TSTP Solution File: SET031-4 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SET031-4 : TPTP v8.2.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n009.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 May 21 03:15:31 EDT 2024
% Result : Unsatisfiable 162.57s 23.61s
% Output : Refutation 162.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 1888
% Syntax : Number of formulae : 5773 ( 152 unt; 0 def)
% Number of atoms : 20784 (1887 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 26660 (11649 ~;13264 |; 0 &)
% (1747 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 6 avg)
% Maximal term depth : 12 ( 2 avg)
% Number of predicates : 1762 (1760 usr;1748 prp; 0-5 aty)
% Number of functors : 60 ( 60 usr; 8 con; 0-5 aty)
% Number of variables : 8631 (8631 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f150137,plain,
$false,
inference(avatar_sat_refutation,[],[f189,f194,f199,f203,f208,f212,f216,f220,f224,f228,f234,f238,f242,f247,f251,f255,f259,f263,f267,f271,f275,f279,f283,f287,f292,f296,f300,f308,f312,f316,f320,f324,f334,f338,f342,f347,f351,f355,f359,f363,f367,f371,f375,f379,f385,f408,f412,f416,f420,f424,f428,f432,f436,f440,f444,f448,f452,f456,f460,f464,f468,f472,f476,f480,f484,f488,f497,f501,f505,f618,f622,f626,f630,f634,f638,f642,f646,f650,f654,f658,f662,f666,f670,f674,f678,f682,f686,f690,f766,f830,f834,f838,f842,f846,f850,f854,f858,f862,f866,f954,f958,f962,f968,f972,f1066,f1070,f1074,f1079,f1083,f1087,f1091,f1161,f1165,f1169,f1173,f1177,f1181,f1268,f1285,f1289,f1293,f1297,f1301,f1344,f1395,f1399,f1403,f1407,f1472,f1481,f1485,f1489,f1546,f1550,f1554,f1636,f1640,f1644,f1747,f1751,f1776,f1780,f1784,f1788,f1920,f1956,f1983,f1987,f2023,f2027,f2032,f2100,f2104,f2201,f2205,f2209,f2214,f2224,f2235,f2241,f2245,f2249,f2253,f2254,f2258,f2262,f2360,f2430,f2434,f2443,f2472,f2479,f2484,f2492,f2496,f2500,f2505,f2509,f2513,f2518,f2524,f2528,f2532,f2544,f2552,f2557,f2561,f2565,f2570,f2575,f2579,f2583,f2587,f2591,f2596,f2606,f2609,f2615,f2619,f2623,f2629,f2645,f2649,f2705,f2735,f2739,f2882,f2886,f2891,f2896,f2900,f2904,f2908,f2912,f2917,f2921,f2925,f2929,f2933,f2937,f2941,f2945,f2949,f2953,f2958,f2963,f2967,f2971,f2975,f2979,f2986,f2990,f2995,f3003,f3039,f3044,f3049,f3054,f3059,f3064,f3069,f3073,f3077,f3082,f3087,f3093,f3098,f3103,f3108,f3113,f3118,f3122,f3126,f3130,f3134,f3138,f3143,f3148,f3154,f3160,f3164,f3168,f3172,f3176,f3180,f3184,f3189,f3194,f3198,f3203,f3208,f3212,f3216,f3220,f3224,f3228,f3232,f3237,f3242,f3406,f3410,f3414,f3418,f3422,f3426,f3430,f3435,f3477,f3481,f3547,f3551,f3626,f3631,f3667,f3672,f3677,f3681,f3685,f3689,f3693,f3697,f3701,f3705,f3709,f3713,f3717,f3721,f3725,f3729,f3733,f3737,f3741,f3745,f3749,f3753,f3757,f3761,f3765,f3769,f3773,f3777,f3781,f3785,f3789,f3793,f3797,f3801,f3805,f3809,f3813,f3817,f3821,f3825,f3829,f3833,f3837,f3841,f3845,f3849,f3853,f3857,f3861,f3865,f3897,f3901,f3905,f3909,f3913,f3918,f3922,f3927,f3931,f3973,f4036,f4224,f4228,f4232,f4236,f4240,f4244,f4248,f4255,f4260,f4266,f4272,f4276,f4280,f4284,f4288,f4292,f4296,f4300,f4305,f4309,f4313,f4317,f4321,f4325,f4330,f4335,f4339,f4343,f4347,f4353,f4357,f4361,f4365,f4369,f4373,f4377,f4381,f4385,f4389,f4394,f4399,f4405,f4411,f4415,f4419,f4423,f4427,f4431,f4435,f4439,f4444,f4448,f4452,f4456,f4460,f4464,f4468,f4472,f4476,f4480,f4484,f4489,f4493,f4497,f4501,f4505,f4509,f4513,f4517,f4523,f4529,f4534,f4539,f5161,f5168,f5172,f5177,f5223,f5229,f5233,f5238,f5269,f5305,f5495,f5499,f5503,f5508,f5512,f5516,f5521,f5525,f5529,f5533,f5537,f5541,f5545,f5550,f5555,f5560,f5566,f5571,f5576,f5581,f5586,f5591,f5596,f5601,f5606,f5611,f5616,f5620,f5625,f5629,f5634,f5638,f5642,f5646,f5650,f5654,f5658,f5662,f5666,f5671,f5676,f5680,f5685,f5689,f5694,f5699,f5704,f5709,f5713,f5717,f5722,f5726,f5730,f5734,f5738,f5742,f5746,f6053,f6772,f6776,f6780,f6784,f6789,f6793,f6797,f6801,f6805,f6809,f6813,f6817,f6821,f6925,f7134,f7138,f7153,f7157,f7161,f7165,f7169,f7194,f7205,f7223,f7229,f7233,f7237,f7241,f7245,f7250,f7254,f7259,f7263,f7268,f7272,f7276,f7280,f7285,f7289,f7293,f7297,f7302,f7307,f7311,f7315,f7319,f7323,f7327,f7331,f7335,f7339,f7343,f7347,f7352,f7356,f7360,f7364,f7368,f7372,f7376,f7380,f7384,f7388,f7392,f7397,f7401,f7405,f7409,f7413,f7417,f7421,f7425,f7429,f7433,f7437,f7442,f7446,f7450,f7454,f7458,f7462,f7466,f7470,f7474,f7483,f7489,f7495,f7501,f7507,f7920,f7924,f8133,f8140,f8147,f8152,f8158,f8165,f8417,f8489,f8493,f8497,f8502,f8507,f8511,f8515,f8519,f8524,f8528,f8532,f8536,f8540,f8544,f8548,f8552,f8556,f8560,f8564,f8569,f8573,f8577,f8581,f8585,f8589,f8593,f8597,f8601,f8605,f8609,f8614,f8618,f8622,f8626,f8630,f8634,f8638,f8642,f8646,f8650,f8654,f8659,f8663,f8667,f8672,f8676,f8680,f8801,f8805,f8809,f8820,f9061,f9272,f9277,f9638,f9802,f9807,f9812,f9816,f9820,f9824,f9828,f9832,f9837,f9841,f9845,f9849,f9853,f9858,f9862,f9866,f9871,f9875,f9879,f9884,f9888,f9892,f9896,f9900,f9904,f9908,f9912,f9916,f9920,f9924,f9929,f9933,f9937,f9941,f9946,f9951,f9955,f9961,f9968,f9972,f9976,f10298,f10771,f11167,f11171,f11175,f11179,f11184,f11188,f11193,f11197,f11201,f11206,f11210,f11215,f11220,f11224,f11229,f11234,f11239,f11243,f11247,f11251,f11255,f11259,f11263,f11294,f11298,f11302,f11306,f11310,f11314,f11318,f11322,f11326,f11330,f11350,f11354,f11358,f11362,f11366,f11370,f11374,f11378,f11382,f11386,f11439,f11443,f11447,f11453,f11457,f11461,f11465,f11469,f11473,f11477,f11530,f11534,f11538,f11542,f11546,f11550,f11554,f11560,f11564,f11568,f11589,f11593,f11597,f11601,f11605,f11784,f11869,f12074,f12159,f12163,f12167,f12171,f12175,f14492,f15964,f16008,f16012,f16017,f16021,f16028,f16032,f16036,f16040,f16045,f16049,f16053,f16057,f16061,f16065,f16069,f16076,f16080,f16084,f16088,f16094,f16098,f16707,f16763,f16767,f16771,f16775,f16779,f16783,f16788,f16792,f16796,f16800,f16807,f16811,f16815,f16819,f16823,f16827,f16831,f16836,f16840,f16844,f16848,f16855,f16859,f16863,f16867,f16871,f16875,f16879,f16883,f16887,f16891,f16895,f16902,f16906,f16910,f17044,f17157,f18354,f18375,f18647,f18690,f18694,f18698,f18702,f18709,f18713,f18717,f18721,f18725,f18729,f18733,f18737,f18741,f18745,f18749,f18756,f18760,f18764,f18768,f18772,f18776,f18780,f18784,f18788,f18792,f18796,f19649,f20914,f21174,f21179,f21183,f21187,f21191,f21195,f21199,f21203,f21210,f21214,f21218,f21222,f21226,f21230,f21234,f21238,f21242,f21246,f21250,f21257,f21261,f21265,f21269,f21273,f21277,f21281,f21285,f21289,f21293,f21297,f21304,f21308,f21312,f21316,f21320,f21324,f21328,f21332,f21336,f21340,f21344,f21351,f21355,f21359,f21363,f21367,f21371,f21375,f21379,f21383,f21387,f21391,f21398,f21402,f21406,f21410,f22152,f22993,f23014,f23037,f23220,f23297,f23301,f23305,f23310,f23314,f23318,f23322,f23329,f23333,f23609,f24220,f24228,f24232,f24236,f24240,f24244,f24248,f24252,f24259,f24263,f24270,f24993,f24997,f25001,f25005,f25012,f25300,f25304,f25308,f25312,f25316,f25320,f25325,f25329,f25333,f25338,f25343,f25348,f25794,f26093,f26097,f26101,f26105,f26109,f26113,f26117,f26122,f26126,f26130,f26134,f26954,f27280,f27284,f27288,f27293,f27299,f27303,f27308,f27312,f27316,f27320,f27324,f27329,f27335,f27339,f27343,f27347,f27352,f27356,f27360,f27364,f27368,f27372,f27686,f27697,f27704,f27708,f27712,f27716,f27720,f27724,f27728,f27732,f27736,f27741,f27749,f27816,f27834,f27838,f27842,f27848,f27853,f27858,f27862,f27866,f27870,f27875,f27879,f27883,f27887,f27891,f27895,f27899,f27903,f27907,f27911,f27915,f27920,f27924,f27928,f27932,f27936,f27940,f27944,f27948,f27952,f27956,f27960,f27965,f27971,f27975,f27989,f28008,f28085,f28150,f28154,f28158,f28162,f28166,f28170,f28203,f28252,f28256,f28260,f28264,f28271,f28275,f28282,f28286,f28291,f28295,f28299,f28637,f28644,f28648,f28653,f28658,f28662,f28666,f28670,f28674,f28678,f28682,f28687,f28691,f28695,f28699,f28703,f28707,f28711,f28715,f28719,f28723,f28727,f28732,f28736,f28740,f28744,f28748,f28752,f28756,f28760,f28764,f28768,f28772,f28777,f28781,f28785,f28789,f28793,f28797,f28801,f28807,f28967,f28971,f28976,f29996,f30022,f30049,f30065,f30069,f30073,f30077,f30081,f30085,f30089,f30093,f30097,f30101,f30105,f30109,f30113,f30292,f31218,f31222,f31226,f31230,f31234,f31238,f31242,f31246,f31250,f31254,f31258,f31262,f31266,f31270,f31274,f31278,f31282,f31286,f31290,f31294,f31298,f31302,f31306,f31310,f31314,f31318,f32418,f32690,f32694,f32700,f32765,f32769,f32773,f32777,f32781,f32785,f33582,f33586,f33590,f33594,f33598,f33602,f33606,f33693,f33697,f33701,f33705,f33709,f33713,f33717,f33721,f33725,f34768,f34772,f34776,f34780,f34784,f34790,f34794,f34798,f34802,f34806,f34810,f34814,f34883,f34922,f34926,f34930,f34934,f34938,f34942,f34946,f34950,f34954,f34958,f34962,f34966,f34970,f36390,f36415,f36419,f36423,f36427,f36431,f36435,f36439,f36885,f36907,f36912,f36916,f36920,f36988,f36992,f36996,f37000,f37004,f37267,f37271,f37275,f37279,f37283,f37287,f37291,f37388,f37392,f37396,f37400,f37404,f37408,f37412,f37416,f37420,f37424,f37428,f37434,f37438,f37442,f37446,f37450,f37454,f37458,f37462,f37466,f37470,f37474,f37481,f37537,f37565,f37650,f37654,f37661,f37665,f37669,f37673,f37677,f37681,f38051,f38147,f38151,f38189,f38194,f38200,f38207,f38211,f38215,f38219,f38223,f38227,f38233,f38239,f38243,f38247,f38251,f38324,f38328,f38332,f38339,f38343,f38347,f38351,f38355,f38359,f38870,f39318,f39322,f39326,f39330,f39336,f39353,f39358,f39363,f39367,f39371,f39375,f39379,f39383,f39387,f40398,f40402,f40406,f40410,f40414,f40421,f40425,f40429,f40433,f41281,f41314,f41318,f41322,f41326,f41330,f41334,f41338,f41342,f41346,f41353,f41357,f41361,f41417,f41442,f41447,f41452,f41456,f41460,f41464,f41468,f41475,f41479,f41483,f41487,f41784,f41793,f41797,f41801,f41805,f41809,f41813,f42173,f42927,f42931,f42935,f42939,f42943,f42947,f42951,f42958,f43775,f43842,f43849,f43853,f43857,f43861,f44643,f44647,f44651,f44658,f44662,f44666,f44670,f44688,f44695,f44699,f44703,f44707,f44711,f44715,f44719,f45309,f46085,f46089,f46093,f46097,f46101,f46105,f46109,f46116,f46120,f46124,f46187,f46238,f46244,f46250,f46254,f46258,f46262,f46266,f46270,f46274,f46281,f46897,f46901,f46905,f46912,f46916,f47704,f47708,f47712,f47716,f47720,f47979,f47983,f48392,f48396,f48400,f48407,f48411,f48415,f48419,f48423,f48427,f48431,f48435,f48439,f48443,f48447,f49809,f49896,f49900,f49904,f49908,f50682,f50689,f50693,f50859,f50863,f51001,f51046,f51053,f51057,f51061,f51065,f51249,f51253,f51257,f51650,f51654,f51658,f51662,f51678,f51685,f51689,f51693,f51697,f51701,f52670,f52677,f52681,f52697,f52701,f52829,f52833,f52837,f53240,f53244,f53638,f53642,f53646,f53650,f53654,f53681,f53685,f53767,f53771,f53775,f53782,f53786,f54601,f54605,f54991,f54998,f55002,f55012,f55016,f55020,f55024,f55032,f55043,f55047,f55051,f55055,f55833,f55840,f55844,f56257,f56261,f56265,f56269,f56678,f57090,f57094,f57488,f57492,f57496,f57500,f57504,f58283,f58290,f58297,f58304,f58311,f58318,f58322,f58326,f58330,f58339,f58345,f58349,f58393,f58400,f58407,f58414,f58421,f58428,f58435,f58442,f58450,f58454,f58461,f58468,f58475,f58482,f58489,f58496,f58503,f58510,f58517,f58525,f58529,f58536,f58548,f58555,f58559,f58573,f58574,f58585,f58595,f58599,f58603,f58607,f58611,f58612,f58672,f59392,f59634,f59638,f59642,f59646,f59650,f59654,f59658,f59662,f59666,f59670,f59675,f59681,f59686,f59690,f59694,f59698,f59702,f59706,f59717,f60210,f60225,f60233,f60241,f60249,f60257,f60265,f60273,f60281,f60289,f60300,f60308,f60316,f60324,f60328,f67942,f68659,f68986,f68990,f68994,f68998,f69002,f69007,f69011,f69017,f69023,f69032,f69036,f69040,f69044,f69048,f69052,f69056,f69060,f69064,f69068,f69069,f77131,f85257,f93963,f93970,f95086,f95091,f95096,f95101,f95107,f95110,f117181,f117186,f117191,f117196,f117201,f117206,f117211,f117216,f117221,f117226,f117228,f117247,f117252,f117257,f117262,f117267,f117272,f117277,f117286,f117288,f117325,f117330,f117335,f117365,f117371,f117376,f117381,f123870,f124766,f129134,f129140,f129146,f129152,f129157,f129162,f129167,f129172,f129177,f129182,f129187,f129192,f129197,f129199,f129438,f129445,f129449,f129455,f129461,f138919,f147009,f147013,f147017,f147022,f147027,f147036,f147040,f147232,f147236,f147240,f147244,f147248,f147252,f147256,f147260,f147264,f147268,f147460,f147464,f147468,f147472,f147476,f147480,f147484,f147488,f147492,f147496,f147501,f147505,f147509,f147513,f147517,f147521,f147525,f147529,f147533,f147537,f147541,f147546,f147550,f147554,f147558,f147562,f147566,f147570,f147574,f147578,f147582,f147586,f147780,f147786,f147792,f147798,f147804,f147810,f147814,f147818,f147823,f147827,f148015,f148019,f148023,f148027,f148031,f148035,f148039,f148043,f148047,f148053,f148068,f148072,f148076,f148080,f148084,f148088,f148092,f148096,f148100,f148104,f148108,f148112,f148116,f148120,f148124,f148128,f148457,f148814,f150136]) ).
fof(f150136,plain,
( spl0_1
| ~ spl0_19
| ~ spl0_1732 ),
inference(avatar_split_clause,[],[f150102,f148065,f265,f186]) ).
fof(f186,plain,
( spl0_1
<=> relation(compose(a,b)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).
fof(f265,plain,
( spl0_19
<=> ! [X3] :
( relation(X3)
| ~ ordered_pair_predicate(f18(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_19])]) ).
fof(f148065,plain,
( spl0_1732
<=> ordered_pair_predicate(f18(compose(a,b))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1732])]) ).
fof(f150102,plain,
( relation(compose(a,b))
| ~ spl0_19
| ~ spl0_1732 ),
inference(resolution,[],[f148067,f266]) ).
fof(f266,plain,
( ! [X3] :
( ~ ordered_pair_predicate(f18(X3))
| relation(X3) )
| ~ spl0_19 ),
inference(avatar_component_clause,[],[f265]) ).
fof(f148067,plain,
( ordered_pair_predicate(f18(compose(a,b)))
| ~ spl0_1732 ),
inference(avatar_component_clause,[],[f148065]) ).
fof(f148814,plain,
( spl0_1
| ~ spl0_422
| spl0_1731 ),
inference(avatar_split_clause,[],[f148530,f148061,f4495,f186]) ).
fof(f4495,plain,
( spl0_422
<=> ! [X0,X1] :
( little_set(f30(f18(compose(X0,X1)),X0,X1))
| relation(compose(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_422])]) ).
fof(f148061,plain,
( spl0_1731
<=> little_set(f30(f18(compose(a,b)),a,b)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1731])]) ).
fof(f148530,plain,
( relation(compose(a,b))
| ~ spl0_422
| spl0_1731 ),
inference(resolution,[],[f148063,f4496]) ).
fof(f4496,plain,
( ! [X0,X1] :
( little_set(f30(f18(compose(X0,X1)),X0,X1))
| relation(compose(X0,X1)) )
| ~ spl0_422 ),
inference(avatar_component_clause,[],[f4495]) ).
fof(f148063,plain,
( ~ little_set(f30(f18(compose(a,b)),a,b))
| spl0_1731 ),
inference(avatar_component_clause,[],[f148061]) ).
fof(f148457,plain,
( spl0_1
| ~ spl0_421
| spl0_1730 ),
inference(avatar_split_clause,[],[f148434,f148057,f4491,f186]) ).
fof(f4491,plain,
( spl0_421
<=> ! [X0,X1] :
( little_set(f29(f18(compose(X0,X1)),X0,X1))
| relation(compose(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_421])]) ).
fof(f148057,plain,
( spl0_1730
<=> little_set(f29(f18(compose(a,b)),a,b)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1730])]) ).
fof(f148434,plain,
( relation(compose(a,b))
| ~ spl0_421
| spl0_1730 ),
inference(resolution,[],[f148059,f4492]) ).
fof(f4492,plain,
( ! [X0,X1] :
( little_set(f29(f18(compose(X0,X1)),X0,X1))
| relation(compose(X0,X1)) )
| ~ spl0_421 ),
inference(avatar_component_clause,[],[f4491]) ).
fof(f148059,plain,
( ~ little_set(f29(f18(compose(a,b)),a,b))
| spl0_1730 ),
inference(avatar_component_clause,[],[f148057]) ).
fof(f148128,plain,
( spl0_1747
| ~ spl0_119
| ~ spl0_175
| ~ spl0_210
| ~ spl0_784 ),
inference(avatar_split_clause,[],[f88751,f16047,f2737,f2469,f1266,f148126]) ).
fof(f148126,plain,
( spl0_1747
<=> ! [X0,X1] :
( ordered_pair_predicate(f1(cross_product(X0,X1),estin))
| estin = cross_product(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1747])]) ).
fof(f1266,plain,
( spl0_119
<=> ! [X0] : ~ member(X0,domain_of(empty_set)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_119])]) ).
fof(f2469,plain,
( spl0_175
<=> empty_set = identity_relation ),
introduced(avatar_definition,[new_symbols(naming,[spl0_175])]) ).
fof(f2737,plain,
( spl0_210
<=> ! [X0] :
( estin = X0
| member(f1(estin,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_210])]) ).
fof(f16047,plain,
( spl0_784
<=> ! [X2,X0,X1] :
( member(f1(cross_product(X0,X1),X2),X2)
| cross_product(X0,X1) = X2
| ordered_pair_predicate(f1(cross_product(X0,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_784])]) ).
fof(f88751,plain,
( ! [X0,X1] :
( ordered_pair_predicate(f1(cross_product(X0,X1),estin))
| estin = cross_product(X0,X1) )
| ~ spl0_119
| ~ spl0_175
| ~ spl0_210
| ~ spl0_784 ),
inference(forward_demodulation,[],[f88750,f85273]) ).
fof(f85273,plain,
( estin = domain_of(identity_relation)
| ~ spl0_119
| ~ spl0_175
| ~ spl0_210 ),
inference(forward_demodulation,[],[f2828,f2471]) ).
fof(f2471,plain,
( empty_set = identity_relation
| ~ spl0_175 ),
inference(avatar_component_clause,[],[f2469]) ).
fof(f2828,plain,
( estin = domain_of(empty_set)
| ~ spl0_119
| ~ spl0_210 ),
inference(resolution,[],[f2738,f1267]) ).
fof(f1267,plain,
( ! [X0] : ~ member(X0,domain_of(empty_set))
| ~ spl0_119 ),
inference(avatar_component_clause,[],[f1266]) ).
fof(f2738,plain,
( ! [X0] :
( member(f1(estin,X0),X0)
| estin = X0 )
| ~ spl0_210 ),
inference(avatar_component_clause,[],[f2737]) ).
fof(f88750,plain,
( ! [X0,X1] :
( ordered_pair_predicate(f1(cross_product(X0,X1),domain_of(identity_relation)))
| estin = cross_product(X0,X1) )
| ~ spl0_119
| ~ spl0_175
| ~ spl0_210
| ~ spl0_784 ),
inference(forward_demodulation,[],[f88749,f2471]) ).
fof(f88749,plain,
( ! [X0,X1] :
( estin = cross_product(X0,X1)
| ordered_pair_predicate(f1(cross_product(X0,X1),domain_of(empty_set))) )
| ~ spl0_119
| ~ spl0_175
| ~ spl0_210
| ~ spl0_784 ),
inference(forward_demodulation,[],[f88748,f85273]) ).
fof(f88748,plain,
( ! [X0,X1] :
( cross_product(X0,X1) = domain_of(identity_relation)
| ordered_pair_predicate(f1(cross_product(X0,X1),domain_of(empty_set))) )
| ~ spl0_119
| ~ spl0_175
| ~ spl0_784 ),
inference(forward_demodulation,[],[f16245,f2471]) ).
fof(f16245,plain,
( ! [X0,X1] :
( cross_product(X0,X1) = domain_of(empty_set)
| ordered_pair_predicate(f1(cross_product(X0,X1),domain_of(empty_set))) )
| ~ spl0_119
| ~ spl0_784 ),
inference(resolution,[],[f16048,f1267]) ).
fof(f16048,plain,
( ! [X2,X0,X1] :
( member(f1(cross_product(X0,X1),X2),X2)
| cross_product(X0,X1) = X2
| ordered_pair_predicate(f1(cross_product(X0,X1),X2)) )
| ~ spl0_784 ),
inference(avatar_component_clause,[],[f16047]) ).
fof(f148124,plain,
( spl0_1746
| ~ spl0_119
| ~ spl0_175
| ~ spl0_210
| ~ spl0_755 ),
inference(avatar_split_clause,[],[f88627,f11548,f2737,f2469,f1266,f148122]) ).
fof(f148122,plain,
( spl0_1746
<=> ! [X0] :
( estin = range_of(X0)
| ordered_pair_predicate(f27(f1(range_of(X0),estin),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1746])]) ).
fof(f11548,plain,
( spl0_755
<=> ! [X0,X1] :
( member(f1(range_of(X0),X1),X1)
| range_of(X0) = X1
| ordered_pair_predicate(f27(f1(range_of(X0),X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_755])]) ).
fof(f88627,plain,
( ! [X0] :
( estin = range_of(X0)
| ordered_pair_predicate(f27(f1(range_of(X0),estin),X0)) )
| ~ spl0_119
| ~ spl0_175
| ~ spl0_210
| ~ spl0_755 ),
inference(forward_demodulation,[],[f88626,f85273]) ).
fof(f88626,plain,
( ! [X0] :
( range_of(X0) = domain_of(identity_relation)
| ordered_pair_predicate(f27(f1(range_of(X0),estin),X0)) )
| ~ spl0_119
| ~ spl0_175
| ~ spl0_210
| ~ spl0_755 ),
inference(forward_demodulation,[],[f88625,f2471]) ).
fof(f88625,plain,
( ! [X0] :
( ordered_pair_predicate(f27(f1(range_of(X0),estin),X0))
| range_of(X0) = domain_of(empty_set) )
| ~ spl0_119
| ~ spl0_175
| ~ spl0_210
| ~ spl0_755 ),
inference(forward_demodulation,[],[f88624,f85273]) ).
fof(f88624,plain,
( ! [X0] :
( ordered_pair_predicate(f27(f1(range_of(X0),domain_of(identity_relation)),X0))
| range_of(X0) = domain_of(empty_set) )
| ~ spl0_119
| ~ spl0_175
| ~ spl0_755 ),
inference(forward_demodulation,[],[f15707,f2471]) ).
fof(f15707,plain,
( ! [X0] :
( ordered_pair_predicate(f27(f1(range_of(X0),domain_of(empty_set)),X0))
| range_of(X0) = domain_of(empty_set) )
| ~ spl0_119
| ~ spl0_755 ),
inference(resolution,[],[f11549,f1267]) ).
fof(f11549,plain,
( ! [X0,X1] :
( ordered_pair_predicate(f27(f1(range_of(X0),X1),X0))
| member(f1(range_of(X0),X1),X1)
| range_of(X0) = X1 )
| ~ spl0_755 ),
inference(avatar_component_clause,[],[f11548]) ).
fof(f148120,plain,
( spl0_1745
| ~ spl0_119
| ~ spl0_175
| ~ spl0_210
| ~ spl0_754 ),
inference(avatar_split_clause,[],[f88583,f11544,f2737,f2469,f1266,f148118]) ).
fof(f148118,plain,
( spl0_1745
<=> ! [X0] :
( estin = flip_range_of(X0)
| little_set(f12(f1(flip_range_of(X0),estin),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1745])]) ).
fof(f11544,plain,
( spl0_754
<=> ! [X0,X1] :
( member(f1(flip_range_of(X0),X1),X1)
| flip_range_of(X0) = X1
| little_set(f12(f1(flip_range_of(X0),X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_754])]) ).
fof(f88583,plain,
( ! [X0] :
( estin = flip_range_of(X0)
| little_set(f12(f1(flip_range_of(X0),estin),X0)) )
| ~ spl0_119
| ~ spl0_175
| ~ spl0_210
| ~ spl0_754 ),
inference(forward_demodulation,[],[f88582,f85273]) ).
fof(f88582,plain,
( ! [X0] :
( flip_range_of(X0) = domain_of(identity_relation)
| little_set(f12(f1(flip_range_of(X0),estin),X0)) )
| ~ spl0_119
| ~ spl0_175
| ~ spl0_210
| ~ spl0_754 ),
inference(forward_demodulation,[],[f88581,f2471]) ).
fof(f88581,plain,
( ! [X0] :
( little_set(f12(f1(flip_range_of(X0),estin),X0))
| flip_range_of(X0) = domain_of(empty_set) )
| ~ spl0_119
| ~ spl0_175
| ~ spl0_210
| ~ spl0_754 ),
inference(forward_demodulation,[],[f88580,f85273]) ).
fof(f88580,plain,
( ! [X0] :
( little_set(f12(f1(flip_range_of(X0),domain_of(identity_relation)),X0))
| flip_range_of(X0) = domain_of(empty_set) )
| ~ spl0_119
| ~ spl0_175
| ~ spl0_754 ),
inference(forward_demodulation,[],[f15586,f2471]) ).
fof(f15586,plain,
( ! [X0] :
( little_set(f12(f1(flip_range_of(X0),domain_of(empty_set)),X0))
| flip_range_of(X0) = domain_of(empty_set) )
| ~ spl0_119
| ~ spl0_754 ),
inference(resolution,[],[f11545,f1267]) ).
fof(f11545,plain,
( ! [X0,X1] :
( little_set(f12(f1(flip_range_of(X0),X1),X0))
| member(f1(flip_range_of(X0),X1),X1)
| flip_range_of(X0) = X1 )
| ~ spl0_754 ),
inference(avatar_component_clause,[],[f11544]) ).
fof(f148116,plain,
( spl0_1744
| ~ spl0_119
| ~ spl0_175
| ~ spl0_210
| ~ spl0_753 ),
inference(avatar_split_clause,[],[f88539,f11540,f2737,f2469,f1266,f148114]) ).
fof(f148114,plain,
( spl0_1744
<=> ! [X0] :
( estin = flip_range_of(X0)
| little_set(f13(f1(flip_range_of(X0),estin),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1744])]) ).
fof(f11540,plain,
( spl0_753
<=> ! [X0,X1] :
( member(f1(flip_range_of(X0),X1),X1)
| flip_range_of(X0) = X1
| little_set(f13(f1(flip_range_of(X0),X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_753])]) ).
fof(f88539,plain,
( ! [X0] :
( estin = flip_range_of(X0)
| little_set(f13(f1(flip_range_of(X0),estin),X0)) )
| ~ spl0_119
| ~ spl0_175
| ~ spl0_210
| ~ spl0_753 ),
inference(forward_demodulation,[],[f88538,f85273]) ).
fof(f88538,plain,
( ! [X0] :
( flip_range_of(X0) = domain_of(identity_relation)
| little_set(f13(f1(flip_range_of(X0),estin),X0)) )
| ~ spl0_119
| ~ spl0_175
| ~ spl0_210
| ~ spl0_753 ),
inference(forward_demodulation,[],[f88537,f2471]) ).
fof(f88537,plain,
( ! [X0] :
( little_set(f13(f1(flip_range_of(X0),estin),X0))
| flip_range_of(X0) = domain_of(empty_set) )
| ~ spl0_119
| ~ spl0_175
| ~ spl0_210
| ~ spl0_753 ),
inference(forward_demodulation,[],[f88536,f85273]) ).
fof(f88536,plain,
( ! [X0] :
( little_set(f13(f1(flip_range_of(X0),domain_of(identity_relation)),X0))
| flip_range_of(X0) = domain_of(empty_set) )
| ~ spl0_119
| ~ spl0_175
| ~ spl0_753 ),
inference(forward_demodulation,[],[f15467,f2471]) ).
fof(f15467,plain,
( ! [X0] :
( little_set(f13(f1(flip_range_of(X0),domain_of(empty_set)),X0))
| flip_range_of(X0) = domain_of(empty_set) )
| ~ spl0_119
| ~ spl0_753 ),
inference(resolution,[],[f11541,f1267]) ).
fof(f11541,plain,
( ! [X0,X1] :
( little_set(f13(f1(flip_range_of(X0),X1),X0))
| member(f1(flip_range_of(X0),X1),X1)
| flip_range_of(X0) = X1 )
| ~ spl0_753 ),
inference(avatar_component_clause,[],[f11540]) ).
fof(f148112,plain,
( spl0_1743
| ~ spl0_119
| ~ spl0_175
| ~ spl0_210
| ~ spl0_752 ),
inference(avatar_split_clause,[],[f88495,f11536,f2737,f2469,f1266,f148110]) ).
fof(f148110,plain,
( spl0_1743
<=> ! [X0] :
( estin = flip_range_of(X0)
| little_set(f14(f1(flip_range_of(X0),estin),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1743])]) ).
fof(f11536,plain,
( spl0_752
<=> ! [X0,X1] :
( member(f1(flip_range_of(X0),X1),X1)
| flip_range_of(X0) = X1
| little_set(f14(f1(flip_range_of(X0),X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_752])]) ).
fof(f88495,plain,
( ! [X0] :
( estin = flip_range_of(X0)
| little_set(f14(f1(flip_range_of(X0),estin),X0)) )
| ~ spl0_119
| ~ spl0_175
| ~ spl0_210
| ~ spl0_752 ),
inference(forward_demodulation,[],[f88494,f85273]) ).
fof(f88494,plain,
( ! [X0] :
( flip_range_of(X0) = domain_of(identity_relation)
| little_set(f14(f1(flip_range_of(X0),estin),X0)) )
| ~ spl0_119
| ~ spl0_175
| ~ spl0_210
| ~ spl0_752 ),
inference(forward_demodulation,[],[f88493,f2471]) ).
fof(f88493,plain,
( ! [X0] :
( little_set(f14(f1(flip_range_of(X0),estin),X0))
| flip_range_of(X0) = domain_of(empty_set) )
| ~ spl0_119
| ~ spl0_175
| ~ spl0_210
| ~ spl0_752 ),
inference(forward_demodulation,[],[f88492,f85273]) ).
fof(f88492,plain,
( ! [X0] :
( little_set(f14(f1(flip_range_of(X0),domain_of(identity_relation)),X0))
| flip_range_of(X0) = domain_of(empty_set) )
| ~ spl0_119
| ~ spl0_175
| ~ spl0_752 ),
inference(forward_demodulation,[],[f15348,f2471]) ).
fof(f15348,plain,
( ! [X0] :
( little_set(f14(f1(flip_range_of(X0),domain_of(empty_set)),X0))
| flip_range_of(X0) = domain_of(empty_set) )
| ~ spl0_119
| ~ spl0_752 ),
inference(resolution,[],[f11537,f1267]) ).
fof(f11537,plain,
( ! [X0,X1] :
( little_set(f14(f1(flip_range_of(X0),X1),X0))
| member(f1(flip_range_of(X0),X1),X1)
| flip_range_of(X0) = X1 )
| ~ spl0_752 ),
inference(avatar_component_clause,[],[f11536]) ).
fof(f148108,plain,
( spl0_1742
| ~ spl0_119
| ~ spl0_175
| ~ spl0_210
| ~ spl0_751 ),
inference(avatar_split_clause,[],[f88451,f11532,f2737,f2469,f1266,f148106]) ).
fof(f148106,plain,
( spl0_1742
<=> ! [X0] :
( estin = rotate_right(X0)
| little_set(f9(f1(rotate_right(X0),estin),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1742])]) ).
fof(f11532,plain,
( spl0_751
<=> ! [X0,X1] :
( member(f1(rotate_right(X0),X1),X1)
| rotate_right(X0) = X1
| little_set(f9(f1(rotate_right(X0),X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_751])]) ).
fof(f88451,plain,
( ! [X0] :
( estin = rotate_right(X0)
| little_set(f9(f1(rotate_right(X0),estin),X0)) )
| ~ spl0_119
| ~ spl0_175
| ~ spl0_210
| ~ spl0_751 ),
inference(forward_demodulation,[],[f88450,f85273]) ).
fof(f88450,plain,
( ! [X0] :
( rotate_right(X0) = domain_of(identity_relation)
| little_set(f9(f1(rotate_right(X0),estin),X0)) )
| ~ spl0_119
| ~ spl0_175
| ~ spl0_210
| ~ spl0_751 ),
inference(forward_demodulation,[],[f88449,f2471]) ).
fof(f88449,plain,
( ! [X0] :
( little_set(f9(f1(rotate_right(X0),estin),X0))
| rotate_right(X0) = domain_of(empty_set) )
| ~ spl0_119
| ~ spl0_175
| ~ spl0_210
| ~ spl0_751 ),
inference(forward_demodulation,[],[f88448,f85273]) ).
fof(f88448,plain,
( ! [X0] :
( little_set(f9(f1(rotate_right(X0),domain_of(identity_relation)),X0))
| rotate_right(X0) = domain_of(empty_set) )
| ~ spl0_119
| ~ spl0_175
| ~ spl0_751 ),
inference(forward_demodulation,[],[f15229,f2471]) ).
fof(f15229,plain,
( ! [X0] :
( little_set(f9(f1(rotate_right(X0),domain_of(empty_set)),X0))
| rotate_right(X0) = domain_of(empty_set) )
| ~ spl0_119
| ~ spl0_751 ),
inference(resolution,[],[f11533,f1267]) ).
fof(f11533,plain,
( ! [X0,X1] :
( little_set(f9(f1(rotate_right(X0),X1),X0))
| member(f1(rotate_right(X0),X1),X1)
| rotate_right(X0) = X1 )
| ~ spl0_751 ),
inference(avatar_component_clause,[],[f11532]) ).
fof(f148104,plain,
( spl0_1741
| ~ spl0_119
| ~ spl0_175
| ~ spl0_210
| ~ spl0_750 ),
inference(avatar_split_clause,[],[f88407,f11528,f2737,f2469,f1266,f148102]) ).
fof(f148102,plain,
( spl0_1741
<=> ! [X0] :
( estin = rotate_right(X0)
| little_set(f10(f1(rotate_right(X0),estin),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1741])]) ).
fof(f11528,plain,
( spl0_750
<=> ! [X0,X1] :
( member(f1(rotate_right(X0),X1),X1)
| rotate_right(X0) = X1
| little_set(f10(f1(rotate_right(X0),X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_750])]) ).
fof(f88407,plain,
( ! [X0] :
( estin = rotate_right(X0)
| little_set(f10(f1(rotate_right(X0),estin),X0)) )
| ~ spl0_119
| ~ spl0_175
| ~ spl0_210
| ~ spl0_750 ),
inference(forward_demodulation,[],[f88406,f85273]) ).
fof(f88406,plain,
( ! [X0] :
( rotate_right(X0) = domain_of(identity_relation)
| little_set(f10(f1(rotate_right(X0),estin),X0)) )
| ~ spl0_119
| ~ spl0_175
| ~ spl0_210
| ~ spl0_750 ),
inference(forward_demodulation,[],[f88405,f2471]) ).
fof(f88405,plain,
( ! [X0] :
( little_set(f10(f1(rotate_right(X0),estin),X0))
| rotate_right(X0) = domain_of(empty_set) )
| ~ spl0_119
| ~ spl0_175
| ~ spl0_210
| ~ spl0_750 ),
inference(forward_demodulation,[],[f88404,f85273]) ).
fof(f88404,plain,
( ! [X0] :
( little_set(f10(f1(rotate_right(X0),domain_of(identity_relation)),X0))
| rotate_right(X0) = domain_of(empty_set) )
| ~ spl0_119
| ~ spl0_175
| ~ spl0_750 ),
inference(forward_demodulation,[],[f15110,f2471]) ).
fof(f15110,plain,
( ! [X0] :
( little_set(f10(f1(rotate_right(X0),domain_of(empty_set)),X0))
| rotate_right(X0) = domain_of(empty_set) )
| ~ spl0_119
| ~ spl0_750 ),
inference(resolution,[],[f11529,f1267]) ).
fof(f11529,plain,
( ! [X0,X1] :
( little_set(f10(f1(rotate_right(X0),X1),X0))
| member(f1(rotate_right(X0),X1),X1)
| rotate_right(X0) = X1 )
| ~ spl0_750 ),
inference(avatar_component_clause,[],[f11528]) ).
fof(f148100,plain,
( spl0_1740
| ~ spl0_119
| ~ spl0_175
| ~ spl0_210
| ~ spl0_749 ),
inference(avatar_split_clause,[],[f88363,f11475,f2737,f2469,f1266,f148098]) ).
fof(f148098,plain,
( spl0_1740
<=> ! [X0] :
( estin = rotate_right(X0)
| little_set(f11(f1(rotate_right(X0),estin),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1740])]) ).
fof(f11475,plain,
( spl0_749
<=> ! [X0,X1] :
( member(f1(rotate_right(X0),X1),X1)
| rotate_right(X0) = X1
| little_set(f11(f1(rotate_right(X0),X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_749])]) ).
fof(f88363,plain,
( ! [X0] :
( estin = rotate_right(X0)
| little_set(f11(f1(rotate_right(X0),estin),X0)) )
| ~ spl0_119
| ~ spl0_175
| ~ spl0_210
| ~ spl0_749 ),
inference(forward_demodulation,[],[f88362,f85273]) ).
fof(f88362,plain,
( ! [X0] :
( rotate_right(X0) = domain_of(identity_relation)
| little_set(f11(f1(rotate_right(X0),estin),X0)) )
| ~ spl0_119
| ~ spl0_175
| ~ spl0_210
| ~ spl0_749 ),
inference(forward_demodulation,[],[f88361,f2471]) ).
fof(f88361,plain,
( ! [X0] :
( little_set(f11(f1(rotate_right(X0),estin),X0))
| rotate_right(X0) = domain_of(empty_set) )
| ~ spl0_119
| ~ spl0_175
| ~ spl0_210
| ~ spl0_749 ),
inference(forward_demodulation,[],[f88360,f85273]) ).
fof(f88360,plain,
( ! [X0] :
( little_set(f11(f1(rotate_right(X0),domain_of(identity_relation)),X0))
| rotate_right(X0) = domain_of(empty_set) )
| ~ spl0_119
| ~ spl0_175
| ~ spl0_749 ),
inference(forward_demodulation,[],[f14991,f2471]) ).
fof(f14991,plain,
( ! [X0] :
( little_set(f11(f1(rotate_right(X0),domain_of(empty_set)),X0))
| rotate_right(X0) = domain_of(empty_set) )
| ~ spl0_119
| ~ spl0_749 ),
inference(resolution,[],[f11476,f1267]) ).
fof(f11476,plain,
( ! [X0,X1] :
( little_set(f11(f1(rotate_right(X0),X1),X0))
| member(f1(rotate_right(X0),X1),X1)
| rotate_right(X0) = X1 )
| ~ spl0_749 ),
inference(avatar_component_clause,[],[f11475]) ).
fof(f148096,plain,
( spl0_1739
| ~ spl0_119
| ~ spl0_175
| ~ spl0_210
| ~ spl0_748 ),
inference(avatar_split_clause,[],[f88319,f11471,f2737,f2469,f1266,f148094]) ).
fof(f148094,plain,
( spl0_1739
<=> ! [X0] :
( estin = domain_of(X0)
| ordered_pair_predicate(f8(f1(domain_of(X0),estin),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1739])]) ).
fof(f11471,plain,
( spl0_748
<=> ! [X0,X1] :
( member(f1(domain_of(X0),X1),X1)
| domain_of(X0) = X1
| ordered_pair_predicate(f8(f1(domain_of(X0),X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_748])]) ).
fof(f88319,plain,
( ! [X0] :
( estin = domain_of(X0)
| ordered_pair_predicate(f8(f1(domain_of(X0),estin),X0)) )
| ~ spl0_119
| ~ spl0_175
| ~ spl0_210
| ~ spl0_748 ),
inference(forward_demodulation,[],[f88318,f85273]) ).
fof(f88318,plain,
( ! [X0] :
( domain_of(X0) = domain_of(identity_relation)
| ordered_pair_predicate(f8(f1(domain_of(X0),estin),X0)) )
| ~ spl0_119
| ~ spl0_175
| ~ spl0_210
| ~ spl0_748 ),
inference(forward_demodulation,[],[f88317,f2471]) ).
fof(f88317,plain,
( ! [X0] :
( ordered_pair_predicate(f8(f1(domain_of(X0),estin),X0))
| domain_of(X0) = domain_of(empty_set) )
| ~ spl0_119
| ~ spl0_175
| ~ spl0_210
| ~ spl0_748 ),
inference(forward_demodulation,[],[f88316,f85273]) ).
fof(f88316,plain,
( ! [X0] :
( ordered_pair_predicate(f8(f1(domain_of(X0),domain_of(identity_relation)),X0))
| domain_of(X0) = domain_of(empty_set) )
| ~ spl0_119
| ~ spl0_175
| ~ spl0_748 ),
inference(forward_demodulation,[],[f14872,f2471]) ).
fof(f14872,plain,
( ! [X0] :
( ordered_pair_predicate(f8(f1(domain_of(X0),domain_of(empty_set)),X0))
| domain_of(X0) = domain_of(empty_set) )
| ~ spl0_119
| ~ spl0_748 ),
inference(resolution,[],[f11472,f1267]) ).
fof(f11472,plain,
( ! [X0,X1] :
( ordered_pair_predicate(f8(f1(domain_of(X0),X1),X0))
| member(f1(domain_of(X0),X1),X1)
| domain_of(X0) = X1 )
| ~ spl0_748 ),
inference(avatar_component_clause,[],[f11471]) ).
fof(f148092,plain,
( spl0_1738
| ~ spl0_119
| ~ spl0_175
| ~ spl0_210
| ~ spl0_747 ),
inference(avatar_split_clause,[],[f88275,f11467,f2737,f2469,f1266,f148090]) ).
fof(f148090,plain,
( spl0_1738
<=> ! [X0] :
( second(X0) = estin
| little_set(f6(f1(second(X0),estin),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1738])]) ).
fof(f11467,plain,
( spl0_747
<=> ! [X0,X1] :
( member(f1(second(X0),X1),X1)
| second(X0) = X1
| little_set(f6(f1(second(X0),X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_747])]) ).
fof(f88275,plain,
( ! [X0] :
( second(X0) = estin
| little_set(f6(f1(second(X0),estin),X0)) )
| ~ spl0_119
| ~ spl0_175
| ~ spl0_210
| ~ spl0_747 ),
inference(forward_demodulation,[],[f88274,f85273]) ).
fof(f88274,plain,
( ! [X0] :
( second(X0) = domain_of(identity_relation)
| little_set(f6(f1(second(X0),estin),X0)) )
| ~ spl0_119
| ~ spl0_175
| ~ spl0_210
| ~ spl0_747 ),
inference(forward_demodulation,[],[f88273,f2471]) ).
fof(f88273,plain,
( ! [X0] :
( little_set(f6(f1(second(X0),estin),X0))
| second(X0) = domain_of(empty_set) )
| ~ spl0_119
| ~ spl0_175
| ~ spl0_210
| ~ spl0_747 ),
inference(forward_demodulation,[],[f88272,f85273]) ).
fof(f88272,plain,
( ! [X0] :
( little_set(f6(f1(second(X0),domain_of(identity_relation)),X0))
| second(X0) = domain_of(empty_set) )
| ~ spl0_119
| ~ spl0_175
| ~ spl0_747 ),
inference(forward_demodulation,[],[f14752,f2471]) ).
fof(f14752,plain,
( ! [X0] :
( little_set(f6(f1(second(X0),domain_of(empty_set)),X0))
| second(X0) = domain_of(empty_set) )
| ~ spl0_119
| ~ spl0_747 ),
inference(resolution,[],[f11468,f1267]) ).
fof(f11468,plain,
( ! [X0,X1] :
( little_set(f6(f1(second(X0),X1),X0))
| member(f1(second(X0),X1),X1)
| second(X0) = X1 )
| ~ spl0_747 ),
inference(avatar_component_clause,[],[f11467]) ).
fof(f148088,plain,
( spl0_1737
| ~ spl0_119
| ~ spl0_175
| ~ spl0_210
| ~ spl0_746 ),
inference(avatar_split_clause,[],[f88231,f11463,f2737,f2469,f1266,f148086]) ).
fof(f148086,plain,
( spl0_1737
<=> ! [X0] :
( second(X0) = estin
| little_set(f7(f1(second(X0),estin),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1737])]) ).
fof(f11463,plain,
( spl0_746
<=> ! [X0,X1] :
( member(f1(second(X0),X1),X1)
| second(X0) = X1
| little_set(f7(f1(second(X0),X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_746])]) ).
fof(f88231,plain,
( ! [X0] :
( second(X0) = estin
| little_set(f7(f1(second(X0),estin),X0)) )
| ~ spl0_119
| ~ spl0_175
| ~ spl0_210
| ~ spl0_746 ),
inference(forward_demodulation,[],[f88230,f85273]) ).
fof(f88230,plain,
( ! [X0] :
( second(X0) = domain_of(identity_relation)
| little_set(f7(f1(second(X0),estin),X0)) )
| ~ spl0_119
| ~ spl0_175
| ~ spl0_210
| ~ spl0_746 ),
inference(forward_demodulation,[],[f88229,f2471]) ).
fof(f88229,plain,
( ! [X0] :
( little_set(f7(f1(second(X0),estin),X0))
| second(X0) = domain_of(empty_set) )
| ~ spl0_119
| ~ spl0_175
| ~ spl0_210
| ~ spl0_746 ),
inference(forward_demodulation,[],[f88228,f85273]) ).
fof(f88228,plain,
( ! [X0] :
( little_set(f7(f1(second(X0),domain_of(identity_relation)),X0))
| second(X0) = domain_of(empty_set) )
| ~ spl0_119
| ~ spl0_175
| ~ spl0_746 ),
inference(forward_demodulation,[],[f14633,f2471]) ).
fof(f14633,plain,
( ! [X0] :
( little_set(f7(f1(second(X0),domain_of(empty_set)),X0))
| second(X0) = domain_of(empty_set) )
| ~ spl0_119
| ~ spl0_746 ),
inference(resolution,[],[f11464,f1267]) ).
fof(f11464,plain,
( ! [X0,X1] :
( little_set(f7(f1(second(X0),X1),X0))
| member(f1(second(X0),X1),X1)
| second(X0) = X1 )
| ~ spl0_746 ),
inference(avatar_component_clause,[],[f11463]) ).
fof(f148084,plain,
( spl0_1736
| ~ spl0_119
| ~ spl0_175
| ~ spl0_210
| ~ spl0_745 ),
inference(avatar_split_clause,[],[f88187,f11459,f2737,f2469,f1266,f148082]) ).
fof(f148082,plain,
( spl0_1736
<=> ! [X0] :
( first(X0) = estin
| little_set(f4(f1(first(X0),estin),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1736])]) ).
fof(f11459,plain,
( spl0_745
<=> ! [X0,X1] :
( member(f1(first(X0),X1),X1)
| first(X0) = X1
| little_set(f4(f1(first(X0),X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_745])]) ).
fof(f88187,plain,
( ! [X0] :
( first(X0) = estin
| little_set(f4(f1(first(X0),estin),X0)) )
| ~ spl0_119
| ~ spl0_175
| ~ spl0_210
| ~ spl0_745 ),
inference(forward_demodulation,[],[f88186,f85273]) ).
fof(f88186,plain,
( ! [X0] :
( first(X0) = domain_of(identity_relation)
| little_set(f4(f1(first(X0),estin),X0)) )
| ~ spl0_119
| ~ spl0_175
| ~ spl0_210
| ~ spl0_745 ),
inference(forward_demodulation,[],[f88185,f2471]) ).
fof(f88185,plain,
( ! [X0] :
( little_set(f4(f1(first(X0),estin),X0))
| first(X0) = domain_of(empty_set) )
| ~ spl0_119
| ~ spl0_175
| ~ spl0_210
| ~ spl0_745 ),
inference(forward_demodulation,[],[f88184,f85273]) ).
fof(f88184,plain,
( ! [X0] :
( little_set(f4(f1(first(X0),domain_of(identity_relation)),X0))
| first(X0) = domain_of(empty_set) )
| ~ spl0_119
| ~ spl0_175
| ~ spl0_745 ),
inference(forward_demodulation,[],[f14512,f2471]) ).
fof(f14512,plain,
( ! [X0] :
( little_set(f4(f1(first(X0),domain_of(empty_set)),X0))
| first(X0) = domain_of(empty_set) )
| ~ spl0_119
| ~ spl0_745 ),
inference(resolution,[],[f11460,f1267]) ).
fof(f11460,plain,
( ! [X0,X1] :
( little_set(f4(f1(first(X0),X1),X0))
| member(f1(first(X0),X1),X1)
| first(X0) = X1 )
| ~ spl0_745 ),
inference(avatar_component_clause,[],[f11459]) ).
fof(f148080,plain,
( spl0_1735
| ~ spl0_119
| ~ spl0_175
| ~ spl0_210
| ~ spl0_744 ),
inference(avatar_split_clause,[],[f88143,f11455,f2737,f2469,f1266,f148078]) ).
fof(f148078,plain,
( spl0_1735
<=> ! [X0] :
( first(X0) = estin
| little_set(f5(f1(first(X0),estin),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1735])]) ).
fof(f11455,plain,
( spl0_744
<=> ! [X0,X1] :
( member(f1(first(X0),X1),X1)
| first(X0) = X1
| little_set(f5(f1(first(X0),X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_744])]) ).
fof(f88143,plain,
( ! [X0] :
( first(X0) = estin
| little_set(f5(f1(first(X0),estin),X0)) )
| ~ spl0_119
| ~ spl0_175
| ~ spl0_210
| ~ spl0_744 ),
inference(forward_demodulation,[],[f88142,f85273]) ).
fof(f88142,plain,
( ! [X0] :
( first(X0) = domain_of(identity_relation)
| little_set(f5(f1(first(X0),estin),X0)) )
| ~ spl0_119
| ~ spl0_175
| ~ spl0_210
| ~ spl0_744 ),
inference(forward_demodulation,[],[f88141,f2471]) ).
fof(f88141,plain,
( ! [X0] :
( little_set(f5(f1(first(X0),estin),X0))
| first(X0) = domain_of(empty_set) )
| ~ spl0_119
| ~ spl0_175
| ~ spl0_210
| ~ spl0_744 ),
inference(forward_demodulation,[],[f88140,f85273]) ).
fof(f88140,plain,
( ! [X0] :
( little_set(f5(f1(first(X0),domain_of(identity_relation)),X0))
| first(X0) = domain_of(empty_set) )
| ~ spl0_119
| ~ spl0_175
| ~ spl0_744 ),
inference(forward_demodulation,[],[f14386,f2471]) ).
fof(f14386,plain,
( ! [X0] :
( little_set(f5(f1(first(X0),domain_of(empty_set)),X0))
| first(X0) = domain_of(empty_set) )
| ~ spl0_119
| ~ spl0_744 ),
inference(resolution,[],[f11456,f1267]) ).
fof(f11456,plain,
( ! [X0,X1] :
( little_set(f5(f1(first(X0),X1),X0))
| member(f1(first(X0),X1),X1)
| first(X0) = X1 )
| ~ spl0_744 ),
inference(avatar_component_clause,[],[f11455]) ).
fof(f148076,plain,
( spl0_1734
| ~ spl0_1181
| ~ spl0_1221 ),
inference(avatar_split_clause,[],[f37053,f36986,f33723,f148074]) ).
fof(f148074,plain,
( spl0_1734
<=> ! [X0,X1] :
( ~ member(X0,rotate_right(complement(sigma(X1))))
| ~ member(complement(sigma(X1)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1734])]) ).
fof(f33723,plain,
( spl0_1181
<=> ! [X2,X0,X1] :
( ~ member(X0,rotate_right(X1))
| ~ member(X1,X2)
| member(non_ordered_pair(non_ordered_pair(f10(X0,X1),f10(X0,X1)),non_ordered_pair(f10(X0,X1),non_ordered_pair(non_ordered_pair(f11(X0,X1),f11(X0,X1)),non_ordered_pair(f11(X0,X1),f9(X0,X1))))),sigma(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1181])]) ).
fof(f36986,plain,
( spl0_1221
<=> ! [X0,X1] :
( ~ member(X0,rotate_right(complement(X1)))
| ~ member(non_ordered_pair(non_ordered_pair(f10(X0,complement(X1)),f10(X0,complement(X1))),non_ordered_pair(f10(X0,complement(X1)),non_ordered_pair(non_ordered_pair(f11(X0,complement(X1)),f11(X0,complement(X1))),non_ordered_pair(f11(X0,complement(X1)),f9(X0,complement(X1)))))),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1221])]) ).
fof(f37053,plain,
( ! [X0,X1] :
( ~ member(X0,rotate_right(complement(sigma(X1))))
| ~ member(complement(sigma(X1)),X1) )
| ~ spl0_1181
| ~ spl0_1221 ),
inference(duplicate_literal_removal,[],[f37043]) ).
fof(f37043,plain,
( ! [X0,X1] :
( ~ member(X0,rotate_right(complement(sigma(X1))))
| ~ member(complement(sigma(X1)),X1)
| ~ member(X0,rotate_right(complement(sigma(X1)))) )
| ~ spl0_1181
| ~ spl0_1221 ),
inference(resolution,[],[f36987,f33724]) ).
fof(f33724,plain,
( ! [X2,X0,X1] :
( member(non_ordered_pair(non_ordered_pair(f10(X0,X1),f10(X0,X1)),non_ordered_pair(f10(X0,X1),non_ordered_pair(non_ordered_pair(f11(X0,X1),f11(X0,X1)),non_ordered_pair(f11(X0,X1),f9(X0,X1))))),sigma(X2))
| ~ member(X1,X2)
| ~ member(X0,rotate_right(X1)) )
| ~ spl0_1181 ),
inference(avatar_component_clause,[],[f33723]) ).
fof(f36987,plain,
( ! [X0,X1] :
( ~ member(non_ordered_pair(non_ordered_pair(f10(X0,complement(X1)),f10(X0,complement(X1))),non_ordered_pair(f10(X0,complement(X1)),non_ordered_pair(non_ordered_pair(f11(X0,complement(X1)),f11(X0,complement(X1))),non_ordered_pair(f11(X0,complement(X1)),f9(X0,complement(X1)))))),X1)
| ~ member(X0,rotate_right(complement(X1))) )
| ~ spl0_1221 ),
inference(avatar_component_clause,[],[f36986]) ).
fof(f148072,plain,
( spl0_1733
| ~ spl0_1180
| ~ spl0_1219 ),
inference(avatar_split_clause,[],[f37040,f36914,f33719,f148070]) ).
fof(f148070,plain,
( spl0_1733
<=> ! [X0,X1] :
( ~ member(X0,flip_range_of(complement(sigma(X1))))
| ~ member(complement(sigma(X1)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1733])]) ).
fof(f33719,plain,
( spl0_1180
<=> ! [X2,X0,X1] :
( ~ member(X0,flip_range_of(X1))
| ~ member(X1,X2)
| member(non_ordered_pair(non_ordered_pair(f12(X0,X1),f12(X0,X1)),non_ordered_pair(f12(X0,X1),non_ordered_pair(non_ordered_pair(f14(X0,X1),f14(X0,X1)),non_ordered_pair(f14(X0,X1),f13(X0,X1))))),sigma(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1180])]) ).
fof(f36914,plain,
( spl0_1219
<=> ! [X0,X1] :
( ~ member(X0,flip_range_of(complement(X1)))
| ~ member(non_ordered_pair(non_ordered_pair(f12(X0,complement(X1)),f12(X0,complement(X1))),non_ordered_pair(f12(X0,complement(X1)),non_ordered_pair(non_ordered_pair(f14(X0,complement(X1)),f14(X0,complement(X1))),non_ordered_pair(f14(X0,complement(X1)),f13(X0,complement(X1)))))),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1219])]) ).
fof(f37040,plain,
( ! [X0,X1] :
( ~ member(X0,flip_range_of(complement(sigma(X1))))
| ~ member(complement(sigma(X1)),X1) )
| ~ spl0_1180
| ~ spl0_1219 ),
inference(duplicate_literal_removal,[],[f37030]) ).
fof(f37030,plain,
( ! [X0,X1] :
( ~ member(X0,flip_range_of(complement(sigma(X1))))
| ~ member(complement(sigma(X1)),X1)
| ~ member(X0,flip_range_of(complement(sigma(X1)))) )
| ~ spl0_1180
| ~ spl0_1219 ),
inference(resolution,[],[f36915,f33720]) ).
fof(f33720,plain,
( ! [X2,X0,X1] :
( member(non_ordered_pair(non_ordered_pair(f12(X0,X1),f12(X0,X1)),non_ordered_pair(f12(X0,X1),non_ordered_pair(non_ordered_pair(f14(X0,X1),f14(X0,X1)),non_ordered_pair(f14(X0,X1),f13(X0,X1))))),sigma(X2))
| ~ member(X1,X2)
| ~ member(X0,flip_range_of(X1)) )
| ~ spl0_1180 ),
inference(avatar_component_clause,[],[f33719]) ).
fof(f36915,plain,
( ! [X0,X1] :
( ~ member(non_ordered_pair(non_ordered_pair(f12(X0,complement(X1)),f12(X0,complement(X1))),non_ordered_pair(f12(X0,complement(X1)),non_ordered_pair(non_ordered_pair(f14(X0,complement(X1)),f14(X0,complement(X1))),non_ordered_pair(f14(X0,complement(X1)),f13(X0,complement(X1)))))),X1)
| ~ member(X0,flip_range_of(complement(X1))) )
| ~ spl0_1219 ),
inference(avatar_component_clause,[],[f36914]) ).
fof(f148068,plain,
( ~ spl0_1730
| ~ spl0_1731
| spl0_1732
| ~ spl0_112
| ~ spl0_1554 ),
inference(avatar_split_clause,[],[f59395,f59389,f1089,f148065,f148061,f148057]) ).
fof(f1089,plain,
( spl0_112
<=> ! [X1,X3] :
( ~ little_set(X1)
| ~ little_set(X3)
| ordered_pair_predicate(non_ordered_pair(non_ordered_pair(X1,X1),non_ordered_pair(X1,X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_112])]) ).
fof(f59389,plain,
( spl0_1554
<=> f18(compose(a,b)) = non_ordered_pair(non_ordered_pair(f29(f18(compose(a,b)),a,b),f29(f18(compose(a,b)),a,b)),non_ordered_pair(f29(f18(compose(a,b)),a,b),f30(f18(compose(a,b)),a,b))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1554])]) ).
fof(f59395,plain,
( ordered_pair_predicate(f18(compose(a,b)))
| ~ little_set(f30(f18(compose(a,b)),a,b))
| ~ little_set(f29(f18(compose(a,b)),a,b))
| ~ spl0_112
| ~ spl0_1554 ),
inference(superposition,[],[f1090,f59391]) ).
fof(f59391,plain,
( f18(compose(a,b)) = non_ordered_pair(non_ordered_pair(f29(f18(compose(a,b)),a,b),f29(f18(compose(a,b)),a,b)),non_ordered_pair(f29(f18(compose(a,b)),a,b),f30(f18(compose(a,b)),a,b)))
| ~ spl0_1554 ),
inference(avatar_component_clause,[],[f59389]) ).
fof(f1090,plain,
( ! [X3,X1] :
( ordered_pair_predicate(non_ordered_pair(non_ordered_pair(X1,X1),non_ordered_pair(X1,X3)))
| ~ little_set(X3)
| ~ little_set(X1) )
| ~ spl0_112 ),
inference(avatar_component_clause,[],[f1089]) ).
fof(f148053,plain,
( spl0_1729
| ~ spl0_23
| ~ spl0_784 ),
inference(avatar_split_clause,[],[f16299,f16047,f281,f148051]) ).
fof(f148051,plain,
( spl0_1729
<=> ! [X0,X1] :
( cross_product(X0,X1) = identity_relation
| ordered_pair_predicate(f1(cross_product(X0,X1),identity_relation)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1729])]) ).
fof(f281,plain,
( spl0_23
<=> ! [X3] :
( ordered_pair_predicate(X3)
| ~ member(X3,identity_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_23])]) ).
fof(f16299,plain,
( ! [X0,X1] :
( cross_product(X0,X1) = identity_relation
| ordered_pair_predicate(f1(cross_product(X0,X1),identity_relation)) )
| ~ spl0_23
| ~ spl0_784 ),
inference(duplicate_literal_removal,[],[f16288]) ).
fof(f16288,plain,
( ! [X0,X1] :
( cross_product(X0,X1) = identity_relation
| ordered_pair_predicate(f1(cross_product(X0,X1),identity_relation))
| ordered_pair_predicate(f1(cross_product(X0,X1),identity_relation)) )
| ~ spl0_23
| ~ spl0_784 ),
inference(resolution,[],[f16048,f282]) ).
fof(f282,plain,
( ! [X3] :
( ~ member(X3,identity_relation)
| ordered_pair_predicate(X3) )
| ~ spl0_23 ),
inference(avatar_component_clause,[],[f281]) ).
fof(f148047,plain,
( spl0_1728
| ~ spl0_23
| ~ spl0_783 ),
inference(avatar_split_clause,[],[f16175,f16043,f281,f148045]) ).
fof(f148045,plain,
( spl0_1728
<=> ! [X0,X1] :
( cross_product(X0,X1) = identity_relation
| ordered_pair_predicate(f1(identity_relation,cross_product(X0,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1728])]) ).
fof(f16043,plain,
( spl0_783
<=> ! [X2,X0,X1] :
( member(f1(X0,cross_product(X1,X2)),X0)
| cross_product(X1,X2) = X0
| ordered_pair_predicate(f1(X0,cross_product(X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_783])]) ).
fof(f16175,plain,
( ! [X0,X1] :
( cross_product(X0,X1) = identity_relation
| ordered_pair_predicate(f1(identity_relation,cross_product(X0,X1))) )
| ~ spl0_23
| ~ spl0_783 ),
inference(duplicate_literal_removal,[],[f16164]) ).
fof(f16164,plain,
( ! [X0,X1] :
( cross_product(X0,X1) = identity_relation
| ordered_pair_predicate(f1(identity_relation,cross_product(X0,X1)))
| ordered_pair_predicate(f1(identity_relation,cross_product(X0,X1))) )
| ~ spl0_23
| ~ spl0_783 ),
inference(resolution,[],[f16044,f282]) ).
fof(f16044,plain,
( ! [X2,X0,X1] :
( member(f1(X0,cross_product(X1,X2)),X0)
| cross_product(X1,X2) = X0
| ordered_pair_predicate(f1(X0,cross_product(X1,X2))) )
| ~ spl0_783 ),
inference(avatar_component_clause,[],[f16043]) ).
fof(f148043,plain,
( spl0_1727
| ~ spl0_667
| ~ spl0_677 ),
inference(avatar_split_clause,[],[f10639,f9898,f9856,f148041]) ).
fof(f148041,plain,
( spl0_1727
<=> ! [X0,X3,X2,X1] :
( ~ member(X0,apply(cross_product(X1,X2),X3))
| member(X0,sigma(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1727])]) ).
fof(f9856,plain,
( spl0_667
<=> ! [X0,X3,X2,X1] :
( ~ member(X0,apply(cross_product(X1,X2),X3))
| member(second(f28(X0,cross_product(X1,X2),X3)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_667])]) ).
fof(f9898,plain,
( spl0_677
<=> ! [X0,X3,X2,X1] :
( ~ member(X0,apply(X1,X2))
| ~ member(second(f28(X0,X1,X2)),X3)
| member(X0,sigma(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_677])]) ).
fof(f10639,plain,
( ! [X2,X3,X0,X1] :
( ~ member(X0,apply(cross_product(X1,X2),X3))
| member(X0,sigma(X2)) )
| ~ spl0_667
| ~ spl0_677 ),
inference(duplicate_literal_removal,[],[f10621]) ).
fof(f10621,plain,
( ! [X2,X3,X0,X1] :
( ~ member(X0,apply(cross_product(X1,X2),X3))
| member(X0,sigma(X2))
| ~ member(X0,apply(cross_product(X1,X2),X3)) )
| ~ spl0_667
| ~ spl0_677 ),
inference(resolution,[],[f9899,f9857]) ).
fof(f9857,plain,
( ! [X2,X3,X0,X1] :
( member(second(f28(X0,cross_product(X1,X2),X3)),X2)
| ~ member(X0,apply(cross_product(X1,X2),X3)) )
| ~ spl0_667 ),
inference(avatar_component_clause,[],[f9856]) ).
fof(f9899,plain,
( ! [X2,X3,X0,X1] :
( ~ member(second(f28(X0,X1,X2)),X3)
| ~ member(X0,apply(X1,X2))
| member(X0,sigma(X3)) )
| ~ spl0_677 ),
inference(avatar_component_clause,[],[f9898]) ).
fof(f148039,plain,
( spl0_1726
| ~ spl0_28
| ~ spl0_643 ),
inference(avatar_split_clause,[],[f9342,f8670,f306,f148037]) ).
fof(f148037,plain,
( spl0_1726
<=> ! [X0,X1] :
( converse(X0) = converse(X1)
| ordered_pair_predicate(f1(converse(X1),converse(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1726])]) ).
fof(f306,plain,
( spl0_28
<=> ! [X0,X3] :
( ordered_pair_predicate(X3)
| ~ member(X3,converse(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_28])]) ).
fof(f8670,plain,
( spl0_643
<=> ! [X0,X1] :
( member(f1(X0,converse(X1)),X0)
| converse(X1) = X0
| ordered_pair_predicate(f1(X0,converse(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_643])]) ).
fof(f9342,plain,
( ! [X0,X1] :
( converse(X0) = converse(X1)
| ordered_pair_predicate(f1(converse(X1),converse(X0))) )
| ~ spl0_28
| ~ spl0_643 ),
inference(duplicate_literal_removal,[],[f9300]) ).
fof(f9300,plain,
( ! [X0,X1] :
( converse(X0) = converse(X1)
| ordered_pair_predicate(f1(converse(X1),converse(X0)))
| ordered_pair_predicate(f1(converse(X1),converse(X0))) )
| ~ spl0_28
| ~ spl0_643 ),
inference(resolution,[],[f8671,f307]) ).
fof(f307,plain,
( ! [X3,X0] :
( ~ member(X3,converse(X0))
| ordered_pair_predicate(X3) )
| ~ spl0_28 ),
inference(avatar_component_clause,[],[f306]) ).
fof(f8671,plain,
( ! [X0,X1] :
( member(f1(X0,converse(X1)),X0)
| converse(X1) = X0
| ordered_pair_predicate(f1(X0,converse(X1))) )
| ~ spl0_643 ),
inference(avatar_component_clause,[],[f8670]) ).
fof(f148035,plain,
( spl0_1725
| ~ spl0_28
| ~ spl0_581 ),
inference(avatar_split_clause,[],[f8361,f7464,f306,f148033]) ).
fof(f148033,plain,
( spl0_1725
<=> ! [X0,X1] :
( converse(X1) = X0
| ordered_pair_predicate(f1(X0,converse(X1)))
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1725])]) ).
fof(f7464,plain,
( spl0_581
<=> ! [X0,X1] :
( member(f1(X0,X1),X1)
| X0 = X1
| ordered_pair_predicate(f1(X0,X1))
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_581])]) ).
fof(f8361,plain,
( ! [X0,X1] :
( converse(X1) = X0
| ordered_pair_predicate(f1(X0,converse(X1)))
| ~ relation(X0) )
| ~ spl0_28
| ~ spl0_581 ),
inference(duplicate_literal_removal,[],[f8319]) ).
fof(f8319,plain,
( ! [X0,X1] :
( converse(X1) = X0
| ordered_pair_predicate(f1(X0,converse(X1)))
| ~ relation(X0)
| ordered_pair_predicate(f1(X0,converse(X1))) )
| ~ spl0_28
| ~ spl0_581 ),
inference(resolution,[],[f7465,f307]) ).
fof(f7465,plain,
( ! [X0,X1] :
( member(f1(X0,X1),X1)
| X0 = X1
| ordered_pair_predicate(f1(X0,X1))
| ~ relation(X0) )
| ~ spl0_581 ),
inference(avatar_component_clause,[],[f7464]) ).
fof(f148031,plain,
( spl0_1724
| ~ spl0_38
| ~ spl0_580 ),
inference(avatar_split_clause,[],[f8247,f7460,f353,f148029]) ).
fof(f148029,plain,
( spl0_1724
<=> ! [X0,X1] :
( X0 = X1
| ordered_pair_predicate(f1(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1724])]) ).
fof(f353,plain,
( spl0_38
<=> ! [X0,X3] :
( ~ relation(X3)
| ordered_pair_predicate(X0)
| ~ member(X0,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_38])]) ).
fof(f7460,plain,
( spl0_580
<=> ! [X0,X1] :
( member(f1(X0,X1),X0)
| X0 = X1
| ordered_pair_predicate(f1(X0,X1))
| ~ relation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_580])]) ).
fof(f8247,plain,
( ! [X0,X1] :
( X0 = X1
| ordered_pair_predicate(f1(X0,X1))
| ~ relation(X1)
| ~ relation(X0) )
| ~ spl0_38
| ~ spl0_580 ),
inference(duplicate_literal_removal,[],[f8183]) ).
fof(f8183,plain,
( ! [X0,X1] :
( X0 = X1
| ordered_pair_predicate(f1(X0,X1))
| ~ relation(X1)
| ordered_pair_predicate(f1(X0,X1))
| ~ relation(X0) )
| ~ spl0_38
| ~ spl0_580 ),
inference(resolution,[],[f7461,f354]) ).
fof(f354,plain,
( ! [X3,X0] :
( ~ member(X0,X3)
| ordered_pair_predicate(X0)
| ~ relation(X3) )
| ~ spl0_38 ),
inference(avatar_component_clause,[],[f353]) ).
fof(f7461,plain,
( ! [X0,X1] :
( member(f1(X0,X1),X0)
| X0 = X1
| ordered_pair_predicate(f1(X0,X1))
| ~ relation(X1) )
| ~ spl0_580 ),
inference(avatar_component_clause,[],[f7460]) ).
fof(f148027,plain,
( spl0_1723
| ~ spl0_28
| ~ spl0_580 ),
inference(avatar_split_clause,[],[f8245,f7460,f306,f148025]) ).
fof(f148025,plain,
( spl0_1723
<=> ! [X0,X1] :
( converse(X0) = X1
| ordered_pair_predicate(f1(converse(X0),X1))
| ~ relation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1723])]) ).
fof(f8245,plain,
( ! [X0,X1] :
( converse(X0) = X1
| ordered_pair_predicate(f1(converse(X0),X1))
| ~ relation(X1) )
| ~ spl0_28
| ~ spl0_580 ),
inference(duplicate_literal_removal,[],[f8203]) ).
fof(f8203,plain,
( ! [X0,X1] :
( converse(X0) = X1
| ordered_pair_predicate(f1(converse(X0),X1))
| ~ relation(X1)
| ordered_pair_predicate(f1(converse(X0),X1)) )
| ~ spl0_28
| ~ spl0_580 ),
inference(resolution,[],[f7461,f307]) ).
fof(f148023,plain,
( spl0_1722
| ~ spl0_348
| ~ spl0_482 ),
inference(avatar_split_clause,[],[f7149,f5674,f3895,f148021]) ).
fof(f148021,plain,
( spl0_1722
<=> ! [X0,X1] :
( ~ member(complement(sigma(X0)),X0)
| ~ member(X1,range_of(complement(sigma(X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1722])]) ).
fof(f3895,plain,
( spl0_348
<=> ! [X0,X1] :
( ~ member(X0,range_of(complement(X1)))
| ~ member(f27(X0,complement(X1)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_348])]) ).
fof(f5674,plain,
( spl0_482
<=> ! [X2,X0,X1] :
( ~ member(X0,X1)
| member(f27(X2,X0),sigma(X1))
| ~ member(X2,range_of(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_482])]) ).
fof(f7149,plain,
( ! [X0,X1] :
( ~ member(complement(sigma(X0)),X0)
| ~ member(X1,range_of(complement(sigma(X0)))) )
| ~ spl0_348
| ~ spl0_482 ),
inference(duplicate_literal_removal,[],[f7140]) ).
fof(f7140,plain,
( ! [X0,X1] :
( ~ member(complement(sigma(X0)),X0)
| ~ member(X1,range_of(complement(sigma(X0))))
| ~ member(X1,range_of(complement(sigma(X0)))) )
| ~ spl0_348
| ~ spl0_482 ),
inference(resolution,[],[f5675,f3896]) ).
fof(f3896,plain,
( ! [X0,X1] :
( ~ member(f27(X0,complement(X1)),X1)
| ~ member(X0,range_of(complement(X1))) )
| ~ spl0_348 ),
inference(avatar_component_clause,[],[f3895]) ).
fof(f5675,plain,
( ! [X2,X0,X1] :
( member(f27(X2,X0),sigma(X1))
| ~ member(X0,X1)
| ~ member(X2,range_of(X0)) )
| ~ spl0_482 ),
inference(avatar_component_clause,[],[f5674]) ).
fof(f148019,plain,
( spl0_1721
| ~ spl0_345
| ~ spl0_479 ),
inference(avatar_split_clause,[],[f7130,f5660,f3855,f148017]) ).
fof(f148017,plain,
( spl0_1721
<=> ! [X0,X1] :
( ~ member(complement(sigma(X0)),X0)
| ~ member(X1,sigma(complement(sigma(X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1721])]) ).
fof(f3855,plain,
( spl0_345
<=> ! [X0,X1] :
( ~ member(X0,sigma(complement(X1)))
| ~ member(f16(X0,complement(X1)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_345])]) ).
fof(f5660,plain,
( spl0_479
<=> ! [X2,X0,X1] :
( ~ member(X0,X1)
| member(f16(X2,X0),sigma(X1))
| ~ member(X2,sigma(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_479])]) ).
fof(f7130,plain,
( ! [X0,X1] :
( ~ member(complement(sigma(X0)),X0)
| ~ member(X1,sigma(complement(sigma(X0)))) )
| ~ spl0_345
| ~ spl0_479 ),
inference(duplicate_literal_removal,[],[f7119]) ).
fof(f7119,plain,
( ! [X0,X1] :
( ~ member(complement(sigma(X0)),X0)
| ~ member(X1,sigma(complement(sigma(X0))))
| ~ member(X1,sigma(complement(sigma(X0)))) )
| ~ spl0_345
| ~ spl0_479 ),
inference(resolution,[],[f5661,f3856]) ).
fof(f3856,plain,
( ! [X0,X1] :
( ~ member(f16(X0,complement(X1)),X1)
| ~ member(X0,sigma(complement(X1))) )
| ~ spl0_345 ),
inference(avatar_component_clause,[],[f3855]) ).
fof(f5661,plain,
( ! [X2,X0,X1] :
( member(f16(X2,X0),sigma(X1))
| ~ member(X0,X1)
| ~ member(X2,sigma(X0)) )
| ~ spl0_479 ),
inference(avatar_component_clause,[],[f5660]) ).
fof(f148015,plain,
( spl0_1720
| ~ spl0_343
| ~ spl0_478 ),
inference(avatar_split_clause,[],[f7118,f5656,f3847,f148013]) ).
fof(f148013,plain,
( spl0_1720
<=> ! [X0,X1] :
( ~ member(complement(sigma(X0)),X0)
| ~ member(X1,domain_of(complement(sigma(X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1720])]) ).
fof(f3847,plain,
( spl0_343
<=> ! [X0,X1] :
( ~ member(X0,domain_of(complement(X1)))
| ~ member(f8(X0,complement(X1)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_343])]) ).
fof(f5656,plain,
( spl0_478
<=> ! [X2,X0,X1] :
( ~ member(X0,X1)
| member(f8(X2,X0),sigma(X1))
| ~ member(X2,domain_of(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_478])]) ).
fof(f7118,plain,
( ! [X0,X1] :
( ~ member(complement(sigma(X0)),X0)
| ~ member(X1,domain_of(complement(sigma(X0)))) )
| ~ spl0_343
| ~ spl0_478 ),
inference(duplicate_literal_removal,[],[f7109]) ).
fof(f7109,plain,
( ! [X0,X1] :
( ~ member(complement(sigma(X0)),X0)
| ~ member(X1,domain_of(complement(sigma(X0))))
| ~ member(X1,domain_of(complement(sigma(X0)))) )
| ~ spl0_343
| ~ spl0_478 ),
inference(resolution,[],[f5657,f3848]) ).
fof(f3848,plain,
( ! [X0,X1] :
( ~ member(f8(X0,complement(X1)),X1)
| ~ member(X0,domain_of(complement(X1))) )
| ~ spl0_343 ),
inference(avatar_component_clause,[],[f3847]) ).
fof(f5657,plain,
( ! [X2,X0,X1] :
( member(f8(X2,X0),sigma(X1))
| ~ member(X0,X1)
| ~ member(X2,domain_of(X0)) )
| ~ spl0_478 ),
inference(avatar_component_clause,[],[f5656]) ).
fof(f147827,plain,
( spl0_1719
| ~ spl0_23
| ~ spl0_435 ),
inference(avatar_split_clause,[],[f5445,f5175,f281,f147825]) ).
fof(f147825,plain,
( spl0_1719
<=> ! [X0] :
( estin = cross_product(X0,identity_relation)
| ordered_pair_predicate(second(f24(cross_product(X0,identity_relation)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1719])]) ).
fof(f5175,plain,
( spl0_435
<=> ! [X0,X1] :
( estin = cross_product(X0,X1)
| member(second(f24(cross_product(X0,X1))),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_435])]) ).
fof(f5445,plain,
( ! [X0] :
( estin = cross_product(X0,identity_relation)
| ordered_pair_predicate(second(f24(cross_product(X0,identity_relation)))) )
| ~ spl0_23
| ~ spl0_435 ),
inference(resolution,[],[f5176,f282]) ).
fof(f5176,plain,
( ! [X0,X1] :
( member(second(f24(cross_product(X0,X1))),X1)
| estin = cross_product(X0,X1) )
| ~ spl0_435 ),
inference(avatar_component_clause,[],[f5175]) ).
fof(f147823,plain,
( spl0_1718
| ~ spl0_11
| ~ spl0_435 ),
inference(avatar_split_clause,[],[f5396,f5175,f232,f147821]) ).
fof(f147821,plain,
( spl0_1718
<=> ! [X0,X1] :
( estin = cross_product(X0,X1)
| little_set(second(f24(cross_product(X0,X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1718])]) ).
fof(f232,plain,
( spl0_11
<=> ! [X0,X1] :
( little_set(X0)
| ~ member(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).
fof(f5396,plain,
( ! [X0,X1] :
( estin = cross_product(X0,X1)
| little_set(second(f24(cross_product(X0,X1)))) )
| ~ spl0_11
| ~ spl0_435 ),
inference(resolution,[],[f5176,f233]) ).
fof(f233,plain,
( ! [X0,X1] :
( ~ member(X0,X1)
| little_set(X0) )
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f232]) ).
fof(f147818,plain,
( spl0_1717
| ~ spl0_23
| ~ spl0_433 ),
inference(avatar_split_clause,[],[f5358,f5166,f281,f147816]) ).
fof(f147816,plain,
( spl0_1717
<=> ! [X0] :
( estin = cross_product(identity_relation,X0)
| ordered_pair_predicate(first(f24(cross_product(identity_relation,X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1717])]) ).
fof(f5166,plain,
( spl0_433
<=> ! [X0,X1] :
( estin = cross_product(X0,X1)
| member(first(f24(cross_product(X0,X1))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_433])]) ).
fof(f5358,plain,
( ! [X0] :
( estin = cross_product(identity_relation,X0)
| ordered_pair_predicate(first(f24(cross_product(identity_relation,X0)))) )
| ~ spl0_23
| ~ spl0_433 ),
inference(resolution,[],[f5167,f282]) ).
fof(f5167,plain,
( ! [X0,X1] :
( member(first(f24(cross_product(X0,X1))),X0)
| estin = cross_product(X0,X1) )
| ~ spl0_433 ),
inference(avatar_component_clause,[],[f5166]) ).
fof(f147814,plain,
( spl0_1716
| ~ spl0_11
| ~ spl0_433 ),
inference(avatar_split_clause,[],[f5309,f5166,f232,f147812]) ).
fof(f147812,plain,
( spl0_1716
<=> ! [X0,X1] :
( estin = cross_product(X0,X1)
| little_set(first(f24(cross_product(X0,X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1716])]) ).
fof(f5309,plain,
( ! [X0,X1] :
( estin = cross_product(X0,X1)
| little_set(first(f24(cross_product(X0,X1)))) )
| ~ spl0_11
| ~ spl0_433 ),
inference(resolution,[],[f5167,f233]) ).
fof(f147810,plain,
( spl0_1715
| ~ spl0_188
| ~ spl0_389 ),
inference(avatar_split_clause,[],[f5192,f4355,f2542,f147808]) ).
fof(f147808,plain,
( spl0_1715
<=> ! [X0,X1] :
( ordered_pair_predicate(f16(estin,cross_product(X0,X1)))
| ~ member(infinity,cross_product(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1715])]) ).
fof(f2542,plain,
( spl0_188
<=> ! [X0] :
( member(estin,sigma(X0))
| ~ member(infinity,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_188])]) ).
fof(f4355,plain,
( spl0_389
<=> ! [X2,X0,X1] :
( ~ member(X0,sigma(cross_product(X1,X2)))
| ordered_pair_predicate(f16(X0,cross_product(X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_389])]) ).
fof(f5192,plain,
( ! [X0,X1] :
( ordered_pair_predicate(f16(estin,cross_product(X0,X1)))
| ~ member(infinity,cross_product(X0,X1)) )
| ~ spl0_188
| ~ spl0_389 ),
inference(resolution,[],[f4356,f2543]) ).
fof(f2543,plain,
( ! [X0] :
( member(estin,sigma(X0))
| ~ member(infinity,X0) )
| ~ spl0_188 ),
inference(avatar_component_clause,[],[f2542]) ).
fof(f4356,plain,
( ! [X2,X0,X1] :
( ~ member(X0,sigma(cross_product(X1,X2)))
| ordered_pair_predicate(f16(X0,cross_product(X1,X2))) )
| ~ spl0_389 ),
inference(avatar_component_clause,[],[f4355]) ).
fof(f147804,plain,
( spl0_1714
| ~ spl0_23
| ~ spl0_364 ),
inference(avatar_split_clause,[],[f5106,f4242,f281,f147802]) ).
fof(f147802,plain,
( spl0_1714
<=> ! [X0,X1] :
( disjoint(X0,intersection(identity_relation,X1))
| ordered_pair_predicate(f23(X0,intersection(identity_relation,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1714])]) ).
fof(f4242,plain,
( spl0_364
<=> ! [X2,X0,X1] :
( disjoint(X0,intersection(X1,X2))
| member(f23(X0,intersection(X1,X2)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_364])]) ).
fof(f5106,plain,
( ! [X0,X1] :
( disjoint(X0,intersection(identity_relation,X1))
| ordered_pair_predicate(f23(X0,intersection(identity_relation,X1))) )
| ~ spl0_23
| ~ spl0_364 ),
inference(resolution,[],[f4243,f282]) ).
fof(f4243,plain,
( ! [X2,X0,X1] :
( member(f23(X0,intersection(X1,X2)),X1)
| disjoint(X0,intersection(X1,X2)) )
| ~ spl0_364 ),
inference(avatar_component_clause,[],[f4242]) ).
fof(f147798,plain,
( spl0_1713
| ~ spl0_23
| ~ spl0_363 ),
inference(avatar_split_clause,[],[f5003,f4238,f281,f147796]) ).
fof(f147796,plain,
( spl0_1713
<=> ! [X0,X1] :
( disjoint(X0,intersection(X1,identity_relation))
| ordered_pair_predicate(f23(X0,intersection(X1,identity_relation))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1713])]) ).
fof(f4238,plain,
( spl0_363
<=> ! [X2,X0,X1] :
( disjoint(X0,intersection(X1,X2))
| member(f23(X0,intersection(X1,X2)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_363])]) ).
fof(f5003,plain,
( ! [X0,X1] :
( disjoint(X0,intersection(X1,identity_relation))
| ordered_pair_predicate(f23(X0,intersection(X1,identity_relation))) )
| ~ spl0_23
| ~ spl0_363 ),
inference(resolution,[],[f4239,f282]) ).
fof(f4239,plain,
( ! [X2,X0,X1] :
( member(f23(X0,intersection(X1,X2)),X2)
| disjoint(X0,intersection(X1,X2)) )
| ~ spl0_363 ),
inference(avatar_component_clause,[],[f4238]) ).
fof(f147792,plain,
( spl0_1712
| ~ spl0_23
| ~ spl0_362 ),
inference(avatar_split_clause,[],[f4900,f4234,f281,f147790]) ).
fof(f147790,plain,
( spl0_1712
<=> ! [X0,X1] :
( disjoint(intersection(identity_relation,X0),X1)
| ordered_pair_predicate(f23(intersection(identity_relation,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1712])]) ).
fof(f4234,plain,
( spl0_362
<=> ! [X2,X0,X1] :
( disjoint(intersection(X0,X1),X2)
| member(f23(intersection(X0,X1),X2),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_362])]) ).
fof(f4900,plain,
( ! [X0,X1] :
( disjoint(intersection(identity_relation,X0),X1)
| ordered_pair_predicate(f23(intersection(identity_relation,X0),X1)) )
| ~ spl0_23
| ~ spl0_362 ),
inference(resolution,[],[f4235,f282]) ).
fof(f4235,plain,
( ! [X2,X0,X1] :
( member(f23(intersection(X0,X1),X2),X0)
| disjoint(intersection(X0,X1),X2) )
| ~ spl0_362 ),
inference(avatar_component_clause,[],[f4234]) ).
fof(f147786,plain,
( spl0_1711
| ~ spl0_23
| ~ spl0_361 ),
inference(avatar_split_clause,[],[f4797,f4230,f281,f147784]) ).
fof(f147784,plain,
( spl0_1711
<=> ! [X0,X1] :
( disjoint(intersection(X0,identity_relation),X1)
| ordered_pair_predicate(f23(intersection(X0,identity_relation),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1711])]) ).
fof(f4230,plain,
( spl0_361
<=> ! [X2,X0,X1] :
( disjoint(intersection(X0,X1),X2)
| member(f23(intersection(X0,X1),X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_361])]) ).
fof(f4797,plain,
( ! [X0,X1] :
( disjoint(intersection(X0,identity_relation),X1)
| ordered_pair_predicate(f23(intersection(X0,identity_relation),X1)) )
| ~ spl0_23
| ~ spl0_361 ),
inference(resolution,[],[f4231,f282]) ).
fof(f4231,plain,
( ! [X2,X0,X1] :
( member(f23(intersection(X0,X1),X2),X1)
| disjoint(intersection(X0,X1),X2) )
| ~ spl0_361 ),
inference(avatar_component_clause,[],[f4230]) ).
fof(f147780,plain,
( spl0_1710
| ~ spl0_23
| ~ spl0_360 ),
inference(avatar_split_clause,[],[f4694,f4226,f281,f147778]) ).
fof(f147778,plain,
( spl0_1710
<=> ! [X0,X1] :
( subset(intersection(identity_relation,X0),X1)
| ordered_pair_predicate(f17(intersection(identity_relation,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1710])]) ).
fof(f4226,plain,
( spl0_360
<=> ! [X2,X0,X1] :
( subset(intersection(X0,X1),X2)
| member(f17(intersection(X0,X1),X2),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_360])]) ).
fof(f4694,plain,
( ! [X0,X1] :
( subset(intersection(identity_relation,X0),X1)
| ordered_pair_predicate(f17(intersection(identity_relation,X0),X1)) )
| ~ spl0_23
| ~ spl0_360 ),
inference(resolution,[],[f4227,f282]) ).
fof(f4227,plain,
( ! [X2,X0,X1] :
( member(f17(intersection(X0,X1),X2),X0)
| subset(intersection(X0,X1),X2) )
| ~ spl0_360 ),
inference(avatar_component_clause,[],[f4226]) ).
fof(f147586,plain,
( spl0_1709
| ~ spl0_23
| ~ spl0_359 ),
inference(avatar_split_clause,[],[f4591,f4222,f281,f147584]) ).
fof(f147584,plain,
( spl0_1709
<=> ! [X0,X1] :
( subset(intersection(X0,identity_relation),X1)
| ordered_pair_predicate(f17(intersection(X0,identity_relation),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1709])]) ).
fof(f4222,plain,
( spl0_359
<=> ! [X2,X0,X1] :
( subset(intersection(X0,X1),X2)
| member(f17(intersection(X0,X1),X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_359])]) ).
fof(f4591,plain,
( ! [X0,X1] :
( subset(intersection(X0,identity_relation),X1)
| ordered_pair_predicate(f17(intersection(X0,identity_relation),X1)) )
| ~ spl0_23
| ~ spl0_359 ),
inference(resolution,[],[f4223,f282]) ).
fof(f4223,plain,
( ! [X2,X0,X1] :
( member(f17(intersection(X0,X1),X2),X1)
| subset(intersection(X0,X1),X2) )
| ~ spl0_359 ),
inference(avatar_component_clause,[],[f4222]) ).
fof(f147582,plain,
( spl0_1708
| ~ spl0_197
| ~ spl0_358 ),
inference(avatar_split_clause,[],[f4215,f4034,f2585,f147580]) ).
fof(f147580,plain,
( spl0_1708
<=> ! [X0,X1] :
( ~ member(X0,X1)
| estin = X0
| little_set(f16(f24(X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1708])]) ).
fof(f2585,plain,
( spl0_197
<=> ! [X0,X1] :
( ~ member(X0,sigma(X1))
| little_set(f16(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_197])]) ).
fof(f4034,plain,
( spl0_358
<=> ! [X0,X1] :
( estin = X0
| ~ member(X0,X1)
| member(f24(X0),sigma(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_358])]) ).
fof(f4215,plain,
( ! [X0,X1] :
( ~ member(X0,X1)
| estin = X0
| little_set(f16(f24(X0),X1)) )
| ~ spl0_197
| ~ spl0_358 ),
inference(resolution,[],[f4035,f2586]) ).
fof(f2586,plain,
( ! [X0,X1] :
( ~ member(X0,sigma(X1))
| little_set(f16(X0,X1)) )
| ~ spl0_197 ),
inference(avatar_component_clause,[],[f2585]) ).
fof(f4035,plain,
( ! [X0,X1] :
( member(f24(X0),sigma(X1))
| ~ member(X0,X1)
| estin = X0 )
| ~ spl0_358 ),
inference(avatar_component_clause,[],[f4034]) ).
fof(f147578,plain,
( spl0_1707
| ~ spl0_30
| ~ spl0_294 ),
inference(avatar_split_clause,[],[f3648,f3545,f314,f147576]) ).
fof(f147576,plain,
( spl0_1707
<=> ! [X0] :
( ~ member(f18(f24(X0)),X0)
| estin = X0
| relation(f24(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1707])]) ).
fof(f314,plain,
( spl0_30
<=> ! [X3] :
( relation(X3)
| member(f18(X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_30])]) ).
fof(f3545,plain,
( spl0_294
<=> ! [X0,X1] :
( estin = X1
| ~ member(X0,X1)
| ~ member(X0,f24(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_294])]) ).
fof(f3648,plain,
( ! [X0] :
( ~ member(f18(f24(X0)),X0)
| estin = X0
| relation(f24(X0)) )
| ~ spl0_30
| ~ spl0_294 ),
inference(resolution,[],[f3546,f315]) ).
fof(f315,plain,
( ! [X3] :
( member(f18(X3),X3)
| relation(X3) )
| ~ spl0_30 ),
inference(avatar_component_clause,[],[f314]) ).
fof(f3546,plain,
( ! [X0,X1] :
( ~ member(X0,f24(X1))
| ~ member(X0,X1)
| estin = X1 )
| ~ spl0_294 ),
inference(avatar_component_clause,[],[f3545]) ).
fof(f147574,plain,
( spl0_1706
| ~ spl0_38
| ~ spl0_275 ),
inference(avatar_split_clause,[],[f3558,f3206,f353,f147572]) ).
fof(f147572,plain,
( spl0_1706
<=> ! [X0,X1] :
( ~ member(X0,X1)
| relation(X0)
| ordered_pair_predicate(f18(X0))
| ~ relation(sigma(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1706])]) ).
fof(f3206,plain,
( spl0_275
<=> ! [X0,X1] :
( ~ member(X0,X1)
| member(f18(X0),sigma(X1))
| relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_275])]) ).
fof(f3558,plain,
( ! [X0,X1] :
( ~ member(X0,X1)
| relation(X0)
| ordered_pair_predicate(f18(X0))
| ~ relation(sigma(X1)) )
| ~ spl0_38
| ~ spl0_275 ),
inference(resolution,[],[f3207,f354]) ).
fof(f3207,plain,
( ! [X0,X1] :
( member(f18(X0),sigma(X1))
| ~ member(X0,X1)
| relation(X0) )
| ~ spl0_275 ),
inference(avatar_component_clause,[],[f3206]) ).
fof(f147570,plain,
( spl0_1705
| ~ spl0_234
| ~ spl0_269 ),
inference(avatar_split_clause,[],[f3513,f3178,f2977,f147568]) ).
fof(f147568,plain,
( spl0_1705
<=> ! [X0,X1] :
( ordered_pair_predicate(f16(X0,converse(X1)))
| ~ member(universal_set,converse(X1))
| ~ little_set(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1705])]) ).
fof(f2977,plain,
( spl0_234
<=> ! [X0,X1] :
( ~ member(universal_set,X0)
| member(X1,sigma(X0))
| ~ little_set(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_234])]) ).
fof(f3178,plain,
( spl0_269
<=> ! [X0,X1] :
( ~ member(X0,sigma(converse(X1)))
| ordered_pair_predicate(f16(X0,converse(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_269])]) ).
fof(f3513,plain,
( ! [X0,X1] :
( ordered_pair_predicate(f16(X0,converse(X1)))
| ~ member(universal_set,converse(X1))
| ~ little_set(X0) )
| ~ spl0_234
| ~ spl0_269 ),
inference(resolution,[],[f3179,f2978]) ).
fof(f2978,plain,
( ! [X0,X1] :
( member(X1,sigma(X0))
| ~ member(universal_set,X0)
| ~ little_set(X1) )
| ~ spl0_234 ),
inference(avatar_component_clause,[],[f2977]) ).
fof(f3179,plain,
( ! [X0,X1] :
( ~ member(X0,sigma(converse(X1)))
| ordered_pair_predicate(f16(X0,converse(X1))) )
| ~ spl0_269 ),
inference(avatar_component_clause,[],[f3178]) ).
fof(f147566,plain,
( spl0_1704
| ~ spl0_30
| ~ spl0_268 ),
inference(avatar_split_clause,[],[f3499,f3174,f314,f147564]) ).
fof(f147564,plain,
( spl0_1704
<=> ! [X0] :
( ordered_pair_predicate(f16(f18(sigma(X0)),X0))
| ~ relation(X0)
| relation(sigma(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1704])]) ).
fof(f3174,plain,
( spl0_268
<=> ! [X0,X1] :
( ~ member(X0,sigma(X1))
| ordered_pair_predicate(f16(X0,X1))
| ~ relation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_268])]) ).
fof(f3499,plain,
( ! [X0] :
( ordered_pair_predicate(f16(f18(sigma(X0)),X0))
| ~ relation(X0)
| relation(sigma(X0)) )
| ~ spl0_30
| ~ spl0_268 ),
inference(resolution,[],[f3175,f315]) ).
fof(f3175,plain,
( ! [X0,X1] :
( ~ member(X0,sigma(X1))
| ordered_pair_predicate(f16(X0,X1))
| ~ relation(X1) )
| ~ spl0_268 ),
inference(avatar_component_clause,[],[f3174]) ).
fof(f147562,plain,
( spl0_1703
| ~ spl0_234
| ~ spl0_268 ),
inference(avatar_split_clause,[],[f3482,f3174,f2977,f147560]) ).
fof(f147560,plain,
( spl0_1703
<=> ! [X0,X1] :
( ordered_pair_predicate(f16(X0,X1))
| ~ relation(X1)
| ~ member(universal_set,X1)
| ~ little_set(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1703])]) ).
fof(f3482,plain,
( ! [X0,X1] :
( ordered_pair_predicate(f16(X0,X1))
| ~ relation(X1)
| ~ member(universal_set,X1)
| ~ little_set(X0) )
| ~ spl0_234
| ~ spl0_268 ),
inference(resolution,[],[f3175,f2978]) ).
fof(f147558,plain,
( spl0_1702
| ~ spl0_28
| ~ spl0_246 ),
inference(avatar_split_clause,[],[f3343,f3071,f306,f147556]) ).
fof(f147556,plain,
( spl0_1702
<=> ! [X0,X1] :
( relation(intersection(X0,converse(X1)))
| ordered_pair_predicate(f18(intersection(X0,converse(X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1702])]) ).
fof(f3071,plain,
( spl0_246
<=> ! [X0,X1] :
( member(f18(intersection(X0,X1)),X1)
| relation(intersection(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_246])]) ).
fof(f3343,plain,
( ! [X0,X1] :
( relation(intersection(X0,converse(X1)))
| ordered_pair_predicate(f18(intersection(X0,converse(X1)))) )
| ~ spl0_28
| ~ spl0_246 ),
inference(resolution,[],[f3072,f307]) ).
fof(f3072,plain,
( ! [X0,X1] :
( member(f18(intersection(X0,X1)),X1)
| relation(intersection(X0,X1)) )
| ~ spl0_246 ),
inference(avatar_component_clause,[],[f3071]) ).
fof(f147554,plain,
( spl0_1701
| ~ spl0_38
| ~ spl0_246 ),
inference(avatar_split_clause,[],[f3324,f3071,f353,f147552]) ).
fof(f147552,plain,
( spl0_1701
<=> ! [X0,X1] :
( relation(intersection(X0,X1))
| ordered_pair_predicate(f18(intersection(X0,X1)))
| ~ relation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1701])]) ).
fof(f3324,plain,
( ! [X0,X1] :
( relation(intersection(X0,X1))
| ordered_pair_predicate(f18(intersection(X0,X1)))
| ~ relation(X1) )
| ~ spl0_38
| ~ spl0_246 ),
inference(resolution,[],[f3072,f354]) ).
fof(f147550,plain,
( spl0_1700
| ~ spl0_28
| ~ spl0_245 ),
inference(avatar_split_clause,[],[f3263,f3067,f306,f147548]) ).
fof(f147548,plain,
( spl0_1700
<=> ! [X0,X1] :
( relation(intersection(converse(X0),X1))
| ordered_pair_predicate(f18(intersection(converse(X0),X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1700])]) ).
fof(f3067,plain,
( spl0_245
<=> ! [X0,X1] :
( member(f18(intersection(X0,X1)),X0)
| relation(intersection(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_245])]) ).
fof(f3263,plain,
( ! [X0,X1] :
( relation(intersection(converse(X0),X1))
| ordered_pair_predicate(f18(intersection(converse(X0),X1))) )
| ~ spl0_28
| ~ spl0_245 ),
inference(resolution,[],[f3068,f307]) ).
fof(f3068,plain,
( ! [X0,X1] :
( member(f18(intersection(X0,X1)),X0)
| relation(intersection(X0,X1)) )
| ~ spl0_245 ),
inference(avatar_component_clause,[],[f3067]) ).
fof(f147546,plain,
( spl0_1699
| ~ spl0_1517
| spl0_1574 ),
inference(avatar_split_clause,[],[f69028,f60207,f58343,f147543]) ).
fof(f147543,plain,
( spl0_1699
<=> estin = second(f18(estin)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1699])]) ).
fof(f58343,plain,
( spl0_1517
<=> ! [X0] :
( little_set(X0)
| second(X0) = estin ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1517])]) ).
fof(f60207,plain,
( spl0_1574
<=> little_set(f18(estin)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1574])]) ).
fof(f69028,plain,
( estin = second(f18(estin))
| ~ spl0_1517
| spl0_1574 ),
inference(resolution,[],[f60209,f58344]) ).
fof(f58344,plain,
( ! [X0] :
( little_set(X0)
| second(X0) = estin )
| ~ spl0_1517 ),
inference(avatar_component_clause,[],[f58343]) ).
fof(f60209,plain,
( ~ little_set(f18(estin))
| spl0_1574 ),
inference(avatar_component_clause,[],[f60207]) ).
fof(f147541,plain,
( spl0_1698
| ~ spl0_38
| ~ spl0_245 ),
inference(avatar_split_clause,[],[f3244,f3067,f353,f147539]) ).
fof(f147539,plain,
( spl0_1698
<=> ! [X0,X1] :
( relation(intersection(X0,X1))
| ordered_pair_predicate(f18(intersection(X0,X1)))
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1698])]) ).
fof(f3244,plain,
( ! [X0,X1] :
( relation(intersection(X0,X1))
| ordered_pair_predicate(f18(intersection(X0,X1)))
| ~ relation(X0) )
| ~ spl0_38
| ~ spl0_245 ),
inference(resolution,[],[f3068,f354]) ).
fof(f147537,plain,
( spl0_1697
| ~ spl0_65
| ~ spl0_210 ),
inference(avatar_split_clause,[],[f2854,f2737,f482,f147535]) ).
fof(f147535,plain,
( spl0_1697
<=> ! [X0] :
( estin = range_of(X0)
| ordered_pair_predicate(f27(f1(estin,range_of(X0)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1697])]) ).
fof(f482,plain,
( spl0_65
<=> ! [X0,X3] :
( ~ member(X3,range_of(X0))
| ordered_pair_predicate(f27(X3,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_65])]) ).
fof(f2854,plain,
( ! [X0] :
( estin = range_of(X0)
| ordered_pair_predicate(f27(f1(estin,range_of(X0)),X0)) )
| ~ spl0_65
| ~ spl0_210 ),
inference(resolution,[],[f2738,f483]) ).
fof(f483,plain,
( ! [X3,X0] :
( ~ member(X3,range_of(X0))
| ordered_pair_predicate(f27(X3,X0)) )
| ~ spl0_65 ),
inference(avatar_component_clause,[],[f482]) ).
fof(f147533,plain,
( spl0_1696
| ~ spl0_203
| ~ spl0_210 ),
inference(avatar_split_clause,[],[f2852,f2737,f2617,f147531]) ).
fof(f147531,plain,
( spl0_1696
<=> ! [X0] :
( estin = range_of(X0)
| little_set(f27(f1(estin,range_of(X0)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1696])]) ).
fof(f2617,plain,
( spl0_203
<=> ! [X0,X1] :
( ~ member(X0,range_of(X1))
| little_set(f27(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_203])]) ).
fof(f2852,plain,
( ! [X0] :
( estin = range_of(X0)
| little_set(f27(f1(estin,range_of(X0)),X0)) )
| ~ spl0_203
| ~ spl0_210 ),
inference(resolution,[],[f2738,f2618]) ).
fof(f2618,plain,
( ! [X0,X1] :
( ~ member(X0,range_of(X1))
| little_set(f27(X0,X1)) )
| ~ spl0_203 ),
inference(avatar_component_clause,[],[f2617]) ).
fof(f147529,plain,
( spl0_1695
| ~ spl0_197
| ~ spl0_210 ),
inference(avatar_split_clause,[],[f2846,f2737,f2585,f147527]) ).
fof(f147527,plain,
( spl0_1695
<=> ! [X0] :
( estin = sigma(X0)
| little_set(f16(f1(estin,sigma(X0)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1695])]) ).
fof(f2846,plain,
( ! [X0] :
( estin = sigma(X0)
| little_set(f16(f1(estin,sigma(X0)),X0)) )
| ~ spl0_197
| ~ spl0_210 ),
inference(resolution,[],[f2738,f2586]) ).
fof(f147525,plain,
( spl0_1694
| ~ spl0_57
| ~ spl0_210 ),
inference(avatar_split_clause,[],[f2842,f2737,f450,f147523]) ).
fof(f147523,plain,
( spl0_1694
<=> ! [X0] :
( estin = flip_range_of(X0)
| little_set(f12(f1(estin,flip_range_of(X0)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1694])]) ).
fof(f450,plain,
( spl0_57
<=> ! [X0,X3] :
( ~ member(X3,flip_range_of(X0))
| little_set(f12(X3,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_57])]) ).
fof(f2842,plain,
( ! [X0] :
( estin = flip_range_of(X0)
| little_set(f12(f1(estin,flip_range_of(X0)),X0)) )
| ~ spl0_57
| ~ spl0_210 ),
inference(resolution,[],[f2738,f451]) ).
fof(f451,plain,
( ! [X3,X0] :
( ~ member(X3,flip_range_of(X0))
| little_set(f12(X3,X0)) )
| ~ spl0_57 ),
inference(avatar_component_clause,[],[f450]) ).
fof(f147521,plain,
( spl0_1693
| ~ spl0_58
| ~ spl0_210 ),
inference(avatar_split_clause,[],[f2841,f2737,f454,f147519]) ).
fof(f147519,plain,
( spl0_1693
<=> ! [X0] :
( estin = flip_range_of(X0)
| little_set(f13(f1(estin,flip_range_of(X0)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1693])]) ).
fof(f454,plain,
( spl0_58
<=> ! [X0,X3] :
( ~ member(X3,flip_range_of(X0))
| little_set(f13(X3,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_58])]) ).
fof(f2841,plain,
( ! [X0] :
( estin = flip_range_of(X0)
| little_set(f13(f1(estin,flip_range_of(X0)),X0)) )
| ~ spl0_58
| ~ spl0_210 ),
inference(resolution,[],[f2738,f455]) ).
fof(f455,plain,
( ! [X3,X0] :
( ~ member(X3,flip_range_of(X0))
| little_set(f13(X3,X0)) )
| ~ spl0_58 ),
inference(avatar_component_clause,[],[f454]) ).
fof(f147517,plain,
( spl0_1692
| ~ spl0_59
| ~ spl0_210 ),
inference(avatar_split_clause,[],[f2840,f2737,f458,f147515]) ).
fof(f147515,plain,
( spl0_1692
<=> ! [X0] :
( estin = flip_range_of(X0)
| little_set(f14(f1(estin,flip_range_of(X0)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1692])]) ).
fof(f458,plain,
( spl0_59
<=> ! [X0,X3] :
( ~ member(X3,flip_range_of(X0))
| little_set(f14(X3,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_59])]) ).
fof(f2840,plain,
( ! [X0] :
( estin = flip_range_of(X0)
| little_set(f14(f1(estin,flip_range_of(X0)),X0)) )
| ~ spl0_59
| ~ spl0_210 ),
inference(resolution,[],[f2738,f459]) ).
fof(f459,plain,
( ! [X3,X0] :
( ~ member(X3,flip_range_of(X0))
| little_set(f14(X3,X0)) )
| ~ spl0_59 ),
inference(avatar_component_clause,[],[f458]) ).
fof(f147513,plain,
( spl0_1691
| ~ spl0_54
| ~ spl0_210 ),
inference(avatar_split_clause,[],[f2837,f2737,f438,f147511]) ).
fof(f147511,plain,
( spl0_1691
<=> ! [X0] :
( estin = rotate_right(X0)
| little_set(f9(f1(estin,rotate_right(X0)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1691])]) ).
fof(f438,plain,
( spl0_54
<=> ! [X0,X3] :
( ~ member(X3,rotate_right(X0))
| little_set(f9(X3,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_54])]) ).
fof(f2837,plain,
( ! [X0] :
( estin = rotate_right(X0)
| little_set(f9(f1(estin,rotate_right(X0)),X0)) )
| ~ spl0_54
| ~ spl0_210 ),
inference(resolution,[],[f2738,f439]) ).
fof(f439,plain,
( ! [X3,X0] :
( ~ member(X3,rotate_right(X0))
| little_set(f9(X3,X0)) )
| ~ spl0_54 ),
inference(avatar_component_clause,[],[f438]) ).
fof(f147509,plain,
( spl0_1690
| ~ spl0_55
| ~ spl0_210 ),
inference(avatar_split_clause,[],[f2836,f2737,f442,f147507]) ).
fof(f147507,plain,
( spl0_1690
<=> ! [X0] :
( estin = rotate_right(X0)
| little_set(f10(f1(estin,rotate_right(X0)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1690])]) ).
fof(f442,plain,
( spl0_55
<=> ! [X0,X3] :
( ~ member(X3,rotate_right(X0))
| little_set(f10(X3,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_55])]) ).
fof(f2836,plain,
( ! [X0] :
( estin = rotate_right(X0)
| little_set(f10(f1(estin,rotate_right(X0)),X0)) )
| ~ spl0_55
| ~ spl0_210 ),
inference(resolution,[],[f2738,f443]) ).
fof(f443,plain,
( ! [X3,X0] :
( ~ member(X3,rotate_right(X0))
| little_set(f10(X3,X0)) )
| ~ spl0_55 ),
inference(avatar_component_clause,[],[f442]) ).
fof(f147505,plain,
( spl0_1689
| ~ spl0_56
| ~ spl0_210 ),
inference(avatar_split_clause,[],[f2835,f2737,f446,f147503]) ).
fof(f147503,plain,
( spl0_1689
<=> ! [X0] :
( estin = rotate_right(X0)
| little_set(f11(f1(estin,rotate_right(X0)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1689])]) ).
fof(f446,plain,
( spl0_56
<=> ! [X0,X3] :
( ~ member(X3,rotate_right(X0))
| little_set(f11(X3,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_56])]) ).
fof(f2835,plain,
( ! [X0] :
( estin = rotate_right(X0)
| little_set(f11(f1(estin,rotate_right(X0)),X0)) )
| ~ spl0_56
| ~ spl0_210 ),
inference(resolution,[],[f2738,f447]) ).
fof(f447,plain,
( ! [X3,X0] :
( ~ member(X3,rotate_right(X0))
| little_set(f11(X3,X0)) )
| ~ spl0_56 ),
inference(avatar_component_clause,[],[f446]) ).
fof(f147501,plain,
( spl0_1688
| ~ spl0_1518
| spl0_1574 ),
inference(avatar_split_clause,[],[f69027,f60207,f58347,f147498]) ).
fof(f147498,plain,
( spl0_1688
<=> estin = first(f18(estin)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1688])]) ).
fof(f58347,plain,
( spl0_1518
<=> ! [X0] :
( little_set(X0)
| first(X0) = estin ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1518])]) ).
fof(f69027,plain,
( estin = first(f18(estin))
| ~ spl0_1518
| spl0_1574 ),
inference(resolution,[],[f60209,f58348]) ).
fof(f58348,plain,
( ! [X0] :
( little_set(X0)
| first(X0) = estin )
| ~ spl0_1518 ),
inference(avatar_component_clause,[],[f58347]) ).
fof(f147496,plain,
( spl0_1687
| ~ spl0_35
| ~ spl0_210 ),
inference(avatar_split_clause,[],[f2831,f2737,f340,f147494]) ).
fof(f147494,plain,
( spl0_1687
<=> ! [X0,X1] :
( estin = cross_product(X0,X1)
| ordered_pair_predicate(f1(estin,cross_product(X0,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1687])]) ).
fof(f340,plain,
( spl0_35
<=> ! [X0,X1,X3] :
( ordered_pair_predicate(X3)
| ~ member(X3,cross_product(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_35])]) ).
fof(f2831,plain,
( ! [X0,X1] :
( estin = cross_product(X0,X1)
| ordered_pair_predicate(f1(estin,cross_product(X0,X1))) )
| ~ spl0_35
| ~ spl0_210 ),
inference(resolution,[],[f2738,f341]) ).
fof(f341,plain,
( ! [X3,X0,X1] :
( ~ member(X3,cross_product(X0,X1))
| ordered_pair_predicate(X3) )
| ~ spl0_35 ),
inference(avatar_component_clause,[],[f340]) ).
fof(f147492,plain,
( spl0_1686
| ~ spl0_53
| ~ spl0_210 ),
inference(avatar_split_clause,[],[f2827,f2737,f434,f147490]) ).
fof(f147490,plain,
( spl0_1686
<=> ! [X0] :
( estin = domain_of(X0)
| ordered_pair_predicate(f8(f1(estin,domain_of(X0)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1686])]) ).
fof(f434,plain,
( spl0_53
<=> ! [X0,X3] :
( ~ member(X3,domain_of(X0))
| ordered_pair_predicate(f8(X3,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_53])]) ).
fof(f2827,plain,
( ! [X0] :
( estin = domain_of(X0)
| ordered_pair_predicate(f8(f1(estin,domain_of(X0)),X0)) )
| ~ spl0_53
| ~ spl0_210 ),
inference(resolution,[],[f2738,f435]) ).
fof(f435,plain,
( ! [X3,X0] :
( ~ member(X3,domain_of(X0))
| ordered_pair_predicate(f8(X3,X0)) )
| ~ spl0_53 ),
inference(avatar_component_clause,[],[f434]) ).
fof(f147488,plain,
( spl0_1685
| ~ spl0_196
| ~ spl0_210 ),
inference(avatar_split_clause,[],[f2825,f2737,f2581,f147486]) ).
fof(f147486,plain,
( spl0_1685
<=> ! [X0] :
( estin = domain_of(X0)
| little_set(f8(f1(estin,domain_of(X0)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1685])]) ).
fof(f2581,plain,
( spl0_196
<=> ! [X0,X1] :
( ~ member(X0,domain_of(X1))
| little_set(f8(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_196])]) ).
fof(f2825,plain,
( ! [X0] :
( estin = domain_of(X0)
| little_set(f8(f1(estin,domain_of(X0)),X0)) )
| ~ spl0_196
| ~ spl0_210 ),
inference(resolution,[],[f2738,f2582]) ).
fof(f2582,plain,
( ! [X0,X1] :
( ~ member(X0,domain_of(X1))
| little_set(f8(X0,X1)) )
| ~ spl0_196 ),
inference(avatar_component_clause,[],[f2581]) ).
fof(f147484,plain,
( spl0_1684
| ~ spl0_48
| ~ spl0_210 ),
inference(avatar_split_clause,[],[f2821,f2737,f414,f147482]) ).
fof(f147482,plain,
( spl0_1684
<=> ! [X0] :
( second(X0) = estin
| little_set(f6(f1(estin,second(X0)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1684])]) ).
fof(f414,plain,
( spl0_48
<=> ! [X0,X3] :
( ~ member(X3,second(X0))
| little_set(f6(X3,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_48])]) ).
fof(f2821,plain,
( ! [X0] :
( second(X0) = estin
| little_set(f6(f1(estin,second(X0)),X0)) )
| ~ spl0_48
| ~ spl0_210 ),
inference(resolution,[],[f2738,f415]) ).
fof(f415,plain,
( ! [X3,X0] :
( ~ member(X3,second(X0))
| little_set(f6(X3,X0)) )
| ~ spl0_48 ),
inference(avatar_component_clause,[],[f414]) ).
fof(f147480,plain,
( spl0_1683
| ~ spl0_49
| ~ spl0_210 ),
inference(avatar_split_clause,[],[f2820,f2737,f418,f147478]) ).
fof(f147478,plain,
( spl0_1683
<=> ! [X0] :
( second(X0) = estin
| little_set(f7(f1(estin,second(X0)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1683])]) ).
fof(f418,plain,
( spl0_49
<=> ! [X0,X3] :
( ~ member(X3,second(X0))
| little_set(f7(X3,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_49])]) ).
fof(f2820,plain,
( ! [X0] :
( second(X0) = estin
| little_set(f7(f1(estin,second(X0)),X0)) )
| ~ spl0_49
| ~ spl0_210 ),
inference(resolution,[],[f2738,f419]) ).
fof(f419,plain,
( ! [X3,X0] :
( ~ member(X3,second(X0))
| little_set(f7(X3,X0)) )
| ~ spl0_49 ),
inference(avatar_component_clause,[],[f418]) ).
fof(f147476,plain,
( spl0_1682
| ~ spl0_46
| ~ spl0_210 ),
inference(avatar_split_clause,[],[f2818,f2737,f406,f147474]) ).
fof(f147474,plain,
( spl0_1682
<=> ! [X0] :
( first(X0) = estin
| little_set(f4(f1(estin,first(X0)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1682])]) ).
fof(f406,plain,
( spl0_46
<=> ! [X0,X3] :
( ~ member(X3,first(X0))
| little_set(f4(X3,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_46])]) ).
fof(f2818,plain,
( ! [X0] :
( first(X0) = estin
| little_set(f4(f1(estin,first(X0)),X0)) )
| ~ spl0_46
| ~ spl0_210 ),
inference(resolution,[],[f2738,f407]) ).
fof(f407,plain,
( ! [X3,X0] :
( ~ member(X3,first(X0))
| little_set(f4(X3,X0)) )
| ~ spl0_46 ),
inference(avatar_component_clause,[],[f406]) ).
fof(f147472,plain,
( spl0_1681
| ~ spl0_47
| ~ spl0_210 ),
inference(avatar_split_clause,[],[f2817,f2737,f410,f147470]) ).
fof(f147470,plain,
( spl0_1681
<=> ! [X0] :
( first(X0) = estin
| little_set(f5(f1(estin,first(X0)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1681])]) ).
fof(f410,plain,
( spl0_47
<=> ! [X0,X3] :
( ~ member(X3,first(X0))
| little_set(f5(X3,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_47])]) ).
fof(f2817,plain,
( ! [X0] :
( first(X0) = estin
| little_set(f5(f1(estin,first(X0)),X0)) )
| ~ spl0_47
| ~ spl0_210 ),
inference(resolution,[],[f2738,f411]) ).
fof(f411,plain,
( ! [X3,X0] :
( ~ member(X3,first(X0))
| little_set(f5(X3,X0)) )
| ~ spl0_47 ),
inference(avatar_component_clause,[],[f410]) ).
fof(f147468,plain,
( spl0_1680
| ~ spl0_203
| ~ spl0_209 ),
inference(avatar_split_clause,[],[f2784,f2733,f2617,f147466]) ).
fof(f147466,plain,
( spl0_1680
<=> ! [X0] :
( estin = range_of(X0)
| little_set(f27(f1(range_of(X0),estin),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1680])]) ).
fof(f2733,plain,
( spl0_209
<=> ! [X0] :
( estin = X0
| member(f1(X0,estin),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_209])]) ).
fof(f2784,plain,
( ! [X0] :
( estin = range_of(X0)
| little_set(f27(f1(range_of(X0),estin),X0)) )
| ~ spl0_203
| ~ spl0_209 ),
inference(resolution,[],[f2734,f2618]) ).
fof(f2734,plain,
( ! [X0] :
( member(f1(X0,estin),X0)
| estin = X0 )
| ~ spl0_209 ),
inference(avatar_component_clause,[],[f2733]) ).
fof(f147464,plain,
( spl0_1679
| ~ spl0_197
| ~ spl0_209 ),
inference(avatar_split_clause,[],[f2778,f2733,f2585,f147462]) ).
fof(f147462,plain,
( spl0_1679
<=> ! [X0] :
( estin = sigma(X0)
| little_set(f16(f1(sigma(X0),estin),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1679])]) ).
fof(f2778,plain,
( ! [X0] :
( estin = sigma(X0)
| little_set(f16(f1(sigma(X0),estin),X0)) )
| ~ spl0_197
| ~ spl0_209 ),
inference(resolution,[],[f2734,f2586]) ).
fof(f147460,plain,
( spl0_1678
| ~ spl0_196
| ~ spl0_209 ),
inference(avatar_split_clause,[],[f2757,f2733,f2581,f147458]) ).
fof(f147458,plain,
( spl0_1678
<=> ! [X0] :
( estin = domain_of(X0)
| little_set(f8(f1(domain_of(X0),estin),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1678])]) ).
fof(f2757,plain,
( ! [X0] :
( estin = domain_of(X0)
| little_set(f8(f1(domain_of(X0),estin),X0)) )
| ~ spl0_196
| ~ spl0_209 ),
inference(resolution,[],[f2734,f2582]) ).
fof(f147268,plain,
( spl0_1677
| ~ spl0_64
| ~ spl0_203 ),
inference(avatar_split_clause,[],[f2723,f2617,f478,f147266]) ).
fof(f147266,plain,
( spl0_1677
<=> ! [X0,X1] :
( little_set(f27(f23(X0,range_of(X1)),X1))
| disjoint(X0,range_of(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1677])]) ).
fof(f478,plain,
( spl0_64
<=> ! [X0,X1] :
( disjoint(X0,X1)
| member(f23(X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_64])]) ).
fof(f2723,plain,
( ! [X0,X1] :
( little_set(f27(f23(X0,range_of(X1)),X1))
| disjoint(X0,range_of(X1)) )
| ~ spl0_64
| ~ spl0_203 ),
inference(resolution,[],[f2618,f479]) ).
fof(f479,plain,
( ! [X0,X1] :
( member(f23(X0,X1),X1)
| disjoint(X0,X1) )
| ~ spl0_64 ),
inference(avatar_component_clause,[],[f478]) ).
fof(f147264,plain,
( spl0_1676
| ~ spl0_63
| ~ spl0_203 ),
inference(avatar_split_clause,[],[f2722,f2617,f474,f147262]) ).
fof(f147262,plain,
( spl0_1676
<=> ! [X0,X1] :
( little_set(f27(f23(range_of(X0),X1),X0))
| disjoint(range_of(X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1676])]) ).
fof(f474,plain,
( spl0_63
<=> ! [X0,X1] :
( disjoint(X0,X1)
| member(f23(X0,X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_63])]) ).
fof(f2722,plain,
( ! [X0,X1] :
( little_set(f27(f23(range_of(X0),X1),X0))
| disjoint(range_of(X0),X1) )
| ~ spl0_63
| ~ spl0_203 ),
inference(resolution,[],[f2618,f475]) ).
fof(f475,plain,
( ! [X0,X1] :
( member(f23(X0,X1),X0)
| disjoint(X0,X1) )
| ~ spl0_63 ),
inference(avatar_component_clause,[],[f474]) ).
fof(f147260,plain,
( spl0_1675
| ~ spl0_60
| ~ spl0_203 ),
inference(avatar_split_clause,[],[f2719,f2617,f462,f147258]) ).
fof(f147258,plain,
( spl0_1675
<=> ! [X0,X1] :
( little_set(f27(f17(range_of(X0),X1),X0))
| subset(range_of(X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1675])]) ).
fof(f462,plain,
( spl0_60
<=> ! [X0,X1] :
( subset(X0,X1)
| member(f17(X0,X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_60])]) ).
fof(f2719,plain,
( ! [X0,X1] :
( little_set(f27(f17(range_of(X0),X1),X0))
| subset(range_of(X0),X1) )
| ~ spl0_60
| ~ spl0_203 ),
inference(resolution,[],[f2618,f463]) ).
fof(f463,plain,
( ! [X0,X1] :
( member(f17(X0,X1),X0)
| subset(X0,X1) )
| ~ spl0_60 ),
inference(avatar_component_clause,[],[f462]) ).
fof(f147256,plain,
( spl0_1674
| ~ spl0_64
| ~ spl0_197 ),
inference(avatar_split_clause,[],[f2693,f2585,f478,f147254]) ).
fof(f147254,plain,
( spl0_1674
<=> ! [X0,X1] :
( little_set(f16(f23(X0,sigma(X1)),X1))
| disjoint(X0,sigma(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1674])]) ).
fof(f2693,plain,
( ! [X0,X1] :
( little_set(f16(f23(X0,sigma(X1)),X1))
| disjoint(X0,sigma(X1)) )
| ~ spl0_64
| ~ spl0_197 ),
inference(resolution,[],[f2586,f479]) ).
fof(f147252,plain,
( spl0_1673
| ~ spl0_63
| ~ spl0_197 ),
inference(avatar_split_clause,[],[f2692,f2585,f474,f147250]) ).
fof(f147250,plain,
( spl0_1673
<=> ! [X0,X1] :
( little_set(f16(f23(sigma(X0),X1),X0))
| disjoint(sigma(X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1673])]) ).
fof(f2692,plain,
( ! [X0,X1] :
( little_set(f16(f23(sigma(X0),X1),X0))
| disjoint(sigma(X0),X1) )
| ~ spl0_63
| ~ spl0_197 ),
inference(resolution,[],[f2586,f475]) ).
fof(f147248,plain,
( spl0_1672
| ~ spl0_60
| ~ spl0_197 ),
inference(avatar_split_clause,[],[f2689,f2585,f462,f147246]) ).
fof(f147246,plain,
( spl0_1672
<=> ! [X0,X1] :
( little_set(f16(f17(sigma(X0),X1),X0))
| subset(sigma(X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1672])]) ).
fof(f2689,plain,
( ! [X0,X1] :
( little_set(f16(f17(sigma(X0),X1),X0))
| subset(sigma(X0),X1) )
| ~ spl0_60
| ~ spl0_197 ),
inference(resolution,[],[f2586,f463]) ).
fof(f147244,plain,
( spl0_1671
| ~ spl0_64
| ~ spl0_196 ),
inference(avatar_split_clause,[],[f2667,f2581,f478,f147242]) ).
fof(f147242,plain,
( spl0_1671
<=> ! [X0,X1] :
( little_set(f8(f23(X0,domain_of(X1)),X1))
| disjoint(X0,domain_of(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1671])]) ).
fof(f2667,plain,
( ! [X0,X1] :
( little_set(f8(f23(X0,domain_of(X1)),X1))
| disjoint(X0,domain_of(X1)) )
| ~ spl0_64
| ~ spl0_196 ),
inference(resolution,[],[f2582,f479]) ).
fof(f147240,plain,
( spl0_1670
| ~ spl0_63
| ~ spl0_196 ),
inference(avatar_split_clause,[],[f2666,f2581,f474,f147238]) ).
fof(f147238,plain,
( spl0_1670
<=> ! [X0,X1] :
( little_set(f8(f23(domain_of(X0),X1),X0))
| disjoint(domain_of(X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1670])]) ).
fof(f2666,plain,
( ! [X0,X1] :
( little_set(f8(f23(domain_of(X0),X1),X0))
| disjoint(domain_of(X0),X1) )
| ~ spl0_63
| ~ spl0_196 ),
inference(resolution,[],[f2582,f475]) ).
fof(f147236,plain,
( spl0_1669
| ~ spl0_60
| ~ spl0_196 ),
inference(avatar_split_clause,[],[f2663,f2581,f462,f147234]) ).
fof(f147234,plain,
( spl0_1669
<=> ! [X0,X1] :
( little_set(f8(f17(domain_of(X0),X1),X0))
| subset(domain_of(X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1669])]) ).
fof(f2663,plain,
( ! [X0,X1] :
( little_set(f8(f17(domain_of(X0),X1),X0))
| subset(domain_of(X0),X1) )
| ~ spl0_60
| ~ spl0_196 ),
inference(resolution,[],[f2582,f463]) ).
fof(f147232,plain,
( spl0_1668
| ~ spl0_80
| ~ spl0_191 ),
inference(avatar_split_clause,[],[f2641,f2559,f652,f147230]) ).
fof(f147230,plain,
( spl0_1668
<=> ! [X0,X1] :
( relation(powerset(X0))
| ~ member(X1,f18(powerset(X0)))
| member(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1668])]) ).
fof(f652,plain,
( spl0_80
<=> ! [X2,X0,X1] :
( ~ subset(X0,X1)
| ~ member(X2,X0)
| member(X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_80])]) ).
fof(f2559,plain,
( spl0_191
<=> ! [X0] :
( subset(f18(powerset(X0)),X0)
| relation(powerset(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_191])]) ).
fof(f2641,plain,
( ! [X0,X1] :
( relation(powerset(X0))
| ~ member(X1,f18(powerset(X0)))
| member(X1,X0) )
| ~ spl0_80
| ~ spl0_191 ),
inference(resolution,[],[f2560,f653]) ).
fof(f653,plain,
( ! [X2,X0,X1] :
( ~ subset(X0,X1)
| ~ member(X2,X0)
| member(X2,X1) )
| ~ spl0_80 ),
inference(avatar_component_clause,[],[f652]) ).
fof(f2560,plain,
( ! [X0] :
( subset(f18(powerset(X0)),X0)
| relation(powerset(X0)) )
| ~ spl0_191 ),
inference(avatar_component_clause,[],[f2559]) ).
fof(f147040,plain,
( spl0_1667
| ~ spl0_93
| ~ spl0_188 ),
inference(avatar_split_clause,[],[f2546,f2542,f836,f147038]) ).
fof(f147038,plain,
( spl0_1667
<=> ! [X0,X1] :
( ~ member(infinity,X0)
| ~ member(sigma(X0),X1)
| member(estin,sigma(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1667])]) ).
fof(f836,plain,
( spl0_93
<=> ! [X0,X1,X3] :
( ~ member(X3,X1)
| ~ member(X1,X0)
| member(X3,sigma(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_93])]) ).
fof(f2546,plain,
( ! [X0,X1] :
( ~ member(infinity,X0)
| ~ member(sigma(X0),X1)
| member(estin,sigma(X1)) )
| ~ spl0_93
| ~ spl0_188 ),
inference(resolution,[],[f2543,f837]) ).
fof(f837,plain,
( ! [X3,X0,X1] :
( ~ member(X3,X1)
| ~ member(X1,X0)
| member(X3,sigma(X0)) )
| ~ spl0_93 ),
inference(avatar_component_clause,[],[f836]) ).
fof(f147036,plain,
( spl0_1666
| ~ spl0_81
| ~ spl0_186 ),
inference(avatar_split_clause,[],[f2539,f2526,f656,f147034]) ).
fof(f147034,plain,
( spl0_1666
<=> ! [X0,X1] :
( ~ closed(X0,X1)
| range_of(X1) = X0
| proper_subset(range_of(X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1666])]) ).
fof(f656,plain,
( spl0_81
<=> ! [X0,X1] :
( ~ subset(X0,X1)
| X0 = X1
| proper_subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_81])]) ).
fof(f2526,plain,
( spl0_186
<=> ! [X0,X1] :
( ~ closed(X0,X1)
| subset(range_of(X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_186])]) ).
fof(f2539,plain,
( ! [X0,X1] :
( ~ closed(X0,X1)
| range_of(X1) = X0
| proper_subset(range_of(X1),X0) )
| ~ spl0_81
| ~ spl0_186 ),
inference(resolution,[],[f2527,f657]) ).
fof(f657,plain,
( ! [X0,X1] :
( ~ subset(X0,X1)
| X0 = X1
| proper_subset(X0,X1) )
| ~ spl0_81 ),
inference(avatar_component_clause,[],[f656]) ).
fof(f2527,plain,
( ! [X0,X1] :
( subset(range_of(X1),X0)
| ~ closed(X0,X1) )
| ~ spl0_186 ),
inference(avatar_component_clause,[],[f2526]) ).
fof(f147027,plain,
( spl0_1665
| ~ spl0_40
| ~ spl0_175
| ~ spl0_203 ),
inference(avatar_split_clause,[],[f85271,f2617,f2469,f361,f147025]) ).
fof(f147025,plain,
( spl0_1665
<=> ! [X0] :
( range_of(X0) = identity_relation
| little_set(f27(f24(range_of(X0)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1665])]) ).
fof(f361,plain,
( spl0_40
<=> ! [X0] :
( empty_set = X0
| member(f24(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_40])]) ).
fof(f85271,plain,
( ! [X0] :
( range_of(X0) = identity_relation
| little_set(f27(f24(range_of(X0)),X0)) )
| ~ spl0_40
| ~ spl0_175
| ~ spl0_203 ),
inference(forward_demodulation,[],[f2724,f2471]) ).
fof(f2724,plain,
( ! [X0] :
( little_set(f27(f24(range_of(X0)),X0))
| empty_set = range_of(X0) )
| ~ spl0_40
| ~ spl0_203 ),
inference(resolution,[],[f2618,f362]) ).
fof(f362,plain,
( ! [X0] :
( member(f24(X0),X0)
| empty_set = X0 )
| ~ spl0_40 ),
inference(avatar_component_clause,[],[f361]) ).
fof(f147022,plain,
( spl0_1664
| ~ spl0_40
| ~ spl0_175
| ~ spl0_197 ),
inference(avatar_split_clause,[],[f85269,f2585,f2469,f361,f147020]) ).
fof(f147020,plain,
( spl0_1664
<=> ! [X0] :
( sigma(X0) = identity_relation
| little_set(f16(f24(sigma(X0)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1664])]) ).
fof(f85269,plain,
( ! [X0] :
( sigma(X0) = identity_relation
| little_set(f16(f24(sigma(X0)),X0)) )
| ~ spl0_40
| ~ spl0_175
| ~ spl0_197 ),
inference(forward_demodulation,[],[f2694,f2471]) ).
fof(f2694,plain,
( ! [X0] :
( little_set(f16(f24(sigma(X0)),X0))
| empty_set = sigma(X0) )
| ~ spl0_40
| ~ spl0_197 ),
inference(resolution,[],[f2586,f362]) ).
fof(f147017,plain,
( spl0_1663
| ~ spl0_40
| ~ spl0_175
| ~ spl0_196 ),
inference(avatar_split_clause,[],[f85267,f2581,f2469,f361,f147015]) ).
fof(f147015,plain,
( spl0_1663
<=> ! [X0] :
( domain_of(X0) = identity_relation
| little_set(f8(f24(domain_of(X0)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1663])]) ).
fof(f85267,plain,
( ! [X0] :
( domain_of(X0) = identity_relation
| little_set(f8(f24(domain_of(X0)),X0)) )
| ~ spl0_40
| ~ spl0_175
| ~ spl0_196 ),
inference(forward_demodulation,[],[f2668,f2471]) ).
fof(f2668,plain,
( ! [X0] :
( little_set(f8(f24(domain_of(X0)),X0))
| domain_of(X0) = empty_set )
| ~ spl0_40
| ~ spl0_196 ),
inference(resolution,[],[f2582,f362]) ).
fof(f147013,plain,
( spl0_1662
| ~ spl0_40
| ~ spl0_197
| ~ spl0_209
| ~ spl0_1550 ),
inference(avatar_split_clause,[],[f84530,f58601,f2733,f2585,f361,f147011]) ).
fof(f147011,plain,
( spl0_1662
<=> ! [X0] :
( estin = sigma(X0)
| little_set(f16(f24(sigma(X0)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1662])]) ).
fof(f58601,plain,
( spl0_1550
<=> ! [X2,X0,X1] : ~ member(X0,image(complement(X1),cross_product(X1,X2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1550])]) ).
fof(f84530,plain,
( ! [X0] :
( estin = sigma(X0)
| little_set(f16(f24(sigma(X0)),X0)) )
| ~ spl0_40
| ~ spl0_197
| ~ spl0_209
| ~ spl0_1550 ),
inference(forward_demodulation,[],[f2694,f59236]) ).
fof(f59236,plain,
( estin = empty_set
| ~ spl0_40
| ~ spl0_209
| ~ spl0_1550 ),
inference(forward_demodulation,[],[f58847,f58690]) ).
fof(f58690,plain,
( ! [X0,X1] : estin = image(complement(X0),cross_product(X0,X1))
| ~ spl0_209
| ~ spl0_1550 ),
inference(resolution,[],[f58602,f2734]) ).
fof(f58602,plain,
( ! [X2,X0,X1] : ~ member(X0,image(complement(X1),cross_product(X1,X2)))
| ~ spl0_1550 ),
inference(avatar_component_clause,[],[f58601]) ).
fof(f58847,plain,
( ! [X0,X1] : empty_set = image(complement(X0),cross_product(X0,X1))
| ~ spl0_40
| ~ spl0_1550 ),
inference(resolution,[],[f58602,f362]) ).
fof(f147009,plain,
( spl0_1661
| ~ spl0_40
| ~ spl0_203
| ~ spl0_209
| ~ spl0_1550 ),
inference(avatar_split_clause,[],[f84528,f58601,f2733,f2617,f361,f147007]) ).
fof(f147007,plain,
( spl0_1661
<=> ! [X0] :
( estin = range_of(X0)
| little_set(f27(f24(range_of(X0)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1661])]) ).
fof(f84528,plain,
( ! [X0] :
( estin = range_of(X0)
| little_set(f27(f24(range_of(X0)),X0)) )
| ~ spl0_40
| ~ spl0_203
| ~ spl0_209
| ~ spl0_1550 ),
inference(forward_demodulation,[],[f2724,f59236]) ).
fof(f138919,plain,
( spl0_1660
| spl0_1516
| ~ spl0_1518 ),
inference(avatar_split_clause,[],[f58385,f58347,f58336,f138916]) ).
fof(f138916,plain,
( spl0_1660
<=> estin = first(f20(estin)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1660])]) ).
fof(f58336,plain,
( spl0_1516
<=> little_set(f20(estin)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1516])]) ).
fof(f58385,plain,
( estin = first(f20(estin))
| spl0_1516
| ~ spl0_1518 ),
inference(resolution,[],[f58348,f58338]) ).
fof(f58338,plain,
( ~ little_set(f20(estin))
| spl0_1516 ),
inference(avatar_component_clause,[],[f58336]) ).
fof(f129461,plain,
( spl0_1659
| ~ spl0_23
| ~ spl0_644 ),
inference(avatar_split_clause,[],[f9455,f8674,f281,f129459]) ).
fof(f129459,plain,
( spl0_1659
<=> ! [X0] :
( converse(X0) = identity_relation
| ordered_pair_predicate(f1(converse(X0),identity_relation)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1659])]) ).
fof(f8674,plain,
( spl0_644
<=> ! [X0,X1] :
( member(f1(converse(X0),X1),X1)
| converse(X0) = X1
| ordered_pair_predicate(f1(converse(X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_644])]) ).
fof(f9455,plain,
( ! [X0] :
( converse(X0) = identity_relation
| ordered_pair_predicate(f1(converse(X0),identity_relation)) )
| ~ spl0_23
| ~ spl0_644 ),
inference(duplicate_literal_removal,[],[f9444]) ).
fof(f9444,plain,
( ! [X0] :
( converse(X0) = identity_relation
| ordered_pair_predicate(f1(converse(X0),identity_relation))
| ordered_pair_predicate(f1(converse(X0),identity_relation)) )
| ~ spl0_23
| ~ spl0_644 ),
inference(resolution,[],[f8675,f282]) ).
fof(f8675,plain,
( ! [X0,X1] :
( member(f1(converse(X0),X1),X1)
| converse(X0) = X1
| ordered_pair_predicate(f1(converse(X0),X1)) )
| ~ spl0_644 ),
inference(avatar_component_clause,[],[f8674]) ).
fof(f129455,plain,
( spl0_1658
| ~ spl0_23
| ~ spl0_643 ),
inference(avatar_split_clause,[],[f9341,f8670,f281,f129453]) ).
fof(f129453,plain,
( spl0_1658
<=> ! [X0] :
( converse(X0) = identity_relation
| ordered_pair_predicate(f1(identity_relation,converse(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1658])]) ).
fof(f9341,plain,
( ! [X0] :
( converse(X0) = identity_relation
| ordered_pair_predicate(f1(identity_relation,converse(X0))) )
| ~ spl0_23
| ~ spl0_643 ),
inference(duplicate_literal_removal,[],[f9330]) ).
fof(f9330,plain,
( ! [X0] :
( converse(X0) = identity_relation
| ordered_pair_predicate(f1(identity_relation,converse(X0)))
| ordered_pair_predicate(f1(identity_relation,converse(X0))) )
| ~ spl0_23
| ~ spl0_643 ),
inference(resolution,[],[f8671,f282]) ).
fof(f129449,plain,
( spl0_1657
| ~ spl0_23
| ~ spl0_581 ),
inference(avatar_split_clause,[],[f8360,f7464,f281,f129447]) ).
fof(f129447,plain,
( spl0_1657
<=> ! [X0] :
( identity_relation = X0
| ordered_pair_predicate(f1(X0,identity_relation))
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1657])]) ).
fof(f8360,plain,
( ! [X0] :
( identity_relation = X0
| ordered_pair_predicate(f1(X0,identity_relation))
| ~ relation(X0) )
| ~ spl0_23
| ~ spl0_581 ),
inference(duplicate_literal_removal,[],[f8349]) ).
fof(f8349,plain,
( ! [X0] :
( identity_relation = X0
| ordered_pair_predicate(f1(X0,identity_relation))
| ~ relation(X0)
| ordered_pair_predicate(f1(X0,identity_relation)) )
| ~ spl0_23
| ~ spl0_581 ),
inference(resolution,[],[f7465,f282]) ).
fof(f129445,plain,
( spl0_1656
| spl0_1515
| ~ spl0_1518 ),
inference(avatar_split_clause,[],[f58384,f58347,f58332,f129442]) ).
fof(f129442,plain,
( spl0_1656
<=> estin = first(f19(estin)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1656])]) ).
fof(f58332,plain,
( spl0_1515
<=> little_set(f19(estin)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1515])]) ).
fof(f58384,plain,
( estin = first(f19(estin))
| spl0_1515
| ~ spl0_1518 ),
inference(resolution,[],[f58348,f58334]) ).
fof(f58334,plain,
( ~ little_set(f19(estin))
| spl0_1515 ),
inference(avatar_component_clause,[],[f58332]) ).
fof(f129438,plain,
( spl0_1655
| ~ spl0_23
| ~ spl0_580 ),
inference(avatar_split_clause,[],[f8244,f7460,f281,f129436]) ).
fof(f129436,plain,
( spl0_1655
<=> ! [X0] :
( identity_relation = X0
| ordered_pair_predicate(f1(identity_relation,X0))
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1655])]) ).
fof(f8244,plain,
( ! [X0] :
( identity_relation = X0
| ordered_pair_predicate(f1(identity_relation,X0))
| ~ relation(X0) )
| ~ spl0_23
| ~ spl0_580 ),
inference(duplicate_literal_removal,[],[f8233]) ).
fof(f8233,plain,
( ! [X0] :
( identity_relation = X0
| ordered_pair_predicate(f1(identity_relation,X0))
| ~ relation(X0)
| ordered_pair_predicate(f1(identity_relation,X0)) )
| ~ spl0_23
| ~ spl0_580 ),
inference(resolution,[],[f7461,f282]) ).
fof(f129199,plain,
( spl0_209
| ~ spl0_119
| ~ spl0_175
| ~ spl0_210
| ~ spl0_804
| ~ spl0_1196 ),
inference(avatar_split_clause,[],[f88836,f34924,f16790,f2737,f2469,f1266,f2733]) ).
fof(f16790,plain,
( spl0_804
<=> ! [X2,X0,X1] :
( member(f1(X0,intersection(X1,X2)),X0)
| intersection(X1,X2) = X0
| member(f1(X0,intersection(X1,X2)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_804])]) ).
fof(f34924,plain,
( spl0_1196
<=> ! [X0] : estin = intersection(X0,estin) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1196])]) ).
fof(f88836,plain,
( ! [X0] :
( estin = X0
| member(f1(X0,estin),X0) )
| ~ spl0_119
| ~ spl0_175
| ~ spl0_210
| ~ spl0_804
| ~ spl0_1196 ),
inference(forward_demodulation,[],[f88835,f34925]) ).
fof(f34925,plain,
( ! [X0] : estin = intersection(X0,estin)
| ~ spl0_1196 ),
inference(avatar_component_clause,[],[f34924]) ).
fof(f88835,plain,
( ! [X0,X1] :
( intersection(X1,estin) = X0
| member(f1(X0,estin),X0) )
| ~ spl0_119
| ~ spl0_175
| ~ spl0_210
| ~ spl0_804
| ~ spl0_1196 ),
inference(forward_demodulation,[],[f88834,f85273]) ).
fof(f88834,plain,
( ! [X0,X1] :
( intersection(X1,domain_of(identity_relation)) = X0
| member(f1(X0,estin),X0) )
| ~ spl0_119
| ~ spl0_175
| ~ spl0_210
| ~ spl0_804
| ~ spl0_1196 ),
inference(forward_demodulation,[],[f88833,f2471]) ).
fof(f88833,plain,
( ! [X0,X1] :
( member(f1(X0,estin),X0)
| intersection(X1,domain_of(empty_set)) = X0 )
| ~ spl0_119
| ~ spl0_175
| ~ spl0_210
| ~ spl0_804
| ~ spl0_1196 ),
inference(forward_demodulation,[],[f88832,f34925]) ).
fof(f88832,plain,
( ! [X0,X1] :
( member(f1(X0,intersection(X1,estin)),X0)
| intersection(X1,domain_of(empty_set)) = X0 )
| ~ spl0_119
| ~ spl0_175
| ~ spl0_210
| ~ spl0_804 ),
inference(forward_demodulation,[],[f88831,f85273]) ).
fof(f88831,plain,
( ! [X0,X1] :
( member(f1(X0,intersection(X1,domain_of(identity_relation))),X0)
| intersection(X1,domain_of(empty_set)) = X0 )
| ~ spl0_119
| ~ spl0_175
| ~ spl0_804 ),
inference(forward_demodulation,[],[f17181,f2471]) ).
fof(f17181,plain,
( ! [X0,X1] :
( member(f1(X0,intersection(X1,domain_of(empty_set))),X0)
| intersection(X1,domain_of(empty_set)) = X0 )
| ~ spl0_119
| ~ spl0_804 ),
inference(resolution,[],[f16791,f1267]) ).
fof(f16791,plain,
( ! [X2,X0,X1] :
( member(f1(X0,intersection(X1,X2)),X2)
| member(f1(X0,intersection(X1,X2)),X0)
| intersection(X1,X2) = X0 )
| ~ spl0_804 ),
inference(avatar_component_clause,[],[f16790]) ).
fof(f129197,plain,
( spl0_1654
| ~ spl0_40
| ~ spl0_119
| ~ spl0_175
| ~ spl0_356 ),
inference(avatar_split_clause,[],[f85353,f3929,f2469,f1266,f361,f129195]) ).
fof(f129195,plain,
( spl0_1654
<=> ! [X0] : estin = intersection(X0,identity_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1654])]) ).
fof(f3929,plain,
( spl0_356
<=> ! [X0,X1] :
( estin = intersection(X0,X1)
| member(f24(intersection(X0,X1)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_356])]) ).
fof(f85353,plain,
( ! [X0] : estin = intersection(X0,identity_relation)
| ~ spl0_40
| ~ spl0_119
| ~ spl0_175
| ~ spl0_356 ),
inference(forward_demodulation,[],[f4186,f2471]) ).
fof(f4186,plain,
( ! [X0] : estin = intersection(X0,empty_set)
| ~ spl0_40
| ~ spl0_119
| ~ spl0_356 ),
inference(forward_demodulation,[],[f4142,f1939]) ).
fof(f1939,plain,
( empty_set = domain_of(empty_set)
| ~ spl0_40
| ~ spl0_119 ),
inference(resolution,[],[f1267,f362]) ).
fof(f4142,plain,
( ! [X0] : estin = intersection(X0,domain_of(empty_set))
| ~ spl0_119
| ~ spl0_356 ),
inference(resolution,[],[f3930,f1267]) ).
fof(f3930,plain,
( ! [X0,X1] :
( member(f24(intersection(X0,X1)),X1)
| estin = intersection(X0,X1) )
| ~ spl0_356 ),
inference(avatar_component_clause,[],[f3929]) ).
fof(f129192,plain,
( spl0_1653
| ~ spl0_40
| ~ spl0_119
| ~ spl0_175
| ~ spl0_355 ),
inference(avatar_split_clause,[],[f85341,f3925,f2469,f1266,f361,f129190]) ).
fof(f129190,plain,
( spl0_1653
<=> ! [X0] : estin = intersection(identity_relation,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1653])]) ).
fof(f3925,plain,
( spl0_355
<=> ! [X0,X1] :
( estin = intersection(X0,X1)
| member(f24(intersection(X0,X1)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_355])]) ).
fof(f85341,plain,
( ! [X0] : estin = intersection(identity_relation,X0)
| ~ spl0_40
| ~ spl0_119
| ~ spl0_175
| ~ spl0_355 ),
inference(forward_demodulation,[],[f4098,f2471]) ).
fof(f4098,plain,
( ! [X0] : estin = intersection(empty_set,X0)
| ~ spl0_40
| ~ spl0_119
| ~ spl0_355 ),
inference(forward_demodulation,[],[f4054,f1939]) ).
fof(f4054,plain,
( ! [X0] : estin = intersection(domain_of(empty_set),X0)
| ~ spl0_119
| ~ spl0_355 ),
inference(resolution,[],[f3926,f1267]) ).
fof(f3926,plain,
( ! [X0,X1] :
( member(f24(intersection(X0,X1)),X0)
| estin = intersection(X0,X1) )
| ~ spl0_355 ),
inference(avatar_component_clause,[],[f3925]) ).
fof(f129187,plain,
( spl0_1652
| ~ spl0_168
| ~ spl0_175
| ~ spl0_210 ),
inference(avatar_split_clause,[],[f85283,f2737,f2469,f2260,f129185]) ).
fof(f129185,plain,
( spl0_1652
<=> ! [X0] : estin = compose(identity_relation,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1652])]) ).
fof(f2260,plain,
( spl0_168
<=> ! [X0,X1] : ~ member(X0,compose(empty_set,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_168])]) ).
fof(f85283,plain,
( ! [X0] : estin = compose(identity_relation,X0)
| ~ spl0_168
| ~ spl0_175
| ~ spl0_210 ),
inference(forward_demodulation,[],[f2866,f2471]) ).
fof(f2866,plain,
( ! [X0] : estin = compose(empty_set,X0)
| ~ spl0_168
| ~ spl0_210 ),
inference(resolution,[],[f2738,f2261]) ).
fof(f2261,plain,
( ! [X0,X1] : ~ member(X0,compose(empty_set,X1))
| ~ spl0_168 ),
inference(avatar_component_clause,[],[f2260]) ).
fof(f129182,plain,
( spl0_1651
| ~ spl0_167
| ~ spl0_175
| ~ spl0_210 ),
inference(avatar_split_clause,[],[f85282,f2737,f2469,f2256,f129180]) ).
fof(f129180,plain,
( spl0_1651
<=> ! [X0] : estin = compose(X0,identity_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1651])]) ).
fof(f2256,plain,
( spl0_167
<=> ! [X0,X1] : ~ member(X0,compose(X1,empty_set)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_167])]) ).
fof(f85282,plain,
( ! [X0] : estin = compose(X0,identity_relation)
| ~ spl0_167
| ~ spl0_175
| ~ spl0_210 ),
inference(forward_demodulation,[],[f2865,f2471]) ).
fof(f2865,plain,
( ! [X0] : estin = compose(X0,empty_set)
| ~ spl0_167
| ~ spl0_210 ),
inference(resolution,[],[f2738,f2257]) ).
fof(f2257,plain,
( ! [X0,X1] : ~ member(X0,compose(X1,empty_set))
| ~ spl0_167 ),
inference(avatar_component_clause,[],[f2256]) ).
fof(f129177,plain,
( spl0_1650
| ~ spl0_165
| ~ spl0_175
| ~ spl0_210 ),
inference(avatar_split_clause,[],[f85281,f2737,f2469,f2247,f129175]) ).
fof(f129175,plain,
( spl0_1650
<=> ! [X0] : estin = apply(identity_relation,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1650])]) ).
fof(f2247,plain,
( spl0_165
<=> ! [X0,X1] : ~ member(X0,apply(empty_set,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_165])]) ).
fof(f85281,plain,
( ! [X0] : estin = apply(identity_relation,X0)
| ~ spl0_165
| ~ spl0_175
| ~ spl0_210 ),
inference(forward_demodulation,[],[f2860,f2471]) ).
fof(f2860,plain,
( ! [X0] : estin = apply(empty_set,X0)
| ~ spl0_165
| ~ spl0_210 ),
inference(resolution,[],[f2738,f2248]) ).
fof(f2248,plain,
( ! [X0,X1] : ~ member(X0,apply(empty_set,X1))
| ~ spl0_165 ),
inference(avatar_component_clause,[],[f2247]) ).
fof(f129172,plain,
( spl0_1649
| ~ spl0_166
| ~ spl0_175
| ~ spl0_210 ),
inference(avatar_split_clause,[],[f85279,f2737,f2469,f2251,f129170]) ).
fof(f129170,plain,
( spl0_1649
<=> ! [X0] : estin = image(identity_relation,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1649])]) ).
fof(f2251,plain,
( spl0_166
<=> ! [X0,X1] : ~ member(X0,image(empty_set,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_166])]) ).
fof(f85279,plain,
( ! [X0] : estin = image(identity_relation,X0)
| ~ spl0_166
| ~ spl0_175
| ~ spl0_210 ),
inference(forward_demodulation,[],[f2851,f2471]) ).
fof(f2851,plain,
( ! [X0] : estin = image(empty_set,X0)
| ~ spl0_166
| ~ spl0_210 ),
inference(resolution,[],[f2738,f2252]) ).
fof(f2252,plain,
( ! [X0,X1] : ~ member(X0,image(empty_set,X1))
| ~ spl0_166 ),
inference(avatar_component_clause,[],[f2251]) ).
fof(f129167,plain,
( spl0_1648
| ~ spl0_164
| ~ spl0_175
| ~ spl0_210 ),
inference(avatar_split_clause,[],[f85278,f2737,f2469,f2243,f129165]) ).
fof(f129165,plain,
( spl0_1648
<=> ! [X0] : estin = image(X0,identity_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1648])]) ).
fof(f2243,plain,
( spl0_164
<=> ! [X0,X1] : ~ member(X0,image(X1,empty_set)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_164])]) ).
fof(f85278,plain,
( ! [X0] : estin = image(X0,identity_relation)
| ~ spl0_164
| ~ spl0_175
| ~ spl0_210 ),
inference(forward_demodulation,[],[f2850,f2471]) ).
fof(f2850,plain,
( ! [X0] : estin = image(X0,empty_set)
| ~ spl0_164
| ~ spl0_210 ),
inference(resolution,[],[f2738,f2244]) ).
fof(f2244,plain,
( ! [X0,X1] : ~ member(X0,image(X1,empty_set))
| ~ spl0_164 ),
inference(avatar_component_clause,[],[f2243]) ).
fof(f129162,plain,
( spl0_1647
| ~ spl0_40
| ~ spl0_119
| ~ spl0_175
| ~ spl0_246 ),
inference(avatar_split_clause,[],[f85313,f3071,f2469,f1266,f361,f129160]) ).
fof(f129160,plain,
( spl0_1647
<=> ! [X0] : relation(intersection(X0,identity_relation)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1647])]) ).
fof(f85313,plain,
( ! [X0] : relation(intersection(X0,identity_relation))
| ~ spl0_40
| ~ spl0_119
| ~ spl0_175
| ~ spl0_246 ),
inference(forward_demodulation,[],[f3378,f2471]) ).
fof(f3378,plain,
( ! [X0] : relation(intersection(X0,empty_set))
| ~ spl0_40
| ~ spl0_119
| ~ spl0_246 ),
inference(forward_demodulation,[],[f3339,f1939]) ).
fof(f3339,plain,
( ! [X0] : relation(intersection(X0,domain_of(empty_set)))
| ~ spl0_119
| ~ spl0_246 ),
inference(resolution,[],[f3072,f1267]) ).
fof(f129157,plain,
( spl0_1646
| ~ spl0_40
| ~ spl0_119
| ~ spl0_175
| ~ spl0_245 ),
inference(avatar_split_clause,[],[f85301,f3067,f2469,f1266,f361,f129155]) ).
fof(f129155,plain,
( spl0_1646
<=> ! [X0] : relation(intersection(identity_relation,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1646])]) ).
fof(f85301,plain,
( ! [X0] : relation(intersection(identity_relation,X0))
| ~ spl0_40
| ~ spl0_119
| ~ spl0_175
| ~ spl0_245 ),
inference(forward_demodulation,[],[f3298,f2471]) ).
fof(f3298,plain,
( ! [X0] : relation(intersection(empty_set,X0))
| ~ spl0_40
| ~ spl0_119
| ~ spl0_245 ),
inference(forward_demodulation,[],[f3259,f1939]) ).
fof(f3259,plain,
( ! [X0] : relation(intersection(domain_of(empty_set),X0))
| ~ spl0_119
| ~ spl0_245 ),
inference(resolution,[],[f3068,f1267]) ).
fof(f129152,plain,
( spl0_1645
| ~ spl0_141
| ~ spl0_175
| ~ spl0_210 ),
inference(avatar_split_clause,[],[f85280,f2737,f2469,f1749,f129149]) ).
fof(f129149,plain,
( spl0_1645
<=> estin = range_of(identity_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1645])]) ).
fof(f1749,plain,
( spl0_141
<=> ! [X0] : ~ member(X0,range_of(empty_set)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_141])]) ).
fof(f85280,plain,
( estin = range_of(identity_relation)
| ~ spl0_141
| ~ spl0_175
| ~ spl0_210 ),
inference(forward_demodulation,[],[f2855,f2471]) ).
fof(f2855,plain,
( estin = range_of(empty_set)
| ~ spl0_141
| ~ spl0_210 ),
inference(resolution,[],[f2738,f1750]) ).
fof(f1750,plain,
( ! [X0] : ~ member(X0,range_of(empty_set))
| ~ spl0_141 ),
inference(avatar_component_clause,[],[f1749]) ).
fof(f129146,plain,
( spl0_1644
| ~ spl0_135
| ~ spl0_175
| ~ spl0_210 ),
inference(avatar_split_clause,[],[f85277,f2737,f2469,f1548,f129143]) ).
fof(f129143,plain,
( spl0_1644
<=> estin = sigma(identity_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1644])]) ).
fof(f1548,plain,
( spl0_135
<=> ! [X0] : ~ member(X0,sigma(empty_set)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_135])]) ).
fof(f85277,plain,
( estin = sigma(identity_relation)
| ~ spl0_135
| ~ spl0_175
| ~ spl0_210 ),
inference(forward_demodulation,[],[f2845,f2471]) ).
fof(f2845,plain,
( estin = sigma(empty_set)
| ~ spl0_135
| ~ spl0_210 ),
inference(resolution,[],[f2738,f1549]) ).
fof(f1549,plain,
( ! [X0] : ~ member(X0,sigma(empty_set))
| ~ spl0_135 ),
inference(avatar_component_clause,[],[f1548]) ).
fof(f129140,plain,
( spl0_1643
| ~ spl0_153
| ~ spl0_175
| ~ spl0_210 ),
inference(avatar_split_clause,[],[f85276,f2737,f2469,f2098,f129137]) ).
fof(f129137,plain,
( spl0_1643
<=> estin = flip_range_of(identity_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1643])]) ).
fof(f2098,plain,
( spl0_153
<=> ! [X0] : ~ member(X0,flip_range_of(empty_set)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_153])]) ).
fof(f85276,plain,
( estin = flip_range_of(identity_relation)
| ~ spl0_153
| ~ spl0_175
| ~ spl0_210 ),
inference(forward_demodulation,[],[f2843,f2471]) ).
fof(f2843,plain,
( estin = flip_range_of(empty_set)
| ~ spl0_153
| ~ spl0_210 ),
inference(resolution,[],[f2738,f2099]) ).
fof(f2099,plain,
( ! [X0] : ~ member(X0,flip_range_of(empty_set))
| ~ spl0_153 ),
inference(avatar_component_clause,[],[f2098]) ).
fof(f129134,plain,
( spl0_1642
| ~ spl0_154
| ~ spl0_175
| ~ spl0_210 ),
inference(avatar_split_clause,[],[f85275,f2737,f2469,f2102,f129131]) ).
fof(f129131,plain,
( spl0_1642
<=> estin = rotate_right(identity_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1642])]) ).
fof(f2102,plain,
( spl0_154
<=> ! [X0] : ~ member(X0,rotate_right(empty_set)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_154])]) ).
fof(f85275,plain,
( estin = rotate_right(identity_relation)
| ~ spl0_154
| ~ spl0_175
| ~ spl0_210 ),
inference(forward_demodulation,[],[f2838,f2471]) ).
fof(f2838,plain,
( estin = rotate_right(empty_set)
| ~ spl0_154
| ~ spl0_210 ),
inference(resolution,[],[f2738,f2103]) ).
fof(f2103,plain,
( ! [X0] : ~ member(X0,rotate_right(empty_set))
| ~ spl0_154 ),
inference(avatar_component_clause,[],[f2102]) ).
fof(f124766,plain,
( spl0_1641
| ~ spl0_151
| ~ spl0_175
| ~ spl0_210 ),
inference(avatar_split_clause,[],[f85274,f2737,f2469,f2025,f124763]) ).
fof(f124763,plain,
( spl0_1641
<=> estin = converse(identity_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1641])]) ).
fof(f2025,plain,
( spl0_151
<=> ! [X0] : ~ member(X0,converse(empty_set)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_151])]) ).
fof(f85274,plain,
( estin = converse(identity_relation)
| ~ spl0_151
| ~ spl0_175
| ~ spl0_210 ),
inference(forward_demodulation,[],[f2833,f2471]) ).
fof(f2833,plain,
( estin = converse(empty_set)
| ~ spl0_151
| ~ spl0_210 ),
inference(resolution,[],[f2738,f2026]) ).
fof(f2026,plain,
( ! [X0] : ~ member(X0,converse(empty_set))
| ~ spl0_151 ),
inference(avatar_component_clause,[],[f2025]) ).
fof(f123870,plain,
( spl0_1640
| ~ spl0_119
| ~ spl0_175
| ~ spl0_210 ),
inference(avatar_split_clause,[],[f85273,f2737,f2469,f1266,f123867]) ).
fof(f123867,plain,
( spl0_1640
<=> estin = domain_of(identity_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1640])]) ).
fof(f117381,plain,
( spl0_1639
| ~ spl0_175
| ~ spl0_399 ),
inference(avatar_split_clause,[],[f85369,f4397,f2469,f117379]) ).
fof(f117379,plain,
( spl0_1639
<=> ! [X0] :
( powerset(X0) = identity_relation
| ~ little_set(powerset(X0))
| subset(f26(powerset(X0)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1639])]) ).
fof(f4397,plain,
( spl0_399
<=> ! [X0] :
( empty_set = powerset(X0)
| ~ little_set(powerset(X0))
| subset(f26(powerset(X0)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_399])]) ).
fof(f85369,plain,
( ! [X0] :
( powerset(X0) = identity_relation
| ~ little_set(powerset(X0))
| subset(f26(powerset(X0)),X0) )
| ~ spl0_175
| ~ spl0_399 ),
inference(forward_demodulation,[],[f4398,f2471]) ).
fof(f4398,plain,
( ! [X0] :
( empty_set = powerset(X0)
| ~ little_set(powerset(X0))
| subset(f26(powerset(X0)),X0) )
| ~ spl0_399 ),
inference(avatar_component_clause,[],[f4397]) ).
fof(f117376,plain,
( spl0_1638
| ~ spl0_175
| ~ spl0_397 ),
inference(avatar_split_clause,[],[f85368,f4387,f2469,f117374]) ).
fof(f117374,plain,
( spl0_1638
<=> ! [X0] :
( complement(X0) = identity_relation
| ~ little_set(complement(X0))
| ~ member(f26(complement(X0)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1638])]) ).
fof(f4387,plain,
( spl0_397
<=> ! [X0] :
( complement(X0) = empty_set
| ~ little_set(complement(X0))
| ~ member(f26(complement(X0)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_397])]) ).
fof(f85368,plain,
( ! [X0] :
( complement(X0) = identity_relation
| ~ little_set(complement(X0))
| ~ member(f26(complement(X0)),X0) )
| ~ spl0_175
| ~ spl0_397 ),
inference(forward_demodulation,[],[f4388,f2471]) ).
fof(f4388,plain,
( ! [X0] :
( complement(X0) = empty_set
| ~ little_set(complement(X0))
| ~ member(f26(complement(X0)),X0) )
| ~ spl0_397 ),
inference(avatar_component_clause,[],[f4387]) ).
fof(f117371,plain,
( spl0_1637
| ~ spl0_175
| ~ spl0_383 ),
inference(avatar_split_clause,[],[f85367,f4328,f2469,f117369]) ).
fof(f117369,plain,
( spl0_1637
<=> ! [X0,X1] :
( cross_product(X0,X1) = identity_relation
| member(second(f24(cross_product(X0,X1))),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1637])]) ).
fof(f4328,plain,
( spl0_383
<=> ! [X0,X1] :
( member(second(f24(cross_product(X0,X1))),X1)
| cross_product(X0,X1) = empty_set ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_383])]) ).
fof(f85367,plain,
( ! [X0,X1] :
( cross_product(X0,X1) = identity_relation
| member(second(f24(cross_product(X0,X1))),X1) )
| ~ spl0_175
| ~ spl0_383 ),
inference(forward_demodulation,[],[f4329,f2471]) ).
fof(f4329,plain,
( ! [X0,X1] :
( member(second(f24(cross_product(X0,X1))),X1)
| cross_product(X0,X1) = empty_set )
| ~ spl0_383 ),
inference(avatar_component_clause,[],[f4328]) ).
fof(f117365,plain,
( spl0_1636
| ~ spl0_175
| ~ spl0_382 ),
inference(avatar_split_clause,[],[f85366,f4323,f2469,f117363]) ).
fof(f117363,plain,
( spl0_1636
<=> ! [X0,X1] :
( cross_product(X0,X1) = identity_relation
| member(first(f24(cross_product(X0,X1))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1636])]) ).
fof(f4323,plain,
( spl0_382
<=> ! [X0,X1] :
( member(first(f24(cross_product(X0,X1))),X0)
| cross_product(X0,X1) = empty_set ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_382])]) ).
fof(f85366,plain,
( ! [X0,X1] :
( cross_product(X0,X1) = identity_relation
| member(first(f24(cross_product(X0,X1))),X0) )
| ~ spl0_175
| ~ spl0_382 ),
inference(forward_demodulation,[],[f4324,f2471]) ).
fof(f4324,plain,
( ! [X0,X1] :
( member(first(f24(cross_product(X0,X1))),X0)
| cross_product(X0,X1) = empty_set )
| ~ spl0_382 ),
inference(avatar_component_clause,[],[f4323]) ).
fof(f117335,plain,
( spl0_1635
| ~ spl0_175
| ~ spl0_352 ),
inference(avatar_split_clause,[],[f85338,f3911,f2469,f117333]) ).
fof(f117333,plain,
( spl0_1635
<=> ! [X0,X1] :
( identity_relation = X0
| ~ member(X0,X1)
| member(f24(X0),sigma(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1635])]) ).
fof(f3911,plain,
( spl0_352
<=> ! [X0,X1] :
( ~ member(X0,X1)
| member(f24(X0),sigma(X1))
| empty_set = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_352])]) ).
fof(f85338,plain,
( ! [X0,X1] :
( identity_relation = X0
| ~ member(X0,X1)
| member(f24(X0),sigma(X1)) )
| ~ spl0_175
| ~ spl0_352 ),
inference(forward_demodulation,[],[f3912,f2471]) ).
fof(f3912,plain,
( ! [X0,X1] :
( ~ member(X0,X1)
| member(f24(X0),sigma(X1))
| empty_set = X0 )
| ~ spl0_352 ),
inference(avatar_component_clause,[],[f3911]) ).
fof(f117330,plain,
( spl0_1634
| ~ spl0_175
| ~ spl0_347 ),
inference(avatar_split_clause,[],[f85337,f3863,f2469,f117328]) ).
fof(f117328,plain,
( spl0_1634
<=> ! [X0] :
( converse(X0) = identity_relation
| ~ little_set(converse(X0))
| ordered_pair_predicate(f26(converse(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1634])]) ).
fof(f3863,plain,
( spl0_347
<=> ! [X0] :
( converse(X0) = empty_set
| ~ little_set(converse(X0))
| ordered_pair_predicate(f26(converse(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_347])]) ).
fof(f85337,plain,
( ! [X0] :
( converse(X0) = identity_relation
| ~ little_set(converse(X0))
| ordered_pair_predicate(f26(converse(X0))) )
| ~ spl0_175
| ~ spl0_347 ),
inference(forward_demodulation,[],[f3864,f2471]) ).
fof(f3864,plain,
( ! [X0] :
( converse(X0) = empty_set
| ~ little_set(converse(X0))
| ordered_pair_predicate(f26(converse(X0))) )
| ~ spl0_347 ),
inference(avatar_component_clause,[],[f3863]) ).
fof(f117325,plain,
( spl0_1633
| ~ spl0_175
| ~ spl0_299 ),
inference(avatar_split_clause,[],[f85336,f3670,f2469,f117323]) ).
fof(f117323,plain,
( spl0_1633
<=> ! [X0,X1] :
( intersection(X0,X1) = identity_relation
| member(f24(intersection(X0,X1)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1633])]) ).
fof(f3670,plain,
( spl0_299
<=> ! [X0,X1] :
( member(f24(intersection(X0,X1)),X1)
| intersection(X0,X1) = empty_set ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_299])]) ).
fof(f85336,plain,
( ! [X0,X1] :
( intersection(X0,X1) = identity_relation
| member(f24(intersection(X0,X1)),X1) )
| ~ spl0_175
| ~ spl0_299 ),
inference(forward_demodulation,[],[f3671,f2471]) ).
fof(f3671,plain,
( ! [X0,X1] :
( member(f24(intersection(X0,X1)),X1)
| intersection(X0,X1) = empty_set )
| ~ spl0_299 ),
inference(avatar_component_clause,[],[f3670]) ).
fof(f117288,plain,
( spl0_173
| ~ spl0_40
| ~ spl0_209
| ~ spl0_1550 ),
inference(avatar_split_clause,[],[f59236,f58601,f2733,f361,f2440]) ).
fof(f2440,plain,
( spl0_173
<=> estin = empty_set ),
introduced(avatar_definition,[new_symbols(naming,[spl0_173])]) ).
fof(f117286,plain,
( spl0_1632
| ~ spl0_175
| ~ spl0_298 ),
inference(avatar_split_clause,[],[f85335,f3665,f2469,f117284]) ).
fof(f117284,plain,
( spl0_1632
<=> ! [X0,X1] :
( intersection(X0,X1) = identity_relation
| member(f24(intersection(X0,X1)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1632])]) ).
fof(f3665,plain,
( spl0_298
<=> ! [X0,X1] :
( member(f24(intersection(X0,X1)),X0)
| intersection(X0,X1) = empty_set ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_298])]) ).
fof(f85335,plain,
( ! [X0,X1] :
( intersection(X0,X1) = identity_relation
| member(f24(intersection(X0,X1)),X0) )
| ~ spl0_175
| ~ spl0_298 ),
inference(forward_demodulation,[],[f3666,f2471]) ).
fof(f3666,plain,
( ! [X0,X1] :
( member(f24(intersection(X0,X1)),X0)
| intersection(X0,X1) = empty_set )
| ~ spl0_298 ),
inference(avatar_component_clause,[],[f3665]) ).
fof(f117277,plain,
( spl0_1631
| ~ spl0_175
| ~ spl0_274 ),
inference(avatar_split_clause,[],[f85300,f3201,f2469,f117275]) ).
fof(f117275,plain,
( spl0_1631
<=> ! [X0] :
( identity_relation = X0
| ~ little_set(X0)
| ordered_pair_predicate(f26(X0))
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1631])]) ).
fof(f3201,plain,
( spl0_274
<=> ! [X0] :
( empty_set = X0
| ~ little_set(X0)
| ordered_pair_predicate(f26(X0))
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_274])]) ).
fof(f85300,plain,
( ! [X0] :
( identity_relation = X0
| ~ little_set(X0)
| ordered_pair_predicate(f26(X0))
| ~ relation(X0) )
| ~ spl0_175
| ~ spl0_274 ),
inference(forward_demodulation,[],[f3202,f2471]) ).
fof(f3202,plain,
( ! [X0] :
( empty_set = X0
| ~ little_set(X0)
| ordered_pair_predicate(f26(X0))
| ~ relation(X0) )
| ~ spl0_274 ),
inference(avatar_component_clause,[],[f3201]) ).
fof(f117272,plain,
( spl0_1630
| ~ spl0_175
| ~ spl0_273 ),
inference(avatar_split_clause,[],[f85299,f3196,f2469,f117270]) ).
fof(f117270,plain,
( spl0_1630
<=> ! [X0,X1] :
( identity_relation = X1
| ~ member(X0,X1)
| ~ member(X0,f24(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1630])]) ).
fof(f3196,plain,
( spl0_273
<=> ! [X0,X1] :
( ~ member(X0,X1)
| ~ member(X0,f24(X1))
| empty_set = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_273])]) ).
fof(f85299,plain,
( ! [X0,X1] :
( identity_relation = X1
| ~ member(X0,X1)
| ~ member(X0,f24(X1)) )
| ~ spl0_175
| ~ spl0_273 ),
inference(forward_demodulation,[],[f3197,f2471]) ).
fof(f3197,plain,
( ! [X0,X1] :
( ~ member(X0,X1)
| ~ member(X0,f24(X1))
| empty_set = X1 )
| ~ spl0_273 ),
inference(avatar_component_clause,[],[f3196]) ).
fof(f117267,plain,
( spl0_1629
| ~ spl0_175
| ~ spl0_262 ),
inference(avatar_split_clause,[],[f85298,f3146,f2469,f117265]) ).
fof(f117265,plain,
( spl0_1629
<=> ! [X0] :
( range_of(X0) = identity_relation
| ordered_pair_predicate(f27(f24(range_of(X0)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1629])]) ).
fof(f3146,plain,
( spl0_262
<=> ! [X0] :
( ordered_pair_predicate(f27(f24(range_of(X0)),X0))
| empty_set = range_of(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_262])]) ).
fof(f85298,plain,
( ! [X0] :
( range_of(X0) = identity_relation
| ordered_pair_predicate(f27(f24(range_of(X0)),X0)) )
| ~ spl0_175
| ~ spl0_262 ),
inference(forward_demodulation,[],[f3147,f2471]) ).
fof(f3147,plain,
( ! [X0] :
( ordered_pair_predicate(f27(f24(range_of(X0)),X0))
| empty_set = range_of(X0) )
| ~ spl0_262 ),
inference(avatar_component_clause,[],[f3146]) ).
fof(f117262,plain,
( spl0_1628
| ~ spl0_175
| ~ spl0_254 ),
inference(avatar_split_clause,[],[f85297,f3111,f2469,f117260]) ).
fof(f117260,plain,
( spl0_1628
<=> ! [X0] :
( flip_range_of(X0) = identity_relation
| little_set(f14(f24(flip_range_of(X0)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1628])]) ).
fof(f3111,plain,
( spl0_254
<=> ! [X0] :
( little_set(f14(f24(flip_range_of(X0)),X0))
| flip_range_of(X0) = empty_set ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_254])]) ).
fof(f85297,plain,
( ! [X0] :
( flip_range_of(X0) = identity_relation
| little_set(f14(f24(flip_range_of(X0)),X0)) )
| ~ spl0_175
| ~ spl0_254 ),
inference(forward_demodulation,[],[f3112,f2471]) ).
fof(f3112,plain,
( ! [X0] :
( little_set(f14(f24(flip_range_of(X0)),X0))
| flip_range_of(X0) = empty_set )
| ~ spl0_254 ),
inference(avatar_component_clause,[],[f3111]) ).
fof(f117257,plain,
( spl0_1627
| ~ spl0_175
| ~ spl0_253 ),
inference(avatar_split_clause,[],[f85296,f3106,f2469,f117255]) ).
fof(f117255,plain,
( spl0_1627
<=> ! [X0] :
( flip_range_of(X0) = identity_relation
| little_set(f13(f24(flip_range_of(X0)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1627])]) ).
fof(f3106,plain,
( spl0_253
<=> ! [X0] :
( little_set(f13(f24(flip_range_of(X0)),X0))
| flip_range_of(X0) = empty_set ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_253])]) ).
fof(f85296,plain,
( ! [X0] :
( flip_range_of(X0) = identity_relation
| little_set(f13(f24(flip_range_of(X0)),X0)) )
| ~ spl0_175
| ~ spl0_253 ),
inference(forward_demodulation,[],[f3107,f2471]) ).
fof(f3107,plain,
( ! [X0] :
( little_set(f13(f24(flip_range_of(X0)),X0))
| flip_range_of(X0) = empty_set )
| ~ spl0_253 ),
inference(avatar_component_clause,[],[f3106]) ).
fof(f117252,plain,
( spl0_1626
| ~ spl0_175
| ~ spl0_252 ),
inference(avatar_split_clause,[],[f85295,f3101,f2469,f117250]) ).
fof(f117250,plain,
( spl0_1626
<=> ! [X0] :
( flip_range_of(X0) = identity_relation
| little_set(f12(f24(flip_range_of(X0)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1626])]) ).
fof(f3101,plain,
( spl0_252
<=> ! [X0] :
( little_set(f12(f24(flip_range_of(X0)),X0))
| flip_range_of(X0) = empty_set ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_252])]) ).
fof(f85295,plain,
( ! [X0] :
( flip_range_of(X0) = identity_relation
| little_set(f12(f24(flip_range_of(X0)),X0)) )
| ~ spl0_175
| ~ spl0_252 ),
inference(forward_demodulation,[],[f3102,f2471]) ).
fof(f3102,plain,
( ! [X0] :
( little_set(f12(f24(flip_range_of(X0)),X0))
| flip_range_of(X0) = empty_set )
| ~ spl0_252 ),
inference(avatar_component_clause,[],[f3101]) ).
fof(f117247,plain,
( spl0_1625
| ~ spl0_175
| ~ spl0_251 ),
inference(avatar_split_clause,[],[f85294,f3096,f2469,f117245]) ).
fof(f117245,plain,
( spl0_1625
<=> ! [X0] :
( rotate_right(X0) = identity_relation
| little_set(f11(f24(rotate_right(X0)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1625])]) ).
fof(f3096,plain,
( spl0_251
<=> ! [X0] :
( little_set(f11(f24(rotate_right(X0)),X0))
| rotate_right(X0) = empty_set ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_251])]) ).
fof(f85294,plain,
( ! [X0] :
( rotate_right(X0) = identity_relation
| little_set(f11(f24(rotate_right(X0)),X0)) )
| ~ spl0_175
| ~ spl0_251 ),
inference(forward_demodulation,[],[f3097,f2471]) ).
fof(f3097,plain,
( ! [X0] :
( little_set(f11(f24(rotate_right(X0)),X0))
| rotate_right(X0) = empty_set )
| ~ spl0_251 ),
inference(avatar_component_clause,[],[f3096]) ).
fof(f117228,plain,
( spl0_177
| ~ spl0_119
| ~ spl0_175
| ~ spl0_210
| ~ spl0_430 ),
inference(avatar_split_clause,[],[f85371,f4531,f2737,f2469,f1266,f2481]) ).
fof(f2481,plain,
( spl0_177
<=> estin = identity_relation ),
introduced(avatar_definition,[new_symbols(naming,[spl0_177])]) ).
fof(f4531,plain,
( spl0_430
<=> empty_set = domain_of(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_430])]) ).
fof(f85371,plain,
( estin = identity_relation
| ~ spl0_119
| ~ spl0_175
| ~ spl0_210
| ~ spl0_430 ),
inference(forward_demodulation,[],[f85370,f85273]) ).
fof(f85370,plain,
( identity_relation = domain_of(identity_relation)
| ~ spl0_175
| ~ spl0_430 ),
inference(forward_demodulation,[],[f4533,f2471]) ).
fof(f4533,plain,
( empty_set = domain_of(empty_set)
| ~ spl0_430 ),
inference(avatar_component_clause,[],[f4531]) ).
fof(f117226,plain,
( spl0_1624
| ~ spl0_175
| ~ spl0_249 ),
inference(avatar_split_clause,[],[f85293,f3085,f2469,f117224]) ).
fof(f117224,plain,
( spl0_1624
<=> ! [X0] :
( rotate_right(X0) = identity_relation
| little_set(f10(f24(rotate_right(X0)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1624])]) ).
fof(f3085,plain,
( spl0_249
<=> ! [X0] :
( little_set(f10(f24(rotate_right(X0)),X0))
| rotate_right(X0) = empty_set ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_249])]) ).
fof(f85293,plain,
( ! [X0] :
( rotate_right(X0) = identity_relation
| little_set(f10(f24(rotate_right(X0)),X0)) )
| ~ spl0_175
| ~ spl0_249 ),
inference(forward_demodulation,[],[f3086,f2471]) ).
fof(f3086,plain,
( ! [X0] :
( little_set(f10(f24(rotate_right(X0)),X0))
| rotate_right(X0) = empty_set )
| ~ spl0_249 ),
inference(avatar_component_clause,[],[f3085]) ).
fof(f117221,plain,
( spl0_1623
| ~ spl0_175
| ~ spl0_248 ),
inference(avatar_split_clause,[],[f85292,f3080,f2469,f117219]) ).
fof(f117219,plain,
( spl0_1623
<=> ! [X0] :
( rotate_right(X0) = identity_relation
| little_set(f9(f24(rotate_right(X0)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1623])]) ).
fof(f3080,plain,
( spl0_248
<=> ! [X0] :
( little_set(f9(f24(rotate_right(X0)),X0))
| rotate_right(X0) = empty_set ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_248])]) ).
fof(f85292,plain,
( ! [X0] :
( rotate_right(X0) = identity_relation
| little_set(f9(f24(rotate_right(X0)),X0)) )
| ~ spl0_175
| ~ spl0_248 ),
inference(forward_demodulation,[],[f3081,f2471]) ).
fof(f3081,plain,
( ! [X0] :
( little_set(f9(f24(rotate_right(X0)),X0))
| rotate_right(X0) = empty_set )
| ~ spl0_248 ),
inference(avatar_component_clause,[],[f3080]) ).
fof(f117216,plain,
( spl0_1622
| ~ spl0_175
| ~ spl0_247 ),
inference(avatar_split_clause,[],[f85291,f3075,f2469,f117214]) ).
fof(f117214,plain,
( spl0_1622
<=> ! [X0] :
( domain_of(X0) = identity_relation
| ordered_pair_predicate(f8(f24(domain_of(X0)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1622])]) ).
fof(f3075,plain,
( spl0_247
<=> ! [X0] :
( ordered_pair_predicate(f8(f24(domain_of(X0)),X0))
| domain_of(X0) = empty_set ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_247])]) ).
fof(f85291,plain,
( ! [X0] :
( domain_of(X0) = identity_relation
| ordered_pair_predicate(f8(f24(domain_of(X0)),X0)) )
| ~ spl0_175
| ~ spl0_247 ),
inference(forward_demodulation,[],[f3076,f2471]) ).
fof(f3076,plain,
( ! [X0] :
( ordered_pair_predicate(f8(f24(domain_of(X0)),X0))
| domain_of(X0) = empty_set )
| ~ spl0_247 ),
inference(avatar_component_clause,[],[f3075]) ).
fof(f117211,plain,
( spl0_1621
| ~ spl0_175
| ~ spl0_244 ),
inference(avatar_split_clause,[],[f85290,f3062,f2469,f117209]) ).
fof(f117209,plain,
( spl0_1621
<=> ! [X0] :
( second(X0) = identity_relation
| little_set(f7(f24(second(X0)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1621])]) ).
fof(f3062,plain,
( spl0_244
<=> ! [X0] :
( little_set(f7(f24(second(X0)),X0))
| second(X0) = empty_set ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_244])]) ).
fof(f85290,plain,
( ! [X0] :
( second(X0) = identity_relation
| little_set(f7(f24(second(X0)),X0)) )
| ~ spl0_175
| ~ spl0_244 ),
inference(forward_demodulation,[],[f3063,f2471]) ).
fof(f3063,plain,
( ! [X0] :
( little_set(f7(f24(second(X0)),X0))
| second(X0) = empty_set )
| ~ spl0_244 ),
inference(avatar_component_clause,[],[f3062]) ).
fof(f117206,plain,
( spl0_1620
| ~ spl0_175
| ~ spl0_243 ),
inference(avatar_split_clause,[],[f85289,f3057,f2469,f117204]) ).
fof(f117204,plain,
( spl0_1620
<=> ! [X0] :
( second(X0) = identity_relation
| little_set(f6(f24(second(X0)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1620])]) ).
fof(f3057,plain,
( spl0_243
<=> ! [X0] :
( little_set(f6(f24(second(X0)),X0))
| second(X0) = empty_set ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_243])]) ).
fof(f85289,plain,
( ! [X0] :
( second(X0) = identity_relation
| little_set(f6(f24(second(X0)),X0)) )
| ~ spl0_175
| ~ spl0_243 ),
inference(forward_demodulation,[],[f3058,f2471]) ).
fof(f3058,plain,
( ! [X0] :
( little_set(f6(f24(second(X0)),X0))
| second(X0) = empty_set )
| ~ spl0_243 ),
inference(avatar_component_clause,[],[f3057]) ).
fof(f117201,plain,
( spl0_1619
| ~ spl0_175
| ~ spl0_242 ),
inference(avatar_split_clause,[],[f85288,f3052,f2469,f117199]) ).
fof(f117199,plain,
( spl0_1619
<=> ! [X0] :
( first(X0) = identity_relation
| little_set(f5(f24(first(X0)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1619])]) ).
fof(f3052,plain,
( spl0_242
<=> ! [X0] :
( little_set(f5(f24(first(X0)),X0))
| first(X0) = empty_set ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_242])]) ).
fof(f85288,plain,
( ! [X0] :
( first(X0) = identity_relation
| little_set(f5(f24(first(X0)),X0)) )
| ~ spl0_175
| ~ spl0_242 ),
inference(forward_demodulation,[],[f3053,f2471]) ).
fof(f3053,plain,
( ! [X0] :
( little_set(f5(f24(first(X0)),X0))
| first(X0) = empty_set )
| ~ spl0_242 ),
inference(avatar_component_clause,[],[f3052]) ).
fof(f117196,plain,
( spl0_1618
| ~ spl0_175
| ~ spl0_241 ),
inference(avatar_split_clause,[],[f85287,f3047,f2469,f117194]) ).
fof(f117194,plain,
( spl0_1618
<=> ! [X0] :
( first(X0) = identity_relation
| little_set(f4(f24(first(X0)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1618])]) ).
fof(f3047,plain,
( spl0_241
<=> ! [X0] :
( little_set(f4(f24(first(X0)),X0))
| first(X0) = empty_set ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_241])]) ).
fof(f85287,plain,
( ! [X0] :
( first(X0) = identity_relation
| little_set(f4(f24(first(X0)),X0)) )
| ~ spl0_175
| ~ spl0_241 ),
inference(forward_demodulation,[],[f3048,f2471]) ).
fof(f3048,plain,
( ! [X0] :
( little_set(f4(f24(first(X0)),X0))
| first(X0) = empty_set )
| ~ spl0_241 ),
inference(avatar_component_clause,[],[f3047]) ).
fof(f117191,plain,
( spl0_1617
| ~ spl0_175
| ~ spl0_240 ),
inference(avatar_split_clause,[],[f85286,f3042,f2469,f117189]) ).
fof(f117189,plain,
( spl0_1617
<=> ! [X0,X1] :
( cross_product(X0,X1) = identity_relation
| ordered_pair_predicate(f24(cross_product(X0,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1617])]) ).
fof(f3042,plain,
( spl0_240
<=> ! [X0,X1] :
( cross_product(X0,X1) = empty_set
| ordered_pair_predicate(f24(cross_product(X0,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_240])]) ).
fof(f85286,plain,
( ! [X0,X1] :
( cross_product(X0,X1) = identity_relation
| ordered_pair_predicate(f24(cross_product(X0,X1))) )
| ~ spl0_175
| ~ spl0_240 ),
inference(forward_demodulation,[],[f3043,f2471]) ).
fof(f3043,plain,
( ! [X0,X1] :
( cross_product(X0,X1) = empty_set
| ordered_pair_predicate(f24(cross_product(X0,X1))) )
| ~ spl0_240 ),
inference(avatar_component_clause,[],[f3042]) ).
fof(f117186,plain,
( spl0_1616
| ~ spl0_175
| ~ spl0_213 ),
inference(avatar_split_clause,[],[f85285,f2889,f2469,f117184]) ).
fof(f117184,plain,
( spl0_1616
<=> ! [X0] :
( powerset(X0) = identity_relation
| subset(f24(powerset(X0)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1616])]) ).
fof(f2889,plain,
( spl0_213
<=> ! [X0] :
( empty_set = powerset(X0)
| subset(f24(powerset(X0)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_213])]) ).
fof(f85285,plain,
( ! [X0] :
( powerset(X0) = identity_relation
| subset(f24(powerset(X0)),X0) )
| ~ spl0_175
| ~ spl0_213 ),
inference(forward_demodulation,[],[f2890,f2471]) ).
fof(f2890,plain,
( ! [X0] :
( empty_set = powerset(X0)
| subset(f24(powerset(X0)),X0) )
| ~ spl0_213 ),
inference(avatar_component_clause,[],[f2889]) ).
fof(f117181,plain,
( spl0_1615
| ~ spl0_175
| ~ spl0_212 ),
inference(avatar_split_clause,[],[f85284,f2884,f2469,f117179]) ).
fof(f117179,plain,
( spl0_1615
<=> ! [X0] :
( complement(X0) = identity_relation
| ~ member(f24(complement(X0)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1615])]) ).
fof(f2884,plain,
( spl0_212
<=> ! [X0] :
( complement(X0) = empty_set
| ~ member(f24(complement(X0)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_212])]) ).
fof(f85284,plain,
( ! [X0] :
( complement(X0) = identity_relation
| ~ member(f24(complement(X0)),X0) )
| ~ spl0_175
| ~ spl0_212 ),
inference(forward_demodulation,[],[f2885,f2471]) ).
fof(f2885,plain,
( ! [X0] :
( complement(X0) = empty_set
| ~ member(f24(complement(X0)),X0) )
| ~ spl0_212 ),
inference(avatar_component_clause,[],[f2884]) ).
fof(f95110,plain,
( spl0_173
| ~ spl0_4
| ~ spl0_210 ),
inference(avatar_split_clause,[],[f2844,f2737,f201,f2440]) ).
fof(f201,plain,
( spl0_4
<=> ! [X3] : ~ member(X3,empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).
fof(f2844,plain,
( estin = empty_set
| ~ spl0_4
| ~ spl0_210 ),
inference(resolution,[],[f2738,f202]) ).
fof(f202,plain,
( ! [X3] : ~ member(X3,empty_set)
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f201]) ).
fof(f95107,plain,
( spl0_1614
| ~ spl0_175
| ~ spl0_205 ),
inference(avatar_split_clause,[],[f85266,f2627,f2469,f95105]) ).
fof(f95105,plain,
( spl0_1614
<=> ! [X0] :
( identity_relation = X0
| member(f1(identity_relation,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1614])]) ).
fof(f2627,plain,
( spl0_205
<=> ! [X0] :
( member(f1(empty_set,X0),X0)
| empty_set = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_205])]) ).
fof(f85266,plain,
( ! [X0] :
( identity_relation = X0
| member(f1(identity_relation,X0),X0) )
| ~ spl0_175
| ~ spl0_205 ),
inference(forward_demodulation,[],[f85265,f2471]) ).
fof(f85265,plain,
( ! [X0] :
( member(f1(identity_relation,X0),X0)
| empty_set = X0 )
| ~ spl0_175
| ~ spl0_205 ),
inference(forward_demodulation,[],[f2628,f2471]) ).
fof(f2628,plain,
( ! [X0] :
( member(f1(empty_set,X0),X0)
| empty_set = X0 )
| ~ spl0_205 ),
inference(avatar_component_clause,[],[f2627]) ).
fof(f95101,plain,
( spl0_1613
| ~ spl0_175
| ~ spl0_204 ),
inference(avatar_split_clause,[],[f85264,f2621,f2469,f95099]) ).
fof(f95099,plain,
( spl0_1613
<=> ! [X0] :
( identity_relation = X0
| member(f1(X0,identity_relation),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1613])]) ).
fof(f2621,plain,
( spl0_204
<=> ! [X0] :
( member(f1(X0,empty_set),X0)
| empty_set = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_204])]) ).
fof(f85264,plain,
( ! [X0] :
( identity_relation = X0
| member(f1(X0,identity_relation),X0) )
| ~ spl0_175
| ~ spl0_204 ),
inference(forward_demodulation,[],[f85263,f2471]) ).
fof(f85263,plain,
( ! [X0] :
( member(f1(X0,identity_relation),X0)
| empty_set = X0 )
| ~ spl0_175
| ~ spl0_204 ),
inference(forward_demodulation,[],[f2622,f2471]) ).
fof(f2622,plain,
( ! [X0] :
( member(f1(X0,empty_set),X0)
| empty_set = X0 )
| ~ spl0_204 ),
inference(avatar_component_clause,[],[f2621]) ).
fof(f95096,plain,
( spl0_1612
| ~ spl0_175
| ~ spl0_199 ),
inference(avatar_split_clause,[],[f85262,f2594,f2469,f95094]) ).
fof(f95094,plain,
( spl0_1612
<=> ! [X0] :
( identity_relation = X0
| ~ little_set(X0)
| little_set(f26(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1612])]) ).
fof(f2594,plain,
( spl0_199
<=> ! [X0] :
( empty_set = X0
| ~ little_set(X0)
| little_set(f26(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_199])]) ).
fof(f85262,plain,
( ! [X0] :
( identity_relation = X0
| ~ little_set(X0)
| little_set(f26(X0)) )
| ~ spl0_175
| ~ spl0_199 ),
inference(forward_demodulation,[],[f2595,f2471]) ).
fof(f2595,plain,
( ! [X0] :
( empty_set = X0
| ~ little_set(X0)
| little_set(f26(X0)) )
| ~ spl0_199 ),
inference(avatar_component_clause,[],[f2594]) ).
fof(f95091,plain,
( spl0_1611
| ~ spl0_175
| ~ spl0_193 ),
inference(avatar_split_clause,[],[f85261,f2568,f2469,f95089]) ).
fof(f95089,plain,
( spl0_1611
<=> ! [X0] :
( converse(X0) = identity_relation
| ordered_pair_predicate(f24(converse(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1611])]) ).
fof(f2568,plain,
( spl0_193
<=> ! [X0] :
( converse(X0) = empty_set
| ordered_pair_predicate(f24(converse(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_193])]) ).
fof(f85261,plain,
( ! [X0] :
( converse(X0) = identity_relation
| ordered_pair_predicate(f24(converse(X0))) )
| ~ spl0_175
| ~ spl0_193 ),
inference(forward_demodulation,[],[f2569,f2471]) ).
fof(f2569,plain,
( ! [X0] :
( converse(X0) = empty_set
| ordered_pair_predicate(f24(converse(X0))) )
| ~ spl0_193 ),
inference(avatar_component_clause,[],[f2568]) ).
fof(f95086,plain,
( spl0_1610
| ~ spl0_175
| ~ spl0_192 ),
inference(avatar_split_clause,[],[f85260,f2563,f2469,f95084]) ).
fof(f95084,plain,
( spl0_1610
<=> ! [X0] :
( identity_relation = X0
| ordered_pair_predicate(f24(X0))
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1610])]) ).
fof(f2563,plain,
( spl0_192
<=> ! [X0] :
( empty_set = X0
| ordered_pair_predicate(f24(X0))
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_192])]) ).
fof(f85260,plain,
( ! [X0] :
( identity_relation = X0
| ordered_pair_predicate(f24(X0))
| ~ relation(X0) )
| ~ spl0_175
| ~ spl0_192 ),
inference(forward_demodulation,[],[f2564,f2471]) ).
fof(f2564,plain,
( ! [X0] :
( empty_set = X0
| ordered_pair_predicate(f24(X0))
| ~ relation(X0) )
| ~ spl0_192 ),
inference(avatar_component_clause,[],[f2563]) ).
fof(f93970,plain,
( spl0_1609
| ~ spl0_175
| ~ spl0_187 ),
inference(avatar_split_clause,[],[f85259,f2530,f2469,f93968]) ).
fof(f93968,plain,
( spl0_1609
<=> ! [X0] :
( member(identity_relation,sigma(X0))
| ~ member(infinity,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1609])]) ).
fof(f2530,plain,
( spl0_187
<=> ! [X0] :
( ~ member(infinity,X0)
| member(empty_set,sigma(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_187])]) ).
fof(f85259,plain,
( ! [X0] :
( member(identity_relation,sigma(X0))
| ~ member(infinity,X0) )
| ~ spl0_175
| ~ spl0_187 ),
inference(forward_demodulation,[],[f2531,f2471]) ).
fof(f2531,plain,
( ! [X0] :
( ~ member(infinity,X0)
| member(empty_set,sigma(X0)) )
| ~ spl0_187 ),
inference(avatar_component_clause,[],[f2530]) ).
fof(f93963,plain,
( spl0_1608
| ~ spl0_175
| ~ spl0_366 ),
inference(avatar_split_clause,[],[f85365,f4252,f2469,f93960]) ).
fof(f93960,plain,
( spl0_1608
<=> function(identity_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1608])]) ).
fof(f4252,plain,
( spl0_366
<=> function(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_366])]) ).
fof(f85365,plain,
( function(identity_relation)
| ~ spl0_175
| ~ spl0_366 ),
inference(forward_demodulation,[],[f4254,f2471]) ).
fof(f4254,plain,
( function(empty_set)
| ~ spl0_366 ),
inference(avatar_component_clause,[],[f4252]) ).
fof(f85257,plain,
( spl0_177
| ~ spl0_40
| ~ spl0_175
| ~ spl0_209
| ~ spl0_1550 ),
inference(avatar_split_clause,[],[f84541,f58601,f2733,f2469,f361,f2481]) ).
fof(f84541,plain,
( estin = identity_relation
| ~ spl0_40
| ~ spl0_175
| ~ spl0_209
| ~ spl0_1550 ),
inference(forward_demodulation,[],[f2471,f59236]) ).
fof(f77131,plain,
( spl0_173
| ~ spl0_175
| ~ spl0_177 ),
inference(avatar_split_clause,[],[f67933,f2481,f2469,f2440]) ).
fof(f67933,plain,
( estin = empty_set
| ~ spl0_175
| ~ spl0_177 ),
inference(forward_demodulation,[],[f2471,f2483]) ).
fof(f2483,plain,
( estin = identity_relation
| ~ spl0_177 ),
inference(avatar_component_clause,[],[f2481]) ).
fof(f69069,plain,
( spl0_173
| ~ spl0_171
| spl0_1573 ),
inference(avatar_split_clause,[],[f60294,f59714,f2432,f2440]) ).
fof(f2432,plain,
( spl0_171
<=> ! [X0] :
( empty_set = X0
| little_set(f24(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_171])]) ).
fof(f59714,plain,
( spl0_1573
<=> little_set(f24(estin)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1573])]) ).
fof(f60294,plain,
( estin = empty_set
| ~ spl0_171
| spl0_1573 ),
inference(resolution,[],[f59716,f2433]) ).
fof(f2433,plain,
( ! [X0] :
( little_set(f24(X0))
| empty_set = X0 )
| ~ spl0_171 ),
inference(avatar_component_clause,[],[f2432]) ).
fof(f59716,plain,
( ~ little_set(f24(estin))
| spl0_1573 ),
inference(avatar_component_clause,[],[f59714]) ).
fof(f69068,plain,
( spl0_1607
| ~ spl0_7
| ~ spl0_1225 ),
inference(avatar_split_clause,[],[f37217,f37002,f214,f69066]) ).
fof(f69066,plain,
( spl0_1607
<=> ! [X0,X1] :
( little_set(f24(compose(X0,X1)))
| estin = compose(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1607])]) ).
fof(f214,plain,
( spl0_7
<=> ! [X0,X1] : little_set(non_ordered_pair(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).
fof(f37002,plain,
( spl0_1225
<=> ! [X0,X1] :
( estin = compose(X0,X1)
| f24(compose(X0,X1)) = non_ordered_pair(non_ordered_pair(f29(f24(compose(X0,X1)),X0,X1),f29(f24(compose(X0,X1)),X0,X1)),non_ordered_pair(f29(f24(compose(X0,X1)),X0,X1),f30(f24(compose(X0,X1)),X0,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1225])]) ).
fof(f37217,plain,
( ! [X0,X1] :
( little_set(f24(compose(X0,X1)))
| estin = compose(X0,X1) )
| ~ spl0_7
| ~ spl0_1225 ),
inference(superposition,[],[f215,f37003]) ).
fof(f37003,plain,
( ! [X0,X1] :
( f24(compose(X0,X1)) = non_ordered_pair(non_ordered_pair(f29(f24(compose(X0,X1)),X0,X1),f29(f24(compose(X0,X1)),X0,X1)),non_ordered_pair(f29(f24(compose(X0,X1)),X0,X1),f30(f24(compose(X0,X1)),X0,X1)))
| estin = compose(X0,X1) )
| ~ spl0_1225 ),
inference(avatar_component_clause,[],[f37002]) ).
fof(f215,plain,
( ! [X0,X1] : little_set(non_ordered_pair(X0,X1))
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f214]) ).
fof(f69064,plain,
( spl0_1606
| ~ spl0_453
| ~ spl0_476 ),
inference(avatar_split_clause,[],[f7092,f5648,f5539,f69062]) ).
fof(f69062,plain,
( spl0_1606
<=> ! [X2,X0,X1] :
( member(X0,sigma(X1))
| ~ member(X0,sigma(intersection(X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1606])]) ).
fof(f5539,plain,
( spl0_453
<=> ! [X2,X0,X1] :
( ~ member(X0,sigma(intersection(X1,X2)))
| member(f16(X0,intersection(X1,X2)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_453])]) ).
fof(f5648,plain,
( spl0_476
<=> ! [X2,X0,X1] :
( ~ member(f16(X0,X1),X2)
| member(X0,sigma(X2))
| ~ member(X0,sigma(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_476])]) ).
fof(f7092,plain,
( ! [X2,X0,X1] :
( member(X0,sigma(X1))
| ~ member(X0,sigma(intersection(X1,X2))) )
| ~ spl0_453
| ~ spl0_476 ),
inference(duplicate_literal_removal,[],[f7074]) ).
fof(f7074,plain,
( ! [X2,X0,X1] :
( member(X0,sigma(X1))
| ~ member(X0,sigma(intersection(X1,X2)))
| ~ member(X0,sigma(intersection(X1,X2))) )
| ~ spl0_453
| ~ spl0_476 ),
inference(resolution,[],[f5649,f5540]) ).
fof(f5540,plain,
( ! [X2,X0,X1] :
( member(f16(X0,intersection(X1,X2)),X1)
| ~ member(X0,sigma(intersection(X1,X2))) )
| ~ spl0_453 ),
inference(avatar_component_clause,[],[f5539]) ).
fof(f5649,plain,
( ! [X2,X0,X1] :
( ~ member(f16(X0,X1),X2)
| member(X0,sigma(X2))
| ~ member(X0,sigma(X1)) )
| ~ spl0_476 ),
inference(avatar_component_clause,[],[f5648]) ).
fof(f69060,plain,
( spl0_1605
| ~ spl0_452
| ~ spl0_476 ),
inference(avatar_split_clause,[],[f7091,f5648,f5535,f69058]) ).
fof(f69058,plain,
( spl0_1605
<=> ! [X2,X0,X1] :
( member(X0,sigma(X1))
| ~ member(X0,sigma(intersection(X2,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1605])]) ).
