc_prod(X7,X6)),c_Product__Type_OPair(tc_prod(X7,X6),tc_prod(X7,X6),c_Product__Type_OPair(X7,X6,X5,X4),c_Product__Type_OPair(X7,X6,X3,X2)),c_Wellfounded_Olex__prod(X7,X6,X1,X0))
| ( ( ~ c_member(tc_prod(X6,X6),c_Product__Type_OPair(X6,X6,X4,X2),X0)
| X3 != X5 )
& ~ c_member(tc_prod(X7,X7),c_Product__Type_OPair(X7,X7,X5,X3),X1) ) )
& ( ( c_member(tc_prod(X6,X6),c_Product__Type_OPair(X6,X6,X4,X2),X0)
& X3 = X5 )
| c_member(tc_prod(X7,X7),c_Product__Type_OPair(X7,X7,X5,X3),X1)
| ~ c_member(tc_prod(tc_prod(X7,X6),tc_prod(X7,X6)),c_Product__Type_OPair(tc_prod(X7,X6),tc_prod(X7,X6),c_Product__Type_OPair(X7,X6,X5,X4),c_Product__Type_OPair(X7,X6,X3,X2)),c_Wellfounded_Olex__prod(X7,X6,X1,X0)) ) ),
inference(nnf_transformation,[],[f1016]) ).
fof(f1016,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( c_member(tc_prod(tc_prod(X7,X6),tc_prod(X7,X6)),c_Product__Type_OPair(tc_prod(X7,X6),tc_prod(X7,X6),c_Product__Type_OPair(X7,X6,X5,X4),c_Product__Type_OPair(X7,X6,X3,X2)),c_Wellfounded_Olex__prod(X7,X6,X1,X0))
<=> ( ( c_member(tc_prod(X6,X6),c_Product__Type_OPair(X6,X6,X4,X2),X0)
& X3 = X5 )
| c_member(tc_prod(X7,X7),c_Product__Type_OPair(X7,X7,X5,X3),X1) ) ),
inference(rectify,[],[f18]) ).
fof(f18,axiom,
! [X30,X3,X22,X23,X8,X9,X15,X4] :
( c_member(tc_prod(tc_prod(X4,X15),tc_prod(X4,X15)),c_Product__Type_OPair(tc_prod(X4,X15),tc_prod(X4,X15),c_Product__Type_OPair(X4,X15,X9,X8),c_Product__Type_OPair(X4,X15,X23,X22)),c_Wellfounded_Olex__prod(X4,X15,X3,X30))
<=> ( ( c_member(tc_prod(X15,X15),c_Product__Type_OPair(X15,X15,X8,X22),X30)
& X9 = X23 )
| c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X9,X23),X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_in__lex__prod) ).
fof(f14596,plain,
( spl104_604
| ~ spl104_442
| ~ spl104_443
| ~ spl104_603 ),
inference(avatar_split_clause,[],[f14592,f14588,f8101,f8097,f14594]) ).
fof(f14594,plain,
( spl104_604
<=> ! [X0,X3,X2,X1] : c_Set_Oinsert(X3,X2,c_Set_Oinsert(X3,X1,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),c_Relation_ORange(X3,X3,X0),c_Relation_ODomain(X3,X3,X0)))) = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),c_Set_Oinsert(X3,X2,c_Relation_ODomain(X3,X3,X0)),c_Set_Oinsert(X3,X1,c_Relation_ORange(X3,X3,X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_604])]) ).
fof(f8097,plain,
( spl104_442
<=> ! [X2,X4,X0,X3,X1] : c_Relation_ORange(X4,X3,c_Set_Oinsert(tc_prod(X4,X3),c_Product__Type_OPair(X4,X3,X2,X1),X0)) = c_Set_Oinsert(X3,X1,c_Relation_ORange(X4,X3,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_442])]) ).
fof(f8101,plain,
( spl104_443
<=> ! [X4,X0,X3,X2,X1] : c_Relation_ODomain(X4,X3,c_Set_Oinsert(tc_prod(X4,X3),c_Product__Type_OPair(X4,X3,X2,X1),X0)) = c_Set_Oinsert(X4,X2,c_Relation_ODomain(X4,X3,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_443])]) ).
fof(f14588,plain,
( spl104_603
<=> ! [X0,X3,X2,X1] : c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),c_Relation_ODomain(X3,X3,c_Set_Oinsert(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X2,X1),X0)),c_Relation_ORange(X3,X3,c_Set_Oinsert(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X2,X1),X0))) = c_Set_Oinsert(X3,X2,c_Set_Oinsert(X3,X1,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),c_Relation_ORange(X3,X3,X0),c_Relation_ODomain(X3,X3,X0)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_603])]) ).
fof(f14592,plain,
( ! [X2,X3,X0,X1] : c_Set_Oinsert(X3,X2,c_Set_Oinsert(X3,X1,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),c_Relation_ORange(X3,X3,X0),c_Relation_ODomain(X3,X3,X0)))) = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),c_Set_Oinsert(X3,X2,c_Relation_ODomain(X3,X3,X0)),c_Set_Oinsert(X3,X1,c_Relation_ORange(X3,X3,X0)))
| ~ spl104_442
| ~ spl104_443
| ~ spl104_603 ),
inference(forward_demodulation,[],[f14591,f8102]) ).
fof(f8102,plain,
( ! [X2,X3,X0,X1,X4] : c_Relation_ODomain(X4,X3,c_Set_Oinsert(tc_prod(X4,X3),c_Product__Type_OPair(X4,X3,X2,X1),X0)) = c_Set_Oinsert(X4,X2,c_Relation_ODomain(X4,X3,X0))
| ~ spl104_443 ),
inference(avatar_component_clause,[],[f8101]) ).
fof(f14591,plain,
( ! [X2,X3,X0,X1] : c_Set_Oinsert(X3,X2,c_Set_Oinsert(X3,X1,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),c_Relation_ORange(X3,X3,X0),c_Relation_ODomain(X3,X3,X0)))) = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),c_Relation_ODomain(X3,X3,c_Set_Oinsert(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X2,X1),X0)),c_Set_Oinsert(X3,X1,c_Relation_ORange(X3,X3,X0)))
| ~ spl104_442
| ~ spl104_603 ),
inference(forward_demodulation,[],[f14589,f8098]) ).
fof(f8098,plain,
( ! [X2,X3,X0,X1,X4] : c_Relation_ORange(X4,X3,c_Set_Oinsert(tc_prod(X4,X3),c_Product__Type_OPair(X4,X3,X2,X1),X0)) = c_Set_Oinsert(X3,X1,c_Relation_ORange(X4,X3,X0))
| ~ spl104_442 ),
inference(avatar_component_clause,[],[f8097]) ).
fof(f14589,plain,
( ! [X2,X3,X0,X1] : c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),c_Relation_ODomain(X3,X3,c_Set_Oinsert(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X2,X1),X0)),c_Relation_ORange(X3,X3,c_Set_Oinsert(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X2,X1),X0))) = c_Set_Oinsert(X3,X2,c_Set_Oinsert(X3,X1,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),c_Relation_ORange(X3,X3,X0),c_Relation_ODomain(X3,X3,X0))))
| ~ spl104_603 ),
inference(avatar_component_clause,[],[f14588]) ).
fof(f14590,plain,
spl104_603,
inference(avatar_split_clause,[],[f2841,f14588]) ).
fof(f2841,plain,
! [X2,X3,X0,X1] : c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),c_Relation_ODomain(X3,X3,c_Set_Oinsert(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X2,X1),X0)),c_Relation_ORange(X3,X3,c_Set_Oinsert(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X2,X1),X0))) = c_Set_Oinsert(X3,X2,c_Set_Oinsert(X3,X1,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),c_Relation_ORange(X3,X3,X0),c_Relation_ODomain(X3,X3,X0)))),
inference(forward_demodulation,[],[f2840,f2058]) ).
fof(f2840,plain,
! [X2,X3,X0,X1] : c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),c_Relation_ODomain(X3,X3,c_Set_Oinsert(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X2,X1),X0)),c_Relation_ORange(X3,X3,c_Set_Oinsert(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X2,X1),X0))) = c_Set_Oinsert(X3,X2,c_Set_Oinsert(X3,X1,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),c_Relation_ODomain(X3,X3,X0),c_Relation_ORange(X3,X3,X0)))),
inference(forward_demodulation,[],[f2839,f2060]) ).
fof(f2060,plain,
! [X2,X0,X1] : c_Set_Oinsert(X2,X1,X0) = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool),c_Set_Oinsert(X2,X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))),X0),
inference(cnf_transformation,[],[f658]) ).
fof(f658,plain,
! [X0,X1,X2] : c_Set_Oinsert(X2,X1,X0) = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool),c_Set_Oinsert(X2,X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))),X0),
inference(rectify,[],[f398]) ).
fof(f398,axiom,
! [X11,X9,X4] : c_Set_Oinsert(X4,X9,X11) = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool),c_Set_Oinsert(X4,X9,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))),X11),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__is__Un) ).
fof(f2839,plain,
! [X2,X3,X0,X1] : c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),c_Relation_ODomain(X3,X3,c_Set_Oinsert(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X2,X1),X0)),c_Relation_ORange(X3,X3,c_Set_Oinsert(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X2,X1),X0))) = c_Set_Oinsert(X3,X2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),c_Set_Oinsert(X3,X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),c_Relation_ODomain(X3,X3,X0),c_Relation_ORange(X3,X3,X0)))),
inference(forward_demodulation,[],[f2658,f2270]) ).
fof(f2270,plain,
! [X2,X3,X0,X1] : c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),c_Set_Oinsert(X3,X2,X1),X0) = c_Set_Oinsert(X3,X2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),X1,X0)),
inference(cnf_transformation,[],[f796]) ).
fof(f796,plain,
! [X0,X1,X2,X3] : c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),c_Set_Oinsert(X3,X2,X1),X0) = c_Set_Oinsert(X3,X2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),X1,X0)),
inference(rectify,[],[f128]) ).
fof(f128,axiom,
! [X53,X10,X9,X4] : c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool),c_Set_Oinsert(X4,X9,X10),X53) = c_Set_Oinsert(X4,X9,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool),X10,X53)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__insert__left) ).
fof(f2658,plain,
! [X2,X3,X0,X1] : c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),c_Relation_ODomain(X3,X3,c_Set_Oinsert(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X2,X1),X0)),c_Relation_ORange(X3,X3,c_Set_Oinsert(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X2,X1),X0))) = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),c_Set_Oinsert(X3,X2,c_Set_Oinsert(X3,X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)))),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),c_Relation_ODomain(X3,X3,X0),c_Relation_ORange(X3,X3,X0))),
inference(definition_unfolding,[],[f2280,f1954,f1954]) ).
fof(f2280,plain,
! [X2,X3,X0,X1] : c_Relation_OField(X3,c_Set_Oinsert(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X2,X1),X0)) = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),c_Set_Oinsert(X3,X2,c_Set_Oinsert(X3,X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)))),c_Relation_OField(X3,X0)),
inference(cnf_transformation,[],[f806]) ).
fof(f806,plain,
! [X0,X1,X2,X3] : c_Relation_OField(X3,c_Set_Oinsert(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X2,X1),X0)) = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),c_Set_Oinsert(X3,X2,c_Set_Oinsert(X3,X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)))),c_Relation_OField(X3,X0)),
inference(rectify,[],[f393]) ).
fof(f393,axiom,
! [X3,X8,X9,X4] : c_Relation_OField(X4,c_Set_Oinsert(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X9,X8),X3)) = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool),c_Set_Oinsert(X4,X9,c_Set_Oinsert(X4,X8,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))),c_Relation_OField(X4,X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Field__insert) ).
fof(f14586,plain,
spl104_602,
inference(avatar_split_clause,[],[f2655,f14584]) ).
fof(f14584,plain,
( spl104_602
<=> ! [X2,X0,X1] :
( c_Transitive__Closure_Otrancl(X2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),X0,c_Relation_OId(X2))) = c_Transitive__Closure_Otrancl(X2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),X1,c_Relation_OId(X2)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),X0,c_Transitive__Closure_Otrancl(X2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),X1,c_Relation_OId(X2))))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_602])]) ).
fof(f2655,plain,
! [X2,X0,X1] :
( c_Transitive__Closure_Otrancl(X2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),X0,c_Relation_OId(X2))) = c_Transitive__Closure_Otrancl(X2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),X1,c_Relation_OId(X2)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),X0,c_Transitive__Closure_Otrancl(X2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),X1,c_Relation_OId(X2))))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),X1,X0) ),
inference(definition_unfolding,[],[f2190,f1949,f1949,f1949]) ).
fof(f2190,plain,
! [X2,X0,X1] :
( c_Transitive__Closure_Ortrancl(X2,X0) = c_Transitive__Closure_Ortrancl(X2,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),X0,c_Transitive__Closure_Ortrancl(X2,X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),X1,X0) ),
inference(cnf_transformation,[],[f1221]) ).
fof(f1221,plain,
! [X0,X1,X2] :
( c_Transitive__Closure_Ortrancl(X2,X0) = c_Transitive__Closure_Ortrancl(X2,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),X0,c_Transitive__Closure_Ortrancl(X2,X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),X1,X0) ),
inference(flattening,[],[f1220]) ).
fof(f1220,plain,
! [X0,X1,X2] :
( c_Transitive__Closure_Ortrancl(X2,X0) = c_Transitive__Closure_Ortrancl(X2,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),X0,c_Transitive__Closure_Ortrancl(X2,X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),X1,X0) ),
inference(ennf_transformation,[],[f761]) ).
fof(f761,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),X1,X0)
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),X0,c_Transitive__Closure_Ortrancl(X2,X1))
=> c_Transitive__Closure_Ortrancl(X2,X0) = c_Transitive__Closure_Ortrancl(X2,X1) ) ),
inference(rectify,[],[f269]) ).
fof(f269,axiom,
! [X54,X14,X4] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),X14,X54)
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),X54,c_Transitive__Closure_Ortrancl(X4,X14))
=> c_Transitive__Closure_Ortrancl(X4,X14) = c_Transitive__Closure_Ortrancl(X4,X54) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__subset) ).
fof(f14516,plain,
( ~ spl104_11
| spl104_601
| ~ spl104_27
| ~ spl104_450 ),
inference(avatar_split_clause,[],[f8439,f8306,f3004,f14514,f2927]) ).
fof(f8439,plain,
( ! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X0,tc_Nat_Onat),X1,X1)
| ~ class_Orderings_Oord(tc_Nat_Onat) )
| ~ spl104_27
| ~ spl104_450 ),
inference(resolution,[],[f8307,f3005]) ).
fof(f14445,plain,
spl104_600,
inference(avatar_split_clause,[],[f2680,f14443]) ).
fof(f14443,plain,
( spl104_600
<=> ! [X0,X3,X2,X1] :
( c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X2,sK65(X0,X1,X2,X3)),c_Transitive__Closure_Otrancl(X3,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X3,X3),tc_HOL_Obool),X0,c_Relation_OId(X3))))
| X1 = X2
| ~ c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X2,X1),c_Transitive__Closure_Otrancl(X3,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X3,X3),tc_HOL_Obool),X0,c_Relation_OId(X3)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_600])]) ).
fof(f2680,plain,
! [X2,X3,X0,X1] :
( c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X2,sK65(X0,X1,X2,X3)),c_Transitive__Closure_Otrancl(X3,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X3,X3),tc_HOL_Obool),X0,c_Relation_OId(X3))))
| X1 = X2
| ~ c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X2,X1),c_Transitive__Closure_Otrancl(X3,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X3,X3),tc_HOL_Obool),X0,c_Relation_OId(X3)))) ),
inference(definition_unfolding,[],[f2415,f1949,f1949]) ).
fof(f2415,plain,
! [X2,X3,X0,X1] :
( c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X2,sK65(X0,X1,X2,X3)),c_Transitive__Closure_Ortrancl(X3,X0))
| X1 = X2
| ~ c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X2,X1),c_Transitive__Closure_Ortrancl(X3,X0)) ),
inference(cnf_transformation,[],[f1730]) ).
fof(f1730,plain,
! [X0,X1,X2,X3] :
( ( c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,sK65(X0,X1,X2,X3),X1),X0)
& c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X2,sK65(X0,X1,X2,X3)),c_Transitive__Closure_Ortrancl(X3,X0)) )
| X1 = X2
| ~ c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X2,X1),c_Transitive__Closure_Ortrancl(X3,X0)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK65])],[f1414,f1729]) ).
fof(f1729,plain,
! [X0,X1,X2,X3] :
( ? [X4] :
( c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X4,X1),X0)
& c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X2,X4),c_Transitive__Closure_Ortrancl(X3,X0)) )
=> ( c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,sK65(X0,X1,X2,X3),X1),X0)
& c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X2,sK65(X0,X1,X2,X3)),c_Transitive__Closure_Ortrancl(X3,X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f1414,plain,
! [X0,X1,X2,X3] :
( ? [X4] :
( c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X4,X1),X0)
& c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X2,X4),c_Transitive__Closure_Ortrancl(X3,X0)) )
| X1 = X2
| ~ c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X2,X1),c_Transitive__Closure_Ortrancl(X3,X0)) ),
inference(flattening,[],[f1413]) ).
fof(f1413,plain,
! [X0,X1,X2,X3] :
( ? [X4] :
( c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X4,X1),X0)
& c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X2,X4),c_Transitive__Closure_Ortrancl(X3,X0)) )
| X1 = X2
| ~ c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X2,X1),c_Transitive__Closure_Ortrancl(X3,X0)) ),
inference(ennf_transformation,[],[f914]) ).
fof(f914,plain,
! [X0,X1,X2,X3] :
( c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X2,X1),c_Transitive__Closure_Ortrancl(X3,X0))
=> ( X1 != X2
=> ~ ! [X4] :
( c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X2,X4),c_Transitive__Closure_Ortrancl(X3,X0))
=> ~ c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X4,X1),X0) ) ) ),
inference(rectify,[],[f72]) ).
fof(f72,axiom,
! [X3,X8,X9,X4] :
( c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X9,X8),c_Transitive__Closure_Ortrancl(X4,X3))
=> ( X8 != X9
=> ~ ! [X5] :
( c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X9,X5),c_Transitive__Closure_Ortrancl(X4,X3))
=> ~ c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X5,X8),X3) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtranclE) ).
fof(f14441,plain,
spl104_599,
inference(avatar_split_clause,[],[f2677,f14439]) ).
fof(f14439,plain,
( spl104_599
<=> ! [X0,X3,X2,X1] :
( c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,sK64(X0,X1,X2,X3),X1),c_Transitive__Closure_Otrancl(X3,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X3,X3),tc_HOL_Obool),X0,c_Relation_OId(X3))))
| X1 = X2
| ~ c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X2,X1),c_Transitive__Closure_Otrancl(X3,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X3,X3),tc_HOL_Obool),X0,c_Relation_OId(X3)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_599])]) ).
fof(f2677,plain,
! [X2,X3,X0,X1] :
( c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,sK64(X0,X1,X2,X3),X1),c_Transitive__Closure_Otrancl(X3,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X3,X3),tc_HOL_Obool),X0,c_Relation_OId(X3))))
| X1 = X2
| ~ c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X2,X1),c_Transitive__Closure_Otrancl(X3,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X3,X3),tc_HOL_Obool),X0,c_Relation_OId(X3)))) ),
inference(definition_unfolding,[],[f2414,f1949,f1949]) ).
fof(f2414,plain,
! [X2,X3,X0,X1] :
( c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,sK64(X0,X1,X2,X3),X1),c_Transitive__Closure_Ortrancl(X3,X0))
| X1 = X2
| ~ c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X2,X1),c_Transitive__Closure_Ortrancl(X3,X0)) ),
inference(cnf_transformation,[],[f1728]) ).
fof(f1728,plain,
! [X0,X1,X2,X3] :
( ( c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,sK64(X0,X1,X2,X3),X1),c_Transitive__Closure_Ortrancl(X3,X0))
& c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X2,sK64(X0,X1,X2,X3)),X0) )
| X1 = X2
| ~ c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X2,X1),c_Transitive__Closure_Ortrancl(X3,X0)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK64])],[f1412,f1727]) ).
fof(f1727,plain,
! [X0,X1,X2,X3] :
( ? [X4] :
( c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X4,X1),c_Transitive__Closure_Ortrancl(X3,X0))
& c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X2,X4),X0) )
=> ( c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,sK64(X0,X1,X2,X3),X1),c_Transitive__Closure_Ortrancl(X3,X0))
& c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X2,sK64(X0,X1,X2,X3)),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f1412,plain,
! [X0,X1,X2,X3] :
( ? [X4] :
( c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X4,X1),c_Transitive__Closure_Ortrancl(X3,X0))
& c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X2,X4),X0) )
| X1 = X2
| ~ c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X2,X1),c_Transitive__Closure_Ortrancl(X3,X0)) ),
inference(flattening,[],[f1411]) ).
fof(f1411,plain,
! [X0,X1,X2,X3] :
( ? [X4] :
( c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X4,X1),c_Transitive__Closure_Ortrancl(X3,X0))
& c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X2,X4),X0) )
| X1 = X2
| ~ c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X2,X1),c_Transitive__Closure_Ortrancl(X3,X0)) ),
inference(ennf_transformation,[],[f913]) ).
fof(f913,plain,
! [X0,X1,X2,X3] :
( c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X2,X1),c_Transitive__Closure_Ortrancl(X3,X0))
=> ( X1 != X2
=> ~ ! [X4] :
( c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X2,X4),X0)
=> ~ c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X4,X1),c_Transitive__Closure_Ortrancl(X3,X0)) ) ) ),
inference(rectify,[],[f73]) ).
fof(f73,axiom,
! [X3,X38,X13,X4] :
( c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X13,X38),c_Transitive__Closure_Ortrancl(X4,X3))
=> ( X13 != X38
=> ~ ! [X5] :
( c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X13,X5),X3)
=> ~ c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X5,X38),c_Transitive__Closure_Ortrancl(X4,X3)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_converse__rtranclE) ).
fof(f14193,plain,
spl104_598,
inference(avatar_split_clause,[],[f2868,f14191]) ).
fof(f14191,plain,
( spl104_598
<=> ! [X0,X3,X2,X1] :
( c_Relation_Orel__comp(X3,X3,X3,X2,X1) != c_Relation_OId__on(X3,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)))
| c_Relation_Orel__comp(X3,X3,X3,X2,X0) != c_Relation_OId__on(X3,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)))
| c_Relation_Orel__comp(X3,X3,X3,X2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X3,X3),tc_HOL_Obool),X1,X0)) = c_Relation_OId__on(X3,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_598])]) ).
fof(f2868,plain,
! [X2,X3,X0,X1] :
( c_Relation_Orel__comp(X3,X3,X3,X2,X1) != c_Relation_OId__on(X3,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)))
| c_Relation_Orel__comp(X3,X3,X3,X2,X0) != c_Relation_OId__on(X3,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)))
| c_Relation_Orel__comp(X3,X3,X3,X2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X3,X3),tc_HOL_Obool),X1,X0)) = c_Relation_OId__on(X3,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))) ),
inference(forward_demodulation,[],[f2867,f1912]) ).
fof(f1912,plain,
! [X0] : c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X0,X0),tc_HOL_Obool)) = c_Relation_OId__on(X0,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool))),
inference(cnf_transformation,[],[f542]) ).
fof(f542,plain,
! [X0] : c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X0,X0),tc_HOL_Obool)) = c_Relation_OId__on(X0,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool))),
inference(rectify,[],[f414]) ).
fof(f414,axiom,
! [X4] : c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X4,X4),tc_HOL_Obool)) = c_Relation_OId__on(X4,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Id__on__empty) ).
fof(f2867,plain,
! [X2,X3,X0,X1] :
( c_Relation_Orel__comp(X3,X3,X3,X2,X0) != c_Relation_OId__on(X3,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)))
| c_Relation_Orel__comp(X3,X3,X3,X2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X3,X3),tc_HOL_Obool),X1,X0)) = c_Relation_OId__on(X3,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)))
| c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X3,X3),tc_HOL_Obool)) != c_Relation_Orel__comp(X3,X3,X3,X2,X1) ),
inference(forward_demodulation,[],[f2866,f1912]) ).
fof(f2866,plain,
! [X2,X3,X0,X1] :
( c_Relation_Orel__comp(X3,X3,X3,X2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X3,X3),tc_HOL_Obool),X1,X0)) = c_Relation_OId__on(X3,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)))
| c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X3,X3),tc_HOL_Obool)) != c_Relation_Orel__comp(X3,X3,X3,X2,X0)
| c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X3,X3),tc_HOL_Obool)) != c_Relation_Orel__comp(X3,X3,X3,X2,X1) ),
inference(forward_demodulation,[],[f2418,f1912]) ).
fof(f2418,plain,
! [X2,X3,X0,X1] :
( c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X3,X3),tc_HOL_Obool)) = c_Relation_Orel__comp(X3,X3,X3,X2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X3,X3),tc_HOL_Obool),X1,X0))
| c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X3,X3),tc_HOL_Obool)) != c_Relation_Orel__comp(X3,X3,X3,X2,X0)
| c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X3,X3),tc_HOL_Obool)) != c_Relation_Orel__comp(X3,X3,X3,X2,X1) ),
inference(cnf_transformation,[],[f1418]) ).
fof(f1418,plain,
! [X0,X1,X2,X3] :
( c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X3,X3),tc_HOL_Obool)) = c_Relation_Orel__comp(X3,X3,X3,X2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X3,X3),tc_HOL_Obool),X1,X0))
| c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X3,X3),tc_HOL_Obool)) != c_Relation_Orel__comp(X3,X3,X3,X2,X0)
| c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X3,X3),tc_HOL_Obool)) != c_Relation_Orel__comp(X3,X3,X3,X2,X1) ),
inference(flattening,[],[f1417]) ).
fof(f1417,plain,
! [X0,X1,X2,X3] :
( c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X3,X3),tc_HOL_Obool)) = c_Relation_Orel__comp(X3,X3,X3,X2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X3,X3),tc_HOL_Obool),X1,X0))
| c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X3,X3),tc_HOL_Obool)) != c_Relation_Orel__comp(X3,X3,X3,X2,X0)
| c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X3,X3),tc_HOL_Obool)) != c_Relation_Orel__comp(X3,X3,X3,X2,X1) ),
inference(ennf_transformation,[],[f916]) ).
fof(f916,plain,
! [X0,X1,X2,X3] :
( c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X3,X3),tc_HOL_Obool)) = c_Relation_Orel__comp(X3,X3,X3,X2,X1)
=> ( c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X3,X3),tc_HOL_Obool)) = c_Relation_Orel__comp(X3,X3,X3,X2,X0)
=> c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X3,X3),tc_HOL_Obool)) = c_Relation_Orel__comp(X3,X3,X3,X2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X3,X3),tc_HOL_Obool),X1,X0)) ) ),
inference(rectify,[],[f494]) ).
fof(f494,axiom,
! [X53,X10,X11,X4] :
( c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X4,X4),tc_HOL_Obool)) = c_Relation_Orel__comp(X4,X4,X4,X11,X10)
=> ( c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X4,X4),tc_HOL_Obool)) = c_Relation_Orel__comp(X4,X4,X4,X11,X53)
=> c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X4,X4),tc_HOL_Obool)) = c_Relation_Orel__comp(X4,X4,X4,X11,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),X10,X53)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_union__comp__emptyR) ).
fof(f14189,plain,
spl104_597,
inference(avatar_split_clause,[],[f2708,f14187]) ).
fof(f14187,plain,
( spl104_597
<=> ! [X2,X4,X0,X3,X1] :
( hBOOL(hAPP(X0,X3))
| c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,sK79(X0,X1,X2,X4),sK80(X0,X1,X2,X4)),X1)
| ~ hBOOL(hAPP(X0,X2))
| ~ c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,X2),c_Transitive__Closure_Otrancl(X4,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),X1,c_Relation_OId(X4)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_597])]) ).
fof(f2708,plain,
! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(X0,X3))
| c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,sK79(X0,X1,X2,X4),sK80(X0,X1,X2,X4)),X1)
| ~ hBOOL(hAPP(X0,X2))
| ~ c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,X2),c_Transitive__Closure_Otrancl(X4,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),X1,c_Relation_OId(X4)))) ),
inference(definition_unfolding,[],[f2547,f1949]) ).
fof(f2547,plain,
! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(X0,X3))
| c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,sK79(X0,X1,X2,X4),sK80(X0,X1,X2,X4)),X1)
| ~ hBOOL(hAPP(X0,X2))
| ~ c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,X2),c_Transitive__Closure_Ortrancl(X4,X1)) ),
inference(cnf_transformation,[],[f1801]) ).
fof(f14183,plain,
spl104_596,
inference(avatar_split_clause,[],[f2703,f14181]) ).
fof(f14181,plain,
( spl104_596
<=> ! [X4,X0,X3,X2,X1] :
( hBOOL(hAPP(X0,X2))
| c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,sK77(X0,X1,X3,X4),sK78(X0,X1,X3,X4)),X1)
| ~ hBOOL(hAPP(X0,X3))
| ~ c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,X2),c_Transitive__Closure_Otrancl(X4,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),X1,c_Relation_OId(X4)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_596])]) ).
fof(f2703,plain,
! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(X0,X2))
| c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,sK77(X0,X1,X3,X4),sK78(X0,X1,X3,X4)),X1)
| ~ hBOOL(hAPP(X0,X3))
| ~ c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,X2),c_Transitive__Closure_Otrancl(X4,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),X1,c_Relation_OId(X4)))) ),
inference(definition_unfolding,[],[f2544,f1949]) ).
fof(f2544,plain,
! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(X0,X2))
| c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,sK77(X0,X1,X3,X4),sK78(X0,X1,X3,X4)),X1)
| ~ hBOOL(hAPP(X0,X3))
| ~ c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,X2),c_Transitive__Closure_Ortrancl(X4,X1)) ),
inference(cnf_transformation,[],[f1799]) ).
fof(f14179,plain,
spl104_595,
inference(avatar_split_clause,[],[f2656,f14177]) ).
fof(f14177,plain,
( spl104_595
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),c_Transitive__Closure_Otrancl(X2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),X1,c_Relation_OId(X2))),c_Transitive__Closure_Otrancl(X2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),X0,c_Relation_OId(X2))))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),X1,c_Transitive__Closure_Otrancl(X2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),X0,c_Relation_OId(X2)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_595])]) ).
fof(f2656,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),c_Transitive__Closure_Otrancl(X2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),X1,c_Relation_OId(X2))),c_Transitive__Closure_Otrancl(X2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),X0,c_Relation_OId(X2))))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),X1,c_Transitive__Closure_Otrancl(X2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),X0,c_Relation_OId(X2)))) ),
inference(definition_unfolding,[],[f2193,f1949,f1949,f1949]) ).
fof(f2193,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),c_Transitive__Closure_Ortrancl(X2,X1),c_Transitive__Closure_Ortrancl(X2,X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),X1,c_Transitive__Closure_Ortrancl(X2,X0)) ),
inference(cnf_transformation,[],[f1223]) ).
fof(f1223,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),c_Transitive__Closure_Ortrancl(X2,X1),c_Transitive__Closure_Ortrancl(X2,X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),X1,c_Transitive__Closure_Ortrancl(X2,X0)) ),
inference(ennf_transformation,[],[f763]) ).
fof(f763,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),X1,c_Transitive__Closure_Ortrancl(X2,X0))
=> c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),c_Transitive__Closure_Ortrancl(X2,X1),c_Transitive__Closure_Ortrancl(X2,X0)) ),
inference(rectify,[],[f268]) ).
fof(f268,axiom,
! [X30,X3,X4] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),X3,c_Transitive__Closure_Ortrancl(X4,X30))
=> c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),c_Transitive__Closure_Ortrancl(X4,X3),c_Transitive__Closure_Ortrancl(X4,X30)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__subset__rtrancl) ).
fof(f14175,plain,
spl104_594,
inference(avatar_split_clause,[],[f2608,f14173]) ).
fof(f14173,plain,
( spl104_594
<=> ! [X2,X3,X4,X0,X6,X5,X1] :
( c_member(tc_prod(tc_prod(X0,X4),tc_prod(X0,X4)),c_Product__Type_OPair(tc_prod(X0,X4),tc_prod(X0,X4),c_Product__Type_OPair(X0,X4,X5,X3),c_Product__Type_OPair(X0,X4,X5,X2)),c_Recdef_Osame__fst(X0,X4,X6,X1))
| ~ c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,X2),hAPP(X1,X5))
| ~ hBOOL(hAPP(X6,X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_594])]) ).
fof(f2608,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( c_member(tc_prod(tc_prod(X0,X4),tc_prod(X0,X4)),c_Product__Type_OPair(tc_prod(X0,X4),tc_prod(X0,X4),c_Product__Type_OPair(X0,X4,X5,X3),c_Product__Type_OPair(X0,X4,X5,X2)),c_Recdef_Osame__fst(X0,X4,X6,X1))
| ~ c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,X2),hAPP(X1,X5))
| ~ hBOOL(hAPP(X6,X5)) ),
inference(cnf_transformation,[],[f1515]) ).
fof(f1515,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( c_member(tc_prod(tc_prod(X0,X4),tc_prod(X0,X4)),c_Product__Type_OPair(tc_prod(X0,X4),tc_prod(X0,X4),c_Product__Type_OPair(X0,X4,X5,X3),c_Product__Type_OPair(X0,X4,X5,X2)),c_Recdef_Osame__fst(X0,X4,X6,X1))
| ~ c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,X2),hAPP(X1,X5))
| ~ hBOOL(hAPP(X6,X5)) ),
inference(flattening,[],[f1514]) ).
fof(f1514,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( c_member(tc_prod(tc_prod(X0,X4),tc_prod(X0,X4)),c_Product__Type_OPair(tc_prod(X0,X4),tc_prod(X0,X4),c_Product__Type_OPair(X0,X4,X5,X3),c_Product__Type_OPair(X0,X4,X5,X2)),c_Recdef_Osame__fst(X0,X4,X6,X1))
| ~ c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,X2),hAPP(X1,X5))
| ~ hBOOL(hAPP(X6,X5)) ),
inference(ennf_transformation,[],[f1009]) ).
fof(f1009,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( hBOOL(hAPP(X6,X5))
=> ( c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,X2),hAPP(X1,X5))
=> c_member(tc_prod(tc_prod(X0,X4),tc_prod(X0,X4)),c_Product__Type_OPair(tc_prod(X0,X4),tc_prod(X0,X4),c_Product__Type_OPair(X0,X4,X5,X3),c_Product__Type_OPair(X0,X4,X5,X2)),c_Recdef_Osame__fst(X0,X4,X6,X1)) ) ),
inference(rectify,[],[f6]) ).
fof(f6,axiom,
! [X4,X14,X12,X16,X15,X13,X17] :
( hBOOL(hAPP(X17,X13))
=> ( c_member(tc_prod(X15,X15),c_Product__Type_OPair(X15,X15,X16,X12),hAPP(X14,X13))
=> c_member(tc_prod(tc_prod(X4,X15),tc_prod(X4,X15)),c_Product__Type_OPair(tc_prod(X4,X15),tc_prod(X4,X15),c_Product__Type_OPair(X4,X15,X13,X16),c_Product__Type_OPair(X4,X15,X13,X12)),c_Recdef_Osame__fst(X4,X15,X17,X14)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_same__fstI) ).
fof(f14017,plain,
spl104_593,
inference(avatar_split_clause,[],[f2711,f14015]) ).
fof(f14015,plain,
( spl104_593
<=> ! [X2,X4,X0,X3,X1] :
( c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,X0),c_Transitive__Closure_Otrancl(X4,X1))
| ~ c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X2,X0),c_Transitive__Closure_Otrancl(X4,X1))
| ~ c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,X2),c_Transitive__Closure_Otrancl(X4,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),X1,c_Relation_OId(X4)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_593])]) ).
fof(f2711,plain,
! [X2,X3,X0,X1,X4] :
( c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,X0),c_Transitive__Closure_Otrancl(X4,X1))
| ~ c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X2,X0),c_Transitive__Closure_Otrancl(X4,X1))
| ~ c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,X2),c_Transitive__Closure_Otrancl(X4,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),X1,c_Relation_OId(X4)))) ),
inference(definition_unfolding,[],[f2553,f1949]) ).
fof(f2553,plain,
! [X2,X3,X0,X1,X4] :
( c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,X0),c_Transitive__Closure_Otrancl(X4,X1))
| ~ c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X2,X0),c_Transitive__Closure_Otrancl(X4,X1))
| ~ c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,X2),c_Transitive__Closure_Ortrancl(X4,X1)) ),
inference(cnf_transformation,[],[f1486]) ).
fof(f1486,plain,
! [X0,X1,X2,X3,X4] :
( c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,X0),c_Transitive__Closure_Otrancl(X4,X1))
| ~ c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X2,X0),c_Transitive__Closure_Otrancl(X4,X1))
| ~ c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,X2),c_Transitive__Closure_Ortrancl(X4,X1)) ),
inference(flattening,[],[f1485]) ).
fof(f1485,plain,
! [X0,X1,X2,X3,X4] :
( c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,X0),c_Transitive__Closure_Otrancl(X4,X1))
| ~ c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X2,X0),c_Transitive__Closure_Otrancl(X4,X1))
| ~ c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,X2),c_Transitive__Closure_Ortrancl(X4,X1)) ),
inference(ennf_transformation,[],[f982]) ).
fof(f982,plain,
! [X0,X1,X2,X3,X4] :
( c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,X2),c_Transitive__Closure_Ortrancl(X4,X1))
=> ( c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X2,X0),c_Transitive__Closure_Otrancl(X4,X1))
=> c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,X0),c_Transitive__Closure_Otrancl(X4,X1)) ) ),
inference(rectify,[],[f95]) ).
fof(f95,axiom,
! [X38,X3,X12,X13,X4] :
( c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X13,X12),c_Transitive__Closure_Ortrancl(X4,X3))
=> ( c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X12,X38),c_Transitive__Closure_Otrancl(X4,X3))
=> c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X13,X38),c_Transitive__Closure_Otrancl(X4,X3)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__trancl__trancl) ).
fof(f14013,plain,
spl104_592,
inference(avatar_split_clause,[],[f2700,f14011]) ).
fof(f14011,plain,
( spl104_592
<=> ! [X2,X4,X0,X3,X1] :
( c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,X0),c_Transitive__Closure_Otrancl(X4,X1))
| ~ c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X2,X0),c_Transitive__Closure_Otrancl(X4,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),X1,c_Relation_OId(X4))))
| ~ c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,X2),c_Transitive__Closure_Otrancl(X4,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_592])]) ).
fof(f2700,plain,
! [X2,X3,X0,X1,X4] :
( c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,X0),c_Transitive__Closure_Otrancl(X4,X1))
| ~ c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X2,X0),c_Transitive__Closure_Otrancl(X4,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),X1,c_Relation_OId(X4))))
| ~ c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,X2),c_Transitive__Closure_Otrancl(X4,X1)) ),
inference(definition_unfolding,[],[f2542,f1949]) ).
fof(f2542,plain,
! [X2,X3,X0,X1,X4] :
( c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,X0),c_Transitive__Closure_Otrancl(X4,X1))
| ~ c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X2,X0),c_Transitive__Closure_Ortrancl(X4,X1))
| ~ c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,X2),c_Transitive__Closure_Otrancl(X4,X1)) ),
inference(cnf_transformation,[],[f1476]) ).
fof(f1476,plain,
! [X0,X1,X2,X3,X4] :
( c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,X0),c_Transitive__Closure_Otrancl(X4,X1))
| ~ c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X2,X0),c_Transitive__Closure_Ortrancl(X4,X1))
| ~ c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,X2),c_Transitive__Closure_Otrancl(X4,X1)) ),
inference(flattening,[],[f1475]) ).
fof(f1475,plain,
! [X0,X1,X2,X3,X4] :
( c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,X0),c_Transitive__Closure_Otrancl(X4,X1))
| ~ c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X2,X0),c_Transitive__Closure_Ortrancl(X4,X1))
| ~ c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,X2),c_Transitive__Closure_Otrancl(X4,X1)) ),
inference(ennf_transformation,[],[f977]) ).
fof(f977,plain,
! [X0,X1,X2,X3,X4] :
( c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,X2),c_Transitive__Closure_Otrancl(X4,X1))
=> ( c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X2,X0),c_Transitive__Closure_Ortrancl(X4,X1))
=> c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,X0),c_Transitive__Closure_Otrancl(X4,X1)) ) ),
inference(rectify,[],[f94]) ).
fof(f94,axiom,
! [X7,X3,X8,X9,X4] :
( c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X9,X8),c_Transitive__Closure_Otrancl(X4,X3))
=> ( c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X8,X7),c_Transitive__Closure_Ortrancl(X4,X3))
=> c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X9,X7),c_Transitive__Closure_Otrancl(X4,X3)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trancl__rtrancl__trancl) ).
fof(f14001,plain,
spl104_591,
inference(avatar_split_clause,[],[f2629,f13999]) ).
fof(f13999,plain,
( spl104_591
<=> ! [X2,X3,X4,X7,X0,X6,X5,X1] :
( X3 = X5
| c_member(tc_prod(X7,X7),c_Product__Type_OPair(X7,X7,X5,X3),X1)
| ~ c_member(tc_prod(tc_prod(X7,X6),tc_prod(X7,X6)),c_Product__Type_OPair(tc_prod(X7,X6),tc_prod(X7,X6),c_Product__Type_OPair(X7,X6,X5,X4),c_Product__Type_OPair(X7,X6,X3,X2)),c_Wellfounded_Olex__prod(X7,X6,X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_591])]) ).
fof(f2629,plain,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( X3 = X5
| c_member(tc_prod(X7,X7),c_Product__Type_OPair(X7,X7,X5,X3),X1)
| ~ c_member(tc_prod(tc_prod(X7,X6),tc_prod(X7,X6)),c_Product__Type_OPair(tc_prod(X7,X6),tc_prod(X7,X6),c_Product__Type_OPair(X7,X6,X5,X4),c_Product__Type_OPair(X7,X6,X3,X2)),c_Wellfounded_Olex__prod(X7,X6,X1,X0)) ),
inference(cnf_transformation,[],[f1851]) ).
fof(f13997,plain,
( spl104_590
| ~ spl104_196
| ~ spl104_389 ),
inference(avatar_split_clause,[],[f7116,f7002,f4032,f13995]) ).
fof(f7116,plain,
( ! [X0,X1] :
( c_Wellfounded_Oacyclic(X0,X1)
| ~ c_Relation_Oirrefl(X0,c_Transitive__Closure_Otrancl(X0,X1)) )
| ~ spl104_196
| ~ spl104_389 ),
inference(resolution,[],[f7003,f4033]) ).
fof(f13993,plain,
spl104_589,
inference(avatar_split_clause,[],[f2602,f13991]) ).
fof(f13991,plain,
( spl104_589
<=> ! [X5,X6,X4,X0,X3,X2,X1] :
( c_Recdef_Owfrec__rel(X5,X4,X3,X2,X1,hAPP(hAPP(X2,X0),X1))
| ~ c_Recdef_Owfrec__rel(X5,X4,X3,X2,sK89(X1,X2,X3,X4,X5,X6),hAPP(X6,sK89(X1,X2,X3,X4,X5,X6)))
| hAPP(hAPP(X2,X6),X1) != hAPP(hAPP(X2,X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_589])]) ).
fof(f2602,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( c_Recdef_Owfrec__rel(X5,X4,X3,X2,X1,hAPP(hAPP(X2,X0),X1))
| ~ c_Recdef_Owfrec__rel(X5,X4,X3,X2,sK89(X1,X2,X3,X4,X5,X6),hAPP(X6,sK89(X1,X2,X3,X4,X5,X6)))
| hAPP(hAPP(X2,X6),X1) != hAPP(hAPP(X2,X0),X1) ),
inference(cnf_transformation,[],[f1831]) ).
fof(f1831,plain,
! [X0,X1,X2,X3,X4,X5] :
( ( c_Recdef_Owfrec__rel(X5,X4,X3,X2,X1,hAPP(hAPP(X2,X0),X1))
| ! [X6] :
( ( ~ c_Recdef_Owfrec__rel(X5,X4,X3,X2,sK89(X1,X2,X3,X4,X5,X6),hAPP(X6,sK89(X1,X2,X3,X4,X5,X6)))
& c_member(tc_prod(X5,X5),c_Product__Type_OPair(X5,X5,sK89(X1,X2,X3,X4,X5,X6),X1),X3) )
| hAPP(hAPP(X2,X6),X1) != hAPP(hAPP(X2,X0),X1) ) )
& ( ( ! [X9] :
( c_Recdef_Owfrec__rel(X5,X4,X3,X2,X9,hAPP(sK90(X0,X1,X2,X3,X4,X5),X9))
| ~ c_member(tc_prod(X5,X5),c_Product__Type_OPair(X5,X5,X9,X1),X3) )
& hAPP(hAPP(X2,X0),X1) = hAPP(hAPP(X2,sK90(X0,X1,X2,X3,X4,X5)),X1) )
| ~ c_Recdef_Owfrec__rel(X5,X4,X3,X2,X1,hAPP(hAPP(X2,X0),X1)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK89,sK90])],[f1828,f1830,f1829]) ).
fof(f1829,plain,
! [X1,X2,X3,X4,X5,X6] :
( ? [X7] :
( ~ c_Recdef_Owfrec__rel(X5,X4,X3,X2,X7,hAPP(X6,X7))
& c_member(tc_prod(X5,X5),c_Product__Type_OPair(X5,X5,X7,X1),X3) )
=> ( ~ c_Recdef_Owfrec__rel(X5,X4,X3,X2,sK89(X1,X2,X3,X4,X5,X6),hAPP(X6,sK89(X1,X2,X3,X4,X5,X6)))
& c_member(tc_prod(X5,X5),c_Product__Type_OPair(X5,X5,sK89(X1,X2,X3,X4,X5,X6),X1),X3) ) ),
introduced(choice_axiom,[]) ).
fof(f1830,plain,
! [X0,X1,X2,X3,X4,X5] :
( ? [X8] :
( ! [X9] :
( c_Recdef_Owfrec__rel(X5,X4,X3,X2,X9,hAPP(X8,X9))
| ~ c_member(tc_prod(X5,X5),c_Product__Type_OPair(X5,X5,X9,X1),X3) )
& hAPP(hAPP(X2,X0),X1) = hAPP(hAPP(X2,X8),X1) )
=> ( ! [X9] :
( c_Recdef_Owfrec__rel(X5,X4,X3,X2,X9,hAPP(sK90(X0,X1,X2,X3,X4,X5),X9))
| ~ c_member(tc_prod(X5,X5),c_Product__Type_OPair(X5,X5,X9,X1),X3) )
& hAPP(hAPP(X2,X0),X1) = hAPP(hAPP(X2,sK90(X0,X1,X2,X3,X4,X5)),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f1828,plain,
! [X0,X1,X2,X3,X4,X5] :
( ( c_Recdef_Owfrec__rel(X5,X4,X3,X2,X1,hAPP(hAPP(X2,X0),X1))
| ! [X6] :
( ? [X7] :
( ~ c_Recdef_Owfrec__rel(X5,X4,X3,X2,X7,hAPP(X6,X7))
& c_member(tc_prod(X5,X5),c_Product__Type_OPair(X5,X5,X7,X1),X3) )
| hAPP(hAPP(X2,X6),X1) != hAPP(hAPP(X2,X0),X1) ) )
& ( ? [X8] :
( ! [X9] :
( c_Recdef_Owfrec__rel(X5,X4,X3,X2,X9,hAPP(X8,X9))
| ~ c_member(tc_prod(X5,X5),c_Product__Type_OPair(X5,X5,X9,X1),X3) )
& hAPP(hAPP(X2,X0),X1) = hAPP(hAPP(X2,X8),X1) )
| ~ c_Recdef_Owfrec__rel(X5,X4,X3,X2,X1,hAPP(hAPP(X2,X0),X1)) ) ),
inference(rectify,[],[f1827]) ).
fof(f1827,plain,
! [X0,X1,X2,X3,X4,X5] :
( ( c_Recdef_Owfrec__rel(X5,X4,X3,X2,X1,hAPP(hAPP(X2,X0),X1))
| ! [X6] :
( ? [X7] :
( ~ c_Recdef_Owfrec__rel(X5,X4,X3,X2,X7,hAPP(X6,X7))
& c_member(tc_prod(X5,X5),c_Product__Type_OPair(X5,X5,X7,X1),X3) )
| hAPP(hAPP(X2,X6),X1) != hAPP(hAPP(X2,X0),X1) ) )
& ( ? [X6] :
( ! [X7] :
( c_Recdef_Owfrec__rel(X5,X4,X3,X2,X7,hAPP(X6,X7))
| ~ c_member(tc_prod(X5,X5),c_Product__Type_OPair(X5,X5,X7,X1),X3) )
& hAPP(hAPP(X2,X6),X1) = hAPP(hAPP(X2,X0),X1) )
| ~ c_Recdef_Owfrec__rel(X5,X4,X3,X2,X1,hAPP(hAPP(X2,X0),X1)) ) ),
inference(nnf_transformation,[],[f1512]) ).
fof(f1512,plain,
! [X0,X1,X2,X3,X4,X5] :
( c_Recdef_Owfrec__rel(X5,X4,X3,X2,X1,hAPP(hAPP(X2,X0),X1))
<=> ? [X6] :
( ! [X7] :
( c_Recdef_Owfrec__rel(X5,X4,X3,X2,X7,hAPP(X6,X7))
| ~ c_member(tc_prod(X5,X5),c_Product__Type_OPair(X5,X5,X7,X1),X3) )
& hAPP(hAPP(X2,X6),X1) = hAPP(hAPP(X2,X0),X1) ) ),
inference(ennf_transformation,[],[f1006]) ).
fof(f1006,plain,
! [X0,X1,X2,X3,X4,X5] :
( c_Recdef_Owfrec__rel(X5,X4,X3,X2,X1,hAPP(hAPP(X2,X0),X1))
<=> ? [X6] :
( ! [X7] :
( c_member(tc_prod(X5,X5),c_Product__Type_OPair(X5,X5,X7,X1),X3)
=> c_Recdef_Owfrec__rel(X5,X4,X3,X2,X7,hAPP(X6,X7)) )
& hAPP(hAPP(X2,X6),X1) = hAPP(hAPP(X2,X0),X1) ) ),
inference(rectify,[],[f43]) ).
fof(f43,axiom,
! [X34,X35,X36,X14,X15,X4] :
( c_Recdef_Owfrec__rel(X4,X15,X14,X36,X35,hAPP(hAPP(X36,X34),X35))
<=> ? [X37] :
( ! [X6] :
( c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X6,X35),X14)
=> c_Recdef_Owfrec__rel(X4,X15,X14,X36,X6,hAPP(X37,X6)) )
& hAPP(hAPP(X36,X34),X35) = hAPP(hAPP(X36,X37),X35) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wfrec__rel_Oequations) ).
fof(f13847,plain,
spl104_588,
inference(avatar_split_clause,[],[f2709,f13845]) ).
fof(f13845,plain,
( spl104_588
<=> ! [X2,X4,X0,X3,X1] :
( c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,X0),c_Transitive__Closure_Otrancl(X4,X1))
| ~ c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X2,X0),X1)
| ~ c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,X2),c_Transitive__Closure_Otrancl(X4,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),X1,c_Relation_OId(X4)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_588])]) ).
fof(f2709,plain,
! [X2,X3,X0,X1,X4] :
( c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,X0),c_Transitive__Closure_Otrancl(X4,X1))
| ~ c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X2,X0),X1)
| ~ c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,X2),c_Transitive__Closure_Otrancl(X4,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),X1,c_Relation_OId(X4)))) ),
inference(definition_unfolding,[],[f2551,f1949]) ).
fof(f2551,plain,
! [X2,X3,X0,X1,X4] :
( c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,X0),c_Transitive__Closure_Otrancl(X4,X1))
| ~ c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X2,X0),X1)
| ~ c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,X2),c_Transitive__Closure_Ortrancl(X4,X1)) ),
inference(cnf_transformation,[],[f1482]) ).
fof(f1482,plain,
! [X0,X1,X2,X3,X4] :
( c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,X0),c_Transitive__Closure_Otrancl(X4,X1))
| ~ c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X2,X0),X1)
| ~ c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,X2),c_Transitive__Closure_Ortrancl(X4,X1)) ),
inference(flattening,[],[f1481]) ).
fof(f1481,plain,
! [X0,X1,X2,X3,X4] :
( c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,X0),c_Transitive__Closure_Otrancl(X4,X1))
| ~ c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X2,X0),X1)
| ~ c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,X2),c_Transitive__Closure_Ortrancl(X4,X1)) ),
inference(ennf_transformation,[],[f980]) ).
fof(f980,plain,
! [X0,X1,X2,X3,X4] :
( c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,X2),c_Transitive__Closure_Ortrancl(X4,X1))
=> ( c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X2,X0),X1)
=> c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,X0),c_Transitive__Closure_Otrancl(X4,X1)) ) ),
inference(rectify,[],[f93]) ).
fof(f93,axiom,
! [X7,X3,X8,X9,X4] :
( c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X9,X8),c_Transitive__Closure_Ortrancl(X4,X3))
=> ( c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X8,X7),X3)
=> c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X9,X7),c_Transitive__Closure_Otrancl(X4,X3)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__into__trancl1) ).
fof(f13843,plain,
spl104_587,
inference(avatar_split_clause,[],[f2698,f13841]) ).
fof(f13841,plain,
( spl104_587
<=> ! [X2,X4,X0,X3,X1] :
( c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,X0),c_Transitive__Closure_Otrancl(X4,X1))
| ~ c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X2,X0),c_Transitive__Closure_Otrancl(X4,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),X1,c_Relation_OId(X4))))
| ~ c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_587])]) ).
fof(f2698,plain,
! [X2,X3,X0,X1,X4] :
( c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,X0),c_Transitive__Closure_Otrancl(X4,X1))
| ~ c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X2,X0),c_Transitive__Closure_Otrancl(X4,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),X1,c_Relation_OId(X4))))
| ~ c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,X2),X1) ),
inference(definition_unfolding,[],[f2538,f1949]) ).
fof(f2538,plain,
! [X2,X3,X0,X1,X4] :
( c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,X0),c_Transitive__Closure_Otrancl(X4,X1))
| ~ c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X2,X0),c_Transitive__Closure_Ortrancl(X4,X1))
| ~ c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,X2),X1) ),
inference(cnf_transformation,[],[f1468]) ).
fof(f1468,plain,
! [X0,X1,X2,X3,X4] :
( c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,X0),c_Transitive__Closure_Otrancl(X4,X1))
| ~ c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X2,X0),c_Transitive__Closure_Ortrancl(X4,X1))
| ~ c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,X2),X1) ),
inference(flattening,[],[f1467]) ).
fof(f1467,plain,
! [X0,X1,X2,X3,X4] :
( c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,X0),c_Transitive__Closure_Otrancl(X4,X1))
| ~ c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X2,X0),c_Transitive__Closure_Ortrancl(X4,X1))
| ~ c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,X2),X1) ),
inference(ennf_transformation,[],[f973]) ).
fof(f973,plain,
! [X0,X1,X2,X3,X4] :
( c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,X2),X1)
=> ( c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X2,X0),c_Transitive__Closure_Ortrancl(X4,X1))
=> c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,X0),c_Transitive__Closure_Otrancl(X4,X1)) ) ),
inference(rectify,[],[f91]) ).
fof(f91,axiom,
! [X7,X3,X8,X9,X4] :
( c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X9,X8),X3)
=> ( c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X8,X7),c_Transitive__Closure_Ortrancl(X4,X3))
=> c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X9,X7),c_Transitive__Closure_Otrancl(X4,X3)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__into__trancl2) ).
fof(f13838,plain,
spl104_586,
inference(avatar_split_clause,[],[f2615,f13836]) ).
fof(f13836,plain,
( spl104_586
<=> ! [X2,X3,X0,X1,X8,X6,X7,X4,X5] :
( sP11(X0,X1,X2,X3,X4,X5,X6)
| ~ c_Nitpick_Ofold__graph_H(X0,X4,X3,X2,c_Groups_Ominus__class_Ominus(tc_fun(X0,tc_HOL_Obool),X1,c_Set_Oinsert(X0,X7,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)))),X8)
| ~ c_member(X0,X7,X1)
| hAPP(hAPP(X3,X6),X5) != hAPP(hAPP(X3,X7),X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_586])]) ).
fof(f2615,plain,
! [X2,X3,X0,X1,X8,X6,X7,X4,X5] :
( sP11(X0,X1,X2,X3,X4,X5,X6)
| ~ c_Nitpick_Ofold__graph_H(X0,X4,X3,X2,c_Groups_Ominus__class_Ominus(tc_fun(X0,tc_HOL_Obool),X1,c_Set_Oinsert(X0,X7,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)))),X8)
| ~ c_member(X0,X7,X1)
| hAPP(hAPP(X3,X6),X5) != hAPP(hAPP(X3,X7),X8) ),
inference(cnf_transformation,[],[f1842]) ).
fof(f1842,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ( sP11(X0,X1,X2,X3,X4,X5,X6)
| ! [X7,X8] :
( ~ c_Nitpick_Ofold__graph_H(X0,X4,X3,X2,c_Groups_Ominus__class_Ominus(tc_fun(X0,tc_HOL_Obool),X1,c_Set_Oinsert(X0,X7,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)))),X8)
| ~ c_member(X0,X7,X1)
| hAPP(hAPP(X3,X6),X5) != hAPP(hAPP(X3,X7),X8) ) )
& ( ( c_Nitpick_Ofold__graph_H(X0,X4,X3,X2,c_Groups_Ominus__class_Ominus(tc_fun(X0,tc_HOL_Obool),X1,c_Set_Oinsert(X0,sK94(X0,X1,X2,X3,X4,X5,X6),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)))),sK95(X0,X1,X2,X3,X4,X5,X6))
& c_member(X0,sK94(X0,X1,X2,X3,X4,X5,X6),X1)
& hAPP(hAPP(X3,X6),X5) = hAPP(hAPP(X3,sK94(X0,X1,X2,X3,X4,X5,X6)),sK95(X0,X1,X2,X3,X4,X5,X6)) )
| ~ sP11(X0,X1,X2,X3,X4,X5,X6) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK94,sK95])],[f1840,f1841]) ).
fof(f1841,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ? [X9,X10] :
( c_Nitpick_Ofold__graph_H(X0,X4,X3,X2,c_Groups_Ominus__class_Ominus(tc_fun(X0,tc_HOL_Obool),X1,c_Set_Oinsert(X0,X9,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)))),X10)
& c_member(X0,X9,X1)
& hAPP(hAPP(X3,X6),X5) = hAPP(hAPP(X3,X9),X10) )
=> ( c_Nitpick_Ofold__graph_H(X0,X4,X3,X2,c_Groups_Ominus__class_Ominus(tc_fun(X0,tc_HOL_Obool),X1,c_Set_Oinsert(X0,sK94(X0,X1,X2,X3,X4,X5,X6),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)))),sK95(X0,X1,X2,X3,X4,X5,X6))
& c_member(X0,sK94(X0,X1,X2,X3,X4,X5,X6),X1)
& hAPP(hAPP(X3,X6),X5) = hAPP(hAPP(X3,sK94(X0,X1,X2,X3,X4,X5,X6)),sK95(X0,X1,X2,X3,X4,X5,X6)) ) ),
introduced(choice_axiom,[]) ).
fof(f1840,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ( sP11(X0,X1,X2,X3,X4,X5,X6)
| ! [X7,X8] :
( ~ c_Nitpick_Ofold__graph_H(X0,X4,X3,X2,c_Groups_Ominus__class_Ominus(tc_fun(X0,tc_HOL_Obool),X1,c_Set_Oinsert(X0,X7,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)))),X8)
| ~ c_member(X0,X7,X1)
| hAPP(hAPP(X3,X6),X5) != hAPP(hAPP(X3,X7),X8) ) )
& ( ? [X9,X10] :
( c_Nitpick_Ofold__graph_H(X0,X4,X3,X2,c_Groups_Ominus__class_Ominus(tc_fun(X0,tc_HOL_Obool),X1,c_Set_Oinsert(X0,X9,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)))),X10)
& c_member(X0,X9,X1)
& hAPP(hAPP(X3,X6),X5) = hAPP(hAPP(X3,X9),X10) )
| ~ sP11(X0,X1,X2,X3,X4,X5,X6) ) ),
inference(rectify,[],[f1839]) ).
fof(f1839,plain,
! [X6,X2,X3,X4,X5,X0,X1] :
( ( sP11(X6,X2,X3,X4,X5,X0,X1)
| ! [X7,X8] :
( ~ c_Nitpick_Ofold__graph_H(X6,X5,X4,X3,c_Groups_Ominus__class_Ominus(tc_fun(X6,tc_HOL_Obool),X2,c_Set_Oinsert(X6,X7,c_Orderings_Obot__class_Obot(tc_fun(X6,tc_HOL_Obool)))),X8)
| ~ c_member(X6,X7,X2)
| hAPP(hAPP(X4,X1),X0) != hAPP(hAPP(X4,X7),X8) ) )
& ( ? [X7,X8] :
( c_Nitpick_Ofold__graph_H(X6,X5,X4,X3,c_Groups_Ominus__class_Ominus(tc_fun(X6,tc_HOL_Obool),X2,c_Set_Oinsert(X6,X7,c_Orderings_Obot__class_Obot(tc_fun(X6,tc_HOL_Obool)))),X8)
& c_member(X6,X7,X2)
& hAPP(hAPP(X4,X1),X0) = hAPP(hAPP(X4,X7),X8) )
| ~ sP11(X6,X2,X3,X4,X5,X0,X1) ) ),
inference(nnf_transformation,[],[f1545]) ).
fof(f1545,plain,
! [X6,X2,X3,X4,X5,X0,X1] :
( sP11(X6,X2,X3,X4,X5,X0,X1)
<=> ? [X7,X8] :
( c_Nitpick_Ofold__graph_H(X6,X5,X4,X3,c_Groups_Ominus__class_Ominus(tc_fun(X6,tc_HOL_Obool),X2,c_Set_Oinsert(X6,X7,c_Orderings_Obot__class_Obot(tc_fun(X6,tc_HOL_Obool)))),X8)
& c_member(X6,X7,X2)
& hAPP(hAPP(X4,X1),X0) = hAPP(hAPP(X4,X7),X8) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP11])]) ).
fof(f13781,plain,
( spl104_585
| ~ spl104_206
| ~ spl104_389 ),
inference(avatar_split_clause,[],[f7115,f7002,f4072,f13779]) ).
fof(f13779,plain,
( spl104_585
<=> ! [X0,X1] :
( c_Wellfounded_Oacyclic(X0,X1)
| ~ c_Wellfounded_Owf(X0,c_Transitive__Closure_Otrancl(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_585])]) ).
fof(f7115,plain,
( ! [X0,X1] :
( c_Wellfounded_Oacyclic(X0,X1)
| ~ c_Wellfounded_Owf(X0,c_Transitive__Closure_Otrancl(X0,X1)) )
| ~ spl104_206
| ~ spl104_389 ),
inference(resolution,[],[f7003,f4073]) ).
fof(f13777,plain,
spl104_584,
inference(avatar_split_clause,[],[f2817,f13775]) ).
fof(f13775,plain,
( spl104_584
<=> ! [X2,X4,X0,X6,X5,X1,X7] :
( c_member(tc_prod(tc_prod(X7,X6),tc_prod(X7,X6)),c_Product__Type_OPair(tc_prod(X7,X6),tc_prod(X7,X6),c_Product__Type_OPair(X7,X6,X5,X4),c_Product__Type_OPair(X7,X6,X5,X2)),c_Wellfounded_Olex__prod(X7,X6,X1,X0))
| ~ c_member(tc_prod(X6,X6),c_Product__Type_OPair(X6,X6,X4,X2),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_584])]) ).
fof(f2817,plain,
! [X2,X0,X1,X6,X7,X4,X5] :
( c_member(tc_prod(tc_prod(X7,X6),tc_prod(X7,X6)),c_Product__Type_OPair(tc_prod(X7,X6),tc_prod(X7,X6),c_Product__Type_OPair(X7,X6,X5,X4),c_Product__Type_OPair(X7,X6,X5,X2)),c_Wellfounded_Olex__prod(X7,X6,X1,X0))
| ~ c_member(tc_prod(X6,X6),c_Product__Type_OPair(X6,X6,X4,X2),X0) ),
inference(equality_resolution,[],[f2632]) ).
fof(f2632,plain,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( c_member(tc_prod(tc_prod(X7,X6),tc_prod(X7,X6)),c_Product__Type_OPair(tc_prod(X7,X6),tc_prod(X7,X6),c_Product__Type_OPair(X7,X6,X5,X4),c_Product__Type_OPair(X7,X6,X3,X2)),c_Wellfounded_Olex__prod(X7,X6,X1,X0))
| ~ c_member(tc_prod(X6,X6),c_Product__Type_OPair(X6,X6,X4,X2),X0)
| X3 != X5 ),
inference(cnf_transformation,[],[f1851]) ).
fof(f13773,plain,
spl104_583,
inference(avatar_split_clause,[],[f2631,f13771]) ).
fof(f13771,plain,
( spl104_583
<=> ! [X2,X3,X4,X0,X6,X5,X1,X7] :
( c_member(tc_prod(tc_prod(X7,X6),tc_prod(X7,X6)),c_Product__Type_OPair(tc_prod(X7,X6),tc_prod(X7,X6),c_Product__Type_OPair(X7,X6,X5,X4),c_Product__Type_OPair(X7,X6,X3,X2)),c_Wellfounded_Olex__prod(X7,X6,X1,X0))
| ~ c_member(tc_prod(X7,X7),c_Product__Type_OPair(X7,X7,X5,X3),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_583])]) ).
fof(f2631,plain,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( c_member(tc_prod(tc_prod(X7,X6),tc_prod(X7,X6)),c_Product__Type_OPair(tc_prod(X7,X6),tc_prod(X7,X6),c_Product__Type_OPair(X7,X6,X5,X4),c_Product__Type_OPair(X7,X6,X3,X2)),c_Wellfounded_Olex__prod(X7,X6,X1,X0))
| ~ c_member(tc_prod(X7,X7),c_Product__Type_OPair(X7,X7,X5,X3),X1) ),
inference(cnf_transformation,[],[f1851]) ).
fof(f13769,plain,
spl104_582,
inference(avatar_split_clause,[],[f2614,f13767]) ).
fof(f13767,plain,
( spl104_582
<=> ! [X5,X4,X2,X0,X6,X3,X1] :
( c_Nitpick_Ofold__graph_H(X0,X4,X3,X2,c_Groups_Ominus__class_Ominus(tc_fun(X0,tc_HOL_Obool),X1,c_Set_Oinsert(X0,sK94(X0,X1,X2,X3,X4,X5,X6),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)))),sK95(X0,X1,X2,X3,X4,X5,X6))
| ~ sP11(X0,X1,X2,X3,X4,X5,X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_582])]) ).
fof(f2614,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( c_Nitpick_Ofold__graph_H(X0,X4,X3,X2,c_Groups_Ominus__class_Ominus(tc_fun(X0,tc_HOL_Obool),X1,c_Set_Oinsert(X0,sK94(X0,X1,X2,X3,X4,X5,X6),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)))),sK95(X0,X1,X2,X3,X4,X5,X6))
| ~ sP11(X0,X1,X2,X3,X4,X5,X6) ),
inference(cnf_transformation,[],[f1842]) ).
fof(f13562,plain,
spl104_581,
inference(avatar_split_clause,[],[f2870,f13560]) ).
fof(f13560,plain,
( spl104_581
<=> ! [X0,X3,X2,X1] :
( c_member(tc_prod(X3,X3),X2,c_Transitive__Closure_Otrancl(X3,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X3,X3),tc_HOL_Obool),c_Relation_OId(X3),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X3,X3),tc_HOL_Obool),X1,X0))))
| ~ c_member(tc_prod(X3,X3),X2,c_Transitive__Closure_Otrancl(X3,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X3,X3),tc_HOL_Obool),X1,c_Relation_OId(X3)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_581])]) ).
fof(f2870,plain,
! [X2,X3,X0,X1] :
( c_member(tc_prod(X3,X3),X2,c_Transitive__Closure_Otrancl(X3,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X3,X3),tc_HOL_Obool),c_Relation_OId(X3),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X3,X3),tc_HOL_Obool),X1,X0))))
| ~ c_member(tc_prod(X3,X3),X2,c_Transitive__Closure_Otrancl(X3,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X3,X3),tc_HOL_Obool),X1,c_Relation_OId(X3)))) ),
inference(forward_demodulation,[],[f2683,f2058]) ).
fof(f2683,plain,
! [X2,X3,X0,X1] :
( c_member(tc_prod(X3,X3),X2,c_Transitive__Closure_Otrancl(X3,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X3,X3),tc_HOL_Obool),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X3,X3),tc_HOL_Obool),X1,X0),c_Relation_OId(X3))))
| ~ c_member(tc_prod(X3,X3),X2,c_Transitive__Closure_Otrancl(X3,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X3,X3),tc_HOL_Obool),X1,c_Relation_OId(X3)))) ),
inference(definition_unfolding,[],[f2420,f1949,f1949]) ).
fof(f2420,plain,
! [X2,X3,X0,X1] :
( c_member(tc_prod(X3,X3),X2,c_Transitive__Closure_Ortrancl(X3,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X3,X3),tc_HOL_Obool),X1,X0)))
| ~ c_member(tc_prod(X3,X3),X2,c_Transitive__Closure_Ortrancl(X3,X1)) ),
inference(cnf_transformation,[],[f1421]) ).
fof(f1421,plain,
! [X0,X1,X2,X3] :
( c_member(tc_prod(X3,X3),X2,c_Transitive__Closure_Ortrancl(X3,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X3,X3),tc_HOL_Obool),X1,X0)))
| ( ~ c_member(tc_prod(X3,X3),X2,c_Transitive__Closure_Ortrancl(X3,X0))
& ~ c_member(tc_prod(X3,X3),X2,c_Transitive__Closure_Ortrancl(X3,X1)) ) ),
inference(ennf_transformation,[],[f918]) ).
fof(f918,plain,
! [X0,X1,X2,X3] :
( ( c_member(tc_prod(X3,X3),X2,c_Transitive__Closure_Ortrancl(X3,X0))
| c_member(tc_prod(X3,X3),X2,c_Transitive__Closure_Ortrancl(X3,X1)) )
=> c_member(tc_prod(X3,X3),X2,c_Transitive__Closure_Ortrancl(X3,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X3,X3),tc_HOL_Obool),X1,X0))) ),
inference(rectify,[],[f148]) ).
fof(f148,axiom,
! [X54,X14,X13,X4] :
( ( c_member(tc_prod(X4,X4),X13,c_Transitive__Closure_Ortrancl(X4,X54))
| c_member(tc_prod(X4,X4),X13,c_Transitive__Closure_Ortrancl(X4,X14)) )
=> c_member(tc_prod(X4,X4),X13,c_Transitive__Closure_Ortrancl(X4,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),X14,X54))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_in__rtrancl__UnI) ).
fof(f13558,plain,
spl104_580,
inference(avatar_split_clause,[],[f2869,f13556]) ).
fof(f13556,plain,
( spl104_580
<=> ! [X0,X3,X2,X1] :
( c_member(tc_prod(X3,X3),X2,c_Transitive__Closure_Otrancl(X3,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X3,X3),tc_HOL_Obool),c_Relation_OId(X3),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X3,X3),tc_HOL_Obool),X1,X0))))
| ~ c_member(tc_prod(X3,X3),X2,c_Transitive__Closure_Otrancl(X3,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X3,X3),tc_HOL_Obool),X0,c_Relation_OId(X3)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_580])]) ).
fof(f2869,plain,
! [X2,X3,X0,X1] :
( c_member(tc_prod(X3,X3),X2,c_Transitive__Closure_Otrancl(X3,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X3,X3),tc_HOL_Obool),c_Relation_OId(X3),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X3,X3),tc_HOL_Obool),X1,X0))))
| ~ c_member(tc_prod(X3,X3),X2,c_Transitive__Closure_Otrancl(X3,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X3,X3),tc_HOL_Obool),X0,c_Relation_OId(X3)))) ),
inference(forward_demodulation,[],[f2682,f2058]) ).
fof(f2682,plain,
! [X2,X3,X0,X1] :
( c_member(tc_prod(X3,X3),X2,c_Transitive__Closure_Otrancl(X3,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X3,X3),tc_HOL_Obool),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X3,X3),tc_HOL_Obool),X1,X0),c_Relation_OId(X3))))
| ~ c_member(tc_prod(X3,X3),X2,c_Transitive__Closure_Otrancl(X3,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X3,X3),tc_HOL_Obool),X0,c_Relation_OId(X3)))) ),
inference(definition_unfolding,[],[f2421,f1949,f1949]) ).
fof(f2421,plain,
! [X2,X3,X0,X1] :
( c_member(tc_prod(X3,X3),X2,c_Transitive__Closure_Ortrancl(X3,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X3,X3),tc_HOL_Obool),X1,X0)))
| ~ c_member(tc_prod(X3,X3),X2,c_Transitive__Closure_Ortrancl(X3,X0)) ),
inference(cnf_transformation,[],[f1421]) ).
fof(f13554,plain,
spl104_579,
inference(avatar_split_clause,[],[f2826,f13552]) ).
fof(f13552,plain,
( spl104_579
<=> ! [X0] :
( c_Relation_OId__on(tc_Nat_Onat,c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) = X0
| c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),X0,c_Relation_OId__on(tc_Nat_Onat,c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))),c_FunDef_Omin__strict) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_579])]) ).
fof(f2826,plain,
! [X0] :
( c_Relation_OId__on(tc_Nat_Onat,c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) = X0
| c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),X0,c_Relation_OId__on(tc_Nat_Onat,c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))),c_FunDef_Omin__strict) ),
inference(forward_demodulation,[],[f2825,f1912]) ).
fof(f2825,plain,
! [X0] :
( c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),X0,c_Relation_OId__on(tc_Nat_Onat,c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))),c_FunDef_Omin__strict)
| c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)) = X0 ),
inference(forward_demodulation,[],[f1915,f1912]) ).
fof(f1915,plain,
! [X0] :
( c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),X0,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),c_FunDef_Omin__strict)
| c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)) = X0 ),
inference(cnf_transformation,[],[f1027]) ).
fof(f1027,plain,
! [X0] :
( c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),X0,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),c_FunDef_Omin__strict)
| c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)) = X0 ),
inference(ennf_transformation,[],[f545]) ).
fof(f545,plain,
! [X0] :
( c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)) != X0
=> c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),X0,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),c_FunDef_Omin__strict) ),
inference(rectify,[],[f452]) ).
fof(f452,axiom,
! [X80] :
( c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)) != X80
=> c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),X80,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),c_FunDef_Omin__strict) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_smin__emptyI) ).
fof(f13460,plain,
spl104_578,
inference(avatar_split_clause,[],[f2601,f13458]) ).
fof(f13458,plain,
( spl104_578
<=> ! [X5,X6,X4,X0,X3,X2,X1] :
( c_Recdef_Owfrec__rel(X5,X4,X3,X2,X1,hAPP(hAPP(X2,X0),X1))
| c_member(tc_prod(X5,X5),c_Product__Type_OPair(X5,X5,sK89(X1,X2,X3,X4,X5,X6),X1),X3)
| hAPP(hAPP(X2,X6),X1) != hAPP(hAPP(X2,X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_578])]) ).
fof(f2601,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( c_Recdef_Owfrec__rel(X5,X4,X3,X2,X1,hAPP(hAPP(X2,X0),X1))
| c_member(tc_prod(X5,X5),c_Product__Type_OPair(X5,X5,sK89(X1,X2,X3,X4,X5,X6),X1),X3)
| hAPP(hAPP(X2,X6),X1) != hAPP(hAPP(X2,X0),X1) ),
inference(cnf_transformation,[],[f1831]) ).
fof(f13456,plain,
spl104_577,
inference(avatar_split_clause,[],[f2405,f13454]) ).
fof(f13454,plain,
( spl104_577
<=> ! [X0,X3,X2,X1] :
( c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X2,sK61(X0,X1,X2,X3)),c_Transitive__Closure_Otrancl(X3,X0))
| c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X2,X1),X0)
| ~ c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X2,X1),c_Transitive__Closure_Otrancl(X3,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_577])]) ).
fof(f2405,plain,
! [X2,X3,X0,X1] :
( c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X2,sK61(X0,X1,X2,X3)),c_Transitive__Closure_Otrancl(X3,X0))
| c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X2,X1),X0)
| ~ c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X2,X1),c_Transitive__Closure_Otrancl(X3,X0)) ),
inference(cnf_transformation,[],[f1722]) ).
fof(f1722,plain,
! [X0,X1,X2,X3] :
( ( c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,sK61(X0,X1,X2,X3),X1),X0)
& c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X2,sK61(X0,X1,X2,X3)),c_Transitive__Closure_Otrancl(X3,X0)) )
| c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X2,X1),X0)
| ~ c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X2,X1),c_Transitive__Closure_Otrancl(X3,X0)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK61])],[f1406,f1721]) ).
fof(f1721,plain,
! [X0,X1,X2,X3] :
( ? [X4] :
( c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X4,X1),X0)
& c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X2,X4),c_Transitive__Closure_Otrancl(X3,X0)) )
=> ( c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,sK61(X0,X1,X2,X3),X1),X0)
& c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X2,sK61(X0,X1,X2,X3)),c_Transitive__Closure_Otrancl(X3,X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f1406,plain,
! [X0,X1,X2,X3] :
( ? [X4] :
( c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X4,X1),X0)
& c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X2,X4),c_Transitive__Closure_Otrancl(X3,X0)) )
| c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X2,X1),X0)
| ~ c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X2,X1),c_Transitive__Closure_Otrancl(X3,X0)) ),
inference(flattening,[],[f1405]) ).
fof(f1405,plain,
! [X0,X1,X2,X3] :
( ? [X4] :
( c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X4,X1),X0)
& c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X2,X4),c_Transitive__Closure_Otrancl(X3,X0)) )
| c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X2,X1),X0)
| ~ c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X2,X1),c_Transitive__Closure_Otrancl(X3,X0)) ),
inference(ennf_transformation,[],[f909]) ).
fof(f909,plain,
! [X0,X1,X2,X3] :
( c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X2,X1),c_Transitive__Closure_Otrancl(X3,X0))
=> ( ~ c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X2,X1),X0)
=> ~ ! [X4] :
( c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X2,X4),c_Transitive__Closure_Otrancl(X3,X0))
=> ~ c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X4,X1),X0) ) ) ),
inference(rectify,[],[f103]) ).
fof(f103,axiom,
! [X3,X8,X9,X4] :
( c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X9,X8),c_Transitive__Closure_Otrancl(X4,X3))
=> ( ~ c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X9,X8),X3)
=> ~ ! [X52] :
( c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X9,X52),c_Transitive__Closure_Otrancl(X4,X3))
=> ~ c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X52,X8),X3) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_tranclE) ).
fof(f13452,plain,
spl104_576,
inference(avatar_split_clause,[],[f2404,f13450]) ).
fof(f13450,plain,
( spl104_576
<=> ! [X0,X3,X2,X1] :
( c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,sK60(X0,X1,X2,X3),X1),c_Transitive__Closure_Otrancl(X3,X0))
| c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X2,X1),X0)
| ~ c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X2,X1),c_Transitive__Closure_Otrancl(X3,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_576])]) ).
fof(f2404,plain,
! [X2,X3,X0,X1] :
( c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,sK60(X0,X1,X2,X3),X1),c_Transitive__Closure_Otrancl(X3,X0))
| c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X2,X1),X0)
| ~ c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X2,X1),c_Transitive__Closure_Otrancl(X3,X0)) ),
inference(cnf_transformation,[],[f1720]) ).
fof(f1720,plain,
! [X0,X1,X2,X3] :
( ( c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,sK60(X0,X1,X2,X3),X1),c_Transitive__Closure_Otrancl(X3,X0))
& c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X2,sK60(X0,X1,X2,X3)),X0) )
| c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X2,X1),X0)
| ~ c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X2,X1),c_Transitive__Closure_Otrancl(X3,X0)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK60])],[f1404,f1719]) ).
fof(f1719,plain,
! [X0,X1,X2,X3] :
( ? [X4] :
( c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X4,X1),c_Transitive__Closure_Otrancl(X3,X0))
& c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X2,X4),X0) )
=> ( c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,sK60(X0,X1,X2,X3),X1),c_Transitive__Closure_Otrancl(X3,X0))
& c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X2,sK60(X0,X1,X2,X3)),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f1404,plain,
! [X0,X1,X2,X3] :
( ? [X4] :
( c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X4,X1),c_Transitive__Closure_Otrancl(X3,X0))
& c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X2,X4),X0) )
| c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X2,X1),X0)
| ~ c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X2,X1),c_Transitive__Closure_Otrancl(X3,X0)) ),
inference(flattening,[],[f1403]) ).
fof(f1403,plain,
! [X0,X1,X2,X3] :
( ? [X4] :
( c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X4,X1),c_Transitive__Closure_Otrancl(X3,X0))
& c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X2,X4),X0) )
| c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X2,X1),X0)
| ~ c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X2,X1),c_Transitive__Closure_Otrancl(X3,X0)) ),
inference(ennf_transformation,[],[f908]) ).
fof(f908,plain,
! [X0,X1,X2,X3] :
( c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X2,X1),c_Transitive__Closure_Otrancl(X3,X0))
=> ( ~ c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X2,X1),X0)
=> ~ ! [X4] :
( c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X2,X4),X0)
=> ~ c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X4,X1),c_Transitive__Closure_Otrancl(X3,X0)) ) ) ),
inference(rectify,[],[f102]) ).
fof(f102,axiom,
! [X3,X38,X13,X4] :
( c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X13,X38),c_Transitive__Closure_Otrancl(X4,X3))
=> ( ~ c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X13,X38),X3)
=> ~ ! [X5] :
( c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X13,X5),X3)
=> ~ c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X5,X38),c_Transitive__Closure_Otrancl(X4,X3)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_converse__tranclE) ).
fof(f13306,plain,
spl104_575,
inference(avatar_split_clause,[],[f2679,f13304]) ).
fof(f13304,plain,
( spl104_575
<=> ! [X0,X3,X2,X1] :
( c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,sK65(X0,X1,X2,X3),X1),X0)
| X1 = X2
| ~ c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X2,X1),c_Transitive__Closure_Otrancl(X3,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X3,X3),tc_HOL_Obool),X0,c_Relation_OId(X3)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_575])]) ).
fof(f2679,plain,
! [X2,X3,X0,X1] :
( c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,sK65(X0,X1,X2,X3),X1),X0)
| X1 = X2
| ~ c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X2,X1),c_Transitive__Closure_Otrancl(X3,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X3,X3),tc_HOL_Obool),X0,c_Relation_OId(X3)))) ),
inference(definition_unfolding,[],[f2416,f1949]) ).
fof(f2416,plain,
! [X2,X3,X0,X1] :
( c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,sK65(X0,X1,X2,X3),X1),X0)
| X1 = X2
| ~ c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X2,X1),c_Transitive__Closure_Ortrancl(X3,X0)) ),
inference(cnf_transformation,[],[f1730]) ).
fof(f13302,plain,
spl104_574,
inference(avatar_split_clause,[],[f2678,f13300]) ).
fof(f13300,plain,
( spl104_574
<=> ! [X0,X3,X2,X1] :
( c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X2,sK64(X0,X1,X2,X3)),X0)
| X1 = X2
| ~ c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X2,X1),c_Transitive__Closure_Otrancl(X3,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X3,X3),tc_HOL_Obool),X0,c_Relation_OId(X3)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_574])]) ).
fof(f2678,plain,
! [X2,X3,X0,X1] :
( c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X2,sK64(X0,X1,X2,X3)),X0)
| X1 = X2
| ~ c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X2,X1),c_Transitive__Closure_Otrancl(X3,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X3,X3),tc_HOL_Obool),X0,c_Relation_OId(X3)))) ),
inference(definition_unfolding,[],[f2413,f1949]) ).
fof(f2413,plain,
! [X2,X3,X0,X1] :
( c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X2,sK64(X0,X1,X2,X3)),X0)
| X1 = X2
| ~ c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X2,X1),c_Transitive__Closure_Ortrancl(X3,X0)) ),
inference(cnf_transformation,[],[f1728]) ).
fof(f12451,plain,
spl104_573,
inference(avatar_split_clause,[],[f2838,f12449]) ).
fof(f12449,plain,
( spl104_573
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool),c_Relation_ORange(X2,X2,X1),c_Relation_ODomain(X2,X2,X1)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool),c_Relation_ORange(X2,X2,X0),c_Relation_ODomain(X2,X2,X0)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_573])]) ).
fof(f2838,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool),c_Relation_ORange(X2,X2,X1),c_Relation_ODomain(X2,X2,X1)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool),c_Relation_ORange(X2,X2,X0),c_Relation_ODomain(X2,X2,X0)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),X1,X0) ),
inference(forward_demodulation,[],[f2837,f2058]) ).
fof(f2837,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool),c_Relation_ODomain(X2,X2,X1),c_Relation_ORange(X2,X2,X1)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool),c_Relation_ORange(X2,X2,X0),c_Relation_ODomain(X2,X2,X0)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),X1,X0) ),
inference(forward_demodulation,[],[f2653,f2058]) ).
fof(f2653,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool),c_Relation_ODomain(X2,X2,X1),c_Relation_ORange(X2,X2,X1)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool),c_Relation_ODomain(X2,X2,X0),c_Relation_ORange(X2,X2,X0)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),X1,X0) ),
inference(definition_unfolding,[],[f2187,f1954,f1954]) ).
fof(f2187,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool),c_Relation_OField(X2,X1),c_Relation_OField(X2,X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),X1,X0) ),
inference(cnf_transformation,[],[f1216]) ).
fof(f1216,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool),c_Relation_OField(X2,X1),c_Relation_OField(X2,X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),X1,X0) ),
inference(ennf_transformation,[],[f758]) ).
fof(f758,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),X1,X0)
=> c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool),c_Relation_OField(X2,X1),c_Relation_OField(X2,X0)) ),
inference(rectify,[],[f239]) ).
fof(f239,axiom,
! [X30,X3,X4] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),X3,X30)
=> c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool),c_Relation_OField(X4,X3),c_Relation_OField(X4,X30)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mono__Field) ).
fof(f12447,plain,
spl104_572,
inference(avatar_split_clause,[],[f2706,f12445]) ).
fof(f12445,plain,
( spl104_572
<=> ! [X4,X0,X3,X2,X1] :
( hBOOL(hAPP(X0,X3))
| hBOOL(hAPP(X0,sK80(X0,X1,X2,X4)))
| ~ hBOOL(hAPP(X0,X2))
| ~ c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,X2),c_Transitive__Closure_Otrancl(X4,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),X1,c_Relation_OId(X4)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_572])]) ).
fof(f2706,plain,
! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(X0,X3))
| hBOOL(hAPP(X0,sK80(X0,X1,X2,X4)))
| ~ hBOOL(hAPP(X0,X2))
| ~ c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,X2),c_Transitive__Closure_Otrancl(X4,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),X1,c_Relation_OId(X4)))) ),
inference(definition_unfolding,[],[f2549,f1949]) ).
fof(f2549,plain,
! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(X0,X3))
| hBOOL(hAPP(X0,sK80(X0,X1,X2,X4)))
| ~ hBOOL(hAPP(X0,X2))
| ~ c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,X2),c_Transitive__Closure_Ortrancl(X4,X1)) ),
inference(cnf_transformation,[],[f1801]) ).
fof(f12443,plain,
spl104_571,
inference(avatar_split_clause,[],[f2705,f12441]) ).
fof(f12441,plain,
( spl104_571
<=> ! [X4,X0,X3,X2,X1] :
( hBOOL(hAPP(X0,X3))
| ~ hBOOL(hAPP(X0,sK79(X0,X1,X2,X4)))
| ~ hBOOL(hAPP(X0,X2))
| ~ c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,X2),c_Transitive__Closure_Otrancl(X4,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),X1,c_Relation_OId(X4)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_571])]) ).
fof(f2705,plain,
! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(X0,X3))
| ~ hBOOL(hAPP(X0,sK79(X0,X1,X2,X4)))
| ~ hBOOL(hAPP(X0,X2))
| ~ c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,X2),c_Transitive__Closure_Otrancl(X4,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),X1,c_Relation_OId(X4)))) ),
inference(definition_unfolding,[],[f2550,f1949]) ).
fof(f2550,plain,
! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(X0,X3))
| ~ hBOOL(hAPP(X0,sK79(X0,X1,X2,X4)))
| ~ hBOOL(hAPP(X0,X2))
| ~ c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,X2),c_Transitive__Closure_Ortrancl(X4,X1)) ),
inference(cnf_transformation,[],[f1801]) ).
fof(f12439,plain,
spl104_570,
inference(avatar_split_clause,[],[f2702,f12437]) ).
fof(f12437,plain,
( spl104_570
<=> ! [X4,X0,X3,X2,X1] :
( hBOOL(hAPP(X0,X2))
| hBOOL(hAPP(X0,sK77(X0,X1,X3,X4)))
| ~ hBOOL(hAPP(X0,X3))
| ~ c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,X2),c_Transitive__Closure_Otrancl(X4,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),X1,c_Relation_OId(X4)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_570])]) ).
fof(f2702,plain,
! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(X0,X2))
| hBOOL(hAPP(X0,sK77(X0,X1,X3,X4)))
| ~ hBOOL(hAPP(X0,X3))
| ~ c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,X2),c_Transitive__Closure_Otrancl(X4,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),X1,c_Relation_OId(X4)))) ),
inference(definition_unfolding,[],[f2545,f1949]) ).
fof(f2545,plain,
! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(X0,X2))
| hBOOL(hAPP(X0,sK77(X0,X1,X3,X4)))
| ~ hBOOL(hAPP(X0,X3))
| ~ c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,X2),c_Transitive__Closure_Ortrancl(X4,X1)) ),
inference(cnf_transformation,[],[f1799]) ).
fof(f12435,plain,
spl104_569,
inference(avatar_split_clause,[],[f2701,f12433]) ).
fof(f12433,plain,
( spl104_569
<=> ! [X4,X0,X3,X2,X1] :
( hBOOL(hAPP(X0,X2))
| ~ hBOOL(hAPP(X0,sK78(X0,X1,X3,X4)))
| ~ hBOOL(hAPP(X0,X3))
| ~ c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,X2),c_Transitive__Closure_Otrancl(X4,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),X1,c_Relation_OId(X4)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_569])]) ).
fof(f2701,plain,
! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(X0,X2))
| ~ hBOOL(hAPP(X0,sK78(X0,X1,X3,X4)))
| ~ hBOOL(hAPP(X0,X3))
| ~ c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,X2),c_Transitive__Closure_Otrancl(X4,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),X1,c_Relation_OId(X4)))) ),
inference(definition_unfolding,[],[f2546,f1949]) ).
fof(f2546,plain,
! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(X0,X2))
| ~ hBOOL(hAPP(X0,sK78(X0,X1,X3,X4)))
| ~ hBOOL(hAPP(X0,X3))
| ~ c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,X2),c_Transitive__Closure_Ortrancl(X4,X1)) ),
inference(cnf_transformation,[],[f1799]) ).
fof(f12431,plain,
spl104_568,
inference(avatar_split_clause,[],[f2674,f12429]) ).
fof(f12429,plain,
( spl104_568
<=> ! [X0,X3,X2,X1] :
( c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X2,sK63(X0,X1,X2,X3)),c_Transitive__Closure_Otrancl(X3,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X3,X3),tc_HOL_Obool),X0,c_Relation_OId(X3))))
| ~ c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X2,X1),c_Transitive__Closure_Otrancl(X3,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_568])]) ).
fof(f2674,plain,
! [X2,X3,X0,X1] :
( c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X2,sK63(X0,X1,X2,X3)),c_Transitive__Closure_Otrancl(X3,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X3,X3),tc_HOL_Obool),X0,c_Relation_OId(X3))))
| ~ c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X2,X1),c_Transitive__Closure_Otrancl(X3,X0)) ),
inference(definition_unfolding,[],[f2409,f1949]) ).
fof(f2409,plain,
! [X2,X3,X0,X1] :
( c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X2,sK63(X0,X1,X2,X3)),c_Transitive__Closure_Ortrancl(X3,X0))
| ~ c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X2,X1),c_Transitive__Closure_Otrancl(X3,X0)) ),
inference(cnf_transformation,[],[f1726]) ).
fof(f1726,plain,
! [X0,X1,X2,X3] :
( ( c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,sK63(X0,X1,X2,X3),X1),X0)
& c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X2,sK63(X0,X1,X2,X3)),c_Transitive__Closure_Ortrancl(X3,X0)) )
| ~ c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X2,X1),c_Transitive__Closure_Otrancl(X3,X0)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK63])],[f1408,f1725]) ).
fof(f1725,plain,
! [X0,X1,X2,X3] :
( ? [X4] :
( c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X4,X1),X0)
& c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X2,X4),c_Transitive__Closure_Ortrancl(X3,X0)) )
=> ( c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,sK63(X0,X1,X2,X3),X1),X0)
& c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X2,sK63(X0,X1,X2,X3)),c_Transitive__Closure_Ortrancl(X3,X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f1408,plain,
! [X0,X1,X2,X3] :
( ? [X4] :
( c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X4,X1),X0)
& c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X2,X4),c_Transitive__Closure_Ortrancl(X3,X0)) )
| ~ c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X2,X1),c_Transitive__Closure_Otrancl(X3,X0)) ),
inference(ennf_transformation,[],[f911]) ).
fof(f911,plain,
! [X0,X1,X2,X3] :
( c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X2,X1),c_Transitive__Closure_Otrancl(X3,X0))
=> ? [X4] :
( c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X4,X1),X0)
& c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X2,X4),c_Transitive__Closure_Ortrancl(X3,X0)) ) ),
inference(rectify,[],[f98]) ).
fof(f98,axiom,
! [X14,X12,X13,X4] :
( c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X13,X12),c_Transitive__Closure_Otrancl(X4,X14))
=> ? [X6] :
( c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X6,X12),X14)
& c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X13,X6),c_Transitive__Closure_Ortrancl(X4,X14)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_tranclD2) ).
fof(f12427,plain,
spl104_567,
inference(avatar_split_clause,[],[f2673,f12425]) ).
fof(f12425,plain,
( spl104_567
<=> ! [X0,X3,X2,X1] :
( c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,sK62(X0,X1,X2,X3),X1),c_Transitive__Closure_Otrancl(X3,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X3,X3),tc_HOL_Obool),X0,c_Relation_OId(X3))))
| ~ c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X2,X1),c_Transitive__Closure_Otrancl(X3,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_567])]) ).
fof(f2673,plain,
! [X2,X3,X0,X1] :
( c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,sK62(X0,X1,X2,X3),X1),c_Transitive__Closure_Otrancl(X3,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X3,X3),tc_HOL_Obool),X0,c_Relation_OId(X3))))
| ~ c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X2,X1),c_Transitive__Closure_Otrancl(X3,X0)) ),
inference(definition_unfolding,[],[f2408,f1949]) ).
fof(f2408,plain,
! [X2,X3,X0,X1] :
( c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,sK62(X0,X1,X2,X3),X1),c_Transitive__Closure_Ortrancl(X3,X0))
| ~ c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X2,X1),c_Transitive__Closure_Otrancl(X3,X0)) ),
inference(cnf_transformation,[],[f1724]) ).
fof(f1724,plain,
! [X0,X1,X2,X3] :
( ( c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,sK62(X0,X1,X2,X3),X1),c_Transitive__Closure_Ortrancl(X3,X0))
& c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X2,sK62(X0,X1,X2,X3)),X0) )
| ~ c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X2,X1),c_Transitive__Closure_Otrancl(X3,X0)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK62])],[f1407,f1723]) ).
fof(f1723,plain,
! [X0,X1,X2,X3] :
( ? [X4] :
( c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X4,X1),c_Transitive__Closure_Ortrancl(X3,X0))
& c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X2,X4),X0) )
=> ( c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,sK62(X0,X1,X2,X3),X1),c_Transitive__Closure_Ortrancl(X3,X0))
& c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X2,sK62(X0,X1,X2,X3)),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f1407,plain,
! [X0,X1,X2,X3] :
( ? [X4] :
( c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X4,X1),c_Transitive__Closure_Ortrancl(X3,X0))
& c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X2,X4),X0) )
| ~ c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X2,X1),c_Transitive__Closure_Otrancl(X3,X0)) ),
inference(ennf_transformation,[],[f910]) ).
fof(f910,plain,
! [X0,X1,X2,X3] :
( c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X2,X1),c_Transitive__Closure_Otrancl(X3,X0))
=> ? [X4] :
( c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X4,X1),c_Transitive__Closure_Ortrancl(X3,X0))
& c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X2,X4),X0) ) ),
inference(rectify,[],[f99]) ).
fof(f99,axiom,
! [X14,X12,X13,X4] :
( c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X13,X12),c_Transitive__Closure_Otrancl(X4,X14))
=> ? [X6] :
( c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X6,X12),c_Transitive__Closure_Ortrancl(X4,X14))
& c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X13,X6),X14) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_tranclD) ).
fof(f12423,plain,
spl104_566,
inference(avatar_split_clause,[],[f2654,f12421]) ).
fof(f12421,plain,
( spl104_566
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),c_Transitive__Closure_Otrancl(X2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),X1,c_Relation_OId(X2))),c_Transitive__Closure_Otrancl(X2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),X0,c_Relation_OId(X2))))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_566])]) ).
fof(f2654,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),c_Transitive__Closure_Otrancl(X2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),X1,c_Relation_OId(X2))),c_Transitive__Closure_Otrancl(X2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),X0,c_Relation_OId(X2))))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),X1,X0) ),
inference(definition_unfolding,[],[f2188,f1949,f1949]) ).
fof(f2188,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),c_Transitive__Closure_Ortrancl(X2,X1),c_Transitive__Closure_Ortrancl(X2,X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),X1,X0) ),
inference(cnf_transformation,[],[f1217]) ).
fof(f1217,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),c_Transitive__Closure_Ortrancl(X2,X1),c_Transitive__Closure_Ortrancl(X2,X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),X1,X0) ),
inference(ennf_transformation,[],[f759]) ).
fof(f759,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),X1,X0)
=> c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),c_Transitive__Closure_Ortrancl(X2,X1),c_Transitive__Closure_Ortrancl(X2,X0)) ),
inference(rectify,[],[f270]) ).
fof(f270,axiom,
! [X30,X3,X4] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),X3,X30)
=> c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),c_Transitive__Closure_Ortrancl(X4,X3),c_Transitive__Closure_Ortrancl(X4,X30)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__mono) ).
fof(f12419,plain,
( spl104_565
| ~ spl104_370
| ~ spl104_391 ),
inference(avatar_split_clause,[],[f11435,f7010,f6473,f12417]) ).
fof(f12417,plain,
( spl104_565
<=> ! [X0,X1] : ~ sP5(X1,X0,c_fequal(X1),c_fequal(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_565])]) ).
fof(f7010,plain,
( spl104_391
<=> ! [X2,X0,X1] : ~ sP5(X0,X1,c_Set_Oinsert(X1,X0,X2),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_391])]) ).
fof(f11435,plain,
( ! [X0,X1] : ~ sP5(X1,X0,c_fequal(X1),c_fequal(X1))
| ~ spl104_370
| ~ spl104_391 ),
inference(superposition,[],[f7011,f6474]) ).
fof(f7011,plain,
( ! [X2,X0,X1] : ~ sP5(X0,X1,c_Set_Oinsert(X1,X0,X2),X2)
| ~ spl104_391 ),
inference(avatar_component_clause,[],[f7010]) ).
fof(f12415,plain,
spl104_564,
inference(avatar_split_clause,[],[f2644,f12413]) ).
fof(f12413,plain,
( spl104_564
<=> ! [X0,X1] : c_Transitive__Closure_Otrancl(X1,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),X0,c_Relation_OId(X1))) = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),c_Relation_OId(X1),c_Relation_Orel__comp(X1,X1,X1,c_Transitive__Closure_Otrancl(X1,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),X0,c_Relation_OId(X1))),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_564])]) ).
fof(f2644,plain,
! [X0,X1] : c_Transitive__Closure_Otrancl(X1,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),X0,c_Relation_OId(X1))) = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),c_Relation_OId(X1),c_Relation_Orel__comp(X1,X1,X1,c_Transitive__Closure_Otrancl(X1,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),X0,c_Relation_OId(X1))),X0)),
inference(definition_unfolding,[],[f1955,f1949,f1949]) ).
