TSTP Solution File: NUM401+1 by Vampire---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : NUM401+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% Computer : n015.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 : Thu Aug 31 12:07:53 EDT 2023
% Result : Theorem 2.65s 0.78s
% Output : Refutation 2.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 720
% Syntax : Number of formulae : 3123 ( 119 unt; 0 def)
% Number of atoms : 10815 ( 586 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 14077 (6385 ~;6805 |; 175 &)
% ( 676 <=>; 35 =>; 0 <=; 1 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 677 ( 675 usr; 664 prp; 0-2 aty)
% Number of functors : 19 ( 19 usr; 11 con; 0-3 aty)
% Number of variables : 1650 (;1611 !; 39 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f10870,plain,
$false,
inference(avatar_sat_refutation,[],[f266,f271,f280,f281,f286,f291,f296,f301,f306,f311,f316,f321,f326,f331,f336,f341,f346,f351,f356,f361,f366,f371,f376,f381,f385,f389,f393,f397,f401,f405,f409,f413,f417,f421,f425,f429,f433,f437,f441,f445,f449,f466,f471,f476,f481,f486,f490,f494,f498,f502,f506,f510,f514,f531,f535,f539,f543,f547,f554,f562,f563,f564,f565,f566,f578,f582,f587,f591,f596,f601,f606,f610,f614,f618,f633,f647,f653,f664,f668,f672,f676,f681,f687,f691,f701,f705,f714,f734,f741,f755,f759,f763,f767,f771,f775,f780,f808,f826,f833,f837,f842,f847,f851,f855,f871,f875,f879,f883,f893,f900,f907,f918,f922,f935,f939,f954,f958,f982,f986,f990,f997,f1013,f1020,f1024,f1038,f1042,f1049,f1053,f1058,f1074,f1084,f1088,f1094,f1112,f1118,f1122,f1128,f1132,f1136,f1155,f1170,f1177,f1191,f1214,f1228,f1233,f1265,f1282,f1286,f1333,f1371,f1415,f1420,f1423,f1461,f1464,f1470,f1492,f1516,f1538,f1576,f1598,f1604,f1622,f1627,f1669,f1697,f1701,f1705,f1712,f1717,f1725,f1738,f1743,f1756,f1760,f1774,f1778,f1792,f1796,f1798,f1802,f1822,f1826,f1830,f1846,f1853,f1858,f1870,f1874,f1878,f1898,f1902,f1906,f1922,f1926,f1948,f1950,f1953,f1955,f1960,f1965,f1969,f1973,f1977,f1981,f1998,f2007,f2013,f2016,f2022,f2039,f2071,f2078,f2096,f2099,f2140,f2162,f2171,f2175,f2182,f2192,f2211,f2226,f2229,f2246,f2253,f2277,f2280,f2283,f2313,f2315,f2318,f2320,f2326,f2334,f2340,f2345,f2346,f2363,f2369,f2372,f2375,f2379,f2386,f2391,f2400,f2403,f2406,f2415,f2427,f2437,f2466,f2477,f2488,f2521,f2533,f2535,f2537,f2539,f2542,f2544,f2547,f2551,f2553,f2586,f2597,f2608,f2628,f2655,f2662,f2668,f2672,f2688,f2695,f2701,f2705,f2728,f2740,f2779,f2781,f2784,f2786,f2805,f2818,f2822,f2826,f2855,f2861,f2875,f2892,f2897,f2928,f2932,f2936,f2940,f2944,f2960,f3006,f3015,f3043,f3045,f3059,f3062,f3064,f3066,f3095,f3100,f3135,f3139,f3176,f3181,f3199,f3254,f3256,f3259,f3261,f3266,f3334,f3342,f3348,f3393,f3416,f3417,f3421,f3425,f3439,f3457,f3511,f3517,f3521,f3526,f3535,f3539,f3611,f3625,f3631,f3635,f3640,f3664,f3668,f3673,f3677,f3681,f3685,f3690,f3694,f3698,f3711,f3721,f3736,f3744,f3749,f3753,f3757,f3761,f3765,f3783,f3787,f3791,f3811,f3848,f3852,f3854,f3856,f3858,f3906,f3908,f3910,f3917,f3919,f3926,f3928,f3930,f3949,f3956,f3959,f3961,f4017,f4024,f4026,f4028,f4045,f4127,f4134,f4136,f4138,f4155,f4157,f4166,f4169,f4177,f4179,f4182,f4185,f4188,f4198,f4199,f4219,f4224,f4245,f4249,f4255,f4266,f4267,f4283,f4292,f4309,f4313,f4349,f4370,f4397,f4402,f4430,f4435,f4437,f4508,f4514,f4519,f4523,f4528,f4536,f4541,f4550,f4555,f4564,f4633,f4640,f4645,f4704,f4793,f4815,f4863,f4896,f4897,f4898,f4909,f4913,f4941,f4949,f4954,f4966,f5124,f5129,f5269,f5278,f5428,f5466,f5471,f5478,f5483,f5509,f5514,f5521,f5526,f5535,f5546,f5592,f5596,f5598,f5600,f5602,f5605,f5607,f5613,f5615,f5619,f5621,f5623,f5646,f5674,f5701,f5713,f5731,f5745,f5758,f5768,f5785,f5804,f5809,f5816,f5821,f5825,f5867,f5915,f5917,f5919,f5921,f5928,f5930,f5932,f5934,f5938,f5940,f5942,f5957,f5964,f6041,f6054,f6076,f6084,f6131,f6135,f6139,f6143,f6157,f6161,f6165,f6169,f6173,f6177,f6181,f6186,f6190,f6212,f6222,f6226,f6230,f6260,f6264,f6270,f6280,f6324,f6334,f6338,f6401,f6416,f6425,f6429,f6443,f6478,f6482,f6491,f6495,f6539,f6548,f6554,f6563,f6739,f6750,f6776,f6827,f6833,f6853,f6887,f6898,f6913,f6920,f6949,f6955,f6975,f6981,f6986,f6991,f6995,f7003,f7007,f7011,f7048,f7052,f7059,f7063,f7067,f7108,f7113,f7122,f7343,f7347,f7357,f7362,f7366,f7378,f7400,f7612,f7621,f7626,f7643,f7648,f7659,f7665,f7669,f7673,f7710,f7748,f7764,f7794,f7800,f7813,f7817,f7843,f7850,f7861,f7910,f7931,f7939,f7954,f7983,f7987,f7991,f8028,f8089,f8093,f8145,f8150,f8172,f8177,f8183,f8187,f8192,f8196,f8200,f8217,f8231,f8235,f8239,f8281,f8285,f8297,f8307,f8311,f8324,f8329,f8334,f8338,f8342,f8346,f8362,f8371,f8379,f8390,f8395,f8401,f8516,f8520,f8535,f8545,f8591,f8640,f8644,f8727,f8731,f8735,f8739,f8749,f8785,f8824,f8839,f8851,f8865,f9008,f9016,f9031,f9035,f9061,f9065,f9069,f9073,f9082,f9086,f9090,f9094,f9098,f9111,f9118,f9146,f9181,f9223,f9231,f9243,f9254,f9311,f9314,f9316,f9340,f9351,f9381,f9383,f9427,f9460,f9518,f9524,f9566,f9571,f9642,f9647,f9718,f9724,f9729,f9738,f9778,f9780,f9782,f9784,f9786,f9799,f9845,f9854,f9861,f9865,f9871,f9880,f9885,f9891,f9895,f9899,f9903,f9907,f9911,f9915,f9919,f9923,f9927,f9931,f9936,f9950,f9963,f9967,f9982,f9995,f10014,f10070,f10076,f10080,f10084,f10159,f10163,f10167,f10239,f10243,f10247,f10251,f10255,f10259,f10263,f10284,f10289,f10314,f10322,f10327,f10351,f10357,f10361,f10366,f10371,f10381,f10385,f10423,f10427,f10431,f10442,f10446,f10457,f10462,f10477,f10502,f10506,f10510,f10535,f10579,f10605,f10610,f10625,f10630,f10634,f10685,f10713,f10728,f10732,f10746,f10751,f10755,f10758,f10788,f10792,f10800,f10804,f10808,f10868]) ).
fof(f10868,plain,
( ~ spl19_3
| spl19_101
| spl19_141
| ~ spl19_622 ),
inference(avatar_contradiction_clause,[],[f10867]) ).
fof(f10867,plain,
( $false
| ~ spl19_3
| spl19_101
| spl19_141
| ~ spl19_622 ),
inference(subsumption_resolution,[],[f10866,f1153]) ).
fof(f1153,plain,
( sK0 != sK1
| spl19_141 ),
inference(avatar_component_clause,[],[f1152]) ).
fof(f1152,plain,
( spl19_141
<=> sK0 = sK1 ),
introduced(avatar_definition,[new_symbols(naming,[spl19_141])]) ).
fof(f10866,plain,
( sK0 = sK1
| ~ spl19_3
| spl19_101
| ~ spl19_622 ),
inference(subsumption_resolution,[],[f10818,f870]) ).
fof(f870,plain,
( ~ in(sK0,sK1)
| spl19_101 ),
inference(avatar_component_clause,[],[f868]) ).
fof(f868,plain,
( spl19_101
<=> in(sK0,sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_101])]) ).
fof(f10818,plain,
( in(sK0,sK1)
| sK0 = sK1
| ~ spl19_3
| ~ spl19_622 ),
inference(resolution,[],[f10288,f275]) ).
fof(f275,plain,
( in(sK0,succ(sK1))
| ~ spl19_3 ),
inference(avatar_component_clause,[],[f273]) ).
fof(f273,plain,
( spl19_3
<=> in(sK0,succ(sK1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_3])]) ).
fof(f10288,plain,
( ! [X2,X3] :
( ~ in(X2,succ(X3))
| in(X2,X3)
| X2 = X3 )
| ~ spl19_622 ),
inference(avatar_component_clause,[],[f10287]) ).
fof(f10287,plain,
( spl19_622
<=> ! [X2,X3] :
( in(X2,X3)
| ~ in(X2,succ(X3))
| X2 = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_622])]) ).
fof(f10808,plain,
( spl19_663
| ~ spl19_280
| ~ spl19_585 ),
inference(avatar_split_clause,[],[f10553,f9869,f3455,f10806]) ).
fof(f10806,plain,
( spl19_663
<=> ! [X29,X27,X28] :
( ~ in(set_union2(powerset(sK0),X27),X28)
| ~ in(set_union2(X28,X29),sK0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_663])]) ).
fof(f3455,plain,
( spl19_280
<=> ! [X6] :
( in(X6,powerset(sK0))
| ~ in(X6,sK0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_280])]) ).
fof(f9869,plain,
( spl19_585
<=> ! [X10,X7,X9,X8] :
( ~ in(set_union2(X7,X8),X9)
| ~ in(set_union2(X9,X10),X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_585])]) ).
fof(f10553,plain,
( ! [X28,X29,X27] :
( ~ in(set_union2(powerset(sK0),X27),X28)
| ~ in(set_union2(X28,X29),sK0) )
| ~ spl19_280
| ~ spl19_585 ),
inference(resolution,[],[f9870,f3456]) ).
fof(f3456,plain,
( ! [X6] :
( in(X6,powerset(sK0))
| ~ in(X6,sK0) )
| ~ spl19_280 ),
inference(avatar_component_clause,[],[f3455]) ).
fof(f9870,plain,
( ! [X10,X8,X9,X7] :
( ~ in(set_union2(X9,X10),X7)
| ~ in(set_union2(X7,X8),X9) )
| ~ spl19_585 ),
inference(avatar_component_clause,[],[f9869]) ).
fof(f10804,plain,
( spl19_662
| ~ spl19_280
| ~ spl19_584 ),
inference(avatar_split_clause,[],[f10518,f9863,f3455,f10802]) ).
fof(f10802,plain,
( spl19_662
<=> ! [X29,X27,X28] :
( ~ in(set_union2(X27,powerset(sK0)),X28)
| ~ in(set_union2(X29,X28),sK0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_662])]) ).
fof(f9863,plain,
( spl19_584
<=> ! [X13,X12,X11,X14] :
( ~ in(set_union2(X11,X12),X13)
| ~ in(set_union2(X14,X13),X12) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_584])]) ).
fof(f10518,plain,
( ! [X28,X29,X27] :
( ~ in(set_union2(X27,powerset(sK0)),X28)
| ~ in(set_union2(X29,X28),sK0) )
| ~ spl19_280
| ~ spl19_584 ),
inference(resolution,[],[f9864,f3456]) ).
fof(f9864,plain,
( ! [X11,X14,X12,X13] :
( ~ in(set_union2(X14,X13),X12)
| ~ in(set_union2(X11,X12),X13) )
| ~ spl19_584 ),
inference(avatar_component_clause,[],[f9863]) ).
fof(f10800,plain,
( spl19_661
| ~ spl19_280
| ~ spl19_582 ),
inference(avatar_split_clause,[],[f10485,f9852,f3455,f10798]) ).
fof(f10798,plain,
( spl19_661
<=> ! [X29,X27,X28] :
( ~ in(set_union2(powerset(sK0),X27),X28)
| ~ in(set_union2(X29,X28),sK0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_661])]) ).
fof(f9852,plain,
( spl19_582
<=> ! [X9,X8,X7,X10] :
( ~ in(set_union2(X7,X8),X9)
| ~ in(set_union2(X10,X9),X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_582])]) ).
fof(f10485,plain,
( ! [X28,X29,X27] :
( ~ in(set_union2(powerset(sK0),X27),X28)
| ~ in(set_union2(X29,X28),sK0) )
| ~ spl19_280
| ~ spl19_582 ),
inference(resolution,[],[f9853,f3456]) ).
fof(f9853,plain,
( ! [X10,X8,X9,X7] :
( ~ in(set_union2(X10,X9),X7)
| ~ in(set_union2(X7,X8),X9) )
| ~ spl19_582 ),
inference(avatar_component_clause,[],[f9852]) ).
fof(f10792,plain,
( spl19_660
| ~ spl19_57
| ~ spl19_658 ),
inference(avatar_split_clause,[],[f10776,f10753,f541,f10790]) ).
fof(f10790,plain,
( spl19_660
<=> ! [X14,X15] :
( ~ in(succ(X14),sK1)
| ~ in(set_union2(X15,sK0),singleton(X14)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_660])]) ).
fof(f541,plain,
( spl19_57
<=> ! [X0] : succ(X0) = set_union2(X0,singleton(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_57])]) ).
fof(f10753,plain,
( spl19_658
<=> ! [X2,X4,X3] :
( ~ in(set_union2(X3,X2),sK1)
| ~ in(set_union2(X4,sK0),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_658])]) ).
fof(f10776,plain,
( ! [X14,X15] :
( ~ in(succ(X14),sK1)
| ~ in(set_union2(X15,sK0),singleton(X14)) )
| ~ spl19_57
| ~ spl19_658 ),
inference(superposition,[],[f10754,f542]) ).
fof(f542,plain,
( ! [X0] : succ(X0) = set_union2(X0,singleton(X0))
| ~ spl19_57 ),
inference(avatar_component_clause,[],[f541]) ).
fof(f10754,plain,
( ! [X2,X3,X4] :
( ~ in(set_union2(X3,X2),sK1)
| ~ in(set_union2(X4,sK0),X2) )
| ~ spl19_658 ),
inference(avatar_component_clause,[],[f10753]) ).
fof(f10788,plain,
( spl19_659
| ~ spl19_57
| ~ spl19_655 ),
inference(avatar_split_clause,[],[f10764,f10726,f541,f10786]) ).
fof(f10786,plain,
( spl19_659
<=> ! [X14,X15] :
( ~ in(succ(X14),sK1)
| ~ in(set_union2(sK0,X15),singleton(X14)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_659])]) ).
fof(f10726,plain,
( spl19_655
<=> ! [X2,X4,X3] :
( ~ in(set_union2(X3,X2),sK1)
| ~ in(set_union2(sK0,X4),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_655])]) ).
fof(f10764,plain,
( ! [X14,X15] :
( ~ in(succ(X14),sK1)
| ~ in(set_union2(sK0,X15),singleton(X14)) )
| ~ spl19_57
| ~ spl19_655 ),
inference(superposition,[],[f10727,f542]) ).
fof(f10727,plain,
( ! [X2,X3,X4] :
( ~ in(set_union2(X3,X2),sK1)
| ~ in(set_union2(sK0,X4),X2) )
| ~ spl19_655 ),
inference(avatar_component_clause,[],[f10726]) ).
fof(f10758,plain,
( spl19_657
| spl19_657
| ~ spl19_481
| ~ spl19_652 ),
inference(avatar_split_clause,[],[f10708,f10632,f7859,f10744,f10744]) ).
fof(f10744,plain,
( spl19_657
<=> ! [X0] : ~ in(set_union2(X0,sK0),sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_657])]) ).
fof(f7859,plain,
( spl19_481
<=> ! [X3] : set_union2(X3,sK0) = set_union2(sK1,set_union2(X3,sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_481])]) ).
fof(f10632,plain,
( spl19_652
<=> ! [X34,X35,X33] :
( ~ in(set_union2(X33,sK0),X34)
| ~ in(set_union2(X34,X35),sK1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_652])]) ).
fof(f10708,plain,
( ! [X24,X23] :
( ~ in(set_union2(X23,sK0),sK1)
| ~ in(set_union2(X24,sK0),sK1) )
| ~ spl19_481
| ~ spl19_652 ),
inference(superposition,[],[f10633,f7860]) ).
fof(f7860,plain,
( ! [X3] : set_union2(X3,sK0) = set_union2(sK1,set_union2(X3,sK0))
| ~ spl19_481 ),
inference(avatar_component_clause,[],[f7859]) ).
fof(f10633,plain,
( ! [X34,X35,X33] :
( ~ in(set_union2(X34,X35),sK1)
| ~ in(set_union2(X33,sK0),X34) )
| ~ spl19_652 ),
inference(avatar_component_clause,[],[f10632]) ).
fof(f10755,plain,
( spl19_658
| ~ spl19_58
| ~ spl19_652 ),
inference(avatar_split_clause,[],[f10699,f10632,f545,f10753]) ).
fof(f545,plain,
( spl19_58
<=> ! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_58])]) ).
fof(f10699,plain,
( ! [X2,X3,X4] :
( ~ in(set_union2(X3,X2),sK1)
| ~ in(set_union2(X4,sK0),X2) )
| ~ spl19_58
| ~ spl19_652 ),
inference(superposition,[],[f10633,f546]) ).
fof(f546,plain,
( ! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0)
| ~ spl19_58 ),
inference(avatar_component_clause,[],[f545]) ).
fof(f10751,plain,
( spl19_656
| spl19_657
| ~ spl19_481
| ~ spl19_651 ),
inference(avatar_split_clause,[],[f10680,f10628,f7859,f10744,f10730]) ).
fof(f10730,plain,
( spl19_656
<=> ! [X22] : ~ in(set_union2(sK0,X22),sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_656])]) ).
fof(f10628,plain,
( spl19_651
<=> ! [X32,X30,X31] :
( ~ in(set_union2(sK0,X30),X31)
| ~ in(set_union2(X31,X32),sK1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_651])]) ).
fof(f10680,plain,
( ! [X24,X23] :
( ~ in(set_union2(X23,sK0),sK1)
| ~ in(set_union2(sK0,X24),sK1) )
| ~ spl19_481
| ~ spl19_651 ),
inference(superposition,[],[f10629,f7860]) ).
fof(f10629,plain,
( ! [X31,X32,X30] :
( ~ in(set_union2(X31,X32),sK1)
| ~ in(set_union2(sK0,X30),X31) )
| ~ spl19_651 ),
inference(avatar_component_clause,[],[f10628]) ).
fof(f10746,plain,
( spl19_657
| ~ spl19_58
| ~ spl19_656 ),
inference(avatar_split_clause,[],[f10735,f10730,f545,f10744]) ).
fof(f10735,plain,
( ! [X0] : ~ in(set_union2(X0,sK0),sK1)
| ~ spl19_58
| ~ spl19_656 ),
inference(superposition,[],[f10731,f546]) ).
fof(f10731,plain,
( ! [X22] : ~ in(set_union2(sK0,X22),sK1)
| ~ spl19_656 ),
inference(avatar_component_clause,[],[f10730]) ).
fof(f10732,plain,
( spl19_656
| spl19_656
| ~ spl19_480
| ~ spl19_651 ),
inference(avatar_split_clause,[],[f10679,f10628,f7848,f10730,f10730]) ).
fof(f7848,plain,
( spl19_480
<=> ! [X1] : set_union2(sK0,X1) = set_union2(sK1,set_union2(sK0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_480])]) ).
fof(f10679,plain,
( ! [X21,X22] :
( ~ in(set_union2(sK0,X21),sK1)
| ~ in(set_union2(sK0,X22),sK1) )
| ~ spl19_480
| ~ spl19_651 ),
inference(superposition,[],[f10629,f7849]) ).
fof(f7849,plain,
( ! [X1] : set_union2(sK0,X1) = set_union2(sK1,set_union2(sK0,X1))
| ~ spl19_480 ),
inference(avatar_component_clause,[],[f7848]) ).
fof(f10728,plain,
( spl19_655
| ~ spl19_58
| ~ spl19_651 ),
inference(avatar_split_clause,[],[f10671,f10628,f545,f10726]) ).
fof(f10671,plain,
( ! [X2,X3,X4] :
( ~ in(set_union2(X3,X2),sK1)
| ~ in(set_union2(sK0,X4),X2) )
| ~ spl19_58
| ~ spl19_651 ),
inference(superposition,[],[f10629,f546]) ).
fof(f10713,plain,
( spl19_654
| ~ spl19_57
| ~ spl19_652 ),
inference(avatar_split_clause,[],[f10703,f10632,f541,f10711]) ).
fof(f10711,plain,
( spl19_654
<=> ! [X14,X15] :
( ~ in(succ(X14),sK1)
| ~ in(set_union2(X15,sK0),X14) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_654])]) ).
fof(f10703,plain,
( ! [X14,X15] :
( ~ in(succ(X14),sK1)
| ~ in(set_union2(X15,sK0),X14) )
| ~ spl19_57
| ~ spl19_652 ),
inference(superposition,[],[f10633,f542]) ).
fof(f10685,plain,
( spl19_653
| ~ spl19_57
| ~ spl19_651 ),
inference(avatar_split_clause,[],[f10675,f10628,f541,f10683]) ).
fof(f10683,plain,
( spl19_653
<=> ! [X14,X15] :
( ~ in(succ(X14),sK1)
| ~ in(set_union2(sK0,X15),X14) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_653])]) ).
fof(f10675,plain,
( ! [X14,X15] :
( ~ in(succ(X14),sK1)
| ~ in(set_union2(sK0,X15),X14) )
| ~ spl19_57
| ~ spl19_651 ),
inference(superposition,[],[f10629,f542]) ).
fof(f10634,plain,
( spl19_652
| ~ spl19_481
| ~ spl19_585 ),
inference(avatar_split_clause,[],[f10565,f9869,f7859,f10632]) ).
fof(f10565,plain,
( ! [X34,X35,X33] :
( ~ in(set_union2(X33,sK0),X34)
| ~ in(set_union2(X34,X35),sK1) )
| ~ spl19_481
| ~ spl19_585 ),
inference(superposition,[],[f9870,f7860]) ).
fof(f10630,plain,
( spl19_651
| ~ spl19_480
| ~ spl19_585 ),
inference(avatar_split_clause,[],[f10564,f9869,f7848,f10628]) ).
fof(f10564,plain,
( ! [X31,X32,X30] :
( ~ in(set_union2(sK0,X30),X31)
| ~ in(set_union2(X31,X32),sK1) )
| ~ spl19_480
| ~ spl19_585 ),
inference(superposition,[],[f9870,f7849]) ).
fof(f10625,plain,
( spl19_650
| spl19_282
| ~ spl19_349
| ~ spl19_588 ),
inference(avatar_split_clause,[],[f10620,f9889,f4951,f3514,f10622]) ).
fof(f10622,plain,
( spl19_650
<=> element(sK3(sK3(empty_set)),sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_650])]) ).
fof(f3514,plain,
( spl19_282
<=> empty(sK3(empty_set)) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_282])]) ).
fof(f4951,plain,
( spl19_349
<=> empty_set = powerset(sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_349])]) ).
fof(f9889,plain,
( spl19_588
<=> ! [X1] :
( element(sK3(sK3(powerset(X1))),X1)
| empty(sK3(powerset(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_588])]) ).
fof(f10620,plain,
( element(sK3(sK3(empty_set)),sK1)
| spl19_282
| ~ spl19_349
| ~ spl19_588 ),
inference(subsumption_resolution,[],[f10617,f3516]) ).
fof(f3516,plain,
( ~ empty(sK3(empty_set))
| spl19_282 ),
inference(avatar_component_clause,[],[f3514]) ).
fof(f10617,plain,
( element(sK3(sK3(empty_set)),sK1)
| empty(sK3(empty_set))
| ~ spl19_349
| ~ spl19_588 ),
inference(superposition,[],[f9890,f4953]) ).
fof(f4953,plain,
( empty_set = powerset(sK1)
| ~ spl19_349 ),
inference(avatar_component_clause,[],[f4951]) ).
fof(f9890,plain,
( ! [X1] :
( element(sK3(sK3(powerset(X1))),X1)
| empty(sK3(powerset(X1))) )
| ~ spl19_588 ),
inference(avatar_component_clause,[],[f9889]) ).
fof(f10610,plain,
( spl19_649
| ~ spl19_310
| ~ spl19_640 ),
inference(avatar_split_clause,[],[f10471,f10454,f3781,f10608]) ).
fof(f10608,plain,
( spl19_649
<=> ! [X0] :
( ~ in(X0,sK5(empty_set,empty_set,sK3(empty_set)))
| in(X0,sK0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_649])]) ).
fof(f3781,plain,
( spl19_310
<=> ! [X0,X1] :
( ~ in(X0,X1)
| ~ in(X1,sK0)
| in(X0,sK0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_310])]) ).
fof(f10454,plain,
( spl19_640
<=> in(sK5(empty_set,empty_set,sK3(empty_set)),sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_640])]) ).
fof(f10471,plain,
( ! [X0] :
( ~ in(X0,sK5(empty_set,empty_set,sK3(empty_set)))
| in(X0,sK0) )
| ~ spl19_310
| ~ spl19_640 ),
inference(resolution,[],[f10456,f3782]) ).
fof(f3782,plain,
( ! [X0,X1] :
( ~ in(X1,sK0)
| ~ in(X0,X1)
| in(X0,sK0) )
| ~ spl19_310 ),
inference(avatar_component_clause,[],[f3781]) ).
fof(f10456,plain,
( in(sK5(empty_set,empty_set,sK3(empty_set)),sK0)
| ~ spl19_640 ),
inference(avatar_component_clause,[],[f10454]) ).
fof(f10605,plain,
( spl19_648
| ~ spl19_57
| ~ spl19_646 ),
inference(avatar_split_clause,[],[f10588,f10533,f541,f10602]) ).
fof(f10602,plain,
( spl19_648
<=> in(sK5(empty_set,empty_set,sK3(empty_set)),succ(sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_648])]) ).
fof(f10533,plain,
( spl19_646
<=> ! [X3] : in(sK5(empty_set,empty_set,sK3(empty_set)),set_union2(sK0,X3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_646])]) ).
fof(f10588,plain,
( in(sK5(empty_set,empty_set,sK3(empty_set)),succ(sK0))
| ~ spl19_57
| ~ spl19_646 ),
inference(superposition,[],[f10534,f542]) ).
fof(f10534,plain,
( ! [X3] : in(sK5(empty_set,empty_set,sK3(empty_set)),set_union2(sK0,X3))
| ~ spl19_646 ),
inference(avatar_component_clause,[],[f10533]) ).
fof(f10579,plain,
( ~ spl19_647
| ~ spl19_57
| ~ spl19_645 ),
inference(avatar_split_clause,[],[f10573,f10508,f541,f10576]) ).
fof(f10576,plain,
( spl19_647
<=> in(succ(sK0),sK5(empty_set,empty_set,sK3(empty_set))) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_647])]) ).
fof(f10508,plain,
( spl19_645
<=> ! [X2] : ~ in(set_union2(sK0,X2),sK5(empty_set,empty_set,sK3(empty_set))) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_645])]) ).
fof(f10573,plain,
( ~ in(succ(sK0),sK5(empty_set,empty_set,sK3(empty_set)))
| ~ spl19_57
| ~ spl19_645 ),
inference(superposition,[],[f10509,f542]) ).
fof(f10509,plain,
( ! [X2] : ~ in(set_union2(sK0,X2),sK5(empty_set,empty_set,sK3(empty_set)))
| ~ spl19_645 ),
inference(avatar_component_clause,[],[f10508]) ).
fof(f10535,plain,
( spl19_646
| ~ spl19_503
| ~ spl19_637 ),
inference(avatar_split_clause,[],[f10450,f10435,f8233,f10533]) ).
fof(f8233,plain,
( spl19_503
<=> ! [X6,X7] :
( in(X7,set_union2(sK0,X6))
| ~ in(X7,sK1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_503])]) ).
fof(f10435,plain,
( spl19_637
<=> in(sK5(empty_set,empty_set,sK3(empty_set)),sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_637])]) ).
fof(f10450,plain,
( ! [X3] : in(sK5(empty_set,empty_set,sK3(empty_set)),set_union2(sK0,X3))
| ~ spl19_503
| ~ spl19_637 ),
inference(resolution,[],[f10437,f8234]) ).
fof(f8234,plain,
( ! [X6,X7] :
( ~ in(X7,sK1)
| in(X7,set_union2(sK0,X6)) )
| ~ spl19_503 ),
inference(avatar_component_clause,[],[f8233]) ).
fof(f10437,plain,
( in(sK5(empty_set,empty_set,sK3(empty_set)),sK1)
| ~ spl19_637 ),
inference(avatar_component_clause,[],[f10435]) ).
fof(f10510,plain,
( spl19_645
| ~ spl19_504
| ~ spl19_637 ),
inference(avatar_split_clause,[],[f10449,f10435,f8237,f10508]) ).
fof(f8237,plain,
( spl19_504
<=> ! [X16,X17] :
( ~ in(set_union2(sK0,X16),X17)
| ~ in(X17,sK1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_504])]) ).
fof(f10449,plain,
( ! [X2] : ~ in(set_union2(sK0,X2),sK5(empty_set,empty_set,sK3(empty_set)))
| ~ spl19_504
| ~ spl19_637 ),
inference(resolution,[],[f10437,f8238]) ).
fof(f8238,plain,
( ! [X16,X17] :
( ~ in(X17,sK1)
| ~ in(set_union2(sK0,X16),X17) )
| ~ spl19_504 ),
inference(avatar_component_clause,[],[f8237]) ).
fof(f10506,plain,
( spl19_644
| ~ spl19_528
| ~ spl19_637 ),
inference(avatar_split_clause,[],[f10448,f10435,f8638,f10504]) ).
fof(f10504,plain,
( spl19_644
<=> ! [X1] : in(sK5(empty_set,empty_set,sK3(empty_set)),set_union2(X1,sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_644])]) ).
fof(f8638,plain,
( spl19_528
<=> ! [X6,X7] :
( in(X7,set_union2(X6,sK0))
| ~ in(X7,sK1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_528])]) ).
fof(f10448,plain,
( ! [X1] : in(sK5(empty_set,empty_set,sK3(empty_set)),set_union2(X1,sK0))
| ~ spl19_528
| ~ spl19_637 ),
inference(resolution,[],[f10437,f8639]) ).
fof(f8639,plain,
( ! [X6,X7] :
( ~ in(X7,sK1)
| in(X7,set_union2(X6,sK0)) )
| ~ spl19_528 ),
inference(avatar_component_clause,[],[f8638]) ).
fof(f10502,plain,
( spl19_643
| ~ spl19_529
| ~ spl19_637 ),
inference(avatar_split_clause,[],[f10447,f10435,f8642,f10500]) ).
fof(f10500,plain,
( spl19_643
<=> ! [X0] : ~ in(set_union2(X0,sK0),sK5(empty_set,empty_set,sK3(empty_set))) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_643])]) ).
fof(f8642,plain,
( spl19_529
<=> ! [X16,X17] :
( ~ in(set_union2(X16,sK0),X17)
| ~ in(X17,sK1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_529])]) ).
fof(f10447,plain,
( ! [X0] : ~ in(set_union2(X0,sK0),sK5(empty_set,empty_set,sK3(empty_set)))
| ~ spl19_529
| ~ spl19_637 ),
inference(resolution,[],[f10437,f8643]) ).
fof(f8643,plain,
( ! [X16,X17] :
( ~ in(X17,sK1)
| ~ in(set_union2(X16,sK0),X17) )
| ~ spl19_529 ),
inference(avatar_component_clause,[],[f8642]) ).
fof(f10477,plain,
( ~ spl19_642
| ~ spl19_52
| ~ spl19_640 ),
inference(avatar_split_clause,[],[f10472,f10454,f508,f10474]) ).
fof(f10474,plain,
( spl19_642
<=> in(sK0,sK5(empty_set,empty_set,sK3(empty_set))) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_642])]) ).
fof(f508,plain,
( spl19_52
<=> ! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_52])]) ).
fof(f10472,plain,
( ~ in(sK0,sK5(empty_set,empty_set,sK3(empty_set)))
| ~ spl19_52
| ~ spl19_640 ),
inference(resolution,[],[f10456,f509]) ).
fof(f509,plain,
( ! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) )
| ~ spl19_52 ),
inference(avatar_component_clause,[],[f508]) ).
fof(f10462,plain,
( ~ spl19_641
| ~ spl19_52
| ~ spl19_637 ),
inference(avatar_split_clause,[],[f10452,f10435,f508,f10459]) ).
fof(f10459,plain,
( spl19_641
<=> in(sK1,sK5(empty_set,empty_set,sK3(empty_set))) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_641])]) ).
fof(f10452,plain,
( ~ in(sK1,sK5(empty_set,empty_set,sK3(empty_set)))
| ~ spl19_52
| ~ spl19_637 ),
inference(resolution,[],[f10437,f509]) ).
fof(f10457,plain,
( spl19_640
| ~ spl19_313
| ~ spl19_637 ),
inference(avatar_split_clause,[],[f10451,f10435,f3809,f10454]) ).
fof(f3809,plain,
( spl19_313
<=> ! [X3] :
( ~ in(X3,sK1)
| in(X3,sK0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_313])]) ).
fof(f10451,plain,
( in(sK5(empty_set,empty_set,sK3(empty_set)),sK0)
| ~ spl19_313
| ~ spl19_637 ),
inference(resolution,[],[f10437,f3810]) ).
fof(f3810,plain,
( ! [X3] :
( ~ in(X3,sK1)
| in(X3,sK0) )
| ~ spl19_313 ),
inference(avatar_component_clause,[],[f3809]) ).
fof(f10446,plain,
( spl19_639
| ~ spl19_14
| ~ spl19_273 ),
inference(avatar_split_clause,[],[f3378,f3346,f328,f10444]) ).
fof(f10444,plain,
( spl19_639
<=> ! [X9] :
( ordinal_subset(X9,succ(sK8))
| ~ ordinal(X9)
| ~ subset(X9,succ(sK8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_639])]) ).
fof(f328,plain,
( spl19_14
<=> ordinal(sK8) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_14])]) ).
fof(f3346,plain,
( spl19_273
<=> ! [X2,X3] :
( ~ subset(X2,succ(X3))
| ordinal_subset(X2,succ(X3))
| ~ ordinal(X2)
| ~ ordinal(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_273])]) ).
fof(f3378,plain,
( ! [X9] :
( ordinal_subset(X9,succ(sK8))
| ~ ordinal(X9)
| ~ subset(X9,succ(sK8)) )
| ~ spl19_14
| ~ spl19_273 ),
inference(resolution,[],[f3347,f330]) ).
fof(f330,plain,
( ordinal(sK8)
| ~ spl19_14 ),
inference(avatar_component_clause,[],[f328]) ).
fof(f3347,plain,
( ! [X2,X3] :
( ~ ordinal(X3)
| ordinal_subset(X2,succ(X3))
| ~ ordinal(X2)
| ~ subset(X2,succ(X3)) )
| ~ spl19_273 ),
inference(avatar_component_clause,[],[f3346]) ).
fof(f10442,plain,
( spl19_637
| spl19_638
| ~ spl19_355
| ~ spl19_544 ),
inference(avatar_split_clause,[],[f9502,f9033,f5426,f10439,f10435]) ).
fof(f10439,plain,
( spl19_638
<=> empty_set = sK3(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_638])]) ).
fof(f5426,plain,
( spl19_355
<=> ! [X0] :
( ~ in(X0,sK3(empty_set))
| in(X0,sK1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_355])]) ).
fof(f9033,plain,
( spl19_544
<=> ! [X12] :
( in(sK5(empty_set,empty_set,X12),X12)
| empty_set = X12 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_544])]) ).
fof(f9502,plain,
( empty_set = sK3(empty_set)
| in(sK5(empty_set,empty_set,sK3(empty_set)),sK1)
| ~ spl19_355
| ~ spl19_544 ),
inference(resolution,[],[f9034,f5427]) ).
fof(f5427,plain,
( ! [X0] :
( ~ in(X0,sK3(empty_set))
| in(X0,sK1) )
| ~ spl19_355 ),
inference(avatar_component_clause,[],[f5426]) ).
fof(f9034,plain,
( ! [X12] :
( in(sK5(empty_set,empty_set,X12),X12)
| empty_set = X12 )
| ~ spl19_544 ),
inference(avatar_component_clause,[],[f9033]) ).
fof(f10431,plain,
( spl19_636
| ~ spl19_8
| ~ spl19_273 ),
inference(avatar_split_clause,[],[f3375,f3346,f298,f10429]) ).
fof(f10429,plain,
( spl19_636
<=> ! [X6] :
( ordinal_subset(X6,succ(empty_set))
| ~ ordinal(X6)
| ~ subset(X6,succ(empty_set)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_636])]) ).
fof(f298,plain,
( spl19_8
<=> ordinal(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_8])]) ).
fof(f3375,plain,
( ! [X6] :
( ordinal_subset(X6,succ(empty_set))
| ~ ordinal(X6)
| ~ subset(X6,succ(empty_set)) )
| ~ spl19_8
| ~ spl19_273 ),
inference(resolution,[],[f3347,f300]) ).
fof(f300,plain,
( ordinal(empty_set)
| ~ spl19_8 ),
inference(avatar_component_clause,[],[f298]) ).
fof(f10427,plain,
( spl19_635
| ~ spl19_490
| ~ spl19_514 ),
inference(avatar_split_clause,[],[f9412,f8340,f8087,f10425]) ).
fof(f10425,plain,
( spl19_635
<=> ! [X18,X19] :
( ~ in(set_union2(succ(sK0),X18),X19)
| ~ in(succ(X19),sK1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_635])]) ).
fof(f8087,plain,
( spl19_490
<=> ! [X1] :
( in(X1,succ(sK0))
| ~ in(X1,sK1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_490])]) ).
fof(f8340,plain,
( spl19_514
<=> ! [X2,X4,X3] :
( ~ in(succ(X2),X3)
| ~ in(set_union2(X3,X4),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_514])]) ).
fof(f9412,plain,
( ! [X18,X19] :
( ~ in(set_union2(succ(sK0),X18),X19)
| ~ in(succ(X19),sK1) )
| ~ spl19_490
| ~ spl19_514 ),
inference(resolution,[],[f8341,f8088]) ).
fof(f8088,plain,
( ! [X1] :
( in(X1,succ(sK0))
| ~ in(X1,sK1) )
| ~ spl19_490 ),
inference(avatar_component_clause,[],[f8087]) ).
fof(f8341,plain,
( ! [X2,X3,X4] :
( ~ in(succ(X2),X3)
| ~ in(set_union2(X3,X4),X2) )
| ~ spl19_514 ),
inference(avatar_component_clause,[],[f8340]) ).
fof(f10423,plain,
( spl19_634
| ~ spl19_490
| ~ spl19_506 ),
inference(avatar_split_clause,[],[f9215,f8283,f8087,f10421]) ).
fof(f10421,plain,
( spl19_634
<=> ! [X18,X19] :
( ~ in(set_union2(X18,succ(sK0)),X19)
| ~ in(succ(X19),sK1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_634])]) ).
fof(f8283,plain,
( spl19_506
<=> ! [X2,X4,X3] :
( ~ in(succ(X2),X3)
| ~ in(set_union2(X4,X3),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_506])]) ).
fof(f9215,plain,
( ! [X18,X19] :
( ~ in(set_union2(X18,succ(sK0)),X19)
| ~ in(succ(X19),sK1) )
| ~ spl19_490
| ~ spl19_506 ),
inference(resolution,[],[f8284,f8088]) ).
fof(f8284,plain,
( ! [X2,X3,X4] :
( ~ in(succ(X2),X3)
| ~ in(set_union2(X4,X3),X2) )
| ~ spl19_506 ),
inference(avatar_component_clause,[],[f8283]) ).
fof(f10385,plain,
( spl19_633
| ~ spl19_310
| ~ spl19_576 ),
inference(avatar_split_clause,[],[f9719,f9715,f3781,f10383]) ).
fof(f10383,plain,
( spl19_633
<=> ! [X0] :
( ~ in(X0,sK5(empty_set,empty_set,sK3(sK1)))
| in(X0,sK0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_633])]) ).
fof(f9715,plain,
( spl19_576
<=> in(sK5(empty_set,empty_set,sK3(sK1)),sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_576])]) ).
fof(f9719,plain,
( ! [X0] :
( ~ in(X0,sK5(empty_set,empty_set,sK3(sK1)))
| in(X0,sK0) )
| ~ spl19_310
| ~ spl19_576 ),
inference(resolution,[],[f9717,f3782]) ).
fof(f9717,plain,
( in(sK5(empty_set,empty_set,sK3(sK1)),sK0)
| ~ spl19_576 ),
inference(avatar_component_clause,[],[f9715]) ).
fof(f10381,plain,
( spl19_632
| ~ spl19_14
| ~ spl19_272 ),
inference(avatar_split_clause,[],[f3368,f3340,f328,f10379]) ).
fof(f10379,plain,
( spl19_632
<=> ! [X9] :
( subset(X9,succ(sK8))
| ~ ordinal(X9)
| ~ ordinal_subset(X9,succ(sK8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_632])]) ).
fof(f3340,plain,
( spl19_272
<=> ! [X2,X3] :
( ~ ordinal_subset(X2,succ(X3))
| subset(X2,succ(X3))
| ~ ordinal(X2)
| ~ ordinal(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_272])]) ).
fof(f3368,plain,
( ! [X9] :
( subset(X9,succ(sK8))
| ~ ordinal(X9)
| ~ ordinal_subset(X9,succ(sK8)) )
| ~ spl19_14
| ~ spl19_272 ),
inference(resolution,[],[f3341,f330]) ).
fof(f3341,plain,
( ! [X2,X3] :
( ~ ordinal(X3)
| subset(X2,succ(X3))
| ~ ordinal(X2)
| ~ ordinal_subset(X2,succ(X3)) )
| ~ spl19_272 ),
inference(avatar_component_clause,[],[f3340]) ).
fof(f10371,plain,
( spl19_631
| ~ spl19_394
| ~ spl19_559 ),
inference(avatar_split_clause,[],[f9207,f9179,f6163,f10369]) ).
fof(f10369,plain,
( spl19_631
<=> ! [X0] :
( succ(sK1) = X0
| ~ empty(X0)
| ordinal_subset(X0,succ(sK1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_631])]) ).
fof(f6163,plain,
( spl19_394
<=> ! [X5] :
( ordinal_subset(X5,succ(sK1))
| ordinal_subset(succ(sK1),X5)
| ~ empty(X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_394])]) ).
fof(f9179,plain,
( spl19_559
<=> ! [X0] :
( succ(sK1) = X0
| ~ ordinal_subset(succ(sK1),X0)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_559])]) ).
fof(f9207,plain,
( ! [X0] :
( succ(sK1) = X0
| ~ empty(X0)
| ordinal_subset(X0,succ(sK1)) )
| ~ spl19_394
| ~ spl19_559 ),
inference(duplicate_literal_removal,[],[f9182]) ).
fof(f9182,plain,
( ! [X0] :
( succ(sK1) = X0
| ~ empty(X0)
| ordinal_subset(X0,succ(sK1))
| ~ empty(X0) )
| ~ spl19_394
| ~ spl19_559 ),
inference(resolution,[],[f9180,f6164]) ).
fof(f6164,plain,
( ! [X5] :
( ordinal_subset(succ(sK1),X5)
| ordinal_subset(X5,succ(sK1))
| ~ empty(X5) )
| ~ spl19_394 ),
inference(avatar_component_clause,[],[f6163]) ).
fof(f9180,plain,
( ! [X0] :
( ~ ordinal_subset(succ(sK1),X0)
| succ(sK1) = X0
| ~ empty(X0) )
| ~ spl19_559 ),
inference(avatar_component_clause,[],[f9179]) ).
fof(f10366,plain,
( spl19_630
| ~ spl19_8
| ~ spl19_272 ),
inference(avatar_split_clause,[],[f3365,f3340,f298,f10364]) ).
fof(f10364,plain,
( spl19_630
<=> ! [X6] :
( subset(X6,succ(empty_set))
| ~ ordinal(X6)
| ~ ordinal_subset(X6,succ(empty_set)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_630])]) ).
fof(f3365,plain,
( ! [X6] :
( subset(X6,succ(empty_set))
| ~ ordinal(X6)
| ~ ordinal_subset(X6,succ(empty_set)) )
| ~ spl19_8
| ~ spl19_272 ),
inference(resolution,[],[f3341,f300]) ).
fof(f10361,plain,
( spl19_629
| ~ spl19_280
| ~ spl19_514 ),
inference(avatar_split_clause,[],[f9415,f8340,f3455,f10359]) ).
fof(f10359,plain,
( spl19_629
<=> ! [X25,X26] :
( ~ in(set_union2(powerset(sK0),X25),X26)
| ~ in(succ(X26),sK0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_629])]) ).
fof(f9415,plain,
( ! [X26,X25] :
( ~ in(set_union2(powerset(sK0),X25),X26)
| ~ in(succ(X26),sK0) )
| ~ spl19_280
| ~ spl19_514 ),
inference(resolution,[],[f8341,f3456]) ).
fof(f10357,plain,
( spl19_628
| ~ spl19_280
| ~ spl19_506 ),
inference(avatar_split_clause,[],[f9218,f8283,f3455,f10355]) ).
fof(f10355,plain,
( spl19_628
<=> ! [X25,X26] :
( ~ in(set_union2(X25,powerset(sK0)),X26)
| ~ in(succ(X26),sK0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_628])]) ).
fof(f9218,plain,
( ! [X26,X25] :
( ~ in(set_union2(X25,powerset(sK0)),X26)
| ~ in(succ(X26),sK0) )
| ~ spl19_280
| ~ spl19_506 ),
inference(resolution,[],[f8284,f3456]) ).
fof(f10351,plain,
( spl19_627
| ~ spl19_14
| ~ spl19_271 ),
inference(avatar_split_clause,[],[f3357,f3332,f328,f10349]) ).
fof(f10349,plain,
( spl19_627
<=> ! [X9] :
( ordinal_subset(succ(sK8),X9)
| ~ ordinal(X9)
| ordinal_subset(X9,succ(sK8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_627])]) ).
fof(f3332,plain,
( spl19_271
<=> ! [X2,X3] :
( ordinal_subset(X2,succ(X3))
| ordinal_subset(succ(X3),X2)
| ~ ordinal(X2)
| ~ ordinal(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_271])]) ).
fof(f3357,plain,
( ! [X9] :
( ordinal_subset(succ(sK8),X9)
| ~ ordinal(X9)
| ordinal_subset(X9,succ(sK8)) )
| ~ spl19_14
| ~ spl19_271 ),
inference(resolution,[],[f3333,f330]) ).
fof(f3333,plain,
( ! [X2,X3] :
( ~ ordinal(X3)
| ordinal_subset(succ(X3),X2)
| ~ ordinal(X2)
| ordinal_subset(X2,succ(X3)) )
| ~ spl19_271 ),
inference(avatar_component_clause,[],[f3332]) ).
fof(f10327,plain,
( spl19_626
| ~ spl19_5
| ~ spl19_616
| spl19_624 ),
inference(avatar_split_clause,[],[f10318,f10311,f10245,f283,f10324]) ).
fof(f10324,plain,
( spl19_626
<=> ordinal_subset(empty_set,succ(sK8)) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_626])]) ).
fof(f283,plain,
( spl19_5
<=> empty(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_5])]) ).
fof(f10245,plain,
( spl19_616
<=> ! [X6] :
( ordinal_subset(X6,succ(sK8))
| ordinal_subset(succ(sK8),X6)
| ~ empty(X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_616])]) ).
fof(f10311,plain,
( spl19_624
<=> ordinal_subset(succ(sK8),empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_624])]) ).
fof(f10318,plain,
( ordinal_subset(empty_set,succ(sK8))
| ~ spl19_5
| ~ spl19_616
| spl19_624 ),
inference(subsumption_resolution,[],[f10315,f285]) ).
fof(f285,plain,
( empty(empty_set)
| ~ spl19_5 ),
inference(avatar_component_clause,[],[f283]) ).
fof(f10315,plain,
( ordinal_subset(empty_set,succ(sK8))
| ~ empty(empty_set)
| ~ spl19_616
| spl19_624 ),
inference(resolution,[],[f10313,f10246]) ).
fof(f10246,plain,
( ! [X6] :
( ordinal_subset(succ(sK8),X6)
| ordinal_subset(X6,succ(sK8))
| ~ empty(X6) )
| ~ spl19_616 ),
inference(avatar_component_clause,[],[f10245]) ).
fof(f10313,plain,
( ~ ordinal_subset(succ(sK8),empty_set)
| spl19_624 ),
inference(avatar_component_clause,[],[f10311]) ).
fof(f10322,plain,
( spl19_625
| ~ spl19_8
| ~ spl19_271 ),
inference(avatar_split_clause,[],[f3354,f3332,f298,f10320]) ).
fof(f10320,plain,
( spl19_625
<=> ! [X6] :
( ordinal_subset(succ(empty_set),X6)
| ~ ordinal(X6)
| ordinal_subset(X6,succ(empty_set)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_625])]) ).
fof(f3354,plain,
( ! [X6] :
( ordinal_subset(succ(empty_set),X6)
| ~ ordinal(X6)
| ordinal_subset(X6,succ(empty_set)) )
| ~ spl19_8
| ~ spl19_271 ),
inference(resolution,[],[f3333,f300]) ).
fof(f10314,plain,
( spl19_623
| ~ spl19_624
| ~ spl19_5
| ~ spl19_362
| ~ spl19_617 ),
inference(avatar_split_clause,[],[f10306,f10249,f5519,f283,f10311,f10308]) ).
fof(f10308,plain,
( spl19_623
<=> ! [X2] : ~ in(X2,succ(sK8)) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_623])]) ).
fof(f5519,plain,
( spl19_362
<=> ! [X2,X1] :
( ~ in(X1,X2)
| ~ subset(X2,empty_set) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_362])]) ).
fof(f10249,plain,
( spl19_617
<=> ! [X7] :
( subset(succ(sK8),X7)
| ~ ordinal_subset(succ(sK8),X7)
| ~ empty(X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_617])]) ).
fof(f10306,plain,
( ! [X2] :
( ~ ordinal_subset(succ(sK8),empty_set)
| ~ in(X2,succ(sK8)) )
| ~ spl19_5
| ~ spl19_362
| ~ spl19_617 ),
inference(subsumption_resolution,[],[f10301,f285]) ).
fof(f10301,plain,
( ! [X2] :
( ~ ordinal_subset(succ(sK8),empty_set)
| ~ empty(empty_set)
| ~ in(X2,succ(sK8)) )
| ~ spl19_362
| ~ spl19_617 ),
inference(resolution,[],[f10250,f5520]) ).
fof(f5520,plain,
( ! [X2,X1] :
( ~ subset(X2,empty_set)
| ~ in(X1,X2) )
| ~ spl19_362 ),
inference(avatar_component_clause,[],[f5519]) ).
fof(f10250,plain,
( ! [X7] :
( subset(succ(sK8),X7)
| ~ ordinal_subset(succ(sK8),X7)
| ~ empty(X7) )
| ~ spl19_617 ),
inference(avatar_component_clause,[],[f10249]) ).
fof(f10289,plain,
( spl19_622
| ~ spl19_70
| ~ spl19_256 ),
inference(avatar_split_clause,[],[f3103,f2930,f616,f10287]) ).
fof(f616,plain,
( spl19_70
<=> ! [X0,X3] :
( X0 = X3
| ~ in(X3,singleton(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_70])]) ).
fof(f2930,plain,
( spl19_256
<=> ! [X9,X8] :
( ~ in(X9,succ(X8))
| in(X9,X8)
| in(X9,singleton(X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_256])]) ).
fof(f3103,plain,
( ! [X2,X3] :
( in(X2,X3)
| ~ in(X2,succ(X3))
| X2 = X3 )
| ~ spl19_70
| ~ spl19_256 ),
inference(resolution,[],[f2931,f617]) ).
fof(f617,plain,
( ! [X3,X0] :
( ~ in(X3,singleton(X0))
| X0 = X3 )
| ~ spl19_70 ),
inference(avatar_component_clause,[],[f616]) ).
fof(f2931,plain,
( ! [X8,X9] :
( in(X9,singleton(X8))
| in(X9,X8)
| ~ in(X9,succ(X8)) )
| ~ spl19_256 ),
inference(avatar_component_clause,[],[f2930]) ).
fof(f10284,plain,
( spl19_621
| ~ spl19_48
| ~ spl19_49
| ~ spl19_614 ),
inference(avatar_split_clause,[],[f10279,f10237,f496,f492,f10281]) ).
fof(f10281,plain,
( spl19_621
<=> epsilon_transitive(succ(succ(sK8))) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_621])]) ).
fof(f492,plain,
( spl19_48
<=> ! [X0] :
( epsilon_transitive(X0)
| in(sK2(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_48])]) ).
fof(f496,plain,
( spl19_49
<=> ! [X0] :
( epsilon_transitive(X0)
| ~ subset(sK2(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_49])]) ).
fof(f10237,plain,
( spl19_614
<=> ! [X5] :
( subset(X5,succ(succ(sK8)))
| ~ in(X5,succ(succ(sK8))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_614])]) ).
fof(f10279,plain,
( epsilon_transitive(succ(succ(sK8)))
| ~ spl19_48
| ~ spl19_49
| ~ spl19_614 ),
inference(subsumption_resolution,[],[f10276,f493]) ).
fof(f493,plain,
( ! [X0] :
( in(sK2(X0),X0)
| epsilon_transitive(X0) )
| ~ spl19_48 ),
inference(avatar_component_clause,[],[f492]) ).
fof(f10276,plain,
( ~ in(sK2(succ(succ(sK8))),succ(succ(sK8)))
| epsilon_transitive(succ(succ(sK8)))
| ~ spl19_49
| ~ spl19_614 ),
inference(resolution,[],[f10238,f497]) ).
fof(f497,plain,
( ! [X0] :
( ~ subset(sK2(X0),X0)
| epsilon_transitive(X0) )
| ~ spl19_49 ),
inference(avatar_component_clause,[],[f496]) ).
fof(f10238,plain,
( ! [X5] :
( subset(X5,succ(succ(sK8)))
| ~ in(X5,succ(succ(sK8))) )
| ~ spl19_614 ),
inference(avatar_component_clause,[],[f10237]) ).
fof(f10263,plain,
( spl19_620
| ~ spl19_32
| ~ spl19_236 ),
inference(avatar_split_clause,[],[f2862,f2670,f411,f10261]) ).
fof(f10261,plain,
( spl19_620
<=> ! [X0,X1] :
( ordinal_subset(X0,X1)
| ~ subset(X0,X1)
| ~ empty(X1)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_620])]) ).
fof(f411,plain,
( spl19_32
<=> ! [X0] :
( ordinal(X0)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_32])]) ).
fof(f2670,plain,
( spl19_236
<=> ! [X0,X1] :
( ~ subset(X0,X1)
| ordinal_subset(X0,X1)
| ~ ordinal(X0)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_236])]) ).
fof(f2862,plain,
( ! [X0,X1] :
( ordinal_subset(X0,X1)
| ~ subset(X0,X1)
| ~ empty(X1)
| ~ empty(X0) )
| ~ spl19_32
| ~ spl19_236 ),
inference(resolution,[],[f2671,f412]) ).
fof(f412,plain,
( ! [X0] :
( ordinal(X0)
| ~ empty(X0) )
| ~ spl19_32 ),
inference(avatar_component_clause,[],[f411]) ).
fof(f2671,plain,
( ! [X0,X1] :
( ~ ordinal(X0)
| ordinal_subset(X0,X1)
| ~ subset(X0,X1)
| ~ empty(X1) )
| ~ spl19_236 ),
inference(avatar_component_clause,[],[f2670]) ).
fof(f10259,plain,
( spl19_619
| ~ spl19_242
| ~ spl19_569 ),
inference(avatar_split_clause,[],[f9474,f9424,f2703,f10257]) ).
fof(f10257,plain,
( spl19_619
<=> ! [X9] :
( in(X9,succ(sK8))
| succ(sK8) = X9
| ~ empty(X9) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_619])]) ).
fof(f2703,plain,
( spl19_242
<=> ! [X0,X1] :
( X0 = X1
| in(X1,X0)
| ~ ordinal(X0)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_242])]) ).
fof(f9424,plain,
( spl19_569
<=> ordinal(succ(sK8)) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_569])]) ).
fof(f9474,plain,
( ! [X9] :
( in(X9,succ(sK8))
| succ(sK8) = X9
| ~ empty(X9) )
| ~ spl19_242
| ~ spl19_569 ),
inference(resolution,[],[f9425,f2704]) ).
fof(f2704,plain,
( ! [X0,X1] :
( ~ ordinal(X0)
| in(X1,X0)
| X0 = X1
| ~ empty(X1) )
| ~ spl19_242 ),
inference(avatar_component_clause,[],[f2703]) ).
fof(f9425,plain,
( ordinal(succ(sK8))
| ~ spl19_569 ),
inference(avatar_component_clause,[],[f9424]) ).
fof(f10255,plain,
( spl19_618
| ~ spl19_236
| ~ spl19_569 ),
inference(avatar_split_clause,[],[f9473,f9424,f2670,f10253]) ).
fof(f10253,plain,
( spl19_618
<=> ! [X8] :
( ordinal_subset(succ(sK8),X8)
| ~ subset(succ(sK8),X8)
| ~ empty(X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_618])]) ).
fof(f9473,plain,
( ! [X8] :
( ordinal_subset(succ(sK8),X8)
| ~ subset(succ(sK8),X8)
| ~ empty(X8) )
| ~ spl19_236
| ~ spl19_569 ),
inference(resolution,[],[f9425,f2671]) ).
fof(f10251,plain,
( spl19_617
| ~ spl19_234
| ~ spl19_569 ),
inference(avatar_split_clause,[],[f9472,f9424,f2660,f10249]) ).
fof(f2660,plain,
( spl19_234
<=> ! [X0,X1] :
( ~ ordinal_subset(X0,X1)
| subset(X0,X1)
| ~ ordinal(X0)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_234])]) ).
fof(f9472,plain,
( ! [X7] :
( subset(succ(sK8),X7)
| ~ ordinal_subset(succ(sK8),X7)
| ~ empty(X7) )
| ~ spl19_234
| ~ spl19_569 ),
inference(resolution,[],[f9425,f2661]) ).
fof(f2661,plain,
( ! [X0,X1] :
( ~ ordinal(X0)
| subset(X0,X1)
| ~ ordinal_subset(X0,X1)
| ~ empty(X1) )
| ~ spl19_234 ),
inference(avatar_component_clause,[],[f2660]) ).
fof(f10247,plain,
( spl19_616
| ~ spl19_230
| ~ spl19_569 ),
inference(avatar_split_clause,[],[f9471,f9424,f2626,f10245]) ).
fof(f2626,plain,
( spl19_230
<=> ! [X0,X1] :
( ordinal_subset(X0,X1)
| ordinal_subset(X1,X0)
| ~ ordinal(X0)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_230])]) ).
fof(f9471,plain,
( ! [X6] :
( ordinal_subset(X6,succ(sK8))
| ordinal_subset(succ(sK8),X6)
| ~ empty(X6) )
| ~ spl19_230
| ~ spl19_569 ),
inference(resolution,[],[f9425,f2627]) ).
fof(f2627,plain,
( ! [X0,X1] :
( ~ ordinal(X0)
| ordinal_subset(X1,X0)
| ordinal_subset(X0,X1)
| ~ empty(X1) )
| ~ spl19_230 ),
inference(avatar_component_clause,[],[f2626]) ).
fof(f10243,plain,
( spl19_615
| ~ spl19_32
| ~ spl19_234 ),
inference(avatar_split_clause,[],[f2827,f2660,f411,f10241]) ).
fof(f10241,plain,
( spl19_615
<=> ! [X0,X1] :
( subset(X0,X1)
| ~ ordinal_subset(X0,X1)
| ~ empty(X1)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_615])]) ).
fof(f2827,plain,
( ! [X0,X1] :
( subset(X0,X1)
| ~ ordinal_subset(X0,X1)
| ~ empty(X1)
| ~ empty(X0) )
| ~ spl19_32
| ~ spl19_234 ),
inference(resolution,[],[f2661,f412]) ).
fof(f10239,plain,
( spl19_614
| ~ spl19_228
| ~ spl19_569 ),
inference(avatar_split_clause,[],[f9470,f9424,f2595,f10237]) ).
fof(f2595,plain,
( spl19_228
<=> ! [X4,X5] :
( ~ in(X4,succ(X5))
| subset(X4,succ(X5))
| ~ ordinal(X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_228])]) ).
fof(f9470,plain,
( ! [X5] :
( subset(X5,succ(succ(sK8)))
| ~ in(X5,succ(succ(sK8))) )
| ~ spl19_228
| ~ spl19_569 ),
inference(resolution,[],[f9425,f2596]) ).
fof(f2596,plain,
( ! [X4,X5] :
( ~ ordinal(X5)
| subset(X4,succ(X5))
| ~ in(X4,succ(X5)) )
| ~ spl19_228 ),
inference(avatar_component_clause,[],[f2595]) ).
fof(f10167,plain,
( spl19_613
| ~ spl19_32
| ~ spl19_230 ),
inference(avatar_split_clause,[],[f2806,f2626,f411,f10165]) ).
fof(f10165,plain,
( spl19_613
<=> ! [X0,X1] :
( ordinal_subset(X0,X1)
| ordinal_subset(X1,X0)
| ~ empty(X0)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_613])]) ).
fof(f2806,plain,
( ! [X0,X1] :
( ordinal_subset(X0,X1)
| ordinal_subset(X1,X0)
| ~ empty(X0)
| ~ empty(X1) )
| ~ spl19_32
| ~ spl19_230 ),
inference(resolution,[],[f2627,f412]) ).
fof(f10163,plain,
( spl19_612
| ~ spl19_310
| ~ spl19_573 ),
inference(avatar_split_clause,[],[f9636,f9568,f3781,f10161]) ).
fof(f10161,plain,
( spl19_612
<=> ! [X0] :
( ~ in(X0,sK5(empty_set,empty_set,sK1))
| in(X0,sK0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_612])]) ).
fof(f9568,plain,
( spl19_573
<=> in(sK5(empty_set,empty_set,sK1),sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_573])]) ).
fof(f9636,plain,
( ! [X0] :
( ~ in(X0,sK5(empty_set,empty_set,sK1))
| in(X0,sK0) )
| ~ spl19_310
| ~ spl19_573 ),
inference(resolution,[],[f9570,f3782]) ).
fof(f9570,plain,
( in(sK5(empty_set,empty_set,sK1),sK0)
| ~ spl19_573 ),
inference(avatar_component_clause,[],[f9568]) ).
fof(f10159,plain,
( spl19_611
| ~ spl19_310
| ~ spl19_572 ),
inference(avatar_split_clause,[],[f9572,f9563,f3781,f10157]) ).
fof(f10157,plain,
( spl19_611
<=> ! [X0] :
( ~ in(X0,sK5(sK1,sK1,empty_set))
| in(X0,sK0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_611])]) ).
fof(f9563,plain,
( spl19_572
<=> in(sK5(sK1,sK1,empty_set),sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_572])]) ).
fof(f9572,plain,
( ! [X0] :
( ~ in(X0,sK5(sK1,sK1,empty_set))
| in(X0,sK0) )
| ~ spl19_310
| ~ spl19_572 ),
inference(resolution,[],[f9565,f3782]) ).
fof(f9565,plain,
( in(sK5(sK1,sK1,empty_set),sK0)
| ~ spl19_572 ),
inference(avatar_component_clause,[],[f9563]) ).
fof(f10084,plain,
( spl19_610
| spl19_146
| ~ spl19_310
| ~ spl19_544 ),
inference(avatar_split_clause,[],[f9507,f9033,f3781,f1326,f10082]) ).
fof(f10082,plain,
( spl19_610
<=> ! [X11] :
( ~ in(X11,sK5(empty_set,empty_set,sK0))
| in(X11,sK0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_610])]) ).
fof(f1326,plain,
( spl19_146
<=> empty_set = sK0 ),
introduced(avatar_definition,[new_symbols(naming,[spl19_146])]) ).
fof(f9507,plain,
( ! [X11] :
( ~ in(X11,sK5(empty_set,empty_set,sK0))
| in(X11,sK0) )
| spl19_146
| ~ spl19_310
| ~ spl19_544 ),
inference(subsumption_resolution,[],[f9495,f1327]) ).
fof(f1327,plain,
( empty_set != sK0
| spl19_146 ),
inference(avatar_component_clause,[],[f1326]) ).
fof(f9495,plain,
( ! [X11] :
( empty_set = sK0
| ~ in(X11,sK5(empty_set,empty_set,sK0))
| in(X11,sK0) )
| ~ spl19_310
| ~ spl19_544 ),
inference(resolution,[],[f9034,f3782]) ).
fof(f10080,plain,
( spl19_609
| spl19_146
| ~ spl19_310
| ~ spl19_543 ),
inference(avatar_split_clause,[],[f9450,f9014,f3781,f1326,f10078]) ).
fof(f10078,plain,
( spl19_609
<=> ! [X9] :
( ~ in(X9,sK5(sK0,sK0,empty_set))
| in(X9,sK0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_609])]) ).
fof(f9014,plain,
( spl19_543
<=> ! [X14] :
( in(sK5(X14,X14,empty_set),X14)
| empty_set = X14 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_543])]) ).
fof(f9450,plain,
( ! [X9] :
( ~ in(X9,sK5(sK0,sK0,empty_set))
| in(X9,sK0) )
| spl19_146
| ~ spl19_310
| ~ spl19_543 ),
inference(subsumption_resolution,[],[f9438,f1327]) ).
fof(f9438,plain,
( ! [X9] :
( empty_set = sK0
| ~ in(X9,sK5(sK0,sK0,empty_set))
| in(X9,sK0) )
| ~ spl19_310
| ~ spl19_543 ),
inference(resolution,[],[f9015,f3782]) ).
fof(f9015,plain,
( ! [X14] :
( in(sK5(X14,X14,empty_set),X14)
| empty_set = X14 )
| ~ spl19_543 ),
inference(avatar_component_clause,[],[f9014]) ).
fof(f10076,plain,
( ~ spl19_608
| ~ spl19_39
| spl19_525
| ~ spl19_604 ),
inference(avatar_split_clause,[],[f10029,f9989,f8532,f439,f10073]) ).
fof(f10073,plain,
( spl19_608
<=> ordinal_subset(sK3(empty_set),sK8) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_608])]) ).
fof(f439,plain,
( spl19_39
<=> ! [X0] :
( empty_set = X0
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_39])]) ).
fof(f8532,plain,
( spl19_525
<=> ordinal_subset(sK3(powerset(sK8)),sK8) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_525])]) ).
fof(f9989,plain,
( spl19_604
<=> empty(powerset(sK8)) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_604])]) ).
fof(f10029,plain,
( ~ ordinal_subset(sK3(empty_set),sK8)
| ~ spl19_39
| spl19_525
| ~ spl19_604 ),
inference(backward_demodulation,[],[f8533,f10015]) ).
fof(f10015,plain,
( empty_set = powerset(sK8)
| ~ spl19_39
| ~ spl19_604 ),
inference(resolution,[],[f9991,f440]) ).
fof(f440,plain,
( ! [X0] :
( ~ empty(X0)
| empty_set = X0 )
| ~ spl19_39 ),
inference(avatar_component_clause,[],[f439]) ).
fof(f9991,plain,
( empty(powerset(sK8))
| ~ spl19_604 ),
inference(avatar_component_clause,[],[f9989]) ).
fof(f8533,plain,
( ~ ordinal_subset(sK3(powerset(sK8)),sK8)
| spl19_525 ),
inference(avatar_component_clause,[],[f8532]) ).
fof(f10070,plain,
( spl19_607
| ~ spl19_57
| ~ spl19_598 ),
inference(avatar_split_clause,[],[f10064,f9929,f541,f10067]) ).
fof(f10067,plain,
( spl19_607
<=> in(sK5(empty_set,empty_set,sK1),succ(sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_607])]) ).
fof(f9929,plain,
( spl19_598
<=> ! [X15] : in(sK5(empty_set,empty_set,sK1),set_union2(sK0,X15)) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_598])]) ).
fof(f10064,plain,
( in(sK5(empty_set,empty_set,sK1),succ(sK0))
| ~ spl19_57
| ~ spl19_598 ),
inference(superposition,[],[f9930,f542]) ).
fof(f9930,plain,
( ! [X15] : in(sK5(empty_set,empty_set,sK1),set_union2(sK0,X15))
| ~ spl19_598 ),
inference(avatar_component_clause,[],[f9929]) ).
fof(f10014,plain,
( ~ spl19_606
| ~ spl19_57
| ~ spl19_596 ),
inference(avatar_split_clause,[],[f10008,f9921,f541,f10011]) ).
fof(f10011,plain,
( spl19_606
<=> in(succ(sK0),sK5(empty_set,empty_set,sK1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_606])]) ).
fof(f9921,plain,
( spl19_596
<=> ! [X14] : ~ in(set_union2(sK0,X14),sK5(empty_set,empty_set,sK1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_596])]) ).
fof(f10008,plain,
( ~ in(succ(sK0),sK5(empty_set,empty_set,sK1))
| ~ spl19_57
| ~ spl19_596 ),
inference(superposition,[],[f9922,f542]) ).
fof(f9922,plain,
( ! [X14] : ~ in(set_union2(sK0,X14),sK5(empty_set,empty_set,sK1))
| ~ spl19_596 ),
inference(avatar_component_clause,[],[f9921]) ).
fof(f9995,plain,
( spl19_604
| spl19_605
| ~ spl19_81
| ~ spl19_229 ),
inference(avatar_split_clause,[],[f2797,f2606,f699,f9993,f9989]) ).
fof(f9993,plain,
( spl19_605
<=> ! [X10] :
( in(X10,powerset(sK8))
| ~ in(X10,sK8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_605])]) ).
fof(f699,plain,
( spl19_81
<=> ! [X7] :
( ~ in(X7,sK8)
| subset(X7,sK8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_81])]) ).
fof(f2606,plain,
( spl19_229
<=> ! [X4,X3] :
( empty(powerset(X3))
| in(X4,powerset(X3))
| ~ subset(X4,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_229])]) ).
fof(f2797,plain,
( ! [X10] :
( in(X10,powerset(sK8))
| empty(powerset(sK8))
| ~ in(X10,sK8) )
| ~ spl19_81
| ~ spl19_229 ),
inference(resolution,[],[f2607,f700]) ).
fof(f700,plain,
( ! [X7] :
( subset(X7,sK8)
| ~ in(X7,sK8) )
| ~ spl19_81 ),
inference(avatar_component_clause,[],[f699]) ).
fof(f2607,plain,
( ! [X3,X4] :
( ~ subset(X4,X3)
| in(X4,powerset(X3))
| empty(powerset(X3)) )
| ~ spl19_229 ),
inference(avatar_component_clause,[],[f2606]) ).
fof(f9982,plain,
( spl19_603
| ~ spl19_57
| ~ spl19_592 ),
inference(avatar_split_clause,[],[f9976,f9905,f541,f9979]) ).
fof(f9979,plain,
( spl19_603
<=> in(sK5(sK1,sK1,empty_set),succ(sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_603])]) ).
fof(f9905,plain,
( spl19_592
<=> ! [X13] : in(sK5(sK1,sK1,empty_set),set_union2(sK0,X13)) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_592])]) ).
fof(f9976,plain,
( in(sK5(sK1,sK1,empty_set),succ(sK0))
| ~ spl19_57
| ~ spl19_592 ),
inference(superposition,[],[f9906,f542]) ).
fof(f9906,plain,
( ! [X13] : in(sK5(sK1,sK1,empty_set),set_union2(sK0,X13))
| ~ spl19_592 ),
inference(avatar_component_clause,[],[f9905]) ).