fof(f5535,plain,
( spl0_452
<=> ! [X2,X0,X1] :
( ~ member(X0,sigma(intersection(X1,X2)))
| member(f16(X0,intersection(X1,X2)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_452])]) ).
fof(f7091,plain,
( ! [X2,X0,X1] :
( member(X0,sigma(X1))
| ~ member(X0,sigma(intersection(X2,X1))) )
| ~ spl0_452
| ~ spl0_476 ),
inference(duplicate_literal_removal,[],[f7075]) ).
fof(f7075,plain,
( ! [X2,X0,X1] :
( member(X0,sigma(X1))
| ~ member(X0,sigma(intersection(X2,X1)))
| ~ member(X0,sigma(intersection(X2,X1))) )
| ~ spl0_452
| ~ spl0_476 ),
inference(resolution,[],[f5649,f5536]) ).
fof(f5536,plain,
( ! [X2,X0,X1] :
( member(f16(X0,intersection(X1,X2)),X2)
| ~ member(X0,sigma(intersection(X1,X2))) )
| ~ spl0_452 ),
inference(avatar_component_clause,[],[f5535]) ).
fof(f69056,plain,
( spl0_1604
| ~ spl0_259
| ~ spl0_417 ),
inference(avatar_split_clause,[],[f5281,f4474,f3132,f69054]) ).
fof(f69054,plain,
( spl0_1604
<=> ! [X0,X1] :
( ~ member(complement(sigma(X0)),X0)
| disjoint(X1,complement(sigma(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1604])]) ).
fof(f3132,plain,
( spl0_259
<=> ! [X0,X1] :
( disjoint(X0,complement(X1))
| ~ member(f23(X0,complement(X1)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_259])]) ).
fof(f4474,plain,
( spl0_417
<=> ! [X2,X0,X1] :
( ~ member(X0,X1)
| member(f23(X2,X0),sigma(X1))
| disjoint(X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_417])]) ).
fof(f5281,plain,
( ! [X0,X1] :
( ~ member(complement(sigma(X0)),X0)
| disjoint(X1,complement(sigma(X0))) )
| ~ spl0_259
| ~ spl0_417 ),
inference(duplicate_literal_removal,[],[f5272]) ).
fof(f5272,plain,
( ! [X0,X1] :
( ~ member(complement(sigma(X0)),X0)
| disjoint(X1,complement(sigma(X0)))
| disjoint(X1,complement(sigma(X0))) )
| ~ spl0_259
| ~ spl0_417 ),
inference(resolution,[],[f4475,f3133]) ).
fof(f3133,plain,
( ! [X0,X1] :
( ~ member(f23(X0,complement(X1)),X1)
| disjoint(X0,complement(X1)) )
| ~ spl0_259 ),
inference(avatar_component_clause,[],[f3132]) ).
fof(f4475,plain,
( ! [X2,X0,X1] :
( member(f23(X2,X0),sigma(X1))
| ~ member(X0,X1)
| disjoint(X2,X0) )
| ~ spl0_417 ),
inference(avatar_component_clause,[],[f4474]) ).
fof(f69052,plain,
( spl0_1603
| ~ spl0_257
| ~ spl0_416 ),
inference(avatar_split_clause,[],[f5265,f4470,f3124,f69050]) ).
fof(f69050,plain,
( spl0_1603
<=> ! [X0,X1] :
( ~ member(complement(sigma(X0)),X0)
| disjoint(complement(sigma(X0)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1603])]) ).
fof(f3124,plain,
( spl0_257
<=> ! [X0,X1] :
( disjoint(complement(X0),X1)
| ~ member(f23(complement(X0),X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_257])]) ).
fof(f4470,plain,
( spl0_416
<=> ! [X2,X0,X1] :
( ~ member(X0,X1)
| member(f23(X0,X2),sigma(X1))
| disjoint(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_416])]) ).
fof(f5265,plain,
( ! [X0,X1] :
( ~ member(complement(sigma(X0)),X0)
| disjoint(complement(sigma(X0)),X1) )
| ~ spl0_257
| ~ spl0_416 ),
inference(duplicate_literal_removal,[],[f5254]) ).
fof(f5254,plain,
( ! [X0,X1] :
( ~ member(complement(sigma(X0)),X0)
| disjoint(complement(sigma(X0)),X1)
| disjoint(complement(sigma(X0)),X1) )
| ~ spl0_257
| ~ spl0_416 ),
inference(resolution,[],[f4471,f3125]) ).
fof(f3125,plain,
( ! [X0,X1] :
( ~ member(f23(complement(X0),X1),X0)
| disjoint(complement(X0),X1) )
| ~ spl0_257 ),
inference(avatar_component_clause,[],[f3124]) ).
fof(f4471,plain,
( ! [X2,X0,X1] :
( member(f23(X0,X2),sigma(X1))
| ~ member(X0,X1)
| disjoint(X0,X2) )
| ~ spl0_416 ),
inference(avatar_component_clause,[],[f4470]) ).
fof(f69048,plain,
( spl0_1602
| ~ spl0_255
| ~ spl0_415 ),
inference(avatar_split_clause,[],[f5252,f4466,f3116,f69046]) ).
fof(f69046,plain,
( spl0_1602
<=> ! [X0,X1] :
( ~ member(complement(sigma(X0)),X0)
| subset(complement(sigma(X0)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1602])]) ).
fof(f3116,plain,
( spl0_255
<=> ! [X0,X1] :
( subset(complement(X0),X1)
| ~ member(f17(complement(X0),X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_255])]) ).
fof(f4466,plain,
( spl0_415
<=> ! [X2,X0,X1] :
( ~ member(X0,X1)
| member(f17(X0,X2),sigma(X1))
| subset(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_415])]) ).
fof(f5252,plain,
( ! [X0,X1] :
( ~ member(complement(sigma(X0)),X0)
| subset(complement(sigma(X0)),X1) )
| ~ spl0_255
| ~ spl0_415 ),
inference(duplicate_literal_removal,[],[f5243]) ).
fof(f5243,plain,
( ! [X0,X1] :
( ~ member(complement(sigma(X0)),X0)
| subset(complement(sigma(X0)),X1)
| subset(complement(sigma(X0)),X1) )
| ~ spl0_255
| ~ spl0_415 ),
inference(resolution,[],[f4467,f3117]) ).
fof(f3117,plain,
( ! [X0,X1] :
( ~ member(f17(complement(X0),X1),X0)
| subset(complement(X0),X1) )
| ~ spl0_255 ),
inference(avatar_component_clause,[],[f3116]) ).
fof(f4467,plain,
( ! [X2,X0,X1] :
( member(f17(X0,X2),sigma(X1))
| ~ member(X0,X1)
| subset(X0,X2) )
| ~ spl0_415 ),
inference(avatar_component_clause,[],[f4466]) ).
fof(f69044,plain,
( spl0_1601
| ~ spl0_235
| ~ spl0_358 ),
inference(avatar_split_clause,[],[f4220,f4034,f2984,f69042]) ).
fof(f69042,plain,
( spl0_1601
<=> ! [X0] :
( ~ member(complement(sigma(X0)),X0)
| estin = complement(sigma(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1601])]) ).
fof(f2984,plain,
( spl0_235
<=> ! [X0] :
( estin = complement(X0)
| ~ member(f24(complement(X0)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_235])]) ).
fof(f4220,plain,
( ! [X0] :
( ~ member(complement(sigma(X0)),X0)
| estin = complement(sigma(X0)) )
| ~ spl0_235
| ~ spl0_358 ),
inference(duplicate_literal_removal,[],[f4212]) ).
fof(f4212,plain,
( ! [X0] :
( ~ member(complement(sigma(X0)),X0)
| estin = complement(sigma(X0))
| estin = complement(sigma(X0)) )
| ~ spl0_235
| ~ spl0_358 ),
inference(resolution,[],[f4035,f2985]) ).
fof(f2985,plain,
( ! [X0] :
( ~ member(f24(complement(X0)),X0)
| estin = complement(X0) )
| ~ spl0_235 ),
inference(avatar_component_clause,[],[f2984]) ).
fof(f69040,plain,
( spl0_1600
| ~ spl0_11
| ~ spl0_355 ),
inference(avatar_split_clause,[],[f4039,f3925,f232,f69038]) ).
fof(f69038,plain,
( spl0_1600
<=> ! [X0,X1] :
( estin = intersection(X0,X1)
| little_set(f24(intersection(X0,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1600])]) ).
fof(f4039,plain,
( ! [X0,X1] :
( estin = intersection(X0,X1)
| little_set(f24(intersection(X0,X1))) )
| ~ spl0_11
| ~ spl0_355 ),
inference(resolution,[],[f3926,f233]) ).
fof(f69036,plain,
( spl0_1599
| ~ spl0_16
| ~ spl0_351 ),
inference(avatar_split_clause,[],[f4027,f3907,f253,f69034]) ).
fof(f69034,plain,
( spl0_1599
<=> ! [X0,X1] :
( member(X0,sigma(universal_set))
| ~ little_set(X0)
| ~ little_set(non_ordered_pair(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1599])]) ).
fof(f253,plain,
( spl0_16
<=> ! [X3] :
( ~ little_set(X3)
| member(X3,universal_set) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_16])]) ).
fof(f3907,plain,
( spl0_351
<=> ! [X2,X0,X1] :
( ~ member(non_ordered_pair(X0,X1),X2)
| member(X1,sigma(X2))
| ~ little_set(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_351])]) ).
fof(f4027,plain,
( ! [X0,X1] :
( member(X0,sigma(universal_set))
| ~ little_set(X0)
| ~ little_set(non_ordered_pair(X1,X0)) )
| ~ spl0_16
| ~ spl0_351 ),
inference(resolution,[],[f3908,f254]) ).
fof(f254,plain,
( ! [X3] :
( member(X3,universal_set)
| ~ little_set(X3) )
| ~ spl0_16 ),
inference(avatar_component_clause,[],[f253]) ).
fof(f3908,plain,
( ! [X2,X0,X1] :
( ~ member(non_ordered_pair(X0,X1),X2)
| member(X1,sigma(X2))
| ~ little_set(X1) )
| ~ spl0_351 ),
inference(avatar_component_clause,[],[f3907]) ).
fof(f69032,plain,
( spl0_1598
| ~ spl0_16
| ~ spl0_350 ),
inference(avatar_split_clause,[],[f4003,f3903,f253,f69030]) ).
fof(f69030,plain,
( spl0_1598
<=> ! [X0,X1] :
( member(X0,sigma(universal_set))
| ~ little_set(X0)
| ~ little_set(non_ordered_pair(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1598])]) ).
fof(f3903,plain,
( spl0_350
<=> ! [X2,X0,X1] :
( ~ member(non_ordered_pair(X0,X1),X2)
| member(X0,sigma(X2))
| ~ little_set(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_350])]) ).
fof(f4003,plain,
( ! [X0,X1] :
( member(X0,sigma(universal_set))
| ~ little_set(X0)
| ~ little_set(non_ordered_pair(X0,X1)) )
| ~ spl0_16
| ~ spl0_350 ),
inference(resolution,[],[f3904,f254]) ).
fof(f3904,plain,
( ! [X2,X0,X1] :
( ~ member(non_ordered_pair(X0,X1),X2)
| member(X0,sigma(X2))
| ~ little_set(X0) )
| ~ spl0_350 ),
inference(avatar_component_clause,[],[f3903]) ).
fof(f69023,plain,
( spl0_1597
| ~ spl0_16
| ~ spl0_348 ),
inference(avatar_split_clause,[],[f3979,f3895,f253,f69021]) ).
fof(f69021,plain,
( spl0_1597
<=> ! [X0] :
( ~ member(X0,range_of(complement(universal_set)))
| ~ little_set(f27(X0,complement(universal_set))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1597])]) ).
fof(f3979,plain,
( ! [X0] :
( ~ member(X0,range_of(complement(universal_set)))
| ~ little_set(f27(X0,complement(universal_set))) )
| ~ spl0_16
| ~ spl0_348 ),
inference(resolution,[],[f3896,f254]) ).
fof(f69017,plain,
( spl0_1596
| ~ spl0_16
| ~ spl0_345 ),
inference(avatar_split_clause,[],[f3964,f3855,f253,f69015]) ).
fof(f69015,plain,
( spl0_1596
<=> ! [X0] :
( ~ member(X0,sigma(complement(universal_set)))
| ~ little_set(f16(X0,complement(universal_set))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1596])]) ).
fof(f3964,plain,
( ! [X0] :
( ~ member(X0,sigma(complement(universal_set)))
| ~ little_set(f16(X0,complement(universal_set))) )
| ~ spl0_16
| ~ spl0_345 ),
inference(resolution,[],[f3856,f254]) ).
fof(f69011,plain,
( spl0_1595
| ~ spl0_16
| ~ spl0_343 ),
inference(avatar_split_clause,[],[f3953,f3847,f253,f69009]) ).
fof(f69009,plain,
( spl0_1595
<=> ! [X0] :
( ~ member(X0,domain_of(complement(universal_set)))
| ~ little_set(f8(X0,complement(universal_set))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1595])]) ).
fof(f3953,plain,
( ! [X0] :
( ~ member(X0,domain_of(complement(universal_set)))
| ~ little_set(f8(X0,complement(universal_set))) )
| ~ spl0_16
| ~ spl0_343 ),
inference(resolution,[],[f3848,f254]) ).
fof(f69007,plain,
( spl0_1594
| ~ spl0_197
| ~ spl0_275 ),
inference(avatar_split_clause,[],[f3555,f3206,f2585,f69005]) ).
fof(f69005,plain,
( spl0_1594
<=> ! [X0,X1] :
( ~ member(X0,X1)
| relation(X0)
| little_set(f16(f18(X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1594])]) ).
fof(f3555,plain,
( ! [X0,X1] :
( ~ member(X0,X1)
| relation(X0)
| little_set(f16(f18(X0),X1)) )
| ~ spl0_197
| ~ spl0_275 ),
inference(resolution,[],[f3207,f2586]) ).
fof(f69002,plain,
( spl0_170
| spl0_1593
| ~ spl0_38
| ~ spl0_234 ),
inference(avatar_split_clause,[],[f3014,f2977,f353,f69000,f2428]) ).
fof(f2428,plain,
( spl0_170
<=> ! [X0] :
( ordered_pair_predicate(X0)
| ~ little_set(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_170])]) ).
fof(f69000,plain,
( spl0_1593
<=> ! [X0] :
( ~ member(universal_set,X0)
| ~ relation(sigma(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1593])]) ).
fof(f3014,plain,
( ! [X0,X1] :
( ~ member(universal_set,X0)
| ~ little_set(X1)
| ordered_pair_predicate(X1)
| ~ relation(sigma(X0)) )
| ~ spl0_38
| ~ spl0_234 ),
inference(resolution,[],[f2978,f354]) ).
fof(f68998,plain,
( spl0_1592
| ~ spl0_37
| ~ spl0_210 ),
inference(avatar_split_clause,[],[f2847,f2737,f349,f68996]) ).
fof(f68996,plain,
( spl0_1592
<=> ! [X0] :
( estin = powerset(X0)
| subset(f1(estin,powerset(X0)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1592])]) ).
fof(f349,plain,
( spl0_37
<=> ! [X0,X3] :
( subset(X3,X0)
| ~ member(X3,powerset(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_37])]) ).
fof(f2847,plain,
( ! [X0] :
( estin = powerset(X0)
| subset(f1(estin,powerset(X0)),X0) )
| ~ spl0_37
| ~ spl0_210 ),
inference(resolution,[],[f2738,f350]) ).
fof(f350,plain,
( ! [X3,X0] :
( ~ member(X3,powerset(X0))
| subset(X3,X0) )
| ~ spl0_37 ),
inference(avatar_component_clause,[],[f349]) ).
fof(f68994,plain,
( spl0_1591
| ~ spl0_34
| ~ spl0_210 ),
inference(avatar_split_clause,[],[f2824,f2737,f336,f68992]) ).
fof(f68992,plain,
( spl0_1591
<=> ! [X0] :
( estin = complement(X0)
| ~ member(f1(estin,complement(X0)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1591])]) ).
fof(f336,plain,
( spl0_34
<=> ! [X0,X3] :
( ~ member(X3,X0)
| ~ member(X3,complement(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_34])]) ).
fof(f2824,plain,
( ! [X0] :
( estin = complement(X0)
| ~ member(f1(estin,complement(X0)),X0) )
| ~ spl0_34
| ~ spl0_210 ),
inference(resolution,[],[f2738,f337]) ).
fof(f337,plain,
( ! [X3,X0] :
( ~ member(X3,complement(X0))
| ~ member(X3,X0) )
| ~ spl0_34 ),
inference(avatar_component_clause,[],[f336]) ).
fof(f68990,plain,
( spl0_1590
| ~ spl0_37
| ~ spl0_209 ),
inference(avatar_split_clause,[],[f2779,f2733,f349,f68988]) ).
fof(f68988,plain,
( spl0_1590
<=> ! [X0] :
( estin = powerset(X0)
| subset(f1(powerset(X0),estin),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1590])]) ).
fof(f2779,plain,
( ! [X0] :
( estin = powerset(X0)
| subset(f1(powerset(X0),estin),X0) )
| ~ spl0_37
| ~ spl0_209 ),
inference(resolution,[],[f2734,f350]) ).
fof(f68986,plain,
( spl0_1589
| ~ spl0_34
| ~ spl0_209 ),
inference(avatar_split_clause,[],[f2756,f2733,f336,f68984]) ).
fof(f68984,plain,
( spl0_1589
<=> ! [X0] :
( estin = complement(X0)
| ~ member(f1(complement(X0),estin),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1589])]) ).
fof(f2756,plain,
( ! [X0] :
( estin = complement(X0)
| ~ member(f1(complement(X0),estin),X0) )
| ~ spl0_34
| ~ spl0_209 ),
inference(resolution,[],[f2734,f337]) ).
fof(f68659,plain,
( spl0_177
| ~ spl0_171
| ~ spl0_175
| spl0_1573 ),
inference(avatar_split_clause,[],[f67943,f59714,f2469,f2432,f2481]) ).
fof(f67943,plain,
( estin = identity_relation
| ~ spl0_171
| ~ spl0_175
| spl0_1573 ),
inference(forward_demodulation,[],[f2471,f60294]) ).
fof(f67942,plain,
( ~ spl0_172
| spl0_174
| ~ spl0_177 ),
inference(avatar_split_clause,[],[f67932,f2481,f2465,f2436]) ).
fof(f2436,plain,
( spl0_172
<=> ordered_pair_predicate(f24(estin)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_172])]) ).
fof(f2465,plain,
( spl0_174
<=> ordered_pair_predicate(f24(identity_relation)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_174])]) ).
fof(f67932,plain,
( ~ ordered_pair_predicate(f24(estin))
| spl0_174
| ~ spl0_177 ),
inference(forward_demodulation,[],[f2466,f2483]) ).
fof(f2466,plain,
( ~ ordered_pair_predicate(f24(identity_relation))
| spl0_174 ),
inference(avatar_component_clause,[],[f2465]) ).
fof(f60328,plain,
( spl0_1588
| ~ spl0_40
| ~ spl0_173
| ~ spl0_196 ),
inference(avatar_split_clause,[],[f2674,f2581,f2440,f361,f60326]) ).
fof(f60326,plain,
( spl0_1588
<=> ! [X0] :
( estin = domain_of(X0)
| little_set(f8(f24(domain_of(X0)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1588])]) ).
fof(f2674,plain,
( ! [X0] :
( estin = domain_of(X0)
| little_set(f8(f24(domain_of(X0)),X0)) )
| ~ spl0_40
| ~ spl0_173
| ~ spl0_196 ),
inference(forward_demodulation,[],[f2668,f2442]) ).
fof(f2442,plain,
( estin = empty_set
| ~ spl0_173 ),
inference(avatar_component_clause,[],[f2440]) ).
fof(f60324,plain,
( spl0_1587
| ~ spl0_80
| ~ spl0_186 ),
inference(avatar_split_clause,[],[f2540,f2526,f652,f60322]) ).
fof(f60322,plain,
( spl0_1587
<=> ! [X2,X0,X1] :
( ~ closed(X0,X1)
| ~ member(X2,range_of(X1))
| member(X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1587])]) ).
fof(f2540,plain,
( ! [X2,X0,X1] :
( ~ closed(X0,X1)
| ~ member(X2,range_of(X1))
| member(X2,X0) )
| ~ spl0_80
| ~ spl0_186 ),
inference(resolution,[],[f2527,f653]) ).
fof(f60316,plain,
( spl0_1586
| ~ spl0_113
| ~ spl0_154 ),
inference(avatar_split_clause,[],[f2168,f2102,f1159,f60314]) ).
fof(f60314,plain,
( spl0_1586
<=> ! [X0] :
( member(f1(rotate_right(empty_set),X0),X0)
| rotate_right(empty_set) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1586])]) ).
fof(f1159,plain,
( spl0_113
<=> ! [X0,X1] :
( X0 = X1
| member(f1(X0,X1),X1)
| member(f1(X0,X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_113])]) ).
fof(f2168,plain,
( ! [X0] :
( member(f1(rotate_right(empty_set),X0),X0)
| rotate_right(empty_set) = X0 )
| ~ spl0_113
| ~ spl0_154 ),
inference(resolution,[],[f2103,f1160]) ).
fof(f1160,plain,
( ! [X0,X1] :
( member(f1(X0,X1),X1)
| member(f1(X0,X1),X0)
| X0 = X1 )
| ~ spl0_113 ),
inference(avatar_component_clause,[],[f1159]) ).
fof(f60308,plain,
( spl0_1585
| ~ spl0_113
| ~ spl0_154 ),
inference(avatar_split_clause,[],[f2167,f2102,f1159,f60306]) ).
fof(f60306,plain,
( spl0_1585
<=> ! [X0] :
( member(f1(X0,rotate_right(empty_set)),X0)
| rotate_right(empty_set) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1585])]) ).
fof(f2167,plain,
( ! [X0] :
( member(f1(X0,rotate_right(empty_set)),X0)
| rotate_right(empty_set) = X0 )
| ~ spl0_113
| ~ spl0_154 ),
inference(resolution,[],[f2103,f1160]) ).
fof(f60300,plain,
( spl0_1584
| ~ spl0_113
| ~ spl0_153 ),
inference(avatar_split_clause,[],[f2137,f2098,f1159,f60298]) ).
fof(f60298,plain,
( spl0_1584
<=> ! [X0] :
( member(f1(flip_range_of(empty_set),X0),X0)
| flip_range_of(empty_set) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1584])]) ).
fof(f2137,plain,
( ! [X0] :
( member(f1(flip_range_of(empty_set),X0),X0)
| flip_range_of(empty_set) = X0 )
| ~ spl0_113
| ~ spl0_153 ),
inference(resolution,[],[f2099,f1160]) ).
fof(f60289,plain,
( spl0_1583
| ~ spl0_113
| ~ spl0_153 ),
inference(avatar_split_clause,[],[f2136,f2098,f1159,f60287]) ).
fof(f60287,plain,
( spl0_1583
<=> ! [X0] :
( member(f1(X0,flip_range_of(empty_set)),X0)
| flip_range_of(empty_set) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1583])]) ).
fof(f2136,plain,
( ! [X0] :
( member(f1(X0,flip_range_of(empty_set)),X0)
| flip_range_of(empty_set) = X0 )
| ~ spl0_113
| ~ spl0_153 ),
inference(resolution,[],[f2099,f1160]) ).
fof(f60281,plain,
( spl0_1582
| ~ spl0_113
| ~ spl0_151 ),
inference(avatar_split_clause,[],[f2106,f2025,f1159,f60279]) ).
fof(f60279,plain,
( spl0_1582
<=> ! [X0] :
( member(f1(converse(empty_set),X0),X0)
| converse(empty_set) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1582])]) ).
fof(f2106,plain,
( ! [X0] :
( member(f1(converse(empty_set),X0),X0)
| converse(empty_set) = X0 )
| ~ spl0_113
| ~ spl0_151 ),
inference(resolution,[],[f2026,f1160]) ).
fof(f60273,plain,
( spl0_1581
| ~ spl0_113
| ~ spl0_151 ),
inference(avatar_split_clause,[],[f2105,f2025,f1159,f60271]) ).
fof(f60271,plain,
( spl0_1581
<=> ! [X0] :
( member(f1(X0,converse(empty_set)),X0)
| converse(empty_set) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1581])]) ).
fof(f2105,plain,
( ! [X0] :
( member(f1(X0,converse(empty_set)),X0)
| converse(empty_set) = X0 )
| ~ spl0_113
| ~ spl0_151 ),
inference(resolution,[],[f2026,f1160]) ).
fof(f60265,plain,
( spl0_1580
| ~ spl0_113
| ~ spl0_141 ),
inference(avatar_split_clause,[],[f2066,f1749,f1159,f60263]) ).
fof(f60263,plain,
( spl0_1580
<=> ! [X0] :
( member(f1(range_of(empty_set),X0),X0)
| range_of(empty_set) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1580])]) ).
fof(f2066,plain,
( ! [X0] :
( member(f1(range_of(empty_set),X0),X0)
| range_of(empty_set) = X0 )
| ~ spl0_113
| ~ spl0_141 ),
inference(resolution,[],[f1750,f1160]) ).
fof(f60257,plain,
( spl0_1579
| ~ spl0_113
| ~ spl0_141 ),
inference(avatar_split_clause,[],[f2065,f1749,f1159,f60255]) ).
fof(f60255,plain,
( spl0_1579
<=> ! [X0] :
( member(f1(X0,range_of(empty_set)),X0)
| range_of(empty_set) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1579])]) ).
fof(f2065,plain,
( ! [X0] :
( member(f1(X0,range_of(empty_set)),X0)
| range_of(empty_set) = X0 )
| ~ spl0_113
| ~ spl0_141 ),
inference(resolution,[],[f1750,f1160]) ).
fof(f60249,plain,
( spl0_1578
| ~ spl0_113
| ~ spl0_135 ),
inference(avatar_split_clause,[],[f2035,f1548,f1159,f60247]) ).
fof(f60247,plain,
( spl0_1578
<=> ! [X0] :
( member(f1(sigma(empty_set),X0),X0)
| sigma(empty_set) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1578])]) ).
fof(f2035,plain,
( ! [X0] :
( member(f1(sigma(empty_set),X0),X0)
| sigma(empty_set) = X0 )
| ~ spl0_113
| ~ spl0_135 ),
inference(resolution,[],[f1549,f1160]) ).
fof(f60241,plain,
( spl0_1577
| ~ spl0_113
| ~ spl0_135 ),
inference(avatar_split_clause,[],[f2034,f1548,f1159,f60239]) ).
fof(f60239,plain,
( spl0_1577
<=> ! [X0] :
( member(f1(X0,sigma(empty_set)),X0)
| sigma(empty_set) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1577])]) ).
fof(f2034,plain,
( ! [X0] :
( member(f1(X0,sigma(empty_set)),X0)
| sigma(empty_set) = X0 )
| ~ spl0_113
| ~ spl0_135 ),
inference(resolution,[],[f1549,f1160]) ).
fof(f60233,plain,
( spl0_1576
| ~ spl0_113
| ~ spl0_119 ),
inference(avatar_split_clause,[],[f1922,f1266,f1159,f60231]) ).
fof(f60231,plain,
( spl0_1576
<=> ! [X0] :
( member(f1(domain_of(empty_set),X0),X0)
| domain_of(empty_set) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1576])]) ).
fof(f1922,plain,
( ! [X0] :
( member(f1(domain_of(empty_set),X0),X0)
| domain_of(empty_set) = X0 )
| ~ spl0_113
| ~ spl0_119 ),
inference(resolution,[],[f1267,f1160]) ).
fof(f60225,plain,
( spl0_1575
| ~ spl0_113
| ~ spl0_119 ),
inference(avatar_split_clause,[],[f1921,f1266,f1159,f60223]) ).
fof(f60223,plain,
( spl0_1575
<=> ! [X0] :
( member(f1(X0,domain_of(empty_set)),X0)
| domain_of(empty_set) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1575])]) ).
fof(f1921,plain,
( ! [X0] :
( member(f1(X0,domain_of(empty_set)),X0)
| domain_of(empty_set) = X0 )
| ~ spl0_113
| ~ spl0_119 ),
inference(resolution,[],[f1267,f1160]) ).
fof(f60210,plain,
( ~ spl0_1574
| spl0_1541
| ~ spl0_1547 ),
inference(avatar_split_clause,[],[f58615,f58582,f58541,f60207]) ).
fof(f58541,plain,
( spl0_1541
<=> little_set(f18(complement(universal_set))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1541])]) ).
fof(f58582,plain,
( spl0_1547
<=> estin = complement(universal_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1547])]) ).
fof(f58615,plain,
( ~ little_set(f18(estin))
| spl0_1541
| ~ spl0_1547 ),
inference(superposition,[],[f58543,f58584]) ).
fof(f58584,plain,
( estin = complement(universal_set)
| ~ spl0_1547 ),
inference(avatar_component_clause,[],[f58582]) ).
fof(f58543,plain,
( ~ little_set(f18(complement(universal_set)))
| spl0_1541 ),
inference(avatar_component_clause,[],[f58541]) ).
fof(f59717,plain,
( ~ spl0_1573
| spl0_1546
| ~ spl0_1547 ),
inference(avatar_split_clause,[],[f58613,f58582,f58578,f59714]) ).
fof(f58578,plain,
( spl0_1546
<=> little_set(f24(complement(universal_set))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1546])]) ).
fof(f58613,plain,
( ~ little_set(f24(estin))
| spl0_1546
| ~ spl0_1547 ),
inference(superposition,[],[f58580,f58584]) ).
fof(f58580,plain,
( ~ little_set(f24(complement(universal_set)))
| spl0_1546 ),
inference(avatar_component_clause,[],[f58578]) ).
fof(f59706,plain,
( spl0_1572
| ~ spl0_809
| ~ spl0_854 ),
inference(avatar_split_clause,[],[f20884,f18762,f16813,f59704]) ).
fof(f59704,plain,
( spl0_1572
<=> ! [X0] :
( single_valued_set(complement(sigma(X0)))
| ~ member(complement(sigma(X0)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1572])]) ).
fof(f16813,plain,
( spl0_809
<=> ! [X0,X1] :
( single_valued_set(X0)
| ~ member(X0,X1)
| member(non_ordered_pair(non_ordered_pair(f19(X0),f19(X0)),non_ordered_pair(f19(X0),f20(X0))),sigma(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_809])]) ).
fof(f18762,plain,
( spl0_854
<=> ! [X0] :
( single_valued_set(complement(X0))
| ~ member(non_ordered_pair(non_ordered_pair(f19(complement(X0)),f19(complement(X0))),non_ordered_pair(f19(complement(X0)),f20(complement(X0)))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_854])]) ).
fof(f20884,plain,
( ! [X0] :
( single_valued_set(complement(sigma(X0)))
| ~ member(complement(sigma(X0)),X0) )
| ~ spl0_809
| ~ spl0_854 ),
inference(duplicate_literal_removal,[],[f20874]) ).
fof(f20874,plain,
( ! [X0] :
( single_valued_set(complement(sigma(X0)))
| ~ member(complement(sigma(X0)),X0)
| single_valued_set(complement(sigma(X0))) )
| ~ spl0_809
| ~ spl0_854 ),
inference(resolution,[],[f18763,f16814]) ).
fof(f16814,plain,
( ! [X0,X1] :
( member(non_ordered_pair(non_ordered_pair(f19(X0),f19(X0)),non_ordered_pair(f19(X0),f20(X0))),sigma(X1))
| ~ member(X0,X1)
| single_valued_set(X0) )
| ~ spl0_809 ),
inference(avatar_component_clause,[],[f16813]) ).
fof(f18763,plain,
( ! [X0] :
( ~ member(non_ordered_pair(non_ordered_pair(f19(complement(X0)),f19(complement(X0))),non_ordered_pair(f19(complement(X0)),f20(complement(X0)))),X0)
| single_valued_set(complement(X0)) )
| ~ spl0_854 ),
inference(avatar_component_clause,[],[f18762]) ).
fof(f59702,plain,
( spl0_1571
| ~ spl0_127
| ~ spl0_787 ),
inference(avatar_split_clause,[],[f16570,f16059,f1397,f59700]) ).
fof(f59700,plain,
( spl0_1571
<=> ! [X0,X1] :
( ~ member(X0,converse(complement(X1)))
| ~ member(X0,converse(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1571])]) ).
fof(f1397,plain,
( spl0_127
<=> ! [X0,X3] :
( ~ member(X3,converse(X0))
| member(non_ordered_pair(non_ordered_pair(second(X3),second(X3)),non_ordered_pair(second(X3),first(X3))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_127])]) ).
fof(f16059,plain,
( spl0_787
<=> ! [X0,X1] :
( ~ member(X0,converse(complement(X1)))
| ~ member(non_ordered_pair(non_ordered_pair(second(X0),second(X0)),non_ordered_pair(second(X0),first(X0))),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_787])]) ).
fof(f16570,plain,
( ! [X0,X1] :
( ~ member(X0,converse(complement(X1)))
| ~ member(X0,converse(X1)) )
| ~ spl0_127
| ~ spl0_787 ),
inference(resolution,[],[f16060,f1398]) ).
fof(f1398,plain,
( ! [X3,X0] :
( member(non_ordered_pair(non_ordered_pair(second(X3),second(X3)),non_ordered_pair(second(X3),first(X3))),X0)
| ~ member(X3,converse(X0)) )
| ~ spl0_127 ),
inference(avatar_component_clause,[],[f1397]) ).
fof(f16060,plain,
( ! [X0,X1] :
( ~ member(non_ordered_pair(non_ordered_pair(second(X0),second(X0)),non_ordered_pair(second(X0),first(X0))),X1)
| ~ member(X0,converse(complement(X1))) )
| ~ spl0_787 ),
inference(avatar_component_clause,[],[f16059]) ).
fof(f59698,plain,
( spl0_1570
| ~ spl0_11
| ~ spl0_358 ),
inference(avatar_split_clause,[],[f4219,f4034,f232,f59696]) ).
fof(f59696,plain,
( spl0_1570
<=> ! [X0,X1] :
( ~ member(X0,X1)
| estin = X0
| little_set(f24(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1570])]) ).
fof(f4219,plain,
( ! [X0,X1] :
( ~ member(X0,X1)
| estin = X0
| little_set(f24(X0)) )
| ~ spl0_11
| ~ spl0_358 ),
inference(resolution,[],[f4035,f233]) ).
fof(f59694,plain,
( spl0_1569
| ~ spl0_189
| ~ spl0_275 ),
inference(avatar_split_clause,[],[f3560,f3206,f2550,f59692]) ).
fof(f59692,plain,
( spl0_1569
<=> ! [X0] :
( ~ member(complement(sigma(X0)),X0)
| relation(complement(sigma(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1569])]) ).
fof(f2550,plain,
( spl0_189
<=> ! [X0] :
( ~ member(f18(complement(X0)),X0)
| relation(complement(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_189])]) ).
fof(f3560,plain,
( ! [X0] :
( ~ member(complement(sigma(X0)),X0)
| relation(complement(sigma(X0))) )
| ~ spl0_189
| ~ spl0_275 ),
inference(duplicate_literal_removal,[],[f3552]) ).
fof(f3552,plain,
( ! [X0] :
( ~ member(complement(sigma(X0)),X0)
| relation(complement(sigma(X0)))
| relation(complement(sigma(X0))) )
| ~ spl0_189
| ~ spl0_275 ),
inference(resolution,[],[f3207,f2551]) ).
fof(f2551,plain,
( ! [X0] :
( ~ member(f18(complement(X0)),X0)
| relation(complement(X0)) )
| ~ spl0_189 ),
inference(avatar_component_clause,[],[f2550]) ).
fof(f59690,plain,
( spl0_1568
| ~ spl0_188
| ~ spl0_269 ),
inference(avatar_split_clause,[],[f3526,f3178,f2542,f59688]) ).
fof(f59688,plain,
( spl0_1568
<=> ! [X0] :
( ordered_pair_predicate(f16(estin,converse(X0)))
| ~ member(infinity,converse(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1568])]) ).
fof(f3526,plain,
( ! [X0] :
( ordered_pair_predicate(f16(estin,converse(X0)))
| ~ member(infinity,converse(X0)) )
| ~ spl0_188
| ~ spl0_269 ),
inference(resolution,[],[f3179,f2543]) ).
fof(f59686,plain,
( spl0_1567
| ~ spl0_188
| ~ spl0_268 ),
inference(avatar_split_clause,[],[f3495,f3174,f2542,f59684]) ).
fof(f59684,plain,
( spl0_1567
<=> ! [X0] :
( ordered_pair_predicate(f16(estin,X0))
| ~ relation(X0)
| ~ member(infinity,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1567])]) ).
fof(f3495,plain,
( ! [X0] :
( ordered_pair_predicate(f16(estin,X0))
| ~ relation(X0)
| ~ member(infinity,X0) )
| ~ spl0_188
| ~ spl0_268 ),
inference(resolution,[],[f3175,f2543]) ).
fof(f59681,plain,
( spl0_1566
| ~ spl0_16
| ~ spl0_259 ),
inference(avatar_split_clause,[],[f3467,f3132,f253,f59679]) ).
fof(f59679,plain,
( spl0_1566
<=> ! [X0] :
( disjoint(X0,complement(universal_set))
| ~ little_set(f23(X0,complement(universal_set))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1566])]) ).
fof(f3467,plain,
( ! [X0] :
( disjoint(X0,complement(universal_set))
| ~ little_set(f23(X0,complement(universal_set))) )
| ~ spl0_16
| ~ spl0_259 ),
inference(resolution,[],[f3133,f254]) ).
fof(f59675,plain,
( spl0_1565
| ~ spl0_16
| ~ spl0_257 ),
inference(avatar_split_clause,[],[f3454,f3124,f253,f59673]) ).
fof(f59673,plain,
( spl0_1565
<=> ! [X0] :
( disjoint(complement(universal_set),X0)
| ~ little_set(f23(complement(universal_set),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1565])]) ).
fof(f3454,plain,
( ! [X0] :
( disjoint(complement(universal_set),X0)
| ~ little_set(f23(complement(universal_set),X0)) )
| ~ spl0_16
| ~ spl0_257 ),
inference(resolution,[],[f3125,f254]) ).
fof(f59670,plain,
( spl0_1564
| ~ spl0_16
| ~ spl0_255 ),
inference(avatar_split_clause,[],[f3442,f3116,f253,f59668]) ).
fof(f59668,plain,
( spl0_1564
<=> ! [X0] :
( subset(complement(universal_set),X0)
| ~ little_set(f17(complement(universal_set),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1564])]) ).
fof(f3442,plain,
( ! [X0] :
( subset(complement(universal_set),X0)
| ~ little_set(f17(complement(universal_set),X0)) )
| ~ spl0_16
| ~ spl0_255 ),
inference(resolution,[],[f3117,f254]) ).
fof(f59666,plain,
( spl0_1563
| ~ spl0_197
| ~ spl0_234 ),
inference(avatar_split_clause,[],[f3012,f2977,f2585,f59664]) ).
fof(f59664,plain,
( spl0_1563
<=> ! [X0,X1] :
( ~ member(universal_set,X0)
| ~ little_set(X1)
| little_set(f16(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1563])]) ).
fof(f3012,plain,
( ! [X0,X1] :
( ~ member(universal_set,X0)
| ~ little_set(X1)
| little_set(f16(X1,X0)) )
| ~ spl0_197
| ~ spl0_234 ),
inference(resolution,[],[f2978,f2586]) ).
fof(f59662,plain,
( spl0_1562
| ~ spl0_28
| ~ spl0_210 ),
inference(avatar_split_clause,[],[f2832,f2737,f306,f59660]) ).
fof(f59660,plain,
( spl0_1562
<=> ! [X0] :
( estin = converse(X0)
| ordered_pair_predicate(f1(estin,converse(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1562])]) ).
fof(f2832,plain,
( ! [X0] :
( estin = converse(X0)
| ordered_pair_predicate(f1(estin,converse(X0))) )
| ~ spl0_28
| ~ spl0_210 ),
inference(resolution,[],[f2738,f307]) ).
fof(f59658,plain,
( spl0_1561
| ~ spl0_38
| ~ spl0_210 ),
inference(avatar_split_clause,[],[f2813,f2737,f353,f59656]) ).
fof(f59656,plain,
( spl0_1561
<=> ! [X0] :
( estin = X0
| ordered_pair_predicate(f1(estin,X0))
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1561])]) ).
fof(f2813,plain,
( ! [X0] :
( estin = X0
| ordered_pair_predicate(f1(estin,X0))
| ~ relation(X0) )
| ~ spl0_38
| ~ spl0_210 ),
inference(resolution,[],[f2738,f354]) ).
fof(f59654,plain,
( spl0_1560
| ~ spl0_28
| ~ spl0_209 ),
inference(avatar_split_clause,[],[f2764,f2733,f306,f59652]) ).
fof(f59652,plain,
( spl0_1560
<=> ! [X0] :
( estin = converse(X0)
| ordered_pair_predicate(f1(converse(X0),estin)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1560])]) ).
fof(f2764,plain,
( ! [X0] :
( estin = converse(X0)
| ordered_pair_predicate(f1(converse(X0),estin)) )
| ~ spl0_28
| ~ spl0_209 ),
inference(resolution,[],[f2734,f307]) ).
fof(f59650,plain,
( spl0_1559
| ~ spl0_38
| ~ spl0_209 ),
inference(avatar_split_clause,[],[f2745,f2733,f353,f59648]) ).
fof(f59648,plain,
( spl0_1559
<=> ! [X0] :
( estin = X0
| ordered_pair_predicate(f1(X0,estin))
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1559])]) ).
fof(f2745,plain,
( ! [X0] :
( estin = X0
| ordered_pair_predicate(f1(X0,estin))
| ~ relation(X0) )
| ~ spl0_38
| ~ spl0_209 ),
inference(resolution,[],[f2734,f354]) ).
fof(f59646,plain,
( spl0_1558
| ~ spl0_30
| ~ spl0_203 ),
inference(avatar_split_clause,[],[f2720,f2617,f314,f59644]) ).
fof(f59644,plain,
( spl0_1558
<=> ! [X0] :
( little_set(f27(f18(range_of(X0)),X0))
| relation(range_of(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1558])]) ).
fof(f2720,plain,
( ! [X0] :
( little_set(f27(f18(range_of(X0)),X0))
| relation(range_of(X0)) )
| ~ spl0_30
| ~ spl0_203 ),
inference(resolution,[],[f2618,f315]) ).
fof(f59642,plain,
( spl0_1557
| ~ spl0_30
| ~ spl0_197 ),
inference(avatar_split_clause,[],[f2690,f2585,f314,f59640]) ).
fof(f59640,plain,
( spl0_1557
<=> ! [X0] :
( little_set(f16(f18(sigma(X0)),X0))
| relation(sigma(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1557])]) ).
fof(f2690,plain,
( ! [X0] :
( little_set(f16(f18(sigma(X0)),X0))
| relation(sigma(X0)) )
| ~ spl0_30
| ~ spl0_197 ),
inference(resolution,[],[f2586,f315]) ).
fof(f59638,plain,
( spl0_1556
| ~ spl0_30
| ~ spl0_196 ),
inference(avatar_split_clause,[],[f2664,f2581,f314,f59636]) ).
fof(f59636,plain,
( spl0_1556
<=> ! [X0] :
( little_set(f8(f18(domain_of(X0)),X0))
| relation(domain_of(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1556])]) ).
fof(f2664,plain,
( ! [X0] :
( little_set(f8(f18(domain_of(X0)),X0))
| relation(domain_of(X0)) )
| ~ spl0_30
| ~ spl0_196 ),
inference(resolution,[],[f2582,f315]) ).
fof(f59634,plain,
( spl0_1555
| ~ spl0_7
| ~ spl0_1554 ),
inference(avatar_split_clause,[],[f59497,f59389,f214,f59631]) ).
fof(f59631,plain,
( spl0_1555
<=> little_set(f18(compose(a,b))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1555])]) ).
fof(f59497,plain,
( little_set(f18(compose(a,b)))
| ~ spl0_7
| ~ spl0_1554 ),
inference(superposition,[],[f215,f59391]) ).
fof(f59392,plain,
( spl0_1554
| spl0_1
| ~ spl0_1210 ),
inference(avatar_split_clause,[],[f36457,f36417,f186,f59389]) ).
fof(f36417,plain,
( spl0_1210
<=> ! [X0,X1] :
( f18(compose(X0,X1)) = non_ordered_pair(non_ordered_pair(f29(f18(compose(X0,X1)),X0,X1),f29(f18(compose(X0,X1)),X0,X1)),non_ordered_pair(f29(f18(compose(X0,X1)),X0,X1),f30(f18(compose(X0,X1)),X0,X1)))
| relation(compose(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1210])]) ).
fof(f36457,plain,
( f18(compose(a,b)) = non_ordered_pair(non_ordered_pair(f29(f18(compose(a,b)),a,b),f29(f18(compose(a,b)),a,b)),non_ordered_pair(f29(f18(compose(a,b)),a,b),f30(f18(compose(a,b)),a,b)))
| spl0_1
| ~ spl0_1210 ),
inference(resolution,[],[f36418,f188]) ).
fof(f188,plain,
( ~ relation(compose(a,b))
| spl0_1 ),
inference(avatar_component_clause,[],[f186]) ).
fof(f36418,plain,
( ! [X0,X1] :
( relation(compose(X0,X1))
| f18(compose(X0,X1)) = non_ordered_pair(non_ordered_pair(f29(f18(compose(X0,X1)),X0,X1),f29(f18(compose(X0,X1)),X0,X1)),non_ordered_pair(f29(f18(compose(X0,X1)),X0,X1),f30(f18(compose(X0,X1)),X0,X1))) )
| ~ spl0_1210 ),
inference(avatar_component_clause,[],[f36417]) ).
fof(f58672,plain,
( spl0_1553
| ~ spl0_7
| ~ spl0_1305 ),
inference(avatar_split_clause,[],[f40328,f39381,f214,f58670]) ).
fof(f58670,plain,
( spl0_1553
<=> ! [X0] :
( little_set(f24(rotate_right(X0)))
| estin = rotate_right(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1553])]) ).
fof(f39381,plain,
( spl0_1305
<=> ! [X0] :
( estin = rotate_right(X0)
| f24(rotate_right(X0)) = non_ordered_pair(non_ordered_pair(f9(f24(rotate_right(X0)),X0),f9(f24(rotate_right(X0)),X0)),non_ordered_pair(f9(f24(rotate_right(X0)),X0),non_ordered_pair(non_ordered_pair(f10(f24(rotate_right(X0)),X0),f10(f24(rotate_right(X0)),X0)),non_ordered_pair(f10(f24(rotate_right(X0)),X0),f11(f24(rotate_right(X0)),X0))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1305])]) ).
fof(f40328,plain,
( ! [X0] :
( little_set(f24(rotate_right(X0)))
| estin = rotate_right(X0) )
| ~ spl0_7
| ~ spl0_1305 ),
inference(superposition,[],[f215,f39382]) ).
fof(f39382,plain,
( ! [X0] :
( f24(rotate_right(X0)) = non_ordered_pair(non_ordered_pair(f9(f24(rotate_right(X0)),X0),f9(f24(rotate_right(X0)),X0)),non_ordered_pair(f9(f24(rotate_right(X0)),X0),non_ordered_pair(non_ordered_pair(f10(f24(rotate_right(X0)),X0),f10(f24(rotate_right(X0)),X0)),non_ordered_pair(f10(f24(rotate_right(X0)),X0),f11(f24(rotate_right(X0)),X0)))))
| estin = rotate_right(X0) )
| ~ spl0_1305 ),
inference(avatar_component_clause,[],[f39381]) ).
fof(f58612,plain,
( spl0_1547
| ~ spl0_171
| ~ spl0_173
| spl0_1546 ),
inference(avatar_split_clause,[],[f58589,f58578,f2440,f2432,f58582]) ).
fof(f58589,plain,
( estin = complement(universal_set)
| ~ spl0_171
| ~ spl0_173
| spl0_1546 ),
inference(forward_demodulation,[],[f58586,f2442]) ).
fof(f58586,plain,
( empty_set = complement(universal_set)
| ~ spl0_171
| spl0_1546 ),
inference(resolution,[],[f58580,f2433]) ).
fof(f58611,plain,
( spl0_1552
| ~ spl0_7
| ~ spl0_1304 ),
inference(avatar_split_clause,[],[f40218,f39377,f214,f58609]) ).
fof(f58609,plain,
( spl0_1552
<=> ! [X0] :
( little_set(f24(flip_range_of(X0)))
| estin = flip_range_of(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1552])]) ).
fof(f39377,plain,
( spl0_1304
<=> ! [X0] :
( estin = flip_range_of(X0)
| f24(flip_range_of(X0)) = non_ordered_pair(non_ordered_pair(f12(f24(flip_range_of(X0)),X0),f12(f24(flip_range_of(X0)),X0)),non_ordered_pair(f12(f24(flip_range_of(X0)),X0),non_ordered_pair(non_ordered_pair(f13(f24(flip_range_of(X0)),X0),f13(f24(flip_range_of(X0)),X0)),non_ordered_pair(f13(f24(flip_range_of(X0)),X0),f14(f24(flip_range_of(X0)),X0))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1304])]) ).
fof(f40218,plain,
( ! [X0] :
( little_set(f24(flip_range_of(X0)))
| estin = flip_range_of(X0) )
| ~ spl0_7
| ~ spl0_1304 ),
inference(superposition,[],[f215,f39378]) ).
fof(f39378,plain,
( ! [X0] :
( f24(flip_range_of(X0)) = non_ordered_pair(non_ordered_pair(f12(f24(flip_range_of(X0)),X0),f12(f24(flip_range_of(X0)),X0)),non_ordered_pair(f12(f24(flip_range_of(X0)),X0),non_ordered_pair(non_ordered_pair(f13(f24(flip_range_of(X0)),X0),f13(f24(flip_range_of(X0)),X0)),non_ordered_pair(f13(f24(flip_range_of(X0)),X0),f14(f24(flip_range_of(X0)),X0)))))
| estin = flip_range_of(X0) )
| ~ spl0_1304 ),
inference(avatar_component_clause,[],[f39377]) ).
fof(f58607,plain,
( spl0_1551
| ~ spl0_7
| ~ spl0_861 ),
inference(avatar_split_clause,[],[f21166,f18790,f214,f58605]) ).
fof(f58605,plain,
( spl0_1551
<=> ! [X0] :
( member(X0,converse(universal_set))
| ~ ordered_pair_predicate(X0)
| ~ little_set(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1551])]) ).
fof(f18790,plain,
( spl0_861
<=> ! [X0] :
( ~ little_set(X0)
| member(X0,converse(universal_set))
| ~ ordered_pair_predicate(X0)
| ~ little_set(non_ordered_pair(non_ordered_pair(second(X0),second(X0)),non_ordered_pair(second(X0),first(X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_861])]) ).
fof(f21166,plain,
( ! [X0] :
( member(X0,converse(universal_set))
| ~ ordered_pair_predicate(X0)
| ~ little_set(X0) )
| ~ spl0_7
| ~ spl0_861 ),
inference(resolution,[],[f18791,f215]) ).
fof(f18791,plain,
( ! [X0] :
( ~ little_set(non_ordered_pair(non_ordered_pair(second(X0),second(X0)),non_ordered_pair(second(X0),first(X0))))
| member(X0,converse(universal_set))
| ~ ordered_pair_predicate(X0)
| ~ little_set(X0) )
| ~ spl0_861 ),
inference(avatar_component_clause,[],[f18790]) ).
fof(f58603,plain,
( spl0_1550
| ~ spl0_577
| ~ spl0_665 ),
inference(avatar_split_clause,[],[f10152,f9847,f7448,f58601]) ).
fof(f7448,plain,
( spl0_577
<=> ! [X2,X0,X1] :
( ~ member(X0,image(complement(X1),X2))
| ~ member(first(f22(X0,complement(X1),X2)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_577])]) ).
fof(f9847,plain,
( spl0_665
<=> ! [X0,X3,X2,X1] :
( ~ member(X0,image(X1,cross_product(X2,X3)))
| member(first(f22(X0,X1,cross_product(X2,X3))),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_665])]) ).
fof(f10152,plain,
( ! [X2,X0,X1] : ~ member(X0,image(complement(X1),cross_product(X1,X2)))
| ~ spl0_577
| ~ spl0_665 ),
inference(duplicate_literal_removal,[],[f10089]) ).
fof(f10089,plain,
( ! [X2,X0,X1] :
( ~ member(X0,image(complement(X1),cross_product(X1,X2)))
| ~ member(X0,image(complement(X1),cross_product(X1,X2))) )
| ~ spl0_577
| ~ spl0_665 ),
inference(resolution,[],[f9848,f7449]) ).
fof(f7449,plain,
( ! [X2,X0,X1] :
( ~ member(first(f22(X0,complement(X1),X2)),X1)
| ~ member(X0,image(complement(X1),X2)) )
| ~ spl0_577 ),
inference(avatar_component_clause,[],[f7448]) ).
fof(f9848,plain,
( ! [X2,X3,X0,X1] :
( member(first(f22(X0,X1,cross_product(X2,X3))),X2)
| ~ member(X0,image(X1,cross_product(X2,X3))) )
| ~ spl0_665 ),
inference(avatar_component_clause,[],[f9847]) ).
fof(f58599,plain,
( spl0_1549
| ~ spl0_257
| ~ spl0_417 ),
inference(avatar_split_clause,[],[f5282,f4474,f3124,f58597]) ).
fof(f58597,plain,
( spl0_1549
<=> ! [X0,X1] :
( ~ member(X0,X1)
| disjoint(complement(sigma(X1)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1549])]) ).
fof(f5282,plain,
( ! [X0,X1] :
( ~ member(X0,X1)
| disjoint(complement(sigma(X1)),X0) )
| ~ spl0_257
| ~ spl0_417 ),
inference(duplicate_literal_removal,[],[f5271]) ).
fof(f5271,plain,
( ! [X0,X1] :
( ~ member(X0,X1)
| disjoint(complement(sigma(X1)),X0)
| disjoint(complement(sigma(X1)),X0) )
| ~ spl0_257
| ~ spl0_417 ),
inference(resolution,[],[f4475,f3125]) ).
fof(f58595,plain,
( spl0_1548
| ~ spl0_259
| ~ spl0_416 ),
inference(avatar_split_clause,[],[f5264,f4470,f3132,f58593]) ).
fof(f58593,plain,
( spl0_1548
<=> ! [X0,X1] :
( ~ member(X0,X1)
| disjoint(X0,complement(sigma(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1548])]) ).
fof(f5264,plain,
( ! [X0,X1] :
( ~ member(X0,X1)
| disjoint(X0,complement(sigma(X1))) )
| ~ spl0_259
| ~ spl0_416 ),
inference(duplicate_literal_removal,[],[f5255]) ).
fof(f5255,plain,
( ! [X0,X1] :
( ~ member(X0,X1)
| disjoint(X0,complement(sigma(X1)))
| disjoint(X0,complement(sigma(X1))) )
| ~ spl0_259
| ~ spl0_416 ),
inference(resolution,[],[f4471,f3133]) ).
fof(f58585,plain,
( ~ spl0_1546
| spl0_1547
| ~ spl0_16
| ~ spl0_235 ),
inference(avatar_split_clause,[],[f3029,f2984,f253,f58582,f58578]) ).
fof(f3029,plain,
( estin = complement(universal_set)
| ~ little_set(f24(complement(universal_set)))
| ~ spl0_16
| ~ spl0_235 ),
inference(resolution,[],[f2985,f254]) ).
fof(f58574,plain,
( spl0_1542
| ~ spl0_157
| spl0_1541 ),
inference(avatar_split_clause,[],[f58549,f58541,f2207,f58545]) ).
fof(f58545,plain,
( spl0_1542
<=> relation(complement(universal_set)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1542])]) ).
fof(f2207,plain,
( spl0_157
<=> ! [X0] :
( relation(X0)
| little_set(f18(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_157])]) ).
fof(f58549,plain,
( relation(complement(universal_set))
| ~ spl0_157
| spl0_1541 ),
inference(resolution,[],[f58543,f2208]) ).
fof(f2208,plain,
( ! [X0] :
( little_set(f18(X0))
| relation(X0) )
| ~ spl0_157 ),
inference(avatar_component_clause,[],[f2207]) ).
fof(f58573,plain,
( spl0_185
| spl0_1545
| ~ spl0_38
| ~ spl0_188 ),
inference(avatar_split_clause,[],[f2547,f2542,f353,f58571,f2521]) ).
fof(f2521,plain,
( spl0_185
<=> ordered_pair_predicate(estin) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_185])]) ).
fof(f58571,plain,
( spl0_1545
<=> ! [X0] :
( ~ member(infinity,X0)
| ~ relation(sigma(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1545])]) ).
fof(f2547,plain,
( ! [X0] :
( ~ member(infinity,X0)
| ordered_pair_predicate(estin)
| ~ relation(sigma(X0)) )
| ~ spl0_38
| ~ spl0_188 ),
inference(resolution,[],[f2543,f354]) ).
fof(f58559,plain,
( spl0_1544
| ~ spl0_61
| ~ spl0_415 ),
inference(avatar_split_clause,[],[f5253,f4466,f466,f58557]) ).
fof(f58557,plain,
( spl0_1544
<=> ! [X0,X1] :
( ~ member(X0,X1)
| subset(X0,sigma(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1544])]) ).
fof(f466,plain,
( spl0_61
<=> ! [X0,X1] :
( subset(X0,X1)
| ~ member(f17(X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_61])]) ).
fof(f5253,plain,
( ! [X0,X1] :
( ~ member(X0,X1)
| subset(X0,sigma(X1)) )
| ~ spl0_61
| ~ spl0_415 ),
inference(duplicate_literal_removal,[],[f5242]) ).
fof(f5242,plain,
( ! [X0,X1] :
( ~ member(X0,X1)
| subset(X0,sigma(X1))
| subset(X0,sigma(X1)) )
| ~ spl0_61
| ~ spl0_415 ),
inference(resolution,[],[f4467,f467]) ).
fof(f467,plain,
( ! [X0,X1] :
( ~ member(f17(X0,X1),X1)
| subset(X0,X1) )
| ~ spl0_61 ),
inference(avatar_component_clause,[],[f466]) ).
fof(f58555,plain,
( spl0_1543
| ~ spl0_188
| ~ spl0_197 ),
inference(avatar_split_clause,[],[f2686,f2585,f2542,f58553]) ).
fof(f58553,plain,
( spl0_1543
<=> ! [X0] :
( little_set(f16(estin,X0))
| ~ member(infinity,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1543])]) ).
fof(f2686,plain,
( ! [X0] :
( little_set(f16(estin,X0))
| ~ member(infinity,X0) )
| ~ spl0_188
| ~ spl0_197 ),
inference(resolution,[],[f2586,f2543]) ).
fof(f58548,plain,
( ~ spl0_1541
| spl0_1542
| ~ spl0_16
| ~ spl0_189 ),
inference(avatar_split_clause,[],[f2637,f2550,f253,f58545,f58541]) ).
fof(f2637,plain,
( relation(complement(universal_set))
| ~ little_set(f18(complement(universal_set)))
| ~ spl0_16
| ~ spl0_189 ),
inference(resolution,[],[f2551,f254]) ).
fof(f58536,plain,
( spl0_1540
| ~ spl0_103
| ~ spl0_168 ),
inference(avatar_split_clause,[],[f2406,f2260,f960,f58534]) ).
fof(f58534,plain,
( spl0_1540
<=> ! [X2,X0,X1] : ~ member(X0,image(X1,compose(empty_set,X2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1540])]) ).
fof(f960,plain,
( spl0_103
<=> ! [X0,X7,X3] :
( ~ member(X3,image(X0,X7))
| member(f22(X3,X0,X7),X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_103])]) ).
fof(f2406,plain,
( ! [X2,X0,X1] : ~ member(X0,image(X1,compose(empty_set,X2)))
| ~ spl0_103
| ~ spl0_168 ),
inference(resolution,[],[f2261,f961]) ).
fof(f961,plain,
( ! [X3,X0,X7] :
( member(f22(X3,X0,X7),X7)
| ~ member(X3,image(X0,X7)) )
| ~ spl0_103 ),
inference(avatar_component_clause,[],[f960]) ).
fof(f58529,plain,
( spl0_1539
| ~ spl0_107
| ~ spl0_168 ),
inference(avatar_split_clause,[],[f2401,f2260,f1068,f58527]) ).
fof(f58527,plain,
( spl0_1539
<=> ! [X2,X0,X1] : ~ member(X0,image(compose(empty_set,X1),X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1539])]) ).
fof(f1068,plain,
( spl0_107
<=> ! [X0,X7,X3] :
( ~ member(X3,image(X0,X7))
| member(first(f22(X3,X0,X7)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_107])]) ).
fof(f2401,plain,
( ! [X2,X0,X1] : ~ member(X0,image(compose(empty_set,X1),X2))
| ~ spl0_107
| ~ spl0_168 ),
inference(resolution,[],[f2261,f1069]) ).
fof(f1069,plain,
( ! [X3,X0,X7] :
( member(first(f22(X3,X0,X7)),X0)
| ~ member(X3,image(X0,X7)) )
| ~ spl0_107 ),
inference(avatar_component_clause,[],[f1068]) ).
fof(f58525,plain,
( spl0_1538
| spl0_1516
| ~ spl0_1517 ),
inference(avatar_split_clause,[],[f58371,f58343,f58336,f58522]) ).
fof(f58522,plain,
( spl0_1538
<=> estin = second(f20(estin)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1538])]) ).
fof(f58371,plain,
( estin = second(f20(estin))
| spl0_1516
| ~ spl0_1517 ),
inference(resolution,[],[f58344,f58338]) ).
fof(f58517,plain,
( spl0_1537
| ~ spl0_138
| ~ spl0_168 ),
inference(avatar_split_clause,[],[f2400,f2260,f1638,f58515]) ).
fof(f58515,plain,
( spl0_1537
<=> ! [X2,X0,X1] : ~ member(X0,compose(X1,compose(empty_set,X2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1537])]) ).
fof(f1638,plain,
( spl0_138
<=> ! [X9,X7,X3] :
( ~ member(X3,compose(X7,X9))
| member(non_ordered_pair(non_ordered_pair(f31(X3,X7,X9),f31(X3,X7,X9)),non_ordered_pair(f31(X3,X7,X9),f30(X3,X7,X9))),X9) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_138])]) ).
fof(f2400,plain,
( ! [X2,X0,X1] : ~ member(X0,compose(X1,compose(empty_set,X2)))
| ~ spl0_138
| ~ spl0_168 ),
inference(resolution,[],[f2261,f1639]) ).
fof(f1639,plain,
( ! [X3,X9,X7] :
( member(non_ordered_pair(non_ordered_pair(f31(X3,X7,X9),f31(X3,X7,X9)),non_ordered_pair(f31(X3,X7,X9),f30(X3,X7,X9))),X9)
| ~ member(X3,compose(X7,X9)) )
| ~ spl0_138 ),
inference(avatar_component_clause,[],[f1638]) ).
fof(f58510,plain,
( spl0_1536
| ~ spl0_139
| ~ spl0_168 ),
inference(avatar_split_clause,[],[f2397,f2260,f1642,f58508]) ).
fof(f58508,plain,
( spl0_1536
<=> ! [X2,X0,X1] : ~ member(X0,compose(compose(empty_set,X1),X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1536])]) ).
fof(f1642,plain,
( spl0_139
<=> ! [X9,X7,X3] :
( ~ member(X3,compose(X7,X9))
| member(non_ordered_pair(non_ordered_pair(f29(X3,X7,X9),f29(X3,X7,X9)),non_ordered_pair(f29(X3,X7,X9),f31(X3,X7,X9))),X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_139])]) ).
fof(f2397,plain,
( ! [X2,X0,X1] : ~ member(X0,compose(compose(empty_set,X1),X2))
| ~ spl0_139
| ~ spl0_168 ),
inference(resolution,[],[f2261,f1643]) ).
fof(f1643,plain,
( ! [X3,X9,X7] :
( member(non_ordered_pair(non_ordered_pair(f29(X3,X7,X9),f29(X3,X7,X9)),non_ordered_pair(f29(X3,X7,X9),f31(X3,X7,X9))),X7)
| ~ member(X3,compose(X7,X9)) )
| ~ spl0_139 ),
inference(avatar_component_clause,[],[f1642]) ).
fof(f58503,plain,
( spl0_1535
| ~ spl0_103
| ~ spl0_167 ),
inference(avatar_split_clause,[],[f2375,f2256,f960,f58501]) ).
fof(f58501,plain,
( spl0_1535
<=> ! [X2,X0,X1] : ~ member(X0,image(X1,compose(X2,empty_set))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1535])]) ).
fof(f2375,plain,
( ! [X2,X0,X1] : ~ member(X0,image(X1,compose(X2,empty_set)))
| ~ spl0_103
| ~ spl0_167 ),
inference(resolution,[],[f2257,f961]) ).
fof(f58496,plain,
( spl0_1534
| ~ spl0_107
| ~ spl0_167 ),
inference(avatar_split_clause,[],[f2370,f2256,f1068,f58494]) ).
fof(f58494,plain,
( spl0_1534
<=> ! [X2,X0,X1] : ~ member(X0,image(compose(X1,empty_set),X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1534])]) ).
fof(f2370,plain,
( ! [X2,X0,X1] : ~ member(X0,image(compose(X1,empty_set),X2))
| ~ spl0_107
| ~ spl0_167 ),
inference(resolution,[],[f2257,f1069]) ).
fof(f58489,plain,
( spl0_1533
| ~ spl0_138
| ~ spl0_167 ),
inference(avatar_split_clause,[],[f2369,f2256,f1638,f58487]) ).
fof(f58487,plain,
( spl0_1533
<=> ! [X2,X0,X1] : ~ member(X0,compose(X1,compose(X2,empty_set))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1533])]) ).
fof(f2369,plain,
( ! [X2,X0,X1] : ~ member(X0,compose(X1,compose(X2,empty_set)))
| ~ spl0_138
| ~ spl0_167 ),
inference(resolution,[],[f2257,f1639]) ).
fof(f58482,plain,
( spl0_1532
| ~ spl0_139
| ~ spl0_167 ),
inference(avatar_split_clause,[],[f2366,f2256,f1642,f58480]) ).
fof(f58480,plain,
( spl0_1532
<=> ! [X2,X0,X1] : ~ member(X0,compose(compose(X1,empty_set),X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1532])]) ).
fof(f2366,plain,
( ! [X2,X0,X1] : ~ member(X0,compose(compose(X1,empty_set),X2))
| ~ spl0_139
| ~ spl0_167 ),
inference(resolution,[],[f2257,f1643]) ).
fof(f58475,plain,
( spl0_1531
| ~ spl0_103
| ~ spl0_166 ),
inference(avatar_split_clause,[],[f2343,f2251,f960,f58473]) ).
fof(f58473,plain,
( spl0_1531
<=> ! [X2,X0,X1] : ~ member(X0,image(X1,image(empty_set,X2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1531])]) ).
fof(f2343,plain,
( ! [X2,X0,X1] : ~ member(X0,image(X1,image(empty_set,X2)))
| ~ spl0_103
| ~ spl0_166 ),
inference(resolution,[],[f2252,f961]) ).
fof(f58468,plain,
( spl0_1530
| ~ spl0_107
| ~ spl0_166 ),
inference(avatar_split_clause,[],[f2337,f2251,f1068,f58466]) ).
fof(f58466,plain,
( spl0_1530
<=> ! [X2,X0,X1] : ~ member(X0,image(image(empty_set,X1),X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1530])]) ).
fof(f2337,plain,
( ! [X2,X0,X1] : ~ member(X0,image(image(empty_set,X1),X2))
| ~ spl0_107
| ~ spl0_166 ),
inference(resolution,[],[f2252,f1069]) ).
fof(f58461,plain,
( spl0_1529
| ~ spl0_138
| ~ spl0_166 ),
inference(avatar_split_clause,[],[f2336,f2251,f1638,f58459]) ).
fof(f58459,plain,
( spl0_1529
<=> ! [X2,X0,X1] : ~ member(X0,compose(X1,image(empty_set,X2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1529])]) ).
fof(f2336,plain,
( ! [X2,X0,X1] : ~ member(X0,compose(X1,image(empty_set,X2)))
| ~ spl0_138
| ~ spl0_166 ),
inference(resolution,[],[f2252,f1639]) ).
fof(f58454,plain,
( spl0_1528
| ~ spl0_139
| ~ spl0_166 ),
inference(avatar_split_clause,[],[f2333,f2251,f1642,f58452]) ).
fof(f58452,plain,
( spl0_1528
<=> ! [X2,X0,X1] : ~ member(X0,compose(image(empty_set,X1),X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1528])]) ).
fof(f2333,plain,
( ! [X2,X0,X1] : ~ member(X0,compose(image(empty_set,X1),X2))
| ~ spl0_139
| ~ spl0_166 ),
inference(resolution,[],[f2252,f1643]) ).
fof(f58450,plain,
( spl0_1527
| spl0_1515
| ~ spl0_1517 ),
inference(avatar_split_clause,[],[f58370,f58343,f58332,f58447]) ).
fof(f58447,plain,
( spl0_1527
<=> estin = second(f19(estin)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1527])]) ).
fof(f58370,plain,
( estin = second(f19(estin))
| spl0_1515
| ~ spl0_1517 ),
inference(resolution,[],[f58344,f58334]) ).
fof(f58442,plain,
( spl0_1526
| ~ spl0_103
| ~ spl0_165 ),
inference(avatar_split_clause,[],[f2311,f2247,f960,f58440]) ).
fof(f58440,plain,
( spl0_1526
<=> ! [X2,X0,X1] : ~ member(X0,image(X1,apply(empty_set,X2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1526])]) ).
fof(f2311,plain,
( ! [X2,X0,X1] : ~ member(X0,image(X1,apply(empty_set,X2)))
| ~ spl0_103
| ~ spl0_165 ),
inference(resolution,[],[f2248,f961]) ).
fof(f58435,plain,
( spl0_1525
| ~ spl0_107
| ~ spl0_165 ),
inference(avatar_split_clause,[],[f2306,f2247,f1068,f58433]) ).
fof(f58433,plain,
( spl0_1525
<=> ! [X2,X0,X1] : ~ member(X0,image(apply(empty_set,X1),X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1525])]) ).
fof(f2306,plain,
( ! [X2,X0,X1] : ~ member(X0,image(apply(empty_set,X1),X2))
| ~ spl0_107
| ~ spl0_165 ),
inference(resolution,[],[f2248,f1069]) ).
fof(f58428,plain,
( spl0_1524
| ~ spl0_138
| ~ spl0_165 ),
inference(avatar_split_clause,[],[f2305,f2247,f1638,f58426]) ).
fof(f58426,plain,
( spl0_1524
<=> ! [X2,X0,X1] : ~ member(X0,compose(X1,apply(empty_set,X2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1524])]) ).
fof(f2305,plain,
( ! [X2,X0,X1] : ~ member(X0,compose(X1,apply(empty_set,X2)))
| ~ spl0_138
| ~ spl0_165 ),
inference(resolution,[],[f2248,f1639]) ).
fof(f58421,plain,
( spl0_1523
| ~ spl0_139
| ~ spl0_165 ),
inference(avatar_split_clause,[],[f2302,f2247,f1642,f58419]) ).
fof(f58419,plain,
( spl0_1523
<=> ! [X2,X0,X1] : ~ member(X0,compose(apply(empty_set,X1),X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1523])]) ).
fof(f2302,plain,
( ! [X2,X0,X1] : ~ member(X0,compose(apply(empty_set,X1),X2))
| ~ spl0_139
| ~ spl0_165 ),
inference(resolution,[],[f2248,f1643]) ).
fof(f58414,plain,
( spl0_1522
| ~ spl0_103
| ~ spl0_164 ),
inference(avatar_split_clause,[],[f2279,f2243,f960,f58412]) ).
fof(f58412,plain,
( spl0_1522
<=> ! [X2,X0,X1] : ~ member(X0,image(X1,image(X2,empty_set))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1522])]) ).
fof(f2279,plain,
( ! [X2,X0,X1] : ~ member(X0,image(X1,image(X2,empty_set)))
| ~ spl0_103
| ~ spl0_164 ),
inference(resolution,[],[f2244,f961]) ).
fof(f58407,plain,
( spl0_1521
| ~ spl0_107
| ~ spl0_164 ),
inference(avatar_split_clause,[],[f2273,f2243,f1068,f58405]) ).
fof(f58405,plain,
( spl0_1521
<=> ! [X2,X0,X1] : ~ member(X0,image(image(X1,empty_set),X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1521])]) ).
fof(f2273,plain,
( ! [X2,X0,X1] : ~ member(X0,image(image(X1,empty_set),X2))
| ~ spl0_107
| ~ spl0_164 ),
inference(resolution,[],[f2244,f1069]) ).
fof(f58400,plain,
( spl0_1520
| ~ spl0_138
| ~ spl0_164 ),
inference(avatar_split_clause,[],[f2272,f2243,f1638,f58398]) ).
fof(f58398,plain,
( spl0_1520
<=> ! [X2,X0,X1] : ~ member(X0,compose(X1,image(X2,empty_set))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1520])]) ).
fof(f2272,plain,
( ! [X2,X0,X1] : ~ member(X0,compose(X1,image(X2,empty_set)))
| ~ spl0_138
| ~ spl0_164 ),
inference(resolution,[],[f2244,f1639]) ).
fof(f58393,plain,
( spl0_1519
| ~ spl0_139
| ~ spl0_164 ),
inference(avatar_split_clause,[],[f2269,f2243,f1642,f58391]) ).
fof(f58391,plain,
( spl0_1519
<=> ! [X2,X0,X1] : ~ member(X0,compose(image(X1,empty_set),X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1519])]) ).
fof(f2269,plain,
( ! [X2,X0,X1] : ~ member(X0,compose(image(X1,empty_set),X2))
| ~ spl0_139
| ~ spl0_164 ),
inference(resolution,[],[f2244,f1643]) ).
fof(f58349,plain,
( spl0_1518
| ~ spl0_7
| ~ spl0_1047 ),
inference(avatar_split_clause,[],[f28107,f27973,f214,f58347]) ).
fof(f27973,plain,
( spl0_1047
<=> ! [X0] :
( first(X0) = estin
| non_ordered_pair(non_ordered_pair(f4(f24(first(X0)),X0),f4(f24(first(X0)),X0)),non_ordered_pair(f4(f24(first(X0)),X0),f5(f24(first(X0)),X0))) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1047])]) ).
fof(f28107,plain,
( ! [X0] :
( little_set(X0)
| first(X0) = estin )
| ~ spl0_7
| ~ spl0_1047 ),
inference(superposition,[],[f215,f27974]) ).
fof(f27974,plain,
( ! [X0] :
( non_ordered_pair(non_ordered_pair(f4(f24(first(X0)),X0),f4(f24(first(X0)),X0)),non_ordered_pair(f4(f24(first(X0)),X0),f5(f24(first(X0)),X0))) = X0
| first(X0) = estin )
| ~ spl0_1047 ),
inference(avatar_component_clause,[],[f27973]) ).
fof(f58345,plain,
( spl0_1517
| ~ spl0_7
| ~ spl0_1046 ),
inference(avatar_split_clause,[],[f28042,f27969,f214,f58343]) ).
fof(f27969,plain,
( spl0_1046
<=> ! [X0] :
( second(X0) = estin
| non_ordered_pair(non_ordered_pair(f6(f24(second(X0)),X0),f6(f24(second(X0)),X0)),non_ordered_pair(f6(f24(second(X0)),X0),f7(f24(second(X0)),X0))) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1046])]) ).
fof(f28042,plain,
( ! [X0] :
( little_set(X0)
| second(X0) = estin )
| ~ spl0_7
| ~ spl0_1046 ),
inference(superposition,[],[f215,f27970]) ).
fof(f27970,plain,
( ! [X0] :
( non_ordered_pair(non_ordered_pair(f6(f24(second(X0)),X0),f6(f24(second(X0)),X0)),non_ordered_pair(f6(f24(second(X0)),X0),f7(f24(second(X0)),X0))) = X0
| second(X0) = estin )
| ~ spl0_1046 ),
inference(avatar_component_clause,[],[f27969]) ).
fof(f58339,plain,
( ~ spl0_1515
| ~ spl0_1516
| ~ spl0_112
| spl0_587 ),
inference(avatar_split_clause,[],[f7496,f7492,f1089,f58336,f58332]) ).
fof(f7492,plain,
( spl0_587
<=> ordered_pair_predicate(non_ordered_pair(non_ordered_pair(f19(estin),f19(estin)),non_ordered_pair(f19(estin),f20(estin)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_587])]) ).
fof(f7496,plain,
( ~ little_set(f20(estin))
| ~ little_set(f19(estin))
| ~ spl0_112
| spl0_587 ),
inference(resolution,[],[f7494,f1090]) ).
fof(f7494,plain,
( ~ ordered_pair_predicate(non_ordered_pair(non_ordered_pair(f19(estin),f19(estin)),non_ordered_pair(f19(estin),f20(estin))))
| spl0_587 ),
inference(avatar_component_clause,[],[f7492]) ).
fof(f58330,plain,
( spl0_1514
| ~ spl0_257
| ~ spl0_364 ),
inference(avatar_split_clause,[],[f5117,f4242,f3124,f58328]) ).
fof(f58328,plain,
( spl0_1514
<=> ! [X0,X1] : disjoint(complement(X0),intersection(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1514])]) ).
fof(f5117,plain,
( ! [X0,X1] : disjoint(complement(X0),intersection(X0,X1))
| ~ spl0_257
| ~ spl0_364 ),
inference(duplicate_literal_removal,[],[f5055]) ).
fof(f5055,plain,
( ! [X0,X1] :
( disjoint(complement(X0),intersection(X0,X1))
| disjoint(complement(X0),intersection(X0,X1)) )
| ~ spl0_257
| ~ spl0_364 ),
inference(resolution,[],[f4243,f3125]) ).
fof(f58326,plain,
( spl0_1513
| ~ spl0_257
| ~ spl0_363 ),
inference(avatar_split_clause,[],[f5014,f4238,f3124,f58324]) ).
fof(f58324,plain,
( spl0_1513
<=> ! [X0,X1] : disjoint(complement(X0),intersection(X1,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1513])]) ).
fof(f5014,plain,
( ! [X0,X1] : disjoint(complement(X0),intersection(X1,X0))
| ~ spl0_257
| ~ spl0_363 ),
inference(duplicate_literal_removal,[],[f4952]) ).
fof(f4952,plain,
( ! [X0,X1] :
( disjoint(complement(X0),intersection(X1,X0))
| disjoint(complement(X0),intersection(X1,X0)) )
| ~ spl0_257
| ~ spl0_363 ),
inference(resolution,[],[f4239,f3125]) ).
fof(f58322,plain,
( spl0_1512
| ~ spl0_259
| ~ spl0_362 ),
inference(avatar_split_clause,[],[f4911,f4234,f3132,f58320]) ).
fof(f58320,plain,
( spl0_1512
<=> ! [X0,X1] : disjoint(intersection(X0,X1),complement(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1512])]) ).
fof(f4911,plain,
( ! [X0,X1] : disjoint(intersection(X0,X1),complement(X0))
| ~ spl0_259
| ~ spl0_362 ),
inference(duplicate_literal_removal,[],[f4849]) ).
fof(f4849,plain,
( ! [X0,X1] :
( disjoint(intersection(X0,X1),complement(X0))
| disjoint(intersection(X0,X1),complement(X0)) )
| ~ spl0_259
| ~ spl0_362 ),
inference(resolution,[],[f4235,f3133]) ).
fof(f58318,plain,
( spl0_1511
| ~ spl0_259
| ~ spl0_361 ),
inference(avatar_split_clause,[],[f4808,f4230,f3132,f58316]) ).
fof(f58316,plain,
( spl0_1511
<=> ! [X0,X1] : disjoint(intersection(X0,X1),complement(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1511])]) ).
fof(f4808,plain,
( ! [X0,X1] : disjoint(intersection(X0,X1),complement(X1))
| ~ spl0_259
| ~ spl0_361 ),
inference(duplicate_literal_removal,[],[f4746]) ).
fof(f4746,plain,
( ! [X0,X1] :
( disjoint(intersection(X0,X1),complement(X1))
| disjoint(intersection(X0,X1),complement(X1)) )
| ~ spl0_259
| ~ spl0_361 ),
inference(resolution,[],[f4231,f3133]) ).
fof(f58311,plain,
( spl0_1510
| ~ spl0_78
| ~ spl0_168 ),
inference(avatar_split_clause,[],[f2403,f2260,f644,f58309]) ).
fof(f58309,plain,
( spl0_1510
<=> ! [X0,X1] : ~ member(X0,sigma(compose(empty_set,X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1510])]) ).
fof(f644,plain,
( spl0_78
<=> ! [X0,X3] :
( ~ member(X3,sigma(X0))
| member(f16(X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_78])]) ).
fof(f2403,plain,
( ! [X0,X1] : ~ member(X0,sigma(compose(empty_set,X1)))
| ~ spl0_78
| ~ spl0_168 ),
inference(resolution,[],[f2261,f645]) ).
fof(f645,plain,
( ! [X3,X0] :
( member(f16(X3,X0),X0)
| ~ member(X3,sigma(X0)) )
| ~ spl0_78 ),
inference(avatar_component_clause,[],[f644]) ).
fof(f58304,plain,
( spl0_1509
| ~ spl0_74
| ~ spl0_168 ),
inference(avatar_split_clause,[],[f2402,f2260,f628,f58302]) ).
fof(f58302,plain,
( spl0_1509
<=> ! [X0,X1] : ~ member(X0,domain_of(compose(empty_set,X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1509])]) ).
fof(f628,plain,
( spl0_74
<=> ! [X0,X3] :
( ~ member(X3,domain_of(X0))
| member(f8(X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_74])]) ).
fof(f2402,plain,
( ! [X0,X1] : ~ member(X0,domain_of(compose(empty_set,X1)))
| ~ spl0_74
| ~ spl0_168 ),
inference(resolution,[],[f2261,f629]) ).
fof(f629,plain,
( ! [X3,X0] :
( member(f8(X3,X0),X0)
| ~ member(X3,domain_of(X0)) )
| ~ spl0_74 ),
inference(avatar_component_clause,[],[f628]) ).
fof(f58297,plain,
( spl0_1508
| ~ spl0_145
| ~ spl0_168 ),
inference(avatar_split_clause,[],[f2399,f2260,f1786,f58295]) ).
fof(f58295,plain,
( spl0_1508
<=> ! [X0,X1] : ~ member(X0,rotate_right(compose(empty_set,X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1508])]) ).
fof(f1786,plain,
( spl0_145
<=> ! [X0,X3] :
( ~ member(X3,rotate_right(X0))
| member(non_ordered_pair(non_ordered_pair(f10(X3,X0),f10(X3,X0)),non_ordered_pair(f10(X3,X0),non_ordered_pair(non_ordered_pair(f11(X3,X0),f11(X3,X0)),non_ordered_pair(f11(X3,X0),f9(X3,X0))))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_145])]) ).
fof(f2399,plain,
( ! [X0,X1] : ~ member(X0,rotate_right(compose(empty_set,X1)))
| ~ spl0_145
| ~ spl0_168 ),
inference(resolution,[],[f2261,f1787]) ).
fof(f1787,plain,
( ! [X3,X0] :
( member(non_ordered_pair(non_ordered_pair(f10(X3,X0),f10(X3,X0)),non_ordered_pair(f10(X3,X0),non_ordered_pair(non_ordered_pair(f11(X3,X0),f11(X3,X0)),non_ordered_pair(f11(X3,X0),f9(X3,X0))))),X0)
| ~ member(X3,rotate_right(X0)) )
| ~ spl0_145 ),
inference(avatar_component_clause,[],[f1786]) ).
fof(f58290,plain,
( spl0_1507
| ~ spl0_144
| ~ spl0_168 ),
inference(avatar_split_clause,[],[f2398,f2260,f1782,f58288]) ).
fof(f58288,plain,
( spl0_1507
<=> ! [X0,X1] : ~ member(X0,flip_range_of(compose(empty_set,X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1507])]) ).
fof(f1782,plain,
( spl0_144
<=> ! [X0,X3] :
( ~ member(X3,flip_range_of(X0))
| member(non_ordered_pair(non_ordered_pair(f12(X3,X0),f12(X3,X0)),non_ordered_pair(f12(X3,X0),non_ordered_pair(non_ordered_pair(f14(X3,X0),f14(X3,X0)),non_ordered_pair(f14(X3,X0),f13(X3,X0))))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_144])]) ).
fof(f2398,plain,
( ! [X0,X1] : ~ member(X0,flip_range_of(compose(empty_set,X1)))
| ~ spl0_144
| ~ spl0_168 ),
inference(resolution,[],[f2261,f1783]) ).
fof(f1783,plain,
( ! [X3,X0] :
( member(non_ordered_pair(non_ordered_pair(f12(X3,X0),f12(X3,X0)),non_ordered_pair(f12(X3,X0),non_ordered_pair(non_ordered_pair(f14(X3,X0),f14(X3,X0)),non_ordered_pair(f14(X3,X0),f13(X3,X0))))),X0)
| ~ member(X3,flip_range_of(X0)) )
| ~ spl0_144 ),
inference(avatar_component_clause,[],[f1782]) ).
fof(f58283,plain,
( spl0_1506
| ~ spl0_127
| ~ spl0_168 ),
inference(avatar_split_clause,[],[f2396,f2260,f1397,f58281]) ).
fof(f58281,plain,
( spl0_1506
<=> ! [X0,X1] : ~ member(X0,converse(compose(empty_set,X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1506])]) ).
fof(f2396,plain,
( ! [X0,X1] : ~ member(X0,converse(compose(empty_set,X1)))
| ~ spl0_127
| ~ spl0_168 ),
inference(resolution,[],[f2261,f1398]) ).
fof(f57504,plain,
( spl0_1505
| ~ spl0_78
| ~ spl0_167 ),
inference(avatar_split_clause,[],[f2372,f2256,f644,f57502]) ).
fof(f57502,plain,
( spl0_1505
<=> ! [X0,X1] : ~ member(X0,sigma(compose(X1,empty_set))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1505])]) ).
fof(f2372,plain,
( ! [X0,X1] : ~ member(X0,sigma(compose(X1,empty_set)))
| ~ spl0_78
| ~ spl0_167 ),
inference(resolution,[],[f2257,f645]) ).
fof(f57500,plain,
( spl0_1504
| ~ spl0_142
| ~ spl0_145 ),
inference(avatar_split_clause,[],[f1899,f1786,f1774,f57498]) ).
fof(f57498,plain,
( spl0_1504
<=> ! [X0,X1] :
( ~ member(X0,rotate_right(flip_range_of(X1)))
| non_ordered_pair(non_ordered_pair(f10(X0,flip_range_of(X1)),f10(X0,flip_range_of(X1))),non_ordered_pair(f10(X0,flip_range_of(X1)),non_ordered_pair(non_ordered_pair(f11(X0,flip_range_of(X1)),f11(X0,flip_range_of(X1))),non_ordered_pair(f11(X0,flip_range_of(X1)),f9(X0,flip_range_of(X1)))))) = non_ordered_pair(non_ordered_pair(f12(non_ordered_pair(non_ordered_pair(f10(X0,flip_range_of(X1)),f10(X0,flip_range_of(X1))),non_ordered_pair(f10(X0,flip_range_of(X1)),non_ordered_pair(non_ordered_pair(f11(X0,flip_range_of(X1)),f11(X0,flip_range_of(X1))),non_ordered_pair(f11(X0,flip_range_of(X1)),f9(X0,flip_range_of(X1)))))),X1),f12(non_ordered_pair(non_ordered_pair(f10(X0,flip_range_of(X1)),f10(X0,flip_range_of(X1))),non_ordered_pair(f10(X0,flip_range_of(X1)),non_ordered_pair(non_ordered_pair(f11(X0,flip_range_of(X1)),f11(X0,flip_range_of(X1))),non_ordered_pair(f11(X0,flip_range_of(X1)),f9(X0,flip_range_of(X1)))))),X1)),non_ordered_pair(f12(non_ordered_pair(non_ordered_pair(f10(X0,flip_range_of(X1)),f10(X0,flip_range_of(X1))),non_ordered_pair(f10(X0,flip_range_of(X1)),non_ordered_pair(non_ordered_pair(f11(X0,flip_range_of(X1)),f11(X0,flip_range_of(X1))),non_ordered_pair(f11(X0,flip_range_of(X1)),f9(X0,flip_range_of(X1)))))),X1),non_ordered_pair(non_ordered_pair(f13(non_ordered_pair(non_ordered_pair(f10(X0,flip_range_of(X1)),f10(X0,flip_range_of(X1))),non_ordered_pair(f10(X0,flip_range_of(X1)),non_ordered_pair(non_ordered_pair(f11(X0,flip_range_of(X1)),f11(X0,flip_range_of(X1))),non_ordered_pair(f11(X0,flip_range_of(X1)),f9(X0,flip_range_of(X1)))))),X1),f13(non_ordered_pair(non_ordered_pair(f10(X0,flip_range_of(X1)),f10(X0,flip_range_of(X1))),non_ordered_pair(f10(X0,flip_range_of(X1)),non_ordered_pair(non_ordered_pair(f11(X0,flip_range_of(X1)),f11(X0,flip_range_of(X1))),non_ordered_pair(f11(X0,flip_range_of(X1)),f9(X0,flip_range_of(X1)))))),X1)),non_ordered_pair(f13(non_ordered_pair(non_ordered_pair(f10(X0,flip_range_of(X1)),f10(X0,flip_range_of(X1))),non_ordered_pair(f10(X0,flip_range_of(X1)),non_ordered_pair(non_ordered_pair(f11(X0,flip_range_of(X1)),f11(X0,flip_range_of(X1))),non_ordered_pair(f11(X0,flip_range_of(X1)),f9(X0,flip_range_of(X1)))))),X1),f14(non_ordered_pair(non_ordered_pair(f10(X0,flip_range_of(X1)),f10(X0,flip_range_of(X1))),non_ordered_pair(f10(X0,flip_range_of(X1)),non_ordered_pair(non_ordered_pair(f11(X0,flip_range_of(X1)),f11(X0,flip_range_of(X1))),non_ordered_pair(f11(X0,flip_range_of(X1)),f9(X0,flip_range_of(X1)))))),X1))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1504])]) ).
fof(f1774,plain,
( spl0_142
<=> ! [X0,X3] :
( ~ member(X3,flip_range_of(X0))
| non_ordered_pair(non_ordered_pair(f12(X3,X0),f12(X3,X0)),non_ordered_pair(f12(X3,X0),non_ordered_pair(non_ordered_pair(f13(X3,X0),f13(X3,X0)),non_ordered_pair(f13(X3,X0),f14(X3,X0))))) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_142])]) ).
fof(f1899,plain,
( ! [X0,X1] :
( ~ member(X0,rotate_right(flip_range_of(X1)))
| non_ordered_pair(non_ordered_pair(f10(X0,flip_range_of(X1)),f10(X0,flip_range_of(X1))),non_ordered_pair(f10(X0,flip_range_of(X1)),non_ordered_pair(non_ordered_pair(f11(X0,flip_range_of(X1)),f11(X0,flip_range_of(X1))),non_ordered_pair(f11(X0,flip_range_of(X1)),f9(X0,flip_range_of(X1)))))) = non_ordered_pair(non_ordered_pair(f12(non_ordered_pair(non_ordered_pair(f10(X0,flip_range_of(X1)),f10(X0,flip_range_of(X1))),non_ordered_pair(f10(X0,flip_range_of(X1)),non_ordered_pair(non_ordered_pair(f11(X0,flip_range_of(X1)),f11(X0,flip_range_of(X1))),non_ordered_pair(f11(X0,flip_range_of(X1)),f9(X0,flip_range_of(X1)))))),X1),f12(non_ordered_pair(non_ordered_pair(f10(X0,flip_range_of(X1)),f10(X0,flip_range_of(X1))),non_ordered_pair(f10(X0,flip_range_of(X1)),non_ordered_pair(non_ordered_pair(f11(X0,flip_range_of(X1)),f11(X0,flip_range_of(X1))),non_ordered_pair(f11(X0,flip_range_of(X1)),f9(X0,flip_range_of(X1)))))),X1)),non_ordered_pair(f12(non_ordered_pair(non_ordered_pair(f10(X0,flip_range_of(X1)),f10(X0,flip_range_of(X1))),non_ordered_pair(f10(X0,flip_range_of(X1)),non_ordered_pair(non_ordered_pair(f11(X0,flip_range_of(X1)),f11(X0,flip_range_of(X1))),non_ordered_pair(f11(X0,flip_range_of(X1)),f9(X0,flip_range_of(X1)))))),X1),non_ordered_pair(non_ordered_pair(f13(non_ordered_pair(non_ordered_pair(f10(X0,flip_range_of(X1)),f10(X0,flip_range_of(X1))),non_ordered_pair(f10(X0,flip_range_of(X1)),non_ordered_pair(non_ordered_pair(f11(X0,flip_range_of(X1)),f11(X0,flip_range_of(X1))),non_ordered_pair(f11(X0,flip_range_of(X1)),f9(X0,flip_range_of(X1)))))),X1),f13(non_ordered_pair(non_ordered_pair(f10(X0,flip_range_of(X1)),f10(X0,flip_range_of(X1))),non_ordered_pair(f10(X0,flip_range_of(X1)),non_ordered_pair(non_ordered_pair(f11(X0,flip_range_of(X1)),f11(X0,flip_range_of(X1))),non_ordered_pair(f11(X0,flip_range_of(X1)),f9(X0,flip_range_of(X1)))))),X1)),non_ordered_pair(f13(non_ordered_pair(non_ordered_pair(f10(X0,flip_range_of(X1)),f10(X0,flip_range_of(X1))),non_ordered_pair(f10(X0,flip_range_of(X1)),non_ordered_pair(non_ordered_pair(f11(X0,flip_range_of(X1)),f11(X0,flip_range_of(X1))),non_ordered_pair(f11(X0,flip_range_of(X1)),f9(X0,flip_range_of(X1)))))),X1),f14(non_ordered_pair(non_ordered_pair(f10(X0,flip_range_of(X1)),f10(X0,flip_range_of(X1))),non_ordered_pair(f10(X0,flip_range_of(X1)),non_ordered_pair(non_ordered_pair(f11(X0,flip_range_of(X1)),f11(X0,flip_range_of(X1))),non_ordered_pair(f11(X0,flip_range_of(X1)),f9(X0,flip_range_of(X1)))))),X1))))) )
| ~ spl0_142
| ~ spl0_145 ),
inference(resolution,[],[f1787,f1775]) ).
fof(f1775,plain,
( ! [X3,X0] :
( ~ member(X3,flip_range_of(X0))
| non_ordered_pair(non_ordered_pair(f12(X3,X0),f12(X3,X0)),non_ordered_pair(f12(X3,X0),non_ordered_pair(non_ordered_pair(f13(X3,X0),f13(X3,X0)),non_ordered_pair(f13(X3,X0),f14(X3,X0))))) = X3 )
| ~ spl0_142 ),
inference(avatar_component_clause,[],[f1774]) ).
fof(f57496,plain,
( spl0_1503
| ~ spl0_143
| ~ spl0_145 ),
inference(avatar_split_clause,[],[f1895,f1786,f1778,f57494]) ).
fof(f57494,plain,
( spl0_1503
<=> ! [X0,X1] :
( ~ member(X0,rotate_right(rotate_right(X1)))
| non_ordered_pair(non_ordered_pair(f10(X0,rotate_right(X1)),f10(X0,rotate_right(X1))),non_ordered_pair(f10(X0,rotate_right(X1)),non_ordered_pair(non_ordered_pair(f11(X0,rotate_right(X1)),f11(X0,rotate_right(X1))),non_ordered_pair(f11(X0,rotate_right(X1)),f9(X0,rotate_right(X1)))))) = non_ordered_pair(non_ordered_pair(f9(non_ordered_pair(non_ordered_pair(f10(X0,rotate_right(X1)),f10(X0,rotate_right(X1))),non_ordered_pair(f10(X0,rotate_right(X1)),non_ordered_pair(non_ordered_pair(f11(X0,rotate_right(X1)),f11(X0,rotate_right(X1))),non_ordered_pair(f11(X0,rotate_right(X1)),f9(X0,rotate_right(X1)))))),X1),f9(non_ordered_pair(non_ordered_pair(f10(X0,rotate_right(X1)),f10(X0,rotate_right(X1))),non_ordered_pair(f10(X0,rotate_right(X1)),non_ordered_pair(non_ordered_pair(f11(X0,rotate_right(X1)),f11(X0,rotate_right(X1))),non_ordered_pair(f11(X0,rotate_right(X1)),f9(X0,rotate_right(X1)))))),X1)),non_ordered_pair(f9(non_ordered_pair(non_ordered_pair(f10(X0,rotate_right(X1)),f10(X0,rotate_right(X1))),non_ordered_pair(f10(X0,rotate_right(X1)),non_ordered_pair(non_ordered_pair(f11(X0,rotate_right(X1)),f11(X0,rotate_right(X1))),non_ordered_pair(f11(X0,rotate_right(X1)),f9(X0,rotate_right(X1)))))),X1),non_ordered_pair(non_ordered_pair(f10(non_ordered_pair(non_ordered_pair(f10(X0,rotate_right(X1)),f10(X0,rotate_right(X1))),non_ordered_pair(f10(X0,rotate_right(X1)),non_ordered_pair(non_ordered_pair(f11(X0,rotate_right(X1)),f11(X0,rotate_right(X1))),non_ordered_pair(f11(X0,rotate_right(X1)),f9(X0,rotate_right(X1)))))),X1),f10(non_ordered_pair(non_ordered_pair(f10(X0,rotate_right(X1)),f10(X0,rotate_right(X1))),non_ordered_pair(f10(X0,rotate_right(X1)),non_ordered_pair(non_ordered_pair(f11(X0,rotate_right(X1)),f11(X0,rotate_right(X1))),non_ordered_pair(f11(X0,rotate_right(X1)),f9(X0,rotate_right(X1)))))),X1)),non_ordered_pair(f10(non_ordered_pair(non_ordered_pair(f10(X0,rotate_right(X1)),f10(X0,rotate_right(X1))),non_ordered_pair(f10(X0,rotate_right(X1)),non_ordered_pair(non_ordered_pair(f11(X0,rotate_right(X1)),f11(X0,rotate_right(X1))),non_ordered_pair(f11(X0,rotate_right(X1)),f9(X0,rotate_right(X1)))))),X1),f11(non_ordered_pair(non_ordered_pair(f10(X0,rotate_right(X1)),f10(X0,rotate_right(X1))),non_ordered_pair(f10(X0,rotate_right(X1)),non_ordered_pair(non_ordered_pair(f11(X0,rotate_right(X1)),f11(X0,rotate_right(X1))),non_ordered_pair(f11(X0,rotate_right(X1)),f9(X0,rotate_right(X1)))))),X1))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1503])]) ).
fof(f1778,plain,
( spl0_143
<=> ! [X0,X3] :
( ~ member(X3,rotate_right(X0))
| non_ordered_pair(non_ordered_pair(f9(X3,X0),f9(X3,X0)),non_ordered_pair(f9(X3,X0),non_ordered_pair(non_ordered_pair(f10(X3,X0),f10(X3,X0)),non_ordered_pair(f10(X3,X0),f11(X3,X0))))) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_143])]) ).
fof(f1895,plain,
( ! [X0,X1] :
( ~ member(X0,rotate_right(rotate_right(X1)))
| non_ordered_pair(non_ordered_pair(f10(X0,rotate_right(X1)),f10(X0,rotate_right(X1))),non_ordered_pair(f10(X0,rotate_right(X1)),non_ordered_pair(non_ordered_pair(f11(X0,rotate_right(X1)),f11(X0,rotate_right(X1))),non_ordered_pair(f11(X0,rotate_right(X1)),f9(X0,rotate_right(X1)))))) = non_ordered_pair(non_ordered_pair(f9(non_ordered_pair(non_ordered_pair(f10(X0,rotate_right(X1)),f10(X0,rotate_right(X1))),non_ordered_pair(f10(X0,rotate_right(X1)),non_ordered_pair(non_ordered_pair(f11(X0,rotate_right(X1)),f11(X0,rotate_right(X1))),non_ordered_pair(f11(X0,rotate_right(X1)),f9(X0,rotate_right(X1)))))),X1),f9(non_ordered_pair(non_ordered_pair(f10(X0,rotate_right(X1)),f10(X0,rotate_right(X1))),non_ordered_pair(f10(X0,rotate_right(X1)),non_ordered_pair(non_ordered_pair(f11(X0,rotate_right(X1)),f11(X0,rotate_right(X1))),non_ordered_pair(f11(X0,rotate_right(X1)),f9(X0,rotate_right(X1)))))),X1)),non_ordered_pair(f9(non_ordered_pair(non_ordered_pair(f10(X0,rotate_right(X1)),f10(X0,rotate_right(X1))),non_ordered_pair(f10(X0,rotate_right(X1)),non_ordered_pair(non_ordered_pair(f11(X0,rotate_right(X1)),f11(X0,rotate_right(X1))),non_ordered_pair(f11(X0,rotate_right(X1)),f9(X0,rotate_right(X1)))))),X1),non_ordered_pair(non_ordered_pair(f10(non_ordered_pair(non_ordered_pair(f10(X0,rotate_right(X1)),f10(X0,rotate_right(X1))),non_ordered_pair(f10(X0,rotate_right(X1)),non_ordered_pair(non_ordered_pair(f11(X0,rotate_right(X1)),f11(X0,rotate_right(X1))),non_ordered_pair(f11(X0,rotate_right(X1)),f9(X0,rotate_right(X1)))))),X1),f10(non_ordered_pair(non_ordered_pair(f10(X0,rotate_right(X1)),f10(X0,rotate_right(X1))),non_ordered_pair(f10(X0,rotate_right(X1)),non_ordered_pair(non_ordered_pair(f11(X0,rotate_right(X1)),f11(X0,rotate_right(X1))),non_ordered_pair(f11(X0,rotate_right(X1)),f9(X0,rotate_right(X1)))))),X1)),non_ordered_pair(f10(non_ordered_pair(non_ordered_pair(f10(X0,rotate_right(X1)),f10(X0,rotate_right(X1))),non_ordered_pair(f10(X0,rotate_right(X1)),non_ordered_pair(non_ordered_pair(f11(X0,rotate_right(X1)),f11(X0,rotate_right(X1))),non_ordered_pair(f11(X0,rotate_right(X1)),f9(X0,rotate_right(X1)))))),X1),f11(non_ordered_pair(non_ordered_pair(f10(X0,rotate_right(X1)),f10(X0,rotate_right(X1))),non_ordered_pair(f10(X0,rotate_right(X1)),non_ordered_pair(non_ordered_pair(f11(X0,rotate_right(X1)),f11(X0,rotate_right(X1))),non_ordered_pair(f11(X0,rotate_right(X1)),f9(X0,rotate_right(X1)))))),X1))))) )
| ~ spl0_143
| ~ spl0_145 ),
inference(resolution,[],[f1787,f1779]) ).
fof(f1779,plain,
( ! [X3,X0] :
( ~ member(X3,rotate_right(X0))
| non_ordered_pair(non_ordered_pair(f9(X3,X0),f9(X3,X0)),non_ordered_pair(f9(X3,X0),non_ordered_pair(non_ordered_pair(f10(X3,X0),f10(X3,X0)),non_ordered_pair(f10(X3,X0),f11(X3,X0))))) = X3 )
| ~ spl0_143 ),
inference(avatar_component_clause,[],[f1778]) ).
fof(f57492,plain,
( spl0_1502
| ~ spl0_142
| ~ spl0_144 ),
inference(avatar_split_clause,[],[f1856,f1782,f1774,f57490]) ).
fof(f57490,plain,
( spl0_1502
<=> ! [X0,X1] :
( ~ member(X0,flip_range_of(flip_range_of(X1)))
| non_ordered_pair(non_ordered_pair(f12(X0,flip_range_of(X1)),f12(X0,flip_range_of(X1))),non_ordered_pair(f12(X0,flip_range_of(X1)),non_ordered_pair(non_ordered_pair(f14(X0,flip_range_of(X1)),f14(X0,flip_range_of(X1))),non_ordered_pair(f14(X0,flip_range_of(X1)),f13(X0,flip_range_of(X1)))))) = non_ordered_pair(non_ordered_pair(f12(non_ordered_pair(non_ordered_pair(f12(X0,flip_range_of(X1)),f12(X0,flip_range_of(X1))),non_ordered_pair(f12(X0,flip_range_of(X1)),non_ordered_pair(non_ordered_pair(f14(X0,flip_range_of(X1)),f14(X0,flip_range_of(X1))),non_ordered_pair(f14(X0,flip_range_of(X1)),f13(X0,flip_range_of(X1)))))),X1),f12(non_ordered_pair(non_ordered_pair(f12(X0,flip_range_of(X1)),f12(X0,flip_range_of(X1))),non_ordered_pair(f12(X0,flip_range_of(X1)),non_ordered_pair(non_ordered_pair(f14(X0,flip_range_of(X1)),f14(X0,flip_range_of(X1))),non_ordered_pair(f14(X0,flip_range_of(X1)),f13(X0,flip_range_of(X1)))))),X1)),non_ordered_pair(f12(non_ordered_pair(non_ordered_pair(f12(X0,flip_range_of(X1)),f12(X0,flip_range_of(X1))),non_ordered_pair(f12(X0,flip_range_of(X1)),non_ordered_pair(non_ordered_pair(f14(X0,flip_range_of(X1)),f14(X0,flip_range_of(X1))),non_ordered_pair(f14(X0,flip_range_of(X1)),f13(X0,flip_range_of(X1)))))),X1),non_ordered_pair(non_ordered_pair(f13(non_ordered_pair(non_ordered_pair(f12(X0,flip_range_of(X1)),f12(X0,flip_range_of(X1))),non_ordered_pair(f12(X0,flip_range_of(X1)),non_ordered_pair(non_ordered_pair(f14(X0,flip_range_of(X1)),f14(X0,flip_range_of(X1))),non_ordered_pair(f14(X0,flip_range_of(X1)),f13(X0,flip_range_of(X1)))))),X1),f13(non_ordered_pair(non_ordered_pair(f12(X0,flip_range_of(X1)),f12(X0,flip_range_of(X1))),non_ordered_pair(f12(X0,flip_range_of(X1)),non_ordered_pair(non_ordered_pair(f14(X0,flip_range_of(X1)),f14(X0,flip_range_of(X1))),non_ordered_pair(f14(X0,flip_range_of(X1)),f13(X0,flip_range_of(X1)))))),X1)),non_ordered_pair(f13(non_ordered_pair(non_ordered_pair(f12(X0,flip_range_of(X1)),f12(X0,flip_range_of(X1))),non_ordered_pair(f12(X0,flip_range_of(X1)),non_ordered_pair(non_ordered_pair(f14(X0,flip_range_of(X1)),f14(X0,flip_range_of(X1))),non_ordered_pair(f14(X0,flip_range_of(X1)),f13(X0,flip_range_of(X1)))))),X1),f14(non_ordered_pair(non_ordered_pair(f12(X0,flip_range_of(X1)),f12(X0,flip_range_of(X1))),non_ordered_pair(f12(X0,flip_range_of(X1)),non_ordered_pair(non_ordered_pair(f14(X0,flip_range_of(X1)),f14(X0,flip_range_of(X1))),non_ordered_pair(f14(X0,flip_range_of(X1)),f13(X0,flip_range_of(X1)))))),X1))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1502])]) ).
fof(f1856,plain,
( ! [X0,X1] :
( ~ member(X0,flip_range_of(flip_range_of(X1)))
| non_ordered_pair(non_ordered_pair(f12(X0,flip_range_of(X1)),f12(X0,flip_range_of(X1))),non_ordered_pair(f12(X0,flip_range_of(X1)),non_ordered_pair(non_ordered_pair(f14(X0,flip_range_of(X1)),f14(X0,flip_range_of(X1))),non_ordered_pair(f14(X0,flip_range_of(X1)),f13(X0,flip_range_of(X1)))))) = non_ordered_pair(non_ordered_pair(f12(non_ordered_pair(non_ordered_pair(f12(X0,flip_range_of(X1)),f12(X0,flip_range_of(X1))),non_ordered_pair(f12(X0,flip_range_of(X1)),non_ordered_pair(non_ordered_pair(f14(X0,flip_range_of(X1)),f14(X0,flip_range_of(X1))),non_ordered_pair(f14(X0,flip_range_of(X1)),f13(X0,flip_range_of(X1)))))),X1),f12(non_ordered_pair(non_ordered_pair(f12(X0,flip_range_of(X1)),f12(X0,flip_range_of(X1))),non_ordered_pair(f12(X0,flip_range_of(X1)),non_ordered_pair(non_ordered_pair(f14(X0,flip_range_of(X1)),f14(X0,flip_range_of(X1))),non_ordered_pair(f14(X0,flip_range_of(X1)),f13(X0,flip_range_of(X1)))))),X1)),non_ordered_pair(f12(non_ordered_pair(non_ordered_pair(f12(X0,flip_range_of(X1)),f12(X0,flip_range_of(X1))),non_ordered_pair(f12(X0,flip_range_of(X1)),non_ordered_pair(non_ordered_pair(f14(X0,flip_range_of(X1)),f14(X0,flip_range_of(X1))),non_ordered_pair(f14(X0,flip_range_of(X1)),f13(X0,flip_range_of(X1)))))),X1),non_ordered_pair(non_ordered_pair(f13(non_ordered_pair(non_ordered_pair(f12(X0,flip_range_of(X1)),f12(X0,flip_range_of(X1))),non_ordered_pair(f12(X0,flip_range_of(X1)),non_ordered_pair(non_ordered_pair(f14(X0,flip_range_of(X1)),f14(X0,flip_range_of(X1))),non_ordered_pair(f14(X0,flip_range_of(X1)),f13(X0,flip_range_of(X1)))))),X1),f13(non_ordered_pair(non_ordered_pair(f12(X0,flip_range_of(X1)),f12(X0,flip_range_of(X1))),non_ordered_pair(f12(X0,flip_range_of(X1)),non_ordered_pair(non_ordered_pair(f14(X0,flip_range_of(X1)),f14(X0,flip_range_of(X1))),non_ordered_pair(f14(X0,flip_range_of(X1)),f13(X0,flip_range_of(X1)))))),X1)),non_ordered_pair(f13(non_ordered_pair(non_ordered_pair(f12(X0,flip_range_of(X1)),f12(X0,flip_range_of(X1))),non_ordered_pair(f12(X0,flip_range_of(X1)),non_ordered_pair(non_ordered_pair(f14(X0,flip_range_of(X1)),f14(X0,flip_range_of(X1))),non_ordered_pair(f14(X0,flip_range_of(X1)),f13(X0,flip_range_of(X1)))))),X1),f14(non_ordered_pair(non_ordered_pair(f12(X0,flip_range_of(X1)),f12(X0,flip_range_of(X1))),non_ordered_pair(f12(X0,flip_range_of(X1)),non_ordered_pair(non_ordered_pair(f14(X0,flip_range_of(X1)),f14(X0,flip_range_of(X1))),non_ordered_pair(f14(X0,flip_range_of(X1)),f13(X0,flip_range_of(X1)))))),X1))))) )
| ~ spl0_142
| ~ spl0_144 ),
inference(resolution,[],[f1783,f1775]) ).
fof(f57488,plain,
( spl0_1501
| ~ spl0_143
| ~ spl0_144 ),
inference(avatar_split_clause,[],[f1852,f1782,f1778,f57486]) ).
fof(f57486,plain,
( spl0_1501
<=> ! [X0,X1] :
( ~ member(X0,flip_range_of(rotate_right(X1)))
| non_ordered_pair(non_ordered_pair(f12(X0,rotate_right(X1)),f12(X0,rotate_right(X1))),non_ordered_pair(f12(X0,rotate_right(X1)),non_ordered_pair(non_ordered_pair(f14(X0,rotate_right(X1)),f14(X0,rotate_right(X1))),non_ordered_pair(f14(X0,rotate_right(X1)),f13(X0,rotate_right(X1)))))) = non_ordered_pair(non_ordered_pair(f9(non_ordered_pair(non_ordered_pair(f12(X0,rotate_right(X1)),f12(X0,rotate_right(X1))),non_ordered_pair(f12(X0,rotate_right(X1)),non_ordered_pair(non_ordered_pair(f14(X0,rotate_right(X1)),f14(X0,rotate_right(X1))),non_ordered_pair(f14(X0,rotate_right(X1)),f13(X0,rotate_right(X1)))))),X1),f9(non_ordered_pair(non_ordered_pair(f12(X0,rotate_right(X1)),f12(X0,rotate_right(X1))),non_ordered_pair(f12(X0,rotate_right(X1)),non_ordered_pair(non_ordered_pair(f14(X0,rotate_right(X1)),f14(X0,rotate_right(X1))),non_ordered_pair(f14(X0,rotate_right(X1)),f13(X0,rotate_right(X1)))))),X1)),non_ordered_pair(f9(non_ordered_pair(non_ordered_pair(f12(X0,rotate_right(X1)),f12(X0,rotate_right(X1))),non_ordered_pair(f12(X0,rotate_right(X1)),non_ordered_pair(non_ordered_pair(f14(X0,rotate_right(X1)),f14(X0,rotate_right(X1))),non_ordered_pair(f14(X0,rotate_right(X1)),f13(X0,rotate_right(X1)))))),X1),non_ordered_pair(non_ordered_pair(f10(non_ordered_pair(non_ordered_pair(f12(X0,rotate_right(X1)),f12(X0,rotate_right(X1))),non_ordered_pair(f12(X0,rotate_right(X1)),non_ordered_pair(non_ordered_pair(f14(X0,rotate_right(X1)),f14(X0,rotate_right(X1))),non_ordered_pair(f14(X0,rotate_right(X1)),f13(X0,rotate_right(X1)))))),X1),f10(non_ordered_pair(non_ordered_pair(f12(X0,rotate_right(X1)),f12(X0,rotate_right(X1))),non_ordered_pair(f12(X0,rotate_right(X1)),non_ordered_pair(non_ordered_pair(f14(X0,rotate_right(X1)),f14(X0,rotate_right(X1))),non_ordered_pair(f14(X0,rotate_right(X1)),f13(X0,rotate_right(X1)))))),X1)),non_ordered_pair(f10(non_ordered_pair(non_ordered_pair(f12(X0,rotate_right(X1)),f12(X0,rotate_right(X1))),non_ordered_pair(f12(X0,rotate_right(X1)),non_ordered_pair(non_ordered_pair(f14(X0,rotate_right(X1)),f14(X0,rotate_right(X1))),non_ordered_pair(f14(X0,rotate_right(X1)),f13(X0,rotate_right(X1)))))),X1),f11(non_ordered_pair(non_ordered_pair(f12(X0,rotate_right(X1)),f12(X0,rotate_right(X1))),non_ordered_pair(f12(X0,rotate_right(X1)),non_ordered_pair(non_ordered_pair(f14(X0,rotate_right(X1)),f14(X0,rotate_right(X1))),non_ordered_pair(f14(X0,rotate_right(X1)),f13(X0,rotate_right(X1)))))),X1))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1501])]) ).
fof(f1852,plain,
( ! [X0,X1] :
( ~ member(X0,flip_range_of(rotate_right(X1)))
| non_ordered_pair(non_ordered_pair(f12(X0,rotate_right(X1)),f12(X0,rotate_right(X1))),non_ordered_pair(f12(X0,rotate_right(X1)),non_ordered_pair(non_ordered_pair(f14(X0,rotate_right(X1)),f14(X0,rotate_right(X1))),non_ordered_pair(f14(X0,rotate_right(X1)),f13(X0,rotate_right(X1)))))) = non_ordered_pair(non_ordered_pair(f9(non_ordered_pair(non_ordered_pair(f12(X0,rotate_right(X1)),f12(X0,rotate_right(X1))),non_ordered_pair(f12(X0,rotate_right(X1)),non_ordered_pair(non_ordered_pair(f14(X0,rotate_right(X1)),f14(X0,rotate_right(X1))),non_ordered_pair(f14(X0,rotate_right(X1)),f13(X0,rotate_right(X1)))))),X1),f9(non_ordered_pair(non_ordered_pair(f12(X0,rotate_right(X1)),f12(X0,rotate_right(X1))),non_ordered_pair(f12(X0,rotate_right(X1)),non_ordered_pair(non_ordered_pair(f14(X0,rotate_right(X1)),f14(X0,rotate_right(X1))),non_ordered_pair(f14(X0,rotate_right(X1)),f13(X0,rotate_right(X1)))))),X1)),non_ordered_pair(f9(non_ordered_pair(non_ordered_pair(f12(X0,rotate_right(X1)),f12(X0,rotate_right(X1))),non_ordered_pair(f12(X0,rotate_right(X1)),non_ordered_pair(non_ordered_pair(f14(X0,rotate_right(X1)),f14(X0,rotate_right(X1))),non_ordered_pair(f14(X0,rotate_right(X1)),f13(X0,rotate_right(X1)))))),X1),non_ordered_pair(non_ordered_pair(f10(non_ordered_pair(non_ordered_pair(f12(X0,rotate_right(X1)),f12(X0,rotate_right(X1))),non_ordered_pair(f12(X0,rotate_right(X1)),non_ordered_pair(non_ordered_pair(f14(X0,rotate_right(X1)),f14(X0,rotate_right(X1))),non_ordered_pair(f14(X0,rotate_right(X1)),f13(X0,rotate_right(X1)))))),X1),f10(non_ordered_pair(non_ordered_pair(f12(X0,rotate_right(X1)),f12(X0,rotate_right(X1))),non_ordered_pair(f12(X0,rotate_right(X1)),non_ordered_pair(non_ordered_pair(f14(X0,rotate_right(X1)),f14(X0,rotate_right(X1))),non_ordered_pair(f14(X0,rotate_right(X1)),f13(X0,rotate_right(X1)))))),X1)),non_ordered_pair(f10(non_ordered_pair(non_ordered_pair(f12(X0,rotate_right(X1)),f12(X0,rotate_right(X1))),non_ordered_pair(f12(X0,rotate_right(X1)),non_ordered_pair(non_ordered_pair(f14(X0,rotate_right(X1)),f14(X0,rotate_right(X1))),non_ordered_pair(f14(X0,rotate_right(X1)),f13(X0,rotate_right(X1)))))),X1),f11(non_ordered_pair(non_ordered_pair(f12(X0,rotate_right(X1)),f12(X0,rotate_right(X1))),non_ordered_pair(f12(X0,rotate_right(X1)),non_ordered_pair(non_ordered_pair(f14(X0,rotate_right(X1)),f14(X0,rotate_right(X1))),non_ordered_pair(f14(X0,rotate_right(X1)),f13(X0,rotate_right(X1)))))),X1))))) )
| ~ spl0_143
| ~ spl0_144 ),
inference(resolution,[],[f1783,f1779]) ).
fof(f57094,plain,
( spl0_1500
| ~ spl0_137
| ~ spl0_145 ),
inference(avatar_split_clause,[],[f1913,f1786,f1634,f57092]) ).
fof(f57092,plain,
( spl0_1500
<=> ! [X2,X0,X1] :
( ~ member(X0,rotate_right(compose(X1,X2)))
| non_ordered_pair(non_ordered_pair(f10(X0,compose(X1,X2)),f10(X0,compose(X1,X2))),non_ordered_pair(f10(X0,compose(X1,X2)),non_ordered_pair(non_ordered_pair(f11(X0,compose(X1,X2)),f11(X0,compose(X1,X2))),non_ordered_pair(f11(X0,compose(X1,X2)),f9(X0,compose(X1,X2)))))) = non_ordered_pair(non_ordered_pair(f29(non_ordered_pair(non_ordered_pair(f10(X0,compose(X1,X2)),f10(X0,compose(X1,X2))),non_ordered_pair(f10(X0,compose(X1,X2)),non_ordered_pair(non_ordered_pair(f11(X0,compose(X1,X2)),f11(X0,compose(X1,X2))),non_ordered_pair(f11(X0,compose(X1,X2)),f9(X0,compose(X1,X2)))))),X1,X2),f29(non_ordered_pair(non_ordered_pair(f10(X0,compose(X1,X2)),f10(X0,compose(X1,X2))),non_ordered_pair(f10(X0,compose(X1,X2)),non_ordered_pair(non_ordered_pair(f11(X0,compose(X1,X2)),f11(X0,compose(X1,X2))),non_ordered_pair(f11(X0,compose(X1,X2)),f9(X0,compose(X1,X2)))))),X1,X2)),non_ordered_pair(f29(non_ordered_pair(non_ordered_pair(f10(X0,compose(X1,X2)),f10(X0,compose(X1,X2))),non_ordered_pair(f10(X0,compose(X1,X2)),non_ordered_pair(non_ordered_pair(f11(X0,compose(X1,X2)),f11(X0,compose(X1,X2))),non_ordered_pair(f11(X0,compose(X1,X2)),f9(X0,compose(X1,X2)))))),X1,X2),f30(non_ordered_pair(non_ordered_pair(f10(X0,compose(X1,X2)),f10(X0,compose(X1,X2))),non_ordered_pair(f10(X0,compose(X1,X2)),non_ordered_pair(non_ordered_pair(f11(X0,compose(X1,X2)),f11(X0,compose(X1,X2))),non_ordered_pair(f11(X0,compose(X1,X2)),f9(X0,compose(X1,X2)))))),X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1500])]) ).
fof(f1634,plain,
( spl0_137
<=> ! [X9,X7,X3] :
( ~ member(X3,compose(X7,X9))
| non_ordered_pair(non_ordered_pair(f29(X3,X7,X9),f29(X3,X7,X9)),non_ordered_pair(f29(X3,X7,X9),f30(X3,X7,X9))) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_137])]) ).
fof(f1913,plain,
( ! [X2,X0,X1] :
( ~ member(X0,rotate_right(compose(X1,X2)))
| non_ordered_pair(non_ordered_pair(f10(X0,compose(X1,X2)),f10(X0,compose(X1,X2))),non_ordered_pair(f10(X0,compose(X1,X2)),non_ordered_pair(non_ordered_pair(f11(X0,compose(X1,X2)),f11(X0,compose(X1,X2))),non_ordered_pair(f11(X0,compose(X1,X2)),f9(X0,compose(X1,X2)))))) = non_ordered_pair(non_ordered_pair(f29(non_ordered_pair(non_ordered_pair(f10(X0,compose(X1,X2)),f10(X0,compose(X1,X2))),non_ordered_pair(f10(X0,compose(X1,X2)),non_ordered_pair(non_ordered_pair(f11(X0,compose(X1,X2)),f11(X0,compose(X1,X2))),non_ordered_pair(f11(X0,compose(X1,X2)),f9(X0,compose(X1,X2)))))),X1,X2),f29(non_ordered_pair(non_ordered_pair(f10(X0,compose(X1,X2)),f10(X0,compose(X1,X2))),non_ordered_pair(f10(X0,compose(X1,X2)),non_ordered_pair(non_ordered_pair(f11(X0,compose(X1,X2)),f11(X0,compose(X1,X2))),non_ordered_pair(f11(X0,compose(X1,X2)),f9(X0,compose(X1,X2)))))),X1,X2)),non_ordered_pair(f29(non_ordered_pair(non_ordered_pair(f10(X0,compose(X1,X2)),f10(X0,compose(X1,X2))),non_ordered_pair(f10(X0,compose(X1,X2)),non_ordered_pair(non_ordered_pair(f11(X0,compose(X1,X2)),f11(X0,compose(X1,X2))),non_ordered_pair(f11(X0,compose(X1,X2)),f9(X0,compose(X1,X2)))))),X1,X2),f30(non_ordered_pair(non_ordered_pair(f10(X0,compose(X1,X2)),f10(X0,compose(X1,X2))),non_ordered_pair(f10(X0,compose(X1,X2)),non_ordered_pair(non_ordered_pair(f11(X0,compose(X1,X2)),f11(X0,compose(X1,X2))),non_ordered_pair(f11(X0,compose(X1,X2)),f9(X0,compose(X1,X2)))))),X1,X2))) )
| ~ spl0_137
| ~ spl0_145 ),
inference(resolution,[],[f1787,f1635]) ).
fof(f1635,plain,
( ! [X3,X9,X7] :
( ~ member(X3,compose(X7,X9))
| non_ordered_pair(non_ordered_pair(f29(X3,X7,X9),f29(X3,X7,X9)),non_ordered_pair(f29(X3,X7,X9),f30(X3,X7,X9))) = X3 )
| ~ spl0_137 ),
inference(avatar_component_clause,[],[f1634]) ).
fof(f57090,plain,
( spl0_1499
| ~ spl0_137
| ~ spl0_144 ),
inference(avatar_split_clause,[],[f1870,f1782,f1634,f57088]) ).
fof(f57088,plain,
( spl0_1499
<=> ! [X2,X0,X1] :
( ~ member(X0,flip_range_of(compose(X1,X2)))
| non_ordered_pair(non_ordered_pair(f12(X0,compose(X1,X2)),f12(X0,compose(X1,X2))),non_ordered_pair(f12(X0,compose(X1,X2)),non_ordered_pair(non_ordered_pair(f14(X0,compose(X1,X2)),f14(X0,compose(X1,X2))),non_ordered_pair(f14(X0,compose(X1,X2)),f13(X0,compose(X1,X2)))))) = non_ordered_pair(non_ordered_pair(f29(non_ordered_pair(non_ordered_pair(f12(X0,compose(X1,X2)),f12(X0,compose(X1,X2))),non_ordered_pair(f12(X0,compose(X1,X2)),non_ordered_pair(non_ordered_pair(f14(X0,compose(X1,X2)),f14(X0,compose(X1,X2))),non_ordered_pair(f14(X0,compose(X1,X2)),f13(X0,compose(X1,X2)))))),X1,X2),f29(non_ordered_pair(non_ordered_pair(f12(X0,compose(X1,X2)),f12(X0,compose(X1,X2))),non_ordered_pair(f12(X0,compose(X1,X2)),non_ordered_pair(non_ordered_pair(f14(X0,compose(X1,X2)),f14(X0,compose(X1,X2))),non_ordered_pair(f14(X0,compose(X1,X2)),f13(X0,compose(X1,X2)))))),X1,X2)),non_ordered_pair(f29(non_ordered_pair(non_ordered_pair(f12(X0,compose(X1,X2)),f12(X0,compose(X1,X2))),non_ordered_pair(f12(X0,compose(X1,X2)),non_ordered_pair(non_ordered_pair(f14(X0,compose(X1,X2)),f14(X0,compose(X1,X2))),non_ordered_pair(f14(X0,compose(X1,X2)),f13(X0,compose(X1,X2)))))),X1,X2),f30(non_ordered_pair(non_ordered_pair(f12(X0,compose(X1,X2)),f12(X0,compose(X1,X2))),non_ordered_pair(f12(X0,compose(X1,X2)),non_ordered_pair(non_ordered_pair(f14(X0,compose(X1,X2)),f14(X0,compose(X1,X2))),non_ordered_pair(f14(X0,compose(X1,X2)),f13(X0,compose(X1,X2)))))),X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1499])]) ).
fof(f1870,plain,
( ! [X2,X0,X1] :
( ~ member(X0,flip_range_of(compose(X1,X2)))
| non_ordered_pair(non_ordered_pair(f12(X0,compose(X1,X2)),f12(X0,compose(X1,X2))),non_ordered_pair(f12(X0,compose(X1,X2)),non_ordered_pair(non_ordered_pair(f14(X0,compose(X1,X2)),f14(X0,compose(X1,X2))),non_ordered_pair(f14(X0,compose(X1,X2)),f13(X0,compose(X1,X2)))))) = non_ordered_pair(non_ordered_pair(f29(non_ordered_pair(non_ordered_pair(f12(X0,compose(X1,X2)),f12(X0,compose(X1,X2))),non_ordered_pair(f12(X0,compose(X1,X2)),non_ordered_pair(non_ordered_pair(f14(X0,compose(X1,X2)),f14(X0,compose(X1,X2))),non_ordered_pair(f14(X0,compose(X1,X2)),f13(X0,compose(X1,X2)))))),X1,X2),f29(non_ordered_pair(non_ordered_pair(f12(X0,compose(X1,X2)),f12(X0,compose(X1,X2))),non_ordered_pair(f12(X0,compose(X1,X2)),non_ordered_pair(non_ordered_pair(f14(X0,compose(X1,X2)),f14(X0,compose(X1,X2))),non_ordered_pair(f14(X0,compose(X1,X2)),f13(X0,compose(X1,X2)))))),X1,X2)),non_ordered_pair(f29(non_ordered_pair(non_ordered_pair(f12(X0,compose(X1,X2)),f12(X0,compose(X1,X2))),non_ordered_pair(f12(X0,compose(X1,X2)),non_ordered_pair(non_ordered_pair(f14(X0,compose(X1,X2)),f14(X0,compose(X1,X2))),non_ordered_pair(f14(X0,compose(X1,X2)),f13(X0,compose(X1,X2)))))),X1,X2),f30(non_ordered_pair(non_ordered_pair(f12(X0,compose(X1,X2)),f12(X0,compose(X1,X2))),non_ordered_pair(f12(X0,compose(X1,X2)),non_ordered_pair(non_ordered_pair(f14(X0,compose(X1,X2)),f14(X0,compose(X1,X2))),non_ordered_pair(f14(X0,compose(X1,X2)),f13(X0,compose(X1,X2)))))),X1,X2))) )
| ~ spl0_137
| ~ spl0_144 ),
inference(resolution,[],[f1783,f1635]) ).
fof(f56678,plain,
( spl0_1498
| ~ spl0_74
| ~ spl0_167 ),
inference(avatar_split_clause,[],[f2371,f2256,f628,f56676]) ).
fof(f56676,plain,
( spl0_1498
<=> ! [X0,X1] : ~ member(X0,domain_of(compose(X1,empty_set))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1498])]) ).
fof(f2371,plain,
( ! [X0,X1] : ~ member(X0,domain_of(compose(X1,empty_set)))
| ~ spl0_74
| ~ spl0_167 ),
inference(resolution,[],[f2257,f629]) ).
fof(f56269,plain,
( spl0_1497
| ~ spl0_138
| ~ spl0_143 ),
inference(avatar_split_clause,[],[f1816,f1778,f1638,f56267]) ).
fof(f56267,plain,
( spl0_1497
<=> ! [X2,X0,X1] :
( non_ordered_pair(non_ordered_pair(f31(X0,X1,rotate_right(X2)),f31(X0,X1,rotate_right(X2))),non_ordered_pair(f31(X0,X1,rotate_right(X2)),f30(X0,X1,rotate_right(X2)))) = non_ordered_pair(non_ordered_pair(f9(non_ordered_pair(non_ordered_pair(f31(X0,X1,rotate_right(X2)),f31(X0,X1,rotate_right(X2))),non_ordered_pair(f31(X0,X1,rotate_right(X2)),f30(X0,X1,rotate_right(X2)))),X2),f9(non_ordered_pair(non_ordered_pair(f31(X0,X1,rotate_right(X2)),f31(X0,X1,rotate_right(X2))),non_ordered_pair(f31(X0,X1,rotate_right(X2)),f30(X0,X1,rotate_right(X2)))),X2)),non_ordered_pair(f9(non_ordered_pair(non_ordered_pair(f31(X0,X1,rotate_right(X2)),f31(X0,X1,rotate_right(X2))),non_ordered_pair(f31(X0,X1,rotate_right(X2)),f30(X0,X1,rotate_right(X2)))),X2),non_ordered_pair(non_ordered_pair(f10(non_ordered_pair(non_ordered_pair(f31(X0,X1,rotate_right(X2)),f31(X0,X1,rotate_right(X2))),non_ordered_pair(f31(X0,X1,rotate_right(X2)),f30(X0,X1,rotate_right(X2)))),X2),f10(non_ordered_pair(non_ordered_pair(f31(X0,X1,rotate_right(X2)),f31(X0,X1,rotate_right(X2))),non_ordered_pair(f31(X0,X1,rotate_right(X2)),f30(X0,X1,rotate_right(X2)))),X2)),non_ordered_pair(f10(non_ordered_pair(non_ordered_pair(f31(X0,X1,rotate_right(X2)),f31(X0,X1,rotate_right(X2))),non_ordered_pair(f31(X0,X1,rotate_right(X2)),f30(X0,X1,rotate_right(X2)))),X2),f11(non_ordered_pair(non_ordered_pair(f31(X0,X1,rotate_right(X2)),f31(X0,X1,rotate_right(X2))),non_ordered_pair(f31(X0,X1,rotate_right(X2)),f30(X0,X1,rotate_right(X2)))),X2)))))
| ~ member(X0,compose(X1,rotate_right(X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1497])]) ).
fof(f1816,plain,
( ! [X2,X0,X1] :
( non_ordered_pair(non_ordered_pair(f31(X0,X1,rotate_right(X2)),f31(X0,X1,rotate_right(X2))),non_ordered_pair(f31(X0,X1,rotate_right(X2)),f30(X0,X1,rotate_right(X2)))) = non_ordered_pair(non_ordered_pair(f9(non_ordered_pair(non_ordered_pair(f31(X0,X1,rotate_right(X2)),f31(X0,X1,rotate_right(X2))),non_ordered_pair(f31(X0,X1,rotate_right(X2)),f30(X0,X1,rotate_right(X2)))),X2),f9(non_ordered_pair(non_ordered_pair(f31(X0,X1,rotate_right(X2)),f31(X0,X1,rotate_right(X2))),non_ordered_pair(f31(X0,X1,rotate_right(X2)),f30(X0,X1,rotate_right(X2)))),X2)),non_ordered_pair(f9(non_ordered_pair(non_ordered_pair(f31(X0,X1,rotate_right(X2)),f31(X0,X1,rotate_right(X2))),non_ordered_pair(f31(X0,X1,rotate_right(X2)),f30(X0,X1,rotate_right(X2)))),X2),non_ordered_pair(non_ordered_pair(f10(non_ordered_pair(non_ordered_pair(f31(X0,X1,rotate_right(X2)),f31(X0,X1,rotate_right(X2))),non_ordered_pair(f31(X0,X1,rotate_right(X2)),f30(X0,X1,rotate_right(X2)))),X2),f10(non_ordered_pair(non_ordered_pair(f31(X0,X1,rotate_right(X2)),f31(X0,X1,rotate_right(X2))),non_ordered_pair(f31(X0,X1,rotate_right(X2)),f30(X0,X1,rotate_right(X2)))),X2)),non_ordered_pair(f10(non_ordered_pair(non_ordered_pair(f31(X0,X1,rotate_right(X2)),f31(X0,X1,rotate_right(X2))),non_ordered_pair(f31(X0,X1,rotate_right(X2)),f30(X0,X1,rotate_right(X2)))),X2),f11(non_ordered_pair(non_ordered_pair(f31(X0,X1,rotate_right(X2)),f31(X0,X1,rotate_right(X2))),non_ordered_pair(f31(X0,X1,rotate_right(X2)),f30(X0,X1,rotate_right(X2)))),X2)))))
| ~ member(X0,compose(X1,rotate_right(X2))) )
| ~ spl0_138
| ~ spl0_143 ),
inference(resolution,[],[f1779,f1639]) ).
fof(f56265,plain,
( spl0_1496
| ~ spl0_139
| ~ spl0_143 ),
inference(avatar_split_clause,[],[f1815,f1778,f1642,f56263]) ).
fof(f56263,plain,
( spl0_1496
<=> ! [X2,X0,X1] :
( non_ordered_pair(non_ordered_pair(f29(X0,rotate_right(X1),X2),f29(X0,rotate_right(X1),X2)),non_ordered_pair(f29(X0,rotate_right(X1),X2),f31(X0,rotate_right(X1),X2))) = non_ordered_pair(non_ordered_pair(f9(non_ordered_pair(non_ordered_pair(f29(X0,rotate_right(X1),X2),f29(X0,rotate_right(X1),X2)),non_ordered_pair(f29(X0,rotate_right(X1),X2),f31(X0,rotate_right(X1),X2))),X1),f9(non_ordered_pair(non_ordered_pair(f29(X0,rotate_right(X1),X2),f29(X0,rotate_right(X1),X2)),non_ordered_pair(f29(X0,rotate_right(X1),X2),f31(X0,rotate_right(X1),X2))),X1)),non_ordered_pair(f9(non_ordered_pair(non_ordered_pair(f29(X0,rotate_right(X1),X2),f29(X0,rotate_right(X1),X2)),non_ordered_pair(f29(X0,rotate_right(X1),X2),f31(X0,rotate_right(X1),X2))),X1),non_ordered_pair(non_ordered_pair(f10(non_ordered_pair(non_ordered_pair(f29(X0,rotate_right(X1),X2),f29(X0,rotate_right(X1),X2)),non_ordered_pair(f29(X0,rotate_right(X1),X2),f31(X0,rotate_right(X1),X2))),X1),f10(non_ordered_pair(non_ordered_pair(f29(X0,rotate_right(X1),X2),f29(X0,rotate_right(X1),X2)),non_ordered_pair(f29(X0,rotate_right(X1),X2),f31(X0,rotate_right(X1),X2))),X1)),non_ordered_pair(f10(non_ordered_pair(non_ordered_pair(f29(X0,rotate_right(X1),X2),f29(X0,rotate_right(X1),X2)),non_ordered_pair(f29(X0,rotate_right(X1),X2),f31(X0,rotate_right(X1),X2))),X1),f11(non_ordered_pair(non_ordered_pair(f29(X0,rotate_right(X1),X2),f29(X0,rotate_right(X1),X2)),non_ordered_pair(f29(X0,rotate_right(X1),X2),f31(X0,rotate_right(X1),X2))),X1)))))
| ~ member(X0,compose(rotate_right(X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1496])]) ).
fof(f1815,plain,
( ! [X2,X0,X1] :
( non_ordered_pair(non_ordered_pair(f29(X0,rotate_right(X1),X2),f29(X0,rotate_right(X1),X2)),non_ordered_pair(f29(X0,rotate_right(X1),X2),f31(X0,rotate_right(X1),X2))) = non_ordered_pair(non_ordered_pair(f9(non_ordered_pair(non_ordered_pair(f29(X0,rotate_right(X1),X2),f29(X0,rotate_right(X1),X2)),non_ordered_pair(f29(X0,rotate_right(X1),X2),f31(X0,rotate_right(X1),X2))),X1),f9(non_ordered_pair(non_ordered_pair(f29(X0,rotate_right(X1),X2),f29(X0,rotate_right(X1),X2)),non_ordered_pair(f29(X0,rotate_right(X1),X2),f31(X0,rotate_right(X1),X2))),X1)),non_ordered_pair(f9(non_ordered_pair(non_ordered_pair(f29(X0,rotate_right(X1),X2),f29(X0,rotate_right(X1),X2)),non_ordered_pair(f29(X0,rotate_right(X1),X2),f31(X0,rotate_right(X1),X2))),X1),non_ordered_pair(non_ordered_pair(f10(non_ordered_pair(non_ordered_pair(f29(X0,rotate_right(X1),X2),f29(X0,rotate_right(X1),X2)),non_ordered_pair(f29(X0,rotate_right(X1),X2),f31(X0,rotate_right(X1),X2))),X1),f10(non_ordered_pair(non_ordered_pair(f29(X0,rotate_right(X1),X2),f29(X0,rotate_right(X1),X2)),non_ordered_pair(f29(X0,rotate_right(X1),X2),f31(X0,rotate_right(X1),X2))),X1)),non_ordered_pair(f10(non_ordered_pair(non_ordered_pair(f29(X0,rotate_right(X1),X2),f29(X0,rotate_right(X1),X2)),non_ordered_pair(f29(X0,rotate_right(X1),X2),f31(X0,rotate_right(X1),X2))),X1),f11(non_ordered_pair(non_ordered_pair(f29(X0,rotate_right(X1),X2),f29(X0,rotate_right(X1),X2)),non_ordered_pair(f29(X0,rotate_right(X1),X2),f31(X0,rotate_right(X1),X2))),X1)))))
| ~ member(X0,compose(rotate_right(X1),X2)) )
| ~ spl0_139
| ~ spl0_143 ),
inference(resolution,[],[f1779,f1643]) ).
fof(f56261,plain,
( spl0_1495
| ~ spl0_138
| ~ spl0_142 ),
inference(avatar_split_clause,[],[f1795,f1774,f1638,f56259]) ).
fof(f56259,plain,
( spl0_1495
<=> ! [X2,X0,X1] :
( non_ordered_pair(non_ordered_pair(f31(X0,X1,flip_range_of(X2)),f31(X0,X1,flip_range_of(X2))),non_ordered_pair(f31(X0,X1,flip_range_of(X2)),f30(X0,X1,flip_range_of(X2)))) = non_ordered_pair(non_ordered_pair(f12(non_ordered_pair(non_ordered_pair(f31(X0,X1,flip_range_of(X2)),f31(X0,X1,flip_range_of(X2))),non_ordered_pair(f31(X0,X1,flip_range_of(X2)),f30(X0,X1,flip_range_of(X2)))),X2),f12(non_ordered_pair(non_ordered_pair(f31(X0,X1,flip_range_of(X2)),f31(X0,X1,flip_range_of(X2))),non_ordered_pair(f31(X0,X1,flip_range_of(X2)),f30(X0,X1,flip_range_of(X2)))),X2)),non_ordered_pair(f12(non_ordered_pair(non_ordered_pair(f31(X0,X1,flip_range_of(X2)),f31(X0,X1,flip_range_of(X2))),non_ordered_pair(f31(X0,X1,flip_range_of(X2)),f30(X0,X1,flip_range_of(X2)))),X2),non_ordered_pair(non_ordered_pair(f13(non_ordered_pair(non_ordered_pair(f31(X0,X1,flip_range_of(X2)),f31(X0,X1,flip_range_of(X2))),non_ordered_pair(f31(X0,X1,flip_range_of(X2)),f30(X0,X1,flip_range_of(X2)))),X2),f13(non_ordered_pair(non_ordered_pair(f31(X0,X1,flip_range_of(X2)),f31(X0,X1,flip_range_of(X2))),non_ordered_pair(f31(X0,X1,flip_range_of(X2)),f30(X0,X1,flip_range_of(X2)))),X2)),non_ordered_pair(f13(non_ordered_pair(non_ordered_pair(f31(X0,X1,flip_range_of(X2)),f31(X0,X1,flip_range_of(X2))),non_ordered_pair(f31(X0,X1,flip_range_of(X2)),f30(X0,X1,flip_range_of(X2)))),X2),f14(non_ordered_pair(non_ordered_pair(f31(X0,X1,flip_range_of(X2)),f31(X0,X1,flip_range_of(X2))),non_ordered_pair(f31(X0,X1,flip_range_of(X2)),f30(X0,X1,flip_range_of(X2)))),X2)))))
| ~ member(X0,compose(X1,flip_range_of(X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1495])]) ).
fof(f1795,plain,
( ! [X2,X0,X1] :
( non_ordered_pair(non_ordered_pair(f31(X0,X1,flip_range_of(X2)),f31(X0,X1,flip_range_of(X2))),non_ordered_pair(f31(X0,X1,flip_range_of(X2)),f30(X0,X1,flip_range_of(X2)))) = non_ordered_pair(non_ordered_pair(f12(non_ordered_pair(non_ordered_pair(f31(X0,X1,flip_range_of(X2)),f31(X0,X1,flip_range_of(X2))),non_ordered_pair(f31(X0,X1,flip_range_of(X2)),f30(X0,X1,flip_range_of(X2)))),X2),f12(non_ordered_pair(non_ordered_pair(f31(X0,X1,flip_range_of(X2)),f31(X0,X1,flip_range_of(X2))),non_ordered_pair(f31(X0,X1,flip_range_of(X2)),f30(X0,X1,flip_range_of(X2)))),X2)),non_ordered_pair(f12(non_ordered_pair(non_ordered_pair(f31(X0,X1,flip_range_of(X2)),f31(X0,X1,flip_range_of(X2))),non_ordered_pair(f31(X0,X1,flip_range_of(X2)),f30(X0,X1,flip_range_of(X2)))),X2),non_ordered_pair(non_ordered_pair(f13(non_ordered_pair(non_ordered_pair(f31(X0,X1,flip_range_of(X2)),f31(X0,X1,flip_range_of(X2))),non_ordered_pair(f31(X0,X1,flip_range_of(X2)),f30(X0,X1,flip_range_of(X2)))),X2),f13(non_ordered_pair(non_ordered_pair(f31(X0,X1,flip_range_of(X2)),f31(X0,X1,flip_range_of(X2))),non_ordered_pair(f31(X0,X1,flip_range_of(X2)),f30(X0,X1,flip_range_of(X2)))),X2)),non_ordered_pair(f13(non_ordered_pair(non_ordered_pair(f31(X0,X1,flip_range_of(X2)),f31(X0,X1,flip_range_of(X2))),non_ordered_pair(f31(X0,X1,flip_range_of(X2)),f30(X0,X1,flip_range_of(X2)))),X2),f14(non_ordered_pair(non_ordered_pair(f31(X0,X1,flip_range_of(X2)),f31(X0,X1,flip_range_of(X2))),non_ordered_pair(f31(X0,X1,flip_range_of(X2)),f30(X0,X1,flip_range_of(X2)))),X2)))))
| ~ member(X0,compose(X1,flip_range_of(X2))) )
| ~ spl0_138
| ~ spl0_142 ),
inference(resolution,[],[f1775,f1639]) ).
fof(f56257,plain,
( spl0_1494
| ~ spl0_139
| ~ spl0_142 ),
inference(avatar_split_clause,[],[f1794,f1774,f1642,f56255]) ).
fof(f56255,plain,
( spl0_1494
<=> ! [X2,X0,X1] :
( non_ordered_pair(non_ordered_pair(f29(X0,flip_range_of(X1),X2),f29(X0,flip_range_of(X1),X2)),non_ordered_pair(f29(X0,flip_range_of(X1),X2),f31(X0,flip_range_of(X1),X2))) = non_ordered_pair(non_ordered_pair(f12(non_ordered_pair(non_ordered_pair(f29(X0,flip_range_of(X1),X2),f29(X0,flip_range_of(X1),X2)),non_ordered_pair(f29(X0,flip_range_of(X1),X2),f31(X0,flip_range_of(X1),X2))),X1),f12(non_ordered_pair(non_ordered_pair(f29(X0,flip_range_of(X1),X2),f29(X0,flip_range_of(X1),X2)),non_ordered_pair(f29(X0,flip_range_of(X1),X2),f31(X0,flip_range_of(X1),X2))),X1)),non_ordered_pair(f12(non_ordered_pair(non_ordered_pair(f29(X0,flip_range_of(X1),X2),f29(X0,flip_range_of(X1),X2)),non_ordered_pair(f29(X0,flip_range_of(X1),X2),f31(X0,flip_range_of(X1),X2))),X1),non_ordered_pair(non_ordered_pair(f13(non_ordered_pair(non_ordered_pair(f29(X0,flip_range_of(X1),X2),f29(X0,flip_range_of(X1),X2)),non_ordered_pair(f29(X0,flip_range_of(X1),X2),f31(X0,flip_range_of(X1),X2))),X1),f13(non_ordered_pair(non_ordered_pair(f29(X0,flip_range_of(X1),X2),f29(X0,flip_range_of(X1),X2)),non_ordered_pair(f29(X0,flip_range_of(X1),X2),f31(X0,flip_range_of(X1),X2))),X1)),non_ordered_pair(f13(non_ordered_pair(non_ordered_pair(f29(X0,flip_range_of(X1),X2),f29(X0,flip_range_of(X1),X2)),non_ordered_pair(f29(X0,flip_range_of(X1),X2),f31(X0,flip_range_of(X1),X2))),X1),f14(non_ordered_pair(non_ordered_pair(f29(X0,flip_range_of(X1),X2),f29(X0,flip_range_of(X1),X2)),non_ordered_pair(f29(X0,flip_range_of(X1),X2),f31(X0,flip_range_of(X1),X2))),X1)))))
| ~ member(X0,compose(flip_range_of(X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1494])]) ).
fof(f1794,plain,
( ! [X2,X0,X1] :
( non_ordered_pair(non_ordered_pair(f29(X0,flip_range_of(X1),X2),f29(X0,flip_range_of(X1),X2)),non_ordered_pair(f29(X0,flip_range_of(X1),X2),f31(X0,flip_range_of(X1),X2))) = non_ordered_pair(non_ordered_pair(f12(non_ordered_pair(non_ordered_pair(f29(X0,flip_range_of(X1),X2),f29(X0,flip_range_of(X1),X2)),non_ordered_pair(f29(X0,flip_range_of(X1),X2),f31(X0,flip_range_of(X1),X2))),X1),f12(non_ordered_pair(non_ordered_pair(f29(X0,flip_range_of(X1),X2),f29(X0,flip_range_of(X1),X2)),non_ordered_pair(f29(X0,flip_range_of(X1),X2),f31(X0,flip_range_of(X1),X2))),X1)),non_ordered_pair(f12(non_ordered_pair(non_ordered_pair(f29(X0,flip_range_of(X1),X2),f29(X0,flip_range_of(X1),X2)),non_ordered_pair(f29(X0,flip_range_of(X1),X2),f31(X0,flip_range_of(X1),X2))),X1),non_ordered_pair(non_ordered_pair(f13(non_ordered_pair(non_ordered_pair(f29(X0,flip_range_of(X1),X2),f29(X0,flip_range_of(X1),X2)),non_ordered_pair(f29(X0,flip_range_of(X1),X2),f31(X0,flip_range_of(X1),X2))),X1),f13(non_ordered_pair(non_ordered_pair(f29(X0,flip_range_of(X1),X2),f29(X0,flip_range_of(X1),X2)),non_ordered_pair(f29(X0,flip_range_of(X1),X2),f31(X0,flip_range_of(X1),X2))),X1)),non_ordered_pair(f13(non_ordered_pair(non_ordered_pair(f29(X0,flip_range_of(X1),X2),f29(X0,flip_range_of(X1),X2)),non_ordered_pair(f29(X0,flip_range_of(X1),X2),f31(X0,flip_range_of(X1),X2))),X1),f14(non_ordered_pair(non_ordered_pair(f29(X0,flip_range_of(X1),X2),f29(X0,flip_range_of(X1),X2)),non_ordered_pair(f29(X0,flip_range_of(X1),X2),f31(X0,flip_range_of(X1),X2))),X1)))))
| ~ member(X0,compose(flip_range_of(X1),X2)) )
| ~ spl0_139
| ~ spl0_142 ),
inference(resolution,[],[f1775,f1643]) ).
fof(f55844,plain,
( spl0_1493
| ~ spl0_137
| ~ spl0_139 ),
inference(avatar_split_clause,[],[f1740,f1642,f1634,f55842]) ).
fof(f55842,plain,
( spl0_1493
<=> ! [X0,X3,X2,X1] :
( ~ member(X0,compose(compose(X1,X2),X3))
| non_ordered_pair(non_ordered_pair(f29(X0,compose(X1,X2),X3),f29(X0,compose(X1,X2),X3)),non_ordered_pair(f29(X0,compose(X1,X2),X3),f31(X0,compose(X1,X2),X3))) = non_ordered_pair(non_ordered_pair(f29(non_ordered_pair(non_ordered_pair(f29(X0,compose(X1,X2),X3),f29(X0,compose(X1,X2),X3)),non_ordered_pair(f29(X0,compose(X1,X2),X3),f31(X0,compose(X1,X2),X3))),X1,X2),f29(non_ordered_pair(non_ordered_pair(f29(X0,compose(X1,X2),X3),f29(X0,compose(X1,X2),X3)),non_ordered_pair(f29(X0,compose(X1,X2),X3),f31(X0,compose(X1,X2),X3))),X1,X2)),non_ordered_pair(f29(non_ordered_pair(non_ordered_pair(f29(X0,compose(X1,X2),X3),f29(X0,compose(X1,X2),X3)),non_ordered_pair(f29(X0,compose(X1,X2),X3),f31(X0,compose(X1,X2),X3))),X1,X2),f30(non_ordered_pair(non_ordered_pair(f29(X0,compose(X1,X2),X3),f29(X0,compose(X1,X2),X3)),non_ordered_pair(f29(X0,compose(X1,X2),X3),f31(X0,compose(X1,X2),X3))),X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1493])]) ).
fof(f1740,plain,
( ! [X2,X3,X0,X1] :
( ~ member(X0,compose(compose(X1,X2),X3))
| non_ordered_pair(non_ordered_pair(f29(X0,compose(X1,X2),X3),f29(X0,compose(X1,X2),X3)),non_ordered_pair(f29(X0,compose(X1,X2),X3),f31(X0,compose(X1,X2),X3))) = non_ordered_pair(non_ordered_pair(f29(non_ordered_pair(non_ordered_pair(f29(X0,compose(X1,X2),X3),f29(X0,compose(X1,X2),X3)),non_ordered_pair(f29(X0,compose(X1,X2),X3),f31(X0,compose(X1,X2),X3))),X1,X2),f29(non_ordered_pair(non_ordered_pair(f29(X0,compose(X1,X2),X3),f29(X0,compose(X1,X2),X3)),non_ordered_pair(f29(X0,compose(X1,X2),X3),f31(X0,compose(X1,X2),X3))),X1,X2)),non_ordered_pair(f29(non_ordered_pair(non_ordered_pair(f29(X0,compose(X1,X2),X3),f29(X0,compose(X1,X2),X3)),non_ordered_pair(f29(X0,compose(X1,X2),X3),f31(X0,compose(X1,X2),X3))),X1,X2),f30(non_ordered_pair(non_ordered_pair(f29(X0,compose(X1,X2),X3),f29(X0,compose(X1,X2),X3)),non_ordered_pair(f29(X0,compose(X1,X2),X3),f31(X0,compose(X1,X2),X3))),X1,X2))) )
| ~ spl0_137
| ~ spl0_139 ),
inference(resolution,[],[f1643,f1635]) ).
fof(f55840,plain,
( spl0_1492
| ~ spl0_137
| ~ spl0_138 ),
inference(avatar_split_clause,[],[f1700,f1638,f1634,f55838]) ).
fof(f55838,plain,
( spl0_1492
<=> ! [X0,X3,X2,X1] :
( ~ member(X0,compose(X1,compose(X2,X3)))
| non_ordered_pair(non_ordered_pair(f31(X0,X1,compose(X2,X3)),f31(X0,X1,compose(X2,X3))),non_ordered_pair(f31(X0,X1,compose(X2,X3)),f30(X0,X1,compose(X2,X3)))) = non_ordered_pair(non_ordered_pair(f29(non_ordered_pair(non_ordered_pair(f31(X0,X1,compose(X2,X3)),f31(X0,X1,compose(X2,X3))),non_ordered_pair(f31(X0,X1,compose(X2,X3)),f30(X0,X1,compose(X2,X3)))),X2,X3),f29(non_ordered_pair(non_ordered_pair(f31(X0,X1,compose(X2,X3)),f31(X0,X1,compose(X2,X3))),non_ordered_pair(f31(X0,X1,compose(X2,X3)),f30(X0,X1,compose(X2,X3)))),X2,X3)),non_ordered_pair(f29(non_ordered_pair(non_ordered_pair(f31(X0,X1,compose(X2,X3)),f31(X0,X1,compose(X2,X3))),non_ordered_pair(f31(X0,X1,compose(X2,X3)),f30(X0,X1,compose(X2,X3)))),X2,X3),f30(non_ordered_pair(non_ordered_pair(f31(X0,X1,compose(X2,X3)),f31(X0,X1,compose(X2,X3))),non_ordered_pair(f31(X0,X1,compose(X2,X3)),f30(X0,X1,compose(X2,X3)))),X2,X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1492])]) ).
fof(f1700,plain,
( ! [X2,X3,X0,X1] :
( ~ member(X0,compose(X1,compose(X2,X3)))
| non_ordered_pair(non_ordered_pair(f31(X0,X1,compose(X2,X3)),f31(X0,X1,compose(X2,X3))),non_ordered_pair(f31(X0,X1,compose(X2,X3)),f30(X0,X1,compose(X2,X3)))) = non_ordered_pair(non_ordered_pair(f29(non_ordered_pair(non_ordered_pair(f31(X0,X1,compose(X2,X3)),f31(X0,X1,compose(X2,X3))),non_ordered_pair(f31(X0,X1,compose(X2,X3)),f30(X0,X1,compose(X2,X3)))),X2,X3),f29(non_ordered_pair(non_ordered_pair(f31(X0,X1,compose(X2,X3)),f31(X0,X1,compose(X2,X3))),non_ordered_pair(f31(X0,X1,compose(X2,X3)),f30(X0,X1,compose(X2,X3)))),X2,X3)),non_ordered_pair(f29(non_ordered_pair(non_ordered_pair(f31(X0,X1,compose(X2,X3)),f31(X0,X1,compose(X2,X3))),non_ordered_pair(f31(X0,X1,compose(X2,X3)),f30(X0,X1,compose(X2,X3)))),X2,X3),f30(non_ordered_pair(non_ordered_pair(f31(X0,X1,compose(X2,X3)),f31(X0,X1,compose(X2,X3))),non_ordered_pair(f31(X0,X1,compose(X2,X3)),f30(X0,X1,compose(X2,X3)))),X2,X3))) )
| ~ spl0_137
| ~ spl0_138 ),
inference(resolution,[],[f1639,f1635]) ).
fof(f55833,plain,
( spl0_1491
| ~ spl0_145
| ~ spl0_167 ),
inference(avatar_split_clause,[],[f2368,f2256,f1786,f55831]) ).
fof(f55831,plain,
( spl0_1491
<=> ! [X0,X1] : ~ member(X0,rotate_right(compose(X1,empty_set))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1491])]) ).
fof(f2368,plain,
( ! [X0,X1] : ~ member(X0,rotate_right(compose(X1,empty_set)))
| ~ spl0_145
| ~ spl0_167 ),
inference(resolution,[],[f2257,f1787]) ).
fof(f55055,plain,
( spl0_1490
| ~ spl0_131
| ~ spl0_145 ),
inference(avatar_split_clause,[],[f1882,f1786,f1479,f55053]) ).
fof(f55053,plain,
( spl0_1490
<=> ! [X0,X1] :
( ~ member(X0,rotate_right(second(X1)))
| non_ordered_pair(non_ordered_pair(f6(non_ordered_pair(non_ordered_pair(f10(X0,second(X1)),f10(X0,second(X1))),non_ordered_pair(f10(X0,second(X1)),non_ordered_pair(non_ordered_pair(f11(X0,second(X1)),f11(X0,second(X1))),non_ordered_pair(f11(X0,second(X1)),f9(X0,second(X1)))))),X1),f6(non_ordered_pair(non_ordered_pair(f10(X0,second(X1)),f10(X0,second(X1))),non_ordered_pair(f10(X0,second(X1)),non_ordered_pair(non_ordered_pair(f11(X0,second(X1)),f11(X0,second(X1))),non_ordered_pair(f11(X0,second(X1)),f9(X0,second(X1)))))),X1)),non_ordered_pair(f6(non_ordered_pair(non_ordered_pair(f10(X0,second(X1)),f10(X0,second(X1))),non_ordered_pair(f10(X0,second(X1)),non_ordered_pair(non_ordered_pair(f11(X0,second(X1)),f11(X0,second(X1))),non_ordered_pair(f11(X0,second(X1)),f9(X0,second(X1)))))),X1),f7(non_ordered_pair(non_ordered_pair(f10(X0,second(X1)),f10(X0,second(X1))),non_ordered_pair(f10(X0,second(X1)),non_ordered_pair(non_ordered_pair(f11(X0,second(X1)),f11(X0,second(X1))),non_ordered_pair(f11(X0,second(X1)),f9(X0,second(X1)))))),X1))) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1490])]) ).
fof(f1479,plain,
( spl0_131
<=> ! [X0,X3] :
( ~ member(X3,second(X0))
| non_ordered_pair(non_ordered_pair(f6(X3,X0),f6(X3,X0)),non_ordered_pair(f6(X3,X0),f7(X3,X0))) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_131])]) ).
fof(f1882,plain,
( ! [X0,X1] :
( ~ member(X0,rotate_right(second(X1)))
| non_ordered_pair(non_ordered_pair(f6(non_ordered_pair(non_ordered_pair(f10(X0,second(X1)),f10(X0,second(X1))),non_ordered_pair(f10(X0,second(X1)),non_ordered_pair(non_ordered_pair(f11(X0,second(X1)),f11(X0,second(X1))),non_ordered_pair(f11(X0,second(X1)),f9(X0,second(X1)))))),X1),f6(non_ordered_pair(non_ordered_pair(f10(X0,second(X1)),f10(X0,second(X1))),non_ordered_pair(f10(X0,second(X1)),non_ordered_pair(non_ordered_pair(f11(X0,second(X1)),f11(X0,second(X1))),non_ordered_pair(f11(X0,second(X1)),f9(X0,second(X1)))))),X1)),non_ordered_pair(f6(non_ordered_pair(non_ordered_pair(f10(X0,second(X1)),f10(X0,second(X1))),non_ordered_pair(f10(X0,second(X1)),non_ordered_pair(non_ordered_pair(f11(X0,second(X1)),f11(X0,second(X1))),non_ordered_pair(f11(X0,second(X1)),f9(X0,second(X1)))))),X1),f7(non_ordered_pair(non_ordered_pair(f10(X0,second(X1)),f10(X0,second(X1))),non_ordered_pair(f10(X0,second(X1)),non_ordered_pair(non_ordered_pair(f11(X0,second(X1)),f11(X0,second(X1))),non_ordered_pair(f11(X0,second(X1)),f9(X0,second(X1)))))),X1))) = X1 )
| ~ spl0_131
| ~ spl0_145 ),
inference(resolution,[],[f1787,f1480]) ).
fof(f1480,plain,
( ! [X3,X0] :
( ~ member(X3,second(X0))
| non_ordered_pair(non_ordered_pair(f6(X3,X0),f6(X3,X0)),non_ordered_pair(f6(X3,X0),f7(X3,X0))) = X0 )
| ~ spl0_131 ),
inference(avatar_component_clause,[],[f1479]) ).
fof(f55051,plain,
( spl0_1489
| ~ spl0_132
| ~ spl0_145 ),
inference(avatar_split_clause,[],[f1879,f1786,f1483,f55049]) ).
fof(f55049,plain,
( spl0_1489
<=> ! [X0,X1] :
( ~ member(X0,rotate_right(first(X1)))
| non_ordered_pair(non_ordered_pair(f4(non_ordered_pair(non_ordered_pair(f10(X0,first(X1)),f10(X0,first(X1))),non_ordered_pair(f10(X0,first(X1)),non_ordered_pair(non_ordered_pair(f11(X0,first(X1)),f11(X0,first(X1))),non_ordered_pair(f11(X0,first(X1)),f9(X0,first(X1)))))),X1),f4(non_ordered_pair(non_ordered_pair(f10(X0,first(X1)),f10(X0,first(X1))),non_ordered_pair(f10(X0,first(X1)),non_ordered_pair(non_ordered_pair(f11(X0,first(X1)),f11(X0,first(X1))),non_ordered_pair(f11(X0,first(X1)),f9(X0,first(X1)))))),X1)),non_ordered_pair(f4(non_ordered_pair(non_ordered_pair(f10(X0,first(X1)),f10(X0,first(X1))),non_ordered_pair(f10(X0,first(X1)),non_ordered_pair(non_ordered_pair(f11(X0,first(X1)),f11(X0,first(X1))),non_ordered_pair(f11(X0,first(X1)),f9(X0,first(X1)))))),X1),f5(non_ordered_pair(non_ordered_pair(f10(X0,first(X1)),f10(X0,first(X1))),non_ordered_pair(f10(X0,first(X1)),non_ordered_pair(non_ordered_pair(f11(X0,first(X1)),f11(X0,first(X1))),non_ordered_pair(f11(X0,first(X1)),f9(X0,first(X1)))))),X1))) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1489])]) ).
fof(f1483,plain,
( spl0_132
<=> ! [X0,X3] :
( ~ member(X3,first(X0))
| non_ordered_pair(non_ordered_pair(f4(X3,X0),f4(X3,X0)),non_ordered_pair(f4(X3,X0),f5(X3,X0))) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_132])]) ).
fof(f1879,plain,
( ! [X0,X1] :
( ~ member(X0,rotate_right(first(X1)))
| non_ordered_pair(non_ordered_pair(f4(non_ordered_pair(non_ordered_pair(f10(X0,first(X1)),f10(X0,first(X1))),non_ordered_pair(f10(X0,first(X1)),non_ordered_pair(non_ordered_pair(f11(X0,first(X1)),f11(X0,first(X1))),non_ordered_pair(f11(X0,first(X1)),f9(X0,first(X1)))))),X1),f4(non_ordered_pair(non_ordered_pair(f10(X0,first(X1)),f10(X0,first(X1))),non_ordered_pair(f10(X0,first(X1)),non_ordered_pair(non_ordered_pair(f11(X0,first(X1)),f11(X0,first(X1))),non_ordered_pair(f11(X0,first(X1)),f9(X0,first(X1)))))),X1)),non_ordered_pair(f4(non_ordered_pair(non_ordered_pair(f10(X0,first(X1)),f10(X0,first(X1))),non_ordered_pair(f10(X0,first(X1)),non_ordered_pair(non_ordered_pair(f11(X0,first(X1)),f11(X0,first(X1))),non_ordered_pair(f11(X0,first(X1)),f9(X0,first(X1)))))),X1),f5(non_ordered_pair(non_ordered_pair(f10(X0,first(X1)),f10(X0,first(X1))),non_ordered_pair(f10(X0,first(X1)),non_ordered_pair(non_ordered_pair(f11(X0,first(X1)),f11(X0,first(X1))),non_ordered_pair(f11(X0,first(X1)),f9(X0,first(X1)))))),X1))) = X1 )
| ~ spl0_132
| ~ spl0_145 ),
inference(resolution,[],[f1787,f1484]) ).
fof(f1484,plain,
( ! [X3,X0] :
( ~ member(X3,first(X0))
| non_ordered_pair(non_ordered_pair(f4(X3,X0),f4(X3,X0)),non_ordered_pair(f4(X3,X0),f5(X3,X0))) = X0 )
| ~ spl0_132 ),
inference(avatar_component_clause,[],[f1483]) ).
fof(f55047,plain,
( spl0_1488
| ~ spl0_131
| ~ spl0_144 ),
inference(avatar_split_clause,[],[f1839,f1782,f1479,f55045]) ).
fof(f55045,plain,
( spl0_1488
<=> ! [X0,X1] :
( ~ member(X0,flip_range_of(second(X1)))
| non_ordered_pair(non_ordered_pair(f6(non_ordered_pair(non_ordered_pair(f12(X0,second(X1)),f12(X0,second(X1))),non_ordered_pair(f12(X0,second(X1)),non_ordered_pair(non_ordered_pair(f14(X0,second(X1)),f14(X0,second(X1))),non_ordered_pair(f14(X0,second(X1)),f13(X0,second(X1)))))),X1),f6(non_ordered_pair(non_ordered_pair(f12(X0,second(X1)),f12(X0,second(X1))),non_ordered_pair(f12(X0,second(X1)),non_ordered_pair(non_ordered_pair(f14(X0,second(X1)),f14(X0,second(X1))),non_ordered_pair(f14(X0,second(X1)),f13(X0,second(X1)))))),X1)),non_ordered_pair(f6(non_ordered_pair(non_ordered_pair(f12(X0,second(X1)),f12(X0,second(X1))),non_ordered_pair(f12(X0,second(X1)),non_ordered_pair(non_ordered_pair(f14(X0,second(X1)),f14(X0,second(X1))),non_ordered_pair(f14(X0,second(X1)),f13(X0,second(X1)))))),X1),f7(non_ordered_pair(non_ordered_pair(f12(X0,second(X1)),f12(X0,second(X1))),non_ordered_pair(f12(X0,second(X1)),non_ordered_pair(non_ordered_pair(f14(X0,second(X1)),f14(X0,second(X1))),non_ordered_pair(f14(X0,second(X1)),f13(X0,second(X1)))))),X1))) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1488])]) ).
fof(f1839,plain,
( ! [X0,X1] :
( ~ member(X0,flip_range_of(second(X1)))
| non_ordered_pair(non_ordered_pair(f6(non_ordered_pair(non_ordered_pair(f12(X0,second(X1)),f12(X0,second(X1))),non_ordered_pair(f12(X0,second(X1)),non_ordered_pair(non_ordered_pair(f14(X0,second(X1)),f14(X0,second(X1))),non_ordered_pair(f14(X0,second(X1)),f13(X0,second(X1)))))),X1),f6(non_ordered_pair(non_ordered_pair(f12(X0,second(X1)),f12(X0,second(X1))),non_ordered_pair(f12(X0,second(X1)),non_ordered_pair(non_ordered_pair(f14(X0,second(X1)),f14(X0,second(X1))),non_ordered_pair(f14(X0,second(X1)),f13(X0,second(X1)))))),X1)),non_ordered_pair(f6(non_ordered_pair(non_ordered_pair(f12(X0,second(X1)),f12(X0,second(X1))),non_ordered_pair(f12(X0,second(X1)),non_ordered_pair(non_ordered_pair(f14(X0,second(X1)),f14(X0,second(X1))),non_ordered_pair(f14(X0,second(X1)),f13(X0,second(X1)))))),X1),f7(non_ordered_pair(non_ordered_pair(f12(X0,second(X1)),f12(X0,second(X1))),non_ordered_pair(f12(X0,second(X1)),non_ordered_pair(non_ordered_pair(f14(X0,second(X1)),f14(X0,second(X1))),non_ordered_pair(f14(X0,second(X1)),f13(X0,second(X1)))))),X1))) = X1 )
| ~ spl0_131
| ~ spl0_144 ),
inference(resolution,[],[f1783,f1480]) ).
fof(f55043,plain,
( spl0_1487
| ~ spl0_132
| ~ spl0_144 ),
inference(avatar_split_clause,[],[f1836,f1782,f1483,f55041]) ).
fof(f55041,plain,
( spl0_1487
<=> ! [X0,X1] :
( ~ member(X0,flip_range_of(first(X1)))
| non_ordered_pair(non_ordered_pair(f4(non_ordered_pair(non_ordered_pair(f12(X0,first(X1)),f12(X0,first(X1))),non_ordered_pair(f12(X0,first(X1)),non_ordered_pair(non_ordered_pair(f14(X0,first(X1)),f14(X0,first(X1))),non_ordered_pair(f14(X0,first(X1)),f13(X0,first(X1)))))),X1),f4(non_ordered_pair(non_ordered_pair(f12(X0,first(X1)),f12(X0,first(X1))),non_ordered_pair(f12(X0,first(X1)),non_ordered_pair(non_ordered_pair(f14(X0,first(X1)),f14(X0,first(X1))),non_ordered_pair(f14(X0,first(X1)),f13(X0,first(X1)))))),X1)),non_ordered_pair(f4(non_ordered_pair(non_ordered_pair(f12(X0,first(X1)),f12(X0,first(X1))),non_ordered_pair(f12(X0,first(X1)),non_ordered_pair(non_ordered_pair(f14(X0,first(X1)),f14(X0,first(X1))),non_ordered_pair(f14(X0,first(X1)),f13(X0,first(X1)))))),X1),f5(non_ordered_pair(non_ordered_pair(f12(X0,first(X1)),f12(X0,first(X1))),non_ordered_pair(f12(X0,first(X1)),non_ordered_pair(non_ordered_pair(f14(X0,first(X1)),f14(X0,first(X1))),non_ordered_pair(f14(X0,first(X1)),f13(X0,first(X1)))))),X1))) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1487])]) ).
fof(f1836,plain,
( ! [X0,X1] :
( ~ member(X0,flip_range_of(first(X1)))
| non_ordered_pair(non_ordered_pair(f4(non_ordered_pair(non_ordered_pair(f12(X0,first(X1)),f12(X0,first(X1))),non_ordered_pair(f12(X0,first(X1)),non_ordered_pair(non_ordered_pair(f14(X0,first(X1)),f14(X0,first(X1))),non_ordered_pair(f14(X0,first(X1)),f13(X0,first(X1)))))),X1),f4(non_ordered_pair(non_ordered_pair(f12(X0,first(X1)),f12(X0,first(X1))),non_ordered_pair(f12(X0,first(X1)),non_ordered_pair(non_ordered_pair(f14(X0,first(X1)),f14(X0,first(X1))),non_ordered_pair(f14(X0,first(X1)),f13(X0,first(X1)))))),X1)),non_ordered_pair(f4(non_ordered_pair(non_ordered_pair(f12(X0,first(X1)),f12(X0,first(X1))),non_ordered_pair(f12(X0,first(X1)),non_ordered_pair(non_ordered_pair(f14(X0,first(X1)),f14(X0,first(X1))),non_ordered_pair(f14(X0,first(X1)),f13(X0,first(X1)))))),X1),f5(non_ordered_pair(non_ordered_pair(f12(X0,first(X1)),f12(X0,first(X1))),non_ordered_pair(f12(X0,first(X1)),non_ordered_pair(non_ordered_pair(f14(X0,first(X1)),f14(X0,first(X1))),non_ordered_pair(f14(X0,first(X1)),f13(X0,first(X1)))))),X1))) = X1 )
| ~ spl0_132
| ~ spl0_144 ),
inference(resolution,[],[f1783,f1484]) ).
fof(f55032,plain,
( spl0_1486
| ~ spl0_144
| ~ spl0_167 ),
inference(avatar_split_clause,[],[f2367,f2256,f1782,f55030]) ).
fof(f55030,plain,
( spl0_1486
<=> ! [X0,X1] : ~ member(X0,flip_range_of(compose(X1,empty_set))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1486])]) ).
fof(f2367,plain,
( ! [X0,X1] : ~ member(X0,flip_range_of(compose(X1,empty_set)))
| ~ spl0_144
| ~ spl0_167 ),
inference(resolution,[],[f2257,f1783]) ).
fof(f55024,plain,
( spl0_1485
| ~ spl0_122
| ~ spl0_143 ),
inference(avatar_split_clause,[],[f1813,f1778,f1291,f55022]) ).
fof(f55022,plain,
( spl0_1485
<=> ! [X0] :
( non_ordered_pair(non_ordered_pair(f19(rotate_right(X0)),f19(rotate_right(X0))),non_ordered_pair(f19(rotate_right(X0)),f21(rotate_right(X0)))) = non_ordered_pair(non_ordered_pair(f9(non_ordered_pair(non_ordered_pair(f19(rotate_right(X0)),f19(rotate_right(X0))),non_ordered_pair(f19(rotate_right(X0)),f21(rotate_right(X0)))),X0),f9(non_ordered_pair(non_ordered_pair(f19(rotate_right(X0)),f19(rotate_right(X0))),non_ordered_pair(f19(rotate_right(X0)),f21(rotate_right(X0)))),X0)),non_ordered_pair(f9(non_ordered_pair(non_ordered_pair(f19(rotate_right(X0)),f19(rotate_right(X0))),non_ordered_pair(f19(rotate_right(X0)),f21(rotate_right(X0)))),X0),non_ordered_pair(non_ordered_pair(f10(non_ordered_pair(non_ordered_pair(f19(rotate_right(X0)),f19(rotate_right(X0))),non_ordered_pair(f19(rotate_right(X0)),f21(rotate_right(X0)))),X0),f10(non_ordered_pair(non_ordered_pair(f19(rotate_right(X0)),f19(rotate_right(X0))),non_ordered_pair(f19(rotate_right(X0)),f21(rotate_right(X0)))),X0)),non_ordered_pair(f10(non_ordered_pair(non_ordered_pair(f19(rotate_right(X0)),f19(rotate_right(X0))),non_ordered_pair(f19(rotate_right(X0)),f21(rotate_right(X0)))),X0),f11(non_ordered_pair(non_ordered_pair(f19(rotate_right(X0)),f19(rotate_right(X0))),non_ordered_pair(f19(rotate_right(X0)),f21(rotate_right(X0)))),X0)))))
| single_valued_set(rotate_right(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1485])]) ).
fof(f1291,plain,
( spl0_122
<=> ! [X0] :
( single_valued_set(X0)
| member(non_ordered_pair(non_ordered_pair(f19(X0),f19(X0)),non_ordered_pair(f19(X0),f21(X0))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_122])]) ).
fof(f1813,plain,
( ! [X0] :
( non_ordered_pair(non_ordered_pair(f19(rotate_right(X0)),f19(rotate_right(X0))),non_ordered_pair(f19(rotate_right(X0)),f21(rotate_right(X0)))) = non_ordered_pair(non_ordered_pair(f9(non_ordered_pair(non_ordered_pair(f19(rotate_right(X0)),f19(rotate_right(X0))),non_ordered_pair(f19(rotate_right(X0)),f21(rotate_right(X0)))),X0),f9(non_ordered_pair(non_ordered_pair(f19(rotate_right(X0)),f19(rotate_right(X0))),non_ordered_pair(f19(rotate_right(X0)),f21(rotate_right(X0)))),X0)),non_ordered_pair(f9(non_ordered_pair(non_ordered_pair(f19(rotate_right(X0)),f19(rotate_right(X0))),non_ordered_pair(f19(rotate_right(X0)),f21(rotate_right(X0)))),X0),non_ordered_pair(non_ordered_pair(f10(non_ordered_pair(non_ordered_pair(f19(rotate_right(X0)),f19(rotate_right(X0))),non_ordered_pair(f19(rotate_right(X0)),f21(rotate_right(X0)))),X0),f10(non_ordered_pair(non_ordered_pair(f19(rotate_right(X0)),f19(rotate_right(X0))),non_ordered_pair(f19(rotate_right(X0)),f21(rotate_right(X0)))),X0)),non_ordered_pair(f10(non_ordered_pair(non_ordered_pair(f19(rotate_right(X0)),f19(rotate_right(X0))),non_ordered_pair(f19(rotate_right(X0)),f21(rotate_right(X0)))),X0),f11(non_ordered_pair(non_ordered_pair(f19(rotate_right(X0)),f19(rotate_right(X0))),non_ordered_pair(f19(rotate_right(X0)),f21(rotate_right(X0)))),X0)))))
| single_valued_set(rotate_right(X0)) )
| ~ spl0_122
| ~ spl0_143 ),
inference(resolution,[],[f1779,f1292]) ).
fof(f1292,plain,
( ! [X0] :
( member(non_ordered_pair(non_ordered_pair(f19(X0),f19(X0)),non_ordered_pair(f19(X0),f21(X0))),X0)
| single_valued_set(X0) )
| ~ spl0_122 ),
inference(avatar_component_clause,[],[f1291]) ).
fof(f55020,plain,
( spl0_1484
| ~ spl0_121
| ~ spl0_143 ),
inference(avatar_split_clause,[],[f1812,f1778,f1287,f55018]) ).
fof(f55018,plain,
( spl0_1484
<=> ! [X0] :
( non_ordered_pair(non_ordered_pair(f19(rotate_right(X0)),f19(rotate_right(X0))),non_ordered_pair(f19(rotate_right(X0)),f20(rotate_right(X0)))) = non_ordered_pair(non_ordered_pair(f9(non_ordered_pair(non_ordered_pair(f19(rotate_right(X0)),f19(rotate_right(X0))),non_ordered_pair(f19(rotate_right(X0)),f20(rotate_right(X0)))),X0),f9(non_ordered_pair(non_ordered_pair(f19(rotate_right(X0)),f19(rotate_right(X0))),non_ordered_pair(f19(rotate_right(X0)),f20(rotate_right(X0)))),X0)),non_ordered_pair(f9(non_ordered_pair(non_ordered_pair(f19(rotate_right(X0)),f19(rotate_right(X0))),non_ordered_pair(f19(rotate_right(X0)),f20(rotate_right(X0)))),X0),non_ordered_pair(non_ordered_pair(f10(non_ordered_pair(non_ordered_pair(f19(rotate_right(X0)),f19(rotate_right(X0))),non_ordered_pair(f19(rotate_right(X0)),f20(rotate_right(X0)))),X0),f10(non_ordered_pair(non_ordered_pair(f19(rotate_right(X0)),f19(rotate_right(X0))),non_ordered_pair(f19(rotate_right(X0)),f20(rotate_right(X0)))),X0)),non_ordered_pair(f10(non_ordered_pair(non_ordered_pair(f19(rotate_right(X0)),f19(rotate_right(X0))),non_ordered_pair(f19(rotate_right(X0)),f20(rotate_right(X0)))),X0),f11(non_ordered_pair(non_ordered_pair(f19(rotate_right(X0)),f19(rotate_right(X0))),non_ordered_pair(f19(rotate_right(X0)),f20(rotate_right(X0)))),X0)))))
| single_valued_set(rotate_right(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1484])]) ).
fof(f1287,plain,
( spl0_121
<=> ! [X0] :
( single_valued_set(X0)
| member(non_ordered_pair(non_ordered_pair(f19(X0),f19(X0)),non_ordered_pair(f19(X0),f20(X0))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_121])]) ).
fof(f1812,plain,
( ! [X0] :
( non_ordered_pair(non_ordered_pair(f19(rotate_right(X0)),f19(rotate_right(X0))),non_ordered_pair(f19(rotate_right(X0)),f20(rotate_right(X0)))) = non_ordered_pair(non_ordered_pair(f9(non_ordered_pair(non_ordered_pair(f19(rotate_right(X0)),f19(rotate_right(X0))),non_ordered_pair(f19(rotate_right(X0)),f20(rotate_right(X0)))),X0),f9(non_ordered_pair(non_ordered_pair(f19(rotate_right(X0)),f19(rotate_right(X0))),non_ordered_pair(f19(rotate_right(X0)),f20(rotate_right(X0)))),X0)),non_ordered_pair(f9(non_ordered_pair(non_ordered_pair(f19(rotate_right(X0)),f19(rotate_right(X0))),non_ordered_pair(f19(rotate_right(X0)),f20(rotate_right(X0)))),X0),non_ordered_pair(non_ordered_pair(f10(non_ordered_pair(non_ordered_pair(f19(rotate_right(X0)),f19(rotate_right(X0))),non_ordered_pair(f19(rotate_right(X0)),f20(rotate_right(X0)))),X0),f10(non_ordered_pair(non_ordered_pair(f19(rotate_right(X0)),f19(rotate_right(X0))),non_ordered_pair(f19(rotate_right(X0)),f20(rotate_right(X0)))),X0)),non_ordered_pair(f10(non_ordered_pair(non_ordered_pair(f19(rotate_right(X0)),f19(rotate_right(X0))),non_ordered_pair(f19(rotate_right(X0)),f20(rotate_right(X0)))),X0),f11(non_ordered_pair(non_ordered_pair(f19(rotate_right(X0)),f19(rotate_right(X0))),non_ordered_pair(f19(rotate_right(X0)),f20(rotate_right(X0)))),X0)))))
| single_valued_set(rotate_right(X0)) )
| ~ spl0_121
| ~ spl0_143 ),
inference(resolution,[],[f1779,f1288]) ).
fof(f1288,plain,
( ! [X0] :
( member(non_ordered_pair(non_ordered_pair(f19(X0),f19(X0)),non_ordered_pair(f19(X0),f20(X0))),X0)
| single_valued_set(X0) )
| ~ spl0_121 ),
inference(avatar_component_clause,[],[f1287]) ).
fof(f55016,plain,
( spl0_1483
| ~ spl0_122
| ~ spl0_142 ),
inference(avatar_split_clause,[],[f1792,f1774,f1291,f55014]) ).
fof(f55014,plain,
( spl0_1483
<=> ! [X0] :
( non_ordered_pair(non_ordered_pair(f19(flip_range_of(X0)),f19(flip_range_of(X0))),non_ordered_pair(f19(flip_range_of(X0)),f21(flip_range_of(X0)))) = non_ordered_pair(non_ordered_pair(f12(non_ordered_pair(non_ordered_pair(f19(flip_range_of(X0)),f19(flip_range_of(X0))),non_ordered_pair(f19(flip_range_of(X0)),f21(flip_range_of(X0)))),X0),f12(non_ordered_pair(non_ordered_pair(f19(flip_range_of(X0)),f19(flip_range_of(X0))),non_ordered_pair(f19(flip_range_of(X0)),f21(flip_range_of(X0)))),X0)),non_ordered_pair(f12(non_ordered_pair(non_ordered_pair(f19(flip_range_of(X0)),f19(flip_range_of(X0))),non_ordered_pair(f19(flip_range_of(X0)),f21(flip_range_of(X0)))),X0),non_ordered_pair(non_ordered_pair(f13(non_ordered_pair(non_ordered_pair(f19(flip_range_of(X0)),f19(flip_range_of(X0))),non_ordered_pair(f19(flip_range_of(X0)),f21(flip_range_of(X0)))),X0),f13(non_ordered_pair(non_ordered_pair(f19(flip_range_of(X0)),f19(flip_range_of(X0))),non_ordered_pair(f19(flip_range_of(X0)),f21(flip_range_of(X0)))),X0)),non_ordered_pair(f13(non_ordered_pair(non_ordered_pair(f19(flip_range_of(X0)),f19(flip_range_of(X0))),non_ordered_pair(f19(flip_range_of(X0)),f21(flip_range_of(X0)))),X0),f14(non_ordered_pair(non_ordered_pair(f19(flip_range_of(X0)),f19(flip_range_of(X0))),non_ordered_pair(f19(flip_range_of(X0)),f21(flip_range_of(X0)))),X0)))))
| single_valued_set(flip_range_of(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1483])]) ).
fof(f1792,plain,
( ! [X0] :
( non_ordered_pair(non_ordered_pair(f19(flip_range_of(X0)),f19(flip_range_of(X0))),non_ordered_pair(f19(flip_range_of(X0)),f21(flip_range_of(X0)))) = non_ordered_pair(non_ordered_pair(f12(non_ordered_pair(non_ordered_pair(f19(flip_range_of(X0)),f19(flip_range_of(X0))),non_ordered_pair(f19(flip_range_of(X0)),f21(flip_range_of(X0)))),X0),f12(non_ordered_pair(non_ordered_pair(f19(flip_range_of(X0)),f19(flip_range_of(X0))),non_ordered_pair(f19(flip_range_of(X0)),f21(flip_range_of(X0)))),X0)),non_ordered_pair(f12(non_ordered_pair(non_ordered_pair(f19(flip_range_of(X0)),f19(flip_range_of(X0))),non_ordered_pair(f19(flip_range_of(X0)),f21(flip_range_of(X0)))),X0),non_ordered_pair(non_ordered_pair(f13(non_ordered_pair(non_ordered_pair(f19(flip_range_of(X0)),f19(flip_range_of(X0))),non_ordered_pair(f19(flip_range_of(X0)),f21(flip_range_of(X0)))),X0),f13(non_ordered_pair(non_ordered_pair(f19(flip_range_of(X0)),f19(flip_range_of(X0))),non_ordered_pair(f19(flip_range_of(X0)),f21(flip_range_of(X0)))),X0)),non_ordered_pair(f13(non_ordered_pair(non_ordered_pair(f19(flip_range_of(X0)),f19(flip_range_of(X0))),non_ordered_pair(f19(flip_range_of(X0)),f21(flip_range_of(X0)))),X0),f14(non_ordered_pair(non_ordered_pair(f19(flip_range_of(X0)),f19(flip_range_of(X0))),non_ordered_pair(f19(flip_range_of(X0)),f21(flip_range_of(X0)))),X0)))))
| single_valued_set(flip_range_of(X0)) )
| ~ spl0_122
| ~ spl0_142 ),
inference(resolution,[],[f1775,f1292]) ).
fof(f55012,plain,
( spl0_1482
| ~ spl0_121
| ~ spl0_142 ),
inference(avatar_split_clause,[],[f1791,f1774,f1287,f55010]) ).
fof(f55010,plain,
( spl0_1482
<=> ! [X0] :
( non_ordered_pair(non_ordered_pair(f19(flip_range_of(X0)),f19(flip_range_of(X0))),non_ordered_pair(f19(flip_range_of(X0)),f20(flip_range_of(X0)))) = non_ordered_pair(non_ordered_pair(f12(non_ordered_pair(non_ordered_pair(f19(flip_range_of(X0)),f19(flip_range_of(X0))),non_ordered_pair(f19(flip_range_of(X0)),f20(flip_range_of(X0)))),X0),f12(non_ordered_pair(non_ordered_pair(f19(flip_range_of(X0)),f19(flip_range_of(X0))),non_ordered_pair(f19(flip_range_of(X0)),f20(flip_range_of(X0)))),X0)),non_ordered_pair(f12(non_ordered_pair(non_ordered_pair(f19(flip_range_of(X0)),f19(flip_range_of(X0))),non_ordered_pair(f19(flip_range_of(X0)),f20(flip_range_of(X0)))),X0),non_ordered_pair(non_ordered_pair(f13(non_ordered_pair(non_ordered_pair(f19(flip_range_of(X0)),f19(flip_range_of(X0))),non_ordered_pair(f19(flip_range_of(X0)),f20(flip_range_of(X0)))),X0),f13(non_ordered_pair(non_ordered_pair(f19(flip_range_of(X0)),f19(flip_range_of(X0))),non_ordered_pair(f19(flip_range_of(X0)),f20(flip_range_of(X0)))),X0)),non_ordered_pair(f13(non_ordered_pair(non_ordered_pair(f19(flip_range_of(X0)),f19(flip_range_of(X0))),non_ordered_pair(f19(flip_range_of(X0)),f20(flip_range_of(X0)))),X0),f14(non_ordered_pair(non_ordered_pair(f19(flip_range_of(X0)),f19(flip_range_of(X0))),non_ordered_pair(f19(flip_range_of(X0)),f20(flip_range_of(X0)))),X0)))))
| single_valued_set(flip_range_of(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1482])]) ).
fof(f1791,plain,
( ! [X0] :
( non_ordered_pair(non_ordered_pair(f19(flip_range_of(X0)),f19(flip_range_of(X0))),non_ordered_pair(f19(flip_range_of(X0)),f20(flip_range_of(X0)))) = non_ordered_pair(non_ordered_pair(f12(non_ordered_pair(non_ordered_pair(f19(flip_range_of(X0)),f19(flip_range_of(X0))),non_ordered_pair(f19(flip_range_of(X0)),f20(flip_range_of(X0)))),X0),f12(non_ordered_pair(non_ordered_pair(f19(flip_range_of(X0)),f19(flip_range_of(X0))),non_ordered_pair(f19(flip_range_of(X0)),f20(flip_range_of(X0)))),X0)),non_ordered_pair(f12(non_ordered_pair(non_ordered_pair(f19(flip_range_of(X0)),f19(flip_range_of(X0))),non_ordered_pair(f19(flip_range_of(X0)),f20(flip_range_of(X0)))),X0),non_ordered_pair(non_ordered_pair(f13(non_ordered_pair(non_ordered_pair(f19(flip_range_of(X0)),f19(flip_range_of(X0))),non_ordered_pair(f19(flip_range_of(X0)),f20(flip_range_of(X0)))),X0),f13(non_ordered_pair(non_ordered_pair(f19(flip_range_of(X0)),f19(flip_range_of(X0))),non_ordered_pair(f19(flip_range_of(X0)),f20(flip_range_of(X0)))),X0)),non_ordered_pair(f13(non_ordered_pair(non_ordered_pair(f19(flip_range_of(X0)),f19(flip_range_of(X0))),non_ordered_pair(f19(flip_range_of(X0)),f20(flip_range_of(X0)))),X0),f14(non_ordered_pair(non_ordered_pair(f19(flip_range_of(X0)),f19(flip_range_of(X0))),non_ordered_pair(f19(flip_range_of(X0)),f20(flip_range_of(X0)))),X0)))))
| single_valued_set(flip_range_of(X0)) )
| ~ spl0_121
| ~ spl0_142 ),
inference(resolution,[],[f1775,f1288]) ).
fof(f55002,plain,
( spl0_1481
| ~ spl0_122
| ~ spl0_137 ),
inference(avatar_split_clause,[],[f1648,f1634,f1291,f55000]) ).
fof(f55000,plain,
( spl0_1481
<=> ! [X0,X1] :
( non_ordered_pair(non_ordered_pair(f19(compose(X0,X1)),f19(compose(X0,X1))),non_ordered_pair(f19(compose(X0,X1)),f21(compose(X0,X1)))) = non_ordered_pair(non_ordered_pair(f29(non_ordered_pair(non_ordered_pair(f19(compose(X0,X1)),f19(compose(X0,X1))),non_ordered_pair(f19(compose(X0,X1)),f21(compose(X0,X1)))),X0,X1),f29(non_ordered_pair(non_ordered_pair(f19(compose(X0,X1)),f19(compose(X0,X1))),non_ordered_pair(f19(compose(X0,X1)),f21(compose(X0,X1)))),X0,X1)),non_ordered_pair(f29(non_ordered_pair(non_ordered_pair(f19(compose(X0,X1)),f19(compose(X0,X1))),non_ordered_pair(f19(compose(X0,X1)),f21(compose(X0,X1)))),X0,X1),f30(non_ordered_pair(non_ordered_pair(f19(compose(X0,X1)),f19(compose(X0,X1))),non_ordered_pair(f19(compose(X0,X1)),f21(compose(X0,X1)))),X0,X1)))
| single_valued_set(compose(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1481])]) ).
fof(f1648,plain,
( ! [X0,X1] :
( non_ordered_pair(non_ordered_pair(f19(compose(X0,X1)),f19(compose(X0,X1))),non_ordered_pair(f19(compose(X0,X1)),f21(compose(X0,X1)))) = non_ordered_pair(non_ordered_pair(f29(non_ordered_pair(non_ordered_pair(f19(compose(X0,X1)),f19(compose(X0,X1))),non_ordered_pair(f19(compose(X0,X1)),f21(compose(X0,X1)))),X0,X1),f29(non_ordered_pair(non_ordered_pair(f19(compose(X0,X1)),f19(compose(X0,X1))),non_ordered_pair(f19(compose(X0,X1)),f21(compose(X0,X1)))),X0,X1)),non_ordered_pair(f29(non_ordered_pair(non_ordered_pair(f19(compose(X0,X1)),f19(compose(X0,X1))),non_ordered_pair(f19(compose(X0,X1)),f21(compose(X0,X1)))),X0,X1),f30(non_ordered_pair(non_ordered_pair(f19(compose(X0,X1)),f19(compose(X0,X1))),non_ordered_pair(f19(compose(X0,X1)),f21(compose(X0,X1)))),X0,X1)))
| single_valued_set(compose(X0,X1)) )
| ~ spl0_122
| ~ spl0_137 ),
inference(resolution,[],[f1635,f1292]) ).
fof(f54998,plain,
( spl0_1480
| ~ spl0_121
| ~ spl0_137 ),
inference(avatar_split_clause,[],[f1647,f1634,f1287,f54996]) ).
fof(f54996,plain,
( spl0_1480
<=> ! [X0,X1] :
( non_ordered_pair(non_ordered_pair(f19(compose(X0,X1)),f19(compose(X0,X1))),non_ordered_pair(f19(compose(X0,X1)),f20(compose(X0,X1)))) = non_ordered_pair(non_ordered_pair(f29(non_ordered_pair(non_ordered_pair(f19(compose(X0,X1)),f19(compose(X0,X1))),non_ordered_pair(f19(compose(X0,X1)),f20(compose(X0,X1)))),X0,X1),f29(non_ordered_pair(non_ordered_pair(f19(compose(X0,X1)),f19(compose(X0,X1))),non_ordered_pair(f19(compose(X0,X1)),f20(compose(X0,X1)))),X0,X1)),non_ordered_pair(f29(non_ordered_pair(non_ordered_pair(f19(compose(X0,X1)),f19(compose(X0,X1))),non_ordered_pair(f19(compose(X0,X1)),f20(compose(X0,X1)))),X0,X1),f30(non_ordered_pair(non_ordered_pair(f19(compose(X0,X1)),f19(compose(X0,X1))),non_ordered_pair(f19(compose(X0,X1)),f20(compose(X0,X1)))),X0,X1)))
| single_valued_set(compose(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1480])]) ).
fof(f1647,plain,
( ! [X0,X1] :
( non_ordered_pair(non_ordered_pair(f19(compose(X0,X1)),f19(compose(X0,X1))),non_ordered_pair(f19(compose(X0,X1)),f20(compose(X0,X1)))) = non_ordered_pair(non_ordered_pair(f29(non_ordered_pair(non_ordered_pair(f19(compose(X0,X1)),f19(compose(X0,X1))),non_ordered_pair(f19(compose(X0,X1)),f20(compose(X0,X1)))),X0,X1),f29(non_ordered_pair(non_ordered_pair(f19(compose(X0,X1)),f19(compose(X0,X1))),non_ordered_pair(f19(compose(X0,X1)),f20(compose(X0,X1)))),X0,X1)),non_ordered_pair(f29(non_ordered_pair(non_ordered_pair(f19(compose(X0,X1)),f19(compose(X0,X1))),non_ordered_pair(f19(compose(X0,X1)),f20(compose(X0,X1)))),X0,X1),f30(non_ordered_pair(non_ordered_pair(f19(compose(X0,X1)),f19(compose(X0,X1))),non_ordered_pair(f19(compose(X0,X1)),f20(compose(X0,X1)))),X0,X1)))
| single_valued_set(compose(X0,X1)) )
| ~ spl0_121
| ~ spl0_137 ),
inference(resolution,[],[f1635,f1288]) ).
fof(f54991,plain,
( spl0_1479
| ~ spl0_127
| ~ spl0_167 ),
inference(avatar_split_clause,[],[f2365,f2256,f1397,f54989]) ).
fof(f54989,plain,
( spl0_1479
<=> ! [X0,X1] : ~ member(X0,converse(compose(X1,empty_set))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1479])]) ).
fof(f2365,plain,
( ! [X0,X1] : ~ member(X0,converse(compose(X1,empty_set)))
| ~ spl0_127
| ~ spl0_167 ),
inference(resolution,[],[f2257,f1398]) ).
fof(f54605,plain,
( spl0_1478
| ~ spl0_127
| ~ spl0_143 ),
inference(avatar_split_clause,[],[f1814,f1778,f1397,f54603]) ).
fof(f54603,plain,
( spl0_1478
<=> ! [X0,X1] :
( non_ordered_pair(non_ordered_pair(second(X0),second(X0)),non_ordered_pair(second(X0),first(X0))) = non_ordered_pair(non_ordered_pair(f9(non_ordered_pair(non_ordered_pair(second(X0),second(X0)),non_ordered_pair(second(X0),first(X0))),X1),f9(non_ordered_pair(non_ordered_pair(second(X0),second(X0)),non_ordered_pair(second(X0),first(X0))),X1)),non_ordered_pair(f9(non_ordered_pair(non_ordered_pair(second(X0),second(X0)),non_ordered_pair(second(X0),first(X0))),X1),non_ordered_pair(non_ordered_pair(f10(non_ordered_pair(non_ordered_pair(second(X0),second(X0)),non_ordered_pair(second(X0),first(X0))),X1),f10(non_ordered_pair(non_ordered_pair(second(X0),second(X0)),non_ordered_pair(second(X0),first(X0))),X1)),non_ordered_pair(f10(non_ordered_pair(non_ordered_pair(second(X0),second(X0)),non_ordered_pair(second(X0),first(X0))),X1),f11(non_ordered_pair(non_ordered_pair(second(X0),second(X0)),non_ordered_pair(second(X0),first(X0))),X1)))))
| ~ member(X0,converse(rotate_right(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1478])]) ).
fof(f1814,plain,
( ! [X0,X1] :
( non_ordered_pair(non_ordered_pair(second(X0),second(X0)),non_ordered_pair(second(X0),first(X0))) = non_ordered_pair(non_ordered_pair(f9(non_ordered_pair(non_ordered_pair(second(X0),second(X0)),non_ordered_pair(second(X0),first(X0))),X1),f9(non_ordered_pair(non_ordered_pair(second(X0),second(X0)),non_ordered_pair(second(X0),first(X0))),X1)),non_ordered_pair(f9(non_ordered_pair(non_ordered_pair(second(X0),second(X0)),non_ordered_pair(second(X0),first(X0))),X1),non_ordered_pair(non_ordered_pair(f10(non_ordered_pair(non_ordered_pair(second(X0),second(X0)),non_ordered_pair(second(X0),first(X0))),X1),f10(non_ordered_pair(non_ordered_pair(second(X0),second(X0)),non_ordered_pair(second(X0),first(X0))),X1)),non_ordered_pair(f10(non_ordered_pair(non_ordered_pair(second(X0),second(X0)),non_ordered_pair(second(X0),first(X0))),X1),f11(non_ordered_pair(non_ordered_pair(second(X0),second(X0)),non_ordered_pair(second(X0),first(X0))),X1)))))
| ~ member(X0,converse(rotate_right(X1))) )
| ~ spl0_127
| ~ spl0_143 ),
inference(resolution,[],[f1779,f1398]) ).
fof(f54601,plain,
( spl0_1477
| ~ spl0_127
| ~ spl0_142 ),
inference(avatar_split_clause,[],[f1793,f1774,f1397,f54599]) ).
fof(f54599,plain,
( spl0_1477
<=> ! [X0,X1] :
( non_ordered_pair(non_ordered_pair(second(X0),second(X0)),non_ordered_pair(second(X0),first(X0))) = non_ordered_pair(non_ordered_pair(f12(non_ordered_pair(non_ordered_pair(second(X0),second(X0)),non_ordered_pair(second(X0),first(X0))),X1),f12(non_ordered_pair(non_ordered_pair(second(X0),second(X0)),non_ordered_pair(second(X0),first(X0))),X1)),non_ordered_pair(f12(non_ordered_pair(non_ordered_pair(second(X0),second(X0)),non_ordered_pair(second(X0),first(X0))),X1),non_ordered_pair(non_ordered_pair(f13(non_ordered_pair(non_ordered_pair(second(X0),second(X0)),non_ordered_pair(second(X0),first(X0))),X1),f13(non_ordered_pair(non_ordered_pair(second(X0),second(X0)),non_ordered_pair(second(X0),first(X0))),X1)),non_ordered_pair(f13(non_ordered_pair(non_ordered_pair(second(X0),second(X0)),non_ordered_pair(second(X0),first(X0))),X1),f14(non_ordered_pair(non_ordered_pair(second(X0),second(X0)),non_ordered_pair(second(X0),first(X0))),X1)))))
| ~ member(X0,converse(flip_range_of(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1477])]) ).
fof(f1793,plain,
( ! [X0,X1] :
( non_ordered_pair(non_ordered_pair(second(X0),second(X0)),non_ordered_pair(second(X0),first(X0))) = non_ordered_pair(non_ordered_pair(f12(non_ordered_pair(non_ordered_pair(second(X0),second(X0)),non_ordered_pair(second(X0),first(X0))),X1),f12(non_ordered_pair(non_ordered_pair(second(X0),second(X0)),non_ordered_pair(second(X0),first(X0))),X1)),non_ordered_pair(f12(non_ordered_pair(non_ordered_pair(second(X0),second(X0)),non_ordered_pair(second(X0),first(X0))),X1),non_ordered_pair(non_ordered_pair(f13(non_ordered_pair(non_ordered_pair(second(X0),second(X0)),non_ordered_pair(second(X0),first(X0))),X1),f13(non_ordered_pair(non_ordered_pair(second(X0),second(X0)),non_ordered_pair(second(X0),first(X0))),X1)),non_ordered_pair(f13(non_ordered_pair(non_ordered_pair(second(X0),second(X0)),non_ordered_pair(second(X0),first(X0))),X1),f14(non_ordered_pair(non_ordered_pair(second(X0),second(X0)),non_ordered_pair(second(X0),first(X0))),X1)))))
| ~ member(X0,converse(flip_range_of(X1))) )
| ~ spl0_127
| ~ spl0_142 ),
inference(resolution,[],[f1775,f1398]) ).
fof(f53786,plain,
( spl0_1476
| ~ spl0_131
| ~ spl0_139 ),
inference(avatar_split_clause,[],[f1711,f1642,f1479,f53784]) ).
fof(f53784,plain,
( spl0_1476
<=> ! [X2,X0,X1] :
( ~ member(X0,compose(second(X1),X2))
| non_ordered_pair(non_ordered_pair(f6(non_ordered_pair(non_ordered_pair(f29(X0,second(X1),X2),f29(X0,second(X1),X2)),non_ordered_pair(f29(X0,second(X1),X2),f31(X0,second(X1),X2))),X1),f6(non_ordered_pair(non_ordered_pair(f29(X0,second(X1),X2),f29(X0,second(X1),X2)),non_ordered_pair(f29(X0,second(X1),X2),f31(X0,second(X1),X2))),X1)),non_ordered_pair(f6(non_ordered_pair(non_ordered_pair(f29(X0,second(X1),X2),f29(X0,second(X1),X2)),non_ordered_pair(f29(X0,second(X1),X2),f31(X0,second(X1),X2))),X1),f7(non_ordered_pair(non_ordered_pair(f29(X0,second(X1),X2),f29(X0,second(X1),X2)),non_ordered_pair(f29(X0,second(X1),X2),f31(X0,second(X1),X2))),X1))) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1476])]) ).
fof(f1711,plain,
( ! [X2,X0,X1] :
( ~ member(X0,compose(second(X1),X2))
| non_ordered_pair(non_ordered_pair(f6(non_ordered_pair(non_ordered_pair(f29(X0,second(X1),X2),f29(X0,second(X1),X2)),non_ordered_pair(f29(X0,second(X1),X2),f31(X0,second(X1),X2))),X1),f6(non_ordered_pair(non_ordered_pair(f29(X0,second(X1),X2),f29(X0,second(X1),X2)),non_ordered_pair(f29(X0,second(X1),X2),f31(X0,second(X1),X2))),X1)),non_ordered_pair(f6(non_ordered_pair(non_ordered_pair(f29(X0,second(X1),X2),f29(X0,second(X1),X2)),non_ordered_pair(f29(X0,second(X1),X2),f31(X0,second(X1),X2))),X1),f7(non_ordered_pair(non_ordered_pair(f29(X0,second(X1),X2),f29(X0,second(X1),X2)),non_ordered_pair(f29(X0,second(X1),X2),f31(X0,second(X1),X2))),X1))) = X1 )
| ~ spl0_131
| ~ spl0_139 ),
inference(resolution,[],[f1643,f1480]) ).
fof(f53782,plain,
( spl0_1475
| ~ spl0_132
| ~ spl0_139 ),
inference(avatar_split_clause,[],[f1708,f1642,f1483,f53780]) ).