fof(f1955,plain,
! [X0,X1] : c_Transitive__Closure_Ortrancl(X1,X0) = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),c_Relation_OId(X1),c_Relation_Orel__comp(X1,X1,X1,c_Transitive__Closure_Ortrancl(X1,X0),X0)),
inference(cnf_transformation,[],[f585]) ).
fof(f585,plain,
! [X0,X1] : c_Transitive__Closure_Ortrancl(X1,X0) = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),c_Relation_OId(X1),c_Relation_Orel__comp(X1,X1,X1,c_Transitive__Closure_Ortrancl(X1,X0),X0)),
inference(rectify,[],[f492]) ).
fof(f492,axiom,
! [X3,X4] : c_Transitive__Closure_Ortrancl(X4,X3) = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),c_Relation_OId(X4),c_Relation_Orel__comp(X4,X4,X4,c_Transitive__Closure_Ortrancl(X4,X3),X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__unfold) ).
fof(f12411,plain,
spl104_563,
inference(avatar_split_clause,[],[f2600,f12409]) ).
fof(f12409,plain,
( spl104_563
<=> ! [X5,X4,X2,X0,X9,X3,X1] :
( c_Recdef_Owfrec__rel(X5,X4,X3,X2,X9,hAPP(sK90(X0,X1,X2,X3,X4,X5),X9))
| ~ c_member(tc_prod(X5,X5),c_Product__Type_OPair(X5,X5,X9,X1),X3)
| ~ c_Recdef_Owfrec__rel(X5,X4,X3,X2,X1,hAPP(hAPP(X2,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_563])]) ).
fof(f2600,plain,
! [X2,X3,X0,X1,X9,X4,X5] :
( c_Recdef_Owfrec__rel(X5,X4,X3,X2,X9,hAPP(sK90(X0,X1,X2,X3,X4,X5),X9))
| ~ c_member(tc_prod(X5,X5),c_Product__Type_OPair(X5,X5,X9,X1),X3)
| ~ c_Recdef_Owfrec__rel(X5,X4,X3,X2,X1,hAPP(hAPP(X2,X0),X1)) ),
inference(cnf_transformation,[],[f1831]) ).
fof(f12407,plain,
spl104_562,
inference(avatar_split_clause,[],[f2541,f12405]) ).
fof(f12405,plain,
( spl104_562
<=> ! [X2,X4,X0,X3,X1] :
( c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,X0),c_Transitive__Closure_Otrancl(X4,X1))
| ~ c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X2,X0),c_Transitive__Closure_Otrancl(X4,X1))
| ~ c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,X2),c_Transitive__Closure_Otrancl(X4,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_562])]) ).
fof(f2541,plain,
! [X2,X3,X0,X1,X4] :
( c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,X0),c_Transitive__Closure_Otrancl(X4,X1))
| ~ c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X2,X0),c_Transitive__Closure_Otrancl(X4,X1))
| ~ c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,X2),c_Transitive__Closure_Otrancl(X4,X1)) ),
inference(cnf_transformation,[],[f1474]) ).
fof(f1474,plain,
! [X0,X1,X2,X3,X4] :
( c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,X0),c_Transitive__Closure_Otrancl(X4,X1))
| ~ c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X2,X0),c_Transitive__Closure_Otrancl(X4,X1))
| ~ c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,X2),c_Transitive__Closure_Otrancl(X4,X1)) ),
inference(flattening,[],[f1473]) ).
fof(f1473,plain,
! [X0,X1,X2,X3,X4] :
( c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,X0),c_Transitive__Closure_Otrancl(X4,X1))
| ~ c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X2,X0),c_Transitive__Closure_Otrancl(X4,X1))
| ~ c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,X2),c_Transitive__Closure_Otrancl(X4,X1)) ),
inference(ennf_transformation,[],[f976]) ).
fof(f976,plain,
! [X0,X1,X2,X3,X4] :
( c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,X2),c_Transitive__Closure_Otrancl(X4,X1))
=> ( c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X2,X0),c_Transitive__Closure_Otrancl(X4,X1))
=> c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,X0),c_Transitive__Closure_Otrancl(X4,X1)) ) ),
inference(rectify,[],[f89]) ).
fof(f89,axiom,
! [X7,X3,X8,X9,X4] :
( c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X9,X8),c_Transitive__Closure_Otrancl(X4,X3))
=> ( c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X8,X7),c_Transitive__Closure_Otrancl(X4,X3))
=> c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X9,X7),c_Transitive__Closure_Otrancl(X4,X3)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trancl__trans) ).
fof(f12403,plain,
spl104_561,
inference(avatar_split_clause,[],[f2406,f12401]) ).
fof(f12401,plain,
( spl104_561
<=> ! [X0,X3,X2,X1] :
( c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,sK61(X0,X1,X2,X3),X1),X0)
| c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X2,X1),X0)
| ~ c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X2,X1),c_Transitive__Closure_Otrancl(X3,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_561])]) ).
fof(f2406,plain,
! [X2,X3,X0,X1] :
( c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,sK61(X0,X1,X2,X3),X1),X0)
| c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X2,X1),X0)
| ~ c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X2,X1),c_Transitive__Closure_Otrancl(X3,X0)) ),
inference(cnf_transformation,[],[f1722]) ).
fof(f12399,plain,
spl104_560,
inference(avatar_split_clause,[],[f2403,f12397]) ).
fof(f12397,plain,
( spl104_560
<=> ! [X0,X3,X2,X1] :
( c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X2,sK60(X0,X1,X2,X3)),X0)
| c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X2,X1),X0)
| ~ c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X2,X1),c_Transitive__Closure_Otrancl(X3,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_560])]) ).
fof(f2403,plain,
! [X2,X3,X0,X1] :
( c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X2,sK60(X0,X1,X2,X3)),X0)
| c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X2,X1),X0)
| ~ c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X2,X1),c_Transitive__Closure_Otrancl(X3,X0)) ),
inference(cnf_transformation,[],[f1720]) ).
fof(f12152,plain,
spl104_559,
inference(avatar_split_clause,[],[f2686,f12150]) ).
fof(f12150,plain,
( spl104_559
<=> ! [X0,X3,X2,X1] :
( c_Wellfounded_Owf(X3,c_Set_Oinsert(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X2,X1),X0))
| c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X1,X2),c_Transitive__Closure_Otrancl(X3,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X3,X3),tc_HOL_Obool),X0,c_Relation_OId(X3))))
| ~ c_Wellfounded_Owf(X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_559])]) ).
fof(f2686,plain,
! [X2,X3,X0,X1] :
( c_Wellfounded_Owf(X3,c_Set_Oinsert(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X2,X1),X0))
| c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X1,X2),c_Transitive__Closure_Otrancl(X3,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X3,X3),tc_HOL_Obool),X0,c_Relation_OId(X3))))
| ~ c_Wellfounded_Owf(X3,X0) ),
inference(definition_unfolding,[],[f2479,f1949]) ).
fof(f2479,plain,
! [X2,X3,X0,X1] :
( c_Wellfounded_Owf(X3,c_Set_Oinsert(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X2,X1),X0))
| c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X1,X2),c_Transitive__Closure_Ortrancl(X3,X0))
| ~ c_Wellfounded_Owf(X3,X0) ),
inference(cnf_transformation,[],[f1768]) ).
fof(f1768,plain,
! [X0,X1,X2,X3] :
( ( c_Wellfounded_Owf(X3,c_Set_Oinsert(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X2,X1),X0))
| c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X1,X2),c_Transitive__Closure_Ortrancl(X3,X0))
| ~ c_Wellfounded_Owf(X3,X0) )
& ( ( ~ c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X1,X2),c_Transitive__Closure_Ortrancl(X3,X0))
& c_Wellfounded_Owf(X3,X0) )
| ~ c_Wellfounded_Owf(X3,c_Set_Oinsert(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X2,X1),X0)) ) ),
inference(flattening,[],[f1767]) ).
fof(f1767,plain,
! [X0,X1,X2,X3] :
( ( c_Wellfounded_Owf(X3,c_Set_Oinsert(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X2,X1),X0))
| c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X1,X2),c_Transitive__Closure_Ortrancl(X3,X0))
| ~ c_Wellfounded_Owf(X3,X0) )
& ( ( ~ c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X1,X2),c_Transitive__Closure_Ortrancl(X3,X0))
& c_Wellfounded_Owf(X3,X0) )
| ~ c_Wellfounded_Owf(X3,c_Set_Oinsert(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X2,X1),X0)) ) ),
inference(nnf_transformation,[],[f935]) ).
fof(f935,plain,
! [X0,X1,X2,X3] :
( c_Wellfounded_Owf(X3,c_Set_Oinsert(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X2,X1),X0))
<=> ( ~ c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X1,X2),c_Transitive__Closure_Ortrancl(X3,X0))
& c_Wellfounded_Owf(X3,X0) ) ),
inference(rectify,[],[f160]) ).
fof(f160,axiom,
! [X3,X13,X12,X4] :
( c_Wellfounded_Owf(X4,c_Set_Oinsert(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X12,X13),X3))
<=> ( ~ c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X13,X12),c_Transitive__Closure_Ortrancl(X4,X3))
& c_Wellfounded_Owf(X4,X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__insert) ).
fof(f12148,plain,
spl104_558,
inference(avatar_split_clause,[],[f2684,f12146]) ).
fof(f12146,plain,
( spl104_558
<=> ! [X0,X3,X2,X1] :
( c_Wellfounded_Oacyclic(X3,c_Set_Oinsert(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X2,X1),X0))
| c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X1,X2),c_Transitive__Closure_Otrancl(X3,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X3,X3),tc_HOL_Obool),X0,c_Relation_OId(X3))))
| ~ c_Wellfounded_Oacyclic(X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_558])]) ).
fof(f2684,plain,
! [X2,X3,X0,X1] :
( c_Wellfounded_Oacyclic(X3,c_Set_Oinsert(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X2,X1),X0))
| c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X1,X2),c_Transitive__Closure_Otrancl(X3,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X3,X3),tc_HOL_Obool),X0,c_Relation_OId(X3))))
| ~ c_Wellfounded_Oacyclic(X3,X0) ),
inference(definition_unfolding,[],[f2476,f1949]) ).
fof(f2476,plain,
! [X2,X3,X0,X1] :
( c_Wellfounded_Oacyclic(X3,c_Set_Oinsert(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X2,X1),X0))
| c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X1,X2),c_Transitive__Closure_Ortrancl(X3,X0))
| ~ c_Wellfounded_Oacyclic(X3,X0) ),
inference(cnf_transformation,[],[f1766]) ).
fof(f1766,plain,
! [X0,X1,X2,X3] :
( ( c_Wellfounded_Oacyclic(X3,c_Set_Oinsert(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X2,X1),X0))
| c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X1,X2),c_Transitive__Closure_Ortrancl(X3,X0))
| ~ c_Wellfounded_Oacyclic(X3,X0) )
& ( ( ~ c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X1,X2),c_Transitive__Closure_Ortrancl(X3,X0))
& c_Wellfounded_Oacyclic(X3,X0) )
| ~ c_Wellfounded_Oacyclic(X3,c_Set_Oinsert(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X2,X1),X0)) ) ),
inference(flattening,[],[f1765]) ).
fof(f1765,plain,
! [X0,X1,X2,X3] :
( ( c_Wellfounded_Oacyclic(X3,c_Set_Oinsert(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X2,X1),X0))
| c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X1,X2),c_Transitive__Closure_Ortrancl(X3,X0))
| ~ c_Wellfounded_Oacyclic(X3,X0) )
& ( ( ~ c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X1,X2),c_Transitive__Closure_Ortrancl(X3,X0))
& c_Wellfounded_Oacyclic(X3,X0) )
| ~ c_Wellfounded_Oacyclic(X3,c_Set_Oinsert(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X2,X1),X0)) ) ),
inference(nnf_transformation,[],[f934]) ).
fof(f934,plain,
! [X0,X1,X2,X3] :
( c_Wellfounded_Oacyclic(X3,c_Set_Oinsert(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X2,X1),X0))
<=> ( ~ c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X1,X2),c_Transitive__Closure_Ortrancl(X3,X0))
& c_Wellfounded_Oacyclic(X3,X0) ) ),
inference(rectify,[],[f111]) ).
fof(f111,axiom,
! [X3,X13,X12,X4] :
( c_Wellfounded_Oacyclic(X4,c_Set_Oinsert(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X12,X13),X3))
<=> ( ~ c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X13,X12),c_Transitive__Closure_Ortrancl(X4,X3))
& c_Wellfounded_Oacyclic(X4,X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_acyclic__insert) ).
fof(f12144,plain,
spl104_557,
inference(avatar_split_clause,[],[f2675,f12142]) ).
fof(f12142,plain,
( spl104_557
<=> ! [X0,X3,X2,X1] :
( c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X2,X1),c_Transitive__Closure_Otrancl(X3,X0))
| X1 = X2
| ~ c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X2,X1),c_Transitive__Closure_Otrancl(X3,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X3,X3),tc_HOL_Obool),X0,c_Relation_OId(X3)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_557])]) ).
fof(f2675,plain,
! [X2,X3,X0,X1] :
( c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X2,X1),c_Transitive__Closure_Otrancl(X3,X0))
| X1 = X2
| ~ c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X2,X1),c_Transitive__Closure_Otrancl(X3,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X3,X3),tc_HOL_Obool),X0,c_Relation_OId(X3)))) ),
inference(definition_unfolding,[],[f2412,f1949]) ).
fof(f2412,plain,
! [X2,X3,X0,X1] :
( c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X2,X1),c_Transitive__Closure_Otrancl(X3,X0))
| X1 = X2
| ~ c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X2,X1),c_Transitive__Closure_Ortrancl(X3,X0)) ),
inference(cnf_transformation,[],[f1410]) ).
fof(f1410,plain,
! [X0,X1,X2,X3] :
( ( c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X2,X1),c_Transitive__Closure_Otrancl(X3,X0))
& X1 != X2 )
| X1 = X2
| ~ c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X2,X1),c_Transitive__Closure_Ortrancl(X3,X0)) ),
inference(flattening,[],[f1409]) ).
fof(f1409,plain,
! [X0,X1,X2,X3] :
( ( c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X2,X1),c_Transitive__Closure_Otrancl(X3,X0))
& X1 != X2 )
| X1 = X2
| ~ c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X2,X1),c_Transitive__Closure_Ortrancl(X3,X0)) ),
inference(ennf_transformation,[],[f912]) ).
fof(f912,plain,
! [X0,X1,X2,X3] :
( c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X2,X1),c_Transitive__Closure_Ortrancl(X3,X0))
=> ( ( c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X2,X1),c_Transitive__Closure_Otrancl(X3,X0))
& X1 != X2 )
| X1 = X2 ) ),
inference(rectify,[],[f92]) ).
fof(f92,axiom,
! [X14,X8,X9,X4] :
( c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X9,X8),c_Transitive__Closure_Ortrancl(X4,X14))
=> ( ( c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X9,X8),c_Transitive__Closure_Otrancl(X4,X14))
& X8 != X9 )
| X8 = X9 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtranclD) ).
fof(f12140,plain,
spl104_556,
inference(avatar_split_clause,[],[f2620,f12138]) ).
fof(f12138,plain,
( spl104_556
<=> ! [X1,X3,X4,X0,X6,X5,X2,X7] :
( c_member(tc_prod(X7,X2),c_Product__Type_OPair(X7,X2,X5,X1),c_Relation_Orel__comp(X7,X6,X2,X3,X0))
| ~ c_member(tc_prod(X6,X2),c_Product__Type_OPair(X6,X2,X4,X1),X0)
| ~ c_member(tc_prod(X7,X6),c_Product__Type_OPair(X7,X6,X5,X4),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_556])]) ).
fof(f2620,plain,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( c_member(tc_prod(X7,X2),c_Product__Type_OPair(X7,X2,X5,X1),c_Relation_Orel__comp(X7,X6,X2,X3,X0))
| ~ c_member(tc_prod(X6,X2),c_Product__Type_OPair(X6,X2,X4,X1),X0)
| ~ c_member(tc_prod(X7,X6),c_Product__Type_OPair(X7,X6,X5,X4),X3) ),
inference(cnf_transformation,[],[f1521]) ).
fof(f1521,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( c_member(tc_prod(X7,X2),c_Product__Type_OPair(X7,X2,X5,X1),c_Relation_Orel__comp(X7,X6,X2,X3,X0))
| ~ c_member(tc_prod(X6,X2),c_Product__Type_OPair(X6,X2,X4,X1),X0)
| ~ c_member(tc_prod(X7,X6),c_Product__Type_OPair(X7,X6,X5,X4),X3) ),
inference(flattening,[],[f1520]) ).
fof(f1520,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( c_member(tc_prod(X7,X2),c_Product__Type_OPair(X7,X2,X5,X1),c_Relation_Orel__comp(X7,X6,X2,X3,X0))
| ~ c_member(tc_prod(X6,X2),c_Product__Type_OPair(X6,X2,X4,X1),X0)
| ~ c_member(tc_prod(X7,X6),c_Product__Type_OPair(X7,X6,X5,X4),X3) ),
inference(ennf_transformation,[],[f1013]) ).
fof(f1013,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( c_member(tc_prod(X7,X6),c_Product__Type_OPair(X7,X6,X5,X4),X3)
=> ( c_member(tc_prod(X6,X2),c_Product__Type_OPair(X6,X2,X4,X1),X0)
=> c_member(tc_prod(X7,X2),c_Product__Type_OPair(X7,X2,X5,X1),c_Relation_Orel__comp(X7,X6,X2,X3,X0)) ) ),
inference(rectify,[],[f491]) ).
fof(f491,axiom,
! [X30,X7,X29,X3,X8,X9,X15,X4] :
( c_member(tc_prod(X4,X15),c_Product__Type_OPair(X4,X15,X9,X8),X3)
=> ( c_member(tc_prod(X15,X29),c_Product__Type_OPair(X15,X29,X8,X7),X30)
=> c_member(tc_prod(X4,X29),c_Product__Type_OPair(X4,X29,X9,X7),c_Relation_Orel__comp(X4,X15,X29,X3,X30)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__compI) ).
fof(f12136,plain,
spl104_555,
inference(avatar_split_clause,[],[f2217,f12134]) ).
fof(f12134,plain,
( spl104_555
<=> ! [X6,X0,X5,X2,X1] :
( c_member(tc_prod(X2,X2),c_Product__Type_OPair(X2,X2,X6,X5),X0)
| c_member(tc_prod(X2,X2),c_Product__Type_OPair(X2,X2,X5,X6),X0)
| X5 = X6
| ~ c_member(X2,X6,X1)
| ~ c_member(X2,X5,X1)
| ~ c_Relation_Ototal__on(X2,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_555])]) ).
fof(f2217,plain,
! [X2,X0,X1,X6,X5] :
( c_member(tc_prod(X2,X2),c_Product__Type_OPair(X2,X2,X6,X5),X0)
| c_member(tc_prod(X2,X2),c_Product__Type_OPair(X2,X2,X5,X6),X0)
| X5 = X6
| ~ c_member(X2,X6,X1)
| ~ c_member(X2,X5,X1)
| ~ c_Relation_Ototal__on(X2,X1,X0) ),
inference(cnf_transformation,[],[f1659]) ).
fof(f1659,plain,
! [X0,X1,X2] :
( ( c_Relation_Ototal__on(X2,X1,X0)
| ( ~ c_member(tc_prod(X2,X2),c_Product__Type_OPair(X2,X2,sK47(X0,X1,X2),sK46(X0,X1,X2)),X0)
& ~ c_member(tc_prod(X2,X2),c_Product__Type_OPair(X2,X2,sK46(X0,X1,X2),sK47(X0,X1,X2)),X0)
& sK46(X0,X1,X2) != sK47(X0,X1,X2)
& c_member(X2,sK47(X0,X1,X2),X1)
& c_member(X2,sK46(X0,X1,X2),X1) ) )
& ( ! [X5] :
( ! [X6] :
( c_member(tc_prod(X2,X2),c_Product__Type_OPair(X2,X2,X6,X5),X0)
| c_member(tc_prod(X2,X2),c_Product__Type_OPair(X2,X2,X5,X6),X0)
| X5 = X6
| ~ c_member(X2,X6,X1) )
| ~ c_member(X2,X5,X1) )
| ~ c_Relation_Ototal__on(X2,X1,X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK46,sK47])],[f1656,f1658,f1657]) ).
fof(f1657,plain,
! [X0,X1,X2] :
( ? [X3] :
( ? [X4] :
( ~ c_member(tc_prod(X2,X2),c_Product__Type_OPair(X2,X2,X4,X3),X0)
& ~ c_member(tc_prod(X2,X2),c_Product__Type_OPair(X2,X2,X3,X4),X0)
& X3 != X4
& c_member(X2,X4,X1) )
& c_member(X2,X3,X1) )
=> ( ? [X4] :
( ~ c_member(tc_prod(X2,X2),c_Product__Type_OPair(X2,X2,X4,sK46(X0,X1,X2)),X0)
& ~ c_member(tc_prod(X2,X2),c_Product__Type_OPair(X2,X2,sK46(X0,X1,X2),X4),X0)
& sK46(X0,X1,X2) != X4
& c_member(X2,X4,X1) )
& c_member(X2,sK46(X0,X1,X2),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f1658,plain,
! [X0,X1,X2] :
( ? [X4] :
( ~ c_member(tc_prod(X2,X2),c_Product__Type_OPair(X2,X2,X4,sK46(X0,X1,X2)),X0)
& ~ c_member(tc_prod(X2,X2),c_Product__Type_OPair(X2,X2,sK46(X0,X1,X2),X4),X0)
& sK46(X0,X1,X2) != X4
& c_member(X2,X4,X1) )
=> ( ~ c_member(tc_prod(X2,X2),c_Product__Type_OPair(X2,X2,sK47(X0,X1,X2),sK46(X0,X1,X2)),X0)
& ~ c_member(tc_prod(X2,X2),c_Product__Type_OPair(X2,X2,sK46(X0,X1,X2),sK47(X0,X1,X2)),X0)
& sK46(X0,X1,X2) != sK47(X0,X1,X2)
& c_member(X2,sK47(X0,X1,X2),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f1656,plain,
! [X0,X1,X2] :
( ( c_Relation_Ototal__on(X2,X1,X0)
| ? [X3] :
( ? [X4] :
( ~ c_member(tc_prod(X2,X2),c_Product__Type_OPair(X2,X2,X4,X3),X0)
& ~ c_member(tc_prod(X2,X2),c_Product__Type_OPair(X2,X2,X3,X4),X0)
& X3 != X4
& c_member(X2,X4,X1) )
& c_member(X2,X3,X1) ) )
& ( ! [X5] :
( ! [X6] :
( c_member(tc_prod(X2,X2),c_Product__Type_OPair(X2,X2,X6,X5),X0)
| c_member(tc_prod(X2,X2),c_Product__Type_OPair(X2,X2,X5,X6),X0)
| X5 = X6
| ~ c_member(X2,X6,X1) )
| ~ c_member(X2,X5,X1) )
| ~ c_Relation_Ototal__on(X2,X1,X0) ) ),
inference(rectify,[],[f1655]) ).
fof(f1655,plain,
! [X0,X1,X2] :
( ( c_Relation_Ototal__on(X2,X1,X0)
| ? [X3] :
( ? [X4] :
( ~ c_member(tc_prod(X2,X2),c_Product__Type_OPair(X2,X2,X4,X3),X0)
& ~ c_member(tc_prod(X2,X2),c_Product__Type_OPair(X2,X2,X3,X4),X0)
& X3 != X4
& c_member(X2,X4,X1) )
& c_member(X2,X3,X1) ) )
& ( ! [X3] :
( ! [X4] :
( c_member(tc_prod(X2,X2),c_Product__Type_OPair(X2,X2,X4,X3),X0)
| c_member(tc_prod(X2,X2),c_Product__Type_OPair(X2,X2,X3,X4),X0)
| X3 = X4
| ~ c_member(X2,X4,X1) )
| ~ c_member(X2,X3,X1) )
| ~ c_Relation_Ototal__on(X2,X1,X0) ) ),
inference(nnf_transformation,[],[f1236]) ).
fof(f1236,plain,
! [X0,X1,X2] :
( c_Relation_Ototal__on(X2,X1,X0)
<=> ! [X3] :
( ! [X4] :
( c_member(tc_prod(X2,X2),c_Product__Type_OPair(X2,X2,X4,X3),X0)
| c_member(tc_prod(X2,X2),c_Product__Type_OPair(X2,X2,X3,X4),X0)
| X3 = X4
| ~ c_member(X2,X4,X1) )
| ~ c_member(X2,X3,X1) ) ),
inference(flattening,[],[f1235]) ).
fof(f1235,plain,
! [X0,X1,X2] :
( c_Relation_Ototal__on(X2,X1,X0)
<=> ! [X3] :
( ! [X4] :
( c_member(tc_prod(X2,X2),c_Product__Type_OPair(X2,X2,X4,X3),X0)
| c_member(tc_prod(X2,X2),c_Product__Type_OPair(X2,X2,X3,X4),X0)
| X3 = X4
| ~ c_member(X2,X4,X1) )
| ~ c_member(X2,X3,X1) ) ),
inference(ennf_transformation,[],[f774]) ).
fof(f774,plain,
! [X0,X1,X2] :
( c_Relation_Ototal__on(X2,X1,X0)
<=> ! [X3] :
( c_member(X2,X3,X1)
=> ! [X4] :
( c_member(X2,X4,X1)
=> ( X3 != X4
=> ( c_member(tc_prod(X2,X2),c_Product__Type_OPair(X2,X2,X4,X3),X0)
| c_member(tc_prod(X2,X2),c_Product__Type_OPair(X2,X2,X3,X4),X0) ) ) ) ) ),
inference(rectify,[],[f25]) ).
fof(f25,axiom,
! [X3,X11,X4] :
( c_Relation_Ototal__on(X4,X11,X3)
<=> ! [X2] :
( c_member(X4,X2,X11)
=> ! [X31] :
( c_member(X4,X31,X11)
=> ( X2 != X31
=> ( c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X31,X2),X3)
| c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X2,X31),X3) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_total__on__def) ).
fof(f12132,plain,
spl104_554,
inference(avatar_split_clause,[],[f1893,f12129]) ).
fof(f12129,plain,
( spl104_554
<=> c_FunDef_Oreduction__pair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),c_Product__Type_OPair(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool),tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool),c_FunDef_Omin__strict,c_FunDef_Omin__weak)) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_554])]) ).
fof(f1893,plain,
c_FunDef_Oreduction__pair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),c_Product__Type_OPair(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool),tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool),c_FunDef_Omin__strict,c_FunDef_Omin__weak)),
inference(cnf_transformation,[],[f484]) ).
fof(f484,axiom,
c_FunDef_Oreduction__pair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),c_Product__Type_OPair(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool),tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool),c_FunDef_Omin__strict,c_FunDef_Omin__weak)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__rpair__set) ).
fof(f12127,plain,
spl104_553,
inference(avatar_split_clause,[],[f1892,f12124]) ).
fof(f12124,plain,
( spl104_553
<=> c_FunDef_Oreduction__pair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),c_Product__Type_OPair(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool),tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool),c_FunDef_Omax__strict,c_FunDef_Omax__weak)) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_553])]) ).
fof(f1892,plain,
c_FunDef_Oreduction__pair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),c_Product__Type_OPair(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool),tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool),c_FunDef_Omax__strict,c_FunDef_Omax__weak)),
inference(cnf_transformation,[],[f471]) ).
fof(f471,axiom,
c_FunDef_Oreduction__pair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),c_Product__Type_OPair(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool),tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool),c_FunDef_Omax__strict,c_FunDef_Omax__weak)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_max__rpair__set) ).
fof(f11976,plain,
spl104_552,
inference(avatar_split_clause,[],[f2540,f11974]) ).
fof(f11974,plain,
( spl104_552
<=> ! [X2,X4,X0,X3,X1] :
( c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,X0),c_Transitive__Closure_Otrancl(X4,X1))
| ~ c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X2,X0),X1)
| ~ c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,X2),c_Transitive__Closure_Otrancl(X4,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_552])]) ).
fof(f2540,plain,
! [X2,X3,X0,X1,X4] :
( c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,X0),c_Transitive__Closure_Otrancl(X4,X1))
| ~ c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X2,X0),X1)
| ~ c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,X2),c_Transitive__Closure_Otrancl(X4,X1)) ),
inference(cnf_transformation,[],[f1472]) ).
fof(f1472,plain,
! [X0,X1,X2,X3,X4] :
( c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,X0),c_Transitive__Closure_Otrancl(X4,X1))
| ~ c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X2,X0),X1)
| ~ c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,X2),c_Transitive__Closure_Otrancl(X4,X1)) ),
inference(flattening,[],[f1471]) ).
fof(f1471,plain,
! [X0,X1,X2,X3,X4] :
( c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,X0),c_Transitive__Closure_Otrancl(X4,X1))
| ~ c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X2,X0),X1)
| ~ c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,X2),c_Transitive__Closure_Otrancl(X4,X1)) ),
inference(ennf_transformation,[],[f975]) ).
fof(f975,plain,
! [X0,X1,X2,X3,X4] :
( c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,X2),c_Transitive__Closure_Otrancl(X4,X1))
=> ( c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X2,X0),X1)
=> c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,X0),c_Transitive__Closure_Otrancl(X4,X1)) ) ),
inference(rectify,[],[f88]) ).
fof(f88,axiom,
! [X7,X3,X8,X9,X4] :
( c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X9,X8),c_Transitive__Closure_Otrancl(X4,X3))
=> ( c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X8,X7),X3)
=> c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X9,X7),c_Transitive__Closure_Otrancl(X4,X3)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Transitive__Closure_Otrancl__into__trancl) ).
fof(f11972,plain,
spl104_551,
inference(avatar_split_clause,[],[f2537,f11970]) ).
fof(f11970,plain,
( spl104_551
<=> ! [X2,X4,X0,X3,X1] :
( c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,X0),c_Transitive__Closure_Otrancl(X4,X1))
| ~ c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X2,X0),c_Transitive__Closure_Otrancl(X4,X1))
| ~ c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_551])]) ).
fof(f2537,plain,
! [X2,X3,X0,X1,X4] :
( c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,X0),c_Transitive__Closure_Otrancl(X4,X1))
| ~ c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X2,X0),c_Transitive__Closure_Otrancl(X4,X1))
| ~ c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,X2),X1) ),
inference(cnf_transformation,[],[f1466]) ).
fof(f1466,plain,
! [X0,X1,X2,X3,X4] :
( c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,X0),c_Transitive__Closure_Otrancl(X4,X1))
| ~ c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X2,X0),c_Transitive__Closure_Otrancl(X4,X1))
| ~ c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,X2),X1) ),
inference(flattening,[],[f1465]) ).
fof(f1465,plain,
! [X0,X1,X2,X3,X4] :
( c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,X0),c_Transitive__Closure_Otrancl(X4,X1))
| ~ c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X2,X0),c_Transitive__Closure_Otrancl(X4,X1))
| ~ c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,X2),X1) ),
inference(ennf_transformation,[],[f972]) ).
fof(f972,plain,
! [X0,X1,X2,X3,X4] :
( c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,X2),X1)
=> ( c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X2,X0),c_Transitive__Closure_Otrancl(X4,X1))
=> c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,X0),c_Transitive__Closure_Otrancl(X4,X1)) ) ),
inference(rectify,[],[f87]) ).
fof(f87,axiom,
! [X7,X3,X8,X9,X4] :
( c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X9,X8),X3)
=> ( c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X8,X7),c_Transitive__Closure_Otrancl(X4,X3))
=> c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X9,X7),c_Transitive__Closure_Otrancl(X4,X3)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trancl__into__trancl2) ).
fof(f11968,plain,
spl104_550,
inference(avatar_split_clause,[],[f2350,f11966]) ).
fof(f2350,plain,
! [X2,X3,X0,X1] :
( c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat,X3,X1),c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat,X2,X0)),c_FunDef_Opair__leq)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X2) ),
inference(cnf_transformation,[],[f1329]) ).
fof(f1329,plain,
! [X0,X1,X2,X3] :
( c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat,X3,X1),c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat,X2,X0)),c_FunDef_Opair__leq)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X2) ),
inference(flattening,[],[f1328]) ).
fof(f1328,plain,
! [X0,X1,X2,X3] :
( c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat,X3,X1),c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat,X2,X0)),c_FunDef_Opair__leq)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X2) ),
inference(ennf_transformation,[],[f862]) ).
fof(f862,plain,
! [X0,X1,X2,X3] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X2)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
=> c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat,X3,X1),c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat,X2,X0)),c_FunDef_Opair__leq) ) ),
inference(rectify,[],[f453]) ).
fof(f453,axiom,
! [X79,X30,X8,X9] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X9,X8)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X30,X79)
=> c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat,X9,X30),c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat,X8,X79)),c_FunDef_Opair__leq) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pair__leqI2) ).
fof(f11964,plain,
spl104_549,
inference(avatar_split_clause,[],[f2349,f11962]) ).
fof(f11962,plain,
( spl104_549
<=> ! [X0,X3,X2,X1] :
( c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat,X3,X1),c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat,X2,X0)),c_FunDef_Opair__less)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_549])]) ).
fof(f2349,plain,
! [X2,X3,X0,X1] :
( c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat,X3,X1),c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat,X2,X0)),c_FunDef_Opair__less)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X2) ),
inference(cnf_transformation,[],[f1327]) ).
fof(f1327,plain,
! [X0,X1,X2,X3] :
( c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat,X3,X1),c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat,X2,X0)),c_FunDef_Opair__less)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X2) ),
inference(flattening,[],[f1326]) ).
fof(f1326,plain,
! [X0,X1,X2,X3] :
( c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat,X3,X1),c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat,X2,X0)),c_FunDef_Opair__less)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X2) ),
inference(ennf_transformation,[],[f861]) ).
fof(f861,plain,
! [X0,X1,X2,X3] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X2)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
=> c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat,X3,X1),c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat,X2,X0)),c_FunDef_Opair__less) ) ),
inference(rectify,[],[f392]) ).
fof(f392,axiom,
! [X79,X30,X8,X9] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X9,X8)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X30,X79)
=> c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat,X9,X30),c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat,X8,X79)),c_FunDef_Opair__less) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pair__lessI2) ).
fof(f11898,plain,
( ~ spl104_548
| ~ spl104_196
| ~ spl104_535 ),
inference(avatar_split_clause,[],[f11516,f11199,f4032,f11895]) ).
fof(f11895,plain,
( spl104_548
<=> c_Relation_Oirrefl(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),c_FunDef_Omin__weak) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_548])]) ).
fof(f11516,plain,
( ~ c_Relation_Oirrefl(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),c_FunDef_Omin__weak)
| ~ spl104_196
| ~ spl104_535 ),
inference(resolution,[],[f11200,f4033]) ).
fof(f11890,plain,
spl104_547,
inference(avatar_split_clause,[],[f2639,f11888]) ).
fof(f11888,plain,
( spl104_547
<=> ! [X0,X1] : c_Transitive__Closure_Otrancl(X1,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),X0,c_Relation_OId(X1))) = c_Transitive__Closure_Otrancl(X1,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),c_Transitive__Closure_Otrancl(X1,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),X0,c_Relation_OId(X1))),c_Relation_OId(X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_547])]) ).
fof(f2639,plain,
! [X0,X1] : c_Transitive__Closure_Otrancl(X1,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),X0,c_Relation_OId(X1))) = c_Transitive__Closure_Otrancl(X1,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),c_Transitive__Closure_Otrancl(X1,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),X0,c_Relation_OId(X1))),c_Relation_OId(X1))),
inference(definition_unfolding,[],[f1935,f1949,f1949,f1949]) ).
fof(f1935,plain,
! [X0,X1] : c_Transitive__Closure_Ortrancl(X1,X0) = c_Transitive__Closure_Ortrancl(X1,c_Transitive__Closure_Ortrancl(X1,X0)),
inference(cnf_transformation,[],[f565]) ).
fof(f565,plain,
! [X0,X1] : c_Transitive__Closure_Ortrancl(X1,X0) = c_Transitive__Closure_Ortrancl(X1,c_Transitive__Closure_Ortrancl(X1,X0)),
inference(rectify,[],[f68]) ).
fof(f68,axiom,
! [X3,X4] : c_Transitive__Closure_Ortrancl(X4,X3) = c_Transitive__Closure_Ortrancl(X4,c_Transitive__Closure_Ortrancl(X4,X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__idemp) ).
fof(f11886,plain,
spl104_546,
inference(avatar_split_clause,[],[f2612,f11884]) ).
fof(f11884,plain,
( spl104_546
<=> ! [X5,X4,X2,X0,X6,X3,X1] :
( hAPP(hAPP(X3,X6),X5) = hAPP(hAPP(X3,sK94(X0,X1,X2,X3,X4,X5,X6)),sK95(X0,X1,X2,X3,X4,X5,X6))
| ~ sP11(X0,X1,X2,X3,X4,X5,X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_546])]) ).
fof(f2612,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( hAPP(hAPP(X3,X6),X5) = hAPP(hAPP(X3,sK94(X0,X1,X2,X3,X4,X5,X6)),sK95(X0,X1,X2,X3,X4,X5,X6))
| ~ sP11(X0,X1,X2,X3,X4,X5,X6) ),
inference(cnf_transformation,[],[f1842]) ).
fof(f11882,plain,
spl104_545,
inference(avatar_split_clause,[],[f2609,f11880]) ).
fof(f11880,plain,
( spl104_545
<=> ! [X3,X4,X0,X6,X5,X2,X1] :
( c_Nitpick_Ofold__graph_H(X6,X3,X2,X1,X4,hAPP(hAPP(X2,X5),X0))
| ~ c_Nitpick_Ofold__graph_H(X6,X3,X2,X1,c_Groups_Ominus__class_Ominus(tc_fun(X6,tc_HOL_Obool),X4,c_Set_Oinsert(X6,X5,c_Orderings_Obot__class_Obot(tc_fun(X6,tc_HOL_Obool)))),X0)
| ~ c_member(X6,X5,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_545])]) ).
fof(f2609,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( c_Nitpick_Ofold__graph_H(X6,X3,X2,X1,X4,hAPP(hAPP(X2,X5),X0))
| ~ c_Nitpick_Ofold__graph_H(X6,X3,X2,X1,c_Groups_Ominus__class_Ominus(tc_fun(X6,tc_HOL_Obool),X4,c_Set_Oinsert(X6,X5,c_Orderings_Obot__class_Obot(tc_fun(X6,tc_HOL_Obool)))),X0)
| ~ c_member(X6,X5,X4) ),
inference(cnf_transformation,[],[f1517]) ).
fof(f1517,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( c_Nitpick_Ofold__graph_H(X6,X3,X2,X1,X4,hAPP(hAPP(X2,X5),X0))
| ~ c_Nitpick_Ofold__graph_H(X6,X3,X2,X1,c_Groups_Ominus__class_Ominus(tc_fun(X6,tc_HOL_Obool),X4,c_Set_Oinsert(X6,X5,c_Orderings_Obot__class_Obot(tc_fun(X6,tc_HOL_Obool)))),X0)
| ~ c_member(X6,X5,X4) ),
inference(flattening,[],[f1516]) ).
fof(f1516,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( c_Nitpick_Ofold__graph_H(X6,X3,X2,X1,X4,hAPP(hAPP(X2,X5),X0))
| ~ c_Nitpick_Ofold__graph_H(X6,X3,X2,X1,c_Groups_Ominus__class_Ominus(tc_fun(X6,tc_HOL_Obool),X4,c_Set_Oinsert(X6,X5,c_Orderings_Obot__class_Obot(tc_fun(X6,tc_HOL_Obool)))),X0)
| ~ c_member(X6,X5,X4) ),
inference(ennf_transformation,[],[f1010]) ).
fof(f1010,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( c_member(X6,X5,X4)
=> ( c_Nitpick_Ofold__graph_H(X6,X3,X2,X1,c_Groups_Ominus__class_Ominus(tc_fun(X6,tc_HOL_Obool),X4,c_Set_Oinsert(X6,X5,c_Orderings_Obot__class_Obot(tc_fun(X6,tc_HOL_Obool)))),X0)
=> c_Nitpick_Ofold__graph_H(X6,X3,X2,X1,X4,hAPP(hAPP(X2,X5),X0)) ) ),
inference(rectify,[],[f467]) ).
fof(f467,axiom,
! [X12,X38,X1,X15,X11,X13,X4] :
( c_member(X4,X13,X11)
=> ( c_Nitpick_Ofold__graph_H(X4,X15,X1,X38,c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool),X11,c_Set_Oinsert(X4,X13,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))),X12)
=> c_Nitpick_Ofold__graph_H(X4,X15,X1,X38,X11,hAPP(hAPP(X1,X13),X12)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold__graph_H_Ointros_I2_J) ).
fof(f11878,plain,
spl104_544,
inference(avatar_split_clause,[],[f2015,f11876]) ).
fof(f11876,plain,
( spl104_544
<=> ! [X6,X0,X5,X1,X7] :
( c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,X5,X7),X0)
| ~ c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,X6,X7),X0)
| ~ c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,X5,X6),X0)
| ~ c_Relation_Otrans(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_544])]) ).
fof(f2015,plain,
! [X0,X1,X6,X7,X5] :
( c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,X5,X7),X0)
| ~ c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,X6,X7),X0)
| ~ c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,X5,X6),X0)
| ~ c_Relation_Otrans(X1,X0) ),
inference(cnf_transformation,[],[f1587]) ).
fof(f1587,plain,
! [X0,X1] :
( ( c_Relation_Otrans(X1,X0)
| ( ~ c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,sK30(X0,X1),sK32(X0,X1)),X0)
& c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,sK31(X0,X1),sK32(X0,X1)),X0)
& c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,sK30(X0,X1),sK31(X0,X1)),X0) ) )
& ( ! [X5,X6] :
( ! [X7] :
( c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,X5,X7),X0)
| ~ c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,X6,X7),X0) )
| ~ c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,X5,X6),X0) )
| ~ c_Relation_Otrans(X1,X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK30,sK31,sK32])],[f1584,f1586,f1585]) ).
fof(f1585,plain,
! [X0,X1] :
( ? [X2,X3] :
( ? [X4] :
( ~ c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,X2,X4),X0)
& c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,X3,X4),X0) )
& c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,X2,X3),X0) )
=> ( ? [X4] :
( ~ c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,sK30(X0,X1),X4),X0)
& c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,sK31(X0,X1),X4),X0) )
& c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,sK30(X0,X1),sK31(X0,X1)),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f1586,plain,
! [X0,X1] :
( ? [X4] :
( ~ c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,sK30(X0,X1),X4),X0)
& c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,sK31(X0,X1),X4),X0) )
=> ( ~ c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,sK30(X0,X1),sK32(X0,X1)),X0)
& c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,sK31(X0,X1),sK32(X0,X1)),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f1584,plain,
! [X0,X1] :
( ( c_Relation_Otrans(X1,X0)
| ? [X2,X3] :
( ? [X4] :
( ~ c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,X2,X4),X0)
& c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,X3,X4),X0) )
& c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,X2,X3),X0) ) )
& ( ! [X5,X6] :
( ! [X7] :
( c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,X5,X7),X0)
| ~ c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,X6,X7),X0) )
| ~ c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,X5,X6),X0) )
| ~ c_Relation_Otrans(X1,X0) ) ),
inference(rectify,[],[f1583]) ).
fof(f1583,plain,
! [X0,X1] :
( ( c_Relation_Otrans(X1,X0)
| ? [X2,X3] :
( ? [X4] :
( ~ c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,X2,X4),X0)
& c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,X3,X4),X0) )
& c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,X2,X3),X0) ) )
& ( ! [X2,X3] :
( ! [X4] :
( c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,X2,X4),X0)
| ~ c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,X3,X4),X0) )
| ~ c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,X2,X3),X0) )
| ~ c_Relation_Otrans(X1,X0) ) ),
inference(nnf_transformation,[],[f1077]) ).
fof(f1077,plain,
! [X0,X1] :
( c_Relation_Otrans(X1,X0)
<=> ! [X2,X3] :
( ! [X4] :
( c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,X2,X4),X0)
| ~ c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,X3,X4),X0) )
| ~ c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,X2,X3),X0) ) ),
inference(ennf_transformation,[],[f634]) ).
fof(f634,plain,
! [X0,X1] :
( c_Relation_Otrans(X1,X0)
<=> ! [X2,X3] :
( c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,X2,X3),X0)
=> ! [X4] :
( c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,X3,X4),X0)
=> c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,X2,X4),X0) ) ) ),
inference(rectify,[],[f2]) ).
fof(f2,axiom,
! [X3,X4] :
( c_Relation_Otrans(X4,X3)
<=> ! [X2,X5] :
( c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X2,X5),X3)
=> ! [X6] :
( c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X5,X6),X3)
=> c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X2,X6),X3) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trans__def) ).
fof(f11628,plain,
( ~ spl104_543
| ~ spl104_206
| ~ spl104_535 ),
inference(avatar_split_clause,[],[f11515,f11199,f4072,f11625]) ).
fof(f11625,plain,
( spl104_543
<=> c_Wellfounded_Owf(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),c_FunDef_Omin__weak) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_543])]) ).
fof(f11515,plain,
( ~ c_Wellfounded_Owf(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),c_FunDef_Omin__weak)
| ~ spl104_206
| ~ spl104_535 ),
inference(resolution,[],[f11200,f4073]) ).
fof(f11560,plain,
spl104_542,
inference(avatar_split_clause,[],[f2811,f11558]) ).
fof(f11558,plain,
( spl104_542
<=> ! [X5,X3,X4,X6,X2,X1] :
( c_Recdef_Owfrec__rel(X5,X4,X3,X2,X1,hAPP(hAPP(X2,X6),X1))
| ~ c_Recdef_Owfrec__rel(X5,X4,X3,X2,sK87(X1,X2,X3,X4,X5,X6),hAPP(X6,sK87(X1,X2,X3,X4,X5,X6))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_542])]) ).
fof(f2811,plain,
! [X2,X3,X1,X6,X4,X5] :
( c_Recdef_Owfrec__rel(X5,X4,X3,X2,X1,hAPP(hAPP(X2,X6),X1))
| ~ c_Recdef_Owfrec__rel(X5,X4,X3,X2,sK87(X1,X2,X3,X4,X5,X6),hAPP(X6,sK87(X1,X2,X3,X4,X5,X6))) ),
inference(equality_resolution,[],[f2595]) ).
fof(f2595,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( c_Recdef_Owfrec__rel(X5,X4,X3,X2,X1,X0)
| ~ c_Recdef_Owfrec__rel(X5,X4,X3,X2,sK87(X1,X2,X3,X4,X5,X6),hAPP(X6,sK87(X1,X2,X3,X4,X5,X6)))
| hAPP(hAPP(X2,X6),X1) != X0 ),
inference(cnf_transformation,[],[f1824]) ).
fof(f1824,plain,
! [X0,X1,X2,X3,X4,X5] :
( ( c_Recdef_Owfrec__rel(X5,X4,X3,X2,X1,X0)
| ! [X6] :
( ( ~ c_Recdef_Owfrec__rel(X5,X4,X3,X2,sK87(X1,X2,X3,X4,X5,X6),hAPP(X6,sK87(X1,X2,X3,X4,X5,X6)))
& c_member(tc_prod(X5,X5),c_Product__Type_OPair(X5,X5,sK87(X1,X2,X3,X4,X5,X6),X1),X3) )
| hAPP(hAPP(X2,X6),X1) != X0 ) )
& ( ( ! [X9] :
( c_Recdef_Owfrec__rel(X5,X4,X3,X2,X9,hAPP(sK88(X0,X1,X2,X3,X4,X5),X9))
| ~ c_member(tc_prod(X5,X5),c_Product__Type_OPair(X5,X5,X9,X1),X3) )
& hAPP(hAPP(X2,sK88(X0,X1,X2,X3,X4,X5)),X1) = X0 )
| ~ c_Recdef_Owfrec__rel(X5,X4,X3,X2,X1,X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK87,sK88])],[f1821,f1823,f1822]) ).
fof(f1822,plain,
! [X1,X2,X3,X4,X5,X6] :
( ? [X7] :
( ~ c_Recdef_Owfrec__rel(X5,X4,X3,X2,X7,hAPP(X6,X7))
& c_member(tc_prod(X5,X5),c_Product__Type_OPair(X5,X5,X7,X1),X3) )
=> ( ~ c_Recdef_Owfrec__rel(X5,X4,X3,X2,sK87(X1,X2,X3,X4,X5,X6),hAPP(X6,sK87(X1,X2,X3,X4,X5,X6)))
& c_member(tc_prod(X5,X5),c_Product__Type_OPair(X5,X5,sK87(X1,X2,X3,X4,X5,X6),X1),X3) ) ),
introduced(choice_axiom,[]) ).
fof(f1823,plain,
! [X0,X1,X2,X3,X4,X5] :
( ? [X8] :
( ! [X9] :
( c_Recdef_Owfrec__rel(X5,X4,X3,X2,X9,hAPP(X8,X9))
| ~ c_member(tc_prod(X5,X5),c_Product__Type_OPair(X5,X5,X9,X1),X3) )
& hAPP(hAPP(X2,X8),X1) = X0 )
=> ( ! [X9] :
( c_Recdef_Owfrec__rel(X5,X4,X3,X2,X9,hAPP(sK88(X0,X1,X2,X3,X4,X5),X9))
| ~ c_member(tc_prod(X5,X5),c_Product__Type_OPair(X5,X5,X9,X1),X3) )
& hAPP(hAPP(X2,sK88(X0,X1,X2,X3,X4,X5)),X1) = X0 ) ),
introduced(choice_axiom,[]) ).
fof(f1821,plain,
! [X0,X1,X2,X3,X4,X5] :
( ( c_Recdef_Owfrec__rel(X5,X4,X3,X2,X1,X0)
| ! [X6] :
( ? [X7] :
( ~ c_Recdef_Owfrec__rel(X5,X4,X3,X2,X7,hAPP(X6,X7))
& c_member(tc_prod(X5,X5),c_Product__Type_OPair(X5,X5,X7,X1),X3) )
| hAPP(hAPP(X2,X6),X1) != X0 ) )
& ( ? [X8] :
( ! [X9] :
( c_Recdef_Owfrec__rel(X5,X4,X3,X2,X9,hAPP(X8,X9))
| ~ c_member(tc_prod(X5,X5),c_Product__Type_OPair(X5,X5,X9,X1),X3) )
& hAPP(hAPP(X2,X8),X1) = X0 )
| ~ c_Recdef_Owfrec__rel(X5,X4,X3,X2,X1,X0) ) ),
inference(rectify,[],[f1820]) ).
fof(f1820,plain,
! [X0,X1,X2,X3,X4,X5] :
( ( c_Recdef_Owfrec__rel(X5,X4,X3,X2,X1,X0)
| ! [X6] :
( ? [X7] :
( ~ c_Recdef_Owfrec__rel(X5,X4,X3,X2,X7,hAPP(X6,X7))
& c_member(tc_prod(X5,X5),c_Product__Type_OPair(X5,X5,X7,X1),X3) )
| hAPP(hAPP(X2,X6),X1) != X0 ) )
& ( ? [X6] :
( ! [X7] :
( c_Recdef_Owfrec__rel(X5,X4,X3,X2,X7,hAPP(X6,X7))
| ~ c_member(tc_prod(X5,X5),c_Product__Type_OPair(X5,X5,X7,X1),X3) )
& hAPP(hAPP(X2,X6),X1) = X0 )
| ~ c_Recdef_Owfrec__rel(X5,X4,X3,X2,X1,X0) ) ),
inference(nnf_transformation,[],[f1511]) ).
fof(f1511,plain,
! [X0,X1,X2,X3,X4,X5] :
( c_Recdef_Owfrec__rel(X5,X4,X3,X2,X1,X0)
<=> ? [X6] :
( ! [X7] :
( c_Recdef_Owfrec__rel(X5,X4,X3,X2,X7,hAPP(X6,X7))
| ~ c_member(tc_prod(X5,X5),c_Product__Type_OPair(X5,X5,X7,X1),X3) )
& hAPP(hAPP(X2,X6),X1) = X0 ) ),
inference(ennf_transformation,[],[f1004]) ).
fof(f1004,plain,
! [X0,X1,X2,X3,X4,X5] :
( c_Recdef_Owfrec__rel(X5,X4,X3,X2,X1,X0)
<=> ? [X6] :
( ! [X7] :
( c_member(tc_prod(X5,X5),c_Product__Type_OPair(X5,X5,X7,X1),X3)
=> c_Recdef_Owfrec__rel(X5,X4,X3,X2,X7,hAPP(X6,X7)) )
& hAPP(hAPP(X2,X6),X1) = X0 ) ),
inference(rectify,[],[f49]) ).
fof(f49,axiom,
! [X34,X35,X36,X14,X15,X4] :
( c_Recdef_Owfrec__rel(X4,X15,X14,X36,X35,X34)
<=> ? [X37] :
( ! [X6] :
( c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X6,X35),X14)
=> c_Recdef_Owfrec__rel(X4,X15,X14,X36,X6,hAPP(X37,X6)) )
& hAPP(hAPP(X36,X37),X35) = X34 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wfrec__rel_Osimps) ).
fof(f11556,plain,
spl104_541,
inference(avatar_split_clause,[],[f2687,f11554]) ).
fof(f11554,plain,
( spl104_541
<=> ! [X0,X3,X2,X1] :
( ~ c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X1,X2),c_Transitive__Closure_Otrancl(X3,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X3,X3),tc_HOL_Obool),X0,c_Relation_OId(X3))))
| ~ c_Wellfounded_Owf(X3,c_Set_Oinsert(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X2,X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_541])]) ).
fof(f2687,plain,
! [X2,X3,X0,X1] :
( ~ c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X1,X2),c_Transitive__Closure_Otrancl(X3,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X3,X3),tc_HOL_Obool),X0,c_Relation_OId(X3))))
| ~ c_Wellfounded_Owf(X3,c_Set_Oinsert(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X2,X1),X0)) ),
inference(definition_unfolding,[],[f2478,f1949]) ).
fof(f2478,plain,
! [X2,X3,X0,X1] :
( ~ c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X1,X2),c_Transitive__Closure_Ortrancl(X3,X0))
| ~ c_Wellfounded_Owf(X3,c_Set_Oinsert(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X2,X1),X0)) ),
inference(cnf_transformation,[],[f1768]) ).
fof(f11552,plain,
spl104_540,
inference(avatar_split_clause,[],[f2685,f11550]) ).
fof(f2685,plain,
! [X2,X3,X0,X1] :
( ~ c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X1,X2),c_Transitive__Closure_Otrancl(X3,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X3,X3),tc_HOL_Obool),X0,c_Relation_OId(X3))))
| ~ c_Wellfounded_Oacyclic(X3,c_Set_Oinsert(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X2,X1),X0)) ),
inference(definition_unfolding,[],[f2475,f1949]) ).
fof(f2475,plain,
! [X2,X3,X0,X1] :
( ~ c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X1,X2),c_Transitive__Closure_Ortrancl(X3,X0))
| ~ c_Wellfounded_Oacyclic(X3,c_Set_Oinsert(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X2,X1),X0)) ),
inference(cnf_transformation,[],[f1766]) ).
fof(f11548,plain,
spl104_539,
inference(avatar_split_clause,[],[f2669,f11546]) ).
fof(f11546,plain,
( spl104_539
<=> ! [X0,X3,X2,X1] :
( c_member(X3,X0,c_Wellfounded_Oacc(X3,X1))
| ~ c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X0,X2),c_Transitive__Closure_Otrancl(X3,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X3,X3),tc_HOL_Obool),X1,c_Relation_OId(X3))))
| ~ c_member(X3,X2,c_Wellfounded_Oacc(X3,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_539])]) ).
fof(f2669,plain,
! [X2,X3,X0,X1] :
( c_member(X3,X0,c_Wellfounded_Oacc(X3,X1))
| ~ c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X0,X2),c_Transitive__Closure_Otrancl(X3,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X3,X3),tc_HOL_Obool),X1,c_Relation_OId(X3))))
| ~ c_member(X3,X2,c_Wellfounded_Oacc(X3,X1)) ),
inference(definition_unfolding,[],[f2386,f1949]) ).
fof(f2386,plain,
! [X2,X3,X0,X1] :
( c_member(X3,X0,c_Wellfounded_Oacc(X3,X1))
| ~ c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X0,X2),c_Transitive__Closure_Ortrancl(X3,X1))
| ~ c_member(X3,X2,c_Wellfounded_Oacc(X3,X1)) ),
inference(cnf_transformation,[],[f1383]) ).
fof(f1383,plain,
! [X0,X1,X2,X3] :
( c_member(X3,X0,c_Wellfounded_Oacc(X3,X1))
| ~ c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X0,X2),c_Transitive__Closure_Ortrancl(X3,X1))
| ~ c_member(X3,X2,c_Wellfounded_Oacc(X3,X1)) ),
inference(flattening,[],[f1382]) ).
fof(f1382,plain,
! [X0,X1,X2,X3] :
( c_member(X3,X0,c_Wellfounded_Oacc(X3,X1))
| ~ c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X0,X2),c_Transitive__Closure_Ortrancl(X3,X1))
| ~ c_member(X3,X2,c_Wellfounded_Oacc(X3,X1)) ),
inference(ennf_transformation,[],[f893]) ).
fof(f893,plain,
! [X0,X1,X2,X3] :
( c_member(X3,X2,c_Wellfounded_Oacc(X3,X1))
=> ( c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X0,X2),c_Transitive__Closure_Ortrancl(X3,X1))
=> c_member(X3,X0,c_Wellfounded_Oacc(X3,X1)) ) ),
inference(rectify,[],[f51]) ).
fof(f51,axiom,
! [X8,X3,X9,X4] :
( c_member(X4,X9,c_Wellfounded_Oacc(X4,X3))
=> ( c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X8,X9),c_Transitive__Closure_Ortrancl(X4,X3))
=> c_member(X4,X8,c_Wellfounded_Oacc(X4,X3)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_acc__downwards) ).
fof(f11544,plain,
spl104_538,
inference(avatar_split_clause,[],[f2593,f11542]) ).
fof(f11542,plain,
( spl104_538
<=> ! [X5,X4,X2,X0,X9,X3,X1] :
( c_Recdef_Owfrec__rel(X5,X4,X3,X2,X9,hAPP(sK88(X0,X1,X2,X3,X4,X5),X9))
| ~ c_member(tc_prod(X5,X5),c_Product__Type_OPair(X5,X5,X9,X1),X3)
| ~ c_Recdef_Owfrec__rel(X5,X4,X3,X2,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_538])]) ).
fof(f2593,plain,
! [X2,X3,X0,X1,X9,X4,X5] :
( c_Recdef_Owfrec__rel(X5,X4,X3,X2,X9,hAPP(sK88(X0,X1,X2,X3,X4,X5),X9))
| ~ c_member(tc_prod(X5,X5),c_Product__Type_OPair(X5,X5,X9,X1),X3)
| ~ c_Recdef_Owfrec__rel(X5,X4,X3,X2,X1,X0) ),
inference(cnf_transformation,[],[f1824]) ).
fof(f11540,plain,
spl104_537,
inference(avatar_split_clause,[],[f2591,f11538]) ).
fof(f11538,plain,
( spl104_537
<=> ! [X2,X4,X0,X3,X5,X1] :
( c_Recdef_Owfrec__rel(X5,X2,X3,X1,X4,hAPP(hAPP(X1,X0),X4))
| ~ c_Recdef_Owfrec__rel(X5,X2,X3,X1,sK86(X0,X1,X2,X3,X4,X5),hAPP(X0,sK86(X0,X1,X2,X3,X4,X5))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_537])]) ).
fof(f2591,plain,
! [X2,X3,X0,X1,X4,X5] :
( c_Recdef_Owfrec__rel(X5,X2,X3,X1,X4,hAPP(hAPP(X1,X0),X4))
| ~ c_Recdef_Owfrec__rel(X5,X2,X3,X1,sK86(X0,X1,X2,X3,X4,X5),hAPP(X0,sK86(X0,X1,X2,X3,X4,X5))) ),
inference(cnf_transformation,[],[f1819]) ).
fof(f1819,plain,
! [X0,X1,X2,X3,X4,X5] :
( c_Recdef_Owfrec__rel(X5,X2,X3,X1,X4,hAPP(hAPP(X1,X0),X4))
| ( ~ c_Recdef_Owfrec__rel(X5,X2,X3,X1,sK86(X0,X1,X2,X3,X4,X5),hAPP(X0,sK86(X0,X1,X2,X3,X4,X5)))
& c_member(tc_prod(X5,X5),c_Product__Type_OPair(X5,X5,sK86(X0,X1,X2,X3,X4,X5),X4),X3) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK86])],[f1510,f1818]) ).
fof(f1818,plain,
! [X0,X1,X2,X3,X4,X5] :
( ? [X6] :
( ~ c_Recdef_Owfrec__rel(X5,X2,X3,X1,X6,hAPP(X0,X6))
& c_member(tc_prod(X5,X5),c_Product__Type_OPair(X5,X5,X6,X4),X3) )
=> ( ~ c_Recdef_Owfrec__rel(X5,X2,X3,X1,sK86(X0,X1,X2,X3,X4,X5),hAPP(X0,sK86(X0,X1,X2,X3,X4,X5)))
& c_member(tc_prod(X5,X5),c_Product__Type_OPair(X5,X5,sK86(X0,X1,X2,X3,X4,X5),X4),X3) ) ),
introduced(choice_axiom,[]) ).
fof(f1510,plain,
! [X0,X1,X2,X3,X4,X5] :
( c_Recdef_Owfrec__rel(X5,X2,X3,X1,X4,hAPP(hAPP(X1,X0),X4))
| ? [X6] :
( ~ c_Recdef_Owfrec__rel(X5,X2,X3,X1,X6,hAPP(X0,X6))
& c_member(tc_prod(X5,X5),c_Product__Type_OPair(X5,X5,X6,X4),X3) ) ),
inference(ennf_transformation,[],[f1003]) ).
fof(f1003,plain,
! [X0,X1,X2,X3,X4,X5] :
( ! [X6] :
( c_member(tc_prod(X5,X5),c_Product__Type_OPair(X5,X5,X6,X4),X3)
=> c_Recdef_Owfrec__rel(X5,X2,X3,X1,X6,hAPP(X0,X6)) )
=> c_Recdef_Owfrec__rel(X5,X2,X3,X1,X4,hAPP(hAPP(X1,X0),X4)) ),
inference(rectify,[],[f48]) ).
fof(f48,axiom,
! [X0,X36,X15,X14,X13,X4] :
( ! [X6] :
( c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X6,X13),X14)
=> c_Recdef_Owfrec__rel(X4,X15,X14,X36,X6,hAPP(X0,X6)) )
=> c_Recdef_Owfrec__rel(X4,X15,X14,X36,X13,hAPP(hAPP(X36,X0),X13)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wfrec__rel_Ointros) ).
fof(f11536,plain,
spl104_536,
inference(avatar_split_clause,[],[f2536,f11534]) ).
fof(f11534,plain,
( spl104_536
<=> ! [X2,X4,X0,X3,X1] :
( c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,X0),c_Transitive__Closure_Otrancl(X4,X1))
| ~ c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X2,X0),X1)
| ~ c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_536])]) ).
fof(f2536,plain,
! [X2,X3,X0,X1,X4] :
( c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,X0),c_Transitive__Closure_Otrancl(X4,X1))
| ~ c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X2,X0),X1)
| ~ c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,X2),X1) ),
inference(cnf_transformation,[],[f1464]) ).
fof(f1464,plain,
! [X0,X1,X2,X3,X4] :
( c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,X0),c_Transitive__Closure_Otrancl(X4,X1))
| ~ c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X2,X0),X1)
| ~ c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,X2),X1) ),
inference(flattening,[],[f1463]) ).
fof(f1463,plain,
! [X0,X1,X2,X3,X4] :
( c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,X0),c_Transitive__Closure_Otrancl(X4,X1))
| ~ c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X2,X0),X1)
| ~ c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,X2),X1) ),
inference(ennf_transformation,[],[f971]) ).
fof(f971,plain,
! [X0,X1,X2,X3,X4] :
( c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,X2),X1)
=> ( c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X2,X0),X1)
=> c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X3,X0),c_Transitive__Closure_Otrancl(X4,X1)) ) ),
inference(rectify,[],[f86]) ).
fof(f86,axiom,
! [X7,X14,X8,X9,X4] :
( c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X9,X8),X14)
=> ( c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X8,X7),X14)
=> c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X9,X7),c_Transitive__Closure_Otrancl(X4,X14)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_r__r__into__trancl) ).
fof(f11201,plain,
spl104_535,
inference(avatar_split_clause,[],[f2824,f11199]) ).
fof(f2824,plain,
! [X0] : c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),X0,c_Relation_OId__on(tc_Nat_Onat,c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))),c_FunDef_Omin__weak),
inference(forward_demodulation,[],[f1914,f1912]) ).
fof(f1914,plain,
! [X0] : c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),X0,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),c_FunDef_Omin__weak),
inference(cnf_transformation,[],[f544]) ).
fof(f544,plain,
! [X0] : c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),X0,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),c_FunDef_Omin__weak),
inference(rectify,[],[f458]) ).
fof(f458,axiom,
! [X80] : c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),X80,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),c_FunDef_Omin__weak),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wmin__emptyI) ).
fof(f11197,plain,
spl104_534,
inference(avatar_split_clause,[],[f2643,f11195]) ).
fof(f11195,plain,
( spl104_534
<=> ! [X0,X1] : c_Transitive__Closure_Otrancl(X1,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),X0,c_Relation_OId(X1))) = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),c_Transitive__Closure_Otrancl(X1,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),X0,c_Relation_OId(X1))),c_Relation_OId(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_534])]) ).
fof(f2643,plain,
! [X0,X1] : c_Transitive__Closure_Otrancl(X1,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),X0,c_Relation_OId(X1))) = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),c_Transitive__Closure_Otrancl(X1,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),X0,c_Relation_OId(X1))),c_Relation_OId(X1)),
inference(definition_unfolding,[],[f1953,f1949,f1949]) ).
fof(f1953,plain,
! [X0,X1] : c_Transitive__Closure_Ortrancl(X1,X0) = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),c_Transitive__Closure_Ortrancl(X1,X0),c_Relation_OId(X1)),
inference(cnf_transformation,[],[f583]) ).
fof(f583,plain,
! [X0,X1] : c_Transitive__Closure_Ortrancl(X1,X0) = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),c_Transitive__Closure_Ortrancl(X1,X0),c_Relation_OId(X1)),
inference(rectify,[],[f151]) ).
fof(f151,axiom,
! [X14,X4] : c_Transitive__Closure_Ortrancl(X4,X14) = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),c_Transitive__Closure_Ortrancl(X4,X14),c_Relation_OId(X4)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__reflcl__absorb) ).
fof(f11193,plain,
spl104_533,
inference(avatar_split_clause,[],[f2641,f11191]) ).
fof(f11191,plain,
( spl104_533
<=> ! [X0,X1] : c_Transitive__Closure_Otrancl(X1,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),X0,c_Relation_OId(X1))) = c_Transitive__Closure_Otrancl(X1,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),X0,c_Relation_OId(X1)),c_Relation_OId(X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_533])]) ).
fof(f2641,plain,
! [X0,X1] : c_Transitive__Closure_Otrancl(X1,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),X0,c_Relation_OId(X1))) = c_Transitive__Closure_Otrancl(X1,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),X0,c_Relation_OId(X1)),c_Relation_OId(X1))),
inference(definition_unfolding,[],[f1951,f1949,f1949]) ).
fof(f1951,plain,
! [X0,X1] : c_Transitive__Closure_Ortrancl(X1,X0) = c_Transitive__Closure_Ortrancl(X1,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),X0,c_Relation_OId(X1))),
inference(cnf_transformation,[],[f581]) ).
fof(f581,plain,
! [X0,X1] : c_Transitive__Closure_Ortrancl(X1,X0) = c_Transitive__Closure_Ortrancl(X1,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),X0,c_Relation_OId(X1))),
inference(rectify,[],[f150]) ).
fof(f150,axiom,
! [X14,X4] : c_Transitive__Closure_Ortrancl(X4,X14) = c_Transitive__Closure_Ortrancl(X4,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),X14,c_Relation_OId(X4))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__reflcl) ).
fof(f11189,plain,
spl104_532,
inference(avatar_split_clause,[],[f2640,f11187]) ).
fof(f11187,plain,
( spl104_532
<=> ! [X0,X1] : c_Transitive__Closure_Otrancl(X1,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),X0,c_Relation_OId(X1))) = c_Transitive__Closure_Otrancl(X1,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),X0,c_Relation_OId(X1)),c_Relation_OId(X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_532])]) ).
fof(f2640,plain,
! [X0,X1] : c_Transitive__Closure_Otrancl(X1,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),X0,c_Relation_OId(X1))) = c_Transitive__Closure_Otrancl(X1,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),X0,c_Relation_OId(X1)),c_Relation_OId(X1))),
inference(definition_unfolding,[],[f1950,f1949,f1949]) ).
fof(f1950,plain,
! [X0,X1] : c_Transitive__Closure_Ortrancl(X1,X0) = c_Transitive__Closure_Ortrancl(X1,c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),X0,c_Relation_OId(X1))),
inference(cnf_transformation,[],[f580]) ).
fof(f580,plain,
! [X0,X1] : c_Transitive__Closure_Ortrancl(X1,X0) = c_Transitive__Closure_Ortrancl(X1,c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),X0,c_Relation_OId(X1))),
inference(rectify,[],[f211]) ).
fof(f211,axiom,
! [X3,X4] : c_Transitive__Closure_Ortrancl(X4,X3) = c_Transitive__Closure_Ortrancl(X4,c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),X3,c_Relation_OId(X4))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__r__diff__Id) ).
fof(f11185,plain,
spl104_531,
inference(avatar_split_clause,[],[f2531,f11183]) ).
fof(f11183,plain,
( spl104_531
<=> ! [X2,X4,X0,X3,X1] :
( c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,X3,X2),c_Wellfounded_Omlex__prod(X1,X4,X0))
| ~ c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,X3,X2),X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(X4,X3),hAPP(X4,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_531])]) ).
fof(f2531,plain,
! [X2,X3,X0,X1,X4] :
( c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,X3,X2),c_Wellfounded_Omlex__prod(X1,X4,X0))
| ~ c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,X3,X2),X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(X4,X3),hAPP(X4,X2)) ),
inference(cnf_transformation,[],[f1459]) ).
fof(f1459,plain,
! [X0,X1,X2,X3,X4] :
( c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,X3,X2),c_Wellfounded_Omlex__prod(X1,X4,X0))
| ~ c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,X3,X2),X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(X4,X3),hAPP(X4,X2)) ),
inference(flattening,[],[f1458]) ).
fof(f1458,plain,
! [X0,X1,X2,X3,X4] :
( c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,X3,X2),c_Wellfounded_Omlex__prod(X1,X4,X0))
| ~ c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,X3,X2),X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(X4,X3),hAPP(X4,X2)) ),
inference(ennf_transformation,[],[f967]) ).
fof(f967,plain,
! [X0,X1,X2,X3,X4] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(X4,X3),hAPP(X4,X2))
=> ( c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,X3,X2),X0)
=> c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,X3,X2),c_Wellfounded_Omlex__prod(X1,X4,X0)) ) ),
inference(rectify,[],[f296]) ).
fof(f296,axiom,
! [X14,X4,X12,X13,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(X1,X13),hAPP(X1,X12))
=> ( c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X13,X12),X14)
=> c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X13,X12),c_Wellfounded_Omlex__prod(X4,X1,X14)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mlex__leq) ).
fof(f11181,plain,
spl104_530,
inference(avatar_split_clause,[],[f2185,f11179]) ).
fof(f11179,plain,
( spl104_530
<=> ! [X2,X0,X1] :
( ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X1,X0),X2)
| ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,X1),X2)
| X0 = X1
| ~ c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),X2,c_Arrow__Order__Mirabelle_OLin) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_530])]) ).
fof(f2185,plain,
! [X2,X0,X1] :
( ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X1,X0),X2)
| ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,X1),X2)
| X0 = X1
| ~ c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),X2,c_Arrow__Order__Mirabelle_OLin) ),
inference(cnf_transformation,[],[f1643]) ).
fof(f1643,plain,
! [X0,X1,X2] :
( ( ( ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X1,X0),X2)
| ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,X1),X2) )
& ( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,X1),X2)
| c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X1,X0),X2) ) )
| X0 = X1
| ~ c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),X2,c_Arrow__Order__Mirabelle_OLin) ),
inference(nnf_transformation,[],[f1214]) ).
fof(f1214,plain,
! [X0,X1,X2] :
( ( ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X1,X0),X2)
<=> c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,X1),X2) )
| X0 = X1
| ~ c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),X2,c_Arrow__Order__Mirabelle_OLin) ),
inference(flattening,[],[f1213]) ).
fof(f1213,plain,
! [X0,X1,X2] :
( ( ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X1,X0),X2)
<=> c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,X1),X2) )
| X0 = X1
| ~ c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),X2,c_Arrow__Order__Mirabelle_OLin) ),
inference(ennf_transformation,[],[f756]) ).
fof(f756,plain,
! [X0,X1,X2] :
( c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),X2,c_Arrow__Order__Mirabelle_OLin)
=> ( X0 != X1
=> ( ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X1,X0),X2)
<=> c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,X1),X2) ) ) ),
inference(rectify,[],[f8]) ).
fof(f8,axiom,
! [X12,X13,X18] :
( c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),X18,c_Arrow__Order__Mirabelle_OLin)
=> ( X12 != X13
=> ( ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X13,X12),X18)
<=> c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X12,X13),X18) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_notin__Lin__iff) ).
fof(f11177,plain,
spl104_529,
inference(avatar_split_clause,[],[f2184,f11175]) ).
fof(f11175,plain,
( spl104_529
<=> ! [X2,X0,X1] :
( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,X1),X2)
| c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X1,X0),X2)
| X0 = X1
| ~ c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),X2,c_Arrow__Order__Mirabelle_OLin) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_529])]) ).
fof(f2184,plain,
! [X2,X0,X1] :
( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,X1),X2)
| c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X1,X0),X2)
| X0 = X1
| ~ c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),X2,c_Arrow__Order__Mirabelle_OLin) ),
inference(cnf_transformation,[],[f1643]) ).
fof(f11173,plain,
spl104_528,
inference(avatar_split_clause,[],[f2155,f11171]) ).
fof(f11171,plain,
( spl104_528
<=> ! [X2,X0,X1] :
( c_FunDef_Oreduction__pair(X2,c_Product__Type_OPair(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),tc_fun(tc_prod(X2,X2),tc_HOL_Obool),X1,X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),c_Relation_Orel__comp(X2,X2,X2,X1,X0),X1)
| ~ c_Wellfounded_Owf(X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_528])]) ).
fof(f2155,plain,
! [X2,X0,X1] :
( c_FunDef_Oreduction__pair(X2,c_Product__Type_OPair(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),tc_fun(tc_prod(X2,X2),tc_HOL_Obool),X1,X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),c_Relation_Orel__comp(X2,X2,X2,X1,X0),X1)
| ~ c_Wellfounded_Owf(X2,X1) ),
inference(cnf_transformation,[],[f1180]) ).
fof(f1180,plain,
! [X0,X1,X2] :
( c_FunDef_Oreduction__pair(X2,c_Product__Type_OPair(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),tc_fun(tc_prod(X2,X2),tc_HOL_Obool),X1,X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),c_Relation_Orel__comp(X2,X2,X2,X1,X0),X1)
| ~ c_Wellfounded_Owf(X2,X1) ),
inference(flattening,[],[f1179]) ).
fof(f1179,plain,
! [X0,X1,X2] :
( c_FunDef_Oreduction__pair(X2,c_Product__Type_OPair(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),tc_fun(tc_prod(X2,X2),tc_HOL_Obool),X1,X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),c_Relation_Orel__comp(X2,X2,X2,X1,X0),X1)
| ~ c_Wellfounded_Owf(X2,X1) ),
inference(ennf_transformation,[],[f731]) ).
fof(f731,plain,
! [X0,X1,X2] :
( c_Wellfounded_Owf(X2,X1)
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),c_Relation_Orel__comp(X2,X2,X2,X1,X0),X1)
=> c_FunDef_Oreduction__pair(X2,c_Product__Type_OPair(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),tc_fun(tc_prod(X2,X2),tc_HOL_Obool),X1,X0)) ) ),
inference(rectify,[],[f489]) ).
fof(f489,axiom,
! [X54,X14,X4] :
( c_Wellfounded_Owf(X4,X14)
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),c_Relation_Orel__comp(X4,X4,X4,X14,X54),X14)
=> c_FunDef_Oreduction__pair(X4,c_Product__Type_OPair(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),tc_fun(tc_prod(X4,X4),tc_HOL_Obool),X14,X54)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_reduction__pairI) ).
fof(f11035,plain,
spl104_527,
inference(avatar_split_clause,[],[f2671,f11033]) ).
fof(f11033,plain,
( spl104_527
<=> ! [X0,X3,X2,X1] :
( X0 = X2
| ~ c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X2,X0),c_Transitive__Closure_Otrancl(X3,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X3,X3),tc_HOL_Obool),X1,c_Relation_OId(X3))))
| c_member(X3,X2,c_Relation_ODomain(X3,X3,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_527])]) ).
fof(f2671,plain,
! [X2,X3,X0,X1] :
( X0 = X2
| ~ c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X2,X0),c_Transitive__Closure_Otrancl(X3,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X3,X3),tc_HOL_Obool),X1,c_Relation_OId(X3))))
| c_member(X3,X2,c_Relation_ODomain(X3,X3,X1)) ),
inference(definition_unfolding,[],[f2387,f1949]) ).
fof(f2387,plain,
! [X2,X3,X0,X1] :
( X0 = X2
| ~ c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X2,X0),c_Transitive__Closure_Ortrancl(X3,X1))
| c_member(X3,X2,c_Relation_ODomain(X3,X3,X1)) ),
inference(cnf_transformation,[],[f1714]) ).
fof(f1714,plain,
! [X0,X1,X2,X3] :
( ( ( c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X2,X0),c_Transitive__Closure_Ortrancl(X3,X1))
| X0 != X2 )
& ( X0 = X2
| ~ c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X2,X0),c_Transitive__Closure_Ortrancl(X3,X1)) ) )
| c_member(X3,X2,c_Relation_ODomain(X3,X3,X1)) ),
inference(nnf_transformation,[],[f1384]) ).
fof(f1384,plain,
! [X0,X1,X2,X3] :
( ( c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X2,X0),c_Transitive__Closure_Ortrancl(X3,X1))
<=> X0 = X2 )
| c_member(X3,X2,c_Relation_ODomain(X3,X3,X1)) ),
inference(ennf_transformation,[],[f894]) ).
fof(f894,plain,
! [X0,X1,X2,X3] :
( ~ c_member(X3,X2,c_Relation_ODomain(X3,X3,X1))
=> ( c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X2,X0),c_Transitive__Closure_Ortrancl(X3,X1))
<=> X0 = X2 ) ),
inference(rectify,[],[f61]) ).
fof(f61,axiom,
! [X12,X14,X13,X4] :
( ~ c_member(X4,X13,c_Relation_ODomain(X4,X4,X14))
=> ( c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X13,X12),c_Transitive__Closure_Ortrancl(X4,X14))
<=> X12 = X13 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Not__Domain__rtrancl) ).
fof(f11031,plain,
spl104_526,
inference(avatar_split_clause,[],[f2605,f11029]) ).
fof(f11029,plain,
( spl104_526
<=> ! [X3,X4,X0,X5,X2,X1] :
( c_Recdef_Ocut(X5,X4,X3,X2,X1) = c_Recdef_Ocut(X5,X4,X0,X2,X1)
| hAPP(X0,sK91(X0,X1,X2,X3,X5)) != hAPP(X3,sK91(X0,X1,X2,X3,X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_526])]) ).
fof(f2605,plain,
! [X2,X3,X0,X1,X4,X5] :
( c_Recdef_Ocut(X5,X4,X3,X2,X1) = c_Recdef_Ocut(X5,X4,X0,X2,X1)
| hAPP(X0,sK91(X0,X1,X2,X3,X5)) != hAPP(X3,sK91(X0,X1,X2,X3,X5)) ),
inference(cnf_transformation,[],[f1835]) ).
fof(f1835,plain,
! [X0,X1,X2,X3,X4,X5] :
( ( c_Recdef_Ocut(X5,X4,X3,X2,X1) = c_Recdef_Ocut(X5,X4,X0,X2,X1)
| ( hAPP(X0,sK91(X0,X1,X2,X3,X5)) != hAPP(X3,sK91(X0,X1,X2,X3,X5))
& c_member(tc_prod(X5,X5),c_Product__Type_OPair(X5,X5,sK91(X0,X1,X2,X3,X5),X1),X2) ) )
& ( ! [X7] :
( hAPP(X0,X7) = hAPP(X3,X7)
| ~ c_member(tc_prod(X5,X5),c_Product__Type_OPair(X5,X5,X7,X1),X2) )
| c_Recdef_Ocut(X5,X4,X3,X2,X1) != c_Recdef_Ocut(X5,X4,X0,X2,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK91])],[f1833,f1834]) ).
fof(f1834,plain,
! [X0,X1,X2,X3,X5] :
( ? [X6] :
( hAPP(X0,X6) != hAPP(X3,X6)
& c_member(tc_prod(X5,X5),c_Product__Type_OPair(X5,X5,X6,X1),X2) )
=> ( hAPP(X0,sK91(X0,X1,X2,X3,X5)) != hAPP(X3,sK91(X0,X1,X2,X3,X5))
& c_member(tc_prod(X5,X5),c_Product__Type_OPair(X5,X5,sK91(X0,X1,X2,X3,X5),X1),X2) ) ),
introduced(choice_axiom,[]) ).
fof(f1833,plain,
! [X0,X1,X2,X3,X4,X5] :
( ( c_Recdef_Ocut(X5,X4,X3,X2,X1) = c_Recdef_Ocut(X5,X4,X0,X2,X1)
| ? [X6] :
( hAPP(X0,X6) != hAPP(X3,X6)
& c_member(tc_prod(X5,X5),c_Product__Type_OPair(X5,X5,X6,X1),X2) ) )
& ( ! [X7] :
( hAPP(X0,X7) = hAPP(X3,X7)
| ~ c_member(tc_prod(X5,X5),c_Product__Type_OPair(X5,X5,X7,X1),X2) )
| c_Recdef_Ocut(X5,X4,X3,X2,X1) != c_Recdef_Ocut(X5,X4,X0,X2,X1) ) ),
inference(rectify,[],[f1832]) ).
fof(f1832,plain,
! [X0,X1,X2,X3,X4,X5] :
( ( c_Recdef_Ocut(X5,X4,X3,X2,X1) = c_Recdef_Ocut(X5,X4,X0,X2,X1)
| ? [X6] :
( hAPP(X0,X6) != hAPP(X3,X6)
& c_member(tc_prod(X5,X5),c_Product__Type_OPair(X5,X5,X6,X1),X2) ) )
& ( ! [X6] :
( hAPP(X0,X6) = hAPP(X3,X6)
| ~ c_member(tc_prod(X5,X5),c_Product__Type_OPair(X5,X5,X6,X1),X2) )
| c_Recdef_Ocut(X5,X4,X3,X2,X1) != c_Recdef_Ocut(X5,X4,X0,X2,X1) ) ),
inference(nnf_transformation,[],[f1513]) ).
fof(f1513,plain,
! [X0,X1,X2,X3,X4,X5] :
( c_Recdef_Ocut(X5,X4,X3,X2,X1) = c_Recdef_Ocut(X5,X4,X0,X2,X1)
<=> ! [X6] :
( hAPP(X0,X6) = hAPP(X3,X6)
| ~ c_member(tc_prod(X5,X5),c_Product__Type_OPair(X5,X5,X6,X1),X2) ) ),
inference(ennf_transformation,[],[f1007]) ).
fof(f1007,plain,
! [X0,X1,X2,X3,X4,X5] :
( c_Recdef_Ocut(X5,X4,X3,X2,X1) = c_Recdef_Ocut(X5,X4,X0,X2,X1)
<=> ! [X6] :
( c_member(tc_prod(X5,X5),c_Product__Type_OPair(X5,X5,X6,X1),X2)
=> hAPP(X0,X6) = hAPP(X3,X6) ) ),
inference(rectify,[],[f97]) ).
fof(f97,axiom,
! [X0,X13,X3,X1,X15,X4] :
( c_Recdef_Ocut(X4,X15,X1,X3,X13) = c_Recdef_Ocut(X4,X15,X0,X3,X13)
<=> ! [X5] :
( c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X5,X13),X3)
=> hAPP(X1,X5) = hAPP(X0,X5) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_cuts__eq) ).
fof(f11027,plain,
spl104_525,
inference(avatar_split_clause,[],[f2603,f11025]) ).
fof(f11025,plain,
( spl104_525
<=> ! [X1,X4,X0,X3,X5,X2,X7] :
( hAPP(X0,X7) = hAPP(X3,X7)
| ~ c_member(tc_prod(X5,X5),c_Product__Type_OPair(X5,X5,X7,X1),X2)
| c_Recdef_Ocut(X5,X4,X3,X2,X1) != c_Recdef_Ocut(X5,X4,X0,X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_525])]) ).
fof(f2603,plain,
! [X2,X3,X0,X1,X7,X4,X5] :
( hAPP(X0,X7) = hAPP(X3,X7)
| ~ c_member(tc_prod(X5,X5),c_Product__Type_OPair(X5,X5,X7,X1),X2)
| c_Recdef_Ocut(X5,X4,X3,X2,X1) != c_Recdef_Ocut(X5,X4,X0,X2,X1) ),
inference(cnf_transformation,[],[f1835]) ).
fof(f11023,plain,
spl104_524,
inference(avatar_split_clause,[],[f2419,f11021]) ).
fof(f11021,plain,
( spl104_524
<=> ! [X0,X3,X2,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X2,c_Set_Oinsert(X3,X1,X0))
| ~ c_member(X3,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),c_Groups_Ominus__class_Ominus(tc_fun(X3,tc_HOL_Obool),X2,c_Set_Oinsert(X3,X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_524])]) ).
fof(f2419,plain,
! [X2,X3,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X2,c_Set_Oinsert(X3,X1,X0))
| ~ c_member(X3,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),c_Groups_Ominus__class_Ominus(tc_fun(X3,tc_HOL_Obool),X2,c_Set_Oinsert(X3,X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)))),X0) ),
inference(cnf_transformation,[],[f1420]) ).
fof(f1420,plain,
! [X0,X1,X2,X3] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X2,c_Set_Oinsert(X3,X1,X0))
| ~ c_member(X3,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),c_Groups_Ominus__class_Ominus(tc_fun(X3,tc_HOL_Obool),X2,c_Set_Oinsert(X3,X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)))),X0) ),
inference(flattening,[],[f1419]) ).
fof(f1419,plain,
! [X0,X1,X2,X3] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X2,c_Set_Oinsert(X3,X1,X0))
| ~ c_member(X3,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),c_Groups_Ominus__class_Ominus(tc_fun(X3,tc_HOL_Obool),X2,c_Set_Oinsert(X3,X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)))),X0) ),
inference(ennf_transformation,[],[f917]) ).
fof(f917,plain,
! [X0,X1,X2,X3] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),c_Groups_Ominus__class_Ominus(tc_fun(X3,tc_HOL_Obool),X2,c_Set_Oinsert(X3,X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)))),X0)
=> ( c_member(X3,X1,X2)
=> c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X2,c_Set_Oinsert(X3,X1,X0)) ) ),
inference(rectify,[],[f447]) ).
fof(f447,axiom,
! [X10,X13,X11,X4] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool),c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool),X11,c_Set_Oinsert(X4,X13,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))),X10)
=> ( c_member(X4,X13,X11)
=> c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool),X11,c_Set_Oinsert(X4,X13,X10)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__single__insert) ).
fof(f11019,plain,
spl104_523,
inference(avatar_split_clause,[],[f2348,f11017]) ).
fof(f11017,plain,
( spl104_523
<=> ! [X0,X3,X2,X1] :
( c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat,X3,X1),c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat,X2,X0)),c_FunDef_Opair__less)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_523])]) ).
fof(f2348,plain,
! [X2,X3,X0,X1] :
( c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat,X3,X1),c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat,X2,X0)),c_FunDef_Opair__less)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X2) ),
inference(cnf_transformation,[],[f1325]) ).
fof(f1325,plain,
! [X0,X1,X2,X3] :
( c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat,X3,X1),c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat,X2,X0)),c_FunDef_Opair__less)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X2) ),
inference(ennf_transformation,[],[f860]) ).
fof(f860,plain,
! [X0,X1,X2,X3] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X2)
=> c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat,X3,X1),c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat,X2,X0)),c_FunDef_Opair__less) ),
inference(rectify,[],[f448]) ).
fof(f448,axiom,
! [X79,X30,X8,X9] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X9,X8)
=> c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat,X9,X30),c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat,X8,X79)),c_FunDef_Opair__less) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pair__lessI1) ).
fof(f11015,plain,
spl104_522,
inference(avatar_split_clause,[],[f2347,f11013]) ).
fof(f11013,plain,
( spl104_522
<=> ! [X0,X3,X2,X1] :
( c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat,X3,X1),c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat,X2,X0)),c_FunDef_Opair__leq)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_522])]) ).
fof(f2347,plain,
! [X2,X3,X0,X1] :
( c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat,X3,X1),c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat,X2,X0)),c_FunDef_Opair__leq)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X2) ),
inference(cnf_transformation,[],[f1324]) ).
fof(f1324,plain,
! [X0,X1,X2,X3] :
( c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat,X3,X1),c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat,X2,X0)),c_FunDef_Opair__leq)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X2) ),
inference(ennf_transformation,[],[f859]) ).
fof(f859,plain,
! [X0,X1,X2,X3] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X2)
=> c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat,X3,X1),c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat,X2,X0)),c_FunDef_Opair__leq) ),
inference(rectify,[],[f454]) ).
fof(f454,axiom,
! [X79,X30,X8,X9] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X9,X8)
=> c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat,X9,X30),c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat,X8,X79)),c_FunDef_Opair__leq) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pair__leqI1) ).
fof(f10959,plain,
spl104_521,
inference(avatar_split_clause,[],[f2607,f10957]) ).
fof(f10957,plain,
( spl104_521
<=> ! [X3,X4,X0,X5,X2,X1] :
( c_member(tc_prod(X5,X5),c_Product__Type_OPair(X5,X5,X4,X3),hAPP(c_Relation_Oinv__image(X2,X5,X1),X0))
| ~ c_member(tc_prod(X2,X2),c_Product__Type_OPair(X2,X2,hAPP(X0,X4),hAPP(X0,X3)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_521])]) ).
fof(f2607,plain,
! [X2,X3,X0,X1,X4,X5] :
( c_member(tc_prod(X5,X5),c_Product__Type_OPair(X5,X5,X4,X3),hAPP(c_Relation_Oinv__image(X2,X5,X1),X0))
| ~ c_member(tc_prod(X2,X2),c_Product__Type_OPair(X2,X2,hAPP(X0,X4),hAPP(X0,X3)),X1) ),
inference(cnf_transformation,[],[f1836]) ).
fof(f1836,plain,
! [X0,X1,X2,X3,X4,X5] :
( ( c_member(tc_prod(X5,X5),c_Product__Type_OPair(X5,X5,X4,X3),hAPP(c_Relation_Oinv__image(X2,X5,X1),X0))
| ~ c_member(tc_prod(X2,X2),c_Product__Type_OPair(X2,X2,hAPP(X0,X4),hAPP(X0,X3)),X1) )
& ( c_member(tc_prod(X2,X2),c_Product__Type_OPair(X2,X2,hAPP(X0,X4),hAPP(X0,X3)),X1)
| ~ c_member(tc_prod(X5,X5),c_Product__Type_OPair(X5,X5,X4,X3),hAPP(c_Relation_Oinv__image(X2,X5,X1),X0)) ) ),
inference(nnf_transformation,[],[f1008]) ).
fof(f1008,plain,
! [X0,X1,X2,X3,X4,X5] :
( c_member(tc_prod(X5,X5),c_Product__Type_OPair(X5,X5,X4,X3),hAPP(c_Relation_Oinv__image(X2,X5,X1),X0))
<=> c_member(tc_prod(X2,X2),c_Product__Type_OPair(X2,X2,hAPP(X0,X4),hAPP(X0,X3)),X1) ),
inference(rectify,[],[f26]) ).
fof(f26,axiom,
! [X1,X3,X15,X12,X13,X4] :
( c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X13,X12),hAPP(c_Relation_Oinv__image(X15,X4,X3),X1))
<=> c_member(tc_prod(X15,X15),c_Product__Type_OPair(X15,X15,hAPP(X1,X13),hAPP(X1,X12)),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_in__inv__image) ).
fof(f10955,plain,
spl104_520,
inference(avatar_split_clause,[],[f2606,f10953]) ).
fof(f10953,plain,
( spl104_520
<=> ! [X2,X4,X0,X3,X5,X1] :
( c_member(tc_prod(X2,X2),c_Product__Type_OPair(X2,X2,hAPP(X0,X4),hAPP(X0,X3)),X1)
| ~ c_member(tc_prod(X5,X5),c_Product__Type_OPair(X5,X5,X4,X3),hAPP(c_Relation_Oinv__image(X2,X5,X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_520])]) ).
fof(f2606,plain,
! [X2,X3,X0,X1,X4,X5] :
( c_member(tc_prod(X2,X2),c_Product__Type_OPair(X2,X2,hAPP(X0,X4),hAPP(X0,X3)),X1)
| ~ c_member(tc_prod(X5,X5),c_Product__Type_OPair(X5,X5,X4,X3),hAPP(c_Relation_Oinv__image(X2,X5,X1),X0)) ),
inference(cnf_transformation,[],[f1836]) ).
fof(f10665,plain,
spl104_519,
inference(avatar_split_clause,[],[f2604,f10663]) ).
fof(f10663,plain,
( spl104_519
<=> ! [X3,X4,X0,X5,X2,X1] :
( c_Recdef_Ocut(X5,X4,X3,X2,X1) = c_Recdef_Ocut(X5,X4,X0,X2,X1)
| c_member(tc_prod(X5,X5),c_Product__Type_OPair(X5,X5,sK91(X0,X1,X2,X3,X5),X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_519])]) ).
fof(f2604,plain,
! [X2,X3,X0,X1,X4,X5] :
( c_Recdef_Ocut(X5,X4,X3,X2,X1) = c_Recdef_Ocut(X5,X4,X0,X2,X1)
| c_member(tc_prod(X5,X5),c_Product__Type_OPair(X5,X5,sK91(X0,X1,X2,X3,X5),X1),X2) ),
inference(cnf_transformation,[],[f1835]) ).
fof(f10661,plain,
spl104_518,
inference(avatar_split_clause,[],[f2599,f10659]) ).
fof(f10659,plain,
( spl104_518
<=> ! [X2,X3,X4,X0,X5,X1] :
( hAPP(hAPP(X2,X0),X1) = hAPP(hAPP(X2,sK90(X0,X1,X2,X3,X4,X5)),X1)
| ~ c_Recdef_Owfrec__rel(X5,X4,X3,X2,X1,hAPP(hAPP(X2,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_518])]) ).
fof(f2599,plain,
! [X2,X3,X0,X1,X4,X5] :
( hAPP(hAPP(X2,X0),X1) = hAPP(hAPP(X2,sK90(X0,X1,X2,X3,X4,X5)),X1)
| ~ c_Recdef_Owfrec__rel(X5,X4,X3,X2,X1,hAPP(hAPP(X2,X0),X1)) ),
inference(cnf_transformation,[],[f1831]) ).
fof(f10657,plain,
spl104_517,
inference(avatar_split_clause,[],[f2584,f10655]) ).
fof(f10655,plain,
( spl104_517
<=> ! [X3,X4,X0,X5,X2,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool),c_Relation_OImage(X5,X4,X3,X1),c_Relation_OImage(X5,X4,X2,X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool),X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X4),tc_HOL_Obool),X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_517])]) ).
fof(f2584,plain,
! [X2,X3,X0,X1,X4,X5] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool),c_Relation_OImage(X5,X4,X3,X1),c_Relation_OImage(X5,X4,X2,X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool),X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X4),tc_HOL_Obool),X3,X2) ),
inference(cnf_transformation,[],[f1504]) ).
fof(f1504,plain,
! [X0,X1,X2,X3,X4,X5] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool),c_Relation_OImage(X5,X4,X3,X1),c_Relation_OImage(X5,X4,X2,X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool),X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X4),tc_HOL_Obool),X3,X2) ),
inference(flattening,[],[f1503]) ).
fof(f1503,plain,
! [X0,X1,X2,X3,X4,X5] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool),c_Relation_OImage(X5,X4,X3,X1),c_Relation_OImage(X5,X4,X2,X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool),X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X4),tc_HOL_Obool),X3,X2) ),
inference(ennf_transformation,[],[f998]) ).
fof(f998,plain,
! [X0,X1,X2,X3,X4,X5] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X4),tc_HOL_Obool),X3,X2)
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool),X1,X0)
=> c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool),c_Relation_OImage(X5,X4,X3,X1),c_Relation_OImage(X5,X4,X2,X0)) ) ),
inference(rectify,[],[f476]) ).
fof(f476,axiom,
! [X11,X84,X3,X85,X15,X4] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X4,X15),tc_HOL_Obool),X85,X3)
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool),X84,X11)
=> c_Orderings_Oord__class_Oless__eq(tc_fun(X15,tc_HOL_Obool),c_Relation_OImage(X4,X15,X85,X84),c_Relation_OImage(X4,X15,X3,X11)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Image__mono) ).
fof(f10653,plain,
spl104_516,
inference(avatar_split_clause,[],[f2526,f10651]) ).
fof(f10651,plain,
( spl104_516
<=> ! [X4,X0,X3,X2,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool),X3,X1),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool),X2,X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool),X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool),X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_516])]) ).
fof(f2526,plain,
! [X2,X3,X0,X1,X4] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool),X3,X1),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool),X2,X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool),X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool),X3,X2) ),
inference(cnf_transformation,[],[f1453]) ).
fof(f1453,plain,
! [X0,X1,X2,X3,X4] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool),X3,X1),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool),X2,X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool),X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool),X3,X2) ),
inference(flattening,[],[f1452]) ).
fof(f1452,plain,
! [X0,X1,X2,X3,X4] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool),X3,X1),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool),X2,X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool),X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool),X3,X2) ),
inference(ennf_transformation,[],[f962]) ).
fof(f962,plain,
! [X0,X1,X2,X3,X4] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool),X3,X2)
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool),X1,X0)
=> c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool),X3,X1),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool),X2,X0)) ) ),
inference(rectify,[],[f224]) ).
fof(f224,axiom,
! [X65,X10,X53,X11,X4] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool),X11,X53)
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool),X10,X65)
=> c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool),X11,X10),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool),X53,X65)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__mono) ).
fof(f10649,plain,
spl104_515,
inference(avatar_split_clause,[],[f2525,f10647]) ).
fof(f10647,plain,
( spl104_515
<=> ! [X4,X0,X3,X2,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool),c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool),X3,X0),c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool),X2,X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool),X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool),X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_515])]) ).
fof(f2525,plain,
! [X2,X3,X0,X1,X4] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool),c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool),X3,X0),c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool),X2,X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool),X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool),X3,X2) ),
inference(cnf_transformation,[],[f1451]) ).
fof(f1451,plain,
! [X0,X1,X2,X3,X4] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool),c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool),X3,X0),c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool),X2,X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool),X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool),X3,X2) ),
inference(flattening,[],[f1450]) ).
fof(f1450,plain,
! [X0,X1,X2,X3,X4] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool),c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool),X3,X0),c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool),X2,X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool),X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool),X3,X2) ),
inference(ennf_transformation,[],[f961]) ).
fof(f961,plain,
! [X0,X1,X2,X3,X4] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool),X3,X2)
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool),X1,X0)
=> c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool),c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool),X3,X0),c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool),X2,X1)) ) ),
inference(rectify,[],[f266]) ).