fof(f9967,plain,
( spl19_602
| ~ spl19_32
| ~ spl19_228 ),
inference(avatar_split_clause,[],[f2729,f2595,f411,f9965]) ).
fof(f9965,plain,
( spl19_602
<=> ! [X0,X1] :
( subset(X0,succ(X1))
| ~ in(X0,succ(X1))
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_602])]) ).
fof(f2729,plain,
( ! [X0,X1] :
( subset(X0,succ(X1))
| ~ in(X0,succ(X1))
| ~ empty(X1) )
| ~ spl19_32
| ~ spl19_228 ),
inference(resolution,[],[f2596,f412]) ).
fof(f9963,plain,
( ~ spl19_601
| ~ spl19_57
| ~ spl19_591 ),
inference(avatar_split_clause,[],[f9957,f9901,f541,f9960]) ).
fof(f9960,plain,
( spl19_601
<=> in(succ(sK0),sK5(sK1,sK1,empty_set)) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_601])]) ).
fof(f9901,plain,
( spl19_591
<=> ! [X12] : ~ in(set_union2(sK0,X12),sK5(sK1,sK1,empty_set)) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_591])]) ).
fof(f9957,plain,
( ~ in(succ(sK0),sK5(sK1,sK1,empty_set))
| ~ spl19_57
| ~ spl19_591 ),
inference(superposition,[],[f9902,f542]) ).
fof(f9902,plain,
( ! [X12] : ~ in(set_union2(sK0,X12),sK5(sK1,sK1,empty_set))
| ~ spl19_591 ),
inference(avatar_component_clause,[],[f9901]) ).
fof(f9950,plain,
( spl19_600
| ~ spl19_99
| ~ spl19_227 ),
inference(avatar_split_clause,[],[f2591,f2584,f849,f9948]) ).
fof(f9948,plain,
( spl19_600
<=> ! [X9,X8,X7] :
( ~ in(X7,X8)
| ~ subset(X8,powerset(empty_set))
| ~ in(X9,X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_600])]) ).
fof(f849,plain,
( spl19_99
<=> ! [X0,X1] :
( ~ element(X0,powerset(empty_set))
| ~ in(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_99])]) ).
fof(f2584,plain,
( spl19_227
<=> ! [X2,X4,X3] :
( element(X2,X3)
| ~ in(X2,X4)
| ~ subset(X4,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_227])]) ).
fof(f2591,plain,
( ! [X8,X9,X7] :
( ~ in(X7,X8)
| ~ subset(X8,powerset(empty_set))
| ~ in(X9,X7) )
| ~ spl19_99
| ~ spl19_227 ),
inference(resolution,[],[f2585,f850]) ).
fof(f850,plain,
( ! [X0,X1] :
( ~ element(X0,powerset(empty_set))
| ~ in(X1,X0) )
| ~ spl19_99 ),
inference(avatar_component_clause,[],[f849]) ).
fof(f2585,plain,
( ! [X2,X3,X4] :
( element(X2,X3)
| ~ in(X2,X4)
| ~ subset(X4,X3) )
| ~ spl19_227 ),
inference(avatar_component_clause,[],[f2584]) ).
fof(f9936,plain,
( ~ spl19_599
| ~ spl19_52
| ~ spl19_587 ),
inference(avatar_split_clause,[],[f9887,f9882,f508,f9933]) ).
fof(f9933,plain,
( spl19_599
<=> in(sK0,sK5(sK3(sK1),sK3(sK1),empty_set)) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_599])]) ).
fof(f9882,plain,
( spl19_587
<=> in(sK5(sK3(sK1),sK3(sK1),empty_set),sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_587])]) ).
fof(f9887,plain,
( ~ in(sK0,sK5(sK3(sK1),sK3(sK1),empty_set))
| ~ spl19_52
| ~ spl19_587 ),
inference(resolution,[],[f9884,f509]) ).
fof(f9884,plain,
( in(sK5(sK3(sK1),sK3(sK1),empty_set),sK0)
| ~ spl19_587 ),
inference(avatar_component_clause,[],[f9882]) ).
fof(f9931,plain,
( spl19_598
| spl19_150
| ~ spl19_503
| ~ spl19_544 ),
inference(avatar_split_clause,[],[f9511,f9033,f8233,f1531,f9929]) ).
fof(f1531,plain,
( spl19_150
<=> empty_set = sK1 ),
introduced(avatar_definition,[new_symbols(naming,[spl19_150])]) ).
fof(f9511,plain,
( ! [X15] : in(sK5(empty_set,empty_set,sK1),set_union2(sK0,X15))
| spl19_150
| ~ spl19_503
| ~ spl19_544 ),
inference(subsumption_resolution,[],[f9499,f1532]) ).
fof(f1532,plain,
( empty_set != sK1
| spl19_150 ),
inference(avatar_component_clause,[],[f1531]) ).
fof(f9499,plain,
( ! [X15] :
( empty_set = sK1
| in(sK5(empty_set,empty_set,sK1),set_union2(sK0,X15)) )
| ~ spl19_503
| ~ spl19_544 ),
inference(resolution,[],[f9034,f8234]) ).
fof(f9927,plain,
( spl19_597
| ~ spl19_62
| ~ spl19_227 ),
inference(avatar_split_clause,[],[f2590,f2584,f580,f9925]) ).
fof(f9925,plain,
( spl19_597
<=> ! [X6,X4,X5] :
( ~ in(X4,X5)
| ~ subset(X5,powerset(X6))
| subset(X4,X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_597])]) ).
fof(f580,plain,
( spl19_62
<=> ! [X0,X1] :
( subset(X0,X1)
| ~ element(X0,powerset(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_62])]) ).
fof(f2590,plain,
( ! [X6,X4,X5] :
( ~ in(X4,X5)
| ~ subset(X5,powerset(X6))
| subset(X4,X6) )
| ~ spl19_62
| ~ spl19_227 ),
inference(resolution,[],[f2585,f581]) ).
fof(f581,plain,
( ! [X0,X1] :
( ~ element(X0,powerset(X1))
| subset(X0,X1) )
| ~ spl19_62 ),
inference(avatar_component_clause,[],[f580]) ).
fof(f9923,plain,
( spl19_596
| spl19_150
| ~ spl19_504
| ~ spl19_544 ),
inference(avatar_split_clause,[],[f9510,f9033,f8237,f1531,f9921]) ).
fof(f9510,plain,
( ! [X14] : ~ in(set_union2(sK0,X14),sK5(empty_set,empty_set,sK1))
| spl19_150
| ~ spl19_504
| ~ spl19_544 ),
inference(subsumption_resolution,[],[f9498,f1532]) ).
fof(f9498,plain,
( ! [X14] :
( empty_set = sK1
| ~ in(set_union2(sK0,X14),sK5(empty_set,empty_set,sK1)) )
| ~ spl19_504
| ~ spl19_544 ),
inference(resolution,[],[f9034,f8238]) ).
fof(f9919,plain,
( spl19_595
| spl19_150
| ~ spl19_528
| ~ spl19_544 ),
inference(avatar_split_clause,[],[f9509,f9033,f8638,f1531,f9917]) ).
fof(f9917,plain,
( spl19_595
<=> ! [X13] : in(sK5(empty_set,empty_set,sK1),set_union2(X13,sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_595])]) ).
fof(f9509,plain,
( ! [X13] : in(sK5(empty_set,empty_set,sK1),set_union2(X13,sK0))
| spl19_150
| ~ spl19_528
| ~ spl19_544 ),
inference(subsumption_resolution,[],[f9497,f1532]) ).
fof(f9497,plain,
( ! [X13] :
( empty_set = sK1
| in(sK5(empty_set,empty_set,sK1),set_union2(X13,sK0)) )
| ~ spl19_528
| ~ spl19_544 ),
inference(resolution,[],[f9034,f8639]) ).
fof(f9915,plain,
( spl19_594
| spl19_150
| ~ spl19_529
| ~ spl19_544 ),
inference(avatar_split_clause,[],[f9508,f9033,f8642,f1531,f9913]) ).
fof(f9913,plain,
( spl19_594
<=> ! [X12] : ~ in(set_union2(X12,sK0),sK5(empty_set,empty_set,sK1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_594])]) ).
fof(f9508,plain,
( ! [X12] : ~ in(set_union2(X12,sK0),sK5(empty_set,empty_set,sK1))
| spl19_150
| ~ spl19_529
| ~ spl19_544 ),
inference(subsumption_resolution,[],[f9496,f1532]) ).
fof(f9496,plain,
( ! [X12] :
( empty_set = sK1
| ~ in(set_union2(X12,sK0),sK5(empty_set,empty_set,sK1)) )
| ~ spl19_529
| ~ spl19_544 ),
inference(resolution,[],[f9034,f8643]) ).
fof(f9911,plain,
( spl19_593
| ~ spl19_38
| ~ spl19_201 ),
inference(avatar_split_clause,[],[f2574,f2020,f435,f9909]) ).
fof(f9909,plain,
( spl19_593
<=> ! [X1] :
( in(empty_set,succ(X1))
| empty_set = succ(X1)
| ~ ordinal(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_593])]) ).
fof(f435,plain,
( spl19_38
<=> ! [X0] :
( ordinal(succ(X0))
| ~ ordinal(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_38])]) ).
fof(f2020,plain,
( spl19_201
<=> ! [X4] :
( empty_set = X4
| in(empty_set,X4)
| ~ ordinal(X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_201])]) ).
fof(f2574,plain,
( ! [X1] :
( in(empty_set,succ(X1))
| empty_set = succ(X1)
| ~ ordinal(X1) )
| ~ spl19_38
| ~ spl19_201 ),
inference(resolution,[],[f2021,f436]) ).
fof(f436,plain,
( ! [X0] :
( ordinal(succ(X0))
| ~ ordinal(X0) )
| ~ spl19_38 ),
inference(avatar_component_clause,[],[f435]) ).
fof(f2021,plain,
( ! [X4] :
( ~ ordinal(X4)
| in(empty_set,X4)
| empty_set = X4 )
| ~ spl19_201 ),
inference(avatar_component_clause,[],[f2020]) ).
fof(f9907,plain,
( spl19_592
| spl19_150
| ~ spl19_503
| ~ spl19_543 ),
inference(avatar_split_clause,[],[f9454,f9014,f8233,f1531,f9905]) ).
fof(f9454,plain,
( ! [X13] : in(sK5(sK1,sK1,empty_set),set_union2(sK0,X13))
| spl19_150
| ~ spl19_503
| ~ spl19_543 ),
inference(subsumption_resolution,[],[f9442,f1532]) ).
fof(f9442,plain,
( ! [X13] :
( empty_set = sK1
| in(sK5(sK1,sK1,empty_set),set_union2(sK0,X13)) )
| ~ spl19_503
| ~ spl19_543 ),
inference(resolution,[],[f9015,f8234]) ).
fof(f9903,plain,
( spl19_591
| spl19_150
| ~ spl19_504
| ~ spl19_543 ),
inference(avatar_split_clause,[],[f9453,f9014,f8237,f1531,f9901]) ).
fof(f9453,plain,
( ! [X12] : ~ in(set_union2(sK0,X12),sK5(sK1,sK1,empty_set))
| spl19_150
| ~ spl19_504
| ~ spl19_543 ),
inference(subsumption_resolution,[],[f9441,f1532]) ).
fof(f9441,plain,
( ! [X12] :
( empty_set = sK1
| ~ in(set_union2(sK0,X12),sK5(sK1,sK1,empty_set)) )
| ~ spl19_504
| ~ spl19_543 ),
inference(resolution,[],[f9015,f8238]) ).
fof(f9899,plain,
( spl19_590
| spl19_150
| ~ spl19_528
| ~ spl19_543 ),
inference(avatar_split_clause,[],[f9452,f9014,f8638,f1531,f9897]) ).
fof(f9897,plain,
( spl19_590
<=> ! [X11] : in(sK5(sK1,sK1,empty_set),set_union2(X11,sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_590])]) ).
fof(f9452,plain,
( ! [X11] : in(sK5(sK1,sK1,empty_set),set_union2(X11,sK0))
| spl19_150
| ~ spl19_528
| ~ spl19_543 ),
inference(subsumption_resolution,[],[f9440,f1532]) ).
fof(f9440,plain,
( ! [X11] :
( empty_set = sK1
| in(sK5(sK1,sK1,empty_set),set_union2(X11,sK0)) )
| ~ spl19_528
| ~ spl19_543 ),
inference(resolution,[],[f9015,f8639]) ).
fof(f9895,plain,
( spl19_589
| spl19_150
| ~ spl19_529
| ~ spl19_543 ),
inference(avatar_split_clause,[],[f9451,f9014,f8642,f1531,f9893]) ).
fof(f9893,plain,
( spl19_589
<=> ! [X10] : ~ in(set_union2(X10,sK0),sK5(sK1,sK1,empty_set)) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_589])]) ).
fof(f9451,plain,
( ! [X10] : ~ in(set_union2(X10,sK0),sK5(sK1,sK1,empty_set))
| spl19_150
| ~ spl19_529
| ~ spl19_543 ),
inference(subsumption_resolution,[],[f9439,f1532]) ).
fof(f9439,plain,
( ! [X10] :
( empty_set = sK1
| ~ in(set_union2(X10,sK0),sK5(sK1,sK1,empty_set)) )
| ~ spl19_529
| ~ spl19_543 ),
inference(resolution,[],[f9015,f8643]) ).
fof(f9891,plain,
( spl19_588
| ~ spl19_83
| ~ spl19_198 ),
inference(avatar_split_clause,[],[f2565,f1996,f712,f9889]) ).
fof(f712,plain,
( spl19_83
<=> ! [X0] :
( empty(X0)
| in(sK3(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_83])]) ).
fof(f1996,plain,
( spl19_198
<=> ! [X0,X1] :
( element(X0,X1)
| ~ in(X0,sK3(powerset(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_198])]) ).
fof(f2565,plain,
( ! [X1] :
( element(sK3(sK3(powerset(X1))),X1)
| empty(sK3(powerset(X1))) )
| ~ spl19_83
| ~ spl19_198 ),
inference(resolution,[],[f1997,f713]) ).
fof(f713,plain,
( ! [X0] :
( in(sK3(X0),X0)
| empty(X0) )
| ~ spl19_83 ),
inference(avatar_component_clause,[],[f712]) ).
fof(f1997,plain,
( ! [X0,X1] :
( ~ in(X0,sK3(powerset(X1)))
| element(X0,X1) )
| ~ spl19_198 ),
inference(avatar_component_clause,[],[f1996]) ).
fof(f9885,plain,
( spl19_587
| ~ spl19_318
| spl19_337
| ~ spl19_543 ),
inference(avatar_split_clause,[],[f9456,f9014,f4630,f4347,f9882]) ).
fof(f4347,plain,
( spl19_318
<=> ! [X0] :
( ~ in(X0,sK3(sK1))
| in(X0,sK0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_318])]) ).
fof(f4630,plain,
( spl19_337
<=> empty_set = sK3(sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_337])]) ).
fof(f9456,plain,
( in(sK5(sK3(sK1),sK3(sK1),empty_set),sK0)
| ~ spl19_318
| spl19_337
| ~ spl19_543 ),
inference(subsumption_resolution,[],[f9447,f4631]) ).
fof(f4631,plain,
( empty_set != sK3(sK1)
| spl19_337 ),
inference(avatar_component_clause,[],[f4630]) ).
fof(f9447,plain,
( empty_set = sK3(sK1)
| in(sK5(sK3(sK1),sK3(sK1),empty_set),sK0)
| ~ spl19_318
| ~ spl19_543 ),
inference(resolution,[],[f9015,f4348]) ).
fof(f4348,plain,
( ! [X0] :
( ~ in(X0,sK3(sK1))
| in(X0,sK0) )
| ~ spl19_318 ),
inference(avatar_component_clause,[],[f4347]) ).
fof(f9880,plain,
( spl19_586
| ~ spl19_48
| ~ spl19_198 ),
inference(avatar_split_clause,[],[f2564,f1996,f492,f9878]) ).
fof(f9878,plain,
( spl19_586
<=> ! [X0] :
( element(sK2(sK3(powerset(X0))),X0)
| epsilon_transitive(sK3(powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_586])]) ).
fof(f2564,plain,
( ! [X0] :
( element(sK2(sK3(powerset(X0))),X0)
| epsilon_transitive(sK3(powerset(X0))) )
| ~ spl19_48
| ~ spl19_198 ),
inference(resolution,[],[f1997,f493]) ).
fof(f9871,plain,
( spl19_585
| ~ spl19_80
| ~ spl19_171 ),
inference(avatar_split_clause,[],[f2144,f1776,f689,f9869]) ).
fof(f689,plain,
( spl19_80
<=> ! [X4,X0,X1] :
( in(X4,set_union2(X0,X1))
| ~ in(X4,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_80])]) ).
fof(f1776,plain,
( spl19_171
<=> ! [X2,X0,X1] :
( ~ in(X0,X1)
| ~ in(set_union2(X1,X2),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_171])]) ).
fof(f2144,plain,
( ! [X10,X8,X9,X7] :
( ~ in(set_union2(X7,X8),X9)
| ~ in(set_union2(X9,X10),X7) )
| ~ spl19_80
| ~ spl19_171 ),
inference(resolution,[],[f1777,f690]) ).
fof(f690,plain,
( ! [X0,X1,X4] :
( in(X4,set_union2(X0,X1))
| ~ in(X4,X0) )
| ~ spl19_80 ),
inference(avatar_component_clause,[],[f689]) ).
fof(f1777,plain,
( ! [X2,X0,X1] :
( ~ in(set_union2(X1,X2),X0)
| ~ in(X0,X1) )
| ~ spl19_171 ),
inference(avatar_component_clause,[],[f1776]) ).
fof(f9865,plain,
( spl19_584
| ~ spl19_79
| ~ spl19_163 ),
inference(avatar_split_clause,[],[f2120,f1741,f685,f9863]) ).
fof(f685,plain,
( spl19_79
<=> ! [X4,X0,X1] :
( in(X4,set_union2(X0,X1))
| ~ in(X4,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_79])]) ).
fof(f1741,plain,
( spl19_163
<=> ! [X2,X0,X1] :
( ~ in(X0,X1)
| ~ in(set_union2(X2,X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_163])]) ).
fof(f2120,plain,
( ! [X11,X14,X12,X13] :
( ~ in(set_union2(X11,X12),X13)
| ~ in(set_union2(X14,X13),X12) )
| ~ spl19_79
| ~ spl19_163 ),
inference(resolution,[],[f1742,f686]) ).
fof(f686,plain,
( ! [X0,X1,X4] :
( in(X4,set_union2(X0,X1))
| ~ in(X4,X1) )
| ~ spl19_79 ),
inference(avatar_component_clause,[],[f685]) ).
fof(f1742,plain,
( ! [X2,X0,X1] :
( ~ in(set_union2(X2,X1),X0)
| ~ in(X0,X1) )
| ~ spl19_163 ),
inference(avatar_component_clause,[],[f1741]) ).
fof(f9861,plain,
( spl19_583
| ~ spl19_109
| ~ spl19_569
| spl19_581 ),
inference(avatar_split_clause,[],[f9850,f9842,f9424,f920,f9858]) ).
fof(f9858,plain,
( spl19_583
<=> ordinal_subset(sK1,succ(sK8)) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_583])]) ).
fof(f920,plain,
( spl19_109
<=> ! [X6] :
( ordinal_subset(X6,sK1)
| ordinal_subset(sK1,X6)
| ~ ordinal(X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_109])]) ).
fof(f9842,plain,
( spl19_581
<=> ordinal_subset(succ(sK8),sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_581])]) ).
fof(f9850,plain,
( ordinal_subset(sK1,succ(sK8))
| ~ spl19_109
| ~ spl19_569
| spl19_581 ),
inference(subsumption_resolution,[],[f9849,f9425]) ).
fof(f9849,plain,
( ordinal_subset(sK1,succ(sK8))
| ~ ordinal(succ(sK8))
| ~ spl19_109
| spl19_581 ),
inference(resolution,[],[f9844,f921]) ).
fof(f921,plain,
( ! [X6] :
( ordinal_subset(sK1,X6)
| ordinal_subset(X6,sK1)
| ~ ordinal(X6) )
| ~ spl19_109 ),
inference(avatar_component_clause,[],[f920]) ).
fof(f9844,plain,
( ~ ordinal_subset(succ(sK8),sK1)
| spl19_581 ),
inference(avatar_component_clause,[],[f9842]) ).
fof(f9854,plain,
( spl19_582
| ~ spl19_80
| ~ spl19_163 ),
inference(avatar_split_clause,[],[f2119,f1741,f689,f9852]) ).
fof(f2119,plain,
( ! [X10,X8,X9,X7] :
( ~ in(set_union2(X7,X8),X9)
| ~ in(set_union2(X10,X9),X7) )
| ~ spl19_80
| ~ spl19_163 ),
inference(resolution,[],[f1742,f690]) ).
fof(f9845,plain,
( ~ spl19_581
| ~ spl19_178
| ~ spl19_428
| spl19_566
| ~ spl19_567
| ~ spl19_569 ),
inference(avatar_split_clause,[],[f9802,f9424,f9348,f9344,f6825,f1824,f9842]) ).
fof(f1824,plain,
( spl19_178
<=> ! [X0] :
( ~ ordinal_subset(X0,sK1)
| ~ ordinal(X0)
| sK1 = X0
| ~ subset(sK1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_178])]) ).
fof(f6825,plain,
( spl19_428
<=> ! [X8] :
( subset(X8,succ(sK8))
| ~ in(X8,succ(sK8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_428])]) ).
fof(f9344,plain,
( spl19_566
<=> sK1 = succ(sK8) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_566])]) ).
fof(f9348,plain,
( spl19_567
<=> in(sK1,succ(sK8)) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_567])]) ).
fof(f9802,plain,
( ~ ordinal_subset(succ(sK8),sK1)
| ~ spl19_178
| ~ spl19_428
| spl19_566
| ~ spl19_567
| ~ spl19_569 ),
inference(subsumption_resolution,[],[f9801,f9345]) ).
fof(f9345,plain,
( sK1 != succ(sK8)
| spl19_566 ),
inference(avatar_component_clause,[],[f9344]) ).
fof(f9801,plain,
( sK1 = succ(sK8)
| ~ ordinal_subset(succ(sK8),sK1)
| ~ spl19_178
| ~ spl19_428
| ~ spl19_567
| ~ spl19_569 ),
inference(subsumption_resolution,[],[f9800,f9425]) ).
fof(f9800,plain,
( ~ ordinal(succ(sK8))
| sK1 = succ(sK8)
| ~ ordinal_subset(succ(sK8),sK1)
| ~ spl19_178
| ~ spl19_428
| ~ spl19_567 ),
inference(subsumption_resolution,[],[f7757,f9350]) ).
fof(f9350,plain,
( in(sK1,succ(sK8))
| ~ spl19_567 ),
inference(avatar_component_clause,[],[f9348]) ).
fof(f7757,plain,
( ~ in(sK1,succ(sK8))
| ~ ordinal(succ(sK8))
| sK1 = succ(sK8)
| ~ ordinal_subset(succ(sK8),sK1)
| ~ spl19_178
| ~ spl19_428 ),
inference(resolution,[],[f6826,f1825]) ).
fof(f1825,plain,
( ! [X0] :
( ~ subset(sK1,X0)
| ~ ordinal(X0)
| sK1 = X0
| ~ ordinal_subset(X0,sK1) )
| ~ spl19_178 ),
inference(avatar_component_clause,[],[f1824]) ).
fof(f6826,plain,
( ! [X8] :
( subset(X8,succ(sK8))
| ~ in(X8,succ(sK8)) )
| ~ spl19_428 ),
inference(avatar_component_clause,[],[f6825]) ).
fof(f9799,plain,
( spl19_152
| ~ spl19_570
| ~ spl19_579 ),
inference(avatar_contradiction_clause,[],[f9798]) ).
fof(f9798,plain,
( $false
| spl19_152
| ~ spl19_570
| ~ spl19_579 ),
inference(subsumption_resolution,[],[f9765,f1597]) ).
fof(f1597,plain,
( ~ ordinal_subset(sK0,empty_set)
| spl19_152 ),
inference(avatar_component_clause,[],[f1595]) ).
fof(f1595,plain,
( spl19_152
<=> ordinal_subset(sK0,empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_152])]) ).
fof(f9765,plain,
( ordinal_subset(sK0,empty_set)
| ~ spl19_570
| ~ spl19_579 ),
inference(backward_demodulation,[],[f9517,f9733]) ).
fof(f9733,plain,
( empty_set = succ(sK8)
| ~ spl19_579 ),
inference(avatar_component_clause,[],[f9731]) ).
fof(f9731,plain,
( spl19_579
<=> empty_set = succ(sK8) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_579])]) ).
fof(f9517,plain,
( ordinal_subset(sK0,succ(sK8))
| ~ spl19_570 ),
inference(avatar_component_clause,[],[f9515]) ).
fof(f9515,plain,
( spl19_570
<=> ordinal_subset(sK0,succ(sK8)) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_570])]) ).
fof(f9786,plain,
( ~ spl19_154
| spl19_568
| ~ spl19_579 ),
inference(avatar_contradiction_clause,[],[f9785]) ).
fof(f9785,plain,
( $false
| ~ spl19_154
| spl19_568
| ~ spl19_579 ),
inference(subsumption_resolution,[],[f9754,f1621]) ).
fof(f1621,plain,
( ordinal_subset(empty_set,sK0)
| ~ spl19_154 ),
inference(avatar_component_clause,[],[f1619]) ).
fof(f1619,plain,
( spl19_154
<=> ordinal_subset(empty_set,sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_154])]) ).
fof(f9754,plain,
( ~ ordinal_subset(empty_set,sK0)
| spl19_568
| ~ spl19_579 ),
inference(backward_demodulation,[],[f9422,f9733]) ).
fof(f9422,plain,
( ~ ordinal_subset(succ(sK8),sK0)
| spl19_568 ),
inference(avatar_component_clause,[],[f9420]) ).
fof(f9420,plain,
( spl19_568
<=> ordinal_subset(succ(sK8),sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_568])]) ).
fof(f9784,plain,
( ~ spl19_46
| ~ spl19_567
| ~ spl19_579 ),
inference(avatar_contradiction_clause,[],[f9783]) ).
fof(f9783,plain,
( $false
| ~ spl19_46
| ~ spl19_567
| ~ spl19_579 ),
inference(subsumption_resolution,[],[f9753,f485]) ).
fof(f485,plain,
( ! [X0] : ~ in(X0,empty_set)
| ~ spl19_46 ),
inference(avatar_component_clause,[],[f484]) ).
fof(f484,plain,
( spl19_46
<=> ! [X0] : ~ in(X0,empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_46])]) ).
fof(f9753,plain,
( in(sK1,empty_set)
| ~ spl19_567
| ~ spl19_579 ),
inference(backward_demodulation,[],[f9350,f9733]) ).
fof(f9782,plain,
( ~ spl19_151
| spl19_565
| ~ spl19_579 ),
inference(avatar_contradiction_clause,[],[f9781]) ).
fof(f9781,plain,
( $false
| ~ spl19_151
| spl19_565
| ~ spl19_579 ),
inference(subsumption_resolution,[],[f9751,f1537]) ).
fof(f1537,plain,
( in(empty_set,sK1)
| ~ spl19_151 ),
inference(avatar_component_clause,[],[f1535]) ).
fof(f1535,plain,
( spl19_151
<=> in(empty_set,sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_151])]) ).
fof(f9751,plain,
( ~ in(empty_set,sK1)
| spl19_565
| ~ spl19_579 ),
inference(backward_demodulation,[],[f9339,f9733]) ).
fof(f9339,plain,
( ~ in(succ(sK8),sK1)
| spl19_565 ),
inference(avatar_component_clause,[],[f9337]) ).
fof(f9337,plain,
( spl19_565
<=> in(succ(sK8),sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_565])]) ).
fof(f9780,plain,
( ~ spl19_46
| ~ spl19_564
| ~ spl19_579 ),
inference(avatar_contradiction_clause,[],[f9779]) ).
fof(f9779,plain,
( $false
| ~ spl19_46
| ~ spl19_564
| ~ spl19_579 ),
inference(subsumption_resolution,[],[f9750,f485]) ).
fof(f9750,plain,
( in(sK0,empty_set)
| ~ spl19_564
| ~ spl19_579 ),
inference(backward_demodulation,[],[f9253,f9733]) ).
fof(f9253,plain,
( in(sK0,succ(sK8))
| ~ spl19_564 ),
inference(avatar_component_clause,[],[f9251]) ).
fof(f9251,plain,
( spl19_564
<=> in(sK0,succ(sK8)) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_564])]) ).
fof(f9778,plain,
( ~ spl19_147
| spl19_562
| ~ spl19_579 ),
inference(avatar_contradiction_clause,[],[f9777]) ).
fof(f9777,plain,
( $false
| ~ spl19_147
| spl19_562
| ~ spl19_579 ),
inference(subsumption_resolution,[],[f9748,f1332]) ).
fof(f1332,plain,
( in(empty_set,sK0)
| ~ spl19_147 ),
inference(avatar_component_clause,[],[f1330]) ).
fof(f1330,plain,
( spl19_147
<=> in(empty_set,sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_147])]) ).
fof(f9748,plain,
( ~ in(empty_set,sK0)
| spl19_562
| ~ spl19_579 ),
inference(backward_demodulation,[],[f9242,f9733]) ).
fof(f9242,plain,
( ~ in(succ(sK8),sK0)
| spl19_562 ),
inference(avatar_component_clause,[],[f9240]) ).
fof(f9240,plain,
( spl19_562
<=> in(succ(sK8),sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_562])]) ).
fof(f9738,plain,
( spl19_579
| spl19_580
| ~ spl19_201
| ~ spl19_569 ),
inference(avatar_split_clause,[],[f9469,f9424,f2020,f9735,f9731]) ).
fof(f9735,plain,
( spl19_580
<=> in(empty_set,succ(sK8)) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_580])]) ).
fof(f9469,plain,
( in(empty_set,succ(sK8))
| empty_set = succ(sK8)
| ~ spl19_201
| ~ spl19_569 ),
inference(resolution,[],[f9425,f2021]) ).
fof(f9729,plain,
( ~ spl19_578
| ~ spl19_52
| ~ spl19_576 ),
inference(avatar_split_clause,[],[f9720,f9715,f508,f9726]) ).
fof(f9726,plain,
( spl19_578
<=> in(sK0,sK5(empty_set,empty_set,sK3(sK1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_578])]) ).
fof(f9720,plain,
( ~ in(sK0,sK5(empty_set,empty_set,sK3(sK1)))
| ~ spl19_52
| ~ spl19_576 ),
inference(resolution,[],[f9717,f509]) ).
fof(f9724,plain,
( spl19_577
| ~ spl19_72
| ~ spl19_89 ),
inference(avatar_split_clause,[],[f810,f765,f645,f9722]) ).
fof(f9722,plain,
( spl19_577
<=> ! [X1] :
( sK3(powerset(X1)) = X1
| ~ subset(X1,sK3(powerset(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_577])]) ).
fof(f645,plain,
( spl19_72
<=> ! [X0] : subset(sK3(powerset(X0)),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_72])]) ).
fof(f765,plain,
( spl19_89
<=> ! [X0,X1] :
( X0 = X1
| ~ subset(X1,X0)
| ~ subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_89])]) ).
fof(f810,plain,
( ! [X1] :
( sK3(powerset(X1)) = X1
| ~ subset(X1,sK3(powerset(X1))) )
| ~ spl19_72
| ~ spl19_89 ),
inference(resolution,[],[f766,f646]) ).
fof(f646,plain,
( ! [X0] : subset(sK3(powerset(X0)),X0)
| ~ spl19_72 ),
inference(avatar_component_clause,[],[f645]) ).
fof(f766,plain,
( ! [X0,X1] :
( ~ subset(X1,X0)
| X0 = X1
| ~ subset(X0,X1) )
| ~ spl19_89 ),
inference(avatar_component_clause,[],[f765]) ).
fof(f9718,plain,
( spl19_576
| ~ spl19_318
| spl19_337
| ~ spl19_544 ),
inference(avatar_split_clause,[],[f9513,f9033,f4630,f4347,f9715]) ).
fof(f9513,plain,
( in(sK5(empty_set,empty_set,sK3(sK1)),sK0)
| ~ spl19_318
| spl19_337
| ~ spl19_544 ),
inference(subsumption_resolution,[],[f9504,f4631]) ).
fof(f9504,plain,
( empty_set = sK3(sK1)
| in(sK5(empty_set,empty_set,sK3(sK1)),sK0)
| ~ spl19_318
| ~ spl19_544 ),
inference(resolution,[],[f9034,f4348]) ).
fof(f9647,plain,
( ~ spl19_575
| ~ spl19_52
| ~ spl19_573 ),
inference(avatar_split_clause,[],[f9637,f9568,f508,f9644]) ).
fof(f9644,plain,
( spl19_575
<=> in(sK0,sK5(empty_set,empty_set,sK1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_575])]) ).
fof(f9637,plain,
( ~ in(sK0,sK5(empty_set,empty_set,sK1))
| ~ spl19_52
| ~ spl19_573 ),
inference(resolution,[],[f9570,f509]) ).
fof(f9642,plain,
( ~ spl19_574
| ~ spl19_52
| ~ spl19_572 ),
inference(avatar_split_clause,[],[f9573,f9563,f508,f9639]) ).
fof(f9639,plain,
( spl19_574
<=> in(sK0,sK5(sK1,sK1,empty_set)) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_574])]) ).
fof(f9573,plain,
( ~ in(sK0,sK5(sK1,sK1,empty_set))
| ~ spl19_52
| ~ spl19_572 ),
inference(resolution,[],[f9565,f509]) ).
fof(f9571,plain,
( spl19_573
| spl19_150
| ~ spl19_313
| ~ spl19_544 ),
inference(avatar_split_clause,[],[f9512,f9033,f3809,f1531,f9568]) ).
fof(f9512,plain,
( in(sK5(empty_set,empty_set,sK1),sK0)
| spl19_150
| ~ spl19_313
| ~ spl19_544 ),
inference(subsumption_resolution,[],[f9500,f1532]) ).
fof(f9500,plain,
( empty_set = sK1
| in(sK5(empty_set,empty_set,sK1),sK0)
| ~ spl19_313
| ~ spl19_544 ),
inference(resolution,[],[f9034,f3810]) ).
fof(f9566,plain,
( spl19_572
| spl19_150
| ~ spl19_313
| ~ spl19_543 ),
inference(avatar_split_clause,[],[f9455,f9014,f3809,f1531,f9563]) ).
fof(f9455,plain,
( in(sK5(sK1,sK1,empty_set),sK0)
| spl19_150
| ~ spl19_313
| ~ spl19_543 ),
inference(subsumption_resolution,[],[f9443,f1532]) ).
fof(f9443,plain,
( empty_set = sK1
| in(sK5(sK1,sK1,empty_set),sK0)
| ~ spl19_313
| ~ spl19_543 ),
inference(resolution,[],[f9015,f3810]) ).
fof(f9524,plain,
( spl19_571
| ~ spl19_60
| ~ spl19_569 ),
inference(avatar_split_clause,[],[f9461,f9424,f552,f9521]) ).
fof(f9521,plain,
( spl19_571
<=> ordinal_subset(succ(sK8),succ(sK8)) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_571])]) ).
fof(f552,plain,
( spl19_60
<=> ! [X0] :
( ordinal_subset(X0,X0)
| ~ ordinal(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_60])]) ).
fof(f9461,plain,
( ordinal_subset(succ(sK8),succ(sK8))
| ~ spl19_60
| ~ spl19_569 ),
inference(resolution,[],[f9425,f553]) ).
fof(f553,plain,
( ! [X0] :
( ~ ordinal(X0)
| ordinal_subset(X0,X0) )
| ~ spl19_60 ),
inference(avatar_component_clause,[],[f552]) ).
fof(f9518,plain,
( spl19_570
| ~ spl19_108
| spl19_568
| ~ spl19_569 ),
inference(avatar_split_clause,[],[f9484,f9424,f9420,f916,f9515]) ).
fof(f916,plain,
( spl19_108
<=> ! [X5] :
( ordinal_subset(X5,sK0)
| ordinal_subset(sK0,X5)
| ~ ordinal(X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_108])]) ).
fof(f9484,plain,
( ordinal_subset(sK0,succ(sK8))
| ~ spl19_108
| spl19_568
| ~ spl19_569 ),
inference(subsumption_resolution,[],[f9483,f9425]) ).
fof(f9483,plain,
( ordinal_subset(sK0,succ(sK8))
| ~ ordinal(succ(sK8))
| ~ spl19_108
| spl19_568 ),
inference(resolution,[],[f9422,f917]) ).
fof(f917,plain,
( ! [X5] :
( ordinal_subset(sK0,X5)
| ordinal_subset(X5,sK0)
| ~ ordinal(X5) )
| ~ spl19_108 ),
inference(avatar_component_clause,[],[f916]) ).
fof(f9460,plain,
( ~ spl19_14
| ~ spl19_38
| spl19_569 ),
inference(avatar_contradiction_clause,[],[f9459]) ).
fof(f9459,plain,
( $false
| ~ spl19_14
| ~ spl19_38
| spl19_569 ),
inference(subsumption_resolution,[],[f9457,f330]) ).
fof(f9457,plain,
( ~ ordinal(sK8)
| ~ spl19_38
| spl19_569 ),
inference(resolution,[],[f9426,f436]) ).
fof(f9426,plain,
( ~ ordinal(succ(sK8))
| spl19_569 ),
inference(avatar_component_clause,[],[f9424]) ).
fof(f9427,plain,
( ~ spl19_568
| ~ spl19_569
| ~ spl19_177
| ~ spl19_428
| spl19_563
| ~ spl19_564 ),
inference(avatar_split_clause,[],[f9385,f9251,f9247,f6825,f1820,f9424,f9420]) ).
fof(f1820,plain,
( spl19_177
<=> ! [X0] :
( ~ ordinal_subset(X0,sK0)
| ~ ordinal(X0)
| sK0 = X0
| ~ subset(sK0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_177])]) ).
fof(f9247,plain,
( spl19_563
<=> sK0 = succ(sK8) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_563])]) ).
fof(f9385,plain,
( ~ ordinal(succ(sK8))
| ~ ordinal_subset(succ(sK8),sK0)
| ~ spl19_177
| ~ spl19_428
| spl19_563
| ~ spl19_564 ),
inference(subsumption_resolution,[],[f9384,f9248]) ).
fof(f9248,plain,
( sK0 != succ(sK8)
| spl19_563 ),
inference(avatar_component_clause,[],[f9247]) ).
fof(f9384,plain,
( ~ ordinal(succ(sK8))
| sK0 = succ(sK8)
| ~ ordinal_subset(succ(sK8),sK0)
| ~ spl19_177
| ~ spl19_428
| ~ spl19_564 ),
inference(subsumption_resolution,[],[f7754,f9253]) ).
fof(f7754,plain,
( ~ in(sK0,succ(sK8))
| ~ ordinal(succ(sK8))
| sK0 = succ(sK8)
| ~ ordinal_subset(succ(sK8),sK0)
| ~ spl19_177
| ~ spl19_428 ),
inference(resolution,[],[f6826,f1821]) ).
fof(f1821,plain,
( ! [X0] :
( ~ subset(sK0,X0)
| ~ ordinal(X0)
| sK0 = X0
| ~ ordinal_subset(X0,sK0) )
| ~ spl19_177 ),
inference(avatar_component_clause,[],[f1820]) ).
fof(f9383,plain,
( spl19_101
| ~ spl19_564
| ~ spl19_566 ),
inference(avatar_contradiction_clause,[],[f9382]) ).
fof(f9382,plain,
( $false
| spl19_101
| ~ spl19_564
| ~ spl19_566 ),
inference(subsumption_resolution,[],[f9364,f870]) ).
fof(f9364,plain,
( in(sK0,sK1)
| ~ spl19_564
| ~ spl19_566 ),
inference(backward_demodulation,[],[f9253,f9346]) ).
fof(f9346,plain,
( sK1 = succ(sK8)
| ~ spl19_566 ),
inference(avatar_component_clause,[],[f9344]) ).
fof(f9381,plain,
( ~ spl19_140
| spl19_562
| ~ spl19_566 ),
inference(avatar_contradiction_clause,[],[f9380]) ).
fof(f9380,plain,
( $false
| ~ spl19_140
| spl19_562
| ~ spl19_566 ),
inference(subsumption_resolution,[],[f9362,f1149]) ).
fof(f1149,plain,
( in(sK1,sK0)
| ~ spl19_140 ),
inference(avatar_component_clause,[],[f1148]) ).
fof(f1148,plain,
( spl19_140
<=> in(sK1,sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_140])]) ).
fof(f9362,plain,
( ~ in(sK1,sK0)
| spl19_562
| ~ spl19_566 ),
inference(backward_demodulation,[],[f9242,f9346]) ).
fof(f9351,plain,
( spl19_566
| spl19_567
| ~ spl19_14
| ~ spl19_185
| spl19_565 ),
inference(avatar_split_clause,[],[f9342,f9337,f1876,f328,f9348,f9344]) ).
fof(f1876,plain,
( spl19_185
<=> ! [X1] :
( in(succ(X1),sK1)
| in(sK1,succ(X1))
| succ(X1) = sK1
| ~ ordinal(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_185])]) ).
fof(f9342,plain,
( in(sK1,succ(sK8))
| sK1 = succ(sK8)
| ~ spl19_14
| ~ spl19_185
| spl19_565 ),
inference(subsumption_resolution,[],[f9341,f330]) ).
fof(f9341,plain,
( in(sK1,succ(sK8))
| sK1 = succ(sK8)
| ~ ordinal(sK8)
| ~ spl19_185
| spl19_565 ),
inference(resolution,[],[f9339,f1877]) ).
fof(f1877,plain,
( ! [X1] :
( in(succ(X1),sK1)
| in(sK1,succ(X1))
| succ(X1) = sK1
| ~ ordinal(X1) )
| ~ spl19_185 ),
inference(avatar_component_clause,[],[f1876]) ).
fof(f9340,plain,
( ~ spl19_565
| ~ spl19_474
| ~ spl19_564 ),
inference(avatar_split_clause,[],[f9334,f9251,f7762,f9337]) ).
fof(f7762,plain,
( spl19_474
<=> ! [X3] :
( ~ in(sK0,X3)
| ~ in(X3,sK1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_474])]) ).
fof(f9334,plain,
( ~ in(succ(sK8),sK1)
| ~ spl19_474
| ~ spl19_564 ),
inference(resolution,[],[f9253,f7763]) ).
fof(f7763,plain,
( ! [X3] :
( ~ in(sK0,X3)
| ~ in(X3,sK1) )
| ~ spl19_474 ),
inference(avatar_component_clause,[],[f7762]) ).
fof(f9316,plain,
( ~ spl19_93
| ~ spl19_269
| ~ spl19_563 ),
inference(avatar_contradiction_clause,[],[f9315]) ).
fof(f9315,plain,
( $false
| ~ spl19_93
| ~ spl19_269
| ~ spl19_563 ),
inference(subsumption_resolution,[],[f9292,f3180]) ).
fof(f3180,plain,
( in(succ(sK0),sK8)
| ~ spl19_269 ),
inference(avatar_component_clause,[],[f3178]) ).
fof(f3178,plain,
( spl19_269
<=> in(succ(sK0),sK8) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_269])]) ).
fof(f9292,plain,
( ~ in(succ(sK0),sK8)
| ~ spl19_93
| ~ spl19_563 ),
inference(superposition,[],[f807,f9249]) ).
fof(f9249,plain,
( sK0 = succ(sK8)
| ~ spl19_563 ),
inference(avatar_component_clause,[],[f9247]) ).
fof(f807,plain,
( ! [X5] : ~ in(succ(succ(X5)),X5)
| ~ spl19_93 ),
inference(avatar_component_clause,[],[f806]) ).
fof(f806,plain,
( spl19_93
<=> ! [X5] : ~ in(succ(succ(X5)),X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_93])]) ).
fof(f9314,plain,
( ~ spl19_54
| ~ spl19_161
| ~ spl19_563 ),
inference(avatar_contradiction_clause,[],[f9313]) ).
fof(f9313,plain,
( $false
| ~ spl19_54
| ~ spl19_161
| ~ spl19_563 ),
inference(subsumption_resolution,[],[f9290,f1733]) ).
fof(f1733,plain,
( in(sK0,sK8)
| ~ spl19_161 ),
inference(avatar_component_clause,[],[f1731]) ).
fof(f1731,plain,
( spl19_161
<=> in(sK0,sK8) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_161])]) ).
fof(f9290,plain,
( ~ in(sK0,sK8)
| ~ spl19_54
| ~ spl19_563 ),
inference(superposition,[],[f530,f9249]) ).
fof(f530,plain,
( ! [X0] : ~ in(succ(X0),X0)
| ~ spl19_54 ),
inference(avatar_component_clause,[],[f529]) ).
fof(f529,plain,
( spl19_54
<=> ! [X0] : ~ in(succ(X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_54])]) ).
fof(f9311,plain,
( ~ spl19_28
| spl19_162
| ~ spl19_563 ),
inference(avatar_contradiction_clause,[],[f9310]) ).
fof(f9310,plain,
( $false
| ~ spl19_28
| spl19_162
| ~ spl19_563 ),
inference(subsumption_resolution,[],[f9286,f1736]) ).
fof(f1736,plain,
( ~ in(sK8,sK0)
| spl19_162 ),
inference(avatar_component_clause,[],[f1735]) ).
fof(f1735,plain,
( spl19_162
<=> in(sK8,sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_162])]) ).
fof(f9286,plain,
( in(sK8,sK0)
| ~ spl19_28
| ~ spl19_563 ),
inference(superposition,[],[f396,f9249]) ).
fof(f396,plain,
( ! [X0] : in(X0,succ(X0))
| ~ spl19_28 ),
inference(avatar_component_clause,[],[f395]) ).
fof(f395,plain,
( spl19_28
<=> ! [X0] : in(X0,succ(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_28])]) ).
fof(f9254,plain,
( spl19_563
| spl19_564
| ~ spl19_14
| ~ spl19_183
| spl19_562 ),
inference(avatar_split_clause,[],[f9245,f9240,f1868,f328,f9251,f9247]) ).
fof(f1868,plain,
( spl19_183
<=> ! [X1] :
( in(succ(X1),sK0)
| in(sK0,succ(X1))
| succ(X1) = sK0
| ~ ordinal(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_183])]) ).
fof(f9245,plain,
( in(sK0,succ(sK8))
| sK0 = succ(sK8)
| ~ spl19_14
| ~ spl19_183
| spl19_562 ),
inference(subsumption_resolution,[],[f9244,f330]) ).
fof(f9244,plain,
( in(sK0,succ(sK8))
| sK0 = succ(sK8)
| ~ ordinal(sK8)
| ~ spl19_183
| spl19_562 ),
inference(resolution,[],[f9242,f1869]) ).
fof(f1869,plain,
( ! [X1] :
( in(succ(X1),sK0)
| in(sK0,succ(X1))
| succ(X1) = sK0
| ~ ordinal(X1) )
| ~ spl19_183 ),
inference(avatar_component_clause,[],[f1868]) ).
fof(f9243,plain,
( ~ spl19_562
| ~ spl19_57
| ~ spl19_561 ),
inference(avatar_split_clause,[],[f9237,f9229,f541,f9240]) ).
fof(f9229,plain,
( spl19_561
<=> ! [X0] : ~ in(set_union2(sK8,X0),sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_561])]) ).
fof(f9237,plain,
( ~ in(succ(sK8),sK0)
| ~ spl19_57
| ~ spl19_561 ),
inference(superposition,[],[f9230,f542]) ).
fof(f9230,plain,
( ! [X0] : ~ in(set_union2(sK8,X0),sK0)
| ~ spl19_561 ),
inference(avatar_component_clause,[],[f9229]) ).
fof(f9231,plain,
( spl19_561
| ~ spl19_58
| ~ spl19_560 ),
inference(avatar_split_clause,[],[f9225,f9221,f545,f9229]) ).
fof(f9221,plain,
( spl19_560
<=> ! [X4] : ~ in(set_union2(X4,sK8),sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_560])]) ).
fof(f9225,plain,
( ! [X0] : ~ in(set_union2(sK8,X0),sK0)
| ~ spl19_58
| ~ spl19_560 ),
inference(superposition,[],[f9222,f546]) ).
fof(f9222,plain,
( ! [X4] : ~ in(set_union2(X4,sK8),sK0)
| ~ spl19_560 ),
inference(avatar_component_clause,[],[f9221]) ).
fof(f9223,plain,
( spl19_560
| ~ spl19_269
| ~ spl19_506 ),
inference(avatar_split_clause,[],[f9210,f8283,f3178,f9221]) ).
fof(f9210,plain,
( ! [X4] : ~ in(set_union2(X4,sK8),sK0)
| ~ spl19_269
| ~ spl19_506 ),
inference(resolution,[],[f8284,f3180]) ).
fof(f9181,plain,
( spl19_559
| ~ spl19_396
| ~ spl19_400
| ~ spl19_550 ),
inference(avatar_split_clause,[],[f9175,f9084,f6188,f6171,f9179]) ).
fof(f6171,plain,
( spl19_396
<=> ! [X5] :
( subset(succ(sK1),X5)
| ~ ordinal_subset(succ(sK1),X5)
| ~ empty(X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_396])]) ).
fof(f6188,plain,
( spl19_400
<=> ! [X5] :
( in(X5,succ(sK1))
| succ(sK1) = X5
| ~ empty(X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_400])]) ).
fof(f9084,plain,
( spl19_550
<=> ! [X1] :
( ~ in(X1,succ(sK1))
| succ(sK1) = X1
| ~ subset(succ(sK1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_550])]) ).
fof(f9175,plain,
( ! [X0] :
( succ(sK1) = X0
| ~ ordinal_subset(succ(sK1),X0)
| ~ empty(X0) )
| ~ spl19_396
| ~ spl19_400
| ~ spl19_550 ),
inference(subsumption_resolution,[],[f9156,f6189]) ).
fof(f6189,plain,
( ! [X5] :
( ~ empty(X5)
| succ(sK1) = X5
| in(X5,succ(sK1)) )
| ~ spl19_400 ),
inference(avatar_component_clause,[],[f6188]) ).
fof(f9156,plain,
( ! [X0] :
( succ(sK1) = X0
| ~ in(X0,succ(sK1))
| ~ ordinal_subset(succ(sK1),X0)
| ~ empty(X0) )
| ~ spl19_396
| ~ spl19_550 ),
inference(resolution,[],[f9085,f6172]) ).
fof(f6172,plain,
( ! [X5] :
( subset(succ(sK1),X5)
| ~ ordinal_subset(succ(sK1),X5)
| ~ empty(X5) )
| ~ spl19_396 ),
inference(avatar_component_clause,[],[f6171]) ).
fof(f9085,plain,
( ! [X1] :
( ~ subset(succ(sK1),X1)
| succ(sK1) = X1
| ~ in(X1,succ(sK1)) )
| ~ spl19_550 ),
inference(avatar_component_clause,[],[f9084]) ).
fof(f9146,plain,
( ~ spl19_558
| ~ spl19_32
| spl19_554 ),
inference(avatar_split_clause,[],[f9141,f9100,f411,f9143]) ).
fof(f9143,plain,
( spl19_558
<=> empty(sK2(powerset(sK0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_558])]) ).
fof(f9100,plain,
( spl19_554
<=> ordinal(sK2(powerset(sK0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_554])]) ).
fof(f9141,plain,
( ~ empty(sK2(powerset(sK0)))
| ~ spl19_32
| spl19_554 ),
inference(resolution,[],[f9102,f412]) ).
fof(f9102,plain,
( ~ ordinal(sK2(powerset(sK0)))
| spl19_554 ),
inference(avatar_component_clause,[],[f9100]) ).
fof(f9118,plain,
( ~ spl19_557
| ~ spl19_29
| spl19_556 ),
inference(avatar_split_clause,[],[f9113,f9108,f399,f9115]) ).
fof(f9115,plain,
( spl19_557
<=> ordinal(powerset(sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_557])]) ).
fof(f399,plain,
( spl19_29
<=> ! [X0] :
( epsilon_transitive(X0)
| ~ ordinal(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_29])]) ).
fof(f9108,plain,
( spl19_556
<=> epsilon_transitive(powerset(sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_556])]) ).
fof(f9113,plain,
( ~ ordinal(powerset(sK0))
| ~ spl19_29
| spl19_556 ),
inference(resolution,[],[f9109,f400]) ).
fof(f400,plain,
( ! [X0] :
( epsilon_transitive(X0)
| ~ ordinal(X0) )
| ~ spl19_29 ),
inference(avatar_component_clause,[],[f399]) ).
fof(f9109,plain,
( ~ epsilon_transitive(powerset(sK0))
| spl19_556 ),
inference(avatar_component_clause,[],[f9108]) ).
fof(f9111,plain,
( ~ spl19_554
| spl19_555
| spl19_556
| ~ spl19_112
| ~ spl19_416 ),
inference(avatar_split_clause,[],[f7386,f6427,f952,f9108,f9104,f9100]) ).
fof(f9104,plain,
( spl19_555
<=> ordinal_subset(sK2(powerset(sK0)),sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_555])]) ).
fof(f952,plain,
( spl19_112
<=> ! [X5] :
( ~ subset(X5,sK0)
| ordinal_subset(X5,sK0)
| ~ ordinal(X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_112])]) ).
fof(f6427,plain,
( spl19_416
<=> ! [X0] :
( subset(sK2(powerset(X0)),X0)
| epsilon_transitive(powerset(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_416])]) ).
fof(f7386,plain,
( epsilon_transitive(powerset(sK0))
| ordinal_subset(sK2(powerset(sK0)),sK0)
| ~ ordinal(sK2(powerset(sK0)))
| ~ spl19_112
| ~ spl19_416 ),
inference(resolution,[],[f6428,f953]) ).
fof(f953,plain,
( ! [X5] :
( ~ subset(X5,sK0)
| ordinal_subset(X5,sK0)
| ~ ordinal(X5) )
| ~ spl19_112 ),
inference(avatar_component_clause,[],[f952]) ).
fof(f6428,plain,
( ! [X0] :
( subset(sK2(powerset(X0)),X0)
| epsilon_transitive(powerset(X0)) )
| ~ spl19_416 ),
inference(avatar_component_clause,[],[f6427]) ).
fof(f9098,plain,
( spl19_553
| ~ spl19_264
| ~ spl19_300 ),
inference(avatar_split_clause,[],[f4332,f3696,f3093,f9096]) ).
fof(f9096,plain,
( spl19_553
<=> ! [X6,X7] : set_union2(X6,X7) = set_union2(X7,set_union2(X6,X7)) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_553])]) ).
fof(f3093,plain,
( spl19_264
<=> ! [X0,X1] :
( in(sK5(X0,X1,X1),X0)
| set_union2(X0,X1) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_264])]) ).
fof(f3696,plain,
( spl19_300
<=> ! [X10,X7,X9,X8] :
( ~ in(sK5(X7,X8,set_union2(X9,X10)),X7)
| set_union2(X9,X10) = set_union2(X7,X8)
| ~ in(sK5(X7,X8,set_union2(X9,X10)),X10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_300])]) ).
fof(f4332,plain,
( ! [X6,X7] : set_union2(X6,X7) = set_union2(X7,set_union2(X6,X7))
| ~ spl19_264
| ~ spl19_300 ),
inference(subsumption_resolution,[],[f4331,f3094]) ).
fof(f3094,plain,
( ! [X0,X1] :
( in(sK5(X0,X1,X1),X0)
| set_union2(X0,X1) = X1 )
| ~ spl19_264 ),
inference(avatar_component_clause,[],[f3093]) ).
fof(f4331,plain,
( ! [X6,X7] :
( set_union2(X6,X7) = set_union2(X7,set_union2(X6,X7))
| ~ in(sK5(X7,set_union2(X6,X7),set_union2(X6,X7)),X7) )
| ~ spl19_264
| ~ spl19_300 ),
inference(duplicate_literal_removal,[],[f4316]) ).
fof(f4316,plain,
( ! [X6,X7] :
( set_union2(X6,X7) = set_union2(X7,set_union2(X6,X7))
| ~ in(sK5(X7,set_union2(X6,X7),set_union2(X6,X7)),X7)
| set_union2(X6,X7) = set_union2(X7,set_union2(X6,X7)) )
| ~ spl19_264
| ~ spl19_300 ),
inference(resolution,[],[f3697,f3094]) ).
fof(f3697,plain,
( ! [X10,X8,X9,X7] :
( ~ in(sK5(X7,X8,set_union2(X9,X10)),X10)
| set_union2(X9,X10) = set_union2(X7,X8)
| ~ in(sK5(X7,X8,set_union2(X9,X10)),X7) )
| ~ spl19_300 ),
inference(avatar_component_clause,[],[f3696]) ).
fof(f9094,plain,
( spl19_552
| ~ spl19_229
| ~ spl19_257 ),
inference(avatar_split_clause,[],[f2963,f2934,f2606,f9092]) ).
fof(f9092,plain,
( spl19_552
<=> ! [X2] :
( ~ ordinal_subset(sK1,X2)
| ~ empty(X2)
| in(sK1,powerset(X2))
| empty(powerset(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_552])]) ).
fof(f2934,plain,
( spl19_257
<=> ! [X8] :
( subset(sK1,X8)
| ~ ordinal_subset(sK1,X8)
| ~ empty(X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_257])]) ).
fof(f2963,plain,
( ! [X2] :
( ~ ordinal_subset(sK1,X2)
| ~ empty(X2)
| in(sK1,powerset(X2))
| empty(powerset(X2)) )
| ~ spl19_229
| ~ spl19_257 ),
inference(resolution,[],[f2935,f2607]) ).
fof(f2935,plain,
( ! [X8] :
( subset(sK1,X8)
| ~ ordinal_subset(sK1,X8)
| ~ empty(X8) )
| ~ spl19_257 ),
inference(avatar_component_clause,[],[f2934]) ).
fof(f9090,plain,
( spl19_551
| ~ spl19_229
| ~ spl19_255 ),
inference(avatar_split_clause,[],[f2947,f2926,f2606,f9088]) ).
fof(f9088,plain,
( spl19_551
<=> ! [X2] :
( ~ ordinal_subset(sK0,X2)
| ~ empty(X2)
| in(sK0,powerset(X2))
| empty(powerset(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_551])]) ).
fof(f2926,plain,
( spl19_255
<=> ! [X7] :
( subset(sK0,X7)
| ~ ordinal_subset(sK0,X7)
| ~ empty(X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_255])]) ).
fof(f2947,plain,
( ! [X2] :
( ~ ordinal_subset(sK0,X2)
| ~ empty(X2)
| in(sK0,powerset(X2))
| empty(powerset(X2)) )
| ~ spl19_229
| ~ spl19_255 ),
inference(resolution,[],[f2927,f2607]) ).
fof(f2927,plain,
( ! [X7] :
( subset(sK0,X7)
| ~ ordinal_subset(sK0,X7)
| ~ empty(X7) )
| ~ spl19_255 ),
inference(avatar_component_clause,[],[f2926]) ).
fof(f9086,plain,
( spl19_550
| ~ spl19_89
| ~ spl19_247 ),
inference(avatar_split_clause,[],[f2837,f2816,f765,f9084]) ).
fof(f2816,plain,
( spl19_247
<=> ! [X7] :
( subset(X7,succ(sK1))
| ~ in(X7,succ(sK1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_247])]) ).
fof(f2837,plain,
( ! [X1] :
( ~ in(X1,succ(sK1))
| succ(sK1) = X1
| ~ subset(succ(sK1),X1) )
| ~ spl19_89
| ~ spl19_247 ),
inference(resolution,[],[f2817,f766]) ).
fof(f2817,plain,
( ! [X7] :
( subset(X7,succ(sK1))
| ~ in(X7,succ(sK1)) )
| ~ spl19_247 ),
inference(avatar_component_clause,[],[f2816]) ).
fof(f9082,plain,
( spl19_549
| ~ spl19_264
| ~ spl19_296 ),
inference(avatar_split_clause,[],[f3830,f3679,f3093,f9080]) ).
fof(f9080,plain,
( spl19_549
<=> ! [X6,X7] : set_union2(X6,X7) = set_union2(X6,set_union2(X6,X7)) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_549])]) ).
fof(f3679,plain,
( spl19_296
<=> ! [X5,X4,X6,X3] :
( ~ in(sK5(X3,X4,set_union2(X5,X6)),X3)
| set_union2(X3,X4) = set_union2(X5,X6)
| ~ in(sK5(X3,X4,set_union2(X5,X6)),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_296])]) ).
fof(f3830,plain,
( ! [X6,X7] : set_union2(X6,X7) = set_union2(X6,set_union2(X6,X7))
| ~ spl19_264
| ~ spl19_296 ),
inference(subsumption_resolution,[],[f3829,f3094]) ).
fof(f3829,plain,
( ! [X6,X7] :
( set_union2(X6,X7) = set_union2(X6,set_union2(X6,X7))
| ~ in(sK5(X6,set_union2(X6,X7),set_union2(X6,X7)),X6) )
| ~ spl19_264
| ~ spl19_296 ),
inference(duplicate_literal_removal,[],[f3814]) ).
fof(f3814,plain,
( ! [X6,X7] :
( set_union2(X6,X7) = set_union2(X6,set_union2(X6,X7))
| ~ in(sK5(X6,set_union2(X6,X7),set_union2(X6,X7)),X6)
| set_union2(X6,X7) = set_union2(X6,set_union2(X6,X7)) )
| ~ spl19_264
| ~ spl19_296 ),
inference(resolution,[],[f3680,f3094]) ).
fof(f3680,plain,
( ! [X3,X6,X4,X5] :
( ~ in(sK5(X3,X4,set_union2(X5,X6)),X5)
| set_union2(X3,X4) = set_union2(X5,X6)
| ~ in(sK5(X3,X4,set_union2(X5,X6)),X3) )
| ~ spl19_296 ),
inference(avatar_component_clause,[],[f3679]) ).
fof(f9073,plain,
( spl19_548
| ~ spl19_256
| ~ spl19_474 ),
inference(avatar_split_clause,[],[f7775,f7762,f2930,f9071]) ).
fof(f9071,plain,
( spl19_548
<=> ! [X5] :
( ~ in(singleton(X5),sK1)
| in(sK0,X5)
| ~ in(sK0,succ(X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_548])]) ).
fof(f7775,plain,
( ! [X5] :
( ~ in(singleton(X5),sK1)
| in(sK0,X5)
| ~ in(sK0,succ(X5)) )
| ~ spl19_256
| ~ spl19_474 ),
inference(resolution,[],[f7763,f2931]) ).
fof(f9069,plain,
( spl19_547
| ~ spl19_70
| ~ spl19_120
| ~ spl19_290 ),
inference(avatar_split_clause,[],[f3660,f3633,f1018,f616,f9067]) ).
fof(f9067,plain,
( spl19_547
<=> ! [X4,X5] :
( singleton(X5) = singleton(X4)
| ~ in(X4,singleton(X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_547])]) ).
fof(f1018,plain,
( spl19_120
<=> ! [X0,X1] :
( singleton(X0) = X1
| sK4(X0,X1) != X0
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_120])]) ).
fof(f3633,plain,
( spl19_290
<=> ! [X6,X7] :
( sK4(X6,singleton(X7)) = X6
| singleton(X6) = singleton(X7)
| sK4(X6,singleton(X7)) = X7 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_290])]) ).
fof(f3660,plain,
( ! [X4,X5] :
( singleton(X5) = singleton(X4)
| ~ in(X4,singleton(X5)) )
| ~ spl19_70
| ~ spl19_120
| ~ spl19_290 ),
inference(subsumption_resolution,[],[f3659,f1019]) ).
fof(f1019,plain,
( ! [X0,X1] :
( sK4(X0,X1) != X0
| singleton(X0) = X1
| ~ in(X0,X1) )
| ~ spl19_120 ),
inference(avatar_component_clause,[],[f1018]) ).
fof(f3659,plain,
( ! [X4,X5] :
( singleton(X5) = singleton(X4)
| ~ in(X4,singleton(X5))
| sK4(X4,singleton(X5)) = X4 )
| ~ spl19_70
| ~ spl19_120
| ~ spl19_290 ),
inference(subsumption_resolution,[],[f3656,f617]) ).
fof(f3656,plain,
( ! [X4,X5] :
( X4 != X5
| singleton(X5) = singleton(X4)
| ~ in(X4,singleton(X5))
| sK4(X4,singleton(X5)) = X4 )
| ~ spl19_120
| ~ spl19_290 ),
inference(duplicate_literal_removal,[],[f3648]) ).
fof(f3648,plain,
( ! [X4,X5] :
( X4 != X5
| singleton(X5) = singleton(X4)
| ~ in(X4,singleton(X5))
| sK4(X4,singleton(X5)) = X4
| singleton(X5) = singleton(X4) )
| ~ spl19_120
| ~ spl19_290 ),
inference(superposition,[],[f1019,f3634]) ).
fof(f3634,plain,
( ! [X6,X7] :
( sK4(X6,singleton(X7)) = X7
| sK4(X6,singleton(X7)) = X6
| singleton(X6) = singleton(X7) )
| ~ spl19_290 ),
inference(avatar_component_clause,[],[f3633]) ).
fof(f9065,plain,
( spl19_546
| ~ spl19_52
| ~ spl19_471 ),
inference(avatar_split_clause,[],[f9043,f7671,f508,f9063]) ).
fof(f9063,plain,
( spl19_546
<=> ! [X6] :
( set_union2(X6,sK1) = X6
| ~ in(sK0,sK5(X6,sK1,X6)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_546])]) ).
fof(f7671,plain,
( spl19_471
<=> ! [X11] :
( in(sK5(X11,sK1,X11),sK0)
| set_union2(X11,sK1) = X11 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_471])]) ).
fof(f9043,plain,
( ! [X6] :
( set_union2(X6,sK1) = X6
| ~ in(sK0,sK5(X6,sK1,X6)) )
| ~ spl19_52
| ~ spl19_471 ),
inference(resolution,[],[f7672,f509]) ).
fof(f7672,plain,
( ! [X11] :
( in(sK5(X11,sK1,X11),sK0)
| set_union2(X11,sK1) = X11 )
| ~ spl19_471 ),
inference(avatar_component_clause,[],[f7671]) ).
fof(f9061,plain,
( spl19_545
| ~ spl19_52
| ~ spl19_470 ),
inference(avatar_split_clause,[],[f7693,f7667,f508,f9059]) ).
fof(f9059,plain,
( spl19_545
<=> ! [X6] :
( set_union2(sK1,X6) = X6
| ~ in(sK0,sK5(sK1,X6,X6)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_545])]) ).
fof(f7667,plain,
( spl19_470
<=> ! [X10] :
( in(sK5(sK1,X10,X10),sK0)
| set_union2(sK1,X10) = X10 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_470])]) ).
fof(f7693,plain,
( ! [X6] :
( set_union2(sK1,X6) = X6
| ~ in(sK0,sK5(sK1,X6,X6)) )
| ~ spl19_52
| ~ spl19_470 ),
inference(resolution,[],[f7668,f509]) ).
fof(f7668,plain,
( ! [X10] :
( in(sK5(sK1,X10,X10),sK0)
| set_union2(sK1,X10) = X10 )
| ~ spl19_470 ),
inference(avatar_component_clause,[],[f7667]) ).
fof(f9035,plain,
( spl19_544
| ~ spl19_46
| ~ spl19_278 ),
inference(avatar_split_clause,[],[f3501,f3437,f484,f9033]) ).
fof(f3437,plain,
( spl19_278
<=> ! [X4,X5] :
( X4 = X5
| in(sK5(X4,X4,X5),X5)
| in(sK5(X4,X4,X5),X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_278])]) ).
fof(f3501,plain,
( ! [X12] :
( in(sK5(empty_set,empty_set,X12),X12)
| empty_set = X12 )
| ~ spl19_46
| ~ spl19_278 ),
inference(resolution,[],[f3438,f485]) ).
fof(f3438,plain,
( ! [X4,X5] :
( in(sK5(X4,X4,X5),X5)
| in(sK5(X4,X4,X5),X4)
| X4 = X5 )
| ~ spl19_278 ),
inference(avatar_component_clause,[],[f3437]) ).
fof(f9031,plain,
( spl19_537
| spl19_538
| ~ spl19_143
| ~ spl19_403
| spl19_475 ),
inference(avatar_split_clause,[],[f8852,f7791,f6219,f1175,f8782,f8778]) ).
fof(f8778,plain,
( spl19_537
<=> sK1 = succ(succ(sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_537])]) ).
fof(f8782,plain,
( spl19_538
<=> in(sK1,succ(succ(sK0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_538])]) ).
fof(f1175,plain,
( spl19_143
<=> ! [X6] :
( sK1 = X6
| in(X6,sK1)
| in(sK1,X6)
| ~ ordinal(X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_143])]) ).
fof(f6219,plain,
( spl19_403
<=> ordinal(succ(succ(sK0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_403])]) ).
fof(f7791,plain,
( spl19_475
<=> in(succ(succ(sK0)),sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_475])]) ).
fof(f8852,plain,
( in(sK1,succ(succ(sK0)))
| sK1 = succ(succ(sK0))
| ~ spl19_143
| ~ spl19_403
| spl19_475 ),
inference(subsumption_resolution,[],[f6237,f7793]) ).
fof(f7793,plain,
( ~ in(succ(succ(sK0)),sK1)
| spl19_475 ),
inference(avatar_component_clause,[],[f7791]) ).
fof(f6237,plain,
( in(succ(succ(sK0)),sK1)
| in(sK1,succ(succ(sK0)))
| sK1 = succ(succ(sK0))
| ~ spl19_143
| ~ spl19_403 ),
inference(resolution,[],[f6220,f1176]) ).
fof(f1176,plain,
( ! [X6] :
( ~ ordinal(X6)
| in(X6,sK1)
| in(sK1,X6)
| sK1 = X6 )
| ~ spl19_143 ),
inference(avatar_component_clause,[],[f1175]) ).
fof(f6220,plain,
( ordinal(succ(succ(sK0)))
| ~ spl19_403 ),
inference(avatar_component_clause,[],[f6219]) ).
fof(f9016,plain,
( spl19_543
| ~ spl19_46
| ~ spl19_278 ),
inference(avatar_split_clause,[],[f3489,f3437,f484,f9014]) ).
fof(f3489,plain,
( ! [X14] :
( in(sK5(X14,X14,empty_set),X14)
| empty_set = X14 )
| ~ spl19_46
| ~ spl19_278 ),
inference(resolution,[],[f3438,f485]) ).
fof(f9008,plain,
( ~ spl19_542
| ~ spl19_539
| spl19_540 ),
inference(avatar_split_clause,[],[f8925,f8858,f8854,f9005]) ).
fof(f9005,plain,
( spl19_542
<=> in(sK8,sK8) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_542])]) ).
fof(f8854,plain,
( spl19_539
<=> sK8 = sK10 ),
introduced(avatar_definition,[new_symbols(naming,[spl19_539])]) ).
fof(f8858,plain,
( spl19_540
<=> in(sK8,sK10) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_540])]) ).
fof(f8925,plain,
( ~ in(sK8,sK8)
| ~ spl19_539
| spl19_540 ),
inference(backward_demodulation,[],[f8859,f8856]) ).
fof(f8856,plain,
( sK8 = sK10
| ~ spl19_539 ),
inference(avatar_component_clause,[],[f8854]) ).
fof(f8859,plain,
( ~ in(sK8,sK10)
| spl19_540 ),
inference(avatar_component_clause,[],[f8858]) ).
fof(f8865,plain,
( spl19_539
| spl19_540
| spl19_541
| ~ spl19_18
| ~ spl19_260 ),
inference(avatar_split_clause,[],[f3168,f2958,f348,f8862,f8858,f8854]) ).
fof(f8862,plain,
( spl19_541
<=> in(sK10,sK8) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_541])]) ).
fof(f348,plain,
( spl19_18
<=> ordinal(sK10) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_18])]) ).
fof(f2958,plain,
( spl19_260
<=> ! [X7] :
( sK8 = X7
| in(X7,sK8)
| in(sK8,X7)
| ~ ordinal(X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_260])]) ).
fof(f3168,plain,
( in(sK10,sK8)
| in(sK8,sK10)
| sK8 = sK10
| ~ spl19_18
| ~ spl19_260 ),
inference(resolution,[],[f2959,f350]) ).
fof(f350,plain,
( ordinal(sK10)
| ~ spl19_18 ),
inference(avatar_component_clause,[],[f348]) ).
fof(f2959,plain,
( ! [X7] :
( ~ ordinal(X7)
| in(X7,sK8)
| in(sK8,X7)
| sK8 = X7 )
| ~ spl19_260 ),
inference(avatar_component_clause,[],[f2958]) ).
fof(f8851,plain,
( spl19_4
| ~ spl19_405
| ~ spl19_537 ),
inference(avatar_contradiction_clause,[],[f8850]) ).