fof(f53780,plain,
( spl0_1475
<=> ! [X2,X0,X1] :
( ~ member(X0,compose(first(X1),X2))
| non_ordered_pair(non_ordered_pair(f4(non_ordered_pair(non_ordered_pair(f29(X0,first(X1),X2),f29(X0,first(X1),X2)),non_ordered_pair(f29(X0,first(X1),X2),f31(X0,first(X1),X2))),X1),f4(non_ordered_pair(non_ordered_pair(f29(X0,first(X1),X2),f29(X0,first(X1),X2)),non_ordered_pair(f29(X0,first(X1),X2),f31(X0,first(X1),X2))),X1)),non_ordered_pair(f4(non_ordered_pair(non_ordered_pair(f29(X0,first(X1),X2),f29(X0,first(X1),X2)),non_ordered_pair(f29(X0,first(X1),X2),f31(X0,first(X1),X2))),X1),f5(non_ordered_pair(non_ordered_pair(f29(X0,first(X1),X2),f29(X0,first(X1),X2)),non_ordered_pair(f29(X0,first(X1),X2),f31(X0,first(X1),X2))),X1))) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1475])]) ).
fof(f1708,plain,
( ! [X2,X0,X1] :
( ~ member(X0,compose(first(X1),X2))
| non_ordered_pair(non_ordered_pair(f4(non_ordered_pair(non_ordered_pair(f29(X0,first(X1),X2),f29(X0,first(X1),X2)),non_ordered_pair(f29(X0,first(X1),X2),f31(X0,first(X1),X2))),X1),f4(non_ordered_pair(non_ordered_pair(f29(X0,first(X1),X2),f29(X0,first(X1),X2)),non_ordered_pair(f29(X0,first(X1),X2),f31(X0,first(X1),X2))),X1)),non_ordered_pair(f4(non_ordered_pair(non_ordered_pair(f29(X0,first(X1),X2),f29(X0,first(X1),X2)),non_ordered_pair(f29(X0,first(X1),X2),f31(X0,first(X1),X2))),X1),f5(non_ordered_pair(non_ordered_pair(f29(X0,first(X1),X2),f29(X0,first(X1),X2)),non_ordered_pair(f29(X0,first(X1),X2),f31(X0,first(X1),X2))),X1))) = X1 )
| ~ spl0_132
| ~ spl0_139 ),
inference(resolution,[],[f1643,f1484]) ).
fof(f53775,plain,
( spl0_1474
| ~ spl0_78
| ~ spl0_166 ),
inference(avatar_split_clause,[],[f2340,f2251,f644,f53773]) ).
fof(f53773,plain,
( spl0_1474
<=> ! [X0,X1] : ~ member(X0,sigma(image(empty_set,X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1474])]) ).
fof(f2340,plain,
( ! [X0,X1] : ~ member(X0,sigma(image(empty_set,X1)))
| ~ spl0_78
| ~ spl0_166 ),
inference(resolution,[],[f2252,f645]) ).
fof(f53771,plain,
( spl0_1473
| ~ spl0_131
| ~ spl0_138 ),
inference(avatar_split_clause,[],[f1671,f1638,f1479,f53769]) ).
fof(f53769,plain,
( spl0_1473
<=> ! [X2,X0,X1] :
( ~ member(X0,compose(X1,second(X2)))
| non_ordered_pair(non_ordered_pair(f6(non_ordered_pair(non_ordered_pair(f31(X0,X1,second(X2)),f31(X0,X1,second(X2))),non_ordered_pair(f31(X0,X1,second(X2)),f30(X0,X1,second(X2)))),X2),f6(non_ordered_pair(non_ordered_pair(f31(X0,X1,second(X2)),f31(X0,X1,second(X2))),non_ordered_pair(f31(X0,X1,second(X2)),f30(X0,X1,second(X2)))),X2)),non_ordered_pair(f6(non_ordered_pair(non_ordered_pair(f31(X0,X1,second(X2)),f31(X0,X1,second(X2))),non_ordered_pair(f31(X0,X1,second(X2)),f30(X0,X1,second(X2)))),X2),f7(non_ordered_pair(non_ordered_pair(f31(X0,X1,second(X2)),f31(X0,X1,second(X2))),non_ordered_pair(f31(X0,X1,second(X2)),f30(X0,X1,second(X2)))),X2))) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1473])]) ).
fof(f1671,plain,
( ! [X2,X0,X1] :
( ~ member(X0,compose(X1,second(X2)))
| non_ordered_pair(non_ordered_pair(f6(non_ordered_pair(non_ordered_pair(f31(X0,X1,second(X2)),f31(X0,X1,second(X2))),non_ordered_pair(f31(X0,X1,second(X2)),f30(X0,X1,second(X2)))),X2),f6(non_ordered_pair(non_ordered_pair(f31(X0,X1,second(X2)),f31(X0,X1,second(X2))),non_ordered_pair(f31(X0,X1,second(X2)),f30(X0,X1,second(X2)))),X2)),non_ordered_pair(f6(non_ordered_pair(non_ordered_pair(f31(X0,X1,second(X2)),f31(X0,X1,second(X2))),non_ordered_pair(f31(X0,X1,second(X2)),f30(X0,X1,second(X2)))),X2),f7(non_ordered_pair(non_ordered_pair(f31(X0,X1,second(X2)),f31(X0,X1,second(X2))),non_ordered_pair(f31(X0,X1,second(X2)),f30(X0,X1,second(X2)))),X2))) = X2 )
| ~ spl0_131
| ~ spl0_138 ),
inference(resolution,[],[f1639,f1480]) ).
fof(f53767,plain,
( spl0_1472
| ~ spl0_132
| ~ spl0_138 ),
inference(avatar_split_clause,[],[f1668,f1638,f1483,f53765]) ).
fof(f53765,plain,
( spl0_1472
<=> ! [X2,X0,X1] :
( ~ member(X0,compose(X1,first(X2)))
| non_ordered_pair(non_ordered_pair(f4(non_ordered_pair(non_ordered_pair(f31(X0,X1,first(X2)),f31(X0,X1,first(X2))),non_ordered_pair(f31(X0,X1,first(X2)),f30(X0,X1,first(X2)))),X2),f4(non_ordered_pair(non_ordered_pair(f31(X0,X1,first(X2)),f31(X0,X1,first(X2))),non_ordered_pair(f31(X0,X1,first(X2)),f30(X0,X1,first(X2)))),X2)),non_ordered_pair(f4(non_ordered_pair(non_ordered_pair(f31(X0,X1,first(X2)),f31(X0,X1,first(X2))),non_ordered_pair(f31(X0,X1,first(X2)),f30(X0,X1,first(X2)))),X2),f5(non_ordered_pair(non_ordered_pair(f31(X0,X1,first(X2)),f31(X0,X1,first(X2))),non_ordered_pair(f31(X0,X1,first(X2)),f30(X0,X1,first(X2)))),X2))) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1472])]) ).
fof(f1668,plain,
( ! [X2,X0,X1] :
( ~ member(X0,compose(X1,first(X2)))
| non_ordered_pair(non_ordered_pair(f4(non_ordered_pair(non_ordered_pair(f31(X0,X1,first(X2)),f31(X0,X1,first(X2))),non_ordered_pair(f31(X0,X1,first(X2)),f30(X0,X1,first(X2)))),X2),f4(non_ordered_pair(non_ordered_pair(f31(X0,X1,first(X2)),f31(X0,X1,first(X2))),non_ordered_pair(f31(X0,X1,first(X2)),f30(X0,X1,first(X2)))),X2)),non_ordered_pair(f4(non_ordered_pair(non_ordered_pair(f31(X0,X1,first(X2)),f31(X0,X1,first(X2))),non_ordered_pair(f31(X0,X1,first(X2)),f30(X0,X1,first(X2)))),X2),f5(non_ordered_pair(non_ordered_pair(f31(X0,X1,first(X2)),f31(X0,X1,first(X2))),non_ordered_pair(f31(X0,X1,first(X2)),f30(X0,X1,first(X2)))),X2))) = X2 )
| ~ spl0_132
| ~ spl0_138 ),
inference(resolution,[],[f1639,f1484]) ).
fof(f53685,plain,
( spl0_1471
| ~ spl0_126
| ~ spl0_149 ),
inference(avatar_split_clause,[],[f2015,f1985,f1393,f53683]) ).
fof(f53683,plain,
( spl0_1471
<=> ! [X4,X0,X3,X2,X1] :
( ~ little_set(X0)
| ~ little_set(X1)
| ~ little_set(X2)
| member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X1)))),flip_range_of(cross_product(X3,X4)))
| ~ little_set(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X1)))))
| ~ little_set(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,non_ordered_pair(non_ordered_pair(X1,X1),non_ordered_pair(X1,X2)))))
| ~ member(first(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,non_ordered_pair(non_ordered_pair(X1,X1),non_ordered_pair(X1,X2))))),X3)
| ~ member(second(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,non_ordered_pair(non_ordered_pair(X1,X1),non_ordered_pair(X1,X2))))),X4)
| ~ ordered_pair_predicate(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,non_ordered_pair(non_ordered_pair(X1,X1),non_ordered_pair(X1,X2))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1471])]) ).
fof(f1393,plain,
( spl0_126
<=> ! [X0,X1,X3] :
( ~ ordered_pair_predicate(X3)
| ~ little_set(X3)
| ~ member(first(X3),X0)
| ~ member(second(X3),X1)
| member(X3,cross_product(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_126])]) ).
fof(f1985,plain,
( spl0_149
<=> ! [X4,X0,X6,X2] :
( ~ little_set(non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,non_ordered_pair(non_ordered_pair(X4,X4),non_ordered_pair(X4,X6)))))
| ~ little_set(X2)
| ~ little_set(X6)
| ~ little_set(X4)
| member(non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,non_ordered_pair(non_ordered_pair(X4,X4),non_ordered_pair(X4,X6)))),flip_range_of(X0))
| ~ member(non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,non_ordered_pair(non_ordered_pair(X6,X6),non_ordered_pair(X6,X4)))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_149])]) ).
fof(f2015,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ little_set(X0)
| ~ little_set(X1)
| ~ little_set(X2)
| member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X1)))),flip_range_of(cross_product(X3,X4)))
| ~ little_set(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X1)))))
| ~ little_set(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,non_ordered_pair(non_ordered_pair(X1,X1),non_ordered_pair(X1,X2)))))
| ~ member(first(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,non_ordered_pair(non_ordered_pair(X1,X1),non_ordered_pair(X1,X2))))),X3)
| ~ member(second(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,non_ordered_pair(non_ordered_pair(X1,X1),non_ordered_pair(X1,X2))))),X4)
| ~ ordered_pair_predicate(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,non_ordered_pair(non_ordered_pair(X1,X1),non_ordered_pair(X1,X2))))) )
| ~ spl0_126
| ~ spl0_149 ),
inference(resolution,[],[f1986,f1394]) ).
fof(f1394,plain,
( ! [X3,X0,X1] :
( member(X3,cross_product(X0,X1))
| ~ little_set(X3)
| ~ member(first(X3),X0)
| ~ member(second(X3),X1)
| ~ ordered_pair_predicate(X3) )
| ~ spl0_126 ),
inference(avatar_component_clause,[],[f1393]) ).
fof(f1986,plain,
( ! [X2,X0,X6,X4] :
( ~ member(non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,non_ordered_pair(non_ordered_pair(X6,X6),non_ordered_pair(X6,X4)))),X0)
| ~ little_set(X2)
| ~ little_set(X6)
| ~ little_set(X4)
| member(non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,non_ordered_pair(non_ordered_pair(X4,X4),non_ordered_pair(X4,X6)))),flip_range_of(X0))
| ~ little_set(non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,non_ordered_pair(non_ordered_pair(X4,X4),non_ordered_pair(X4,X6))))) )
| ~ spl0_149 ),
inference(avatar_component_clause,[],[f1985]) ).
fof(f53681,plain,
( spl0_1470
| ~ spl0_126
| ~ spl0_148 ),
inference(avatar_split_clause,[],[f1999,f1981,f1393,f53679]) ).
fof(f53679,plain,
( spl0_1470
<=> ! [X4,X0,X3,X2,X1] :
( ~ little_set(X0)
| ~ little_set(X1)
| ~ little_set(X2)
| member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X1)))),rotate_right(cross_product(X3,X4)))
| ~ little_set(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X1)))))
| ~ little_set(non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,non_ordered_pair(non_ordered_pair(X1,X1),non_ordered_pair(X1,X0)))))
| ~ member(first(non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,non_ordered_pair(non_ordered_pair(X1,X1),non_ordered_pair(X1,X0))))),X3)
| ~ member(second(non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,non_ordered_pair(non_ordered_pair(X1,X1),non_ordered_pair(X1,X0))))),X4)
| ~ ordered_pair_predicate(non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,non_ordered_pair(non_ordered_pair(X1,X1),non_ordered_pair(X1,X0))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1470])]) ).
fof(f1981,plain,
( spl0_148
<=> ! [X4,X0,X6,X2] :
( ~ little_set(non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,non_ordered_pair(non_ordered_pair(X4,X4),non_ordered_pair(X4,X6)))))
| ~ little_set(X2)
| ~ little_set(X6)
| ~ little_set(X4)
| member(non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,non_ordered_pair(non_ordered_pair(X4,X4),non_ordered_pair(X4,X6)))),rotate_right(X0))
| ~ member(non_ordered_pair(non_ordered_pair(X4,X4),non_ordered_pair(X4,non_ordered_pair(non_ordered_pair(X6,X6),non_ordered_pair(X6,X2)))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_148])]) ).
fof(f1999,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ little_set(X0)
| ~ little_set(X1)
| ~ little_set(X2)
| member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X1)))),rotate_right(cross_product(X3,X4)))
| ~ little_set(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X1)))))
| ~ little_set(non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,non_ordered_pair(non_ordered_pair(X1,X1),non_ordered_pair(X1,X0)))))
| ~ member(first(non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,non_ordered_pair(non_ordered_pair(X1,X1),non_ordered_pair(X1,X0))))),X3)
| ~ member(second(non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,non_ordered_pair(non_ordered_pair(X1,X1),non_ordered_pair(X1,X0))))),X4)
| ~ ordered_pair_predicate(non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,non_ordered_pair(non_ordered_pair(X1,X1),non_ordered_pair(X1,X0))))) )
| ~ spl0_126
| ~ spl0_148 ),
inference(resolution,[],[f1982,f1394]) ).
fof(f1982,plain,
( ! [X2,X0,X6,X4] :
( ~ member(non_ordered_pair(non_ordered_pair(X4,X4),non_ordered_pair(X4,non_ordered_pair(non_ordered_pair(X6,X6),non_ordered_pair(X6,X2)))),X0)
| ~ little_set(X2)
| ~ little_set(X6)
| ~ little_set(X4)
| member(non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,non_ordered_pair(non_ordered_pair(X4,X4),non_ordered_pair(X4,X6)))),rotate_right(X0))
| ~ little_set(non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,non_ordered_pair(non_ordered_pair(X4,X4),non_ordered_pair(X4,X6))))) )
| ~ spl0_148 ),
inference(avatar_component_clause,[],[f1981]) ).
fof(f53654,plain,
( spl0_1469
| ~ spl0_74
| ~ spl0_166 ),
inference(avatar_split_clause,[],[f2339,f2251,f628,f53652]) ).
fof(f53652,plain,
( spl0_1469
<=> ! [X0,X1] : ~ member(X0,domain_of(image(empty_set,X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1469])]) ).
fof(f2339,plain,
( ! [X0,X1] : ~ member(X0,domain_of(image(empty_set,X1)))
| ~ spl0_74
| ~ spl0_166 ),
inference(resolution,[],[f2252,f629]) ).
fof(f53650,plain,
( spl0_1468
| ~ spl0_136
| ~ spl0_143 ),
inference(avatar_split_clause,[],[f1830,f1778,f1552,f53648]) ).
fof(f53648,plain,
( spl0_1468
<=> ! [X4,X0,X3,X2,X1] :
( f33(X0,rotate_right(X1),X2,X3,X4) = non_ordered_pair(non_ordered_pair(f9(f33(X0,rotate_right(X1),X2,X3,X4),X1),f9(f33(X0,rotate_right(X1),X2,X3,X4),X1)),non_ordered_pair(f9(f33(X0,rotate_right(X1),X2,X3,X4),X1),non_ordered_pair(non_ordered_pair(f10(f33(X0,rotate_right(X1),X2,X3,X4),X1),f10(f33(X0,rotate_right(X1),X2,X3,X4),X1)),non_ordered_pair(f10(f33(X0,rotate_right(X1),X2,X3,X4),X1),f11(f33(X0,rotate_right(X1),X2,X3,X4),X1)))))
| ~ closed(X3,X4)
| ~ maps(X0,rotate_right(X1),X3)
| homomorphism(X0,rotate_right(X1),X2,X3,X4)
| ~ closed(rotate_right(X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1468])]) ).
fof(f1552,plain,
( spl0_136
<=> ! [X10,X11,X14,X13,X12] :
( ~ closed(X11,X12)
| ~ closed(X13,X14)
| ~ maps(X10,X11,X13)
| homomorphism(X10,X11,X12,X13,X14)
| member(f33(X10,X11,X12,X13,X14),X11) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_136])]) ).
fof(f1830,plain,
( ! [X2,X3,X0,X1,X4] :
( f33(X0,rotate_right(X1),X2,X3,X4) = non_ordered_pair(non_ordered_pair(f9(f33(X0,rotate_right(X1),X2,X3,X4),X1),f9(f33(X0,rotate_right(X1),X2,X3,X4),X1)),non_ordered_pair(f9(f33(X0,rotate_right(X1),X2,X3,X4),X1),non_ordered_pair(non_ordered_pair(f10(f33(X0,rotate_right(X1),X2,X3,X4),X1),f10(f33(X0,rotate_right(X1),X2,X3,X4),X1)),non_ordered_pair(f10(f33(X0,rotate_right(X1),X2,X3,X4),X1),f11(f33(X0,rotate_right(X1),X2,X3,X4),X1)))))
| ~ closed(X3,X4)
| ~ maps(X0,rotate_right(X1),X3)
| homomorphism(X0,rotate_right(X1),X2,X3,X4)
| ~ closed(rotate_right(X1),X2) )
| ~ spl0_136
| ~ spl0_143 ),
inference(resolution,[],[f1779,f1553]) ).
fof(f1553,plain,
( ! [X10,X11,X14,X12,X13] :
( member(f33(X10,X11,X12,X13,X14),X11)
| ~ closed(X13,X14)
| ~ maps(X10,X11,X13)
| homomorphism(X10,X11,X12,X13,X14)
| ~ closed(X11,X12) )
| ~ spl0_136 ),
inference(avatar_component_clause,[],[f1552]) ).
fof(f53646,plain,
( spl0_1467
| ~ spl0_134
| ~ spl0_143 ),
inference(avatar_split_clause,[],[f1829,f1778,f1544,f53644]) ).
fof(f53644,plain,
( spl0_1467
<=> ! [X4,X0,X3,X2,X1] :
( f32(X0,rotate_right(X1),X2,X3,X4) = non_ordered_pair(non_ordered_pair(f9(f32(X0,rotate_right(X1),X2,X3,X4),X1),f9(f32(X0,rotate_right(X1),X2,X3,X4),X1)),non_ordered_pair(f9(f32(X0,rotate_right(X1),X2,X3,X4),X1),non_ordered_pair(non_ordered_pair(f10(f32(X0,rotate_right(X1),X2,X3,X4),X1),f10(f32(X0,rotate_right(X1),X2,X3,X4),X1)),non_ordered_pair(f10(f32(X0,rotate_right(X1),X2,X3,X4),X1),f11(f32(X0,rotate_right(X1),X2,X3,X4),X1)))))
| ~ closed(X3,X4)
| ~ maps(X0,rotate_right(X1),X3)
| homomorphism(X0,rotate_right(X1),X2,X3,X4)
| ~ closed(rotate_right(X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1467])]) ).
fof(f1544,plain,
( spl0_134
<=> ! [X10,X11,X14,X13,X12] :
( ~ closed(X11,X12)
| ~ closed(X13,X14)
| ~ maps(X10,X11,X13)
| homomorphism(X10,X11,X12,X13,X14)
| member(f32(X10,X11,X12,X13,X14),X11) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_134])]) ).
fof(f1829,plain,
( ! [X2,X3,X0,X1,X4] :
( f32(X0,rotate_right(X1),X2,X3,X4) = non_ordered_pair(non_ordered_pair(f9(f32(X0,rotate_right(X1),X2,X3,X4),X1),f9(f32(X0,rotate_right(X1),X2,X3,X4),X1)),non_ordered_pair(f9(f32(X0,rotate_right(X1),X2,X3,X4),X1),non_ordered_pair(non_ordered_pair(f10(f32(X0,rotate_right(X1),X2,X3,X4),X1),f10(f32(X0,rotate_right(X1),X2,X3,X4),X1)),non_ordered_pair(f10(f32(X0,rotate_right(X1),X2,X3,X4),X1),f11(f32(X0,rotate_right(X1),X2,X3,X4),X1)))))
| ~ closed(X3,X4)
| ~ maps(X0,rotate_right(X1),X3)
| homomorphism(X0,rotate_right(X1),X2,X3,X4)
| ~ closed(rotate_right(X1),X2) )
| ~ spl0_134
| ~ spl0_143 ),
inference(resolution,[],[f1779,f1545]) ).
fof(f1545,plain,
( ! [X10,X11,X14,X12,X13] :
( member(f32(X10,X11,X12,X13,X14),X11)
| ~ closed(X13,X14)
| ~ maps(X10,X11,X13)
| homomorphism(X10,X11,X12,X13,X14)
| ~ closed(X11,X12) )
| ~ spl0_134 ),
inference(avatar_component_clause,[],[f1544]) ).
fof(f53642,plain,
( spl0_1466
| ~ spl0_136
| ~ spl0_142 ),
inference(avatar_split_clause,[],[f1809,f1774,f1552,f53640]) ).
fof(f53640,plain,
( spl0_1466
<=> ! [X4,X0,X3,X2,X1] :
( f33(X0,flip_range_of(X1),X2,X3,X4) = non_ordered_pair(non_ordered_pair(f12(f33(X0,flip_range_of(X1),X2,X3,X4),X1),f12(f33(X0,flip_range_of(X1),X2,X3,X4),X1)),non_ordered_pair(f12(f33(X0,flip_range_of(X1),X2,X3,X4),X1),non_ordered_pair(non_ordered_pair(f13(f33(X0,flip_range_of(X1),X2,X3,X4),X1),f13(f33(X0,flip_range_of(X1),X2,X3,X4),X1)),non_ordered_pair(f13(f33(X0,flip_range_of(X1),X2,X3,X4),X1),f14(f33(X0,flip_range_of(X1),X2,X3,X4),X1)))))
| ~ closed(X3,X4)
| ~ maps(X0,flip_range_of(X1),X3)
| homomorphism(X0,flip_range_of(X1),X2,X3,X4)
| ~ closed(flip_range_of(X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1466])]) ).
fof(f1809,plain,
( ! [X2,X3,X0,X1,X4] :
( f33(X0,flip_range_of(X1),X2,X3,X4) = non_ordered_pair(non_ordered_pair(f12(f33(X0,flip_range_of(X1),X2,X3,X4),X1),f12(f33(X0,flip_range_of(X1),X2,X3,X4),X1)),non_ordered_pair(f12(f33(X0,flip_range_of(X1),X2,X3,X4),X1),non_ordered_pair(non_ordered_pair(f13(f33(X0,flip_range_of(X1),X2,X3,X4),X1),f13(f33(X0,flip_range_of(X1),X2,X3,X4),X1)),non_ordered_pair(f13(f33(X0,flip_range_of(X1),X2,X3,X4),X1),f14(f33(X0,flip_range_of(X1),X2,X3,X4),X1)))))
| ~ closed(X3,X4)
| ~ maps(X0,flip_range_of(X1),X3)
| homomorphism(X0,flip_range_of(X1),X2,X3,X4)
| ~ closed(flip_range_of(X1),X2) )
| ~ spl0_136
| ~ spl0_142 ),
inference(resolution,[],[f1775,f1553]) ).
fof(f53638,plain,
( spl0_1465
| ~ spl0_134
| ~ spl0_142 ),
inference(avatar_split_clause,[],[f1808,f1774,f1544,f53636]) ).
fof(f53636,plain,
( spl0_1465
<=> ! [X4,X0,X3,X2,X1] :
( f32(X0,flip_range_of(X1),X2,X3,X4) = non_ordered_pair(non_ordered_pair(f12(f32(X0,flip_range_of(X1),X2,X3,X4),X1),f12(f32(X0,flip_range_of(X1),X2,X3,X4),X1)),non_ordered_pair(f12(f32(X0,flip_range_of(X1),X2,X3,X4),X1),non_ordered_pair(non_ordered_pair(f13(f32(X0,flip_range_of(X1),X2,X3,X4),X1),f13(f32(X0,flip_range_of(X1),X2,X3,X4),X1)),non_ordered_pair(f13(f32(X0,flip_range_of(X1),X2,X3,X4),X1),f14(f32(X0,flip_range_of(X1),X2,X3,X4),X1)))))
| ~ closed(X3,X4)
| ~ maps(X0,flip_range_of(X1),X3)
| homomorphism(X0,flip_range_of(X1),X2,X3,X4)
| ~ closed(flip_range_of(X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1465])]) ).
fof(f1808,plain,
( ! [X2,X3,X0,X1,X4] :
( f32(X0,flip_range_of(X1),X2,X3,X4) = non_ordered_pair(non_ordered_pair(f12(f32(X0,flip_range_of(X1),X2,X3,X4),X1),f12(f32(X0,flip_range_of(X1),X2,X3,X4),X1)),non_ordered_pair(f12(f32(X0,flip_range_of(X1),X2,X3,X4),X1),non_ordered_pair(non_ordered_pair(f13(f32(X0,flip_range_of(X1),X2,X3,X4),X1),f13(f32(X0,flip_range_of(X1),X2,X3,X4),X1)),non_ordered_pair(f13(f32(X0,flip_range_of(X1),X2,X3,X4),X1),f14(f32(X0,flip_range_of(X1),X2,X3,X4),X1)))))
| ~ closed(X3,X4)
| ~ maps(X0,flip_range_of(X1),X3)
| homomorphism(X0,flip_range_of(X1),X2,X3,X4)
| ~ closed(flip_range_of(X1),X2) )
| ~ spl0_134
| ~ spl0_142 ),
inference(resolution,[],[f1775,f1545]) ).
fof(f53244,plain,
( spl0_1464
| ~ spl0_108
| ~ spl0_145 ),
inference(avatar_split_clause,[],[f1905,f1786,f1072,f53242]) ).
fof(f53242,plain,
( spl0_1464
<=> ! [X2,X0,X1] :
( ~ member(X0,rotate_right(image(X1,X2)))
| non_ordered_pair(non_ordered_pair(f10(X0,image(X1,X2)),f10(X0,image(X1,X2))),non_ordered_pair(f10(X0,image(X1,X2)),non_ordered_pair(non_ordered_pair(f11(X0,image(X1,X2)),f11(X0,image(X1,X2))),non_ordered_pair(f11(X0,image(X1,X2)),f9(X0,image(X1,X2)))))) = second(f22(non_ordered_pair(non_ordered_pair(f10(X0,image(X1,X2)),f10(X0,image(X1,X2))),non_ordered_pair(f10(X0,image(X1,X2)),non_ordered_pair(non_ordered_pair(f11(X0,image(X1,X2)),f11(X0,image(X1,X2))),non_ordered_pair(f11(X0,image(X1,X2)),f9(X0,image(X1,X2)))))),X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1464])]) ).
fof(f1072,plain,
( spl0_108
<=> ! [X0,X7,X3] :
( ~ member(X3,image(X0,X7))
| second(f22(X3,X0,X7)) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_108])]) ).
fof(f1905,plain,
( ! [X2,X0,X1] :
( ~ member(X0,rotate_right(image(X1,X2)))
| non_ordered_pair(non_ordered_pair(f10(X0,image(X1,X2)),f10(X0,image(X1,X2))),non_ordered_pair(f10(X0,image(X1,X2)),non_ordered_pair(non_ordered_pair(f11(X0,image(X1,X2)),f11(X0,image(X1,X2))),non_ordered_pair(f11(X0,image(X1,X2)),f9(X0,image(X1,X2)))))) = second(f22(non_ordered_pair(non_ordered_pair(f10(X0,image(X1,X2)),f10(X0,image(X1,X2))),non_ordered_pair(f10(X0,image(X1,X2)),non_ordered_pair(non_ordered_pair(f11(X0,image(X1,X2)),f11(X0,image(X1,X2))),non_ordered_pair(f11(X0,image(X1,X2)),f9(X0,image(X1,X2)))))),X1,X2)) )
| ~ spl0_108
| ~ spl0_145 ),
inference(resolution,[],[f1787,f1073]) ).
fof(f1073,plain,
( ! [X3,X0,X7] :
( ~ member(X3,image(X0,X7))
| second(f22(X3,X0,X7)) = X3 )
| ~ spl0_108 ),
inference(avatar_component_clause,[],[f1072]) ).
fof(f53240,plain,
( spl0_1463
| ~ spl0_108
| ~ spl0_144 ),
inference(avatar_split_clause,[],[f1862,f1782,f1072,f53238]) ).
fof(f53238,plain,
( spl0_1463
<=> ! [X2,X0,X1] :
( ~ member(X0,flip_range_of(image(X1,X2)))
| non_ordered_pair(non_ordered_pair(f12(X0,image(X1,X2)),f12(X0,image(X1,X2))),non_ordered_pair(f12(X0,image(X1,X2)),non_ordered_pair(non_ordered_pair(f14(X0,image(X1,X2)),f14(X0,image(X1,X2))),non_ordered_pair(f14(X0,image(X1,X2)),f13(X0,image(X1,X2)))))) = second(f22(non_ordered_pair(non_ordered_pair(f12(X0,image(X1,X2)),f12(X0,image(X1,X2))),non_ordered_pair(f12(X0,image(X1,X2)),non_ordered_pair(non_ordered_pair(f14(X0,image(X1,X2)),f14(X0,image(X1,X2))),non_ordered_pair(f14(X0,image(X1,X2)),f13(X0,image(X1,X2)))))),X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1463])]) ).
fof(f1862,plain,
( ! [X2,X0,X1] :
( ~ member(X0,flip_range_of(image(X1,X2)))
| non_ordered_pair(non_ordered_pair(f12(X0,image(X1,X2)),f12(X0,image(X1,X2))),non_ordered_pair(f12(X0,image(X1,X2)),non_ordered_pair(non_ordered_pair(f14(X0,image(X1,X2)),f14(X0,image(X1,X2))),non_ordered_pair(f14(X0,image(X1,X2)),f13(X0,image(X1,X2)))))) = second(f22(non_ordered_pair(non_ordered_pair(f12(X0,image(X1,X2)),f12(X0,image(X1,X2))),non_ordered_pair(f12(X0,image(X1,X2)),non_ordered_pair(non_ordered_pair(f14(X0,image(X1,X2)),f14(X0,image(X1,X2))),non_ordered_pair(f14(X0,image(X1,X2)),f13(X0,image(X1,X2)))))),X1,X2)) )
| ~ spl0_108
| ~ spl0_144 ),
inference(resolution,[],[f1783,f1073]) ).
fof(f52837,plain,
( spl0_1462
| ~ spl0_145
| ~ spl0_166 ),
inference(avatar_split_clause,[],[f2335,f2251,f1786,f52835]) ).
fof(f52835,plain,
( spl0_1462
<=> ! [X0,X1] : ~ member(X0,rotate_right(image(empty_set,X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1462])]) ).
fof(f2335,plain,
( ! [X0,X1] : ~ member(X0,rotate_right(image(empty_set,X1)))
| ~ spl0_145
| ~ spl0_166 ),
inference(resolution,[],[f2252,f1787]) ).
fof(f52833,plain,
( spl0_1461
| ~ spl0_101
| ~ spl0_145 ),
inference(avatar_split_clause,[],[f1878,f1786,f952,f52831]) ).
fof(f52831,plain,
( spl0_1461
<=> ! [X2,X0,X1] :
( ~ member(X0,rotate_right(non_ordered_pair(X1,X2)))
| non_ordered_pair(non_ordered_pair(f10(X0,non_ordered_pair(X1,X2)),f10(X0,non_ordered_pair(X1,X2))),non_ordered_pair(f10(X0,non_ordered_pair(X1,X2)),non_ordered_pair(non_ordered_pair(f11(X0,non_ordered_pair(X1,X2)),f11(X0,non_ordered_pair(X1,X2))),non_ordered_pair(f11(X0,non_ordered_pair(X1,X2)),f9(X0,non_ordered_pair(X1,X2)))))) = X1
| non_ordered_pair(non_ordered_pair(f10(X0,non_ordered_pair(X1,X2)),f10(X0,non_ordered_pair(X1,X2))),non_ordered_pair(f10(X0,non_ordered_pair(X1,X2)),non_ordered_pair(non_ordered_pair(f11(X0,non_ordered_pair(X1,X2)),f11(X0,non_ordered_pair(X1,X2))),non_ordered_pair(f11(X0,non_ordered_pair(X1,X2)),f9(X0,non_ordered_pair(X1,X2)))))) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1461])]) ).
fof(f952,plain,
( spl0_101
<=> ! [X2,X0,X1] :
( X1 = X2
| X0 = X2
| ~ member(X2,non_ordered_pair(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_101])]) ).
fof(f1878,plain,
( ! [X2,X0,X1] :
( ~ member(X0,rotate_right(non_ordered_pair(X1,X2)))
| non_ordered_pair(non_ordered_pair(f10(X0,non_ordered_pair(X1,X2)),f10(X0,non_ordered_pair(X1,X2))),non_ordered_pair(f10(X0,non_ordered_pair(X1,X2)),non_ordered_pair(non_ordered_pair(f11(X0,non_ordered_pair(X1,X2)),f11(X0,non_ordered_pair(X1,X2))),non_ordered_pair(f11(X0,non_ordered_pair(X1,X2)),f9(X0,non_ordered_pair(X1,X2)))))) = X1
| non_ordered_pair(non_ordered_pair(f10(X0,non_ordered_pair(X1,X2)),f10(X0,non_ordered_pair(X1,X2))),non_ordered_pair(f10(X0,non_ordered_pair(X1,X2)),non_ordered_pair(non_ordered_pair(f11(X0,non_ordered_pair(X1,X2)),f11(X0,non_ordered_pair(X1,X2))),non_ordered_pair(f11(X0,non_ordered_pair(X1,X2)),f9(X0,non_ordered_pair(X1,X2)))))) = X2 )
| ~ spl0_101
| ~ spl0_145 ),
inference(resolution,[],[f1787,f953]) ).
fof(f953,plain,
( ! [X2,X0,X1] :
( ~ member(X2,non_ordered_pair(X0,X1))
| X0 = X2
| X1 = X2 )
| ~ spl0_101 ),
inference(avatar_component_clause,[],[f952]) ).
fof(f52829,plain,
( spl0_1460
| ~ spl0_101
| ~ spl0_144 ),
inference(avatar_split_clause,[],[f1835,f1782,f952,f52827]) ).
fof(f52827,plain,
( spl0_1460
<=> ! [X2,X0,X1] :
( ~ member(X0,flip_range_of(non_ordered_pair(X1,X2)))
| non_ordered_pair(non_ordered_pair(f12(X0,non_ordered_pair(X1,X2)),f12(X0,non_ordered_pair(X1,X2))),non_ordered_pair(f12(X0,non_ordered_pair(X1,X2)),non_ordered_pair(non_ordered_pair(f14(X0,non_ordered_pair(X1,X2)),f14(X0,non_ordered_pair(X1,X2))),non_ordered_pair(f14(X0,non_ordered_pair(X1,X2)),f13(X0,non_ordered_pair(X1,X2)))))) = X1
| non_ordered_pair(non_ordered_pair(f12(X0,non_ordered_pair(X1,X2)),f12(X0,non_ordered_pair(X1,X2))),non_ordered_pair(f12(X0,non_ordered_pair(X1,X2)),non_ordered_pair(non_ordered_pair(f14(X0,non_ordered_pair(X1,X2)),f14(X0,non_ordered_pair(X1,X2))),non_ordered_pair(f14(X0,non_ordered_pair(X1,X2)),f13(X0,non_ordered_pair(X1,X2)))))) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1460])]) ).
fof(f1835,plain,
( ! [X2,X0,X1] :
( ~ member(X0,flip_range_of(non_ordered_pair(X1,X2)))
| non_ordered_pair(non_ordered_pair(f12(X0,non_ordered_pair(X1,X2)),f12(X0,non_ordered_pair(X1,X2))),non_ordered_pair(f12(X0,non_ordered_pair(X1,X2)),non_ordered_pair(non_ordered_pair(f14(X0,non_ordered_pair(X1,X2)),f14(X0,non_ordered_pair(X1,X2))),non_ordered_pair(f14(X0,non_ordered_pair(X1,X2)),f13(X0,non_ordered_pair(X1,X2)))))) = X1
| non_ordered_pair(non_ordered_pair(f12(X0,non_ordered_pair(X1,X2)),f12(X0,non_ordered_pair(X1,X2))),non_ordered_pair(f12(X0,non_ordered_pair(X1,X2)),non_ordered_pair(non_ordered_pair(f14(X0,non_ordered_pair(X1,X2)),f14(X0,non_ordered_pair(X1,X2))),non_ordered_pair(f14(X0,non_ordered_pair(X1,X2)),f13(X0,non_ordered_pair(X1,X2)))))) = X2 )
| ~ spl0_101
| ~ spl0_144 ),
inference(resolution,[],[f1783,f953]) ).
fof(f52701,plain,
( spl0_1459
| ~ spl0_145
| ~ spl0_147 ),
inference(avatar_split_clause,[],[f1962,f1954,f1786,f52699]) ).
fof(f52699,plain,
( spl0_1459
<=> ! [X0,X3,X2,X1] :
( ~ little_set(X0)
| ~ little_set(non_ordered_pair(non_ordered_pair(f11(X1,X2),f11(X1,X2)),non_ordered_pair(f11(X1,X2),f9(X1,X2))))
| ~ little_set(f10(X1,X2))
| ~ member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,f10(X1,X2))),X3)
| ~ little_set(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,non_ordered_pair(non_ordered_pair(f11(X1,X2),f11(X1,X2)),non_ordered_pair(f11(X1,X2),f9(X1,X2))))))
| member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,non_ordered_pair(non_ordered_pair(f11(X1,X2),f11(X1,X2)),non_ordered_pair(f11(X1,X2),f9(X1,X2))))),compose(X3,X2))
| ~ member(X1,rotate_right(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1459])]) ).
fof(f1954,plain,
( spl0_147
<=> ! [X9,X0,X6,X1,X7] :
( ~ little_set(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X1)))
| ~ little_set(X0)
| ~ little_set(X1)
| ~ little_set(X6)
| ~ member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X6)),X7)
| ~ member(non_ordered_pair(non_ordered_pair(X6,X6),non_ordered_pair(X6,X1)),X9)
| member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X1)),compose(X7,X9)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_147])]) ).
fof(f1962,plain,
( ! [X2,X3,X0,X1] :
( ~ little_set(X0)
| ~ little_set(non_ordered_pair(non_ordered_pair(f11(X1,X2),f11(X1,X2)),non_ordered_pair(f11(X1,X2),f9(X1,X2))))
| ~ little_set(f10(X1,X2))
| ~ member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,f10(X1,X2))),X3)
| ~ little_set(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,non_ordered_pair(non_ordered_pair(f11(X1,X2),f11(X1,X2)),non_ordered_pair(f11(X1,X2),f9(X1,X2))))))
| member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,non_ordered_pair(non_ordered_pair(f11(X1,X2),f11(X1,X2)),non_ordered_pair(f11(X1,X2),f9(X1,X2))))),compose(X3,X2))
| ~ member(X1,rotate_right(X2)) )
| ~ spl0_145
| ~ spl0_147 ),
inference(resolution,[],[f1955,f1787]) ).
fof(f1955,plain,
( ! [X0,X1,X6,X9,X7] :
( ~ member(non_ordered_pair(non_ordered_pair(X6,X6),non_ordered_pair(X6,X1)),X9)
| ~ little_set(X0)
| ~ little_set(X1)
| ~ little_set(X6)
| ~ member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X6)),X7)
| ~ little_set(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X1)))
| member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X1)),compose(X7,X9)) )
| ~ spl0_147 ),
inference(avatar_component_clause,[],[f1954]) ).
fof(f52697,plain,
( spl0_1458
| ~ spl0_144
| ~ spl0_147 ),
inference(avatar_split_clause,[],[f1961,f1954,f1782,f52695]) ).
fof(f52695,plain,
( spl0_1458
<=> ! [X0,X3,X2,X1] :
( ~ little_set(X0)
| ~ little_set(non_ordered_pair(non_ordered_pair(f14(X1,X2),f14(X1,X2)),non_ordered_pair(f14(X1,X2),f13(X1,X2))))
| ~ little_set(f12(X1,X2))
| ~ member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,f12(X1,X2))),X3)
| ~ little_set(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,non_ordered_pair(non_ordered_pair(f14(X1,X2),f14(X1,X2)),non_ordered_pair(f14(X1,X2),f13(X1,X2))))))
| member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,non_ordered_pair(non_ordered_pair(f14(X1,X2),f14(X1,X2)),non_ordered_pair(f14(X1,X2),f13(X1,X2))))),compose(X3,X2))
| ~ member(X1,flip_range_of(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1458])]) ).
fof(f1961,plain,
( ! [X2,X3,X0,X1] :
( ~ little_set(X0)
| ~ little_set(non_ordered_pair(non_ordered_pair(f14(X1,X2),f14(X1,X2)),non_ordered_pair(f14(X1,X2),f13(X1,X2))))
| ~ little_set(f12(X1,X2))
| ~ member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,f12(X1,X2))),X3)
| ~ little_set(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,non_ordered_pair(non_ordered_pair(f14(X1,X2),f14(X1,X2)),non_ordered_pair(f14(X1,X2),f13(X1,X2))))))
| member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,non_ordered_pair(non_ordered_pair(f14(X1,X2),f14(X1,X2)),non_ordered_pair(f14(X1,X2),f13(X1,X2))))),compose(X3,X2))
| ~ member(X1,flip_range_of(X2)) )
| ~ spl0_144
| ~ spl0_147 ),
inference(resolution,[],[f1955,f1783]) ).
fof(f52681,plain,
( spl0_1457
| ~ spl0_136
| ~ spl0_137 ),
inference(avatar_split_clause,[],[f1663,f1634,f1552,f52679]) ).
fof(f52679,plain,
( spl0_1457
<=> ! [X3,X4,X0,X5,X2,X1] :
( f33(X0,compose(X1,X2),X3,X4,X5) = non_ordered_pair(non_ordered_pair(f29(f33(X0,compose(X1,X2),X3,X4,X5),X1,X2),f29(f33(X0,compose(X1,X2),X3,X4,X5),X1,X2)),non_ordered_pair(f29(f33(X0,compose(X1,X2),X3,X4,X5),X1,X2),f30(f33(X0,compose(X1,X2),X3,X4,X5),X1,X2)))
| ~ closed(X4,X5)
| ~ maps(X0,compose(X1,X2),X4)
| homomorphism(X0,compose(X1,X2),X3,X4,X5)
| ~ closed(compose(X1,X2),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1457])]) ).
fof(f1663,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( f33(X0,compose(X1,X2),X3,X4,X5) = non_ordered_pair(non_ordered_pair(f29(f33(X0,compose(X1,X2),X3,X4,X5),X1,X2),f29(f33(X0,compose(X1,X2),X3,X4,X5),X1,X2)),non_ordered_pair(f29(f33(X0,compose(X1,X2),X3,X4,X5),X1,X2),f30(f33(X0,compose(X1,X2),X3,X4,X5),X1,X2)))
| ~ closed(X4,X5)
| ~ maps(X0,compose(X1,X2),X4)
| homomorphism(X0,compose(X1,X2),X3,X4,X5)
| ~ closed(compose(X1,X2),X3) )
| ~ spl0_136
| ~ spl0_137 ),
inference(resolution,[],[f1635,f1553]) ).
fof(f52677,plain,
( spl0_1456
| ~ spl0_134
| ~ spl0_137 ),
inference(avatar_split_clause,[],[f1662,f1634,f1544,f52675]) ).
fof(f52675,plain,
( spl0_1456
<=> ! [X3,X4,X0,X5,X2,X1] :
( f32(X0,compose(X1,X2),X3,X4,X5) = non_ordered_pair(non_ordered_pair(f29(f32(X0,compose(X1,X2),X3,X4,X5),X1,X2),f29(f32(X0,compose(X1,X2),X3,X4,X5),X1,X2)),non_ordered_pair(f29(f32(X0,compose(X1,X2),X3,X4,X5),X1,X2),f30(f32(X0,compose(X1,X2),X3,X4,X5),X1,X2)))
| ~ closed(X4,X5)
| ~ maps(X0,compose(X1,X2),X4)
| homomorphism(X0,compose(X1,X2),X3,X4,X5)
| ~ closed(compose(X1,X2),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1456])]) ).
fof(f1662,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( f32(X0,compose(X1,X2),X3,X4,X5) = non_ordered_pair(non_ordered_pair(f29(f32(X0,compose(X1,X2),X3,X4,X5),X1,X2),f29(f32(X0,compose(X1,X2),X3,X4,X5),X1,X2)),non_ordered_pair(f29(f32(X0,compose(X1,X2),X3,X4,X5),X1,X2),f30(f32(X0,compose(X1,X2),X3,X4,X5),X1,X2)))
| ~ closed(X4,X5)
| ~ maps(X0,compose(X1,X2),X4)
| homomorphism(X0,compose(X1,X2),X3,X4,X5)
| ~ closed(compose(X1,X2),X3) )
| ~ spl0_134
| ~ spl0_137 ),
inference(resolution,[],[f1635,f1545]) ).
fof(f52670,plain,
( spl0_1455
| ~ spl0_144
| ~ spl0_166 ),
inference(avatar_split_clause,[],[f2334,f2251,f1782,f52668]) ).
fof(f52668,plain,
( spl0_1455
<=> ! [X0,X1] : ~ member(X0,flip_range_of(image(empty_set,X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1455])]) ).
fof(f2334,plain,
( ! [X0,X1] : ~ member(X0,flip_range_of(image(empty_set,X1)))
| ~ spl0_144
| ~ spl0_166 ),
inference(resolution,[],[f2252,f1783]) ).
fof(f51701,plain,
( spl0_1454
| ~ spl0_95
| ~ spl0_145 ),
inference(avatar_split_clause,[],[f1907,f1786,f844,f51699]) ).
fof(f51699,plain,
( spl0_1454
<=> ! [X0,X1] :
( ~ member(X0,rotate_right(range_of(X1)))
| non_ordered_pair(non_ordered_pair(f10(X0,range_of(X1)),f10(X0,range_of(X1))),non_ordered_pair(f10(X0,range_of(X1)),non_ordered_pair(non_ordered_pair(f11(X0,range_of(X1)),f11(X0,range_of(X1))),non_ordered_pair(f11(X0,range_of(X1)),f9(X0,range_of(X1)))))) = second(f27(non_ordered_pair(non_ordered_pair(f10(X0,range_of(X1)),f10(X0,range_of(X1))),non_ordered_pair(f10(X0,range_of(X1)),non_ordered_pair(non_ordered_pair(f11(X0,range_of(X1)),f11(X0,range_of(X1))),non_ordered_pair(f11(X0,range_of(X1)),f9(X0,range_of(X1)))))),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1454])]) ).
fof(f844,plain,
( spl0_95
<=> ! [X0,X3] :
( ~ member(X3,range_of(X0))
| second(f27(X3,X0)) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_95])]) ).
fof(f1907,plain,
( ! [X0,X1] :
( ~ member(X0,rotate_right(range_of(X1)))
| non_ordered_pair(non_ordered_pair(f10(X0,range_of(X1)),f10(X0,range_of(X1))),non_ordered_pair(f10(X0,range_of(X1)),non_ordered_pair(non_ordered_pair(f11(X0,range_of(X1)),f11(X0,range_of(X1))),non_ordered_pair(f11(X0,range_of(X1)),f9(X0,range_of(X1)))))) = second(f27(non_ordered_pair(non_ordered_pair(f10(X0,range_of(X1)),f10(X0,range_of(X1))),non_ordered_pair(f10(X0,range_of(X1)),non_ordered_pair(non_ordered_pair(f11(X0,range_of(X1)),f11(X0,range_of(X1))),non_ordered_pair(f11(X0,range_of(X1)),f9(X0,range_of(X1)))))),X1)) )
| ~ spl0_95
| ~ spl0_145 ),
inference(resolution,[],[f1787,f845]) ).
fof(f845,plain,
( ! [X3,X0] :
( ~ member(X3,range_of(X0))
| second(f27(X3,X0)) = X3 )
| ~ spl0_95 ),
inference(avatar_component_clause,[],[f844]) ).
fof(f51697,plain,
( spl0_1453
| ~ spl0_91
| ~ spl0_145 ),
inference(avatar_split_clause,[],[f1889,f1786,f828,f51695]) ).
fof(f51695,plain,
( spl0_1453
<=> ! [X0,X1] :
( ~ member(X0,rotate_right(domain_of(X1)))
| non_ordered_pair(non_ordered_pair(f10(X0,domain_of(X1)),f10(X0,domain_of(X1))),non_ordered_pair(f10(X0,domain_of(X1)),non_ordered_pair(non_ordered_pair(f11(X0,domain_of(X1)),f11(X0,domain_of(X1))),non_ordered_pair(f11(X0,domain_of(X1)),f9(X0,domain_of(X1)))))) = first(f8(non_ordered_pair(non_ordered_pair(f10(X0,domain_of(X1)),f10(X0,domain_of(X1))),non_ordered_pair(f10(X0,domain_of(X1)),non_ordered_pair(non_ordered_pair(f11(X0,domain_of(X1)),f11(X0,domain_of(X1))),non_ordered_pair(f11(X0,domain_of(X1)),f9(X0,domain_of(X1)))))),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1453])]) ).
fof(f828,plain,
( spl0_91
<=> ! [X0,X3] :
( ~ member(X3,domain_of(X0))
| first(f8(X3,X0)) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_91])]) ).
fof(f1889,plain,
( ! [X0,X1] :
( ~ member(X0,rotate_right(domain_of(X1)))
| non_ordered_pair(non_ordered_pair(f10(X0,domain_of(X1)),f10(X0,domain_of(X1))),non_ordered_pair(f10(X0,domain_of(X1)),non_ordered_pair(non_ordered_pair(f11(X0,domain_of(X1)),f11(X0,domain_of(X1))),non_ordered_pair(f11(X0,domain_of(X1)),f9(X0,domain_of(X1)))))) = first(f8(non_ordered_pair(non_ordered_pair(f10(X0,domain_of(X1)),f10(X0,domain_of(X1))),non_ordered_pair(f10(X0,domain_of(X1)),non_ordered_pair(non_ordered_pair(f11(X0,domain_of(X1)),f11(X0,domain_of(X1))),non_ordered_pair(f11(X0,domain_of(X1)),f9(X0,domain_of(X1)))))),X1)) )
| ~ spl0_91
| ~ spl0_145 ),
inference(resolution,[],[f1787,f829]) ).
fof(f829,plain,
( ! [X3,X0] :
( ~ member(X3,domain_of(X0))
| first(f8(X3,X0)) = X3 )
| ~ spl0_91 ),
inference(avatar_component_clause,[],[f828]) ).
fof(f51693,plain,
( spl0_1452
| ~ spl0_95
| ~ spl0_144 ),
inference(avatar_split_clause,[],[f1864,f1782,f844,f51691]) ).
fof(f51691,plain,
( spl0_1452
<=> ! [X0,X1] :
( ~ member(X0,flip_range_of(range_of(X1)))
| non_ordered_pair(non_ordered_pair(f12(X0,range_of(X1)),f12(X0,range_of(X1))),non_ordered_pair(f12(X0,range_of(X1)),non_ordered_pair(non_ordered_pair(f14(X0,range_of(X1)),f14(X0,range_of(X1))),non_ordered_pair(f14(X0,range_of(X1)),f13(X0,range_of(X1)))))) = second(f27(non_ordered_pair(non_ordered_pair(f12(X0,range_of(X1)),f12(X0,range_of(X1))),non_ordered_pair(f12(X0,range_of(X1)),non_ordered_pair(non_ordered_pair(f14(X0,range_of(X1)),f14(X0,range_of(X1))),non_ordered_pair(f14(X0,range_of(X1)),f13(X0,range_of(X1)))))),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1452])]) ).
fof(f1864,plain,
( ! [X0,X1] :
( ~ member(X0,flip_range_of(range_of(X1)))
| non_ordered_pair(non_ordered_pair(f12(X0,range_of(X1)),f12(X0,range_of(X1))),non_ordered_pair(f12(X0,range_of(X1)),non_ordered_pair(non_ordered_pair(f14(X0,range_of(X1)),f14(X0,range_of(X1))),non_ordered_pair(f14(X0,range_of(X1)),f13(X0,range_of(X1)))))) = second(f27(non_ordered_pair(non_ordered_pair(f12(X0,range_of(X1)),f12(X0,range_of(X1))),non_ordered_pair(f12(X0,range_of(X1)),non_ordered_pair(non_ordered_pair(f14(X0,range_of(X1)),f14(X0,range_of(X1))),non_ordered_pair(f14(X0,range_of(X1)),f13(X0,range_of(X1)))))),X1)) )
| ~ spl0_95
| ~ spl0_144 ),
inference(resolution,[],[f1783,f845]) ).
fof(f51689,plain,
( spl0_1451
| ~ spl0_91
| ~ spl0_144 ),
inference(avatar_split_clause,[],[f1846,f1782,f828,f51687]) ).
fof(f51687,plain,
( spl0_1451
<=> ! [X0,X1] :
( ~ member(X0,flip_range_of(domain_of(X1)))
| non_ordered_pair(non_ordered_pair(f12(X0,domain_of(X1)),f12(X0,domain_of(X1))),non_ordered_pair(f12(X0,domain_of(X1)),non_ordered_pair(non_ordered_pair(f14(X0,domain_of(X1)),f14(X0,domain_of(X1))),non_ordered_pair(f14(X0,domain_of(X1)),f13(X0,domain_of(X1)))))) = first(f8(non_ordered_pair(non_ordered_pair(f12(X0,domain_of(X1)),f12(X0,domain_of(X1))),non_ordered_pair(f12(X0,domain_of(X1)),non_ordered_pair(non_ordered_pair(f14(X0,domain_of(X1)),f14(X0,domain_of(X1))),non_ordered_pair(f14(X0,domain_of(X1)),f13(X0,domain_of(X1)))))),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1451])]) ).
fof(f1846,plain,
( ! [X0,X1] :
( ~ member(X0,flip_range_of(domain_of(X1)))
| non_ordered_pair(non_ordered_pair(f12(X0,domain_of(X1)),f12(X0,domain_of(X1))),non_ordered_pair(f12(X0,domain_of(X1)),non_ordered_pair(non_ordered_pair(f14(X0,domain_of(X1)),f14(X0,domain_of(X1))),non_ordered_pair(f14(X0,domain_of(X1)),f13(X0,domain_of(X1)))))) = first(f8(non_ordered_pair(non_ordered_pair(f12(X0,domain_of(X1)),f12(X0,domain_of(X1))),non_ordered_pair(f12(X0,domain_of(X1)),non_ordered_pair(non_ordered_pair(f14(X0,domain_of(X1)),f14(X0,domain_of(X1))),non_ordered_pair(f14(X0,domain_of(X1)),f13(X0,domain_of(X1)))))),X1)) )
| ~ spl0_91
| ~ spl0_144 ),
inference(resolution,[],[f1783,f829]) ).
fof(f51685,plain,
( spl0_1450
| ~ spl0_127
| ~ spl0_137 ),
inference(avatar_split_clause,[],[f1649,f1634,f1397,f51683]) ).
fof(f51683,plain,
( spl0_1450
<=> ! [X2,X0,X1] :
( non_ordered_pair(non_ordered_pair(second(X0),second(X0)),non_ordered_pair(second(X0),first(X0))) = non_ordered_pair(non_ordered_pair(f29(non_ordered_pair(non_ordered_pair(second(X0),second(X0)),non_ordered_pair(second(X0),first(X0))),X1,X2),f29(non_ordered_pair(non_ordered_pair(second(X0),second(X0)),non_ordered_pair(second(X0),first(X0))),X1,X2)),non_ordered_pair(f29(non_ordered_pair(non_ordered_pair(second(X0),second(X0)),non_ordered_pair(second(X0),first(X0))),X1,X2),f30(non_ordered_pair(non_ordered_pair(second(X0),second(X0)),non_ordered_pair(second(X0),first(X0))),X1,X2)))
| ~ member(X0,converse(compose(X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1450])]) ).
fof(f1649,plain,
( ! [X2,X0,X1] :
( non_ordered_pair(non_ordered_pair(second(X0),second(X0)),non_ordered_pair(second(X0),first(X0))) = non_ordered_pair(non_ordered_pair(f29(non_ordered_pair(non_ordered_pair(second(X0),second(X0)),non_ordered_pair(second(X0),first(X0))),X1,X2),f29(non_ordered_pair(non_ordered_pair(second(X0),second(X0)),non_ordered_pair(second(X0),first(X0))),X1,X2)),non_ordered_pair(f29(non_ordered_pair(non_ordered_pair(second(X0),second(X0)),non_ordered_pair(second(X0),first(X0))),X1,X2),f30(non_ordered_pair(non_ordered_pair(second(X0),second(X0)),non_ordered_pair(second(X0),first(X0))),X1,X2)))
| ~ member(X0,converse(compose(X1,X2))) )
| ~ spl0_127
| ~ spl0_137 ),
inference(resolution,[],[f1635,f1398]) ).
fof(f51678,plain,
( spl0_1449
| ~ spl0_127
| ~ spl0_166 ),
inference(avatar_split_clause,[],[f2332,f2251,f1397,f51676]) ).
fof(f51676,plain,
( spl0_1449
<=> ! [X0,X1] : ~ member(X0,converse(image(empty_set,X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1449])]) ).
fof(f2332,plain,
( ! [X0,X1] : ~ member(X0,converse(image(empty_set,X1)))
| ~ spl0_127
| ~ spl0_166 ),
inference(resolution,[],[f2252,f1398]) ).
fof(f51662,plain,
( spl0_1448
| ~ spl0_122
| ~ spl0_132 ),
inference(avatar_split_clause,[],[f1514,f1483,f1291,f51660]) ).
fof(f51660,plain,
( spl0_1448
<=> ! [X0] :
( non_ordered_pair(non_ordered_pair(f4(non_ordered_pair(non_ordered_pair(f19(first(X0)),f19(first(X0))),non_ordered_pair(f19(first(X0)),f21(first(X0)))),X0),f4(non_ordered_pair(non_ordered_pair(f19(first(X0)),f19(first(X0))),non_ordered_pair(f19(first(X0)),f21(first(X0)))),X0)),non_ordered_pair(f4(non_ordered_pair(non_ordered_pair(f19(first(X0)),f19(first(X0))),non_ordered_pair(f19(first(X0)),f21(first(X0)))),X0),f5(non_ordered_pair(non_ordered_pair(f19(first(X0)),f19(first(X0))),non_ordered_pair(f19(first(X0)),f21(first(X0)))),X0))) = X0
| single_valued_set(first(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1448])]) ).
fof(f1514,plain,
( ! [X0] :
( non_ordered_pair(non_ordered_pair(f4(non_ordered_pair(non_ordered_pair(f19(first(X0)),f19(first(X0))),non_ordered_pair(f19(first(X0)),f21(first(X0)))),X0),f4(non_ordered_pair(non_ordered_pair(f19(first(X0)),f19(first(X0))),non_ordered_pair(f19(first(X0)),f21(first(X0)))),X0)),non_ordered_pair(f4(non_ordered_pair(non_ordered_pair(f19(first(X0)),f19(first(X0))),non_ordered_pair(f19(first(X0)),f21(first(X0)))),X0),f5(non_ordered_pair(non_ordered_pair(f19(first(X0)),f19(first(X0))),non_ordered_pair(f19(first(X0)),f21(first(X0)))),X0))) = X0
| single_valued_set(first(X0)) )
| ~ spl0_122
| ~ spl0_132 ),
inference(resolution,[],[f1484,f1292]) ).
fof(f51658,plain,
( spl0_1447
| ~ spl0_121
| ~ spl0_132 ),
inference(avatar_split_clause,[],[f1513,f1483,f1287,f51656]) ).
fof(f51656,plain,
( spl0_1447
<=> ! [X0] :
( non_ordered_pair(non_ordered_pair(f4(non_ordered_pair(non_ordered_pair(f19(first(X0)),f19(first(X0))),non_ordered_pair(f19(first(X0)),f20(first(X0)))),X0),f4(non_ordered_pair(non_ordered_pair(f19(first(X0)),f19(first(X0))),non_ordered_pair(f19(first(X0)),f20(first(X0)))),X0)),non_ordered_pair(f4(non_ordered_pair(non_ordered_pair(f19(first(X0)),f19(first(X0))),non_ordered_pair(f19(first(X0)),f20(first(X0)))),X0),f5(non_ordered_pair(non_ordered_pair(f19(first(X0)),f19(first(X0))),non_ordered_pair(f19(first(X0)),f20(first(X0)))),X0))) = X0
| single_valued_set(first(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1447])]) ).
fof(f1513,plain,
( ! [X0] :
( non_ordered_pair(non_ordered_pair(f4(non_ordered_pair(non_ordered_pair(f19(first(X0)),f19(first(X0))),non_ordered_pair(f19(first(X0)),f20(first(X0)))),X0),f4(non_ordered_pair(non_ordered_pair(f19(first(X0)),f19(first(X0))),non_ordered_pair(f19(first(X0)),f20(first(X0)))),X0)),non_ordered_pair(f4(non_ordered_pair(non_ordered_pair(f19(first(X0)),f19(first(X0))),non_ordered_pair(f19(first(X0)),f20(first(X0)))),X0),f5(non_ordered_pair(non_ordered_pair(f19(first(X0)),f19(first(X0))),non_ordered_pair(f19(first(X0)),f20(first(X0)))),X0))) = X0
| single_valued_set(first(X0)) )
| ~ spl0_121
| ~ spl0_132 ),
inference(resolution,[],[f1484,f1288]) ).
fof(f51654,plain,
( spl0_1446
| ~ spl0_122
| ~ spl0_131 ),
inference(avatar_split_clause,[],[f1495,f1479,f1291,f51652]) ).
fof(f51652,plain,
( spl0_1446
<=> ! [X0] :
( non_ordered_pair(non_ordered_pair(f6(non_ordered_pair(non_ordered_pair(f19(second(X0)),f19(second(X0))),non_ordered_pair(f19(second(X0)),f21(second(X0)))),X0),f6(non_ordered_pair(non_ordered_pair(f19(second(X0)),f19(second(X0))),non_ordered_pair(f19(second(X0)),f21(second(X0)))),X0)),non_ordered_pair(f6(non_ordered_pair(non_ordered_pair(f19(second(X0)),f19(second(X0))),non_ordered_pair(f19(second(X0)),f21(second(X0)))),X0),f7(non_ordered_pair(non_ordered_pair(f19(second(X0)),f19(second(X0))),non_ordered_pair(f19(second(X0)),f21(second(X0)))),X0))) = X0
| single_valued_set(second(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1446])]) ).
fof(f1495,plain,
( ! [X0] :
( non_ordered_pair(non_ordered_pair(f6(non_ordered_pair(non_ordered_pair(f19(second(X0)),f19(second(X0))),non_ordered_pair(f19(second(X0)),f21(second(X0)))),X0),f6(non_ordered_pair(non_ordered_pair(f19(second(X0)),f19(second(X0))),non_ordered_pair(f19(second(X0)),f21(second(X0)))),X0)),non_ordered_pair(f6(non_ordered_pair(non_ordered_pair(f19(second(X0)),f19(second(X0))),non_ordered_pair(f19(second(X0)),f21(second(X0)))),X0),f7(non_ordered_pair(non_ordered_pair(f19(second(X0)),f19(second(X0))),non_ordered_pair(f19(second(X0)),f21(second(X0)))),X0))) = X0
| single_valued_set(second(X0)) )
| ~ spl0_122
| ~ spl0_131 ),
inference(resolution,[],[f1480,f1292]) ).
fof(f51650,plain,
( spl0_1445
| ~ spl0_121
| ~ spl0_131 ),
inference(avatar_split_clause,[],[f1494,f1479,f1287,f51648]) ).
fof(f51648,plain,
( spl0_1445
<=> ! [X0] :
( non_ordered_pair(non_ordered_pair(f6(non_ordered_pair(non_ordered_pair(f19(second(X0)),f19(second(X0))),non_ordered_pair(f19(second(X0)),f20(second(X0)))),X0),f6(non_ordered_pair(non_ordered_pair(f19(second(X0)),f19(second(X0))),non_ordered_pair(f19(second(X0)),f20(second(X0)))),X0)),non_ordered_pair(f6(non_ordered_pair(non_ordered_pair(f19(second(X0)),f19(second(X0))),non_ordered_pair(f19(second(X0)),f20(second(X0)))),X0),f7(non_ordered_pair(non_ordered_pair(f19(second(X0)),f19(second(X0))),non_ordered_pair(f19(second(X0)),f20(second(X0)))),X0))) = X0
| single_valued_set(second(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1445])]) ).
fof(f1494,plain,
( ! [X0] :
( non_ordered_pair(non_ordered_pair(f6(non_ordered_pair(non_ordered_pair(f19(second(X0)),f19(second(X0))),non_ordered_pair(f19(second(X0)),f20(second(X0)))),X0),f6(non_ordered_pair(non_ordered_pair(f19(second(X0)),f19(second(X0))),non_ordered_pair(f19(second(X0)),f20(second(X0)))),X0)),non_ordered_pair(f6(non_ordered_pair(non_ordered_pair(f19(second(X0)),f19(second(X0))),non_ordered_pair(f19(second(X0)),f20(second(X0)))),X0),f7(non_ordered_pair(non_ordered_pair(f19(second(X0)),f19(second(X0))),non_ordered_pair(f19(second(X0)),f20(second(X0)))),X0))) = X0
| single_valued_set(second(X0)) )
| ~ spl0_121
| ~ spl0_131 ),
inference(resolution,[],[f1480,f1288]) ).
fof(f51257,plain,
( spl0_1444
| ~ spl0_78
| ~ spl0_165 ),
inference(avatar_split_clause,[],[f2308,f2247,f644,f51255]) ).
fof(f51255,plain,
( spl0_1444
<=> ! [X0,X1] : ~ member(X0,sigma(apply(empty_set,X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1444])]) ).
fof(f2308,plain,
( ! [X0,X1] : ~ member(X0,sigma(apply(empty_set,X1)))
| ~ spl0_78
| ~ spl0_165 ),
inference(resolution,[],[f2248,f645]) ).
fof(f51253,plain,
( spl0_1443
| ~ spl0_107
| ~ spl0_143 ),
inference(avatar_split_clause,[],[f1817,f1778,f1068,f51251]) ).
fof(f51251,plain,
( spl0_1443
<=> ! [X2,X0,X1] :
( first(f22(X0,rotate_right(X1),X2)) = non_ordered_pair(non_ordered_pair(f9(first(f22(X0,rotate_right(X1),X2)),X1),f9(first(f22(X0,rotate_right(X1),X2)),X1)),non_ordered_pair(f9(first(f22(X0,rotate_right(X1),X2)),X1),non_ordered_pair(non_ordered_pair(f10(first(f22(X0,rotate_right(X1),X2)),X1),f10(first(f22(X0,rotate_right(X1),X2)),X1)),non_ordered_pair(f10(first(f22(X0,rotate_right(X1),X2)),X1),f11(first(f22(X0,rotate_right(X1),X2)),X1)))))
| ~ member(X0,image(rotate_right(X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1443])]) ).
fof(f1817,plain,
( ! [X2,X0,X1] :
( first(f22(X0,rotate_right(X1),X2)) = non_ordered_pair(non_ordered_pair(f9(first(f22(X0,rotate_right(X1),X2)),X1),f9(first(f22(X0,rotate_right(X1),X2)),X1)),non_ordered_pair(f9(first(f22(X0,rotate_right(X1),X2)),X1),non_ordered_pair(non_ordered_pair(f10(first(f22(X0,rotate_right(X1),X2)),X1),f10(first(f22(X0,rotate_right(X1),X2)),X1)),non_ordered_pair(f10(first(f22(X0,rotate_right(X1),X2)),X1),f11(first(f22(X0,rotate_right(X1),X2)),X1)))))
| ~ member(X0,image(rotate_right(X1),X2)) )
| ~ spl0_107
| ~ spl0_143 ),
inference(resolution,[],[f1779,f1069]) ).
fof(f51249,plain,
( spl0_1442
| ~ spl0_107
| ~ spl0_142 ),
inference(avatar_split_clause,[],[f1796,f1774,f1068,f51247]) ).
fof(f51247,plain,
( spl0_1442
<=> ! [X2,X0,X1] :
( first(f22(X0,flip_range_of(X1),X2)) = non_ordered_pair(non_ordered_pair(f12(first(f22(X0,flip_range_of(X1),X2)),X1),f12(first(f22(X0,flip_range_of(X1),X2)),X1)),non_ordered_pair(f12(first(f22(X0,flip_range_of(X1),X2)),X1),non_ordered_pair(non_ordered_pair(f13(first(f22(X0,flip_range_of(X1),X2)),X1),f13(first(f22(X0,flip_range_of(X1),X2)),X1)),non_ordered_pair(f13(first(f22(X0,flip_range_of(X1),X2)),X1),f14(first(f22(X0,flip_range_of(X1),X2)),X1)))))
| ~ member(X0,image(flip_range_of(X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1442])]) ).
fof(f1796,plain,
( ! [X2,X0,X1] :
( first(f22(X0,flip_range_of(X1),X2)) = non_ordered_pair(non_ordered_pair(f12(first(f22(X0,flip_range_of(X1),X2)),X1),f12(first(f22(X0,flip_range_of(X1),X2)),X1)),non_ordered_pair(f12(first(f22(X0,flip_range_of(X1),X2)),X1),non_ordered_pair(non_ordered_pair(f13(first(f22(X0,flip_range_of(X1),X2)),X1),f13(first(f22(X0,flip_range_of(X1),X2)),X1)),non_ordered_pair(f13(first(f22(X0,flip_range_of(X1),X2)),X1),f14(first(f22(X0,flip_range_of(X1),X2)),X1)))))
| ~ member(X0,image(flip_range_of(X1),X2)) )
| ~ spl0_107
| ~ spl0_142 ),
inference(resolution,[],[f1775,f1069]) ).
fof(f51065,plain,
( spl0_1441
| ~ spl0_145
| ~ spl0_149 ),
inference(avatar_split_clause,[],[f2005,f1985,f1786,f51063]) ).
fof(f51063,plain,
( spl0_1441
<=> ! [X0,X1] :
( ~ little_set(f10(X0,X1))
| ~ little_set(f11(X0,X1))
| ~ little_set(f9(X0,X1))
| member(non_ordered_pair(non_ordered_pair(f10(X0,X1),f10(X0,X1)),non_ordered_pair(f10(X0,X1),non_ordered_pair(non_ordered_pair(f9(X0,X1),f9(X0,X1)),non_ordered_pair(f9(X0,X1),f11(X0,X1))))),flip_range_of(X1))
| ~ little_set(non_ordered_pair(non_ordered_pair(f10(X0,X1),f10(X0,X1)),non_ordered_pair(f10(X0,X1),non_ordered_pair(non_ordered_pair(f9(X0,X1),f9(X0,X1)),non_ordered_pair(f9(X0,X1),f11(X0,X1))))))
| ~ member(X0,rotate_right(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1441])]) ).
fof(f2005,plain,
( ! [X0,X1] :
( ~ little_set(f10(X0,X1))
| ~ little_set(f11(X0,X1))
| ~ little_set(f9(X0,X1))
| member(non_ordered_pair(non_ordered_pair(f10(X0,X1),f10(X0,X1)),non_ordered_pair(f10(X0,X1),non_ordered_pair(non_ordered_pair(f9(X0,X1),f9(X0,X1)),non_ordered_pair(f9(X0,X1),f11(X0,X1))))),flip_range_of(X1))
| ~ little_set(non_ordered_pair(non_ordered_pair(f10(X0,X1),f10(X0,X1)),non_ordered_pair(f10(X0,X1),non_ordered_pair(non_ordered_pair(f9(X0,X1),f9(X0,X1)),non_ordered_pair(f9(X0,X1),f11(X0,X1))))))
| ~ member(X0,rotate_right(X1)) )
| ~ spl0_145
| ~ spl0_149 ),
inference(resolution,[],[f1986,f1787]) ).
fof(f51061,plain,
( spl0_1440
| ~ spl0_144
| ~ spl0_149 ),
inference(avatar_split_clause,[],[f2004,f1985,f1782,f51059]) ).
fof(f51059,plain,
( spl0_1440
<=> ! [X0,X1] :
( ~ little_set(f12(X0,X1))
| ~ little_set(f14(X0,X1))
| ~ little_set(f13(X0,X1))
| member(non_ordered_pair(non_ordered_pair(f12(X0,X1),f12(X0,X1)),non_ordered_pair(f12(X0,X1),non_ordered_pair(non_ordered_pair(f13(X0,X1),f13(X0,X1)),non_ordered_pair(f13(X0,X1),f14(X0,X1))))),flip_range_of(X1))
| ~ little_set(non_ordered_pair(non_ordered_pair(f12(X0,X1),f12(X0,X1)),non_ordered_pair(f12(X0,X1),non_ordered_pair(non_ordered_pair(f13(X0,X1),f13(X0,X1)),non_ordered_pair(f13(X0,X1),f14(X0,X1))))))
| ~ member(X0,flip_range_of(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1440])]) ).
fof(f2004,plain,
( ! [X0,X1] :
( ~ little_set(f12(X0,X1))
| ~ little_set(f14(X0,X1))
| ~ little_set(f13(X0,X1))
| member(non_ordered_pair(non_ordered_pair(f12(X0,X1),f12(X0,X1)),non_ordered_pair(f12(X0,X1),non_ordered_pair(non_ordered_pair(f13(X0,X1),f13(X0,X1)),non_ordered_pair(f13(X0,X1),f14(X0,X1))))),flip_range_of(X1))
| ~ little_set(non_ordered_pair(non_ordered_pair(f12(X0,X1),f12(X0,X1)),non_ordered_pair(f12(X0,X1),non_ordered_pair(non_ordered_pair(f13(X0,X1),f13(X0,X1)),non_ordered_pair(f13(X0,X1),f14(X0,X1))))))
| ~ member(X0,flip_range_of(X1)) )
| ~ spl0_144
| ~ spl0_149 ),
inference(resolution,[],[f1986,f1783]) ).
fof(f51057,plain,
( spl0_1439
| ~ spl0_145
| ~ spl0_148 ),
inference(avatar_split_clause,[],[f1989,f1981,f1786,f51055]) ).
fof(f51055,plain,
( spl0_1439
<=> ! [X0,X1] :
( ~ little_set(f9(X0,X1))
| ~ little_set(f11(X0,X1))
| ~ little_set(f10(X0,X1))
| member(non_ordered_pair(non_ordered_pair(f9(X0,X1),f9(X0,X1)),non_ordered_pair(f9(X0,X1),non_ordered_pair(non_ordered_pair(f10(X0,X1),f10(X0,X1)),non_ordered_pair(f10(X0,X1),f11(X0,X1))))),rotate_right(X1))
| ~ little_set(non_ordered_pair(non_ordered_pair(f9(X0,X1),f9(X0,X1)),non_ordered_pair(f9(X0,X1),non_ordered_pair(non_ordered_pair(f10(X0,X1),f10(X0,X1)),non_ordered_pair(f10(X0,X1),f11(X0,X1))))))
| ~ member(X0,rotate_right(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1439])]) ).
fof(f1989,plain,
( ! [X0,X1] :
( ~ little_set(f9(X0,X1))
| ~ little_set(f11(X0,X1))
| ~ little_set(f10(X0,X1))
| member(non_ordered_pair(non_ordered_pair(f9(X0,X1),f9(X0,X1)),non_ordered_pair(f9(X0,X1),non_ordered_pair(non_ordered_pair(f10(X0,X1),f10(X0,X1)),non_ordered_pair(f10(X0,X1),f11(X0,X1))))),rotate_right(X1))
| ~ little_set(non_ordered_pair(non_ordered_pair(f9(X0,X1),f9(X0,X1)),non_ordered_pair(f9(X0,X1),non_ordered_pair(non_ordered_pair(f10(X0,X1),f10(X0,X1)),non_ordered_pair(f10(X0,X1),f11(X0,X1))))))
| ~ member(X0,rotate_right(X1)) )
| ~ spl0_145
| ~ spl0_148 ),
inference(resolution,[],[f1982,f1787]) ).
fof(f51053,plain,
( spl0_1438
| ~ spl0_144
| ~ spl0_148 ),
inference(avatar_split_clause,[],[f1988,f1981,f1782,f51051]) ).
fof(f51051,plain,
( spl0_1438
<=> ! [X0,X1] :
( ~ little_set(f13(X0,X1))
| ~ little_set(f14(X0,X1))
| ~ little_set(f12(X0,X1))
| member(non_ordered_pair(non_ordered_pair(f13(X0,X1),f13(X0,X1)),non_ordered_pair(f13(X0,X1),non_ordered_pair(non_ordered_pair(f12(X0,X1),f12(X0,X1)),non_ordered_pair(f12(X0,X1),f14(X0,X1))))),rotate_right(X1))
| ~ little_set(non_ordered_pair(non_ordered_pair(f13(X0,X1),f13(X0,X1)),non_ordered_pair(f13(X0,X1),non_ordered_pair(non_ordered_pair(f12(X0,X1),f12(X0,X1)),non_ordered_pair(f12(X0,X1),f14(X0,X1))))))
| ~ member(X0,flip_range_of(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1438])]) ).
fof(f1988,plain,
( ! [X0,X1] :
( ~ little_set(f13(X0,X1))
| ~ little_set(f14(X0,X1))
| ~ little_set(f12(X0,X1))
| member(non_ordered_pair(non_ordered_pair(f13(X0,X1),f13(X0,X1)),non_ordered_pair(f13(X0,X1),non_ordered_pair(non_ordered_pair(f12(X0,X1),f12(X0,X1)),non_ordered_pair(f12(X0,X1),f14(X0,X1))))),rotate_right(X1))
| ~ little_set(non_ordered_pair(non_ordered_pair(f13(X0,X1),f13(X0,X1)),non_ordered_pair(f13(X0,X1),non_ordered_pair(non_ordered_pair(f12(X0,X1),f12(X0,X1)),non_ordered_pair(f12(X0,X1),f14(X0,X1))))))
| ~ member(X0,flip_range_of(X1)) )
| ~ spl0_144
| ~ spl0_148 ),
inference(resolution,[],[f1982,f1783]) ).
fof(f51046,plain,
( spl0_1437
| ~ spl0_74
| ~ spl0_165 ),
inference(avatar_split_clause,[],[f2307,f2247,f628,f51044]) ).
fof(f51044,plain,
( spl0_1437
<=> ! [X0,X1] : ~ member(X0,domain_of(apply(empty_set,X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1437])]) ).
fof(f2307,plain,
( ! [X0,X1] : ~ member(X0,domain_of(apply(empty_set,X1)))
| ~ spl0_74
| ~ spl0_165 ),
inference(resolution,[],[f2248,f629]) ).
fof(f51001,plain,
( spl0_1436
| ~ spl0_126
| ~ spl0_147 ),
inference(avatar_split_clause,[],[f1974,f1954,f1393,f50999]) ).
fof(f50999,plain,
( spl0_1436
<=> ! [X5,X4,X0,X3,X2,X1] :
( ~ little_set(X0)
| ~ little_set(X1)
| ~ little_set(X2)
| ~ member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X2)),X3)
| ~ little_set(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X1)))
| member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X1)),compose(X3,cross_product(X4,X5)))
| ~ little_set(non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X1)))
| ~ member(first(non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X1))),X4)
| ~ member(second(non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X1))),X5)
| ~ ordered_pair_predicate(non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1436])]) ).
fof(f1974,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ little_set(X0)
| ~ little_set(X1)
| ~ little_set(X2)
| ~ member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X2)),X3)
| ~ little_set(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X1)))
| member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X1)),compose(X3,cross_product(X4,X5)))
| ~ little_set(non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X1)))
| ~ member(first(non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X1))),X4)
| ~ member(second(non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X1))),X5)
| ~ ordered_pair_predicate(non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X1))) )
| ~ spl0_126
| ~ spl0_147 ),
inference(resolution,[],[f1955,f1394]) ).
fof(f50863,plain,
( spl0_1435
| ~ spl0_111
| ~ spl0_149 ),
inference(avatar_split_clause,[],[f2010,f1985,f1085,f50861]) ).
fof(f50861,plain,
( spl0_1435
<=> ! [X4,X0,X3,X2,X1] :
( ~ little_set(X0)
| ~ little_set(X1)
| ~ little_set(X2)
| member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X1)))),flip_range_of(second(f28(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,non_ordered_pair(non_ordered_pair(X1,X1),non_ordered_pair(X1,X2)))),X3,X4))))
| ~ little_set(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X1)))))
| ~ member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,non_ordered_pair(non_ordered_pair(X1,X1),non_ordered_pair(X1,X2)))),apply(X3,X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1435])]) ).
fof(f1085,plain,
( spl0_111
<=> ! [X1,X7,X3] :
( ~ member(X3,apply(X7,X1))
| member(X3,second(f28(X3,X7,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_111])]) ).
fof(f2010,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ little_set(X0)
| ~ little_set(X1)
| ~ little_set(X2)
| member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X1)))),flip_range_of(second(f28(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,non_ordered_pair(non_ordered_pair(X1,X1),non_ordered_pair(X1,X2)))),X3,X4))))
| ~ little_set(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X1)))))
| ~ member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,non_ordered_pair(non_ordered_pair(X1,X1),non_ordered_pair(X1,X2)))),apply(X3,X4)) )
| ~ spl0_111
| ~ spl0_149 ),
inference(resolution,[],[f1986,f1086]) ).
fof(f1086,plain,
( ! [X3,X1,X7] :
( member(X3,second(f28(X3,X7,X1)))
| ~ member(X3,apply(X7,X1)) )
| ~ spl0_111 ),
inference(avatar_component_clause,[],[f1085]) ).
fof(f50859,plain,
( spl0_1434
| ~ spl0_111
| ~ spl0_148 ),
inference(avatar_split_clause,[],[f1994,f1981,f1085,f50857]) ).
fof(f50857,plain,
( spl0_1434
<=> ! [X4,X0,X3,X2,X1] :
( ~ little_set(X0)
| ~ little_set(X1)
| ~ little_set(X2)
| member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X1)))),rotate_right(second(f28(non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,non_ordered_pair(non_ordered_pair(X1,X1),non_ordered_pair(X1,X0)))),X3,X4))))
| ~ little_set(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X1)))))
| ~ member(non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,non_ordered_pair(non_ordered_pair(X1,X1),non_ordered_pair(X1,X0)))),apply(X3,X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1434])]) ).
fof(f1994,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ little_set(X0)
| ~ little_set(X1)
| ~ little_set(X2)
| member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X1)))),rotate_right(second(f28(non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,non_ordered_pair(non_ordered_pair(X1,X1),non_ordered_pair(X1,X0)))),X3,X4))))
| ~ little_set(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X1)))))
| ~ member(non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,non_ordered_pair(non_ordered_pair(X1,X1),non_ordered_pair(X1,X0)))),apply(X3,X4)) )
| ~ spl0_111
| ~ spl0_148 ),
inference(resolution,[],[f1982,f1086]) ).
fof(f50693,plain,
( spl0_1433
| ~ spl0_102
| ~ spl0_149 ),
inference(avatar_split_clause,[],[f2013,f1985,f956,f50691]) ).
fof(f50691,plain,
( spl0_1433
<=> ! [X4,X0,X3,X2,X1] :
( ~ little_set(X0)
| ~ little_set(X1)
| ~ little_set(X2)
| member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X1)))),flip_range_of(intersection(X3,X4)))
| ~ little_set(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X1)))))
| ~ member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,non_ordered_pair(non_ordered_pair(X1,X1),non_ordered_pair(X1,X2)))),X3)
| ~ member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,non_ordered_pair(non_ordered_pair(X1,X1),non_ordered_pair(X1,X2)))),X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1433])]) ).
fof(f956,plain,
( spl0_102
<=> ! [X0,X1,X3] :
( ~ member(X3,X1)
| ~ member(X3,X0)
| member(X3,intersection(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_102])]) ).
fof(f2013,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ little_set(X0)
| ~ little_set(X1)
| ~ little_set(X2)
| member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X1)))),flip_range_of(intersection(X3,X4)))
| ~ little_set(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X1)))))
| ~ member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,non_ordered_pair(non_ordered_pair(X1,X1),non_ordered_pair(X1,X2)))),X3)
| ~ member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,non_ordered_pair(non_ordered_pair(X1,X1),non_ordered_pair(X1,X2)))),X4) )
| ~ spl0_102
| ~ spl0_149 ),
inference(resolution,[],[f1986,f957]) ).
fof(f957,plain,
( ! [X3,X0,X1] :
( member(X3,intersection(X0,X1))
| ~ member(X3,X0)
| ~ member(X3,X1) )
| ~ spl0_102 ),
inference(avatar_component_clause,[],[f956]) ).
fof(f50689,plain,
( spl0_1432
| ~ spl0_102
| ~ spl0_148 ),
inference(avatar_split_clause,[],[f1997,f1981,f956,f50687]) ).
fof(f50687,plain,
( spl0_1432
<=> ! [X4,X0,X3,X2,X1] :
( ~ little_set(X0)
| ~ little_set(X1)
| ~ little_set(X2)
| member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X1)))),rotate_right(intersection(X3,X4)))
| ~ little_set(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X1)))))
| ~ member(non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,non_ordered_pair(non_ordered_pair(X1,X1),non_ordered_pair(X1,X0)))),X3)
| ~ member(non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,non_ordered_pair(non_ordered_pair(X1,X1),non_ordered_pair(X1,X0)))),X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1432])]) ).
fof(f1997,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ little_set(X0)
| ~ little_set(X1)
| ~ little_set(X2)
| member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X1)))),rotate_right(intersection(X3,X4)))
| ~ little_set(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X1)))))
| ~ member(non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,non_ordered_pair(non_ordered_pair(X1,X1),non_ordered_pair(X1,X0)))),X3)
| ~ member(non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,non_ordered_pair(non_ordered_pair(X1,X1),non_ordered_pair(X1,X0)))),X4) )
| ~ spl0_102
| ~ spl0_148 ),
inference(resolution,[],[f1982,f957]) ).
fof(f50682,plain,
( spl0_1431
| ~ spl0_145
| ~ spl0_165 ),
inference(avatar_split_clause,[],[f2304,f2247,f1786,f50680]) ).
fof(f50680,plain,
( spl0_1431
<=> ! [X0,X1] : ~ member(X0,rotate_right(apply(empty_set,X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1431])]) ).
fof(f2304,plain,
( ! [X0,X1] : ~ member(X0,rotate_right(apply(empty_set,X1)))
| ~ spl0_145
| ~ spl0_165 ),
inference(resolution,[],[f2248,f1787]) ).
fof(f49908,plain,
( spl0_1430
| ~ spl0_104
| ~ spl0_143 ),
inference(avatar_split_clause,[],[f1828,f1778,f966,f49906]) ).
fof(f49906,plain,
( spl0_1430
<=> ! [X2,X0,X1] :
( f28(X0,rotate_right(X1),X2) = non_ordered_pair(non_ordered_pair(f9(f28(X0,rotate_right(X1),X2),X1),f9(f28(X0,rotate_right(X1),X2),X1)),non_ordered_pair(f9(f28(X0,rotate_right(X1),X2),X1),non_ordered_pair(non_ordered_pair(f10(f28(X0,rotate_right(X1),X2),X1),f10(f28(X0,rotate_right(X1),X2),X1)),non_ordered_pair(f10(f28(X0,rotate_right(X1),X2),X1),f11(f28(X0,rotate_right(X1),X2),X1)))))
| ~ member(X0,apply(rotate_right(X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1430])]) ).
fof(f966,plain,
( spl0_104
<=> ! [X1,X7,X3] :
( ~ member(X3,apply(X7,X1))
| member(f28(X3,X7,X1),X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_104])]) ).
fof(f1828,plain,
( ! [X2,X0,X1] :
( f28(X0,rotate_right(X1),X2) = non_ordered_pair(non_ordered_pair(f9(f28(X0,rotate_right(X1),X2),X1),f9(f28(X0,rotate_right(X1),X2),X1)),non_ordered_pair(f9(f28(X0,rotate_right(X1),X2),X1),non_ordered_pair(non_ordered_pair(f10(f28(X0,rotate_right(X1),X2),X1),f10(f28(X0,rotate_right(X1),X2),X1)),non_ordered_pair(f10(f28(X0,rotate_right(X1),X2),X1),f11(f28(X0,rotate_right(X1),X2),X1)))))
| ~ member(X0,apply(rotate_right(X1),X2)) )
| ~ spl0_104
| ~ spl0_143 ),
inference(resolution,[],[f1779,f967]) ).
fof(f967,plain,
( ! [X3,X1,X7] :
( member(f28(X3,X7,X1),X7)
| ~ member(X3,apply(X7,X1)) )
| ~ spl0_104 ),
inference(avatar_component_clause,[],[f966]) ).
fof(f49904,plain,
( spl0_1429
| ~ spl0_103
| ~ spl0_143 ),
inference(avatar_split_clause,[],[f1822,f1778,f960,f49902]) ).
fof(f49902,plain,
( spl0_1429
<=> ! [X2,X0,X1] :
( f22(X0,X1,rotate_right(X2)) = non_ordered_pair(non_ordered_pair(f9(f22(X0,X1,rotate_right(X2)),X2),f9(f22(X0,X1,rotate_right(X2)),X2)),non_ordered_pair(f9(f22(X0,X1,rotate_right(X2)),X2),non_ordered_pair(non_ordered_pair(f10(f22(X0,X1,rotate_right(X2)),X2),f10(f22(X0,X1,rotate_right(X2)),X2)),non_ordered_pair(f10(f22(X0,X1,rotate_right(X2)),X2),f11(f22(X0,X1,rotate_right(X2)),X2)))))
| ~ member(X0,image(X1,rotate_right(X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1429])]) ).
fof(f1822,plain,
( ! [X2,X0,X1] :
( f22(X0,X1,rotate_right(X2)) = non_ordered_pair(non_ordered_pair(f9(f22(X0,X1,rotate_right(X2)),X2),f9(f22(X0,X1,rotate_right(X2)),X2)),non_ordered_pair(f9(f22(X0,X1,rotate_right(X2)),X2),non_ordered_pair(non_ordered_pair(f10(f22(X0,X1,rotate_right(X2)),X2),f10(f22(X0,X1,rotate_right(X2)),X2)),non_ordered_pair(f10(f22(X0,X1,rotate_right(X2)),X2),f11(f22(X0,X1,rotate_right(X2)),X2)))))
| ~ member(X0,image(X1,rotate_right(X2))) )
| ~ spl0_103
| ~ spl0_143 ),
inference(resolution,[],[f1779,f961]) ).
fof(f49900,plain,
( spl0_1428
| ~ spl0_104
| ~ spl0_142 ),
inference(avatar_split_clause,[],[f1807,f1774,f966,f49898]) ).
fof(f49898,plain,
( spl0_1428
<=> ! [X2,X0,X1] :
( f28(X0,flip_range_of(X1),X2) = non_ordered_pair(non_ordered_pair(f12(f28(X0,flip_range_of(X1),X2),X1),f12(f28(X0,flip_range_of(X1),X2),X1)),non_ordered_pair(f12(f28(X0,flip_range_of(X1),X2),X1),non_ordered_pair(non_ordered_pair(f13(f28(X0,flip_range_of(X1),X2),X1),f13(f28(X0,flip_range_of(X1),X2),X1)),non_ordered_pair(f13(f28(X0,flip_range_of(X1),X2),X1),f14(f28(X0,flip_range_of(X1),X2),X1)))))
| ~ member(X0,apply(flip_range_of(X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1428])]) ).
fof(f1807,plain,
( ! [X2,X0,X1] :
( f28(X0,flip_range_of(X1),X2) = non_ordered_pair(non_ordered_pair(f12(f28(X0,flip_range_of(X1),X2),X1),f12(f28(X0,flip_range_of(X1),X2),X1)),non_ordered_pair(f12(f28(X0,flip_range_of(X1),X2),X1),non_ordered_pair(non_ordered_pair(f13(f28(X0,flip_range_of(X1),X2),X1),f13(f28(X0,flip_range_of(X1),X2),X1)),non_ordered_pair(f13(f28(X0,flip_range_of(X1),X2),X1),f14(f28(X0,flip_range_of(X1),X2),X1)))))
| ~ member(X0,apply(flip_range_of(X1),X2)) )
| ~ spl0_104
| ~ spl0_142 ),
inference(resolution,[],[f1775,f967]) ).
fof(f49896,plain,
( spl0_1427
| ~ spl0_103
| ~ spl0_142 ),
inference(avatar_split_clause,[],[f1801,f1774,f960,f49894]) ).
fof(f49894,plain,
( spl0_1427
<=> ! [X2,X0,X1] :
( f22(X0,X1,flip_range_of(X2)) = non_ordered_pair(non_ordered_pair(f12(f22(X0,X1,flip_range_of(X2)),X2),f12(f22(X0,X1,flip_range_of(X2)),X2)),non_ordered_pair(f12(f22(X0,X1,flip_range_of(X2)),X2),non_ordered_pair(non_ordered_pair(f13(f22(X0,X1,flip_range_of(X2)),X2),f13(f22(X0,X1,flip_range_of(X2)),X2)),non_ordered_pair(f13(f22(X0,X1,flip_range_of(X2)),X2),f14(f22(X0,X1,flip_range_of(X2)),X2)))))
| ~ member(X0,image(X1,flip_range_of(X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1427])]) ).
fof(f1801,plain,
( ! [X2,X0,X1] :
( f22(X0,X1,flip_range_of(X2)) = non_ordered_pair(non_ordered_pair(f12(f22(X0,X1,flip_range_of(X2)),X2),f12(f22(X0,X1,flip_range_of(X2)),X2)),non_ordered_pair(f12(f22(X0,X1,flip_range_of(X2)),X2),non_ordered_pair(non_ordered_pair(f13(f22(X0,X1,flip_range_of(X2)),X2),f13(f22(X0,X1,flip_range_of(X2)),X2)),non_ordered_pair(f13(f22(X0,X1,flip_range_of(X2)),X2),f14(f22(X0,X1,flip_range_of(X2)),X2)))))
| ~ member(X0,image(X1,flip_range_of(X2))) )
| ~ spl0_103
| ~ spl0_142 ),
inference(resolution,[],[f1775,f961]) ).
fof(f49809,plain,
( spl0_1426
| ~ spl0_144
| ~ spl0_165 ),
inference(avatar_split_clause,[],[f2303,f2247,f1782,f49807]) ).
fof(f49807,plain,
( spl0_1426
<=> ! [X0,X1] : ~ member(X0,flip_range_of(apply(empty_set,X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1426])]) ).
fof(f2303,plain,
( ! [X0,X1] : ~ member(X0,flip_range_of(apply(empty_set,X1)))
| ~ spl0_144
| ~ spl0_165 ),
inference(resolution,[],[f2248,f1783]) ).
fof(f48447,plain,
( spl0_1425
| ~ spl0_127
| ~ spl0_165 ),
inference(avatar_split_clause,[],[f2301,f2247,f1397,f48445]) ).
fof(f48445,plain,
( spl0_1425
<=> ! [X0,X1] : ~ member(X0,converse(apply(empty_set,X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1425])]) ).
fof(f2301,plain,
( ! [X0,X1] : ~ member(X0,converse(apply(empty_set,X1)))
| ~ spl0_127
| ~ spl0_165 ),
inference(resolution,[],[f2248,f1398]) ).
fof(f48443,plain,
( spl0_1424
| ~ spl0_82
| ~ spl0_149 ),
inference(avatar_split_clause,[],[f2018,f1985,f660,f48441]) ).
fof(f48441,plain,
( spl0_1424
<=> ! [X0,X3,X2,X1] :
( ~ little_set(X0)
| ~ little_set(X1)
| ~ little_set(X2)
| member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X1)))),flip_range_of(powerset(X3)))
| ~ little_set(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X1)))))
| ~ subset(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,non_ordered_pair(non_ordered_pair(X1,X1),non_ordered_pair(X1,X2)))),X3)
| ~ little_set(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,non_ordered_pair(non_ordered_pair(X1,X1),non_ordered_pair(X1,X2))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1424])]) ).
fof(f660,plain,
( spl0_82
<=> ! [X0,X3] :
( ~ little_set(X3)
| ~ subset(X3,X0)
| member(X3,powerset(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_82])]) ).
fof(f2018,plain,
( ! [X2,X3,X0,X1] :
( ~ little_set(X0)
| ~ little_set(X1)
| ~ little_set(X2)
| member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X1)))),flip_range_of(powerset(X3)))
| ~ little_set(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X1)))))
| ~ subset(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,non_ordered_pair(non_ordered_pair(X1,X1),non_ordered_pair(X1,X2)))),X3)
| ~ little_set(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,non_ordered_pair(non_ordered_pair(X1,X1),non_ordered_pair(X1,X2))))) )
| ~ spl0_82
| ~ spl0_149 ),
inference(resolution,[],[f1986,f661]) ).
fof(f661,plain,
( ! [X3,X0] :
( member(X3,powerset(X0))
| ~ subset(X3,X0)
| ~ little_set(X3) )
| ~ spl0_82 ),
inference(avatar_component_clause,[],[f660]) ).
fof(f48439,plain,
( spl0_1423
| ~ spl0_79
| ~ spl0_149 ),
inference(avatar_split_clause,[],[f2017,f1985,f648,f48437]) ).
fof(f48437,plain,
( spl0_1423
<=> ! [X0,X3,X2,X1] :
( ~ little_set(X0)
| ~ little_set(X1)
| ~ little_set(X2)
| member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X1)))),flip_range_of(f16(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,non_ordered_pair(non_ordered_pair(X1,X1),non_ordered_pair(X1,X2)))),X3)))
| ~ little_set(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X1)))))
| ~ member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,non_ordered_pair(non_ordered_pair(X1,X1),non_ordered_pair(X1,X2)))),sigma(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1423])]) ).
fof(f648,plain,
( spl0_79
<=> ! [X0,X3] :
( ~ member(X3,sigma(X0))
| member(X3,f16(X3,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_79])]) ).
fof(f2017,plain,
( ! [X2,X3,X0,X1] :
( ~ little_set(X0)
| ~ little_set(X1)
| ~ little_set(X2)
| member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X1)))),flip_range_of(f16(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,non_ordered_pair(non_ordered_pair(X1,X1),non_ordered_pair(X1,X2)))),X3)))
| ~ little_set(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X1)))))
| ~ member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,non_ordered_pair(non_ordered_pair(X1,X1),non_ordered_pair(X1,X2)))),sigma(X3)) )
| ~ spl0_79
| ~ spl0_149 ),
inference(resolution,[],[f1986,f649]) ).
fof(f649,plain,
( ! [X3,X0] :
( member(X3,f16(X3,X0))
| ~ member(X3,sigma(X0)) )
| ~ spl0_79 ),
inference(avatar_component_clause,[],[f648]) ).
fof(f48435,plain,
( spl0_1422
| ~ spl0_73
| ~ spl0_149 ),
inference(avatar_split_clause,[],[f2014,f1985,f624,f48433]) ).
fof(f48433,plain,
( spl0_1422
<=> ! [X0,X3,X2,X1] :
( ~ little_set(X0)
| ~ little_set(X1)
| ~ little_set(X2)
| member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X1)))),flip_range_of(complement(X3)))
| ~ little_set(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X1)))))
| member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,non_ordered_pair(non_ordered_pair(X1,X1),non_ordered_pair(X1,X2)))),X3)
| ~ little_set(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,non_ordered_pair(non_ordered_pair(X1,X1),non_ordered_pair(X1,X2))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1422])]) ).
fof(f624,plain,
( spl0_73
<=> ! [X0,X3] :
( ~ little_set(X3)
| member(X3,X0)
| member(X3,complement(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_73])]) ).
fof(f2014,plain,
( ! [X2,X3,X0,X1] :
( ~ little_set(X0)
| ~ little_set(X1)
| ~ little_set(X2)
| member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X1)))),flip_range_of(complement(X3)))
| ~ little_set(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X1)))))
| member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,non_ordered_pair(non_ordered_pair(X1,X1),non_ordered_pair(X1,X2)))),X3)
| ~ little_set(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,non_ordered_pair(non_ordered_pair(X1,X1),non_ordered_pair(X1,X2))))) )
| ~ spl0_73
| ~ spl0_149 ),
inference(resolution,[],[f1986,f625]) ).
fof(f625,plain,
( ! [X3,X0] :
( member(X3,complement(X0))
| member(X3,X0)
| ~ little_set(X3) )
| ~ spl0_73 ),
inference(avatar_component_clause,[],[f624]) ).
fof(f48431,plain,
( spl0_1421
| ~ spl0_72
| ~ spl0_149 ),
inference(avatar_split_clause,[],[f2012,f1985,f620,f48429]) ).
fof(f48429,plain,
( spl0_1421
<=> ! [X0,X3,X2,X1] :
( ~ little_set(X0)
| ~ little_set(X1)
| ~ little_set(X2)
| member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X1)))),flip_range_of(f7(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,non_ordered_pair(non_ordered_pair(X1,X1),non_ordered_pair(X1,X2)))),X3)))
| ~ little_set(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X1)))))
| ~ member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,non_ordered_pair(non_ordered_pair(X1,X1),non_ordered_pair(X1,X2)))),second(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1421])]) ).
fof(f620,plain,
( spl0_72
<=> ! [X0,X3] :
( ~ member(X3,second(X0))
| member(X3,f7(X3,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_72])]) ).
fof(f2012,plain,
( ! [X2,X3,X0,X1] :
( ~ little_set(X0)
| ~ little_set(X1)
| ~ little_set(X2)
| member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X1)))),flip_range_of(f7(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,non_ordered_pair(non_ordered_pair(X1,X1),non_ordered_pair(X1,X2)))),X3)))
| ~ little_set(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X1)))))
| ~ member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,non_ordered_pair(non_ordered_pair(X1,X1),non_ordered_pair(X1,X2)))),second(X3)) )
| ~ spl0_72
| ~ spl0_149 ),
inference(resolution,[],[f1986,f621]) ).
fof(f621,plain,
( ! [X3,X0] :
( member(X3,f7(X3,X0))
| ~ member(X3,second(X0)) )
| ~ spl0_72 ),
inference(avatar_component_clause,[],[f620]) ).
fof(f48427,plain,
( spl0_1420
| ~ spl0_71
| ~ spl0_149 ),
inference(avatar_split_clause,[],[f2009,f1985,f616,f48425]) ).
fof(f48425,plain,
( spl0_1420
<=> ! [X0,X3,X2,X1] :
( ~ little_set(X0)
| ~ little_set(X1)
| ~ little_set(X2)
| member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X1)))),flip_range_of(f4(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,non_ordered_pair(non_ordered_pair(X1,X1),non_ordered_pair(X1,X2)))),X3)))
| ~ little_set(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X1)))))
| ~ member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,non_ordered_pair(non_ordered_pair(X1,X1),non_ordered_pair(X1,X2)))),first(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1420])]) ).
fof(f616,plain,
( spl0_71
<=> ! [X0,X3] :
( ~ member(X3,first(X0))
| member(X3,f4(X3,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_71])]) ).
fof(f2009,plain,
( ! [X2,X3,X0,X1] :
( ~ little_set(X0)
| ~ little_set(X1)
| ~ little_set(X2)
| member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X1)))),flip_range_of(f4(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,non_ordered_pair(non_ordered_pair(X1,X1),non_ordered_pair(X1,X2)))),X3)))
| ~ little_set(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X1)))))
| ~ member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,non_ordered_pair(non_ordered_pair(X1,X1),non_ordered_pair(X1,X2)))),first(X3)) )
| ~ spl0_71
| ~ spl0_149 ),
inference(resolution,[],[f1986,f617]) ).
fof(f617,plain,
( ! [X3,X0] :
( member(X3,f4(X3,X0))
| ~ member(X3,first(X0)) )
| ~ spl0_71 ),
inference(avatar_component_clause,[],[f616]) ).
fof(f48423,plain,
( spl0_1419
| ~ spl0_82
| ~ spl0_148 ),
inference(avatar_split_clause,[],[f2002,f1981,f660,f48421]) ).
fof(f48421,plain,
( spl0_1419
<=> ! [X0,X3,X2,X1] :
( ~ little_set(X0)
| ~ little_set(X1)
| ~ little_set(X2)
| member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X1)))),rotate_right(powerset(X3)))
| ~ little_set(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X1)))))
| ~ subset(non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,non_ordered_pair(non_ordered_pair(X1,X1),non_ordered_pair(X1,X0)))),X3)
| ~ little_set(non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,non_ordered_pair(non_ordered_pair(X1,X1),non_ordered_pair(X1,X0))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1419])]) ).
fof(f2002,plain,
( ! [X2,X3,X0,X1] :
( ~ little_set(X0)
| ~ little_set(X1)
| ~ little_set(X2)
| member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X1)))),rotate_right(powerset(X3)))
| ~ little_set(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X1)))))
| ~ subset(non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,non_ordered_pair(non_ordered_pair(X1,X1),non_ordered_pair(X1,X0)))),X3)
| ~ little_set(non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,non_ordered_pair(non_ordered_pair(X1,X1),non_ordered_pair(X1,X0))))) )
| ~ spl0_82
| ~ spl0_148 ),
inference(resolution,[],[f1982,f661]) ).
fof(f48419,plain,
( spl0_1418
| ~ spl0_79
| ~ spl0_148 ),
inference(avatar_split_clause,[],[f2001,f1981,f648,f48417]) ).
fof(f48417,plain,
( spl0_1418
<=> ! [X0,X3,X2,X1] :
( ~ little_set(X0)
| ~ little_set(X1)
| ~ little_set(X2)
| member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X1)))),rotate_right(f16(non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,non_ordered_pair(non_ordered_pair(X1,X1),non_ordered_pair(X1,X0)))),X3)))
| ~ little_set(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X1)))))
| ~ member(non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,non_ordered_pair(non_ordered_pair(X1,X1),non_ordered_pair(X1,X0)))),sigma(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1418])]) ).
fof(f2001,plain,
( ! [X2,X3,X0,X1] :
( ~ little_set(X0)
| ~ little_set(X1)
| ~ little_set(X2)
| member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X1)))),rotate_right(f16(non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,non_ordered_pair(non_ordered_pair(X1,X1),non_ordered_pair(X1,X0)))),X3)))
| ~ little_set(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X1)))))
| ~ member(non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,non_ordered_pair(non_ordered_pair(X1,X1),non_ordered_pair(X1,X0)))),sigma(X3)) )
| ~ spl0_79
| ~ spl0_148 ),
inference(resolution,[],[f1982,f649]) ).
fof(f48415,plain,
( spl0_1417
| ~ spl0_73
| ~ spl0_148 ),
inference(avatar_split_clause,[],[f1998,f1981,f624,f48413]) ).
fof(f48413,plain,
( spl0_1417
<=> ! [X0,X3,X2,X1] :
( ~ little_set(X0)
| ~ little_set(X1)
| ~ little_set(X2)
| member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X1)))),rotate_right(complement(X3)))
| ~ little_set(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X1)))))
| member(non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,non_ordered_pair(non_ordered_pair(X1,X1),non_ordered_pair(X1,X0)))),X3)
| ~ little_set(non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,non_ordered_pair(non_ordered_pair(X1,X1),non_ordered_pair(X1,X0))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1417])]) ).
fof(f1998,plain,
( ! [X2,X3,X0,X1] :
( ~ little_set(X0)
| ~ little_set(X1)
| ~ little_set(X2)
| member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X1)))),rotate_right(complement(X3)))
| ~ little_set(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X1)))))
| member(non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,non_ordered_pair(non_ordered_pair(X1,X1),non_ordered_pair(X1,X0)))),X3)
| ~ little_set(non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,non_ordered_pair(non_ordered_pair(X1,X1),non_ordered_pair(X1,X0))))) )
| ~ spl0_73
| ~ spl0_148 ),
inference(resolution,[],[f1982,f625]) ).
fof(f48411,plain,
( spl0_1416
| ~ spl0_72
| ~ spl0_148 ),
inference(avatar_split_clause,[],[f1996,f1981,f620,f48409]) ).
fof(f48409,plain,
( spl0_1416
<=> ! [X0,X3,X2,X1] :
( ~ little_set(X0)
| ~ little_set(X1)
| ~ little_set(X2)
| member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X1)))),rotate_right(f7(non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,non_ordered_pair(non_ordered_pair(X1,X1),non_ordered_pair(X1,X0)))),X3)))
| ~ little_set(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X1)))))
| ~ member(non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,non_ordered_pair(non_ordered_pair(X1,X1),non_ordered_pair(X1,X0)))),second(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1416])]) ).
fof(f1996,plain,
( ! [X2,X3,X0,X1] :
( ~ little_set(X0)
| ~ little_set(X1)
| ~ little_set(X2)
| member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X1)))),rotate_right(f7(non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,non_ordered_pair(non_ordered_pair(X1,X1),non_ordered_pair(X1,X0)))),X3)))
| ~ little_set(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X1)))))
| ~ member(non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,non_ordered_pair(non_ordered_pair(X1,X1),non_ordered_pair(X1,X0)))),second(X3)) )
| ~ spl0_72
| ~ spl0_148 ),
inference(resolution,[],[f1982,f621]) ).
fof(f48407,plain,
( spl0_1415
| ~ spl0_71
| ~ spl0_148 ),
inference(avatar_split_clause,[],[f1993,f1981,f616,f48405]) ).
fof(f48405,plain,
( spl0_1415
<=> ! [X0,X3,X2,X1] :
( ~ little_set(X0)
| ~ little_set(X1)
| ~ little_set(X2)
| member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X1)))),rotate_right(f4(non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,non_ordered_pair(non_ordered_pair(X1,X1),non_ordered_pair(X1,X0)))),X3)))
| ~ little_set(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X1)))))
| ~ member(non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,non_ordered_pair(non_ordered_pair(X1,X1),non_ordered_pair(X1,X0)))),first(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1415])]) ).
fof(f1993,plain,
( ! [X2,X3,X0,X1] :
( ~ little_set(X0)
| ~ little_set(X1)
| ~ little_set(X2)
| member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X1)))),rotate_right(f4(non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,non_ordered_pair(non_ordered_pair(X1,X1),non_ordered_pair(X1,X0)))),X3)))
| ~ little_set(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X1)))))
| ~ member(non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,non_ordered_pair(non_ordered_pair(X1,X1),non_ordered_pair(X1,X0)))),first(X3)) )
| ~ spl0_71
| ~ spl0_148 ),
inference(resolution,[],[f1982,f617]) ).
fof(f48400,plain,
( spl0_1414
| ~ spl0_78
| ~ spl0_164 ),
inference(avatar_split_clause,[],[f2276,f2243,f644,f48398]) ).
fof(f48398,plain,
( spl0_1414
<=> ! [X0,X1] : ~ member(X0,sigma(image(X1,empty_set))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1414])]) ).
fof(f2276,plain,
( ! [X0,X1] : ~ member(X0,sigma(image(X1,empty_set)))
| ~ spl0_78
| ~ spl0_164 ),
inference(resolution,[],[f2244,f645]) ).
fof(f48396,plain,
( spl0_1413
| ~ spl0_108
| ~ spl0_139 ),
inference(avatar_split_clause,[],[f1732,f1642,f1072,f48394]) ).
fof(f48394,plain,
( spl0_1413
<=> ! [X0,X3,X2,X1] :
( ~ member(X0,compose(image(X1,X2),X3))
| non_ordered_pair(non_ordered_pair(f29(X0,image(X1,X2),X3),f29(X0,image(X1,X2),X3)),non_ordered_pair(f29(X0,image(X1,X2),X3),f31(X0,image(X1,X2),X3))) = second(f22(non_ordered_pair(non_ordered_pair(f29(X0,image(X1,X2),X3),f29(X0,image(X1,X2),X3)),non_ordered_pair(f29(X0,image(X1,X2),X3),f31(X0,image(X1,X2),X3))),X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1413])]) ).
fof(f1732,plain,
( ! [X2,X3,X0,X1] :
( ~ member(X0,compose(image(X1,X2),X3))
| non_ordered_pair(non_ordered_pair(f29(X0,image(X1,X2),X3),f29(X0,image(X1,X2),X3)),non_ordered_pair(f29(X0,image(X1,X2),X3),f31(X0,image(X1,X2),X3))) = second(f22(non_ordered_pair(non_ordered_pair(f29(X0,image(X1,X2),X3),f29(X0,image(X1,X2),X3)),non_ordered_pair(f29(X0,image(X1,X2),X3),f31(X0,image(X1,X2),X3))),X1,X2)) )
| ~ spl0_108
| ~ spl0_139 ),
inference(resolution,[],[f1643,f1073]) ).
fof(f48392,plain,
( spl0_1412
| ~ spl0_108
| ~ spl0_138 ),
inference(avatar_split_clause,[],[f1692,f1638,f1072,f48390]) ).
fof(f48390,plain,
( spl0_1412
<=> ! [X0,X3,X2,X1] :
( ~ member(X0,compose(X1,image(X2,X3)))
| non_ordered_pair(non_ordered_pair(f31(X0,X1,image(X2,X3)),f31(X0,X1,image(X2,X3))),non_ordered_pair(f31(X0,X1,image(X2,X3)),f30(X0,X1,image(X2,X3)))) = second(f22(non_ordered_pair(non_ordered_pair(f31(X0,X1,image(X2,X3)),f31(X0,X1,image(X2,X3))),non_ordered_pair(f31(X0,X1,image(X2,X3)),f30(X0,X1,image(X2,X3)))),X2,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1412])]) ).
fof(f1692,plain,
( ! [X2,X3,X0,X1] :
( ~ member(X0,compose(X1,image(X2,X3)))
| non_ordered_pair(non_ordered_pair(f31(X0,X1,image(X2,X3)),f31(X0,X1,image(X2,X3))),non_ordered_pair(f31(X0,X1,image(X2,X3)),f30(X0,X1,image(X2,X3)))) = second(f22(non_ordered_pair(non_ordered_pair(f31(X0,X1,image(X2,X3)),f31(X0,X1,image(X2,X3))),non_ordered_pair(f31(X0,X1,image(X2,X3)),f30(X0,X1,image(X2,X3)))),X2,X3)) )
| ~ spl0_108
| ~ spl0_138 ),
inference(resolution,[],[f1639,f1073]) ).
fof(f47983,plain,
( spl0_1411
| ~ spl0_101
| ~ spl0_139 ),
inference(avatar_split_clause,[],[f1707,f1642,f952,f47981]) ).
fof(f47981,plain,
( spl0_1411
<=> ! [X0,X3,X2,X1] :
( ~ member(X0,compose(non_ordered_pair(X1,X2),X3))
| non_ordered_pair(non_ordered_pair(f29(X0,non_ordered_pair(X1,X2),X3),f29(X0,non_ordered_pair(X1,X2),X3)),non_ordered_pair(f29(X0,non_ordered_pair(X1,X2),X3),f31(X0,non_ordered_pair(X1,X2),X3))) = X1
| non_ordered_pair(non_ordered_pair(f29(X0,non_ordered_pair(X1,X2),X3),f29(X0,non_ordered_pair(X1,X2),X3)),non_ordered_pair(f29(X0,non_ordered_pair(X1,X2),X3),f31(X0,non_ordered_pair(X1,X2),X3))) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1411])]) ).
fof(f1707,plain,
( ! [X2,X3,X0,X1] :
( ~ member(X0,compose(non_ordered_pair(X1,X2),X3))
| non_ordered_pair(non_ordered_pair(f29(X0,non_ordered_pair(X1,X2),X3),f29(X0,non_ordered_pair(X1,X2),X3)),non_ordered_pair(f29(X0,non_ordered_pair(X1,X2),X3),f31(X0,non_ordered_pair(X1,X2),X3))) = X1
| non_ordered_pair(non_ordered_pair(f29(X0,non_ordered_pair(X1,X2),X3),f29(X0,non_ordered_pair(X1,X2),X3)),non_ordered_pair(f29(X0,non_ordered_pair(X1,X2),X3),f31(X0,non_ordered_pair(X1,X2),X3))) = X2 )
| ~ spl0_101
| ~ spl0_139 ),
inference(resolution,[],[f1643,f953]) ).
fof(f47979,plain,
( spl0_1410
| ~ spl0_101
| ~ spl0_138 ),
inference(avatar_split_clause,[],[f1667,f1638,f952,f47977]) ).
fof(f47977,plain,
( spl0_1410
<=> ! [X0,X3,X2,X1] :
( ~ member(X0,compose(X1,non_ordered_pair(X2,X3)))
| non_ordered_pair(non_ordered_pair(f31(X0,X1,non_ordered_pair(X2,X3)),f31(X0,X1,non_ordered_pair(X2,X3))),non_ordered_pair(f31(X0,X1,non_ordered_pair(X2,X3)),f30(X0,X1,non_ordered_pair(X2,X3)))) = X2
| non_ordered_pair(non_ordered_pair(f31(X0,X1,non_ordered_pair(X2,X3)),f31(X0,X1,non_ordered_pair(X2,X3))),non_ordered_pair(f31(X0,X1,non_ordered_pair(X2,X3)),f30(X0,X1,non_ordered_pair(X2,X3)))) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1410])]) ).
fof(f1667,plain,
( ! [X2,X3,X0,X1] :
( ~ member(X0,compose(X1,non_ordered_pair(X2,X3)))
| non_ordered_pair(non_ordered_pair(f31(X0,X1,non_ordered_pair(X2,X3)),f31(X0,X1,non_ordered_pair(X2,X3))),non_ordered_pair(f31(X0,X1,non_ordered_pair(X2,X3)),f30(X0,X1,non_ordered_pair(X2,X3)))) = X2
| non_ordered_pair(non_ordered_pair(f31(X0,X1,non_ordered_pair(X2,X3)),f31(X0,X1,non_ordered_pair(X2,X3))),non_ordered_pair(f31(X0,X1,non_ordered_pair(X2,X3)),f30(X0,X1,non_ordered_pair(X2,X3)))) = X3 )
| ~ spl0_101
| ~ spl0_138 ),
inference(resolution,[],[f1639,f953]) ).
fof(f47720,plain,
( spl0_1409
| ~ spl0_74
| ~ spl0_164 ),
inference(avatar_split_clause,[],[f2275,f2243,f628,f47718]) ).
fof(f47718,plain,
( spl0_1409
<=> ! [X0,X1] : ~ member(X0,domain_of(image(X1,empty_set))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1409])]) ).
fof(f2275,plain,
( ! [X0,X1] : ~ member(X0,domain_of(image(X1,empty_set)))
| ~ spl0_74
| ~ spl0_164 ),
inference(resolution,[],[f2244,f629]) ).
fof(f47716,plain,
( spl0_1408
| ~ spl0_44
| ~ spl0_149 ),
inference(avatar_split_clause,[],[f2007,f1985,f377,f47714]) ).
fof(f47714,plain,
( spl0_1408
<=> ! [X0,X3,X2,X1] :
( ~ little_set(X0)
| ~ little_set(X1)
| ~ little_set(X2)
| member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X1)))),flip_range_of(non_ordered_pair(X3,non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,non_ordered_pair(non_ordered_pair(X1,X1),non_ordered_pair(X1,X2)))))))
| ~ little_set(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X1)))))
| ~ little_set(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,non_ordered_pair(non_ordered_pair(X1,X1),non_ordered_pair(X1,X2))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1408])]) ).
fof(f377,plain,
( spl0_44
<=> ! [X2,X0] :
( ~ little_set(X2)
| member(X2,non_ordered_pair(X0,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_44])]) ).
fof(f2007,plain,
( ! [X2,X3,X0,X1] :
( ~ little_set(X0)
| ~ little_set(X1)
| ~ little_set(X2)
| member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X1)))),flip_range_of(non_ordered_pair(X3,non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,non_ordered_pair(non_ordered_pair(X1,X1),non_ordered_pair(X1,X2)))))))
| ~ little_set(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X1)))))
| ~ little_set(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,non_ordered_pair(non_ordered_pair(X1,X1),non_ordered_pair(X1,X2))))) )
| ~ spl0_44
| ~ spl0_149 ),
inference(resolution,[],[f1986,f378]) ).
fof(f378,plain,
( ! [X2,X0] :
( member(X2,non_ordered_pair(X0,X2))
| ~ little_set(X2) )
| ~ spl0_44 ),
inference(avatar_component_clause,[],[f377]) ).
fof(f47712,plain,
( spl0_1407
| ~ spl0_43
| ~ spl0_149 ),
inference(avatar_split_clause,[],[f2006,f1985,f373,f47710]) ).
fof(f47710,plain,
( spl0_1407
<=> ! [X0,X3,X2,X1] :
( ~ little_set(X0)
| ~ little_set(X1)
| ~ little_set(X2)
| member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X1)))),flip_range_of(non_ordered_pair(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,non_ordered_pair(non_ordered_pair(X1,X1),non_ordered_pair(X1,X2)))),X3)))
| ~ little_set(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X1)))))
| ~ little_set(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,non_ordered_pair(non_ordered_pair(X1,X1),non_ordered_pair(X1,X2))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1407])]) ).
fof(f373,plain,
( spl0_43
<=> ! [X2,X1] :
( ~ little_set(X2)
| member(X2,non_ordered_pair(X2,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_43])]) ).
fof(f2006,plain,
( ! [X2,X3,X0,X1] :
( ~ little_set(X0)
| ~ little_set(X1)
| ~ little_set(X2)
| member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X1)))),flip_range_of(non_ordered_pair(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,non_ordered_pair(non_ordered_pair(X1,X1),non_ordered_pair(X1,X2)))),X3)))
| ~ little_set(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X1)))))
| ~ little_set(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,non_ordered_pair(non_ordered_pair(X1,X1),non_ordered_pair(X1,X2))))) )
| ~ spl0_43
| ~ spl0_149 ),
inference(resolution,[],[f1986,f374]) ).
fof(f374,plain,
( ! [X2,X1] :
( member(X2,non_ordered_pair(X2,X1))
| ~ little_set(X2) )
| ~ spl0_43 ),
inference(avatar_component_clause,[],[f373]) ).
fof(f47708,plain,
( spl0_1406
| ~ spl0_44
| ~ spl0_148 ),
inference(avatar_split_clause,[],[f1991,f1981,f377,f47706]) ).
fof(f47706,plain,
( spl0_1406
<=> ! [X0,X3,X2,X1] :
( ~ little_set(X0)
| ~ little_set(X1)
| ~ little_set(X2)
| member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X1)))),rotate_right(non_ordered_pair(X3,non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,non_ordered_pair(non_ordered_pair(X1,X1),non_ordered_pair(X1,X0)))))))
| ~ little_set(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X1)))))
| ~ little_set(non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,non_ordered_pair(non_ordered_pair(X1,X1),non_ordered_pair(X1,X0))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1406])]) ).
fof(f1991,plain,
( ! [X2,X3,X0,X1] :
( ~ little_set(X0)
| ~ little_set(X1)
| ~ little_set(X2)
| member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X1)))),rotate_right(non_ordered_pair(X3,non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,non_ordered_pair(non_ordered_pair(X1,X1),non_ordered_pair(X1,X0)))))))
| ~ little_set(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X1)))))
| ~ little_set(non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,non_ordered_pair(non_ordered_pair(X1,X1),non_ordered_pair(X1,X0))))) )
| ~ spl0_44
| ~ spl0_148 ),
inference(resolution,[],[f1982,f378]) ).
fof(f47704,plain,
( spl0_1405
| ~ spl0_43
| ~ spl0_148 ),
inference(avatar_split_clause,[],[f1990,f1981,f373,f47702]) ).
fof(f47702,plain,
( spl0_1405
<=> ! [X0,X3,X2,X1] :
( ~ little_set(X0)
| ~ little_set(X1)
| ~ little_set(X2)
| member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X1)))),rotate_right(non_ordered_pair(non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,non_ordered_pair(non_ordered_pair(X1,X1),non_ordered_pair(X1,X0)))),X3)))
| ~ little_set(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X1)))))
| ~ little_set(non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,non_ordered_pair(non_ordered_pair(X1,X1),non_ordered_pair(X1,X0))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1405])]) ).
fof(f1990,plain,
( ! [X2,X3,X0,X1] :
( ~ little_set(X0)
| ~ little_set(X1)
| ~ little_set(X2)
| member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X1)))),rotate_right(non_ordered_pair(non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,non_ordered_pair(non_ordered_pair(X1,X1),non_ordered_pair(X1,X0)))),X3)))
| ~ little_set(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X1)))))
| ~ little_set(non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,non_ordered_pair(non_ordered_pair(X1,X1),non_ordered_pair(X1,X0))))) )
| ~ spl0_43
| ~ spl0_148 ),
inference(resolution,[],[f1982,f374]) ).
fof(f46916,plain,
( spl0_1404
| ~ spl0_113
| ~ spl0_143 ),
inference(avatar_split_clause,[],[f1811,f1778,f1159,f46914]) ).
fof(f46914,plain,
( spl0_1404
<=> ! [X0,X1] :
( f1(rotate_right(X0),X1) = non_ordered_pair(non_ordered_pair(f9(f1(rotate_right(X0),X1),X0),f9(f1(rotate_right(X0),X1),X0)),non_ordered_pair(f9(f1(rotate_right(X0),X1),X0),non_ordered_pair(non_ordered_pair(f10(f1(rotate_right(X0),X1),X0),f10(f1(rotate_right(X0),X1),X0)),non_ordered_pair(f10(f1(rotate_right(X0),X1),X0),f11(f1(rotate_right(X0),X1),X0)))))
| member(f1(rotate_right(X0),X1),X1)
| rotate_right(X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1404])]) ).
fof(f1811,plain,
( ! [X0,X1] :
( f1(rotate_right(X0),X1) = non_ordered_pair(non_ordered_pair(f9(f1(rotate_right(X0),X1),X0),f9(f1(rotate_right(X0),X1),X0)),non_ordered_pair(f9(f1(rotate_right(X0),X1),X0),non_ordered_pair(non_ordered_pair(f10(f1(rotate_right(X0),X1),X0),f10(f1(rotate_right(X0),X1),X0)),non_ordered_pair(f10(f1(rotate_right(X0),X1),X0),f11(f1(rotate_right(X0),X1),X0)))))
| member(f1(rotate_right(X0),X1),X1)
| rotate_right(X0) = X1 )
| ~ spl0_113
| ~ spl0_143 ),
inference(resolution,[],[f1779,f1160]) ).
fof(f46912,plain,
( spl0_1403
| ~ spl0_113
| ~ spl0_143 ),
inference(avatar_split_clause,[],[f1810,f1778,f1159,f46910]) ).
fof(f46910,plain,
( spl0_1403
<=> ! [X0,X1] :
( f1(X0,rotate_right(X1)) = non_ordered_pair(non_ordered_pair(f9(f1(X0,rotate_right(X1)),X1),f9(f1(X0,rotate_right(X1)),X1)),non_ordered_pair(f9(f1(X0,rotate_right(X1)),X1),non_ordered_pair(non_ordered_pair(f10(f1(X0,rotate_right(X1)),X1),f10(f1(X0,rotate_right(X1)),X1)),non_ordered_pair(f10(f1(X0,rotate_right(X1)),X1),f11(f1(X0,rotate_right(X1)),X1)))))
| member(f1(X0,rotate_right(X1)),X0)
| rotate_right(X1) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1403])]) ).
fof(f1810,plain,
( ! [X0,X1] :
( f1(X0,rotate_right(X1)) = non_ordered_pair(non_ordered_pair(f9(f1(X0,rotate_right(X1)),X1),f9(f1(X0,rotate_right(X1)),X1)),non_ordered_pair(f9(f1(X0,rotate_right(X1)),X1),non_ordered_pair(non_ordered_pair(f10(f1(X0,rotate_right(X1)),X1),f10(f1(X0,rotate_right(X1)),X1)),non_ordered_pair(f10(f1(X0,rotate_right(X1)),X1),f11(f1(X0,rotate_right(X1)),X1)))))
| member(f1(X0,rotate_right(X1)),X0)
| rotate_right(X1) = X0 )
| ~ spl0_113
| ~ spl0_143 ),
inference(resolution,[],[f1779,f1160]) ).
fof(f46905,plain,
( spl0_1402
| ~ spl0_145
| ~ spl0_164 ),
inference(avatar_split_clause,[],[f2271,f2243,f1786,f46903]) ).
fof(f46903,plain,
( spl0_1402
<=> ! [X0,X1] : ~ member(X0,rotate_right(image(X1,empty_set))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1402])]) ).
fof(f2271,plain,
( ! [X0,X1] : ~ member(X0,rotate_right(image(X1,empty_set)))
| ~ spl0_145
| ~ spl0_164 ),
inference(resolution,[],[f2244,f1787]) ).
fof(f46901,plain,
( spl0_1401
| ~ spl0_113
| ~ spl0_142 ),
inference(avatar_split_clause,[],[f1790,f1774,f1159,f46899]) ).
fof(f46899,plain,
( spl0_1401
<=> ! [X0,X1] :
( f1(flip_range_of(X0),X1) = non_ordered_pair(non_ordered_pair(f12(f1(flip_range_of(X0),X1),X0),f12(f1(flip_range_of(X0),X1),X0)),non_ordered_pair(f12(f1(flip_range_of(X0),X1),X0),non_ordered_pair(non_ordered_pair(f13(f1(flip_range_of(X0),X1),X0),f13(f1(flip_range_of(X0),X1),X0)),non_ordered_pair(f13(f1(flip_range_of(X0),X1),X0),f14(f1(flip_range_of(X0),X1),X0)))))
| member(f1(flip_range_of(X0),X1),X1)
| flip_range_of(X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1401])]) ).
fof(f1790,plain,
( ! [X0,X1] :
( f1(flip_range_of(X0),X1) = non_ordered_pair(non_ordered_pair(f12(f1(flip_range_of(X0),X1),X0),f12(f1(flip_range_of(X0),X1),X0)),non_ordered_pair(f12(f1(flip_range_of(X0),X1),X0),non_ordered_pair(non_ordered_pair(f13(f1(flip_range_of(X0),X1),X0),f13(f1(flip_range_of(X0),X1),X0)),non_ordered_pair(f13(f1(flip_range_of(X0),X1),X0),f14(f1(flip_range_of(X0),X1),X0)))))
| member(f1(flip_range_of(X0),X1),X1)
| flip_range_of(X0) = X1 )
| ~ spl0_113
| ~ spl0_142 ),
inference(resolution,[],[f1775,f1160]) ).
fof(f46897,plain,
( spl0_1400
| ~ spl0_113
| ~ spl0_142 ),
inference(avatar_split_clause,[],[f1789,f1774,f1159,f46895]) ).
fof(f46895,plain,
( spl0_1400
<=> ! [X0,X1] :
( f1(X0,flip_range_of(X1)) = non_ordered_pair(non_ordered_pair(f12(f1(X0,flip_range_of(X1)),X1),f12(f1(X0,flip_range_of(X1)),X1)),non_ordered_pair(f12(f1(X0,flip_range_of(X1)),X1),non_ordered_pair(non_ordered_pair(f13(f1(X0,flip_range_of(X1)),X1),f13(f1(X0,flip_range_of(X1)),X1)),non_ordered_pair(f13(f1(X0,flip_range_of(X1)),X1),f14(f1(X0,flip_range_of(X1)),X1)))))
| member(f1(X0,flip_range_of(X1)),X0)
| flip_range_of(X1) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1400])]) ).
fof(f1789,plain,
( ! [X0,X1] :
( f1(X0,flip_range_of(X1)) = non_ordered_pair(non_ordered_pair(f12(f1(X0,flip_range_of(X1)),X1),f12(f1(X0,flip_range_of(X1)),X1)),non_ordered_pair(f12(f1(X0,flip_range_of(X1)),X1),non_ordered_pair(non_ordered_pair(f13(f1(X0,flip_range_of(X1)),X1),f13(f1(X0,flip_range_of(X1)),X1)),non_ordered_pair(f13(f1(X0,flip_range_of(X1)),X1),f14(f1(X0,flip_range_of(X1)),X1)))))
| member(f1(X0,flip_range_of(X1)),X0)
| flip_range_of(X1) = X0 )
| ~ spl0_113
| ~ spl0_142 ),
inference(resolution,[],[f1775,f1160]) ).
fof(f46281,plain,
( spl0_1399
| ~ spl0_128
| ~ spl0_149 ),
inference(avatar_split_clause,[],[f2011,f1985,f1401,f46279]) ).
fof(f46279,plain,
( spl0_1399
<=> ! [X4,X0,X3,X2,X1] :
( ~ little_set(X0)
| ~ little_set(X1)
| ~ little_set(X2)
| member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X1)))),flip_range_of(second(non_ordered_pair(non_ordered_pair(X3,X3),non_ordered_pair(X3,X4)))))
| ~ little_set(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X1)))))
| ~ little_set(X4)
| ~ member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,non_ordered_pair(non_ordered_pair(X1,X1),non_ordered_pair(X1,X2)))),X4)
| ~ little_set(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1399])]) ).
fof(f1401,plain,
( spl0_128
<=> ! [X2,X3,X4] :
( ~ little_set(X2)
| ~ little_set(X4)
| ~ member(X3,X4)
| member(X3,second(non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X4)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_128])]) ).
fof(f2011,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ little_set(X0)
| ~ little_set(X1)
| ~ little_set(X2)
| member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X1)))),flip_range_of(second(non_ordered_pair(non_ordered_pair(X3,X3),non_ordered_pair(X3,X4)))))
| ~ little_set(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X1)))))
| ~ little_set(X4)
| ~ member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,non_ordered_pair(non_ordered_pair(X1,X1),non_ordered_pair(X1,X2)))),X4)
| ~ little_set(X3) )
| ~ spl0_128
| ~ spl0_149 ),
inference(resolution,[],[f1986,f1402]) ).
fof(f1402,plain,
( ! [X2,X3,X4] :
( member(X3,second(non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X4))))
| ~ little_set(X4)
| ~ member(X3,X4)
| ~ little_set(X2) )
| ~ spl0_128 ),
inference(avatar_component_clause,[],[f1401]) ).
fof(f46274,plain,
( spl0_1398
| ~ spl0_144
| ~ spl0_164 ),
inference(avatar_split_clause,[],[f2270,f2243,f1782,f46272]) ).
fof(f46272,plain,
( spl0_1398
<=> ! [X0,X1] : ~ member(X0,flip_range_of(image(X1,empty_set))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1398])]) ).
fof(f2270,plain,
( ! [X0,X1] : ~ member(X0,flip_range_of(image(X1,empty_set)))
| ~ spl0_144
| ~ spl0_164 ),
inference(resolution,[],[f2244,f1783]) ).
fof(f46270,plain,
( spl0_1397
| ~ spl0_129
| ~ spl0_149 ),
inference(avatar_split_clause,[],[f2008,f1985,f1405,f46268]) ).
fof(f46268,plain,
( spl0_1397
<=> ! [X4,X0,X3,X2,X1] :
( ~ little_set(X0)
| ~ little_set(X1)
| ~ little_set(X2)
| member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X1)))),flip_range_of(first(non_ordered_pair(non_ordered_pair(X3,X3),non_ordered_pair(X3,X4)))))
| ~ little_set(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X1)))))
| ~ little_set(X4)
| ~ member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,non_ordered_pair(non_ordered_pair(X1,X1),non_ordered_pair(X1,X2)))),X3)
| ~ little_set(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1397])]) ).
fof(f1405,plain,
( spl0_129
<=> ! [X2,X3,X4] :
( ~ little_set(X2)
| ~ little_set(X4)
| ~ member(X3,X2)
| member(X3,first(non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X4)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_129])]) ).
fof(f2008,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ little_set(X0)
| ~ little_set(X1)
| ~ little_set(X2)
| member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X1)))),flip_range_of(first(non_ordered_pair(non_ordered_pair(X3,X3),non_ordered_pair(X3,X4)))))
| ~ little_set(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X1)))))
| ~ little_set(X4)
| ~ member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,non_ordered_pair(non_ordered_pair(X1,X1),non_ordered_pair(X1,X2)))),X3)
| ~ little_set(X3) )
| ~ spl0_129
| ~ spl0_149 ),
inference(resolution,[],[f1986,f1406]) ).
fof(f1406,plain,
( ! [X2,X3,X4] :
( member(X3,first(non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X4))))
| ~ little_set(X4)
| ~ member(X3,X2)
| ~ little_set(X2) )
| ~ spl0_129 ),
inference(avatar_component_clause,[],[f1405]) ).
fof(f46266,plain,
( spl0_1396
| ~ spl0_128
| ~ spl0_148 ),
inference(avatar_split_clause,[],[f1995,f1981,f1401,f46264]) ).
fof(f46264,plain,
( spl0_1396
<=> ! [X4,X0,X3,X2,X1] :
( ~ little_set(X0)
| ~ little_set(X1)
| ~ little_set(X2)
| member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X1)))),rotate_right(second(non_ordered_pair(non_ordered_pair(X3,X3),non_ordered_pair(X3,X4)))))
| ~ little_set(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X1)))))
| ~ little_set(X4)
| ~ member(non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,non_ordered_pair(non_ordered_pair(X1,X1),non_ordered_pair(X1,X0)))),X4)
| ~ little_set(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1396])]) ).
fof(f1995,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ little_set(X0)
| ~ little_set(X1)
| ~ little_set(X2)
| member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X1)))),rotate_right(second(non_ordered_pair(non_ordered_pair(X3,X3),non_ordered_pair(X3,X4)))))
| ~ little_set(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X1)))))
| ~ little_set(X4)
| ~ member(non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,non_ordered_pair(non_ordered_pair(X1,X1),non_ordered_pair(X1,X0)))),X4)
| ~ little_set(X3) )
| ~ spl0_128
| ~ spl0_148 ),
inference(resolution,[],[f1982,f1402]) ).
fof(f46262,plain,
( spl0_1395
| ~ spl0_129
| ~ spl0_148 ),
inference(avatar_split_clause,[],[f1992,f1981,f1405,f46260]) ).
fof(f46260,plain,
( spl0_1395
<=> ! [X4,X0,X3,X2,X1] :
( ~ little_set(X0)
| ~ little_set(X1)
| ~ little_set(X2)
| member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X1)))),rotate_right(first(non_ordered_pair(non_ordered_pair(X3,X3),non_ordered_pair(X3,X4)))))
| ~ little_set(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X1)))))
| ~ little_set(X4)
| ~ member(non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,non_ordered_pair(non_ordered_pair(X1,X1),non_ordered_pair(X1,X0)))),X3)
| ~ little_set(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1395])]) ).
fof(f1992,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ little_set(X0)
| ~ little_set(X1)
| ~ little_set(X2)
| member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X1)))),rotate_right(first(non_ordered_pair(non_ordered_pair(X3,X3),non_ordered_pair(X3,X4)))))
| ~ little_set(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X1)))))
| ~ little_set(X4)
| ~ member(non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,non_ordered_pair(non_ordered_pair(X1,X1),non_ordered_pair(X1,X0)))),X3)
| ~ little_set(X3) )
| ~ spl0_129
| ~ spl0_148 ),
inference(resolution,[],[f1982,f1406]) ).
fof(f46258,plain,
( spl0_1394
| ~ spl0_126
| ~ spl0_133 ),
inference(avatar_split_clause,[],[f1538,f1487,f1393,f46256]) ).
fof(f46256,plain,
( spl0_1394
<=> ! [X2,X0,X1] :
( ~ little_set(X0)
| member(X0,converse(cross_product(X1,X2)))
| ~ ordered_pair_predicate(X0)
| ~ little_set(non_ordered_pair(non_ordered_pair(second(X0),second(X0)),non_ordered_pair(second(X0),first(X0))))
| ~ member(first(non_ordered_pair(non_ordered_pair(second(X0),second(X0)),non_ordered_pair(second(X0),first(X0)))),X1)
| ~ member(second(non_ordered_pair(non_ordered_pair(second(X0),second(X0)),non_ordered_pair(second(X0),first(X0)))),X2)
| ~ ordered_pair_predicate(non_ordered_pair(non_ordered_pair(second(X0),second(X0)),non_ordered_pair(second(X0),first(X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1394])]) ).
fof(f1487,plain,
( spl0_133
<=> ! [X0,X3] :
( ~ ordered_pair_predicate(X3)
| ~ little_set(X3)
| member(X3,converse(X0))
| ~ member(non_ordered_pair(non_ordered_pair(second(X3),second(X3)),non_ordered_pair(second(X3),first(X3))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_133])]) ).
fof(f1538,plain,
( ! [X2,X0,X1] :
( ~ little_set(X0)
| member(X0,converse(cross_product(X1,X2)))
| ~ ordered_pair_predicate(X0)
| ~ little_set(non_ordered_pair(non_ordered_pair(second(X0),second(X0)),non_ordered_pair(second(X0),first(X0))))
| ~ member(first(non_ordered_pair(non_ordered_pair(second(X0),second(X0)),non_ordered_pair(second(X0),first(X0)))),X1)
| ~ member(second(non_ordered_pair(non_ordered_pair(second(X0),second(X0)),non_ordered_pair(second(X0),first(X0)))),X2)
| ~ ordered_pair_predicate(non_ordered_pair(non_ordered_pair(second(X0),second(X0)),non_ordered_pair(second(X0),first(X0)))) )
| ~ spl0_126
| ~ spl0_133 ),
inference(resolution,[],[f1488,f1394]) ).
fof(f1488,plain,
( ! [X3,X0] :
( ~ member(non_ordered_pair(non_ordered_pair(second(X3),second(X3)),non_ordered_pair(second(X3),first(X3))),X0)
| ~ little_set(X3)
| member(X3,converse(X0))
| ~ ordered_pair_predicate(X3) )
| ~ spl0_133 ),
inference(avatar_component_clause,[],[f1487]) ).
fof(f46254,plain,
( spl0_1393
| ~ spl0_127
| ~ spl0_132 ),
inference(avatar_split_clause,[],[f1515,f1483,f1397,f46252]) ).
fof(f46252,plain,
( spl0_1393
<=> ! [X0,X1] :
( non_ordered_pair(non_ordered_pair(f4(non_ordered_pair(non_ordered_pair(second(X0),second(X0)),non_ordered_pair(second(X0),first(X0))),X1),f4(non_ordered_pair(non_ordered_pair(second(X0),second(X0)),non_ordered_pair(second(X0),first(X0))),X1)),non_ordered_pair(f4(non_ordered_pair(non_ordered_pair(second(X0),second(X0)),non_ordered_pair(second(X0),first(X0))),X1),f5(non_ordered_pair(non_ordered_pair(second(X0),second(X0)),non_ordered_pair(second(X0),first(X0))),X1))) = X1
| ~ member(X0,converse(first(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1393])]) ).
fof(f1515,plain,
( ! [X0,X1] :
( non_ordered_pair(non_ordered_pair(f4(non_ordered_pair(non_ordered_pair(second(X0),second(X0)),non_ordered_pair(second(X0),first(X0))),X1),f4(non_ordered_pair(non_ordered_pair(second(X0),second(X0)),non_ordered_pair(second(X0),first(X0))),X1)),non_ordered_pair(f4(non_ordered_pair(non_ordered_pair(second(X0),second(X0)),non_ordered_pair(second(X0),first(X0))),X1),f5(non_ordered_pair(non_ordered_pair(second(X0),second(X0)),non_ordered_pair(second(X0),first(X0))),X1))) = X1
| ~ member(X0,converse(first(X1))) )
| ~ spl0_127
| ~ spl0_132 ),
inference(resolution,[],[f1484,f1398]) ).
fof(f46250,plain,
( spl0_1392
| ~ spl0_127
| ~ spl0_131 ),
inference(avatar_split_clause,[],[f1496,f1479,f1397,f46248]) ).
fof(f46248,plain,
( spl0_1392
<=> ! [X0,X1] :
( non_ordered_pair(non_ordered_pair(f6(non_ordered_pair(non_ordered_pair(second(X0),second(X0)),non_ordered_pair(second(X0),first(X0))),X1),f6(non_ordered_pair(non_ordered_pair(second(X0),second(X0)),non_ordered_pair(second(X0),first(X0))),X1)),non_ordered_pair(f6(non_ordered_pair(non_ordered_pair(second(X0),second(X0)),non_ordered_pair(second(X0),first(X0))),X1),f7(non_ordered_pair(non_ordered_pair(second(X0),second(X0)),non_ordered_pair(second(X0),first(X0))),X1))) = X1
| ~ member(X0,converse(second(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1392])]) ).
fof(f1496,plain,
( ! [X0,X1] :
( non_ordered_pair(non_ordered_pair(f6(non_ordered_pair(non_ordered_pair(second(X0),second(X0)),non_ordered_pair(second(X0),first(X0))),X1),f6(non_ordered_pair(non_ordered_pair(second(X0),second(X0)),non_ordered_pair(second(X0),first(X0))),X1)),non_ordered_pair(f6(non_ordered_pair(non_ordered_pair(second(X0),second(X0)),non_ordered_pair(second(X0),first(X0))),X1),f7(non_ordered_pair(non_ordered_pair(second(X0),second(X0)),non_ordered_pair(second(X0),first(X0))),X1))) = X1
| ~ member(X0,converse(second(X1))) )
| ~ spl0_127
| ~ spl0_131 ),
inference(resolution,[],[f1480,f1398]) ).
fof(f46244,plain,
( spl0_1391
| ~ spl0_66
| ~ spl0_145 ),
inference(avatar_split_clause,[],[f1909,f1786,f486,f46242]) ).
fof(f46242,plain,
( spl0_1391
<=> ! [X0] :
( ~ member(X0,rotate_right(identity_relation))
| first(non_ordered_pair(non_ordered_pair(f10(X0,identity_relation),f10(X0,identity_relation)),non_ordered_pair(f10(X0,identity_relation),non_ordered_pair(non_ordered_pair(f11(X0,identity_relation),f11(X0,identity_relation)),non_ordered_pair(f11(X0,identity_relation),f9(X0,identity_relation)))))) = second(non_ordered_pair(non_ordered_pair(f10(X0,identity_relation),f10(X0,identity_relation)),non_ordered_pair(f10(X0,identity_relation),non_ordered_pair(non_ordered_pair(f11(X0,identity_relation),f11(X0,identity_relation)),non_ordered_pair(f11(X0,identity_relation),f9(X0,identity_relation)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1391])]) ).
fof(f486,plain,
( spl0_66
<=> ! [X3] :
( ~ member(X3,identity_relation)
| first(X3) = second(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_66])]) ).
fof(f1909,plain,
( ! [X0] :
( ~ member(X0,rotate_right(identity_relation))
| first(non_ordered_pair(non_ordered_pair(f10(X0,identity_relation),f10(X0,identity_relation)),non_ordered_pair(f10(X0,identity_relation),non_ordered_pair(non_ordered_pair(f11(X0,identity_relation),f11(X0,identity_relation)),non_ordered_pair(f11(X0,identity_relation),f9(X0,identity_relation)))))) = second(non_ordered_pair(non_ordered_pair(f10(X0,identity_relation),f10(X0,identity_relation)),non_ordered_pair(f10(X0,identity_relation),non_ordered_pair(non_ordered_pair(f11(X0,identity_relation),f11(X0,identity_relation)),non_ordered_pair(f11(X0,identity_relation),f9(X0,identity_relation)))))) )
| ~ spl0_66
| ~ spl0_145 ),
inference(resolution,[],[f1787,f487]) ).
fof(f487,plain,
( ! [X3] :
( ~ member(X3,identity_relation)
| first(X3) = second(X3) )
| ~ spl0_66 ),
inference(avatar_component_clause,[],[f486]) ).
fof(f46238,plain,
( spl0_1390
| ~ spl0_66
| ~ spl0_144 ),
inference(avatar_split_clause,[],[f1866,f1782,f486,f46236]) ).
fof(f46236,plain,
( spl0_1390
<=> ! [X0] :
( ~ member(X0,flip_range_of(identity_relation))
| first(non_ordered_pair(non_ordered_pair(f12(X0,identity_relation),f12(X0,identity_relation)),non_ordered_pair(f12(X0,identity_relation),non_ordered_pair(non_ordered_pair(f14(X0,identity_relation),f14(X0,identity_relation)),non_ordered_pair(f14(X0,identity_relation),f13(X0,identity_relation)))))) = second(non_ordered_pair(non_ordered_pair(f12(X0,identity_relation),f12(X0,identity_relation)),non_ordered_pair(f12(X0,identity_relation),non_ordered_pair(non_ordered_pair(f14(X0,identity_relation),f14(X0,identity_relation)),non_ordered_pair(f14(X0,identity_relation),f13(X0,identity_relation)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1390])]) ).
fof(f1866,plain,
( ! [X0] :
( ~ member(X0,flip_range_of(identity_relation))
| first(non_ordered_pair(non_ordered_pair(f12(X0,identity_relation),f12(X0,identity_relation)),non_ordered_pair(f12(X0,identity_relation),non_ordered_pair(non_ordered_pair(f14(X0,identity_relation),f14(X0,identity_relation)),non_ordered_pair(f14(X0,identity_relation),f13(X0,identity_relation)))))) = second(non_ordered_pair(non_ordered_pair(f12(X0,identity_relation),f12(X0,identity_relation)),non_ordered_pair(f12(X0,identity_relation),non_ordered_pair(non_ordered_pair(f14(X0,identity_relation),f14(X0,identity_relation)),non_ordered_pair(f14(X0,identity_relation),f13(X0,identity_relation)))))) )
| ~ spl0_66
| ~ spl0_144 ),
inference(resolution,[],[f1783,f487]) ).
fof(f46187,plain,
( spl0_1389
| ~ spl0_127
| ~ spl0_164 ),
inference(avatar_split_clause,[],[f2268,f2243,f1397,f46185]) ).
fof(f46185,plain,
( spl0_1389
<=> ! [X0,X1] : ~ member(X0,converse(image(X1,empty_set))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1389])]) ).
fof(f2268,plain,
( ! [X0,X1] : ~ member(X0,converse(image(X1,empty_set)))
| ~ spl0_127
| ~ spl0_164 ),
inference(resolution,[],[f2244,f1398]) ).
fof(f46124,plain,
( spl0_1388
| ~ spl0_124
| ~ spl0_149 ),
inference(avatar_split_clause,[],[f2019,f1985,f1299,f46122]) ).
fof(f46122,plain,
( spl0_1388
<=> ! [X4,X0,X3,X2,X1] :
( ~ little_set(X0)
| ~ little_set(X1)
| ~ little_set(X2)
| member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X1)))),flip_range_of(apply(X3,first(X4))))
| ~ little_set(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X1)))))
| ~ member(X4,X3)
| ~ member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,non_ordered_pair(non_ordered_pair(X1,X1),non_ordered_pair(X1,X2)))),second(X4))
| ~ ordered_pair_predicate(X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1388])]) ).
fof(f1299,plain,
( spl0_124
<=> ! [X6,X7,X3] :
( ~ ordered_pair_predicate(X6)
| ~ member(X6,X7)
| ~ member(X3,second(X6))
| member(X3,apply(X7,first(X6))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_124])]) ).
fof(f2019,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ little_set(X0)
| ~ little_set(X1)
| ~ little_set(X2)
| member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X1)))),flip_range_of(apply(X3,first(X4))))
| ~ little_set(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X1)))))
| ~ member(X4,X3)
| ~ member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,non_ordered_pair(non_ordered_pair(X1,X1),non_ordered_pair(X1,X2)))),second(X4))
| ~ ordered_pair_predicate(X4) )
| ~ spl0_124
| ~ spl0_149 ),
inference(resolution,[],[f1986,f1300]) ).
fof(f1300,plain,
( ! [X3,X6,X7] :
( member(X3,apply(X7,first(X6)))
| ~ member(X6,X7)
| ~ member(X3,second(X6))
| ~ ordered_pair_predicate(X6) )
| ~ spl0_124 ),
inference(avatar_component_clause,[],[f1299]) ).
fof(f46120,plain,
( spl0_1387
| ~ spl0_124
| ~ spl0_148 ),
inference(avatar_split_clause,[],[f2003,f1981,f1299,f46118]) ).
fof(f46118,plain,
( spl0_1387
<=> ! [X4,X0,X3,X2,X1] :
( ~ little_set(X0)
| ~ little_set(X1)
| ~ little_set(X2)
| member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X1)))),rotate_right(apply(X3,first(X4))))
| ~ little_set(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X1)))))
| ~ member(X4,X3)
| ~ member(non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,non_ordered_pair(non_ordered_pair(X1,X1),non_ordered_pair(X1,X0)))),second(X4))
| ~ ordered_pair_predicate(X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1387])]) ).
fof(f2003,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ little_set(X0)
| ~ little_set(X1)
| ~ little_set(X2)
| member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X1)))),rotate_right(apply(X3,first(X4))))
| ~ little_set(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X1)))))
| ~ member(X4,X3)
| ~ member(non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,non_ordered_pair(non_ordered_pair(X1,X1),non_ordered_pair(X1,X0)))),second(X4))
| ~ ordered_pair_predicate(X4) )
| ~ spl0_124
| ~ spl0_148 ),
inference(resolution,[],[f1982,f1300]) ).
fof(f46116,plain,
( spl0_1386
| ~ spl0_140
| ~ spl0_145 ),
inference(avatar_split_clause,[],[f1874,f1786,f1745,f46114]) ).
fof(f46114,plain,
( spl0_1386
<=> ! [X2,X0,X1] :
( ~ member(X0,rotate_right(X1))
| ~ little_set(f10(X0,X1))
| ~ little_set(X2)
| ~ little_set(non_ordered_pair(non_ordered_pair(f11(X0,X1),f11(X0,X1)),non_ordered_pair(f11(X0,X1),f9(X0,X1))))
| non_ordered_pair(non_ordered_pair(f11(X0,X1),f11(X0,X1)),non_ordered_pair(f11(X0,X1),f9(X0,X1))) = X2
| ~ member(non_ordered_pair(non_ordered_pair(f10(X0,X1),f10(X0,X1)),non_ordered_pair(f10(X0,X1),X2)),X1)
| ~ single_valued_set(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1386])]) ).
fof(f1745,plain,
( spl0_140
<=> ! [X4,X0,X6,X2] :
( ~ single_valued_set(X0)
| ~ little_set(X2)
| ~ little_set(X4)
| ~ little_set(X6)
| X4 = X6
| ~ member(non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X4)),X0)
| ~ member(non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X6)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_140])]) ).
fof(f1874,plain,
( ! [X2,X0,X1] :
( ~ member(X0,rotate_right(X1))
| ~ little_set(f10(X0,X1))
| ~ little_set(X2)
| ~ little_set(non_ordered_pair(non_ordered_pair(f11(X0,X1),f11(X0,X1)),non_ordered_pair(f11(X0,X1),f9(X0,X1))))
| non_ordered_pair(non_ordered_pair(f11(X0,X1),f11(X0,X1)),non_ordered_pair(f11(X0,X1),f9(X0,X1))) = X2
| ~ member(non_ordered_pair(non_ordered_pair(f10(X0,X1),f10(X0,X1)),non_ordered_pair(f10(X0,X1),X2)),X1)
| ~ single_valued_set(X1) )
| ~ spl0_140
| ~ spl0_145 ),
inference(resolution,[],[f1787,f1746]) ).
fof(f1746,plain,
( ! [X2,X0,X6,X4] :
( ~ member(non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X6)),X0)
| ~ little_set(X2)
| ~ little_set(X4)
| ~ little_set(X6)
| X4 = X6
| ~ member(non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X4)),X0)
| ~ single_valued_set(X0) )
| ~ spl0_140 ),
inference(avatar_component_clause,[],[f1745]) ).
fof(f46109,plain,
( spl0_1385
| ~ spl0_103
| ~ spl0_154 ),
inference(avatar_split_clause,[],[f2181,f2102,f960,f46107]) ).
fof(f46107,plain,
( spl0_1385
<=> ! [X0,X1] : ~ member(X0,image(X1,rotate_right(empty_set))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1385])]) ).
fof(f2181,plain,
( ! [X0,X1] : ~ member(X0,image(X1,rotate_right(empty_set)))
| ~ spl0_103
| ~ spl0_154 ),
inference(resolution,[],[f2103,f961]) ).
fof(f46105,plain,
( spl0_1384
| ~ spl0_140
| ~ spl0_144 ),
inference(avatar_split_clause,[],[f1831,f1782,f1745,f46103]) ).
fof(f46103,plain,
( spl0_1384
<=> ! [X2,X0,X1] :
( ~ member(X0,flip_range_of(X1))
| ~ little_set(f12(X0,X1))
| ~ little_set(X2)
| ~ little_set(non_ordered_pair(non_ordered_pair(f14(X0,X1),f14(X0,X1)),non_ordered_pair(f14(X0,X1),f13(X0,X1))))
| non_ordered_pair(non_ordered_pair(f14(X0,X1),f14(X0,X1)),non_ordered_pair(f14(X0,X1),f13(X0,X1))) = X2
| ~ member(non_ordered_pair(non_ordered_pair(f12(X0,X1),f12(X0,X1)),non_ordered_pair(f12(X0,X1),X2)),X1)
| ~ single_valued_set(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1384])]) ).
fof(f1831,plain,
( ! [X2,X0,X1] :
( ~ member(X0,flip_range_of(X1))
| ~ little_set(f12(X0,X1))
| ~ little_set(X2)
| ~ little_set(non_ordered_pair(non_ordered_pair(f14(X0,X1),f14(X0,X1)),non_ordered_pair(f14(X0,X1),f13(X0,X1))))
| non_ordered_pair(non_ordered_pair(f14(X0,X1),f14(X0,X1)),non_ordered_pair(f14(X0,X1),f13(X0,X1))) = X2
| ~ member(non_ordered_pair(non_ordered_pair(f12(X0,X1),f12(X0,X1)),non_ordered_pair(f12(X0,X1),X2)),X1)
| ~ single_valued_set(X1) )
| ~ spl0_140
| ~ spl0_144 ),
inference(resolution,[],[f1783,f1746]) ).
fof(f46101,plain,
( spl0_1383
| ~ spl0_126
| ~ spl0_140 ),
inference(avatar_split_clause,[],[f1767,f1745,f1393,f46099]) ).
fof(f46099,plain,
( spl0_1383
<=> ! [X4,X0,X3,X2,X1] :
( ~ little_set(X0)
| ~ little_set(X1)
| ~ little_set(X2)
| X1 = X2
| ~ member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X1)),cross_product(X3,X4))
| ~ single_valued_set(cross_product(X3,X4))
| ~ little_set(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X2)))
| ~ member(first(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X2))),X3)
| ~ member(second(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X2))),X4)
| ~ ordered_pair_predicate(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1383])]) ).
fof(f1767,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ little_set(X0)
| ~ little_set(X1)
| ~ little_set(X2)
| X1 = X2
| ~ member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X1)),cross_product(X3,X4))
| ~ single_valued_set(cross_product(X3,X4))
| ~ little_set(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X2)))
| ~ member(first(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X2))),X3)
| ~ member(second(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X2))),X4)
| ~ ordered_pair_predicate(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X2))) )
| ~ spl0_126
| ~ spl0_140 ),
inference(resolution,[],[f1746,f1394]) ).
fof(f46097,plain,
( spl0_1382
| ~ spl0_131
| ~ spl0_136 ),
inference(avatar_split_clause,[],[f1601,f1552,f1479,f46095]) ).
fof(f46095,plain,
( spl0_1382
<=> ! [X4,X0,X3,X2,X1] :
( ~ closed(X0,X1)
| ~ maps(X2,second(X3),X0)
| homomorphism(X2,second(X3),X4,X0,X1)
| ~ closed(second(X3),X4)
| non_ordered_pair(non_ordered_pair(f6(f33(X2,second(X3),X4,X0,X1),X3),f6(f33(X2,second(X3),X4,X0,X1),X3)),non_ordered_pair(f6(f33(X2,second(X3),X4,X0,X1),X3),f7(f33(X2,second(X3),X4,X0,X1),X3))) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1382])]) ).
fof(f1601,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ closed(X0,X1)
| ~ maps(X2,second(X3),X0)
| homomorphism(X2,second(X3),X4,X0,X1)
| ~ closed(second(X3),X4)
| non_ordered_pair(non_ordered_pair(f6(f33(X2,second(X3),X4,X0,X1),X3),f6(f33(X2,second(X3),X4,X0,X1),X3)),non_ordered_pair(f6(f33(X2,second(X3),X4,X0,X1),X3),f7(f33(X2,second(X3),X4,X0,X1),X3))) = X3 )
| ~ spl0_131
| ~ spl0_136 ),
inference(resolution,[],[f1553,f1480]) ).
fof(f46093,plain,
( spl0_1381
| ~ spl0_132
| ~ spl0_136 ),
inference(avatar_split_clause,[],[f1598,f1552,f1483,f46091]) ).
fof(f46091,plain,
( spl0_1381
<=> ! [X4,X0,X3,X2,X1] :
( ~ closed(X0,X1)
| ~ maps(X2,first(X3),X0)
| homomorphism(X2,first(X3),X4,X0,X1)
| ~ closed(first(X3),X4)
| non_ordered_pair(non_ordered_pair(f4(f33(X2,first(X3),X4,X0,X1),X3),f4(f33(X2,first(X3),X4,X0,X1),X3)),non_ordered_pair(f4(f33(X2,first(X3),X4,X0,X1),X3),f5(f33(X2,first(X3),X4,X0,X1),X3))) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1381])]) ).
fof(f1598,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ closed(X0,X1)
| ~ maps(X2,first(X3),X0)
| homomorphism(X2,first(X3),X4,X0,X1)
| ~ closed(first(X3),X4)
| non_ordered_pair(non_ordered_pair(f4(f33(X2,first(X3),X4,X0,X1),X3),f4(f33(X2,first(X3),X4,X0,X1),X3)),non_ordered_pair(f4(f33(X2,first(X3),X4,X0,X1),X3),f5(f33(X2,first(X3),X4,X0,X1),X3))) = X3 )
| ~ spl0_132
| ~ spl0_136 ),
inference(resolution,[],[f1553,f1484]) ).
fof(f46089,plain,
( spl0_1380
| ~ spl0_131
| ~ spl0_134 ),
inference(avatar_split_clause,[],[f1562,f1544,f1479,f46087]) ).
fof(f46087,plain,
( spl0_1380
<=> ! [X4,X0,X3,X2,X1] :
( ~ closed(X0,X1)
| ~ maps(X2,second(X3),X0)
| homomorphism(X2,second(X3),X4,X0,X1)
| ~ closed(second(X3),X4)
| non_ordered_pair(non_ordered_pair(f6(f32(X2,second(X3),X4,X0,X1),X3),f6(f32(X2,second(X3),X4,X0,X1),X3)),non_ordered_pair(f6(f32(X2,second(X3),X4,X0,X1),X3),f7(f32(X2,second(X3),X4,X0,X1),X3))) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1380])]) ).
fof(f1562,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ closed(X0,X1)
| ~ maps(X2,second(X3),X0)
| homomorphism(X2,second(X3),X4,X0,X1)
| ~ closed(second(X3),X4)
| non_ordered_pair(non_ordered_pair(f6(f32(X2,second(X3),X4,X0,X1),X3),f6(f32(X2,second(X3),X4,X0,X1),X3)),non_ordered_pair(f6(f32(X2,second(X3),X4,X0,X1),X3),f7(f32(X2,second(X3),X4,X0,X1),X3))) = X3 )
| ~ spl0_131
| ~ spl0_134 ),
inference(resolution,[],[f1545,f1480]) ).
fof(f46085,plain,
( spl0_1379
| ~ spl0_132
| ~ spl0_134 ),
inference(avatar_split_clause,[],[f1559,f1544,f1483,f46083]) ).
fof(f46083,plain,
( spl0_1379
<=> ! [X4,X0,X3,X2,X1] :
( ~ closed(X0,X1)
| ~ maps(X2,first(X3),X0)
| homomorphism(X2,first(X3),X4,X0,X1)
| ~ closed(first(X3),X4)
| non_ordered_pair(non_ordered_pair(f4(f32(X2,first(X3),X4,X0,X1),X3),f4(f32(X2,first(X3),X4,X0,X1),X3)),non_ordered_pair(f4(f32(X2,first(X3),X4,X0,X1),X3),f5(f32(X2,first(X3),X4,X0,X1),X3))) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1379])]) ).
fof(f1559,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ closed(X0,X1)
| ~ maps(X2,first(X3),X0)
| homomorphism(X2,first(X3),X4,X0,X1)
| ~ closed(first(X3),X4)
| non_ordered_pair(non_ordered_pair(f4(f32(X2,first(X3),X4,X0,X1),X3),f4(f32(X2,first(X3),X4,X0,X1),X3)),non_ordered_pair(f4(f32(X2,first(X3),X4,X0,X1),X3),f5(f32(X2,first(X3),X4,X0,X1),X3))) = X3 )
| ~ spl0_132
| ~ spl0_134 ),
inference(resolution,[],[f1545,f1484]) ).
fof(f45309,plain,
( spl0_1378
| ~ spl0_107
| ~ spl0_154 ),
inference(avatar_split_clause,[],[f2176,f2102,f1068,f45307]) ).
fof(f45307,plain,
( spl0_1378
<=> ! [X0,X1] : ~ member(X0,image(rotate_right(empty_set),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1378])]) ).
fof(f2176,plain,
( ! [X0,X1] : ~ member(X0,image(rotate_right(empty_set),X1))
| ~ spl0_107
| ~ spl0_154 ),
inference(resolution,[],[f2103,f1069]) ).
fof(f44719,plain,
( spl0_1377
| ~ spl0_85
| ~ spl0_143 ),
inference(avatar_split_clause,[],[f1827,f1778,f672,f44717]) ).
fof(f44717,plain,
( spl0_1377
<=> ! [X0,X1] :
( f27(X0,rotate_right(X1)) = non_ordered_pair(non_ordered_pair(f9(f27(X0,rotate_right(X1)),X1),f9(f27(X0,rotate_right(X1)),X1)),non_ordered_pair(f9(f27(X0,rotate_right(X1)),X1),non_ordered_pair(non_ordered_pair(f10(f27(X0,rotate_right(X1)),X1),f10(f27(X0,rotate_right(X1)),X1)),non_ordered_pair(f10(f27(X0,rotate_right(X1)),X1),f11(f27(X0,rotate_right(X1)),X1)))))
| ~ member(X0,range_of(rotate_right(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1377])]) ).
fof(f672,plain,
( spl0_85
<=> ! [X0,X3] :
( ~ member(X3,range_of(X0))
| member(f27(X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_85])]) ).
fof(f1827,plain,
( ! [X0,X1] :
( f27(X0,rotate_right(X1)) = non_ordered_pair(non_ordered_pair(f9(f27(X0,rotate_right(X1)),X1),f9(f27(X0,rotate_right(X1)),X1)),non_ordered_pair(f9(f27(X0,rotate_right(X1)),X1),non_ordered_pair(non_ordered_pair(f10(f27(X0,rotate_right(X1)),X1),f10(f27(X0,rotate_right(X1)),X1)),non_ordered_pair(f10(f27(X0,rotate_right(X1)),X1),f11(f27(X0,rotate_right(X1)),X1)))))
| ~ member(X0,range_of(rotate_right(X1))) )
| ~ spl0_85
| ~ spl0_143 ),
inference(resolution,[],[f1779,f673]) ).
fof(f673,plain,
( ! [X3,X0] :
( member(f27(X3,X0),X0)
| ~ member(X3,range_of(X0)) )
| ~ spl0_85 ),
inference(avatar_component_clause,[],[f672]) ).
fof(f44715,plain,
( spl0_1376
| ~ spl0_78
| ~ spl0_143 ),
inference(avatar_split_clause,[],[f1819,f1778,f644,f44713]) ).
fof(f44713,plain,
( spl0_1376
<=> ! [X0,X1] :
( f16(X0,rotate_right(X1)) = non_ordered_pair(non_ordered_pair(f9(f16(X0,rotate_right(X1)),X1),f9(f16(X0,rotate_right(X1)),X1)),non_ordered_pair(f9(f16(X0,rotate_right(X1)),X1),non_ordered_pair(non_ordered_pair(f10(f16(X0,rotate_right(X1)),X1),f10(f16(X0,rotate_right(X1)),X1)),non_ordered_pair(f10(f16(X0,rotate_right(X1)),X1),f11(f16(X0,rotate_right(X1)),X1)))))
| ~ member(X0,sigma(rotate_right(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1376])]) ).
fof(f1819,plain,
( ! [X0,X1] :
( f16(X0,rotate_right(X1)) = non_ordered_pair(non_ordered_pair(f9(f16(X0,rotate_right(X1)),X1),f9(f16(X0,rotate_right(X1)),X1)),non_ordered_pair(f9(f16(X0,rotate_right(X1)),X1),non_ordered_pair(non_ordered_pair(f10(f16(X0,rotate_right(X1)),X1),f10(f16(X0,rotate_right(X1)),X1)),non_ordered_pair(f10(f16(X0,rotate_right(X1)),X1),f11(f16(X0,rotate_right(X1)),X1)))))
| ~ member(X0,sigma(rotate_right(X1))) )
| ~ spl0_78
| ~ spl0_143 ),
inference(resolution,[],[f1779,f645]) ).
fof(f44711,plain,
( spl0_1375
| ~ spl0_74
| ~ spl0_143 ),
inference(avatar_split_clause,[],[f1818,f1778,f628,f44709]) ).
fof(f44709,plain,
( spl0_1375
<=> ! [X0,X1] :
( f8(X0,rotate_right(X1)) = non_ordered_pair(non_ordered_pair(f9(f8(X0,rotate_right(X1)),X1),f9(f8(X0,rotate_right(X1)),X1)),non_ordered_pair(f9(f8(X0,rotate_right(X1)),X1),non_ordered_pair(non_ordered_pair(f10(f8(X0,rotate_right(X1)),X1),f10(f8(X0,rotate_right(X1)),X1)),non_ordered_pair(f10(f8(X0,rotate_right(X1)),X1),f11(f8(X0,rotate_right(X1)),X1)))))
| ~ member(X0,domain_of(rotate_right(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1375])]) ).
fof(f1818,plain,
( ! [X0,X1] :
( f8(X0,rotate_right(X1)) = non_ordered_pair(non_ordered_pair(f9(f8(X0,rotate_right(X1)),X1),f9(f8(X0,rotate_right(X1)),X1)),non_ordered_pair(f9(f8(X0,rotate_right(X1)),X1),non_ordered_pair(non_ordered_pair(f10(f8(X0,rotate_right(X1)),X1),f10(f8(X0,rotate_right(X1)),X1)),non_ordered_pair(f10(f8(X0,rotate_right(X1)),X1),f11(f8(X0,rotate_right(X1)),X1)))))
| ~ member(X0,domain_of(rotate_right(X1))) )
| ~ spl0_74
| ~ spl0_143 ),
inference(resolution,[],[f1779,f629]) ).
fof(f44707,plain,
( spl0_1374
| ~ spl0_85
| ~ spl0_142 ),
inference(avatar_split_clause,[],[f1806,f1774,f672,f44705]) ).
fof(f44705,plain,
( spl0_1374
<=> ! [X0,X1] :
( f27(X0,flip_range_of(X1)) = non_ordered_pair(non_ordered_pair(f12(f27(X0,flip_range_of(X1)),X1),f12(f27(X0,flip_range_of(X1)),X1)),non_ordered_pair(f12(f27(X0,flip_range_of(X1)),X1),non_ordered_pair(non_ordered_pair(f13(f27(X0,flip_range_of(X1)),X1),f13(f27(X0,flip_range_of(X1)),X1)),non_ordered_pair(f13(f27(X0,flip_range_of(X1)),X1),f14(f27(X0,flip_range_of(X1)),X1)))))
| ~ member(X0,range_of(flip_range_of(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1374])]) ).
fof(f1806,plain,
( ! [X0,X1] :
( f27(X0,flip_range_of(X1)) = non_ordered_pair(non_ordered_pair(f12(f27(X0,flip_range_of(X1)),X1),f12(f27(X0,flip_range_of(X1)),X1)),non_ordered_pair(f12(f27(X0,flip_range_of(X1)),X1),non_ordered_pair(non_ordered_pair(f13(f27(X0,flip_range_of(X1)),X1),f13(f27(X0,flip_range_of(X1)),X1)),non_ordered_pair(f13(f27(X0,flip_range_of(X1)),X1),f14(f27(X0,flip_range_of(X1)),X1)))))
| ~ member(X0,range_of(flip_range_of(X1))) )
| ~ spl0_85
| ~ spl0_142 ),
inference(resolution,[],[f1775,f673]) ).
fof(f44703,plain,
( spl0_1373
| ~ spl0_78
| ~ spl0_142 ),
inference(avatar_split_clause,[],[f1798,f1774,f644,f44701]) ).
fof(f44701,plain,
( spl0_1373
<=> ! [X0,X1] :
( f16(X0,flip_range_of(X1)) = non_ordered_pair(non_ordered_pair(f12(f16(X0,flip_range_of(X1)),X1),f12(f16(X0,flip_range_of(X1)),X1)),non_ordered_pair(f12(f16(X0,flip_range_of(X1)),X1),non_ordered_pair(non_ordered_pair(f13(f16(X0,flip_range_of(X1)),X1),f13(f16(X0,flip_range_of(X1)),X1)),non_ordered_pair(f13(f16(X0,flip_range_of(X1)),X1),f14(f16(X0,flip_range_of(X1)),X1)))))
| ~ member(X0,sigma(flip_range_of(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1373])]) ).
fof(f1798,plain,
( ! [X0,X1] :
( f16(X0,flip_range_of(X1)) = non_ordered_pair(non_ordered_pair(f12(f16(X0,flip_range_of(X1)),X1),f12(f16(X0,flip_range_of(X1)),X1)),non_ordered_pair(f12(f16(X0,flip_range_of(X1)),X1),non_ordered_pair(non_ordered_pair(f13(f16(X0,flip_range_of(X1)),X1),f13(f16(X0,flip_range_of(X1)),X1)),non_ordered_pair(f13(f16(X0,flip_range_of(X1)),X1),f14(f16(X0,flip_range_of(X1)),X1)))))
| ~ member(X0,sigma(flip_range_of(X1))) )
| ~ spl0_78
| ~ spl0_142 ),
inference(resolution,[],[f1775,f645]) ).
fof(f44699,plain,
( spl0_1372
| ~ spl0_74
| ~ spl0_142 ),
inference(avatar_split_clause,[],[f1797,f1774,f628,f44697]) ).
fof(f44697,plain,
( spl0_1372
<=> ! [X0,X1] :
( f8(X0,flip_range_of(X1)) = non_ordered_pair(non_ordered_pair(f12(f8(X0,flip_range_of(X1)),X1),f12(f8(X0,flip_range_of(X1)),X1)),non_ordered_pair(f12(f8(X0,flip_range_of(X1)),X1),non_ordered_pair(non_ordered_pair(f13(f8(X0,flip_range_of(X1)),X1),f13(f8(X0,flip_range_of(X1)),X1)),non_ordered_pair(f13(f8(X0,flip_range_of(X1)),X1),f14(f8(X0,flip_range_of(X1)),X1)))))
| ~ member(X0,domain_of(flip_range_of(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1372])]) ).
fof(f1797,plain,
( ! [X0,X1] :
( f8(X0,flip_range_of(X1)) = non_ordered_pair(non_ordered_pair(f12(f8(X0,flip_range_of(X1)),X1),f12(f8(X0,flip_range_of(X1)),X1)),non_ordered_pair(f12(f8(X0,flip_range_of(X1)),X1),non_ordered_pair(non_ordered_pair(f13(f8(X0,flip_range_of(X1)),X1),f13(f8(X0,flip_range_of(X1)),X1)),non_ordered_pair(f13(f8(X0,flip_range_of(X1)),X1),f14(f8(X0,flip_range_of(X1)),X1)))))
| ~ member(X0,domain_of(flip_range_of(X1))) )
| ~ spl0_74
| ~ spl0_142 ),
inference(resolution,[],[f1775,f629]) ).
fof(f44695,plain,
( spl0_1371
| ~ spl0_107
| ~ spl0_137 ),
inference(avatar_split_clause,[],[f1650,f1634,f1068,f44693]) ).
fof(f44693,plain,
( spl0_1371
<=> ! [X0,X3,X2,X1] :
( first(f22(X0,compose(X1,X2),X3)) = non_ordered_pair(non_ordered_pair(f29(first(f22(X0,compose(X1,X2),X3)),X1,X2),f29(first(f22(X0,compose(X1,X2),X3)),X1,X2)),non_ordered_pair(f29(first(f22(X0,compose(X1,X2),X3)),X1,X2),f30(first(f22(X0,compose(X1,X2),X3)),X1,X2)))
| ~ member(X0,image(compose(X1,X2),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1371])]) ).
fof(f1650,plain,
( ! [X2,X3,X0,X1] :
( first(f22(X0,compose(X1,X2),X3)) = non_ordered_pair(non_ordered_pair(f29(first(f22(X0,compose(X1,X2),X3)),X1,X2),f29(first(f22(X0,compose(X1,X2),X3)),X1,X2)),non_ordered_pair(f29(first(f22(X0,compose(X1,X2),X3)),X1,X2),f30(first(f22(X0,compose(X1,X2),X3)),X1,X2)))
| ~ member(X0,image(compose(X1,X2),X3)) )
| ~ spl0_107
| ~ spl0_137 ),
inference(resolution,[],[f1635,f1069]) ).
fof(f44688,plain,
( spl0_1370
| ~ spl0_138
| ~ spl0_154 ),
inference(avatar_split_clause,[],[f2175,f2102,f1638,f44686]) ).
fof(f44686,plain,
( spl0_1370
<=> ! [X0,X1] : ~ member(X0,compose(X1,rotate_right(empty_set))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1370])]) ).
fof(f2175,plain,
( ! [X0,X1] : ~ member(X0,compose(X1,rotate_right(empty_set)))
| ~ spl0_138
| ~ spl0_154 ),
inference(resolution,[],[f2103,f1639]) ).
fof(f44670,plain,
( spl0_1369
| ~ spl0_64
| ~ spl0_143 ),
inference(avatar_split_clause,[],[f1824,f1778,f478,f44668]) ).
fof(f44668,plain,
( spl0_1369
<=> ! [X0,X1] :
( f23(X0,rotate_right(X1)) = non_ordered_pair(non_ordered_pair(f9(f23(X0,rotate_right(X1)),X1),f9(f23(X0,rotate_right(X1)),X1)),non_ordered_pair(f9(f23(X0,rotate_right(X1)),X1),non_ordered_pair(non_ordered_pair(f10(f23(X0,rotate_right(X1)),X1),f10(f23(X0,rotate_right(X1)),X1)),non_ordered_pair(f10(f23(X0,rotate_right(X1)),X1),f11(f23(X0,rotate_right(X1)),X1)))))
| disjoint(X0,rotate_right(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1369])]) ).
fof(f1824,plain,
( ! [X0,X1] :
( f23(X0,rotate_right(X1)) = non_ordered_pair(non_ordered_pair(f9(f23(X0,rotate_right(X1)),X1),f9(f23(X0,rotate_right(X1)),X1)),non_ordered_pair(f9(f23(X0,rotate_right(X1)),X1),non_ordered_pair(non_ordered_pair(f10(f23(X0,rotate_right(X1)),X1),f10(f23(X0,rotate_right(X1)),X1)),non_ordered_pair(f10(f23(X0,rotate_right(X1)),X1),f11(f23(X0,rotate_right(X1)),X1)))))
| disjoint(X0,rotate_right(X1)) )
| ~ spl0_64
| ~ spl0_143 ),
inference(resolution,[],[f1779,f479]) ).
fof(f44666,plain,
( spl0_1368
| ~ spl0_63
| ~ spl0_143 ),
inference(avatar_split_clause,[],[f1823,f1778,f474,f44664]) ).
fof(f44664,plain,
( spl0_1368
<=> ! [X0,X1] :
( f23(rotate_right(X0),X1) = non_ordered_pair(non_ordered_pair(f9(f23(rotate_right(X0),X1),X0),f9(f23(rotate_right(X0),X1),X0)),non_ordered_pair(f9(f23(rotate_right(X0),X1),X0),non_ordered_pair(non_ordered_pair(f10(f23(rotate_right(X0),X1),X0),f10(f23(rotate_right(X0),X1),X0)),non_ordered_pair(f10(f23(rotate_right(X0),X1),X0),f11(f23(rotate_right(X0),X1),X0)))))
| disjoint(rotate_right(X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1368])]) ).
fof(f1823,plain,
( ! [X0,X1] :
( f23(rotate_right(X0),X1) = non_ordered_pair(non_ordered_pair(f9(f23(rotate_right(X0),X1),X0),f9(f23(rotate_right(X0),X1),X0)),non_ordered_pair(f9(f23(rotate_right(X0),X1),X0),non_ordered_pair(non_ordered_pair(f10(f23(rotate_right(X0),X1),X0),f10(f23(rotate_right(X0),X1),X0)),non_ordered_pair(f10(f23(rotate_right(X0),X1),X0),f11(f23(rotate_right(X0),X1),X0)))))
| disjoint(rotate_right(X0),X1) )
| ~ spl0_63
| ~ spl0_143 ),
inference(resolution,[],[f1779,f475]) ).
fof(f44662,plain,
( spl0_1367
| ~ spl0_60
| ~ spl0_143 ),
inference(avatar_split_clause,[],[f1820,f1778,f462,f44660]) ).
fof(f44660,plain,
( spl0_1367
<=> ! [X0,X1] :
( f17(rotate_right(X0),X1) = non_ordered_pair(non_ordered_pair(f9(f17(rotate_right(X0),X1),X0),f9(f17(rotate_right(X0),X1),X0)),non_ordered_pair(f9(f17(rotate_right(X0),X1),X0),non_ordered_pair(non_ordered_pair(f10(f17(rotate_right(X0),X1),X0),f10(f17(rotate_right(X0),X1),X0)),non_ordered_pair(f10(f17(rotate_right(X0),X1),X0),f11(f17(rotate_right(X0),X1),X0)))))
| subset(rotate_right(X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1367])]) ).
fof(f1820,plain,
( ! [X0,X1] :
( f17(rotate_right(X0),X1) = non_ordered_pair(non_ordered_pair(f9(f17(rotate_right(X0),X1),X0),f9(f17(rotate_right(X0),X1),X0)),non_ordered_pair(f9(f17(rotate_right(X0),X1),X0),non_ordered_pair(non_ordered_pair(f10(f17(rotate_right(X0),X1),X0),f10(f17(rotate_right(X0),X1),X0)),non_ordered_pair(f10(f17(rotate_right(X0),X1),X0),f11(f17(rotate_right(X0),X1),X0)))))
| subset(rotate_right(X0),X1) )
| ~ spl0_60
| ~ spl0_143 ),
inference(resolution,[],[f1779,f463]) ).
fof(f44658,plain,
( spl0_1366
| ~ spl0_64
| ~ spl0_142 ),
inference(avatar_split_clause,[],[f1803,f1774,f478,f44656]) ).
fof(f44656,plain,
( spl0_1366
<=> ! [X0,X1] :
( f23(X0,flip_range_of(X1)) = non_ordered_pair(non_ordered_pair(f12(f23(X0,flip_range_of(X1)),X1),f12(f23(X0,flip_range_of(X1)),X1)),non_ordered_pair(f12(f23(X0,flip_range_of(X1)),X1),non_ordered_pair(non_ordered_pair(f13(f23(X0,flip_range_of(X1)),X1),f13(f23(X0,flip_range_of(X1)),X1)),non_ordered_pair(f13(f23(X0,flip_range_of(X1)),X1),f14(f23(X0,flip_range_of(X1)),X1)))))
| disjoint(X0,flip_range_of(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1366])]) ).
fof(f1803,plain,
( ! [X0,X1] :
( f23(X0,flip_range_of(X1)) = non_ordered_pair(non_ordered_pair(f12(f23(X0,flip_range_of(X1)),X1),f12(f23(X0,flip_range_of(X1)),X1)),non_ordered_pair(f12(f23(X0,flip_range_of(X1)),X1),non_ordered_pair(non_ordered_pair(f13(f23(X0,flip_range_of(X1)),X1),f13(f23(X0,flip_range_of(X1)),X1)),non_ordered_pair(f13(f23(X0,flip_range_of(X1)),X1),f14(f23(X0,flip_range_of(X1)),X1)))))
| disjoint(X0,flip_range_of(X1)) )
| ~ spl0_64
| ~ spl0_142 ),
inference(resolution,[],[f1775,f479]) ).
fof(f44651,plain,
( spl0_1365
| ~ spl0_139
| ~ spl0_154 ),
inference(avatar_split_clause,[],[f2172,f2102,f1642,f44649]) ).
fof(f44649,plain,
( spl0_1365
<=> ! [X0,X1] : ~ member(X0,compose(rotate_right(empty_set),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1365])]) ).
fof(f2172,plain,
( ! [X0,X1] : ~ member(X0,compose(rotate_right(empty_set),X1))
| ~ spl0_139
| ~ spl0_154 ),
inference(resolution,[],[f2103,f1643]) ).
fof(f44647,plain,
( spl0_1364
| ~ spl0_63
| ~ spl0_142 ),
inference(avatar_split_clause,[],[f1802,f1774,f474,f44645]) ).
fof(f44645,plain,
( spl0_1364
<=> ! [X0,X1] :
( f23(flip_range_of(X0),X1) = non_ordered_pair(non_ordered_pair(f12(f23(flip_range_of(X0),X1),X0),f12(f23(flip_range_of(X0),X1),X0)),non_ordered_pair(f12(f23(flip_range_of(X0),X1),X0),non_ordered_pair(non_ordered_pair(f13(f23(flip_range_of(X0),X1),X0),f13(f23(flip_range_of(X0),X1),X0)),non_ordered_pair(f13(f23(flip_range_of(X0),X1),X0),f14(f23(flip_range_of(X0),X1),X0)))))
| disjoint(flip_range_of(X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1364])]) ).
fof(f1802,plain,
( ! [X0,X1] :
( f23(flip_range_of(X0),X1) = non_ordered_pair(non_ordered_pair(f12(f23(flip_range_of(X0),X1),X0),f12(f23(flip_range_of(X0),X1),X0)),non_ordered_pair(f12(f23(flip_range_of(X0),X1),X0),non_ordered_pair(non_ordered_pair(f13(f23(flip_range_of(X0),X1),X0),f13(f23(flip_range_of(X0),X1),X0)),non_ordered_pair(f13(f23(flip_range_of(X0),X1),X0),f14(f23(flip_range_of(X0),X1),X0)))))
| disjoint(flip_range_of(X0),X1) )
| ~ spl0_63
| ~ spl0_142 ),
inference(resolution,[],[f1775,f475]) ).
fof(f44643,plain,
( spl0_1363
| ~ spl0_60
| ~ spl0_142 ),
inference(avatar_split_clause,[],[f1799,f1774,f462,f44641]) ).
fof(f44641,plain,
( spl0_1363
<=> ! [X0,X1] :
( f17(flip_range_of(X0),X1) = non_ordered_pair(non_ordered_pair(f12(f17(flip_range_of(X0),X1),X0),f12(f17(flip_range_of(X0),X1),X0)),non_ordered_pair(f12(f17(flip_range_of(X0),X1),X0),non_ordered_pair(non_ordered_pair(f13(f17(flip_range_of(X0),X1),X0),f13(f17(flip_range_of(X0),X1),X0)),non_ordered_pair(f13(f17(flip_range_of(X0),X1),X0),f14(f17(flip_range_of(X0),X1),X0)))))
| subset(flip_range_of(X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1363])]) ).
fof(f1799,plain,
( ! [X0,X1] :
( f17(flip_range_of(X0),X1) = non_ordered_pair(non_ordered_pair(f12(f17(flip_range_of(X0),X1),X0),f12(f17(flip_range_of(X0),X1),X0)),non_ordered_pair(f12(f17(flip_range_of(X0),X1),X0),non_ordered_pair(non_ordered_pair(f13(f17(flip_range_of(X0),X1),X0),f13(f17(flip_range_of(X0),X1),X0)),non_ordered_pair(f13(f17(flip_range_of(X0),X1),X0),f14(f17(flip_range_of(X0),X1),X0)))))
| subset(flip_range_of(X0),X1) )
| ~ spl0_60
| ~ spl0_142 ),
inference(resolution,[],[f1775,f463]) ).
fof(f43861,plain,
( spl0_1362
| ~ spl0_95
| ~ spl0_139 ),
inference(avatar_split_clause,[],[f1734,f1642,f844,f43859]) ).
fof(f43859,plain,
( spl0_1362
<=> ! [X2,X0,X1] :
( ~ member(X0,compose(range_of(X1),X2))
| non_ordered_pair(non_ordered_pair(f29(X0,range_of(X1),X2),f29(X0,range_of(X1),X2)),non_ordered_pair(f29(X0,range_of(X1),X2),f31(X0,range_of(X1),X2))) = second(f27(non_ordered_pair(non_ordered_pair(f29(X0,range_of(X1),X2),f29(X0,range_of(X1),X2)),non_ordered_pair(f29(X0,range_of(X1),X2),f31(X0,range_of(X1),X2))),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1362])]) ).
fof(f1734,plain,
( ! [X2,X0,X1] :
( ~ member(X0,compose(range_of(X1),X2))
| non_ordered_pair(non_ordered_pair(f29(X0,range_of(X1),X2),f29(X0,range_of(X1),X2)),non_ordered_pair(f29(X0,range_of(X1),X2),f31(X0,range_of(X1),X2))) = second(f27(non_ordered_pair(non_ordered_pair(f29(X0,range_of(X1),X2),f29(X0,range_of(X1),X2)),non_ordered_pair(f29(X0,range_of(X1),X2),f31(X0,range_of(X1),X2))),X1)) )
| ~ spl0_95
| ~ spl0_139 ),
inference(resolution,[],[f1643,f845]) ).
fof(f43857,plain,
( spl0_1361
| ~ spl0_91
| ~ spl0_139 ),
inference(avatar_split_clause,[],[f1718,f1642,f828,f43855]) ).
fof(f43855,plain,
( spl0_1361
<=> ! [X2,X0,X1] :
( ~ member(X0,compose(domain_of(X1),X2))
| non_ordered_pair(non_ordered_pair(f29(X0,domain_of(X1),X2),f29(X0,domain_of(X1),X2)),non_ordered_pair(f29(X0,domain_of(X1),X2),f31(X0,domain_of(X1),X2))) = first(f8(non_ordered_pair(non_ordered_pair(f29(X0,domain_of(X1),X2),f29(X0,domain_of(X1),X2)),non_ordered_pair(f29(X0,domain_of(X1),X2),f31(X0,domain_of(X1),X2))),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1361])]) ).
fof(f1718,plain,
( ! [X2,X0,X1] :
( ~ member(X0,compose(domain_of(X1),X2))
| non_ordered_pair(non_ordered_pair(f29(X0,domain_of(X1),X2),f29(X0,domain_of(X1),X2)),non_ordered_pair(f29(X0,domain_of(X1),X2),f31(X0,domain_of(X1),X2))) = first(f8(non_ordered_pair(non_ordered_pair(f29(X0,domain_of(X1),X2),f29(X0,domain_of(X1),X2)),non_ordered_pair(f29(X0,domain_of(X1),X2),f31(X0,domain_of(X1),X2))),X1)) )
| ~ spl0_91
| ~ spl0_139 ),
inference(resolution,[],[f1643,f829]) ).
fof(f43853,plain,
( spl0_1360
| ~ spl0_95
| ~ spl0_138 ),
inference(avatar_split_clause,[],[f1694,f1638,f844,f43851]) ).
fof(f43851,plain,
( spl0_1360
<=> ! [X2,X0,X1] :
( ~ member(X0,compose(X1,range_of(X2)))
| non_ordered_pair(non_ordered_pair(f31(X0,X1,range_of(X2)),f31(X0,X1,range_of(X2))),non_ordered_pair(f31(X0,X1,range_of(X2)),f30(X0,X1,range_of(X2)))) = second(f27(non_ordered_pair(non_ordered_pair(f31(X0,X1,range_of(X2)),f31(X0,X1,range_of(X2))),non_ordered_pair(f31(X0,X1,range_of(X2)),f30(X0,X1,range_of(X2)))),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1360])]) ).
fof(f1694,plain,
( ! [X2,X0,X1] :
( ~ member(X0,compose(X1,range_of(X2)))
| non_ordered_pair(non_ordered_pair(f31(X0,X1,range_of(X2)),f31(X0,X1,range_of(X2))),non_ordered_pair(f31(X0,X1,range_of(X2)),f30(X0,X1,range_of(X2)))) = second(f27(non_ordered_pair(non_ordered_pair(f31(X0,X1,range_of(X2)),f31(X0,X1,range_of(X2))),non_ordered_pair(f31(X0,X1,range_of(X2)),f30(X0,X1,range_of(X2)))),X2)) )
| ~ spl0_95
| ~ spl0_138 ),
inference(resolution,[],[f1639,f845]) ).
fof(f43849,plain,
( spl0_1359
| ~ spl0_91
| ~ spl0_138 ),
inference(avatar_split_clause,[],[f1678,f1638,f828,f43847]) ).
fof(f43847,plain,
( spl0_1359
<=> ! [X2,X0,X1] :
( ~ member(X0,compose(X1,domain_of(X2)))
| non_ordered_pair(non_ordered_pair(f31(X0,X1,domain_of(X2)),f31(X0,X1,domain_of(X2))),non_ordered_pair(f31(X0,X1,domain_of(X2)),f30(X0,X1,domain_of(X2)))) = first(f8(non_ordered_pair(non_ordered_pair(f31(X0,X1,domain_of(X2)),f31(X0,X1,domain_of(X2))),non_ordered_pair(f31(X0,X1,domain_of(X2)),f30(X0,X1,domain_of(X2)))),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1359])]) ).
fof(f1678,plain,
( ! [X2,X0,X1] :
( ~ member(X0,compose(X1,domain_of(X2)))
| non_ordered_pair(non_ordered_pair(f31(X0,X1,domain_of(X2)),f31(X0,X1,domain_of(X2))),non_ordered_pair(f31(X0,X1,domain_of(X2)),f30(X0,X1,domain_of(X2)))) = first(f8(non_ordered_pair(non_ordered_pair(f31(X0,X1,domain_of(X2)),f31(X0,X1,domain_of(X2))),non_ordered_pair(f31(X0,X1,domain_of(X2)),f30(X0,X1,domain_of(X2)))),X2)) )
| ~ spl0_91
| ~ spl0_138 ),
inference(resolution,[],[f1639,f829]) ).
fof(f43842,plain,
( spl0_1358
| ~ spl0_103
| ~ spl0_153 ),
inference(avatar_split_clause,[],[f2150,f2098,f960,f43840]) ).
fof(f43840,plain,
( spl0_1358
<=> ! [X0,X1] : ~ member(X0,image(X1,flip_range_of(empty_set))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1358])]) ).
fof(f2150,plain,
( ! [X0,X1] : ~ member(X0,image(X1,flip_range_of(empty_set)))
| ~ spl0_103
| ~ spl0_153 ),
inference(resolution,[],[f2099,f961]) ).
fof(f43775,plain,
( spl0_1357
| ~ spl0_111
| ~ spl0_147 ),
inference(avatar_split_clause,[],[f1969,f1954,f1085,f43773]) ).
fof(f43773,plain,
( spl0_1357
<=> ! [X5,X4,X0,X3,X2,X1] :
( ~ little_set(X0)
| ~ little_set(X1)
| ~ little_set(X2)
| ~ member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X2)),X3)
| ~ little_set(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X1)))
| member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X1)),compose(X3,second(f28(non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X1)),X4,X5))))
| ~ member(non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X1)),apply(X4,X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1357])]) ).
fof(f1969,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ little_set(X0)
| ~ little_set(X1)
| ~ little_set(X2)
| ~ member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X2)),X3)
| ~ little_set(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X1)))
| member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X1)),compose(X3,second(f28(non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X1)),X4,X5))))
| ~ member(non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X1)),apply(X4,X5)) )
| ~ spl0_111
| ~ spl0_147 ),
inference(resolution,[],[f1955,f1086]) ).
fof(f42958,plain,
( spl0_1356
| ~ spl0_102
| ~ spl0_147 ),
inference(avatar_split_clause,[],[f1972,f1954,f956,f42956]) ).
fof(f42956,plain,
( spl0_1356
<=> ! [X5,X4,X0,X3,X2,X1] :
( ~ little_set(X0)
| ~ little_set(X1)
| ~ little_set(X2)
| ~ member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X2)),X3)
| ~ little_set(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X1)))
| member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X1)),compose(X3,intersection(X4,X5)))
| ~ member(non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X1)),X4)
| ~ member(non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X1)),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1356])]) ).
fof(f1972,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ little_set(X0)
| ~ little_set(X1)
| ~ little_set(X2)
| ~ member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X2)),X3)
| ~ little_set(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X1)))
| member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X1)),compose(X3,intersection(X4,X5)))
| ~ member(non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X1)),X4)
| ~ member(non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X1)),X5) )
| ~ spl0_102
| ~ spl0_147 ),
inference(resolution,[],[f1955,f957]) ).
fof(f42951,plain,
( spl0_1355
| ~ spl0_107
| ~ spl0_153 ),
inference(avatar_split_clause,[],[f2145,f2098,f1068,f42949]) ).
fof(f42949,plain,
( spl0_1355
<=> ! [X0,X1] : ~ member(X0,image(flip_range_of(empty_set),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1355])]) ).
fof(f2145,plain,
( ! [X0,X1] : ~ member(X0,image(flip_range_of(empty_set),X1))
| ~ spl0_107
| ~ spl0_153 ),
inference(resolution,[],[f2099,f1069]) ).
fof(f42947,plain,
( spl0_1354
| ~ spl0_128
| ~ spl0_147 ),
inference(avatar_split_clause,[],[f1970,f1954,f1401,f42945]) ).
fof(f42945,plain,
( spl0_1354
<=> ! [X5,X4,X0,X3,X2,X1] :
( ~ little_set(X0)
| ~ little_set(X1)
| ~ little_set(X2)
| ~ member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X2)),X3)
| ~ little_set(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X1)))
| member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X1)),compose(X3,second(non_ordered_pair(non_ordered_pair(X4,X4),non_ordered_pair(X4,X5)))))
| ~ little_set(X5)
| ~ member(non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X1)),X5)
| ~ little_set(X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1354])]) ).
fof(f1970,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ little_set(X0)
| ~ little_set(X1)
| ~ little_set(X2)
| ~ member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X2)),X3)
| ~ little_set(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X1)))
| member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X1)),compose(X3,second(non_ordered_pair(non_ordered_pair(X4,X4),non_ordered_pair(X4,X5)))))
| ~ little_set(X5)
| ~ member(non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X1)),X5)
| ~ little_set(X4) )
| ~ spl0_128
| ~ spl0_147 ),
inference(resolution,[],[f1955,f1402]) ).
fof(f42943,plain,
( spl0_1353
| ~ spl0_129
| ~ spl0_147 ),
inference(avatar_split_clause,[],[f1967,f1954,f1405,f42941]) ).
fof(f42941,plain,
( spl0_1353
<=> ! [X5,X4,X0,X3,X2,X1] :
( ~ little_set(X0)
| ~ little_set(X1)
| ~ little_set(X2)
| ~ member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X2)),X3)
| ~ little_set(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X1)))
| member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X1)),compose(X3,first(non_ordered_pair(non_ordered_pair(X4,X4),non_ordered_pair(X4,X5)))))
| ~ little_set(X5)
| ~ member(non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X1)),X4)
| ~ little_set(X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1353])]) ).
fof(f1967,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ little_set(X0)
| ~ little_set(X1)
| ~ little_set(X2)
| ~ member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X2)),X3)
| ~ little_set(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X1)))
| member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X1)),compose(X3,first(non_ordered_pair(non_ordered_pair(X4,X4),non_ordered_pair(X4,X5)))))
| ~ little_set(X5)
| ~ member(non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X1)),X4)
| ~ little_set(X4) )
| ~ spl0_129
| ~ spl0_147 ),
inference(resolution,[],[f1955,f1406]) ).
fof(f42939,plain,
( spl0_1352
| ~ spl0_138
| ~ spl0_147 ),
inference(avatar_split_clause,[],[f1963,f1954,f1638,f42937]) ).
fof(f42937,plain,
( spl0_1352
<=> ! [X4,X0,X3,X2,X1] :
( ~ little_set(X0)
| ~ little_set(f30(X1,X2,X3))
| ~ little_set(f31(X1,X2,X3))
| ~ member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,f31(X1,X2,X3))),X4)
| ~ little_set(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,f30(X1,X2,X3))))
| member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,f30(X1,X2,X3))),compose(X4,X3))
| ~ member(X1,compose(X2,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1352])]) ).
fof(f1963,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ little_set(X0)
| ~ little_set(f30(X1,X2,X3))
| ~ little_set(f31(X1,X2,X3))
| ~ member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,f31(X1,X2,X3))),X4)
| ~ little_set(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,f30(X1,X2,X3))))
| member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,f30(X1,X2,X3))),compose(X4,X3))
| ~ member(X1,compose(X2,X3)) )
| ~ spl0_138
| ~ spl0_147 ),
inference(resolution,[],[f1955,f1639]) ).
fof(f42935,plain,
( spl0_1351
| ~ spl0_139
| ~ spl0_147 ),
inference(avatar_split_clause,[],[f1960,f1954,f1642,f42933]) ).
fof(f42933,plain,
( spl0_1351
<=> ! [X4,X0,X3,X2,X1] :
( ~ little_set(X0)
| ~ little_set(f31(X1,X2,X3))
| ~ little_set(f29(X1,X2,X3))
| ~ member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,f29(X1,X2,X3))),X4)
| ~ little_set(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,f31(X1,X2,X3))))
| member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,f31(X1,X2,X3))),compose(X4,X2))
| ~ member(X1,compose(X2,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1351])]) ).
fof(f1960,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ little_set(X0)
| ~ little_set(f31(X1,X2,X3))
| ~ little_set(f29(X1,X2,X3))
| ~ member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,f29(X1,X2,X3))),X4)
| ~ little_set(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,f31(X1,X2,X3))))
| member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,f31(X1,X2,X3))),compose(X4,X2))
| ~ member(X1,compose(X2,X3)) )
| ~ spl0_139
| ~ spl0_147 ),
inference(resolution,[],[f1955,f1643]) ).
fof(f42931,plain,
( spl0_1350
| ~ spl0_129
| ~ spl0_132 ),
inference(avatar_split_clause,[],[f1510,f1483,f1405,f42929]) ).
fof(f42929,plain,
( spl0_1350
<=> ! [X2,X0,X1] :
( non_ordered_pair(non_ordered_pair(X1,X1),non_ordered_pair(X1,X2)) = non_ordered_pair(non_ordered_pair(f4(X0,non_ordered_pair(non_ordered_pair(X1,X1),non_ordered_pair(X1,X2))),f4(X0,non_ordered_pair(non_ordered_pair(X1,X1),non_ordered_pair(X1,X2)))),non_ordered_pair(f4(X0,non_ordered_pair(non_ordered_pair(X1,X1),non_ordered_pair(X1,X2))),f5(X0,non_ordered_pair(non_ordered_pair(X1,X1),non_ordered_pair(X1,X2)))))
| ~ little_set(X2)
| ~ member(X0,X1)
| ~ little_set(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1350])]) ).
fof(f1510,plain,
( ! [X2,X0,X1] :
( non_ordered_pair(non_ordered_pair(X1,X1),non_ordered_pair(X1,X2)) = non_ordered_pair(non_ordered_pair(f4(X0,non_ordered_pair(non_ordered_pair(X1,X1),non_ordered_pair(X1,X2))),f4(X0,non_ordered_pair(non_ordered_pair(X1,X1),non_ordered_pair(X1,X2)))),non_ordered_pair(f4(X0,non_ordered_pair(non_ordered_pair(X1,X1),non_ordered_pair(X1,X2))),f5(X0,non_ordered_pair(non_ordered_pair(X1,X1),non_ordered_pair(X1,X2)))))
| ~ little_set(X2)
| ~ member(X0,X1)
| ~ little_set(X1) )
| ~ spl0_129
| ~ spl0_132 ),
inference(resolution,[],[f1484,f1406]) ).
fof(f42927,plain,
( spl0_1349
| ~ spl0_128
| ~ spl0_131 ),
inference(avatar_split_clause,[],[f1491,f1479,f1401,f42925]) ).
fof(f42925,plain,
( spl0_1349
<=> ! [X2,X0,X1] :
( non_ordered_pair(non_ordered_pair(X1,X1),non_ordered_pair(X1,X2)) = non_ordered_pair(non_ordered_pair(f6(X0,non_ordered_pair(non_ordered_pair(X1,X1),non_ordered_pair(X1,X2))),f6(X0,non_ordered_pair(non_ordered_pair(X1,X1),non_ordered_pair(X1,X2)))),non_ordered_pair(f6(X0,non_ordered_pair(non_ordered_pair(X1,X1),non_ordered_pair(X1,X2))),f7(X0,non_ordered_pair(non_ordered_pair(X1,X1),non_ordered_pair(X1,X2)))))
| ~ little_set(X2)
| ~ member(X0,X2)
| ~ little_set(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1349])]) ).
fof(f1491,plain,
( ! [X2,X0,X1] :
( non_ordered_pair(non_ordered_pair(X1,X1),non_ordered_pair(X1,X2)) = non_ordered_pair(non_ordered_pair(f6(X0,non_ordered_pair(non_ordered_pair(X1,X1),non_ordered_pair(X1,X2))),f6(X0,non_ordered_pair(non_ordered_pair(X1,X1),non_ordered_pair(X1,X2)))),non_ordered_pair(f6(X0,non_ordered_pair(non_ordered_pair(X1,X1),non_ordered_pair(X1,X2))),f7(X0,non_ordered_pair(non_ordered_pair(X1,X1),non_ordered_pair(X1,X2)))))
| ~ little_set(X2)
| ~ member(X0,X2)
| ~ little_set(X1) )
| ~ spl0_128
| ~ spl0_131 ),
inference(resolution,[],[f1480,f1402]) ).
fof(f42173,plain,
( spl0_1348
| ~ spl0_138
| ~ spl0_153 ),
inference(avatar_split_clause,[],[f2144,f2098,f1638,f42171]) ).
fof(f42171,plain,
( spl0_1348
<=> ! [X0,X1] : ~ member(X0,compose(X1,flip_range_of(empty_set))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1348])]) ).
fof(f2144,plain,
( ! [X0,X1] : ~ member(X0,compose(X1,flip_range_of(empty_set)))
| ~ spl0_138
| ~ spl0_153 ),
inference(resolution,[],[f2099,f1639]) ).