fof(f266,axiom,
! [X10,X65,X53,X11,X4] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool),X11,X53)
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool),X65,X10)
=> c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool),c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool),X11,X10),c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool),X53,X65)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Diff__mono) ).
fof(f10644,plain,
spl104_514,
inference(avatar_split_clause,[],[f2452,f10642]) ).
fof(f10642,plain,
( spl104_514
<=> ! [X0,X3,X2,X1] :
( sP4(X0,X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool),X1,X0)
| ~ c_Orderings_Oord__class_Oless(tc_fun(X2,tc_HOL_Obool),c_Groups_Ominus__class_Ominus(tc_fun(X2,tc_HOL_Obool),X1,c_Set_Oinsert(X2,X3,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_514])]) ).
fof(f2452,plain,
! [X2,X3,X0,X1] :
( sP4(X0,X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool),X1,X0)
| ~ c_Orderings_Oord__class_Oless(tc_fun(X2,tc_HOL_Obool),c_Groups_Ominus__class_Ominus(tc_fun(X2,tc_HOL_Obool),X1,c_Set_Oinsert(X2,X3,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)))),X0) ),
inference(cnf_transformation,[],[f1752]) ).
fof(f1752,plain,
! [X0,X1,X2,X3] :
( ( sP4(X0,X1,X2,X3)
| ( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool),X1,X0)
& ~ c_member(X2,X3,X1) )
| ( ~ c_Orderings_Oord__class_Oless(tc_fun(X2,tc_HOL_Obool),c_Groups_Ominus__class_Ominus(tc_fun(X2,tc_HOL_Obool),X1,c_Set_Oinsert(X2,X3,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)))),X0)
& c_member(X2,X3,X1) ) )
& ( ( ( c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool),X1,X0)
| c_member(X2,X3,X1) )
& ( c_Orderings_Oord__class_Oless(tc_fun(X2,tc_HOL_Obool),c_Groups_Ominus__class_Ominus(tc_fun(X2,tc_HOL_Obool),X1,c_Set_Oinsert(X2,X3,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)))),X0)
| ~ c_member(X2,X3,X1) ) )
| ~ sP4(X0,X1,X2,X3) ) ),
inference(rectify,[],[f1751]) ).
fof(f1751,plain,
! [X0,X2,X3,X1] :
( ( sP4(X0,X2,X3,X1)
| ( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X2,X0)
& ~ c_member(X3,X1,X2) )
| ( ~ c_Orderings_Oord__class_Oless(tc_fun(X3,tc_HOL_Obool),c_Groups_Ominus__class_Ominus(tc_fun(X3,tc_HOL_Obool),X2,c_Set_Oinsert(X3,X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)))),X0)
& c_member(X3,X1,X2) ) )
& ( ( ( c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X2,X0)
| c_member(X3,X1,X2) )
& ( c_Orderings_Oord__class_Oless(tc_fun(X3,tc_HOL_Obool),c_Groups_Ominus__class_Ominus(tc_fun(X3,tc_HOL_Obool),X2,c_Set_Oinsert(X3,X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)))),X0)
| ~ c_member(X3,X1,X2) ) )
| ~ sP4(X0,X2,X3,X1) ) ),
inference(flattening,[],[f1750]) ).
fof(f1750,plain,
! [X0,X2,X3,X1] :
( ( sP4(X0,X2,X3,X1)
| ( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X2,X0)
& ~ c_member(X3,X1,X2) )
| ( ~ c_Orderings_Oord__class_Oless(tc_fun(X3,tc_HOL_Obool),c_Groups_Ominus__class_Ominus(tc_fun(X3,tc_HOL_Obool),X2,c_Set_Oinsert(X3,X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)))),X0)
& c_member(X3,X1,X2) ) )
& ( ( ( c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X2,X0)
| c_member(X3,X1,X2) )
& ( c_Orderings_Oord__class_Oless(tc_fun(X3,tc_HOL_Obool),c_Groups_Ominus__class_Ominus(tc_fun(X3,tc_HOL_Obool),X2,c_Set_Oinsert(X3,X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)))),X0)
| ~ c_member(X3,X1,X2) ) )
| ~ sP4(X0,X2,X3,X1) ) ),
inference(nnf_transformation,[],[f1533]) ).
fof(f1533,plain,
! [X0,X2,X3,X1] :
( sP4(X0,X2,X3,X1)
<=> ( ( c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X2,X0)
| c_member(X3,X1,X2) )
& ( c_Orderings_Oord__class_Oless(tc_fun(X3,tc_HOL_Obool),c_Groups_Ominus__class_Ominus(tc_fun(X3,tc_HOL_Obool),X2,c_Set_Oinsert(X3,X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)))),X0)
| ~ c_member(X3,X1,X2) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP4])]) ).
fof(f10640,plain,
spl104_513,
inference(avatar_split_clause,[],[f2279,f10638]) ).
fof(f10638,plain,
( spl104_513
<=> ! [X0,X3,X2,X1] : c_Groups_Ominus__class_Ominus(tc_fun(X3,tc_HOL_Obool),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),X2,X1),X0) = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),c_Groups_Ominus__class_Ominus(tc_fun(X3,tc_HOL_Obool),X2,X0),c_Groups_Ominus__class_Ominus(tc_fun(X3,tc_HOL_Obool),X1,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_513])]) ).
fof(f2279,plain,
! [X2,X3,X0,X1] : c_Groups_Ominus__class_Ominus(tc_fun(X3,tc_HOL_Obool),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),X2,X1),X0) = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),c_Groups_Ominus__class_Ominus(tc_fun(X3,tc_HOL_Obool),X2,X0),c_Groups_Ominus__class_Ominus(tc_fun(X3,tc_HOL_Obool),X1,X0)),
inference(cnf_transformation,[],[f805]) ).
fof(f805,plain,
! [X0,X1,X2,X3] : c_Groups_Ominus__class_Ominus(tc_fun(X3,tc_HOL_Obool),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),X2,X1),X0) = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),c_Groups_Ominus__class_Ominus(tc_fun(X3,tc_HOL_Obool),X2,X0),c_Groups_Ominus__class_Ominus(tc_fun(X3,tc_HOL_Obool),X1,X0)),
inference(rectify,[],[f206]) ).
fof(f206,axiom,
! [X53,X10,X11,X4] : c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool),X11,X10),X53) = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool),c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool),X11,X53),c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool),X10,X53)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__Diff) ).
fof(f10302,plain,
( spl104_512
| ~ spl104_107
| ~ spl104_370 ),
inference(avatar_split_clause,[],[f10174,f6473,f3367,f10300]) ).
fof(f10300,plain,
( spl104_512
<=> ! [X0,X1] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)) != c_fequal(X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_512])]) ).
fof(f10174,plain,
( ! [X0,X1] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)) != c_fequal(X1)
| ~ spl104_107
| ~ spl104_370 ),
inference(superposition,[],[f3368,f6474]) ).
fof(f10233,plain,
spl104_511,
inference(avatar_split_clause,[],[f2812,f10231]) ).
fof(f10231,plain,
( spl104_511
<=> ! [X5,X3,X4,X6,X2,X1] :
( c_Recdef_Owfrec__rel(X5,X4,X3,X2,X1,hAPP(hAPP(X2,X6),X1))
| c_member(tc_prod(X5,X5),c_Product__Type_OPair(X5,X5,sK87(X1,X2,X3,X4,X5,X6),X1),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_511])]) ).
fof(f2812,plain,
! [X2,X3,X1,X6,X4,X5] :
( c_Recdef_Owfrec__rel(X5,X4,X3,X2,X1,hAPP(hAPP(X2,X6),X1))
| c_member(tc_prod(X5,X5),c_Product__Type_OPair(X5,X5,sK87(X1,X2,X3,X4,X5,X6),X1),X3) ),
inference(equality_resolution,[],[f2594]) ).
fof(f2594,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( c_Recdef_Owfrec__rel(X5,X4,X3,X2,X1,X0)
| c_member(tc_prod(X5,X5),c_Product__Type_OPair(X5,X5,sK87(X1,X2,X3,X4,X5,X6),X1),X3)
| hAPP(hAPP(X2,X6),X1) != X0 ),
inference(cnf_transformation,[],[f1824]) ).
fof(f10229,plain,
spl104_510,
inference(avatar_split_clause,[],[f2657,f10227]) ).
fof(f10227,plain,
( spl104_510
<=> ! [X2,X0,X1] :
( c_Relation_OImage(X2,X2,c_Transitive__Closure_Otrancl(X2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),X1,c_Relation_OId(X2))),X0) = X0
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool),c_Relation_OImage(X2,X2,X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_510])]) ).
fof(f2657,plain,
! [X2,X0,X1] :
( c_Relation_OImage(X2,X2,c_Transitive__Closure_Otrancl(X2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),X1,c_Relation_OId(X2))),X0) = X0
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool),c_Relation_OImage(X2,X2,X1,X0),X0) ),
inference(definition_unfolding,[],[f2195,f1949]) ).
fof(f2195,plain,
! [X2,X0,X1] :
( c_Relation_OImage(X2,X2,c_Transitive__Closure_Ortrancl(X2,X1),X0) = X0
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool),c_Relation_OImage(X2,X2,X1,X0),X0) ),
inference(cnf_transformation,[],[f1225]) ).
fof(f1225,plain,
! [X0,X1,X2] :
( c_Relation_OImage(X2,X2,c_Transitive__Closure_Ortrancl(X2,X1),X0) = X0
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool),c_Relation_OImage(X2,X2,X1,X0),X0) ),
inference(ennf_transformation,[],[f765]) ).
fof(f765,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool),c_Relation_OImage(X2,X2,X1,X0),X0)
=> c_Relation_OImage(X2,X2,c_Transitive__Closure_Ortrancl(X2,X1),X0) = X0 ),
inference(rectify,[],[f477]) ).
fof(f477,axiom,
! [X80,X3,X4] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool),c_Relation_OImage(X4,X4,X3,X80),X80)
=> c_Relation_OImage(X4,X4,c_Transitive__Closure_Ortrancl(X4,X3),X80) = X80 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Image__closed__trancl) ).
fof(f10223,plain,
spl104_509,
inference(avatar_split_clause,[],[f2634,f10221]) ).
fof(f10221,plain,
( spl104_509
<=> ! [X0] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)) = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X0,tc_HOL_Obool),c_Relation_ODomain(X0,X0,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X0,X0),tc_HOL_Obool))),c_Relation_ORange(X0,X0,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X0,X0),tc_HOL_Obool)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_509])]) ).
fof(f2634,plain,
! [X0] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)) = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X0,tc_HOL_Obool),c_Relation_ODomain(X0,X0,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X0,X0),tc_HOL_Obool))),c_Relation_ORange(X0,X0,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X0,X0),tc_HOL_Obool)))),
inference(definition_unfolding,[],[f1911,f1954]) ).
fof(f1911,plain,
! [X0] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)) = c_Relation_OField(X0,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X0,X0),tc_HOL_Obool))),
inference(cnf_transformation,[],[f541]) ).
fof(f541,plain,
! [X0] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)) = c_Relation_OField(X0,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X0,X0),tc_HOL_Obool))),
inference(rectify,[],[f432]) ).
fof(f432,axiom,
! [X4] : c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)) = c_Relation_OField(X4,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X4,X4),tc_HOL_Obool))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Field__empty) ).
fof(f10219,plain,
spl104_508,
inference(avatar_split_clause,[],[f2590,f10217]) ).
fof(f10217,plain,
( spl104_508
<=> ! [X2,X4,X0,X3,X5,X1] :
( c_Recdef_Owfrec__rel(X5,X2,X3,X1,X4,hAPP(hAPP(X1,X0),X4))
| c_member(tc_prod(X5,X5),c_Product__Type_OPair(X5,X5,sK86(X0,X1,X2,X3,X4,X5),X4),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_508])]) ).
fof(f2590,plain,
! [X2,X3,X0,X1,X4,X5] :
( c_Recdef_Owfrec__rel(X5,X2,X3,X1,X4,hAPP(hAPP(X1,X0),X4))
| c_member(tc_prod(X5,X5),c_Product__Type_OPair(X5,X5,sK86(X0,X1,X2,X3,X4,X5),X4),X3) ),
inference(cnf_transformation,[],[f1819]) ).
fof(f10215,plain,
spl104_507,
inference(avatar_split_clause,[],[f2513,f10213]) ).
fof(f10213,plain,
( spl104_507
<=> ! [X2,X4,X0,X3,X1] : c_Relation_OImage(X4,X3,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X4,X3),tc_HOL_Obool),X2,X1),X0) = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),c_Relation_OImage(X4,X3,X2,X0),c_Relation_OImage(X4,X3,X1,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_507])]) ).
fof(f2513,plain,
! [X2,X3,X0,X1,X4] : c_Relation_OImage(X4,X3,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X4,X3),tc_HOL_Obool),X2,X1),X0) = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),c_Relation_OImage(X4,X3,X2,X0),c_Relation_OImage(X4,X3,X1,X0)),
inference(cnf_transformation,[],[f945]) ).
fof(f945,plain,
! [X0,X1,X2,X3,X4] : c_Relation_OImage(X4,X3,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X4,X3),tc_HOL_Obool),X2,X1),X0) = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),c_Relation_OImage(X4,X3,X2,X0),c_Relation_OImage(X4,X3,X1,X0)),
inference(rectify,[],[f480]) ).
fof(f480,axiom,
! [X11,X54,X14,X4,X15] : c_Relation_OImage(X15,X4,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X15,X4),tc_HOL_Obool),X14,X54),X11) = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool),c_Relation_OImage(X15,X4,X14,X11),c_Relation_OImage(X15,X4,X54,X11)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__Image) ).
fof(f10211,plain,
spl104_506,
inference(avatar_split_clause,[],[f2278,f10209]) ).
fof(f10209,plain,
( spl104_506
<=> ! [X0,X3,X2,X1] : c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),c_Groups_Ominus__class_Ominus(tc_fun(X3,tc_HOL_Obool),c_Relation_ODomain(X3,X2,X1),c_Relation_ODomain(X3,X2,X0)),c_Relation_ODomain(X3,X2,c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X3,X2),tc_HOL_Obool),X1,X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_506])]) ).
fof(f2278,plain,
! [X2,X3,X0,X1] : c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),c_Groups_Ominus__class_Ominus(tc_fun(X3,tc_HOL_Obool),c_Relation_ODomain(X3,X2,X1),c_Relation_ODomain(X3,X2,X0)),c_Relation_ODomain(X3,X2,c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X3,X2),tc_HOL_Obool),X1,X0))),
inference(cnf_transformation,[],[f804]) ).
fof(f804,plain,
! [X0,X1,X2,X3] : c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),c_Groups_Ominus__class_Ominus(tc_fun(X3,tc_HOL_Obool),c_Relation_ODomain(X3,X2,X1),c_Relation_ODomain(X3,X2,X0)),c_Relation_ODomain(X3,X2,c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X3,X2),tc_HOL_Obool),X1,X0))),
inference(rectify,[],[f282]) ).
fof(f282,axiom,
! [X10,X11,X15,X4] : c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool),c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool),c_Relation_ODomain(X4,X15,X11),c_Relation_ODomain(X4,X15,X10)),c_Relation_ODomain(X4,X15,c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X4,X15),tc_HOL_Obool),X11,X10))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Domain__Diff__subset) ).
fof(f10207,plain,
spl104_505,
inference(avatar_split_clause,[],[f2277,f10205]) ).
fof(f10205,plain,
( spl104_505
<=> ! [X0,X3,X2,X1] : c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),c_Groups_Ominus__class_Ominus(tc_fun(X3,tc_HOL_Obool),c_Relation_ORange(X2,X3,X1),c_Relation_ORange(X2,X3,X0)),c_Relation_ORange(X2,X3,c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X2,X3),tc_HOL_Obool),X1,X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_505])]) ).
fof(f2277,plain,
! [X2,X3,X0,X1] : c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),c_Groups_Ominus__class_Ominus(tc_fun(X3,tc_HOL_Obool),c_Relation_ORange(X2,X3,X1),c_Relation_ORange(X2,X3,X0)),c_Relation_ORange(X2,X3,c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X2,X3),tc_HOL_Obool),X1,X0))),
inference(cnf_transformation,[],[f803]) ).
fof(f803,plain,
! [X0,X1,X2,X3] : c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),c_Groups_Ominus__class_Ominus(tc_fun(X3,tc_HOL_Obool),c_Relation_ORange(X2,X3,X1),c_Relation_ORange(X2,X3,X0)),c_Relation_ORange(X2,X3,c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X2,X3),tc_HOL_Obool),X1,X0))),
inference(rectify,[],[f219]) ).
fof(f219,axiom,
! [X10,X11,X15,X4] : c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool),c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool),c_Relation_ORange(X15,X4,X11),c_Relation_ORange(X15,X4,X10)),c_Relation_ORange(X15,X4,c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X15,X4),tc_HOL_Obool),X11,X10))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Range__Diff__subset) ).
fof(f10203,plain,
spl104_504,
inference(avatar_split_clause,[],[f2276,f10201]) ).
fof(f10201,plain,
( spl104_504
<=> ! [X0,X3,X2,X1] : c_Groups_Ominus__class_Ominus(tc_fun(X3,tc_HOL_Obool),X2,c_Set_Oinsert(X3,X1,X0)) = c_Groups_Ominus__class_Ominus(tc_fun(X3,tc_HOL_Obool),c_Groups_Ominus__class_Ominus(tc_fun(X3,tc_HOL_Obool),X2,c_Set_Oinsert(X3,X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)))),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_504])]) ).
fof(f2276,plain,
! [X2,X3,X0,X1] : c_Groups_Ominus__class_Ominus(tc_fun(X3,tc_HOL_Obool),X2,c_Set_Oinsert(X3,X1,X0)) = c_Groups_Ominus__class_Ominus(tc_fun(X3,tc_HOL_Obool),c_Groups_Ominus__class_Ominus(tc_fun(X3,tc_HOL_Obool),X2,c_Set_Oinsert(X3,X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)))),X0),
inference(cnf_transformation,[],[f802]) ).
fof(f802,plain,
! [X0,X1,X2,X3] : c_Groups_Ominus__class_Ominus(tc_fun(X3,tc_HOL_Obool),X2,c_Set_Oinsert(X3,X1,X0)) = c_Groups_Ominus__class_Ominus(tc_fun(X3,tc_HOL_Obool),c_Groups_Ominus__class_Ominus(tc_fun(X3,tc_HOL_Obool),X2,c_Set_Oinsert(X3,X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)))),X0),
inference(rectify,[],[f400]) ).
fof(f400,axiom,
! [X10,X9,X11,X4] : c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool),X11,c_Set_Oinsert(X4,X9,X10)) = c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool),c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool),X11,c_Set_Oinsert(X4,X9,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))),X10),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Diff__insert2) ).
fof(f10172,plain,
spl104_503,
inference(avatar_split_clause,[],[f2275,f10170]) ).
fof(f10170,plain,
( spl104_503
<=> ! [X0,X3,X2,X1] : c_Groups_Ominus__class_Ominus(tc_fun(X3,tc_HOL_Obool),X2,c_Set_Oinsert(X3,X1,X0)) = c_Groups_Ominus__class_Ominus(tc_fun(X3,tc_HOL_Obool),c_Groups_Ominus__class_Ominus(tc_fun(X3,tc_HOL_Obool),X2,X0),c_Set_Oinsert(X3,X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_503])]) ).
fof(f2275,plain,
! [X2,X3,X0,X1] : c_Groups_Ominus__class_Ominus(tc_fun(X3,tc_HOL_Obool),X2,c_Set_Oinsert(X3,X1,X0)) = c_Groups_Ominus__class_Ominus(tc_fun(X3,tc_HOL_Obool),c_Groups_Ominus__class_Ominus(tc_fun(X3,tc_HOL_Obool),X2,X0),c_Set_Oinsert(X3,X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)))),
inference(cnf_transformation,[],[f801]) ).
fof(f801,plain,
! [X0,X1,X2,X3] : c_Groups_Ominus__class_Ominus(tc_fun(X3,tc_HOL_Obool),X2,c_Set_Oinsert(X3,X1,X0)) = c_Groups_Ominus__class_Ominus(tc_fun(X3,tc_HOL_Obool),c_Groups_Ominus__class_Ominus(tc_fun(X3,tc_HOL_Obool),X2,X0),c_Set_Oinsert(X3,X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)))),
inference(rectify,[],[f401]) ).
fof(f401,axiom,
! [X10,X9,X11,X4] : c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool),X11,c_Set_Oinsert(X4,X9,X10)) = c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool),c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool),X11,X10),c_Set_Oinsert(X4,X9,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Diff__insert) ).
fof(f10168,plain,
spl104_502,
inference(avatar_split_clause,[],[f2232,f10166]) ).
fof(f10166,plain,
( spl104_502
<=> ! [X1,X2,X0,X6,X8,X7] :
( X7 = X8
| ~ c_member(tc_prod(X2,X1),c_Product__Type_OPair(X2,X1,X6,X8),X0)
| ~ c_member(tc_prod(X2,X1),c_Product__Type_OPair(X2,X1,X6,X7),X0)
| ~ c_Relation_Osingle__valued(X2,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_502])]) ).
fof(f2232,plain,
! [X2,X0,X1,X8,X6,X7] :
( X7 = X8
| ~ c_member(tc_prod(X2,X1),c_Product__Type_OPair(X2,X1,X6,X8),X0)
| ~ c_member(tc_prod(X2,X1),c_Product__Type_OPair(X2,X1,X6,X7),X0)
| ~ c_Relation_Osingle__valued(X2,X1,X0) ),
inference(cnf_transformation,[],[f1670]) ).
fof(f1670,plain,
! [X0,X1,X2] :
( ( c_Relation_Osingle__valued(X2,X1,X0)
| ( sK49(X0,X1,X2) != sK50(X0,X1,X2)
& c_member(tc_prod(X2,X1),c_Product__Type_OPair(X2,X1,sK48(X0,X1,X2),sK50(X0,X1,X2)),X0)
& c_member(tc_prod(X2,X1),c_Product__Type_OPair(X2,X1,sK48(X0,X1,X2),sK49(X0,X1,X2)),X0) ) )
& ( ! [X6,X7] :
( ! [X8] :
( X7 = X8
| ~ c_member(tc_prod(X2,X1),c_Product__Type_OPair(X2,X1,X6,X8),X0) )
| ~ c_member(tc_prod(X2,X1),c_Product__Type_OPair(X2,X1,X6,X7),X0) )
| ~ c_Relation_Osingle__valued(X2,X1,X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK48,sK49,sK50])],[f1667,f1669,f1668]) ).
fof(f1668,plain,
! [X0,X1,X2] :
( ? [X3,X4] :
( ? [X5] :
( X4 != X5
& c_member(tc_prod(X2,X1),c_Product__Type_OPair(X2,X1,X3,X5),X0) )
& c_member(tc_prod(X2,X1),c_Product__Type_OPair(X2,X1,X3,X4),X0) )
=> ( ? [X5] :
( sK49(X0,X1,X2) != X5
& c_member(tc_prod(X2,X1),c_Product__Type_OPair(X2,X1,sK48(X0,X1,X2),X5),X0) )
& c_member(tc_prod(X2,X1),c_Product__Type_OPair(X2,X1,sK48(X0,X1,X2),sK49(X0,X1,X2)),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f1669,plain,
! [X0,X1,X2] :
( ? [X5] :
( sK49(X0,X1,X2) != X5
& c_member(tc_prod(X2,X1),c_Product__Type_OPair(X2,X1,sK48(X0,X1,X2),X5),X0) )
=> ( sK49(X0,X1,X2) != sK50(X0,X1,X2)
& c_member(tc_prod(X2,X1),c_Product__Type_OPair(X2,X1,sK48(X0,X1,X2),sK50(X0,X1,X2)),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f1667,plain,
! [X0,X1,X2] :
( ( c_Relation_Osingle__valued(X2,X1,X0)
| ? [X3,X4] :
( ? [X5] :
( X4 != X5
& c_member(tc_prod(X2,X1),c_Product__Type_OPair(X2,X1,X3,X5),X0) )
& c_member(tc_prod(X2,X1),c_Product__Type_OPair(X2,X1,X3,X4),X0) ) )
& ( ! [X6,X7] :
( ! [X8] :
( X7 = X8
| ~ c_member(tc_prod(X2,X1),c_Product__Type_OPair(X2,X1,X6,X8),X0) )
| ~ c_member(tc_prod(X2,X1),c_Product__Type_OPair(X2,X1,X6,X7),X0) )
| ~ c_Relation_Osingle__valued(X2,X1,X0) ) ),
inference(rectify,[],[f1666]) ).
fof(f1666,plain,
! [X0,X1,X2] :
( ( c_Relation_Osingle__valued(X2,X1,X0)
| ? [X3,X4] :
( ? [X5] :
( X4 != X5
& c_member(tc_prod(X2,X1),c_Product__Type_OPair(X2,X1,X3,X5),X0) )
& c_member(tc_prod(X2,X1),c_Product__Type_OPair(X2,X1,X3,X4),X0) ) )
& ( ! [X3,X4] :
( ! [X5] :
( X4 = X5
| ~ c_member(tc_prod(X2,X1),c_Product__Type_OPair(X2,X1,X3,X5),X0) )
| ~ c_member(tc_prod(X2,X1),c_Product__Type_OPair(X2,X1,X3,X4),X0) )
| ~ c_Relation_Osingle__valued(X2,X1,X0) ) ),
inference(nnf_transformation,[],[f1237]) ).
fof(f1237,plain,
! [X0,X1,X2] :
( c_Relation_Osingle__valued(X2,X1,X0)
<=> ! [X3,X4] :
( ! [X5] :
( X4 = X5
| ~ c_member(tc_prod(X2,X1),c_Product__Type_OPair(X2,X1,X3,X5),X0) )
| ~ c_member(tc_prod(X2,X1),c_Product__Type_OPair(X2,X1,X3,X4),X0) ) ),
inference(ennf_transformation,[],[f778]) ).
fof(f778,plain,
! [X0,X1,X2] :
( c_Relation_Osingle__valued(X2,X1,X0)
<=> ! [X3,X4] :
( c_member(tc_prod(X2,X1),c_Product__Type_OPair(X2,X1,X3,X4),X0)
=> ! [X5] :
( c_member(tc_prod(X2,X1),c_Product__Type_OPair(X2,X1,X3,X5),X0)
=> X4 = X5 ) ) ),
inference(rectify,[],[f54]) ).
fof(f54,axiom,
! [X3,X15,X4] :
( c_Relation_Osingle__valued(X4,X15,X3)
<=> ! [X2,X5] :
( c_member(tc_prod(X4,X15),c_Product__Type_OPair(X4,X15,X2,X5),X3)
=> ! [X6] :
( c_member(tc_prod(X4,X15),c_Product__Type_OPair(X4,X15,X2,X6),X3)
=> X5 = X6 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_single__valued__def) ).
fof(f10164,plain,
spl104_501,
inference(avatar_split_clause,[],[f2196,f10162]) ).
fof(f10162,plain,
( spl104_501
<=> ! [X2,X0,X1] :
( c_Set_Oinsert(X2,X0,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))) = X1
| c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) = X1
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool),X1,c_Set_Oinsert(X2,X0,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_501])]) ).
fof(f2196,plain,
! [X2,X0,X1] :
( c_Set_Oinsert(X2,X0,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))) = X1
| c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) = X1
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool),X1,c_Set_Oinsert(X2,X0,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)))) ),
inference(cnf_transformation,[],[f1227]) ).
fof(f1227,plain,
! [X0,X1,X2] :
( c_Set_Oinsert(X2,X0,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))) = X1
| c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) = X1
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool),X1,c_Set_Oinsert(X2,X0,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)))) ),
inference(flattening,[],[f1226]) ).
fof(f1226,plain,
! [X0,X1,X2] :
( c_Set_Oinsert(X2,X0,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))) = X1
| c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) = X1
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool),X1,c_Set_Oinsert(X2,X0,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)))) ),
inference(ennf_transformation,[],[f766]) ).
fof(f766,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool),X1,c_Set_Oinsert(X2,X0,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))))
=> ( c_Set_Oinsert(X2,X0,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))) = X1
| c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) = X1 ) ),
inference(rectify,[],[f434]) ).
fof(f434,axiom,
! [X13,X11,X4] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool),X11,c_Set_Oinsert(X4,X13,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))
=> ( c_Set_Oinsert(X4,X13,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))) = X11
| c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)) = X11 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__singletonD) ).
fof(f9868,plain,
spl104_500,
inference(avatar_split_clause,[],[f2800,f9866]) ).
fof(f9866,plain,
( spl104_500
<=> ! [X2,X1,X3] :
( ~ c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X1,X1),X2)
| c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,sK66(X2,X3),sK66(X2,X3)),c_Transitive__Closure_Otrancl(X3,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_500])]) ).
fof(f2800,plain,
! [X2,X3,X1] :
( ~ c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X1,X1),X2)
| c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,sK66(X2,X3),sK66(X2,X3)),c_Transitive__Closure_Otrancl(X3,X2)) ),
inference(equality_resolution,[],[f2428]) ).
fof(f2428,plain,
! [X2,X3,X0,X1] :
( X0 != X1
| ~ c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X1,X0),X2)
| c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,sK66(X2,X3),sK66(X2,X3)),c_Transitive__Closure_Otrancl(X3,X2)) ),
inference(cnf_transformation,[],[f1732]) ).
fof(f1732,plain,
! [X0,X1,X2,X3] :
( X0 != X1
| ~ c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X1,X0),X2)
| c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,sK66(X2,X3),sK66(X2,X3)),c_Transitive__Closure_Otrancl(X3,X2)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK66])],[f1426,f1731]) ).
fof(f1731,plain,
! [X2,X3] :
( ? [X4] : c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X4,X4),c_Transitive__Closure_Otrancl(X3,X2))
=> c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,sK66(X2,X3),sK66(X2,X3)),c_Transitive__Closure_Otrancl(X3,X2)) ),
introduced(choice_axiom,[]) ).
fof(f1426,plain,
! [X0,X1,X2,X3] :
( X0 != X1
| ~ c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X1,X0),X2)
| ? [X4] : c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X4,X4),c_Transitive__Closure_Otrancl(X3,X2)) ),
inference(flattening,[],[f1425]) ).
fof(f1425,plain,
! [X0,X1,X2,X3] :
( X0 != X1
| ~ c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X1,X0),X2)
| ? [X4] : c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X4,X4),c_Transitive__Closure_Otrancl(X3,X2)) ),
inference(ennf_transformation,[],[f922]) ).
fof(f922,plain,
! [X0,X1,X2,X3] :
( ! [X4] : ~ c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X4,X4),c_Transitive__Closure_Otrancl(X3,X2))
=> ( c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X1,X0),X2)
=> X0 != X1 ) ),
inference(rectify,[],[f101]) ).
fof(f101,axiom,
! [X12,X13,X3,X4] :
( ! [X2] : ~ c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X2,X2),c_Transitive__Closure_Otrancl(X4,X3))
=> ( c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X13,X12),X3)
=> X12 != X13 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_irrefl__trancl__rD) ).
fof(f9864,plain,
spl104_499,
inference(avatar_split_clause,[],[f2617,f9862]) ).
fof(f9862,plain,
( spl104_499
<=> ! [X2,X3,X4,X0,X6,X5,X1] :
( sP11(X6,X2,X3,X4,X5,X0,X1)
| hAPP(hAPP(X4,X1),X0) = X3
| ~ c_Nitpick_Ofold__graph_H(X6,X5,X4,X3,X2,hAPP(hAPP(X4,X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_499])]) ).
fof(f2617,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( sP11(X6,X2,X3,X4,X5,X0,X1)
| hAPP(hAPP(X4,X1),X0) = X3
| ~ c_Nitpick_Ofold__graph_H(X6,X5,X4,X3,X2,hAPP(hAPP(X4,X1),X0)) ),
inference(cnf_transformation,[],[f1844]) ).
fof(f1844,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ( c_Nitpick_Ofold__graph_H(X6,X5,X4,X3,X2,hAPP(hAPP(X4,X1),X0))
| ( ~ sP11(X6,X2,X3,X4,X5,X0,X1)
& ( hAPP(hAPP(X4,X1),X0) != X3
| c_Orderings_Obot__class_Obot(tc_fun(X6,tc_HOL_Obool)) != X2 ) ) )
& ( sP11(X6,X2,X3,X4,X5,X0,X1)
| ( hAPP(hAPP(X4,X1),X0) = X3
& c_Orderings_Obot__class_Obot(tc_fun(X6,tc_HOL_Obool)) = X2 )
| ~ c_Nitpick_Ofold__graph_H(X6,X5,X4,X3,X2,hAPP(hAPP(X4,X1),X0)) ) ),
inference(flattening,[],[f1843]) ).
fof(f1843,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ( c_Nitpick_Ofold__graph_H(X6,X5,X4,X3,X2,hAPP(hAPP(X4,X1),X0))
| ( ~ sP11(X6,X2,X3,X4,X5,X0,X1)
& ( hAPP(hAPP(X4,X1),X0) != X3
| c_Orderings_Obot__class_Obot(tc_fun(X6,tc_HOL_Obool)) != X2 ) ) )
& ( sP11(X6,X2,X3,X4,X5,X0,X1)
| ( hAPP(hAPP(X4,X1),X0) = X3
& c_Orderings_Obot__class_Obot(tc_fun(X6,tc_HOL_Obool)) = X2 )
| ~ c_Nitpick_Ofold__graph_H(X6,X5,X4,X3,X2,hAPP(hAPP(X4,X1),X0)) ) ),
inference(nnf_transformation,[],[f1546]) ).
fof(f1546,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( c_Nitpick_Ofold__graph_H(X6,X5,X4,X3,X2,hAPP(hAPP(X4,X1),X0))
<=> ( sP11(X6,X2,X3,X4,X5,X0,X1)
| ( hAPP(hAPP(X4,X1),X0) = X3
& c_Orderings_Obot__class_Obot(tc_fun(X6,tc_HOL_Obool)) = X2 ) ) ),
inference(definition_folding,[],[f1012,f1545]) ).
fof(f1012,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( c_Nitpick_Ofold__graph_H(X6,X5,X4,X3,X2,hAPP(hAPP(X4,X1),X0))
<=> ( ? [X7,X8] :
( c_Nitpick_Ofold__graph_H(X6,X5,X4,X3,c_Groups_Ominus__class_Ominus(tc_fun(X6,tc_HOL_Obool),X2,c_Set_Oinsert(X6,X7,c_Orderings_Obot__class_Obot(tc_fun(X6,tc_HOL_Obool)))),X8)
& c_member(X6,X7,X2)
& hAPP(hAPP(X4,X1),X0) = hAPP(hAPP(X4,X7),X8) )
| ( hAPP(hAPP(X4,X1),X0) = X3
& c_Orderings_Obot__class_Obot(tc_fun(X6,tc_HOL_Obool)) = X2 ) ) ),
inference(rectify,[],[f486]) ).
fof(f486,axiom,
! [X86,X35,X34,X87,X88,X15,X4] :
( c_Nitpick_Ofold__graph_H(X4,X15,X88,X87,X34,hAPP(hAPP(X88,X35),X86))
<=> ( ? [X2,X5] :
( c_Nitpick_Ofold__graph_H(X4,X15,X88,X87,c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool),X34,c_Set_Oinsert(X4,X2,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))),X5)
& c_member(X4,X2,X34)
& hAPP(hAPP(X88,X35),X86) = hAPP(hAPP(X88,X2),X5) )
| ( hAPP(hAPP(X88,X35),X86) = X87
& c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)) = X34 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold__graph_H_Oequations_I2_J) ).
fof(f9860,plain,
spl104_498,
inference(avatar_split_clause,[],[f2575,f9858]) ).
fof(f9858,plain,
( spl104_498
<=> ! [X2,X4,X0,X3,X1] :
( c_Set_Oinsert(X4,X3,c_Set_Oinsert(X4,X2,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))) = c_Set_Oinsert(X4,X1,c_Set_Oinsert(X4,X0,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))
| ~ sP10(X2,X1,X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_498])]) ).
fof(f2575,plain,
! [X2,X3,X0,X1,X4] :
( c_Set_Oinsert(X4,X3,c_Set_Oinsert(X4,X2,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))) = c_Set_Oinsert(X4,X1,c_Set_Oinsert(X4,X0,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))
| ~ sP10(X2,X1,X3,X0) ),
inference(cnf_transformation,[],[f1817]) ).
fof(f1817,plain,
! [X0,X1,X2,X3,X4] :
( ( c_Set_Oinsert(X4,X3,c_Set_Oinsert(X4,X2,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))) = c_Set_Oinsert(X4,X1,c_Set_Oinsert(X4,X0,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))
| ~ sP10(X2,X1,X3,X0) )
& ( sP10(X2,X1,X3,X0)
| c_Set_Oinsert(X4,X3,c_Set_Oinsert(X4,X2,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))) != c_Set_Oinsert(X4,X1,c_Set_Oinsert(X4,X0,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))) ) ),
inference(nnf_transformation,[],[f1544]) ).
fof(f1544,plain,
! [X0,X1,X2,X3,X4] :
( c_Set_Oinsert(X4,X3,c_Set_Oinsert(X4,X2,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))) = c_Set_Oinsert(X4,X1,c_Set_Oinsert(X4,X0,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))
<=> sP10(X2,X1,X3,X0) ),
inference(definition_folding,[],[f989,f1543]) ).
fof(f1543,plain,
! [X2,X1,X3,X0] :
( sP10(X2,X1,X3,X0)
<=> ( ( X1 = X2
& X0 = X3 )
| ( X0 = X2
& X1 = X3 ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP10])]) ).
fof(f989,plain,
! [X0,X1,X2,X3,X4] :
( c_Set_Oinsert(X4,X3,c_Set_Oinsert(X4,X2,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))) = c_Set_Oinsert(X4,X1,c_Set_Oinsert(X4,X0,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))
<=> ( ( X1 = X2
& X0 = X3 )
| ( X0 = X2
& X1 = X3 ) ) ),
inference(rectify,[],[f429]) ).
fof(f429,axiom,
! [X69,X7,X8,X9,X4] :
( c_Set_Oinsert(X4,X9,c_Set_Oinsert(X4,X8,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))) = c_Set_Oinsert(X4,X7,c_Set_Oinsert(X4,X69,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))
<=> ( ( X7 = X8
& X9 = X69 )
| ( X8 = X69
& X7 = X9 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_doubleton__eq__iff) ).
fof(f9856,plain,
spl104_497,
inference(avatar_split_clause,[],[f2574,f9854]) ).
fof(f9854,plain,
( spl104_497
<=> ! [X4,X0,X3,X2,X1] :
( sP10(X2,X1,X3,X0)
| c_Set_Oinsert(X4,X3,c_Set_Oinsert(X4,X2,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))) != c_Set_Oinsert(X4,X1,c_Set_Oinsert(X4,X0,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_497])]) ).
fof(f2574,plain,
! [X2,X3,X0,X1,X4] :
( sP10(X2,X1,X3,X0)
| c_Set_Oinsert(X4,X3,c_Set_Oinsert(X4,X2,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))) != c_Set_Oinsert(X4,X1,c_Set_Oinsert(X4,X0,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))) ),
inference(cnf_transformation,[],[f1817]) ).
fof(f9852,plain,
spl104_496,
inference(avatar_split_clause,[],[f2458,f9850]) ).
fof(f9850,plain,
( spl104_496
<=> ! [X0,X3,X2,X1] :
( sP6(X0,X1,X2,X3)
| ~ c_member(X2,X3,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool),c_Groups_Ominus__class_Ominus(tc_fun(X2,tc_HOL_Obool),X1,c_Set_Oinsert(X2,X3,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_496])]) ).
fof(f2458,plain,
! [X2,X3,X0,X1] :
( sP6(X0,X1,X2,X3)
| ~ c_member(X2,X3,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool),c_Groups_Ominus__class_Ominus(tc_fun(X2,tc_HOL_Obool),X1,c_Set_Oinsert(X2,X3,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)))),X0) ),
inference(cnf_transformation,[],[f1756]) ).
fof(f1756,plain,
! [X0,X1,X2,X3] :
( ( sP6(X0,X1,X2,X3)
| ( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool),X1,X0)
& ~ c_member(X2,X3,X1) )
| ( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool),c_Groups_Ominus__class_Ominus(tc_fun(X2,tc_HOL_Obool),X1,c_Set_Oinsert(X2,X3,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)))),X0)
& c_member(X2,X3,X1) ) )
& ( ( ( c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool),X1,X0)
| c_member(X2,X3,X1) )
& ( c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool),c_Groups_Ominus__class_Ominus(tc_fun(X2,tc_HOL_Obool),X1,c_Set_Oinsert(X2,X3,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)))),X0)
| ~ c_member(X2,X3,X1) ) )
| ~ sP6(X0,X1,X2,X3) ) ),
inference(rectify,[],[f1755]) ).
fof(f1755,plain,
! [X0,X2,X3,X1] :
( ( sP6(X0,X2,X3,X1)
| ( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X2,X0)
& ~ c_member(X3,X1,X2) )
| ( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),c_Groups_Ominus__class_Ominus(tc_fun(X3,tc_HOL_Obool),X2,c_Set_Oinsert(X3,X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)))),X0)
& c_member(X3,X1,X2) ) )
& ( ( ( c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X2,X0)
| c_member(X3,X1,X2) )
& ( c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),c_Groups_Ominus__class_Ominus(tc_fun(X3,tc_HOL_Obool),X2,c_Set_Oinsert(X3,X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)))),X0)
| ~ c_member(X3,X1,X2) ) )
| ~ sP6(X0,X2,X3,X1) ) ),
inference(flattening,[],[f1754]) ).
fof(f1754,plain,
! [X0,X2,X3,X1] :
( ( sP6(X0,X2,X3,X1)
| ( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X2,X0)
& ~ c_member(X3,X1,X2) )
| ( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),c_Groups_Ominus__class_Ominus(tc_fun(X3,tc_HOL_Obool),X2,c_Set_Oinsert(X3,X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)))),X0)
& c_member(X3,X1,X2) ) )
& ( ( ( c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X2,X0)
| c_member(X3,X1,X2) )
& ( c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),c_Groups_Ominus__class_Ominus(tc_fun(X3,tc_HOL_Obool),X2,c_Set_Oinsert(X3,X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)))),X0)
| ~ c_member(X3,X1,X2) ) )
| ~ sP6(X0,X2,X3,X1) ) ),
inference(nnf_transformation,[],[f1536]) ).
fof(f1536,plain,
! [X0,X2,X3,X1] :
( sP6(X0,X2,X3,X1)
<=> ( ( c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X2,X0)
| c_member(X3,X1,X2) )
& ( c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),c_Groups_Ominus__class_Ominus(tc_fun(X3,tc_HOL_Obool),X2,c_Set_Oinsert(X3,X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)))),X0)
| ~ c_member(X3,X1,X2) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP6])]) ).
fof(f9848,plain,
spl104_495,
inference(avatar_split_clause,[],[f2455,f9846]) ).
fof(f9846,plain,
( spl104_495
<=> ! [X0,X3,X2,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool),c_Groups_Ominus__class_Ominus(tc_fun(X2,tc_HOL_Obool),X1,c_Set_Oinsert(X2,X3,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)))),X0)
| ~ c_member(X2,X3,X1)
| ~ sP6(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_495])]) ).
fof(f2455,plain,
! [X2,X3,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool),c_Groups_Ominus__class_Ominus(tc_fun(X2,tc_HOL_Obool),X1,c_Set_Oinsert(X2,X3,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)))),X0)
| ~ c_member(X2,X3,X1)
| ~ sP6(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f1756]) ).
fof(f9844,plain,
( spl104_494
| ~ spl104_145
| ~ spl104_355 ),
inference(avatar_split_clause,[],[f6386,f5977,f3586,f9842]) ).
fof(f6386,plain,
( ! [X0,X1] : c_member(X0,X1,c_Relation_ODomain(X0,X0,c_Relation_OId(X0)))
| ~ spl104_145
| ~ spl104_355 ),
inference(resolution,[],[f5978,f3587]) ).
fof(f9840,plain,
spl104_493,
inference(avatar_split_clause,[],[f2450,f9838]) ).
fof(f9838,plain,
( spl104_493
<=> ! [X0,X3,X2,X1] :
( sP4(X0,X1,X2,X3)
| ~ c_member(X2,X3,X1)
| ~ c_Orderings_Oord__class_Oless(tc_fun(X2,tc_HOL_Obool),c_Groups_Ominus__class_Ominus(tc_fun(X2,tc_HOL_Obool),X1,c_Set_Oinsert(X2,X3,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_493])]) ).
fof(f2450,plain,
! [X2,X3,X0,X1] :
( sP4(X0,X1,X2,X3)
| ~ c_member(X2,X3,X1)
| ~ c_Orderings_Oord__class_Oless(tc_fun(X2,tc_HOL_Obool),c_Groups_Ominus__class_Ominus(tc_fun(X2,tc_HOL_Obool),X1,c_Set_Oinsert(X2,X3,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)))),X0) ),
inference(cnf_transformation,[],[f1752]) ).
fof(f9836,plain,
spl104_492,
inference(avatar_split_clause,[],[f2447,f9834]) ).
fof(f2447,plain,
! [X2,X3,X0,X1] :
( c_Orderings_Oord__class_Oless(tc_fun(X2,tc_HOL_Obool),c_Groups_Ominus__class_Ominus(tc_fun(X2,tc_HOL_Obool),X1,c_Set_Oinsert(X2,X3,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)))),X0)
| ~ c_member(X2,X3,X1)
| ~ sP4(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f1752]) ).
fof(f9832,plain,
spl104_491,
inference(avatar_split_clause,[],[f2410,f9830]) ).
fof(f9830,plain,
( spl104_491
<=> ! [X0,X3,X2,X1] :
( c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,sK63(X0,X1,X2,X3),X1),X0)
| ~ c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X2,X1),c_Transitive__Closure_Otrancl(X3,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_491])]) ).
fof(f2410,plain,
! [X2,X3,X0,X1] :
( c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,sK63(X0,X1,X2,X3),X1),X0)
| ~ c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X2,X1),c_Transitive__Closure_Otrancl(X3,X0)) ),
inference(cnf_transformation,[],[f1726]) ).
fof(f9828,plain,
spl104_490,
inference(avatar_split_clause,[],[f2407,f9826]) ).
fof(f9826,plain,
( spl104_490
<=> ! [X0,X3,X2,X1] :
( c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X2,sK62(X0,X1,X2,X3)),X0)
| ~ c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X2,X1),c_Transitive__Closure_Otrancl(X3,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_490])]) ).
fof(f2407,plain,
! [X2,X3,X0,X1] :
( c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X2,sK62(X0,X1,X2,X3)),X0)
| ~ c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X2,X1),c_Transitive__Closure_Otrancl(X3,X0)) ),
inference(cnf_transformation,[],[f1724]) ).
fof(f9824,plain,
spl104_489,
inference(avatar_split_clause,[],[f2011,f9822]) ).
fof(f9822,plain,
( spl104_489
<=> ! [X4,X0,X5,X1] :
( X4 = X5
| ~ c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,X5,X4),X0)
| ~ c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,X4,X5),X0)
| ~ c_Relation_Oantisym(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_489])]) ).
fof(f2011,plain,
! [X0,X1,X4,X5] :
( X4 = X5
| ~ c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,X5,X4),X0)
| ~ c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,X4,X5),X0)
| ~ c_Relation_Oantisym(X1,X0) ),
inference(cnf_transformation,[],[f1582]) ).
fof(f1582,plain,
! [X0,X1] :
( ( c_Relation_Oantisym(X1,X0)
| ( sK28(X0,X1) != sK29(X0,X1)
& c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,sK29(X0,X1),sK28(X0,X1)),X0)
& c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,sK28(X0,X1),sK29(X0,X1)),X0) ) )
& ( ! [X4,X5] :
( X4 = X5
| ~ c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,X5,X4),X0)
| ~ c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,X4,X5),X0) )
| ~ c_Relation_Oantisym(X1,X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK28,sK29])],[f1580,f1581]) ).
fof(f1581,plain,
! [X0,X1] :
( ? [X2,X3] :
( X2 != X3
& c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,X3,X2),X0)
& c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,X2,X3),X0) )
=> ( sK28(X0,X1) != sK29(X0,X1)
& c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,sK29(X0,X1),sK28(X0,X1)),X0)
& c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,sK28(X0,X1),sK29(X0,X1)),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f1580,plain,
! [X0,X1] :
( ( c_Relation_Oantisym(X1,X0)
| ? [X2,X3] :
( X2 != X3
& c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,X3,X2),X0)
& c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,X2,X3),X0) ) )
& ( ! [X4,X5] :
( X4 = X5
| ~ c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,X5,X4),X0)
| ~ c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,X4,X5),X0) )
| ~ c_Relation_Oantisym(X1,X0) ) ),
inference(rectify,[],[f1579]) ).
fof(f1579,plain,
! [X0,X1] :
( ( c_Relation_Oantisym(X1,X0)
| ? [X2,X3] :
( X2 != X3
& c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,X3,X2),X0)
& c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,X2,X3),X0) ) )
& ( ! [X2,X3] :
( X2 = X3
| ~ c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,X3,X2),X0)
| ~ c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,X2,X3),X0) )
| ~ c_Relation_Oantisym(X1,X0) ) ),
inference(nnf_transformation,[],[f1076]) ).
fof(f1076,plain,
! [X0,X1] :
( c_Relation_Oantisym(X1,X0)
<=> ! [X2,X3] :
( X2 = X3
| ~ c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,X3,X2),X0)
| ~ c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,X2,X3),X0) ) ),
inference(flattening,[],[f1075]) ).
fof(f1075,plain,
! [X0,X1] :
( c_Relation_Oantisym(X1,X0)
<=> ! [X2,X3] :
( X2 = X3
| ~ c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,X3,X2),X0)
| ~ c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,X2,X3),X0) ) ),
inference(ennf_transformation,[],[f633]) ).
fof(f633,plain,
! [X0,X1] :
( c_Relation_Oantisym(X1,X0)
<=> ! [X2,X3] :
( c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,X2,X3),X0)
=> ( c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,X3,X2),X0)
=> X2 = X3 ) ) ),
inference(rectify,[],[f153]) ).
fof(f153,axiom,
! [X3,X4] :
( c_Relation_Oantisym(X4,X3)
<=> ! [X2,X5] :
( c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X2,X5),X3)
=> ( c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X5,X2),X3)
=> X2 = X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_antisym__def) ).
fof(f9722,plain,
spl104_488,
inference(avatar_split_clause,[],[f2638,f9720]) ).
fof(f9720,plain,
( spl104_488
<=> ! [X0,X1] : c_Transitive__Closure_Otrancl(X1,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),X0,c_Relation_OId(X1))) = c_Transitive__Closure_Otrancl(X1,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),c_Transitive__Closure_Otrancl(X1,X0),c_Relation_OId(X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_488])]) ).
fof(f2638,plain,
! [X0,X1] : c_Transitive__Closure_Otrancl(X1,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),X0,c_Relation_OId(X1))) = c_Transitive__Closure_Otrancl(X1,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),c_Transitive__Closure_Otrancl(X1,X0),c_Relation_OId(X1))),
inference(definition_unfolding,[],[f1934,f1949,f1949]) ).
fof(f1934,plain,
! [X0,X1] : c_Transitive__Closure_Ortrancl(X1,X0) = c_Transitive__Closure_Ortrancl(X1,c_Transitive__Closure_Otrancl(X1,X0)),
inference(cnf_transformation,[],[f564]) ).
fof(f564,plain,
! [X0,X1] : c_Transitive__Closure_Ortrancl(X1,X0) = c_Transitive__Closure_Ortrancl(X1,c_Transitive__Closure_Otrancl(X1,X0)),
inference(rectify,[],[f80]) ).
fof(f80,axiom,
! [X14,X4] : c_Transitive__Closure_Ortrancl(X4,X14) = c_Transitive__Closure_Ortrancl(X4,c_Transitive__Closure_Otrancl(X4,X14)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trancl__rtrancl__absorb) ).
fof(f9717,plain,
spl104_487,
inference(avatar_split_clause,[],[f2616,f9715]) ).
fof(f9715,plain,
( spl104_487
<=> ! [X2,X3,X4,X0,X6,X5,X1] :
( sP11(X6,X2,X3,X4,X5,X0,X1)
| c_Orderings_Obot__class_Obot(tc_fun(X6,tc_HOL_Obool)) = X2
| ~ c_Nitpick_Ofold__graph_H(X6,X5,X4,X3,X2,hAPP(hAPP(X4,X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_487])]) ).
fof(f2616,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( sP11(X6,X2,X3,X4,X5,X0,X1)
| c_Orderings_Obot__class_Obot(tc_fun(X6,tc_HOL_Obool)) = X2
| ~ c_Nitpick_Ofold__graph_H(X6,X5,X4,X3,X2,hAPP(hAPP(X4,X1),X0)) ),
inference(cnf_transformation,[],[f1844]) ).
fof(f9713,plain,
spl104_486,
inference(avatar_split_clause,[],[f2512,f9711]) ).
fof(f9711,plain,
( spl104_486
<=> ! [X4,X0,X3,X2,X1] : c_Relation_OImage(X4,X3,X2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool),X1,X0)) = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),c_Relation_OImage(X4,X3,X2,X1),c_Relation_OImage(X4,X3,X2,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_486])]) ).
fof(f2512,plain,
! [X2,X3,X0,X1,X4] : c_Relation_OImage(X4,X3,X2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool),X1,X0)) = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),c_Relation_OImage(X4,X3,X2,X1),c_Relation_OImage(X4,X3,X2,X0)),
inference(cnf_transformation,[],[f944]) ).
fof(f944,plain,
! [X0,X1,X2,X3,X4] : c_Relation_OImage(X4,X3,X2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool),X1,X0)) = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),c_Relation_OImage(X4,X3,X2,X1),c_Relation_OImage(X4,X3,X2,X0)),
inference(rectify,[],[f479]) ).
fof(f479,axiom,
! [X10,X11,X14,X4,X15] : c_Relation_OImage(X15,X4,X14,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X15,tc_HOL_Obool),X11,X10)) = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool),c_Relation_OImage(X15,X4,X14,X11),c_Relation_OImage(X15,X4,X14,X10)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Image__Un) ).
fof(f9709,plain,
spl104_485,
inference(avatar_split_clause,[],[f2374,f9707]) ).
fof(f9707,plain,
( spl104_485
<=> ! [X0,X3,X2,X1] :
( c_Groups_Ominus__class_Ominus(tc_fun(X3,tc_HOL_Obool),X1,c_Groups_Ominus__class_Ominus(tc_fun(X3,tc_HOL_Obool),X0,X2)) = X2
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_485])]) ).
fof(f2374,plain,
! [X2,X3,X0,X1] :
( c_Groups_Ominus__class_Ominus(tc_fun(X3,tc_HOL_Obool),X1,c_Groups_Ominus__class_Ominus(tc_fun(X3,tc_HOL_Obool),X0,X2)) = X2
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X2,X1) ),
inference(cnf_transformation,[],[f1371]) ).
fof(f1371,plain,
! [X0,X1,X2,X3] :
( c_Groups_Ominus__class_Ominus(tc_fun(X3,tc_HOL_Obool),X1,c_Groups_Ominus__class_Ominus(tc_fun(X3,tc_HOL_Obool),X0,X2)) = X2
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X2,X1) ),
inference(flattening,[],[f1370]) ).
fof(f1370,plain,
! [X0,X1,X2,X3] :
( c_Groups_Ominus__class_Ominus(tc_fun(X3,tc_HOL_Obool),X1,c_Groups_Ominus__class_Ominus(tc_fun(X3,tc_HOL_Obool),X0,X2)) = X2
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X2,X1) ),
inference(ennf_transformation,[],[f887]) ).
fof(f887,plain,
! [X0,X1,X2,X3] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X2,X1)
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X1,X0)
=> c_Groups_Ominus__class_Ominus(tc_fun(X3,tc_HOL_Obool),X1,c_Groups_Ominus__class_Ominus(tc_fun(X3,tc_HOL_Obool),X0,X2)) = X2 ) ),
inference(rectify,[],[f267]) ).
fof(f267,axiom,
! [X53,X10,X11,X4] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool),X11,X10)
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool),X10,X53)
=> c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool),X10,c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool),X53,X11)) = X11 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_double__diff) ).
fof(f9705,plain,
spl104_484,
inference(avatar_split_clause,[],[f2339,f9703]) ).
fof(f9703,plain,
( spl104_484
<=> ! [X4,X0,X3,X2,X1] :
( hAPP(c_Recdef_Owfrec(X1,X0,X3,X2),X4) = hAPP(hAPP(X2,c_Recdef_Ocut(X1,X0,c_Recdef_Owfrec(X1,X0,X3,X2),X3,X4)),X4)
| ~ c_Wellfounded_Owf(X1,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_484])]) ).
fof(f2339,plain,
! [X2,X3,X0,X1,X4] :
( hAPP(c_Recdef_Owfrec(X1,X0,X3,X2),X4) = hAPP(hAPP(X2,c_Recdef_Ocut(X1,X0,c_Recdef_Owfrec(X1,X0,X3,X2),X3,X4)),X4)
| ~ c_Wellfounded_Owf(X1,X3) ),
inference(cnf_transformation,[],[f1316]) ).
fof(f1316,plain,
! [X0,X1,X2,X3] :
( ! [X4] : hAPP(c_Recdef_Owfrec(X1,X0,X3,X2),X4) = hAPP(hAPP(X2,c_Recdef_Ocut(X1,X0,c_Recdef_Owfrec(X1,X0,X3,X2),X3,X4)),X4)
| ~ c_Wellfounded_Owf(X1,X3) ),
inference(ennf_transformation,[],[f853]) ).
fof(f853,plain,
! [X0,X1,X2,X3] :
( c_Wellfounded_Owf(X1,X3)
=> ! [X4] : hAPP(c_Recdef_Owfrec(X1,X0,X3,X2),X4) = hAPP(hAPP(X2,c_Recdef_Ocut(X1,X0,c_Recdef_Owfrec(X1,X0,X3,X2),X3,X4)),X4) ),
inference(rectify,[],[f192]) ).
fof(f192,axiom,
! [X15,X4,X63,X51] :
( c_Wellfounded_Owf(X4,X51)
=> ! [X2] : hAPP(c_Recdef_Owfrec(X4,X15,X51,X63),X2) = hAPP(hAPP(X63,c_Recdef_Ocut(X4,X15,c_Recdef_Owfrec(X4,X15,X51,X63),X51,X2)),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_tfl__wfrec) ).
fof(f9447,plain,
( spl104_483
| ~ spl104_33
| ~ spl104_468 ),
inference(avatar_split_clause,[],[f9327,f9240,f3030,f9444]) ).
fof(f9444,plain,
( spl104_483
<=> c_Relation_Otrans(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__leq) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_483])]) ).
fof(f9240,plain,
( spl104_468
<=> c_FunDef_Opair__leq = c_Transitive__Closure_Otrancl(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__leq) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_468])]) ).
fof(f9327,plain,
( c_Relation_Otrans(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__leq)
| ~ spl104_33
| ~ spl104_468 ),
inference(superposition,[],[f3031,f9242]) ).
fof(f9242,plain,
( c_FunDef_Opair__leq = c_Transitive__Closure_Otrancl(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__leq)
| ~ spl104_468 ),
inference(avatar_component_clause,[],[f9240]) ).
fof(f9387,plain,
( spl104_482
| ~ spl104_28
| ~ spl104_464
| ~ spl104_481 ),
inference(avatar_split_clause,[],[f9383,f9380,f8651,f3008,f9385]) ).
fof(f9385,plain,
( spl104_482
<=> ! [X0,X1] :
( ~ c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat,X1,X0),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),c_Wellfounded_Oless__than,c_Relation_OId(tc_Nat_Onat)))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_482])]) ).
fof(f9380,plain,
( spl104_481
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| ~ c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat,X1,X0),c_Transitive__Closure_Otrancl(tc_Nat_Onat,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),c_Wellfounded_Opred__nat,c_Relation_OId(tc_Nat_Onat)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_481])]) ).
fof(f9383,plain,
( ! [X0,X1] :
( ~ c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat,X1,X0),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),c_Wellfounded_Oless__than,c_Relation_OId(tc_Nat_Onat)))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) )
| ~ spl104_28
| ~ spl104_464
| ~ spl104_481 ),
inference(forward_demodulation,[],[f9381,f9147]) ).
fof(f9147,plain,
( c_Transitive__Closure_Otrancl(tc_Nat_Onat,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),c_Wellfounded_Opred__nat,c_Relation_OId(tc_Nat_Onat))) = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),c_Wellfounded_Oless__than,c_Relation_OId(tc_Nat_Onat))
| ~ spl104_28
| ~ spl104_464 ),
inference(superposition,[],[f8652,f3010]) ).
fof(f9381,plain,
( ! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| ~ c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat,X1,X0),c_Transitive__Closure_Otrancl(tc_Nat_Onat,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),c_Wellfounded_Opred__nat,c_Relation_OId(tc_Nat_Onat)))) )
| ~ spl104_481 ),
inference(avatar_component_clause,[],[f9380]) ).
fof(f9382,plain,
spl104_481,
inference(avatar_split_clause,[],[f2647,f9380]) ).
fof(f2647,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| ~ c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat,X1,X0),c_Transitive__Closure_Otrancl(tc_Nat_Onat,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),c_Wellfounded_Opred__nat,c_Relation_OId(tc_Nat_Onat)))) ),
inference(definition_unfolding,[],[f2042,f1949]) ).
fof(f2042,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| ~ c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat,X1,X0),c_Transitive__Closure_Ortrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat)) ),
inference(cnf_transformation,[],[f1608]) ).
fof(f1608,plain,
! [X0,X1] :
( ( c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat,X1,X0),c_Transitive__Closure_Ortrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| ~ c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat,X1,X0),c_Transitive__Closure_Ortrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat)) ) ),
inference(nnf_transformation,[],[f643]) ).
fof(f643,plain,
! [X0,X1] :
( c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat,X1,X0),c_Transitive__Closure_Ortrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ),
inference(rectify,[],[f355]) ).
fof(f355,axiom,
! [X67,X68] :
( c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat,X68,X67),c_Transitive__Closure_Ortrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X68,X67) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pred__nat__trancl__eq__le) ).
fof(f9356,plain,
( spl104_480
| ~ spl104_28
| ~ spl104_464
| ~ spl104_479 ),
inference(avatar_split_clause,[],[f9352,f9349,f8651,f3008,f9354]) ).
fof(f9354,plain,
( spl104_480
<=> ! [X0,X1] :
( c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat,X1,X0),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),c_Wellfounded_Oless__than,c_Relation_OId(tc_Nat_Onat)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_480])]) ).
fof(f9349,plain,
( spl104_479
<=> ! [X0,X1] :
( c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat,X1,X0),c_Transitive__Closure_Otrancl(tc_Nat_Onat,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),c_Wellfounded_Opred__nat,c_Relation_OId(tc_Nat_Onat))))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_479])]) ).
fof(f9352,plain,
( ! [X0,X1] :
( c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat,X1,X0),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),c_Wellfounded_Oless__than,c_Relation_OId(tc_Nat_Onat)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) )
| ~ spl104_28
| ~ spl104_464
| ~ spl104_479 ),
inference(forward_demodulation,[],[f9350,f9147]) ).
fof(f9350,plain,
( ! [X0,X1] :
( c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat,X1,X0),c_Transitive__Closure_Otrancl(tc_Nat_Onat,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),c_Wellfounded_Opred__nat,c_Relation_OId(tc_Nat_Onat))))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) )
| ~ spl104_479 ),
inference(avatar_component_clause,[],[f9349]) ).
fof(f9351,plain,
spl104_479,
inference(avatar_split_clause,[],[f2646,f9349]) ).
fof(f2646,plain,
! [X0,X1] :
( c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat,X1,X0),c_Transitive__Closure_Otrancl(tc_Nat_Onat,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),c_Wellfounded_Opred__nat,c_Relation_OId(tc_Nat_Onat))))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ),
inference(definition_unfolding,[],[f2043,f1949]) ).
fof(f2043,plain,
! [X0,X1] :
( c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat,X1,X0),c_Transitive__Closure_Ortrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ),
inference(cnf_transformation,[],[f1608]) ).
fof(f9347,plain,
spl104_478,
inference(avatar_split_clause,[],[f2567,f9345]) ).
fof(f9345,plain,
( spl104_478
<=> ! [X4,X0,X3,X2,X1] :
( c_member(X4,X3,c_Relation_OImage(X2,X4,X1,c_Set_Oinsert(X2,X0,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)))))
| ~ c_member(tc_prod(X2,X4),c_Product__Type_OPair(X2,X4,X0,X3),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_478])]) ).
fof(f2567,plain,
! [X2,X3,X0,X1,X4] :
( c_member(X4,X3,c_Relation_OImage(X2,X4,X1,c_Set_Oinsert(X2,X0,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)))))
| ~ c_member(tc_prod(X2,X4),c_Product__Type_OPair(X2,X4,X0,X3),X1) ),
inference(cnf_transformation,[],[f1813]) ).
fof(f1813,plain,
! [X0,X1,X2,X3,X4] :
( ( c_member(X4,X3,c_Relation_OImage(X2,X4,X1,c_Set_Oinsert(X2,X0,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)))))
| ~ c_member(tc_prod(X2,X4),c_Product__Type_OPair(X2,X4,X0,X3),X1) )
& ( c_member(tc_prod(X2,X4),c_Product__Type_OPair(X2,X4,X0,X3),X1)
| ~ c_member(X4,X3,c_Relation_OImage(X2,X4,X1,c_Set_Oinsert(X2,X0,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))))) ) ),
inference(nnf_transformation,[],[f988]) ).
fof(f988,plain,
! [X0,X1,X2,X3,X4] :
( c_member(X4,X3,c_Relation_OImage(X2,X4,X1,c_Set_Oinsert(X2,X0,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)))))
<=> c_member(tc_prod(X2,X4),c_Product__Type_OPair(X2,X4,X0,X3),X1) ),
inference(rectify,[],[f481]) ).
fof(f481,axiom,
! [X9,X3,X15,X8,X4] :
( c_member(X4,X8,c_Relation_OImage(X15,X4,X3,c_Set_Oinsert(X15,X9,c_Orderings_Obot__class_Obot(tc_fun(X15,tc_HOL_Obool)))))
<=> c_member(tc_prod(X15,X4),c_Product__Type_OPair(X15,X4,X9,X8),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Image__singleton__iff) ).
fof(f9343,plain,
spl104_477,
inference(avatar_split_clause,[],[f2566,f9341]) ).
fof(f9341,plain,
( spl104_477
<=> ! [X2,X4,X0,X3,X1] :
( c_member(tc_prod(X2,X4),c_Product__Type_OPair(X2,X4,X0,X3),X1)
| ~ c_member(X4,X3,c_Relation_OImage(X2,X4,X1,c_Set_Oinsert(X2,X0,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_477])]) ).
fof(f2566,plain,
! [X2,X3,X0,X1,X4] :
( c_member(tc_prod(X2,X4),c_Product__Type_OPair(X2,X4,X0,X3),X1)
| ~ c_member(X4,X3,c_Relation_OImage(X2,X4,X1,c_Set_Oinsert(X2,X0,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))))) ),
inference(cnf_transformation,[],[f1813]) ).
fof(f9339,plain,
spl104_476,
inference(avatar_split_clause,[],[f2521,f9337]) ).
fof(f9337,plain,
( spl104_476
<=> ! [X4,X0,X3,X2,X1] :
( c_Relation_Orefl__on(X4,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool),X3,X1),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),X2,X0))
| ~ c_Relation_Orefl__on(X4,X1,X0)
| ~ c_Relation_Orefl__on(X4,X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_476])]) ).
fof(f2521,plain,
! [X2,X3,X0,X1,X4] :
( c_Relation_Orefl__on(X4,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool),X3,X1),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),X2,X0))
| ~ c_Relation_Orefl__on(X4,X1,X0)
| ~ c_Relation_Orefl__on(X4,X3,X2) ),
inference(cnf_transformation,[],[f1443]) ).
fof(f1443,plain,
! [X0,X1,X2,X3,X4] :
( c_Relation_Orefl__on(X4,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool),X3,X1),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),X2,X0))
| ~ c_Relation_Orefl__on(X4,X1,X0)
| ~ c_Relation_Orefl__on(X4,X3,X2) ),
inference(flattening,[],[f1442]) ).
fof(f1442,plain,
! [X0,X1,X2,X3,X4] :
( c_Relation_Orefl__on(X4,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool),X3,X1),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),X2,X0))
| ~ c_Relation_Orefl__on(X4,X1,X0)
| ~ c_Relation_Orefl__on(X4,X3,X2) ),
inference(ennf_transformation,[],[f957]) ).
fof(f957,plain,
! [X0,X1,X2,X3,X4] :
( c_Relation_Orefl__on(X4,X3,X2)
=> ( c_Relation_Orefl__on(X4,X1,X0)
=> c_Relation_Orefl__on(X4,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool),X3,X1),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),X2,X0)) ) ),
inference(rectify,[],[f133]) ).
fof(f133,axiom,
! [X30,X10,X3,X11,X4] :
( c_Relation_Orefl__on(X4,X11,X3)
=> ( c_Relation_Orefl__on(X4,X10,X30)
=> c_Relation_Orefl__on(X4,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool),X11,X10),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),X3,X30)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_refl__on__Un) ).
fof(f9326,plain,
spl104_475,
inference(avatar_split_clause,[],[f2394,f9324]) ).
fof(f9324,plain,
( spl104_475
<=> ! [X0,X3,X2,X1] :
( c_member(tc_prod(X3,X3),X2,c_Transitive__Closure_Otrancl(X3,X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X3,X3),tc_HOL_Obool),X1,X0)
| ~ c_member(tc_prod(X3,X3),X2,c_Transitive__Closure_Otrancl(X3,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_475])]) ).
fof(f2394,plain,
! [X2,X3,X0,X1] :
( c_member(tc_prod(X3,X3),X2,c_Transitive__Closure_Otrancl(X3,X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X3,X3),tc_HOL_Obool),X1,X0)
| ~ c_member(tc_prod(X3,X3),X2,c_Transitive__Closure_Otrancl(X3,X1)) ),
inference(cnf_transformation,[],[f1393]) ).
fof(f1393,plain,
! [X0,X1,X2,X3] :
( c_member(tc_prod(X3,X3),X2,c_Transitive__Closure_Otrancl(X3,X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X3,X3),tc_HOL_Obool),X1,X0)
| ~ c_member(tc_prod(X3,X3),X2,c_Transitive__Closure_Otrancl(X3,X1)) ),
inference(flattening,[],[f1392]) ).
fof(f1392,plain,
! [X0,X1,X2,X3] :
( c_member(tc_prod(X3,X3),X2,c_Transitive__Closure_Otrancl(X3,X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X3,X3),tc_HOL_Obool),X1,X0)
| ~ c_member(tc_prod(X3,X3),X2,c_Transitive__Closure_Otrancl(X3,X1)) ),
inference(ennf_transformation,[],[f900]) ).
fof(f900,plain,
! [X0,X1,X2,X3] :
( c_member(tc_prod(X3,X3),X2,c_Transitive__Closure_Otrancl(X3,X1))
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X3,X3),tc_HOL_Obool),X1,X0)
=> c_member(tc_prod(X3,X3),X2,c_Transitive__Closure_Otrancl(X3,X0)) ) ),
inference(rectify,[],[f279]) ).
fof(f279,axiom,
! [X30,X3,X39,X4] :
( c_member(tc_prod(X4,X4),X39,c_Transitive__Closure_Otrancl(X4,X3))
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),X3,X30)
=> c_member(tc_prod(X4,X4),X39,c_Transitive__Closure_Otrancl(X4,X30)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trancl__mono) ).
fof(f9322,plain,
spl104_474,
inference(avatar_split_clause,[],[f2274,f9320]) ).
fof(f9320,plain,
( spl104_474
<=> ! [X0,X3,X2,X1] : c_Relation_ODomain(X3,X2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X3,X2),tc_HOL_Obool),X1,X0)) = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),c_Relation_ODomain(X3,X2,X1),c_Relation_ODomain(X3,X2,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_474])]) ).
fof(f2274,plain,
! [X2,X3,X0,X1] : c_Relation_ODomain(X3,X2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X3,X2),tc_HOL_Obool),X1,X0)) = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),c_Relation_ODomain(X3,X2,X1),c_Relation_ODomain(X3,X2,X0)),
inference(cnf_transformation,[],[f800]) ).
fof(f800,plain,
! [X0,X1,X2,X3] : c_Relation_ODomain(X3,X2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X3,X2),tc_HOL_Obool),X1,X0)) = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),c_Relation_ODomain(X3,X2,X1),c_Relation_ODomain(X3,X2,X0)),
inference(rectify,[],[f135]) ).
fof(f135,axiom,
! [X10,X11,X15,X4] : c_Relation_ODomain(X4,X15,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X4,X15),tc_HOL_Obool),X11,X10)) = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool),c_Relation_ODomain(X4,X15,X11),c_Relation_ODomain(X4,X15,X10)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Domain__Un__eq) ).
fof(f9318,plain,
spl104_473,
inference(avatar_split_clause,[],[f2273,f9316]) ).
fof(f9316,plain,
( spl104_473
<=> ! [X0,X3,X2,X1] : c_Relation_ORange(X3,X2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X3,X2),tc_HOL_Obool),X1,X0)) = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool),c_Relation_ORange(X3,X2,X1),c_Relation_ORange(X3,X2,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_473])]) ).
fof(f2273,plain,
! [X2,X3,X0,X1] : c_Relation_ORange(X3,X2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X3,X2),tc_HOL_Obool),X1,X0)) = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool),c_Relation_ORange(X3,X2,X1),c_Relation_ORange(X3,X2,X0)),
inference(cnf_transformation,[],[f799]) ).
fof(f799,plain,
! [X0,X1,X2,X3] : c_Relation_ORange(X3,X2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X3,X2),tc_HOL_Obool),X1,X0)) = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool),c_Relation_ORange(X3,X2,X1),c_Relation_ORange(X3,X2,X0)),
inference(rectify,[],[f134]) ).
fof(f134,axiom,
! [X10,X11,X4,X15] : c_Relation_ORange(X15,X4,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X15,X4),tc_HOL_Obool),X11,X10)) = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool),c_Relation_ORange(X15,X4,X11),c_Relation_ORange(X15,X4,X10)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Range__Un__eq) ).
fof(f9314,plain,
spl104_472,
inference(avatar_split_clause,[],[f2022,f9312]) ).
fof(f9312,plain,
( spl104_472
<=> ! [X9,X0,X8,X6,X1] :
( ~ c_member(X0,X8,X6)
| ~ c_member(tc_prod(X0,X0),c_Product__Type_OPair(X0,X0,X8,sK37(X0,X1,X6)),X1)
| ~ c_member(X0,X9,X6)
| ~ sP2(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_472])]) ).
fof(f2022,plain,
! [X0,X1,X8,X6,X9] :
( ~ c_member(X0,X8,X6)
| ~ c_member(tc_prod(X0,X0),c_Product__Type_OPair(X0,X0,X8,sK37(X0,X1,X6)),X1)
| ~ c_member(X0,X9,X6)
| ~ sP2(X0,X1) ),
inference(cnf_transformation,[],[f1598]) ).
fof(f1598,plain,
! [X0,X1] :
( ( sP2(X0,X1)
| ( ! [X3] :
( ( c_member(X0,sK35(X0,X1,X3),sK34(X0,X1))
& c_member(tc_prod(X0,X0),c_Product__Type_OPair(X0,X0,sK35(X0,X1,X3),X3),X1) )
| ~ c_member(X0,X3,sK34(X0,X1)) )
& c_member(X0,sK36(X0,X1),sK34(X0,X1)) ) )
& ( ! [X6] :
( ( ! [X8] :
( ~ c_member(X0,X8,X6)
| ~ c_member(tc_prod(X0,X0),c_Product__Type_OPair(X0,X0,X8,sK37(X0,X1,X6)),X1) )
& c_member(X0,sK37(X0,X1,X6),X6) )
| ! [X9] : ~ c_member(X0,X9,X6) )
| ~ sP2(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK34,sK35,sK36,sK37])],[f1593,f1597,f1596,f1595,f1594]) ).
fof(f1594,plain,
! [X0,X1] :
( ? [X2] :
( ! [X3] :
( ? [X4] :
( c_member(X0,X4,X2)
& c_member(tc_prod(X0,X0),c_Product__Type_OPair(X0,X0,X4,X3),X1) )
| ~ c_member(X0,X3,X2) )
& ? [X5] : c_member(X0,X5,X2) )
=> ( ! [X3] :
( ? [X4] :
( c_member(X0,X4,sK34(X0,X1))
& c_member(tc_prod(X0,X0),c_Product__Type_OPair(X0,X0,X4,X3),X1) )
| ~ c_member(X0,X3,sK34(X0,X1)) )
& ? [X5] : c_member(X0,X5,sK34(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f1595,plain,
! [X0,X1,X3] :
( ? [X4] :
( c_member(X0,X4,sK34(X0,X1))
& c_member(tc_prod(X0,X0),c_Product__Type_OPair(X0,X0,X4,X3),X1) )
=> ( c_member(X0,sK35(X0,X1,X3),sK34(X0,X1))
& c_member(tc_prod(X0,X0),c_Product__Type_OPair(X0,X0,sK35(X0,X1,X3),X3),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f1596,plain,
! [X0,X1] :
( ? [X5] : c_member(X0,X5,sK34(X0,X1))
=> c_member(X0,sK36(X0,X1),sK34(X0,X1)) ),
introduced(choice_axiom,[]) ).
fof(f1597,plain,
! [X0,X1,X6] :
( ? [X7] :
( ! [X8] :
( ~ c_member(X0,X8,X6)
| ~ c_member(tc_prod(X0,X0),c_Product__Type_OPair(X0,X0,X8,X7),X1) )
& c_member(X0,X7,X6) )
=> ( ! [X8] :
( ~ c_member(X0,X8,X6)
| ~ c_member(tc_prod(X0,X0),c_Product__Type_OPair(X0,X0,X8,sK37(X0,X1,X6)),X1) )
& c_member(X0,sK37(X0,X1,X6),X6) ) ),
introduced(choice_axiom,[]) ).
fof(f1593,plain,
! [X0,X1] :
( ( sP2(X0,X1)
| ? [X2] :
( ! [X3] :
( ? [X4] :
( c_member(X0,X4,X2)
& c_member(tc_prod(X0,X0),c_Product__Type_OPair(X0,X0,X4,X3),X1) )
| ~ c_member(X0,X3,X2) )
& ? [X5] : c_member(X0,X5,X2) ) )
& ( ! [X6] :
( ? [X7] :
( ! [X8] :
( ~ c_member(X0,X8,X6)
| ~ c_member(tc_prod(X0,X0),c_Product__Type_OPair(X0,X0,X8,X7),X1) )
& c_member(X0,X7,X6) )
| ! [X9] : ~ c_member(X0,X9,X6) )
| ~ sP2(X0,X1) ) ),
inference(rectify,[],[f1592]) ).
fof(f1592,plain,
! [X1,X0] :
( ( sP2(X1,X0)
| ? [X2] :
( ! [X4] :
( ? [X5] :
( c_member(X1,X5,X2)
& c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,X5,X4),X0) )
| ~ c_member(X1,X4,X2) )
& ? [X3] : c_member(X1,X3,X2) ) )
& ( ! [X2] :
( ? [X4] :
( ! [X5] :
( ~ c_member(X1,X5,X2)
| ~ c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,X5,X4),X0) )
& c_member(X1,X4,X2) )
| ! [X3] : ~ c_member(X1,X3,X2) )
| ~ sP2(X1,X0) ) ),
inference(nnf_transformation,[],[f1529]) ).
fof(f1529,plain,
! [X1,X0] :
( sP2(X1,X0)
<=> ! [X2] :
( ? [X4] :
( ! [X5] :
( ~ c_member(X1,X5,X2)
| ~ c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,X5,X4),X0) )
& c_member(X1,X4,X2) )
| ! [X3] : ~ c_member(X1,X3,X2) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP2])]) ).
fof(f9304,plain,
( ~ spl104_23
| spl104_323
| ~ spl104_471
| spl104_1 ),
inference(avatar_split_clause,[],[f1863,f2878,f9301,f5847,f2987]) ).
fof(f1863,plain,
( sP0
| ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,sK15,sK16),v_L)
| c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,sK17,sK17),v_L)
| ~ c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,v_L) ),
inference(cnf_transformation,[],[f1558]) ).
fof(f9293,plain,
( ~ spl104_23
| spl104_323
| ~ spl104_470
| spl104_1 ),
inference(avatar_split_clause,[],[f1862,f2878,f9290,f5847,f2987]) ).
fof(f1862,plain,
( sP0
| ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,sK16,sK15),v_L)
| c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,sK17,sK17),v_L)
| ~ c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,v_L) ),
inference(cnf_transformation,[],[f1558]) ).
fof(f9247,plain,
( ~ spl104_2
| spl104_469 ),
inference(avatar_split_clause,[],[f1854,f9245,f2882]) ).
fof(f1854,plain,
! [X3,X4] :
( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X4,X3),v_L)
| c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X3,X4),v_L)
| X3 = X4
| ~ sP1 ),
inference(cnf_transformation,[],[f1552]) ).
fof(f9243,plain,
( spl104_468
| ~ spl104_325
| ~ spl104_421
| ~ spl104_464 ),
inference(avatar_split_clause,[],[f9196,f8651,f7559,f5856,f9240]) ).
fof(f7559,plain,
( spl104_421
<=> c_FunDef_Opair__less = c_Transitive__Closure_Otrancl(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_421])]) ).
fof(f9196,plain,
( c_FunDef_Opair__leq = c_Transitive__Closure_Otrancl(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__leq)
| ~ spl104_325
| ~ spl104_421
| ~ spl104_464 ),
inference(forward_demodulation,[],[f9145,f5858]) ).
fof(f9145,plain,
( c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),tc_HOL_Obool),c_FunDef_Opair__less,c_Relation_OId(tc_prod(tc_Nat_Onat,tc_Nat_Onat))) = c_Transitive__Closure_Otrancl(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),tc_HOL_Obool),c_FunDef_Opair__less,c_Relation_OId(tc_prod(tc_Nat_Onat,tc_Nat_Onat))))
| ~ spl104_421
| ~ spl104_464 ),
inference(superposition,[],[f8652,f7561]) ).
fof(f7561,plain,
( c_FunDef_Opair__less = c_Transitive__Closure_Otrancl(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less)
| ~ spl104_421 ),
inference(avatar_component_clause,[],[f7559]) ).
fof(f8686,plain,
( spl104_467
| ~ spl104_145
| ~ spl104_354 ),
inference(avatar_split_clause,[],[f6364,f5973,f3586,f8684]) ).
fof(f6364,plain,
( ! [X0,X1] : c_member(X0,X1,c_Relation_ORange(X0,X0,c_Relation_OId(X0)))
| ~ spl104_145
| ~ spl104_354 ),
inference(resolution,[],[f5974,f3587]) ).
fof(f8661,plain,
spl104_466,
inference(avatar_split_clause,[],[f2693,f8659]) ).
fof(f8659,plain,
( spl104_466
<=> ! [X0,X3,X2,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(X0,X2),hAPP(X0,X1))
| ~ c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X2,X1),hAPP(c_Relation_Oinv__image(tc_Nat_Onat,X3,c_Wellfounded_Oless__than),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_466])]) ).
fof(f2693,plain,
! [X2,X3,X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(X0,X2),hAPP(X0,X1))
| ~ c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X2,X1),hAPP(c_Relation_Oinv__image(tc_Nat_Onat,X3,c_Wellfounded_Oless__than),X0)) ),
inference(definition_unfolding,[],[f2487,f1902]) ).
fof(f1902,plain,
! [X0] : c_Wellfounded_Omeasure(X0) = c_Relation_Oinv__image(tc_Nat_Onat,X0,c_Wellfounded_Oless__than),
inference(cnf_transformation,[],[f532]) ).
fof(f532,plain,
! [X0] : c_Wellfounded_Omeasure(X0) = c_Relation_Oinv__image(tc_Nat_Onat,X0,c_Wellfounded_Oless__than),
inference(rectify,[],[f218]) ).
fof(f218,axiom,
! [X4] : c_Wellfounded_Omeasure(X4) = c_Relation_Oinv__image(tc_Nat_Onat,X4,c_Wellfounded_Oless__than),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_measure__def) ).
fof(f2487,plain,
! [X2,X3,X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(X0,X2),hAPP(X0,X1))
| ~ c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X2,X1),hAPP(c_Wellfounded_Omeasure(X3),X0)) ),
inference(cnf_transformation,[],[f1773]) ).
fof(f1773,plain,
! [X0,X1,X2,X3] :
( ( c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X2,X1),hAPP(c_Wellfounded_Omeasure(X3),X0))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(X0,X2),hAPP(X0,X1)) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(X0,X2),hAPP(X0,X1))
| ~ c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X2,X1),hAPP(c_Wellfounded_Omeasure(X3),X0)) ) ),
inference(nnf_transformation,[],[f938]) ).
fof(f938,plain,
! [X0,X1,X2,X3] :
( c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X2,X1),hAPP(c_Wellfounded_Omeasure(X3),X0))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(X0,X2),hAPP(X0,X1)) ),
inference(rectify,[],[f217]) ).
fof(f217,axiom,
! [X1,X12,X13,X4] :
( c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X13,X12),hAPP(c_Wellfounded_Omeasure(X4),X1))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(X1,X13),hAPP(X1,X12)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_in__measure) ).
fof(f8657,plain,
spl104_465,
inference(avatar_split_clause,[],[f2692,f8655]) ).
fof(f8655,plain,
( spl104_465
<=> ! [X0,X3,X2,X1] :
( c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X2,X1),hAPP(c_Relation_Oinv__image(tc_Nat_Onat,X3,c_Wellfounded_Oless__than),X0))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(X0,X2),hAPP(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_465])]) ).
fof(f2692,plain,
! [X2,X3,X0,X1] :
( c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X2,X1),hAPP(c_Relation_Oinv__image(tc_Nat_Onat,X3,c_Wellfounded_Oless__than),X0))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(X0,X2),hAPP(X0,X1)) ),
inference(definition_unfolding,[],[f2488,f1902]) ).
fof(f2488,plain,
! [X2,X3,X0,X1] :
( c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X2,X1),hAPP(c_Wellfounded_Omeasure(X3),X0))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(X0,X2),hAPP(X0,X1)) ),
inference(cnf_transformation,[],[f1773]) ).
fof(f8653,plain,
spl104_464,
inference(avatar_split_clause,[],[f2642,f8651]) ).
fof(f2642,plain,
! [X0,X1] : c_Transitive__Closure_Otrancl(X1,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),X0,c_Relation_OId(X1))) = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),c_Transitive__Closure_Otrancl(X1,X0),c_Relation_OId(X1)),
inference(definition_unfolding,[],[f1952,f1949]) ).
fof(f1952,plain,
! [X0,X1] : c_Transitive__Closure_Ortrancl(X1,X0) = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),c_Transitive__Closure_Otrancl(X1,X0),c_Relation_OId(X1)),
inference(cnf_transformation,[],[f582]) ).
fof(f582,plain,
! [X0,X1] : c_Transitive__Closure_Ortrancl(X1,X0) = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),c_Transitive__Closure_Otrancl(X1,X0),c_Relation_OId(X1)),
inference(rectify,[],[f114]) ).
fof(f114,axiom,
! [X3,X4] : c_Transitive__Closure_Ortrancl(X4,X3) = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),c_Transitive__Closure_Otrancl(X4,X3),c_Relation_OId(X4)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_reflcl__trancl) ).
fof(f8649,plain,
spl104_463,
inference(avatar_split_clause,[],[f2562,f8647]) ).
fof(f2562,plain,
! [X2,X3,X0,X1,X4] :
( c_member(tc_prod(X2,X4),c_Product__Type_OPair(X2,X4,sK85(X0,X1,X2,X3,X4),X3),X1)
| ~ c_member(X4,X3,c_Relation_OImage(X2,X4,X1,X0)) ),
inference(cnf_transformation,[],[f1811]) ).
fof(f1811,plain,
! [X0,X1,X2,X3,X4] :
( ( c_member(X4,X3,c_Relation_OImage(X2,X4,X1,X0))
| ! [X5] :
( ~ c_member(tc_prod(X2,X4),c_Product__Type_OPair(X2,X4,X5,X3),X1)
| ~ c_member(X2,X5,X0) ) )
& ( ( c_member(tc_prod(X2,X4),c_Product__Type_OPair(X2,X4,sK85(X0,X1,X2,X3,X4),X3),X1)
& c_member(X2,sK85(X0,X1,X2,X3,X4),X0) )
| ~ c_member(X4,X3,c_Relation_OImage(X2,X4,X1,X0)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK85])],[f1809,f1810]) ).
fof(f1810,plain,
! [X0,X1,X2,X3,X4] :
( ? [X6] :
( c_member(tc_prod(X2,X4),c_Product__Type_OPair(X2,X4,X6,X3),X1)
& c_member(X2,X6,X0) )
=> ( c_member(tc_prod(X2,X4),c_Product__Type_OPair(X2,X4,sK85(X0,X1,X2,X3,X4),X3),X1)
& c_member(X2,sK85(X0,X1,X2,X3,X4),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f1809,plain,
! [X0,X1,X2,X3,X4] :
( ( c_member(X4,X3,c_Relation_OImage(X2,X4,X1,X0))
| ! [X5] :
( ~ c_member(tc_prod(X2,X4),c_Product__Type_OPair(X2,X4,X5,X3),X1)
| ~ c_member(X2,X5,X0) ) )
& ( ? [X6] :
( c_member(tc_prod(X2,X4),c_Product__Type_OPair(X2,X4,X6,X3),X1)
& c_member(X2,X6,X0) )
| ~ c_member(X4,X3,c_Relation_OImage(X2,X4,X1,X0)) ) ),
inference(rectify,[],[f1808]) ).
fof(f1808,plain,
! [X0,X1,X2,X3,X4] :
( ( c_member(X4,X3,c_Relation_OImage(X2,X4,X1,X0))
| ! [X5] :
( ~ c_member(tc_prod(X2,X4),c_Product__Type_OPair(X2,X4,X5,X3),X1)
| ~ c_member(X2,X5,X0) ) )
& ( ? [X5] :
( c_member(tc_prod(X2,X4),c_Product__Type_OPair(X2,X4,X5,X3),X1)
& c_member(X2,X5,X0) )
| ~ c_member(X4,X3,c_Relation_OImage(X2,X4,X1,X0)) ) ),
inference(nnf_transformation,[],[f986]) ).
fof(f986,plain,
! [X0,X1,X2,X3,X4] :
( c_member(X4,X3,c_Relation_OImage(X2,X4,X1,X0))
<=> ? [X5] :
( c_member(tc_prod(X2,X4),c_Product__Type_OPair(X2,X4,X5,X3),X1)
& c_member(X2,X5,X0) ) ),
inference(rectify,[],[f473]) ).
fof(f473,axiom,
! [X11,X3,X15,X8,X4] :
( c_member(X4,X8,c_Relation_OImage(X15,X4,X3,X11))
<=> ? [X2] :
( c_member(tc_prod(X15,X4),c_Product__Type_OPair(X15,X4,X2,X8),X3)
& c_member(X15,X2,X11) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Image__iff) ).
fof(f8645,plain,
spl104_462,
inference(avatar_split_clause,[],[f2532,f8643]) ).
fof(f2532,plain,
! [X2,X3,X0,X1,X4] :
( c_member(tc_prod(X2,X4),c_Product__Type_OPair(X2,X4,sK76(X0,X1,X2,X3,X4),X3),X1)
| ~ c_member(X4,X3,c_Relation_OImage(X2,X4,X1,X0)) ),
inference(cnf_transformation,[],[f1796]) ).
fof(f1796,plain,
! [X0,X1,X2,X3,X4] :
( ( c_member(X2,sK76(X0,X1,X2,X3,X4),X0)
& c_member(tc_prod(X2,X4),c_Product__Type_OPair(X2,X4,sK76(X0,X1,X2,X3,X4),X3),X1) )
| ~ c_member(X4,X3,c_Relation_OImage(X2,X4,X1,X0)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK76])],[f1460,f1795]) ).
fof(f1795,plain,
! [X0,X1,X2,X3,X4] :
( ? [X5] :
( c_member(X2,X5,X0)
& c_member(tc_prod(X2,X4),c_Product__Type_OPair(X2,X4,X5,X3),X1) )
=> ( c_member(X2,sK76(X0,X1,X2,X3,X4),X0)
& c_member(tc_prod(X2,X4),c_Product__Type_OPair(X2,X4,sK76(X0,X1,X2,X3,X4),X3),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f1460,plain,
! [X0,X1,X2,X3,X4] :
( ? [X5] :
( c_member(X2,X5,X0)
& c_member(tc_prod(X2,X4),c_Product__Type_OPair(X2,X4,X5,X3),X1) )
| ~ c_member(X4,X3,c_Relation_OImage(X2,X4,X1,X0)) ),
inference(ennf_transformation,[],[f968]) ).
fof(f968,plain,
! [X0,X1,X2,X3,X4] :
( c_member(X4,X3,c_Relation_OImage(X2,X4,X1,X0))
=> ~ ! [X5] :
( c_member(tc_prod(X2,X4),c_Product__Type_OPair(X2,X4,X5,X3),X1)
=> ~ c_member(X2,X5,X0) ) ),
inference(rectify,[],[f488]) ).
fof(f488,axiom,
! [X11,X3,X15,X8,X4] :
( c_member(X4,X8,c_Relation_OImage(X15,X4,X3,X11))
=> ~ ! [X2] :
( c_member(tc_prod(X15,X4),c_Product__Type_OPair(X15,X4,X2,X8),X3)
=> ~ c_member(X15,X2,X11) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ImageE) ).
fof(f8641,plain,
spl104_461,
inference(avatar_split_clause,[],[f2373,f8639]) ).
fof(f8639,plain,
( spl104_461
<=> ! [X0,X3,X2,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),X2,X0),X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X0,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_461])]) ).
fof(f2373,plain,
! [X2,X3,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),X2,X0),X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X0,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X2,X1) ),
inference(cnf_transformation,[],[f1369]) ).
fof(f1369,plain,
! [X0,X1,X2,X3] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),X2,X0),X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X0,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X2,X1) ),
inference(flattening,[],[f1368]) ).
fof(f1368,plain,
! [X0,X1,X2,X3] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),X2,X0),X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X0,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X2,X1) ),
inference(ennf_transformation,[],[f886]) ).
fof(f886,plain,
! [X0,X1,X2,X3] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X2,X1)
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X0,X1)
=> c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),X2,X0),X1) ) ),
inference(rectify,[],[f225]) ).
fof(f225,axiom,
! [X10,X53,X11,X4] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool),X11,X53)
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool),X10,X53)
=> c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool),X11,X10),X53) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__least) ).
fof(f8637,plain,
spl104_460,
inference(avatar_split_clause,[],[f2337,f8635]) ).
fof(f8635,plain,
( spl104_460
<=> ! [X0,X3,X2,X1] :
( ~ c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X0,X1),X2)
| ~ c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X1,X0),X2)
| ~ c_Wellfounded_Owf(X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_460])]) ).
fof(f2337,plain,
! [X2,X3,X0,X1] :
( ~ c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X0,X1),X2)
| ~ c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X1,X0),X2)
| ~ c_Wellfounded_Owf(X3,X2) ),
inference(cnf_transformation,[],[f1313]) ).
fof(f1313,plain,
! [X0,X1,X2,X3] :
( ~ c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X0,X1),X2)
| ~ c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X1,X0),X2)
| ~ c_Wellfounded_Owf(X3,X2) ),
inference(flattening,[],[f1312]) ).
fof(f1312,plain,
! [X0,X1,X2,X3] :
( ~ c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X0,X1),X2)
| ~ c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X1,X0),X2)
| ~ c_Wellfounded_Owf(X3,X2) ),
inference(ennf_transformation,[],[f851]) ).
fof(f851,plain,
! [X0,X1,X2,X3] :
( c_Wellfounded_Owf(X3,X2)
=> ( c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X1,X0),X2)
=> ~ c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X0,X1),X2) ) ),
inference(rectify,[],[f166]) ).
fof(f166,axiom,
! [X13,X9,X3,X4] :
( c_Wellfounded_Owf(X4,X3)
=> ( c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X9,X13),X3)
=> ~ c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X13,X9),X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__asym) ).
fof(f8633,plain,
spl104_459,
inference(avatar_split_clause,[],[f2282,f8631]) ).
fof(f8631,plain,
( spl104_459
<=> ! [X0,X3,X2,X1] :
( c_Groups_Ominus__class_Ominus(tc_fun(X3,tc_HOL_Obool),c_Set_Oinsert(X3,X2,X0),X1) = c_Set_Oinsert(X3,X2,c_Groups_Ominus__class_Ominus(tc_fun(X3,tc_HOL_Obool),X0,X1))
| c_member(X3,X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_459])]) ).
fof(f2282,plain,
! [X2,X3,X0,X1] :
( c_Groups_Ominus__class_Ominus(tc_fun(X3,tc_HOL_Obool),c_Set_Oinsert(X3,X2,X0),X1) = c_Set_Oinsert(X3,X2,c_Groups_Ominus__class_Ominus(tc_fun(X3,tc_HOL_Obool),X0,X1))
| c_member(X3,X2,X1) ),
inference(cnf_transformation,[],[f1239]) ).
fof(f1239,plain,
! [X0,X1,X2,X3] :
( ( c_Groups_Ominus__class_Ominus(tc_fun(X3,tc_HOL_Obool),c_Set_Oinsert(X3,X2,X0),X1) = c_Set_Oinsert(X3,X2,c_Groups_Ominus__class_Ominus(tc_fun(X3,tc_HOL_Obool),X0,X1))
| c_member(X3,X2,X1) )
& ( c_Groups_Ominus__class_Ominus(tc_fun(X3,tc_HOL_Obool),c_Set_Oinsert(X3,X2,X0),X1) = c_Groups_Ominus__class_Ominus(tc_fun(X3,tc_HOL_Obool),X0,X1)
| ~ c_member(X3,X2,X1) ) ),
inference(ennf_transformation,[],[f807]) ).
fof(f807,plain,
! [X0,X1,X2,X3] :
( ( ~ c_member(X3,X2,X1)
=> c_Groups_Ominus__class_Ominus(tc_fun(X3,tc_HOL_Obool),c_Set_Oinsert(X3,X2,X0),X1) = c_Set_Oinsert(X3,X2,c_Groups_Ominus__class_Ominus(tc_fun(X3,tc_HOL_Obool),X0,X1)) )
& ( c_member(X3,X2,X1)
=> c_Groups_Ominus__class_Ominus(tc_fun(X3,tc_HOL_Obool),c_Set_Oinsert(X3,X2,X0),X1) = c_Groups_Ominus__class_Ominus(tc_fun(X3,tc_HOL_Obool),X0,X1) ) ),
inference(rectify,[],[f210]) ).
fof(f210,axiom,
! [X11,X10,X13,X4] :
( ( ~ c_member(X4,X13,X10)
=> c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool),c_Set_Oinsert(X4,X13,X11),X10) = c_Set_Oinsert(X4,X13,c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool),X11,X10)) )
& ( c_member(X4,X13,X10)
=> c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool),X11,X10) = c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool),c_Set_Oinsert(X4,X13,X11),X10) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__Diff__if) ).
fof(f8629,plain,
spl104_458,
inference(avatar_split_clause,[],[f2272,f8627]) ).
fof(f8623,plain,
spl104_457,
inference(avatar_split_clause,[],[f2271,f8621]) ).
fof(f2271,plain,
! [X2,X3,X0,X1] : c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),X2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),X1,X0)) = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),X1,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),X2,X0)),
inference(cnf_transformation,[],[f797]) ).
fof(f797,plain,
! [X0,X1,X2,X3] : c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),X2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),X1,X0)) = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),X1,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),X2,X0)),
inference(rectify,[],[f127]) ).
fof(f127,axiom,
! [X53,X10,X11,X4] : c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool),X11,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool),X10,X53)) = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool),X10,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool),X11,X53)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__left__commute) ).
fof(f8619,plain,
spl104_456,
inference(avatar_split_clause,[],[f2163,f8617]) ).
fof(f8617,plain,
( spl104_456
<=> ! [X2,X0,X1] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_456])]) ).