fof(f8850,plain,
( $false
| spl19_4
| ~ spl19_405
| ~ spl19_537 ),
inference(subsumption_resolution,[],[f8809,f278]) ).
fof(f278,plain,
( ~ ordinal_subset(sK0,sK1)
| spl19_4 ),
inference(avatar_component_clause,[],[f277]) ).
fof(f277,plain,
( spl19_4
<=> ordinal_subset(sK0,sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_4])]) ).
fof(f8809,plain,
( ordinal_subset(sK0,sK1)
| ~ spl19_405
| ~ spl19_537 ),
inference(backward_demodulation,[],[f6259,f8780]) ).
fof(f8780,plain,
( sK1 = succ(succ(sK0))
| ~ spl19_537 ),
inference(avatar_component_clause,[],[f8778]) ).
fof(f6259,plain,
( ordinal_subset(sK0,succ(succ(sK0)))
| ~ spl19_405 ),
inference(avatar_component_clause,[],[f6257]) ).
fof(f6257,plain,
( spl19_405
<=> ordinal_subset(sK0,succ(succ(sK0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_405])]) ).
fof(f8839,plain,
( ~ spl19_148
| spl19_402
| ~ spl19_537 ),
inference(avatar_contradiction_clause,[],[f8838]) ).
fof(f8838,plain,
( $false
| ~ spl19_148
| spl19_402
| ~ spl19_537 ),
inference(subsumption_resolution,[],[f8796,f1413]) ).
fof(f1413,plain,
( ordinal_subset(sK1,sK0)
| ~ spl19_148 ),
inference(avatar_component_clause,[],[f1412]) ).
fof(f1412,plain,
( spl19_148
<=> ordinal_subset(sK1,sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_148])]) ).
fof(f8796,plain,
( ~ ordinal_subset(sK1,sK0)
| spl19_402
| ~ spl19_537 ),
inference(backward_demodulation,[],[f6217,f8780]) ).
fof(f6217,plain,
( ~ ordinal_subset(succ(succ(sK0)),sK0)
| spl19_402 ),
inference(avatar_component_clause,[],[f6215]) ).
fof(f6215,plain,
( spl19_402
<=> ordinal_subset(succ(succ(sK0)),sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_402])]) ).
fof(f8824,plain,
( spl19_101
| ~ spl19_188
| ~ spl19_537 ),
inference(avatar_contradiction_clause,[],[f8823]) ).
fof(f8823,plain,
( $false
| spl19_101
| ~ spl19_188
| ~ spl19_537 ),
inference(subsumption_resolution,[],[f8787,f870]) ).
fof(f8787,plain,
( in(sK0,sK1)
| ~ spl19_188
| ~ spl19_537 ),
inference(backward_demodulation,[],[f1897,f8780]) ).
fof(f1897,plain,
( in(sK0,succ(succ(sK0)))
| ~ spl19_188 ),
inference(avatar_component_clause,[],[f1895]) ).
fof(f1895,plain,
( spl19_188
<=> in(sK0,succ(succ(sK0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_188])]) ).
fof(f8785,plain,
( spl19_537
| spl19_538
| ~ spl19_185
| ~ spl19_186
| spl19_475 ),
inference(avatar_split_clause,[],[f7796,f7791,f1887,f1876,f8782,f8778]) ).
fof(f1887,plain,
( spl19_186
<=> ordinal(succ(sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_186])]) ).
fof(f7796,plain,
( in(sK1,succ(succ(sK0)))
| sK1 = succ(succ(sK0))
| ~ spl19_185
| ~ spl19_186
| spl19_475 ),
inference(subsumption_resolution,[],[f7795,f1888]) ).
fof(f1888,plain,
( ordinal(succ(sK0))
| ~ spl19_186 ),
inference(avatar_component_clause,[],[f1887]) ).
fof(f7795,plain,
( in(sK1,succ(succ(sK0)))
| sK1 = succ(succ(sK0))
| ~ ordinal(succ(sK0))
| ~ spl19_185
| spl19_475 ),
inference(resolution,[],[f7793,f1877]) ).
fof(f8749,plain,
( spl19_535
| ~ spl19_536
| ~ spl19_408
| ~ spl19_491 ),
inference(avatar_split_clause,[],[f8167,f8091,f6278,f8746,f8742]) ).
fof(f8742,plain,
( spl19_535
<=> empty(powerset(succ(sK0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_535])]) ).
fof(f8746,plain,
( spl19_536
<=> in(powerset(succ(sK0)),sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_536])]) ).
fof(f6278,plain,
( spl19_408
<=> ! [X0] :
( in(X0,powerset(X0))
| empty(powerset(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_408])]) ).
fof(f8091,plain,
( spl19_491
<=> ! [X4] :
( ~ in(succ(sK0),X4)
| ~ in(X4,sK1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_491])]) ).
fof(f8167,plain,
( ~ in(powerset(succ(sK0)),sK1)
| empty(powerset(succ(sK0)))
| ~ spl19_408
| ~ spl19_491 ),
inference(resolution,[],[f8092,f6279]) ).
fof(f6279,plain,
( ! [X0] :
( in(X0,powerset(X0))
| empty(powerset(X0)) )
| ~ spl19_408 ),
inference(avatar_component_clause,[],[f6278]) ).
fof(f8092,plain,
( ! [X4] :
( ~ in(succ(sK0),X4)
| ~ in(X4,sK1) )
| ~ spl19_491 ),
inference(avatar_component_clause,[],[f8091]) ).
fof(f8739,plain,
( spl19_534
| ~ spl19_420
| ~ spl19_490 ),
inference(avatar_split_clause,[],[f8102,f8087,f6480,f8737]) ).
fof(f8737,plain,
( spl19_534
<=> ! [X7] :
( ~ in(succ(X7),sK1)
| ~ in(succ(sK0),singleton(X7)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_534])]) ).
fof(f6480,plain,
( spl19_420
<=> ! [X9,X8] :
( ~ in(succ(X8),X9)
| ~ in(X9,singleton(X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_420])]) ).
fof(f8102,plain,
( ! [X7] :
( ~ in(succ(X7),sK1)
| ~ in(succ(sK0),singleton(X7)) )
| ~ spl19_420
| ~ spl19_490 ),
inference(resolution,[],[f8088,f6481]) ).
fof(f6481,plain,
( ! [X8,X9] :
( ~ in(succ(X8),X9)
| ~ in(X9,singleton(X8)) )
| ~ spl19_420 ),
inference(avatar_component_clause,[],[f6480]) ).
fof(f8735,plain,
( spl19_533
| ~ spl19_163
| ~ spl19_490 ),
inference(avatar_split_clause,[],[f8096,f8087,f1741,f8733]) ).
fof(f8733,plain,
( spl19_533
<=> ! [X4,X3] :
( ~ in(set_union2(X3,X4),sK1)
| ~ in(succ(sK0),X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_533])]) ).
fof(f8096,plain,
( ! [X3,X4] :
( ~ in(set_union2(X3,X4),sK1)
| ~ in(succ(sK0),X4) )
| ~ spl19_163
| ~ spl19_490 ),
inference(resolution,[],[f8088,f1742]) ).
fof(f8731,plain,
( spl19_532
| ~ spl19_171
| ~ spl19_490 ),
inference(avatar_split_clause,[],[f8095,f8087,f1776,f8729]) ).
fof(f8729,plain,
( spl19_532
<=> ! [X2,X1] :
( ~ in(set_union2(X1,X2),sK1)
| ~ in(succ(sK0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_532])]) ).
fof(f8095,plain,
( ! [X2,X1] :
( ~ in(set_union2(X1,X2),sK1)
| ~ in(succ(sK0),X1) )
| ~ spl19_171
| ~ spl19_490 ),
inference(resolution,[],[f8088,f1777]) ).
fof(f8727,plain,
( ~ spl19_530
| spl19_531
| ~ spl19_72
| ~ spl19_196 ),
inference(avatar_split_clause,[],[f2482,f1975,f645,f8724,f8720]) ).
fof(f8720,plain,
( spl19_530
<=> ordinal(sK3(powerset(sK10))) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_530])]) ).
fof(f8724,plain,
( spl19_531
<=> ordinal_subset(sK3(powerset(sK10)),sK10) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_531])]) ).
fof(f1975,plain,
( spl19_196
<=> ! [X8] :
( ~ subset(X8,sK10)
| ordinal_subset(X8,sK10)
| ~ ordinal(X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_196])]) ).
fof(f2482,plain,
( ordinal_subset(sK3(powerset(sK10)),sK10)
| ~ ordinal(sK3(powerset(sK10)))
| ~ spl19_72
| ~ spl19_196 ),
inference(resolution,[],[f1976,f646]) ).
fof(f1976,plain,
( ! [X8] :
( ~ subset(X8,sK10)
| ordinal_subset(X8,sK10)
| ~ ordinal(X8) )
| ~ spl19_196 ),
inference(avatar_component_clause,[],[f1975]) ).
fof(f8644,plain,
( spl19_529
| ~ spl19_171
| ~ spl19_481 ),
inference(avatar_split_clause,[],[f8607,f7859,f1776,f8642]) ).
fof(f8607,plain,
( ! [X16,X17] :
( ~ in(set_union2(X16,sK0),X17)
| ~ in(X17,sK1) )
| ~ spl19_171
| ~ spl19_481 ),
inference(superposition,[],[f1777,f7860]) ).
fof(f8640,plain,
( spl19_528
| ~ spl19_80
| ~ spl19_481 ),
inference(avatar_split_clause,[],[f8600,f7859,f689,f8638]) ).
fof(f8600,plain,
( ! [X6,X7] :
( in(X7,set_union2(X6,sK0))
| ~ in(X7,sK1) )
| ~ spl19_80
| ~ spl19_481 ),
inference(superposition,[],[f690,f7860]) ).
fof(f8591,plain,
( spl19_527
| ~ spl19_404
| ~ spl19_490 ),
inference(avatar_split_clause,[],[f8103,f8087,f6228,f8589]) ).
fof(f8589,plain,
( spl19_527
<=> ! [X8] :
( ~ in(succ(X8),sK1)
| ~ in(succ(sK0),X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_527])]) ).
fof(f6228,plain,
( spl19_404
<=> ! [X2,X1] :
( ~ in(X1,X2)
| ~ in(succ(X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_404])]) ).
fof(f8103,plain,
( ! [X8] :
( ~ in(succ(X8),sK1)
| ~ in(succ(sK0),X8) )
| ~ spl19_404
| ~ spl19_490 ),
inference(resolution,[],[f8088,f6229]) ).
fof(f6229,plain,
( ! [X2,X1] :
( ~ in(succ(X2),X1)
| ~ in(X1,X2) )
| ~ spl19_404 ),
inference(avatar_component_clause,[],[f6228]) ).
fof(f8545,plain,
( spl19_526
| ~ spl19_58
| ~ spl19_522 ),
inference(avatar_split_clause,[],[f8523,f8514,f545,f8543]) ).
fof(f8543,plain,
( spl19_526
<=> ! [X0] : ~ in(set_union2(X0,sK0),sK3(sK3(empty_set))) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_526])]) ).
fof(f8514,plain,
( spl19_522
<=> ! [X1] : ~ in(set_union2(sK0,X1),sK3(sK3(empty_set))) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_522])]) ).
fof(f8523,plain,
( ! [X0] : ~ in(set_union2(X0,sK0),sK3(sK3(empty_set)))
| ~ spl19_58
| ~ spl19_522 ),
inference(superposition,[],[f8515,f546]) ).
fof(f8515,plain,
( ! [X1] : ~ in(set_union2(sK0,X1),sK3(sK3(empty_set)))
| ~ spl19_522 ),
inference(avatar_component_clause,[],[f8514]) ).
fof(f8535,plain,
( ~ spl19_524
| spl19_525
| ~ spl19_72
| ~ spl19_192 ),
inference(avatar_split_clause,[],[f2470,f1958,f645,f8532,f8528]) ).
fof(f8528,plain,
( spl19_524
<=> ordinal(sK3(powerset(sK8))) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_524])]) ).
fof(f1958,plain,
( spl19_192
<=> ! [X7] :
( ~ subset(X7,sK8)
| ordinal_subset(X7,sK8)
| ~ ordinal(X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_192])]) ).
fof(f2470,plain,
( ordinal_subset(sK3(powerset(sK8)),sK8)
| ~ ordinal(sK3(powerset(sK8)))
| ~ spl19_72
| ~ spl19_192 ),
inference(resolution,[],[f1959,f646]) ).
fof(f1959,plain,
( ! [X7] :
( ~ subset(X7,sK8)
| ordinal_subset(X7,sK8)
| ~ ordinal(X7) )
| ~ spl19_192 ),
inference(avatar_component_clause,[],[f1958]) ).
fof(f8520,plain,
( spl19_523
| ~ spl19_58
| ~ spl19_519 ),
inference(avatar_split_clause,[],[f8384,f8377,f545,f8518]) ).
fof(f8518,plain,
( spl19_523
<=> ! [X0] : in(sK3(sK3(empty_set)),set_union2(X0,sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_523])]) ).
fof(f8377,plain,
( spl19_519
<=> ! [X8] : in(sK3(sK3(empty_set)),set_union2(sK0,X8)) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_519])]) ).
fof(f8384,plain,
( ! [X0] : in(sK3(sK3(empty_set)),set_union2(X0,sK0))
| ~ spl19_58
| ~ spl19_519 ),
inference(superposition,[],[f8378,f546]) ).
fof(f8378,plain,
( ! [X8] : in(sK3(sK3(empty_set)),set_union2(sK0,X8))
| ~ spl19_519 ),
inference(avatar_component_clause,[],[f8377]) ).
fof(f8516,plain,
( spl19_522
| ~ spl19_52
| ~ spl19_519 ),
inference(avatar_split_clause,[],[f8381,f8377,f508,f8514]) ).
fof(f8381,plain,
( ! [X1] : ~ in(set_union2(sK0,X1),sK3(sK3(empty_set)))
| ~ spl19_52
| ~ spl19_519 ),
inference(resolution,[],[f8378,f509]) ).
fof(f8401,plain,
( ~ spl19_521
| ~ spl19_52
| ~ spl19_520 ),
inference(avatar_split_clause,[],[f8396,f8392,f508,f8398]) ).
fof(f8398,plain,
( spl19_521
<=> in(succ(sK0),sK3(sK3(empty_set))) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_521])]) ).
fof(f8392,plain,
( spl19_520
<=> in(sK3(sK3(empty_set)),succ(sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_520])]) ).
fof(f8396,plain,
( ~ in(succ(sK0),sK3(sK3(empty_set)))
| ~ spl19_52
| ~ spl19_520 ),
inference(resolution,[],[f8394,f509]) ).
fof(f8394,plain,
( in(sK3(sK3(empty_set)),succ(sK0))
| ~ spl19_520 ),
inference(avatar_component_clause,[],[f8392]) ).
fof(f8395,plain,
( spl19_520
| ~ spl19_57
| ~ spl19_519 ),
inference(avatar_split_clause,[],[f8386,f8377,f541,f8392]) ).
fof(f8386,plain,
( in(sK3(sK3(empty_set)),succ(sK0))
| ~ spl19_57
| ~ spl19_519 ),
inference(superposition,[],[f8378,f542]) ).
fof(f8390,plain,
( ~ spl19_32
| ~ spl19_83
| ~ spl19_106
| spl19_517 ),
inference(avatar_contradiction_clause,[],[f8389]) ).
fof(f8389,plain,
( $false
| ~ spl19_32
| ~ spl19_83
| ~ spl19_106
| spl19_517 ),
inference(subsumption_resolution,[],[f8388,f902]) ).
fof(f902,plain,
( empty(sK3(powerset(empty_set)))
| ~ spl19_83
| ~ spl19_106 ),
inference(resolution,[],[f899,f713]) ).
fof(f899,plain,
( ! [X0] : ~ in(X0,sK3(powerset(empty_set)))
| ~ spl19_106 ),
inference(avatar_component_clause,[],[f898]) ).
fof(f898,plain,
( spl19_106
<=> ! [X0] : ~ in(X0,sK3(powerset(empty_set))) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_106])]) ).
fof(f8388,plain,
( ~ empty(sK3(powerset(empty_set)))
| ~ spl19_32
| spl19_517 ),
inference(resolution,[],[f8366,f412]) ).
fof(f8366,plain,
( ~ ordinal(sK3(powerset(empty_set)))
| spl19_517 ),
inference(avatar_component_clause,[],[f8364]) ).
fof(f8364,plain,
( spl19_517
<=> ordinal(sK3(powerset(empty_set))) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_517])]) ).
fof(f8379,plain,
( spl19_519
| ~ spl19_357
| ~ spl19_503 ),
inference(avatar_split_clause,[],[f8245,f8233,f5468,f8377]) ).
fof(f5468,plain,
( spl19_357
<=> in(sK3(sK3(empty_set)),sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_357])]) ).
fof(f8245,plain,
( ! [X8] : in(sK3(sK3(empty_set)),set_union2(sK0,X8))
| ~ spl19_357
| ~ spl19_503 ),
inference(resolution,[],[f8234,f5470]) ).
fof(f5470,plain,
( in(sK3(sK3(empty_set)),sK1)
| ~ spl19_357 ),
inference(avatar_component_clause,[],[f5468]) ).
fof(f8371,plain,
( ~ spl19_517
| spl19_518
| ~ spl19_72
| ~ spl19_191 ),
inference(avatar_split_clause,[],[f2432,f1924,f645,f8368,f8364]) ).
fof(f8368,plain,
( spl19_518
<=> ordinal_subset(sK3(powerset(empty_set)),empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_518])]) ).
fof(f1924,plain,
( spl19_191
<=> ! [X4] :
( ~ subset(X4,empty_set)
| ordinal_subset(X4,empty_set)
| ~ ordinal(X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_191])]) ).
fof(f2432,plain,
( ordinal_subset(sK3(powerset(empty_set)),empty_set)
| ~ ordinal(sK3(powerset(empty_set)))
| ~ spl19_72
| ~ spl19_191 ),
inference(resolution,[],[f1925,f646]) ).
fof(f1925,plain,
( ! [X4] :
( ~ subset(X4,empty_set)
| ordinal_subset(X4,empty_set)
| ~ ordinal(X4) )
| ~ spl19_191 ),
inference(avatar_component_clause,[],[f1924]) ).
fof(f8362,plain,
( spl19_516
| ~ spl19_58
| ~ spl19_513 ),
inference(avatar_split_clause,[],[f8349,f8336,f545,f8360]) ).
fof(f8360,plain,
( spl19_516
<=> ! [X0] : ~ in(set_union2(X0,sK0),sK3(sK1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_516])]) ).
fof(f8336,plain,
( spl19_513
<=> ! [X1] : ~ in(set_union2(sK0,X1),sK3(sK1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_513])]) ).
fof(f8349,plain,
( ! [X0] : ~ in(set_union2(X0,sK0),sK3(sK1))
| ~ spl19_58
| ~ spl19_513 ),
inference(superposition,[],[f8337,f546]) ).
fof(f8337,plain,
( ! [X1] : ~ in(set_union2(sK0,X1),sK3(sK1))
| ~ spl19_513 ),
inference(avatar_component_clause,[],[f8336]) ).
fof(f8346,plain,
( spl19_515
| ~ spl19_58
| ~ spl19_509 ),
inference(avatar_split_clause,[],[f8316,f8309,f545,f8344]) ).
fof(f8344,plain,
( spl19_515
<=> ! [X0] : in(sK3(sK1),set_union2(X0,sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_515])]) ).
fof(f8309,plain,
( spl19_509
<=> ! [X9] : in(sK3(sK1),set_union2(sK0,X9)) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_509])]) ).
fof(f8316,plain,
( ! [X0] : in(sK3(sK1),set_union2(X0,sK0))
| ~ spl19_58
| ~ spl19_509 ),
inference(superposition,[],[f8310,f546]) ).
fof(f8310,plain,
( ! [X9] : in(sK3(sK1),set_union2(sK0,X9))
| ~ spl19_509 ),
inference(avatar_component_clause,[],[f8309]) ).
fof(f8342,plain,
( spl19_514
| ~ spl19_98
| ~ spl19_171 ),
inference(avatar_split_clause,[],[f2142,f1776,f845,f8340]) ).
fof(f845,plain,
( spl19_98
<=> ! [X9,X8] :
( in(X9,succ(X8))
| ~ in(X9,X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_98])]) ).
fof(f2142,plain,
( ! [X2,X3,X4] :
( ~ in(succ(X2),X3)
| ~ in(set_union2(X3,X4),X2) )
| ~ spl19_98
| ~ spl19_171 ),
inference(resolution,[],[f1777,f846]) ).
fof(f846,plain,
( ! [X8,X9] :
( in(X9,succ(X8))
| ~ in(X9,X8) )
| ~ spl19_98 ),
inference(avatar_component_clause,[],[f845]) ).
fof(f8338,plain,
( spl19_513
| ~ spl19_52
| ~ spl19_509 ),
inference(avatar_split_clause,[],[f8313,f8309,f508,f8336]) ).
fof(f8313,plain,
( ! [X1] : ~ in(set_union2(sK0,X1),sK3(sK1))
| ~ spl19_52
| ~ spl19_509 ),
inference(resolution,[],[f8310,f509]) ).
fof(f8334,plain,
( ~ spl19_512
| ~ spl19_52
| ~ spl19_510 ),
inference(avatar_split_clause,[],[f8325,f8321,f508,f8331]) ).
fof(f8331,plain,
( spl19_512
<=> in(succ(sK0),sK3(sK1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_512])]) ).
fof(f8321,plain,
( spl19_510
<=> in(sK3(sK1),succ(sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_510])]) ).
fof(f8325,plain,
( ~ in(succ(sK0),sK3(sK1))
| ~ spl19_52
| ~ spl19_510 ),
inference(resolution,[],[f8323,f509]) ).
fof(f8323,plain,
( in(sK3(sK1),succ(sK0))
| ~ spl19_510 ),
inference(avatar_component_clause,[],[f8321]) ).
fof(f8329,plain,
( spl19_511
| ~ spl19_83
| ~ spl19_167 ),
inference(avatar_split_clause,[],[f2130,f1758,f712,f8327]) ).
fof(f8327,plain,
( spl19_511
<=> ! [X2] :
( in(sK3(singleton(X2)),succ(X2))
| empty(singleton(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_511])]) ).
fof(f1758,plain,
( spl19_167
<=> ! [X9,X8] :
( in(X9,succ(X8))
| ~ in(X9,singleton(X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_167])]) ).
fof(f2130,plain,
( ! [X2] :
( in(sK3(singleton(X2)),succ(X2))
| empty(singleton(X2)) )
| ~ spl19_83
| ~ spl19_167 ),
inference(resolution,[],[f1759,f713]) ).
fof(f1759,plain,
( ! [X8,X9] :
( ~ in(X9,singleton(X8))
| in(X9,succ(X8)) )
| ~ spl19_167 ),
inference(avatar_component_clause,[],[f1758]) ).
fof(f8324,plain,
( spl19_510
| ~ spl19_57
| ~ spl19_509 ),
inference(avatar_split_clause,[],[f8318,f8309,f541,f8321]) ).
fof(f8318,plain,
( in(sK3(sK1),succ(sK0))
| ~ spl19_57
| ~ spl19_509 ),
inference(superposition,[],[f8310,f542]) ).
fof(f8311,plain,
( spl19_509
| ~ spl19_83
| spl19_314
| ~ spl19_503 ),
inference(avatar_split_clause,[],[f8275,f8233,f4276,f712,f8309]) ).
fof(f4276,plain,
( spl19_314
<=> empty(sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_314])]) ).
fof(f8275,plain,
( ! [X9] : in(sK3(sK1),set_union2(sK0,X9))
| ~ spl19_83
| spl19_314
| ~ spl19_503 ),
inference(subsumption_resolution,[],[f8246,f4277]) ).
fof(f4277,plain,
( ~ empty(sK1)
| spl19_314 ),
inference(avatar_component_clause,[],[f4276]) ).
fof(f8246,plain,
( ! [X9] :
( in(sK3(sK1),set_union2(sK0,X9))
| empty(sK1) )
| ~ spl19_83
| ~ spl19_503 ),
inference(resolution,[],[f8234,f713]) ).
fof(f8307,plain,
( spl19_508
| ~ spl19_48
| ~ spl19_167 ),
inference(avatar_split_clause,[],[f2129,f1758,f492,f8305]) ).
fof(f8305,plain,
( spl19_508
<=> ! [X1] :
( in(sK2(singleton(X1)),succ(X1))
| epsilon_transitive(singleton(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_508])]) ).
fof(f2129,plain,
( ! [X1] :
( in(sK2(singleton(X1)),succ(X1))
| epsilon_transitive(singleton(X1)) )
| ~ spl19_48
| ~ spl19_167 ),
inference(resolution,[],[f1759,f493]) ).
fof(f8297,plain,
( spl19_507
| ~ spl19_58
| ~ spl19_505 ),
inference(avatar_split_clause,[],[f8290,f8279,f545,f8295]) ).
fof(f8295,plain,
( spl19_507
<=> ! [X0] : in(empty_set,set_union2(X0,sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_507])]) ).
fof(f8279,plain,
( spl19_505
<=> ! [X2] : in(empty_set,set_union2(sK0,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_505])]) ).
fof(f8290,plain,
( ! [X0] : in(empty_set,set_union2(X0,sK0))
| ~ spl19_58
| ~ spl19_505 ),
inference(superposition,[],[f8280,f546]) ).
fof(f8280,plain,
( ! [X2] : in(empty_set,set_union2(sK0,X2))
| ~ spl19_505 ),
inference(avatar_component_clause,[],[f8279]) ).
fof(f8285,plain,
( spl19_506
| ~ spl19_98
| ~ spl19_163 ),
inference(avatar_split_clause,[],[f2117,f1741,f845,f8283]) ).
fof(f2117,plain,
( ! [X2,X3,X4] :
( ~ in(succ(X2),X3)
| ~ in(set_union2(X4,X3),X2) )
| ~ spl19_98
| ~ spl19_163 ),
inference(resolution,[],[f1742,f846]) ).
fof(f8281,plain,
( spl19_505
| ~ spl19_151
| ~ spl19_503 ),
inference(avatar_split_clause,[],[f8241,f8233,f1535,f8279]) ).
fof(f8241,plain,
( ! [X2] : in(empty_set,set_union2(sK0,X2))
| ~ spl19_151
| ~ spl19_503 ),
inference(resolution,[],[f8234,f1537]) ).
fof(f8239,plain,
( spl19_504
| ~ spl19_171
| ~ spl19_480 ),
inference(avatar_split_clause,[],[f7878,f7848,f1776,f8237]) ).
fof(f7878,plain,
( ! [X16,X17] :
( ~ in(set_union2(sK0,X16),X17)
| ~ in(X17,sK1) )
| ~ spl19_171
| ~ spl19_480 ),
inference(superposition,[],[f1777,f7849]) ).
fof(f8235,plain,
( spl19_503
| ~ spl19_80
| ~ spl19_480 ),
inference(avatar_split_clause,[],[f7871,f7848,f689,f8233]) ).
fof(f7871,plain,
( ! [X6,X7] :
( in(X7,set_union2(sK0,X6))
| ~ in(X7,sK1) )
| ~ spl19_80
| ~ spl19_480 ),
inference(superposition,[],[f690,f7849]) ).
fof(f8231,plain,
( spl19_502
| ~ spl19_46
| ~ spl19_131 ),
inference(avatar_split_clause,[],[f1099,f1086,f484,f8229]) ).
fof(f8229,plain,
( spl19_502
<=> ! [X8] :
( sK4(X8,empty_set) = X8
| empty_set = singleton(X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_502])]) ).
fof(f1086,plain,
( spl19_131
<=> ! [X0,X1] :
( singleton(X0) = X1
| sK4(X0,X1) = X0
| in(sK4(X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_131])]) ).
fof(f1099,plain,
( ! [X8] :
( sK4(X8,empty_set) = X8
| empty_set = singleton(X8) )
| ~ spl19_46
| ~ spl19_131 ),
inference(resolution,[],[f1087,f485]) ).
fof(f1087,plain,
( ! [X0,X1] :
( in(sK4(X0,X1),X1)
| sK4(X0,X1) = X0
| singleton(X0) = X1 )
| ~ spl19_131 ),
inference(avatar_component_clause,[],[f1086]) ).
fof(f8217,plain,
( spl19_501
| ~ spl19_82
| ~ spl19_89 ),
inference(avatar_split_clause,[],[f812,f765,f703,f8215]) ).
fof(f8215,plain,
( spl19_501
<=> ! [X3] :
( sK10 = X3
| ~ subset(sK10,X3)
| ~ in(X3,sK10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_501])]) ).
fof(f703,plain,
( spl19_82
<=> ! [X8] :
( ~ in(X8,sK10)
| subset(X8,sK10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_82])]) ).
fof(f812,plain,
( ! [X3] :
( sK10 = X3
| ~ subset(sK10,X3)
| ~ in(X3,sK10) )
| ~ spl19_82
| ~ spl19_89 ),
inference(resolution,[],[f766,f704]) ).
fof(f704,plain,
( ! [X8] :
( subset(X8,sK10)
| ~ in(X8,sK10) )
| ~ spl19_82 ),
inference(avatar_component_clause,[],[f703]) ).
fof(f8200,plain,
( spl19_500
| ~ spl19_88
| ~ spl19_490 ),
inference(avatar_split_clause,[],[f8108,f8087,f761,f8198]) ).
fof(f8198,plain,
( spl19_500
<=> ! [X10] : ~ in(singleton(set_union2(X10,succ(sK0))),sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_500])]) ).
fof(f761,plain,
( spl19_88
<=> ! [X6,X5] : ~ in(singleton(set_union2(X5,X6)),X6) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_88])]) ).
fof(f8108,plain,
( ! [X10] : ~ in(singleton(set_union2(X10,succ(sK0))),sK1)
| ~ spl19_88
| ~ spl19_490 ),
inference(resolution,[],[f8088,f762]) ).
fof(f762,plain,
( ! [X6,X5] : ~ in(singleton(set_union2(X5,X6)),X6)
| ~ spl19_88 ),
inference(avatar_component_clause,[],[f761]) ).
fof(f8196,plain,
( spl19_499
| ~ spl19_81
| ~ spl19_89 ),
inference(avatar_split_clause,[],[f811,f765,f699,f8194]) ).
fof(f8194,plain,
( spl19_499
<=> ! [X2] :
( sK8 = X2
| ~ subset(sK8,X2)
| ~ in(X2,sK8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_499])]) ).
fof(f811,plain,
( ! [X2] :
( sK8 = X2
| ~ subset(sK8,X2)
| ~ in(X2,sK8) )
| ~ spl19_81
| ~ spl19_89 ),
inference(resolution,[],[f766,f700]) ).
fof(f8192,plain,
( ~ spl19_498
| ~ spl19_104
| ~ spl19_490 ),
inference(avatar_split_clause,[],[f8107,f8087,f881,f8189]) ).
fof(f8189,plain,
( spl19_498
<=> in(singleton(succ(succ(succ(sK0)))),sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_498])]) ).
fof(f881,plain,
( spl19_104
<=> ! [X12] : ~ in(singleton(succ(succ(X12))),X12) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_104])]) ).
fof(f8107,plain,
( ~ in(singleton(succ(succ(succ(sK0)))),sK1)
| ~ spl19_104
| ~ spl19_490 ),
inference(resolution,[],[f8088,f882]) ).
fof(f882,plain,
( ! [X12] : ~ in(singleton(succ(succ(X12))),X12)
| ~ spl19_104 ),
inference(avatar_component_clause,[],[f881]) ).
fof(f8187,plain,
( spl19_497
| ~ spl19_91
| ~ spl19_490 ),
inference(avatar_split_clause,[],[f8105,f8087,f773,f8185]) ).
fof(f8185,plain,
( spl19_497
<=> ! [X9] : ~ in(singleton(set_union2(succ(sK0),X9)),sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_497])]) ).
fof(f773,plain,
( spl19_91
<=> ! [X6,X5] : ~ in(singleton(set_union2(X5,X6)),X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_91])]) ).
fof(f8105,plain,
( ! [X9] : ~ in(singleton(set_union2(succ(sK0),X9)),sK1)
| ~ spl19_91
| ~ spl19_490 ),
inference(resolution,[],[f8088,f774]) ).
fof(f774,plain,
( ! [X6,X5] : ~ in(singleton(set_union2(X5,X6)),X5)
| ~ spl19_91 ),
inference(avatar_component_clause,[],[f773]) ).
fof(f8183,plain,
( spl19_496
| ~ spl19_87
| ~ spl19_490 ),
inference(avatar_split_clause,[],[f8101,f8087,f757,f8181]) ).
fof(f8181,plain,
( spl19_496
<=> ! [X6] : ~ in(succ(set_union2(X6,succ(sK0))),sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_496])]) ).
fof(f757,plain,
( spl19_87
<=> ! [X4,X3] : ~ in(succ(set_union2(X3,X4)),X4) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_87])]) ).
fof(f8101,plain,
( ! [X6] : ~ in(succ(set_union2(X6,succ(sK0))),sK1)
| ~ spl19_87
| ~ spl19_490 ),
inference(resolution,[],[f8088,f758]) ).
fof(f758,plain,
( ! [X3,X4] : ~ in(succ(set_union2(X3,X4)),X4)
| ~ spl19_87 ),
inference(avatar_component_clause,[],[f757]) ).
fof(f8177,plain,
( ~ spl19_495
| ~ spl19_102
| ~ spl19_490 ),
inference(avatar_split_clause,[],[f8100,f8087,f873,f8174]) ).
fof(f8174,plain,
( spl19_495
<=> in(succ(succ(succ(succ(sK0)))),sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_495])]) ).
fof(f873,plain,
( spl19_102
<=> ! [X6] : ~ in(succ(succ(succ(X6))),X6) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_102])]) ).
fof(f8100,plain,
( ~ in(succ(succ(succ(succ(sK0)))),sK1)
| ~ spl19_102
| ~ spl19_490 ),
inference(resolution,[],[f8088,f874]) ).
fof(f874,plain,
( ! [X6] : ~ in(succ(succ(succ(X6))),X6)
| ~ spl19_102 ),
inference(avatar_component_clause,[],[f873]) ).
fof(f8172,plain,
( spl19_494
| ~ spl19_90
| ~ spl19_490 ),
inference(avatar_split_clause,[],[f8098,f8087,f769,f8170]) ).
fof(f8170,plain,
( spl19_494
<=> ! [X5] : ~ in(succ(set_union2(succ(sK0),X5)),sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_494])]) ).
fof(f769,plain,
( spl19_90
<=> ! [X4,X3] : ~ in(succ(set_union2(X3,X4)),X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_90])]) ).
fof(f8098,plain,
( ! [X5] : ~ in(succ(set_union2(succ(sK0),X5)),sK1)
| ~ spl19_90
| ~ spl19_490 ),
inference(resolution,[],[f8088,f770]) ).
fof(f770,plain,
( ! [X3,X4] : ~ in(succ(set_union2(X3,X4)),X3)
| ~ spl19_90 ),
inference(avatar_component_clause,[],[f769]) ).
fof(f8150,plain,
( ~ spl19_493
| ~ spl19_94
| ~ spl19_490 ),
inference(avatar_split_clause,[],[f8106,f8087,f824,f8147]) ).
fof(f8147,plain,
( spl19_493
<=> in(singleton(succ(succ(sK0))),sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_493])]) ).
fof(f824,plain,
( spl19_94
<=> ! [X5] : ~ in(singleton(succ(X5)),X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_94])]) ).
fof(f8106,plain,
( ~ in(singleton(succ(succ(sK0))),sK1)
| ~ spl19_94
| ~ spl19_490 ),
inference(resolution,[],[f8088,f825]) ).
fof(f825,plain,
( ! [X5] : ~ in(singleton(succ(X5)),X5)
| ~ spl19_94 ),
inference(avatar_component_clause,[],[f824]) ).
fof(f8145,plain,
( ~ spl19_492
| ~ spl19_93
| ~ spl19_490 ),
inference(avatar_split_clause,[],[f8099,f8087,f806,f8142]) ).
fof(f8142,plain,
( spl19_492
<=> in(succ(succ(succ(sK0))),sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_492])]) ).
fof(f8099,plain,
( ~ in(succ(succ(succ(sK0))),sK1)
| ~ spl19_93
| ~ spl19_490 ),
inference(resolution,[],[f8088,f807]) ).
fof(f8093,plain,
( spl19_491
| ~ spl19_171
| ~ spl19_489 ),
inference(avatar_split_clause,[],[f8061,f8025,f1776,f8091]) ).
fof(f8025,plain,
( spl19_489
<=> succ(sK0) = set_union2(sK1,succ(sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_489])]) ).
fof(f8061,plain,
( ! [X4] :
( ~ in(succ(sK0),X4)
| ~ in(X4,sK1) )
| ~ spl19_171
| ~ spl19_489 ),
inference(superposition,[],[f1777,f8027]) ).
fof(f8027,plain,
( succ(sK0) = set_union2(sK1,succ(sK0))
| ~ spl19_489 ),
inference(avatar_component_clause,[],[f8025]) ).
fof(f8089,plain,
( spl19_490
| ~ spl19_80
| ~ spl19_489 ),
inference(avatar_split_clause,[],[f8054,f8025,f689,f8087]) ).
fof(f8054,plain,
( ! [X1] :
( in(X1,succ(sK0))
| ~ in(X1,sK1) )
| ~ spl19_80
| ~ spl19_489 ),
inference(superposition,[],[f690,f8027]) ).
fof(f8028,plain,
( spl19_489
| ~ spl19_57
| ~ spl19_480 ),
inference(avatar_split_clause,[],[f7866,f7848,f541,f8025]) ).
fof(f7866,plain,
( succ(sK0) = set_union2(sK1,succ(sK0))
| ~ spl19_57
| ~ spl19_480 ),
inference(superposition,[],[f7849,f542]) ).
fof(f7991,plain,
( spl19_488
| ~ spl19_58
| ~ spl19_485 ),
inference(avatar_split_clause,[],[f7964,f7952,f545,f7989]) ).
fof(f7989,plain,
( spl19_488
<=> ! [X0] : ~ in(singleton(set_union2(X0,sK0)),sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_488])]) ).
fof(f7952,plain,
( spl19_485
<=> ! [X11] : ~ in(singleton(set_union2(sK0,X11)),sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_485])]) ).
fof(f7964,plain,
( ! [X0] : ~ in(singleton(set_union2(X0,sK0)),sK1)
| ~ spl19_58
| ~ spl19_485 ),
inference(superposition,[],[f7953,f546]) ).
fof(f7953,plain,
( ! [X11] : ~ in(singleton(set_union2(sK0,X11)),sK1)
| ~ spl19_485 ),
inference(avatar_component_clause,[],[f7952]) ).
fof(f7987,plain,
( spl19_487
| ~ spl19_58
| ~ spl19_484 ),
inference(avatar_split_clause,[],[f7958,f7937,f545,f7985]) ).
fof(f7985,plain,
( spl19_487
<=> ! [X0] : ~ in(succ(set_union2(X0,sK0)),sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_487])]) ).
fof(f7937,plain,
( spl19_484
<=> ! [X10] : ~ in(succ(set_union2(sK0,X10)),sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_484])]) ).
fof(f7958,plain,
( ! [X0] : ~ in(succ(set_union2(X0,sK0)),sK1)
| ~ spl19_58
| ~ spl19_484 ),
inference(superposition,[],[f7938,f546]) ).
fof(f7938,plain,
( ! [X10] : ~ in(succ(set_union2(sK0,X10)),sK1)
| ~ spl19_484 ),
inference(avatar_component_clause,[],[f7937]) ).
fof(f7983,plain,
( ~ spl19_486
| ~ spl19_57
| ~ spl19_485 ),
inference(avatar_split_clause,[],[f7966,f7952,f541,f7980]) ).
fof(f7980,plain,
( spl19_486
<=> in(singleton(succ(sK0)),sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_486])]) ).
fof(f7966,plain,
( ~ in(singleton(succ(sK0)),sK1)
| ~ spl19_57
| ~ spl19_485 ),
inference(superposition,[],[f7953,f542]) ).
fof(f7954,plain,
( spl19_485
| ~ spl19_91
| ~ spl19_480 ),
inference(avatar_split_clause,[],[f7875,f7848,f773,f7952]) ).
fof(f7875,plain,
( ! [X11] : ~ in(singleton(set_union2(sK0,X11)),sK1)
| ~ spl19_91
| ~ spl19_480 ),
inference(superposition,[],[f774,f7849]) ).
fof(f7939,plain,
( spl19_484
| ~ spl19_90
| ~ spl19_480 ),
inference(avatar_split_clause,[],[f7874,f7848,f769,f7937]) ).
fof(f7874,plain,
( ! [X10] : ~ in(succ(set_union2(sK0,X10)),sK1)
| ~ spl19_90
| ~ spl19_480 ),
inference(superposition,[],[f770,f7849]) ).
fof(f7931,plain,
( spl19_483
| ~ spl19_58
| ~ spl19_482 ),
inference(avatar_split_clause,[],[f7924,f7908,f545,f7929]) ).
fof(f7929,plain,
( spl19_483
<=> ! [X0] : ~ empty(set_union2(X0,sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_483])]) ).
fof(f7908,plain,
( spl19_482
<=> ! [X0] : ~ empty(set_union2(sK0,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_482])]) ).
fof(f7924,plain,
( ! [X0] : ~ empty(set_union2(X0,sK0))
| ~ spl19_58
| ~ spl19_482 ),
inference(superposition,[],[f7909,f546]) ).
fof(f7909,plain,
( ! [X0] : ~ empty(set_union2(sK0,X0))
| ~ spl19_482 ),
inference(avatar_component_clause,[],[f7908]) ).
fof(f7910,plain,
( spl19_482
| ~ spl19_50
| spl19_314
| ~ spl19_480 ),
inference(avatar_split_clause,[],[f7906,f7848,f4276,f500,f7908]) ).
fof(f500,plain,
( spl19_50
<=> ! [X0,X1] :
( ~ empty(set_union2(X0,X1))
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_50])]) ).
fof(f7906,plain,
( ! [X0] : ~ empty(set_union2(sK0,X0))
| ~ spl19_50
| spl19_314
| ~ spl19_480 ),
inference(subsumption_resolution,[],[f7868,f4277]) ).
fof(f7868,plain,
( ! [X0] :
( ~ empty(set_union2(sK0,X0))
| empty(sK1) )
| ~ spl19_50
| ~ spl19_480 ),
inference(superposition,[],[f501,f7849]) ).
fof(f501,plain,
( ! [X0,X1] :
( ~ empty(set_union2(X0,X1))
| empty(X0) )
| ~ spl19_50 ),
inference(avatar_component_clause,[],[f500]) ).
fof(f7861,plain,
( spl19_481
| ~ spl19_264
| ~ spl19_300
| ~ spl19_470 ),
inference(avatar_split_clause,[],[f7705,f7667,f3696,f3093,f7859]) ).
fof(f7705,plain,
( ! [X3] : set_union2(X3,sK0) = set_union2(sK1,set_union2(X3,sK0))
| ~ spl19_264
| ~ spl19_300
| ~ spl19_470 ),
inference(subsumption_resolution,[],[f7694,f3094]) ).
fof(f7694,plain,
( ! [X3] :
( set_union2(X3,sK0) = set_union2(sK1,set_union2(X3,sK0))
| ~ in(sK5(sK1,set_union2(X3,sK0),set_union2(X3,sK0)),sK1) )
| ~ spl19_300
| ~ spl19_470 ),
inference(duplicate_literal_removal,[],[f7691]) ).
fof(f7691,plain,
( ! [X3] :
( set_union2(X3,sK0) = set_union2(sK1,set_union2(X3,sK0))
| set_union2(X3,sK0) = set_union2(sK1,set_union2(X3,sK0))
| ~ in(sK5(sK1,set_union2(X3,sK0),set_union2(X3,sK0)),sK1) )
| ~ spl19_300
| ~ spl19_470 ),
inference(resolution,[],[f7668,f3697]) ).
fof(f7850,plain,
( spl19_480
| ~ spl19_264
| ~ spl19_296
| ~ spl19_470 ),
inference(avatar_split_clause,[],[f7704,f7667,f3679,f3093,f7848]) ).
fof(f7704,plain,
( ! [X1] : set_union2(sK0,X1) = set_union2(sK1,set_union2(sK0,X1))
| ~ spl19_264
| ~ spl19_296
| ~ spl19_470 ),
inference(subsumption_resolution,[],[f7696,f3094]) ).
fof(f7696,plain,
( ! [X1] :
( set_union2(sK0,X1) = set_union2(sK1,set_union2(sK0,X1))
| ~ in(sK5(sK1,set_union2(sK0,X1),set_union2(sK0,X1)),sK1) )
| ~ spl19_296
| ~ spl19_470 ),
inference(duplicate_literal_removal,[],[f7689]) ).
fof(f7689,plain,
( ! [X1] :
( set_union2(sK0,X1) = set_union2(sK1,set_union2(sK0,X1))
| set_union2(sK0,X1) = set_union2(sK1,set_union2(sK0,X1))
| ~ in(sK5(sK1,set_union2(sK0,X1),set_union2(sK0,X1)),sK1) )
| ~ spl19_296
| ~ spl19_470 ),
inference(resolution,[],[f7668,f3680]) ).
fof(f7843,plain,
( spl19_479
| ~ spl19_57
| ~ spl19_478 ),
inference(avatar_split_clause,[],[f7835,f7815,f541,f7841]) ).
fof(f7841,plain,
( spl19_479
<=> ! [X5] :
( ~ in(succ(X5),sK1)
| ~ in(sK0,singleton(X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_479])]) ).
fof(f7815,plain,
( spl19_478
<=> ! [X2,X3] :
( ~ in(set_union2(X2,X3),sK1)
| ~ in(sK0,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_478])]) ).
fof(f7835,plain,
( ! [X5] :
( ~ in(succ(X5),sK1)
| ~ in(sK0,singleton(X5)) )
| ~ spl19_57
| ~ spl19_478 ),
inference(superposition,[],[f7816,f542]) ).
fof(f7816,plain,
( ! [X2,X3] :
( ~ in(set_union2(X2,X3),sK1)
| ~ in(sK0,X3) )
| ~ spl19_478 ),
inference(avatar_component_clause,[],[f7815]) ).
fof(f7817,plain,
( spl19_478
| ~ spl19_79
| ~ spl19_474 ),
inference(avatar_split_clause,[],[f7771,f7762,f685,f7815]) ).
fof(f7771,plain,
( ! [X2,X3] :
( ~ in(set_union2(X2,X3),sK1)
| ~ in(sK0,X3) )
| ~ spl19_79
| ~ spl19_474 ),
inference(resolution,[],[f7763,f686]) ).
fof(f7813,plain,
( spl19_477
| ~ spl19_80
| ~ spl19_474 ),
inference(avatar_split_clause,[],[f7770,f7762,f689,f7811]) ).
fof(f7811,plain,
( spl19_477
<=> ! [X0,X1] :
( ~ in(set_union2(X0,X1),sK1)
| ~ in(sK0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_477])]) ).
fof(f7770,plain,
( ! [X0,X1] :
( ~ in(set_union2(X0,X1),sK1)
| ~ in(sK0,X0) )
| ~ spl19_80
| ~ spl19_474 ),
inference(resolution,[],[f7763,f690]) ).
fof(f7800,plain,
( spl19_476
| ~ spl19_98
| ~ spl19_474 ),
inference(avatar_split_clause,[],[f7773,f7762,f845,f7798]) ).
fof(f7798,plain,
( spl19_476
<=> ! [X4] :
( ~ in(succ(X4),sK1)
| ~ in(sK0,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_476])]) ).
fof(f7773,plain,
( ! [X4] :
( ~ in(succ(X4),sK1)
| ~ in(sK0,X4) )
| ~ spl19_98
| ~ spl19_474 ),
inference(resolution,[],[f7763,f846]) ).
fof(f7794,plain,
( ~ spl19_475
| ~ spl19_188
| ~ spl19_474 ),
inference(avatar_split_clause,[],[f7766,f7762,f1895,f7791]) ).
fof(f7766,plain,
( ~ in(succ(succ(sK0)),sK1)
| ~ spl19_188
| ~ spl19_474 ),
inference(resolution,[],[f7763,f1897]) ).
fof(f7764,plain,
( spl19_474
| ~ spl19_163
| ~ spl19_472 ),
inference(avatar_split_clause,[],[f7720,f7707,f1741,f7762]) ).
fof(f7707,plain,
( spl19_472
<=> sK0 = set_union2(sK0,sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_472])]) ).
fof(f7720,plain,
( ! [X3] :
( ~ in(sK0,X3)
| ~ in(X3,sK1) )
| ~ spl19_163
| ~ spl19_472 ),
inference(superposition,[],[f1742,f7709]) ).
fof(f7709,plain,
( sK0 = set_union2(sK0,sK1)
| ~ spl19_472 ),
inference(avatar_component_clause,[],[f7707]) ).
fof(f7748,plain,
( ~ spl19_473
| ~ spl19_88
| ~ spl19_472 ),
inference(avatar_split_clause,[],[f7716,f7707,f761,f7745]) ).
fof(f7745,plain,
( spl19_473
<=> in(singleton(sK0),sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_473])]) ).
fof(f7716,plain,
( ~ in(singleton(sK0),sK1)
| ~ spl19_88
| ~ spl19_472 ),
inference(superposition,[],[f762,f7709]) ).
fof(f7710,plain,
( spl19_472
| ~ spl19_58
| ~ spl19_138
| ~ spl19_470 ),
inference(avatar_split_clause,[],[f7701,f7667,f1130,f545,f7707]) ).
fof(f1130,plain,
( spl19_138
<=> ! [X2,X0,X1] :
( set_union2(X0,X1) = X2
| ~ in(sK5(X0,X1,X2),X1)
| ~ in(sK5(X0,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_138])]) ).
fof(f7701,plain,
( sK0 = set_union2(sK0,sK1)
| ~ spl19_58
| ~ spl19_138
| ~ spl19_470 ),
inference(forward_demodulation,[],[f7700,f546]) ).
fof(f7700,plain,
( sK0 = set_union2(sK1,sK0)
| ~ spl19_138
| ~ spl19_470 ),
inference(subsumption_resolution,[],[f7699,f7668]) ).
fof(f7699,plain,
( sK0 = set_union2(sK1,sK0)
| ~ in(sK5(sK1,sK0,sK0),sK0)
| ~ spl19_138
| ~ spl19_470 ),
inference(duplicate_literal_removal,[],[f7686]) ).
fof(f7686,plain,
( sK0 = set_union2(sK1,sK0)
| ~ in(sK5(sK1,sK0,sK0),sK0)
| sK0 = set_union2(sK1,sK0)
| ~ spl19_138
| ~ spl19_470 ),
inference(resolution,[],[f7668,f1131]) ).
fof(f1131,plain,
( ! [X2,X0,X1] :
( ~ in(sK5(X0,X1,X2),X2)
| ~ in(sK5(X0,X1,X2),X1)
| set_union2(X0,X1) = X2 )
| ~ spl19_138 ),
inference(avatar_component_clause,[],[f1130]) ).
fof(f7673,plain,
( spl19_471
| ~ spl19_265
| ~ spl19_313 ),
inference(avatar_split_clause,[],[f3843,f3809,f3098,f7671]) ).
fof(f3098,plain,
( spl19_265
<=> ! [X2,X3] :
( in(sK5(X2,X3,X2),X3)
| set_union2(X2,X3) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_265])]) ).
fof(f3843,plain,
( ! [X11] :
( in(sK5(X11,sK1,X11),sK0)
| set_union2(X11,sK1) = X11 )
| ~ spl19_265
| ~ spl19_313 ),
inference(resolution,[],[f3810,f3099]) ).
fof(f3099,plain,
( ! [X2,X3] :
( in(sK5(X2,X3,X2),X3)
| set_union2(X2,X3) = X2 )
| ~ spl19_265 ),
inference(avatar_component_clause,[],[f3098]) ).
fof(f7669,plain,
( spl19_470
| ~ spl19_264
| ~ spl19_313 ),
inference(avatar_split_clause,[],[f3842,f3809,f3093,f7667]) ).
fof(f3842,plain,
( ! [X10] :
( in(sK5(sK1,X10,X10),sK0)
| set_union2(sK1,X10) = X10 )
| ~ spl19_264
| ~ spl19_313 ),
inference(resolution,[],[f3810,f3094]) ).
fof(f7665,plain,
( spl19_469
| ~ spl19_32
| ~ spl19_178
| ~ spl19_257 ),
inference(avatar_split_clause,[],[f2971,f2934,f1824,f411,f7663]) ).
fof(f7663,plain,
( spl19_469
<=> ! [X0] :
( ~ ordinal_subset(sK1,X0)
| ~ empty(X0)
| sK1 = X0
| ~ ordinal_subset(X0,sK1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_469])]) ).
fof(f2971,plain,
( ! [X0] :
( ~ ordinal_subset(sK1,X0)
| ~ empty(X0)
| sK1 = X0
| ~ ordinal_subset(X0,sK1) )
| ~ spl19_32
| ~ spl19_178
| ~ spl19_257 ),
inference(subsumption_resolution,[],[f2961,f412]) ).
fof(f2961,plain,
( ! [X0] :
( ~ ordinal_subset(sK1,X0)
| ~ empty(X0)
| ~ ordinal(X0)
| sK1 = X0
| ~ ordinal_subset(X0,sK1) )
| ~ spl19_178
| ~ spl19_257 ),
inference(resolution,[],[f2935,f1825]) ).
fof(f7659,plain,
( spl19_468
| ~ spl19_32
| ~ spl19_177
| ~ spl19_255 ),
inference(avatar_split_clause,[],[f2955,f2926,f1820,f411,f7657]) ).
fof(f7657,plain,
( spl19_468
<=> ! [X0] :
( ~ ordinal_subset(sK0,X0)
| ~ empty(X0)
| sK0 = X0
| ~ ordinal_subset(X0,sK0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_468])]) ).
fof(f2955,plain,
( ! [X0] :
( ~ ordinal_subset(sK0,X0)
| ~ empty(X0)
| sK0 = X0
| ~ ordinal_subset(X0,sK0) )
| ~ spl19_32
| ~ spl19_177
| ~ spl19_255 ),
inference(subsumption_resolution,[],[f2945,f412]) ).
fof(f2945,plain,
( ! [X0] :
( ~ ordinal_subset(sK0,X0)
| ~ empty(X0)
| ~ ordinal(X0)
| sK0 = X0
| ~ ordinal_subset(X0,sK0) )
| ~ spl19_177
| ~ spl19_255 ),
inference(resolution,[],[f2927,f1821]) ).
fof(f7648,plain,
( ~ spl19_467
| ~ spl19_270
| ~ spl19_420 ),
inference(avatar_split_clause,[],[f7630,f6480,f3196,f7645]) ).
fof(f7645,plain,
( spl19_467
<=> in(sK10,singleton(sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_467])]) ).
fof(f3196,plain,
( spl19_270
<=> in(succ(sK0),sK10) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_270])]) ).
fof(f7630,plain,
( ~ in(sK10,singleton(sK0))
| ~ spl19_270
| ~ spl19_420 ),
inference(resolution,[],[f6481,f3198]) ).
fof(f3198,plain,
( in(succ(sK0),sK10)
| ~ spl19_270 ),
inference(avatar_component_clause,[],[f3196]) ).
fof(f7643,plain,
( ~ spl19_466
| ~ spl19_269
| ~ spl19_420 ),
inference(avatar_split_clause,[],[f7629,f6480,f3178,f7640]) ).
fof(f7640,plain,
( spl19_466
<=> in(sK8,singleton(sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_466])]) ).
fof(f7629,plain,
( ~ in(sK8,singleton(sK0))
| ~ spl19_269
| ~ spl19_420 ),
inference(resolution,[],[f6481,f3180]) ).
fof(f7626,plain,
( spl19_465
| ~ spl19_83
| spl19_335
| ~ spl19_463 ),
inference(avatar_split_clause,[],[f7616,f7609,f4557,f712,f7623]) ).
fof(f7623,plain,
( spl19_465
<=> in(empty_set,sK3(sK1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_465])]) ).
fof(f4557,plain,
( spl19_335
<=> empty(sK3(sK1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_335])]) ).
fof(f7609,plain,
( spl19_463
<=> empty_set = sK3(sK3(sK1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_463])]) ).
fof(f7616,plain,
( in(empty_set,sK3(sK1))
| ~ spl19_83
| spl19_335
| ~ spl19_463 ),
inference(subsumption_resolution,[],[f7614,f4558]) ).
fof(f4558,plain,
( ~ empty(sK3(sK1))
| spl19_335 ),
inference(avatar_component_clause,[],[f4557]) ).
fof(f7614,plain,
( in(empty_set,sK3(sK1))
| empty(sK3(sK1))
| ~ spl19_83
| ~ spl19_463 ),
inference(superposition,[],[f713,f7611]) ).
fof(f7611,plain,
( empty_set = sK3(sK3(sK1))
| ~ spl19_463 ),
inference(avatar_component_clause,[],[f7609]) ).
fof(f7621,plain,
( spl19_464
| ~ spl19_33
| ~ spl19_463 ),
inference(avatar_split_clause,[],[f7615,f7609,f415,f7618]) ).
fof(f7618,plain,
( spl19_464
<=> element(empty_set,sK3(sK1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_464])]) ).
fof(f415,plain,
( spl19_33
<=> ! [X0] : element(sK3(X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_33])]) ).
fof(f7615,plain,
( element(empty_set,sK3(sK1))
| ~ spl19_33
| ~ spl19_463 ),
inference(superposition,[],[f416,f7611]) ).
fof(f416,plain,
( ! [X0] : element(sK3(X0),X0)
| ~ spl19_33 ),
inference(avatar_component_clause,[],[f415]) ).
fof(f7612,plain,
( spl19_463
| ~ spl19_39
| ~ spl19_461 ),
inference(avatar_split_clause,[],[f7401,f7393,f439,f7609]) ).
fof(f7393,plain,
( spl19_461
<=> empty(sK3(sK3(sK1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_461])]) ).
fof(f7401,plain,
( empty_set = sK3(sK3(sK1))
| ~ spl19_39
| ~ spl19_461 ),
inference(resolution,[],[f7395,f440]) ).
fof(f7395,plain,
( empty(sK3(sK3(sK1)))
| ~ spl19_461 ),
inference(avatar_component_clause,[],[f7393]) ).
fof(f7400,plain,
( spl19_461
| spl19_462
| ~ spl19_83
| ~ spl19_342 ),
inference(avatar_split_clause,[],[f4876,f4861,f712,f7397,f7393]) ).
fof(f7397,plain,
( spl19_462
<=> in(sK3(sK3(sK3(sK1))),sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_462])]) ).
fof(f4861,plain,
( spl19_342
<=> ! [X0] :
( ~ in(X0,sK3(sK3(sK1)))
| in(X0,sK0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_342])]) ).
fof(f4876,plain,
( in(sK3(sK3(sK3(sK1))),sK0)
| empty(sK3(sK3(sK1)))
| ~ spl19_83
| ~ spl19_342 ),
inference(resolution,[],[f4862,f713]) ).
fof(f4862,plain,
( ! [X0] :
( ~ in(X0,sK3(sK3(sK1)))
| in(X0,sK0) )
| ~ spl19_342 ),
inference(avatar_component_clause,[],[f4861]) ).
fof(f7378,plain,
( spl19_459
| spl19_460
| ~ spl19_48
| ~ spl19_342 ),
inference(avatar_split_clause,[],[f4873,f4861,f492,f7375,f7371]) ).
fof(f7371,plain,
( spl19_459
<=> epsilon_transitive(sK3(sK3(sK1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_459])]) ).
fof(f7375,plain,
( spl19_460
<=> in(sK2(sK3(sK3(sK1))),sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_460])]) ).
fof(f4873,plain,
( in(sK2(sK3(sK3(sK1))),sK0)
| epsilon_transitive(sK3(sK3(sK1)))
| ~ spl19_48
| ~ spl19_342 ),
inference(resolution,[],[f4862,f493]) ).
fof(f7366,plain,
( spl19_458
| ~ spl19_18
| ~ spl19_242 ),
inference(avatar_split_clause,[],[f2906,f2703,f348,f7364]) ).
fof(f7364,plain,
( spl19_458
<=> ! [X10] :
( in(X10,sK10)
| sK10 = X10
| ~ empty(X10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_458])]) ).
fof(f2906,plain,
( ! [X10] :
( in(X10,sK10)
| sK10 = X10
| ~ empty(X10) )
| ~ spl19_18
| ~ spl19_242 ),
inference(resolution,[],[f2704,f350]) ).
fof(f7362,plain,
( spl19_457
| ~ spl19_48
| spl19_375
| ~ spl19_454 ),
inference(avatar_split_clause,[],[f7352,f7340,f5778,f492,f7359]) ).
fof(f7359,plain,
( spl19_457
<=> in(empty_set,sK3(empty_set)) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_457])]) ).
fof(f5778,plain,
( spl19_375
<=> epsilon_transitive(sK3(empty_set)) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_375])]) ).
fof(f7340,plain,
( spl19_454
<=> empty_set = sK2(sK3(empty_set)) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_454])]) ).
fof(f7352,plain,
( in(empty_set,sK3(empty_set))
| ~ spl19_48
| spl19_375
| ~ spl19_454 ),
inference(subsumption_resolution,[],[f7350,f5779]) ).
fof(f5779,plain,
( ~ epsilon_transitive(sK3(empty_set))
| spl19_375 ),
inference(avatar_component_clause,[],[f5778]) ).
fof(f7350,plain,
( in(empty_set,sK3(empty_set))
| epsilon_transitive(sK3(empty_set))
| ~ spl19_48
| ~ spl19_454 ),
inference(superposition,[],[f493,f7342]) ).
fof(f7342,plain,
( empty_set = sK2(sK3(empty_set))
| ~ spl19_454 ),
inference(avatar_component_clause,[],[f7340]) ).
fof(f7357,plain,
( ~ spl19_456
| ~ spl19_49
| spl19_375
| ~ spl19_454 ),
inference(avatar_split_clause,[],[f7351,f7340,f5778,f496,f7354]) ).
fof(f7354,plain,
( spl19_456
<=> subset(empty_set,sK3(empty_set)) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_456])]) ).
fof(f7351,plain,
( ~ subset(empty_set,sK3(empty_set))
| ~ spl19_49
| spl19_375
| ~ spl19_454 ),
inference(subsumption_resolution,[],[f7349,f5779]) ).
fof(f7349,plain,
( ~ subset(empty_set,sK3(empty_set))
| epsilon_transitive(sK3(empty_set))
| ~ spl19_49
| ~ spl19_454 ),
inference(superposition,[],[f497,f7342]) ).
fof(f7347,plain,
( spl19_455
| ~ spl19_14
| ~ spl19_242 ),
inference(avatar_split_clause,[],[f2905,f2703,f328,f7345]) ).
fof(f7345,plain,
( spl19_455
<=> ! [X9] :
( in(X9,sK8)
| sK8 = X9
| ~ empty(X9) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_455])]) ).
fof(f2905,plain,
( ! [X9] :
( in(X9,sK8)
| sK8 = X9
| ~ empty(X9) )
| ~ spl19_14
| ~ spl19_242 ),
inference(resolution,[],[f2704,f330]) ).
fof(f7343,plain,
( spl19_454
| ~ spl19_39
| ~ spl19_452 ),
inference(avatar_split_clause,[],[f7123,f7115,f439,f7340]) ).
fof(f7115,plain,
( spl19_452
<=> empty(sK2(sK3(empty_set))) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_452])]) ).
fof(f7123,plain,
( empty_set = sK2(sK3(empty_set))
| ~ spl19_39
| ~ spl19_452 ),
inference(resolution,[],[f7117,f440]) ).
fof(f7117,plain,
( empty(sK2(sK3(empty_set)))
| ~ spl19_452 ),
inference(avatar_component_clause,[],[f7115]) ).
fof(f7122,plain,
( spl19_452
| spl19_453
| ~ spl19_83
| ~ spl19_381 ),
inference(avatar_split_clause,[],[f6008,f5823,f712,f7119,f7115]) ).
fof(f7119,plain,
( spl19_453
<=> in(sK3(sK2(sK3(empty_set))),sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_453])]) ).
fof(f5823,plain,
( spl19_381
<=> ! [X0] :
( ~ in(X0,sK2(sK3(empty_set)))
| in(X0,sK0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_381])]) ).
fof(f6008,plain,
( in(sK3(sK2(sK3(empty_set))),sK0)
| empty(sK2(sK3(empty_set)))
| ~ spl19_83
| ~ spl19_381 ),
inference(resolution,[],[f5824,f713]) ).
fof(f5824,plain,
( ! [X0] :
( ~ in(X0,sK2(sK3(empty_set)))
| in(X0,sK0) )
| ~ spl19_381 ),
inference(avatar_component_clause,[],[f5823]) ).
fof(f7113,plain,
( spl19_451
| ~ spl19_18
| ~ spl19_236 ),
inference(avatar_split_clause,[],[f2870,f2670,f348,f7111]) ).
fof(f7111,plain,
( spl19_451
<=> ! [X10] :
( ordinal_subset(sK10,X10)
| ~ subset(sK10,X10)
| ~ empty(X10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_451])]) ).
fof(f2870,plain,
( ! [X10] :
( ordinal_subset(sK10,X10)
| ~ subset(sK10,X10)
| ~ empty(X10) )
| ~ spl19_18
| ~ spl19_236 ),
inference(resolution,[],[f2671,f350]) ).
fof(f7108,plain,
( spl19_449
| spl19_450
| ~ spl19_48
| ~ spl19_381 ),
inference(avatar_split_clause,[],[f6005,f5823,f492,f7105,f7101]) ).
fof(f7101,plain,
( spl19_449
<=> epsilon_transitive(sK2(sK3(empty_set))) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_449])]) ).
fof(f7105,plain,
( spl19_450
<=> in(sK2(sK2(sK3(empty_set))),sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_450])]) ).
fof(f6005,plain,
( in(sK2(sK2(sK3(empty_set))),sK0)
| epsilon_transitive(sK2(sK3(empty_set)))
| ~ spl19_48
| ~ spl19_381 ),
inference(resolution,[],[f5824,f493]) ).
fof(f7067,plain,
( spl19_448
| ~ spl19_14
| ~ spl19_236 ),
inference(avatar_split_clause,[],[f2869,f2670,f328,f7065]) ).
fof(f7065,plain,
( spl19_448
<=> ! [X9] :
( ordinal_subset(sK8,X9)
| ~ subset(sK8,X9)
| ~ empty(X9) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_448])]) ).
fof(f2869,plain,
( ! [X9] :
( ordinal_subset(sK8,X9)
| ~ subset(sK8,X9)
| ~ empty(X9) )
| ~ spl19_14
| ~ spl19_236 ),
inference(resolution,[],[f2671,f330]) ).
fof(f7063,plain,
( spl19_447
| ~ spl19_310
| ~ spl19_444 ),
inference(avatar_split_clause,[],[f7053,f7045,f3781,f7061]) ).
fof(f7061,plain,
( spl19_447
<=> ! [X0] :
( ~ in(X0,sK3(sK3(sK3(empty_set))))
| in(X0,sK0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_447])]) ).
fof(f7045,plain,
( spl19_444
<=> in(sK3(sK3(sK3(empty_set))),sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_444])]) ).
fof(f7053,plain,
( ! [X0] :
( ~ in(X0,sK3(sK3(sK3(empty_set))))
| in(X0,sK0) )
| ~ spl19_310
| ~ spl19_444 ),
inference(resolution,[],[f7047,f3782]) ).
fof(f7047,plain,
( in(sK3(sK3(sK3(empty_set))),sK0)
| ~ spl19_444 ),
inference(avatar_component_clause,[],[f7045]) ).
fof(f7059,plain,
( ~ spl19_446
| ~ spl19_52
| ~ spl19_444 ),
inference(avatar_split_clause,[],[f7054,f7045,f508,f7056]) ).
fof(f7056,plain,
( spl19_446
<=> in(sK0,sK3(sK3(sK3(empty_set)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_446])]) ).
fof(f7054,plain,
( ~ in(sK0,sK3(sK3(sK3(empty_set))))
| ~ spl19_52
| ~ spl19_444 ),
inference(resolution,[],[f7047,f509]) ).
fof(f7052,plain,
( spl19_445
| ~ spl19_8
| ~ spl19_236 ),
inference(avatar_split_clause,[],[f2866,f2670,f298,f7050]) ).
fof(f7050,plain,
( spl19_445
<=> ! [X6] :
( ordinal_subset(empty_set,X6)
| ~ subset(empty_set,X6)
| ~ empty(X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_445])]) ).
fof(f2866,plain,
( ! [X6] :
( ordinal_subset(empty_set,X6)
| ~ subset(empty_set,X6)
| ~ empty(X6) )
| ~ spl19_8
| ~ spl19_236 ),
inference(resolution,[],[f2671,f300]) ).
fof(f7048,plain,
( spl19_438
| spl19_444
| ~ spl19_83
| ~ spl19_380 ),
inference(avatar_split_clause,[],[f5829,f5819,f712,f7045,f6983]) ).
fof(f6983,plain,
( spl19_438
<=> empty(sK3(sK3(empty_set))) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_438])]) ).
fof(f5819,plain,
( spl19_380
<=> ! [X0] :
( ~ in(X0,sK3(sK3(empty_set)))
| in(X0,sK0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_380])]) ).
fof(f5829,plain,
( in(sK3(sK3(sK3(empty_set))),sK0)
| empty(sK3(sK3(empty_set)))
| ~ spl19_83
| ~ spl19_380 ),
inference(resolution,[],[f5820,f713]) ).
fof(f5820,plain,
( ! [X0] :
( ~ in(X0,sK3(sK3(empty_set)))
| in(X0,sK0) )
| ~ spl19_380 ),
inference(avatar_component_clause,[],[f5819]) ).
fof(f7011,plain,
( spl19_443
| ~ spl19_310
| ~ spl19_436 ),
inference(avatar_split_clause,[],[f6997,f6972,f3781,f7009]) ).
fof(f7009,plain,
( spl19_443
<=> ! [X0] :
( ~ in(X0,sK2(sK3(sK3(empty_set))))
| in(X0,sK0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_443])]) ).
fof(f6972,plain,
( spl19_436
<=> in(sK2(sK3(sK3(empty_set))),sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_436])]) ).
fof(f6997,plain,
( ! [X0] :
( ~ in(X0,sK2(sK3(sK3(empty_set))))
| in(X0,sK0) )
| ~ spl19_310
| ~ spl19_436 ),
inference(resolution,[],[f6974,f3782]) ).
fof(f6974,plain,
( in(sK2(sK3(sK3(empty_set))),sK0)
| ~ spl19_436 ),
inference(avatar_component_clause,[],[f6972]) ).
fof(f7007,plain,
( spl19_442
| ~ spl19_18
| ~ spl19_234 ),
inference(avatar_split_clause,[],[f2835,f2660,f348,f7005]) ).
fof(f7005,plain,
( spl19_442
<=> ! [X10] :
( subset(sK10,X10)
| ~ ordinal_subset(sK10,X10)
| ~ empty(X10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_442])]) ).
fof(f2835,plain,
( ! [X10] :
( subset(sK10,X10)
| ~ ordinal_subset(sK10,X10)
| ~ empty(X10) )
| ~ spl19_18
| ~ spl19_234 ),
inference(resolution,[],[f2661,f350]) ).
fof(f7003,plain,
( ~ spl19_441
| ~ spl19_52
| ~ spl19_436 ),
inference(avatar_split_clause,[],[f6998,f6972,f508,f7000]) ).
fof(f7000,plain,
( spl19_441
<=> in(sK0,sK2(sK3(sK3(empty_set)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_441])]) ).
fof(f6998,plain,
( ~ in(sK0,sK2(sK3(sK3(empty_set))))
| ~ spl19_52
| ~ spl19_436 ),
inference(resolution,[],[f6974,f509]) ).
fof(f6995,plain,
( spl19_440
| ~ spl19_14
| ~ spl19_234 ),
inference(avatar_split_clause,[],[f2834,f2660,f328,f6993]) ).
fof(f6993,plain,
( spl19_440
<=> ! [X9] :
( subset(sK8,X9)
| ~ ordinal_subset(sK8,X9)
| ~ empty(X9) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_440])]) ).
fof(f2834,plain,
( ! [X9] :
( subset(sK8,X9)
| ~ ordinal_subset(sK8,X9)
| ~ empty(X9) )
| ~ spl19_14
| ~ spl19_234 ),
inference(resolution,[],[f2661,f330]) ).
fof(f6991,plain,
( ~ spl19_439
| ~ spl19_29
| spl19_435 ),
inference(avatar_split_clause,[],[f6977,f6968,f399,f6988]) ).
fof(f6988,plain,
( spl19_439
<=> ordinal(sK3(sK3(empty_set))) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_439])]) ).
fof(f6968,plain,
( spl19_435
<=> epsilon_transitive(sK3(sK3(empty_set))) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_435])]) ).