fof(f41813,plain,
( spl0_1347
| ~ spl0_110
| ~ spl0_145 ),
inference(avatar_split_clause,[],[f1911,f1786,f1081,f41811]) ).
fof(f41811,plain,
( spl0_1347
<=> ! [X2,X0,X1] :
( ~ member(X0,rotate_right(apply(X1,X2)))
| first(f28(non_ordered_pair(non_ordered_pair(f10(X0,apply(X1,X2)),f10(X0,apply(X1,X2))),non_ordered_pair(f10(X0,apply(X1,X2)),non_ordered_pair(non_ordered_pair(f11(X0,apply(X1,X2)),f11(X0,apply(X1,X2))),non_ordered_pair(f11(X0,apply(X1,X2)),f9(X0,apply(X1,X2)))))),X1,X2)) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1347])]) ).
fof(f1081,plain,
( spl0_110
<=> ! [X1,X7,X3] :
( ~ member(X3,apply(X7,X1))
| first(f28(X3,X7,X1)) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_110])]) ).
fof(f1911,plain,
( ! [X2,X0,X1] :
( ~ member(X0,rotate_right(apply(X1,X2)))
| first(f28(non_ordered_pair(non_ordered_pair(f10(X0,apply(X1,X2)),f10(X0,apply(X1,X2))),non_ordered_pair(f10(X0,apply(X1,X2)),non_ordered_pair(non_ordered_pair(f11(X0,apply(X1,X2)),f11(X0,apply(X1,X2))),non_ordered_pair(f11(X0,apply(X1,X2)),f9(X0,apply(X1,X2)))))),X1,X2)) = X2 )
| ~ spl0_110
| ~ spl0_145 ),
inference(resolution,[],[f1787,f1082]) ).
fof(f1082,plain,
( ! [X3,X1,X7] :
( ~ member(X3,apply(X7,X1))
| first(f28(X3,X7,X1)) = X1 )
| ~ spl0_110 ),
inference(avatar_component_clause,[],[f1081]) ).
fof(f41809,plain,
( spl0_1346
| ~ spl0_110
| ~ spl0_144 ),
inference(avatar_split_clause,[],[f1868,f1782,f1081,f41807]) ).
fof(f41807,plain,
( spl0_1346
<=> ! [X2,X0,X1] :
( ~ member(X0,flip_range_of(apply(X1,X2)))
| first(f28(non_ordered_pair(non_ordered_pair(f12(X0,apply(X1,X2)),f12(X0,apply(X1,X2))),non_ordered_pair(f12(X0,apply(X1,X2)),non_ordered_pair(non_ordered_pair(f14(X0,apply(X1,X2)),f14(X0,apply(X1,X2))),non_ordered_pair(f14(X0,apply(X1,X2)),f13(X0,apply(X1,X2)))))),X1,X2)) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1346])]) ).
fof(f1868,plain,
( ! [X2,X0,X1] :
( ~ member(X0,flip_range_of(apply(X1,X2)))
| first(f28(non_ordered_pair(non_ordered_pair(f12(X0,apply(X1,X2)),f12(X0,apply(X1,X2))),non_ordered_pair(f12(X0,apply(X1,X2)),non_ordered_pair(non_ordered_pair(f14(X0,apply(X1,X2)),f14(X0,apply(X1,X2))),non_ordered_pair(f14(X0,apply(X1,X2)),f13(X0,apply(X1,X2)))))),X1,X2)) = X2 )
| ~ spl0_110
| ~ spl0_144 ),
inference(resolution,[],[f1783,f1082]) ).
fof(f41805,plain,
( spl0_1345
| ~ spl0_104
| ~ spl0_137 ),
inference(avatar_split_clause,[],[f1661,f1634,f966,f41803]) ).
fof(f41803,plain,
( spl0_1345
<=> ! [X0,X3,X2,X1] :
( f28(X0,compose(X1,X2),X3) = non_ordered_pair(non_ordered_pair(f29(f28(X0,compose(X1,X2),X3),X1,X2),f29(f28(X0,compose(X1,X2),X3),X1,X2)),non_ordered_pair(f29(f28(X0,compose(X1,X2),X3),X1,X2),f30(f28(X0,compose(X1,X2),X3),X1,X2)))
| ~ member(X0,apply(compose(X1,X2),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1345])]) ).
fof(f1661,plain,
( ! [X2,X3,X0,X1] :
( f28(X0,compose(X1,X2),X3) = non_ordered_pair(non_ordered_pair(f29(f28(X0,compose(X1,X2),X3),X1,X2),f29(f28(X0,compose(X1,X2),X3),X1,X2)),non_ordered_pair(f29(f28(X0,compose(X1,X2),X3),X1,X2),f30(f28(X0,compose(X1,X2),X3),X1,X2)))
| ~ member(X0,apply(compose(X1,X2),X3)) )
| ~ spl0_104
| ~ spl0_137 ),
inference(resolution,[],[f1635,f967]) ).
fof(f41801,plain,
( spl0_1344
| ~ spl0_103
| ~ spl0_137 ),
inference(avatar_split_clause,[],[f1655,f1634,f960,f41799]) ).
fof(f41799,plain,
( spl0_1344
<=> ! [X0,X3,X2,X1] :
( f22(X0,X1,compose(X2,X3)) = non_ordered_pair(non_ordered_pair(f29(f22(X0,X1,compose(X2,X3)),X2,X3),f29(f22(X0,X1,compose(X2,X3)),X2,X3)),non_ordered_pair(f29(f22(X0,X1,compose(X2,X3)),X2,X3),f30(f22(X0,X1,compose(X2,X3)),X2,X3)))
| ~ member(X0,image(X1,compose(X2,X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1344])]) ).
fof(f1655,plain,
( ! [X2,X3,X0,X1] :
( f22(X0,X1,compose(X2,X3)) = non_ordered_pair(non_ordered_pair(f29(f22(X0,X1,compose(X2,X3)),X2,X3),f29(f22(X0,X1,compose(X2,X3)),X2,X3)),non_ordered_pair(f29(f22(X0,X1,compose(X2,X3)),X2,X3),f30(f22(X0,X1,compose(X2,X3)),X2,X3)))
| ~ member(X0,image(X1,compose(X2,X3))) )
| ~ spl0_103
| ~ spl0_137 ),
inference(resolution,[],[f1635,f961]) ).
fof(f41797,plain,
( spl0_1343
| ~ spl0_113
| ~ spl0_137 ),
inference(avatar_split_clause,[],[f1646,f1634,f1159,f41795]) ).
fof(f41795,plain,
( spl0_1343
<=> ! [X2,X0,X1] :
( f1(compose(X0,X1),X2) = non_ordered_pair(non_ordered_pair(f29(f1(compose(X0,X1),X2),X0,X1),f29(f1(compose(X0,X1),X2),X0,X1)),non_ordered_pair(f29(f1(compose(X0,X1),X2),X0,X1),f30(f1(compose(X0,X1),X2),X0,X1)))
| member(f1(compose(X0,X1),X2),X2)
| compose(X0,X1) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1343])]) ).
fof(f1646,plain,
( ! [X2,X0,X1] :
( f1(compose(X0,X1),X2) = non_ordered_pair(non_ordered_pair(f29(f1(compose(X0,X1),X2),X0,X1),f29(f1(compose(X0,X1),X2),X0,X1)),non_ordered_pair(f29(f1(compose(X0,X1),X2),X0,X1),f30(f1(compose(X0,X1),X2),X0,X1)))
| member(f1(compose(X0,X1),X2),X2)
| compose(X0,X1) = X2 )
| ~ spl0_113
| ~ spl0_137 ),
inference(resolution,[],[f1635,f1160]) ).
fof(f41793,plain,
( spl0_1342
| ~ spl0_113
| ~ spl0_137 ),
inference(avatar_split_clause,[],[f1645,f1634,f1159,f41791]) ).
fof(f41791,plain,
( spl0_1342
<=> ! [X2,X0,X1] :
( f1(X0,compose(X1,X2)) = non_ordered_pair(non_ordered_pair(f29(f1(X0,compose(X1,X2)),X1,X2),f29(f1(X0,compose(X1,X2)),X1,X2)),non_ordered_pair(f29(f1(X0,compose(X1,X2)),X1,X2),f30(f1(X0,compose(X1,X2)),X1,X2)))
| member(f1(X0,compose(X1,X2)),X0)
| compose(X1,X2) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1342])]) ).
fof(f1645,plain,
( ! [X2,X0,X1] :
( f1(X0,compose(X1,X2)) = non_ordered_pair(non_ordered_pair(f29(f1(X0,compose(X1,X2)),X1,X2),f29(f1(X0,compose(X1,X2)),X1,X2)),non_ordered_pair(f29(f1(X0,compose(X1,X2)),X1,X2),f30(f1(X0,compose(X1,X2)),X1,X2)))
| member(f1(X0,compose(X1,X2)),X0)
| compose(X1,X2) = X0 )
| ~ spl0_113
| ~ spl0_137 ),
inference(resolution,[],[f1635,f1160]) ).
fof(f41784,plain,
( spl0_1341
| ~ spl0_139
| ~ spl0_153 ),
inference(avatar_split_clause,[],[f2141,f2098,f1642,f41782]) ).
fof(f41782,plain,
( spl0_1341
<=> ! [X0,X1] : ~ member(X0,compose(flip_range_of(empty_set),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1341])]) ).
fof(f2141,plain,
( ! [X0,X1] : ~ member(X0,compose(flip_range_of(empty_set),X1))
| ~ spl0_139
| ~ spl0_153 ),
inference(resolution,[],[f2099,f1643]) ).
fof(f41487,plain,
( spl0_1340
| ~ spl0_173
| ~ spl0_1331 ),
inference(avatar_split_clause,[],[f41448,f41445,f2440,f41485]) ).
fof(f41485,plain,
( spl0_1340
<=> ! [X0] :
( estin = rotate_right(X0)
| f26(rotate_right(X0)) = non_ordered_pair(non_ordered_pair(f9(f26(rotate_right(X0)),X0),f9(f26(rotate_right(X0)),X0)),non_ordered_pair(f9(f26(rotate_right(X0)),X0),non_ordered_pair(non_ordered_pair(f10(f26(rotate_right(X0)),X0),f10(f26(rotate_right(X0)),X0)),non_ordered_pair(f10(f26(rotate_right(X0)),X0),f11(f26(rotate_right(X0)),X0)))))
| ~ little_set(rotate_right(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1340])]) ).
fof(f41445,plain,
( spl0_1331
<=> ! [X0] :
( f26(rotate_right(X0)) = non_ordered_pair(non_ordered_pair(f9(f26(rotate_right(X0)),X0),f9(f26(rotate_right(X0)),X0)),non_ordered_pair(f9(f26(rotate_right(X0)),X0),non_ordered_pair(non_ordered_pair(f10(f26(rotate_right(X0)),X0),f10(f26(rotate_right(X0)),X0)),non_ordered_pair(f10(f26(rotate_right(X0)),X0),f11(f26(rotate_right(X0)),X0)))))
| rotate_right(X0) = empty_set
| ~ little_set(rotate_right(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1331])]) ).
fof(f41448,plain,
( ! [X0] :
( estin = rotate_right(X0)
| f26(rotate_right(X0)) = non_ordered_pair(non_ordered_pair(f9(f26(rotate_right(X0)),X0),f9(f26(rotate_right(X0)),X0)),non_ordered_pair(f9(f26(rotate_right(X0)),X0),non_ordered_pair(non_ordered_pair(f10(f26(rotate_right(X0)),X0),f10(f26(rotate_right(X0)),X0)),non_ordered_pair(f10(f26(rotate_right(X0)),X0),f11(f26(rotate_right(X0)),X0)))))
| ~ little_set(rotate_right(X0)) )
| ~ spl0_173
| ~ spl0_1331 ),
inference(forward_demodulation,[],[f41446,f2442]) ).
fof(f41446,plain,
( ! [X0] :
( f26(rotate_right(X0)) = non_ordered_pair(non_ordered_pair(f9(f26(rotate_right(X0)),X0),f9(f26(rotate_right(X0)),X0)),non_ordered_pair(f9(f26(rotate_right(X0)),X0),non_ordered_pair(non_ordered_pair(f10(f26(rotate_right(X0)),X0),f10(f26(rotate_right(X0)),X0)),non_ordered_pair(f10(f26(rotate_right(X0)),X0),f11(f26(rotate_right(X0)),X0)))))
| rotate_right(X0) = empty_set
| ~ little_set(rotate_right(X0)) )
| ~ spl0_1331 ),
inference(avatar_component_clause,[],[f41445]) ).
fof(f41483,plain,
( spl0_1339
| ~ spl0_173
| ~ spl0_1330 ),
inference(avatar_split_clause,[],[f41443,f41440,f2440,f41481]) ).
fof(f41481,plain,
( spl0_1339
<=> ! [X0] :
( estin = flip_range_of(X0)
| f26(flip_range_of(X0)) = non_ordered_pair(non_ordered_pair(f12(f26(flip_range_of(X0)),X0),f12(f26(flip_range_of(X0)),X0)),non_ordered_pair(f12(f26(flip_range_of(X0)),X0),non_ordered_pair(non_ordered_pair(f13(f26(flip_range_of(X0)),X0),f13(f26(flip_range_of(X0)),X0)),non_ordered_pair(f13(f26(flip_range_of(X0)),X0),f14(f26(flip_range_of(X0)),X0)))))
| ~ little_set(flip_range_of(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1339])]) ).
fof(f41440,plain,
( spl0_1330
<=> ! [X0] :
( f26(flip_range_of(X0)) = non_ordered_pair(non_ordered_pair(f12(f26(flip_range_of(X0)),X0),f12(f26(flip_range_of(X0)),X0)),non_ordered_pair(f12(f26(flip_range_of(X0)),X0),non_ordered_pair(non_ordered_pair(f13(f26(flip_range_of(X0)),X0),f13(f26(flip_range_of(X0)),X0)),non_ordered_pair(f13(f26(flip_range_of(X0)),X0),f14(f26(flip_range_of(X0)),X0)))))
| flip_range_of(X0) = empty_set
| ~ little_set(flip_range_of(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1330])]) ).
fof(f41443,plain,
( ! [X0] :
( estin = flip_range_of(X0)
| f26(flip_range_of(X0)) = non_ordered_pair(non_ordered_pair(f12(f26(flip_range_of(X0)),X0),f12(f26(flip_range_of(X0)),X0)),non_ordered_pair(f12(f26(flip_range_of(X0)),X0),non_ordered_pair(non_ordered_pair(f13(f26(flip_range_of(X0)),X0),f13(f26(flip_range_of(X0)),X0)),non_ordered_pair(f13(f26(flip_range_of(X0)),X0),f14(f26(flip_range_of(X0)),X0)))))
| ~ little_set(flip_range_of(X0)) )
| ~ spl0_173
| ~ spl0_1330 ),
inference(forward_demodulation,[],[f41441,f2442]) ).
fof(f41441,plain,
( ! [X0] :
( f26(flip_range_of(X0)) = non_ordered_pair(non_ordered_pair(f12(f26(flip_range_of(X0)),X0),f12(f26(flip_range_of(X0)),X0)),non_ordered_pair(f12(f26(flip_range_of(X0)),X0),non_ordered_pair(non_ordered_pair(f13(f26(flip_range_of(X0)),X0),f13(f26(flip_range_of(X0)),X0)),non_ordered_pair(f13(f26(flip_range_of(X0)),X0),f14(f26(flip_range_of(X0)),X0)))))
| flip_range_of(X0) = empty_set
| ~ little_set(flip_range_of(X0)) )
| ~ spl0_1330 ),
inference(avatar_component_clause,[],[f41440]) ).
fof(f41479,plain,
( spl0_1338
| ~ spl0_124
| ~ spl0_147 ),
inference(avatar_split_clause,[],[f1978,f1954,f1299,f41477]) ).
fof(f41477,plain,
( spl0_1338
<=> ! [X5,X4,X0,X3,X2,X1] :
( ~ little_set(X0)
| ~ little_set(X1)
| ~ little_set(X2)
| ~ member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X2)),X3)
| ~ little_set(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X1)))
| member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X1)),compose(X3,apply(X4,first(X5))))
| ~ member(X5,X4)
| ~ member(non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X1)),second(X5))
| ~ ordered_pair_predicate(X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1338])]) ).
fof(f1978,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ little_set(X0)
| ~ little_set(X1)
| ~ little_set(X2)
| ~ member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X2)),X3)
| ~ little_set(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X1)))
| member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X1)),compose(X3,apply(X4,first(X5))))
| ~ member(X5,X4)
| ~ member(non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X1)),second(X5))
| ~ ordered_pair_predicate(X5) )
| ~ spl0_124
| ~ spl0_147 ),
inference(resolution,[],[f1955,f1300]) ).
fof(f41475,plain,
( spl0_1337
| ~ spl0_82
| ~ spl0_147 ),
inference(avatar_split_clause,[],[f1977,f1954,f660,f41473]) ).
fof(f41473,plain,
( spl0_1337
<=> ! [X4,X0,X3,X2,X1] :
( ~ little_set(X0)
| ~ little_set(X1)
| ~ little_set(X2)
| ~ member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X2)),X3)
| ~ little_set(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X1)))
| member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X1)),compose(X3,powerset(X4)))
| ~ subset(non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X1)),X4)
| ~ little_set(non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1337])]) ).
fof(f1977,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ little_set(X0)
| ~ little_set(X1)
| ~ little_set(X2)
| ~ member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X2)),X3)
| ~ little_set(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X1)))
| member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X1)),compose(X3,powerset(X4)))
| ~ subset(non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X1)),X4)
| ~ little_set(non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X1))) )
| ~ spl0_82
| ~ spl0_147 ),
inference(resolution,[],[f1955,f661]) ).
fof(f41468,plain,
( spl0_1336
| ~ spl0_103
| ~ spl0_151 ),
inference(avatar_split_clause,[],[f2119,f2025,f960,f41466]) ).
fof(f41466,plain,
( spl0_1336
<=> ! [X0,X1] : ~ member(X0,image(X1,converse(empty_set))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1336])]) ).
fof(f2119,plain,
( ! [X0,X1] : ~ member(X0,image(X1,converse(empty_set)))
| ~ spl0_103
| ~ spl0_151 ),
inference(resolution,[],[f2026,f961]) ).
fof(f41464,plain,
( spl0_1335
| ~ spl0_79
| ~ spl0_147 ),
inference(avatar_split_clause,[],[f1976,f1954,f648,f41462]) ).
fof(f41462,plain,
( spl0_1335
<=> ! [X4,X0,X3,X2,X1] :
( ~ little_set(X0)
| ~ little_set(X1)
| ~ little_set(X2)
| ~ member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X2)),X3)
| ~ little_set(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X1)))
| member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X1)),compose(X3,f16(non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X1)),X4)))
| ~ member(non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X1)),sigma(X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1335])]) ).
fof(f1976,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ little_set(X0)
| ~ little_set(X1)
| ~ little_set(X2)
| ~ member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X2)),X3)
| ~ little_set(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X1)))
| member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X1)),compose(X3,f16(non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X1)),X4)))
| ~ member(non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X1)),sigma(X4)) )
| ~ spl0_79
| ~ spl0_147 ),
inference(resolution,[],[f1955,f649]) ).
fof(f41460,plain,
( spl0_1334
| ~ spl0_73
| ~ spl0_147 ),
inference(avatar_split_clause,[],[f1973,f1954,f624,f41458]) ).
fof(f41458,plain,
( spl0_1334
<=> ! [X4,X0,X3,X2,X1] :
( ~ little_set(X0)
| ~ little_set(X1)
| ~ little_set(X2)
| ~ member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X2)),X3)
| ~ little_set(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X1)))
| member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X1)),compose(X3,complement(X4)))
| member(non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X1)),X4)
| ~ little_set(non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1334])]) ).
fof(f1973,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ little_set(X0)
| ~ little_set(X1)
| ~ little_set(X2)
| ~ member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X2)),X3)
| ~ little_set(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X1)))
| member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X1)),compose(X3,complement(X4)))
| member(non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X1)),X4)
| ~ little_set(non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X1))) )
| ~ spl0_73
| ~ spl0_147 ),
inference(resolution,[],[f1955,f625]) ).
fof(f41456,plain,
( spl0_1333
| ~ spl0_72
| ~ spl0_147 ),
inference(avatar_split_clause,[],[f1971,f1954,f620,f41454]) ).
fof(f41454,plain,
( spl0_1333
<=> ! [X4,X0,X3,X2,X1] :
( ~ little_set(X0)
| ~ little_set(X1)
| ~ little_set(X2)
| ~ member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X2)),X3)
| ~ little_set(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X1)))
| member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X1)),compose(X3,f7(non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X1)),X4)))
| ~ member(non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X1)),second(X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1333])]) ).
fof(f1971,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ little_set(X0)
| ~ little_set(X1)
| ~ little_set(X2)
| ~ member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X2)),X3)
| ~ little_set(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X1)))
| member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X1)),compose(X3,f7(non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X1)),X4)))
| ~ member(non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X1)),second(X4)) )
| ~ spl0_72
| ~ spl0_147 ),
inference(resolution,[],[f1955,f621]) ).
fof(f41452,plain,
( spl0_1332
| ~ spl0_71
| ~ spl0_147 ),
inference(avatar_split_clause,[],[f1968,f1954,f616,f41450]) ).
fof(f41450,plain,
( spl0_1332
<=> ! [X4,X0,X3,X2,X1] :
( ~ little_set(X0)
| ~ little_set(X1)
| ~ little_set(X2)
| ~ member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X2)),X3)
| ~ little_set(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X1)))
| member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X1)),compose(X3,f4(non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X1)),X4)))
| ~ member(non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X1)),first(X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1332])]) ).
fof(f1968,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ little_set(X0)
| ~ little_set(X1)
| ~ little_set(X2)
| ~ member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X2)),X3)
| ~ little_set(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X1)))
| member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X1)),compose(X3,f4(non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X1)),X4)))
| ~ member(non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X1)),first(X4)) )
| ~ spl0_71
| ~ spl0_147 ),
inference(resolution,[],[f1955,f617]) ).
fof(f41447,plain,
( spl0_1331
| ~ spl0_84
| ~ spl0_143 ),
inference(avatar_split_clause,[],[f1826,f1778,f668,f41445]) ).
fof(f668,plain,
( spl0_84
<=> ! [X0] :
( ~ little_set(X0)
| empty_set = X0
| member(f26(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_84])]) ).
fof(f1826,plain,
( ! [X0] :
( f26(rotate_right(X0)) = non_ordered_pair(non_ordered_pair(f9(f26(rotate_right(X0)),X0),f9(f26(rotate_right(X0)),X0)),non_ordered_pair(f9(f26(rotate_right(X0)),X0),non_ordered_pair(non_ordered_pair(f10(f26(rotate_right(X0)),X0),f10(f26(rotate_right(X0)),X0)),non_ordered_pair(f10(f26(rotate_right(X0)),X0),f11(f26(rotate_right(X0)),X0)))))
| rotate_right(X0) = empty_set
| ~ little_set(rotate_right(X0)) )
| ~ spl0_84
| ~ spl0_143 ),
inference(resolution,[],[f1779,f669]) ).
fof(f669,plain,
( ! [X0] :
( member(f26(X0),X0)
| empty_set = X0
| ~ little_set(X0) )
| ~ spl0_84 ),
inference(avatar_component_clause,[],[f668]) ).
fof(f41442,plain,
( spl0_1330
| ~ spl0_84
| ~ spl0_142 ),
inference(avatar_split_clause,[],[f1805,f1774,f668,f41440]) ).
fof(f1805,plain,
( ! [X0] :
( f26(flip_range_of(X0)) = non_ordered_pair(non_ordered_pair(f12(f26(flip_range_of(X0)),X0),f12(f26(flip_range_of(X0)),X0)),non_ordered_pair(f12(f26(flip_range_of(X0)),X0),non_ordered_pair(non_ordered_pair(f13(f26(flip_range_of(X0)),X0),f13(f26(flip_range_of(X0)),X0)),non_ordered_pair(f13(f26(flip_range_of(X0)),X0),f14(f26(flip_range_of(X0)),X0)))))
| flip_range_of(X0) = empty_set
| ~ little_set(flip_range_of(X0)) )
| ~ spl0_84
| ~ spl0_142 ),
inference(resolution,[],[f1775,f669]) ).
fof(f41417,plain,
( spl0_1329
| ~ spl0_107
| ~ spl0_151 ),
inference(avatar_split_clause,[],[f2114,f2025,f1068,f41415]) ).
fof(f41415,plain,
( spl0_1329
<=> ! [X0,X1] : ~ member(X0,image(converse(empty_set),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1329])]) ).
fof(f2114,plain,
( ! [X0,X1] : ~ member(X0,image(converse(empty_set),X1))
| ~ spl0_107
| ~ spl0_151 ),
inference(resolution,[],[f2026,f1069]) ).
fof(f41361,plain,
( spl0_1328
| ~ spl0_97
| ~ spl0_145 ),
inference(avatar_split_clause,[],[f1916,f1786,f852,f41359]) ).
fof(f41359,plain,
( spl0_1328
<=> ! [X2,X0,X1] :
( ~ member(X0,rotate_right(compose(X1,X2)))
| little_set(f29(non_ordered_pair(non_ordered_pair(f10(X0,compose(X1,X2)),f10(X0,compose(X1,X2))),non_ordered_pair(f10(X0,compose(X1,X2)),non_ordered_pair(non_ordered_pair(f11(X0,compose(X1,X2)),f11(X0,compose(X1,X2))),non_ordered_pair(f11(X0,compose(X1,X2)),f9(X0,compose(X1,X2)))))),X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1328])]) ).
fof(f852,plain,
( spl0_97
<=> ! [X9,X7,X3] :
( ~ member(X3,compose(X7,X9))
| little_set(f29(X3,X7,X9)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_97])]) ).
fof(f1916,plain,
( ! [X2,X0,X1] :
( ~ member(X0,rotate_right(compose(X1,X2)))
| little_set(f29(non_ordered_pair(non_ordered_pair(f10(X0,compose(X1,X2)),f10(X0,compose(X1,X2))),non_ordered_pair(f10(X0,compose(X1,X2)),non_ordered_pair(non_ordered_pair(f11(X0,compose(X1,X2)),f11(X0,compose(X1,X2))),non_ordered_pair(f11(X0,compose(X1,X2)),f9(X0,compose(X1,X2)))))),X1,X2)) )
| ~ spl0_97
| ~ spl0_145 ),
inference(resolution,[],[f1787,f853]) ).
fof(f853,plain,
( ! [X3,X9,X7] :
( ~ member(X3,compose(X7,X9))
| little_set(f29(X3,X7,X9)) )
| ~ spl0_97 ),
inference(avatar_component_clause,[],[f852]) ).
fof(f41357,plain,
( spl0_1327
| ~ spl0_98
| ~ spl0_145 ),
inference(avatar_split_clause,[],[f1915,f1786,f856,f41355]) ).
fof(f41355,plain,
( spl0_1327
<=> ! [X2,X0,X1] :
( ~ member(X0,rotate_right(compose(X1,X2)))
| little_set(f30(non_ordered_pair(non_ordered_pair(f10(X0,compose(X1,X2)),f10(X0,compose(X1,X2))),non_ordered_pair(f10(X0,compose(X1,X2)),non_ordered_pair(non_ordered_pair(f11(X0,compose(X1,X2)),f11(X0,compose(X1,X2))),non_ordered_pair(f11(X0,compose(X1,X2)),f9(X0,compose(X1,X2)))))),X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1327])]) ).
fof(f856,plain,
( spl0_98
<=> ! [X9,X7,X3] :
( ~ member(X3,compose(X7,X9))
| little_set(f30(X3,X7,X9)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_98])]) ).
fof(f1915,plain,
( ! [X2,X0,X1] :
( ~ member(X0,rotate_right(compose(X1,X2)))
| little_set(f30(non_ordered_pair(non_ordered_pair(f10(X0,compose(X1,X2)),f10(X0,compose(X1,X2))),non_ordered_pair(f10(X0,compose(X1,X2)),non_ordered_pair(non_ordered_pair(f11(X0,compose(X1,X2)),f11(X0,compose(X1,X2))),non_ordered_pair(f11(X0,compose(X1,X2)),f9(X0,compose(X1,X2)))))),X1,X2)) )
| ~ spl0_98
| ~ spl0_145 ),
inference(resolution,[],[f1787,f857]) ).
fof(f857,plain,
( ! [X3,X9,X7] :
( ~ member(X3,compose(X7,X9))
| little_set(f30(X3,X7,X9)) )
| ~ spl0_98 ),
inference(avatar_component_clause,[],[f856]) ).
fof(f41353,plain,
( spl0_1326
| ~ spl0_99
| ~ spl0_145 ),
inference(avatar_split_clause,[],[f1914,f1786,f860,f41351]) ).
fof(f41351,plain,
( spl0_1326
<=> ! [X2,X0,X1] :
( ~ member(X0,rotate_right(compose(X1,X2)))
| little_set(f31(non_ordered_pair(non_ordered_pair(f10(X0,compose(X1,X2)),f10(X0,compose(X1,X2))),non_ordered_pair(f10(X0,compose(X1,X2)),non_ordered_pair(non_ordered_pair(f11(X0,compose(X1,X2)),f11(X0,compose(X1,X2))),non_ordered_pair(f11(X0,compose(X1,X2)),f9(X0,compose(X1,X2)))))),X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1326])]) ).
fof(f860,plain,
( spl0_99
<=> ! [X9,X7,X3] :
( ~ member(X3,compose(X7,X9))
| little_set(f31(X3,X7,X9)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_99])]) ).
fof(f1914,plain,
( ! [X2,X0,X1] :
( ~ member(X0,rotate_right(compose(X1,X2)))
| little_set(f31(non_ordered_pair(non_ordered_pair(f10(X0,compose(X1,X2)),f10(X0,compose(X1,X2))),non_ordered_pair(f10(X0,compose(X1,X2)),non_ordered_pair(non_ordered_pair(f11(X0,compose(X1,X2)),f11(X0,compose(X1,X2))),non_ordered_pair(f11(X0,compose(X1,X2)),f9(X0,compose(X1,X2)))))),X1,X2)) )
| ~ spl0_99
| ~ spl0_145 ),
inference(resolution,[],[f1787,f861]) ).
fof(f861,plain,
( ! [X3,X9,X7] :
( ~ member(X3,compose(X7,X9))
| little_set(f31(X3,X7,X9)) )
| ~ spl0_99 ),
inference(avatar_component_clause,[],[f860]) ).
fof(f41346,plain,
( spl0_1325
| ~ spl0_138
| ~ spl0_151 ),
inference(avatar_split_clause,[],[f2113,f2025,f1638,f41344]) ).
fof(f41344,plain,
( spl0_1325
<=> ! [X0,X1] : ~ member(X0,compose(X1,converse(empty_set))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1325])]) ).
fof(f2113,plain,
( ! [X0,X1] : ~ member(X0,compose(X1,converse(empty_set)))
| ~ spl0_138
| ~ spl0_151 ),
inference(resolution,[],[f2026,f1639]) ).
fof(f41342,plain,
( spl0_1324
| ~ spl0_96
| ~ spl0_145 ),
inference(avatar_split_clause,[],[f1912,f1786,f848,f41340]) ).
fof(f41340,plain,
( spl0_1324
<=> ! [X2,X0,X1] :
( ~ member(X0,rotate_right(apply(X1,X2)))
| ordered_pair_predicate(f28(non_ordered_pair(non_ordered_pair(f10(X0,apply(X1,X2)),f10(X0,apply(X1,X2))),non_ordered_pair(f10(X0,apply(X1,X2)),non_ordered_pair(non_ordered_pair(f11(X0,apply(X1,X2)),f11(X0,apply(X1,X2))),non_ordered_pair(f11(X0,apply(X1,X2)),f9(X0,apply(X1,X2)))))),X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1324])]) ).
fof(f848,plain,
( spl0_96
<=> ! [X1,X7,X3] :
( ~ member(X3,apply(X7,X1))
| ordered_pair_predicate(f28(X3,X7,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_96])]) ).
fof(f1912,plain,
( ! [X2,X0,X1] :
( ~ member(X0,rotate_right(apply(X1,X2)))
| ordered_pair_predicate(f28(non_ordered_pair(non_ordered_pair(f10(X0,apply(X1,X2)),f10(X0,apply(X1,X2))),non_ordered_pair(f10(X0,apply(X1,X2)),non_ordered_pair(non_ordered_pair(f11(X0,apply(X1,X2)),f11(X0,apply(X1,X2))),non_ordered_pair(f11(X0,apply(X1,X2)),f9(X0,apply(X1,X2)))))),X1,X2)) )
| ~ spl0_96
| ~ spl0_145 ),
inference(resolution,[],[f1787,f849]) ).
fof(f849,plain,
( ! [X3,X1,X7] :
( ~ member(X3,apply(X7,X1))
| ordered_pair_predicate(f28(X3,X7,X1)) )
| ~ spl0_96 ),
inference(avatar_component_clause,[],[f848]) ).
fof(f41338,plain,
( spl0_1323
| ~ spl0_94
| ~ spl0_145 ),
inference(avatar_split_clause,[],[f1906,f1786,f840,f41336]) ).
fof(f41336,plain,
( spl0_1323
<=> ! [X2,X0,X1] :
( ~ member(X0,rotate_right(image(X1,X2)))
| ordered_pair_predicate(f22(non_ordered_pair(non_ordered_pair(f10(X0,image(X1,X2)),f10(X0,image(X1,X2))),non_ordered_pair(f10(X0,image(X1,X2)),non_ordered_pair(non_ordered_pair(f11(X0,image(X1,X2)),f11(X0,image(X1,X2))),non_ordered_pair(f11(X0,image(X1,X2)),f9(X0,image(X1,X2)))))),X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1323])]) ).
fof(f840,plain,
( spl0_94
<=> ! [X0,X7,X3] :
( ~ member(X3,image(X0,X7))
| ordered_pair_predicate(f22(X3,X0,X7)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_94])]) ).
fof(f1906,plain,
( ! [X2,X0,X1] :
( ~ member(X0,rotate_right(image(X1,X2)))
| ordered_pair_predicate(f22(non_ordered_pair(non_ordered_pair(f10(X0,image(X1,X2)),f10(X0,image(X1,X2))),non_ordered_pair(f10(X0,image(X1,X2)),non_ordered_pair(non_ordered_pair(f11(X0,image(X1,X2)),f11(X0,image(X1,X2))),non_ordered_pair(f11(X0,image(X1,X2)),f9(X0,image(X1,X2)))))),X1,X2)) )
| ~ spl0_94
| ~ spl0_145 ),
inference(resolution,[],[f1787,f841]) ).
fof(f841,plain,
( ! [X3,X0,X7] :
( ~ member(X3,image(X0,X7))
| ordered_pair_predicate(f22(X3,X0,X7)) )
| ~ spl0_94 ),
inference(avatar_component_clause,[],[f840]) ).
fof(f41334,plain,
( spl0_1322
| ~ spl0_97
| ~ spl0_144 ),
inference(avatar_split_clause,[],[f1873,f1782,f852,f41332]) ).
fof(f41332,plain,
( spl0_1322
<=> ! [X2,X0,X1] :
( ~ member(X0,flip_range_of(compose(X1,X2)))
| little_set(f29(non_ordered_pair(non_ordered_pair(f12(X0,compose(X1,X2)),f12(X0,compose(X1,X2))),non_ordered_pair(f12(X0,compose(X1,X2)),non_ordered_pair(non_ordered_pair(f14(X0,compose(X1,X2)),f14(X0,compose(X1,X2))),non_ordered_pair(f14(X0,compose(X1,X2)),f13(X0,compose(X1,X2)))))),X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1322])]) ).
fof(f1873,plain,
( ! [X2,X0,X1] :
( ~ member(X0,flip_range_of(compose(X1,X2)))
| little_set(f29(non_ordered_pair(non_ordered_pair(f12(X0,compose(X1,X2)),f12(X0,compose(X1,X2))),non_ordered_pair(f12(X0,compose(X1,X2)),non_ordered_pair(non_ordered_pair(f14(X0,compose(X1,X2)),f14(X0,compose(X1,X2))),non_ordered_pair(f14(X0,compose(X1,X2)),f13(X0,compose(X1,X2)))))),X1,X2)) )
| ~ spl0_97
| ~ spl0_144 ),
inference(resolution,[],[f1783,f853]) ).
fof(f41330,plain,
( spl0_1321
| ~ spl0_98
| ~ spl0_144 ),
inference(avatar_split_clause,[],[f1872,f1782,f856,f41328]) ).
fof(f41328,plain,
( spl0_1321
<=> ! [X2,X0,X1] :
( ~ member(X0,flip_range_of(compose(X1,X2)))
| little_set(f30(non_ordered_pair(non_ordered_pair(f12(X0,compose(X1,X2)),f12(X0,compose(X1,X2))),non_ordered_pair(f12(X0,compose(X1,X2)),non_ordered_pair(non_ordered_pair(f14(X0,compose(X1,X2)),f14(X0,compose(X1,X2))),non_ordered_pair(f14(X0,compose(X1,X2)),f13(X0,compose(X1,X2)))))),X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1321])]) ).
fof(f1872,plain,
( ! [X2,X0,X1] :
( ~ member(X0,flip_range_of(compose(X1,X2)))
| little_set(f30(non_ordered_pair(non_ordered_pair(f12(X0,compose(X1,X2)),f12(X0,compose(X1,X2))),non_ordered_pair(f12(X0,compose(X1,X2)),non_ordered_pair(non_ordered_pair(f14(X0,compose(X1,X2)),f14(X0,compose(X1,X2))),non_ordered_pair(f14(X0,compose(X1,X2)),f13(X0,compose(X1,X2)))))),X1,X2)) )
| ~ spl0_98
| ~ spl0_144 ),
inference(resolution,[],[f1783,f857]) ).
fof(f41326,plain,
( spl0_1320
| ~ spl0_99
| ~ spl0_144 ),
inference(avatar_split_clause,[],[f1871,f1782,f860,f41324]) ).
fof(f41324,plain,
( spl0_1320
<=> ! [X2,X0,X1] :
( ~ member(X0,flip_range_of(compose(X1,X2)))
| little_set(f31(non_ordered_pair(non_ordered_pair(f12(X0,compose(X1,X2)),f12(X0,compose(X1,X2))),non_ordered_pair(f12(X0,compose(X1,X2)),non_ordered_pair(non_ordered_pair(f14(X0,compose(X1,X2)),f14(X0,compose(X1,X2))),non_ordered_pair(f14(X0,compose(X1,X2)),f13(X0,compose(X1,X2)))))),X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1320])]) ).
fof(f1871,plain,
( ! [X2,X0,X1] :
( ~ member(X0,flip_range_of(compose(X1,X2)))
| little_set(f31(non_ordered_pair(non_ordered_pair(f12(X0,compose(X1,X2)),f12(X0,compose(X1,X2))),non_ordered_pair(f12(X0,compose(X1,X2)),non_ordered_pair(non_ordered_pair(f14(X0,compose(X1,X2)),f14(X0,compose(X1,X2))),non_ordered_pair(f14(X0,compose(X1,X2)),f13(X0,compose(X1,X2)))))),X1,X2)) )
| ~ spl0_99
| ~ spl0_144 ),
inference(resolution,[],[f1783,f861]) ).
fof(f41322,plain,
( spl0_1319
| ~ spl0_96
| ~ spl0_144 ),
inference(avatar_split_clause,[],[f1869,f1782,f848,f41320]) ).
fof(f41320,plain,
( spl0_1319
<=> ! [X2,X0,X1] :
( ~ member(X0,flip_range_of(apply(X1,X2)))
| ordered_pair_predicate(f28(non_ordered_pair(non_ordered_pair(f12(X0,apply(X1,X2)),f12(X0,apply(X1,X2))),non_ordered_pair(f12(X0,apply(X1,X2)),non_ordered_pair(non_ordered_pair(f14(X0,apply(X1,X2)),f14(X0,apply(X1,X2))),non_ordered_pair(f14(X0,apply(X1,X2)),f13(X0,apply(X1,X2)))))),X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1319])]) ).
fof(f1869,plain,
( ! [X2,X0,X1] :
( ~ member(X0,flip_range_of(apply(X1,X2)))
| ordered_pair_predicate(f28(non_ordered_pair(non_ordered_pair(f12(X0,apply(X1,X2)),f12(X0,apply(X1,X2))),non_ordered_pair(f12(X0,apply(X1,X2)),non_ordered_pair(non_ordered_pair(f14(X0,apply(X1,X2)),f14(X0,apply(X1,X2))),non_ordered_pair(f14(X0,apply(X1,X2)),f13(X0,apply(X1,X2)))))),X1,X2)) )
| ~ spl0_96
| ~ spl0_144 ),
inference(resolution,[],[f1783,f849]) ).
fof(f41318,plain,
( spl0_1318
| ~ spl0_94
| ~ spl0_144 ),
inference(avatar_split_clause,[],[f1863,f1782,f840,f41316]) ).
fof(f41316,plain,
( spl0_1318
<=> ! [X2,X0,X1] :
( ~ member(X0,flip_range_of(image(X1,X2)))
| ordered_pair_predicate(f22(non_ordered_pair(non_ordered_pair(f12(X0,image(X1,X2)),f12(X0,image(X1,X2))),non_ordered_pair(f12(X0,image(X1,X2)),non_ordered_pair(non_ordered_pair(f14(X0,image(X1,X2)),f14(X0,image(X1,X2))),non_ordered_pair(f14(X0,image(X1,X2)),f13(X0,image(X1,X2)))))),X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1318])]) ).
fof(f1863,plain,
( ! [X2,X0,X1] :
( ~ member(X0,flip_range_of(image(X1,X2)))
| ordered_pair_predicate(f22(non_ordered_pair(non_ordered_pair(f12(X0,image(X1,X2)),f12(X0,image(X1,X2))),non_ordered_pair(f12(X0,image(X1,X2)),non_ordered_pair(non_ordered_pair(f14(X0,image(X1,X2)),f14(X0,image(X1,X2))),non_ordered_pair(f14(X0,image(X1,X2)),f13(X0,image(X1,X2)))))),X1,X2)) )
| ~ spl0_94
| ~ spl0_144 ),
inference(resolution,[],[f1783,f841]) ).
fof(f41314,plain,
( spl0_1317
| ~ spl0_111
| ~ spl0_140 ),
inference(avatar_split_clause,[],[f1762,f1745,f1085,f41312]) ).
fof(f41312,plain,
( spl0_1317
<=> ! [X4,X0,X3,X2,X1] :
( ~ little_set(X0)
| ~ little_set(X1)
| ~ little_set(X2)
| X1 = X2
| ~ member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X1)),second(f28(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X2)),X3,X4)))
| ~ single_valued_set(second(f28(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X2)),X3,X4)))
| ~ member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X2)),apply(X3,X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1317])]) ).
fof(f1762,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ little_set(X0)
| ~ little_set(X1)
| ~ little_set(X2)
| X1 = X2
| ~ member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X1)),second(f28(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X2)),X3,X4)))
| ~ single_valued_set(second(f28(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X2)),X3,X4)))
| ~ member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X2)),apply(X3,X4)) )
| ~ spl0_111
| ~ spl0_140 ),
inference(resolution,[],[f1746,f1086]) ).
fof(f41281,plain,
( spl0_1316
| ~ spl0_139
| ~ spl0_151 ),
inference(avatar_split_clause,[],[f2110,f2025,f1642,f41279]) ).
fof(f41279,plain,
( spl0_1316
<=> ! [X0,X1] : ~ member(X0,compose(converse(empty_set),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1316])]) ).
fof(f2110,plain,
( ! [X0,X1] : ~ member(X0,compose(converse(empty_set),X1))
| ~ spl0_139
| ~ spl0_151 ),
inference(resolution,[],[f2026,f1643]) ).
fof(f40433,plain,
( spl0_1315
| ~ spl0_16
| ~ spl0_149 ),
inference(avatar_split_clause,[],[f2016,f1985,f253,f40431]) ).
fof(f40431,plain,
( spl0_1315
<=> ! [X2,X0,X1] :
( ~ little_set(X0)
| ~ little_set(X1)
| ~ little_set(X2)
| member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X1)))),flip_range_of(universal_set))
| ~ little_set(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X1)))))
| ~ little_set(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,non_ordered_pair(non_ordered_pair(X1,X1),non_ordered_pair(X1,X2))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1315])]) ).
fof(f2016,plain,
( ! [X2,X0,X1] :
( ~ little_set(X0)
| ~ little_set(X1)
| ~ little_set(X2)
| member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X1)))),flip_range_of(universal_set))
| ~ little_set(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X1)))))
| ~ little_set(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,non_ordered_pair(non_ordered_pair(X1,X1),non_ordered_pair(X1,X2))))) )
| ~ spl0_16
| ~ spl0_149 ),
inference(resolution,[],[f1986,f254]) ).
fof(f40429,plain,
( spl0_1314
| ~ spl0_16
| ~ spl0_148 ),
inference(avatar_split_clause,[],[f2000,f1981,f253,f40427]) ).
fof(f40427,plain,
( spl0_1314
<=> ! [X2,X0,X1] :
( ~ little_set(X0)
| ~ little_set(X1)
| ~ little_set(X2)
| member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X1)))),rotate_right(universal_set))
| ~ little_set(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X1)))))
| ~ little_set(non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,non_ordered_pair(non_ordered_pair(X1,X1),non_ordered_pair(X1,X0))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1314])]) ).
fof(f2000,plain,
( ! [X2,X0,X1] :
( ~ little_set(X0)
| ~ little_set(X1)
| ~ little_set(X2)
| member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X1)))),rotate_right(universal_set))
| ~ little_set(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X1)))))
| ~ little_set(non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,non_ordered_pair(non_ordered_pair(X1,X1),non_ordered_pair(X1,X0))))) )
| ~ spl0_16
| ~ spl0_148 ),
inference(resolution,[],[f1982,f254]) ).
fof(f40425,plain,
( spl0_1313
| ~ spl0_44
| ~ spl0_147 ),
inference(avatar_split_clause,[],[f1966,f1954,f377,f40423]) ).
fof(f40423,plain,
( spl0_1313
<=> ! [X4,X0,X3,X2,X1] :
( ~ little_set(X0)
| ~ little_set(X1)
| ~ little_set(X2)
| ~ member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X2)),X3)
| ~ little_set(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X1)))
| member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X1)),compose(X3,non_ordered_pair(X4,non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X1)))))
| ~ little_set(non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1313])]) ).
fof(f1966,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ little_set(X0)
| ~ little_set(X1)
| ~ little_set(X2)
| ~ member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X2)),X3)
| ~ little_set(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X1)))
| member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X1)),compose(X3,non_ordered_pair(X4,non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X1)))))
| ~ little_set(non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X1))) )
| ~ spl0_44
| ~ spl0_147 ),
inference(resolution,[],[f1955,f378]) ).
fof(f40421,plain,
( spl0_1312
| ~ spl0_43
| ~ spl0_147 ),
inference(avatar_split_clause,[],[f1965,f1954,f373,f40419]) ).
fof(f40419,plain,
( spl0_1312
<=> ! [X4,X0,X3,X2,X1] :
( ~ little_set(X0)
| ~ little_set(X1)
| ~ little_set(X2)
| ~ member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X2)),X3)
| ~ little_set(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X1)))
| member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X1)),compose(X3,non_ordered_pair(non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X1)),X4)))
| ~ little_set(non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1312])]) ).
fof(f1965,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ little_set(X0)
| ~ little_set(X1)
| ~ little_set(X2)
| ~ member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X2)),X3)
| ~ little_set(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X1)))
| member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X1)),compose(X3,non_ordered_pair(non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X1)),X4)))
| ~ little_set(non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X1))) )
| ~ spl0_43
| ~ spl0_147 ),
inference(resolution,[],[f1955,f374]) ).
fof(f40414,plain,
( spl0_1311
| ~ spl0_103
| ~ spl0_141 ),
inference(avatar_split_clause,[],[f2080,f1749,f960,f40412]) ).
fof(f40412,plain,
( spl0_1311
<=> ! [X0,X1] : ~ member(X0,image(X1,range_of(empty_set))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1311])]) ).
fof(f2080,plain,
( ! [X0,X1] : ~ member(X0,image(X1,range_of(empty_set)))
| ~ spl0_103
| ~ spl0_141 ),
inference(resolution,[],[f1750,f961]) ).
fof(f40410,plain,
( spl0_1310
| ~ spl0_75
| ~ spl0_145 ),
inference(avatar_split_clause,[],[f1892,f1786,f632,f40408]) ).
fof(f40408,plain,
( spl0_1310
<=> ! [X2,X0,X1] :
( ~ member(X0,rotate_right(cross_product(X1,X2)))
| member(first(non_ordered_pair(non_ordered_pair(f10(X0,cross_product(X1,X2)),f10(X0,cross_product(X1,X2))),non_ordered_pair(f10(X0,cross_product(X1,X2)),non_ordered_pair(non_ordered_pair(f11(X0,cross_product(X1,X2)),f11(X0,cross_product(X1,X2))),non_ordered_pair(f11(X0,cross_product(X1,X2)),f9(X0,cross_product(X1,X2))))))),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1310])]) ).
fof(f632,plain,
( spl0_75
<=> ! [X0,X1,X3] :
( member(first(X3),X0)
| ~ member(X3,cross_product(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_75])]) ).
fof(f1892,plain,
( ! [X2,X0,X1] :
( ~ member(X0,rotate_right(cross_product(X1,X2)))
| member(first(non_ordered_pair(non_ordered_pair(f10(X0,cross_product(X1,X2)),f10(X0,cross_product(X1,X2))),non_ordered_pair(f10(X0,cross_product(X1,X2)),non_ordered_pair(non_ordered_pair(f11(X0,cross_product(X1,X2)),f11(X0,cross_product(X1,X2))),non_ordered_pair(f11(X0,cross_product(X1,X2)),f9(X0,cross_product(X1,X2))))))),X1) )
| ~ spl0_75
| ~ spl0_145 ),
inference(resolution,[],[f1787,f633]) ).
fof(f633,plain,
( ! [X3,X0,X1] :
( ~ member(X3,cross_product(X0,X1))
| member(first(X3),X0) )
| ~ spl0_75 ),
inference(avatar_component_clause,[],[f632]) ).
fof(f40406,plain,
( spl0_1309
| ~ spl0_77
| ~ spl0_145 ),
inference(avatar_split_clause,[],[f1891,f1786,f640,f40404]) ).
fof(f40404,plain,
( spl0_1309
<=> ! [X2,X0,X1] :
( ~ member(X0,rotate_right(cross_product(X1,X2)))
| member(second(non_ordered_pair(non_ordered_pair(f10(X0,cross_product(X1,X2)),f10(X0,cross_product(X1,X2))),non_ordered_pair(f10(X0,cross_product(X1,X2)),non_ordered_pair(non_ordered_pair(f11(X0,cross_product(X1,X2)),f11(X0,cross_product(X1,X2))),non_ordered_pair(f11(X0,cross_product(X1,X2)),f9(X0,cross_product(X1,X2))))))),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1309])]) ).
fof(f640,plain,
( spl0_77
<=> ! [X0,X1,X3] :
( member(second(X3),X1)
| ~ member(X3,cross_product(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_77])]) ).
fof(f1891,plain,
( ! [X2,X0,X1] :
( ~ member(X0,rotate_right(cross_product(X1,X2)))
| member(second(non_ordered_pair(non_ordered_pair(f10(X0,cross_product(X1,X2)),f10(X0,cross_product(X1,X2))),non_ordered_pair(f10(X0,cross_product(X1,X2)),non_ordered_pair(non_ordered_pair(f11(X0,cross_product(X1,X2)),f11(X0,cross_product(X1,X2))),non_ordered_pair(f11(X0,cross_product(X1,X2)),f9(X0,cross_product(X1,X2))))))),X2) )
| ~ spl0_77
| ~ spl0_145 ),
inference(resolution,[],[f1787,f641]) ).
fof(f641,plain,
( ! [X3,X0,X1] :
( ~ member(X3,cross_product(X0,X1))
| member(second(X3),X1) )
| ~ spl0_77 ),
inference(avatar_component_clause,[],[f640]) ).
fof(f40402,plain,
( spl0_1308
| ~ spl0_75
| ~ spl0_144 ),
inference(avatar_split_clause,[],[f1849,f1782,f632,f40400]) ).
fof(f40400,plain,
( spl0_1308
<=> ! [X2,X0,X1] :
( ~ member(X0,flip_range_of(cross_product(X1,X2)))
| member(first(non_ordered_pair(non_ordered_pair(f12(X0,cross_product(X1,X2)),f12(X0,cross_product(X1,X2))),non_ordered_pair(f12(X0,cross_product(X1,X2)),non_ordered_pair(non_ordered_pair(f14(X0,cross_product(X1,X2)),f14(X0,cross_product(X1,X2))),non_ordered_pair(f14(X0,cross_product(X1,X2)),f13(X0,cross_product(X1,X2))))))),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1308])]) ).
fof(f1849,plain,
( ! [X2,X0,X1] :
( ~ member(X0,flip_range_of(cross_product(X1,X2)))
| member(first(non_ordered_pair(non_ordered_pair(f12(X0,cross_product(X1,X2)),f12(X0,cross_product(X1,X2))),non_ordered_pair(f12(X0,cross_product(X1,X2)),non_ordered_pair(non_ordered_pair(f14(X0,cross_product(X1,X2)),f14(X0,cross_product(X1,X2))),non_ordered_pair(f14(X0,cross_product(X1,X2)),f13(X0,cross_product(X1,X2))))))),X1) )
| ~ spl0_75
| ~ spl0_144 ),
inference(resolution,[],[f1783,f633]) ).
fof(f40398,plain,
( spl0_1307
| ~ spl0_77
| ~ spl0_144 ),
inference(avatar_split_clause,[],[f1848,f1782,f640,f40396]) ).
fof(f40396,plain,
( spl0_1307
<=> ! [X2,X0,X1] :
( ~ member(X0,flip_range_of(cross_product(X1,X2)))
| member(second(non_ordered_pair(non_ordered_pair(f12(X0,cross_product(X1,X2)),f12(X0,cross_product(X1,X2))),non_ordered_pair(f12(X0,cross_product(X1,X2)),non_ordered_pair(non_ordered_pair(f14(X0,cross_product(X1,X2)),f14(X0,cross_product(X1,X2))),non_ordered_pair(f14(X0,cross_product(X1,X2)),f13(X0,cross_product(X1,X2))))))),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1307])]) ).
fof(f1848,plain,
( ! [X2,X0,X1] :
( ~ member(X0,flip_range_of(cross_product(X1,X2)))
| member(second(non_ordered_pair(non_ordered_pair(f12(X0,cross_product(X1,X2)),f12(X0,cross_product(X1,X2))),non_ordered_pair(f12(X0,cross_product(X1,X2)),non_ordered_pair(non_ordered_pair(f14(X0,cross_product(X1,X2)),f14(X0,cross_product(X1,X2))),non_ordered_pair(f14(X0,cross_product(X1,X2)),f13(X0,cross_product(X1,X2))))))),X2) )
| ~ spl0_77
| ~ spl0_144 ),
inference(resolution,[],[f1783,f641]) ).
fof(f39387,plain,
( spl0_1306
| ~ spl0_107
| ~ spl0_141 ),
inference(avatar_split_clause,[],[f2074,f1749,f1068,f39385]) ).
fof(f39385,plain,
( spl0_1306
<=> ! [X0,X1] : ~ member(X0,image(range_of(empty_set),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1306])]) ).
fof(f2074,plain,
( ! [X0,X1] : ~ member(X0,image(range_of(empty_set),X1))
| ~ spl0_107
| ~ spl0_141 ),
inference(resolution,[],[f1750,f1069]) ).
fof(f39383,plain,
( spl0_1305
| ~ spl0_173
| ~ spl0_1299 ),
inference(avatar_split_clause,[],[f39359,f39356,f2440,f39381]) ).
fof(f39356,plain,
( spl0_1299
<=> ! [X0] :
( f24(rotate_right(X0)) = non_ordered_pair(non_ordered_pair(f9(f24(rotate_right(X0)),X0),f9(f24(rotate_right(X0)),X0)),non_ordered_pair(f9(f24(rotate_right(X0)),X0),non_ordered_pair(non_ordered_pair(f10(f24(rotate_right(X0)),X0),f10(f24(rotate_right(X0)),X0)),non_ordered_pair(f10(f24(rotate_right(X0)),X0),f11(f24(rotate_right(X0)),X0)))))
| rotate_right(X0) = empty_set ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1299])]) ).
fof(f39359,plain,
( ! [X0] :
( estin = rotate_right(X0)
| f24(rotate_right(X0)) = non_ordered_pair(non_ordered_pair(f9(f24(rotate_right(X0)),X0),f9(f24(rotate_right(X0)),X0)),non_ordered_pair(f9(f24(rotate_right(X0)),X0),non_ordered_pair(non_ordered_pair(f10(f24(rotate_right(X0)),X0),f10(f24(rotate_right(X0)),X0)),non_ordered_pair(f10(f24(rotate_right(X0)),X0),f11(f24(rotate_right(X0)),X0))))) )
| ~ spl0_173
| ~ spl0_1299 ),
inference(forward_demodulation,[],[f39357,f2442]) ).
fof(f39357,plain,
( ! [X0] :
( f24(rotate_right(X0)) = non_ordered_pair(non_ordered_pair(f9(f24(rotate_right(X0)),X0),f9(f24(rotate_right(X0)),X0)),non_ordered_pair(f9(f24(rotate_right(X0)),X0),non_ordered_pair(non_ordered_pair(f10(f24(rotate_right(X0)),X0),f10(f24(rotate_right(X0)),X0)),non_ordered_pair(f10(f24(rotate_right(X0)),X0),f11(f24(rotate_right(X0)),X0)))))
| rotate_right(X0) = empty_set )
| ~ spl0_1299 ),
inference(avatar_component_clause,[],[f39356]) ).
fof(f39379,plain,
( spl0_1304
| ~ spl0_173
| ~ spl0_1298 ),
inference(avatar_split_clause,[],[f39354,f39351,f2440,f39377]) ).
fof(f39351,plain,
( spl0_1298
<=> ! [X0] :
( f24(flip_range_of(X0)) = non_ordered_pair(non_ordered_pair(f12(f24(flip_range_of(X0)),X0),f12(f24(flip_range_of(X0)),X0)),non_ordered_pair(f12(f24(flip_range_of(X0)),X0),non_ordered_pair(non_ordered_pair(f13(f24(flip_range_of(X0)),X0),f13(f24(flip_range_of(X0)),X0)),non_ordered_pair(f13(f24(flip_range_of(X0)),X0),f14(f24(flip_range_of(X0)),X0)))))
| flip_range_of(X0) = empty_set ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1298])]) ).
fof(f39354,plain,
( ! [X0] :
( estin = flip_range_of(X0)
| f24(flip_range_of(X0)) = non_ordered_pair(non_ordered_pair(f12(f24(flip_range_of(X0)),X0),f12(f24(flip_range_of(X0)),X0)),non_ordered_pair(f12(f24(flip_range_of(X0)),X0),non_ordered_pair(non_ordered_pair(f13(f24(flip_range_of(X0)),X0),f13(f24(flip_range_of(X0)),X0)),non_ordered_pair(f13(f24(flip_range_of(X0)),X0),f14(f24(flip_range_of(X0)),X0))))) )
| ~ spl0_173
| ~ spl0_1298 ),
inference(forward_demodulation,[],[f39352,f2442]) ).
fof(f39352,plain,
( ! [X0] :
( f24(flip_range_of(X0)) = non_ordered_pair(non_ordered_pair(f12(f24(flip_range_of(X0)),X0),f12(f24(flip_range_of(X0)),X0)),non_ordered_pair(f12(f24(flip_range_of(X0)),X0),non_ordered_pair(non_ordered_pair(f13(f24(flip_range_of(X0)),X0),f13(f24(flip_range_of(X0)),X0)),non_ordered_pair(f13(f24(flip_range_of(X0)),X0),f14(f24(flip_range_of(X0)),X0)))))
| flip_range_of(X0) = empty_set )
| ~ spl0_1298 ),
inference(avatar_component_clause,[],[f39351]) ).
fof(f39375,plain,
( spl0_1303
| ~ spl0_51
| ~ spl0_145 ),
inference(avatar_split_clause,[],[f1887,f1786,f426,f39373]) ).
fof(f39373,plain,
( spl0_1303
<=> ! [X2,X0,X1] :
( ~ member(X0,rotate_right(intersection(X1,X2)))
| member(non_ordered_pair(non_ordered_pair(f10(X0,intersection(X1,X2)),f10(X0,intersection(X1,X2))),non_ordered_pair(f10(X0,intersection(X1,X2)),non_ordered_pair(non_ordered_pair(f11(X0,intersection(X1,X2)),f11(X0,intersection(X1,X2))),non_ordered_pair(f11(X0,intersection(X1,X2)),f9(X0,intersection(X1,X2)))))),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1303])]) ).
fof(f426,plain,
( spl0_51
<=> ! [X0,X1,X3] :
( member(X3,X0)
| ~ member(X3,intersection(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_51])]) ).
fof(f1887,plain,
( ! [X2,X0,X1] :
( ~ member(X0,rotate_right(intersection(X1,X2)))
| member(non_ordered_pair(non_ordered_pair(f10(X0,intersection(X1,X2)),f10(X0,intersection(X1,X2))),non_ordered_pair(f10(X0,intersection(X1,X2)),non_ordered_pair(non_ordered_pair(f11(X0,intersection(X1,X2)),f11(X0,intersection(X1,X2))),non_ordered_pair(f11(X0,intersection(X1,X2)),f9(X0,intersection(X1,X2)))))),X1) )
| ~ spl0_51
| ~ spl0_145 ),
inference(resolution,[],[f1787,f427]) ).
fof(f427,plain,
( ! [X3,X0,X1] :
( ~ member(X3,intersection(X0,X1))
| member(X3,X0) )
| ~ spl0_51 ),
inference(avatar_component_clause,[],[f426]) ).
fof(f39371,plain,
( spl0_1302
| ~ spl0_52
| ~ spl0_145 ),
inference(avatar_split_clause,[],[f1886,f1786,f430,f39369]) ).
fof(f39369,plain,
( spl0_1302
<=> ! [X2,X0,X1] :
( ~ member(X0,rotate_right(intersection(X1,X2)))
| member(non_ordered_pair(non_ordered_pair(f10(X0,intersection(X1,X2)),f10(X0,intersection(X1,X2))),non_ordered_pair(f10(X0,intersection(X1,X2)),non_ordered_pair(non_ordered_pair(f11(X0,intersection(X1,X2)),f11(X0,intersection(X1,X2))),non_ordered_pair(f11(X0,intersection(X1,X2)),f9(X0,intersection(X1,X2)))))),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1302])]) ).
fof(f430,plain,
( spl0_52
<=> ! [X0,X1,X3] :
( member(X3,X1)
| ~ member(X3,intersection(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_52])]) ).
fof(f1886,plain,
( ! [X2,X0,X1] :
( ~ member(X0,rotate_right(intersection(X1,X2)))
| member(non_ordered_pair(non_ordered_pair(f10(X0,intersection(X1,X2)),f10(X0,intersection(X1,X2))),non_ordered_pair(f10(X0,intersection(X1,X2)),non_ordered_pair(non_ordered_pair(f11(X0,intersection(X1,X2)),f11(X0,intersection(X1,X2))),non_ordered_pair(f11(X0,intersection(X1,X2)),f9(X0,intersection(X1,X2)))))),X2) )
| ~ spl0_52
| ~ spl0_145 ),
inference(resolution,[],[f1787,f431]) ).
fof(f431,plain,
( ! [X3,X0,X1] :
( ~ member(X3,intersection(X0,X1))
| member(X3,X1) )
| ~ spl0_52 ),
inference(avatar_component_clause,[],[f430]) ).
fof(f39367,plain,
( spl0_1301
| ~ spl0_51
| ~ spl0_144 ),
inference(avatar_split_clause,[],[f1844,f1782,f426,f39365]) ).
fof(f39365,plain,
( spl0_1301
<=> ! [X2,X0,X1] :
( ~ member(X0,flip_range_of(intersection(X1,X2)))
| member(non_ordered_pair(non_ordered_pair(f12(X0,intersection(X1,X2)),f12(X0,intersection(X1,X2))),non_ordered_pair(f12(X0,intersection(X1,X2)),non_ordered_pair(non_ordered_pair(f14(X0,intersection(X1,X2)),f14(X0,intersection(X1,X2))),non_ordered_pair(f14(X0,intersection(X1,X2)),f13(X0,intersection(X1,X2)))))),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1301])]) ).
fof(f1844,plain,
( ! [X2,X0,X1] :
( ~ member(X0,flip_range_of(intersection(X1,X2)))
| member(non_ordered_pair(non_ordered_pair(f12(X0,intersection(X1,X2)),f12(X0,intersection(X1,X2))),non_ordered_pair(f12(X0,intersection(X1,X2)),non_ordered_pair(non_ordered_pair(f14(X0,intersection(X1,X2)),f14(X0,intersection(X1,X2))),non_ordered_pair(f14(X0,intersection(X1,X2)),f13(X0,intersection(X1,X2)))))),X1) )
| ~ spl0_51
| ~ spl0_144 ),
inference(resolution,[],[f1783,f427]) ).
fof(f39363,plain,
( spl0_1300
| ~ spl0_52
| ~ spl0_144 ),
inference(avatar_split_clause,[],[f1843,f1782,f430,f39361]) ).
fof(f39361,plain,
( spl0_1300
<=> ! [X2,X0,X1] :
( ~ member(X0,flip_range_of(intersection(X1,X2)))
| member(non_ordered_pair(non_ordered_pair(f12(X0,intersection(X1,X2)),f12(X0,intersection(X1,X2))),non_ordered_pair(f12(X0,intersection(X1,X2)),non_ordered_pair(non_ordered_pair(f14(X0,intersection(X1,X2)),f14(X0,intersection(X1,X2))),non_ordered_pair(f14(X0,intersection(X1,X2)),f13(X0,intersection(X1,X2)))))),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1300])]) ).
fof(f1843,plain,
( ! [X2,X0,X1] :
( ~ member(X0,flip_range_of(intersection(X1,X2)))
| member(non_ordered_pair(non_ordered_pair(f12(X0,intersection(X1,X2)),f12(X0,intersection(X1,X2))),non_ordered_pair(f12(X0,intersection(X1,X2)),non_ordered_pair(non_ordered_pair(f14(X0,intersection(X1,X2)),f14(X0,intersection(X1,X2))),non_ordered_pair(f14(X0,intersection(X1,X2)),f13(X0,intersection(X1,X2)))))),X2) )
| ~ spl0_52
| ~ spl0_144 ),
inference(resolution,[],[f1783,f431]) ).
fof(f39358,plain,
( spl0_1299
| ~ spl0_40
| ~ spl0_143 ),
inference(avatar_split_clause,[],[f1825,f1778,f361,f39356]) ).
fof(f1825,plain,
( ! [X0] :
( f24(rotate_right(X0)) = non_ordered_pair(non_ordered_pair(f9(f24(rotate_right(X0)),X0),f9(f24(rotate_right(X0)),X0)),non_ordered_pair(f9(f24(rotate_right(X0)),X0),non_ordered_pair(non_ordered_pair(f10(f24(rotate_right(X0)),X0),f10(f24(rotate_right(X0)),X0)),non_ordered_pair(f10(f24(rotate_right(X0)),X0),f11(f24(rotate_right(X0)),X0)))))
| rotate_right(X0) = empty_set )
| ~ spl0_40
| ~ spl0_143 ),
inference(resolution,[],[f1779,f362]) ).
fof(f39353,plain,
( spl0_1298
| ~ spl0_40
| ~ spl0_142 ),
inference(avatar_split_clause,[],[f1804,f1774,f361,f39351]) ).
fof(f1804,plain,
( ! [X0] :
( f24(flip_range_of(X0)) = non_ordered_pair(non_ordered_pair(f12(f24(flip_range_of(X0)),X0),f12(f24(flip_range_of(X0)),X0)),non_ordered_pair(f12(f24(flip_range_of(X0)),X0),non_ordered_pair(non_ordered_pair(f13(f24(flip_range_of(X0)),X0),f13(f24(flip_range_of(X0)),X0)),non_ordered_pair(f13(f24(flip_range_of(X0)),X0),f14(f24(flip_range_of(X0)),X0)))))
| flip_range_of(X0) = empty_set )
| ~ spl0_40
| ~ spl0_142 ),
inference(resolution,[],[f1775,f362]) ).
fof(f39336,plain,
( spl0_1297
| ~ spl0_138
| ~ spl0_141 ),
inference(avatar_split_clause,[],[f2073,f1749,f1638,f39334]) ).
fof(f39334,plain,
( spl0_1297
<=> ! [X0,X1] : ~ member(X0,compose(X1,range_of(empty_set))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1297])]) ).
fof(f2073,plain,
( ! [X0,X1] : ~ member(X0,compose(X1,range_of(empty_set)))
| ~ spl0_138
| ~ spl0_141 ),
inference(resolution,[],[f1750,f1639]) ).
fof(f39330,plain,
( spl0_1296
| ~ spl0_35
| ~ spl0_145 ),
inference(avatar_split_clause,[],[f1893,f1786,f340,f39328]) ).
fof(f39328,plain,
( spl0_1296
<=> ! [X2,X0,X1] :
( ~ member(X0,rotate_right(cross_product(X1,X2)))
| ordered_pair_predicate(non_ordered_pair(non_ordered_pair(f10(X0,cross_product(X1,X2)),f10(X0,cross_product(X1,X2))),non_ordered_pair(f10(X0,cross_product(X1,X2)),non_ordered_pair(non_ordered_pair(f11(X0,cross_product(X1,X2)),f11(X0,cross_product(X1,X2))),non_ordered_pair(f11(X0,cross_product(X1,X2)),f9(X0,cross_product(X1,X2))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1296])]) ).
fof(f1893,plain,
( ! [X2,X0,X1] :
( ~ member(X0,rotate_right(cross_product(X1,X2)))
| ordered_pair_predicate(non_ordered_pair(non_ordered_pair(f10(X0,cross_product(X1,X2)),f10(X0,cross_product(X1,X2))),non_ordered_pair(f10(X0,cross_product(X1,X2)),non_ordered_pair(non_ordered_pair(f11(X0,cross_product(X1,X2)),f11(X0,cross_product(X1,X2))),non_ordered_pair(f11(X0,cross_product(X1,X2)),f9(X0,cross_product(X1,X2))))))) )
| ~ spl0_35
| ~ spl0_145 ),
inference(resolution,[],[f1787,f341]) ).
fof(f39326,plain,
( spl0_1295
| ~ spl0_35
| ~ spl0_144 ),
inference(avatar_split_clause,[],[f1850,f1782,f340,f39324]) ).
fof(f39324,plain,
( spl0_1295
<=> ! [X2,X0,X1] :
( ~ member(X0,flip_range_of(cross_product(X1,X2)))
| ordered_pair_predicate(non_ordered_pair(non_ordered_pair(f12(X0,cross_product(X1,X2)),f12(X0,cross_product(X1,X2))),non_ordered_pair(f12(X0,cross_product(X1,X2)),non_ordered_pair(non_ordered_pair(f14(X0,cross_product(X1,X2)),f14(X0,cross_product(X1,X2))),non_ordered_pair(f14(X0,cross_product(X1,X2)),f13(X0,cross_product(X1,X2))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1295])]) ).
fof(f1850,plain,
( ! [X2,X0,X1] :
( ~ member(X0,flip_range_of(cross_product(X1,X2)))
| ordered_pair_predicate(non_ordered_pair(non_ordered_pair(f12(X0,cross_product(X1,X2)),f12(X0,cross_product(X1,X2))),non_ordered_pair(f12(X0,cross_product(X1,X2)),non_ordered_pair(non_ordered_pair(f14(X0,cross_product(X1,X2)),f14(X0,cross_product(X1,X2))),non_ordered_pair(f14(X0,cross_product(X1,X2)),f13(X0,cross_product(X1,X2))))))) )
| ~ spl0_35
| ~ spl0_144 ),
inference(resolution,[],[f1783,f341]) ).
fof(f39322,plain,
( spl0_1294
| ~ spl0_30
| ~ spl0_143 ),
inference(avatar_split_clause,[],[f1821,f1778,f314,f39320]) ).
fof(f39320,plain,
( spl0_1294
<=> ! [X0] :
( f18(rotate_right(X0)) = non_ordered_pair(non_ordered_pair(f9(f18(rotate_right(X0)),X0),f9(f18(rotate_right(X0)),X0)),non_ordered_pair(f9(f18(rotate_right(X0)),X0),non_ordered_pair(non_ordered_pair(f10(f18(rotate_right(X0)),X0),f10(f18(rotate_right(X0)),X0)),non_ordered_pair(f10(f18(rotate_right(X0)),X0),f11(f18(rotate_right(X0)),X0)))))
| relation(rotate_right(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1294])]) ).
fof(f1821,plain,
( ! [X0] :
( f18(rotate_right(X0)) = non_ordered_pair(non_ordered_pair(f9(f18(rotate_right(X0)),X0),f9(f18(rotate_right(X0)),X0)),non_ordered_pair(f9(f18(rotate_right(X0)),X0),non_ordered_pair(non_ordered_pair(f10(f18(rotate_right(X0)),X0),f10(f18(rotate_right(X0)),X0)),non_ordered_pair(f10(f18(rotate_right(X0)),X0),f11(f18(rotate_right(X0)),X0)))))
| relation(rotate_right(X0)) )
| ~ spl0_30
| ~ spl0_143 ),
inference(resolution,[],[f1779,f315]) ).
fof(f39318,plain,
( spl0_1293
| ~ spl0_30
| ~ spl0_142 ),
inference(avatar_split_clause,[],[f1800,f1774,f314,f39316]) ).
fof(f39316,plain,
( spl0_1293
<=> ! [X0] :
( f18(flip_range_of(X0)) = non_ordered_pair(non_ordered_pair(f12(f18(flip_range_of(X0)),X0),f12(f18(flip_range_of(X0)),X0)),non_ordered_pair(f12(f18(flip_range_of(X0)),X0),non_ordered_pair(non_ordered_pair(f13(f18(flip_range_of(X0)),X0),f13(f18(flip_range_of(X0)),X0)),non_ordered_pair(f13(f18(flip_range_of(X0)),X0),f14(f18(flip_range_of(X0)),X0)))))
| relation(flip_range_of(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1293])]) ).
fof(f1800,plain,
( ! [X0] :
( f18(flip_range_of(X0)) = non_ordered_pair(non_ordered_pair(f12(f18(flip_range_of(X0)),X0),f12(f18(flip_range_of(X0)),X0)),non_ordered_pair(f12(f18(flip_range_of(X0)),X0),non_ordered_pair(non_ordered_pair(f13(f18(flip_range_of(X0)),X0),f13(f18(flip_range_of(X0)),X0)),non_ordered_pair(f13(f18(flip_range_of(X0)),X0),f14(f18(flip_range_of(X0)),X0)))))
| relation(flip_range_of(X0)) )
| ~ spl0_30
| ~ spl0_142 ),
inference(resolution,[],[f1775,f315]) ).
fof(f38870,plain,
( spl0_1292
| ~ spl0_139
| ~ spl0_141 ),
inference(avatar_split_clause,[],[f2070,f1749,f1642,f38868]) ).
fof(f38868,plain,
( spl0_1292
<=> ! [X0,X1] : ~ member(X0,compose(range_of(empty_set),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1292])]) ).
fof(f2070,plain,
( ! [X0,X1] : ~ member(X0,compose(range_of(empty_set),X1))
| ~ spl0_139
| ~ spl0_141 ),
inference(resolution,[],[f1750,f1643]) ).
fof(f38359,plain,
( spl0_1291
| ~ spl0_128
| ~ spl0_140 ),
inference(avatar_split_clause,[],[f1763,f1745,f1401,f38357]) ).
fof(f38357,plain,
( spl0_1291
<=> ! [X4,X0,X3,X2,X1] :
( ~ little_set(X0)
| ~ little_set(X1)
| ~ little_set(X2)
| X1 = X2
| ~ member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X1)),second(non_ordered_pair(non_ordered_pair(X3,X3),non_ordered_pair(X3,X4))))
| ~ single_valued_set(second(non_ordered_pair(non_ordered_pair(X3,X3),non_ordered_pair(X3,X4))))
| ~ little_set(X4)
| ~ member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X2)),X4)
| ~ little_set(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1291])]) ).
fof(f1763,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ little_set(X0)
| ~ little_set(X1)
| ~ little_set(X2)
| X1 = X2
| ~ member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X1)),second(non_ordered_pair(non_ordered_pair(X3,X3),non_ordered_pair(X3,X4))))
| ~ single_valued_set(second(non_ordered_pair(non_ordered_pair(X3,X3),non_ordered_pair(X3,X4))))
| ~ little_set(X4)
| ~ member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X2)),X4)
| ~ little_set(X3) )
| ~ spl0_128
| ~ spl0_140 ),
inference(resolution,[],[f1746,f1402]) ).
fof(f38355,plain,
( spl0_1290
| ~ spl0_129
| ~ spl0_140 ),
inference(avatar_split_clause,[],[f1760,f1745,f1405,f38353]) ).
fof(f38353,plain,
( spl0_1290
<=> ! [X4,X0,X3,X2,X1] :
( ~ little_set(X0)
| ~ little_set(X1)
| ~ little_set(X2)
| X1 = X2
| ~ member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X1)),first(non_ordered_pair(non_ordered_pair(X3,X3),non_ordered_pair(X3,X4))))
| ~ single_valued_set(first(non_ordered_pair(non_ordered_pair(X3,X3),non_ordered_pair(X3,X4))))
| ~ little_set(X4)
| ~ member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X2)),X3)
| ~ little_set(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1290])]) ).
fof(f1760,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ little_set(X0)
| ~ little_set(X1)
| ~ little_set(X2)
| X1 = X2
| ~ member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X1)),first(non_ordered_pair(non_ordered_pair(X3,X3),non_ordered_pair(X3,X4))))
| ~ single_valued_set(first(non_ordered_pair(non_ordered_pair(X3,X3),non_ordered_pair(X3,X4))))
| ~ little_set(X4)
| ~ member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X2)),X3)
| ~ little_set(X3) )
| ~ spl0_129
| ~ spl0_140 ),
inference(resolution,[],[f1746,f1406]) ).
fof(f38351,plain,
( spl0_1289
| ~ spl0_85
| ~ spl0_137 ),
inference(avatar_split_clause,[],[f1660,f1634,f672,f38349]) ).
fof(f38349,plain,
( spl0_1289
<=> ! [X2,X0,X1] :
( f27(X0,compose(X1,X2)) = non_ordered_pair(non_ordered_pair(f29(f27(X0,compose(X1,X2)),X1,X2),f29(f27(X0,compose(X1,X2)),X1,X2)),non_ordered_pair(f29(f27(X0,compose(X1,X2)),X1,X2),f30(f27(X0,compose(X1,X2)),X1,X2)))
| ~ member(X0,range_of(compose(X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1289])]) ).
fof(f1660,plain,
( ! [X2,X0,X1] :
( f27(X0,compose(X1,X2)) = non_ordered_pair(non_ordered_pair(f29(f27(X0,compose(X1,X2)),X1,X2),f29(f27(X0,compose(X1,X2)),X1,X2)),non_ordered_pair(f29(f27(X0,compose(X1,X2)),X1,X2),f30(f27(X0,compose(X1,X2)),X1,X2)))
| ~ member(X0,range_of(compose(X1,X2))) )
| ~ spl0_85
| ~ spl0_137 ),
inference(resolution,[],[f1635,f673]) ).
fof(f38347,plain,
( spl0_1288
| ~ spl0_78
| ~ spl0_137 ),
inference(avatar_split_clause,[],[f1652,f1634,f644,f38345]) ).
fof(f38345,plain,
( spl0_1288
<=> ! [X2,X0,X1] :
( f16(X0,compose(X1,X2)) = non_ordered_pair(non_ordered_pair(f29(f16(X0,compose(X1,X2)),X1,X2),f29(f16(X0,compose(X1,X2)),X1,X2)),non_ordered_pair(f29(f16(X0,compose(X1,X2)),X1,X2),f30(f16(X0,compose(X1,X2)),X1,X2)))
| ~ member(X0,sigma(compose(X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1288])]) ).
fof(f1652,plain,
( ! [X2,X0,X1] :
( f16(X0,compose(X1,X2)) = non_ordered_pair(non_ordered_pair(f29(f16(X0,compose(X1,X2)),X1,X2),f29(f16(X0,compose(X1,X2)),X1,X2)),non_ordered_pair(f29(f16(X0,compose(X1,X2)),X1,X2),f30(f16(X0,compose(X1,X2)),X1,X2)))
| ~ member(X0,sigma(compose(X1,X2))) )
| ~ spl0_78
| ~ spl0_137 ),
inference(resolution,[],[f1635,f645]) ).
fof(f38343,plain,
( spl0_1287
| ~ spl0_74
| ~ spl0_137 ),
inference(avatar_split_clause,[],[f1651,f1634,f628,f38341]) ).
fof(f38341,plain,
( spl0_1287
<=> ! [X2,X0,X1] :
( f8(X0,compose(X1,X2)) = non_ordered_pair(non_ordered_pair(f29(f8(X0,compose(X1,X2)),X1,X2),f29(f8(X0,compose(X1,X2)),X1,X2)),non_ordered_pair(f29(f8(X0,compose(X1,X2)),X1,X2),f30(f8(X0,compose(X1,X2)),X1,X2)))
| ~ member(X0,domain_of(compose(X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1287])]) ).
fof(f1651,plain,
( ! [X2,X0,X1] :
( f8(X0,compose(X1,X2)) = non_ordered_pair(non_ordered_pair(f29(f8(X0,compose(X1,X2)),X1,X2),f29(f8(X0,compose(X1,X2)),X1,X2)),non_ordered_pair(f29(f8(X0,compose(X1,X2)),X1,X2),f30(f8(X0,compose(X1,X2)),X1,X2)))
| ~ member(X0,domain_of(compose(X1,X2))) )
| ~ spl0_74
| ~ spl0_137 ),
inference(resolution,[],[f1635,f629]) ).
fof(f38339,plain,
( spl0_1286
| ~ spl0_108
| ~ spl0_122 ),
inference(avatar_split_clause,[],[f1371,f1291,f1072,f38337]) ).
fof(f38337,plain,
( spl0_1286
<=> ! [X0,X1] :
( single_valued_set(image(X0,X1))
| non_ordered_pair(non_ordered_pair(f19(image(X0,X1)),f19(image(X0,X1))),non_ordered_pair(f19(image(X0,X1)),f21(image(X0,X1)))) = second(f22(non_ordered_pair(non_ordered_pair(f19(image(X0,X1)),f19(image(X0,X1))),non_ordered_pair(f19(image(X0,X1)),f21(image(X0,X1)))),X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1286])]) ).
fof(f1371,plain,
( ! [X0,X1] :
( single_valued_set(image(X0,X1))
| non_ordered_pair(non_ordered_pair(f19(image(X0,X1)),f19(image(X0,X1))),non_ordered_pair(f19(image(X0,X1)),f21(image(X0,X1)))) = second(f22(non_ordered_pair(non_ordered_pair(f19(image(X0,X1)),f19(image(X0,X1))),non_ordered_pair(f19(image(X0,X1)),f21(image(X0,X1)))),X0,X1)) )
| ~ spl0_108
| ~ spl0_122 ),
inference(resolution,[],[f1292,f1073]) ).
fof(f38332,plain,
( spl0_1285
| ~ spl0_103
| ~ spl0_135 ),
inference(avatar_split_clause,[],[f2048,f1548,f960,f38330]) ).
fof(f38330,plain,
( spl0_1285
<=> ! [X0,X1] : ~ member(X0,image(X1,sigma(empty_set))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1285])]) ).
fof(f2048,plain,
( ! [X0,X1] : ~ member(X0,image(X1,sigma(empty_set)))
| ~ spl0_103
| ~ spl0_135 ),
inference(resolution,[],[f1549,f961]) ).
fof(f38328,plain,
( spl0_1284
| ~ spl0_108
| ~ spl0_121 ),
inference(avatar_split_clause,[],[f1329,f1287,f1072,f38326]) ).
fof(f38326,plain,
( spl0_1284
<=> ! [X0,X1] :
( single_valued_set(image(X0,X1))
| non_ordered_pair(non_ordered_pair(f19(image(X0,X1)),f19(image(X0,X1))),non_ordered_pair(f19(image(X0,X1)),f20(image(X0,X1)))) = second(f22(non_ordered_pair(non_ordered_pair(f19(image(X0,X1)),f19(image(X0,X1))),non_ordered_pair(f19(image(X0,X1)),f20(image(X0,X1)))),X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1284])]) ).
fof(f1329,plain,
( ! [X0,X1] :
( single_valued_set(image(X0,X1))
| non_ordered_pair(non_ordered_pair(f19(image(X0,X1)),f19(image(X0,X1))),non_ordered_pair(f19(image(X0,X1)),f20(image(X0,X1)))) = second(f22(non_ordered_pair(non_ordered_pair(f19(image(X0,X1)),f19(image(X0,X1))),non_ordered_pair(f19(image(X0,X1)),f20(image(X0,X1)))),X0,X1)) )
| ~ spl0_108
| ~ spl0_121 ),
inference(resolution,[],[f1288,f1073]) ).
fof(f38324,plain,
( spl0_1283
| ~ spl0_112
| ~ spl0_120 ),
inference(avatar_split_clause,[],[f1302,f1283,f1089,f38322]) ).
fof(f38322,plain,
( spl0_1283
<=> ! [X0,X1] :
( non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X1)) = non_ordered_pair(non_ordered_pair(f2(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X1))),f2(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X1)))),non_ordered_pair(f2(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X1))),f3(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X1)))))
| ~ little_set(X1)
| ~ little_set(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1283])]) ).
fof(f1283,plain,
( spl0_120
<=> ! [X0] :
( ~ ordered_pair_predicate(X0)
| non_ordered_pair(non_ordered_pair(f2(X0),f2(X0)),non_ordered_pair(f2(X0),f3(X0))) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_120])]) ).
fof(f1302,plain,
( ! [X0,X1] :
( non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X1)) = non_ordered_pair(non_ordered_pair(f2(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X1))),f2(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X1)))),non_ordered_pair(f2(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X1))),f3(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X1)))))
| ~ little_set(X1)
| ~ little_set(X0) )
| ~ spl0_112
| ~ spl0_120 ),
inference(resolution,[],[f1284,f1090]) ).
fof(f1284,plain,
( ! [X0] :
( ~ ordered_pair_predicate(X0)
| non_ordered_pair(non_ordered_pair(f2(X0),f2(X0)),non_ordered_pair(f2(X0),f3(X0))) = X0 )
| ~ spl0_120 ),
inference(avatar_component_clause,[],[f1283]) ).
fof(f38251,plain,
( spl0_1282
| ~ spl0_107
| ~ spl0_135 ),
inference(avatar_split_clause,[],[f2043,f1548,f1068,f38249]) ).
fof(f38249,plain,
( spl0_1282
<=> ! [X0,X1] : ~ member(X0,image(sigma(empty_set),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1282])]) ).
fof(f2043,plain,
( ! [X0,X1] : ~ member(X0,image(sigma(empty_set),X1))
| ~ spl0_107
| ~ spl0_135 ),
inference(resolution,[],[f1549,f1069]) ).
fof(f38247,plain,
( spl0_1281
| ~ spl0_79
| ~ spl0_140 ),
inference(avatar_split_clause,[],[f1769,f1745,f648,f38245]) ).
fof(f38245,plain,
( spl0_1281
<=> ! [X0,X3,X2,X1] :
( ~ little_set(X0)
| ~ little_set(X1)
| ~ little_set(X2)
| X1 = X2
| ~ member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X1)),f16(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X2)),X3))
| ~ single_valued_set(f16(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X2)),X3))
| ~ member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X2)),sigma(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1281])]) ).
fof(f1769,plain,
( ! [X2,X3,X0,X1] :
( ~ little_set(X0)
| ~ little_set(X1)
| ~ little_set(X2)
| X1 = X2
| ~ member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X1)),f16(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X2)),X3))
| ~ single_valued_set(f16(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X2)),X3))
| ~ member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X2)),sigma(X3)) )
| ~ spl0_79
| ~ spl0_140 ),
inference(resolution,[],[f1746,f649]) ).
fof(f38243,plain,
( spl0_1280
| ~ spl0_72
| ~ spl0_140 ),
inference(avatar_split_clause,[],[f1764,f1745,f620,f38241]) ).
fof(f38241,plain,
( spl0_1280
<=> ! [X0,X3,X2,X1] :
( ~ little_set(X0)
| ~ little_set(X1)
| ~ little_set(X2)
| X1 = X2
| ~ member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X1)),f7(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X2)),X3))
| ~ single_valued_set(f7(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X2)),X3))
| ~ member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X2)),second(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1280])]) ).
fof(f1764,plain,
( ! [X2,X3,X0,X1] :
( ~ little_set(X0)
| ~ little_set(X1)
| ~ little_set(X2)
| X1 = X2
| ~ member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X1)),f7(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X2)),X3))
| ~ single_valued_set(f7(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X2)),X3))
| ~ member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X2)),second(X3)) )
| ~ spl0_72
| ~ spl0_140 ),
inference(resolution,[],[f1746,f621]) ).
fof(f38239,plain,
( spl0_1279
| ~ spl0_71
| ~ spl0_140 ),
inference(avatar_split_clause,[],[f1761,f1745,f616,f38237]) ).
fof(f38237,plain,
( spl0_1279
<=> ! [X0,X3,X2,X1] :
( ~ little_set(X0)
| ~ little_set(X1)
| ~ little_set(X2)
| X1 = X2
| ~ member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X1)),f4(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X2)),X3))
| ~ single_valued_set(f4(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X2)),X3))
| ~ member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X2)),first(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1279])]) ).
fof(f1761,plain,
( ! [X2,X3,X0,X1] :
( ~ little_set(X0)
| ~ little_set(X1)
| ~ little_set(X2)
| X1 = X2
| ~ member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X1)),f4(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X2)),X3))
| ~ single_valued_set(f4(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X2)),X3))
| ~ member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X2)),first(X3)) )
| ~ spl0_71
| ~ spl0_140 ),
inference(resolution,[],[f1746,f617]) ).
fof(f38233,plain,
( spl0_1278
| ~ spl0_66
| ~ spl0_139 ),
inference(avatar_split_clause,[],[f1736,f1642,f486,f38231]) ).
fof(f38231,plain,
( spl0_1278
<=> ! [X0,X1] :
( ~ member(X0,compose(identity_relation,X1))
| first(non_ordered_pair(non_ordered_pair(f29(X0,identity_relation,X1),f29(X0,identity_relation,X1)),non_ordered_pair(f29(X0,identity_relation,X1),f31(X0,identity_relation,X1)))) = second(non_ordered_pair(non_ordered_pair(f29(X0,identity_relation,X1),f29(X0,identity_relation,X1)),non_ordered_pair(f29(X0,identity_relation,X1),f31(X0,identity_relation,X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1278])]) ).
fof(f1736,plain,
( ! [X0,X1] :
( ~ member(X0,compose(identity_relation,X1))
| first(non_ordered_pair(non_ordered_pair(f29(X0,identity_relation,X1),f29(X0,identity_relation,X1)),non_ordered_pair(f29(X0,identity_relation,X1),f31(X0,identity_relation,X1)))) = second(non_ordered_pair(non_ordered_pair(f29(X0,identity_relation,X1),f29(X0,identity_relation,X1)),non_ordered_pair(f29(X0,identity_relation,X1),f31(X0,identity_relation,X1)))) )
| ~ spl0_66
| ~ spl0_139 ),
inference(resolution,[],[f1643,f487]) ).
fof(f38227,plain,
( spl0_1277
| ~ spl0_66
| ~ spl0_138 ),
inference(avatar_split_clause,[],[f1696,f1638,f486,f38225]) ).
fof(f38225,plain,
( spl0_1277
<=> ! [X0,X1] :
( ~ member(X0,compose(X1,identity_relation))
| first(non_ordered_pair(non_ordered_pair(f31(X0,X1,identity_relation),f31(X0,X1,identity_relation)),non_ordered_pair(f31(X0,X1,identity_relation),f30(X0,X1,identity_relation)))) = second(non_ordered_pair(non_ordered_pair(f31(X0,X1,identity_relation),f31(X0,X1,identity_relation)),non_ordered_pair(f31(X0,X1,identity_relation),f30(X0,X1,identity_relation)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1277])]) ).
fof(f1696,plain,
( ! [X0,X1] :
( ~ member(X0,compose(X1,identity_relation))
| first(non_ordered_pair(non_ordered_pair(f31(X0,X1,identity_relation),f31(X0,X1,identity_relation)),non_ordered_pair(f31(X0,X1,identity_relation),f30(X0,X1,identity_relation)))) = second(non_ordered_pair(non_ordered_pair(f31(X0,X1,identity_relation),f31(X0,X1,identity_relation)),non_ordered_pair(f31(X0,X1,identity_relation),f30(X0,X1,identity_relation)))) )
| ~ spl0_66
| ~ spl0_138 ),
inference(resolution,[],[f1639,f487]) ).
fof(f38223,plain,
( spl0_1276
| ~ spl0_64
| ~ spl0_137 ),
inference(avatar_split_clause,[],[f1657,f1634,f478,f38221]) ).
fof(f38221,plain,
( spl0_1276
<=> ! [X2,X0,X1] :
( f23(X0,compose(X1,X2)) = non_ordered_pair(non_ordered_pair(f29(f23(X0,compose(X1,X2)),X1,X2),f29(f23(X0,compose(X1,X2)),X1,X2)),non_ordered_pair(f29(f23(X0,compose(X1,X2)),X1,X2),f30(f23(X0,compose(X1,X2)),X1,X2)))
| disjoint(X0,compose(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1276])]) ).
fof(f1657,plain,
( ! [X2,X0,X1] :
( f23(X0,compose(X1,X2)) = non_ordered_pair(non_ordered_pair(f29(f23(X0,compose(X1,X2)),X1,X2),f29(f23(X0,compose(X1,X2)),X1,X2)),non_ordered_pair(f29(f23(X0,compose(X1,X2)),X1,X2),f30(f23(X0,compose(X1,X2)),X1,X2)))
| disjoint(X0,compose(X1,X2)) )
| ~ spl0_64
| ~ spl0_137 ),
inference(resolution,[],[f1635,f479]) ).
fof(f38219,plain,
( spl0_1275
| ~ spl0_63
| ~ spl0_137 ),
inference(avatar_split_clause,[],[f1656,f1634,f474,f38217]) ).
fof(f38217,plain,
( spl0_1275
<=> ! [X2,X0,X1] :
( f23(compose(X0,X1),X2) = non_ordered_pair(non_ordered_pair(f29(f23(compose(X0,X1),X2),X0,X1),f29(f23(compose(X0,X1),X2),X0,X1)),non_ordered_pair(f29(f23(compose(X0,X1),X2),X0,X1),f30(f23(compose(X0,X1),X2),X0,X1)))
| disjoint(compose(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1275])]) ).
fof(f1656,plain,
( ! [X2,X0,X1] :
( f23(compose(X0,X1),X2) = non_ordered_pair(non_ordered_pair(f29(f23(compose(X0,X1),X2),X0,X1),f29(f23(compose(X0,X1),X2),X0,X1)),non_ordered_pair(f29(f23(compose(X0,X1),X2),X0,X1),f30(f23(compose(X0,X1),X2),X0,X1)))
| disjoint(compose(X0,X1),X2) )
| ~ spl0_63
| ~ spl0_137 ),
inference(resolution,[],[f1635,f475]) ).
fof(f38215,plain,
( spl0_1274
| ~ spl0_60
| ~ spl0_137 ),
inference(avatar_split_clause,[],[f1653,f1634,f462,f38213]) ).
fof(f38213,plain,
( spl0_1274
<=> ! [X2,X0,X1] :
( f17(compose(X0,X1),X2) = non_ordered_pair(non_ordered_pair(f29(f17(compose(X0,X1),X2),X0,X1),f29(f17(compose(X0,X1),X2),X0,X1)),non_ordered_pair(f29(f17(compose(X0,X1),X2),X0,X1),f30(f17(compose(X0,X1),X2),X0,X1)))
| subset(compose(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1274])]) ).
fof(f1653,plain,
( ! [X2,X0,X1] :
( f17(compose(X0,X1),X2) = non_ordered_pair(non_ordered_pair(f29(f17(compose(X0,X1),X2),X0,X1),f29(f17(compose(X0,X1),X2),X0,X1)),non_ordered_pair(f29(f17(compose(X0,X1),X2),X0,X1),f30(f17(compose(X0,X1),X2),X0,X1)))
| subset(compose(X0,X1),X2) )
| ~ spl0_60
| ~ spl0_137 ),
inference(resolution,[],[f1635,f463]) ).
fof(f38211,plain,
( spl0_1273
| ~ spl0_101
| ~ spl0_122 ),
inference(avatar_split_clause,[],[f1348,f1291,f952,f38209]) ).
fof(f38209,plain,
( spl0_1273
<=> ! [X0,X1] :
( single_valued_set(non_ordered_pair(X0,X1))
| non_ordered_pair(non_ordered_pair(f19(non_ordered_pair(X0,X1)),f19(non_ordered_pair(X0,X1))),non_ordered_pair(f19(non_ordered_pair(X0,X1)),f21(non_ordered_pair(X0,X1)))) = X0
| non_ordered_pair(non_ordered_pair(f19(non_ordered_pair(X0,X1)),f19(non_ordered_pair(X0,X1))),non_ordered_pair(f19(non_ordered_pair(X0,X1)),f21(non_ordered_pair(X0,X1)))) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1273])]) ).
fof(f1348,plain,
( ! [X0,X1] :
( single_valued_set(non_ordered_pair(X0,X1))
| non_ordered_pair(non_ordered_pair(f19(non_ordered_pair(X0,X1)),f19(non_ordered_pair(X0,X1))),non_ordered_pair(f19(non_ordered_pair(X0,X1)),f21(non_ordered_pair(X0,X1)))) = X0
| non_ordered_pair(non_ordered_pair(f19(non_ordered_pair(X0,X1)),f19(non_ordered_pair(X0,X1))),non_ordered_pair(f19(non_ordered_pair(X0,X1)),f21(non_ordered_pair(X0,X1)))) = X1 )
| ~ spl0_101
| ~ spl0_122 ),
inference(resolution,[],[f1292,f953]) ).
fof(f38207,plain,
( spl0_1272
| ~ spl0_101
| ~ spl0_121 ),
inference(avatar_split_clause,[],[f1306,f1287,f952,f38205]) ).
fof(f38205,plain,
( spl0_1272
<=> ! [X0,X1] :
( single_valued_set(non_ordered_pair(X0,X1))
| non_ordered_pair(non_ordered_pair(f19(non_ordered_pair(X0,X1)),f19(non_ordered_pair(X0,X1))),non_ordered_pair(f19(non_ordered_pair(X0,X1)),f20(non_ordered_pair(X0,X1)))) = X0
| non_ordered_pair(non_ordered_pair(f19(non_ordered_pair(X0,X1)),f19(non_ordered_pair(X0,X1))),non_ordered_pair(f19(non_ordered_pair(X0,X1)),f20(non_ordered_pair(X0,X1)))) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1272])]) ).
fof(f1306,plain,
( ! [X0,X1] :
( single_valued_set(non_ordered_pair(X0,X1))
| non_ordered_pair(non_ordered_pair(f19(non_ordered_pair(X0,X1)),f19(non_ordered_pair(X0,X1))),non_ordered_pair(f19(non_ordered_pair(X0,X1)),f20(non_ordered_pair(X0,X1)))) = X0
| non_ordered_pair(non_ordered_pair(f19(non_ordered_pair(X0,X1)),f19(non_ordered_pair(X0,X1))),non_ordered_pair(f19(non_ordered_pair(X0,X1)),f20(non_ordered_pair(X0,X1)))) = X1 )
| ~ spl0_101
| ~ spl0_121 ),
inference(resolution,[],[f1288,f953]) ).
fof(f38200,plain,
( spl0_1271
| ~ spl0_135
| ~ spl0_138 ),
inference(avatar_split_clause,[],[f2042,f1638,f1548,f38198]) ).
fof(f38198,plain,
( spl0_1271
<=> ! [X0,X1] : ~ member(X0,compose(X1,sigma(empty_set))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1271])]) ).
fof(f2042,plain,
( ! [X0,X1] : ~ member(X0,compose(X1,sigma(empty_set)))
| ~ spl0_135
| ~ spl0_138 ),
inference(resolution,[],[f1549,f1639]) ).
fof(f38194,plain,
( spl0_1270
| ~ spl0_173
| ~ spl0_1269 ),
inference(avatar_split_clause,[],[f38190,f38187,f2440,f38192]) ).
fof(f38192,plain,
( spl0_1270
<=> ! [X0,X1] :
( estin = compose(X0,X1)
| f26(compose(X0,X1)) = non_ordered_pair(non_ordered_pair(f29(f26(compose(X0,X1)),X0,X1),f29(f26(compose(X0,X1)),X0,X1)),non_ordered_pair(f29(f26(compose(X0,X1)),X0,X1),f30(f26(compose(X0,X1)),X0,X1)))
| ~ little_set(compose(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1270])]) ).
fof(f38187,plain,
( spl0_1269
<=> ! [X0,X1] :
( f26(compose(X0,X1)) = non_ordered_pair(non_ordered_pair(f29(f26(compose(X0,X1)),X0,X1),f29(f26(compose(X0,X1)),X0,X1)),non_ordered_pair(f29(f26(compose(X0,X1)),X0,X1),f30(f26(compose(X0,X1)),X0,X1)))
| empty_set = compose(X0,X1)
| ~ little_set(compose(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1269])]) ).
fof(f38190,plain,
( ! [X0,X1] :
( estin = compose(X0,X1)
| f26(compose(X0,X1)) = non_ordered_pair(non_ordered_pair(f29(f26(compose(X0,X1)),X0,X1),f29(f26(compose(X0,X1)),X0,X1)),non_ordered_pair(f29(f26(compose(X0,X1)),X0,X1),f30(f26(compose(X0,X1)),X0,X1)))
| ~ little_set(compose(X0,X1)) )
| ~ spl0_173
| ~ spl0_1269 ),
inference(forward_demodulation,[],[f38188,f2442]) ).
fof(f38188,plain,
( ! [X0,X1] :
( f26(compose(X0,X1)) = non_ordered_pair(non_ordered_pair(f29(f26(compose(X0,X1)),X0,X1),f29(f26(compose(X0,X1)),X0,X1)),non_ordered_pair(f29(f26(compose(X0,X1)),X0,X1),f30(f26(compose(X0,X1)),X0,X1)))
| empty_set = compose(X0,X1)
| ~ little_set(compose(X0,X1)) )
| ~ spl0_1269 ),
inference(avatar_component_clause,[],[f38187]) ).
fof(f38189,plain,
( spl0_1269
| ~ spl0_84
| ~ spl0_137 ),
inference(avatar_split_clause,[],[f1659,f1634,f668,f38187]) ).
fof(f1659,plain,
( ! [X0,X1] :
( f26(compose(X0,X1)) = non_ordered_pair(non_ordered_pair(f29(f26(compose(X0,X1)),X0,X1),f29(f26(compose(X0,X1)),X0,X1)),non_ordered_pair(f29(f26(compose(X0,X1)),X0,X1),f30(f26(compose(X0,X1)),X0,X1)))
| empty_set = compose(X0,X1)
| ~ little_set(compose(X0,X1)) )
| ~ spl0_84
| ~ spl0_137 ),
inference(resolution,[],[f1635,f669]) ).
fof(f38151,plain,
( spl0_1268
| ~ spl0_44
| ~ spl0_140 ),
inference(avatar_split_clause,[],[f1759,f1745,f377,f38149]) ).
fof(f38149,plain,
( spl0_1268
<=> ! [X0,X3,X2,X1] :
( ~ little_set(X0)
| ~ little_set(X1)
| ~ little_set(X2)
| X1 = X2
| ~ member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X1)),non_ordered_pair(X3,non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X2))))
| ~ single_valued_set(non_ordered_pair(X3,non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X2))))
| ~ little_set(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1268])]) ).
fof(f1759,plain,
( ! [X2,X3,X0,X1] :
( ~ little_set(X0)
| ~ little_set(X1)
| ~ little_set(X2)
| X1 = X2
| ~ member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X1)),non_ordered_pair(X3,non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X2))))
| ~ single_valued_set(non_ordered_pair(X3,non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X2))))
| ~ little_set(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X2))) )
| ~ spl0_44
| ~ spl0_140 ),
inference(resolution,[],[f1746,f378]) ).
fof(f38147,plain,
( spl0_1267
| ~ spl0_43
| ~ spl0_140 ),
inference(avatar_split_clause,[],[f1758,f1745,f373,f38145]) ).
fof(f38145,plain,
( spl0_1267
<=> ! [X0,X3,X2,X1] :
( ~ little_set(X0)
| ~ little_set(X1)
| ~ little_set(X2)
| X1 = X2
| ~ member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X1)),non_ordered_pair(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X2)),X3))
| ~ single_valued_set(non_ordered_pair(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X2)),X3))
| ~ little_set(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1267])]) ).
fof(f1758,plain,
( ! [X2,X3,X0,X1] :
( ~ little_set(X0)
| ~ little_set(X1)
| ~ little_set(X2)
| X1 = X2
| ~ member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X1)),non_ordered_pair(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X2)),X3))
| ~ single_valued_set(non_ordered_pair(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X2)),X3))
| ~ little_set(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X2))) )
| ~ spl0_43
| ~ spl0_140 ),
inference(resolution,[],[f1746,f374]) ).
fof(f38051,plain,
( spl0_1266
| ~ spl0_135
| ~ spl0_139 ),
inference(avatar_split_clause,[],[f2039,f1642,f1548,f38049]) ).
fof(f38049,plain,
( spl0_1266
<=> ! [X0,X1] : ~ member(X0,compose(sigma(empty_set),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1266])]) ).
fof(f2039,plain,
( ! [X0,X1] : ~ member(X0,compose(sigma(empty_set),X1))
| ~ spl0_135
| ~ spl0_139 ),
inference(resolution,[],[f1549,f1643]) ).
fof(f37681,plain,
( spl0_1265
| ~ spl0_127
| ~ spl0_147 ),
inference(avatar_split_clause,[],[f1959,f1954,f1397,f37679]) ).
fof(f37679,plain,
( spl0_1265
<=> ! [X0,X3,X2,X1] :
( ~ little_set(X0)
| ~ little_set(first(X1))
| ~ little_set(second(X1))
| ~ member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,second(X1))),X2)
| ~ little_set(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,first(X1))))
| member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,first(X1))),compose(X2,X3))
| ~ member(X1,converse(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1265])]) ).
fof(f1959,plain,
( ! [X2,X3,X0,X1] :
( ~ little_set(X0)
| ~ little_set(first(X1))
| ~ little_set(second(X1))
| ~ member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,second(X1))),X2)
| ~ little_set(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,first(X1))))
| member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,first(X1))),compose(X2,X3))
| ~ member(X1,converse(X3)) )
| ~ spl0_127
| ~ spl0_147 ),
inference(resolution,[],[f1955,f1398]) ).
fof(f37677,plain,
( spl0_1264
| ~ spl0_138
| ~ spl0_140 ),
inference(avatar_split_clause,[],[f1756,f1745,f1638,f37675]) ).
fof(f37675,plain,
( spl0_1264
<=> ! [X0,X3,X2,X1] :
( ~ little_set(f31(X0,X1,X2))
| ~ little_set(X3)
| ~ little_set(f30(X0,X1,X2))
| f30(X0,X1,X2) = X3
| ~ member(non_ordered_pair(non_ordered_pair(f31(X0,X1,X2),f31(X0,X1,X2)),non_ordered_pair(f31(X0,X1,X2),X3)),X2)
| ~ single_valued_set(X2)
| ~ member(X0,compose(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1264])]) ).
fof(f1756,plain,
( ! [X2,X3,X0,X1] :
( ~ little_set(f31(X0,X1,X2))
| ~ little_set(X3)
| ~ little_set(f30(X0,X1,X2))
| f30(X0,X1,X2) = X3
| ~ member(non_ordered_pair(non_ordered_pair(f31(X0,X1,X2),f31(X0,X1,X2)),non_ordered_pair(f31(X0,X1,X2),X3)),X2)
| ~ single_valued_set(X2)
| ~ member(X0,compose(X1,X2)) )
| ~ spl0_138
| ~ spl0_140 ),
inference(resolution,[],[f1746,f1639]) ).
fof(f37673,plain,
( spl0_1263
| ~ spl0_139
| ~ spl0_140 ),
inference(avatar_split_clause,[],[f1755,f1745,f1642,f37671]) ).
fof(f37671,plain,
( spl0_1263
<=> ! [X0,X3,X2,X1] :
( ~ little_set(f29(X0,X1,X2))
| ~ little_set(X3)
| ~ little_set(f31(X0,X1,X2))
| f31(X0,X1,X2) = X3
| ~ member(non_ordered_pair(non_ordered_pair(f29(X0,X1,X2),f29(X0,X1,X2)),non_ordered_pair(f29(X0,X1,X2),X3)),X1)
| ~ single_valued_set(X1)
| ~ member(X0,compose(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1263])]) ).
fof(f1755,plain,
( ! [X2,X3,X0,X1] :
( ~ little_set(f29(X0,X1,X2))
| ~ little_set(X3)
| ~ little_set(f31(X0,X1,X2))
| f31(X0,X1,X2) = X3
| ~ member(non_ordered_pair(non_ordered_pair(f29(X0,X1,X2),f29(X0,X1,X2)),non_ordered_pair(f29(X0,X1,X2),X3)),X1)
| ~ single_valued_set(X1)
| ~ member(X0,compose(X1,X2)) )
| ~ spl0_139
| ~ spl0_140 ),
inference(resolution,[],[f1746,f1643]) ).
fof(f37669,plain,
( spl0_1262
| ~ spl0_108
| ~ spl0_136 ),
inference(avatar_split_clause,[],[f1622,f1552,f1072,f37667]) ).
fof(f37667,plain,
( spl0_1262
<=> ! [X2,X4,X0,X3,X5,X1] :
( ~ closed(X0,X1)
| ~ maps(X2,image(X3,X4),X0)
| homomorphism(X2,image(X3,X4),X5,X0,X1)
| ~ closed(image(X3,X4),X5)
| f33(X2,image(X3,X4),X5,X0,X1) = second(f22(f33(X2,image(X3,X4),X5,X0,X1),X3,X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1262])]) ).
fof(f1622,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ closed(X0,X1)
| ~ maps(X2,image(X3,X4),X0)
| homomorphism(X2,image(X3,X4),X5,X0,X1)
| ~ closed(image(X3,X4),X5)
| f33(X2,image(X3,X4),X5,X0,X1) = second(f22(f33(X2,image(X3,X4),X5,X0,X1),X3,X4)) )
| ~ spl0_108
| ~ spl0_136 ),
inference(resolution,[],[f1553,f1073]) ).
fof(f37665,plain,
( spl0_1261
| ~ spl0_108
| ~ spl0_134 ),
inference(avatar_split_clause,[],[f1583,f1544,f1072,f37663]) ).
fof(f37663,plain,
( spl0_1261
<=> ! [X2,X4,X0,X3,X5,X1] :
( ~ closed(X0,X1)
| ~ maps(X2,image(X3,X4),X0)
| homomorphism(X2,image(X3,X4),X5,X0,X1)
| ~ closed(image(X3,X4),X5)
| f32(X2,image(X3,X4),X5,X0,X1) = second(f22(f32(X2,image(X3,X4),X5,X0,X1),X3,X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1261])]) ).
fof(f1583,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ closed(X0,X1)
| ~ maps(X2,image(X3,X4),X0)
| homomorphism(X2,image(X3,X4),X5,X0,X1)
| ~ closed(image(X3,X4),X5)
| f32(X2,image(X3,X4),X5,X0,X1) = second(f22(f32(X2,image(X3,X4),X5,X0,X1),X3,X4)) )
| ~ spl0_108
| ~ spl0_134 ),
inference(resolution,[],[f1545,f1073]) ).
fof(f37661,plain,
( spl0_1260
| ~ spl0_107
| ~ spl0_132 ),
inference(avatar_split_clause,[],[f1516,f1483,f1068,f37659]) ).
fof(f37659,plain,
( spl0_1260
<=> ! [X2,X0,X1] :
( non_ordered_pair(non_ordered_pair(f4(first(f22(X0,first(X1),X2)),X1),f4(first(f22(X0,first(X1),X2)),X1)),non_ordered_pair(f4(first(f22(X0,first(X1),X2)),X1),f5(first(f22(X0,first(X1),X2)),X1))) = X1
| ~ member(X0,image(first(X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1260])]) ).
fof(f1516,plain,
( ! [X2,X0,X1] :
( non_ordered_pair(non_ordered_pair(f4(first(f22(X0,first(X1),X2)),X1),f4(first(f22(X0,first(X1),X2)),X1)),non_ordered_pair(f4(first(f22(X0,first(X1),X2)),X1),f5(first(f22(X0,first(X1),X2)),X1))) = X1
| ~ member(X0,image(first(X1),X2)) )
| ~ spl0_107
| ~ spl0_132 ),
inference(resolution,[],[f1484,f1069]) ).
fof(f37654,plain,
( spl0_1259
| ~ spl0_103
| ~ spl0_119 ),
inference(avatar_split_clause,[],[f1936,f1266,f960,f37652]) ).
fof(f37652,plain,
( spl0_1259
<=> ! [X0,X1] : ~ member(X0,image(X1,domain_of(empty_set))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1259])]) ).
fof(f1936,plain,
( ! [X0,X1] : ~ member(X0,image(X1,domain_of(empty_set)))
| ~ spl0_103
| ~ spl0_119 ),
inference(resolution,[],[f1267,f961]) ).
fof(f37650,plain,
( spl0_1258
| ~ spl0_107
| ~ spl0_131 ),
inference(avatar_split_clause,[],[f1498,f1479,f1068,f37648]) ).
fof(f37648,plain,
( spl0_1258
<=> ! [X2,X0,X1] :
( non_ordered_pair(non_ordered_pair(f6(first(f22(X0,second(X1),X2)),X1),f6(first(f22(X0,second(X1),X2)),X1)),non_ordered_pair(f6(first(f22(X0,second(X1),X2)),X1),f7(first(f22(X0,second(X1),X2)),X1))) = X1
| ~ member(X0,image(second(X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1258])]) ).
fof(f1498,plain,
( ! [X2,X0,X1] :
( non_ordered_pair(non_ordered_pair(f6(first(f22(X0,second(X1),X2)),X1),f6(first(f22(X0,second(X1),X2)),X1)),non_ordered_pair(f6(first(f22(X0,second(X1),X2)),X1),f7(first(f22(X0,second(X1),X2)),X1))) = X1
| ~ member(X0,image(second(X1),X2)) )
| ~ spl0_107
| ~ spl0_131 ),
inference(resolution,[],[f1480,f1069]) ).
fof(f37565,plain,
( spl0_1257
| ~ spl0_107
| ~ spl0_119 ),
inference(avatar_split_clause,[],[f1931,f1266,f1068,f37563]) ).
fof(f37563,plain,
( spl0_1257
<=> ! [X0,X1] : ~ member(X0,image(domain_of(empty_set),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1257])]) ).
fof(f1931,plain,
( ! [X0,X1] : ~ member(X0,image(domain_of(empty_set),X1))
| ~ spl0_107
| ~ spl0_119 ),
inference(resolution,[],[f1267,f1069]) ).
fof(f37537,plain,
( spl0_1256
| ~ spl0_119
| ~ spl0_138 ),
inference(avatar_split_clause,[],[f1929,f1638,f1266,f37535]) ).
fof(f37535,plain,
( spl0_1256
<=> ! [X0,X1] : ~ member(X0,compose(X1,domain_of(empty_set))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1256])]) ).
fof(f1929,plain,
( ! [X0,X1] : ~ member(X0,compose(X1,domain_of(empty_set)))
| ~ spl0_119
| ~ spl0_138 ),
inference(resolution,[],[f1267,f1639]) ).
fof(f37481,plain,
( spl0_1255
| ~ spl0_16
| ~ spl0_147 ),
inference(avatar_split_clause,[],[f1975,f1954,f253,f37479]) ).
fof(f37479,plain,
( spl0_1255
<=> ! [X0,X3,X2,X1] :
( ~ little_set(X0)
| ~ little_set(X1)
| ~ little_set(X2)
| ~ member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X2)),X3)
| ~ little_set(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X1)))
| member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X1)),compose(X3,universal_set))
| ~ little_set(non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1255])]) ).
fof(f1975,plain,
( ! [X2,X3,X0,X1] :
( ~ little_set(X0)
| ~ little_set(X1)
| ~ little_set(X2)
| ~ member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X2)),X3)
| ~ little_set(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X1)))
| member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X1)),compose(X3,universal_set))
| ~ little_set(non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X1))) )
| ~ spl0_16
| ~ spl0_147 ),
inference(resolution,[],[f1955,f254]) ).
fof(f37474,plain,
( spl0_1254
| ~ spl0_119
| ~ spl0_139 ),
inference(avatar_split_clause,[],[f1926,f1642,f1266,f37472]) ).
fof(f37472,plain,
( spl0_1254
<=> ! [X0,X1] : ~ member(X0,compose(domain_of(empty_set),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1254])]) ).
fof(f1926,plain,
( ! [X0,X1] : ~ member(X0,compose(domain_of(empty_set),X1))
| ~ spl0_119
| ~ spl0_139 ),
inference(resolution,[],[f1267,f1643]) ).
fof(f37470,plain,
( spl0_1253
| ~ spl0_65
| ~ spl0_145 ),
inference(avatar_split_clause,[],[f1908,f1786,f482,f37468]) ).
fof(f37468,plain,
( spl0_1253
<=> ! [X0,X1] :
( ~ member(X0,rotate_right(range_of(X1)))
| ordered_pair_predicate(f27(non_ordered_pair(non_ordered_pair(f10(X0,range_of(X1)),f10(X0,range_of(X1))),non_ordered_pair(f10(X0,range_of(X1)),non_ordered_pair(non_ordered_pair(f11(X0,range_of(X1)),f11(X0,range_of(X1))),non_ordered_pair(f11(X0,range_of(X1)),f9(X0,range_of(X1)))))),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1253])]) ).
fof(f1908,plain,
( ! [X0,X1] :
( ~ member(X0,rotate_right(range_of(X1)))
| ordered_pair_predicate(f27(non_ordered_pair(non_ordered_pair(f10(X0,range_of(X1)),f10(X0,range_of(X1))),non_ordered_pair(f10(X0,range_of(X1)),non_ordered_pair(non_ordered_pair(f11(X0,range_of(X1)),f11(X0,range_of(X1))),non_ordered_pair(f11(X0,range_of(X1)),f9(X0,range_of(X1)))))),X1)) )
| ~ spl0_65
| ~ spl0_145 ),
inference(resolution,[],[f1787,f483]) ).
fof(f37466,plain,
( spl0_1252
| ~ spl0_57
| ~ spl0_145 ),
inference(avatar_split_clause,[],[f1902,f1786,f450,f37464]) ).
fof(f37464,plain,
( spl0_1252
<=> ! [X0,X1] :
( ~ member(X0,rotate_right(flip_range_of(X1)))
| little_set(f12(non_ordered_pair(non_ordered_pair(f10(X0,flip_range_of(X1)),f10(X0,flip_range_of(X1))),non_ordered_pair(f10(X0,flip_range_of(X1)),non_ordered_pair(non_ordered_pair(f11(X0,flip_range_of(X1)),f11(X0,flip_range_of(X1))),non_ordered_pair(f11(X0,flip_range_of(X1)),f9(X0,flip_range_of(X1)))))),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1252])]) ).
fof(f1902,plain,
( ! [X0,X1] :
( ~ member(X0,rotate_right(flip_range_of(X1)))
| little_set(f12(non_ordered_pair(non_ordered_pair(f10(X0,flip_range_of(X1)),f10(X0,flip_range_of(X1))),non_ordered_pair(f10(X0,flip_range_of(X1)),non_ordered_pair(non_ordered_pair(f11(X0,flip_range_of(X1)),f11(X0,flip_range_of(X1))),non_ordered_pair(f11(X0,flip_range_of(X1)),f9(X0,flip_range_of(X1)))))),X1)) )
| ~ spl0_57
| ~ spl0_145 ),
inference(resolution,[],[f1787,f451]) ).
fof(f37462,plain,
( spl0_1251
| ~ spl0_58
| ~ spl0_145 ),
inference(avatar_split_clause,[],[f1901,f1786,f454,f37460]) ).
fof(f37460,plain,
( spl0_1251
<=> ! [X0,X1] :
( ~ member(X0,rotate_right(flip_range_of(X1)))
| little_set(f13(non_ordered_pair(non_ordered_pair(f10(X0,flip_range_of(X1)),f10(X0,flip_range_of(X1))),non_ordered_pair(f10(X0,flip_range_of(X1)),non_ordered_pair(non_ordered_pair(f11(X0,flip_range_of(X1)),f11(X0,flip_range_of(X1))),non_ordered_pair(f11(X0,flip_range_of(X1)),f9(X0,flip_range_of(X1)))))),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1251])]) ).
fof(f1901,plain,
( ! [X0,X1] :
( ~ member(X0,rotate_right(flip_range_of(X1)))
| little_set(f13(non_ordered_pair(non_ordered_pair(f10(X0,flip_range_of(X1)),f10(X0,flip_range_of(X1))),non_ordered_pair(f10(X0,flip_range_of(X1)),non_ordered_pair(non_ordered_pair(f11(X0,flip_range_of(X1)),f11(X0,flip_range_of(X1))),non_ordered_pair(f11(X0,flip_range_of(X1)),f9(X0,flip_range_of(X1)))))),X1)) )
| ~ spl0_58
| ~ spl0_145 ),
inference(resolution,[],[f1787,f455]) ).
fof(f37458,plain,
( spl0_1250
| ~ spl0_59
| ~ spl0_145 ),
inference(avatar_split_clause,[],[f1900,f1786,f458,f37456]) ).
fof(f37456,plain,
( spl0_1250
<=> ! [X0,X1] :
( ~ member(X0,rotate_right(flip_range_of(X1)))
| little_set(f14(non_ordered_pair(non_ordered_pair(f10(X0,flip_range_of(X1)),f10(X0,flip_range_of(X1))),non_ordered_pair(f10(X0,flip_range_of(X1)),non_ordered_pair(non_ordered_pair(f11(X0,flip_range_of(X1)),f11(X0,flip_range_of(X1))),non_ordered_pair(f11(X0,flip_range_of(X1)),f9(X0,flip_range_of(X1)))))),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1250])]) ).
fof(f1900,plain,
( ! [X0,X1] :
( ~ member(X0,rotate_right(flip_range_of(X1)))
| little_set(f14(non_ordered_pair(non_ordered_pair(f10(X0,flip_range_of(X1)),f10(X0,flip_range_of(X1))),non_ordered_pair(f10(X0,flip_range_of(X1)),non_ordered_pair(non_ordered_pair(f11(X0,flip_range_of(X1)),f11(X0,flip_range_of(X1))),non_ordered_pair(f11(X0,flip_range_of(X1)),f9(X0,flip_range_of(X1)))))),X1)) )
| ~ spl0_59
| ~ spl0_145 ),
inference(resolution,[],[f1787,f459]) ).
fof(f37454,plain,
( spl0_1249
| ~ spl0_54
| ~ spl0_145 ),
inference(avatar_split_clause,[],[f1898,f1786,f438,f37452]) ).
fof(f37452,plain,
( spl0_1249
<=> ! [X0,X1] :
( ~ member(X0,rotate_right(rotate_right(X1)))
| little_set(f9(non_ordered_pair(non_ordered_pair(f10(X0,rotate_right(X1)),f10(X0,rotate_right(X1))),non_ordered_pair(f10(X0,rotate_right(X1)),non_ordered_pair(non_ordered_pair(f11(X0,rotate_right(X1)),f11(X0,rotate_right(X1))),non_ordered_pair(f11(X0,rotate_right(X1)),f9(X0,rotate_right(X1)))))),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1249])]) ).
fof(f1898,plain,
( ! [X0,X1] :
( ~ member(X0,rotate_right(rotate_right(X1)))
| little_set(f9(non_ordered_pair(non_ordered_pair(f10(X0,rotate_right(X1)),f10(X0,rotate_right(X1))),non_ordered_pair(f10(X0,rotate_right(X1)),non_ordered_pair(non_ordered_pair(f11(X0,rotate_right(X1)),f11(X0,rotate_right(X1))),non_ordered_pair(f11(X0,rotate_right(X1)),f9(X0,rotate_right(X1)))))),X1)) )
| ~ spl0_54
| ~ spl0_145 ),
inference(resolution,[],[f1787,f439]) ).
fof(f37450,plain,
( spl0_1248
| ~ spl0_55
| ~ spl0_145 ),
inference(avatar_split_clause,[],[f1897,f1786,f442,f37448]) ).
fof(f37448,plain,
( spl0_1248
<=> ! [X0,X1] :
( ~ member(X0,rotate_right(rotate_right(X1)))
| little_set(f10(non_ordered_pair(non_ordered_pair(f10(X0,rotate_right(X1)),f10(X0,rotate_right(X1))),non_ordered_pair(f10(X0,rotate_right(X1)),non_ordered_pair(non_ordered_pair(f11(X0,rotate_right(X1)),f11(X0,rotate_right(X1))),non_ordered_pair(f11(X0,rotate_right(X1)),f9(X0,rotate_right(X1)))))),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1248])]) ).
fof(f1897,plain,
( ! [X0,X1] :
( ~ member(X0,rotate_right(rotate_right(X1)))
| little_set(f10(non_ordered_pair(non_ordered_pair(f10(X0,rotate_right(X1)),f10(X0,rotate_right(X1))),non_ordered_pair(f10(X0,rotate_right(X1)),non_ordered_pair(non_ordered_pair(f11(X0,rotate_right(X1)),f11(X0,rotate_right(X1))),non_ordered_pair(f11(X0,rotate_right(X1)),f9(X0,rotate_right(X1)))))),X1)) )
| ~ spl0_55
| ~ spl0_145 ),
inference(resolution,[],[f1787,f443]) ).
fof(f37446,plain,
( spl0_1247
| ~ spl0_56
| ~ spl0_145 ),
inference(avatar_split_clause,[],[f1896,f1786,f446,f37444]) ).
fof(f37444,plain,
( spl0_1247
<=> ! [X0,X1] :
( ~ member(X0,rotate_right(rotate_right(X1)))
| little_set(f11(non_ordered_pair(non_ordered_pair(f10(X0,rotate_right(X1)),f10(X0,rotate_right(X1))),non_ordered_pair(f10(X0,rotate_right(X1)),non_ordered_pair(non_ordered_pair(f11(X0,rotate_right(X1)),f11(X0,rotate_right(X1))),non_ordered_pair(f11(X0,rotate_right(X1)),f9(X0,rotate_right(X1)))))),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1247])]) ).
fof(f1896,plain,
( ! [X0,X1] :
( ~ member(X0,rotate_right(rotate_right(X1)))
| little_set(f11(non_ordered_pair(non_ordered_pair(f10(X0,rotate_right(X1)),f10(X0,rotate_right(X1))),non_ordered_pair(f10(X0,rotate_right(X1)),non_ordered_pair(non_ordered_pair(f11(X0,rotate_right(X1)),f11(X0,rotate_right(X1))),non_ordered_pair(f11(X0,rotate_right(X1)),f9(X0,rotate_right(X1)))))),X1)) )
| ~ spl0_56
| ~ spl0_145 ),
inference(resolution,[],[f1787,f447]) ).
fof(f37442,plain,
( spl0_1246
| ~ spl0_53
| ~ spl0_145 ),
inference(avatar_split_clause,[],[f1890,f1786,f434,f37440]) ).
fof(f37440,plain,
( spl0_1246
<=> ! [X0,X1] :
( ~ member(X0,rotate_right(domain_of(X1)))
| ordered_pair_predicate(f8(non_ordered_pair(non_ordered_pair(f10(X0,domain_of(X1)),f10(X0,domain_of(X1))),non_ordered_pair(f10(X0,domain_of(X1)),non_ordered_pair(non_ordered_pair(f11(X0,domain_of(X1)),f11(X0,domain_of(X1))),non_ordered_pair(f11(X0,domain_of(X1)),f9(X0,domain_of(X1)))))),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1246])]) ).
fof(f1890,plain,
( ! [X0,X1] :
( ~ member(X0,rotate_right(domain_of(X1)))
| ordered_pair_predicate(f8(non_ordered_pair(non_ordered_pair(f10(X0,domain_of(X1)),f10(X0,domain_of(X1))),non_ordered_pair(f10(X0,domain_of(X1)),non_ordered_pair(non_ordered_pair(f11(X0,domain_of(X1)),f11(X0,domain_of(X1))),non_ordered_pair(f11(X0,domain_of(X1)),f9(X0,domain_of(X1)))))),X1)) )
| ~ spl0_53
| ~ spl0_145 ),
inference(resolution,[],[f1787,f435]) ).
fof(f37438,plain,
( spl0_1245
| ~ spl0_48
| ~ spl0_145 ),
inference(avatar_split_clause,[],[f1884,f1786,f414,f37436]) ).
fof(f37436,plain,
( spl0_1245
<=> ! [X0,X1] :
( ~ member(X0,rotate_right(second(X1)))
| little_set(f6(non_ordered_pair(non_ordered_pair(f10(X0,second(X1)),f10(X0,second(X1))),non_ordered_pair(f10(X0,second(X1)),non_ordered_pair(non_ordered_pair(f11(X0,second(X1)),f11(X0,second(X1))),non_ordered_pair(f11(X0,second(X1)),f9(X0,second(X1)))))),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1245])]) ).
fof(f1884,plain,
( ! [X0,X1] :
( ~ member(X0,rotate_right(second(X1)))
| little_set(f6(non_ordered_pair(non_ordered_pair(f10(X0,second(X1)),f10(X0,second(X1))),non_ordered_pair(f10(X0,second(X1)),non_ordered_pair(non_ordered_pair(f11(X0,second(X1)),f11(X0,second(X1))),non_ordered_pair(f11(X0,second(X1)),f9(X0,second(X1)))))),X1)) )
| ~ spl0_48
| ~ spl0_145 ),
inference(resolution,[],[f1787,f415]) ).
fof(f37434,plain,
( spl0_1244
| ~ spl0_49
| ~ spl0_145 ),
inference(avatar_split_clause,[],[f1883,f1786,f418,f37432]) ).
fof(f37432,plain,
( spl0_1244
<=> ! [X0,X1] :
( ~ member(X0,rotate_right(second(X1)))
| little_set(f7(non_ordered_pair(non_ordered_pair(f10(X0,second(X1)),f10(X0,second(X1))),non_ordered_pair(f10(X0,second(X1)),non_ordered_pair(non_ordered_pair(f11(X0,second(X1)),f11(X0,second(X1))),non_ordered_pair(f11(X0,second(X1)),f9(X0,second(X1)))))),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1244])]) ).
fof(f1883,plain,
( ! [X0,X1] :
( ~ member(X0,rotate_right(second(X1)))
| little_set(f7(non_ordered_pair(non_ordered_pair(f10(X0,second(X1)),f10(X0,second(X1))),non_ordered_pair(f10(X0,second(X1)),non_ordered_pair(non_ordered_pair(f11(X0,second(X1)),f11(X0,second(X1))),non_ordered_pair(f11(X0,second(X1)),f9(X0,second(X1)))))),X1)) )
| ~ spl0_49
| ~ spl0_145 ),
inference(resolution,[],[f1787,f419]) ).
fof(f37428,plain,
( spl0_1243
| ~ spl0_76
| ~ spl0_81 ),
inference(avatar_split_clause,[],[f895,f656,f636,f37426]) ).
fof(f37426,plain,
( spl0_1243
<=> ! [X0] :
( empty_set = X0
| proper_subset(empty_set,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1243])]) ).
fof(f636,plain,
( spl0_76
<=> ! [X0] : subset(empty_set,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_76])]) ).
fof(f895,plain,
( ! [X0] :
( empty_set = X0
| proper_subset(empty_set,X0) )
| ~ spl0_76
| ~ spl0_81 ),
inference(resolution,[],[f637,f657]) ).
fof(f637,plain,
( ! [X0] : subset(empty_set,X0)
| ~ spl0_76 ),
inference(avatar_component_clause,[],[f636]) ).
fof(f37424,plain,
( spl0_1242
| ~ spl0_46
| ~ spl0_145 ),
inference(avatar_split_clause,[],[f1881,f1786,f406,f37422]) ).
fof(f37422,plain,
( spl0_1242
<=> ! [X0,X1] :
( ~ member(X0,rotate_right(first(X1)))
| little_set(f4(non_ordered_pair(non_ordered_pair(f10(X0,first(X1)),f10(X0,first(X1))),non_ordered_pair(f10(X0,first(X1)),non_ordered_pair(non_ordered_pair(f11(X0,first(X1)),f11(X0,first(X1))),non_ordered_pair(f11(X0,first(X1)),f9(X0,first(X1)))))),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1242])]) ).
fof(f1881,plain,
( ! [X0,X1] :
( ~ member(X0,rotate_right(first(X1)))
| little_set(f4(non_ordered_pair(non_ordered_pair(f10(X0,first(X1)),f10(X0,first(X1))),non_ordered_pair(f10(X0,first(X1)),non_ordered_pair(non_ordered_pair(f11(X0,first(X1)),f11(X0,first(X1))),non_ordered_pair(f11(X0,first(X1)),f9(X0,first(X1)))))),X1)) )
| ~ spl0_46
| ~ spl0_145 ),
inference(resolution,[],[f1787,f407]) ).
fof(f37420,plain,
( spl0_1241
| ~ spl0_47
| ~ spl0_145 ),
inference(avatar_split_clause,[],[f1880,f1786,f410,f37418]) ).
fof(f37418,plain,
( spl0_1241
<=> ! [X0,X1] :
( ~ member(X0,rotate_right(first(X1)))
| little_set(f5(non_ordered_pair(non_ordered_pair(f10(X0,first(X1)),f10(X0,first(X1))),non_ordered_pair(f10(X0,first(X1)),non_ordered_pair(non_ordered_pair(f11(X0,first(X1)),f11(X0,first(X1))),non_ordered_pair(f11(X0,first(X1)),f9(X0,first(X1)))))),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1241])]) ).
fof(f1880,plain,
( ! [X0,X1] :
( ~ member(X0,rotate_right(first(X1)))
| little_set(f5(non_ordered_pair(non_ordered_pair(f10(X0,first(X1)),f10(X0,first(X1))),non_ordered_pair(f10(X0,first(X1)),non_ordered_pair(non_ordered_pair(f11(X0,first(X1)),f11(X0,first(X1))),non_ordered_pair(f11(X0,first(X1)),f9(X0,first(X1)))))),X1)) )
| ~ spl0_47
| ~ spl0_145 ),
inference(resolution,[],[f1787,f411]) ).
fof(f37416,plain,
( spl0_1240
| ~ spl0_65
| ~ spl0_144 ),
inference(avatar_split_clause,[],[f1865,f1782,f482,f37414]) ).
fof(f37414,plain,
( spl0_1240
<=> ! [X0,X1] :
( ~ member(X0,flip_range_of(range_of(X1)))
| ordered_pair_predicate(f27(non_ordered_pair(non_ordered_pair(f12(X0,range_of(X1)),f12(X0,range_of(X1))),non_ordered_pair(f12(X0,range_of(X1)),non_ordered_pair(non_ordered_pair(f14(X0,range_of(X1)),f14(X0,range_of(X1))),non_ordered_pair(f14(X0,range_of(X1)),f13(X0,range_of(X1)))))),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1240])]) ).
fof(f1865,plain,
( ! [X0,X1] :
( ~ member(X0,flip_range_of(range_of(X1)))
| ordered_pair_predicate(f27(non_ordered_pair(non_ordered_pair(f12(X0,range_of(X1)),f12(X0,range_of(X1))),non_ordered_pair(f12(X0,range_of(X1)),non_ordered_pair(non_ordered_pair(f14(X0,range_of(X1)),f14(X0,range_of(X1))),non_ordered_pair(f14(X0,range_of(X1)),f13(X0,range_of(X1)))))),X1)) )
| ~ spl0_65
| ~ spl0_144 ),
inference(resolution,[],[f1783,f483]) ).
fof(f37412,plain,
( spl0_1239
| ~ spl0_57
| ~ spl0_144 ),
inference(avatar_split_clause,[],[f1859,f1782,f450,f37410]) ).
fof(f37410,plain,
( spl0_1239
<=> ! [X0,X1] :
( ~ member(X0,flip_range_of(flip_range_of(X1)))
| little_set(f12(non_ordered_pair(non_ordered_pair(f12(X0,flip_range_of(X1)),f12(X0,flip_range_of(X1))),non_ordered_pair(f12(X0,flip_range_of(X1)),non_ordered_pair(non_ordered_pair(f14(X0,flip_range_of(X1)),f14(X0,flip_range_of(X1))),non_ordered_pair(f14(X0,flip_range_of(X1)),f13(X0,flip_range_of(X1)))))),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1239])]) ).
fof(f1859,plain,
( ! [X0,X1] :
( ~ member(X0,flip_range_of(flip_range_of(X1)))
| little_set(f12(non_ordered_pair(non_ordered_pair(f12(X0,flip_range_of(X1)),f12(X0,flip_range_of(X1))),non_ordered_pair(f12(X0,flip_range_of(X1)),non_ordered_pair(non_ordered_pair(f14(X0,flip_range_of(X1)),f14(X0,flip_range_of(X1))),non_ordered_pair(f14(X0,flip_range_of(X1)),f13(X0,flip_range_of(X1)))))),X1)) )
| ~ spl0_57
| ~ spl0_144 ),
inference(resolution,[],[f1783,f451]) ).
fof(f37408,plain,
( spl0_1238
| ~ spl0_58
| ~ spl0_144 ),
inference(avatar_split_clause,[],[f1858,f1782,f454,f37406]) ).
fof(f37406,plain,
( spl0_1238
<=> ! [X0,X1] :
( ~ member(X0,flip_range_of(flip_range_of(X1)))
| little_set(f13(non_ordered_pair(non_ordered_pair(f12(X0,flip_range_of(X1)),f12(X0,flip_range_of(X1))),non_ordered_pair(f12(X0,flip_range_of(X1)),non_ordered_pair(non_ordered_pair(f14(X0,flip_range_of(X1)),f14(X0,flip_range_of(X1))),non_ordered_pair(f14(X0,flip_range_of(X1)),f13(X0,flip_range_of(X1)))))),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1238])]) ).
fof(f1858,plain,
( ! [X0,X1] :
( ~ member(X0,flip_range_of(flip_range_of(X1)))
| little_set(f13(non_ordered_pair(non_ordered_pair(f12(X0,flip_range_of(X1)),f12(X0,flip_range_of(X1))),non_ordered_pair(f12(X0,flip_range_of(X1)),non_ordered_pair(non_ordered_pair(f14(X0,flip_range_of(X1)),f14(X0,flip_range_of(X1))),non_ordered_pair(f14(X0,flip_range_of(X1)),f13(X0,flip_range_of(X1)))))),X1)) )
| ~ spl0_58
| ~ spl0_144 ),
inference(resolution,[],[f1783,f455]) ).
fof(f37404,plain,
( spl0_1237
| ~ spl0_59
| ~ spl0_144 ),
inference(avatar_split_clause,[],[f1857,f1782,f458,f37402]) ).
fof(f37402,plain,
( spl0_1237
<=> ! [X0,X1] :
( ~ member(X0,flip_range_of(flip_range_of(X1)))
| little_set(f14(non_ordered_pair(non_ordered_pair(f12(X0,flip_range_of(X1)),f12(X0,flip_range_of(X1))),non_ordered_pair(f12(X0,flip_range_of(X1)),non_ordered_pair(non_ordered_pair(f14(X0,flip_range_of(X1)),f14(X0,flip_range_of(X1))),non_ordered_pair(f14(X0,flip_range_of(X1)),f13(X0,flip_range_of(X1)))))),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1237])]) ).
fof(f1857,plain,
( ! [X0,X1] :
( ~ member(X0,flip_range_of(flip_range_of(X1)))
| little_set(f14(non_ordered_pair(non_ordered_pair(f12(X0,flip_range_of(X1)),f12(X0,flip_range_of(X1))),non_ordered_pair(f12(X0,flip_range_of(X1)),non_ordered_pair(non_ordered_pair(f14(X0,flip_range_of(X1)),f14(X0,flip_range_of(X1))),non_ordered_pair(f14(X0,flip_range_of(X1)),f13(X0,flip_range_of(X1)))))),X1)) )
| ~ spl0_59
| ~ spl0_144 ),
inference(resolution,[],[f1783,f459]) ).
fof(f37400,plain,
( spl0_1236
| ~ spl0_54
| ~ spl0_144 ),
inference(avatar_split_clause,[],[f1855,f1782,f438,f37398]) ).
fof(f37398,plain,
( spl0_1236
<=> ! [X0,X1] :
( ~ member(X0,flip_range_of(rotate_right(X1)))
| little_set(f9(non_ordered_pair(non_ordered_pair(f12(X0,rotate_right(X1)),f12(X0,rotate_right(X1))),non_ordered_pair(f12(X0,rotate_right(X1)),non_ordered_pair(non_ordered_pair(f14(X0,rotate_right(X1)),f14(X0,rotate_right(X1))),non_ordered_pair(f14(X0,rotate_right(X1)),f13(X0,rotate_right(X1)))))),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1236])]) ).
fof(f1855,plain,
( ! [X0,X1] :
( ~ member(X0,flip_range_of(rotate_right(X1)))
| little_set(f9(non_ordered_pair(non_ordered_pair(f12(X0,rotate_right(X1)),f12(X0,rotate_right(X1))),non_ordered_pair(f12(X0,rotate_right(X1)),non_ordered_pair(non_ordered_pair(f14(X0,rotate_right(X1)),f14(X0,rotate_right(X1))),non_ordered_pair(f14(X0,rotate_right(X1)),f13(X0,rotate_right(X1)))))),X1)) )
| ~ spl0_54
| ~ spl0_144 ),
inference(resolution,[],[f1783,f439]) ).
fof(f37396,plain,
( spl0_1235
| ~ spl0_55
| ~ spl0_144 ),
inference(avatar_split_clause,[],[f1854,f1782,f442,f37394]) ).
fof(f37394,plain,
( spl0_1235
<=> ! [X0,X1] :
( ~ member(X0,flip_range_of(rotate_right(X1)))
| little_set(f10(non_ordered_pair(non_ordered_pair(f12(X0,rotate_right(X1)),f12(X0,rotate_right(X1))),non_ordered_pair(f12(X0,rotate_right(X1)),non_ordered_pair(non_ordered_pair(f14(X0,rotate_right(X1)),f14(X0,rotate_right(X1))),non_ordered_pair(f14(X0,rotate_right(X1)),f13(X0,rotate_right(X1)))))),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1235])]) ).
fof(f1854,plain,
( ! [X0,X1] :
( ~ member(X0,flip_range_of(rotate_right(X1)))
| little_set(f10(non_ordered_pair(non_ordered_pair(f12(X0,rotate_right(X1)),f12(X0,rotate_right(X1))),non_ordered_pair(f12(X0,rotate_right(X1)),non_ordered_pair(non_ordered_pair(f14(X0,rotate_right(X1)),f14(X0,rotate_right(X1))),non_ordered_pair(f14(X0,rotate_right(X1)),f13(X0,rotate_right(X1)))))),X1)) )
| ~ spl0_55
| ~ spl0_144 ),
inference(resolution,[],[f1783,f443]) ).
fof(f37392,plain,
( spl0_1234
| ~ spl0_56
| ~ spl0_144 ),
inference(avatar_split_clause,[],[f1853,f1782,f446,f37390]) ).
fof(f37390,plain,
( spl0_1234
<=> ! [X0,X1] :
( ~ member(X0,flip_range_of(rotate_right(X1)))
| little_set(f11(non_ordered_pair(non_ordered_pair(f12(X0,rotate_right(X1)),f12(X0,rotate_right(X1))),non_ordered_pair(f12(X0,rotate_right(X1)),non_ordered_pair(non_ordered_pair(f14(X0,rotate_right(X1)),f14(X0,rotate_right(X1))),non_ordered_pair(f14(X0,rotate_right(X1)),f13(X0,rotate_right(X1)))))),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1234])]) ).
fof(f1853,plain,
( ! [X0,X1] :
( ~ member(X0,flip_range_of(rotate_right(X1)))
| little_set(f11(non_ordered_pair(non_ordered_pair(f12(X0,rotate_right(X1)),f12(X0,rotate_right(X1))),non_ordered_pair(f12(X0,rotate_right(X1)),non_ordered_pair(non_ordered_pair(f14(X0,rotate_right(X1)),f14(X0,rotate_right(X1))),non_ordered_pair(f14(X0,rotate_right(X1)),f13(X0,rotate_right(X1)))))),X1)) )
| ~ spl0_56
| ~ spl0_144 ),
inference(resolution,[],[f1783,f447]) ).
fof(f37388,plain,
( spl0_1233
| ~ spl0_53
| ~ spl0_144 ),
inference(avatar_split_clause,[],[f1847,f1782,f434,f37386]) ).
fof(f37386,plain,
( spl0_1233
<=> ! [X0,X1] :
( ~ member(X0,flip_range_of(domain_of(X1)))
| ordered_pair_predicate(f8(non_ordered_pair(non_ordered_pair(f12(X0,domain_of(X1)),f12(X0,domain_of(X1))),non_ordered_pair(f12(X0,domain_of(X1)),non_ordered_pair(non_ordered_pair(f14(X0,domain_of(X1)),f14(X0,domain_of(X1))),non_ordered_pair(f14(X0,domain_of(X1)),f13(X0,domain_of(X1)))))),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1233])]) ).
fof(f1847,plain,
( ! [X0,X1] :
( ~ member(X0,flip_range_of(domain_of(X1)))
| ordered_pair_predicate(f8(non_ordered_pair(non_ordered_pair(f12(X0,domain_of(X1)),f12(X0,domain_of(X1))),non_ordered_pair(f12(X0,domain_of(X1)),non_ordered_pair(non_ordered_pair(f14(X0,domain_of(X1)),f14(X0,domain_of(X1))),non_ordered_pair(f14(X0,domain_of(X1)),f13(X0,domain_of(X1)))))),X1)) )
| ~ spl0_53
| ~ spl0_144 ),
inference(resolution,[],[f1783,f435]) ).
fof(f37291,plain,
( spl0_1232
| ~ spl0_48
| ~ spl0_144 ),
inference(avatar_split_clause,[],[f1841,f1782,f414,f37289]) ).
fof(f37289,plain,
( spl0_1232
<=> ! [X0,X1] :
( ~ member(X0,flip_range_of(second(X1)))
| little_set(f6(non_ordered_pair(non_ordered_pair(f12(X0,second(X1)),f12(X0,second(X1))),non_ordered_pair(f12(X0,second(X1)),non_ordered_pair(non_ordered_pair(f14(X0,second(X1)),f14(X0,second(X1))),non_ordered_pair(f14(X0,second(X1)),f13(X0,second(X1)))))),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1232])]) ).
fof(f1841,plain,
( ! [X0,X1] :
( ~ member(X0,flip_range_of(second(X1)))
| little_set(f6(non_ordered_pair(non_ordered_pair(f12(X0,second(X1)),f12(X0,second(X1))),non_ordered_pair(f12(X0,second(X1)),non_ordered_pair(non_ordered_pair(f14(X0,second(X1)),f14(X0,second(X1))),non_ordered_pair(f14(X0,second(X1)),f13(X0,second(X1)))))),X1)) )
| ~ spl0_48
| ~ spl0_144 ),
inference(resolution,[],[f1783,f415]) ).
fof(f37287,plain,
( spl0_1231
| ~ spl0_49
| ~ spl0_144 ),
inference(avatar_split_clause,[],[f1840,f1782,f418,f37285]) ).
fof(f37285,plain,
( spl0_1231
<=> ! [X0,X1] :
( ~ member(X0,flip_range_of(second(X1)))
| little_set(f7(non_ordered_pair(non_ordered_pair(f12(X0,second(X1)),f12(X0,second(X1))),non_ordered_pair(f12(X0,second(X1)),non_ordered_pair(non_ordered_pair(f14(X0,second(X1)),f14(X0,second(X1))),non_ordered_pair(f14(X0,second(X1)),f13(X0,second(X1)))))),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1231])]) ).
fof(f1840,plain,
( ! [X0,X1] :
( ~ member(X0,flip_range_of(second(X1)))
| little_set(f7(non_ordered_pair(non_ordered_pair(f12(X0,second(X1)),f12(X0,second(X1))),non_ordered_pair(f12(X0,second(X1)),non_ordered_pair(non_ordered_pair(f14(X0,second(X1)),f14(X0,second(X1))),non_ordered_pair(f14(X0,second(X1)),f13(X0,second(X1)))))),X1)) )
| ~ spl0_49
| ~ spl0_144 ),
inference(resolution,[],[f1783,f419]) ).
fof(f37283,plain,
( spl0_1230
| ~ spl0_46
| ~ spl0_144 ),
inference(avatar_split_clause,[],[f1838,f1782,f406,f37281]) ).
fof(f37281,plain,
( spl0_1230
<=> ! [X0,X1] :
( ~ member(X0,flip_range_of(first(X1)))
| little_set(f4(non_ordered_pair(non_ordered_pair(f12(X0,first(X1)),f12(X0,first(X1))),non_ordered_pair(f12(X0,first(X1)),non_ordered_pair(non_ordered_pair(f14(X0,first(X1)),f14(X0,first(X1))),non_ordered_pair(f14(X0,first(X1)),f13(X0,first(X1)))))),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1230])]) ).
fof(f1838,plain,
( ! [X0,X1] :
( ~ member(X0,flip_range_of(first(X1)))
| little_set(f4(non_ordered_pair(non_ordered_pair(f12(X0,first(X1)),f12(X0,first(X1))),non_ordered_pair(f12(X0,first(X1)),non_ordered_pair(non_ordered_pair(f14(X0,first(X1)),f14(X0,first(X1))),non_ordered_pair(f14(X0,first(X1)),f13(X0,first(X1)))))),X1)) )
| ~ spl0_46
| ~ spl0_144 ),
inference(resolution,[],[f1783,f407]) ).
fof(f37279,plain,
( spl0_1229
| ~ spl0_47
| ~ spl0_144 ),
inference(avatar_split_clause,[],[f1837,f1782,f410,f37277]) ).
fof(f37277,plain,
( spl0_1229
<=> ! [X0,X1] :
( ~ member(X0,flip_range_of(first(X1)))
| little_set(f5(non_ordered_pair(non_ordered_pair(f12(X0,first(X1)),f12(X0,first(X1))),non_ordered_pair(f12(X0,first(X1)),non_ordered_pair(non_ordered_pair(f14(X0,first(X1)),f14(X0,first(X1))),non_ordered_pair(f14(X0,first(X1)),f13(X0,first(X1)))))),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1229])]) ).
fof(f1837,plain,
( ! [X0,X1] :
( ~ member(X0,flip_range_of(first(X1)))
| little_set(f5(non_ordered_pair(non_ordered_pair(f12(X0,first(X1)),f12(X0,first(X1))),non_ordered_pair(f12(X0,first(X1)),non_ordered_pair(non_ordered_pair(f14(X0,first(X1)),f14(X0,first(X1))),non_ordered_pair(f14(X0,first(X1)),f13(X0,first(X1)))))),X1)) )
| ~ spl0_47
| ~ spl0_144 ),
inference(resolution,[],[f1783,f411]) ).
fof(f37275,plain,
( spl0_1228
| ~ spl0_102
| ~ spl0_140 ),
inference(avatar_split_clause,[],[f1765,f1745,f956,f37273]) ).
fof(f37273,plain,
( spl0_1228
<=> ! [X4,X0,X3,X2,X1] :
( ~ little_set(X0)
| ~ little_set(X1)
| ~ little_set(X2)
| X1 = X2
| ~ member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X1)),intersection(X3,X4))
| ~ single_valued_set(intersection(X3,X4))
| ~ member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X2)),X3)
| ~ member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X2)),X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1228])]) ).
fof(f1765,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ little_set(X0)
| ~ little_set(X1)
| ~ little_set(X2)
| X1 = X2
| ~ member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X1)),intersection(X3,X4))
| ~ single_valued_set(intersection(X3,X4))
| ~ member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X2)),X3)
| ~ member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X2)),X4) )
| ~ spl0_102
| ~ spl0_140 ),
inference(resolution,[],[f1746,f957]) ).
fof(f37271,plain,
( spl0_1227
| ~ spl0_101
| ~ spl0_136 ),
inference(avatar_split_clause,[],[f1597,f1552,f952,f37269]) ).
fof(f37269,plain,
( spl0_1227
<=> ! [X2,X4,X0,X3,X5,X1] :
( ~ closed(X0,X1)
| ~ maps(X2,non_ordered_pair(X3,X4),X0)
| homomorphism(X2,non_ordered_pair(X3,X4),X5,X0,X1)
| ~ closed(non_ordered_pair(X3,X4),X5)
| f33(X2,non_ordered_pair(X3,X4),X5,X0,X1) = X3
| f33(X2,non_ordered_pair(X3,X4),X5,X0,X1) = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1227])]) ).
fof(f1597,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ closed(X0,X1)
| ~ maps(X2,non_ordered_pair(X3,X4),X0)
| homomorphism(X2,non_ordered_pair(X3,X4),X5,X0,X1)
| ~ closed(non_ordered_pair(X3,X4),X5)
| f33(X2,non_ordered_pair(X3,X4),X5,X0,X1) = X3
| f33(X2,non_ordered_pair(X3,X4),X5,X0,X1) = X4 )
| ~ spl0_101
| ~ spl0_136 ),
inference(resolution,[],[f1553,f953]) ).
fof(f37267,plain,
( spl0_1226
| ~ spl0_101
| ~ spl0_134 ),
inference(avatar_split_clause,[],[f1558,f1544,f952,f37265]) ).
fof(f37265,plain,
( spl0_1226
<=> ! [X2,X4,X0,X3,X5,X1] :
( ~ closed(X0,X1)
| ~ maps(X2,non_ordered_pair(X3,X4),X0)
| homomorphism(X2,non_ordered_pair(X3,X4),X5,X0,X1)
| ~ closed(non_ordered_pair(X3,X4),X5)
| f32(X2,non_ordered_pair(X3,X4),X5,X0,X1) = X3
| f32(X2,non_ordered_pair(X3,X4),X5,X0,X1) = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1226])]) ).
fof(f1558,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ closed(X0,X1)
| ~ maps(X2,non_ordered_pair(X3,X4),X0)
| homomorphism(X2,non_ordered_pair(X3,X4),X5,X0,X1)
| ~ closed(non_ordered_pair(X3,X4),X5)
| f32(X2,non_ordered_pair(X3,X4),X5,X0,X1) = X3
| f32(X2,non_ordered_pair(X3,X4),X5,X0,X1) = X4 )
| ~ spl0_101
| ~ spl0_134 ),
inference(resolution,[],[f1545,f953]) ).
fof(f37004,plain,
( spl0_1225
| ~ spl0_173
| ~ spl0_1217 ),
inference(avatar_split_clause,[],[f36908,f36905,f2440,f37002]) ).
fof(f36905,plain,
( spl0_1217
<=> ! [X0,X1] :
( f24(compose(X0,X1)) = non_ordered_pair(non_ordered_pair(f29(f24(compose(X0,X1)),X0,X1),f29(f24(compose(X0,X1)),X0,X1)),non_ordered_pair(f29(f24(compose(X0,X1)),X0,X1),f30(f24(compose(X0,X1)),X0,X1)))
| empty_set = compose(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1217])]) ).
fof(f36908,plain,
( ! [X0,X1] :
( estin = compose(X0,X1)
| f24(compose(X0,X1)) = non_ordered_pair(non_ordered_pair(f29(f24(compose(X0,X1)),X0,X1),f29(f24(compose(X0,X1)),X0,X1)),non_ordered_pair(f29(f24(compose(X0,X1)),X0,X1),f30(f24(compose(X0,X1)),X0,X1))) )
| ~ spl0_173
| ~ spl0_1217 ),
inference(forward_demodulation,[],[f36906,f2442]) ).
fof(f36906,plain,
( ! [X0,X1] :
( f24(compose(X0,X1)) = non_ordered_pair(non_ordered_pair(f29(f24(compose(X0,X1)),X0,X1),f29(f24(compose(X0,X1)),X0,X1)),non_ordered_pair(f29(f24(compose(X0,X1)),X0,X1),f30(f24(compose(X0,X1)),X0,X1)))
| empty_set = compose(X0,X1) )
| ~ spl0_1217 ),
inference(avatar_component_clause,[],[f36905]) ).
fof(f37000,plain,
( spl0_1224
| ~ spl0_122
| ~ spl0_147 ),
inference(avatar_split_clause,[],[f1958,f1954,f1291,f36998]) ).
fof(f36998,plain,
( spl0_1224
<=> ! [X2,X0,X1] :
( ~ little_set(X0)
| ~ little_set(f21(X1))
| ~ little_set(f19(X1))
| ~ member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,f19(X1))),X2)
| ~ little_set(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,f21(X1))))
| member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,f21(X1))),compose(X2,X1))
| single_valued_set(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1224])]) ).
fof(f1958,plain,
( ! [X2,X0,X1] :
( ~ little_set(X0)
| ~ little_set(f21(X1))
| ~ little_set(f19(X1))
| ~ member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,f19(X1))),X2)
| ~ little_set(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,f21(X1))))
| member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,f21(X1))),compose(X2,X1))
| single_valued_set(X1) )
| ~ spl0_122
| ~ spl0_147 ),
inference(resolution,[],[f1955,f1292]) ).
fof(f36996,plain,
( spl0_1223
| ~ spl0_121
| ~ spl0_147 ),
inference(avatar_split_clause,[],[f1957,f1954,f1287,f36994]) ).
fof(f36994,plain,
( spl0_1223
<=> ! [X2,X0,X1] :
( ~ little_set(X0)
| ~ little_set(f20(X1))
| ~ little_set(f19(X1))
| ~ member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,f19(X1))),X2)
| ~ little_set(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,f20(X1))))
| member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,f20(X1))),compose(X2,X1))
| single_valued_set(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1223])]) ).
fof(f1957,plain,
( ! [X2,X0,X1] :
( ~ little_set(X0)
| ~ little_set(f20(X1))
| ~ little_set(f19(X1))
| ~ member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,f19(X1))),X2)
| ~ little_set(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,f20(X1))))
| member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,f20(X1))),compose(X2,X1))
| single_valued_set(X1) )
| ~ spl0_121
| ~ spl0_147 ),
inference(resolution,[],[f1955,f1288]) ).
fof(f36992,plain,
( spl0_1222
| ~ spl0_37
| ~ spl0_145 ),
inference(avatar_split_clause,[],[f1904,f1786,f349,f36990]) ).
fof(f36990,plain,
( spl0_1222
<=> ! [X0,X1] :
( ~ member(X0,rotate_right(powerset(X1)))
| subset(non_ordered_pair(non_ordered_pair(f10(X0,powerset(X1)),f10(X0,powerset(X1))),non_ordered_pair(f10(X0,powerset(X1)),non_ordered_pair(non_ordered_pair(f11(X0,powerset(X1)),f11(X0,powerset(X1))),non_ordered_pair(f11(X0,powerset(X1)),f9(X0,powerset(X1)))))),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1222])]) ).
fof(f1904,plain,
( ! [X0,X1] :
( ~ member(X0,rotate_right(powerset(X1)))
| subset(non_ordered_pair(non_ordered_pair(f10(X0,powerset(X1)),f10(X0,powerset(X1))),non_ordered_pair(f10(X0,powerset(X1)),non_ordered_pair(non_ordered_pair(f11(X0,powerset(X1)),f11(X0,powerset(X1))),non_ordered_pair(f11(X0,powerset(X1)),f9(X0,powerset(X1)))))),X1) )
| ~ spl0_37
| ~ spl0_145 ),
inference(resolution,[],[f1787,f350]) ).
fof(f36988,plain,
( spl0_1221
| ~ spl0_34
| ~ spl0_145 ),
inference(avatar_split_clause,[],[f1888,f1786,f336,f36986]) ).
fof(f1888,plain,
( ! [X0,X1] :
( ~ member(X0,rotate_right(complement(X1)))
| ~ member(non_ordered_pair(non_ordered_pair(f10(X0,complement(X1)),f10(X0,complement(X1))),non_ordered_pair(f10(X0,complement(X1)),non_ordered_pair(non_ordered_pair(f11(X0,complement(X1)),f11(X0,complement(X1))),non_ordered_pair(f11(X0,complement(X1)),f9(X0,complement(X1)))))),X1) )
| ~ spl0_34
| ~ spl0_145 ),
inference(resolution,[],[f1787,f337]) ).
fof(f36920,plain,
( spl0_1220
| ~ spl0_37
| ~ spl0_144 ),
inference(avatar_split_clause,[],[f1861,f1782,f349,f36918]) ).
fof(f36918,plain,
( spl0_1220
<=> ! [X0,X1] :
( ~ member(X0,flip_range_of(powerset(X1)))
| subset(non_ordered_pair(non_ordered_pair(f12(X0,powerset(X1)),f12(X0,powerset(X1))),non_ordered_pair(f12(X0,powerset(X1)),non_ordered_pair(non_ordered_pair(f14(X0,powerset(X1)),f14(X0,powerset(X1))),non_ordered_pair(f14(X0,powerset(X1)),f13(X0,powerset(X1)))))),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1220])]) ).
fof(f1861,plain,
( ! [X0,X1] :
( ~ member(X0,flip_range_of(powerset(X1)))
| subset(non_ordered_pair(non_ordered_pair(f12(X0,powerset(X1)),f12(X0,powerset(X1))),non_ordered_pair(f12(X0,powerset(X1)),non_ordered_pair(non_ordered_pair(f14(X0,powerset(X1)),f14(X0,powerset(X1))),non_ordered_pair(f14(X0,powerset(X1)),f13(X0,powerset(X1)))))),X1) )
| ~ spl0_37
| ~ spl0_144 ),
inference(resolution,[],[f1783,f350]) ).
fof(f36916,plain,
( spl0_1219
| ~ spl0_34
| ~ spl0_144 ),
inference(avatar_split_clause,[],[f1845,f1782,f336,f36914]) ).
fof(f1845,plain,
( ! [X0,X1] :
( ~ member(X0,flip_range_of(complement(X1)))
| ~ member(non_ordered_pair(non_ordered_pair(f12(X0,complement(X1)),f12(X0,complement(X1))),non_ordered_pair(f12(X0,complement(X1)),non_ordered_pair(non_ordered_pair(f14(X0,complement(X1)),f14(X0,complement(X1))),non_ordered_pair(f14(X0,complement(X1)),f13(X0,complement(X1)))))),X1) )
| ~ spl0_34
| ~ spl0_144 ),
inference(resolution,[],[f1783,f337]) ).
fof(f36912,plain,
( spl0_1218
| ~ spl0_124
| ~ spl0_140 ),
inference(avatar_split_clause,[],[f1771,f1745,f1299,f36910]) ).
fof(f36910,plain,
( spl0_1218
<=> ! [X4,X0,X3,X2,X1] :
( ~ little_set(X0)
| ~ little_set(X1)
| ~ little_set(X2)
| X1 = X2
| ~ member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X1)),apply(X3,first(X4)))
| ~ single_valued_set(apply(X3,first(X4)))
| ~ member(X4,X3)
| ~ member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X2)),second(X4))
| ~ ordered_pair_predicate(X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1218])]) ).
fof(f1771,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ little_set(X0)
| ~ little_set(X1)
| ~ little_set(X2)
| X1 = X2
| ~ member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X1)),apply(X3,first(X4)))
| ~ single_valued_set(apply(X3,first(X4)))
| ~ member(X4,X3)
| ~ member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X2)),second(X4))
| ~ ordered_pair_predicate(X4) )
| ~ spl0_124
| ~ spl0_140 ),
inference(resolution,[],[f1746,f1300]) ).
fof(f36907,plain,
( spl0_1217
| ~ spl0_40
| ~ spl0_137 ),
inference(avatar_split_clause,[],[f1658,f1634,f361,f36905]) ).
fof(f1658,plain,
( ! [X0,X1] :
( f24(compose(X0,X1)) = non_ordered_pair(non_ordered_pair(f29(f24(compose(X0,X1)),X0,X1),f29(f24(compose(X0,X1)),X0,X1)),non_ordered_pair(f29(f24(compose(X0,X1)),X0,X1),f30(f24(compose(X0,X1)),X0,X1)))
| empty_set = compose(X0,X1) )
| ~ spl0_40
| ~ spl0_137 ),
inference(resolution,[],[f1635,f362]) ).
fof(f36885,plain,
( spl0_1216
| ~ spl0_173
| ~ spl0_1215 ),
inference(avatar_split_clause,[],[f36440,f36437,f2440,f36883]) ).
fof(f36883,plain,
( spl0_1216
<=> ! [X2,X0,X1] :
( estin = X1
| ~ little_set(X0)
| ~ little_set(f26(X1))
| ~ little_set(X1)
| ~ member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X1)),X2)
| ~ little_set(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,f26(X1))))
| member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,f26(X1))),compose(X2,f25)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1216])]) ).
fof(f36437,plain,
( spl0_1215
<=> ! [X2,X0,X1] :
( ~ little_set(X0)
| ~ little_set(f26(X1))
| ~ little_set(X1)
| ~ member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X1)),X2)
| ~ little_set(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,f26(X1))))
| member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,f26(X1))),compose(X2,f25))
| empty_set = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1215])]) ).
fof(f36440,plain,
( ! [X2,X0,X1] :
( estin = X1
| ~ little_set(X0)
| ~ little_set(f26(X1))
| ~ little_set(X1)
| ~ member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X1)),X2)
| ~ little_set(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,f26(X1))))
| member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,f26(X1))),compose(X2,f25)) )
| ~ spl0_173
| ~ spl0_1215 ),
inference(forward_demodulation,[],[f36438,f2442]) ).
fof(f36438,plain,
( ! [X2,X0,X1] :
( ~ little_set(X0)
| ~ little_set(f26(X1))
| ~ little_set(X1)
| ~ member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X1)),X2)
| ~ little_set(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,f26(X1))))
| member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,f26(X1))),compose(X2,f25))
| empty_set = X1 )
| ~ spl0_1215 ),
inference(avatar_component_clause,[],[f36437]) ).
fof(f36439,plain,
( spl0_1215
| ~ spl0_123
| ~ spl0_147 ),
inference(avatar_split_clause,[],[f1979,f1954,f1295,f36437]) ).
fof(f1295,plain,
( spl0_123
<=> ! [X0] :
( ~ little_set(X0)
| empty_set = X0
| member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,f26(X0))),f25) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_123])]) ).
fof(f1979,plain,
( ! [X2,X0,X1] :
( ~ little_set(X0)
| ~ little_set(f26(X1))
| ~ little_set(X1)
| ~ member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X1)),X2)
| ~ little_set(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,f26(X1))))
| member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,f26(X1))),compose(X2,f25))
| empty_set = X1 )
| ~ spl0_123
| ~ spl0_147 ),
inference(duplicate_literal_removal,[],[f1964]) ).
fof(f1964,plain,
( ! [X2,X0,X1] :
( ~ little_set(X0)
| ~ little_set(f26(X1))
| ~ little_set(X1)
| ~ member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X1)),X2)
| ~ little_set(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,f26(X1))))
| member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,f26(X1))),compose(X2,f25))
| empty_set = X1
| ~ little_set(X1) )
| ~ spl0_123
| ~ spl0_147 ),
inference(resolution,[],[f1955,f1296]) ).
fof(f1296,plain,
( ! [X0] :
( member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,f26(X0))),f25)
| empty_set = X0
| ~ little_set(X0) )
| ~ spl0_123 ),
inference(avatar_component_clause,[],[f1295]) ).
fof(f36435,plain,
( spl0_1214
| ~ spl0_28
| ~ spl0_145 ),
inference(avatar_split_clause,[],[f1894,f1786,f306,f36433]) ).
fof(f36433,plain,
( spl0_1214
<=> ! [X0,X1] :
( ~ member(X0,rotate_right(converse(X1)))
| ordered_pair_predicate(non_ordered_pair(non_ordered_pair(f10(X0,converse(X1)),f10(X0,converse(X1))),non_ordered_pair(f10(X0,converse(X1)),non_ordered_pair(non_ordered_pair(f11(X0,converse(X1)),f11(X0,converse(X1))),non_ordered_pair(f11(X0,converse(X1)),f9(X0,converse(X1))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1214])]) ).
fof(f1894,plain,
( ! [X0,X1] :
( ~ member(X0,rotate_right(converse(X1)))
| ordered_pair_predicate(non_ordered_pair(non_ordered_pair(f10(X0,converse(X1)),f10(X0,converse(X1))),non_ordered_pair(f10(X0,converse(X1)),non_ordered_pair(non_ordered_pair(f11(X0,converse(X1)),f11(X0,converse(X1))),non_ordered_pair(f11(X0,converse(X1)),f9(X0,converse(X1))))))) )
| ~ spl0_28
| ~ spl0_145 ),
inference(resolution,[],[f1787,f307]) ).
fof(f36431,plain,
( spl0_1213
| ~ spl0_28
| ~ spl0_144 ),
inference(avatar_split_clause,[],[f1851,f1782,f306,f36429]) ).
fof(f36429,plain,
( spl0_1213
<=> ! [X0,X1] :
( ~ member(X0,flip_range_of(converse(X1)))
| ordered_pair_predicate(non_ordered_pair(non_ordered_pair(f12(X0,converse(X1)),f12(X0,converse(X1))),non_ordered_pair(f12(X0,converse(X1)),non_ordered_pair(non_ordered_pair(f14(X0,converse(X1)),f14(X0,converse(X1))),non_ordered_pair(f14(X0,converse(X1)),f13(X0,converse(X1))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1213])]) ).
fof(f1851,plain,
( ! [X0,X1] :
( ~ member(X0,flip_range_of(converse(X1)))
| ordered_pair_predicate(non_ordered_pair(non_ordered_pair(f12(X0,converse(X1)),f12(X0,converse(X1))),non_ordered_pair(f12(X0,converse(X1)),non_ordered_pair(non_ordered_pair(f14(X0,converse(X1)),f14(X0,converse(X1))),non_ordered_pair(f14(X0,converse(X1)),f13(X0,converse(X1))))))) )
| ~ spl0_28
| ~ spl0_144 ),
inference(resolution,[],[f1783,f307]) ).
fof(f36427,plain,
( spl0_1212
| ~ spl0_110
| ~ spl0_139 ),
inference(avatar_split_clause,[],[f1738,f1642,f1081,f36425]) ).
fof(f36425,plain,
( spl0_1212
<=> ! [X0,X3,X2,X1] :
( ~ member(X0,compose(apply(X1,X2),X3))
| first(f28(non_ordered_pair(non_ordered_pair(f29(X0,apply(X1,X2),X3),f29(X0,apply(X1,X2),X3)),non_ordered_pair(f29(X0,apply(X1,X2),X3),f31(X0,apply(X1,X2),X3))),X1,X2)) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1212])]) ).
fof(f1738,plain,
( ! [X2,X3,X0,X1] :
( ~ member(X0,compose(apply(X1,X2),X3))
| first(f28(non_ordered_pair(non_ordered_pair(f29(X0,apply(X1,X2),X3),f29(X0,apply(X1,X2),X3)),non_ordered_pair(f29(X0,apply(X1,X2),X3),f31(X0,apply(X1,X2),X3))),X1,X2)) = X2 )
| ~ spl0_110
| ~ spl0_139 ),
inference(resolution,[],[f1643,f1082]) ).
fof(f36423,plain,
( spl0_1211
| ~ spl0_110
| ~ spl0_138 ),
inference(avatar_split_clause,[],[f1698,f1638,f1081,f36421]) ).
fof(f36421,plain,
( spl0_1211
<=> ! [X0,X3,X2,X1] :
( ~ member(X0,compose(X1,apply(X2,X3)))
| first(f28(non_ordered_pair(non_ordered_pair(f31(X0,X1,apply(X2,X3)),f31(X0,X1,apply(X2,X3))),non_ordered_pair(f31(X0,X1,apply(X2,X3)),f30(X0,X1,apply(X2,X3)))),X2,X3)) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1211])]) ).
fof(f1698,plain,
( ! [X2,X3,X0,X1] :
( ~ member(X0,compose(X1,apply(X2,X3)))
| first(f28(non_ordered_pair(non_ordered_pair(f31(X0,X1,apply(X2,X3)),f31(X0,X1,apply(X2,X3))),non_ordered_pair(f31(X0,X1,apply(X2,X3)),f30(X0,X1,apply(X2,X3)))),X2,X3)) = X3 )
| ~ spl0_110
| ~ spl0_138 ),
inference(resolution,[],[f1639,f1082]) ).
fof(f36419,plain,
( spl0_1210
| ~ spl0_30
| ~ spl0_137 ),
inference(avatar_split_clause,[],[f1654,f1634,f314,f36417]) ).
fof(f1654,plain,
( ! [X0,X1] :
( f18(compose(X0,X1)) = non_ordered_pair(non_ordered_pair(f29(f18(compose(X0,X1)),X0,X1),f29(f18(compose(X0,X1)),X0,X1)),non_ordered_pair(f29(f18(compose(X0,X1)),X0,X1),f30(f18(compose(X0,X1)),X0,X1)))
| relation(compose(X0,X1)) )
| ~ spl0_30
| ~ spl0_137 ),
inference(resolution,[],[f1635,f315]) ).
fof(f36415,plain,
( spl0_1209
| ~ spl0_114
| ~ spl0_126 ),
inference(avatar_split_clause,[],[f1414,f1393,f1163,f36413]) ).
fof(f36413,plain,
( spl0_1209
<=> ! [X2,X0,X1] :
( ~ little_set(f1(X0,cross_product(X1,X2)))
| ~ member(first(f1(X0,cross_product(X1,X2))),X1)
| ~ member(second(f1(X0,cross_product(X1,X2))),X2)
| ~ ordered_pair_predicate(f1(X0,cross_product(X1,X2)))
| cross_product(X1,X2) = X0
| ~ member(f1(X0,cross_product(X1,X2)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1209])]) ).
fof(f1163,plain,
( spl0_114
<=> ! [X0,X1] :
( X0 = X1
| ~ member(f1(X0,X1),X1)
| ~ member(f1(X0,X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_114])]) ).
fof(f1414,plain,
( ! [X2,X0,X1] :
( ~ little_set(f1(X0,cross_product(X1,X2)))
| ~ member(first(f1(X0,cross_product(X1,X2))),X1)
| ~ member(second(f1(X0,cross_product(X1,X2))),X2)
| ~ ordered_pair_predicate(f1(X0,cross_product(X1,X2)))
| cross_product(X1,X2) = X0
| ~ member(f1(X0,cross_product(X1,X2)),X0) )
| ~ spl0_114
| ~ spl0_126 ),
inference(resolution,[],[f1394,f1164]) ).
fof(f1164,plain,
( ! [X0,X1] :
( ~ member(f1(X0,X1),X1)
| X0 = X1
| ~ member(f1(X0,X1),X0) )
| ~ spl0_114 ),
inference(avatar_component_clause,[],[f1163]) ).
fof(f36390,plain,
( spl0_1208
| ~ spl0_293
| ~ spl0_435 ),
inference(avatar_split_clause,[],[f5404,f5175,f3479,f36388]) ).
fof(f36388,plain,
( spl0_1208
<=> ! [X0] : estin = cross_product(X0,estin) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1208])]) ).
fof(f3479,plain,
( spl0_293
<=> ! [X0] : ~ member(X0,estin) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_293])]) ).
fof(f5404,plain,
( ! [X0] : estin = cross_product(X0,estin)
| ~ spl0_293
| ~ spl0_435 ),
inference(resolution,[],[f5176,f3480]) ).
fof(f3480,plain,
( ! [X0] : ~ member(X0,estin)
| ~ spl0_293 ),
inference(avatar_component_clause,[],[f3479]) ).
fof(f34970,plain,
( spl0_1207
| ~ spl0_293
| ~ spl0_433 ),
inference(avatar_split_clause,[],[f5317,f5166,f3479,f34968]) ).
fof(f34968,plain,
( spl0_1207
<=> ! [X0] : estin = cross_product(estin,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1207])]) ).
fof(f5317,plain,
( ! [X0] : estin = cross_product(estin,X0)
| ~ spl0_293
| ~ spl0_433 ),
inference(resolution,[],[f5167,f3480]) ).
fof(f34966,plain,
( spl0_1206
| ~ spl0_82
| ~ spl0_140 ),
inference(avatar_split_clause,[],[f1770,f1745,f660,f34964]) ).
fof(f34964,plain,
( spl0_1206
<=> ! [X0,X3,X2,X1] :
( ~ little_set(X0)
| ~ little_set(X1)
| ~ little_set(X2)
| X1 = X2
| ~ member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X1)),powerset(X3))
| ~ single_valued_set(powerset(X3))
| ~ subset(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X2)),X3)
| ~ little_set(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1206])]) ).
fof(f1770,plain,
( ! [X2,X3,X0,X1] :
( ~ little_set(X0)
| ~ little_set(X1)
| ~ little_set(X2)
| X1 = X2
| ~ member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X1)),powerset(X3))
| ~ single_valued_set(powerset(X3))
| ~ subset(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X2)),X3)
| ~ little_set(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X2))) )
| ~ spl0_82
| ~ spl0_140 ),
inference(resolution,[],[f1746,f661]) ).
fof(f34962,plain,
( spl0_1205
| ~ spl0_73
| ~ spl0_140 ),
inference(avatar_split_clause,[],[f1766,f1745,f624,f34960]) ).
fof(f34960,plain,
( spl0_1205
<=> ! [X0,X3,X2,X1] :
( ~ little_set(X0)
| ~ little_set(X1)
| ~ little_set(X2)
| X1 = X2
| ~ member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X1)),complement(X3))
| ~ single_valued_set(complement(X3))
| member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X2)),X3)
| ~ little_set(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1205])]) ).
fof(f1766,plain,
( ! [X2,X3,X0,X1] :
( ~ little_set(X0)
| ~ little_set(X1)
| ~ little_set(X2)
| X1 = X2
| ~ member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X1)),complement(X3))
| ~ single_valued_set(complement(X3))
| member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X2)),X3)
| ~ little_set(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X2))) )
| ~ spl0_73
| ~ spl0_140 ),
inference(resolution,[],[f1746,f625]) ).
fof(f34958,plain,
( spl0_1204
| ~ spl0_104
| ~ spl0_132 ),
inference(avatar_split_clause,[],[f1527,f1483,f966,f34956]) ).
fof(f34956,plain,
( spl0_1204
<=> ! [X2,X0,X1] :
( non_ordered_pair(non_ordered_pair(f4(f28(X0,first(X1),X2),X1),f4(f28(X0,first(X1),X2),X1)),non_ordered_pair(f4(f28(X0,first(X1),X2),X1),f5(f28(X0,first(X1),X2),X1))) = X1
| ~ member(X0,apply(first(X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1204])]) ).
fof(f1527,plain,
( ! [X2,X0,X1] :
( non_ordered_pair(non_ordered_pair(f4(f28(X0,first(X1),X2),X1),f4(f28(X0,first(X1),X2),X1)),non_ordered_pair(f4(f28(X0,first(X1),X2),X1),f5(f28(X0,first(X1),X2),X1))) = X1
| ~ member(X0,apply(first(X1),X2)) )
| ~ spl0_104
| ~ spl0_132 ),
inference(resolution,[],[f1484,f967]) ).
fof(f34954,plain,
( spl0_1203
| ~ spl0_103
| ~ spl0_132 ),
inference(avatar_split_clause,[],[f1521,f1483,f960,f34952]) ).
fof(f34952,plain,
( spl0_1203
<=> ! [X2,X0,X1] :
( non_ordered_pair(non_ordered_pair(f4(f22(X0,X1,first(X2)),X2),f4(f22(X0,X1,first(X2)),X2)),non_ordered_pair(f4(f22(X0,X1,first(X2)),X2),f5(f22(X0,X1,first(X2)),X2))) = X2
| ~ member(X0,image(X1,first(X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1203])]) ).
fof(f1521,plain,
( ! [X2,X0,X1] :
( non_ordered_pair(non_ordered_pair(f4(f22(X0,X1,first(X2)),X2),f4(f22(X0,X1,first(X2)),X2)),non_ordered_pair(f4(f22(X0,X1,first(X2)),X2),f5(f22(X0,X1,first(X2)),X2))) = X2
| ~ member(X0,image(X1,first(X2))) )
| ~ spl0_103
| ~ spl0_132 ),
inference(resolution,[],[f1484,f961]) ).
fof(f34950,plain,
( spl0_1202
| ~ spl0_113
| ~ spl0_132 ),
inference(avatar_split_clause,[],[f1512,f1483,f1159,f34948]) ).
fof(f34948,plain,
( spl0_1202
<=> ! [X0,X1] :
( non_ordered_pair(non_ordered_pair(f4(f1(first(X0),X1),X0),f4(f1(first(X0),X1),X0)),non_ordered_pair(f4(f1(first(X0),X1),X0),f5(f1(first(X0),X1),X0))) = X0
| member(f1(first(X0),X1),X1)
| first(X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1202])]) ).
fof(f1512,plain,
( ! [X0,X1] :
( non_ordered_pair(non_ordered_pair(f4(f1(first(X0),X1),X0),f4(f1(first(X0),X1),X0)),non_ordered_pair(f4(f1(first(X0),X1),X0),f5(f1(first(X0),X1),X0))) = X0
| member(f1(first(X0),X1),X1)
| first(X0) = X1 )
| ~ spl0_113
| ~ spl0_132 ),
inference(resolution,[],[f1484,f1160]) ).
fof(f34946,plain,
( spl0_1201
| ~ spl0_113
| ~ spl0_132 ),
inference(avatar_split_clause,[],[f1511,f1483,f1159,f34944]) ).
fof(f34944,plain,
( spl0_1201
<=> ! [X0,X1] :
( non_ordered_pair(non_ordered_pair(f4(f1(X0,first(X1)),X1),f4(f1(X0,first(X1)),X1)),non_ordered_pair(f4(f1(X0,first(X1)),X1),f5(f1(X0,first(X1)),X1))) = X1
| member(f1(X0,first(X1)),X0)
| first(X1) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1201])]) ).
fof(f1511,plain,
( ! [X0,X1] :
( non_ordered_pair(non_ordered_pair(f4(f1(X0,first(X1)),X1),f4(f1(X0,first(X1)),X1)),non_ordered_pair(f4(f1(X0,first(X1)),X1),f5(f1(X0,first(X1)),X1))) = X1
| member(f1(X0,first(X1)),X0)
| first(X1) = X0 )
| ~ spl0_113
| ~ spl0_132 ),
inference(resolution,[],[f1484,f1160]) ).
fof(f34942,plain,
( spl0_1200
| ~ spl0_104
| ~ spl0_131 ),
inference(avatar_split_clause,[],[f1509,f1479,f966,f34940]) ).
fof(f34940,plain,
( spl0_1200
<=> ! [X2,X0,X1] :
( non_ordered_pair(non_ordered_pair(f6(f28(X0,second(X1),X2),X1),f6(f28(X0,second(X1),X2),X1)),non_ordered_pair(f6(f28(X0,second(X1),X2),X1),f7(f28(X0,second(X1),X2),X1))) = X1
| ~ member(X0,apply(second(X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1200])]) ).
fof(f1509,plain,
( ! [X2,X0,X1] :
( non_ordered_pair(non_ordered_pair(f6(f28(X0,second(X1),X2),X1),f6(f28(X0,second(X1),X2),X1)),non_ordered_pair(f6(f28(X0,second(X1),X2),X1),f7(f28(X0,second(X1),X2),X1))) = X1
| ~ member(X0,apply(second(X1),X2)) )
| ~ spl0_104
| ~ spl0_131 ),
inference(resolution,[],[f1480,f967]) ).
fof(f34938,plain,
( spl0_1199
| ~ spl0_103
| ~ spl0_131 ),
inference(avatar_split_clause,[],[f1503,f1479,f960,f34936]) ).
fof(f34936,plain,
( spl0_1199
<=> ! [X2,X0,X1] :
( non_ordered_pair(non_ordered_pair(f6(f22(X0,X1,second(X2)),X2),f6(f22(X0,X1,second(X2)),X2)),non_ordered_pair(f6(f22(X0,X1,second(X2)),X2),f7(f22(X0,X1,second(X2)),X2))) = X2
| ~ member(X0,image(X1,second(X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1199])]) ).
fof(f1503,plain,
( ! [X2,X0,X1] :
( non_ordered_pair(non_ordered_pair(f6(f22(X0,X1,second(X2)),X2),f6(f22(X0,X1,second(X2)),X2)),non_ordered_pair(f6(f22(X0,X1,second(X2)),X2),f7(f22(X0,X1,second(X2)),X2))) = X2
| ~ member(X0,image(X1,second(X2))) )
| ~ spl0_103
| ~ spl0_131 ),
inference(resolution,[],[f1480,f961]) ).
fof(f34934,plain,
( spl0_1198
| ~ spl0_113
| ~ spl0_131 ),
inference(avatar_split_clause,[],[f1493,f1479,f1159,f34932]) ).
fof(f34932,plain,
( spl0_1198
<=> ! [X0,X1] :
( non_ordered_pair(non_ordered_pair(f6(f1(second(X0),X1),X0),f6(f1(second(X0),X1),X0)),non_ordered_pair(f6(f1(second(X0),X1),X0),f7(f1(second(X0),X1),X0))) = X0
| member(f1(second(X0),X1),X1)
| second(X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1198])]) ).
fof(f1493,plain,
( ! [X0,X1] :
( non_ordered_pair(non_ordered_pair(f6(f1(second(X0),X1),X0),f6(f1(second(X0),X1),X0)),non_ordered_pair(f6(f1(second(X0),X1),X0),f7(f1(second(X0),X1),X0))) = X0
| member(f1(second(X0),X1),X1)
| second(X0) = X1 )
| ~ spl0_113
| ~ spl0_131 ),
inference(resolution,[],[f1480,f1160]) ).
fof(f34930,plain,
( spl0_1197
| ~ spl0_113
| ~ spl0_131 ),
inference(avatar_split_clause,[],[f1492,f1479,f1159,f34928]) ).
fof(f34928,plain,
( spl0_1197
<=> ! [X0,X1] :
( non_ordered_pair(non_ordered_pair(f6(f1(X0,second(X1)),X1),f6(f1(X0,second(X1)),X1)),non_ordered_pair(f6(f1(X0,second(X1)),X1),f7(f1(X0,second(X1)),X1))) = X1
| member(f1(X0,second(X1)),X0)
| second(X1) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1197])]) ).
fof(f1492,plain,
( ! [X0,X1] :
( non_ordered_pair(non_ordered_pair(f6(f1(X0,second(X1)),X1),f6(f1(X0,second(X1)),X1)),non_ordered_pair(f6(f1(X0,second(X1)),X1),f7(f1(X0,second(X1)),X1))) = X1
| member(f1(X0,second(X1)),X0)
| second(X1) = X0 )
| ~ spl0_113
| ~ spl0_131 ),
inference(resolution,[],[f1480,f1160]) ).
fof(f34926,plain,
( spl0_1196
| ~ spl0_293
| ~ spl0_356 ),
inference(avatar_split_clause,[],[f4135,f3929,f3479,f34924]) ).
fof(f4135,plain,
( ! [X0] : estin = intersection(X0,estin)
| ~ spl0_293
| ~ spl0_356 ),
inference(resolution,[],[f3930,f3480]) ).
fof(f34922,plain,
( spl0_1195
| ~ spl0_106
| ~ spl0_128 ),
inference(avatar_split_clause,[],[f1459,f1401,f1064,f34920]) ).
fof(f34920,plain,
( spl0_1195
<=> ! [X0,X1] :
( ~ little_set(X0)
| ~ member(first(non_ordered_pair(non_ordered_pair(X1,X1),non_ordered_pair(X1,X0))),X0)
| ~ little_set(X1)
| ~ little_set(non_ordered_pair(non_ordered_pair(X1,X1),non_ordered_pair(X1,X0)))
| member(non_ordered_pair(non_ordered_pair(X1,X1),non_ordered_pair(X1,X0)),estin)
| ~ ordered_pair_predicate(non_ordered_pair(non_ordered_pair(X1,X1),non_ordered_pair(X1,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1195])]) ).
fof(f1064,plain,
( spl0_106
<=> ! [X3] :
( ~ ordered_pair_predicate(X3)
| ~ little_set(X3)
| member(X3,estin)
| ~ member(first(X3),second(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_106])]) ).
fof(f1459,plain,
( ! [X0,X1] :
( ~ little_set(X0)
| ~ member(first(non_ordered_pair(non_ordered_pair(X1,X1),non_ordered_pair(X1,X0))),X0)
| ~ little_set(X1)
| ~ little_set(non_ordered_pair(non_ordered_pair(X1,X1),non_ordered_pair(X1,X0)))
| member(non_ordered_pair(non_ordered_pair(X1,X1),non_ordered_pair(X1,X0)),estin)
| ~ ordered_pair_predicate(non_ordered_pair(non_ordered_pair(X1,X1),non_ordered_pair(X1,X0))) )
| ~ spl0_106
| ~ spl0_128 ),
inference(resolution,[],[f1402,f1065]) ).
fof(f1065,plain,
( ! [X3] :
( ~ member(first(X3),second(X3))
| ~ little_set(X3)
| member(X3,estin)
| ~ ordered_pair_predicate(X3) )
| ~ spl0_106 ),
inference(avatar_component_clause,[],[f1064]) ).
fof(f34883,plain,
( spl0_1194
| ~ spl0_293
| ~ spl0_355 ),
inference(avatar_split_clause,[],[f4047,f3925,f3479,f34881]) ).
fof(f34881,plain,
( spl0_1194
<=> ! [X0] : estin = intersection(estin,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1194])]) ).
fof(f4047,plain,
( ! [X0] : estin = intersection(estin,X0)
| ~ spl0_293
| ~ spl0_355 ),
inference(resolution,[],[f3926,f3480]) ).
fof(f34814,plain,
( spl0_1193
| ~ spl0_97
| ~ spl0_139 ),
inference(avatar_split_clause,[],[f1743,f1642,f852,f34812]) ).
fof(f34812,plain,
( spl0_1193
<=> ! [X0,X3,X2,X1] :
( ~ member(X0,compose(compose(X1,X2),X3))
| little_set(f29(non_ordered_pair(non_ordered_pair(f29(X0,compose(X1,X2),X3),f29(X0,compose(X1,X2),X3)),non_ordered_pair(f29(X0,compose(X1,X2),X3),f31(X0,compose(X1,X2),X3))),X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1193])]) ).
fof(f1743,plain,
( ! [X2,X3,X0,X1] :
( ~ member(X0,compose(compose(X1,X2),X3))
| little_set(f29(non_ordered_pair(non_ordered_pair(f29(X0,compose(X1,X2),X3),f29(X0,compose(X1,X2),X3)),non_ordered_pair(f29(X0,compose(X1,X2),X3),f31(X0,compose(X1,X2),X3))),X1,X2)) )
| ~ spl0_97
| ~ spl0_139 ),
inference(resolution,[],[f1643,f853]) ).
fof(f34810,plain,
( spl0_1192
| ~ spl0_98
| ~ spl0_139 ),
inference(avatar_split_clause,[],[f1742,f1642,f856,f34808]) ).
fof(f34808,plain,
( spl0_1192
<=> ! [X0,X3,X2,X1] :
( ~ member(X0,compose(compose(X1,X2),X3))
| little_set(f30(non_ordered_pair(non_ordered_pair(f29(X0,compose(X1,X2),X3),f29(X0,compose(X1,X2),X3)),non_ordered_pair(f29(X0,compose(X1,X2),X3),f31(X0,compose(X1,X2),X3))),X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1192])]) ).
fof(f1742,plain,
( ! [X2,X3,X0,X1] :
( ~ member(X0,compose(compose(X1,X2),X3))
| little_set(f30(non_ordered_pair(non_ordered_pair(f29(X0,compose(X1,X2),X3),f29(X0,compose(X1,X2),X3)),non_ordered_pair(f29(X0,compose(X1,X2),X3),f31(X0,compose(X1,X2),X3))),X1,X2)) )
| ~ spl0_98
| ~ spl0_139 ),
inference(resolution,[],[f1643,f857]) ).
fof(f34806,plain,
( spl0_1191
| ~ spl0_99
| ~ spl0_139 ),
inference(avatar_split_clause,[],[f1741,f1642,f860,f34804]) ).
fof(f34804,plain,
( spl0_1191
<=> ! [X0,X3,X2,X1] :
( ~ member(X0,compose(compose(X1,X2),X3))
| little_set(f31(non_ordered_pair(non_ordered_pair(f29(X0,compose(X1,X2),X3),f29(X0,compose(X1,X2),X3)),non_ordered_pair(f29(X0,compose(X1,X2),X3),f31(X0,compose(X1,X2),X3))),X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1191])]) ).
fof(f1741,plain,
( ! [X2,X3,X0,X1] :
( ~ member(X0,compose(compose(X1,X2),X3))
| little_set(f31(non_ordered_pair(non_ordered_pair(f29(X0,compose(X1,X2),X3),f29(X0,compose(X1,X2),X3)),non_ordered_pair(f29(X0,compose(X1,X2),X3),f31(X0,compose(X1,X2),X3))),X1,X2)) )
| ~ spl0_99
| ~ spl0_139 ),
inference(resolution,[],[f1643,f861]) ).
fof(f34802,plain,
( spl0_1190
| ~ spl0_96
| ~ spl0_139 ),
inference(avatar_split_clause,[],[f1739,f1642,f848,f34800]) ).
fof(f34800,plain,
( spl0_1190
<=> ! [X0,X3,X2,X1] :
( ~ member(X0,compose(apply(X1,X2),X3))
| ordered_pair_predicate(f28(non_ordered_pair(non_ordered_pair(f29(X0,apply(X1,X2),X3),f29(X0,apply(X1,X2),X3)),non_ordered_pair(f29(X0,apply(X1,X2),X3),f31(X0,apply(X1,X2),X3))),X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1190])]) ).
fof(f1739,plain,
( ! [X2,X3,X0,X1] :
( ~ member(X0,compose(apply(X1,X2),X3))
| ordered_pair_predicate(f28(non_ordered_pair(non_ordered_pair(f29(X0,apply(X1,X2),X3),f29(X0,apply(X1,X2),X3)),non_ordered_pair(f29(X0,apply(X1,X2),X3),f31(X0,apply(X1,X2),X3))),X1,X2)) )
| ~ spl0_96
| ~ spl0_139 ),
inference(resolution,[],[f1643,f849]) ).
fof(f34798,plain,
( spl0_1189
| ~ spl0_94
| ~ spl0_139 ),
inference(avatar_split_clause,[],[f1733,f1642,f840,f34796]) ).
fof(f34796,plain,
( spl0_1189
<=> ! [X0,X3,X2,X1] :
( ~ member(X0,compose(image(X1,X2),X3))
| ordered_pair_predicate(f22(non_ordered_pair(non_ordered_pair(f29(X0,image(X1,X2),X3),f29(X0,image(X1,X2),X3)),non_ordered_pair(f29(X0,image(X1,X2),X3),f31(X0,image(X1,X2),X3))),X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1189])]) ).
fof(f1733,plain,
( ! [X2,X3,X0,X1] :
( ~ member(X0,compose(image(X1,X2),X3))
| ordered_pair_predicate(f22(non_ordered_pair(non_ordered_pair(f29(X0,image(X1,X2),X3),f29(X0,image(X1,X2),X3)),non_ordered_pair(f29(X0,image(X1,X2),X3),f31(X0,image(X1,X2),X3))),X1,X2)) )
| ~ spl0_94
| ~ spl0_139 ),
inference(resolution,[],[f1643,f841]) ).
fof(f34794,plain,
( spl0_1188
| ~ spl0_97
| ~ spl0_138 ),
inference(avatar_split_clause,[],[f1703,f1638,f852,f34792]) ).
fof(f34792,plain,
( spl0_1188
<=> ! [X0,X3,X2,X1] :
( ~ member(X0,compose(X1,compose(X2,X3)))
| little_set(f29(non_ordered_pair(non_ordered_pair(f31(X0,X1,compose(X2,X3)),f31(X0,X1,compose(X2,X3))),non_ordered_pair(f31(X0,X1,compose(X2,X3)),f30(X0,X1,compose(X2,X3)))),X2,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1188])]) ).
fof(f1703,plain,
( ! [X2,X3,X0,X1] :
( ~ member(X0,compose(X1,compose(X2,X3)))
| little_set(f29(non_ordered_pair(non_ordered_pair(f31(X0,X1,compose(X2,X3)),f31(X0,X1,compose(X2,X3))),non_ordered_pair(f31(X0,X1,compose(X2,X3)),f30(X0,X1,compose(X2,X3)))),X2,X3)) )
| ~ spl0_97
| ~ spl0_138 ),
inference(resolution,[],[f1639,f853]) ).
fof(f34790,plain,
( spl0_1187
| ~ spl0_98
| ~ spl0_138 ),
inference(avatar_split_clause,[],[f1702,f1638,f856,f34788]) ).
fof(f34788,plain,
( spl0_1187
<=> ! [X0,X3,X2,X1] :
( ~ member(X0,compose(X1,compose(X2,X3)))
| little_set(f30(non_ordered_pair(non_ordered_pair(f31(X0,X1,compose(X2,X3)),f31(X0,X1,compose(X2,X3))),non_ordered_pair(f31(X0,X1,compose(X2,X3)),f30(X0,X1,compose(X2,X3)))),X2,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1187])]) ).
fof(f1702,plain,
( ! [X2,X3,X0,X1] :
( ~ member(X0,compose(X1,compose(X2,X3)))
| little_set(f30(non_ordered_pair(non_ordered_pair(f31(X0,X1,compose(X2,X3)),f31(X0,X1,compose(X2,X3))),non_ordered_pair(f31(X0,X1,compose(X2,X3)),f30(X0,X1,compose(X2,X3)))),X2,X3)) )
| ~ spl0_98
| ~ spl0_138 ),
inference(resolution,[],[f1639,f857]) ).
fof(f34784,plain,
( spl0_1186
| ~ spl0_99
| ~ spl0_138 ),
inference(avatar_split_clause,[],[f1701,f1638,f860,f34782]) ).
fof(f34782,plain,
( spl0_1186
<=> ! [X0,X3,X2,X1] :
( ~ member(X0,compose(X1,compose(X2,X3)))
| little_set(f31(non_ordered_pair(non_ordered_pair(f31(X0,X1,compose(X2,X3)),f31(X0,X1,compose(X2,X3))),non_ordered_pair(f31(X0,X1,compose(X2,X3)),f30(X0,X1,compose(X2,X3)))),X2,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1186])]) ).
fof(f1701,plain,
( ! [X2,X3,X0,X1] :
( ~ member(X0,compose(X1,compose(X2,X3)))
| little_set(f31(non_ordered_pair(non_ordered_pair(f31(X0,X1,compose(X2,X3)),f31(X0,X1,compose(X2,X3))),non_ordered_pair(f31(X0,X1,compose(X2,X3)),f30(X0,X1,compose(X2,X3)))),X2,X3)) )
| ~ spl0_99
| ~ spl0_138 ),
inference(resolution,[],[f1639,f861]) ).
fof(f34780,plain,
( spl0_1185
| ~ spl0_96
| ~ spl0_138 ),
inference(avatar_split_clause,[],[f1699,f1638,f848,f34778]) ).
fof(f34778,plain,
( spl0_1185
<=> ! [X0,X3,X2,X1] :
( ~ member(X0,compose(X1,apply(X2,X3)))
| ordered_pair_predicate(f28(non_ordered_pair(non_ordered_pair(f31(X0,X1,apply(X2,X3)),f31(X0,X1,apply(X2,X3))),non_ordered_pair(f31(X0,X1,apply(X2,X3)),f30(X0,X1,apply(X2,X3)))),X2,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1185])]) ).
fof(f1699,plain,
( ! [X2,X3,X0,X1] :
( ~ member(X0,compose(X1,apply(X2,X3)))
| ordered_pair_predicate(f28(non_ordered_pair(non_ordered_pair(f31(X0,X1,apply(X2,X3)),f31(X0,X1,apply(X2,X3))),non_ordered_pair(f31(X0,X1,apply(X2,X3)),f30(X0,X1,apply(X2,X3)))),X2,X3)) )
| ~ spl0_96
| ~ spl0_138 ),
inference(resolution,[],[f1639,f849]) ).
fof(f34776,plain,
( spl0_1184
| ~ spl0_94
| ~ spl0_138 ),
inference(avatar_split_clause,[],[f1693,f1638,f840,f34774]) ).
fof(f34774,plain,
( spl0_1184
<=> ! [X0,X3,X2,X1] :
( ~ member(X0,compose(X1,image(X2,X3)))
| ordered_pair_predicate(f22(non_ordered_pair(non_ordered_pair(f31(X0,X1,image(X2,X3)),f31(X0,X1,image(X2,X3))),non_ordered_pair(f31(X0,X1,image(X2,X3)),f30(X0,X1,image(X2,X3)))),X2,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1184])]) ).
fof(f1693,plain,
( ! [X2,X3,X0,X1] :
( ~ member(X0,compose(X1,image(X2,X3)))
| ordered_pair_predicate(f22(non_ordered_pair(non_ordered_pair(f31(X0,X1,image(X2,X3)),f31(X0,X1,image(X2,X3))),non_ordered_pair(f31(X0,X1,image(X2,X3)),f30(X0,X1,image(X2,X3)))),X2,X3)) )
| ~ spl0_94
| ~ spl0_138 ),
inference(resolution,[],[f1639,f841]) ).
fof(f34772,plain,
( spl0_1183
| ~ spl0_114
| ~ spl0_129 ),
inference(avatar_split_clause,[],[f1467,f1405,f1163,f34770]) ).
fof(f34770,plain,
( spl0_1183
<=> ! [X2,X0,X1] :
( ~ little_set(X0)
| ~ member(f1(X1,first(non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X0)))),X2)
| ~ little_set(X2)
| first(non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X0))) = X1
| ~ member(f1(X1,first(non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X0)))),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1183])]) ).
fof(f1467,plain,
( ! [X2,X0,X1] :
( ~ little_set(X0)
| ~ member(f1(X1,first(non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X0)))),X2)
| ~ little_set(X2)
| first(non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X0))) = X1
| ~ member(f1(X1,first(non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X0)))),X1) )
| ~ spl0_114
| ~ spl0_129 ),
inference(resolution,[],[f1406,f1164]) ).
fof(f34768,plain,
( spl0_1182
| ~ spl0_114
| ~ spl0_128 ),
inference(avatar_split_clause,[],[f1458,f1401,f1163,f34766]) ).
fof(f34766,plain,
( spl0_1182
<=> ! [X2,X0,X1] :
( ~ little_set(X0)
| ~ member(f1(X1,second(non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X0)))),X0)
| ~ little_set(X2)
| second(non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X0))) = X1
| ~ member(f1(X1,second(non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X0)))),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1182])]) ).
fof(f1458,plain,
( ! [X2,X0,X1] :
( ~ little_set(X0)
| ~ member(f1(X1,second(non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X0)))),X0)
| ~ little_set(X2)
| second(non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X0))) = X1
| ~ member(f1(X1,second(non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X0)))),X1) )
| ~ spl0_114
| ~ spl0_128 ),
inference(resolution,[],[f1402,f1164]) ).
fof(f33725,plain,
( spl0_1181
| ~ spl0_93
| ~ spl0_145 ),
inference(avatar_split_clause,[],[f1875,f1786,f836,f33723]) ).
fof(f1875,plain,
( ! [X2,X0,X1] :
( ~ member(X0,rotate_right(X1))
| ~ member(X1,X2)
| member(non_ordered_pair(non_ordered_pair(f10(X0,X1),f10(X0,X1)),non_ordered_pair(f10(X0,X1),non_ordered_pair(non_ordered_pair(f11(X0,X1),f11(X0,X1)),non_ordered_pair(f11(X0,X1),f9(X0,X1))))),sigma(X2)) )
| ~ spl0_93
| ~ spl0_145 ),
inference(resolution,[],[f1787,f837]) ).
fof(f33721,plain,
( spl0_1180
| ~ spl0_93
| ~ spl0_144 ),
inference(avatar_split_clause,[],[f1832,f1782,f836,f33719]) ).
fof(f1832,plain,
( ! [X2,X0,X1] :
( ~ member(X0,flip_range_of(X1))
| ~ member(X1,X2)
| member(non_ordered_pair(non_ordered_pair(f12(X0,X1),f12(X0,X1)),non_ordered_pair(f12(X0,X1),non_ordered_pair(non_ordered_pair(f14(X0,X1),f14(X0,X1)),non_ordered_pair(f14(X0,X1),f13(X0,X1))))),sigma(X2)) )
| ~ spl0_93
| ~ spl0_144 ),
inference(resolution,[],[f1783,f837]) ).
fof(f33717,plain,
( spl0_1179
| ~ spl0_75
| ~ spl0_139 ),
inference(avatar_split_clause,[],[f1721,f1642,f632,f33715]) ).
fof(f33715,plain,
( spl0_1179
<=> ! [X0,X3,X2,X1] :
( ~ member(X0,compose(cross_product(X1,X2),X3))
| member(first(non_ordered_pair(non_ordered_pair(f29(X0,cross_product(X1,X2),X3),f29(X0,cross_product(X1,X2),X3)),non_ordered_pair(f29(X0,cross_product(X1,X2),X3),f31(X0,cross_product(X1,X2),X3)))),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1179])]) ).
fof(f1721,plain,
( ! [X2,X3,X0,X1] :
( ~ member(X0,compose(cross_product(X1,X2),X3))
| member(first(non_ordered_pair(non_ordered_pair(f29(X0,cross_product(X1,X2),X3),f29(X0,cross_product(X1,X2),X3)),non_ordered_pair(f29(X0,cross_product(X1,X2),X3),f31(X0,cross_product(X1,X2),X3)))),X1) )
| ~ spl0_75
| ~ spl0_139 ),
inference(resolution,[],[f1643,f633]) ).
fof(f33713,plain,
( spl0_1178
| ~ spl0_77
| ~ spl0_139 ),
inference(avatar_split_clause,[],[f1720,f1642,f640,f33711]) ).