fof(f2163,plain,
! [X2,X0,X1] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
inference(cnf_transformation,[],[f1192]) ).
fof(f1192,plain,
! [X0,X1,X2] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
inference(flattening,[],[f1191]) ).
fof(f1191,plain,
! [X0,X1,X2] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
inference(ennf_transformation,[],[f739]) ).
fof(f739,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X0)
=> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X2)) ) ),
inference(rectify,[],[f381]) ).
fof(f381,axiom,
! [X70,X71,X75] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X75,X71)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X75,X70)
=> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X71,X75),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X70,X75)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X71,X70) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat_Odiff__diff__eq) ).
fof(f8328,plain,
spl104_455,
inference(avatar_split_clause,[],[f2652,f8326]) ).
fof(f8326,plain,
( spl104_455
<=> ! [X2,X0,X1] :
( c_member(tc_prod(X2,X2),X1,c_Transitive__Closure_Otrancl(X2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),X0,c_Relation_OId(X2))))
| ~ c_member(tc_prod(X2,X2),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_455])]) ).
fof(f2652,plain,
! [X2,X0,X1] :
( c_member(tc_prod(X2,X2),X1,c_Transitive__Closure_Otrancl(X2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),X0,c_Relation_OId(X2))))
| ~ c_member(tc_prod(X2,X2),X1,X0) ),
inference(definition_unfolding,[],[f2182,f1949]) ).
fof(f2182,plain,
! [X2,X0,X1] :
( c_member(tc_prod(X2,X2),X1,c_Transitive__Closure_Ortrancl(X2,X0))
| ~ c_member(tc_prod(X2,X2),X1,X0) ),
inference(cnf_transformation,[],[f1211]) ).
fof(f1211,plain,
! [X0,X1,X2] :
( c_member(tc_prod(X2,X2),X1,c_Transitive__Closure_Ortrancl(X2,X0))
| ~ c_member(tc_prod(X2,X2),X1,X0) ),
inference(ennf_transformation,[],[f754]) ).
fof(f754,plain,
! [X0,X1,X2] :
( c_member(tc_prod(X2,X2),X1,X0)
=> c_member(tc_prod(X2,X2),X1,c_Transitive__Closure_Ortrancl(X2,X0)) ),
inference(rectify,[],[f60]) ).
fof(f60,axiom,
! [X3,X39,X4] :
( c_member(tc_prod(X4,X4),X39,X3)
=> c_member(tc_prod(X4,X4),X39,c_Transitive__Closure_Ortrancl(X4,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_r__into__rtrancl) ).
fof(f8324,plain,
spl104_454,
inference(avatar_split_clause,[],[f2585,f8322]) ).
fof(f2585,plain,
! [X2,X3,X0,X1,X4,X5] :
( hAPP(X0,X4) = hAPP(c_Recdef_Ocut(X5,X1,X0,X2,X3),X4)
| ~ c_member(tc_prod(X5,X5),c_Product__Type_OPair(X5,X5,X4,X3),X2) ),
inference(cnf_transformation,[],[f1505]) ).
fof(f1505,plain,
! [X0,X1,X2,X3,X4,X5] :
( hAPP(X0,X4) = hAPP(c_Recdef_Ocut(X5,X1,X0,X2,X3),X4)
| ~ c_member(tc_prod(X5,X5),c_Product__Type_OPair(X5,X5,X4,X3),X2) ),
inference(ennf_transformation,[],[f999]) ).
fof(f999,plain,
! [X0,X1,X2,X3,X4,X5] :
( c_member(tc_prod(X5,X5),c_Product__Type_OPair(X5,X5,X4,X3),X2)
=> hAPP(X0,X4) = hAPP(c_Recdef_Ocut(X5,X1,X0,X2,X3),X4) ),
inference(rectify,[],[f77]) ).
fof(f77,axiom,
! [X1,X15,X3,X9,X13,X4] :
( c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X13,X9),X3)
=> hAPP(X1,X13) = hAPP(c_Recdef_Ocut(X4,X15,X1,X3,X9),X13) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_cut__apply) ).
fof(f8320,plain,
spl104_453,
inference(avatar_split_clause,[],[f2563,f8318]) ).
fof(f2563,plain,
! [X2,X3,X0,X1,X4,X5] :
( c_member(X4,X3,c_Relation_OImage(X2,X4,X1,X0))
| ~ c_member(tc_prod(X2,X4),c_Product__Type_OPair(X2,X4,X5,X3),X1)
| ~ c_member(X2,X5,X0) ),
inference(cnf_transformation,[],[f1811]) ).
fof(f8316,plain,
spl104_452,
inference(avatar_split_clause,[],[f2473,f8314]) ).
fof(f8314,plain,
( spl104_452
<=> ! [X0,X3,X2,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),c_Groups_Ominus__class_Ominus(tc_fun(X3,tc_HOL_Obool),X2,X1),X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_452])]) ).
fof(f2473,plain,
! [X2,X3,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),c_Groups_Ominus__class_Ominus(tc_fun(X3,tc_HOL_Obool),X2,X1),X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),X1,X0)) ),
inference(cnf_transformation,[],[f1764]) ).
fof(f1764,plain,
! [X0,X1,X2,X3] :
( ( c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),c_Groups_Ominus__class_Ominus(tc_fun(X3,tc_HOL_Obool),X2,X1),X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),X1,X0)) )
& ( c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),X1,X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),c_Groups_Ominus__class_Ominus(tc_fun(X3,tc_HOL_Obool),X2,X1),X0) ) ),
inference(nnf_transformation,[],[f933]) ).
fof(f933,plain,
! [X0,X1,X2,X3] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),c_Groups_Ominus__class_Ominus(tc_fun(X3,tc_HOL_Obool),X2,X1),X0)
<=> c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),X1,X0)) ),
inference(rectify,[],[f277]) ).
fof(f277,axiom,
! [X53,X10,X11,X4] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool),c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool),X11,X10),X53)
<=> c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool),X11,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool),X10,X53)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Diff__subset__conv) ).
fof(f8312,plain,
spl104_451,
inference(avatar_split_clause,[],[f2472,f8310]) ).
fof(f8310,plain,
( spl104_451
<=> ! [X0,X3,X2,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),X1,X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),c_Groups_Ominus__class_Ominus(tc_fun(X3,tc_HOL_Obool),X2,X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_451])]) ).
fof(f2472,plain,
! [X2,X3,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),X1,X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),c_Groups_Ominus__class_Ominus(tc_fun(X3,tc_HOL_Obool),X2,X1),X0) ),
inference(cnf_transformation,[],[f1764]) ).
fof(f8308,plain,
spl104_450,
inference(avatar_split_clause,[],[f2293,f8306]) ).
fof(f2293,plain,
! [X2,X3,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X2,X3),X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(X3,hAPP(X1,sK55(X0,X1,X3)),hAPP(X0,sK55(X0,X1,X3)))
| ~ class_Orderings_Oord(X3) ),
inference(cnf_transformation,[],[f1699]) ).
fof(f1699,plain,
! [X0,X1,X2,X3] :
( ( ( c_Orderings_Oord__class_Oless__eq(tc_fun(X2,X3),X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(X3,hAPP(X1,sK55(X0,X1,X3)),hAPP(X0,sK55(X0,X1,X3))) )
& ( ! [X5] : c_Orderings_Oord__class_Oless__eq(X3,hAPP(X1,X5),hAPP(X0,X5))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X2,X3),X1,X0) ) )
| ~ class_Orderings_Oord(X3) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK55])],[f1697,f1698]) ).
fof(f1698,plain,
! [X0,X1,X3] :
( ? [X4] : ~ c_Orderings_Oord__class_Oless__eq(X3,hAPP(X1,X4),hAPP(X0,X4))
=> ~ c_Orderings_Oord__class_Oless__eq(X3,hAPP(X1,sK55(X0,X1,X3)),hAPP(X0,sK55(X0,X1,X3))) ),
introduced(choice_axiom,[]) ).
fof(f1697,plain,
! [X0,X1,X2,X3] :
( ( ( c_Orderings_Oord__class_Oless__eq(tc_fun(X2,X3),X1,X0)
| ? [X4] : ~ c_Orderings_Oord__class_Oless__eq(X3,hAPP(X1,X4),hAPP(X0,X4)) )
& ( ! [X5] : c_Orderings_Oord__class_Oless__eq(X3,hAPP(X1,X5),hAPP(X0,X5))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X2,X3),X1,X0) ) )
| ~ class_Orderings_Oord(X3) ),
inference(rectify,[],[f1696]) ).
fof(f1696,plain,
! [X0,X1,X2,X3] :
( ( ( c_Orderings_Oord__class_Oless__eq(tc_fun(X2,X3),X1,X0)
| ? [X4] : ~ c_Orderings_Oord__class_Oless__eq(X3,hAPP(X1,X4),hAPP(X0,X4)) )
& ( ! [X4] : c_Orderings_Oord__class_Oless__eq(X3,hAPP(X1,X4),hAPP(X0,X4))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X2,X3),X1,X0) ) )
| ~ class_Orderings_Oord(X3) ),
inference(nnf_transformation,[],[f1251]) ).
fof(f1251,plain,
! [X0,X1,X2,X3] :
( ( c_Orderings_Oord__class_Oless__eq(tc_fun(X2,X3),X1,X0)
<=> ! [X4] : c_Orderings_Oord__class_Oless__eq(X3,hAPP(X1,X4),hAPP(X0,X4)) )
| ~ class_Orderings_Oord(X3) ),
inference(ennf_transformation,[],[f815]) ).
fof(f815,plain,
! [X0,X1,X2,X3] :
( class_Orderings_Oord(X3)
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(X2,X3),X1,X0)
<=> ! [X4] : c_Orderings_Oord__class_Oless__eq(X3,hAPP(X1,X4),hAPP(X0,X4)) ) ),
inference(rectify,[],[f353]) ).
fof(f353,axiom,
! [X0,X1,X4,X15] :
( class_Orderings_Oord(X15)
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(X4,X15),X1,X0)
<=> ! [X2] : c_Orderings_Oord__class_Oless__eq(X15,hAPP(X1,X2),hAPP(X0,X2)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__fun__def) ).
fof(f8304,plain,
spl104_449,
inference(avatar_split_clause,[],[f2248,f8302]) ).
fof(f2248,plain,
! [X2,X0,X1,X4] :
( c_member(X2,X4,c_Wellfounded_Oacc(X2,X0))
| ~ c_member(tc_prod(X2,X2),c_Product__Type_OPair(X2,X2,X4,X1),X0)
| ~ c_member(X2,X1,c_Wellfounded_Oacc(X2,X0)) ),
inference(cnf_transformation,[],[f1681]) ).
fof(f1681,plain,
! [X0,X1,X2] :
( ( c_member(X2,X1,c_Wellfounded_Oacc(X2,X0))
| ( ~ c_member(X2,sK51(X0,X1,X2),c_Wellfounded_Oacc(X2,X0))
& c_member(tc_prod(X2,X2),c_Product__Type_OPair(X2,X2,sK51(X0,X1,X2),X1),X0) ) )
& ( ! [X4] :
( c_member(X2,X4,c_Wellfounded_Oacc(X2,X0))
| ~ c_member(tc_prod(X2,X2),c_Product__Type_OPair(X2,X2,X4,X1),X0) )
| ~ c_member(X2,X1,c_Wellfounded_Oacc(X2,X0)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK51])],[f1679,f1680]) ).
fof(f1680,plain,
! [X0,X1,X2] :
( ? [X3] :
( ~ c_member(X2,X3,c_Wellfounded_Oacc(X2,X0))
& c_member(tc_prod(X2,X2),c_Product__Type_OPair(X2,X2,X3,X1),X0) )
=> ( ~ c_member(X2,sK51(X0,X1,X2),c_Wellfounded_Oacc(X2,X0))
& c_member(tc_prod(X2,X2),c_Product__Type_OPair(X2,X2,sK51(X0,X1,X2),X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f1679,plain,
! [X0,X1,X2] :
( ( c_member(X2,X1,c_Wellfounded_Oacc(X2,X0))
| ? [X3] :
( ~ c_member(X2,X3,c_Wellfounded_Oacc(X2,X0))
& c_member(tc_prod(X2,X2),c_Product__Type_OPair(X2,X2,X3,X1),X0) ) )
& ( ! [X4] :
( c_member(X2,X4,c_Wellfounded_Oacc(X2,X0))
| ~ c_member(tc_prod(X2,X2),c_Product__Type_OPair(X2,X2,X4,X1),X0) )
| ~ c_member(X2,X1,c_Wellfounded_Oacc(X2,X0)) ) ),
inference(rectify,[],[f1678]) ).
fof(f1678,plain,
! [X0,X1,X2] :
( ( c_member(X2,X1,c_Wellfounded_Oacc(X2,X0))
| ? [X3] :
( ~ c_member(X2,X3,c_Wellfounded_Oacc(X2,X0))
& c_member(tc_prod(X2,X2),c_Product__Type_OPair(X2,X2,X3,X1),X0) ) )
& ( ! [X3] :
( c_member(X2,X3,c_Wellfounded_Oacc(X2,X0))
| ~ c_member(tc_prod(X2,X2),c_Product__Type_OPair(X2,X2,X3,X1),X0) )
| ~ c_member(X2,X1,c_Wellfounded_Oacc(X2,X0)) ) ),
inference(nnf_transformation,[],[f1238]) ).
fof(f1238,plain,
! [X0,X1,X2] :
( c_member(X2,X1,c_Wellfounded_Oacc(X2,X0))
<=> ! [X3] :
( c_member(X2,X3,c_Wellfounded_Oacc(X2,X0))
| ~ c_member(tc_prod(X2,X2),c_Product__Type_OPair(X2,X2,X3,X1),X0) ) ),
inference(ennf_transformation,[],[f784]) ).
fof(f784,plain,
! [X0,X1,X2] :
( c_member(X2,X1,c_Wellfounded_Oacc(X2,X0))
<=> ! [X3] :
( c_member(tc_prod(X2,X2),c_Product__Type_OPair(X2,X2,X3,X1),X0)
=> c_member(X2,X3,c_Wellfounded_Oacc(X2,X0)) ) ),
inference(rectify,[],[f38]) ).
fof(f38,axiom,
! [X3,X9,X4] :
( c_member(X4,X9,c_Wellfounded_Oacc(X4,X3))
<=> ! [X2] :
( c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X2,X9),X3)
=> c_member(X4,X2,c_Wellfounded_Oacc(X4,X3)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_acc_Osimps) ).
fof(f8300,plain,
spl104_448,
inference(avatar_split_clause,[],[f2168,f8298]) ).
fof(f8298,plain,
( spl104_448
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_448])]) ).
fof(f2168,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
inference(cnf_transformation,[],[f1640]) ).
fof(f1640,plain,
! [X0,X1,X2] :
( ( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X2)) ) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
inference(nnf_transformation,[],[f1198]) ).
fof(f1198,plain,
! [X0,X1,X2] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X2))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
inference(flattening,[],[f1197]) ).
fof(f1197,plain,
! [X0,X1,X2] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X2))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
inference(ennf_transformation,[],[f742]) ).
fof(f742,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X0)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X2))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ) ) ),
inference(rectify,[],[f380]) ).
fof(f380,axiom,
! [X67,X68,X78] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X78,X68)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X78,X67)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X68,X78),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X67,X78))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X68,X67) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__diff__iff) ).
fof(f8296,plain,
( spl104_447
| ~ spl104_219
| ~ spl104_325 ),
inference(avatar_split_clause,[],[f5997,f5856,f4124,f8294]) ).
fof(f8294,plain,
( spl104_447
<=> ! [X0] :
( hBOOL(hAPP(c_FunDef_Opair__leq,X0))
| ~ hBOOL(hAPP(c_FunDef_Opair__less,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_447])]) ).
fof(f5997,plain,
( ! [X0] :
( hBOOL(hAPP(c_FunDef_Opair__leq,X0))
| ~ hBOOL(hAPP(c_FunDef_Opair__less,X0)) )
| ~ spl104_219
| ~ spl104_325 ),
inference(superposition,[],[f4125,f5858]) ).
fof(f8292,plain,
spl104_446,
inference(avatar_split_clause,[],[f2166,f8290]) ).
fof(f8290,plain,
( spl104_446
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_446])]) ).
fof(f2166,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
inference(cnf_transformation,[],[f1639]) ).
fof(f1639,plain,
! [X0,X1,X2] :
( ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X2))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X2)) ) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
inference(nnf_transformation,[],[f1196]) ).
fof(f1196,plain,
! [X0,X1,X2] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X2))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
inference(flattening,[],[f1195]) ).
fof(f1195,plain,
! [X0,X1,X2] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X2))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
inference(ennf_transformation,[],[f741]) ).
fof(f741,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X0)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X2))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ) ) ),
inference(rectify,[],[f388]) ).
fof(f388,axiom,
! [X67,X68,X78] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X78,X68)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X78,X67)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X68,X78),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X67,X78))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X68,X67) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__diff__iff) ).
fof(f8288,plain,
spl104_445,
inference(avatar_split_clause,[],[f2024,f8286]) ).
fof(f8286,plain,
( spl104_445
<=> ! [X0,X1,X3] :
( sP2(X0,X1)
| c_member(tc_prod(X0,X0),c_Product__Type_OPair(X0,X0,sK35(X0,X1,X3),X3),X1)
| ~ c_member(X0,X3,sK34(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_445])]) ).
fof(f2024,plain,
! [X3,X0,X1] :
( sP2(X0,X1)
| c_member(tc_prod(X0,X0),c_Product__Type_OPair(X0,X0,sK35(X0,X1,X3),X3),X1)
| ~ c_member(X0,X3,sK34(X0,X1)) ),
inference(cnf_transformation,[],[f1598]) ).
fof(f8107,plain,
spl104_444,
inference(avatar_split_clause,[],[f2530,f8105]) ).
fof(f8105,plain,
( spl104_444
<=> ! [X2,X4,X0,X3,X1] :
( c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,X3,X2),c_Wellfounded_Omlex__prod(X1,X4,X0))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(X4,X3),hAPP(X4,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_444])]) ).
fof(f2530,plain,
! [X2,X3,X0,X1,X4] :
( c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,X3,X2),c_Wellfounded_Omlex__prod(X1,X4,X0))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(X4,X3),hAPP(X4,X2)) ),
inference(cnf_transformation,[],[f1457]) ).
fof(f1457,plain,
! [X0,X1,X2,X3,X4] :
( c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,X3,X2),c_Wellfounded_Omlex__prod(X1,X4,X0))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(X4,X3),hAPP(X4,X2)) ),
inference(ennf_transformation,[],[f966]) ).
fof(f966,plain,
! [X0,X1,X2,X3,X4] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(X4,X3),hAPP(X4,X2))
=> c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,X3,X2),c_Wellfounded_Omlex__prod(X1,X4,X0)) ),
inference(rectify,[],[f284]) ).
fof(f284,axiom,
! [X14,X4,X12,X13,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(X1,X13),hAPP(X1,X12))
=> c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X13,X12),c_Wellfounded_Omlex__prod(X4,X1,X14)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mlex__less) ).
fof(f8103,plain,
spl104_443,
inference(avatar_split_clause,[],[f2511,f8101]) ).
fof(f2511,plain,
! [X2,X3,X0,X1,X4] : c_Relation_ODomain(X4,X3,c_Set_Oinsert(tc_prod(X4,X3),c_Product__Type_OPair(X4,X3,X2,X1),X0)) = c_Set_Oinsert(X4,X2,c_Relation_ODomain(X4,X3,X0)),
inference(cnf_transformation,[],[f943]) ).
fof(f943,plain,
! [X0,X1,X2,X3,X4] : c_Relation_ODomain(X4,X3,c_Set_Oinsert(tc_prod(X4,X3),c_Product__Type_OPair(X4,X3,X2,X1),X0)) = c_Set_Oinsert(X4,X2,c_Relation_ODomain(X4,X3,X0)),
inference(rectify,[],[f136]) ).
fof(f136,axiom,
! [X3,X8,X9,X15,X4] : c_Relation_ODomain(X4,X15,c_Set_Oinsert(tc_prod(X4,X15),c_Product__Type_OPair(X4,X15,X9,X8),X3)) = c_Set_Oinsert(X4,X9,c_Relation_ODomain(X4,X15,X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Domain__insert) ).
fof(f8099,plain,
spl104_442,
inference(avatar_split_clause,[],[f2510,f8097]) ).
fof(f2510,plain,
! [X2,X3,X0,X1,X4] : c_Relation_ORange(X4,X3,c_Set_Oinsert(tc_prod(X4,X3),c_Product__Type_OPair(X4,X3,X2,X1),X0)) = c_Set_Oinsert(X3,X1,c_Relation_ORange(X4,X3,X0)),
inference(cnf_transformation,[],[f942]) ).
fof(f942,plain,
! [X0,X1,X2,X3,X4] : c_Relation_ORange(X4,X3,c_Set_Oinsert(tc_prod(X4,X3),c_Product__Type_OPair(X4,X3,X2,X1),X0)) = c_Set_Oinsert(X3,X1,c_Relation_ORange(X4,X3,X0)),
inference(rectify,[],[f137]) ).
fof(f137,axiom,
! [X3,X8,X9,X4,X15] : c_Relation_ORange(X15,X4,c_Set_Oinsert(tc_prod(X15,X4),c_Product__Type_OPair(X15,X4,X9,X8),X3)) = c_Set_Oinsert(X4,X8,c_Relation_ORange(X15,X4,X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Range__insert) ).
fof(f8095,plain,
spl104_441,
inference(avatar_split_clause,[],[f2436,f8093]) ).
fof(f2436,plain,
! [X2,X3,X0,X1] :
( c_member(tc_prod(X3,X1),c_Product__Type_OPair(X3,X1,X2,sK69(X0,X1,X2,X3)),X0)
| ~ c_member(X3,X2,c_Relation_ODomain(X3,X1,X0)) ),
inference(cnf_transformation,[],[f1744]) ).
fof(f1744,plain,
! [X0,X1,X2,X3] :
( ( c_member(X3,X2,c_Relation_ODomain(X3,X1,X0))
| ! [X4] : ~ c_member(tc_prod(X3,X1),c_Product__Type_OPair(X3,X1,X2,X4),X0) )
& ( c_member(tc_prod(X3,X1),c_Product__Type_OPair(X3,X1,X2,sK69(X0,X1,X2,X3)),X0)
| ~ c_member(X3,X2,c_Relation_ODomain(X3,X1,X0)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK69])],[f1742,f1743]) ).
fof(f1743,plain,
! [X0,X1,X2,X3] :
( ? [X5] : c_member(tc_prod(X3,X1),c_Product__Type_OPair(X3,X1,X2,X5),X0)
=> c_member(tc_prod(X3,X1),c_Product__Type_OPair(X3,X1,X2,sK69(X0,X1,X2,X3)),X0) ),
introduced(choice_axiom,[]) ).
fof(f1742,plain,
! [X0,X1,X2,X3] :
( ( c_member(X3,X2,c_Relation_ODomain(X3,X1,X0))
| ! [X4] : ~ c_member(tc_prod(X3,X1),c_Product__Type_OPair(X3,X1,X2,X4),X0) )
& ( ? [X5] : c_member(tc_prod(X3,X1),c_Product__Type_OPair(X3,X1,X2,X5),X0)
| ~ c_member(X3,X2,c_Relation_ODomain(X3,X1,X0)) ) ),
inference(rectify,[],[f1741]) ).
fof(f1741,plain,
! [X0,X1,X2,X3] :
( ( c_member(X3,X2,c_Relation_ODomain(X3,X1,X0))
| ! [X4] : ~ c_member(tc_prod(X3,X1),c_Product__Type_OPair(X3,X1,X2,X4),X0) )
& ( ? [X4] : c_member(tc_prod(X3,X1),c_Product__Type_OPair(X3,X1,X2,X4),X0)
| ~ c_member(X3,X2,c_Relation_ODomain(X3,X1,X0)) ) ),
inference(nnf_transformation,[],[f926]) ).
fof(f926,plain,
! [X0,X1,X2,X3] :
( c_member(X3,X2,c_Relation_ODomain(X3,X1,X0))
<=> ? [X4] : c_member(tc_prod(X3,X1),c_Product__Type_OPair(X3,X1,X2,X4),X0) ),
inference(rectify,[],[f32]) ).
fof(f32,axiom,
! [X3,X15,X9,X4] :
( c_member(X4,X9,c_Relation_ODomain(X4,X15,X3))
<=> ? [X5] : c_member(tc_prod(X4,X15),c_Product__Type_OPair(X4,X15,X9,X5),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Domain__iff) ).
fof(f8091,plain,
spl104_440,
inference(avatar_split_clause,[],[f2434,f8089]) ).
fof(f2434,plain,
! [X2,X3,X0,X1] :
( c_member(tc_prod(X1,X3),c_Product__Type_OPair(X1,X3,sK68(X0,X1,X2,X3),X2),X0)
| ~ c_member(X3,X2,c_Relation_ORange(X1,X3,X0)) ),
inference(cnf_transformation,[],[f1740]) ).
fof(f1740,plain,
! [X0,X1,X2,X3] :
( ( c_member(X3,X2,c_Relation_ORange(X1,X3,X0))
| ! [X4] : ~ c_member(tc_prod(X1,X3),c_Product__Type_OPair(X1,X3,X4,X2),X0) )
& ( c_member(tc_prod(X1,X3),c_Product__Type_OPair(X1,X3,sK68(X0,X1,X2,X3),X2),X0)
| ~ c_member(X3,X2,c_Relation_ORange(X1,X3,X0)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK68])],[f1738,f1739]) ).
fof(f1739,plain,
! [X0,X1,X2,X3] :
( ? [X5] : c_member(tc_prod(X1,X3),c_Product__Type_OPair(X1,X3,X5,X2),X0)
=> c_member(tc_prod(X1,X3),c_Product__Type_OPair(X1,X3,sK68(X0,X1,X2,X3),X2),X0) ),
introduced(choice_axiom,[]) ).
fof(f1738,plain,
! [X0,X1,X2,X3] :
( ( c_member(X3,X2,c_Relation_ORange(X1,X3,X0))
| ! [X4] : ~ c_member(tc_prod(X1,X3),c_Product__Type_OPair(X1,X3,X4,X2),X0) )
& ( ? [X5] : c_member(tc_prod(X1,X3),c_Product__Type_OPair(X1,X3,X5,X2),X0)
| ~ c_member(X3,X2,c_Relation_ORange(X1,X3,X0)) ) ),
inference(rectify,[],[f1737]) ).
fof(f1737,plain,
! [X0,X1,X2,X3] :
( ( c_member(X3,X2,c_Relation_ORange(X1,X3,X0))
| ! [X4] : ~ c_member(tc_prod(X1,X3),c_Product__Type_OPair(X1,X3,X4,X2),X0) )
& ( ? [X4] : c_member(tc_prod(X1,X3),c_Product__Type_OPair(X1,X3,X4,X2),X0)
| ~ c_member(X3,X2,c_Relation_ORange(X1,X3,X0)) ) ),
inference(nnf_transformation,[],[f925]) ).
fof(f925,plain,
! [X0,X1,X2,X3] :
( c_member(X3,X2,c_Relation_ORange(X1,X3,X0))
<=> ? [X4] : c_member(tc_prod(X1,X3),c_Product__Type_OPair(X1,X3,X4,X2),X0) ),
inference(rectify,[],[f33]) ).
fof(f33,axiom,
! [X3,X15,X9,X4] :
( c_member(X4,X9,c_Relation_ORange(X15,X4,X3))
<=> ? [X5] : c_member(tc_prod(X15,X4),c_Product__Type_OPair(X15,X4,X5,X9),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Range__iff) ).
fof(f8087,plain,
spl104_439,
inference(avatar_split_clause,[],[f2390,f8085]) ).
fof(f2390,plain,
! [X2,X3,X0,X1] :
( c_member(tc_prod(X3,X1),c_Product__Type_OPair(X3,X1,X2,sK59(X0,X1,X2,X3)),X0)
| ~ c_member(X3,X2,c_Relation_ODomain(X3,X1,X0)) ),
inference(cnf_transformation,[],[f1718]) ).
fof(f1718,plain,
! [X0,X1,X2,X3] :
( c_member(tc_prod(X3,X1),c_Product__Type_OPair(X3,X1,X2,sK59(X0,X1,X2,X3)),X0)
| ~ c_member(X3,X2,c_Relation_ODomain(X3,X1,X0)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK59])],[f1386,f1717]) ).
fof(f1717,plain,
! [X0,X1,X2,X3] :
( ? [X4] : c_member(tc_prod(X3,X1),c_Product__Type_OPair(X3,X1,X2,X4),X0)
=> c_member(tc_prod(X3,X1),c_Product__Type_OPair(X3,X1,X2,sK59(X0,X1,X2,X3)),X0) ),
introduced(choice_axiom,[]) ).
fof(f1386,plain,
! [X0,X1,X2,X3] :
( ? [X4] : c_member(tc_prod(X3,X1),c_Product__Type_OPair(X3,X1,X2,X4),X0)
| ~ c_member(X3,X2,c_Relation_ODomain(X3,X1,X0)) ),
inference(ennf_transformation,[],[f896]) ).
fof(f896,plain,
! [X0,X1,X2,X3] :
( c_member(X3,X2,c_Relation_ODomain(X3,X1,X0))
=> ~ ! [X4] : ~ c_member(tc_prod(X3,X1),c_Product__Type_OPair(X3,X1,X2,X4),X0) ),
inference(rectify,[],[f37]) ).
fof(f37,axiom,
! [X3,X15,X9,X4] :
( c_member(X4,X9,c_Relation_ODomain(X4,X15,X3))
=> ~ ! [X5] : ~ c_member(tc_prod(X4,X15),c_Product__Type_OPair(X4,X15,X9,X5),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_DomainE) ).
fof(f8083,plain,
spl104_438,
inference(avatar_split_clause,[],[f2389,f8081]) ).
fof(f2389,plain,
! [X2,X3,X0,X1] :
( c_member(tc_prod(X1,X3),c_Product__Type_OPair(X1,X3,sK58(X0,X1,X2,X3),X2),X0)
| ~ c_member(X3,X2,c_Relation_ORange(X1,X3,X0)) ),
inference(cnf_transformation,[],[f1716]) ).
fof(f1716,plain,
! [X0,X1,X2,X3] :
( c_member(tc_prod(X1,X3),c_Product__Type_OPair(X1,X3,sK58(X0,X1,X2,X3),X2),X0)
| ~ c_member(X3,X2,c_Relation_ORange(X1,X3,X0)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK58])],[f1385,f1715]) ).
fof(f1715,plain,
! [X0,X1,X2,X3] :
( ? [X4] : c_member(tc_prod(X1,X3),c_Product__Type_OPair(X1,X3,X4,X2),X0)
=> c_member(tc_prod(X1,X3),c_Product__Type_OPair(X1,X3,sK58(X0,X1,X2,X3),X2),X0) ),
introduced(choice_axiom,[]) ).
fof(f1385,plain,
! [X0,X1,X2,X3] :
( ? [X4] : c_member(tc_prod(X1,X3),c_Product__Type_OPair(X1,X3,X4,X2),X0)
| ~ c_member(X3,X2,c_Relation_ORange(X1,X3,X0)) ),
inference(ennf_transformation,[],[f895]) ).
fof(f895,plain,
! [X0,X1,X2,X3] :
( c_member(X3,X2,c_Relation_ORange(X1,X3,X0))
=> ~ ! [X4] : ~ c_member(tc_prod(X1,X3),c_Product__Type_OPair(X1,X3,X4,X2),X0) ),
inference(rectify,[],[f36]) ).
fof(f36,axiom,
! [X3,X15,X8,X4] :
( c_member(X4,X8,c_Relation_ORange(X15,X4,X3))
=> ~ ! [X2] : ~ c_member(tc_prod(X15,X4),c_Product__Type_OPair(X15,X4,X2,X8),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_RangeE) ).
fof(f8079,plain,
spl104_437,
inference(avatar_split_clause,[],[f2192,f8077]) ).
fof(f8077,plain,
( spl104_437
<=> ! [X2,X0,X1] :
( c_Product__Type_OPair(X2,X2,sK41(X0,X1,X2),sK41(X0,X1,X2)) = X1
| ~ c_member(tc_prod(X2,X2),X1,c_Relation_OId__on(X2,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_437])]) ).
fof(f2192,plain,
! [X2,X0,X1] :
( c_Product__Type_OPair(X2,X2,sK41(X0,X1,X2),sK41(X0,X1,X2)) = X1
| ~ c_member(tc_prod(X2,X2),X1,c_Relation_OId__on(X2,X0)) ),
inference(cnf_transformation,[],[f1645]) ).
fof(f1645,plain,
! [X0,X1,X2] :
( ( c_Product__Type_OPair(X2,X2,sK41(X0,X1,X2),sK41(X0,X1,X2)) = X1
& c_member(X2,sK41(X0,X1,X2),X0) )
| ~ c_member(tc_prod(X2,X2),X1,c_Relation_OId__on(X2,X0)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK41])],[f1222,f1644]) ).
fof(f1644,plain,
! [X0,X1,X2] :
( ? [X3] :
( c_Product__Type_OPair(X2,X2,X3,X3) = X1
& c_member(X2,X3,X0) )
=> ( c_Product__Type_OPair(X2,X2,sK41(X0,X1,X2),sK41(X0,X1,X2)) = X1
& c_member(X2,sK41(X0,X1,X2),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f1222,plain,
! [X0,X1,X2] :
( ? [X3] :
( c_Product__Type_OPair(X2,X2,X3,X3) = X1
& c_member(X2,X3,X0) )
| ~ c_member(tc_prod(X2,X2),X1,c_Relation_OId__on(X2,X0)) ),
inference(ennf_transformation,[],[f762]) ).
fof(f762,plain,
! [X0,X1,X2] :
( c_member(tc_prod(X2,X2),X1,c_Relation_OId__on(X2,X0))
=> ~ ! [X3] :
( c_member(X2,X3,X0)
=> c_Product__Type_OPair(X2,X2,X3,X3) != X1 ) ),
inference(rectify,[],[f35]) ).
fof(f35,axiom,
! [X11,X7,X4] :
( c_member(tc_prod(X4,X4),X7,c_Relation_OId__on(X4,X11))
=> ~ ! [X2] :
( c_member(X4,X2,X11)
=> c_Product__Type_OPair(X4,X4,X2,X2) != X7 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Id__onE) ).
fof(f8018,plain,
( spl104_436
| ~ spl104_198
| ~ spl104_427
| ~ spl104_435 ),
inference(avatar_split_clause,[],[f8009,f8006,f7584,f4040,f8016]) ).
fof(f8016,plain,
( spl104_436
<=> ! [X2,X0,X1] :
( c_Groups_Ominus__class_Ominus(tc_fun(X2,tc_HOL_Obool),X0,c_Set_Oinsert(X2,X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)))) = X0
| c_member(X2,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_436])]) ).
fof(f4040,plain,
( spl104_198
<=> ! [X2,X0,X1,X3] : c_member(X0,X1,c_Set_Oinsert(X2,X1,X3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_198])]) ).
fof(f7584,plain,
( spl104_427
<=> ! [X0,X3,X2,X1] :
( c_Groups_Ominus__class_Ominus(tc_fun(X3,tc_HOL_Obool),c_Set_Oinsert(X3,X2,X0),X1) = c_Groups_Ominus__class_Ominus(tc_fun(X3,tc_HOL_Obool),X0,X1)
| ~ c_member(X3,X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_427])]) ).
fof(f8006,plain,
( spl104_435
<=> ! [X2,X0,X1] :
( c_Groups_Ominus__class_Ominus(tc_fun(X2,tc_HOL_Obool),c_Set_Oinsert(X2,X1,X0),c_Set_Oinsert(X2,X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)))) = X0
| c_member(X2,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_435])]) ).
fof(f8009,plain,
( ! [X2,X0,X1] :
( c_Groups_Ominus__class_Ominus(tc_fun(X2,tc_HOL_Obool),X0,c_Set_Oinsert(X2,X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)))) = X0
| c_member(X2,X1,X0) )
| ~ spl104_198
| ~ spl104_427
| ~ spl104_435 ),
inference(forward_demodulation,[],[f8007,f7778]) ).
fof(f7778,plain,
( ! [X2,X3,X0,X1,X4] : c_Groups_Ominus__class_Ominus(tc_fun(X0,tc_HOL_Obool),c_Set_Oinsert(X0,X1,X2),c_Set_Oinsert(X3,X1,X4)) = c_Groups_Ominus__class_Ominus(tc_fun(X0,tc_HOL_Obool),X2,c_Set_Oinsert(X3,X1,X4))
| ~ spl104_198
| ~ spl104_427 ),
inference(resolution,[],[f7585,f4041]) ).
fof(f4041,plain,
( ! [X2,X3,X0,X1] : c_member(X0,X1,c_Set_Oinsert(X2,X1,X3))
| ~ spl104_198 ),
inference(avatar_component_clause,[],[f4040]) ).
fof(f7585,plain,
( ! [X2,X3,X0,X1] :
( ~ c_member(X3,X2,X1)
| c_Groups_Ominus__class_Ominus(tc_fun(X3,tc_HOL_Obool),c_Set_Oinsert(X3,X2,X0),X1) = c_Groups_Ominus__class_Ominus(tc_fun(X3,tc_HOL_Obool),X0,X1) )
| ~ spl104_427 ),
inference(avatar_component_clause,[],[f7584]) ).
fof(f8007,plain,
( ! [X2,X0,X1] :
( c_Groups_Ominus__class_Ominus(tc_fun(X2,tc_HOL_Obool),c_Set_Oinsert(X2,X1,X0),c_Set_Oinsert(X2,X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)))) = X0
| c_member(X2,X1,X0) )
| ~ spl104_435 ),
inference(avatar_component_clause,[],[f8006]) ).
fof(f8008,plain,
spl104_435,
inference(avatar_split_clause,[],[f2156,f8006]) ).
fof(f2156,plain,
! [X2,X0,X1] :
( c_Groups_Ominus__class_Ominus(tc_fun(X2,tc_HOL_Obool),c_Set_Oinsert(X2,X1,X0),c_Set_Oinsert(X2,X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)))) = X0
| c_member(X2,X1,X0) ),
inference(cnf_transformation,[],[f1181]) ).
fof(f1181,plain,
! [X0,X1,X2] :
( c_Groups_Ominus__class_Ominus(tc_fun(X2,tc_HOL_Obool),c_Set_Oinsert(X2,X1,X0),c_Set_Oinsert(X2,X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)))) = X0
| c_member(X2,X1,X0) ),
inference(ennf_transformation,[],[f732]) ).
fof(f732,plain,
! [X0,X1,X2] :
( ~ c_member(X2,X1,X0)
=> c_Groups_Ominus__class_Ominus(tc_fun(X2,tc_HOL_Obool),c_Set_Oinsert(X2,X1,X0),c_Set_Oinsert(X2,X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)))) = X0 ),
inference(rectify,[],[f445]) ).
fof(f445,axiom,
! [X11,X13,X4] :
( ~ c_member(X4,X13,X11)
=> c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool),c_Set_Oinsert(X4,X13,X11),c_Set_Oinsert(X4,X13,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))) = X11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Diff__insert__absorb) ).
fof(f7620,plain,
spl104_434,
inference(avatar_split_clause,[],[f2648,f7618]) ).
fof(f2648,plain,
! [X2,X0,X1] : c_member(tc_prod(X2,X2),c_Product__Type_OPair(X2,X2,X1,X1),c_Transitive__Closure_Otrancl(X2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),X0,c_Relation_OId(X2)))),
inference(definition_unfolding,[],[f2056,f1949]) ).
fof(f2056,plain,
! [X2,X0,X1] : c_member(tc_prod(X2,X2),c_Product__Type_OPair(X2,X2,X1,X1),c_Transitive__Closure_Ortrancl(X2,X0)),
inference(cnf_transformation,[],[f654]) ).
fof(f654,plain,
! [X0,X1,X2] : c_member(tc_prod(X2,X2),c_Product__Type_OPair(X2,X2,X1,X1),c_Transitive__Closure_Ortrancl(X2,X0)),
inference(rectify,[],[f59]) ).
fof(f59,axiom,
! [X3,X9,X4] : c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X9,X9),c_Transitive__Closure_Ortrancl(X4,X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl_Ortrancl__refl) ).
fof(f7616,plain,
spl104_433,
inference(avatar_split_clause,[],[f2592,f7614]) ).
fof(f7614,plain,
( spl104_433
<=> ! [X2,X3,X4,X0,X5,X1] :
( hAPP(hAPP(X2,sK88(X0,X1,X2,X3,X4,X5)),X1) = X0
| ~ c_Recdef_Owfrec__rel(X5,X4,X3,X2,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_433])]) ).
fof(f2592,plain,
! [X2,X3,X0,X1,X4,X5] :
( hAPP(hAPP(X2,sK88(X0,X1,X2,X3,X4,X5)),X1) = X0
| ~ c_Recdef_Owfrec__rel(X5,X4,X3,X2,X1,X0) ),
inference(cnf_transformation,[],[f1824]) ).
fof(f7612,plain,
spl104_432,
inference(avatar_split_clause,[],[f2581,f7610]) ).
fof(f7610,plain,
( spl104_432
<=> ! [X2,X4,X0,X5,X3,X1] :
( hBOOL(hAPP(hAPP(X0,X4),X3))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_fun(X1,tc_HOL_Obool)),X5,X0)
| ~ hBOOL(hAPP(hAPP(X5,X4),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_432])]) ).
fof(f2581,plain,
! [X2,X3,X0,X1,X4,X5] :
( hBOOL(hAPP(hAPP(X0,X4),X3))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_fun(X1,tc_HOL_Obool)),X5,X0)
| ~ hBOOL(hAPP(hAPP(X5,X4),X3)) ),
inference(cnf_transformation,[],[f1498]) ).
fof(f1498,plain,
! [X0,X1,X2,X3,X4,X5] :
( hBOOL(hAPP(hAPP(X0,X4),X3))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_fun(X1,tc_HOL_Obool)),X5,X0)
| ~ hBOOL(hAPP(hAPP(X5,X4),X3)) ),
inference(flattening,[],[f1497]) ).
fof(f1497,plain,
! [X0,X1,X2,X3,X4,X5] :
( hBOOL(hAPP(hAPP(X0,X4),X3))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_fun(X1,tc_HOL_Obool)),X5,X0)
| ~ hBOOL(hAPP(hAPP(X5,X4),X3)) ),
inference(ennf_transformation,[],[f995]) ).
fof(f995,plain,
! [X0,X1,X2,X3,X4,X5] :
( hBOOL(hAPP(hAPP(X5,X4),X3))
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_fun(X1,tc_HOL_Obool)),X5,X0)
=> hBOOL(hAPP(hAPP(X0,X4),X3)) ) ),
inference(rectify,[],[f358]) ).
fof(f358,axiom,
! [X55,X15,X4,X12,X13,X17] :
( hBOOL(hAPP(hAPP(X17,X13),X12))
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_fun(X15,tc_HOL_Obool)),X17,X55)
=> hBOOL(hAPP(hAPP(X55,X13),X12)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rev__predicate2D) ).
fof(f7602,plain,
spl104_431,
inference(avatar_split_clause,[],[f2518,f7600]) ).
fof(f7600,plain,
( spl104_431
<=> ! [X4,X0,X3,X2,X1] :
( c_Orderings_Oord__class_Oless__eq(X4,c_Lattices_Osemilattice__sup__class_Osup(X4,X3,X1),c_Lattices_Osemilattice__sup__class_Osup(X4,X2,X0))
| ~ c_Orderings_Oord__class_Oless__eq(X4,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(X4,X3,X2)
| ~ class_Lattices_Osemilattice__sup(X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_431])]) ).
fof(f2518,plain,
! [X2,X3,X0,X1,X4] :
( c_Orderings_Oord__class_Oless__eq(X4,c_Lattices_Osemilattice__sup__class_Osup(X4,X3,X1),c_Lattices_Osemilattice__sup__class_Osup(X4,X2,X0))
| ~ c_Orderings_Oord__class_Oless__eq(X4,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(X4,X3,X2)
| ~ class_Lattices_Osemilattice__sup(X4) ),
inference(cnf_transformation,[],[f1438]) ).
fof(f1438,plain,
! [X0,X1,X2,X3,X4] :
( c_Orderings_Oord__class_Oless__eq(X4,c_Lattices_Osemilattice__sup__class_Osup(X4,X3,X1),c_Lattices_Osemilattice__sup__class_Osup(X4,X2,X0))
| ~ c_Orderings_Oord__class_Oless__eq(X4,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(X4,X3,X2)
| ~ class_Lattices_Osemilattice__sup(X4) ),
inference(flattening,[],[f1437]) ).
fof(f1437,plain,
! [X0,X1,X2,X3,X4] :
( c_Orderings_Oord__class_Oless__eq(X4,c_Lattices_Osemilattice__sup__class_Osup(X4,X3,X1),c_Lattices_Osemilattice__sup__class_Osup(X4,X2,X0))
| ~ c_Orderings_Oord__class_Oless__eq(X4,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(X4,X3,X2)
| ~ class_Lattices_Osemilattice__sup(X4) ),
inference(ennf_transformation,[],[f953]) ).
fof(f953,plain,
! [X0,X1,X2,X3,X4] :
( class_Lattices_Osemilattice__sup(X4)
=> ( c_Orderings_Oord__class_Oless__eq(X4,X3,X2)
=> ( c_Orderings_Oord__class_Oless__eq(X4,X1,X0)
=> c_Orderings_Oord__class_Oless__eq(X4,c_Lattices_Osemilattice__sup__class_Osup(X4,X3,X1),c_Lattices_Osemilattice__sup__class_Osup(X4,X2,X0)) ) ) ),
inference(rectify,[],[f247]) ).
fof(f247,axiom,
! [X66,X26,X60,X27,X4] :
( class_Lattices_Osemilattice__sup(X4)
=> ( c_Orderings_Oord__class_Oless__eq(X4,X27,X60)
=> ( c_Orderings_Oord__class_Oless__eq(X4,X26,X66)
=> c_Orderings_Oord__class_Oless__eq(X4,c_Lattices_Osemilattice__sup__class_Osup(X4,X27,X26),c_Lattices_Osemilattice__sup__class_Osup(X4,X60,X66)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup__mono) ).
fof(f7598,plain,
spl104_430,
inference(avatar_split_clause,[],[f2392,f7596]) ).
fof(f7596,plain,
( spl104_430
<=> ! [X0,X3,X2,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),c_Relation_ODomain(X3,X2,X1),c_Relation_ODomain(X3,X2,X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X3,X2),tc_HOL_Obool),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_430])]) ).
fof(f2392,plain,
! [X2,X3,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),c_Relation_ODomain(X3,X2,X1),c_Relation_ODomain(X3,X2,X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X3,X2),tc_HOL_Obool),X1,X0) ),
inference(cnf_transformation,[],[f1389]) ).
fof(f1389,plain,
! [X0,X1,X2,X3] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),c_Relation_ODomain(X3,X2,X1),c_Relation_ODomain(X3,X2,X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X3,X2),tc_HOL_Obool),X1,X0) ),
inference(ennf_transformation,[],[f898]) ).
fof(f898,plain,
! [X0,X1,X2,X3] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X3,X2),tc_HOL_Obool),X1,X0)
=> c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),c_Relation_ODomain(X3,X2,X1),c_Relation_ODomain(X3,X2,X0)) ),
inference(rectify,[],[f233]) ).
fof(f233,axiom,
! [X30,X3,X15,X4] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X4,X15),tc_HOL_Obool),X3,X30)
=> c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool),c_Relation_ODomain(X4,X15,X3),c_Relation_ODomain(X4,X15,X30)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Domain__mono) ).
fof(f7594,plain,
spl104_429,
inference(avatar_split_clause,[],[f2340,f7592]) ).
fof(f7592,plain,
( spl104_429
<=> ! [X0,X3,X2,X1] :
( X0 = X1
| c_Set_Oinsert(X3,X2,X0) != c_Set_Oinsert(X3,X2,X1)
| c_member(X3,X2,X0)
| c_member(X3,X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_429])]) ).
fof(f2340,plain,
! [X2,X3,X0,X1] :
( X0 = X1
| c_Set_Oinsert(X3,X2,X0) != c_Set_Oinsert(X3,X2,X1)
| c_member(X3,X2,X0)
| c_member(X3,X2,X1) ),
inference(cnf_transformation,[],[f1704]) ).
fof(f1704,plain,
! [X0,X1,X2,X3] :
( ( ( c_Set_Oinsert(X3,X2,X0) = c_Set_Oinsert(X3,X2,X1)
| X0 != X1 )
& ( X0 = X1
| c_Set_Oinsert(X3,X2,X0) != c_Set_Oinsert(X3,X2,X1) ) )
| c_member(X3,X2,X0)
| c_member(X3,X2,X1) ),
inference(nnf_transformation,[],[f1318]) ).
fof(f1318,plain,
! [X0,X1,X2,X3] :
( ( c_Set_Oinsert(X3,X2,X0) = c_Set_Oinsert(X3,X2,X1)
<=> X0 = X1 )
| c_member(X3,X2,X0)
| c_member(X3,X2,X1) ),
inference(flattening,[],[f1317]) ).
fof(f1317,plain,
! [X0,X1,X2,X3] :
( ( c_Set_Oinsert(X3,X2,X0) = c_Set_Oinsert(X3,X2,X1)
<=> X0 = X1 )
| c_member(X3,X2,X0)
| c_member(X3,X2,X1) ),
inference(ennf_transformation,[],[f854]) ).
fof(f854,plain,
! [X0,X1,X2,X3] :
( ~ c_member(X3,X2,X1)
=> ( ~ c_member(X3,X2,X0)
=> ( c_Set_Oinsert(X3,X2,X0) = c_Set_Oinsert(X3,X2,X1)
<=> X0 = X1 ) ) ),
inference(rectify,[],[f143]) ).
fof(f143,axiom,
! [X10,X11,X13,X4] :
( ~ c_member(X4,X13,X11)
=> ( ~ c_member(X4,X13,X10)
=> ( c_Set_Oinsert(X4,X13,X11) = c_Set_Oinsert(X4,X13,X10)
<=> X10 = X11 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__ident) ).
fof(f7590,plain,
spl104_428,
inference(avatar_split_clause,[],[f2291,f7588]) ).
fof(f7588,plain,
( spl104_428
<=> ! [X0,X3,X2,X1] :
( c_Orderings_Oord__class_Oless(tc_fun(X2,X3),X1,X0)
| c_Orderings_Oord__class_Oless__eq(tc_fun(X2,X3),X0,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X2,X3),X1,X0)
| ~ class_Orderings_Oord(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_428])]) ).
fof(f2291,plain,
! [X2,X3,X0,X1] :
( c_Orderings_Oord__class_Oless(tc_fun(X2,X3),X1,X0)
| c_Orderings_Oord__class_Oless__eq(tc_fun(X2,X3),X0,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X2,X3),X1,X0)
| ~ class_Orderings_Oord(X3) ),
inference(cnf_transformation,[],[f1695]) ).
fof(f1695,plain,
! [X0,X1,X2,X3] :
( ( ( c_Orderings_Oord__class_Oless(tc_fun(X2,X3),X1,X0)
| c_Orderings_Oord__class_Oless__eq(tc_fun(X2,X3),X0,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X2,X3),X1,X0) )
& ( ( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X2,X3),X0,X1)
& c_Orderings_Oord__class_Oless__eq(tc_fun(X2,X3),X1,X0) )
| ~ c_Orderings_Oord__class_Oless(tc_fun(X2,X3),X1,X0) ) )
| ~ class_Orderings_Oord(X3) ),
inference(flattening,[],[f1694]) ).
fof(f1694,plain,
! [X0,X1,X2,X3] :
( ( ( c_Orderings_Oord__class_Oless(tc_fun(X2,X3),X1,X0)
| c_Orderings_Oord__class_Oless__eq(tc_fun(X2,X3),X0,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X2,X3),X1,X0) )
& ( ( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X2,X3),X0,X1)
& c_Orderings_Oord__class_Oless__eq(tc_fun(X2,X3),X1,X0) )
| ~ c_Orderings_Oord__class_Oless(tc_fun(X2,X3),X1,X0) ) )
| ~ class_Orderings_Oord(X3) ),
inference(nnf_transformation,[],[f1250]) ).
fof(f1250,plain,
! [X0,X1,X2,X3] :
( ( c_Orderings_Oord__class_Oless(tc_fun(X2,X3),X1,X0)
<=> ( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X2,X3),X0,X1)
& c_Orderings_Oord__class_Oless__eq(tc_fun(X2,X3),X1,X0) ) )
| ~ class_Orderings_Oord(X3) ),
inference(ennf_transformation,[],[f814]) ).
fof(f814,plain,
! [X0,X1,X2,X3] :
( class_Orderings_Oord(X3)
=> ( c_Orderings_Oord__class_Oless(tc_fun(X2,X3),X1,X0)
<=> ( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X2,X3),X0,X1)
& c_Orderings_Oord__class_Oless__eq(tc_fun(X2,X3),X1,X0) ) ) ),
inference(rectify,[],[f293]) ).
fof(f293,axiom,
! [X0,X1,X4,X15] :
( class_Orderings_Oord(X15)
=> ( c_Orderings_Oord__class_Oless(tc_fun(X4,X15),X1,X0)
<=> ( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X4,X15),X0,X1)
& c_Orderings_Oord__class_Oless__eq(tc_fun(X4,X15),X1,X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__fun__def) ).
fof(f7586,plain,
spl104_427,
inference(avatar_split_clause,[],[f2281,f7584]) ).
fof(f2281,plain,
! [X2,X3,X0,X1] :
( c_Groups_Ominus__class_Ominus(tc_fun(X3,tc_HOL_Obool),c_Set_Oinsert(X3,X2,X0),X1) = c_Groups_Ominus__class_Ominus(tc_fun(X3,tc_HOL_Obool),X0,X1)
| ~ c_member(X3,X2,X1) ),
inference(cnf_transformation,[],[f1239]) ).
fof(f7582,plain,
spl104_426,
inference(avatar_split_clause,[],[f2234,f7580]) ).
fof(f7580,plain,
( spl104_426
<=> ! [X2,X0,X1] :
( c_Relation_Osingle__valued(X2,X1,X0)
| c_member(tc_prod(X2,X1),c_Product__Type_OPair(X2,X1,sK48(X0,X1,X2),sK50(X0,X1,X2)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_426])]) ).
fof(f2234,plain,
! [X2,X0,X1] :
( c_Relation_Osingle__valued(X2,X1,X0)
| c_member(tc_prod(X2,X1),c_Product__Type_OPair(X2,X1,sK48(X0,X1,X2),sK50(X0,X1,X2)),X0) ),
inference(cnf_transformation,[],[f1670]) ).
fof(f7578,plain,
spl104_425,
inference(avatar_split_clause,[],[f2233,f7576]) ).
fof(f7576,plain,
( spl104_425
<=> ! [X2,X0,X1] :
( c_Relation_Osingle__valued(X2,X1,X0)
| c_member(tc_prod(X2,X1),c_Product__Type_OPair(X2,X1,sK48(X0,X1,X2),sK49(X0,X1,X2)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_425])]) ).
fof(f2233,plain,
! [X2,X0,X1] :
( c_Relation_Osingle__valued(X2,X1,X0)
| c_member(tc_prod(X2,X1),c_Product__Type_OPair(X2,X1,sK48(X0,X1,X2),sK49(X0,X1,X2)),X0) ),
inference(cnf_transformation,[],[f1670]) ).
fof(f7574,plain,
spl104_424,
inference(avatar_split_clause,[],[f2222,f7572]) ).
fof(f7572,plain,
( spl104_424
<=> ! [X2,X0,X1] :
( c_Relation_Ototal__on(X2,X1,X0)
| ~ c_member(tc_prod(X2,X2),c_Product__Type_OPair(X2,X2,sK47(X0,X1,X2),sK46(X0,X1,X2)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_424])]) ).
fof(f2222,plain,
! [X2,X0,X1] :
( c_Relation_Ototal__on(X2,X1,X0)
| ~ c_member(tc_prod(X2,X2),c_Product__Type_OPair(X2,X2,sK47(X0,X1,X2),sK46(X0,X1,X2)),X0) ),
inference(cnf_transformation,[],[f1659]) ).
fof(f7570,plain,
spl104_423,
inference(avatar_split_clause,[],[f2221,f7568]) ).
fof(f2221,plain,
! [X2,X0,X1] :
( c_Relation_Ototal__on(X2,X1,X0)
| ~ c_member(tc_prod(X2,X2),c_Product__Type_OPair(X2,X2,sK46(X0,X1,X2),sK47(X0,X1,X2)),X0) ),
inference(cnf_transformation,[],[f1659]) ).
fof(f7566,plain,
spl104_422,
inference(avatar_split_clause,[],[f2207,f7564]) ).
fof(f7564,plain,
( spl104_422
<=> ! [X2,X0,X1] :
( c_Relation_Osingle__valued(X2,X1,X0)
| c_member(tc_prod(X2,X1),c_Product__Type_OPair(X2,X1,sK43(X0,X1,X2),sK45(X0,X1,X2)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_422])]) ).
fof(f2207,plain,
! [X2,X0,X1] :
( c_Relation_Osingle__valued(X2,X1,X0)
| c_member(tc_prod(X2,X1),c_Product__Type_OPair(X2,X1,sK43(X0,X1,X2),sK45(X0,X1,X2)),X0) ),
inference(cnf_transformation,[],[f1652]) ).
fof(f1652,plain,
! [X0,X1,X2] :
( c_Relation_Osingle__valued(X2,X1,X0)
| ( sK44(X0,X1,X2) != sK45(X0,X1,X2)
& c_member(tc_prod(X2,X1),c_Product__Type_OPair(X2,X1,sK43(X0,X1,X2),sK45(X0,X1,X2)),X0)
& c_member(tc_prod(X2,X1),c_Product__Type_OPair(X2,X1,sK43(X0,X1,X2),sK44(X0,X1,X2)),X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK43,sK44,sK45])],[f1232,f1651,f1650]) ).
fof(f1650,plain,
! [X0,X1,X2] :
( ? [X3,X4] :
( ? [X5] :
( X4 != X5
& c_member(tc_prod(X2,X1),c_Product__Type_OPair(X2,X1,X3,X5),X0) )
& c_member(tc_prod(X2,X1),c_Product__Type_OPair(X2,X1,X3,X4),X0) )
=> ( ? [X5] :
( sK44(X0,X1,X2) != X5
& c_member(tc_prod(X2,X1),c_Product__Type_OPair(X2,X1,sK43(X0,X1,X2),X5),X0) )
& c_member(tc_prod(X2,X1),c_Product__Type_OPair(X2,X1,sK43(X0,X1,X2),sK44(X0,X1,X2)),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f1651,plain,
! [X0,X1,X2] :
( ? [X5] :
( sK44(X0,X1,X2) != X5
& c_member(tc_prod(X2,X1),c_Product__Type_OPair(X2,X1,sK43(X0,X1,X2),X5),X0) )
=> ( sK44(X0,X1,X2) != sK45(X0,X1,X2)
& c_member(tc_prod(X2,X1),c_Product__Type_OPair(X2,X1,sK43(X0,X1,X2),sK45(X0,X1,X2)),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f1232,plain,
! [X0,X1,X2] :
( c_Relation_Osingle__valued(X2,X1,X0)
| ? [X3,X4] :
( ? [X5] :
( X4 != X5
& c_member(tc_prod(X2,X1),c_Product__Type_OPair(X2,X1,X3,X5),X0) )
& c_member(tc_prod(X2,X1),c_Product__Type_OPair(X2,X1,X3,X4),X0) ) ),
inference(ennf_transformation,[],[f770]) ).
fof(f770,plain,
! [X0,X1,X2] :
( ! [X3,X4] :
( c_member(tc_prod(X2,X1),c_Product__Type_OPair(X2,X1,X3,X4),X0)
=> ! [X5] :
( c_member(tc_prod(X2,X1),c_Product__Type_OPair(X2,X1,X3,X5),X0)
=> X4 = X5 ) )
=> c_Relation_Osingle__valued(X2,X1,X0) ),
inference(rectify,[],[f67]) ).
fof(f67,axiom,
! [X3,X15,X4] :
( ! [X2,X5] :
( c_member(tc_prod(X4,X15),c_Product__Type_OPair(X4,X15,X2,X5),X3)
=> ! [X6] :
( c_member(tc_prod(X4,X15),c_Product__Type_OPair(X4,X15,X2,X6),X3)
=> X5 = X6 ) )
=> c_Relation_Osingle__valued(X4,X15,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_single__valuedI) ).
fof(f7562,plain,
( spl104_421
| ~ spl104_85
| ~ spl104_417 ),
inference(avatar_split_clause,[],[f7468,f7292,f3254,f7559]) ).
fof(f7292,plain,
( spl104_417
<=> c_Relation_Otrans(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_417])]) ).
fof(f7468,plain,
( c_FunDef_Opair__less = c_Transitive__Closure_Otrancl(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less)
| ~ spl104_85
| ~ spl104_417 ),
inference(resolution,[],[f7294,f3255]) ).
fof(f7294,plain,
( c_Relation_Otrans(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less)
| ~ spl104_417 ),
inference(avatar_component_clause,[],[f7292]) ).
fof(f7557,plain,
spl104_420,
inference(avatar_split_clause,[],[f2206,f7555]) ).
fof(f2206,plain,
! [X2,X0,X1] :
( c_Relation_Osingle__valued(X2,X1,X0)
| c_member(tc_prod(X2,X1),c_Product__Type_OPair(X2,X1,sK43(X0,X1,X2),sK44(X0,X1,X2)),X0) ),
inference(cnf_transformation,[],[f1652]) ).
fof(f7553,plain,
spl104_419,
inference(avatar_split_clause,[],[f2164,f7551]) ).
fof(f7551,plain,
( spl104_419
<=> ! [X2,X0,X1] :
( X0 = X1
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X2) != c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_419])]) ).
fof(f2164,plain,
! [X2,X0,X1] :
( X0 = X1
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X2) != c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
inference(cnf_transformation,[],[f1638]) ).
fof(f1638,plain,
! [X0,X1,X2] :
( ( ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X2) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2)
| X0 != X1 )
& ( X0 = X1
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X2) != c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2) ) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
inference(nnf_transformation,[],[f1194]) ).
fof(f1194,plain,
! [X0,X1,X2] :
( ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X2) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2)
<=> X0 = X1 )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
inference(flattening,[],[f1193]) ).
fof(f1193,plain,
! [X0,X1,X2] :
( ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X2) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2)
<=> X0 = X1 )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
inference(ennf_transformation,[],[f740]) ).
fof(f740,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X0)
=> ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X2) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2)
<=> X0 = X1 ) ) ),
inference(rectify,[],[f382]) ).
fof(f382,axiom,
! [X67,X68,X78] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X78,X68)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X78,X67)
=> ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X68,X78) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X67,X78)
<=> X67 = X68 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__diff__iff) ).
fof(f7549,plain,
spl104_418,
inference(avatar_split_clause,[],[f2065,f7547]) ).
fof(f7547,plain,
( spl104_418
<=> ! [X2,X0,X1] : c_Set_Oinsert(X2,X1,X0) = c_Set_Oinsert(X2,X1,c_Groups_Ominus__class_Ominus(tc_fun(X2,tc_HOL_Obool),X0,c_Set_Oinsert(X2,X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_418])]) ).
fof(f2065,plain,
! [X2,X0,X1] : c_Set_Oinsert(X2,X1,X0) = c_Set_Oinsert(X2,X1,c_Groups_Ominus__class_Ominus(tc_fun(X2,tc_HOL_Obool),X0,c_Set_Oinsert(X2,X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))))),
inference(cnf_transformation,[],[f663]) ).
fof(f663,plain,
! [X0,X1,X2] : c_Set_Oinsert(X2,X1,X0) = c_Set_Oinsert(X2,X1,c_Groups_Ominus__class_Ominus(tc_fun(X2,tc_HOL_Obool),X0,c_Set_Oinsert(X2,X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))))),
inference(rectify,[],[f399]) ).
fof(f399,axiom,
! [X11,X9,X4] : c_Set_Oinsert(X4,X9,X11) = c_Set_Oinsert(X4,X9,c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool),X11,c_Set_Oinsert(X4,X9,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__Diff__single) ).
fof(f7295,plain,
( ~ spl104_20
| spl104_417
| ~ spl104_62
| ~ spl104_298 ),
inference(avatar_split_clause,[],[f5617,f5435,f3156,f7292,f2972]) ).
fof(f2972,plain,
( spl104_20
<=> c_Relation_Otrans(tc_Nat_Onat,c_Wellfounded_Oless__than) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_20])]) ).
fof(f3156,plain,
( spl104_62
<=> c_FunDef_Opair__less = c_Wellfounded_Olex__prod(tc_Nat_Onat,tc_Nat_Onat,c_Wellfounded_Oless__than,c_Wellfounded_Oless__than) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_62])]) ).
fof(f5435,plain,
( spl104_298
<=> ! [X0,X3,X2,X1] :
( c_Relation_Otrans(tc_prod(X3,X1),c_Wellfounded_Olex__prod(X3,X1,X2,X0))
| ~ c_Relation_Otrans(X1,X0)
| ~ c_Relation_Otrans(X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_298])]) ).
fof(f5617,plain,
( c_Relation_Otrans(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less)
| ~ c_Relation_Otrans(tc_Nat_Onat,c_Wellfounded_Oless__than)
| ~ spl104_62
| ~ spl104_298 ),
inference(duplicate_literal_removal,[],[f5616]) ).
fof(f5616,plain,
( c_Relation_Otrans(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less)
| ~ c_Relation_Otrans(tc_Nat_Onat,c_Wellfounded_Oless__than)
| ~ c_Relation_Otrans(tc_Nat_Onat,c_Wellfounded_Oless__than)
| ~ spl104_62
| ~ spl104_298 ),
inference(superposition,[],[f5436,f3158]) ).
fof(f3158,plain,
( c_FunDef_Opair__less = c_Wellfounded_Olex__prod(tc_Nat_Onat,tc_Nat_Onat,c_Wellfounded_Oless__than,c_Wellfounded_Oless__than)
| ~ spl104_62 ),
inference(avatar_component_clause,[],[f3156]) ).
fof(f5436,plain,
( ! [X2,X3,X0,X1] :
( c_Relation_Otrans(tc_prod(X3,X1),c_Wellfounded_Olex__prod(X3,X1,X2,X0))
| ~ c_Relation_Otrans(X1,X0)
| ~ c_Relation_Otrans(X3,X2) )
| ~ spl104_298 ),
inference(avatar_component_clause,[],[f5435]) ).
fof(f7112,plain,
spl104_416,
inference(avatar_split_clause,[],[f2633,f7110]) ).
fof(f7110,plain,
( spl104_416
<=> ! [X0] : c_Relation_OId(X0) = c_Transitive__Closure_Otrancl(X0,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X0,X0),tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X0,X0),tc_HOL_Obool)),c_Relation_OId(X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_416])]) ).
fof(f2633,plain,
! [X0] : c_Relation_OId(X0) = c_Transitive__Closure_Otrancl(X0,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X0,X0),tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X0,X0),tc_HOL_Obool)),c_Relation_OId(X0))),
inference(definition_unfolding,[],[f1905,f1949]) ).
fof(f1905,plain,
! [X0] : c_Relation_OId(X0) = c_Transitive__Closure_Ortrancl(X0,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X0,X0),tc_HOL_Obool))),
inference(cnf_transformation,[],[f535]) ).
fof(f535,plain,
! [X0] : c_Relation_OId(X0) = c_Transitive__Closure_Ortrancl(X0,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X0,X0),tc_HOL_Obool))),
inference(rectify,[],[f442]) ).
fof(f442,axiom,
! [X4] : c_Relation_OId(X4) = c_Transitive__Closure_Ortrancl(X4,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X4,X4),tc_HOL_Obool))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__empty) ).
fof(f7108,plain,
spl104_415,
inference(avatar_split_clause,[],[f2619,f7106]) ).
fof(f7106,plain,
( spl104_415
<=> ! [X2,X6,X4,X0,X3,X5,X1] :
( c_Nitpick_Ofold__graph_H(X6,X5,X4,X3,X2,hAPP(hAPP(X4,X1),X0))
| ~ sP11(X6,X2,X3,X4,X5,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_415])]) ).
fof(f2619,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( c_Nitpick_Ofold__graph_H(X6,X5,X4,X3,X2,hAPP(hAPP(X4,X1),X0))
| ~ sP11(X6,X2,X3,X4,X5,X0,X1) ),
inference(cnf_transformation,[],[f1844]) ).
fof(f7104,plain,
spl104_414,
inference(avatar_split_clause,[],[f2613,f7102]) ).
fof(f2613,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( c_member(X0,sK94(X0,X1,X2,X3,X4,X5,X6),X1)
| ~ sP11(X0,X1,X2,X3,X4,X5,X6) ),
inference(cnf_transformation,[],[f1842]) ).
fof(f7100,plain,
( spl104_413
| ~ spl104_101
| ~ spl104_279 ),
inference(avatar_split_clause,[],[f5345,f4810,f3342,f7098]) ).
fof(f7098,plain,
( spl104_413
<=> ! [X2,X0,X1] : sP6(X0,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),X1,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_413])]) ).
fof(f5345,plain,
( ! [X2,X0,X1] : sP6(X0,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),X1,X2)
| ~ spl104_101
| ~ spl104_279 ),
inference(resolution,[],[f4811,f3343]) ).
fof(f7096,plain,
spl104_412,
inference(avatar_split_clause,[],[f2565,f7094]) ).
fof(f2565,plain,
! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(X4,X3,X2),X1),X0))
| ~ c_member(tc_prod(X4,X3),c_Product__Type_OPair(X4,X3,X1,X0),X2) ),
inference(cnf_transformation,[],[f1812]) ).
fof(f1812,plain,
! [X0,X1,X2,X3,X4] :
( ( hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(X4,X3,X2),X1),X0))
| ~ c_member(tc_prod(X4,X3),c_Product__Type_OPair(X4,X3,X1,X0),X2) )
& ( c_member(tc_prod(X4,X3),c_Product__Type_OPair(X4,X3,X1,X0),X2)
| ~ hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(X4,X3,X2),X1),X0)) ) ),
inference(nnf_transformation,[],[f987]) ).
fof(f987,plain,
! [X0,X1,X2,X3,X4] :
( hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(X4,X3,X2),X1),X0))
<=> c_member(tc_prod(X4,X3),c_Product__Type_OPair(X4,X3,X1,X0),X2) ),
inference(rectify,[],[f5]) ).
fof(f5,axiom,
! [X12,X13,X14,X15,X4] :
( hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(X4,X15,X14),X13),X12))
<=> c_member(tc_prod(X4,X15),c_Product__Type_OPair(X4,X15,X13,X12),X14) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_in__rel__def) ).
fof(f7092,plain,
spl104_411,
inference(avatar_split_clause,[],[f2564,f7090]) ).
fof(f2564,plain,
! [X2,X3,X0,X1,X4] :
( c_member(tc_prod(X4,X3),c_Product__Type_OPair(X4,X3,X1,X0),X2)
| ~ hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(X4,X3,X2),X1),X0)) ),
inference(cnf_transformation,[],[f1812]) ).
fof(f7088,plain,
spl104_410,
inference(avatar_split_clause,[],[f2515,f7086]) ).
fof(f7086,plain,
( spl104_410
<=> ! [X4,X0,X3,X2,X1] :
( hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,X4),X2,X1),X0) = c_Lattices_Osemilattice__sup__class_Osup(X4,hAPP(X2,X0),hAPP(X1,X0))
| ~ class_Lattices_Olattice(X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_410])]) ).
fof(f2515,plain,
! [X2,X3,X0,X1,X4] :
( hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,X4),X2,X1),X0) = c_Lattices_Osemilattice__sup__class_Osup(X4,hAPP(X2,X0),hAPP(X1,X0))
| ~ class_Lattices_Olattice(X4) ),
inference(cnf_transformation,[],[f1432]) ).
fof(f1432,plain,
! [X0,X1,X2,X3,X4] :
( hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,X4),X2,X1),X0) = c_Lattices_Osemilattice__sup__class_Osup(X4,hAPP(X2,X0),hAPP(X1,X0))
| ~ class_Lattices_Olattice(X4) ),
inference(ennf_transformation,[],[f950]) ).
fof(f950,plain,
! [X0,X1,X2,X3,X4] :
( class_Lattices_Olattice(X4)
=> hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,X4),X2,X1),X0) = c_Lattices_Osemilattice__sup__class_Osup(X4,hAPP(X2,X0),hAPP(X1,X0)) ),
inference(rectify,[],[f156]) ).
fof(f156,axiom,
! [X13,X0,X1,X15,X4] :
( class_Lattices_Olattice(X4)
=> hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X15,X4),X1,X0),X13) = c_Lattices_Osemilattice__sup__class_Osup(X4,hAPP(X1,X13),hAPP(X0,X13)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup__apply) ).
fof(f7084,plain,
spl104_409,
inference(avatar_split_clause,[],[f2514,f7082]) ).
fof(f7082,plain,
( spl104_409
<=> ! [X4,X0,X3,X2,X1] :
( hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X3,X4),X2,X1),X0) = c_Groups_Ominus__class_Ominus(X4,hAPP(X2,X0),hAPP(X1,X0))
| ~ class_Groups_Ominus(X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_409])]) ).
fof(f2514,plain,
! [X2,X3,X0,X1,X4] :
( hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X3,X4),X2,X1),X0) = c_Groups_Ominus__class_Ominus(X4,hAPP(X2,X0),hAPP(X1,X0))
| ~ class_Groups_Ominus(X4) ),
inference(cnf_transformation,[],[f1431]) ).
fof(f1431,plain,
! [X0,X1,X2,X3,X4] :
( hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X3,X4),X2,X1),X0) = c_Groups_Ominus__class_Ominus(X4,hAPP(X2,X0),hAPP(X1,X0))
| ~ class_Groups_Ominus(X4) ),
inference(ennf_transformation,[],[f949]) ).
fof(f949,plain,
! [X0,X1,X2,X3,X4] :
( class_Groups_Ominus(X4)
=> hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X3,X4),X2,X1),X0) = c_Groups_Ominus__class_Ominus(X4,hAPP(X2,X0),hAPP(X1,X0)) ),
inference(rectify,[],[f208]) ).
fof(f208,axiom,
! [X13,X10,X11,X15,X4] :
( class_Groups_Ominus(X4)
=> hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X15,X4),X11,X10),X13) = c_Groups_Ominus__class_Ominus(X4,hAPP(X11,X13),hAPP(X10,X13)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__apply) ).
fof(f7080,plain,
spl104_408,
inference(avatar_split_clause,[],[f2501,f7078]) ).
fof(f7078,plain,
( spl104_408
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP(X0,sK73(X0,X1,X2)))
| hBOOL(hAPP(X0,sK74(X0,X2,X3)))
| ~ sP9(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_408])]) ).
fof(f2501,plain,
! [X2,X3,X0,X1] :
( hBOOL(hAPP(X0,sK73(X0,X1,X2)))
| hBOOL(hAPP(X0,sK74(X0,X2,X3)))
| ~ sP9(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f1789]) ).
fof(f1789,plain,
! [X0,X1,X2,X3] :
( ( sP9(X0,X1,X2,X3)
| ( ! [X4] :
( ~ hBOOL(hAPP(X0,X4))
| ~ c_member(X2,X4,X1) )
& ! [X5] :
( ~ hBOOL(hAPP(X0,X5))
| ~ c_member(X2,X5,X3) ) ) )
& ( ( hBOOL(hAPP(X0,sK73(X0,X1,X2)))
& c_member(X2,sK73(X0,X1,X2),X1) )
| ( hBOOL(hAPP(X0,sK74(X0,X2,X3)))
& c_member(X2,sK74(X0,X2,X3),X3) )
| ~ sP9(X0,X1,X2,X3) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK73,sK74])],[f1786,f1788,f1787]) ).
fof(f1787,plain,
! [X0,X1,X2] :
( ? [X6] :
( hBOOL(hAPP(X0,X6))
& c_member(X2,X6,X1) )
=> ( hBOOL(hAPP(X0,sK73(X0,X1,X2)))
& c_member(X2,sK73(X0,X1,X2),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f1788,plain,
! [X0,X2,X3] :
( ? [X7] :
( hBOOL(hAPP(X0,X7))
& c_member(X2,X7,X3) )
=> ( hBOOL(hAPP(X0,sK74(X0,X2,X3)))
& c_member(X2,sK74(X0,X2,X3),X3) ) ),
introduced(choice_axiom,[]) ).
fof(f1786,plain,
! [X0,X1,X2,X3] :
( ( sP9(X0,X1,X2,X3)
| ( ! [X4] :
( ~ hBOOL(hAPP(X0,X4))
| ~ c_member(X2,X4,X1) )
& ! [X5] :
( ~ hBOOL(hAPP(X0,X5))
| ~ c_member(X2,X5,X3) ) ) )
& ( ? [X6] :
( hBOOL(hAPP(X0,X6))
& c_member(X2,X6,X1) )
| ? [X7] :
( hBOOL(hAPP(X0,X7))
& c_member(X2,X7,X3) )
| ~ sP9(X0,X1,X2,X3) ) ),
inference(rectify,[],[f1785]) ).
fof(f1785,plain,
! [X0,X1,X3,X2] :
( ( sP9(X0,X1,X3,X2)
| ( ! [X5] :
( ~ hBOOL(hAPP(X0,X5))
| ~ c_member(X3,X5,X1) )
& ! [X6] :
( ~ hBOOL(hAPP(X0,X6))
| ~ c_member(X3,X6,X2) ) ) )
& ( ? [X5] :
( hBOOL(hAPP(X0,X5))
& c_member(X3,X5,X1) )
| ? [X6] :
( hBOOL(hAPP(X0,X6))
& c_member(X3,X6,X2) )
| ~ sP9(X0,X1,X3,X2) ) ),
inference(flattening,[],[f1784]) ).
fof(f1784,plain,
! [X0,X1,X3,X2] :
( ( sP9(X0,X1,X3,X2)
| ( ! [X5] :
( ~ hBOOL(hAPP(X0,X5))
| ~ c_member(X3,X5,X1) )
& ! [X6] :
( ~ hBOOL(hAPP(X0,X6))
| ~ c_member(X3,X6,X2) ) ) )
& ( ? [X5] :
( hBOOL(hAPP(X0,X5))
& c_member(X3,X5,X1) )
| ? [X6] :
( hBOOL(hAPP(X0,X6))
& c_member(X3,X6,X2) )
| ~ sP9(X0,X1,X3,X2) ) ),
inference(nnf_transformation,[],[f1541]) ).
fof(f1541,plain,
! [X0,X1,X3,X2] :
( sP9(X0,X1,X3,X2)
<=> ( ? [X5] :
( hBOOL(hAPP(X0,X5))
& c_member(X3,X5,X1) )
| ? [X6] :
( hBOOL(hAPP(X0,X6))
& c_member(X3,X6,X2) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP9])]) ).
fof(f7076,plain,
spl104_407,
inference(avatar_split_clause,[],[f2500,f7074]) ).
fof(f7074,plain,
( spl104_407
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP(X0,sK73(X0,X1,X2)))
| c_member(X2,sK74(X0,X2,X3),X3)
| ~ sP9(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_407])]) ).
fof(f2500,plain,
! [X2,X3,X0,X1] :
( hBOOL(hAPP(X0,sK73(X0,X1,X2)))
| c_member(X2,sK74(X0,X2,X3),X3)
| ~ sP9(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f1789]) ).
fof(f7072,plain,
spl104_406,
inference(avatar_split_clause,[],[f2499,f7070]) ).
fof(f7070,plain,
( spl104_406
<=> ! [X0,X3,X2,X1] :
( c_member(X2,sK73(X0,X1,X2),X1)
| hBOOL(hAPP(X0,sK74(X0,X2,X3)))
| ~ sP9(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_406])]) ).
fof(f2499,plain,
! [X2,X3,X0,X1] :
( c_member(X2,sK73(X0,X1,X2),X1)
| hBOOL(hAPP(X0,sK74(X0,X2,X3)))
| ~ sP9(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f1789]) ).
fof(f7068,plain,
spl104_405,
inference(avatar_split_clause,[],[f2498,f7066]) ).
fof(f7066,plain,
( spl104_405
<=> ! [X0,X3,X2,X1] :
( c_member(X2,sK73(X0,X1,X2),X1)
| c_member(X2,sK74(X0,X2,X3),X3)
| ~ sP9(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_405])]) ).
fof(f2498,plain,
! [X2,X3,X0,X1] :
( c_member(X2,sK73(X0,X1,X2),X1)
| c_member(X2,sK74(X0,X2,X3),X3)
| ~ sP9(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f1789]) ).
fof(f7064,plain,
spl104_404,
inference(avatar_split_clause,[],[f2494,f7062]) ).
fof(f7062,plain,
( spl104_404
<=> ! [X0,X3,X2,X1] :
( sP7(X0,X1,X2,X3)
| ~ hBOOL(hAPP(X0,sK70(X0,X1,X2)))
| ~ hBOOL(hAPP(X0,sK71(X0,X2,X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_404])]) ).
fof(f2494,plain,
! [X2,X3,X0,X1] :
( sP7(X0,X1,X2,X3)
| ~ hBOOL(hAPP(X0,sK70(X0,X1,X2)))
| ~ hBOOL(hAPP(X0,sK71(X0,X2,X3))) ),
inference(cnf_transformation,[],[f1779]) ).
fof(f1779,plain,
! [X0,X1,X2,X3] :
( ( sP7(X0,X1,X2,X3)
| ( ~ hBOOL(hAPP(X0,sK70(X0,X1,X2)))
& c_member(X2,sK70(X0,X1,X2),X1) )
| ( ~ hBOOL(hAPP(X0,sK71(X0,X2,X3)))
& c_member(X2,sK71(X0,X2,X3),X3) ) )
& ( ( ! [X6] :
( hBOOL(hAPP(X0,X6))
| ~ c_member(X2,X6,X1) )
& ! [X7] :
( hBOOL(hAPP(X0,X7))
| ~ c_member(X2,X7,X3) ) )
| ~ sP7(X0,X1,X2,X3) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK70,sK71])],[f1776,f1778,f1777]) ).
fof(f1777,plain,
! [X0,X1,X2] :
( ? [X4] :
( ~ hBOOL(hAPP(X0,X4))
& c_member(X2,X4,X1) )
=> ( ~ hBOOL(hAPP(X0,sK70(X0,X1,X2)))
& c_member(X2,sK70(X0,X1,X2),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f1778,plain,
! [X0,X2,X3] :
( ? [X5] :
( ~ hBOOL(hAPP(X0,X5))
& c_member(X2,X5,X3) )
=> ( ~ hBOOL(hAPP(X0,sK71(X0,X2,X3)))
& c_member(X2,sK71(X0,X2,X3),X3) ) ),
introduced(choice_axiom,[]) ).
fof(f1776,plain,
! [X0,X1,X2,X3] :
( ( sP7(X0,X1,X2,X3)
| ? [X4] :
( ~ hBOOL(hAPP(X0,X4))
& c_member(X2,X4,X1) )
| ? [X5] :
( ~ hBOOL(hAPP(X0,X5))
& c_member(X2,X5,X3) ) )
& ( ( ! [X6] :
( hBOOL(hAPP(X0,X6))
| ~ c_member(X2,X6,X1) )
& ! [X7] :
( hBOOL(hAPP(X0,X7))
| ~ c_member(X2,X7,X3) ) )
| ~ sP7(X0,X1,X2,X3) ) ),
inference(rectify,[],[f1775]) ).
fof(f1775,plain,
! [X0,X1,X3,X2] :
( ( sP7(X0,X1,X3,X2)
| ? [X5] :
( ~ hBOOL(hAPP(X0,X5))
& c_member(X3,X5,X1) )
| ? [X6] :
( ~ hBOOL(hAPP(X0,X6))
& c_member(X3,X6,X2) ) )
& ( ( ! [X5] :
( hBOOL(hAPP(X0,X5))
| ~ c_member(X3,X5,X1) )
& ! [X6] :
( hBOOL(hAPP(X0,X6))
| ~ c_member(X3,X6,X2) ) )
| ~ sP7(X0,X1,X3,X2) ) ),
inference(flattening,[],[f1774]) ).
fof(f1774,plain,
! [X0,X1,X3,X2] :
( ( sP7(X0,X1,X3,X2)
| ? [X5] :
( ~ hBOOL(hAPP(X0,X5))
& c_member(X3,X5,X1) )
| ? [X6] :
( ~ hBOOL(hAPP(X0,X6))
& c_member(X3,X6,X2) ) )
& ( ( ! [X5] :
( hBOOL(hAPP(X0,X5))
| ~ c_member(X3,X5,X1) )
& ! [X6] :
( hBOOL(hAPP(X0,X6))
| ~ c_member(X3,X6,X2) ) )
| ~ sP7(X0,X1,X3,X2) ) ),
inference(nnf_transformation,[],[f1538]) ).
fof(f1538,plain,
! [X0,X1,X3,X2] :
( sP7(X0,X1,X3,X2)
<=> ( ! [X5] :
( hBOOL(hAPP(X0,X5))
| ~ c_member(X3,X5,X1) )
& ! [X6] :
( hBOOL(hAPP(X0,X6))
| ~ c_member(X3,X6,X2) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP7])]) ).
fof(f7060,plain,
spl104_403,
inference(avatar_split_clause,[],[f2493,f7058]) ).
fof(f7058,plain,
( spl104_403
<=> ! [X0,X3,X2,X1] :
( sP7(X0,X1,X2,X3)
| ~ hBOOL(hAPP(X0,sK70(X0,X1,X2)))
| c_member(X2,sK71(X0,X2,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_403])]) ).
fof(f2493,plain,
! [X2,X3,X0,X1] :
( sP7(X0,X1,X2,X3)
| ~ hBOOL(hAPP(X0,sK70(X0,X1,X2)))
| c_member(X2,sK71(X0,X2,X3),X3) ),
inference(cnf_transformation,[],[f1779]) ).
fof(f7056,plain,
( spl104_402
| ~ spl104_38
| ~ spl104_279 ),
inference(avatar_split_clause,[],[f5344,f4810,f3051,f7054]) ).
fof(f7054,plain,
( spl104_402
<=> ! [X2,X0,X1] : sP6(X0,c_Set_Oinsert(X1,X2,X0),X1,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_402])]) ).
fof(f5344,plain,
( ! [X2,X0,X1] : sP6(X0,c_Set_Oinsert(X1,X2,X0),X1,X2)
| ~ spl104_38
| ~ spl104_279 ),
inference(resolution,[],[f4811,f3052]) ).
fof(f7052,plain,
spl104_401,
inference(avatar_split_clause,[],[f2492,f7050]) ).
fof(f7050,plain,
( spl104_401
<=> ! [X0,X3,X2,X1] :
( sP7(X0,X1,X2,X3)
| c_member(X2,sK70(X0,X1,X2),X1)
| ~ hBOOL(hAPP(X0,sK71(X0,X2,X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_401])]) ).
fof(f2492,plain,
! [X2,X3,X0,X1] :
( sP7(X0,X1,X2,X3)
| c_member(X2,sK70(X0,X1,X2),X1)
| ~ hBOOL(hAPP(X0,sK71(X0,X2,X3))) ),
inference(cnf_transformation,[],[f1779]) ).
fof(f7048,plain,
spl104_400,
inference(avatar_split_clause,[],[f2491,f7046]) ).
fof(f7046,plain,
( spl104_400
<=> ! [X0,X3,X2,X1] :
( sP7(X0,X1,X2,X3)
| c_member(X2,sK70(X0,X1,X2),X1)
| c_member(X2,sK71(X0,X2,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_400])]) ).
fof(f2491,plain,
! [X2,X3,X0,X1] :
( sP7(X0,X1,X2,X3)
| c_member(X2,sK70(X0,X1,X2),X1)
| c_member(X2,sK71(X0,X2,X3),X3) ),
inference(cnf_transformation,[],[f1779]) ).
fof(f7044,plain,
spl104_399,
inference(avatar_split_clause,[],[f2465,f7042]) ).
fof(f7042,plain,
( spl104_399
<=> ! [X0,X3,X2,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),c_Set_Oinsert(X3,X2,X1),X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X1,X0)
| ~ c_member(X3,X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_399])]) ).
fof(f2465,plain,
! [X2,X3,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),c_Set_Oinsert(X3,X2,X1),X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X1,X0)
| ~ c_member(X3,X2,X0) ),
inference(cnf_transformation,[],[f1759]) ).
fof(f1759,plain,
! [X0,X1,X2,X3] :
( ( c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),c_Set_Oinsert(X3,X2,X1),X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X1,X0)
| ~ c_member(X3,X2,X0) )
& ( ( c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X1,X0)
& c_member(X3,X2,X0) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),c_Set_Oinsert(X3,X2,X1),X0) ) ),
inference(flattening,[],[f1758]) ).
fof(f1758,plain,
! [X0,X1,X2,X3] :
( ( c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),c_Set_Oinsert(X3,X2,X1),X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X1,X0)
| ~ c_member(X3,X2,X0) )
& ( ( c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X1,X0)
& c_member(X3,X2,X0) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),c_Set_Oinsert(X3,X2,X1),X0) ) ),
inference(nnf_transformation,[],[f930]) ).
fof(f930,plain,
! [X0,X1,X2,X3] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),c_Set_Oinsert(X3,X2,X1),X0)
<=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X1,X0)
& c_member(X3,X2,X0) ) ),
inference(rectify,[],[f275]) ).
fof(f275,axiom,
! [X10,X11,X13,X4] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool),c_Set_Oinsert(X4,X13,X11),X10)
<=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool),X11,X10)
& c_member(X4,X13,X10) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__subset) ).
fof(f7040,plain,
spl104_398,
inference(avatar_split_clause,[],[f2342,f7038]) ).
fof(f7038,plain,
( spl104_398
<=> ! [X0,X3,X2,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X1,c_Set_Oinsert(X3,X2,X0))
| c_member(X3,X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_398])]) ).
fof(f2342,plain,
! [X2,X3,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X1,c_Set_Oinsert(X3,X2,X0))
| c_member(X3,X2,X1) ),
inference(cnf_transformation,[],[f1705]) ).
fof(f1705,plain,
! [X0,X1,X2,X3] :
( ( ( c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X1,c_Set_Oinsert(X3,X2,X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X1,X0) )
& ( c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X1,c_Set_Oinsert(X3,X2,X0)) ) )
| c_member(X3,X2,X1) ),
inference(nnf_transformation,[],[f1319]) ).
fof(f1319,plain,
! [X0,X1,X2,X3] :
( ( c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X1,c_Set_Oinsert(X3,X2,X0))
<=> c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X1,X0) )
| c_member(X3,X2,X1) ),
inference(ennf_transformation,[],[f855]) ).
fof(f855,plain,
! [X0,X1,X2,X3] :
( ~ c_member(X3,X2,X1)
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X1,c_Set_Oinsert(X3,X2,X0))
<=> c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X1,X0) ) ),
inference(rectify,[],[f276]) ).
fof(f276,axiom,
! [X10,X11,X13,X4] :
( ~ c_member(X4,X13,X11)
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool),X11,c_Set_Oinsert(X4,X13,X10))
<=> c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool),X11,X10) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__insert) ).
fof(f7036,plain,
spl104_397,
inference(avatar_split_clause,[],[f2270,f7034]) ).
fof(f7034,plain,
( spl104_397
<=> ! [X0,X3,X2,X1] : c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),c_Set_Oinsert(X3,X2,X1),X0) = c_Set_Oinsert(X3,X2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),X1,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_397])]) ).
fof(f7032,plain,
spl104_396,
inference(avatar_split_clause,[],[f2269,f7030]) ).
fof(f7030,plain,
( spl104_396
<=> ! [X0,X3,X2,X1] : c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),X2,c_Set_Oinsert(X3,X1,X0)) = c_Set_Oinsert(X3,X1,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),X2,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_396])]) ).
fof(f2269,plain,
! [X2,X3,X0,X1] : c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),X2,c_Set_Oinsert(X3,X1,X0)) = c_Set_Oinsert(X3,X1,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),X2,X0)),
inference(cnf_transformation,[],[f795]) ).
fof(f795,plain,
! [X0,X1,X2,X3] : c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),X2,c_Set_Oinsert(X3,X1,X0)) = c_Set_Oinsert(X3,X1,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),X2,X0)),
inference(rectify,[],[f126]) ).
fof(f126,axiom,
! [X10,X9,X11,X4] : c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool),X11,c_Set_Oinsert(X4,X9,X10)) = c_Set_Oinsert(X4,X9,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool),X11,X10)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__insert__right) ).
fof(f7028,plain,
spl104_395,
inference(avatar_split_clause,[],[f2249,f7026]) ).
fof(f2249,plain,
! [X2,X0,X1] :
( c_member(X2,X1,c_Wellfounded_Oacc(X2,X0))
| c_member(tc_prod(X2,X2),c_Product__Type_OPair(X2,X2,sK51(X0,X1,X2),X1),X0) ),
inference(cnf_transformation,[],[f1681]) ).
fof(f7024,plain,
spl104_394,
inference(avatar_split_clause,[],[f2204,f7022]) ).
fof(f2204,plain,
! [X2,X0,X1] :
( c_member(X2,X1,c_Wellfounded_Oacc(X2,X0))
| c_member(tc_prod(X2,X2),c_Product__Type_OPair(X2,X2,sK42(X0,X1,X2),X1),X0) ),
inference(cnf_transformation,[],[f1649]) ).
fof(f1649,plain,
! [X0,X1,X2] :
( c_member(X2,X1,c_Wellfounded_Oacc(X2,X0))
| ( ~ c_member(X2,sK42(X0,X1,X2),c_Wellfounded_Oacc(X2,X0))
& c_member(tc_prod(X2,X2),c_Product__Type_OPair(X2,X2,sK42(X0,X1,X2),X1),X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK42])],[f1231,f1648]) ).
fof(f1648,plain,
! [X0,X1,X2] :
( ? [X3] :
( ~ c_member(X2,X3,c_Wellfounded_Oacc(X2,X0))
& c_member(tc_prod(X2,X2),c_Product__Type_OPair(X2,X2,X3,X1),X0) )
=> ( ~ c_member(X2,sK42(X0,X1,X2),c_Wellfounded_Oacc(X2,X0))
& c_member(tc_prod(X2,X2),c_Product__Type_OPair(X2,X2,sK42(X0,X1,X2),X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f1231,plain,
! [X0,X1,X2] :
( c_member(X2,X1,c_Wellfounded_Oacc(X2,X0))
| ? [X3] :
( ~ c_member(X2,X3,c_Wellfounded_Oacc(X2,X0))
& c_member(tc_prod(X2,X2),c_Product__Type_OPair(X2,X2,X3,X1),X0) ) ),
inference(ennf_transformation,[],[f769]) ).
fof(f769,plain,
! [X0,X1,X2] :
( ! [X3] :
( c_member(tc_prod(X2,X2),c_Product__Type_OPair(X2,X2,X3,X1),X0)
=> c_member(X2,X3,c_Wellfounded_Oacc(X2,X0)) )
=> c_member(X2,X1,c_Wellfounded_Oacc(X2,X0)) ),
inference(rectify,[],[f47]) ).
fof(f47,axiom,
! [X3,X13,X4] :
( ! [X5] :
( c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X5,X13),X3)
=> c_member(X4,X5,c_Wellfounded_Oacc(X4,X3)) )
=> c_member(X4,X13,c_Wellfounded_Oacc(X4,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_acc_OaccI) ).
fof(f7020,plain,
spl104_393,
inference(avatar_split_clause,[],[f2173,f7018]) ).
fof(f2173,plain,
! [X2,X0,X1] :
( c_member(tc_prod(X2,X2),c_Product__Type_OPair(X2,X2,sK40(X0,X1,X2),X1),X0)
| c_member(X2,X1,c_Wellfounded_Oacc(X2,X0)) ),
inference(cnf_transformation,[],[f1642]) ).
fof(f1642,plain,
! [X0,X1,X2] :
( ( ~ c_member(X2,sK40(X0,X1,X2),c_Wellfounded_Oacc(X2,X0))
& c_member(tc_prod(X2,X2),c_Product__Type_OPair(X2,X2,sK40(X0,X1,X2),X1),X0) )
| c_member(X2,X1,c_Wellfounded_Oacc(X2,X0)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK40])],[f1202,f1641]) ).
fof(f1641,plain,
! [X0,X1,X2] :
( ? [X3] :
( ~ c_member(X2,X3,c_Wellfounded_Oacc(X2,X0))
& c_member(tc_prod(X2,X2),c_Product__Type_OPair(X2,X2,X3,X1),X0) )
=> ( ~ c_member(X2,sK40(X0,X1,X2),c_Wellfounded_Oacc(X2,X0))
& c_member(tc_prod(X2,X2),c_Product__Type_OPair(X2,X2,sK40(X0,X1,X2),X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f1202,plain,
! [X0,X1,X2] :
( ? [X3] :
( ~ c_member(X2,X3,c_Wellfounded_Oacc(X2,X0))
& c_member(tc_prod(X2,X2),c_Product__Type_OPair(X2,X2,X3,X1),X0) )
| c_member(X2,X1,c_Wellfounded_Oacc(X2,X0)) ),
inference(ennf_transformation,[],[f746]) ).
fof(f746,plain,
! [X0,X1,X2] :
( ~ c_member(X2,X1,c_Wellfounded_Oacc(X2,X0))
=> ~ ! [X3] :
( c_member(tc_prod(X2,X2),c_Product__Type_OPair(X2,X2,X3,X1),X0)
=> c_member(X2,X3,c_Wellfounded_Oacc(X2,X0)) ) ),
inference(rectify,[],[f46]) ).
fof(f46,axiom,
! [X14,X13,X4] :
( ~ c_member(X4,X13,c_Wellfounded_Oacc(X4,X14))
=> ~ ! [X6] :
( c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X6,X13),X14)
=> c_member(X4,X6,c_Wellfounded_Oacc(X4,X14)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__acc__down) ).
fof(f7016,plain,
spl104_392,
inference(avatar_split_clause,[],[f2154,f7014]) ).
fof(f7014,plain,
( spl104_392
<=> ! [X2,X0,X1] :
( c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) = X0
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool),X0,c_Relation_OImage(X2,X2,X1,X0))
| ~ c_Wellfounded_Owf(X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_392])]) ).
fof(f2154,plain,
! [X2,X0,X1] :
( c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) = X0
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool),X0,c_Relation_OImage(X2,X2,X1,X0))
| ~ c_Wellfounded_Owf(X2,X1) ),
inference(cnf_transformation,[],[f1178]) ).
fof(f1178,plain,
! [X0,X1,X2] :
( c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) = X0
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool),X0,c_Relation_OImage(X2,X2,X1,X0))
| ~ c_Wellfounded_Owf(X2,X1) ),
inference(flattening,[],[f1177]) ).
fof(f1177,plain,
! [X0,X1,X2] :
( c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) = X0
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool),X0,c_Relation_OImage(X2,X2,X1,X0))
| ~ c_Wellfounded_Owf(X2,X1) ),
inference(ennf_transformation,[],[f730]) ).
fof(f730,plain,
! [X0,X1,X2] :
( c_Wellfounded_Owf(X2,X1)
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool),X0,c_Relation_OImage(X2,X2,X1,X0))
=> c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) = X0 ) ),
inference(rectify,[],[f472]) ).
fof(f472,axiom,
! [X11,X14,X4] :
( c_Wellfounded_Owf(X4,X14)
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool),X11,c_Relation_OImage(X4,X4,X14,X11))
=> c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)) = X11 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wfE__pf) ).
fof(f7012,plain,
( spl104_391
| ~ spl104_58
| ~ spl104_278 ),
inference(avatar_split_clause,[],[f5329,f4806,f3131,f7010]) ).
fof(f3131,plain,
( spl104_58
<=> ! [X2,X1] : ~ c_Orderings_Oord__class_Oless(tc_fun(X2,tc_HOL_Obool),X1,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_58])]) ).
fof(f4806,plain,
( spl104_278
<=> ! [X0,X3,X2,X1] :
( c_Orderings_Oord__class_Oless(tc_fun(X3,tc_HOL_Obool),X2,c_Set_Oinsert(X3,X1,X0))
| ~ sP5(X1,X3,X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_278])]) ).
fof(f5329,plain,
( ! [X2,X0,X1] : ~ sP5(X0,X1,c_Set_Oinsert(X1,X0,X2),X2)
| ~ spl104_58
| ~ spl104_278 ),
inference(resolution,[],[f4807,f3132]) ).