fof(f6977,plain,
( ~ ordinal(sK3(sK3(empty_set)))
| ~ spl19_29
| spl19_435 ),
inference(resolution,[],[f6969,f400]) ).
fof(f6969,plain,
( ~ epsilon_transitive(sK3(sK3(empty_set)))
| spl19_435 ),
inference(avatar_component_clause,[],[f6968]) ).
fof(f6986,plain,
( ~ spl19_438
| ~ spl19_30
| spl19_435 ),
inference(avatar_split_clause,[],[f6976,f6968,f403,f6983]) ).
fof(f403,plain,
( spl19_30
<=> ! [X0] :
( epsilon_transitive(X0)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_30])]) ).
fof(f6976,plain,
( ~ empty(sK3(sK3(empty_set)))
| ~ spl19_30
| spl19_435 ),
inference(resolution,[],[f6969,f404]) ).
fof(f404,plain,
( ! [X0] :
( epsilon_transitive(X0)
| ~ empty(X0) )
| ~ spl19_30 ),
inference(avatar_component_clause,[],[f403]) ).
fof(f6981,plain,
( spl19_437
| ~ spl19_8
| ~ spl19_234 ),
inference(avatar_split_clause,[],[f2831,f2660,f298,f6979]) ).
fof(f6979,plain,
( spl19_437
<=> ! [X6] :
( subset(empty_set,X6)
| ~ ordinal_subset(empty_set,X6)
| ~ empty(X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_437])]) ).
fof(f2831,plain,
( ! [X6] :
( subset(empty_set,X6)
| ~ ordinal_subset(empty_set,X6)
| ~ empty(X6) )
| ~ spl19_8
| ~ spl19_234 ),
inference(resolution,[],[f2661,f300]) ).
fof(f6975,plain,
( spl19_435
| spl19_436
| ~ spl19_48
| ~ spl19_380 ),
inference(avatar_split_clause,[],[f5826,f5819,f492,f6972,f6968]) ).
fof(f5826,plain,
( in(sK2(sK3(sK3(empty_set))),sK0)
| epsilon_transitive(sK3(sK3(empty_set)))
| ~ spl19_48
| ~ spl19_380 ),
inference(resolution,[],[f5820,f493]) ).
fof(f6955,plain,
( spl19_434
| ~ spl19_18
| ~ spl19_230 ),
inference(avatar_split_clause,[],[f2814,f2626,f348,f6953]) ).
fof(f6953,plain,
( spl19_434
<=> ! [X10] :
( ordinal_subset(X10,sK10)
| ordinal_subset(sK10,X10)
| ~ empty(X10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_434])]) ).
fof(f2814,plain,
( ! [X10] :
( ordinal_subset(X10,sK10)
| ordinal_subset(sK10,X10)
| ~ empty(X10) )
| ~ spl19_18
| ~ spl19_230 ),
inference(resolution,[],[f2627,f350]) ).
fof(f6949,plain,
( spl19_433
| ~ spl19_14
| ~ spl19_230 ),
inference(avatar_split_clause,[],[f2813,f2626,f328,f6947]) ).
fof(f6947,plain,
( spl19_433
<=> ! [X9] :
( ordinal_subset(X9,sK8)
| ordinal_subset(sK8,X9)
| ~ empty(X9) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_433])]) ).
fof(f2813,plain,
( ! [X9] :
( ordinal_subset(X9,sK8)
| ordinal_subset(sK8,X9)
| ~ empty(X9) )
| ~ spl19_14
| ~ spl19_230 ),
inference(resolution,[],[f2627,f330]) ).
fof(f6920,plain,
( spl19_432
| ~ spl19_8
| ~ spl19_230 ),
inference(avatar_split_clause,[],[f2810,f2626,f298,f6918]) ).
fof(f6918,plain,
( spl19_432
<=> ! [X6] :
( ordinal_subset(X6,empty_set)
| ordinal_subset(empty_set,X6)
| ~ empty(X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_432])]) ).
fof(f2810,plain,
( ! [X6] :
( ordinal_subset(X6,empty_set)
| ordinal_subset(empty_set,X6)
| ~ empty(X6) )
| ~ spl19_8
| ~ spl19_230 ),
inference(resolution,[],[f2627,f300]) ).
fof(f6913,plain,
( spl19_212
| ~ spl19_412
| ~ spl19_430 ),
inference(avatar_contradiction_clause,[],[f6912]) ).
fof(f6912,plain,
( $false
| spl19_212
| ~ spl19_412
| ~ spl19_430 ),
inference(subsumption_resolution,[],[f6880,f2225]) ).
fof(f2225,plain,
( ~ ordinal_subset(sK1,empty_set)
| spl19_212 ),
inference(avatar_component_clause,[],[f2223]) ).
fof(f2223,plain,
( spl19_212
<=> ordinal_subset(sK1,empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_212])]) ).
fof(f6880,plain,
( ordinal_subset(sK1,empty_set)
| ~ spl19_412
| ~ spl19_430 ),
inference(backward_demodulation,[],[f6400,f6848]) ).
fof(f6848,plain,
( empty_set = succ(succ(sK1))
| ~ spl19_430 ),
inference(avatar_component_clause,[],[f6846]) ).
fof(f6846,plain,
( spl19_430
<=> empty_set = succ(succ(sK1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_430])]) ).
fof(f6400,plain,
( ordinal_subset(sK1,succ(succ(sK1)))
| ~ spl19_412 ),
inference(avatar_component_clause,[],[f6398]) ).
fof(f6398,plain,
( spl19_412
<=> ordinal_subset(sK1,succ(succ(sK1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_412])]) ).
fof(f6898,plain,
( ~ spl19_155
| spl19_410
| ~ spl19_430 ),
inference(avatar_contradiction_clause,[],[f6897]) ).
fof(f6897,plain,
( $false
| ~ spl19_155
| spl19_410
| ~ spl19_430 ),
inference(subsumption_resolution,[],[f6866,f1668]) ).
fof(f1668,plain,
( ordinal_subset(empty_set,sK1)
| ~ spl19_155 ),
inference(avatar_component_clause,[],[f1666]) ).
fof(f1666,plain,
( spl19_155
<=> ordinal_subset(empty_set,sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_155])]) ).
fof(f6866,plain,
( ~ ordinal_subset(empty_set,sK1)
| spl19_410
| ~ spl19_430 ),
inference(backward_demodulation,[],[f6329,f6848]) ).
fof(f6329,plain,
( ~ ordinal_subset(succ(succ(sK1)),sK1)
| spl19_410 ),
inference(avatar_component_clause,[],[f6327]) ).
fof(f6327,plain,
( spl19_410
<=> ordinal_subset(succ(succ(sK1)),sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_410])]) ).
fof(f6887,plain,
( ~ spl19_46
| ~ spl19_245
| ~ spl19_430 ),
inference(avatar_contradiction_clause,[],[f6886]) ).
fof(f6886,plain,
( $false
| ~ spl19_46
| ~ spl19_245
| ~ spl19_430 ),
inference(subsumption_resolution,[],[f6856,f485]) ).
fof(f6856,plain,
( in(sK1,empty_set)
| ~ spl19_245
| ~ spl19_430 ),
inference(backward_demodulation,[],[f2727,f6848]) ).
fof(f2727,plain,
( in(sK1,succ(succ(sK1)))
| ~ spl19_245 ),
inference(avatar_component_clause,[],[f2725]) ).
fof(f2725,plain,
( spl19_245
<=> in(sK1,succ(succ(sK1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_245])]) ).
fof(f6853,plain,
( spl19_430
| spl19_431
| ~ spl19_201
| ~ spl19_411 ),
inference(avatar_split_clause,[],[f6380,f6331,f2020,f6850,f6846]) ).
fof(f6850,plain,
( spl19_431
<=> in(empty_set,succ(succ(sK1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_431])]) ).
fof(f6331,plain,
( spl19_411
<=> ordinal(succ(succ(sK1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_411])]) ).
fof(f6380,plain,
( in(empty_set,succ(succ(sK1)))
| empty_set = succ(succ(sK1))
| ~ spl19_201
| ~ spl19_411 ),
inference(resolution,[],[f6332,f2021]) ).
fof(f6332,plain,
( ordinal(succ(succ(sK1)))
| ~ spl19_411 ),
inference(avatar_component_clause,[],[f6331]) ).
fof(f6833,plain,
( spl19_429
| ~ spl19_18
| ~ spl19_228 ),
inference(avatar_split_clause,[],[f2736,f2595,f348,f6831]) ).
fof(f6831,plain,
( spl19_429
<=> ! [X9] :
( subset(X9,succ(sK10))
| ~ in(X9,succ(sK10)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_429])]) ).
fof(f2736,plain,
( ! [X9] :
( subset(X9,succ(sK10))
| ~ in(X9,succ(sK10)) )
| ~ spl19_18
| ~ spl19_228 ),
inference(resolution,[],[f2596,f350]) ).
fof(f6827,plain,
( spl19_428
| ~ spl19_14
| ~ spl19_228 ),
inference(avatar_split_clause,[],[f2735,f2595,f328,f6825]) ).
fof(f2735,plain,
( ! [X8] :
( subset(X8,succ(sK8))
| ~ in(X8,succ(sK8)) )
| ~ spl19_14
| ~ spl19_228 ),
inference(resolution,[],[f2596,f330]) ).
fof(f6776,plain,
( spl19_152
| ~ spl19_405
| ~ spl19_426 ),
inference(avatar_contradiction_clause,[],[f6775]) ).
fof(f6775,plain,
( $false
| spl19_152
| ~ spl19_405
| ~ spl19_426 ),
inference(subsumption_resolution,[],[f6590,f1597]) ).
fof(f6590,plain,
( ordinal_subset(sK0,empty_set)
| ~ spl19_405
| ~ spl19_426 ),
inference(backward_demodulation,[],[f6259,f6558]) ).
fof(f6558,plain,
( empty_set = succ(succ(sK0))
| ~ spl19_426 ),
inference(avatar_component_clause,[],[f6556]) ).
fof(f6556,plain,
( spl19_426
<=> empty_set = succ(succ(sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_426])]) ).
fof(f6750,plain,
( ~ spl19_154
| spl19_402
| ~ spl19_426 ),
inference(avatar_contradiction_clause,[],[f6749]) ).
fof(f6749,plain,
( $false
| ~ spl19_154
| spl19_402
| ~ spl19_426 ),
inference(subsumption_resolution,[],[f6576,f1621]) ).
fof(f6576,plain,
( ~ ordinal_subset(empty_set,sK0)
| spl19_402
| ~ spl19_426 ),
inference(backward_demodulation,[],[f6217,f6558]) ).
fof(f6739,plain,
( ~ spl19_46
| ~ spl19_188
| ~ spl19_426 ),
inference(avatar_contradiction_clause,[],[f6738]) ).
fof(f6738,plain,
( $false
| ~ spl19_46
| ~ spl19_188
| ~ spl19_426 ),
inference(subsumption_resolution,[],[f6566,f485]) ).
fof(f6566,plain,
( in(sK0,empty_set)
| ~ spl19_188
| ~ spl19_426 ),
inference(backward_demodulation,[],[f1897,f6558]) ).
fof(f6563,plain,
( spl19_426
| spl19_427
| ~ spl19_201
| ~ spl19_403 ),
inference(avatar_split_clause,[],[f6239,f6219,f2020,f6560,f6556]) ).
fof(f6560,plain,
( spl19_427
<=> in(empty_set,succ(succ(sK0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_427])]) ).
fof(f6239,plain,
( in(empty_set,succ(succ(sK0)))
| empty_set = succ(succ(sK0))
| ~ spl19_201
| ~ spl19_403 ),
inference(resolution,[],[f6220,f2021]) ).
fof(f6554,plain,
( spl19_425
| ~ spl19_8
| ~ spl19_228 ),
inference(avatar_split_clause,[],[f2732,f2595,f298,f6552]) ).
fof(f6552,plain,
( spl19_425
<=> ! [X5] :
( subset(X5,succ(empty_set))
| ~ in(X5,succ(empty_set)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_425])]) ).
fof(f2732,plain,
( ! [X5] :
( subset(X5,succ(empty_set))
| ~ in(X5,succ(empty_set)) )
| ~ spl19_8
| ~ spl19_228 ),
inference(resolution,[],[f2596,f300]) ).
fof(f6548,plain,
( spl19_424
| ~ spl19_247
| ~ spl19_391 ),
inference(avatar_split_clause,[],[f6291,f6141,f2816,f6546]) ).
fof(f6546,plain,
( spl19_424
<=> ! [X1] :
( ordinal_subset(X1,succ(sK1))
| ~ ordinal(X1)
| ~ in(X1,succ(sK1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_424])]) ).
fof(f6141,plain,
( spl19_391
<=> ! [X2] :
( ~ subset(X2,succ(sK1))
| ordinal_subset(X2,succ(sK1))
| ~ ordinal(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_391])]) ).
fof(f6291,plain,
( ! [X1] :
( ordinal_subset(X1,succ(sK1))
| ~ ordinal(X1)
| ~ in(X1,succ(sK1)) )
| ~ spl19_247
| ~ spl19_391 ),
inference(resolution,[],[f6142,f2817]) ).
fof(f6142,plain,
( ! [X2] :
( ~ subset(X2,succ(sK1))
| ordinal_subset(X2,succ(sK1))
| ~ ordinal(X2) )
| ~ spl19_391 ),
inference(avatar_component_clause,[],[f6141]) ).
fof(f6539,plain,
( spl19_423
| ~ spl19_82
| ~ spl19_196 ),
inference(avatar_split_clause,[],[f2480,f1975,f703,f6537]) ).
fof(f6537,plain,
( spl19_423
<=> ! [X1] :
( ordinal_subset(X1,sK10)
| ~ ordinal(X1)
| ~ in(X1,sK10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_423])]) ).
fof(f2480,plain,
( ! [X1] :
( ordinal_subset(X1,sK10)
| ~ ordinal(X1)
| ~ in(X1,sK10) )
| ~ spl19_82
| ~ spl19_196 ),
inference(resolution,[],[f1976,f704]) ).
fof(f6495,plain,
( spl19_422
| ~ spl19_81
| ~ spl19_192 ),
inference(avatar_split_clause,[],[f2468,f1958,f699,f6493]) ).
fof(f6493,plain,
( spl19_422
<=> ! [X1] :
( ordinal_subset(X1,sK8)
| ~ ordinal(X1)
| ~ in(X1,sK8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_422])]) ).
fof(f2468,plain,
( ! [X1] :
( ordinal_subset(X1,sK8)
| ~ ordinal(X1)
| ~ in(X1,sK8) )
| ~ spl19_81
| ~ spl19_192 ),
inference(resolution,[],[f1959,f700]) ).
fof(f6491,plain,
( spl19_421
| ~ spl19_5
| ~ spl19_394
| spl19_419 ),
inference(avatar_split_clause,[],[f6486,f6475,f6163,f283,f6488]) ).
fof(f6488,plain,
( spl19_421
<=> ordinal_subset(empty_set,succ(sK1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_421])]) ).
fof(f6475,plain,
( spl19_419
<=> ordinal_subset(succ(sK1),empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_419])]) ).
fof(f6486,plain,
( ordinal_subset(empty_set,succ(sK1))
| ~ spl19_5
| ~ spl19_394
| spl19_419 ),
inference(subsumption_resolution,[],[f6483,f285]) ).
fof(f6483,plain,
( ordinal_subset(empty_set,succ(sK1))
| ~ empty(empty_set)
| ~ spl19_394
| spl19_419 ),
inference(resolution,[],[f6477,f6164]) ).
fof(f6477,plain,
( ~ ordinal_subset(succ(sK1),empty_set)
| spl19_419 ),
inference(avatar_component_clause,[],[f6475]) ).
fof(f6482,plain,
( spl19_420
| ~ spl19_57
| ~ spl19_163 ),
inference(avatar_split_clause,[],[f2124,f1741,f541,f6480]) ).
fof(f2124,plain,
( ! [X8,X9] :
( ~ in(succ(X8),X9)
| ~ in(X9,singleton(X8)) )
| ~ spl19_57
| ~ spl19_163 ),
inference(superposition,[],[f1742,f542]) ).
fof(f6478,plain,
( spl19_418
| ~ spl19_419
| ~ spl19_5
| ~ spl19_362
| ~ spl19_396 ),
inference(avatar_split_clause,[],[f6470,f6171,f5519,f283,f6475,f6472]) ).
fof(f6472,plain,
( spl19_418
<=> ! [X2] : ~ in(X2,succ(sK1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_418])]) ).
fof(f6470,plain,
( ! [X2] :
( ~ ordinal_subset(succ(sK1),empty_set)
| ~ in(X2,succ(sK1)) )
| ~ spl19_5
| ~ spl19_362
| ~ spl19_396 ),
inference(subsumption_resolution,[],[f6464,f285]) ).
fof(f6464,plain,
( ! [X2] :
( ~ ordinal_subset(succ(sK1),empty_set)
| ~ empty(empty_set)
| ~ in(X2,succ(sK1)) )
| ~ spl19_362
| ~ spl19_396 ),
inference(resolution,[],[f6172,f5520]) ).
fof(f6443,plain,
( spl19_417
| ~ spl19_70
| ~ spl19_83 ),
inference(avatar_split_clause,[],[f717,f712,f616,f6441]) ).
fof(f6441,plain,
( spl19_417
<=> ! [X1] :
( empty(singleton(X1))
| sK3(singleton(X1)) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_417])]) ).
fof(f717,plain,
( ! [X1] :
( empty(singleton(X1))
| sK3(singleton(X1)) = X1 )
| ~ spl19_70
| ~ spl19_83 ),
inference(resolution,[],[f713,f617]) ).
fof(f6429,plain,
( spl19_416
| ~ spl19_48
| ~ spl19_76 ),
inference(avatar_split_clause,[],[f677,f670,f492,f6427]) ).
fof(f670,plain,
( spl19_76
<=> ! [X2,X1] :
( subset(X1,X2)
| ~ in(X1,powerset(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_76])]) ).
fof(f677,plain,
( ! [X0] :
( subset(sK2(powerset(X0)),X0)
| epsilon_transitive(powerset(X0)) )
| ~ spl19_48
| ~ spl19_76 ),
inference(resolution,[],[f671,f493]) ).
fof(f671,plain,
( ! [X2,X1] :
( ~ in(X1,powerset(X2))
| subset(X1,X2) )
| ~ spl19_76 ),
inference(avatar_component_clause,[],[f670]) ).
fof(f6425,plain,
( ~ spl19_414
| spl19_415
| ~ spl19_292
| ~ spl19_408 ),
inference(avatar_split_clause,[],[f6409,f6278,f3662,f6422,f6418]) ).
fof(f6418,plain,
( spl19_414
<=> in(powerset(powerset(sK0)),sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_414])]) ).
fof(f6422,plain,
( spl19_415
<=> empty(powerset(powerset(sK0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_415])]) ).
fof(f3662,plain,
( spl19_292
<=> ! [X3] :
( ~ in(X3,sK0)
| ~ in(powerset(sK0),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_292])]) ).
fof(f6409,plain,
( empty(powerset(powerset(sK0)))
| ~ in(powerset(powerset(sK0)),sK0)
| ~ spl19_292
| ~ spl19_408 ),
inference(resolution,[],[f6279,f3663]) ).
fof(f3663,plain,
( ! [X3] :
( ~ in(powerset(sK0),X3)
| ~ in(X3,sK0) )
| ~ spl19_292 ),
inference(avatar_component_clause,[],[f3662]) ).
fof(f6416,plain,
( spl19_413
| ~ spl19_60
| ~ spl19_411 ),
inference(avatar_split_clause,[],[f6372,f6331,f552,f6413]) ).
fof(f6413,plain,
( spl19_413
<=> ordinal_subset(succ(succ(sK1)),succ(succ(sK1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_413])]) ).
fof(f6372,plain,
( ordinal_subset(succ(succ(sK1)),succ(succ(sK1)))
| ~ spl19_60
| ~ spl19_411 ),
inference(resolution,[],[f6332,f553]) ).
fof(f6401,plain,
( spl19_412
| ~ spl19_109
| spl19_410
| ~ spl19_411 ),
inference(avatar_split_clause,[],[f6396,f6331,f6327,f920,f6398]) ).
fof(f6396,plain,
( ordinal_subset(sK1,succ(succ(sK1)))
| ~ spl19_109
| spl19_410
| ~ spl19_411 ),
inference(subsumption_resolution,[],[f6395,f6332]) ).
fof(f6395,plain,
( ordinal_subset(sK1,succ(succ(sK1)))
| ~ ordinal(succ(succ(sK1)))
| ~ spl19_109
| spl19_410 ),
inference(resolution,[],[f6329,f921]) ).
fof(f6338,plain,
( ~ spl19_38
| ~ spl19_243
| spl19_411 ),
inference(avatar_contradiction_clause,[],[f6337]) ).
fof(f6337,plain,
( $false
| ~ spl19_38
| ~ spl19_243
| spl19_411 ),
inference(subsumption_resolution,[],[f6335,f2718]) ).
fof(f2718,plain,
( ordinal(succ(sK1))
| ~ spl19_243 ),
inference(avatar_component_clause,[],[f2717]) ).
fof(f2717,plain,
( spl19_243
<=> ordinal(succ(sK1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_243])]) ).
fof(f6335,plain,
( ~ ordinal(succ(sK1))
| ~ spl19_38
| spl19_411 ),
inference(resolution,[],[f6333,f436]) ).
fof(f6333,plain,
( ~ ordinal(succ(succ(sK1)))
| spl19_411 ),
inference(avatar_component_clause,[],[f6331]) ).
fof(f6334,plain,
( ~ spl19_410
| ~ spl19_411
| ~ spl19_178
| spl19_244
| ~ spl19_245
| ~ spl19_392 ),
inference(avatar_split_clause,[],[f6307,f6155,f2725,f2721,f1824,f6331,f6327]) ).
fof(f2721,plain,
( spl19_244
<=> sK1 = succ(succ(sK1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_244])]) ).
fof(f6155,plain,
( spl19_392
<=> ! [X5] :
( subset(X5,succ(succ(sK1)))
| ~ in(X5,succ(succ(sK1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_392])]) ).
fof(f6307,plain,
( ~ ordinal(succ(succ(sK1)))
| ~ ordinal_subset(succ(succ(sK1)),sK1)
| ~ spl19_178
| spl19_244
| ~ spl19_245
| ~ spl19_392 ),
inference(subsumption_resolution,[],[f6306,f2722]) ).
fof(f2722,plain,
( sK1 != succ(succ(sK1))
| spl19_244 ),
inference(avatar_component_clause,[],[f2721]) ).
fof(f6306,plain,
( ~ ordinal(succ(succ(sK1)))
| sK1 = succ(succ(sK1))
| ~ ordinal_subset(succ(succ(sK1)),sK1)
| ~ spl19_178
| ~ spl19_245
| ~ spl19_392 ),
inference(subsumption_resolution,[],[f6303,f2727]) ).
fof(f6303,plain,
( ~ in(sK1,succ(succ(sK1)))
| ~ ordinal(succ(succ(sK1)))
| sK1 = succ(succ(sK1))
| ~ ordinal_subset(succ(succ(sK1)),sK1)
| ~ spl19_178
| ~ spl19_392 ),
inference(resolution,[],[f6156,f1825]) ).
fof(f6156,plain,
( ! [X5] :
( subset(X5,succ(succ(sK1)))
| ~ in(X5,succ(succ(sK1))) )
| ~ spl19_392 ),
inference(avatar_component_clause,[],[f6155]) ).
fof(f6324,plain,
( spl19_409
| ~ spl19_48
| ~ spl19_49
| ~ spl19_392 ),
inference(avatar_split_clause,[],[f6308,f6155,f496,f492,f6321]) ).
fof(f6321,plain,
( spl19_409
<=> epsilon_transitive(succ(succ(sK1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_409])]) ).
fof(f6308,plain,
( epsilon_transitive(succ(succ(sK1)))
| ~ spl19_48
| ~ spl19_49
| ~ spl19_392 ),
inference(subsumption_resolution,[],[f6305,f493]) ).
fof(f6305,plain,
( ~ in(sK2(succ(succ(sK1))),succ(succ(sK1)))
| epsilon_transitive(succ(succ(sK1)))
| ~ spl19_49
| ~ spl19_392 ),
inference(resolution,[],[f6156,f497]) ).
fof(f6280,plain,
( spl19_408
| ~ spl19_26
| ~ spl19_229 ),
inference(avatar_split_clause,[],[f2787,f2606,f387,f6278]) ).
fof(f387,plain,
( spl19_26
<=> ! [X0] : subset(X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_26])]) ).
fof(f2787,plain,
( ! [X0] :
( in(X0,powerset(X0))
| empty(powerset(X0)) )
| ~ spl19_26
| ~ spl19_229 ),
inference(resolution,[],[f2607,f388]) ).
fof(f388,plain,
( ! [X0] : subset(X0,X0)
| ~ spl19_26 ),
inference(avatar_component_clause,[],[f387]) ).
fof(f6270,plain,
( spl19_407
| ~ spl19_60
| ~ spl19_403 ),
inference(avatar_split_clause,[],[f6231,f6219,f552,f6267]) ).
fof(f6267,plain,
( spl19_407
<=> ordinal_subset(succ(succ(sK0)),succ(succ(sK0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_407])]) ).
fof(f6231,plain,
( ordinal_subset(succ(succ(sK0)),succ(succ(sK0)))
| ~ spl19_60
| ~ spl19_403 ),
inference(resolution,[],[f6220,f553]) ).
fof(f6264,plain,
( spl19_406
| ~ spl19_53
| ~ spl19_99 ),
inference(avatar_split_clause,[],[f896,f849,f512,f6262]) ).
fof(f6262,plain,
( spl19_406
<=> ! [X4,X3] :
( ~ in(X3,X4)
| ~ in(X4,powerset(empty_set)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_406])]) ).
fof(f512,plain,
( spl19_53
<=> ! [X0,X1] :
( element(X0,X1)
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_53])]) ).
fof(f896,plain,
( ! [X3,X4] :
( ~ in(X3,X4)
| ~ in(X4,powerset(empty_set)) )
| ~ spl19_53
| ~ spl19_99 ),
inference(resolution,[],[f850,f513]) ).
fof(f513,plain,
( ! [X0,X1] :
( element(X0,X1)
| ~ in(X0,X1) )
| ~ spl19_53 ),
inference(avatar_component_clause,[],[f512]) ).
fof(f6260,plain,
( spl19_405
| ~ spl19_108
| spl19_402
| ~ spl19_403 ),
inference(avatar_split_clause,[],[f6255,f6219,f6215,f916,f6257]) ).
fof(f6255,plain,
( ordinal_subset(sK0,succ(succ(sK0)))
| ~ spl19_108
| spl19_402
| ~ spl19_403 ),
inference(subsumption_resolution,[],[f6254,f6220]) ).
fof(f6254,plain,
( ordinal_subset(sK0,succ(succ(sK0)))
| ~ ordinal(succ(succ(sK0)))
| ~ spl19_108
| spl19_402 ),
inference(resolution,[],[f6217,f917]) ).
fof(f6230,plain,
( spl19_404
| ~ spl19_52
| ~ spl19_98 ),
inference(avatar_split_clause,[],[f857,f845,f508,f6228]) ).
fof(f857,plain,
( ! [X2,X1] :
( ~ in(X1,X2)
| ~ in(succ(X2),X1) )
| ~ spl19_52
| ~ spl19_98 ),
inference(resolution,[],[f846,f509]) ).
fof(f6226,plain,
( ~ spl19_38
| ~ spl19_186
| spl19_403 ),
inference(avatar_contradiction_clause,[],[f6225]) ).
fof(f6225,plain,
( $false
| ~ spl19_38
| ~ spl19_186
| spl19_403 ),
inference(subsumption_resolution,[],[f6223,f1888]) ).
fof(f6223,plain,
( ~ ordinal(succ(sK0))
| ~ spl19_38
| spl19_403 ),
inference(resolution,[],[f6221,f436]) ).
fof(f6221,plain,
( ~ ordinal(succ(succ(sK0)))
| spl19_403 ),
inference(avatar_component_clause,[],[f6219]) ).
fof(f6222,plain,
( ~ spl19_402
| ~ spl19_403
| ~ spl19_177
| spl19_187
| ~ spl19_188
| ~ spl19_388 ),
inference(avatar_split_clause,[],[f6201,f6129,f1895,f1891,f1820,f6219,f6215]) ).
fof(f1891,plain,
( spl19_187
<=> sK0 = succ(succ(sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_187])]) ).
fof(f6129,plain,
( spl19_388
<=> ! [X4] :
( subset(X4,succ(succ(sK0)))
| ~ in(X4,succ(succ(sK0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_388])]) ).
fof(f6201,plain,
( ~ ordinal(succ(succ(sK0)))
| ~ ordinal_subset(succ(succ(sK0)),sK0)
| ~ spl19_177
| spl19_187
| ~ spl19_188
| ~ spl19_388 ),
inference(subsumption_resolution,[],[f6200,f1892]) ).
fof(f1892,plain,
( sK0 != succ(succ(sK0))
| spl19_187 ),
inference(avatar_component_clause,[],[f1891]) ).
fof(f6200,plain,
( ~ ordinal(succ(succ(sK0)))
| sK0 = succ(succ(sK0))
| ~ ordinal_subset(succ(succ(sK0)),sK0)
| ~ spl19_177
| ~ spl19_188
| ~ spl19_388 ),
inference(subsumption_resolution,[],[f6194,f1897]) ).
fof(f6194,plain,
( ~ in(sK0,succ(succ(sK0)))
| ~ ordinal(succ(succ(sK0)))
| sK0 = succ(succ(sK0))
| ~ ordinal_subset(succ(succ(sK0)),sK0)
| ~ spl19_177
| ~ spl19_388 ),
inference(resolution,[],[f6130,f1821]) ).
fof(f6130,plain,
( ! [X4] :
( subset(X4,succ(succ(sK0)))
| ~ in(X4,succ(succ(sK0))) )
| ~ spl19_388 ),
inference(avatar_component_clause,[],[f6129]) ).
fof(f6212,plain,
( spl19_401
| ~ spl19_48
| ~ spl19_49
| ~ spl19_388 ),
inference(avatar_split_clause,[],[f6202,f6129,f496,f492,f6209]) ).
fof(f6209,plain,
( spl19_401
<=> epsilon_transitive(succ(succ(sK0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_401])]) ).
fof(f6202,plain,
( epsilon_transitive(succ(succ(sK0)))
| ~ spl19_48
| ~ spl19_49
| ~ spl19_388 ),
inference(subsumption_resolution,[],[f6199,f493]) ).
fof(f6199,plain,
( ~ in(sK2(succ(succ(sK0))),succ(succ(sK0)))
| epsilon_transitive(succ(succ(sK0)))
| ~ spl19_49
| ~ spl19_388 ),
inference(resolution,[],[f6130,f497]) ).
fof(f6190,plain,
( spl19_400
| ~ spl19_242
| ~ spl19_243 ),
inference(avatar_split_clause,[],[f2901,f2717,f2703,f6188]) ).
fof(f2901,plain,
( ! [X5] :
( in(X5,succ(sK1))
| succ(sK1) = X5
| ~ empty(X5) )
| ~ spl19_242
| ~ spl19_243 ),
inference(resolution,[],[f2704,f2718]) ).
fof(f6186,plain,
( spl19_399
| ~ spl19_186
| ~ spl19_242 ),
inference(avatar_split_clause,[],[f2900,f2703,f1887,f6184]) ).
fof(f6184,plain,
( spl19_399
<=> ! [X4] :
( in(X4,succ(sK0))
| succ(sK0) = X4
| ~ empty(X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_399])]) ).
fof(f2900,plain,
( ! [X4] :
( in(X4,succ(sK0))
| succ(sK0) = X4
| ~ empty(X4) )
| ~ spl19_186
| ~ spl19_242 ),
inference(resolution,[],[f2704,f1888]) ).
fof(f6181,plain,
( spl19_398
| ~ spl19_236
| ~ spl19_243 ),
inference(avatar_split_clause,[],[f2865,f2717,f2670,f6179]) ).
fof(f6179,plain,
( spl19_398
<=> ! [X5] :
( ordinal_subset(succ(sK1),X5)
| ~ subset(succ(sK1),X5)
| ~ empty(X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_398])]) ).
fof(f2865,plain,
( ! [X5] :
( ordinal_subset(succ(sK1),X5)
| ~ subset(succ(sK1),X5)
| ~ empty(X5) )
| ~ spl19_236
| ~ spl19_243 ),
inference(resolution,[],[f2671,f2718]) ).
fof(f6177,plain,
( spl19_397
| ~ spl19_186
| ~ spl19_236 ),
inference(avatar_split_clause,[],[f2864,f2670,f1887,f6175]) ).
fof(f6175,plain,
( spl19_397
<=> ! [X4] :
( ordinal_subset(succ(sK0),X4)
| ~ subset(succ(sK0),X4)
| ~ empty(X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_397])]) ).
fof(f2864,plain,
( ! [X4] :
( ordinal_subset(succ(sK0),X4)
| ~ subset(succ(sK0),X4)
| ~ empty(X4) )
| ~ spl19_186
| ~ spl19_236 ),
inference(resolution,[],[f2671,f1888]) ).
fof(f6173,plain,
( spl19_396
| ~ spl19_234
| ~ spl19_243 ),
inference(avatar_split_clause,[],[f2830,f2717,f2660,f6171]) ).
fof(f2830,plain,
( ! [X5] :
( subset(succ(sK1),X5)
| ~ ordinal_subset(succ(sK1),X5)
| ~ empty(X5) )
| ~ spl19_234
| ~ spl19_243 ),
inference(resolution,[],[f2661,f2718]) ).
fof(f6169,plain,
( spl19_395
| ~ spl19_186
| ~ spl19_234 ),
inference(avatar_split_clause,[],[f2829,f2660,f1887,f6167]) ).
fof(f6167,plain,
( spl19_395
<=> ! [X4] :
( subset(succ(sK0),X4)
| ~ ordinal_subset(succ(sK0),X4)
| ~ empty(X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_395])]) ).
fof(f2829,plain,
( ! [X4] :
( subset(succ(sK0),X4)
| ~ ordinal_subset(succ(sK0),X4)
| ~ empty(X4) )
| ~ spl19_186
| ~ spl19_234 ),
inference(resolution,[],[f2661,f1888]) ).
fof(f6165,plain,
( spl19_394
| ~ spl19_230
| ~ spl19_243 ),
inference(avatar_split_clause,[],[f2809,f2717,f2626,f6163]) ).
fof(f2809,plain,
( ! [X5] :
( ordinal_subset(X5,succ(sK1))
| ordinal_subset(succ(sK1),X5)
| ~ empty(X5) )
| ~ spl19_230
| ~ spl19_243 ),
inference(resolution,[],[f2627,f2718]) ).
fof(f6161,plain,
( spl19_393
| ~ spl19_186
| ~ spl19_230 ),
inference(avatar_split_clause,[],[f2808,f2626,f1887,f6159]) ).
fof(f6159,plain,
( spl19_393
<=> ! [X4] :
( ordinal_subset(X4,succ(sK0))
| ordinal_subset(succ(sK0),X4)
| ~ empty(X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_393])]) ).
fof(f2808,plain,
( ! [X4] :
( ordinal_subset(X4,succ(sK0))
| ordinal_subset(succ(sK0),X4)
| ~ empty(X4) )
| ~ spl19_186
| ~ spl19_230 ),
inference(resolution,[],[f2627,f1888]) ).
fof(f6157,plain,
( spl19_392
| ~ spl19_228
| ~ spl19_243 ),
inference(avatar_split_clause,[],[f2754,f2717,f2595,f6155]) ).
fof(f2754,plain,
( ! [X5] :
( subset(X5,succ(succ(sK1)))
| ~ in(X5,succ(succ(sK1))) )
| ~ spl19_228
| ~ spl19_243 ),
inference(resolution,[],[f2718,f2596]) ).
fof(f6143,plain,
( spl19_391
| ~ spl19_103
| ~ spl19_243 ),
inference(avatar_split_clause,[],[f2748,f2717,f877,f6141]) ).
fof(f877,plain,
( spl19_103
<=> ! [X0,X1] :
( ordinal_subset(X0,X1)
| ~ subset(X0,X1)
| ~ ordinal(X1)
| ~ ordinal(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_103])]) ).
fof(f2748,plain,
( ! [X2] :
( ~ subset(X2,succ(sK1))
| ordinal_subset(X2,succ(sK1))
| ~ ordinal(X2) )
| ~ spl19_103
| ~ spl19_243 ),
inference(resolution,[],[f2718,f878]) ).
fof(f878,plain,
( ! [X0,X1] :
( ~ ordinal(X1)
| ~ subset(X0,X1)
| ordinal_subset(X0,X1)
| ~ ordinal(X0) )
| ~ spl19_103 ),
inference(avatar_component_clause,[],[f877]) ).
fof(f6139,plain,
( spl19_390
| ~ spl19_100
| ~ spl19_243 ),
inference(avatar_split_clause,[],[f2747,f2717,f853,f6137]) ).
fof(f6137,plain,
( spl19_390
<=> ! [X1] :
( ~ ordinal_subset(X1,succ(sK1))
| subset(X1,succ(sK1))
| ~ ordinal(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_390])]) ).
fof(f853,plain,
( spl19_100
<=> ! [X0,X1] :
( subset(X0,X1)
| ~ ordinal_subset(X0,X1)
| ~ ordinal(X1)
| ~ ordinal(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_100])]) ).
fof(f2747,plain,
( ! [X1] :
( ~ ordinal_subset(X1,succ(sK1))
| subset(X1,succ(sK1))
| ~ ordinal(X1) )
| ~ spl19_100
| ~ spl19_243 ),
inference(resolution,[],[f2718,f854]) ).
fof(f854,plain,
( ! [X0,X1] :
( ~ ordinal(X1)
| ~ ordinal_subset(X0,X1)
| subset(X0,X1)
| ~ ordinal(X0) )
| ~ spl19_100 ),
inference(avatar_component_clause,[],[f853]) ).
fof(f6135,plain,
( spl19_389
| ~ spl19_97
| ~ spl19_243 ),
inference(avatar_split_clause,[],[f2746,f2717,f840,f6133]) ).
fof(f6133,plain,
( spl19_389
<=> ! [X0] :
( ordinal_subset(X0,succ(sK1))
| ordinal_subset(succ(sK1),X0)
| ~ ordinal(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_389])]) ).
fof(f840,plain,
( spl19_97
<=> ! [X0,X1] :
( ordinal_subset(X1,X0)
| ordinal_subset(X0,X1)
| ~ ordinal(X1)
| ~ ordinal(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_97])]) ).
fof(f2746,plain,
( ! [X0] :
( ordinal_subset(X0,succ(sK1))
| ordinal_subset(succ(sK1),X0)
| ~ ordinal(X0) )
| ~ spl19_97
| ~ spl19_243 ),
inference(resolution,[],[f2718,f841]) ).
fof(f841,plain,
( ! [X0,X1] :
( ~ ordinal(X1)
| ordinal_subset(X0,X1)
| ordinal_subset(X1,X0)
| ~ ordinal(X0) )
| ~ spl19_97 ),
inference(avatar_component_clause,[],[f840]) ).
fof(f6131,plain,
( spl19_388
| ~ spl19_186
| ~ spl19_228 ),
inference(avatar_split_clause,[],[f2731,f2595,f1887,f6129]) ).
fof(f2731,plain,
( ! [X4] :
( subset(X4,succ(succ(sK0)))
| ~ in(X4,succ(succ(sK0))) )
| ~ spl19_186
| ~ spl19_228 ),
inference(resolution,[],[f2596,f1888]) ).
fof(f6084,plain,
( spl19_387
| ~ spl19_32
| ~ spl19_276
| ~ spl19_356 ),
inference(avatar_split_clause,[],[f5500,f5464,f3419,f411,f6082]) ).
fof(f6082,plain,
( spl19_387
<=> ! [X0] :
( in(X0,powerset(sK0))
| sK0 = X0
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_387])]) ).
fof(f3419,plain,
( spl19_276
<=> ! [X0] :
( ~ empty(X0)
| sK0 = X0
| ordinal_subset(X0,sK0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_276])]) ).
fof(f5464,plain,
( spl19_356
<=> ! [X5] :
( in(X5,powerset(sK0))
| ~ ordinal(X5)
| ~ ordinal_subset(X5,sK0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_356])]) ).
fof(f5500,plain,
( ! [X0] :
( in(X0,powerset(sK0))
| sK0 = X0
| ~ empty(X0) )
| ~ spl19_32
| ~ spl19_276
| ~ spl19_356 ),
inference(subsumption_resolution,[],[f5484,f412]) ).
fof(f5484,plain,
( ! [X0] :
( ~ ordinal(X0)
| in(X0,powerset(sK0))
| sK0 = X0
| ~ empty(X0) )
| ~ spl19_276
| ~ spl19_356 ),
inference(resolution,[],[f5465,f3420]) ).
fof(f3420,plain,
( ! [X0] :
( ordinal_subset(X0,sK0)
| sK0 = X0
| ~ empty(X0) )
| ~ spl19_276 ),
inference(avatar_component_clause,[],[f3419]) ).
fof(f5465,plain,
( ! [X5] :
( ~ ordinal_subset(X5,sK0)
| ~ ordinal(X5)
| in(X5,powerset(sK0)) )
| ~ spl19_356 ),
inference(avatar_component_clause,[],[f5464]) ).
fof(f6076,plain,
( spl19_386
| ~ spl19_105
| ~ spl19_349 ),
inference(avatar_split_clause,[],[f4959,f4951,f891,f6074]) ).
fof(f6074,plain,
( spl19_386
<=> ! [X4,X3] :
( ~ element(X3,empty_set)
| element(X4,sK1)
| ~ in(X4,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_386])]) ).
fof(f891,plain,
( spl19_105
<=> ! [X2,X0,X1] :
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_105])]) ).
fof(f4959,plain,
( ! [X3,X4] :
( ~ element(X3,empty_set)
| element(X4,sK1)
| ~ in(X4,X3) )
| ~ spl19_105
| ~ spl19_349 ),
inference(superposition,[],[f892,f4953]) ).
fof(f892,plain,
( ! [X2,X0,X1] :
( ~ element(X1,powerset(X2))
| element(X0,X2)
| ~ in(X0,X1) )
| ~ spl19_105 ),
inference(avatar_component_clause,[],[f891]) ).
fof(f6054,plain,
( spl19_385
| ~ spl19_32
| ~ spl19_248
| ~ spl19_356 ),
inference(avatar_split_clause,[],[f5501,f5464,f2820,f411,f6052]) ).
fof(f6052,plain,
( spl19_385
<=> ! [X1] :
( in(X1,powerset(sK0))
| ordinal_subset(sK0,X1)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_385])]) ).
fof(f2820,plain,
( spl19_248
<=> ! [X7] :
( ordinal_subset(X7,sK0)
| ordinal_subset(sK0,X7)
| ~ empty(X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_248])]) ).
fof(f5501,plain,
( ! [X1] :
( in(X1,powerset(sK0))
| ordinal_subset(sK0,X1)
| ~ empty(X1) )
| ~ spl19_32
| ~ spl19_248
| ~ spl19_356 ),
inference(subsumption_resolution,[],[f5485,f412]) ).
fof(f5485,plain,
( ! [X1] :
( ~ ordinal(X1)
| in(X1,powerset(sK0))
| ordinal_subset(sK0,X1)
| ~ empty(X1) )
| ~ spl19_248
| ~ spl19_356 ),
inference(resolution,[],[f5465,f2821]) ).
fof(f2821,plain,
( ! [X7] :
( ordinal_subset(sK0,X7)
| ordinal_subset(X7,sK0)
| ~ empty(X7) )
| ~ spl19_248 ),
inference(avatar_component_clause,[],[f2820]) ).
fof(f6041,plain,
( spl19_384
| ~ spl19_108
| ~ spl19_356 ),
inference(avatar_split_clause,[],[f5498,f5464,f916,f6039]) ).
fof(f6039,plain,
( spl19_384
<=> ! [X3] :
( ~ ordinal(X3)
| in(X3,powerset(sK0))
| ordinal_subset(sK0,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_384])]) ).
fof(f5498,plain,
( ! [X3] :
( ~ ordinal(X3)
| in(X3,powerset(sK0))
| ordinal_subset(sK0,X3) )
| ~ spl19_108
| ~ spl19_356 ),
inference(duplicate_literal_removal,[],[f5487]) ).
fof(f5487,plain,
( ! [X3] :
( ~ ordinal(X3)
| in(X3,powerset(sK0))
| ordinal_subset(sK0,X3)
| ~ ordinal(X3) )
| ~ spl19_108
| ~ spl19_356 ),
inference(resolution,[],[f5465,f917]) ).
fof(f5964,plain,
( ~ spl19_46
| ~ spl19_270
| ~ spl19_382 ),
inference(avatar_contradiction_clause,[],[f5963]) ).
fof(f5963,plain,
( $false
| ~ spl19_46
| ~ spl19_270
| ~ spl19_382 ),
inference(subsumption_resolution,[],[f5906,f485]) ).
fof(f5906,plain,
( in(succ(sK0),empty_set)
| ~ spl19_270
| ~ spl19_382 ),
inference(backward_demodulation,[],[f3198,f5862]) ).
fof(f5862,plain,
( empty_set = sK10
| ~ spl19_382 ),
inference(avatar_component_clause,[],[f5860]) ).
fof(f5860,plain,
( spl19_382
<=> empty_set = sK10 ),
introduced(avatar_definition,[new_symbols(naming,[spl19_382])]) ).
fof(f5957,plain,
( ~ spl19_5
| spl19_268
| ~ spl19_382 ),
inference(avatar_contradiction_clause,[],[f5956]) ).
fof(f5956,plain,
( $false
| ~ spl19_5
| spl19_268
| ~ spl19_382 ),
inference(subsumption_resolution,[],[f5903,f285]) ).
fof(f5903,plain,
( ~ empty(empty_set)
| spl19_268
| ~ spl19_382 ),
inference(backward_demodulation,[],[f3175,f5862]) ).
fof(f3175,plain,
( ~ empty(sK10)
| spl19_268 ),
inference(avatar_component_clause,[],[f3173]) ).
fof(f3173,plain,
( spl19_268
<=> empty(sK10) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_268])]) ).
fof(f5942,plain,
( ~ spl19_226
| spl19_241
| ~ spl19_382 ),
inference(avatar_contradiction_clause,[],[f5941]) ).
fof(f5941,plain,
( $false
| ~ spl19_226
| spl19_241
| ~ spl19_382 ),
inference(subsumption_resolution,[],[f5893,f2487]) ).
fof(f2487,plain,
( ordinal_subset(empty_set,succ(sK0))
| ~ spl19_226 ),
inference(avatar_component_clause,[],[f2485]) ).
fof(f2485,plain,
( spl19_226
<=> ordinal_subset(empty_set,succ(sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_226])]) ).
fof(f5893,plain,
( ~ ordinal_subset(empty_set,succ(sK0))
| spl19_241
| ~ spl19_382 ),
inference(backward_demodulation,[],[f2699,f5862]) ).
fof(f2699,plain,
( ~ ordinal_subset(sK10,succ(sK0))
| spl19_241 ),
inference(avatar_component_clause,[],[f2698]) ).
fof(f2698,plain,
( spl19_241
<=> ordinal_subset(sK10,succ(sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_241])]) ).
fof(f5940,plain,
( ~ spl19_224
| spl19_238
| ~ spl19_382 ),
inference(avatar_contradiction_clause,[],[f5939]) ).
fof(f5939,plain,
( $false
| ~ spl19_224
| spl19_238
| ~ spl19_382 ),
inference(subsumption_resolution,[],[f5891,f2460]) ).
fof(f2460,plain,
( in(empty_set,succ(sK0))
| ~ spl19_224 ),
inference(avatar_component_clause,[],[f2459]) ).
fof(f2459,plain,
( spl19_224
<=> in(empty_set,succ(sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_224])]) ).
fof(f5891,plain,
( ~ in(empty_set,succ(sK0))
| spl19_238
| ~ spl19_382 ),
inference(backward_demodulation,[],[f2683,f5862]) ).
fof(f2683,plain,
( ~ in(sK10,succ(sK0))
| spl19_238 ),
inference(avatar_component_clause,[],[f2681]) ).
fof(f2681,plain,
( spl19_238
<=> in(sK10,succ(sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_238])]) ).
fof(f5938,plain,
( spl19_223
| ~ spl19_237
| ~ spl19_382 ),
inference(avatar_contradiction_clause,[],[f5937]) ).
fof(f5937,plain,
( $false
| spl19_223
| ~ spl19_237
| ~ spl19_382 ),
inference(subsumption_resolution,[],[f5890,f2457]) ).
fof(f2457,plain,
( ~ ordinal_subset(succ(sK0),empty_set)
| spl19_223 ),
inference(avatar_component_clause,[],[f2455]) ).
fof(f2455,plain,
( spl19_223
<=> ordinal_subset(succ(sK0),empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_223])]) ).
fof(f5890,plain,
( ordinal_subset(succ(sK0),empty_set)
| ~ spl19_237
| ~ spl19_382 ),
inference(backward_demodulation,[],[f2678,f5862]) ).
fof(f2678,plain,
( ordinal_subset(succ(sK0),sK10)
| ~ spl19_237 ),
inference(avatar_component_clause,[],[f2677]) ).
fof(f2677,plain,
( spl19_237
<=> ordinal_subset(succ(sK0),sK10) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_237])]) ).
fof(f5934,plain,
( ~ spl19_155
| spl19_218
| ~ spl19_382 ),
inference(avatar_contradiction_clause,[],[f5933]) ).
fof(f5933,plain,
( $false
| ~ spl19_155
| spl19_218
| ~ spl19_382 ),
inference(subsumption_resolution,[],[f5887,f1668]) ).
fof(f5887,plain,
( ~ ordinal_subset(empty_set,sK1)
| spl19_218
| ~ spl19_382 ),
inference(backward_demodulation,[],[f2390,f5862]) ).
fof(f2390,plain,
( ~ ordinal_subset(sK10,sK1)
| spl19_218 ),
inference(avatar_component_clause,[],[f2388]) ).
fof(f2388,plain,
( spl19_218
<=> ordinal_subset(sK10,sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_218])]) ).
fof(f5932,plain,
( ~ spl19_154
| spl19_217
| ~ spl19_382 ),
inference(avatar_contradiction_clause,[],[f5931]) ).
fof(f5931,plain,
( $false
| ~ spl19_154
| spl19_217
| ~ spl19_382 ),
inference(subsumption_resolution,[],[f5886,f1621]) ).
fof(f5886,plain,
( ~ ordinal_subset(empty_set,sK0)
| spl19_217
| ~ spl19_382 ),
inference(backward_demodulation,[],[f2362,f5862]) ).
fof(f2362,plain,
( ~ ordinal_subset(sK10,sK0)
| spl19_217 ),
inference(avatar_component_clause,[],[f2360]) ).
fof(f2360,plain,
( spl19_217
<=> ordinal_subset(sK10,sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_217])]) ).
fof(f5930,plain,
( spl19_212
| ~ spl19_216
| ~ spl19_382 ),
inference(avatar_contradiction_clause,[],[f5929]) ).
fof(f5929,plain,
( $false
| spl19_212
| ~ spl19_216
| ~ spl19_382 ),
inference(subsumption_resolution,[],[f5885,f2225]) ).
fof(f5885,plain,
( ordinal_subset(sK1,empty_set)
| ~ spl19_216
| ~ spl19_382 ),
inference(backward_demodulation,[],[f2343,f5862]) ).
fof(f2343,plain,
( ordinal_subset(sK1,sK10)
| ~ spl19_216 ),
inference(avatar_component_clause,[],[f2342]) ).
fof(f2342,plain,
( spl19_216
<=> ordinal_subset(sK1,sK10) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_216])]) ).
fof(f5928,plain,
( spl19_152
| ~ spl19_215
| ~ spl19_382 ),
inference(avatar_contradiction_clause,[],[f5927]) ).
fof(f5927,plain,
( $false
| spl19_152
| ~ spl19_215
| ~ spl19_382 ),
inference(subsumption_resolution,[],[f5884,f1597]) ).
fof(f5884,plain,
( ordinal_subset(sK0,empty_set)
| ~ spl19_215
| ~ spl19_382 ),
inference(backward_demodulation,[],[f2338,f5862]) ).
fof(f2338,plain,
( ordinal_subset(sK0,sK10)
| ~ spl19_215 ),
inference(avatar_component_clause,[],[f2337]) ).
fof(f2337,plain,
( spl19_215
<=> ordinal_subset(sK0,sK10) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_215])]) ).
fof(f5921,plain,
( ~ spl19_151
| spl19_174
| ~ spl19_382 ),
inference(avatar_contradiction_clause,[],[f5920]) ).
fof(f5920,plain,
( $false
| ~ spl19_151
| spl19_174
| ~ spl19_382 ),
inference(subsumption_resolution,[],[f5879,f1537]) ).
fof(f5879,plain,
( ~ in(empty_set,sK1)
| spl19_174
| ~ spl19_382 ),
inference(backward_demodulation,[],[f1790,f5862]) ).
fof(f1790,plain,
( ~ in(sK10,sK1)
| spl19_174 ),
inference(avatar_component_clause,[],[f1789]) ).
fof(f1789,plain,
( spl19_174
<=> in(sK10,sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_174])]) ).
fof(f5919,plain,
( ~ spl19_46
| ~ spl19_173
| ~ spl19_382 ),
inference(avatar_contradiction_clause,[],[f5918]) ).
fof(f5918,plain,
( $false
| ~ spl19_46
| ~ spl19_173
| ~ spl19_382 ),
inference(subsumption_resolution,[],[f5878,f485]) ).
fof(f5878,plain,
( in(sK1,empty_set)
| ~ spl19_173
| ~ spl19_382 ),
inference(backward_demodulation,[],[f1787,f5862]) ).
fof(f1787,plain,
( in(sK1,sK10)
| ~ spl19_173 ),
inference(avatar_component_clause,[],[f1785]) ).
fof(f1785,plain,
( spl19_173
<=> in(sK1,sK10) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_173])]) ).
fof(f5917,plain,
( ~ spl19_147
| spl19_166
| ~ spl19_382 ),
inference(avatar_contradiction_clause,[],[f5916]) ).
fof(f5916,plain,
( $false
| ~ spl19_147
| spl19_166
| ~ spl19_382 ),
inference(subsumption_resolution,[],[f5876,f1332]) ).
fof(f5876,plain,
( ~ in(empty_set,sK0)
| spl19_166
| ~ spl19_382 ),
inference(backward_demodulation,[],[f1754,f5862]) ).
fof(f1754,plain,
( ~ in(sK10,sK0)
| spl19_166 ),
inference(avatar_component_clause,[],[f1753]) ).
fof(f1753,plain,
( spl19_166
<=> in(sK10,sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_166])]) ).
fof(f5915,plain,
( ~ spl19_46
| ~ spl19_165
| ~ spl19_382 ),
inference(avatar_contradiction_clause,[],[f5914]) ).
fof(f5914,plain,
( $false
| ~ spl19_46
| ~ spl19_165
| ~ spl19_382 ),
inference(subsumption_resolution,[],[f5875,f485]) ).
fof(f5875,plain,
( in(sK0,empty_set)
| ~ spl19_165
| ~ spl19_382 ),
inference(backward_demodulation,[],[f1751,f5862]) ).
fof(f1751,plain,
( in(sK0,sK10)
| ~ spl19_165 ),
inference(avatar_component_clause,[],[f1749]) ).
fof(f1749,plain,
( spl19_165
<=> in(sK0,sK10) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_165])]) ).
fof(f5867,plain,
( spl19_382
| spl19_383
| ~ spl19_18
| ~ spl19_201 ),
inference(avatar_split_clause,[],[f2580,f2020,f348,f5864,f5860]) ).
fof(f5864,plain,
( spl19_383
<=> in(empty_set,sK10) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_383])]) ).
fof(f2580,plain,
( in(empty_set,sK10)
| empty_set = sK10
| ~ spl19_18
| ~ spl19_201 ),
inference(resolution,[],[f2021,f350]) ).
fof(f5825,plain,
( spl19_381
| ~ spl19_310
| ~ spl19_377 ),
inference(avatar_split_clause,[],[f5810,f5801,f3781,f5823]) ).
fof(f5801,plain,
( spl19_377
<=> in(sK2(sK3(empty_set)),sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_377])]) ).
fof(f5810,plain,
( ! [X0] :
( ~ in(X0,sK2(sK3(empty_set)))
| in(X0,sK0) )
| ~ spl19_310
| ~ spl19_377 ),
inference(resolution,[],[f5803,f3782]) ).
fof(f5803,plain,
( in(sK2(sK3(empty_set)),sK0)
| ~ spl19_377 ),
inference(avatar_component_clause,[],[f5801]) ).
fof(f5821,plain,
( spl19_380
| ~ spl19_310
| ~ spl19_358 ),
inference(avatar_split_clause,[],[f5739,f5475,f3781,f5819]) ).
fof(f5475,plain,
( spl19_358
<=> in(sK3(sK3(empty_set)),sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_358])]) ).
fof(f5739,plain,
( ! [X0] :
( ~ in(X0,sK3(sK3(empty_set)))
| in(X0,sK0) )
| ~ spl19_310
| ~ spl19_358 ),
inference(resolution,[],[f5477,f3782]) ).
fof(f5477,plain,
( in(sK3(sK3(empty_set)),sK0)
| ~ spl19_358 ),
inference(avatar_component_clause,[],[f5475]) ).
fof(f5816,plain,
( ~ spl19_379
| ~ spl19_52
| ~ spl19_377 ),
inference(avatar_split_clause,[],[f5811,f5801,f508,f5813]) ).
fof(f5813,plain,
( spl19_379
<=> in(sK0,sK2(sK3(empty_set))) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_379])]) ).
fof(f5811,plain,
( ~ in(sK0,sK2(sK3(empty_set)))
| ~ spl19_52
| ~ spl19_377 ),
inference(resolution,[],[f5803,f509]) ).
fof(f5809,plain,
( ~ spl19_378
| ~ spl19_52
| ~ spl19_376 ),
inference(avatar_split_clause,[],[f5799,f5782,f508,f5806]) ).
fof(f5806,plain,
( spl19_378
<=> in(sK1,sK2(sK3(empty_set))) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_378])]) ).
fof(f5782,plain,
( spl19_376
<=> in(sK2(sK3(empty_set)),sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_376])]) ).
fof(f5799,plain,
( ~ in(sK1,sK2(sK3(empty_set)))
| ~ spl19_52
| ~ spl19_376 ),
inference(resolution,[],[f5784,f509]) ).
fof(f5784,plain,
( in(sK2(sK3(empty_set)),sK1)
| ~ spl19_376 ),
inference(avatar_component_clause,[],[f5782]) ).
fof(f5804,plain,
( spl19_377
| ~ spl19_313
| ~ spl19_376 ),
inference(avatar_split_clause,[],[f5798,f5782,f3809,f5801]) ).
fof(f5798,plain,
( in(sK2(sK3(empty_set)),sK0)
| ~ spl19_313
| ~ spl19_376 ),
inference(resolution,[],[f5784,f3810]) ).
fof(f5785,plain,
( spl19_375
| spl19_376
| ~ spl19_48
| ~ spl19_355 ),
inference(avatar_split_clause,[],[f5429,f5426,f492,f5782,f5778]) ).
fof(f5429,plain,
( in(sK2(sK3(empty_set)),sK1)
| epsilon_transitive(sK3(empty_set))
| ~ spl19_48
| ~ spl19_355 ),
inference(resolution,[],[f5427,f493]) ).
fof(f5768,plain,
( ~ spl19_373
| spl19_374
| ~ spl19_89
| ~ spl19_350 ),
inference(avatar_split_clause,[],[f4969,f4963,f765,f5765,f5761]) ).
fof(f5761,plain,
( spl19_373
<=> subset(sK1,sK3(empty_set)) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_373])]) ).
fof(f5765,plain,
( spl19_374
<=> sK1 = sK3(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_374])]) ).
fof(f4963,plain,
( spl19_350
<=> subset(sK3(empty_set),sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_350])]) ).
fof(f4969,plain,
( sK1 = sK3(empty_set)
| ~ subset(sK1,sK3(empty_set))
| ~ spl19_89
| ~ spl19_350 ),
inference(resolution,[],[f4965,f766]) ).
fof(f4965,plain,
( subset(sK3(empty_set),sK1)
| ~ spl19_350 ),
inference(avatar_component_clause,[],[f4963]) ).
fof(f5758,plain,
( spl19_372
| ~ spl19_240
| ~ spl19_367 ),
inference(avatar_split_clause,[],[f5675,f5671,f2693,f5756]) ).
fof(f5756,plain,
( spl19_372
<=> ! [X0] :
( ~ in(X0,sK1)
| element(X0,sK0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_372])]) ).
fof(f2693,plain,
( spl19_240
<=> ! [X6,X5,X7] :
( element(X5,X6)
| ~ in(X5,X7)
| ~ in(X7,powerset(X6)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_240])]) ).
fof(f5671,plain,
( spl19_367
<=> in(sK1,powerset(sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_367])]) ).
fof(f5675,plain,
( ! [X0] :
( ~ in(X0,sK1)
| element(X0,sK0) )
| ~ spl19_240
| ~ spl19_367 ),
inference(resolution,[],[f5673,f2694]) ).
fof(f2694,plain,
( ! [X6,X7,X5] :
( ~ in(X7,powerset(X6))
| ~ in(X5,X7)
| element(X5,X6) )
| ~ spl19_240 ),
inference(avatar_component_clause,[],[f2693]) ).
fof(f5673,plain,
( in(sK1,powerset(sK0))
| ~ spl19_367 ),
inference(avatar_component_clause,[],[f5671]) ).
fof(f5745,plain,
( ~ spl19_371
| ~ spl19_52
| ~ spl19_358 ),
inference(avatar_split_clause,[],[f5740,f5475,f508,f5742]) ).
fof(f5742,plain,
( spl19_371
<=> in(sK0,sK3(sK3(empty_set))) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_371])]) ).
fof(f5740,plain,
( ~ in(sK0,sK3(sK3(empty_set)))
| ~ spl19_52
| ~ spl19_358 ),
inference(resolution,[],[f5477,f509]) ).
fof(f5731,plain,
( ~ spl19_370
| ~ spl19_52
| ~ spl19_367 ),
inference(avatar_split_clause,[],[f5677,f5671,f508,f5728]) ).
fof(f5728,plain,
( spl19_370
<=> in(powerset(sK0),sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_370])]) ).
fof(f5677,plain,
( ~ in(powerset(sK0),sK1)
| ~ spl19_52
| ~ spl19_367 ),
inference(resolution,[],[f5673,f509]) ).
fof(f5713,plain,
( ~ spl19_369
| ~ spl19_89
| spl19_141
| ~ spl19_368 ),
inference(avatar_split_clause,[],[f5708,f5698,f1152,f765,f5710]) ).
fof(f5710,plain,
( spl19_369
<=> subset(sK0,sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_369])]) ).
fof(f5698,plain,
( spl19_368
<=> subset(sK1,sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_368])]) ).
fof(f5708,plain,
( ~ subset(sK0,sK1)
| ~ spl19_89
| spl19_141
| ~ spl19_368 ),
inference(subsumption_resolution,[],[f5707,f1153]) ).
fof(f5707,plain,
( sK0 = sK1
| ~ subset(sK0,sK1)
| ~ spl19_89
| ~ spl19_368 ),
inference(resolution,[],[f5700,f766]) ).
fof(f5700,plain,
( subset(sK1,sK0)
| ~ spl19_368 ),
inference(avatar_component_clause,[],[f5698]) ).
fof(f5701,plain,
( spl19_368
| ~ spl19_76
| ~ spl19_367 ),
inference(avatar_split_clause,[],[f5676,f5671,f670,f5698]) ).
fof(f5676,plain,
( subset(sK1,sK0)
| ~ spl19_76
| ~ spl19_367 ),
inference(resolution,[],[f5673,f671]) ).
fof(f5674,plain,
( spl19_367
| ~ spl19_2
| ~ spl19_148
| ~ spl19_356 ),
inference(avatar_split_clause,[],[f5504,f5464,f1412,f268,f5671]) ).
fof(f268,plain,
( spl19_2
<=> ordinal(sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_2])]) ).
fof(f5504,plain,
( in(sK1,powerset(sK0))
| ~ spl19_2
| ~ spl19_148
| ~ spl19_356 ),
inference(subsumption_resolution,[],[f5493,f270]) ).
fof(f270,plain,
( ordinal(sK1)
| ~ spl19_2 ),
inference(avatar_component_clause,[],[f268]) ).
fof(f5493,plain,
( ~ ordinal(sK1)
| in(sK1,powerset(sK0))
| ~ spl19_148
| ~ spl19_356 ),
inference(resolution,[],[f5465,f1413]) ).
fof(f5646,plain,
( ~ spl19_46
| ~ spl19_269
| ~ spl19_365 ),
inference(avatar_contradiction_clause,[],[f5645]) ).
fof(f5645,plain,
( $false
| ~ spl19_46
| ~ spl19_269
| ~ spl19_365 ),
inference(subsumption_resolution,[],[f5585,f485]) ).
fof(f5585,plain,
( in(succ(sK0),empty_set)
| ~ spl19_269
| ~ spl19_365 ),
inference(backward_demodulation,[],[f3180,f5541]) ).
fof(f5541,plain,
( empty_set = sK8
| ~ spl19_365 ),
inference(avatar_component_clause,[],[f5539]) ).
fof(f5539,plain,
( spl19_365
<=> empty_set = sK8 ),
introduced(avatar_definition,[new_symbols(naming,[spl19_365])]) ).
fof(f5623,plain,
( ~ spl19_226
| spl19_235
| ~ spl19_365 ),
inference(avatar_contradiction_clause,[],[f5622]) ).
fof(f5622,plain,
( $false
| ~ spl19_226
| spl19_235
| ~ spl19_365 ),
inference(subsumption_resolution,[],[f5573,f2487]) ).
fof(f5573,plain,
( ~ ordinal_subset(empty_set,succ(sK0))
| spl19_235
| ~ spl19_365 ),
inference(backward_demodulation,[],[f2666,f5541]) ).
fof(f2666,plain,
( ~ ordinal_subset(sK8,succ(sK0))
| spl19_235 ),
inference(avatar_component_clause,[],[f2665]) ).
fof(f2665,plain,
( spl19_235
<=> ordinal_subset(sK8,succ(sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_235])]) ).
fof(f5621,plain,
( ~ spl19_224
| spl19_232
| ~ spl19_365 ),
inference(avatar_contradiction_clause,[],[f5620]) ).
fof(f5620,plain,
( $false
| ~ spl19_224
| spl19_232
| ~ spl19_365 ),
inference(subsumption_resolution,[],[f5571,f2460]) ).
fof(f5571,plain,
( ~ in(empty_set,succ(sK0))
| spl19_232
| ~ spl19_365 ),
inference(backward_demodulation,[],[f2650,f5541]) ).
fof(f2650,plain,
( ~ in(sK8,succ(sK0))
| spl19_232 ),
inference(avatar_component_clause,[],[f2648]) ).
fof(f2648,plain,
( spl19_232
<=> in(sK8,succ(sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_232])]) ).
fof(f5619,plain,
( spl19_223
| ~ spl19_231
| ~ spl19_365 ),
inference(avatar_contradiction_clause,[],[f5618]) ).
fof(f5618,plain,
( $false
| spl19_223
| ~ spl19_231
| ~ spl19_365 ),
inference(subsumption_resolution,[],[f5570,f2457]) ).
fof(f5570,plain,
( ordinal_subset(succ(sK0),empty_set)
| ~ spl19_231
| ~ spl19_365 ),
inference(backward_demodulation,[],[f2645,f5541]) ).
fof(f2645,plain,
( ordinal_subset(succ(sK0),sK8)
| ~ spl19_231 ),
inference(avatar_component_clause,[],[f2644]) ).
fof(f2644,plain,
( spl19_231
<=> ordinal_subset(succ(sK0),sK8) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_231])]) ).
fof(f5615,plain,
( ~ spl19_155
| spl19_214
| ~ spl19_365 ),
inference(avatar_contradiction_clause,[],[f5614]) ).
fof(f5614,plain,
( $false
| ~ spl19_155
| spl19_214
| ~ spl19_365 ),
inference(subsumption_resolution,[],[f5567,f1668]) ).
fof(f5567,plain,
( ~ ordinal_subset(empty_set,sK1)
| spl19_214
| ~ spl19_365 ),
inference(backward_demodulation,[],[f2252,f5541]) ).
fof(f2252,plain,
( ~ ordinal_subset(sK8,sK1)
| spl19_214 ),
inference(avatar_component_clause,[],[f2250]) ).
fof(f2250,plain,
( spl19_214
<=> ordinal_subset(sK8,sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_214])]) ).
fof(f5613,plain,
( spl19_212
| ~ spl19_213
| ~ spl19_365 ),
inference(avatar_contradiction_clause,[],[f5612]) ).
fof(f5612,plain,
( $false
| spl19_212
| ~ spl19_213
| ~ spl19_365 ),
inference(subsumption_resolution,[],[f5566,f2225]) ).
fof(f5566,plain,
( ordinal_subset(sK1,empty_set)
| ~ spl19_213
| ~ spl19_365 ),
inference(backward_demodulation,[],[f2244,f5541]) ).
fof(f2244,plain,
( ordinal_subset(sK1,sK8)
| ~ spl19_213 ),
inference(avatar_component_clause,[],[f2243]) ).
fof(f2243,plain,
( spl19_213
<=> ordinal_subset(sK1,sK8) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_213])]) ).
fof(f5607,plain,
( spl19_152
| ~ spl19_182
| ~ spl19_365 ),
inference(avatar_contradiction_clause,[],[f5606]) ).
fof(f5606,plain,
( $false
| spl19_152
| ~ spl19_182
| ~ spl19_365 ),
inference(subsumption_resolution,[],[f5562,f1597]) ).
fof(f5562,plain,
( ordinal_subset(sK0,empty_set)
| ~ spl19_182
| ~ spl19_365 ),
inference(backward_demodulation,[],[f1857,f5541]) ).
fof(f1857,plain,
( ordinal_subset(sK0,sK8)
| ~ spl19_182 ),
inference(avatar_component_clause,[],[f1855]) ).
fof(f1855,plain,
( spl19_182
<=> ordinal_subset(sK0,sK8) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_182])]) ).
fof(f5605,plain,
( ~ spl19_154
| spl19_180
| ~ spl19_365 ),
inference(avatar_contradiction_clause,[],[f5604]) ).
fof(f5604,plain,
( $false
| ~ spl19_154
| spl19_180
| ~ spl19_365 ),
inference(subsumption_resolution,[],[f5561,f1621]) ).
fof(f5561,plain,
( ~ ordinal_subset(empty_set,sK0)
| spl19_180
| ~ spl19_365 ),
inference(backward_demodulation,[],[f1845,f5541]) ).
fof(f1845,plain,
( ~ ordinal_subset(sK8,sK0)
| spl19_180 ),
inference(avatar_component_clause,[],[f1843]) ).
fof(f1843,plain,
( spl19_180
<=> ordinal_subset(sK8,sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_180])]) ).
fof(f5602,plain,
( ~ spl19_151
| spl19_170
| ~ spl19_365 ),
inference(avatar_contradiction_clause,[],[f5601]) ).
fof(f5601,plain,
( $false
| ~ spl19_151
| spl19_170
| ~ spl19_365 ),
inference(subsumption_resolution,[],[f5559,f1537]) ).
fof(f5559,plain,
( ~ in(empty_set,sK1)
| spl19_170
| ~ spl19_365 ),
inference(backward_demodulation,[],[f1772,f5541]) ).
fof(f1772,plain,
( ~ in(sK8,sK1)
| spl19_170 ),
inference(avatar_component_clause,[],[f1771]) ).
fof(f1771,plain,
( spl19_170
<=> in(sK8,sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_170])]) ).
fof(f5600,plain,
( ~ spl19_46
| ~ spl19_169
| ~ spl19_365 ),
inference(avatar_contradiction_clause,[],[f5599]) ).
fof(f5599,plain,
( $false
| ~ spl19_46
| ~ spl19_169
| ~ spl19_365 ),
inference(subsumption_resolution,[],[f5558,f485]) ).
fof(f5558,plain,
( in(sK1,empty_set)
| ~ spl19_169
| ~ spl19_365 ),
inference(backward_demodulation,[],[f1769,f5541]) ).
fof(f1769,plain,
( in(sK1,sK8)
| ~ spl19_169 ),
inference(avatar_component_clause,[],[f1767]) ).
fof(f1767,plain,
( spl19_169
<=> in(sK1,sK8) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_169])]) ).
fof(f5598,plain,
( ~ spl19_147
| spl19_162
| ~ spl19_365 ),
inference(avatar_contradiction_clause,[],[f5597]) ).
fof(f5597,plain,
( $false
| ~ spl19_147
| spl19_162
| ~ spl19_365 ),
inference(subsumption_resolution,[],[f5556,f1332]) ).