fof(f33711,plain,
( spl0_1178
<=> ! [X0,X3,X2,X1] :
( ~ member(X0,compose(cross_product(X1,X2),X3))
| member(second(non_ordered_pair(non_ordered_pair(f29(X0,cross_product(X1,X2),X3),f29(X0,cross_product(X1,X2),X3)),non_ordered_pair(f29(X0,cross_product(X1,X2),X3),f31(X0,cross_product(X1,X2),X3)))),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1178])]) ).
fof(f1720,plain,
( ! [X2,X3,X0,X1] :
( ~ member(X0,compose(cross_product(X1,X2),X3))
| member(second(non_ordered_pair(non_ordered_pair(f29(X0,cross_product(X1,X2),X3),f29(X0,cross_product(X1,X2),X3)),non_ordered_pair(f29(X0,cross_product(X1,X2),X3),f31(X0,cross_product(X1,X2),X3)))),X2) )
| ~ spl0_77
| ~ spl0_139 ),
inference(resolution,[],[f1643,f641]) ).
fof(f33709,plain,
( spl0_1177
| ~ spl0_75
| ~ spl0_138 ),
inference(avatar_split_clause,[],[f1681,f1638,f632,f33707]) ).
fof(f33707,plain,
( spl0_1177
<=> ! [X0,X3,X2,X1] :
( ~ member(X0,compose(X1,cross_product(X2,X3)))
| member(first(non_ordered_pair(non_ordered_pair(f31(X0,X1,cross_product(X2,X3)),f31(X0,X1,cross_product(X2,X3))),non_ordered_pair(f31(X0,X1,cross_product(X2,X3)),f30(X0,X1,cross_product(X2,X3))))),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1177])]) ).
fof(f1681,plain,
( ! [X2,X3,X0,X1] :
( ~ member(X0,compose(X1,cross_product(X2,X3)))
| member(first(non_ordered_pair(non_ordered_pair(f31(X0,X1,cross_product(X2,X3)),f31(X0,X1,cross_product(X2,X3))),non_ordered_pair(f31(X0,X1,cross_product(X2,X3)),f30(X0,X1,cross_product(X2,X3))))),X2) )
| ~ spl0_75
| ~ spl0_138 ),
inference(resolution,[],[f1639,f633]) ).
fof(f33705,plain,
( spl0_1176
| ~ spl0_77
| ~ spl0_138 ),
inference(avatar_split_clause,[],[f1680,f1638,f640,f33703]) ).
fof(f33703,plain,
( spl0_1176
<=> ! [X0,X3,X2,X1] :
( ~ member(X0,compose(X1,cross_product(X2,X3)))
| member(second(non_ordered_pair(non_ordered_pair(f31(X0,X1,cross_product(X2,X3)),f31(X0,X1,cross_product(X2,X3))),non_ordered_pair(f31(X0,X1,cross_product(X2,X3)),f30(X0,X1,cross_product(X2,X3))))),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1176])]) ).
fof(f1680,plain,
( ! [X2,X3,X0,X1] :
( ~ member(X0,compose(X1,cross_product(X2,X3)))
| member(second(non_ordered_pair(non_ordered_pair(f31(X0,X1,cross_product(X2,X3)),f31(X0,X1,cross_product(X2,X3))),non_ordered_pair(f31(X0,X1,cross_product(X2,X3)),f30(X0,X1,cross_product(X2,X3))))),X3) )
| ~ spl0_77
| ~ spl0_138 ),
inference(resolution,[],[f1639,f641]) ).
fof(f33701,plain,
( spl0_1175
| ~ spl0_95
| ~ spl0_136 ),
inference(avatar_split_clause,[],[f1624,f1552,f844,f33699]) ).
fof(f33699,plain,
( spl0_1175
<=> ! [X4,X0,X3,X2,X1] :
( ~ closed(X0,X1)
| ~ maps(X2,range_of(X3),X0)
| homomorphism(X2,range_of(X3),X4,X0,X1)
| ~ closed(range_of(X3),X4)
| f33(X2,range_of(X3),X4,X0,X1) = second(f27(f33(X2,range_of(X3),X4,X0,X1),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1175])]) ).
fof(f1624,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ closed(X0,X1)
| ~ maps(X2,range_of(X3),X0)
| homomorphism(X2,range_of(X3),X4,X0,X1)
| ~ closed(range_of(X3),X4)
| f33(X2,range_of(X3),X4,X0,X1) = second(f27(f33(X2,range_of(X3),X4,X0,X1),X3)) )
| ~ spl0_95
| ~ spl0_136 ),
inference(resolution,[],[f1553,f845]) ).
fof(f33697,plain,
( spl0_1174
| ~ spl0_91
| ~ spl0_136 ),
inference(avatar_split_clause,[],[f1608,f1552,f828,f33695]) ).
fof(f33695,plain,
( spl0_1174
<=> ! [X4,X0,X3,X2,X1] :
( ~ closed(X0,X1)
| ~ maps(X2,domain_of(X3),X0)
| homomorphism(X2,domain_of(X3),X4,X0,X1)
| ~ closed(domain_of(X3),X4)
| f33(X2,domain_of(X3),X4,X0,X1) = first(f8(f33(X2,domain_of(X3),X4,X0,X1),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1174])]) ).
fof(f1608,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ closed(X0,X1)
| ~ maps(X2,domain_of(X3),X0)
| homomorphism(X2,domain_of(X3),X4,X0,X1)
| ~ closed(domain_of(X3),X4)
| f33(X2,domain_of(X3),X4,X0,X1) = first(f8(f33(X2,domain_of(X3),X4,X0,X1),X3)) )
| ~ spl0_91
| ~ spl0_136 ),
inference(resolution,[],[f1553,f829]) ).
fof(f33693,plain,
( spl0_1173
| ~ spl0_95
| ~ spl0_134 ),
inference(avatar_split_clause,[],[f1585,f1544,f844,f33691]) ).
fof(f33691,plain,
( spl0_1173
<=> ! [X4,X0,X3,X2,X1] :
( ~ closed(X0,X1)
| ~ maps(X2,range_of(X3),X0)
| homomorphism(X2,range_of(X3),X4,X0,X1)
| ~ closed(range_of(X3),X4)
| f32(X2,range_of(X3),X4,X0,X1) = second(f27(f32(X2,range_of(X3),X4,X0,X1),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1173])]) ).
fof(f1585,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ closed(X0,X1)
| ~ maps(X2,range_of(X3),X0)
| homomorphism(X2,range_of(X3),X4,X0,X1)
| ~ closed(range_of(X3),X4)
| f32(X2,range_of(X3),X4,X0,X1) = second(f27(f32(X2,range_of(X3),X4,X0,X1),X3)) )
| ~ spl0_95
| ~ spl0_134 ),
inference(resolution,[],[f1545,f845]) ).
fof(f33606,plain,
( spl0_1172
| ~ spl0_91
| ~ spl0_134 ),
inference(avatar_split_clause,[],[f1569,f1544,f828,f33604]) ).
fof(f33604,plain,
( spl0_1172
<=> ! [X4,X0,X3,X2,X1] :
( ~ closed(X0,X1)
| ~ maps(X2,domain_of(X3),X0)
| homomorphism(X2,domain_of(X3),X4,X0,X1)
| ~ closed(domain_of(X3),X4)
| f32(X2,domain_of(X3),X4,X0,X1) = first(f8(f32(X2,domain_of(X3),X4,X0,X1),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1172])]) ).
fof(f1569,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ closed(X0,X1)
| ~ maps(X2,domain_of(X3),X0)
| homomorphism(X2,domain_of(X3),X4,X0,X1)
| ~ closed(domain_of(X3),X4)
| f32(X2,domain_of(X3),X4,X0,X1) = first(f8(f32(X2,domain_of(X3),X4,X0,X1),X3)) )
| ~ spl0_91
| ~ spl0_134 ),
inference(resolution,[],[f1545,f829]) ).
fof(f33602,plain,
( spl0_1171
| ~ spl0_111
| ~ spl0_133 ),
inference(avatar_split_clause,[],[f1533,f1487,f1085,f33600]) ).
fof(f33600,plain,
( spl0_1171
<=> ! [X2,X0,X1] :
( ~ little_set(X0)
| member(X0,converse(second(f28(non_ordered_pair(non_ordered_pair(second(X0),second(X0)),non_ordered_pair(second(X0),first(X0))),X1,X2))))
| ~ ordered_pair_predicate(X0)
| ~ member(non_ordered_pair(non_ordered_pair(second(X0),second(X0)),non_ordered_pair(second(X0),first(X0))),apply(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1171])]) ).
fof(f1533,plain,
( ! [X2,X0,X1] :
( ~ little_set(X0)
| member(X0,converse(second(f28(non_ordered_pair(non_ordered_pair(second(X0),second(X0)),non_ordered_pair(second(X0),first(X0))),X1,X2))))
| ~ ordered_pair_predicate(X0)
| ~ member(non_ordered_pair(non_ordered_pair(second(X0),second(X0)),non_ordered_pair(second(X0),first(X0))),apply(X1,X2)) )
| ~ spl0_111
| ~ spl0_133 ),
inference(resolution,[],[f1488,f1086]) ).
fof(f33598,plain,
( spl0_1170
| ~ spl0_111
| ~ spl0_131 ),
inference(avatar_split_clause,[],[f1490,f1479,f1085,f33596]) ).
fof(f33596,plain,
( spl0_1170
<=> ! [X2,X0,X1] :
( f28(X0,X1,X2) = non_ordered_pair(non_ordered_pair(f6(X0,f28(X0,X1,X2)),f6(X0,f28(X0,X1,X2))),non_ordered_pair(f6(X0,f28(X0,X1,X2)),f7(X0,f28(X0,X1,X2))))
| ~ member(X0,apply(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1170])]) ).
fof(f1490,plain,
( ! [X2,X0,X1] :
( f28(X0,X1,X2) = non_ordered_pair(non_ordered_pair(f6(X0,f28(X0,X1,X2)),f6(X0,f28(X0,X1,X2))),non_ordered_pair(f6(X0,f28(X0,X1,X2)),f7(X0,f28(X0,X1,X2))))
| ~ member(X0,apply(X1,X2)) )
| ~ spl0_111
| ~ spl0_131 ),
inference(resolution,[],[f1480,f1086]) ).
fof(f33594,plain,
( spl0_1169
| ~ spl0_95
| ~ spl0_122 ),
inference(avatar_split_clause,[],[f1373,f1291,f844,f33592]) ).
fof(f33592,plain,
( spl0_1169
<=> ! [X0] :
( single_valued_set(range_of(X0))
| non_ordered_pair(non_ordered_pair(f19(range_of(X0)),f19(range_of(X0))),non_ordered_pair(f19(range_of(X0)),f21(range_of(X0)))) = second(f27(non_ordered_pair(non_ordered_pair(f19(range_of(X0)),f19(range_of(X0))),non_ordered_pair(f19(range_of(X0)),f21(range_of(X0)))),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1169])]) ).
fof(f1373,plain,
( ! [X0] :
( single_valued_set(range_of(X0))
| non_ordered_pair(non_ordered_pair(f19(range_of(X0)),f19(range_of(X0))),non_ordered_pair(f19(range_of(X0)),f21(range_of(X0)))) = second(f27(non_ordered_pair(non_ordered_pair(f19(range_of(X0)),f19(range_of(X0))),non_ordered_pair(f19(range_of(X0)),f21(range_of(X0)))),X0)) )
| ~ spl0_95
| ~ spl0_122 ),
inference(resolution,[],[f1292,f845]) ).
fof(f33590,plain,
( spl0_1168
| ~ spl0_91
| ~ spl0_122 ),
inference(avatar_split_clause,[],[f1357,f1291,f828,f33588]) ).
fof(f33588,plain,
( spl0_1168
<=> ! [X0] :
( single_valued_set(domain_of(X0))
| non_ordered_pair(non_ordered_pair(f19(domain_of(X0)),f19(domain_of(X0))),non_ordered_pair(f19(domain_of(X0)),f21(domain_of(X0)))) = first(f8(non_ordered_pair(non_ordered_pair(f19(domain_of(X0)),f19(domain_of(X0))),non_ordered_pair(f19(domain_of(X0)),f21(domain_of(X0)))),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1168])]) ).
fof(f1357,plain,
( ! [X0] :
( single_valued_set(domain_of(X0))
| non_ordered_pair(non_ordered_pair(f19(domain_of(X0)),f19(domain_of(X0))),non_ordered_pair(f19(domain_of(X0)),f21(domain_of(X0)))) = first(f8(non_ordered_pair(non_ordered_pair(f19(domain_of(X0)),f19(domain_of(X0))),non_ordered_pair(f19(domain_of(X0)),f21(domain_of(X0)))),X0)) )
| ~ spl0_91
| ~ spl0_122 ),
inference(resolution,[],[f1292,f829]) ).
fof(f33586,plain,
( spl0_1167
| ~ spl0_95
| ~ spl0_121 ),
inference(avatar_split_clause,[],[f1331,f1287,f844,f33584]) ).
fof(f33584,plain,
( spl0_1167
<=> ! [X0] :
( single_valued_set(range_of(X0))
| non_ordered_pair(non_ordered_pair(f19(range_of(X0)),f19(range_of(X0))),non_ordered_pair(f19(range_of(X0)),f20(range_of(X0)))) = second(f27(non_ordered_pair(non_ordered_pair(f19(range_of(X0)),f19(range_of(X0))),non_ordered_pair(f19(range_of(X0)),f20(range_of(X0)))),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1167])]) ).
fof(f1331,plain,
( ! [X0] :
( single_valued_set(range_of(X0))
| non_ordered_pair(non_ordered_pair(f19(range_of(X0)),f19(range_of(X0))),non_ordered_pair(f19(range_of(X0)),f20(range_of(X0)))) = second(f27(non_ordered_pair(non_ordered_pair(f19(range_of(X0)),f19(range_of(X0))),non_ordered_pair(f19(range_of(X0)),f20(range_of(X0)))),X0)) )
| ~ spl0_95
| ~ spl0_121 ),
inference(resolution,[],[f1288,f845]) ).
fof(f33582,plain,
( spl0_1166
| ~ spl0_91
| ~ spl0_121 ),
inference(avatar_split_clause,[],[f1315,f1287,f828,f33580]) ).
fof(f33580,plain,
( spl0_1166
<=> ! [X0] :
( single_valued_set(domain_of(X0))
| non_ordered_pair(non_ordered_pair(f19(domain_of(X0)),f19(domain_of(X0))),non_ordered_pair(f19(domain_of(X0)),f20(domain_of(X0)))) = first(f8(non_ordered_pair(non_ordered_pair(f19(domain_of(X0)),f19(domain_of(X0))),non_ordered_pair(f19(domain_of(X0)),f20(domain_of(X0)))),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1166])]) ).
fof(f1315,plain,
( ! [X0] :
( single_valued_set(domain_of(X0))
| non_ordered_pair(non_ordered_pair(f19(domain_of(X0)),f19(domain_of(X0))),non_ordered_pair(f19(domain_of(X0)),f20(domain_of(X0)))) = first(f8(non_ordered_pair(non_ordered_pair(f19(domain_of(X0)),f19(domain_of(X0))),non_ordered_pair(f19(domain_of(X0)),f20(domain_of(X0)))),X0)) )
| ~ spl0_91
| ~ spl0_121 ),
inference(resolution,[],[f1288,f829]) ).
fof(f32785,plain,
( spl0_1165
| ~ spl0_51
| ~ spl0_139 ),
inference(avatar_split_clause,[],[f1716,f1642,f426,f32783]) ).
fof(f32783,plain,
( spl0_1165
<=> ! [X0,X3,X2,X1] :
( ~ member(X0,compose(intersection(X1,X2),X3))
| member(non_ordered_pair(non_ordered_pair(f29(X0,intersection(X1,X2),X3),f29(X0,intersection(X1,X2),X3)),non_ordered_pair(f29(X0,intersection(X1,X2),X3),f31(X0,intersection(X1,X2),X3))),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1165])]) ).
fof(f1716,plain,
( ! [X2,X3,X0,X1] :
( ~ member(X0,compose(intersection(X1,X2),X3))
| member(non_ordered_pair(non_ordered_pair(f29(X0,intersection(X1,X2),X3),f29(X0,intersection(X1,X2),X3)),non_ordered_pair(f29(X0,intersection(X1,X2),X3),f31(X0,intersection(X1,X2),X3))),X1) )
| ~ spl0_51
| ~ spl0_139 ),
inference(resolution,[],[f1643,f427]) ).
fof(f32781,plain,
( spl0_1164
| ~ spl0_52
| ~ spl0_139 ),
inference(avatar_split_clause,[],[f1715,f1642,f430,f32779]) ).
fof(f32779,plain,
( spl0_1164
<=> ! [X0,X3,X2,X1] :
( ~ member(X0,compose(intersection(X1,X2),X3))
| member(non_ordered_pair(non_ordered_pair(f29(X0,intersection(X1,X2),X3),f29(X0,intersection(X1,X2),X3)),non_ordered_pair(f29(X0,intersection(X1,X2),X3),f31(X0,intersection(X1,X2),X3))),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1164])]) ).
fof(f1715,plain,
( ! [X2,X3,X0,X1] :
( ~ member(X0,compose(intersection(X1,X2),X3))
| member(non_ordered_pair(non_ordered_pair(f29(X0,intersection(X1,X2),X3),f29(X0,intersection(X1,X2),X3)),non_ordered_pair(f29(X0,intersection(X1,X2),X3),f31(X0,intersection(X1,X2),X3))),X2) )
| ~ spl0_52
| ~ spl0_139 ),
inference(resolution,[],[f1643,f431]) ).
fof(f32777,plain,
( spl0_1163
| ~ spl0_51
| ~ spl0_138 ),
inference(avatar_split_clause,[],[f1676,f1638,f426,f32775]) ).
fof(f32775,plain,
( spl0_1163
<=> ! [X0,X3,X2,X1] :
( ~ member(X0,compose(X1,intersection(X2,X3)))
| member(non_ordered_pair(non_ordered_pair(f31(X0,X1,intersection(X2,X3)),f31(X0,X1,intersection(X2,X3))),non_ordered_pair(f31(X0,X1,intersection(X2,X3)),f30(X0,X1,intersection(X2,X3)))),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1163])]) ).
fof(f1676,plain,
( ! [X2,X3,X0,X1] :
( ~ member(X0,compose(X1,intersection(X2,X3)))
| member(non_ordered_pair(non_ordered_pair(f31(X0,X1,intersection(X2,X3)),f31(X0,X1,intersection(X2,X3))),non_ordered_pair(f31(X0,X1,intersection(X2,X3)),f30(X0,X1,intersection(X2,X3)))),X2) )
| ~ spl0_51
| ~ spl0_138 ),
inference(resolution,[],[f1639,f427]) ).
fof(f32773,plain,
( spl0_1162
| ~ spl0_52
| ~ spl0_138 ),
inference(avatar_split_clause,[],[f1675,f1638,f430,f32771]) ).
fof(f32771,plain,
( spl0_1162
<=> ! [X0,X3,X2,X1] :
( ~ member(X0,compose(X1,intersection(X2,X3)))
| member(non_ordered_pair(non_ordered_pair(f31(X0,X1,intersection(X2,X3)),f31(X0,X1,intersection(X2,X3))),non_ordered_pair(f31(X0,X1,intersection(X2,X3)),f30(X0,X1,intersection(X2,X3)))),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1162])]) ).
fof(f1675,plain,
( ! [X2,X3,X0,X1] :
( ~ member(X0,compose(X1,intersection(X2,X3)))
| member(non_ordered_pair(non_ordered_pair(f31(X0,X1,intersection(X2,X3)),f31(X0,X1,intersection(X2,X3))),non_ordered_pair(f31(X0,X1,intersection(X2,X3)),f30(X0,X1,intersection(X2,X3)))),X3) )
| ~ spl0_52
| ~ spl0_138 ),
inference(resolution,[],[f1639,f431]) ).
fof(f32769,plain,
( spl0_1161
| ~ spl0_110
| ~ spl0_136 ),
inference(avatar_split_clause,[],[f1628,f1552,f1081,f32767]) ).
fof(f32767,plain,
( spl0_1161
<=> ! [X2,X4,X0,X3,X5,X1] :
( ~ closed(X0,X1)
| ~ maps(X2,apply(X3,X4),X0)
| homomorphism(X2,apply(X3,X4),X5,X0,X1)
| ~ closed(apply(X3,X4),X5)
| first(f28(f33(X2,apply(X3,X4),X5,X0,X1),X3,X4)) = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1161])]) ).
fof(f1628,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ closed(X0,X1)
| ~ maps(X2,apply(X3,X4),X0)
| homomorphism(X2,apply(X3,X4),X5,X0,X1)
| ~ closed(apply(X3,X4),X5)
| first(f28(f33(X2,apply(X3,X4),X5,X0,X1),X3,X4)) = X4 )
| ~ spl0_110
| ~ spl0_136 ),
inference(resolution,[],[f1553,f1082]) ).
fof(f32765,plain,
( spl0_1160
| ~ spl0_110
| ~ spl0_134 ),
inference(avatar_split_clause,[],[f1589,f1544,f1081,f32763]) ).
fof(f32763,plain,
( spl0_1160
<=> ! [X2,X4,X0,X3,X5,X1] :
( ~ closed(X0,X1)
| ~ maps(X2,apply(X3,X4),X0)
| homomorphism(X2,apply(X3,X4),X5,X0,X1)
| ~ closed(apply(X3,X4),X5)
| first(f28(f32(X2,apply(X3,X4),X5,X0,X1),X3,X4)) = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1160])]) ).
fof(f1589,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ closed(X0,X1)
| ~ maps(X2,apply(X3,X4),X0)
| homomorphism(X2,apply(X3,X4),X5,X0,X1)
| ~ closed(apply(X3,X4),X5)
| first(f28(f32(X2,apply(X3,X4),X5,X0,X1),X3,X4)) = X4 )
| ~ spl0_110
| ~ spl0_134 ),
inference(resolution,[],[f1545,f1082]) ).
fof(f32700,plain,
( spl0_1159
| ~ spl0_102
| ~ spl0_133 ),
inference(avatar_split_clause,[],[f1536,f1487,f956,f32698]) ).
fof(f32698,plain,
( spl0_1159
<=> ! [X2,X0,X1] :
( ~ little_set(X0)
| member(X0,converse(intersection(X1,X2)))
| ~ ordered_pair_predicate(X0)
| ~ member(non_ordered_pair(non_ordered_pair(second(X0),second(X0)),non_ordered_pair(second(X0),first(X0))),X1)
| ~ member(non_ordered_pair(non_ordered_pair(second(X0),second(X0)),non_ordered_pair(second(X0),first(X0))),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1159])]) ).
fof(f1536,plain,
( ! [X2,X0,X1] :
( ~ little_set(X0)
| member(X0,converse(intersection(X1,X2)))
| ~ ordered_pair_predicate(X0)
| ~ member(non_ordered_pair(non_ordered_pair(second(X0),second(X0)),non_ordered_pair(second(X0),first(X0))),X1)
| ~ member(non_ordered_pair(non_ordered_pair(second(X0),second(X0)),non_ordered_pair(second(X0),first(X0))),X2) )
| ~ spl0_102
| ~ spl0_133 ),
inference(resolution,[],[f1488,f957]) ).
fof(f32694,plain,
( spl0_1158
| ~ spl0_35
| ~ spl0_139 ),
inference(avatar_split_clause,[],[f1722,f1642,f340,f32692]) ).
fof(f32692,plain,
( spl0_1158
<=> ! [X0,X3,X2,X1] :
( ~ member(X0,compose(cross_product(X1,X2),X3))
| ordered_pair_predicate(non_ordered_pair(non_ordered_pair(f29(X0,cross_product(X1,X2),X3),f29(X0,cross_product(X1,X2),X3)),non_ordered_pair(f29(X0,cross_product(X1,X2),X3),f31(X0,cross_product(X1,X2),X3)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1158])]) ).
fof(f1722,plain,
( ! [X2,X3,X0,X1] :
( ~ member(X0,compose(cross_product(X1,X2),X3))
| ordered_pair_predicate(non_ordered_pair(non_ordered_pair(f29(X0,cross_product(X1,X2),X3),f29(X0,cross_product(X1,X2),X3)),non_ordered_pair(f29(X0,cross_product(X1,X2),X3),f31(X0,cross_product(X1,X2),X3)))) )
| ~ spl0_35
| ~ spl0_139 ),
inference(resolution,[],[f1643,f341]) ).
fof(f32690,plain,
( spl0_1157
| ~ spl0_35
| ~ spl0_138 ),
inference(avatar_split_clause,[],[f1682,f1638,f340,f32688]) ).
fof(f32688,plain,
( spl0_1157
<=> ! [X0,X3,X2,X1] :
( ~ member(X0,compose(X1,cross_product(X2,X3)))
| ordered_pair_predicate(non_ordered_pair(non_ordered_pair(f31(X0,X1,cross_product(X2,X3)),f31(X0,X1,cross_product(X2,X3))),non_ordered_pair(f31(X0,X1,cross_product(X2,X3)),f30(X0,X1,cross_product(X2,X3))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1157])]) ).
fof(f1682,plain,
( ! [X2,X3,X0,X1] :
( ~ member(X0,compose(X1,cross_product(X2,X3)))
| ordered_pair_predicate(non_ordered_pair(non_ordered_pair(f31(X0,X1,cross_product(X2,X3)),f31(X0,X1,cross_product(X2,X3))),non_ordered_pair(f31(X0,X1,cross_product(X2,X3)),f30(X0,X1,cross_product(X2,X3))))) )
| ~ spl0_35
| ~ spl0_138 ),
inference(resolution,[],[f1639,f341]) ).
fof(f32418,plain,
( spl0_1156
| ~ spl0_61
| ~ spl0_360 ),
inference(avatar_split_clause,[],[f4705,f4226,f466,f32416]) ).
fof(f32416,plain,
( spl0_1156
<=> ! [X0,X1] : subset(intersection(X0,X1),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1156])]) ).
fof(f4705,plain,
( ! [X0,X1] : subset(intersection(X0,X1),X0)
| ~ spl0_61
| ~ spl0_360 ),
inference(duplicate_literal_removal,[],[f4643]) ).
fof(f4643,plain,
( ! [X0,X1] :
( subset(intersection(X0,X1),X0)
| subset(intersection(X0,X1),X0) )
| ~ spl0_61
| ~ spl0_360 ),
inference(resolution,[],[f4227,f467]) ).
fof(f31318,plain,
( spl0_1155
| ~ spl0_38
| ~ spl0_145 ),
inference(avatar_split_clause,[],[f1876,f1786,f353,f31316]) ).
fof(f31316,plain,
( spl0_1155
<=> ! [X0,X1] :
( ~ member(X0,rotate_right(X1))
| ordered_pair_predicate(non_ordered_pair(non_ordered_pair(f10(X0,X1),f10(X0,X1)),non_ordered_pair(f10(X0,X1),non_ordered_pair(non_ordered_pair(f11(X0,X1),f11(X0,X1)),non_ordered_pair(f11(X0,X1),f9(X0,X1))))))
| ~ relation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1155])]) ).
fof(f1876,plain,
( ! [X0,X1] :
( ~ member(X0,rotate_right(X1))
| ordered_pair_predicate(non_ordered_pair(non_ordered_pair(f10(X0,X1),f10(X0,X1)),non_ordered_pair(f10(X0,X1),non_ordered_pair(non_ordered_pair(f11(X0,X1),f11(X0,X1)),non_ordered_pair(f11(X0,X1),f9(X0,X1))))))
| ~ relation(X1) )
| ~ spl0_38
| ~ spl0_145 ),
inference(resolution,[],[f1787,f354]) ).
fof(f31314,plain,
( spl0_1154
| ~ spl0_38
| ~ spl0_144 ),
inference(avatar_split_clause,[],[f1833,f1782,f353,f31312]) ).
fof(f31312,plain,
( spl0_1154
<=> ! [X0,X1] :
( ~ member(X0,flip_range_of(X1))
| ordered_pair_predicate(non_ordered_pair(non_ordered_pair(f12(X0,X1),f12(X0,X1)),non_ordered_pair(f12(X0,X1),non_ordered_pair(non_ordered_pair(f14(X0,X1),f14(X0,X1)),non_ordered_pair(f14(X0,X1),f13(X0,X1))))))
| ~ relation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1154])]) ).
fof(f1833,plain,
( ! [X0,X1] :
( ~ member(X0,flip_range_of(X1))
| ordered_pair_predicate(non_ordered_pair(non_ordered_pair(f12(X0,X1),f12(X0,X1)),non_ordered_pair(f12(X0,X1),non_ordered_pair(non_ordered_pair(f14(X0,X1),f14(X0,X1)),non_ordered_pair(f14(X0,X1),f13(X0,X1))))))
| ~ relation(X1) )
| ~ spl0_38
| ~ spl0_144 ),
inference(resolution,[],[f1783,f354]) ).
fof(f31310,plain,
( spl0_1153
| ~ spl0_61
| ~ spl0_359 ),
inference(avatar_split_clause,[],[f4602,f4222,f466,f31308]) ).
fof(f31308,plain,
( spl0_1153
<=> ! [X0,X1] : subset(intersection(X0,X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1153])]) ).
fof(f4602,plain,
( ! [X0,X1] : subset(intersection(X0,X1),X1)
| ~ spl0_61
| ~ spl0_359 ),
inference(duplicate_literal_removal,[],[f4540]) ).
fof(f4540,plain,
( ! [X0,X1] :
( subset(intersection(X0,X1),X1)
| subset(intersection(X0,X1),X1) )
| ~ spl0_61
| ~ spl0_359 ),
inference(resolution,[],[f4223,f467]) ).
fof(f31306,plain,
( spl0_1152
| ~ spl0_97
| ~ spl0_136 ),
inference(avatar_split_clause,[],[f1632,f1552,f852,f31304]) ).
fof(f31304,plain,
( spl0_1152
<=> ! [X2,X4,X0,X3,X5,X1] :
( ~ closed(X0,X1)
| ~ maps(X2,compose(X3,X4),X0)
| homomorphism(X2,compose(X3,X4),X5,X0,X1)
| ~ closed(compose(X3,X4),X5)
| little_set(f29(f33(X2,compose(X3,X4),X5,X0,X1),X3,X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1152])]) ).
fof(f1632,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ closed(X0,X1)
| ~ maps(X2,compose(X3,X4),X0)
| homomorphism(X2,compose(X3,X4),X5,X0,X1)
| ~ closed(compose(X3,X4),X5)
| little_set(f29(f33(X2,compose(X3,X4),X5,X0,X1),X3,X4)) )
| ~ spl0_97
| ~ spl0_136 ),
inference(resolution,[],[f1553,f853]) ).
fof(f31302,plain,
( spl0_1151
| ~ spl0_98
| ~ spl0_136 ),
inference(avatar_split_clause,[],[f1631,f1552,f856,f31300]) ).
fof(f31300,plain,
( spl0_1151
<=> ! [X2,X4,X0,X3,X5,X1] :
( ~ closed(X0,X1)
| ~ maps(X2,compose(X3,X4),X0)
| homomorphism(X2,compose(X3,X4),X5,X0,X1)
| ~ closed(compose(X3,X4),X5)
| little_set(f30(f33(X2,compose(X3,X4),X5,X0,X1),X3,X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1151])]) ).
fof(f1631,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ closed(X0,X1)
| ~ maps(X2,compose(X3,X4),X0)
| homomorphism(X2,compose(X3,X4),X5,X0,X1)
| ~ closed(compose(X3,X4),X5)
| little_set(f30(f33(X2,compose(X3,X4),X5,X0,X1),X3,X4)) )
| ~ spl0_98
| ~ spl0_136 ),
inference(resolution,[],[f1553,f857]) ).
fof(f31298,plain,
( spl0_1150
| ~ spl0_99
| ~ spl0_136 ),
inference(avatar_split_clause,[],[f1630,f1552,f860,f31296]) ).
fof(f31296,plain,
( spl0_1150
<=> ! [X2,X4,X0,X3,X5,X1] :
( ~ closed(X0,X1)
| ~ maps(X2,compose(X3,X4),X0)
| homomorphism(X2,compose(X3,X4),X5,X0,X1)
| ~ closed(compose(X3,X4),X5)
| little_set(f31(f33(X2,compose(X3,X4),X5,X0,X1),X3,X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1150])]) ).
fof(f1630,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ closed(X0,X1)
| ~ maps(X2,compose(X3,X4),X0)
| homomorphism(X2,compose(X3,X4),X5,X0,X1)
| ~ closed(compose(X3,X4),X5)
| little_set(f31(f33(X2,compose(X3,X4),X5,X0,X1),X3,X4)) )
| ~ spl0_99
| ~ spl0_136 ),
inference(resolution,[],[f1553,f861]) ).
fof(f31294,plain,
( spl0_1149
| ~ spl0_96
| ~ spl0_136 ),
inference(avatar_split_clause,[],[f1629,f1552,f848,f31292]) ).
fof(f31292,plain,
( spl0_1149
<=> ! [X2,X4,X0,X3,X5,X1] :
( ~ closed(X0,X1)
| ~ maps(X2,apply(X3,X4),X0)
| homomorphism(X2,apply(X3,X4),X5,X0,X1)
| ~ closed(apply(X3,X4),X5)
| ordered_pair_predicate(f28(f33(X2,apply(X3,X4),X5,X0,X1),X3,X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1149])]) ).
fof(f1629,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ closed(X0,X1)
| ~ maps(X2,apply(X3,X4),X0)
| homomorphism(X2,apply(X3,X4),X5,X0,X1)
| ~ closed(apply(X3,X4),X5)
| ordered_pair_predicate(f28(f33(X2,apply(X3,X4),X5,X0,X1),X3,X4)) )
| ~ spl0_96
| ~ spl0_136 ),
inference(resolution,[],[f1553,f849]) ).
fof(f31290,plain,
( spl0_1148
| ~ spl0_94
| ~ spl0_136 ),
inference(avatar_split_clause,[],[f1623,f1552,f840,f31288]) ).
fof(f31288,plain,
( spl0_1148
<=> ! [X2,X4,X0,X3,X5,X1] :
( ~ closed(X0,X1)
| ~ maps(X2,image(X3,X4),X0)
| homomorphism(X2,image(X3,X4),X5,X0,X1)
| ~ closed(image(X3,X4),X5)
| ordered_pair_predicate(f22(f33(X2,image(X3,X4),X5,X0,X1),X3,X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1148])]) ).
fof(f1623,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ closed(X0,X1)
| ~ maps(X2,image(X3,X4),X0)
| homomorphism(X2,image(X3,X4),X5,X0,X1)
| ~ closed(image(X3,X4),X5)
| ordered_pair_predicate(f22(f33(X2,image(X3,X4),X5,X0,X1),X3,X4)) )
| ~ spl0_94
| ~ spl0_136 ),
inference(resolution,[],[f1553,f841]) ).
fof(f31286,plain,
( spl0_1147
| ~ spl0_97
| ~ spl0_134 ),
inference(avatar_split_clause,[],[f1593,f1544,f852,f31284]) ).
fof(f31284,plain,
( spl0_1147
<=> ! [X2,X4,X0,X3,X5,X1] :
( ~ closed(X0,X1)
| ~ maps(X2,compose(X3,X4),X0)
| homomorphism(X2,compose(X3,X4),X5,X0,X1)
| ~ closed(compose(X3,X4),X5)
| little_set(f29(f32(X2,compose(X3,X4),X5,X0,X1),X3,X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1147])]) ).
fof(f1593,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ closed(X0,X1)
| ~ maps(X2,compose(X3,X4),X0)
| homomorphism(X2,compose(X3,X4),X5,X0,X1)
| ~ closed(compose(X3,X4),X5)
| little_set(f29(f32(X2,compose(X3,X4),X5,X0,X1),X3,X4)) )
| ~ spl0_97
| ~ spl0_134 ),
inference(resolution,[],[f1545,f853]) ).
fof(f31282,plain,
( spl0_1146
| ~ spl0_98
| ~ spl0_134 ),
inference(avatar_split_clause,[],[f1592,f1544,f856,f31280]) ).
fof(f31280,plain,
( spl0_1146
<=> ! [X2,X4,X0,X3,X5,X1] :
( ~ closed(X0,X1)
| ~ maps(X2,compose(X3,X4),X0)
| homomorphism(X2,compose(X3,X4),X5,X0,X1)
| ~ closed(compose(X3,X4),X5)
| little_set(f30(f32(X2,compose(X3,X4),X5,X0,X1),X3,X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1146])]) ).
fof(f1592,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ closed(X0,X1)
| ~ maps(X2,compose(X3,X4),X0)
| homomorphism(X2,compose(X3,X4),X5,X0,X1)
| ~ closed(compose(X3,X4),X5)
| little_set(f30(f32(X2,compose(X3,X4),X5,X0,X1),X3,X4)) )
| ~ spl0_98
| ~ spl0_134 ),
inference(resolution,[],[f1545,f857]) ).
fof(f31278,plain,
( spl0_1145
| ~ spl0_99
| ~ spl0_134 ),
inference(avatar_split_clause,[],[f1591,f1544,f860,f31276]) ).
fof(f31276,plain,
( spl0_1145
<=> ! [X2,X4,X0,X3,X5,X1] :
( ~ closed(X0,X1)
| ~ maps(X2,compose(X3,X4),X0)
| homomorphism(X2,compose(X3,X4),X5,X0,X1)
| ~ closed(compose(X3,X4),X5)
| little_set(f31(f32(X2,compose(X3,X4),X5,X0,X1),X3,X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1145])]) ).
fof(f1591,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ closed(X0,X1)
| ~ maps(X2,compose(X3,X4),X0)
| homomorphism(X2,compose(X3,X4),X5,X0,X1)
| ~ closed(compose(X3,X4),X5)
| little_set(f31(f32(X2,compose(X3,X4),X5,X0,X1),X3,X4)) )
| ~ spl0_99
| ~ spl0_134 ),
inference(resolution,[],[f1545,f861]) ).
fof(f31274,plain,
( spl0_1144
| ~ spl0_96
| ~ spl0_134 ),
inference(avatar_split_clause,[],[f1590,f1544,f848,f31272]) ).
fof(f31272,plain,
( spl0_1144
<=> ! [X2,X4,X0,X3,X5,X1] :
( ~ closed(X0,X1)
| ~ maps(X2,apply(X3,X4),X0)
| homomorphism(X2,apply(X3,X4),X5,X0,X1)
| ~ closed(apply(X3,X4),X5)
| ordered_pair_predicate(f28(f32(X2,apply(X3,X4),X5,X0,X1),X3,X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1144])]) ).
fof(f1590,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ closed(X0,X1)
| ~ maps(X2,apply(X3,X4),X0)
| homomorphism(X2,apply(X3,X4),X5,X0,X1)
| ~ closed(apply(X3,X4),X5)
| ordered_pair_predicate(f28(f32(X2,apply(X3,X4),X5,X0,X1),X3,X4)) )
| ~ spl0_96
| ~ spl0_134 ),
inference(resolution,[],[f1545,f849]) ).
fof(f31270,plain,
( spl0_1143
| ~ spl0_94
| ~ spl0_134 ),
inference(avatar_split_clause,[],[f1584,f1544,f840,f31268]) ).
fof(f31268,plain,
( spl0_1143
<=> ! [X2,X4,X0,X3,X5,X1] :
( ~ closed(X0,X1)
| ~ maps(X2,image(X3,X4),X0)
| homomorphism(X2,image(X3,X4),X5,X0,X1)
| ~ closed(image(X3,X4),X5)
| ordered_pair_predicate(f22(f32(X2,image(X3,X4),X5,X0,X1),X3,X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1143])]) ).
fof(f1584,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ closed(X0,X1)
| ~ maps(X2,image(X3,X4),X0)
| homomorphism(X2,image(X3,X4),X5,X0,X1)
| ~ closed(image(X3,X4),X5)
| ordered_pair_predicate(f22(f32(X2,image(X3,X4),X5,X0,X1),X3,X4)) )
| ~ spl0_94
| ~ spl0_134 ),
inference(resolution,[],[f1545,f841]) ).
fof(f31266,plain,
( spl0_1142
| ~ spl0_168
| ~ spl0_173
| ~ spl0_209 ),
inference(avatar_split_clause,[],[f2810,f2733,f2440,f2260,f31264]) ).
fof(f31264,plain,
( spl0_1142
<=> ! [X0] : estin = compose(estin,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1142])]) ).
fof(f2810,plain,
( ! [X0] : estin = compose(estin,X0)
| ~ spl0_168
| ~ spl0_173
| ~ spl0_209 ),
inference(forward_demodulation,[],[f2798,f2442]) ).
fof(f2798,plain,
( ! [X0] : estin = compose(empty_set,X0)
| ~ spl0_168
| ~ spl0_209 ),
inference(resolution,[],[f2734,f2261]) ).
fof(f31262,plain,
( spl0_1141
| ~ spl0_82
| ~ spl0_133 ),
inference(avatar_split_clause,[],[f1541,f1487,f660,f31260]) ).
fof(f31260,plain,
( spl0_1141
<=> ! [X0,X1] :
( ~ little_set(X0)
| member(X0,converse(powerset(X1)))
| ~ ordered_pair_predicate(X0)
| ~ subset(non_ordered_pair(non_ordered_pair(second(X0),second(X0)),non_ordered_pair(second(X0),first(X0))),X1)
| ~ little_set(non_ordered_pair(non_ordered_pair(second(X0),second(X0)),non_ordered_pair(second(X0),first(X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1141])]) ).
fof(f1541,plain,
( ! [X0,X1] :
( ~ little_set(X0)
| member(X0,converse(powerset(X1)))
| ~ ordered_pair_predicate(X0)
| ~ subset(non_ordered_pair(non_ordered_pair(second(X0),second(X0)),non_ordered_pair(second(X0),first(X0))),X1)
| ~ little_set(non_ordered_pair(non_ordered_pair(second(X0),second(X0)),non_ordered_pair(second(X0),first(X0)))) )
| ~ spl0_82
| ~ spl0_133 ),
inference(resolution,[],[f1488,f661]) ).
fof(f31258,plain,
( spl0_1140
| ~ spl0_79
| ~ spl0_133 ),
inference(avatar_split_clause,[],[f1540,f1487,f648,f31256]) ).
fof(f31256,plain,
( spl0_1140
<=> ! [X0,X1] :
( ~ little_set(X0)
| member(X0,converse(f16(non_ordered_pair(non_ordered_pair(second(X0),second(X0)),non_ordered_pair(second(X0),first(X0))),X1)))
| ~ ordered_pair_predicate(X0)
| ~ member(non_ordered_pair(non_ordered_pair(second(X0),second(X0)),non_ordered_pair(second(X0),first(X0))),sigma(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1140])]) ).
fof(f1540,plain,
( ! [X0,X1] :
( ~ little_set(X0)
| member(X0,converse(f16(non_ordered_pair(non_ordered_pair(second(X0),second(X0)),non_ordered_pair(second(X0),first(X0))),X1)))
| ~ ordered_pair_predicate(X0)
| ~ member(non_ordered_pair(non_ordered_pair(second(X0),second(X0)),non_ordered_pair(second(X0),first(X0))),sigma(X1)) )
| ~ spl0_79
| ~ spl0_133 ),
inference(resolution,[],[f1488,f649]) ).
fof(f31254,plain,
( spl0_1139
| ~ spl0_73
| ~ spl0_133 ),
inference(avatar_split_clause,[],[f1537,f1487,f624,f31252]) ).
fof(f31252,plain,
( spl0_1139
<=> ! [X0,X1] :
( ~ little_set(X0)
| member(X0,converse(complement(X1)))
| ~ ordered_pair_predicate(X0)
| member(non_ordered_pair(non_ordered_pair(second(X0),second(X0)),non_ordered_pair(second(X0),first(X0))),X1)
| ~ little_set(non_ordered_pair(non_ordered_pair(second(X0),second(X0)),non_ordered_pair(second(X0),first(X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1139])]) ).
fof(f1537,plain,
( ! [X0,X1] :
( ~ little_set(X0)
| member(X0,converse(complement(X1)))
| ~ ordered_pair_predicate(X0)
| member(non_ordered_pair(non_ordered_pair(second(X0),second(X0)),non_ordered_pair(second(X0),first(X0))),X1)
| ~ little_set(non_ordered_pair(non_ordered_pair(second(X0),second(X0)),non_ordered_pair(second(X0),first(X0)))) )
| ~ spl0_73
| ~ spl0_133 ),
inference(resolution,[],[f1488,f625]) ).
fof(f31250,plain,
( spl0_1138
| ~ spl0_72
| ~ spl0_133 ),
inference(avatar_split_clause,[],[f1535,f1487,f620,f31248]) ).
fof(f31248,plain,
( spl0_1138
<=> ! [X0,X1] :
( ~ little_set(X0)
| member(X0,converse(f7(non_ordered_pair(non_ordered_pair(second(X0),second(X0)),non_ordered_pair(second(X0),first(X0))),X1)))
| ~ ordered_pair_predicate(X0)
| ~ member(non_ordered_pair(non_ordered_pair(second(X0),second(X0)),non_ordered_pair(second(X0),first(X0))),second(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1138])]) ).
fof(f1535,plain,
( ! [X0,X1] :
( ~ little_set(X0)
| member(X0,converse(f7(non_ordered_pair(non_ordered_pair(second(X0),second(X0)),non_ordered_pair(second(X0),first(X0))),X1)))
| ~ ordered_pair_predicate(X0)
| ~ member(non_ordered_pair(non_ordered_pair(second(X0),second(X0)),non_ordered_pair(second(X0),first(X0))),second(X1)) )
| ~ spl0_72
| ~ spl0_133 ),
inference(resolution,[],[f1488,f621]) ).
fof(f31246,plain,
( spl0_1137
| ~ spl0_71
| ~ spl0_133 ),
inference(avatar_split_clause,[],[f1532,f1487,f616,f31244]) ).
fof(f31244,plain,
( spl0_1137
<=> ! [X0,X1] :
( ~ little_set(X0)
| member(X0,converse(f4(non_ordered_pair(non_ordered_pair(second(X0),second(X0)),non_ordered_pair(second(X0),first(X0))),X1)))
| ~ ordered_pair_predicate(X0)
| ~ member(non_ordered_pair(non_ordered_pair(second(X0),second(X0)),non_ordered_pair(second(X0),first(X0))),first(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1137])]) ).
fof(f1532,plain,
( ! [X0,X1] :
( ~ little_set(X0)
| member(X0,converse(f4(non_ordered_pair(non_ordered_pair(second(X0),second(X0)),non_ordered_pair(second(X0),first(X0))),X1)))
| ~ ordered_pair_predicate(X0)
| ~ member(non_ordered_pair(non_ordered_pair(second(X0),second(X0)),non_ordered_pair(second(X0),first(X0))),first(X1)) )
| ~ spl0_71
| ~ spl0_133 ),
inference(resolution,[],[f1488,f617]) ).
fof(f31242,plain,
( spl0_1136
| ~ spl0_85
| ~ spl0_132 ),
inference(avatar_split_clause,[],[f1526,f1483,f672,f31240]) ).
fof(f31240,plain,
( spl0_1136
<=> ! [X0,X1] :
( non_ordered_pair(non_ordered_pair(f4(f27(X0,first(X1)),X1),f4(f27(X0,first(X1)),X1)),non_ordered_pair(f4(f27(X0,first(X1)),X1),f5(f27(X0,first(X1)),X1))) = X1
| ~ member(X0,range_of(first(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1136])]) ).
fof(f1526,plain,
( ! [X0,X1] :
( non_ordered_pair(non_ordered_pair(f4(f27(X0,first(X1)),X1),f4(f27(X0,first(X1)),X1)),non_ordered_pair(f4(f27(X0,first(X1)),X1),f5(f27(X0,first(X1)),X1))) = X1
| ~ member(X0,range_of(first(X1))) )
| ~ spl0_85
| ~ spl0_132 ),
inference(resolution,[],[f1484,f673]) ).
fof(f31238,plain,
( spl0_1135
| ~ spl0_78
| ~ spl0_132 ),
inference(avatar_split_clause,[],[f1518,f1483,f644,f31236]) ).
fof(f31236,plain,
( spl0_1135
<=> ! [X0,X1] :
( non_ordered_pair(non_ordered_pair(f4(f16(X0,first(X1)),X1),f4(f16(X0,first(X1)),X1)),non_ordered_pair(f4(f16(X0,first(X1)),X1),f5(f16(X0,first(X1)),X1))) = X1
| ~ member(X0,sigma(first(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1135])]) ).
fof(f1518,plain,
( ! [X0,X1] :
( non_ordered_pair(non_ordered_pair(f4(f16(X0,first(X1)),X1),f4(f16(X0,first(X1)),X1)),non_ordered_pair(f4(f16(X0,first(X1)),X1),f5(f16(X0,first(X1)),X1))) = X1
| ~ member(X0,sigma(first(X1))) )
| ~ spl0_78
| ~ spl0_132 ),
inference(resolution,[],[f1484,f645]) ).
fof(f31234,plain,
( spl0_1134
| ~ spl0_74
| ~ spl0_132 ),
inference(avatar_split_clause,[],[f1517,f1483,f628,f31232]) ).
fof(f31232,plain,
( spl0_1134
<=> ! [X0,X1] :
( non_ordered_pair(non_ordered_pair(f4(f8(X0,first(X1)),X1),f4(f8(X0,first(X1)),X1)),non_ordered_pair(f4(f8(X0,first(X1)),X1),f5(f8(X0,first(X1)),X1))) = X1
| ~ member(X0,domain_of(first(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1134])]) ).
fof(f1517,plain,
( ! [X0,X1] :
( non_ordered_pair(non_ordered_pair(f4(f8(X0,first(X1)),X1),f4(f8(X0,first(X1)),X1)),non_ordered_pair(f4(f8(X0,first(X1)),X1),f5(f8(X0,first(X1)),X1))) = X1
| ~ member(X0,domain_of(first(X1))) )
| ~ spl0_74
| ~ spl0_132 ),
inference(resolution,[],[f1484,f629]) ).
fof(f31230,plain,
( spl0_1133
| ~ spl0_85
| ~ spl0_131 ),
inference(avatar_split_clause,[],[f1508,f1479,f672,f31228]) ).
fof(f31228,plain,
( spl0_1133
<=> ! [X0,X1] :
( non_ordered_pair(non_ordered_pair(f6(f27(X0,second(X1)),X1),f6(f27(X0,second(X1)),X1)),non_ordered_pair(f6(f27(X0,second(X1)),X1),f7(f27(X0,second(X1)),X1))) = X1
| ~ member(X0,range_of(second(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1133])]) ).
fof(f1508,plain,
( ! [X0,X1] :
( non_ordered_pair(non_ordered_pair(f6(f27(X0,second(X1)),X1),f6(f27(X0,second(X1)),X1)),non_ordered_pair(f6(f27(X0,second(X1)),X1),f7(f27(X0,second(X1)),X1))) = X1
| ~ member(X0,range_of(second(X1))) )
| ~ spl0_85
| ~ spl0_131 ),
inference(resolution,[],[f1480,f673]) ).
fof(f31226,plain,
( spl0_1132
| ~ spl0_78
| ~ spl0_131 ),
inference(avatar_split_clause,[],[f1500,f1479,f644,f31224]) ).
fof(f31224,plain,
( spl0_1132
<=> ! [X0,X1] :
( non_ordered_pair(non_ordered_pair(f6(f16(X0,second(X1)),X1),f6(f16(X0,second(X1)),X1)),non_ordered_pair(f6(f16(X0,second(X1)),X1),f7(f16(X0,second(X1)),X1))) = X1
| ~ member(X0,sigma(second(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1132])]) ).
fof(f1500,plain,
( ! [X0,X1] :
( non_ordered_pair(non_ordered_pair(f6(f16(X0,second(X1)),X1),f6(f16(X0,second(X1)),X1)),non_ordered_pair(f6(f16(X0,second(X1)),X1),f7(f16(X0,second(X1)),X1))) = X1
| ~ member(X0,sigma(second(X1))) )
| ~ spl0_78
| ~ spl0_131 ),
inference(resolution,[],[f1480,f645]) ).
fof(f31222,plain,
( spl0_1131
| ~ spl0_167
| ~ spl0_173
| ~ spl0_209 ),
inference(avatar_split_clause,[],[f2809,f2733,f2440,f2256,f31220]) ).
fof(f31220,plain,
( spl0_1131
<=> ! [X0] : estin = compose(X0,estin) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1131])]) ).
fof(f2809,plain,
( ! [X0] : estin = compose(X0,estin)
| ~ spl0_167
| ~ spl0_173
| ~ spl0_209 ),
inference(forward_demodulation,[],[f2797,f2442]) ).
fof(f2797,plain,
( ! [X0] : estin = compose(X0,empty_set)
| ~ spl0_167
| ~ spl0_209 ),
inference(resolution,[],[f2734,f2257]) ).
fof(f31218,plain,
( spl0_1130
| ~ spl0_74
| ~ spl0_131 ),
inference(avatar_split_clause,[],[f1499,f1479,f628,f31216]) ).
fof(f31216,plain,
( spl0_1130
<=> ! [X0,X1] :
( non_ordered_pair(non_ordered_pair(f6(f8(X0,second(X1)),X1),f6(f8(X0,second(X1)),X1)),non_ordered_pair(f6(f8(X0,second(X1)),X1),f7(f8(X0,second(X1)),X1))) = X1
| ~ member(X0,domain_of(second(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1130])]) ).
fof(f1499,plain,
( ! [X0,X1] :
( non_ordered_pair(non_ordered_pair(f6(f8(X0,second(X1)),X1),f6(f8(X0,second(X1)),X1)),non_ordered_pair(f6(f8(X0,second(X1)),X1),f7(f8(X0,second(X1)),X1))) = X1
| ~ member(X0,domain_of(second(X1))) )
| ~ spl0_74
| ~ spl0_131 ),
inference(resolution,[],[f1480,f629]) ).
fof(f30292,plain,
( spl0_1129
| ~ spl0_165
| ~ spl0_173
| ~ spl0_209 ),
inference(avatar_split_clause,[],[f2808,f2733,f2440,f2247,f30290]) ).
fof(f30290,plain,
( spl0_1129
<=> ! [X0] : estin = apply(estin,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1129])]) ).
fof(f2808,plain,
( ! [X0] : estin = apply(estin,X0)
| ~ spl0_165
| ~ spl0_173
| ~ spl0_209 ),
inference(forward_demodulation,[],[f2792,f2442]) ).
fof(f2792,plain,
( ! [X0] : estin = apply(empty_set,X0)
| ~ spl0_165
| ~ spl0_209 ),
inference(resolution,[],[f2734,f2248]) ).
fof(f30113,plain,
( spl0_1128
| ~ spl0_75
| ~ spl0_136 ),
inference(avatar_split_clause,[],[f1611,f1552,f632,f30111]) ).
fof(f30111,plain,
( spl0_1128
<=> ! [X2,X4,X0,X3,X5,X1] :
( ~ closed(X0,X1)
| ~ maps(X2,cross_product(X3,X4),X0)
| homomorphism(X2,cross_product(X3,X4),X5,X0,X1)
| ~ closed(cross_product(X3,X4),X5)
| member(first(f33(X2,cross_product(X3,X4),X5,X0,X1)),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1128])]) ).
fof(f1611,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ closed(X0,X1)
| ~ maps(X2,cross_product(X3,X4),X0)
| homomorphism(X2,cross_product(X3,X4),X5,X0,X1)
| ~ closed(cross_product(X3,X4),X5)
| member(first(f33(X2,cross_product(X3,X4),X5,X0,X1)),X3) )
| ~ spl0_75
| ~ spl0_136 ),
inference(resolution,[],[f1553,f633]) ).
fof(f30109,plain,
( spl0_1127
| ~ spl0_77
| ~ spl0_136 ),
inference(avatar_split_clause,[],[f1610,f1552,f640,f30107]) ).
fof(f30107,plain,
( spl0_1127
<=> ! [X2,X4,X0,X3,X5,X1] :
( ~ closed(X0,X1)
| ~ maps(X2,cross_product(X3,X4),X0)
| homomorphism(X2,cross_product(X3,X4),X5,X0,X1)
| ~ closed(cross_product(X3,X4),X5)
| member(second(f33(X2,cross_product(X3,X4),X5,X0,X1)),X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1127])]) ).
fof(f1610,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ closed(X0,X1)
| ~ maps(X2,cross_product(X3,X4),X0)
| homomorphism(X2,cross_product(X3,X4),X5,X0,X1)
| ~ closed(cross_product(X3,X4),X5)
| member(second(f33(X2,cross_product(X3,X4),X5,X0,X1)),X4) )
| ~ spl0_77
| ~ spl0_136 ),
inference(resolution,[],[f1553,f641]) ).
fof(f30105,plain,
( spl0_1126
| ~ spl0_75
| ~ spl0_134 ),
inference(avatar_split_clause,[],[f1572,f1544,f632,f30103]) ).
fof(f30103,plain,
( spl0_1126
<=> ! [X2,X4,X0,X3,X5,X1] :
( ~ closed(X0,X1)
| ~ maps(X2,cross_product(X3,X4),X0)
| homomorphism(X2,cross_product(X3,X4),X5,X0,X1)
| ~ closed(cross_product(X3,X4),X5)
| member(first(f32(X2,cross_product(X3,X4),X5,X0,X1)),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1126])]) ).
fof(f1572,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ closed(X0,X1)
| ~ maps(X2,cross_product(X3,X4),X0)
| homomorphism(X2,cross_product(X3,X4),X5,X0,X1)
| ~ closed(cross_product(X3,X4),X5)
| member(first(f32(X2,cross_product(X3,X4),X5,X0,X1)),X3) )
| ~ spl0_75
| ~ spl0_134 ),
inference(resolution,[],[f1545,f633]) ).
fof(f30101,plain,
( spl0_1125
| ~ spl0_77
| ~ spl0_134 ),
inference(avatar_split_clause,[],[f1571,f1544,f640,f30099]) ).
fof(f30099,plain,
( spl0_1125
<=> ! [X2,X4,X0,X3,X5,X1] :
( ~ closed(X0,X1)
| ~ maps(X2,cross_product(X3,X4),X0)
| homomorphism(X2,cross_product(X3,X4),X5,X0,X1)
| ~ closed(cross_product(X3,X4),X5)
| member(second(f32(X2,cross_product(X3,X4),X5,X0,X1)),X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1125])]) ).
fof(f1571,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ closed(X0,X1)
| ~ maps(X2,cross_product(X3,X4),X0)
| homomorphism(X2,cross_product(X3,X4),X5,X0,X1)
| ~ closed(cross_product(X3,X4),X5)
| member(second(f32(X2,cross_product(X3,X4),X5,X0,X1)),X4) )
| ~ spl0_77
| ~ spl0_134 ),
inference(resolution,[],[f1545,f641]) ).
fof(f30097,plain,
( spl0_1124
| ~ spl0_64
| ~ spl0_132 ),
inference(avatar_split_clause,[],[f1523,f1483,f478,f30095]) ).
fof(f30095,plain,
( spl0_1124
<=> ! [X0,X1] :
( non_ordered_pair(non_ordered_pair(f4(f23(X0,first(X1)),X1),f4(f23(X0,first(X1)),X1)),non_ordered_pair(f4(f23(X0,first(X1)),X1),f5(f23(X0,first(X1)),X1))) = X1
| disjoint(X0,first(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1124])]) ).
fof(f1523,plain,
( ! [X0,X1] :
( non_ordered_pair(non_ordered_pair(f4(f23(X0,first(X1)),X1),f4(f23(X0,first(X1)),X1)),non_ordered_pair(f4(f23(X0,first(X1)),X1),f5(f23(X0,first(X1)),X1))) = X1
| disjoint(X0,first(X1)) )
| ~ spl0_64
| ~ spl0_132 ),
inference(resolution,[],[f1484,f479]) ).
fof(f30093,plain,
( spl0_1123
| ~ spl0_63
| ~ spl0_132 ),
inference(avatar_split_clause,[],[f1522,f1483,f474,f30091]) ).
fof(f30091,plain,
( spl0_1123
<=> ! [X0,X1] :
( non_ordered_pair(non_ordered_pair(f4(f23(first(X0),X1),X0),f4(f23(first(X0),X1),X0)),non_ordered_pair(f4(f23(first(X0),X1),X0),f5(f23(first(X0),X1),X0))) = X0
| disjoint(first(X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1123])]) ).
fof(f1522,plain,
( ! [X0,X1] :
( non_ordered_pair(non_ordered_pair(f4(f23(first(X0),X1),X0),f4(f23(first(X0),X1),X0)),non_ordered_pair(f4(f23(first(X0),X1),X0),f5(f23(first(X0),X1),X0))) = X0
| disjoint(first(X0),X1) )
| ~ spl0_63
| ~ spl0_132 ),
inference(resolution,[],[f1484,f475]) ).
fof(f30089,plain,
( spl0_1122
| ~ spl0_60
| ~ spl0_132 ),
inference(avatar_split_clause,[],[f1519,f1483,f462,f30087]) ).
fof(f30087,plain,
( spl0_1122
<=> ! [X0,X1] :
( non_ordered_pair(non_ordered_pair(f4(f17(first(X0),X1),X0),f4(f17(first(X0),X1),X0)),non_ordered_pair(f4(f17(first(X0),X1),X0),f5(f17(first(X0),X1),X0))) = X0
| subset(first(X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1122])]) ).
fof(f1519,plain,
( ! [X0,X1] :
( non_ordered_pair(non_ordered_pair(f4(f17(first(X0),X1),X0),f4(f17(first(X0),X1),X0)),non_ordered_pair(f4(f17(first(X0),X1),X0),f5(f17(first(X0),X1),X0))) = X0
| subset(first(X0),X1) )
| ~ spl0_60
| ~ spl0_132 ),
inference(resolution,[],[f1484,f463]) ).
fof(f30085,plain,
( spl0_1121
| ~ spl0_166
| ~ spl0_173
| ~ spl0_209 ),
inference(avatar_split_clause,[],[f2806,f2733,f2440,f2251,f30083]) ).
fof(f30083,plain,
( spl0_1121
<=> ! [X0] : estin = image(estin,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1121])]) ).
fof(f2806,plain,
( ! [X0] : estin = image(estin,X0)
| ~ spl0_166
| ~ spl0_173
| ~ spl0_209 ),
inference(forward_demodulation,[],[f2783,f2442]) ).
fof(f2783,plain,
( ! [X0] : estin = image(empty_set,X0)
| ~ spl0_166
| ~ spl0_209 ),
inference(resolution,[],[f2734,f2252]) ).
fof(f30081,plain,
( spl0_1120
| ~ spl0_64
| ~ spl0_131 ),
inference(avatar_split_clause,[],[f1505,f1479,f478,f30079]) ).
fof(f30079,plain,
( spl0_1120
<=> ! [X0,X1] :
( non_ordered_pair(non_ordered_pair(f6(f23(X0,second(X1)),X1),f6(f23(X0,second(X1)),X1)),non_ordered_pair(f6(f23(X0,second(X1)),X1),f7(f23(X0,second(X1)),X1))) = X1
| disjoint(X0,second(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1120])]) ).
fof(f1505,plain,
( ! [X0,X1] :
( non_ordered_pair(non_ordered_pair(f6(f23(X0,second(X1)),X1),f6(f23(X0,second(X1)),X1)),non_ordered_pair(f6(f23(X0,second(X1)),X1),f7(f23(X0,second(X1)),X1))) = X1
| disjoint(X0,second(X1)) )
| ~ spl0_64
| ~ spl0_131 ),
inference(resolution,[],[f1480,f479]) ).
fof(f30077,plain,
( spl0_1119
| ~ spl0_63
| ~ spl0_131 ),
inference(avatar_split_clause,[],[f1504,f1479,f474,f30075]) ).
fof(f30075,plain,
( spl0_1119
<=> ! [X0,X1] :
( non_ordered_pair(non_ordered_pair(f6(f23(second(X0),X1),X0),f6(f23(second(X0),X1),X0)),non_ordered_pair(f6(f23(second(X0),X1),X0),f7(f23(second(X0),X1),X0))) = X0
| disjoint(second(X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1119])]) ).
fof(f1504,plain,
( ! [X0,X1] :
( non_ordered_pair(non_ordered_pair(f6(f23(second(X0),X1),X0),f6(f23(second(X0),X1),X0)),non_ordered_pair(f6(f23(second(X0),X1),X0),f7(f23(second(X0),X1),X0))) = X0
| disjoint(second(X0),X1) )
| ~ spl0_63
| ~ spl0_131 ),
inference(resolution,[],[f1480,f475]) ).
fof(f30073,plain,
( spl0_1118
| ~ spl0_60
| ~ spl0_131 ),
inference(avatar_split_clause,[],[f1501,f1479,f462,f30071]) ).
fof(f30071,plain,
( spl0_1118
<=> ! [X0,X1] :
( non_ordered_pair(non_ordered_pair(f6(f17(second(X0),X1),X0),f6(f17(second(X0),X1),X0)),non_ordered_pair(f6(f17(second(X0),X1),X0),f7(f17(second(X0),X1),X0))) = X0
| subset(second(X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1118])]) ).
fof(f1501,plain,
( ! [X0,X1] :
( non_ordered_pair(non_ordered_pair(f6(f17(second(X0),X1),X0),f6(f17(second(X0),X1),X0)),non_ordered_pair(f6(f17(second(X0),X1),X0),f7(f17(second(X0),X1),X0))) = X0
| subset(second(X0),X1) )
| ~ spl0_60
| ~ spl0_131 ),
inference(resolution,[],[f1480,f463]) ).
fof(f30069,plain,
( spl0_1117
| ~ spl0_108
| ~ spl0_127 ),
inference(avatar_split_clause,[],[f1442,f1397,f1072,f30067]) ).
fof(f30067,plain,
( spl0_1117
<=> ! [X2,X0,X1] :
( ~ member(X0,converse(image(X1,X2)))
| non_ordered_pair(non_ordered_pair(second(X0),second(X0)),non_ordered_pair(second(X0),first(X0))) = second(f22(non_ordered_pair(non_ordered_pair(second(X0),second(X0)),non_ordered_pair(second(X0),first(X0))),X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1117])]) ).
fof(f1442,plain,
( ! [X2,X0,X1] :
( ~ member(X0,converse(image(X1,X2)))
| non_ordered_pair(non_ordered_pair(second(X0),second(X0)),non_ordered_pair(second(X0),first(X0))) = second(f22(non_ordered_pair(non_ordered_pair(second(X0),second(X0)),non_ordered_pair(second(X0),first(X0))),X1,X2)) )
| ~ spl0_108
| ~ spl0_127 ),
inference(resolution,[],[f1398,f1073]) ).
fof(f30065,plain,
( spl0_1116
| ~ spl0_61
| ~ spl0_126 ),
inference(avatar_split_clause,[],[f1415,f1393,f466,f30063]) ).
fof(f30063,plain,
( spl0_1116
<=> ! [X2,X0,X1] :
( ~ little_set(f17(X0,cross_product(X1,X2)))
| ~ member(first(f17(X0,cross_product(X1,X2))),X1)
| ~ member(second(f17(X0,cross_product(X1,X2))),X2)
| ~ ordered_pair_predicate(f17(X0,cross_product(X1,X2)))
| subset(X0,cross_product(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1116])]) ).
fof(f1415,plain,
( ! [X2,X0,X1] :
( ~ little_set(f17(X0,cross_product(X1,X2)))
| ~ member(first(f17(X0,cross_product(X1,X2))),X1)
| ~ member(second(f17(X0,cross_product(X1,X2))),X2)
| ~ ordered_pair_predicate(f17(X0,cross_product(X1,X2)))
| subset(X0,cross_product(X1,X2)) )
| ~ spl0_61
| ~ spl0_126 ),
inference(resolution,[],[f1394,f467]) ).
fof(f30049,plain,
( spl0_1115
| ~ spl0_164
| ~ spl0_173
| ~ spl0_209 ),
inference(avatar_split_clause,[],[f2805,f2733,f2440,f2243,f30047]) ).
fof(f30047,plain,
( spl0_1115
<=> ! [X0] : estin = image(X0,estin) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1115])]) ).
fof(f2805,plain,
( ! [X0] : estin = image(X0,estin)
| ~ spl0_164
| ~ spl0_173
| ~ spl0_209 ),
inference(forward_demodulation,[],[f2782,f2442]) ).
fof(f2782,plain,
( ! [X0] : estin = image(X0,empty_set)
| ~ spl0_164
| ~ spl0_209 ),
inference(resolution,[],[f2734,f2244]) ).
fof(f30022,plain,
( spl0_1114
| ~ spl0_168
| ~ spl0_173 ),
inference(avatar_split_clause,[],[f2463,f2440,f2260,f30020]) ).
fof(f30020,plain,
( spl0_1114
<=> ! [X0,X1] : ~ member(X0,compose(estin,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1114])]) ).
fof(f2463,plain,
( ! [X0,X1] : ~ member(X0,compose(estin,X1))
| ~ spl0_168
| ~ spl0_173 ),
inference(superposition,[],[f2261,f2442]) ).
fof(f29996,plain,
( spl0_1113
| ~ spl0_167
| ~ spl0_173 ),
inference(avatar_split_clause,[],[f2462,f2440,f2256,f29994]) ).
fof(f29994,plain,
( spl0_1113
<=> ! [X0,X1] : ~ member(X0,compose(X1,estin)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1113])]) ).
fof(f2462,plain,
( ! [X0,X1] : ~ member(X0,compose(X1,estin))
| ~ spl0_167
| ~ spl0_173 ),
inference(superposition,[],[f2257,f2442]) ).
fof(f28976,plain,
( spl0_1112
| ~ spl0_173
| ~ spl0_1072 ),
inference(avatar_split_clause,[],[f28654,f28651,f2440,f28974]) ).
fof(f28974,plain,
( spl0_1112
<=> ! [X0] :
( first(X0) = estin
| non_ordered_pair(non_ordered_pair(f4(f26(first(X0)),X0),f4(f26(first(X0)),X0)),non_ordered_pair(f4(f26(first(X0)),X0),f5(f26(first(X0)),X0))) = X0
| ~ little_set(first(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1112])]) ).
fof(f28651,plain,
( spl0_1072
<=> ! [X0] :
( non_ordered_pair(non_ordered_pair(f4(f26(first(X0)),X0),f4(f26(first(X0)),X0)),non_ordered_pair(f4(f26(first(X0)),X0),f5(f26(first(X0)),X0))) = X0
| first(X0) = empty_set
| ~ little_set(first(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1072])]) ).
fof(f28654,plain,
( ! [X0] :
( first(X0) = estin
| non_ordered_pair(non_ordered_pair(f4(f26(first(X0)),X0),f4(f26(first(X0)),X0)),non_ordered_pair(f4(f26(first(X0)),X0),f5(f26(first(X0)),X0))) = X0
| ~ little_set(first(X0)) )
| ~ spl0_173
| ~ spl0_1072 ),
inference(forward_demodulation,[],[f28652,f2442]) ).
fof(f28652,plain,
( ! [X0] :
( non_ordered_pair(non_ordered_pair(f4(f26(first(X0)),X0),f4(f26(first(X0)),X0)),non_ordered_pair(f4(f26(first(X0)),X0),f5(f26(first(X0)),X0))) = X0
| first(X0) = empty_set
| ~ little_set(first(X0)) )
| ~ spl0_1072 ),
inference(avatar_component_clause,[],[f28651]) ).
fof(f28971,plain,
( spl0_1111
| ~ spl0_166
| ~ spl0_173 ),
inference(avatar_split_clause,[],[f2461,f2440,f2251,f28969]) ).
fof(f28969,plain,
( spl0_1111
<=> ! [X0,X1] : ~ member(X0,image(estin,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1111])]) ).
fof(f2461,plain,
( ! [X0,X1] : ~ member(X0,image(estin,X1))
| ~ spl0_166
| ~ spl0_173 ),
inference(superposition,[],[f2252,f2442]) ).
fof(f28967,plain,
( spl0_1110
| ~ spl0_173
| ~ spl0_1071 ),
inference(avatar_split_clause,[],[f28649,f28646,f2440,f28965]) ).
fof(f28965,plain,
( spl0_1110
<=> ! [X0] :
( second(X0) = estin
| non_ordered_pair(non_ordered_pair(f6(f26(second(X0)),X0),f6(f26(second(X0)),X0)),non_ordered_pair(f6(f26(second(X0)),X0),f7(f26(second(X0)),X0))) = X0
| ~ little_set(second(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1110])]) ).
fof(f28646,plain,
( spl0_1071
<=> ! [X0] :
( non_ordered_pair(non_ordered_pair(f6(f26(second(X0)),X0),f6(f26(second(X0)),X0)),non_ordered_pair(f6(f26(second(X0)),X0),f7(f26(second(X0)),X0))) = X0
| second(X0) = empty_set
| ~ little_set(second(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1071])]) ).
fof(f28649,plain,
( ! [X0] :
( second(X0) = estin
| non_ordered_pair(non_ordered_pair(f6(f26(second(X0)),X0),f6(f26(second(X0)),X0)),non_ordered_pair(f6(f26(second(X0)),X0),f7(f26(second(X0)),X0))) = X0
| ~ little_set(second(X0)) )
| ~ spl0_173
| ~ spl0_1071 ),
inference(forward_demodulation,[],[f28647,f2442]) ).
fof(f28647,plain,
( ! [X0] :
( non_ordered_pair(non_ordered_pair(f6(f26(second(X0)),X0),f6(f26(second(X0)),X0)),non_ordered_pair(f6(f26(second(X0)),X0),f7(f26(second(X0)),X0))) = X0
| second(X0) = empty_set
| ~ little_set(second(X0)) )
| ~ spl0_1071 ),
inference(avatar_component_clause,[],[f28646]) ).
fof(f28807,plain,
( spl0_1109
| ~ spl0_23
| ~ spl0_145 ),
inference(avatar_split_clause,[],[f1910,f1786,f281,f28805]) ).
fof(f28805,plain,
( spl0_1109
<=> ! [X0] :
( ~ member(X0,rotate_right(identity_relation))
| ordered_pair_predicate(non_ordered_pair(non_ordered_pair(f10(X0,identity_relation),f10(X0,identity_relation)),non_ordered_pair(f10(X0,identity_relation),non_ordered_pair(non_ordered_pair(f11(X0,identity_relation),f11(X0,identity_relation)),non_ordered_pair(f11(X0,identity_relation),f9(X0,identity_relation)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1109])]) ).
fof(f1910,plain,
( ! [X0] :
( ~ member(X0,rotate_right(identity_relation))
| ordered_pair_predicate(non_ordered_pair(non_ordered_pair(f10(X0,identity_relation),f10(X0,identity_relation)),non_ordered_pair(f10(X0,identity_relation),non_ordered_pair(non_ordered_pair(f11(X0,identity_relation),f11(X0,identity_relation)),non_ordered_pair(f11(X0,identity_relation),f9(X0,identity_relation)))))) )
| ~ spl0_23
| ~ spl0_145 ),
inference(resolution,[],[f1787,f282]) ).
fof(f28801,plain,
( spl0_1108
| ~ spl0_23
| ~ spl0_144 ),
inference(avatar_split_clause,[],[f1867,f1782,f281,f28799]) ).
fof(f28799,plain,
( spl0_1108
<=> ! [X0] :
( ~ member(X0,flip_range_of(identity_relation))
| ordered_pair_predicate(non_ordered_pair(non_ordered_pair(f12(X0,identity_relation),f12(X0,identity_relation)),non_ordered_pair(f12(X0,identity_relation),non_ordered_pair(non_ordered_pair(f14(X0,identity_relation),f14(X0,identity_relation)),non_ordered_pair(f14(X0,identity_relation),f13(X0,identity_relation)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1108])]) ).
fof(f1867,plain,
( ! [X0] :
( ~ member(X0,flip_range_of(identity_relation))
| ordered_pair_predicate(non_ordered_pair(non_ordered_pair(f12(X0,identity_relation),f12(X0,identity_relation)),non_ordered_pair(f12(X0,identity_relation),non_ordered_pair(non_ordered_pair(f14(X0,identity_relation),f14(X0,identity_relation)),non_ordered_pair(f14(X0,identity_relation),f13(X0,identity_relation)))))) )
| ~ spl0_23
| ~ spl0_144 ),
inference(resolution,[],[f1783,f282]) ).
fof(f28797,plain,
( spl0_1107
| ~ spl0_65
| ~ spl0_139 ),
inference(avatar_split_clause,[],[f1735,f1642,f482,f28795]) ).
fof(f28795,plain,
( spl0_1107
<=> ! [X2,X0,X1] :
( ~ member(X0,compose(range_of(X1),X2))
| ordered_pair_predicate(f27(non_ordered_pair(non_ordered_pair(f29(X0,range_of(X1),X2),f29(X0,range_of(X1),X2)),non_ordered_pair(f29(X0,range_of(X1),X2),f31(X0,range_of(X1),X2))),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1107])]) ).
fof(f1735,plain,
( ! [X2,X0,X1] :
( ~ member(X0,compose(range_of(X1),X2))
| ordered_pair_predicate(f27(non_ordered_pair(non_ordered_pair(f29(X0,range_of(X1),X2),f29(X0,range_of(X1),X2)),non_ordered_pair(f29(X0,range_of(X1),X2),f31(X0,range_of(X1),X2))),X1)) )
| ~ spl0_65
| ~ spl0_139 ),
inference(resolution,[],[f1643,f483]) ).
fof(f28793,plain,
( spl0_1106
| ~ spl0_57
| ~ spl0_139 ),
inference(avatar_split_clause,[],[f1729,f1642,f450,f28791]) ).
fof(f28791,plain,
( spl0_1106
<=> ! [X2,X0,X1] :
( ~ member(X0,compose(flip_range_of(X1),X2))
| little_set(f12(non_ordered_pair(non_ordered_pair(f29(X0,flip_range_of(X1),X2),f29(X0,flip_range_of(X1),X2)),non_ordered_pair(f29(X0,flip_range_of(X1),X2),f31(X0,flip_range_of(X1),X2))),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1106])]) ).
fof(f1729,plain,
( ! [X2,X0,X1] :
( ~ member(X0,compose(flip_range_of(X1),X2))
| little_set(f12(non_ordered_pair(non_ordered_pair(f29(X0,flip_range_of(X1),X2),f29(X0,flip_range_of(X1),X2)),non_ordered_pair(f29(X0,flip_range_of(X1),X2),f31(X0,flip_range_of(X1),X2))),X1)) )
| ~ spl0_57
| ~ spl0_139 ),
inference(resolution,[],[f1643,f451]) ).
fof(f28789,plain,
( spl0_1105
| ~ spl0_58
| ~ spl0_139 ),
inference(avatar_split_clause,[],[f1728,f1642,f454,f28787]) ).
fof(f28787,plain,
( spl0_1105
<=> ! [X2,X0,X1] :
( ~ member(X0,compose(flip_range_of(X1),X2))
| little_set(f13(non_ordered_pair(non_ordered_pair(f29(X0,flip_range_of(X1),X2),f29(X0,flip_range_of(X1),X2)),non_ordered_pair(f29(X0,flip_range_of(X1),X2),f31(X0,flip_range_of(X1),X2))),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1105])]) ).
fof(f1728,plain,
( ! [X2,X0,X1] :
( ~ member(X0,compose(flip_range_of(X1),X2))
| little_set(f13(non_ordered_pair(non_ordered_pair(f29(X0,flip_range_of(X1),X2),f29(X0,flip_range_of(X1),X2)),non_ordered_pair(f29(X0,flip_range_of(X1),X2),f31(X0,flip_range_of(X1),X2))),X1)) )
| ~ spl0_58
| ~ spl0_139 ),
inference(resolution,[],[f1643,f455]) ).
fof(f28785,plain,
( spl0_1104
| ~ spl0_59
| ~ spl0_139 ),
inference(avatar_split_clause,[],[f1727,f1642,f458,f28783]) ).
fof(f28783,plain,
( spl0_1104
<=> ! [X2,X0,X1] :
( ~ member(X0,compose(flip_range_of(X1),X2))
| little_set(f14(non_ordered_pair(non_ordered_pair(f29(X0,flip_range_of(X1),X2),f29(X0,flip_range_of(X1),X2)),non_ordered_pair(f29(X0,flip_range_of(X1),X2),f31(X0,flip_range_of(X1),X2))),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1104])]) ).
fof(f1727,plain,
( ! [X2,X0,X1] :
( ~ member(X0,compose(flip_range_of(X1),X2))
| little_set(f14(non_ordered_pair(non_ordered_pair(f29(X0,flip_range_of(X1),X2),f29(X0,flip_range_of(X1),X2)),non_ordered_pair(f29(X0,flip_range_of(X1),X2),f31(X0,flip_range_of(X1),X2))),X1)) )
| ~ spl0_59
| ~ spl0_139 ),
inference(resolution,[],[f1643,f459]) ).
fof(f28781,plain,
( spl0_1103
| ~ spl0_54
| ~ spl0_139 ),
inference(avatar_split_clause,[],[f1726,f1642,f438,f28779]) ).
fof(f28779,plain,
( spl0_1103
<=> ! [X2,X0,X1] :
( ~ member(X0,compose(rotate_right(X1),X2))
| little_set(f9(non_ordered_pair(non_ordered_pair(f29(X0,rotate_right(X1),X2),f29(X0,rotate_right(X1),X2)),non_ordered_pair(f29(X0,rotate_right(X1),X2),f31(X0,rotate_right(X1),X2))),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1103])]) ).
fof(f1726,plain,
( ! [X2,X0,X1] :
( ~ member(X0,compose(rotate_right(X1),X2))
| little_set(f9(non_ordered_pair(non_ordered_pair(f29(X0,rotate_right(X1),X2),f29(X0,rotate_right(X1),X2)),non_ordered_pair(f29(X0,rotate_right(X1),X2),f31(X0,rotate_right(X1),X2))),X1)) )
| ~ spl0_54
| ~ spl0_139 ),
inference(resolution,[],[f1643,f439]) ).
fof(f28777,plain,
( spl0_1102
| ~ spl0_55
| ~ spl0_139 ),
inference(avatar_split_clause,[],[f1725,f1642,f442,f28775]) ).
fof(f28775,plain,
( spl0_1102
<=> ! [X2,X0,X1] :
( ~ member(X0,compose(rotate_right(X1),X2))
| little_set(f10(non_ordered_pair(non_ordered_pair(f29(X0,rotate_right(X1),X2),f29(X0,rotate_right(X1),X2)),non_ordered_pair(f29(X0,rotate_right(X1),X2),f31(X0,rotate_right(X1),X2))),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1102])]) ).
fof(f1725,plain,
( ! [X2,X0,X1] :
( ~ member(X0,compose(rotate_right(X1),X2))
| little_set(f10(non_ordered_pair(non_ordered_pair(f29(X0,rotate_right(X1),X2),f29(X0,rotate_right(X1),X2)),non_ordered_pair(f29(X0,rotate_right(X1),X2),f31(X0,rotate_right(X1),X2))),X1)) )
| ~ spl0_55
| ~ spl0_139 ),
inference(resolution,[],[f1643,f443]) ).
fof(f28772,plain,
( spl0_1101
| ~ spl0_165
| ~ spl0_173 ),
inference(avatar_split_clause,[],[f2460,f2440,f2247,f28770]) ).
fof(f28770,plain,
( spl0_1101
<=> ! [X0,X1] : ~ member(X0,apply(estin,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1101])]) ).
fof(f2460,plain,
( ! [X0,X1] : ~ member(X0,apply(estin,X1))
| ~ spl0_165
| ~ spl0_173 ),
inference(superposition,[],[f2248,f2442]) ).
fof(f28768,plain,
( spl0_1100
| ~ spl0_56
| ~ spl0_139 ),
inference(avatar_split_clause,[],[f1724,f1642,f446,f28766]) ).
fof(f28766,plain,
( spl0_1100
<=> ! [X2,X0,X1] :
( ~ member(X0,compose(rotate_right(X1),X2))
| little_set(f11(non_ordered_pair(non_ordered_pair(f29(X0,rotate_right(X1),X2),f29(X0,rotate_right(X1),X2)),non_ordered_pair(f29(X0,rotate_right(X1),X2),f31(X0,rotate_right(X1),X2))),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1100])]) ).
fof(f1724,plain,
( ! [X2,X0,X1] :
( ~ member(X0,compose(rotate_right(X1),X2))
| little_set(f11(non_ordered_pair(non_ordered_pair(f29(X0,rotate_right(X1),X2),f29(X0,rotate_right(X1),X2)),non_ordered_pair(f29(X0,rotate_right(X1),X2),f31(X0,rotate_right(X1),X2))),X1)) )
| ~ spl0_56
| ~ spl0_139 ),
inference(resolution,[],[f1643,f447]) ).
fof(f28764,plain,
( spl0_1099
| ~ spl0_53
| ~ spl0_139 ),
inference(avatar_split_clause,[],[f1719,f1642,f434,f28762]) ).
fof(f28762,plain,
( spl0_1099
<=> ! [X2,X0,X1] :
( ~ member(X0,compose(domain_of(X1),X2))
| ordered_pair_predicate(f8(non_ordered_pair(non_ordered_pair(f29(X0,domain_of(X1),X2),f29(X0,domain_of(X1),X2)),non_ordered_pair(f29(X0,domain_of(X1),X2),f31(X0,domain_of(X1),X2))),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1099])]) ).
fof(f1719,plain,
( ! [X2,X0,X1] :
( ~ member(X0,compose(domain_of(X1),X2))
| ordered_pair_predicate(f8(non_ordered_pair(non_ordered_pair(f29(X0,domain_of(X1),X2),f29(X0,domain_of(X1),X2)),non_ordered_pair(f29(X0,domain_of(X1),X2),f31(X0,domain_of(X1),X2))),X1)) )
| ~ spl0_53
| ~ spl0_139 ),
inference(resolution,[],[f1643,f435]) ).
fof(f28760,plain,
( spl0_1098
| ~ spl0_48
| ~ spl0_139 ),
inference(avatar_split_clause,[],[f1713,f1642,f414,f28758]) ).
fof(f28758,plain,
( spl0_1098
<=> ! [X2,X0,X1] :
( ~ member(X0,compose(second(X1),X2))
| little_set(f6(non_ordered_pair(non_ordered_pair(f29(X0,second(X1),X2),f29(X0,second(X1),X2)),non_ordered_pair(f29(X0,second(X1),X2),f31(X0,second(X1),X2))),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1098])]) ).
fof(f1713,plain,
( ! [X2,X0,X1] :
( ~ member(X0,compose(second(X1),X2))
| little_set(f6(non_ordered_pair(non_ordered_pair(f29(X0,second(X1),X2),f29(X0,second(X1),X2)),non_ordered_pair(f29(X0,second(X1),X2),f31(X0,second(X1),X2))),X1)) )
| ~ spl0_48
| ~ spl0_139 ),
inference(resolution,[],[f1643,f415]) ).
fof(f28756,plain,
( spl0_1097
| ~ spl0_49
| ~ spl0_139 ),
inference(avatar_split_clause,[],[f1712,f1642,f418,f28754]) ).
fof(f28754,plain,
( spl0_1097
<=> ! [X2,X0,X1] :
( ~ member(X0,compose(second(X1),X2))
| little_set(f7(non_ordered_pair(non_ordered_pair(f29(X0,second(X1),X2),f29(X0,second(X1),X2)),non_ordered_pair(f29(X0,second(X1),X2),f31(X0,second(X1),X2))),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1097])]) ).
fof(f1712,plain,
( ! [X2,X0,X1] :
( ~ member(X0,compose(second(X1),X2))
| little_set(f7(non_ordered_pair(non_ordered_pair(f29(X0,second(X1),X2),f29(X0,second(X1),X2)),non_ordered_pair(f29(X0,second(X1),X2),f31(X0,second(X1),X2))),X1)) )
| ~ spl0_49
| ~ spl0_139 ),
inference(resolution,[],[f1643,f419]) ).
fof(f28752,plain,
( spl0_1096
| ~ spl0_46
| ~ spl0_139 ),
inference(avatar_split_clause,[],[f1710,f1642,f406,f28750]) ).
fof(f28750,plain,
( spl0_1096
<=> ! [X2,X0,X1] :
( ~ member(X0,compose(first(X1),X2))
| little_set(f4(non_ordered_pair(non_ordered_pair(f29(X0,first(X1),X2),f29(X0,first(X1),X2)),non_ordered_pair(f29(X0,first(X1),X2),f31(X0,first(X1),X2))),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1096])]) ).
fof(f1710,plain,
( ! [X2,X0,X1] :
( ~ member(X0,compose(first(X1),X2))
| little_set(f4(non_ordered_pair(non_ordered_pair(f29(X0,first(X1),X2),f29(X0,first(X1),X2)),non_ordered_pair(f29(X0,first(X1),X2),f31(X0,first(X1),X2))),X1)) )
| ~ spl0_46
| ~ spl0_139 ),
inference(resolution,[],[f1643,f407]) ).
fof(f28748,plain,
( spl0_1095
| ~ spl0_47
| ~ spl0_139 ),
inference(avatar_split_clause,[],[f1709,f1642,f410,f28746]) ).
fof(f28746,plain,
( spl0_1095
<=> ! [X2,X0,X1] :
( ~ member(X0,compose(first(X1),X2))
| little_set(f5(non_ordered_pair(non_ordered_pair(f29(X0,first(X1),X2),f29(X0,first(X1),X2)),non_ordered_pair(f29(X0,first(X1),X2),f31(X0,first(X1),X2))),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1095])]) ).
fof(f1709,plain,
( ! [X2,X0,X1] :
( ~ member(X0,compose(first(X1),X2))
| little_set(f5(non_ordered_pair(non_ordered_pair(f29(X0,first(X1),X2),f29(X0,first(X1),X2)),non_ordered_pair(f29(X0,first(X1),X2),f31(X0,first(X1),X2))),X1)) )
| ~ spl0_47
| ~ spl0_139 ),
inference(resolution,[],[f1643,f411]) ).
fof(f28744,plain,
( spl0_1094
| ~ spl0_65
| ~ spl0_138 ),
inference(avatar_split_clause,[],[f1695,f1638,f482,f28742]) ).
fof(f28742,plain,
( spl0_1094
<=> ! [X2,X0,X1] :
( ~ member(X0,compose(X1,range_of(X2)))
| ordered_pair_predicate(f27(non_ordered_pair(non_ordered_pair(f31(X0,X1,range_of(X2)),f31(X0,X1,range_of(X2))),non_ordered_pair(f31(X0,X1,range_of(X2)),f30(X0,X1,range_of(X2)))),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1094])]) ).
fof(f1695,plain,
( ! [X2,X0,X1] :
( ~ member(X0,compose(X1,range_of(X2)))
| ordered_pair_predicate(f27(non_ordered_pair(non_ordered_pair(f31(X0,X1,range_of(X2)),f31(X0,X1,range_of(X2))),non_ordered_pair(f31(X0,X1,range_of(X2)),f30(X0,X1,range_of(X2)))),X2)) )
| ~ spl0_65
| ~ spl0_138 ),
inference(resolution,[],[f1639,f483]) ).
fof(f28740,plain,
( spl0_1093
| ~ spl0_57
| ~ spl0_138 ),
inference(avatar_split_clause,[],[f1689,f1638,f450,f28738]) ).
fof(f28738,plain,
( spl0_1093
<=> ! [X2,X0,X1] :
( ~ member(X0,compose(X1,flip_range_of(X2)))
| little_set(f12(non_ordered_pair(non_ordered_pair(f31(X0,X1,flip_range_of(X2)),f31(X0,X1,flip_range_of(X2))),non_ordered_pair(f31(X0,X1,flip_range_of(X2)),f30(X0,X1,flip_range_of(X2)))),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1093])]) ).
fof(f1689,plain,
( ! [X2,X0,X1] :
( ~ member(X0,compose(X1,flip_range_of(X2)))
| little_set(f12(non_ordered_pair(non_ordered_pair(f31(X0,X1,flip_range_of(X2)),f31(X0,X1,flip_range_of(X2))),non_ordered_pair(f31(X0,X1,flip_range_of(X2)),f30(X0,X1,flip_range_of(X2)))),X2)) )
| ~ spl0_57
| ~ spl0_138 ),
inference(resolution,[],[f1639,f451]) ).
fof(f28736,plain,
( spl0_1092
| ~ spl0_58
| ~ spl0_138 ),
inference(avatar_split_clause,[],[f1688,f1638,f454,f28734]) ).
fof(f28734,plain,
( spl0_1092
<=> ! [X2,X0,X1] :
( ~ member(X0,compose(X1,flip_range_of(X2)))
| little_set(f13(non_ordered_pair(non_ordered_pair(f31(X0,X1,flip_range_of(X2)),f31(X0,X1,flip_range_of(X2))),non_ordered_pair(f31(X0,X1,flip_range_of(X2)),f30(X0,X1,flip_range_of(X2)))),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1092])]) ).
fof(f1688,plain,
( ! [X2,X0,X1] :
( ~ member(X0,compose(X1,flip_range_of(X2)))
| little_set(f13(non_ordered_pair(non_ordered_pair(f31(X0,X1,flip_range_of(X2)),f31(X0,X1,flip_range_of(X2))),non_ordered_pair(f31(X0,X1,flip_range_of(X2)),f30(X0,X1,flip_range_of(X2)))),X2)) )
| ~ spl0_58
| ~ spl0_138 ),
inference(resolution,[],[f1639,f455]) ).
fof(f28732,plain,
( spl0_1091
| ~ spl0_59
| ~ spl0_138 ),
inference(avatar_split_clause,[],[f1687,f1638,f458,f28730]) ).
fof(f28730,plain,
( spl0_1091
<=> ! [X2,X0,X1] :
( ~ member(X0,compose(X1,flip_range_of(X2)))
| little_set(f14(non_ordered_pair(non_ordered_pair(f31(X0,X1,flip_range_of(X2)),f31(X0,X1,flip_range_of(X2))),non_ordered_pair(f31(X0,X1,flip_range_of(X2)),f30(X0,X1,flip_range_of(X2)))),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1091])]) ).
fof(f1687,plain,
( ! [X2,X0,X1] :
( ~ member(X0,compose(X1,flip_range_of(X2)))
| little_set(f14(non_ordered_pair(non_ordered_pair(f31(X0,X1,flip_range_of(X2)),f31(X0,X1,flip_range_of(X2))),non_ordered_pair(f31(X0,X1,flip_range_of(X2)),f30(X0,X1,flip_range_of(X2)))),X2)) )
| ~ spl0_59
| ~ spl0_138 ),
inference(resolution,[],[f1639,f459]) ).
fof(f28727,plain,
( spl0_1090
| ~ spl0_164
| ~ spl0_173 ),
inference(avatar_split_clause,[],[f2459,f2440,f2243,f28725]) ).
fof(f28725,plain,
( spl0_1090
<=> ! [X0,X1] : ~ member(X0,image(X1,estin)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1090])]) ).
fof(f2459,plain,
( ! [X0,X1] : ~ member(X0,image(X1,estin))
| ~ spl0_164
| ~ spl0_173 ),
inference(superposition,[],[f2244,f2442]) ).
fof(f28723,plain,
( spl0_1089
| ~ spl0_54
| ~ spl0_138 ),
inference(avatar_split_clause,[],[f1686,f1638,f438,f28721]) ).
fof(f28721,plain,
( spl0_1089
<=> ! [X2,X0,X1] :
( ~ member(X0,compose(X1,rotate_right(X2)))
| little_set(f9(non_ordered_pair(non_ordered_pair(f31(X0,X1,rotate_right(X2)),f31(X0,X1,rotate_right(X2))),non_ordered_pair(f31(X0,X1,rotate_right(X2)),f30(X0,X1,rotate_right(X2)))),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1089])]) ).
fof(f1686,plain,
( ! [X2,X0,X1] :
( ~ member(X0,compose(X1,rotate_right(X2)))
| little_set(f9(non_ordered_pair(non_ordered_pair(f31(X0,X1,rotate_right(X2)),f31(X0,X1,rotate_right(X2))),non_ordered_pair(f31(X0,X1,rotate_right(X2)),f30(X0,X1,rotate_right(X2)))),X2)) )
| ~ spl0_54
| ~ spl0_138 ),
inference(resolution,[],[f1639,f439]) ).
fof(f28719,plain,
( spl0_1088
| ~ spl0_55
| ~ spl0_138 ),
inference(avatar_split_clause,[],[f1685,f1638,f442,f28717]) ).
fof(f28717,plain,
( spl0_1088
<=> ! [X2,X0,X1] :
( ~ member(X0,compose(X1,rotate_right(X2)))
| little_set(f10(non_ordered_pair(non_ordered_pair(f31(X0,X1,rotate_right(X2)),f31(X0,X1,rotate_right(X2))),non_ordered_pair(f31(X0,X1,rotate_right(X2)),f30(X0,X1,rotate_right(X2)))),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1088])]) ).
fof(f1685,plain,
( ! [X2,X0,X1] :
( ~ member(X0,compose(X1,rotate_right(X2)))
| little_set(f10(non_ordered_pair(non_ordered_pair(f31(X0,X1,rotate_right(X2)),f31(X0,X1,rotate_right(X2))),non_ordered_pair(f31(X0,X1,rotate_right(X2)),f30(X0,X1,rotate_right(X2)))),X2)) )
| ~ spl0_55
| ~ spl0_138 ),
inference(resolution,[],[f1639,f443]) ).
fof(f28715,plain,
( spl0_1087
| ~ spl0_56
| ~ spl0_138 ),
inference(avatar_split_clause,[],[f1684,f1638,f446,f28713]) ).
fof(f28713,plain,
( spl0_1087
<=> ! [X2,X0,X1] :
( ~ member(X0,compose(X1,rotate_right(X2)))
| little_set(f11(non_ordered_pair(non_ordered_pair(f31(X0,X1,rotate_right(X2)),f31(X0,X1,rotate_right(X2))),non_ordered_pair(f31(X0,X1,rotate_right(X2)),f30(X0,X1,rotate_right(X2)))),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1087])]) ).
fof(f1684,plain,
( ! [X2,X0,X1] :
( ~ member(X0,compose(X1,rotate_right(X2)))
| little_set(f11(non_ordered_pair(non_ordered_pair(f31(X0,X1,rotate_right(X2)),f31(X0,X1,rotate_right(X2))),non_ordered_pair(f31(X0,X1,rotate_right(X2)),f30(X0,X1,rotate_right(X2)))),X2)) )
| ~ spl0_56
| ~ spl0_138 ),
inference(resolution,[],[f1639,f447]) ).
fof(f28711,plain,
( spl0_1086
| ~ spl0_53
| ~ spl0_138 ),
inference(avatar_split_clause,[],[f1679,f1638,f434,f28709]) ).
fof(f28709,plain,
( spl0_1086
<=> ! [X2,X0,X1] :
( ~ member(X0,compose(X1,domain_of(X2)))
| ordered_pair_predicate(f8(non_ordered_pair(non_ordered_pair(f31(X0,X1,domain_of(X2)),f31(X0,X1,domain_of(X2))),non_ordered_pair(f31(X0,X1,domain_of(X2)),f30(X0,X1,domain_of(X2)))),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1086])]) ).
fof(f1679,plain,
( ! [X2,X0,X1] :
( ~ member(X0,compose(X1,domain_of(X2)))
| ordered_pair_predicate(f8(non_ordered_pair(non_ordered_pair(f31(X0,X1,domain_of(X2)),f31(X0,X1,domain_of(X2))),non_ordered_pair(f31(X0,X1,domain_of(X2)),f30(X0,X1,domain_of(X2)))),X2)) )
| ~ spl0_53
| ~ spl0_138 ),
inference(resolution,[],[f1639,f435]) ).
fof(f28707,plain,
( spl0_1085
| ~ spl0_48
| ~ spl0_138 ),
inference(avatar_split_clause,[],[f1673,f1638,f414,f28705]) ).
fof(f28705,plain,
( spl0_1085
<=> ! [X2,X0,X1] :
( ~ member(X0,compose(X1,second(X2)))
| little_set(f6(non_ordered_pair(non_ordered_pair(f31(X0,X1,second(X2)),f31(X0,X1,second(X2))),non_ordered_pair(f31(X0,X1,second(X2)),f30(X0,X1,second(X2)))),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1085])]) ).
fof(f1673,plain,
( ! [X2,X0,X1] :
( ~ member(X0,compose(X1,second(X2)))
| little_set(f6(non_ordered_pair(non_ordered_pair(f31(X0,X1,second(X2)),f31(X0,X1,second(X2))),non_ordered_pair(f31(X0,X1,second(X2)),f30(X0,X1,second(X2)))),X2)) )
| ~ spl0_48
| ~ spl0_138 ),
inference(resolution,[],[f1639,f415]) ).
fof(f28703,plain,
( spl0_1084
| ~ spl0_49
| ~ spl0_138 ),
inference(avatar_split_clause,[],[f1672,f1638,f418,f28701]) ).
fof(f28701,plain,
( spl0_1084
<=> ! [X2,X0,X1] :
( ~ member(X0,compose(X1,second(X2)))
| little_set(f7(non_ordered_pair(non_ordered_pair(f31(X0,X1,second(X2)),f31(X0,X1,second(X2))),non_ordered_pair(f31(X0,X1,second(X2)),f30(X0,X1,second(X2)))),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1084])]) ).
fof(f1672,plain,
( ! [X2,X0,X1] :
( ~ member(X0,compose(X1,second(X2)))
| little_set(f7(non_ordered_pair(non_ordered_pair(f31(X0,X1,second(X2)),f31(X0,X1,second(X2))),non_ordered_pair(f31(X0,X1,second(X2)),f30(X0,X1,second(X2)))),X2)) )
| ~ spl0_49
| ~ spl0_138 ),
inference(resolution,[],[f1639,f419]) ).
fof(f28699,plain,
( spl0_1083
| ~ spl0_46
| ~ spl0_138 ),
inference(avatar_split_clause,[],[f1670,f1638,f406,f28697]) ).
fof(f28697,plain,
( spl0_1083
<=> ! [X2,X0,X1] :
( ~ member(X0,compose(X1,first(X2)))
| little_set(f4(non_ordered_pair(non_ordered_pair(f31(X0,X1,first(X2)),f31(X0,X1,first(X2))),non_ordered_pair(f31(X0,X1,first(X2)),f30(X0,X1,first(X2)))),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1083])]) ).
fof(f1670,plain,
( ! [X2,X0,X1] :
( ~ member(X0,compose(X1,first(X2)))
| little_set(f4(non_ordered_pair(non_ordered_pair(f31(X0,X1,first(X2)),f31(X0,X1,first(X2))),non_ordered_pair(f31(X0,X1,first(X2)),f30(X0,X1,first(X2)))),X2)) )
| ~ spl0_46
| ~ spl0_138 ),
inference(resolution,[],[f1639,f407]) ).
fof(f28695,plain,
( spl0_1082
| ~ spl0_47
| ~ spl0_138 ),
inference(avatar_split_clause,[],[f1669,f1638,f410,f28693]) ).
fof(f28693,plain,
( spl0_1082
<=> ! [X2,X0,X1] :
( ~ member(X0,compose(X1,first(X2)))
| little_set(f5(non_ordered_pair(non_ordered_pair(f31(X0,X1,first(X2)),f31(X0,X1,first(X2))),non_ordered_pair(f31(X0,X1,first(X2)),f30(X0,X1,first(X2)))),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1082])]) ).
fof(f1669,plain,
( ! [X2,X0,X1] :
( ~ member(X0,compose(X1,first(X2)))
| little_set(f5(non_ordered_pair(non_ordered_pair(f31(X0,X1,first(X2)),f31(X0,X1,first(X2))),non_ordered_pair(f31(X0,X1,first(X2)),f30(X0,X1,first(X2)))),X2)) )
| ~ spl0_47
| ~ spl0_138 ),
inference(resolution,[],[f1639,f411]) ).
fof(f28691,plain,
( spl0_1081
| ~ spl0_51
| ~ spl0_136 ),
inference(avatar_split_clause,[],[f1606,f1552,f426,f28689]) ).
fof(f28689,plain,
( spl0_1081
<=> ! [X2,X4,X0,X3,X5,X1] :
( ~ closed(X0,X1)
| ~ maps(X2,intersection(X3,X4),X0)
| homomorphism(X2,intersection(X3,X4),X5,X0,X1)
| ~ closed(intersection(X3,X4),X5)
| member(f33(X2,intersection(X3,X4),X5,X0,X1),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1081])]) ).
fof(f1606,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ closed(X0,X1)
| ~ maps(X2,intersection(X3,X4),X0)
| homomorphism(X2,intersection(X3,X4),X5,X0,X1)
| ~ closed(intersection(X3,X4),X5)
| member(f33(X2,intersection(X3,X4),X5,X0,X1),X3) )
| ~ spl0_51
| ~ spl0_136 ),
inference(resolution,[],[f1553,f427]) ).
fof(f28687,plain,
( spl0_1080
| ~ spl0_52
| ~ spl0_136 ),
inference(avatar_split_clause,[],[f1605,f1552,f430,f28685]) ).
fof(f28685,plain,
( spl0_1080
<=> ! [X2,X4,X0,X3,X5,X1] :
( ~ closed(X0,X1)
| ~ maps(X2,intersection(X3,X4),X0)
| homomorphism(X2,intersection(X3,X4),X5,X0,X1)
| ~ closed(intersection(X3,X4),X5)
| member(f33(X2,intersection(X3,X4),X5,X0,X1),X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1080])]) ).
fof(f1605,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ closed(X0,X1)
| ~ maps(X2,intersection(X3,X4),X0)
| homomorphism(X2,intersection(X3,X4),X5,X0,X1)
| ~ closed(intersection(X3,X4),X5)
| member(f33(X2,intersection(X3,X4),X5,X0,X1),X4) )
| ~ spl0_52
| ~ spl0_136 ),
inference(resolution,[],[f1553,f431]) ).
fof(f28682,plain,
( spl0_1079
| ~ spl0_40
| ~ spl0_168 ),
inference(avatar_split_clause,[],[f2409,f2260,f361,f28680]) ).
fof(f28680,plain,
( spl0_1079
<=> ! [X0] : empty_set = compose(empty_set,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1079])]) ).
fof(f2409,plain,
( ! [X0] : empty_set = compose(empty_set,X0)
| ~ spl0_40
| ~ spl0_168 ),
inference(resolution,[],[f2261,f362]) ).
fof(f28678,plain,
( spl0_1078
| ~ spl0_51
| ~ spl0_134 ),
inference(avatar_split_clause,[],[f1567,f1544,f426,f28676]) ).
fof(f28676,plain,
( spl0_1078
<=> ! [X2,X4,X0,X3,X5,X1] :
( ~ closed(X0,X1)
| ~ maps(X2,intersection(X3,X4),X0)
| homomorphism(X2,intersection(X3,X4),X5,X0,X1)
| ~ closed(intersection(X3,X4),X5)
| member(f32(X2,intersection(X3,X4),X5,X0,X1),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1078])]) ).
fof(f1567,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ closed(X0,X1)
| ~ maps(X2,intersection(X3,X4),X0)
| homomorphism(X2,intersection(X3,X4),X5,X0,X1)
| ~ closed(intersection(X3,X4),X5)
| member(f32(X2,intersection(X3,X4),X5,X0,X1),X3) )
| ~ spl0_51
| ~ spl0_134 ),
inference(resolution,[],[f1545,f427]) ).
fof(f28674,plain,
( spl0_1077
| ~ spl0_52
| ~ spl0_134 ),
inference(avatar_split_clause,[],[f1566,f1544,f430,f28672]) ).
fof(f28672,plain,
( spl0_1077
<=> ! [X2,X4,X0,X3,X5,X1] :
( ~ closed(X0,X1)
| ~ maps(X2,intersection(X3,X4),X0)
| homomorphism(X2,intersection(X3,X4),X5,X0,X1)
| ~ closed(intersection(X3,X4),X5)
| member(f32(X2,intersection(X3,X4),X5,X0,X1),X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1077])]) ).
fof(f1566,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ closed(X0,X1)
| ~ maps(X2,intersection(X3,X4),X0)
| homomorphism(X2,intersection(X3,X4),X5,X0,X1)
| ~ closed(intersection(X3,X4),X5)
| member(f32(X2,intersection(X3,X4),X5,X0,X1),X4) )
| ~ spl0_52
| ~ spl0_134 ),
inference(resolution,[],[f1545,f431]) ).
fof(f28670,plain,
( spl0_1076
| ~ spl0_128
| ~ spl0_133 ),
inference(avatar_split_clause,[],[f1534,f1487,f1401,f28668]) ).
fof(f28668,plain,
( spl0_1076
<=> ! [X2,X0,X1] :
( ~ little_set(X0)
| member(X0,converse(second(non_ordered_pair(non_ordered_pair(X1,X1),non_ordered_pair(X1,X2)))))
| ~ ordered_pair_predicate(X0)
| ~ little_set(X2)
| ~ member(non_ordered_pair(non_ordered_pair(second(X0),second(X0)),non_ordered_pair(second(X0),first(X0))),X2)
| ~ little_set(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1076])]) ).
fof(f1534,plain,
( ! [X2,X0,X1] :
( ~ little_set(X0)
| member(X0,converse(second(non_ordered_pair(non_ordered_pair(X1,X1),non_ordered_pair(X1,X2)))))
| ~ ordered_pair_predicate(X0)
| ~ little_set(X2)
| ~ member(non_ordered_pair(non_ordered_pair(second(X0),second(X0)),non_ordered_pair(second(X0),first(X0))),X2)
| ~ little_set(X1) )
| ~ spl0_128
| ~ spl0_133 ),
inference(resolution,[],[f1488,f1402]) ).
fof(f28666,plain,
( spl0_1075
| ~ spl0_129
| ~ spl0_133 ),
inference(avatar_split_clause,[],[f1531,f1487,f1405,f28664]) ).
fof(f28664,plain,
( spl0_1075
<=> ! [X2,X0,X1] :
( ~ little_set(X0)
| member(X0,converse(first(non_ordered_pair(non_ordered_pair(X1,X1),non_ordered_pair(X1,X2)))))
| ~ ordered_pair_predicate(X0)
| ~ little_set(X2)
| ~ member(non_ordered_pair(non_ordered_pair(second(X0),second(X0)),non_ordered_pair(second(X0),first(X0))),X1)
| ~ little_set(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1075])]) ).
fof(f1531,plain,
( ! [X2,X0,X1] :
( ~ little_set(X0)
| member(X0,converse(first(non_ordered_pair(non_ordered_pair(X1,X1),non_ordered_pair(X1,X2)))))
| ~ ordered_pair_predicate(X0)
| ~ little_set(X2)
| ~ member(non_ordered_pair(non_ordered_pair(second(X0),second(X0)),non_ordered_pair(second(X0),first(X0))),X1)
| ~ little_set(X1) )
| ~ spl0_129
| ~ spl0_133 ),
inference(resolution,[],[f1488,f1406]) ).
fof(f28662,plain,
( spl0_1074
| ~ spl0_44
| ~ spl0_133 ),
inference(avatar_split_clause,[],[f1530,f1487,f377,f28660]) ).
fof(f28660,plain,
( spl0_1074
<=> ! [X0,X1] :
( ~ little_set(X0)
| member(X0,converse(non_ordered_pair(X1,non_ordered_pair(non_ordered_pair(second(X0),second(X0)),non_ordered_pair(second(X0),first(X0))))))
| ~ ordered_pair_predicate(X0)
| ~ little_set(non_ordered_pair(non_ordered_pair(second(X0),second(X0)),non_ordered_pair(second(X0),first(X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1074])]) ).
fof(f1530,plain,
( ! [X0,X1] :
( ~ little_set(X0)
| member(X0,converse(non_ordered_pair(X1,non_ordered_pair(non_ordered_pair(second(X0),second(X0)),non_ordered_pair(second(X0),first(X0))))))
| ~ ordered_pair_predicate(X0)
| ~ little_set(non_ordered_pair(non_ordered_pair(second(X0),second(X0)),non_ordered_pair(second(X0),first(X0)))) )
| ~ spl0_44
| ~ spl0_133 ),
inference(resolution,[],[f1488,f378]) ).
fof(f28658,plain,
( spl0_1073
| ~ spl0_43
| ~ spl0_133 ),
inference(avatar_split_clause,[],[f1529,f1487,f373,f28656]) ).
fof(f28656,plain,
( spl0_1073
<=> ! [X0,X1] :
( ~ little_set(X0)
| member(X0,converse(non_ordered_pair(non_ordered_pair(non_ordered_pair(second(X0),second(X0)),non_ordered_pair(second(X0),first(X0))),X1)))
| ~ ordered_pair_predicate(X0)
| ~ little_set(non_ordered_pair(non_ordered_pair(second(X0),second(X0)),non_ordered_pair(second(X0),first(X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1073])]) ).
fof(f1529,plain,
( ! [X0,X1] :
( ~ little_set(X0)
| member(X0,converse(non_ordered_pair(non_ordered_pair(non_ordered_pair(second(X0),second(X0)),non_ordered_pair(second(X0),first(X0))),X1)))
| ~ ordered_pair_predicate(X0)
| ~ little_set(non_ordered_pair(non_ordered_pair(second(X0),second(X0)),non_ordered_pair(second(X0),first(X0)))) )
| ~ spl0_43
| ~ spl0_133 ),
inference(resolution,[],[f1488,f374]) ).
fof(f28653,plain,
( spl0_1072
| ~ spl0_84
| ~ spl0_132 ),
inference(avatar_split_clause,[],[f1525,f1483,f668,f28651]) ).
fof(f1525,plain,
( ! [X0] :
( non_ordered_pair(non_ordered_pair(f4(f26(first(X0)),X0),f4(f26(first(X0)),X0)),non_ordered_pair(f4(f26(first(X0)),X0),f5(f26(first(X0)),X0))) = X0
| first(X0) = empty_set
| ~ little_set(first(X0)) )
| ~ spl0_84
| ~ spl0_132 ),
inference(resolution,[],[f1484,f669]) ).
fof(f28648,plain,
( spl0_1071
| ~ spl0_84
| ~ spl0_131 ),
inference(avatar_split_clause,[],[f1507,f1479,f668,f28646]) ).
fof(f1507,plain,
( ! [X0] :
( non_ordered_pair(non_ordered_pair(f6(f26(second(X0)),X0),f6(f26(second(X0)),X0)),non_ordered_pair(f6(f26(second(X0)),X0),f7(f26(second(X0)),X0))) = X0
| second(X0) = empty_set
| ~ little_set(second(X0)) )
| ~ spl0_84
| ~ spl0_131 ),
inference(resolution,[],[f1480,f669]) ).
fof(f28644,plain,
( spl0_1070
| ~ spl0_101
| ~ spl0_127 ),
inference(avatar_split_clause,[],[f1419,f1397,f952,f28642]) ).
fof(f28642,plain,
( spl0_1070
<=> ! [X2,X0,X1] :
( ~ member(X0,converse(non_ordered_pair(X1,X2)))
| non_ordered_pair(non_ordered_pair(second(X0),second(X0)),non_ordered_pair(second(X0),first(X0))) = X1
| non_ordered_pair(non_ordered_pair(second(X0),second(X0)),non_ordered_pair(second(X0),first(X0))) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1070])]) ).
fof(f1419,plain,
( ! [X2,X0,X1] :
( ~ member(X0,converse(non_ordered_pair(X1,X2)))
| non_ordered_pair(non_ordered_pair(second(X0),second(X0)),non_ordered_pair(second(X0),first(X0))) = X1
| non_ordered_pair(non_ordered_pair(second(X0),second(X0)),non_ordered_pair(second(X0),first(X0))) = X2 )
| ~ spl0_101
| ~ spl0_127 ),
inference(resolution,[],[f1398,f953]) ).
fof(f28637,plain,
( spl0_1069
| ~ spl0_64
| ~ spl0_168 ),
inference(avatar_split_clause,[],[f2408,f2260,f478,f28635]) ).
fof(f28635,plain,
( spl0_1069
<=> ! [X0,X1] : disjoint(X0,compose(empty_set,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1069])]) ).
fof(f2408,plain,
( ! [X0,X1] : disjoint(X0,compose(empty_set,X1))
| ~ spl0_64
| ~ spl0_168 ),
inference(resolution,[],[f2261,f479]) ).
fof(f28299,plain,
( spl0_1068
| ~ spl0_37
| ~ spl0_139 ),
inference(avatar_split_clause,[],[f1731,f1642,f349,f28297]) ).
fof(f28297,plain,
( spl0_1068
<=> ! [X2,X0,X1] :
( ~ member(X0,compose(powerset(X1),X2))
| subset(non_ordered_pair(non_ordered_pair(f29(X0,powerset(X1),X2),f29(X0,powerset(X1),X2)),non_ordered_pair(f29(X0,powerset(X1),X2),f31(X0,powerset(X1),X2))),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1068])]) ).
fof(f1731,plain,
( ! [X2,X0,X1] :
( ~ member(X0,compose(powerset(X1),X2))
| subset(non_ordered_pair(non_ordered_pair(f29(X0,powerset(X1),X2),f29(X0,powerset(X1),X2)),non_ordered_pair(f29(X0,powerset(X1),X2),f31(X0,powerset(X1),X2))),X1) )
| ~ spl0_37
| ~ spl0_139 ),
inference(resolution,[],[f1643,f350]) ).
fof(f28295,plain,
( spl0_1067
| ~ spl0_34
| ~ spl0_139 ),
inference(avatar_split_clause,[],[f1717,f1642,f336,f28293]) ).
fof(f28293,plain,
( spl0_1067
<=> ! [X2,X0,X1] :
( ~ member(X0,compose(complement(X1),X2))
| ~ member(non_ordered_pair(non_ordered_pair(f29(X0,complement(X1),X2),f29(X0,complement(X1),X2)),non_ordered_pair(f29(X0,complement(X1),X2),f31(X0,complement(X1),X2))),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1067])]) ).
fof(f1717,plain,
( ! [X2,X0,X1] :
( ~ member(X0,compose(complement(X1),X2))
| ~ member(non_ordered_pair(non_ordered_pair(f29(X0,complement(X1),X2),f29(X0,complement(X1),X2)),non_ordered_pair(f29(X0,complement(X1),X2),f31(X0,complement(X1),X2))),X1) )
| ~ spl0_34
| ~ spl0_139 ),
inference(resolution,[],[f1643,f337]) ).
fof(f28291,plain,
( spl0_1066
| ~ spl0_37
| ~ spl0_138 ),
inference(avatar_split_clause,[],[f1691,f1638,f349,f28289]) ).
fof(f28289,plain,
( spl0_1066
<=> ! [X2,X0,X1] :
( ~ member(X0,compose(X1,powerset(X2)))
| subset(non_ordered_pair(non_ordered_pair(f31(X0,X1,powerset(X2)),f31(X0,X1,powerset(X2))),non_ordered_pair(f31(X0,X1,powerset(X2)),f30(X0,X1,powerset(X2)))),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1066])]) ).
fof(f1691,plain,
( ! [X2,X0,X1] :
( ~ member(X0,compose(X1,powerset(X2)))
| subset(non_ordered_pair(non_ordered_pair(f31(X0,X1,powerset(X2)),f31(X0,X1,powerset(X2))),non_ordered_pair(f31(X0,X1,powerset(X2)),f30(X0,X1,powerset(X2)))),X2) )
| ~ spl0_37
| ~ spl0_138 ),
inference(resolution,[],[f1639,f350]) ).
fof(f28286,plain,
( spl0_1065
| ~ spl0_63
| ~ spl0_168 ),
inference(avatar_split_clause,[],[f2407,f2260,f474,f28284]) ).
fof(f28284,plain,
( spl0_1065
<=> ! [X0,X1] : disjoint(compose(empty_set,X0),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1065])]) ).
fof(f2407,plain,
( ! [X0,X1] : disjoint(compose(empty_set,X0),X1)
| ~ spl0_63
| ~ spl0_168 ),
inference(resolution,[],[f2261,f475]) ).
fof(f28282,plain,
( spl0_1064
| ~ spl0_34
| ~ spl0_138 ),
inference(avatar_split_clause,[],[f1677,f1638,f336,f28280]) ).
fof(f28280,plain,
( spl0_1064
<=> ! [X2,X0,X1] :
( ~ member(X0,compose(X1,complement(X2)))
| ~ member(non_ordered_pair(non_ordered_pair(f31(X0,X1,complement(X2)),f31(X0,X1,complement(X2))),non_ordered_pair(f31(X0,X1,complement(X2)),f30(X0,X1,complement(X2)))),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1064])]) ).
fof(f1677,plain,
( ! [X2,X0,X1] :
( ~ member(X0,compose(X1,complement(X2)))
| ~ member(non_ordered_pair(non_ordered_pair(f31(X0,X1,complement(X2)),f31(X0,X1,complement(X2))),non_ordered_pair(f31(X0,X1,complement(X2)),f30(X0,X1,complement(X2)))),X2) )
| ~ spl0_34
| ~ spl0_138 ),
inference(resolution,[],[f1639,f337]) ).
fof(f28275,plain,
( spl0_1063
| ~ spl0_66
| ~ spl0_136 ),
inference(avatar_split_clause,[],[f1626,f1552,f486,f28273]) ).
fof(f28273,plain,
( spl0_1063
<=> ! [X0,X3,X2,X1] :
( ~ closed(X0,X1)
| ~ maps(X2,identity_relation,X0)
| homomorphism(X2,identity_relation,X3,X0,X1)
| ~ closed(identity_relation,X3)
| first(f33(X2,identity_relation,X3,X0,X1)) = second(f33(X2,identity_relation,X3,X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1063])]) ).
fof(f1626,plain,
( ! [X2,X3,X0,X1] :
( ~ closed(X0,X1)
| ~ maps(X2,identity_relation,X0)
| homomorphism(X2,identity_relation,X3,X0,X1)
| ~ closed(identity_relation,X3)
| first(f33(X2,identity_relation,X3,X0,X1)) = second(f33(X2,identity_relation,X3,X0,X1)) )
| ~ spl0_66
| ~ spl0_136 ),
inference(resolution,[],[f1553,f487]) ).
fof(f28271,plain,
( spl0_1062
| ~ spl0_35
| ~ spl0_136 ),
inference(avatar_split_clause,[],[f1612,f1552,f340,f28269]) ).
fof(f28269,plain,
( spl0_1062
<=> ! [X2,X4,X0,X3,X5,X1] :
( ~ closed(X0,X1)
| ~ maps(X2,cross_product(X3,X4),X0)
| homomorphism(X2,cross_product(X3,X4),X5,X0,X1)
| ~ closed(cross_product(X3,X4),X5)
| ordered_pair_predicate(f33(X2,cross_product(X3,X4),X5,X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1062])]) ).
fof(f1612,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ closed(X0,X1)
| ~ maps(X2,cross_product(X3,X4),X0)
| homomorphism(X2,cross_product(X3,X4),X5,X0,X1)
| ~ closed(cross_product(X3,X4),X5)
| ordered_pair_predicate(f33(X2,cross_product(X3,X4),X5,X0,X1)) )
| ~ spl0_35
| ~ spl0_136 ),
inference(resolution,[],[f1553,f341]) ).
fof(f28264,plain,
( spl0_1061
| ~ spl0_66
| ~ spl0_134 ),
inference(avatar_split_clause,[],[f1587,f1544,f486,f28262]) ).
fof(f28262,plain,
( spl0_1061
<=> ! [X0,X3,X2,X1] :
( ~ closed(X0,X1)
| ~ maps(X2,identity_relation,X0)
| homomorphism(X2,identity_relation,X3,X0,X1)
| ~ closed(identity_relation,X3)
| first(f32(X2,identity_relation,X3,X0,X1)) = second(f32(X2,identity_relation,X3,X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1061])]) ).
fof(f1587,plain,
( ! [X2,X3,X0,X1] :
( ~ closed(X0,X1)
| ~ maps(X2,identity_relation,X0)
| homomorphism(X2,identity_relation,X3,X0,X1)
| ~ closed(identity_relation,X3)
| first(f32(X2,identity_relation,X3,X0,X1)) = second(f32(X2,identity_relation,X3,X0,X1)) )
| ~ spl0_66
| ~ spl0_134 ),
inference(resolution,[],[f1545,f487]) ).
fof(f28260,plain,
( spl0_1060
| ~ spl0_35
| ~ spl0_134 ),
inference(avatar_split_clause,[],[f1573,f1544,f340,f28258]) ).
fof(f28258,plain,
( spl0_1060
<=> ! [X2,X4,X0,X3,X5,X1] :
( ~ closed(X0,X1)
| ~ maps(X2,cross_product(X3,X4),X0)
| homomorphism(X2,cross_product(X3,X4),X5,X0,X1)
| ~ closed(cross_product(X3,X4),X5)
| ordered_pair_predicate(f32(X2,cross_product(X3,X4),X5,X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1060])]) ).
fof(f1573,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ closed(X0,X1)
| ~ maps(X2,cross_product(X3,X4),X0)
| homomorphism(X2,cross_product(X3,X4),X5,X0,X1)
| ~ closed(cross_product(X3,X4),X5)
| ordered_pair_predicate(f32(X2,cross_product(X3,X4),X5,X0,X1)) )
| ~ spl0_35
| ~ spl0_134 ),
inference(resolution,[],[f1545,f341]) ).
fof(f28256,plain,
( spl0_1059
| ~ spl0_95
| ~ spl0_127 ),
inference(avatar_split_clause,[],[f1444,f1397,f844,f28254]) ).
fof(f28254,plain,
( spl0_1059
<=> ! [X0,X1] :
( ~ member(X0,converse(range_of(X1)))
| non_ordered_pair(non_ordered_pair(second(X0),second(X0)),non_ordered_pair(second(X0),first(X0))) = second(f27(non_ordered_pair(non_ordered_pair(second(X0),second(X0)),non_ordered_pair(second(X0),first(X0))),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1059])]) ).
fof(f1444,plain,
( ! [X0,X1] :
( ~ member(X0,converse(range_of(X1)))
| non_ordered_pair(non_ordered_pair(second(X0),second(X0)),non_ordered_pair(second(X0),first(X0))) = second(f27(non_ordered_pair(non_ordered_pair(second(X0),second(X0)),non_ordered_pair(second(X0),first(X0))),X1)) )
| ~ spl0_95
| ~ spl0_127 ),
inference(resolution,[],[f1398,f845]) ).
fof(f28252,plain,
( spl0_1058
| ~ spl0_91
| ~ spl0_127 ),
inference(avatar_split_clause,[],[f1428,f1397,f828,f28250]) ).
fof(f28250,plain,
( spl0_1058
<=> ! [X0,X1] :
( ~ member(X0,converse(domain_of(X1)))
| non_ordered_pair(non_ordered_pair(second(X0),second(X0)),non_ordered_pair(second(X0),first(X0))) = first(f8(non_ordered_pair(non_ordered_pair(second(X0),second(X0)),non_ordered_pair(second(X0),first(X0))),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1058])]) ).
fof(f1428,plain,
( ! [X0,X1] :
( ~ member(X0,converse(domain_of(X1)))
| non_ordered_pair(non_ordered_pair(second(X0),second(X0)),non_ordered_pair(second(X0),first(X0))) = first(f8(non_ordered_pair(non_ordered_pair(second(X0),second(X0)),non_ordered_pair(second(X0),first(X0))),X1)) )
| ~ spl0_91
| ~ spl0_127 ),
inference(resolution,[],[f1398,f829]) ).
fof(f28203,plain,
( spl0_1057
| ~ spl0_60
| ~ spl0_168 ),
inference(avatar_split_clause,[],[f2404,f2260,f462,f28201]) ).
fof(f28201,plain,
( spl0_1057
<=> ! [X0,X1] : subset(compose(empty_set,X0),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1057])]) ).
fof(f2404,plain,
( ! [X0,X1] : subset(compose(empty_set,X0),X1)
| ~ spl0_60
| ~ spl0_168 ),
inference(resolution,[],[f2261,f463]) ).
fof(f28170,plain,
( spl0_1056
| ~ spl0_127
| ~ spl0_140 ),
inference(avatar_split_clause,[],[f1754,f1745,f1397,f28168]) ).
fof(f28168,plain,
( spl0_1056
<=> ! [X2,X0,X1] :
( ~ little_set(second(X0))
| ~ little_set(X1)
| ~ little_set(first(X0))
| first(X0) = X1
| ~ member(non_ordered_pair(non_ordered_pair(second(X0),second(X0)),non_ordered_pair(second(X0),X1)),X2)
| ~ single_valued_set(X2)
| ~ member(X0,converse(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1056])]) ).
fof(f1754,plain,
( ! [X2,X0,X1] :
( ~ little_set(second(X0))
| ~ little_set(X1)
| ~ little_set(first(X0))
| first(X0) = X1
| ~ member(non_ordered_pair(non_ordered_pair(second(X0),second(X0)),non_ordered_pair(second(X0),X1)),X2)
| ~ single_valued_set(X2)
| ~ member(X0,converse(X2)) )
| ~ spl0_127
| ~ spl0_140 ),
inference(resolution,[],[f1746,f1398]) ).
fof(f28166,plain,
( spl0_1055
| ~ spl0_28
| ~ spl0_139 ),
inference(avatar_split_clause,[],[f1723,f1642,f306,f28164]) ).
fof(f28164,plain,
( spl0_1055
<=> ! [X2,X0,X1] :
( ~ member(X0,compose(converse(X1),X2))
| ordered_pair_predicate(non_ordered_pair(non_ordered_pair(f29(X0,converse(X1),X2),f29(X0,converse(X1),X2)),non_ordered_pair(f29(X0,converse(X1),X2),f31(X0,converse(X1),X2)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1055])]) ).
fof(f1723,plain,
( ! [X2,X0,X1] :
( ~ member(X0,compose(converse(X1),X2))
| ordered_pair_predicate(non_ordered_pair(non_ordered_pair(f29(X0,converse(X1),X2),f29(X0,converse(X1),X2)),non_ordered_pair(f29(X0,converse(X1),X2),f31(X0,converse(X1),X2)))) )
| ~ spl0_28
| ~ spl0_139 ),
inference(resolution,[],[f1643,f307]) ).
fof(f28162,plain,
( spl0_1054
| ~ spl0_93
| ~ spl0_139 ),
inference(avatar_split_clause,[],[f1704,f1642,f836,f28160]) ).
fof(f28160,plain,
( spl0_1054
<=> ! [X0,X3,X2,X1] :
( ~ member(X0,compose(X1,X2))
| ~ member(X1,X3)
| member(non_ordered_pair(non_ordered_pair(f29(X0,X1,X2),f29(X0,X1,X2)),non_ordered_pair(f29(X0,X1,X2),f31(X0,X1,X2))),sigma(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1054])]) ).
fof(f1704,plain,
( ! [X2,X3,X0,X1] :
( ~ member(X0,compose(X1,X2))
| ~ member(X1,X3)
| member(non_ordered_pair(non_ordered_pair(f29(X0,X1,X2),f29(X0,X1,X2)),non_ordered_pair(f29(X0,X1,X2),f31(X0,X1,X2))),sigma(X3)) )
| ~ spl0_93
| ~ spl0_139 ),
inference(resolution,[],[f1643,f837]) ).
fof(f28158,plain,
( spl0_1053
| ~ spl0_28
| ~ spl0_138 ),
inference(avatar_split_clause,[],[f1683,f1638,f306,f28156]) ).
fof(f28156,plain,
( spl0_1053
<=> ! [X2,X0,X1] :
( ~ member(X0,compose(X1,converse(X2)))
| ordered_pair_predicate(non_ordered_pair(non_ordered_pair(f31(X0,X1,converse(X2)),f31(X0,X1,converse(X2))),non_ordered_pair(f31(X0,X1,converse(X2)),f30(X0,X1,converse(X2))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1053])]) ).
fof(f1683,plain,
( ! [X2,X0,X1] :
( ~ member(X0,compose(X1,converse(X2)))
| ordered_pair_predicate(non_ordered_pair(non_ordered_pair(f31(X0,X1,converse(X2)),f31(X0,X1,converse(X2))),non_ordered_pair(f31(X0,X1,converse(X2)),f30(X0,X1,converse(X2))))) )
| ~ spl0_28
| ~ spl0_138 ),
inference(resolution,[],[f1639,f307]) ).
fof(f28154,plain,
( spl0_1052
| ~ spl0_93
| ~ spl0_138 ),
inference(avatar_split_clause,[],[f1664,f1638,f836,f28152]) ).
fof(f28152,plain,
( spl0_1052
<=> ! [X0,X3,X2,X1] :
( ~ member(X0,compose(X1,X2))
| ~ member(X2,X3)
| member(non_ordered_pair(non_ordered_pair(f31(X0,X1,X2),f31(X0,X1,X2)),non_ordered_pair(f31(X0,X1,X2),f30(X0,X1,X2))),sigma(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1052])]) ).
fof(f1664,plain,
( ! [X2,X3,X0,X1] :
( ~ member(X0,compose(X1,X2))
| ~ member(X2,X3)
| member(non_ordered_pair(non_ordered_pair(f31(X0,X1,X2),f31(X0,X1,X2)),non_ordered_pair(f31(X0,X1,X2),f30(X0,X1,X2))),sigma(X3)) )
| ~ spl0_93
| ~ spl0_138 ),
inference(resolution,[],[f1639,f837]) ).
fof(f28150,plain,
( spl0_1051
| ~ spl0_124
| ~ spl0_133 ),
inference(avatar_split_clause,[],[f1542,f1487,f1299,f28148]) ).
fof(f28148,plain,
( spl0_1051
<=> ! [X2,X0,X1] :
( ~ little_set(X0)
| member(X0,converse(apply(X1,first(X2))))
| ~ ordered_pair_predicate(X0)
| ~ member(X2,X1)
| ~ member(non_ordered_pair(non_ordered_pair(second(X0),second(X0)),non_ordered_pair(second(X0),first(X0))),second(X2))
| ~ ordered_pair_predicate(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1051])]) ).
fof(f1542,plain,
( ! [X2,X0,X1] :
( ~ little_set(X0)
| member(X0,converse(apply(X1,first(X2))))
| ~ ordered_pair_predicate(X0)
| ~ member(X2,X1)
| ~ member(non_ordered_pair(non_ordered_pair(second(X0),second(X0)),non_ordered_pair(second(X0),first(X0))),second(X2))
| ~ ordered_pair_predicate(X2) )
| ~ spl0_124
| ~ spl0_133 ),
inference(resolution,[],[f1488,f1300]) ).
fof(f28085,plain,
( spl0_1050
| ~ spl0_40
| ~ spl0_167 ),
inference(avatar_split_clause,[],[f2378,f2256,f361,f28083]) ).
fof(f28083,plain,
( spl0_1050
<=> ! [X0] : empty_set = compose(X0,empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1050])]) ).
fof(f2378,plain,
( ! [X0] : empty_set = compose(X0,empty_set)
| ~ spl0_40
| ~ spl0_167 ),
inference(resolution,[],[f2257,f362]) ).
fof(f28008,plain,
( spl0_1049
| ~ spl0_64
| ~ spl0_167 ),
inference(avatar_split_clause,[],[f2377,f2256,f478,f28006]) ).
fof(f28006,plain,
( spl0_1049
<=> ! [X0,X1] : disjoint(X0,compose(X1,empty_set)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1049])]) ).
fof(f2377,plain,
( ! [X0,X1] : disjoint(X0,compose(X1,empty_set))
| ~ spl0_64
| ~ spl0_167 ),
inference(resolution,[],[f2257,f479]) ).
fof(f27989,plain,
( spl0_1048
| ~ spl0_63
| ~ spl0_167 ),
inference(avatar_split_clause,[],[f2376,f2256,f474,f27987]) ).
fof(f27987,plain,
( spl0_1048
<=> ! [X0,X1] : disjoint(compose(X0,empty_set),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1048])]) ).
fof(f2376,plain,
( ! [X0,X1] : disjoint(compose(X0,empty_set),X1)
| ~ spl0_63
| ~ spl0_167 ),
inference(resolution,[],[f2257,f475]) ).
fof(f27975,plain,
( spl0_1047
| ~ spl0_173
| ~ spl0_1018 ),
inference(avatar_split_clause,[],[f27854,f27851,f2440,f27973]) ).
fof(f27851,plain,
( spl0_1018
<=> ! [X0] :
( non_ordered_pair(non_ordered_pair(f4(f24(first(X0)),X0),f4(f24(first(X0)),X0)),non_ordered_pair(f4(f24(first(X0)),X0),f5(f24(first(X0)),X0))) = X0
| first(X0) = empty_set ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1018])]) ).
fof(f27854,plain,
( ! [X0] :
( first(X0) = estin
| non_ordered_pair(non_ordered_pair(f4(f24(first(X0)),X0),f4(f24(first(X0)),X0)),non_ordered_pair(f4(f24(first(X0)),X0),f5(f24(first(X0)),X0))) = X0 )
| ~ spl0_173
| ~ spl0_1018 ),
inference(forward_demodulation,[],[f27852,f2442]) ).
fof(f27852,plain,
( ! [X0] :
( non_ordered_pair(non_ordered_pair(f4(f24(first(X0)),X0),f4(f24(first(X0)),X0)),non_ordered_pair(f4(f24(first(X0)),X0),f5(f24(first(X0)),X0))) = X0
| first(X0) = empty_set )
| ~ spl0_1018 ),
inference(avatar_component_clause,[],[f27851]) ).
fof(f27971,plain,
( spl0_1046
| ~ spl0_173
| ~ spl0_1017 ),
inference(avatar_split_clause,[],[f27849,f27846,f2440,f27969]) ).
fof(f27846,plain,
( spl0_1017
<=> ! [X0] :
( non_ordered_pair(non_ordered_pair(f6(f24(second(X0)),X0),f6(f24(second(X0)),X0)),non_ordered_pair(f6(f24(second(X0)),X0),f7(f24(second(X0)),X0))) = X0
| second(X0) = empty_set ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1017])]) ).
fof(f27849,plain,
( ! [X0] :
( second(X0) = estin
| non_ordered_pair(non_ordered_pair(f6(f24(second(X0)),X0),f6(f24(second(X0)),X0)),non_ordered_pair(f6(f24(second(X0)),X0),f7(f24(second(X0)),X0))) = X0 )
| ~ spl0_173
| ~ spl0_1017 ),
inference(forward_demodulation,[],[f27847,f2442]) ).
fof(f27847,plain,
( ! [X0] :
( non_ordered_pair(non_ordered_pair(f6(f24(second(X0)),X0),f6(f24(second(X0)),X0)),non_ordered_pair(f6(f24(second(X0)),X0),f7(f24(second(X0)),X0))) = X0
| second(X0) = empty_set )
| ~ spl0_1017 ),
inference(avatar_component_clause,[],[f27846]) ).
fof(f27965,plain,
( spl0_1045
| ~ spl0_65
| ~ spl0_136 ),
inference(avatar_split_clause,[],[f1625,f1552,f482,f27963]) ).
fof(f27963,plain,
( spl0_1045
<=> ! [X4,X0,X3,X2,X1] :
( ~ closed(X0,X1)
| ~ maps(X2,range_of(X3),X0)
| homomorphism(X2,range_of(X3),X4,X0,X1)
| ~ closed(range_of(X3),X4)
| ordered_pair_predicate(f27(f33(X2,range_of(X3),X4,X0,X1),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1045])]) ).
fof(f1625,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ closed(X0,X1)
| ~ maps(X2,range_of(X3),X0)
| homomorphism(X2,range_of(X3),X4,X0,X1)
| ~ closed(range_of(X3),X4)
| ordered_pair_predicate(f27(f33(X2,range_of(X3),X4,X0,X1),X3)) )
| ~ spl0_65
| ~ spl0_136 ),
inference(resolution,[],[f1553,f483]) ).
fof(f27960,plain,
( spl0_1044
| ~ spl0_60
| ~ spl0_167 ),
inference(avatar_split_clause,[],[f2373,f2256,f462,f27958]) ).
fof(f27958,plain,
( spl0_1044
<=> ! [X0,X1] : subset(compose(X0,empty_set),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1044])]) ).
fof(f2373,plain,
( ! [X0,X1] : subset(compose(X0,empty_set),X1)
| ~ spl0_60
| ~ spl0_167 ),
inference(resolution,[],[f2257,f463]) ).
fof(f27956,plain,
( spl0_1043
| ~ spl0_57
| ~ spl0_136 ),
inference(avatar_split_clause,[],[f1619,f1552,f450,f27954]) ).
fof(f27954,plain,
( spl0_1043
<=> ! [X4,X0,X3,X2,X1] :
( ~ closed(X0,X1)
| ~ maps(X2,flip_range_of(X3),X0)
| homomorphism(X2,flip_range_of(X3),X4,X0,X1)
| ~ closed(flip_range_of(X3),X4)
| little_set(f12(f33(X2,flip_range_of(X3),X4,X0,X1),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1043])]) ).
fof(f1619,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ closed(X0,X1)
| ~ maps(X2,flip_range_of(X3),X0)
| homomorphism(X2,flip_range_of(X3),X4,X0,X1)
| ~ closed(flip_range_of(X3),X4)
| little_set(f12(f33(X2,flip_range_of(X3),X4,X0,X1),X3)) )
| ~ spl0_57
| ~ spl0_136 ),
inference(resolution,[],[f1553,f451]) ).
fof(f27952,plain,
( spl0_1042
| ~ spl0_58
| ~ spl0_136 ),
inference(avatar_split_clause,[],[f1618,f1552,f454,f27950]) ).
fof(f27950,plain,
( spl0_1042
<=> ! [X4,X0,X3,X2,X1] :
( ~ closed(X0,X1)
| ~ maps(X2,flip_range_of(X3),X0)
| homomorphism(X2,flip_range_of(X3),X4,X0,X1)
| ~ closed(flip_range_of(X3),X4)
| little_set(f13(f33(X2,flip_range_of(X3),X4,X0,X1),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1042])]) ).
fof(f1618,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ closed(X0,X1)
| ~ maps(X2,flip_range_of(X3),X0)
| homomorphism(X2,flip_range_of(X3),X4,X0,X1)
| ~ closed(flip_range_of(X3),X4)
| little_set(f13(f33(X2,flip_range_of(X3),X4,X0,X1),X3)) )
| ~ spl0_58
| ~ spl0_136 ),
inference(resolution,[],[f1553,f455]) ).
fof(f27948,plain,
( spl0_1041
| ~ spl0_59
| ~ spl0_136 ),
inference(avatar_split_clause,[],[f1617,f1552,f458,f27946]) ).
fof(f27946,plain,
( spl0_1041
<=> ! [X4,X0,X3,X2,X1] :
( ~ closed(X0,X1)
| ~ maps(X2,flip_range_of(X3),X0)
| homomorphism(X2,flip_range_of(X3),X4,X0,X1)
| ~ closed(flip_range_of(X3),X4)
| little_set(f14(f33(X2,flip_range_of(X3),X4,X0,X1),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1041])]) ).
fof(f1617,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ closed(X0,X1)
| ~ maps(X2,flip_range_of(X3),X0)
| homomorphism(X2,flip_range_of(X3),X4,X0,X1)
| ~ closed(flip_range_of(X3),X4)
| little_set(f14(f33(X2,flip_range_of(X3),X4,X0,X1),X3)) )
| ~ spl0_59
| ~ spl0_136 ),
inference(resolution,[],[f1553,f459]) ).
fof(f27944,plain,
( spl0_1040
| ~ spl0_54
| ~ spl0_136 ),
inference(avatar_split_clause,[],[f1616,f1552,f438,f27942]) ).
fof(f27942,plain,
( spl0_1040
<=> ! [X4,X0,X3,X2,X1] :
( ~ closed(X0,X1)
| ~ maps(X2,rotate_right(X3),X0)
| homomorphism(X2,rotate_right(X3),X4,X0,X1)
| ~ closed(rotate_right(X3),X4)
| little_set(f9(f33(X2,rotate_right(X3),X4,X0,X1),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1040])]) ).
fof(f1616,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ closed(X0,X1)
| ~ maps(X2,rotate_right(X3),X0)
| homomorphism(X2,rotate_right(X3),X4,X0,X1)
| ~ closed(rotate_right(X3),X4)
| little_set(f9(f33(X2,rotate_right(X3),X4,X0,X1),X3)) )
| ~ spl0_54
| ~ spl0_136 ),
inference(resolution,[],[f1553,f439]) ).
fof(f27940,plain,
( spl0_1039
| ~ spl0_55
| ~ spl0_136 ),
inference(avatar_split_clause,[],[f1615,f1552,f442,f27938]) ).
fof(f27938,plain,
( spl0_1039
<=> ! [X4,X0,X3,X2,X1] :
( ~ closed(X0,X1)
| ~ maps(X2,rotate_right(X3),X0)
| homomorphism(X2,rotate_right(X3),X4,X0,X1)
| ~ closed(rotate_right(X3),X4)
| little_set(f10(f33(X2,rotate_right(X3),X4,X0,X1),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1039])]) ).
fof(f1615,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ closed(X0,X1)
| ~ maps(X2,rotate_right(X3),X0)
| homomorphism(X2,rotate_right(X3),X4,X0,X1)
| ~ closed(rotate_right(X3),X4)
| little_set(f10(f33(X2,rotate_right(X3),X4,X0,X1),X3)) )
| ~ spl0_55
| ~ spl0_136 ),
inference(resolution,[],[f1553,f443]) ).
fof(f27936,plain,
( spl0_1038
| ~ spl0_56
| ~ spl0_136 ),
inference(avatar_split_clause,[],[f1614,f1552,f446,f27934]) ).
fof(f27934,plain,
( spl0_1038
<=> ! [X4,X0,X3,X2,X1] :
( ~ closed(X0,X1)
| ~ maps(X2,rotate_right(X3),X0)
| homomorphism(X2,rotate_right(X3),X4,X0,X1)
| ~ closed(rotate_right(X3),X4)
| little_set(f11(f33(X2,rotate_right(X3),X4,X0,X1),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1038])]) ).
fof(f1614,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ closed(X0,X1)
| ~ maps(X2,rotate_right(X3),X0)
| homomorphism(X2,rotate_right(X3),X4,X0,X1)
| ~ closed(rotate_right(X3),X4)
| little_set(f11(f33(X2,rotate_right(X3),X4,X0,X1),X3)) )
| ~ spl0_56
| ~ spl0_136 ),
inference(resolution,[],[f1553,f447]) ).
fof(f27932,plain,
( spl0_1037
| ~ spl0_53
| ~ spl0_136 ),
inference(avatar_split_clause,[],[f1609,f1552,f434,f27930]) ).
fof(f27930,plain,
( spl0_1037
<=> ! [X4,X0,X3,X2,X1] :
( ~ closed(X0,X1)
| ~ maps(X2,domain_of(X3),X0)
| homomorphism(X2,domain_of(X3),X4,X0,X1)
| ~ closed(domain_of(X3),X4)
| ordered_pair_predicate(f8(f33(X2,domain_of(X3),X4,X0,X1),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1037])]) ).
fof(f1609,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ closed(X0,X1)
| ~ maps(X2,domain_of(X3),X0)
| homomorphism(X2,domain_of(X3),X4,X0,X1)
| ~ closed(domain_of(X3),X4)
| ordered_pair_predicate(f8(f33(X2,domain_of(X3),X4,X0,X1),X3)) )
| ~ spl0_53
| ~ spl0_136 ),
inference(resolution,[],[f1553,f435]) ).
fof(f27928,plain,
( spl0_1036
| ~ spl0_48
| ~ spl0_136 ),
inference(avatar_split_clause,[],[f1603,f1552,f414,f27926]) ).
fof(f27926,plain,
( spl0_1036
<=> ! [X4,X0,X3,X2,X1] :
( ~ closed(X0,X1)
| ~ maps(X2,second(X3),X0)
| homomorphism(X2,second(X3),X4,X0,X1)
| ~ closed(second(X3),X4)
| little_set(f6(f33(X2,second(X3),X4,X0,X1),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1036])]) ).
fof(f1603,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ closed(X0,X1)
| ~ maps(X2,second(X3),X0)
| homomorphism(X2,second(X3),X4,X0,X1)
| ~ closed(second(X3),X4)
| little_set(f6(f33(X2,second(X3),X4,X0,X1),X3)) )
| ~ spl0_48
| ~ spl0_136 ),
inference(resolution,[],[f1553,f415]) ).
fof(f27924,plain,
( spl0_1035
| ~ spl0_49
| ~ spl0_136 ),
inference(avatar_split_clause,[],[f1602,f1552,f418,f27922]) ).
fof(f27922,plain,
( spl0_1035
<=> ! [X4,X0,X3,X2,X1] :
( ~ closed(X0,X1)
| ~ maps(X2,second(X3),X0)
| homomorphism(X2,second(X3),X4,X0,X1)
| ~ closed(second(X3),X4)
| little_set(f7(f33(X2,second(X3),X4,X0,X1),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1035])]) ).
fof(f1602,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ closed(X0,X1)
| ~ maps(X2,second(X3),X0)
| homomorphism(X2,second(X3),X4,X0,X1)
| ~ closed(second(X3),X4)
| little_set(f7(f33(X2,second(X3),X4,X0,X1),X3)) )
| ~ spl0_49
| ~ spl0_136 ),
inference(resolution,[],[f1553,f419]) ).
fof(f27920,plain,
( spl0_1034
| ~ spl0_46
| ~ spl0_136 ),
inference(avatar_split_clause,[],[f1600,f1552,f406,f27918]) ).
fof(f27918,plain,
( spl0_1034
<=> ! [X4,X0,X3,X2,X1] :
( ~ closed(X0,X1)
| ~ maps(X2,first(X3),X0)
| homomorphism(X2,first(X3),X4,X0,X1)
| ~ closed(first(X3),X4)
| little_set(f4(f33(X2,first(X3),X4,X0,X1),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1034])]) ).
fof(f1600,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ closed(X0,X1)
| ~ maps(X2,first(X3),X0)
| homomorphism(X2,first(X3),X4,X0,X1)
| ~ closed(first(X3),X4)
| little_set(f4(f33(X2,first(X3),X4,X0,X1),X3)) )
| ~ spl0_46
| ~ spl0_136 ),
inference(resolution,[],[f1553,f407]) ).
fof(f27915,plain,
( spl0_1033
| ~ spl0_40
| ~ spl0_166 ),
inference(avatar_split_clause,[],[f2346,f2251,f361,f27913]) ).
fof(f27913,plain,
( spl0_1033
<=> ! [X0] : empty_set = image(empty_set,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1033])]) ).
fof(f2346,plain,
( ! [X0] : empty_set = image(empty_set,X0)
| ~ spl0_40
| ~ spl0_166 ),
inference(resolution,[],[f2252,f362]) ).
fof(f27911,plain,
( spl0_1032
| ~ spl0_47
| ~ spl0_136 ),
inference(avatar_split_clause,[],[f1599,f1552,f410,f27909]) ).
fof(f27909,plain,
( spl0_1032
<=> ! [X4,X0,X3,X2,X1] :
( ~ closed(X0,X1)
| ~ maps(X2,first(X3),X0)
| homomorphism(X2,first(X3),X4,X0,X1)
| ~ closed(first(X3),X4)
| little_set(f5(f33(X2,first(X3),X4,X0,X1),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1032])]) ).
fof(f1599,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ closed(X0,X1)
| ~ maps(X2,first(X3),X0)
| homomorphism(X2,first(X3),X4,X0,X1)
| ~ closed(first(X3),X4)
| little_set(f5(f33(X2,first(X3),X4,X0,X1),X3)) )
| ~ spl0_47
| ~ spl0_136 ),
inference(resolution,[],[f1553,f411]) ).
fof(f27907,plain,
( spl0_1031
| ~ spl0_65
| ~ spl0_134 ),
inference(avatar_split_clause,[],[f1586,f1544,f482,f27905]) ).
fof(f27905,plain,
( spl0_1031
<=> ! [X4,X0,X3,X2,X1] :
( ~ closed(X0,X1)
| ~ maps(X2,range_of(X3),X0)
| homomorphism(X2,range_of(X3),X4,X0,X1)
| ~ closed(range_of(X3),X4)
| ordered_pair_predicate(f27(f32(X2,range_of(X3),X4,X0,X1),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1031])]) ).
fof(f1586,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ closed(X0,X1)
| ~ maps(X2,range_of(X3),X0)
| homomorphism(X2,range_of(X3),X4,X0,X1)
| ~ closed(range_of(X3),X4)
| ordered_pair_predicate(f27(f32(X2,range_of(X3),X4,X0,X1),X3)) )
| ~ spl0_65
| ~ spl0_134 ),
inference(resolution,[],[f1545,f483]) ).
fof(f27903,plain,
( spl0_1030
| ~ spl0_57
| ~ spl0_134 ),
inference(avatar_split_clause,[],[f1580,f1544,f450,f27901]) ).
fof(f27901,plain,
( spl0_1030
<=> ! [X4,X0,X3,X2,X1] :
( ~ closed(X0,X1)
| ~ maps(X2,flip_range_of(X3),X0)
| homomorphism(X2,flip_range_of(X3),X4,X0,X1)
| ~ closed(flip_range_of(X3),X4)
| little_set(f12(f32(X2,flip_range_of(X3),X4,X0,X1),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1030])]) ).
fof(f1580,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ closed(X0,X1)
| ~ maps(X2,flip_range_of(X3),X0)
| homomorphism(X2,flip_range_of(X3),X4,X0,X1)
| ~ closed(flip_range_of(X3),X4)
| little_set(f12(f32(X2,flip_range_of(X3),X4,X0,X1),X3)) )
| ~ spl0_57
| ~ spl0_134 ),
inference(resolution,[],[f1545,f451]) ).
fof(f27899,plain,
( spl0_1029
| ~ spl0_58
| ~ spl0_134 ),
inference(avatar_split_clause,[],[f1579,f1544,f454,f27897]) ).
fof(f27897,plain,
( spl0_1029
<=> ! [X4,X0,X3,X2,X1] :
( ~ closed(X0,X1)
| ~ maps(X2,flip_range_of(X3),X0)
| homomorphism(X2,flip_range_of(X3),X4,X0,X1)
| ~ closed(flip_range_of(X3),X4)
| little_set(f13(f32(X2,flip_range_of(X3),X4,X0,X1),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1029])]) ).
fof(f1579,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ closed(X0,X1)
| ~ maps(X2,flip_range_of(X3),X0)
| homomorphism(X2,flip_range_of(X3),X4,X0,X1)
| ~ closed(flip_range_of(X3),X4)
| little_set(f13(f32(X2,flip_range_of(X3),X4,X0,X1),X3)) )
| ~ spl0_58
| ~ spl0_134 ),
inference(resolution,[],[f1545,f455]) ).
fof(f27895,plain,
( spl0_1028
| ~ spl0_59
| ~ spl0_134 ),
inference(avatar_split_clause,[],[f1578,f1544,f458,f27893]) ).
fof(f27893,plain,
( spl0_1028
<=> ! [X4,X0,X3,X2,X1] :
( ~ closed(X0,X1)
| ~ maps(X2,flip_range_of(X3),X0)
| homomorphism(X2,flip_range_of(X3),X4,X0,X1)
| ~ closed(flip_range_of(X3),X4)
| little_set(f14(f32(X2,flip_range_of(X3),X4,X0,X1),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1028])]) ).
fof(f1578,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ closed(X0,X1)
| ~ maps(X2,flip_range_of(X3),X0)
| homomorphism(X2,flip_range_of(X3),X4,X0,X1)
| ~ closed(flip_range_of(X3),X4)
| little_set(f14(f32(X2,flip_range_of(X3),X4,X0,X1),X3)) )
| ~ spl0_59
| ~ spl0_134 ),
inference(resolution,[],[f1545,f459]) ).
fof(f27891,plain,
( spl0_1027
| ~ spl0_54
| ~ spl0_134 ),
inference(avatar_split_clause,[],[f1577,f1544,f438,f27889]) ).
fof(f27889,plain,
( spl0_1027
<=> ! [X4,X0,X3,X2,X1] :
( ~ closed(X0,X1)
| ~ maps(X2,rotate_right(X3),X0)
| homomorphism(X2,rotate_right(X3),X4,X0,X1)
| ~ closed(rotate_right(X3),X4)
| little_set(f9(f32(X2,rotate_right(X3),X4,X0,X1),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1027])]) ).
fof(f1577,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ closed(X0,X1)
| ~ maps(X2,rotate_right(X3),X0)
| homomorphism(X2,rotate_right(X3),X4,X0,X1)
| ~ closed(rotate_right(X3),X4)
| little_set(f9(f32(X2,rotate_right(X3),X4,X0,X1),X3)) )
| ~ spl0_54
| ~ spl0_134 ),
inference(resolution,[],[f1545,f439]) ).
fof(f27887,plain,
( spl0_1026
| ~ spl0_55
| ~ spl0_134 ),
inference(avatar_split_clause,[],[f1576,f1544,f442,f27885]) ).
fof(f27885,plain,
( spl0_1026
<=> ! [X4,X0,X3,X2,X1] :
( ~ closed(X0,X1)
| ~ maps(X2,rotate_right(X3),X0)
| homomorphism(X2,rotate_right(X3),X4,X0,X1)
| ~ closed(rotate_right(X3),X4)
| little_set(f10(f32(X2,rotate_right(X3),X4,X0,X1),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1026])]) ).
fof(f1576,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ closed(X0,X1)
| ~ maps(X2,rotate_right(X3),X0)
| homomorphism(X2,rotate_right(X3),X4,X0,X1)
| ~ closed(rotate_right(X3),X4)
| little_set(f10(f32(X2,rotate_right(X3),X4,X0,X1),X3)) )
| ~ spl0_55
| ~ spl0_134 ),
inference(resolution,[],[f1545,f443]) ).
fof(f27883,plain,
( spl0_1025
| ~ spl0_56
| ~ spl0_134 ),
inference(avatar_split_clause,[],[f1575,f1544,f446,f27881]) ).
fof(f27881,plain,
( spl0_1025
<=> ! [X4,X0,X3,X2,X1] :
( ~ closed(X0,X1)
| ~ maps(X2,rotate_right(X3),X0)
| homomorphism(X2,rotate_right(X3),X4,X0,X1)
| ~ closed(rotate_right(X3),X4)
| little_set(f11(f32(X2,rotate_right(X3),X4,X0,X1),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1025])]) ).
fof(f1575,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ closed(X0,X1)
| ~ maps(X2,rotate_right(X3),X0)
| homomorphism(X2,rotate_right(X3),X4,X0,X1)
| ~ closed(rotate_right(X3),X4)
| little_set(f11(f32(X2,rotate_right(X3),X4,X0,X1),X3)) )
| ~ spl0_56
| ~ spl0_134 ),
inference(resolution,[],[f1545,f447]) ).
fof(f27879,plain,
( spl0_1024
| ~ spl0_53
| ~ spl0_134 ),
inference(avatar_split_clause,[],[f1570,f1544,f434,f27877]) ).
fof(f27877,plain,
( spl0_1024
<=> ! [X4,X0,X3,X2,X1] :
( ~ closed(X0,X1)
| ~ maps(X2,domain_of(X3),X0)
| homomorphism(X2,domain_of(X3),X4,X0,X1)
| ~ closed(domain_of(X3),X4)
| ordered_pair_predicate(f8(f32(X2,domain_of(X3),X4,X0,X1),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1024])]) ).
fof(f1570,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ closed(X0,X1)
| ~ maps(X2,domain_of(X3),X0)
| homomorphism(X2,domain_of(X3),X4,X0,X1)
| ~ closed(domain_of(X3),X4)
| ordered_pair_predicate(f8(f32(X2,domain_of(X3),X4,X0,X1),X3)) )
| ~ spl0_53
| ~ spl0_134 ),
inference(resolution,[],[f1545,f435]) ).
fof(f27875,plain,
( spl0_1023
| ~ spl0_48
| ~ spl0_134 ),
inference(avatar_split_clause,[],[f1564,f1544,f414,f27873]) ).
fof(f27873,plain,
( spl0_1023
<=> ! [X4,X0,X3,X2,X1] :
( ~ closed(X0,X1)
| ~ maps(X2,second(X3),X0)
| homomorphism(X2,second(X3),X4,X0,X1)
| ~ closed(second(X3),X4)
| little_set(f6(f32(X2,second(X3),X4,X0,X1),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1023])]) ).
fof(f1564,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ closed(X0,X1)
| ~ maps(X2,second(X3),X0)
| homomorphism(X2,second(X3),X4,X0,X1)
| ~ closed(second(X3),X4)
| little_set(f6(f32(X2,second(X3),X4,X0,X1),X3)) )
| ~ spl0_48
| ~ spl0_134 ),
inference(resolution,[],[f1545,f415]) ).
fof(f27870,plain,
( spl0_1022
| ~ spl0_64
| ~ spl0_166 ),
inference(avatar_split_clause,[],[f2345,f2251,f478,f27868]) ).
fof(f27868,plain,
( spl0_1022
<=> ! [X0,X1] : disjoint(X0,image(empty_set,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1022])]) ).
fof(f2345,plain,
( ! [X0,X1] : disjoint(X0,image(empty_set,X1))
| ~ spl0_64
| ~ spl0_166 ),
inference(resolution,[],[f2252,f479]) ).
fof(f27866,plain,
( spl0_1021
| ~ spl0_49
| ~ spl0_134 ),
inference(avatar_split_clause,[],[f1563,f1544,f418,f27864]) ).
fof(f27864,plain,
( spl0_1021
<=> ! [X4,X0,X3,X2,X1] :
( ~ closed(X0,X1)
| ~ maps(X2,second(X3),X0)
| homomorphism(X2,second(X3),X4,X0,X1)
| ~ closed(second(X3),X4)
| little_set(f7(f32(X2,second(X3),X4,X0,X1),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1021])]) ).
fof(f1563,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ closed(X0,X1)
| ~ maps(X2,second(X3),X0)
| homomorphism(X2,second(X3),X4,X0,X1)
| ~ closed(second(X3),X4)
| little_set(f7(f32(X2,second(X3),X4,X0,X1),X3)) )
| ~ spl0_49
| ~ spl0_134 ),
inference(resolution,[],[f1545,f419]) ).
fof(f27862,plain,
( spl0_1020
| ~ spl0_46
| ~ spl0_134 ),
inference(avatar_split_clause,[],[f1561,f1544,f406,f27860]) ).
fof(f27860,plain,
( spl0_1020
<=> ! [X4,X0,X3,X2,X1] :
( ~ closed(X0,X1)
| ~ maps(X2,first(X3),X0)
| homomorphism(X2,first(X3),X4,X0,X1)
| ~ closed(first(X3),X4)
| little_set(f4(f32(X2,first(X3),X4,X0,X1),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1020])]) ).
fof(f1561,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ closed(X0,X1)
| ~ maps(X2,first(X3),X0)
| homomorphism(X2,first(X3),X4,X0,X1)
| ~ closed(first(X3),X4)
| little_set(f4(f32(X2,first(X3),X4,X0,X1),X3)) )
| ~ spl0_46
| ~ spl0_134 ),
inference(resolution,[],[f1545,f407]) ).
fof(f27858,plain,
( spl0_1019
| ~ spl0_47
| ~ spl0_134 ),
inference(avatar_split_clause,[],[f1560,f1544,f410,f27856]) ).
fof(f27856,plain,
( spl0_1019
<=> ! [X4,X0,X3,X2,X1] :
( ~ closed(X0,X1)
| ~ maps(X2,first(X3),X0)
| homomorphism(X2,first(X3),X4,X0,X1)
| ~ closed(first(X3),X4)
| little_set(f5(f32(X2,first(X3),X4,X0,X1),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1019])]) ).
fof(f1560,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ closed(X0,X1)
| ~ maps(X2,first(X3),X0)
| homomorphism(X2,first(X3),X4,X0,X1)
| ~ closed(first(X3),X4)
| little_set(f5(f32(X2,first(X3),X4,X0,X1),X3)) )
| ~ spl0_47
| ~ spl0_134 ),
inference(resolution,[],[f1545,f411]) ).
fof(f27853,plain,
( spl0_1018
| ~ spl0_40
| ~ spl0_132 ),
inference(avatar_split_clause,[],[f1524,f1483,f361,f27851]) ).
fof(f1524,plain,
( ! [X0] :
( non_ordered_pair(non_ordered_pair(f4(f24(first(X0)),X0),f4(f24(first(X0)),X0)),non_ordered_pair(f4(f24(first(X0)),X0),f5(f24(first(X0)),X0))) = X0
| first(X0) = empty_set )
| ~ spl0_40
| ~ spl0_132 ),
inference(resolution,[],[f1484,f362]) ).
fof(f27848,plain,
( spl0_1017
| ~ spl0_40
| ~ spl0_131 ),
inference(avatar_split_clause,[],[f1506,f1479,f361,f27846]) ).
fof(f1506,plain,
( ! [X0] :
( non_ordered_pair(non_ordered_pair(f6(f24(second(X0)),X0),f6(f24(second(X0)),X0)),non_ordered_pair(f6(f24(second(X0)),X0),f7(f24(second(X0)),X0))) = X0
| second(X0) = empty_set )
| ~ spl0_40
| ~ spl0_131 ),
inference(resolution,[],[f1480,f362]) ).
fof(f27842,plain,
( spl0_1016
| ~ spl0_66
| ~ spl0_127 ),
inference(avatar_split_clause,[],[f1446,f1397,f486,f27840]) ).
fof(f27840,plain,
( spl0_1016
<=> ! [X0] :
( ~ member(X0,converse(identity_relation))
| second(non_ordered_pair(non_ordered_pair(second(X0),second(X0)),non_ordered_pair(second(X0),first(X0)))) = first(non_ordered_pair(non_ordered_pair(second(X0),second(X0)),non_ordered_pair(second(X0),first(X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1016])]) ).
fof(f1446,plain,
( ! [X0] :
( ~ member(X0,converse(identity_relation))
| second(non_ordered_pair(non_ordered_pair(second(X0),second(X0)),non_ordered_pair(second(X0),first(X0)))) = first(non_ordered_pair(non_ordered_pair(second(X0),second(X0)),non_ordered_pair(second(X0),first(X0)))) )
| ~ spl0_66
| ~ spl0_127 ),
inference(resolution,[],[f1398,f487]) ).
fof(f27838,plain,
( spl0_1015
| ~ spl0_110
| ~ spl0_122 ),
inference(avatar_split_clause,[],[f1377,f1291,f1081,f27836]) ).
fof(f27836,plain,
( spl0_1015
<=> ! [X0,X1] :
( single_valued_set(apply(X0,X1))
| first(f28(non_ordered_pair(non_ordered_pair(f19(apply(X0,X1)),f19(apply(X0,X1))),non_ordered_pair(f19(apply(X0,X1)),f21(apply(X0,X1)))),X0,X1)) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1015])]) ).
fof(f1377,plain,
( ! [X0,X1] :
( single_valued_set(apply(X0,X1))
| first(f28(non_ordered_pair(non_ordered_pair(f19(apply(X0,X1)),f19(apply(X0,X1))),non_ordered_pair(f19(apply(X0,X1)),f21(apply(X0,X1)))),X0,X1)) = X1 )
| ~ spl0_110
| ~ spl0_122 ),
inference(resolution,[],[f1292,f1082]) ).
fof(f27834,plain,
( spl0_1014
| ~ spl0_110
| ~ spl0_121 ),
inference(avatar_split_clause,[],[f1335,f1287,f1081,f27832]) ).
fof(f27832,plain,
( spl0_1014
<=> ! [X0,X1] :
( single_valued_set(apply(X0,X1))
| first(f28(non_ordered_pair(non_ordered_pair(f19(apply(X0,X1)),f19(apply(X0,X1))),non_ordered_pair(f19(apply(X0,X1)),f20(apply(X0,X1)))),X0,X1)) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1014])]) ).
fof(f1335,plain,
( ! [X0,X1] :
( single_valued_set(apply(X0,X1))
| first(f28(non_ordered_pair(non_ordered_pair(f19(apply(X0,X1)),f19(apply(X0,X1))),non_ordered_pair(f19(apply(X0,X1)),f20(apply(X0,X1)))),X0,X1)) = X1 )
| ~ spl0_110
| ~ spl0_121 ),
inference(resolution,[],[f1288,f1082]) ).
fof(f27816,plain,
( spl0_1013
| ~ spl0_63
| ~ spl0_166 ),
inference(avatar_split_clause,[],[f2344,f2251,f474,f27814]) ).
fof(f27814,plain,
( spl0_1013
<=> ! [X0,X1] : disjoint(image(empty_set,X0),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1013])]) ).
fof(f2344,plain,
( ! [X0,X1] : disjoint(image(empty_set,X0),X1)
| ~ spl0_63
| ~ spl0_166 ),
inference(resolution,[],[f2252,f475]) ).
fof(f27749,plain,
( ~ spl0_1011
| spl0_1012
| ~ spl0_16
| ~ spl0_140 ),
inference(avatar_split_clause,[],[f1768,f1745,f253,f27747,f27743]) ).
fof(f27743,plain,
( spl0_1011
<=> single_valued_set(universal_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1011])]) ).
fof(f27747,plain,
( spl0_1012
<=> ! [X2,X0,X1] :
( ~ little_set(X0)
| ~ little_set(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X2)))
| ~ member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X1)),universal_set)
| ~ little_set(X2)
| ~ little_set(X1)
| X1 = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1012])]) ).
fof(f1768,plain,
( ! [X2,X0,X1] :
( ~ little_set(X0)
| ~ little_set(X1)
| ~ little_set(X2)
| X1 = X2
| ~ member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X1)),universal_set)
| ~ single_valued_set(universal_set)
| ~ little_set(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X2))) )
| ~ spl0_16
| ~ spl0_140 ),
inference(resolution,[],[f1746,f254]) ).
fof(f27741,plain,
( spl0_1010
| ~ spl0_37
| ~ spl0_136 ),
inference(avatar_split_clause,[],[f1621,f1552,f349,f27739]) ).
fof(f27739,plain,
( spl0_1010
<=> ! [X4,X0,X3,X2,X1] :
( ~ closed(X0,X1)
| ~ maps(X2,powerset(X3),X0)
| homomorphism(X2,powerset(X3),X4,X0,X1)
| ~ closed(powerset(X3),X4)
| subset(f33(X2,powerset(X3),X4,X0,X1),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1010])]) ).
fof(f1621,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ closed(X0,X1)
| ~ maps(X2,powerset(X3),X0)
| homomorphism(X2,powerset(X3),X4,X0,X1)
| ~ closed(powerset(X3),X4)
| subset(f33(X2,powerset(X3),X4,X0,X1),X3) )
| ~ spl0_37
| ~ spl0_136 ),
inference(resolution,[],[f1553,f350]) ).
fof(f27736,plain,
( spl0_1009
| ~ spl0_60
| ~ spl0_166 ),
inference(avatar_split_clause,[],[f2341,f2251,f462,f27734]) ).
fof(f27734,plain,
( spl0_1009
<=> ! [X0,X1] : subset(image(empty_set,X0),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1009])]) ).
fof(f2341,plain,
( ! [X0,X1] : subset(image(empty_set,X0),X1)
| ~ spl0_60
| ~ spl0_166 ),
inference(resolution,[],[f2252,f463]) ).
fof(f27732,plain,
( spl0_1008
| ~ spl0_34
| ~ spl0_136 ),
inference(avatar_split_clause,[],[f1607,f1552,f336,f27730]) ).
fof(f27730,plain,
( spl0_1008
<=> ! [X4,X0,X3,X2,X1] :
( ~ closed(X0,X1)
| ~ maps(X2,complement(X3),X0)
| homomorphism(X2,complement(X3),X4,X0,X1)
| ~ closed(complement(X3),X4)
| ~ member(f33(X2,complement(X3),X4,X0,X1),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1008])]) ).
fof(f1607,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ closed(X0,X1)
| ~ maps(X2,complement(X3),X0)
| homomorphism(X2,complement(X3),X4,X0,X1)
| ~ closed(complement(X3),X4)
| ~ member(f33(X2,complement(X3),X4,X0,X1),X3) )
| ~ spl0_34
| ~ spl0_136 ),
inference(resolution,[],[f1553,f337]) ).
fof(f27728,plain,
( spl0_1007
| ~ spl0_93
| ~ spl0_136 ),
inference(avatar_split_clause,[],[f1594,f1552,f836,f27726]) ).
fof(f27726,plain,
( spl0_1007
<=> ! [X5,X4,X0,X3,X2,X1] :
( ~ closed(X0,X1)
| ~ maps(X2,X3,X0)
| homomorphism(X2,X3,X4,X0,X1)
| ~ closed(X3,X4)
| ~ member(X3,X5)
| member(f33(X2,X3,X4,X0,X1),sigma(X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1007])]) ).
fof(f1594,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ closed(X0,X1)
| ~ maps(X2,X3,X0)
| homomorphism(X2,X3,X4,X0,X1)
| ~ closed(X3,X4)
| ~ member(X3,X5)
| member(f33(X2,X3,X4,X0,X1),sigma(X5)) )
| ~ spl0_93
| ~ spl0_136 ),
inference(resolution,[],[f1553,f837]) ).
fof(f27724,plain,
( spl0_1006
| ~ spl0_37
| ~ spl0_134 ),
inference(avatar_split_clause,[],[f1582,f1544,f349,f27722]) ).
fof(f27722,plain,
( spl0_1006
<=> ! [X4,X0,X3,X2,X1] :
( ~ closed(X0,X1)
| ~ maps(X2,powerset(X3),X0)
| homomorphism(X2,powerset(X3),X4,X0,X1)
| ~ closed(powerset(X3),X4)
| subset(f32(X2,powerset(X3),X4,X0,X1),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1006])]) ).
fof(f1582,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ closed(X0,X1)
| ~ maps(X2,powerset(X3),X0)
| homomorphism(X2,powerset(X3),X4,X0,X1)
| ~ closed(powerset(X3),X4)
| subset(f32(X2,powerset(X3),X4,X0,X1),X3) )
| ~ spl0_37
| ~ spl0_134 ),
inference(resolution,[],[f1545,f350]) ).
fof(f27720,plain,
( spl0_1005
| ~ spl0_34
| ~ spl0_134 ),
inference(avatar_split_clause,[],[f1568,f1544,f336,f27718]) ).
fof(f27718,plain,
( spl0_1005
<=> ! [X4,X0,X3,X2,X1] :
( ~ closed(X0,X1)
| ~ maps(X2,complement(X3),X0)
| homomorphism(X2,complement(X3),X4,X0,X1)
| ~ closed(complement(X3),X4)
| ~ member(f32(X2,complement(X3),X4,X0,X1),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1005])]) ).
fof(f1568,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ closed(X0,X1)
| ~ maps(X2,complement(X3),X0)
| homomorphism(X2,complement(X3),X4,X0,X1)
| ~ closed(complement(X3),X4)
| ~ member(f32(X2,complement(X3),X4,X0,X1),X3) )
| ~ spl0_34
| ~ spl0_134 ),
inference(resolution,[],[f1545,f337]) ).
fof(f27716,plain,
( spl0_1004
| ~ spl0_93
| ~ spl0_134 ),
inference(avatar_split_clause,[],[f1555,f1544,f836,f27714]) ).
fof(f27714,plain,
( spl0_1004
<=> ! [X5,X4,X0,X3,X2,X1] :
( ~ closed(X0,X1)
| ~ maps(X2,X3,X0)
| homomorphism(X2,X3,X4,X0,X1)
| ~ closed(X3,X4)
| ~ member(X3,X5)
| member(f32(X2,X3,X4,X0,X1),sigma(X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1004])]) ).
fof(f1555,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ closed(X0,X1)
| ~ maps(X2,X3,X0)
| homomorphism(X2,X3,X4,X0,X1)
| ~ closed(X3,X4)
| ~ member(X3,X5)
| member(f32(X2,X3,X4,X0,X1),sigma(X5)) )
| ~ spl0_93
| ~ spl0_134 ),
inference(resolution,[],[f1545,f837]) ).
fof(f27712,plain,
( spl0_1003
| ~ spl0_30
| ~ spl0_132 ),
inference(avatar_split_clause,[],[f1520,f1483,f314,f27710]) ).
fof(f27710,plain,
( spl0_1003
<=> ! [X0] :
( non_ordered_pair(non_ordered_pair(f4(f18(first(X0)),X0),f4(f18(first(X0)),X0)),non_ordered_pair(f4(f18(first(X0)),X0),f5(f18(first(X0)),X0))) = X0
| relation(first(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1003])]) ).
fof(f1520,plain,
( ! [X0] :
( non_ordered_pair(non_ordered_pair(f4(f18(first(X0)),X0),f4(f18(first(X0)),X0)),non_ordered_pair(f4(f18(first(X0)),X0),f5(f18(first(X0)),X0))) = X0
| relation(first(X0)) )
| ~ spl0_30
| ~ spl0_132 ),
inference(resolution,[],[f1484,f315]) ).
fof(f27708,plain,
( spl0_1002
| ~ spl0_30
| ~ spl0_131 ),
inference(avatar_split_clause,[],[f1502,f1479,f314,f27706]) ).
fof(f27706,plain,
( spl0_1002
<=> ! [X0] :
( non_ordered_pair(non_ordered_pair(f6(f18(second(X0)),X0),f6(f18(second(X0)),X0)),non_ordered_pair(f6(f18(second(X0)),X0),f7(f18(second(X0)),X0))) = X0
| relation(second(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1002])]) ).
fof(f1502,plain,
( ! [X0] :
( non_ordered_pair(non_ordered_pair(f6(f18(second(X0)),X0),f6(f18(second(X0)),X0)),non_ordered_pair(f6(f18(second(X0)),X0),f7(f18(second(X0)),X0))) = X0
| relation(second(X0)) )
| ~ spl0_30
| ~ spl0_131 ),
inference(resolution,[],[f1480,f315]) ).
fof(f27704,plain,
( spl0_1001
| ~ spl0_114
| ~ spl0_124 ),
inference(avatar_split_clause,[],[f1390,f1299,f1163,f27702]) ).
fof(f27702,plain,
( spl0_1001
<=> ! [X2,X0,X1] :
( ~ member(X0,X1)
| ~ member(f1(X2,apply(X1,first(X0))),second(X0))
| ~ ordered_pair_predicate(X0)
| apply(X1,first(X0)) = X2
| ~ member(f1(X2,apply(X1,first(X0))),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1001])]) ).
fof(f1390,plain,
( ! [X2,X0,X1] :
( ~ member(X0,X1)
| ~ member(f1(X2,apply(X1,first(X0))),second(X0))
| ~ ordered_pair_predicate(X0)
| apply(X1,first(X0)) = X2
| ~ member(f1(X2,apply(X1,first(X0))),X2) )
| ~ spl0_114
| ~ spl0_124 ),
inference(resolution,[],[f1300,f1164]) ).
fof(f27697,plain,
( spl0_1000
| ~ spl0_40
| ~ spl0_165 ),
inference(avatar_split_clause,[],[f2314,f2247,f361,f27695]) ).
fof(f27695,plain,
( spl0_1000
<=> ! [X0] : empty_set = apply(empty_set,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1000])]) ).
fof(f2314,plain,
( ! [X0] : empty_set = apply(empty_set,X0)
| ~ spl0_40
| ~ spl0_165 ),
inference(resolution,[],[f2248,f362]) ).
fof(f27686,plain,
( spl0_999
| ~ spl0_64
| ~ spl0_165 ),
inference(avatar_split_clause,[],[f2313,f2247,f478,f27684]) ).
fof(f27684,plain,
( spl0_999
<=> ! [X0,X1] : disjoint(X0,apply(empty_set,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_999])]) ).
fof(f2313,plain,
( ! [X0,X1] : disjoint(X0,apply(empty_set,X1))
| ~ spl0_64
| ~ spl0_165 ),
inference(resolution,[],[f2248,f479]) ).
fof(f27372,plain,
( spl0_998
| ~ spl0_38
| ~ spl0_139 ),
inference(avatar_split_clause,[],[f1705,f1642,f353,f27370]) ).
fof(f27370,plain,
( spl0_998
<=> ! [X2,X0,X1] :
( ~ member(X0,compose(X1,X2))
| ordered_pair_predicate(non_ordered_pair(non_ordered_pair(f29(X0,X1,X2),f29(X0,X1,X2)),non_ordered_pair(f29(X0,X1,X2),f31(X0,X1,X2))))
| ~ relation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_998])]) ).
fof(f1705,plain,
( ! [X2,X0,X1] :
( ~ member(X0,compose(X1,X2))
| ordered_pair_predicate(non_ordered_pair(non_ordered_pair(f29(X0,X1,X2),f29(X0,X1,X2)),non_ordered_pair(f29(X0,X1,X2),f31(X0,X1,X2))))
| ~ relation(X1) )
| ~ spl0_38
| ~ spl0_139 ),
inference(resolution,[],[f1643,f354]) ).
fof(f27368,plain,
( spl0_997
| ~ spl0_38
| ~ spl0_138 ),
inference(avatar_split_clause,[],[f1665,f1638,f353,f27366]) ).
fof(f27366,plain,
( spl0_997
<=> ! [X2,X0,X1] :
( ~ member(X0,compose(X1,X2))
| ordered_pair_predicate(non_ordered_pair(non_ordered_pair(f31(X0,X1,X2),f31(X0,X1,X2)),non_ordered_pair(f31(X0,X1,X2),f30(X0,X1,X2))))
| ~ relation(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_997])]) ).
fof(f1665,plain,
( ! [X2,X0,X1] :
( ~ member(X0,compose(X1,X2))
| ordered_pair_predicate(non_ordered_pair(non_ordered_pair(f31(X0,X1,X2),f31(X0,X1,X2)),non_ordered_pair(f31(X0,X1,X2),f30(X0,X1,X2))))
| ~ relation(X2) )
| ~ spl0_38
| ~ spl0_138 ),
inference(resolution,[],[f1639,f354]) ).
fof(f27364,plain,
( spl0_996
| ~ spl0_28
| ~ spl0_136 ),
inference(avatar_split_clause,[],[f1613,f1552,f306,f27362]) ).
fof(f27362,plain,
( spl0_996
<=> ! [X4,X0,X3,X2,X1] :
( ~ closed(X0,X1)
| ~ maps(X2,converse(X3),X0)
| homomorphism(X2,converse(X3),X4,X0,X1)
| ~ closed(converse(X3),X4)
| ordered_pair_predicate(f33(X2,converse(X3),X4,X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_996])]) ).
fof(f1613,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ closed(X0,X1)
| ~ maps(X2,converse(X3),X0)
| homomorphism(X2,converse(X3),X4,X0,X1)
| ~ closed(converse(X3),X4)
| ordered_pair_predicate(f33(X2,converse(X3),X4,X0,X1)) )
| ~ spl0_28
| ~ spl0_136 ),
inference(resolution,[],[f1553,f307]) ).
fof(f27360,plain,
( spl0_995
| ~ spl0_28
| ~ spl0_134 ),
inference(avatar_split_clause,[],[f1574,f1544,f306,f27358]) ).
fof(f27358,plain,
( spl0_995
<=> ! [X4,X0,X3,X2,X1] :
( ~ closed(X0,X1)
| ~ maps(X2,converse(X3),X0)
| homomorphism(X2,converse(X3),X4,X0,X1)
| ~ closed(converse(X3),X4)
| ordered_pair_predicate(f32(X2,converse(X3),X4,X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_995])]) ).
fof(f1574,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ closed(X0,X1)
| ~ maps(X2,converse(X3),X0)
| homomorphism(X2,converse(X3),X4,X0,X1)
| ~ closed(converse(X3),X4)
| ordered_pair_predicate(f32(X2,converse(X3),X4,X0,X1)) )
| ~ spl0_28
| ~ spl0_134 ),
inference(resolution,[],[f1545,f307]) ).
fof(f27356,plain,
( spl0_994
| ~ spl0_97
| ~ spl0_122 ),
inference(avatar_split_clause,[],[f1381,f1291,f852,f27354]) ).
fof(f27354,plain,
( spl0_994
<=> ! [X0,X1] :
( single_valued_set(compose(X0,X1))
| little_set(f29(non_ordered_pair(non_ordered_pair(f19(compose(X0,X1)),f19(compose(X0,X1))),non_ordered_pair(f19(compose(X0,X1)),f21(compose(X0,X1)))),X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_994])]) ).
fof(f1381,plain,
( ! [X0,X1] :
( single_valued_set(compose(X0,X1))
| little_set(f29(non_ordered_pair(non_ordered_pair(f19(compose(X0,X1)),f19(compose(X0,X1))),non_ordered_pair(f19(compose(X0,X1)),f21(compose(X0,X1)))),X0,X1)) )
| ~ spl0_97
| ~ spl0_122 ),
inference(resolution,[],[f1292,f853]) ).
fof(f27352,plain,
( spl0_993
| ~ spl0_98
| ~ spl0_122 ),
inference(avatar_split_clause,[],[f1380,f1291,f856,f27350]) ).
fof(f27350,plain,
( spl0_993
<=> ! [X0,X1] :
( single_valued_set(compose(X0,X1))
| little_set(f30(non_ordered_pair(non_ordered_pair(f19(compose(X0,X1)),f19(compose(X0,X1))),non_ordered_pair(f19(compose(X0,X1)),f21(compose(X0,X1)))),X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_993])]) ).
fof(f1380,plain,
( ! [X0,X1] :
( single_valued_set(compose(X0,X1))
| little_set(f30(non_ordered_pair(non_ordered_pair(f19(compose(X0,X1)),f19(compose(X0,X1))),non_ordered_pair(f19(compose(X0,X1)),f21(compose(X0,X1)))),X0,X1)) )
| ~ spl0_98
| ~ spl0_122 ),
inference(resolution,[],[f1292,f857]) ).
fof(f27347,plain,
( spl0_992
| ~ spl0_63
| ~ spl0_165 ),
inference(avatar_split_clause,[],[f2312,f2247,f474,f27345]) ).
fof(f27345,plain,
( spl0_992
<=> ! [X0,X1] : disjoint(apply(empty_set,X0),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_992])]) ).
fof(f2312,plain,
( ! [X0,X1] : disjoint(apply(empty_set,X0),X1)
| ~ spl0_63
| ~ spl0_165 ),
inference(resolution,[],[f2248,f475]) ).
fof(f27343,plain,
( spl0_991
| ~ spl0_99
| ~ spl0_122 ),
inference(avatar_split_clause,[],[f1379,f1291,f860,f27341]) ).
fof(f27341,plain,
( spl0_991
<=> ! [X0,X1] :
( single_valued_set(compose(X0,X1))
| little_set(f31(non_ordered_pair(non_ordered_pair(f19(compose(X0,X1)),f19(compose(X0,X1))),non_ordered_pair(f19(compose(X0,X1)),f21(compose(X0,X1)))),X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_991])]) ).
fof(f1379,plain,
( ! [X0,X1] :
( single_valued_set(compose(X0,X1))
| little_set(f31(non_ordered_pair(non_ordered_pair(f19(compose(X0,X1)),f19(compose(X0,X1))),non_ordered_pair(f19(compose(X0,X1)),f21(compose(X0,X1)))),X0,X1)) )
| ~ spl0_99
| ~ spl0_122 ),
inference(resolution,[],[f1292,f861]) ).
fof(f27339,plain,
( spl0_990
| ~ spl0_96
| ~ spl0_122 ),
inference(avatar_split_clause,[],[f1378,f1291,f848,f27337]) ).
fof(f27337,plain,
( spl0_990
<=> ! [X0,X1] :
( single_valued_set(apply(X0,X1))
| ordered_pair_predicate(f28(non_ordered_pair(non_ordered_pair(f19(apply(X0,X1)),f19(apply(X0,X1))),non_ordered_pair(f19(apply(X0,X1)),f21(apply(X0,X1)))),X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_990])]) ).
fof(f1378,plain,
( ! [X0,X1] :
( single_valued_set(apply(X0,X1))
| ordered_pair_predicate(f28(non_ordered_pair(non_ordered_pair(f19(apply(X0,X1)),f19(apply(X0,X1))),non_ordered_pair(f19(apply(X0,X1)),f21(apply(X0,X1)))),X0,X1)) )
| ~ spl0_96
| ~ spl0_122 ),
inference(resolution,[],[f1292,f849]) ).
fof(f27335,plain,
( ~ spl0_989
| ~ spl0_177
| spl0_988 ),
inference(avatar_split_clause,[],[f27330,f27326,f2481,f27332]) ).
fof(f27332,plain,
( spl0_989
<=> first(non_ordered_pair(non_ordered_pair(f19(estin),f19(estin)),non_ordered_pair(f19(estin),f21(estin)))) = second(non_ordered_pair(non_ordered_pair(f19(estin),f19(estin)),non_ordered_pair(f19(estin),f21(estin)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_989])]) ).
fof(f27326,plain,
( spl0_988
<=> first(non_ordered_pair(non_ordered_pair(f19(identity_relation),f19(identity_relation)),non_ordered_pair(f19(identity_relation),f21(identity_relation)))) = second(non_ordered_pair(non_ordered_pair(f19(identity_relation),f19(identity_relation)),non_ordered_pair(f19(identity_relation),f21(identity_relation)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_988])]) ).
fof(f27330,plain,
( first(non_ordered_pair(non_ordered_pair(f19(estin),f19(estin)),non_ordered_pair(f19(estin),f21(estin)))) != second(non_ordered_pair(non_ordered_pair(f19(estin),f19(estin)),non_ordered_pair(f19(estin),f21(estin))))
| ~ spl0_177
| spl0_988 ),
inference(forward_demodulation,[],[f27327,f2483]) ).
fof(f27327,plain,
( first(non_ordered_pair(non_ordered_pair(f19(identity_relation),f19(identity_relation)),non_ordered_pair(f19(identity_relation),f21(identity_relation)))) != second(non_ordered_pair(non_ordered_pair(f19(identity_relation),f19(identity_relation)),non_ordered_pair(f19(identity_relation),f21(identity_relation))))
| spl0_988 ),
inference(avatar_component_clause,[],[f27326]) ).
fof(f27329,plain,
( spl0_988
| spl0_585
| ~ spl0_66
| ~ spl0_122 ),
inference(avatar_split_clause,[],[f1375,f1291,f486,f7480,f27326]) ).
fof(f7480,plain,
( spl0_585
<=> single_valued_set(identity_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_585])]) ).
fof(f1375,plain,
( single_valued_set(identity_relation)
| first(non_ordered_pair(non_ordered_pair(f19(identity_relation),f19(identity_relation)),non_ordered_pair(f19(identity_relation),f21(identity_relation)))) = second(non_ordered_pair(non_ordered_pair(f19(identity_relation),f19(identity_relation)),non_ordered_pair(f19(identity_relation),f21(identity_relation))))
| ~ spl0_66
| ~ spl0_122 ),
inference(resolution,[],[f1292,f487]) ).
fof(f27324,plain,
( spl0_987
| ~ spl0_94
| ~ spl0_122 ),
inference(avatar_split_clause,[],[f1372,f1291,f840,f27322]) ).
fof(f27322,plain,
( spl0_987
<=> ! [X0,X1] :
( single_valued_set(image(X0,X1))
| ordered_pair_predicate(f22(non_ordered_pair(non_ordered_pair(f19(image(X0,X1)),f19(image(X0,X1))),non_ordered_pair(f19(image(X0,X1)),f21(image(X0,X1)))),X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_987])]) ).
fof(f1372,plain,
( ! [X0,X1] :
( single_valued_set(image(X0,X1))
| ordered_pair_predicate(f22(non_ordered_pair(non_ordered_pair(f19(image(X0,X1)),f19(image(X0,X1))),non_ordered_pair(f19(image(X0,X1)),f21(image(X0,X1)))),X0,X1)) )
| ~ spl0_94
| ~ spl0_122 ),
inference(resolution,[],[f1292,f841]) ).
fof(f27320,plain,
( spl0_986
| ~ spl0_97
| ~ spl0_121 ),
inference(avatar_split_clause,[],[f1339,f1287,f852,f27318]) ).
fof(f27318,plain,
( spl0_986
<=> ! [X0,X1] :
( single_valued_set(compose(X0,X1))
| little_set(f29(non_ordered_pair(non_ordered_pair(f19(compose(X0,X1)),f19(compose(X0,X1))),non_ordered_pair(f19(compose(X0,X1)),f20(compose(X0,X1)))),X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_986])]) ).
fof(f1339,plain,
( ! [X0,X1] :
( single_valued_set(compose(X0,X1))
| little_set(f29(non_ordered_pair(non_ordered_pair(f19(compose(X0,X1)),f19(compose(X0,X1))),non_ordered_pair(f19(compose(X0,X1)),f20(compose(X0,X1)))),X0,X1)) )
| ~ spl0_97
| ~ spl0_121 ),
inference(resolution,[],[f1288,f853]) ).
fof(f27316,plain,
( spl0_985
| ~ spl0_98
| ~ spl0_121 ),
inference(avatar_split_clause,[],[f1338,f1287,f856,f27314]) ).
fof(f27314,plain,
( spl0_985
<=> ! [X0,X1] :
( single_valued_set(compose(X0,X1))
| little_set(f30(non_ordered_pair(non_ordered_pair(f19(compose(X0,X1)),f19(compose(X0,X1))),non_ordered_pair(f19(compose(X0,X1)),f20(compose(X0,X1)))),X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_985])]) ).
fof(f1338,plain,
( ! [X0,X1] :
( single_valued_set(compose(X0,X1))
| little_set(f30(non_ordered_pair(non_ordered_pair(f19(compose(X0,X1)),f19(compose(X0,X1))),non_ordered_pair(f19(compose(X0,X1)),f20(compose(X0,X1)))),X0,X1)) )
| ~ spl0_98
| ~ spl0_121 ),
inference(resolution,[],[f1288,f857]) ).
fof(f27312,plain,
( spl0_984
| ~ spl0_99
| ~ spl0_121 ),
inference(avatar_split_clause,[],[f1337,f1287,f860,f27310]) ).
fof(f27310,plain,
( spl0_984
<=> ! [X0,X1] :
( single_valued_set(compose(X0,X1))
| little_set(f31(non_ordered_pair(non_ordered_pair(f19(compose(X0,X1)),f19(compose(X0,X1))),non_ordered_pair(f19(compose(X0,X1)),f20(compose(X0,X1)))),X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_984])]) ).
fof(f1337,plain,
( ! [X0,X1] :
( single_valued_set(compose(X0,X1))
| little_set(f31(non_ordered_pair(non_ordered_pair(f19(compose(X0,X1)),f19(compose(X0,X1))),non_ordered_pair(f19(compose(X0,X1)),f20(compose(X0,X1)))),X0,X1)) )
| ~ spl0_99
| ~ spl0_121 ),
inference(resolution,[],[f1288,f861]) ).
fof(f27308,plain,
( spl0_983
| ~ spl0_96
| ~ spl0_121 ),
inference(avatar_split_clause,[],[f1336,f1287,f848,f27306]) ).
fof(f27306,plain,
( spl0_983
<=> ! [X0,X1] :
( single_valued_set(apply(X0,X1))
| ordered_pair_predicate(f28(non_ordered_pair(non_ordered_pair(f19(apply(X0,X1)),f19(apply(X0,X1))),non_ordered_pair(f19(apply(X0,X1)),f20(apply(X0,X1)))),X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_983])]) ).
fof(f1336,plain,
( ! [X0,X1] :
( single_valued_set(apply(X0,X1))
| ordered_pair_predicate(f28(non_ordered_pair(non_ordered_pair(f19(apply(X0,X1)),f19(apply(X0,X1))),non_ordered_pair(f19(apply(X0,X1)),f20(apply(X0,X1)))),X0,X1)) )
| ~ spl0_96
| ~ spl0_121 ),
inference(resolution,[],[f1288,f849]) ).
fof(f27303,plain,
( spl0_982
| ~ spl0_60
| ~ spl0_165 ),
inference(avatar_split_clause,[],[f2309,f2247,f462,f27301]) ).
fof(f27301,plain,
( spl0_982
<=> ! [X0,X1] : subset(apply(empty_set,X0),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_982])]) ).
fof(f2309,plain,
( ! [X0,X1] : subset(apply(empty_set,X0),X1)
| ~ spl0_60
| ~ spl0_165 ),
inference(resolution,[],[f2248,f463]) ).
fof(f27299,plain,
( ~ spl0_981
| ~ spl0_177
| spl0_980 ),
inference(avatar_split_clause,[],[f27294,f27290,f2481,f27296]) ).
fof(f27296,plain,
( spl0_981
<=> first(non_ordered_pair(non_ordered_pair(f19(estin),f19(estin)),non_ordered_pair(f19(estin),f20(estin)))) = second(non_ordered_pair(non_ordered_pair(f19(estin),f19(estin)),non_ordered_pair(f19(estin),f20(estin)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_981])]) ).
fof(f27290,plain,
( spl0_980
<=> first(non_ordered_pair(non_ordered_pair(f19(identity_relation),f19(identity_relation)),non_ordered_pair(f19(identity_relation),f20(identity_relation)))) = second(non_ordered_pair(non_ordered_pair(f19(identity_relation),f19(identity_relation)),non_ordered_pair(f19(identity_relation),f20(identity_relation)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_980])]) ).
fof(f27294,plain,
( first(non_ordered_pair(non_ordered_pair(f19(estin),f19(estin)),non_ordered_pair(f19(estin),f20(estin)))) != second(non_ordered_pair(non_ordered_pair(f19(estin),f19(estin)),non_ordered_pair(f19(estin),f20(estin))))
| ~ spl0_177
| spl0_980 ),
inference(forward_demodulation,[],[f27291,f2483]) ).
fof(f27291,plain,
( first(non_ordered_pair(non_ordered_pair(f19(identity_relation),f19(identity_relation)),non_ordered_pair(f19(identity_relation),f20(identity_relation)))) != second(non_ordered_pair(non_ordered_pair(f19(identity_relation),f19(identity_relation)),non_ordered_pair(f19(identity_relation),f20(identity_relation))))
| spl0_980 ),
inference(avatar_component_clause,[],[f27290]) ).
fof(f27293,plain,
( spl0_980
| spl0_585
| ~ spl0_66
| ~ spl0_121 ),
inference(avatar_split_clause,[],[f1333,f1287,f486,f7480,f27290]) ).
fof(f1333,plain,
( single_valued_set(identity_relation)
| first(non_ordered_pair(non_ordered_pair(f19(identity_relation),f19(identity_relation)),non_ordered_pair(f19(identity_relation),f20(identity_relation)))) = second(non_ordered_pair(non_ordered_pair(f19(identity_relation),f19(identity_relation)),non_ordered_pair(f19(identity_relation),f20(identity_relation))))
| ~ spl0_66
| ~ spl0_121 ),
inference(resolution,[],[f1288,f487]) ).
fof(f27288,plain,
( spl0_979
| ~ spl0_94
| ~ spl0_121 ),
inference(avatar_split_clause,[],[f1330,f1287,f840,f27286]) ).
fof(f27286,plain,
( spl0_979
<=> ! [X0,X1] :
( single_valued_set(image(X0,X1))
| ordered_pair_predicate(f22(non_ordered_pair(non_ordered_pair(f19(image(X0,X1)),f19(image(X0,X1))),non_ordered_pair(f19(image(X0,X1)),f20(image(X0,X1)))),X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_979])]) ).
fof(f1330,plain,
( ! [X0,X1] :
( single_valued_set(image(X0,X1))
| ordered_pair_predicate(f22(non_ordered_pair(non_ordered_pair(f19(image(X0,X1)),f19(image(X0,X1))),non_ordered_pair(f19(image(X0,X1)),f20(image(X0,X1)))),X0,X1)) )
| ~ spl0_94
| ~ spl0_121 ),
inference(resolution,[],[f1288,f841]) ).
fof(f27284,plain,
( spl0_978
| ~ spl0_108
| ~ spl0_113 ),
inference(avatar_split_clause,[],[f1245,f1159,f1072,f27282]) ).
fof(f27282,plain,
( spl0_978
<=> ! [X2,X0,X1] :
( member(f1(image(X0,X1),X2),X2)
| image(X0,X1) = X2
| f1(image(X0,X1),X2) = second(f22(f1(image(X0,X1),X2),X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_978])]) ).
fof(f1245,plain,
( ! [X2,X0,X1] :
( member(f1(image(X0,X1),X2),X2)
| image(X0,X1) = X2
| f1(image(X0,X1),X2) = second(f22(f1(image(X0,X1),X2),X0,X1)) )
| ~ spl0_108
| ~ spl0_113 ),
inference(resolution,[],[f1160,f1073]) ).
fof(f27280,plain,
( spl0_977
| ~ spl0_108
| ~ spl0_113 ),
inference(avatar_split_clause,[],[f1208,f1159,f1072,f27278]) ).
fof(f27278,plain,
( spl0_977
<=> ! [X2,X0,X1] :
( member(f1(X0,image(X1,X2)),X0)
| image(X1,X2) = X0
| f1(X0,image(X1,X2)) = second(f22(f1(X0,image(X1,X2)),X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_977])]) ).
fof(f1208,plain,
( ! [X2,X0,X1] :
( member(f1(X0,image(X1,X2)),X0)
| image(X1,X2) = X0
| f1(X0,image(X1,X2)) = second(f22(f1(X0,image(X1,X2)),X1,X2)) )
| ~ spl0_108
| ~ spl0_113 ),
inference(resolution,[],[f1160,f1073]) ).
fof(f26954,plain,
( spl0_976
| ~ spl0_40
| ~ spl0_164 ),
inference(avatar_split_clause,[],[f2282,f2243,f361,f26952]) ).
fof(f26952,plain,
( spl0_976
<=> ! [X0] : empty_set = image(X0,empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_976])]) ).
fof(f2282,plain,
( ! [X0] : empty_set = image(X0,empty_set)
| ~ spl0_40
| ~ spl0_164 ),
inference(resolution,[],[f2244,f362]) ).
fof(f26134,plain,
( spl0_975
| ~ spl0_61
| ~ spl0_129 ),
inference(avatar_split_clause,[],[f1468,f1405,f466,f26132]) ).
fof(f26132,plain,
( spl0_975
<=> ! [X2,X0,X1] :
( ~ little_set(X0)
| ~ member(f17(X1,first(non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X0)))),X2)
| ~ little_set(X2)
| subset(X1,first(non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_975])]) ).
fof(f1468,plain,
( ! [X2,X0,X1] :
( ~ little_set(X0)
| ~ member(f17(X1,first(non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X0)))),X2)
| ~ little_set(X2)
| subset(X1,first(non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X0)))) )
| ~ spl0_61
| ~ spl0_129 ),
inference(resolution,[],[f1406,f467]) ).
fof(f26130,plain,
( spl0_974
| ~ spl0_61
| ~ spl0_128 ),
inference(avatar_split_clause,[],[f1460,f1401,f466,f26128]) ).
fof(f26128,plain,
( spl0_974
<=> ! [X2,X0,X1] :
( ~ little_set(X0)
| ~ member(f17(X1,second(non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X0)))),X0)
| ~ little_set(X2)
| subset(X1,second(non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_974])]) ).
fof(f1460,plain,
( ! [X2,X0,X1] :
( ~ little_set(X0)
| ~ member(f17(X1,second(non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X0)))),X0)
| ~ little_set(X2)
| subset(X1,second(non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X0)))) )
| ~ spl0_61
| ~ spl0_128 ),
inference(resolution,[],[f1402,f467]) ).
fof(f26126,plain,
( spl0_973
| ~ spl0_75
| ~ spl0_122 ),
inference(avatar_split_clause,[],[f1360,f1291,f632,f26124]) ).
fof(f26124,plain,
( spl0_973
<=> ! [X0,X1] :
( single_valued_set(cross_product(X0,X1))
| member(first(non_ordered_pair(non_ordered_pair(f19(cross_product(X0,X1)),f19(cross_product(X0,X1))),non_ordered_pair(f19(cross_product(X0,X1)),f21(cross_product(X0,X1))))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_973])]) ).
fof(f1360,plain,
( ! [X0,X1] :
( single_valued_set(cross_product(X0,X1))
| member(first(non_ordered_pair(non_ordered_pair(f19(cross_product(X0,X1)),f19(cross_product(X0,X1))),non_ordered_pair(f19(cross_product(X0,X1)),f21(cross_product(X0,X1))))),X0) )
| ~ spl0_75
| ~ spl0_122 ),
inference(resolution,[],[f1292,f633]) ).
fof(f26122,plain,
( spl0_972
| ~ spl0_77
| ~ spl0_122 ),
inference(avatar_split_clause,[],[f1359,f1291,f640,f26120]) ).
fof(f26120,plain,
( spl0_972
<=> ! [X0,X1] :
( single_valued_set(cross_product(X0,X1))
| member(second(non_ordered_pair(non_ordered_pair(f19(cross_product(X0,X1)),f19(cross_product(X0,X1))),non_ordered_pair(f19(cross_product(X0,X1)),f21(cross_product(X0,X1))))),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_972])]) ).
fof(f1359,plain,
( ! [X0,X1] :
( single_valued_set(cross_product(X0,X1))
| member(second(non_ordered_pair(non_ordered_pair(f19(cross_product(X0,X1)),f19(cross_product(X0,X1))),non_ordered_pair(f19(cross_product(X0,X1)),f21(cross_product(X0,X1))))),X1) )
| ~ spl0_77
| ~ spl0_122 ),
inference(resolution,[],[f1292,f641]) ).
fof(f26117,plain,
( spl0_971
| ~ spl0_64
| ~ spl0_164 ),
inference(avatar_split_clause,[],[f2281,f2243,f478,f26115]) ).
fof(f26115,plain,
( spl0_971
<=> ! [X0,X1] : disjoint(X0,image(X1,empty_set)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_971])]) ).
fof(f2281,plain,
( ! [X0,X1] : disjoint(X0,image(X1,empty_set))
| ~ spl0_64
| ~ spl0_164 ),
inference(resolution,[],[f2244,f479]) ).
fof(f26113,plain,
( spl0_970
| ~ spl0_75
| ~ spl0_121 ),
inference(avatar_split_clause,[],[f1318,f1287,f632,f26111]) ).
fof(f26111,plain,
( spl0_970
<=> ! [X0,X1] :
( single_valued_set(cross_product(X0,X1))
| member(first(non_ordered_pair(non_ordered_pair(f19(cross_product(X0,X1)),f19(cross_product(X0,X1))),non_ordered_pair(f19(cross_product(X0,X1)),f20(cross_product(X0,X1))))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_970])]) ).
fof(f1318,plain,
( ! [X0,X1] :
( single_valued_set(cross_product(X0,X1))
| member(first(non_ordered_pair(non_ordered_pair(f19(cross_product(X0,X1)),f19(cross_product(X0,X1))),non_ordered_pair(f19(cross_product(X0,X1)),f20(cross_product(X0,X1))))),X0) )
| ~ spl0_75
| ~ spl0_121 ),
inference(resolution,[],[f1288,f633]) ).
fof(f26109,plain,
( spl0_969
| ~ spl0_77
| ~ spl0_121 ),
inference(avatar_split_clause,[],[f1317,f1287,f640,f26107]) ).
fof(f26107,plain,
( spl0_969
<=> ! [X0,X1] :
( single_valued_set(cross_product(X0,X1))
| member(second(non_ordered_pair(non_ordered_pair(f19(cross_product(X0,X1)),f19(cross_product(X0,X1))),non_ordered_pair(f19(cross_product(X0,X1)),f20(cross_product(X0,X1))))),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_969])]) ).