fof(f3132,plain,
( ! [X2,X1] : ~ c_Orderings_Oord__class_Oless(tc_fun(X2,tc_HOL_Obool),X1,X1)
| ~ spl104_58 ),
inference(avatar_component_clause,[],[f3131]) ).
fof(f4807,plain,
( ! [X2,X3,X0,X1] :
( c_Orderings_Oord__class_Oless(tc_fun(X3,tc_HOL_Obool),X2,c_Set_Oinsert(X3,X1,X0))
| ~ sP5(X1,X3,X2,X0) )
| ~ spl104_278 ),
inference(avatar_component_clause,[],[f4806]) ).
fof(f7008,plain,
spl104_390,
inference(avatar_split_clause,[],[f2010,f7006]) ).
fof(f2010,plain,
! [X0,X1] :
( c_Wellfounded_Oacyclic(X1,X0)
| c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,sK27(X0,X1),sK27(X0,X1)),c_Transitive__Closure_Otrancl(X1,X0)) ),
inference(cnf_transformation,[],[f1578]) ).
fof(f1578,plain,
! [X0,X1] :
( ( c_Wellfounded_Oacyclic(X1,X0)
| c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,sK27(X0,X1),sK27(X0,X1)),c_Transitive__Closure_Otrancl(X1,X0)) )
& ( ! [X3] : ~ c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,X3,X3),c_Transitive__Closure_Otrancl(X1,X0))
| ~ c_Wellfounded_Oacyclic(X1,X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK27])],[f1576,f1577]) ).
fof(f1577,plain,
! [X0,X1] :
( ? [X2] : c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,X2,X2),c_Transitive__Closure_Otrancl(X1,X0))
=> c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,sK27(X0,X1),sK27(X0,X1)),c_Transitive__Closure_Otrancl(X1,X0)) ),
introduced(choice_axiom,[]) ).
fof(f1576,plain,
! [X0,X1] :
( ( c_Wellfounded_Oacyclic(X1,X0)
| ? [X2] : c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,X2,X2),c_Transitive__Closure_Otrancl(X1,X0)) )
& ( ! [X3] : ~ c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,X3,X3),c_Transitive__Closure_Otrancl(X1,X0))
| ~ c_Wellfounded_Oacyclic(X1,X0) ) ),
inference(rectify,[],[f1575]) ).
fof(f1575,plain,
! [X0,X1] :
( ( c_Wellfounded_Oacyclic(X1,X0)
| ? [X2] : c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,X2,X2),c_Transitive__Closure_Otrancl(X1,X0)) )
& ( ! [X2] : ~ c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,X2,X2),c_Transitive__Closure_Otrancl(X1,X0))
| ~ c_Wellfounded_Oacyclic(X1,X0) ) ),
inference(nnf_transformation,[],[f632]) ).
fof(f632,plain,
! [X0,X1] :
( c_Wellfounded_Oacyclic(X1,X0)
<=> ! [X2] : ~ c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,X2,X2),c_Transitive__Closure_Otrancl(X1,X0)) ),
inference(rectify,[],[f100]) ).
fof(f100,axiom,
! [X3,X4] :
( c_Wellfounded_Oacyclic(X4,X3)
<=> ! [X2] : ~ c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X2,X2),c_Transitive__Closure_Otrancl(X4,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_acyclic__def) ).
fof(f7004,plain,
spl104_389,
inference(avatar_split_clause,[],[f1998,f7002]) ).
fof(f1998,plain,
! [X0,X1] :
( c_Wellfounded_Oacyclic(X1,X0)
| c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,sK21(X0,X1),sK21(X0,X1)),c_Transitive__Closure_Otrancl(X1,X0)) ),
inference(cnf_transformation,[],[f1567]) ).
fof(f1567,plain,
! [X0,X1] :
( c_Wellfounded_Oacyclic(X1,X0)
| c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,sK21(X0,X1),sK21(X0,X1)),c_Transitive__Closure_Otrancl(X1,X0)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK21])],[f1070,f1566]) ).
fof(f1566,plain,
! [X0,X1] :
( ? [X2] : c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,X2,X2),c_Transitive__Closure_Otrancl(X1,X0))
=> c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,sK21(X0,X1),sK21(X0,X1)),c_Transitive__Closure_Otrancl(X1,X0)) ),
introduced(choice_axiom,[]) ).
fof(f1070,plain,
! [X0,X1] :
( c_Wellfounded_Oacyclic(X1,X0)
| ? [X2] : c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,X2,X2),c_Transitive__Closure_Otrancl(X1,X0)) ),
inference(ennf_transformation,[],[f626]) ).
fof(f626,plain,
! [X0,X1] :
( ! [X2] : ~ c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,X2,X2),c_Transitive__Closure_Otrancl(X1,X0))
=> c_Wellfounded_Oacyclic(X1,X0) ),
inference(rectify,[],[f109]) ).
fof(f109,axiom,
! [X3,X4] :
( ! [X2] : ~ c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X2,X2),c_Transitive__Closure_Otrancl(X4,X3))
=> c_Wellfounded_Oacyclic(X4,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_acyclicI) ).
fof(f6834,plain,
( spl104_388
| ~ spl104_35
| ~ spl104_206 ),
inference(avatar_split_clause,[],[f4361,f4072,f3038,f6832]) ).
fof(f6832,plain,
( spl104_388
<=> ! [X0,X1] : ~ c_Wellfounded_Owf(X0,c_fequal(c_Product__Type_OPair(X0,X0,X1,X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_388])]) ).
fof(f4361,plain,
( ! [X0,X1] : ~ c_Wellfounded_Owf(X0,c_fequal(c_Product__Type_OPair(X0,X0,X1,X1)))
| ~ spl104_35
| ~ spl104_206 ),
inference(resolution,[],[f4073,f3039]) ).
fof(f6649,plain,
( spl104_387
| ~ spl104_35
| ~ spl104_196 ),
inference(avatar_split_clause,[],[f4215,f4032,f3038,f6647]) ).
fof(f6647,plain,
( spl104_387
<=> ! [X0,X1] : ~ c_Relation_Oirrefl(X0,c_fequal(c_Product__Type_OPair(X0,X0,X1,X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_387])]) ).
fof(f4215,plain,
( ! [X0,X1] : ~ c_Relation_Oirrefl(X0,c_fequal(c_Product__Type_OPair(X0,X0,X1,X1)))
| ~ spl104_35
| ~ spl104_196 ),
inference(resolution,[],[f4033,f3039]) ).
fof(f6539,plain,
spl104_386,
inference(avatar_split_clause,[],[f2523,f6537]) ).
fof(f2523,plain,
! [X2,X3,X0,X1,X4] :
( c_member(X4,X1,X3)
| ~ c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X1,X0),X2)
| ~ c_Relation_Orefl__on(X4,X3,X2) ),
inference(cnf_transformation,[],[f1447]) ).
fof(f1447,plain,
! [X0,X1,X2,X3,X4] :
( c_member(X4,X1,X3)
| ~ c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X1,X0),X2)
| ~ c_Relation_Orefl__on(X4,X3,X2) ),
inference(flattening,[],[f1446]) ).
fof(f1446,plain,
! [X0,X1,X2,X3,X4] :
( c_member(X4,X1,X3)
| ~ c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X1,X0),X2)
| ~ c_Relation_Orefl__on(X4,X3,X2) ),
inference(ennf_transformation,[],[f959]) ).
fof(f959,plain,
! [X0,X1,X2,X3,X4] :
( c_Relation_Orefl__on(X4,X3,X2)
=> ( c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X1,X0),X2)
=> c_member(X4,X1,X3) ) ),
inference(rectify,[],[f41]) ).
fof(f41,axiom,
! [X12,X13,X3,X11,X4] :
( c_Relation_Orefl__on(X4,X11,X3)
=> ( c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X13,X12),X3)
=> c_member(X4,X13,X11) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_refl__onD1) ).
fof(f6535,plain,
spl104_385,
inference(avatar_split_clause,[],[f2522,f6533]) ).
fof(f2522,plain,
! [X2,X3,X0,X1,X4] :
( c_member(X4,X0,X3)
| ~ c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X1,X0),X2)
| ~ c_Relation_Orefl__on(X4,X3,X2) ),
inference(cnf_transformation,[],[f1445]) ).
fof(f1445,plain,
! [X0,X1,X2,X3,X4] :
( c_member(X4,X0,X3)
| ~ c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X1,X0),X2)
| ~ c_Relation_Orefl__on(X4,X3,X2) ),
inference(flattening,[],[f1444]) ).
fof(f1444,plain,
! [X0,X1,X2,X3,X4] :
( c_member(X4,X0,X3)
| ~ c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X1,X0),X2)
| ~ c_Relation_Orefl__on(X4,X3,X2) ),
inference(ennf_transformation,[],[f958]) ).
fof(f958,plain,
! [X0,X1,X2,X3,X4] :
( c_Relation_Orefl__on(X4,X3,X2)
=> ( c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X1,X0),X2)
=> c_member(X4,X0,X3) ) ),
inference(rectify,[],[f42]) ).
fof(f42,axiom,
! [X12,X13,X3,X11,X4] :
( c_Relation_Orefl__on(X4,X11,X3)
=> ( c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X13,X12),X3)
=> c_member(X4,X12,X11) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_refl__onD2) ).
fof(f6531,plain,
spl104_384,
inference(avatar_split_clause,[],[f2506,f6529]) ).
fof(f2506,plain,
! [X2,X3,X0,X1,X4] :
( sP8(X0,X1,X2,X3)
| ~ hBOOL(hAPP(X0,X4))
| ~ c_member(X3,X4,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),X2,X1)) ),
inference(cnf_transformation,[],[f1793]) ).
fof(f1793,plain,
! [X0,X1,X2,X3] :
( ( sP8(X0,X1,X2,X3)
| ! [X4] :
( ~ hBOOL(hAPP(X0,X4))
| ~ c_member(X3,X4,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),X2,X1)) ) )
& ( ( hBOOL(hAPP(X0,sK75(X0,X1,X2,X3)))
& c_member(X3,sK75(X0,X1,X2,X3),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),X2,X1)) )
| ~ sP8(X0,X1,X2,X3) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK75])],[f1791,f1792]) ).
fof(f1792,plain,
! [X0,X1,X2,X3] :
( ? [X5] :
( hBOOL(hAPP(X0,X5))
& c_member(X3,X5,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),X2,X1)) )
=> ( hBOOL(hAPP(X0,sK75(X0,X1,X2,X3)))
& c_member(X3,sK75(X0,X1,X2,X3),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),X2,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f1791,plain,
! [X0,X1,X2,X3] :
( ( sP8(X0,X1,X2,X3)
| ! [X4] :
( ~ hBOOL(hAPP(X0,X4))
| ~ c_member(X3,X4,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),X2,X1)) ) )
& ( ? [X5] :
( hBOOL(hAPP(X0,X5))
& c_member(X3,X5,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),X2,X1)) )
| ~ sP8(X0,X1,X2,X3) ) ),
inference(rectify,[],[f1790]) ).
fof(f1790,plain,
! [X0,X1,X2,X3] :
( ( sP8(X0,X1,X2,X3)
| ! [X4] :
( ~ hBOOL(hAPP(X0,X4))
| ~ c_member(X3,X4,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),X2,X1)) ) )
& ( ? [X4] :
( hBOOL(hAPP(X0,X4))
& c_member(X3,X4,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),X2,X1)) )
| ~ sP8(X0,X1,X2,X3) ) ),
inference(nnf_transformation,[],[f1540]) ).
fof(f1540,plain,
! [X0,X1,X2,X3] :
( sP8(X0,X1,X2,X3)
<=> ? [X4] :
( hBOOL(hAPP(X0,X4))
& c_member(X3,X4,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),X2,X1)) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP8])]) ).
fof(f6527,plain,
spl104_383,
inference(avatar_split_clause,[],[f2504,f6525]) ).
fof(f2504,plain,
! [X2,X3,X0,X1] :
( c_member(X3,sK75(X0,X1,X2,X3),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),X2,X1))
| ~ sP8(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f1793]) ).
fof(f6523,plain,
spl104_382,
inference(avatar_split_clause,[],[f2497,f6521]) ).
fof(f6521,plain,
( spl104_382
<=> ! [X2,X4,X0,X3,X1] :
( hBOOL(hAPP(X0,X4))
| ~ c_member(X3,X4,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),X2,X1))
| ~ sP7(X0,X1,X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_382])]) ).
fof(f2497,plain,
! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(X0,X4))
| ~ c_member(X3,X4,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),X2,X1))
| ~ sP7(X0,X1,X3,X2) ),
inference(cnf_transformation,[],[f1783]) ).
fof(f1783,plain,
! [X0,X1,X2,X3] :
( ( ! [X4] :
( hBOOL(hAPP(X0,X4))
| ~ c_member(X3,X4,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),X2,X1)) )
| ~ sP7(X0,X1,X3,X2) )
& ( sP7(X0,X1,X3,X2)
| ( ~ hBOOL(hAPP(X0,sK72(X0,X1,X2,X3)))
& c_member(X3,sK72(X0,X1,X2,X3),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),X2,X1)) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK72])],[f1781,f1782]) ).
fof(f1782,plain,
! [X0,X1,X2,X3] :
( ? [X5] :
( ~ hBOOL(hAPP(X0,X5))
& c_member(X3,X5,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),X2,X1)) )
=> ( ~ hBOOL(hAPP(X0,sK72(X0,X1,X2,X3)))
& c_member(X3,sK72(X0,X1,X2,X3),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),X2,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f1781,plain,
! [X0,X1,X2,X3] :
( ( ! [X4] :
( hBOOL(hAPP(X0,X4))
| ~ c_member(X3,X4,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),X2,X1)) )
| ~ sP7(X0,X1,X3,X2) )
& ( sP7(X0,X1,X3,X2)
| ? [X5] :
( ~ hBOOL(hAPP(X0,X5))
& c_member(X3,X5,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),X2,X1)) ) ) ),
inference(rectify,[],[f1780]) ).
fof(f1780,plain,
! [X0,X1,X2,X3] :
( ( ! [X4] :
( hBOOL(hAPP(X0,X4))
| ~ c_member(X3,X4,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),X2,X1)) )
| ~ sP7(X0,X1,X3,X2) )
& ( sP7(X0,X1,X3,X2)
| ? [X4] :
( ~ hBOOL(hAPP(X0,X4))
& c_member(X3,X4,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),X2,X1)) ) ) ),
inference(nnf_transformation,[],[f1539]) ).
fof(f1539,plain,
! [X0,X1,X2,X3] :
( ! [X4] :
( hBOOL(hAPP(X0,X4))
| ~ c_member(X3,X4,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),X2,X1)) )
<=> sP7(X0,X1,X3,X2) ),
inference(definition_folding,[],[f1430,f1538]) ).
fof(f1430,plain,
! [X0,X1,X2,X3] :
( ! [X4] :
( hBOOL(hAPP(X0,X4))
| ~ c_member(X3,X4,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),X2,X1)) )
<=> ( ! [X5] :
( hBOOL(hAPP(X0,X5))
| ~ c_member(X3,X5,X1) )
& ! [X6] :
( hBOOL(hAPP(X0,X6))
| ~ c_member(X3,X6,X2) ) ) ),
inference(ennf_transformation,[],[f939]) ).
fof(f939,plain,
! [X0,X1,X2,X3] :
( ! [X4] :
( c_member(X3,X4,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),X2,X1))
=> hBOOL(hAPP(X0,X4)) )
<=> ( ! [X5] :
( c_member(X3,X5,X1)
=> hBOOL(hAPP(X0,X5)) )
& ! [X6] :
( c_member(X3,X6,X2)
=> hBOOL(hAPP(X0,X6)) ) ) ),
inference(rectify,[],[f131]) ).
fof(f131,axiom,
! [X17,X10,X11,X4] :
( ! [X2] :
( c_member(X4,X2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool),X11,X10))
=> hBOOL(hAPP(X17,X2)) )
<=> ( ! [X2] :
( c_member(X4,X2,X10)
=> hBOOL(hAPP(X17,X2)) )
& ! [X2] :
( c_member(X4,X2,X11)
=> hBOOL(hAPP(X17,X2)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ball__Un) ).
fof(f6519,plain,
( spl104_381
| ~ spl104_137
| ~ spl104_144 ),
inference(avatar_split_clause,[],[f3712,f3582,f3552,f6517]) ).
fof(f6517,plain,
( spl104_381
<=> ! [X0] : c_Relation_Oirrefl(X0,c_Relation_OId__on(X0,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_381])]) ).
fof(f3552,plain,
( spl104_137
<=> ! [X0,X1] : c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) = c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool),X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_137])]) ).
fof(f3582,plain,
( spl104_144
<=> ! [X0,X1] : c_Relation_Oirrefl(X1,c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),X0,c_Relation_OId(X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_144])]) ).
fof(f3712,plain,
( ! [X0] : c_Relation_Oirrefl(X0,c_Relation_OId__on(X0,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool))))
| ~ spl104_137
| ~ spl104_144 ),
inference(forward_demodulation,[],[f3711,f1912]) ).
fof(f3711,plain,
( ! [X0] : c_Relation_Oirrefl(X0,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X0,X0),tc_HOL_Obool)))
| ~ spl104_137
| ~ spl104_144 ),
inference(superposition,[],[f3583,f3553]) ).
fof(f3553,plain,
( ! [X0,X1] : c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) = c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool),X0,X0)
| ~ spl104_137 ),
inference(avatar_component_clause,[],[f3552]) ).
fof(f3583,plain,
( ! [X0,X1] : c_Relation_Oirrefl(X1,c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),X0,c_Relation_OId(X1)))
| ~ spl104_144 ),
inference(avatar_component_clause,[],[f3582]) ).
fof(f6515,plain,
spl104_380,
inference(avatar_split_clause,[],[f2495,f6513]) ).
fof(f2495,plain,
! [X2,X3,X0,X1] :
( sP7(X0,X1,X3,X2)
| c_member(X3,sK72(X0,X1,X2,X3),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),X2,X1)) ),
inference(cnf_transformation,[],[f1783]) ).
fof(f6511,plain,
spl104_379,
inference(avatar_split_clause,[],[f2372,f6509]) ).
fof(f6509,plain,
( spl104_379
<=> ! [X0,X3,X2,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X2,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_379])]) ).
fof(f2372,plain,
! [X2,X3,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X2,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X2,X1) ),
inference(cnf_transformation,[],[f1367]) ).
fof(f1367,plain,
! [X0,X1,X2,X3] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X2,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X2,X1) ),
inference(flattening,[],[f1366]) ).
fof(f1366,plain,
! [X0,X1,X2,X3] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X2,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X2,X1) ),
inference(ennf_transformation,[],[f885]) ).
fof(f885,plain,
! [X0,X1,X2,X3] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X2,X1)
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X1,X0)
=> c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X2,X0) ) ),
inference(rectify,[],[f240]) ).
fof(f240,axiom,
! [X53,X10,X11,X4] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool),X11,X10)
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool),X10,X53)
=> c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool),X11,X53) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__trans) ).
fof(f6507,plain,
spl104_378,
inference(avatar_split_clause,[],[f2371,f6505]) ).
fof(f6505,plain,
( spl104_378
<=> ! [X0,X3,X2,X1] :
( c_Orderings_Oord__class_Oless(tc_fun(X3,tc_HOL_Obool),X2,X0)
| ~ c_Orderings_Oord__class_Oless(tc_fun(X3,tc_HOL_Obool),X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_378])]) ).
fof(f2371,plain,
! [X2,X3,X0,X1] :
( c_Orderings_Oord__class_Oless(tc_fun(X3,tc_HOL_Obool),X2,X0)
| ~ c_Orderings_Oord__class_Oless(tc_fun(X3,tc_HOL_Obool),X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X2,X1) ),
inference(cnf_transformation,[],[f1365]) ).
fof(f1365,plain,
! [X0,X1,X2,X3] :
( c_Orderings_Oord__class_Oless(tc_fun(X3,tc_HOL_Obool),X2,X0)
| ~ c_Orderings_Oord__class_Oless(tc_fun(X3,tc_HOL_Obool),X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X2,X1) ),
inference(flattening,[],[f1364]) ).
fof(f1364,plain,
! [X0,X1,X2,X3] :
( c_Orderings_Oord__class_Oless(tc_fun(X3,tc_HOL_Obool),X2,X0)
| ~ c_Orderings_Oord__class_Oless(tc_fun(X3,tc_HOL_Obool),X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X2,X1) ),
inference(ennf_transformation,[],[f884]) ).
fof(f884,plain,
! [X0,X1,X2,X3] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X2,X1)
=> ( c_Orderings_Oord__class_Oless(tc_fun(X3,tc_HOL_Obool),X1,X0)
=> c_Orderings_Oord__class_Oless(tc_fun(X3,tc_HOL_Obool),X2,X0) ) ),
inference(rectify,[],[f292]) ).
fof(f292,axiom,
! [X53,X10,X11,X4] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool),X11,X10)
=> ( c_Orderings_Oord__class_Oless(tc_fun(X4,tc_HOL_Obool),X10,X53)
=> c_Orderings_Oord__class_Oless(tc_fun(X4,tc_HOL_Obool),X11,X53) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__psubset__trans) ).
fof(f6503,plain,
spl104_377,
inference(avatar_split_clause,[],[f2366,f6501]) ).
fof(f6501,plain,
( spl104_377
<=> ! [X0,X3,X2,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),c_Set_Oinsert(X3,X0,X2),c_Set_Oinsert(X3,X0,X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_377])]) ).
fof(f2366,plain,
! [X2,X3,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),c_Set_Oinsert(X3,X0,X2),c_Set_Oinsert(X3,X0,X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X2,X1) ),
inference(cnf_transformation,[],[f1355]) ).
fof(f1355,plain,
! [X0,X1,X2,X3] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),c_Set_Oinsert(X3,X0,X2),c_Set_Oinsert(X3,X0,X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X2,X1) ),
inference(ennf_transformation,[],[f879]) ).
fof(f879,plain,
! [X0,X1,X2,X3] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X2,X1)
=> c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),c_Set_Oinsert(X3,X0,X2),c_Set_Oinsert(X3,X0,X1)) ),
inference(rectify,[],[f243]) ).
fof(f243,axiom,
! [X9,X65,X53,X4] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool),X53,X65)
=> c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool),c_Set_Oinsert(X4,X9,X53),c_Set_Oinsert(X4,X9,X65)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__mono) ).
fof(f6499,plain,
spl104_376,
inference(avatar_split_clause,[],[f2364,f6497]) ).
fof(f6497,plain,
( spl104_376
<=> ! [X0,X3,X2,X1] :
( c_Orderings_Oord__class_Oless(tc_fun(X3,tc_HOL_Obool),X2,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X1,X0)
| ~ c_Orderings_Oord__class_Oless(tc_fun(X3,tc_HOL_Obool),X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_376])]) ).
fof(f2364,plain,
! [X2,X3,X0,X1] :
( c_Orderings_Oord__class_Oless(tc_fun(X3,tc_HOL_Obool),X2,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X1,X0)
| ~ c_Orderings_Oord__class_Oless(tc_fun(X3,tc_HOL_Obool),X2,X1) ),
inference(cnf_transformation,[],[f1353]) ).
fof(f1353,plain,
! [X0,X1,X2,X3] :
( c_Orderings_Oord__class_Oless(tc_fun(X3,tc_HOL_Obool),X2,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X1,X0)
| ~ c_Orderings_Oord__class_Oless(tc_fun(X3,tc_HOL_Obool),X2,X1) ),
inference(flattening,[],[f1352]) ).
fof(f1352,plain,
! [X0,X1,X2,X3] :
( c_Orderings_Oord__class_Oless(tc_fun(X3,tc_HOL_Obool),X2,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X1,X0)
| ~ c_Orderings_Oord__class_Oless(tc_fun(X3,tc_HOL_Obool),X2,X1) ),
inference(ennf_transformation,[],[f877]) ).
fof(f877,plain,
! [X0,X1,X2,X3] :
( c_Orderings_Oord__class_Oless(tc_fun(X3,tc_HOL_Obool),X2,X1)
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X1,X0)
=> c_Orderings_Oord__class_Oless(tc_fun(X3,tc_HOL_Obool),X2,X0) ) ),
inference(rectify,[],[f291]) ).
fof(f291,axiom,
! [X53,X10,X11,X4] :
( c_Orderings_Oord__class_Oless(tc_fun(X4,tc_HOL_Obool),X11,X10)
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool),X10,X53)
=> c_Orderings_Oord__class_Oless(tc_fun(X4,tc_HOL_Obool),X11,X53) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_psubset__subset__trans) ).
fof(f6495,plain,
spl104_375,
inference(avatar_split_clause,[],[f2363,f6493]) ).
fof(f6493,plain,
( spl104_375
<=> ! [X0,X3,X2,X1] :
( c_Orderings_Oord__class_Oless(tc_fun(X3,tc_HOL_Obool),X2,X0)
| ~ c_Orderings_Oord__class_Oless(tc_fun(X3,tc_HOL_Obool),X1,X0)
| ~ c_Orderings_Oord__class_Oless(tc_fun(X3,tc_HOL_Obool),X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_375])]) ).
fof(f2363,plain,
! [X2,X3,X0,X1] :
( c_Orderings_Oord__class_Oless(tc_fun(X3,tc_HOL_Obool),X2,X0)
| ~ c_Orderings_Oord__class_Oless(tc_fun(X3,tc_HOL_Obool),X1,X0)
| ~ c_Orderings_Oord__class_Oless(tc_fun(X3,tc_HOL_Obool),X2,X1) ),
inference(cnf_transformation,[],[f1351]) ).
fof(f1351,plain,
! [X0,X1,X2,X3] :
( c_Orderings_Oord__class_Oless(tc_fun(X3,tc_HOL_Obool),X2,X0)
| ~ c_Orderings_Oord__class_Oless(tc_fun(X3,tc_HOL_Obool),X1,X0)
| ~ c_Orderings_Oord__class_Oless(tc_fun(X3,tc_HOL_Obool),X2,X1) ),
inference(flattening,[],[f1350]) ).
fof(f1350,plain,
! [X0,X1,X2,X3] :
( c_Orderings_Oord__class_Oless(tc_fun(X3,tc_HOL_Obool),X2,X0)
| ~ c_Orderings_Oord__class_Oless(tc_fun(X3,tc_HOL_Obool),X1,X0)
| ~ c_Orderings_Oord__class_Oless(tc_fun(X3,tc_HOL_Obool),X2,X1) ),
inference(ennf_transformation,[],[f876]) ).
fof(f876,plain,
! [X0,X1,X2,X3] :
( c_Orderings_Oord__class_Oless(tc_fun(X3,tc_HOL_Obool),X2,X1)
=> ( c_Orderings_Oord__class_Oless(tc_fun(X3,tc_HOL_Obool),X1,X0)
=> c_Orderings_Oord__class_Oless(tc_fun(X3,tc_HOL_Obool),X2,X0) ) ),
inference(rectify,[],[f359]) ).
fof(f359,axiom,
! [X53,X10,X11,X4] :
( c_Orderings_Oord__class_Oless(tc_fun(X4,tc_HOL_Obool),X11,X10)
=> ( c_Orderings_Oord__class_Oless(tc_fun(X4,tc_HOL_Obool),X10,X53)
=> c_Orderings_Oord__class_Oless(tc_fun(X4,tc_HOL_Obool),X11,X53) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_psubset__trans) ).
fof(f6491,plain,
spl104_374,
inference(avatar_split_clause,[],[f2351,f6489]) ).
fof(f6489,plain,
( spl104_374
<=> ! [X0,X3,X2,X1] :
( c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X0,X0),X1)
| ~ c_member(X3,X0,X2)
| ~ c_Relation_Orefl__on(X3,X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_374])]) ).
fof(f2351,plain,
! [X2,X3,X0,X1] :
( c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X0,X0),X1)
| ~ c_member(X3,X0,X2)
| ~ c_Relation_Orefl__on(X3,X2,X1) ),
inference(cnf_transformation,[],[f1331]) ).
fof(f1331,plain,
! [X0,X1,X2,X3] :
( c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X0,X0),X1)
| ~ c_member(X3,X0,X2)
| ~ c_Relation_Orefl__on(X3,X2,X1) ),
inference(flattening,[],[f1330]) ).
fof(f1330,plain,
! [X0,X1,X2,X3] :
( c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X0,X0),X1)
| ~ c_member(X3,X0,X2)
| ~ c_Relation_Orefl__on(X3,X2,X1) ),
inference(ennf_transformation,[],[f864]) ).
fof(f864,plain,
! [X0,X1,X2,X3] :
( c_Relation_Orefl__on(X3,X2,X1)
=> ( c_member(X3,X0,X2)
=> c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X0,X0),X1) ) ),
inference(rectify,[],[f40]) ).
fof(f40,axiom,
! [X9,X3,X11,X4] :
( c_Relation_Orefl__on(X4,X11,X3)
=> ( c_member(X4,X9,X11)
=> c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X9,X9),X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_refl__onD) ).
fof(f6487,plain,
spl104_373,
inference(avatar_split_clause,[],[f2265,f6485]) ).
fof(f6485,plain,
( spl104_373
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP(X2,X3))
| ~ hBOOL(hAPP(X2,c_Product__Type_OPair(X1,X0,sK52(X0,X1,X2),sK53(X0,X1,X2)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_373])]) ).
fof(f2265,plain,
! [X2,X3,X0,X1] :
( hBOOL(hAPP(X2,X3))
| ~ hBOOL(hAPP(X2,c_Product__Type_OPair(X1,X0,sK52(X0,X1,X2),sK53(X0,X1,X2)))) ),
inference(cnf_transformation,[],[f1693]) ).
fof(f1693,plain,
! [X0,X1,X2] :
( ( ! [X3] : hBOOL(hAPP(X2,X3))
| ~ hBOOL(hAPP(X2,c_Product__Type_OPair(X1,X0,sK52(X0,X1,X2),sK53(X0,X1,X2)))) )
& ( ! [X6,X7] : hBOOL(hAPP(X2,c_Product__Type_OPair(X1,X0,X6,X7)))
| ~ hBOOL(hAPP(X2,sK54(X2))) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK52,sK53,sK54])],[f1690,f1692,f1691]) ).
fof(f1691,plain,
! [X0,X1,X2] :
( ? [X4,X5] : ~ hBOOL(hAPP(X2,c_Product__Type_OPair(X1,X0,X4,X5)))
=> ~ hBOOL(hAPP(X2,c_Product__Type_OPair(X1,X0,sK52(X0,X1,X2),sK53(X0,X1,X2)))) ),
introduced(choice_axiom,[]) ).
fof(f1692,plain,
! [X2] :
( ? [X8] : ~ hBOOL(hAPP(X2,X8))
=> ~ hBOOL(hAPP(X2,sK54(X2))) ),
introduced(choice_axiom,[]) ).
fof(f1690,plain,
! [X0,X1,X2] :
( ( ! [X3] : hBOOL(hAPP(X2,X3))
| ? [X4,X5] : ~ hBOOL(hAPP(X2,c_Product__Type_OPair(X1,X0,X4,X5))) )
& ( ! [X6,X7] : hBOOL(hAPP(X2,c_Product__Type_OPair(X1,X0,X6,X7)))
| ? [X8] : ~ hBOOL(hAPP(X2,X8)) ) ),
inference(rectify,[],[f1689]) ).
fof(f1689,plain,
! [X0,X1,X2] :
( ( ! [X3] : hBOOL(hAPP(X2,X3))
| ? [X4,X5] : ~ hBOOL(hAPP(X2,c_Product__Type_OPair(X1,X0,X4,X5))) )
& ( ! [X4,X5] : hBOOL(hAPP(X2,c_Product__Type_OPair(X1,X0,X4,X5)))
| ? [X3] : ~ hBOOL(hAPP(X2,X3)) ) ),
inference(nnf_transformation,[],[f791]) ).
fof(f791,plain,
! [X0,X1,X2] :
( ! [X3] : hBOOL(hAPP(X2,X3))
<=> ! [X4,X5] : hBOOL(hAPP(X2,c_Product__Type_OPair(X1,X0,X4,X5))) ),
inference(rectify,[],[f9]) ).
fof(f9,axiom,
! [X15,X4,X17] :
( ! [X19] : hBOOL(hAPP(X17,X19))
<=> ! [X20,X21] : hBOOL(hAPP(X17,c_Product__Type_OPair(X4,X15,X20,X21))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_split__paired__All) ).
fof(f6483,plain,
spl104_372,
inference(avatar_split_clause,[],[f2197,f6481]) ).
fof(f6481,plain,
( spl104_372
<=> ! [X2,X0,X1] :
( X0 = X1
| c_Set_Oinsert(X2,X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))) != c_Set_Oinsert(X2,X0,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_372])]) ).
fof(f2197,plain,
! [X2,X0,X1] :
( X0 = X1
| c_Set_Oinsert(X2,X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))) != c_Set_Oinsert(X2,X0,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))) ),
inference(cnf_transformation,[],[f1228]) ).
fof(f1228,plain,
! [X0,X1,X2] :
( X0 = X1
| c_Set_Oinsert(X2,X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))) != c_Set_Oinsert(X2,X0,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))) ),
inference(ennf_transformation,[],[f767]) ).
fof(f767,plain,
! [X0,X1,X2] :
( c_Set_Oinsert(X2,X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))) = c_Set_Oinsert(X2,X0,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)))
=> X0 = X1 ),
inference(rectify,[],[f428]) ).
fof(f428,axiom,
! [X8,X9,X4] :
( c_Set_Oinsert(X4,X8,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))) = c_Set_Oinsert(X4,X9,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))
=> X8 = X9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_singleton__inject) ).
fof(f6479,plain,
spl104_371,
inference(avatar_split_clause,[],[f2186,f6477]) ).
fof(f6477,plain,
( spl104_371
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool),c_Wellfounded_Oacc(X2,X0),c_Wellfounded_Oacc(X2,X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_371])]) ).
fof(f2186,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool),c_Wellfounded_Oacc(X2,X0),c_Wellfounded_Oacc(X2,X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),X1,X0) ),
inference(cnf_transformation,[],[f1215]) ).
fof(f1215,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool),c_Wellfounded_Oacc(X2,X0),c_Wellfounded_Oacc(X2,X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),X1,X0) ),
inference(ennf_transformation,[],[f757]) ).
fof(f757,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),X1,X0)
=> c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool),c_Wellfounded_Oacc(X2,X0),c_Wellfounded_Oacc(X2,X1)) ),
inference(rectify,[],[f234]) ).
fof(f234,axiom,
! [X32,X33,X4] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),X33,X32)
=> c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool),c_Wellfounded_Oacc(X4,X32),c_Wellfounded_Oacc(X4,X33)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_acc__subset) ).
fof(f6475,plain,
( spl104_370
| ~ spl104_35
| ~ spl104_130 ),
inference(avatar_split_clause,[],[f3542,f3473,f3038,f6473]) ).
fof(f3542,plain,
( ! [X0,X1] : c_fequal(X1) = c_Set_Oinsert(X0,X1,c_fequal(X1))
| ~ spl104_35
| ~ spl104_130 ),
inference(resolution,[],[f3474,f3039]) ).
fof(f6471,plain,
spl104_369,
inference(avatar_split_clause,[],[f2159,f6469]) ).
fof(f6469,plain,
( spl104_369
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X0),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_369])]) ).
fof(f2159,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X0),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1) ),
inference(cnf_transformation,[],[f1186]) ).
fof(f1186,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X0),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1) ),
inference(flattening,[],[f1185]) ).
fof(f1185,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X0),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1) ),
inference(ennf_transformation,[],[f735]) ).
fof(f735,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X2)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X0),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0)) ) ),
inference(rectify,[],[f387]) ).
fof(f387,axiom,
! [X60,X26,X27] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X27,X26)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X60,X27)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X27,X60),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X26,X60)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__less__mono) ).
fof(f6467,plain,
spl104_368,
inference(avatar_split_clause,[],[f2158,f6465]) ).
fof(f6465,plain,
( spl104_368
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X2))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_368])]) ).
fof(f2158,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X2))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1) ),
inference(cnf_transformation,[],[f1184]) ).
fof(f1184,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X2))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1) ),
inference(flattening,[],[f1183]) ).
fof(f1183,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X2))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1) ),
inference(ennf_transformation,[],[f734]) ).
fof(f734,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X0)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X2)) ) ),
inference(rectify,[],[f373]) ).
fof(f373,axiom,
! [X74,X70,X71] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X71,X70)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X71,X74)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X74,X70),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X74,X71)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__less__mono2) ).
fof(f6463,plain,
spl104_367,
inference(avatar_split_clause,[],[f2064,f6461]) ).
fof(f6461,plain,
( spl104_367
<=> ! [X2,X0,X1] : c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool),X1,X0) = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool),c_Groups_Ominus__class_Ominus(tc_fun(X2,tc_HOL_Obool),X1,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_367])]) ).
fof(f2064,plain,
! [X2,X0,X1] : c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool),X1,X0) = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool),c_Groups_Ominus__class_Ominus(tc_fun(X2,tc_HOL_Obool),X1,X0),X0),
inference(cnf_transformation,[],[f662]) ).
fof(f662,plain,
! [X0,X1,X2] : c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool),X1,X0) = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool),c_Groups_Ominus__class_Ominus(tc_fun(X2,tc_HOL_Obool),X1,X0),X0),
inference(rectify,[],[f205]) ).
fof(f205,axiom,
! [X11,X10,X4] : c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool),X10,X11) = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool),c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool),X10,X11),X11),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__Diff__cancel2) ).
fof(f6459,plain,
spl104_366,
inference(avatar_split_clause,[],[f2063,f6457]) ).
fof(f2063,plain,
! [X2,X0,X1] : c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool),X1,X0) = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool),X1,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool),X1,X0)),
inference(cnf_transformation,[],[f661]) ).
fof(f661,plain,
! [X0,X1,X2] : c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool),X1,X0) = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool),X1,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool),X1,X0)),
inference(rectify,[],[f124]) ).
fof(f124,axiom,
! [X10,X11,X4] : c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool),X11,X10) = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool),X11,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool),X11,X10)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__left__absorb) ).
fof(f6455,plain,
spl104_365,
inference(avatar_split_clause,[],[f2062,f6453]) ).
fof(f6453,plain,
( spl104_365
<=> ! [X2,X0,X1] : c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool),X1,X0) = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool),X1,c_Groups_Ominus__class_Ominus(tc_fun(X2,tc_HOL_Obool),X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_365])]) ).
fof(f2062,plain,
! [X2,X0,X1] : c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool),X1,X0) = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool),X1,c_Groups_Ominus__class_Ominus(tc_fun(X2,tc_HOL_Obool),X0,X1)),
inference(cnf_transformation,[],[f660]) ).
fof(f660,plain,
! [X0,X1,X2] : c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool),X1,X0) = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool),X1,c_Groups_Ominus__class_Ominus(tc_fun(X2,tc_HOL_Obool),X0,X1)),
inference(rectify,[],[f204]) ).
fof(f204,axiom,
! [X10,X11,X4] : c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool),X11,X10) = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool),X11,c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool),X10,X11)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__Diff__cancel) ).
fof(f6451,plain,
spl104_364,
inference(avatar_split_clause,[],[f2061,f6449]) ).
fof(f6449,plain,
( spl104_364
<=> ! [X2,X0,X1] : c_Groups_Ominus__class_Ominus(tc_fun(X2,tc_HOL_Obool),X1,X0) = c_Groups_Ominus__class_Ominus(tc_fun(X2,tc_HOL_Obool),c_Groups_Ominus__class_Ominus(tc_fun(X2,tc_HOL_Obool),X1,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_364])]) ).
fof(f2061,plain,
! [X2,X0,X1] : c_Groups_Ominus__class_Ominus(tc_fun(X2,tc_HOL_Obool),X1,X0) = c_Groups_Ominus__class_Ominus(tc_fun(X2,tc_HOL_Obool),c_Groups_Ominus__class_Ominus(tc_fun(X2,tc_HOL_Obool),X1,X0),X0),
inference(cnf_transformation,[],[f659]) ).
fof(f659,plain,
! [X0,X1,X2] : c_Groups_Ominus__class_Ominus(tc_fun(X2,tc_HOL_Obool),X1,X0) = c_Groups_Ominus__class_Ominus(tc_fun(X2,tc_HOL_Obool),c_Groups_Ominus__class_Ominus(tc_fun(X2,tc_HOL_Obool),X1,X0),X0),
inference(rectify,[],[f207]) ).
fof(f207,axiom,
! [X10,X11,X4] : c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool),X11,X10) = c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool),c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool),X11,X10),X10),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Diff__idemp) ).
fof(f6447,plain,
spl104_363,
inference(avatar_split_clause,[],[f2025,f6445]) ).
fof(f6445,plain,
( spl104_363
<=> ! [X0,X1,X3] :
( sP2(X0,X1)
| c_member(X0,sK35(X0,X1,X3),sK34(X0,X1))
| ~ c_member(X0,X3,sK34(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_363])]) ).
fof(f2025,plain,
! [X3,X0,X1] :
( sP2(X0,X1)
| c_member(X0,sK35(X0,X1,X3),sK34(X0,X1))
| ~ c_member(X0,X3,sK34(X0,X1)) ),
inference(cnf_transformation,[],[f1598]) ).
fof(f6443,plain,
spl104_362,
inference(avatar_split_clause,[],[f1993,f6441]) ).
fof(f6441,plain,
( spl104_362
<=> ! [X0,X1] :
( c_Product__Type_OPair(X1,X1,sK18(X0,X1),sK18(X0,X1)) = X0
| ~ c_member(tc_prod(X1,X1),X0,c_Relation_OId(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_362])]) ).
fof(f1993,plain,
! [X0,X1] :
( c_Product__Type_OPair(X1,X1,sK18(X0,X1),sK18(X0,X1)) = X0
| ~ c_member(tc_prod(X1,X1),X0,c_Relation_OId(X1)) ),
inference(cnf_transformation,[],[f1561]) ).
fof(f1561,plain,
! [X0,X1] :
( c_Product__Type_OPair(X1,X1,sK18(X0,X1),sK18(X0,X1)) = X0
| ~ c_member(tc_prod(X1,X1),X0,c_Relation_OId(X1)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK18])],[f1066,f1560]) ).
fof(f1560,plain,
! [X0,X1] :
( ? [X2] : c_Product__Type_OPair(X1,X1,X2,X2) = X0
=> c_Product__Type_OPair(X1,X1,sK18(X0,X1),sK18(X0,X1)) = X0 ),
introduced(choice_axiom,[]) ).
fof(f1066,plain,
! [X0,X1] :
( ? [X2] : c_Product__Type_OPair(X1,X1,X2,X2) = X0
| ~ c_member(tc_prod(X1,X1),X0,c_Relation_OId(X1)) ),
inference(ennf_transformation,[],[f623]) ).
fof(f623,plain,
! [X0,X1] :
( c_member(tc_prod(X1,X1),X0,c_Relation_OId(X1))
=> ~ ! [X2] : c_Product__Type_OPair(X1,X1,X2,X2) != X0 ),
inference(rectify,[],[f110]) ).
fof(f110,axiom,
! [X39,X4] :
( c_member(tc_prod(X4,X4),X39,c_Relation_OId(X4))
=> ~ ! [X2] : c_Product__Type_OPair(X4,X4,X2,X2) != X39 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_IdE) ).
fof(f6411,plain,
( spl104_361
| ~ spl104_52
| ~ spl104_99 ),
inference(avatar_split_clause,[],[f3336,f3310,f3107,f6409]) ).
fof(f6409,plain,
( spl104_361
<=> ! [X0] : c_Wellfounded_Oacyclic(X0,c_Relation_OId__on(X0,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_361])]) ).
fof(f3310,plain,
( spl104_99
<=> ! [X0] : c_Wellfounded_Owf(X0,c_Relation_OId__on(X0,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_99])]) ).
fof(f3336,plain,
( ! [X0] : c_Wellfounded_Oacyclic(X0,c_Relation_OId__on(X0,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool))))
| ~ spl104_52
| ~ spl104_99 ),
inference(resolution,[],[f3311,f3108]) ).
fof(f3311,plain,
( ! [X0] : c_Wellfounded_Owf(X0,c_Relation_OId__on(X0,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool))))
| ~ spl104_99 ),
inference(avatar_component_clause,[],[f3310]) ).
fof(f6252,plain,
( spl104_360
| ~ spl104_53
| ~ spl104_99 ),
inference(avatar_split_clause,[],[f3335,f3310,f3111,f6250]) ).
fof(f6250,plain,
( spl104_360
<=> ! [X0] : sP2(X0,c_Relation_OId__on(X0,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_360])]) ).
fof(f3335,plain,
( ! [X0] : sP2(X0,c_Relation_OId__on(X0,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool))))
| ~ spl104_53
| ~ spl104_99 ),
inference(resolution,[],[f3311,f3112]) ).
fof(f6142,plain,
( spl104_359
| ~ spl104_52
| ~ spl104_98 ),
inference(avatar_split_clause,[],[f3334,f3306,f3107,f6140]) ).
fof(f6140,plain,
( spl104_359
<=> ! [X0,X1] : c_Wellfounded_Oacyclic(X0,hAPP(c_Relation_Oinv__image(tc_Nat_Onat,X0,c_Wellfounded_Oless__than),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_359])]) ).
fof(f3334,plain,
( ! [X0,X1] : c_Wellfounded_Oacyclic(X0,hAPP(c_Relation_Oinv__image(tc_Nat_Onat,X0,c_Wellfounded_Oless__than),X1))
| ~ spl104_52
| ~ spl104_98 ),
inference(resolution,[],[f3307,f3108]) ).
fof(f5991,plain,
spl104_358,
inference(avatar_split_clause,[],[f2561,f5989]) ).
fof(f5989,plain,
( spl104_358
<=> ! [X4,X0,X3,X2,X1] :
( c_member(X2,sK85(X0,X1,X2,X3,X4),X0)
| ~ c_member(X4,X3,c_Relation_OImage(X2,X4,X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_358])]) ).
fof(f2561,plain,
! [X2,X3,X0,X1,X4] :
( c_member(X2,sK85(X0,X1,X2,X3,X4),X0)
| ~ c_member(X4,X3,c_Relation_OImage(X2,X4,X1,X0)) ),
inference(cnf_transformation,[],[f1811]) ).
fof(f5987,plain,
( spl104_357
| ~ spl104_53
| ~ spl104_98 ),
inference(avatar_split_clause,[],[f3333,f3306,f3111,f5985]) ).
fof(f5985,plain,
( spl104_357
<=> ! [X0,X1] : sP2(X0,hAPP(c_Relation_Oinv__image(tc_Nat_Onat,X0,c_Wellfounded_Oless__than),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_357])]) ).
fof(f3333,plain,
( ! [X0,X1] : sP2(X0,hAPP(c_Relation_Oinv__image(tc_Nat_Onat,X0,c_Wellfounded_Oless__than),X1))
| ~ spl104_53
| ~ spl104_98 ),
inference(resolution,[],[f3307,f3112]) ).
fof(f5983,plain,
spl104_356,
inference(avatar_split_clause,[],[f2533,f5981]) ).
fof(f5981,plain,
( spl104_356
<=> ! [X4,X0,X3,X2,X1] :
( c_member(X2,sK76(X0,X1,X2,X3,X4),X0)
| ~ c_member(X4,X3,c_Relation_OImage(X2,X4,X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_356])]) ).
fof(f2533,plain,
! [X2,X3,X0,X1,X4] :
( c_member(X2,sK76(X0,X1,X2,X3,X4),X0)
| ~ c_member(X4,X3,c_Relation_OImage(X2,X4,X1,X0)) ),
inference(cnf_transformation,[],[f1796]) ).
fof(f5979,plain,
spl104_355,
inference(avatar_split_clause,[],[f2437,f5977]) ).
fof(f2437,plain,
! [X2,X3,X0,X1,X4] :
( c_member(X3,X2,c_Relation_ODomain(X3,X1,X0))
| ~ c_member(tc_prod(X3,X1),c_Product__Type_OPair(X3,X1,X2,X4),X0) ),
inference(cnf_transformation,[],[f1744]) ).
fof(f5975,plain,
spl104_354,
inference(avatar_split_clause,[],[f2435,f5973]) ).
fof(f2435,plain,
! [X2,X3,X0,X1,X4] :
( c_member(X3,X2,c_Relation_ORange(X1,X3,X0))
| ~ c_member(tc_prod(X1,X3),c_Product__Type_OPair(X1,X3,X4,X2),X0) ),
inference(cnf_transformation,[],[f1740]) ).
fof(f5971,plain,
spl104_353,
inference(avatar_split_clause,[],[f2430,f5969]) ).
fof(f2430,plain,
! [X2,X3,X0,X1] :
( c_Wellfounded_Owf(tc_prod(X0,X2),c_Recdef_Osame__fst(X0,X2,X3,X1))
| ~ c_Wellfounded_Owf(X2,hAPP(X1,sK67(X1,X2,X3))) ),
inference(cnf_transformation,[],[f1734]) ).
fof(f1734,plain,
! [X0,X1,X2,X3] :
( c_Wellfounded_Owf(tc_prod(X0,X2),c_Recdef_Osame__fst(X0,X2,X3,X1))
| ( ~ c_Wellfounded_Owf(X2,hAPP(X1,sK67(X1,X2,X3)))
& hBOOL(hAPP(X3,sK67(X1,X2,X3))) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK67])],[f1427,f1733]) ).
fof(f1733,plain,
! [X1,X2,X3] :
( ? [X4] :
( ~ c_Wellfounded_Owf(X2,hAPP(X1,X4))
& hBOOL(hAPP(X3,X4)) )
=> ( ~ c_Wellfounded_Owf(X2,hAPP(X1,sK67(X1,X2,X3)))
& hBOOL(hAPP(X3,sK67(X1,X2,X3))) ) ),
introduced(choice_axiom,[]) ).
fof(f1427,plain,
! [X0,X1,X2,X3] :
( c_Wellfounded_Owf(tc_prod(X0,X2),c_Recdef_Osame__fst(X0,X2,X3,X1))
| ? [X4] :
( ~ c_Wellfounded_Owf(X2,hAPP(X1,X4))
& hBOOL(hAPP(X3,X4)) ) ),
inference(ennf_transformation,[],[f923]) ).
fof(f923,plain,
! [X0,X1,X2,X3] :
( ! [X4] :
( hBOOL(hAPP(X3,X4))
=> c_Wellfounded_Owf(X2,hAPP(X1,X4)) )
=> c_Wellfounded_Owf(tc_prod(X0,X2),c_Recdef_Osame__fst(X0,X2,X3,X1)) ),
inference(rectify,[],[f194]) ).
fof(f194,axiom,
! [X4,X14,X15,X17] :
( ! [X2] :
( hBOOL(hAPP(X17,X2))
=> c_Wellfounded_Owf(X15,hAPP(X14,X2)) )
=> c_Wellfounded_Owf(tc_prod(X4,X15),c_Recdef_Osame__fst(X4,X15,X17,X14)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__same__fst) ).
fof(f5967,plain,
spl104_352,
inference(avatar_split_clause,[],[f2400,f5965]) ).
fof(f5965,plain,
( spl104_352
<=> ! [X0,X3,X2,X1] :
( c_member(X3,X2,X0)
| c_member(X3,X2,X1)
| ~ c_member(X3,X2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_352])]) ).
fof(f2400,plain,
! [X2,X3,X0,X1] :
( c_member(X3,X2,X0)
| c_member(X3,X2,X1)
| ~ c_member(X3,X2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),X1,X0)) ),
inference(cnf_transformation,[],[f1400]) ).
fof(f1400,plain,
! [X0,X1,X2,X3] :
( c_member(X3,X2,X0)
| c_member(X3,X2,X1)
| ~ c_member(X3,X2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),X1,X0)) ),
inference(flattening,[],[f1399]) ).
fof(f1399,plain,
! [X0,X1,X2,X3] :
( c_member(X3,X2,X0)
| c_member(X3,X2,X1)
| ~ c_member(X3,X2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),X1,X0)) ),
inference(ennf_transformation,[],[f905]) ).
fof(f905,plain,
! [X0,X1,X2,X3] :
( c_member(X3,X2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),X1,X0))
=> ( ~ c_member(X3,X2,X1)
=> c_member(X3,X2,X0) ) ),
inference(rectify,[],[f118]) ).
fof(f118,axiom,
! [X10,X11,X7,X4] :
( c_member(X4,X7,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool),X11,X10))
=> ( ~ c_member(X4,X7,X11)
=> c_member(X4,X7,X10) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UnE) ).
fof(f5963,plain,
spl104_351,
inference(avatar_split_clause,[],[f2395,f5961]) ).
fof(f5961,plain,
( spl104_351
<=> ! [X2,X0,X1,X3] :
( hBOOL(hAPP(X1,X0))
| hBOOL(hAPP(X2,X0))
| ~ hBOOL(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),X2,X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_351])]) ).
fof(f2395,plain,
! [X2,X3,X0,X1] :
( hBOOL(hAPP(X1,X0))
| hBOOL(hAPP(X2,X0))
| ~ hBOOL(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),X2,X1),X0)) ),
inference(cnf_transformation,[],[f1395]) ).
fof(f1395,plain,
! [X0,X1,X2,X3] :
( hBOOL(hAPP(X1,X0))
| hBOOL(hAPP(X2,X0))
| ~ hBOOL(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),X2,X1),X0)) ),
inference(flattening,[],[f1394]) ).
fof(f1394,plain,
! [X0,X1,X2,X3] :
( hBOOL(hAPP(X1,X0))
| hBOOL(hAPP(X2,X0))
| ~ hBOOL(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),X2,X1),X0)) ),
inference(ennf_transformation,[],[f901]) ).
fof(f901,plain,
! [X0,X1,X2,X3] :
( hBOOL(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),X2,X1),X0))
=> ( ~ hBOOL(hAPP(X2,X0))
=> hBOOL(hAPP(X1,X0)) ) ),
inference(rectify,[],[f155]) ).
fof(f155,axiom,
! [X13,X10,X11,X4] :
( hBOOL(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool),X11,X10),X13))
=> ( ~ hBOOL(hAPP(X11,X13))
=> hBOOL(hAPP(X10,X13)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup1E) ).
fof(f5959,plain,
spl104_350,
inference(avatar_split_clause,[],[f2356,f5957]) ).
fof(f5957,plain,
( spl104_350
<=> ! [X0,X3,X2,X1] :
( c_member(X3,X2,c_Groups_Ominus__class_Ominus(tc_fun(X3,tc_HOL_Obool),X1,X0))
| c_member(X3,X2,X0)
| ~ c_member(X3,X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_350])]) ).
fof(f2356,plain,
! [X2,X3,X0,X1] :
( c_member(X3,X2,c_Groups_Ominus__class_Ominus(tc_fun(X3,tc_HOL_Obool),X1,X0))
| c_member(X3,X2,X0)
| ~ c_member(X3,X2,X1) ),
inference(cnf_transformation,[],[f1337]) ).
fof(f1337,plain,
! [X0,X1,X2,X3] :
( c_member(X3,X2,c_Groups_Ominus__class_Ominus(tc_fun(X3,tc_HOL_Obool),X1,X0))
| c_member(X3,X2,X0)
| ~ c_member(X3,X2,X1) ),
inference(flattening,[],[f1336]) ).
fof(f1336,plain,
! [X0,X1,X2,X3] :
( c_member(X3,X2,c_Groups_Ominus__class_Ominus(tc_fun(X3,tc_HOL_Obool),X1,X0))
| c_member(X3,X2,X0)
| ~ c_member(X3,X2,X1) ),
inference(ennf_transformation,[],[f869]) ).
fof(f869,plain,
! [X0,X1,X2,X3] :
( c_member(X3,X2,X1)
=> ( ~ c_member(X3,X2,X0)
=> c_member(X3,X2,c_Groups_Ominus__class_Ominus(tc_fun(X3,tc_HOL_Obool),X1,X0)) ) ),
inference(rectify,[],[f200]) ).
fof(f200,axiom,
! [X10,X11,X7,X4] :
( c_member(X4,X7,X11)
=> ( ~ c_member(X4,X7,X10)
=> c_member(X4,X7,c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool),X11,X10)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_DiffI) ).
fof(f5955,plain,
spl104_349,
inference(avatar_split_clause,[],[f2314,f5953]) ).
fof(f5953,plain,
( spl104_349
<=> ! [X0,X3,X2,X1] :
( c_Orderings_Oord__class_Oless__eq(X3,c_Lattices_Osemilattice__sup__class_Osup(X3,X2,X0),X1)
| ~ c_Orderings_Oord__class_Oless__eq(X3,X0,X1)
| ~ c_Orderings_Oord__class_Oless__eq(X3,X2,X1)
| ~ class_Lattices_Osemilattice__sup(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_349])]) ).
fof(f2314,plain,
! [X2,X3,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X3,c_Lattices_Osemilattice__sup__class_Osup(X3,X2,X0),X1)
| ~ c_Orderings_Oord__class_Oless__eq(X3,X0,X1)
| ~ c_Orderings_Oord__class_Oless__eq(X3,X2,X1)
| ~ class_Lattices_Osemilattice__sup(X3) ),
inference(cnf_transformation,[],[f1289]) ).
fof(f1289,plain,
! [X0,X1,X2,X3] :
( c_Orderings_Oord__class_Oless__eq(X3,c_Lattices_Osemilattice__sup__class_Osup(X3,X2,X0),X1)
| ~ c_Orderings_Oord__class_Oless__eq(X3,X0,X1)
| ~ c_Orderings_Oord__class_Oless__eq(X3,X2,X1)
| ~ class_Lattices_Osemilattice__sup(X3) ),
inference(flattening,[],[f1288]) ).
fof(f1288,plain,
! [X0,X1,X2,X3] :
( c_Orderings_Oord__class_Oless__eq(X3,c_Lattices_Osemilattice__sup__class_Osup(X3,X2,X0),X1)
| ~ c_Orderings_Oord__class_Oless__eq(X3,X0,X1)
| ~ c_Orderings_Oord__class_Oless__eq(X3,X2,X1)
| ~ class_Lattices_Osemilattice__sup(X3) ),
inference(ennf_transformation,[],[f836]) ).
fof(f836,plain,
! [X0,X1,X2,X3] :
( class_Lattices_Osemilattice__sup(X3)
=> ( c_Orderings_Oord__class_Oless__eq(X3,X2,X1)
=> ( c_Orderings_Oord__class_Oless__eq(X3,X0,X1)
=> c_Orderings_Oord__class_Oless__eq(X3,c_Lattices_Osemilattice__sup__class_Osup(X3,X2,X0),X1) ) ) ),
inference(rectify,[],[f249]) ).
fof(f249,axiom,
! [X26,X58,X27,X4] :
( class_Lattices_Osemilattice__sup(X4)
=> ( c_Orderings_Oord__class_Oless__eq(X4,X27,X58)
=> ( c_Orderings_Oord__class_Oless__eq(X4,X26,X58)
=> c_Orderings_Oord__class_Oless__eq(X4,c_Lattices_Osemilattice__sup__class_Osup(X4,X27,X26),X58) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__supI) ).
fof(f5951,plain,
spl104_348,
inference(avatar_split_clause,[],[f2300,f5949]) ).
fof(f5949,plain,
( spl104_348
<=> ! [X0,X3,X2,X1] :
( c_Lattices_Osemilattice__sup__class_Osup(X3,X2,c_Lattices_Osemilattice__sup__class_Osup(X3,X1,X0)) = c_Lattices_Osemilattice__sup__class_Osup(X3,c_Lattices_Osemilattice__sup__class_Osup(X3,X2,X1),X0)
| ~ class_Lattices_Osemilattice__sup(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_348])]) ).
fof(f2300,plain,
! [X2,X3,X0,X1] :
( c_Lattices_Osemilattice__sup__class_Osup(X3,X2,c_Lattices_Osemilattice__sup__class_Osup(X3,X1,X0)) = c_Lattices_Osemilattice__sup__class_Osup(X3,c_Lattices_Osemilattice__sup__class_Osup(X3,X2,X1),X0)
| ~ class_Lattices_Osemilattice__sup(X3) ),
inference(cnf_transformation,[],[f1262]) ).
fof(f1262,plain,
! [X0,X1,X2,X3] :
( c_Lattices_Osemilattice__sup__class_Osup(X3,X2,c_Lattices_Osemilattice__sup__class_Osup(X3,X1,X0)) = c_Lattices_Osemilattice__sup__class_Osup(X3,c_Lattices_Osemilattice__sup__class_Osup(X3,X2,X1),X0)
| ~ class_Lattices_Osemilattice__sup(X3) ),
inference(ennf_transformation,[],[f822]) ).
fof(f822,plain,
! [X0,X1,X2,X3] :
( class_Lattices_Osemilattice__sup(X3)
=> c_Lattices_Osemilattice__sup__class_Osup(X3,X2,c_Lattices_Osemilattice__sup__class_Osup(X3,X1,X0)) = c_Lattices_Osemilattice__sup__class_Osup(X3,c_Lattices_Osemilattice__sup__class_Osup(X3,X2,X1),X0) ),
inference(rectify,[],[f185]) ).
fof(f185,axiom,
! [X61,X59,X58,X4] :
( class_Lattices_Osemilattice__sup(X4)
=> c_Lattices_Osemilattice__sup__class_Osup(X4,X58,c_Lattices_Osemilattice__sup__class_Osup(X4,X59,X61)) = c_Lattices_Osemilattice__sup__class_Osup(X4,c_Lattices_Osemilattice__sup__class_Osup(X4,X58,X59),X61) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup__assoc) ).
fof(f5947,plain,
spl104_347,
inference(avatar_split_clause,[],[f2298,f5945]) ).
fof(f5945,plain,
( spl104_347
<=> ! [X0,X3,X2,X1] :
( c_Lattices_Osemilattice__sup__class_Osup(X3,X2,c_Lattices_Osemilattice__sup__class_Osup(X3,X1,X0)) = c_Lattices_Osemilattice__sup__class_Osup(X3,X1,c_Lattices_Osemilattice__sup__class_Osup(X3,X2,X0))
| ~ class_Lattices_Osemilattice__sup(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_347])]) ).
fof(f2298,plain,
! [X2,X3,X0,X1] :
( c_Lattices_Osemilattice__sup__class_Osup(X3,X2,c_Lattices_Osemilattice__sup__class_Osup(X3,X1,X0)) = c_Lattices_Osemilattice__sup__class_Osup(X3,X1,c_Lattices_Osemilattice__sup__class_Osup(X3,X2,X0))
| ~ class_Lattices_Osemilattice__sup(X3) ),
inference(cnf_transformation,[],[f1260]) ).
fof(f1260,plain,
! [X0,X1,X2,X3] :
( c_Lattices_Osemilattice__sup__class_Osup(X3,X2,c_Lattices_Osemilattice__sup__class_Osup(X3,X1,X0)) = c_Lattices_Osemilattice__sup__class_Osup(X3,X1,c_Lattices_Osemilattice__sup__class_Osup(X3,X2,X0))
| ~ class_Lattices_Osemilattice__sup(X3) ),
inference(ennf_transformation,[],[f820]) ).
fof(f820,plain,
! [X0,X1,X2,X3] :
( class_Lattices_Osemilattice__sup(X3)
=> c_Lattices_Osemilattice__sup__class_Osup(X3,X2,c_Lattices_Osemilattice__sup__class_Osup(X3,X1,X0)) = c_Lattices_Osemilattice__sup__class_Osup(X3,X1,c_Lattices_Osemilattice__sup__class_Osup(X3,X2,X0)) ),
inference(rectify,[],[f182]) ).
fof(f182,axiom,
! [X61,X59,X58,X4] :
( class_Lattices_Osemilattice__sup(X4)
=> c_Lattices_Osemilattice__sup__class_Osup(X4,X58,c_Lattices_Osemilattice__sup__class_Osup(X4,X59,X61)) = c_Lattices_Osemilattice__sup__class_Osup(X4,X59,c_Lattices_Osemilattice__sup__class_Osup(X4,X58,X61)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup__left__commute) ).
fof(f5943,plain,
( spl104_346
| ~ spl104_52
| ~ spl104_86 ),
inference(avatar_split_clause,[],[f3325,f3258,f3107,f5941]) ).
fof(f5941,plain,
( spl104_346
<=> ! [X0,X1] :
( ~ c_Wellfounded_Owf(X0,X1)
| c_Wellfounded_Oacyclic(X0,c_Transitive__Closure_Otrancl(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_346])]) ).
fof(f3258,plain,
( spl104_86
<=> ! [X0,X1] :
( c_Wellfounded_Owf(X1,c_Transitive__Closure_Otrancl(X1,X0))
| ~ c_Wellfounded_Owf(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_86])]) ).
fof(f3325,plain,
( ! [X0,X1] :
( ~ c_Wellfounded_Owf(X0,X1)
| c_Wellfounded_Oacyclic(X0,c_Transitive__Closure_Otrancl(X0,X1)) )
| ~ spl104_52
| ~ spl104_86 ),
inference(resolution,[],[f3259,f3108]) ).
fof(f3259,plain,
( ! [X0,X1] :
( c_Wellfounded_Owf(X1,c_Transitive__Closure_Otrancl(X1,X0))
| ~ c_Wellfounded_Owf(X1,X0) )
| ~ spl104_86 ),
inference(avatar_component_clause,[],[f3258]) ).
fof(f5939,plain,
spl104_345,
inference(avatar_split_clause,[],[f2284,f5937]) ).
fof(f5937,plain,
( spl104_345
<=> ! [X0,X3,X2,X1] :
( c_Lattices_Osemilattice__sup__class_Osup(X3,X2,c_Lattices_Osemilattice__sup__class_Osup(X3,X1,X0)) = c_Lattices_Osemilattice__sup__class_Osup(X3,c_Lattices_Osemilattice__sup__class_Osup(X3,X2,X1),X0)
| ~ class_Lattices_Olattice(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_345])]) ).
fof(f2284,plain,
! [X2,X3,X0,X1] :
( c_Lattices_Osemilattice__sup__class_Osup(X3,X2,c_Lattices_Osemilattice__sup__class_Osup(X3,X1,X0)) = c_Lattices_Osemilattice__sup__class_Osup(X3,c_Lattices_Osemilattice__sup__class_Osup(X3,X2,X1),X0)
| ~ class_Lattices_Olattice(X3) ),
inference(cnf_transformation,[],[f1241]) ).
fof(f1241,plain,
! [X0,X1,X2,X3] :
( c_Lattices_Osemilattice__sup__class_Osup(X3,X2,c_Lattices_Osemilattice__sup__class_Osup(X3,X1,X0)) = c_Lattices_Osemilattice__sup__class_Osup(X3,c_Lattices_Osemilattice__sup__class_Osup(X3,X2,X1),X0)
| ~ class_Lattices_Olattice(X3) ),
inference(ennf_transformation,[],[f809]) ).
fof(f809,plain,
! [X0,X1,X2,X3] :
( class_Lattices_Olattice(X3)
=> c_Lattices_Osemilattice__sup__class_Osup(X3,X2,c_Lattices_Osemilattice__sup__class_Osup(X3,X1,X0)) = c_Lattices_Osemilattice__sup__class_Osup(X3,c_Lattices_Osemilattice__sup__class_Osup(X3,X2,X1),X0) ),
inference(rectify,[],[f184]) ).
fof(f184,axiom,
! [X61,X59,X58,X4] :
( class_Lattices_Olattice(X4)
=> c_Lattices_Osemilattice__sup__class_Osup(X4,X58,c_Lattices_Osemilattice__sup__class_Osup(X4,X59,X61)) = c_Lattices_Osemilattice__sup__class_Osup(X4,c_Lattices_Osemilattice__sup__class_Osup(X4,X58,X59),X61) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__sup__aci_I6_J) ).
fof(f5935,plain,
spl104_344,
inference(avatar_split_clause,[],[f2283,f5933]) ).
fof(f5933,plain,
( spl104_344
<=> ! [X0,X3,X2,X1] :
( c_Lattices_Osemilattice__sup__class_Osup(X3,X2,c_Lattices_Osemilattice__sup__class_Osup(X3,X1,X0)) = c_Lattices_Osemilattice__sup__class_Osup(X3,X1,c_Lattices_Osemilattice__sup__class_Osup(X3,X2,X0))
| ~ class_Lattices_Olattice(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_344])]) ).
fof(f2283,plain,
! [X2,X3,X0,X1] :
( c_Lattices_Osemilattice__sup__class_Osup(X3,X2,c_Lattices_Osemilattice__sup__class_Osup(X3,X1,X0)) = c_Lattices_Osemilattice__sup__class_Osup(X3,X1,c_Lattices_Osemilattice__sup__class_Osup(X3,X2,X0))
| ~ class_Lattices_Olattice(X3) ),
inference(cnf_transformation,[],[f1240]) ).
fof(f1240,plain,
! [X0,X1,X2,X3] :
( c_Lattices_Osemilattice__sup__class_Osup(X3,X2,c_Lattices_Osemilattice__sup__class_Osup(X3,X1,X0)) = c_Lattices_Osemilattice__sup__class_Osup(X3,X1,c_Lattices_Osemilattice__sup__class_Osup(X3,X2,X0))
| ~ class_Lattices_Olattice(X3) ),
inference(ennf_transformation,[],[f808]) ).
fof(f808,plain,
! [X0,X1,X2,X3] :
( class_Lattices_Olattice(X3)
=> c_Lattices_Osemilattice__sup__class_Osup(X3,X2,c_Lattices_Osemilattice__sup__class_Osup(X3,X1,X0)) = c_Lattices_Osemilattice__sup__class_Osup(X3,X1,c_Lattices_Osemilattice__sup__class_Osup(X3,X2,X0)) ),
inference(rectify,[],[f181]) ).
fof(f181,axiom,
! [X61,X59,X58,X4] :
( class_Lattices_Olattice(X4)
=> c_Lattices_Osemilattice__sup__class_Osup(X4,X58,c_Lattices_Osemilattice__sup__class_Osup(X4,X59,X61)) = c_Lattices_Osemilattice__sup__class_Osup(X4,X59,c_Lattices_Osemilattice__sup__class_Osup(X4,X58,X61)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__sup__aci_I7_J) ).
fof(f5931,plain,
spl104_343,
inference(avatar_split_clause,[],[f2258,f5929]) ).
fof(f5929,plain,
( spl104_343
<=> ! [X2,X0,X1] :
( c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) = X0
| c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) != c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_343])]) ).
fof(f2258,plain,
! [X2,X0,X1] :
( c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) = X0
| c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) != c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool),X1,X0) ),
inference(cnf_transformation,[],[f1686]) ).
fof(f1686,plain,
! [X0,X1,X2] :
( ( c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool),X1,X0)
| c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) != X0
| c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) != X1 )
& ( ( c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) = X0
& c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) = X1 )
| c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) != c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool),X1,X0) ) ),
inference(flattening,[],[f1685]) ).
fof(f1685,plain,
! [X0,X1,X2] :
( ( c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool),X1,X0)
| c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) != X0
| c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) != X1 )
& ( ( c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) = X0
& c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) = X1 )
| c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) != c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool),X1,X0) ) ),
inference(nnf_transformation,[],[f788]) ).
fof(f788,plain,
! [X0,X1,X2] :
( c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool),X1,X0)
<=> ( c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) = X0
& c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) = X1 ) ),
inference(rectify,[],[f425]) ).
fof(f425,axiom,
! [X10,X11,X4] :
( c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool),X11,X10) = c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))
<=> ( c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)) = X10
& c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)) = X11 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__empty) ).
fof(f5927,plain,
spl104_342,
inference(avatar_split_clause,[],[f2257,f5925]) ).
fof(f5925,plain,
( spl104_342
<=> ! [X2,X0,X1] :
( c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) = X1
| c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) != c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_342])]) ).
fof(f2257,plain,
! [X2,X0,X1] :
( c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) = X1
| c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) != c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool),X1,X0) ),
inference(cnf_transformation,[],[f1686]) ).
fof(f5923,plain,
spl104_341,
inference(avatar_split_clause,[],[f2253,f5921]) ).
fof(f5921,plain,
( spl104_341
<=> ! [X2,X0,X1] :
( c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X1),tc_HOL_Obool)) = X0
| c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) != c_Relation_ODomain(X2,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_341])]) ).
fof(f2253,plain,
! [X2,X0,X1] :
( c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X1),tc_HOL_Obool)) = X0
| c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) != c_Relation_ODomain(X2,X1,X0) ),
inference(cnf_transformation,[],[f1683]) ).
fof(f1683,plain,
! [X0,X1,X2] :
( ( c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) = c_Relation_ODomain(X2,X1,X0)
| c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X1),tc_HOL_Obool)) != X0 )
& ( c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X1),tc_HOL_Obool)) = X0
| c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) != c_Relation_ODomain(X2,X1,X0) ) ),
inference(nnf_transformation,[],[f786]) ).
fof(f786,plain,
! [X0,X1,X2] :
( c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) = c_Relation_ODomain(X2,X1,X0)
<=> c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X1),tc_HOL_Obool)) = X0 ),
inference(rectify,[],[f416]) ).
fof(f416,axiom,
! [X3,X15,X4] :
( c_Relation_ODomain(X4,X15,X3) = c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))
<=> c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X4,X15),tc_HOL_Obool)) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Domain__empty__iff) ).
fof(f5919,plain,
spl104_340,
inference(avatar_split_clause,[],[f2251,f5917]) ).
fof(f5917,plain,
( spl104_340
<=> ! [X2,X0,X1] :
( c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X1),tc_HOL_Obool)) = X0
| c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) != c_Relation_ORange(X2,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_340])]) ).
fof(f2251,plain,
! [X2,X0,X1] :
( c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X1),tc_HOL_Obool)) = X0
| c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) != c_Relation_ORange(X2,X1,X0) ),
inference(cnf_transformation,[],[f1682]) ).
fof(f1682,plain,
! [X0,X1,X2] :
( ( c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) = c_Relation_ORange(X2,X1,X0)
| c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X1),tc_HOL_Obool)) != X0 )
& ( c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X1),tc_HOL_Obool)) = X0
| c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) != c_Relation_ORange(X2,X1,X0) ) ),
inference(nnf_transformation,[],[f785]) ).
fof(f785,plain,
! [X0,X1,X2] :
( c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) = c_Relation_ORange(X2,X1,X0)
<=> c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X1),tc_HOL_Obool)) = X0 ),
inference(rectify,[],[f418]) ).
fof(f418,axiom,
! [X3,X4,X15] :
( c_Relation_ORange(X15,X4,X3) = c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))
<=> c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X15,X4),tc_HOL_Obool)) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Range__empty__iff) ).
fof(f5915,plain,
spl104_339,
inference(avatar_split_clause,[],[f2200,f5913]) ).
fof(f5913,plain,
( spl104_339
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(X0,X1),X2))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| X1 = X2
| sP3(X2,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_339])]) ).
fof(f2200,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(X0,X1),X2))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| X1 = X2
| sP3(X2,X1,X0) ),
inference(cnf_transformation,[],[f1532]) ).
fof(f1532,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(hAPP(X0,X1),X2))
| ( ~ hBOOL(hAPP(hAPP(X0,X1),X2))
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) )
| ( ~ hBOOL(hAPP(hAPP(X0,X1),X2))
& X1 = X2 )
| sP3(X2,X1,X0) ),
inference(definition_folding,[],[f1230,f1531]) ).
fof(f1531,plain,
! [X2,X1,X0] :
( ( ~ hBOOL(hAPP(hAPP(X0,X1),X2))
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1) )
| ~ sP3(X2,X1,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP3])]) ).
fof(f1230,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(hAPP(X0,X1),X2))
| ( ~ hBOOL(hAPP(hAPP(X0,X1),X2))
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) )
| ( ~ hBOOL(hAPP(hAPP(X0,X1),X2))
& X1 = X2 )
| ( ~ hBOOL(hAPP(hAPP(X0,X1),X2))
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1) ) ),
inference(flattening,[],[f1229]) ).
fof(f1229,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(hAPP(X0,X1),X2))
| ( ~ hBOOL(hAPP(hAPP(X0,X1),X2))
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) )
| ( ~ hBOOL(hAPP(hAPP(X0,X1),X2))
& X1 = X2 )
| ( ~ hBOOL(hAPP(hAPP(X0,X1),X2))
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1) ) ),
inference(ennf_transformation,[],[f768]) ).
fof(f768,plain,
! [X0,X1,X2] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1)
=> hBOOL(hAPP(hAPP(X0,X1),X2)) )
=> ( ( X1 = X2
=> hBOOL(hAPP(hAPP(X0,X1),X2)) )
=> ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
=> hBOOL(hAPP(hAPP(X0,X1),X2)) )
=> hBOOL(hAPP(hAPP(X0,X1),X2)) ) ) ),
inference(rectify,[],[f372]) ).
fof(f372,axiom,
! [X17,X67,X68] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X68,X67)
=> hBOOL(hAPP(hAPP(X17,X67),X68)) )
=> ( ( X67 = X68
=> hBOOL(hAPP(hAPP(X17,X67),X68)) )
=> ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X67,X68)
=> hBOOL(hAPP(hAPP(X17,X67),X68)) )
=> hBOOL(hAPP(hAPP(X17,X67),X68)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__less__cases) ).
fof(f5911,plain,
spl104_338,
inference(avatar_split_clause,[],[f2060,f5909]) ).
fof(f5909,plain,
( spl104_338
<=> ! [X2,X0,X1] : c_Set_Oinsert(X2,X1,X0) = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool),c_Set_Oinsert(X2,X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_338])]) ).
fof(f5907,plain,
spl104_337,
inference(avatar_split_clause,[],[f2018,f5905]) ).
fof(f5905,plain,
( spl104_337
<=> ! [X0,X1] :
( c_Relation_Otrans(X1,X0)
| ~ c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,sK30(X0,X1),sK32(X0,X1)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_337])]) ).
fof(f2018,plain,
! [X0,X1] :
( c_Relation_Otrans(X1,X0)
| ~ c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,sK30(X0,X1),sK32(X0,X1)),X0) ),
inference(cnf_transformation,[],[f1587]) ).
fof(f5903,plain,
spl104_336,
inference(avatar_split_clause,[],[f2017,f5901]) ).
fof(f2017,plain,
! [X0,X1] :
( c_Relation_Otrans(X1,X0)
| c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,sK31(X0,X1),sK32(X0,X1)),X0) ),
inference(cnf_transformation,[],[f1587]) ).
fof(f5899,plain,
( spl104_335
| ~ spl104_53
| ~ spl104_86 ),
inference(avatar_split_clause,[],[f3324,f3258,f3111,f5897]) ).
fof(f5897,plain,
( spl104_335
<=> ! [X0,X1] :
( ~ c_Wellfounded_Owf(X0,X1)
| sP2(X0,c_Transitive__Closure_Otrancl(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_335])]) ).
fof(f3324,plain,
( ! [X0,X1] :
( ~ c_Wellfounded_Owf(X0,X1)
| sP2(X0,c_Transitive__Closure_Otrancl(X0,X1)) )
| ~ spl104_53
| ~ spl104_86 ),
inference(resolution,[],[f3259,f3112]) ).
fof(f5895,plain,
spl104_334,
inference(avatar_split_clause,[],[f2016,f5893]) ).
fof(f2016,plain,
! [X0,X1] :
( c_Relation_Otrans(X1,X0)
| c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,sK30(X0,X1),sK31(X0,X1)),X0) ),
inference(cnf_transformation,[],[f1587]) ).
fof(f5891,plain,
spl104_333,
inference(avatar_split_clause,[],[f2013,f5889]) ).
fof(f2013,plain,
! [X0,X1] :
( c_Relation_Oantisym(X1,X0)
| c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,sK29(X0,X1),sK28(X0,X1)),X0) ),
inference(cnf_transformation,[],[f1582]) ).
fof(f5887,plain,
spl104_332,
inference(avatar_split_clause,[],[f2012,f5885]) ).
fof(f2012,plain,
! [X0,X1] :
( c_Relation_Oantisym(X1,X0)
| c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,sK28(X0,X1),sK29(X0,X1)),X0) ),
inference(cnf_transformation,[],[f1582]) ).
fof(f5883,plain,
spl104_331,
inference(avatar_split_clause,[],[f2004,f5881]) ).
fof(f2004,plain,
! [X0,X1] :
( c_Relation_Otrans(X1,X0)
| ~ c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,sK24(X0,X1),sK26(X0,X1)),X0) ),
inference(cnf_transformation,[],[f1572]) ).
fof(f1572,plain,
! [X0,X1] :
( c_Relation_Otrans(X1,X0)
| ( ~ c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,sK24(X0,X1),sK26(X0,X1)),X0)
& c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,sK25(X0,X1),sK26(X0,X1)),X0)
& c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,sK24(X0,X1),sK25(X0,X1)),X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK24,sK25,sK26])],[f1073,f1571,f1570]) ).
fof(f1570,plain,
! [X0,X1] :
( ? [X2,X3] :
( ? [X4] :
( ~ c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,X2,X4),X0)
& c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,X3,X4),X0) )
& c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,X2,X3),X0) )
=> ( ? [X4] :
( ~ c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,sK24(X0,X1),X4),X0)
& c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,sK25(X0,X1),X4),X0) )
& c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,sK24(X0,X1),sK25(X0,X1)),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f1571,plain,
! [X0,X1] :
( ? [X4] :
( ~ c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,sK24(X0,X1),X4),X0)
& c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,sK25(X0,X1),X4),X0) )
=> ( ~ c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,sK24(X0,X1),sK26(X0,X1)),X0)
& c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,sK25(X0,X1),sK26(X0,X1)),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f1073,plain,
! [X0,X1] :
( c_Relation_Otrans(X1,X0)
| ? [X2,X3] :
( ? [X4] :
( ~ c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,X2,X4),X0)
& c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,X3,X4),X0) )
& c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,X2,X3),X0) ) ),
inference(ennf_transformation,[],[f628]) ).
fof(f628,plain,
! [X0,X1] :
( ! [X2,X3] :
( c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,X2,X3),X0)
=> ! [X4] :
( c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,X3,X4),X0)
=> c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,X2,X4),X0) ) )
=> c_Relation_Otrans(X1,X0) ),
inference(rectify,[],[f24]) ).
fof(f24,axiom,
! [X3,X4] :
( ! [X2,X5] :
( c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X2,X5),X3)
=> ! [X6] :
( c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X5,X6),X3)
=> c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X2,X6),X3) ) )
=> c_Relation_Otrans(X4,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transI) ).
fof(f5879,plain,
spl104_330,
inference(avatar_split_clause,[],[f2003,f5877]) ).
fof(f2003,plain,
! [X0,X1] :
( c_Relation_Otrans(X1,X0)
| c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,sK25(X0,X1),sK26(X0,X1)),X0) ),
inference(cnf_transformation,[],[f1572]) ).
fof(f5875,plain,
spl104_329,
inference(avatar_split_clause,[],[f2002,f5873]) ).
fof(f2002,plain,
! [X0,X1] :
( c_Relation_Otrans(X1,X0)
| c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,sK24(X0,X1),sK25(X0,X1)),X0) ),
inference(cnf_transformation,[],[f1572]) ).
fof(f5871,plain,
spl104_328,
inference(avatar_split_clause,[],[f2000,f5869]) ).
fof(f2000,plain,
! [X0,X1] :
( c_Relation_Oantisym(X1,X0)
| c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,sK23(X0,X1),sK22(X0,X1)),X0) ),
inference(cnf_transformation,[],[f1569]) ).
fof(f1569,plain,
! [X0,X1] :
( c_Relation_Oantisym(X1,X0)
| ( sK22(X0,X1) != sK23(X0,X1)
& c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,sK23(X0,X1),sK22(X0,X1)),X0)
& c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,sK22(X0,X1),sK23(X0,X1)),X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK22,sK23])],[f1072,f1568]) ).
fof(f1568,plain,
! [X0,X1] :
( ? [X2,X3] :
( X2 != X3
& c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,X3,X2),X0)
& c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,X2,X3),X0) )
=> ( sK22(X0,X1) != sK23(X0,X1)
& c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,sK23(X0,X1),sK22(X0,X1)),X0)
& c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,sK22(X0,X1),sK23(X0,X1)),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f1072,plain,
! [X0,X1] :
( c_Relation_Oantisym(X1,X0)
| ? [X2,X3] :
( X2 != X3
& c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,X3,X2),X0)
& c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,X2,X3),X0) ) ),
inference(flattening,[],[f1071]) ).
fof(f1071,plain,
! [X0,X1] :
( c_Relation_Oantisym(X1,X0)
| ? [X2,X3] :
( X2 != X3
& c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,X3,X2),X0)
& c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,X2,X3),X0) ) ),
inference(ennf_transformation,[],[f627]) ).
fof(f627,plain,
! [X0,X1] :
( ! [X2,X3] :
( c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,X2,X3),X0)
=> ( c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,X3,X2),X0)
=> X2 = X3 ) )
=> c_Relation_Oantisym(X1,X0) ),
inference(rectify,[],[f197]) ).
fof(f197,axiom,
! [X3,X4] :
( ! [X2,X5] :
( c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X2,X5),X3)
=> ( c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X5,X2),X3)
=> X2 = X5 ) )
=> c_Relation_Oantisym(X4,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_antisymI) ).
fof(f5867,plain,
spl104_327,
inference(avatar_split_clause,[],[f1999,f5865]) ).
fof(f1999,plain,
! [X0,X1] :
( c_Relation_Oantisym(X1,X0)
| c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,sK22(X0,X1),sK23(X0,X1)),X0) ),
inference(cnf_transformation,[],[f1569]) ).
fof(f5863,plain,
spl104_326,
inference(avatar_split_clause,[],[f1980,f5861]) ).
fof(f5861,plain,
( spl104_326
<=> ! [X0,X1] :
( c_Relation_Otrans(X1,c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),X0,c_Relation_OId(X1)))
| ~ c_Relation_Oantisym(X1,X0)
| ~ c_Relation_Otrans(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_326])]) ).
fof(f1980,plain,
! [X0,X1] :
( c_Relation_Otrans(X1,c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),X0,c_Relation_OId(X1)))
| ~ c_Relation_Oantisym(X1,X0)
| ~ c_Relation_Otrans(X1,X0) ),
inference(cnf_transformation,[],[f1051]) ).
fof(f1051,plain,
! [X0,X1] :
( c_Relation_Otrans(X1,c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),X0,c_Relation_OId(X1)))
| ~ c_Relation_Oantisym(X1,X0)
| ~ c_Relation_Otrans(X1,X0) ),
inference(flattening,[],[f1050]) ).
fof(f1050,plain,
! [X0,X1] :
( c_Relation_Otrans(X1,c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),X0,c_Relation_OId(X1)))
| ~ c_Relation_Oantisym(X1,X0)
| ~ c_Relation_Otrans(X1,X0) ),
inference(ennf_transformation,[],[f610]) ).
fof(f610,plain,
! [X0,X1] :
( c_Relation_Otrans(X1,X0)
=> ( c_Relation_Oantisym(X1,X0)
=> c_Relation_Otrans(X1,c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),X0,c_Relation_OId(X1))) ) ),
inference(rectify,[],[f214]) ).
fof(f214,axiom,
! [X3,X4] :
( c_Relation_Otrans(X4,X3)
=> ( c_Relation_Oantisym(X4,X3)
=> c_Relation_Otrans(X4,c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),X3,c_Relation_OId(X4))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trans__diff__Id) ).
fof(f5859,plain,
spl104_325,
inference(avatar_split_clause,[],[f1891,f5856]) ).
fof(f1891,plain,
c_FunDef_Opair__leq = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),tc_HOL_Obool),c_FunDef_Opair__less,c_Relation_OId(tc_prod(tc_Nat_Onat,tc_Nat_Onat))),
inference(cnf_transformation,[],[f455]) ).
fof(f455,axiom,
c_FunDef_Opair__leq = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),tc_HOL_Obool),c_FunDef_Opair__less,c_Relation_OId(tc_prod(tc_Nat_Onat,tc_Nat_Onat))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pair__leq__def) ).
fof(f5854,plain,
( ~ spl104_23
| spl104_323
| ~ spl104_324
| spl104_1 ),
inference(avatar_split_clause,[],[f1861,f2878,f5851,f5847,f2987]) ).
fof(f1861,plain,
( sP0
| sK15 != sK16
| c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,sK17,sK17),v_L)
| ~ c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,v_L) ),
inference(cnf_transformation,[],[f1558]) ).
fof(f5757,plain,
spl104_322,
inference(avatar_split_clause,[],[f2785,f5755]) ).
fof(f2785,plain,
! [X3,X0,X1] :
( c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,X3,X3),c_Relation_OId__on(X1,X0))
| ~ c_member(X1,X3,X0) ),
inference(equality_resolution,[],[f2322]) ).
fof(f2322,plain,
! [X2,X3,X0,X1] :
( c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,X3,X2),c_Relation_OId__on(X1,X0))
| ~ c_member(X1,X3,X0)
| X2 != X3 ),
inference(cnf_transformation,[],[f1298]) ).
fof(f1298,plain,
! [X0,X1,X2,X3] :
( c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,X3,X2),c_Relation_OId__on(X1,X0))
| ~ c_member(X1,X3,X0)
| X2 != X3 ),
inference(flattening,[],[f1297]) ).
fof(f1297,plain,
! [X0,X1,X2,X3] :
( c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,X3,X2),c_Relation_OId__on(X1,X0))
| ~ c_member(X1,X3,X0)
| X2 != X3 ),
inference(ennf_transformation,[],[f841]) ).
fof(f841,plain,
! [X0,X1,X2,X3] :
( X2 = X3
=> ( c_member(X1,X3,X0)
=> c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,X3,X2),c_Relation_OId__on(X1,X0)) ) ),
inference(rectify,[],[f22]) ).
fof(f22,axiom,
! [X11,X4,X8,X9] :
( X8 = X9
=> ( c_member(X4,X9,X11)
=> c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X9,X8),c_Relation_OId__on(X4,X11)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Id__on__eqI) ).
fof(f5753,plain,
spl104_321,
inference(avatar_split_clause,[],[f2645,f5751]) ).
fof(f5751,plain,
( spl104_321
<=> ! [X0,X1] :
( c_Relation_Oantisym(X1,c_Transitive__Closure_Otrancl(X1,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),X0,c_Relation_OId(X1))))
| ~ c_Wellfounded_Oacyclic(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_321])]) ).
fof(f2645,plain,
! [X0,X1] :
( c_Relation_Oantisym(X1,c_Transitive__Closure_Otrancl(X1,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),X0,c_Relation_OId(X1))))
| ~ c_Wellfounded_Oacyclic(X1,X0) ),
inference(definition_unfolding,[],[f1977,f1949]) ).
fof(f1977,plain,
! [X0,X1] :
( c_Relation_Oantisym(X1,c_Transitive__Closure_Ortrancl(X1,X0))
| ~ c_Wellfounded_Oacyclic(X1,X0) ),
inference(cnf_transformation,[],[f1047]) ).
fof(f1047,plain,
! [X0,X1] :
( c_Relation_Oantisym(X1,c_Transitive__Closure_Ortrancl(X1,X0))
| ~ c_Wellfounded_Oacyclic(X1,X0) ),
inference(ennf_transformation,[],[f607]) ).
fof(f607,plain,
! [X0,X1] :
( c_Wellfounded_Oacyclic(X1,X0)
=> c_Relation_Oantisym(X1,c_Transitive__Closure_Ortrancl(X1,X0)) ),
inference(rectify,[],[f112]) ).
fof(f112,axiom,
! [X3,X4] :
( c_Wellfounded_Oacyclic(X4,X3)
=> c_Relation_Oantisym(X4,c_Transitive__Closure_Ortrancl(X4,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_acyclic__impl__antisym__rtrancl) ).
fof(f5749,plain,
spl104_320,
inference(avatar_split_clause,[],[f2578,f5747]) ).
fof(f5747,plain,
( spl104_320
<=> ! [X2,X3,X4,X0,X5,X1] : hAPP(hAPP(X2,X1),X0) = c_Product__Type_Oprod_Oprod__rec(X5,X4,X3,X2,c_Product__Type_OPair(X5,X4,X1,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_320])]) ).
fof(f2578,plain,
! [X2,X3,X0,X1,X4,X5] : hAPP(hAPP(X2,X1),X0) = c_Product__Type_Oprod_Oprod__rec(X5,X4,X3,X2,c_Product__Type_OPair(X5,X4,X1,X0)),
inference(cnf_transformation,[],[f992]) ).
fof(f992,plain,
! [X0,X1,X2,X3,X4,X5] : hAPP(hAPP(X2,X1),X0) = c_Product__Type_Oprod_Oprod__rec(X5,X4,X3,X2,c_Product__Type_OPair(X5,X4,X1,X0)),
inference(rectify,[],[f16]) ).
fof(f16,axiom,
! [X8,X9,X28,X4,X29,X15] : c_Product__Type_Oprod_Oprod__rec(X15,X29,X4,X28,c_Product__Type_OPair(X15,X29,X9,X8)) = hAPP(hAPP(X28,X9),X8),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_prod_Orecs) ).
fof(f5745,plain,
spl104_319,
inference(avatar_split_clause,[],[f2577,f5743]) ).
fof(f5743,plain,
( spl104_319
<=> ! [X3,X4,X0,X5,X2,X1] : c_Product__Type_Ointernal__split(X5,X4,X3,X2,c_Product__Type_OPair(X5,X4,X1,X0)) = hAPP(hAPP(X2,X1),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_319])]) ).
fof(f2577,plain,
! [X2,X3,X0,X1,X4,X5] : c_Product__Type_Ointernal__split(X5,X4,X3,X2,c_Product__Type_OPair(X5,X4,X1,X0)) = hAPP(hAPP(X2,X1),X0),
inference(cnf_transformation,[],[f991]) ).
fof(f991,plain,
! [X0,X1,X2,X3,X4,X5] : c_Product__Type_Ointernal__split(X5,X4,X3,X2,c_Product__Type_OPair(X5,X4,X1,X0)) = hAPP(hAPP(X2,X1),X0),
inference(rectify,[],[f19]) ).
fof(f19,axiom,
! [X8,X9,X7,X4,X29,X15] : c_Product__Type_Ointernal__split(X15,X29,X4,X7,c_Product__Type_OPair(X15,X29,X9,X8)) = hAPP(hAPP(X7,X9),X8),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_internal__split__conv) ).
fof(f5741,plain,
spl104_318,
inference(avatar_split_clause,[],[f2481,f5739]) ).
fof(f5739,plain,
( spl104_318
<=> ! [X0,X3,X2,X1] :
( c_member(X3,X2,X0)
| ~ c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X2,X1),c_Relation_OId__on(X3,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_318])]) ).
fof(f2481,plain,
! [X2,X3,X0,X1] :
( c_member(X3,X2,X0)
| ~ c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X2,X1),c_Relation_OId__on(X3,X0)) ),
inference(cnf_transformation,[],[f1770]) ).
fof(f1770,plain,
! [X0,X1,X2,X3] :
( ( c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X2,X1),c_Relation_OId__on(X3,X0))
| ~ c_member(X3,X2,X0)
| X1 != X2 )
& ( ( c_member(X3,X2,X0)
& X1 = X2 )
| ~ c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X2,X1),c_Relation_OId__on(X3,X0)) ) ),
inference(flattening,[],[f1769]) ).
fof(f1769,plain,
! [X0,X1,X2,X3] :
( ( c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X2,X1),c_Relation_OId__on(X3,X0))
| ~ c_member(X3,X2,X0)
| X1 != X2 )
& ( ( c_member(X3,X2,X0)
& X1 = X2 )
| ~ c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X2,X1),c_Relation_OId__on(X3,X0)) ) ),
inference(nnf_transformation,[],[f936]) ).
fof(f936,plain,
! [X0,X1,X2,X3] :
( c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X2,X1),c_Relation_OId__on(X3,X0))
<=> ( c_member(X3,X2,X0)
& X1 = X2 ) ),
inference(rectify,[],[f21]) ).
fof(f21,axiom,
! [X11,X12,X13,X4] :
( c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X13,X12),c_Relation_OId__on(X4,X11))
<=> ( c_member(X4,X13,X11)
& X12 = X13 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Id__on__iff) ).
fof(f5737,plain,
spl104_317,
inference(avatar_split_clause,[],[f2446,f5735]) ).
fof(f5735,plain,
( spl104_317
<=> ! [X0,X3,X2,X1] :
( sP5(X0,X1,X2,X3)
| ~ sP4(X3,X2,X1,X0)
| ~ c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool),X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_317])]) ).
fof(f2446,plain,
! [X2,X3,X0,X1] :
( sP5(X0,X1,X2,X3)
| ~ sP4(X3,X2,X1,X0)
| ~ c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool),X2,X3) ),
inference(cnf_transformation,[],[f1749]) ).
fof(f1749,plain,
! [X0,X1,X2,X3] :
( ( sP5(X0,X1,X2,X3)
| ( ~ sP4(X3,X2,X1,X0)
& ~ c_member(X1,X0,X3) )
| ( ~ c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool),X2,X3)
& c_member(X1,X0,X3) ) )
& ( ( ( sP4(X3,X2,X1,X0)
| c_member(X1,X0,X3) )
& ( c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool),X2,X3)
| ~ c_member(X1,X0,X3) ) )
| ~ sP5(X0,X1,X2,X3) ) ),
inference(rectify,[],[f1748]) ).
fof(f1748,plain,
! [X1,X3,X2,X0] :
( ( sP5(X1,X3,X2,X0)
| ( ~ sP4(X0,X2,X3,X1)
& ~ c_member(X3,X1,X0) )
| ( ~ c_Orderings_Oord__class_Oless(tc_fun(X3,tc_HOL_Obool),X2,X0)
& c_member(X3,X1,X0) ) )
& ( ( ( sP4(X0,X2,X3,X1)
| c_member(X3,X1,X0) )
& ( c_Orderings_Oord__class_Oless(tc_fun(X3,tc_HOL_Obool),X2,X0)
| ~ c_member(X3,X1,X0) ) )
| ~ sP5(X1,X3,X2,X0) ) ),
inference(flattening,[],[f1747]) ).
fof(f1747,plain,
! [X1,X3,X2,X0] :
( ( sP5(X1,X3,X2,X0)
| ( ~ sP4(X0,X2,X3,X1)
& ~ c_member(X3,X1,X0) )
| ( ~ c_Orderings_Oord__class_Oless(tc_fun(X3,tc_HOL_Obool),X2,X0)
& c_member(X3,X1,X0) ) )
& ( ( ( sP4(X0,X2,X3,X1)
| c_member(X3,X1,X0) )
& ( c_Orderings_Oord__class_Oless(tc_fun(X3,tc_HOL_Obool),X2,X0)
| ~ c_member(X3,X1,X0) ) )
| ~ sP5(X1,X3,X2,X0) ) ),
inference(nnf_transformation,[],[f1534]) ).
fof(f1534,plain,
! [X1,X3,X2,X0] :
( sP5(X1,X3,X2,X0)
<=> ( ( sP4(X0,X2,X3,X1)
| c_member(X3,X1,X0) )
& ( c_Orderings_Oord__class_Oless(tc_fun(X3,tc_HOL_Obool),X2,X0)
| ~ c_member(X3,X1,X0) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP5])]) ).
fof(f5733,plain,
spl104_316,
inference(avatar_split_clause,[],[f2429,f5731]) ).
fof(f5731,plain,
( spl104_316
<=> ! [X0,X3,X2,X1] :
( c_Wellfounded_Owf(tc_prod(X0,X2),c_Recdef_Osame__fst(X0,X2,X3,X1))
| hBOOL(hAPP(X3,sK67(X1,X2,X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_316])]) ).
fof(f2429,plain,
! [X2,X3,X0,X1] :
( c_Wellfounded_Owf(tc_prod(X0,X2),c_Recdef_Osame__fst(X0,X2,X3,X1))
| hBOOL(hAPP(X3,sK67(X1,X2,X3))) ),
inference(cnf_transformation,[],[f1734]) ).
fof(f5729,plain,
( ~ spl104_15
| spl104_310
| ~ spl104_127
| ~ spl104_285 ),
inference(avatar_split_clause,[],[f5463,f5291,f3461,f5558,f2947]) ).
fof(f2947,plain,
( spl104_15
<=> class_Orderings_Opreorder(tc_HOL_Obool) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_15])]) ).
fof(f5558,plain,
( spl104_310
<=> ! [X0] : ~ c_Orderings_Oord__class_Oless(tc_HOL_Obool,X0,c_Orderings_Obot__class_Obot(tc_HOL_Obool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_310])]) ).