fof(f5556,plain,
( ~ in(empty_set,sK0)
| spl19_162
| ~ spl19_365 ),
inference(backward_demodulation,[],[f1736,f5541]) ).
fof(f5596,plain,
( ~ spl19_46
| ~ spl19_161
| ~ spl19_365 ),
inference(avatar_contradiction_clause,[],[f5595]) ).
fof(f5595,plain,
( $false
| ~ spl19_46
| ~ spl19_161
| ~ spl19_365 ),
inference(subsumption_resolution,[],[f5555,f485]) ).
fof(f5555,plain,
( in(sK0,empty_set)
| ~ spl19_161
| ~ spl19_365 ),
inference(backward_demodulation,[],[f1733,f5541]) ).
fof(f5592,plain,
( ~ spl19_5
| spl19_11
| ~ spl19_365 ),
inference(avatar_contradiction_clause,[],[f5591]) ).
fof(f5591,plain,
( $false
| ~ spl19_5
| spl19_11
| ~ spl19_365 ),
inference(subsumption_resolution,[],[f5547,f285]) ).
fof(f5547,plain,
( ~ empty(empty_set)
| spl19_11
| ~ spl19_365 ),
inference(backward_demodulation,[],[f315,f5541]) ).
fof(f315,plain,
( ~ empty(sK8)
| spl19_11 ),
inference(avatar_component_clause,[],[f313]) ).
fof(f313,plain,
( spl19_11
<=> empty(sK8) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_11])]) ).
fof(f5546,plain,
( spl19_365
| spl19_366
| ~ spl19_14
| ~ spl19_201 ),
inference(avatar_split_clause,[],[f2579,f2020,f328,f5543,f5539]) ).
fof(f5543,plain,
( spl19_366
<=> in(empty_set,sK8) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_366])]) ).
fof(f2579,plain,
( in(empty_set,sK8)
| empty_set = sK8
| ~ spl19_14
| ~ spl19_201 ),
inference(resolution,[],[f2021,f330]) ).
fof(f5535,plain,
( ~ spl19_364
| ~ spl19_89
| spl19_146
| ~ spl19_363 ),
inference(avatar_split_clause,[],[f5530,f5523,f1326,f765,f5532]) ).
fof(f5532,plain,
( spl19_364
<=> subset(sK0,empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_364])]) ).
fof(f5523,plain,
( spl19_363
<=> subset(empty_set,sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_363])]) ).
fof(f5530,plain,
( ~ subset(sK0,empty_set)
| ~ spl19_89
| spl19_146
| ~ spl19_363 ),
inference(subsumption_resolution,[],[f5529,f1327]) ).
fof(f5529,plain,
( empty_set = sK0
| ~ subset(sK0,empty_set)
| ~ spl19_89
| ~ spl19_363 ),
inference(resolution,[],[f5525,f766]) ).
fof(f5525,plain,
( subset(empty_set,sK0)
| ~ spl19_363 ),
inference(avatar_component_clause,[],[f5523]) ).
fof(f5526,plain,
( spl19_363
| ~ spl19_76
| ~ spl19_360 ),
inference(avatar_split_clause,[],[f5516,f5506,f670,f5523]) ).
fof(f5506,plain,
( spl19_360
<=> in(empty_set,powerset(sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_360])]) ).
fof(f5516,plain,
( subset(empty_set,sK0)
| ~ spl19_76
| ~ spl19_360 ),
inference(resolution,[],[f5508,f671]) ).
fof(f5508,plain,
( in(empty_set,powerset(sK0))
| ~ spl19_360 ),
inference(avatar_component_clause,[],[f5506]) ).
fof(f5521,plain,
( spl19_362
| ~ spl19_64
| ~ spl19_99 ),
inference(avatar_split_clause,[],[f895,f849,f589,f5519]) ).
fof(f589,plain,
( spl19_64
<=> ! [X0,X1] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_64])]) ).
fof(f895,plain,
( ! [X2,X1] :
( ~ in(X1,X2)
| ~ subset(X2,empty_set) )
| ~ spl19_64
| ~ spl19_99 ),
inference(resolution,[],[f850,f590]) ).
fof(f590,plain,
( ! [X0,X1] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) )
| ~ spl19_64 ),
inference(avatar_component_clause,[],[f589]) ).
fof(f5514,plain,
( spl19_361
| ~ spl19_1
| ~ spl19_61
| ~ spl19_356 ),
inference(avatar_split_clause,[],[f5503,f5464,f575,f263,f5511]) ).
fof(f5511,plain,
( spl19_361
<=> in(sK0,powerset(sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_361])]) ).
fof(f263,plain,
( spl19_1
<=> ordinal(sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_1])]) ).
fof(f575,plain,
( spl19_61
<=> ordinal_subset(sK0,sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_61])]) ).
fof(f5503,plain,
( in(sK0,powerset(sK0))
| ~ spl19_1
| ~ spl19_61
| ~ spl19_356 ),
inference(subsumption_resolution,[],[f5490,f265]) ).
fof(f265,plain,
( ordinal(sK0)
| ~ spl19_1 ),
inference(avatar_component_clause,[],[f263]) ).
fof(f5490,plain,
( ~ ordinal(sK0)
| in(sK0,powerset(sK0))
| ~ spl19_61
| ~ spl19_356 ),
inference(resolution,[],[f5465,f577]) ).
fof(f577,plain,
( ordinal_subset(sK0,sK0)
| ~ spl19_61 ),
inference(avatar_component_clause,[],[f575]) ).
fof(f5509,plain,
( spl19_360
| ~ spl19_8
| ~ spl19_154
| ~ spl19_356 ),
inference(avatar_split_clause,[],[f5502,f5464,f1619,f298,f5506]) ).
fof(f5502,plain,
( in(empty_set,powerset(sK0))
| ~ spl19_8
| ~ spl19_154
| ~ spl19_356 ),
inference(subsumption_resolution,[],[f5488,f300]) ).
fof(f5488,plain,
( ~ ordinal(empty_set)
| in(empty_set,powerset(sK0))
| ~ spl19_154
| ~ spl19_356 ),
inference(resolution,[],[f5465,f1621]) ).
fof(f5483,plain,
( ~ spl19_359
| ~ spl19_52
| ~ spl19_357 ),
inference(avatar_split_clause,[],[f5473,f5468,f508,f5480]) ).
fof(f5480,plain,
( spl19_359
<=> in(sK1,sK3(sK3(empty_set))) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_359])]) ).
fof(f5473,plain,
( ~ in(sK1,sK3(sK3(empty_set)))
| ~ spl19_52
| ~ spl19_357 ),
inference(resolution,[],[f5470,f509]) ).
fof(f5478,plain,
( spl19_358
| ~ spl19_313
| ~ spl19_357 ),
inference(avatar_split_clause,[],[f5472,f5468,f3809,f5475]) ).
fof(f5472,plain,
( in(sK3(sK3(empty_set)),sK0)
| ~ spl19_313
| ~ spl19_357 ),
inference(resolution,[],[f5470,f3810]) ).
fof(f5471,plain,
( spl19_357
| ~ spl19_83
| spl19_282
| ~ spl19_355 ),
inference(avatar_split_clause,[],[f5461,f5426,f3514,f712,f5468]) ).
fof(f5461,plain,
( in(sK3(sK3(empty_set)),sK1)
| ~ spl19_83
| spl19_282
| ~ spl19_355 ),
inference(subsumption_resolution,[],[f5432,f3516]) ).
fof(f5432,plain,
( in(sK3(sK3(empty_set)),sK1)
| empty(sK3(empty_set))
| ~ spl19_83
| ~ spl19_355 ),
inference(resolution,[],[f5427,f713]) ).
fof(f5466,plain,
( spl19_279
| spl19_356
| ~ spl19_110
| ~ spl19_229 ),
inference(avatar_split_clause,[],[f2792,f2606,f933,f5464,f3451]) ).
fof(f3451,plain,
( spl19_279
<=> empty(powerset(sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_279])]) ).
fof(f933,plain,
( spl19_110
<=> ! [X5] :
( ~ ordinal_subset(X5,sK0)
| subset(X5,sK0)
| ~ ordinal(X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_110])]) ).
fof(f2792,plain,
( ! [X5] :
( in(X5,powerset(sK0))
| empty(powerset(sK0))
| ~ ordinal_subset(X5,sK0)
| ~ ordinal(X5) )
| ~ spl19_110
| ~ spl19_229 ),
inference(resolution,[],[f2607,f934]) ).
fof(f934,plain,
( ! [X5] :
( subset(X5,sK0)
| ~ ordinal_subset(X5,sK0)
| ~ ordinal(X5) )
| ~ spl19_110 ),
inference(avatar_component_clause,[],[f933]) ).
fof(f5428,plain,
( spl19_355
| ~ spl19_77
| spl19_314
| ~ spl19_354 ),
inference(avatar_split_clause,[],[f5424,f5276,f4276,f674,f5426]) ).
fof(f674,plain,
( spl19_77
<=> ! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_77])]) ).
fof(f5276,plain,
( spl19_354
<=> ! [X5] :
( ~ in(X5,sK3(empty_set))
| element(X5,sK1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_354])]) ).
fof(f5424,plain,
( ! [X0] :
( ~ in(X0,sK3(empty_set))
| in(X0,sK1) )
| ~ spl19_77
| spl19_314
| ~ spl19_354 ),
inference(subsumption_resolution,[],[f5423,f4277]) ).
fof(f5423,plain,
( ! [X0] :
( ~ in(X0,sK3(empty_set))
| empty(sK1)
| in(X0,sK1) )
| ~ spl19_77
| ~ spl19_354 ),
inference(resolution,[],[f5277,f675]) ).
fof(f675,plain,
( ! [X0,X1] :
( ~ element(X0,X1)
| empty(X1)
| in(X0,X1) )
| ~ spl19_77 ),
inference(avatar_component_clause,[],[f674]) ).
fof(f5277,plain,
( ! [X5] :
( element(X5,sK1)
| ~ in(X5,sK3(empty_set)) )
| ~ spl19_354 ),
inference(avatar_component_clause,[],[f5276]) ).
fof(f5278,plain,
( spl19_354
| ~ spl19_198
| ~ spl19_349 ),
inference(avatar_split_clause,[],[f4960,f4951,f1996,f5276]) ).
fof(f4960,plain,
( ! [X5] :
( ~ in(X5,sK3(empty_set))
| element(X5,sK1) )
| ~ spl19_198
| ~ spl19_349 ),
inference(superposition,[],[f1997,f4953]) ).
fof(f5269,plain,
( spl19_353
| ~ spl19_64
| ~ spl19_349 ),
inference(avatar_split_clause,[],[f4956,f4951,f589,f5267]) ).
fof(f5267,plain,
( spl19_353
<=> ! [X1] :
( element(X1,empty_set)
| ~ subset(X1,sK1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_353])]) ).
fof(f4956,plain,
( ! [X1] :
( element(X1,empty_set)
| ~ subset(X1,sK1) )
| ~ spl19_64
| ~ spl19_349 ),
inference(superposition,[],[f590,f4953]) ).
fof(f5129,plain,
( spl19_352
| ~ spl19_62
| ~ spl19_349 ),
inference(avatar_split_clause,[],[f4955,f4951,f580,f5127]) ).
fof(f5127,plain,
( spl19_352
<=> ! [X0] :
( ~ element(X0,empty_set)
| subset(X0,sK1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_352])]) ).
fof(f4955,plain,
( ! [X0] :
( ~ element(X0,empty_set)
| subset(X0,sK1) )
| ~ spl19_62
| ~ spl19_349 ),
inference(superposition,[],[f581,f4953]) ).
fof(f5124,plain,
( spl19_351
| ~ spl19_39
| ~ spl19_156
| ~ spl19_344 ),
inference(avatar_split_clause,[],[f4924,f4903,f1694,f439,f5121]) ).
fof(f5121,plain,
( spl19_351
<=> ordinal_subset(sK3(empty_set),sK3(empty_set)) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_351])]) ).
fof(f1694,plain,
( spl19_156
<=> ordinal_subset(sK3(powerset(sK1)),sK3(powerset(sK1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_156])]) ).
fof(f4903,plain,
( spl19_344
<=> empty(powerset(sK1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_344])]) ).
fof(f4924,plain,
( ordinal_subset(sK3(empty_set),sK3(empty_set))
| ~ spl19_39
| ~ spl19_156
| ~ spl19_344 ),
inference(backward_demodulation,[],[f1696,f4914]) ).
fof(f4914,plain,
( empty_set = powerset(sK1)
| ~ spl19_39
| ~ spl19_344 ),
inference(resolution,[],[f4905,f440]) ).
fof(f4905,plain,
( empty(powerset(sK1))
| ~ spl19_344 ),
inference(avatar_component_clause,[],[f4903]) ).
fof(f1696,plain,
( ordinal_subset(sK3(powerset(sK1)),sK3(powerset(sK1)))
| ~ spl19_156 ),
inference(avatar_component_clause,[],[f1694]) ).
fof(f4966,plain,
( spl19_350
| ~ spl19_72
| ~ spl19_349 ),
inference(avatar_split_clause,[],[f4957,f4951,f645,f4963]) ).
fof(f4957,plain,
( subset(sK3(empty_set),sK1)
| ~ spl19_72
| ~ spl19_349 ),
inference(superposition,[],[f646,f4953]) ).
fof(f4954,plain,
( spl19_349
| ~ spl19_39
| ~ spl19_344 ),
inference(avatar_split_clause,[],[f4914,f4903,f439,f4951]) ).
fof(f4949,plain,
( spl19_348
| ~ spl19_117
| ~ spl19_145 ),
inference(avatar_split_clause,[],[f1309,f1284,f988,f4947]) ).
fof(f4947,plain,
( spl19_348
<=> ! [X10,X7,X9,X8] :
( in(sK5(set_union2(X7,X8),X9,X10),X10)
| in(sK5(set_union2(X7,X8),X9,X10),X9)
| set_union2(set_union2(X7,X8),X9) = X10
| in(sK5(set_union2(X7,X8),X9,X10),X7)
| in(sK5(set_union2(X7,X8),X9,X10),X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_348])]) ).
fof(f988,plain,
( spl19_117
<=> ! [X4,X0,X1] :
( in(X4,X1)
| in(X4,X0)
| ~ in(X4,set_union2(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_117])]) ).
fof(f1284,plain,
( spl19_145
<=> ! [X2,X0,X1] :
( set_union2(X0,X1) = X2
| in(sK5(X0,X1,X2),X1)
| in(sK5(X0,X1,X2),X0)
| in(sK5(X0,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_145])]) ).
fof(f1309,plain,
( ! [X10,X8,X9,X7] :
( in(sK5(set_union2(X7,X8),X9,X10),X10)
| in(sK5(set_union2(X7,X8),X9,X10),X9)
| set_union2(set_union2(X7,X8),X9) = X10
| in(sK5(set_union2(X7,X8),X9,X10),X7)
| in(sK5(set_union2(X7,X8),X9,X10),X8) )
| ~ spl19_117
| ~ spl19_145 ),
inference(resolution,[],[f1285,f989]) ).
fof(f989,plain,
( ! [X0,X1,X4] :
( ~ in(X4,set_union2(X0,X1))
| in(X4,X0)
| in(X4,X1) )
| ~ spl19_117 ),
inference(avatar_component_clause,[],[f988]) ).
fof(f1285,plain,
( ! [X2,X0,X1] :
( in(sK5(X0,X1,X2),X2)
| in(sK5(X0,X1,X2),X1)
| in(sK5(X0,X1,X2),X0)
| set_union2(X0,X1) = X2 )
| ~ spl19_145 ),
inference(avatar_component_clause,[],[f1284]) ).
fof(f4941,plain,
( ~ spl19_347
| ~ spl19_39
| spl19_134
| ~ spl19_344 ),
inference(avatar_split_clause,[],[f4922,f4903,f1109,f439,f4938]) ).
fof(f4938,plain,
( spl19_347
<=> ordinal_subset(sK3(empty_set),sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_347])]) ).
fof(f1109,plain,
( spl19_134
<=> ordinal_subset(sK3(powerset(sK1)),sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_134])]) ).
fof(f4922,plain,
( ~ ordinal_subset(sK3(empty_set),sK1)
| ~ spl19_39
| spl19_134
| ~ spl19_344 ),
inference(backward_demodulation,[],[f1110,f4914]) ).
fof(f1110,plain,
( ~ ordinal_subset(sK3(powerset(sK1)),sK1)
| spl19_134 ),
inference(avatar_component_clause,[],[f1109]) ).
fof(f4913,plain,
( spl19_346
| ~ spl19_117
| ~ spl19_145 ),
inference(avatar_split_clause,[],[f1300,f1284,f988,f4911]) ).
fof(f4911,plain,
( spl19_346
<=> ! [X10,X7,X9,X8] :
( in(sK5(X7,set_union2(X8,X9),X10),X10)
| in(sK5(X7,set_union2(X8,X9),X10),X7)
| set_union2(X7,set_union2(X8,X9)) = X10
| in(sK5(X7,set_union2(X8,X9),X10),X8)
| in(sK5(X7,set_union2(X8,X9),X10),X9) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_346])]) ).
fof(f1300,plain,
( ! [X10,X8,X9,X7] :
( in(sK5(X7,set_union2(X8,X9),X10),X10)
| in(sK5(X7,set_union2(X8,X9),X10),X7)
| set_union2(X7,set_union2(X8,X9)) = X10
| in(sK5(X7,set_union2(X8,X9),X10),X8)
| in(sK5(X7,set_union2(X8,X9),X10),X9) )
| ~ spl19_117
| ~ spl19_145 ),
inference(resolution,[],[f1285,f989]) ).
fof(f4909,plain,
( spl19_344
| spl19_345
| ~ spl19_127
| ~ spl19_229 ),
inference(avatar_split_clause,[],[f2794,f2606,f1056,f4907,f4903]) ).
fof(f4907,plain,
( spl19_345
<=> ! [X7] :
( in(X7,powerset(sK1))
| ~ in(X7,sK1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_345])]) ).
fof(f1056,plain,
( spl19_127
<=> ! [X0] :
( ~ in(X0,sK1)
| subset(X0,sK1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_127])]) ).
fof(f2794,plain,
( ! [X7] :
( in(X7,powerset(sK1))
| empty(powerset(sK1))
| ~ in(X7,sK1) )
| ~ spl19_127
| ~ spl19_229 ),
inference(resolution,[],[f2607,f1057]) ).
fof(f1057,plain,
( ! [X0] :
( subset(X0,sK1)
| ~ in(X0,sK1) )
| ~ spl19_127 ),
inference(avatar_component_clause,[],[f1056]) ).
fof(f4898,plain,
( ~ spl19_174
| spl19_172
| ~ spl19_216
| ~ spl19_2
| ~ spl19_139
| ~ spl19_189 ),
inference(avatar_split_clause,[],[f2269,f1900,f1134,f268,f2342,f1781,f1789]) ).
fof(f1781,plain,
( spl19_172
<=> sK1 = sK10 ),
introduced(avatar_definition,[new_symbols(naming,[spl19_172])]) ).
fof(f1134,plain,
( spl19_139
<=> ! [X1] :
( ~ in(X1,sK1)
| sK1 = X1
| ~ subset(sK1,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_139])]) ).
fof(f1900,plain,
( spl19_189
<=> ! [X8] :
( ~ ordinal_subset(X8,sK10)
| subset(X8,sK10)
| ~ ordinal(X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_189])]) ).
fof(f2269,plain,
( ~ ordinal_subset(sK1,sK10)
| sK1 = sK10
| ~ in(sK10,sK1)
| ~ spl19_2
| ~ spl19_139
| ~ spl19_189 ),
inference(subsumption_resolution,[],[f2258,f270]) ).
fof(f2258,plain,
( ~ ordinal_subset(sK1,sK10)
| ~ ordinal(sK1)
| sK1 = sK10
| ~ in(sK10,sK1)
| ~ spl19_139
| ~ spl19_189 ),
inference(resolution,[],[f1901,f1135]) ).
fof(f1135,plain,
( ! [X1] :
( ~ subset(sK1,X1)
| sK1 = X1
| ~ in(X1,sK1) )
| ~ spl19_139 ),
inference(avatar_component_clause,[],[f1134]) ).
fof(f1901,plain,
( ! [X8] :
( subset(X8,sK10)
| ~ ordinal_subset(X8,sK10)
| ~ ordinal(X8) )
| ~ spl19_189 ),
inference(avatar_component_clause,[],[f1900]) ).
fof(f4897,plain,
( ~ spl19_218
| spl19_172
| ~ spl19_216
| ~ spl19_2
| ~ spl19_18
| ~ spl19_178
| ~ spl19_189 ),
inference(avatar_split_clause,[],[f2267,f1900,f1824,f348,f268,f2342,f1781,f2388]) ).
fof(f2267,plain,
( ~ ordinal_subset(sK1,sK10)
| sK1 = sK10
| ~ ordinal_subset(sK10,sK1)
| ~ spl19_2
| ~ spl19_18
| ~ spl19_178
| ~ spl19_189 ),
inference(subsumption_resolution,[],[f2266,f350]) ).
fof(f2266,plain,
( ~ ordinal_subset(sK1,sK10)
| ~ ordinal(sK10)
| sK1 = sK10
| ~ ordinal_subset(sK10,sK1)
| ~ spl19_2
| ~ spl19_178
| ~ spl19_189 ),
inference(subsumption_resolution,[],[f2257,f270]) ).
fof(f2257,plain,
( ~ ordinal_subset(sK1,sK10)
| ~ ordinal(sK1)
| ~ ordinal(sK10)
| sK1 = sK10
| ~ ordinal_subset(sK10,sK1)
| ~ spl19_178
| ~ spl19_189 ),
inference(resolution,[],[f1901,f1825]) ).
fof(f4896,plain,
( spl19_343
| ~ spl19_117
| ~ spl19_145 ),
inference(avatar_split_clause,[],[f1291,f1284,f988,f4894]) ).
fof(f4894,plain,
( spl19_343
<=> ! [X10,X11,X12,X9] :
( in(sK5(X9,X10,set_union2(X11,X12)),X10)
| in(sK5(X9,X10,set_union2(X11,X12)),X9)
| set_union2(X9,X10) = set_union2(X11,X12)
| in(sK5(X9,X10,set_union2(X11,X12)),X11)
| in(sK5(X9,X10,set_union2(X11,X12)),X12) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_343])]) ).
fof(f1291,plain,
( ! [X10,X11,X9,X12] :
( in(sK5(X9,X10,set_union2(X11,X12)),X10)
| in(sK5(X9,X10,set_union2(X11,X12)),X9)
| set_union2(X9,X10) = set_union2(X11,X12)
| in(sK5(X9,X10,set_union2(X11,X12)),X11)
| in(sK5(X9,X10,set_union2(X11,X12)),X12) )
| ~ spl19_117
| ~ spl19_145 ),
inference(resolution,[],[f1285,f989]) ).
fof(f4863,plain,
( spl19_342
| ~ spl19_310
| ~ spl19_336 ),
inference(avatar_split_clause,[],[f4748,f4561,f3781,f4861]) ).
fof(f4561,plain,
( spl19_336
<=> in(sK3(sK3(sK1)),sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_336])]) ).
fof(f4748,plain,
( ! [X0] :
( ~ in(X0,sK3(sK3(sK1)))
| in(X0,sK0) )
| ~ spl19_310
| ~ spl19_336 ),
inference(resolution,[],[f4563,f3782]) ).
fof(f4563,plain,
( in(sK3(sK3(sK1)),sK0)
| ~ spl19_336 ),
inference(avatar_component_clause,[],[f4561]) ).
fof(f4815,plain,
( spl19_341
| ~ spl19_74
| ~ spl19_332 ),
inference(avatar_split_clause,[],[f4551,f4543,f662,f4813]) ).
fof(f4813,plain,
( spl19_341
<=> ! [X0] :
( ~ in(X0,sK3(sK1))
| subset(X0,sK3(sK1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_341])]) ).
fof(f662,plain,
( spl19_74
<=> ! [X2,X0] :
( subset(X2,X0)
| ~ in(X2,X0)
| ~ epsilon_transitive(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_74])]) ).
fof(f4543,plain,
( spl19_332
<=> epsilon_transitive(sK3(sK1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_332])]) ).
fof(f4551,plain,
( ! [X0] :
( ~ in(X0,sK3(sK1))
| subset(X0,sK3(sK1)) )
| ~ spl19_74
| ~ spl19_332 ),
inference(resolution,[],[f4545,f663]) ).
fof(f663,plain,
( ! [X2,X0] :
( ~ epsilon_transitive(X0)
| ~ in(X2,X0)
| subset(X2,X0) )
| ~ spl19_74 ),
inference(avatar_component_clause,[],[f662]) ).
fof(f4545,plain,
( epsilon_transitive(sK3(sK1))
| ~ spl19_332 ),
inference(avatar_component_clause,[],[f4543]) ).
fof(f4793,plain,
( ~ spl19_340
| ~ spl19_52
| ~ spl19_336 ),
inference(avatar_split_clause,[],[f4749,f4561,f508,f4790]) ).
fof(f4790,plain,
( spl19_340
<=> in(sK0,sK3(sK3(sK1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_340])]) ).
fof(f4749,plain,
( ~ in(sK0,sK3(sK3(sK1)))
| ~ spl19_52
| ~ spl19_336 ),
inference(resolution,[],[f4563,f509]) ).
fof(f4704,plain,
( ~ spl19_53
| ~ spl19_151
| spl19_339 ),
inference(avatar_contradiction_clause,[],[f4703]) ).
fof(f4703,plain,
( $false
| ~ spl19_53
| ~ spl19_151
| spl19_339 ),
inference(subsumption_resolution,[],[f4702,f1537]) ).
fof(f4702,plain,
( ~ in(empty_set,sK1)
| ~ spl19_53
| spl19_339 ),
inference(resolution,[],[f4643,f513]) ).
fof(f4643,plain,
( ~ element(empty_set,sK1)
| spl19_339 ),
inference(avatar_component_clause,[],[f4642]) ).
fof(f4642,plain,
( spl19_339
<=> element(empty_set,sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_339])]) ).
fof(f4645,plain,
( spl19_339
| ~ spl19_33
| ~ spl19_337 ),
inference(avatar_split_clause,[],[f4636,f4630,f415,f4642]) ).
fof(f4636,plain,
( element(empty_set,sK1)
| ~ spl19_33
| ~ spl19_337 ),
inference(superposition,[],[f416,f4632]) ).
fof(f4632,plain,
( empty_set = sK3(sK1)
| ~ spl19_337 ),
inference(avatar_component_clause,[],[f4630]) ).
fof(f4640,plain,
( spl19_338
| ~ spl19_70
| ~ spl19_145 ),
inference(avatar_split_clause,[],[f1311,f1284,f616,f4638]) ).
fof(f4638,plain,
( spl19_338
<=> ! [X13,X14,X15] :
( in(sK5(singleton(X13),X14,X15),X15)
| in(sK5(singleton(X13),X14,X15),X14)
| set_union2(singleton(X13),X14) = X15
| sK5(singleton(X13),X14,X15) = X13 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_338])]) ).
fof(f1311,plain,
( ! [X14,X15,X13] :
( in(sK5(singleton(X13),X14,X15),X15)
| in(sK5(singleton(X13),X14,X15),X14)
| set_union2(singleton(X13),X14) = X15
| sK5(singleton(X13),X14,X15) = X13 )
| ~ spl19_70
| ~ spl19_145 ),
inference(resolution,[],[f1285,f617]) ).
fof(f4633,plain,
( spl19_337
| ~ spl19_39
| ~ spl19_335 ),
inference(avatar_split_clause,[],[f4565,f4557,f439,f4630]) ).
fof(f4565,plain,
( empty_set = sK3(sK1)
| ~ spl19_39
| ~ spl19_335 ),
inference(resolution,[],[f4559,f440]) ).
fof(f4559,plain,
( empty(sK3(sK1))
| ~ spl19_335 ),
inference(avatar_component_clause,[],[f4557]) ).
fof(f4564,plain,
( spl19_335
| spl19_336
| ~ spl19_83
| ~ spl19_318 ),
inference(avatar_split_clause,[],[f4353,f4347,f712,f4561,f4557]) ).
fof(f4353,plain,
( in(sK3(sK3(sK1)),sK0)
| empty(sK3(sK1))
| ~ spl19_83
| ~ spl19_318 ),
inference(resolution,[],[f4348,f713]) ).
fof(f4555,plain,
( spl19_334
| ~ spl19_70
| ~ spl19_145 ),
inference(avatar_split_clause,[],[f1302,f1284,f616,f4553]) ).
fof(f4553,plain,
( spl19_334
<=> ! [X13,X14,X15] :
( in(sK5(X13,singleton(X14),X15),X15)
| in(sK5(X13,singleton(X14),X15),X13)
| set_union2(X13,singleton(X14)) = X15
| sK5(X13,singleton(X14),X15) = X14 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_334])]) ).
fof(f1302,plain,
( ! [X14,X15,X13] :
( in(sK5(X13,singleton(X14),X15),X15)
| in(sK5(X13,singleton(X14),X15),X13)
| set_union2(X13,singleton(X14)) = X15
| sK5(X13,singleton(X14),X15) = X14 )
| ~ spl19_70
| ~ spl19_145 ),
inference(resolution,[],[f1285,f617]) ).
fof(f4550,plain,
( spl19_332
| spl19_333
| ~ spl19_48
| ~ spl19_318 ),
inference(avatar_split_clause,[],[f4350,f4347,f492,f4547,f4543]) ).
fof(f4547,plain,
( spl19_333
<=> in(sK2(sK3(sK1)),sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_333])]) ).
fof(f4350,plain,
( in(sK2(sK3(sK1)),sK0)
| epsilon_transitive(sK3(sK1))
| ~ spl19_48
| ~ spl19_318 ),
inference(resolution,[],[f4348,f493]) ).
fof(f4541,plain,
( spl19_331
| ~ spl19_70
| ~ spl19_145 ),
inference(avatar_split_clause,[],[f1293,f1284,f616,f4539]) ).
fof(f4539,plain,
( spl19_331
<=> ! [X16,X17,X15] :
( in(sK5(X15,X16,singleton(X17)),X16)
| in(sK5(X15,X16,singleton(X17)),X15)
| singleton(X17) = set_union2(X15,X16)
| sK5(X15,X16,singleton(X17)) = X17 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_331])]) ).
fof(f1293,plain,
( ! [X16,X17,X15] :
( in(sK5(X15,X16,singleton(X17)),X16)
| in(sK5(X15,X16,singleton(X17)),X15)
| singleton(X17) = set_union2(X15,X16)
| sK5(X15,X16,singleton(X17)) = X17 )
| ~ spl19_70
| ~ spl19_145 ),
inference(resolution,[],[f1285,f617]) ).
fof(f4536,plain,
( spl19_330
| ~ spl19_33
| ~ spl19_329 ),
inference(avatar_split_clause,[],[f4531,f4525,f415,f4533]) ).
fof(f4533,plain,
( spl19_330
<=> element(empty_set,sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_330])]) ).
fof(f4525,plain,
( spl19_329
<=> empty_set = sK3(sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_329])]) ).
fof(f4531,plain,
( element(empty_set,sK0)
| ~ spl19_33
| ~ spl19_329 ),
inference(superposition,[],[f416,f4527]) ).
fof(f4527,plain,
( empty_set = sK3(sK0)
| ~ spl19_329 ),
inference(avatar_component_clause,[],[f4525]) ).
fof(f4528,plain,
( spl19_329
| ~ spl19_39
| ~ spl19_321 ),
inference(avatar_split_clause,[],[f4439,f4394,f439,f4525]) ).
fof(f4394,plain,
( spl19_321
<=> empty(sK3(sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_321])]) ).
fof(f4439,plain,
( empty_set = sK3(sK0)
| ~ spl19_39
| ~ spl19_321 ),
inference(resolution,[],[f4395,f440]) ).
fof(f4395,plain,
( empty(sK3(sK0))
| ~ spl19_321 ),
inference(avatar_component_clause,[],[f4394]) ).
fof(f4523,plain,
( spl19_328
| ~ spl19_117
| ~ spl19_131 ),
inference(avatar_split_clause,[],[f1096,f1086,f988,f4521]) ).
fof(f4521,plain,
( spl19_328
<=> ! [X2,X3,X4] :
( sK4(X2,set_union2(X3,X4)) = X2
| set_union2(X3,X4) = singleton(X2)
| in(sK4(X2,set_union2(X3,X4)),X3)
| in(sK4(X2,set_union2(X3,X4)),X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_328])]) ).
fof(f1096,plain,
( ! [X2,X3,X4] :
( sK4(X2,set_union2(X3,X4)) = X2
| set_union2(X3,X4) = singleton(X2)
| in(sK4(X2,set_union2(X3,X4)),X3)
| in(sK4(X2,set_union2(X3,X4)),X4) )
| ~ spl19_117
| ~ spl19_131 ),
inference(resolution,[],[f1087,f989]) ).
fof(f4519,plain,
( ~ spl19_327
| ~ spl19_39
| ~ spl19_321
| spl19_323 ),
inference(avatar_split_clause,[],[f4462,f4427,f4394,f439,f4516]) ).
fof(f4516,plain,
( spl19_327
<=> in(sK0,sK2(empty_set)) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_327])]) ).
fof(f4427,plain,
( spl19_323
<=> in(sK0,sK2(sK3(sK0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_323])]) ).
fof(f4462,plain,
( ~ in(sK0,sK2(empty_set))
| ~ spl19_39
| ~ spl19_321
| spl19_323 ),
inference(backward_demodulation,[],[f4429,f4439]) ).
fof(f4429,plain,
( ~ in(sK0,sK2(sK3(sK0)))
| spl19_323 ),
inference(avatar_component_clause,[],[f4427]) ).
fof(f4514,plain,
( ~ spl19_326
| ~ spl19_39
| ~ spl19_321
| spl19_324 ),
inference(avatar_split_clause,[],[f4463,f4432,f4394,f439,f4511]) ).
fof(f4511,plain,
( spl19_326
<=> in(sK3(empty_set),sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_326])]) ).
fof(f4432,plain,
( spl19_324
<=> in(sK3(sK3(sK0)),sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_324])]) ).
fof(f4463,plain,
( ~ in(sK3(empty_set),sK0)
| ~ spl19_39
| ~ spl19_321
| spl19_324 ),
inference(backward_demodulation,[],[f4433,f4439]) ).
fof(f4433,plain,
( ~ in(sK3(sK3(sK0)),sK0)
| spl19_324 ),
inference(avatar_component_clause,[],[f4432]) ).
fof(f4508,plain,
( spl19_325
| ~ spl19_39
| ~ spl19_320
| ~ spl19_321 ),
inference(avatar_split_clause,[],[f4458,f4394,f4367,f439,f4505]) ).
fof(f4505,plain,
( spl19_325
<=> in(sK2(empty_set),sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_325])]) ).
fof(f4367,plain,
( spl19_320
<=> in(sK2(sK3(sK0)),sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_320])]) ).
fof(f4458,plain,
( in(sK2(empty_set),sK0)
| ~ spl19_39
| ~ spl19_320
| ~ spl19_321 ),
inference(backward_demodulation,[],[f4369,f4439]) ).
fof(f4369,plain,
( in(sK2(sK3(sK0)),sK0)
| ~ spl19_320 ),
inference(avatar_component_clause,[],[f4367]) ).
fof(f4437,plain,
( ~ spl19_32
| ~ spl19_321
| spl19_322 ),
inference(avatar_contradiction_clause,[],[f4436]) ).
fof(f4436,plain,
( $false
| ~ spl19_32
| ~ spl19_321
| spl19_322 ),
inference(subsumption_resolution,[],[f4395,f4423]) ).
fof(f4423,plain,
( ~ empty(sK3(sK0))
| ~ spl19_32
| spl19_322 ),
inference(resolution,[],[f4401,f412]) ).
fof(f4401,plain,
( ~ ordinal(sK3(sK0))
| spl19_322 ),
inference(avatar_component_clause,[],[f4399]) ).
fof(f4399,plain,
( spl19_322
<=> ordinal(sK3(sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_322])]) ).
fof(f4435,plain,
( spl19_321
| spl19_324
| ~ spl19_83
| ~ spl19_317 ),
inference(avatar_split_clause,[],[f4337,f4311,f712,f4432,f4394]) ).
fof(f4311,plain,
( spl19_317
<=> ! [X9] :
( ~ in(X9,sK3(sK0))
| in(X9,sK0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_317])]) ).
fof(f4337,plain,
( in(sK3(sK3(sK0)),sK0)
| empty(sK3(sK0))
| ~ spl19_83
| ~ spl19_317 ),
inference(resolution,[],[f4312,f713]) ).
fof(f4312,plain,
( ! [X9] :
( ~ in(X9,sK3(sK0))
| in(X9,sK0) )
| ~ spl19_317 ),
inference(avatar_component_clause,[],[f4311]) ).
fof(f4430,plain,
( ~ spl19_323
| ~ spl19_52
| ~ spl19_320 ),
inference(avatar_split_clause,[],[f4425,f4367,f508,f4427]) ).
fof(f4425,plain,
( ~ in(sK0,sK2(sK3(sK0)))
| ~ spl19_52
| ~ spl19_320 ),
inference(resolution,[],[f4369,f509]) ).
fof(f4402,plain,
( ~ spl19_322
| ~ spl19_29
| spl19_319 ),
inference(avatar_split_clause,[],[f4392,f4363,f399,f4399]) ).
fof(f4363,plain,
( spl19_319
<=> epsilon_transitive(sK3(sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_319])]) ).
fof(f4392,plain,
( ~ ordinal(sK3(sK0))
| ~ spl19_29
| spl19_319 ),
inference(resolution,[],[f4364,f400]) ).
fof(f4364,plain,
( ~ epsilon_transitive(sK3(sK0))
| spl19_319 ),
inference(avatar_component_clause,[],[f4363]) ).
fof(f4397,plain,
( ~ spl19_321
| ~ spl19_30
| spl19_319 ),
inference(avatar_split_clause,[],[f4391,f4363,f403,f4394]) ).
fof(f4391,plain,
( ~ empty(sK3(sK0))
| ~ spl19_30
| spl19_319 ),
inference(resolution,[],[f4364,f404]) ).
fof(f4370,plain,
( spl19_319
| spl19_320
| ~ spl19_48
| ~ spl19_317 ),
inference(avatar_split_clause,[],[f4334,f4311,f492,f4367,f4363]) ).
fof(f4334,plain,
( in(sK2(sK3(sK0)),sK0)
| epsilon_transitive(sK3(sK0))
| ~ spl19_48
| ~ spl19_317 ),
inference(resolution,[],[f4312,f493]) ).
fof(f4349,plain,
( spl19_318
| ~ spl19_310
| ~ spl19_315 ),
inference(avatar_split_clause,[],[f4293,f4280,f3781,f4347]) ).
fof(f4280,plain,
( spl19_315
<=> in(sK3(sK1),sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_315])]) ).
fof(f4293,plain,
( ! [X0] :
( ~ in(X0,sK3(sK1))
| in(X0,sK0) )
| ~ spl19_310
| ~ spl19_315 ),
inference(resolution,[],[f4282,f3782]) ).
fof(f4282,plain,
( in(sK3(sK1),sK0)
| ~ spl19_315 ),
inference(avatar_component_clause,[],[f4280]) ).
fof(f4313,plain,
( spl19_317
| ~ spl19_83
| spl19_275
| ~ spl19_310 ),
inference(avatar_split_clause,[],[f3807,f3781,f3413,f712,f4311]) ).
fof(f3413,plain,
( spl19_275
<=> empty(sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_275])]) ).
fof(f3807,plain,
( ! [X9] :
( ~ in(X9,sK3(sK0))
| in(X9,sK0) )
| ~ spl19_83
| spl19_275
| ~ spl19_310 ),
inference(subsumption_resolution,[],[f3798,f3415]) ).
fof(f3415,plain,
( ~ empty(sK0)
| spl19_275 ),
inference(avatar_component_clause,[],[f3413]) ).
fof(f3798,plain,
( ! [X9] :
( ~ in(X9,sK3(sK0))
| in(X9,sK0)
| empty(sK0) )
| ~ spl19_83
| ~ spl19_310 ),
inference(resolution,[],[f3782,f713]) ).
fof(f4309,plain,
( ~ spl19_316
| ~ spl19_52
| ~ spl19_315 ),
inference(avatar_split_clause,[],[f4294,f4280,f508,f4306]) ).
fof(f4306,plain,
( spl19_316
<=> in(sK0,sK3(sK1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_316])]) ).
fof(f4294,plain,
( ~ in(sK0,sK3(sK1))
| ~ spl19_52
| ~ spl19_315 ),
inference(resolution,[],[f4282,f509]) ).
fof(f4292,plain,
( ~ spl19_39
| spl19_150
| ~ spl19_314 ),
inference(avatar_contradiction_clause,[],[f4291]) ).
fof(f4291,plain,
( $false
| ~ spl19_39
| spl19_150
| ~ spl19_314 ),
inference(subsumption_resolution,[],[f4284,f1532]) ).
fof(f4284,plain,
( empty_set = sK1
| ~ spl19_39
| ~ spl19_314 ),
inference(resolution,[],[f4278,f440]) ).
fof(f4278,plain,
( empty(sK1)
| ~ spl19_314 ),
inference(avatar_component_clause,[],[f4276]) ).
fof(f4283,plain,
( spl19_314
| spl19_315
| ~ spl19_83
| ~ spl19_313 ),
inference(avatar_split_clause,[],[f3837,f3809,f712,f4280,f4276]) ).
fof(f3837,plain,
( in(sK3(sK1),sK0)
| empty(sK1)
| ~ spl19_83
| ~ spl19_313 ),
inference(resolution,[],[f3810,f713]) ).
fof(f4267,plain,
( ~ spl19_174
| ~ spl19_216
| ~ spl19_2
| ~ spl19_139
| spl19_172
| ~ spl19_189 ),
inference(avatar_split_clause,[],[f2270,f1900,f1781,f1134,f268,f2342,f1789]) ).
fof(f2270,plain,
( ~ ordinal_subset(sK1,sK10)
| ~ in(sK10,sK1)
| ~ spl19_2
| ~ spl19_139
| spl19_172
| ~ spl19_189 ),
inference(subsumption_resolution,[],[f2269,f1782]) ).
fof(f1782,plain,
( sK1 != sK10
| spl19_172 ),
inference(avatar_component_clause,[],[f1781]) ).
fof(f4266,plain,
( ~ spl19_218
| ~ spl19_216
| ~ spl19_2
| ~ spl19_18
| spl19_172
| ~ spl19_178
| ~ spl19_189 ),
inference(avatar_split_clause,[],[f2268,f1900,f1824,f1781,f348,f268,f2342,f2388]) ).
fof(f2268,plain,
( ~ ordinal_subset(sK1,sK10)
| ~ ordinal_subset(sK10,sK1)
| ~ spl19_2
| ~ spl19_18
| spl19_172
| ~ spl19_178
| ~ spl19_189 ),
inference(subsumption_resolution,[],[f2267,f1782]) ).
fof(f4255,plain,
( spl19_215
| ~ spl19_18
| ~ spl19_108
| spl19_217 ),
inference(avatar_split_clause,[],[f2377,f2360,f916,f348,f2337]) ).
fof(f2377,plain,
( ordinal_subset(sK0,sK10)
| ~ spl19_18
| ~ spl19_108
| spl19_217 ),
inference(subsumption_resolution,[],[f2366,f350]) ).
fof(f2366,plain,
( ordinal_subset(sK0,sK10)
| ~ ordinal(sK10)
| ~ spl19_108
| spl19_217 ),
inference(resolution,[],[f2362,f917]) ).
fof(f4249,plain,
( ~ spl19_217
| ~ spl19_18
| ~ spl19_82
| spl19_164
| ~ spl19_165
| ~ spl19_177 ),
inference(avatar_split_clause,[],[f4248,f1820,f1749,f1745,f703,f348,f2360]) ).
fof(f1745,plain,
( spl19_164
<=> sK0 = sK10 ),
introduced(avatar_definition,[new_symbols(naming,[spl19_164])]) ).
fof(f4248,plain,
( ~ ordinal_subset(sK10,sK0)
| ~ spl19_18
| ~ spl19_82
| spl19_164
| ~ spl19_165
| ~ spl19_177 ),
inference(subsumption_resolution,[],[f4247,f1746]) ).
fof(f1746,plain,
( sK0 != sK10
| spl19_164 ),
inference(avatar_component_clause,[],[f1745]) ).
fof(f4247,plain,
( sK0 = sK10
| ~ ordinal_subset(sK10,sK0)
| ~ spl19_18
| ~ spl19_82
| ~ spl19_165
| ~ spl19_177 ),
inference(subsumption_resolution,[],[f4246,f350]) ).
fof(f4246,plain,
( ~ ordinal(sK10)
| sK0 = sK10
| ~ ordinal_subset(sK10,sK0)
| ~ spl19_82
| ~ spl19_165
| ~ spl19_177 ),
inference(subsumption_resolution,[],[f4232,f1751]) ).
fof(f4232,plain,
( ~ in(sK0,sK10)
| ~ ordinal(sK10)
| sK0 = sK10
| ~ ordinal_subset(sK10,sK0)
| ~ spl19_82
| ~ spl19_177 ),
inference(resolution,[],[f704,f1821]) ).
fof(f4245,plain,
( spl19_164
| ~ spl19_18
| ~ spl19_82
| ~ spl19_165
| ~ spl19_177
| ~ spl19_217 ),
inference(avatar_split_clause,[],[f4190,f2360,f1820,f1749,f703,f348,f1745]) ).
fof(f4190,plain,
( ~ ordinal(sK10)
| sK0 = sK10
| ~ spl19_82
| ~ spl19_165
| ~ spl19_177
| ~ spl19_217 ),
inference(subsumption_resolution,[],[f4189,f1751]) ).
fof(f4189,plain,
( ~ ordinal(sK10)
| sK0 = sK10
| ~ in(sK0,sK10)
| ~ spl19_82
| ~ spl19_177
| ~ spl19_217 ),
inference(subsumption_resolution,[],[f1837,f2361]) ).
fof(f2361,plain,
( ordinal_subset(sK10,sK0)
| ~ spl19_217 ),
inference(avatar_component_clause,[],[f2360]) ).
fof(f1837,plain,
( ~ ordinal(sK10)
| sK0 = sK10
| ~ ordinal_subset(sK10,sK0)
| ~ in(sK0,sK10)
| ~ spl19_82
| ~ spl19_177 ),
inference(resolution,[],[f1821,f704]) ).
fof(f4224,plain,
( spl19_216
| ~ spl19_18
| ~ spl19_109
| spl19_218 ),
inference(avatar_split_clause,[],[f4193,f2388,f920,f348,f2342]) ).
fof(f4193,plain,
( ordinal_subset(sK1,sK10)
| ~ spl19_18
| ~ spl19_109
| spl19_218 ),
inference(subsumption_resolution,[],[f2397,f350]) ).
fof(f2397,plain,
( ordinal_subset(sK1,sK10)
| ~ ordinal(sK10)
| ~ spl19_109
| spl19_218 ),
inference(resolution,[],[f2390,f921]) ).
fof(f4219,plain,
( ~ spl19_218
| ~ spl19_18
| ~ spl19_82
| spl19_172
| ~ spl19_173
| ~ spl19_178 ),
inference(avatar_split_clause,[],[f4192,f1824,f1785,f1781,f703,f348,f2388]) ).
fof(f4192,plain,
( ~ ordinal_subset(sK10,sK1)
| ~ spl19_18
| ~ spl19_82
| spl19_172
| ~ spl19_173
| ~ spl19_178 ),
inference(subsumption_resolution,[],[f4191,f1787]) ).
fof(f4191,plain,
( ~ ordinal_subset(sK10,sK1)
| ~ in(sK1,sK10)
| ~ spl19_18
| ~ spl19_82
| spl19_172
| ~ spl19_178 ),
inference(subsumption_resolution,[],[f4063,f1782]) ).
fof(f4063,plain,
( sK1 = sK10
| ~ ordinal_subset(sK10,sK1)
| ~ in(sK1,sK10)
| ~ spl19_18
| ~ spl19_82
| ~ spl19_178 ),
inference(subsumption_resolution,[],[f1865,f350]) ).
fof(f1865,plain,
( ~ ordinal(sK10)
| sK1 = sK10
| ~ ordinal_subset(sK10,sK1)
| ~ in(sK1,sK10)
| ~ spl19_82
| ~ spl19_178 ),
inference(resolution,[],[f1825,f704]) ).
fof(f4199,plain,
( ~ spl19_215
| ~ spl19_1
| ~ spl19_18
| spl19_164
| ~ spl19_177
| ~ spl19_189
| ~ spl19_217 ),
inference(avatar_split_clause,[],[f4061,f2360,f1900,f1820,f1745,f348,f263,f2337]) ).
fof(f4061,plain,
( ~ ordinal_subset(sK0,sK10)
| ~ spl19_1
| ~ spl19_18
| spl19_164
| ~ spl19_177
| ~ spl19_189
| ~ spl19_217 ),
inference(subsumption_resolution,[],[f3963,f1746]) ).
fof(f3963,plain,
( ~ ordinal_subset(sK0,sK10)
| sK0 = sK10
| ~ spl19_1
| ~ spl19_18
| ~ spl19_177
| ~ spl19_189
| ~ spl19_217 ),
inference(subsumption_resolution,[],[f2261,f2361]) ).
fof(f2261,plain,
( ~ ordinal_subset(sK0,sK10)
| sK0 = sK10
| ~ ordinal_subset(sK10,sK0)
| ~ spl19_1
| ~ spl19_18
| ~ spl19_177
| ~ spl19_189 ),
inference(subsumption_resolution,[],[f2260,f350]) ).
fof(f2260,plain,
( ~ ordinal_subset(sK0,sK10)
| ~ ordinal(sK10)
| sK0 = sK10
| ~ ordinal_subset(sK10,sK0)
| ~ spl19_1
| ~ spl19_177
| ~ spl19_189 ),
inference(subsumption_resolution,[],[f2255,f265]) ).
fof(f2255,plain,
( ~ ordinal_subset(sK0,sK10)
| ~ ordinal(sK0)
| ~ ordinal(sK10)
| sK0 = sK10
| ~ ordinal_subset(sK10,sK0)
| ~ spl19_177
| ~ spl19_189 ),
inference(resolution,[],[f1901,f1821]) ).
fof(f4198,plain,
( ~ spl19_166
| ~ spl19_52
| ~ spl19_165 ),
inference(avatar_split_clause,[],[f2378,f1749,f508,f1753]) ).
fof(f2378,plain,
( ~ in(sK10,sK0)
| ~ spl19_52
| ~ spl19_165 ),
inference(resolution,[],[f1751,f509]) ).
fof(f4188,plain,
( ~ spl19_2
| ~ spl19_18
| ~ spl19_82
| spl19_101
| ~ spl19_165
| spl19_174
| ~ spl19_178
| ~ spl19_218
| ~ spl19_261 ),
inference(avatar_contradiction_clause,[],[f4187]) ).
fof(f4187,plain,
( $false
| ~ spl19_2
| ~ spl19_18
| ~ spl19_82
| spl19_101
| ~ spl19_165
| spl19_174
| ~ spl19_178
| ~ spl19_218
| ~ spl19_261 ),
inference(subsumption_resolution,[],[f4186,f870]) ).
fof(f4186,plain,
( in(sK0,sK1)
| ~ spl19_2
| ~ spl19_18
| ~ spl19_82
| ~ spl19_165
| spl19_174
| ~ spl19_178
| ~ spl19_218
| ~ spl19_261 ),
inference(forward_demodulation,[],[f1751,f4065]) ).
fof(f4065,plain,
( sK1 = sK10
| ~ spl19_2
| ~ spl19_18
| ~ spl19_82
| spl19_174
| ~ spl19_178
| ~ spl19_218
| ~ spl19_261 ),
inference(subsumption_resolution,[],[f4064,f4062]) ).
fof(f4062,plain,
( in(sK1,sK10)
| sK1 = sK10
| ~ spl19_2
| spl19_174
| ~ spl19_261 ),
inference(subsumption_resolution,[],[f3188,f1790]) ).
fof(f3188,plain,
( in(sK1,sK10)
| in(sK10,sK1)
| sK1 = sK10
| ~ spl19_2
| ~ spl19_261 ),
inference(resolution,[],[f3005,f270]) ).
fof(f3005,plain,
( ! [X8] :
( ~ ordinal(X8)
| in(X8,sK10)
| in(sK10,X8)
| sK10 = X8 )
| ~ spl19_261 ),
inference(avatar_component_clause,[],[f3004]) ).
fof(f3004,plain,
( spl19_261
<=> ! [X8] :
( sK10 = X8
| in(X8,sK10)
| in(sK10,X8)
| ~ ordinal(X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_261])]) ).
fof(f4064,plain,
( sK1 = sK10
| ~ in(sK1,sK10)
| ~ spl19_18
| ~ spl19_82
| ~ spl19_178
| ~ spl19_218 ),
inference(subsumption_resolution,[],[f4063,f2389]) ).
fof(f2389,plain,
( ordinal_subset(sK10,sK1)
| ~ spl19_218 ),
inference(avatar_component_clause,[],[f2388]) ).
fof(f4185,plain,
( ~ spl19_2
| ~ spl19_18
| ~ spl19_52
| ~ spl19_82
| ~ spl19_140
| ~ spl19_165
| spl19_174
| ~ spl19_178
| ~ spl19_218
| ~ spl19_261 ),
inference(avatar_contradiction_clause,[],[f4184]) ).
fof(f4184,plain,
( $false
| ~ spl19_2
| ~ spl19_18
| ~ spl19_52
| ~ spl19_82
| ~ spl19_140
| ~ spl19_165
| spl19_174
| ~ spl19_178
| ~ spl19_218
| ~ spl19_261 ),
inference(subsumption_resolution,[],[f4183,f1149]) ).
fof(f4183,plain,
( ~ in(sK1,sK0)
| ~ spl19_2
| ~ spl19_18
| ~ spl19_52
| ~ spl19_82
| ~ spl19_165
| spl19_174
| ~ spl19_178
| ~ spl19_218
| ~ spl19_261 ),
inference(forward_demodulation,[],[f2378,f4065]) ).
fof(f4182,plain,
( ~ spl19_2
| ~ spl19_18
| ~ spl19_82
| ~ spl19_140
| spl19_166
| spl19_174
| ~ spl19_178
| ~ spl19_218
| ~ spl19_261 ),
inference(avatar_contradiction_clause,[],[f4181]) ).
fof(f4181,plain,
( $false
| ~ spl19_2
| ~ spl19_18
| ~ spl19_82
| ~ spl19_140
| spl19_166
| spl19_174
| ~ spl19_178
| ~ spl19_218
| ~ spl19_261 ),
inference(subsumption_resolution,[],[f4180,f1149]) ).
fof(f4180,plain,
( ~ in(sK1,sK0)
| ~ spl19_2
| ~ spl19_18
| ~ spl19_82
| spl19_166
| spl19_174
| ~ spl19_178
| ~ spl19_218
| ~ spl19_261 ),
inference(forward_demodulation,[],[f1754,f4065]) ).
fof(f4179,plain,
( ~ spl19_2
| ~ spl19_18
| ~ spl19_82
| spl19_172
| spl19_174
| ~ spl19_178
| ~ spl19_218
| ~ spl19_261 ),
inference(avatar_contradiction_clause,[],[f4178]) ).
fof(f4178,plain,
( $false
| ~ spl19_2
| ~ spl19_18
| ~ spl19_82
| spl19_172
| spl19_174
| ~ spl19_178
| ~ spl19_218
| ~ spl19_261 ),
inference(subsumption_resolution,[],[f1782,f4065]) ).
fof(f4177,plain,
( ~ spl19_2
| ~ spl19_18
| ~ spl19_63
| ~ spl19_82
| spl19_172
| spl19_174
| ~ spl19_178
| ~ spl19_189
| ~ spl19_218
| ~ spl19_261 ),
inference(avatar_contradiction_clause,[],[f4176]) ).
fof(f4176,plain,
( $false
| ~ spl19_2
| ~ spl19_18
| ~ spl19_63
| ~ spl19_82
| spl19_172
| spl19_174
| ~ spl19_178
| ~ spl19_189
| ~ spl19_218
| ~ spl19_261 ),
inference(subsumption_resolution,[],[f4175,f586]) ).
fof(f586,plain,
( ordinal_subset(sK1,sK1)
| ~ spl19_63 ),
inference(avatar_component_clause,[],[f584]) ).
fof(f584,plain,
( spl19_63
<=> ordinal_subset(sK1,sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_63])]) ).
fof(f4175,plain,
( ~ ordinal_subset(sK1,sK1)
| ~ spl19_2
| ~ spl19_18
| ~ spl19_63
| ~ spl19_82
| spl19_172
| spl19_174
| ~ spl19_178
| ~ spl19_189
| ~ spl19_218
| ~ spl19_261 ),
inference(forward_demodulation,[],[f4174,f4065]) ).
fof(f4174,plain,
( ~ ordinal_subset(sK10,sK1)
| ~ spl19_2
| ~ spl19_18
| ~ spl19_63
| ~ spl19_82
| spl19_172
| spl19_174
| ~ spl19_178
| ~ spl19_189
| ~ spl19_218
| ~ spl19_261 ),
inference(subsumption_resolution,[],[f4173,f586]) ).
fof(f4173,plain,
( ~ ordinal_subset(sK1,sK1)
| ~ ordinal_subset(sK10,sK1)
| ~ spl19_2
| ~ spl19_18
| ~ spl19_82
| spl19_172
| spl19_174
| ~ spl19_178
| ~ spl19_189
| ~ spl19_218
| ~ spl19_261 ),
inference(forward_demodulation,[],[f2268,f4065]) ).
fof(f4169,plain,
( ~ spl19_2
| ~ spl19_18
| ~ spl19_82
| ~ spl19_173
| spl19_174
| ~ spl19_178
| spl19_205
| ~ spl19_218
| ~ spl19_261 ),
inference(avatar_contradiction_clause,[],[f4168]) ).
fof(f4168,plain,
( $false
| ~ spl19_2
| ~ spl19_18
| ~ spl19_82
| ~ spl19_173
| spl19_174
| ~ spl19_178
| spl19_205
| ~ spl19_218
| ~ spl19_261 ),
inference(subsumption_resolution,[],[f4167,f2070]) ).
fof(f2070,plain,
( ~ in(sK1,sK1)
| spl19_205 ),
inference(avatar_component_clause,[],[f2068]) ).
fof(f2068,plain,
( spl19_205
<=> in(sK1,sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_205])]) ).
fof(f4167,plain,
( in(sK1,sK1)
| ~ spl19_2
| ~ spl19_18
| ~ spl19_82
| ~ spl19_173
| spl19_174
| ~ spl19_178
| ~ spl19_218
| ~ spl19_261 ),
inference(forward_demodulation,[],[f1787,f4065]) ).
fof(f4166,plain,
( ~ spl19_1
| ~ spl19_2
| ~ spl19_18
| ~ spl19_82
| ~ spl19_98
| spl19_101
| spl19_141
| spl19_174
| ~ spl19_178
| ~ spl19_218
| spl19_238
| ~ spl19_261 ),
inference(avatar_contradiction_clause,[],[f4165]) ).
fof(f4165,plain,
( $false
| ~ spl19_1
| ~ spl19_2
| ~ spl19_18
| ~ spl19_82
| ~ spl19_98
| spl19_101
| spl19_141
| spl19_174
| ~ spl19_178
| ~ spl19_218
| spl19_238
| ~ spl19_261 ),
inference(subsumption_resolution,[],[f4164,f870]) ).
fof(f4164,plain,
( in(sK0,sK1)
| ~ spl19_1
| ~ spl19_2
| ~ spl19_18
| ~ spl19_82
| ~ spl19_98
| spl19_141
| spl19_174
| ~ spl19_178
| ~ spl19_218
| spl19_238
| ~ spl19_261 ),
inference(forward_demodulation,[],[f4163,f4065]) ).
fof(f4163,plain,
( in(sK0,sK10)
| ~ spl19_1
| ~ spl19_2
| ~ spl19_18
| ~ spl19_82
| ~ spl19_98
| spl19_141
| spl19_174
| ~ spl19_178
| ~ spl19_218
| spl19_238
| ~ spl19_261 ),
inference(subsumption_resolution,[],[f4108,f1153]) ).
fof(f4108,plain,
( sK0 = sK1
| in(sK0,sK10)
| ~ spl19_1
| ~ spl19_2
| ~ spl19_18
| ~ spl19_82
| ~ spl19_98
| spl19_174
| ~ spl19_178
| ~ spl19_218
| spl19_238
| ~ spl19_261 ),
inference(backward_demodulation,[],[f4060,f4065]) ).
fof(f4060,plain,
( in(sK0,sK10)
| sK0 = sK10
| ~ spl19_1
| ~ spl19_98
| spl19_238
| ~ spl19_261 ),
inference(subsumption_resolution,[],[f3187,f3349]) ).
fof(f3349,plain,
( ~ in(sK10,sK0)
| ~ spl19_98
| spl19_238 ),
inference(resolution,[],[f2683,f846]) ).
fof(f3187,plain,
( in(sK0,sK10)
| in(sK10,sK0)
| sK0 = sK10
| ~ spl19_1
| ~ spl19_261 ),
inference(resolution,[],[f3005,f265]) ).
fof(f4157,plain,
( ~ spl19_2
| ~ spl19_18
| ~ spl19_82
| ~ spl19_98
| ~ spl19_140
| spl19_174
| ~ spl19_178
| ~ spl19_218
| spl19_238
| ~ spl19_261 ),
inference(avatar_contradiction_clause,[],[f4156]) ).
fof(f4156,plain,
( $false
| ~ spl19_2
| ~ spl19_18
| ~ spl19_82
| ~ spl19_98
| ~ spl19_140
| spl19_174
| ~ spl19_178
| ~ spl19_218
| spl19_238
| ~ spl19_261 ),
inference(subsumption_resolution,[],[f4103,f1149]) ).
fof(f4103,plain,
( ~ in(sK1,sK0)
| ~ spl19_2
| ~ spl19_18
| ~ spl19_82
| ~ spl19_98
| spl19_174
| ~ spl19_178
| ~ spl19_218
| spl19_238
| ~ spl19_261 ),
inference(backward_demodulation,[],[f3349,f4065]) ).
fof(f4155,plain,
( ~ spl19_2
| ~ spl19_18
| ~ spl19_82
| spl19_174
| ~ spl19_178
| spl19_204
| ~ spl19_218
| ~ spl19_261
| ~ spl19_270 ),
inference(avatar_contradiction_clause,[],[f4154]) ).
fof(f4154,plain,
( $false
| ~ spl19_2
| ~ spl19_18
| ~ spl19_82
| spl19_174
| ~ spl19_178
| spl19_204
| ~ spl19_218
| ~ spl19_261
| ~ spl19_270 ),
inference(subsumption_resolution,[],[f4102,f2037]) ).
fof(f2037,plain,
( ~ in(succ(sK0),sK1)
| spl19_204 ),
inference(avatar_component_clause,[],[f2036]) ).
fof(f2036,plain,
( spl19_204
<=> in(succ(sK0),sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_204])]) ).
fof(f4102,plain,
( in(succ(sK0),sK1)
| ~ spl19_2
| ~ spl19_18
| ~ spl19_82
| spl19_174
| ~ spl19_178
| ~ spl19_218
| ~ spl19_261
| ~ spl19_270 ),
inference(backward_demodulation,[],[f3198,f4065]) ).
fof(f4138,plain,
( ~ spl19_2
| ~ spl19_18
| ~ spl19_82
| spl19_174
| ~ spl19_178
| ~ spl19_210
| ~ spl19_218
| spl19_241
| ~ spl19_261 ),
inference(avatar_contradiction_clause,[],[f4137]) ).
fof(f4137,plain,
( $false
| ~ spl19_2
| ~ spl19_18
| ~ spl19_82
| spl19_174
| ~ spl19_178
| ~ spl19_210
| ~ spl19_218
| spl19_241
| ~ spl19_261 ),
inference(subsumption_resolution,[],[f4089,f2191]) ).
fof(f2191,plain,
( ordinal_subset(sK1,succ(sK0))
| ~ spl19_210 ),
inference(avatar_component_clause,[],[f2189]) ).
fof(f2189,plain,
( spl19_210
<=> ordinal_subset(sK1,succ(sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_210])]) ).
fof(f4089,plain,
( ~ ordinal_subset(sK1,succ(sK0))
| ~ spl19_2
| ~ spl19_18
| ~ spl19_82
| spl19_174
| ~ spl19_178
| ~ spl19_218
| spl19_241
| ~ spl19_261 ),
inference(backward_demodulation,[],[f2699,f4065]) ).
fof(f4136,plain,
( ~ spl19_2
| ~ spl19_18
| ~ spl19_82
| spl19_174
| ~ spl19_178
| ~ spl19_203
| ~ spl19_218
| spl19_238
| ~ spl19_261 ),
inference(avatar_contradiction_clause,[],[f4135]) ).
fof(f4135,plain,
( $false
| ~ spl19_2
| ~ spl19_18
| ~ spl19_82
| spl19_174
| ~ spl19_178
| ~ spl19_203
| ~ spl19_218
| spl19_238
| ~ spl19_261 ),
inference(subsumption_resolution,[],[f4087,f2034]) ).
fof(f2034,plain,
( in(sK1,succ(sK0))
| ~ spl19_203 ),
inference(avatar_component_clause,[],[f2032]) ).
fof(f2032,plain,
( spl19_203
<=> in(sK1,succ(sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_203])]) ).
fof(f4087,plain,
( ~ in(sK1,succ(sK0))
| ~ spl19_2
| ~ spl19_18
| ~ spl19_82
| spl19_174
| ~ spl19_178
| ~ spl19_218
| spl19_238
| ~ spl19_261 ),
inference(backward_demodulation,[],[f2683,f4065]) ).
fof(f4134,plain,
( ~ spl19_2
| ~ spl19_18
| ~ spl19_82
| spl19_174
| ~ spl19_178
| spl19_209
| ~ spl19_218
| ~ spl19_237
| ~ spl19_261 ),
inference(avatar_contradiction_clause,[],[f4133]) ).
fof(f4133,plain,
( $false
| ~ spl19_2
| ~ spl19_18
| ~ spl19_82
| spl19_174
| ~ spl19_178
| spl19_209
| ~ spl19_218
| ~ spl19_237
| ~ spl19_261 ),
inference(subsumption_resolution,[],[f4086,f2181]) ).
fof(f2181,plain,
( ~ ordinal_subset(succ(sK0),sK1)
| spl19_209 ),
inference(avatar_component_clause,[],[f2179]) ).
fof(f2179,plain,
( spl19_209
<=> ordinal_subset(succ(sK0),sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_209])]) ).
fof(f4086,plain,
( ordinal_subset(succ(sK0),sK1)
| ~ spl19_2
| ~ spl19_18
| ~ spl19_82
| spl19_174
| ~ spl19_178
| ~ spl19_218
| ~ spl19_237
| ~ spl19_261 ),
inference(backward_demodulation,[],[f2678,f4065]) ).
fof(f4127,plain,
( ~ spl19_2
| ~ spl19_18
| ~ spl19_63
| ~ spl19_82
| spl19_174
| ~ spl19_178
| spl19_216
| ~ spl19_218
| ~ spl19_261 ),
inference(avatar_contradiction_clause,[],[f4126]) ).
fof(f4126,plain,
( $false
| ~ spl19_2
| ~ spl19_18
| ~ spl19_63
| ~ spl19_82
| spl19_174
| ~ spl19_178
| spl19_216
| ~ spl19_218
| ~ spl19_261 ),
inference(subsumption_resolution,[],[f4080,f586]) ).
fof(f4080,plain,
( ~ ordinal_subset(sK1,sK1)
| ~ spl19_2
| ~ spl19_18
| ~ spl19_82
| spl19_174
| ~ spl19_178
| spl19_216
| ~ spl19_218
| ~ spl19_261 ),
inference(backward_demodulation,[],[f2344,f4065]) ).
fof(f2344,plain,
( ~ ordinal_subset(sK1,sK10)
| spl19_216 ),
inference(avatar_component_clause,[],[f2342]) ).
fof(f4045,plain,
( ~ spl19_172
| spl19_204
| ~ spl19_270 ),
inference(avatar_contradiction_clause,[],[f4044]) ).
fof(f4044,plain,
( $false
| ~ spl19_172
| spl19_204
| ~ spl19_270 ),
inference(subsumption_resolution,[],[f4001,f2037]) ).
fof(f4001,plain,
( in(succ(sK0),sK1)
| ~ spl19_172
| ~ spl19_270 ),
inference(backward_demodulation,[],[f3198,f1783]) ).
fof(f1783,plain,
( sK1 = sK10
| ~ spl19_172 ),
inference(avatar_component_clause,[],[f1781]) ).
fof(f4028,plain,
( ~ spl19_172
| ~ spl19_210
| spl19_241 ),
inference(avatar_contradiction_clause,[],[f4027]) ).
fof(f4027,plain,
( $false
| ~ spl19_172
| ~ spl19_210
| spl19_241 ),
inference(subsumption_resolution,[],[f3988,f2191]) ).
fof(f3988,plain,
( ~ ordinal_subset(sK1,succ(sK0))
| ~ spl19_172
| spl19_241 ),
inference(backward_demodulation,[],[f2699,f1783]) ).
fof(f4026,plain,
( ~ spl19_172
| ~ spl19_203
| spl19_238 ),
inference(avatar_contradiction_clause,[],[f4025]) ).
fof(f4025,plain,
( $false
| ~ spl19_172
| ~ spl19_203
| spl19_238 ),
inference(subsumption_resolution,[],[f3986,f2034]) ).
fof(f3986,plain,
( ~ in(sK1,succ(sK0))
| ~ spl19_172
| spl19_238 ),
inference(backward_demodulation,[],[f2683,f1783]) ).
fof(f4024,plain,
( ~ spl19_172
| spl19_209
| ~ spl19_237 ),
inference(avatar_contradiction_clause,[],[f4023]) ).
fof(f4023,plain,
( $false
| ~ spl19_172
| spl19_209
| ~ spl19_237 ),
inference(subsumption_resolution,[],[f3985,f2181]) ).
fof(f3985,plain,
( ordinal_subset(succ(sK0),sK1)
| ~ spl19_172
| ~ spl19_237 ),
inference(backward_demodulation,[],[f2678,f1783]) ).
fof(f4017,plain,
( ~ spl19_63
| ~ spl19_172
| spl19_216 ),
inference(avatar_contradiction_clause,[],[f4016]) ).
fof(f4016,plain,
( $false
| ~ spl19_63
| ~ spl19_172
| spl19_216 ),
inference(subsumption_resolution,[],[f3979,f586]) ).
fof(f3979,plain,
( ~ ordinal_subset(sK1,sK1)
| ~ spl19_172
| spl19_216 ),
inference(backward_demodulation,[],[f2344,f1783]) ).
fof(f3961,plain,
( ~ spl19_98
| ~ spl19_166
| spl19_238 ),
inference(avatar_contradiction_clause,[],[f3960]) ).
fof(f3960,plain,
( $false
| ~ spl19_98
| ~ spl19_166
| spl19_238 ),
inference(subsumption_resolution,[],[f3349,f1755]) ).
fof(f1755,plain,
( in(sK10,sK0)
| ~ spl19_166 ),
inference(avatar_component_clause,[],[f1753]) ).
fof(f3959,plain,
( ~ spl19_98
| ~ spl19_166
| spl19_238 ),
inference(avatar_contradiction_clause,[],[f3958]) ).
fof(f3958,plain,
( $false
| ~ spl19_98
| ~ spl19_166
| spl19_238 ),
inference(subsumption_resolution,[],[f2696,f1755]) ).
fof(f2696,plain,
( ~ in(sK10,sK0)
| ~ spl19_98
| spl19_238 ),
inference(resolution,[],[f2683,f846]) ).
fof(f3956,plain,
( ~ spl19_164
| ~ spl19_174
| spl19_190
| ~ spl19_313 ),
inference(avatar_contradiction_clause,[],[f3955]) ).
fof(f3955,plain,
( $false
| ~ spl19_164
| ~ spl19_174
| spl19_190
| ~ spl19_313 ),
inference(subsumption_resolution,[],[f3901,f1921]) ).
fof(f1921,plain,
( ~ in(sK0,sK0)
| spl19_190 ),
inference(avatar_component_clause,[],[f1919]) ).
fof(f1919,plain,
( spl19_190
<=> in(sK0,sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_190])]) ).
fof(f3901,plain,
( in(sK0,sK0)
| ~ spl19_164
| ~ spl19_174
| ~ spl19_313 ),
inference(backward_demodulation,[],[f3846,f1747]) ).
fof(f1747,plain,
( sK0 = sK10
| ~ spl19_164 ),
inference(avatar_component_clause,[],[f1745]) ).
fof(f3846,plain,
( in(sK10,sK0)
| ~ spl19_174
| ~ spl19_313 ),
inference(resolution,[],[f3810,f1791]) ).