fof(f1317,plain,
( ! [X0,X1] :
( single_valued_set(cross_product(X0,X1))
| member(second(non_ordered_pair(non_ordered_pair(f19(cross_product(X0,X1)),f19(cross_product(X0,X1))),non_ordered_pair(f19(cross_product(X0,X1)),f20(cross_product(X0,X1))))),X1) )
| ~ spl0_77
| ~ spl0_121 ),
inference(resolution,[],[f1288,f641]) ).
fof(f26105,plain,
( spl0_968
| ~ spl0_102
| ~ spl0_114 ),
inference(avatar_split_clause,[],[f1259,f1163,f956,f26103]) ).
fof(f26103,plain,
( spl0_968
<=> ! [X2,X0,X1] :
( intersection(X1,X2) = X0
| ~ member(f1(X0,intersection(X1,X2)),X0)
| ~ member(f1(X0,intersection(X1,X2)),X1)
| ~ member(f1(X0,intersection(X1,X2)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_968])]) ).
fof(f1259,plain,
( ! [X2,X0,X1] :
( intersection(X1,X2) = X0
| ~ member(f1(X0,intersection(X1,X2)),X0)
| ~ member(f1(X0,intersection(X1,X2)),X1)
| ~ member(f1(X0,intersection(X1,X2)),X2) )
| ~ spl0_102
| ~ spl0_114 ),
inference(resolution,[],[f1164,f957]) ).
fof(f26101,plain,
( spl0_967
| ~ spl0_101
| ~ spl0_113 ),
inference(avatar_split_clause,[],[f1222,f1159,f952,f26099]) ).
fof(f26099,plain,
( spl0_967
<=> ! [X2,X0,X1] :
( member(f1(non_ordered_pair(X0,X1),X2),X2)
| non_ordered_pair(X0,X1) = X2
| f1(non_ordered_pair(X0,X1),X2) = X0
| f1(non_ordered_pair(X0,X1),X2) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_967])]) ).
fof(f1222,plain,
( ! [X2,X0,X1] :
( member(f1(non_ordered_pair(X0,X1),X2),X2)
| non_ordered_pair(X0,X1) = X2
| f1(non_ordered_pair(X0,X1),X2) = X0
| f1(non_ordered_pair(X0,X1),X2) = X1 )
| ~ spl0_101
| ~ spl0_113 ),
inference(resolution,[],[f1160,f953]) ).
fof(f26097,plain,
( spl0_966
| ~ spl0_101
| ~ spl0_113 ),
inference(avatar_split_clause,[],[f1185,f1159,f952,f26095]) ).
fof(f26095,plain,
( spl0_966
<=> ! [X2,X0,X1] :
( member(f1(X0,non_ordered_pair(X1,X2)),X0)
| non_ordered_pair(X1,X2) = X0
| f1(X0,non_ordered_pair(X1,X2)) = X1
| f1(X0,non_ordered_pair(X1,X2)) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_966])]) ).
fof(f1185,plain,
( ! [X2,X0,X1] :
( member(f1(X0,non_ordered_pair(X1,X2)),X0)
| non_ordered_pair(X1,X2) = X0
| f1(X0,non_ordered_pair(X1,X2)) = X1
| f1(X0,non_ordered_pair(X1,X2)) = X2 )
| ~ spl0_101
| ~ spl0_113 ),
inference(resolution,[],[f1160,f953]) ).
fof(f26093,plain,
( spl0_965
| ~ spl0_107
| ~ spl0_108 ),
inference(avatar_split_clause,[],[f1128,f1072,f1068,f26091]) ).
fof(f26091,plain,
( spl0_965
<=> ! [X0,X3,X2,X1] :
( first(f22(X0,image(X1,X2),X3)) = second(f22(first(f22(X0,image(X1,X2),X3)),X1,X2))
| ~ member(X0,image(image(X1,X2),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_965])]) ).
fof(f1128,plain,
( ! [X2,X3,X0,X1] :
( first(f22(X0,image(X1,X2),X3)) = second(f22(first(f22(X0,image(X1,X2),X3)),X1,X2))
| ~ member(X0,image(image(X1,X2),X3)) )
| ~ spl0_107
| ~ spl0_108 ),
inference(resolution,[],[f1073,f1069]) ).
fof(f25794,plain,
( spl0_964
| ~ spl0_63
| ~ spl0_164 ),
inference(avatar_split_clause,[],[f2280,f2243,f474,f25792]) ).
fof(f25792,plain,
( spl0_964
<=> ! [X0,X1] : disjoint(image(X0,empty_set),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_964])]) ).
fof(f2280,plain,
( ! [X0,X1] : disjoint(image(X0,empty_set),X1)
| ~ spl0_63
| ~ spl0_164 ),
inference(resolution,[],[f2244,f475]) ).
fof(f25348,plain,
( spl0_963
| ~ spl0_173
| ~ spl0_962 ),
inference(avatar_split_clause,[],[f25344,f25341,f2440,f25346]) ).
fof(f25346,plain,
( spl0_963
<=> ! [X0,X1] :
( estin = X0
| ~ little_set(X0)
| ~ member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X1)),f25)
| f26(X0) = X1
| ~ little_set(f26(X0))
| ~ little_set(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_963])]) ).
fof(f25341,plain,
( spl0_962
<=> ! [X0,X1] :
( ~ little_set(X0)
| empty_set = X0
| ~ member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X1)),f25)
| f26(X0) = X1
| ~ little_set(f26(X0))
| ~ little_set(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_962])]) ).
fof(f25344,plain,
( ! [X0,X1] :
( estin = X0
| ~ little_set(X0)
| ~ member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X1)),f25)
| f26(X0) = X1
| ~ little_set(f26(X0))
| ~ little_set(X1) )
| ~ spl0_173
| ~ spl0_962 ),
inference(forward_demodulation,[],[f25342,f2442]) ).
fof(f25342,plain,
( ! [X0,X1] :
( ~ little_set(X0)
| empty_set = X0
| ~ member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X1)),f25)
| f26(X0) = X1
| ~ little_set(f26(X0))
| ~ little_set(X1) )
| ~ spl0_962 ),
inference(avatar_component_clause,[],[f25341]) ).
fof(f25343,plain,
( ~ spl0_25
| spl0_962
| ~ spl0_123
| ~ spl0_140 ),
inference(avatar_split_clause,[],[f1772,f1745,f1295,f25341,f289]) ).
fof(f289,plain,
( spl0_25
<=> single_valued_set(f25) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_25])]) ).
fof(f1772,plain,
( ! [X0,X1] :
( ~ little_set(X0)
| ~ little_set(X1)
| ~ little_set(f26(X0))
| f26(X0) = X1
| ~ member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X1)),f25)
| ~ single_valued_set(f25)
| empty_set = X0 )
| ~ spl0_123
| ~ spl0_140 ),
inference(duplicate_literal_removal,[],[f1757]) ).
fof(f1757,plain,
( ! [X0,X1] :
( ~ little_set(X0)
| ~ little_set(X1)
| ~ little_set(f26(X0))
| f26(X0) = X1
| ~ member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X1)),f25)
| ~ single_valued_set(f25)
| empty_set = X0
| ~ little_set(X0) )
| ~ spl0_123
| ~ spl0_140 ),
inference(resolution,[],[f1746,f1296]) ).
fof(f25338,plain,
( spl0_961
| ~ spl0_23
| ~ spl0_139 ),
inference(avatar_split_clause,[],[f1737,f1642,f281,f25336]) ).
fof(f25336,plain,
( spl0_961
<=> ! [X0,X1] :
( ~ member(X0,compose(identity_relation,X1))
| ordered_pair_predicate(non_ordered_pair(non_ordered_pair(f29(X0,identity_relation,X1),f29(X0,identity_relation,X1)),non_ordered_pair(f29(X0,identity_relation,X1),f31(X0,identity_relation,X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_961])]) ).
fof(f1737,plain,
( ! [X0,X1] :
( ~ member(X0,compose(identity_relation,X1))
| ordered_pair_predicate(non_ordered_pair(non_ordered_pair(f29(X0,identity_relation,X1),f29(X0,identity_relation,X1)),non_ordered_pair(f29(X0,identity_relation,X1),f31(X0,identity_relation,X1)))) )
| ~ spl0_23
| ~ spl0_139 ),
inference(resolution,[],[f1643,f282]) ).
fof(f25333,plain,
( spl0_960
| ~ spl0_23
| ~ spl0_138 ),
inference(avatar_split_clause,[],[f1697,f1638,f281,f25331]) ).
fof(f25331,plain,
( spl0_960
<=> ! [X0,X1] :
( ~ member(X0,compose(X1,identity_relation))
| ordered_pair_predicate(non_ordered_pair(non_ordered_pair(f31(X0,X1,identity_relation),f31(X0,X1,identity_relation)),non_ordered_pair(f31(X0,X1,identity_relation),f30(X0,X1,identity_relation)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_960])]) ).
fof(f1697,plain,
( ! [X0,X1] :
( ~ member(X0,compose(X1,identity_relation))
| ordered_pair_predicate(non_ordered_pair(non_ordered_pair(f31(X0,X1,identity_relation),f31(X0,X1,identity_relation)),non_ordered_pair(f31(X0,X1,identity_relation),f30(X0,X1,identity_relation)))) )
| ~ spl0_23
| ~ spl0_138 ),
inference(resolution,[],[f1639,f282]) ).
fof(f25329,plain,
( spl0_959
| ~ spl0_38
| ~ spl0_136 ),
inference(avatar_split_clause,[],[f1595,f1552,f353,f25327]) ).
fof(f25327,plain,
( spl0_959
<=> ! [X4,X0,X3,X2,X1] :
( ~ closed(X0,X1)
| ~ maps(X2,X3,X0)
| homomorphism(X2,X3,X4,X0,X1)
| ~ closed(X3,X4)
| ordered_pair_predicate(f33(X2,X3,X4,X0,X1))
| ~ relation(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_959])]) ).
fof(f1595,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ closed(X0,X1)
| ~ maps(X2,X3,X0)
| homomorphism(X2,X3,X4,X0,X1)
| ~ closed(X3,X4)
| ordered_pair_predicate(f33(X2,X3,X4,X0,X1))
| ~ relation(X3) )
| ~ spl0_38
| ~ spl0_136 ),
inference(resolution,[],[f1553,f354]) ).
fof(f25325,plain,
( spl0_958
| ~ spl0_38
| ~ spl0_134 ),
inference(avatar_split_clause,[],[f1556,f1544,f353,f25323]) ).
fof(f25323,plain,
( spl0_958
<=> ! [X4,X0,X3,X2,X1] :
( ~ closed(X0,X1)
| ~ maps(X2,X3,X0)
| homomorphism(X2,X3,X4,X0,X1)
| ~ closed(X3,X4)
| ordered_pair_predicate(f32(X2,X3,X4,X0,X1))
| ~ relation(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_958])]) ).
fof(f1556,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ closed(X0,X1)
| ~ maps(X2,X3,X0)
| homomorphism(X2,X3,X4,X0,X1)
| ~ closed(X3,X4)
| ordered_pair_predicate(f32(X2,X3,X4,X0,X1))
| ~ relation(X3) )
| ~ spl0_38
| ~ spl0_134 ),
inference(resolution,[],[f1545,f354]) ).
fof(f25320,plain,
( spl0_957
| ~ spl0_60
| ~ spl0_164 ),
inference(avatar_split_clause,[],[f2277,f2243,f462,f25318]) ).
fof(f25318,plain,
( spl0_957
<=> ! [X0,X1] : subset(image(X0,empty_set),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_957])]) ).
fof(f2277,plain,
( ! [X0,X1] : subset(image(X0,empty_set),X1)
| ~ spl0_60
| ~ spl0_164 ),
inference(resolution,[],[f2244,f463]) ).
fof(f25316,plain,
( spl0_956
| ~ spl0_51
| ~ spl0_122 ),
inference(avatar_split_clause,[],[f1355,f1291,f426,f25314]) ).
fof(f25314,plain,
( spl0_956
<=> ! [X0,X1] :
( single_valued_set(intersection(X0,X1))
| member(non_ordered_pair(non_ordered_pair(f19(intersection(X0,X1)),f19(intersection(X0,X1))),non_ordered_pair(f19(intersection(X0,X1)),f21(intersection(X0,X1)))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_956])]) ).
fof(f1355,plain,
( ! [X0,X1] :
( single_valued_set(intersection(X0,X1))
| member(non_ordered_pair(non_ordered_pair(f19(intersection(X0,X1)),f19(intersection(X0,X1))),non_ordered_pair(f19(intersection(X0,X1)),f21(intersection(X0,X1)))),X0) )
| ~ spl0_51
| ~ spl0_122 ),
inference(resolution,[],[f1292,f427]) ).
fof(f25312,plain,
( spl0_955
| ~ spl0_52
| ~ spl0_122 ),
inference(avatar_split_clause,[],[f1354,f1291,f430,f25310]) ).
fof(f25310,plain,
( spl0_955
<=> ! [X0,X1] :
( single_valued_set(intersection(X0,X1))
| member(non_ordered_pair(non_ordered_pair(f19(intersection(X0,X1)),f19(intersection(X0,X1))),non_ordered_pair(f19(intersection(X0,X1)),f21(intersection(X0,X1)))),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_955])]) ).
fof(f1354,plain,
( ! [X0,X1] :
( single_valued_set(intersection(X0,X1))
| member(non_ordered_pair(non_ordered_pair(f19(intersection(X0,X1)),f19(intersection(X0,X1))),non_ordered_pair(f19(intersection(X0,X1)),f21(intersection(X0,X1)))),X1) )
| ~ spl0_52
| ~ spl0_122 ),
inference(resolution,[],[f1292,f431]) ).
fof(f25308,plain,
( spl0_954
| ~ spl0_51
| ~ spl0_121 ),
inference(avatar_split_clause,[],[f1313,f1287,f426,f25306]) ).
fof(f25306,plain,
( spl0_954
<=> ! [X0,X1] :
( single_valued_set(intersection(X0,X1))
| member(non_ordered_pair(non_ordered_pair(f19(intersection(X0,X1)),f19(intersection(X0,X1))),non_ordered_pair(f19(intersection(X0,X1)),f20(intersection(X0,X1)))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_954])]) ).
fof(f1313,plain,
( ! [X0,X1] :
( single_valued_set(intersection(X0,X1))
| member(non_ordered_pair(non_ordered_pair(f19(intersection(X0,X1)),f19(intersection(X0,X1))),non_ordered_pair(f19(intersection(X0,X1)),f20(intersection(X0,X1)))),X0) )
| ~ spl0_51
| ~ spl0_121 ),
inference(resolution,[],[f1288,f427]) ).
fof(f25304,plain,
( spl0_953
| ~ spl0_52
| ~ spl0_121 ),
inference(avatar_split_clause,[],[f1312,f1287,f430,f25302]) ).
fof(f25302,plain,
( spl0_953
<=> ! [X0,X1] :
( single_valued_set(intersection(X0,X1))
| member(non_ordered_pair(non_ordered_pair(f19(intersection(X0,X1)),f19(intersection(X0,X1))),non_ordered_pair(f19(intersection(X0,X1)),f20(intersection(X0,X1)))),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_953])]) ).
fof(f1312,plain,
( ! [X0,X1] :
( single_valued_set(intersection(X0,X1))
| member(non_ordered_pair(non_ordered_pair(f19(intersection(X0,X1)),f19(intersection(X0,X1))),non_ordered_pair(f19(intersection(X0,X1)),f20(intersection(X0,X1)))),X1) )
| ~ spl0_52
| ~ spl0_121 ),
inference(resolution,[],[f1288,f431]) ).
fof(f25300,plain,
( spl0_952
| ~ spl0_101
| ~ spl0_107 ),
inference(avatar_split_clause,[],[f1096,f1068,f952,f25298]) ).
fof(f25298,plain,
( spl0_952
<=> ! [X0,X3,X2,X1] :
( ~ member(X0,image(non_ordered_pair(X1,X2),X3))
| first(f22(X0,non_ordered_pair(X1,X2),X3)) = X1
| first(f22(X0,non_ordered_pair(X1,X2),X3)) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_952])]) ).
fof(f1096,plain,
( ! [X2,X3,X0,X1] :
( ~ member(X0,image(non_ordered_pair(X1,X2),X3))
| first(f22(X0,non_ordered_pair(X1,X2),X3)) = X1
| first(f22(X0,non_ordered_pair(X1,X2),X3)) = X2 )
| ~ spl0_101
| ~ spl0_107 ),
inference(resolution,[],[f1069,f953]) ).
fof(f25012,plain,
( spl0_951
| ~ spl0_35
| ~ spl0_122 ),
inference(avatar_split_clause,[],[f1361,f1291,f340,f25010]) ).
fof(f25010,plain,
( spl0_951
<=> ! [X0,X1] :
( single_valued_set(cross_product(X0,X1))
| ordered_pair_predicate(non_ordered_pair(non_ordered_pair(f19(cross_product(X0,X1)),f19(cross_product(X0,X1))),non_ordered_pair(f19(cross_product(X0,X1)),f21(cross_product(X0,X1))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_951])]) ).
fof(f1361,plain,
( ! [X0,X1] :
( single_valued_set(cross_product(X0,X1))
| ordered_pair_predicate(non_ordered_pair(non_ordered_pair(f19(cross_product(X0,X1)),f19(cross_product(X0,X1))),non_ordered_pair(f19(cross_product(X0,X1)),f21(cross_product(X0,X1))))) )
| ~ spl0_35
| ~ spl0_122 ),
inference(resolution,[],[f1292,f341]) ).
fof(f25005,plain,
( spl0_950
| ~ spl0_78
| ~ spl0_154 ),
inference(avatar_split_clause,[],[f2178,f2102,f644,f25003]) ).
fof(f25003,plain,
( spl0_950
<=> ! [X0] : ~ member(X0,sigma(rotate_right(empty_set))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_950])]) ).
fof(f2178,plain,
( ! [X0] : ~ member(X0,sigma(rotate_right(empty_set)))
| ~ spl0_78
| ~ spl0_154 ),
inference(resolution,[],[f2103,f645]) ).
fof(f25001,plain,
( spl0_949
| ~ spl0_35
| ~ spl0_121 ),
inference(avatar_split_clause,[],[f1319,f1287,f340,f24999]) ).
fof(f24999,plain,
( spl0_949
<=> ! [X0,X1] :
( single_valued_set(cross_product(X0,X1))
| ordered_pair_predicate(non_ordered_pair(non_ordered_pair(f19(cross_product(X0,X1)),f19(cross_product(X0,X1))),non_ordered_pair(f19(cross_product(X0,X1)),f20(cross_product(X0,X1))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_949])]) ).
fof(f1319,plain,
( ! [X0,X1] :
( single_valued_set(cross_product(X0,X1))
| ordered_pair_predicate(non_ordered_pair(non_ordered_pair(f19(cross_product(X0,X1)),f19(cross_product(X0,X1))),non_ordered_pair(f19(cross_product(X0,X1)),f20(cross_product(X0,X1))))) )
| ~ spl0_35
| ~ spl0_121 ),
inference(resolution,[],[f1288,f341]) ).
fof(f24997,plain,
( spl0_948
| ~ spl0_104
| ~ spl0_108 ),
inference(avatar_split_clause,[],[f1139,f1072,f966,f24995]) ).
fof(f24995,plain,
( spl0_948
<=> ! [X0,X3,X2,X1] :
( f28(X0,image(X1,X2),X3) = second(f22(f28(X0,image(X1,X2),X3),X1,X2))
| ~ member(X0,apply(image(X1,X2),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_948])]) ).
fof(f1139,plain,
( ! [X2,X3,X0,X1] :
( f28(X0,image(X1,X2),X3) = second(f22(f28(X0,image(X1,X2),X3),X1,X2))
| ~ member(X0,apply(image(X1,X2),X3)) )
| ~ spl0_104
| ~ spl0_108 ),
inference(resolution,[],[f1073,f967]) ).
fof(f24993,plain,
( spl0_947
| ~ spl0_103
| ~ spl0_108 ),
inference(avatar_split_clause,[],[f1133,f1072,f960,f24991]) ).
fof(f24991,plain,
( spl0_947
<=> ! [X0,X3,X2,X1] :
( f22(X0,X1,image(X2,X3)) = second(f22(f22(X0,X1,image(X2,X3)),X2,X3))
| ~ member(X0,image(X1,image(X2,X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_947])]) ).
fof(f1133,plain,
( ! [X2,X3,X0,X1] :
( f22(X0,X1,image(X2,X3)) = second(f22(f22(X0,X1,image(X2,X3)),X2,X3))
| ~ member(X0,image(X1,image(X2,X3))) )
| ~ spl0_103
| ~ spl0_108 ),
inference(resolution,[],[f1073,f961]) ).
fof(f24270,plain,
( spl0_946
| ~ spl0_74
| ~ spl0_154 ),
inference(avatar_split_clause,[],[f2177,f2102,f628,f24268]) ).
fof(f24268,plain,
( spl0_946
<=> ! [X0] : ~ member(X0,domain_of(rotate_right(empty_set))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_946])]) ).
fof(f2177,plain,
( ! [X0] : ~ member(X0,domain_of(rotate_right(empty_set)))
| ~ spl0_74
| ~ spl0_154 ),
inference(resolution,[],[f2103,f629]) ).
fof(f24263,plain,
( spl0_945
| ~ spl0_23
| ~ spl0_136 ),
inference(avatar_split_clause,[],[f1627,f1552,f281,f24261]) ).
fof(f24261,plain,
( spl0_945
<=> ! [X0,X3,X2,X1] :
( ~ closed(X0,X1)
| ~ maps(X2,identity_relation,X0)
| homomorphism(X2,identity_relation,X3,X0,X1)
| ~ closed(identity_relation,X3)
| ordered_pair_predicate(f33(X2,identity_relation,X3,X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_945])]) ).
fof(f1627,plain,
( ! [X2,X3,X0,X1] :
( ~ closed(X0,X1)
| ~ maps(X2,identity_relation,X0)
| homomorphism(X2,identity_relation,X3,X0,X1)
| ~ closed(identity_relation,X3)
| ordered_pair_predicate(f33(X2,identity_relation,X3,X0,X1)) )
| ~ spl0_23
| ~ spl0_136 ),
inference(resolution,[],[f1553,f282]) ).
fof(f24259,plain,
( spl0_944
| ~ spl0_11
| ~ spl0_136 ),
inference(avatar_split_clause,[],[f1596,f1552,f232,f24257]) ).
fof(f24257,plain,
( spl0_944
<=> ! [X4,X0,X3,X2,X1] :
( ~ closed(X0,X1)
| ~ maps(X2,X3,X0)
| homomorphism(X2,X3,X4,X0,X1)
| ~ closed(X3,X4)
| little_set(f33(X2,X3,X4,X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_944])]) ).
fof(f1596,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ closed(X0,X1)
| ~ maps(X2,X3,X0)
| homomorphism(X2,X3,X4,X0,X1)
| ~ closed(X3,X4)
| little_set(f33(X2,X3,X4,X0,X1)) )
| ~ spl0_11
| ~ spl0_136 ),
inference(resolution,[],[f1553,f233]) ).
fof(f24252,plain,
( spl0_943
| ~ spl0_23
| ~ spl0_134 ),
inference(avatar_split_clause,[],[f1588,f1544,f281,f24250]) ).
fof(f24250,plain,
( spl0_943
<=> ! [X0,X3,X2,X1] :
( ~ closed(X0,X1)
| ~ maps(X2,identity_relation,X0)
| homomorphism(X2,identity_relation,X3,X0,X1)
| ~ closed(identity_relation,X3)
| ordered_pair_predicate(f32(X2,identity_relation,X3,X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_943])]) ).
fof(f1588,plain,
( ! [X2,X3,X0,X1] :
( ~ closed(X0,X1)
| ~ maps(X2,identity_relation,X0)
| homomorphism(X2,identity_relation,X3,X0,X1)
| ~ closed(identity_relation,X3)
| ordered_pair_predicate(f32(X2,identity_relation,X3,X0,X1)) )
| ~ spl0_23
| ~ spl0_134 ),
inference(resolution,[],[f1545,f282]) ).
fof(f24248,plain,
( spl0_942
| ~ spl0_11
| ~ spl0_134 ),
inference(avatar_split_clause,[],[f1557,f1544,f232,f24246]) ).
fof(f24246,plain,
( spl0_942
<=> ! [X4,X0,X3,X2,X1] :
( ~ closed(X0,X1)
| ~ maps(X2,X3,X0)
| homomorphism(X2,X3,X4,X0,X1)
| ~ closed(X3,X4)
| little_set(f32(X2,X3,X4,X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_942])]) ).
fof(f1557,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ closed(X0,X1)
| ~ maps(X2,X3,X0)
| homomorphism(X2,X3,X4,X0,X1)
| ~ closed(X3,X4)
| little_set(f32(X2,X3,X4,X0,X1)) )
| ~ spl0_11
| ~ spl0_134 ),
inference(resolution,[],[f1545,f233]) ).
fof(f24244,plain,
( spl0_941
| ~ spl0_110
| ~ spl0_127 ),
inference(avatar_split_clause,[],[f1448,f1397,f1081,f24242]) ).
fof(f24242,plain,
( spl0_941
<=> ! [X2,X0,X1] :
( ~ member(X0,converse(apply(X1,X2)))
| first(f28(non_ordered_pair(non_ordered_pair(second(X0),second(X0)),non_ordered_pair(second(X0),first(X0))),X1,X2)) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_941])]) ).
fof(f1448,plain,
( ! [X2,X0,X1] :
( ~ member(X0,converse(apply(X1,X2)))
| first(f28(non_ordered_pair(non_ordered_pair(second(X0),second(X0)),non_ordered_pair(second(X0),first(X0))),X1,X2)) = X2 )
| ~ spl0_110
| ~ spl0_127 ),
inference(resolution,[],[f1398,f1082]) ).
fof(f24240,plain,
( spl0_940
| ~ spl0_110
| ~ spl0_113 ),
inference(avatar_split_clause,[],[f1251,f1159,f1081,f24238]) ).
fof(f24238,plain,
( spl0_940
<=> ! [X2,X0,X1] :
( member(f1(apply(X0,X1),X2),X2)
| apply(X0,X1) = X2
| first(f28(f1(apply(X0,X1),X2),X0,X1)) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_940])]) ).
fof(f1251,plain,
( ! [X2,X0,X1] :
( member(f1(apply(X0,X1),X2),X2)
| apply(X0,X1) = X2
| first(f28(f1(apply(X0,X1),X2),X0,X1)) = X1 )
| ~ spl0_110
| ~ spl0_113 ),
inference(resolution,[],[f1160,f1082]) ).
fof(f24236,plain,
( spl0_939
| ~ spl0_110
| ~ spl0_113 ),
inference(avatar_split_clause,[],[f1214,f1159,f1081,f24234]) ).
fof(f24234,plain,
( spl0_939
<=> ! [X2,X0,X1] :
( member(f1(X0,apply(X1,X2)),X0)
| apply(X1,X2) = X0
| first(f28(f1(X0,apply(X1,X2)),X1,X2)) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_939])]) ).
fof(f1214,plain,
( ! [X2,X0,X1] :
( member(f1(X0,apply(X1,X2)),X0)
| apply(X1,X2) = X0
| first(f28(f1(X0,apply(X1,X2)),X1,X2)) = X2 )
| ~ spl0_110
| ~ spl0_113 ),
inference(resolution,[],[f1160,f1082]) ).
fof(f24232,plain,
( spl0_938
| ~ spl0_101
| ~ spl0_104 ),
inference(avatar_split_clause,[],[f1028,f966,f952,f24230]) ).
fof(f24230,plain,
( spl0_938
<=> ! [X0,X3,X2,X1] :
( ~ member(X0,apply(non_ordered_pair(X1,X2),X3))
| f28(X0,non_ordered_pair(X1,X2),X3) = X1
| f28(X0,non_ordered_pair(X1,X2),X3) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_938])]) ).
fof(f1028,plain,
( ! [X2,X3,X0,X1] :
( ~ member(X0,apply(non_ordered_pair(X1,X2),X3))
| f28(X0,non_ordered_pair(X1,X2),X3) = X1
| f28(X0,non_ordered_pair(X1,X2),X3) = X2 )
| ~ spl0_101
| ~ spl0_104 ),
inference(resolution,[],[f967,f953]) ).
fof(f24228,plain,
( spl0_937
| ~ spl0_101
| ~ spl0_103 ),
inference(avatar_split_clause,[],[f993,f960,f952,f24226]) ).
fof(f24226,plain,
( spl0_937
<=> ! [X0,X3,X2,X1] :
( ~ member(X0,image(X1,non_ordered_pair(X2,X3)))
| f22(X0,X1,non_ordered_pair(X2,X3)) = X2
| f22(X0,X1,non_ordered_pair(X2,X3)) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_937])]) ).
fof(f993,plain,
( ! [X2,X3,X0,X1] :
( ~ member(X0,image(X1,non_ordered_pair(X2,X3)))
| f22(X0,X1,non_ordered_pair(X2,X3)) = X2
| f22(X0,X1,non_ordered_pair(X2,X3)) = X3 )
| ~ spl0_101
| ~ spl0_103 ),
inference(resolution,[],[f961,f953]) ).
fof(f24220,plain,
( spl0_936
| ~ spl0_145
| ~ spl0_154 ),
inference(avatar_split_clause,[],[f2174,f2102,f1786,f24218]) ).
fof(f24218,plain,
( spl0_936
<=> ! [X0] : ~ member(X0,rotate_right(rotate_right(empty_set))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_936])]) ).
fof(f2174,plain,
( ! [X0] : ~ member(X0,rotate_right(rotate_right(empty_set)))
| ~ spl0_145
| ~ spl0_154 ),
inference(resolution,[],[f2103,f1787]) ).
fof(f23609,plain,
( spl0_935
| ~ spl0_173
| ~ spl0_928 ),
inference(avatar_split_clause,[],[f23306,f23303,f2440,f23607]) ).
fof(f23607,plain,
( spl0_935
<=> ! [X0,X1] :
( estin = image(X0,X1)
| f26(image(X0,X1)) = second(f22(f26(image(X0,X1)),X0,X1))
| ~ little_set(image(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_935])]) ).
fof(f23303,plain,
( spl0_928
<=> ! [X0,X1] :
( f26(image(X0,X1)) = second(f22(f26(image(X0,X1)),X0,X1))
| empty_set = image(X0,X1)
| ~ little_set(image(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_928])]) ).
fof(f23306,plain,
( ! [X0,X1] :
( estin = image(X0,X1)
| f26(image(X0,X1)) = second(f22(f26(image(X0,X1)),X0,X1))
| ~ little_set(image(X0,X1)) )
| ~ spl0_173
| ~ spl0_928 ),
inference(forward_demodulation,[],[f23304,f2442]) ).
fof(f23304,plain,
( ! [X0,X1] :
( f26(image(X0,X1)) = second(f22(f26(image(X0,X1)),X0,X1))
| empty_set = image(X0,X1)
| ~ little_set(image(X0,X1)) )
| ~ spl0_928 ),
inference(avatar_component_clause,[],[f23303]) ).
fof(f23333,plain,
( spl0_934
| ~ spl0_93
| ~ spl0_130 ),
inference(avatar_split_clause,[],[f1475,f1470,f836,f23331]) ).
fof(f23331,plain,
( spl0_934
<=> ! [X0,X3,X2,X1] :
( ~ little_set(second(X0))
| ~ member(X0,X1)
| ~ member(first(X0),X2)
| ~ ordered_pair_predicate(X0)
| ~ member(image(X2,X1),X3)
| member(second(X0),sigma(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_934])]) ).
fof(f1470,plain,
( spl0_130
<=> ! [X0,X1,X7] :
( ~ ordered_pair_predicate(X1)
| ~ little_set(second(X1))
| ~ member(X1,X7)
| ~ member(first(X1),X0)
| member(second(X1),image(X0,X7)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_130])]) ).
fof(f1475,plain,
( ! [X2,X3,X0,X1] :
( ~ little_set(second(X0))
| ~ member(X0,X1)
| ~ member(first(X0),X2)
| ~ ordered_pair_predicate(X0)
| ~ member(image(X2,X1),X3)
| member(second(X0),sigma(X3)) )
| ~ spl0_93
| ~ spl0_130 ),
inference(resolution,[],[f1471,f837]) ).
fof(f1471,plain,
( ! [X0,X1,X7] :
( member(second(X1),image(X0,X7))
| ~ little_set(second(X1))
| ~ member(X1,X7)
| ~ member(first(X1),X0)
| ~ ordered_pair_predicate(X1) )
| ~ spl0_130 ),
inference(avatar_component_clause,[],[f1470]) ).
fof(f23329,plain,
( spl0_933
| ~ spl0_95
| ~ spl0_113 ),
inference(avatar_split_clause,[],[f1247,f1159,f844,f23327]) ).
fof(f23327,plain,
( spl0_933
<=> ! [X0,X1] :
( member(f1(range_of(X0),X1),X1)
| range_of(X0) = X1
| f1(range_of(X0),X1) = second(f27(f1(range_of(X0),X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_933])]) ).
fof(f1247,plain,
( ! [X0,X1] :
( member(f1(range_of(X0),X1),X1)
| range_of(X0) = X1
| f1(range_of(X0),X1) = second(f27(f1(range_of(X0),X1),X0)) )
| ~ spl0_95
| ~ spl0_113 ),
inference(resolution,[],[f1160,f845]) ).
fof(f23322,plain,
( spl0_932
| ~ spl0_144
| ~ spl0_154 ),
inference(avatar_split_clause,[],[f2173,f2102,f1782,f23320]) ).
fof(f23320,plain,
( spl0_932
<=> ! [X0] : ~ member(X0,flip_range_of(rotate_right(empty_set))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_932])]) ).
fof(f2173,plain,
( ! [X0] : ~ member(X0,flip_range_of(rotate_right(empty_set)))
| ~ spl0_144
| ~ spl0_154 ),
inference(resolution,[],[f2103,f1783]) ).
fof(f23318,plain,
( spl0_931
| ~ spl0_91
| ~ spl0_113 ),
inference(avatar_split_clause,[],[f1231,f1159,f828,f23316]) ).
fof(f23316,plain,
( spl0_931
<=> ! [X0,X1] :
( member(f1(domain_of(X0),X1),X1)
| domain_of(X0) = X1
| f1(domain_of(X0),X1) = first(f8(f1(domain_of(X0),X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_931])]) ).
fof(f1231,plain,
( ! [X0,X1] :
( member(f1(domain_of(X0),X1),X1)
| domain_of(X0) = X1
| f1(domain_of(X0),X1) = first(f8(f1(domain_of(X0),X1),X0)) )
| ~ spl0_91
| ~ spl0_113 ),
inference(resolution,[],[f1160,f829]) ).
fof(f23314,plain,
( spl0_930
| ~ spl0_95
| ~ spl0_113 ),
inference(avatar_split_clause,[],[f1210,f1159,f844,f23312]) ).
fof(f23312,plain,
( spl0_930
<=> ! [X0,X1] :
( member(f1(X0,range_of(X1)),X0)
| range_of(X1) = X0
| f1(X0,range_of(X1)) = second(f27(f1(X0,range_of(X1)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_930])]) ).
fof(f1210,plain,
( ! [X0,X1] :
( member(f1(X0,range_of(X1)),X0)
| range_of(X1) = X0
| f1(X0,range_of(X1)) = second(f27(f1(X0,range_of(X1)),X1)) )
| ~ spl0_95
| ~ spl0_113 ),
inference(resolution,[],[f1160,f845]) ).
fof(f23310,plain,
( spl0_929
| ~ spl0_91
| ~ spl0_113 ),
inference(avatar_split_clause,[],[f1194,f1159,f828,f23308]) ).
fof(f23308,plain,
( spl0_929
<=> ! [X0,X1] :
( member(f1(X0,domain_of(X1)),X0)
| domain_of(X1) = X0
| f1(X0,domain_of(X1)) = first(f8(f1(X0,domain_of(X1)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_929])]) ).
fof(f1194,plain,
( ! [X0,X1] :
( member(f1(X0,domain_of(X1)),X0)
| domain_of(X1) = X0
| f1(X0,domain_of(X1)) = first(f8(f1(X0,domain_of(X1)),X1)) )
| ~ spl0_91
| ~ spl0_113 ),
inference(resolution,[],[f1160,f829]) ).
fof(f23305,plain,
( spl0_928
| ~ spl0_84
| ~ spl0_108 ),
inference(avatar_split_clause,[],[f1137,f1072,f668,f23303]) ).
fof(f1137,plain,
( ! [X0,X1] :
( f26(image(X0,X1)) = second(f22(f26(image(X0,X1)),X0,X1))
| empty_set = image(X0,X1)
| ~ little_set(image(X0,X1)) )
| ~ spl0_84
| ~ spl0_108 ),
inference(resolution,[],[f1073,f669]) ).
fof(f23301,plain,
( spl0_927
| ~ spl0_95
| ~ spl0_107 ),
inference(avatar_split_clause,[],[f1120,f1068,f844,f23299]) ).
fof(f23299,plain,
( spl0_927
<=> ! [X2,X0,X1] :
( ~ member(X0,image(range_of(X1),X2))
| first(f22(X0,range_of(X1),X2)) = second(f27(first(f22(X0,range_of(X1),X2)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_927])]) ).
fof(f1120,plain,
( ! [X2,X0,X1] :
( ~ member(X0,image(range_of(X1),X2))
| first(f22(X0,range_of(X1),X2)) = second(f27(first(f22(X0,range_of(X1),X2)),X1)) )
| ~ spl0_95
| ~ spl0_107 ),
inference(resolution,[],[f1069,f845]) ).
fof(f23297,plain,
( spl0_926
| ~ spl0_91
| ~ spl0_107 ),
inference(avatar_split_clause,[],[f1105,f1068,f828,f23295]) ).
fof(f23295,plain,
( spl0_926
<=> ! [X2,X0,X1] :
( ~ member(X0,image(domain_of(X1),X2))
| first(f22(X0,domain_of(X1),X2)) = first(f8(first(f22(X0,domain_of(X1),X2)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_926])]) ).
fof(f1105,plain,
( ! [X2,X0,X1] :
( ~ member(X0,image(domain_of(X1),X2))
| first(f22(X0,domain_of(X1),X2)) = first(f8(first(f22(X0,domain_of(X1),X2)),X1)) )
| ~ spl0_91
| ~ spl0_107 ),
inference(resolution,[],[f1069,f829]) ).
fof(f23220,plain,
( spl0_925
| ~ spl0_127
| ~ spl0_154 ),
inference(avatar_split_clause,[],[f2171,f2102,f1397,f23218]) ).
fof(f23218,plain,
( spl0_925
<=> ! [X0] : ~ member(X0,converse(rotate_right(empty_set))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_925])]) ).
fof(f2171,plain,
( ! [X0] : ~ member(X0,converse(rotate_right(empty_set)))
| ~ spl0_127
| ~ spl0_154 ),
inference(resolution,[],[f2103,f1398]) ).
fof(f23037,plain,
( spl0_924
| ~ spl0_78
| ~ spl0_153 ),
inference(avatar_split_clause,[],[f2147,f2098,f644,f23035]) ).
fof(f23035,plain,
( spl0_924
<=> ! [X0] : ~ member(X0,sigma(flip_range_of(empty_set))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_924])]) ).
fof(f2147,plain,
( ! [X0] : ~ member(X0,sigma(flip_range_of(empty_set)))
| ~ spl0_78
| ~ spl0_153 ),
inference(resolution,[],[f2099,f645]) ).
fof(f23014,plain,
( spl0_923
| ~ spl0_74
| ~ spl0_153 ),
inference(avatar_split_clause,[],[f2146,f2098,f628,f23012]) ).
fof(f23012,plain,
( spl0_923
<=> ! [X0] : ~ member(X0,domain_of(flip_range_of(empty_set))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_923])]) ).
fof(f2146,plain,
( ! [X0] : ~ member(X0,domain_of(flip_range_of(empty_set)))
| ~ spl0_74
| ~ spl0_153 ),
inference(resolution,[],[f2099,f629]) ).
fof(f22993,plain,
( spl0_922
| ~ spl0_145
| ~ spl0_153 ),
inference(avatar_split_clause,[],[f2143,f2098,f1786,f22991]) ).
fof(f22991,plain,
( spl0_922
<=> ! [X0] : ~ member(X0,rotate_right(flip_range_of(empty_set))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_922])]) ).
fof(f2143,plain,
( ! [X0] : ~ member(X0,rotate_right(flip_range_of(empty_set)))
| ~ spl0_145
| ~ spl0_153 ),
inference(resolution,[],[f2099,f1787]) ).
fof(f22152,plain,
( spl0_921
| ~ spl0_144
| ~ spl0_153 ),
inference(avatar_split_clause,[],[f2142,f2098,f1782,f22150]) ).
fof(f22150,plain,
( spl0_921
<=> ! [X0] : ~ member(X0,flip_range_of(flip_range_of(empty_set))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_921])]) ).
fof(f2142,plain,
( ! [X0] : ~ member(X0,flip_range_of(flip_range_of(empty_set)))
| ~ spl0_144
| ~ spl0_153 ),
inference(resolution,[],[f2099,f1783]) ).
fof(f21410,plain,
( spl0_920
| ~ spl0_173
| ~ spl0_865 ),
inference(avatar_split_clause,[],[f21175,f21172,f2440,f21408]) ).
fof(f21408,plain,
( spl0_920
<=> ! [X0,X1] :
( non_ordered_pair(X0,X1) = estin
| f26(non_ordered_pair(X0,X1)) = X0
| f26(non_ordered_pair(X0,X1)) = X1
| ~ little_set(non_ordered_pair(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_920])]) ).
fof(f21172,plain,
( spl0_865
<=> ! [X0,X1] :
( f26(non_ordered_pair(X0,X1)) = X0
| f26(non_ordered_pair(X0,X1)) = X1
| non_ordered_pair(X0,X1) = empty_set
| ~ little_set(non_ordered_pair(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_865])]) ).
fof(f21175,plain,
( ! [X0,X1] :
( non_ordered_pair(X0,X1) = estin
| f26(non_ordered_pair(X0,X1)) = X0
| f26(non_ordered_pair(X0,X1)) = X1
| ~ little_set(non_ordered_pair(X0,X1)) )
| ~ spl0_173
| ~ spl0_865 ),
inference(forward_demodulation,[],[f21173,f2442]) ).
fof(f21173,plain,
( ! [X0,X1] :
( f26(non_ordered_pair(X0,X1)) = X0
| f26(non_ordered_pair(X0,X1)) = X1
| non_ordered_pair(X0,X1) = empty_set
| ~ little_set(non_ordered_pair(X0,X1)) )
| ~ spl0_865 ),
inference(avatar_component_clause,[],[f21172]) ).
fof(f21406,plain,
( spl0_919
| ~ spl0_108
| ~ spl0_130 ),
inference(avatar_split_clause,[],[f1473,f1470,f1072,f21404]) ).
fof(f21404,plain,
( spl0_919
<=> ! [X2,X0,X1] :
( ~ little_set(second(X0))
| ~ member(X0,X1)
| ~ member(first(X0),X2)
| ~ ordered_pair_predicate(X0)
| second(X0) = second(f22(second(X0),X2,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_919])]) ).
fof(f1473,plain,
( ! [X2,X0,X1] :
( ~ little_set(second(X0))
| ~ member(X0,X1)
| ~ member(first(X0),X2)
| ~ ordered_pair_predicate(X0)
| second(X0) = second(f22(second(X0),X2,X1)) )
| ~ spl0_108
| ~ spl0_130 ),
inference(resolution,[],[f1471,f1073]) ).
fof(f21402,plain,
( spl0_918
| ~ spl0_93
| ~ spl0_129 ),
inference(avatar_split_clause,[],[f1464,f1405,f836,f21400]) ).
fof(f21400,plain,
( spl0_918
<=> ! [X0,X3,X2,X1] :
( ~ little_set(X0)
| ~ member(X1,X2)
| ~ little_set(X2)
| ~ member(first(non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X0))),X3)
| member(X1,sigma(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_918])]) ).
fof(f1464,plain,
( ! [X2,X3,X0,X1] :
( ~ little_set(X0)
| ~ member(X1,X2)
| ~ little_set(X2)
| ~ member(first(non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X0))),X3)
| member(X1,sigma(X3)) )
| ~ spl0_93
| ~ spl0_129 ),
inference(resolution,[],[f1406,f837]) ).
fof(f21398,plain,
( spl0_917
| ~ spl0_93
| ~ spl0_128 ),
inference(avatar_split_clause,[],[f1455,f1401,f836,f21396]) ).
fof(f21396,plain,
( spl0_917
<=> ! [X0,X3,X2,X1] :
( ~ little_set(X0)
| ~ member(X1,X0)
| ~ little_set(X2)
| ~ member(second(non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X0))),X3)
| member(X1,sigma(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_917])]) ).
fof(f1455,plain,
( ! [X2,X3,X0,X1] :
( ~ little_set(X0)
| ~ member(X1,X0)
| ~ little_set(X2)
| ~ member(second(non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X0))),X3)
| member(X1,sigma(X3)) )
| ~ spl0_93
| ~ spl0_128 ),
inference(resolution,[],[f1402,f837]) ).
fof(f21391,plain,
( spl0_916
| ~ spl0_127
| ~ spl0_153 ),
inference(avatar_split_clause,[],[f2140,f2098,f1397,f21389]) ).
fof(f21389,plain,
( spl0_916
<=> ! [X0] : ~ member(X0,converse(flip_range_of(empty_set))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_916])]) ).
fof(f2140,plain,
( ! [X0] : ~ member(X0,converse(flip_range_of(empty_set)))
| ~ spl0_127
| ~ spl0_153 ),
inference(resolution,[],[f2099,f1398]) ).
fof(f21387,plain,
( spl0_915
| ~ spl0_97
| ~ spl0_127 ),
inference(avatar_split_clause,[],[f1452,f1397,f852,f21385]) ).
fof(f21385,plain,
( spl0_915
<=> ! [X2,X0,X1] :
( ~ member(X0,converse(compose(X1,X2)))
| little_set(f29(non_ordered_pair(non_ordered_pair(second(X0),second(X0)),non_ordered_pair(second(X0),first(X0))),X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_915])]) ).
fof(f1452,plain,
( ! [X2,X0,X1] :
( ~ member(X0,converse(compose(X1,X2)))
| little_set(f29(non_ordered_pair(non_ordered_pair(second(X0),second(X0)),non_ordered_pair(second(X0),first(X0))),X1,X2)) )
| ~ spl0_97
| ~ spl0_127 ),
inference(resolution,[],[f1398,f853]) ).
fof(f21383,plain,
( spl0_914
| ~ spl0_98
| ~ spl0_127 ),
inference(avatar_split_clause,[],[f1451,f1397,f856,f21381]) ).
fof(f21381,plain,
( spl0_914
<=> ! [X2,X0,X1] :
( ~ member(X0,converse(compose(X1,X2)))
| little_set(f30(non_ordered_pair(non_ordered_pair(second(X0),second(X0)),non_ordered_pair(second(X0),first(X0))),X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_914])]) ).
fof(f1451,plain,
( ! [X2,X0,X1] :
( ~ member(X0,converse(compose(X1,X2)))
| little_set(f30(non_ordered_pair(non_ordered_pair(second(X0),second(X0)),non_ordered_pair(second(X0),first(X0))),X1,X2)) )
| ~ spl0_98
| ~ spl0_127 ),
inference(resolution,[],[f1398,f857]) ).
fof(f21379,plain,
( spl0_913
| ~ spl0_99
| ~ spl0_127 ),
inference(avatar_split_clause,[],[f1450,f1397,f860,f21377]) ).
fof(f21377,plain,
( spl0_913
<=> ! [X2,X0,X1] :
( ~ member(X0,converse(compose(X1,X2)))
| little_set(f31(non_ordered_pair(non_ordered_pair(second(X0),second(X0)),non_ordered_pair(second(X0),first(X0))),X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_913])]) ).
fof(f1450,plain,
( ! [X2,X0,X1] :
( ~ member(X0,converse(compose(X1,X2)))
| little_set(f31(non_ordered_pair(non_ordered_pair(second(X0),second(X0)),non_ordered_pair(second(X0),first(X0))),X1,X2)) )
| ~ spl0_99
| ~ spl0_127 ),
inference(resolution,[],[f1398,f861]) ).
fof(f21375,plain,
( spl0_912
| ~ spl0_96
| ~ spl0_127 ),
inference(avatar_split_clause,[],[f1449,f1397,f848,f21373]) ).
fof(f21373,plain,
( spl0_912
<=> ! [X2,X0,X1] :
( ~ member(X0,converse(apply(X1,X2)))
| ordered_pair_predicate(f28(non_ordered_pair(non_ordered_pair(second(X0),second(X0)),non_ordered_pair(second(X0),first(X0))),X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_912])]) ).
fof(f1449,plain,
( ! [X2,X0,X1] :
( ~ member(X0,converse(apply(X1,X2)))
| ordered_pair_predicate(f28(non_ordered_pair(non_ordered_pair(second(X0),second(X0)),non_ordered_pair(second(X0),first(X0))),X1,X2)) )
| ~ spl0_96
| ~ spl0_127 ),
inference(resolution,[],[f1398,f849]) ).
fof(f21371,plain,
( spl0_911
| ~ spl0_94
| ~ spl0_127 ),
inference(avatar_split_clause,[],[f1443,f1397,f840,f21369]) ).
fof(f21369,plain,
( spl0_911
<=> ! [X2,X0,X1] :
( ~ member(X0,converse(image(X1,X2)))
| ordered_pair_predicate(f22(non_ordered_pair(non_ordered_pair(second(X0),second(X0)),non_ordered_pair(second(X0),first(X0))),X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_911])]) ).
fof(f1443,plain,
( ! [X2,X0,X1] :
( ~ member(X0,converse(image(X1,X2)))
| ordered_pair_predicate(f22(non_ordered_pair(non_ordered_pair(second(X0),second(X0)),non_ordered_pair(second(X0),first(X0))),X1,X2)) )
| ~ spl0_94
| ~ spl0_127 ),
inference(resolution,[],[f1398,f841]) ).
fof(f21367,plain,
( spl0_910
| ~ spl0_93
| ~ spl0_127 ),
inference(avatar_split_clause,[],[f1416,f1397,f836,f21365]) ).
fof(f21365,plain,
( spl0_910
<=> ! [X2,X0,X1] :
( ~ member(X0,converse(X1))
| ~ member(X1,X2)
| member(non_ordered_pair(non_ordered_pair(second(X0),second(X0)),non_ordered_pair(second(X0),first(X0))),sigma(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_910])]) ).
fof(f1416,plain,
( ! [X2,X0,X1] :
( ~ member(X0,converse(X1))
| ~ member(X1,X2)
| member(non_ordered_pair(non_ordered_pair(second(X0),second(X0)),non_ordered_pair(second(X0),first(X0))),sigma(X2)) )
| ~ spl0_93
| ~ spl0_127 ),
inference(resolution,[],[f1398,f837]) ).
fof(f21363,plain,
( spl0_909
| ~ spl0_93
| ~ spl0_126 ),
inference(avatar_split_clause,[],[f1411,f1393,f836,f21361]) ).
fof(f21361,plain,
( spl0_909
<=> ! [X0,X3,X2,X1] :
( ~ little_set(X0)
| ~ member(first(X0),X1)
| ~ member(second(X0),X2)
| ~ ordered_pair_predicate(X0)
| ~ member(cross_product(X1,X2),X3)
| member(X0,sigma(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_909])]) ).
fof(f1411,plain,
( ! [X2,X3,X0,X1] :
( ~ little_set(X0)
| ~ member(first(X0),X1)
| ~ member(second(X0),X2)
| ~ ordered_pair_predicate(X0)
| ~ member(cross_product(X1,X2),X3)
| member(X0,sigma(X3)) )
| ~ spl0_93
| ~ spl0_126 ),
inference(resolution,[],[f1394,f837]) ).
fof(f21359,plain,
( spl0_908
| ~ spl0_65
| ~ spl0_122 ),
inference(avatar_split_clause,[],[f1374,f1291,f482,f21357]) ).
fof(f21357,plain,
( spl0_908
<=> ! [X0] :
( single_valued_set(range_of(X0))
| ordered_pair_predicate(f27(non_ordered_pair(non_ordered_pair(f19(range_of(X0)),f19(range_of(X0))),non_ordered_pair(f19(range_of(X0)),f21(range_of(X0)))),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_908])]) ).
fof(f1374,plain,
( ! [X0] :
( single_valued_set(range_of(X0))
| ordered_pair_predicate(f27(non_ordered_pair(non_ordered_pair(f19(range_of(X0)),f19(range_of(X0))),non_ordered_pair(f19(range_of(X0)),f21(range_of(X0)))),X0)) )
| ~ spl0_65
| ~ spl0_122 ),
inference(resolution,[],[f1292,f483]) ).
fof(f21355,plain,
( spl0_907
| ~ spl0_57
| ~ spl0_122 ),
inference(avatar_split_clause,[],[f1368,f1291,f450,f21353]) ).
fof(f21353,plain,
( spl0_907
<=> ! [X0] :
( single_valued_set(flip_range_of(X0))
| little_set(f12(non_ordered_pair(non_ordered_pair(f19(flip_range_of(X0)),f19(flip_range_of(X0))),non_ordered_pair(f19(flip_range_of(X0)),f21(flip_range_of(X0)))),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_907])]) ).
fof(f1368,plain,
( ! [X0] :
( single_valued_set(flip_range_of(X0))
| little_set(f12(non_ordered_pair(non_ordered_pair(f19(flip_range_of(X0)),f19(flip_range_of(X0))),non_ordered_pair(f19(flip_range_of(X0)),f21(flip_range_of(X0)))),X0)) )
| ~ spl0_57
| ~ spl0_122 ),
inference(resolution,[],[f1292,f451]) ).
fof(f21351,plain,
( spl0_906
| ~ spl0_58
| ~ spl0_122 ),
inference(avatar_split_clause,[],[f1367,f1291,f454,f21349]) ).
fof(f21349,plain,
( spl0_906
<=> ! [X0] :
( single_valued_set(flip_range_of(X0))
| little_set(f13(non_ordered_pair(non_ordered_pair(f19(flip_range_of(X0)),f19(flip_range_of(X0))),non_ordered_pair(f19(flip_range_of(X0)),f21(flip_range_of(X0)))),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_906])]) ).
fof(f1367,plain,
( ! [X0] :
( single_valued_set(flip_range_of(X0))
| little_set(f13(non_ordered_pair(non_ordered_pair(f19(flip_range_of(X0)),f19(flip_range_of(X0))),non_ordered_pair(f19(flip_range_of(X0)),f21(flip_range_of(X0)))),X0)) )
| ~ spl0_58
| ~ spl0_122 ),
inference(resolution,[],[f1292,f455]) ).
fof(f21344,plain,
( spl0_905
| ~ spl0_78
| ~ spl0_151 ),
inference(avatar_split_clause,[],[f2116,f2025,f644,f21342]) ).
fof(f21342,plain,
( spl0_905
<=> ! [X0] : ~ member(X0,sigma(converse(empty_set))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_905])]) ).
fof(f2116,plain,
( ! [X0] : ~ member(X0,sigma(converse(empty_set)))
| ~ spl0_78
| ~ spl0_151 ),
inference(resolution,[],[f2026,f645]) ).
fof(f21340,plain,
( spl0_904
| ~ spl0_59
| ~ spl0_122 ),
inference(avatar_split_clause,[],[f1366,f1291,f458,f21338]) ).
fof(f21338,plain,
( spl0_904
<=> ! [X0] :
( single_valued_set(flip_range_of(X0))
| little_set(f14(non_ordered_pair(non_ordered_pair(f19(flip_range_of(X0)),f19(flip_range_of(X0))),non_ordered_pair(f19(flip_range_of(X0)),f21(flip_range_of(X0)))),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_904])]) ).
fof(f1366,plain,
( ! [X0] :
( single_valued_set(flip_range_of(X0))
| little_set(f14(non_ordered_pair(non_ordered_pair(f19(flip_range_of(X0)),f19(flip_range_of(X0))),non_ordered_pair(f19(flip_range_of(X0)),f21(flip_range_of(X0)))),X0)) )
| ~ spl0_59
| ~ spl0_122 ),
inference(resolution,[],[f1292,f459]) ).
fof(f21336,plain,
( spl0_903
| ~ spl0_54
| ~ spl0_122 ),
inference(avatar_split_clause,[],[f1365,f1291,f438,f21334]) ).
fof(f21334,plain,
( spl0_903
<=> ! [X0] :
( single_valued_set(rotate_right(X0))
| little_set(f9(non_ordered_pair(non_ordered_pair(f19(rotate_right(X0)),f19(rotate_right(X0))),non_ordered_pair(f19(rotate_right(X0)),f21(rotate_right(X0)))),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_903])]) ).
fof(f1365,plain,
( ! [X0] :
( single_valued_set(rotate_right(X0))
| little_set(f9(non_ordered_pair(non_ordered_pair(f19(rotate_right(X0)),f19(rotate_right(X0))),non_ordered_pair(f19(rotate_right(X0)),f21(rotate_right(X0)))),X0)) )
| ~ spl0_54
| ~ spl0_122 ),
inference(resolution,[],[f1292,f439]) ).
fof(f21332,plain,
( spl0_902
| ~ spl0_55
| ~ spl0_122 ),
inference(avatar_split_clause,[],[f1364,f1291,f442,f21330]) ).
fof(f21330,plain,
( spl0_902
<=> ! [X0] :
( single_valued_set(rotate_right(X0))
| little_set(f10(non_ordered_pair(non_ordered_pair(f19(rotate_right(X0)),f19(rotate_right(X0))),non_ordered_pair(f19(rotate_right(X0)),f21(rotate_right(X0)))),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_902])]) ).
fof(f1364,plain,
( ! [X0] :
( single_valued_set(rotate_right(X0))
| little_set(f10(non_ordered_pair(non_ordered_pair(f19(rotate_right(X0)),f19(rotate_right(X0))),non_ordered_pair(f19(rotate_right(X0)),f21(rotate_right(X0)))),X0)) )
| ~ spl0_55
| ~ spl0_122 ),
inference(resolution,[],[f1292,f443]) ).
fof(f21328,plain,
( spl0_901
| ~ spl0_56
| ~ spl0_122 ),
inference(avatar_split_clause,[],[f1363,f1291,f446,f21326]) ).
fof(f21326,plain,
( spl0_901
<=> ! [X0] :
( single_valued_set(rotate_right(X0))
| little_set(f11(non_ordered_pair(non_ordered_pair(f19(rotate_right(X0)),f19(rotate_right(X0))),non_ordered_pair(f19(rotate_right(X0)),f21(rotate_right(X0)))),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_901])]) ).
fof(f1363,plain,
( ! [X0] :
( single_valued_set(rotate_right(X0))
| little_set(f11(non_ordered_pair(non_ordered_pair(f19(rotate_right(X0)),f19(rotate_right(X0))),non_ordered_pair(f19(rotate_right(X0)),f21(rotate_right(X0)))),X0)) )
| ~ spl0_56
| ~ spl0_122 ),
inference(resolution,[],[f1292,f447]) ).
fof(f21324,plain,
( spl0_900
| ~ spl0_53
| ~ spl0_122 ),
inference(avatar_split_clause,[],[f1358,f1291,f434,f21322]) ).
fof(f21322,plain,
( spl0_900
<=> ! [X0] :
( single_valued_set(domain_of(X0))
| ordered_pair_predicate(f8(non_ordered_pair(non_ordered_pair(f19(domain_of(X0)),f19(domain_of(X0))),non_ordered_pair(f19(domain_of(X0)),f21(domain_of(X0)))),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_900])]) ).
fof(f1358,plain,
( ! [X0] :
( single_valued_set(domain_of(X0))
| ordered_pair_predicate(f8(non_ordered_pair(non_ordered_pair(f19(domain_of(X0)),f19(domain_of(X0))),non_ordered_pair(f19(domain_of(X0)),f21(domain_of(X0)))),X0)) )
| ~ spl0_53
| ~ spl0_122 ),
inference(resolution,[],[f1292,f435]) ).
fof(f21320,plain,
( spl0_899
| ~ spl0_48
| ~ spl0_122 ),
inference(avatar_split_clause,[],[f1352,f1291,f414,f21318]) ).
fof(f21318,plain,
( spl0_899
<=> ! [X0] :
( single_valued_set(second(X0))
| little_set(f6(non_ordered_pair(non_ordered_pair(f19(second(X0)),f19(second(X0))),non_ordered_pair(f19(second(X0)),f21(second(X0)))),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_899])]) ).
fof(f1352,plain,
( ! [X0] :
( single_valued_set(second(X0))
| little_set(f6(non_ordered_pair(non_ordered_pair(f19(second(X0)),f19(second(X0))),non_ordered_pair(f19(second(X0)),f21(second(X0)))),X0)) )
| ~ spl0_48
| ~ spl0_122 ),
inference(resolution,[],[f1292,f415]) ).
fof(f21316,plain,
( spl0_898
| ~ spl0_49
| ~ spl0_122 ),
inference(avatar_split_clause,[],[f1351,f1291,f418,f21314]) ).
fof(f21314,plain,
( spl0_898
<=> ! [X0] :
( single_valued_set(second(X0))
| little_set(f7(non_ordered_pair(non_ordered_pair(f19(second(X0)),f19(second(X0))),non_ordered_pair(f19(second(X0)),f21(second(X0)))),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_898])]) ).
fof(f1351,plain,
( ! [X0] :
( single_valued_set(second(X0))
| little_set(f7(non_ordered_pair(non_ordered_pair(f19(second(X0)),f19(second(X0))),non_ordered_pair(f19(second(X0)),f21(second(X0)))),X0)) )
| ~ spl0_49
| ~ spl0_122 ),
inference(resolution,[],[f1292,f419]) ).
fof(f21312,plain,
( spl0_897
| ~ spl0_46
| ~ spl0_122 ),
inference(avatar_split_clause,[],[f1350,f1291,f406,f21310]) ).
fof(f21310,plain,
( spl0_897
<=> ! [X0] :
( single_valued_set(first(X0))
| little_set(f4(non_ordered_pair(non_ordered_pair(f19(first(X0)),f19(first(X0))),non_ordered_pair(f19(first(X0)),f21(first(X0)))),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_897])]) ).
fof(f1350,plain,
( ! [X0] :
( single_valued_set(first(X0))
| little_set(f4(non_ordered_pair(non_ordered_pair(f19(first(X0)),f19(first(X0))),non_ordered_pair(f19(first(X0)),f21(first(X0)))),X0)) )
| ~ spl0_46
| ~ spl0_122 ),
inference(resolution,[],[f1292,f407]) ).
fof(f21308,plain,
( spl0_896
| ~ spl0_47
| ~ spl0_122 ),
inference(avatar_split_clause,[],[f1349,f1291,f410,f21306]) ).
fof(f21306,plain,
( spl0_896
<=> ! [X0] :
( single_valued_set(first(X0))
| little_set(f5(non_ordered_pair(non_ordered_pair(f19(first(X0)),f19(first(X0))),non_ordered_pair(f19(first(X0)),f21(first(X0)))),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_896])]) ).
fof(f1349,plain,
( ! [X0] :
( single_valued_set(first(X0))
| little_set(f5(non_ordered_pair(non_ordered_pair(f19(first(X0)),f19(first(X0))),non_ordered_pair(f19(first(X0)),f21(first(X0)))),X0)) )
| ~ spl0_47
| ~ spl0_122 ),
inference(resolution,[],[f1292,f411]) ).
fof(f21304,plain,
( spl0_895
| ~ spl0_65
| ~ spl0_121 ),
inference(avatar_split_clause,[],[f1332,f1287,f482,f21302]) ).
fof(f21302,plain,
( spl0_895
<=> ! [X0] :
( single_valued_set(range_of(X0))
| ordered_pair_predicate(f27(non_ordered_pair(non_ordered_pair(f19(range_of(X0)),f19(range_of(X0))),non_ordered_pair(f19(range_of(X0)),f20(range_of(X0)))),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_895])]) ).
fof(f1332,plain,
( ! [X0] :
( single_valued_set(range_of(X0))
| ordered_pair_predicate(f27(non_ordered_pair(non_ordered_pair(f19(range_of(X0)),f19(range_of(X0))),non_ordered_pair(f19(range_of(X0)),f20(range_of(X0)))),X0)) )
| ~ spl0_65
| ~ spl0_121 ),
inference(resolution,[],[f1288,f483]) ).
fof(f21297,plain,
( spl0_894
| ~ spl0_74
| ~ spl0_151 ),
inference(avatar_split_clause,[],[f2115,f2025,f628,f21295]) ).
fof(f21295,plain,
( spl0_894
<=> ! [X0] : ~ member(X0,domain_of(converse(empty_set))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_894])]) ).
fof(f2115,plain,
( ! [X0] : ~ member(X0,domain_of(converse(empty_set)))
| ~ spl0_74
| ~ spl0_151 ),
inference(resolution,[],[f2026,f629]) ).
fof(f21293,plain,
( spl0_893
| ~ spl0_57
| ~ spl0_121 ),
inference(avatar_split_clause,[],[f1326,f1287,f450,f21291]) ).
fof(f21291,plain,
( spl0_893
<=> ! [X0] :
( single_valued_set(flip_range_of(X0))
| little_set(f12(non_ordered_pair(non_ordered_pair(f19(flip_range_of(X0)),f19(flip_range_of(X0))),non_ordered_pair(f19(flip_range_of(X0)),f20(flip_range_of(X0)))),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_893])]) ).
fof(f1326,plain,
( ! [X0] :
( single_valued_set(flip_range_of(X0))
| little_set(f12(non_ordered_pair(non_ordered_pair(f19(flip_range_of(X0)),f19(flip_range_of(X0))),non_ordered_pair(f19(flip_range_of(X0)),f20(flip_range_of(X0)))),X0)) )
| ~ spl0_57
| ~ spl0_121 ),
inference(resolution,[],[f1288,f451]) ).
fof(f21289,plain,
( spl0_892
| ~ spl0_58
| ~ spl0_121 ),
inference(avatar_split_clause,[],[f1325,f1287,f454,f21287]) ).
fof(f21287,plain,
( spl0_892
<=> ! [X0] :
( single_valued_set(flip_range_of(X0))
| little_set(f13(non_ordered_pair(non_ordered_pair(f19(flip_range_of(X0)),f19(flip_range_of(X0))),non_ordered_pair(f19(flip_range_of(X0)),f20(flip_range_of(X0)))),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_892])]) ).
fof(f1325,plain,
( ! [X0] :
( single_valued_set(flip_range_of(X0))
| little_set(f13(non_ordered_pair(non_ordered_pair(f19(flip_range_of(X0)),f19(flip_range_of(X0))),non_ordered_pair(f19(flip_range_of(X0)),f20(flip_range_of(X0)))),X0)) )
| ~ spl0_58
| ~ spl0_121 ),
inference(resolution,[],[f1288,f455]) ).
fof(f21285,plain,
( spl0_891
| ~ spl0_59
| ~ spl0_121 ),
inference(avatar_split_clause,[],[f1324,f1287,f458,f21283]) ).
fof(f21283,plain,
( spl0_891
<=> ! [X0] :
( single_valued_set(flip_range_of(X0))
| little_set(f14(non_ordered_pair(non_ordered_pair(f19(flip_range_of(X0)),f19(flip_range_of(X0))),non_ordered_pair(f19(flip_range_of(X0)),f20(flip_range_of(X0)))),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_891])]) ).
fof(f1324,plain,
( ! [X0] :
( single_valued_set(flip_range_of(X0))
| little_set(f14(non_ordered_pair(non_ordered_pair(f19(flip_range_of(X0)),f19(flip_range_of(X0))),non_ordered_pair(f19(flip_range_of(X0)),f20(flip_range_of(X0)))),X0)) )
| ~ spl0_59
| ~ spl0_121 ),
inference(resolution,[],[f1288,f459]) ).
fof(f21281,plain,
( spl0_890
| ~ spl0_54
| ~ spl0_121 ),
inference(avatar_split_clause,[],[f1323,f1287,f438,f21279]) ).
fof(f21279,plain,
( spl0_890
<=> ! [X0] :
( single_valued_set(rotate_right(X0))
| little_set(f9(non_ordered_pair(non_ordered_pair(f19(rotate_right(X0)),f19(rotate_right(X0))),non_ordered_pair(f19(rotate_right(X0)),f20(rotate_right(X0)))),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_890])]) ).
fof(f1323,plain,
( ! [X0] :
( single_valued_set(rotate_right(X0))
| little_set(f9(non_ordered_pair(non_ordered_pair(f19(rotate_right(X0)),f19(rotate_right(X0))),non_ordered_pair(f19(rotate_right(X0)),f20(rotate_right(X0)))),X0)) )
| ~ spl0_54
| ~ spl0_121 ),
inference(resolution,[],[f1288,f439]) ).
fof(f21277,plain,
( spl0_889
| ~ spl0_55
| ~ spl0_121 ),
inference(avatar_split_clause,[],[f1322,f1287,f442,f21275]) ).
fof(f21275,plain,
( spl0_889
<=> ! [X0] :
( single_valued_set(rotate_right(X0))
| little_set(f10(non_ordered_pair(non_ordered_pair(f19(rotate_right(X0)),f19(rotate_right(X0))),non_ordered_pair(f19(rotate_right(X0)),f20(rotate_right(X0)))),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_889])]) ).
fof(f1322,plain,
( ! [X0] :
( single_valued_set(rotate_right(X0))
| little_set(f10(non_ordered_pair(non_ordered_pair(f19(rotate_right(X0)),f19(rotate_right(X0))),non_ordered_pair(f19(rotate_right(X0)),f20(rotate_right(X0)))),X0)) )
| ~ spl0_55
| ~ spl0_121 ),
inference(resolution,[],[f1288,f443]) ).
fof(f21273,plain,
( spl0_888
| ~ spl0_56
| ~ spl0_121 ),
inference(avatar_split_clause,[],[f1321,f1287,f446,f21271]) ).
fof(f21271,plain,
( spl0_888
<=> ! [X0] :
( single_valued_set(rotate_right(X0))
| little_set(f11(non_ordered_pair(non_ordered_pair(f19(rotate_right(X0)),f19(rotate_right(X0))),non_ordered_pair(f19(rotate_right(X0)),f20(rotate_right(X0)))),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_888])]) ).
fof(f1321,plain,
( ! [X0] :
( single_valued_set(rotate_right(X0))
| little_set(f11(non_ordered_pair(non_ordered_pair(f19(rotate_right(X0)),f19(rotate_right(X0))),non_ordered_pair(f19(rotate_right(X0)),f20(rotate_right(X0)))),X0)) )
| ~ spl0_56
| ~ spl0_121 ),
inference(resolution,[],[f1288,f447]) ).
fof(f21269,plain,
( spl0_887
| ~ spl0_53
| ~ spl0_121 ),
inference(avatar_split_clause,[],[f1316,f1287,f434,f21267]) ).
fof(f21267,plain,
( spl0_887
<=> ! [X0] :
( single_valued_set(domain_of(X0))
| ordered_pair_predicate(f8(non_ordered_pair(non_ordered_pair(f19(domain_of(X0)),f19(domain_of(X0))),non_ordered_pair(f19(domain_of(X0)),f20(domain_of(X0)))),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_887])]) ).
fof(f1316,plain,
( ! [X0] :
( single_valued_set(domain_of(X0))
| ordered_pair_predicate(f8(non_ordered_pair(non_ordered_pair(f19(domain_of(X0)),f19(domain_of(X0))),non_ordered_pair(f19(domain_of(X0)),f20(domain_of(X0)))),X0)) )
| ~ spl0_53
| ~ spl0_121 ),
inference(resolution,[],[f1288,f435]) ).
fof(f21265,plain,
( spl0_886
| ~ spl0_48
| ~ spl0_121 ),
inference(avatar_split_clause,[],[f1310,f1287,f414,f21263]) ).
fof(f21263,plain,
( spl0_886
<=> ! [X0] :
( single_valued_set(second(X0))
| little_set(f6(non_ordered_pair(non_ordered_pair(f19(second(X0)),f19(second(X0))),non_ordered_pair(f19(second(X0)),f20(second(X0)))),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_886])]) ).
fof(f1310,plain,
( ! [X0] :
( single_valued_set(second(X0))
| little_set(f6(non_ordered_pair(non_ordered_pair(f19(second(X0)),f19(second(X0))),non_ordered_pair(f19(second(X0)),f20(second(X0)))),X0)) )
| ~ spl0_48
| ~ spl0_121 ),
inference(resolution,[],[f1288,f415]) ).
fof(f21261,plain,
( spl0_885
| ~ spl0_49
| ~ spl0_121 ),
inference(avatar_split_clause,[],[f1309,f1287,f418,f21259]) ).
fof(f21259,plain,
( spl0_885
<=> ! [X0] :
( single_valued_set(second(X0))
| little_set(f7(non_ordered_pair(non_ordered_pair(f19(second(X0)),f19(second(X0))),non_ordered_pair(f19(second(X0)),f20(second(X0)))),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_885])]) ).
fof(f1309,plain,
( ! [X0] :
( single_valued_set(second(X0))
| little_set(f7(non_ordered_pair(non_ordered_pair(f19(second(X0)),f19(second(X0))),non_ordered_pair(f19(second(X0)),f20(second(X0)))),X0)) )
| ~ spl0_49
| ~ spl0_121 ),
inference(resolution,[],[f1288,f419]) ).
fof(f21257,plain,
( spl0_884
| ~ spl0_46
| ~ spl0_121 ),
inference(avatar_split_clause,[],[f1308,f1287,f406,f21255]) ).
fof(f21255,plain,
( spl0_884
<=> ! [X0] :
( single_valued_set(first(X0))
| little_set(f4(non_ordered_pair(non_ordered_pair(f19(first(X0)),f19(first(X0))),non_ordered_pair(f19(first(X0)),f20(first(X0)))),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_884])]) ).
fof(f1308,plain,
( ! [X0] :
( single_valued_set(first(X0))
| little_set(f4(non_ordered_pair(non_ordered_pair(f19(first(X0)),f19(first(X0))),non_ordered_pair(f19(first(X0)),f20(first(X0)))),X0)) )
| ~ spl0_46
| ~ spl0_121 ),
inference(resolution,[],[f1288,f407]) ).
fof(f21250,plain,
( spl0_883
| ~ spl0_145
| ~ spl0_151 ),
inference(avatar_split_clause,[],[f2112,f2025,f1786,f21248]) ).
fof(f21248,plain,
( spl0_883
<=> ! [X0] : ~ member(X0,rotate_right(converse(empty_set))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_883])]) ).
fof(f2112,plain,
( ! [X0] : ~ member(X0,rotate_right(converse(empty_set)))
| ~ spl0_145
| ~ spl0_151 ),
inference(resolution,[],[f2026,f1787]) ).
fof(f21246,plain,
( spl0_882
| ~ spl0_47
| ~ spl0_121 ),
inference(avatar_split_clause,[],[f1307,f1287,f410,f21244]) ).
fof(f21244,plain,
( spl0_882
<=> ! [X0] :
( single_valued_set(first(X0))
| little_set(f5(non_ordered_pair(non_ordered_pair(f19(first(X0)),f19(first(X0))),non_ordered_pair(f19(first(X0)),f20(first(X0)))),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_882])]) ).
fof(f1307,plain,
( ! [X0] :
( single_valued_set(first(X0))
| little_set(f5(non_ordered_pair(non_ordered_pair(f19(first(X0)),f19(first(X0))),non_ordered_pair(f19(first(X0)),f20(first(X0)))),X0)) )
| ~ spl0_47
| ~ spl0_121 ),
inference(resolution,[],[f1288,f411]) ).
fof(f21242,plain,
( spl0_881
| ~ spl0_82
| ~ spl0_114 ),
inference(avatar_split_clause,[],[f1262,f1163,f660,f21240]) ).
fof(f21240,plain,
( spl0_881
<=> ! [X0,X1] :
( powerset(X1) = X0
| ~ member(f1(X0,powerset(X1)),X0)
| ~ subset(f1(X0,powerset(X1)),X1)
| ~ little_set(f1(X0,powerset(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_881])]) ).
fof(f1262,plain,
( ! [X0,X1] :
( powerset(X1) = X0
| ~ member(f1(X0,powerset(X1)),X0)
| ~ subset(f1(X0,powerset(X1)),X1)
| ~ little_set(f1(X0,powerset(X1))) )
| ~ spl0_82
| ~ spl0_114 ),
inference(resolution,[],[f1164,f661]) ).
fof(f21238,plain,
( spl0_880
| ~ spl0_73
| ~ spl0_114 ),
inference(avatar_split_clause,[],[f1260,f1163,f624,f21236]) ).
fof(f21236,plain,
( spl0_880
<=> ! [X0,X1] :
( complement(X1) = X0
| ~ member(f1(X0,complement(X1)),X0)
| member(f1(X0,complement(X1)),X1)
| ~ little_set(f1(X0,complement(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_880])]) ).
fof(f1260,plain,
( ! [X0,X1] :
( complement(X1) = X0
| ~ member(f1(X0,complement(X1)),X0)
| member(f1(X0,complement(X1)),X1)
| ~ little_set(f1(X0,complement(X1))) )
| ~ spl0_73
| ~ spl0_114 ),
inference(resolution,[],[f1164,f625]) ).
fof(f21234,plain,
( spl0_879
| ~ spl0_97
| ~ spl0_113 ),
inference(avatar_split_clause,[],[f1255,f1159,f852,f21232]) ).
fof(f21232,plain,
( spl0_879
<=> ! [X2,X0,X1] :
( member(f1(compose(X0,X1),X2),X2)
| compose(X0,X1) = X2
| little_set(f29(f1(compose(X0,X1),X2),X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_879])]) ).
fof(f1255,plain,
( ! [X2,X0,X1] :
( member(f1(compose(X0,X1),X2),X2)
| compose(X0,X1) = X2
| little_set(f29(f1(compose(X0,X1),X2),X0,X1)) )
| ~ spl0_97
| ~ spl0_113 ),
inference(resolution,[],[f1160,f853]) ).
fof(f21230,plain,
( spl0_878
| ~ spl0_98
| ~ spl0_113 ),
inference(avatar_split_clause,[],[f1254,f1159,f856,f21228]) ).
fof(f21228,plain,
( spl0_878
<=> ! [X2,X0,X1] :
( member(f1(compose(X0,X1),X2),X2)
| compose(X0,X1) = X2
| little_set(f30(f1(compose(X0,X1),X2),X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_878])]) ).
fof(f1254,plain,
( ! [X2,X0,X1] :
( member(f1(compose(X0,X1),X2),X2)
| compose(X0,X1) = X2
| little_set(f30(f1(compose(X0,X1),X2),X0,X1)) )
| ~ spl0_98
| ~ spl0_113 ),
inference(resolution,[],[f1160,f857]) ).
fof(f21226,plain,
( spl0_877
| ~ spl0_99
| ~ spl0_113 ),
inference(avatar_split_clause,[],[f1253,f1159,f860,f21224]) ).
fof(f21224,plain,
( spl0_877
<=> ! [X2,X0,X1] :
( member(f1(compose(X0,X1),X2),X2)
| compose(X0,X1) = X2
| little_set(f31(f1(compose(X0,X1),X2),X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_877])]) ).
fof(f1253,plain,
( ! [X2,X0,X1] :
( member(f1(compose(X0,X1),X2),X2)
| compose(X0,X1) = X2
| little_set(f31(f1(compose(X0,X1),X2),X0,X1)) )
| ~ spl0_99
| ~ spl0_113 ),
inference(resolution,[],[f1160,f861]) ).
fof(f21222,plain,
( spl0_876
| ~ spl0_96
| ~ spl0_113 ),
inference(avatar_split_clause,[],[f1252,f1159,f848,f21220]) ).
fof(f21220,plain,
( spl0_876
<=> ! [X2,X0,X1] :
( member(f1(apply(X0,X1),X2),X2)
| apply(X0,X1) = X2
| ordered_pair_predicate(f28(f1(apply(X0,X1),X2),X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_876])]) ).
fof(f1252,plain,
( ! [X2,X0,X1] :
( member(f1(apply(X0,X1),X2),X2)
| apply(X0,X1) = X2
| ordered_pair_predicate(f28(f1(apply(X0,X1),X2),X0,X1)) )
| ~ spl0_96
| ~ spl0_113 ),
inference(resolution,[],[f1160,f849]) ).
fof(f21218,plain,
( spl0_875
| ~ spl0_94
| ~ spl0_113 ),
inference(avatar_split_clause,[],[f1246,f1159,f840,f21216]) ).
fof(f21216,plain,
( spl0_875
<=> ! [X2,X0,X1] :
( member(f1(image(X0,X1),X2),X2)
| image(X0,X1) = X2
| ordered_pair_predicate(f22(f1(image(X0,X1),X2),X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_875])]) ).
fof(f1246,plain,
( ! [X2,X0,X1] :
( member(f1(image(X0,X1),X2),X2)
| image(X0,X1) = X2
| ordered_pair_predicate(f22(f1(image(X0,X1),X2),X0,X1)) )
| ~ spl0_94
| ~ spl0_113 ),
inference(resolution,[],[f1160,f841]) ).
fof(f21214,plain,
( spl0_874
| ~ spl0_97
| ~ spl0_113 ),
inference(avatar_split_clause,[],[f1218,f1159,f852,f21212]) ).
fof(f21212,plain,
( spl0_874
<=> ! [X2,X0,X1] :
( member(f1(X0,compose(X1,X2)),X0)
| compose(X1,X2) = X0
| little_set(f29(f1(X0,compose(X1,X2)),X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_874])]) ).
fof(f1218,plain,
( ! [X2,X0,X1] :
( member(f1(X0,compose(X1,X2)),X0)
| compose(X1,X2) = X0
| little_set(f29(f1(X0,compose(X1,X2)),X1,X2)) )
| ~ spl0_97
| ~ spl0_113 ),
inference(resolution,[],[f1160,f853]) ).
fof(f21210,plain,
( spl0_873
| ~ spl0_98
| ~ spl0_113 ),
inference(avatar_split_clause,[],[f1217,f1159,f856,f21208]) ).
fof(f21208,plain,
( spl0_873
<=> ! [X2,X0,X1] :
( member(f1(X0,compose(X1,X2)),X0)
| compose(X1,X2) = X0
| little_set(f30(f1(X0,compose(X1,X2)),X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_873])]) ).
fof(f1217,plain,
( ! [X2,X0,X1] :
( member(f1(X0,compose(X1,X2)),X0)
| compose(X1,X2) = X0
| little_set(f30(f1(X0,compose(X1,X2)),X1,X2)) )
| ~ spl0_98
| ~ spl0_113 ),
inference(resolution,[],[f1160,f857]) ).
fof(f21203,plain,
( spl0_872
| ~ spl0_144
| ~ spl0_151 ),
inference(avatar_split_clause,[],[f2111,f2025,f1782,f21201]) ).
fof(f21201,plain,
( spl0_872
<=> ! [X0] : ~ member(X0,flip_range_of(converse(empty_set))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_872])]) ).
fof(f2111,plain,
( ! [X0] : ~ member(X0,flip_range_of(converse(empty_set)))
| ~ spl0_144
| ~ spl0_151 ),
inference(resolution,[],[f2026,f1783]) ).
fof(f21199,plain,
( spl0_871
| ~ spl0_99
| ~ spl0_113 ),
inference(avatar_split_clause,[],[f1216,f1159,f860,f21197]) ).
fof(f21197,plain,
( spl0_871
<=> ! [X2,X0,X1] :
( member(f1(X0,compose(X1,X2)),X0)
| compose(X1,X2) = X0
| little_set(f31(f1(X0,compose(X1,X2)),X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_871])]) ).
fof(f1216,plain,
( ! [X2,X0,X1] :
( member(f1(X0,compose(X1,X2)),X0)
| compose(X1,X2) = X0
| little_set(f31(f1(X0,compose(X1,X2)),X1,X2)) )
| ~ spl0_99
| ~ spl0_113 ),
inference(resolution,[],[f1160,f861]) ).
fof(f21195,plain,
( spl0_870
| ~ spl0_96
| ~ spl0_113 ),
inference(avatar_split_clause,[],[f1215,f1159,f848,f21193]) ).
fof(f21193,plain,
( spl0_870
<=> ! [X2,X0,X1] :
( member(f1(X0,apply(X1,X2)),X0)
| apply(X1,X2) = X0
| ordered_pair_predicate(f28(f1(X0,apply(X1,X2)),X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_870])]) ).
fof(f1215,plain,
( ! [X2,X0,X1] :
( member(f1(X0,apply(X1,X2)),X0)
| apply(X1,X2) = X0
| ordered_pair_predicate(f28(f1(X0,apply(X1,X2)),X1,X2)) )
| ~ spl0_96
| ~ spl0_113 ),
inference(resolution,[],[f1160,f849]) ).
fof(f21191,plain,
( spl0_869
| ~ spl0_94
| ~ spl0_113 ),
inference(avatar_split_clause,[],[f1209,f1159,f840,f21189]) ).
fof(f21189,plain,
( spl0_869
<=> ! [X2,X0,X1] :
( member(f1(X0,image(X1,X2)),X0)
| image(X1,X2) = X0
| ordered_pair_predicate(f22(f1(X0,image(X1,X2)),X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_869])]) ).
fof(f1209,plain,
( ! [X2,X0,X1] :
( member(f1(X0,image(X1,X2)),X0)
| image(X1,X2) = X0
| ordered_pair_predicate(f22(f1(X0,image(X1,X2)),X1,X2)) )
| ~ spl0_94
| ~ spl0_113 ),
inference(resolution,[],[f1160,f841]) ).
fof(f21187,plain,
( spl0_868
| ~ spl0_85
| ~ spl0_108 ),
inference(avatar_split_clause,[],[f1138,f1072,f672,f21185]) ).
fof(f21185,plain,
( spl0_868
<=> ! [X2,X0,X1] :
( f27(X0,image(X1,X2)) = second(f22(f27(X0,image(X1,X2)),X1,X2))
| ~ member(X0,range_of(image(X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_868])]) ).
fof(f1138,plain,
( ! [X2,X0,X1] :
( f27(X0,image(X1,X2)) = second(f22(f27(X0,image(X1,X2)),X1,X2))
| ~ member(X0,range_of(image(X1,X2))) )
| ~ spl0_85
| ~ spl0_108 ),
inference(resolution,[],[f1073,f673]) ).
fof(f21183,plain,
( spl0_867
| ~ spl0_78
| ~ spl0_108 ),
inference(avatar_split_clause,[],[f1130,f1072,f644,f21181]) ).
fof(f21181,plain,
( spl0_867
<=> ! [X2,X0,X1] :
( f16(X0,image(X1,X2)) = second(f22(f16(X0,image(X1,X2)),X1,X2))
| ~ member(X0,sigma(image(X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_867])]) ).
fof(f1130,plain,
( ! [X2,X0,X1] :
( f16(X0,image(X1,X2)) = second(f22(f16(X0,image(X1,X2)),X1,X2))
| ~ member(X0,sigma(image(X1,X2))) )
| ~ spl0_78
| ~ spl0_108 ),
inference(resolution,[],[f1073,f645]) ).
fof(f21179,plain,
( spl0_866
| ~ spl0_74
| ~ spl0_108 ),
inference(avatar_split_clause,[],[f1129,f1072,f628,f21177]) ).
fof(f21177,plain,
( spl0_866
<=> ! [X2,X0,X1] :
( f8(X0,image(X1,X2)) = second(f22(f8(X0,image(X1,X2)),X1,X2))
| ~ member(X0,domain_of(image(X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_866])]) ).
fof(f1129,plain,
( ! [X2,X0,X1] :
( f8(X0,image(X1,X2)) = second(f22(f8(X0,image(X1,X2)),X1,X2))
| ~ member(X0,domain_of(image(X1,X2))) )
| ~ spl0_74
| ~ spl0_108 ),
inference(resolution,[],[f1073,f629]) ).
fof(f21174,plain,
( spl0_865
| ~ spl0_84
| ~ spl0_101 ),
inference(avatar_split_clause,[],[f982,f952,f668,f21172]) ).
fof(f982,plain,
( ! [X0,X1] :
( f26(non_ordered_pair(X0,X1)) = X0
| f26(non_ordered_pair(X0,X1)) = X1
| non_ordered_pair(X0,X1) = empty_set
| ~ little_set(non_ordered_pair(X0,X1)) )
| ~ spl0_84
| ~ spl0_101 ),
inference(resolution,[],[f953,f669]) ).
fof(f20914,plain,
( spl0_864
| ~ spl0_127
| ~ spl0_151 ),
inference(avatar_split_clause,[],[f2109,f2025,f1397,f20912]) ).
fof(f20912,plain,
( spl0_864
<=> ! [X0] : ~ member(X0,converse(converse(empty_set))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_864])]) ).
fof(f2109,plain,
( ! [X0] : ~ member(X0,converse(converse(empty_set)))
| ~ spl0_127
| ~ spl0_151 ),
inference(resolution,[],[f2026,f1398]) ).
fof(f19649,plain,
( spl0_863
| ~ spl0_78
| ~ spl0_141 ),
inference(avatar_split_clause,[],[f2077,f1749,f644,f19647]) ).
fof(f19647,plain,
( spl0_863
<=> ! [X0] : ~ member(X0,sigma(range_of(empty_set))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_863])]) ).
fof(f2077,plain,
( ! [X0] : ~ member(X0,sigma(range_of(empty_set)))
| ~ spl0_78
| ~ spl0_141 ),
inference(resolution,[],[f1750,f645]) ).
fof(f18796,plain,
( spl0_862
| ~ spl0_74
| ~ spl0_141 ),
inference(avatar_split_clause,[],[f2076,f1749,f628,f18794]) ).
fof(f18794,plain,
( spl0_862
<=> ! [X0] : ~ member(X0,domain_of(range_of(empty_set))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_862])]) ).
fof(f2076,plain,
( ! [X0] : ~ member(X0,domain_of(range_of(empty_set)))
| ~ spl0_74
| ~ spl0_141 ),
inference(resolution,[],[f1750,f629]) ).
fof(f18792,plain,
( spl0_861
| ~ spl0_16
| ~ spl0_133 ),
inference(avatar_split_clause,[],[f1539,f1487,f253,f18790]) ).
fof(f1539,plain,
( ! [X0] :
( ~ little_set(X0)
| member(X0,converse(universal_set))
| ~ ordered_pair_predicate(X0)
| ~ little_set(non_ordered_pair(non_ordered_pair(second(X0),second(X0)),non_ordered_pair(second(X0),first(X0)))) )
| ~ spl0_16
| ~ spl0_133 ),
inference(resolution,[],[f1488,f254]) ).
fof(f18788,plain,
( spl0_860
| ~ spl0_75
| ~ spl0_127 ),
inference(avatar_split_clause,[],[f1431,f1397,f632,f18786]) ).
fof(f18786,plain,
( spl0_860
<=> ! [X2,X0,X1] :
( ~ member(X0,converse(cross_product(X1,X2)))
| member(first(non_ordered_pair(non_ordered_pair(second(X0),second(X0)),non_ordered_pair(second(X0),first(X0)))),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_860])]) ).
fof(f1431,plain,
( ! [X2,X0,X1] :
( ~ member(X0,converse(cross_product(X1,X2)))
| member(first(non_ordered_pair(non_ordered_pair(second(X0),second(X0)),non_ordered_pair(second(X0),first(X0)))),X1) )
| ~ spl0_75
| ~ spl0_127 ),
inference(resolution,[],[f1398,f633]) ).
fof(f18784,plain,
( spl0_859
| ~ spl0_77
| ~ spl0_127 ),
inference(avatar_split_clause,[],[f1430,f1397,f640,f18782]) ).
fof(f18782,plain,
( spl0_859
<=> ! [X2,X0,X1] :
( ~ member(X0,converse(cross_product(X1,X2)))
| member(second(non_ordered_pair(non_ordered_pair(second(X0),second(X0)),non_ordered_pair(second(X0),first(X0)))),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_859])]) ).
fof(f1430,plain,
( ! [X2,X0,X1] :
( ~ member(X0,converse(cross_product(X1,X2)))
| member(second(non_ordered_pair(non_ordered_pair(second(X0),second(X0)),non_ordered_pair(second(X0),first(X0)))),X2) )
| ~ spl0_77
| ~ spl0_127 ),
inference(resolution,[],[f1398,f641]) ).
fof(f18780,plain,
( spl0_858
| ~ spl0_61
| ~ spl0_124 ),
inference(avatar_split_clause,[],[f1391,f1299,f466,f18778]) ).
fof(f18778,plain,
( spl0_858
<=> ! [X2,X0,X1] :
( ~ member(X0,X1)
| ~ member(f17(X2,apply(X1,first(X0))),second(X0))
| ~ ordered_pair_predicate(X0)
| subset(X2,apply(X1,first(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_858])]) ).
fof(f1391,plain,
( ! [X2,X0,X1] :
( ~ member(X0,X1)
| ~ member(f17(X2,apply(X1,first(X0))),second(X0))
| ~ ordered_pair_predicate(X0)
| subset(X2,apply(X1,first(X0))) )
| ~ spl0_61
| ~ spl0_124 ),
inference(resolution,[],[f1300,f467]) ).
fof(f18776,plain,
( spl0_857
| ~ spl0_37
| ~ spl0_122 ),
inference(avatar_split_clause,[],[f1370,f1291,f349,f18774]) ).
fof(f18774,plain,
( spl0_857
<=> ! [X0] :
( single_valued_set(powerset(X0))
| subset(non_ordered_pair(non_ordered_pair(f19(powerset(X0)),f19(powerset(X0))),non_ordered_pair(f19(powerset(X0)),f21(powerset(X0)))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_857])]) ).
fof(f1370,plain,
( ! [X0] :
( single_valued_set(powerset(X0))
| subset(non_ordered_pair(non_ordered_pair(f19(powerset(X0)),f19(powerset(X0))),non_ordered_pair(f19(powerset(X0)),f21(powerset(X0)))),X0) )
| ~ spl0_37
| ~ spl0_122 ),
inference(resolution,[],[f1292,f350]) ).
fof(f18772,plain,
( spl0_856
| ~ spl0_34
| ~ spl0_122 ),
inference(avatar_split_clause,[],[f1356,f1291,f336,f18770]) ).
fof(f18770,plain,
( spl0_856
<=> ! [X0] :
( single_valued_set(complement(X0))
| ~ member(non_ordered_pair(non_ordered_pair(f19(complement(X0)),f19(complement(X0))),non_ordered_pair(f19(complement(X0)),f21(complement(X0)))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_856])]) ).
fof(f1356,plain,
( ! [X0] :
( single_valued_set(complement(X0))
| ~ member(non_ordered_pair(non_ordered_pair(f19(complement(X0)),f19(complement(X0))),non_ordered_pair(f19(complement(X0)),f21(complement(X0)))),X0) )
| ~ spl0_34
| ~ spl0_122 ),
inference(resolution,[],[f1292,f337]) ).
fof(f18768,plain,
( spl0_855
| ~ spl0_37
| ~ spl0_121 ),
inference(avatar_split_clause,[],[f1328,f1287,f349,f18766]) ).
fof(f18766,plain,
( spl0_855
<=> ! [X0] :
( single_valued_set(powerset(X0))
| subset(non_ordered_pair(non_ordered_pair(f19(powerset(X0)),f19(powerset(X0))),non_ordered_pair(f19(powerset(X0)),f20(powerset(X0)))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_855])]) ).
fof(f1328,plain,
( ! [X0] :
( single_valued_set(powerset(X0))
| subset(non_ordered_pair(non_ordered_pair(f19(powerset(X0)),f19(powerset(X0))),non_ordered_pair(f19(powerset(X0)),f20(powerset(X0)))),X0) )
| ~ spl0_37
| ~ spl0_121 ),
inference(resolution,[],[f1288,f350]) ).
fof(f18764,plain,
( spl0_854
| ~ spl0_34
| ~ spl0_121 ),
inference(avatar_split_clause,[],[f1314,f1287,f336,f18762]) ).
fof(f1314,plain,
( ! [X0] :
( single_valued_set(complement(X0))
| ~ member(non_ordered_pair(non_ordered_pair(f19(complement(X0)),f19(complement(X0))),non_ordered_pair(f19(complement(X0)),f20(complement(X0)))),X0) )
| ~ spl0_34
| ~ spl0_121 ),
inference(resolution,[],[f1288,f337]) ).
fof(f18760,plain,
( spl0_853
| ~ spl0_75
| ~ spl0_113 ),
inference(avatar_split_clause,[],[f1234,f1159,f632,f18758]) ).
fof(f18758,plain,
( spl0_853
<=> ! [X2,X0,X1] :
( member(f1(cross_product(X0,X1),X2),X2)
| cross_product(X0,X1) = X2
| member(first(f1(cross_product(X0,X1),X2)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_853])]) ).
fof(f1234,plain,
( ! [X2,X0,X1] :
( member(f1(cross_product(X0,X1),X2),X2)
| cross_product(X0,X1) = X2
| member(first(f1(cross_product(X0,X1),X2)),X0) )
| ~ spl0_75
| ~ spl0_113 ),
inference(resolution,[],[f1160,f633]) ).
fof(f18756,plain,
( spl0_852
| ~ spl0_77
| ~ spl0_113 ),
inference(avatar_split_clause,[],[f1233,f1159,f640,f18754]) ).
fof(f18754,plain,
( spl0_852
<=> ! [X2,X0,X1] :
( member(f1(cross_product(X0,X1),X2),X2)
| cross_product(X0,X1) = X2
| member(second(f1(cross_product(X0,X1),X2)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_852])]) ).
fof(f1233,plain,
( ! [X2,X0,X1] :
( member(f1(cross_product(X0,X1),X2),X2)
| cross_product(X0,X1) = X2
| member(second(f1(cross_product(X0,X1),X2)),X1) )
| ~ spl0_77
| ~ spl0_113 ),
inference(resolution,[],[f1160,f641]) ).
fof(f18749,plain,
( spl0_851
| ~ spl0_141
| ~ spl0_145 ),
inference(avatar_split_clause,[],[f2072,f1786,f1749,f18747]) ).
fof(f18747,plain,
( spl0_851
<=> ! [X0] : ~ member(X0,rotate_right(range_of(empty_set))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_851])]) ).
fof(f2072,plain,
( ! [X0] : ~ member(X0,rotate_right(range_of(empty_set)))
| ~ spl0_141
| ~ spl0_145 ),
inference(resolution,[],[f1750,f1787]) ).
fof(f18745,plain,
( spl0_850
| ~ spl0_75
| ~ spl0_113 ),
inference(avatar_split_clause,[],[f1197,f1159,f632,f18743]) ).
fof(f18743,plain,
( spl0_850
<=> ! [X2,X0,X1] :
( member(f1(X0,cross_product(X1,X2)),X0)
| cross_product(X1,X2) = X0
| member(first(f1(X0,cross_product(X1,X2))),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_850])]) ).
fof(f1197,plain,
( ! [X2,X0,X1] :
( member(f1(X0,cross_product(X1,X2)),X0)
| cross_product(X1,X2) = X0
| member(first(f1(X0,cross_product(X1,X2))),X1) )
| ~ spl0_75
| ~ spl0_113 ),
inference(resolution,[],[f1160,f633]) ).
fof(f18741,plain,
( spl0_849
| ~ spl0_77
| ~ spl0_113 ),
inference(avatar_split_clause,[],[f1196,f1159,f640,f18739]) ).
fof(f18739,plain,
( spl0_849
<=> ! [X2,X0,X1] :
( member(f1(X0,cross_product(X1,X2)),X0)
| cross_product(X1,X2) = X0
| member(second(f1(X0,cross_product(X1,X2))),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_849])]) ).
fof(f1196,plain,
( ! [X2,X0,X1] :
( member(f1(X0,cross_product(X1,X2)),X0)
| cross_product(X1,X2) = X0
| member(second(f1(X0,cross_product(X1,X2))),X2) )
| ~ spl0_77
| ~ spl0_113 ),
inference(resolution,[],[f1160,f641]) ).
fof(f18737,plain,
( spl0_848
| ~ spl0_107
| ~ spl0_110 ),
inference(avatar_split_clause,[],[f1140,f1081,f1068,f18735]) ).
fof(f18735,plain,
( spl0_848
<=> ! [X0,X3,X2,X1] :
( first(f28(first(f22(X0,apply(X1,X2),X3)),X1,X2)) = X2
| ~ member(X0,image(apply(X1,X2),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_848])]) ).
fof(f1140,plain,
( ! [X2,X3,X0,X1] :
( first(f28(first(f22(X0,apply(X1,X2),X3)),X1,X2)) = X2
| ~ member(X0,image(apply(X1,X2),X3)) )
| ~ spl0_107
| ~ spl0_110 ),
inference(resolution,[],[f1082,f1069]) ).
fof(f18733,plain,
( spl0_847
| ~ spl0_64
| ~ spl0_108 ),
inference(avatar_split_clause,[],[f1135,f1072,f478,f18731]) ).
fof(f18731,plain,
( spl0_847
<=> ! [X2,X0,X1] :
( f23(X0,image(X1,X2)) = second(f22(f23(X0,image(X1,X2)),X1,X2))
| disjoint(X0,image(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_847])]) ).
fof(f1135,plain,
( ! [X2,X0,X1] :
( f23(X0,image(X1,X2)) = second(f22(f23(X0,image(X1,X2)),X1,X2))
| disjoint(X0,image(X1,X2)) )
| ~ spl0_64
| ~ spl0_108 ),
inference(resolution,[],[f1073,f479]) ).
fof(f18729,plain,
( spl0_846
| ~ spl0_63
| ~ spl0_108 ),
inference(avatar_split_clause,[],[f1134,f1072,f474,f18727]) ).
fof(f18727,plain,
( spl0_846
<=> ! [X2,X0,X1] :
( f23(image(X0,X1),X2) = second(f22(f23(image(X0,X1),X2),X0,X1))
| disjoint(image(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_846])]) ).
fof(f1134,plain,
( ! [X2,X0,X1] :
( f23(image(X0,X1),X2) = second(f22(f23(image(X0,X1),X2),X0,X1))
| disjoint(image(X0,X1),X2) )
| ~ spl0_63
| ~ spl0_108 ),
inference(resolution,[],[f1073,f475]) ).
fof(f18725,plain,
( spl0_845
| ~ spl0_60
| ~ spl0_108 ),
inference(avatar_split_clause,[],[f1131,f1072,f462,f18723]) ).
fof(f18723,plain,
( spl0_845
<=> ! [X2,X0,X1] :
( f17(image(X0,X1),X2) = second(f22(f17(image(X0,X1),X2),X0,X1))
| subset(image(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_845])]) ).
fof(f1131,plain,
( ! [X2,X0,X1] :
( f17(image(X0,X1),X2) = second(f22(f17(image(X0,X1),X2),X0,X1))
| subset(image(X0,X1),X2) )
| ~ spl0_60
| ~ spl0_108 ),
inference(resolution,[],[f1073,f463]) ).
fof(f18721,plain,
( spl0_844
| ~ spl0_95
| ~ spl0_104 ),
inference(avatar_split_clause,[],[f1052,f966,f844,f18719]) ).
fof(f18719,plain,
( spl0_844
<=> ! [X2,X0,X1] :
( ~ member(X0,apply(range_of(X1),X2))
| f28(X0,range_of(X1),X2) = second(f27(f28(X0,range_of(X1),X2),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_844])]) ).
fof(f1052,plain,
( ! [X2,X0,X1] :
( ~ member(X0,apply(range_of(X1),X2))
| f28(X0,range_of(X1),X2) = second(f27(f28(X0,range_of(X1),X2),X1)) )
| ~ spl0_95
| ~ spl0_104 ),
inference(resolution,[],[f967,f845]) ).
fof(f18717,plain,
( spl0_843
| ~ spl0_91
| ~ spl0_104 ),
inference(avatar_split_clause,[],[f1037,f966,f828,f18715]) ).
fof(f18715,plain,
( spl0_843
<=> ! [X2,X0,X1] :
( ~ member(X0,apply(domain_of(X1),X2))
| f28(X0,domain_of(X1),X2) = first(f8(f28(X0,domain_of(X1),X2),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_843])]) ).
fof(f1037,plain,
( ! [X2,X0,X1] :
( ~ member(X0,apply(domain_of(X1),X2))
| f28(X0,domain_of(X1),X2) = first(f8(f28(X0,domain_of(X1),X2),X1)) )
| ~ spl0_91
| ~ spl0_104 ),
inference(resolution,[],[f967,f829]) ).
fof(f18713,plain,
( spl0_842
| ~ spl0_95
| ~ spl0_103 ),
inference(avatar_split_clause,[],[f1017,f960,f844,f18711]) ).
fof(f18711,plain,
( spl0_842
<=> ! [X2,X0,X1] :
( ~ member(X0,image(X1,range_of(X2)))
| f22(X0,X1,range_of(X2)) = second(f27(f22(X0,X1,range_of(X2)),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_842])]) ).
fof(f1017,plain,
( ! [X2,X0,X1] :
( ~ member(X0,image(X1,range_of(X2)))
| f22(X0,X1,range_of(X2)) = second(f27(f22(X0,X1,range_of(X2)),X2)) )
| ~ spl0_95
| ~ spl0_103 ),
inference(resolution,[],[f961,f845]) ).
fof(f18709,plain,
( spl0_841
| ~ spl0_91
| ~ spl0_103 ),
inference(avatar_split_clause,[],[f1002,f960,f828,f18707]) ).
fof(f18707,plain,
( spl0_841
<=> ! [X2,X0,X1] :
( ~ member(X0,image(X1,domain_of(X2)))
| f22(X0,X1,domain_of(X2)) = first(f8(f22(X0,X1,domain_of(X2)),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_841])]) ).
fof(f1002,plain,
( ! [X2,X0,X1] :
( ~ member(X0,image(X1,domain_of(X2)))
| f22(X0,X1,domain_of(X2)) = first(f8(f22(X0,X1,domain_of(X2)),X2)) )
| ~ spl0_91
| ~ spl0_103 ),
inference(resolution,[],[f961,f829]) ).
fof(f18702,plain,
( spl0_840
| ~ spl0_141
| ~ spl0_144 ),
inference(avatar_split_clause,[],[f2071,f1782,f1749,f18700]) ).
fof(f18700,plain,
( spl0_840
<=> ! [X0] : ~ member(X0,flip_range_of(range_of(empty_set))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_840])]) ).
fof(f2071,plain,
( ! [X0] : ~ member(X0,flip_range_of(range_of(empty_set)))
| ~ spl0_141
| ~ spl0_144 ),
inference(resolution,[],[f1750,f1783]) ).
fof(f18698,plain,
( spl0_839
| ~ spl0_85
| ~ spl0_101 ),
inference(avatar_split_clause,[],[f983,f952,f672,f18696]) ).
fof(f18696,plain,
( spl0_839
<=> ! [X2,X0,X1] :
( f27(X1,non_ordered_pair(X0,X2)) = X0
| f27(X1,non_ordered_pair(X0,X2)) = X2
| ~ member(X1,range_of(non_ordered_pair(X0,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_839])]) ).
fof(f983,plain,
( ! [X2,X0,X1] :
( f27(X1,non_ordered_pair(X0,X2)) = X0
| f27(X1,non_ordered_pair(X0,X2)) = X2
| ~ member(X1,range_of(non_ordered_pair(X0,X2))) )
| ~ spl0_85
| ~ spl0_101 ),
inference(resolution,[],[f953,f673]) ).
fof(f18694,plain,
( spl0_838
| ~ spl0_78
| ~ spl0_101 ),
inference(avatar_split_clause,[],[f976,f952,f644,f18692]) ).
fof(f18692,plain,
( spl0_838
<=> ! [X2,X0,X1] :
( f16(X1,non_ordered_pair(X0,X2)) = X0
| f16(X1,non_ordered_pair(X0,X2)) = X2
| ~ member(X1,sigma(non_ordered_pair(X0,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_838])]) ).
fof(f976,plain,
( ! [X2,X0,X1] :
( f16(X1,non_ordered_pair(X0,X2)) = X0
| f16(X1,non_ordered_pair(X0,X2)) = X2
| ~ member(X1,sigma(non_ordered_pair(X0,X2))) )
| ~ spl0_78
| ~ spl0_101 ),
inference(resolution,[],[f953,f645]) ).
fof(f18690,plain,
( spl0_837
| ~ spl0_74
| ~ spl0_101 ),
inference(avatar_split_clause,[],[f975,f952,f628,f18688]) ).
fof(f18688,plain,
( spl0_837
<=> ! [X2,X0,X1] :
( f8(X1,non_ordered_pair(X0,X2)) = X0
| f8(X1,non_ordered_pair(X0,X2)) = X2
| ~ member(X1,domain_of(non_ordered_pair(X0,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_837])]) ).
fof(f975,plain,
( ! [X2,X0,X1] :
( f8(X1,non_ordered_pair(X0,X2)) = X0
| f8(X1,non_ordered_pair(X0,X2)) = X2
| ~ member(X1,domain_of(non_ordered_pair(X0,X2))) )
| ~ spl0_74
| ~ spl0_101 ),
inference(resolution,[],[f953,f629]) ).
fof(f18647,plain,
( spl0_836
| ~ spl0_127
| ~ spl0_141 ),
inference(avatar_split_clause,[],[f2069,f1749,f1397,f18645]) ).
fof(f18645,plain,
( spl0_836
<=> ! [X0] : ~ member(X0,converse(range_of(empty_set))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_836])]) ).
fof(f2069,plain,
( ! [X0] : ~ member(X0,converse(range_of(empty_set)))
| ~ spl0_127
| ~ spl0_141 ),
inference(resolution,[],[f1750,f1398]) ).
fof(f18375,plain,
( spl0_835
| ~ spl0_78
| ~ spl0_135 ),
inference(avatar_split_clause,[],[f2045,f1548,f644,f18373]) ).
fof(f18373,plain,
( spl0_835
<=> ! [X0] : ~ member(X0,sigma(sigma(empty_set))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_835])]) ).
fof(f2045,plain,
( ! [X0] : ~ member(X0,sigma(sigma(empty_set)))
| ~ spl0_78
| ~ spl0_135 ),
inference(resolution,[],[f1549,f645]) ).
fof(f18354,plain,
( spl0_834
| ~ spl0_173
| ~ spl0_813 ),
inference(avatar_split_clause,[],[f16832,f16829,f2440,f18352]) ).
fof(f18352,plain,
( spl0_834
<=> ! [X0,X1] :
( estin = X0
| ~ little_set(X0)
| ~ member(f25,X1)
| member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,f26(X0))),sigma(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_834])]) ).
fof(f16829,plain,
( spl0_813
<=> ! [X0,X1] :
( empty_set = X0
| ~ little_set(X0)
| ~ member(f25,X1)
| member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,f26(X0))),sigma(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_813])]) ).
fof(f16832,plain,
( ! [X0,X1] :
( estin = X0
| ~ little_set(X0)
| ~ member(f25,X1)
| member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,f26(X0))),sigma(X1)) )
| ~ spl0_173
| ~ spl0_813 ),
inference(forward_demodulation,[],[f16830,f2442]) ).
fof(f16830,plain,
( ! [X0,X1] :
( empty_set = X0
| ~ little_set(X0)
| ~ member(f25,X1)
| member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,f26(X0))),sigma(X1)) )
| ~ spl0_813 ),
inference(avatar_component_clause,[],[f16829]) ).
fof(f17157,plain,
( spl0_833
| ~ spl0_74
| ~ spl0_135 ),
inference(avatar_split_clause,[],[f2044,f1548,f628,f17155]) ).
fof(f17155,plain,
( spl0_833
<=> ! [X0] : ~ member(X0,domain_of(sigma(empty_set))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_833])]) ).
fof(f2044,plain,
( ! [X0] : ~ member(X0,domain_of(sigma(empty_set)))
| ~ spl0_74
| ~ spl0_135 ),
inference(resolution,[],[f1549,f629]) ).
fof(f17044,plain,
( spl0_832
| ~ spl0_173
| ~ spl0_802 ),
inference(avatar_split_clause,[],[f16784,f16781,f2440,f17042]) ).
fof(f17042,plain,
( spl0_832
<=> ! [X0,X1] :
( estin = apply(X0,X1)
| first(f28(f26(apply(X0,X1)),X0,X1)) = X1
| ~ little_set(apply(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_832])]) ).
fof(f16781,plain,
( spl0_802
<=> ! [X0,X1] :
( first(f28(f26(apply(X0,X1)),X0,X1)) = X1
| empty_set = apply(X0,X1)
| ~ little_set(apply(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_802])]) ).
fof(f16784,plain,
( ! [X0,X1] :
( estin = apply(X0,X1)
| first(f28(f26(apply(X0,X1)),X0,X1)) = X1
| ~ little_set(apply(X0,X1)) )
| ~ spl0_173
| ~ spl0_802 ),
inference(forward_demodulation,[],[f16782,f2442]) ).
fof(f16782,plain,
( ! [X0,X1] :
( first(f28(f26(apply(X0,X1)),X0,X1)) = X1
| empty_set = apply(X0,X1)
| ~ little_set(apply(X0,X1)) )
| ~ spl0_802 ),
inference(avatar_component_clause,[],[f16781]) ).
fof(f16910,plain,
( spl0_831
| ~ spl0_38
| ~ spl0_130 ),
inference(avatar_split_clause,[],[f1476,f1470,f353,f16908]) ).
fof(f16908,plain,
( spl0_831
<=> ! [X2,X0,X1] :
( ~ little_set(second(X0))
| ~ member(X0,X1)
| ~ member(first(X0),X2)
| ~ ordered_pair_predicate(X0)
| ordered_pair_predicate(second(X0))
| ~ relation(image(X2,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_831])]) ).
fof(f1476,plain,
( ! [X2,X0,X1] :
( ~ little_set(second(X0))
| ~ member(X0,X1)
| ~ member(first(X0),X2)
| ~ ordered_pair_predicate(X0)
| ordered_pair_predicate(second(X0))
| ~ relation(image(X2,X1)) )
| ~ spl0_38
| ~ spl0_130 ),
inference(resolution,[],[f1471,f354]) ).
fof(f16906,plain,
( spl0_830
| ~ spl0_65
| ~ spl0_127 ),
inference(avatar_split_clause,[],[f1445,f1397,f482,f16904]) ).
fof(f16904,plain,
( spl0_830
<=> ! [X0,X1] :
( ~ member(X0,converse(range_of(X1)))
| ordered_pair_predicate(f27(non_ordered_pair(non_ordered_pair(second(X0),second(X0)),non_ordered_pair(second(X0),first(X0))),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_830])]) ).
fof(f1445,plain,
( ! [X0,X1] :
( ~ member(X0,converse(range_of(X1)))
| ordered_pair_predicate(f27(non_ordered_pair(non_ordered_pair(second(X0),second(X0)),non_ordered_pair(second(X0),first(X0))),X1)) )
| ~ spl0_65
| ~ spl0_127 ),
inference(resolution,[],[f1398,f483]) ).
fof(f16902,plain,
( spl0_829
| ~ spl0_57
| ~ spl0_127 ),
inference(avatar_split_clause,[],[f1439,f1397,f450,f16900]) ).
fof(f16900,plain,
( spl0_829
<=> ! [X0,X1] :
( ~ member(X0,converse(flip_range_of(X1)))
| little_set(f12(non_ordered_pair(non_ordered_pair(second(X0),second(X0)),non_ordered_pair(second(X0),first(X0))),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_829])]) ).
fof(f1439,plain,
( ! [X0,X1] :
( ~ member(X0,converse(flip_range_of(X1)))
| little_set(f12(non_ordered_pair(non_ordered_pair(second(X0),second(X0)),non_ordered_pair(second(X0),first(X0))),X1)) )
| ~ spl0_57
| ~ spl0_127 ),
inference(resolution,[],[f1398,f451]) ).
fof(f16895,plain,
( spl0_828
| ~ spl0_135
| ~ spl0_145 ),
inference(avatar_split_clause,[],[f2041,f1786,f1548,f16893]) ).
fof(f16893,plain,
( spl0_828
<=> ! [X0] : ~ member(X0,rotate_right(sigma(empty_set))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_828])]) ).
fof(f2041,plain,
( ! [X0] : ~ member(X0,rotate_right(sigma(empty_set)))
| ~ spl0_135
| ~ spl0_145 ),
inference(resolution,[],[f1549,f1787]) ).
fof(f16891,plain,
( spl0_827
| ~ spl0_58
| ~ spl0_127 ),
inference(avatar_split_clause,[],[f1438,f1397,f454,f16889]) ).
fof(f16889,plain,
( spl0_827
<=> ! [X0,X1] :
( ~ member(X0,converse(flip_range_of(X1)))
| little_set(f13(non_ordered_pair(non_ordered_pair(second(X0),second(X0)),non_ordered_pair(second(X0),first(X0))),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_827])]) ).
fof(f1438,plain,
( ! [X0,X1] :
( ~ member(X0,converse(flip_range_of(X1)))
| little_set(f13(non_ordered_pair(non_ordered_pair(second(X0),second(X0)),non_ordered_pair(second(X0),first(X0))),X1)) )
| ~ spl0_58
| ~ spl0_127 ),
inference(resolution,[],[f1398,f455]) ).
fof(f16887,plain,
( spl0_826
| ~ spl0_59
| ~ spl0_127 ),
inference(avatar_split_clause,[],[f1437,f1397,f458,f16885]) ).
fof(f16885,plain,
( spl0_826
<=> ! [X0,X1] :
( ~ member(X0,converse(flip_range_of(X1)))
| little_set(f14(non_ordered_pair(non_ordered_pair(second(X0),second(X0)),non_ordered_pair(second(X0),first(X0))),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_826])]) ).
fof(f1437,plain,
( ! [X0,X1] :
( ~ member(X0,converse(flip_range_of(X1)))
| little_set(f14(non_ordered_pair(non_ordered_pair(second(X0),second(X0)),non_ordered_pair(second(X0),first(X0))),X1)) )
| ~ spl0_59
| ~ spl0_127 ),
inference(resolution,[],[f1398,f459]) ).
fof(f16883,plain,
( spl0_825
| ~ spl0_54
| ~ spl0_127 ),
inference(avatar_split_clause,[],[f1436,f1397,f438,f16881]) ).
fof(f16881,plain,
( spl0_825
<=> ! [X0,X1] :
( ~ member(X0,converse(rotate_right(X1)))
| little_set(f9(non_ordered_pair(non_ordered_pair(second(X0),second(X0)),non_ordered_pair(second(X0),first(X0))),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_825])]) ).
fof(f1436,plain,
( ! [X0,X1] :
( ~ member(X0,converse(rotate_right(X1)))
| little_set(f9(non_ordered_pair(non_ordered_pair(second(X0),second(X0)),non_ordered_pair(second(X0),first(X0))),X1)) )
| ~ spl0_54
| ~ spl0_127 ),
inference(resolution,[],[f1398,f439]) ).
fof(f16879,plain,
( spl0_824
| ~ spl0_55
| ~ spl0_127 ),
inference(avatar_split_clause,[],[f1435,f1397,f442,f16877]) ).
fof(f16877,plain,
( spl0_824
<=> ! [X0,X1] :
( ~ member(X0,converse(rotate_right(X1)))
| little_set(f10(non_ordered_pair(non_ordered_pair(second(X0),second(X0)),non_ordered_pair(second(X0),first(X0))),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_824])]) ).
fof(f1435,plain,
( ! [X0,X1] :
( ~ member(X0,converse(rotate_right(X1)))
| little_set(f10(non_ordered_pair(non_ordered_pair(second(X0),second(X0)),non_ordered_pair(second(X0),first(X0))),X1)) )
| ~ spl0_55
| ~ spl0_127 ),
inference(resolution,[],[f1398,f443]) ).
fof(f16875,plain,
( spl0_823
| ~ spl0_56
| ~ spl0_127 ),
inference(avatar_split_clause,[],[f1434,f1397,f446,f16873]) ).
fof(f16873,plain,
( spl0_823
<=> ! [X0,X1] :
( ~ member(X0,converse(rotate_right(X1)))
| little_set(f11(non_ordered_pair(non_ordered_pair(second(X0),second(X0)),non_ordered_pair(second(X0),first(X0))),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_823])]) ).
fof(f1434,plain,
( ! [X0,X1] :
( ~ member(X0,converse(rotate_right(X1)))
| little_set(f11(non_ordered_pair(non_ordered_pair(second(X0),second(X0)),non_ordered_pair(second(X0),first(X0))),X1)) )
| ~ spl0_56
| ~ spl0_127 ),
inference(resolution,[],[f1398,f447]) ).
fof(f16871,plain,
( spl0_822
| ~ spl0_53
| ~ spl0_127 ),
inference(avatar_split_clause,[],[f1429,f1397,f434,f16869]) ).
fof(f16869,plain,
( spl0_822
<=> ! [X0,X1] :
( ~ member(X0,converse(domain_of(X1)))
| ordered_pair_predicate(f8(non_ordered_pair(non_ordered_pair(second(X0),second(X0)),non_ordered_pair(second(X0),first(X0))),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_822])]) ).
fof(f1429,plain,
( ! [X0,X1] :
( ~ member(X0,converse(domain_of(X1)))
| ordered_pair_predicate(f8(non_ordered_pair(non_ordered_pair(second(X0),second(X0)),non_ordered_pair(second(X0),first(X0))),X1)) )
| ~ spl0_53
| ~ spl0_127 ),
inference(resolution,[],[f1398,f435]) ).
fof(f16867,plain,
( spl0_821
| ~ spl0_51
| ~ spl0_127 ),
inference(avatar_split_clause,[],[f1426,f1397,f426,f16865]) ).
fof(f16865,plain,
( spl0_821
<=> ! [X2,X0,X1] :
( ~ member(X0,converse(intersection(X1,X2)))
| member(non_ordered_pair(non_ordered_pair(second(X0),second(X0)),non_ordered_pair(second(X0),first(X0))),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_821])]) ).
fof(f1426,plain,
( ! [X2,X0,X1] :
( ~ member(X0,converse(intersection(X1,X2)))
| member(non_ordered_pair(non_ordered_pair(second(X0),second(X0)),non_ordered_pair(second(X0),first(X0))),X1) )
| ~ spl0_51
| ~ spl0_127 ),
inference(resolution,[],[f1398,f427]) ).
fof(f16863,plain,
( spl0_820
| ~ spl0_52
| ~ spl0_127 ),
inference(avatar_split_clause,[],[f1425,f1397,f430,f16861]) ).
fof(f16861,plain,
( spl0_820
<=> ! [X2,X0,X1] :
( ~ member(X0,converse(intersection(X1,X2)))
| member(non_ordered_pair(non_ordered_pair(second(X0),second(X0)),non_ordered_pair(second(X0),first(X0))),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_820])]) ).
fof(f1425,plain,
( ! [X2,X0,X1] :
( ~ member(X0,converse(intersection(X1,X2)))
| member(non_ordered_pair(non_ordered_pair(second(X0),second(X0)),non_ordered_pair(second(X0),first(X0))),X2) )
| ~ spl0_52
| ~ spl0_127 ),
inference(resolution,[],[f1398,f431]) ).
fof(f16859,plain,
( spl0_819
| ~ spl0_48
| ~ spl0_127 ),
inference(avatar_split_clause,[],[f1423,f1397,f414,f16857]) ).
fof(f16857,plain,
( spl0_819
<=> ! [X0,X1] :
( ~ member(X0,converse(second(X1)))
| little_set(f6(non_ordered_pair(non_ordered_pair(second(X0),second(X0)),non_ordered_pair(second(X0),first(X0))),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_819])]) ).
fof(f1423,plain,
( ! [X0,X1] :
( ~ member(X0,converse(second(X1)))
| little_set(f6(non_ordered_pair(non_ordered_pair(second(X0),second(X0)),non_ordered_pair(second(X0),first(X0))),X1)) )
| ~ spl0_48
| ~ spl0_127 ),
inference(resolution,[],[f1398,f415]) ).
fof(f16855,plain,
( spl0_818
| ~ spl0_49
| ~ spl0_127 ),
inference(avatar_split_clause,[],[f1422,f1397,f418,f16853]) ).
fof(f16853,plain,
( spl0_818
<=> ! [X0,X1] :
( ~ member(X0,converse(second(X1)))
| little_set(f7(non_ordered_pair(non_ordered_pair(second(X0),second(X0)),non_ordered_pair(second(X0),first(X0))),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_818])]) ).
fof(f1422,plain,
( ! [X0,X1] :
( ~ member(X0,converse(second(X1)))
| little_set(f7(non_ordered_pair(non_ordered_pair(second(X0),second(X0)),non_ordered_pair(second(X0),first(X0))),X1)) )
| ~ spl0_49
| ~ spl0_127 ),
inference(resolution,[],[f1398,f419]) ).
fof(f16848,plain,
( spl0_817
| ~ spl0_135
| ~ spl0_144 ),
inference(avatar_split_clause,[],[f2040,f1782,f1548,f16846]) ).
fof(f16846,plain,
( spl0_817
<=> ! [X0] : ~ member(X0,flip_range_of(sigma(empty_set))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_817])]) ).
fof(f2040,plain,
( ! [X0] : ~ member(X0,flip_range_of(sigma(empty_set)))
| ~ spl0_135
| ~ spl0_144 ),
inference(resolution,[],[f1549,f1783]) ).
fof(f16844,plain,
( spl0_816
| ~ spl0_46
| ~ spl0_127 ),
inference(avatar_split_clause,[],[f1421,f1397,f406,f16842]) ).
fof(f16842,plain,
( spl0_816
<=> ! [X0,X1] :
( ~ member(X0,converse(first(X1)))
| little_set(f4(non_ordered_pair(non_ordered_pair(second(X0),second(X0)),non_ordered_pair(second(X0),first(X0))),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_816])]) ).
fof(f1421,plain,
( ! [X0,X1] :
( ~ member(X0,converse(first(X1)))
| little_set(f4(non_ordered_pair(non_ordered_pair(second(X0),second(X0)),non_ordered_pair(second(X0),first(X0))),X1)) )
| ~ spl0_46
| ~ spl0_127 ),
inference(resolution,[],[f1398,f407]) ).
fof(f16840,plain,
( spl0_815
| ~ spl0_47
| ~ spl0_127 ),
inference(avatar_split_clause,[],[f1420,f1397,f410,f16838]) ).
fof(f16838,plain,
( spl0_815
<=> ! [X0,X1] :
( ~ member(X0,converse(first(X1)))
| little_set(f5(non_ordered_pair(non_ordered_pair(second(X0),second(X0)),non_ordered_pair(second(X0),first(X0))),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_815])]) ).
fof(f1420,plain,
( ! [X0,X1] :
( ~ member(X0,converse(first(X1)))
| little_set(f5(non_ordered_pair(non_ordered_pair(second(X0),second(X0)),non_ordered_pair(second(X0),first(X0))),X1)) )
| ~ spl0_47
| ~ spl0_127 ),
inference(resolution,[],[f1398,f411]) ).
fof(f16836,plain,
( spl0_814
| ~ spl0_93
| ~ spl0_124 ),
inference(avatar_split_clause,[],[f1387,f1299,f836,f16834]) ).
fof(f16834,plain,
( spl0_814
<=> ! [X0,X3,X2,X1] :
( ~ member(X0,X1)
| ~ member(X2,second(X0))
| ~ ordered_pair_predicate(X0)
| ~ member(apply(X1,first(X0)),X3)
| member(X2,sigma(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_814])]) ).
fof(f1387,plain,
( ! [X2,X3,X0,X1] :
( ~ member(X0,X1)
| ~ member(X2,second(X0))
| ~ ordered_pair_predicate(X0)
| ~ member(apply(X1,first(X0)),X3)
| member(X2,sigma(X3)) )
| ~ spl0_93
| ~ spl0_124 ),
inference(resolution,[],[f1300,f837]) ).
fof(f16831,plain,
( spl0_813
| ~ spl0_93
| ~ spl0_123 ),
inference(avatar_split_clause,[],[f1382,f1295,f836,f16829]) ).
fof(f1382,plain,
( ! [X0,X1] :
( empty_set = X0
| ~ little_set(X0)
| ~ member(f25,X1)
| member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,f26(X0))),sigma(X1)) )
| ~ spl0_93
| ~ spl0_123 ),
inference(resolution,[],[f1296,f837]) ).
fof(f16827,plain,
( spl0_812
| ~ spl0_28
| ~ spl0_122 ),
inference(avatar_split_clause,[],[f1362,f1291,f306,f16825]) ).
fof(f16825,plain,
( spl0_812
<=> ! [X0] :
( single_valued_set(converse(X0))
| ordered_pair_predicate(non_ordered_pair(non_ordered_pair(f19(converse(X0)),f19(converse(X0))),non_ordered_pair(f19(converse(X0)),f21(converse(X0))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_812])]) ).
fof(f1362,plain,
( ! [X0] :
( single_valued_set(converse(X0))
| ordered_pair_predicate(non_ordered_pair(non_ordered_pair(f19(converse(X0)),f19(converse(X0))),non_ordered_pair(f19(converse(X0)),f21(converse(X0))))) )
| ~ spl0_28
| ~ spl0_122 ),
inference(resolution,[],[f1292,f307]) ).
fof(f16823,plain,
( spl0_811
| ~ spl0_93
| ~ spl0_122 ),
inference(avatar_split_clause,[],[f1345,f1291,f836,f16821]) ).
fof(f16821,plain,
( spl0_811
<=> ! [X0,X1] :
( single_valued_set(X0)
| ~ member(X0,X1)
| member(non_ordered_pair(non_ordered_pair(f19(X0),f19(X0)),non_ordered_pair(f19(X0),f21(X0))),sigma(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_811])]) ).
fof(f1345,plain,
( ! [X0,X1] :
( single_valued_set(X0)
| ~ member(X0,X1)
| member(non_ordered_pair(non_ordered_pair(f19(X0),f19(X0)),non_ordered_pair(f19(X0),f21(X0))),sigma(X1)) )
| ~ spl0_93
| ~ spl0_122 ),
inference(resolution,[],[f1292,f837]) ).
fof(f16819,plain,
( spl0_810
| ~ spl0_28
| ~ spl0_121 ),
inference(avatar_split_clause,[],[f1320,f1287,f306,f16817]) ).
fof(f16817,plain,
( spl0_810
<=> ! [X0] :
( single_valued_set(converse(X0))
| ordered_pair_predicate(non_ordered_pair(non_ordered_pair(f19(converse(X0)),f19(converse(X0))),non_ordered_pair(f19(converse(X0)),f20(converse(X0))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_810])]) ).
fof(f1320,plain,
( ! [X0] :
( single_valued_set(converse(X0))
| ordered_pair_predicate(non_ordered_pair(non_ordered_pair(f19(converse(X0)),f19(converse(X0))),non_ordered_pair(f19(converse(X0)),f20(converse(X0))))) )
| ~ spl0_28
| ~ spl0_121 ),
inference(resolution,[],[f1288,f307]) ).
fof(f16815,plain,
( spl0_809
| ~ spl0_93
| ~ spl0_121 ),
inference(avatar_split_clause,[],[f1303,f1287,f836,f16813]) ).
fof(f1303,plain,
( ! [X0,X1] :
( single_valued_set(X0)
| ~ member(X0,X1)
| member(non_ordered_pair(non_ordered_pair(f19(X0),f19(X0)),non_ordered_pair(f19(X0),f20(X0))),sigma(X1)) )
| ~ spl0_93
| ~ spl0_121 ),
inference(resolution,[],[f1288,f837]) ).
fof(f16811,plain,
( spl0_808
| ~ spl0_51
| ~ spl0_113 ),
inference(avatar_split_clause,[],[f1229,f1159,f426,f16809]) ).
fof(f16809,plain,
( spl0_808
<=> ! [X2,X0,X1] :
( member(f1(intersection(X0,X1),X2),X2)
| intersection(X0,X1) = X2
| member(f1(intersection(X0,X1),X2),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_808])]) ).
fof(f1229,plain,
( ! [X2,X0,X1] :
( member(f1(intersection(X0,X1),X2),X2)
| intersection(X0,X1) = X2
| member(f1(intersection(X0,X1),X2),X0) )
| ~ spl0_51
| ~ spl0_113 ),
inference(resolution,[],[f1160,f427]) ).
fof(f16807,plain,
( spl0_807
| ~ spl0_52
| ~ spl0_113 ),
inference(avatar_split_clause,[],[f1228,f1159,f430,f16805]) ).
fof(f16805,plain,
( spl0_807
<=> ! [X2,X0,X1] :
( member(f1(intersection(X0,X1),X2),X2)
| intersection(X0,X1) = X2
| member(f1(intersection(X0,X1),X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_807])]) ).
fof(f1228,plain,
( ! [X2,X0,X1] :
( member(f1(intersection(X0,X1),X2),X2)
| intersection(X0,X1) = X2
| member(f1(intersection(X0,X1),X2),X1) )
| ~ spl0_52
| ~ spl0_113 ),
inference(resolution,[],[f1160,f431]) ).
fof(f16800,plain,
( spl0_806
| ~ spl0_127
| ~ spl0_135 ),
inference(avatar_split_clause,[],[f2038,f1548,f1397,f16798]) ).
fof(f16798,plain,
( spl0_806
<=> ! [X0] : ~ member(X0,converse(sigma(empty_set))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_806])]) ).
fof(f2038,plain,
( ! [X0] : ~ member(X0,converse(sigma(empty_set)))
| ~ spl0_127
| ~ spl0_135 ),
inference(resolution,[],[f1549,f1398]) ).
fof(f16796,plain,
( spl0_805
| ~ spl0_51
| ~ spl0_113 ),
inference(avatar_split_clause,[],[f1192,f1159,f426,f16794]) ).
fof(f16794,plain,
( spl0_805
<=> ! [X2,X0,X1] :
( member(f1(X0,intersection(X1,X2)),X0)
| intersection(X1,X2) = X0
| member(f1(X0,intersection(X1,X2)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_805])]) ).
fof(f1192,plain,
( ! [X2,X0,X1] :
( member(f1(X0,intersection(X1,X2)),X0)
| intersection(X1,X2) = X0
| member(f1(X0,intersection(X1,X2)),X1) )
| ~ spl0_51
| ~ spl0_113 ),
inference(resolution,[],[f1160,f427]) ).
fof(f16792,plain,
( spl0_804
| ~ spl0_52
| ~ spl0_113 ),
inference(avatar_split_clause,[],[f1191,f1159,f430,f16790]) ).
fof(f1191,plain,
( ! [X2,X0,X1] :
( member(f1(X0,intersection(X1,X2)),X0)
| intersection(X1,X2) = X0
| member(f1(X0,intersection(X1,X2)),X2) )
| ~ spl0_52
| ~ spl0_113 ),
inference(resolution,[],[f1160,f431]) ).
fof(f16788,plain,
( spl0_803
| ~ spl0_104
| ~ spl0_110 ),
inference(avatar_split_clause,[],[f1151,f1081,f966,f16786]) ).
fof(f16786,plain,
( spl0_803
<=> ! [X0,X3,X2,X1] :
( first(f28(f28(X0,apply(X1,X2),X3),X1,X2)) = X2
| ~ member(X0,apply(apply(X1,X2),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_803])]) ).
fof(f1151,plain,
( ! [X2,X3,X0,X1] :
( first(f28(f28(X0,apply(X1,X2),X3),X1,X2)) = X2
| ~ member(X0,apply(apply(X1,X2),X3)) )
| ~ spl0_104
| ~ spl0_110 ),
inference(resolution,[],[f1082,f967]) ).
fof(f16783,plain,
( spl0_802
| ~ spl0_84
| ~ spl0_110 ),
inference(avatar_split_clause,[],[f1149,f1081,f668,f16781]) ).
fof(f1149,plain,
( ! [X0,X1] :
( first(f28(f26(apply(X0,X1)),X0,X1)) = X1
| empty_set = apply(X0,X1)
| ~ little_set(apply(X0,X1)) )
| ~ spl0_84
| ~ spl0_110 ),
inference(resolution,[],[f1082,f669]) ).
fof(f16779,plain,
( spl0_801
| ~ spl0_103
| ~ spl0_110 ),
inference(avatar_split_clause,[],[f1145,f1081,f960,f16777]) ).
fof(f16777,plain,
( spl0_801
<=> ! [X0,X3,X2,X1] :
( first(f28(f22(X0,X1,apply(X2,X3)),X2,X3)) = X3
| ~ member(X0,image(X1,apply(X2,X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_801])]) ).
fof(f1145,plain,
( ! [X2,X3,X0,X1] :
( first(f28(f22(X0,X1,apply(X2,X3)),X2,X3)) = X3
| ~ member(X0,image(X1,apply(X2,X3))) )
| ~ spl0_103
| ~ spl0_110 ),
inference(resolution,[],[f1082,f961]) ).
fof(f16775,plain,
( spl0_800
| ~ spl0_61
| ~ spl0_102 ),
inference(avatar_split_clause,[],[f989,f956,f466,f16773]) ).
fof(f16773,plain,
( spl0_800
<=> ! [X2,X0,X1] :
( ~ member(f17(X0,intersection(X1,X2)),X1)
| ~ member(f17(X0,intersection(X1,X2)),X2)
| subset(X0,intersection(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_800])]) ).
fof(f989,plain,
( ! [X2,X0,X1] :
( ~ member(f17(X0,intersection(X1,X2)),X1)
| ~ member(f17(X0,intersection(X1,X2)),X2)
| subset(X0,intersection(X1,X2)) )
| ~ spl0_61
| ~ spl0_102 ),
inference(resolution,[],[f957,f467]) ).
fof(f16771,plain,
( spl0_799
| ~ spl0_64
| ~ spl0_101 ),
inference(avatar_split_clause,[],[f980,f952,f478,f16769]) ).
fof(f16769,plain,
( spl0_799
<=> ! [X2,X0,X1] :
( f23(X1,non_ordered_pair(X0,X2)) = X0
| f23(X1,non_ordered_pair(X0,X2)) = X2
| disjoint(X1,non_ordered_pair(X0,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_799])]) ).
fof(f980,plain,
( ! [X2,X0,X1] :
( f23(X1,non_ordered_pair(X0,X2)) = X0
| f23(X1,non_ordered_pair(X0,X2)) = X2
| disjoint(X1,non_ordered_pair(X0,X2)) )
| ~ spl0_64
| ~ spl0_101 ),
inference(resolution,[],[f953,f479]) ).
fof(f16767,plain,
( spl0_798
| ~ spl0_63
| ~ spl0_101 ),
inference(avatar_split_clause,[],[f979,f952,f474,f16765]) ).
fof(f16765,plain,
( spl0_798
<=> ! [X2,X0,X1] :
( f23(non_ordered_pair(X0,X1),X2) = X0
| f23(non_ordered_pair(X0,X1),X2) = X1
| disjoint(non_ordered_pair(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_798])]) ).
fof(f979,plain,
( ! [X2,X0,X1] :
( f23(non_ordered_pair(X0,X1),X2) = X0
| f23(non_ordered_pair(X0,X1),X2) = X1
| disjoint(non_ordered_pair(X0,X1),X2) )
| ~ spl0_63
| ~ spl0_101 ),
inference(resolution,[],[f953,f475]) ).
fof(f16763,plain,
( spl0_797
| ~ spl0_60
| ~ spl0_101 ),
inference(avatar_split_clause,[],[f977,f952,f462,f16761]) ).
fof(f16761,plain,
( spl0_797
<=> ! [X2,X0,X1] :
( f17(non_ordered_pair(X0,X1),X2) = X0
| f17(non_ordered_pair(X0,X1),X2) = X1
| subset(non_ordered_pair(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_797])]) ).
fof(f977,plain,
( ! [X2,X0,X1] :
( f17(non_ordered_pair(X0,X1),X2) = X0
| f17(non_ordered_pair(X0,X1),X2) = X1
| subset(non_ordered_pair(X0,X1),X2) )
| ~ spl0_60
| ~ spl0_101 ),
inference(resolution,[],[f953,f463]) ).
fof(f16707,plain,
( spl0_796
| ~ spl0_78
| ~ spl0_119 ),
inference(avatar_split_clause,[],[f1933,f1266,f644,f16705]) ).
fof(f16705,plain,
( spl0_796
<=> ! [X0] : ~ member(X0,sigma(domain_of(empty_set))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_796])]) ).
fof(f1933,plain,
( ! [X0] : ~ member(X0,sigma(domain_of(empty_set)))
| ~ spl0_78
| ~ spl0_119 ),
inference(resolution,[],[f1267,f645]) ).
fof(f16098,plain,
( spl0_795
| ~ spl0_74
| ~ spl0_119 ),
inference(avatar_split_clause,[],[f1932,f1266,f628,f16096]) ).
fof(f16096,plain,
( spl0_795
<=> ! [X0] : ~ member(X0,domain_of(domain_of(empty_set))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_795])]) ).
fof(f1932,plain,
( ! [X0] : ~ member(X0,domain_of(domain_of(empty_set)))
| ~ spl0_74
| ~ spl0_119 ),
inference(resolution,[],[f1267,f629]) ).
fof(f16094,plain,
( spl0_794
| ~ spl0_173
| ~ spl0_782 ),
inference(avatar_split_clause,[],[f16041,f16038,f2440,f16092]) ).
fof(f16092,plain,
( spl0_794
<=> ! [X0,X1] :
( estin = image(X0,X1)
| f24(image(X0,X1)) = second(f22(f24(image(X0,X1)),X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_794])]) ).
fof(f16038,plain,
( spl0_782
<=> ! [X0,X1] :
( f24(image(X0,X1)) = second(f22(f24(image(X0,X1)),X0,X1))
| empty_set = image(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_782])]) ).
fof(f16041,plain,
( ! [X0,X1] :
( estin = image(X0,X1)
| f24(image(X0,X1)) = second(f22(f24(image(X0,X1)),X0,X1)) )
| ~ spl0_173
| ~ spl0_782 ),
inference(forward_demodulation,[],[f16039,f2442]) ).
fof(f16039,plain,
( ! [X0,X1] :
( f24(image(X0,X1)) = second(f22(f24(image(X0,X1)),X0,X1))
| empty_set = image(X0,X1) )
| ~ spl0_782 ),
inference(avatar_component_clause,[],[f16038]) ).
fof(f16088,plain,
( spl0_793
| ~ spl0_94
| ~ spl0_130 ),
inference(avatar_split_clause,[],[f1474,f1470,f840,f16086]) ).
fof(f16086,plain,
( spl0_793
<=> ! [X2,X0,X1] :
( ~ little_set(second(X0))
| ~ member(X0,X1)
| ~ member(first(X0),X2)
| ~ ordered_pair_predicate(X0)
| ordered_pair_predicate(f22(second(X0),X2,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_793])]) ).
fof(f1474,plain,
( ! [X2,X0,X1] :
( ~ little_set(second(X0))
| ~ member(X0,X1)
| ~ member(first(X0),X2)
| ~ ordered_pair_predicate(X0)
| ordered_pair_predicate(f22(second(X0),X2,X1)) )
| ~ spl0_94
| ~ spl0_130 ),
inference(resolution,[],[f1471,f841]) ).
fof(f16084,plain,
( spl0_792
| ~ spl0_38
| ~ spl0_129 ),
inference(avatar_split_clause,[],[f1465,f1405,f353,f16082]) ).
fof(f16082,plain,
( spl0_792
<=> ! [X2,X0,X1] :
( ~ little_set(X0)
| ~ member(X1,X2)
| ~ little_set(X2)
| ordered_pair_predicate(X1)
| ~ relation(first(non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_792])]) ).
fof(f1465,plain,
( ! [X2,X0,X1] :
( ~ little_set(X0)
| ~ member(X1,X2)
| ~ little_set(X2)
| ordered_pair_predicate(X1)
| ~ relation(first(non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X0)))) )
| ~ spl0_38
| ~ spl0_129 ),
inference(resolution,[],[f1406,f354]) ).
fof(f16080,plain,
( spl0_791
| ~ spl0_38
| ~ spl0_128 ),
inference(avatar_split_clause,[],[f1456,f1401,f353,f16078]) ).
fof(f16078,plain,
( spl0_791
<=> ! [X2,X0,X1] :
( ~ little_set(X0)
| ~ member(X1,X0)
| ~ little_set(X2)
| ordered_pair_predicate(X1)
| ~ relation(second(non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_791])]) ).
fof(f1456,plain,
( ! [X2,X0,X1] :
( ~ little_set(X0)
| ~ member(X1,X0)
| ~ little_set(X2)
| ordered_pair_predicate(X1)
| ~ relation(second(non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X0)))) )
| ~ spl0_38
| ~ spl0_128 ),
inference(resolution,[],[f1402,f354]) ).
fof(f16076,plain,
( spl0_790
| ~ spl0_37
| ~ spl0_127 ),
inference(avatar_split_clause,[],[f1441,f1397,f349,f16074]) ).
fof(f16074,plain,
( spl0_790
<=> ! [X0,X1] :
( ~ member(X0,converse(powerset(X1)))
| subset(non_ordered_pair(non_ordered_pair(second(X0),second(X0)),non_ordered_pair(second(X0),first(X0))),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_790])]) ).
fof(f1441,plain,
( ! [X0,X1] :
( ~ member(X0,converse(powerset(X1)))
| subset(non_ordered_pair(non_ordered_pair(second(X0),second(X0)),non_ordered_pair(second(X0),first(X0))),X1) )
| ~ spl0_37
| ~ spl0_127 ),
inference(resolution,[],[f1398,f350]) ).
fof(f16069,plain,
( spl0_789
| ~ spl0_119
| ~ spl0_145 ),
inference(avatar_split_clause,[],[f1928,f1786,f1266,f16067]) ).
fof(f16067,plain,
( spl0_789
<=> ! [X0] : ~ member(X0,rotate_right(domain_of(empty_set))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_789])]) ).
fof(f1928,plain,
( ! [X0] : ~ member(X0,rotate_right(domain_of(empty_set)))
| ~ spl0_119
| ~ spl0_145 ),
inference(resolution,[],[f1267,f1787]) ).
fof(f16065,plain,
( spl0_788
| ~ spl0_35
| ~ spl0_127 ),
inference(avatar_split_clause,[],[f1432,f1397,f340,f16063]) ).
fof(f16063,plain,
( spl0_788
<=> ! [X2,X0,X1] :
( ~ member(X0,converse(cross_product(X1,X2)))
| ordered_pair_predicate(non_ordered_pair(non_ordered_pair(second(X0),second(X0)),non_ordered_pair(second(X0),first(X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_788])]) ).
fof(f1432,plain,
( ! [X2,X0,X1] :
( ~ member(X0,converse(cross_product(X1,X2)))
| ordered_pair_predicate(non_ordered_pair(non_ordered_pair(second(X0),second(X0)),non_ordered_pair(second(X0),first(X0)))) )
| ~ spl0_35
| ~ spl0_127 ),
inference(resolution,[],[f1398,f341]) ).
fof(f16061,plain,
( spl0_787
| ~ spl0_34
| ~ spl0_127 ),
inference(avatar_split_clause,[],[f1427,f1397,f336,f16059]) ).
fof(f1427,plain,
( ! [X0,X1] :
( ~ member(X0,converse(complement(X1)))
| ~ member(non_ordered_pair(non_ordered_pair(second(X0),second(X0)),non_ordered_pair(second(X0),first(X0))),X1) )
| ~ spl0_34
| ~ spl0_127 ),
inference(resolution,[],[f1398,f337]) ).
fof(f16057,plain,
( spl0_786
| ~ spl0_38
| ~ spl0_127 ),
inference(avatar_split_clause,[],[f1417,f1397,f353,f16055]) ).
fof(f16055,plain,
( spl0_786
<=> ! [X0,X1] :
( ~ member(X0,converse(X1))
| ordered_pair_predicate(non_ordered_pair(non_ordered_pair(second(X0),second(X0)),non_ordered_pair(second(X0),first(X0))))
| ~ relation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_786])]) ).
fof(f1417,plain,
( ! [X0,X1] :
( ~ member(X0,converse(X1))
| ordered_pair_predicate(non_ordered_pair(non_ordered_pair(second(X0),second(X0)),non_ordered_pair(second(X0),first(X0))))
| ~ relation(X1) )
| ~ spl0_38
| ~ spl0_127 ),
inference(resolution,[],[f1398,f354]) ).
fof(f16053,plain,
( spl0_785
| ~ spl0_110
| ~ spl0_124 ),
inference(avatar_split_clause,[],[f1385,f1299,f1081,f16051]) ).
fof(f16051,plain,
( spl0_785
<=> ! [X2,X0,X1] :
( ~ member(X0,X1)
| ~ member(X2,second(X0))
| ~ ordered_pair_predicate(X0)
| first(X0) = first(f28(X2,X1,first(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_785])]) ).
fof(f1385,plain,
( ! [X2,X0,X1] :
( ~ member(X0,X1)
| ~ member(X2,second(X0))
| ~ ordered_pair_predicate(X0)
| first(X0) = first(f28(X2,X1,first(X0))) )
| ~ spl0_110
| ~ spl0_124 ),
inference(resolution,[],[f1300,f1082]) ).
fof(f16049,plain,
( spl0_784
| ~ spl0_35
| ~ spl0_113 ),
inference(avatar_split_clause,[],[f1235,f1159,f340,f16047]) ).
fof(f1235,plain,
( ! [X2,X0,X1] :
( member(f1(cross_product(X0,X1),X2),X2)
| cross_product(X0,X1) = X2
| ordered_pair_predicate(f1(cross_product(X0,X1),X2)) )
| ~ spl0_35
| ~ spl0_113 ),
inference(resolution,[],[f1160,f341]) ).
fof(f16045,plain,
( spl0_783
| ~ spl0_35
| ~ spl0_113 ),
inference(avatar_split_clause,[],[f1198,f1159,f340,f16043]) ).
fof(f1198,plain,
( ! [X2,X0,X1] :
( member(f1(X0,cross_product(X1,X2)),X0)
| cross_product(X1,X2) = X0
| ordered_pair_predicate(f1(X0,cross_product(X1,X2))) )
| ~ spl0_35
| ~ spl0_113 ),
inference(resolution,[],[f1160,f341]) ).
fof(f16040,plain,
( spl0_782
| ~ spl0_40
| ~ spl0_108 ),
inference(avatar_split_clause,[],[f1136,f1072,f361,f16038]) ).
fof(f1136,plain,
( ! [X0,X1] :
( f24(image(X0,X1)) = second(f22(f24(image(X0,X1)),X0,X1))
| empty_set = image(X0,X1) )
| ~ spl0_40
| ~ spl0_108 ),
inference(resolution,[],[f1073,f362]) ).
fof(f16036,plain,
( spl0_781
| ~ spl0_97
| ~ spl0_107 ),
inference(avatar_split_clause,[],[f1127,f1068,f852,f16034]) ).
fof(f16034,plain,
( spl0_781
<=> ! [X0,X3,X2,X1] :
( ~ member(X0,image(compose(X1,X2),X3))
| little_set(f29(first(f22(X0,compose(X1,X2),X3)),X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_781])]) ).
fof(f1127,plain,
( ! [X2,X3,X0,X1] :
( ~ member(X0,image(compose(X1,X2),X3))
| little_set(f29(first(f22(X0,compose(X1,X2),X3)),X1,X2)) )
| ~ spl0_97
| ~ spl0_107 ),
inference(resolution,[],[f1069,f853]) ).
fof(f16032,plain,
( spl0_780
| ~ spl0_98
| ~ spl0_107 ),
inference(avatar_split_clause,[],[f1126,f1068,f856,f16030]) ).
fof(f16030,plain,
( spl0_780
<=> ! [X0,X3,X2,X1] :
( ~ member(X0,image(compose(X1,X2),X3))
| little_set(f30(first(f22(X0,compose(X1,X2),X3)),X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_780])]) ).
fof(f1126,plain,
( ! [X2,X3,X0,X1] :
( ~ member(X0,image(compose(X1,X2),X3))
| little_set(f30(first(f22(X0,compose(X1,X2),X3)),X1,X2)) )
| ~ spl0_98
| ~ spl0_107 ),
inference(resolution,[],[f1069,f857]) ).
fof(f16028,plain,
( spl0_779
| ~ spl0_99
| ~ spl0_107 ),
inference(avatar_split_clause,[],[f1125,f1068,f860,f16026]) ).
fof(f16026,plain,
( spl0_779
<=> ! [X0,X3,X2,X1] :
( ~ member(X0,image(compose(X1,X2),X3))
| little_set(f31(first(f22(X0,compose(X1,X2),X3)),X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_779])]) ).
fof(f1125,plain,
( ! [X2,X3,X0,X1] :
( ~ member(X0,image(compose(X1,X2),X3))
| little_set(f31(first(f22(X0,compose(X1,X2),X3)),X1,X2)) )
| ~ spl0_99
| ~ spl0_107 ),
inference(resolution,[],[f1069,f861]) ).
fof(f16021,plain,
( spl0_778
| ~ spl0_119
| ~ spl0_144 ),
inference(avatar_split_clause,[],[f1927,f1782,f1266,f16019]) ).
fof(f16019,plain,
( spl0_778
<=> ! [X0] : ~ member(X0,flip_range_of(domain_of(empty_set))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_778])]) ).
fof(f1927,plain,
( ! [X0] : ~ member(X0,flip_range_of(domain_of(empty_set)))
| ~ spl0_119
| ~ spl0_144 ),
inference(resolution,[],[f1267,f1783]) ).
fof(f16017,plain,
( spl0_777
| ~ spl0_96
| ~ spl0_107 ),
inference(avatar_split_clause,[],[f1124,f1068,f848,f16015]) ).
fof(f16015,plain,
( spl0_777
<=> ! [X0,X3,X2,X1] :
( ~ member(X0,image(apply(X1,X2),X3))
| ordered_pair_predicate(f28(first(f22(X0,apply(X1,X2),X3)),X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_777])]) ).
fof(f1124,plain,
( ! [X2,X3,X0,X1] :
( ~ member(X0,image(apply(X1,X2),X3))
| ordered_pair_predicate(f28(first(f22(X0,apply(X1,X2),X3)),X1,X2)) )
| ~ spl0_96
| ~ spl0_107 ),
inference(resolution,[],[f1069,f849]) ).
fof(f16012,plain,
( spl0_776
| ~ spl0_66
| ~ spl0_107 ),
inference(avatar_split_clause,[],[f1122,f1068,f486,f16010]) ).
fof(f16010,plain,
( spl0_776
<=> ! [X0,X1] :
( ~ member(X0,image(identity_relation,X1))
| first(first(f22(X0,identity_relation,X1))) = second(first(f22(X0,identity_relation,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_776])]) ).
fof(f1122,plain,
( ! [X0,X1] :
( ~ member(X0,image(identity_relation,X1))
| first(first(f22(X0,identity_relation,X1))) = second(first(f22(X0,identity_relation,X1))) )
| ~ spl0_66
| ~ spl0_107 ),
inference(resolution,[],[f1069,f487]) ).
fof(f16008,plain,
( spl0_775
| ~ spl0_94
| ~ spl0_107 ),
inference(avatar_split_clause,[],[f1119,f1068,f840,f16006]) ).
fof(f16006,plain,
( spl0_775
<=> ! [X0,X3,X2,X1] :
( ~ member(X0,image(image(X1,X2),X3))
| ordered_pair_predicate(f22(first(f22(X0,image(X1,X2),X3)),X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_775])]) ).
fof(f1119,plain,
( ! [X2,X3,X0,X1] :
( ~ member(X0,image(image(X1,X2),X3))
| ordered_pair_predicate(f22(first(f22(X0,image(X1,X2),X3)),X1,X2)) )
| ~ spl0_94
| ~ spl0_107 ),
inference(resolution,[],[f1069,f841]) ).
fof(f15964,plain,
( spl0_774
| ~ spl0_119
| ~ spl0_127 ),
inference(avatar_split_clause,[],[f1925,f1397,f1266,f15962]) ).
fof(f15962,plain,
( spl0_774
<=> ! [X0] : ~ member(X0,converse(domain_of(empty_set))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_774])]) ).
fof(f1925,plain,
( ! [X0] : ~ member(X0,converse(domain_of(empty_set)))
| ~ spl0_119
| ~ spl0_127 ),
inference(resolution,[],[f1267,f1398]) ).
fof(f14492,plain,
( spl0_773
| ~ spl0_377
| ~ spl0_42
| ~ spl0_651 ),
inference(avatar_split_clause,[],[f11345,f9269,f369,f4302,f14489]) ).
fof(f14489,plain,
( spl0_773
<=> one_to_one_function(estin) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_773])]) ).
fof(f4302,plain,
( spl0_377
<=> function(estin) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_377])]) ).
fof(f369,plain,
( spl0_42
<=> ! [X7] :
( ~ function(X7)
| one_to_one_function(X7)
| ~ function(converse(X7)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_42])]) ).
fof(f9269,plain,
( spl0_651
<=> estin = converse(estin) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_651])]) ).
fof(f11345,plain,
( ~ function(estin)
| one_to_one_function(estin)
| ~ spl0_42
| ~ spl0_651 ),
inference(duplicate_literal_removal,[],[f11333]) ).
fof(f11333,plain,
( ~ function(estin)
| one_to_one_function(estin)
| ~ function(estin)
| ~ spl0_42
| ~ spl0_651 ),
inference(superposition,[],[f370,f9271]) ).
fof(f9271,plain,
( estin = converse(estin)
| ~ spl0_651 ),
inference(avatar_component_clause,[],[f9269]) ).
fof(f370,plain,
( ! [X7] :
( ~ function(converse(X7))
| one_to_one_function(X7)
| ~ function(X7) )
| ~ spl0_42 ),
inference(avatar_component_clause,[],[f369]) ).
fof(f12175,plain,
( spl0_772
| ~ spl0_173
| ~ spl0_712 ),
inference(avatar_split_clause,[],[f11235,f11232,f2440,f12173]) ).
fof(f12173,plain,
( spl0_772
<=> ! [X0,X1] :
( non_ordered_pair(X0,X1) = estin
| f24(non_ordered_pair(X0,X1)) = X0
| f24(non_ordered_pair(X0,X1)) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_772])]) ).
fof(f11232,plain,
( spl0_712
<=> ! [X0,X1] :
( f24(non_ordered_pair(X0,X1)) = X0
| f24(non_ordered_pair(X0,X1)) = X1
| non_ordered_pair(X0,X1) = empty_set ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_712])]) ).
fof(f11235,plain,
( ! [X0,X1] :
( non_ordered_pair(X0,X1) = estin
| f24(non_ordered_pair(X0,X1)) = X0
| f24(non_ordered_pair(X0,X1)) = X1 )
| ~ spl0_173
| ~ spl0_712 ),
inference(forward_demodulation,[],[f11233,f2442]) ).
fof(f11233,plain,
( ! [X0,X1] :
( f24(non_ordered_pair(X0,X1)) = X0
| f24(non_ordered_pair(X0,X1)) = X1
| non_ordered_pair(X0,X1) = empty_set )
| ~ spl0_712 ),
inference(avatar_component_clause,[],[f11232]) ).
fof(f12171,plain,
( spl0_771
| ~ spl0_173
| ~ spl0_711 ),
inference(avatar_split_clause,[],[f11230,f11227,f2440,f12169]) ).
fof(f12169,plain,
( spl0_771
<=> ! [X0,X1] :
( estin = compose(X0,X1)
| little_set(f31(f26(compose(X0,X1)),X0,X1))
| ~ little_set(compose(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_771])]) ).
fof(f11227,plain,
( spl0_711
<=> ! [X0,X1] :
( little_set(f31(f26(compose(X0,X1)),X0,X1))
| empty_set = compose(X0,X1)
| ~ little_set(compose(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_711])]) ).
fof(f11230,plain,
( ! [X0,X1] :
( estin = compose(X0,X1)
| little_set(f31(f26(compose(X0,X1)),X0,X1))
| ~ little_set(compose(X0,X1)) )
| ~ spl0_173
| ~ spl0_711 ),
inference(forward_demodulation,[],[f11228,f2442]) ).
fof(f11228,plain,
( ! [X0,X1] :
( little_set(f31(f26(compose(X0,X1)),X0,X1))
| empty_set = compose(X0,X1)
| ~ little_set(compose(X0,X1)) )
| ~ spl0_711 ),
inference(avatar_component_clause,[],[f11227]) ).
fof(f12167,plain,
( spl0_770
| ~ spl0_173
| ~ spl0_710 ),
inference(avatar_split_clause,[],[f11225,f11222,f2440,f12165]) ).
fof(f12165,plain,
( spl0_770
<=> ! [X0,X1] :
( estin = compose(X0,X1)
| little_set(f30(f26(compose(X0,X1)),X0,X1))
| ~ little_set(compose(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_770])]) ).
fof(f11222,plain,
( spl0_710
<=> ! [X0,X1] :
( little_set(f30(f26(compose(X0,X1)),X0,X1))
| empty_set = compose(X0,X1)
| ~ little_set(compose(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_710])]) ).
fof(f11225,plain,
( ! [X0,X1] :
( estin = compose(X0,X1)
| little_set(f30(f26(compose(X0,X1)),X0,X1))
| ~ little_set(compose(X0,X1)) )
| ~ spl0_173
| ~ spl0_710 ),
inference(forward_demodulation,[],[f11223,f2442]) ).
fof(f11223,plain,
( ! [X0,X1] :
( little_set(f30(f26(compose(X0,X1)),X0,X1))
| empty_set = compose(X0,X1)
| ~ little_set(compose(X0,X1)) )
| ~ spl0_710 ),
inference(avatar_component_clause,[],[f11222]) ).
fof(f12163,plain,
( spl0_769
| ~ spl0_173
| ~ spl0_708 ),
inference(avatar_split_clause,[],[f11216,f11213,f2440,f12161]) ).
fof(f12161,plain,
( spl0_769
<=> ! [X0,X1] :
( estin = compose(X0,X1)
| little_set(f29(f26(compose(X0,X1)),X0,X1))
| ~ little_set(compose(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_769])]) ).
fof(f11213,plain,
( spl0_708
<=> ! [X0,X1] :
( little_set(f29(f26(compose(X0,X1)),X0,X1))
| empty_set = compose(X0,X1)
| ~ little_set(compose(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_708])]) ).
fof(f11216,plain,
( ! [X0,X1] :
( estin = compose(X0,X1)
| little_set(f29(f26(compose(X0,X1)),X0,X1))
| ~ little_set(compose(X0,X1)) )
| ~ spl0_173
| ~ spl0_708 ),
inference(forward_demodulation,[],[f11214,f2442]) ).
fof(f11214,plain,
( ! [X0,X1] :
( little_set(f29(f26(compose(X0,X1)),X0,X1))
| empty_set = compose(X0,X1)
| ~ little_set(compose(X0,X1)) )
| ~ spl0_708 ),
inference(avatar_component_clause,[],[f11213]) ).
fof(f12159,plain,
( spl0_768
| ~ spl0_173
| ~ spl0_707 ),
inference(avatar_split_clause,[],[f11211,f11208,f2440,f12157]) ).
fof(f12157,plain,
( spl0_768
<=> ! [X0,X1] :
( estin = apply(X0,X1)
| ordered_pair_predicate(f28(f26(apply(X0,X1)),X0,X1))
| ~ little_set(apply(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_768])]) ).
fof(f11208,plain,
( spl0_707
<=> ! [X0,X1] :
( ordered_pair_predicate(f28(f26(apply(X0,X1)),X0,X1))
| empty_set = apply(X0,X1)
| ~ little_set(apply(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_707])]) ).
fof(f11211,plain,
( ! [X0,X1] :
( estin = apply(X0,X1)
| ordered_pair_predicate(f28(f26(apply(X0,X1)),X0,X1))
| ~ little_set(apply(X0,X1)) )
| ~ spl0_173
| ~ spl0_707 ),
inference(forward_demodulation,[],[f11209,f2442]) ).
fof(f11209,plain,
( ! [X0,X1] :
( ordered_pair_predicate(f28(f26(apply(X0,X1)),X0,X1))
| empty_set = apply(X0,X1)
| ~ little_set(apply(X0,X1)) )
| ~ spl0_707 ),
inference(avatar_component_clause,[],[f11208]) ).
fof(f12074,plain,
( spl0_767
| ~ spl0_173
| ~ spl0_705 ),
inference(avatar_split_clause,[],[f11202,f11199,f2440,f12072]) ).
fof(f12072,plain,
( spl0_767
<=> ! [X0] :
( estin = range_of(X0)
| f26(range_of(X0)) = second(f27(f26(range_of(X0)),X0))
| ~ little_set(range_of(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_767])]) ).
fof(f11199,plain,
( spl0_705
<=> ! [X0] :
( f26(range_of(X0)) = second(f27(f26(range_of(X0)),X0))
| empty_set = range_of(X0)
| ~ little_set(range_of(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_705])]) ).
fof(f11202,plain,
( ! [X0] :
( estin = range_of(X0)
| f26(range_of(X0)) = second(f27(f26(range_of(X0)),X0))
| ~ little_set(range_of(X0)) )
| ~ spl0_173
| ~ spl0_705 ),
inference(forward_demodulation,[],[f11200,f2442]) ).
fof(f11200,plain,
( ! [X0] :
( f26(range_of(X0)) = second(f27(f26(range_of(X0)),X0))
| empty_set = range_of(X0)
| ~ little_set(range_of(X0)) )
| ~ spl0_705 ),
inference(avatar_component_clause,[],[f11199]) ).
fof(f11869,plain,
( spl0_766
| ~ spl0_173
| ~ spl0_702 ),
inference(avatar_split_clause,[],[f11189,f11186,f2440,f11867]) ).
fof(f11867,plain,
( spl0_766
<=> ! [X0,X1] :
( estin = image(X0,X1)
| ordered_pair_predicate(f22(f26(image(X0,X1)),X0,X1))
| ~ little_set(image(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_766])]) ).
fof(f11186,plain,
( spl0_702
<=> ! [X0,X1] :
( ordered_pair_predicate(f22(f26(image(X0,X1)),X0,X1))
| empty_set = image(X0,X1)
| ~ little_set(image(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_702])]) ).
fof(f11189,plain,
( ! [X0,X1] :
( estin = image(X0,X1)
| ordered_pair_predicate(f22(f26(image(X0,X1)),X0,X1))
| ~ little_set(image(X0,X1)) )
| ~ spl0_173
| ~ spl0_702 ),
inference(forward_demodulation,[],[f11187,f2442]) ).
fof(f11187,plain,
( ! [X0,X1] :
( ordered_pair_predicate(f22(f26(image(X0,X1)),X0,X1))
| empty_set = image(X0,X1)
| ~ little_set(image(X0,X1)) )
| ~ spl0_702 ),
inference(avatar_component_clause,[],[f11186]) ).
fof(f11784,plain,
( spl0_765
| ~ spl0_173
| ~ spl0_700 ),
inference(avatar_split_clause,[],[f11180,f11177,f2440,f11782]) ).
fof(f11782,plain,
( spl0_765
<=> ! [X0] :
( estin = domain_of(X0)
| f26(domain_of(X0)) = first(f8(f26(domain_of(X0)),X0))
| ~ little_set(domain_of(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_765])]) ).
fof(f11177,plain,
( spl0_700
<=> ! [X0] :
( f26(domain_of(X0)) = first(f8(f26(domain_of(X0)),X0))
| domain_of(X0) = empty_set
| ~ little_set(domain_of(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_700])]) ).
fof(f11180,plain,
( ! [X0] :
( estin = domain_of(X0)
| f26(domain_of(X0)) = first(f8(f26(domain_of(X0)),X0))
| ~ little_set(domain_of(X0)) )
| ~ spl0_173
| ~ spl0_700 ),
inference(forward_demodulation,[],[f11178,f2442]) ).
fof(f11178,plain,
( ! [X0] :
( f26(domain_of(X0)) = first(f8(f26(domain_of(X0)),X0))
| domain_of(X0) = empty_set
| ~ little_set(domain_of(X0)) )
| ~ spl0_700 ),
inference(avatar_component_clause,[],[f11177]) ).
fof(f11605,plain,
( spl0_764
| ~ spl0_46
| ~ spl0_129 ),
inference(avatar_split_clause,[],[f1463,f1405,f406,f11603]) ).
fof(f11603,plain,
( spl0_764
<=> ! [X2,X0,X1] :
( ~ little_set(X0)
| ~ member(X1,X2)
| ~ little_set(X2)
| little_set(f4(X1,non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_764])]) ).
fof(f1463,plain,
( ! [X2,X0,X1] :
( ~ little_set(X0)
| ~ member(X1,X2)
| ~ little_set(X2)
| little_set(f4(X1,non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X0)))) )
| ~ spl0_46
| ~ spl0_129 ),
inference(resolution,[],[f1406,f407]) ).
fof(f11601,plain,
( spl0_763
| ~ spl0_47
| ~ spl0_129 ),
inference(avatar_split_clause,[],[f1462,f1405,f410,f11599]) ).
fof(f11599,plain,
( spl0_763
<=> ! [X2,X0,X1] :
( ~ little_set(X0)
| ~ member(X1,X2)
| ~ little_set(X2)
| little_set(f5(X1,non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_763])]) ).
fof(f1462,plain,
( ! [X2,X0,X1] :
( ~ little_set(X0)
| ~ member(X1,X2)
| ~ little_set(X2)
| little_set(f5(X1,non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X0)))) )
| ~ spl0_47
| ~ spl0_129 ),
inference(resolution,[],[f1406,f411]) ).
fof(f11597,plain,
( spl0_762
| ~ spl0_48
| ~ spl0_128 ),
inference(avatar_split_clause,[],[f1454,f1401,f414,f11595]) ).
fof(f11595,plain,
( spl0_762
<=> ! [X2,X0,X1] :
( ~ little_set(X0)
| ~ member(X1,X0)
| ~ little_set(X2)
| little_set(f6(X1,non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_762])]) ).
fof(f1454,plain,
( ! [X2,X0,X1] :
( ~ little_set(X0)
| ~ member(X1,X0)
| ~ little_set(X2)
| little_set(f6(X1,non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X0)))) )
| ~ spl0_48
| ~ spl0_128 ),
inference(resolution,[],[f1402,f415]) ).
fof(f11593,plain,
( spl0_761
| ~ spl0_49
| ~ spl0_128 ),
inference(avatar_split_clause,[],[f1453,f1401,f418,f11591]) ).
fof(f11591,plain,
( spl0_761
<=> ! [X2,X0,X1] :
( ~ little_set(X0)
| ~ member(X1,X0)
| ~ little_set(X2)
| little_set(f7(X1,non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_761])]) ).
fof(f1453,plain,
( ! [X2,X0,X1] :
( ~ little_set(X0)
| ~ member(X1,X0)
| ~ little_set(X2)
| little_set(f7(X1,non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X0)))) )
| ~ spl0_49
| ~ spl0_128 ),
inference(resolution,[],[f1402,f419]) ).
fof(f11589,plain,
( spl0_760
| ~ spl0_28
| ~ spl0_127 ),
inference(avatar_split_clause,[],[f1433,f1397,f306,f11587]) ).
fof(f11587,plain,
( spl0_760
<=> ! [X0,X1] :
( ~ member(X0,converse(converse(X1)))
| ordered_pair_predicate(non_ordered_pair(non_ordered_pair(second(X0),second(X0)),non_ordered_pair(second(X0),first(X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_760])]) ).
fof(f1433,plain,
( ! [X0,X1] :
( ~ member(X0,converse(converse(X1)))
| ordered_pair_predicate(non_ordered_pair(non_ordered_pair(second(X0),second(X0)),non_ordered_pair(second(X0),first(X0)))) )
| ~ spl0_28
| ~ spl0_127 ),
inference(resolution,[],[f1398,f307]) ).
fof(f11568,plain,
( spl0_759
| ~ spl0_93
| ~ spl0_118 ),
inference(avatar_split_clause,[],[f1279,f1179,f836,f11566]) ).
fof(f11566,plain,
( spl0_759
<=> ! [X2,X0,X1] :
( ~ little_set(second(X0))
| ~ member(X0,X1)
| ~ ordered_pair_predicate(X0)
| ~ member(range_of(X1),X2)
| member(second(X0),sigma(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_759])]) ).
fof(f1179,plain,
( spl0_118
<=> ! [X5,X0] :
( ~ ordered_pair_predicate(X5)
| ~ little_set(second(X5))
| ~ member(X5,X0)
| member(second(X5),range_of(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_118])]) ).
fof(f1279,plain,
( ! [X2,X0,X1] :
( ~ little_set(second(X0))
| ~ member(X0,X1)
| ~ ordered_pair_predicate(X0)
| ~ member(range_of(X1),X2)
| member(second(X0),sigma(X2)) )
| ~ spl0_93
| ~ spl0_118 ),
inference(resolution,[],[f1180,f837]) ).
fof(f1180,plain,
( ! [X0,X5] :
( member(second(X5),range_of(X0))
| ~ little_set(second(X5))
| ~ member(X5,X0)
| ~ ordered_pair_predicate(X5) )
| ~ spl0_118 ),
inference(avatar_component_clause,[],[f1179]) ).
fof(f11564,plain,
( spl0_758
| ~ spl0_93
| ~ spl0_117 ),
inference(avatar_split_clause,[],[f1274,f1175,f836,f11562]) ).
fof(f11562,plain,
( spl0_758
<=> ! [X2,X0,X1] :
( ~ little_set(first(X0))
| ~ member(X0,X1)
| ~ ordered_pair_predicate(X0)
| ~ member(domain_of(X1),X2)
| member(first(X0),sigma(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_758])]) ).
fof(f1175,plain,
( spl0_117
<=> ! [X5,X0] :
( ~ ordered_pair_predicate(X5)
| ~ little_set(first(X5))
| ~ member(X5,X0)
| member(first(X5),domain_of(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_117])]) ).
fof(f1274,plain,
( ! [X2,X0,X1] :
( ~ little_set(first(X0))
| ~ member(X0,X1)
| ~ ordered_pair_predicate(X0)
| ~ member(domain_of(X1),X2)
| member(first(X0),sigma(X2)) )
| ~ spl0_93
| ~ spl0_117 ),
inference(resolution,[],[f1176,f837]) ).
fof(f1176,plain,
( ! [X0,X5] :
( member(first(X5),domain_of(X0))
| ~ little_set(first(X5))
| ~ member(X5,X0)
| ~ ordered_pair_predicate(X5) )
| ~ spl0_117 ),
inference(avatar_component_clause,[],[f1175]) ).
fof(f11560,plain,
( spl0_757
| ~ spl0_93
| ~ spl0_116 ),
inference(avatar_split_clause,[],[f1269,f1171,f836,f11558]) ).
fof(f11558,plain,
( spl0_757
<=> ! [X0,X1] :
( ~ member(X0,infinity)
| ~ member(infinity,X1)
| member(complement(intersection(complement(X0),complement(non_ordered_pair(X0,X0)))),sigma(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_757])]) ).
fof(f1171,plain,
( spl0_116
<=> ! [X0] :
( ~ member(X0,infinity)
| member(complement(intersection(complement(X0),complement(non_ordered_pair(X0,X0)))),infinity) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_116])]) ).
fof(f1269,plain,
( ! [X0,X1] :
( ~ member(X0,infinity)
| ~ member(infinity,X1)
| member(complement(intersection(complement(X0),complement(non_ordered_pair(X0,X0)))),sigma(X1)) )
| ~ spl0_93
| ~ spl0_116 ),
inference(resolution,[],[f1172,f837]) ).
fof(f1172,plain,
( ! [X0] :
( member(complement(intersection(complement(X0),complement(non_ordered_pair(X0,X0)))),infinity)
| ~ member(X0,infinity) )
| ~ spl0_116 ),
inference(avatar_component_clause,[],[f1171]) ).
fof(f11554,plain,
( spl0_756
| ~ spl0_66
| ~ spl0_113 ),
inference(avatar_split_clause,[],[f1249,f1159,f486,f11552]) ).
fof(f11552,plain,
( spl0_756
<=> ! [X0] :
( member(f1(identity_relation,X0),X0)
| identity_relation = X0
| first(f1(identity_relation,X0)) = second(f1(identity_relation,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_756])]) ).
fof(f1249,plain,
( ! [X0] :
( member(f1(identity_relation,X0),X0)
| identity_relation = X0
| first(f1(identity_relation,X0)) = second(f1(identity_relation,X0)) )
| ~ spl0_66
| ~ spl0_113 ),
inference(resolution,[],[f1160,f487]) ).
fof(f11550,plain,
( spl0_755
| ~ spl0_65
| ~ spl0_113 ),
inference(avatar_split_clause,[],[f1248,f1159,f482,f11548]) ).
fof(f1248,plain,
( ! [X0,X1] :
( member(f1(range_of(X0),X1),X1)
| range_of(X0) = X1
| ordered_pair_predicate(f27(f1(range_of(X0),X1),X0)) )
| ~ spl0_65
| ~ spl0_113 ),
inference(resolution,[],[f1160,f483]) ).
fof(f11546,plain,
( spl0_754
| ~ spl0_57
| ~ spl0_113 ),
inference(avatar_split_clause,[],[f1242,f1159,f450,f11544]) ).
fof(f1242,plain,
( ! [X0,X1] :
( member(f1(flip_range_of(X0),X1),X1)
| flip_range_of(X0) = X1
| little_set(f12(f1(flip_range_of(X0),X1),X0)) )
| ~ spl0_57
| ~ spl0_113 ),
inference(resolution,[],[f1160,f451]) ).
fof(f11542,plain,
( spl0_753
| ~ spl0_58
| ~ spl0_113 ),
inference(avatar_split_clause,[],[f1241,f1159,f454,f11540]) ).
fof(f1241,plain,
( ! [X0,X1] :
( member(f1(flip_range_of(X0),X1),X1)
| flip_range_of(X0) = X1
| little_set(f13(f1(flip_range_of(X0),X1),X0)) )
| ~ spl0_58
| ~ spl0_113 ),
inference(resolution,[],[f1160,f455]) ).
fof(f11538,plain,
( spl0_752
| ~ spl0_59
| ~ spl0_113 ),
inference(avatar_split_clause,[],[f1240,f1159,f458,f11536]) ).
fof(f1240,plain,
( ! [X0,X1] :
( member(f1(flip_range_of(X0),X1),X1)
| flip_range_of(X0) = X1
| little_set(f14(f1(flip_range_of(X0),X1),X0)) )
| ~ spl0_59
| ~ spl0_113 ),
inference(resolution,[],[f1160,f459]) ).
fof(f11534,plain,
( spl0_751
| ~ spl0_54
| ~ spl0_113 ),
inference(avatar_split_clause,[],[f1239,f1159,f438,f11532]) ).
fof(f1239,plain,
( ! [X0,X1] :
( member(f1(rotate_right(X0),X1),X1)
| rotate_right(X0) = X1
| little_set(f9(f1(rotate_right(X0),X1),X0)) )
| ~ spl0_54
| ~ spl0_113 ),
inference(resolution,[],[f1160,f439]) ).
fof(f11530,plain,
( spl0_750
| ~ spl0_55
| ~ spl0_113 ),
inference(avatar_split_clause,[],[f1238,f1159,f442,f11528]) ).
fof(f1238,plain,
( ! [X0,X1] :
( member(f1(rotate_right(X0),X1),X1)
| rotate_right(X0) = X1
| little_set(f10(f1(rotate_right(X0),X1),X0)) )
| ~ spl0_55
| ~ spl0_113 ),
inference(resolution,[],[f1160,f443]) ).
fof(f11477,plain,
( spl0_749
| ~ spl0_56
| ~ spl0_113 ),
inference(avatar_split_clause,[],[f1237,f1159,f446,f11475]) ).
fof(f1237,plain,
( ! [X0,X1] :
( member(f1(rotate_right(X0),X1),X1)
| rotate_right(X0) = X1
| little_set(f11(f1(rotate_right(X0),X1),X0)) )
| ~ spl0_56
| ~ spl0_113 ),
inference(resolution,[],[f1160,f447]) ).
fof(f11473,plain,
( spl0_748
| ~ spl0_53
| ~ spl0_113 ),
inference(avatar_split_clause,[],[f1232,f1159,f434,f11471]) ).
fof(f1232,plain,
( ! [X0,X1] :
( member(f1(domain_of(X0),X1),X1)
| domain_of(X0) = X1
| ordered_pair_predicate(f8(f1(domain_of(X0),X1),X0)) )
| ~ spl0_53
| ~ spl0_113 ),
inference(resolution,[],[f1160,f435]) ).
fof(f11469,plain,
( spl0_747
| ~ spl0_48
| ~ spl0_113 ),
inference(avatar_split_clause,[],[f1226,f1159,f414,f11467]) ).
fof(f1226,plain,
( ! [X0,X1] :
( member(f1(second(X0),X1),X1)
| second(X0) = X1
| little_set(f6(f1(second(X0),X1),X0)) )
| ~ spl0_48
| ~ spl0_113 ),
inference(resolution,[],[f1160,f415]) ).
fof(f11465,plain,
( spl0_746
| ~ spl0_49
| ~ spl0_113 ),
inference(avatar_split_clause,[],[f1225,f1159,f418,f11463]) ).
fof(f1225,plain,
( ! [X0,X1] :
( member(f1(second(X0),X1),X1)
| second(X0) = X1
| little_set(f7(f1(second(X0),X1),X0)) )
| ~ spl0_49
| ~ spl0_113 ),
inference(resolution,[],[f1160,f419]) ).
fof(f11461,plain,
( spl0_745
| ~ spl0_46
| ~ spl0_113 ),
inference(avatar_split_clause,[],[f1224,f1159,f406,f11459]) ).
fof(f1224,plain,
( ! [X0,X1] :
( member(f1(first(X0),X1),X1)
| first(X0) = X1
| little_set(f4(f1(first(X0),X1),X0)) )
| ~ spl0_46
| ~ spl0_113 ),
inference(resolution,[],[f1160,f407]) ).
fof(f11457,plain,
( spl0_744
| ~ spl0_47
| ~ spl0_113 ),
inference(avatar_split_clause,[],[f1223,f1159,f410,f11455]) ).
fof(f1223,plain,
( ! [X0,X1] :
( member(f1(first(X0),X1),X1)
| first(X0) = X1
| little_set(f5(f1(first(X0),X1),X0)) )
| ~ spl0_47
| ~ spl0_113 ),
inference(resolution,[],[f1160,f411]) ).
fof(f11453,plain,
( spl0_743
| ~ spl0_93
| ~ spl0_113 ),
inference(avatar_split_clause,[],[f1219,f1159,f836,f11451]) ).
fof(f11451,plain,
( spl0_743
<=> ! [X2,X0,X1] :
( member(f1(X0,X1),X1)
| X0 = X1
| ~ member(X0,X2)
| member(f1(X0,X1),sigma(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_743])]) ).
fof(f1219,plain,
( ! [X2,X0,X1] :
( member(f1(X0,X1),X1)
| X0 = X1
| ~ member(X0,X2)
| member(f1(X0,X1),sigma(X2)) )
| ~ spl0_93
| ~ spl0_113 ),
inference(resolution,[],[f1160,f837]) ).
fof(f11447,plain,
( spl0_742
| ~ spl0_66
| ~ spl0_113 ),
inference(avatar_split_clause,[],[f1212,f1159,f486,f11445]) ).
fof(f11445,plain,
( spl0_742
<=> ! [X0] :
( member(f1(X0,identity_relation),X0)
| identity_relation = X0
| first(f1(X0,identity_relation)) = second(f1(X0,identity_relation)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_742])]) ).
fof(f1212,plain,
( ! [X0] :
( member(f1(X0,identity_relation),X0)
| identity_relation = X0
| first(f1(X0,identity_relation)) = second(f1(X0,identity_relation)) )
| ~ spl0_66
| ~ spl0_113 ),
inference(resolution,[],[f1160,f487]) ).
fof(f11443,plain,
( spl0_741
| ~ spl0_65
| ~ spl0_113 ),
inference(avatar_split_clause,[],[f1211,f1159,f482,f11441]) ).
fof(f11441,plain,
( spl0_741
<=> ! [X0,X1] :
( member(f1(X0,range_of(X1)),X0)
| range_of(X1) = X0
| ordered_pair_predicate(f27(f1(X0,range_of(X1)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_741])]) ).
fof(f1211,plain,
( ! [X0,X1] :
( member(f1(X0,range_of(X1)),X0)
| range_of(X1) = X0
| ordered_pair_predicate(f27(f1(X0,range_of(X1)),X1)) )
| ~ spl0_65
| ~ spl0_113 ),
inference(resolution,[],[f1160,f483]) ).
fof(f11439,plain,
( spl0_740
| ~ spl0_57
| ~ spl0_113 ),
inference(avatar_split_clause,[],[f1205,f1159,f450,f11437]) ).
fof(f11437,plain,
( spl0_740
<=> ! [X0,X1] :
( member(f1(X0,flip_range_of(X1)),X0)
| flip_range_of(X1) = X0
| little_set(f12(f1(X0,flip_range_of(X1)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_740])]) ).
fof(f1205,plain,
( ! [X0,X1] :
( member(f1(X0,flip_range_of(X1)),X0)
| flip_range_of(X1) = X0
| little_set(f12(f1(X0,flip_range_of(X1)),X1)) )
| ~ spl0_57
| ~ spl0_113 ),
inference(resolution,[],[f1160,f451]) ).
fof(f11386,plain,
( spl0_739
| ~ spl0_58
| ~ spl0_113 ),
inference(avatar_split_clause,[],[f1204,f1159,f454,f11384]) ).
fof(f11384,plain,
( spl0_739
<=> ! [X0,X1] :
( member(f1(X0,flip_range_of(X1)),X0)
| flip_range_of(X1) = X0
| little_set(f13(f1(X0,flip_range_of(X1)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_739])]) ).
fof(f1204,plain,
( ! [X0,X1] :
( member(f1(X0,flip_range_of(X1)),X0)
| flip_range_of(X1) = X0
| little_set(f13(f1(X0,flip_range_of(X1)),X1)) )
| ~ spl0_58
| ~ spl0_113 ),
inference(resolution,[],[f1160,f455]) ).
fof(f11382,plain,
( spl0_738
| ~ spl0_59
| ~ spl0_113 ),
inference(avatar_split_clause,[],[f1203,f1159,f458,f11380]) ).
fof(f11380,plain,
( spl0_738
<=> ! [X0,X1] :
( member(f1(X0,flip_range_of(X1)),X0)
| flip_range_of(X1) = X0
| little_set(f14(f1(X0,flip_range_of(X1)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_738])]) ).
fof(f1203,plain,
( ! [X0,X1] :
( member(f1(X0,flip_range_of(X1)),X0)
| flip_range_of(X1) = X0
| little_set(f14(f1(X0,flip_range_of(X1)),X1)) )
| ~ spl0_59
| ~ spl0_113 ),
inference(resolution,[],[f1160,f459]) ).
fof(f11378,plain,
( spl0_737
| ~ spl0_54
| ~ spl0_113 ),
inference(avatar_split_clause,[],[f1202,f1159,f438,f11376]) ).
fof(f11376,plain,
( spl0_737
<=> ! [X0,X1] :
( member(f1(X0,rotate_right(X1)),X0)
| rotate_right(X1) = X0
| little_set(f9(f1(X0,rotate_right(X1)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_737])]) ).
fof(f1202,plain,
( ! [X0,X1] :
( member(f1(X0,rotate_right(X1)),X0)
| rotate_right(X1) = X0
| little_set(f9(f1(X0,rotate_right(X1)),X1)) )
| ~ spl0_54
| ~ spl0_113 ),
inference(resolution,[],[f1160,f439]) ).
fof(f11374,plain,
( spl0_736
| ~ spl0_55
| ~ spl0_113 ),
inference(avatar_split_clause,[],[f1201,f1159,f442,f11372]) ).
fof(f11372,plain,
( spl0_736
<=> ! [X0,X1] :
( member(f1(X0,rotate_right(X1)),X0)
| rotate_right(X1) = X0
| little_set(f10(f1(X0,rotate_right(X1)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_736])]) ).
fof(f1201,plain,
( ! [X0,X1] :
( member(f1(X0,rotate_right(X1)),X0)
| rotate_right(X1) = X0
| little_set(f10(f1(X0,rotate_right(X1)),X1)) )
| ~ spl0_55
| ~ spl0_113 ),
inference(resolution,[],[f1160,f443]) ).
fof(f11370,plain,
( spl0_735
| ~ spl0_56
| ~ spl0_113 ),
inference(avatar_split_clause,[],[f1200,f1159,f446,f11368]) ).
fof(f11368,plain,
( spl0_735
<=> ! [X0,X1] :
( member(f1(X0,rotate_right(X1)),X0)
| rotate_right(X1) = X0
| little_set(f11(f1(X0,rotate_right(X1)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_735])]) ).
fof(f1200,plain,
( ! [X0,X1] :
( member(f1(X0,rotate_right(X1)),X0)
| rotate_right(X1) = X0
| little_set(f11(f1(X0,rotate_right(X1)),X1)) )
| ~ spl0_56
| ~ spl0_113 ),
inference(resolution,[],[f1160,f447]) ).
fof(f11366,plain,
( spl0_734
| ~ spl0_53
| ~ spl0_113 ),
inference(avatar_split_clause,[],[f1195,f1159,f434,f11364]) ).
fof(f11364,plain,
( spl0_734
<=> ! [X0,X1] :
( member(f1(X0,domain_of(X1)),X0)
| domain_of(X1) = X0
| ordered_pair_predicate(f8(f1(X0,domain_of(X1)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_734])]) ).
fof(f1195,plain,
( ! [X0,X1] :
( member(f1(X0,domain_of(X1)),X0)
| domain_of(X1) = X0
| ordered_pair_predicate(f8(f1(X0,domain_of(X1)),X1)) )
| ~ spl0_53
| ~ spl0_113 ),
inference(resolution,[],[f1160,f435]) ).
fof(f11362,plain,
( spl0_733
| ~ spl0_48
| ~ spl0_113 ),
inference(avatar_split_clause,[],[f1189,f1159,f414,f11360]) ).
fof(f11360,plain,
( spl0_733
<=> ! [X0,X1] :
( member(f1(X0,second(X1)),X0)
| second(X1) = X0
| little_set(f6(f1(X0,second(X1)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_733])]) ).
fof(f1189,plain,
( ! [X0,X1] :
( member(f1(X0,second(X1)),X0)
| second(X1) = X0
| little_set(f6(f1(X0,second(X1)),X1)) )
| ~ spl0_48
| ~ spl0_113 ),
inference(resolution,[],[f1160,f415]) ).
fof(f11358,plain,
( spl0_732
| ~ spl0_49
| ~ spl0_113 ),
inference(avatar_split_clause,[],[f1188,f1159,f418,f11356]) ).
fof(f11356,plain,
( spl0_732
<=> ! [X0,X1] :
( member(f1(X0,second(X1)),X0)
| second(X1) = X0
| little_set(f7(f1(X0,second(X1)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_732])]) ).
fof(f1188,plain,
( ! [X0,X1] :
( member(f1(X0,second(X1)),X0)
| second(X1) = X0
| little_set(f7(f1(X0,second(X1)),X1)) )
| ~ spl0_49
| ~ spl0_113 ),
inference(resolution,[],[f1160,f419]) ).
fof(f11354,plain,
( spl0_731
| ~ spl0_46
| ~ spl0_113 ),
inference(avatar_split_clause,[],[f1187,f1159,f406,f11352]) ).
fof(f11352,plain,
( spl0_731
<=> ! [X0,X1] :
( member(f1(X0,first(X1)),X0)
| first(X1) = X0
| little_set(f4(f1(X0,first(X1)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_731])]) ).
fof(f1187,plain,
( ! [X0,X1] :
( member(f1(X0,first(X1)),X0)
| first(X1) = X0
| little_set(f4(f1(X0,first(X1)),X1)) )
| ~ spl0_46
| ~ spl0_113 ),
inference(resolution,[],[f1160,f407]) ).
fof(f11350,plain,
( spl0_730
| ~ spl0_47
| ~ spl0_113 ),
inference(avatar_split_clause,[],[f1186,f1159,f410,f11348]) ).
fof(f11348,plain,
( spl0_730
<=> ! [X0,X1] :
( member(f1(X0,first(X1)),X0)
| first(X1) = X0
| little_set(f5(f1(X0,first(X1)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_730])]) ).
fof(f1186,plain,
( ! [X0,X1] :
( member(f1(X0,first(X1)),X0)
| first(X1) = X0
| little_set(f5(f1(X0,first(X1)),X1)) )
| ~ spl0_47
| ~ spl0_113 ),
inference(resolution,[],[f1160,f411]) ).
fof(f11330,plain,
( spl0_729
| ~ spl0_93
| ~ spl0_113 ),
inference(avatar_split_clause,[],[f1182,f1159,f836,f11328]) ).
fof(f11328,plain,
( spl0_729
<=> ! [X2,X0,X1] :
( member(f1(X0,X1),X0)
| X0 = X1
| ~ member(X1,X2)
| member(f1(X0,X1),sigma(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_729])]) ).
fof(f1182,plain,
( ! [X2,X0,X1] :
( member(f1(X0,X1),X0)
| X0 = X1
| ~ member(X1,X2)
| member(f1(X0,X1),sigma(X2)) )
| ~ spl0_93
| ~ spl0_113 ),
inference(resolution,[],[f1160,f837]) ).
fof(f11326,plain,
( spl0_728
| ~ spl0_85
| ~ spl0_110 ),
inference(avatar_split_clause,[],[f1150,f1081,f672,f11324]) ).
fof(f11324,plain,
( spl0_728
<=> ! [X2,X0,X1] :
( first(f28(f27(X0,apply(X1,X2)),X1,X2)) = X2
| ~ member(X0,range_of(apply(X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_728])]) ).
fof(f1150,plain,
( ! [X2,X0,X1] :
( first(f28(f27(X0,apply(X1,X2)),X1,X2)) = X2
| ~ member(X0,range_of(apply(X1,X2))) )
| ~ spl0_85
| ~ spl0_110 ),
inference(resolution,[],[f1082,f673]) ).
fof(f11322,plain,
( spl0_727
| ~ spl0_78
| ~ spl0_110 ),
inference(avatar_split_clause,[],[f1142,f1081,f644,f11320]) ).
fof(f11320,plain,
( spl0_727
<=> ! [X2,X0,X1] :
( first(f28(f16(X0,apply(X1,X2)),X1,X2)) = X2
| ~ member(X0,sigma(apply(X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_727])]) ).
fof(f1142,plain,
( ! [X2,X0,X1] :
( first(f28(f16(X0,apply(X1,X2)),X1,X2)) = X2
| ~ member(X0,sigma(apply(X1,X2))) )
| ~ spl0_78
| ~ spl0_110 ),
inference(resolution,[],[f1082,f645]) ).
fof(f11318,plain,
( spl0_726
| ~ spl0_74
| ~ spl0_110 ),
inference(avatar_split_clause,[],[f1141,f1081,f628,f11316]) ).
fof(f11316,plain,
( spl0_726
<=> ! [X2,X0,X1] :
( first(f28(f8(X0,apply(X1,X2)),X1,X2)) = X2
| ~ member(X0,domain_of(apply(X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_726])]) ).
fof(f1141,plain,
( ! [X2,X0,X1] :
( first(f28(f8(X0,apply(X1,X2)),X1,X2)) = X2
| ~ member(X0,domain_of(apply(X1,X2))) )
| ~ spl0_74
| ~ spl0_110 ),
inference(resolution,[],[f1082,f629]) ).
fof(f11314,plain,
( spl0_725
| ~ spl0_30
| ~ spl0_108 ),
inference(avatar_split_clause,[],[f1132,f1072,f314,f11312]) ).
fof(f11312,plain,
( spl0_725
<=> ! [X0,X1] :
( f18(image(X0,X1)) = second(f22(f18(image(X0,X1)),X0,X1))
| relation(image(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_725])]) ).
fof(f1132,plain,
( ! [X0,X1] :
( f18(image(X0,X1)) = second(f22(f18(image(X0,X1)),X0,X1))
| relation(image(X0,X1)) )
| ~ spl0_30
| ~ spl0_108 ),
inference(resolution,[],[f1073,f315]) ).
fof(f11310,plain,
( spl0_724
| ~ spl0_75
| ~ spl0_107 ),
inference(avatar_split_clause,[],[f1108,f1068,f632,f11308]) ).
fof(f11308,plain,
( spl0_724
<=> ! [X0,X3,X2,X1] :
( ~ member(X0,image(cross_product(X1,X2),X3))
| member(first(first(f22(X0,cross_product(X1,X2),X3))),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_724])]) ).
fof(f1108,plain,
( ! [X2,X3,X0,X1] :
( ~ member(X0,image(cross_product(X1,X2),X3))
| member(first(first(f22(X0,cross_product(X1,X2),X3))),X1) )
| ~ spl0_75
| ~ spl0_107 ),
inference(resolution,[],[f1069,f633]) ).
fof(f11306,plain,
( spl0_723
| ~ spl0_77
| ~ spl0_107 ),
inference(avatar_split_clause,[],[f1107,f1068,f640,f11304]) ).
fof(f11304,plain,
( spl0_723
<=> ! [X0,X3,X2,X1] :
( ~ member(X0,image(cross_product(X1,X2),X3))
| member(second(first(f22(X0,cross_product(X1,X2),X3))),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_723])]) ).
fof(f1107,plain,
( ! [X2,X3,X0,X1] :
( ~ member(X0,image(cross_product(X1,X2),X3))
| member(second(first(f22(X0,cross_product(X1,X2),X3))),X2) )
| ~ spl0_77
| ~ spl0_107 ),
inference(resolution,[],[f1069,f641]) ).
fof(f11302,plain,
( spl0_722
| ~ spl0_97
| ~ spl0_104 ),
inference(avatar_split_clause,[],[f1059,f966,f852,f11300]) ).
fof(f11300,plain,
( spl0_722
<=> ! [X0,X3,X2,X1] :
( ~ member(X0,apply(compose(X1,X2),X3))
| little_set(f29(f28(X0,compose(X1,X2),X3),X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_722])]) ).
fof(f1059,plain,
( ! [X2,X3,X0,X1] :
( ~ member(X0,apply(compose(X1,X2),X3))
| little_set(f29(f28(X0,compose(X1,X2),X3),X1,X2)) )
| ~ spl0_97
| ~ spl0_104 ),
inference(resolution,[],[f967,f853]) ).
fof(f11298,plain,
( spl0_721
| ~ spl0_98
| ~ spl0_104 ),
inference(avatar_split_clause,[],[f1058,f966,f856,f11296]) ).
fof(f11296,plain,
( spl0_721
<=> ! [X0,X3,X2,X1] :
( ~ member(X0,apply(compose(X1,X2),X3))
| little_set(f30(f28(X0,compose(X1,X2),X3),X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_721])]) ).
fof(f1058,plain,
( ! [X2,X3,X0,X1] :
( ~ member(X0,apply(compose(X1,X2),X3))
| little_set(f30(f28(X0,compose(X1,X2),X3),X1,X2)) )
| ~ spl0_98
| ~ spl0_104 ),
inference(resolution,[],[f967,f857]) ).
fof(f11294,plain,
( spl0_720
| ~ spl0_99
| ~ spl0_104 ),
inference(avatar_split_clause,[],[f1057,f966,f860,f11292]) ).
fof(f11292,plain,
( spl0_720
<=> ! [X0,X3,X2,X1] :
( ~ member(X0,apply(compose(X1,X2),X3))
| little_set(f31(f28(X0,compose(X1,X2),X3),X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_720])]) ).
fof(f1057,plain,
( ! [X2,X3,X0,X1] :
( ~ member(X0,apply(compose(X1,X2),X3))
| little_set(f31(f28(X0,compose(X1,X2),X3),X1,X2)) )
| ~ spl0_99
| ~ spl0_104 ),
inference(resolution,[],[f967,f861]) ).
fof(f11263,plain,
( spl0_719
| ~ spl0_96
| ~ spl0_104 ),
inference(avatar_split_clause,[],[f1056,f966,f848,f11261]) ).
fof(f11261,plain,
( spl0_719
<=> ! [X0,X3,X2,X1] :
( ~ member(X0,apply(apply(X1,X2),X3))
| ordered_pair_predicate(f28(f28(X0,apply(X1,X2),X3),X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_719])]) ).
fof(f1056,plain,
( ! [X2,X3,X0,X1] :
( ~ member(X0,apply(apply(X1,X2),X3))
| ordered_pair_predicate(f28(f28(X0,apply(X1,X2),X3),X1,X2)) )
| ~ spl0_96
| ~ spl0_104 ),
inference(resolution,[],[f967,f849]) ).
fof(f11259,plain,
( spl0_718
| ~ spl0_94
| ~ spl0_104 ),
inference(avatar_split_clause,[],[f1051,f966,f840,f11257]) ).
fof(f11257,plain,
( spl0_718
<=> ! [X0,X3,X2,X1] :
( ~ member(X0,apply(image(X1,X2),X3))
| ordered_pair_predicate(f22(f28(X0,image(X1,X2),X3),X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_718])]) ).
fof(f1051,plain,
( ! [X2,X3,X0,X1] :
( ~ member(X0,apply(image(X1,X2),X3))
| ordered_pair_predicate(f22(f28(X0,image(X1,X2),X3),X1,X2)) )
| ~ spl0_94
| ~ spl0_104 ),
inference(resolution,[],[f967,f841]) ).
fof(f11255,plain,
( spl0_717
| ~ spl0_97
| ~ spl0_103 ),
inference(avatar_split_clause,[],[f1024,f960,f852,f11253]) ).
fof(f11253,plain,
( spl0_717
<=> ! [X0,X3,X2,X1] :
( ~ member(X0,image(X1,compose(X2,X3)))
| little_set(f29(f22(X0,X1,compose(X2,X3)),X2,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_717])]) ).
fof(f1024,plain,
( ! [X2,X3,X0,X1] :
( ~ member(X0,image(X1,compose(X2,X3)))
| little_set(f29(f22(X0,X1,compose(X2,X3)),X2,X3)) )
| ~ spl0_97
| ~ spl0_103 ),
inference(resolution,[],[f961,f853]) ).
fof(f11251,plain,
( spl0_716
| ~ spl0_98
| ~ spl0_103 ),
inference(avatar_split_clause,[],[f1023,f960,f856,f11249]) ).
fof(f11249,plain,
( spl0_716
<=> ! [X0,X3,X2,X1] :
( ~ member(X0,image(X1,compose(X2,X3)))
| little_set(f30(f22(X0,X1,compose(X2,X3)),X2,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_716])]) ).
fof(f1023,plain,
( ! [X2,X3,X0,X1] :
( ~ member(X0,image(X1,compose(X2,X3)))
| little_set(f30(f22(X0,X1,compose(X2,X3)),X2,X3)) )
| ~ spl0_98
| ~ spl0_103 ),
inference(resolution,[],[f961,f857]) ).
fof(f11247,plain,
( spl0_715
| ~ spl0_99
| ~ spl0_103 ),
inference(avatar_split_clause,[],[f1022,f960,f860,f11245]) ).
fof(f11245,plain,
( spl0_715
<=> ! [X0,X3,X2,X1] :
( ~ member(X0,image(X1,compose(X2,X3)))
| little_set(f31(f22(X0,X1,compose(X2,X3)),X2,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_715])]) ).
fof(f1022,plain,
( ! [X2,X3,X0,X1] :
( ~ member(X0,image(X1,compose(X2,X3)))
| little_set(f31(f22(X0,X1,compose(X2,X3)),X2,X3)) )
| ~ spl0_99
| ~ spl0_103 ),
inference(resolution,[],[f961,f861]) ).
fof(f11243,plain,
( spl0_714
| ~ spl0_96
| ~ spl0_103 ),
inference(avatar_split_clause,[],[f1021,f960,f848,f11241]) ).
fof(f11241,plain,
( spl0_714
<=> ! [X0,X3,X2,X1] :
( ~ member(X0,image(X1,apply(X2,X3)))
| ordered_pair_predicate(f28(f22(X0,X1,apply(X2,X3)),X2,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_714])]) ).
fof(f1021,plain,
( ! [X2,X3,X0,X1] :
( ~ member(X0,image(X1,apply(X2,X3)))
| ordered_pair_predicate(f28(f22(X0,X1,apply(X2,X3)),X2,X3)) )
| ~ spl0_96
| ~ spl0_103 ),
inference(resolution,[],[f961,f849]) ).
fof(f11239,plain,
( spl0_713
| ~ spl0_94
| ~ spl0_103 ),
inference(avatar_split_clause,[],[f1016,f960,f840,f11237]) ).
fof(f11237,plain,
( spl0_713
<=> ! [X0,X3,X2,X1] :
( ~ member(X0,image(X1,image(X2,X3)))
| ordered_pair_predicate(f22(f22(X0,X1,image(X2,X3)),X2,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_713])]) ).
fof(f1016,plain,
( ! [X2,X3,X0,X1] :
( ~ member(X0,image(X1,image(X2,X3)))
| ordered_pair_predicate(f22(f22(X0,X1,image(X2,X3)),X2,X3)) )
| ~ spl0_94
| ~ spl0_103 ),
inference(resolution,[],[f961,f841]) ).
fof(f11234,plain,
( spl0_712
| ~ spl0_40
| ~ spl0_101 ),
inference(avatar_split_clause,[],[f981,f952,f361,f11232]) ).
fof(f981,plain,
( ! [X0,X1] :
( f24(non_ordered_pair(X0,X1)) = X0
| f24(non_ordered_pair(X0,X1)) = X1
| non_ordered_pair(X0,X1) = empty_set )
| ~ spl0_40
| ~ spl0_101 ),
inference(resolution,[],[f953,f362]) ).
fof(f11229,plain,
( spl0_711
| ~ spl0_84
| ~ spl0_99 ),
inference(avatar_split_clause,[],[f949,f860,f668,f11227]) ).
fof(f949,plain,
( ! [X0,X1] :
( little_set(f31(f26(compose(X0,X1)),X0,X1))
| empty_set = compose(X0,X1)
| ~ little_set(compose(X0,X1)) )
| ~ spl0_84
| ~ spl0_99 ),
inference(resolution,[],[f861,f669]) ).
fof(f11224,plain,
( spl0_710
| ~ spl0_84
| ~ spl0_98 ),
inference(avatar_split_clause,[],[f940,f856,f668,f11222]) ).
fof(f940,plain,
( ! [X0,X1] :
( little_set(f30(f26(compose(X0,X1)),X0,X1))
| empty_set = compose(X0,X1)
| ~ little_set(compose(X0,X1)) )
| ~ spl0_84
| ~ spl0_98 ),
inference(resolution,[],[f857,f669]) ).
fof(f11220,plain,
( spl0_709
| ~ spl0_63
| ~ spl0_259 ),
inference(avatar_split_clause,[],[f3471,f3132,f474,f11218]) ).
fof(f11218,plain,
( spl0_709
<=> ! [X0] : disjoint(X0,complement(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_709])]) ).
fof(f3471,plain,
( ! [X0] : disjoint(X0,complement(X0))
| ~ spl0_63
| ~ spl0_259 ),
inference(duplicate_literal_removal,[],[f3461]) ).