fof(f5291,plain,
( spl104_285
<=> ! [X0] : c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,c_Orderings_Obot__class_Obot(tc_HOL_Obool),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_285])]) ).
fof(f5463,plain,
( ! [X0] :
( ~ c_Orderings_Oord__class_Oless(tc_HOL_Obool,X0,c_Orderings_Obot__class_Obot(tc_HOL_Obool))
| ~ class_Orderings_Opreorder(tc_HOL_Obool) )
| ~ spl104_127
| ~ spl104_285 ),
inference(resolution,[],[f5292,f3462]) ).
fof(f5292,plain,
( ! [X0] : c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,c_Orderings_Obot__class_Obot(tc_HOL_Obool),X0)
| ~ spl104_285 ),
inference(avatar_component_clause,[],[f5291]) ).
fof(f5728,plain,
spl104_315,
inference(avatar_split_clause,[],[f2393,f5726]) ).
fof(f2393,plain,
! [X2,X3,X0,X1] :
( c_Relation_Osingle__valued(X3,X2,X1)
| ~ c_Relation_Osingle__valued(X3,X2,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X3,X2),tc_HOL_Obool),X1,X0) ),
inference(cnf_transformation,[],[f1391]) ).
fof(f1391,plain,
! [X0,X1,X2,X3] :
( c_Relation_Osingle__valued(X3,X2,X1)
| ~ c_Relation_Osingle__valued(X3,X2,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X3,X2),tc_HOL_Obool),X1,X0) ),
inference(flattening,[],[f1390]) ).
fof(f1390,plain,
! [X0,X1,X2,X3] :
( c_Relation_Osingle__valued(X3,X2,X1)
| ~ c_Relation_Osingle__valued(X3,X2,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X3,X2),tc_HOL_Obool),X1,X0) ),
inference(ennf_transformation,[],[f899]) ).
fof(f899,plain,
! [X0,X1,X2,X3] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X3,X2),tc_HOL_Obool),X1,X0)
=> ( c_Relation_Osingle__valued(X3,X2,X0)
=> c_Relation_Osingle__valued(X3,X2,X1) ) ),
inference(rectify,[],[f274]) ).
fof(f274,axiom,
! [X30,X3,X15,X4] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X4,X15),tc_HOL_Obool),X3,X30)
=> ( c_Relation_Osingle__valued(X4,X15,X30)
=> c_Relation_Osingle__valued(X4,X15,X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_single__valued__subset) ).
fof(f5724,plain,
spl104_314,
inference(avatar_split_clause,[],[f2292,f5722]) ).
fof(f2292,plain,
! [X2,X3,X0,X1,X5] :
( c_Orderings_Oord__class_Oless__eq(X3,hAPP(X1,X5),hAPP(X0,X5))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X2,X3),X1,X0)
| ~ class_Orderings_Oord(X3) ),
inference(cnf_transformation,[],[f1699]) ).
fof(f5720,plain,
spl104_313,
inference(avatar_split_clause,[],[f2263,f5718]) ).
fof(f5718,plain,
( spl104_313
<=> ! [X2,X0,X1] :
( c_Relation_Ototal__on(X2,X1,c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),X0,c_Relation_OId(X2)))
| ~ c_Relation_Ototal__on(X2,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_313])]) ).
fof(f2263,plain,
! [X2,X0,X1] :
( c_Relation_Ototal__on(X2,X1,c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),X0,c_Relation_OId(X2)))
| ~ c_Relation_Ototal__on(X2,X1,X0) ),
inference(cnf_transformation,[],[f1688]) ).
fof(f1688,plain,
! [X0,X1,X2] :
( ( c_Relation_Ototal__on(X2,X1,c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),X0,c_Relation_OId(X2)))
| ~ c_Relation_Ototal__on(X2,X1,X0) )
& ( c_Relation_Ototal__on(X2,X1,X0)
| ~ c_Relation_Ototal__on(X2,X1,c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),X0,c_Relation_OId(X2))) ) ),
inference(nnf_transformation,[],[f790]) ).
fof(f790,plain,
! [X0,X1,X2] :
( c_Relation_Ototal__on(X2,X1,c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),X0,c_Relation_OId(X2)))
<=> c_Relation_Ototal__on(X2,X1,X0) ),
inference(rectify,[],[f212]) ).
fof(f212,axiom,
! [X3,X11,X4] :
( c_Relation_Ototal__on(X4,X11,c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),X3,c_Relation_OId(X4)))
<=> c_Relation_Ototal__on(X4,X11,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_total__on__diff__Id) ).
fof(f5716,plain,
spl104_312,
inference(avatar_split_clause,[],[f2262,f5714]) ).
fof(f5714,plain,
( spl104_312
<=> ! [X2,X0,X1] :
( c_Relation_Ototal__on(X2,X1,X0)
| ~ c_Relation_Ototal__on(X2,X1,c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),X0,c_Relation_OId(X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_312])]) ).
fof(f2262,plain,
! [X2,X0,X1] :
( c_Relation_Ototal__on(X2,X1,X0)
| ~ c_Relation_Ototal__on(X2,X1,c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),X0,c_Relation_OId(X2))) ),
inference(cnf_transformation,[],[f1688]) ).
fof(f5712,plain,
spl104_311,
inference(avatar_split_clause,[],[f2170,f5710]) ).
fof(f5710,plain,
( spl104_311
<=> ! [X2,X0,X1] :
( c_Order__Relation_Ostrict__linear__order__on(X2,X1,c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),X0,c_Relation_OId(X2)))
| ~ c_Order__Relation_Olinear__order__on(X2,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_311])]) ).
fof(f2170,plain,
! [X2,X0,X1] :
( c_Order__Relation_Ostrict__linear__order__on(X2,X1,c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),X0,c_Relation_OId(X2)))
| ~ c_Order__Relation_Olinear__order__on(X2,X1,X0) ),
inference(cnf_transformation,[],[f1199]) ).
fof(f1199,plain,
! [X0,X1,X2] :
( c_Order__Relation_Ostrict__linear__order__on(X2,X1,c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),X0,c_Relation_OId(X2)))
| ~ c_Order__Relation_Olinear__order__on(X2,X1,X0) ),
inference(ennf_transformation,[],[f743]) ).
fof(f743,plain,
! [X0,X1,X2] :
( c_Order__Relation_Olinear__order__on(X2,X1,X0)
=> c_Order__Relation_Ostrict__linear__order__on(X2,X1,c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),X0,c_Relation_OId(X2))) ),
inference(rectify,[],[f196]) ).
fof(f196,axiom,
! [X3,X11,X4] :
( c_Order__Relation_Olinear__order__on(X4,X11,X3)
=> c_Order__Relation_Ostrict__linear__order__on(X4,X11,c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),X3,c_Relation_OId(X4))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_strict__linear__order__on__diff__Id) ).
fof(f5560,plain,
( ~ spl104_309
| spl104_310
| ~ spl104_122
| ~ spl104_285 ),
inference(avatar_split_clause,[],[f5462,f5291,f3440,f5558,f5554]) ).
fof(f5554,plain,
( spl104_309
<=> class_Orderings_Olinorder(tc_HOL_Obool) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_309])]) ).
fof(f5462,plain,
( ! [X0] :
( ~ c_Orderings_Oord__class_Oless(tc_HOL_Obool,X0,c_Orderings_Obot__class_Obot(tc_HOL_Obool))
| ~ class_Orderings_Olinorder(tc_HOL_Obool) )
| ~ spl104_122
| ~ spl104_285 ),
inference(resolution,[],[f5292,f3441]) ).
fof(f5491,plain,
spl104_308,
inference(avatar_split_clause,[],[f2480,f5489]) ).
fof(f2480,plain,
! [X2,X3,X0,X1] :
( X1 = X2
| ~ c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X2,X1),c_Relation_OId__on(X3,X0)) ),
inference(cnf_transformation,[],[f1770]) ).
fof(f5487,plain,
spl104_307,
inference(avatar_split_clause,[],[f2464,f5485]) ).
fof(f2464,plain,
! [X2,X3,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),c_Set_Oinsert(X3,X2,X1),X0) ),
inference(cnf_transformation,[],[f1759]) ).
fof(f5483,plain,
spl104_306,
inference(avatar_split_clause,[],[f2459,f5481]) ).
fof(f5481,plain,
( spl104_306
<=> ! [X0,X3,X2,X1] :
( sP6(X0,X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool),X1,X0)
| c_member(X2,X3,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_306])]) ).
fof(f2459,plain,
! [X2,X3,X0,X1] :
( sP6(X0,X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool),X1,X0)
| c_member(X2,X3,X1) ),
inference(cnf_transformation,[],[f1756]) ).
fof(f5479,plain,
spl104_305,
inference(avatar_split_clause,[],[f2456,f5477]) ).
fof(f5477,plain,
( spl104_305
<=> ! [X0,X3,X2,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool),X1,X0)
| c_member(X2,X3,X1)
| ~ sP6(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_305])]) ).
fof(f2456,plain,
! [X2,X3,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool),X1,X0)
| c_member(X2,X3,X1)
| ~ sP6(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f1756]) ).
fof(f5461,plain,
spl104_304,
inference(avatar_split_clause,[],[f2451,f5459]) ).
fof(f2451,plain,
! [X2,X3,X0,X1] :
( sP4(X0,X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool),X1,X0)
| c_member(X2,X3,X1) ),
inference(cnf_transformation,[],[f1752]) ).
fof(f5457,plain,
spl104_303,
inference(avatar_split_clause,[],[f2448,f5455]) ).
fof(f5455,plain,
( spl104_303
<=> ! [X0,X3,X2,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool),X1,X0)
| c_member(X2,X3,X1)
| ~ sP4(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_303])]) ).
fof(f2448,plain,
! [X2,X3,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool),X1,X0)
| c_member(X2,X3,X1)
| ~ sP4(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f1752]) ).
fof(f5453,plain,
spl104_302,
inference(avatar_split_clause,[],[f2444,f5451]) ).
fof(f5451,plain,
( spl104_302
<=> ! [X0,X3,X2,X1] :
( sP5(X0,X1,X2,X3)
| ~ c_member(X1,X0,X3)
| ~ c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool),X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_302])]) ).
fof(f2444,plain,
! [X2,X3,X0,X1] :
( sP5(X0,X1,X2,X3)
| ~ c_member(X1,X0,X3)
| ~ c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool),X2,X3) ),
inference(cnf_transformation,[],[f1749]) ).
fof(f5449,plain,
spl104_301,
inference(avatar_split_clause,[],[f2441,f5447]) ).
fof(f5447,plain,
( spl104_301
<=> ! [X0,X3,X2,X1] :
( c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool),X2,X3)
| ~ c_member(X1,X0,X3)
| ~ sP5(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_301])]) ).
fof(f2441,plain,
! [X2,X3,X0,X1] :
( c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool),X2,X3)
| ~ c_member(X1,X0,X3)
| ~ sP5(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f1749]) ).
fof(f5445,plain,
spl104_300,
inference(avatar_split_clause,[],[f2365,f5443]) ).
fof(f2365,plain,
! [X2,X3,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X2,c_Set_Oinsert(X3,X0,X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X2,X1) ),
inference(cnf_transformation,[],[f1354]) ).
fof(f1354,plain,
! [X0,X1,X2,X3] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X2,c_Set_Oinsert(X3,X0,X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X2,X1) ),
inference(ennf_transformation,[],[f878]) ).
fof(f878,plain,
! [X0,X1,X2,X3] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X2,X1)
=> c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X2,c_Set_Oinsert(X3,X0,X1)) ),
inference(rectify,[],[f244]) ).
fof(f244,axiom,
! [X8,X10,X11,X4] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool),X11,X10)
=> c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool),X11,c_Set_Oinsert(X4,X8,X10)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__insertI2) ).
fof(f5441,plain,
spl104_299,
inference(avatar_split_clause,[],[f2336,f5439]) ).
fof(f5439,plain,
( spl104_299
<=> ! [X0,X3,X2,X1] :
( c_Wellfounded_Owf(tc_prod(X3,X1),c_Wellfounded_Olex__prod(X3,X1,X2,X0))
| ~ c_Wellfounded_Owf(X1,X0)
| ~ c_Wellfounded_Owf(X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_299])]) ).
fof(f2336,plain,
! [X2,X3,X0,X1] :
( c_Wellfounded_Owf(tc_prod(X3,X1),c_Wellfounded_Olex__prod(X3,X1,X2,X0))
| ~ c_Wellfounded_Owf(X1,X0)
| ~ c_Wellfounded_Owf(X3,X2) ),
inference(cnf_transformation,[],[f1311]) ).
fof(f1311,plain,
! [X0,X1,X2,X3] :
( c_Wellfounded_Owf(tc_prod(X3,X1),c_Wellfounded_Olex__prod(X3,X1,X2,X0))
| ~ c_Wellfounded_Owf(X1,X0)
| ~ c_Wellfounded_Owf(X3,X2) ),
inference(flattening,[],[f1310]) ).
fof(f1310,plain,
! [X0,X1,X2,X3] :
( c_Wellfounded_Owf(tc_prod(X3,X1),c_Wellfounded_Olex__prod(X3,X1,X2,X0))
| ~ c_Wellfounded_Owf(X1,X0)
| ~ c_Wellfounded_Owf(X3,X2) ),
inference(ennf_transformation,[],[f850]) ).
fof(f850,plain,
! [X0,X1,X2,X3] :
( c_Wellfounded_Owf(X3,X2)
=> ( c_Wellfounded_Owf(X1,X0)
=> c_Wellfounded_Owf(tc_prod(X3,X1),c_Wellfounded_Olex__prod(X3,X1,X2,X0)) ) ),
inference(rectify,[],[f162]) ).
fof(f162,axiom,
! [X56,X15,X57,X4] :
( c_Wellfounded_Owf(X4,X57)
=> ( c_Wellfounded_Owf(X15,X56)
=> c_Wellfounded_Owf(tc_prod(X4,X15),c_Wellfounded_Olex__prod(X4,X15,X57,X56)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__lex__prod) ).
fof(f5437,plain,
spl104_298,
inference(avatar_split_clause,[],[f2334,f5435]) ).
fof(f2334,plain,
! [X2,X3,X0,X1] :
( c_Relation_Otrans(tc_prod(X3,X1),c_Wellfounded_Olex__prod(X3,X1,X2,X0))
| ~ c_Relation_Otrans(X1,X0)
| ~ c_Relation_Otrans(X3,X2) ),
inference(cnf_transformation,[],[f1308]) ).
fof(f1308,plain,
! [X0,X1,X2,X3] :
( c_Relation_Otrans(tc_prod(X3,X1),c_Wellfounded_Olex__prod(X3,X1,X2,X0))
| ~ c_Relation_Otrans(X1,X0)
| ~ c_Relation_Otrans(X3,X2) ),
inference(flattening,[],[f1307]) ).
fof(f1307,plain,
! [X0,X1,X2,X3] :
( c_Relation_Otrans(tc_prod(X3,X1),c_Wellfounded_Olex__prod(X3,X1,X2,X0))
| ~ c_Relation_Otrans(X1,X0)
| ~ c_Relation_Otrans(X3,X2) ),
inference(ennf_transformation,[],[f848]) ).
fof(f848,plain,
! [X0,X1,X2,X3] :
( c_Relation_Otrans(X3,X2)
=> ( c_Relation_Otrans(X1,X0)
=> c_Relation_Otrans(tc_prod(X3,X1),c_Wellfounded_Olex__prod(X3,X1,X2,X0)) ) ),
inference(rectify,[],[f27]) ).
fof(f27,axiom,
! [X32,X15,X33,X4] :
( c_Relation_Otrans(X4,X33)
=> ( c_Relation_Otrans(X15,X32)
=> c_Relation_Otrans(tc_prod(X4,X15),c_Wellfounded_Olex__prod(X4,X15,X33,X32)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trans__lex__prod) ).
fof(f5433,plain,
spl104_297,
inference(avatar_split_clause,[],[f2268,f5431]) ).
fof(f2268,plain,
! [X2,X3,X0,X1] : c_Set_Oinsert(X3,X2,c_Set_Oinsert(X3,X1,X0)) = c_Set_Oinsert(X3,X1,c_Set_Oinsert(X3,X2,X0)),
inference(cnf_transformation,[],[f794]) ).
fof(f794,plain,
! [X0,X1,X2,X3] : c_Set_Oinsert(X3,X2,c_Set_Oinsert(X3,X1,X0)) = c_Set_Oinsert(X3,X1,c_Set_Oinsert(X3,X2,X0)),
inference(rectify,[],[f125]) ).
fof(f125,axiom,
! [X11,X12,X13,X4] : c_Set_Oinsert(X4,X13,c_Set_Oinsert(X4,X12,X11)) = c_Set_Oinsert(X4,X12,c_Set_Oinsert(X4,X13,X11)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__commute) ).
fof(f5429,plain,
spl104_296,
inference(avatar_split_clause,[],[f2250,f5427]) ).
fof(f5427,plain,
( spl104_296
<=> ! [X2,X0,X1] :
( c_member(X2,X1,c_Wellfounded_Oacc(X2,X0))
| ~ c_member(X2,sK51(X0,X1,X2),c_Wellfounded_Oacc(X2,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_296])]) ).
fof(f2250,plain,
! [X2,X0,X1] :
( c_member(X2,X1,c_Wellfounded_Oacc(X2,X0))
| ~ c_member(X2,sK51(X0,X1,X2),c_Wellfounded_Oacc(X2,X0)) ),
inference(cnf_transformation,[],[f1681]) ).
fof(f5425,plain,
spl104_295,
inference(avatar_split_clause,[],[f2242,f5423]) ).
fof(f5423,plain,
( spl104_295
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless(tc_fun(X2,tc_HOL_Obool),X1,X0)
| X0 = X1
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_295])]) ).
fof(f2242,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless(tc_fun(X2,tc_HOL_Obool),X1,X0)
| X0 = X1
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool),X1,X0) ),
inference(cnf_transformation,[],[f1674]) ).
fof(f1674,plain,
! [X0,X1,X2] :
( ( c_Orderings_Oord__class_Oless(tc_fun(X2,tc_HOL_Obool),X1,X0)
| X0 = X1
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool),X1,X0) )
& ( ( X0 != X1
& c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool),X1,X0) )
| ~ c_Orderings_Oord__class_Oless(tc_fun(X2,tc_HOL_Obool),X1,X0) ) ),
inference(flattening,[],[f1673]) ).
fof(f1673,plain,
! [X0,X1,X2] :
( ( c_Orderings_Oord__class_Oless(tc_fun(X2,tc_HOL_Obool),X1,X0)
| X0 = X1
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool),X1,X0) )
& ( ( X0 != X1
& c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool),X1,X0) )
| ~ c_Orderings_Oord__class_Oless(tc_fun(X2,tc_HOL_Obool),X1,X0) ) ),
inference(nnf_transformation,[],[f781]) ).
fof(f781,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless(tc_fun(X2,tc_HOL_Obool),X1,X0)
<=> ( X0 != X1
& c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool),X1,X0) ) ),
inference(rectify,[],[f287]) ).
fof(f287,axiom,
! [X10,X11,X4] :
( c_Orderings_Oord__class_Oless(tc_fun(X4,tc_HOL_Obool),X11,X10)
<=> ( X10 != X11
& c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool),X11,X10) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_psubset__eq) ).
fof(f5421,plain,
spl104_294,
inference(avatar_split_clause,[],[f2216,f5419]) ).
fof(f5419,plain,
( spl104_294
<=> ! [X2,X0,X1] :
( c_Wellfounded_Owf(X2,c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),X0,c_Relation_OId(X2)))
| ~ c_Order__Relation_Owell__order__on(X2,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_294])]) ).
fof(f2216,plain,
! [X2,X0,X1] :
( c_Wellfounded_Owf(X2,c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),X0,c_Relation_OId(X2)))
| ~ c_Order__Relation_Owell__order__on(X2,X1,X0) ),
inference(cnf_transformation,[],[f1234]) ).
fof(f1234,plain,
! [X0,X1,X2] :
( ( c_Wellfounded_Owf(X2,c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),X0,c_Relation_OId(X2)))
& c_Order__Relation_Olinear__order__on(X2,X1,X0) )
| ~ c_Order__Relation_Owell__order__on(X2,X1,X0) ),
inference(ennf_transformation,[],[f1017]) ).
fof(f1017,plain,
! [X0,X1,X2] :
( c_Order__Relation_Owell__order__on(X2,X1,X0)
=> ( c_Wellfounded_Owf(X2,c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),X0,c_Relation_OId(X2)))
& c_Order__Relation_Olinear__order__on(X2,X1,X0) ) ),
inference(unused_predicate_definition_removal,[],[f773]) ).
fof(f773,plain,
! [X0,X1,X2] :
( c_Order__Relation_Owell__order__on(X2,X1,X0)
<=> ( c_Wellfounded_Owf(X2,c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),X0,c_Relation_OId(X2)))
& c_Order__Relation_Olinear__order__on(X2,X1,X0) ) ),
inference(rectify,[],[f215]) ).
fof(f215,axiom,
! [X3,X11,X4] :
( c_Order__Relation_Owell__order__on(X4,X11,X3)
<=> ( c_Wellfounded_Owf(X4,c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),X3,c_Relation_OId(X4)))
& c_Order__Relation_Olinear__order__on(X4,X11,X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_well__order__on__def) ).
fof(f5417,plain,
spl104_293,
inference(avatar_split_clause,[],[f2205,f5415]) ).
fof(f5415,plain,
( spl104_293
<=> ! [X2,X0,X1] :
( c_member(X2,X1,c_Wellfounded_Oacc(X2,X0))
| ~ c_member(X2,sK42(X0,X1,X2),c_Wellfounded_Oacc(X2,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_293])]) ).
fof(f2205,plain,
! [X2,X0,X1] :
( c_member(X2,X1,c_Wellfounded_Oacc(X2,X0))
| ~ c_member(X2,sK42(X0,X1,X2),c_Wellfounded_Oacc(X2,X0)) ),
inference(cnf_transformation,[],[f1649]) ).
fof(f5413,plain,
spl104_292,
inference(avatar_split_clause,[],[f2191,f5411]) ).
fof(f5411,plain,
( spl104_292
<=> ! [X2,X0,X1] :
( c_member(X2,sK41(X0,X1,X2),X0)
| ~ c_member(tc_prod(X2,X2),X1,c_Relation_OId__on(X2,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_292])]) ).
fof(f2191,plain,
! [X2,X0,X1] :
( c_member(X2,sK41(X0,X1,X2),X0)
| ~ c_member(tc_prod(X2,X2),X1,c_Relation_OId__on(X2,X0)) ),
inference(cnf_transformation,[],[f1645]) ).
fof(f5409,plain,
spl104_291,
inference(avatar_split_clause,[],[f2180,f5407]) ).
fof(f5407,plain,
( spl104_291
<=> ! [X2,X0,X1] :
( X0 = X1
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool),X0,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_291])]) ).
fof(f2180,plain,
! [X2,X0,X1] :
( X0 = X1
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool),X0,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool),X1,X0) ),
inference(cnf_transformation,[],[f1209]) ).
fof(f1209,plain,
! [X0,X1,X2] :
( X0 = X1
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool),X0,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool),X1,X0) ),
inference(flattening,[],[f1208]) ).
fof(f1208,plain,
! [X0,X1,X2] :
( X0 = X1
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool),X0,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool),X1,X0) ),
inference(ennf_transformation,[],[f752]) ).
fof(f752,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool),X1,X0)
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool),X0,X1)
=> X0 = X1 ) ),
inference(rectify,[],[f220]) ).
fof(f220,axiom,
! [X10,X11,X4] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool),X11,X10)
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool),X10,X11)
=> X10 = X11 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_equalityI) ).
fof(f5405,plain,
spl104_290,
inference(avatar_split_clause,[],[f2174,f5403]) ).
fof(f5403,plain,
( spl104_290
<=> ! [X2,X0,X1] :
( ~ c_member(X2,sK40(X0,X1,X2),c_Wellfounded_Oacc(X2,X0))
| c_member(X2,X1,c_Wellfounded_Oacc(X2,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_290])]) ).
fof(f2174,plain,
! [X2,X0,X1] :
( ~ c_member(X2,sK40(X0,X1,X2),c_Wellfounded_Oacc(X2,X0))
| c_member(X2,X1,c_Wellfounded_Oacc(X2,X0)) ),
inference(cnf_transformation,[],[f1642]) ).
fof(f5401,plain,
spl104_289,
inference(avatar_split_clause,[],[f2059,f5399]) ).
fof(f2059,plain,
! [X2,X0,X1] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),X0) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X0),X1),
inference(cnf_transformation,[],[f657]) ).
fof(f657,plain,
! [X0,X1,X2] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),X0) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X0),X1),
inference(rectify,[],[f397]) ).
fof(f397,axiom,
! [X75,X76,X77] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X77,X76),X75) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X77,X75),X76),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__commute) ).
fof(f5397,plain,
spl104_288,
inference(avatar_split_clause,[],[f2034,f5395]) ).
fof(f5395,plain,
( spl104_288
<=> ! [X0,X1] :
( c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) = X0
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X0,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_288])]) ).
fof(f2034,plain,
! [X0,X1] :
( c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) = X0
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X0,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))) ),
inference(cnf_transformation,[],[f1604]) ).
fof(f1604,plain,
! [X0,X1] :
( ( c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X0,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))
| c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) != X0 )
& ( c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) = X0
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X0,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))) ) ),
inference(nnf_transformation,[],[f639]) ).
fof(f639,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X0,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))
<=> c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) = X0 ),
inference(rectify,[],[f440]) ).
fof(f440,axiom,
! [X11,X4] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool),X11,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))
<=> c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)) = X11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__empty) ).
fof(f5393,plain,
spl104_287,
inference(avatar_split_clause,[],[f2009,f5391]) ).
fof(f2009,plain,
! [X3,X0,X1] :
( ~ c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,X3,X3),c_Transitive__Closure_Otrancl(X1,X0))
| ~ c_Wellfounded_Oacyclic(X1,X0) ),
inference(cnf_transformation,[],[f1578]) ).
fof(f5387,plain,
( spl104_286
| ~ spl104_108
| ~ spl104_279 ),
inference(avatar_split_clause,[],[f5343,f4810,f3371,f5385]) ).
fof(f5385,plain,
( spl104_286
<=> ! [X2,X0,X1] : sP6(X0,X0,X1,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_286])]) ).
fof(f5343,plain,
( ! [X2,X0,X1] : sP6(X0,X0,X1,X2)
| ~ spl104_108
| ~ spl104_279 ),
inference(resolution,[],[f4811,f3372]) ).
fof(f5293,plain,
( ~ spl104_13
| spl104_285
| ~ spl104_109
| ~ spl104_209 ),
inference(avatar_split_clause,[],[f4738,f4084,f3375,f5291,f2937]) ).
fof(f4084,plain,
( spl104_209
<=> ! [X0] : c_Lattices_Osemilattice__sup__class_Osup(tc_HOL_Obool,X0,c_Orderings_Obot__class_Obot(tc_HOL_Obool)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl104_209])]) ).
fof(f4738,plain,
( ! [X0] :
( c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,c_Orderings_Obot__class_Obot(tc_HOL_Obool),X0)
| ~ class_Lattices_Olattice(tc_HOL_Obool) )
| ~ spl104_109
| ~ spl104_209 ),
inference(superposition,[],[f3376,f4085]) ).
fof(f4085,plain,
( ! [X0] : c_Lattices_Osemilattice__sup__class_Osup(tc_HOL_Obool,X0,c_Orderings_Obot__class_Obot(tc_HOL_Obool)) = X0
| ~ spl104_209 ),
inference(avatar_component_clause,[],[f4084]) ).
fof(f4948,plain,
( spl104_283
| ~ spl104_284
| ~ spl104_9
| ~ spl104_142
| ~ spl104_156
| ~ spl104_219 ),
inference(avatar_split_clause,[],[f4518,f4124,f3630,f3574,f2917,f4945,f4942]) ).
fof(f4942,plain,
( spl104_283
<=> ! [X2,X1] : hBOOL(hAPP(X1,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_283])]) ).
fof(f4945,plain,
( spl104_284
<=> hBOOL(c_Orderings_Obot__class_Obot(tc_HOL_Obool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_284])]) ).
fof(f3574,plain,
( spl104_142
<=> ! [X0,X1] : c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl104_142])]) ).
fof(f4518,plain,
( ! [X2,X1] :
( ~ hBOOL(c_Orderings_Obot__class_Obot(tc_HOL_Obool))
| hBOOL(hAPP(X1,X2)) )
| ~ spl104_9
| ~ spl104_142
| ~ spl104_156
| ~ spl104_219 ),
inference(forward_demodulation,[],[f4517,f3787]) ).
fof(f4517,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)),X2)) )
| ~ spl104_142
| ~ spl104_219 ),
inference(superposition,[],[f4125,f3575]) ).
fof(f3575,plain,
( ! [X0,X1] : c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),X0) = X0
| ~ spl104_142 ),
inference(avatar_component_clause,[],[f3574]) ).
fof(f4824,plain,
spl104_282,
inference(avatar_split_clause,[],[f2588,f4822]) ).
fof(f4822,plain,
( spl104_282
<=> ! [X5,X4,X0,X3,X2,X1] :
( X0 = X2
| c_Product__Type_OPair(X5,X4,X1,X0) != c_Product__Type_OPair(X5,X4,X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_282])]) ).
fof(f2588,plain,
! [X2,X3,X0,X1,X4,X5] :
( X0 = X2
| c_Product__Type_OPair(X5,X4,X1,X0) != c_Product__Type_OPair(X5,X4,X3,X2) ),
inference(cnf_transformation,[],[f1507]) ).
fof(f1507,plain,
! [X0,X1,X2,X3,X4,X5] :
( ( X0 = X2
& X1 = X3 )
| c_Product__Type_OPair(X5,X4,X1,X0) != c_Product__Type_OPair(X5,X4,X3,X2) ),
inference(ennf_transformation,[],[f1001]) ).
fof(f1001,plain,
! [X0,X1,X2,X3,X4,X5] :
( c_Product__Type_OPair(X5,X4,X1,X0) = c_Product__Type_OPair(X5,X4,X3,X2)
=> ~ ( X1 = X3
=> X0 != X2 ) ),
inference(rectify,[],[f11]) ).
fof(f11,axiom,
! [X24,X25,X26,X27,X15,X4] :
( c_Product__Type_OPair(X4,X15,X27,X26) = c_Product__Type_OPair(X4,X15,X25,X24)
=> ~ ( X25 = X27
=> X24 != X26 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Pair__inject) ).
fof(f4820,plain,
spl104_281,
inference(avatar_split_clause,[],[f2587,f4818]) ).
fof(f4818,plain,
( spl104_281
<=> ! [X5,X4,X0,X3,X2,X1] :
( X1 = X3
| c_Product__Type_OPair(X5,X4,X1,X0) != c_Product__Type_OPair(X5,X4,X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_281])]) ).
fof(f2587,plain,
! [X2,X3,X0,X1,X4,X5] :
( X1 = X3
| c_Product__Type_OPair(X5,X4,X1,X0) != c_Product__Type_OPair(X5,X4,X3,X2) ),
inference(cnf_transformation,[],[f1507]) ).
fof(f4816,plain,
spl104_280,
inference(avatar_split_clause,[],[f2462,f4814]) ).
fof(f4814,plain,
( spl104_280
<=> ! [X0,X3,X2,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X2,c_Set_Oinsert(X3,X1,X0))
| ~ sP6(X0,X2,X3,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_280])]) ).
fof(f2462,plain,
! [X2,X3,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X2,c_Set_Oinsert(X3,X1,X0))
| ~ sP6(X0,X2,X3,X1) ),
inference(cnf_transformation,[],[f1757]) ).
fof(f1757,plain,
! [X0,X1,X2,X3] :
( ( c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X2,c_Set_Oinsert(X3,X1,X0))
| ~ sP6(X0,X2,X3,X1) )
& ( sP6(X0,X2,X3,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X2,c_Set_Oinsert(X3,X1,X0)) ) ),
inference(nnf_transformation,[],[f1537]) ).
fof(f1537,plain,
! [X0,X1,X2,X3] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X2,c_Set_Oinsert(X3,X1,X0))
<=> sP6(X0,X2,X3,X1) ),
inference(definition_folding,[],[f1429,f1536]) ).
fof(f1429,plain,
! [X0,X1,X2,X3] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X2,c_Set_Oinsert(X3,X1,X0))
<=> ( ( c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X2,X0)
| c_member(X3,X1,X2) )
& ( c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),c_Groups_Ominus__class_Ominus(tc_fun(X3,tc_HOL_Obool),X2,c_Set_Oinsert(X3,X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)))),X0)
| ~ c_member(X3,X1,X2) ) ) ),
inference(ennf_transformation,[],[f929]) ).
fof(f929,plain,
! [X0,X1,X2,X3] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X2,c_Set_Oinsert(X3,X1,X0))
<=> ( ( ~ c_member(X3,X1,X2)
=> c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X2,X0) )
& ( c_member(X3,X1,X2)
=> c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),c_Groups_Ominus__class_Ominus(tc_fun(X3,tc_HOL_Obool),X2,c_Set_Oinsert(X3,X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)))),X0) ) ) ),
inference(rectify,[],[f446]) ).
fof(f446,axiom,
! [X10,X13,X11,X4] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool),X11,c_Set_Oinsert(X4,X13,X10))
<=> ( ( ~ c_member(X4,X13,X11)
=> c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool),X11,X10) )
& ( c_member(X4,X13,X11)
=> c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool),c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool),X11,c_Set_Oinsert(X4,X13,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))),X10) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__insert__iff) ).
fof(f4812,plain,
spl104_279,
inference(avatar_split_clause,[],[f2461,f4810]) ).
fof(f2461,plain,
! [X2,X3,X0,X1] :
( sP6(X0,X2,X3,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X2,c_Set_Oinsert(X3,X1,X0)) ),
inference(cnf_transformation,[],[f1757]) ).
fof(f4808,plain,
spl104_278,
inference(avatar_split_clause,[],[f2454,f4806]) ).
fof(f2454,plain,
! [X2,X3,X0,X1] :
( c_Orderings_Oord__class_Oless(tc_fun(X3,tc_HOL_Obool),X2,c_Set_Oinsert(X3,X1,X0))
| ~ sP5(X1,X3,X2,X0) ),
inference(cnf_transformation,[],[f1753]) ).
fof(f1753,plain,
! [X0,X1,X2,X3] :
( ( c_Orderings_Oord__class_Oless(tc_fun(X3,tc_HOL_Obool),X2,c_Set_Oinsert(X3,X1,X0))
| ~ sP5(X1,X3,X2,X0) )
& ( sP5(X1,X3,X2,X0)
| ~ c_Orderings_Oord__class_Oless(tc_fun(X3,tc_HOL_Obool),X2,c_Set_Oinsert(X3,X1,X0)) ) ),
inference(nnf_transformation,[],[f1535]) ).
fof(f1535,plain,
! [X0,X1,X2,X3] :
( c_Orderings_Oord__class_Oless(tc_fun(X3,tc_HOL_Obool),X2,c_Set_Oinsert(X3,X1,X0))
<=> sP5(X1,X3,X2,X0) ),
inference(definition_folding,[],[f1428,f1534,f1533]) ).
fof(f1428,plain,
! [X0,X1,X2,X3] :
( c_Orderings_Oord__class_Oless(tc_fun(X3,tc_HOL_Obool),X2,c_Set_Oinsert(X3,X1,X0))
<=> ( ( ( ( c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X2,X0)
| c_member(X3,X1,X2) )
& ( c_Orderings_Oord__class_Oless(tc_fun(X3,tc_HOL_Obool),c_Groups_Ominus__class_Ominus(tc_fun(X3,tc_HOL_Obool),X2,c_Set_Oinsert(X3,X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)))),X0)
| ~ c_member(X3,X1,X2) ) )
| c_member(X3,X1,X0) )
& ( c_Orderings_Oord__class_Oless(tc_fun(X3,tc_HOL_Obool),X2,X0)
| ~ c_member(X3,X1,X0) ) ) ),
inference(ennf_transformation,[],[f928]) ).
fof(f928,plain,
! [X0,X1,X2,X3] :
( c_Orderings_Oord__class_Oless(tc_fun(X3,tc_HOL_Obool),X2,c_Set_Oinsert(X3,X1,X0))
<=> ( ( ~ c_member(X3,X1,X0)
=> ( ( ~ c_member(X3,X1,X2)
=> c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X2,X0) )
& ( c_member(X3,X1,X2)
=> c_Orderings_Oord__class_Oless(tc_fun(X3,tc_HOL_Obool),c_Groups_Ominus__class_Ominus(tc_fun(X3,tc_HOL_Obool),X2,c_Set_Oinsert(X3,X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)))),X0) ) ) )
& ( c_member(X3,X1,X0)
=> c_Orderings_Oord__class_Oless(tc_fun(X3,tc_HOL_Obool),X2,X0) ) ) ),
inference(rectify,[],[f449]) ).
fof(f449,axiom,
! [X10,X13,X11,X4] :
( c_Orderings_Oord__class_Oless(tc_fun(X4,tc_HOL_Obool),X11,c_Set_Oinsert(X4,X13,X10))
<=> ( ( ~ c_member(X4,X13,X10)
=> ( ( ~ c_member(X4,X13,X11)
=> c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool),X11,X10) )
& ( c_member(X4,X13,X11)
=> c_Orderings_Oord__class_Oless(tc_fun(X4,tc_HOL_Obool),c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool),X11,c_Set_Oinsert(X4,X13,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))),X10) ) ) )
& ( c_member(X4,X13,X10)
=> c_Orderings_Oord__class_Oless(tc_fun(X4,tc_HOL_Obool),X11,X10) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_psubset__insert__iff) ).
fof(f4790,plain,
spl104_277,
inference(avatar_split_clause,[],[f2453,f4788]) ).
fof(f4788,plain,
( spl104_277
<=> ! [X0,X3,X2,X1] :
( sP5(X1,X3,X2,X0)
| ~ c_Orderings_Oord__class_Oless(tc_fun(X3,tc_HOL_Obool),X2,c_Set_Oinsert(X3,X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_277])]) ).
fof(f2453,plain,
! [X2,X3,X0,X1] :
( sP5(X1,X3,X2,X0)
| ~ c_Orderings_Oord__class_Oless(tc_fun(X3,tc_HOL_Obool),X2,c_Set_Oinsert(X3,X1,X0)) ),
inference(cnf_transformation,[],[f1753]) ).
fof(f4786,plain,
spl104_276,
inference(avatar_split_clause,[],[f2445,f4784]) ).
fof(f4784,plain,
( spl104_276
<=> ! [X0,X3,X2,X1] :
( sP5(X0,X1,X2,X3)
| ~ sP4(X3,X2,X1,X0)
| c_member(X1,X0,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_276])]) ).
fof(f2445,plain,
! [X2,X3,X0,X1] :
( sP5(X0,X1,X2,X3)
| ~ sP4(X3,X2,X1,X0)
| c_member(X1,X0,X3) ),
inference(cnf_transformation,[],[f1749]) ).
fof(f4782,plain,
spl104_275,
inference(avatar_split_clause,[],[f2442,f4780]) ).
fof(f4780,plain,
( spl104_275
<=> ! [X0,X3,X2,X1] :
( sP4(X3,X2,X1,X0)
| c_member(X1,X0,X3)
| ~ sP5(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_275])]) ).
fof(f2442,plain,
! [X2,X3,X0,X1] :
( sP4(X3,X2,X1,X0)
| c_member(X1,X0,X3)
| ~ sP5(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f1749]) ).
fof(f4778,plain,
spl104_274,
inference(avatar_split_clause,[],[f2431,f4776]) ).
fof(f4776,plain,
( spl104_274
<=> ! [X2,X0,X1,X3] :
( hBOOL(hAPP(X1,X0))
| X0 = X2
| ~ hBOOL(hAPP(c_Set_Oinsert(X3,X2,X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_274])]) ).
fof(f2431,plain,
! [X2,X3,X0,X1] :
( hBOOL(hAPP(X1,X0))
| X0 = X2
| ~ hBOOL(hAPP(c_Set_Oinsert(X3,X2,X1),X0)) ),
inference(cnf_transformation,[],[f1736]) ).
fof(f1736,plain,
! [X0,X1,X2,X3] :
( ( hBOOL(hAPP(c_Set_Oinsert(X3,X2,X1),X0))
| ( ~ hBOOL(hAPP(X1,X0))
& X0 != X2 ) )
& ( hBOOL(hAPP(X1,X0))
| X0 = X2
| ~ hBOOL(hAPP(c_Set_Oinsert(X3,X2,X1),X0)) ) ),
inference(flattening,[],[f1735]) ).
fof(f1735,plain,
! [X0,X1,X2,X3] :
( ( hBOOL(hAPP(c_Set_Oinsert(X3,X2,X1),X0))
| ( ~ hBOOL(hAPP(X1,X0))
& X0 != X2 ) )
& ( hBOOL(hAPP(X1,X0))
| X0 = X2
| ~ hBOOL(hAPP(c_Set_Oinsert(X3,X2,X1),X0)) ) ),
inference(nnf_transformation,[],[f924]) ).
fof(f924,plain,
! [X0,X1,X2,X3] :
( hBOOL(hAPP(c_Set_Oinsert(X3,X2,X1),X0))
<=> ( hBOOL(hAPP(X1,X0))
| X0 = X2 ) ),
inference(rectify,[],[f132]) ).
fof(f132,axiom,
! [X13,X11,X12,X4] :
( hBOOL(hAPP(c_Set_Oinsert(X4,X12,X11),X13))
<=> ( hBOOL(hAPP(X11,X13))
| X12 = X13 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__code) ).
fof(f4774,plain,
spl104_273,
inference(avatar_split_clause,[],[f2391,f4772]) ).
fof(f4772,plain,
( spl104_273
<=> ! [X0,X3,X2,X1] :
( c_member(X3,X2,X0)
| X1 = X2
| ~ c_member(X3,X2,c_Set_Oinsert(X3,X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_273])]) ).
fof(f2391,plain,
! [X2,X3,X0,X1] :
( c_member(X3,X2,X0)
| X1 = X2
| ~ c_member(X3,X2,c_Set_Oinsert(X3,X1,X0)) ),
inference(cnf_transformation,[],[f1388]) ).
fof(f1388,plain,
! [X0,X1,X2,X3] :
( c_member(X3,X2,X0)
| X1 = X2
| ~ c_member(X3,X2,c_Set_Oinsert(X3,X1,X0)) ),
inference(flattening,[],[f1387]) ).
fof(f1387,plain,
! [X0,X1,X2,X3] :
( c_member(X3,X2,X0)
| X1 = X2
| ~ c_member(X3,X2,c_Set_Oinsert(X3,X1,X0)) ),
inference(ennf_transformation,[],[f897]) ).
fof(f897,plain,
! [X0,X1,X2,X3] :
( c_member(X3,X2,c_Set_Oinsert(X3,X1,X0))
=> ( X1 != X2
=> c_member(X3,X2,X0) ) ),
inference(rectify,[],[f116]) ).
fof(f116,axiom,
! [X11,X8,X9,X4] :
( c_member(X4,X9,c_Set_Oinsert(X4,X8,X11))
=> ( X8 != X9
=> c_member(X4,X9,X11) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insertE) ).
fof(f4770,plain,
spl104_272,
inference(avatar_split_clause,[],[f2362,f4768]) ).
fof(f4768,plain,
( spl104_272
<=> ! [X0,X3,X2,X1] :
( c_member(X3,X0,X1)
| ~ c_member(X3,X0,X2)
| ~ c_Orderings_Oord__class_Oless(tc_fun(X3,tc_HOL_Obool),X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_272])]) ).
fof(f2362,plain,
! [X2,X3,X0,X1] :
( c_member(X3,X0,X1)
| ~ c_member(X3,X0,X2)
| ~ c_Orderings_Oord__class_Oless(tc_fun(X3,tc_HOL_Obool),X2,X1) ),
inference(cnf_transformation,[],[f1349]) ).
fof(f1349,plain,
! [X0,X1,X2,X3] :
( c_member(X3,X0,X1)
| ~ c_member(X3,X0,X2)
| ~ c_Orderings_Oord__class_Oless(tc_fun(X3,tc_HOL_Obool),X2,X1) ),
inference(flattening,[],[f1348]) ).
fof(f1348,plain,
! [X0,X1,X2,X3] :
( c_member(X3,X0,X1)
| ~ c_member(X3,X0,X2)
| ~ c_Orderings_Oord__class_Oless(tc_fun(X3,tc_HOL_Obool),X2,X1) ),
inference(ennf_transformation,[],[f875]) ).
fof(f875,plain,
! [X0,X1,X2,X3] :
( c_Orderings_Oord__class_Oless(tc_fun(X3,tc_HOL_Obool),X2,X1)
=> ( c_member(X3,X0,X2)
=> c_member(X3,X0,X1) ) ),
inference(rectify,[],[f294]) ).
fof(f294,axiom,
! [X7,X10,X11,X4] :
( c_Orderings_Oord__class_Oless(tc_fun(X4,tc_HOL_Obool),X11,X10)
=> ( c_member(X4,X7,X11)
=> c_member(X4,X7,X10) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_psubsetD) ).
fof(f4766,plain,
spl104_271,
inference(avatar_split_clause,[],[f2357,f4764]) ).
fof(f4764,plain,
( spl104_271
<=> ! [X0,X3,X2,X1] :
( c_member(X3,X2,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X1,X0)
| ~ c_member(X3,X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_271])]) ).
fof(f2357,plain,
! [X2,X3,X0,X1] :
( c_member(X3,X2,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X1,X0)
| ~ c_member(X3,X2,X1) ),
inference(cnf_transformation,[],[f1339]) ).
fof(f1339,plain,
! [X0,X1,X2,X3] :
( c_member(X3,X2,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X1,X0)
| ~ c_member(X3,X2,X1) ),
inference(flattening,[],[f1338]) ).
fof(f1338,plain,
! [X0,X1,X2,X3] :
( c_member(X3,X2,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X1,X0)
| ~ c_member(X3,X2,X1) ),
inference(ennf_transformation,[],[f870]) ).
fof(f870,plain,
! [X0,X1,X2,X3] :
( c_member(X3,X2,X1)
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X1,X0)
=> c_member(X3,X2,X0) ) ),
inference(rectify,[],[f263]) ).
fof(f263,axiom,
! [X10,X11,X13,X4] :
( c_member(X4,X13,X11)
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool),X11,X10)
=> c_member(X4,X13,X10) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__rev__mp) ).
fof(f4762,plain,
spl104_270,
inference(avatar_split_clause,[],[f2346,f4760]) ).
fof(f2346,plain,
! [X2,X3,X0,X1] :
( hBOOL(hAPP(X0,X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X3,X0)
| ~ hBOOL(hAPP(X3,X2)) ),
inference(cnf_transformation,[],[f1323]) ).
fof(f1323,plain,
! [X0,X1,X2,X3] :
( hBOOL(hAPP(X0,X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X3,X0)
| ~ hBOOL(hAPP(X3,X2)) ),
inference(flattening,[],[f1322]) ).
fof(f1322,plain,
! [X0,X1,X2,X3] :
( hBOOL(hAPP(X0,X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X3,X0)
| ~ hBOOL(hAPP(X3,X2)) ),
inference(ennf_transformation,[],[f858]) ).
fof(f858,plain,
! [X0,X1,X2,X3] :
( hBOOL(hAPP(X3,X2))
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X3,X0)
=> hBOOL(hAPP(X0,X2)) ) ),
inference(rectify,[],[f231]) ).
fof(f231,axiom,
! [X55,X4,X13,X17] :
( hBOOL(hAPP(X17,X13))
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool),X17,X55)
=> hBOOL(hAPP(X55,X13)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rev__predicate1D) ).
fof(f4758,plain,
spl104_269,
inference(avatar_split_clause,[],[f2313,f4756]) ).
fof(f2313,plain,
! [X2,X3,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X3,X0,X1)
| ~ c_Orderings_Oord__class_Oless__eq(X3,X0,X2)
| ~ c_Orderings_Oord__class_Oless__eq(X3,X2,X1)
| ~ class_Orderings_Oorder(X3) ),
inference(cnf_transformation,[],[f1287]) ).
fof(f1287,plain,
! [X0,X1,X2,X3] :
( c_Orderings_Oord__class_Oless__eq(X3,X0,X1)
| ~ c_Orderings_Oord__class_Oless__eq(X3,X0,X2)
| ~ c_Orderings_Oord__class_Oless__eq(X3,X2,X1)
| ~ class_Orderings_Oorder(X3) ),
inference(flattening,[],[f1286]) ).
fof(f1286,plain,
! [X0,X1,X2,X3] :
( c_Orderings_Oord__class_Oless__eq(X3,X0,X1)
| ~ c_Orderings_Oord__class_Oless__eq(X3,X0,X2)
| ~ c_Orderings_Oord__class_Oless__eq(X3,X2,X1)
| ~ class_Orderings_Oorder(X3) ),
inference(ennf_transformation,[],[f835]) ).
fof(f835,plain,
! [X0,X1,X2,X3] :
( class_Orderings_Oorder(X3)
=> ( c_Orderings_Oord__class_Oless__eq(X3,X2,X1)
=> ( c_Orderings_Oord__class_Oless__eq(X3,X0,X2)
=> c_Orderings_Oord__class_Oless__eq(X3,X0,X1) ) ) ),
inference(rectify,[],[f308]) ).
fof(f308,axiom,
! [X61,X58,X59,X4] :
( class_Orderings_Oorder(X4)
=> ( c_Orderings_Oord__class_Oless__eq(X4,X59,X58)
=> ( c_Orderings_Oord__class_Oless__eq(X4,X61,X59)
=> c_Orderings_Oord__class_Oless__eq(X4,X61,X58) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I6_J) ).
fof(f4754,plain,
spl104_268,
inference(avatar_split_clause,[],[f2312,f4752]) ).
fof(f2312,plain,
! [X2,X3,X0,X1] :
( c_Orderings_Oord__class_Oless(X3,X0,X1)
| ~ c_Orderings_Oord__class_Oless(X3,X0,X2)
| ~ c_Orderings_Oord__class_Oless__eq(X3,X2,X1)
| ~ class_Orderings_Oorder(X3) ),
inference(cnf_transformation,[],[f1285]) ).
fof(f1285,plain,
! [X0,X1,X2,X3] :
( c_Orderings_Oord__class_Oless(X3,X0,X1)
| ~ c_Orderings_Oord__class_Oless(X3,X0,X2)
| ~ c_Orderings_Oord__class_Oless__eq(X3,X2,X1)
| ~ class_Orderings_Oorder(X3) ),
inference(flattening,[],[f1284]) ).
fof(f1284,plain,
! [X0,X1,X2,X3] :
( c_Orderings_Oord__class_Oless(X3,X0,X1)
| ~ c_Orderings_Oord__class_Oless(X3,X0,X2)
| ~ c_Orderings_Oord__class_Oless__eq(X3,X2,X1)
| ~ class_Orderings_Oorder(X3) ),
inference(ennf_transformation,[],[f834]) ).
fof(f834,plain,
! [X0,X1,X2,X3] :
( class_Orderings_Oorder(X3)
=> ( c_Orderings_Oord__class_Oless__eq(X3,X2,X1)
=> ( c_Orderings_Oord__class_Oless(X3,X0,X2)
=> c_Orderings_Oord__class_Oless(X3,X0,X1) ) ) ),
inference(rectify,[],[f352]) ).
fof(f352,axiom,
! [X61,X58,X59,X4] :
( class_Orderings_Oorder(X4)
=> ( c_Orderings_Oord__class_Oless__eq(X4,X59,X58)
=> ( c_Orderings_Oord__class_Oless(X4,X61,X59)
=> c_Orderings_Oord__class_Oless(X4,X61,X58) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I8_J) ).
fof(f4737,plain,
spl104_267,
inference(avatar_split_clause,[],[f2308,f4735]) ).
fof(f2308,plain,
! [X2,X3,X0,X1] :
( c_Orderings_Oord__class_Oless(X3,X0,X1)
| ~ c_Orderings_Oord__class_Oless__eq(X3,X0,X2)
| ~ c_Orderings_Oord__class_Oless(X3,X2,X1)
| ~ class_Orderings_Oorder(X3) ),
inference(cnf_transformation,[],[f1277]) ).
fof(f1277,plain,
! [X0,X1,X2,X3] :
( c_Orderings_Oord__class_Oless(X3,X0,X1)
| ~ c_Orderings_Oord__class_Oless__eq(X3,X0,X2)
| ~ c_Orderings_Oord__class_Oless(X3,X2,X1)
| ~ class_Orderings_Oorder(X3) ),
inference(flattening,[],[f1276]) ).
fof(f1276,plain,
! [X0,X1,X2,X3] :
( c_Orderings_Oord__class_Oless(X3,X0,X1)
| ~ c_Orderings_Oord__class_Oless__eq(X3,X0,X2)
| ~ c_Orderings_Oord__class_Oless(X3,X2,X1)
| ~ class_Orderings_Oorder(X3) ),
inference(ennf_transformation,[],[f830]) ).
fof(f830,plain,
! [X0,X1,X2,X3] :
( class_Orderings_Oorder(X3)
=> ( c_Orderings_Oord__class_Oless(X3,X2,X1)
=> ( c_Orderings_Oord__class_Oless__eq(X3,X0,X2)
=> c_Orderings_Oord__class_Oless(X3,X0,X1) ) ) ),
inference(rectify,[],[f350]) ).
fof(f350,axiom,
! [X61,X58,X59,X4] :
( class_Orderings_Oorder(X4)
=> ( c_Orderings_Oord__class_Oless(X4,X59,X58)
=> ( c_Orderings_Oord__class_Oless__eq(X4,X61,X59)
=> c_Orderings_Oord__class_Oless(X4,X61,X58) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I7_J) ).
fof(f4733,plain,
spl104_266,
inference(avatar_split_clause,[],[f2307,f4731]) ).
fof(f4731,plain,
( spl104_266
<=> ! [X0,X3,X2,X1] :
( c_Orderings_Oord__class_Oless(X3,X0,X1)
| ~ c_Orderings_Oord__class_Oless(X3,X0,X2)
| ~ c_Orderings_Oord__class_Oless(X3,X2,X1)
| ~ class_Orderings_Oorder(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_266])]) ).
fof(f2307,plain,
! [X2,X3,X0,X1] :
( c_Orderings_Oord__class_Oless(X3,X0,X1)
| ~ c_Orderings_Oord__class_Oless(X3,X0,X2)
| ~ c_Orderings_Oord__class_Oless(X3,X2,X1)
| ~ class_Orderings_Oorder(X3) ),
inference(cnf_transformation,[],[f1275]) ).
fof(f1275,plain,
! [X0,X1,X2,X3] :
( c_Orderings_Oord__class_Oless(X3,X0,X1)
| ~ c_Orderings_Oord__class_Oless(X3,X0,X2)
| ~ c_Orderings_Oord__class_Oless(X3,X2,X1)
| ~ class_Orderings_Oorder(X3) ),
inference(flattening,[],[f1274]) ).
fof(f1274,plain,
! [X0,X1,X2,X3] :
( c_Orderings_Oord__class_Oless(X3,X0,X1)
| ~ c_Orderings_Oord__class_Oless(X3,X0,X2)
| ~ c_Orderings_Oord__class_Oless(X3,X2,X1)
| ~ class_Orderings_Oorder(X3) ),
inference(ennf_transformation,[],[f829]) ).
fof(f829,plain,
! [X0,X1,X2,X3] :
( class_Orderings_Oorder(X3)
=> ( c_Orderings_Oord__class_Oless(X3,X2,X1)
=> ( c_Orderings_Oord__class_Oless(X3,X0,X2)
=> c_Orderings_Oord__class_Oless(X3,X0,X1) ) ) ),
inference(rectify,[],[f328]) ).
fof(f328,axiom,
! [X61,X58,X59,X4] :
( class_Orderings_Oorder(X4)
=> ( c_Orderings_Oord__class_Oless(X4,X59,X58)
=> ( c_Orderings_Oord__class_Oless(X4,X61,X59)
=> c_Orderings_Oord__class_Oless(X4,X61,X58) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I10_J) ).
fof(f4729,plain,
spl104_265,
inference(avatar_split_clause,[],[f2297,f4727]) ).
fof(f4727,plain,
( spl104_265
<=> ! [X0,X3,X2,X1] :
( c_Orderings_Oord__class_Oless__eq(X3,X2,X0)
| ~ c_Orderings_Oord__class_Oless__eq(X3,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(X3,X2,X1)
| ~ class_Orderings_Opreorder(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_265])]) ).
fof(f2297,plain,
! [X2,X3,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X3,X2,X0)
| ~ c_Orderings_Oord__class_Oless__eq(X3,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(X3,X2,X1)
| ~ class_Orderings_Opreorder(X3) ),
inference(cnf_transformation,[],[f1259]) ).
fof(f1259,plain,
! [X0,X1,X2,X3] :
( c_Orderings_Oord__class_Oless__eq(X3,X2,X0)
| ~ c_Orderings_Oord__class_Oless__eq(X3,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(X3,X2,X1)
| ~ class_Orderings_Opreorder(X3) ),
inference(flattening,[],[f1258]) ).
fof(f1258,plain,
! [X0,X1,X2,X3] :
( c_Orderings_Oord__class_Oless__eq(X3,X2,X0)
| ~ c_Orderings_Oord__class_Oless__eq(X3,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(X3,X2,X1)
| ~ class_Orderings_Opreorder(X3) ),
inference(ennf_transformation,[],[f819]) ).
fof(f819,plain,
! [X0,X1,X2,X3] :
( class_Orderings_Opreorder(X3)
=> ( c_Orderings_Oord__class_Oless__eq(X3,X2,X1)
=> ( c_Orderings_Oord__class_Oless__eq(X3,X1,X0)
=> c_Orderings_Oord__class_Oless__eq(X3,X2,X0) ) ) ),
inference(rectify,[],[f306]) ).
fof(f306,axiom,
! [X61,X59,X58,X4] :
( class_Orderings_Opreorder(X4)
=> ( c_Orderings_Oord__class_Oless__eq(X4,X58,X59)
=> ( c_Orderings_Oord__class_Oless__eq(X4,X59,X61)
=> c_Orderings_Oord__class_Oless__eq(X4,X58,X61) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__trans) ).
fof(f4725,plain,
spl104_264,
inference(avatar_split_clause,[],[f2296,f4723]) ).
fof(f2296,plain,
! [X2,X3,X0,X1] :
( c_Orderings_Oord__class_Oless(X3,X2,X0)
| ~ c_Orderings_Oord__class_Oless(X3,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(X3,X2,X1)
| ~ class_Orderings_Opreorder(X3) ),
inference(cnf_transformation,[],[f1257]) ).
fof(f1257,plain,
! [X0,X1,X2,X3] :
( c_Orderings_Oord__class_Oless(X3,X2,X0)
| ~ c_Orderings_Oord__class_Oless(X3,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(X3,X2,X1)
| ~ class_Orderings_Opreorder(X3) ),
inference(flattening,[],[f1256]) ).
fof(f1256,plain,
! [X0,X1,X2,X3] :
( c_Orderings_Oord__class_Oless(X3,X2,X0)
| ~ c_Orderings_Oord__class_Oless(X3,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(X3,X2,X1)
| ~ class_Orderings_Opreorder(X3) ),
inference(ennf_transformation,[],[f818]) ).
fof(f818,plain,
! [X0,X1,X2,X3] :
( class_Orderings_Opreorder(X3)
=> ( c_Orderings_Oord__class_Oless__eq(X3,X2,X1)
=> ( c_Orderings_Oord__class_Oless(X3,X1,X0)
=> c_Orderings_Oord__class_Oless(X3,X2,X0) ) ) ),
inference(rectify,[],[f351]) ).
fof(f351,axiom,
! [X61,X59,X58,X4] :
( class_Orderings_Opreorder(X4)
=> ( c_Orderings_Oord__class_Oless__eq(X4,X58,X59)
=> ( c_Orderings_Oord__class_Oless(X4,X59,X61)
=> c_Orderings_Oord__class_Oless(X4,X58,X61) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__le__less__trans) ).
fof(f4721,plain,
spl104_263,
inference(avatar_split_clause,[],[f2295,f4719]) ).
fof(f2295,plain,
! [X2,X3,X0,X1] :
( c_Orderings_Oord__class_Oless(X3,X2,X0)
| ~ c_Orderings_Oord__class_Oless__eq(X3,X1,X0)
| ~ c_Orderings_Oord__class_Oless(X3,X2,X1)
| ~ class_Orderings_Opreorder(X3) ),
inference(cnf_transformation,[],[f1255]) ).
fof(f1255,plain,
! [X0,X1,X2,X3] :
( c_Orderings_Oord__class_Oless(X3,X2,X0)
| ~ c_Orderings_Oord__class_Oless__eq(X3,X1,X0)
| ~ c_Orderings_Oord__class_Oless(X3,X2,X1)
| ~ class_Orderings_Opreorder(X3) ),
inference(flattening,[],[f1254]) ).
fof(f1254,plain,
! [X0,X1,X2,X3] :
( c_Orderings_Oord__class_Oless(X3,X2,X0)
| ~ c_Orderings_Oord__class_Oless__eq(X3,X1,X0)
| ~ c_Orderings_Oord__class_Oless(X3,X2,X1)
| ~ class_Orderings_Opreorder(X3) ),
inference(ennf_transformation,[],[f817]) ).
fof(f817,plain,
! [X0,X1,X2,X3] :
( class_Orderings_Opreorder(X3)
=> ( c_Orderings_Oord__class_Oless(X3,X2,X1)
=> ( c_Orderings_Oord__class_Oless__eq(X3,X1,X0)
=> c_Orderings_Oord__class_Oless(X3,X2,X0) ) ) ),
inference(rectify,[],[f349]) ).
fof(f349,axiom,
! [X61,X59,X58,X4] :
( class_Orderings_Opreorder(X4)
=> ( c_Orderings_Oord__class_Oless(X4,X58,X59)
=> ( c_Orderings_Oord__class_Oless__eq(X4,X59,X61)
=> c_Orderings_Oord__class_Oless(X4,X58,X61) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__le__trans) ).
fof(f4717,plain,
spl104_262,
inference(avatar_split_clause,[],[f2294,f4715]) ).
fof(f4715,plain,
( spl104_262
<=> ! [X0,X3,X2,X1] :
( c_Orderings_Oord__class_Oless(X3,X2,X0)
| ~ c_Orderings_Oord__class_Oless(X3,X1,X0)
| ~ c_Orderings_Oord__class_Oless(X3,X2,X1)
| ~ class_Orderings_Opreorder(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_262])]) ).
fof(f2294,plain,
! [X2,X3,X0,X1] :
( c_Orderings_Oord__class_Oless(X3,X2,X0)
| ~ c_Orderings_Oord__class_Oless(X3,X1,X0)
| ~ c_Orderings_Oord__class_Oless(X3,X2,X1)
| ~ class_Orderings_Opreorder(X3) ),
inference(cnf_transformation,[],[f1253]) ).
fof(f1253,plain,
! [X0,X1,X2,X3] :
( c_Orderings_Oord__class_Oless(X3,X2,X0)
| ~ c_Orderings_Oord__class_Oless(X3,X1,X0)
| ~ c_Orderings_Oord__class_Oless(X3,X2,X1)
| ~ class_Orderings_Opreorder(X3) ),
inference(flattening,[],[f1252]) ).
fof(f1252,plain,
! [X0,X1,X2,X3] :
( c_Orderings_Oord__class_Oless(X3,X2,X0)
| ~ c_Orderings_Oord__class_Oless(X3,X1,X0)
| ~ c_Orderings_Oord__class_Oless(X3,X2,X1)
| ~ class_Orderings_Opreorder(X3) ),
inference(ennf_transformation,[],[f816]) ).
fof(f816,plain,
! [X0,X1,X2,X3] :
( class_Orderings_Opreorder(X3)
=> ( c_Orderings_Oord__class_Oless(X3,X2,X1)
=> ( c_Orderings_Oord__class_Oless(X3,X1,X0)
=> c_Orderings_Oord__class_Oless(X3,X2,X0) ) ) ),
inference(rectify,[],[f327]) ).
fof(f327,axiom,
! [X61,X59,X58,X4] :
( class_Orderings_Opreorder(X4)
=> ( c_Orderings_Oord__class_Oless(X4,X58,X59)
=> ( c_Orderings_Oord__class_Oless(X4,X59,X61)
=> c_Orderings_Oord__class_Oless(X4,X58,X61) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__trans) ).
fof(f4713,plain,
spl104_261,
inference(avatar_split_clause,[],[f2290,f4711]) ).
fof(f2290,plain,
! [X2,X3,X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X2,X3),X0,X1)
| ~ c_Orderings_Oord__class_Oless(tc_fun(X2,X3),X1,X0)
| ~ class_Orderings_Oord(X3) ),
inference(cnf_transformation,[],[f1695]) ).
fof(f4709,plain,
spl104_260,
inference(avatar_split_clause,[],[f2289,f4707]) ).
fof(f4707,plain,
( spl104_260
<=> ! [X0,X3,X2,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X2,X3),X1,X0)
| ~ c_Orderings_Oord__class_Oless(tc_fun(X2,X3),X1,X0)
| ~ class_Orderings_Oord(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_260])]) ).
fof(f2289,plain,
! [X2,X3,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X2,X3),X1,X0)
| ~ c_Orderings_Oord__class_Oless(tc_fun(X2,X3),X1,X0)
| ~ class_Orderings_Oord(X3) ),
inference(cnf_transformation,[],[f1695]) ).
fof(f4705,plain,
spl104_259,
inference(avatar_split_clause,[],[f2260,f4703]) ).
fof(f2260,plain,
! [X2,X0,X1] :
( X0 = X1
| ~ c_member(tc_prod(X2,X2),c_Product__Type_OPair(X2,X2,X1,X0),c_Relation_OId(X2)) ),
inference(cnf_transformation,[],[f1687]) ).
fof(f1687,plain,
! [X0,X1,X2] :
( ( c_member(tc_prod(X2,X2),c_Product__Type_OPair(X2,X2,X1,X0),c_Relation_OId(X2))
| X0 != X1 )
& ( X0 = X1
| ~ c_member(tc_prod(X2,X2),c_Product__Type_OPair(X2,X2,X1,X0),c_Relation_OId(X2)) ) ),
inference(nnf_transformation,[],[f789]) ).
fof(f789,plain,
! [X0,X1,X2] :
( c_member(tc_prod(X2,X2),c_Product__Type_OPair(X2,X2,X1,X0),c_Relation_OId(X2))
<=> X0 = X1 ),
inference(rectify,[],[f108]) ).
fof(f108,axiom,
! [X8,X9,X4] :
( c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X9,X8),c_Relation_OId(X4))
<=> X8 = X9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pair__in__Id__conv) ).
fof(f4701,plain,
spl104_258,
inference(avatar_split_clause,[],[f2244,f4699]) ).
fof(f4699,plain,
( spl104_258
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool),X1,X0)
| c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool),X1,X0) != X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_258])]) ).
fof(f2244,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool),X1,X0)
| c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool),X1,X0) != X0 ),
inference(cnf_transformation,[],[f1675]) ).
fof(f1675,plain,
! [X0,X1,X2] :
( ( c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool),X1,X0)
| c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool),X1,X0) != X0 )
& ( c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool),X1,X0) = X0
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool),X1,X0) ) ),
inference(nnf_transformation,[],[f782]) ).
fof(f782,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool),X1,X0)
<=> c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool),X1,X0) = X0 ),
inference(rectify,[],[f228]) ).
fof(f228,axiom,
! [X10,X11,X4] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool),X11,X10)
<=> c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool),X11,X10) = X10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__Un__eq) ).
fof(f4691,plain,
spl104_257,
inference(avatar_split_clause,[],[f2189,f4689]) ).
fof(f2189,plain,
! [X2,X0,X1] :
( c_Relation_Oantisym(X2,X1)
| ~ c_Relation_Oantisym(X2,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),X1,X0) ),
inference(cnf_transformation,[],[f1219]) ).
fof(f1219,plain,
! [X0,X1,X2] :
( c_Relation_Oantisym(X2,X1)
| ~ c_Relation_Oantisym(X2,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),X1,X0) ),
inference(flattening,[],[f1218]) ).
fof(f1218,plain,
! [X0,X1,X2] :
( c_Relation_Oantisym(X2,X1)
| ~ c_Relation_Oantisym(X2,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),X1,X0) ),
inference(ennf_transformation,[],[f760]) ).
fof(f760,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),X1,X0)
=> ( c_Relation_Oantisym(X2,X0)
=> c_Relation_Oantisym(X2,X1) ) ),
inference(rectify,[],[f272]) ).
fof(f272,axiom,
! [X30,X3,X4] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),X3,X30)
=> ( c_Relation_Oantisym(X4,X30)
=> c_Relation_Oantisym(X4,X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_antisym__subset) ).
fof(f4687,plain,
spl104_256,
inference(avatar_split_clause,[],[f2181,f4685]) ).
fof(f2181,plain,
! [X2,X0,X1] :
( c_member(tc_prod(X2,X2),X1,c_Transitive__Closure_Otrancl(X2,X0))
| ~ c_member(tc_prod(X2,X2),X1,X0) ),
inference(cnf_transformation,[],[f1210]) ).
fof(f1210,plain,
! [X0,X1,X2] :
( c_member(tc_prod(X2,X2),X1,c_Transitive__Closure_Otrancl(X2,X0))
| ~ c_member(tc_prod(X2,X2),X1,X0) ),
inference(ennf_transformation,[],[f753]) ).
fof(f753,plain,
! [X0,X1,X2] :
( c_member(tc_prod(X2,X2),X1,X0)
=> c_member(tc_prod(X2,X2),X1,c_Transitive__Closure_Otrancl(X2,X0)) ),
inference(rectify,[],[f79]) ).
fof(f79,axiom,
! [X3,X39,X4] :
( c_member(tc_prod(X4,X4),X39,X3)
=> c_member(tc_prod(X4,X4),X39,c_Transitive__Closure_Otrancl(X4,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_r__into__trancl_H) ).
fof(f4683,plain,
spl104_255,
inference(avatar_split_clause,[],[f2178,f4681]) ).
fof(f2178,plain,
! [X2,X0,X1] :
( c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool),X0,X1) = X0
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool),X1,X0) ),
inference(cnf_transformation,[],[f1206]) ).
fof(f1206,plain,
! [X0,X1,X2] :
( c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool),X0,X1) = X0
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool),X1,X0) ),
inference(ennf_transformation,[],[f750]) ).
fof(f750,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool),X1,X0)
=> c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool),X0,X1) = X0 ),
inference(rectify,[],[f226]) ).
fof(f226,axiom,
! [X11,X10,X4] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool),X10,X11)
=> c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool),X11,X10) = X11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__absorb2) ).
fof(f4679,plain,
spl104_254,
inference(avatar_split_clause,[],[f2177,f4677]) ).
fof(f2177,plain,
! [X2,X0,X1] :
( c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool),X1,X0) = X0
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool),X1,X0) ),
inference(cnf_transformation,[],[f1205]) ).
fof(f1205,plain,
! [X0,X1,X2] :
( c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool),X1,X0) = X0
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool),X1,X0) ),
inference(ennf_transformation,[],[f749]) ).
fof(f749,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool),X1,X0)
=> c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool),X1,X0) = X0 ),
inference(rectify,[],[f227]) ).
fof(f227,axiom,
! [X10,X11,X4] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool),X11,X10)
=> c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool),X11,X10) = X10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__absorb1) ).
fof(f4675,plain,
spl104_253,
inference(avatar_split_clause,[],[f2161,f4673]) ).
fof(f4673,plain,
( spl104_253
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_253])]) ).
fof(f2161,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
inference(cnf_transformation,[],[f1188]) ).
fof(f1188,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
inference(ennf_transformation,[],[f737]) ).
fof(f737,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X2)) ),
inference(rectify,[],[f385]) ).
fof(f385,axiom,
! [X74,X70,X71] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X71,X70)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X74,X70),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X74,X71)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__le__mono2) ).
fof(f4671,plain,
spl104_252,
inference(avatar_split_clause,[],[f2160,f4669]) ).
fof(f4669,plain,
( spl104_252
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X0),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_252])]) ).
fof(f2160,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X0),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
inference(cnf_transformation,[],[f1187]) ).
fof(f1187,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X0),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
inference(ennf_transformation,[],[f736]) ).
fof(f736,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X0),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0)) ),
inference(rectify,[],[f384]) ).
fof(f384,axiom,
! [X74,X70,X71] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X71,X70)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X71,X74),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X70,X74)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__le__mono) ).
fof(f4667,plain,
spl104_251,
inference(avatar_split_clause,[],[f2153,f4665]) ).
fof(f2153,plain,
! [X2,X0,X1] :
( c_Wellfounded_Owf(X2,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),X0,X1)
| ~ c_Wellfounded_Owf(X2,X1) ),
inference(cnf_transformation,[],[f1176]) ).
fof(f1176,plain,
! [X0,X1,X2] :
( c_Wellfounded_Owf(X2,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),X0,X1)
| ~ c_Wellfounded_Owf(X2,X1) ),
inference(flattening,[],[f1175]) ).
fof(f1175,plain,
! [X0,X1,X2] :
( c_Wellfounded_Owf(X2,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),X0,X1)
| ~ c_Wellfounded_Owf(X2,X1) ),
inference(ennf_transformation,[],[f729]) ).
fof(f729,plain,
! [X0,X1,X2] :
( c_Wellfounded_Owf(X2,X1)
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),X0,X1)
=> c_Wellfounded_Owf(X2,X0) ) ),
inference(rectify,[],[f271]) ).
fof(f271,axiom,
! [X39,X3,X4] :
( c_Wellfounded_Owf(X4,X3)
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),X39,X3)
=> c_Wellfounded_Owf(X4,X39) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__subset) ).
fof(f4663,plain,
spl104_250,
inference(avatar_split_clause,[],[f2148,f4661]) ).
fof(f2148,plain,
! [X2,X0,X1] :
( c_Wellfounded_Oacyclic(X2,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),X0,X1)
| ~ c_Wellfounded_Oacyclic(X2,X1) ),
inference(cnf_transformation,[],[f1170]) ).
fof(f1170,plain,
! [X0,X1,X2] :
( c_Wellfounded_Oacyclic(X2,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),X0,X1)
| ~ c_Wellfounded_Oacyclic(X2,X1) ),
inference(flattening,[],[f1169]) ).
fof(f1169,plain,
! [X0,X1,X2] :
( c_Wellfounded_Oacyclic(X2,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),X0,X1)
| ~ c_Wellfounded_Oacyclic(X2,X1) ),
inference(ennf_transformation,[],[f724]) ).
fof(f724,plain,
! [X0,X1,X2] :
( c_Wellfounded_Oacyclic(X2,X1)
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),X0,X1)
=> c_Wellfounded_Oacyclic(X2,X0) ) ),
inference(rectify,[],[f273]) ).
fof(f273,axiom,
! [X3,X30,X4] :
( c_Wellfounded_Oacyclic(X4,X30)
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),X3,X30)
=> c_Wellfounded_Oacyclic(X4,X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_acyclic__subset) ).
fof(f4659,plain,
spl104_249,
inference(avatar_split_clause,[],[f2147,f4657]) ).
fof(f4657,plain,
( spl104_249
<=> ! [X2,X0,X1] :
( c_Wellfounded_OwfP(X2,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_fun(X2,tc_HOL_Obool)),X0,X1)
| ~ c_Wellfounded_OwfP(X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_249])]) ).
fof(f2147,plain,
! [X2,X0,X1] :
( c_Wellfounded_OwfP(X2,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_fun(X2,tc_HOL_Obool)),X0,X1)
| ~ c_Wellfounded_OwfP(X2,X1) ),
inference(cnf_transformation,[],[f1168]) ).
fof(f1168,plain,
! [X0,X1,X2] :
( c_Wellfounded_OwfP(X2,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_fun(X2,tc_HOL_Obool)),X0,X1)
| ~ c_Wellfounded_OwfP(X2,X1) ),
inference(flattening,[],[f1167]) ).
fof(f1167,plain,
! [X0,X1,X2] :
( c_Wellfounded_OwfP(X2,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_fun(X2,tc_HOL_Obool)),X0,X1)
| ~ c_Wellfounded_OwfP(X2,X1) ),
inference(ennf_transformation,[],[f723]) ).
fof(f723,plain,
! [X0,X1,X2] :
( c_Wellfounded_OwfP(X2,X1)
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_fun(X2,tc_HOL_Obool)),X0,X1)
=> c_Wellfounded_OwfP(X2,X0) ) ),
inference(rectify,[],[f295]) ).
fof(f295,axiom,
! [X39,X3,X4] :
( c_Wellfounded_OwfP(X4,X3)
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_fun(X4,tc_HOL_Obool)),X39,X3)
=> c_Wellfounded_OwfP(X4,X39) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wfP__subset) ).
fof(f4655,plain,
spl104_248,
inference(avatar_split_clause,[],[f2115,f4653]) ).
fof(f4653,plain,
( spl104_248
<=> ! [X2,X0,X1] :
( c_Lattices_Osemilattice__sup__class_Osup(X2,X1,X0) = c_Lattices_Osemilattice__sup__class_Osup(X2,X1,c_Lattices_Osemilattice__sup__class_Osup(X2,X1,X0))
| ~ class_Lattices_Osemilattice__sup(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_248])]) ).
fof(f2115,plain,
! [X2,X0,X1] :
( c_Lattices_Osemilattice__sup__class_Osup(X2,X1,X0) = c_Lattices_Osemilattice__sup__class_Osup(X2,X1,c_Lattices_Osemilattice__sup__class_Osup(X2,X1,X0))
| ~ class_Lattices_Osemilattice__sup(X2) ),
inference(cnf_transformation,[],[f1130]) ).
fof(f1130,plain,
! [X0,X1,X2] :
( c_Lattices_Osemilattice__sup__class_Osup(X2,X1,X0) = c_Lattices_Osemilattice__sup__class_Osup(X2,X1,c_Lattices_Osemilattice__sup__class_Osup(X2,X1,X0))
| ~ class_Lattices_Osemilattice__sup(X2) ),
inference(ennf_transformation,[],[f700]) ).
fof(f700,plain,
! [X0,X1,X2] :
( class_Lattices_Osemilattice__sup(X2)
=> c_Lattices_Osemilattice__sup__class_Osup(X2,X1,X0) = c_Lattices_Osemilattice__sup__class_Osup(X2,X1,c_Lattices_Osemilattice__sup__class_Osup(X2,X1,X0)) ),
inference(rectify,[],[f177]) ).
fof(f177,axiom,
! [X26,X27,X4] :
( class_Lattices_Osemilattice__sup(X4)
=> c_Lattices_Osemilattice__sup__class_Osup(X4,X27,X26) = c_Lattices_Osemilattice__sup__class_Osup(X4,X27,c_Lattices_Osemilattice__sup__class_Osup(X4,X27,X26)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup_Oleft__idem) ).
fof(f4649,plain,
spl104_247,
inference(avatar_split_clause,[],[f2110,f4647]) ).
fof(f2110,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless(X2,X1,X0)
| c_Orderings_Oord__class_Oless__eq(X2,X0,X1)
| ~ c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
| ~ class_Orderings_Opreorder(X2) ),
inference(cnf_transformation,[],[f1629]) ).
fof(f1629,plain,
! [X0,X1,X2] :
( ( ( c_Orderings_Oord__class_Oless(X2,X1,X0)
| c_Orderings_Oord__class_Oless__eq(X2,X0,X1)
| ~ c_Orderings_Oord__class_Oless__eq(X2,X1,X0) )
& ( ( ~ c_Orderings_Oord__class_Oless__eq(X2,X0,X1)
& c_Orderings_Oord__class_Oless__eq(X2,X1,X0) )
| ~ c_Orderings_Oord__class_Oless(X2,X1,X0) ) )
| ~ class_Orderings_Opreorder(X2) ),
inference(flattening,[],[f1628]) ).
fof(f1628,plain,
! [X0,X1,X2] :
( ( ( c_Orderings_Oord__class_Oless(X2,X1,X0)
| c_Orderings_Oord__class_Oless__eq(X2,X0,X1)
| ~ c_Orderings_Oord__class_Oless__eq(X2,X1,X0) )
& ( ( ~ c_Orderings_Oord__class_Oless__eq(X2,X0,X1)
& c_Orderings_Oord__class_Oless__eq(X2,X1,X0) )
| ~ c_Orderings_Oord__class_Oless(X2,X1,X0) ) )
| ~ class_Orderings_Opreorder(X2) ),
inference(nnf_transformation,[],[f1125]) ).
fof(f1125,plain,
! [X0,X1,X2] :
( ( c_Orderings_Oord__class_Oless(X2,X1,X0)
<=> ( ~ c_Orderings_Oord__class_Oless__eq(X2,X0,X1)
& c_Orderings_Oord__class_Oless__eq(X2,X1,X0) ) )
| ~ class_Orderings_Opreorder(X2) ),
inference(ennf_transformation,[],[f695]) ).
fof(f695,plain,
! [X0,X1,X2] :
( class_Orderings_Opreorder(X2)
=> ( c_Orderings_Oord__class_Oless(X2,X1,X0)
<=> ( ~ c_Orderings_Oord__class_Oless__eq(X2,X0,X1)
& c_Orderings_Oord__class_Oless__eq(X2,X1,X0) ) ) ),
inference(rectify,[],[f336]) ).
fof(f336,axiom,
! [X12,X13,X4] :
( class_Orderings_Opreorder(X4)
=> ( c_Orderings_Oord__class_Oless(X4,X13,X12)
<=> ( ~ c_Orderings_Oord__class_Oless__eq(X4,X12,X13)
& c_Orderings_Oord__class_Oless__eq(X4,X13,X12) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__le__not__le) ).
fof(f4645,plain,
spl104_246,
inference(avatar_split_clause,[],[f2101,f4643]) ).
fof(f2101,plain,
! [X2,X0,X1] :
( c_Lattices_Osemilattice__sup__class_Osup(X2,X1,X0) = c_Lattices_Osemilattice__sup__class_Osup(X2,X1,c_Lattices_Osemilattice__sup__class_Osup(X2,X1,X0))
| ~ class_Lattices_Olattice(X2) ),
inference(cnf_transformation,[],[f1112]) ).
fof(f1112,plain,
! [X0,X1,X2] :
( c_Lattices_Osemilattice__sup__class_Osup(X2,X1,X0) = c_Lattices_Osemilattice__sup__class_Osup(X2,X1,c_Lattices_Osemilattice__sup__class_Osup(X2,X1,X0))
| ~ class_Lattices_Olattice(X2) ),
inference(ennf_transformation,[],[f688]) ).
fof(f688,plain,
! [X0,X1,X2] :
( class_Lattices_Olattice(X2)
=> c_Lattices_Osemilattice__sup__class_Osup(X2,X1,X0) = c_Lattices_Osemilattice__sup__class_Osup(X2,X1,c_Lattices_Osemilattice__sup__class_Osup(X2,X1,X0)) ),
inference(rectify,[],[f178]) ).
fof(f178,axiom,
! [X59,X58,X4] :
( class_Lattices_Olattice(X4)
=> c_Lattices_Osemilattice__sup__class_Osup(X4,X58,X59) = c_Lattices_Osemilattice__sup__class_Osup(X4,X58,c_Lattices_Osemilattice__sup__class_Osup(X4,X58,X59)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__sup__aci_I8_J) ).
fof(f4641,plain,
spl104_245,
inference(avatar_split_clause,[],[f2039,f4639]) ).
fof(f2039,plain,
! [X0,X1] :
( c_Relation_Oantisym(X1,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),X0,c_Relation_OId(X1)))
| ~ c_Relation_Oantisym(X1,X0) ),
inference(cnf_transformation,[],[f1606]) ).
fof(f1606,plain,
! [X0,X1] :
( ( c_Relation_Oantisym(X1,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),X0,c_Relation_OId(X1)))
| ~ c_Relation_Oantisym(X1,X0) )
& ( c_Relation_Oantisym(X1,X0)
| ~ c_Relation_Oantisym(X1,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),X0,c_Relation_OId(X1))) ) ),
inference(nnf_transformation,[],[f641]) ).
fof(f641,plain,
! [X0,X1] :
( c_Relation_Oantisym(X1,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),X0,c_Relation_OId(X1)))
<=> c_Relation_Oantisym(X1,X0) ),
inference(rectify,[],[f120]) ).
fof(f120,axiom,
! [X3,X4] :
( c_Relation_Oantisym(X4,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),X3,c_Relation_OId(X4)))
<=> c_Relation_Oantisym(X4,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_antisym__reflcl) ).
fof(f4637,plain,
spl104_244,
inference(avatar_split_clause,[],[f2038,f4635]) ).
fof(f4635,plain,
( spl104_244
<=> ! [X0,X1] :
( c_Relation_Oantisym(X1,X0)
| ~ c_Relation_Oantisym(X1,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),X0,c_Relation_OId(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_244])]) ).
fof(f2038,plain,
! [X0,X1] :
( c_Relation_Oantisym(X1,X0)
| ~ c_Relation_Oantisym(X1,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),X0,c_Relation_OId(X1))) ),
inference(cnf_transformation,[],[f1606]) ).
fof(f4633,plain,
spl104_243,
inference(avatar_split_clause,[],[f2037,f4631]) ).
fof(f2037,plain,
! [X0,X1] :
( c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat,X1,X0),c_Wellfounded_Oless__than)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ),
inference(cnf_transformation,[],[f1605]) ).
fof(f1605,plain,
! [X0,X1] :
( ( c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat,X1,X0),c_Wellfounded_Oless__than)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| ~ c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat,X1,X0),c_Wellfounded_Oless__than) ) ),
inference(nnf_transformation,[],[f640]) ).
fof(f640,plain,
! [X0,X1] :
( c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat,X1,X0),c_Wellfounded_Oless__than)
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ),
inference(rectify,[],[f242]) ).
fof(f242,axiom,
! [X12,X13] :
( c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat,X13,X12),c_Wellfounded_Oless__than)
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X13,X12) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__than__iff) ).
fof(f4629,plain,
spl104_242,
inference(avatar_split_clause,[],[f2036,f4627]) ).
fof(f2036,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| ~ c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat,X1,X0),c_Wellfounded_Oless__than) ),
inference(cnf_transformation,[],[f1605]) ).
fof(f4625,plain,
spl104_241,
inference(avatar_split_clause,[],[f2021,f4623]) ).
fof(f2021,plain,
! [X0,X1,X6,X9] :
( c_member(X0,sK37(X0,X1,X6),X6)
| ~ c_member(X0,X9,X6)
| ~ sP2(X0,X1) ),
inference(cnf_transformation,[],[f1598]) ).
fof(f4621,plain,
spl104_240,
inference(avatar_split_clause,[],[f1997,f4619]) ).
fof(f4619,plain,
( spl104_240
<=> ! [X0,X1] :
( X0 = X1
| hAPP(X1,sK20(X0,X1)) != hAPP(X0,sK20(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_240])]) ).
fof(f1997,plain,
! [X0,X1] :
( X0 = X1
| hAPP(X1,sK20(X0,X1)) != hAPP(X0,sK20(X0,X1)) ),
inference(cnf_transformation,[],[f1565]) ).
fof(f1565,plain,
! [X0,X1] :
( X0 = X1
| hAPP(X1,sK20(X0,X1)) != hAPP(X0,sK20(X0,X1)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK20])],[f1069,f1564]) ).
fof(f1564,plain,
! [X0,X1] :
( ? [X2] : hAPP(X1,X2) != hAPP(X0,X2)
=> hAPP(X1,sK20(X0,X1)) != hAPP(X0,sK20(X0,X1)) ),
introduced(choice_axiom,[]) ).
fof(f1069,plain,
! [X0,X1] :
( X0 = X1
| ? [X2] : hAPP(X1,X2) != hAPP(X0,X2) ),
inference(ennf_transformation,[],[f1]) ).
fof(f1,axiom,
! [X0,X1] :
( ! [X2] : hAPP(X1,X2) = hAPP(X0,X2)
=> X0 = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ext) ).
fof(f4617,plain,
spl104_239,
inference(avatar_split_clause,[],[f1979,f4615]) ).
fof(f4615,plain,
( spl104_239
<=> ! [X0,X1] :
( c_Relation_Otrans(X1,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),X0,c_Relation_OId(X1)))
| ~ c_Relation_Otrans(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_239])]) ).
fof(f1979,plain,
! [X0,X1] :
( c_Relation_Otrans(X1,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),X0,c_Relation_OId(X1)))
| ~ c_Relation_Otrans(X1,X0) ),
inference(cnf_transformation,[],[f1049]) ).
fof(f1049,plain,
! [X0,X1] :
( c_Relation_Otrans(X1,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),X0,c_Relation_OId(X1)))
| ~ c_Relation_Otrans(X1,X0) ),
inference(ennf_transformation,[],[f609]) ).
fof(f609,plain,
! [X0,X1] :
( c_Relation_Otrans(X1,X0)
=> c_Relation_Otrans(X1,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),X0,c_Relation_OId(X1))) ),
inference(rectify,[],[f152]) ).
fof(f152,axiom,
! [X3,X4] :
( c_Relation_Otrans(X4,X3)
=> c_Relation_Otrans(X4,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),X3,c_Relation_OId(X4))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trans__reflclI) ).
fof(f4613,plain,
spl104_238,
inference(avatar_split_clause,[],[f1948,f4611]) ).
fof(f4611,plain,
( spl104_238
<=> ! [X0,X1] : c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) = c_Relation_ODomain(X1,X0,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X0),tc_HOL_Obool))) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_238])]) ).
fof(f1948,plain,
! [X0,X1] : c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) = c_Relation_ODomain(X1,X0,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X0),tc_HOL_Obool))),
inference(cnf_transformation,[],[f578]) ).
fof(f578,plain,
! [X0,X1] : c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) = c_Relation_ODomain(X1,X0,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X0),tc_HOL_Obool))),
inference(rectify,[],[f417]) ).
fof(f417,axiom,
! [X15,X4] : c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)) = c_Relation_ODomain(X4,X15,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X4,X15),tc_HOL_Obool))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Domain__empty) ).
fof(f4609,plain,
spl104_237,
inference(avatar_split_clause,[],[f1947,f4607]) ).
fof(f4607,plain,
( spl104_237
<=> ! [X0,X1] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)) = c_Relation_ORange(X1,X0,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X0),tc_HOL_Obool))) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_237])]) ).
fof(f1947,plain,
! [X0,X1] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)) = c_Relation_ORange(X1,X0,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X0),tc_HOL_Obool))),
inference(cnf_transformation,[],[f577]) ).
fof(f577,plain,
! [X0,X1] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)) = c_Relation_ORange(X1,X0,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X0),tc_HOL_Obool))),
inference(rectify,[],[f419]) ).
fof(f419,axiom,
! [X4,X15] : c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)) = c_Relation_ORange(X15,X4,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X15,X4),tc_HOL_Obool))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Range__empty) ).
fof(f4605,plain,
spl104_236,
inference(avatar_split_clause,[],[f1946,f4603]) ).
fof(f4603,plain,
( spl104_236
<=> ! [X0,X1] : c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) = c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_236])]) ).
fof(f1946,plain,
! [X0,X1] : c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) = c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),X0),
inference(cnf_transformation,[],[f576]) ).
fof(f576,plain,
! [X0,X1] : c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) = c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),X0),
inference(rectify,[],[f424]) ).
fof(f424,axiom,
! [X11,X4] : c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)) = c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)),X11),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_empty__Diff) ).
fof(f4554,plain,
( spl104_235
| ~ spl104_145
| ~ spl104_206 ),
inference(avatar_split_clause,[],[f4360,f4072,f3586,f4552]) ).
fof(f4552,plain,
( spl104_235
<=> ! [X0] : ~ c_Wellfounded_Owf(X0,c_Relation_OId(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_235])]) ).
fof(f4360,plain,
( ! [X0] : ~ c_Wellfounded_Owf(X0,c_Relation_OId(X0))
| ~ spl104_145
| ~ spl104_206 ),
inference(resolution,[],[f4073,f3587]) ).
fof(f4306,plain,
( spl104_234
| ~ spl104_145
| ~ spl104_196 ),
inference(avatar_split_clause,[],[f4214,f4032,f3586,f4304]) ).
fof(f4304,plain,
( spl104_234
<=> ! [X0] : ~ c_Relation_Oirrefl(X0,c_Relation_OId(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_234])]) ).
fof(f4214,plain,
( ! [X0] : ~ c_Relation_Oirrefl(X0,c_Relation_OId(X0))
| ~ spl104_145
| ~ spl104_196 ),
inference(resolution,[],[f4033,f3587]) ).
fof(f4182,plain,
spl104_233,
inference(avatar_split_clause,[],[f2505,f4180]) ).
fof(f2505,plain,
! [X2,X3,X0,X1] :
( hBOOL(hAPP(X0,sK75(X0,X1,X2,X3)))
| ~ sP8(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f1793]) ).
fof(f4178,plain,
spl104_232,
inference(avatar_split_clause,[],[f2503,f4176]) ).
fof(f2503,plain,
! [X2,X3,X0,X1,X4] :
( sP9(X0,X1,X2,X3)
| ~ hBOOL(hAPP(X0,X4))
| ~ c_member(X2,X4,X1) ),
inference(cnf_transformation,[],[f1789]) ).
fof(f4174,plain,
( spl104_231
| ~ spl104_24
| ~ spl104_159 ),
inference(avatar_split_clause,[],[f3799,f3642,f2992,f4172]) ).
fof(f3799,plain,
( ! [X0,X1] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1))
| ~ spl104_24
| ~ spl104_159 ),
inference(resolution,[],[f3643,f2993]) ).
fof(f4170,plain,
spl104_230,
inference(avatar_split_clause,[],[f2502,f4168]) ).
fof(f2502,plain,
! [X2,X3,X0,X1,X5] :
( sP9(X0,X1,X2,X3)
| ~ hBOOL(hAPP(X0,X5))
| ~ c_member(X2,X5,X3) ),
inference(cnf_transformation,[],[f1789]) ).
fof(f4166,plain,
spl104_229,
inference(avatar_split_clause,[],[f2496,f4164]) ).
fof(f4164,plain,
( spl104_229
<=> ! [X0,X3,X2,X1] :
( sP7(X0,X1,X3,X2)
| ~ hBOOL(hAPP(X0,sK72(X0,X1,X2,X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_229])]) ).
fof(f2496,plain,
! [X2,X3,X0,X1] :
( sP7(X0,X1,X3,X2)
| ~ hBOOL(hAPP(X0,sK72(X0,X1,X2,X3))) ),
inference(cnf_transformation,[],[f1783]) ).
fof(f4162,plain,
spl104_228,
inference(avatar_split_clause,[],[f2490,f4160]) ).
fof(f4160,plain,
( spl104_228
<=> ! [X3,X0,X6,X2,X1] :
( hBOOL(hAPP(X0,X6))
| ~ c_member(X2,X6,X1)
| ~ sP7(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_228])]) ).
fof(f2490,plain,
! [X2,X3,X0,X1,X6] :
( hBOOL(hAPP(X0,X6))
| ~ c_member(X2,X6,X1)
| ~ sP7(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f1779]) ).
fof(f4158,plain,
spl104_227,
inference(avatar_split_clause,[],[f2489,f4156]) ).
fof(f4156,plain,
( spl104_227
<=> ! [X1,X0,X3,X2,X7] :
( hBOOL(hAPP(X0,X7))
| ~ c_member(X2,X7,X3)
| ~ sP7(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_227])]) ).
fof(f2489,plain,
! [X2,X3,X0,X1,X7] :
( hBOOL(hAPP(X0,X7))
| ~ c_member(X2,X7,X3)
| ~ sP7(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f1779]) ).
fof(f4154,plain,
spl104_226,
inference(avatar_split_clause,[],[f2463,f4152]) ).
fof(f4152,plain,
( spl104_226
<=> ! [X0,X3,X2,X1] :
( c_member(X3,X2,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),c_Set_Oinsert(X3,X2,X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_226])]) ).
fof(f2463,plain,
! [X2,X3,X0,X1] :
( c_member(X3,X2,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),c_Set_Oinsert(X3,X2,X1),X0) ),
inference(cnf_transformation,[],[f1759]) ).
fof(f4150,plain,
spl104_225,
inference(avatar_split_clause,[],[f2397,f4148]) ).
fof(f4148,plain,
( spl104_225
<=> ! [X0,X3,X2,X1] :
( c_member(X3,X2,X1)
| ~ c_member(X3,X2,c_Groups_Ominus__class_Ominus(tc_fun(X3,tc_HOL_Obool),X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_225])]) ).
fof(f2397,plain,
! [X2,X3,X0,X1] :
( c_member(X3,X2,X1)
| ~ c_member(X3,X2,c_Groups_Ominus__class_Ominus(tc_fun(X3,tc_HOL_Obool),X1,X0)) ),
inference(cnf_transformation,[],[f1397]) ).
fof(f1397,plain,
! [X0,X1,X2,X3] :
( c_member(X3,X2,X1)
| ~ c_member(X3,X2,c_Groups_Ominus__class_Ominus(tc_fun(X3,tc_HOL_Obool),X1,X0)) ),
inference(ennf_transformation,[],[f903]) ).
fof(f903,plain,
! [X0,X1,X2,X3] :
( c_member(X3,X2,c_Groups_Ominus__class_Ominus(tc_fun(X3,tc_HOL_Obool),X1,X0))
=> c_member(X3,X2,X1) ),
inference(rectify,[],[f202]) ).
fof(f202,axiom,
! [X10,X11,X7,X4] :
( c_member(X4,X7,c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool),X11,X10))
=> c_member(X4,X7,X11) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_DiffD1) ).
fof(f4146,plain,
spl104_224,
inference(avatar_split_clause,[],[f2396,f4144]) ).
fof(f4144,plain,
( spl104_224
<=> ! [X0,X3,X2,X1] :
( ~ c_member(X3,X2,X0)
| ~ c_member(X3,X2,c_Groups_Ominus__class_Ominus(tc_fun(X3,tc_HOL_Obool),X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_224])]) ).
fof(f2396,plain,
! [X2,X3,X0,X1] :
( ~ c_member(X3,X2,X0)
| ~ c_member(X3,X2,c_Groups_Ominus__class_Ominus(tc_fun(X3,tc_HOL_Obool),X1,X0)) ),
inference(cnf_transformation,[],[f1396]) ).
fof(f1396,plain,
! [X0,X1,X2,X3] :
( ~ c_member(X3,X2,X0)
| ~ c_member(X3,X2,c_Groups_Ominus__class_Ominus(tc_fun(X3,tc_HOL_Obool),X1,X0)) ),
inference(ennf_transformation,[],[f902]) ).
fof(f902,plain,
! [X0,X1,X2,X3] :
( c_member(X3,X2,c_Groups_Ominus__class_Ominus(tc_fun(X3,tc_HOL_Obool),X1,X0))
=> ~ c_member(X3,X2,X0) ),
inference(rectify,[],[f203]) ).
fof(f203,axiom,
! [X10,X11,X7,X4] :
( c_member(X4,X7,c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool),X11,X10))
=> ~ c_member(X4,X7,X10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_DiffD2) ).
fof(f4142,plain,
spl104_223,
inference(avatar_split_clause,[],[f2354,f4140]) ).
fof(f2354,plain,
! [X2,X3,X0,X1] :
( c_member(X3,X2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),X0,X1))
| ~ c_member(X3,X2,X1) ),
inference(cnf_transformation,[],[f1334]) ).
fof(f1334,plain,
! [X0,X1,X2,X3] :
( c_member(X3,X2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),X0,X1))
| ~ c_member(X3,X2,X1) ),
inference(ennf_transformation,[],[f867]) ).
fof(f867,plain,
! [X0,X1,X2,X3] :
( c_member(X3,X2,X1)
=> c_member(X3,X2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),X0,X1)) ),
inference(rectify,[],[f140]) ).
fof(f140,axiom,
! [X11,X10,X7,X4] :
( c_member(X4,X7,X10)
=> c_member(X4,X7,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool),X11,X10)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UnI2) ).
fof(f4138,plain,
spl104_222,
inference(avatar_split_clause,[],[f2353,f4136]) ).