fof(f1791,plain,
( in(sK10,sK1)
| ~ spl19_174 ),
inference(avatar_component_clause,[],[f1789]) ).
fof(f3949,plain,
( ~ spl19_54
| ~ spl19_164
| ~ spl19_270 ),
inference(avatar_contradiction_clause,[],[f3948]) ).
fof(f3948,plain,
( $false
| ~ spl19_54
| ~ spl19_164
| ~ spl19_270 ),
inference(subsumption_resolution,[],[f3896,f530]) ).
fof(f3896,plain,
( in(succ(sK0),sK0)
| ~ spl19_164
| ~ spl19_270 ),
inference(backward_demodulation,[],[f3198,f1747]) ).
fof(f3930,plain,
( ~ spl19_164
| ~ spl19_200
| spl19_241 ),
inference(avatar_contradiction_clause,[],[f3929]) ).
fof(f3929,plain,
( $false
| ~ spl19_164
| ~ spl19_200
| spl19_241 ),
inference(subsumption_resolution,[],[f3883,f2005]) ).
fof(f2005,plain,
( ordinal_subset(sK0,succ(sK0))
| ~ spl19_200 ),
inference(avatar_component_clause,[],[f2004]) ).
fof(f2004,plain,
( spl19_200
<=> ordinal_subset(sK0,succ(sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_200])]) ).
fof(f3883,plain,
( ~ ordinal_subset(sK0,succ(sK0))
| ~ spl19_164
| spl19_241 ),
inference(backward_demodulation,[],[f2699,f1747]) ).
fof(f3928,plain,
( ~ spl19_28
| ~ spl19_164
| spl19_238 ),
inference(avatar_contradiction_clause,[],[f3927]) ).
fof(f3927,plain,
( $false
| ~ spl19_28
| ~ spl19_164
| spl19_238 ),
inference(subsumption_resolution,[],[f3881,f396]) ).
fof(f3881,plain,
( ~ in(sK0,succ(sK0))
| ~ spl19_164
| spl19_238 ),
inference(backward_demodulation,[],[f2683,f1747]) ).
fof(f3926,plain,
( ~ spl19_164
| spl19_199
| ~ spl19_237 ),
inference(avatar_contradiction_clause,[],[f3925]) ).
fof(f3925,plain,
( $false
| ~ spl19_164
| spl19_199
| ~ spl19_237 ),
inference(subsumption_resolution,[],[f3880,f2002]) ).
fof(f2002,plain,
( ~ ordinal_subset(succ(sK0),sK0)
| spl19_199 ),
inference(avatar_component_clause,[],[f2000]) ).
fof(f2000,plain,
( spl19_199
<=> ordinal_subset(succ(sK0),sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_199])]) ).
fof(f3880,plain,
( ordinal_subset(succ(sK0),sK0)
| ~ spl19_164
| ~ spl19_237 ),
inference(backward_demodulation,[],[f2678,f1747]) ).
fof(f3919,plain,
( spl19_4
| ~ spl19_164
| ~ spl19_218 ),
inference(avatar_contradiction_clause,[],[f3918]) ).
fof(f3918,plain,
( $false
| spl19_4
| ~ spl19_164
| ~ spl19_218 ),
inference(subsumption_resolution,[],[f3876,f278]) ).
fof(f3876,plain,
( ordinal_subset(sK0,sK1)
| ~ spl19_164
| ~ spl19_218 ),
inference(backward_demodulation,[],[f2389,f1747]) ).
fof(f3917,plain,
( ~ spl19_148
| ~ spl19_164
| spl19_216 ),
inference(avatar_contradiction_clause,[],[f3916]) ).
fof(f3916,plain,
( $false
| ~ spl19_148
| ~ spl19_164
| spl19_216 ),
inference(subsumption_resolution,[],[f3874,f1413]) ).
fof(f3874,plain,
( ~ ordinal_subset(sK1,sK0)
| ~ spl19_164
| spl19_216 ),
inference(backward_demodulation,[],[f2344,f1747]) ).
fof(f3910,plain,
( spl19_101
| ~ spl19_164
| ~ spl19_174 ),
inference(avatar_contradiction_clause,[],[f3909]) ).
fof(f3909,plain,
( $false
| spl19_101
| ~ spl19_164
| ~ spl19_174 ),
inference(subsumption_resolution,[],[f3868,f870]) ).
fof(f3868,plain,
( in(sK0,sK1)
| ~ spl19_164
| ~ spl19_174 ),
inference(backward_demodulation,[],[f1791,f1747]) ).
fof(f3908,plain,
( ~ spl19_140
| ~ spl19_164
| spl19_173 ),
inference(avatar_contradiction_clause,[],[f3907]) ).
fof(f3907,plain,
( $false
| ~ spl19_140
| ~ spl19_164
| spl19_173 ),
inference(subsumption_resolution,[],[f3867,f1149]) ).
fof(f3867,plain,
( ~ in(sK1,sK0)
| ~ spl19_164
| spl19_173 ),
inference(backward_demodulation,[],[f1786,f1747]) ).
fof(f1786,plain,
( ~ in(sK1,sK10)
| spl19_173 ),
inference(avatar_component_clause,[],[f1785]) ).
fof(f3906,plain,
( ~ spl19_164
| ~ spl19_165
| spl19_190 ),
inference(avatar_contradiction_clause,[],[f3905]) ).
fof(f3905,plain,
( $false
| ~ spl19_164
| ~ spl19_165
| spl19_190 ),
inference(subsumption_resolution,[],[f3865,f1921]) ).
fof(f3865,plain,
( in(sK0,sK0)
| ~ spl19_164
| ~ spl19_165 ),
inference(backward_demodulation,[],[f1751,f1747]) ).
fof(f3858,plain,
( ~ spl19_52
| ~ spl19_165
| ~ spl19_166 ),
inference(avatar_contradiction_clause,[],[f3857]) ).
fof(f3857,plain,
( $false
| ~ spl19_52
| ~ spl19_165
| ~ spl19_166 ),
inference(subsumption_resolution,[],[f1761,f1751]) ).
fof(f1761,plain,
( ~ in(sK0,sK10)
| ~ spl19_52
| ~ spl19_166 ),
inference(resolution,[],[f1755,f509]) ).
fof(f3856,plain,
( ~ spl19_52
| ~ spl19_165
| ~ spl19_174
| ~ spl19_313 ),
inference(avatar_contradiction_clause,[],[f3855]) ).
fof(f3855,plain,
( $false
| ~ spl19_52
| ~ spl19_165
| ~ spl19_174
| ~ spl19_313 ),
inference(subsumption_resolution,[],[f2378,f3846]) ).
fof(f3854,plain,
( ~ spl19_98
| ~ spl19_174
| spl19_238
| ~ spl19_313 ),
inference(avatar_contradiction_clause,[],[f3853]) ).
fof(f3853,plain,
( $false
| ~ spl19_98
| ~ spl19_174
| spl19_238
| ~ spl19_313 ),
inference(subsumption_resolution,[],[f2696,f3846]) ).
fof(f3852,plain,
( ~ spl19_98
| ~ spl19_174
| spl19_238
| ~ spl19_313 ),
inference(avatar_contradiction_clause,[],[f3851]) ).
fof(f3851,plain,
( $false
| ~ spl19_98
| ~ spl19_174
| spl19_238
| ~ spl19_313 ),
inference(subsumption_resolution,[],[f3349,f3846]) ).
fof(f3848,plain,
( spl19_166
| ~ spl19_174
| ~ spl19_313 ),
inference(avatar_contradiction_clause,[],[f3847]) ).
fof(f3847,plain,
( $false
| spl19_166
| ~ spl19_174
| ~ spl19_313 ),
inference(subsumption_resolution,[],[f3846,f1754]) ).
fof(f3811,plain,
( spl19_313
| ~ spl19_140
| ~ spl19_310 ),
inference(avatar_split_clause,[],[f3794,f3781,f1148,f3809]) ).
fof(f3794,plain,
( ! [X3] :
( ~ in(X3,sK1)
| in(X3,sK0) )
| ~ spl19_140
| ~ spl19_310 ),
inference(resolution,[],[f3782,f1149]) ).
fof(f3791,plain,
( spl19_312
| ~ spl19_57
| ~ spl19_308 ),
inference(avatar_split_clause,[],[f3777,f3759,f541,f3789]) ).
fof(f3789,plain,
( spl19_312
<=> ! [X5] :
( ~ in(succ(X5),sK0)
| ~ in(powerset(sK0),singleton(X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_312])]) ).
fof(f3759,plain,
( spl19_308
<=> ! [X6,X7] :
( ~ in(set_union2(X6,X7),sK0)
| ~ in(powerset(sK0),X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_308])]) ).
fof(f3777,plain,
( ! [X5] :
( ~ in(succ(X5),sK0)
| ~ in(powerset(sK0),singleton(X5)) )
| ~ spl19_57
| ~ spl19_308 ),
inference(superposition,[],[f3760,f542]) ).
fof(f3760,plain,
( ! [X6,X7] :
( ~ in(set_union2(X6,X7),sK0)
| ~ in(powerset(sK0),X7) )
| ~ spl19_308 ),
inference(avatar_component_clause,[],[f3759]) ).
fof(f3787,plain,
( spl19_311
| ~ spl19_52
| ~ spl19_145 ),
inference(avatar_split_clause,[],[f1308,f1284,f508,f3785]) ).
fof(f3785,plain,
( spl19_311
<=> ! [X6,X4,X5] :
( in(sK5(X4,X5,X6),X6)
| in(sK5(X4,X5,X6),X5)
| set_union2(X4,X5) = X6
| ~ in(X4,sK5(X4,X5,X6)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_311])]) ).
fof(f1308,plain,
( ! [X6,X4,X5] :
( in(sK5(X4,X5,X6),X6)
| in(sK5(X4,X5,X6),X5)
| set_union2(X4,X5) = X6
| ~ in(X4,sK5(X4,X5,X6)) )
| ~ spl19_52
| ~ spl19_145 ),
inference(resolution,[],[f1285,f509]) ).
fof(f3783,plain,
( spl19_310
| ~ spl19_77
| spl19_275
| ~ spl19_306 ),
inference(avatar_split_clause,[],[f3767,f3751,f3413,f674,f3781]) ).
fof(f3751,plain,
( spl19_306
<=> ! [X0,X1] :
( ~ in(X0,sK0)
| ~ in(X1,X0)
| element(X1,sK0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_306])]) ).
fof(f3767,plain,
( ! [X0,X1] :
( ~ in(X0,X1)
| ~ in(X1,sK0)
| in(X0,sK0) )
| ~ spl19_77
| spl19_275
| ~ spl19_306 ),
inference(subsumption_resolution,[],[f3766,f3415]) ).
fof(f3766,plain,
( ! [X0,X1] :
( ~ in(X0,X1)
| ~ in(X1,sK0)
| empty(sK0)
| in(X0,sK0) )
| ~ spl19_77
| ~ spl19_306 ),
inference(resolution,[],[f3752,f675]) ).
fof(f3752,plain,
( ! [X0,X1] :
( element(X1,sK0)
| ~ in(X1,X0)
| ~ in(X0,sK0) )
| ~ spl19_306 ),
inference(avatar_component_clause,[],[f3751]) ).
fof(f3765,plain,
( spl19_309
| ~ spl19_52
| ~ spl19_145 ),
inference(avatar_split_clause,[],[f1299,f1284,f508,f3763]) ).
fof(f3763,plain,
( spl19_309
<=> ! [X6,X4,X5] :
( in(sK5(X4,X5,X6),X6)
| in(sK5(X4,X5,X6),X4)
| set_union2(X4,X5) = X6
| ~ in(X5,sK5(X4,X5,X6)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_309])]) ).
fof(f1299,plain,
( ! [X6,X4,X5] :
( in(sK5(X4,X5,X6),X6)
| in(sK5(X4,X5,X6),X4)
| set_union2(X4,X5) = X6
| ~ in(X5,sK5(X4,X5,X6)) )
| ~ spl19_52
| ~ spl19_145 ),
inference(resolution,[],[f1285,f509]) ).
fof(f3761,plain,
( spl19_308
| ~ spl19_163
| ~ spl19_280 ),
inference(avatar_split_clause,[],[f3594,f3455,f1741,f3759]) ).
fof(f3594,plain,
( ! [X6,X7] :
( ~ in(set_union2(X6,X7),sK0)
| ~ in(powerset(sK0),X7) )
| ~ spl19_163
| ~ spl19_280 ),
inference(resolution,[],[f3456,f1742]) ).
fof(f3757,plain,
( spl19_307
| ~ spl19_171
| ~ spl19_280 ),
inference(avatar_split_clause,[],[f3593,f3455,f1776,f3755]) ).
fof(f3755,plain,
( spl19_307
<=> ! [X4,X5] :
( ~ in(set_union2(X4,X5),sK0)
| ~ in(powerset(sK0),X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_307])]) ).
fof(f3593,plain,
( ! [X4,X5] :
( ~ in(set_union2(X4,X5),sK0)
| ~ in(powerset(sK0),X4) )
| ~ spl19_171
| ~ spl19_280 ),
inference(resolution,[],[f3456,f1777]) ).
fof(f3753,plain,
( spl19_306
| ~ spl19_240
| ~ spl19_280 ),
inference(avatar_split_clause,[],[f3590,f3455,f2693,f3751]) ).
fof(f3590,plain,
( ! [X0,X1] :
( ~ in(X0,sK0)
| ~ in(X1,X0)
| element(X1,sK0) )
| ~ spl19_240
| ~ spl19_280 ),
inference(resolution,[],[f3456,f2694]) ).
fof(f3749,plain,
( spl19_305
| ~ spl19_52
| ~ spl19_145 ),
inference(avatar_split_clause,[],[f1290,f1284,f508,f3747]) ).
fof(f3747,plain,
( spl19_305
<=> ! [X6,X7,X8] :
( in(sK5(X6,X7,X8),X7)
| in(sK5(X6,X7,X8),X6)
| set_union2(X6,X7) = X8
| ~ in(X8,sK5(X6,X7,X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_305])]) ).
fof(f1290,plain,
( ! [X8,X6,X7] :
( in(sK5(X6,X7,X8),X7)
| in(sK5(X6,X7,X8),X6)
| set_union2(X6,X7) = X8
| ~ in(X8,sK5(X6,X7,X8)) )
| ~ spl19_52
| ~ spl19_145 ),
inference(resolution,[],[f1285,f509]) ).
fof(f3744,plain,
( spl19_304
| ~ spl19_98
| ~ spl19_292 ),
inference(avatar_split_clause,[],[f3702,f3662,f845,f3742]) ).
fof(f3742,plain,
( spl19_304
<=> ! [X4] :
( ~ in(succ(X4),sK0)
| ~ in(powerset(sK0),X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_304])]) ).
fof(f3702,plain,
( ! [X4] :
( ~ in(succ(X4),sK0)
| ~ in(powerset(sK0),X4) )
| ~ spl19_98
| ~ spl19_292 ),
inference(resolution,[],[f3663,f846]) ).
fof(f3736,plain,
( spl19_303
| ~ spl19_79
| ~ spl19_138 ),
inference(avatar_split_clause,[],[f1173,f1130,f685,f3734]) ).
fof(f3734,plain,
( spl19_303
<=> ! [X10,X7,X9,X8] :
( ~ in(sK5(X7,X8,set_union2(X9,X10)),X8)
| set_union2(X9,X10) = set_union2(X7,X8)
| ~ in(sK5(X7,X8,set_union2(X9,X10)),X10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_303])]) ).
fof(f1173,plain,
( ! [X10,X8,X9,X7] :
( ~ in(sK5(X7,X8,set_union2(X9,X10)),X8)
| set_union2(X9,X10) = set_union2(X7,X8)
| ~ in(sK5(X7,X8,set_union2(X9,X10)),X10) )
| ~ spl19_79
| ~ spl19_138 ),
inference(resolution,[],[f1131,f686]) ).
fof(f3721,plain,
( spl19_302
| ~ spl19_80
| ~ spl19_138 ),
inference(avatar_split_clause,[],[f1172,f1130,f689,f3719]) ).
fof(f3719,plain,
( spl19_302
<=> ! [X5,X4,X6,X3] :
( ~ in(sK5(X3,X4,set_union2(X5,X6)),X4)
| set_union2(X3,X4) = set_union2(X5,X6)
| ~ in(sK5(X3,X4,set_union2(X5,X6)),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_302])]) ).
fof(f1172,plain,
( ! [X3,X6,X4,X5] :
( ~ in(sK5(X3,X4,set_union2(X5,X6)),X4)
| set_union2(X3,X4) = set_union2(X5,X6)
| ~ in(sK5(X3,X4,set_union2(X5,X6)),X5) )
| ~ spl19_80
| ~ spl19_138 ),
inference(resolution,[],[f1131,f690]) ).
fof(f3711,plain,
( ~ spl19_301
| ~ spl19_280
| ~ spl19_292 ),
inference(avatar_split_clause,[],[f3706,f3662,f3455,f3708]) ).
fof(f3708,plain,
( spl19_301
<=> in(powerset(sK0),sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_301])]) ).
fof(f3706,plain,
( ~ in(powerset(sK0),sK0)
| ~ spl19_280
| ~ spl19_292 ),
inference(duplicate_literal_removal,[],[f3705]) ).
fof(f3705,plain,
( ~ in(powerset(sK0),sK0)
| ~ in(powerset(sK0),sK0)
| ~ spl19_280
| ~ spl19_292 ),
inference(resolution,[],[f3663,f3456]) ).
fof(f3698,plain,
( spl19_300
| ~ spl19_79
| ~ spl19_136 ),
inference(avatar_split_clause,[],[f1158,f1120,f685,f3696]) ).
fof(f1120,plain,
( spl19_136
<=> ! [X2,X0,X1] :
( set_union2(X0,X1) = X2
| ~ in(sK5(X0,X1,X2),X0)
| ~ in(sK5(X0,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_136])]) ).
fof(f1158,plain,
( ! [X10,X8,X9,X7] :
( ~ in(sK5(X7,X8,set_union2(X9,X10)),X7)
| set_union2(X9,X10) = set_union2(X7,X8)
| ~ in(sK5(X7,X8,set_union2(X9,X10)),X10) )
| ~ spl19_79
| ~ spl19_136 ),
inference(resolution,[],[f1121,f686]) ).
fof(f1121,plain,
( ! [X2,X0,X1] :
( ~ in(sK5(X0,X1,X2),X2)
| ~ in(sK5(X0,X1,X2),X0)
| set_union2(X0,X1) = X2 )
| ~ spl19_136 ),
inference(avatar_component_clause,[],[f1120]) ).
fof(f3694,plain,
( spl19_299
| ~ spl19_88
| ~ spl19_280 ),
inference(avatar_split_clause,[],[f3604,f3455,f761,f3692]) ).
fof(f3692,plain,
( spl19_299
<=> ! [X11] : ~ in(singleton(set_union2(X11,powerset(sK0))),sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_299])]) ).
fof(f3604,plain,
( ! [X11] : ~ in(singleton(set_union2(X11,powerset(sK0))),sK0)
| ~ spl19_88
| ~ spl19_280 ),
inference(resolution,[],[f3456,f762]) ).
fof(f3690,plain,
( ~ spl19_298
| ~ spl19_104
| ~ spl19_280 ),
inference(avatar_split_clause,[],[f3603,f3455,f881,f3687]) ).
fof(f3687,plain,
( spl19_298
<=> in(singleton(succ(succ(powerset(sK0)))),sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_298])]) ).
fof(f3603,plain,
( ~ in(singleton(succ(succ(powerset(sK0)))),sK0)
| ~ spl19_104
| ~ spl19_280 ),
inference(resolution,[],[f3456,f882]) ).
fof(f3685,plain,
( spl19_297
| ~ spl19_91
| ~ spl19_280 ),
inference(avatar_split_clause,[],[f3601,f3455,f773,f3683]) ).
fof(f3683,plain,
( spl19_297
<=> ! [X10] : ~ in(singleton(set_union2(powerset(sK0),X10)),sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_297])]) ).
fof(f3601,plain,
( ! [X10] : ~ in(singleton(set_union2(powerset(sK0),X10)),sK0)
| ~ spl19_91
| ~ spl19_280 ),
inference(resolution,[],[f3456,f774]) ).
fof(f3681,plain,
( spl19_296
| ~ spl19_80
| ~ spl19_136 ),
inference(avatar_split_clause,[],[f1157,f1120,f689,f3679]) ).
fof(f1157,plain,
( ! [X3,X6,X4,X5] :
( ~ in(sK5(X3,X4,set_union2(X5,X6)),X3)
| set_union2(X3,X4) = set_union2(X5,X6)
| ~ in(sK5(X3,X4,set_union2(X5,X6)),X5) )
| ~ spl19_80
| ~ spl19_136 ),
inference(resolution,[],[f1121,f690]) ).
fof(f3677,plain,
( spl19_295
| ~ spl19_87
| ~ spl19_280 ),
inference(avatar_split_clause,[],[f3599,f3455,f757,f3675]) ).
fof(f3675,plain,
( spl19_295
<=> ! [X9] : ~ in(succ(set_union2(X9,powerset(sK0))),sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_295])]) ).
fof(f3599,plain,
( ! [X9] : ~ in(succ(set_union2(X9,powerset(sK0))),sK0)
| ~ spl19_87
| ~ spl19_280 ),
inference(resolution,[],[f3456,f758]) ).
fof(f3673,plain,
( ~ spl19_294
| ~ spl19_102
| ~ spl19_280 ),
inference(avatar_split_clause,[],[f3598,f3455,f873,f3670]) ).
fof(f3670,plain,
( spl19_294
<=> in(succ(succ(succ(powerset(sK0)))),sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_294])]) ).
fof(f3598,plain,
( ~ in(succ(succ(succ(powerset(sK0)))),sK0)
| ~ spl19_102
| ~ spl19_280 ),
inference(resolution,[],[f3456,f874]) ).
fof(f3668,plain,
( spl19_293
| ~ spl19_90
| ~ spl19_280 ),
inference(avatar_split_clause,[],[f3596,f3455,f769,f3666]) ).
fof(f3666,plain,
( spl19_293
<=> ! [X8] : ~ in(succ(set_union2(powerset(sK0),X8)),sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_293])]) ).
fof(f3596,plain,
( ! [X8] : ~ in(succ(set_union2(powerset(sK0),X8)),sK0)
| ~ spl19_90
| ~ spl19_280 ),
inference(resolution,[],[f3456,f770]) ).
fof(f3664,plain,
( spl19_292
| ~ spl19_52
| ~ spl19_280 ),
inference(avatar_split_clause,[],[f3592,f3455,f508,f3662]) ).
fof(f3592,plain,
( ! [X3] :
( ~ in(X3,sK0)
| ~ in(powerset(sK0),X3) )
| ~ spl19_52
| ~ spl19_280 ),
inference(resolution,[],[f3456,f509]) ).
fof(f3640,plain,
( ~ spl19_291
| ~ spl19_94
| ~ spl19_280 ),
inference(avatar_split_clause,[],[f3602,f3455,f824,f3637]) ).
fof(f3637,plain,
( spl19_291
<=> in(singleton(succ(powerset(sK0))),sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_291])]) ).
fof(f3602,plain,
( ~ in(singleton(succ(powerset(sK0))),sK0)
| ~ spl19_94
| ~ spl19_280 ),
inference(resolution,[],[f3456,f825]) ).
fof(f3635,plain,
( spl19_290
| ~ spl19_70
| ~ spl19_131 ),
inference(avatar_split_clause,[],[f1098,f1086,f616,f3633]) ).
fof(f1098,plain,
( ! [X6,X7] :
( sK4(X6,singleton(X7)) = X6
| singleton(X6) = singleton(X7)
| sK4(X6,singleton(X7)) = X7 )
| ~ spl19_70
| ~ spl19_131 ),
inference(resolution,[],[f1087,f617]) ).
fof(f3631,plain,
( ~ spl19_289
| ~ spl19_93
| ~ spl19_280 ),
inference(avatar_split_clause,[],[f3597,f3455,f806,f3628]) ).
fof(f3628,plain,
( spl19_289
<=> in(succ(succ(powerset(sK0))),sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_289])]) ).
fof(f3597,plain,
( ~ in(succ(succ(powerset(sK0))),sK0)
| ~ spl19_93
| ~ spl19_280 ),
inference(resolution,[],[f3456,f807]) ).
fof(f3625,plain,
( ~ spl19_288
| ~ spl19_55
| ~ spl19_280 ),
inference(avatar_split_clause,[],[f3600,f3455,f533,f3622]) ).
fof(f3622,plain,
( spl19_288
<=> in(singleton(powerset(sK0)),sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_288])]) ).
fof(f533,plain,
( spl19_55
<=> ! [X1] : ~ in(singleton(X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_55])]) ).
fof(f3600,plain,
( ~ in(singleton(powerset(sK0)),sK0)
| ~ spl19_55
| ~ spl19_280 ),
inference(resolution,[],[f3456,f534]) ).
fof(f534,plain,
( ! [X1] : ~ in(singleton(X1),X1)
| ~ spl19_55 ),
inference(avatar_component_clause,[],[f533]) ).
fof(f3611,plain,
( ~ spl19_287
| ~ spl19_54
| ~ spl19_280 ),
inference(avatar_split_clause,[],[f3595,f3455,f529,f3608]) ).
fof(f3608,plain,
( spl19_287
<=> in(succ(powerset(sK0)),sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_287])]) ).
fof(f3595,plain,
( ~ in(succ(powerset(sK0)),sK0)
| ~ spl19_54
| ~ spl19_280 ),
inference(resolution,[],[f3456,f530]) ).
fof(f3539,plain,
( spl19_286
| ~ spl19_38
| ~ spl19_126 ),
inference(avatar_split_clause,[],[f1060,f1051,f435,f3537]) ).
fof(f3537,plain,
( spl19_286
<=> ! [X2,X3] :
( succ(X3) = X2
| in(X2,succ(X3))
| in(succ(X3),X2)
| ~ ordinal(X2)
| ~ ordinal(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_286])]) ).
fof(f1051,plain,
( spl19_126
<=> ! [X0,X1] :
( in(X1,X0)
| X0 = X1
| in(X0,X1)
| ~ ordinal(X1)
| ~ ordinal(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_126])]) ).
fof(f1060,plain,
( ! [X2,X3] :
( succ(X3) = X2
| in(X2,succ(X3))
| in(succ(X3),X2)
| ~ ordinal(X2)
| ~ ordinal(X3) )
| ~ spl19_38
| ~ spl19_126 ),
inference(resolution,[],[f1052,f436]) ).
fof(f1052,plain,
( ! [X0,X1] :
( ~ ordinal(X1)
| X0 = X1
| in(X0,X1)
| in(X1,X0)
| ~ ordinal(X0) )
| ~ spl19_126 ),
inference(avatar_component_clause,[],[f1051]) ).
fof(f3535,plain,
( spl19_285
| ~ spl19_39
| ~ spl19_279 ),
inference(avatar_split_clause,[],[f3458,f3451,f439,f3532]) ).
fof(f3532,plain,
( spl19_285
<=> empty_set = powerset(sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_285])]) ).
fof(f3458,plain,
( empty_set = powerset(sK0)
| ~ spl19_39
| ~ spl19_279 ),
inference(resolution,[],[f3453,f440]) ).
fof(f3453,plain,
( empty(powerset(sK0))
| ~ spl19_279 ),
inference(avatar_component_clause,[],[f3451]) ).
fof(f3526,plain,
( ~ spl19_284
| ~ spl19_39
| spl19_130
| ~ spl19_279 ),
inference(avatar_split_clause,[],[f3466,f3451,f1081,f439,f3523]) ).
fof(f3523,plain,
( spl19_284
<=> ordinal_subset(sK3(empty_set),sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_284])]) ).
fof(f1081,plain,
( spl19_130
<=> ordinal_subset(sK3(powerset(sK0)),sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_130])]) ).
fof(f3466,plain,
( ~ ordinal_subset(sK3(empty_set),sK0)
| ~ spl19_39
| spl19_130
| ~ spl19_279 ),
inference(backward_demodulation,[],[f1082,f3458]) ).
fof(f1082,plain,
( ~ ordinal_subset(sK3(powerset(sK0)),sK0)
| spl19_130 ),
inference(avatar_component_clause,[],[f1081]) ).
fof(f3521,plain,
( spl19_283
| ~ spl19_48
| ~ spl19_117 ),
inference(avatar_split_clause,[],[f1000,f988,f492,f3519]) ).
fof(f3519,plain,
( spl19_283
<=> ! [X6,X7] :
( in(sK2(set_union2(X6,X7)),X6)
| in(sK2(set_union2(X6,X7)),X7)
| epsilon_transitive(set_union2(X6,X7)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_283])]) ).
fof(f1000,plain,
( ! [X6,X7] :
( in(sK2(set_union2(X6,X7)),X6)
| in(sK2(set_union2(X6,X7)),X7)
| epsilon_transitive(set_union2(X6,X7)) )
| ~ spl19_48
| ~ spl19_117 ),
inference(resolution,[],[f989,f493]) ).
fof(f3517,plain,
( ~ spl19_282
| ~ spl19_39
| spl19_132
| ~ spl19_279 ),
inference(avatar_split_clause,[],[f3467,f3451,f1091,f439,f3514]) ).
fof(f1091,plain,
( spl19_132
<=> empty(sK3(powerset(sK0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_132])]) ).
fof(f3467,plain,
( ~ empty(sK3(empty_set))
| ~ spl19_39
| spl19_132
| ~ spl19_279 ),
inference(backward_demodulation,[],[f1093,f3458]) ).
fof(f1093,plain,
( ~ empty(sK3(powerset(sK0)))
| spl19_132 ),
inference(avatar_component_clause,[],[f1091]) ).
fof(f3511,plain,
( ~ spl19_281
| ~ spl19_39
| spl19_129
| ~ spl19_279 ),
inference(avatar_split_clause,[],[f3465,f3451,f1077,f439,f3508]) ).
fof(f3508,plain,
( spl19_281
<=> ordinal(sK3(empty_set)) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_281])]) ).
fof(f1077,plain,
( spl19_129
<=> ordinal(sK3(powerset(sK0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_129])]) ).
fof(f3465,plain,
( ~ ordinal(sK3(empty_set))
| ~ spl19_39
| spl19_129
| ~ spl19_279 ),
inference(backward_demodulation,[],[f1079,f3458]) ).
fof(f1079,plain,
( ~ ordinal(sK3(powerset(sK0)))
| spl19_129 ),
inference(avatar_component_clause,[],[f1077]) ).
fof(f3457,plain,
( spl19_279
| spl19_280
| ~ spl19_119
| ~ spl19_229 ),
inference(avatar_split_clause,[],[f2793,f2606,f1011,f3455,f3451]) ).
fof(f1011,plain,
( spl19_119
<=> ! [X0] :
( ~ in(X0,sK0)
| subset(X0,sK0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_119])]) ).
fof(f2793,plain,
( ! [X6] :
( in(X6,powerset(sK0))
| empty(powerset(sK0))
| ~ in(X6,sK0) )
| ~ spl19_119
| ~ spl19_229 ),
inference(resolution,[],[f2607,f1012]) ).
fof(f1012,plain,
( ! [X0] :
( subset(X0,sK0)
| ~ in(X0,sK0) )
| ~ spl19_119 ),
inference(avatar_component_clause,[],[f1011]) ).
fof(f3439,plain,
( spl19_278
| ~ spl19_40
| ~ spl19_145 ),
inference(avatar_split_clause,[],[f1324,f1284,f443,f3437]) ).
fof(f443,plain,
( spl19_40
<=> ! [X0] : set_union2(X0,X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl19_40])]) ).
fof(f1324,plain,
( ! [X4,X5] :
( X4 = X5
| in(sK5(X4,X4,X5),X5)
| in(sK5(X4,X4,X5),X4) )
| ~ spl19_40
| ~ spl19_145 ),
inference(forward_demodulation,[],[f1317,f444]) ).
fof(f444,plain,
( ! [X0] : set_union2(X0,X0) = X0
| ~ spl19_40 ),
inference(avatar_component_clause,[],[f443]) ).
fof(f1317,plain,
( ! [X4,X5] :
( in(sK5(X4,X4,X5),X5)
| in(sK5(X4,X4,X5),X4)
| set_union2(X4,X4) = X5 )
| ~ spl19_145 ),
inference(factoring,[],[f1285]) ).
fof(f3425,plain,
( spl19_277
| ~ spl19_249
| ~ spl19_267 ),
inference(avatar_split_clause,[],[f3410,f3137,f2824,f3423]) ).
fof(f3423,plain,
( spl19_277
<=> ! [X0] :
( ~ empty(X0)
| sK1 = X0
| ordinal_subset(X0,sK1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_277])]) ).
fof(f2824,plain,
( spl19_249
<=> ! [X8] :
( ordinal_subset(X8,sK1)
| ordinal_subset(sK1,X8)
| ~ empty(X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_249])]) ).
fof(f3137,plain,
( spl19_267
<=> ! [X1] :
( ~ ordinal_subset(sK1,X1)
| ~ empty(X1)
| sK1 = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_267])]) ).
fof(f3410,plain,
( ! [X0] :
( ~ empty(X0)
| sK1 = X0
| ordinal_subset(X0,sK1) )
| ~ spl19_249
| ~ spl19_267 ),
inference(duplicate_literal_removal,[],[f3394]) ).
fof(f3394,plain,
( ! [X0] :
( ~ empty(X0)
| sK1 = X0
| ordinal_subset(X0,sK1)
| ~ empty(X0) )
| ~ spl19_249
| ~ spl19_267 ),
inference(resolution,[],[f3138,f2825]) ).
fof(f2825,plain,
( ! [X8] :
( ordinal_subset(sK1,X8)
| ordinal_subset(X8,sK1)
| ~ empty(X8) )
| ~ spl19_249 ),
inference(avatar_component_clause,[],[f2824]) ).
fof(f3138,plain,
( ! [X1] :
( ~ ordinal_subset(sK1,X1)
| ~ empty(X1)
| sK1 = X1 )
| ~ spl19_267 ),
inference(avatar_component_clause,[],[f3137]) ).
fof(f3421,plain,
( spl19_276
| ~ spl19_248
| ~ spl19_266 ),
inference(avatar_split_clause,[],[f3158,f3133,f2820,f3419]) ).
fof(f3133,plain,
( spl19_266
<=> ! [X1] :
( ~ ordinal_subset(sK0,X1)
| ~ empty(X1)
| sK0 = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_266])]) ).
fof(f3158,plain,
( ! [X0] :
( ~ empty(X0)
| sK0 = X0
| ordinal_subset(X0,sK0) )
| ~ spl19_248
| ~ spl19_266 ),
inference(duplicate_literal_removal,[],[f3140]) ).
fof(f3140,plain,
( ! [X0] :
( ~ empty(X0)
| sK0 = X0
| ordinal_subset(X0,sK0)
| ~ empty(X0) )
| ~ spl19_248
| ~ spl19_266 ),
inference(resolution,[],[f3134,f2821]) ).
fof(f3134,plain,
( ! [X1] :
( ~ ordinal_subset(sK0,X1)
| ~ empty(X1)
| sK0 = X1 )
| ~ spl19_266 ),
inference(avatar_component_clause,[],[f3133]) ).
fof(f3417,plain,
( spl19_239
| spl19_270
| ~ spl19_186
| spl19_238
| ~ spl19_261 ),
inference(avatar_split_clause,[],[f3192,f3004,f2681,f1887,f3196,f2685]) ).
fof(f2685,plain,
( spl19_239
<=> sK10 = succ(sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_239])]) ).
fof(f3192,plain,
( in(succ(sK0),sK10)
| sK10 = succ(sK0)
| ~ spl19_186
| spl19_238
| ~ spl19_261 ),
inference(subsumption_resolution,[],[f3184,f2683]) ).
fof(f3184,plain,
( in(succ(sK0),sK10)
| in(sK10,succ(sK0))
| sK10 = succ(sK0)
| ~ spl19_186
| ~ spl19_261 ),
inference(resolution,[],[f3005,f1888]) ).
fof(f3416,plain,
( ~ spl19_275
| spl19_141
| ~ spl19_148
| ~ spl19_267 ),
inference(avatar_split_clause,[],[f3411,f3137,f1412,f1152,f3413]) ).
fof(f3411,plain,
( ~ empty(sK0)
| spl19_141
| ~ spl19_148
| ~ spl19_267 ),
inference(subsumption_resolution,[],[f3398,f1153]) ).
fof(f3398,plain,
( ~ empty(sK0)
| sK0 = sK1
| ~ spl19_148
| ~ spl19_267 ),
inference(resolution,[],[f3138,f1413]) ).
fof(f3393,plain,
( spl19_274
| ~ spl19_52
| ~ spl19_131 ),
inference(avatar_split_clause,[],[f1095,f1086,f508,f3391]) ).
fof(f3391,plain,
( spl19_274
<=> ! [X0,X1] :
( sK4(X0,X1) = X0
| singleton(X0) = X1
| ~ in(X1,sK4(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_274])]) ).
fof(f1095,plain,
( ! [X0,X1] :
( sK4(X0,X1) = X0
| singleton(X0) = X1
| ~ in(X1,sK4(X0,X1)) )
| ~ spl19_52
| ~ spl19_131 ),
inference(resolution,[],[f1087,f509]) ).
fof(f3348,plain,
( spl19_273
| ~ spl19_38
| ~ spl19_103 ),
inference(avatar_split_clause,[],[f943,f877,f435,f3346]) ).
fof(f943,plain,
( ! [X2,X3] :
( ~ subset(X2,succ(X3))
| ordinal_subset(X2,succ(X3))
| ~ ordinal(X2)
| ~ ordinal(X3) )
| ~ spl19_38
| ~ spl19_103 ),
inference(resolution,[],[f878,f436]) ).
fof(f3342,plain,
( spl19_272
| ~ spl19_38
| ~ spl19_100 ),
inference(avatar_split_clause,[],[f925,f853,f435,f3340]) ).
fof(f925,plain,
( ! [X2,X3] :
( ~ ordinal_subset(X2,succ(X3))
| subset(X2,succ(X3))
| ~ ordinal(X2)
| ~ ordinal(X3) )
| ~ spl19_38
| ~ spl19_100 ),
inference(resolution,[],[f854,f436]) ).
fof(f3334,plain,
( spl19_271
| ~ spl19_38
| ~ spl19_97 ),
inference(avatar_split_clause,[],[f909,f840,f435,f3332]) ).
fof(f909,plain,
( ! [X2,X3] :
( ordinal_subset(X2,succ(X3))
| ordinal_subset(succ(X3),X2)
| ~ ordinal(X2)
| ~ ordinal(X3) )
| ~ spl19_38
| ~ spl19_97 ),
inference(resolution,[],[f841,f436]) ).
fof(f3266,plain,
( ~ spl19_67
| ~ spl19_239
| spl19_241 ),
inference(avatar_contradiction_clause,[],[f3265]) ).
fof(f3265,plain,
( $false
| ~ spl19_67
| ~ spl19_239
| spl19_241 ),
inference(subsumption_resolution,[],[f3234,f605]) ).
fof(f605,plain,
( ordinal_subset(sK10,sK10)
| ~ spl19_67 ),
inference(avatar_component_clause,[],[f603]) ).
fof(f603,plain,
( spl19_67
<=> ordinal_subset(sK10,sK10) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_67])]) ).
fof(f3234,plain,
( ~ ordinal_subset(sK10,sK10)
| ~ spl19_239
| spl19_241 ),
inference(backward_demodulation,[],[f2699,f2687]) ).
fof(f2687,plain,
( sK10 = succ(sK0)
| ~ spl19_239 ),
inference(avatar_component_clause,[],[f2685]) ).
fof(f3261,plain,
( ~ spl19_210
| spl19_216
| ~ spl19_239 ),
inference(avatar_contradiction_clause,[],[f3260]) ).
fof(f3260,plain,
( $false
| ~ spl19_210
| spl19_216
| ~ spl19_239 ),
inference(subsumption_resolution,[],[f3218,f2344]) ).
fof(f3218,plain,
( ordinal_subset(sK1,sK10)
| ~ spl19_210
| ~ spl19_239 ),
inference(backward_demodulation,[],[f2191,f2687]) ).
fof(f3259,plain,
( spl19_209
| ~ spl19_218
| ~ spl19_239 ),
inference(avatar_contradiction_clause,[],[f3258]) ).
fof(f3258,plain,
( $false
| spl19_209
| ~ spl19_218
| ~ spl19_239 ),
inference(subsumption_resolution,[],[f3217,f2389]) ).
fof(f3217,plain,
( ~ ordinal_subset(sK10,sK1)
| spl19_209
| ~ spl19_239 ),
inference(backward_demodulation,[],[f2181,f2687]) ).
fof(f3256,plain,
( ~ spl19_174
| spl19_204
| ~ spl19_239 ),
inference(avatar_contradiction_clause,[],[f3255]) ).
fof(f3255,plain,
( $false
| ~ spl19_174
| spl19_204
| ~ spl19_239 ),
inference(subsumption_resolution,[],[f3214,f1791]) ).
fof(f3214,plain,
( ~ in(sK10,sK1)
| spl19_204
| ~ spl19_239 ),
inference(backward_demodulation,[],[f2037,f2687]) ).
fof(f3254,plain,
( spl19_173
| ~ spl19_203
| ~ spl19_239 ),
inference(avatar_contradiction_clause,[],[f3253]) ).
fof(f3253,plain,
( $false
| spl19_173
| ~ spl19_203
| ~ spl19_239 ),
inference(subsumption_resolution,[],[f3213,f1786]) ).
fof(f3213,plain,
( in(sK1,sK10)
| ~ spl19_203
| ~ spl19_239 ),
inference(backward_demodulation,[],[f2034,f2687]) ).
fof(f3199,plain,
( spl19_270
| ~ spl19_186
| spl19_238
| spl19_239
| ~ spl19_261 ),
inference(avatar_split_clause,[],[f3193,f3004,f2685,f2681,f1887,f3196]) ).
fof(f3193,plain,
( in(succ(sK0),sK10)
| ~ spl19_186
| spl19_238
| spl19_239
| ~ spl19_261 ),
inference(subsumption_resolution,[],[f3192,f2686]) ).
fof(f2686,plain,
( sK10 != succ(sK0)
| spl19_239 ),
inference(avatar_component_clause,[],[f2685]) ).
fof(f3181,plain,
( spl19_269
| ~ spl19_186
| spl19_232
| spl19_233
| ~ spl19_260 ),
inference(avatar_split_clause,[],[f3171,f2958,f2652,f2648,f1887,f3178]) ).
fof(f2652,plain,
( spl19_233
<=> sK8 = succ(sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_233])]) ).
fof(f3171,plain,
( in(succ(sK0),sK8)
| ~ spl19_186
| spl19_232
| spl19_233
| ~ spl19_260 ),
inference(subsumption_resolution,[],[f3170,f2653]) ).
fof(f2653,plain,
( sK8 != succ(sK0)
| spl19_233 ),
inference(avatar_component_clause,[],[f2652]) ).
fof(f3170,plain,
( in(succ(sK0),sK8)
| sK8 = succ(sK0)
| ~ spl19_186
| spl19_232
| ~ spl19_260 ),
inference(subsumption_resolution,[],[f3162,f2650]) ).
fof(f3162,plain,
( in(succ(sK0),sK8)
| in(sK8,succ(sK0))
| sK8 = succ(sK0)
| ~ spl19_186
| ~ spl19_260 ),
inference(resolution,[],[f2959,f1888]) ).
fof(f3176,plain,
( ~ spl19_268
| spl19_164
| ~ spl19_215
| ~ spl19_266 ),
inference(avatar_split_clause,[],[f3159,f3133,f2337,f1745,f3173]) ).
fof(f3159,plain,
( ~ empty(sK10)
| spl19_164
| ~ spl19_215
| ~ spl19_266 ),
inference(subsumption_resolution,[],[f3146,f1746]) ).
fof(f3146,plain,
( ~ empty(sK10)
| sK0 = sK10
| ~ spl19_215
| ~ spl19_266 ),
inference(resolution,[],[f3134,f2338]) ).
fof(f3139,plain,
( spl19_267
| ~ spl19_139
| ~ spl19_157
| ~ spl19_257 ),
inference(avatar_split_clause,[],[f2972,f2934,f1699,f1134,f3137]) ).
fof(f1699,plain,
( spl19_157
<=> ! [X0] :
( in(X0,sK1)
| sK1 = X0
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_157])]) ).
fof(f2972,plain,
( ! [X1] :
( ~ ordinal_subset(sK1,X1)
| ~ empty(X1)
| sK1 = X1 )
| ~ spl19_139
| ~ spl19_157
| ~ spl19_257 ),
inference(subsumption_resolution,[],[f2962,f1700]) ).
fof(f1700,plain,
( ! [X0] :
( ~ empty(X0)
| sK1 = X0
| in(X0,sK1) )
| ~ spl19_157 ),
inference(avatar_component_clause,[],[f1699]) ).
fof(f2962,plain,
( ! [X1] :
( ~ ordinal_subset(sK1,X1)
| ~ empty(X1)
| sK1 = X1
| ~ in(X1,sK1) )
| ~ spl19_139
| ~ spl19_257 ),
inference(resolution,[],[f2935,f1135]) ).
fof(f3135,plain,
( spl19_266
| ~ spl19_137
| ~ spl19_149
| ~ spl19_255 ),
inference(avatar_split_clause,[],[f2956,f2926,f1514,f1126,f3133]) ).
fof(f1126,plain,
( spl19_137
<=> ! [X1] :
( ~ in(X1,sK0)
| sK0 = X1
| ~ subset(sK0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_137])]) ).
fof(f1514,plain,
( spl19_149
<=> ! [X0] :
( in(X0,sK0)
| sK0 = X0
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_149])]) ).
fof(f2956,plain,
( ! [X1] :
( ~ ordinal_subset(sK0,X1)
| ~ empty(X1)
| sK0 = X1 )
| ~ spl19_137
| ~ spl19_149
| ~ spl19_255 ),
inference(subsumption_resolution,[],[f2946,f1515]) ).
fof(f1515,plain,
( ! [X0] :
( ~ empty(X0)
| sK0 = X0
| in(X0,sK0) )
| ~ spl19_149 ),
inference(avatar_component_clause,[],[f1514]) ).
fof(f2946,plain,
( ! [X1] :
( ~ ordinal_subset(sK0,X1)
| ~ empty(X1)
| sK0 = X1
| ~ in(X1,sK0) )
| ~ spl19_137
| ~ spl19_255 ),
inference(resolution,[],[f2927,f1127]) ).
fof(f1127,plain,
( ! [X1] :
( ~ subset(sK0,X1)
| sK0 = X1
| ~ in(X1,sK0) )
| ~ spl19_137 ),
inference(avatar_component_clause,[],[f1126]) ).
fof(f3100,plain,
( spl19_265
| ~ spl19_136
| ~ spl19_145 ),
inference(avatar_split_clause,[],[f1323,f1284,f1120,f3098]) ).
fof(f1323,plain,
( ! [X2,X3] :
( in(sK5(X2,X3,X2),X3)
| set_union2(X2,X3) = X2 )
| ~ spl19_136
| ~ spl19_145 ),
inference(subsumption_resolution,[],[f1316,f1121]) ).
fof(f1316,plain,
( ! [X2,X3] :
( in(sK5(X2,X3,X2),X2)
| in(sK5(X2,X3,X2),X3)
| set_union2(X2,X3) = X2 )
| ~ spl19_145 ),
inference(factoring,[],[f1285]) ).
fof(f3095,plain,
( spl19_264
| ~ spl19_138
| ~ spl19_145 ),
inference(avatar_split_clause,[],[f1322,f1284,f1130,f3093]) ).
fof(f1322,plain,
( ! [X0,X1] :
( in(sK5(X0,X1,X1),X0)
| set_union2(X0,X1) = X1 )
| ~ spl19_138
| ~ spl19_145 ),
inference(subsumption_resolution,[],[f1315,f1131]) ).
fof(f1315,plain,
( ! [X0,X1] :
( in(sK5(X0,X1,X1),X1)
| in(sK5(X0,X1,X1),X0)
| set_union2(X0,X1) = X1 )
| ~ spl19_145 ),
inference(factoring,[],[f1285]) ).
fof(f3066,plain,
( spl19_212
| ~ spl19_254
| ~ spl19_262 ),
inference(avatar_contradiction_clause,[],[f3065]) ).
fof(f3065,plain,
( $false
| spl19_212
| ~ spl19_254
| ~ spl19_262 ),
inference(subsumption_resolution,[],[f3039,f2225]) ).
fof(f3039,plain,
( ordinal_subset(sK1,empty_set)
| ~ spl19_254
| ~ spl19_262 ),
inference(backward_demodulation,[],[f2896,f3010]) ).
fof(f3010,plain,
( empty_set = succ(sK1)
| ~ spl19_262 ),
inference(avatar_component_clause,[],[f3008]) ).
fof(f3008,plain,
( spl19_262
<=> empty_set = succ(sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_262])]) ).
fof(f2896,plain,
( ordinal_subset(sK1,succ(sK1))
| ~ spl19_254 ),
inference(avatar_component_clause,[],[f2894]) ).
fof(f2894,plain,
( spl19_254
<=> ordinal_subset(sK1,succ(sK1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_254])]) ).
fof(f3064,plain,
( spl19_152
| ~ spl19_253
| ~ spl19_262 ),
inference(avatar_contradiction_clause,[],[f3063]) ).
fof(f3063,plain,
( $false
| spl19_152
| ~ spl19_253
| ~ spl19_262 ),
inference(subsumption_resolution,[],[f3038,f1597]) ).
fof(f3038,plain,
( ordinal_subset(sK0,empty_set)
| ~ spl19_253
| ~ spl19_262 ),
inference(backward_demodulation,[],[f2891,f3010]) ).
fof(f2891,plain,
( ordinal_subset(sK0,succ(sK1))
| ~ spl19_253 ),
inference(avatar_component_clause,[],[f2889]) ).
fof(f2889,plain,
( spl19_253
<=> ordinal_subset(sK0,succ(sK1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_253])]) ).
fof(f3062,plain,
( ~ spl19_155
| spl19_252
| ~ spl19_262 ),
inference(avatar_contradiction_clause,[],[f3061]) ).
fof(f3061,plain,
( $false
| ~ spl19_155
| spl19_252
| ~ spl19_262 ),
inference(subsumption_resolution,[],[f3037,f1668]) ).
fof(f3037,plain,
( ~ ordinal_subset(empty_set,sK1)
| spl19_252
| ~ spl19_262 ),
inference(backward_demodulation,[],[f2874,f3010]) ).
fof(f2874,plain,
( ~ ordinal_subset(succ(sK1),sK1)
| spl19_252 ),
inference(avatar_component_clause,[],[f2872]) ).
fof(f2872,plain,
( spl19_252
<=> ordinal_subset(succ(sK1),sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_252])]) ).
fof(f3059,plain,
( ~ spl19_154
| spl19_251
| ~ spl19_262 ),
inference(avatar_contradiction_clause,[],[f3058]) ).
fof(f3058,plain,
( $false
| ~ spl19_154
| spl19_251
| ~ spl19_262 ),
inference(subsumption_resolution,[],[f3035,f1621]) ).
fof(f3035,plain,
( ~ ordinal_subset(empty_set,sK0)
| spl19_251
| ~ spl19_262 ),
inference(backward_demodulation,[],[f2860,f3010]) ).
fof(f2860,plain,
( ~ ordinal_subset(succ(sK1),sK0)
| spl19_251 ),
inference(avatar_component_clause,[],[f2858]) ).
fof(f2858,plain,
( spl19_251
<=> ordinal_subset(succ(sK1),sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_251])]) ).
fof(f3045,plain,
( spl19_144
| ~ spl19_147
| ~ spl19_262 ),
inference(avatar_contradiction_clause,[],[f3044]) ).
fof(f3044,plain,
( $false
| spl19_144
| ~ spl19_147
| ~ spl19_262 ),
inference(subsumption_resolution,[],[f3017,f1332]) ).
fof(f3017,plain,
( ~ in(empty_set,sK0)
| spl19_144
| ~ spl19_262 ),
inference(backward_demodulation,[],[f1281,f3010]) ).
fof(f1281,plain,
( ~ in(succ(sK1),sK0)
| spl19_144 ),
inference(avatar_component_clause,[],[f1279]) ).
fof(f1279,plain,
( spl19_144
<=> in(succ(sK1),sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_144])]) ).
fof(f3043,plain,
( ~ spl19_3
| ~ spl19_46
| ~ spl19_262 ),
inference(avatar_contradiction_clause,[],[f3042]) ).
fof(f3042,plain,
( $false
| ~ spl19_3
| ~ spl19_46
| ~ spl19_262 ),
inference(subsumption_resolution,[],[f3016,f485]) ).
fof(f3016,plain,
( in(sK0,empty_set)
| ~ spl19_3
| ~ spl19_262 ),
inference(backward_demodulation,[],[f275,f3010]) ).
fof(f3015,plain,
( spl19_262
| spl19_263
| ~ spl19_201
| ~ spl19_243 ),
inference(avatar_split_clause,[],[f2753,f2717,f2020,f3012,f3008]) ).
fof(f3012,plain,
( spl19_263
<=> in(empty_set,succ(sK1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_263])]) ).
fof(f2753,plain,
( in(empty_set,succ(sK1))
| empty_set = succ(sK1)
| ~ spl19_201
| ~ spl19_243 ),
inference(resolution,[],[f2718,f2021]) ).
fof(f3006,plain,
( spl19_261
| ~ spl19_18
| ~ spl19_126 ),
inference(avatar_split_clause,[],[f1065,f1051,f348,f3004]) ).
fof(f1065,plain,
( ! [X8] :
( sK10 = X8
| in(X8,sK10)
| in(sK10,X8)
| ~ ordinal(X8) )
| ~ spl19_18
| ~ spl19_126 ),
inference(resolution,[],[f1052,f350]) ).
fof(f2960,plain,
( spl19_260
| ~ spl19_14
| ~ spl19_126 ),
inference(avatar_split_clause,[],[f1064,f1051,f328,f2958]) ).
fof(f1064,plain,
( ! [X7] :
( sK8 = X7
| in(X7,sK8)
| in(sK8,X7)
| ~ ordinal(X7) )
| ~ spl19_14
| ~ spl19_126 ),
inference(resolution,[],[f1052,f330]) ).
fof(f2944,plain,
( spl19_259
| ~ spl19_2
| ~ spl19_236 ),
inference(avatar_split_clause,[],[f2868,f2670,f268,f2942]) ).
fof(f2942,plain,
( spl19_259
<=> ! [X8] :
( ordinal_subset(sK1,X8)
| ~ subset(sK1,X8)
| ~ empty(X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_259])]) ).
fof(f2868,plain,
( ! [X8] :
( ordinal_subset(sK1,X8)
| ~ subset(sK1,X8)
| ~ empty(X8) )
| ~ spl19_2
| ~ spl19_236 ),
inference(resolution,[],[f2671,f270]) ).
fof(f2940,plain,
( spl19_258
| ~ spl19_1
| ~ spl19_236 ),
inference(avatar_split_clause,[],[f2867,f2670,f263,f2938]) ).
fof(f2938,plain,
( spl19_258
<=> ! [X7] :
( ordinal_subset(sK0,X7)
| ~ subset(sK0,X7)
| ~ empty(X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_258])]) ).
fof(f2867,plain,
( ! [X7] :
( ordinal_subset(sK0,X7)
| ~ subset(sK0,X7)
| ~ empty(X7) )
| ~ spl19_1
| ~ spl19_236 ),
inference(resolution,[],[f2671,f265]) ).
fof(f2936,plain,
( spl19_257
| ~ spl19_2
| ~ spl19_234 ),
inference(avatar_split_clause,[],[f2833,f2660,f268,f2934]) ).
fof(f2833,plain,
( ! [X8] :
( subset(sK1,X8)
| ~ ordinal_subset(sK1,X8)
| ~ empty(X8) )
| ~ spl19_2
| ~ spl19_234 ),
inference(resolution,[],[f2661,f270]) ).
fof(f2932,plain,
( spl19_256
| ~ spl19_57
| ~ spl19_117 ),
inference(avatar_split_clause,[],[f1005,f988,f541,f2930]) ).
fof(f1005,plain,
( ! [X8,X9] :
( ~ in(X9,succ(X8))
| in(X9,X8)
| in(X9,singleton(X8)) )
| ~ spl19_57
| ~ spl19_117 ),
inference(superposition,[],[f989,f542]) ).
fof(f2928,plain,
( spl19_255
| ~ spl19_1
| ~ spl19_234 ),
inference(avatar_split_clause,[],[f2832,f2660,f263,f2926]) ).
fof(f2832,plain,
( ! [X7] :
( subset(sK0,X7)
| ~ ordinal_subset(sK0,X7)
| ~ empty(X7) )
| ~ spl19_1
| ~ spl19_234 ),
inference(resolution,[],[f2661,f265]) ).
fof(f2897,plain,
( spl19_254
| ~ spl19_109
| ~ spl19_243
| spl19_252 ),
inference(avatar_split_clause,[],[f2881,f2872,f2717,f920,f2894]) ).
fof(f2881,plain,
( ordinal_subset(sK1,succ(sK1))
| ~ spl19_109
| ~ spl19_243
| spl19_252 ),
inference(subsumption_resolution,[],[f2880,f2718]) ).
fof(f2880,plain,
( ordinal_subset(sK1,succ(sK1))
| ~ ordinal(succ(sK1))
| ~ spl19_109
| spl19_252 ),
inference(resolution,[],[f2874,f921]) ).
fof(f2892,plain,
( spl19_253
| ~ spl19_108
| ~ spl19_243
| spl19_251 ),
inference(avatar_split_clause,[],[f2878,f2858,f2717,f916,f2889]) ).
fof(f2878,plain,
( ordinal_subset(sK0,succ(sK1))
| ~ spl19_108
| ~ spl19_243
| spl19_251 ),
inference(subsumption_resolution,[],[f2877,f2718]) ).
fof(f2877,plain,
( ordinal_subset(sK0,succ(sK1))
| ~ ordinal(succ(sK1))
| ~ spl19_108
| spl19_251 ),
inference(resolution,[],[f2860,f917]) ).
fof(f2875,plain,
( ~ spl19_252
| ~ spl19_27
| ~ spl19_28
| ~ spl19_178
| ~ spl19_243
| ~ spl19_247 ),
inference(avatar_split_clause,[],[f2849,f2816,f2717,f1824,f395,f391,f2872]) ).
fof(f391,plain,
( spl19_27
<=> ! [X0] : succ(X0) != X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl19_27])]) ).
fof(f2849,plain,
( ~ ordinal_subset(succ(sK1),sK1)
| ~ spl19_27
| ~ spl19_28
| ~ spl19_178
| ~ spl19_243
| ~ spl19_247 ),
inference(subsumption_resolution,[],[f2848,f392]) ).
fof(f392,plain,
( ! [X0] : succ(X0) != X0
| ~ spl19_27 ),
inference(avatar_component_clause,[],[f391]) ).
fof(f2848,plain,
( sK1 = succ(sK1)
| ~ ordinal_subset(succ(sK1),sK1)
| ~ spl19_28
| ~ spl19_178
| ~ spl19_243
| ~ spl19_247 ),
inference(subsumption_resolution,[],[f2847,f2718]) ).
fof(f2847,plain,
( ~ ordinal(succ(sK1))
| sK1 = succ(sK1)
| ~ ordinal_subset(succ(sK1),sK1)
| ~ spl19_28
| ~ spl19_178
| ~ spl19_247 ),
inference(subsumption_resolution,[],[f2841,f396]) ).
fof(f2841,plain,
( ~ in(sK1,succ(sK1))
| ~ ordinal(succ(sK1))
| sK1 = succ(sK1)
| ~ ordinal_subset(succ(sK1),sK1)
| ~ spl19_178
| ~ spl19_247 ),
inference(resolution,[],[f2817,f1825]) ).
fof(f2861,plain,
( ~ spl19_251
| ~ spl19_3
| ~ spl19_177
| spl19_206
| ~ spl19_243
| ~ spl19_247 ),
inference(avatar_split_clause,[],[f2846,f2816,f2717,f2075,f1820,f273,f2858]) ).
fof(f2075,plain,
( spl19_206
<=> sK0 = succ(sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_206])]) ).
fof(f2846,plain,
( ~ ordinal_subset(succ(sK1),sK0)
| ~ spl19_3
| ~ spl19_177
| spl19_206
| ~ spl19_243
| ~ spl19_247 ),
inference(subsumption_resolution,[],[f2845,f2077]) ).
fof(f2077,plain,
( sK0 != succ(sK1)
| spl19_206 ),
inference(avatar_component_clause,[],[f2075]) ).
fof(f2845,plain,
( sK0 = succ(sK1)
| ~ ordinal_subset(succ(sK1),sK0)
| ~ spl19_3
| ~ spl19_177
| ~ spl19_243
| ~ spl19_247 ),
inference(subsumption_resolution,[],[f2844,f2718]) ).
fof(f2844,plain,
( ~ ordinal(succ(sK1))
| sK0 = succ(sK1)
| ~ ordinal_subset(succ(sK1),sK0)
| ~ spl19_3
| ~ spl19_177
| ~ spl19_247 ),
inference(subsumption_resolution,[],[f2839,f275]) ).
fof(f2839,plain,
( ~ in(sK0,succ(sK1))
| ~ ordinal(succ(sK1))
| sK0 = succ(sK1)
| ~ ordinal_subset(succ(sK1),sK0)
| ~ spl19_177
| ~ spl19_247 ),
inference(resolution,[],[f2817,f1821]) ).
fof(f2855,plain,
( spl19_250
| ~ spl19_48
| ~ spl19_49
| ~ spl19_247 ),
inference(avatar_split_clause,[],[f2850,f2816,f496,f492,f2852]) ).
fof(f2852,plain,
( spl19_250
<=> epsilon_transitive(succ(sK1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_250])]) ).
fof(f2850,plain,
( epsilon_transitive(succ(sK1))
| ~ spl19_48
| ~ spl19_49
| ~ spl19_247 ),
inference(subsumption_resolution,[],[f2843,f493]) ).
fof(f2843,plain,
( ~ in(sK2(succ(sK1)),succ(sK1))
| epsilon_transitive(succ(sK1))
| ~ spl19_49
| ~ spl19_247 ),
inference(resolution,[],[f2817,f497]) ).
fof(f2826,plain,
( spl19_249
| ~ spl19_2
| ~ spl19_230 ),
inference(avatar_split_clause,[],[f2812,f2626,f268,f2824]) ).
fof(f2812,plain,
( ! [X8] :
( ordinal_subset(X8,sK1)
| ordinal_subset(sK1,X8)
| ~ empty(X8) )
| ~ spl19_2
| ~ spl19_230 ),
inference(resolution,[],[f2627,f270]) ).
fof(f2822,plain,
( spl19_248
| ~ spl19_1
| ~ spl19_230 ),
inference(avatar_split_clause,[],[f2811,f2626,f263,f2820]) ).
fof(f2811,plain,
( ! [X7] :
( ordinal_subset(X7,sK0)
| ordinal_subset(sK0,X7)
| ~ empty(X7) )
| ~ spl19_1
| ~ spl19_230 ),
inference(resolution,[],[f2627,f265]) ).
fof(f2818,plain,
( spl19_247
| ~ spl19_2
| ~ spl19_228 ),
inference(avatar_split_clause,[],[f2734,f2595,f268,f2816]) ).
fof(f2734,plain,
( ! [X7] :
( subset(X7,succ(sK1))
| ~ in(X7,succ(sK1)) )
| ~ spl19_2
| ~ spl19_228 ),
inference(resolution,[],[f2596,f270]) ).
fof(f2805,plain,
( spl19_246
| ~ spl19_60
| ~ spl19_243 ),
inference(avatar_split_clause,[],[f2745,f2717,f552,f2802]) ).
fof(f2802,plain,
( spl19_246
<=> ordinal_subset(succ(sK1),succ(sK1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_246])]) ).
fof(f2745,plain,
( ordinal_subset(succ(sK1),succ(sK1))
| ~ spl19_60
| ~ spl19_243 ),
inference(resolution,[],[f2718,f553]) ).
fof(f2786,plain,
( ~ spl19_34
| ~ spl19_95
| ~ spl19_244 ),
inference(avatar_contradiction_clause,[],[f2785]) ).
fof(f2785,plain,
( $false
| ~ spl19_34
| ~ spl19_95
| ~ spl19_244 ),
inference(subsumption_resolution,[],[f2771,f420]) ).
fof(f420,plain,
( ! [X3] : in(X3,singleton(X3))
| ~ spl19_34 ),
inference(avatar_component_clause,[],[f419]) ).
fof(f419,plain,
( spl19_34
<=> ! [X3] : in(X3,singleton(X3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_34])]) ).
fof(f2771,plain,
( ~ in(succ(sK1),singleton(succ(sK1)))
| ~ spl19_95
| ~ spl19_244 ),
inference(superposition,[],[f832,f2723]) ).
fof(f2723,plain,
( sK1 = succ(succ(sK1))
| ~ spl19_244 ),
inference(avatar_component_clause,[],[f2721]) ).
fof(f832,plain,
( ! [X5] : ~ in(succ(succ(X5)),singleton(X5))
| ~ spl19_95 ),
inference(avatar_component_clause,[],[f831]) ).
fof(f831,plain,
( spl19_95
<=> ! [X5] : ~ in(succ(succ(X5)),singleton(X5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_95])]) ).
fof(f2784,plain,
( ~ spl19_28
| ~ spl19_54
| ~ spl19_244 ),
inference(avatar_contradiction_clause,[],[f2783]) ).
fof(f2783,plain,
( $false
| ~ spl19_28
| ~ spl19_54
| ~ spl19_244 ),
inference(subsumption_resolution,[],[f2767,f396]) ).
fof(f2767,plain,
( ~ in(sK1,succ(sK1))
| ~ spl19_54
| ~ spl19_244 ),
inference(superposition,[],[f530,f2723]) ).
fof(f2781,plain,
( ~ spl19_28
| ~ spl19_54
| ~ spl19_244 ),
inference(avatar_contradiction_clause,[],[f2780]) ).
fof(f2780,plain,
( $false
| ~ spl19_28
| ~ spl19_54
| ~ spl19_244 ),
inference(subsumption_resolution,[],[f2763,f530]) ).
fof(f2763,plain,
( in(succ(sK1),sK1)
| ~ spl19_28
| ~ spl19_244 ),
inference(superposition,[],[f396,f2723]) ).
fof(f2779,plain,
( ~ spl19_34
| ~ spl19_95
| ~ spl19_244 ),
inference(avatar_contradiction_clause,[],[f2778]) ).
fof(f2778,plain,
( $false
| ~ spl19_34
| ~ spl19_95
| ~ spl19_244 ),
inference(subsumption_resolution,[],[f2759,f420]) ).
fof(f2759,plain,
( ~ in(sK1,singleton(sK1))
| ~ spl19_95
| ~ spl19_244 ),
inference(superposition,[],[f832,f2723]) ).
fof(f2740,plain,
( ~ spl19_2
| ~ spl19_38
| spl19_243 ),
inference(avatar_contradiction_clause,[],[f2739]) ).
fof(f2739,plain,
( $false
| ~ spl19_2
| ~ spl19_38
| spl19_243 ),
inference(subsumption_resolution,[],[f2737,f270]) ).
fof(f2737,plain,
( ~ ordinal(sK1)
| ~ spl19_38
| spl19_243 ),
inference(resolution,[],[f2719,f436]) ).
fof(f2719,plain,
( ~ ordinal(succ(sK1))
| spl19_243 ),
inference(avatar_component_clause,[],[f2717]) ).
fof(f2728,plain,
( ~ spl19_243
| spl19_244
| spl19_245
| ~ spl19_93
| ~ spl19_185 ),
inference(avatar_split_clause,[],[f2712,f1876,f806,f2725,f2721,f2717]) ).
fof(f2712,plain,
( in(sK1,succ(succ(sK1)))
| sK1 = succ(succ(sK1))
| ~ ordinal(succ(sK1))
| ~ spl19_93
| ~ spl19_185 ),
inference(resolution,[],[f1877,f807]) ).
fof(f2705,plain,
( spl19_242
| ~ spl19_32
| ~ spl19_41
| ~ spl19_126 ),
inference(avatar_split_clause,[],[f1066,f1051,f447,f411,f2703]) ).
fof(f447,plain,
( spl19_41
<=> ! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_41])]) ).
fof(f1066,plain,
( ! [X0,X1] :
( X0 = X1
| in(X1,X0)
| ~ ordinal(X0)
| ~ empty(X1) )
| ~ spl19_32
| ~ spl19_41
| ~ spl19_126 ),
inference(subsumption_resolution,[],[f1059,f448]) ).
fof(f448,plain,
( ! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) )
| ~ spl19_41 ),
inference(avatar_component_clause,[],[f447]) ).
fof(f1059,plain,
( ! [X0,X1] :
( X0 = X1
| in(X0,X1)
| in(X1,X0)
| ~ ordinal(X0)
| ~ empty(X1) )
| ~ spl19_32
| ~ spl19_126 ),
inference(resolution,[],[f1052,f412]) ).
fof(f2701,plain,
( spl19_241
| ~ spl19_18
| ~ spl19_194
| spl19_237 ),
inference(avatar_split_clause,[],[f2691,f2677,f1967,f348,f2698]) ).
fof(f1967,plain,
( spl19_194
<=> ! [X0] :
( ordinal_subset(X0,succ(sK0))
| ordinal_subset(succ(sK0),X0)
| ~ ordinal(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_194])]) ).
fof(f2691,plain,
( ordinal_subset(sK10,succ(sK0))
| ~ spl19_18
| ~ spl19_194
| spl19_237 ),
inference(subsumption_resolution,[],[f2689,f350]) ).
fof(f2689,plain,
( ordinal_subset(sK10,succ(sK0))
| ~ ordinal(sK10)
| ~ spl19_194
| spl19_237 ),
inference(resolution,[],[f2679,f1968]) ).
fof(f1968,plain,
( ! [X0] :
( ordinal_subset(succ(sK0),X0)
| ordinal_subset(X0,succ(sK0))
| ~ ordinal(X0) )
| ~ spl19_194 ),
inference(avatar_component_clause,[],[f1967]) ).
fof(f2679,plain,
( ~ ordinal_subset(succ(sK0),sK10)
| spl19_237 ),
inference(avatar_component_clause,[],[f2677]) ).
fof(f2695,plain,
( spl19_240
| ~ spl19_53
| ~ spl19_105 ),
inference(avatar_split_clause,[],[f961,f891,f512,f2693]) ).
fof(f961,plain,
( ! [X6,X7,X5] :
( element(X5,X6)
| ~ in(X5,X7)
| ~ in(X7,powerset(X6)) )
| ~ spl19_53
| ~ spl19_105 ),
inference(resolution,[],[f892,f513]) ).
fof(f2688,plain,
( ~ spl19_237
| ~ spl19_238
| spl19_239
| ~ spl19_186
| ~ spl19_189
| ~ spl19_222 ),
inference(avatar_split_clause,[],[f2453,f2435,f1900,f1887,f2685,f2681,f2677]) ).
fof(f2435,plain,
( spl19_222
<=> ! [X0] :
( ~ in(X0,succ(sK0))
| succ(sK0) = X0
| ~ subset(succ(sK0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_222])]) ).
fof(f2453,plain,
( sK10 = succ(sK0)
| ~ in(sK10,succ(sK0))
| ~ ordinal_subset(succ(sK0),sK10)
| ~ spl19_186
| ~ spl19_189
| ~ spl19_222 ),
inference(subsumption_resolution,[],[f2448,f1888]) ).
fof(f2448,plain,
( sK10 = succ(sK0)
| ~ in(sK10,succ(sK0))
| ~ ordinal_subset(succ(sK0),sK10)
| ~ ordinal(succ(sK0))
| ~ spl19_189
| ~ spl19_222 ),
inference(resolution,[],[f2436,f1901]) ).
fof(f2436,plain,
( ! [X0] :
( ~ subset(succ(sK0),X0)
| succ(sK0) = X0
| ~ in(X0,succ(sK0)) )
| ~ spl19_222 ),
inference(avatar_component_clause,[],[f2435]) ).
fof(f2672,plain,
( spl19_236
| ~ spl19_32
| ~ spl19_103 ),
inference(avatar_split_clause,[],[f942,f877,f411,f2670]) ).
fof(f942,plain,
( ! [X0,X1] :
( ~ subset(X0,X1)
| ordinal_subset(X0,X1)
| ~ ordinal(X0)
| ~ empty(X1) )
| ~ spl19_32
| ~ spl19_103 ),
inference(resolution,[],[f878,f412]) ).
fof(f2668,plain,
( spl19_235
| ~ spl19_14
| ~ spl19_194
| spl19_231 ),
inference(avatar_split_clause,[],[f2658,f2644,f1967,f328,f2665]) ).
fof(f2658,plain,
( ordinal_subset(sK8,succ(sK0))
| ~ spl19_14
| ~ spl19_194
| spl19_231 ),
inference(subsumption_resolution,[],[f2656,f330]) ).