fof(f3461,plain,
( ! [X0] :
( disjoint(X0,complement(X0))
| disjoint(X0,complement(X0)) )
| ~ spl0_63
| ~ spl0_259 ),
inference(resolution,[],[f3133,f475]) ).
fof(f11215,plain,
( spl0_708
| ~ spl0_84
| ~ spl0_97 ),
inference(avatar_split_clause,[],[f931,f852,f668,f11213]) ).
fof(f931,plain,
( ! [X0,X1] :
( little_set(f29(f26(compose(X0,X1)),X0,X1))
| empty_set = compose(X0,X1)
| ~ little_set(compose(X0,X1)) )
| ~ spl0_84
| ~ spl0_97 ),
inference(resolution,[],[f853,f669]) ).
fof(f11210,plain,
( spl0_707
| ~ spl0_84
| ~ spl0_96 ),
inference(avatar_split_clause,[],[f922,f848,f668,f11208]) ).
fof(f922,plain,
( ! [X0,X1] :
( ordered_pair_predicate(f28(f26(apply(X0,X1)),X0,X1))
| empty_set = apply(X0,X1)
| ~ little_set(apply(X0,X1)) )
| ~ spl0_84
| ~ spl0_96 ),
inference(resolution,[],[f849,f669]) ).
fof(f11206,plain,
( spl0_706
| ~ spl0_85
| ~ spl0_95 ),
inference(avatar_split_clause,[],[f914,f844,f672,f11204]) ).
fof(f11204,plain,
( spl0_706
<=> ! [X0,X1] :
( f27(X0,range_of(X1)) = second(f27(f27(X0,range_of(X1)),X1))
| ~ member(X0,range_of(range_of(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_706])]) ).
fof(f914,plain,
( ! [X0,X1] :
( f27(X0,range_of(X1)) = second(f27(f27(X0,range_of(X1)),X1))
| ~ member(X0,range_of(range_of(X1))) )
| ~ spl0_85
| ~ spl0_95 ),
inference(resolution,[],[f845,f673]) ).
fof(f11201,plain,
( spl0_705
| ~ spl0_84
| ~ spl0_95 ),
inference(avatar_split_clause,[],[f913,f844,f668,f11199]) ).
fof(f913,plain,
( ! [X0] :
( f26(range_of(X0)) = second(f27(f26(range_of(X0)),X0))
| empty_set = range_of(X0)
| ~ little_set(range_of(X0)) )
| ~ spl0_84
| ~ spl0_95 ),
inference(resolution,[],[f845,f669]) ).
fof(f11197,plain,
( spl0_704
| ~ spl0_78
| ~ spl0_95 ),
inference(avatar_split_clause,[],[f907,f844,f644,f11195]) ).
fof(f11195,plain,
( spl0_704
<=> ! [X0,X1] :
( f16(X0,range_of(X1)) = second(f27(f16(X0,range_of(X1)),X1))
| ~ member(X0,sigma(range_of(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_704])]) ).
fof(f907,plain,
( ! [X0,X1] :
( f16(X0,range_of(X1)) = second(f27(f16(X0,range_of(X1)),X1))
| ~ member(X0,sigma(range_of(X1))) )
| ~ spl0_78
| ~ spl0_95 ),
inference(resolution,[],[f845,f645]) ).
fof(f11193,plain,
( spl0_703
| ~ spl0_74
| ~ spl0_95 ),
inference(avatar_split_clause,[],[f906,f844,f628,f11191]) ).
fof(f11191,plain,
( spl0_703
<=> ! [X0,X1] :
( f8(X0,range_of(X1)) = second(f27(f8(X0,range_of(X1)),X1))
| ~ member(X0,domain_of(range_of(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_703])]) ).
fof(f906,plain,
( ! [X0,X1] :
( f8(X0,range_of(X1)) = second(f27(f8(X0,range_of(X1)),X1))
| ~ member(X0,domain_of(range_of(X1))) )
| ~ spl0_74
| ~ spl0_95 ),
inference(resolution,[],[f845,f629]) ).
fof(f11188,plain,
( spl0_702
| ~ spl0_84
| ~ spl0_94 ),
inference(avatar_split_clause,[],[f904,f840,f668,f11186]) ).
fof(f904,plain,
( ! [X0,X1] :
( ordered_pair_predicate(f22(f26(image(X0,X1)),X0,X1))
| empty_set = image(X0,X1)
| ~ little_set(image(X0,X1)) )
| ~ spl0_84
| ~ spl0_94 ),
inference(resolution,[],[f841,f669]) ).
fof(f11184,plain,
( spl0_701
| ~ spl0_85
| ~ spl0_91 ),
inference(avatar_split_clause,[],[f875,f828,f672,f11182]) ).
fof(f11182,plain,
( spl0_701
<=> ! [X0,X1] :
( f27(X0,domain_of(X1)) = first(f8(f27(X0,domain_of(X1)),X1))
| ~ member(X0,range_of(domain_of(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_701])]) ).
fof(f875,plain,
( ! [X0,X1] :
( f27(X0,domain_of(X1)) = first(f8(f27(X0,domain_of(X1)),X1))
| ~ member(X0,range_of(domain_of(X1))) )
| ~ spl0_85
| ~ spl0_91 ),
inference(resolution,[],[f829,f673]) ).
fof(f11179,plain,
( spl0_700
| ~ spl0_84
| ~ spl0_91 ),
inference(avatar_split_clause,[],[f874,f828,f668,f11177]) ).
fof(f874,plain,
( ! [X0] :
( f26(domain_of(X0)) = first(f8(f26(domain_of(X0)),X0))
| domain_of(X0) = empty_set
| ~ little_set(domain_of(X0)) )
| ~ spl0_84
| ~ spl0_91 ),
inference(resolution,[],[f829,f669]) ).
fof(f11175,plain,
( spl0_699
| ~ spl0_78
| ~ spl0_91 ),
inference(avatar_split_clause,[],[f868,f828,f644,f11173]) ).
fof(f11173,plain,
( spl0_699
<=> ! [X0,X1] :
( f16(X0,domain_of(X1)) = first(f8(f16(X0,domain_of(X1)),X1))
| ~ member(X0,sigma(domain_of(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_699])]) ).
fof(f868,plain,
( ! [X0,X1] :
( f16(X0,domain_of(X1)) = first(f8(f16(X0,domain_of(X1)),X1))
| ~ member(X0,sigma(domain_of(X1))) )
| ~ spl0_78
| ~ spl0_91 ),
inference(resolution,[],[f829,f645]) ).
fof(f11171,plain,
( spl0_698
| ~ spl0_64
| ~ spl0_257 ),
inference(avatar_split_clause,[],[f3458,f3124,f478,f11169]) ).
fof(f11169,plain,
( spl0_698
<=> ! [X0] : disjoint(complement(X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_698])]) ).
fof(f3458,plain,
( ! [X0] : disjoint(complement(X0),X0)
| ~ spl0_64
| ~ spl0_257 ),
inference(duplicate_literal_removal,[],[f3448]) ).
fof(f3448,plain,
( ! [X0] :
( disjoint(complement(X0),X0)
| disjoint(complement(X0),X0) )
| ~ spl0_64
| ~ spl0_257 ),
inference(resolution,[],[f3125,f479]) ).
fof(f11167,plain,
( spl0_697
| ~ spl0_74
| ~ spl0_91 ),
inference(avatar_split_clause,[],[f867,f828,f628,f11165]) ).
fof(f11165,plain,
( spl0_697
<=> ! [X0,X1] :
( f8(X0,domain_of(X1)) = first(f8(f8(X0,domain_of(X1)),X1))
| ~ member(X0,domain_of(domain_of(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_697])]) ).
fof(f867,plain,
( ! [X0,X1] :
( f8(X0,domain_of(X1)) = first(f8(f8(X0,domain_of(X1)),X1))
| ~ member(X0,domain_of(domain_of(X1))) )
| ~ spl0_74
| ~ spl0_91 ),
inference(resolution,[],[f829,f629]) ).
fof(f10771,plain,
( spl0_696
| ~ spl0_40
| ~ spl0_119
| ~ spl0_173
| ~ spl0_246 ),
inference(avatar_split_clause,[],[f3379,f3071,f2440,f1266,f361,f10769]) ).
fof(f10769,plain,
( spl0_696
<=> ! [X0] : relation(intersection(X0,estin)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_696])]) ).
fof(f3379,plain,
( ! [X0] : relation(intersection(X0,estin))
| ~ spl0_40
| ~ spl0_119
| ~ spl0_173
| ~ spl0_246 ),
inference(forward_demodulation,[],[f3378,f2442]) ).
fof(f10298,plain,
( spl0_695
| ~ spl0_40
| ~ spl0_119
| ~ spl0_173
| ~ spl0_245 ),
inference(avatar_split_clause,[],[f3299,f3067,f2440,f1266,f361,f10296]) ).
fof(f10296,plain,
( spl0_695
<=> ! [X0] : relation(intersection(estin,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_695])]) ).
fof(f3299,plain,
( ! [X0] : relation(intersection(estin,X0))
| ~ spl0_40
| ~ spl0_119
| ~ spl0_173
| ~ spl0_245 ),
inference(forward_demodulation,[],[f3298,f2442]) ).
fof(f9976,plain,
( spl0_694
| ~ spl0_19
| ~ spl0_211 ),
inference(avatar_split_clause,[],[f2982,f2880,f265,f9974]) ).
fof(f9974,plain,
( spl0_694
<=> ! [X0,X1] : relation(cross_product(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_694])]) ).
fof(f2880,plain,
( spl0_211
<=> ! [X0,X1] :
( ordered_pair_predicate(f18(cross_product(X0,X1)))
| relation(cross_product(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_211])]) ).
fof(f2982,plain,
( ! [X0,X1] : relation(cross_product(X0,X1))
| ~ spl0_19
| ~ spl0_211 ),
inference(duplicate_literal_removal,[],[f2980]) ).
fof(f2980,plain,
( ! [X0,X1] :
( relation(cross_product(X0,X1))
| relation(cross_product(X0,X1)) )
| ~ spl0_19
| ~ spl0_211 ),
inference(resolution,[],[f2881,f266]) ).
fof(f2881,plain,
( ! [X0,X1] :
( ordered_pair_predicate(f18(cross_product(X0,X1)))
| relation(cross_product(X0,X1)) )
| ~ spl0_211 ),
inference(avatar_component_clause,[],[f2880]) ).
fof(f9972,plain,
( spl0_693
| ~ spl0_173
| ~ spl0_655 ),
inference(avatar_split_clause,[],[f9808,f9805,f2440,f9970]) ).
fof(f9970,plain,
( spl0_693
<=> ! [X0,X1] :
( estin = cross_product(X0,X1)
| ~ little_set(cross_product(X0,X1))
| member(first(f26(cross_product(X0,X1))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_693])]) ).
fof(f9805,plain,
( spl0_655
<=> ! [X0,X1] :
( cross_product(X0,X1) = empty_set
| ~ little_set(cross_product(X0,X1))
| member(first(f26(cross_product(X0,X1))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_655])]) ).
fof(f9808,plain,
( ! [X0,X1] :
( estin = cross_product(X0,X1)
| ~ little_set(cross_product(X0,X1))
| member(first(f26(cross_product(X0,X1))),X0) )
| ~ spl0_173
| ~ spl0_655 ),
inference(forward_demodulation,[],[f9806,f2442]) ).
fof(f9806,plain,
( ! [X0,X1] :
( cross_product(X0,X1) = empty_set
| ~ little_set(cross_product(X0,X1))
| member(first(f26(cross_product(X0,X1))),X0) )
| ~ spl0_655 ),
inference(avatar_component_clause,[],[f9805]) ).
fof(f9968,plain,
( spl0_692
| ~ spl0_173
| ~ spl0_654 ),
inference(avatar_split_clause,[],[f9803,f9800,f2440,f9966]) ).
fof(f9966,plain,
( spl0_692
<=> ! [X0,X1] :
( estin = cross_product(X0,X1)
| ~ little_set(cross_product(X0,X1))
| member(second(f26(cross_product(X0,X1))),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_692])]) ).
fof(f9800,plain,
( spl0_654
<=> ! [X0,X1] :
( cross_product(X0,X1) = empty_set
| ~ little_set(cross_product(X0,X1))
| member(second(f26(cross_product(X0,X1))),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_654])]) ).
fof(f9803,plain,
( ! [X0,X1] :
( estin = cross_product(X0,X1)
| ~ little_set(cross_product(X0,X1))
| member(second(f26(cross_product(X0,X1))),X1) )
| ~ spl0_173
| ~ spl0_654 ),
inference(forward_demodulation,[],[f9801,f2442]) ).
fof(f9801,plain,
( ! [X0,X1] :
( cross_product(X0,X1) = empty_set
| ~ little_set(cross_product(X0,X1))
| member(second(f26(cross_product(X0,X1))),X1) )
| ~ spl0_654 ),
inference(avatar_component_clause,[],[f9800]) ).
fof(f9961,plain,
( spl0_691
| ~ spl0_4
| ~ spl0_134 ),
inference(avatar_split_clause,[],[f1581,f1544,f201,f9959]) ).
fof(f9959,plain,
( spl0_691
<=> ! [X0,X3,X2,X1] :
( ~ closed(X0,X1)
| ~ maps(X2,empty_set,X0)
| homomorphism(X2,empty_set,X3,X0,X1)
| ~ closed(empty_set,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_691])]) ).
fof(f1581,plain,
( ! [X2,X3,X0,X1] :
( ~ closed(X0,X1)
| ~ maps(X2,empty_set,X0)
| homomorphism(X2,empty_set,X3,X0,X1)
| ~ closed(empty_set,X3) )
| ~ spl0_4
| ~ spl0_134 ),
inference(resolution,[],[f1545,f202]) ).
fof(f9955,plain,
( spl0_690
| ~ spl0_23
| ~ spl0_127 ),
inference(avatar_split_clause,[],[f1447,f1397,f281,f9953]) ).
fof(f9953,plain,
( spl0_690
<=> ! [X0] :
( ~ member(X0,converse(identity_relation))
| ordered_pair_predicate(non_ordered_pair(non_ordered_pair(second(X0),second(X0)),non_ordered_pair(second(X0),first(X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_690])]) ).
fof(f1447,plain,
( ! [X0] :
( ~ member(X0,converse(identity_relation))
| ordered_pair_predicate(non_ordered_pair(non_ordered_pair(second(X0),second(X0)),non_ordered_pair(second(X0),first(X0)))) )
| ~ spl0_23
| ~ spl0_127 ),
inference(resolution,[],[f1398,f282]) ).
fof(f9951,plain,
( spl0_689
| ~ spl0_38
| ~ spl0_124 ),
inference(avatar_split_clause,[],[f1388,f1299,f353,f9949]) ).
fof(f9949,plain,
( spl0_689
<=> ! [X2,X0,X1] :
( ~ member(X0,X1)
| ~ member(X2,second(X0))
| ~ ordered_pair_predicate(X0)
| ordered_pair_predicate(X2)
| ~ relation(apply(X1,first(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_689])]) ).
fof(f1388,plain,
( ! [X2,X0,X1] :
( ~ member(X0,X1)
| ~ member(X2,second(X0))
| ~ ordered_pair_predicate(X0)
| ordered_pair_predicate(X2)
| ~ relation(apply(X1,first(X0))) )
| ~ spl0_38
| ~ spl0_124 ),
inference(resolution,[],[f1300,f354]) ).
fof(f9946,plain,
( spl0_688
| ~ spl0_173
| ~ spl0_687 ),
inference(avatar_split_clause,[],[f9942,f9939,f2440,f9944]) ).
fof(f9944,plain,
( spl0_688
<=> ! [X0] :
( estin = X0
| ordered_pair_predicate(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,f26(X0))))
| ~ little_set(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_688])]) ).
fof(f9939,plain,
( spl0_687
<=> ! [X0] :
( empty_set = X0
| ordered_pair_predicate(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,f26(X0))))
| ~ little_set(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_687])]) ).
fof(f9942,plain,
( ! [X0] :
( estin = X0
| ordered_pair_predicate(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,f26(X0))))
| ~ little_set(X0) )
| ~ spl0_173
| ~ spl0_687 ),
inference(forward_demodulation,[],[f9940,f2442]) ).
fof(f9940,plain,
( ! [X0] :
( empty_set = X0
| ordered_pair_predicate(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,f26(X0))))
| ~ little_set(X0) )
| ~ spl0_687 ),
inference(avatar_component_clause,[],[f9939]) ).
fof(f9941,plain,
( ~ spl0_14
| spl0_687
| ~ spl0_38
| ~ spl0_123 ),
inference(avatar_split_clause,[],[f1383,f1295,f353,f9939,f244]) ).
fof(f244,plain,
( spl0_14
<=> relation(f25) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).
fof(f1383,plain,
( ! [X0] :
( empty_set = X0
| ~ little_set(X0)
| ordered_pair_predicate(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,f26(X0))))
| ~ relation(f25) )
| ~ spl0_38
| ~ spl0_123 ),
inference(resolution,[],[f1296,f354]) ).
fof(f9937,plain,
( spl0_686
| ~ spl0_38
| ~ spl0_122 ),
inference(avatar_split_clause,[],[f1346,f1291,f353,f9935]) ).
fof(f9935,plain,
( spl0_686
<=> ! [X0] :
( single_valued_set(X0)
| ordered_pair_predicate(non_ordered_pair(non_ordered_pair(f19(X0),f19(X0)),non_ordered_pair(f19(X0),f21(X0))))
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_686])]) ).
fof(f1346,plain,
( ! [X0] :
( single_valued_set(X0)
| ordered_pair_predicate(non_ordered_pair(non_ordered_pair(f19(X0),f19(X0)),non_ordered_pair(f19(X0),f21(X0))))
| ~ relation(X0) )
| ~ spl0_38
| ~ spl0_122 ),
inference(resolution,[],[f1292,f354]) ).
fof(f9933,plain,
( spl0_685
| ~ spl0_38
| ~ spl0_121 ),
inference(avatar_split_clause,[],[f1304,f1287,f353,f9931]) ).
fof(f9931,plain,
( spl0_685
<=> ! [X0] :
( single_valued_set(X0)
| ordered_pair_predicate(non_ordered_pair(non_ordered_pair(f19(X0),f19(X0)),non_ordered_pair(f19(X0),f20(X0))))
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_685])]) ).
fof(f1304,plain,
( ! [X0] :
( single_valued_set(X0)
| ordered_pair_predicate(non_ordered_pair(non_ordered_pair(f19(X0),f19(X0)),non_ordered_pair(f19(X0),f20(X0))))
| ~ relation(X0) )
| ~ spl0_38
| ~ spl0_121 ),
inference(resolution,[],[f1288,f354]) ).
fof(f9929,plain,
( spl0_684
| ~ spl0_141
| ~ spl0_173
| ~ spl0_209 ),
inference(avatar_split_clause,[],[f2807,f2733,f2440,f1749,f9926]) ).
fof(f9926,plain,
( spl0_684
<=> estin = range_of(estin) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_684])]) ).
fof(f2807,plain,
( estin = range_of(estin)
| ~ spl0_141
| ~ spl0_173
| ~ spl0_209 ),
inference(forward_demodulation,[],[f2787,f2442]) ).
fof(f2787,plain,
( estin = range_of(empty_set)
| ~ spl0_141
| ~ spl0_209 ),
inference(resolution,[],[f2734,f1750]) ).
fof(f9924,plain,
( spl0_683
| ~ spl0_95
| ~ spl0_118 ),
inference(avatar_split_clause,[],[f1277,f1179,f844,f9922]) ).
fof(f9922,plain,
( spl0_683
<=> ! [X0,X1] :
( ~ little_set(second(X0))
| ~ member(X0,X1)
| ~ ordered_pair_predicate(X0)
| second(X0) = second(f27(second(X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_683])]) ).
fof(f1277,plain,
( ! [X0,X1] :
( ~ little_set(second(X0))
| ~ member(X0,X1)
| ~ ordered_pair_predicate(X0)
| second(X0) = second(f27(second(X0),X1)) )
| ~ spl0_95
| ~ spl0_118 ),
inference(resolution,[],[f1180,f845]) ).
fof(f9920,plain,
( spl0_682
| ~ spl0_91
| ~ spl0_117 ),
inference(avatar_split_clause,[],[f1272,f1175,f828,f9918]) ).
fof(f9918,plain,
( spl0_682
<=> ! [X0,X1] :
( ~ little_set(first(X0))
| ~ member(X0,X1)
| ~ ordered_pair_predicate(X0)
| first(X0) = first(f8(first(X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_682])]) ).
fof(f1272,plain,
( ! [X0,X1] :
( ~ little_set(first(X0))
| ~ member(X0,X1)
| ~ ordered_pair_predicate(X0)
| first(X0) = first(f8(first(X0),X1)) )
| ~ spl0_91
| ~ spl0_117 ),
inference(resolution,[],[f1176,f829]) ).
fof(f9916,plain,
( spl0_681
| ~ spl0_37
| ~ spl0_113 ),
inference(avatar_split_clause,[],[f1244,f1159,f349,f9914]) ).
fof(f9914,plain,
( spl0_681
<=> ! [X0,X1] :
( member(f1(powerset(X0),X1),X1)
| powerset(X0) = X1
| subset(f1(powerset(X0),X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_681])]) ).
fof(f1244,plain,
( ! [X0,X1] :
( member(f1(powerset(X0),X1),X1)
| powerset(X0) = X1
| subset(f1(powerset(X0),X1),X0) )
| ~ spl0_37
| ~ spl0_113 ),
inference(resolution,[],[f1160,f350]) ).
fof(f9912,plain,
( spl0_680
| ~ spl0_34
| ~ spl0_113 ),
inference(avatar_split_clause,[],[f1230,f1159,f336,f9910]) ).
fof(f9910,plain,
( spl0_680
<=> ! [X0,X1] :
( member(f1(complement(X0),X1),X1)
| complement(X0) = X1
| ~ member(f1(complement(X0),X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_680])]) ).
fof(f1230,plain,
( ! [X0,X1] :
( member(f1(complement(X0),X1),X1)
| complement(X0) = X1
| ~ member(f1(complement(X0),X1),X0) )
| ~ spl0_34
| ~ spl0_113 ),
inference(resolution,[],[f1160,f337]) ).
fof(f9908,plain,
( spl0_679
| ~ spl0_37
| ~ spl0_113 ),
inference(avatar_split_clause,[],[f1207,f1159,f349,f9906]) ).
fof(f9906,plain,
( spl0_679
<=> ! [X0,X1] :
( member(f1(X0,powerset(X1)),X0)
| powerset(X1) = X0
| subset(f1(X0,powerset(X1)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_679])]) ).
fof(f1207,plain,
( ! [X0,X1] :
( member(f1(X0,powerset(X1)),X0)
| powerset(X1) = X0
| subset(f1(X0,powerset(X1)),X1) )
| ~ spl0_37
| ~ spl0_113 ),
inference(resolution,[],[f1160,f350]) ).
fof(f9904,plain,
( spl0_678
| ~ spl0_34
| ~ spl0_113 ),
inference(avatar_split_clause,[],[f1193,f1159,f336,f9902]) ).
fof(f9902,plain,
( spl0_678
<=> ! [X0,X1] :
( member(f1(X0,complement(X1)),X0)
| complement(X1) = X0
| ~ member(f1(X0,complement(X1)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_678])]) ).
fof(f1193,plain,
( ! [X0,X1] :
( member(f1(X0,complement(X1)),X0)
| complement(X1) = X0
| ~ member(f1(X0,complement(X1)),X1) )
| ~ spl0_34
| ~ spl0_113 ),
inference(resolution,[],[f1160,f337]) ).
fof(f9900,plain,
( spl0_677
| ~ spl0_93
| ~ spl0_111 ),
inference(avatar_split_clause,[],[f1154,f1085,f836,f9898]) ).
fof(f1154,plain,
( ! [X2,X3,X0,X1] :
( ~ member(X0,apply(X1,X2))
| ~ member(second(f28(X0,X1,X2)),X3)
| member(X0,sigma(X3)) )
| ~ spl0_93
| ~ spl0_111 ),
inference(resolution,[],[f1086,f837]) ).
fof(f9896,plain,
( spl0_676
| ~ spl0_64
| ~ spl0_110 ),
inference(avatar_split_clause,[],[f1147,f1081,f478,f9894]) ).
fof(f9894,plain,
( spl0_676
<=> ! [X2,X0,X1] :
( first(f28(f23(X0,apply(X1,X2)),X1,X2)) = X2
| disjoint(X0,apply(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_676])]) ).
fof(f1147,plain,
( ! [X2,X0,X1] :
( first(f28(f23(X0,apply(X1,X2)),X1,X2)) = X2
| disjoint(X0,apply(X1,X2)) )
| ~ spl0_64
| ~ spl0_110 ),
inference(resolution,[],[f1082,f479]) ).
fof(f9892,plain,
( spl0_675
| ~ spl0_63
| ~ spl0_110 ),
inference(avatar_split_clause,[],[f1146,f1081,f474,f9890]) ).
fof(f9890,plain,
( spl0_675
<=> ! [X2,X0,X1] :
( first(f28(f23(apply(X0,X1),X2),X0,X1)) = X1
| disjoint(apply(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_675])]) ).
fof(f1146,plain,
( ! [X2,X0,X1] :
( first(f28(f23(apply(X0,X1),X2),X0,X1)) = X1
| disjoint(apply(X0,X1),X2) )
| ~ spl0_63
| ~ spl0_110 ),
inference(resolution,[],[f1082,f475]) ).
fof(f9888,plain,
( spl0_674
| ~ spl0_60
| ~ spl0_110 ),
inference(avatar_split_clause,[],[f1143,f1081,f462,f9886]) ).
fof(f9886,plain,
( spl0_674
<=> ! [X2,X0,X1] :
( first(f28(f17(apply(X0,X1),X2),X0,X1)) = X1
| subset(apply(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_674])]) ).
fof(f1143,plain,
( ! [X2,X0,X1] :
( first(f28(f17(apply(X0,X1),X2),X0,X1)) = X1
| subset(apply(X0,X1),X2) )
| ~ spl0_60
| ~ spl0_110 ),
inference(resolution,[],[f1082,f463]) ).
fof(f9884,plain,
( spl0_673
| ~ spl0_135
| ~ spl0_173
| ~ spl0_209 ),
inference(avatar_split_clause,[],[f2804,f2733,f2440,f1548,f9881]) ).
fof(f9881,plain,
( spl0_673
<=> estin = sigma(estin) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_673])]) ).
fof(f2804,plain,
( estin = sigma(estin)
| ~ spl0_135
| ~ spl0_173
| ~ spl0_209 ),
inference(forward_demodulation,[],[f2777,f2442]) ).
fof(f2777,plain,
( estin = sigma(empty_set)
| ~ spl0_135
| ~ spl0_209 ),
inference(resolution,[],[f2734,f1549]) ).
fof(f9879,plain,
( spl0_672
| ~ spl0_51
| ~ spl0_107 ),
inference(avatar_split_clause,[],[f1103,f1068,f426,f9877]) ).
fof(f9877,plain,
( spl0_672
<=> ! [X0,X3,X2,X1] :
( ~ member(X0,image(intersection(X1,X2),X3))
| member(first(f22(X0,intersection(X1,X2),X3)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_672])]) ).
fof(f1103,plain,
( ! [X2,X3,X0,X1] :
( ~ member(X0,image(intersection(X1,X2),X3))
| member(first(f22(X0,intersection(X1,X2),X3)),X1) )
| ~ spl0_51
| ~ spl0_107 ),
inference(resolution,[],[f1069,f427]) ).
fof(f9875,plain,
( spl0_671
| ~ spl0_52
| ~ spl0_107 ),
inference(avatar_split_clause,[],[f1102,f1068,f430,f9873]) ).
fof(f9873,plain,
( spl0_671
<=> ! [X0,X3,X2,X1] :
( ~ member(X0,image(intersection(X1,X2),X3))
| member(first(f22(X0,intersection(X1,X2),X3)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_671])]) ).
fof(f1102,plain,
( ! [X2,X3,X0,X1] :
( ~ member(X0,image(intersection(X1,X2),X3))
| member(first(f22(X0,intersection(X1,X2),X3)),X2) )
| ~ spl0_52
| ~ spl0_107 ),
inference(resolution,[],[f1069,f431]) ).
fof(f9871,plain,
( spl0_670
| ~ spl0_93
| ~ spl0_107 ),
inference(avatar_split_clause,[],[f1093,f1068,f836,f9869]) ).
fof(f9869,plain,
( spl0_670
<=> ! [X0,X3,X2,X1] :
( ~ member(X0,image(X1,X2))
| ~ member(X1,X3)
| member(first(f22(X0,X1,X2)),sigma(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_670])]) ).
fof(f1093,plain,
( ! [X2,X3,X0,X1] :
( ~ member(X0,image(X1,X2))
| ~ member(X1,X3)
| member(first(f22(X0,X1,X2)),sigma(X3)) )
| ~ spl0_93
| ~ spl0_107 ),
inference(resolution,[],[f1069,f837]) ).
fof(f9866,plain,
( spl0_669
| ~ spl0_66
| ~ spl0_104 ),
inference(avatar_split_clause,[],[f1054,f966,f486,f9864]) ).
fof(f9864,plain,
( spl0_669
<=> ! [X0,X1] :
( ~ member(X0,apply(identity_relation,X1))
| first(f28(X0,identity_relation,X1)) = second(f28(X0,identity_relation,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_669])]) ).
fof(f1054,plain,
( ! [X0,X1] :
( ~ member(X0,apply(identity_relation,X1))
| first(f28(X0,identity_relation,X1)) = second(f28(X0,identity_relation,X1)) )
| ~ spl0_66
| ~ spl0_104 ),
inference(resolution,[],[f967,f487]) ).
fof(f9862,plain,
( spl0_668
| ~ spl0_75
| ~ spl0_104 ),
inference(avatar_split_clause,[],[f1040,f966,f632,f9860]) ).
fof(f9860,plain,
( spl0_668
<=> ! [X0,X3,X2,X1] :
( ~ member(X0,apply(cross_product(X1,X2),X3))
| member(first(f28(X0,cross_product(X1,X2),X3)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_668])]) ).
fof(f1040,plain,
( ! [X2,X3,X0,X1] :
( ~ member(X0,apply(cross_product(X1,X2),X3))
| member(first(f28(X0,cross_product(X1,X2),X3)),X1) )
| ~ spl0_75
| ~ spl0_104 ),
inference(resolution,[],[f967,f633]) ).
fof(f9858,plain,
( spl0_667
| ~ spl0_77
| ~ spl0_104 ),
inference(avatar_split_clause,[],[f1039,f966,f640,f9856]) ).
fof(f1039,plain,
( ! [X2,X3,X0,X1] :
( ~ member(X0,apply(cross_product(X1,X2),X3))
| member(second(f28(X0,cross_product(X1,X2),X3)),X2) )
| ~ spl0_77
| ~ spl0_104 ),
inference(resolution,[],[f967,f641]) ).
fof(f9853,plain,
( spl0_666
| ~ spl0_66
| ~ spl0_103 ),
inference(avatar_split_clause,[],[f1019,f960,f486,f9851]) ).
fof(f9851,plain,
( spl0_666
<=> ! [X0,X1] :
( ~ member(X0,image(X1,identity_relation))
| first(f22(X0,X1,identity_relation)) = second(f22(X0,X1,identity_relation)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_666])]) ).
fof(f1019,plain,
( ! [X0,X1] :
( ~ member(X0,image(X1,identity_relation))
| first(f22(X0,X1,identity_relation)) = second(f22(X0,X1,identity_relation)) )
| ~ spl0_66
| ~ spl0_103 ),
inference(resolution,[],[f961,f487]) ).
fof(f9849,plain,
( spl0_665
| ~ spl0_75
| ~ spl0_103 ),
inference(avatar_split_clause,[],[f1005,f960,f632,f9847]) ).
fof(f1005,plain,
( ! [X2,X3,X0,X1] :
( ~ member(X0,image(X1,cross_product(X2,X3)))
| member(first(f22(X0,X1,cross_product(X2,X3))),X2) )
| ~ spl0_75
| ~ spl0_103 ),
inference(resolution,[],[f961,f633]) ).
fof(f9845,plain,
( spl0_664
| ~ spl0_77
| ~ spl0_103 ),
inference(avatar_split_clause,[],[f1004,f960,f640,f9843]) ).
fof(f9843,plain,
( spl0_664
<=> ! [X0,X3,X2,X1] :
( ~ member(X0,image(X1,cross_product(X2,X3)))
| member(second(f22(X0,X1,cross_product(X2,X3))),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_664])]) ).
fof(f1004,plain,
( ! [X2,X3,X0,X1] :
( ~ member(X0,image(X1,cross_product(X2,X3)))
| member(second(f22(X0,X1,cross_product(X2,X3))),X3) )
| ~ spl0_77
| ~ spl0_103 ),
inference(resolution,[],[f961,f641]) ).
fof(f9841,plain,
( spl0_663
| ~ spl0_30
| ~ spl0_101 ),
inference(avatar_split_clause,[],[f978,f952,f314,f9839]) ).
fof(f9839,plain,
( spl0_663
<=> ! [X0,X1] :
( f18(non_ordered_pair(X0,X1)) = X0
| f18(non_ordered_pair(X0,X1)) = X1
| relation(non_ordered_pair(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_663])]) ).
fof(f978,plain,
( ! [X0,X1] :
( f18(non_ordered_pair(X0,X1)) = X0
| f18(non_ordered_pair(X0,X1)) = X1
| relation(non_ordered_pair(X0,X1)) )
| ~ spl0_30
| ~ spl0_101 ),
inference(resolution,[],[f953,f315]) ).
fof(f9837,plain,
( spl0_662
| ~ spl0_153
| ~ spl0_173
| ~ spl0_209 ),
inference(avatar_split_clause,[],[f2803,f2733,f2440,f2098,f9834]) ).
fof(f9834,plain,
( spl0_662
<=> estin = flip_range_of(estin) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_662])]) ).
fof(f2803,plain,
( estin = flip_range_of(estin)
| ~ spl0_153
| ~ spl0_173
| ~ spl0_209 ),
inference(forward_demodulation,[],[f2775,f2442]) ).
fof(f2775,plain,
( estin = flip_range_of(empty_set)
| ~ spl0_153
| ~ spl0_209 ),
inference(resolution,[],[f2734,f2099]) ).
fof(f9832,plain,
( spl0_661
| ~ spl0_64
| ~ spl0_95 ),
inference(avatar_split_clause,[],[f911,f844,f478,f9830]) ).
fof(f9830,plain,
( spl0_661
<=> ! [X0,X1] :
( f23(X0,range_of(X1)) = second(f27(f23(X0,range_of(X1)),X1))
| disjoint(X0,range_of(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_661])]) ).
fof(f911,plain,
( ! [X0,X1] :
( f23(X0,range_of(X1)) = second(f27(f23(X0,range_of(X1)),X1))
| disjoint(X0,range_of(X1)) )
| ~ spl0_64
| ~ spl0_95 ),
inference(resolution,[],[f845,f479]) ).
fof(f9828,plain,
( spl0_660
| ~ spl0_63
| ~ spl0_95 ),
inference(avatar_split_clause,[],[f910,f844,f474,f9826]) ).
fof(f9826,plain,
( spl0_660
<=> ! [X0,X1] :
( f23(range_of(X0),X1) = second(f27(f23(range_of(X0),X1),X0))
| disjoint(range_of(X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_660])]) ).
fof(f910,plain,
( ! [X0,X1] :
( f23(range_of(X0),X1) = second(f27(f23(range_of(X0),X1),X0))
| disjoint(range_of(X0),X1) )
| ~ spl0_63
| ~ spl0_95 ),
inference(resolution,[],[f845,f475]) ).
fof(f9824,plain,
( spl0_659
| ~ spl0_60
| ~ spl0_95 ),
inference(avatar_split_clause,[],[f908,f844,f462,f9822]) ).
fof(f9822,plain,
( spl0_659
<=> ! [X0,X1] :
( f17(range_of(X0),X1) = second(f27(f17(range_of(X0),X1),X0))
| subset(range_of(X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_659])]) ).
fof(f908,plain,
( ! [X0,X1] :
( f17(range_of(X0),X1) = second(f27(f17(range_of(X0),X1),X0))
| subset(range_of(X0),X1) )
| ~ spl0_60
| ~ spl0_95 ),
inference(resolution,[],[f845,f463]) ).
fof(f9820,plain,
( spl0_658
| ~ spl0_64
| ~ spl0_91 ),
inference(avatar_split_clause,[],[f872,f828,f478,f9818]) ).
fof(f9818,plain,
( spl0_658
<=> ! [X0,X1] :
( f23(X0,domain_of(X1)) = first(f8(f23(X0,domain_of(X1)),X1))
| disjoint(X0,domain_of(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_658])]) ).
fof(f872,plain,
( ! [X0,X1] :
( f23(X0,domain_of(X1)) = first(f8(f23(X0,domain_of(X1)),X1))
| disjoint(X0,domain_of(X1)) )
| ~ spl0_64
| ~ spl0_91 ),
inference(resolution,[],[f829,f479]) ).
fof(f9816,plain,
( spl0_657
| ~ spl0_63
| ~ spl0_91 ),
inference(avatar_split_clause,[],[f871,f828,f474,f9814]) ).
fof(f9814,plain,
( spl0_657
<=> ! [X0,X1] :
( f23(domain_of(X0),X1) = first(f8(f23(domain_of(X0),X1),X0))
| disjoint(domain_of(X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_657])]) ).
fof(f871,plain,
( ! [X0,X1] :
( f23(domain_of(X0),X1) = first(f8(f23(domain_of(X0),X1),X0))
| disjoint(domain_of(X0),X1) )
| ~ spl0_63
| ~ spl0_91 ),
inference(resolution,[],[f829,f475]) ).
fof(f9812,plain,
( spl0_656
| ~ spl0_60
| ~ spl0_91 ),
inference(avatar_split_clause,[],[f869,f828,f462,f9810]) ).
fof(f9810,plain,
( spl0_656
<=> ! [X0,X1] :
( f17(domain_of(X0),X1) = first(f8(f17(domain_of(X0),X1),X0))
| subset(domain_of(X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_656])]) ).
fof(f869,plain,
( ! [X0,X1] :
( f17(domain_of(X0),X1) = first(f8(f17(domain_of(X0),X1),X0))
| subset(domain_of(X0),X1) )
| ~ spl0_60
| ~ spl0_91 ),
inference(resolution,[],[f829,f463]) ).
fof(f9807,plain,
( spl0_655
| ~ spl0_75
| ~ spl0_84 ),
inference(avatar_split_clause,[],[f784,f668,f632,f9805]) ).
fof(f784,plain,
( ! [X0,X1] :
( cross_product(X0,X1) = empty_set
| ~ little_set(cross_product(X0,X1))
| member(first(f26(cross_product(X0,X1))),X0) )
| ~ spl0_75
| ~ spl0_84 ),
inference(resolution,[],[f669,f633]) ).
fof(f9802,plain,
( spl0_654
| ~ spl0_77
| ~ spl0_84 ),
inference(avatar_split_clause,[],[f783,f668,f640,f9800]) ).
fof(f783,plain,
( ! [X0,X1] :
( cross_product(X0,X1) = empty_set
| ~ little_set(cross_product(X0,X1))
| member(second(f26(cross_product(X0,X1))),X1) )
| ~ spl0_77
| ~ spl0_84 ),
inference(resolution,[],[f669,f641]) ).
fof(f9638,plain,
( spl0_653
| ~ spl0_154
| ~ spl0_173
| ~ spl0_209 ),
inference(avatar_split_clause,[],[f2802,f2733,f2440,f2102,f9635]) ).
fof(f9635,plain,
( spl0_653
<=> estin = rotate_right(estin) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_653])]) ).
fof(f2802,plain,
( estin = rotate_right(estin)
| ~ spl0_154
| ~ spl0_173
| ~ spl0_209 ),
inference(forward_demodulation,[],[f2770,f2442]) ).
fof(f2770,plain,
( estin = rotate_right(empty_set)
| ~ spl0_154
| ~ spl0_209 ),
inference(resolution,[],[f2734,f2103]) ).
fof(f9277,plain,
( spl0_652
| ~ spl0_173
| ~ spl0_642 ),
inference(avatar_split_clause,[],[f8668,f8665,f2440,f9275]) ).
fof(f9275,plain,
( spl0_652
<=> ! [X0,X1] :
( estin = apply(X0,X1)
| first(f28(f24(apply(X0,X1)),X0,X1)) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_652])]) ).
fof(f8665,plain,
( spl0_642
<=> ! [X0,X1] :
( first(f28(f24(apply(X0,X1)),X0,X1)) = X1
| empty_set = apply(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_642])]) ).
fof(f8668,plain,
( ! [X0,X1] :
( estin = apply(X0,X1)
| first(f28(f24(apply(X0,X1)),X0,X1)) = X1 )
| ~ spl0_173
| ~ spl0_642 ),
inference(forward_demodulation,[],[f8666,f2442]) ).
fof(f8666,plain,
( ! [X0,X1] :
( first(f28(f24(apply(X0,X1)),X0,X1)) = X1
| empty_set = apply(X0,X1) )
| ~ spl0_642 ),
inference(avatar_component_clause,[],[f8665]) ).
fof(f9272,plain,
( spl0_651
| ~ spl0_151
| ~ spl0_173
| ~ spl0_209 ),
inference(avatar_split_clause,[],[f2801,f2733,f2440,f2025,f9269]) ).
fof(f2801,plain,
( estin = converse(estin)
| ~ spl0_151
| ~ spl0_173
| ~ spl0_209 ),
inference(forward_demodulation,[],[f2765,f2442]) ).
fof(f2765,plain,
( estin = converse(empty_set)
| ~ spl0_151
| ~ spl0_209 ),
inference(resolution,[],[f2734,f2026]) ).
fof(f9061,plain,
( spl0_650
| ~ spl0_119
| ~ spl0_173
| ~ spl0_209 ),
inference(avatar_split_clause,[],[f2800,f2733,f2440,f1266,f9058]) ).
fof(f9058,plain,
( spl0_650
<=> estin = domain_of(estin) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_650])]) ).
fof(f2800,plain,
( estin = domain_of(estin)
| ~ spl0_119
| ~ spl0_173
| ~ spl0_209 ),
inference(forward_demodulation,[],[f2760,f2442]) ).
fof(f2760,plain,
( estin = domain_of(empty_set)
| ~ spl0_119
| ~ spl0_209 ),
inference(resolution,[],[f2734,f1267]) ).
fof(f8820,plain,
( spl0_649
| ~ spl0_154
| ~ spl0_173 ),
inference(avatar_split_clause,[],[f2458,f2440,f2102,f8818]) ).
fof(f8818,plain,
( spl0_649
<=> ! [X0] : ~ member(X0,rotate_right(estin)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_649])]) ).
fof(f2458,plain,
( ! [X0] : ~ member(X0,rotate_right(estin))
| ~ spl0_154
| ~ spl0_173 ),
inference(superposition,[],[f2103,f2442]) ).
fof(f8809,plain,
( spl0_648
| ~ spl0_153
| ~ spl0_173 ),
inference(avatar_split_clause,[],[f2457,f2440,f2098,f8807]) ).
fof(f8807,plain,
( spl0_648
<=> ! [X0] : ~ member(X0,flip_range_of(estin)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_648])]) ).
fof(f2457,plain,
( ! [X0] : ~ member(X0,flip_range_of(estin))
| ~ spl0_153
| ~ spl0_173 ),
inference(superposition,[],[f2099,f2442]) ).
fof(f8805,plain,
( spl0_647
| ~ spl0_173
| ~ spl0_602 ),
inference(avatar_split_clause,[],[f8503,f8500,f2440,f8803]) ).
fof(f8803,plain,
( spl0_647
<=> ! [X0,X1] :
( estin = intersection(X0,X1)
| ~ little_set(intersection(X0,X1))
| member(f26(intersection(X0,X1)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_647])]) ).
fof(f8500,plain,
( spl0_602
<=> ! [X0,X1] :
( intersection(X0,X1) = empty_set
| ~ little_set(intersection(X0,X1))
| member(f26(intersection(X0,X1)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_602])]) ).
fof(f8503,plain,
( ! [X0,X1] :
( estin = intersection(X0,X1)
| ~ little_set(intersection(X0,X1))
| member(f26(intersection(X0,X1)),X0) )
| ~ spl0_173
| ~ spl0_602 ),
inference(forward_demodulation,[],[f8501,f2442]) ).
fof(f8501,plain,
( ! [X0,X1] :
( intersection(X0,X1) = empty_set
| ~ little_set(intersection(X0,X1))
| member(f26(intersection(X0,X1)),X0) )
| ~ spl0_602 ),
inference(avatar_component_clause,[],[f8500]) ).
fof(f8801,plain,
( spl0_646
| ~ spl0_173
| ~ spl0_601 ),
inference(avatar_split_clause,[],[f8498,f8495,f2440,f8799]) ).
fof(f8799,plain,
( spl0_646
<=> ! [X0,X1] :
( estin = intersection(X0,X1)
| ~ little_set(intersection(X0,X1))
| member(f26(intersection(X0,X1)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_646])]) ).
fof(f8495,plain,
( spl0_601
<=> ! [X0,X1] :
( intersection(X0,X1) = empty_set
| ~ little_set(intersection(X0,X1))
| member(f26(intersection(X0,X1)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_601])]) ).
fof(f8498,plain,
( ! [X0,X1] :
( estin = intersection(X0,X1)
| ~ little_set(intersection(X0,X1))
| member(f26(intersection(X0,X1)),X1) )
| ~ spl0_173
| ~ spl0_601 ),
inference(forward_demodulation,[],[f8496,f2442]) ).
fof(f8496,plain,
( ! [X0,X1] :
( intersection(X0,X1) = empty_set
| ~ little_set(intersection(X0,X1))
| member(f26(intersection(X0,X1)),X1) )
| ~ spl0_601 ),
inference(avatar_component_clause,[],[f8495]) ).
fof(f8680,plain,
( spl0_645
| ~ spl0_96
| ~ spl0_124 ),
inference(avatar_split_clause,[],[f1386,f1299,f848,f8678]) ).
fof(f8678,plain,
( spl0_645
<=> ! [X2,X0,X1] :
( ~ member(X0,X1)
| ~ member(X2,second(X0))
| ~ ordered_pair_predicate(X0)
| ordered_pair_predicate(f28(X2,X1,first(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_645])]) ).
fof(f1386,plain,
( ! [X2,X0,X1] :
( ~ member(X0,X1)
| ~ member(X2,second(X0))
| ~ ordered_pair_predicate(X0)
| ordered_pair_predicate(f28(X2,X1,first(X0))) )
| ~ spl0_96
| ~ spl0_124 ),
inference(resolution,[],[f1300,f849]) ).
fof(f8676,plain,
( spl0_644
| ~ spl0_28
| ~ spl0_113 ),
inference(avatar_split_clause,[],[f1236,f1159,f306,f8674]) ).
fof(f1236,plain,
( ! [X0,X1] :
( member(f1(converse(X0),X1),X1)
| converse(X0) = X1
| ordered_pair_predicate(f1(converse(X0),X1)) )
| ~ spl0_28
| ~ spl0_113 ),
inference(resolution,[],[f1160,f307]) ).
fof(f8672,plain,
( spl0_643
| ~ spl0_28
| ~ spl0_113 ),
inference(avatar_split_clause,[],[f1199,f1159,f306,f8670]) ).
fof(f1199,plain,
( ! [X0,X1] :
( member(f1(X0,converse(X1)),X0)
| converse(X1) = X0
| ordered_pair_predicate(f1(X0,converse(X1))) )
| ~ spl0_28
| ~ spl0_113 ),
inference(resolution,[],[f1160,f307]) ).
fof(f8667,plain,
( spl0_642
| ~ spl0_40
| ~ spl0_110 ),
inference(avatar_split_clause,[],[f1148,f1081,f361,f8665]) ).
fof(f1148,plain,
( ! [X0,X1] :
( first(f28(f24(apply(X0,X1)),X0,X1)) = X1
| empty_set = apply(X0,X1) )
| ~ spl0_40
| ~ spl0_110 ),
inference(resolution,[],[f1082,f362]) ).
fof(f8663,plain,
( spl0_641
| ~ spl0_65
| ~ spl0_107 ),
inference(avatar_split_clause,[],[f1121,f1068,f482,f8661]) ).
fof(f8661,plain,
( spl0_641
<=> ! [X2,X0,X1] :
( ~ member(X0,image(range_of(X1),X2))
| ordered_pair_predicate(f27(first(f22(X0,range_of(X1),X2)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_641])]) ).
fof(f1121,plain,
( ! [X2,X0,X1] :
( ~ member(X0,image(range_of(X1),X2))
| ordered_pair_predicate(f27(first(f22(X0,range_of(X1),X2)),X1)) )
| ~ spl0_65
| ~ spl0_107 ),
inference(resolution,[],[f1069,f483]) ).
fof(f8659,plain,
( spl0_640
| ~ spl0_57
| ~ spl0_107 ),
inference(avatar_split_clause,[],[f1116,f1068,f450,f8657]) ).
fof(f8657,plain,
( spl0_640
<=> ! [X2,X0,X1] :
( ~ member(X0,image(flip_range_of(X1),X2))
| little_set(f12(first(f22(X0,flip_range_of(X1),X2)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_640])]) ).
fof(f1116,plain,
( ! [X2,X0,X1] :
( ~ member(X0,image(flip_range_of(X1),X2))
| little_set(f12(first(f22(X0,flip_range_of(X1),X2)),X1)) )
| ~ spl0_57
| ~ spl0_107 ),
inference(resolution,[],[f1069,f451]) ).
fof(f8654,plain,
( spl0_639
| ~ spl0_151
| ~ spl0_173 ),
inference(avatar_split_clause,[],[f2456,f2440,f2025,f8652]) ).
fof(f8652,plain,
( spl0_639
<=> ! [X0] : ~ member(X0,converse(estin)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_639])]) ).
fof(f2456,plain,
( ! [X0] : ~ member(X0,converse(estin))
| ~ spl0_151
| ~ spl0_173 ),
inference(superposition,[],[f2026,f2442]) ).
fof(f8650,plain,
( spl0_638
| ~ spl0_58
| ~ spl0_107 ),
inference(avatar_split_clause,[],[f1115,f1068,f454,f8648]) ).
fof(f8648,plain,
( spl0_638
<=> ! [X2,X0,X1] :
( ~ member(X0,image(flip_range_of(X1),X2))
| little_set(f13(first(f22(X0,flip_range_of(X1),X2)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_638])]) ).
fof(f1115,plain,
( ! [X2,X0,X1] :
( ~ member(X0,image(flip_range_of(X1),X2))
| little_set(f13(first(f22(X0,flip_range_of(X1),X2)),X1)) )
| ~ spl0_58
| ~ spl0_107 ),
inference(resolution,[],[f1069,f455]) ).
fof(f8646,plain,
( spl0_637
| ~ spl0_59
| ~ spl0_107 ),
inference(avatar_split_clause,[],[f1114,f1068,f458,f8644]) ).
fof(f8644,plain,
( spl0_637
<=> ! [X2,X0,X1] :
( ~ member(X0,image(flip_range_of(X1),X2))
| little_set(f14(first(f22(X0,flip_range_of(X1),X2)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_637])]) ).
fof(f1114,plain,
( ! [X2,X0,X1] :
( ~ member(X0,image(flip_range_of(X1),X2))
| little_set(f14(first(f22(X0,flip_range_of(X1),X2)),X1)) )
| ~ spl0_59
| ~ spl0_107 ),
inference(resolution,[],[f1069,f459]) ).
fof(f8642,plain,
( spl0_636
| ~ spl0_54
| ~ spl0_107 ),
inference(avatar_split_clause,[],[f1113,f1068,f438,f8640]) ).
fof(f8640,plain,
( spl0_636
<=> ! [X2,X0,X1] :
( ~ member(X0,image(rotate_right(X1),X2))
| little_set(f9(first(f22(X0,rotate_right(X1),X2)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_636])]) ).
fof(f1113,plain,
( ! [X2,X0,X1] :
( ~ member(X0,image(rotate_right(X1),X2))
| little_set(f9(first(f22(X0,rotate_right(X1),X2)),X1)) )
| ~ spl0_54
| ~ spl0_107 ),
inference(resolution,[],[f1069,f439]) ).
fof(f8638,plain,
( spl0_635
| ~ spl0_55
| ~ spl0_107 ),
inference(avatar_split_clause,[],[f1112,f1068,f442,f8636]) ).
fof(f8636,plain,
( spl0_635
<=> ! [X2,X0,X1] :
( ~ member(X0,image(rotate_right(X1),X2))
| little_set(f10(first(f22(X0,rotate_right(X1),X2)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_635])]) ).
fof(f1112,plain,
( ! [X2,X0,X1] :
( ~ member(X0,image(rotate_right(X1),X2))
| little_set(f10(first(f22(X0,rotate_right(X1),X2)),X1)) )
| ~ spl0_55
| ~ spl0_107 ),
inference(resolution,[],[f1069,f443]) ).
fof(f8634,plain,
( spl0_634
| ~ spl0_56
| ~ spl0_107 ),
inference(avatar_split_clause,[],[f1111,f1068,f446,f8632]) ).
fof(f8632,plain,
( spl0_634
<=> ! [X2,X0,X1] :
( ~ member(X0,image(rotate_right(X1),X2))
| little_set(f11(first(f22(X0,rotate_right(X1),X2)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_634])]) ).
fof(f1111,plain,
( ! [X2,X0,X1] :
( ~ member(X0,image(rotate_right(X1),X2))
| little_set(f11(first(f22(X0,rotate_right(X1),X2)),X1)) )
| ~ spl0_56
| ~ spl0_107 ),
inference(resolution,[],[f1069,f447]) ).
fof(f8630,plain,
( spl0_633
| ~ spl0_35
| ~ spl0_107 ),
inference(avatar_split_clause,[],[f1109,f1068,f340,f8628]) ).
fof(f8628,plain,
( spl0_633
<=> ! [X0,X3,X2,X1] :
( ~ member(X0,image(cross_product(X1,X2),X3))
| ordered_pair_predicate(first(f22(X0,cross_product(X1,X2),X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_633])]) ).
fof(f1109,plain,
( ! [X2,X3,X0,X1] :
( ~ member(X0,image(cross_product(X1,X2),X3))
| ordered_pair_predicate(first(f22(X0,cross_product(X1,X2),X3))) )
| ~ spl0_35
| ~ spl0_107 ),
inference(resolution,[],[f1069,f341]) ).
fof(f8626,plain,
( spl0_632
| ~ spl0_53
| ~ spl0_107 ),
inference(avatar_split_clause,[],[f1106,f1068,f434,f8624]) ).
fof(f8624,plain,
( spl0_632
<=> ! [X2,X0,X1] :
( ~ member(X0,image(domain_of(X1),X2))
| ordered_pair_predicate(f8(first(f22(X0,domain_of(X1),X2)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_632])]) ).
fof(f1106,plain,
( ! [X2,X0,X1] :
( ~ member(X0,image(domain_of(X1),X2))
| ordered_pair_predicate(f8(first(f22(X0,domain_of(X1),X2)),X1)) )
| ~ spl0_53
| ~ spl0_107 ),
inference(resolution,[],[f1069,f435]) ).
fof(f8622,plain,
( spl0_631
| ~ spl0_48
| ~ spl0_107 ),
inference(avatar_split_clause,[],[f1100,f1068,f414,f8620]) ).
fof(f8620,plain,
( spl0_631
<=> ! [X2,X0,X1] :
( ~ member(X0,image(second(X1),X2))
| little_set(f6(first(f22(X0,second(X1),X2)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_631])]) ).
fof(f1100,plain,
( ! [X2,X0,X1] :
( ~ member(X0,image(second(X1),X2))
| little_set(f6(first(f22(X0,second(X1),X2)),X1)) )
| ~ spl0_48
| ~ spl0_107 ),
inference(resolution,[],[f1069,f415]) ).
fof(f8618,plain,
( spl0_630
| ~ spl0_49
| ~ spl0_107 ),
inference(avatar_split_clause,[],[f1099,f1068,f418,f8616]) ).
fof(f8616,plain,
( spl0_630
<=> ! [X2,X0,X1] :
( ~ member(X0,image(second(X1),X2))
| little_set(f7(first(f22(X0,second(X1),X2)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_630])]) ).
fof(f1099,plain,
( ! [X2,X0,X1] :
( ~ member(X0,image(second(X1),X2))
| little_set(f7(first(f22(X0,second(X1),X2)),X1)) )
| ~ spl0_49
| ~ spl0_107 ),
inference(resolution,[],[f1069,f419]) ).
fof(f8614,plain,
( spl0_629
| ~ spl0_46
| ~ spl0_107 ),
inference(avatar_split_clause,[],[f1098,f1068,f406,f8612]) ).
fof(f8612,plain,
( spl0_629
<=> ! [X2,X0,X1] :
( ~ member(X0,image(first(X1),X2))
| little_set(f4(first(f22(X0,first(X1),X2)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_629])]) ).
fof(f1098,plain,
( ! [X2,X0,X1] :
( ~ member(X0,image(first(X1),X2))
| little_set(f4(first(f22(X0,first(X1),X2)),X1)) )
| ~ spl0_46
| ~ spl0_107 ),
inference(resolution,[],[f1069,f407]) ).
fof(f8609,plain,
( spl0_628
| ~ spl0_141
| ~ spl0_173 ),
inference(avatar_split_clause,[],[f2455,f2440,f1749,f8607]) ).
fof(f8607,plain,
( spl0_628
<=> ! [X0] : ~ member(X0,range_of(estin)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_628])]) ).
fof(f2455,plain,
( ! [X0] : ~ member(X0,range_of(estin))
| ~ spl0_141
| ~ spl0_173 ),
inference(superposition,[],[f1750,f2442]) ).
fof(f8605,plain,
( spl0_627
| ~ spl0_47
| ~ spl0_107 ),
inference(avatar_split_clause,[],[f1097,f1068,f410,f8603]) ).
fof(f8603,plain,
( spl0_627
<=> ! [X2,X0,X1] :
( ~ member(X0,image(first(X1),X2))
| little_set(f5(first(f22(X0,first(X1),X2)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_627])]) ).
fof(f1097,plain,
( ! [X2,X0,X1] :
( ~ member(X0,image(first(X1),X2))
| little_set(f5(first(f22(X0,first(X1),X2)),X1)) )
| ~ spl0_47
| ~ spl0_107 ),
inference(resolution,[],[f1069,f411]) ).
fof(f8601,plain,
( spl0_626
| ~ spl0_51
| ~ spl0_104 ),
inference(avatar_split_clause,[],[f1035,f966,f426,f8599]) ).
fof(f8599,plain,
( spl0_626
<=> ! [X0,X3,X2,X1] :
( ~ member(X0,apply(intersection(X1,X2),X3))
| member(f28(X0,intersection(X1,X2),X3),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_626])]) ).
fof(f1035,plain,
( ! [X2,X3,X0,X1] :
( ~ member(X0,apply(intersection(X1,X2),X3))
| member(f28(X0,intersection(X1,X2),X3),X1) )
| ~ spl0_51
| ~ spl0_104 ),
inference(resolution,[],[f967,f427]) ).
fof(f8597,plain,
( spl0_625
| ~ spl0_52
| ~ spl0_104 ),
inference(avatar_split_clause,[],[f1034,f966,f430,f8595]) ).
fof(f8595,plain,
( spl0_625
<=> ! [X0,X3,X2,X1] :
( ~ member(X0,apply(intersection(X1,X2),X3))
| member(f28(X0,intersection(X1,X2),X3),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_625])]) ).
fof(f1034,plain,
( ! [X2,X3,X0,X1] :
( ~ member(X0,apply(intersection(X1,X2),X3))
| member(f28(X0,intersection(X1,X2),X3),X2) )
| ~ spl0_52
| ~ spl0_104 ),
inference(resolution,[],[f967,f431]) ).
fof(f8593,plain,
( spl0_624
| ~ spl0_93
| ~ spl0_104 ),
inference(avatar_split_clause,[],[f1025,f966,f836,f8591]) ).
fof(f8591,plain,
( spl0_624
<=> ! [X0,X3,X2,X1] :
( ~ member(X0,apply(X1,X2))
| ~ member(X1,X3)
| member(f28(X0,X1,X2),sigma(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_624])]) ).
fof(f1025,plain,
( ! [X2,X3,X0,X1] :
( ~ member(X0,apply(X1,X2))
| ~ member(X1,X3)
| member(f28(X0,X1,X2),sigma(X3)) )
| ~ spl0_93
| ~ spl0_104 ),
inference(resolution,[],[f967,f837]) ).
fof(f8589,plain,
( spl0_623
| ~ spl0_51
| ~ spl0_103 ),
inference(avatar_split_clause,[],[f1000,f960,f426,f8587]) ).
fof(f8587,plain,
( spl0_623
<=> ! [X0,X3,X2,X1] :
( ~ member(X0,image(X1,intersection(X2,X3)))
| member(f22(X0,X1,intersection(X2,X3)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_623])]) ).
fof(f1000,plain,
( ! [X2,X3,X0,X1] :
( ~ member(X0,image(X1,intersection(X2,X3)))
| member(f22(X0,X1,intersection(X2,X3)),X2) )
| ~ spl0_51
| ~ spl0_103 ),
inference(resolution,[],[f961,f427]) ).
fof(f8585,plain,
( spl0_622
| ~ spl0_52
| ~ spl0_103 ),
inference(avatar_split_clause,[],[f999,f960,f430,f8583]) ).
fof(f8583,plain,
( spl0_622
<=> ! [X0,X3,X2,X1] :
( ~ member(X0,image(X1,intersection(X2,X3)))
| member(f22(X0,X1,intersection(X2,X3)),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_622])]) ).
fof(f999,plain,
( ! [X2,X3,X0,X1] :
( ~ member(X0,image(X1,intersection(X2,X3)))
| member(f22(X0,X1,intersection(X2,X3)),X3) )
| ~ spl0_52
| ~ spl0_103 ),
inference(resolution,[],[f961,f431]) ).
fof(f8581,plain,
( spl0_621
| ~ spl0_93
| ~ spl0_103 ),
inference(avatar_split_clause,[],[f990,f960,f836,f8579]) ).
fof(f8579,plain,
( spl0_621
<=> ! [X0,X3,X2,X1] :
( ~ member(X0,image(X1,X2))
| ~ member(X2,X3)
| member(f22(X0,X1,X2),sigma(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_621])]) ).
fof(f990,plain,
( ! [X2,X3,X0,X1] :
( ~ member(X0,image(X1,X2))
| ~ member(X2,X3)
| member(f22(X0,X1,X2),sigma(X3)) )
| ~ spl0_93
| ~ spl0_103 ),
inference(resolution,[],[f961,f837]) ).
fof(f8577,plain,
( spl0_620
| ~ spl0_93
| ~ spl0_102 ),
inference(avatar_split_clause,[],[f986,f956,f836,f8575]) ).
fof(f8575,plain,
( spl0_620
<=> ! [X0,X3,X2,X1] :
( ~ member(X0,X1)
| ~ member(X0,X2)
| ~ member(intersection(X1,X2),X3)
| member(X0,sigma(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_620])]) ).
fof(f986,plain,
( ! [X2,X3,X0,X1] :
( ~ member(X0,X1)
| ~ member(X0,X2)
| ~ member(intersection(X1,X2),X3)
| member(X0,sigma(X3)) )
| ~ spl0_93
| ~ spl0_102 ),
inference(resolution,[],[f957,f837]) ).
fof(f8573,plain,
( spl0_619
| ~ spl0_85
| ~ spl0_99 ),
inference(avatar_split_clause,[],[f950,f860,f672,f8571]) ).
fof(f8571,plain,
( spl0_619
<=> ! [X2,X0,X1] :
( little_set(f31(f27(X0,compose(X1,X2)),X1,X2))
| ~ member(X0,range_of(compose(X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_619])]) ).
fof(f950,plain,
( ! [X2,X0,X1] :
( little_set(f31(f27(X0,compose(X1,X2)),X1,X2))
| ~ member(X0,range_of(compose(X1,X2))) )
| ~ spl0_85
| ~ spl0_99 ),
inference(resolution,[],[f861,f673]) ).
fof(f8569,plain,
( spl0_618
| ~ spl0_78
| ~ spl0_99 ),
inference(avatar_split_clause,[],[f943,f860,f644,f8567]) ).
fof(f8567,plain,
( spl0_618
<=> ! [X2,X0,X1] :
( little_set(f31(f16(X0,compose(X1,X2)),X1,X2))
| ~ member(X0,sigma(compose(X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_618])]) ).
fof(f943,plain,
( ! [X2,X0,X1] :
( little_set(f31(f16(X0,compose(X1,X2)),X1,X2))
| ~ member(X0,sigma(compose(X1,X2))) )
| ~ spl0_78
| ~ spl0_99 ),
inference(resolution,[],[f861,f645]) ).
fof(f8564,plain,
( spl0_617
| ~ spl0_135
| ~ spl0_173 ),
inference(avatar_split_clause,[],[f2454,f2440,f1548,f8562]) ).
fof(f8562,plain,
( spl0_617
<=> ! [X0] : ~ member(X0,sigma(estin)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_617])]) ).
fof(f2454,plain,
( ! [X0] : ~ member(X0,sigma(estin))
| ~ spl0_135
| ~ spl0_173 ),
inference(superposition,[],[f1549,f2442]) ).
fof(f8560,plain,
( spl0_616
| ~ spl0_74
| ~ spl0_99 ),
inference(avatar_split_clause,[],[f942,f860,f628,f8558]) ).
fof(f8558,plain,
( spl0_616
<=> ! [X2,X0,X1] :
( little_set(f31(f8(X0,compose(X1,X2)),X1,X2))
| ~ member(X0,domain_of(compose(X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_616])]) ).
fof(f942,plain,
( ! [X2,X0,X1] :
( little_set(f31(f8(X0,compose(X1,X2)),X1,X2))
| ~ member(X0,domain_of(compose(X1,X2))) )
| ~ spl0_74
| ~ spl0_99 ),
inference(resolution,[],[f861,f629]) ).
fof(f8556,plain,
( spl0_615
| ~ spl0_85
| ~ spl0_98 ),
inference(avatar_split_clause,[],[f941,f856,f672,f8554]) ).
fof(f8554,plain,
( spl0_615
<=> ! [X2,X0,X1] :
( little_set(f30(f27(X0,compose(X1,X2)),X1,X2))
| ~ member(X0,range_of(compose(X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_615])]) ).
fof(f941,plain,
( ! [X2,X0,X1] :
( little_set(f30(f27(X0,compose(X1,X2)),X1,X2))
| ~ member(X0,range_of(compose(X1,X2))) )
| ~ spl0_85
| ~ spl0_98 ),
inference(resolution,[],[f857,f673]) ).
fof(f8552,plain,
( spl0_614
| ~ spl0_78
| ~ spl0_98 ),
inference(avatar_split_clause,[],[f934,f856,f644,f8550]) ).
fof(f8550,plain,
( spl0_614
<=> ! [X2,X0,X1] :
( little_set(f30(f16(X0,compose(X1,X2)),X1,X2))
| ~ member(X0,sigma(compose(X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_614])]) ).
fof(f934,plain,
( ! [X2,X0,X1] :
( little_set(f30(f16(X0,compose(X1,X2)),X1,X2))
| ~ member(X0,sigma(compose(X1,X2))) )
| ~ spl0_78
| ~ spl0_98 ),
inference(resolution,[],[f857,f645]) ).
fof(f8548,plain,
( spl0_613
| ~ spl0_74
| ~ spl0_98 ),
inference(avatar_split_clause,[],[f933,f856,f628,f8546]) ).
fof(f8546,plain,
( spl0_613
<=> ! [X2,X0,X1] :
( little_set(f30(f8(X0,compose(X1,X2)),X1,X2))
| ~ member(X0,domain_of(compose(X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_613])]) ).
fof(f933,plain,
( ! [X2,X0,X1] :
( little_set(f30(f8(X0,compose(X1,X2)),X1,X2))
| ~ member(X0,domain_of(compose(X1,X2))) )
| ~ spl0_74
| ~ spl0_98 ),
inference(resolution,[],[f857,f629]) ).
fof(f8544,plain,
( spl0_612
| ~ spl0_85
| ~ spl0_97 ),
inference(avatar_split_clause,[],[f932,f852,f672,f8542]) ).
fof(f8542,plain,
( spl0_612
<=> ! [X2,X0,X1] :
( little_set(f29(f27(X0,compose(X1,X2)),X1,X2))
| ~ member(X0,range_of(compose(X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_612])]) ).
fof(f932,plain,
( ! [X2,X0,X1] :
( little_set(f29(f27(X0,compose(X1,X2)),X1,X2))
| ~ member(X0,range_of(compose(X1,X2))) )
| ~ spl0_85
| ~ spl0_97 ),
inference(resolution,[],[f853,f673]) ).
fof(f8540,plain,
( spl0_611
| ~ spl0_78
| ~ spl0_97 ),
inference(avatar_split_clause,[],[f925,f852,f644,f8538]) ).
fof(f8538,plain,
( spl0_611
<=> ! [X2,X0,X1] :
( little_set(f29(f16(X0,compose(X1,X2)),X1,X2))
| ~ member(X0,sigma(compose(X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_611])]) ).
fof(f925,plain,
( ! [X2,X0,X1] :
( little_set(f29(f16(X0,compose(X1,X2)),X1,X2))
| ~ member(X0,sigma(compose(X1,X2))) )
| ~ spl0_78
| ~ spl0_97 ),
inference(resolution,[],[f853,f645]) ).
fof(f8536,plain,
( spl0_610
| ~ spl0_74
| ~ spl0_97 ),
inference(avatar_split_clause,[],[f924,f852,f628,f8534]) ).
fof(f8534,plain,
( spl0_610
<=> ! [X2,X0,X1] :
( little_set(f29(f8(X0,compose(X1,X2)),X1,X2))
| ~ member(X0,domain_of(compose(X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_610])]) ).
fof(f924,plain,
( ! [X2,X0,X1] :
( little_set(f29(f8(X0,compose(X1,X2)),X1,X2))
| ~ member(X0,domain_of(compose(X1,X2))) )
| ~ spl0_74
| ~ spl0_97 ),
inference(resolution,[],[f853,f629]) ).
fof(f8532,plain,
( spl0_609
| ~ spl0_85
| ~ spl0_96 ),
inference(avatar_split_clause,[],[f923,f848,f672,f8530]) ).
fof(f8530,plain,
( spl0_609
<=> ! [X2,X0,X1] :
( ordered_pair_predicate(f28(f27(X0,apply(X1,X2)),X1,X2))
| ~ member(X0,range_of(apply(X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_609])]) ).
fof(f923,plain,
( ! [X2,X0,X1] :
( ordered_pair_predicate(f28(f27(X0,apply(X1,X2)),X1,X2))
| ~ member(X0,range_of(apply(X1,X2))) )
| ~ spl0_85
| ~ spl0_96 ),
inference(resolution,[],[f849,f673]) ).
fof(f8528,plain,
( spl0_608
| ~ spl0_78
| ~ spl0_96 ),
inference(avatar_split_clause,[],[f916,f848,f644,f8526]) ).
fof(f8526,plain,
( spl0_608
<=> ! [X2,X0,X1] :
( ordered_pair_predicate(f28(f16(X0,apply(X1,X2)),X1,X2))
| ~ member(X0,sigma(apply(X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_608])]) ).
fof(f916,plain,
( ! [X2,X0,X1] :
( ordered_pair_predicate(f28(f16(X0,apply(X1,X2)),X1,X2))
| ~ member(X0,sigma(apply(X1,X2))) )
| ~ spl0_78
| ~ spl0_96 ),
inference(resolution,[],[f849,f645]) ).
fof(f8524,plain,
( spl0_607
| ~ spl0_74
| ~ spl0_96 ),
inference(avatar_split_clause,[],[f915,f848,f628,f8522]) ).
fof(f8522,plain,
( spl0_607
<=> ! [X2,X0,X1] :
( ordered_pair_predicate(f28(f8(X0,apply(X1,X2)),X1,X2))
| ~ member(X0,domain_of(apply(X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_607])]) ).
fof(f915,plain,
( ! [X2,X0,X1] :
( ordered_pair_predicate(f28(f8(X0,apply(X1,X2)),X1,X2))
| ~ member(X0,domain_of(apply(X1,X2))) )
| ~ spl0_74
| ~ spl0_96 ),
inference(resolution,[],[f849,f629]) ).
fof(f8519,plain,
( spl0_606
| ~ spl0_119
| ~ spl0_173 ),
inference(avatar_split_clause,[],[f2452,f2440,f1266,f8517]) ).
fof(f8517,plain,
( spl0_606
<=> ! [X0] : ~ member(X0,domain_of(estin)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_606])]) ).
fof(f2452,plain,
( ! [X0] : ~ member(X0,domain_of(estin))
| ~ spl0_119
| ~ spl0_173 ),
inference(superposition,[],[f1267,f2442]) ).
fof(f8515,plain,
( spl0_605
| ~ spl0_85
| ~ spl0_94 ),
inference(avatar_split_clause,[],[f905,f840,f672,f8513]) ).
fof(f8513,plain,
( spl0_605
<=> ! [X2,X0,X1] :
( ordered_pair_predicate(f22(f27(X0,image(X1,X2)),X1,X2))
| ~ member(X0,range_of(image(X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_605])]) ).
fof(f905,plain,
( ! [X2,X0,X1] :
( ordered_pair_predicate(f22(f27(X0,image(X1,X2)),X1,X2))
| ~ member(X0,range_of(image(X1,X2))) )
| ~ spl0_85
| ~ spl0_94 ),
inference(resolution,[],[f841,f673]) ).
fof(f8511,plain,
( spl0_604
| ~ spl0_78
| ~ spl0_94 ),
inference(avatar_split_clause,[],[f898,f840,f644,f8509]) ).
fof(f8509,plain,
( spl0_604
<=> ! [X2,X0,X1] :
( ordered_pair_predicate(f22(f16(X0,image(X1,X2)),X1,X2))
| ~ member(X0,sigma(image(X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_604])]) ).
fof(f898,plain,
( ! [X2,X0,X1] :
( ordered_pair_predicate(f22(f16(X0,image(X1,X2)),X1,X2))
| ~ member(X0,sigma(image(X1,X2))) )
| ~ spl0_78
| ~ spl0_94 ),
inference(resolution,[],[f841,f645]) ).
fof(f8507,plain,
( spl0_603
| ~ spl0_74
| ~ spl0_94 ),
inference(avatar_split_clause,[],[f897,f840,f628,f8505]) ).
fof(f8505,plain,
( spl0_603
<=> ! [X2,X0,X1] :
( ordered_pair_predicate(f22(f8(X0,image(X1,X2)),X1,X2))
| ~ member(X0,domain_of(image(X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_603])]) ).
fof(f897,plain,
( ! [X2,X0,X1] :
( ordered_pair_predicate(f22(f8(X0,image(X1,X2)),X1,X2))
| ~ member(X0,domain_of(image(X1,X2))) )
| ~ spl0_74
| ~ spl0_94 ),
inference(resolution,[],[f841,f629]) ).
fof(f8502,plain,
( spl0_602
| ~ spl0_51
| ~ spl0_84 ),
inference(avatar_split_clause,[],[f780,f668,f426,f8500]) ).
fof(f780,plain,
( ! [X0,X1] :
( intersection(X0,X1) = empty_set
| ~ little_set(intersection(X0,X1))
| member(f26(intersection(X0,X1)),X0) )
| ~ spl0_51
| ~ spl0_84 ),
inference(resolution,[],[f669,f427]) ).
fof(f8497,plain,
( spl0_601
| ~ spl0_52
| ~ spl0_84 ),
inference(avatar_split_clause,[],[f779,f668,f430,f8495]) ).
fof(f779,plain,
( ! [X0,X1] :
( intersection(X0,X1) = empty_set
| ~ little_set(intersection(X0,X1))
| member(f26(intersection(X0,X1)),X1) )
| ~ spl0_52
| ~ spl0_84 ),
inference(resolution,[],[f669,f431]) ).
fof(f8493,plain,
( spl0_600
| ~ spl0_61
| ~ spl0_82 ),
inference(avatar_split_clause,[],[f770,f660,f466,f8491]) ).
fof(f8491,plain,
( spl0_600
<=> ! [X0,X1] :
( ~ subset(f17(X0,powerset(X1)),X1)
| ~ little_set(f17(X0,powerset(X1)))
| subset(X0,powerset(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_600])]) ).
fof(f770,plain,
( ! [X0,X1] :
( ~ subset(f17(X0,powerset(X1)),X1)
| ~ little_set(f17(X0,powerset(X1)))
| subset(X0,powerset(X1)) )
| ~ spl0_61
| ~ spl0_82 ),
inference(resolution,[],[f661,f467]) ).
fof(f8489,plain,
( spl0_599
| ~ spl0_61
| ~ spl0_73 ),
inference(avatar_split_clause,[],[f698,f624,f466,f8487]) ).
fof(f8487,plain,
( spl0_599
<=> ! [X0,X1] :
( member(f17(X0,complement(X1)),X1)
| ~ little_set(f17(X0,complement(X1)))
| subset(X0,complement(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_599])]) ).
fof(f698,plain,
( ! [X0,X1] :
( member(f17(X0,complement(X1)),X1)
| ~ little_set(f17(X0,complement(X1)))
| subset(X0,complement(X1)) )
| ~ spl0_61
| ~ spl0_73 ),
inference(resolution,[],[f625,f467]) ).
fof(f8417,plain,
( spl0_598
| ~ spl0_30
| ~ spl0_168 ),
inference(avatar_split_clause,[],[f2405,f2260,f314,f8415]) ).
fof(f8415,plain,
( spl0_598
<=> ! [X0] : relation(compose(empty_set,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_598])]) ).
fof(f2405,plain,
( ! [X0] : relation(compose(empty_set,X0))
| ~ spl0_30
| ~ spl0_168 ),
inference(resolution,[],[f2261,f315]) ).
fof(f8165,plain,
( spl0_597
| ~ spl0_121
| ~ spl0_168 ),
inference(avatar_split_clause,[],[f2394,f2260,f1287,f8163]) ).
fof(f8163,plain,
( spl0_597
<=> ! [X0] : single_valued_set(compose(empty_set,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_597])]) ).
fof(f2394,plain,
( ! [X0] : single_valued_set(compose(empty_set,X0))
| ~ spl0_121
| ~ spl0_168 ),
inference(resolution,[],[f2261,f1288]) ).
fof(f8158,plain,
( spl0_596
| ~ spl0_30
| ~ spl0_167 ),
inference(avatar_split_clause,[],[f2374,f2256,f314,f8156]) ).
fof(f8156,plain,
( spl0_596
<=> ! [X0] : relation(compose(X0,empty_set)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_596])]) ).
fof(f2374,plain,
( ! [X0] : relation(compose(X0,empty_set))
| ~ spl0_30
| ~ spl0_167 ),
inference(resolution,[],[f2257,f315]) ).
fof(f8152,plain,
( spl0_595
| ~ spl0_121
| ~ spl0_167 ),
inference(avatar_split_clause,[],[f2363,f2256,f1287,f8150]) ).
fof(f8150,plain,
( spl0_595
<=> ! [X0] : single_valued_set(compose(X0,empty_set)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_595])]) ).
fof(f2363,plain,
( ! [X0] : single_valued_set(compose(X0,empty_set))
| ~ spl0_121
| ~ spl0_167 ),
inference(resolution,[],[f2257,f1288]) ).
fof(f8147,plain,
( spl0_594
| ~ spl0_30
| ~ spl0_166 ),
inference(avatar_split_clause,[],[f2342,f2251,f314,f8145]) ).
fof(f8145,plain,
( spl0_594
<=> ! [X0] : relation(image(empty_set,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_594])]) ).
fof(f2342,plain,
( ! [X0] : relation(image(empty_set,X0))
| ~ spl0_30
| ~ spl0_166 ),
inference(resolution,[],[f2252,f315]) ).
fof(f8140,plain,
( spl0_593
| ~ spl0_173
| ~ spl0_536 ),
inference(avatar_split_clause,[],[f7281,f7278,f2440,f8138]) ).
fof(f8138,plain,
( spl0_593
<=> ! [X0] :
( estin = range_of(X0)
| f24(range_of(X0)) = second(f27(f24(range_of(X0)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_593])]) ).
fof(f7278,plain,
( spl0_536
<=> ! [X0] :
( f24(range_of(X0)) = second(f27(f24(range_of(X0)),X0))
| empty_set = range_of(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_536])]) ).
fof(f7281,plain,
( ! [X0] :
( estin = range_of(X0)
| f24(range_of(X0)) = second(f27(f24(range_of(X0)),X0)) )
| ~ spl0_173
| ~ spl0_536 ),
inference(forward_demodulation,[],[f7279,f2442]) ).
fof(f7279,plain,
( ! [X0] :
( f24(range_of(X0)) = second(f27(f24(range_of(X0)),X0))
| empty_set = range_of(X0) )
| ~ spl0_536 ),
inference(avatar_component_clause,[],[f7278]) ).
fof(f8133,plain,
( spl0_592
| ~ spl0_173
| ~ spl0_532 ),
inference(avatar_split_clause,[],[f7264,f7261,f2440,f8131]) ).
fof(f8131,plain,
( spl0_592
<=> ! [X0] :
( estin = domain_of(X0)
| f24(domain_of(X0)) = first(f8(f24(domain_of(X0)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_592])]) ).
fof(f7261,plain,
( spl0_532
<=> ! [X0] :
( f24(domain_of(X0)) = first(f8(f24(domain_of(X0)),X0))
| domain_of(X0) = empty_set ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_532])]) ).
fof(f7264,plain,
( ! [X0] :
( estin = domain_of(X0)
| f24(domain_of(X0)) = first(f8(f24(domain_of(X0)),X0)) )
| ~ spl0_173
| ~ spl0_532 ),
inference(forward_demodulation,[],[f7262,f2442]) ).
fof(f7262,plain,
( ! [X0] :
( f24(domain_of(X0)) = first(f8(f24(domain_of(X0)),X0))
| domain_of(X0) = empty_set )
| ~ spl0_532 ),
inference(avatar_component_clause,[],[f7261]) ).
fof(f7924,plain,
( spl0_591
| ~ spl0_121
| ~ spl0_166 ),
inference(avatar_split_clause,[],[f2330,f2251,f1287,f7922]) ).
fof(f7922,plain,
( spl0_591
<=> ! [X0] : single_valued_set(image(empty_set,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_591])]) ).
fof(f2330,plain,
( ! [X0] : single_valued_set(image(empty_set,X0))
| ~ spl0_121
| ~ spl0_166 ),
inference(resolution,[],[f2252,f1288]) ).
fof(f7920,plain,
( spl0_590
| ~ spl0_173
| ~ spl0_528 ),
inference(avatar_split_clause,[],[f7246,f7243,f2440,f7918]) ).
fof(f7918,plain,
( spl0_590
<=> ! [X0,X1] :
( estin = cross_product(X0,X1)
| ~ little_set(cross_product(X0,X1))
| ordered_pair_predicate(f26(cross_product(X0,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_590])]) ).
fof(f7243,plain,
( spl0_528
<=> ! [X0,X1] :
( cross_product(X0,X1) = empty_set
| ~ little_set(cross_product(X0,X1))
| ordered_pair_predicate(f26(cross_product(X0,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_528])]) ).
fof(f7246,plain,
( ! [X0,X1] :
( estin = cross_product(X0,X1)
| ~ little_set(cross_product(X0,X1))
| ordered_pair_predicate(f26(cross_product(X0,X1))) )
| ~ spl0_173
| ~ spl0_528 ),
inference(forward_demodulation,[],[f7244,f2442]) ).
fof(f7244,plain,
( ! [X0,X1] :
( cross_product(X0,X1) = empty_set
| ~ little_set(cross_product(X0,X1))
| ordered_pair_predicate(f26(cross_product(X0,X1))) )
| ~ spl0_528 ),
inference(avatar_component_clause,[],[f7243]) ).
fof(f7507,plain,
( ~ spl0_589
| ~ spl0_177
| spl0_588 ),
inference(avatar_split_clause,[],[f7502,f7498,f2481,f7504]) ).
fof(f7504,plain,
( spl0_589
<=> ordered_pair_predicate(non_ordered_pair(non_ordered_pair(f19(estin),f19(estin)),non_ordered_pair(f19(estin),f21(estin)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_589])]) ).
fof(f7498,plain,
( spl0_588
<=> ordered_pair_predicate(non_ordered_pair(non_ordered_pair(f19(identity_relation),f19(identity_relation)),non_ordered_pair(f19(identity_relation),f21(identity_relation)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_588])]) ).
fof(f7502,plain,
( ~ ordered_pair_predicate(non_ordered_pair(non_ordered_pair(f19(estin),f19(estin)),non_ordered_pair(f19(estin),f21(estin))))
| ~ spl0_177
| spl0_588 ),
inference(forward_demodulation,[],[f7499,f2483]) ).
fof(f7499,plain,
( ~ ordered_pair_predicate(non_ordered_pair(non_ordered_pair(f19(identity_relation),f19(identity_relation)),non_ordered_pair(f19(identity_relation),f21(identity_relation))))
| spl0_588 ),
inference(avatar_component_clause,[],[f7498]) ).
fof(f7501,plain,
( spl0_588
| spl0_585
| ~ spl0_23
| ~ spl0_122 ),
inference(avatar_split_clause,[],[f1376,f1291,f281,f7480,f7498]) ).
fof(f1376,plain,
( single_valued_set(identity_relation)
| ordered_pair_predicate(non_ordered_pair(non_ordered_pair(f19(identity_relation),f19(identity_relation)),non_ordered_pair(f19(identity_relation),f21(identity_relation))))
| ~ spl0_23
| ~ spl0_122 ),
inference(resolution,[],[f1292,f282]) ).
fof(f7495,plain,
( ~ spl0_587
| ~ spl0_177
| spl0_584 ),
inference(avatar_split_clause,[],[f7485,f7476,f2481,f7492]) ).
fof(f7476,plain,
( spl0_584
<=> ordered_pair_predicate(non_ordered_pair(non_ordered_pair(f19(identity_relation),f19(identity_relation)),non_ordered_pair(f19(identity_relation),f20(identity_relation)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_584])]) ).
fof(f7485,plain,
( ~ ordered_pair_predicate(non_ordered_pair(non_ordered_pair(f19(estin),f19(estin)),non_ordered_pair(f19(estin),f20(estin))))
| ~ spl0_177
| spl0_584 ),
inference(forward_demodulation,[],[f7477,f2483]) ).
fof(f7477,plain,
( ~ ordered_pair_predicate(non_ordered_pair(non_ordered_pair(f19(identity_relation),f19(identity_relation)),non_ordered_pair(f19(identity_relation),f20(identity_relation))))
| spl0_584 ),
inference(avatar_component_clause,[],[f7476]) ).
fof(f7489,plain,
( spl0_586
| ~ spl0_30
| ~ spl0_165 ),
inference(avatar_split_clause,[],[f2310,f2247,f314,f7487]) ).
fof(f7487,plain,
( spl0_586
<=> ! [X0] : relation(apply(empty_set,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_586])]) ).
fof(f2310,plain,
( ! [X0] : relation(apply(empty_set,X0))
| ~ spl0_30
| ~ spl0_165 ),
inference(resolution,[],[f2248,f315]) ).
fof(f7483,plain,
( spl0_584
| spl0_585
| ~ spl0_23
| ~ spl0_121 ),
inference(avatar_split_clause,[],[f1334,f1287,f281,f7480,f7476]) ).
fof(f1334,plain,
( single_valued_set(identity_relation)
| ordered_pair_predicate(non_ordered_pair(non_ordered_pair(f19(identity_relation),f19(identity_relation)),non_ordered_pair(f19(identity_relation),f20(identity_relation))))
| ~ spl0_23
| ~ spl0_121 ),
inference(resolution,[],[f1288,f282]) ).
fof(f7474,plain,
( spl0_583
| ~ spl0_38
| ~ spl0_118 ),
inference(avatar_split_clause,[],[f1280,f1179,f353,f7472]) ).
fof(f7472,plain,
( spl0_583
<=> ! [X0,X1] :
( ~ little_set(second(X0))
| ~ member(X0,X1)
| ~ ordered_pair_predicate(X0)
| ordered_pair_predicate(second(X0))
| ~ relation(range_of(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_583])]) ).
fof(f1280,plain,
( ! [X0,X1] :
( ~ little_set(second(X0))
| ~ member(X0,X1)
| ~ ordered_pair_predicate(X0)
| ordered_pair_predicate(second(X0))
| ~ relation(range_of(X1)) )
| ~ spl0_38
| ~ spl0_118 ),
inference(resolution,[],[f1180,f354]) ).
fof(f7470,plain,
( spl0_582
| ~ spl0_38
| ~ spl0_117 ),
inference(avatar_split_clause,[],[f1275,f1175,f353,f7468]) ).
fof(f7468,plain,
( spl0_582
<=> ! [X0,X1] :
( ~ little_set(first(X0))
| ~ member(X0,X1)
| ~ ordered_pair_predicate(X0)
| ordered_pair_predicate(first(X0))
| ~ relation(domain_of(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_582])]) ).
fof(f1275,plain,
( ! [X0,X1] :
( ~ little_set(first(X0))
| ~ member(X0,X1)
| ~ ordered_pair_predicate(X0)
| ordered_pair_predicate(first(X0))
| ~ relation(domain_of(X1)) )
| ~ spl0_38
| ~ spl0_117 ),
inference(resolution,[],[f1176,f354]) ).
fof(f7466,plain,
( spl0_581
| ~ spl0_38
| ~ spl0_113 ),
inference(avatar_split_clause,[],[f1220,f1159,f353,f7464]) ).
fof(f1220,plain,
( ! [X0,X1] :
( member(f1(X0,X1),X1)
| X0 = X1
| ordered_pair_predicate(f1(X0,X1))
| ~ relation(X0) )
| ~ spl0_38
| ~ spl0_113 ),
inference(resolution,[],[f1160,f354]) ).
fof(f7462,plain,
( spl0_580
| ~ spl0_38
| ~ spl0_113 ),
inference(avatar_split_clause,[],[f1183,f1159,f353,f7460]) ).
fof(f1183,plain,
( ! [X0,X1] :
( member(f1(X0,X1),X0)
| X0 = X1
| ordered_pair_predicate(f1(X0,X1))
| ~ relation(X1) )
| ~ spl0_38
| ~ spl0_113 ),
inference(resolution,[],[f1160,f354]) ).
fof(f7458,plain,
( spl0_579
| ~ spl0_30
| ~ spl0_110 ),
inference(avatar_split_clause,[],[f1144,f1081,f314,f7456]) ).
fof(f7456,plain,
( spl0_579
<=> ! [X0,X1] :
( first(f28(f18(apply(X0,X1)),X0,X1)) = X1
| relation(apply(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_579])]) ).
fof(f1144,plain,
( ! [X0,X1] :
( first(f28(f18(apply(X0,X1)),X0,X1)) = X1
| relation(apply(X0,X1)) )
| ~ spl0_30
| ~ spl0_110 ),
inference(resolution,[],[f1082,f315]) ).
fof(f7454,plain,
( spl0_578
| ~ spl0_37
| ~ spl0_107 ),
inference(avatar_split_clause,[],[f1118,f1068,f349,f7452]) ).
fof(f7452,plain,
( spl0_578
<=> ! [X2,X0,X1] :
( ~ member(X0,image(powerset(X1),X2))
| subset(first(f22(X0,powerset(X1),X2)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_578])]) ).
fof(f1118,plain,
( ! [X2,X0,X1] :
( ~ member(X0,image(powerset(X1),X2))
| subset(first(f22(X0,powerset(X1),X2)),X1) )
| ~ spl0_37
| ~ spl0_107 ),
inference(resolution,[],[f1069,f350]) ).
fof(f7450,plain,
( spl0_577
| ~ spl0_34
| ~ spl0_107 ),
inference(avatar_split_clause,[],[f1104,f1068,f336,f7448]) ).
fof(f1104,plain,
( ! [X2,X0,X1] :
( ~ member(X0,image(complement(X1),X2))
| ~ member(first(f22(X0,complement(X1),X2)),X1) )
| ~ spl0_34
| ~ spl0_107 ),
inference(resolution,[],[f1069,f337]) ).
fof(f7446,plain,
( spl0_576
| ~ spl0_65
| ~ spl0_104 ),
inference(avatar_split_clause,[],[f1053,f966,f482,f7444]) ).
fof(f7444,plain,
( spl0_576
<=> ! [X2,X0,X1] :
( ~ member(X0,apply(range_of(X1),X2))
| ordered_pair_predicate(f27(f28(X0,range_of(X1),X2),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_576])]) ).
fof(f1053,plain,
( ! [X2,X0,X1] :
( ~ member(X0,apply(range_of(X1),X2))
| ordered_pair_predicate(f27(f28(X0,range_of(X1),X2),X1)) )
| ~ spl0_65
| ~ spl0_104 ),
inference(resolution,[],[f967,f483]) ).
fof(f7442,plain,
( spl0_575
| ~ spl0_57
| ~ spl0_104 ),
inference(avatar_split_clause,[],[f1048,f966,f450,f7440]) ).
fof(f7440,plain,
( spl0_575
<=> ! [X2,X0,X1] :
( ~ member(X0,apply(flip_range_of(X1),X2))
| little_set(f12(f28(X0,flip_range_of(X1),X2),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_575])]) ).
fof(f1048,plain,
( ! [X2,X0,X1] :
( ~ member(X0,apply(flip_range_of(X1),X2))
| little_set(f12(f28(X0,flip_range_of(X1),X2),X1)) )
| ~ spl0_57
| ~ spl0_104 ),
inference(resolution,[],[f967,f451]) ).
fof(f7437,plain,
( spl0_574
| ~ spl0_121
| ~ spl0_165 ),
inference(avatar_split_clause,[],[f2299,f2247,f1287,f7435]) ).
fof(f7435,plain,
( spl0_574
<=> ! [X0] : single_valued_set(apply(empty_set,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_574])]) ).
fof(f2299,plain,
( ! [X0] : single_valued_set(apply(empty_set,X0))
| ~ spl0_121
| ~ spl0_165 ),
inference(resolution,[],[f2248,f1288]) ).
fof(f7433,plain,
( spl0_573
| ~ spl0_58
| ~ spl0_104 ),
inference(avatar_split_clause,[],[f1047,f966,f454,f7431]) ).
fof(f7431,plain,
( spl0_573
<=> ! [X2,X0,X1] :
( ~ member(X0,apply(flip_range_of(X1),X2))
| little_set(f13(f28(X0,flip_range_of(X1),X2),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_573])]) ).
fof(f1047,plain,
( ! [X2,X0,X1] :
( ~ member(X0,apply(flip_range_of(X1),X2))
| little_set(f13(f28(X0,flip_range_of(X1),X2),X1)) )
| ~ spl0_58
| ~ spl0_104 ),
inference(resolution,[],[f967,f455]) ).
fof(f7429,plain,
( spl0_572
| ~ spl0_59
| ~ spl0_104 ),
inference(avatar_split_clause,[],[f1046,f966,f458,f7427]) ).
fof(f7427,plain,
( spl0_572
<=> ! [X2,X0,X1] :
( ~ member(X0,apply(flip_range_of(X1),X2))
| little_set(f14(f28(X0,flip_range_of(X1),X2),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_572])]) ).
fof(f1046,plain,
( ! [X2,X0,X1] :
( ~ member(X0,apply(flip_range_of(X1),X2))
| little_set(f14(f28(X0,flip_range_of(X1),X2),X1)) )
| ~ spl0_59
| ~ spl0_104 ),
inference(resolution,[],[f967,f459]) ).
fof(f7425,plain,
( spl0_571
| ~ spl0_54
| ~ spl0_104 ),
inference(avatar_split_clause,[],[f1045,f966,f438,f7423]) ).
fof(f7423,plain,
( spl0_571
<=> ! [X2,X0,X1] :
( ~ member(X0,apply(rotate_right(X1),X2))
| little_set(f9(f28(X0,rotate_right(X1),X2),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_571])]) ).
fof(f1045,plain,
( ! [X2,X0,X1] :
( ~ member(X0,apply(rotate_right(X1),X2))
| little_set(f9(f28(X0,rotate_right(X1),X2),X1)) )
| ~ spl0_54
| ~ spl0_104 ),
inference(resolution,[],[f967,f439]) ).
fof(f7421,plain,
( spl0_570
| ~ spl0_55
| ~ spl0_104 ),
inference(avatar_split_clause,[],[f1044,f966,f442,f7419]) ).
fof(f7419,plain,
( spl0_570
<=> ! [X2,X0,X1] :
( ~ member(X0,apply(rotate_right(X1),X2))
| little_set(f10(f28(X0,rotate_right(X1),X2),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_570])]) ).
fof(f1044,plain,
( ! [X2,X0,X1] :
( ~ member(X0,apply(rotate_right(X1),X2))
| little_set(f10(f28(X0,rotate_right(X1),X2),X1)) )
| ~ spl0_55
| ~ spl0_104 ),
inference(resolution,[],[f967,f443]) ).
fof(f7417,plain,
( spl0_569
| ~ spl0_56
| ~ spl0_104 ),
inference(avatar_split_clause,[],[f1043,f966,f446,f7415]) ).
fof(f7415,plain,
( spl0_569
<=> ! [X2,X0,X1] :
( ~ member(X0,apply(rotate_right(X1),X2))
| little_set(f11(f28(X0,rotate_right(X1),X2),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_569])]) ).
fof(f1043,plain,
( ! [X2,X0,X1] :
( ~ member(X0,apply(rotate_right(X1),X2))
| little_set(f11(f28(X0,rotate_right(X1),X2),X1)) )
| ~ spl0_56
| ~ spl0_104 ),
inference(resolution,[],[f967,f447]) ).
fof(f7413,plain,
( spl0_568
| ~ spl0_53
| ~ spl0_104 ),
inference(avatar_split_clause,[],[f1038,f966,f434,f7411]) ).
fof(f7411,plain,
( spl0_568
<=> ! [X2,X0,X1] :
( ~ member(X0,apply(domain_of(X1),X2))
| ordered_pair_predicate(f8(f28(X0,domain_of(X1),X2),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_568])]) ).
fof(f1038,plain,
( ! [X2,X0,X1] :
( ~ member(X0,apply(domain_of(X1),X2))
| ordered_pair_predicate(f8(f28(X0,domain_of(X1),X2),X1)) )
| ~ spl0_53
| ~ spl0_104 ),
inference(resolution,[],[f967,f435]) ).
fof(f7409,plain,
( spl0_567
| ~ spl0_48
| ~ spl0_104 ),
inference(avatar_split_clause,[],[f1032,f966,f414,f7407]) ).
fof(f7407,plain,
( spl0_567
<=> ! [X2,X0,X1] :
( ~ member(X0,apply(second(X1),X2))
| little_set(f6(f28(X0,second(X1),X2),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_567])]) ).
fof(f1032,plain,
( ! [X2,X0,X1] :
( ~ member(X0,apply(second(X1),X2))
| little_set(f6(f28(X0,second(X1),X2),X1)) )
| ~ spl0_48
| ~ spl0_104 ),
inference(resolution,[],[f967,f415]) ).
fof(f7405,plain,
( spl0_566
| ~ spl0_49
| ~ spl0_104 ),
inference(avatar_split_clause,[],[f1031,f966,f418,f7403]) ).
fof(f7403,plain,
( spl0_566
<=> ! [X2,X0,X1] :
( ~ member(X0,apply(second(X1),X2))
| little_set(f7(f28(X0,second(X1),X2),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_566])]) ).
fof(f1031,plain,
( ! [X2,X0,X1] :
( ~ member(X0,apply(second(X1),X2))
| little_set(f7(f28(X0,second(X1),X2),X1)) )
| ~ spl0_49
| ~ spl0_104 ),
inference(resolution,[],[f967,f419]) ).
fof(f7401,plain,
( spl0_565
| ~ spl0_46
| ~ spl0_104 ),
inference(avatar_split_clause,[],[f1030,f966,f406,f7399]) ).
fof(f7399,plain,
( spl0_565
<=> ! [X2,X0,X1] :
( ~ member(X0,apply(first(X1),X2))
| little_set(f4(f28(X0,first(X1),X2),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_565])]) ).
fof(f1030,plain,
( ! [X2,X0,X1] :
( ~ member(X0,apply(first(X1),X2))
| little_set(f4(f28(X0,first(X1),X2),X1)) )
| ~ spl0_46
| ~ spl0_104 ),
inference(resolution,[],[f967,f407]) ).
fof(f7397,plain,
( spl0_564
| ~ spl0_47
| ~ spl0_104 ),
inference(avatar_split_clause,[],[f1029,f966,f410,f7395]) ).
fof(f7395,plain,
( spl0_564
<=> ! [X2,X0,X1] :
( ~ member(X0,apply(first(X1),X2))
| little_set(f5(f28(X0,first(X1),X2),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_564])]) ).
fof(f1029,plain,
( ! [X2,X0,X1] :
( ~ member(X0,apply(first(X1),X2))
| little_set(f5(f28(X0,first(X1),X2),X1)) )
| ~ spl0_47
| ~ spl0_104 ),
inference(resolution,[],[f967,f411]) ).
fof(f7392,plain,
( spl0_563
| ~ spl0_30
| ~ spl0_164 ),
inference(avatar_split_clause,[],[f2278,f2243,f314,f7390]) ).
fof(f7390,plain,
( spl0_563
<=> ! [X0] : relation(image(X0,empty_set)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_563])]) ).
fof(f2278,plain,
( ! [X0] : relation(image(X0,empty_set))
| ~ spl0_30
| ~ spl0_164 ),
inference(resolution,[],[f2244,f315]) ).
fof(f7388,plain,
( spl0_562
| ~ spl0_65
| ~ spl0_103 ),
inference(avatar_split_clause,[],[f1018,f960,f482,f7386]) ).
fof(f7386,plain,
( spl0_562
<=> ! [X2,X0,X1] :
( ~ member(X0,image(X1,range_of(X2)))
| ordered_pair_predicate(f27(f22(X0,X1,range_of(X2)),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_562])]) ).
fof(f1018,plain,
( ! [X2,X0,X1] :
( ~ member(X0,image(X1,range_of(X2)))
| ordered_pair_predicate(f27(f22(X0,X1,range_of(X2)),X2)) )
| ~ spl0_65
| ~ spl0_103 ),
inference(resolution,[],[f961,f483]) ).
fof(f7384,plain,
( spl0_561
| ~ spl0_57
| ~ spl0_103 ),
inference(avatar_split_clause,[],[f1013,f960,f450,f7382]) ).
fof(f7382,plain,
( spl0_561
<=> ! [X2,X0,X1] :
( ~ member(X0,image(X1,flip_range_of(X2)))
| little_set(f12(f22(X0,X1,flip_range_of(X2)),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_561])]) ).
fof(f1013,plain,
( ! [X2,X0,X1] :
( ~ member(X0,image(X1,flip_range_of(X2)))
| little_set(f12(f22(X0,X1,flip_range_of(X2)),X2)) )
| ~ spl0_57
| ~ spl0_103 ),
inference(resolution,[],[f961,f451]) ).
fof(f7380,plain,
( spl0_560
| ~ spl0_58
| ~ spl0_103 ),
inference(avatar_split_clause,[],[f1012,f960,f454,f7378]) ).
fof(f7378,plain,
( spl0_560
<=> ! [X2,X0,X1] :
( ~ member(X0,image(X1,flip_range_of(X2)))
| little_set(f13(f22(X0,X1,flip_range_of(X2)),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_560])]) ).
fof(f1012,plain,
( ! [X2,X0,X1] :
( ~ member(X0,image(X1,flip_range_of(X2)))
| little_set(f13(f22(X0,X1,flip_range_of(X2)),X2)) )
| ~ spl0_58
| ~ spl0_103 ),
inference(resolution,[],[f961,f455]) ).
fof(f7376,plain,
( spl0_559
| ~ spl0_59
| ~ spl0_103 ),
inference(avatar_split_clause,[],[f1011,f960,f458,f7374]) ).
fof(f7374,plain,
( spl0_559
<=> ! [X2,X0,X1] :
( ~ member(X0,image(X1,flip_range_of(X2)))
| little_set(f14(f22(X0,X1,flip_range_of(X2)),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_559])]) ).
fof(f1011,plain,
( ! [X2,X0,X1] :
( ~ member(X0,image(X1,flip_range_of(X2)))
| little_set(f14(f22(X0,X1,flip_range_of(X2)),X2)) )
| ~ spl0_59
| ~ spl0_103 ),
inference(resolution,[],[f961,f459]) ).
fof(f7372,plain,
( spl0_558
| ~ spl0_54
| ~ spl0_103 ),
inference(avatar_split_clause,[],[f1010,f960,f438,f7370]) ).
fof(f7370,plain,
( spl0_558
<=> ! [X2,X0,X1] :
( ~ member(X0,image(X1,rotate_right(X2)))
| little_set(f9(f22(X0,X1,rotate_right(X2)),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_558])]) ).
fof(f1010,plain,
( ! [X2,X0,X1] :
( ~ member(X0,image(X1,rotate_right(X2)))
| little_set(f9(f22(X0,X1,rotate_right(X2)),X2)) )
| ~ spl0_54
| ~ spl0_103 ),
inference(resolution,[],[f961,f439]) ).
fof(f7368,plain,
( spl0_557
| ~ spl0_55
| ~ spl0_103 ),
inference(avatar_split_clause,[],[f1009,f960,f442,f7366]) ).
fof(f7366,plain,
( spl0_557
<=> ! [X2,X0,X1] :
( ~ member(X0,image(X1,rotate_right(X2)))
| little_set(f10(f22(X0,X1,rotate_right(X2)),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_557])]) ).
fof(f1009,plain,
( ! [X2,X0,X1] :
( ~ member(X0,image(X1,rotate_right(X2)))
| little_set(f10(f22(X0,X1,rotate_right(X2)),X2)) )
| ~ spl0_55
| ~ spl0_103 ),
inference(resolution,[],[f961,f443]) ).
fof(f7364,plain,
( spl0_556
| ~ spl0_56
| ~ spl0_103 ),
inference(avatar_split_clause,[],[f1008,f960,f446,f7362]) ).
fof(f7362,plain,
( spl0_556
<=> ! [X2,X0,X1] :
( ~ member(X0,image(X1,rotate_right(X2)))
| little_set(f11(f22(X0,X1,rotate_right(X2)),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_556])]) ).
fof(f1008,plain,
( ! [X2,X0,X1] :
( ~ member(X0,image(X1,rotate_right(X2)))
| little_set(f11(f22(X0,X1,rotate_right(X2)),X2)) )
| ~ spl0_56
| ~ spl0_103 ),
inference(resolution,[],[f961,f447]) ).
fof(f7360,plain,
( spl0_555
| ~ spl0_53
| ~ spl0_103 ),
inference(avatar_split_clause,[],[f1003,f960,f434,f7358]) ).
fof(f7358,plain,
( spl0_555
<=> ! [X2,X0,X1] :
( ~ member(X0,image(X1,domain_of(X2)))
| ordered_pair_predicate(f8(f22(X0,X1,domain_of(X2)),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_555])]) ).
fof(f1003,plain,
( ! [X2,X0,X1] :
( ~ member(X0,image(X1,domain_of(X2)))
| ordered_pair_predicate(f8(f22(X0,X1,domain_of(X2)),X2)) )
| ~ spl0_53
| ~ spl0_103 ),
inference(resolution,[],[f961,f435]) ).
fof(f7356,plain,
( spl0_554
| ~ spl0_48
| ~ spl0_103 ),
inference(avatar_split_clause,[],[f997,f960,f414,f7354]) ).
fof(f7354,plain,
( spl0_554
<=> ! [X2,X0,X1] :
( ~ member(X0,image(X1,second(X2)))
| little_set(f6(f22(X0,X1,second(X2)),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_554])]) ).
fof(f997,plain,
( ! [X2,X0,X1] :
( ~ member(X0,image(X1,second(X2)))
| little_set(f6(f22(X0,X1,second(X2)),X2)) )
| ~ spl0_48
| ~ spl0_103 ),
inference(resolution,[],[f961,f415]) ).
fof(f7352,plain,
( spl0_553
| ~ spl0_49
| ~ spl0_103 ),
inference(avatar_split_clause,[],[f996,f960,f418,f7350]) ).
fof(f7350,plain,
( spl0_553
<=> ! [X2,X0,X1] :
( ~ member(X0,image(X1,second(X2)))
| little_set(f7(f22(X0,X1,second(X2)),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_553])]) ).
fof(f996,plain,
( ! [X2,X0,X1] :
( ~ member(X0,image(X1,second(X2)))
| little_set(f7(f22(X0,X1,second(X2)),X2)) )
| ~ spl0_49
| ~ spl0_103 ),
inference(resolution,[],[f961,f419]) ).
fof(f7347,plain,
( spl0_552
| ~ spl0_121
| ~ spl0_164 ),
inference(avatar_split_clause,[],[f2266,f2243,f1287,f7345]) ).
fof(f7345,plain,
( spl0_552
<=> ! [X0] : single_valued_set(image(X0,empty_set)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_552])]) ).
fof(f2266,plain,
( ! [X0] : single_valued_set(image(X0,empty_set))
| ~ spl0_121
| ~ spl0_164 ),
inference(resolution,[],[f2244,f1288]) ).
fof(f7343,plain,
( spl0_551
| ~ spl0_46
| ~ spl0_103 ),
inference(avatar_split_clause,[],[f995,f960,f406,f7341]) ).
fof(f7341,plain,
( spl0_551
<=> ! [X2,X0,X1] :
( ~ member(X0,image(X1,first(X2)))
| little_set(f4(f22(X0,X1,first(X2)),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_551])]) ).
fof(f995,plain,
( ! [X2,X0,X1] :
( ~ member(X0,image(X1,first(X2)))
| little_set(f4(f22(X0,X1,first(X2)),X2)) )
| ~ spl0_46
| ~ spl0_103 ),
inference(resolution,[],[f961,f407]) ).
fof(f7339,plain,
( spl0_550
| ~ spl0_47
| ~ spl0_103 ),
inference(avatar_split_clause,[],[f994,f960,f410,f7337]) ).
fof(f7337,plain,
( spl0_550
<=> ! [X2,X0,X1] :
( ~ member(X0,image(X1,first(X2)))
| little_set(f5(f22(X0,X1,first(X2)),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_550])]) ).
fof(f994,plain,
( ! [X2,X0,X1] :
( ~ member(X0,image(X1,first(X2)))
| little_set(f5(f22(X0,X1,first(X2)),X2)) )
| ~ spl0_47
| ~ spl0_103 ),
inference(resolution,[],[f961,f411]) ).
fof(f7335,plain,
( spl0_549
| ~ spl0_64
| ~ spl0_99 ),
inference(avatar_split_clause,[],[f947,f860,f478,f7333]) ).
fof(f7333,plain,
( spl0_549
<=> ! [X2,X0,X1] :
( little_set(f31(f23(X0,compose(X1,X2)),X1,X2))
| disjoint(X0,compose(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_549])]) ).
fof(f947,plain,
( ! [X2,X0,X1] :
( little_set(f31(f23(X0,compose(X1,X2)),X1,X2))
| disjoint(X0,compose(X1,X2)) )
| ~ spl0_64
| ~ spl0_99 ),
inference(resolution,[],[f861,f479]) ).
fof(f7331,plain,
( spl0_548
| ~ spl0_63
| ~ spl0_99 ),
inference(avatar_split_clause,[],[f946,f860,f474,f7329]) ).
fof(f7329,plain,
( spl0_548
<=> ! [X2,X0,X1] :
( little_set(f31(f23(compose(X0,X1),X2),X0,X1))
| disjoint(compose(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_548])]) ).
fof(f946,plain,
( ! [X2,X0,X1] :
( little_set(f31(f23(compose(X0,X1),X2),X0,X1))
| disjoint(compose(X0,X1),X2) )
| ~ spl0_63
| ~ spl0_99 ),
inference(resolution,[],[f861,f475]) ).
fof(f7327,plain,
( spl0_547
| ~ spl0_60
| ~ spl0_99 ),
inference(avatar_split_clause,[],[f944,f860,f462,f7325]) ).
fof(f7325,plain,
( spl0_547
<=> ! [X2,X0,X1] :
( little_set(f31(f17(compose(X0,X1),X2),X0,X1))
| subset(compose(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_547])]) ).
fof(f944,plain,
( ! [X2,X0,X1] :
( little_set(f31(f17(compose(X0,X1),X2),X0,X1))
| subset(compose(X0,X1),X2) )
| ~ spl0_60
| ~ spl0_99 ),
inference(resolution,[],[f861,f463]) ).
fof(f7323,plain,
( spl0_546
| ~ spl0_64
| ~ spl0_98 ),
inference(avatar_split_clause,[],[f938,f856,f478,f7321]) ).
fof(f7321,plain,
( spl0_546
<=> ! [X2,X0,X1] :
( little_set(f30(f23(X0,compose(X1,X2)),X1,X2))
| disjoint(X0,compose(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_546])]) ).
fof(f938,plain,
( ! [X2,X0,X1] :
( little_set(f30(f23(X0,compose(X1,X2)),X1,X2))
| disjoint(X0,compose(X1,X2)) )
| ~ spl0_64
| ~ spl0_98 ),
inference(resolution,[],[f857,f479]) ).
fof(f7319,plain,
( spl0_545
| ~ spl0_63
| ~ spl0_98 ),
inference(avatar_split_clause,[],[f937,f856,f474,f7317]) ).
fof(f7317,plain,
( spl0_545
<=> ! [X2,X0,X1] :
( little_set(f30(f23(compose(X0,X1),X2),X0,X1))
| disjoint(compose(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_545])]) ).
fof(f937,plain,
( ! [X2,X0,X1] :
( little_set(f30(f23(compose(X0,X1),X2),X0,X1))
| disjoint(compose(X0,X1),X2) )
| ~ spl0_63
| ~ spl0_98 ),
inference(resolution,[],[f857,f475]) ).
fof(f7315,plain,
( spl0_544
| ~ spl0_60
| ~ spl0_98 ),
inference(avatar_split_clause,[],[f935,f856,f462,f7313]) ).
fof(f7313,plain,
( spl0_544
<=> ! [X2,X0,X1] :
( little_set(f30(f17(compose(X0,X1),X2),X0,X1))
| subset(compose(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_544])]) ).
fof(f935,plain,
( ! [X2,X0,X1] :
( little_set(f30(f17(compose(X0,X1),X2),X0,X1))
| subset(compose(X0,X1),X2) )
| ~ spl0_60
| ~ spl0_98 ),
inference(resolution,[],[f857,f463]) ).
fof(f7311,plain,
( spl0_543
| ~ spl0_64
| ~ spl0_97 ),
inference(avatar_split_clause,[],[f929,f852,f478,f7309]) ).
fof(f7309,plain,
( spl0_543
<=> ! [X2,X0,X1] :
( little_set(f29(f23(X0,compose(X1,X2)),X1,X2))
| disjoint(X0,compose(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_543])]) ).
fof(f929,plain,
( ! [X2,X0,X1] :
( little_set(f29(f23(X0,compose(X1,X2)),X1,X2))
| disjoint(X0,compose(X1,X2)) )
| ~ spl0_64
| ~ spl0_97 ),
inference(resolution,[],[f853,f479]) ).
fof(f7307,plain,
( spl0_542
| ~ spl0_63
| ~ spl0_97 ),
inference(avatar_split_clause,[],[f928,f852,f474,f7305]) ).
fof(f7305,plain,
( spl0_542
<=> ! [X2,X0,X1] :
( little_set(f29(f23(compose(X0,X1),X2),X0,X1))
| disjoint(compose(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_542])]) ).
fof(f928,plain,
( ! [X2,X0,X1] :
( little_set(f29(f23(compose(X0,X1),X2),X0,X1))
| disjoint(compose(X0,X1),X2) )
| ~ spl0_63
| ~ spl0_97 ),
inference(resolution,[],[f853,f475]) ).
fof(f7302,plain,
( spl0_541
| ~ spl0_40
| ~ spl0_154 ),
inference(avatar_split_clause,[],[f2184,f2102,f361,f7299]) ).
fof(f7299,plain,
( spl0_541
<=> empty_set = rotate_right(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_541])]) ).
fof(f2184,plain,
( empty_set = rotate_right(empty_set)
| ~ spl0_40
| ~ spl0_154 ),
inference(resolution,[],[f2103,f362]) ).
fof(f7297,plain,
( spl0_540
| ~ spl0_60
| ~ spl0_97 ),
inference(avatar_split_clause,[],[f926,f852,f462,f7295]) ).
fof(f7295,plain,
( spl0_540
<=> ! [X2,X0,X1] :
( little_set(f29(f17(compose(X0,X1),X2),X0,X1))
| subset(compose(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_540])]) ).
fof(f926,plain,
( ! [X2,X0,X1] :
( little_set(f29(f17(compose(X0,X1),X2),X0,X1))
| subset(compose(X0,X1),X2) )
| ~ spl0_60
| ~ spl0_97 ),
inference(resolution,[],[f853,f463]) ).
fof(f7293,plain,
( spl0_539
| ~ spl0_64
| ~ spl0_96 ),
inference(avatar_split_clause,[],[f920,f848,f478,f7291]) ).
fof(f7291,plain,
( spl0_539
<=> ! [X2,X0,X1] :
( ordered_pair_predicate(f28(f23(X0,apply(X1,X2)),X1,X2))
| disjoint(X0,apply(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_539])]) ).
fof(f920,plain,
( ! [X2,X0,X1] :
( ordered_pair_predicate(f28(f23(X0,apply(X1,X2)),X1,X2))
| disjoint(X0,apply(X1,X2)) )
| ~ spl0_64
| ~ spl0_96 ),
inference(resolution,[],[f849,f479]) ).
fof(f7289,plain,
( spl0_538
| ~ spl0_63
| ~ spl0_96 ),
inference(avatar_split_clause,[],[f919,f848,f474,f7287]) ).
fof(f7287,plain,
( spl0_538
<=> ! [X2,X0,X1] :
( ordered_pair_predicate(f28(f23(apply(X0,X1),X2),X0,X1))
| disjoint(apply(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_538])]) ).
fof(f919,plain,
( ! [X2,X0,X1] :
( ordered_pair_predicate(f28(f23(apply(X0,X1),X2),X0,X1))
| disjoint(apply(X0,X1),X2) )
| ~ spl0_63
| ~ spl0_96 ),
inference(resolution,[],[f849,f475]) ).
fof(f7285,plain,
( spl0_537
| ~ spl0_60
| ~ spl0_96 ),
inference(avatar_split_clause,[],[f917,f848,f462,f7283]) ).
fof(f7283,plain,
( spl0_537
<=> ! [X2,X0,X1] :
( ordered_pair_predicate(f28(f17(apply(X0,X1),X2),X0,X1))
| subset(apply(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_537])]) ).
fof(f917,plain,
( ! [X2,X0,X1] :
( ordered_pair_predicate(f28(f17(apply(X0,X1),X2),X0,X1))
| subset(apply(X0,X1),X2) )
| ~ spl0_60
| ~ spl0_96 ),
inference(resolution,[],[f849,f463]) ).
fof(f7280,plain,
( spl0_536
| ~ spl0_40
| ~ spl0_95 ),
inference(avatar_split_clause,[],[f912,f844,f361,f7278]) ).
fof(f912,plain,
( ! [X0] :
( f24(range_of(X0)) = second(f27(f24(range_of(X0)),X0))
| empty_set = range_of(X0) )
| ~ spl0_40
| ~ spl0_95 ),
inference(resolution,[],[f845,f362]) ).
fof(f7276,plain,
( spl0_535
| ~ spl0_64
| ~ spl0_94 ),
inference(avatar_split_clause,[],[f902,f840,f478,f7274]) ).
fof(f7274,plain,
( spl0_535
<=> ! [X2,X0,X1] :
( ordered_pair_predicate(f22(f23(X0,image(X1,X2)),X1,X2))
| disjoint(X0,image(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_535])]) ).
fof(f902,plain,
( ! [X2,X0,X1] :
( ordered_pair_predicate(f22(f23(X0,image(X1,X2)),X1,X2))
| disjoint(X0,image(X1,X2)) )
| ~ spl0_64
| ~ spl0_94 ),
inference(resolution,[],[f841,f479]) ).
fof(f7272,plain,
( spl0_534
| ~ spl0_63
| ~ spl0_94 ),
inference(avatar_split_clause,[],[f901,f840,f474,f7270]) ).
fof(f7270,plain,
( spl0_534
<=> ! [X2,X0,X1] :
( ordered_pair_predicate(f22(f23(image(X0,X1),X2),X0,X1))
| disjoint(image(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_534])]) ).
fof(f901,plain,
( ! [X2,X0,X1] :
( ordered_pair_predicate(f22(f23(image(X0,X1),X2),X0,X1))
| disjoint(image(X0,X1),X2) )
| ~ spl0_63
| ~ spl0_94 ),
inference(resolution,[],[f841,f475]) ).
fof(f7268,plain,
( spl0_533
| ~ spl0_60
| ~ spl0_94 ),
inference(avatar_split_clause,[],[f899,f840,f462,f7266]) ).
fof(f7266,plain,
( spl0_533
<=> ! [X2,X0,X1] :
( ordered_pair_predicate(f22(f17(image(X0,X1),X2),X0,X1))
| subset(image(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_533])]) ).
fof(f899,plain,
( ! [X2,X0,X1] :
( ordered_pair_predicate(f22(f17(image(X0,X1),X2),X0,X1))
| subset(image(X0,X1),X2) )
| ~ spl0_60
| ~ spl0_94 ),
inference(resolution,[],[f841,f463]) ).
fof(f7263,plain,
( spl0_532
| ~ spl0_40
| ~ spl0_91 ),
inference(avatar_split_clause,[],[f873,f828,f361,f7261]) ).
fof(f873,plain,
( ! [X0] :
( f24(domain_of(X0)) = first(f8(f24(domain_of(X0)),X0))
| domain_of(X0) = empty_set )
| ~ spl0_40
| ~ spl0_91 ),
inference(resolution,[],[f829,f362]) ).
fof(f7259,plain,
( spl0_531
| ~ spl0_75
| ~ spl0_85 ),
inference(avatar_split_clause,[],[f810,f672,f632,f7257]) ).
fof(f7257,plain,
( spl0_531
<=> ! [X2,X0,X1] :
( ~ member(X0,range_of(cross_product(X1,X2)))
| member(first(f27(X0,cross_product(X1,X2))),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_531])]) ).
fof(f810,plain,
( ! [X2,X0,X1] :
( ~ member(X0,range_of(cross_product(X1,X2)))
| member(first(f27(X0,cross_product(X1,X2))),X1) )
| ~ spl0_75
| ~ spl0_85 ),
inference(resolution,[],[f673,f633]) ).
fof(f7254,plain,
( spl0_530
| ~ spl0_64
| ~ spl0_154 ),
inference(avatar_split_clause,[],[f2183,f2102,f478,f7252]) ).
fof(f7252,plain,
( spl0_530
<=> ! [X0] : disjoint(X0,rotate_right(empty_set)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_530])]) ).
fof(f2183,plain,
( ! [X0] : disjoint(X0,rotate_right(empty_set))
| ~ spl0_64
| ~ spl0_154 ),
inference(resolution,[],[f2103,f479]) ).
fof(f7250,plain,
( spl0_529
| ~ spl0_77
| ~ spl0_85 ),
inference(avatar_split_clause,[],[f809,f672,f640,f7248]) ).
fof(f7248,plain,
( spl0_529
<=> ! [X2,X0,X1] :
( ~ member(X0,range_of(cross_product(X1,X2)))
| member(second(f27(X0,cross_product(X1,X2))),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_529])]) ).
fof(f809,plain,
( ! [X2,X0,X1] :
( ~ member(X0,range_of(cross_product(X1,X2)))
| member(second(f27(X0,cross_product(X1,X2))),X2) )
| ~ spl0_77
| ~ spl0_85 ),
inference(resolution,[],[f673,f641]) ).
fof(f7245,plain,
( spl0_528
| ~ spl0_35
| ~ spl0_84 ),
inference(avatar_split_clause,[],[f785,f668,f340,f7243]) ).
fof(f785,plain,
( ! [X0,X1] :
( cross_product(X0,X1) = empty_set
| ~ little_set(cross_product(X0,X1))
| ordered_pair_predicate(f26(cross_product(X0,X1))) )
| ~ spl0_35
| ~ spl0_84 ),
inference(resolution,[],[f669,f341]) ).
fof(f7241,plain,
( spl0_527
| ~ spl0_75
| ~ spl0_78 ),
inference(avatar_split_clause,[],[f747,f644,f632,f7239]) ).
fof(f7239,plain,
( spl0_527
<=> ! [X2,X0,X1] :
( ~ member(X0,sigma(cross_product(X1,X2)))
| member(first(f16(X0,cross_product(X1,X2))),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_527])]) ).
fof(f747,plain,
( ! [X2,X0,X1] :
( ~ member(X0,sigma(cross_product(X1,X2)))
| member(first(f16(X0,cross_product(X1,X2))),X1) )
| ~ spl0_75
| ~ spl0_78 ),
inference(resolution,[],[f645,f633]) ).
fof(f7237,plain,
( spl0_526
| ~ spl0_77
| ~ spl0_78 ),
inference(avatar_split_clause,[],[f746,f644,f640,f7235]) ).
fof(f7235,plain,
( spl0_526
<=> ! [X2,X0,X1] :
( ~ member(X0,sigma(cross_product(X1,X2)))
| member(second(f16(X0,cross_product(X1,X2))),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_526])]) ).
fof(f746,plain,
( ! [X2,X0,X1] :
( ~ member(X0,sigma(cross_product(X1,X2)))
| member(second(f16(X0,cross_product(X1,X2))),X2) )
| ~ spl0_77
| ~ spl0_78 ),
inference(resolution,[],[f645,f641]) ).
fof(f7233,plain,
( spl0_525
| ~ spl0_74
| ~ spl0_77 ),
inference(avatar_split_clause,[],[f729,f640,f628,f7231]) ).
fof(f7231,plain,
( spl0_525
<=> ! [X2,X0,X1] :
( member(second(f8(X0,cross_product(X1,X2))),X2)
| ~ member(X0,domain_of(cross_product(X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_525])]) ).
fof(f729,plain,
( ! [X2,X0,X1] :
( member(second(f8(X0,cross_product(X1,X2))),X2)
| ~ member(X0,domain_of(cross_product(X1,X2))) )
| ~ spl0_74
| ~ spl0_77 ),
inference(resolution,[],[f641,f629]) ).
fof(f7229,plain,
( spl0_524
| ~ spl0_74
| ~ spl0_75 ),
inference(avatar_split_clause,[],[f723,f632,f628,f7227]) ).
fof(f7227,plain,
( spl0_524
<=> ! [X2,X0,X1] :
( member(first(f8(X0,cross_product(X1,X2))),X1)
| ~ member(X0,domain_of(cross_product(X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_524])]) ).
fof(f723,plain,
( ! [X2,X0,X1] :
( member(first(f8(X0,cross_product(X1,X2))),X1)
| ~ member(X0,domain_of(cross_product(X1,X2))) )
| ~ spl0_74
| ~ spl0_75 ),
inference(resolution,[],[f633,f629]) ).
fof(f7223,plain,
( spl0_523
| ~ spl0_63
| ~ spl0_154 ),
inference(avatar_split_clause,[],[f2182,f2102,f474,f7221]) ).
fof(f7221,plain,
( spl0_523
<=> ! [X0] : disjoint(rotate_right(empty_set),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_523])]) ).
fof(f2182,plain,
( ! [X0] : disjoint(rotate_right(empty_set),X0)
| ~ spl0_63
| ~ spl0_154 ),
inference(resolution,[],[f2103,f475]) ).
fof(f7205,plain,
( spl0_522
| ~ spl0_60
| ~ spl0_154 ),
inference(avatar_split_clause,[],[f2179,f2102,f462,f7203]) ).
fof(f7203,plain,
( spl0_522
<=> ! [X0] : subset(rotate_right(empty_set),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_522])]) ).
fof(f2179,plain,
( ! [X0] : subset(rotate_right(empty_set),X0)
| ~ spl0_60
| ~ spl0_154 ),
inference(resolution,[],[f2103,f463]) ).
fof(f7194,plain,
( spl0_521
| ~ spl0_40
| ~ spl0_153 ),
inference(avatar_split_clause,[],[f2153,f2098,f361,f7191]) ).
fof(f7191,plain,
( spl0_521
<=> empty_set = flip_range_of(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_521])]) ).
fof(f2153,plain,
( empty_set = flip_range_of(empty_set)
| ~ spl0_40
| ~ spl0_153 ),
inference(resolution,[],[f2099,f362]) ).
fof(f7169,plain,
( spl0_520
| ~ spl0_173
| ~ spl0_488 ),
inference(avatar_split_clause,[],[f5705,f5702,f2440,f7167]) ).
fof(f7167,plain,
( spl0_520
<=> ! [X0,X1] :
( estin = compose(X0,X1)
| little_set(f31(f24(compose(X0,X1)),X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_520])]) ).
fof(f5702,plain,
( spl0_488
<=> ! [X0,X1] :
( little_set(f31(f24(compose(X0,X1)),X0,X1))
| empty_set = compose(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_488])]) ).
fof(f5705,plain,
( ! [X0,X1] :
( estin = compose(X0,X1)
| little_set(f31(f24(compose(X0,X1)),X0,X1)) )
| ~ spl0_173
| ~ spl0_488 ),
inference(forward_demodulation,[],[f5703,f2442]) ).
fof(f5703,plain,
( ! [X0,X1] :
( little_set(f31(f24(compose(X0,X1)),X0,X1))
| empty_set = compose(X0,X1) )
| ~ spl0_488 ),
inference(avatar_component_clause,[],[f5702]) ).
fof(f7165,plain,
( spl0_519
| ~ spl0_173
| ~ spl0_487 ),
inference(avatar_split_clause,[],[f5700,f5697,f2440,f7163]) ).
fof(f7163,plain,
( spl0_519
<=> ! [X0,X1] :
( estin = compose(X0,X1)
| little_set(f30(f24(compose(X0,X1)),X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_519])]) ).
fof(f5697,plain,
( spl0_487
<=> ! [X0,X1] :
( little_set(f30(f24(compose(X0,X1)),X0,X1))
| empty_set = compose(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_487])]) ).
fof(f5700,plain,
( ! [X0,X1] :
( estin = compose(X0,X1)
| little_set(f30(f24(compose(X0,X1)),X0,X1)) )
| ~ spl0_173
| ~ spl0_487 ),
inference(forward_demodulation,[],[f5698,f2442]) ).
fof(f5698,plain,
( ! [X0,X1] :
( little_set(f30(f24(compose(X0,X1)),X0,X1))
| empty_set = compose(X0,X1) )
| ~ spl0_487 ),
inference(avatar_component_clause,[],[f5697]) ).
fof(f7161,plain,
( spl0_518
| ~ spl0_173
| ~ spl0_486 ),
inference(avatar_split_clause,[],[f5695,f5692,f2440,f7159]) ).
fof(f7159,plain,
( spl0_518
<=> ! [X0,X1] :
( estin = compose(X0,X1)
| little_set(f29(f24(compose(X0,X1)),X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_518])]) ).
fof(f5692,plain,
( spl0_486
<=> ! [X0,X1] :
( little_set(f29(f24(compose(X0,X1)),X0,X1))
| empty_set = compose(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_486])]) ).
fof(f5695,plain,
( ! [X0,X1] :
( estin = compose(X0,X1)
| little_set(f29(f24(compose(X0,X1)),X0,X1)) )
| ~ spl0_173
| ~ spl0_486 ),
inference(forward_demodulation,[],[f5693,f2442]) ).
fof(f5693,plain,
( ! [X0,X1] :
( little_set(f29(f24(compose(X0,X1)),X0,X1))
| empty_set = compose(X0,X1) )
| ~ spl0_486 ),
inference(avatar_component_clause,[],[f5692]) ).
fof(f7157,plain,
( spl0_517
| ~ spl0_173
| ~ spl0_485 ),
inference(avatar_split_clause,[],[f5690,f5687,f2440,f7155]) ).
fof(f7155,plain,
( spl0_517
<=> ! [X0,X1] :
( estin = apply(X0,X1)
| ordered_pair_predicate(f28(f24(apply(X0,X1)),X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_517])]) ).
fof(f5687,plain,
( spl0_485
<=> ! [X0,X1] :
( ordered_pair_predicate(f28(f24(apply(X0,X1)),X0,X1))
| empty_set = apply(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_485])]) ).
fof(f5690,plain,
( ! [X0,X1] :
( estin = apply(X0,X1)
| ordered_pair_predicate(f28(f24(apply(X0,X1)),X0,X1)) )
| ~ spl0_173
| ~ spl0_485 ),
inference(forward_demodulation,[],[f5688,f2442]) ).
fof(f5688,plain,
( ! [X0,X1] :
( ordered_pair_predicate(f28(f24(apply(X0,X1)),X0,X1))
| empty_set = apply(X0,X1) )
| ~ spl0_485 ),
inference(avatar_component_clause,[],[f5687]) ).
fof(f7153,plain,
( spl0_516
| ~ spl0_173
| ~ spl0_483 ),
inference(avatar_split_clause,[],[f5681,f5678,f2440,f7151]) ).
fof(f7151,plain,
( spl0_516
<=> ! [X0,X1] :
( estin = image(X0,X1)
| ordered_pair_predicate(f22(f24(image(X0,X1)),X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_516])]) ).
fof(f5678,plain,
( spl0_483
<=> ! [X0,X1] :
( ordered_pair_predicate(f22(f24(image(X0,X1)),X0,X1))
| empty_set = image(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_483])]) ).
fof(f5681,plain,
( ! [X0,X1] :
( estin = image(X0,X1)
| ordered_pair_predicate(f22(f24(image(X0,X1)),X0,X1)) )
| ~ spl0_173
| ~ spl0_483 ),
inference(forward_demodulation,[],[f5679,f2442]) ).
fof(f5679,plain,
( ! [X0,X1] :
( ordered_pair_predicate(f22(f24(image(X0,X1)),X0,X1))
| empty_set = image(X0,X1) )
| ~ spl0_483 ),
inference(avatar_component_clause,[],[f5678]) ).
fof(f7138,plain,
( spl0_515
| ~ spl0_64
| ~ spl0_153 ),
inference(avatar_split_clause,[],[f2152,f2098,f478,f7136]) ).
fof(f7136,plain,
( spl0_515
<=> ! [X0] : disjoint(X0,flip_range_of(empty_set)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_515])]) ).
fof(f2152,plain,
( ! [X0] : disjoint(X0,flip_range_of(empty_set))
| ~ spl0_64
| ~ spl0_153 ),
inference(resolution,[],[f2099,f479]) ).
fof(f7134,plain,
( spl0_514
| ~ spl0_173
| ~ spl0_481 ),
inference(avatar_split_clause,[],[f5672,f5669,f2440,f7132]) ).
fof(f7132,plain,
( spl0_514
<=> ! [X0,X1] :
( estin = X0
| ~ member(X0,X1)
| member(f26(X0),sigma(X1))
| ~ little_set(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_514])]) ).
fof(f5669,plain,
( spl0_481
<=> ! [X0,X1] :
( ~ member(X0,X1)
| member(f26(X0),sigma(X1))
| empty_set = X0
| ~ little_set(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_481])]) ).
fof(f5672,plain,
( ! [X0,X1] :
( estin = X0
| ~ member(X0,X1)
| member(f26(X0),sigma(X1))
| ~ little_set(X0) )
| ~ spl0_173
| ~ spl0_481 ),
inference(forward_demodulation,[],[f5670,f2442]) ).
fof(f5670,plain,
( ! [X0,X1] :
( ~ member(X0,X1)
| member(f26(X0),sigma(X1))
| empty_set = X0
| ~ little_set(X0) )
| ~ spl0_481 ),
inference(avatar_component_clause,[],[f5669]) ).
fof(f6925,plain,
( spl0_513
| ~ spl0_63
| ~ spl0_153 ),
inference(avatar_split_clause,[],[f2151,f2098,f474,f6923]) ).
fof(f6923,plain,
( spl0_513
<=> ! [X0] : disjoint(flip_range_of(empty_set),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_513])]) ).
fof(f2151,plain,
( ! [X0] : disjoint(flip_range_of(empty_set),X0)
| ~ spl0_63
| ~ spl0_153 ),
inference(resolution,[],[f2099,f475]) ).
fof(f6821,plain,
( spl0_512
| ~ spl0_173
| ~ spl0_467 ),
inference(avatar_split_clause,[],[f5612,f5609,f2440,f6819]) ).
fof(f6819,plain,
( spl0_512
<=> ! [X0] :
( estin = range_of(X0)
| ~ little_set(range_of(X0))
| ordered_pair_predicate(f27(f26(range_of(X0)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_512])]) ).
fof(f5609,plain,
( spl0_467
<=> ! [X0] :
( empty_set = range_of(X0)
| ~ little_set(range_of(X0))
| ordered_pair_predicate(f27(f26(range_of(X0)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_467])]) ).
fof(f5612,plain,
( ! [X0] :
( estin = range_of(X0)
| ~ little_set(range_of(X0))
| ordered_pair_predicate(f27(f26(range_of(X0)),X0)) )
| ~ spl0_173
| ~ spl0_467 ),
inference(forward_demodulation,[],[f5610,f2442]) ).
fof(f5610,plain,
( ! [X0] :
( empty_set = range_of(X0)
| ~ little_set(range_of(X0))
| ordered_pair_predicate(f27(f26(range_of(X0)),X0)) )
| ~ spl0_467 ),
inference(avatar_component_clause,[],[f5609]) ).
fof(f6817,plain,
( spl0_511
| ~ spl0_173
| ~ spl0_466 ),
inference(avatar_split_clause,[],[f5607,f5604,f2440,f6815]) ).
fof(f6815,plain,
( spl0_511
<=> ! [X0] :
( estin = flip_range_of(X0)
| ~ little_set(flip_range_of(X0))
| little_set(f12(f26(flip_range_of(X0)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_511])]) ).
fof(f5604,plain,
( spl0_466
<=> ! [X0] :
( flip_range_of(X0) = empty_set
| ~ little_set(flip_range_of(X0))
| little_set(f12(f26(flip_range_of(X0)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_466])]) ).
fof(f5607,plain,
( ! [X0] :
( estin = flip_range_of(X0)
| ~ little_set(flip_range_of(X0))
| little_set(f12(f26(flip_range_of(X0)),X0)) )
| ~ spl0_173
| ~ spl0_466 ),
inference(forward_demodulation,[],[f5605,f2442]) ).
fof(f5605,plain,
( ! [X0] :
( flip_range_of(X0) = empty_set
| ~ little_set(flip_range_of(X0))
| little_set(f12(f26(flip_range_of(X0)),X0)) )
| ~ spl0_466 ),
inference(avatar_component_clause,[],[f5604]) ).
fof(f6813,plain,
( spl0_510
| ~ spl0_173
| ~ spl0_465 ),
inference(avatar_split_clause,[],[f5602,f5599,f2440,f6811]) ).
fof(f6811,plain,
( spl0_510
<=> ! [X0] :
( estin = flip_range_of(X0)
| ~ little_set(flip_range_of(X0))
| little_set(f13(f26(flip_range_of(X0)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_510])]) ).
fof(f5599,plain,
( spl0_465
<=> ! [X0] :
( flip_range_of(X0) = empty_set
| ~ little_set(flip_range_of(X0))
| little_set(f13(f26(flip_range_of(X0)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_465])]) ).
fof(f5602,plain,
( ! [X0] :
( estin = flip_range_of(X0)
| ~ little_set(flip_range_of(X0))
| little_set(f13(f26(flip_range_of(X0)),X0)) )
| ~ spl0_173
| ~ spl0_465 ),
inference(forward_demodulation,[],[f5600,f2442]) ).
fof(f5600,plain,
( ! [X0] :
( flip_range_of(X0) = empty_set
| ~ little_set(flip_range_of(X0))
| little_set(f13(f26(flip_range_of(X0)),X0)) )
| ~ spl0_465 ),
inference(avatar_component_clause,[],[f5599]) ).
fof(f6809,plain,
( spl0_509
| ~ spl0_173
| ~ spl0_464 ),
inference(avatar_split_clause,[],[f5597,f5594,f2440,f6807]) ).
fof(f6807,plain,
( spl0_509
<=> ! [X0] :
( estin = flip_range_of(X0)
| ~ little_set(flip_range_of(X0))
| little_set(f14(f26(flip_range_of(X0)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_509])]) ).
fof(f5594,plain,
( spl0_464
<=> ! [X0] :
( flip_range_of(X0) = empty_set
| ~ little_set(flip_range_of(X0))
| little_set(f14(f26(flip_range_of(X0)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_464])]) ).
fof(f5597,plain,
( ! [X0] :
( estin = flip_range_of(X0)
| ~ little_set(flip_range_of(X0))
| little_set(f14(f26(flip_range_of(X0)),X0)) )
| ~ spl0_173
| ~ spl0_464 ),
inference(forward_demodulation,[],[f5595,f2442]) ).
fof(f5595,plain,
( ! [X0] :
( flip_range_of(X0) = empty_set
| ~ little_set(flip_range_of(X0))
| little_set(f14(f26(flip_range_of(X0)),X0)) )
| ~ spl0_464 ),
inference(avatar_component_clause,[],[f5594]) ).
fof(f6805,plain,
( spl0_508
| ~ spl0_173
| ~ spl0_463 ),
inference(avatar_split_clause,[],[f5592,f5589,f2440,f6803]) ).
fof(f6803,plain,
( spl0_508
<=> ! [X0] :
( estin = rotate_right(X0)
| ~ little_set(rotate_right(X0))
| little_set(f9(f26(rotate_right(X0)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_508])]) ).
fof(f5589,plain,
( spl0_463
<=> ! [X0] :
( rotate_right(X0) = empty_set
| ~ little_set(rotate_right(X0))
| little_set(f9(f26(rotate_right(X0)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_463])]) ).
fof(f5592,plain,
( ! [X0] :
( estin = rotate_right(X0)
| ~ little_set(rotate_right(X0))
| little_set(f9(f26(rotate_right(X0)),X0)) )
| ~ spl0_173
| ~ spl0_463 ),
inference(forward_demodulation,[],[f5590,f2442]) ).
fof(f5590,plain,
( ! [X0] :
( rotate_right(X0) = empty_set
| ~ little_set(rotate_right(X0))
| little_set(f9(f26(rotate_right(X0)),X0)) )
| ~ spl0_463 ),
inference(avatar_component_clause,[],[f5589]) ).
fof(f6801,plain,
( spl0_507
| ~ spl0_173
| ~ spl0_462 ),
inference(avatar_split_clause,[],[f5587,f5584,f2440,f6799]) ).
fof(f6799,plain,
( spl0_507
<=> ! [X0] :
( estin = rotate_right(X0)
| ~ little_set(rotate_right(X0))
| little_set(f10(f26(rotate_right(X0)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_507])]) ).
fof(f5584,plain,
( spl0_462
<=> ! [X0] :
( rotate_right(X0) = empty_set
| ~ little_set(rotate_right(X0))
| little_set(f10(f26(rotate_right(X0)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_462])]) ).
fof(f5587,plain,
( ! [X0] :
( estin = rotate_right(X0)
| ~ little_set(rotate_right(X0))
| little_set(f10(f26(rotate_right(X0)),X0)) )
| ~ spl0_173
| ~ spl0_462 ),
inference(forward_demodulation,[],[f5585,f2442]) ).
fof(f5585,plain,
( ! [X0] :
( rotate_right(X0) = empty_set
| ~ little_set(rotate_right(X0))
| little_set(f10(f26(rotate_right(X0)),X0)) )
| ~ spl0_462 ),
inference(avatar_component_clause,[],[f5584]) ).
fof(f6797,plain,
( spl0_506
| ~ spl0_173
| ~ spl0_461 ),
inference(avatar_split_clause,[],[f5582,f5579,f2440,f6795]) ).
fof(f6795,plain,
( spl0_506
<=> ! [X0] :
( estin = rotate_right(X0)
| ~ little_set(rotate_right(X0))
| little_set(f11(f26(rotate_right(X0)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_506])]) ).
fof(f5579,plain,
( spl0_461
<=> ! [X0] :
( rotate_right(X0) = empty_set
| ~ little_set(rotate_right(X0))
| little_set(f11(f26(rotate_right(X0)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_461])]) ).
fof(f5582,plain,
( ! [X0] :
( estin = rotate_right(X0)
| ~ little_set(rotate_right(X0))
| little_set(f11(f26(rotate_right(X0)),X0)) )
| ~ spl0_173
| ~ spl0_461 ),
inference(forward_demodulation,[],[f5580,f2442]) ).
fof(f5580,plain,
( ! [X0] :
( rotate_right(X0) = empty_set
| ~ little_set(rotate_right(X0))
| little_set(f11(f26(rotate_right(X0)),X0)) )
| ~ spl0_461 ),
inference(avatar_component_clause,[],[f5579]) ).
fof(f6793,plain,
( spl0_505
| ~ spl0_173
| ~ spl0_460 ),
inference(avatar_split_clause,[],[f5577,f5574,f2440,f6791]) ).
fof(f6791,plain,
( spl0_505
<=> ! [X0] :
( estin = domain_of(X0)
| ~ little_set(domain_of(X0))
| ordered_pair_predicate(f8(f26(domain_of(X0)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_505])]) ).
fof(f5574,plain,
( spl0_460
<=> ! [X0] :
( domain_of(X0) = empty_set
| ~ little_set(domain_of(X0))
| ordered_pair_predicate(f8(f26(domain_of(X0)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_460])]) ).
fof(f5577,plain,
( ! [X0] :
( estin = domain_of(X0)
| ~ little_set(domain_of(X0))
| ordered_pair_predicate(f8(f26(domain_of(X0)),X0)) )
| ~ spl0_173
| ~ spl0_460 ),
inference(forward_demodulation,[],[f5575,f2442]) ).
fof(f5575,plain,
( ! [X0] :
( domain_of(X0) = empty_set
| ~ little_set(domain_of(X0))
| ordered_pair_predicate(f8(f26(domain_of(X0)),X0)) )
| ~ spl0_460 ),
inference(avatar_component_clause,[],[f5574]) ).
fof(f6789,plain,
( spl0_504
| ~ spl0_173
| ~ spl0_459 ),
inference(avatar_split_clause,[],[f5572,f5569,f2440,f6787]) ).
fof(f6787,plain,
( spl0_504
<=> ! [X0] :
( second(X0) = estin
| ~ little_set(second(X0))
| little_set(f6(f26(second(X0)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_504])]) ).
fof(f5569,plain,
( spl0_459
<=> ! [X0] :
( second(X0) = empty_set
| ~ little_set(second(X0))
| little_set(f6(f26(second(X0)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_459])]) ).
fof(f5572,plain,
( ! [X0] :
( second(X0) = estin
| ~ little_set(second(X0))
| little_set(f6(f26(second(X0)),X0)) )
| ~ spl0_173
| ~ spl0_459 ),
inference(forward_demodulation,[],[f5570,f2442]) ).
fof(f5570,plain,
( ! [X0] :
( second(X0) = empty_set
| ~ little_set(second(X0))
| little_set(f6(f26(second(X0)),X0)) )
| ~ spl0_459 ),
inference(avatar_component_clause,[],[f5569]) ).
fof(f6784,plain,
( spl0_503
| ~ spl0_60
| ~ spl0_153 ),
inference(avatar_split_clause,[],[f2148,f2098,f462,f6782]) ).
fof(f6782,plain,
( spl0_503
<=> ! [X0] : subset(flip_range_of(empty_set),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_503])]) ).
fof(f2148,plain,
( ! [X0] : subset(flip_range_of(empty_set),X0)
| ~ spl0_60
| ~ spl0_153 ),
inference(resolution,[],[f2099,f463]) ).
fof(f6780,plain,
( spl0_502
| ~ spl0_173
| ~ spl0_457 ),
inference(avatar_split_clause,[],[f5561,f5558,f2440,f6778]) ).
fof(f6778,plain,
( spl0_502
<=> ! [X0] :
( second(X0) = estin
| ~ little_set(second(X0))
| little_set(f7(f26(second(X0)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_502])]) ).
fof(f5558,plain,
( spl0_457
<=> ! [X0] :
( second(X0) = empty_set
| ~ little_set(second(X0))
| little_set(f7(f26(second(X0)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_457])]) ).
fof(f5561,plain,
( ! [X0] :
( second(X0) = estin
| ~ little_set(second(X0))
| little_set(f7(f26(second(X0)),X0)) )
| ~ spl0_173
| ~ spl0_457 ),
inference(forward_demodulation,[],[f5559,f2442]) ).
fof(f5559,plain,
( ! [X0] :
( second(X0) = empty_set
| ~ little_set(second(X0))
| little_set(f7(f26(second(X0)),X0)) )
| ~ spl0_457 ),
inference(avatar_component_clause,[],[f5558]) ).
fof(f6776,plain,
( spl0_501
| ~ spl0_173
| ~ spl0_456 ),
inference(avatar_split_clause,[],[f5556,f5553,f2440,f6774]) ).
fof(f6774,plain,
( spl0_501
<=> ! [X0] :
( first(X0) = estin
| ~ little_set(first(X0))
| little_set(f4(f26(first(X0)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_501])]) ).
fof(f5553,plain,
( spl0_456
<=> ! [X0] :
( first(X0) = empty_set
| ~ little_set(first(X0))
| little_set(f4(f26(first(X0)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_456])]) ).
fof(f5556,plain,
( ! [X0] :
( first(X0) = estin
| ~ little_set(first(X0))
| little_set(f4(f26(first(X0)),X0)) )
| ~ spl0_173
| ~ spl0_456 ),
inference(forward_demodulation,[],[f5554,f2442]) ).
fof(f5554,plain,
( ! [X0] :
( first(X0) = empty_set
| ~ little_set(first(X0))
| little_set(f4(f26(first(X0)),X0)) )
| ~ spl0_456 ),
inference(avatar_component_clause,[],[f5553]) ).
fof(f6772,plain,
( spl0_500
| ~ spl0_173
| ~ spl0_455 ),
inference(avatar_split_clause,[],[f5551,f5548,f2440,f6770]) ).
fof(f6770,plain,
( spl0_500
<=> ! [X0] :
( first(X0) = estin
| ~ little_set(first(X0))
| little_set(f5(f26(first(X0)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_500])]) ).
fof(f5548,plain,
( spl0_455
<=> ! [X0] :
( first(X0) = empty_set
| ~ little_set(first(X0))
| little_set(f5(f26(first(X0)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_455])]) ).
fof(f5551,plain,
( ! [X0] :
( first(X0) = estin
| ~ little_set(first(X0))
| little_set(f5(f26(first(X0)),X0)) )
| ~ spl0_173
| ~ spl0_455 ),
inference(forward_demodulation,[],[f5549,f2442]) ).
fof(f5549,plain,
( ! [X0] :
( first(X0) = empty_set
| ~ little_set(first(X0))
| little_set(f5(f26(first(X0)),X0)) )
| ~ spl0_455 ),
inference(avatar_component_clause,[],[f5548]) ).
fof(f6053,plain,
( spl0_499
| ~ spl0_40
| ~ spl0_151 ),
inference(avatar_split_clause,[],[f2122,f2025,f361,f6050]) ).
fof(f6050,plain,
( spl0_499
<=> empty_set = converse(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_499])]) ).
fof(f2122,plain,
( empty_set = converse(empty_set)
| ~ spl0_40
| ~ spl0_151 ),
inference(resolution,[],[f2026,f362]) ).
fof(f5746,plain,
( spl0_498
| ~ spl0_65
| ~ spl0_118 ),
inference(avatar_split_clause,[],[f1278,f1179,f482,f5744]) ).
fof(f5744,plain,
( spl0_498
<=> ! [X0,X1] :
( ~ little_set(second(X0))
| ~ member(X0,X1)
| ~ ordered_pair_predicate(X0)
| ordered_pair_predicate(f27(second(X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_498])]) ).
fof(f1278,plain,
( ! [X0,X1] :
( ~ little_set(second(X0))
| ~ member(X0,X1)
| ~ ordered_pair_predicate(X0)
| ordered_pair_predicate(f27(second(X0),X1)) )
| ~ spl0_65
| ~ spl0_118 ),
inference(resolution,[],[f1180,f483]) ).
fof(f5742,plain,
( spl0_497
| ~ spl0_53
| ~ spl0_117 ),
inference(avatar_split_clause,[],[f1273,f1175,f434,f5740]) ).
fof(f5740,plain,
( spl0_497
<=> ! [X0,X1] :
( ~ little_set(first(X0))
| ~ member(X0,X1)
| ~ ordered_pair_predicate(X0)
| ordered_pair_predicate(f8(first(X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_497])]) ).
fof(f1273,plain,
( ! [X0,X1] :
( ~ little_set(first(X0))
| ~ member(X0,X1)
| ~ ordered_pair_predicate(X0)
| ordered_pair_predicate(f8(first(X0),X1)) )
| ~ spl0_53
| ~ spl0_117 ),
inference(resolution,[],[f1176,f435]) ).
fof(f5738,plain,
( spl0_496
| ~ spl0_38
| ~ spl0_111 ),
inference(avatar_split_clause,[],[f1155,f1085,f353,f5736]) ).
fof(f5736,plain,
( spl0_496
<=> ! [X2,X0,X1] :
( ~ member(X0,apply(X1,X2))
| ordered_pair_predicate(X0)
| ~ relation(second(f28(X0,X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_496])]) ).
fof(f1155,plain,
( ! [X2,X0,X1] :
( ~ member(X0,apply(X1,X2))
| ordered_pair_predicate(X0)
| ~ relation(second(f28(X0,X1,X2))) )
| ~ spl0_38
| ~ spl0_111 ),
inference(resolution,[],[f1086,f354]) ).
fof(f5734,plain,
( spl0_495
| ~ spl0_28
| ~ spl0_107 ),
inference(avatar_split_clause,[],[f1110,f1068,f306,f5732]) ).
fof(f5732,plain,
( spl0_495
<=> ! [X2,X0,X1] :
( ~ member(X0,image(converse(X1),X2))
| ordered_pair_predicate(first(f22(X0,converse(X1),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_495])]) ).
fof(f1110,plain,
( ! [X2,X0,X1] :
( ~ member(X0,image(converse(X1),X2))
| ordered_pair_predicate(first(f22(X0,converse(X1),X2))) )
| ~ spl0_28
| ~ spl0_107 ),
inference(resolution,[],[f1069,f307]) ).
fof(f5730,plain,
( spl0_494
| ~ spl0_38
| ~ spl0_107 ),
inference(avatar_split_clause,[],[f1094,f1068,f353,f5728]) ).
fof(f5728,plain,
( spl0_494
<=> ! [X2,X0,X1] :
( ~ member(X0,image(X1,X2))
| ordered_pair_predicate(first(f22(X0,X1,X2)))
| ~ relation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_494])]) ).
fof(f1094,plain,
( ! [X2,X0,X1] :
( ~ member(X0,image(X1,X2))
| ordered_pair_predicate(first(f22(X0,X1,X2)))
| ~ relation(X1) )
| ~ spl0_38
| ~ spl0_107 ),
inference(resolution,[],[f1069,f354]) ).
fof(f5726,plain,
( spl0_493
| ~ spl0_37
| ~ spl0_104 ),
inference(avatar_split_clause,[],[f1050,f966,f349,f5724]) ).
fof(f5724,plain,
( spl0_493
<=> ! [X2,X0,X1] :
( ~ member(X0,apply(powerset(X1),X2))
| subset(f28(X0,powerset(X1),X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_493])]) ).
fof(f1050,plain,
( ! [X2,X0,X1] :
( ~ member(X0,apply(powerset(X1),X2))
| subset(f28(X0,powerset(X1),X2),X1) )
| ~ spl0_37
| ~ spl0_104 ),
inference(resolution,[],[f967,f350]) ).
fof(f5722,plain,
( spl0_492
| ~ spl0_34
| ~ spl0_104 ),
inference(avatar_split_clause,[],[f1036,f966,f336,f5720]) ).
fof(f5720,plain,
( spl0_492
<=> ! [X2,X0,X1] :
( ~ member(X0,apply(complement(X1),X2))
| ~ member(f28(X0,complement(X1),X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_492])]) ).
fof(f1036,plain,
( ! [X2,X0,X1] :
( ~ member(X0,apply(complement(X1),X2))
| ~ member(f28(X0,complement(X1),X2),X1) )
| ~ spl0_34
| ~ spl0_104 ),
inference(resolution,[],[f967,f337]) ).
fof(f5717,plain,
( spl0_491
| ~ spl0_64
| ~ spl0_151 ),
inference(avatar_split_clause,[],[f2121,f2025,f478,f5715]) ).
fof(f5715,plain,
( spl0_491
<=> ! [X0] : disjoint(X0,converse(empty_set)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_491])]) ).
fof(f2121,plain,
( ! [X0] : disjoint(X0,converse(empty_set))
| ~ spl0_64
| ~ spl0_151 ),
inference(resolution,[],[f2026,f479]) ).
fof(f5713,plain,
( spl0_490
| ~ spl0_37
| ~ spl0_103 ),
inference(avatar_split_clause,[],[f1015,f960,f349,f5711]) ).
fof(f5711,plain,
( spl0_490
<=> ! [X2,X0,X1] :
( ~ member(X0,image(X1,powerset(X2)))
| subset(f22(X0,X1,powerset(X2)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_490])]) ).
fof(f1015,plain,
( ! [X2,X0,X1] :
( ~ member(X0,image(X1,powerset(X2)))
| subset(f22(X0,X1,powerset(X2)),X2) )
| ~ spl0_37
| ~ spl0_103 ),
inference(resolution,[],[f961,f350]) ).
fof(f5709,plain,
( spl0_489
| ~ spl0_34
| ~ spl0_103 ),
inference(avatar_split_clause,[],[f1001,f960,f336,f5707]) ).
fof(f5707,plain,
( spl0_489
<=> ! [X2,X0,X1] :
( ~ member(X0,image(X1,complement(X2)))
| ~ member(f22(X0,X1,complement(X2)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_489])]) ).
fof(f1001,plain,
( ! [X2,X0,X1] :
( ~ member(X0,image(X1,complement(X2)))
| ~ member(f22(X0,X1,complement(X2)),X2) )
| ~ spl0_34
| ~ spl0_103 ),
inference(resolution,[],[f961,f337]) ).
fof(f5704,plain,
( spl0_488
| ~ spl0_40
| ~ spl0_99 ),
inference(avatar_split_clause,[],[f948,f860,f361,f5702]) ).
fof(f948,plain,
( ! [X0,X1] :
( little_set(f31(f24(compose(X0,X1)),X0,X1))
| empty_set = compose(X0,X1) )
| ~ spl0_40
| ~ spl0_99 ),
inference(resolution,[],[f861,f362]) ).
fof(f5699,plain,
( spl0_487
| ~ spl0_40
| ~ spl0_98 ),
inference(avatar_split_clause,[],[f939,f856,f361,f5697]) ).
fof(f939,plain,
( ! [X0,X1] :
( little_set(f30(f24(compose(X0,X1)),X0,X1))
| empty_set = compose(X0,X1) )
| ~ spl0_40
| ~ spl0_98 ),
inference(resolution,[],[f857,f362]) ).
fof(f5694,plain,
( spl0_486
| ~ spl0_40
| ~ spl0_97 ),
inference(avatar_split_clause,[],[f930,f852,f361,f5692]) ).
fof(f930,plain,
( ! [X0,X1] :
( little_set(f29(f24(compose(X0,X1)),X0,X1))
| empty_set = compose(X0,X1) )
| ~ spl0_40
| ~ spl0_97 ),
inference(resolution,[],[f853,f362]) ).
fof(f5689,plain,
( spl0_485
| ~ spl0_40
| ~ spl0_96 ),
inference(avatar_split_clause,[],[f921,f848,f361,f5687]) ).
fof(f921,plain,
( ! [X0,X1] :
( ordered_pair_predicate(f28(f24(apply(X0,X1)),X0,X1))
| empty_set = apply(X0,X1) )
| ~ spl0_40
| ~ spl0_96 ),
inference(resolution,[],[f849,f362]) ).
fof(f5685,plain,
( spl0_484
| ~ spl0_30
| ~ spl0_95 ),
inference(avatar_split_clause,[],[f909,f844,f314,f5683]) ).
fof(f5683,plain,
( spl0_484
<=> ! [X0] :
( f18(range_of(X0)) = second(f27(f18(range_of(X0)),X0))
| relation(range_of(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_484])]) ).
fof(f909,plain,
( ! [X0] :
( f18(range_of(X0)) = second(f27(f18(range_of(X0)),X0))
| relation(range_of(X0)) )
| ~ spl0_30
| ~ spl0_95 ),
inference(resolution,[],[f845,f315]) ).
fof(f5680,plain,
( spl0_483
| ~ spl0_40
| ~ spl0_94 ),
inference(avatar_split_clause,[],[f903,f840,f361,f5678]) ).
fof(f903,plain,
( ! [X0,X1] :
( ordered_pair_predicate(f22(f24(image(X0,X1)),X0,X1))
| empty_set = image(X0,X1) )
| ~ spl0_40
| ~ spl0_94 ),
inference(resolution,[],[f841,f362]) ).
fof(f5676,plain,
( spl0_482
| ~ spl0_85
| ~ spl0_93 ),
inference(avatar_split_clause,[],[f894,f836,f672,f5674]) ).
fof(f894,plain,
( ! [X2,X0,X1] :
( ~ member(X0,X1)
| member(f27(X2,X0),sigma(X1))
| ~ member(X2,range_of(X0)) )
| ~ spl0_85
| ~ spl0_93 ),
inference(resolution,[],[f837,f673]) ).
fof(f5671,plain,
( spl0_481
| ~ spl0_84
| ~ spl0_93 ),
inference(avatar_split_clause,[],[f893,f836,f668,f5669]) ).
fof(f893,plain,
( ! [X0,X1] :
( ~ member(X0,X1)
| member(f26(X0),sigma(X1))
| empty_set = X0
| ~ little_set(X0) )
| ~ spl0_84
| ~ spl0_93 ),
inference(resolution,[],[f837,f669]) ).
fof(f5666,plain,
( spl0_480
| ~ spl0_63
| ~ spl0_151 ),
inference(avatar_split_clause,[],[f2120,f2025,f474,f5664]) ).
fof(f5664,plain,
( spl0_480
<=> ! [X0] : disjoint(converse(empty_set),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_480])]) ).
fof(f2120,plain,
( ! [X0] : disjoint(converse(empty_set),X0)
| ~ spl0_63
| ~ spl0_151 ),
inference(resolution,[],[f2026,f475]) ).
fof(f5662,plain,
( spl0_479
| ~ spl0_78
| ~ spl0_93 ),
inference(avatar_split_clause,[],[f887,f836,f644,f5660]) ).
fof(f887,plain,
( ! [X2,X0,X1] :
( ~ member(X0,X1)
| member(f16(X2,X0),sigma(X1))
| ~ member(X2,sigma(X0)) )
| ~ spl0_78
| ~ spl0_93 ),
inference(resolution,[],[f837,f645]) ).
fof(f5658,plain,
( spl0_478
| ~ spl0_74
| ~ spl0_93 ),
inference(avatar_split_clause,[],[f885,f836,f628,f5656]) ).
fof(f885,plain,
( ! [X2,X0,X1] :
( ~ member(X0,X1)
| member(f8(X2,X0),sigma(X1))
| ~ member(X2,domain_of(X0)) )
| ~ spl0_74
| ~ spl0_93 ),
inference(resolution,[],[f837,f629]) ).
fof(f5654,plain,
( spl0_477
| ~ spl0_82
| ~ spl0_93 ),
inference(avatar_split_clause,[],[f883,f836,f660,f5652]) ).
fof(f5652,plain,
( spl0_477
<=> ! [X2,X0,X1] :
( ~ member(powerset(X0),X1)
| member(X2,sigma(X1))
| ~ subset(X2,X0)
| ~ little_set(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_477])]) ).
fof(f883,plain,
( ! [X2,X0,X1] :
( ~ member(powerset(X0),X1)
| member(X2,sigma(X1))
| ~ subset(X2,X0)
| ~ little_set(X2) )
| ~ spl0_82
| ~ spl0_93 ),
inference(resolution,[],[f837,f661]) ).
fof(f5650,plain,
( spl0_476
| ~ spl0_79
| ~ spl0_93 ),
inference(avatar_split_clause,[],[f882,f836,f648,f5648]) ).
fof(f882,plain,
( ! [X2,X0,X1] :
( ~ member(f16(X0,X1),X2)
| member(X0,sigma(X2))
| ~ member(X0,sigma(X1)) )
| ~ spl0_79
| ~ spl0_93 ),
inference(resolution,[],[f837,f649]) ).
fof(f5646,plain,
( spl0_475
| ~ spl0_73
| ~ spl0_93 ),
inference(avatar_split_clause,[],[f880,f836,f624,f5644]) ).
fof(f5644,plain,
( spl0_475
<=> ! [X2,X0,X1] :
( ~ member(complement(X0),X1)
| member(X2,sigma(X1))
| member(X2,X0)
| ~ little_set(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_475])]) ).
fof(f880,plain,
( ! [X2,X0,X1] :
( ~ member(complement(X0),X1)
| member(X2,sigma(X1))
| member(X2,X0)
| ~ little_set(X2) )
| ~ spl0_73
| ~ spl0_93 ),
inference(resolution,[],[f837,f625]) ).
fof(f5642,plain,
( spl0_474
| ~ spl0_72
| ~ spl0_93 ),
inference(avatar_split_clause,[],[f879,f836,f620,f5640]) ).
fof(f5640,plain,
( spl0_474
<=> ! [X2,X0,X1] :
( ~ member(f7(X0,X1),X2)
| member(X0,sigma(X2))
| ~ member(X0,second(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_474])]) ).
fof(f879,plain,
( ! [X2,X0,X1] :
( ~ member(f7(X0,X1),X2)
| member(X0,sigma(X2))
| ~ member(X0,second(X1)) )
| ~ spl0_72
| ~ spl0_93 ),
inference(resolution,[],[f837,f621]) ).
fof(f5638,plain,
( spl0_473
| ~ spl0_71
| ~ spl0_93 ),
inference(avatar_split_clause,[],[f878,f836,f616,f5636]) ).
fof(f5636,plain,
( spl0_473
<=> ! [X2,X0,X1] :
( ~ member(f4(X0,X1),X2)
| member(X0,sigma(X2))
| ~ member(X0,first(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_473])]) ).
fof(f878,plain,
( ! [X2,X0,X1] :
( ~ member(f4(X0,X1),X2)
| member(X0,sigma(X2))
| ~ member(X0,first(X1)) )
| ~ spl0_71
| ~ spl0_93 ),
inference(resolution,[],[f837,f617]) ).
fof(f5634,plain,
( spl0_472
| ~ spl0_30
| ~ spl0_91 ),
inference(avatar_split_clause,[],[f870,f828,f314,f5632]) ).
fof(f5632,plain,
( spl0_472
<=> ! [X0] :
( f18(domain_of(X0)) = first(f8(f18(domain_of(X0)),X0))
| relation(domain_of(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_472])]) ).
fof(f870,plain,
( ! [X0] :
( f18(domain_of(X0)) = first(f8(f18(domain_of(X0)),X0))
| relation(domain_of(X0)) )
| ~ spl0_30
| ~ spl0_91 ),
inference(resolution,[],[f829,f315]) ).
fof(f5629,plain,
( spl0_471
| ~ spl0_66
| ~ spl0_85 ),
inference(avatar_split_clause,[],[f822,f672,f486,f5627]) ).
fof(f5627,plain,
( spl0_471
<=> ! [X0] :
( ~ member(X0,range_of(identity_relation))
| first(f27(X0,identity_relation)) = second(f27(X0,identity_relation)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_471])]) ).
fof(f822,plain,
( ! [X0] :
( ~ member(X0,range_of(identity_relation))
| first(f27(X0,identity_relation)) = second(f27(X0,identity_relation)) )
| ~ spl0_66
| ~ spl0_85 ),
inference(resolution,[],[f673,f487]) ).
fof(f5625,plain,
( spl0_470
| ~ spl0_51
| ~ spl0_85 ),
inference(avatar_split_clause,[],[f806,f672,f426,f5623]) ).
fof(f5623,plain,
( spl0_470
<=> ! [X2,X0,X1] :
( ~ member(X0,range_of(intersection(X1,X2)))
| member(f27(X0,intersection(X1,X2)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_470])]) ).
fof(f806,plain,
( ! [X2,X0,X1] :
( ~ member(X0,range_of(intersection(X1,X2)))
| member(f27(X0,intersection(X1,X2)),X1) )
| ~ spl0_51
| ~ spl0_85 ),
inference(resolution,[],[f673,f427]) ).
fof(f5620,plain,
( spl0_469
| ~ spl0_60
| ~ spl0_151 ),
inference(avatar_split_clause,[],[f2117,f2025,f462,f5618]) ).
fof(f5618,plain,
( spl0_469
<=> ! [X0] : subset(converse(empty_set),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_469])]) ).
fof(f2117,plain,
( ! [X0] : subset(converse(empty_set),X0)
| ~ spl0_60
| ~ spl0_151 ),
inference(resolution,[],[f2026,f463]) ).
fof(f5616,plain,
( spl0_468
| ~ spl0_52
| ~ spl0_85 ),
inference(avatar_split_clause,[],[f805,f672,f430,f5614]) ).
fof(f5614,plain,
( spl0_468
<=> ! [X2,X0,X1] :
( ~ member(X0,range_of(intersection(X1,X2)))
| member(f27(X0,intersection(X1,X2)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_468])]) ).
fof(f805,plain,
( ! [X2,X0,X1] :
( ~ member(X0,range_of(intersection(X1,X2)))
| member(f27(X0,intersection(X1,X2)),X2) )
| ~ spl0_52
| ~ spl0_85 ),
inference(resolution,[],[f673,f431]) ).
fof(f5611,plain,
( spl0_467
| ~ spl0_65
| ~ spl0_84 ),
inference(avatar_split_clause,[],[f795,f668,f482,f5609]) ).
fof(f795,plain,
( ! [X0] :
( empty_set = range_of(X0)
| ~ little_set(range_of(X0))
| ordered_pair_predicate(f27(f26(range_of(X0)),X0)) )
| ~ spl0_65
| ~ spl0_84 ),
inference(resolution,[],[f669,f483]) ).
fof(f5606,plain,
( spl0_466
| ~ spl0_57
| ~ spl0_84 ),
inference(avatar_split_clause,[],[f792,f668,f450,f5604]) ).
fof(f792,plain,
( ! [X0] :
( flip_range_of(X0) = empty_set
| ~ little_set(flip_range_of(X0))
| little_set(f12(f26(flip_range_of(X0)),X0)) )
| ~ spl0_57
| ~ spl0_84 ),
inference(resolution,[],[f669,f451]) ).
fof(f5601,plain,
( spl0_465
| ~ spl0_58
| ~ spl0_84 ),
inference(avatar_split_clause,[],[f791,f668,f454,f5599]) ).
fof(f791,plain,
( ! [X0] :
( flip_range_of(X0) = empty_set
| ~ little_set(flip_range_of(X0))
| little_set(f13(f26(flip_range_of(X0)),X0)) )
| ~ spl0_58
| ~ spl0_84 ),
inference(resolution,[],[f669,f455]) ).
fof(f5596,plain,
( spl0_464
| ~ spl0_59
| ~ spl0_84 ),
inference(avatar_split_clause,[],[f790,f668,f458,f5594]) ).
fof(f790,plain,
( ! [X0] :
( flip_range_of(X0) = empty_set
| ~ little_set(flip_range_of(X0))
| little_set(f14(f26(flip_range_of(X0)),X0)) )
| ~ spl0_59
| ~ spl0_84 ),
inference(resolution,[],[f669,f459]) ).
fof(f5591,plain,
( spl0_463
| ~ spl0_54
| ~ spl0_84 ),
inference(avatar_split_clause,[],[f789,f668,f438,f5589]) ).
fof(f789,plain,
( ! [X0] :
( rotate_right(X0) = empty_set
| ~ little_set(rotate_right(X0))
| little_set(f9(f26(rotate_right(X0)),X0)) )
| ~ spl0_54
| ~ spl0_84 ),
inference(resolution,[],[f669,f439]) ).
fof(f5586,plain,
( spl0_462
| ~ spl0_55
| ~ spl0_84 ),
inference(avatar_split_clause,[],[f788,f668,f442,f5584]) ).
fof(f788,plain,
( ! [X0] :
( rotate_right(X0) = empty_set
| ~ little_set(rotate_right(X0))
| little_set(f10(f26(rotate_right(X0)),X0)) )
| ~ spl0_55
| ~ spl0_84 ),
inference(resolution,[],[f669,f443]) ).
fof(f5581,plain,
( spl0_461
| ~ spl0_56
| ~ spl0_84 ),
inference(avatar_split_clause,[],[f787,f668,f446,f5579]) ).
fof(f787,plain,
( ! [X0] :
( rotate_right(X0) = empty_set
| ~ little_set(rotate_right(X0))
| little_set(f11(f26(rotate_right(X0)),X0)) )
| ~ spl0_56
| ~ spl0_84 ),
inference(resolution,[],[f669,f447]) ).
fof(f5576,plain,
( spl0_460
| ~ spl0_53
| ~ spl0_84 ),
inference(avatar_split_clause,[],[f782,f668,f434,f5574]) ).
fof(f782,plain,
( ! [X0] :
( domain_of(X0) = empty_set
| ~ little_set(domain_of(X0))
| ordered_pair_predicate(f8(f26(domain_of(X0)),X0)) )
| ~ spl0_53
| ~ spl0_84 ),
inference(resolution,[],[f669,f435]) ).
fof(f5571,plain,
( spl0_459
| ~ spl0_48
| ~ spl0_84 ),
inference(avatar_split_clause,[],[f777,f668,f414,f5569]) ).
fof(f777,plain,
( ! [X0] :
( second(X0) = empty_set
| ~ little_set(second(X0))
| little_set(f6(f26(second(X0)),X0)) )
| ~ spl0_48
| ~ spl0_84 ),
inference(resolution,[],[f669,f415]) ).
fof(f5566,plain,
( spl0_458
| ~ spl0_40
| ~ spl0_141 ),
inference(avatar_split_clause,[],[f2083,f1749,f361,f5563]) ).
fof(f5563,plain,
( spl0_458
<=> empty_set = range_of(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_458])]) ).
fof(f2083,plain,
( empty_set = range_of(empty_set)
| ~ spl0_40
| ~ spl0_141 ),
inference(resolution,[],[f1750,f362]) ).
fof(f5560,plain,
( spl0_457
| ~ spl0_49
| ~ spl0_84 ),
inference(avatar_split_clause,[],[f776,f668,f418,f5558]) ).
fof(f776,plain,
( ! [X0] :
( second(X0) = empty_set
| ~ little_set(second(X0))
| little_set(f7(f26(second(X0)),X0)) )
| ~ spl0_49
| ~ spl0_84 ),
inference(resolution,[],[f669,f419]) ).
fof(f5555,plain,
( spl0_456
| ~ spl0_46
| ~ spl0_84 ),
inference(avatar_split_clause,[],[f775,f668,f406,f5553]) ).
fof(f775,plain,
( ! [X0] :
( first(X0) = empty_set
| ~ little_set(first(X0))
| little_set(f4(f26(first(X0)),X0)) )
| ~ spl0_46
| ~ spl0_84 ),
inference(resolution,[],[f669,f407]) ).
fof(f5550,plain,
( spl0_455
| ~ spl0_47
| ~ spl0_84 ),
inference(avatar_split_clause,[],[f774,f668,f410,f5548]) ).
fof(f774,plain,
( ! [X0] :
( first(X0) = empty_set
| ~ little_set(first(X0))
| little_set(f5(f26(first(X0)),X0)) )
| ~ spl0_47
| ~ spl0_84 ),
inference(resolution,[],[f669,f411]) ).
fof(f5545,plain,
( spl0_454
| ~ spl0_66
| ~ spl0_78 ),
inference(avatar_split_clause,[],[f759,f644,f486,f5543]) ).
fof(f5543,plain,
( spl0_454
<=> ! [X0] :
( ~ member(X0,sigma(identity_relation))
| first(f16(X0,identity_relation)) = second(f16(X0,identity_relation)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_454])]) ).
fof(f759,plain,
( ! [X0] :
( ~ member(X0,sigma(identity_relation))
| first(f16(X0,identity_relation)) = second(f16(X0,identity_relation)) )
| ~ spl0_66
| ~ spl0_78 ),
inference(resolution,[],[f645,f487]) ).
fof(f5541,plain,
( spl0_453
| ~ spl0_51
| ~ spl0_78 ),
inference(avatar_split_clause,[],[f743,f644,f426,f5539]) ).
fof(f743,plain,
( ! [X2,X0,X1] :
( ~ member(X0,sigma(intersection(X1,X2)))
| member(f16(X0,intersection(X1,X2)),X1) )
| ~ spl0_51
| ~ spl0_78 ),
inference(resolution,[],[f645,f427]) ).
fof(f5537,plain,
( spl0_452
| ~ spl0_52
| ~ spl0_78 ),
inference(avatar_split_clause,[],[f742,f644,f430,f5535]) ).
fof(f742,plain,
( ! [X2,X0,X1] :
( ~ member(X0,sigma(intersection(X1,X2)))
| member(f16(X0,intersection(X1,X2)),X2) )
| ~ spl0_52
| ~ spl0_78 ),
inference(resolution,[],[f645,f431]) ).
fof(f5533,plain,
( spl0_451
| ~ spl0_64
| ~ spl0_77 ),
inference(avatar_split_clause,[],[f733,f640,f478,f5531]) ).
fof(f5531,plain,
( spl0_451
<=> ! [X2,X0,X1] :
( member(second(f23(X0,cross_product(X1,X2))),X2)
| disjoint(X0,cross_product(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_451])]) ).
fof(f733,plain,
( ! [X2,X0,X1] :
( member(second(f23(X0,cross_product(X1,X2))),X2)
| disjoint(X0,cross_product(X1,X2)) )
| ~ spl0_64
| ~ spl0_77 ),
inference(resolution,[],[f641,f479]) ).
fof(f5529,plain,
( spl0_450
| ~ spl0_63
| ~ spl0_77 ),
inference(avatar_split_clause,[],[f732,f640,f474,f5527]) ).
fof(f5527,plain,
( spl0_450
<=> ! [X2,X0,X1] :
( member(second(f23(cross_product(X0,X1),X2)),X1)
| disjoint(cross_product(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_450])]) ).
fof(f732,plain,
( ! [X2,X0,X1] :
( member(second(f23(cross_product(X0,X1),X2)),X1)
| disjoint(cross_product(X0,X1),X2) )
| ~ spl0_63
| ~ spl0_77 ),
inference(resolution,[],[f641,f475]) ).
fof(f5525,plain,
( spl0_449
| ~ spl0_60
| ~ spl0_77 ),
inference(avatar_split_clause,[],[f730,f640,f462,f5523]) ).
fof(f5523,plain,
( spl0_449
<=> ! [X2,X0,X1] :
( member(second(f17(cross_product(X0,X1),X2)),X1)
| subset(cross_product(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_449])]) ).
fof(f730,plain,
( ! [X2,X0,X1] :
( member(second(f17(cross_product(X0,X1),X2)),X1)
| subset(cross_product(X0,X1),X2) )
| ~ spl0_60
| ~ spl0_77 ),
inference(resolution,[],[f641,f463]) ).
fof(f5521,plain,
( spl0_448
| ~ spl0_64
| ~ spl0_75 ),
inference(avatar_split_clause,[],[f727,f632,f478,f5519]) ).
fof(f5519,plain,
( spl0_448
<=> ! [X2,X0,X1] :
( member(first(f23(X0,cross_product(X1,X2))),X1)
| disjoint(X0,cross_product(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_448])]) ).
fof(f727,plain,
( ! [X2,X0,X1] :
( member(first(f23(X0,cross_product(X1,X2))),X1)
| disjoint(X0,cross_product(X1,X2)) )
| ~ spl0_64
| ~ spl0_75 ),
inference(resolution,[],[f633,f479]) ).
fof(f5516,plain,
( spl0_447
| ~ spl0_64
| ~ spl0_141 ),
inference(avatar_split_clause,[],[f2082,f1749,f478,f5514]) ).
fof(f5514,plain,
( spl0_447
<=> ! [X0] : disjoint(X0,range_of(empty_set)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_447])]) ).
fof(f2082,plain,
( ! [X0] : disjoint(X0,range_of(empty_set))
| ~ spl0_64
| ~ spl0_141 ),
inference(resolution,[],[f1750,f479]) ).
fof(f5512,plain,
( spl0_446
| ~ spl0_63
| ~ spl0_75 ),
inference(avatar_split_clause,[],[f726,f632,f474,f5510]) ).
fof(f5510,plain,
( spl0_446
<=> ! [X2,X0,X1] :
( member(first(f23(cross_product(X0,X1),X2)),X0)
| disjoint(cross_product(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_446])]) ).
fof(f726,plain,
( ! [X2,X0,X1] :
( member(first(f23(cross_product(X0,X1),X2)),X0)
| disjoint(cross_product(X0,X1),X2) )
| ~ spl0_63
| ~ spl0_75 ),
inference(resolution,[],[f633,f475]) ).
fof(f5508,plain,
( spl0_445
| ~ spl0_60
| ~ spl0_75 ),
inference(avatar_split_clause,[],[f724,f632,f462,f5506]) ).
fof(f5506,plain,
( spl0_445
<=> ! [X2,X0,X1] :
( member(first(f17(cross_product(X0,X1),X2)),X0)
| subset(cross_product(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_445])]) ).
fof(f724,plain,
( ! [X2,X0,X1] :
( member(first(f17(cross_product(X0,X1),X2)),X0)
| subset(cross_product(X0,X1),X2) )
| ~ spl0_60
| ~ spl0_75 ),
inference(resolution,[],[f633,f463]) ).
fof(f5503,plain,
( spl0_444
| ~ spl0_66
| ~ spl0_74 ),
inference(avatar_split_clause,[],[f721,f628,f486,f5501]) ).
fof(f5501,plain,
( spl0_444
<=> ! [X0] :
( ~ member(X0,domain_of(identity_relation))
| first(f8(X0,identity_relation)) = second(f8(X0,identity_relation)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_444])]) ).
fof(f721,plain,
( ! [X0] :
( ~ member(X0,domain_of(identity_relation))
| first(f8(X0,identity_relation)) = second(f8(X0,identity_relation)) )
| ~ spl0_66
| ~ spl0_74 ),
inference(resolution,[],[f629,f487]) ).
fof(f5499,plain,
( spl0_443
| ~ spl0_51
| ~ spl0_74 ),
inference(avatar_split_clause,[],[f707,f628,f426,f5497]) ).
fof(f5497,plain,
( spl0_443
<=> ! [X2,X0,X1] :
( ~ member(X0,domain_of(intersection(X1,X2)))
| member(f8(X0,intersection(X1,X2)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_443])]) ).
fof(f707,plain,
( ! [X2,X0,X1] :
( ~ member(X0,domain_of(intersection(X1,X2)))
| member(f8(X0,intersection(X1,X2)),X1) )
| ~ spl0_51
| ~ spl0_74 ),
inference(resolution,[],[f629,f427]) ).
fof(f5495,plain,
( spl0_442
| ~ spl0_52
| ~ spl0_74 ),
inference(avatar_split_clause,[],[f706,f628,f430,f5493]) ).
fof(f5493,plain,
( spl0_442
<=> ! [X2,X0,X1] :
( ~ member(X0,domain_of(intersection(X1,X2)))
| member(f8(X0,intersection(X1,X2)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_442])]) ).
fof(f706,plain,
( ! [X2,X0,X1] :
( ~ member(X0,domain_of(intersection(X1,X2)))
| member(f8(X0,intersection(X1,X2)),X2) )
| ~ spl0_52
| ~ spl0_74 ),
inference(resolution,[],[f629,f431]) ).
fof(f5305,plain,
( spl0_441
| ~ spl0_63
| ~ spl0_141 ),
inference(avatar_split_clause,[],[f2081,f1749,f474,f5303]) ).
fof(f5303,plain,
( spl0_441
<=> ! [X0] : disjoint(range_of(empty_set),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_441])]) ).
fof(f2081,plain,
( ! [X0] : disjoint(range_of(empty_set),X0)
| ~ spl0_63
| ~ spl0_141 ),
inference(resolution,[],[f1750,f475]) ).
fof(f5269,plain,
( spl0_440
| ~ spl0_60
| ~ spl0_141 ),
inference(avatar_split_clause,[],[f2078,f1749,f462,f5267]) ).
fof(f5267,plain,
( spl0_440
<=> ! [X0] : subset(range_of(empty_set),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_440])]) ).
fof(f2078,plain,
( ! [X0] : subset(range_of(empty_set),X0)
| ~ spl0_60
| ~ spl0_141 ),
inference(resolution,[],[f1750,f463]) ).
fof(f5238,plain,
( spl0_439
| ~ spl0_40
| ~ spl0_135 ),
inference(avatar_split_clause,[],[f2051,f1548,f361,f5235]) ).
fof(f5235,plain,
( spl0_439
<=> empty_set = sigma(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_439])]) ).
fof(f2051,plain,
( empty_set = sigma(empty_set)
| ~ spl0_40
| ~ spl0_135 ),
inference(resolution,[],[f1549,f362]) ).
fof(f5233,plain,
( spl0_438
| ~ spl0_173
| ~ spl0_399 ),
inference(avatar_split_clause,[],[f4400,f4397,f2440,f5231]) ).
fof(f5231,plain,
( spl0_438
<=> ! [X0] :
( estin = powerset(X0)
| ~ little_set(powerset(X0))
| subset(f26(powerset(X0)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_438])]) ).
fof(f4400,plain,
( ! [X0] :
( estin = powerset(X0)
| ~ little_set(powerset(X0))
| subset(f26(powerset(X0)),X0) )
| ~ spl0_173
| ~ spl0_399 ),
inference(forward_demodulation,[],[f4398,f2442]) ).
fof(f5229,plain,
( spl0_437
| ~ spl0_173
| ~ spl0_397 ),
inference(avatar_split_clause,[],[f4390,f4387,f2440,f5227]) ).
fof(f5227,plain,
( spl0_437
<=> ! [X0] :
( estin = complement(X0)
| ~ little_set(complement(X0))
| ~ member(f26(complement(X0)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_437])]) ).
fof(f4390,plain,
( ! [X0] :
( estin = complement(X0)
| ~ little_set(complement(X0))
| ~ member(f26(complement(X0)),X0) )
| ~ spl0_173
| ~ spl0_397 ),
inference(forward_demodulation,[],[f4388,f2442]) ).
fof(f5223,plain,
( spl0_436
| ~ spl0_64
| ~ spl0_135 ),
inference(avatar_split_clause,[],[f2050,f1548,f478,f5221]) ).
fof(f5221,plain,
( spl0_436
<=> ! [X0] : disjoint(X0,sigma(empty_set)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_436])]) ).
fof(f2050,plain,
( ! [X0] : disjoint(X0,sigma(empty_set))
| ~ spl0_64
| ~ spl0_135 ),
inference(resolution,[],[f1549,f479]) ).
fof(f5177,plain,
( spl0_435
| ~ spl0_173
| ~ spl0_383 ),
inference(avatar_split_clause,[],[f4331,f4328,f2440,f5175]) ).
fof(f4331,plain,
( ! [X0,X1] :
( estin = cross_product(X0,X1)
| member(second(f24(cross_product(X0,X1))),X1) )
| ~ spl0_173
| ~ spl0_383 ),
inference(forward_demodulation,[],[f4329,f2442]) ).
fof(f5172,plain,
( spl0_434
| ~ spl0_63
| ~ spl0_135 ),
inference(avatar_split_clause,[],[f2049,f1548,f474,f5170]) ).
fof(f5170,plain,
( spl0_434
<=> ! [X0] : disjoint(sigma(empty_set),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_434])]) ).
fof(f2049,plain,
( ! [X0] : disjoint(sigma(empty_set),X0)
| ~ spl0_63
| ~ spl0_135 ),
inference(resolution,[],[f1549,f475]) ).
fof(f5168,plain,
( spl0_433
| ~ spl0_173
| ~ spl0_382 ),
inference(avatar_split_clause,[],[f4326,f4323,f2440,f5166]) ).
fof(f4326,plain,
( ! [X0,X1] :
( estin = cross_product(X0,X1)
| member(first(f24(cross_product(X0,X1))),X0) )
| ~ spl0_173
| ~ spl0_382 ),
inference(forward_demodulation,[],[f4324,f2442]) ).
fof(f5161,plain,
( spl0_432
| ~ spl0_60
| ~ spl0_135 ),
inference(avatar_split_clause,[],[f2046,f1548,f462,f5159]) ).
fof(f5159,plain,
( spl0_432
<=> ! [X0] : subset(sigma(empty_set),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_432])]) ).
fof(f2046,plain,
( ! [X0] : subset(sigma(empty_set),X0)
| ~ spl0_60
| ~ spl0_135 ),
inference(resolution,[],[f1549,f463]) ).
fof(f4539,plain,
( spl0_431
| ~ spl0_11
| ~ spl0_116 ),
inference(avatar_split_clause,[],[f1271,f1171,f232,f4537]) ).
fof(f4537,plain,
( spl0_431
<=> ! [X0] :
( ~ member(X0,infinity)
| little_set(complement(intersection(complement(X0),complement(non_ordered_pair(X0,X0))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_431])]) ).
fof(f1271,plain,
( ! [X0] :
( ~ member(X0,infinity)
| little_set(complement(intersection(complement(X0),complement(non_ordered_pair(X0,X0))))) )
| ~ spl0_11
| ~ spl0_116 ),
inference(resolution,[],[f1172,f233]) ).
fof(f4534,plain,
( spl0_430
| ~ spl0_40
| ~ spl0_119 ),
inference(avatar_split_clause,[],[f1939,f1266,f361,f4531]) ).
fof(f4529,plain,
( spl0_429
| ~ spl0_16
| ~ spl0_114 ),
inference(avatar_split_clause,[],[f1261,f1163,f253,f4527]) ).
fof(f4527,plain,
( spl0_429
<=> ! [X0] :
( universal_set = X0
| ~ member(f1(X0,universal_set),X0)
| ~ little_set(f1(X0,universal_set)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_429])]) ).
fof(f1261,plain,
( ! [X0] :
( universal_set = X0
| ~ member(f1(X0,universal_set),X0)
| ~ little_set(f1(X0,universal_set)) )
| ~ spl0_16
| ~ spl0_114 ),
inference(resolution,[],[f1164,f254]) ).
fof(f4523,plain,
( spl0_428
| ~ spl0_23
| ~ spl0_113 ),
inference(avatar_split_clause,[],[f1250,f1159,f281,f4521]) ).
fof(f4521,plain,
( spl0_428
<=> ! [X0] :
( member(f1(identity_relation,X0),X0)
| identity_relation = X0
| ordered_pair_predicate(f1(identity_relation,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_428])]) ).
fof(f1250,plain,
( ! [X0] :
( member(f1(identity_relation,X0),X0)
| identity_relation = X0
| ordered_pair_predicate(f1(identity_relation,X0)) )
| ~ spl0_23
| ~ spl0_113 ),
inference(resolution,[],[f1160,f282]) ).
fof(f4517,plain,
( spl0_427
| ~ spl0_23
| ~ spl0_113 ),
inference(avatar_split_clause,[],[f1213,f1159,f281,f4515]) ).
fof(f4515,plain,
( spl0_427
<=> ! [X0] :
( member(f1(X0,identity_relation),X0)
| identity_relation = X0
| ordered_pair_predicate(f1(X0,identity_relation)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_427])]) ).
fof(f1213,plain,
( ! [X0] :
( member(f1(X0,identity_relation),X0)
| identity_relation = X0
| ordered_pair_predicate(f1(X0,identity_relation)) )
| ~ spl0_23
| ~ spl0_113 ),
inference(resolution,[],[f1160,f282]) ).
fof(f4513,plain,
( spl0_426
| ~ spl0_48
| ~ spl0_111 ),
inference(avatar_split_clause,[],[f1153,f1085,f414,f4511]) ).
fof(f4511,plain,
( spl0_426
<=> ! [X2,X0,X1] :
( ~ member(X0,apply(X1,X2))
| little_set(f6(X0,f28(X0,X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_426])]) ).
fof(f1153,plain,
( ! [X2,X0,X1] :
( ~ member(X0,apply(X1,X2))
| little_set(f6(X0,f28(X0,X1,X2))) )
| ~ spl0_48
| ~ spl0_111 ),
inference(resolution,[],[f1086,f415]) ).
fof(f4509,plain,
( spl0_425
| ~ spl0_49
| ~ spl0_111 ),
inference(avatar_split_clause,[],[f1152,f1085,f418,f4507]) ).
fof(f4507,plain,
( spl0_425
<=> ! [X2,X0,X1] :
( ~ member(X0,apply(X1,X2))
| little_set(f7(X0,f28(X0,X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_425])]) ).
fof(f1152,plain,
( ! [X2,X0,X1] :
( ~ member(X0,apply(X1,X2))
| little_set(f7(X0,f28(X0,X1,X2))) )
| ~ spl0_49
| ~ spl0_111 ),
inference(resolution,[],[f1086,f419]) ).
fof(f4505,plain,
( spl0_424
| ~ spl0_38
| ~ spl0_102 ),
inference(avatar_split_clause,[],[f987,f956,f353,f4503]) ).
fof(f4503,plain,
( spl0_424
<=> ! [X2,X0,X1] :
( ~ member(X0,X1)
| ~ member(X0,X2)
| ordered_pair_predicate(X0)
| ~ relation(intersection(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_424])]) ).
fof(f987,plain,
( ! [X2,X0,X1] :
( ~ member(X0,X1)
| ~ member(X0,X2)
| ordered_pair_predicate(X0)
| ~ relation(intersection(X1,X2)) )
| ~ spl0_38
| ~ spl0_102 ),
inference(resolution,[],[f957,f354]) ).
fof(f4501,plain,
( spl0_423
| ~ spl0_30
| ~ spl0_99 ),
inference(avatar_split_clause,[],[f945,f860,f314,f4499]) ).
fof(f4499,plain,
( spl0_423
<=> ! [X0,X1] :
( little_set(f31(f18(compose(X0,X1)),X0,X1))
| relation(compose(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_423])]) ).
fof(f945,plain,
( ! [X0,X1] :
( little_set(f31(f18(compose(X0,X1)),X0,X1))
| relation(compose(X0,X1)) )
| ~ spl0_30
| ~ spl0_99 ),
inference(resolution,[],[f861,f315]) ).
fof(f4497,plain,
( spl0_422
| ~ spl0_30
| ~ spl0_98 ),
inference(avatar_split_clause,[],[f936,f856,f314,f4495]) ).
fof(f936,plain,
( ! [X0,X1] :
( little_set(f30(f18(compose(X0,X1)),X0,X1))
| relation(compose(X0,X1)) )
| ~ spl0_30
| ~ spl0_98 ),
inference(resolution,[],[f857,f315]) ).
fof(f4493,plain,
( spl0_421
| ~ spl0_30
| ~ spl0_97 ),
inference(avatar_split_clause,[],[f927,f852,f314,f4491]) ).
fof(f927,plain,
( ! [X0,X1] :
( little_set(f29(f18(compose(X0,X1)),X0,X1))
| relation(compose(X0,X1)) )
| ~ spl0_30
| ~ spl0_97 ),
inference(resolution,[],[f853,f315]) ).
fof(f4489,plain,
( spl0_420
| ~ spl0_30
| ~ spl0_96 ),
inference(avatar_split_clause,[],[f918,f848,f314,f4487]) ).
fof(f4487,plain,
( spl0_420
<=> ! [X0,X1] :
( ordered_pair_predicate(f28(f18(apply(X0,X1)),X0,X1))
| relation(apply(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_420])]) ).
fof(f918,plain,
( ! [X0,X1] :
( ordered_pair_predicate(f28(f18(apply(X0,X1)),X0,X1))
| relation(apply(X0,X1)) )
| ~ spl0_30
| ~ spl0_96 ),
inference(resolution,[],[f849,f315]) ).
fof(f4484,plain,
( spl0_419
| ~ spl0_64
| ~ spl0_119 ),
inference(avatar_split_clause,[],[f1938,f1266,f478,f4482]) ).
fof(f4482,plain,
( spl0_419
<=> ! [X0] : disjoint(X0,domain_of(empty_set)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_419])]) ).
fof(f1938,plain,
( ! [X0] : disjoint(X0,domain_of(empty_set))
| ~ spl0_64
| ~ spl0_119 ),
inference(resolution,[],[f1267,f479]) ).
fof(f4480,plain,
( spl0_418
| ~ spl0_30
| ~ spl0_94 ),
inference(avatar_split_clause,[],[f900,f840,f314,f4478]) ).
fof(f4478,plain,
( spl0_418
<=> ! [X0,X1] :
( ordered_pair_predicate(f22(f18(image(X0,X1)),X0,X1))
| relation(image(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_418])]) ).
fof(f900,plain,
( ! [X0,X1] :
( ordered_pair_predicate(f22(f18(image(X0,X1)),X0,X1))
| relation(image(X0,X1)) )
| ~ spl0_30
| ~ spl0_94 ),
inference(resolution,[],[f841,f315]) ).
fof(f4476,plain,
( spl0_417
| ~ spl0_64
| ~ spl0_93 ),
inference(avatar_split_clause,[],[f891,f836,f478,f4474]) ).
fof(f891,plain,
( ! [X2,X0,X1] :
( ~ member(X0,X1)
| member(f23(X2,X0),sigma(X1))
| disjoint(X2,X0) )
| ~ spl0_64
| ~ spl0_93 ),
inference(resolution,[],[f837,f479]) ).
fof(f4472,plain,
( spl0_416
| ~ spl0_63
| ~ spl0_93 ),
inference(avatar_split_clause,[],[f890,f836,f474,f4470]) ).
fof(f890,plain,
( ! [X2,X0,X1] :
( ~ member(X0,X1)
| member(f23(X0,X2),sigma(X1))
| disjoint(X0,X2) )
| ~ spl0_63
| ~ spl0_93 ),
inference(resolution,[],[f837,f475]) ).
fof(f4468,plain,
( spl0_415
| ~ spl0_60
| ~ spl0_93 ),
inference(avatar_split_clause,[],[f888,f836,f462,f4466]) ).
fof(f888,plain,
( ! [X2,X0,X1] :
( ~ member(X0,X1)
| member(f17(X0,X2),sigma(X1))
| subset(X0,X2) )
| ~ spl0_60
| ~ spl0_93 ),
inference(resolution,[],[f837,f463]) ).
fof(f4464,plain,
( spl0_414
| ~ spl0_65
| ~ spl0_85 ),
inference(avatar_split_clause,[],[f821,f672,f482,f4462]) ).
fof(f4462,plain,
( spl0_414
<=> ! [X0,X1] :
( ~ member(X0,range_of(range_of(X1)))
| ordered_pair_predicate(f27(f27(X0,range_of(X1)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_414])]) ).
fof(f821,plain,
( ! [X0,X1] :
( ~ member(X0,range_of(range_of(X1)))
| ordered_pair_predicate(f27(f27(X0,range_of(X1)),X1)) )
| ~ spl0_65
| ~ spl0_85 ),
inference(resolution,[],[f673,f483]) ).
fof(f4460,plain,
( spl0_413
| ~ spl0_57
| ~ spl0_85 ),
inference(avatar_split_clause,[],[f818,f672,f450,f4458]) ).
fof(f4458,plain,
( spl0_413
<=> ! [X0,X1] :
( ~ member(X0,range_of(flip_range_of(X1)))
| little_set(f12(f27(X0,flip_range_of(X1)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_413])]) ).
fof(f818,plain,
( ! [X0,X1] :
( ~ member(X0,range_of(flip_range_of(X1)))
| little_set(f12(f27(X0,flip_range_of(X1)),X1)) )
| ~ spl0_57
| ~ spl0_85 ),
inference(resolution,[],[f673,f451]) ).
fof(f4456,plain,
( spl0_412
| ~ spl0_58
| ~ spl0_85 ),
inference(avatar_split_clause,[],[f817,f672,f454,f4454]) ).
fof(f4454,plain,
( spl0_412
<=> ! [X0,X1] :
( ~ member(X0,range_of(flip_range_of(X1)))
| little_set(f13(f27(X0,flip_range_of(X1)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_412])]) ).
fof(f817,plain,
( ! [X0,X1] :
( ~ member(X0,range_of(flip_range_of(X1)))
| little_set(f13(f27(X0,flip_range_of(X1)),X1)) )
| ~ spl0_58
| ~ spl0_85 ),
inference(resolution,[],[f673,f455]) ).
fof(f4452,plain,
( spl0_411
| ~ spl0_59
| ~ spl0_85 ),
inference(avatar_split_clause,[],[f816,f672,f458,f4450]) ).
fof(f4450,plain,
( spl0_411
<=> ! [X0,X1] :
( ~ member(X0,range_of(flip_range_of(X1)))
| little_set(f14(f27(X0,flip_range_of(X1)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_411])]) ).
fof(f816,plain,
( ! [X0,X1] :
( ~ member(X0,range_of(flip_range_of(X1)))
| little_set(f14(f27(X0,flip_range_of(X1)),X1)) )
| ~ spl0_59
| ~ spl0_85 ),
inference(resolution,[],[f673,f459]) ).
fof(f4448,plain,
( spl0_410
| ~ spl0_54
| ~ spl0_85 ),
inference(avatar_split_clause,[],[f815,f672,f438,f4446]) ).
fof(f4446,plain,
( spl0_410
<=> ! [X0,X1] :
( ~ member(X0,range_of(rotate_right(X1)))
| little_set(f9(f27(X0,rotate_right(X1)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_410])]) ).
fof(f815,plain,
( ! [X0,X1] :
( ~ member(X0,range_of(rotate_right(X1)))
| little_set(f9(f27(X0,rotate_right(X1)),X1)) )
| ~ spl0_54
| ~ spl0_85 ),
inference(resolution,[],[f673,f439]) ).
fof(f4444,plain,
( spl0_409
| ~ spl0_55
| ~ spl0_85 ),
inference(avatar_split_clause,[],[f814,f672,f442,f4442]) ).
fof(f4442,plain,
( spl0_409
<=> ! [X0,X1] :
( ~ member(X0,range_of(rotate_right(X1)))
| little_set(f10(f27(X0,rotate_right(X1)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_409])]) ).
fof(f814,plain,
( ! [X0,X1] :
( ~ member(X0,range_of(rotate_right(X1)))
| little_set(f10(f27(X0,rotate_right(X1)),X1)) )
| ~ spl0_55
| ~ spl0_85 ),
inference(resolution,[],[f673,f443]) ).
fof(f4439,plain,
( spl0_408
| ~ spl0_63
| ~ spl0_119 ),
inference(avatar_split_clause,[],[f1937,f1266,f474,f4437]) ).
fof(f4437,plain,
( spl0_408
<=> ! [X0] : disjoint(domain_of(empty_set),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_408])]) ).
fof(f1937,plain,
( ! [X0] : disjoint(domain_of(empty_set),X0)
| ~ spl0_63
| ~ spl0_119 ),
inference(resolution,[],[f1267,f475]) ).
fof(f4435,plain,
( spl0_407
| ~ spl0_56
| ~ spl0_85 ),
inference(avatar_split_clause,[],[f813,f672,f446,f4433]) ).
fof(f4433,plain,
( spl0_407
<=> ! [X0,X1] :
( ~ member(X0,range_of(rotate_right(X1)))
| little_set(f11(f27(X0,rotate_right(X1)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_407])]) ).
fof(f813,plain,
( ! [X0,X1] :
( ~ member(X0,range_of(rotate_right(X1)))
| little_set(f11(f27(X0,rotate_right(X1)),X1)) )
| ~ spl0_56
| ~ spl0_85 ),
inference(resolution,[],[f673,f447]) ).
fof(f4431,plain,
( spl0_406
| ~ spl0_53
| ~ spl0_85 ),
inference(avatar_split_clause,[],[f808,f672,f434,f4429]) ).
fof(f4429,plain,
( spl0_406
<=> ! [X0,X1] :
( ~ member(X0,range_of(domain_of(X1)))
| ordered_pair_predicate(f8(f27(X0,domain_of(X1)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_406])]) ).
fof(f808,plain,
( ! [X0,X1] :
( ~ member(X0,range_of(domain_of(X1)))
| ordered_pair_predicate(f8(f27(X0,domain_of(X1)),X1)) )
| ~ spl0_53
| ~ spl0_85 ),
inference(resolution,[],[f673,f435]) ).
fof(f4427,plain,
( spl0_405
| ~ spl0_48
| ~ spl0_85 ),
inference(avatar_split_clause,[],[f803,f672,f414,f4425]) ).
fof(f4425,plain,
( spl0_405
<=> ! [X0,X1] :
( ~ member(X0,range_of(second(X1)))
| little_set(f6(f27(X0,second(X1)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_405])]) ).
fof(f803,plain,
( ! [X0,X1] :
( ~ member(X0,range_of(second(X1)))
| little_set(f6(f27(X0,second(X1)),X1)) )
| ~ spl0_48
| ~ spl0_85 ),
inference(resolution,[],[f673,f415]) ).
fof(f4423,plain,
( spl0_404
| ~ spl0_49
| ~ spl0_85 ),
inference(avatar_split_clause,[],[f802,f672,f418,f4421]) ).
fof(f4421,plain,
( spl0_404
<=> ! [X0,X1] :
( ~ member(X0,range_of(second(X1)))
| little_set(f7(f27(X0,second(X1)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_404])]) ).
fof(f802,plain,
( ! [X0,X1] :
( ~ member(X0,range_of(second(X1)))
| little_set(f7(f27(X0,second(X1)),X1)) )
| ~ spl0_49
| ~ spl0_85 ),
inference(resolution,[],[f673,f419]) ).
fof(f4419,plain,
( spl0_403
| ~ spl0_46
| ~ spl0_85 ),
inference(avatar_split_clause,[],[f801,f672,f406,f4417]) ).
fof(f4417,plain,
( spl0_403
<=> ! [X0,X1] :
( ~ member(X0,range_of(first(X1)))
| little_set(f4(f27(X0,first(X1)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_403])]) ).
fof(f801,plain,
( ! [X0,X1] :
( ~ member(X0,range_of(first(X1)))
| little_set(f4(f27(X0,first(X1)),X1)) )
| ~ spl0_46
| ~ spl0_85 ),
inference(resolution,[],[f673,f407]) ).