fof(f2353,plain,
! [X2,X3,X0,X1] :
( c_member(X3,X2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),X1,X0))
| ~ c_member(X3,X2,X1) ),
inference(cnf_transformation,[],[f1333]) ).
fof(f1333,plain,
! [X0,X1,X2,X3] :
( c_member(X3,X2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),X1,X0))
| ~ c_member(X3,X2,X1) ),
inference(ennf_transformation,[],[f866]) ).
fof(f866,plain,
! [X0,X1,X2,X3] :
( c_member(X3,X2,X1)
=> c_member(X3,X2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),X1,X0)) ),
inference(rectify,[],[f139]) ).
fof(f139,axiom,
! [X10,X11,X7,X4] :
( c_member(X4,X7,X11)
=> c_member(X4,X7,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool),X11,X10)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UnI1) ).
fof(f4134,plain,
spl104_221,
inference(avatar_split_clause,[],[f2345,f4132]) ).
fof(f2345,plain,
! [X2,X3,X0,X1] :
( hBOOL(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool),X0,X3),X2))
| ~ hBOOL(hAPP(X3,X2)) ),
inference(cnf_transformation,[],[f1321]) ).
fof(f1321,plain,
! [X0,X1,X2,X3] :
( hBOOL(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool),X0,X3),X2))
| ~ hBOOL(hAPP(X3,X2)) ),
inference(ennf_transformation,[],[f857]) ).
fof(f857,plain,
! [X0,X1,X2,X3] :
( hBOOL(hAPP(X3,X2))
=> hBOOL(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool),X0,X3),X2)) ),
inference(rectify,[],[f187]) ).
fof(f187,axiom,
! [X11,X4,X13,X10] :
( hBOOL(hAPP(X10,X13))
=> hBOOL(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool),X11,X10),X13)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup1I2) ).
fof(f4130,plain,
( spl104_220
| ~ spl104_5
| ~ spl104_103 ),
inference(avatar_split_clause,[],[f3401,f3350,f2897,f4128]) ).
fof(f4128,plain,
( spl104_220
<=> ! [X0] : c_Lattices_Osemilattice__sup__class_Osup(tc_HOL_Obool,c_Orderings_Obot__class_Obot(tc_HOL_Obool),X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl104_220])]) ).
fof(f2897,plain,
( spl104_5
<=> class_Lattices_Obounded__lattice__bot(tc_HOL_Obool) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_5])]) ).
fof(f3401,plain,
( ! [X0] : c_Lattices_Osemilattice__sup__class_Osup(tc_HOL_Obool,c_Orderings_Obot__class_Obot(tc_HOL_Obool),X0) = X0
| ~ spl104_5
| ~ spl104_103 ),
inference(resolution,[],[f3351,f2899]) ).
fof(f2899,plain,
( class_Lattices_Obounded__lattice__bot(tc_HOL_Obool)
| ~ spl104_5 ),
inference(avatar_component_clause,[],[f2897]) ).
fof(f4126,plain,
spl104_219,
inference(avatar_split_clause,[],[f2344,f4124]) ).
fof(f2344,plain,
! [X2,X3,X0,X1] :
( hBOOL(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool),X3,X0),X2))
| ~ hBOOL(hAPP(X3,X2)) ),
inference(cnf_transformation,[],[f1320]) ).
fof(f1320,plain,
! [X0,X1,X2,X3] :
( hBOOL(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool),X3,X0),X2))
| ~ hBOOL(hAPP(X3,X2)) ),
inference(ennf_transformation,[],[f856]) ).
fof(f856,plain,
! [X0,X1,X2,X3] :
( hBOOL(hAPP(X3,X2))
=> hBOOL(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool),X3,X0),X2)) ),
inference(rectify,[],[f186]) ).
fof(f186,axiom,
! [X10,X4,X13,X11] :
( hBOOL(hAPP(X11,X13))
=> hBOOL(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool),X11,X10),X13)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup1I1) ).
fof(f4122,plain,
spl104_218,
inference(avatar_split_clause,[],[f2317,f4120]) ).
fof(f2317,plain,
! [X2,X3,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X3,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(X3,c_Lattices_Osemilattice__sup__class_Osup(X3,X2,X1),X0)
| ~ class_Lattices_Osemilattice__sup(X3) ),
inference(cnf_transformation,[],[f1293]) ).
fof(f1293,plain,
! [X0,X1,X2,X3] :
( ( c_Orderings_Oord__class_Oless__eq(X3,X1,X0)
& c_Orderings_Oord__class_Oless__eq(X3,X2,X0) )
| ~ c_Orderings_Oord__class_Oless__eq(X3,c_Lattices_Osemilattice__sup__class_Osup(X3,X2,X1),X0)
| ~ class_Lattices_Osemilattice__sup(X3) ),
inference(flattening,[],[f1292]) ).
fof(f1292,plain,
! [X0,X1,X2,X3] :
( ( c_Orderings_Oord__class_Oless__eq(X3,X1,X0)
& c_Orderings_Oord__class_Oless__eq(X3,X2,X0) )
| ~ c_Orderings_Oord__class_Oless__eq(X3,c_Lattices_Osemilattice__sup__class_Osup(X3,X2,X1),X0)
| ~ class_Lattices_Osemilattice__sup(X3) ),
inference(ennf_transformation,[],[f838]) ).
fof(f838,plain,
! [X0,X1,X2,X3] :
( class_Lattices_Osemilattice__sup(X3)
=> ( c_Orderings_Oord__class_Oless__eq(X3,c_Lattices_Osemilattice__sup__class_Osup(X3,X2,X1),X0)
=> ~ ( c_Orderings_Oord__class_Oless__eq(X3,X2,X0)
=> ~ c_Orderings_Oord__class_Oless__eq(X3,X1,X0) ) ) ),
inference(rectify,[],[f246]) ).
fof(f246,axiom,
! [X58,X26,X27,X4] :
( class_Lattices_Osemilattice__sup(X4)
=> ( c_Orderings_Oord__class_Oless__eq(X4,c_Lattices_Osemilattice__sup__class_Osup(X4,X27,X26),X58)
=> ~ ( c_Orderings_Oord__class_Oless__eq(X4,X27,X58)
=> ~ c_Orderings_Oord__class_Oless__eq(X4,X26,X58) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__supE) ).
fof(f4118,plain,
spl104_217,
inference(avatar_split_clause,[],[f2316,f4116]) ).
fof(f2316,plain,
! [X2,X3,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X3,X2,X0)
| ~ c_Orderings_Oord__class_Oless__eq(X3,c_Lattices_Osemilattice__sup__class_Osup(X3,X2,X1),X0)
| ~ class_Lattices_Osemilattice__sup(X3) ),
inference(cnf_transformation,[],[f1293]) ).
fof(f4114,plain,
spl104_216,
inference(avatar_split_clause,[],[f2310,f4112]) ).
fof(f4112,plain,
( spl104_216
<=> ! [X0,X3,X2,X1] :
( c_Orderings_Oord__class_Oless__eq(X3,X2,c_Lattices_Osemilattice__sup__class_Osup(X3,X1,X0))
| ~ c_Orderings_Oord__class_Oless__eq(X3,X2,X1)
| ~ class_Lattices_Osemilattice__sup(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_216])]) ).
fof(f2310,plain,
! [X2,X3,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X3,X2,c_Lattices_Osemilattice__sup__class_Osup(X3,X1,X0))
| ~ c_Orderings_Oord__class_Oless__eq(X3,X2,X1)
| ~ class_Lattices_Osemilattice__sup(X3) ),
inference(cnf_transformation,[],[f1281]) ).
fof(f1281,plain,
! [X0,X1,X2,X3] :
( c_Orderings_Oord__class_Oless__eq(X3,X2,c_Lattices_Osemilattice__sup__class_Osup(X3,X1,X0))
| ~ c_Orderings_Oord__class_Oless__eq(X3,X2,X1)
| ~ class_Lattices_Osemilattice__sup(X3) ),
inference(flattening,[],[f1280]) ).
fof(f1280,plain,
! [X0,X1,X2,X3] :
( c_Orderings_Oord__class_Oless__eq(X3,X2,c_Lattices_Osemilattice__sup__class_Osup(X3,X1,X0))
| ~ c_Orderings_Oord__class_Oless__eq(X3,X2,X1)
| ~ class_Lattices_Osemilattice__sup(X3) ),
inference(ennf_transformation,[],[f832]) ).
fof(f832,plain,
! [X0,X1,X2,X3] :
( class_Lattices_Osemilattice__sup(X3)
=> ( c_Orderings_Oord__class_Oless__eq(X3,X2,X1)
=> c_Orderings_Oord__class_Oless__eq(X3,X2,c_Lattices_Osemilattice__sup__class_Osup(X3,X1,X0)) ) ),
inference(rectify,[],[f253]) ).
fof(f253,axiom,
! [X26,X27,X58,X4] :
( class_Lattices_Osemilattice__sup(X4)
=> ( c_Orderings_Oord__class_Oless__eq(X4,X58,X27)
=> c_Orderings_Oord__class_Oless__eq(X4,X58,c_Lattices_Osemilattice__sup__class_Osup(X4,X27,X26)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__supI1) ).
fof(f4110,plain,
spl104_215,
inference(avatar_split_clause,[],[f2309,f4108]) ).
fof(f4108,plain,
( spl104_215
<=> ! [X0,X3,X2,X1] :
( c_Orderings_Oord__class_Oless__eq(X3,X2,c_Lattices_Osemilattice__sup__class_Osup(X3,X0,X1))
| ~ c_Orderings_Oord__class_Oless__eq(X3,X2,X1)
| ~ class_Lattices_Osemilattice__sup(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_215])]) ).
fof(f2309,plain,
! [X2,X3,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X3,X2,c_Lattices_Osemilattice__sup__class_Osup(X3,X0,X1))
| ~ c_Orderings_Oord__class_Oless__eq(X3,X2,X1)
| ~ class_Lattices_Osemilattice__sup(X3) ),
inference(cnf_transformation,[],[f1279]) ).
fof(f1279,plain,
! [X0,X1,X2,X3] :
( c_Orderings_Oord__class_Oless__eq(X3,X2,c_Lattices_Osemilattice__sup__class_Osup(X3,X0,X1))
| ~ c_Orderings_Oord__class_Oless__eq(X3,X2,X1)
| ~ class_Lattices_Osemilattice__sup(X3) ),
inference(flattening,[],[f1278]) ).
fof(f1278,plain,
! [X0,X1,X2,X3] :
( c_Orderings_Oord__class_Oless__eq(X3,X2,c_Lattices_Osemilattice__sup__class_Osup(X3,X0,X1))
| ~ c_Orderings_Oord__class_Oless__eq(X3,X2,X1)
| ~ class_Lattices_Osemilattice__sup(X3) ),
inference(ennf_transformation,[],[f831]) ).
fof(f831,plain,
! [X0,X1,X2,X3] :
( class_Lattices_Osemilattice__sup(X3)
=> ( c_Orderings_Oord__class_Oless__eq(X3,X2,X1)
=> c_Orderings_Oord__class_Oless__eq(X3,X2,c_Lattices_Osemilattice__sup__class_Osup(X3,X0,X1)) ) ),
inference(rectify,[],[f252]) ).
fof(f252,axiom,
! [X27,X26,X58,X4] :
( class_Lattices_Osemilattice__sup(X4)
=> ( c_Orderings_Oord__class_Oless__eq(X4,X58,X26)
=> c_Orderings_Oord__class_Oless__eq(X4,X58,c_Lattices_Osemilattice__sup__class_Osup(X4,X27,X26)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__supI2) ).
fof(f4106,plain,
spl104_214,
inference(avatar_split_clause,[],[f2305,f4104]) ).
fof(f2305,plain,
! [X2,X3,X0,X1] :
( c_Orderings_Oord__class_Oless(X3,X2,c_Lattices_Osemilattice__sup__class_Osup(X3,X1,X0))
| ~ c_Orderings_Oord__class_Oless(X3,X2,X1)
| ~ class_Lattices_Osemilattice__sup(X3) ),
inference(cnf_transformation,[],[f1271]) ).
fof(f1271,plain,
! [X0,X1,X2,X3] :
( c_Orderings_Oord__class_Oless(X3,X2,c_Lattices_Osemilattice__sup__class_Osup(X3,X1,X0))
| ~ c_Orderings_Oord__class_Oless(X3,X2,X1)
| ~ class_Lattices_Osemilattice__sup(X3) ),
inference(flattening,[],[f1270]) ).
fof(f1270,plain,
! [X0,X1,X2,X3] :
( c_Orderings_Oord__class_Oless(X3,X2,c_Lattices_Osemilattice__sup__class_Osup(X3,X1,X0))
| ~ c_Orderings_Oord__class_Oless(X3,X2,X1)
| ~ class_Lattices_Osemilattice__sup(X3) ),
inference(ennf_transformation,[],[f827]) ).
fof(f827,plain,
! [X0,X1,X2,X3] :
( class_Lattices_Osemilattice__sup(X3)
=> ( c_Orderings_Oord__class_Oless(X3,X2,X1)
=> c_Orderings_Oord__class_Oless(X3,X2,c_Lattices_Osemilattice__sup__class_Osup(X3,X1,X0)) ) ),
inference(rectify,[],[f261]) ).
fof(f261,axiom,
! [X26,X27,X58,X4] :
( class_Lattices_Osemilattice__sup(X4)
=> ( c_Orderings_Oord__class_Oless(X4,X58,X27)
=> c_Orderings_Oord__class_Oless(X4,X58,c_Lattices_Osemilattice__sup__class_Osup(X4,X27,X26)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__supI1) ).
fof(f4102,plain,
spl104_213,
inference(avatar_split_clause,[],[f2304,f4100]) ).
fof(f2304,plain,
! [X2,X3,X0,X1] :
( c_Orderings_Oord__class_Oless(X3,X2,c_Lattices_Osemilattice__sup__class_Osup(X3,X0,X1))
| ~ c_Orderings_Oord__class_Oless(X3,X2,X1)
| ~ class_Lattices_Osemilattice__sup(X3) ),
inference(cnf_transformation,[],[f1269]) ).
fof(f1269,plain,
! [X0,X1,X2,X3] :
( c_Orderings_Oord__class_Oless(X3,X2,c_Lattices_Osemilattice__sup__class_Osup(X3,X0,X1))
| ~ c_Orderings_Oord__class_Oless(X3,X2,X1)
| ~ class_Lattices_Osemilattice__sup(X3) ),
inference(flattening,[],[f1268]) ).
fof(f1268,plain,
! [X0,X1,X2,X3] :
( c_Orderings_Oord__class_Oless(X3,X2,c_Lattices_Osemilattice__sup__class_Osup(X3,X0,X1))
| ~ c_Orderings_Oord__class_Oless(X3,X2,X1)
| ~ class_Lattices_Osemilattice__sup(X3) ),
inference(ennf_transformation,[],[f826]) ).
fof(f826,plain,
! [X0,X1,X2,X3] :
( class_Lattices_Osemilattice__sup(X3)
=> ( c_Orderings_Oord__class_Oless(X3,X2,X1)
=> c_Orderings_Oord__class_Oless(X3,X2,c_Lattices_Osemilattice__sup__class_Osup(X3,X0,X1)) ) ),
inference(rectify,[],[f260]) ).
fof(f260,axiom,
! [X27,X26,X58,X4] :
( class_Lattices_Osemilattice__sup(X4)
=> ( c_Orderings_Oord__class_Oless(X4,X58,X26)
=> c_Orderings_Oord__class_Oless(X4,X58,c_Lattices_Osemilattice__sup__class_Osup(X4,X27,X26)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__supI2) ).
fof(f4098,plain,
spl104_212,
inference(avatar_split_clause,[],[f2264,f4096]) ).
fof(f4096,plain,
( spl104_212
<=> ! [X2,X0,X6,X1,X7] :
( hBOOL(hAPP(X2,c_Product__Type_OPair(X1,X0,X6,X7)))
| ~ hBOOL(hAPP(X2,sK54(X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_212])]) ).
fof(f2264,plain,
! [X2,X0,X1,X6,X7] :
( hBOOL(hAPP(X2,c_Product__Type_OPair(X1,X0,X6,X7)))
| ~ hBOOL(hAPP(X2,sK54(X2))) ),
inference(cnf_transformation,[],[f1693]) ).
fof(f4094,plain,
spl104_211,
inference(avatar_split_clause,[],[f2235,f4092]) ).
fof(f4092,plain,
( spl104_211
<=> ! [X2,X0,X1] :
( c_Relation_Osingle__valued(X2,X1,X0)
| sK49(X0,X1,X2) != sK50(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_211])]) ).
fof(f2235,plain,
! [X2,X0,X1] :
( c_Relation_Osingle__valued(X2,X1,X0)
| sK49(X0,X1,X2) != sK50(X0,X1,X2) ),
inference(cnf_transformation,[],[f1670]) ).
fof(f4090,plain,
spl104_210,
inference(avatar_split_clause,[],[f2220,f4088]) ).
fof(f4088,plain,
( spl104_210
<=> ! [X2,X0,X1] :
( c_Relation_Ototal__on(X2,X1,X0)
| sK46(X0,X1,X2) != sK47(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_210])]) ).
fof(f2220,plain,
! [X2,X0,X1] :
( c_Relation_Ototal__on(X2,X1,X0)
| sK46(X0,X1,X2) != sK47(X0,X1,X2) ),
inference(cnf_transformation,[],[f1659]) ).
fof(f4086,plain,
( spl104_209
| ~ spl104_5
| ~ spl104_102 ),
inference(avatar_split_clause,[],[f3399,f3346,f2897,f4084]) ).
fof(f3399,plain,
( ! [X0] : c_Lattices_Osemilattice__sup__class_Osup(tc_HOL_Obool,X0,c_Orderings_Obot__class_Obot(tc_HOL_Obool)) = X0
| ~ spl104_5
| ~ spl104_102 ),
inference(resolution,[],[f3347,f2899]) ).
fof(f4082,plain,
spl104_208,
inference(avatar_split_clause,[],[f2208,f4080]) ).
fof(f4080,plain,
( spl104_208
<=> ! [X2,X0,X1] :
( c_Relation_Osingle__valued(X2,X1,X0)
| sK44(X0,X1,X2) != sK45(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_208])]) ).
fof(f2208,plain,
! [X2,X0,X1] :
( c_Relation_Osingle__valued(X2,X1,X0)
| sK44(X0,X1,X2) != sK45(X0,X1,X2) ),
inference(cnf_transformation,[],[f1652]) ).
fof(f4078,plain,
spl104_207,
inference(avatar_split_clause,[],[f2194,f4076]) ).
fof(f4076,plain,
( spl104_207
<=> ! [X2,X0,X1] :
( X0 = X1
| ~ c_member(X2,X1,c_Set_Oinsert(X2,X0,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_207])]) ).
fof(f2194,plain,
! [X2,X0,X1] :
( X0 = X1
| ~ c_member(X2,X1,c_Set_Oinsert(X2,X0,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)))) ),
inference(cnf_transformation,[],[f1224]) ).
fof(f1224,plain,
! [X0,X1,X2] :
( X0 = X1
| ~ c_member(X2,X1,c_Set_Oinsert(X2,X0,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)))) ),
inference(ennf_transformation,[],[f764]) ).
fof(f764,plain,
! [X0,X1,X2] :
( c_member(X2,X1,c_Set_Oinsert(X2,X0,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))))
=> X0 = X1 ),
inference(rectify,[],[f435]) ).
fof(f435,axiom,
! [X9,X8,X4] :
( c_member(X4,X8,c_Set_Oinsert(X4,X9,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))
=> X8 = X9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_singletonE) ).
fof(f4074,plain,
spl104_206,
inference(avatar_split_clause,[],[f2151,f4072]) ).
fof(f2151,plain,
! [X2,X0,X1] :
( ~ c_member(tc_prod(X2,X2),c_Product__Type_OPair(X2,X2,X0,X0),X1)
| ~ c_Wellfounded_Owf(X2,X1) ),
inference(cnf_transformation,[],[f1173]) ).
fof(f1173,plain,
! [X0,X1,X2] :
( ~ c_member(tc_prod(X2,X2),c_Product__Type_OPair(X2,X2,X0,X0),X1)
| ~ c_Wellfounded_Owf(X2,X1) ),
inference(ennf_transformation,[],[f727]) ).
fof(f727,plain,
! [X0,X1,X2] :
( c_Wellfounded_Owf(X2,X1)
=> ~ c_member(tc_prod(X2,X2),c_Product__Type_OPair(X2,X2,X0,X0),X1) ),
inference(rectify,[],[f165]) ).
fof(f165,axiom,
! [X9,X3,X4] :
( c_Wellfounded_Owf(X4,X3)
=> ~ c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X9,X9),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__irrefl) ).
fof(f4070,plain,
spl104_205,
inference(avatar_split_clause,[],[f2128,f4068]) ).
fof(f2128,plain,
! [X2,X0,X1] :
( X0 = X1
| ~ c_Orderings_Oord__class_Oless__eq(X2,X0,X1)
| ~ c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
| ~ class_Orderings_Oorder(X2) ),
inference(cnf_transformation,[],[f1155]) ).
fof(f1155,plain,
! [X0,X1,X2] :
( X0 = X1
| ~ c_Orderings_Oord__class_Oless__eq(X2,X0,X1)
| ~ c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
| ~ class_Orderings_Oorder(X2) ),
inference(flattening,[],[f1154]) ).
fof(f1154,plain,
! [X0,X1,X2] :
( X0 = X1
| ~ c_Orderings_Oord__class_Oless__eq(X2,X0,X1)
| ~ c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
| ~ class_Orderings_Oorder(X2) ),
inference(ennf_transformation,[],[f713]) ).
fof(f713,plain,
! [X0,X1,X2] :
( class_Orderings_Oorder(X2)
=> ( c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
=> ( c_Orderings_Oord__class_Oless__eq(X2,X0,X1)
=> X0 = X1 ) ) ),
inference(rectify,[],[f305]) ).
fof(f305,axiom,
! [X59,X58,X4] :
( class_Orderings_Oorder(X4)
=> ( c_Orderings_Oord__class_Oless__eq(X4,X58,X59)
=> ( c_Orderings_Oord__class_Oless__eq(X4,X59,X58)
=> X58 = X59 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__antisym) ).
fof(f4066,plain,
spl104_204,
inference(avatar_split_clause,[],[f2117,f4064]) ).
fof(f2117,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless(X2,X0,X1)
| ~ c_Orderings_Oord__class_Oless__eq(X2,X0,X1)
| X0 = X1
| ~ class_Orderings_Oorder(X2) ),
inference(cnf_transformation,[],[f1133]) ).
fof(f1133,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless(X2,X0,X1)
| ~ c_Orderings_Oord__class_Oless__eq(X2,X0,X1)
| X0 = X1
| ~ class_Orderings_Oorder(X2) ),
inference(flattening,[],[f1132]) ).
fof(f1132,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless(X2,X0,X1)
| ~ c_Orderings_Oord__class_Oless__eq(X2,X0,X1)
| X0 = X1
| ~ class_Orderings_Oorder(X2) ),
inference(ennf_transformation,[],[f702]) ).
fof(f702,plain,
! [X0,X1,X2] :
( class_Orderings_Oorder(X2)
=> ( X0 != X1
=> ( c_Orderings_Oord__class_Oless__eq(X2,X0,X1)
=> c_Orderings_Oord__class_Oless(X2,X0,X1) ) ) ),
inference(rectify,[],[f342]) ).
fof(f342,axiom,
! [X26,X27,X4] :
( class_Orderings_Oorder(X4)
=> ( X26 != X27
=> ( c_Orderings_Oord__class_Oless__eq(X4,X26,X27)
=> c_Orderings_Oord__class_Oless(X4,X26,X27) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I12_J) ).
fof(f4062,plain,
spl104_203,
inference(avatar_split_clause,[],[f2095,f4060]) ).
fof(f4060,plain,
( spl104_203
<=> ! [X2,X0,X1] :
( c_Orderings_Obot__class_Obot(X2) = X0
| c_Lattices_Osemilattice__sup__class_Osup(X2,X1,X0) != c_Orderings_Obot__class_Obot(X2)
| ~ class_Lattices_Obounded__lattice__bot(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_203])]) ).
fof(f2095,plain,
! [X2,X0,X1] :
( c_Orderings_Obot__class_Obot(X2) = X0
| c_Lattices_Osemilattice__sup__class_Osup(X2,X1,X0) != c_Orderings_Obot__class_Obot(X2)
| ~ class_Lattices_Obounded__lattice__bot(X2) ),
inference(cnf_transformation,[],[f1627]) ).
fof(f1627,plain,
! [X0,X1,X2] :
( ( ( c_Lattices_Osemilattice__sup__class_Osup(X2,X1,X0) = c_Orderings_Obot__class_Obot(X2)
| c_Orderings_Obot__class_Obot(X2) != X0
| c_Orderings_Obot__class_Obot(X2) != X1 )
& ( ( c_Orderings_Obot__class_Obot(X2) = X0
& c_Orderings_Obot__class_Obot(X2) = X1 )
| c_Lattices_Osemilattice__sup__class_Osup(X2,X1,X0) != c_Orderings_Obot__class_Obot(X2) ) )
| ~ class_Lattices_Obounded__lattice__bot(X2) ),
inference(flattening,[],[f1626]) ).
fof(f1626,plain,
! [X0,X1,X2] :
( ( ( c_Lattices_Osemilattice__sup__class_Osup(X2,X1,X0) = c_Orderings_Obot__class_Obot(X2)
| c_Orderings_Obot__class_Obot(X2) != X0
| c_Orderings_Obot__class_Obot(X2) != X1 )
& ( ( c_Orderings_Obot__class_Obot(X2) = X0
& c_Orderings_Obot__class_Obot(X2) = X1 )
| c_Lattices_Osemilattice__sup__class_Osup(X2,X1,X0) != c_Orderings_Obot__class_Obot(X2) ) )
| ~ class_Lattices_Obounded__lattice__bot(X2) ),
inference(nnf_transformation,[],[f1107]) ).
fof(f1107,plain,
! [X0,X1,X2] :
( ( c_Lattices_Osemilattice__sup__class_Osup(X2,X1,X0) = c_Orderings_Obot__class_Obot(X2)
<=> ( c_Orderings_Obot__class_Obot(X2) = X0
& c_Orderings_Obot__class_Obot(X2) = X1 ) )
| ~ class_Lattices_Obounded__lattice__bot(X2) ),
inference(ennf_transformation,[],[f683]) ).
fof(f683,plain,
! [X0,X1,X2] :
( class_Lattices_Obounded__lattice__bot(X2)
=> ( c_Lattices_Osemilattice__sup__class_Osup(X2,X1,X0) = c_Orderings_Obot__class_Obot(X2)
<=> ( c_Orderings_Obot__class_Obot(X2) = X0
& c_Orderings_Obot__class_Obot(X2) = X1 ) ) ),
inference(rectify,[],[f410]) ).
fof(f410,axiom,
! [X12,X13,X4] :
( class_Lattices_Obounded__lattice__bot(X4)
=> ( c_Lattices_Osemilattice__sup__class_Osup(X4,X13,X12) = c_Orderings_Obot__class_Obot(X4)
<=> ( c_Orderings_Obot__class_Obot(X4) = X12
& c_Orderings_Obot__class_Obot(X4) = X13 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup__eq__bot__iff) ).
fof(f4058,plain,
spl104_202,
inference(avatar_split_clause,[],[f2094,f4056]) ).
fof(f4056,plain,
( spl104_202
<=> ! [X2,X0,X1] :
( c_Orderings_Obot__class_Obot(X2) = X1
| c_Lattices_Osemilattice__sup__class_Osup(X2,X1,X0) != c_Orderings_Obot__class_Obot(X2)
| ~ class_Lattices_Obounded__lattice__bot(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_202])]) ).
fof(f2094,plain,
! [X2,X0,X1] :
( c_Orderings_Obot__class_Obot(X2) = X1
| c_Lattices_Osemilattice__sup__class_Osup(X2,X1,X0) != c_Orderings_Obot__class_Obot(X2)
| ~ class_Lattices_Obounded__lattice__bot(X2) ),
inference(cnf_transformation,[],[f1627]) ).
fof(f4054,plain,
spl104_201,
inference(avatar_split_clause,[],[f2077,f4052]) ).
fof(f2077,plain,
! [X2,X0,X1] :
( X0 = X1
| ~ c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
| c_Orderings_Oord__class_Oless(X2,X1,X0)
| ~ class_Orderings_Olinorder(X2) ),
inference(cnf_transformation,[],[f1618]) ).
fof(f1618,plain,
! [X0,X1,X2] :
( ( ( c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
| X0 != X1 )
& ( X0 = X1
| ~ c_Orderings_Oord__class_Oless__eq(X2,X1,X0) ) )
| c_Orderings_Oord__class_Oless(X2,X1,X0)
| ~ class_Orderings_Olinorder(X2) ),
inference(nnf_transformation,[],[f1094]) ).
fof(f1094,plain,
! [X0,X1,X2] :
( ( c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
<=> X0 = X1 )
| c_Orderings_Oord__class_Oless(X2,X1,X0)
| ~ class_Orderings_Olinorder(X2) ),
inference(flattening,[],[f1093]) ).
fof(f1093,plain,
! [X0,X1,X2] :
( ( c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
<=> X0 = X1 )
| c_Orderings_Oord__class_Oless(X2,X1,X0)
| ~ class_Orderings_Olinorder(X2) ),
inference(ennf_transformation,[],[f674]) ).
fof(f674,plain,
! [X0,X1,X2] :
( class_Orderings_Olinorder(X2)
=> ( ~ c_Orderings_Oord__class_Oless(X2,X1,X0)
=> ( c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
<=> X0 = X1 ) ) ),
inference(rectify,[],[f340]) ).
fof(f340,axiom,
! [X12,X13,X4] :
( class_Orderings_Olinorder(X4)
=> ( ~ c_Orderings_Oord__class_Oless(X4,X13,X12)
=> ( c_Orderings_Oord__class_Oless__eq(X4,X13,X12)
<=> X12 = X13 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__antisym__conv1) ).
fof(f4050,plain,
spl104_200,
inference(avatar_split_clause,[],[f2069,f4048]) ).
fof(f4048,plain,
( spl104_200
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless(X2,X0,X1)
| X0 = X1
| c_Orderings_Oord__class_Oless(X2,X1,X0)
| ~ class_Orderings_Olinorder(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_200])]) ).
fof(f2069,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless(X2,X0,X1)
| X0 = X1
| c_Orderings_Oord__class_Oless(X2,X1,X0)
| ~ class_Orderings_Olinorder(X2) ),
inference(cnf_transformation,[],[f1080]) ).
fof(f1080,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless(X2,X0,X1)
| X0 = X1
| c_Orderings_Oord__class_Oless(X2,X1,X0)
| ~ class_Orderings_Olinorder(X2) ),
inference(flattening,[],[f1079]) ).
fof(f1079,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless(X2,X0,X1)
| X0 = X1
| c_Orderings_Oord__class_Oless(X2,X1,X0)
| ~ class_Orderings_Olinorder(X2) ),
inference(ennf_transformation,[],[f667]) ).
fof(f667,plain,
! [X0,X1,X2] :
( class_Orderings_Olinorder(X2)
=> ( c_Orderings_Oord__class_Oless(X2,X0,X1)
| X0 = X1
| c_Orderings_Oord__class_Oless(X2,X1,X0) ) ),
inference(rectify,[],[f313]) ).
fof(f313,axiom,
! [X59,X58,X4] :
( class_Orderings_Olinorder(X4)
=> ( c_Orderings_Oord__class_Oless(X4,X59,X58)
| X58 = X59
| c_Orderings_Oord__class_Oless(X4,X58,X59) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__less__linear) ).
fof(f4046,plain,
spl104_199,
inference(avatar_split_clause,[],[f2058,f4044]) ).
fof(f4044,plain,
( spl104_199
<=> ! [X2,X0,X1] : c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool),X0,X1) = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool),X1,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_199])]) ).
fof(f4042,plain,
( spl104_198
| ~ spl104_73
| ~ spl104_96 ),
inference(avatar_split_clause,[],[f3331,f3298,f3202,f4040]) ).
fof(f3331,plain,
( ! [X2,X3,X0,X1] : c_member(X0,X1,c_Set_Oinsert(X2,X1,X3))
| ~ spl104_73
| ~ spl104_96 ),
inference(resolution,[],[f3299,f3203]) ).
fof(f4038,plain,
spl104_197,
inference(avatar_split_clause,[],[f2057,f4036]) ).
fof(f4036,plain,
( spl104_197
<=> ! [X2,X0,X1] : c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) = c_Relation_OImage(X2,X1,X0,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_197])]) ).
fof(f2057,plain,
! [X2,X0,X1] : c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) = c_Relation_OImage(X2,X1,X0,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))),
inference(cnf_transformation,[],[f655]) ).
fof(f655,plain,
! [X0,X1,X2] : c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) = c_Relation_OImage(X2,X1,X0,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))),
inference(rectify,[],[f478]) ).
fof(f478,axiom,
! [X14,X4,X15] : c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)) = c_Relation_OImage(X15,X4,X14,c_Orderings_Obot__class_Obot(tc_fun(X15,tc_HOL_Obool))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Image__empty) ).
fof(f4034,plain,
spl104_196,
inference(avatar_split_clause,[],[f2008,f4032]) ).
fof(f2008,plain,
! [X2,X0,X1] :
( ~ c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,X2,X2),X0)
| ~ c_Relation_Oirrefl(X1,X0) ),
inference(cnf_transformation,[],[f1074]) ).
fof(f1074,plain,
! [X0,X1] :
( ! [X2] : ~ c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,X2,X2),X0)
| ~ c_Relation_Oirrefl(X1,X0) ),
inference(ennf_transformation,[],[f1019]) ).
fof(f1019,plain,
! [X0,X1] :
( c_Relation_Oirrefl(X1,X0)
=> ! [X2] : ~ c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,X2,X2),X0) ),
inference(unused_predicate_definition_removal,[],[f631]) ).
fof(f631,plain,
! [X0,X1] :
( c_Relation_Oirrefl(X1,X0)
<=> ! [X2] : ~ c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,X2,X2),X0) ),
inference(rectify,[],[f17]) ).
fof(f17,axiom,
! [X3,X4] :
( c_Relation_Oirrefl(X4,X3)
<=> ! [X2] : ~ c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X2,X2),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_irrefl__def) ).
fof(f4030,plain,
spl104_195,
inference(avatar_split_clause,[],[f1990,f4028]) ).
fof(f1990,plain,
! [X0,X1] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1)) = X1
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ),
inference(cnf_transformation,[],[f1061]) ).
fof(f1061,plain,
! [X0,X1] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1)) = X1
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ),
inference(ennf_transformation,[],[f620]) ).
fof(f620,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
=> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1)) = X1 ),
inference(rectify,[],[f383]) ).
fof(f383,axiom,
! [X70,X77] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X77,X70)
=> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X70,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X70,X77)) = X77 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__diff__cancel) ).
fof(f4026,plain,
spl104_194,
inference(avatar_split_clause,[],[f1912,f4024]) ).
fof(f4013,plain,
( spl104_193
| ~ spl104_26
| ~ spl104_85 ),
inference(avatar_split_clause,[],[f3321,f3254,f3000,f4011]) ).
fof(f4011,plain,
( spl104_193
<=> ! [X0] : c_Relation_OId(X0) = c_Transitive__Closure_Otrancl(X0,c_Relation_OId(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_193])]) ).
fof(f3000,plain,
( spl104_26
<=> ! [X0] : c_Relation_Otrans(X0,c_Relation_OId(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_26])]) ).
fof(f3321,plain,
( ! [X0] : c_Relation_OId(X0) = c_Transitive__Closure_Otrancl(X0,c_Relation_OId(X0))
| ~ spl104_26
| ~ spl104_85 ),
inference(resolution,[],[f3255,f3001]) ).
fof(f3001,plain,
( ! [X0] : c_Relation_Otrans(X0,c_Relation_OId(X0))
| ~ spl104_26 ),
inference(avatar_component_clause,[],[f3000]) ).
fof(f3919,plain,
( spl104_192
| ~ spl104_177 ),
inference(avatar_split_clause,[],[f3856,f3853,f3917]) ).
fof(f3917,plain,
( spl104_192
<=> ! [X0] : c_Order__Relation_Opreorder__on(X0,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)),c_Relation_OId__on(X0,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_192])]) ).
fof(f3853,plain,
( spl104_177
<=> ! [X0] : c_Order__Relation_Opreorder__on(X0,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X0,X0),tc_HOL_Obool))) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_177])]) ).
fof(f3856,plain,
( ! [X0] : c_Order__Relation_Opreorder__on(X0,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)),c_Relation_OId__on(X0,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool))))
| ~ spl104_177 ),
inference(forward_demodulation,[],[f3854,f1912]) ).
fof(f3854,plain,
( ! [X0] : c_Order__Relation_Opreorder__on(X0,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X0,X0),tc_HOL_Obool)))
| ~ spl104_177 ),
inference(avatar_component_clause,[],[f3853]) ).
fof(f3915,plain,
( spl104_191
| ~ spl104_176 ),
inference(avatar_split_clause,[],[f3851,f3848,f3913]) ).
fof(f3913,plain,
( spl104_191
<=> ! [X0] : c_Order__Relation_Olinear__order__on(X0,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)),c_Relation_OId__on(X0,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_191])]) ).
fof(f3848,plain,
( spl104_176
<=> ! [X0] : c_Order__Relation_Olinear__order__on(X0,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X0,X0),tc_HOL_Obool))) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_176])]) ).
fof(f3851,plain,
( ! [X0] : c_Order__Relation_Olinear__order__on(X0,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)),c_Relation_OId__on(X0,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool))))
| ~ spl104_176 ),
inference(forward_demodulation,[],[f3849,f1912]) ).
fof(f3849,plain,
( ! [X0] : c_Order__Relation_Olinear__order__on(X0,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X0,X0),tc_HOL_Obool)))
| ~ spl104_176 ),
inference(avatar_component_clause,[],[f3848]) ).
fof(f3911,plain,
( spl104_190
| ~ spl104_175 ),
inference(avatar_split_clause,[],[f3846,f3843,f3909]) ).
fof(f3909,plain,
( spl104_190
<=> ! [X0] : c_Order__Relation_Opartial__order__on(X0,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)),c_Relation_OId__on(X0,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_190])]) ).
fof(f3843,plain,
( spl104_175
<=> ! [X0] : c_Order__Relation_Opartial__order__on(X0,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X0,X0),tc_HOL_Obool))) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_175])]) ).
fof(f3846,plain,
( ! [X0] : c_Order__Relation_Opartial__order__on(X0,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)),c_Relation_OId__on(X0,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool))))
| ~ spl104_175 ),
inference(forward_demodulation,[],[f3844,f1912]) ).
fof(f3844,plain,
( ! [X0] : c_Order__Relation_Opartial__order__on(X0,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X0,X0),tc_HOL_Obool)))
| ~ spl104_175 ),
inference(avatar_component_clause,[],[f3843]) ).
fof(f3905,plain,
( spl104_189
| ~ spl104_174 ),
inference(avatar_split_clause,[],[f3841,f3838,f3903]) ).
fof(f3903,plain,
( spl104_189
<=> ! [X0] : c_Order__Relation_Owell__order__on(X0,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)),c_Relation_OId__on(X0,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_189])]) ).
fof(f3838,plain,
( spl104_174
<=> ! [X0] : c_Order__Relation_Owell__order__on(X0,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X0,X0),tc_HOL_Obool))) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_174])]) ).
fof(f3841,plain,
( ! [X0] : c_Order__Relation_Owell__order__on(X0,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)),c_Relation_OId__on(X0,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool))))
| ~ spl104_174 ),
inference(forward_demodulation,[],[f3839,f1912]) ).
fof(f3839,plain,
( ! [X0] : c_Order__Relation_Owell__order__on(X0,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X0,X0),tc_HOL_Obool)))
| ~ spl104_174 ),
inference(avatar_component_clause,[],[f3838]) ).
fof(f3901,plain,
spl104_188,
inference(avatar_split_clause,[],[f2225,f3899]) ).
fof(f3899,plain,
( spl104_188
<=> ! [X2,X0,X1] :
( c_Order__Relation_Olinear__order__on(X2,X1,X0)
| ~ c_Relation_Ototal__on(X2,X1,X0)
| ~ c_Order__Relation_Opartial__order__on(X2,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_188])]) ).
fof(f2225,plain,
! [X2,X0,X1] :
( c_Order__Relation_Olinear__order__on(X2,X1,X0)
| ~ c_Relation_Ototal__on(X2,X1,X0)
| ~ c_Order__Relation_Opartial__order__on(X2,X1,X0) ),
inference(cnf_transformation,[],[f1661]) ).
fof(f1661,plain,
! [X0,X1,X2] :
( ( c_Order__Relation_Olinear__order__on(X2,X1,X0)
| ~ c_Relation_Ototal__on(X2,X1,X0)
| ~ c_Order__Relation_Opartial__order__on(X2,X1,X0) )
& ( ( c_Relation_Ototal__on(X2,X1,X0)
& c_Order__Relation_Opartial__order__on(X2,X1,X0) )
| ~ c_Order__Relation_Olinear__order__on(X2,X1,X0) ) ),
inference(flattening,[],[f1660]) ).
fof(f1660,plain,
! [X0,X1,X2] :
( ( c_Order__Relation_Olinear__order__on(X2,X1,X0)
| ~ c_Relation_Ototal__on(X2,X1,X0)
| ~ c_Order__Relation_Opartial__order__on(X2,X1,X0) )
& ( ( c_Relation_Ototal__on(X2,X1,X0)
& c_Order__Relation_Opartial__order__on(X2,X1,X0) )
| ~ c_Order__Relation_Olinear__order__on(X2,X1,X0) ) ),
inference(nnf_transformation,[],[f775]) ).
fof(f775,plain,
! [X0,X1,X2] :
( c_Order__Relation_Olinear__order__on(X2,X1,X0)
<=> ( c_Relation_Ototal__on(X2,X1,X0)
& c_Order__Relation_Opartial__order__on(X2,X1,X0) ) ),
inference(rectify,[],[f189]) ).
fof(f189,axiom,
! [X3,X11,X4] :
( c_Order__Relation_Olinear__order__on(X4,X11,X3)
<=> ( c_Relation_Ototal__on(X4,X11,X3)
& c_Order__Relation_Opartial__order__on(X4,X11,X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linear__order__on__def) ).
fof(f3897,plain,
spl104_187,
inference(avatar_split_clause,[],[f2176,f3895]) ).
fof(f3895,plain,
( spl104_187
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool),X1,X0)
| ~ c_Orderings_Oord__class_Oless(tc_fun(X2,tc_HOL_Obool),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_187])]) ).
fof(f2176,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool),X1,X0)
| ~ c_Orderings_Oord__class_Oless(tc_fun(X2,tc_HOL_Obool),X1,X0) ),
inference(cnf_transformation,[],[f1204]) ).
fof(f1204,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool),X1,X0)
| ~ c_Orderings_Oord__class_Oless(tc_fun(X2,tc_HOL_Obool),X1,X0) ),
inference(ennf_transformation,[],[f748]) ).
fof(f748,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless(tc_fun(X2,tc_HOL_Obool),X1,X0)
=> c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool),X1,X0) ),
inference(rectify,[],[f289]) ).
fof(f289,axiom,
! [X10,X11,X4] :
( c_Orderings_Oord__class_Oless(tc_fun(X4,tc_HOL_Obool),X11,X10)
=> c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool),X11,X10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_psubset__imp__subset) ).
fof(f3893,plain,
spl104_186,
inference(avatar_split_clause,[],[f2162,f3891]) ).
fof(f2162,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
inference(cnf_transformation,[],[f1190]) ).
fof(f1190,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
inference(flattening,[],[f1189]) ).
fof(f1189,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
inference(ennf_transformation,[],[f738]) ).
fof(f738,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X0) ) ),
inference(rectify,[],[f378]) ).
fof(f378,axiom,
! [X75,X76,X77] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X77,X76)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X76,X75)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X77,X75) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__trans) ).
fof(f3889,plain,
spl104_185,
inference(avatar_split_clause,[],[f2139,f3887]) ).
fof(f3887,plain,
( spl104_185
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
| c_Lattices_Osemilattice__sup__class_Osup(X2,X1,X0) != X0
| ~ class_Lattices_Osemilattice__sup(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_185])]) ).
fof(f2139,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
| c_Lattices_Osemilattice__sup__class_Osup(X2,X1,X0) != X0
| ~ class_Lattices_Osemilattice__sup(X2) ),
inference(cnf_transformation,[],[f1635]) ).
fof(f1635,plain,
! [X0,X1,X2] :
( ( ( c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
| c_Lattices_Osemilattice__sup__class_Osup(X2,X1,X0) != X0 )
& ( c_Lattices_Osemilattice__sup__class_Osup(X2,X1,X0) = X0
| ~ c_Orderings_Oord__class_Oless__eq(X2,X1,X0) ) )
| ~ class_Lattices_Osemilattice__sup(X2) ),
inference(nnf_transformation,[],[f1162]) ).
fof(f1162,plain,
! [X0,X1,X2] :
( ( c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
<=> c_Lattices_Osemilattice__sup__class_Osup(X2,X1,X0) = X0 )
| ~ class_Lattices_Osemilattice__sup(X2) ),
inference(ennf_transformation,[],[f718]) ).
fof(f718,plain,
! [X0,X1,X2] :
( class_Lattices_Osemilattice__sup(X2)
=> ( c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
<=> c_Lattices_Osemilattice__sup__class_Osup(X2,X1,X0) = X0 ) ),
inference(rectify,[],[f255]) ).
fof(f255,axiom,
! [X12,X13,X4] :
( class_Lattices_Osemilattice__sup(X4)
=> ( c_Orderings_Oord__class_Oless__eq(X4,X13,X12)
<=> c_Lattices_Osemilattice__sup__class_Osup(X4,X13,X12) = X12 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__iff__sup) ).
fof(f3885,plain,
spl104_184,
inference(avatar_split_clause,[],[f2124,f3883]) ).
fof(f2124,plain,
! [X2,X0,X1] :
( c_Lattices_Osemilattice__sup__class_Osup(X2,X0,X1) = X0
| ~ c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
| ~ class_Lattices_Osemilattice__sup(X2) ),
inference(cnf_transformation,[],[f1147]) ).
fof(f1147,plain,
! [X0,X1,X2] :
( c_Lattices_Osemilattice__sup__class_Osup(X2,X0,X1) = X0
| ~ c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
| ~ class_Lattices_Osemilattice__sup(X2) ),
inference(flattening,[],[f1146]) ).
fof(f1146,plain,
! [X0,X1,X2] :
( c_Lattices_Osemilattice__sup__class_Osup(X2,X0,X1) = X0
| ~ c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
| ~ class_Lattices_Osemilattice__sup(X2) ),
inference(ennf_transformation,[],[f709]) ).
fof(f709,plain,
! [X0,X1,X2] :
( class_Lattices_Osemilattice__sup(X2)
=> ( c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
=> c_Lattices_Osemilattice__sup__class_Osup(X2,X0,X1) = X0 ) ),
inference(rectify,[],[f250]) ).
fof(f250,axiom,
! [X58,X59,X4] :
( class_Lattices_Osemilattice__sup(X4)
=> ( c_Orderings_Oord__class_Oless__eq(X4,X59,X58)
=> c_Lattices_Osemilattice__sup__class_Osup(X4,X58,X59) = X58 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup__absorb1) ).
fof(f3881,plain,
spl104_183,
inference(avatar_split_clause,[],[f2123,f3879]) ).
fof(f2123,plain,
! [X2,X0,X1] :
( c_Lattices_Osemilattice__sup__class_Osup(X2,X1,X0) = X0
| ~ c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
| ~ class_Lattices_Osemilattice__sup(X2) ),
inference(cnf_transformation,[],[f1145]) ).
fof(f1145,plain,
! [X0,X1,X2] :
( c_Lattices_Osemilattice__sup__class_Osup(X2,X1,X0) = X0
| ~ c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
| ~ class_Lattices_Osemilattice__sup(X2) ),
inference(flattening,[],[f1144]) ).
fof(f1144,plain,
! [X0,X1,X2] :
( c_Lattices_Osemilattice__sup__class_Osup(X2,X1,X0) = X0
| ~ c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
| ~ class_Lattices_Osemilattice__sup(X2) ),
inference(ennf_transformation,[],[f708]) ).
fof(f708,plain,
! [X0,X1,X2] :
( class_Lattices_Osemilattice__sup(X2)
=> ( c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
=> c_Lattices_Osemilattice__sup__class_Osup(X2,X1,X0) = X0 ) ),
inference(rectify,[],[f251]) ).
fof(f251,axiom,
! [X59,X58,X4] :
( class_Lattices_Osemilattice__sup(X4)
=> ( c_Orderings_Oord__class_Oless__eq(X4,X58,X59)
=> c_Lattices_Osemilattice__sup__class_Osup(X4,X58,X59) = X59 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup__absorb2) ).
fof(f3877,plain,
spl104_182,
inference(avatar_split_clause,[],[f2055,f3875]) ).
fof(f3875,plain,
( spl104_182
<=> ! [X2,X0,X1] : c_Set_Oinsert(X2,X1,X0) = c_Set_Oinsert(X2,X1,c_Set_Oinsert(X2,X1,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_182])]) ).
fof(f2055,plain,
! [X2,X0,X1] : c_Set_Oinsert(X2,X1,X0) = c_Set_Oinsert(X2,X1,c_Set_Oinsert(X2,X1,X0)),
inference(cnf_transformation,[],[f653]) ).
fof(f653,plain,
! [X0,X1,X2] : c_Set_Oinsert(X2,X1,X0) = c_Set_Oinsert(X2,X1,c_Set_Oinsert(X2,X1,X0)),
inference(rectify,[],[f123]) ).
fof(f123,axiom,
! [X11,X13,X4] : c_Set_Oinsert(X4,X13,X11) = c_Set_Oinsert(X4,X13,c_Set_Oinsert(X4,X13,X11)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__absorb2) ).
fof(f3873,plain,
spl104_181,
inference(avatar_split_clause,[],[f2047,f3871]) ).
fof(f2047,plain,
! [X0,X1] :
( c_member(X1,sK39(X0,X1),X0)
| c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) = X0 ),
inference(cnf_transformation,[],[f1616]) ).
fof(f1616,plain,
! [X0,X1] :
( ( c_member(X1,sK39(X0,X1),X0)
| c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) = X0 )
& ( c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) != X0
| ! [X3] : ~ c_member(X1,X3,X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK39])],[f1614,f1615]) ).
fof(f1615,plain,
! [X0,X1] :
( ? [X2] : c_member(X1,X2,X0)
=> c_member(X1,sK39(X0,X1),X0) ),
introduced(choice_axiom,[]) ).
fof(f1614,plain,
! [X0,X1] :
( ( ? [X2] : c_member(X1,X2,X0)
| c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) = X0 )
& ( c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) != X0
| ! [X3] : ~ c_member(X1,X3,X0) ) ),
inference(rectify,[],[f1613]) ).
fof(f1613,plain,
! [X0,X1] :
( ( ? [X2] : c_member(X1,X2,X0)
| c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) = X0 )
& ( c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) != X0
| ! [X2] : ~ c_member(X1,X2,X0) ) ),
inference(nnf_transformation,[],[f645]) ).
fof(f645,plain,
! [X0,X1] :
( ? [X2] : c_member(X1,X2,X0)
<=> c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) != X0 ),
inference(rectify,[],[f404]) ).
fof(f404,axiom,
! [X11,X4] :
( ? [X2] : c_member(X4,X2,X11)
<=> c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)) != X11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ex__in__conv) ).
fof(f3869,plain,
spl104_180,
inference(avatar_split_clause,[],[f2044,f3867]) ).
fof(f2044,plain,
! [X0,X1] :
( c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) = X0
| c_member(X1,sK38(X0,X1),X0) ),
inference(cnf_transformation,[],[f1612]) ).
fof(f1612,plain,
! [X0,X1] :
( ( ! [X2] : ~ c_member(X1,X2,X0)
| c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) != X0 )
& ( c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) = X0
| c_member(X1,sK38(X0,X1),X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK38])],[f1610,f1611]) ).
fof(f1611,plain,
! [X0,X1] :
( ? [X3] : c_member(X1,X3,X0)
=> c_member(X1,sK38(X0,X1),X0) ),
introduced(choice_axiom,[]) ).
fof(f1610,plain,
! [X0,X1] :
( ( ! [X2] : ~ c_member(X1,X2,X0)
| c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) != X0 )
& ( c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) = X0
| ? [X3] : c_member(X1,X3,X0) ) ),
inference(rectify,[],[f1609]) ).
fof(f1609,plain,
! [X0,X1] :
( ( ! [X2] : ~ c_member(X1,X2,X0)
| c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) != X0 )
& ( c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) = X0
| ? [X2] : c_member(X1,X2,X0) ) ),
inference(nnf_transformation,[],[f644]) ).
fof(f644,plain,
! [X0,X1] :
( ! [X2] : ~ c_member(X1,X2,X0)
<=> c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) = X0 ),
inference(rectify,[],[f403]) ).
fof(f403,axiom,
! [X11,X4] :
( ! [X2] : ~ c_member(X4,X2,X11)
<=> c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)) = X11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_all__not__in__conv) ).
fof(f3865,plain,
( ~ spl104_18
| spl104_179
| ~ spl104_112
| ~ spl104_161 ),
inference(avatar_split_clause,[],[f3789,f3650,f3387,f3863,f2962]) ).
fof(f2962,plain,
( spl104_18
<=> class_Lattices_Osemilattice__sup(tc_HOL_Obool) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_18])]) ).
fof(f3863,plain,
( spl104_179
<=> ! [X0] : c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_179])]) ).
fof(f3650,plain,
( spl104_161
<=> ! [X0] : c_Lattices_Osemilattice__sup__class_Osup(tc_HOL_Obool,X0,X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl104_161])]) ).
fof(f3789,plain,
( ! [X0] :
( c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,X0,X0)
| ~ class_Lattices_Osemilattice__sup(tc_HOL_Obool) )
| ~ spl104_112
| ~ spl104_161 ),
inference(superposition,[],[f3388,f3651]) ).
fof(f3651,plain,
( ! [X0] : c_Lattices_Osemilattice__sup__class_Osup(tc_HOL_Obool,X0,X0) = X0
| ~ spl104_161 ),
inference(avatar_component_clause,[],[f3650]) ).
fof(f3860,plain,
spl104_178,
inference(avatar_split_clause,[],[f1910,f3858]) ).
fof(f3858,plain,
( spl104_178
<=> ! [X0] : c_Relation_Orefl__on(X0,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X0,X0),tc_HOL_Obool))) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_178])]) ).
fof(f1910,plain,
! [X0] : c_Relation_Orefl__on(X0,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X0,X0),tc_HOL_Obool))),
inference(cnf_transformation,[],[f540]) ).
fof(f540,plain,
! [X0] : c_Relation_Orefl__on(X0,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X0,X0),tc_HOL_Obool))),
inference(rectify,[],[f420]) ).
fof(f420,axiom,
! [X4] : c_Relation_Orefl__on(X4,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X4,X4),tc_HOL_Obool))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_refl__on__empty) ).
fof(f3855,plain,
spl104_177,
inference(avatar_split_clause,[],[f1909,f3853]) ).
fof(f1909,plain,
! [X0] : c_Order__Relation_Opreorder__on(X0,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X0,X0),tc_HOL_Obool))),
inference(cnf_transformation,[],[f539]) ).
fof(f539,plain,
! [X0] : c_Order__Relation_Opreorder__on(X0,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X0,X0),tc_HOL_Obool))),
inference(rectify,[],[f415]) ).
fof(f415,axiom,
! [X4] : c_Order__Relation_Opreorder__on(X4,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X4,X4),tc_HOL_Obool))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_preorder__on__empty) ).
fof(f3850,plain,
spl104_176,
inference(avatar_split_clause,[],[f1908,f3848]) ).
fof(f1908,plain,
! [X0] : c_Order__Relation_Olinear__order__on(X0,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X0,X0),tc_HOL_Obool))),
inference(cnf_transformation,[],[f538]) ).
fof(f538,plain,
! [X0] : c_Order__Relation_Olinear__order__on(X0,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X0,X0),tc_HOL_Obool))),
inference(rectify,[],[f421]) ).
fof(f421,axiom,
! [X4] : c_Order__Relation_Olinear__order__on(X4,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X4,X4),tc_HOL_Obool))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lnear__order__on__empty) ).
fof(f3845,plain,
spl104_175,
inference(avatar_split_clause,[],[f1907,f3843]) ).
fof(f1907,plain,
! [X0] : c_Order__Relation_Opartial__order__on(X0,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X0,X0),tc_HOL_Obool))),
inference(cnf_transformation,[],[f537]) ).
fof(f537,plain,
! [X0] : c_Order__Relation_Opartial__order__on(X0,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X0,X0),tc_HOL_Obool))),
inference(rectify,[],[f413]) ).
fof(f413,axiom,
! [X4] : c_Order__Relation_Opartial__order__on(X4,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X4,X4),tc_HOL_Obool))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_partial__order__on__empty) ).
fof(f3840,plain,
spl104_174,
inference(avatar_split_clause,[],[f1906,f3838]) ).
fof(f1906,plain,
! [X0] : c_Order__Relation_Owell__order__on(X0,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X0,X0),tc_HOL_Obool))),
inference(cnf_transformation,[],[f536]) ).
fof(f536,plain,
! [X0] : c_Order__Relation_Owell__order__on(X0,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X0,X0),tc_HOL_Obool))),
inference(rectify,[],[f433]) ).
fof(f433,axiom,
! [X4] : c_Order__Relation_Owell__order__on(X4,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X4,X4),tc_HOL_Obool))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_well__order__on__empty) ).
fof(f3700,plain,
spl104_173,
inference(avatar_split_clause,[],[f2571,f3698]) ).
fof(f3698,plain,
( spl104_173
<=> ! [X0,X3,X2,X1] :
( X0 = X1
| X0 = X3
| ~ sP10(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_173])]) ).
fof(f2571,plain,
! [X2,X3,X0,X1] :
( X0 = X1
| X0 = X3
| ~ sP10(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f1816]) ).
fof(f1816,plain,
! [X0,X1,X2,X3] :
( ( sP10(X0,X1,X2,X3)
| ( ( X0 != X1
| X2 != X3 )
& ( X0 != X3
| X1 != X2 ) ) )
& ( ( X0 = X1
& X2 = X3 )
| ( X0 = X3
& X1 = X2 )
| ~ sP10(X0,X1,X2,X3) ) ),
inference(rectify,[],[f1815]) ).
fof(f1815,plain,
! [X2,X1,X3,X0] :
( ( sP10(X2,X1,X3,X0)
| ( ( X1 != X2
| X0 != X3 )
& ( X0 != X2
| X1 != X3 ) ) )
& ( ( X1 = X2
& X0 = X3 )
| ( X0 = X2
& X1 = X3 )
| ~ sP10(X2,X1,X3,X0) ) ),
inference(flattening,[],[f1814]) ).
fof(f1814,plain,
! [X2,X1,X3,X0] :
( ( sP10(X2,X1,X3,X0)
| ( ( X1 != X2
| X0 != X3 )
& ( X0 != X2
| X1 != X3 ) ) )
& ( ( X1 = X2
& X0 = X3 )
| ( X0 = X2
& X1 = X3 )
| ~ sP10(X2,X1,X3,X0) ) ),
inference(nnf_transformation,[],[f1543]) ).
fof(f3696,plain,
( spl104_172
| ~ spl104_121 ),
inference(avatar_split_clause,[],[f3502,f3436,f3694]) ).
fof(f3694,plain,
( spl104_172
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X0,X1,X1)
| ~ class_Orderings_Olinorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_172])]) ).
fof(f3502,plain,
( ! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X0,X1,X1)
| ~ class_Orderings_Olinorder(X0) )
| ~ spl104_121 ),
inference(factoring,[],[f3437]) ).
fof(f3692,plain,
spl104_171,
inference(avatar_split_clause,[],[f2570,f3690]) ).
fof(f3690,plain,
( spl104_171
<=> ! [X0,X3,X2,X1] :
( X0 = X1
| X1 = X2
| ~ sP10(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_171])]) ).
fof(f2570,plain,
! [X2,X3,X0,X1] :
( X0 = X1
| X1 = X2
| ~ sP10(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f1816]) ).
fof(f3688,plain,
spl104_170,
inference(avatar_split_clause,[],[f2569,f3686]) ).
fof(f3686,plain,
( spl104_170
<=> ! [X0,X3,X2,X1] :
( X2 = X3
| X0 = X3
| ~ sP10(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_170])]) ).
fof(f2569,plain,
! [X2,X3,X0,X1] :
( X2 = X3
| X0 = X3
| ~ sP10(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f1816]) ).
fof(f3684,plain,
spl104_169,
inference(avatar_split_clause,[],[f2568,f3682]) ).
fof(f3682,plain,
( spl104_169
<=> ! [X2,X0,X1,X3] :
( X2 = X3
| X1 = X2
| ~ sP10(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_169])]) ).
fof(f2568,plain,
! [X2,X3,X0,X1] :
( X2 = X3
| X1 = X2
| ~ sP10(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f1816]) ).
fof(f3680,plain,
spl104_168,
inference(avatar_split_clause,[],[f2433,f3678]) ).
fof(f2433,plain,
! [X2,X3,X0,X1] :
( hBOOL(hAPP(c_Set_Oinsert(X3,X2,X1),X0))
| ~ hBOOL(hAPP(X1,X0)) ),
inference(cnf_transformation,[],[f1736]) ).
fof(f3676,plain,
spl104_167,
inference(avatar_split_clause,[],[f2352,f3674]) ).
fof(f2352,plain,
! [X2,X3,X0,X1] :
( c_member(X3,X2,c_Set_Oinsert(X3,X0,X1))
| ~ c_member(X3,X2,X1) ),
inference(cnf_transformation,[],[f1332]) ).
fof(f1332,plain,
! [X0,X1,X2,X3] :
( c_member(X3,X2,c_Set_Oinsert(X3,X0,X1))
| ~ c_member(X3,X2,X1) ),
inference(ennf_transformation,[],[f865]) ).
fof(f865,plain,
! [X0,X1,X2,X3] :
( c_member(X3,X2,X1)
=> c_member(X3,X2,c_Set_Oinsert(X3,X0,X1)) ),
inference(rectify,[],[f144]) ).
fof(f144,axiom,
! [X8,X10,X9,X4] :
( c_member(X4,X9,X10)
=> c_member(X4,X9,c_Set_Oinsert(X4,X8,X10)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insertI2) ).
fof(f3672,plain,
spl104_166,
inference(avatar_split_clause,[],[f2335,f3670]) ).
fof(f2335,plain,
! [X2,X3,X0,X1] :
( c_Wellfounded_Owf(X1,hAPP(c_Relation_Oinv__image(X3,X1,X2),X0))
| ~ c_Wellfounded_Owf(X3,X2) ),
inference(cnf_transformation,[],[f1309]) ).
fof(f1309,plain,
! [X0,X1,X2,X3] :
( c_Wellfounded_Owf(X1,hAPP(c_Relation_Oinv__image(X3,X1,X2),X0))
| ~ c_Wellfounded_Owf(X3,X2) ),
inference(ennf_transformation,[],[f849]) ).
fof(f849,plain,
! [X0,X1,X2,X3] :
( c_Wellfounded_Owf(X3,X2)
=> c_Wellfounded_Owf(X1,hAPP(c_Relation_Oinv__image(X3,X1,X2),X0)) ),
inference(rectify,[],[f161]) ).
fof(f161,axiom,
! [X1,X15,X3,X4] :
( c_Wellfounded_Owf(X4,X3)
=> c_Wellfounded_Owf(X15,hAPP(c_Relation_Oinv__image(X4,X15,X3),X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__inv__image) ).
fof(f3668,plain,
spl104_165,
inference(avatar_split_clause,[],[f2333,f3666]) ).
fof(f3666,plain,
( spl104_165
<=> ! [X0,X3,X2,X1] :
( c_Relation_Otrans(X1,hAPP(c_Relation_Oinv__image(X3,X1,X2),X0))
| ~ c_Relation_Otrans(X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_165])]) ).
fof(f2333,plain,
! [X2,X3,X0,X1] :
( c_Relation_Otrans(X1,hAPP(c_Relation_Oinv__image(X3,X1,X2),X0))
| ~ c_Relation_Otrans(X3,X2) ),
inference(cnf_transformation,[],[f1306]) ).
fof(f1306,plain,
! [X0,X1,X2,X3] :
( c_Relation_Otrans(X1,hAPP(c_Relation_Oinv__image(X3,X1,X2),X0))
| ~ c_Relation_Otrans(X3,X2) ),
inference(ennf_transformation,[],[f847]) ).
fof(f847,plain,
! [X0,X1,X2,X3] :
( c_Relation_Otrans(X3,X2)
=> c_Relation_Otrans(X1,hAPP(c_Relation_Oinv__image(X3,X1,X2),X0)) ),
inference(rectify,[],[f31]) ).
fof(f31,axiom,
! [X1,X15,X3,X4] :
( c_Relation_Otrans(X4,X3)
=> c_Relation_Otrans(X15,hAPP(c_Relation_Oinv__image(X4,X15,X3),X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trans__inv__image) ).
fof(f3664,plain,
spl104_164,
inference(avatar_split_clause,[],[f2231,f3662]) ).
fof(f2231,plain,
! [X2,X0,X1] :
( c_Order__Relation_Opreorder__on(X2,X1,X0)
| ~ c_Relation_Otrans(X2,X0)
| ~ c_Relation_Orefl__on(X2,X1,X0) ),
inference(cnf_transformation,[],[f1665]) ).
fof(f1665,plain,
! [X0,X1,X2] :
( ( c_Order__Relation_Opreorder__on(X2,X1,X0)
| ~ c_Relation_Otrans(X2,X0)
| ~ c_Relation_Orefl__on(X2,X1,X0) )
& ( ( c_Relation_Otrans(X2,X0)
& c_Relation_Orefl__on(X2,X1,X0) )
| ~ c_Order__Relation_Opreorder__on(X2,X1,X0) ) ),
inference(flattening,[],[f1664]) ).
fof(f1664,plain,
! [X0,X1,X2] :
( ( c_Order__Relation_Opreorder__on(X2,X1,X0)
| ~ c_Relation_Otrans(X2,X0)
| ~ c_Relation_Orefl__on(X2,X1,X0) )
& ( ( c_Relation_Otrans(X2,X0)
& c_Relation_Orefl__on(X2,X1,X0) )
| ~ c_Order__Relation_Opreorder__on(X2,X1,X0) ) ),
inference(nnf_transformation,[],[f777]) ).
fof(f777,plain,
! [X0,X1,X2] :
( c_Order__Relation_Opreorder__on(X2,X1,X0)
<=> ( c_Relation_Otrans(X2,X0)
& c_Relation_Orefl__on(X2,X1,X0) ) ),
inference(rectify,[],[f45]) ).
fof(f45,axiom,
! [X3,X11,X4] :
( c_Order__Relation_Opreorder__on(X4,X11,X3)
<=> ( c_Relation_Otrans(X4,X3)
& c_Relation_Orefl__on(X4,X11,X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_preorder__on__def) ).
fof(f3660,plain,
spl104_163,
inference(avatar_split_clause,[],[f2228,f3658]) ).
fof(f3658,plain,
( spl104_163
<=> ! [X2,X0,X1] :
( c_Order__Relation_Opartial__order__on(X2,X1,X0)
| ~ c_Relation_Oantisym(X2,X0)
| ~ c_Order__Relation_Opreorder__on(X2,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_163])]) ).
fof(f2228,plain,
! [X2,X0,X1] :
( c_Order__Relation_Opartial__order__on(X2,X1,X0)
| ~ c_Relation_Oantisym(X2,X0)
| ~ c_Order__Relation_Opreorder__on(X2,X1,X0) ),
inference(cnf_transformation,[],[f1663]) ).
fof(f1663,plain,
! [X0,X1,X2] :
( ( c_Order__Relation_Opartial__order__on(X2,X1,X0)
| ~ c_Relation_Oantisym(X2,X0)
| ~ c_Order__Relation_Opreorder__on(X2,X1,X0) )
& ( ( c_Relation_Oantisym(X2,X0)
& c_Order__Relation_Opreorder__on(X2,X1,X0) )
| ~ c_Order__Relation_Opartial__order__on(X2,X1,X0) ) ),
inference(flattening,[],[f1662]) ).
fof(f1662,plain,
! [X0,X1,X2] :
( ( c_Order__Relation_Opartial__order__on(X2,X1,X0)
| ~ c_Relation_Oantisym(X2,X0)
| ~ c_Order__Relation_Opreorder__on(X2,X1,X0) )
& ( ( c_Relation_Oantisym(X2,X0)
& c_Order__Relation_Opreorder__on(X2,X1,X0) )
| ~ c_Order__Relation_Opartial__order__on(X2,X1,X0) ) ),
inference(nnf_transformation,[],[f776]) ).
fof(f776,plain,
! [X0,X1,X2] :
( c_Order__Relation_Opartial__order__on(X2,X1,X0)
<=> ( c_Relation_Oantisym(X2,X0)
& c_Order__Relation_Opreorder__on(X2,X1,X0) ) ),
inference(rectify,[],[f157]) ).
fof(f157,axiom,
! [X3,X11,X4] :
( c_Order__Relation_Opartial__order__on(X4,X11,X3)
<=> ( c_Relation_Oantisym(X4,X3)
& c_Order__Relation_Opreorder__on(X4,X11,X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_partial__order__on__def) ).
fof(f3656,plain,
spl104_162,
inference(avatar_split_clause,[],[f2219,f3654]) ).
fof(f2219,plain,
! [X2,X0,X1] :
( c_Relation_Ototal__on(X2,X1,X0)
| c_member(X2,sK47(X0,X1,X2),X1) ),
inference(cnf_transformation,[],[f1659]) ).
fof(f3652,plain,
( spl104_161
| ~ spl104_18
| ~ spl104_84 ),
inference(avatar_split_clause,[],[f3317,f3250,f2962,f3650]) ).
fof(f3317,plain,
( ! [X0] : c_Lattices_Osemilattice__sup__class_Osup(tc_HOL_Obool,X0,X0) = X0
| ~ spl104_18
| ~ spl104_84 ),
inference(resolution,[],[f3251,f2964]) ).
fof(f2964,plain,
( class_Lattices_Osemilattice__sup(tc_HOL_Obool)
| ~ spl104_18 ),
inference(avatar_component_clause,[],[f2962]) ).
fof(f3648,plain,
spl104_160,
inference(avatar_split_clause,[],[f2218,f3646]) ).
fof(f2218,plain,
! [X2,X0,X1] :
( c_Relation_Ototal__on(X2,X1,X0)
| c_member(X2,sK46(X0,X1,X2),X1) ),
inference(cnf_transformation,[],[f1659]) ).
fof(f3644,plain,
spl104_159,
inference(avatar_split_clause,[],[f2157,f3642]) ).
fof(f2157,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X0),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1) ),
inference(cnf_transformation,[],[f1182]) ).
fof(f1182,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X0),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1) ),
inference(ennf_transformation,[],[f733]) ).
fof(f733,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X0),X1) ),
inference(rectify,[],[f374]) ).
fof(f374,axiom,
! [X70,X75,X76] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X76,X75)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X76,X70),X75) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__imp__diff__less) ).
fof(f3640,plain,
spl104_158,
inference(avatar_split_clause,[],[f2113,f3638]) ).
fof(f3638,plain,
( spl104_158
<=> ! [X2,X0,X1] :
( c_Lattices_Osemilattice__sup__class_Osup(X2,X1,X0) = c_Lattices_Osemilattice__sup__class_Osup(X2,X0,X1)
| ~ class_Lattices_Osemilattice__sup(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_158])]) ).
fof(f2113,plain,
! [X2,X0,X1] :
( c_Lattices_Osemilattice__sup__class_Osup(X2,X1,X0) = c_Lattices_Osemilattice__sup__class_Osup(X2,X0,X1)
| ~ class_Lattices_Osemilattice__sup(X2) ),
inference(cnf_transformation,[],[f1128]) ).
fof(f1128,plain,
! [X0,X1,X2] :
( c_Lattices_Osemilattice__sup__class_Osup(X2,X1,X0) = c_Lattices_Osemilattice__sup__class_Osup(X2,X0,X1)
| ~ class_Lattices_Osemilattice__sup(X2) ),
inference(ennf_transformation,[],[f698]) ).
fof(f698,plain,
! [X0,X1,X2] :
( class_Lattices_Osemilattice__sup(X2)
=> c_Lattices_Osemilattice__sup__class_Osup(X2,X1,X0) = c_Lattices_Osemilattice__sup__class_Osup(X2,X0,X1) ),
inference(rectify,[],[f176]) ).
fof(f176,axiom,
! [X59,X58,X4] :
( class_Lattices_Osemilattice__sup(X4)
=> c_Lattices_Osemilattice__sup__class_Osup(X4,X58,X59) = c_Lattices_Osemilattice__sup__class_Osup(X4,X59,X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup__commute) ).
fof(f3636,plain,
spl104_157,
inference(avatar_split_clause,[],[f2100,f3634]) ).
fof(f2100,plain,
! [X2,X0,X1] :
( c_Lattices_Osemilattice__sup__class_Osup(X2,X1,X0) = c_Lattices_Osemilattice__sup__class_Osup(X2,X0,X1)
| ~ class_Lattices_Olattice(X2) ),
inference(cnf_transformation,[],[f1111]) ).
fof(f1111,plain,
! [X0,X1,X2] :
( c_Lattices_Osemilattice__sup__class_Osup(X2,X1,X0) = c_Lattices_Osemilattice__sup__class_Osup(X2,X0,X1)
| ~ class_Lattices_Olattice(X2) ),
inference(ennf_transformation,[],[f687]) ).
fof(f687,plain,
! [X0,X1,X2] :
( class_Lattices_Olattice(X2)
=> c_Lattices_Osemilattice__sup__class_Osup(X2,X1,X0) = c_Lattices_Osemilattice__sup__class_Osup(X2,X0,X1) ),
inference(rectify,[],[f175]) ).
fof(f175,axiom,
! [X59,X58,X4] :
( class_Lattices_Olattice(X4)
=> c_Lattices_Osemilattice__sup__class_Osup(X4,X58,X59) = c_Lattices_Osemilattice__sup__class_Osup(X4,X59,X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__sup__aci_I5_J) ).
fof(f3632,plain,
spl104_156,
inference(avatar_split_clause,[],[f2097,f3630]) ).
fof(f2097,plain,
! [X2,X0,X1] :
( c_Orderings_Obot__class_Obot(X2) = hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,X2)),X0)
| ~ class_Orderings_Obot(X2) ),
inference(cnf_transformation,[],[f1108]) ).
fof(f1108,plain,
! [X0,X1,X2] :
( c_Orderings_Obot__class_Obot(X2) = hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,X2)),X0)
| ~ class_Orderings_Obot(X2) ),
inference(ennf_transformation,[],[f684]) ).
fof(f684,plain,
! [X0,X1,X2] :
( class_Orderings_Obot(X2)
=> c_Orderings_Obot__class_Obot(X2) = hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,X2)),X0) ),
inference(rectify,[],[f407]) ).
fof(f407,axiom,
! [X13,X15,X4] :
( class_Orderings_Obot(X4)
=> hAPP(c_Orderings_Obot__class_Obot(tc_fun(X15,X4)),X13) = c_Orderings_Obot__class_Obot(X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bot__apply) ).
fof(f3628,plain,
spl104_155,
inference(avatar_split_clause,[],[f2054,f3626]) ).
fof(f2054,plain,
! [X2,X0,X1] : c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool),c_Groups_Ominus__class_Ominus(tc_fun(X2,tc_HOL_Obool),X1,X0),X1),
inference(cnf_transformation,[],[f652]) ).
fof(f652,plain,
! [X0,X1,X2] : c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool),c_Groups_Ominus__class_Ominus(tc_fun(X2,tc_HOL_Obool),X1,X0),X1),
inference(rectify,[],[f265]) ).
fof(f265,axiom,
! [X10,X11,X4] : c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool),c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool),X11,X10),X11),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Diff__subset) ).
fof(f3624,plain,
spl104_154,
inference(avatar_split_clause,[],[f2053,f3622]) ).
fof(f2053,plain,
! [X2,X0,X1] : c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool),X1,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool),X1,X0)),
inference(cnf_transformation,[],[f651]) ).
fof(f651,plain,
! [X0,X1,X2] : c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool),X1,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool),X1,X0)),
inference(rectify,[],[f230]) ).
fof(f230,axiom,
! [X10,X11,X4] : c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool),X11,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool),X11,X10)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__upper1) ).
fof(f3620,plain,
spl104_153,
inference(avatar_split_clause,[],[f2052,f3618]) ).
fof(f2052,plain,
! [X2,X0,X1] : c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool),X1,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool),X0,X1)),
inference(cnf_transformation,[],[f650]) ).
fof(f650,plain,
! [X0,X1,X2] : c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool),X1,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool),X0,X1)),
inference(rectify,[],[f229]) ).
fof(f229,axiom,
! [X11,X10,X4] : c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool),X10,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool),X11,X10)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__upper2) ).
fof(f3616,plain,
spl104_152,
inference(avatar_split_clause,[],[f2023,f3614]) ).
fof(f2023,plain,
! [X0,X1] :
( sP2(X0,X1)
| c_member(X0,sK36(X0,X1),sK34(X0,X1)) ),
inference(cnf_transformation,[],[f1598]) ).
fof(f3612,plain,
spl104_151,
inference(avatar_split_clause,[],[f2020,f3610]) ).
fof(f3610,plain,
( spl104_151
<=> ! [X0,X1] :
( c_Wellfounded_Owf(X1,X0)
| ~ c_member(X1,sK33(X0,X1),c_Wellfounded_Oacc(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_151])]) ).
fof(f2020,plain,
! [X0,X1] :
( c_Wellfounded_Owf(X1,X0)
| ~ c_member(X1,sK33(X0,X1),c_Wellfounded_Oacc(X1,X0)) ),
inference(cnf_transformation,[],[f1591]) ).
fof(f1591,plain,
! [X0,X1] :
( ( c_Wellfounded_Owf(X1,X0)
| ~ c_member(X1,sK33(X0,X1),c_Wellfounded_Oacc(X1,X0)) )
& ( ! [X3] : c_member(X1,X3,c_Wellfounded_Oacc(X1,X0))
| ~ c_Wellfounded_Owf(X1,X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK33])],[f1589,f1590]) ).
fof(f1590,plain,
! [X0,X1] :
( ? [X2] : ~ c_member(X1,X2,c_Wellfounded_Oacc(X1,X0))
=> ~ c_member(X1,sK33(X0,X1),c_Wellfounded_Oacc(X1,X0)) ),
introduced(choice_axiom,[]) ).
fof(f1589,plain,
! [X0,X1] :
( ( c_Wellfounded_Owf(X1,X0)
| ? [X2] : ~ c_member(X1,X2,c_Wellfounded_Oacc(X1,X0)) )
& ( ! [X3] : c_member(X1,X3,c_Wellfounded_Oacc(X1,X0))
| ~ c_Wellfounded_Owf(X1,X0) ) ),
inference(rectify,[],[f1588]) ).
fof(f1588,plain,
! [X0,X1] :
( ( c_Wellfounded_Owf(X1,X0)
| ? [X2] : ~ c_member(X1,X2,c_Wellfounded_Oacc(X1,X0)) )
& ( ! [X2] : c_member(X1,X2,c_Wellfounded_Oacc(X1,X0))
| ~ c_Wellfounded_Owf(X1,X0) ) ),
inference(nnf_transformation,[],[f635]) ).
fof(f635,plain,
! [X0,X1] :
( c_Wellfounded_Owf(X1,X0)
<=> ! [X2] : c_member(X1,X2,c_Wellfounded_Oacc(X1,X0)) ),
inference(rectify,[],[f170]) ).
fof(f170,axiom,
! [X3,X4] :
( c_Wellfounded_Owf(X4,X3)
<=> ! [X2] : c_member(X4,X2,c_Wellfounded_Oacc(X4,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__acc__iff) ).
fof(f3608,plain,
( spl104_150
| ~ spl104_16
| ~ spl104_84 ),
inference(avatar_split_clause,[],[f3316,f3250,f2952,f3606]) ).
fof(f3606,plain,
( spl104_150
<=> ! [X0] : c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat,X0,X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl104_150])]) ).
fof(f3316,plain,
( ! [X0] : c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat,X0,X0) = X0
| ~ spl104_16
| ~ spl104_84 ),
inference(resolution,[],[f3251,f2954]) ).
fof(f2954,plain,
( class_Lattices_Osemilattice__sup(tc_Nat_Onat)
| ~ spl104_16 ),
inference(avatar_component_clause,[],[f2952]) ).
fof(f3604,plain,
spl104_149,
inference(avatar_split_clause,[],[f1996,f3602]) ).
fof(f3602,plain,
( spl104_149
<=> ! [X0,X1] :
( c_Wellfounded_Owf(X1,X0)
| ~ c_member(X1,sK19(X0,X1),c_Wellfounded_Oacc(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_149])]) ).
fof(f1996,plain,
! [X0,X1] :
( c_Wellfounded_Owf(X1,X0)
| ~ c_member(X1,sK19(X0,X1),c_Wellfounded_Oacc(X1,X0)) ),
inference(cnf_transformation,[],[f1563]) ).
fof(f1563,plain,
! [X0,X1] :
( c_Wellfounded_Owf(X1,X0)
| ~ c_member(X1,sK19(X0,X1),c_Wellfounded_Oacc(X1,X0)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK19])],[f1068,f1562]) ).
fof(f1562,plain,
! [X0,X1] :
( ? [X2] : ~ c_member(X1,X2,c_Wellfounded_Oacc(X1,X0))
=> ~ c_member(X1,sK19(X0,X1),c_Wellfounded_Oacc(X1,X0)) ),
introduced(choice_axiom,[]) ).
fof(f1068,plain,
! [X0,X1] :
( c_Wellfounded_Owf(X1,X0)
| ? [X2] : ~ c_member(X1,X2,c_Wellfounded_Oacc(X1,X0)) ),
inference(ennf_transformation,[],[f625]) ).
fof(f625,plain,
! [X0,X1] :
( ! [X2] : c_member(X1,X2,c_Wellfounded_Oacc(X1,X0))
=> c_Wellfounded_Owf(X1,X0) ),
inference(rectify,[],[f198]) ).
fof(f198,axiom,
! [X3,X4] :
( ! [X2] : c_member(X4,X2,c_Wellfounded_Oacc(X4,X3))
=> c_Wellfounded_Owf(X4,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_acc__wfI) ).
fof(f3600,plain,
spl104_148,
inference(avatar_split_clause,[],[f1992,f3598]) ).
fof(f1992,plain,
! [X0,X1] :
( X0 = X1
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ),
inference(cnf_transformation,[],[f1065]) ).
fof(f1065,plain,
! [X0,X1] :
( X0 = X1
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ),
inference(flattening,[],[f1064]) ).
fof(f1064,plain,
! [X0,X1] :
( X0 = X1
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ),
inference(ennf_transformation,[],[f622]) ).
fof(f622,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1)
=> X0 = X1 ) ),
inference(rectify,[],[f379]) ).
fof(f379,axiom,
! [X70,X71] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X71,X70)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X70,X71)
=> X70 = X71 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__antisym) ).
fof(f3596,plain,
spl104_147,
inference(avatar_split_clause,[],[f1991,f3594]) ).
fof(f1991,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| X0 = X1
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ),
inference(cnf_transformation,[],[f1063]) ).
fof(f1063,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| X0 = X1
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ),
inference(flattening,[],[f1062]) ).
fof(f1062,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| X0 = X1
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ),
inference(ennf_transformation,[],[f621]) ).
fof(f621,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
=> ( X0 != X1
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ) ),
inference(rectify,[],[f390]) ).
fof(f390,axiom,
! [X70,X71] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X71,X70)
=> ( X70 != X71
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X71,X70) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__neq__implies__less) ).
fof(f3592,plain,
spl104_146,
inference(avatar_split_clause,[],[f1975,f3590]) ).
fof(f3590,plain,
( spl104_146
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| X0 = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_146])]) ).
fof(f1975,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| X0 = X1 ),
inference(cnf_transformation,[],[f1045]) ).
fof(f1045,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| X0 = X1 ),
inference(flattening,[],[f1044]) ).
fof(f1044,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| X0 = X1 ),
inference(ennf_transformation,[],[f605]) ).
fof(f605,plain,
! [X0,X1] :
( X0 != X1
=> ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1) ) ),
inference(rectify,[],[f368]) ).
fof(f368,axiom,
! [X59,X58] :
( X58 != X59
=> ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X58,X59)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X59,X58) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__neqE__nat) ).
fof(f3588,plain,
spl104_145,
inference(avatar_split_clause,[],[f1945,f3586]) ).
fof(f1945,plain,
! [X0,X1] : c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,X0,X0),c_Relation_OId(X1)),
inference(cnf_transformation,[],[f575]) ).
fof(f575,plain,
! [X0,X1] : c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,X0,X0),c_Relation_OId(X1)),
inference(rectify,[],[f105]) ).
fof(f105,axiom,
! [X9,X4] : c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X9,X9),c_Relation_OId(X4)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_IdI) ).
fof(f3584,plain,
spl104_144,
inference(avatar_split_clause,[],[f1944,f3582]) ).
fof(f1944,plain,
! [X0,X1] : c_Relation_Oirrefl(X1,c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),X0,c_Relation_OId(X1))),
inference(cnf_transformation,[],[f574]) ).
fof(f574,plain,
! [X0,X1] : c_Relation_Oirrefl(X1,c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),X0,c_Relation_OId(X1))),
inference(rectify,[],[f213]) ).
fof(f213,axiom,
! [X3,X4] : c_Relation_Oirrefl(X4,c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),X3,c_Relation_OId(X4))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_irrefl__diff__Id) ).
fof(f3580,plain,
spl104_143,
inference(avatar_split_clause,[],[f1943,f3578]) ).
fof(f3578,plain,
( spl104_143
<=> ! [X0,X1] : c_Set_Othe__elem(X1,c_Set_Oinsert(X1,X0,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl104_143])]) ).
fof(f1943,plain,
! [X0,X1] : c_Set_Othe__elem(X1,c_Set_Oinsert(X1,X0,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))) = X0,
inference(cnf_transformation,[],[f573]) ).
fof(f573,plain,
! [X0,X1] : c_Set_Othe__elem(X1,c_Set_Oinsert(X1,X0,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))) = X0,
inference(rectify,[],[f466]) ).
fof(f466,axiom,
! [X13,X4] : c_Set_Othe__elem(X4,c_Set_Oinsert(X4,X13,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))) = X13,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_the__elem__eq) ).
fof(f3576,plain,
spl104_142,
inference(avatar_split_clause,[],[f1942,f3574]) ).
fof(f1942,plain,
! [X0,X1] : c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),X0) = X0,
inference(cnf_transformation,[],[f572]) ).
fof(f572,plain,
! [X0,X1] : c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),X0) = X0,
inference(rectify,[],[f427]) ).
fof(f427,axiom,
! [X10,X4] : c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)),X10) = X10,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__empty__left) ).
fof(f3572,plain,
spl104_141,
inference(avatar_split_clause,[],[f1941,f3570]) ).
fof(f3570,plain,
( spl104_141
<=> ! [X0,X1] : c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool),X0,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl104_141])]) ).
fof(f1941,plain,
! [X0,X1] : c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool),X0,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))) = X0,
inference(cnf_transformation,[],[f571]) ).
fof(f571,plain,
! [X0,X1] : c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool),X0,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))) = X0,
inference(rectify,[],[f426]) ).
fof(f426,axiom,
! [X11,X4] : c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool),X11,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))) = X11,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__empty__right) ).
fof(f3568,plain,
spl104_140,
inference(avatar_split_clause,[],[f1940,f3566]) ).
fof(f3566,plain,
( spl104_140
<=> ! [X0,X1] : c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool),X0,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl104_140])]) ).
fof(f1940,plain,
! [X0,X1] : c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool),X0,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))) = X0,
inference(cnf_transformation,[],[f570]) ).
fof(f570,plain,
! [X0,X1] : c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool),X0,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))) = X0,
inference(rectify,[],[f423]) ).
fof(f423,axiom,
! [X11,X4] : c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool),X11,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))) = X11,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Diff__empty) ).
fof(f3562,plain,
spl104_139,
inference(avatar_split_clause,[],[f1939,f3560]) ).
fof(f1939,plain,
! [X0,X1] : c_Relation_ODomain(X1,X1,c_Transitive__Closure_Otrancl(X1,X0)) = c_Relation_ODomain(X1,X1,X0),
inference(cnf_transformation,[],[f569]) ).
fof(f569,plain,
! [X0,X1] : c_Relation_ODomain(X1,X1,c_Transitive__Closure_Otrancl(X1,X0)) = c_Relation_ODomain(X1,X1,X0),
inference(rectify,[],[f82]) ).
fof(f82,axiom,
! [X3,X4] : c_Relation_ODomain(X4,X4,c_Transitive__Closure_Otrancl(X4,X3)) = c_Relation_ODomain(X4,X4,X3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trancl__domain) ).
fof(f3558,plain,
spl104_138,
inference(avatar_split_clause,[],[f1938,f3556]) ).
fof(f1938,plain,
! [X0,X1] : c_Relation_ORange(X1,X1,c_Transitive__Closure_Otrancl(X1,X0)) = c_Relation_ORange(X1,X1,X0),
inference(cnf_transformation,[],[f568]) ).
fof(f568,plain,
! [X0,X1] : c_Relation_ORange(X1,X1,c_Transitive__Closure_Otrancl(X1,X0)) = c_Relation_ORange(X1,X1,X0),
inference(rectify,[],[f85]) ).
fof(f85,axiom,
! [X3,X4] : c_Relation_ORange(X4,X4,c_Transitive__Closure_Otrancl(X4,X3)) = c_Relation_ORange(X4,X4,X3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trancl__range) ).
fof(f3554,plain,
spl104_137,
inference(avatar_split_clause,[],[f1937,f3552]) ).
fof(f1937,plain,
! [X0,X1] : c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) = c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool),X0,X0),
inference(cnf_transformation,[],[f567]) ).
fof(f567,plain,
! [X0,X1] : c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) = c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool),X0,X0),
inference(rectify,[],[f422]) ).
fof(f422,axiom,
! [X11,X4] : c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)) = c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool),X11,X11),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Diff__cancel) ).
fof(f3550,plain,
( ~ spl104_1
| spl104_136 ),
inference(avatar_split_clause,[],[f1859,f3547,f2878]) ).
fof(f1859,plain,
! [X5] :
( ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X5,X5),v_L)
| ~ sP0 ),
inference(cnf_transformation,[],[f1558]) ).
fof(f3549,plain,
( ~ spl104_2
| spl104_136 ),
inference(avatar_split_clause,[],[f1853,f3547,f2882]) ).
fof(f1853,plain,
! [X5] :
( ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X5,X5),v_L)
| ~ sP1 ),
inference(cnf_transformation,[],[f1552]) ).
fof(f3495,plain,
spl104_135,
inference(avatar_split_clause,[],[f2508,f3493]) ).
fof(f3493,plain,
( spl104_135
<=> ! [X0,X3,X2,X1] :
( sP8(X0,X1,X2,X3)
| ~ sP9(X0,X1,X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_135])]) ).
fof(f2508,plain,
! [X2,X3,X0,X1] :
( sP8(X0,X1,X2,X3)
| ~ sP9(X0,X1,X3,X2) ),
inference(cnf_transformation,[],[f1794]) ).
fof(f1794,plain,
! [X0,X1,X2,X3] :
( ( sP8(X0,X1,X2,X3)
| ~ sP9(X0,X1,X3,X2) )
& ( sP9(X0,X1,X3,X2)
| ~ sP8(X0,X1,X2,X3) ) ),
inference(nnf_transformation,[],[f1542]) ).
fof(f1542,plain,
! [X0,X1,X2,X3] :
( sP8(X0,X1,X2,X3)
<=> sP9(X0,X1,X3,X2) ),
inference(definition_folding,[],[f940,f1541,f1540]) ).
fof(f940,plain,
! [X0,X1,X2,X3] :
( ? [X4] :
( hBOOL(hAPP(X0,X4))
& c_member(X3,X4,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool),X2,X1)) )
<=> ( ? [X5] :
( hBOOL(hAPP(X0,X5))
& c_member(X3,X5,X1) )
| ? [X6] :
( hBOOL(hAPP(X0,X6))
& c_member(X3,X6,X2) ) ) ),
inference(rectify,[],[f130]) ).
fof(f130,axiom,
! [X17,X10,X11,X4] :
( ? [X2] :
( hBOOL(hAPP(X17,X2))
& c_member(X4,X2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool),X11,X10)) )
<=> ( ? [X2] :
( hBOOL(hAPP(X17,X2))
& c_member(X4,X2,X10) )
| ? [X2] :
( hBOOL(hAPP(X17,X2))
& c_member(X4,X2,X11) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bex__Un) ).
fof(f3491,plain,
spl104_134,
inference(avatar_split_clause,[],[f2507,f3489]) ).
fof(f3489,plain,
( spl104_134
<=> ! [X0,X3,X2,X1] :
( sP9(X0,X1,X3,X2)
| ~ sP8(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_134])]) ).
fof(f2507,plain,
! [X2,X3,X0,X1] :
( sP9(X0,X1,X3,X2)
| ~ sP8(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f1794]) ).
fof(f3487,plain,
spl104_133,
inference(avatar_split_clause,[],[f2331,f3485]) ).
fof(f3485,plain,
( spl104_133
<=> ! [X0,X3,X2,X1] :
( c_FunDef_Oreduction__pair(X1,c_FunDef_Orp__inv__image(X3,X1,X2,X0))
| ~ c_FunDef_Oreduction__pair(X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_133])]) ).
fof(f2331,plain,
! [X2,X3,X0,X1] :
( c_FunDef_Oreduction__pair(X1,c_FunDef_Orp__inv__image(X3,X1,X2,X0))
| ~ c_FunDef_Oreduction__pair(X3,X2) ),
inference(cnf_transformation,[],[f1303]) ).
fof(f1303,plain,
! [X0,X1,X2,X3] :
( c_FunDef_Oreduction__pair(X1,c_FunDef_Orp__inv__image(X3,X1,X2,X0))
| ~ c_FunDef_Oreduction__pair(X3,X2) ),
inference(ennf_transformation,[],[f845]) ).
fof(f845,plain,
! [X0,X1,X2,X3] :
( c_FunDef_Oreduction__pair(X3,X2)
=> c_FunDef_Oreduction__pair(X1,c_FunDef_Orp__inv__image(X3,X1,X2,X0)) ),
inference(rectify,[],[f487]) ).
fof(f487,axiom,
! [X1,X15,X17,X4] :
( c_FunDef_Oreduction__pair(X4,X17)
=> c_FunDef_Oreduction__pair(X15,c_FunDef_Orp__inv__image(X4,X15,X17,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rp__inv__image__rp) ).
fof(f3483,plain,
spl104_132,
inference(avatar_split_clause,[],[f2266,f3481]) ).
fof(f3481,plain,
( spl104_132
<=> ! [X0,X3,X2,X1] : c_Nitpick_Ofold__graph_H(X3,X2,X1,X0,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_132])]) ).
fof(f2266,plain,
! [X2,X3,X0,X1] : c_Nitpick_Ofold__graph_H(X3,X2,X1,X0,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)),X0),
inference(cnf_transformation,[],[f792]) ).
fof(f792,plain,
! [X0,X1,X2,X3] : c_Nitpick_Ofold__graph_H(X3,X2,X1,X0,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)),X0),
inference(rectify,[],[f469]) ).
fof(f469,axiom,
! [X34,X35,X15,X4] : c_Nitpick_Ofold__graph_H(X4,X15,X35,X34,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)),X34),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold__graph_H_Oequations_I1_J) ).
fof(f3479,plain,
spl104_131,
inference(avatar_split_clause,[],[f2199,f3477]) ).
fof(f2199,plain,
! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(X2,X1),X0))
| ~ sP3(X0,X1,X2) ),
inference(cnf_transformation,[],[f1647]) ).
fof(f1647,plain,
! [X0,X1,X2] :
( ( ~ hBOOL(hAPP(hAPP(X2,X1),X0))
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1) )
| ~ sP3(X0,X1,X2) ),
inference(rectify,[],[f1646]) ).
fof(f1646,plain,
! [X2,X1,X0] :
( ( ~ hBOOL(hAPP(hAPP(X0,X1),X2))
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1) )
| ~ sP3(X2,X1,X0) ),
inference(nnf_transformation,[],[f1531]) ).
fof(f3475,plain,
spl104_130,
inference(avatar_split_clause,[],[f2171,f3473]) ).
fof(f2171,plain,
! [X2,X0,X1] :
( c_Set_Oinsert(X2,X1,X0) = X0
| ~ c_member(X2,X1,X0) ),
inference(cnf_transformation,[],[f1200]) ).
fof(f1200,plain,
! [X0,X1,X2] :
( c_Set_Oinsert(X2,X1,X0) = X0
| ~ c_member(X2,X1,X0) ),
inference(ennf_transformation,[],[f744]) ).
fof(f744,plain,
! [X0,X1,X2] :
( c_member(X2,X1,X0)
=> c_Set_Oinsert(X2,X1,X0) = X0 ),
inference(rectify,[],[f145]) ).
fof(f145,axiom,
! [X11,X9,X4] :
( c_member(X4,X9,X11)
=> c_Set_Oinsert(X4,X9,X11) = X11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__absorb) ).
fof(f3471,plain,
spl104_129,
inference(avatar_split_clause,[],[f2135,f3469]) ).
fof(f3469,plain,
( spl104_129
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
| ~ c_Orderings_Oord__class_Oless(X2,X1,X0)
| ~ class_Orderings_Oorder(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_129])]) ).
fof(f2135,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
| ~ c_Orderings_Oord__class_Oless(X2,X1,X0)
| ~ class_Orderings_Oorder(X2) ),
inference(cnf_transformation,[],[f1634]) ).
fof(f1634,plain,
! [X0,X1,X2] :
( ( ( c_Orderings_Oord__class_Oless(X2,X1,X0)
| X0 = X1
| ~ c_Orderings_Oord__class_Oless__eq(X2,X1,X0) )
& ( ( X0 != X1
& c_Orderings_Oord__class_Oless__eq(X2,X1,X0) )
| ~ c_Orderings_Oord__class_Oless(X2,X1,X0) ) )
| ~ class_Orderings_Oorder(X2) ),
inference(flattening,[],[f1633]) ).
fof(f1633,plain,
! [X0,X1,X2] :
( ( ( c_Orderings_Oord__class_Oless(X2,X1,X0)
| X0 = X1
| ~ c_Orderings_Oord__class_Oless__eq(X2,X1,X0) )
& ( ( X0 != X1
& c_Orderings_Oord__class_Oless__eq(X2,X1,X0) )
| ~ c_Orderings_Oord__class_Oless(X2,X1,X0) ) )
| ~ class_Orderings_Oorder(X2) ),
inference(nnf_transformation,[],[f1161]) ).
fof(f1161,plain,
! [X0,X1,X2] :
( ( c_Orderings_Oord__class_Oless(X2,X1,X0)
<=> ( X0 != X1
& c_Orderings_Oord__class_Oless__eq(X2,X1,X0) ) )
| ~ class_Orderings_Oorder(X2) ),
inference(ennf_transformation,[],[f717]) ).
fof(f717,plain,
! [X0,X1,X2] :
( class_Orderings_Oorder(X2)
=> ( c_Orderings_Oord__class_Oless(X2,X1,X0)
<=> ( X0 != X1
& c_Orderings_Oord__class_Oless__eq(X2,X1,X0) ) ) ),
inference(rectify,[],[f335]) ).
fof(f335,axiom,
! [X12,X13,X4] :
( class_Orderings_Oorder(X4)
=> ( c_Orderings_Oord__class_Oless(X4,X13,X12)
<=> ( X12 != X13
& c_Orderings_Oord__class_Oless__eq(X4,X13,X12) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__le) ).
fof(f3467,plain,
spl104_128,
inference(avatar_split_clause,[],[f2122,f3465]) ).
fof(f2122,plain,
! [X2,X0,X1] :
( ~ c_Orderings_Oord__class_Oless(X2,X0,X1)
| ~ c_Orderings_Oord__class_Oless(X2,X1,X0)
| ~ class_Orderings_Oorder(X2) ),
inference(cnf_transformation,[],[f1143]) ).