fof(f2656,plain,
( ordinal_subset(sK8,succ(sK0))
| ~ ordinal(sK8)
| ~ spl19_194
| spl19_231 ),
inference(resolution,[],[f2646,f1968]) ).
fof(f2646,plain,
( ~ ordinal_subset(succ(sK0),sK8)
| spl19_231 ),
inference(avatar_component_clause,[],[f2644]) ).
fof(f2662,plain,
( spl19_234
| ~ spl19_32
| ~ spl19_100 ),
inference(avatar_split_clause,[],[f924,f853,f411,f2660]) ).
fof(f924,plain,
( ! [X0,X1] :
( ~ ordinal_subset(X0,X1)
| subset(X0,X1)
| ~ ordinal(X0)
| ~ empty(X1) )
| ~ spl19_32
| ~ spl19_100 ),
inference(resolution,[],[f854,f412]) ).
fof(f2655,plain,
( ~ spl19_231
| ~ spl19_232
| spl19_233
| ~ spl19_184
| ~ spl19_186
| ~ spl19_222 ),
inference(avatar_split_clause,[],[f2452,f2435,f1887,f1872,f2652,f2648,f2644]) ).
fof(f1872,plain,
( spl19_184
<=> ! [X7] :
( ~ ordinal_subset(X7,sK8)
| subset(X7,sK8)
| ~ ordinal(X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_184])]) ).
fof(f2452,plain,
( sK8 = succ(sK0)
| ~ in(sK8,succ(sK0))
| ~ ordinal_subset(succ(sK0),sK8)
| ~ spl19_184
| ~ spl19_186
| ~ spl19_222 ),
inference(subsumption_resolution,[],[f2446,f1888]) ).
fof(f2446,plain,
( sK8 = succ(sK0)
| ~ in(sK8,succ(sK0))
| ~ ordinal_subset(succ(sK0),sK8)
| ~ ordinal(succ(sK0))
| ~ spl19_184
| ~ spl19_222 ),
inference(resolution,[],[f2436,f1873]) ).
fof(f1873,plain,
( ! [X7] :
( subset(X7,sK8)
| ~ ordinal_subset(X7,sK8)
| ~ ordinal(X7) )
| ~ spl19_184 ),
inference(avatar_component_clause,[],[f1872]) ).
fof(f2628,plain,
( spl19_230
| ~ spl19_32
| ~ spl19_97 ),
inference(avatar_split_clause,[],[f908,f840,f411,f2626]) ).
fof(f908,plain,
( ! [X0,X1] :
( ordinal_subset(X0,X1)
| ordinal_subset(X1,X0)
| ~ ordinal(X0)
| ~ empty(X1) )
| ~ spl19_32
| ~ spl19_97 ),
inference(resolution,[],[f841,f412]) ).
fof(f2608,plain,
( spl19_229
| ~ spl19_64
| ~ spl19_77 ),
inference(avatar_split_clause,[],[f708,f674,f589,f2606]) ).
fof(f708,plain,
( ! [X3,X4] :
( empty(powerset(X3))
| in(X4,powerset(X3))
| ~ subset(X4,X3) )
| ~ spl19_64
| ~ spl19_77 ),
inference(resolution,[],[f675,f590]) ).
fof(f2597,plain,
( spl19_228
| ~ spl19_36
| ~ spl19_74 ),
inference(avatar_split_clause,[],[f694,f662,f427,f2595]) ).
fof(f427,plain,
( spl19_36
<=> ! [X0] :
( epsilon_transitive(succ(X0))
| ~ ordinal(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_36])]) ).
fof(f694,plain,
( ! [X4,X5] :
( ~ in(X4,succ(X5))
| subset(X4,succ(X5))
| ~ ordinal(X5) )
| ~ spl19_36
| ~ spl19_74 ),
inference(resolution,[],[f663,f428]) ).
fof(f428,plain,
( ! [X0] :
( epsilon_transitive(succ(X0))
| ~ ordinal(X0) )
| ~ spl19_36 ),
inference(avatar_component_clause,[],[f427]) ).
fof(f2586,plain,
( spl19_227
| ~ spl19_64
| ~ spl19_105 ),
inference(avatar_split_clause,[],[f960,f891,f589,f2584]) ).
fof(f960,plain,
( ! [X2,X3,X4] :
( element(X2,X3)
| ~ in(X2,X4)
| ~ subset(X4,X3) )
| ~ spl19_64
| ~ spl19_105 ),
inference(resolution,[],[f892,f590]) ).
fof(f2553,plain,
( ~ spl19_65
| ~ spl19_225
| spl19_226 ),
inference(avatar_contradiction_clause,[],[f2552]) ).
fof(f2552,plain,
( $false
| ~ spl19_65
| ~ spl19_225
| spl19_226 ),
inference(subsumption_resolution,[],[f2517,f595]) ).
fof(f595,plain,
( ordinal_subset(empty_set,empty_set)
| ~ spl19_65 ),
inference(avatar_component_clause,[],[f593]) ).
fof(f593,plain,
( spl19_65
<=> ordinal_subset(empty_set,empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_65])]) ).
fof(f2517,plain,
( ~ ordinal_subset(empty_set,empty_set)
| ~ spl19_225
| spl19_226 ),
inference(backward_demodulation,[],[f2486,f2465]) ).
fof(f2465,plain,
( empty_set = succ(sK0)
| ~ spl19_225 ),
inference(avatar_component_clause,[],[f2463]) ).
fof(f2463,plain,
( spl19_225
<=> empty_set = succ(sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_225])]) ).
fof(f2486,plain,
( ~ ordinal_subset(empty_set,succ(sK0))
| spl19_226 ),
inference(avatar_component_clause,[],[f2485]) ).
fof(f2551,plain,
( ~ spl19_46
| ~ spl19_224
| ~ spl19_225 ),
inference(avatar_contradiction_clause,[],[f2550]) ).
fof(f2550,plain,
( $false
| ~ spl19_46
| ~ spl19_224
| ~ spl19_225 ),
inference(subsumption_resolution,[],[f2516,f485]) ).
fof(f2516,plain,
( in(empty_set,empty_set)
| ~ spl19_224
| ~ spl19_225 ),
inference(backward_demodulation,[],[f2460,f2465]) ).
fof(f2547,plain,
( ~ spl19_83
| ~ spl19_106
| spl19_221
| ~ spl19_225 ),
inference(avatar_contradiction_clause,[],[f2546]) ).
fof(f2546,plain,
( $false
| ~ spl19_83
| ~ spl19_106
| spl19_221
| ~ spl19_225 ),
inference(subsumption_resolution,[],[f2512,f902]) ).
fof(f2512,plain,
( ~ empty(sK3(powerset(empty_set)))
| spl19_221
| ~ spl19_225 ),
inference(backward_demodulation,[],[f2426,f2465]) ).
fof(f2426,plain,
( ~ empty(sK3(powerset(succ(sK0))))
| spl19_221 ),
inference(avatar_component_clause,[],[f2424]) ).
fof(f2424,plain,
( spl19_221
<=> empty(sK3(powerset(succ(sK0)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_221])]) ).
fof(f2544,plain,
( ~ spl19_210
| spl19_212
| ~ spl19_225 ),
inference(avatar_contradiction_clause,[],[f2543]) ).
fof(f2543,plain,
( $false
| ~ spl19_210
| spl19_212
| ~ spl19_225 ),
inference(subsumption_resolution,[],[f2508,f2225]) ).
fof(f2508,plain,
( ordinal_subset(sK1,empty_set)
| ~ spl19_210
| ~ spl19_225 ),
inference(backward_demodulation,[],[f2191,f2465]) ).
fof(f2542,plain,
( ~ spl19_155
| spl19_209
| ~ spl19_225 ),
inference(avatar_contradiction_clause,[],[f2541]) ).
fof(f2541,plain,
( $false
| ~ spl19_155
| spl19_209
| ~ spl19_225 ),
inference(subsumption_resolution,[],[f2507,f1668]) ).
fof(f2507,plain,
( ~ ordinal_subset(empty_set,sK1)
| spl19_209
| ~ spl19_225 ),
inference(backward_demodulation,[],[f2181,f2465]) ).
fof(f2539,plain,
( ~ spl19_151
| spl19_204
| ~ spl19_225 ),
inference(avatar_contradiction_clause,[],[f2538]) ).
fof(f2538,plain,
( $false
| ~ spl19_151
| spl19_204
| ~ spl19_225 ),
inference(subsumption_resolution,[],[f2504,f1537]) ).
fof(f2504,plain,
( ~ in(empty_set,sK1)
| spl19_204
| ~ spl19_225 ),
inference(backward_demodulation,[],[f2037,f2465]) ).
fof(f2537,plain,
( ~ spl19_46
| ~ spl19_203
| ~ spl19_225 ),
inference(avatar_contradiction_clause,[],[f2536]) ).
fof(f2536,plain,
( $false
| ~ spl19_46
| ~ spl19_203
| ~ spl19_225 ),
inference(subsumption_resolution,[],[f2503,f485]) ).
fof(f2503,plain,
( in(sK1,empty_set)
| ~ spl19_203
| ~ spl19_225 ),
inference(backward_demodulation,[],[f2034,f2465]) ).
fof(f2535,plain,
( spl19_152
| ~ spl19_200
| ~ spl19_225 ),
inference(avatar_contradiction_clause,[],[f2534]) ).
fof(f2534,plain,
( $false
| spl19_152
| ~ spl19_200
| ~ spl19_225 ),
inference(subsumption_resolution,[],[f2501,f1597]) ).
fof(f2501,plain,
( ordinal_subset(sK0,empty_set)
| ~ spl19_200
| ~ spl19_225 ),
inference(backward_demodulation,[],[f2005,f2465]) ).
fof(f2533,plain,
( ~ spl19_154
| spl19_199
| ~ spl19_225 ),
inference(avatar_contradiction_clause,[],[f2532]) ).
fof(f2532,plain,
( $false
| ~ spl19_154
| spl19_199
| ~ spl19_225 ),
inference(subsumption_resolution,[],[f2500,f1621]) ).
fof(f2500,plain,
( ~ ordinal_subset(empty_set,sK0)
| spl19_199
| ~ spl19_225 ),
inference(backward_demodulation,[],[f2002,f2465]) ).
fof(f2521,plain,
( spl19_153
| ~ spl19_188
| ~ spl19_225 ),
inference(avatar_contradiction_clause,[],[f2520]) ).
fof(f2520,plain,
( $false
| spl19_153
| ~ spl19_188
| ~ spl19_225 ),
inference(subsumption_resolution,[],[f2492,f1602]) ).
fof(f1602,plain,
( ~ in(sK0,succ(empty_set))
| spl19_153 ),
inference(avatar_component_clause,[],[f1601]) ).
fof(f1601,plain,
( spl19_153
<=> in(sK0,succ(empty_set)) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_153])]) ).
fof(f2492,plain,
( in(sK0,succ(empty_set))
| ~ spl19_188
| ~ spl19_225 ),
inference(backward_demodulation,[],[f1897,f2465]) ).
fof(f2488,plain,
( spl19_226
| ~ spl19_8
| ~ spl19_194
| spl19_223 ),
inference(avatar_split_clause,[],[f2474,f2455,f1967,f298,f2485]) ).
fof(f2474,plain,
( ordinal_subset(empty_set,succ(sK0))
| ~ spl19_8
| ~ spl19_194
| spl19_223 ),
inference(subsumption_resolution,[],[f2472,f300]) ).
fof(f2472,plain,
( ordinal_subset(empty_set,succ(sK0))
| ~ ordinal(empty_set)
| ~ spl19_194
| spl19_223 ),
inference(resolution,[],[f2457,f1968]) ).
fof(f2477,plain,
( ~ spl19_98
| ~ spl19_147
| spl19_224 ),
inference(avatar_contradiction_clause,[],[f2476]) ).
fof(f2476,plain,
( $false
| ~ spl19_98
| ~ spl19_147
| spl19_224 ),
inference(subsumption_resolution,[],[f2475,f1332]) ).
fof(f2475,plain,
( ~ in(empty_set,sK0)
| ~ spl19_98
| spl19_224 ),
inference(resolution,[],[f2461,f846]) ).
fof(f2461,plain,
( ~ in(empty_set,succ(sK0))
| spl19_224 ),
inference(avatar_component_clause,[],[f2459]) ).
fof(f2466,plain,
( ~ spl19_223
| ~ spl19_224
| spl19_225
| ~ spl19_181
| ~ spl19_186
| ~ spl19_222 ),
inference(avatar_split_clause,[],[f2451,f2435,f1887,f1851,f2463,f2459,f2455]) ).
fof(f1851,plain,
( spl19_181
<=> ! [X4] :
( ~ ordinal_subset(X4,empty_set)
| subset(X4,empty_set)
| ~ ordinal(X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_181])]) ).
fof(f2451,plain,
( empty_set = succ(sK0)
| ~ in(empty_set,succ(sK0))
| ~ ordinal_subset(succ(sK0),empty_set)
| ~ spl19_181
| ~ spl19_186
| ~ spl19_222 ),
inference(subsumption_resolution,[],[f2441,f1888]) ).
fof(f2441,plain,
( empty_set = succ(sK0)
| ~ in(empty_set,succ(sK0))
| ~ ordinal_subset(succ(sK0),empty_set)
| ~ ordinal(succ(sK0))
| ~ spl19_181
| ~ spl19_222 ),
inference(resolution,[],[f2436,f1852]) ).
fof(f1852,plain,
( ! [X4] :
( subset(X4,empty_set)
| ~ ordinal_subset(X4,empty_set)
| ~ ordinal(X4) )
| ~ spl19_181 ),
inference(avatar_component_clause,[],[f1851]) ).
fof(f2437,plain,
( spl19_222
| ~ spl19_89
| ~ spl19_207 ),
inference(avatar_split_clause,[],[f2152,f2138,f765,f2435]) ).
fof(f2138,plain,
( spl19_207
<=> ! [X4] :
( subset(X4,succ(sK0))
| ~ in(X4,succ(sK0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_207])]) ).
fof(f2152,plain,
( ! [X0] :
( ~ in(X0,succ(sK0))
| succ(sK0) = X0
| ~ subset(succ(sK0),X0) )
| ~ spl19_89
| ~ spl19_207 ),
inference(resolution,[],[f2139,f766]) ).
fof(f2139,plain,
( ! [X4] :
( subset(X4,succ(sK0))
| ~ in(X4,succ(sK0)) )
| ~ spl19_207 ),
inference(avatar_component_clause,[],[f2138]) ).
fof(f2427,plain,
( ~ spl19_221
| ~ spl19_32
| spl19_219 ),
inference(avatar_split_clause,[],[f2422,f2408,f411,f2424]) ).
fof(f2408,plain,
( spl19_219
<=> ordinal(sK3(powerset(succ(sK0)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_219])]) ).
fof(f2422,plain,
( ~ empty(sK3(powerset(succ(sK0))))
| ~ spl19_32
| spl19_219 ),
inference(resolution,[],[f2410,f412]) ).
fof(f2410,plain,
( ~ ordinal(sK3(powerset(succ(sK0))))
| spl19_219 ),
inference(avatar_component_clause,[],[f2408]) ).
fof(f2415,plain,
( ~ spl19_219
| spl19_220
| ~ spl19_72
| ~ spl19_197 ),
inference(avatar_split_clause,[],[f2025,f1979,f645,f2412,f2408]) ).
fof(f2412,plain,
( spl19_220
<=> ordinal_subset(sK3(powerset(succ(sK0))),succ(sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_220])]) ).
fof(f1979,plain,
( spl19_197
<=> ! [X2] :
( ~ subset(X2,succ(sK0))
| ordinal_subset(X2,succ(sK0))
| ~ ordinal(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_197])]) ).
fof(f2025,plain,
( ordinal_subset(sK3(powerset(succ(sK0))),succ(sK0))
| ~ ordinal(sK3(powerset(succ(sK0))))
| ~ spl19_72
| ~ spl19_197 ),
inference(resolution,[],[f1980,f646]) ).
fof(f1980,plain,
( ! [X2] :
( ~ subset(X2,succ(sK0))
| ordinal_subset(X2,succ(sK0))
| ~ ordinal(X2) )
| ~ spl19_197 ),
inference(avatar_component_clause,[],[f1979]) ).
fof(f2406,plain,
( ~ spl19_18
| ~ spl19_109
| spl19_216
| spl19_218 ),
inference(avatar_contradiction_clause,[],[f2405]) ).
fof(f2405,plain,
( $false
| ~ spl19_18
| ~ spl19_109
| spl19_216
| spl19_218 ),
inference(subsumption_resolution,[],[f2404,f350]) ).
fof(f2404,plain,
( ~ ordinal(sK10)
| ~ spl19_109
| spl19_216
| spl19_218 ),
inference(subsumption_resolution,[],[f2397,f2344]) ).
fof(f2403,plain,
( ~ spl19_18
| ~ spl19_128
| ~ spl19_174
| spl19_218 ),
inference(avatar_contradiction_clause,[],[f2402]) ).
fof(f2402,plain,
( $false
| ~ spl19_18
| ~ spl19_128
| ~ spl19_174
| spl19_218 ),
inference(subsumption_resolution,[],[f2401,f350]) ).
fof(f2401,plain,
( ~ ordinal(sK10)
| ~ spl19_128
| ~ spl19_174
| spl19_218 ),
inference(subsumption_resolution,[],[f2396,f1791]) ).
fof(f2396,plain,
( ~ in(sK10,sK1)
| ~ ordinal(sK10)
| ~ spl19_128
| spl19_218 ),
inference(resolution,[],[f2390,f1073]) ).
fof(f1073,plain,
( ! [X0] :
( ordinal_subset(X0,sK1)
| ~ in(X0,sK1)
| ~ ordinal(X0) )
| ~ spl19_128 ),
inference(avatar_component_clause,[],[f1072]) ).
fof(f1072,plain,
( spl19_128
<=> ! [X0] :
( ~ in(X0,sK1)
| ordinal_subset(X0,sK1)
| ~ ordinal(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_128])]) ).
fof(f2400,plain,
( ~ spl19_2
| ~ spl19_179
| spl19_216
| spl19_218 ),
inference(avatar_contradiction_clause,[],[f2399]) ).
fof(f2399,plain,
( $false
| ~ spl19_2
| ~ spl19_179
| spl19_216
| spl19_218 ),
inference(subsumption_resolution,[],[f2398,f270]) ).
fof(f2398,plain,
( ~ ordinal(sK1)
| ~ spl19_179
| spl19_216
| spl19_218 ),
inference(subsumption_resolution,[],[f2395,f2344]) ).
fof(f2395,plain,
( ordinal_subset(sK1,sK10)
| ~ ordinal(sK1)
| ~ spl19_179
| spl19_218 ),
inference(resolution,[],[f2390,f1829]) ).
fof(f1829,plain,
( ! [X8] :
( ordinal_subset(sK10,X8)
| ordinal_subset(X8,sK10)
| ~ ordinal(X8) )
| ~ spl19_179 ),
inference(avatar_component_clause,[],[f1828]) ).
fof(f1828,plain,
( spl19_179
<=> ! [X8] :
( ordinal_subset(X8,sK10)
| ordinal_subset(sK10,X8)
| ~ ordinal(X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_179])]) ).
fof(f2391,plain,
( ~ spl19_218
| ~ spl19_216
| ~ spl19_2
| ~ spl19_18
| spl19_172
| ~ spl19_178
| ~ spl19_189 ),
inference(avatar_split_clause,[],[f2268,f1900,f1824,f1781,f348,f268,f2342,f2388]) ).
fof(f2386,plain,
( ~ spl19_166
| ~ spl19_18
| ~ spl19_121
| spl19_217 ),
inference(avatar_split_clause,[],[f2376,f2360,f1022,f348,f1753]) ).
fof(f1022,plain,
( spl19_121
<=> ! [X0] :
( ~ in(X0,sK0)
| ordinal_subset(X0,sK0)
| ~ ordinal(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_121])]) ).
fof(f2376,plain,
( ~ in(sK10,sK0)
| ~ spl19_18
| ~ spl19_121
| spl19_217 ),
inference(subsumption_resolution,[],[f2365,f350]) ).
fof(f2365,plain,
( ~ in(sK10,sK0)
| ~ ordinal(sK10)
| ~ spl19_121
| spl19_217 ),
inference(resolution,[],[f2362,f1023]) ).
fof(f1023,plain,
( ! [X0] :
( ordinal_subset(X0,sK0)
| ~ in(X0,sK0)
| ~ ordinal(X0) )
| ~ spl19_121 ),
inference(avatar_component_clause,[],[f1022]) ).
fof(f2379,plain,
( spl19_215
| ~ spl19_18
| ~ spl19_108
| spl19_217 ),
inference(avatar_split_clause,[],[f2377,f2360,f916,f348,f2337]) ).
fof(f2375,plain,
( ~ spl19_18
| ~ spl19_108
| spl19_215
| spl19_217 ),
inference(avatar_contradiction_clause,[],[f2374]) ).
fof(f2374,plain,
( $false
| ~ spl19_18
| ~ spl19_108
| spl19_215
| spl19_217 ),
inference(subsumption_resolution,[],[f2373,f350]) ).
fof(f2373,plain,
( ~ ordinal(sK10)
| ~ spl19_108
| spl19_215
| spl19_217 ),
inference(subsumption_resolution,[],[f2366,f2339]) ).
fof(f2339,plain,
( ~ ordinal_subset(sK0,sK10)
| spl19_215 ),
inference(avatar_component_clause,[],[f2337]) ).
fof(f2372,plain,
( ~ spl19_18
| ~ spl19_121
| ~ spl19_166
| spl19_217 ),
inference(avatar_contradiction_clause,[],[f2371]) ).
fof(f2371,plain,
( $false
| ~ spl19_18
| ~ spl19_121
| ~ spl19_166
| spl19_217 ),
inference(subsumption_resolution,[],[f2370,f350]) ).
fof(f2370,plain,
( ~ ordinal(sK10)
| ~ spl19_121
| ~ spl19_166
| spl19_217 ),
inference(subsumption_resolution,[],[f2365,f1755]) ).
fof(f2369,plain,
( ~ spl19_1
| ~ spl19_179
| spl19_215
| spl19_217 ),
inference(avatar_contradiction_clause,[],[f2368]) ).
fof(f2368,plain,
( $false
| ~ spl19_1
| ~ spl19_179
| spl19_215
| spl19_217 ),
inference(subsumption_resolution,[],[f2367,f265]) ).
fof(f2367,plain,
( ~ ordinal(sK0)
| ~ spl19_179
| spl19_215
| spl19_217 ),
inference(subsumption_resolution,[],[f2364,f2339]) ).
fof(f2364,plain,
( ordinal_subset(sK0,sK10)
| ~ ordinal(sK0)
| ~ spl19_179
| spl19_217 ),
inference(resolution,[],[f2362,f1829]) ).
fof(f2363,plain,
( ~ spl19_217
| ~ spl19_215
| ~ spl19_1
| ~ spl19_18
| spl19_164
| ~ spl19_177
| ~ spl19_189 ),
inference(avatar_split_clause,[],[f2262,f1900,f1820,f1745,f348,f263,f2337,f2360]) ).
fof(f2262,plain,
( ~ ordinal_subset(sK0,sK10)
| ~ ordinal_subset(sK10,sK0)
| ~ spl19_1
| ~ spl19_18
| spl19_164
| ~ spl19_177
| ~ spl19_189 ),
inference(subsumption_resolution,[],[f2261,f1746]) ).
fof(f2346,plain,
( ~ spl19_170
| ~ spl19_14
| ~ spl19_128
| spl19_214 ),
inference(avatar_split_clause,[],[f2284,f2250,f1072,f328,f1771]) ).
fof(f2284,plain,
( ~ in(sK8,sK1)
| ~ spl19_14
| ~ spl19_128
| spl19_214 ),
inference(subsumption_resolution,[],[f2273,f330]) ).
fof(f2273,plain,
( ~ in(sK8,sK1)
| ~ ordinal(sK8)
| ~ spl19_128
| spl19_214 ),
inference(resolution,[],[f2252,f1073]) ).
fof(f2345,plain,
( ~ spl19_216
| ~ spl19_2
| ~ spl19_139
| spl19_172
| ~ spl19_174
| ~ spl19_189 ),
inference(avatar_split_clause,[],[f2271,f1900,f1789,f1781,f1134,f268,f2342]) ).
fof(f2271,plain,
( ~ ordinal_subset(sK1,sK10)
| ~ spl19_2
| ~ spl19_139
| spl19_172
| ~ spl19_174
| ~ spl19_189 ),
inference(subsumption_resolution,[],[f2270,f1791]) ).
fof(f2340,plain,
( ~ spl19_215
| ~ spl19_1
| ~ spl19_137
| spl19_164
| ~ spl19_166
| ~ spl19_189 ),
inference(avatar_split_clause,[],[f2265,f1900,f1753,f1745,f1126,f263,f2337]) ).
fof(f2265,plain,
( ~ ordinal_subset(sK0,sK10)
| ~ spl19_1
| ~ spl19_137
| spl19_164
| ~ spl19_166
| ~ spl19_189 ),
inference(subsumption_resolution,[],[f2264,f1755]) ).
fof(f2264,plain,
( ~ ordinal_subset(sK0,sK10)
| ~ in(sK10,sK0)
| ~ spl19_1
| ~ spl19_137
| spl19_164
| ~ spl19_189 ),
inference(subsumption_resolution,[],[f2263,f1746]) ).
fof(f2263,plain,
( ~ ordinal_subset(sK0,sK10)
| sK0 = sK10
| ~ in(sK10,sK0)
| ~ spl19_1
| ~ spl19_137
| ~ spl19_189 ),
inference(subsumption_resolution,[],[f2256,f265]) ).
fof(f2256,plain,
( ~ ordinal_subset(sK0,sK10)
| ~ ordinal(sK0)
| sK0 = sK10
| ~ in(sK10,sK0)
| ~ spl19_137
| ~ spl19_189 ),
inference(resolution,[],[f1901,f1127]) ).
fof(f2334,plain,
( spl19_213
| ~ spl19_14
| ~ spl19_109
| spl19_214 ),
inference(avatar_split_clause,[],[f2285,f2250,f920,f328,f2243]) ).
fof(f2285,plain,
( ordinal_subset(sK1,sK8)
| ~ spl19_14
| ~ spl19_109
| spl19_214 ),
inference(subsumption_resolution,[],[f2274,f330]) ).
fof(f2274,plain,
( ordinal_subset(sK1,sK8)
| ~ ordinal(sK8)
| ~ spl19_109
| spl19_214 ),
inference(resolution,[],[f2252,f921]) ).
fof(f2326,plain,
( ~ spl19_63
| ~ spl19_168
| spl19_214 ),
inference(avatar_contradiction_clause,[],[f2325]) ).
fof(f2325,plain,
( $false
| ~ spl19_63
| ~ spl19_168
| spl19_214 ),
inference(subsumption_resolution,[],[f2304,f586]) ).
fof(f2304,plain,
( ~ ordinal_subset(sK1,sK1)
| ~ spl19_168
| spl19_214 ),
inference(backward_demodulation,[],[f2252,f1765]) ).
fof(f1765,plain,
( sK1 = sK8
| ~ spl19_168 ),
inference(avatar_component_clause,[],[f1763]) ).
fof(f1763,plain,
( spl19_168
<=> sK1 = sK8 ),
introduced(avatar_definition,[new_symbols(naming,[spl19_168])]) ).
fof(f2320,plain,
( spl19_4
| ~ spl19_168
| ~ spl19_182 ),
inference(avatar_contradiction_clause,[],[f2319]) ).
fof(f2319,plain,
( $false
| spl19_4
| ~ spl19_168
| ~ spl19_182 ),
inference(subsumption_resolution,[],[f2300,f278]) ).
fof(f2300,plain,
( ordinal_subset(sK0,sK1)
| ~ spl19_168
| ~ spl19_182 ),
inference(backward_demodulation,[],[f1857,f1765]) ).
fof(f2318,plain,
( ~ spl19_148
| ~ spl19_168
| spl19_180 ),
inference(avatar_contradiction_clause,[],[f2317]) ).
fof(f2317,plain,
( $false
| ~ spl19_148
| ~ spl19_168
| spl19_180 ),
inference(subsumption_resolution,[],[f2299,f1413]) ).
fof(f2299,plain,
( ~ ordinal_subset(sK1,sK0)
| ~ spl19_168
| spl19_180 ),
inference(backward_demodulation,[],[f1845,f1765]) ).
fof(f2315,plain,
( ~ spl19_140
| spl19_162
| ~ spl19_168 ),
inference(avatar_contradiction_clause,[],[f2314]) ).
fof(f2314,plain,
( $false
| ~ spl19_140
| spl19_162
| ~ spl19_168 ),
inference(subsumption_resolution,[],[f2296,f1149]) ).
fof(f2296,plain,
( ~ in(sK1,sK0)
| spl19_162
| ~ spl19_168 ),
inference(backward_demodulation,[],[f1736,f1765]) ).
fof(f2313,plain,
( spl19_101
| ~ spl19_161
| ~ spl19_168 ),
inference(avatar_contradiction_clause,[],[f2312]) ).
fof(f2312,plain,
( $false
| spl19_101
| ~ spl19_161
| ~ spl19_168 ),
inference(subsumption_resolution,[],[f2295,f870]) ).
fof(f2295,plain,
( in(sK0,sK1)
| ~ spl19_161
| ~ spl19_168 ),
inference(backward_demodulation,[],[f1733,f1765]) ).
fof(f2283,plain,
( ~ spl19_14
| ~ spl19_109
| spl19_213
| spl19_214 ),
inference(avatar_contradiction_clause,[],[f2282]) ).
fof(f2282,plain,
( $false
| ~ spl19_14
| ~ spl19_109
| spl19_213
| spl19_214 ),
inference(subsumption_resolution,[],[f2281,f330]) ).
fof(f2281,plain,
( ~ ordinal(sK8)
| ~ spl19_109
| spl19_213
| spl19_214 ),
inference(subsumption_resolution,[],[f2274,f2245]) ).
fof(f2245,plain,
( ~ ordinal_subset(sK1,sK8)
| spl19_213 ),
inference(avatar_component_clause,[],[f2243]) ).
fof(f2280,plain,
( ~ spl19_14
| ~ spl19_128
| ~ spl19_170
| spl19_214 ),
inference(avatar_contradiction_clause,[],[f2279]) ).
fof(f2279,plain,
( $false
| ~ spl19_14
| ~ spl19_128
| ~ spl19_170
| spl19_214 ),
inference(subsumption_resolution,[],[f2278,f330]) ).
fof(f2278,plain,
( ~ ordinal(sK8)
| ~ spl19_128
| ~ spl19_170
| spl19_214 ),
inference(subsumption_resolution,[],[f2273,f1773]) ).
fof(f1773,plain,
( in(sK8,sK1)
| ~ spl19_170 ),
inference(avatar_component_clause,[],[f1771]) ).
fof(f2277,plain,
( ~ spl19_2
| ~ spl19_176
| spl19_213
| spl19_214 ),
inference(avatar_contradiction_clause,[],[f2276]) ).
fof(f2276,plain,
( $false
| ~ spl19_2
| ~ spl19_176
| spl19_213
| spl19_214 ),
inference(subsumption_resolution,[],[f2275,f270]) ).
fof(f2275,plain,
( ~ ordinal(sK1)
| ~ spl19_176
| spl19_213
| spl19_214 ),
inference(subsumption_resolution,[],[f2272,f2245]) ).
fof(f2272,plain,
( ordinal_subset(sK1,sK8)
| ~ ordinal(sK1)
| ~ spl19_176
| spl19_214 ),
inference(resolution,[],[f2252,f1801]) ).
fof(f1801,plain,
( ! [X7] :
( ordinal_subset(sK8,X7)
| ordinal_subset(X7,sK8)
| ~ ordinal(X7) )
| ~ spl19_176 ),
inference(avatar_component_clause,[],[f1800]) ).
fof(f1800,plain,
( spl19_176
<=> ! [X7] :
( ordinal_subset(X7,sK8)
| ordinal_subset(sK8,X7)
| ~ ordinal(X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_176])]) ).
fof(f2253,plain,
( ~ spl19_214
| ~ spl19_213
| ~ spl19_2
| ~ spl19_14
| spl19_168
| ~ spl19_178
| ~ spl19_184 ),
inference(avatar_split_clause,[],[f2238,f1872,f1824,f1763,f328,f268,f2243,f2250]) ).
fof(f2238,plain,
( ~ ordinal_subset(sK1,sK8)
| ~ ordinal_subset(sK8,sK1)
| ~ spl19_2
| ~ spl19_14
| spl19_168
| ~ spl19_178
| ~ spl19_184 ),
inference(subsumption_resolution,[],[f2237,f1764]) ).
fof(f1764,plain,
( sK1 != sK8
| spl19_168 ),
inference(avatar_component_clause,[],[f1763]) ).
fof(f2237,plain,
( ~ ordinal_subset(sK1,sK8)
| sK1 = sK8
| ~ ordinal_subset(sK8,sK1)
| ~ spl19_2
| ~ spl19_14
| ~ spl19_178
| ~ spl19_184 ),
inference(subsumption_resolution,[],[f2236,f330]) ).
fof(f2236,plain,
( ~ ordinal_subset(sK1,sK8)
| ~ ordinal(sK8)
| sK1 = sK8
| ~ ordinal_subset(sK8,sK1)
| ~ spl19_2
| ~ spl19_178
| ~ spl19_184 ),
inference(subsumption_resolution,[],[f2233,f270]) ).
fof(f2233,plain,
( ~ ordinal_subset(sK1,sK8)
| ~ ordinal(sK1)
| ~ ordinal(sK8)
| sK1 = sK8
| ~ ordinal_subset(sK8,sK1)
| ~ spl19_178
| ~ spl19_184 ),
inference(resolution,[],[f1873,f1825]) ).
fof(f2246,plain,
( ~ spl19_213
| ~ spl19_2
| ~ spl19_139
| spl19_168
| ~ spl19_170
| ~ spl19_184 ),
inference(avatar_split_clause,[],[f2241,f1872,f1771,f1763,f1134,f268,f2243]) ).
fof(f2241,plain,
( ~ ordinal_subset(sK1,sK8)
| ~ spl19_2
| ~ spl19_139
| spl19_168
| ~ spl19_170
| ~ spl19_184 ),
inference(subsumption_resolution,[],[f2240,f1773]) ).
fof(f2240,plain,
( ~ ordinal_subset(sK1,sK8)
| ~ in(sK8,sK1)
| ~ spl19_2
| ~ spl19_139
| spl19_168
| ~ spl19_184 ),
inference(subsumption_resolution,[],[f2239,f1764]) ).
fof(f2239,plain,
( ~ ordinal_subset(sK1,sK8)
| sK1 = sK8
| ~ in(sK8,sK1)
| ~ spl19_2
| ~ spl19_139
| ~ spl19_184 ),
inference(subsumption_resolution,[],[f2234,f270]) ).
fof(f2234,plain,
( ~ ordinal_subset(sK1,sK8)
| ~ ordinal(sK1)
| sK1 = sK8
| ~ in(sK8,sK1)
| ~ spl19_139
| ~ spl19_184 ),
inference(resolution,[],[f1873,f1135]) ).
fof(f2229,plain,
( ~ spl19_209
| spl19_202
| ~ spl19_210
| ~ spl19_2
| ~ spl19_178
| ~ spl19_186
| ~ spl19_195 ),
inference(avatar_split_clause,[],[f1993,f1971,f1887,f1824,f268,f2189,f2028,f2179]) ).
fof(f2028,plain,
( spl19_202
<=> sK1 = succ(sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_202])]) ).
fof(f1971,plain,
( spl19_195
<=> ! [X1] :
( ~ ordinal_subset(X1,succ(sK0))
| subset(X1,succ(sK0))
| ~ ordinal(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_195])]) ).
fof(f1993,plain,
( ~ ordinal_subset(sK1,succ(sK0))
| sK1 = succ(sK0)
| ~ ordinal_subset(succ(sK0),sK1)
| ~ spl19_2
| ~ spl19_178
| ~ spl19_186
| ~ spl19_195 ),
inference(subsumption_resolution,[],[f1992,f1888]) ).
fof(f1992,plain,
( ~ ordinal_subset(sK1,succ(sK0))
| ~ ordinal(succ(sK0))
| sK1 = succ(sK0)
| ~ ordinal_subset(succ(sK0),sK1)
| ~ spl19_2
| ~ spl19_178
| ~ spl19_195 ),
inference(subsumption_resolution,[],[f1986,f270]) ).
fof(f1986,plain,
( ~ ordinal_subset(sK1,succ(sK0))
| ~ ordinal(sK1)
| ~ ordinal(succ(sK0))
| sK1 = succ(sK0)
| ~ ordinal_subset(succ(sK0),sK1)
| ~ spl19_178
| ~ spl19_195 ),
inference(resolution,[],[f1972,f1825]) ).
fof(f1972,plain,
( ! [X1] :
( subset(X1,succ(sK0))
| ~ ordinal_subset(X1,succ(sK0))
| ~ ordinal(X1) )
| ~ spl19_195 ),
inference(avatar_component_clause,[],[f1971]) ).
fof(f2226,plain,
( ~ spl19_212
| ~ spl19_2
| ~ spl19_8
| spl19_150
| ~ spl19_155
| ~ spl19_178
| ~ spl19_181 ),
inference(avatar_split_clause,[],[f2221,f1851,f1824,f1666,f1531,f298,f268,f2223]) ).
fof(f2221,plain,
( ~ ordinal_subset(sK1,empty_set)
| ~ spl19_2
| ~ spl19_8
| spl19_150
| ~ spl19_155
| ~ spl19_178
| ~ spl19_181 ),
inference(subsumption_resolution,[],[f2220,f1668]) ).
fof(f2220,plain,
( ~ ordinal_subset(sK1,empty_set)
| ~ ordinal_subset(empty_set,sK1)
| ~ spl19_2
| ~ spl19_8
| spl19_150
| ~ spl19_178
| ~ spl19_181 ),
inference(subsumption_resolution,[],[f2219,f1532]) ).
fof(f2219,plain,
( ~ ordinal_subset(sK1,empty_set)
| empty_set = sK1
| ~ ordinal_subset(empty_set,sK1)
| ~ spl19_2
| ~ spl19_8
| ~ spl19_178
| ~ spl19_181 ),
inference(subsumption_resolution,[],[f2218,f300]) ).
fof(f2218,plain,
( ~ ordinal_subset(sK1,empty_set)
| ~ ordinal(empty_set)
| empty_set = sK1
| ~ ordinal_subset(empty_set,sK1)
| ~ spl19_2
| ~ spl19_178
| ~ spl19_181 ),
inference(subsumption_resolution,[],[f2215,f270]) ).
fof(f2215,plain,
( ~ ordinal_subset(sK1,empty_set)
| ~ ordinal(sK1)
| ~ ordinal(empty_set)
| empty_set = sK1
| ~ ordinal_subset(empty_set,sK1)
| ~ spl19_178
| ~ spl19_181 ),
inference(resolution,[],[f1852,f1825]) ).
fof(f2211,plain,
( spl19_211
| ~ spl19_197
| ~ spl19_207 ),
inference(avatar_split_clause,[],[f2204,f2138,f1979,f2209]) ).
fof(f2209,plain,
( spl19_211
<=> ! [X1] :
( ordinal_subset(X1,succ(sK0))
| ~ ordinal(X1)
| ~ in(X1,succ(sK0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_211])]) ).
fof(f2204,plain,
( ! [X1] :
( ordinal_subset(X1,succ(sK0))
| ~ ordinal(X1)
| ~ in(X1,succ(sK0)) )
| ~ spl19_197
| ~ spl19_207 ),
inference(resolution,[],[f1980,f2139]) ).
fof(f2192,plain,
( spl19_210
| ~ spl19_109
| ~ spl19_186
| spl19_209 ),
inference(avatar_split_clause,[],[f2187,f2179,f1887,f920,f2189]) ).
fof(f2187,plain,
( ordinal_subset(sK1,succ(sK0))
| ~ spl19_109
| ~ spl19_186
| spl19_209 ),
inference(subsumption_resolution,[],[f2186,f1888]) ).
fof(f2186,plain,
( ordinal_subset(sK1,succ(sK0))
| ~ ordinal(succ(sK0))
| ~ spl19_109
| spl19_209 ),
inference(resolution,[],[f2181,f921]) ).
fof(f2182,plain,
( ~ spl19_209
| ~ spl19_178
| ~ spl19_186
| spl19_202
| ~ spl19_203
| ~ spl19_207 ),
inference(avatar_split_clause,[],[f2165,f2138,f2032,f2028,f1887,f1824,f2179]) ).
fof(f2165,plain,
( ~ ordinal_subset(succ(sK0),sK1)
| ~ spl19_178
| ~ spl19_186
| spl19_202
| ~ spl19_203
| ~ spl19_207 ),
inference(subsumption_resolution,[],[f2164,f2029]) ).
fof(f2029,plain,
( sK1 != succ(sK0)
| spl19_202 ),
inference(avatar_component_clause,[],[f2028]) ).
fof(f2164,plain,
( sK1 = succ(sK0)
| ~ ordinal_subset(succ(sK0),sK1)
| ~ spl19_178
| ~ spl19_186
| ~ spl19_203
| ~ spl19_207 ),
inference(subsumption_resolution,[],[f2163,f1888]) ).
fof(f2163,plain,
( ~ ordinal(succ(sK0))
| sK1 = succ(sK0)
| ~ ordinal_subset(succ(sK0),sK1)
| ~ spl19_178
| ~ spl19_203
| ~ spl19_207 ),
inference(subsumption_resolution,[],[f2155,f2034]) ).
fof(f2155,plain,
( ~ in(sK1,succ(sK0))
| ~ ordinal(succ(sK0))
| sK1 = succ(sK0)
| ~ ordinal_subset(succ(sK0),sK1)
| ~ spl19_178
| ~ spl19_207 ),
inference(resolution,[],[f2139,f1825]) ).
fof(f2175,plain,
( ~ spl19_199
| ~ spl19_27
| ~ spl19_28
| ~ spl19_177
| ~ spl19_186
| ~ spl19_207 ),
inference(avatar_split_clause,[],[f2160,f2138,f1887,f1820,f395,f391,f2000]) ).
fof(f2160,plain,
( ~ ordinal_subset(succ(sK0),sK0)
| ~ spl19_27
| ~ spl19_28
| ~ spl19_177
| ~ spl19_186
| ~ spl19_207 ),
inference(subsumption_resolution,[],[f2159,f392]) ).
fof(f2159,plain,
( sK0 = succ(sK0)
| ~ ordinal_subset(succ(sK0),sK0)
| ~ spl19_28
| ~ spl19_177
| ~ spl19_186
| ~ spl19_207 ),
inference(subsumption_resolution,[],[f2158,f1888]) ).
fof(f2158,plain,
( ~ ordinal(succ(sK0))
| sK0 = succ(sK0)
| ~ ordinal_subset(succ(sK0),sK0)
| ~ spl19_28
| ~ spl19_177
| ~ spl19_207 ),
inference(subsumption_resolution,[],[f2153,f396]) ).
fof(f2153,plain,
( ~ in(sK0,succ(sK0))
| ~ ordinal(succ(sK0))
| sK0 = succ(sK0)
| ~ ordinal_subset(succ(sK0),sK0)
| ~ spl19_177
| ~ spl19_207 ),
inference(resolution,[],[f2139,f1821]) ).
fof(f2171,plain,
( spl19_208
| ~ spl19_48
| ~ spl19_49
| ~ spl19_207 ),
inference(avatar_split_clause,[],[f2166,f2138,f496,f492,f2168]) ).
fof(f2168,plain,
( spl19_208
<=> epsilon_transitive(succ(sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_208])]) ).
fof(f2166,plain,
( epsilon_transitive(succ(sK0))
| ~ spl19_48
| ~ spl19_49
| ~ spl19_207 ),
inference(subsumption_resolution,[],[f2157,f493]) ).
fof(f2157,plain,
( ~ in(sK2(succ(sK0)),succ(sK0))
| epsilon_transitive(succ(sK0))
| ~ spl19_49
| ~ spl19_207 ),
inference(resolution,[],[f2139,f497]) ).
fof(f2162,plain,
( ~ spl19_27
| ~ spl19_28
| ~ spl19_177
| ~ spl19_186
| ~ spl19_199
| ~ spl19_207 ),
inference(avatar_contradiction_clause,[],[f2161]) ).
fof(f2161,plain,
( $false
| ~ spl19_27
| ~ spl19_28
| ~ spl19_177
| ~ spl19_186
| ~ spl19_199
| ~ spl19_207 ),
inference(subsumption_resolution,[],[f2160,f2001]) ).
fof(f2001,plain,
( ordinal_subset(succ(sK0),sK0)
| ~ spl19_199 ),
inference(avatar_component_clause,[],[f2000]) ).
fof(f2140,plain,
( spl19_207
| ~ spl19_159
| ~ spl19_186 ),
inference(avatar_split_clause,[],[f2114,f1887,f1723,f2138]) ).
fof(f1723,plain,
( spl19_159
<=> ! [X2,X3] :
( ~ in(X2,X3)
| subset(X2,X3)
| ~ ordinal(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_159])]) ).
fof(f2114,plain,
( ! [X4] :
( subset(X4,succ(sK0))
| ~ in(X4,succ(sK0)) )
| ~ spl19_159
| ~ spl19_186 ),
inference(resolution,[],[f1888,f1724]) ).
fof(f1724,plain,
( ! [X2,X3] :
( ~ ordinal(X3)
| subset(X2,X3)
| ~ in(X2,X3) )
| ~ spl19_159 ),
inference(avatar_component_clause,[],[f1723]) ).
fof(f2099,plain,
( ~ spl19_54
| ~ spl19_140
| ~ spl19_202 ),
inference(avatar_contradiction_clause,[],[f2098]) ).
fof(f2098,plain,
( $false
| ~ spl19_54
| ~ spl19_140
| ~ spl19_202 ),
inference(subsumption_resolution,[],[f2085,f1149]) ).
fof(f2085,plain,
( ~ in(sK1,sK0)
| ~ spl19_54
| ~ spl19_202 ),
inference(superposition,[],[f530,f2030]) ).
fof(f2030,plain,
( sK1 = succ(sK0)
| ~ spl19_202 ),
inference(avatar_component_clause,[],[f2028]) ).
fof(f2096,plain,
( ~ spl19_28
| spl19_101
| ~ spl19_202 ),
inference(avatar_contradiction_clause,[],[f2095]) ).
fof(f2095,plain,
( $false
| ~ spl19_28
| spl19_101
| ~ spl19_202 ),
inference(subsumption_resolution,[],[f2081,f870]) ).
fof(f2081,plain,
( in(sK0,sK1)
| ~ spl19_28
| ~ spl19_202 ),
inference(superposition,[],[f396,f2030]) ).
fof(f2078,plain,
( ~ spl19_206
| spl19_187
| ~ spl19_202 ),
inference(avatar_split_clause,[],[f2042,f2028,f1891,f2075]) ).
fof(f2042,plain,
( sK0 != succ(sK1)
| spl19_187
| ~ spl19_202 ),
inference(backward_demodulation,[],[f1892,f2030]) ).
fof(f2071,plain,
( ~ spl19_205
| ~ spl19_202
| spl19_203 ),
inference(avatar_split_clause,[],[f2054,f2032,f2028,f2068]) ).
fof(f2054,plain,
( ~ in(sK1,sK1)
| ~ spl19_202
| spl19_203 ),
inference(backward_demodulation,[],[f2033,f2030]) ).
fof(f2033,plain,
( ~ in(sK1,succ(sK0))
| spl19_203 ),
inference(avatar_component_clause,[],[f2032]) ).
fof(f2039,plain,
( spl19_202
| spl19_203
| spl19_204
| ~ spl19_143
| ~ spl19_186 ),
inference(avatar_split_clause,[],[f1917,f1887,f1175,f2036,f2032,f2028]) ).
fof(f1917,plain,
( in(succ(sK0),sK1)
| in(sK1,succ(sK0))
| sK1 = succ(sK0)
| ~ spl19_143
| ~ spl19_186 ),
inference(resolution,[],[f1888,f1176]) ).
fof(f2022,plain,
( spl19_201
| ~ spl19_8
| ~ spl19_46
| ~ spl19_126 ),
inference(avatar_split_clause,[],[f1067,f1051,f484,f298,f2020]) ).
fof(f1067,plain,
( ! [X4] :
( empty_set = X4
| in(empty_set,X4)
| ~ ordinal(X4) )
| ~ spl19_8
| ~ spl19_46
| ~ spl19_126 ),
inference(subsumption_resolution,[],[f1061,f485]) ).
fof(f1061,plain,
( ! [X4] :
( empty_set = X4
| in(X4,empty_set)
| in(empty_set,X4)
| ~ ordinal(X4) )
| ~ spl19_8
| ~ spl19_126 ),
inference(resolution,[],[f1052,f300]) ).
fof(f2016,plain,
( ~ spl19_108
| ~ spl19_186
| spl19_199
| spl19_200 ),
inference(avatar_contradiction_clause,[],[f2015]) ).
fof(f2015,plain,
( $false
| ~ spl19_108
| ~ spl19_186
| spl19_199
| spl19_200 ),
inference(subsumption_resolution,[],[f2014,f1888]) ).
fof(f2014,plain,
( ~ ordinal(succ(sK0))
| ~ spl19_108
| spl19_199
| spl19_200 ),
inference(subsumption_resolution,[],[f2010,f2006]) ).
fof(f2006,plain,
( ~ ordinal_subset(sK0,succ(sK0))
| spl19_200 ),
inference(avatar_component_clause,[],[f2004]) ).
fof(f2010,plain,
( ordinal_subset(sK0,succ(sK0))
| ~ ordinal(succ(sK0))
| ~ spl19_108
| spl19_199 ),
inference(resolution,[],[f2002,f917]) ).
fof(f2013,plain,
( ~ spl19_1
| ~ spl19_194
| spl19_199
| spl19_200 ),
inference(avatar_contradiction_clause,[],[f2012]) ).
fof(f2012,plain,
( $false
| ~ spl19_1
| ~ spl19_194
| spl19_199
| spl19_200 ),
inference(subsumption_resolution,[],[f2011,f265]) ).
fof(f2011,plain,
( ~ ordinal(sK0)
| ~ spl19_194
| spl19_199
| spl19_200 ),
inference(subsumption_resolution,[],[f2008,f2006]) ).
fof(f2008,plain,
( ordinal_subset(sK0,succ(sK0))
| ~ ordinal(sK0)
| ~ spl19_194
| spl19_199 ),
inference(resolution,[],[f2002,f1968]) ).
fof(f2007,plain,
( ~ spl19_199
| ~ spl19_200
| ~ spl19_1
| ~ spl19_27
| ~ spl19_177
| ~ spl19_186
| ~ spl19_195 ),
inference(avatar_split_clause,[],[f1991,f1971,f1887,f1820,f391,f263,f2004,f2000]) ).
fof(f1991,plain,
( ~ ordinal_subset(sK0,succ(sK0))
| ~ ordinal_subset(succ(sK0),sK0)
| ~ spl19_1
| ~ spl19_27
| ~ spl19_177
| ~ spl19_186
| ~ spl19_195 ),
inference(subsumption_resolution,[],[f1990,f392]) ).
fof(f1990,plain,
( ~ ordinal_subset(sK0,succ(sK0))
| sK0 = succ(sK0)
| ~ ordinal_subset(succ(sK0),sK0)
| ~ spl19_1
| ~ spl19_177
| ~ spl19_186
| ~ spl19_195 ),
inference(subsumption_resolution,[],[f1989,f1888]) ).
fof(f1989,plain,
( ~ ordinal_subset(sK0,succ(sK0))
| ~ ordinal(succ(sK0))
| sK0 = succ(sK0)
| ~ ordinal_subset(succ(sK0),sK0)
| ~ spl19_1
| ~ spl19_177
| ~ spl19_195 ),
inference(subsumption_resolution,[],[f1984,f265]) ).
fof(f1984,plain,
( ~ ordinal_subset(sK0,succ(sK0))
| ~ ordinal(sK0)
| ~ ordinal(succ(sK0))
| sK0 = succ(sK0)
| ~ ordinal_subset(succ(sK0),sK0)
| ~ spl19_177
| ~ spl19_195 ),
inference(resolution,[],[f1972,f1821]) ).
fof(f1998,plain,
( spl19_198
| ~ spl19_33
| ~ spl19_105 ),
inference(avatar_split_clause,[],[f959,f891,f415,f1996]) ).
fof(f959,plain,
( ! [X0,X1] :
( element(X0,X1)
| ~ in(X0,sK3(powerset(X1))) )
| ~ spl19_33
| ~ spl19_105 ),
inference(resolution,[],[f892,f416]) ).
fof(f1981,plain,
( spl19_197
| ~ spl19_103
| ~ spl19_186 ),
inference(avatar_split_clause,[],[f1914,f1887,f877,f1979]) ).
fof(f1914,plain,
( ! [X2] :
( ~ subset(X2,succ(sK0))
| ordinal_subset(X2,succ(sK0))
| ~ ordinal(X2) )
| ~ spl19_103
| ~ spl19_186 ),
inference(resolution,[],[f1888,f878]) ).
fof(f1977,plain,
( spl19_196
| ~ spl19_18
| ~ spl19_103 ),
inference(avatar_split_clause,[],[f948,f877,f348,f1975]) ).
fof(f948,plain,
( ! [X8] :
( ~ subset(X8,sK10)
| ordinal_subset(X8,sK10)
| ~ ordinal(X8) )
| ~ spl19_18
| ~ spl19_103 ),
inference(resolution,[],[f878,f350]) ).
fof(f1973,plain,
( spl19_195
| ~ spl19_100
| ~ spl19_186 ),
inference(avatar_split_clause,[],[f1913,f1887,f853,f1971]) ).
fof(f1913,plain,
( ! [X1] :
( ~ ordinal_subset(X1,succ(sK0))
| subset(X1,succ(sK0))
| ~ ordinal(X1) )
| ~ spl19_100
| ~ spl19_186 ),
inference(resolution,[],[f1888,f854]) ).
fof(f1969,plain,
( spl19_194
| ~ spl19_97
| ~ spl19_186 ),
inference(avatar_split_clause,[],[f1912,f1887,f840,f1967]) ).
fof(f1912,plain,
( ! [X0] :
( ordinal_subset(X0,succ(sK0))
| ordinal_subset(succ(sK0),X0)
| ~ ordinal(X0) )
| ~ spl19_97
| ~ spl19_186 ),
inference(resolution,[],[f1888,f841]) ).
fof(f1965,plain,
( spl19_193
| ~ spl19_60
| ~ spl19_186 ),
inference(avatar_split_clause,[],[f1911,f1887,f552,f1962]) ).
fof(f1962,plain,
( spl19_193
<=> ordinal_subset(succ(sK0),succ(sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_193])]) ).
fof(f1911,plain,
( ordinal_subset(succ(sK0),succ(sK0))
| ~ spl19_60
| ~ spl19_186 ),
inference(resolution,[],[f1888,f553]) ).
fof(f1960,plain,
( spl19_192
| ~ spl19_14
| ~ spl19_103 ),
inference(avatar_split_clause,[],[f947,f877,f328,f1958]) ).
fof(f947,plain,
( ! [X7] :
( ~ subset(X7,sK8)
| ordinal_subset(X7,sK8)
| ~ ordinal(X7) )
| ~ spl19_14
| ~ spl19_103 ),
inference(resolution,[],[f878,f330]) ).
fof(f1955,plain,
( ~ spl19_34
| ~ spl19_95
| ~ spl19_187 ),
inference(avatar_contradiction_clause,[],[f1954]) ).
fof(f1954,plain,
( $false
| ~ spl19_34
| ~ spl19_95
| ~ spl19_187 ),
inference(subsumption_resolution,[],[f1941,f420]) ).
fof(f1941,plain,
( ~ in(succ(sK0),singleton(succ(sK0)))
| ~ spl19_95
| ~ spl19_187 ),
inference(superposition,[],[f832,f1893]) ).
fof(f1893,plain,
( sK0 = succ(succ(sK0))
| ~ spl19_187 ),
inference(avatar_component_clause,[],[f1891]) ).
fof(f1953,plain,
( ~ spl19_28
| ~ spl19_54
| ~ spl19_187 ),
inference(avatar_contradiction_clause,[],[f1952]) ).
fof(f1952,plain,
( $false
| ~ spl19_28
| ~ spl19_54
| ~ spl19_187 ),
inference(subsumption_resolution,[],[f1937,f396]) ).
fof(f1937,plain,
( ~ in(sK0,succ(sK0))
| ~ spl19_54
| ~ spl19_187 ),
inference(superposition,[],[f530,f1893]) ).
fof(f1950,plain,
( ~ spl19_28
| ~ spl19_54
| ~ spl19_187 ),
inference(avatar_contradiction_clause,[],[f1949]) ).
fof(f1949,plain,
( $false
| ~ spl19_28
| ~ spl19_54
| ~ spl19_187 ),
inference(subsumption_resolution,[],[f1933,f530]) ).
fof(f1933,plain,
( in(succ(sK0),sK0)
| ~ spl19_28
| ~ spl19_187 ),
inference(superposition,[],[f396,f1893]) ).
fof(f1948,plain,
( ~ spl19_34
| ~ spl19_95
| ~ spl19_187 ),
inference(avatar_contradiction_clause,[],[f1947]) ).
fof(f1947,plain,
( $false
| ~ spl19_34
| ~ spl19_95
| ~ spl19_187 ),
inference(subsumption_resolution,[],[f1929,f420]) ).
fof(f1929,plain,
( ~ in(sK0,singleton(sK0))
| ~ spl19_95
| ~ spl19_187 ),
inference(superposition,[],[f832,f1893]) ).
fof(f1926,plain,
( spl19_191
| ~ spl19_8
| ~ spl19_103 ),
inference(avatar_split_clause,[],[f944,f877,f298,f1924]) ).
fof(f944,plain,
( ! [X4] :
( ~ subset(X4,empty_set)
| ordinal_subset(X4,empty_set)
| ~ ordinal(X4) )
| ~ spl19_8
| ~ spl19_103 ),
inference(resolution,[],[f878,f300]) ).
fof(f1922,plain,
( ~ spl19_190
| ~ spl19_187
| spl19_188 ),
inference(avatar_split_clause,[],[f1907,f1895,f1891,f1919]) ).
fof(f1907,plain,
( ~ in(sK0,sK0)
| ~ spl19_187
| spl19_188 ),
inference(backward_demodulation,[],[f1896,f1893]) ).
fof(f1896,plain,
( ~ in(sK0,succ(succ(sK0)))
| spl19_188 ),
inference(avatar_component_clause,[],[f1895]) ).
fof(f1906,plain,
( ~ spl19_1
| ~ spl19_38
| spl19_186 ),
inference(avatar_contradiction_clause,[],[f1905]) ).
fof(f1905,plain,
( $false
| ~ spl19_1
| ~ spl19_38
| spl19_186 ),
inference(subsumption_resolution,[],[f1903,f265]) ).
fof(f1903,plain,
( ~ ordinal(sK0)
| ~ spl19_38
| spl19_186 ),
inference(resolution,[],[f1889,f436]) ).
fof(f1889,plain,
( ~ ordinal(succ(sK0))
| spl19_186 ),
inference(avatar_component_clause,[],[f1887]) ).
fof(f1902,plain,
( spl19_189
| ~ spl19_18
| ~ spl19_100 ),
inference(avatar_split_clause,[],[f930,f853,f348,f1900]) ).
fof(f930,plain,
( ! [X8] :
( ~ ordinal_subset(X8,sK10)
| subset(X8,sK10)
| ~ ordinal(X8) )
| ~ spl19_18
| ~ spl19_100 ),
inference(resolution,[],[f854,f350]) ).
fof(f1898,plain,
( ~ spl19_186
| spl19_187
| spl19_188
| ~ spl19_93
| ~ spl19_183 ),
inference(avatar_split_clause,[],[f1882,f1868,f806,f1895,f1891,f1887]) ).
fof(f1882,plain,
( in(sK0,succ(succ(sK0)))
| sK0 = succ(succ(sK0))
| ~ ordinal(succ(sK0))
| ~ spl19_93
| ~ spl19_183 ),
inference(resolution,[],[f1869,f807]) ).
fof(f1878,plain,
( spl19_185
| ~ spl19_38
| ~ spl19_143 ),
inference(avatar_split_clause,[],[f1521,f1175,f435,f1876]) ).
fof(f1521,plain,
( ! [X1] :
( in(succ(X1),sK1)
| in(sK1,succ(X1))
| succ(X1) = sK1
| ~ ordinal(X1) )
| ~ spl19_38
| ~ spl19_143 ),
inference(resolution,[],[f1176,f436]) ).
fof(f1874,plain,
( spl19_184
| ~ spl19_14
| ~ spl19_100 ),
inference(avatar_split_clause,[],[f929,f853,f328,f1872]) ).
fof(f929,plain,
( ! [X7] :
( ~ ordinal_subset(X7,sK8)
| subset(X7,sK8)
| ~ ordinal(X7) )
| ~ spl19_14
| ~ spl19_100 ),
inference(resolution,[],[f854,f330]) ).
fof(f1870,plain,
( spl19_183
| ~ spl19_38
| ~ spl19_142 ),
inference(avatar_split_clause,[],[f1179,f1168,f435,f1868]) ).
fof(f1168,plain,
( spl19_142
<=> ! [X5] :
( sK0 = X5
| in(X5,sK0)
| in(sK0,X5)
| ~ ordinal(X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_142])]) ).
fof(f1179,plain,
( ! [X1] :
( in(succ(X1),sK0)
| in(sK0,succ(X1))
| succ(X1) = sK0
| ~ ordinal(X1) )
| ~ spl19_38
| ~ spl19_142 ),
inference(resolution,[],[f1169,f436]) ).
fof(f1169,plain,
( ! [X5] :
( ~ ordinal(X5)
| in(X5,sK0)
| in(sK0,X5)
| sK0 = X5 )
| ~ spl19_142 ),
inference(avatar_component_clause,[],[f1168]) ).
fof(f1858,plain,
( spl19_182
| ~ spl19_14
| ~ spl19_108
| spl19_180 ),
inference(avatar_split_clause,[],[f1849,f1843,f916,f328,f1855]) ).
fof(f1849,plain,
( ordinal_subset(sK0,sK8)
| ~ spl19_14
| ~ spl19_108
| spl19_180 ),
inference(subsumption_resolution,[],[f1848,f330]) ).
fof(f1848,plain,
( ordinal_subset(sK0,sK8)
| ~ ordinal(sK8)
| ~ spl19_108
| spl19_180 ),
inference(resolution,[],[f1845,f917]) ).
fof(f1853,plain,
( spl19_181
| ~ spl19_8
| ~ spl19_100 ),
inference(avatar_split_clause,[],[f926,f853,f298,f1851]) ).
fof(f926,plain,
( ! [X4] :
( ~ ordinal_subset(X4,empty_set)
| subset(X4,empty_set)
| ~ ordinal(X4) )
| ~ spl19_8
| ~ spl19_100 ),
inference(resolution,[],[f854,f300]) ).
fof(f1846,plain,
( ~ spl19_180
| ~ spl19_14
| ~ spl19_81
| spl19_160
| ~ spl19_161
| ~ spl19_177 ),
inference(avatar_split_clause,[],[f1841,f1820,f1731,f1727,f699,f328,f1843]) ).
fof(f1727,plain,
( spl19_160
<=> sK0 = sK8 ),
introduced(avatar_definition,[new_symbols(naming,[spl19_160])]) ).
fof(f1841,plain,
( ~ ordinal_subset(sK8,sK0)
| ~ spl19_14
| ~ spl19_81
| spl19_160
| ~ spl19_161
| ~ spl19_177 ),
inference(subsumption_resolution,[],[f1840,f1733]) ).
fof(f1840,plain,
( ~ ordinal_subset(sK8,sK0)
| ~ in(sK0,sK8)
| ~ spl19_14
| ~ spl19_81
| spl19_160
| ~ spl19_177 ),
inference(subsumption_resolution,[],[f1839,f1728]) ).
fof(f1728,plain,
( sK0 != sK8
| spl19_160 ),
inference(avatar_component_clause,[],[f1727]) ).
fof(f1839,plain,
( sK0 = sK8
| ~ ordinal_subset(sK8,sK0)
| ~ in(sK0,sK8)
| ~ spl19_14
| ~ spl19_81
| ~ spl19_177 ),
inference(subsumption_resolution,[],[f1836,f330]) ).
fof(f1836,plain,
( ~ ordinal(sK8)
| sK0 = sK8
| ~ ordinal_subset(sK8,sK0)
| ~ in(sK0,sK8)
| ~ spl19_81
| ~ spl19_177 ),
inference(resolution,[],[f1821,f700]) ).
fof(f1830,plain,
( spl19_179
| ~ spl19_18
| ~ spl19_97 ),
inference(avatar_split_clause,[],[f914,f840,f348,f1828]) ).
fof(f914,plain,
( ! [X8] :
( ordinal_subset(X8,sK10)
| ordinal_subset(sK10,X8)
| ~ ordinal(X8) )
| ~ spl19_18
| ~ spl19_97 ),
inference(resolution,[],[f841,f350]) ).
fof(f1826,plain,
( spl19_178
| ~ spl19_89
| ~ spl19_111 ),
inference(avatar_split_clause,[],[f950,f937,f765,f1824]) ).
fof(f937,plain,
( spl19_111
<=> ! [X6] :
( ~ ordinal_subset(X6,sK1)
| subset(X6,sK1)
| ~ ordinal(X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_111])]) ).
fof(f950,plain,
( ! [X0] :
( ~ ordinal_subset(X0,sK1)
| ~ ordinal(X0)
| sK1 = X0
| ~ subset(sK1,X0) )
| ~ spl19_89
| ~ spl19_111 ),
inference(resolution,[],[f938,f766]) ).
fof(f938,plain,
( ! [X6] :
( subset(X6,sK1)
| ~ ordinal_subset(X6,sK1)
| ~ ordinal(X6) )
| ~ spl19_111 ),
inference(avatar_component_clause,[],[f937]) ).
fof(f1822,plain,
( spl19_177
| ~ spl19_89
| ~ spl19_110 ),
inference(avatar_split_clause,[],[f941,f933,f765,f1820]) ).
fof(f941,plain,
( ! [X0] :
( ~ ordinal_subset(X0,sK0)
| ~ ordinal(X0)
| sK0 = X0
| ~ subset(sK0,X0) )
| ~ spl19_89
| ~ spl19_110 ),
inference(resolution,[],[f934,f766]) ).
fof(f1802,plain,
( spl19_176
| ~ spl19_14
| ~ spl19_97 ),
inference(avatar_split_clause,[],[f913,f840,f328,f1800]) ).
fof(f913,plain,
( ! [X7] :
( ordinal_subset(X7,sK8)
| ordinal_subset(sK8,X7)
| ~ ordinal(X7) )
| ~ spl19_14
| ~ spl19_97 ),
inference(resolution,[],[f841,f330]) ).
fof(f1798,plain,
( ~ spl19_133
| spl19_134
| ~ spl19_72
| ~ spl19_113 ),
inference(avatar_split_clause,[],[f1673,f956,f645,f1109,f1105]) ).
fof(f1105,plain,
( spl19_133
<=> ordinal(sK3(powerset(sK1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_133])]) ).
fof(f956,plain,
( spl19_113
<=> ! [X6] :
( ~ subset(X6,sK1)
| ordinal_subset(X6,sK1)
| ~ ordinal(X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_113])]) ).
fof(f1673,plain,
( ordinal_subset(sK3(powerset(sK1)),sK1)
| ~ ordinal(sK3(powerset(sK1)))
| ~ spl19_72
| ~ spl19_113 ),
inference(resolution,[],[f957,f646]) ).
fof(f957,plain,
( ! [X6] :
( ~ subset(X6,sK1)
| ordinal_subset(X6,sK1)
| ~ ordinal(X6) )
| ~ spl19_113 ),
inference(avatar_component_clause,[],[f956]) ).
fof(f1796,plain,
( spl19_175
| ~ spl19_8
| ~ spl19_97 ),
inference(avatar_split_clause,[],[f910,f840,f298,f1794]) ).
fof(f1794,plain,
( spl19_175
<=> ! [X4] :
( ordinal_subset(X4,empty_set)
| ordinal_subset(empty_set,X4)
| ~ ordinal(X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_175])]) ).
fof(f910,plain,
( ! [X4] :
( ordinal_subset(X4,empty_set)
| ordinal_subset(empty_set,X4)
| ~ ordinal(X4) )
| ~ spl19_8
| ~ spl19_97 ),
inference(resolution,[],[f841,f300]) ).
fof(f1792,plain,
( spl19_172
| spl19_173
| spl19_174
| ~ spl19_18
| ~ spl19_143 ),
inference(avatar_split_clause,[],[f1526,f1175,f348,f1789,f1785,f1781]) ).
fof(f1526,plain,
( in(sK10,sK1)
| in(sK1,sK10)
| sK1 = sK10
| ~ spl19_18
| ~ spl19_143 ),
inference(resolution,[],[f1176,f350]) ).
fof(f1778,plain,
( spl19_171
| ~ spl19_52
| ~ spl19_80 ),
inference(avatar_split_clause,[],[f742,f689,f508,f1776]) ).
fof(f742,plain,
( ! [X2,X0,X1] :
( ~ in(X0,X1)
| ~ in(set_union2(X1,X2),X0) )
| ~ spl19_52
| ~ spl19_80 ),
inference(resolution,[],[f690,f509]) ).
fof(f1774,plain,
( spl19_168
| spl19_169
| spl19_170
| ~ spl19_14
| ~ spl19_143 ),
inference(avatar_split_clause,[],[f1525,f1175,f328,f1771,f1767,f1763]) ).
fof(f1525,plain,
( in(sK8,sK1)
| in(sK1,sK8)
| sK1 = sK8
| ~ spl19_14
| ~ spl19_143 ),
inference(resolution,[],[f1176,f330]) ).
fof(f1760,plain,
( spl19_167
| ~ spl19_57
| ~ spl19_79 ),
inference(avatar_split_clause,[],[f727,f685,f541,f1758]) ).
fof(f727,plain,
( ! [X8,X9] :
( in(X9,succ(X8))
| ~ in(X9,singleton(X8)) )
| ~ spl19_57
| ~ spl19_79 ),
inference(superposition,[],[f686,f542]) ).
fof(f1756,plain,
( spl19_164
| spl19_165
| spl19_166
| ~ spl19_18
| ~ spl19_142 ),
inference(avatar_split_clause,[],[f1184,f1168,f348,f1753,f1749,f1745]) ).
fof(f1184,plain,
( in(sK10,sK0)
| in(sK0,sK10)
| sK0 = sK10
| ~ spl19_18
| ~ spl19_142 ),
inference(resolution,[],[f1169,f350]) ).
fof(f1743,plain,
( spl19_163
| ~ spl19_52
| ~ spl19_79 ),
inference(avatar_split_clause,[],[f721,f685,f508,f1741]) ).
fof(f721,plain,
( ! [X2,X0,X1] :
( ~ in(X0,X1)
| ~ in(set_union2(X2,X1),X0) )
| ~ spl19_52
| ~ spl19_79 ),
inference(resolution,[],[f686,f509]) ).
fof(f1738,plain,
( spl19_160
| spl19_161
| spl19_162
| ~ spl19_14
| ~ spl19_142 ),
inference(avatar_split_clause,[],[f1183,f1168,f328,f1735,f1731,f1727]) ).
fof(f1183,plain,
( in(sK8,sK0)
| in(sK0,sK8)
| sK0 = sK8
| ~ spl19_14
| ~ spl19_142 ),
inference(resolution,[],[f1169,f330]) ).
fof(f1725,plain,
( spl19_159
| ~ spl19_29
| ~ spl19_74 ),
inference(avatar_split_clause,[],[f693,f662,f399,f1723]) ).
fof(f693,plain,
( ! [X2,X3] :
( ~ in(X2,X3)
| subset(X2,X3)
| ~ ordinal(X3) )
| ~ spl19_29
| ~ spl19_74 ),
inference(resolution,[],[f663,f400]) ).
fof(f1717,plain,
( ~ spl19_78
| spl19_146
| ~ spl19_153 ),
inference(avatar_contradiction_clause,[],[f1716]) ).
fof(f1716,plain,
( $false
| ~ spl19_78
| spl19_146
| ~ spl19_153 ),
inference(subsumption_resolution,[],[f1714,f1327]) ).
fof(f1714,plain,
( empty_set = sK0
| ~ spl19_78
| ~ spl19_153 ),
inference(resolution,[],[f1603,f680]) ).
fof(f680,plain,
( ! [X0] :
( ~ in(X0,succ(empty_set))
| empty_set = X0 )
| ~ spl19_78 ),
inference(avatar_component_clause,[],[f679]) ).
fof(f679,plain,
( spl19_78
<=> ! [X0] :
( ~ in(X0,succ(empty_set))
| empty_set = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_78])]) ).