fof(f4415,plain,
( spl0_402
| ~ spl0_47
| ~ spl0_85 ),
inference(avatar_split_clause,[],[f800,f672,f410,f4413]) ).
fof(f4413,plain,
( spl0_402
<=> ! [X0,X1] :
( ~ member(X0,range_of(first(X1)))
| little_set(f5(f27(X0,first(X1)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_402])]) ).
fof(f800,plain,
( ! [X0,X1] :
( ~ member(X0,range_of(first(X1)))
| little_set(f5(f27(X0,first(X1)),X1)) )
| ~ spl0_47
| ~ spl0_85 ),
inference(resolution,[],[f673,f411]) ).
fof(f4411,plain,
( ~ spl0_401
| ~ spl0_177
| spl0_400 ),
inference(avatar_split_clause,[],[f4406,f4402,f2481,f4408]) ).
fof(f4408,plain,
( spl0_401
<=> first(f26(estin)) = second(f26(estin)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_401])]) ).
fof(f4402,plain,
( spl0_400
<=> first(f26(identity_relation)) = second(f26(identity_relation)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_400])]) ).
fof(f4406,plain,
( first(f26(estin)) != second(f26(estin))
| ~ spl0_177
| spl0_400 ),
inference(forward_demodulation,[],[f4403,f2483]) ).
fof(f4403,plain,
( first(f26(identity_relation)) != second(f26(identity_relation))
| spl0_400 ),
inference(avatar_component_clause,[],[f4402]) ).
fof(f4405,plain,
( spl0_400
| ~ spl0_201
| spl0_175
| ~ spl0_66
| ~ spl0_84 ),
inference(avatar_split_clause,[],[f796,f668,f486,f2469,f2603,f4402]) ).
fof(f2603,plain,
( spl0_201
<=> little_set(identity_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_201])]) ).
fof(f796,plain,
( empty_set = identity_relation
| ~ little_set(identity_relation)
| first(f26(identity_relation)) = second(f26(identity_relation))
| ~ spl0_66
| ~ spl0_84 ),
inference(resolution,[],[f669,f487]) ).
fof(f4399,plain,
( spl0_399
| ~ spl0_37
| ~ spl0_84 ),
inference(avatar_split_clause,[],[f794,f668,f349,f4397]) ).
fof(f794,plain,
( ! [X0] :
( empty_set = powerset(X0)
| ~ little_set(powerset(X0))
| subset(f26(powerset(X0)),X0) )
| ~ spl0_37
| ~ spl0_84 ),
inference(resolution,[],[f669,f350]) ).
fof(f4394,plain,
( spl0_398
| ~ spl0_60
| ~ spl0_119 ),
inference(avatar_split_clause,[],[f1934,f1266,f462,f4392]) ).
fof(f4392,plain,
( spl0_398
<=> ! [X0] : subset(domain_of(empty_set),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_398])]) ).
fof(f1934,plain,
( ! [X0] : subset(domain_of(empty_set),X0)
| ~ spl0_60
| ~ spl0_119 ),
inference(resolution,[],[f1267,f463]) ).
fof(f4389,plain,
( spl0_397
| ~ spl0_34
| ~ spl0_84 ),
inference(avatar_split_clause,[],[f781,f668,f336,f4387]) ).
fof(f781,plain,
( ! [X0] :
( complement(X0) = empty_set
| ~ little_set(complement(X0))
| ~ member(f26(complement(X0)),X0) )
| ~ spl0_34
| ~ spl0_84 ),
inference(resolution,[],[f669,f337]) ).
fof(f4385,plain,
( spl0_396
| ~ spl0_65
| ~ spl0_78 ),
inference(avatar_split_clause,[],[f758,f644,f482,f4383]) ).
fof(f4383,plain,
( spl0_396
<=> ! [X0,X1] :
( ~ member(X0,sigma(range_of(X1)))
| ordered_pair_predicate(f27(f16(X0,range_of(X1)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_396])]) ).
fof(f758,plain,
( ! [X0,X1] :
( ~ member(X0,sigma(range_of(X1)))
| ordered_pair_predicate(f27(f16(X0,range_of(X1)),X1)) )
| ~ spl0_65
| ~ spl0_78 ),
inference(resolution,[],[f645,f483]) ).
fof(f4381,plain,
( spl0_395
| ~ spl0_57
| ~ spl0_78 ),
inference(avatar_split_clause,[],[f755,f644,f450,f4379]) ).
fof(f4379,plain,
( spl0_395
<=> ! [X0,X1] :
( ~ member(X0,sigma(flip_range_of(X1)))
| little_set(f12(f16(X0,flip_range_of(X1)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_395])]) ).
fof(f755,plain,
( ! [X0,X1] :
( ~ member(X0,sigma(flip_range_of(X1)))
| little_set(f12(f16(X0,flip_range_of(X1)),X1)) )
| ~ spl0_57
| ~ spl0_78 ),
inference(resolution,[],[f645,f451]) ).
fof(f4377,plain,
( spl0_394
| ~ spl0_58
| ~ spl0_78 ),
inference(avatar_split_clause,[],[f754,f644,f454,f4375]) ).
fof(f4375,plain,
( spl0_394
<=> ! [X0,X1] :
( ~ member(X0,sigma(flip_range_of(X1)))
| little_set(f13(f16(X0,flip_range_of(X1)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_394])]) ).
fof(f754,plain,
( ! [X0,X1] :
( ~ member(X0,sigma(flip_range_of(X1)))
| little_set(f13(f16(X0,flip_range_of(X1)),X1)) )
| ~ spl0_58
| ~ spl0_78 ),
inference(resolution,[],[f645,f455]) ).
fof(f4373,plain,
( spl0_393
| ~ spl0_59
| ~ spl0_78 ),
inference(avatar_split_clause,[],[f753,f644,f458,f4371]) ).
fof(f4371,plain,
( spl0_393
<=> ! [X0,X1] :
( ~ member(X0,sigma(flip_range_of(X1)))
| little_set(f14(f16(X0,flip_range_of(X1)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_393])]) ).
fof(f753,plain,
( ! [X0,X1] :
( ~ member(X0,sigma(flip_range_of(X1)))
| little_set(f14(f16(X0,flip_range_of(X1)),X1)) )
| ~ spl0_59
| ~ spl0_78 ),
inference(resolution,[],[f645,f459]) ).
fof(f4369,plain,
( spl0_392
| ~ spl0_54
| ~ spl0_78 ),
inference(avatar_split_clause,[],[f752,f644,f438,f4367]) ).
fof(f4367,plain,
( spl0_392
<=> ! [X0,X1] :
( ~ member(X0,sigma(rotate_right(X1)))
| little_set(f9(f16(X0,rotate_right(X1)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_392])]) ).
fof(f752,plain,
( ! [X0,X1] :
( ~ member(X0,sigma(rotate_right(X1)))
| little_set(f9(f16(X0,rotate_right(X1)),X1)) )
| ~ spl0_54
| ~ spl0_78 ),
inference(resolution,[],[f645,f439]) ).
fof(f4365,plain,
( spl0_391
| ~ spl0_55
| ~ spl0_78 ),
inference(avatar_split_clause,[],[f751,f644,f442,f4363]) ).
fof(f4363,plain,
( spl0_391
<=> ! [X0,X1] :
( ~ member(X0,sigma(rotate_right(X1)))
| little_set(f10(f16(X0,rotate_right(X1)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_391])]) ).
fof(f751,plain,
( ! [X0,X1] :
( ~ member(X0,sigma(rotate_right(X1)))
| little_set(f10(f16(X0,rotate_right(X1)),X1)) )
| ~ spl0_55
| ~ spl0_78 ),
inference(resolution,[],[f645,f443]) ).
fof(f4361,plain,
( spl0_390
| ~ spl0_56
| ~ spl0_78 ),
inference(avatar_split_clause,[],[f750,f644,f446,f4359]) ).
fof(f4359,plain,
( spl0_390
<=> ! [X0,X1] :
( ~ member(X0,sigma(rotate_right(X1)))
| little_set(f11(f16(X0,rotate_right(X1)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_390])]) ).
fof(f750,plain,
( ! [X0,X1] :
( ~ member(X0,sigma(rotate_right(X1)))
| little_set(f11(f16(X0,rotate_right(X1)),X1)) )
| ~ spl0_56
| ~ spl0_78 ),
inference(resolution,[],[f645,f447]) ).
fof(f4357,plain,
( spl0_389
| ~ spl0_35
| ~ spl0_78 ),
inference(avatar_split_clause,[],[f748,f644,f340,f4355]) ).
fof(f748,plain,
( ! [X2,X0,X1] :
( ~ member(X0,sigma(cross_product(X1,X2)))
| ordered_pair_predicate(f16(X0,cross_product(X1,X2))) )
| ~ spl0_35
| ~ spl0_78 ),
inference(resolution,[],[f645,f341]) ).
fof(f4353,plain,
( spl0_388
| ~ spl0_53
| ~ spl0_78 ),
inference(avatar_split_clause,[],[f745,f644,f434,f4351]) ).
fof(f4351,plain,
( spl0_388
<=> ! [X0,X1] :
( ~ member(X0,sigma(domain_of(X1)))
| ordered_pair_predicate(f8(f16(X0,domain_of(X1)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_388])]) ).
fof(f745,plain,
( ! [X0,X1] :
( ~ member(X0,sigma(domain_of(X1)))
| ordered_pair_predicate(f8(f16(X0,domain_of(X1)),X1)) )
| ~ spl0_53
| ~ spl0_78 ),
inference(resolution,[],[f645,f435]) ).
fof(f4347,plain,
( spl0_387
| ~ spl0_48
| ~ spl0_78 ),
inference(avatar_split_clause,[],[f740,f644,f414,f4345]) ).
fof(f4345,plain,
( spl0_387
<=> ! [X0,X1] :
( ~ member(X0,sigma(second(X1)))
| little_set(f6(f16(X0,second(X1)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_387])]) ).
fof(f740,plain,
( ! [X0,X1] :
( ~ member(X0,sigma(second(X1)))
| little_set(f6(f16(X0,second(X1)),X1)) )
| ~ spl0_48
| ~ spl0_78 ),
inference(resolution,[],[f645,f415]) ).
fof(f4343,plain,
( spl0_386
| ~ spl0_49
| ~ spl0_78 ),
inference(avatar_split_clause,[],[f739,f644,f418,f4341]) ).
fof(f4341,plain,
( spl0_386
<=> ! [X0,X1] :
( ~ member(X0,sigma(second(X1)))
| little_set(f7(f16(X0,second(X1)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_386])]) ).
fof(f739,plain,
( ! [X0,X1] :
( ~ member(X0,sigma(second(X1)))
| little_set(f7(f16(X0,second(X1)),X1)) )
| ~ spl0_49
| ~ spl0_78 ),
inference(resolution,[],[f645,f419]) ).
fof(f4339,plain,
( spl0_385
| ~ spl0_46
| ~ spl0_78 ),
inference(avatar_split_clause,[],[f738,f644,f406,f4337]) ).
fof(f4337,plain,
( spl0_385
<=> ! [X0,X1] :
( ~ member(X0,sigma(first(X1)))
| little_set(f4(f16(X0,first(X1)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_385])]) ).
fof(f738,plain,
( ! [X0,X1] :
( ~ member(X0,sigma(first(X1)))
| little_set(f4(f16(X0,first(X1)),X1)) )
| ~ spl0_46
| ~ spl0_78 ),
inference(resolution,[],[f645,f407]) ).
fof(f4335,plain,
( spl0_384
| ~ spl0_47
| ~ spl0_78 ),
inference(avatar_split_clause,[],[f737,f644,f410,f4333]) ).
fof(f4333,plain,
( spl0_384
<=> ! [X0,X1] :
( ~ member(X0,sigma(first(X1)))
| little_set(f5(f16(X0,first(X1)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_384])]) ).
fof(f737,plain,
( ! [X0,X1] :
( ~ member(X0,sigma(first(X1)))
| little_set(f5(f16(X0,first(X1)),X1)) )
| ~ spl0_47
| ~ spl0_78 ),
inference(resolution,[],[f645,f411]) ).
fof(f4330,plain,
( spl0_383
| ~ spl0_40
| ~ spl0_77 ),
inference(avatar_split_clause,[],[f734,f640,f361,f4328]) ).
fof(f734,plain,
( ! [X0,X1] :
( member(second(f24(cross_product(X0,X1))),X1)
| cross_product(X0,X1) = empty_set )
| ~ spl0_40
| ~ spl0_77 ),
inference(resolution,[],[f641,f362]) ).
fof(f4325,plain,
( spl0_382
| ~ spl0_40
| ~ spl0_75 ),
inference(avatar_split_clause,[],[f728,f632,f361,f4323]) ).
fof(f728,plain,
( ! [X0,X1] :
( member(first(f24(cross_product(X0,X1))),X0)
| cross_product(X0,X1) = empty_set )
| ~ spl0_40
| ~ spl0_75 ),
inference(resolution,[],[f633,f362]) ).
fof(f4321,plain,
( spl0_381
| ~ spl0_65
| ~ spl0_74 ),
inference(avatar_split_clause,[],[f720,f628,f482,f4319]) ).
fof(f4319,plain,
( spl0_381
<=> ! [X0,X1] :
( ~ member(X0,domain_of(range_of(X1)))
| ordered_pair_predicate(f27(f8(X0,range_of(X1)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_381])]) ).
fof(f720,plain,
( ! [X0,X1] :
( ~ member(X0,domain_of(range_of(X1)))
| ordered_pair_predicate(f27(f8(X0,range_of(X1)),X1)) )
| ~ spl0_65
| ~ spl0_74 ),
inference(resolution,[],[f629,f483]) ).
fof(f4317,plain,
( spl0_380
| ~ spl0_57
| ~ spl0_74 ),
inference(avatar_split_clause,[],[f717,f628,f450,f4315]) ).
fof(f4315,plain,
( spl0_380
<=> ! [X0,X1] :
( ~ member(X0,domain_of(flip_range_of(X1)))
| little_set(f12(f8(X0,flip_range_of(X1)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_380])]) ).
fof(f717,plain,
( ! [X0,X1] :
( ~ member(X0,domain_of(flip_range_of(X1)))
| little_set(f12(f8(X0,flip_range_of(X1)),X1)) )
| ~ spl0_57
| ~ spl0_74 ),
inference(resolution,[],[f629,f451]) ).
fof(f4313,plain,
( spl0_379
| ~ spl0_58
| ~ spl0_74 ),
inference(avatar_split_clause,[],[f716,f628,f454,f4311]) ).
fof(f4311,plain,
( spl0_379
<=> ! [X0,X1] :
( ~ member(X0,domain_of(flip_range_of(X1)))
| little_set(f13(f8(X0,flip_range_of(X1)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_379])]) ).
fof(f716,plain,
( ! [X0,X1] :
( ~ member(X0,domain_of(flip_range_of(X1)))
| little_set(f13(f8(X0,flip_range_of(X1)),X1)) )
| ~ spl0_58
| ~ spl0_74 ),
inference(resolution,[],[f629,f455]) ).
fof(f4309,plain,
( spl0_378
| ~ spl0_59
| ~ spl0_74 ),
inference(avatar_split_clause,[],[f715,f628,f458,f4307]) ).
fof(f4307,plain,
( spl0_378
<=> ! [X0,X1] :
( ~ member(X0,domain_of(flip_range_of(X1)))
| little_set(f14(f8(X0,flip_range_of(X1)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_378])]) ).
fof(f715,plain,
( ! [X0,X1] :
( ~ member(X0,domain_of(flip_range_of(X1)))
| little_set(f14(f8(X0,flip_range_of(X1)),X1)) )
| ~ spl0_59
| ~ spl0_74 ),
inference(resolution,[],[f629,f459]) ).
fof(f4305,plain,
( spl0_377
| ~ spl0_173
| ~ spl0_366 ),
inference(avatar_split_clause,[],[f4256,f4252,f2440,f4302]) ).
fof(f4256,plain,
( function(estin)
| ~ spl0_173
| ~ spl0_366 ),
inference(forward_demodulation,[],[f4254,f2442]) ).
fof(f4300,plain,
( spl0_376
| ~ spl0_54
| ~ spl0_74 ),
inference(avatar_split_clause,[],[f714,f628,f438,f4298]) ).
fof(f4298,plain,
( spl0_376
<=> ! [X0,X1] :
( ~ member(X0,domain_of(rotate_right(X1)))
| little_set(f9(f8(X0,rotate_right(X1)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_376])]) ).
fof(f714,plain,
( ! [X0,X1] :
( ~ member(X0,domain_of(rotate_right(X1)))
| little_set(f9(f8(X0,rotate_right(X1)),X1)) )
| ~ spl0_54
| ~ spl0_74 ),
inference(resolution,[],[f629,f439]) ).
fof(f4296,plain,
( spl0_375
| ~ spl0_55
| ~ spl0_74 ),
inference(avatar_split_clause,[],[f713,f628,f442,f4294]) ).
fof(f4294,plain,
( spl0_375
<=> ! [X0,X1] :
( ~ member(X0,domain_of(rotate_right(X1)))
| little_set(f10(f8(X0,rotate_right(X1)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_375])]) ).
fof(f713,plain,
( ! [X0,X1] :
( ~ member(X0,domain_of(rotate_right(X1)))
| little_set(f10(f8(X0,rotate_right(X1)),X1)) )
| ~ spl0_55
| ~ spl0_74 ),
inference(resolution,[],[f629,f443]) ).
fof(f4292,plain,
( spl0_374
| ~ spl0_56
| ~ spl0_74 ),
inference(avatar_split_clause,[],[f712,f628,f446,f4290]) ).
fof(f4290,plain,
( spl0_374
<=> ! [X0,X1] :
( ~ member(X0,domain_of(rotate_right(X1)))
| little_set(f11(f8(X0,rotate_right(X1)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_374])]) ).
fof(f712,plain,
( ! [X0,X1] :
( ~ member(X0,domain_of(rotate_right(X1)))
| little_set(f11(f8(X0,rotate_right(X1)),X1)) )
| ~ spl0_56
| ~ spl0_74 ),
inference(resolution,[],[f629,f447]) ).
fof(f4288,plain,
( spl0_373
| ~ spl0_53
| ~ spl0_74 ),
inference(avatar_split_clause,[],[f709,f628,f434,f4286]) ).
fof(f4286,plain,
( spl0_373
<=> ! [X0,X1] :
( ~ member(X0,domain_of(domain_of(X1)))
| ordered_pair_predicate(f8(f8(X0,domain_of(X1)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_373])]) ).
fof(f709,plain,
( ! [X0,X1] :
( ~ member(X0,domain_of(domain_of(X1)))
| ordered_pair_predicate(f8(f8(X0,domain_of(X1)),X1)) )
| ~ spl0_53
| ~ spl0_74 ),
inference(resolution,[],[f629,f435]) ).
fof(f4284,plain,
( spl0_372
| ~ spl0_48
| ~ spl0_74 ),
inference(avatar_split_clause,[],[f704,f628,f414,f4282]) ).
fof(f4282,plain,
( spl0_372
<=> ! [X0,X1] :
( ~ member(X0,domain_of(second(X1)))
| little_set(f6(f8(X0,second(X1)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_372])]) ).
fof(f704,plain,
( ! [X0,X1] :
( ~ member(X0,domain_of(second(X1)))
| little_set(f6(f8(X0,second(X1)),X1)) )
| ~ spl0_48
| ~ spl0_74 ),
inference(resolution,[],[f629,f415]) ).
fof(f4280,plain,
( spl0_371
| ~ spl0_49
| ~ spl0_74 ),
inference(avatar_split_clause,[],[f703,f628,f418,f4278]) ).
fof(f4278,plain,
( spl0_371
<=> ! [X0,X1] :
( ~ member(X0,domain_of(second(X1)))
| little_set(f7(f8(X0,second(X1)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_371])]) ).
fof(f703,plain,
( ! [X0,X1] :
( ~ member(X0,domain_of(second(X1)))
| little_set(f7(f8(X0,second(X1)),X1)) )
| ~ spl0_49
| ~ spl0_74 ),
inference(resolution,[],[f629,f419]) ).
fof(f4276,plain,
( spl0_370
| ~ spl0_46
| ~ spl0_74 ),
inference(avatar_split_clause,[],[f702,f628,f406,f4274]) ).
fof(f4274,plain,
( spl0_370
<=> ! [X0,X1] :
( ~ member(X0,domain_of(first(X1)))
| little_set(f4(f8(X0,first(X1)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_370])]) ).
fof(f702,plain,
( ! [X0,X1] :
( ~ member(X0,domain_of(first(X1)))
| little_set(f4(f8(X0,first(X1)),X1)) )
| ~ spl0_46
| ~ spl0_74 ),
inference(resolution,[],[f629,f407]) ).
fof(f4272,plain,
( spl0_369
| ~ spl0_47
| ~ spl0_74 ),
inference(avatar_split_clause,[],[f701,f628,f410,f4270]) ).
fof(f4270,plain,
( spl0_369
<=> ! [X0,X1] :
( ~ member(X0,domain_of(first(X1)))
| little_set(f5(f8(X0,first(X1)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_369])]) ).
fof(f701,plain,
( ! [X0,X1] :
( ~ member(X0,domain_of(first(X1)))
| little_set(f5(f8(X0,first(X1)),X1)) )
| ~ spl0_47
| ~ spl0_74 ),
inference(resolution,[],[f629,f411]) ).
fof(f4266,plain,
( spl0_368
| ~ spl0_64
| ~ spl0_66 ),
inference(avatar_split_clause,[],[f613,f486,f478,f4264]) ).
fof(f4264,plain,
( spl0_368
<=> ! [X0] :
( first(f23(X0,identity_relation)) = second(f23(X0,identity_relation))
| disjoint(X0,identity_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_368])]) ).
fof(f613,plain,
( ! [X0] :
( first(f23(X0,identity_relation)) = second(f23(X0,identity_relation))
| disjoint(X0,identity_relation) )
| ~ spl0_64
| ~ spl0_66 ),
inference(resolution,[],[f487,f479]) ).
fof(f4260,plain,
( spl0_367
| ~ spl0_63
| ~ spl0_66 ),
inference(avatar_split_clause,[],[f612,f486,f474,f4258]) ).
fof(f4258,plain,
( spl0_367
<=> ! [X0] :
( first(f23(identity_relation,X0)) = second(f23(identity_relation,X0))
| disjoint(identity_relation,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_367])]) ).
fof(f612,plain,
( ! [X0] :
( first(f23(identity_relation,X0)) = second(f23(identity_relation,X0))
| disjoint(identity_relation,X0) )
| ~ spl0_63
| ~ spl0_66 ),
inference(resolution,[],[f487,f475]) ).
fof(f4255,plain,
( spl0_366
| ~ spl0_45
| ~ spl0_31
| ~ spl0_125 ),
inference(avatar_split_clause,[],[f1461,f1341,f318,f382,f4252]) ).
fof(f382,plain,
( spl0_45
<=> relation(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_45])]) ).
fof(f318,plain,
( spl0_31
<=> ! [X7] :
( ~ relation(X7)
| ~ single_valued_set(X7)
| function(X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_31])]) ).
fof(f1341,plain,
( spl0_125
<=> single_valued_set(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_125])]) ).
fof(f1461,plain,
( ~ relation(empty_set)
| function(empty_set)
| ~ spl0_31
| ~ spl0_125 ),
inference(resolution,[],[f1343,f319]) ).
fof(f319,plain,
( ! [X7] :
( ~ single_valued_set(X7)
| ~ relation(X7)
| function(X7) )
| ~ spl0_31 ),
inference(avatar_component_clause,[],[f318]) ).
fof(f1343,plain,
( single_valued_set(empty_set)
| ~ spl0_125 ),
inference(avatar_component_clause,[],[f1341]) ).
fof(f4248,plain,
( spl0_365
| ~ spl0_60
| ~ spl0_66 ),
inference(avatar_split_clause,[],[f610,f486,f462,f4246]) ).
fof(f4246,plain,
( spl0_365
<=> ! [X0] :
( first(f17(identity_relation,X0)) = second(f17(identity_relation,X0))
| subset(identity_relation,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_365])]) ).
fof(f610,plain,
( ! [X0] :
( first(f17(identity_relation,X0)) = second(f17(identity_relation,X0))
| subset(identity_relation,X0) )
| ~ spl0_60
| ~ spl0_66 ),
inference(resolution,[],[f487,f463]) ).
fof(f4244,plain,
( spl0_364
| ~ spl0_51
| ~ spl0_64 ),
inference(avatar_split_clause,[],[f591,f478,f426,f4242]) ).
fof(f591,plain,
( ! [X2,X0,X1] :
( disjoint(X0,intersection(X1,X2))
| member(f23(X0,intersection(X1,X2)),X1) )
| ~ spl0_51
| ~ spl0_64 ),
inference(resolution,[],[f479,f427]) ).
fof(f4240,plain,
( spl0_363
| ~ spl0_52
| ~ spl0_64 ),
inference(avatar_split_clause,[],[f590,f478,f430,f4238]) ).
fof(f590,plain,
( ! [X2,X0,X1] :
( disjoint(X0,intersection(X1,X2))
| member(f23(X0,intersection(X1,X2)),X2) )
| ~ spl0_52
| ~ spl0_64 ),
inference(resolution,[],[f479,f431]) ).
fof(f4236,plain,
( spl0_362
| ~ spl0_51
| ~ spl0_63 ),
inference(avatar_split_clause,[],[f569,f474,f426,f4234]) ).
fof(f569,plain,
( ! [X2,X0,X1] :
( disjoint(intersection(X0,X1),X2)
| member(f23(intersection(X0,X1),X2),X0) )
| ~ spl0_51
| ~ spl0_63 ),
inference(resolution,[],[f475,f427]) ).
fof(f4232,plain,
( spl0_361
| ~ spl0_52
| ~ spl0_63 ),
inference(avatar_split_clause,[],[f568,f474,f430,f4230]) ).
fof(f568,plain,
( ! [X2,X0,X1] :
( disjoint(intersection(X0,X1),X2)
| member(f23(intersection(X0,X1),X2),X1) )
| ~ spl0_52
| ~ spl0_63 ),
inference(resolution,[],[f475,f431]) ).
fof(f4228,plain,
( spl0_360
| ~ spl0_51
| ~ spl0_60 ),
inference(avatar_split_clause,[],[f544,f462,f426,f4226]) ).
fof(f544,plain,
( ! [X2,X0,X1] :
( subset(intersection(X0,X1),X2)
| member(f17(intersection(X0,X1),X2),X0) )
| ~ spl0_51
| ~ spl0_60 ),
inference(resolution,[],[f463,f427]) ).
fof(f4224,plain,
( spl0_359
| ~ spl0_52
| ~ spl0_60 ),
inference(avatar_split_clause,[],[f543,f462,f430,f4222]) ).
fof(f543,plain,
( ! [X2,X0,X1] :
( subset(intersection(X0,X1),X2)
| member(f17(intersection(X0,X1),X2),X1) )
| ~ spl0_52
| ~ spl0_60 ),
inference(resolution,[],[f463,f431]) ).
fof(f4036,plain,
( spl0_358
| ~ spl0_173
| ~ spl0_352 ),
inference(avatar_split_clause,[],[f3914,f3911,f2440,f4034]) ).
fof(f3914,plain,
( ! [X0,X1] :
( estin = X0
| ~ member(X0,X1)
| member(f24(X0),sigma(X1)) )
| ~ spl0_173
| ~ spl0_352 ),
inference(forward_demodulation,[],[f3912,f2442]) ).
fof(f3973,plain,
( spl0_357
| ~ spl0_173
| ~ spl0_347 ),
inference(avatar_split_clause,[],[f3866,f3863,f2440,f3971]) ).
fof(f3971,plain,
( spl0_357
<=> ! [X0] :
( estin = converse(X0)
| ~ little_set(converse(X0))
| ordered_pair_predicate(f26(converse(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_357])]) ).
fof(f3866,plain,
( ! [X0] :
( estin = converse(X0)
| ~ little_set(converse(X0))
| ordered_pair_predicate(f26(converse(X0))) )
| ~ spl0_173
| ~ spl0_347 ),
inference(forward_demodulation,[],[f3864,f2442]) ).
fof(f3931,plain,
( spl0_356
| ~ spl0_173
| ~ spl0_299 ),
inference(avatar_split_clause,[],[f3673,f3670,f2440,f3929]) ).
fof(f3673,plain,
( ! [X0,X1] :
( estin = intersection(X0,X1)
| member(f24(intersection(X0,X1)),X1) )
| ~ spl0_173
| ~ spl0_299 ),
inference(forward_demodulation,[],[f3671,f2442]) ).
fof(f3927,plain,
( spl0_355
| ~ spl0_173
| ~ spl0_298 ),
inference(avatar_split_clause,[],[f3668,f3665,f2440,f3925]) ).
fof(f3668,plain,
( ! [X0,X1] :
( estin = intersection(X0,X1)
| member(f24(intersection(X0,X1)),X0) )
| ~ spl0_173
| ~ spl0_298 ),
inference(forward_demodulation,[],[f3666,f2442]) ).
fof(f3922,plain,
( spl0_354
| ~ spl0_23
| ~ spl0_107 ),
inference(avatar_split_clause,[],[f1123,f1068,f281,f3920]) ).
fof(f3920,plain,
( spl0_354
<=> ! [X0,X1] :
( ~ member(X0,image(identity_relation,X1))
| ordered_pair_predicate(first(f22(X0,identity_relation,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_354])]) ).
fof(f1123,plain,
( ! [X0,X1] :
( ~ member(X0,image(identity_relation,X1))
| ordered_pair_predicate(first(f22(X0,identity_relation,X1))) )
| ~ spl0_23
| ~ spl0_107 ),
inference(resolution,[],[f1069,f282]) ).
fof(f3918,plain,
( spl0_353
| ~ spl0_11
| ~ spl0_107 ),
inference(avatar_split_clause,[],[f1095,f1068,f232,f3916]) ).
fof(f3916,plain,
( spl0_353
<=> ! [X2,X0,X1] :
( ~ member(X0,image(X1,X2))
| little_set(first(f22(X0,X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_353])]) ).
fof(f1095,plain,
( ! [X2,X0,X1] :
( ~ member(X0,image(X1,X2))
| little_set(first(f22(X0,X1,X2))) )
| ~ spl0_11
| ~ spl0_107 ),
inference(resolution,[],[f1069,f233]) ).
fof(f3913,plain,
( spl0_352
| ~ spl0_40
| ~ spl0_93 ),
inference(avatar_split_clause,[],[f892,f836,f361,f3911]) ).
fof(f892,plain,
( ! [X0,X1] :
( ~ member(X0,X1)
| member(f24(X0),sigma(X1))
| empty_set = X0 )
| ~ spl0_40
| ~ spl0_93 ),
inference(resolution,[],[f837,f362]) ).
fof(f3909,plain,
( spl0_351
| ~ spl0_44
| ~ spl0_93 ),
inference(avatar_split_clause,[],[f877,f836,f377,f3907]) ).
fof(f877,plain,
( ! [X2,X0,X1] :
( ~ member(non_ordered_pair(X0,X1),X2)
| member(X1,sigma(X2))
| ~ little_set(X1) )
| ~ spl0_44
| ~ spl0_93 ),
inference(resolution,[],[f837,f378]) ).
fof(f3905,plain,
( spl0_350
| ~ spl0_43
| ~ spl0_93 ),
inference(avatar_split_clause,[],[f876,f836,f373,f3903]) ).
fof(f876,plain,
( ! [X2,X0,X1] :
( ~ member(non_ordered_pair(X0,X1),X2)
| member(X0,sigma(X2))
| ~ little_set(X0) )
| ~ spl0_43
| ~ spl0_93 ),
inference(resolution,[],[f837,f374]) ).
fof(f3901,plain,
( spl0_349
| ~ spl0_37
| ~ spl0_85 ),
inference(avatar_split_clause,[],[f820,f672,f349,f3899]) ).
fof(f3899,plain,
( spl0_349
<=> ! [X0,X1] :
( ~ member(X0,range_of(powerset(X1)))
| subset(f27(X0,powerset(X1)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_349])]) ).
fof(f820,plain,
( ! [X0,X1] :
( ~ member(X0,range_of(powerset(X1)))
| subset(f27(X0,powerset(X1)),X1) )
| ~ spl0_37
| ~ spl0_85 ),
inference(resolution,[],[f673,f350]) ).
fof(f3897,plain,
( spl0_348
| ~ spl0_34
| ~ spl0_85 ),
inference(avatar_split_clause,[],[f807,f672,f336,f3895]) ).
fof(f807,plain,
( ! [X0,X1] :
( ~ member(X0,range_of(complement(X1)))
| ~ member(f27(X0,complement(X1)),X1) )
| ~ spl0_34
| ~ spl0_85 ),
inference(resolution,[],[f673,f337]) ).
fof(f3865,plain,
( spl0_347
| ~ spl0_28
| ~ spl0_84 ),
inference(avatar_split_clause,[],[f786,f668,f306,f3863]) ).
fof(f786,plain,
( ! [X0] :
( converse(X0) = empty_set
| ~ little_set(converse(X0))
| ordered_pair_predicate(f26(converse(X0))) )
| ~ spl0_28
| ~ spl0_84 ),
inference(resolution,[],[f669,f307]) ).
fof(f3861,plain,
( spl0_346
| ~ spl0_37
| ~ spl0_78 ),
inference(avatar_split_clause,[],[f757,f644,f349,f3859]) ).
fof(f3859,plain,
( spl0_346
<=> ! [X0,X1] :
( ~ member(X0,sigma(powerset(X1)))
| subset(f16(X0,powerset(X1)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_346])]) ).
fof(f757,plain,
( ! [X0,X1] :
( ~ member(X0,sigma(powerset(X1)))
| subset(f16(X0,powerset(X1)),X1) )
| ~ spl0_37
| ~ spl0_78 ),
inference(resolution,[],[f645,f350]) ).
fof(f3857,plain,
( spl0_345
| ~ spl0_34
| ~ spl0_78 ),
inference(avatar_split_clause,[],[f744,f644,f336,f3855]) ).
fof(f744,plain,
( ! [X0,X1] :
( ~ member(X0,sigma(complement(X1)))
| ~ member(f16(X0,complement(X1)),X1) )
| ~ spl0_34
| ~ spl0_78 ),
inference(resolution,[],[f645,f337]) ).
fof(f3853,plain,
( spl0_344
| ~ spl0_37
| ~ spl0_74 ),
inference(avatar_split_clause,[],[f719,f628,f349,f3851]) ).
fof(f3851,plain,
( spl0_344
<=> ! [X0,X1] :
( ~ member(X0,domain_of(powerset(X1)))
| subset(f8(X0,powerset(X1)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_344])]) ).
fof(f719,plain,
( ! [X0,X1] :
( ~ member(X0,domain_of(powerset(X1)))
| subset(f8(X0,powerset(X1)),X1) )
| ~ spl0_37
| ~ spl0_74 ),
inference(resolution,[],[f629,f350]) ).
fof(f3849,plain,
( spl0_343
| ~ spl0_34
| ~ spl0_74 ),
inference(avatar_split_clause,[],[f708,f628,f336,f3847]) ).
fof(f708,plain,
( ! [X0,X1] :
( ~ member(X0,domain_of(complement(X1)))
| ~ member(f8(X0,complement(X1)),X1) )
| ~ spl0_34
| ~ spl0_74 ),
inference(resolution,[],[f629,f337]) ).
fof(f3845,plain,
( spl0_342
| ~ spl0_64
| ~ spl0_65 ),
inference(avatar_split_clause,[],[f608,f482,f478,f3843]) ).
fof(f3843,plain,
( spl0_342
<=> ! [X0,X1] :
( ordered_pair_predicate(f27(f23(X0,range_of(X1)),X1))
| disjoint(X0,range_of(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_342])]) ).
fof(f608,plain,
( ! [X0,X1] :
( ordered_pair_predicate(f27(f23(X0,range_of(X1)),X1))
| disjoint(X0,range_of(X1)) )
| ~ spl0_64
| ~ spl0_65 ),
inference(resolution,[],[f483,f479]) ).
fof(f3841,plain,
( spl0_341
| ~ spl0_63
| ~ spl0_65 ),
inference(avatar_split_clause,[],[f607,f482,f474,f3839]) ).
fof(f3839,plain,
( spl0_341
<=> ! [X0,X1] :
( ordered_pair_predicate(f27(f23(range_of(X0),X1),X0))
| disjoint(range_of(X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_341])]) ).
fof(f607,plain,
( ! [X0,X1] :
( ordered_pair_predicate(f27(f23(range_of(X0),X1),X0))
| disjoint(range_of(X0),X1) )
| ~ spl0_63
| ~ spl0_65 ),
inference(resolution,[],[f483,f475]) ).
fof(f3837,plain,
( spl0_340
| ~ spl0_60
| ~ spl0_65 ),
inference(avatar_split_clause,[],[f605,f482,f462,f3835]) ).
fof(f3835,plain,
( spl0_340
<=> ! [X0,X1] :
( ordered_pair_predicate(f27(f17(range_of(X0),X1),X0))
| subset(range_of(X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_340])]) ).
fof(f605,plain,
( ! [X0,X1] :
( ordered_pair_predicate(f27(f17(range_of(X0),X1),X0))
| subset(range_of(X0),X1) )
| ~ spl0_60
| ~ spl0_65 ),
inference(resolution,[],[f483,f463]) ).
fof(f3833,plain,
( spl0_339
| ~ spl0_57
| ~ spl0_64 ),
inference(avatar_split_clause,[],[f601,f478,f450,f3831]) ).
fof(f3831,plain,
( spl0_339
<=> ! [X0,X1] :
( disjoint(X0,flip_range_of(X1))
| little_set(f12(f23(X0,flip_range_of(X1)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_339])]) ).
fof(f601,plain,
( ! [X0,X1] :
( disjoint(X0,flip_range_of(X1))
| little_set(f12(f23(X0,flip_range_of(X1)),X1)) )
| ~ spl0_57
| ~ spl0_64 ),
inference(resolution,[],[f479,f451]) ).
fof(f3829,plain,
( spl0_338
| ~ spl0_58
| ~ spl0_64 ),
inference(avatar_split_clause,[],[f600,f478,f454,f3827]) ).
fof(f3827,plain,
( spl0_338
<=> ! [X0,X1] :
( disjoint(X0,flip_range_of(X1))
| little_set(f13(f23(X0,flip_range_of(X1)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_338])]) ).
fof(f600,plain,
( ! [X0,X1] :
( disjoint(X0,flip_range_of(X1))
| little_set(f13(f23(X0,flip_range_of(X1)),X1)) )
| ~ spl0_58
| ~ spl0_64 ),
inference(resolution,[],[f479,f455]) ).
fof(f3825,plain,
( spl0_337
| ~ spl0_179
| ~ spl0_181 ),
inference(avatar_split_clause,[],[f2538,f2503,f2494,f3823]) ).
fof(f3823,plain,
( spl0_337
<=> ! [X0] : subset(X0,universal_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_337])]) ).
fof(f2494,plain,
( spl0_179
<=> ! [X0,X1] :
( subset(X0,X1)
| little_set(f17(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_179])]) ).
fof(f2503,plain,
( spl0_181
<=> ! [X0] :
( subset(X0,universal_set)
| ~ little_set(f17(X0,universal_set)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_181])]) ).
fof(f2538,plain,
( ! [X0] : subset(X0,universal_set)
| ~ spl0_179
| ~ spl0_181 ),
inference(duplicate_literal_removal,[],[f2537]) ).
fof(f2537,plain,
( ! [X0] :
( subset(X0,universal_set)
| subset(X0,universal_set) )
| ~ spl0_179
| ~ spl0_181 ),
inference(resolution,[],[f2504,f2495]) ).
fof(f2495,plain,
( ! [X0,X1] :
( little_set(f17(X0,X1))
| subset(X0,X1) )
| ~ spl0_179 ),
inference(avatar_component_clause,[],[f2494]) ).
fof(f2504,plain,
( ! [X0] :
( ~ little_set(f17(X0,universal_set))
| subset(X0,universal_set) )
| ~ spl0_181 ),
inference(avatar_component_clause,[],[f2503]) ).
fof(f3821,plain,
( spl0_336
| ~ spl0_59
| ~ spl0_64 ),
inference(avatar_split_clause,[],[f599,f478,f458,f3819]) ).
fof(f3819,plain,
( spl0_336
<=> ! [X0,X1] :
( disjoint(X0,flip_range_of(X1))
| little_set(f14(f23(X0,flip_range_of(X1)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_336])]) ).
fof(f599,plain,
( ! [X0,X1] :
( disjoint(X0,flip_range_of(X1))
| little_set(f14(f23(X0,flip_range_of(X1)),X1)) )
| ~ spl0_59
| ~ spl0_64 ),
inference(resolution,[],[f479,f459]) ).
fof(f3817,plain,
( spl0_335
| ~ spl0_54
| ~ spl0_64 ),
inference(avatar_split_clause,[],[f598,f478,f438,f3815]) ).
fof(f3815,plain,
( spl0_335
<=> ! [X0,X1] :
( disjoint(X0,rotate_right(X1))
| little_set(f9(f23(X0,rotate_right(X1)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_335])]) ).
fof(f598,plain,
( ! [X0,X1] :
( disjoint(X0,rotate_right(X1))
| little_set(f9(f23(X0,rotate_right(X1)),X1)) )
| ~ spl0_54
| ~ spl0_64 ),
inference(resolution,[],[f479,f439]) ).
fof(f3813,plain,
( spl0_334
| ~ spl0_55
| ~ spl0_64 ),
inference(avatar_split_clause,[],[f597,f478,f442,f3811]) ).
fof(f3811,plain,
( spl0_334
<=> ! [X0,X1] :
( disjoint(X0,rotate_right(X1))
| little_set(f10(f23(X0,rotate_right(X1)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_334])]) ).
fof(f597,plain,
( ! [X0,X1] :
( disjoint(X0,rotate_right(X1))
| little_set(f10(f23(X0,rotate_right(X1)),X1)) )
| ~ spl0_55
| ~ spl0_64 ),
inference(resolution,[],[f479,f443]) ).
fof(f3809,plain,
( spl0_333
| ~ spl0_56
| ~ spl0_64 ),
inference(avatar_split_clause,[],[f596,f478,f446,f3807]) ).
fof(f3807,plain,
( spl0_333
<=> ! [X0,X1] :
( disjoint(X0,rotate_right(X1))
| little_set(f11(f23(X0,rotate_right(X1)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_333])]) ).
fof(f596,plain,
( ! [X0,X1] :
( disjoint(X0,rotate_right(X1))
| little_set(f11(f23(X0,rotate_right(X1)),X1)) )
| ~ spl0_56
| ~ spl0_64 ),
inference(resolution,[],[f479,f447]) ).
fof(f3805,plain,
( spl0_332
| ~ spl0_35
| ~ spl0_64 ),
inference(avatar_split_clause,[],[f594,f478,f340,f3803]) ).
fof(f3803,plain,
( spl0_332
<=> ! [X2,X0,X1] :
( disjoint(X0,cross_product(X1,X2))
| ordered_pair_predicate(f23(X0,cross_product(X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_332])]) ).
fof(f594,plain,
( ! [X2,X0,X1] :
( disjoint(X0,cross_product(X1,X2))
| ordered_pair_predicate(f23(X0,cross_product(X1,X2))) )
| ~ spl0_35
| ~ spl0_64 ),
inference(resolution,[],[f479,f341]) ).
fof(f3801,plain,
( spl0_331
| ~ spl0_53
| ~ spl0_64 ),
inference(avatar_split_clause,[],[f593,f478,f434,f3799]) ).
fof(f3799,plain,
( spl0_331
<=> ! [X0,X1] :
( disjoint(X0,domain_of(X1))
| ordered_pair_predicate(f8(f23(X0,domain_of(X1)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_331])]) ).
fof(f593,plain,
( ! [X0,X1] :
( disjoint(X0,domain_of(X1))
| ordered_pair_predicate(f8(f23(X0,domain_of(X1)),X1)) )
| ~ spl0_53
| ~ spl0_64 ),
inference(resolution,[],[f479,f435]) ).
fof(f3797,plain,
( spl0_330
| ~ spl0_48
| ~ spl0_64 ),
inference(avatar_split_clause,[],[f588,f478,f414,f3795]) ).
fof(f3795,plain,
( spl0_330
<=> ! [X0,X1] :
( disjoint(X0,second(X1))
| little_set(f6(f23(X0,second(X1)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_330])]) ).
fof(f588,plain,
( ! [X0,X1] :
( disjoint(X0,second(X1))
| little_set(f6(f23(X0,second(X1)),X1)) )
| ~ spl0_48
| ~ spl0_64 ),
inference(resolution,[],[f479,f415]) ).
fof(f3793,plain,
( spl0_329
| ~ spl0_49
| ~ spl0_64 ),
inference(avatar_split_clause,[],[f587,f478,f418,f3791]) ).
fof(f3791,plain,
( spl0_329
<=> ! [X0,X1] :
( disjoint(X0,second(X1))
| little_set(f7(f23(X0,second(X1)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_329])]) ).
fof(f587,plain,
( ! [X0,X1] :
( disjoint(X0,second(X1))
| little_set(f7(f23(X0,second(X1)),X1)) )
| ~ spl0_49
| ~ spl0_64 ),
inference(resolution,[],[f479,f419]) ).
fof(f3789,plain,
( spl0_328
| ~ spl0_46
| ~ spl0_64 ),
inference(avatar_split_clause,[],[f586,f478,f406,f3787]) ).
fof(f3787,plain,
( spl0_328
<=> ! [X0,X1] :
( disjoint(X0,first(X1))
| little_set(f4(f23(X0,first(X1)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_328])]) ).
fof(f586,plain,
( ! [X0,X1] :
( disjoint(X0,first(X1))
| little_set(f4(f23(X0,first(X1)),X1)) )
| ~ spl0_46
| ~ spl0_64 ),
inference(resolution,[],[f479,f407]) ).
fof(f3785,plain,
( spl0_327
| ~ spl0_47
| ~ spl0_64 ),
inference(avatar_split_clause,[],[f585,f478,f410,f3783]) ).
fof(f3783,plain,
( spl0_327
<=> ! [X0,X1] :
( disjoint(X0,first(X1))
| little_set(f5(f23(X0,first(X1)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_327])]) ).
fof(f585,plain,
( ! [X0,X1] :
( disjoint(X0,first(X1))
| little_set(f5(f23(X0,first(X1)),X1)) )
| ~ spl0_47
| ~ spl0_64 ),
inference(resolution,[],[f479,f411]) ).
fof(f3781,plain,
( spl0_326
| ~ spl0_19
| ~ spl0_178 ),
inference(avatar_split_clause,[],[f2536,f2490,f265,f3779]) ).
fof(f3779,plain,
( spl0_326
<=> ! [X0] : relation(converse(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_326])]) ).
fof(f2490,plain,
( spl0_178
<=> ! [X0] :
( relation(converse(X0))
| ordered_pair_predicate(f18(converse(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_178])]) ).
fof(f2536,plain,
( ! [X0] : relation(converse(X0))
| ~ spl0_19
| ~ spl0_178 ),
inference(duplicate_literal_removal,[],[f2534]) ).
fof(f2534,plain,
( ! [X0] :
( relation(converse(X0))
| relation(converse(X0)) )
| ~ spl0_19
| ~ spl0_178 ),
inference(resolution,[],[f2491,f266]) ).
fof(f2491,plain,
( ! [X0] :
( ordered_pair_predicate(f18(converse(X0)))
| relation(converse(X0)) )
| ~ spl0_178 ),
inference(avatar_component_clause,[],[f2490]) ).
fof(f3777,plain,
( spl0_325
| ~ spl0_57
| ~ spl0_63 ),
inference(avatar_split_clause,[],[f579,f474,f450,f3775]) ).
fof(f3775,plain,
( spl0_325
<=> ! [X0,X1] :
( disjoint(flip_range_of(X0),X1)
| little_set(f12(f23(flip_range_of(X0),X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_325])]) ).
fof(f579,plain,
( ! [X0,X1] :
( disjoint(flip_range_of(X0),X1)
| little_set(f12(f23(flip_range_of(X0),X1),X0)) )
| ~ spl0_57
| ~ spl0_63 ),
inference(resolution,[],[f475,f451]) ).
fof(f3773,plain,
( spl0_324
| ~ spl0_58
| ~ spl0_63 ),
inference(avatar_split_clause,[],[f578,f474,f454,f3771]) ).
fof(f3771,plain,
( spl0_324
<=> ! [X0,X1] :
( disjoint(flip_range_of(X0),X1)
| little_set(f13(f23(flip_range_of(X0),X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_324])]) ).
fof(f578,plain,
( ! [X0,X1] :
( disjoint(flip_range_of(X0),X1)
| little_set(f13(f23(flip_range_of(X0),X1),X0)) )
| ~ spl0_58
| ~ spl0_63 ),
inference(resolution,[],[f475,f455]) ).
fof(f3769,plain,
( spl0_323
| ~ spl0_59
| ~ spl0_63 ),
inference(avatar_split_clause,[],[f577,f474,f458,f3767]) ).
fof(f3767,plain,
( spl0_323
<=> ! [X0,X1] :
( disjoint(flip_range_of(X0),X1)
| little_set(f14(f23(flip_range_of(X0),X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_323])]) ).
fof(f577,plain,
( ! [X0,X1] :
( disjoint(flip_range_of(X0),X1)
| little_set(f14(f23(flip_range_of(X0),X1),X0)) )
| ~ spl0_59
| ~ spl0_63 ),
inference(resolution,[],[f475,f459]) ).
fof(f3765,plain,
( spl0_322
| ~ spl0_54
| ~ spl0_63 ),
inference(avatar_split_clause,[],[f576,f474,f438,f3763]) ).
fof(f3763,plain,
( spl0_322
<=> ! [X0,X1] :
( disjoint(rotate_right(X0),X1)
| little_set(f9(f23(rotate_right(X0),X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_322])]) ).
fof(f576,plain,
( ! [X0,X1] :
( disjoint(rotate_right(X0),X1)
| little_set(f9(f23(rotate_right(X0),X1),X0)) )
| ~ spl0_54
| ~ spl0_63 ),
inference(resolution,[],[f475,f439]) ).
fof(f3761,plain,
( spl0_321
| ~ spl0_55
| ~ spl0_63 ),
inference(avatar_split_clause,[],[f575,f474,f442,f3759]) ).
fof(f3759,plain,
( spl0_321
<=> ! [X0,X1] :
( disjoint(rotate_right(X0),X1)
| little_set(f10(f23(rotate_right(X0),X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_321])]) ).
fof(f575,plain,
( ! [X0,X1] :
( disjoint(rotate_right(X0),X1)
| little_set(f10(f23(rotate_right(X0),X1),X0)) )
| ~ spl0_55
| ~ spl0_63 ),
inference(resolution,[],[f475,f443]) ).
fof(f3757,plain,
( spl0_320
| ~ spl0_56
| ~ spl0_63 ),
inference(avatar_split_clause,[],[f574,f474,f446,f3755]) ).
fof(f3755,plain,
( spl0_320
<=> ! [X0,X1] :
( disjoint(rotate_right(X0),X1)
| little_set(f11(f23(rotate_right(X0),X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_320])]) ).
fof(f574,plain,
( ! [X0,X1] :
( disjoint(rotate_right(X0),X1)
| little_set(f11(f23(rotate_right(X0),X1),X0)) )
| ~ spl0_56
| ~ spl0_63 ),
inference(resolution,[],[f475,f447]) ).
fof(f3753,plain,
( spl0_319
| ~ spl0_35
| ~ spl0_63 ),
inference(avatar_split_clause,[],[f572,f474,f340,f3751]) ).
fof(f3751,plain,
( spl0_319
<=> ! [X2,X0,X1] :
( disjoint(cross_product(X0,X1),X2)
| ordered_pair_predicate(f23(cross_product(X0,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_319])]) ).
fof(f572,plain,
( ! [X2,X0,X1] :
( disjoint(cross_product(X0,X1),X2)
| ordered_pair_predicate(f23(cross_product(X0,X1),X2)) )
| ~ spl0_35
| ~ spl0_63 ),
inference(resolution,[],[f475,f341]) ).
fof(f3749,plain,
( spl0_318
| ~ spl0_53
| ~ spl0_63 ),
inference(avatar_split_clause,[],[f571,f474,f434,f3747]) ).
fof(f3747,plain,
( spl0_318
<=> ! [X0,X1] :
( disjoint(domain_of(X0),X1)
| ordered_pair_predicate(f8(f23(domain_of(X0),X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_318])]) ).
fof(f571,plain,
( ! [X0,X1] :
( disjoint(domain_of(X0),X1)
| ordered_pair_predicate(f8(f23(domain_of(X0),X1),X0)) )
| ~ spl0_53
| ~ spl0_63 ),
inference(resolution,[],[f475,f435]) ).
fof(f3745,plain,
( spl0_317
| ~ spl0_48
| ~ spl0_63 ),
inference(avatar_split_clause,[],[f566,f474,f414,f3743]) ).
fof(f3743,plain,
( spl0_317
<=> ! [X0,X1] :
( disjoint(second(X0),X1)
| little_set(f6(f23(second(X0),X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_317])]) ).
fof(f566,plain,
( ! [X0,X1] :
( disjoint(second(X0),X1)
| little_set(f6(f23(second(X0),X1),X0)) )
| ~ spl0_48
| ~ spl0_63 ),
inference(resolution,[],[f475,f415]) ).
fof(f3741,plain,
( spl0_316
| ~ spl0_49
| ~ spl0_63 ),
inference(avatar_split_clause,[],[f565,f474,f418,f3739]) ).
fof(f3739,plain,
( spl0_316
<=> ! [X0,X1] :
( disjoint(second(X0),X1)
| little_set(f7(f23(second(X0),X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_316])]) ).
fof(f565,plain,
( ! [X0,X1] :
( disjoint(second(X0),X1)
| little_set(f7(f23(second(X0),X1),X0)) )
| ~ spl0_49
| ~ spl0_63 ),
inference(resolution,[],[f475,f419]) ).
fof(f3737,plain,
( spl0_315
| ~ spl0_92
| ~ spl0_173 ),
inference(avatar_split_clause,[],[f2451,f2440,f832,f3735]) ).
fof(f3735,plain,
( spl0_315
<=> ! [X0] : disjoint(X0,estin) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_315])]) ).
fof(f832,plain,
( spl0_92
<=> ! [X0] : disjoint(X0,empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_92])]) ).
fof(f2451,plain,
( ! [X0] : disjoint(X0,estin)
| ~ spl0_92
| ~ spl0_173 ),
inference(superposition,[],[f833,f2442]) ).
fof(f833,plain,
( ! [X0] : disjoint(X0,empty_set)
| ~ spl0_92 ),
inference(avatar_component_clause,[],[f832]) ).
fof(f3733,plain,
( spl0_314
| ~ spl0_46
| ~ spl0_63 ),
inference(avatar_split_clause,[],[f564,f474,f406,f3731]) ).
fof(f3731,plain,
( spl0_314
<=> ! [X0,X1] :
( disjoint(first(X0),X1)
| little_set(f4(f23(first(X0),X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_314])]) ).
fof(f564,plain,
( ! [X0,X1] :
( disjoint(first(X0),X1)
| little_set(f4(f23(first(X0),X1),X0)) )
| ~ spl0_46
| ~ spl0_63 ),
inference(resolution,[],[f475,f407]) ).
fof(f3729,plain,
( spl0_313
| ~ spl0_47
| ~ spl0_63 ),
inference(avatar_split_clause,[],[f563,f474,f410,f3727]) ).
fof(f3727,plain,
( spl0_313
<=> ! [X0,X1] :
( disjoint(first(X0),X1)
| little_set(f5(f23(first(X0),X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_313])]) ).
fof(f563,plain,
( ! [X0,X1] :
( disjoint(first(X0),X1)
| little_set(f5(f23(first(X0),X1),X0)) )
| ~ spl0_47
| ~ spl0_63 ),
inference(resolution,[],[f475,f411]) ).
fof(f3725,plain,
( spl0_312
| ~ spl0_57
| ~ spl0_60 ),
inference(avatar_split_clause,[],[f554,f462,f450,f3723]) ).
fof(f3723,plain,
( spl0_312
<=> ! [X0,X1] :
( subset(flip_range_of(X0),X1)
| little_set(f12(f17(flip_range_of(X0),X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_312])]) ).
fof(f554,plain,
( ! [X0,X1] :
( subset(flip_range_of(X0),X1)
| little_set(f12(f17(flip_range_of(X0),X1),X0)) )
| ~ spl0_57
| ~ spl0_60 ),
inference(resolution,[],[f463,f451]) ).
fof(f3721,plain,
( spl0_311
| ~ spl0_58
| ~ spl0_60 ),
inference(avatar_split_clause,[],[f553,f462,f454,f3719]) ).
fof(f3719,plain,
( spl0_311
<=> ! [X0,X1] :
( subset(flip_range_of(X0),X1)
| little_set(f13(f17(flip_range_of(X0),X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_311])]) ).
fof(f553,plain,
( ! [X0,X1] :
( subset(flip_range_of(X0),X1)
| little_set(f13(f17(flip_range_of(X0),X1),X0)) )
| ~ spl0_58
| ~ spl0_60 ),
inference(resolution,[],[f463,f455]) ).
fof(f3717,plain,
( spl0_310
| ~ spl0_59
| ~ spl0_60 ),
inference(avatar_split_clause,[],[f552,f462,f458,f3715]) ).
fof(f3715,plain,
( spl0_310
<=> ! [X0,X1] :
( subset(flip_range_of(X0),X1)
| little_set(f14(f17(flip_range_of(X0),X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_310])]) ).
fof(f552,plain,
( ! [X0,X1] :
( subset(flip_range_of(X0),X1)
| little_set(f14(f17(flip_range_of(X0),X1),X0)) )
| ~ spl0_59
| ~ spl0_60 ),
inference(resolution,[],[f463,f459]) ).
fof(f3713,plain,
( spl0_309
| ~ spl0_54
| ~ spl0_60 ),
inference(avatar_split_clause,[],[f551,f462,f438,f3711]) ).
fof(f3711,plain,
( spl0_309
<=> ! [X0,X1] :
( subset(rotate_right(X0),X1)
| little_set(f9(f17(rotate_right(X0),X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_309])]) ).
fof(f551,plain,
( ! [X0,X1] :
( subset(rotate_right(X0),X1)
| little_set(f9(f17(rotate_right(X0),X1),X0)) )
| ~ spl0_54
| ~ spl0_60 ),
inference(resolution,[],[f463,f439]) ).
fof(f3709,plain,
( spl0_308
| ~ spl0_55
| ~ spl0_60 ),
inference(avatar_split_clause,[],[f550,f462,f442,f3707]) ).
fof(f3707,plain,
( spl0_308
<=> ! [X0,X1] :
( subset(rotate_right(X0),X1)
| little_set(f10(f17(rotate_right(X0),X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_308])]) ).
fof(f550,plain,
( ! [X0,X1] :
( subset(rotate_right(X0),X1)
| little_set(f10(f17(rotate_right(X0),X1),X0)) )
| ~ spl0_55
| ~ spl0_60 ),
inference(resolution,[],[f463,f443]) ).
fof(f3705,plain,
( spl0_307
| ~ spl0_56
| ~ spl0_60 ),
inference(avatar_split_clause,[],[f549,f462,f446,f3703]) ).
fof(f3703,plain,
( spl0_307
<=> ! [X0,X1] :
( subset(rotate_right(X0),X1)
| little_set(f11(f17(rotate_right(X0),X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_307])]) ).
fof(f549,plain,
( ! [X0,X1] :
( subset(rotate_right(X0),X1)
| little_set(f11(f17(rotate_right(X0),X1),X0)) )
| ~ spl0_56
| ~ spl0_60 ),
inference(resolution,[],[f463,f447]) ).
fof(f3701,plain,
( spl0_306
| ~ spl0_35
| ~ spl0_60 ),
inference(avatar_split_clause,[],[f547,f462,f340,f3699]) ).
fof(f3699,plain,
( spl0_306
<=> ! [X2,X0,X1] :
( subset(cross_product(X0,X1),X2)
| ordered_pair_predicate(f17(cross_product(X0,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_306])]) ).
fof(f547,plain,
( ! [X2,X0,X1] :
( subset(cross_product(X0,X1),X2)
| ordered_pair_predicate(f17(cross_product(X0,X1),X2)) )
| ~ spl0_35
| ~ spl0_60 ),
inference(resolution,[],[f463,f341]) ).
fof(f3697,plain,
( spl0_305
| ~ spl0_53
| ~ spl0_60 ),
inference(avatar_split_clause,[],[f546,f462,f434,f3695]) ).
fof(f3695,plain,
( spl0_305
<=> ! [X0,X1] :
( subset(domain_of(X0),X1)
| ordered_pair_predicate(f8(f17(domain_of(X0),X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_305])]) ).
fof(f546,plain,
( ! [X0,X1] :
( subset(domain_of(X0),X1)
| ordered_pair_predicate(f8(f17(domain_of(X0),X1),X0)) )
| ~ spl0_53
| ~ spl0_60 ),
inference(resolution,[],[f463,f435]) ).
fof(f3693,plain,
( spl0_304
| ~ spl0_90
| ~ spl0_173 ),
inference(avatar_split_clause,[],[f2450,f2440,f764,f3691]) ).
fof(f3691,plain,
( spl0_304
<=> ! [X0] : disjoint(estin,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_304])]) ).
fof(f764,plain,
( spl0_90
<=> ! [X0] : disjoint(empty_set,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_90])]) ).
fof(f2450,plain,
( ! [X0] : disjoint(estin,X0)
| ~ spl0_90
| ~ spl0_173 ),
inference(superposition,[],[f765,f2442]) ).
fof(f765,plain,
( ! [X0] : disjoint(empty_set,X0)
| ~ spl0_90 ),
inference(avatar_component_clause,[],[f764]) ).
fof(f3689,plain,
( spl0_303
| ~ spl0_48
| ~ spl0_60 ),
inference(avatar_split_clause,[],[f541,f462,f414,f3687]) ).
fof(f3687,plain,
( spl0_303
<=> ! [X0,X1] :
( subset(second(X0),X1)
| little_set(f6(f17(second(X0),X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_303])]) ).
fof(f541,plain,
( ! [X0,X1] :
( subset(second(X0),X1)
| little_set(f6(f17(second(X0),X1),X0)) )
| ~ spl0_48
| ~ spl0_60 ),
inference(resolution,[],[f463,f415]) ).
fof(f3685,plain,
( spl0_302
| ~ spl0_49
| ~ spl0_60 ),
inference(avatar_split_clause,[],[f540,f462,f418,f3683]) ).
fof(f3683,plain,
( spl0_302
<=> ! [X0,X1] :
( subset(second(X0),X1)
| little_set(f7(f17(second(X0),X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_302])]) ).
fof(f540,plain,
( ! [X0,X1] :
( subset(second(X0),X1)
| little_set(f7(f17(second(X0),X1),X0)) )
| ~ spl0_49
| ~ spl0_60 ),
inference(resolution,[],[f463,f419]) ).
fof(f3681,plain,
( spl0_301
| ~ spl0_46
| ~ spl0_60 ),
inference(avatar_split_clause,[],[f539,f462,f406,f3679]) ).
fof(f3679,plain,
( spl0_301
<=> ! [X0,X1] :
( subset(first(X0),X1)
| little_set(f4(f17(first(X0),X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_301])]) ).
fof(f539,plain,
( ! [X0,X1] :
( subset(first(X0),X1)
| little_set(f4(f17(first(X0),X1),X0)) )
| ~ spl0_46
| ~ spl0_60 ),
inference(resolution,[],[f463,f407]) ).
fof(f3677,plain,
( spl0_300
| ~ spl0_47
| ~ spl0_60 ),
inference(avatar_split_clause,[],[f538,f462,f410,f3675]) ).
fof(f3675,plain,
( spl0_300
<=> ! [X0,X1] :
( subset(first(X0),X1)
| little_set(f5(f17(first(X0),X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_300])]) ).
fof(f538,plain,
( ! [X0,X1] :
( subset(first(X0),X1)
| little_set(f5(f17(first(X0),X1),X0)) )
| ~ spl0_47
| ~ spl0_60 ),
inference(resolution,[],[f463,f411]) ).
fof(f3672,plain,
( spl0_299
| ~ spl0_40
| ~ spl0_52 ),
inference(avatar_split_clause,[],[f521,f430,f361,f3670]) ).
fof(f521,plain,
( ! [X0,X1] :
( member(f24(intersection(X0,X1)),X1)
| intersection(X0,X1) = empty_set )
| ~ spl0_40
| ~ spl0_52 ),
inference(resolution,[],[f431,f362]) ).
fof(f3667,plain,
( spl0_298
| ~ spl0_40
| ~ spl0_51 ),
inference(avatar_split_clause,[],[f519,f426,f361,f3665]) ).
fof(f519,plain,
( ! [X0,X1] :
( member(f24(intersection(X0,X1)),X0)
| intersection(X0,X1) = empty_set )
| ~ spl0_40
| ~ spl0_51 ),
inference(resolution,[],[f427,f362]) ).
fof(f3631,plain,
( spl0_297
| ~ spl0_76
| ~ spl0_173 ),
inference(avatar_split_clause,[],[f2449,f2440,f636,f3629]) ).
fof(f3629,plain,
( spl0_297
<=> ! [X0] : subset(estin,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_297])]) ).
fof(f2449,plain,
( ! [X0] : subset(estin,X0)
| ~ spl0_76
| ~ spl0_173 ),
inference(superposition,[],[f637,f2442]) ).
fof(f3626,plain,
( spl0_296
| ~ spl0_5
| ~ spl0_173 ),
inference(avatar_split_clause,[],[f2445,f2440,f205,f3623]) ).
fof(f3623,plain,
( spl0_296
<=> member(estin,infinity) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_296])]) ).
fof(f205,plain,
( spl0_5
<=> member(empty_set,infinity) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).
fof(f2445,plain,
( member(estin,infinity)
| ~ spl0_5
| ~ spl0_173 ),
inference(superposition,[],[f207,f2442]) ).
fof(f207,plain,
( member(empty_set,infinity)
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f205]) ).
fof(f3551,plain,
( spl0_295
| ~ spl0_173
| ~ spl0_274 ),
inference(avatar_split_clause,[],[f3204,f3201,f2440,f3549]) ).
fof(f3549,plain,
( spl0_295
<=> ! [X0] :
( estin = X0
| ~ little_set(X0)
| ordered_pair_predicate(f26(X0))
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_295])]) ).
fof(f3204,plain,
( ! [X0] :
( estin = X0
| ~ little_set(X0)
| ordered_pair_predicate(f26(X0))
| ~ relation(X0) )
| ~ spl0_173
| ~ spl0_274 ),
inference(forward_demodulation,[],[f3202,f2442]) ).
fof(f3547,plain,
( spl0_294
| ~ spl0_173
| ~ spl0_273 ),
inference(avatar_split_clause,[],[f3199,f3196,f2440,f3545]) ).
fof(f3199,plain,
( ! [X0,X1] :
( estin = X1
| ~ member(X0,X1)
| ~ member(X0,f24(X1)) )
| ~ spl0_173
| ~ spl0_273 ),
inference(forward_demodulation,[],[f3197,f2442]) ).
fof(f3481,plain,
( spl0_293
| ~ spl0_4
| ~ spl0_173 ),
inference(avatar_split_clause,[],[f2444,f2440,f201,f3479]) ).
fof(f2444,plain,
( ! [X0] : ~ member(X0,estin)
| ~ spl0_4
| ~ spl0_173 ),
inference(superposition,[],[f202,f2442]) ).
fof(f3477,plain,
( spl0_292
| ~ spl0_173
| ~ spl0_262 ),
inference(avatar_split_clause,[],[f3149,f3146,f2440,f3475]) ).
fof(f3475,plain,
( spl0_292
<=> ! [X0] :
( estin = range_of(X0)
| ordered_pair_predicate(f27(f24(range_of(X0)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_292])]) ).
fof(f3149,plain,
( ! [X0] :
( estin = range_of(X0)
| ordered_pair_predicate(f27(f24(range_of(X0)),X0)) )
| ~ spl0_173
| ~ spl0_262 ),
inference(forward_demodulation,[],[f3147,f2442]) ).
fof(f3435,plain,
( spl0_291
| ~ spl0_30
| ~ spl0_154 ),
inference(avatar_split_clause,[],[f2180,f2102,f314,f3432]) ).
fof(f3432,plain,
( spl0_291
<=> relation(rotate_right(empty_set)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_291])]) ).
fof(f2180,plain,
( relation(rotate_right(empty_set))
| ~ spl0_30
| ~ spl0_154 ),
inference(resolution,[],[f2103,f315]) ).
fof(f3430,plain,
( spl0_290
| ~ spl0_173
| ~ spl0_254 ),
inference(avatar_split_clause,[],[f3114,f3111,f2440,f3428]) ).
fof(f3428,plain,
( spl0_290
<=> ! [X0] :
( estin = flip_range_of(X0)
| little_set(f14(f24(flip_range_of(X0)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_290])]) ).
fof(f3114,plain,
( ! [X0] :
( estin = flip_range_of(X0)
| little_set(f14(f24(flip_range_of(X0)),X0)) )
| ~ spl0_173
| ~ spl0_254 ),
inference(forward_demodulation,[],[f3112,f2442]) ).
fof(f3426,plain,
( spl0_289
| ~ spl0_173
| ~ spl0_253 ),
inference(avatar_split_clause,[],[f3109,f3106,f2440,f3424]) ).
fof(f3424,plain,
( spl0_289
<=> ! [X0] :
( estin = flip_range_of(X0)
| little_set(f13(f24(flip_range_of(X0)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_289])]) ).
fof(f3109,plain,
( ! [X0] :
( estin = flip_range_of(X0)
| little_set(f13(f24(flip_range_of(X0)),X0)) )
| ~ spl0_173
| ~ spl0_253 ),
inference(forward_demodulation,[],[f3107,f2442]) ).
fof(f3422,plain,
( spl0_288
| ~ spl0_173
| ~ spl0_252 ),
inference(avatar_split_clause,[],[f3104,f3101,f2440,f3420]) ).
fof(f3420,plain,
( spl0_288
<=> ! [X0] :
( estin = flip_range_of(X0)
| little_set(f12(f24(flip_range_of(X0)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_288])]) ).
fof(f3104,plain,
( ! [X0] :
( estin = flip_range_of(X0)
| little_set(f12(f24(flip_range_of(X0)),X0)) )
| ~ spl0_173
| ~ spl0_252 ),
inference(forward_demodulation,[],[f3102,f2442]) ).
fof(f3418,plain,
( spl0_287
| ~ spl0_173
| ~ spl0_251 ),
inference(avatar_split_clause,[],[f3099,f3096,f2440,f3416]) ).
fof(f3416,plain,
( spl0_287
<=> ! [X0] :
( estin = rotate_right(X0)
| little_set(f11(f24(rotate_right(X0)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_287])]) ).
fof(f3099,plain,
( ! [X0] :
( estin = rotate_right(X0)
| little_set(f11(f24(rotate_right(X0)),X0)) )
| ~ spl0_173
| ~ spl0_251 ),
inference(forward_demodulation,[],[f3097,f2442]) ).
fof(f3414,plain,
( spl0_286
| ~ spl0_173
| ~ spl0_249 ),
inference(avatar_split_clause,[],[f3088,f3085,f2440,f3412]) ).
fof(f3412,plain,
( spl0_286
<=> ! [X0] :
( estin = rotate_right(X0)
| little_set(f10(f24(rotate_right(X0)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_286])]) ).
fof(f3088,plain,
( ! [X0] :
( estin = rotate_right(X0)
| little_set(f10(f24(rotate_right(X0)),X0)) )
| ~ spl0_173
| ~ spl0_249 ),
inference(forward_demodulation,[],[f3086,f2442]) ).
fof(f3410,plain,
( spl0_285
| ~ spl0_173
| ~ spl0_248 ),
inference(avatar_split_clause,[],[f3083,f3080,f2440,f3408]) ).
fof(f3408,plain,
( spl0_285
<=> ! [X0] :
( estin = rotate_right(X0)
| little_set(f9(f24(rotate_right(X0)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_285])]) ).
fof(f3083,plain,
( ! [X0] :
( estin = rotate_right(X0)
| little_set(f9(f24(rotate_right(X0)),X0)) )
| ~ spl0_173
| ~ spl0_248 ),
inference(forward_demodulation,[],[f3081,f2442]) ).
fof(f3406,plain,
( spl0_284
| ~ spl0_173
| ~ spl0_247 ),
inference(avatar_split_clause,[],[f3078,f3075,f2440,f3404]) ).
fof(f3404,plain,
( spl0_284
<=> ! [X0] :
( estin = domain_of(X0)
| ordered_pair_predicate(f8(f24(domain_of(X0)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_284])]) ).
fof(f3078,plain,
( ! [X0] :
( estin = domain_of(X0)
| ordered_pair_predicate(f8(f24(domain_of(X0)),X0)) )
| ~ spl0_173
| ~ spl0_247 ),
inference(forward_demodulation,[],[f3076,f2442]) ).
fof(f3242,plain,
( spl0_283
| ~ spl0_173
| ~ spl0_244 ),
inference(avatar_split_clause,[],[f3065,f3062,f2440,f3240]) ).
fof(f3240,plain,
( spl0_283
<=> ! [X0] :
( second(X0) = estin
| little_set(f7(f24(second(X0)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_283])]) ).
fof(f3065,plain,
( ! [X0] :
( second(X0) = estin
| little_set(f7(f24(second(X0)),X0)) )
| ~ spl0_173
| ~ spl0_244 ),
inference(forward_demodulation,[],[f3063,f2442]) ).
fof(f3237,plain,
( spl0_282
| ~ spl0_121
| ~ spl0_154 ),
inference(avatar_split_clause,[],[f2169,f2102,f1287,f3234]) ).
fof(f3234,plain,
( spl0_282
<=> single_valued_set(rotate_right(empty_set)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_282])]) ).
fof(f2169,plain,
( single_valued_set(rotate_right(empty_set))
| ~ spl0_121
| ~ spl0_154 ),
inference(resolution,[],[f2103,f1288]) ).
fof(f3232,plain,
( spl0_281
| ~ spl0_173
| ~ spl0_243 ),
inference(avatar_split_clause,[],[f3060,f3057,f2440,f3230]) ).
fof(f3230,plain,
( spl0_281
<=> ! [X0] :
( second(X0) = estin
| little_set(f6(f24(second(X0)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_281])]) ).
fof(f3060,plain,
( ! [X0] :
( second(X0) = estin
| little_set(f6(f24(second(X0)),X0)) )
| ~ spl0_173
| ~ spl0_243 ),
inference(forward_demodulation,[],[f3058,f2442]) ).
fof(f3228,plain,
( spl0_280
| ~ spl0_173
| ~ spl0_242 ),
inference(avatar_split_clause,[],[f3055,f3052,f2440,f3226]) ).
fof(f3226,plain,
( spl0_280
<=> ! [X0] :
( first(X0) = estin
| little_set(f5(f24(first(X0)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_280])]) ).
fof(f3055,plain,
( ! [X0] :
( first(X0) = estin
| little_set(f5(f24(first(X0)),X0)) )
| ~ spl0_173
| ~ spl0_242 ),
inference(forward_demodulation,[],[f3053,f2442]) ).
fof(f3224,plain,
( spl0_279
| ~ spl0_173
| ~ spl0_241 ),
inference(avatar_split_clause,[],[f3050,f3047,f2440,f3222]) ).
fof(f3222,plain,
( spl0_279
<=> ! [X0] :
( first(X0) = estin
| little_set(f4(f24(first(X0)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_279])]) ).
fof(f3050,plain,
( ! [X0] :
( first(X0) = estin
| little_set(f4(f24(first(X0)),X0)) )
| ~ spl0_173
| ~ spl0_241 ),
inference(forward_demodulation,[],[f3048,f2442]) ).
fof(f3220,plain,
( spl0_278
| ~ spl0_173
| ~ spl0_240 ),
inference(avatar_split_clause,[],[f3045,f3042,f2440,f3218]) ).
fof(f3218,plain,
( spl0_278
<=> ! [X0,X1] :
( estin = cross_product(X0,X1)
| ordered_pair_predicate(f24(cross_product(X0,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_278])]) ).
fof(f3045,plain,
( ! [X0,X1] :
( estin = cross_product(X0,X1)
| ordered_pair_predicate(f24(cross_product(X0,X1))) )
| ~ spl0_173
| ~ spl0_240 ),
inference(forward_demodulation,[],[f3043,f2442]) ).
fof(f3216,plain,
( spl0_277
| ~ spl0_11
| ~ spl0_104 ),
inference(avatar_split_clause,[],[f1027,f966,f232,f3214]) ).
fof(f3214,plain,
( spl0_277
<=> ! [X2,X0,X1] :
( ~ member(X0,apply(X1,X2))
| little_set(f28(X0,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_277])]) ).
fof(f1027,plain,
( ! [X2,X0,X1] :
( ~ member(X0,apply(X1,X2))
| little_set(f28(X0,X1,X2)) )
| ~ spl0_11
| ~ spl0_104 ),
inference(resolution,[],[f967,f233]) ).
fof(f3212,plain,
( spl0_276
| ~ spl0_11
| ~ spl0_103 ),
inference(avatar_split_clause,[],[f992,f960,f232,f3210]) ).
fof(f3210,plain,
( spl0_276
<=> ! [X2,X0,X1] :
( ~ member(X0,image(X1,X2))
| little_set(f22(X0,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_276])]) ).
fof(f992,plain,
( ! [X2,X0,X1] :
( ~ member(X0,image(X1,X2))
| little_set(f22(X0,X1,X2)) )
| ~ spl0_11
| ~ spl0_103 ),
inference(resolution,[],[f961,f233]) ).
fof(f3208,plain,
( spl0_275
| ~ spl0_30
| ~ spl0_93 ),
inference(avatar_split_clause,[],[f889,f836,f314,f3206]) ).
fof(f889,plain,
( ! [X0,X1] :
( ~ member(X0,X1)
| member(f18(X0),sigma(X1))
| relation(X0) )
| ~ spl0_30
| ~ spl0_93 ),
inference(resolution,[],[f837,f315]) ).
fof(f3203,plain,
( spl0_274
| ~ spl0_38
| ~ spl0_84 ),
inference(avatar_split_clause,[],[f772,f668,f353,f3201]) ).
fof(f772,plain,
( ! [X0] :
( empty_set = X0
| ~ little_set(X0)
| ordered_pair_predicate(f26(X0))
| ~ relation(X0) )
| ~ spl0_38
| ~ spl0_84 ),
inference(resolution,[],[f669,f354]) ).
fof(f3198,plain,
( spl0_273
| ~ spl0_41
| ~ spl0_83 ),
inference(avatar_split_clause,[],[f771,f664,f365,f3196]) ).
fof(f365,plain,
( spl0_41
<=> ! [X0] :
( empty_set = X0
| disjoint(f24(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_41])]) ).
fof(f664,plain,
( spl0_83
<=> ! [X2,X0,X1] :
( ~ disjoint(X0,X1)
| ~ member(X2,X1)
| ~ member(X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_83])]) ).
fof(f771,plain,
( ! [X0,X1] :
( ~ member(X0,X1)
| ~ member(X0,f24(X1))
| empty_set = X1 )
| ~ spl0_41
| ~ spl0_83 ),
inference(resolution,[],[f665,f366]) ).
fof(f366,plain,
( ! [X0] :
( disjoint(f24(X0),X0)
| empty_set = X0 )
| ~ spl0_41 ),
inference(avatar_component_clause,[],[f365]) ).
fof(f665,plain,
( ! [X2,X0,X1] :
( ~ disjoint(X0,X1)
| ~ member(X2,X1)
| ~ member(X2,X0) )
| ~ spl0_83 ),
inference(avatar_component_clause,[],[f664]) ).
fof(f3194,plain,
( spl0_272
| ~ spl0_38
| ~ spl0_82 ),
inference(avatar_split_clause,[],[f768,f660,f353,f3192]) ).
fof(f3192,plain,
( spl0_272
<=> ! [X0,X1] :
( ~ subset(X0,X1)
| ~ little_set(X0)
| ordered_pair_predicate(X0)
| ~ relation(powerset(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_272])]) ).
fof(f768,plain,
( ! [X0,X1] :
( ~ subset(X0,X1)
| ~ little_set(X0)
| ordered_pair_predicate(X0)
| ~ relation(powerset(X1)) )
| ~ spl0_38
| ~ spl0_82 ),
inference(resolution,[],[f661,f354]) ).
fof(f3189,plain,
( spl0_271
| ~ spl0_30
| ~ spl0_153 ),
inference(avatar_split_clause,[],[f2149,f2098,f314,f3186]) ).
fof(f3186,plain,
( spl0_271
<=> relation(flip_range_of(empty_set)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_271])]) ).
fof(f2149,plain,
( relation(flip_range_of(empty_set))
| ~ spl0_30
| ~ spl0_153 ),
inference(resolution,[],[f2099,f315]) ).
fof(f3184,plain,
( spl0_270
| ~ spl0_38
| ~ spl0_79 ),
inference(avatar_split_clause,[],[f761,f648,f353,f3182]) ).
fof(f3182,plain,
( spl0_270
<=> ! [X0,X1] :
( ~ member(X0,sigma(X1))
| ordered_pair_predicate(X0)
| ~ relation(f16(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_270])]) ).
fof(f761,plain,
( ! [X0,X1] :
( ~ member(X0,sigma(X1))
| ordered_pair_predicate(X0)
| ~ relation(f16(X0,X1)) )
| ~ spl0_38
| ~ spl0_79 ),
inference(resolution,[],[f649,f354]) ).
fof(f3180,plain,
( spl0_269
| ~ spl0_28
| ~ spl0_78 ),
inference(avatar_split_clause,[],[f749,f644,f306,f3178]) ).
fof(f749,plain,
( ! [X0,X1] :
( ~ member(X0,sigma(converse(X1)))
| ordered_pair_predicate(f16(X0,converse(X1))) )
| ~ spl0_28
| ~ spl0_78 ),
inference(resolution,[],[f645,f307]) ).
fof(f3176,plain,
( spl0_268
| ~ spl0_38
| ~ spl0_78 ),
inference(avatar_split_clause,[],[f735,f644,f353,f3174]) ).
fof(f735,plain,
( ! [X0,X1] :
( ~ member(X0,sigma(X1))
| ordered_pair_predicate(f16(X0,X1))
| ~ relation(X1) )
| ~ spl0_38
| ~ spl0_78 ),
inference(resolution,[],[f645,f354]) ).
fof(f3172,plain,
( spl0_267
| ~ spl0_38
| ~ spl0_73 ),
inference(avatar_split_clause,[],[f696,f624,f353,f3170]) ).
fof(f3170,plain,
( spl0_267
<=> ! [X0,X1] :
( member(X0,X1)
| ~ little_set(X0)
| ordered_pair_predicate(X0)
| ~ relation(complement(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_267])]) ).
fof(f696,plain,
( ! [X0,X1] :
( member(X0,X1)
| ~ little_set(X0)
| ordered_pair_predicate(X0)
| ~ relation(complement(X1)) )
| ~ spl0_38
| ~ spl0_73 ),
inference(resolution,[],[f625,f354]) ).
fof(f3168,plain,
( spl0_266
| ~ spl0_38
| ~ spl0_72 ),
inference(avatar_split_clause,[],[f693,f620,f353,f3166]) ).
fof(f3166,plain,
( spl0_266
<=> ! [X0,X1] :
( ~ member(X0,second(X1))
| ordered_pair_predicate(X0)
| ~ relation(f7(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_266])]) ).
fof(f693,plain,
( ! [X0,X1] :
( ~ member(X0,second(X1))
| ordered_pair_predicate(X0)
| ~ relation(f7(X0,X1)) )
| ~ spl0_38
| ~ spl0_72 ),
inference(resolution,[],[f621,f354]) ).
fof(f3164,plain,
( spl0_265
| ~ spl0_38
| ~ spl0_71 ),
inference(avatar_split_clause,[],[f691,f616,f353,f3162]) ).
fof(f3162,plain,
( spl0_265
<=> ! [X0,X1] :
( ~ member(X0,first(X1))
| ordered_pair_predicate(X0)
| ~ relation(f4(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_265])]) ).
fof(f691,plain,
( ! [X0,X1] :
( ~ member(X0,first(X1))
| ordered_pair_predicate(X0)
| ~ relation(f4(X0,X1)) )
| ~ spl0_38
| ~ spl0_71 ),
inference(resolution,[],[f617,f354]) ).
fof(f3160,plain,
( ~ spl0_264
| ~ spl0_177
| spl0_263 ),
inference(avatar_split_clause,[],[f3155,f3151,f2481,f3157]) ).
fof(f3157,plain,
( spl0_264
<=> first(f24(estin)) = second(f24(estin)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_264])]) ).
fof(f3151,plain,
( spl0_263
<=> first(f24(identity_relation)) = second(f24(identity_relation)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_263])]) ).
fof(f3155,plain,
( first(f24(estin)) != second(f24(estin))
| ~ spl0_177
| spl0_263 ),
inference(forward_demodulation,[],[f3152,f2483]) ).
fof(f3152,plain,
( first(f24(identity_relation)) != second(f24(identity_relation))
| spl0_263 ),
inference(avatar_component_clause,[],[f3151]) ).
fof(f3154,plain,
( spl0_175
| spl0_263
| ~ spl0_40
| ~ spl0_66 ),
inference(avatar_split_clause,[],[f614,f486,f361,f3151,f2469]) ).
fof(f614,plain,
( first(f24(identity_relation)) = second(f24(identity_relation))
| empty_set = identity_relation
| ~ spl0_40
| ~ spl0_66 ),
inference(resolution,[],[f487,f362]) ).
fof(f3148,plain,
( spl0_262
| ~ spl0_40
| ~ spl0_65 ),
inference(avatar_split_clause,[],[f609,f482,f361,f3146]) ).
fof(f609,plain,
( ! [X0] :
( ordered_pair_predicate(f27(f24(range_of(X0)),X0))
| empty_set = range_of(X0) )
| ~ spl0_40
| ~ spl0_65 ),
inference(resolution,[],[f483,f362]) ).
fof(f3143,plain,
( spl0_261
| ~ spl0_121
| ~ spl0_153 ),
inference(avatar_split_clause,[],[f2138,f2098,f1287,f3140]) ).
fof(f3140,plain,
( spl0_261
<=> single_valued_set(flip_range_of(empty_set)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_261])]) ).
fof(f2138,plain,
( single_valued_set(flip_range_of(empty_set))
| ~ spl0_121
| ~ spl0_153 ),
inference(resolution,[],[f2099,f1288]) ).
fof(f3138,plain,
( spl0_260
| ~ spl0_37
| ~ spl0_64 ),
inference(avatar_split_clause,[],[f603,f478,f349,f3136]) ).
fof(f3136,plain,
( spl0_260
<=> ! [X0,X1] :
( disjoint(X0,powerset(X1))
| subset(f23(X0,powerset(X1)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_260])]) ).
fof(f603,plain,
( ! [X0,X1] :
( disjoint(X0,powerset(X1))
| subset(f23(X0,powerset(X1)),X1) )
| ~ spl0_37
| ~ spl0_64 ),
inference(resolution,[],[f479,f350]) ).
fof(f3134,plain,
( spl0_259
| ~ spl0_34
| ~ spl0_64 ),
inference(avatar_split_clause,[],[f592,f478,f336,f3132]) ).
fof(f592,plain,
( ! [X0,X1] :
( disjoint(X0,complement(X1))
| ~ member(f23(X0,complement(X1)),X1) )
| ~ spl0_34
| ~ spl0_64 ),
inference(resolution,[],[f479,f337]) ).
fof(f3130,plain,
( spl0_258
| ~ spl0_37
| ~ spl0_63 ),
inference(avatar_split_clause,[],[f581,f474,f349,f3128]) ).
fof(f3128,plain,
( spl0_258
<=> ! [X0,X1] :
( disjoint(powerset(X0),X1)
| subset(f23(powerset(X0),X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_258])]) ).
fof(f581,plain,
( ! [X0,X1] :
( disjoint(powerset(X0),X1)
| subset(f23(powerset(X0),X1),X0) )
| ~ spl0_37
| ~ spl0_63 ),
inference(resolution,[],[f475,f350]) ).
fof(f3126,plain,
( spl0_257
| ~ spl0_34
| ~ spl0_63 ),
inference(avatar_split_clause,[],[f570,f474,f336,f3124]) ).
fof(f570,plain,
( ! [X0,X1] :
( disjoint(complement(X0),X1)
| ~ member(f23(complement(X0),X1),X0) )
| ~ spl0_34
| ~ spl0_63 ),
inference(resolution,[],[f475,f337]) ).
fof(f3122,plain,
( spl0_256
| ~ spl0_37
| ~ spl0_60 ),
inference(avatar_split_clause,[],[f556,f462,f349,f3120]) ).
fof(f3120,plain,
( spl0_256
<=> ! [X0,X1] :
( subset(powerset(X0),X1)
| subset(f17(powerset(X0),X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_256])]) ).
fof(f556,plain,
( ! [X0,X1] :
( subset(powerset(X0),X1)
| subset(f17(powerset(X0),X1),X0) )
| ~ spl0_37
| ~ spl0_60 ),
inference(resolution,[],[f463,f350]) ).
fof(f3118,plain,
( spl0_255
| ~ spl0_34
| ~ spl0_60 ),
inference(avatar_split_clause,[],[f545,f462,f336,f3116]) ).
fof(f545,plain,
( ! [X0,X1] :
( subset(complement(X0),X1)
| ~ member(f17(complement(X0),X1),X0) )
| ~ spl0_34
| ~ spl0_60 ),
inference(resolution,[],[f463,f337]) ).
fof(f3113,plain,
( spl0_254
| ~ spl0_40
| ~ spl0_59 ),
inference(avatar_split_clause,[],[f535,f458,f361,f3111]) ).
fof(f535,plain,
( ! [X0] :
( little_set(f14(f24(flip_range_of(X0)),X0))
| flip_range_of(X0) = empty_set )
| ~ spl0_40
| ~ spl0_59 ),
inference(resolution,[],[f459,f362]) ).
fof(f3108,plain,
( spl0_253
| ~ spl0_40
| ~ spl0_58 ),
inference(avatar_split_clause,[],[f533,f454,f361,f3106]) ).
fof(f533,plain,
( ! [X0] :
( little_set(f13(f24(flip_range_of(X0)),X0))
| flip_range_of(X0) = empty_set )
| ~ spl0_40
| ~ spl0_58 ),
inference(resolution,[],[f455,f362]) ).
fof(f3103,plain,
( spl0_252
| ~ spl0_40
| ~ spl0_57 ),
inference(avatar_split_clause,[],[f531,f450,f361,f3101]) ).
fof(f531,plain,
( ! [X0] :
( little_set(f12(f24(flip_range_of(X0)),X0))
| flip_range_of(X0) = empty_set )
| ~ spl0_40
| ~ spl0_57 ),
inference(resolution,[],[f451,f362]) ).
fof(f3098,plain,
( spl0_251
| ~ spl0_40
| ~ spl0_56 ),
inference(avatar_split_clause,[],[f529,f446,f361,f3096]) ).
fof(f529,plain,
( ! [X0] :
( little_set(f11(f24(rotate_right(X0)),X0))
| rotate_right(X0) = empty_set )
| ~ spl0_40
| ~ spl0_56 ),
inference(resolution,[],[f447,f362]) ).
fof(f3093,plain,
( spl0_250
| ~ spl0_121
| ~ spl0_151 ),
inference(avatar_split_clause,[],[f2107,f2025,f1287,f3090]) ).
fof(f3090,plain,
( spl0_250
<=> single_valued_set(converse(empty_set)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_250])]) ).
fof(f2107,plain,
( single_valued_set(converse(empty_set))
| ~ spl0_121
| ~ spl0_151 ),
inference(resolution,[],[f2026,f1288]) ).
fof(f3087,plain,
( spl0_249
| ~ spl0_40
| ~ spl0_55 ),
inference(avatar_split_clause,[],[f527,f442,f361,f3085]) ).
fof(f527,plain,
( ! [X0] :
( little_set(f10(f24(rotate_right(X0)),X0))
| rotate_right(X0) = empty_set )
| ~ spl0_40
| ~ spl0_55 ),
inference(resolution,[],[f443,f362]) ).
fof(f3082,plain,
( spl0_248
| ~ spl0_40
| ~ spl0_54 ),
inference(avatar_split_clause,[],[f525,f438,f361,f3080]) ).
fof(f525,plain,
( ! [X0] :
( little_set(f9(f24(rotate_right(X0)),X0))
| rotate_right(X0) = empty_set )
| ~ spl0_40
| ~ spl0_54 ),
inference(resolution,[],[f439,f362]) ).
fof(f3077,plain,
( spl0_247
| ~ spl0_40
| ~ spl0_53 ),
inference(avatar_split_clause,[],[f523,f434,f361,f3075]) ).
fof(f523,plain,
( ! [X0] :
( ordered_pair_predicate(f8(f24(domain_of(X0)),X0))
| domain_of(X0) = empty_set )
| ~ spl0_40
| ~ spl0_53 ),
inference(resolution,[],[f435,f362]) ).
fof(f3073,plain,
( spl0_246
| ~ spl0_30
| ~ spl0_52 ),
inference(avatar_split_clause,[],[f520,f430,f314,f3071]) ).
fof(f520,plain,
( ! [X0,X1] :
( member(f18(intersection(X0,X1)),X1)
| relation(intersection(X0,X1)) )
| ~ spl0_30
| ~ spl0_52 ),
inference(resolution,[],[f431,f315]) ).
fof(f3069,plain,
( spl0_245
| ~ spl0_30
| ~ spl0_51 ),
inference(avatar_split_clause,[],[f518,f426,f314,f3067]) ).
fof(f518,plain,
( ! [X0,X1] :
( member(f18(intersection(X0,X1)),X0)
| relation(intersection(X0,X1)) )
| ~ spl0_30
| ~ spl0_51 ),
inference(resolution,[],[f427,f315]) ).
fof(f3064,plain,
( spl0_244
| ~ spl0_40
| ~ spl0_49 ),
inference(avatar_split_clause,[],[f513,f418,f361,f3062]) ).
fof(f513,plain,
( ! [X0] :
( little_set(f7(f24(second(X0)),X0))
| second(X0) = empty_set )
| ~ spl0_40
| ~ spl0_49 ),
inference(resolution,[],[f419,f362]) ).
fof(f3059,plain,
( spl0_243
| ~ spl0_40
| ~ spl0_48 ),
inference(avatar_split_clause,[],[f511,f414,f361,f3057]) ).
fof(f511,plain,
( ! [X0] :
( little_set(f6(f24(second(X0)),X0))
| second(X0) = empty_set )
| ~ spl0_40
| ~ spl0_48 ),
inference(resolution,[],[f415,f362]) ).
fof(f3054,plain,
( spl0_242
| ~ spl0_40
| ~ spl0_47 ),
inference(avatar_split_clause,[],[f509,f410,f361,f3052]) ).
fof(f509,plain,
( ! [X0] :
( little_set(f5(f24(first(X0)),X0))
| first(X0) = empty_set )
| ~ spl0_40
| ~ spl0_47 ),
inference(resolution,[],[f411,f362]) ).
fof(f3049,plain,
( spl0_241
| ~ spl0_40
| ~ spl0_46 ),
inference(avatar_split_clause,[],[f507,f406,f361,f3047]) ).
fof(f507,plain,
( ! [X0] :
( little_set(f4(f24(first(X0)),X0))
| first(X0) = empty_set )
| ~ spl0_40
| ~ spl0_46 ),
inference(resolution,[],[f407,f362]) ).
fof(f3044,plain,
( spl0_240
| ~ spl0_35
| ~ spl0_40 ),
inference(avatar_split_clause,[],[f395,f361,f340,f3042]) ).
fof(f395,plain,
( ! [X0,X1] :
( cross_product(X0,X1) = empty_set
| ordered_pair_predicate(f24(cross_product(X0,X1))) )
| ~ spl0_35
| ~ spl0_40 ),
inference(resolution,[],[f362,f341]) ).
fof(f3039,plain,
( spl0_239
| ~ spl0_30
| ~ spl0_141 ),
inference(avatar_split_clause,[],[f2079,f1749,f314,f3036]) ).
fof(f3036,plain,
( spl0_239
<=> relation(range_of(empty_set)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_239])]) ).
fof(f2079,plain,
( relation(range_of(empty_set))
| ~ spl0_30
| ~ spl0_141 ),
inference(resolution,[],[f1750,f315]) ).
fof(f3003,plain,
( spl0_238
| ~ spl0_121
| ~ spl0_141 ),
inference(avatar_split_clause,[],[f2067,f1749,f1287,f3000]) ).
fof(f3000,plain,
( spl0_238
<=> single_valued_set(range_of(empty_set)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_238])]) ).
fof(f2067,plain,
( single_valued_set(range_of(empty_set))
| ~ spl0_121
| ~ spl0_141 ),
inference(resolution,[],[f1750,f1288]) ).
fof(f2995,plain,
( spl0_237
| ~ spl0_30
| ~ spl0_135 ),
inference(avatar_split_clause,[],[f2047,f1548,f314,f2992]) ).
fof(f2992,plain,
( spl0_237
<=> relation(sigma(empty_set)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_237])]) ).
fof(f2047,plain,
( relation(sigma(empty_set))
| ~ spl0_30
| ~ spl0_135 ),
inference(resolution,[],[f1549,f315]) ).
fof(f2990,plain,
( spl0_236
| ~ spl0_173
| ~ spl0_213 ),
inference(avatar_split_clause,[],[f2892,f2889,f2440,f2988]) ).
fof(f2988,plain,
( spl0_236
<=> ! [X0] :
( estin = powerset(X0)
| subset(f24(powerset(X0)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_236])]) ).
fof(f2892,plain,
( ! [X0] :
( estin = powerset(X0)
| subset(f24(powerset(X0)),X0) )
| ~ spl0_173
| ~ spl0_213 ),
inference(forward_demodulation,[],[f2890,f2442]) ).
fof(f2986,plain,
( spl0_235
| ~ spl0_173
| ~ spl0_212 ),
inference(avatar_split_clause,[],[f2887,f2884,f2440,f2984]) ).
fof(f2887,plain,
( ! [X0] :
( estin = complement(X0)
| ~ member(f24(complement(X0)),X0) )
| ~ spl0_173
| ~ spl0_212 ),
inference(forward_demodulation,[],[f2885,f2442]) ).
fof(f2979,plain,
( spl0_234
| ~ spl0_16
| ~ spl0_93 ),
inference(avatar_split_clause,[],[f881,f836,f253,f2977]) ).
fof(f881,plain,
( ! [X0,X1] :
( ~ member(universal_set,X0)
| member(X1,sigma(X0))
| ~ little_set(X1) )
| ~ spl0_16
| ~ spl0_93 ),
inference(resolution,[],[f837,f254]) ).
fof(f2975,plain,
( spl0_233
| ~ spl0_69
| ~ spl0_86 ),
inference(avatar_split_clause,[],[f825,f676,f499,f2973]) ).
fof(f2973,plain,
( spl0_233
<=> ! [X0,X1] :
( ~ closed(X0,X1)
| domain_of(X1) = cross_product(X0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_233])]) ).
fof(f499,plain,
( spl0_69
<=> ! [X0,X1,X7] :
( ~ maps(X7,X0,X1)
| domain_of(X7) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_69])]) ).
fof(f676,plain,
( spl0_86
<=> ! [X7,X8] :
( ~ closed(X8,X7)
| maps(X7,cross_product(X8,X8),X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_86])]) ).
fof(f825,plain,
( ! [X0,X1] :
( ~ closed(X0,X1)
| domain_of(X1) = cross_product(X0,X0) )
| ~ spl0_69
| ~ spl0_86 ),
inference(resolution,[],[f677,f500]) ).
fof(f500,plain,
( ! [X0,X1,X7] :
( ~ maps(X7,X0,X1)
| domain_of(X7) = X0 )
| ~ spl0_69 ),
inference(avatar_component_clause,[],[f499]) ).
fof(f677,plain,
( ! [X8,X7] :
( maps(X7,cross_product(X8,X8),X8)
| ~ closed(X8,X7) )
| ~ spl0_86 ),
inference(avatar_component_clause,[],[f676]) ).
fof(f2971,plain,
( spl0_232
| ~ spl0_30
| ~ spl0_65 ),
inference(avatar_split_clause,[],[f606,f482,f314,f2969]) ).
fof(f2969,plain,
( spl0_232
<=> ! [X0] :
( ordered_pair_predicate(f27(f18(range_of(X0)),X0))
| relation(range_of(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_232])]) ).
fof(f606,plain,
( ! [X0] :
( ordered_pair_predicate(f27(f18(range_of(X0)),X0))
| relation(range_of(X0)) )
| ~ spl0_30
| ~ spl0_65 ),
inference(resolution,[],[f483,f315]) ).
fof(f2967,plain,
( spl0_231
| ~ spl0_28
| ~ spl0_64 ),
inference(avatar_split_clause,[],[f595,f478,f306,f2965]) ).
fof(f2965,plain,
( spl0_231
<=> ! [X0,X1] :
( disjoint(X0,converse(X1))
| ordered_pair_predicate(f23(X0,converse(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_231])]) ).
fof(f595,plain,
( ! [X0,X1] :
( disjoint(X0,converse(X1))
| ordered_pair_predicate(f23(X0,converse(X1))) )
| ~ spl0_28
| ~ spl0_64 ),
inference(resolution,[],[f479,f307]) ).
fof(f2963,plain,
( spl0_230
| ~ spl0_38
| ~ spl0_64 ),
inference(avatar_split_clause,[],[f583,f478,f353,f2961]) ).
fof(f2961,plain,
( spl0_230
<=> ! [X0,X1] :
( disjoint(X0,X1)
| ordered_pair_predicate(f23(X0,X1))
| ~ relation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_230])]) ).
fof(f583,plain,
( ! [X0,X1] :
( disjoint(X0,X1)
| ordered_pair_predicate(f23(X0,X1))
| ~ relation(X1) )
| ~ spl0_38
| ~ spl0_64 ),
inference(resolution,[],[f479,f354]) ).
fof(f2958,plain,
( spl0_229
| ~ spl0_121
| ~ spl0_135 ),
inference(avatar_split_clause,[],[f2036,f1548,f1287,f2955]) ).
fof(f2955,plain,
( spl0_229
<=> single_valued_set(sigma(empty_set)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_229])]) ).
fof(f2036,plain,
( single_valued_set(sigma(empty_set))
| ~ spl0_121
| ~ spl0_135 ),
inference(resolution,[],[f1549,f1288]) ).
fof(f2953,plain,
( spl0_228
| ~ spl0_28
| ~ spl0_63 ),
inference(avatar_split_clause,[],[f573,f474,f306,f2951]) ).
fof(f2951,plain,
( spl0_228
<=> ! [X0,X1] :
( disjoint(converse(X0),X1)
| ordered_pair_predicate(f23(converse(X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_228])]) ).
fof(f573,plain,
( ! [X0,X1] :
( disjoint(converse(X0),X1)
| ordered_pair_predicate(f23(converse(X0),X1)) )
| ~ spl0_28
| ~ spl0_63 ),
inference(resolution,[],[f475,f307]) ).
fof(f2949,plain,
( spl0_227
| ~ spl0_38
| ~ spl0_63 ),
inference(avatar_split_clause,[],[f561,f474,f353,f2947]) ).
fof(f2947,plain,
( spl0_227
<=> ! [X0,X1] :
( disjoint(X0,X1)
| ordered_pair_predicate(f23(X0,X1))
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_227])]) ).
fof(f561,plain,
( ! [X0,X1] :
( disjoint(X0,X1)
| ordered_pair_predicate(f23(X0,X1))
| ~ relation(X0) )
| ~ spl0_38
| ~ spl0_63 ),
inference(resolution,[],[f475,f354]) ).
fof(f2945,plain,
( spl0_226
| ~ spl0_28
| ~ spl0_60 ),
inference(avatar_split_clause,[],[f548,f462,f306,f2943]) ).
fof(f2943,plain,
( spl0_226
<=> ! [X0,X1] :
( subset(converse(X0),X1)
| ordered_pair_predicate(f17(converse(X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_226])]) ).
fof(f548,plain,
( ! [X0,X1] :
( subset(converse(X0),X1)
| ordered_pair_predicate(f17(converse(X0),X1)) )
| ~ spl0_28
| ~ spl0_60 ),
inference(resolution,[],[f463,f307]) ).
fof(f2941,plain,
( spl0_225
| ~ spl0_38
| ~ spl0_60 ),
inference(avatar_split_clause,[],[f536,f462,f353,f2939]) ).
fof(f2939,plain,
( spl0_225
<=> ! [X0,X1] :
( subset(X0,X1)
| ordered_pair_predicate(f17(X0,X1))
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_225])]) ).
fof(f536,plain,
( ! [X0,X1] :
( subset(X0,X1)
| ordered_pair_predicate(f17(X0,X1))
| ~ relation(X0) )
| ~ spl0_38
| ~ spl0_60 ),
inference(resolution,[],[f463,f354]) ).
fof(f2937,plain,
( spl0_224
| ~ spl0_30
| ~ spl0_59 ),
inference(avatar_split_clause,[],[f534,f458,f314,f2935]) ).
fof(f2935,plain,
( spl0_224
<=> ! [X0] :
( little_set(f14(f18(flip_range_of(X0)),X0))
| relation(flip_range_of(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_224])]) ).
fof(f534,plain,
( ! [X0] :
( little_set(f14(f18(flip_range_of(X0)),X0))
| relation(flip_range_of(X0)) )
| ~ spl0_30
| ~ spl0_59 ),
inference(resolution,[],[f459,f315]) ).
fof(f2933,plain,
( spl0_223
| ~ spl0_30
| ~ spl0_58 ),
inference(avatar_split_clause,[],[f532,f454,f314,f2931]) ).
fof(f2931,plain,
( spl0_223
<=> ! [X0] :
( little_set(f13(f18(flip_range_of(X0)),X0))
| relation(flip_range_of(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_223])]) ).
fof(f532,plain,
( ! [X0] :
( little_set(f13(f18(flip_range_of(X0)),X0))
| relation(flip_range_of(X0)) )
| ~ spl0_30
| ~ spl0_58 ),
inference(resolution,[],[f455,f315]) ).
fof(f2929,plain,
( spl0_222
| ~ spl0_30
| ~ spl0_57 ),
inference(avatar_split_clause,[],[f530,f450,f314,f2927]) ).
fof(f2927,plain,
( spl0_222
<=> ! [X0] :
( little_set(f12(f18(flip_range_of(X0)),X0))
| relation(flip_range_of(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_222])]) ).
fof(f530,plain,
( ! [X0] :
( little_set(f12(f18(flip_range_of(X0)),X0))
| relation(flip_range_of(X0)) )
| ~ spl0_30
| ~ spl0_57 ),
inference(resolution,[],[f451,f315]) ).
fof(f2925,plain,
( spl0_221
| ~ spl0_30
| ~ spl0_56 ),
inference(avatar_split_clause,[],[f528,f446,f314,f2923]) ).
fof(f2923,plain,
( spl0_221
<=> ! [X0] :
( little_set(f11(f18(rotate_right(X0)),X0))
| relation(rotate_right(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_221])]) ).
fof(f528,plain,
( ! [X0] :
( little_set(f11(f18(rotate_right(X0)),X0))
| relation(rotate_right(X0)) )
| ~ spl0_30
| ~ spl0_56 ),
inference(resolution,[],[f447,f315]) ).
fof(f2921,plain,
( spl0_220
| ~ spl0_30
| ~ spl0_55 ),
inference(avatar_split_clause,[],[f526,f442,f314,f2919]) ).
fof(f2919,plain,
( spl0_220
<=> ! [X0] :
( little_set(f10(f18(rotate_right(X0)),X0))
| relation(rotate_right(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_220])]) ).
fof(f526,plain,
( ! [X0] :
( little_set(f10(f18(rotate_right(X0)),X0))
| relation(rotate_right(X0)) )
| ~ spl0_30
| ~ spl0_55 ),
inference(resolution,[],[f443,f315]) ).
fof(f2917,plain,
( spl0_219
| ~ spl0_30
| ~ spl0_54 ),
inference(avatar_split_clause,[],[f524,f438,f314,f2915]) ).
fof(f2915,plain,
( spl0_219
<=> ! [X0] :
( little_set(f9(f18(rotate_right(X0)),X0))
| relation(rotate_right(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_219])]) ).
fof(f524,plain,
( ! [X0] :
( little_set(f9(f18(rotate_right(X0)),X0))
| relation(rotate_right(X0)) )
| ~ spl0_30
| ~ spl0_54 ),
inference(resolution,[],[f439,f315]) ).
fof(f2912,plain,
( spl0_218
| ~ spl0_30
| ~ spl0_53 ),
inference(avatar_split_clause,[],[f522,f434,f314,f2910]) ).
fof(f2910,plain,
( spl0_218
<=> ! [X0] :
( ordered_pair_predicate(f8(f18(domain_of(X0)),X0))
| relation(domain_of(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_218])]) ).
fof(f522,plain,
( ! [X0] :
( ordered_pair_predicate(f8(f18(domain_of(X0)),X0))
| relation(domain_of(X0)) )
| ~ spl0_30
| ~ spl0_53 ),
inference(resolution,[],[f435,f315]) ).
fof(f2908,plain,
( spl0_217
| ~ spl0_30
| ~ spl0_49 ),
inference(avatar_split_clause,[],[f512,f418,f314,f2906]) ).
fof(f2906,plain,
( spl0_217
<=> ! [X0] :
( little_set(f7(f18(second(X0)),X0))
| relation(second(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_217])]) ).
fof(f512,plain,
( ! [X0] :
( little_set(f7(f18(second(X0)),X0))
| relation(second(X0)) )
| ~ spl0_30
| ~ spl0_49 ),
inference(resolution,[],[f419,f315]) ).
fof(f2904,plain,
( spl0_216
| ~ spl0_30
| ~ spl0_48 ),
inference(avatar_split_clause,[],[f510,f414,f314,f2902]) ).
fof(f2902,plain,
( spl0_216
<=> ! [X0] :
( little_set(f6(f18(second(X0)),X0))
| relation(second(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_216])]) ).
fof(f510,plain,
( ! [X0] :
( little_set(f6(f18(second(X0)),X0))
| relation(second(X0)) )
| ~ spl0_30
| ~ spl0_48 ),
inference(resolution,[],[f415,f315]) ).
fof(f2900,plain,
( spl0_215
| ~ spl0_30
| ~ spl0_47 ),
inference(avatar_split_clause,[],[f508,f410,f314,f2898]) ).
fof(f2898,plain,
( spl0_215
<=> ! [X0] :
( little_set(f5(f18(first(X0)),X0))
| relation(first(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_215])]) ).
fof(f508,plain,
( ! [X0] :
( little_set(f5(f18(first(X0)),X0))
| relation(first(X0)) )
| ~ spl0_30
| ~ spl0_47 ),
inference(resolution,[],[f411,f315]) ).
fof(f2896,plain,
( spl0_214
| ~ spl0_30
| ~ spl0_46 ),
inference(avatar_split_clause,[],[f506,f406,f314,f2894]) ).
fof(f2894,plain,
( spl0_214
<=> ! [X0] :
( little_set(f4(f18(first(X0)),X0))
| relation(first(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_214])]) ).
fof(f506,plain,
( ! [X0] :
( little_set(f4(f18(first(X0)),X0))
| relation(first(X0)) )
| ~ spl0_30
| ~ spl0_46 ),
inference(resolution,[],[f407,f315]) ).
fof(f2891,plain,
( spl0_213
| ~ spl0_37
| ~ spl0_40 ),
inference(avatar_split_clause,[],[f398,f361,f349,f2889]) ).
fof(f398,plain,
( ! [X0] :
( empty_set = powerset(X0)
| subset(f24(powerset(X0)),X0) )
| ~ spl0_37
| ~ spl0_40 ),
inference(resolution,[],[f362,f350]) ).
fof(f2886,plain,
( spl0_212
| ~ spl0_34
| ~ spl0_40 ),
inference(avatar_split_clause,[],[f394,f361,f336,f2884]) ).
fof(f394,plain,
( ! [X0] :
( complement(X0) = empty_set
| ~ member(f24(complement(X0)),X0) )
| ~ spl0_34
| ~ spl0_40 ),
inference(resolution,[],[f362,f337]) ).
fof(f2882,plain,
( spl0_211
| ~ spl0_30
| ~ spl0_35 ),
inference(avatar_split_clause,[],[f386,f340,f314,f2880]) ).
fof(f386,plain,
( ! [X0,X1] :
( ordered_pair_predicate(f18(cross_product(X0,X1)))
| relation(cross_product(X0,X1)) )
| ~ spl0_30
| ~ spl0_35 ),
inference(resolution,[],[f341,f315]) ).
fof(f2739,plain,
( spl0_210
| ~ spl0_173
| ~ spl0_205 ),
inference(avatar_split_clause,[],[f2631,f2627,f2440,f2737]) ).
fof(f2631,plain,
( ! [X0] :
( estin = X0
| member(f1(estin,X0),X0) )
| ~ spl0_173
| ~ spl0_205 ),
inference(forward_demodulation,[],[f2630,f2442]) ).
fof(f2630,plain,
( ! [X0] :
( member(f1(estin,X0),X0)
| empty_set = X0 )
| ~ spl0_173
| ~ spl0_205 ),
inference(forward_demodulation,[],[f2628,f2442]) ).
fof(f2735,plain,
( spl0_209
| ~ spl0_173
| ~ spl0_204 ),
inference(avatar_split_clause,[],[f2625,f2621,f2440,f2733]) ).
fof(f2625,plain,
( ! [X0] :
( estin = X0
| member(f1(X0,estin),X0) )
| ~ spl0_173
| ~ spl0_204 ),
inference(forward_demodulation,[],[f2624,f2442]) ).
fof(f2624,plain,
( ! [X0] :
( member(f1(X0,estin),X0)
| empty_set = X0 )
| ~ spl0_173
| ~ spl0_204 ),
inference(forward_demodulation,[],[f2622,f2442]) ).
fof(f2705,plain,
( spl0_208
| ~ spl0_173
| ~ spl0_199 ),
inference(avatar_split_clause,[],[f2597,f2594,f2440,f2703]) ).
fof(f2703,plain,
( spl0_208
<=> ! [X0] :
( estin = X0
| ~ little_set(X0)
| little_set(f26(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_208])]) ).
fof(f2597,plain,
( ! [X0] :
( estin = X0
| ~ little_set(X0)
| little_set(f26(X0)) )
| ~ spl0_173
| ~ spl0_199 ),
inference(forward_demodulation,[],[f2595,f2442]) ).
fof(f2649,plain,
( spl0_207
| ~ spl0_173
| ~ spl0_193 ),
inference(avatar_split_clause,[],[f2571,f2568,f2440,f2647]) ).
fof(f2647,plain,
( spl0_207
<=> ! [X0] :
( estin = converse(X0)
| ordered_pair_predicate(f24(converse(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_207])]) ).
fof(f2571,plain,
( ! [X0] :
( estin = converse(X0)
| ordered_pair_predicate(f24(converse(X0))) )
| ~ spl0_173
| ~ spl0_193 ),
inference(forward_demodulation,[],[f2569,f2442]) ).
fof(f2645,plain,
( spl0_206
| ~ spl0_173
| ~ spl0_192 ),
inference(avatar_split_clause,[],[f2566,f2563,f2440,f2643]) ).
fof(f2643,plain,
( spl0_206
<=> ! [X0] :
( estin = X0
| ordered_pair_predicate(f24(X0))
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_206])]) ).
fof(f2566,plain,
( ! [X0] :
( estin = X0
| ordered_pair_predicate(f24(X0))
| ~ relation(X0) )
| ~ spl0_173
| ~ spl0_192 ),
inference(forward_demodulation,[],[f2564,f2442]) ).
fof(f2629,plain,
( spl0_205
| ~ spl0_4
| ~ spl0_113 ),
inference(avatar_split_clause,[],[f1243,f1159,f201,f2627]) ).
fof(f1243,plain,
( ! [X0] :
( member(f1(empty_set,X0),X0)
| empty_set = X0 )
| ~ spl0_4
| ~ spl0_113 ),
inference(resolution,[],[f1160,f202]) ).
fof(f2623,plain,
( spl0_204
| ~ spl0_4
| ~ spl0_113 ),
inference(avatar_split_clause,[],[f1206,f1159,f201,f2621]) ).
fof(f1206,plain,
( ! [X0] :
( member(f1(X0,empty_set),X0)
| empty_set = X0 )
| ~ spl0_4
| ~ spl0_113 ),
inference(resolution,[],[f1160,f202]) ).
fof(f2619,plain,
( spl0_203
| ~ spl0_11
| ~ spl0_85 ),
inference(avatar_split_clause,[],[f799,f672,f232,f2617]) ).
fof(f799,plain,
( ! [X0,X1] :
( ~ member(X0,range_of(X1))
| little_set(f27(X0,X1)) )
| ~ spl0_11
| ~ spl0_85 ),
inference(resolution,[],[f673,f233]) ).
fof(f2615,plain,
( ~ spl0_202
| ~ spl0_177
| spl0_200 ),
inference(avatar_split_clause,[],[f2608,f2599,f2481,f2612]) ).
fof(f2612,plain,
( spl0_202
<=> ordered_pair_predicate(f26(estin)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_202])]) ).
fof(f2599,plain,
( spl0_200
<=> ordered_pair_predicate(f26(identity_relation)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_200])]) ).
fof(f2608,plain,
( ~ ordered_pair_predicate(f26(estin))
| ~ spl0_177
| spl0_200 ),
inference(forward_demodulation,[],[f2600,f2483]) ).
fof(f2600,plain,
( ~ ordered_pair_predicate(f26(identity_relation))
| spl0_200 ),
inference(avatar_component_clause,[],[f2599]) ).
fof(f2609,plain,
( ~ spl0_176
| ~ spl0_177
| spl0_201 ),
inference(avatar_split_clause,[],[f2607,f2603,f2481,f2476]) ).
fof(f2476,plain,
( spl0_176
<=> little_set(estin) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_176])]) ).
fof(f2607,plain,
( ~ little_set(estin)
| ~ spl0_177
| spl0_201 ),
inference(forward_demodulation,[],[f2605,f2483]) ).
fof(f2605,plain,
( ~ little_set(identity_relation)
| spl0_201 ),
inference(avatar_component_clause,[],[f2603]) ).
fof(f2606,plain,
( spl0_200
| ~ spl0_201
| spl0_175
| ~ spl0_23
| ~ spl0_84 ),
inference(avatar_split_clause,[],[f797,f668,f281,f2469,f2603,f2599]) ).
fof(f797,plain,
( empty_set = identity_relation
| ~ little_set(identity_relation)
| ordered_pair_predicate(f26(identity_relation))
| ~ spl0_23
| ~ spl0_84 ),
inference(resolution,[],[f669,f282]) ).
fof(f2596,plain,
( spl0_199
| ~ spl0_11
| ~ spl0_84 ),
inference(avatar_split_clause,[],[f773,f668,f232,f2594]) ).
fof(f773,plain,
( ! [X0] :
( empty_set = X0
| ~ little_set(X0)
| little_set(f26(X0)) )
| ~ spl0_11
| ~ spl0_84 ),
inference(resolution,[],[f669,f233]) ).
fof(f2591,plain,
( spl0_198
| ~ spl0_23
| ~ spl0_78 ),
inference(avatar_split_clause,[],[f760,f644,f281,f2589]) ).
fof(f2589,plain,
( spl0_198
<=> ! [X0] :
( ~ member(X0,sigma(identity_relation))
| ordered_pair_predicate(f16(X0,identity_relation)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_198])]) ).
fof(f760,plain,
( ! [X0] :
( ~ member(X0,sigma(identity_relation))
| ordered_pair_predicate(f16(X0,identity_relation)) )
| ~ spl0_23
| ~ spl0_78 ),
inference(resolution,[],[f645,f282]) ).
fof(f2587,plain,
( spl0_197
| ~ spl0_11
| ~ spl0_78 ),
inference(avatar_split_clause,[],[f736,f644,f232,f2585]) ).
fof(f736,plain,
( ! [X0,X1] :
( ~ member(X0,sigma(X1))
| little_set(f16(X0,X1)) )
| ~ spl0_11
| ~ spl0_78 ),
inference(resolution,[],[f645,f233]) ).
fof(f2583,plain,
( spl0_196
| ~ spl0_11
| ~ spl0_74 ),
inference(avatar_split_clause,[],[f700,f628,f232,f2581]) ).
fof(f700,plain,
( ! [X0,X1] :
( ~ member(X0,domain_of(X1))
| little_set(f8(X0,X1)) )
| ~ spl0_11
| ~ spl0_74 ),
inference(resolution,[],[f629,f233]) ).
fof(f2579,plain,
( spl0_195
| ~ spl0_38
| ~ spl0_44 ),
inference(avatar_split_clause,[],[f403,f377,f353,f2577]) ).
fof(f2577,plain,
( spl0_195
<=> ! [X0,X1] :
( ~ little_set(X0)
| ordered_pair_predicate(X0)
| ~ relation(non_ordered_pair(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_195])]) ).
fof(f403,plain,
( ! [X0,X1] :
( ~ little_set(X0)
| ordered_pair_predicate(X0)
| ~ relation(non_ordered_pair(X1,X0)) )
| ~ spl0_38
| ~ spl0_44 ),
inference(resolution,[],[f378,f354]) ).
fof(f2575,plain,
( spl0_194
| ~ spl0_38
| ~ spl0_43 ),
inference(avatar_split_clause,[],[f401,f373,f353,f2573]) ).
fof(f2573,plain,
( spl0_194
<=> ! [X0,X1] :
( ~ little_set(X0)
| ordered_pair_predicate(X0)
| ~ relation(non_ordered_pair(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_194])]) ).
fof(f401,plain,
( ! [X0,X1] :
( ~ little_set(X0)
| ordered_pair_predicate(X0)
| ~ relation(non_ordered_pair(X0,X1)) )
| ~ spl0_38
| ~ spl0_43 ),
inference(resolution,[],[f374,f354]) ).
fof(f2570,plain,
( spl0_193
| ~ spl0_28
| ~ spl0_40 ),
inference(avatar_split_clause,[],[f396,f361,f306,f2568]) ).
fof(f396,plain,
( ! [X0] :
( converse(X0) = empty_set
| ordered_pair_predicate(f24(converse(X0))) )
| ~ spl0_28
| ~ spl0_40 ),
inference(resolution,[],[f362,f307]) ).
fof(f2565,plain,
( spl0_192
| ~ spl0_38
| ~ spl0_40 ),
inference(avatar_split_clause,[],[f391,f361,f353,f2563]) ).
fof(f391,plain,
( ! [X0] :
( empty_set = X0
| ordered_pair_predicate(f24(X0))
| ~ relation(X0) )
| ~ spl0_38
| ~ spl0_40 ),
inference(resolution,[],[f362,f354]) ).
fof(f2561,plain,
( spl0_191
| ~ spl0_30
| ~ spl0_37 ),
inference(avatar_split_clause,[],[f387,f349,f314,f2559]) ).
fof(f387,plain,
( ! [X0] :
( subset(f18(powerset(X0)),X0)
| relation(powerset(X0)) )
| ~ spl0_30
| ~ spl0_37 ),
inference(resolution,[],[f350,f315]) ).
fof(f2557,plain,
( spl0_190
| ~ spl0_125
| ~ spl0_173 ),
inference(avatar_split_clause,[],[f2453,f2440,f1341,f2554]) ).
fof(f2554,plain,
( spl0_190
<=> single_valued_set(estin) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_190])]) ).
fof(f2453,plain,
( single_valued_set(estin)
| ~ spl0_125
| ~ spl0_173 ),
inference(superposition,[],[f1343,f2442]) ).
fof(f2552,plain,
( spl0_189
| ~ spl0_30
| ~ spl0_34 ),
inference(avatar_split_clause,[],[f380,f336,f314,f2550]) ).
fof(f380,plain,
( ! [X0] :
( ~ member(f18(complement(X0)),X0)
| relation(complement(X0)) )
| ~ spl0_30
| ~ spl0_34 ),
inference(resolution,[],[f337,f315]) ).
fof(f2544,plain,
( spl0_188
| ~ spl0_173
| ~ spl0_187 ),
inference(avatar_split_clause,[],[f2533,f2530,f2440,f2542]) ).
fof(f2533,plain,
( ! [X0] :
( member(estin,sigma(X0))
| ~ member(infinity,X0) )
| ~ spl0_173
| ~ spl0_187 ),
inference(forward_demodulation,[],[f2531,f2442]) ).
fof(f2532,plain,
( spl0_187
| ~ spl0_5
| ~ spl0_93 ),
inference(avatar_split_clause,[],[f886,f836,f205,f2530]) ).
fof(f886,plain,
( ! [X0] :
( ~ member(infinity,X0)
| member(empty_set,sigma(X0)) )
| ~ spl0_5
| ~ spl0_93 ),
inference(resolution,[],[f837,f207]) ).
fof(f2528,plain,
( spl0_186
| ~ spl0_70
| ~ spl0_86 ),
inference(avatar_split_clause,[],[f824,f676,f503,f2526]) ).
fof(f503,plain,
( spl0_70
<=> ! [X0,X1,X7] :
( ~ maps(X7,X0,X1)
| subset(range_of(X7),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_70])]) ).
fof(f824,plain,
( ! [X0,X1] :
( ~ closed(X0,X1)
| subset(range_of(X1),X0) )
| ~ spl0_70
| ~ spl0_86 ),
inference(resolution,[],[f677,f504]) ).
fof(f504,plain,
( ! [X0,X1,X7] :
( ~ maps(X7,X0,X1)
| subset(range_of(X7),X1) )
| ~ spl0_70 ),
inference(avatar_component_clause,[],[f503]) ).
fof(f2524,plain,
( ~ spl0_185
| spl0_68
| ~ spl0_173 ),
inference(avatar_split_clause,[],[f2448,f2440,f494,f2521]) ).
fof(f494,plain,
( spl0_68
<=> ordered_pair_predicate(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_68])]) ).
fof(f2448,plain,
( ~ ordered_pair_predicate(estin)
| spl0_68
| ~ spl0_173 ),
inference(superposition,[],[f495,f2442]) ).
fof(f495,plain,
( ~ ordered_pair_predicate(empty_set)
| spl0_68 ),
inference(avatar_component_clause,[],[f494]) ).
fof(f2518,plain,
( spl0_184
| ~ spl0_23
| ~ spl0_64 ),
inference(avatar_split_clause,[],[f604,f478,f281,f2516]) ).
fof(f2516,plain,
( spl0_184
<=> ! [X0] :
( disjoint(X0,identity_relation)
| ordered_pair_predicate(f23(X0,identity_relation)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_184])]) ).
fof(f604,plain,
( ! [X0] :
( disjoint(X0,identity_relation)
| ordered_pair_predicate(f23(X0,identity_relation)) )
| ~ spl0_23
| ~ spl0_64 ),
inference(resolution,[],[f479,f282]) ).
fof(f2513,plain,
( spl0_183
| ~ spl0_23
| ~ spl0_63 ),
inference(avatar_split_clause,[],[f582,f474,f281,f2511]) ).
fof(f2511,plain,
( spl0_183
<=> ! [X0] :
( disjoint(identity_relation,X0)
| ordered_pair_predicate(f23(identity_relation,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_183])]) ).
fof(f582,plain,
( ! [X0] :
( disjoint(identity_relation,X0)
| ordered_pair_predicate(f23(identity_relation,X0)) )
| ~ spl0_23
| ~ spl0_63 ),
inference(resolution,[],[f475,f282]) ).
fof(f2509,plain,
( spl0_182
| ~ spl0_11
| ~ spl0_63 ),
inference(avatar_split_clause,[],[f562,f474,f232,f2507]) ).
fof(f2507,plain,
( spl0_182
<=> ! [X0,X1] :
( disjoint(X0,X1)
| little_set(f23(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_182])]) ).
fof(f562,plain,
( ! [X0,X1] :
( disjoint(X0,X1)
| little_set(f23(X0,X1)) )
| ~ spl0_11
| ~ spl0_63 ),
inference(resolution,[],[f475,f233]) ).
fof(f2505,plain,
( spl0_181
| ~ spl0_16
| ~ spl0_61 ),
inference(avatar_split_clause,[],[f559,f466,f253,f2503]) ).
fof(f559,plain,
( ! [X0] :
( subset(X0,universal_set)
| ~ little_set(f17(X0,universal_set)) )
| ~ spl0_16
| ~ spl0_61 ),
inference(resolution,[],[f467,f254]) ).
fof(f2500,plain,
( spl0_180
| ~ spl0_23
| ~ spl0_60 ),
inference(avatar_split_clause,[],[f557,f462,f281,f2498]) ).
fof(f2498,plain,
( spl0_180
<=> ! [X0] :
( subset(identity_relation,X0)
| ordered_pair_predicate(f17(identity_relation,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_180])]) ).
fof(f557,plain,
( ! [X0] :
( subset(identity_relation,X0)
| ordered_pair_predicate(f17(identity_relation,X0)) )
| ~ spl0_23
| ~ spl0_60 ),
inference(resolution,[],[f463,f282]) ).
fof(f2496,plain,
( spl0_179
| ~ spl0_11
| ~ spl0_60 ),
inference(avatar_split_clause,[],[f537,f462,f232,f2494]) ).
fof(f537,plain,
( ! [X0,X1] :
( subset(X0,X1)
| little_set(f17(X0,X1)) )
| ~ spl0_11
| ~ spl0_60 ),
inference(resolution,[],[f463,f233]) ).
fof(f2492,plain,
( spl0_178
| ~ spl0_28
| ~ spl0_30 ),
inference(avatar_split_clause,[],[f327,f314,f306,f2490]) ).
fof(f327,plain,
( ! [X0] :
( relation(converse(X0))
| ordered_pair_predicate(f18(converse(X0))) )
| ~ spl0_28
| ~ spl0_30 ),
inference(resolution,[],[f315,f307]) ).
fof(f2484,plain,
( spl0_177
| ~ spl0_173
| ~ spl0_175 ),
inference(avatar_split_clause,[],[f2473,f2469,f2440,f2481]) ).
fof(f2473,plain,
( estin = identity_relation
| ~ spl0_173
| ~ spl0_175 ),
inference(forward_demodulation,[],[f2471,f2442]) ).
fof(f2479,plain,
( spl0_176
| ~ spl0_36
| ~ spl0_173 ),
inference(avatar_split_clause,[],[f2446,f2440,f344,f2476]) ).
fof(f344,plain,
( spl0_36
<=> little_set(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_36])]) ).
fof(f2446,plain,
( little_set(estin)
| ~ spl0_36
| ~ spl0_173 ),
inference(superposition,[],[f346,f2442]) ).
fof(f346,plain,
( little_set(empty_set)
| ~ spl0_36 ),
inference(avatar_component_clause,[],[f344]) ).
fof(f2472,plain,
( spl0_174
| spl0_175
| ~ spl0_23
| ~ spl0_40 ),
inference(avatar_split_clause,[],[f399,f361,f281,f2469,f2465]) ).
fof(f399,plain,
( empty_set = identity_relation
| ordered_pair_predicate(f24(identity_relation))
| ~ spl0_23
| ~ spl0_40 ),
inference(resolution,[],[f362,f282]) ).
fof(f2443,plain,
( spl0_172
| spl0_173
| ~ spl0_15
| ~ spl0_40 ),
inference(avatar_split_clause,[],[f393,f361,f249,f2440,f2436]) ).
fof(f249,plain,
( spl0_15
<=> ! [X3] :
( ordered_pair_predicate(X3)
| ~ member(X3,estin) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_15])]) ).
fof(f393,plain,
( estin = empty_set
| ordered_pair_predicate(f24(estin))
| ~ spl0_15
| ~ spl0_40 ),
inference(resolution,[],[f362,f250]) ).
fof(f250,plain,
( ! [X3] :
( ~ member(X3,estin)
| ordered_pair_predicate(X3) )
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f249]) ).
fof(f2434,plain,
( spl0_171
| ~ spl0_11
| ~ spl0_40 ),
inference(avatar_split_clause,[],[f392,f361,f232,f2432]) ).
fof(f392,plain,
( ! [X0] :
( empty_set = X0
| little_set(f24(X0)) )
| ~ spl0_11
| ~ spl0_40 ),
inference(resolution,[],[f362,f233]) ).
fof(f2430,plain,
( ~ spl0_169
| spl0_170
| ~ spl0_16
| ~ spl0_38 ),
inference(avatar_split_clause,[],[f389,f353,f253,f2428,f2424]) ).
fof(f2424,plain,
( spl0_169
<=> relation(universal_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_169])]) ).
fof(f389,plain,
( ! [X0] :
( ordered_pair_predicate(X0)
| ~ relation(universal_set)
| ~ little_set(X0) )
| ~ spl0_16
| ~ spl0_38 ),
inference(resolution,[],[f354,f254]) ).
fof(f2360,plain,
( spl0_162
| ~ spl0_19
| ~ spl0_161 ),
inference(avatar_split_clause,[],[f2236,f2228,f265,f2232]) ).
fof(f2232,plain,
( spl0_162
<=> relation(identity_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_162])]) ).
fof(f2228,plain,
( spl0_161
<=> ordered_pair_predicate(f18(identity_relation)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_161])]) ).
fof(f2236,plain,
( relation(identity_relation)
| ~ spl0_19
| ~ spl0_161 ),
inference(resolution,[],[f2230,f266]) ).
fof(f2230,plain,
( ordered_pair_predicate(f18(identity_relation))
| ~ spl0_161 ),
inference(avatar_component_clause,[],[f2228]) ).
fof(f2262,plain,
( spl0_168
| ~ spl0_4
| ~ spl0_139 ),
inference(avatar_split_clause,[],[f1730,f1642,f201,f2260]) ).
fof(f1730,plain,
( ! [X0,X1] : ~ member(X0,compose(empty_set,X1))
| ~ spl0_4
| ~ spl0_139 ),
inference(resolution,[],[f1643,f202]) ).
fof(f2258,plain,
( spl0_167
| ~ spl0_4
| ~ spl0_138 ),
inference(avatar_split_clause,[],[f1690,f1638,f201,f2256]) ).
fof(f1690,plain,
( ! [X0,X1] : ~ member(X0,compose(X1,empty_set))
| ~ spl0_4
| ~ spl0_138 ),
inference(resolution,[],[f1639,f202]) ).
fof(f2254,plain,
( spl0_160
| ~ spl0_19
| ~ spl0_159 ),
inference(avatar_split_clause,[],[f2225,f2217,f265,f2221]) ).
fof(f2221,plain,
( spl0_160
<=> relation(estin) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_160])]) ).
fof(f2217,plain,
( spl0_159
<=> ordered_pair_predicate(f18(estin)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_159])]) ).
fof(f2225,plain,
( relation(estin)
| ~ spl0_19
| ~ spl0_159 ),
inference(resolution,[],[f2219,f266]) ).
fof(f2219,plain,
( ordered_pair_predicate(f18(estin))
| ~ spl0_159 ),
inference(avatar_component_clause,[],[f2217]) ).
fof(f2253,plain,
( spl0_166
| ~ spl0_4
| ~ spl0_107 ),
inference(avatar_split_clause,[],[f1117,f1068,f201,f2251]) ).
fof(f1117,plain,
( ! [X0,X1] : ~ member(X0,image(empty_set,X1))
| ~ spl0_4
| ~ spl0_107 ),
inference(resolution,[],[f1069,f202]) ).
fof(f2249,plain,
( spl0_165
| ~ spl0_4
| ~ spl0_104 ),
inference(avatar_split_clause,[],[f1049,f966,f201,f2247]) ).
fof(f1049,plain,
( ! [X0,X1] : ~ member(X0,apply(empty_set,X1))
| ~ spl0_4
| ~ spl0_104 ),
inference(resolution,[],[f967,f202]) ).
fof(f2245,plain,
( spl0_164
| ~ spl0_4
| ~ spl0_103 ),
inference(avatar_split_clause,[],[f1014,f960,f201,f2243]) ).
fof(f1014,plain,
( ! [X0,X1] : ~ member(X0,image(X1,empty_set))
| ~ spl0_4
| ~ spl0_103 ),
inference(resolution,[],[f961,f202]) ).
fof(f2241,plain,
( spl0_163
| ~ spl0_32
| ~ spl0_86 ),
inference(avatar_split_clause,[],[f826,f676,f322,f2239]) ).
fof(f2239,plain,
( spl0_163
<=> ! [X0,X1] :
( ~ closed(X0,X1)
| function(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_163])]) ).
fof(f322,plain,
( spl0_32
<=> ! [X0,X1,X7] :
( function(X7)
| ~ maps(X7,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_32])]) ).
fof(f826,plain,
( ! [X0,X1] :
( ~ closed(X0,X1)
| function(X1) )
| ~ spl0_32
| ~ spl0_86 ),
inference(resolution,[],[f677,f323]) ).
fof(f323,plain,
( ! [X0,X1,X7] :
( ~ maps(X7,X0,X1)
| function(X7) )
| ~ spl0_32 ),
inference(avatar_component_clause,[],[f322]) ).
fof(f2235,plain,
( spl0_161
| spl0_162
| ~ spl0_23
| ~ spl0_30 ),
inference(avatar_split_clause,[],[f329,f314,f281,f2232,f2228]) ).
fof(f329,plain,
( relation(identity_relation)
| ordered_pair_predicate(f18(identity_relation))
| ~ spl0_23
| ~ spl0_30 ),
inference(resolution,[],[f315,f282]) ).
fof(f2224,plain,
( spl0_159
| spl0_160
| ~ spl0_15
| ~ spl0_30 ),
inference(avatar_split_clause,[],[f326,f314,f249,f2221,f2217]) ).
fof(f326,plain,
( relation(estin)
| ordered_pair_predicate(f18(estin))
| ~ spl0_15
| ~ spl0_30 ),
inference(resolution,[],[f315,f250]) ).
fof(f2214,plain,
( spl0_158
| ~ spl0_30
| ~ spl0_119 ),
inference(avatar_split_clause,[],[f1935,f1266,f314,f2211]) ).
fof(f2211,plain,
( spl0_158
<=> relation(domain_of(empty_set)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_158])]) ).
fof(f1935,plain,
( relation(domain_of(empty_set))
| ~ spl0_30
| ~ spl0_119 ),
inference(resolution,[],[f1267,f315]) ).
fof(f2209,plain,
( spl0_157
| ~ spl0_11
| ~ spl0_30 ),
inference(avatar_split_clause,[],[f325,f314,f232,f2207]) ).
fof(f325,plain,
( ! [X0] :
( relation(X0)
| little_set(f18(X0)) )
| ~ spl0_11
| ~ spl0_30 ),
inference(resolution,[],[f315,f233]) ).
fof(f2205,plain,
( spl0_156
| ~ spl0_8
| ~ spl0_24 ),
inference(avatar_split_clause,[],[f304,f285,f218,f2203]) ).
fof(f2203,plain,
( spl0_156
<=> ! [X0] :
( ~ one_to_one_function(X0)
| relation(converse(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_156])]) ).
fof(f218,plain,
( spl0_8
<=> ! [X7] :
( ~ function(X7)
| relation(X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).
fof(f285,plain,
( spl0_24
<=> ! [X7] :
( ~ one_to_one_function(X7)
| function(converse(X7)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_24])]) ).
fof(f304,plain,
( ! [X0] :
( ~ one_to_one_function(X0)
| relation(converse(X0)) )
| ~ spl0_8
| ~ spl0_24 ),
inference(resolution,[],[f286,f219]) ).
fof(f219,plain,
( ! [X7] :
( ~ function(X7)
| relation(X7) )
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f218]) ).
fof(f286,plain,
( ! [X7] :
( function(converse(X7))
| ~ one_to_one_function(X7) )
| ~ spl0_24 ),
inference(avatar_component_clause,[],[f285]) ).
fof(f2201,plain,
( spl0_155
| ~ spl0_9
| ~ spl0_24 ),
inference(avatar_split_clause,[],[f303,f285,f222,f2199]) ).
fof(f2199,plain,
( spl0_155
<=> ! [X0] :
( ~ one_to_one_function(X0)
| single_valued_set(converse(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_155])]) ).
fof(f222,plain,
( spl0_9
<=> ! [X7] :
( ~ function(X7)
| single_valued_set(X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).
fof(f303,plain,
( ! [X0] :
( ~ one_to_one_function(X0)
| single_valued_set(converse(X0)) )
| ~ spl0_9
| ~ spl0_24 ),
inference(resolution,[],[f286,f223]) ).
fof(f223,plain,
( ! [X7] :
( ~ function(X7)
| single_valued_set(X7) )
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f222]) ).
fof(f2104,plain,
( spl0_154
| ~ spl0_4
| ~ spl0_145 ),
inference(avatar_split_clause,[],[f1903,f1786,f201,f2102]) ).
fof(f1903,plain,
( ! [X0] : ~ member(X0,rotate_right(empty_set))
| ~ spl0_4
| ~ spl0_145 ),
inference(resolution,[],[f1787,f202]) ).
fof(f2100,plain,
( spl0_153
| ~ spl0_4
| ~ spl0_144 ),
inference(avatar_split_clause,[],[f1860,f1782,f201,f2098]) ).
fof(f1860,plain,
( ! [X0] : ~ member(X0,flip_range_of(empty_set))
| ~ spl0_4
| ~ spl0_144 ),
inference(resolution,[],[f1783,f202]) ).
fof(f2032,plain,
( spl0_152
| ~ spl0_119
| ~ spl0_121 ),
inference(avatar_split_clause,[],[f1923,f1287,f1266,f2029]) ).
fof(f2029,plain,
( spl0_152
<=> single_valued_set(domain_of(empty_set)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_152])]) ).
fof(f1923,plain,
( single_valued_set(domain_of(empty_set))
| ~ spl0_119
| ~ spl0_121 ),
inference(resolution,[],[f1267,f1288]) ).
fof(f2027,plain,
( spl0_151
| ~ spl0_4
| ~ spl0_127 ),
inference(avatar_split_clause,[],[f1440,f1397,f201,f2025]) ).
fof(f1440,plain,
( ! [X0] : ~ member(X0,converse(empty_set))
| ~ spl0_4
| ~ spl0_127 ),
inference(resolution,[],[f1398,f202]) ).
fof(f2023,plain,
spl0_150,
inference(avatar_split_clause,[],[f166,f2021]) ).
fof(f2021,plain,
( spl0_150
<=> ! [X10,X11,X14,X13,X12] :
( ~ closed(X11,X12)
| ~ closed(X13,X14)
| ~ maps(X10,X11,X13)
| homomorphism(X10,X11,X12,X13,X14)
| apply(X10,apply(X12,non_ordered_pair(non_ordered_pair(f32(X10,X11,X12,X13,X14),f32(X10,X11,X12,X13,X14)),non_ordered_pair(f32(X10,X11,X12,X13,X14),f33(X10,X11,X12,X13,X14))))) != apply(X14,non_ordered_pair(non_ordered_pair(apply(X10,f32(X10,X11,X12,X13,X14)),apply(X10,f32(X10,X11,X12,X13,X14))),non_ordered_pair(apply(X10,f32(X10,X11,X12,X13,X14)),apply(X10,f33(X10,X11,X12,X13,X14))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_150])]) ).
fof(f166,plain,
! [X10,X11,X14,X12,X13] :
( ~ closed(X11,X12)
| ~ closed(X13,X14)
| ~ maps(X10,X11,X13)
| homomorphism(X10,X11,X12,X13,X14)
| apply(X10,apply(X12,non_ordered_pair(non_ordered_pair(f32(X10,X11,X12,X13,X14),f32(X10,X11,X12,X13,X14)),non_ordered_pair(f32(X10,X11,X12,X13,X14),f33(X10,X11,X12,X13,X14))))) != apply(X14,non_ordered_pair(non_ordered_pair(apply(X10,f32(X10,X11,X12,X13,X14)),apply(X10,f32(X10,X11,X12,X13,X14))),non_ordered_pair(apply(X10,f32(X10,X11,X12,X13,X14)),apply(X10,f33(X10,X11,X12,X13,X14))))) ),
inference(definition_unfolding,[],[f141,f145,f145]) ).
fof(f145,plain,
! [X0,X1,X7] : apply_to_two_arguments(X7,X0,X1) = apply(X7,non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X1))),
inference(definition_unfolding,[],[f119,f144]) ).
fof(f144,plain,
! [X0,X1] : ordered_pair(X0,X1) = non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X1)),
inference(definition_unfolding,[],[f10,f9]) ).
fof(f9,axiom,
! [X0] : singleton_set(X0) = non_ordered_pair(X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singleton_set) ).
fof(f10,axiom,
! [X0,X1] : ordered_pair(X0,X1) = non_ordered_pair(singleton_set(X0),non_ordered_pair(X0,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ordered_pair) ).
fof(f119,axiom,
! [X0,X1,X7] : apply_to_two_arguments(X7,X0,X1) = apply(X7,ordered_pair(X0,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',apply_to_two_arguments) ).
fof(f141,axiom,
! [X10,X11,X14,X12,X13] :
( ~ closed(X11,X12)
| ~ closed(X13,X14)
| ~ maps(X10,X11,X13)
| homomorphism(X10,X11,X12,X13,X14)
| apply(X10,apply_to_two_arguments(X12,f32(X10,X11,X12,X13,X14),f33(X10,X11,X12,X13,X14))) != apply_to_two_arguments(X14,apply(X10,f32(X10,X11,X12,X13,X14)),apply(X10,f33(X10,X11,X12,X13,X14))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',homomorphism7) ).
fof(f1987,plain,
spl0_149,
inference(avatar_split_clause,[],[f183,f1985]) ).
fof(f183,plain,
! [X2,X0,X6,X4] :
( ~ little_set(non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,non_ordered_pair(non_ordered_pair(X4,X4),non_ordered_pair(X4,X6)))))
| ~ little_set(X2)
| ~ little_set(X6)
| ~ little_set(X4)
| member(non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,non_ordered_pair(non_ordered_pair(X4,X4),non_ordered_pair(X4,X6)))),flip_range_of(X0))
| ~ member(non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,non_ordered_pair(non_ordered_pair(X6,X6),non_ordered_pair(X6,X4)))),X0) ),
inference(equality_resolution,[],[f169]) ).
fof(f169,plain,
! [X2,X3,X0,X6,X4] :
( ~ little_set(X3)
| ~ little_set(X2)
| ~ little_set(X6)
| ~ little_set(X4)
| member(X3,flip_range_of(X0))
| non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,non_ordered_pair(non_ordered_pair(X4,X4),non_ordered_pair(X4,X6)))) != X3
| ~ member(non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,non_ordered_pair(non_ordered_pair(X6,X6),non_ordered_pair(X6,X4)))),X0) ),
inference(definition_unfolding,[],[f56,f144,f144,f144,f144]) ).
fof(f56,axiom,
! [X2,X3,X0,X6,X4] :
( ~ little_set(X3)
| ~ little_set(X2)
| ~ little_set(X6)
| ~ little_set(X4)
| member(X3,flip_range_of(X0))
| ordered_pair(X2,ordered_pair(X4,X6)) != X3
| ~ member(ordered_pair(X2,ordered_pair(X6,X4)),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',flip_range6) ).
fof(f1983,plain,
spl0_148,
inference(avatar_split_clause,[],[f182,f1981]) ).
fof(f182,plain,
! [X2,X0,X6,X4] :
( ~ little_set(non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,non_ordered_pair(non_ordered_pair(X4,X4),non_ordered_pair(X4,X6)))))
| ~ little_set(X2)
| ~ little_set(X6)
| ~ little_set(X4)
| member(non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,non_ordered_pair(non_ordered_pair(X4,X4),non_ordered_pair(X4,X6)))),rotate_right(X0))
| ~ member(non_ordered_pair(non_ordered_pair(X4,X4),non_ordered_pair(X4,non_ordered_pair(non_ordered_pair(X6,X6),non_ordered_pair(X6,X2)))),X0) ),
inference(equality_resolution,[],[f168]) ).
fof(f168,plain,
! [X2,X3,X0,X6,X4] :
( ~ little_set(X3)
| ~ little_set(X2)
| ~ little_set(X6)
| ~ little_set(X4)
| member(X3,rotate_right(X0))
| non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,non_ordered_pair(non_ordered_pair(X4,X4),non_ordered_pair(X4,X6)))) != X3
| ~ member(non_ordered_pair(non_ordered_pair(X4,X4),non_ordered_pair(X4,non_ordered_pair(non_ordered_pair(X6,X6),non_ordered_pair(X6,X2)))),X0) ),
inference(definition_unfolding,[],[f50,f144,f144,f144,f144]) ).
fof(f50,axiom,
! [X2,X3,X0,X6,X4] :
( ~ little_set(X3)
| ~ little_set(X2)
| ~ little_set(X6)
| ~ little_set(X4)
| member(X3,rotate_right(X0))
| ordered_pair(X2,ordered_pair(X4,X6)) != X3
| ~ member(ordered_pair(X4,ordered_pair(X6,X2)),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rotate_right6) ).
fof(f1956,plain,
spl0_147,
inference(avatar_split_clause,[],[f184,f1954]) ).
fof(f184,plain,
! [X0,X1,X6,X9,X7] :
( ~ little_set(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X1)))
| ~ little_set(X0)
| ~ little_set(X1)
| ~ little_set(X6)
| ~ member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X6)),X7)
| ~ member(non_ordered_pair(non_ordered_pair(X6,X6),non_ordered_pair(X6,X1)),X9)
| member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X1)),compose(X7,X9)) ),
inference(equality_resolution,[],[f170]) ).
fof(f170,plain,
! [X3,X0,X1,X6,X9,X7] :
( ~ little_set(X3)
| ~ little_set(X0)
| ~ little_set(X1)
| ~ little_set(X6)
| non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X1)) != X3
| ~ member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X6)),X7)
| ~ member(non_ordered_pair(non_ordered_pair(X6,X6),non_ordered_pair(X6,X1)),X9)
| member(X3,compose(X7,X9)) ),
inference(definition_unfolding,[],[f134,f144,f144,f144]) ).
fof(f134,axiom,
! [X3,X0,X1,X6,X9,X7] :
( ~ little_set(X3)
| ~ little_set(X0)
| ~ little_set(X1)
| ~ little_set(X6)
| ordered_pair(X0,X1) != X3
| ~ member(ordered_pair(X0,X6),X7)
| ~ member(ordered_pair(X6,X1),X9)
| member(X3,compose(X7,X9)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',compose7) ).
fof(f1920,plain,
spl0_146,
inference(avatar_split_clause,[],[f163,f1918]) ).
fof(f1918,plain,
( spl0_146
<=> ! [X10,X11,X0,X14,X13,X12,X1] :
( ~ member(X0,X11)
| ~ member(X1,X11)
| ~ homomorphism(X10,X11,X12,X13,X14)
| apply(X10,apply(X12,non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X1)))) = apply(X14,non_ordered_pair(non_ordered_pair(apply(X10,X0),apply(X10,X0)),non_ordered_pair(apply(X10,X0),apply(X10,X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_146])]) ).
fof(f163,plain,
! [X10,X0,X11,X1,X14,X12,X13] :
( ~ member(X0,X11)
| ~ member(X1,X11)
| ~ homomorphism(X10,X11,X12,X13,X14)
| apply(X10,apply(X12,non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X1)))) = apply(X14,non_ordered_pair(non_ordered_pair(apply(X10,X0),apply(X10,X0)),non_ordered_pair(apply(X10,X0),apply(X10,X1)))) ),
inference(definition_unfolding,[],[f138,f145,f145]) ).
fof(f138,axiom,
! [X10,X0,X11,X1,X14,X12,X13] :
( ~ member(X0,X11)
| ~ member(X1,X11)
| ~ homomorphism(X10,X11,X12,X13,X14)
| apply(X10,apply_to_two_arguments(X12,X0,X1)) = apply_to_two_arguments(X14,apply(X10,X0),apply(X10,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',homomorphism4) ).
fof(f1788,plain,
spl0_145,
inference(avatar_split_clause,[],[f154,f1786]) ).
fof(f154,plain,
! [X3,X0] :
( ~ member(X3,rotate_right(X0))
| member(non_ordered_pair(non_ordered_pair(f10(X3,X0),f10(X3,X0)),non_ordered_pair(f10(X3,X0),non_ordered_pair(non_ordered_pair(f11(X3,X0),f11(X3,X0)),non_ordered_pair(f11(X3,X0),f9(X3,X0))))),X0) ),
inference(definition_unfolding,[],[f49,f144,f144]) ).
fof(f49,axiom,
! [X3,X0] :
( ~ member(X3,rotate_right(X0))
| member(ordered_pair(f10(X3,X0),ordered_pair(f11(X3,X0),f9(X3,X0))),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rotate_right5) ).
fof(f1784,plain,
spl0_144,
inference(avatar_split_clause,[],[f153,f1782]) ).
fof(f153,plain,
! [X3,X0] :
( ~ member(X3,flip_range_of(X0))
| member(non_ordered_pair(non_ordered_pair(f12(X3,X0),f12(X3,X0)),non_ordered_pair(f12(X3,X0),non_ordered_pair(non_ordered_pair(f14(X3,X0),f14(X3,X0)),non_ordered_pair(f14(X3,X0),f13(X3,X0))))),X0) ),
inference(definition_unfolding,[],[f55,f144,f144]) ).
fof(f55,axiom,
! [X3,X0] :
( ~ member(X3,flip_range_of(X0))
| member(ordered_pair(f12(X3,X0),ordered_pair(f14(X3,X0),f13(X3,X0))),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',flip_range5) ).
fof(f1780,plain,
spl0_143,
inference(avatar_split_clause,[],[f152,f1778]) ).
fof(f152,plain,
! [X3,X0] :
( ~ member(X3,rotate_right(X0))
| non_ordered_pair(non_ordered_pair(f9(X3,X0),f9(X3,X0)),non_ordered_pair(f9(X3,X0),non_ordered_pair(non_ordered_pair(f10(X3,X0),f10(X3,X0)),non_ordered_pair(f10(X3,X0),f11(X3,X0))))) = X3 ),
inference(definition_unfolding,[],[f48,f144,f144]) ).
fof(f48,axiom,
! [X3,X0] :
( ~ member(X3,rotate_right(X0))
| ordered_pair(f9(X3,X0),ordered_pair(f10(X3,X0),f11(X3,X0))) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rotate_right4) ).
fof(f1776,plain,
spl0_142,
inference(avatar_split_clause,[],[f151,f1774]) ).
fof(f151,plain,
! [X3,X0] :
( ~ member(X3,flip_range_of(X0))
| non_ordered_pair(non_ordered_pair(f12(X3,X0),f12(X3,X0)),non_ordered_pair(f12(X3,X0),non_ordered_pair(non_ordered_pair(f13(X3,X0),f13(X3,X0)),non_ordered_pair(f13(X3,X0),f14(X3,X0))))) = X3 ),
inference(definition_unfolding,[],[f54,f144,f144]) ).
fof(f54,axiom,
! [X3,X0] :
( ~ member(X3,flip_range_of(X0))
| ordered_pair(f12(X3,X0),ordered_pair(f13(X3,X0),f14(X3,X0))) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',flip_range4) ).
fof(f1751,plain,
( spl0_141
| ~ spl0_4
| ~ spl0_85 ),
inference(avatar_split_clause,[],[f819,f672,f201,f1749]) ).
fof(f819,plain,
( ! [X0] : ~ member(X0,range_of(empty_set))
| ~ spl0_4
| ~ spl0_85 ),
inference(resolution,[],[f673,f202]) ).
fof(f1747,plain,
spl0_140,
inference(avatar_split_clause,[],[f167,f1745]) ).
fof(f167,plain,
! [X2,X0,X6,X4] :
( ~ single_valued_set(X0)
| ~ little_set(X2)
| ~ little_set(X4)
| ~ little_set(X6)
| X4 = X6
| ~ member(non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X4)),X0)
| ~ member(non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X6)),X0) ),
inference(definition_unfolding,[],[f79,f144,f144]) ).
fof(f79,axiom,
! [X2,X0,X6,X4] :
( ~ single_valued_set(X0)
| ~ little_set(X2)
| ~ little_set(X4)
| ~ little_set(X6)
| X4 = X6
| ~ member(ordered_pair(X2,X4),X0)
| ~ member(ordered_pair(X2,X6),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',single_valued_set1) ).
fof(f1644,plain,
spl0_139,
inference(avatar_split_clause,[],[f159,f1642]) ).
fof(f159,plain,
! [X3,X9,X7] :
( ~ member(X3,compose(X7,X9))
| member(non_ordered_pair(non_ordered_pair(f29(X3,X7,X9),f29(X3,X7,X9)),non_ordered_pair(f29(X3,X7,X9),f31(X3,X7,X9))),X7) ),
inference(definition_unfolding,[],[f132,f144]) ).
fof(f132,axiom,
! [X3,X9,X7] :
( ~ member(X3,compose(X7,X9))
| member(ordered_pair(f29(X3,X7,X9),f31(X3,X7,X9)),X7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',compose5) ).
fof(f1640,plain,
spl0_138,
inference(avatar_split_clause,[],[f158,f1638]) ).
fof(f158,plain,
! [X3,X9,X7] :
( ~ member(X3,compose(X7,X9))
| member(non_ordered_pair(non_ordered_pair(f31(X3,X7,X9),f31(X3,X7,X9)),non_ordered_pair(f31(X3,X7,X9),f30(X3,X7,X9))),X9) ),
inference(definition_unfolding,[],[f133,f144]) ).
fof(f133,axiom,
! [X3,X9,X7] :
( ~ member(X3,compose(X7,X9))
| member(ordered_pair(f31(X3,X7,X9),f30(X3,X7,X9)),X9) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',compose6) ).
fof(f1636,plain,
spl0_137,
inference(avatar_split_clause,[],[f157,f1634]) ).
fof(f157,plain,
! [X3,X9,X7] :
( ~ member(X3,compose(X7,X9))
| non_ordered_pair(non_ordered_pair(f29(X3,X7,X9),f29(X3,X7,X9)),non_ordered_pair(f29(X3,X7,X9),f30(X3,X7,X9))) = X3 ),
inference(definition_unfolding,[],[f131,f144]) ).
fof(f131,axiom,
! [X3,X9,X7] :
( ~ member(X3,compose(X7,X9))
| ordered_pair(f29(X3,X7,X9),f30(X3,X7,X9)) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',compose4) ).
fof(f1554,plain,
spl0_136,
inference(avatar_split_clause,[],[f140,f1552]) ).
fof(f140,axiom,
! [X10,X11,X14,X12,X13] :
( ~ closed(X11,X12)
| ~ closed(X13,X14)
| ~ maps(X10,X11,X13)
| homomorphism(X10,X11,X12,X13,X14)
| member(f33(X10,X11,X12,X13,X14),X11) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',homomorphism6) ).
fof(f1550,plain,
( spl0_135
| ~ spl0_4
| ~ spl0_78 ),
inference(avatar_split_clause,[],[f756,f644,f201,f1548]) ).
fof(f756,plain,
( ! [X0] : ~ member(X0,sigma(empty_set))
| ~ spl0_4
| ~ spl0_78 ),
inference(resolution,[],[f645,f202]) ).
fof(f1546,plain,
spl0_134,
inference(avatar_split_clause,[],[f139,f1544]) ).
fof(f139,axiom,
! [X10,X11,X14,X12,X13] :
( ~ closed(X11,X12)
| ~ closed(X13,X14)
| ~ maps(X10,X11,X13)
| homomorphism(X10,X11,X12,X13,X14)
| member(f32(X10,X11,X12,X13,X14),X11) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',homomorphism5) ).
fof(f1489,plain,
spl0_133,
inference(avatar_split_clause,[],[f161,f1487]) ).
fof(f161,plain,
! [X3,X0] :
( ~ ordered_pair_predicate(X3)
| ~ little_set(X3)
| member(X3,converse(X0))
| ~ member(non_ordered_pair(non_ordered_pair(second(X3),second(X3)),non_ordered_pair(second(X3),first(X3))),X0) ),
inference(definition_unfolding,[],[f44,f144]) ).
fof(f44,axiom,
! [X3,X0] :
( ~ ordered_pair_predicate(X3)
| ~ little_set(X3)
| member(X3,converse(X0))
| ~ member(ordered_pair(second(X3),first(X3)),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',converse3) ).
fof(f1485,plain,
spl0_132,
inference(avatar_split_clause,[],[f156,f1483]) ).
fof(f156,plain,
! [X3,X0] :
( ~ member(X3,first(X0))
| non_ordered_pair(non_ordered_pair(f4(X3,X0),f4(X3,X0)),non_ordered_pair(f4(X3,X0),f5(X3,X0))) = X0 ),
inference(definition_unfolding,[],[f17,f144]) ).
fof(f17,axiom,
! [X3,X0] :
( ~ member(X3,first(X0))
| ordered_pair(f4(X3,X0),f5(X3,X0)) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',first3) ).
fof(f1481,plain,
spl0_131,
inference(avatar_split_clause,[],[f155,f1479]) ).
fof(f155,plain,
! [X3,X0] :
( ~ member(X3,second(X0))
| non_ordered_pair(non_ordered_pair(f6(X3,X0),f6(X3,X0)),non_ordered_pair(f6(X3,X0),f7(X3,X0))) = X0 ),
inference(definition_unfolding,[],[f22,f144]) ).
fof(f22,axiom,
! [X3,X0] :
( ~ member(X3,second(X0))
| ordered_pair(f6(X3,X0),f7(X3,X0)) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',second3) ).
fof(f1472,plain,
spl0_130,
inference(avatar_split_clause,[],[f181,f1470]) ).
fof(f181,plain,
! [X0,X1,X7] :
( ~ ordered_pair_predicate(X1)
| ~ little_set(second(X1))
| ~ member(X1,X7)
| ~ member(first(X1),X0)
| member(second(X1),image(X0,X7)) ),
inference(equality_resolution,[],[f93]) ).
fof(f93,axiom,
! [X3,X0,X1,X7] :
( ~ ordered_pair_predicate(X1)
| ~ little_set(X3)
| ~ member(X1,X7)
| second(X1) != X3
| ~ member(first(X1),X0)
| member(X3,image(X0,X7)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',image_and_substitution5) ).
fof(f1407,plain,
spl0_129,
inference(avatar_split_clause,[],[f180,f1405]) ).
fof(f180,plain,
! [X2,X3,X4] :
( ~ little_set(X2)
| ~ little_set(X4)
| ~ member(X3,X2)
| member(X3,first(non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X4)))) ),
inference(equality_resolution,[],[f165]) ).
fof(f165,plain,
! [X2,X3,X0,X4] :
( ~ little_set(X2)
| ~ little_set(X4)
| ~ member(X3,X2)
| member(X3,first(X0))
| non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X4)) != X0 ),
inference(definition_unfolding,[],[f19,f144]) ).
fof(f19,axiom,
! [X2,X3,X0,X4] :
( ~ little_set(X2)
| ~ little_set(X4)
| ~ member(X3,X2)
| member(X3,first(X0))
| ordered_pair(X2,X4) != X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',first5) ).
fof(f1403,plain,
spl0_128,
inference(avatar_split_clause,[],[f179,f1401]) ).
fof(f179,plain,
! [X2,X3,X4] :
( ~ little_set(X2)
| ~ little_set(X4)
| ~ member(X3,X4)
| member(X3,second(non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X4)))) ),
inference(equality_resolution,[],[f164]) ).
fof(f164,plain,
! [X2,X3,X0,X4] :
( ~ little_set(X2)
| ~ little_set(X4)
| ~ member(X3,X4)
| member(X3,second(X0))
| non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X4)) != X0 ),
inference(definition_unfolding,[],[f24,f144]) ).
fof(f24,axiom,
! [X2,X3,X0,X4] :
( ~ little_set(X2)
| ~ little_set(X4)
| ~ member(X3,X4)
| member(X3,second(X0))
| ordered_pair(X2,X4) != X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',second5) ).
fof(f1399,plain,
spl0_127,
inference(avatar_split_clause,[],[f150,f1397]) ).
fof(f150,plain,
! [X3,X0] :
( ~ member(X3,converse(X0))
| member(non_ordered_pair(non_ordered_pair(second(X3),second(X3)),non_ordered_pair(second(X3),first(X3))),X0) ),
inference(definition_unfolding,[],[f43,f144]) ).
fof(f43,axiom,
! [X3,X0] :
( ~ member(X3,converse(X0))
| member(ordered_pair(second(X3),first(X3)),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',converse2) ).
fof(f1395,plain,
spl0_126,
inference(avatar_split_clause,[],[f41,f1393]) ).
fof(f41,axiom,
! [X3,X0,X1] :
( ~ ordered_pair_predicate(X3)
| ~ little_set(X3)
| ~ member(first(X3),X0)
| ~ member(second(X3),X1)
| member(X3,cross_product(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cross_product4) ).
fof(f1344,plain,
( spl0_125
| ~ spl0_4
| ~ spl0_121 ),
inference(avatar_split_clause,[],[f1327,f1287,f201,f1341]) ).
fof(f1327,plain,
( single_valued_set(empty_set)
| ~ spl0_4
| ~ spl0_121 ),
inference(resolution,[],[f1288,f202]) ).
fof(f1301,plain,
spl0_124,
inference(avatar_split_clause,[],[f178,f1299]) ).
fof(f178,plain,
! [X3,X6,X7] :
( ~ ordered_pair_predicate(X6)
| ~ member(X6,X7)
| ~ member(X3,second(X6))
| member(X3,apply(X7,first(X6))) ),
inference(equality_resolution,[],[f118]) ).
fof(f118,axiom,
! [X3,X1,X6,X7] :
( ~ ordered_pair_predicate(X6)
| ~ member(X6,X7)
| first(X6) != X1
| ~ member(X3,second(X6))
| member(X3,apply(X7,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',apply5) ).
fof(f1297,plain,
spl0_123,
inference(avatar_split_clause,[],[f160,f1295]) ).
fof(f160,plain,
! [X0] :
( ~ little_set(X0)
| empty_set = X0
| member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,f26(X0))),f25) ),
inference(definition_unfolding,[],[f102,f144]) ).
fof(f102,axiom,
! [X0] :
( ~ little_set(X0)
| empty_set = X0
| member(ordered_pair(X0,f26(X0)),f25) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',choice3) ).
fof(f1293,plain,
spl0_122,
inference(avatar_split_clause,[],[f148,f1291]) ).
fof(f148,plain,
! [X0] :
( single_valued_set(X0)
| member(non_ordered_pair(non_ordered_pair(f19(X0),f19(X0)),non_ordered_pair(f19(X0),f21(X0))),X0) ),
inference(definition_unfolding,[],[f84,f144]) ).
fof(f84,axiom,
! [X0] :
( single_valued_set(X0)
| member(ordered_pair(f19(X0),f21(X0)),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',single_valued_set6) ).
fof(f1289,plain,
spl0_121,
inference(avatar_split_clause,[],[f147,f1287]) ).
fof(f147,plain,
! [X0] :
( single_valued_set(X0)
| member(non_ordered_pair(non_ordered_pair(f19(X0),f19(X0)),non_ordered_pair(f19(X0),f20(X0))),X0) ),
inference(definition_unfolding,[],[f83,f144]) ).
fof(f83,axiom,
! [X0] :
( single_valued_set(X0)
| member(ordered_pair(f19(X0),f20(X0)),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',single_valued_set5) ).
fof(f1285,plain,
spl0_120,
inference(avatar_split_clause,[],[f146,f1283]) ).
fof(f146,plain,
! [X0] :
( ~ ordered_pair_predicate(X0)
| non_ordered_pair(non_ordered_pair(f2(X0),f2(X0)),non_ordered_pair(f2(X0),f3(X0))) = X0 ),
inference(definition_unfolding,[],[f13,f144]) ).
fof(f13,axiom,
! [X0] :
( ~ ordered_pair_predicate(X0)
| ordered_pair(f2(X0),f3(X0)) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ordered_pair_predicate3) ).
fof(f1268,plain,
( spl0_119
| ~ spl0_4
| ~ spl0_74 ),
inference(avatar_split_clause,[],[f718,f628,f201,f1266]) ).
fof(f718,plain,
( ! [X0] : ~ member(X0,domain_of(empty_set))
| ~ spl0_4
| ~ spl0_74 ),
inference(resolution,[],[f629,f202]) ).
fof(f1181,plain,
spl0_118,
inference(avatar_split_clause,[],[f177,f1179]) ).
fof(f177,plain,
! [X0,X5] :
( ~ ordered_pair_predicate(X5)
| ~ little_set(second(X5))
| ~ member(X5,X0)
| member(second(X5),range_of(X0)) ),
inference(equality_resolution,[],[f106]) ).
fof(f106,axiom,
! [X3,X0,X5] :
( ~ ordered_pair_predicate(X5)
| ~ little_set(X3)
| ~ member(X5,X0)
| second(X5) != X3
| member(X3,range_of(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',range_of4) ).
fof(f1177,plain,
spl0_117,
inference(avatar_split_clause,[],[f176,f1175]) ).
fof(f176,plain,
! [X0,X5] :
( ~ ordered_pair_predicate(X5)
| ~ little_set(first(X5))
| ~ member(X5,X0)
| member(first(X5),domain_of(X0)) ),
inference(equality_resolution,[],[f37]) ).
fof(f37,axiom,
! [X3,X0,X5] :
( ~ ordered_pair_predicate(X5)
| ~ little_set(X3)
| ~ member(X5,X0)
| first(X5) != X3
| member(X3,domain_of(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain4) ).
fof(f1173,plain,
spl0_116,
inference(avatar_split_clause,[],[f149,f1171]) ).
fof(f149,plain,
! [X0] :
( ~ member(X0,infinity)
| member(complement(intersection(complement(X0),complement(non_ordered_pair(X0,X0)))),infinity) ),
inference(definition_unfolding,[],[f62,f143]) ).
fof(f143,plain,
! [X0] : successor(X0) = complement(intersection(complement(X0),complement(non_ordered_pair(X0,X0)))),
inference(definition_unfolding,[],[f57,f33,f9]) ).
fof(f33,axiom,
! [X0,X1] : union(X0,X1) = complement(intersection(complement(X0),complement(X1))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',union) ).
fof(f57,axiom,
! [X0] : successor(X0) = union(X0,singleton_set(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',successor) ).
fof(f62,axiom,
! [X0] :
( ~ member(X0,infinity)
| member(successor(X0),infinity) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',infinity3) ).
fof(f1169,plain,
spl0_115,
inference(avatar_split_clause,[],[f127,f1167]) ).
fof(f1167,plain,
( spl0_115
<=> ! [X8,X7] :
( ~ little_set(X8)
| ~ little_set(X7)
| closed(X8,X7)
| ~ maps(X7,cross_product(X8,X8),X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_115])]) ).
fof(f127,axiom,
! [X8,X7] :
( ~ little_set(X8)
| ~ little_set(X7)
| closed(X8,X7)
| ~ maps(X7,cross_product(X8,X8),X8) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',closed4) ).
fof(f1165,plain,
spl0_114,
inference(avatar_split_clause,[],[f4,f1163]) ).
fof(f4,axiom,
! [X0,X1] :
( X0 = X1
| ~ member(f1(X0,X1),X1)
| ~ member(f1(X0,X1),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',extensionality3) ).
fof(f1161,plain,
spl0_113,
inference(avatar_split_clause,[],[f3,f1159]) ).
fof(f3,axiom,
! [X0,X1] :
( X0 = X1
| member(f1(X0,X1),X1)
| member(f1(X0,X1),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',extensionality2) ).
fof(f1091,plain,
spl0_112,
inference(avatar_split_clause,[],[f175,f1089]) ).
fof(f175,plain,
! [X3,X1] :
( ~ little_set(X1)
| ~ little_set(X3)
| ordered_pair_predicate(non_ordered_pair(non_ordered_pair(X1,X1),non_ordered_pair(X1,X3))) ),
inference(equality_resolution,[],[f162]) ).
fof(f162,plain,
! [X3,X0,X1] :
( ~ little_set(X1)
| ~ little_set(X3)
| ordered_pair_predicate(X0)
| non_ordered_pair(non_ordered_pair(X1,X1),non_ordered_pair(X1,X3)) != X0 ),
inference(definition_unfolding,[],[f14,f144]) ).
fof(f14,axiom,
! [X3,X0,X1] :
( ~ little_set(X1)
| ~ little_set(X3)
| ordered_pair_predicate(X0)
| ordered_pair(X1,X3) != X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ordered_pair_predicate4) ).
fof(f1087,plain,
spl0_111,
inference(avatar_split_clause,[],[f117,f1085]) ).
fof(f117,axiom,
! [X3,X1,X7] :
( ~ member(X3,apply(X7,X1))
| member(X3,second(f28(X3,X7,X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',apply4) ).
fof(f1083,plain,
spl0_110,
inference(avatar_split_clause,[],[f116,f1081]) ).
fof(f116,axiom,
! [X3,X1,X7] :
( ~ member(X3,apply(X7,X1))
| first(f28(X3,X7,X1)) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',apply3) ).
fof(f1079,plain,
spl0_109,
inference(avatar_split_clause,[],[f109,f1077]) ).
fof(f1077,plain,
( spl0_109
<=> ! [X3] :
( ~ ordered_pair_predicate(X3)
| ~ little_set(X3)
| member(X3,identity_relation)
| first(X3) != second(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_109])]) ).
fof(f109,axiom,
! [X3] :
( ~ ordered_pair_predicate(X3)
| ~ little_set(X3)
| member(X3,identity_relation)
| first(X3) != second(X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity_relation3) ).
fof(f1074,plain,
spl0_108,
inference(avatar_split_clause,[],[f92,f1072]) ).
fof(f92,axiom,
! [X3,X0,X7] :
( ~ member(X3,image(X0,X7))
| second(f22(X3,X0,X7)) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',image_and_substitution4) ).
fof(f1070,plain,
spl0_107,
inference(avatar_split_clause,[],[f91,f1068]) ).
fof(f91,axiom,
! [X3,X0,X7] :
( ~ member(X3,image(X0,X7))
| member(first(f22(X3,X0,X7)),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',image_and_substitution3) ).
fof(f1066,plain,
spl0_106,
inference(avatar_split_clause,[],[f27,f1064]) ).
fof(f27,axiom,
! [X3] :
( ~ ordered_pair_predicate(X3)
| ~ little_set(X3)
| member(X3,estin)
| ~ member(first(X3),second(X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_relation3) ).
fof(f972,plain,
spl0_105,
inference(avatar_split_clause,[],[f174,f970]) ).
fof(f970,plain,
( spl0_105
<=> ! [X1,X7] :
( ~ function(X7)
| ~ subset(range_of(X7),X1)
| maps(X7,domain_of(X7),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_105])]) ).
fof(f174,plain,
! [X1,X7] :
( ~ function(X7)
| ~ subset(range_of(X7),X1)
| maps(X7,domain_of(X7),X1) ),
inference(equality_resolution,[],[f123]) ).
fof(f123,axiom,
! [X0,X1,X7] :
( ~ function(X7)
| domain_of(X7) != X0
| ~ subset(range_of(X7),X1)
| maps(X7,X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',maps4) ).
fof(f968,plain,
spl0_104,
inference(avatar_split_clause,[],[f115,f966]) ).
fof(f115,axiom,
! [X3,X1,X7] :
( ~ member(X3,apply(X7,X1))
| member(f28(X3,X7,X1),X7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',apply2) ).
fof(f962,plain,
spl0_103,
inference(avatar_split_clause,[],[f90,f960]) ).
fof(f90,axiom,
! [X3,X0,X7] :
( ~ member(X3,image(X0,X7))
| member(f22(X3,X0,X7),X7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',image_and_substitution2) ).
fof(f958,plain,
spl0_102,
inference(avatar_split_clause,[],[f30,f956]) ).
fof(f30,axiom,
! [X3,X0,X1] :
( ~ member(X3,X1)
| ~ member(X3,X0)
| member(X3,intersection(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection3) ).
fof(f954,plain,
spl0_101,
inference(avatar_split_clause,[],[f5,f952]) ).
fof(f5,axiom,
! [X2,X0,X1] :
( X1 = X2
| X0 = X2
| ~ member(X2,non_ordered_pair(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',non_ordered_pair1) ).
fof(f866,plain,
spl0_100,
inference(avatar_split_clause,[],[f137,f864]) ).
fof(f864,plain,
( spl0_100
<=> ! [X11,X13,X14,X12,X10] :
( maps(X10,X11,X13)
| ~ homomorphism(X10,X11,X12,X13,X14) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_100])]) ).
fof(f137,axiom,
! [X10,X11,X14,X12,X13] :
( maps(X10,X11,X13)
| ~ homomorphism(X10,X11,X12,X13,X14) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',homomorphism3) ).
fof(f862,plain,
spl0_99,
inference(avatar_split_clause,[],[f130,f860]) ).
fof(f130,axiom,
! [X3,X9,X7] :
( ~ member(X3,compose(X7,X9))
| little_set(f31(X3,X7,X9)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',compose3) ).
fof(f858,plain,
spl0_98,
inference(avatar_split_clause,[],[f129,f856]) ).
fof(f129,axiom,
! [X3,X9,X7] :
( ~ member(X3,compose(X7,X9))
| little_set(f30(X3,X7,X9)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',compose2) ).
fof(f854,plain,
spl0_97,
inference(avatar_split_clause,[],[f128,f852]) ).
fof(f128,axiom,
! [X3,X9,X7] :
( ~ member(X3,compose(X7,X9))
| little_set(f29(X3,X7,X9)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',compose1) ).
fof(f850,plain,
spl0_96,
inference(avatar_split_clause,[],[f114,f848]) ).
fof(f114,axiom,
! [X3,X1,X7] :
( ~ member(X3,apply(X7,X1))
| ordered_pair_predicate(f28(X3,X7,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',apply1) ).
fof(f846,plain,
spl0_95,
inference(avatar_split_clause,[],[f105,f844]) ).
fof(f105,axiom,
! [X3,X0] :
( ~ member(X3,range_of(X0))
| second(f27(X3,X0)) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',range_of3) ).
fof(f842,plain,
spl0_94,
inference(avatar_split_clause,[],[f89,f840]) ).
fof(f89,axiom,
! [X3,X0,X7] :
( ~ member(X3,image(X0,X7))
| ordered_pair_predicate(f22(X3,X0,X7)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',image_and_substitution1) ).
fof(f838,plain,
spl0_93,
inference(avatar_split_clause,[],[f65,f836]) ).
fof(f65,axiom,
! [X3,X0,X1] :
( ~ member(X3,X1)
| ~ member(X1,X0)
| member(X3,sigma(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sigma3) ).
fof(f834,plain,
( spl0_92
| ~ spl0_4
| ~ spl0_64 ),
inference(avatar_split_clause,[],[f602,f478,f201,f832]) ).
fof(f602,plain,
( ! [X0] : disjoint(X0,empty_set)
| ~ spl0_4
| ~ spl0_64 ),
inference(resolution,[],[f479,f202]) ).
fof(f830,plain,
spl0_91,
inference(avatar_split_clause,[],[f36,f828]) ).
fof(f36,axiom,
! [X3,X0] :
( ~ member(X3,domain_of(X0))
| first(f8(X3,X0)) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain3) ).
fof(f766,plain,
( spl0_90
| ~ spl0_4
| ~ spl0_63 ),
inference(avatar_split_clause,[],[f580,f474,f201,f764]) ).
fof(f580,plain,
( ! [X0] : disjoint(empty_set,X0)
| ~ spl0_4
| ~ spl0_63 ),
inference(resolution,[],[f475,f202]) ).
fof(f690,plain,
spl0_89,
inference(avatar_split_clause,[],[f136,f688]) ).
fof(f688,plain,
( spl0_89
<=> ! [X10,X11,X13,X14,X12] :
( closed(X13,X14)
| ~ homomorphism(X10,X11,X12,X13,X14) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_89])]) ).
fof(f136,axiom,
! [X10,X11,X14,X12,X13] :
( closed(X13,X14)
| ~ homomorphism(X10,X11,X12,X13,X14) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',homomorphism2) ).
fof(f686,plain,
spl0_88,
inference(avatar_split_clause,[],[f135,f684]) ).
fof(f684,plain,
( spl0_88
<=> ! [X10,X11,X14,X13,X12] :
( closed(X11,X12)
| ~ homomorphism(X10,X11,X12,X13,X14) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_88])]) ).
fof(f135,axiom,
! [X10,X11,X14,X12,X13] :
( closed(X11,X12)
| ~ homomorphism(X10,X11,X12,X13,X14) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',homomorphism1) ).
fof(f682,plain,
( spl0_87
| ~ spl0_60
| ~ spl0_61 ),
inference(avatar_split_clause,[],[f560,f466,f462,f680]) ).
fof(f680,plain,
( spl0_87
<=> ! [X0] : subset(X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_87])]) ).
fof(f560,plain,
( ! [X0] : subset(X0,X0)
| ~ spl0_60
| ~ spl0_61 ),
inference(duplicate_literal_removal,[],[f558]) ).
fof(f558,plain,
( ! [X0] :
( subset(X0,X0)
| subset(X0,X0) )
| ~ spl0_60
| ~ spl0_61 ),
inference(resolution,[],[f467,f463]) ).
fof(f678,plain,
spl0_86,
inference(avatar_split_clause,[],[f126,f676]) ).
fof(f126,axiom,
! [X8,X7] :
( ~ closed(X8,X7)
| maps(X7,cross_product(X8,X8),X8) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',closed3) ).
fof(f674,plain,
spl0_85,
inference(avatar_split_clause,[],[f104,f672]) ).
fof(f104,axiom,
! [X3,X0] :
( ~ member(X3,range_of(X0))
| member(f27(X3,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',range_of2) ).
fof(f670,plain,
spl0_84,
inference(avatar_split_clause,[],[f101,f668]) ).
fof(f101,axiom,
! [X0] :
( ~ little_set(X0)
| empty_set = X0
| member(f26(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',choice2) ).
fof(f666,plain,
spl0_83,
inference(avatar_split_clause,[],[f95,f664]) ).
fof(f95,axiom,
! [X2,X0,X1] :
( ~ disjoint(X0,X1)
| ~ member(X2,X1)
| ~ member(X2,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',disjoint1) ).
fof(f662,plain,
spl0_82,
inference(avatar_split_clause,[],[f74,f660]) ).
fof(f74,axiom,
! [X3,X0] :
( ~ little_set(X3)
| ~ subset(X3,X0)
| member(X3,powerset(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powerset2) ).
fof(f658,plain,
spl0_81,
inference(avatar_split_clause,[],[f72,f656]) ).
fof(f72,axiom,
! [X0,X1] :
( ~ subset(X0,X1)
| X0 = X1
| proper_subset(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',proper_subset3) ).
fof(f654,plain,
spl0_80,
inference(avatar_split_clause,[],[f67,f652]) ).
fof(f67,axiom,
! [X2,X0,X1] :
( ~ subset(X0,X1)
| ~ member(X2,X0)
| member(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset1) ).
fof(f650,plain,
spl0_79,
inference(avatar_split_clause,[],[f64,f648]) ).
fof(f64,axiom,
! [X3,X0] :
( ~ member(X3,sigma(X0))
| member(X3,f16(X3,X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sigma2) ).
fof(f646,plain,
spl0_78,
inference(avatar_split_clause,[],[f63,f644]) ).
fof(f63,axiom,
! [X3,X0] :
( ~ member(X3,sigma(X0))
| member(f16(X3,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sigma1) ).
fof(f642,plain,
spl0_77,
inference(avatar_split_clause,[],[f40,f640]) ).
fof(f40,axiom,
! [X3,X0,X1] :
( member(second(X3),X1)
| ~ member(X3,cross_product(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cross_product3) ).
fof(f638,plain,
( spl0_76
| ~ spl0_4
| ~ spl0_60 ),
inference(avatar_split_clause,[],[f555,f462,f201,f636]) ).
fof(f555,plain,
( ! [X0] : subset(empty_set,X0)
| ~ spl0_4
| ~ spl0_60 ),
inference(resolution,[],[f463,f202]) ).
fof(f634,plain,
spl0_75,
inference(avatar_split_clause,[],[f39,f632]) ).
fof(f39,axiom,
! [X3,X0,X1] :
( member(first(X3),X0)
| ~ member(X3,cross_product(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cross_product2) ).
fof(f630,plain,
spl0_74,
inference(avatar_split_clause,[],[f35,f628]) ).
fof(f35,axiom,
! [X3,X0] :
( ~ member(X3,domain_of(X0))
| member(f8(X3,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain2) ).
fof(f626,plain,
spl0_73,
inference(avatar_split_clause,[],[f32,f624]) ).
fof(f32,axiom,
! [X3,X0] :
( ~ little_set(X3)
| member(X3,X0)
| member(X3,complement(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complement2) ).
fof(f622,plain,
spl0_72,
inference(avatar_split_clause,[],[f23,f620]) ).
fof(f23,axiom,
! [X3,X0] :
( ~ member(X3,second(X0))
| member(X3,f7(X3,X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',second4) ).
fof(f618,plain,
spl0_71,
inference(avatar_split_clause,[],[f18,f616]) ).
fof(f18,axiom,
! [X3,X0] :
( ~ member(X3,first(X0))
| member(X3,f4(X3,X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',first4) ).
fof(f505,plain,
spl0_70,
inference(avatar_split_clause,[],[f122,f503]) ).
fof(f122,axiom,
! [X0,X1,X7] :
( ~ maps(X7,X0,X1)
| subset(range_of(X7),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',maps3) ).
fof(f501,plain,
spl0_69,
inference(avatar_split_clause,[],[f121,f499]) ).
fof(f121,axiom,
! [X0,X1,X7] :
( ~ maps(X7,X0,X1)
| domain_of(X7) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',maps2) ).
fof(f497,plain,
( ~ spl0_67
| spl0_68
| ~ spl0_5
| ~ spl0_38 ),
inference(avatar_split_clause,[],[f388,f353,f205,f494,f490]) ).
fof(f490,plain,
( spl0_67
<=> relation(infinity) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_67])]) ).
fof(f388,plain,
( ordered_pair_predicate(empty_set)
| ~ relation(infinity)
| ~ spl0_5
| ~ spl0_38 ),
inference(resolution,[],[f354,f207]) ).
fof(f488,plain,
spl0_66,
inference(avatar_split_clause,[],[f108,f486]) ).
fof(f108,axiom,
! [X3] :
( ~ member(X3,identity_relation)
| first(X3) = second(X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity_relation2) ).
fof(f484,plain,
spl0_65,
inference(avatar_split_clause,[],[f103,f482]) ).
fof(f103,axiom,
! [X3,X0] :
( ~ member(X3,range_of(X0))
| ordered_pair_predicate(f27(X3,X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',range_of1) ).
fof(f480,plain,
spl0_64,
inference(avatar_split_clause,[],[f97,f478]) ).
fof(f97,axiom,
! [X0,X1] :
( disjoint(X0,X1)
| member(f23(X0,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',disjoint3) ).
fof(f476,plain,
spl0_63,
inference(avatar_split_clause,[],[f96,f474]) ).
fof(f96,axiom,
! [X0,X1] :
( disjoint(X0,X1)
| member(f23(X0,X1),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',disjoint2) ).
fof(f472,plain,
spl0_62,
inference(avatar_split_clause,[],[f94,f470]) ).
fof(f470,plain,
( spl0_62
<=> ! [X0,X7] :
( ~ function(X7)
| ~ little_set(X0)
| little_set(image(X0,X7)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_62])]) ).
fof(f94,axiom,
! [X0,X7] :
( ~ function(X7)
| ~ little_set(X0)
| little_set(image(X0,X7)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',image_and_substitution6) ).
fof(f468,plain,
spl0_61,
inference(avatar_split_clause,[],[f69,f466]) ).
fof(f69,axiom,
! [X0,X1] :
( subset(X0,X1)
| ~ member(f17(X0,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset3) ).
fof(f464,plain,
spl0_60,
inference(avatar_split_clause,[],[f68,f462]) ).
fof(f68,axiom,
! [X0,X1] :
( subset(X0,X1)
| member(f17(X0,X1),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset2) ).
fof(f460,plain,
spl0_59,
inference(avatar_split_clause,[],[f53,f458]) ).
fof(f53,axiom,
! [X3,X0] :
( ~ member(X3,flip_range_of(X0))
| little_set(f14(X3,X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',flip_range3) ).
fof(f456,plain,
spl0_58,
inference(avatar_split_clause,[],[f52,f454]) ).
fof(f52,axiom,
! [X3,X0] :
( ~ member(X3,flip_range_of(X0))
| little_set(f13(X3,X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',flip_range2) ).
fof(f452,plain,
spl0_57,
inference(avatar_split_clause,[],[f51,f450]) ).
fof(f51,axiom,
! [X3,X0] :
( ~ member(X3,flip_range_of(X0))
| little_set(f12(X3,X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',flip_range1) ).
fof(f448,plain,
spl0_56,
inference(avatar_split_clause,[],[f47,f446]) ).
fof(f47,axiom,
! [X3,X0] :
( ~ member(X3,rotate_right(X0))
| little_set(f11(X3,X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rotate_right3) ).
fof(f444,plain,
spl0_55,
inference(avatar_split_clause,[],[f46,f442]) ).
fof(f46,axiom,
! [X3,X0] :
( ~ member(X3,rotate_right(X0))
| little_set(f10(X3,X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rotate_right2) ).
fof(f440,plain,
spl0_54,
inference(avatar_split_clause,[],[f45,f438]) ).
fof(f45,axiom,
! [X3,X0] :
( ~ member(X3,rotate_right(X0))
| little_set(f9(X3,X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rotate_right1) ).
fof(f436,plain,
spl0_53,
inference(avatar_split_clause,[],[f34,f434]) ).
fof(f34,axiom,
! [X3,X0] :
( ~ member(X3,domain_of(X0))
| ordered_pair_predicate(f8(X3,X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain1) ).
fof(f432,plain,
spl0_52,
inference(avatar_split_clause,[],[f29,f430]) ).
fof(f29,axiom,
! [X3,X0,X1] :
( member(X3,X1)
| ~ member(X3,intersection(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection2) ).
fof(f428,plain,
spl0_51,
inference(avatar_split_clause,[],[f28,f426]) ).
fof(f28,axiom,
! [X3,X0,X1] :
( member(X3,X0)
| ~ member(X3,intersection(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection1) ).
fof(f424,plain,
spl0_50,
inference(avatar_split_clause,[],[f26,f422]) ).
fof(f422,plain,
( spl0_50
<=> ! [X3] :
( ~ member(X3,estin)
| member(first(X3),second(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_50])]) ).
fof(f26,axiom,
! [X3] :
( ~ member(X3,estin)
| member(first(X3),second(X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_relation2) ).
fof(f420,plain,
spl0_49,
inference(avatar_split_clause,[],[f21,f418]) ).
fof(f21,axiom,
! [X3,X0] :
( ~ member(X3,second(X0))
| little_set(f7(X3,X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',second2) ).
fof(f416,plain,
spl0_48,
inference(avatar_split_clause,[],[f20,f414]) ).
fof(f20,axiom,
! [X3,X0] :
( ~ member(X3,second(X0))
| little_set(f6(X3,X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',second1) ).
fof(f412,plain,
spl0_47,
inference(avatar_split_clause,[],[f16,f410]) ).
fof(f16,axiom,
! [X3,X0] :
( ~ member(X3,first(X0))
| little_set(f5(X3,X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',first2) ).
fof(f408,plain,
spl0_46,
inference(avatar_split_clause,[],[f15,f406]) ).
fof(f15,axiom,
! [X3,X0] :
( ~ member(X3,first(X0))
| little_set(f4(X3,X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',first1) ).
fof(f385,plain,
( spl0_45
| ~ spl0_4
| ~ spl0_30 ),
inference(avatar_split_clause,[],[f328,f314,f201,f382]) ).
fof(f328,plain,
( relation(empty_set)
| ~ spl0_4
| ~ spl0_30 ),
inference(resolution,[],[f315,f202]) ).
fof(f379,plain,
spl0_44,
inference(avatar_split_clause,[],[f173,f377]) ).
fof(f173,plain,
! [X2,X0] :
( ~ little_set(X2)
| member(X2,non_ordered_pair(X0,X2)) ),
inference(equality_resolution,[],[f7]) ).
fof(f7,axiom,
! [X2,X0,X1] :
( ~ little_set(X2)
| X1 != X2
| member(X2,non_ordered_pair(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',non_ordered_pair3) ).
fof(f375,plain,
spl0_43,
inference(avatar_split_clause,[],[f172,f373]) ).
fof(f172,plain,
! [X2,X1] :
( ~ little_set(X2)
| member(X2,non_ordered_pair(X2,X1)) ),
inference(equality_resolution,[],[f6]) ).
fof(f6,axiom,
! [X2,X0,X1] :
( ~ little_set(X2)
| X0 != X2
| member(X2,non_ordered_pair(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',non_ordered_pair2) ).
fof(f371,plain,
spl0_42,
inference(avatar_split_clause,[],[f113,f369]) ).
fof(f113,axiom,
! [X7] :
( ~ function(X7)
| one_to_one_function(X7)
| ~ function(converse(X7)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',one_to_one_function3) ).
fof(f367,plain,
spl0_41,
inference(avatar_split_clause,[],[f99,f365]) ).
fof(f99,axiom,
! [X0] :
( empty_set = X0
| disjoint(f24(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',regularity2) ).
fof(f363,plain,
spl0_40,
inference(avatar_split_clause,[],[f98,f361]) ).
fof(f98,axiom,
! [X0] :
( empty_set = X0
| member(f24(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',regularity1) ).
fof(f359,plain,
spl0_39,
inference(avatar_split_clause,[],[f85,f357]) ).
fof(f357,plain,
( spl0_39
<=> ! [X0] :
( single_valued_set(X0)
| f20(X0) != f21(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_39])]) ).
fof(f85,axiom,
! [X0] :
( single_valued_set(X0)
| f20(X0) != f21(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',single_valued_set7) ).
fof(f355,plain,
spl0_38,
inference(avatar_split_clause,[],[f76,f353]) ).
fof(f76,axiom,
! [X3,X0] :
( ~ relation(X3)
| ordered_pair_predicate(X0)
| ~ member(X0,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',relation1) ).
fof(f351,plain,
spl0_37,
inference(avatar_split_clause,[],[f73,f349]) ).
fof(f73,axiom,
! [X3,X0] :
( subset(X3,X0)
| ~ member(X3,powerset(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powerset1) ).
fof(f347,plain,
( spl0_36
| ~ spl0_5
| ~ spl0_11 ),
inference(avatar_split_clause,[],[f301,f232,f205,f344]) ).
fof(f301,plain,
( little_set(empty_set)
| ~ spl0_5
| ~ spl0_11 ),
inference(resolution,[],[f233,f207]) ).
fof(f342,plain,
spl0_35,
inference(avatar_split_clause,[],[f38,f340]) ).
fof(f38,axiom,
! [X3,X0,X1] :
( ordered_pair_predicate(X3)
| ~ member(X3,cross_product(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cross_product1) ).
fof(f338,plain,
spl0_34,
inference(avatar_split_clause,[],[f31,f336]) ).
fof(f31,axiom,
! [X3,X0] :
( ~ member(X3,X0)
| ~ member(X3,complement(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complement1) ).
fof(f334,plain,
spl0_33,
inference(avatar_split_clause,[],[f2,f332]) ).
fof(f332,plain,
( spl0_33
<=> ! [X0,X1] :
( X0 = X1
| little_set(f1(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_33])]) ).
fof(f2,axiom,
! [X0,X1] :
( X0 = X1
| little_set(f1(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',extensionality1) ).
fof(f324,plain,
spl0_32,
inference(avatar_split_clause,[],[f120,f322]) ).
fof(f120,axiom,
! [X0,X1,X7] :
( function(X7)
| ~ maps(X7,X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',maps1) ).
fof(f320,plain,
spl0_31,
inference(avatar_split_clause,[],[f88,f318]) ).
fof(f88,axiom,
! [X7] :
( ~ relation(X7)
| ~ single_valued_set(X7)
| function(X7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',function3) ).
fof(f316,plain,
spl0_30,
inference(avatar_split_clause,[],[f77,f314]) ).
fof(f77,axiom,
! [X3] :
( relation(X3)
| member(f18(X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',relation2) ).
fof(f312,plain,
spl0_29,
inference(avatar_split_clause,[],[f70,f310]) ).
fof(f310,plain,
( spl0_29
<=> ! [X0,X1] :
( ~ proper_subset(X0,X1)
| subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_29])]) ).
fof(f70,axiom,
! [X0,X1] :
( ~ proper_subset(X0,X1)
| subset(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',proper_subset1) ).
fof(f308,plain,
spl0_28,
inference(avatar_split_clause,[],[f42,f306]) ).
fof(f42,axiom,
! [X3,X0] :
( ordered_pair_predicate(X3)
| ~ member(X3,converse(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',converse1) ).
fof(f300,plain,
spl0_27,
inference(avatar_split_clause,[],[f125,f298]) ).
fof(f298,plain,
( spl0_27
<=> ! [X7,X8] :
( little_set(X7)
| ~ closed(X8,X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_27])]) ).
fof(f125,axiom,
! [X8,X7] :
( little_set(X7)
| ~ closed(X8,X7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',closed2) ).
fof(f296,plain,
spl0_26,
inference(avatar_split_clause,[],[f124,f294]) ).
fof(f294,plain,
( spl0_26
<=> ! [X8,X7] :
( little_set(X8)
| ~ closed(X8,X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_26])]) ).
fof(f124,axiom,
! [X8,X7] :
( little_set(X8)
| ~ closed(X8,X7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',closed1) ).
fof(f292,plain,
( spl0_25
| ~ spl0_3
| ~ spl0_9 ),
inference(avatar_split_clause,[],[f230,f222,f196,f289]) ).
fof(f196,plain,
( spl0_3
<=> function(f25) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).
fof(f230,plain,
( single_valued_set(f25)
| ~ spl0_3
| ~ spl0_9 ),
inference(resolution,[],[f223,f198]) ).
fof(f198,plain,
( function(f25)
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f196]) ).
fof(f287,plain,
spl0_24,
inference(avatar_split_clause,[],[f112,f285]) ).
fof(f112,axiom,
! [X7] :
( ~ one_to_one_function(X7)
| function(converse(X7)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',one_to_one_function2) ).
fof(f283,plain,
spl0_23,
inference(avatar_split_clause,[],[f107,f281]) ).
fof(f107,axiom,
! [X3] :
( ordered_pair_predicate(X3)
| ~ member(X3,identity_relation) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity_relation1) ).
fof(f279,plain,
spl0_22,
inference(avatar_split_clause,[],[f82,f277]) ).
fof(f277,plain,
( spl0_22
<=> ! [X0] :
( single_valued_set(X0)
| little_set(f21(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_22])]) ).
fof(f82,axiom,
! [X0] :
( single_valued_set(X0)
| little_set(f21(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',single_valued_set4) ).
fof(f275,plain,
spl0_21,
inference(avatar_split_clause,[],[f81,f273]) ).
fof(f273,plain,
( spl0_21
<=> ! [X0] :
( single_valued_set(X0)
| little_set(f20(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_21])]) ).
fof(f81,axiom,
! [X0] :
( single_valued_set(X0)
| little_set(f20(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',single_valued_set3) ).
fof(f271,plain,
spl0_20,
inference(avatar_split_clause,[],[f80,f269]) ).
fof(f269,plain,
( spl0_20
<=> ! [X0] :
( single_valued_set(X0)
| little_set(f19(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_20])]) ).
fof(f80,axiom,
! [X0] :
( single_valued_set(X0)
| little_set(f19(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',single_valued_set2) ).
fof(f267,plain,
spl0_19,
inference(avatar_split_clause,[],[f78,f265]) ).
fof(f78,axiom,
! [X3] :
( relation(X3)
| ~ ordered_pair_predicate(f18(X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',relation3) ).
fof(f263,plain,
spl0_18,
inference(avatar_split_clause,[],[f75,f261]) ).
fof(f261,plain,
( spl0_18
<=> ! [X2] :
( ~ little_set(X2)
| little_set(powerset(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_18])]) ).
fof(f75,axiom,
! [X2] :
( ~ little_set(X2)
| little_set(powerset(X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powerset3) ).
fof(f259,plain,
spl0_17,
inference(avatar_split_clause,[],[f66,f257]) ).
fof(f257,plain,
( spl0_17
<=> ! [X2] :
( ~ little_set(X2)
| little_set(sigma(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_17])]) ).
fof(f66,axiom,
! [X2] :
( ~ little_set(X2)
| little_set(sigma(X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sigma4) ).
fof(f255,plain,
spl0_16,
inference(avatar_split_clause,[],[f59,f253]) ).
fof(f59,axiom,
! [X3] :
( ~ little_set(X3)
| member(X3,universal_set) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',universal_set) ).
fof(f251,plain,
spl0_15,
inference(avatar_split_clause,[],[f25,f249]) ).
fof(f25,axiom,
! [X3] :
( ordered_pair_predicate(X3)
| ~ member(X3,estin) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_relation1) ).
fof(f247,plain,
( spl0_14
| ~ spl0_3
| ~ spl0_8 ),
inference(avatar_split_clause,[],[f229,f218,f196,f244]) ).
fof(f229,plain,
( relation(f25)
| ~ spl0_3
| ~ spl0_8 ),
inference(resolution,[],[f219,f198]) ).
fof(f242,plain,
spl0_13,
inference(avatar_split_clause,[],[f12,f240]) ).
fof(f240,plain,
( spl0_13
<=> ! [X0] :
( ~ ordered_pair_predicate(X0)
| little_set(f3(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).
fof(f12,axiom,
! [X0] :
( ~ ordered_pair_predicate(X0)
| little_set(f3(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ordered_pair_predicate2) ).
fof(f238,plain,
spl0_12,
inference(avatar_split_clause,[],[f11,f236]) ).
fof(f236,plain,
( spl0_12
<=> ! [X0] :
( ~ ordered_pair_predicate(X0)
| little_set(f2(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_12])]) ).
fof(f11,axiom,
! [X0] :
( ~ ordered_pair_predicate(X0)
| little_set(f2(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ordered_pair_predicate1) ).
fof(f234,plain,
spl0_11,
inference(avatar_split_clause,[],[f1,f232]) ).
fof(f1,axiom,
! [X0,X1] :
( little_set(X0)
| ~ member(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a2) ).
fof(f228,plain,
spl0_10,
inference(avatar_split_clause,[],[f111,f226]) ).
fof(f226,plain,
( spl0_10
<=> ! [X7] :
( ~ one_to_one_function(X7)
| function(X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).
fof(f111,axiom,
! [X7] :
( ~ one_to_one_function(X7)
| function(X7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',one_to_one_function1) ).
fof(f224,plain,
spl0_9,
inference(avatar_split_clause,[],[f87,f222]) ).
fof(f87,axiom,
! [X7] :
( ~ function(X7)
| single_valued_set(X7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',function2) ).
fof(f220,plain,
spl0_8,
inference(avatar_split_clause,[],[f86,f218]) ).
fof(f86,axiom,
! [X7] :
( ~ function(X7)
| relation(X7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',function1) ).
fof(f216,plain,
spl0_7,
inference(avatar_split_clause,[],[f8,f214]) ).
fof(f8,axiom,
! [X0,X1] : little_set(non_ordered_pair(X0,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',non_ordered_pair4) ).
fof(f212,plain,
spl0_6,
inference(avatar_split_clause,[],[f171,f210]) ).
fof(f210,plain,
( spl0_6
<=> ! [X1] : ~ proper_subset(X1,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).
fof(f171,plain,
! [X1] : ~ proper_subset(X1,X1),
inference(equality_resolution,[],[f71]) ).
fof(f71,axiom,
! [X0,X1] :
( X0 != X1
| ~ proper_subset(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',proper_subset2) ).
fof(f208,plain,
spl0_5,
inference(avatar_split_clause,[],[f61,f205]) ).
fof(f61,axiom,
member(empty_set,infinity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',infinity2) ).
fof(f203,plain,
spl0_4,
inference(avatar_split_clause,[],[f58,f201]) ).
fof(f58,axiom,
! [X3] : ~ member(X3,empty_set),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',empty_set) ).
fof(f199,plain,
spl0_3,
inference(avatar_split_clause,[],[f100,f196]) ).
fof(f100,axiom,
function(f25),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',choice1) ).
fof(f194,plain,
spl0_2,
inference(avatar_split_clause,[],[f60,f191]) ).
fof(f191,plain,
( spl0_2
<=> little_set(infinity) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).
fof(f60,axiom,
little_set(infinity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',infinity1) ).
fof(f189,plain,
~ spl0_1,
inference(avatar_split_clause,[],[f142,f186]) ).
fof(f142,axiom,
~ relation(compose(a,b)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_composition_is_a_relation) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SET031-4 : TPTP v8.2.0. Released v1.0.0.
% 0.06/0.13 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.13/0.34 % Computer : n009.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon May 20 11:28:08 EDT 2024
% 0.13/0.34 % CPUTime :
% 0.13/0.34 % (2399)Running in auto input_syntax mode. Trying TPTP
% 0.13/0.36 % (2402)WARNING: value z3 for option sas not known
% 0.13/0.36 % (2401)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.13/0.36 % (2402)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)
% 0.13/0.36 % (2400)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.13/0.36 % (2404)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)
% 0.13/0.36 % (2405)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)
% 0.13/0.36 % (2406)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.13/0.36 % (2403)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.13/0.38 TRYING [1]
% 0.13/0.39 TRYING [2]
% 0.19/0.42 TRYING [1]
% 0.19/0.43 TRYING [2]
% 0.19/0.45 TRYING [3]
% 0.19/0.58 TRYING [3]
% 6.19/1.21 TRYING [4]
% 6.40/1.29 TRYING [4]
% 7.88/1.47 TRYING [1]
% 7.88/1.47 TRYING [2]
% 7.88/1.51 TRYING [3]
% 10.13/1.82 TRYING [4]
% 30.38/4.74 TRYING [5]
% 34.47/5.27 TRYING [5]
% 72.47/10.75 TRYING [5]
% 157.91/23.00 TRYING [6]
% 161.09/23.44 % (2404)First to succeed.
% 161.97/23.56 % (2404)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2399"
% 162.57/23.61 % (2404)Refutation found. Thanks to Tanya!
% 162.57/23.61 % SZS status Unsatisfiable for theBenchmark
% 162.57/23.61 % SZS output start Proof for theBenchmark
% See solution above
% 162.57/23.67 % (2404)------------------------------
% 162.57/23.67 % (2404)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 162.57/23.67 % (2404)Termination reason: Refutation
% 162.57/23.67
% 162.57/23.67 % (2404)Memory used [KB]: 106169
% 162.57/23.67 % (2404)Time elapsed: 23.194 s
% 162.57/23.67 % (2404)Instructions burned: 31367 (million)
% 162.57/23.67 % (2399)Success in time 23.303 s
%------------------------------------------------------------------------------