fof(f1143,plain,
! [X0,X1,X2] :
( ~ c_Orderings_Oord__class_Oless(X2,X0,X1)
| ~ c_Orderings_Oord__class_Oless(X2,X1,X0)
| ~ class_Orderings_Oorder(X2) ),
inference(flattening,[],[f1142]) ).
fof(f1142,plain,
! [X0,X1,X2] :
( ~ c_Orderings_Oord__class_Oless(X2,X0,X1)
| ~ c_Orderings_Oord__class_Oless(X2,X1,X0)
| ~ class_Orderings_Oorder(X2) ),
inference(ennf_transformation,[],[f707]) ).
fof(f707,plain,
! [X0,X1,X2] :
( class_Orderings_Oorder(X2)
=> ( c_Orderings_Oord__class_Oless(X2,X1,X0)
=> ~ c_Orderings_Oord__class_Oless(X2,X0,X1) ) ),
inference(rectify,[],[f322]) ).
fof(f322,axiom,
! [X27,X26,X4] :
( class_Orderings_Oorder(X4)
=> ( c_Orderings_Oord__class_Oless(X4,X26,X27)
=> ~ c_Orderings_Oord__class_Oless(X4,X27,X26) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I9_J) ).
fof(f3463,plain,
spl104_127,
inference(avatar_split_clause,[],[f2109,f3461]) ).
fof(f2109,plain,
! [X2,X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(X2,X0,X1)
| ~ c_Orderings_Oord__class_Oless(X2,X1,X0)
| ~ class_Orderings_Opreorder(X2) ),
inference(cnf_transformation,[],[f1629]) ).
fof(f3459,plain,
spl104_126,
inference(avatar_split_clause,[],[f2107,f3457]) ).
fof(f3457,plain,
( spl104_126
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
| ~ c_Orderings_Oord__class_Oless(X2,X1,X0)
| ~ class_Orderings_Opreorder(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_126])]) ).
fof(f2107,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
| ~ c_Orderings_Oord__class_Oless(X2,X1,X0)
| ~ class_Orderings_Opreorder(X2) ),
inference(cnf_transformation,[],[f1124]) ).
fof(f1124,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
| ~ c_Orderings_Oord__class_Oless(X2,X1,X0)
| ~ class_Orderings_Opreorder(X2) ),
inference(flattening,[],[f1123]) ).
fof(f1123,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
| ~ c_Orderings_Oord__class_Oless(X2,X1,X0)
| ~ class_Orderings_Opreorder(X2) ),
inference(ennf_transformation,[],[f694]) ).
fof(f694,plain,
! [X0,X1,X2] :
( class_Orderings_Opreorder(X2)
=> ( c_Orderings_Oord__class_Oless(X2,X1,X0)
=> c_Orderings_Oord__class_Oless__eq(X2,X1,X0) ) ),
inference(rectify,[],[f344]) ).
fof(f344,axiom,
! [X59,X58,X4] :
( class_Orderings_Opreorder(X4)
=> ( c_Orderings_Oord__class_Oless(X4,X58,X59)
=> c_Orderings_Oord__class_Oless__eq(X4,X58,X59) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__imp__le) ).
fof(f3455,plain,
spl104_125,
inference(avatar_split_clause,[],[f2103,f3453]) ).
fof(f3453,plain,
( spl104_125
<=> ! [X2,X0,X1] :
( ~ c_Orderings_Oord__class_Oless(X2,X0,X1)
| ~ c_Orderings_Oord__class_Oless(X2,X1,X0)
| ~ class_Orderings_Opreorder(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_125])]) ).
fof(f2103,plain,
! [X2,X0,X1] :
( ~ c_Orderings_Oord__class_Oless(X2,X0,X1)
| ~ c_Orderings_Oord__class_Oless(X2,X1,X0)
| ~ class_Orderings_Opreorder(X2) ),
inference(cnf_transformation,[],[f1116]) ).
fof(f1116,plain,
! [X0,X1,X2] :
( ~ c_Orderings_Oord__class_Oless(X2,X0,X1)
| ~ c_Orderings_Oord__class_Oless(X2,X1,X0)
| ~ class_Orderings_Opreorder(X2) ),
inference(flattening,[],[f1115]) ).
fof(f1115,plain,
! [X0,X1,X2] :
( ~ c_Orderings_Oord__class_Oless(X2,X0,X1)
| ~ c_Orderings_Oord__class_Oless(X2,X1,X0)
| ~ class_Orderings_Opreorder(X2) ),
inference(ennf_transformation,[],[f690]) ).
fof(f690,plain,
! [X0,X1,X2] :
( class_Orderings_Opreorder(X2)
=> ( c_Orderings_Oord__class_Oless(X2,X1,X0)
=> ~ c_Orderings_Oord__class_Oless(X2,X0,X1) ) ),
inference(rectify,[],[f317]) ).
fof(f317,axiom,
! [X59,X58,X4] :
( class_Orderings_Opreorder(X4)
=> ( c_Orderings_Oord__class_Oless(X4,X58,X59)
=> ~ c_Orderings_Oord__class_Oless(X4,X59,X58) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__not__sym) ).
fof(f3451,plain,
( spl104_124
| ~ spl104_23
| ~ spl104_85 ),
inference(avatar_split_clause,[],[f3320,f3254,f2987,f3448]) ).
fof(f3320,plain,
( v_L = c_Transitive__Closure_Otrancl(tc_Arrow__Order__Mirabelle_Oalt,v_L)
| ~ spl104_23
| ~ spl104_85 ),
inference(resolution,[],[f3255,f2989]) ).
fof(f2989,plain,
( c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,v_L)
| ~ spl104_23 ),
inference(avatar_component_clause,[],[f2987]) ).
fof(f3446,plain,
spl104_123,
inference(avatar_split_clause,[],[f2090,f3444]) ).
fof(f3444,plain,
( spl104_123
<=> ! [X2,X0,X1] :
( ~ c_Orderings_Oord__class_Oless(X2,X1,X0)
| ~ c_Orderings_Oord__class_Oless(X2,X0,X1)
| ~ class_Orderings_Olinorder(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_123])]) ).
fof(f2090,plain,
! [X2,X0,X1] :
( ~ c_Orderings_Oord__class_Oless(X2,X1,X0)
| ~ c_Orderings_Oord__class_Oless(X2,X0,X1)
| ~ class_Orderings_Olinorder(X2) ),
inference(cnf_transformation,[],[f1624]) ).
fof(f1624,plain,
! [X0,X1,X2] :
( ( ( ~ c_Orderings_Oord__class_Oless(X2,X1,X0)
| ( X0 != X1
& ~ c_Orderings_Oord__class_Oless(X2,X0,X1) ) )
& ( X0 = X1
| c_Orderings_Oord__class_Oless(X2,X0,X1)
| c_Orderings_Oord__class_Oless(X2,X1,X0) ) )
| ~ class_Orderings_Olinorder(X2) ),
inference(flattening,[],[f1623]) ).
fof(f1623,plain,
! [X0,X1,X2] :
( ( ( ~ c_Orderings_Oord__class_Oless(X2,X1,X0)
| ( X0 != X1
& ~ c_Orderings_Oord__class_Oless(X2,X0,X1) ) )
& ( X0 = X1
| c_Orderings_Oord__class_Oless(X2,X0,X1)
| c_Orderings_Oord__class_Oless(X2,X1,X0) ) )
| ~ class_Orderings_Olinorder(X2) ),
inference(nnf_transformation,[],[f1105]) ).
fof(f1105,plain,
! [X0,X1,X2] :
( ( ~ c_Orderings_Oord__class_Oless(X2,X1,X0)
<=> ( X0 = X1
| c_Orderings_Oord__class_Oless(X2,X0,X1) ) )
| ~ class_Orderings_Olinorder(X2) ),
inference(ennf_transformation,[],[f681]) ).
fof(f681,plain,
! [X0,X1,X2] :
( class_Orderings_Olinorder(X2)
=> ( ~ c_Orderings_Oord__class_Oless(X2,X1,X0)
<=> ( X0 = X1
| c_Orderings_Oord__class_Oless(X2,X0,X1) ) ) ),
inference(rectify,[],[f312]) ).
fof(f312,axiom,
! [X12,X13,X4] :
( class_Orderings_Olinorder(X4)
=> ( ~ c_Orderings_Oord__class_Oless(X4,X13,X12)
<=> ( X12 = X13
| c_Orderings_Oord__class_Oless(X4,X12,X13) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__less__iff__gr__or__eq) ).
fof(f3442,plain,
spl104_122,
inference(avatar_split_clause,[],[f2081,f3440]) ).
fof(f2081,plain,
! [X2,X0,X1] :
( ~ c_Orderings_Oord__class_Oless(X2,X0,X1)
| ~ c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
| ~ class_Orderings_Olinorder(X2) ),
inference(cnf_transformation,[],[f1100]) ).
fof(f1100,plain,
! [X0,X1,X2] :
( ~ c_Orderings_Oord__class_Oless(X2,X0,X1)
| ~ c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
| ~ class_Orderings_Olinorder(X2) ),
inference(flattening,[],[f1099]) ).
fof(f1099,plain,
! [X0,X1,X2] :
( ~ c_Orderings_Oord__class_Oless(X2,X0,X1)
| ~ c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
| ~ class_Orderings_Olinorder(X2) ),
inference(ennf_transformation,[],[f677]) ).
fof(f677,plain,
! [X0,X1,X2] :
( class_Orderings_Olinorder(X2)
=> ( c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
=> ~ c_Orderings_Oord__class_Oless(X2,X0,X1) ) ),
inference(rectify,[],[f343]) ).
fof(f343,axiom,
! [X58,X59,X4] :
( class_Orderings_Olinorder(X4)
=> ( c_Orderings_Oord__class_Oless__eq(X4,X59,X58)
=> ~ c_Orderings_Oord__class_Oless(X4,X58,X59) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_leD) ).
fof(f3438,plain,
spl104_121,
inference(avatar_split_clause,[],[f2071,f3436]) ).
fof(f2071,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X2,X0,X1)
| c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
| ~ class_Orderings_Olinorder(X2) ),
inference(cnf_transformation,[],[f1084]) ).
fof(f1084,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(X2,X0,X1)
| c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
| ~ class_Orderings_Olinorder(X2) ),
inference(flattening,[],[f1083]) ).
fof(f1083,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(X2,X0,X1)
| c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
| ~ class_Orderings_Olinorder(X2) ),
inference(ennf_transformation,[],[f669]) ).
fof(f669,plain,
! [X0,X1,X2] :
( class_Orderings_Olinorder(X2)
=> ( c_Orderings_Oord__class_Oless__eq(X2,X0,X1)
| c_Orderings_Oord__class_Oless__eq(X2,X1,X0) ) ),
inference(rectify,[],[f297]) ).
fof(f297,axiom,
! [X59,X58,X4] :
( class_Orderings_Olinorder(X4)
=> ( c_Orderings_Oord__class_Oless__eq(X4,X59,X58)
| c_Orderings_Oord__class_Oless__eq(X4,X58,X59) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__linear) ).
fof(f3434,plain,
spl104_120,
inference(avatar_split_clause,[],[f2070,f3432]) ).
fof(f3432,plain,
( spl104_120
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless(X2,X0,X1)
| c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
| ~ class_Orderings_Olinorder(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_120])]) ).
fof(f2070,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless(X2,X0,X1)
| c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
| ~ class_Orderings_Olinorder(X2) ),
inference(cnf_transformation,[],[f1082]) ).
fof(f1082,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless(X2,X0,X1)
| c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
| ~ class_Orderings_Olinorder(X2) ),
inference(flattening,[],[f1081]) ).
fof(f1081,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless(X2,X0,X1)
| c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
| ~ class_Orderings_Olinorder(X2) ),
inference(ennf_transformation,[],[f668]) ).
fof(f668,plain,
! [X0,X1,X2] :
( class_Orderings_Olinorder(X2)
=> ( c_Orderings_Oord__class_Oless(X2,X0,X1)
| c_Orderings_Oord__class_Oless__eq(X2,X1,X0) ) ),
inference(rectify,[],[f334]) ).
fof(f334,axiom,
! [X59,X58,X4] :
( class_Orderings_Olinorder(X4)
=> ( c_Orderings_Oord__class_Oless(X4,X59,X58)
| c_Orderings_Oord__class_Oless__eq(X4,X58,X59) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__le__less__linear) ).
fof(f3430,plain,
spl104_119,
inference(avatar_split_clause,[],[f2014,f3428]) ).
fof(f3428,plain,
( spl104_119
<=> ! [X0,X1] :
( c_Relation_Oantisym(X1,X0)
| sK28(X0,X1) != sK29(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_119])]) ).
fof(f2014,plain,
! [X0,X1] :
( c_Relation_Oantisym(X1,X0)
| sK28(X0,X1) != sK29(X0,X1) ),
inference(cnf_transformation,[],[f1582]) ).
fof(f3426,plain,
spl104_118,
inference(avatar_split_clause,[],[f2001,f3424]) ).
fof(f3424,plain,
( spl104_118
<=> ! [X0,X1] :
( c_Relation_Oantisym(X1,X0)
| sK22(X0,X1) != sK23(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_118])]) ).
fof(f2001,plain,
! [X0,X1] :
( c_Relation_Oantisym(X1,X0)
| sK22(X0,X1) != sK23(X0,X1) ),
inference(cnf_transformation,[],[f1569]) ).
fof(f3422,plain,
spl104_117,
inference(avatar_split_clause,[],[f1985,f3420]) ).
fof(f1985,plain,
! [X0,X1] :
( c_Wellfounded_Owf(tc_fun(X1,tc_HOL_Obool),c_Wellfounded_Omax__ext(X1,X0))
| ~ c_Wellfounded_Owf(X1,X0) ),
inference(cnf_transformation,[],[f1056]) ).
fof(f1056,plain,
! [X0,X1] :
( c_Wellfounded_Owf(tc_fun(X1,tc_HOL_Obool),c_Wellfounded_Omax__ext(X1,X0))
| ~ c_Wellfounded_Owf(X1,X0) ),
inference(ennf_transformation,[],[f615]) ).
fof(f615,plain,
! [X0,X1] :
( c_Wellfounded_Owf(X1,X0)
=> c_Wellfounded_Owf(tc_fun(X1,tc_HOL_Obool),c_Wellfounded_Omax__ext(X1,X0)) ),
inference(rectify,[],[f461]) ).
fof(f461,axiom,
! [X3,X4] :
( c_Wellfounded_Owf(X4,X3)
=> c_Wellfounded_Owf(tc_fun(X4,tc_HOL_Obool),c_Wellfounded_Omax__ext(X4,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_max__ext__wf) ).
fof(f3418,plain,
spl104_116,
inference(avatar_split_clause,[],[f1984,f3416]) ).
fof(f1984,plain,
! [X0,X1] :
( c_Wellfounded_Owf(tc_fun(X1,tc_HOL_Obool),c_Wellfounded_Omin__ext(X1,X0))
| ~ c_Wellfounded_Owf(X1,X0) ),
inference(cnf_transformation,[],[f1055]) ).
fof(f1055,plain,
! [X0,X1] :
( c_Wellfounded_Owf(tc_fun(X1,tc_HOL_Obool),c_Wellfounded_Omin__ext(X1,X0))
| ~ c_Wellfounded_Owf(X1,X0) ),
inference(ennf_transformation,[],[f614]) ).
fof(f614,plain,
! [X0,X1] :
( c_Wellfounded_Owf(X1,X0)
=> c_Wellfounded_Owf(tc_fun(X1,tc_HOL_Obool),c_Wellfounded_Omin__ext(X1,X0)) ),
inference(rectify,[],[f462]) ).
fof(f462,axiom,
! [X3,X4] :
( c_Wellfounded_Owf(X4,X3)
=> c_Wellfounded_Owf(tc_fun(X4,tc_HOL_Obool),c_Wellfounded_Omin__ext(X4,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__ext__wf) ).
fof(f3411,plain,
( spl104_115
| ~ spl104_20
| ~ spl104_85 ),
inference(avatar_split_clause,[],[f3319,f3254,f2972,f3408]) ).
fof(f3408,plain,
( spl104_115
<=> c_Wellfounded_Oless__than = c_Transitive__Closure_Otrancl(tc_Nat_Onat,c_Wellfounded_Oless__than) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_115])]) ).
fof(f3319,plain,
( c_Wellfounded_Oless__than = c_Transitive__Closure_Otrancl(tc_Nat_Onat,c_Wellfounded_Oless__than)
| ~ spl104_20
| ~ spl104_85 ),
inference(resolution,[],[f3255,f2974]) ).
fof(f2974,plain,
( c_Relation_Otrans(tc_Nat_Onat,c_Wellfounded_Oless__than)
| ~ spl104_20 ),
inference(avatar_component_clause,[],[f2972]) ).
fof(f3398,plain,
( spl104_114
| ~ spl104_29
| ~ spl104_53 ),
inference(avatar_split_clause,[],[f3139,f3111,f3013,f3395]) ).
fof(f3395,plain,
( spl104_114
<=> sP2(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_114])]) ).
fof(f3139,plain,
( sP2(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less)
| ~ spl104_29
| ~ spl104_53 ),
inference(resolution,[],[f3112,f3015]) ).
fof(f3015,plain,
( c_Wellfounded_Owf(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less)
| ~ spl104_29 ),
inference(avatar_component_clause,[],[f3013]) ).
fof(f3393,plain,
spl104_113,
inference(avatar_split_clause,[],[f2149,f3391]) ).
fof(f2149,plain,
! [X2,X0,X1] :
( c_Wellfounded_Owf(X2,c_Wellfounded_Omlex__prod(X2,X0,X1))
| ~ c_Wellfounded_Owf(X2,X1) ),
inference(cnf_transformation,[],[f1171]) ).
fof(f1171,plain,
! [X0,X1,X2] :
( c_Wellfounded_Owf(X2,c_Wellfounded_Omlex__prod(X2,X0,X1))
| ~ c_Wellfounded_Owf(X2,X1) ),
inference(ennf_transformation,[],[f725]) ).
fof(f725,plain,
! [X0,X1,X2] :
( c_Wellfounded_Owf(X2,X1)
=> c_Wellfounded_Owf(X2,c_Wellfounded_Omlex__prod(X2,X0,X1)) ),
inference(rectify,[],[f331]) ).
fof(f331,axiom,
! [X1,X14,X4] :
( c_Wellfounded_Owf(X4,X14)
=> c_Wellfounded_Owf(X4,c_Wellfounded_Omlex__prod(X4,X1,X14)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__mlex) ).
fof(f3389,plain,
spl104_112,
inference(avatar_split_clause,[],[f2112,f3387]) ).
fof(f2112,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X2,X1,c_Lattices_Osemilattice__sup__class_Osup(X2,X1,X0))
| ~ class_Lattices_Osemilattice__sup(X2) ),
inference(cnf_transformation,[],[f1127]) ).
fof(f1127,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(X2,X1,c_Lattices_Osemilattice__sup__class_Osup(X2,X1,X0))
| ~ class_Lattices_Osemilattice__sup(X2) ),
inference(ennf_transformation,[],[f697]) ).
fof(f697,plain,
! [X0,X1,X2] :
( class_Lattices_Osemilattice__sup(X2)
=> c_Orderings_Oord__class_Oless__eq(X2,X1,c_Lattices_Osemilattice__sup__class_Osup(X2,X1,X0)) ),
inference(rectify,[],[f258]) ).
fof(f258,axiom,
! [X59,X58,X4] :
( class_Lattices_Osemilattice__sup(X4)
=> c_Orderings_Oord__class_Oless__eq(X4,X58,c_Lattices_Osemilattice__sup__class_Osup(X4,X58,X59)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup__ge1) ).
fof(f3385,plain,
spl104_111,
inference(avatar_split_clause,[],[f2111,f3383]) ).
fof(f2111,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X2,X1,c_Lattices_Osemilattice__sup__class_Osup(X2,X0,X1))
| ~ class_Lattices_Osemilattice__sup(X2) ),
inference(cnf_transformation,[],[f1126]) ).
fof(f1126,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(X2,X1,c_Lattices_Osemilattice__sup__class_Osup(X2,X0,X1))
| ~ class_Lattices_Osemilattice__sup(X2) ),
inference(ennf_transformation,[],[f696]) ).
fof(f696,plain,
! [X0,X1,X2] :
( class_Lattices_Osemilattice__sup(X2)
=> c_Orderings_Oord__class_Oless__eq(X2,X1,c_Lattices_Osemilattice__sup__class_Osup(X2,X0,X1)) ),
inference(rectify,[],[f256]) ).
fof(f256,axiom,
! [X58,X59,X4] :
( class_Lattices_Osemilattice__sup(X4)
=> c_Orderings_Oord__class_Oless__eq(X4,X59,c_Lattices_Osemilattice__sup__class_Osup(X4,X58,X59)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup__ge2) ).
fof(f3381,plain,
spl104_110,
inference(avatar_split_clause,[],[f2099,f3379]) ).
fof(f2099,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X2,X1,c_Lattices_Osemilattice__sup__class_Osup(X2,X1,X0))
| ~ class_Lattices_Olattice(X2) ),
inference(cnf_transformation,[],[f1110]) ).
fof(f1110,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(X2,X1,c_Lattices_Osemilattice__sup__class_Osup(X2,X1,X0))
| ~ class_Lattices_Olattice(X2) ),
inference(ennf_transformation,[],[f686]) ).
fof(f686,plain,
! [X0,X1,X2] :
( class_Lattices_Olattice(X2)
=> c_Orderings_Oord__class_Oless__eq(X2,X1,c_Lattices_Osemilattice__sup__class_Osup(X2,X1,X0)) ),
inference(rectify,[],[f259]) ).
fof(f259,axiom,
! [X59,X58,X4] :
( class_Lattices_Olattice(X4)
=> c_Orderings_Oord__class_Oless__eq(X4,X58,c_Lattices_Osemilattice__sup__class_Osup(X4,X58,X59)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__sup__ord_I3_J) ).
fof(f3377,plain,
spl104_109,
inference(avatar_split_clause,[],[f2098,f3375]) ).
fof(f2098,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X2,X1,c_Lattices_Osemilattice__sup__class_Osup(X2,X0,X1))
| ~ class_Lattices_Olattice(X2) ),
inference(cnf_transformation,[],[f1109]) ).
fof(f1109,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(X2,X1,c_Lattices_Osemilattice__sup__class_Osup(X2,X0,X1))
| ~ class_Lattices_Olattice(X2) ),
inference(ennf_transformation,[],[f685]) ).
fof(f685,plain,
! [X0,X1,X2] :
( class_Lattices_Olattice(X2)
=> c_Orderings_Oord__class_Oless__eq(X2,X1,c_Lattices_Osemilattice__sup__class_Osup(X2,X0,X1)) ),
inference(rectify,[],[f257]) ).
fof(f257,axiom,
! [X58,X59,X4] :
( class_Lattices_Olattice(X4)
=> c_Orderings_Oord__class_Oless__eq(X4,X59,c_Lattices_Osemilattice__sup__class_Osup(X4,X58,X59)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__sup__ord_I4_J) ).
fof(f3373,plain,
spl104_108,
inference(avatar_split_clause,[],[f2051,f3371]) ).
fof(f2051,plain,
! [X2,X0,X1] : c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool),X1,c_Set_Oinsert(X2,X0,X1)),
inference(cnf_transformation,[],[f649]) ).
fof(f649,plain,
! [X0,X1,X2] : c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool),X1,c_Set_Oinsert(X2,X0,X1)),
inference(rectify,[],[f245]) ).
fof(f245,axiom,
! [X9,X10,X4] : c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool),X10,c_Set_Oinsert(X4,X9,X10)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__insertI) ).
fof(f3369,plain,
spl104_107,
inference(avatar_split_clause,[],[f2049,f3367]) ).
fof(f2049,plain,
! [X2,X0,X1] : c_Set_Oinsert(X2,X1,X0) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)),
inference(cnf_transformation,[],[f647]) ).
fof(f647,plain,
! [X0,X1,X2] : c_Set_Oinsert(X2,X1,X0) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)),
inference(rectify,[],[f431]) ).
fof(f431,axiom,
! [X11,X9,X4] : c_Set_Oinsert(X4,X9,X11) != c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_empty__not__insert) ).
fof(f3365,plain,
spl104_106,
inference(avatar_split_clause,[],[f2019,f3363]) ).
fof(f2019,plain,
! [X3,X0,X1] :
( c_member(X1,X3,c_Wellfounded_Oacc(X1,X0))
| ~ c_Wellfounded_Owf(X1,X0) ),
inference(cnf_transformation,[],[f1591]) ).
fof(f3361,plain,
spl104_105,
inference(avatar_split_clause,[],[f1983,f3359]) ).
fof(f3359,plain,
( spl104_105
<=> ! [X0,X1] :
( c_Wellfounded_OwfP(X1,c_FunDef_Oin__rel(X1,X1,X0))
| ~ c_Wellfounded_Owf(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_105])]) ).
fof(f1983,plain,
! [X0,X1] :
( c_Wellfounded_OwfP(X1,c_FunDef_Oin__rel(X1,X1,X0))
| ~ c_Wellfounded_Owf(X1,X0) ),
inference(cnf_transformation,[],[f1054]) ).
fof(f1054,plain,
! [X0,X1] :
( c_Wellfounded_OwfP(X1,c_FunDef_Oin__rel(X1,X1,X0))
| ~ c_Wellfounded_Owf(X1,X0) ),
inference(ennf_transformation,[],[f613]) ).
fof(f613,plain,
! [X0,X1] :
( c_Wellfounded_Owf(X1,X0)
=> c_Wellfounded_OwfP(X1,c_FunDef_Oin__rel(X1,X1,X0)) ),
inference(rectify,[],[f195]) ).
fof(f195,axiom,
! [X14,X4] :
( c_Wellfounded_Owf(X4,X14)
=> c_Wellfounded_OwfP(X4,c_FunDef_Oin__rel(X4,X4,X14)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__in__rel) ).
fof(f3357,plain,
( spl104_104
| ~ spl104_29
| ~ spl104_52 ),
inference(avatar_split_clause,[],[f3136,f3107,f3013,f3354]) ).
fof(f3354,plain,
( spl104_104
<=> c_Wellfounded_Oacyclic(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_104])]) ).
fof(f3136,plain,
( c_Wellfounded_Oacyclic(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less)
| ~ spl104_29
| ~ spl104_52 ),
inference(resolution,[],[f3108,f3015]) ).
fof(f3352,plain,
spl104_103,
inference(avatar_split_clause,[],[f1962,f3350]) ).
fof(f1962,plain,
! [X0,X1] :
( c_Lattices_Osemilattice__sup__class_Osup(X1,c_Orderings_Obot__class_Obot(X1),X0) = X0
| ~ class_Lattices_Obounded__lattice__bot(X1) ),
inference(cnf_transformation,[],[f1031]) ).
fof(f1031,plain,
! [X0,X1] :
( c_Lattices_Osemilattice__sup__class_Osup(X1,c_Orderings_Obot__class_Obot(X1),X0) = X0
| ~ class_Lattices_Obounded__lattice__bot(X1) ),
inference(ennf_transformation,[],[f592]) ).
fof(f592,plain,
! [X0,X1] :
( class_Lattices_Obounded__lattice__bot(X1)
=> c_Lattices_Osemilattice__sup__class_Osup(X1,c_Orderings_Obot__class_Obot(X1),X0) = X0 ),
inference(rectify,[],[f412]) ).
fof(f412,axiom,
! [X58,X4] :
( class_Lattices_Obounded__lattice__bot(X4)
=> c_Lattices_Osemilattice__sup__class_Osup(X4,c_Orderings_Obot__class_Obot(X4),X58) = X58 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup__bot__left) ).
fof(f3348,plain,
spl104_102,
inference(avatar_split_clause,[],[f1961,f3346]) ).
fof(f1961,plain,
! [X0,X1] :
( c_Lattices_Osemilattice__sup__class_Osup(X1,X0,c_Orderings_Obot__class_Obot(X1)) = X0
| ~ class_Lattices_Obounded__lattice__bot(X1) ),
inference(cnf_transformation,[],[f1030]) ).
fof(f1030,plain,
! [X0,X1] :
( c_Lattices_Osemilattice__sup__class_Osup(X1,X0,c_Orderings_Obot__class_Obot(X1)) = X0
| ~ class_Lattices_Obounded__lattice__bot(X1) ),
inference(ennf_transformation,[],[f591]) ).
fof(f591,plain,
! [X0,X1] :
( class_Lattices_Obounded__lattice__bot(X1)
=> c_Lattices_Osemilattice__sup__class_Osup(X1,X0,c_Orderings_Obot__class_Obot(X1)) = X0 ),
inference(rectify,[],[f411]) ).
fof(f411,axiom,
! [X58,X4] :
( class_Lattices_Obounded__lattice__bot(X4)
=> c_Lattices_Osemilattice__sup__class_Osup(X4,X58,c_Orderings_Obot__class_Obot(X4)) = X58 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup__bot__right) ).
fof(f3344,plain,
spl104_101,
inference(avatar_split_clause,[],[f1936,f3342]) ).
fof(f1936,plain,
! [X0,X1] : c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),X0),
inference(cnf_transformation,[],[f566]) ).
fof(f566,plain,
! [X0,X1] : c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),X0),
inference(rectify,[],[f396]) ).
fof(f396,axiom,
! [X11,X4] : c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)),X11),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_empty__subsetI) ).
fof(f3340,plain,
spl104_100,
inference(avatar_split_clause,[],[f1932,f3338]) ).
fof(f1932,plain,
! [X0,X1] : ~ c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool),X0,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),
inference(cnf_transformation,[],[f562]) ).
fof(f562,plain,
! [X0,X1] : ~ c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool),X0,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),
inference(rectify,[],[f441]) ).
fof(f441,axiom,
! [X11,X4] : ~ c_Orderings_Oord__class_Oless(tc_fun(X4,tc_HOL_Obool),X11,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__psubset__empty) ).
fof(f3312,plain,
( spl104_99
| ~ spl104_77 ),
inference(avatar_split_clause,[],[f3224,f3221,f3310]) ).
fof(f3221,plain,
( spl104_77
<=> ! [X0] : c_Wellfounded_Owf(X0,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X0,X0),tc_HOL_Obool))) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_77])]) ).
fof(f3224,plain,
( ! [X0] : c_Wellfounded_Owf(X0,c_Relation_OId__on(X0,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool))))
| ~ spl104_77 ),
inference(forward_demodulation,[],[f3222,f1912]) ).
fof(f3222,plain,
( ! [X0] : c_Wellfounded_Owf(X0,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X0,X0),tc_HOL_Obool)))
| ~ spl104_77 ),
inference(avatar_component_clause,[],[f3221]) ).
fof(f3308,plain,
spl104_98,
inference(avatar_split_clause,[],[f2636,f3306]) ).
fof(f2636,plain,
! [X0,X1] : c_Wellfounded_Owf(X1,hAPP(c_Relation_Oinv__image(tc_Nat_Onat,X1,c_Wellfounded_Oless__than),X0)),
inference(definition_unfolding,[],[f1920,f1902]) ).
fof(f1920,plain,
! [X0,X1] : c_Wellfounded_Owf(X1,hAPP(c_Wellfounded_Omeasure(X1),X0)),
inference(cnf_transformation,[],[f550]) ).
fof(f550,plain,
! [X0,X1] : c_Wellfounded_Owf(X1,hAPP(c_Wellfounded_Omeasure(X1),X0)),
inference(rectify,[],[f188]) ).
fof(f188,axiom,
! [X1,X4] : c_Wellfounded_Owf(X4,hAPP(c_Wellfounded_Omeasure(X4),X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__measure) ).
fof(f3304,plain,
spl104_97,
inference(avatar_split_clause,[],[f2238,f3302]) ).
fof(f2238,plain,
! [X2,X0,X1] :
( X0 = X1
| ~ c_member(X2,X1,c_fequal(X0)) ),
inference(cnf_transformation,[],[f1672]) ).
fof(f1672,plain,
! [X0,X1,X2] :
( ( c_member(X2,X1,c_fequal(X0))
| X0 != X1 )
& ( X0 = X1
| ~ c_member(X2,X1,c_fequal(X0)) ) ),
inference(nnf_transformation,[],[f780]) ).
fof(f780,plain,
! [X0,X1,X2] :
( c_member(X2,X1,c_fequal(X0))
<=> X0 = X1 ),
inference(rectify,[],[f171]) ).
fof(f171,axiom,
! [X12,X13,X4] :
( c_member(X4,X13,c_fequal(X12))
<=> X12 = X13 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__mem) ).
fof(f3300,plain,
spl104_96,
inference(avatar_split_clause,[],[f2237,f3298]) ).
fof(f2237,plain,
! [X2,X0,X1] :
( c_member(X2,X1,X0)
| ~ hBOOL(hAPP(X0,X1)) ),
inference(cnf_transformation,[],[f1671]) ).
fof(f1671,plain,
! [X0,X1,X2] :
( ( c_member(X2,X1,X0)
| ~ hBOOL(hAPP(X0,X1)) )
& ( hBOOL(hAPP(X0,X1))
| ~ c_member(X2,X1,X0) ) ),
inference(nnf_transformation,[],[f779]) ).
fof(f779,plain,
! [X0,X1,X2] :
( c_member(X2,X1,X0)
<=> hBOOL(hAPP(X0,X1)) ),
inference(rectify,[],[f12]) ).
fof(f12,axiom,
! [X11,X13,X4] :
( c_member(X4,X13,X11)
<=> hBOOL(hAPP(X11,X13)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mem__def) ).
fof(f3296,plain,
spl104_95,
inference(avatar_split_clause,[],[f2236,f3294]) ).
fof(f2236,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(X0,X1))
| ~ c_member(X2,X1,X0) ),
inference(cnf_transformation,[],[f1671]) ).
fof(f3292,plain,
spl104_94,
inference(avatar_split_clause,[],[f2229,f3290]) ).
fof(f3290,plain,
( spl104_94
<=> ! [X2,X0,X1] :
( c_Relation_Orefl__on(X2,X1,X0)
| ~ c_Order__Relation_Opreorder__on(X2,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_94])]) ).
fof(f2229,plain,
! [X2,X0,X1] :
( c_Relation_Orefl__on(X2,X1,X0)
| ~ c_Order__Relation_Opreorder__on(X2,X1,X0) ),
inference(cnf_transformation,[],[f1665]) ).
fof(f3288,plain,
spl104_93,
inference(avatar_split_clause,[],[f2226,f3286]) ).
fof(f3286,plain,
( spl104_93
<=> ! [X2,X0,X1] :
( c_Order__Relation_Opreorder__on(X2,X1,X0)
| ~ c_Order__Relation_Opartial__order__on(X2,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_93])]) ).
fof(f2226,plain,
! [X2,X0,X1] :
( c_Order__Relation_Opreorder__on(X2,X1,X0)
| ~ c_Order__Relation_Opartial__order__on(X2,X1,X0) ),
inference(cnf_transformation,[],[f1663]) ).
fof(f3284,plain,
spl104_92,
inference(avatar_split_clause,[],[f2224,f3282]) ).
fof(f3282,plain,
( spl104_92
<=> ! [X2,X0,X1] :
( c_Relation_Ototal__on(X2,X1,X0)
| ~ c_Order__Relation_Olinear__order__on(X2,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_92])]) ).
fof(f2224,plain,
! [X2,X0,X1] :
( c_Relation_Ototal__on(X2,X1,X0)
| ~ c_Order__Relation_Olinear__order__on(X2,X1,X0) ),
inference(cnf_transformation,[],[f1661]) ).
fof(f3280,plain,
spl104_91,
inference(avatar_split_clause,[],[f2223,f3278]) ).
fof(f3278,plain,
( spl104_91
<=> ! [X2,X0,X1] :
( c_Order__Relation_Opartial__order__on(X2,X1,X0)
| ~ c_Order__Relation_Olinear__order__on(X2,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_91])]) ).
fof(f2223,plain,
! [X2,X0,X1] :
( c_Order__Relation_Opartial__order__on(X2,X1,X0)
| ~ c_Order__Relation_Olinear__order__on(X2,X1,X0) ),
inference(cnf_transformation,[],[f1661]) ).
fof(f3276,plain,
spl104_90,
inference(avatar_split_clause,[],[f2215,f3274]) ).
fof(f3274,plain,
( spl104_90
<=> ! [X2,X0,X1] :
( c_Order__Relation_Olinear__order__on(X2,X1,X0)
| ~ c_Order__Relation_Owell__order__on(X2,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_90])]) ).
fof(f2215,plain,
! [X2,X0,X1] :
( c_Order__Relation_Olinear__order__on(X2,X1,X0)
| ~ c_Order__Relation_Owell__order__on(X2,X1,X0) ),
inference(cnf_transformation,[],[f1234]) ).
fof(f3272,plain,
spl104_89,
inference(avatar_split_clause,[],[f2214,f3270]) ).
fof(f3270,plain,
( spl104_89
<=> ! [X2,X0,X1] :
( c_Relation_Ototal__on(X2,X1,X0)
| ~ c_Order__Relation_Ostrict__linear__order__on(X2,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_89])]) ).
fof(f2214,plain,
! [X2,X0,X1] :
( c_Relation_Ototal__on(X2,X1,X0)
| ~ c_Order__Relation_Ostrict__linear__order__on(X2,X1,X0) ),
inference(cnf_transformation,[],[f1233]) ).
fof(f1233,plain,
! [X0,X1,X2] :
( ( c_Relation_Ototal__on(X2,X1,X0)
& c_Relation_Oirrefl(X2,X0)
& c_Relation_Otrans(X2,X0) )
| ~ c_Order__Relation_Ostrict__linear__order__on(X2,X1,X0) ),
inference(ennf_transformation,[],[f1018]) ).
fof(f1018,plain,
! [X0,X1,X2] :
( c_Order__Relation_Ostrict__linear__order__on(X2,X1,X0)
=> ( c_Relation_Ototal__on(X2,X1,X0)
& c_Relation_Oirrefl(X2,X0)
& c_Relation_Otrans(X2,X0) ) ),
inference(unused_predicate_definition_removal,[],[f772]) ).
fof(f772,plain,
! [X0,X1,X2] :
( c_Order__Relation_Ostrict__linear__order__on(X2,X1,X0)
<=> ( c_Relation_Ototal__on(X2,X1,X0)
& c_Relation_Oirrefl(X2,X0)
& c_Relation_Otrans(X2,X0) ) ),
inference(rectify,[],[f34]) ).
fof(f34,axiom,
! [X3,X11,X4] :
( c_Order__Relation_Ostrict__linear__order__on(X4,X11,X3)
<=> ( c_Relation_Ototal__on(X4,X11,X3)
& c_Relation_Oirrefl(X4,X3)
& c_Relation_Otrans(X4,X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_strict__linear__order__on__def) ).
fof(f3268,plain,
spl104_88,
inference(avatar_split_clause,[],[f2198,f3266]) ).
fof(f3266,plain,
( spl104_88
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1)
| ~ sP3(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_88])]) ).
fof(f2198,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1)
| ~ sP3(X0,X1,X2) ),
inference(cnf_transformation,[],[f1647]) ).
fof(f3264,plain,
spl104_87,
inference(avatar_split_clause,[],[f1988,f3262]) ).
fof(f1988,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ),
inference(cnf_transformation,[],[f1059]) ).
fof(f1059,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ),
inference(ennf_transformation,[],[f618]) ).
fof(f618,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ),
inference(rectify,[],[f290]) ).
fof(f290,axiom,
! [X59,X58] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X58,X59)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X58,X59) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_termination__basic__simps_I5_J) ).
fof(f3260,plain,
spl104_86,
inference(avatar_split_clause,[],[f1982,f3258]) ).
fof(f1982,plain,
! [X0,X1] :
( c_Wellfounded_Owf(X1,c_Transitive__Closure_Otrancl(X1,X0))
| ~ c_Wellfounded_Owf(X1,X0) ),
inference(cnf_transformation,[],[f1053]) ).
fof(f1053,plain,
! [X0,X1] :
( c_Wellfounded_Owf(X1,c_Transitive__Closure_Otrancl(X1,X0))
| ~ c_Wellfounded_Owf(X1,X0) ),
inference(ennf_transformation,[],[f612]) ).
fof(f612,plain,
! [X0,X1] :
( c_Wellfounded_Owf(X1,X0)
=> c_Wellfounded_Owf(X1,c_Transitive__Closure_Otrancl(X1,X0)) ),
inference(rectify,[],[f163]) ).
fof(f163,axiom,
! [X3,X4] :
( c_Wellfounded_Owf(X4,X3)
=> c_Wellfounded_Owf(X4,c_Transitive__Closure_Otrancl(X4,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__trancl) ).
fof(f3256,plain,
spl104_85,
inference(avatar_split_clause,[],[f1978,f3254]) ).
fof(f1978,plain,
! [X0,X1] :
( c_Transitive__Closure_Otrancl(X1,X0) = X0
| ~ c_Relation_Otrans(X1,X0) ),
inference(cnf_transformation,[],[f1048]) ).
fof(f1048,plain,
! [X0,X1] :
( c_Transitive__Closure_Otrancl(X1,X0) = X0
| ~ c_Relation_Otrans(X1,X0) ),
inference(ennf_transformation,[],[f608]) ).
fof(f608,plain,
! [X0,X1] :
( c_Relation_Otrans(X1,X0)
=> c_Transitive__Closure_Otrancl(X1,X0) = X0 ),
inference(rectify,[],[f84]) ).
fof(f84,axiom,
! [X3,X4] :
( c_Relation_Otrans(X4,X3)
=> c_Transitive__Closure_Otrancl(X4,X3) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trancl__id) ).
fof(f3252,plain,
spl104_84,
inference(avatar_split_clause,[],[f1973,f3250]) ).
fof(f1973,plain,
! [X0,X1] :
( c_Lattices_Osemilattice__sup__class_Osup(X1,X0,X0) = X0
| ~ class_Lattices_Osemilattice__sup(X1) ),
inference(cnf_transformation,[],[f1042]) ).
fof(f1042,plain,
! [X0,X1] :
( c_Lattices_Osemilattice__sup__class_Osup(X1,X0,X0) = X0
| ~ class_Lattices_Osemilattice__sup(X1) ),
inference(ennf_transformation,[],[f603]) ).
fof(f603,plain,
! [X0,X1] :
( class_Lattices_Osemilattice__sup(X1)
=> c_Lattices_Osemilattice__sup__class_Osup(X1,X0,X0) = X0 ),
inference(rectify,[],[f172]) ).
fof(f172,axiom,
! [X27,X4] :
( class_Lattices_Osemilattice__sup(X4)
=> c_Lattices_Osemilattice__sup__class_Osup(X4,X27,X27) = X27 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup_Oidem) ).
fof(f3248,plain,
spl104_83,
inference(avatar_split_clause,[],[f1958,f3246]) ).
fof(f3246,plain,
( spl104_83
<=> ! [X0,X1] :
( X0 = X1
| ~ hBOOL(hAPP(c_fequal(X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_83])]) ).
fof(f1958,plain,
! [X0,X1] :
( X0 = X1
| ~ hBOOL(hAPP(c_fequal(X1),X0)) ),
inference(cnf_transformation,[],[f588]) ).
fof(f588,plain,
! [X0,X1] :
( X0 = X1
| ~ hBOOL(hAPP(c_fequal(X1),X0)) ),
inference(rectify,[],[f521]) ).
fof(f521,axiom,
! [X12,X13] :
( X12 = X13
| ~ hBOOL(hAPP(c_fequal(X13),X12)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__fequal__1) ).
fof(f3244,plain,
spl104_82,
inference(avatar_split_clause,[],[f1957,f3242]) ).
fof(f1957,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ),
inference(cnf_transformation,[],[f587]) ).
fof(f587,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ),
inference(rectify,[],[f376]) ).
fof(f376,axiom,
! [X70,X71] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X70,X71)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X71,X70) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__le__linear) ).
fof(f3240,plain,
spl104_81,
inference(avatar_split_clause,[],[f1931,f3238]) ).
fof(f1931,plain,
! [X0,X1] : c_Relation_OImage(X1,X1,c_Relation_OId(X1),X0) = X0,
inference(cnf_transformation,[],[f561]) ).
fof(f561,plain,
! [X0,X1] : c_Relation_OImage(X1,X1,c_Relation_OId(X1),X0) = X0,
inference(rectify,[],[f475]) ).
fof(f475,axiom,
! [X11,X4] : c_Relation_OImage(X4,X4,c_Relation_OId(X4),X11) = X11,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Image__Id) ).
fof(f3236,plain,
spl104_80,
inference(avatar_split_clause,[],[f1930,f3234]) ).
fof(f1930,plain,
! [X0,X1] : c_Relation_ODomain(X1,X1,c_Relation_OId__on(X1,X0)) = X0,
inference(cnf_transformation,[],[f560]) ).
fof(f560,plain,
! [X0,X1] : c_Relation_ODomain(X1,X1,c_Relation_OId__on(X1,X0)) = X0,
inference(rectify,[],[f29]) ).
fof(f29,axiom,
! [X11,X4] : c_Relation_ODomain(X4,X4,c_Relation_OId__on(X4,X11)) = X11,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Domain__Id__on) ).
fof(f3232,plain,
spl104_79,
inference(avatar_split_clause,[],[f1929,f3230]) ).
fof(f1929,plain,
! [X0,X1] : c_Relation_ORange(X1,X1,c_Relation_OId__on(X1,X0)) = X0,
inference(cnf_transformation,[],[f559]) ).
fof(f559,plain,
! [X0,X1] : c_Relation_ORange(X1,X1,c_Relation_OId__on(X1,X0)) = X0,
inference(rectify,[],[f28]) ).
fof(f28,axiom,
! [X11,X4] : c_Relation_ORange(X4,X4,c_Relation_OId__on(X4,X11)) = X11,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Range__Id__on) ).
fof(f3228,plain,
spl104_78,
inference(avatar_split_clause,[],[f1928,f3226]) ).
fof(f1928,plain,
! [X0,X1] : c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool),X0,X0) = X0,
inference(cnf_transformation,[],[f558]) ).
fof(f558,plain,
! [X0,X1] : c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool),X0,X0) = X0,
inference(rectify,[],[f121]) ).
fof(f121,axiom,
! [X11,X4] : c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool),X11,X11) = X11,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__absorb) ).
fof(f3223,plain,
spl104_77,
inference(avatar_split_clause,[],[f1904,f3221]) ).
fof(f1904,plain,
! [X0] : c_Wellfounded_Owf(X0,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X0,X0),tc_HOL_Obool))),
inference(cnf_transformation,[],[f534]) ).
fof(f534,plain,
! [X0] : c_Wellfounded_Owf(X0,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X0,X0),tc_HOL_Obool))),
inference(rectify,[],[f394]) ).
fof(f394,axiom,
! [X4] : c_Wellfounded_Owf(X4,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X4,X4),tc_HOL_Obool))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__empty) ).
fof(f3218,plain,
spl104_76,
inference(avatar_split_clause,[],[f1903,f3216]) ).
fof(f3216,plain,
( spl104_76
<=> ! [X0] : c_Relation_Oantisym(X0,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X0,X0),tc_HOL_Obool))) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_76])]) ).
fof(f1903,plain,
! [X0] : c_Relation_Oantisym(X0,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X0,X0),tc_HOL_Obool))),
inference(cnf_transformation,[],[f533]) ).
fof(f533,plain,
! [X0] : c_Relation_Oantisym(X0,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X0,X0),tc_HOL_Obool))),
inference(rectify,[],[f408]) ).
fof(f408,axiom,
! [X4] : c_Relation_Oantisym(X4,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X4,X4),tc_HOL_Obool))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_antisym__empty) ).
fof(f3214,plain,
( spl104_75
| ~ spl104_22
| ~ spl104_53 ),
inference(avatar_split_clause,[],[f3138,f3111,f2982,f3211]) ).
fof(f3211,plain,
( spl104_75
<=> sP2(tc_Nat_Onat,c_Wellfounded_Oless__than) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_75])]) ).
fof(f2982,plain,
( spl104_22
<=> c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Oless__than) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_22])]) ).
fof(f3138,plain,
( sP2(tc_Nat_Onat,c_Wellfounded_Oless__than)
| ~ spl104_22
| ~ spl104_53 ),
inference(resolution,[],[f3112,f2984]) ).
fof(f2984,plain,
( c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Oless__than)
| ~ spl104_22 ),
inference(avatar_component_clause,[],[f2982]) ).
fof(f3209,plain,
( spl104_74
| ~ spl104_21
| ~ spl104_53 ),
inference(avatar_split_clause,[],[f3137,f3111,f2977,f3206]) ).
fof(f3206,plain,
( spl104_74
<=> sP2(tc_Nat_Onat,c_Wellfounded_Opred__nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_74])]) ).
fof(f2977,plain,
( spl104_21
<=> c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Opred__nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_21])]) ).
fof(f3137,plain,
( sP2(tc_Nat_Onat,c_Wellfounded_Opred__nat)
| ~ spl104_21
| ~ spl104_53 ),
inference(resolution,[],[f3112,f2979]) ).
fof(f2979,plain,
( c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Opred__nat)
| ~ spl104_21 ),
inference(avatar_component_clause,[],[f2977]) ).
fof(f3204,plain,
spl104_73,
inference(avatar_split_clause,[],[f2801,f3202]) ).
fof(f2801,plain,
! [X2,X3,X1] : hBOOL(hAPP(c_Set_Oinsert(X3,X2,X1),X2)),
inference(equality_resolution,[],[f2432]) ).
fof(f2432,plain,
! [X2,X3,X0,X1] :
( hBOOL(hAPP(c_Set_Oinsert(X3,X2,X1),X0))
| X0 != X2 ),
inference(cnf_transformation,[],[f1736]) ).
fof(f3200,plain,
spl104_72,
inference(avatar_split_clause,[],[f2230,f3198]) ).
fof(f3198,plain,
( spl104_72
<=> ! [X2,X0,X1] :
( c_Relation_Otrans(X2,X0)
| ~ c_Order__Relation_Opreorder__on(X2,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_72])]) ).
fof(f2230,plain,
! [X2,X0,X1] :
( c_Relation_Otrans(X2,X0)
| ~ c_Order__Relation_Opreorder__on(X2,X1,X0) ),
inference(cnf_transformation,[],[f1665]) ).
fof(f3196,plain,
spl104_71,
inference(avatar_split_clause,[],[f2227,f3194]) ).
fof(f3194,plain,
( spl104_71
<=> ! [X2,X0,X1] :
( c_Relation_Oantisym(X2,X0)
| ~ c_Order__Relation_Opartial__order__on(X2,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_71])]) ).
fof(f2227,plain,
! [X2,X0,X1] :
( c_Relation_Oantisym(X2,X0)
| ~ c_Order__Relation_Opartial__order__on(X2,X1,X0) ),
inference(cnf_transformation,[],[f1663]) ).
fof(f3192,plain,
spl104_70,
inference(avatar_split_clause,[],[f2213,f3190]) ).
fof(f3190,plain,
( spl104_70
<=> ! [X2,X0,X1] :
( c_Relation_Oirrefl(X2,X0)
| ~ c_Order__Relation_Ostrict__linear__order__on(X2,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_70])]) ).
fof(f2213,plain,
! [X2,X0,X1] :
( c_Relation_Oirrefl(X2,X0)
| ~ c_Order__Relation_Ostrict__linear__order__on(X2,X1,X0) ),
inference(cnf_transformation,[],[f1233]) ).
fof(f3188,plain,
spl104_69,
inference(avatar_split_clause,[],[f2212,f3186]) ).
fof(f3186,plain,
( spl104_69
<=> ! [X2,X0,X1] :
( c_Relation_Otrans(X2,X0)
| ~ c_Order__Relation_Ostrict__linear__order__on(X2,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_69])]) ).
fof(f2212,plain,
! [X2,X0,X1] :
( c_Relation_Otrans(X2,X0)
| ~ c_Order__Relation_Ostrict__linear__order__on(X2,X1,X0) ),
inference(cnf_transformation,[],[f1233]) ).
fof(f3184,plain,
spl104_68,
inference(avatar_split_clause,[],[f2048,f3182]) ).
fof(f3182,plain,
( spl104_68
<=> ! [X2,X0,X1] : c_member(X2,X1,c_Set_Oinsert(X2,X1,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_68])]) ).
fof(f2048,plain,
! [X2,X0,X1] : c_member(X2,X1,c_Set_Oinsert(X2,X1,X0)),
inference(cnf_transformation,[],[f646]) ).
fof(f646,plain,
! [X0,X1,X2] : c_member(X2,X1,c_Set_Oinsert(X2,X1,X0)),
inference(rectify,[],[f141]) ).
fof(f141,axiom,
! [X10,X9,X4] : c_member(X4,X9,c_Set_Oinsert(X4,X9,X10)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insertI1) ).
fof(f3180,plain,
spl104_67,
inference(avatar_split_clause,[],[f1965,f3178]) ).
fof(f1965,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X1,c_Orderings_Obot__class_Obot(X1),X0)
| ~ class_Orderings_Obot(X1) ),
inference(cnf_transformation,[],[f1034]) ).
fof(f1034,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X1,c_Orderings_Obot__class_Obot(X1),X0)
| ~ class_Orderings_Obot(X1) ),
inference(ennf_transformation,[],[f595]) ).
fof(f595,plain,
! [X0,X1] :
( class_Orderings_Obot(X1)
=> c_Orderings_Oord__class_Oless__eq(X1,c_Orderings_Obot__class_Obot(X1),X0) ),
inference(rectify,[],[f438]) ).
fof(f438,axiom,
! [X58,X4] :
( class_Orderings_Obot(X4)
=> c_Orderings_Oord__class_Oless__eq(X4,c_Orderings_Obot__class_Obot(X4),X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bot__least) ).
fof(f3176,plain,
( spl104_66
| ~ spl104_22
| ~ spl104_52 ),
inference(avatar_split_clause,[],[f3135,f3107,f2982,f3173]) ).
fof(f3173,plain,
( spl104_66
<=> c_Wellfounded_Oacyclic(tc_Nat_Onat,c_Wellfounded_Oless__than) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_66])]) ).
fof(f3135,plain,
( c_Wellfounded_Oacyclic(tc_Nat_Onat,c_Wellfounded_Oless__than)
| ~ spl104_22
| ~ spl104_52 ),
inference(resolution,[],[f3108,f2984]) ).
fof(f3171,plain,
spl104_65,
inference(avatar_split_clause,[],[f1927,f3169]) ).
fof(f1927,plain,
! [X0,X1] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0),X1),
inference(cnf_transformation,[],[f557]) ).
fof(f557,plain,
! [X0,X1] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0),X1),
inference(rectify,[],[f386]) ).
fof(f386,axiom,
! [X70,X71] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X71,X70),X71),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__le__self) ).
fof(f3167,plain,
spl104_64,
inference(avatar_split_clause,[],[f1926,f3165]) ).
fof(f1926,plain,
! [X0,X1] : c_Relation_Ototal__on(X1,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),X0),
inference(cnf_transformation,[],[f556]) ).
fof(f556,plain,
! [X0,X1] : c_Relation_Ototal__on(X1,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),X0),
inference(rectify,[],[f409]) ).
fof(f409,axiom,
! [X3,X4] : c_Relation_Ototal__on(X4,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)),X3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_total__on__empty) ).
fof(f3163,plain,
spl104_63,
inference(avatar_split_clause,[],[f1924,f3161]) ).
fof(f1924,plain,
! [X0,X1] : ~ c_member(X1,X0,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),
inference(cnf_transformation,[],[f554]) ).
fof(f554,plain,
! [X0,X1] : ~ c_member(X1,X0,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),
inference(rectify,[],[f405]) ).
fof(f405,axiom,
! [X7,X4] : ~ c_member(X4,X7,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_empty__iff) ).
fof(f3159,plain,
spl104_62,
inference(avatar_split_clause,[],[f1890,f3156]) ).
fof(f1890,plain,
c_FunDef_Opair__less = c_Wellfounded_Olex__prod(tc_Nat_Onat,tc_Nat_Onat,c_Wellfounded_Oless__than,c_Wellfounded_Oless__than),
inference(cnf_transformation,[],[f443]) ).
fof(f443,axiom,
c_FunDef_Opair__less = c_Wellfounded_Olex__prod(tc_Nat_Onat,tc_Nat_Onat,c_Wellfounded_Oless__than,c_Wellfounded_Oless__than),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pair__less__def) ).
fof(f3154,plain,
spl104_61,
inference(avatar_split_clause,[],[f1889,f3151]) ).
fof(f1889,plain,
c_FunDef_Omin__strict = c_Wellfounded_Omin__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less),
inference(cnf_transformation,[],[f465]) ).
fof(f465,axiom,
c_FunDef_Omin__strict = c_Wellfounded_Omin__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__strict__def) ).
fof(f3149,plain,
spl104_60,
inference(avatar_split_clause,[],[f1888,f3146]) ).
fof(f1888,plain,
c_FunDef_Omax__strict = c_Wellfounded_Omax__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less),
inference(cnf_transformation,[],[f463]) ).
fof(f463,axiom,
c_FunDef_Omax__strict = c_Wellfounded_Omax__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_max__strict__def) ).
fof(f3144,plain,
( spl104_59
| ~ spl104_21
| ~ spl104_52 ),
inference(avatar_split_clause,[],[f3134,f3107,f2977,f3141]) ).
fof(f3134,plain,
( c_Wellfounded_Oacyclic(tc_Nat_Onat,c_Wellfounded_Opred__nat)
| ~ spl104_21
| ~ spl104_52 ),
inference(resolution,[],[f3108,f2979]) ).
fof(f3133,plain,
spl104_58,
inference(avatar_split_clause,[],[f2768,f3131]) ).
fof(f2768,plain,
! [X2,X1] : ~ c_Orderings_Oord__class_Oless(tc_fun(X2,tc_HOL_Obool),X1,X1),
inference(equality_resolution,[],[f2241]) ).
fof(f2241,plain,
! [X2,X0,X1] :
( X0 != X1
| ~ c_Orderings_Oord__class_Oless(tc_fun(X2,tc_HOL_Obool),X1,X0) ),
inference(cnf_transformation,[],[f1674]) ).
fof(f3129,plain,
spl104_57,
inference(avatar_split_clause,[],[f2754,f3127]) ).
fof(f2754,plain,
! [X2,X1] :
( c_Orderings_Oord__class_Oless__eq(X2,X1,X1)
| ~ class_Orderings_Oorder(X2) ),
inference(equality_resolution,[],[f2133]) ).
fof(f2133,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X2,X0,X1)
| X0 != X1
| ~ class_Orderings_Oorder(X2) ),
inference(cnf_transformation,[],[f1632]) ).
fof(f1632,plain,
! [X0,X1,X2] :
( ( ( X0 = X1
| ~ c_Orderings_Oord__class_Oless__eq(X2,X0,X1)
| ~ c_Orderings_Oord__class_Oless__eq(X2,X1,X0) )
& ( ( c_Orderings_Oord__class_Oless__eq(X2,X0,X1)
& c_Orderings_Oord__class_Oless__eq(X2,X1,X0) )
| X0 != X1 ) )
| ~ class_Orderings_Oorder(X2) ),
inference(flattening,[],[f1631]) ).
fof(f1631,plain,
! [X0,X1,X2] :
( ( ( X0 = X1
| ~ c_Orderings_Oord__class_Oless__eq(X2,X0,X1)
| ~ c_Orderings_Oord__class_Oless__eq(X2,X1,X0) )
& ( ( c_Orderings_Oord__class_Oless__eq(X2,X0,X1)
& c_Orderings_Oord__class_Oless__eq(X2,X1,X0) )
| X0 != X1 ) )
| ~ class_Orderings_Oorder(X2) ),
inference(nnf_transformation,[],[f1160]) ).
fof(f1160,plain,
! [X0,X1,X2] :
( ( X0 = X1
<=> ( c_Orderings_Oord__class_Oless__eq(X2,X0,X1)
& c_Orderings_Oord__class_Oless__eq(X2,X1,X0) ) )
| ~ class_Orderings_Oorder(X2) ),
inference(ennf_transformation,[],[f716]) ).
fof(f716,plain,
! [X0,X1,X2] :
( class_Orderings_Oorder(X2)
=> ( X0 = X1
<=> ( c_Orderings_Oord__class_Oless__eq(X2,X0,X1)
& c_Orderings_Oord__class_Oless__eq(X2,X1,X0) ) ) ),
inference(rectify,[],[f298]) ).
fof(f298,axiom,
! [X12,X13,X4] :
( class_Orderings_Oorder(X4)
=> ( X12 = X13
<=> ( c_Orderings_Oord__class_Oless__eq(X4,X12,X13)
& c_Orderings_Oord__class_Oless__eq(X4,X13,X12) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__eq__iff) ).
fof(f3125,plain,
spl104_56,
inference(avatar_split_clause,[],[f2750,f3123]) ).
fof(f2750,plain,
! [X2,X1] :
( ~ c_Orderings_Oord__class_Oless(X2,X1,X1)
| ~ class_Orderings_Oorder(X2) ),
inference(equality_resolution,[],[f2119]) ).
fof(f2119,plain,
! [X2,X0,X1] :
( X0 != X1
| ~ c_Orderings_Oord__class_Oless(X2,X1,X0)
| ~ class_Orderings_Oorder(X2) ),
inference(cnf_transformation,[],[f1137]) ).
fof(f1137,plain,
! [X0,X1,X2] :
( X0 != X1
| ~ c_Orderings_Oord__class_Oless(X2,X1,X0)
| ~ class_Orderings_Oorder(X2) ),
inference(flattening,[],[f1136]) ).
fof(f1136,plain,
! [X0,X1,X2] :
( X0 != X1
| ~ c_Orderings_Oord__class_Oless(X2,X1,X0)
| ~ class_Orderings_Oorder(X2) ),
inference(ennf_transformation,[],[f704]) ).
fof(f704,plain,
! [X0,X1,X2] :
( class_Orderings_Oorder(X2)
=> ( c_Orderings_Oord__class_Oless(X2,X1,X0)
=> X0 != X1 ) ),
inference(rectify,[],[f320]) ).
fof(f320,axiom,
! [X59,X58,X4] :
( class_Orderings_Oorder(X4)
=> ( c_Orderings_Oord__class_Oless(X4,X58,X59)
=> X58 != X59 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__imp__not__eq2) ).
fof(f3121,plain,
spl104_55,
inference(avatar_split_clause,[],[f2744,f3119]) ).
fof(f3119,plain,
( spl104_55
<=> ! [X2,X1] :
( ~ c_Orderings_Oord__class_Oless(X2,X1,X1)
| ~ class_Orderings_Olinorder(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_55])]) ).
fof(f2744,plain,
! [X2,X1] :
( ~ c_Orderings_Oord__class_Oless(X2,X1,X1)
| ~ class_Orderings_Olinorder(X2) ),
inference(equality_resolution,[],[f2086]) ).
fof(f2086,plain,
! [X2,X0,X1] :
( X0 != X1
| ~ c_Orderings_Oord__class_Oless(X2,X0,X1)
| ~ class_Orderings_Olinorder(X2) ),
inference(cnf_transformation,[],[f1621]) ).
fof(f1621,plain,
! [X0,X1,X2] :
( ( ( X0 != X1
| ( ~ c_Orderings_Oord__class_Oless(X2,X0,X1)
& ~ c_Orderings_Oord__class_Oless(X2,X1,X0) ) )
& ( c_Orderings_Oord__class_Oless(X2,X0,X1)
| c_Orderings_Oord__class_Oless(X2,X1,X0)
| X0 = X1 ) )
| ~ class_Orderings_Olinorder(X2) ),
inference(flattening,[],[f1620]) ).
fof(f1620,plain,
! [X0,X1,X2] :
( ( ( X0 != X1
| ( ~ c_Orderings_Oord__class_Oless(X2,X0,X1)
& ~ c_Orderings_Oord__class_Oless(X2,X1,X0) ) )
& ( c_Orderings_Oord__class_Oless(X2,X0,X1)
| c_Orderings_Oord__class_Oless(X2,X1,X0)
| X0 = X1 ) )
| ~ class_Orderings_Olinorder(X2) ),
inference(nnf_transformation,[],[f1103]) ).
fof(f1103,plain,
! [X0,X1,X2] :
( ( X0 != X1
<=> ( c_Orderings_Oord__class_Oless(X2,X0,X1)
| c_Orderings_Oord__class_Oless(X2,X1,X0) ) )
| ~ class_Orderings_Olinorder(X2) ),
inference(ennf_transformation,[],[f679]) ).
fof(f679,plain,
! [X0,X1,X2] :
( class_Orderings_Olinorder(X2)
=> ( X0 != X1
<=> ( c_Orderings_Oord__class_Oless(X2,X0,X1)
| c_Orderings_Oord__class_Oless(X2,X1,X0) ) ) ),
inference(rectify,[],[f311]) ).
fof(f311,axiom,
! [X12,X13,X4] :
( class_Orderings_Olinorder(X4)
=> ( X12 != X13
<=> ( c_Orderings_Oord__class_Oless(X4,X12,X13)
| c_Orderings_Oord__class_Oless(X4,X13,X12) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__neq__iff) ).
fof(f3117,plain,
spl104_54,
inference(avatar_split_clause,[],[f2027,f3115]) ).
fof(f3115,plain,
( spl104_54
<=> ! [X0,X1] :
( c_Wellfounded_Owf(X1,X0)
| ~ sP2(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_54])]) ).
fof(f2027,plain,
! [X0,X1] :
( c_Wellfounded_Owf(X1,X0)
| ~ sP2(X1,X0) ),
inference(cnf_transformation,[],[f1599]) ).
fof(f1599,plain,
! [X0,X1] :
( ( c_Wellfounded_Owf(X1,X0)
| ~ sP2(X1,X0) )
& ( sP2(X1,X0)
| ~ c_Wellfounded_Owf(X1,X0) ) ),
inference(nnf_transformation,[],[f1530]) ).
fof(f1530,plain,
! [X0,X1] :
( c_Wellfounded_Owf(X1,X0)
<=> sP2(X1,X0) ),
inference(definition_folding,[],[f1078,f1529]) ).
fof(f1078,plain,
! [X0,X1] :
( c_Wellfounded_Owf(X1,X0)
<=> ! [X2] :
( ? [X4] :
( ! [X5] :
( ~ c_member(X1,X5,X2)
| ~ c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,X5,X4),X0) )
& c_member(X1,X4,X2) )
| ! [X3] : ~ c_member(X1,X3,X2) ) ),
inference(ennf_transformation,[],[f636]) ).
fof(f636,plain,
! [X0,X1] :
( c_Wellfounded_Owf(X1,X0)
<=> ! [X2] :
( ? [X3] : c_member(X1,X3,X2)
=> ? [X4] :
( ! [X5] :
( c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,X5,X4),X0)
=> ~ c_member(X1,X5,X2) )
& c_member(X1,X4,X2) ) ) ),
inference(rectify,[],[f193]) ).
fof(f193,axiom,
! [X3,X4] :
( c_Wellfounded_Owf(X4,X3)
<=> ! [X64] :
( ? [X2] : c_member(X4,X2,X64)
=> ? [X2] :
( ! [X5] :
( c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X5,X2),X3)
=> ~ c_member(X4,X5,X64) )
& c_member(X4,X2,X64) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__eq__minimal) ).
fof(f3113,plain,
spl104_53,
inference(avatar_split_clause,[],[f2026,f3111]) ).
fof(f2026,plain,
! [X0,X1] :
( sP2(X1,X0)
| ~ c_Wellfounded_Owf(X1,X0) ),
inference(cnf_transformation,[],[f1599]) ).
fof(f3109,plain,
spl104_52,
inference(avatar_split_clause,[],[f1981,f3107]) ).
fof(f1981,plain,
! [X0,X1] :
( c_Wellfounded_Oacyclic(X1,X0)
| ~ c_Wellfounded_Owf(X1,X0) ),
inference(cnf_transformation,[],[f1052]) ).
fof(f1052,plain,
! [X0,X1] :
( c_Wellfounded_Oacyclic(X1,X0)
| ~ c_Wellfounded_Owf(X1,X0) ),
inference(ennf_transformation,[],[f611]) ).
fof(f611,plain,
! [X0,X1] :
( c_Wellfounded_Owf(X1,X0)
=> c_Wellfounded_Oacyclic(X1,X0) ),
inference(rectify,[],[f164]) ).
fof(f164,axiom,
! [X3,X4] :
( c_Wellfounded_Owf(X4,X3)
=> c_Wellfounded_Oacyclic(X4,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__acyclic) ).
fof(f3105,plain,
spl104_51,
inference(avatar_split_clause,[],[f1972,f3103]) ).
fof(f3103,plain,
( spl104_51
<=> ! [X0,X1] :
( class_Orderings_Oorder(tc_fun(X0,X1))
| ~ class_Orderings_Oorder(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_51])]) ).
fof(f1972,plain,
! [X0,X1] :
( class_Orderings_Oorder(tc_fun(X0,X1))
| ~ class_Orderings_Oorder(X1) ),
inference(cnf_transformation,[],[f1041]) ).
fof(f1041,plain,
! [X0,X1] :
( class_Orderings_Oorder(tc_fun(X0,X1))
| ~ class_Orderings_Oorder(X1) ),
inference(ennf_transformation,[],[f602]) ).
fof(f602,plain,
! [X0,X1] :
( class_Orderings_Oorder(X1)
=> class_Orderings_Oorder(tc_fun(X0,X1)) ),
inference(rectify,[],[f501]) ).
fof(f501,axiom,
! [X89,X90] :
( class_Orderings_Oorder(X90)
=> class_Orderings_Oorder(tc_fun(X89,X90)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Orderings_Oorder) ).
fof(f3101,plain,
spl104_50,
inference(avatar_split_clause,[],[f1971,f3099]) ).
fof(f1971,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X1,X0,X0)
| ~ class_Orderings_Opreorder(X1) ),
inference(cnf_transformation,[],[f1040]) ).
fof(f1040,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X1,X0,X0)
| ~ class_Orderings_Opreorder(X1) ),
inference(ennf_transformation,[],[f601]) ).
fof(f601,plain,
! [X0,X1] :
( class_Orderings_Opreorder(X1)
=> c_Orderings_Oord__class_Oless__eq(X1,X0,X0) ),
inference(rectify,[],[f283]) ).
fof(f283,axiom,
! [X58,X4] :
( class_Orderings_Opreorder(X4)
=> c_Orderings_Oord__class_Oless__eq(X4,X58,X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__refl) ).
fof(f3097,plain,
spl104_49,
inference(avatar_split_clause,[],[f1970,f3095]) ).
fof(f3095,plain,
( spl104_49
<=> ! [X0,X1] :
( class_Orderings_Opreorder(tc_fun(X0,X1))
| ~ class_Orderings_Opreorder(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_49])]) ).
fof(f1970,plain,
! [X0,X1] :
( class_Orderings_Opreorder(tc_fun(X0,X1))
| ~ class_Orderings_Opreorder(X1) ),
inference(cnf_transformation,[],[f1039]) ).
fof(f1039,plain,
! [X0,X1] :
( class_Orderings_Opreorder(tc_fun(X0,X1))
| ~ class_Orderings_Opreorder(X1) ),
inference(ennf_transformation,[],[f600]) ).
fof(f600,plain,
! [X0,X1] :
( class_Orderings_Opreorder(X1)
=> class_Orderings_Opreorder(tc_fun(X0,X1)) ),
inference(rectify,[],[f499]) ).
fof(f499,axiom,
! [X89,X90] :
( class_Orderings_Opreorder(X90)
=> class_Orderings_Opreorder(tc_fun(X89,X90)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Orderings_Opreorder) ).
fof(f3093,plain,
spl104_48,
inference(avatar_split_clause,[],[f1969,f3091]) ).
fof(f3091,plain,
( spl104_48
<=> ! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless(X1,X0,X0)
| ~ class_Orderings_Opreorder(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_48])]) ).
fof(f1969,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless(X1,X0,X0)
| ~ class_Orderings_Opreorder(X1) ),
inference(cnf_transformation,[],[f1038]) ).
fof(f1038,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless(X1,X0,X0)
| ~ class_Orderings_Opreorder(X1) ),
inference(ennf_transformation,[],[f599]) ).
fof(f599,plain,
! [X0,X1] :
( class_Orderings_Opreorder(X1)
=> ~ c_Orderings_Oord__class_Oless(X1,X0,X0) ),
inference(rectify,[],[f310]) ).
fof(f310,axiom,
! [X58,X4] :
( class_Orderings_Opreorder(X4)
=> ~ c_Orderings_Oord__class_Oless(X4,X58,X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__irrefl) ).
fof(f3089,plain,
spl104_47,
inference(avatar_split_clause,[],[f1968,f3087]) ).
fof(f1968,plain,
! [X0,X1] :
( class_Lattices_Osemilattice__sup(tc_fun(X0,X1))
| ~ class_Lattices_Olattice(X1) ),
inference(cnf_transformation,[],[f1037]) ).
fof(f1037,plain,
! [X0,X1] :
( class_Lattices_Osemilattice__sup(tc_fun(X0,X1))
| ~ class_Lattices_Olattice(X1) ),
inference(ennf_transformation,[],[f598]) ).
fof(f598,plain,
! [X0,X1] :
( class_Lattices_Olattice(X1)
=> class_Lattices_Osemilattice__sup(tc_fun(X0,X1)) ),
inference(rectify,[],[f498]) ).
fof(f498,axiom,
! [X89,X90] :
( class_Lattices_Olattice(X90)
=> class_Lattices_Osemilattice__sup(tc_fun(X89,X90)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Lattices_Osemilattice__sup) ).
fof(f3085,plain,
spl104_46,
inference(avatar_split_clause,[],[f1967,f3083]) ).
fof(f3083,plain,
( spl104_46
<=> ! [X0,X1] :
( class_Orderings_Oord(tc_fun(X0,X1))
| ~ class_Orderings_Oord(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_46])]) ).
fof(f1967,plain,
! [X0,X1] :
( class_Orderings_Oord(tc_fun(X0,X1))
| ~ class_Orderings_Oord(X1) ),
inference(cnf_transformation,[],[f1036]) ).
fof(f1036,plain,
! [X0,X1] :
( class_Orderings_Oord(tc_fun(X0,X1))
| ~ class_Orderings_Oord(X1) ),
inference(ennf_transformation,[],[f597]) ).
fof(f597,plain,
! [X0,X1] :
( class_Orderings_Oord(X1)
=> class_Orderings_Oord(tc_fun(X0,X1)) ),
inference(rectify,[],[f502]) ).
fof(f502,axiom,
! [X89,X90] :
( class_Orderings_Oord(X90)
=> class_Orderings_Oord(tc_fun(X89,X90)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Orderings_Oord) ).
fof(f3081,plain,
spl104_45,
inference(avatar_split_clause,[],[f1966,f3079]) ).
fof(f3079,plain,
( spl104_45
<=> ! [X0,X1] :
( class_Lattices_Olattice(tc_fun(X0,X1))
| ~ class_Lattices_Olattice(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_45])]) ).
fof(f1966,plain,
! [X0,X1] :
( class_Lattices_Olattice(tc_fun(X0,X1))
| ~ class_Lattices_Olattice(X1) ),
inference(cnf_transformation,[],[f1035]) ).
fof(f1035,plain,
! [X0,X1] :
( class_Lattices_Olattice(tc_fun(X0,X1))
| ~ class_Lattices_Olattice(X1) ),
inference(ennf_transformation,[],[f596]) ).
fof(f596,plain,
! [X0,X1] :
( class_Lattices_Olattice(X1)
=> class_Lattices_Olattice(tc_fun(X0,X1)) ),
inference(rectify,[],[f500]) ).
fof(f500,axiom,
! [X89,X90] :
( class_Lattices_Olattice(X90)
=> class_Lattices_Olattice(tc_fun(X89,X90)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Lattices_Olattice) ).
fof(f3077,plain,
spl104_44,
inference(avatar_split_clause,[],[f1964,f3075]) ).
fof(f3075,plain,
( spl104_44
<=> ! [X0,X1] :
( class_Orderings_Obot(tc_fun(X0,X1))
| ~ class_Orderings_Obot(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_44])]) ).
fof(f1964,plain,
! [X0,X1] :
( class_Orderings_Obot(tc_fun(X0,X1))
| ~ class_Orderings_Obot(X1) ),
inference(cnf_transformation,[],[f1033]) ).
fof(f1033,plain,
! [X0,X1] :
( class_Orderings_Obot(tc_fun(X0,X1))
| ~ class_Orderings_Obot(X1) ),
inference(ennf_transformation,[],[f594]) ).
fof(f594,plain,
! [X0,X1] :
( class_Orderings_Obot(X1)
=> class_Orderings_Obot(tc_fun(X0,X1)) ),
inference(rectify,[],[f503]) ).
fof(f503,axiom,
! [X89,X90] :
( class_Orderings_Obot(X90)
=> class_Orderings_Obot(tc_fun(X89,X90)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Orderings_Obot) ).
fof(f3073,plain,
spl104_43,
inference(avatar_split_clause,[],[f1963,f3071]) ).
fof(f3071,plain,
( spl104_43
<=> ! [X0,X1] :
( class_Groups_Ominus(tc_fun(X0,X1))
| ~ class_Groups_Ominus(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_43])]) ).
fof(f1963,plain,
! [X0,X1] :
( class_Groups_Ominus(tc_fun(X0,X1))
| ~ class_Groups_Ominus(X1) ),
inference(cnf_transformation,[],[f1032]) ).
fof(f1032,plain,
! [X0,X1] :
( class_Groups_Ominus(tc_fun(X0,X1))
| ~ class_Groups_Ominus(X1) ),
inference(ennf_transformation,[],[f593]) ).
fof(f593,plain,
! [X0,X1] :
( class_Groups_Ominus(X1)
=> class_Groups_Ominus(tc_fun(X0,X1)) ),
inference(rectify,[],[f504]) ).
fof(f504,axiom,
! [X89,X90] :
( class_Groups_Ominus(X90)
=> class_Groups_Ominus(tc_fun(X89,X90)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Groups_Ominus) ).
fof(f3069,plain,
spl104_42,
inference(avatar_split_clause,[],[f1960,f3067]) ).
fof(f1960,plain,
! [X0,X1] :
( class_Lattices_Obounded__lattice__bot(tc_fun(X0,X1))
| ~ class_Lattices_Obounded__lattice(X1) ),
inference(cnf_transformation,[],[f1029]) ).
fof(f1029,plain,
! [X0,X1] :
( class_Lattices_Obounded__lattice__bot(tc_fun(X0,X1))
| ~ class_Lattices_Obounded__lattice(X1) ),
inference(ennf_transformation,[],[f590]) ).
fof(f590,plain,
! [X0,X1] :
( class_Lattices_Obounded__lattice(X1)
=> class_Lattices_Obounded__lattice__bot(tc_fun(X0,X1)) ),
inference(rectify,[],[f497]) ).
fof(f497,axiom,
! [X89,X90] :
( class_Lattices_Obounded__lattice(X90)
=> class_Lattices_Obounded__lattice__bot(tc_fun(X89,X90)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Lattices_Obounded__lattice__bot) ).
fof(f3065,plain,
spl104_41,
inference(avatar_split_clause,[],[f1959,f3063]) ).
fof(f3063,plain,
( spl104_41
<=> ! [X0,X1] :
( class_Lattices_Obounded__lattice(tc_fun(X0,X1))
| ~ class_Lattices_Obounded__lattice(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_41])]) ).
fof(f1959,plain,
! [X0,X1] :
( class_Lattices_Obounded__lattice(tc_fun(X0,X1))
| ~ class_Lattices_Obounded__lattice(X1) ),
inference(cnf_transformation,[],[f1028]) ).
fof(f1028,plain,
! [X0,X1] :
( class_Lattices_Obounded__lattice(tc_fun(X0,X1))
| ~ class_Lattices_Obounded__lattice(X1) ),
inference(ennf_transformation,[],[f589]) ).
fof(f589,plain,
! [X0,X1] :
( class_Lattices_Obounded__lattice(X1)
=> class_Lattices_Obounded__lattice(tc_fun(X0,X1)) ),
inference(rectify,[],[f496]) ).
fof(f496,axiom,
! [X89,X90] :
( class_Lattices_Obounded__lattice(X90)
=> class_Lattices_Obounded__lattice(tc_fun(X89,X90)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Lattices_Obounded__lattice) ).
fof(f3061,plain,
spl104_40,
inference(avatar_split_clause,[],[f1923,f3059]) ).
fof(f3059,plain,
( spl104_40
<=> ! [X0,X1] : c_Relation_Osingle__valued(X1,X1,c_Relation_OId__on(X1,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_40])]) ).
fof(f1923,plain,
! [X0,X1] : c_Relation_Osingle__valued(X1,X1,c_Relation_OId__on(X1,X0)),
inference(cnf_transformation,[],[f553]) ).
fof(f553,plain,
! [X0,X1] : c_Relation_Osingle__valued(X1,X1,c_Relation_OId__on(X1,X0)),
inference(rectify,[],[f57]) ).
fof(f57,axiom,
! [X11,X4] : c_Relation_Osingle__valued(X4,X4,c_Relation_OId__on(X4,X11)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_single__valued__Id__on) ).
fof(f3057,plain,
spl104_39,
inference(avatar_split_clause,[],[f1922,f3055]) ).
fof(f1922,plain,
! [X0,X1] : c_Relation_Orefl__on(X1,X0,c_Relation_OId__on(X1,X0)),
inference(cnf_transformation,[],[f552]) ).
fof(f552,plain,
! [X0,X1] : c_Relation_Orefl__on(X1,X0,c_Relation_OId__on(X1,X0)),
inference(rectify,[],[f44]) ).
fof(f44,axiom,
! [X11,X4] : c_Relation_Orefl__on(X4,X11,c_Relation_OId__on(X4,X11)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_refl__on__Id__on) ).
fof(f3053,plain,
spl104_38,
inference(avatar_split_clause,[],[f1921,f3051]) ).
fof(f1921,plain,
! [X0,X1] : c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X0,X0),
inference(cnf_transformation,[],[f551]) ).
fof(f551,plain,
! [X0,X1] : c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X0,X0),
inference(rectify,[],[f235]) ).
fof(f235,axiom,
! [X11,X4] : c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool),X11,X11),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__refl) ).
fof(f3048,plain,
spl104_37,
inference(avatar_split_clause,[],[f2809,f3046]) ).
fof(f3046,plain,
( spl104_37
<=> ! [X2,X3] : sP10(X3,X2,X2,X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_37])]) ).
fof(f2809,plain,
! [X2,X3] : sP10(X3,X2,X2,X3),
inference(equality_resolution,[],[f2808]) ).
fof(f2808,plain,
! [X2,X3,X1] :
( sP10(X3,X1,X2,X3)
| X1 != X2 ),
inference(equality_resolution,[],[f2572]) ).
fof(f2572,plain,
! [X2,X3,X0,X1] :
( sP10(X0,X1,X2,X3)
| X0 != X3
| X1 != X2 ),
inference(cnf_transformation,[],[f1816]) ).
fof(f3044,plain,
spl104_36,
inference(avatar_split_clause,[],[f2807,f3042]) ).
fof(f3042,plain,
( spl104_36
<=> ! [X1,X3] : sP10(X1,X1,X3,X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_36])]) ).
fof(f2807,plain,
! [X3,X1] : sP10(X1,X1,X3,X3),
inference(equality_resolution,[],[f2806]) ).
fof(f2806,plain,
! [X2,X3,X1] :
( sP10(X1,X1,X2,X3)
| X2 != X3 ),
inference(equality_resolution,[],[f2573]) ).
fof(f2573,plain,
! [X2,X3,X0,X1] :
( sP10(X0,X1,X2,X3)
| X0 != X1
| X2 != X3 ),
inference(cnf_transformation,[],[f1816]) ).
fof(f3040,plain,
spl104_35,
inference(avatar_split_clause,[],[f2767,f3038]) ).
fof(f2767,plain,
! [X2,X1] : c_member(X2,X1,c_fequal(X1)),
inference(equality_resolution,[],[f2239]) ).
fof(f2239,plain,
! [X2,X0,X1] :
( c_member(X2,X1,c_fequal(X0))
| X0 != X1 ),
inference(cnf_transformation,[],[f1672]) ).
fof(f3036,plain,
spl104_34,
inference(avatar_split_clause,[],[f2729,f3034]) ).
fof(f2729,plain,
! [X1] : hBOOL(hAPP(c_fequal(X1),X1)),
inference(equality_resolution,[],[f1956]) ).
fof(f1956,plain,
! [X0,X1] :
( hBOOL(hAPP(c_fequal(X1),X0))
| X0 != X1 ),
inference(cnf_transformation,[],[f586]) ).
fof(f586,plain,
! [X0,X1] :
( hBOOL(hAPP(c_fequal(X1),X0))
| X0 != X1 ),
inference(rectify,[],[f522]) ).
fof(f522,axiom,
! [X12,X13] :
( hBOOL(hAPP(c_fequal(X13),X12))
| X12 != X13 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__fequal__2) ).
fof(f3032,plain,
spl104_33,
inference(avatar_split_clause,[],[f1918,f3030]) ).
fof(f1918,plain,
! [X0,X1] : c_Relation_Otrans(X1,c_Transitive__Closure_Otrancl(X1,X0)),
inference(cnf_transformation,[],[f548]) ).
fof(f548,plain,
! [X0,X1] : c_Relation_Otrans(X1,c_Transitive__Closure_Otrancl(X1,X0)),
inference(rectify,[],[f83]) ).
fof(f83,axiom,
! [X3,X4] : c_Relation_Otrans(X4,c_Transitive__Closure_Otrancl(X4,X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trans__trancl) ).
fof(f3028,plain,
spl104_32,
inference(avatar_split_clause,[],[f1917,f3026]) ).
fof(f1917,plain,
! [X0,X1] : c_Relation_Otrans(X1,c_Relation_OId__on(X1,X0)),
inference(cnf_transformation,[],[f547]) ).
fof(f547,plain,
! [X0,X1] : c_Relation_Otrans(X1,c_Relation_OId__on(X1,X0)),
inference(rectify,[],[f30]) ).
fof(f30,axiom,
! [X11,X4] : c_Relation_Otrans(X4,c_Relation_OId__on(X4,X11)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trans__Id__on) ).
fof(f3024,plain,
spl104_31,
inference(avatar_split_clause,[],[f1916,f3022]) ).
fof(f3022,plain,
( spl104_31
<=> ! [X0,X1] : c_Relation_Oantisym(X1,c_Relation_OId__on(X1,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_31])]) ).
fof(f1916,plain,
! [X0,X1] : c_Relation_Oantisym(X1,c_Relation_OId__on(X1,X0)),
inference(cnf_transformation,[],[f546]) ).
fof(f546,plain,
! [X0,X1] : c_Relation_Oantisym(X1,c_Relation_OId__on(X1,X0)),
inference(rectify,[],[f149]) ).
fof(f149,axiom,
! [X11,X4] : c_Relation_Oantisym(X4,c_Relation_OId__on(X4,X11)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_antisym__Id__on) ).
fof(f3020,plain,
spl104_30,
inference(avatar_split_clause,[],[f1901,f3018]) ).
fof(f3018,plain,
( spl104_30
<=> ! [X0] : c_Relation_Osingle__valued(X0,X0,c_Relation_OId(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_30])]) ).
fof(f1901,plain,
! [X0] : c_Relation_Osingle__valued(X0,X0,c_Relation_OId(X0)),
inference(cnf_transformation,[],[f531]) ).
fof(f531,plain,
! [X0] : c_Relation_Osingle__valued(X0,X0,c_Relation_OId(X0)),
inference(rectify,[],[f107]) ).
fof(f107,axiom,
! [X4] : c_Relation_Osingle__valued(X4,X4,c_Relation_OId(X4)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_single__valued__Id) ).
fof(f3016,plain,
spl104_29,
inference(avatar_split_clause,[],[f1887,f3013]) ).
fof(f1887,plain,
c_Wellfounded_Owf(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less),
inference(cnf_transformation,[],[f402]) ).
fof(f402,axiom,
c_Wellfounded_Owf(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__pair__less) ).
fof(f3011,plain,
spl104_28,
inference(avatar_split_clause,[],[f1886,f3008]) ).
fof(f1886,plain,
c_Wellfounded_Oless__than = c_Transitive__Closure_Otrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat),
inference(cnf_transformation,[],[f361]) ).
fof(f361,axiom,
c_Wellfounded_Oless__than = c_Transitive__Closure_Otrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__than__def) ).
fof(f3006,plain,
spl104_27,
inference(avatar_split_clause,[],[f1900,f3004]) ).
fof(f1900,plain,
! [X0] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X0),
inference(cnf_transformation,[],[f530]) ).
fof(f530,plain,
! [X0] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X0),
inference(rectify,[],[f375]) ).
fof(f375,axiom,
! [X70] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X70,X70),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__refl) ).
fof(f3002,plain,
spl104_26,
inference(avatar_split_clause,[],[f1899,f3000]) ).
fof(f1899,plain,
! [X0] : c_Relation_Otrans(X0,c_Relation_OId(X0)),
inference(cnf_transformation,[],[f529]) ).
fof(f529,plain,
! [X0] : c_Relation_Otrans(X0,c_Relation_OId(X0)),
inference(rectify,[],[f106]) ).
fof(f106,axiom,
! [X4] : c_Relation_Otrans(X4,c_Relation_OId(X4)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trans__Id) ).
fof(f2998,plain,
spl104_25,
inference(avatar_split_clause,[],[f1898,f2996]) ).
fof(f2996,plain,
( spl104_25
<=> ! [X0] : c_Relation_Oantisym(X0,c_Relation_OId(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_25])]) ).
fof(f1898,plain,
! [X0] : c_Relation_Oantisym(X0,c_Relation_OId(X0)),
inference(cnf_transformation,[],[f528]) ).
fof(f528,plain,
! [X0] : c_Relation_Oantisym(X0,c_Relation_OId(X0)),
inference(rectify,[],[f147]) ).
fof(f147,axiom,
! [X4] : c_Relation_Oantisym(X4,c_Relation_OId(X4)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_antisym__Id) ).
fof(f2994,plain,
spl104_24,
inference(avatar_split_clause,[],[f1896,f2992]) ).
fof(f1896,plain,
! [X0] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X0),
inference(cnf_transformation,[],[f526]) ).
fof(f526,plain,
! [X0] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X0),
inference(rectify,[],[f366]) ).
fof(f366,axiom,
! [X70] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X70,X70),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__not__refl) ).
fof(f2990,plain,
( ~ spl104_2
| spl104_23 ),
inference(avatar_split_clause,[],[f1852,f2987,f2882]) ).
fof(f1852,plain,
( c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,v_L)
| ~ sP1 ),
inference(cnf_transformation,[],[f1552]) ).
fof(f2985,plain,
spl104_22,
inference(avatar_split_clause,[],[f1885,f2982]) ).
fof(f1885,plain,
c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Oless__than),
inference(cnf_transformation,[],[f222]) ).
fof(f222,axiom,
c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Oless__than),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__less__than) ).
fof(f2980,plain,
spl104_21,
inference(avatar_split_clause,[],[f1884,f2977]) ).
fof(f1884,plain,
c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Opred__nat),
inference(cnf_transformation,[],[f362]) ).
fof(f362,axiom,
c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Opred__nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__pred__nat) ).
fof(f2975,plain,
spl104_20,
inference(avatar_split_clause,[],[f1883,f2972]) ).
fof(f1883,plain,
c_Relation_Otrans(tc_Nat_Onat,c_Wellfounded_Oless__than),
inference(cnf_transformation,[],[f221]) ).
fof(f221,axiom,
c_Relation_Otrans(tc_Nat_Onat,c_Wellfounded_Oless__than),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trans__less__than) ).
fof(f2970,plain,
spl104_19,
inference(avatar_split_clause,[],[f1882,f2967]) ).
fof(f2967,plain,
( spl104_19
<=> class_Orderings_Oorder(tc_HOL_Obool) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_19])]) ).
fof(f1882,plain,
class_Orderings_Oorder(tc_HOL_Obool),
inference(cnf_transformation,[],[f517]) ).
fof(f517,axiom,
class_Orderings_Oorder(tc_HOL_Obool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Orderings_Oorder) ).
fof(f2965,plain,
spl104_18,
inference(avatar_split_clause,[],[f1881,f2962]) ).
fof(f1881,plain,
class_Lattices_Osemilattice__sup(tc_HOL_Obool),
inference(cnf_transformation,[],[f514]) ).
fof(f514,axiom,
class_Lattices_Osemilattice__sup(tc_HOL_Obool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Lattices_Osemilattice__sup) ).
fof(f2960,plain,
spl104_17,
inference(avatar_split_clause,[],[f1880,f2957]) ).
fof(f1880,plain,
class_Orderings_Oorder(tc_Nat_Onat),
inference(cnf_transformation,[],[f509]) ).
fof(f509,axiom,
class_Orderings_Oorder(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Oorder) ).
fof(f2955,plain,
spl104_16,
inference(avatar_split_clause,[],[f1879,f2952]) ).
fof(f1879,plain,
class_Lattices_Osemilattice__sup(tc_Nat_Onat),
inference(cnf_transformation,[],[f505]) ).
fof(f505,axiom,
class_Lattices_Osemilattice__sup(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Lattices_Osemilattice__sup) ).
fof(f2950,plain,
spl104_15,
inference(avatar_split_clause,[],[f1878,f2947]) ).
fof(f1878,plain,
class_Orderings_Opreorder(tc_HOL_Obool),
inference(cnf_transformation,[],[f515]) ).
fof(f515,axiom,
class_Orderings_Opreorder(tc_HOL_Obool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Orderings_Opreorder) ).
fof(f2945,plain,
spl104_14,
inference(avatar_split_clause,[],[f1877,f2942]) ).
fof(f1877,plain,
class_Orderings_Opreorder(tc_Nat_Onat),
inference(cnf_transformation,[],[f506]) ).
fof(f506,axiom,
class_Orderings_Opreorder(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Opreorder) ).
fof(f2940,plain,
spl104_13,
inference(avatar_split_clause,[],[f1876,f2937]) ).
fof(f1876,plain,
class_Lattices_Olattice(tc_HOL_Obool),
inference(cnf_transformation,[],[f516]) ).
fof(f516,axiom,
class_Lattices_Olattice(tc_HOL_Obool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Lattices_Olattice) ).
fof(f2935,plain,
spl104_12,
inference(avatar_split_clause,[],[f1875,f2932]) ).
fof(f1875,plain,
class_Orderings_Oord(tc_HOL_Obool),
inference(cnf_transformation,[],[f518]) ).
fof(f518,axiom,
class_Orderings_Oord(tc_HOL_Obool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Orderings_Oord) ).
fof(f2930,plain,
spl104_11,
inference(avatar_split_clause,[],[f1874,f2927]) ).
fof(f1874,plain,
class_Orderings_Oord(tc_Nat_Onat),
inference(cnf_transformation,[],[f510]) ).
fof(f510,axiom,
class_Orderings_Oord(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Oord) ).
fof(f2925,plain,
spl104_10,
inference(avatar_split_clause,[],[f1873,f2922]) ).
fof(f1873,plain,
class_Lattices_Olattice(tc_Nat_Onat),
inference(cnf_transformation,[],[f508]) ).
fof(f508,axiom,
class_Lattices_Olattice(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Lattices_Olattice) ).
fof(f2920,plain,
spl104_9,
inference(avatar_split_clause,[],[f1872,f2917]) ).
fof(f1872,plain,
class_Orderings_Obot(tc_HOL_Obool),
inference(cnf_transformation,[],[f519]) ).
fof(f519,axiom,
class_Orderings_Obot(tc_HOL_Obool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Orderings_Obot) ).
fof(f2915,plain,
spl104_8,
inference(avatar_split_clause,[],[f1871,f2912]) ).
fof(f1871,plain,
class_Orderings_Obot(tc_Nat_Onat),
inference(cnf_transformation,[],[f511]) ).
fof(f511,axiom,
class_Orderings_Obot(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Obot) ).
fof(f2910,plain,
spl104_7,
inference(avatar_split_clause,[],[f1870,f2907]) ).
fof(f2907,plain,
( spl104_7
<=> class_Groups_Ominus(tc_HOL_Obool) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_7])]) ).
fof(f1870,plain,
class_Groups_Ominus(tc_HOL_Obool),
inference(cnf_transformation,[],[f520]) ).
fof(f520,axiom,
class_Groups_Ominus(tc_HOL_Obool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Groups_Ominus) ).
fof(f2905,plain,
spl104_6,
inference(avatar_split_clause,[],[f1869,f2902]) ).
fof(f2902,plain,
( spl104_6
<=> class_Groups_Ominus(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_6])]) ).
fof(f1869,plain,
class_Groups_Ominus(tc_Nat_Onat),
inference(cnf_transformation,[],[f512]) ).
fof(f512,axiom,
class_Groups_Ominus(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ominus) ).
fof(f2900,plain,
spl104_5,
inference(avatar_split_clause,[],[f1868,f2897]) ).
fof(f1868,plain,
class_Lattices_Obounded__lattice__bot(tc_HOL_Obool),
inference(cnf_transformation,[],[f513]) ).
fof(f513,axiom,
class_Lattices_Obounded__lattice__bot(tc_HOL_Obool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Lattices_Obounded__lattice__bot) ).
fof(f2895,plain,
spl104_4,
inference(avatar_split_clause,[],[f1867,f2892]) ).
fof(f2892,plain,
( spl104_4
<=> class_Lattices_Obounded__lattice(tc_HOL_Obool) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_4])]) ).
fof(f1867,plain,
class_Lattices_Obounded__lattice(tc_HOL_Obool),
inference(cnf_transformation,[],[f495]) ).
fof(f495,axiom,
class_Lattices_Obounded__lattice(tc_HOL_Obool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Lattices_Obounded__lattice) ).
fof(f2890,plain,
spl104_3,
inference(avatar_split_clause,[],[f1866,f2887]) ).
fof(f2887,plain,
( spl104_3
<=> class_Orderings_Olinorder(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_3])]) ).
fof(f1866,plain,
class_Orderings_Olinorder(tc_Nat_Onat),
inference(cnf_transformation,[],[f507]) ).
fof(f507,axiom,
class_Orderings_Olinorder(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Olinorder) ).
fof(f2885,plain,
( spl104_1
| spl104_2 ),
inference(avatar_split_clause,[],[f1864,f2882,f2878]) ).
fof(f1864,plain,
( sP1
| sP0 ),
inference(cnf_transformation,[],[f1559]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.15 % Problem : SCT105+1 : TPTP v8.1.2. Released v5.2.0.
% 0.07/0.17 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.38 % Computer : n027.cluster.edu
% 0.14/0.38 % Model : x86_64 x86_64
% 0.14/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.38 % Memory : 8042.1875MB
% 0.14/0.38 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.38 % CPULimit : 300
% 0.14/0.38 % WCLimit : 300
% 0.14/0.38 % DateTime : Mon Apr 29 23:38:02 EDT 2024
% 0.14/0.39 % CPUTime :
% 0.14/0.39 % (3468)Running in auto input_syntax mode. Trying TPTP
% 0.22/0.43 % (3492)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.22/0.43 % (3491)WARNING: value z3 for option sas not known
% 0.22/0.43 % (3489)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.22/0.44 % (3491)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)
% 0.22/0.44 % (3493)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)
% 0.22/0.44 % (3494)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)
% 0.22/0.44 % (3490)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.22/0.44 % (3495)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 1.40/0.61 TRYING [1]
% 1.64/0.63 TRYING [2]
% 4.33/1.03 TRYING [1]
% 4.33/1.04 TRYING [3]
% 4.79/1.12 TRYING [2]
% 7.76/1.51 % (3493)First to succeed.
% 7.99/1.57 % (3493)Refutation found. Thanks to Tanya!
% 7.99/1.57 % SZS status Theorem for theBenchmark
% 7.99/1.57 % SZS output start Proof for theBenchmark
% See solution above
% 7.99/1.59 % (3493)------------------------------
% 7.99/1.59 % (3493)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 7.99/1.59 % (3493)Termination reason: Refutation
% 7.99/1.59
% 7.99/1.59 % (3493)Memory used [KB]: 15472
% 7.99/1.59 % (3493)Time elapsed: 1.130 s
% 7.99/1.59 % (3493)Instructions burned: 3318 (million)
% 7.99/1.59 % (3493)------------------------------
% 7.99/1.59 % (3493)------------------------------
% 7.99/1.59 % (3468)Success in time 1.182 s
%------------------------------------------------------------------------------