fof(f1603,plain,
( in(sK0,succ(empty_set))
| ~ spl19_153 ),
inference(avatar_component_clause,[],[f1601]) ).
fof(f1712,plain,
( ~ spl19_8
| ~ spl19_128
| ~ spl19_151
| spl19_155 ),
inference(avatar_contradiction_clause,[],[f1711]) ).
fof(f1711,plain,
( $false
| ~ spl19_8
| ~ spl19_128
| ~ spl19_151
| spl19_155 ),
inference(subsumption_resolution,[],[f1710,f300]) ).
fof(f1710,plain,
( ~ ordinal(empty_set)
| ~ spl19_128
| ~ spl19_151
| spl19_155 ),
inference(subsumption_resolution,[],[f1707,f1537]) ).
fof(f1707,plain,
( ~ in(empty_set,sK1)
| ~ ordinal(empty_set)
| ~ spl19_128
| spl19_155 ),
inference(resolution,[],[f1073,f1667]) ).
fof(f1667,plain,
( ~ ordinal_subset(empty_set,sK1)
| spl19_155 ),
inference(avatar_component_clause,[],[f1666]) ).
fof(f1705,plain,
( spl19_158
| ~ spl19_48
| ~ spl19_70 ),
inference(avatar_split_clause,[],[f659,f616,f492,f1703]) ).
fof(f1703,plain,
( spl19_158
<=> ! [X1] :
( sK2(singleton(X1)) = X1
| epsilon_transitive(singleton(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_158])]) ).
fof(f659,plain,
( ! [X1] :
( sK2(singleton(X1)) = X1
| epsilon_transitive(singleton(X1)) )
| ~ spl19_48
| ~ spl19_70 ),
inference(resolution,[],[f617,f493]) ).
fof(f1701,plain,
( spl19_157
| ~ spl19_32
| ~ spl19_41
| ~ spl19_143 ),
inference(avatar_split_clause,[],[f1528,f1175,f447,f411,f1699]) ).
fof(f1528,plain,
( ! [X0] :
( in(X0,sK1)
| sK1 = X0
| ~ empty(X0) )
| ~ spl19_32
| ~ spl19_41
| ~ spl19_143 ),
inference(subsumption_resolution,[],[f1520,f448]) ).
fof(f1520,plain,
( ! [X0] :
( in(X0,sK1)
| in(sK1,X0)
| sK1 = X0
| ~ empty(X0) )
| ~ spl19_32
| ~ spl19_143 ),
inference(resolution,[],[f1176,f412]) ).
fof(f1697,plain,
( spl19_156
| ~ spl19_60
| ~ spl19_133 ),
inference(avatar_split_clause,[],[f1634,f1105,f552,f1694]) ).
fof(f1634,plain,
( ordinal_subset(sK3(powerset(sK1)),sK3(powerset(sK1)))
| ~ spl19_60
| ~ spl19_133 ),
inference(resolution,[],[f1106,f553]) ).
fof(f1106,plain,
( ordinal(sK3(powerset(sK1)))
| ~ spl19_133 ),
inference(avatar_component_clause,[],[f1105]) ).
fof(f1669,plain,
( spl19_155
| ~ spl19_39
| ~ spl19_134
| ~ spl19_135 ),
inference(avatar_split_clause,[],[f1647,f1115,f1109,f439,f1666]) ).
fof(f1115,plain,
( spl19_135
<=> empty(sK3(powerset(sK1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_135])]) ).
fof(f1647,plain,
( ordinal_subset(empty_set,sK1)
| ~ spl19_39
| ~ spl19_134
| ~ spl19_135 ),
inference(backward_demodulation,[],[f1111,f1645]) ).
fof(f1645,plain,
( empty_set = sK3(powerset(sK1))
| ~ spl19_39
| ~ spl19_135 ),
inference(resolution,[],[f1116,f440]) ).
fof(f1116,plain,
( empty(sK3(powerset(sK1)))
| ~ spl19_135 ),
inference(avatar_component_clause,[],[f1115]) ).
fof(f1111,plain,
( ordinal_subset(sK3(powerset(sK1)),sK1)
| ~ spl19_134 ),
inference(avatar_component_clause,[],[f1109]) ).
fof(f1627,plain,
( ~ spl19_8
| ~ spl19_121
| ~ spl19_147
| spl19_154 ),
inference(avatar_contradiction_clause,[],[f1626]) ).
fof(f1626,plain,
( $false
| ~ spl19_8
| ~ spl19_121
| ~ spl19_147
| spl19_154 ),
inference(subsumption_resolution,[],[f1625,f300]) ).
fof(f1625,plain,
( ~ ordinal(empty_set)
| ~ spl19_121
| ~ spl19_147
| spl19_154 ),
inference(subsumption_resolution,[],[f1623,f1332]) ).
fof(f1623,plain,
( ~ in(empty_set,sK0)
| ~ ordinal(empty_set)
| ~ spl19_121
| spl19_154 ),
inference(resolution,[],[f1620,f1023]) ).
fof(f1620,plain,
( ~ ordinal_subset(empty_set,sK0)
| spl19_154 ),
inference(avatar_component_clause,[],[f1619]) ).
fof(f1622,plain,
( spl19_154
| ~ spl19_8
| ~ spl19_108
| spl19_152 ),
inference(avatar_split_clause,[],[f1605,f1595,f916,f298,f1619]) ).
fof(f1605,plain,
( ordinal_subset(empty_set,sK0)
| ~ spl19_8
| ~ spl19_108
| spl19_152 ),
inference(subsumption_resolution,[],[f1599,f300]) ).
fof(f1599,plain,
( ordinal_subset(empty_set,sK0)
| ~ ordinal(empty_set)
| ~ spl19_108
| spl19_152 ),
inference(resolution,[],[f1597,f917]) ).
fof(f1604,plain,
( spl19_153
| ~ spl19_3
| ~ spl19_150 ),
inference(avatar_split_clause,[],[f1540,f1531,f273,f1601]) ).
fof(f1540,plain,
( in(sK0,succ(empty_set))
| ~ spl19_3
| ~ spl19_150 ),
inference(backward_demodulation,[],[f275,f1533]) ).
fof(f1533,plain,
( empty_set = sK1
| ~ spl19_150 ),
inference(avatar_component_clause,[],[f1531]) ).
fof(f1598,plain,
( ~ spl19_152
| spl19_4
| ~ spl19_150 ),
inference(avatar_split_clause,[],[f1541,f1531,f277,f1595]) ).
fof(f1541,plain,
( ~ ordinal_subset(sK0,empty_set)
| spl19_4
| ~ spl19_150 ),
inference(backward_demodulation,[],[f278,f1533]) ).
fof(f1576,plain,
( ~ spl19_83
| ~ spl19_106
| spl19_135
| ~ spl19_150 ),
inference(avatar_contradiction_clause,[],[f1575]) ).
fof(f1575,plain,
( $false
| ~ spl19_83
| ~ spl19_106
| spl19_135
| ~ spl19_150 ),
inference(subsumption_resolution,[],[f1556,f902]) ).
fof(f1556,plain,
( ~ empty(sK3(powerset(empty_set)))
| spl19_135
| ~ spl19_150 ),
inference(backward_demodulation,[],[f1117,f1533]) ).
fof(f1117,plain,
( ~ empty(sK3(powerset(sK1)))
| spl19_135 ),
inference(avatar_component_clause,[],[f1115]) ).
fof(f1538,plain,
( spl19_150
| spl19_151
| ~ spl19_8
| ~ spl19_46
| ~ spl19_143 ),
inference(avatar_split_clause,[],[f1529,f1175,f484,f298,f1535,f1531]) ).
fof(f1529,plain,
( in(empty_set,sK1)
| empty_set = sK1
| ~ spl19_8
| ~ spl19_46
| ~ spl19_143 ),
inference(subsumption_resolution,[],[f1522,f485]) ).
fof(f1522,plain,
( in(empty_set,sK1)
| in(sK1,empty_set)
| empty_set = sK1
| ~ spl19_8
| ~ spl19_143 ),
inference(resolution,[],[f1176,f300]) ).
fof(f1516,plain,
( spl19_149
| ~ spl19_32
| ~ spl19_41
| ~ spl19_142 ),
inference(avatar_split_clause,[],[f1186,f1168,f447,f411,f1514]) ).
fof(f1186,plain,
( ! [X0] :
( in(X0,sK0)
| sK0 = X0
| ~ empty(X0) )
| ~ spl19_32
| ~ spl19_41
| ~ spl19_142 ),
inference(subsumption_resolution,[],[f1178,f448]) ).
fof(f1178,plain,
( ! [X0] :
( in(X0,sK0)
| in(sK0,X0)
| sK0 = X0
| ~ empty(X0) )
| ~ spl19_32
| ~ spl19_142 ),
inference(resolution,[],[f1169,f412]) ).
fof(f1492,plain,
( ~ spl19_4
| spl19_141
| ~ spl19_1
| ~ spl19_111
| ~ spl19_137
| ~ spl19_140 ),
inference(avatar_split_clause,[],[f1472,f1148,f1126,f937,f263,f1152,f277]) ).
fof(f1472,plain,
( sK0 = sK1
| ~ ordinal_subset(sK0,sK1)
| ~ spl19_1
| ~ spl19_111
| ~ spl19_137
| ~ spl19_140 ),
inference(subsumption_resolution,[],[f1471,f265]) ).
fof(f1471,plain,
( sK0 = sK1
| ~ ordinal_subset(sK0,sK1)
| ~ ordinal(sK0)
| ~ spl19_111
| ~ spl19_137
| ~ spl19_140 ),
inference(subsumption_resolution,[],[f1141,f1149]) ).
fof(f1141,plain,
( sK0 = sK1
| ~ in(sK1,sK0)
| ~ ordinal_subset(sK0,sK1)
| ~ ordinal(sK0)
| ~ spl19_111
| ~ spl19_137 ),
inference(resolution,[],[f1127,f938]) ).
fof(f1470,plain,
( spl19_3
| ~ spl19_28
| ~ spl19_141 ),
inference(avatar_contradiction_clause,[],[f1469]) ).
fof(f1469,plain,
( $false
| spl19_3
| ~ spl19_28
| ~ spl19_141 ),
inference(subsumption_resolution,[],[f1468,f396]) ).
fof(f1468,plain,
( ~ in(sK0,succ(sK0))
| spl19_3
| ~ spl19_141 ),
inference(forward_demodulation,[],[f274,f1154]) ).
fof(f1154,plain,
( sK0 = sK1
| ~ spl19_141 ),
inference(avatar_component_clause,[],[f1152]) ).
fof(f274,plain,
( ~ in(sK0,succ(sK1))
| spl19_3 ),
inference(avatar_component_clause,[],[f273]) ).
fof(f1464,plain,
( ~ spl19_52
| ~ spl19_140
| ~ spl19_141 ),
inference(avatar_contradiction_clause,[],[f1463]) ).
fof(f1463,plain,
( $false
| ~ spl19_52
| ~ spl19_140
| ~ spl19_141 ),
inference(subsumption_resolution,[],[f1462,f509]) ).
fof(f1462,plain,
( in(sK0,sK0)
| ~ spl19_140
| ~ spl19_141 ),
inference(forward_demodulation,[],[f1149,f1154]) ).
fof(f1461,plain,
( ~ spl19_61
| ~ spl19_141
| spl19_148 ),
inference(avatar_contradiction_clause,[],[f1460]) ).
fof(f1460,plain,
( $false
| ~ spl19_61
| ~ spl19_141
| spl19_148 ),
inference(subsumption_resolution,[],[f1446,f577]) ).
fof(f1446,plain,
( ~ ordinal_subset(sK0,sK0)
| ~ spl19_141
| spl19_148 ),
inference(backward_demodulation,[],[f1414,f1154]) ).
fof(f1414,plain,
( ~ ordinal_subset(sK1,sK0)
| spl19_148 ),
inference(avatar_component_clause,[],[f1412]) ).
fof(f1423,plain,
( ~ spl19_2
| spl19_4
| ~ spl19_108
| spl19_148 ),
inference(avatar_contradiction_clause,[],[f1422]) ).
fof(f1422,plain,
( $false
| ~ spl19_2
| spl19_4
| ~ spl19_108
| spl19_148 ),
inference(subsumption_resolution,[],[f1421,f270]) ).
fof(f1421,plain,
( ~ ordinal(sK1)
| spl19_4
| ~ spl19_108
| spl19_148 ),
inference(subsumption_resolution,[],[f1417,f278]) ).
fof(f1417,plain,
( ordinal_subset(sK0,sK1)
| ~ ordinal(sK1)
| ~ spl19_108
| spl19_148 ),
inference(resolution,[],[f1414,f917]) ).
fof(f1420,plain,
( ~ spl19_1
| spl19_4
| ~ spl19_109
| spl19_148 ),
inference(avatar_contradiction_clause,[],[f1419]) ).
fof(f1419,plain,
( $false
| ~ spl19_1
| spl19_4
| ~ spl19_109
| spl19_148 ),
inference(subsumption_resolution,[],[f1418,f265]) ).
fof(f1418,plain,
( ~ ordinal(sK0)
| spl19_4
| ~ spl19_109
| spl19_148 ),
inference(subsumption_resolution,[],[f1416,f278]) ).
fof(f1416,plain,
( ordinal_subset(sK0,sK1)
| ~ ordinal(sK0)
| ~ spl19_109
| spl19_148 ),
inference(resolution,[],[f1414,f921]) ).
fof(f1415,plain,
( ~ spl19_148
| spl19_141
| ~ spl19_2
| ~ spl19_101
| ~ spl19_110
| ~ spl19_139 ),
inference(avatar_split_clause,[],[f1387,f1134,f933,f868,f268,f1152,f1412]) ).
fof(f1387,plain,
( sK0 = sK1
| ~ ordinal_subset(sK1,sK0)
| ~ spl19_2
| ~ spl19_101
| ~ spl19_110
| ~ spl19_139 ),
inference(subsumption_resolution,[],[f1266,f270]) ).
fof(f1266,plain,
( sK0 = sK1
| ~ ordinal_subset(sK1,sK0)
| ~ ordinal(sK1)
| ~ spl19_101
| ~ spl19_110
| ~ spl19_139 ),
inference(subsumption_resolution,[],[f1161,f869]) ).
fof(f869,plain,
( in(sK0,sK1)
| ~ spl19_101 ),
inference(avatar_component_clause,[],[f868]) ).
fof(f1161,plain,
( sK0 = sK1
| ~ in(sK0,sK1)
| ~ ordinal_subset(sK1,sK0)
| ~ ordinal(sK1)
| ~ spl19_110
| ~ spl19_139 ),
inference(resolution,[],[f1135,f934]) ).
fof(f1371,plain,
( ~ spl19_83
| ~ spl19_106
| spl19_132
| ~ spl19_146 ),
inference(avatar_contradiction_clause,[],[f1370]) ).
fof(f1370,plain,
( $false
| ~ spl19_83
| ~ spl19_106
| spl19_132
| ~ spl19_146 ),
inference(subsumption_resolution,[],[f1351,f902]) ).
fof(f1351,plain,
( ~ empty(sK3(powerset(empty_set)))
| spl19_132
| ~ spl19_146 ),
inference(backward_demodulation,[],[f1093,f1328]) ).
fof(f1328,plain,
( empty_set = sK0
| ~ spl19_146 ),
inference(avatar_component_clause,[],[f1326]) ).
fof(f1333,plain,
( spl19_146
| spl19_147
| ~ spl19_8
| ~ spl19_46
| ~ spl19_142 ),
inference(avatar_split_clause,[],[f1187,f1168,f484,f298,f1330,f1326]) ).
fof(f1187,plain,
( in(empty_set,sK0)
| empty_set = sK0
| ~ spl19_8
| ~ spl19_46
| ~ spl19_142 ),
inference(subsumption_resolution,[],[f1180,f485]) ).
fof(f1180,plain,
( in(empty_set,sK0)
| in(sK0,empty_set)
| empty_set = sK0
| ~ spl19_8
| ~ spl19_142 ),
inference(resolution,[],[f1169,f300]) ).
fof(f1286,plain,
spl19_145,
inference(avatar_split_clause,[],[f218,f1284]) ).
fof(f218,plain,
! [X2,X0,X1] :
( set_union2(X0,X1) = X2
| in(sK5(X0,X1,X2),X1)
| in(sK5(X0,X1,X2),X0)
| in(sK5(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f123]) ).
fof(f123,plain,
! [X0,X1,X2] :
( ( set_union2(X0,X1) = X2
| ( ( ( ~ in(sK5(X0,X1,X2),X1)
& ~ in(sK5(X0,X1,X2),X0) )
| ~ in(sK5(X0,X1,X2),X2) )
& ( in(sK5(X0,X1,X2),X1)
| in(sK5(X0,X1,X2),X0)
| in(sK5(X0,X1,X2),X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ( ~ in(X4,X1)
& ~ in(X4,X0) ) )
& ( in(X4,X1)
| in(X4,X0)
| ~ in(X4,X2) ) )
| set_union2(X0,X1) != X2 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5])],[f121,f122]) ).
fof(f122,plain,
! [X0,X1,X2] :
( ? [X3] :
( ( ( ~ in(X3,X1)
& ~ in(X3,X0) )
| ~ in(X3,X2) )
& ( in(X3,X1)
| in(X3,X0)
| in(X3,X2) ) )
=> ( ( ( ~ in(sK5(X0,X1,X2),X1)
& ~ in(sK5(X0,X1,X2),X0) )
| ~ in(sK5(X0,X1,X2),X2) )
& ( in(sK5(X0,X1,X2),X1)
| in(sK5(X0,X1,X2),X0)
| in(sK5(X0,X1,X2),X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f121,plain,
! [X0,X1,X2] :
( ( set_union2(X0,X1) = X2
| ? [X3] :
( ( ( ~ in(X3,X1)
& ~ in(X3,X0) )
| ~ in(X3,X2) )
& ( in(X3,X1)
| in(X3,X0)
| in(X3,X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ( ~ in(X4,X1)
& ~ in(X4,X0) ) )
& ( in(X4,X1)
| in(X4,X0)
| ~ in(X4,X2) ) )
| set_union2(X0,X1) != X2 ) ),
inference(rectify,[],[f120]) ).
fof(f120,plain,
! [X0,X1,X2] :
( ( set_union2(X0,X1) = X2
| ? [X3] :
( ( ( ~ in(X3,X1)
& ~ in(X3,X0) )
| ~ in(X3,X2) )
& ( in(X3,X1)
| in(X3,X0)
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ( ~ in(X3,X1)
& ~ in(X3,X0) ) )
& ( in(X3,X1)
| in(X3,X0)
| ~ in(X3,X2) ) )
| set_union2(X0,X1) != X2 ) ),
inference(flattening,[],[f119]) ).
fof(f119,plain,
! [X0,X1,X2] :
( ( set_union2(X0,X1) = X2
| ? [X3] :
( ( ( ~ in(X3,X1)
& ~ in(X3,X0) )
| ~ in(X3,X2) )
& ( in(X3,X1)
| in(X3,X0)
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ( ~ in(X3,X1)
& ~ in(X3,X0) ) )
& ( in(X3,X1)
| in(X3,X0)
| ~ in(X3,X2) ) )
| set_union2(X0,X1) != X2 ) ),
inference(nnf_transformation,[],[f14]) ).
fof(f14,axiom,
! [X0,X1,X2] :
( set_union2(X0,X1) = X2
<=> ! [X3] :
( in(X3,X2)
<=> ( in(X3,X1)
| in(X3,X0) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.woznqBvrsC/Vampire---4.8_317',d2_xboole_0) ).
fof(f1282,plain,
( ~ spl19_144
| ~ spl19_3
| ~ spl19_52 ),
inference(avatar_split_clause,[],[f1277,f508,f273,f1279]) ).
fof(f1277,plain,
( ~ in(succ(sK1),sK0)
| ~ spl19_3
| ~ spl19_52 ),
inference(resolution,[],[f275,f509]) ).
fof(f1265,plain,
( ~ spl19_101
| spl19_140
| ~ spl19_141 ),
inference(avatar_contradiction_clause,[],[f1264]) ).
fof(f1264,plain,
( $false
| ~ spl19_101
| spl19_140
| ~ spl19_141 ),
inference(subsumption_resolution,[],[f1263,f1237]) ).
fof(f1237,plain,
( ~ in(sK0,sK0)
| spl19_140
| ~ spl19_141 ),
inference(forward_demodulation,[],[f1150,f1154]) ).
fof(f1150,plain,
( ~ in(sK1,sK0)
| spl19_140 ),
inference(avatar_component_clause,[],[f1148]) ).
fof(f1263,plain,
( in(sK0,sK0)
| ~ spl19_101
| ~ spl19_141 ),
inference(forward_demodulation,[],[f869,f1154]) ).
fof(f1233,plain,
( spl19_4
| ~ spl19_61
| ~ spl19_141 ),
inference(avatar_contradiction_clause,[],[f1232]) ).
fof(f1232,plain,
( $false
| spl19_4
| ~ spl19_61
| ~ spl19_141 ),
inference(subsumption_resolution,[],[f1230,f577]) ).
fof(f1230,plain,
( ~ ordinal_subset(sK0,sK0)
| spl19_4
| ~ spl19_141 ),
inference(backward_demodulation,[],[f278,f1154]) ).
fof(f1228,plain,
( ~ spl19_2
| spl19_4
| ~ spl19_61
| spl19_101
| spl19_140
| ~ spl19_142 ),
inference(avatar_contradiction_clause,[],[f1227]) ).
fof(f1227,plain,
( $false
| ~ spl19_2
| spl19_4
| ~ spl19_61
| spl19_101
| spl19_140
| ~ spl19_142 ),
inference(subsumption_resolution,[],[f1226,f577]) ).
fof(f1226,plain,
( ~ ordinal_subset(sK0,sK0)
| ~ spl19_2
| spl19_4
| spl19_101
| spl19_140
| ~ spl19_142 ),
inference(forward_demodulation,[],[f278,f1189]) ).
fof(f1189,plain,
( sK0 = sK1
| ~ spl19_2
| spl19_101
| spl19_140
| ~ spl19_142 ),
inference(subsumption_resolution,[],[f1188,f870]) ).
fof(f1188,plain,
( in(sK0,sK1)
| sK0 = sK1
| ~ spl19_2
| spl19_140
| ~ spl19_142 ),
inference(subsumption_resolution,[],[f1182,f1150]) ).
fof(f1182,plain,
( in(sK1,sK0)
| in(sK0,sK1)
| sK0 = sK1
| ~ spl19_2
| ~ spl19_142 ),
inference(resolution,[],[f1169,f270]) ).
fof(f1214,plain,
( ~ spl19_2
| spl19_3
| ~ spl19_28
| spl19_101
| spl19_140
| ~ spl19_142 ),
inference(avatar_contradiction_clause,[],[f1213]) ).
fof(f1213,plain,
( $false
| ~ spl19_2
| spl19_3
| ~ spl19_28
| spl19_101
| spl19_140
| ~ spl19_142 ),
inference(subsumption_resolution,[],[f1193,f396]) ).
fof(f1193,plain,
( ~ in(sK0,succ(sK0))
| ~ spl19_2
| spl19_3
| spl19_101
| spl19_140
| ~ spl19_142 ),
inference(backward_demodulation,[],[f274,f1189]) ).
fof(f1191,plain,
( ~ spl19_2
| spl19_101
| spl19_140
| spl19_141
| ~ spl19_142 ),
inference(avatar_contradiction_clause,[],[f1190]) ).
fof(f1190,plain,
( $false
| ~ spl19_2
| spl19_101
| spl19_140
| spl19_141
| ~ spl19_142 ),
inference(subsumption_resolution,[],[f1189,f1153]) ).
fof(f1177,plain,
( spl19_143
| ~ spl19_2
| ~ spl19_126 ),
inference(avatar_split_clause,[],[f1063,f1051,f268,f1175]) ).
fof(f1063,plain,
( ! [X6] :
( sK1 = X6
| in(X6,sK1)
| in(sK1,X6)
| ~ ordinal(X6) )
| ~ spl19_2
| ~ spl19_126 ),
inference(resolution,[],[f1052,f270]) ).
fof(f1170,plain,
( spl19_142
| ~ spl19_1
| ~ spl19_126 ),
inference(avatar_split_clause,[],[f1062,f1051,f263,f1168]) ).
fof(f1062,plain,
( ! [X5] :
( sK0 = X5
| in(X5,sK0)
| in(sK0,X5)
| ~ ordinal(X5) )
| ~ spl19_1
| ~ spl19_126 ),
inference(resolution,[],[f1052,f265]) ).
fof(f1155,plain,
( ~ spl19_140
| spl19_141
| ~ spl19_1
| ~ spl19_4
| ~ spl19_111
| ~ spl19_137 ),
inference(avatar_split_clause,[],[f1146,f1126,f937,f277,f263,f1152,f1148]) ).
fof(f1146,plain,
( sK0 = sK1
| ~ in(sK1,sK0)
| ~ spl19_1
| ~ spl19_4
| ~ spl19_111
| ~ spl19_137 ),
inference(subsumption_resolution,[],[f1145,f265]) ).
fof(f1145,plain,
( sK0 = sK1
| ~ in(sK1,sK0)
| ~ ordinal(sK0)
| ~ spl19_4
| ~ spl19_111
| ~ spl19_137 ),
inference(subsumption_resolution,[],[f1141,f279]) ).
fof(f279,plain,
( ordinal_subset(sK0,sK1)
| ~ spl19_4 ),
inference(avatar_component_clause,[],[f277]) ).
fof(f1136,plain,
( spl19_139
| ~ spl19_89
| ~ spl19_127 ),
inference(avatar_split_clause,[],[f1070,f1056,f765,f1134]) ).
fof(f1070,plain,
( ! [X1] :
( ~ in(X1,sK1)
| sK1 = X1
| ~ subset(sK1,X1) )
| ~ spl19_89
| ~ spl19_127 ),
inference(resolution,[],[f1057,f766]) ).
fof(f1132,plain,
spl19_138,
inference(avatar_split_clause,[],[f220,f1130]) ).
fof(f220,plain,
! [X2,X0,X1] :
( set_union2(X0,X1) = X2
| ~ in(sK5(X0,X1,X2),X1)
| ~ in(sK5(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f123]) ).
fof(f1128,plain,
( spl19_137
| ~ spl19_89
| ~ spl19_119 ),
inference(avatar_split_clause,[],[f1016,f1011,f765,f1126]) ).
fof(f1016,plain,
( ! [X1] :
( ~ in(X1,sK0)
| sK0 = X1
| ~ subset(sK0,X1) )
| ~ spl19_89
| ~ spl19_119 ),
inference(resolution,[],[f1012,f766]) ).
fof(f1122,plain,
spl19_136,
inference(avatar_split_clause,[],[f219,f1120]) ).
fof(f219,plain,
! [X2,X0,X1] :
( set_union2(X0,X1) = X2
| ~ in(sK5(X0,X1,X2),X0)
| ~ in(sK5(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f123]) ).
fof(f1118,plain,
( ~ spl19_135
| ~ spl19_32
| spl19_133 ),
inference(avatar_split_clause,[],[f1113,f1105,f411,f1115]) ).
fof(f1113,plain,
( ~ empty(sK3(powerset(sK1)))
| ~ spl19_32
| spl19_133 ),
inference(resolution,[],[f1107,f412]) ).
fof(f1107,plain,
( ~ ordinal(sK3(powerset(sK1)))
| spl19_133 ),
inference(avatar_component_clause,[],[f1105]) ).
fof(f1112,plain,
( ~ spl19_133
| spl19_134
| ~ spl19_72
| ~ spl19_113 ),
inference(avatar_split_clause,[],[f968,f956,f645,f1109,f1105]) ).
fof(f968,plain,
( ordinal_subset(sK3(powerset(sK1)),sK1)
| ~ ordinal(sK3(powerset(sK1)))
| ~ spl19_72
| ~ spl19_113 ),
inference(resolution,[],[f957,f646]) ).
fof(f1094,plain,
( ~ spl19_132
| ~ spl19_32
| spl19_129 ),
inference(avatar_split_clause,[],[f1089,f1077,f411,f1091]) ).
fof(f1089,plain,
( ~ empty(sK3(powerset(sK0)))
| ~ spl19_32
| spl19_129 ),
inference(resolution,[],[f1079,f412]) ).
fof(f1088,plain,
spl19_131,
inference(avatar_split_clause,[],[f208,f1086]) ).
fof(f208,plain,
! [X0,X1] :
( singleton(X0) = X1
| sK4(X0,X1) = X0
| in(sK4(X0,X1),X1) ),
inference(cnf_transformation,[],[f117]) ).
fof(f117,plain,
! [X0,X1] :
( ( singleton(X0) = X1
| ( ( sK4(X0,X1) != X0
| ~ in(sK4(X0,X1),X1) )
& ( sK4(X0,X1) = X0
| in(sK4(X0,X1),X1) ) ) )
& ( ! [X3] :
( ( in(X3,X1)
| X0 != X3 )
& ( X0 = X3
| ~ in(X3,X1) ) )
| singleton(X0) != X1 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f115,f116]) ).
fof(f116,plain,
! [X0,X1] :
( ? [X2] :
( ( X0 != X2
| ~ in(X2,X1) )
& ( X0 = X2
| in(X2,X1) ) )
=> ( ( sK4(X0,X1) != X0
| ~ in(sK4(X0,X1),X1) )
& ( sK4(X0,X1) = X0
| in(sK4(X0,X1),X1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f115,plain,
! [X0,X1] :
( ( singleton(X0) = X1
| ? [X2] :
( ( X0 != X2
| ~ in(X2,X1) )
& ( X0 = X2
| in(X2,X1) ) ) )
& ( ! [X3] :
( ( in(X3,X1)
| X0 != X3 )
& ( X0 = X3
| ~ in(X3,X1) ) )
| singleton(X0) != X1 ) ),
inference(rectify,[],[f114]) ).
fof(f114,plain,
! [X0,X1] :
( ( singleton(X0) = X1
| ? [X2] :
( ( X0 != X2
| ~ in(X2,X1) )
& ( X0 = X2
| in(X2,X1) ) ) )
& ( ! [X2] :
( ( in(X2,X1)
| X0 != X2 )
& ( X0 = X2
| ~ in(X2,X1) ) )
| singleton(X0) != X1 ) ),
inference(nnf_transformation,[],[f12]) ).
fof(f12,axiom,
! [X0,X1] :
( singleton(X0) = X1
<=> ! [X2] :
( in(X2,X1)
<=> X0 = X2 ) ),
file('/export/starexec/sandbox2/tmp/tmp.woznqBvrsC/Vampire---4.8_317',d1_tarski) ).
fof(f1084,plain,
( ~ spl19_129
| spl19_130
| ~ spl19_72
| ~ spl19_112 ),
inference(avatar_split_clause,[],[f964,f952,f645,f1081,f1077]) ).
fof(f964,plain,
( ordinal_subset(sK3(powerset(sK0)),sK0)
| ~ ordinal(sK3(powerset(sK0)))
| ~ spl19_72
| ~ spl19_112 ),
inference(resolution,[],[f953,f646]) ).
fof(f1074,plain,
( spl19_128
| ~ spl19_113
| ~ spl19_127 ),
inference(avatar_split_clause,[],[f1069,f1056,f956,f1072]) ).
fof(f1069,plain,
( ! [X0] :
( ~ in(X0,sK1)
| ordinal_subset(X0,sK1)
| ~ ordinal(X0) )
| ~ spl19_113
| ~ spl19_127 ),
inference(resolution,[],[f1057,f957]) ).
fof(f1058,plain,
( spl19_127
| ~ spl19_74
| ~ spl19_122 ),
inference(avatar_split_clause,[],[f1043,f1027,f662,f1056]) ).
fof(f1027,plain,
( spl19_122
<=> epsilon_transitive(sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_122])]) ).
fof(f1043,plain,
( ! [X0] :
( ~ in(X0,sK1)
| subset(X0,sK1) )
| ~ spl19_74
| ~ spl19_122 ),
inference(resolution,[],[f1029,f663]) ).
fof(f1029,plain,
( epsilon_transitive(sK1)
| ~ spl19_122 ),
inference(avatar_component_clause,[],[f1027]) ).
fof(f1053,plain,
spl19_126,
inference(avatar_split_clause,[],[f176,f1051]) ).
fof(f176,plain,
! [X0,X1] :
( in(X1,X0)
| X0 = X1
| in(X0,X1)
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f71]) ).
fof(f71,plain,
! [X0] :
( ! [X1] :
( in(X1,X0)
| X0 = X1
| in(X0,X1)
| ~ ordinal(X1) )
| ~ ordinal(X0) ),
inference(flattening,[],[f70]) ).
fof(f70,plain,
! [X0] :
( ! [X1] :
( in(X1,X0)
| X0 = X1
| in(X0,X1)
| ~ ordinal(X1) )
| ~ ordinal(X0) ),
inference(ennf_transformation,[],[f46]) ).
fof(f46,axiom,
! [X0] :
( ordinal(X0)
=> ! [X1] :
( ordinal(X1)
=> ~ ( ~ in(X1,X0)
& X0 != X1
& ~ in(X0,X1) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.woznqBvrsC/Vampire---4.8_317',t24_ordinal1) ).
fof(f1049,plain,
( ~ spl19_125
| ~ spl19_32
| spl19_123 ),
inference(avatar_split_clause,[],[f1044,f1031,f411,f1046]) ).
fof(f1046,plain,
( spl19_125
<=> empty(sK2(sK1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_125])]) ).
fof(f1031,plain,
( spl19_123
<=> ordinal(sK2(sK1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_123])]) ).
fof(f1044,plain,
( ~ empty(sK2(sK1))
| ~ spl19_32
| spl19_123 ),
inference(resolution,[],[f1033,f412]) ).
fof(f1033,plain,
( ~ ordinal(sK2(sK1))
| spl19_123 ),
inference(avatar_component_clause,[],[f1031]) ).
fof(f1042,plain,
( ~ spl19_2
| ~ spl19_29
| spl19_122 ),
inference(avatar_contradiction_clause,[],[f1041]) ).
fof(f1041,plain,
( $false
| ~ spl19_2
| ~ spl19_29
| spl19_122 ),
inference(subsumption_resolution,[],[f1040,f270]) ).
fof(f1040,plain,
( ~ ordinal(sK1)
| ~ spl19_29
| spl19_122 ),
inference(resolution,[],[f1028,f400]) ).
fof(f1028,plain,
( ~ epsilon_transitive(sK1)
| spl19_122 ),
inference(avatar_component_clause,[],[f1027]) ).
fof(f1038,plain,
( spl19_122
| ~ spl19_123
| ~ spl19_124
| ~ spl19_49
| ~ spl19_111 ),
inference(avatar_split_clause,[],[f949,f937,f496,f1035,f1031,f1027]) ).
fof(f1035,plain,
( spl19_124
<=> ordinal_subset(sK2(sK1),sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_124])]) ).
fof(f949,plain,
( ~ ordinal_subset(sK2(sK1),sK1)
| ~ ordinal(sK2(sK1))
| epsilon_transitive(sK1)
| ~ spl19_49
| ~ spl19_111 ),
inference(resolution,[],[f938,f497]) ).
fof(f1024,plain,
( spl19_121
| ~ spl19_112
| ~ spl19_119 ),
inference(avatar_split_clause,[],[f1015,f1011,f952,f1022]) ).
fof(f1015,plain,
( ! [X0] :
( ~ in(X0,sK0)
| ordinal_subset(X0,sK0)
| ~ ordinal(X0) )
| ~ spl19_112
| ~ spl19_119 ),
inference(resolution,[],[f1012,f953]) ).
fof(f1020,plain,
spl19_120,
inference(avatar_split_clause,[],[f261,f1018]) ).
fof(f261,plain,
! [X0,X1] :
( singleton(X0) = X1
| sK4(X0,X1) != X0
| ~ in(X0,X1) ),
inference(inner_rewriting,[],[f209]) ).
fof(f209,plain,
! [X0,X1] :
( singleton(X0) = X1
| sK4(X0,X1) != X0
| ~ in(sK4(X0,X1),X1) ),
inference(cnf_transformation,[],[f117]) ).
fof(f1013,plain,
( spl19_119
| ~ spl19_74
| ~ spl19_114 ),
inference(avatar_split_clause,[],[f991,f971,f662,f1011]) ).
fof(f971,plain,
( spl19_114
<=> epsilon_transitive(sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_114])]) ).
fof(f991,plain,
( ! [X0] :
( ~ in(X0,sK0)
| subset(X0,sK0) )
| ~ spl19_74
| ~ spl19_114 ),
inference(resolution,[],[f973,f663]) ).
fof(f973,plain,
( epsilon_transitive(sK0)
| ~ spl19_114 ),
inference(avatar_component_clause,[],[f971]) ).
fof(f997,plain,
( ~ spl19_118
| ~ spl19_32
| spl19_115 ),
inference(avatar_split_clause,[],[f992,f975,f411,f994]) ).
fof(f994,plain,
( spl19_118
<=> empty(sK2(sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_118])]) ).
fof(f975,plain,
( spl19_115
<=> ordinal(sK2(sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_115])]) ).
fof(f992,plain,
( ~ empty(sK2(sK0))
| ~ spl19_32
| spl19_115 ),
inference(resolution,[],[f977,f412]) ).
fof(f977,plain,
( ~ ordinal(sK2(sK0))
| spl19_115 ),
inference(avatar_component_clause,[],[f975]) ).
fof(f990,plain,
spl19_117,
inference(avatar_split_clause,[],[f260,f988]) ).
fof(f260,plain,
! [X0,X1,X4] :
( in(X4,X1)
| in(X4,X0)
| ~ in(X4,set_union2(X0,X1)) ),
inference(equality_resolution,[],[f215]) ).
fof(f215,plain,
! [X2,X0,X1,X4] :
( in(X4,X1)
| in(X4,X0)
| ~ in(X4,X2)
| set_union2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f123]) ).
fof(f986,plain,
( ~ spl19_1
| ~ spl19_29
| spl19_114 ),
inference(avatar_contradiction_clause,[],[f985]) ).
fof(f985,plain,
( $false
| ~ spl19_1
| ~ spl19_29
| spl19_114 ),
inference(subsumption_resolution,[],[f984,f265]) ).
fof(f984,plain,
( ~ ordinal(sK0)
| ~ spl19_29
| spl19_114 ),
inference(resolution,[],[f972,f400]) ).
fof(f972,plain,
( ~ epsilon_transitive(sK0)
| spl19_114 ),
inference(avatar_component_clause,[],[f971]) ).
fof(f982,plain,
( spl19_114
| ~ spl19_115
| ~ spl19_116
| ~ spl19_49
| ~ spl19_110 ),
inference(avatar_split_clause,[],[f940,f933,f496,f979,f975,f971]) ).
fof(f979,plain,
( spl19_116
<=> ordinal_subset(sK2(sK0),sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_116])]) ).
fof(f940,plain,
( ~ ordinal_subset(sK2(sK0),sK0)
| ~ ordinal(sK2(sK0))
| epsilon_transitive(sK0)
| ~ spl19_49
| ~ spl19_110 ),
inference(resolution,[],[f934,f497]) ).
fof(f958,plain,
( spl19_113
| ~ spl19_2
| ~ spl19_103 ),
inference(avatar_split_clause,[],[f946,f877,f268,f956]) ).
fof(f946,plain,
( ! [X6] :
( ~ subset(X6,sK1)
| ordinal_subset(X6,sK1)
| ~ ordinal(X6) )
| ~ spl19_2
| ~ spl19_103 ),
inference(resolution,[],[f878,f270]) ).
fof(f954,plain,
( spl19_112
| ~ spl19_1
| ~ spl19_103 ),
inference(avatar_split_clause,[],[f945,f877,f263,f952]) ).
fof(f945,plain,
( ! [X5] :
( ~ subset(X5,sK0)
| ordinal_subset(X5,sK0)
| ~ ordinal(X5) )
| ~ spl19_1
| ~ spl19_103 ),
inference(resolution,[],[f878,f265]) ).
fof(f939,plain,
( spl19_111
| ~ spl19_2
| ~ spl19_100 ),
inference(avatar_split_clause,[],[f928,f853,f268,f937]) ).
fof(f928,plain,
( ! [X6] :
( ~ ordinal_subset(X6,sK1)
| subset(X6,sK1)
| ~ ordinal(X6) )
| ~ spl19_2
| ~ spl19_100 ),
inference(resolution,[],[f854,f270]) ).
fof(f935,plain,
( spl19_110
| ~ spl19_1
| ~ spl19_100 ),
inference(avatar_split_clause,[],[f927,f853,f263,f933]) ).
fof(f927,plain,
( ! [X5] :
( ~ ordinal_subset(X5,sK0)
| subset(X5,sK0)
| ~ ordinal(X5) )
| ~ spl19_1
| ~ spl19_100 ),
inference(resolution,[],[f854,f265]) ).
fof(f922,plain,
( spl19_109
| ~ spl19_2
| ~ spl19_97 ),
inference(avatar_split_clause,[],[f912,f840,f268,f920]) ).
fof(f912,plain,
( ! [X6] :
( ordinal_subset(X6,sK1)
| ordinal_subset(sK1,X6)
| ~ ordinal(X6) )
| ~ spl19_2
| ~ spl19_97 ),
inference(resolution,[],[f841,f270]) ).
fof(f918,plain,
( spl19_108
| ~ spl19_1
| ~ spl19_97 ),
inference(avatar_split_clause,[],[f911,f840,f263,f916]) ).
fof(f911,plain,
( ! [X5] :
( ordinal_subset(X5,sK0)
| ordinal_subset(sK0,X5)
| ~ ordinal(X5) )
| ~ spl19_1
| ~ spl19_97 ),
inference(resolution,[],[f841,f265]) ).
fof(f907,plain,
( spl19_107
| ~ spl19_48
| ~ spl19_106 ),
inference(avatar_split_clause,[],[f901,f898,f492,f904]) ).
fof(f904,plain,
( spl19_107
<=> epsilon_transitive(sK3(powerset(empty_set))) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_107])]) ).
fof(f901,plain,
( epsilon_transitive(sK3(powerset(empty_set)))
| ~ spl19_48
| ~ spl19_106 ),
inference(resolution,[],[f899,f493]) ).
fof(f900,plain,
( spl19_106
| ~ spl19_33
| ~ spl19_99 ),
inference(avatar_split_clause,[],[f894,f849,f415,f898]) ).
fof(f894,plain,
( ! [X0] : ~ in(X0,sK3(powerset(empty_set)))
| ~ spl19_33
| ~ spl19_99 ),
inference(resolution,[],[f850,f416]) ).
fof(f893,plain,
spl19_105,
inference(avatar_split_clause,[],[f214,f891]) ).
fof(f214,plain,
! [X2,X0,X1] :
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f98]) ).
fof(f98,plain,
! [X0,X1,X2] :
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(flattening,[],[f97]) ).
fof(f97,plain,
! [X0,X1,X2] :
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f51]) ).
fof(f51,axiom,
! [X0,X1,X2] :
( ( element(X1,powerset(X2))
& in(X0,X1) )
=> element(X0,X2) ),
file('/export/starexec/sandbox2/tmp/tmp.woznqBvrsC/Vampire---4.8_317',t4_subset) ).
fof(f883,plain,
( spl19_104
| ~ spl19_94
| ~ spl19_98 ),
inference(avatar_split_clause,[],[f864,f845,f824,f881]) ).
fof(f864,plain,
( ! [X12] : ~ in(singleton(succ(succ(X12))),X12)
| ~ spl19_94
| ~ spl19_98 ),
inference(resolution,[],[f846,f825]) ).
fof(f879,plain,
spl19_103,
inference(avatar_split_clause,[],[f201,f877]) ).
fof(f201,plain,
! [X0,X1] :
( ordinal_subset(X0,X1)
| ~ subset(X0,X1)
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f111]) ).
fof(f111,plain,
! [X0,X1] :
( ( ( ordinal_subset(X0,X1)
| ~ subset(X0,X1) )
& ( subset(X0,X1)
| ~ ordinal_subset(X0,X1) ) )
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(nnf_transformation,[],[f92]) ).
fof(f92,plain,
! [X0,X1] :
( ( ordinal_subset(X0,X1)
<=> subset(X0,X1) )
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(flattening,[],[f91]) ).
fof(f91,plain,
! [X0,X1] :
( ( ordinal_subset(X0,X1)
<=> subset(X0,X1) )
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(ennf_transformation,[],[f39]) ).
fof(f39,axiom,
! [X0,X1] :
( ( ordinal(X1)
& ordinal(X0) )
=> ( ordinal_subset(X0,X1)
<=> subset(X0,X1) ) ),
file('/export/starexec/sandbox2/tmp/tmp.woznqBvrsC/Vampire---4.8_317',redefinition_r1_ordinal1) ).
fof(f875,plain,
( spl19_102
| ~ spl19_93
| ~ spl19_98 ),
inference(avatar_split_clause,[],[f860,f845,f806,f873]) ).
fof(f860,plain,
( ! [X6] : ~ in(succ(succ(succ(X6))),X6)
| ~ spl19_93
| ~ spl19_98 ),
inference(resolution,[],[f846,f807]) ).
fof(f871,plain,
( ~ spl19_101
| spl19_3
| ~ spl19_98 ),
inference(avatar_split_clause,[],[f866,f845,f273,f868]) ).
fof(f866,plain,
( ~ in(sK0,sK1)
| spl19_3
| ~ spl19_98 ),
inference(resolution,[],[f846,f274]) ).
fof(f855,plain,
spl19_100,
inference(avatar_split_clause,[],[f200,f853]) ).
fof(f200,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ ordinal_subset(X0,X1)
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f111]) ).
fof(f851,plain,
( spl19_99
| ~ spl19_5
| ~ spl19_92 ),
inference(avatar_split_clause,[],[f827,f778,f283,f849]) ).
fof(f778,plain,
( spl19_92
<=> ! [X2,X0,X1] :
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_92])]) ).
fof(f827,plain,
( ! [X0,X1] :
( ~ element(X0,powerset(empty_set))
| ~ in(X1,X0) )
| ~ spl19_5
| ~ spl19_92 ),
inference(resolution,[],[f779,f285]) ).
fof(f779,plain,
( ! [X2,X0,X1] :
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) )
| ~ spl19_92 ),
inference(avatar_component_clause,[],[f778]) ).
fof(f847,plain,
( spl19_98
| ~ spl19_57
| ~ spl19_80 ),
inference(avatar_split_clause,[],[f748,f689,f541,f845]) ).
fof(f748,plain,
( ! [X8,X9] :
( in(X9,succ(X8))
| ~ in(X9,X8) )
| ~ spl19_57
| ~ spl19_80 ),
inference(superposition,[],[f690,f542]) ).
fof(f842,plain,
spl19_97,
inference(avatar_split_clause,[],[f199,f840]) ).
fof(f199,plain,
! [X0,X1] :
( ordinal_subset(X1,X0)
| ordinal_subset(X0,X1)
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f90]) ).
fof(f90,plain,
! [X0,X1] :
( ordinal_subset(X1,X0)
| ordinal_subset(X0,X1)
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(flattening,[],[f89]) ).
fof(f89,plain,
! [X0,X1] :
( ordinal_subset(X1,X0)
| ordinal_subset(X0,X1)
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(ennf_transformation,[],[f9]) ).
fof(f9,axiom,
! [X0,X1] :
( ( ordinal(X1)
& ordinal(X0) )
=> ( ordinal_subset(X1,X0)
| ordinal_subset(X0,X1) ) ),
file('/export/starexec/sandbox2/tmp/tmp.woznqBvrsC/Vampire---4.8_317',connectedness_r1_ordinal1) ).
fof(f837,plain,
( spl19_96
| ~ spl19_57
| ~ spl19_88 ),
inference(avatar_split_clause,[],[f794,f761,f541,f835]) ).
fof(f835,plain,
( spl19_96
<=> ! [X5] : ~ in(singleton(succ(X5)),singleton(X5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_96])]) ).
fof(f794,plain,
( ! [X5] : ~ in(singleton(succ(X5)),singleton(X5))
| ~ spl19_57
| ~ spl19_88 ),
inference(superposition,[],[f762,f542]) ).
fof(f833,plain,
( spl19_95
| ~ spl19_57
| ~ spl19_87 ),
inference(avatar_split_clause,[],[f786,f757,f541,f831]) ).
fof(f786,plain,
( ! [X5] : ~ in(succ(succ(X5)),singleton(X5))
| ~ spl19_57
| ~ spl19_87 ),
inference(superposition,[],[f758,f542]) ).
fof(f826,plain,
( spl19_94
| ~ spl19_57
| ~ spl19_91 ),
inference(avatar_split_clause,[],[f820,f773,f541,f824]) ).
fof(f820,plain,
( ! [X5] : ~ in(singleton(succ(X5)),X5)
| ~ spl19_57
| ~ spl19_91 ),
inference(superposition,[],[f774,f542]) ).
fof(f808,plain,
( spl19_93
| ~ spl19_57
| ~ spl19_90 ),
inference(avatar_split_clause,[],[f802,f769,f541,f806]) ).
fof(f802,plain,
( ! [X5] : ~ in(succ(succ(X5)),X5)
| ~ spl19_57
| ~ spl19_90 ),
inference(superposition,[],[f770,f542]) ).
fof(f780,plain,
spl19_92,
inference(avatar_split_clause,[],[f221,f778]) ).
fof(f221,plain,
! [X2,X0,X1] :
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f99]) ).
fof(f99,plain,
! [X0,X1,X2] :
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f52]) ).
fof(f52,axiom,
! [X0,X1,X2] :
~ ( empty(X2)
& element(X1,powerset(X2))
& in(X0,X1) ),
file('/export/starexec/sandbox2/tmp/tmp.woznqBvrsC/Vampire---4.8_317',t5_subset) ).
fof(f775,plain,
( spl19_91
| ~ spl19_55
| ~ spl19_80 ),
inference(avatar_split_clause,[],[f744,f689,f533,f773]) ).
fof(f744,plain,
( ! [X6,X5] : ~ in(singleton(set_union2(X5,X6)),X5)
| ~ spl19_55
| ~ spl19_80 ),
inference(resolution,[],[f690,f534]) ).
fof(f771,plain,
( spl19_90
| ~ spl19_54
| ~ spl19_80 ),
inference(avatar_split_clause,[],[f743,f689,f529,f769]) ).
fof(f743,plain,
( ! [X3,X4] : ~ in(succ(set_union2(X3,X4)),X3)
| ~ spl19_54
| ~ spl19_80 ),
inference(resolution,[],[f690,f530]) ).
fof(f767,plain,
spl19_89,
inference(avatar_split_clause,[],[f205,f765]) ).
fof(f205,plain,
! [X0,X1] :
( X0 = X1
| ~ subset(X1,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f113]) ).
fof(f113,plain,
! [X0,X1] :
( ( X0 = X1
| ~ subset(X1,X0)
| ~ subset(X0,X1) )
& ( ( subset(X1,X0)
& subset(X0,X1) )
| X0 != X1 ) ),
inference(flattening,[],[f112]) ).
fof(f112,plain,
! [X0,X1] :
( ( X0 = X1
| ~ subset(X1,X0)
| ~ subset(X0,X1) )
& ( ( subset(X1,X0)
& subset(X0,X1) )
| X0 != X1 ) ),
inference(nnf_transformation,[],[f10]) ).
fof(f10,axiom,
! [X0,X1] :
( X0 = X1
<=> ( subset(X1,X0)
& subset(X0,X1) ) ),
file('/export/starexec/sandbox2/tmp/tmp.woznqBvrsC/Vampire---4.8_317',d10_xboole_0) ).
fof(f763,plain,
( spl19_88
| ~ spl19_55
| ~ spl19_79 ),
inference(avatar_split_clause,[],[f723,f685,f533,f761]) ).
fof(f723,plain,
( ! [X6,X5] : ~ in(singleton(set_union2(X5,X6)),X6)
| ~ spl19_55
| ~ spl19_79 ),
inference(resolution,[],[f686,f534]) ).
fof(f759,plain,
( spl19_87
| ~ spl19_54
| ~ spl19_79 ),
inference(avatar_split_clause,[],[f722,f685,f529,f757]) ).
fof(f722,plain,
( ! [X3,X4] : ~ in(succ(set_union2(X3,X4)),X4)
| ~ spl19_54
| ~ spl19_79 ),
inference(resolution,[],[f686,f530]) ).
fof(f755,plain,
( spl19_86
| ~ spl19_52
| ~ spl19_83 ),
inference(avatar_split_clause,[],[f715,f712,f508,f753]) ).
fof(f753,plain,
( spl19_86
<=> ! [X0] :
( empty(X0)
| ~ in(X0,sK3(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_86])]) ).
fof(f715,plain,
( ! [X0] :
( empty(X0)
| ~ in(X0,sK3(X0)) )
| ~ spl19_52
| ~ spl19_83 ),
inference(resolution,[],[f713,f509]) ).
fof(f741,plain,
( spl19_85
| ~ spl19_33
| ~ spl19_84 ),
inference(avatar_split_clause,[],[f736,f731,f415,f738]) ).
fof(f738,plain,
( spl19_85
<=> element(empty_set,succ(empty_set)) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_85])]) ).
fof(f731,plain,
( spl19_84
<=> empty_set = sK3(succ(empty_set)) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_84])]) ).
fof(f736,plain,
( element(empty_set,succ(empty_set))
| ~ spl19_33
| ~ spl19_84 ),
inference(superposition,[],[f416,f733]) ).
fof(f733,plain,
( empty_set = sK3(succ(empty_set))
| ~ spl19_84 ),
inference(avatar_component_clause,[],[f731]) ).
fof(f734,plain,
( spl19_84
| ~ spl19_25
| ~ spl19_78
| ~ spl19_83 ),
inference(avatar_split_clause,[],[f720,f712,f679,f383,f731]) ).
fof(f383,plain,
( spl19_25
<=> ! [X0] : ~ empty(succ(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_25])]) ).
fof(f720,plain,
( empty_set = sK3(succ(empty_set))
| ~ spl19_25
| ~ spl19_78
| ~ spl19_83 ),
inference(subsumption_resolution,[],[f716,f384]) ).
fof(f384,plain,
( ! [X0] : ~ empty(succ(X0))
| ~ spl19_25 ),
inference(avatar_component_clause,[],[f383]) ).
fof(f716,plain,
( empty(succ(empty_set))
| empty_set = sK3(succ(empty_set))
| ~ spl19_78
| ~ spl19_83 ),
inference(resolution,[],[f713,f680]) ).
fof(f714,plain,
( spl19_83
| ~ spl19_33
| ~ spl19_77 ),
inference(avatar_split_clause,[],[f706,f674,f415,f712]) ).
fof(f706,plain,
( ! [X0] :
( empty(X0)
| in(sK3(X0),X0) )
| ~ spl19_33
| ~ spl19_77 ),
inference(resolution,[],[f675,f416]) ).
fof(f705,plain,
( spl19_82
| ~ spl19_16
| ~ spl19_74 ),
inference(avatar_split_clause,[],[f697,f662,f338,f703]) ).
fof(f338,plain,
( spl19_16
<=> epsilon_transitive(sK10) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_16])]) ).
fof(f697,plain,
( ! [X8] :
( ~ in(X8,sK10)
| subset(X8,sK10) )
| ~ spl19_16
| ~ spl19_74 ),
inference(resolution,[],[f663,f340]) ).
fof(f340,plain,
( epsilon_transitive(sK10)
| ~ spl19_16 ),
inference(avatar_component_clause,[],[f338]) ).
fof(f701,plain,
( spl19_81
| ~ spl19_12
| ~ spl19_74 ),
inference(avatar_split_clause,[],[f696,f662,f318,f699]) ).
fof(f318,plain,
( spl19_12
<=> epsilon_transitive(sK8) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_12])]) ).
fof(f696,plain,
( ! [X7] :
( ~ in(X7,sK8)
| subset(X7,sK8) )
| ~ spl19_12
| ~ spl19_74 ),
inference(resolution,[],[f663,f320]) ).
fof(f320,plain,
( epsilon_transitive(sK8)
| ~ spl19_12 ),
inference(avatar_component_clause,[],[f318]) ).
fof(f691,plain,
spl19_80,
inference(avatar_split_clause,[],[f259,f689]) ).
fof(f259,plain,
! [X0,X1,X4] :
( in(X4,set_union2(X0,X1))
| ~ in(X4,X0) ),
inference(equality_resolution,[],[f216]) ).
fof(f216,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| ~ in(X4,X0)
| set_union2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f123]) ).
fof(f687,plain,
spl19_79,
inference(avatar_split_clause,[],[f258,f685]) ).
fof(f258,plain,
! [X0,X1,X4] :
( in(X4,set_union2(X0,X1))
| ~ in(X4,X1) ),
inference(equality_resolution,[],[f217]) ).
fof(f217,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| ~ in(X4,X1)
| set_union2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f123]) ).
fof(f681,plain,
( spl19_78
| ~ spl19_70
| ~ spl19_73 ),
inference(avatar_split_clause,[],[f660,f650,f616,f679]) ).
fof(f650,plain,
( spl19_73
<=> singleton(empty_set) = succ(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_73])]) ).
fof(f660,plain,
( ! [X0] :
( ~ in(X0,succ(empty_set))
| empty_set = X0 )
| ~ spl19_70
| ~ spl19_73 ),
inference(superposition,[],[f617,f652]) ).
fof(f652,plain,
( singleton(empty_set) = succ(empty_set)
| ~ spl19_73 ),
inference(avatar_component_clause,[],[f650]) ).
fof(f676,plain,
spl19_77,
inference(avatar_split_clause,[],[f195,f674]) ).
fof(f195,plain,
! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(cnf_transformation,[],[f84]) ).
fof(f84,plain,
! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(flattening,[],[f83]) ).
fof(f83,plain,
! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(ennf_transformation,[],[f47]) ).
fof(f47,axiom,
! [X0,X1] :
( element(X0,X1)
=> ( in(X0,X1)
| empty(X1) ) ),
file('/export/starexec/sandbox2/tmp/tmp.woznqBvrsC/Vampire---4.8_317',t2_subset) ).
fof(f672,plain,
( spl19_76
| ~ spl19_53
| ~ spl19_62 ),
inference(avatar_split_clause,[],[f635,f580,f512,f670]) ).
fof(f635,plain,
( ! [X2,X1] :
( subset(X1,X2)
| ~ in(X1,powerset(X2)) )
| ~ spl19_53
| ~ spl19_62 ),
inference(resolution,[],[f581,f513]) ).
fof(f668,plain,
( spl19_75
| ~ spl19_38
| ~ spl19_60 ),
inference(avatar_split_clause,[],[f568,f552,f435,f666]) ).
fof(f666,plain,
( spl19_75
<=> ! [X1] :
( ordinal_subset(succ(X1),succ(X1))
| ~ ordinal(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_75])]) ).
fof(f568,plain,
( ! [X1] :
( ordinal_subset(succ(X1),succ(X1))
| ~ ordinal(X1) )
| ~ spl19_38
| ~ spl19_60 ),
inference(resolution,[],[f553,f436]) ).
fof(f664,plain,
spl19_74,
inference(avatar_split_clause,[],[f186,f662]) ).
fof(f186,plain,
! [X2,X0] :
( subset(X2,X0)
| ~ in(X2,X0)
| ~ epsilon_transitive(X0) ),
inference(cnf_transformation,[],[f108]) ).
fof(f108,plain,
! [X0] :
( ( epsilon_transitive(X0)
| ( ~ subset(sK2(X0),X0)
& in(sK2(X0),X0) ) )
& ( ! [X2] :
( subset(X2,X0)
| ~ in(X2,X0) )
| ~ epsilon_transitive(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f106,f107]) ).
fof(f107,plain,
! [X0] :
( ? [X1] :
( ~ subset(X1,X0)
& in(X1,X0) )
=> ( ~ subset(sK2(X0),X0)
& in(sK2(X0),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f106,plain,
! [X0] :
( ( epsilon_transitive(X0)
| ? [X1] :
( ~ subset(X1,X0)
& in(X1,X0) ) )
& ( ! [X2] :
( subset(X2,X0)
| ~ in(X2,X0) )
| ~ epsilon_transitive(X0) ) ),
inference(rectify,[],[f105]) ).
fof(f105,plain,
! [X0] :
( ( epsilon_transitive(X0)
| ? [X1] :
( ~ subset(X1,X0)
& in(X1,X0) ) )
& ( ! [X1] :
( subset(X1,X0)
| ~ in(X1,X0) )
| ~ epsilon_transitive(X0) ) ),
inference(nnf_transformation,[],[f80]) ).
fof(f80,plain,
! [X0] :
( epsilon_transitive(X0)
<=> ! [X1] :
( subset(X1,X0)
| ~ in(X1,X0) ) ),
inference(ennf_transformation,[],[f13]) ).
fof(f13,axiom,
! [X0] :
( epsilon_transitive(X0)
<=> ! [X1] :
( in(X1,X0)
=> subset(X1,X0) ) ),
file('/export/starexec/sandbox2/tmp/tmp.woznqBvrsC/Vampire---4.8_317',d2_ordinal1) ).
fof(f653,plain,
( spl19_73
| ~ spl19_57
| ~ spl19_71 ),
inference(avatar_split_clause,[],[f638,f631,f541,f650]) ).
fof(f631,plain,
( spl19_71
<=> ! [X6] : set_union2(empty_set,X6) = X6 ),
introduced(avatar_definition,[new_symbols(naming,[spl19_71])]) ).
fof(f638,plain,
( singleton(empty_set) = succ(empty_set)
| ~ spl19_57
| ~ spl19_71 ),
inference(superposition,[],[f632,f542]) ).
fof(f632,plain,
( ! [X6] : set_union2(empty_set,X6) = X6
| ~ spl19_71 ),
inference(avatar_component_clause,[],[f631]) ).
fof(f647,plain,
( spl19_72
| ~ spl19_33
| ~ spl19_62 ),
inference(avatar_split_clause,[],[f634,f580,f415,f645]) ).
fof(f634,plain,
( ! [X0] : subset(sK3(powerset(X0)),X0)
| ~ spl19_33
| ~ spl19_62 ),
inference(resolution,[],[f581,f416]) ).
fof(f633,plain,
( spl19_71
| ~ spl19_35
| ~ spl19_58 ),
inference(avatar_split_clause,[],[f622,f545,f423,f631]) ).
fof(f423,plain,
( spl19_35
<=> ! [X0] : set_union2(X0,empty_set) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl19_35])]) ).
fof(f622,plain,
( ! [X6] : set_union2(empty_set,X6) = X6
| ~ spl19_35
| ~ spl19_58 ),
inference(superposition,[],[f546,f424]) ).
fof(f424,plain,
( ! [X0] : set_union2(X0,empty_set) = X0
| ~ spl19_35 ),
inference(avatar_component_clause,[],[f423]) ).
fof(f618,plain,
spl19_70,
inference(avatar_split_clause,[],[f257,f616]) ).
fof(f257,plain,
! [X3,X0] :
( X0 = X3
| ~ in(X3,singleton(X0)) ),
inference(equality_resolution,[],[f206]) ).
fof(f206,plain,
! [X3,X0,X1] :
( X0 = X3
| ~ in(X3,X1)
| singleton(X0) != X1 ),
inference(cnf_transformation,[],[f117]) ).
fof(f614,plain,
( spl19_69
| ~ spl19_32
| ~ spl19_60 ),
inference(avatar_split_clause,[],[f567,f552,f411,f612]) ).
fof(f612,plain,
( spl19_69
<=> ! [X0] :
( ordinal_subset(X0,X0)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_69])]) ).
fof(f567,plain,
( ! [X0] :
( ordinal_subset(X0,X0)
| ~ empty(X0) )
| ~ spl19_32
| ~ spl19_60 ),
inference(resolution,[],[f553,f412]) ).
fof(f610,plain,
spl19_68,
inference(avatar_split_clause,[],[f212,f608]) ).
fof(f608,plain,
( spl19_68
<=> ! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_68])]) ).
fof(f212,plain,
! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) ),
inference(cnf_transformation,[],[f95]) ).
fof(f95,plain,
! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) ),
inference(ennf_transformation,[],[f55]) ).
fof(f55,axiom,
! [X0,X1] :
~ ( empty(X1)
& X0 != X1
& empty(X0) ),
file('/export/starexec/sandbox2/tmp/tmp.woznqBvrsC/Vampire---4.8_317',t8_boole) ).
fof(f606,plain,
( spl19_67
| ~ spl19_18
| ~ spl19_60 ),
inference(avatar_split_clause,[],[f573,f552,f348,f603]) ).
fof(f573,plain,
( ordinal_subset(sK10,sK10)
| ~ spl19_18
| ~ spl19_60 ),
inference(resolution,[],[f553,f350]) ).
fof(f601,plain,
( spl19_66
| ~ spl19_14
| ~ spl19_60 ),
inference(avatar_split_clause,[],[f572,f552,f328,f598]) ).
fof(f598,plain,
( spl19_66
<=> ordinal_subset(sK8,sK8) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_66])]) ).
fof(f572,plain,
( ordinal_subset(sK8,sK8)
| ~ spl19_14
| ~ spl19_60 ),
inference(resolution,[],[f553,f330]) ).
fof(f596,plain,
( spl19_65
| ~ spl19_8
| ~ spl19_60 ),
inference(avatar_split_clause,[],[f569,f552,f298,f593]) ).
fof(f569,plain,
( ordinal_subset(empty_set,empty_set)
| ~ spl19_8
| ~ spl19_60 ),
inference(resolution,[],[f553,f300]) ).
fof(f591,plain,
spl19_64,
inference(avatar_split_clause,[],[f211,f589]) ).
fof(f211,plain,
! [X0,X1] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f118]) ).
fof(f118,plain,
! [X0,X1] :
( ( element(X0,powerset(X1))
| ~ subset(X0,X1) )
& ( subset(X0,X1)
| ~ element(X0,powerset(X1)) ) ),
inference(nnf_transformation,[],[f50]) ).
fof(f50,axiom,
! [X0,X1] :
( element(X0,powerset(X1))
<=> subset(X0,X1) ),
file('/export/starexec/sandbox2/tmp/tmp.woznqBvrsC/Vampire---4.8_317',t3_subset) ).
fof(f587,plain,
( spl19_63
| ~ spl19_2
| ~ spl19_60 ),
inference(avatar_split_clause,[],[f571,f552,f268,f584]) ).
fof(f571,plain,
( ordinal_subset(sK1,sK1)
| ~ spl19_2
| ~ spl19_60 ),
inference(resolution,[],[f553,f270]) ).
fof(f582,plain,
spl19_62,
inference(avatar_split_clause,[],[f210,f580]) ).
fof(f210,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f118]) ).
fof(f578,plain,
( spl19_61
| ~ spl19_1
| ~ spl19_60 ),
inference(avatar_split_clause,[],[f570,f552,f263,f575]) ).
fof(f570,plain,
( ordinal_subset(sK0,sK0)
| ~ spl19_1
| ~ spl19_60 ),
inference(resolution,[],[f553,f265]) ).
fof(f566,plain,
( ~ spl19_8
| ~ spl19_59 ),
inference(avatar_contradiction_clause,[],[f557]) ).
fof(f557,plain,
( $false
| ~ spl19_8
| ~ spl19_59 ),
inference(resolution,[],[f550,f300]) ).
fof(f550,plain,
( ! [X1] : ~ ordinal(X1)
| ~ spl19_59 ),
inference(avatar_component_clause,[],[f549]) ).
fof(f549,plain,
( spl19_59
<=> ! [X1] : ~ ordinal(X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_59])]) ).
fof(f565,plain,
( ~ spl19_1
| ~ spl19_59 ),
inference(avatar_contradiction_clause,[],[f558]) ).
fof(f558,plain,
( $false
| ~ spl19_1
| ~ spl19_59 ),
inference(resolution,[],[f550,f265]) ).
fof(f564,plain,
( ~ spl19_2
| ~ spl19_59 ),
inference(avatar_contradiction_clause,[],[f559]) ).
fof(f559,plain,
( $false
| ~ spl19_2
| ~ spl19_59 ),
inference(resolution,[],[f550,f270]) ).
fof(f563,plain,
( ~ spl19_14
| ~ spl19_59 ),
inference(avatar_contradiction_clause,[],[f560]) ).
fof(f560,plain,
( $false
| ~ spl19_14
| ~ spl19_59 ),
inference(resolution,[],[f550,f330]) ).
fof(f562,plain,
( ~ spl19_18
| ~ spl19_59 ),
inference(avatar_contradiction_clause,[],[f561]) ).
fof(f561,plain,
( $false
| ~ spl19_18
| ~ spl19_59 ),
inference(resolution,[],[f550,f350]) ).
fof(f554,plain,
( spl19_59
| spl19_60 ),
inference(avatar_split_clause,[],[f198,f552,f549]) ).
fof(f198,plain,
! [X0,X1] :
( ordinal_subset(X0,X0)
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f88]) ).
fof(f88,plain,
! [X0,X1] :
( ordinal_subset(X0,X0)
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(flattening,[],[f87]) ).
fof(f87,plain,
! [X0,X1] :
( ordinal_subset(X0,X0)
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(ennf_transformation,[],[f40]) ).
fof(f40,axiom,
! [X0,X1] :
( ( ordinal(X1)
& ordinal(X0) )
=> ordinal_subset(X0,X0) ),
file('/export/starexec/sandbox2/tmp/tmp.woznqBvrsC/Vampire---4.8_317',reflexivity_r1_ordinal1) ).
fof(f547,plain,
spl19_58,
inference(avatar_split_clause,[],[f192,f545]) ).
fof(f192,plain,
! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
inference(cnf_transformation,[],[f8]) ).
fof(f8,axiom,
! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
file('/export/starexec/sandbox2/tmp/tmp.woznqBvrsC/Vampire---4.8_317',commutativity_k2_xboole_0) ).
fof(f543,plain,
spl19_57,
inference(avatar_split_clause,[],[f169,f541]) ).
fof(f169,plain,
! [X0] : succ(X0) = set_union2(X0,singleton(X0)),
inference(cnf_transformation,[],[f11]) ).
fof(f11,axiom,
! [X0] : succ(X0) = set_union2(X0,singleton(X0)),
file('/export/starexec/sandbox2/tmp/tmp.woznqBvrsC/Vampire---4.8_317',d1_ordinal1) ).
fof(f539,plain,
( spl19_56
| ~ spl19_48
| ~ spl19_52 ),
inference(avatar_split_clause,[],[f527,f508,f492,f537]) ).
fof(f537,plain,
( spl19_56
<=> ! [X2] :
( ~ in(X2,sK2(X2))
| epsilon_transitive(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_56])]) ).
fof(f527,plain,
( ! [X2] :
( ~ in(X2,sK2(X2))
| epsilon_transitive(X2) )
| ~ spl19_48
| ~ spl19_52 ),
inference(resolution,[],[f509,f493]) ).
fof(f535,plain,
( spl19_55
| ~ spl19_34
| ~ spl19_52 ),
inference(avatar_split_clause,[],[f526,f508,f419,f533]) ).
fof(f526,plain,
( ! [X1] : ~ in(singleton(X1),X1)
| ~ spl19_34
| ~ spl19_52 ),
inference(resolution,[],[f509,f420]) ).
fof(f531,plain,
( spl19_54
| ~ spl19_28
| ~ spl19_52 ),
inference(avatar_split_clause,[],[f525,f508,f395,f529]) ).
fof(f525,plain,
( ! [X0] : ~ in(succ(X0),X0)
| ~ spl19_28
| ~ spl19_52 ),
inference(resolution,[],[f509,f396]) ).
fof(f514,plain,
spl19_53,
inference(avatar_split_clause,[],[f197,f512]) ).
fof(f197,plain,
! [X0,X1] :
( element(X0,X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f86]) ).
fof(f86,plain,
! [X0,X1] :
( element(X0,X1)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f45]) ).
fof(f45,axiom,
! [X0,X1] :
( in(X0,X1)
=> element(X0,X1) ),
file('/export/starexec/sandbox2/tmp/tmp.woznqBvrsC/Vampire---4.8_317',t1_subset) ).
fof(f510,plain,
spl19_52,
inference(avatar_split_clause,[],[f196,f508]) ).
fof(f196,plain,
! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f85]) ).
fof(f85,plain,
! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f1]) ).
fof(f1,axiom,
! [X0,X1] :
( in(X0,X1)
=> ~ in(X1,X0) ),
file('/export/starexec/sandbox2/tmp/tmp.woznqBvrsC/Vampire---4.8_317',antisymmetry_r2_hidden) ).
fof(f506,plain,
spl19_51,
inference(avatar_split_clause,[],[f194,f504]) ).
fof(f504,plain,
( spl19_51
<=> ! [X0,X1] :
( ~ empty(set_union2(X1,X0))
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_51])]) ).
fof(f194,plain,
! [X0,X1] :
( ~ empty(set_union2(X1,X0))
| empty(X0) ),
inference(cnf_transformation,[],[f82]) ).
fof(f82,plain,
! [X0,X1] :
( ~ empty(set_union2(X1,X0))
| empty(X0) ),
inference(ennf_transformation,[],[f23]) ).
fof(f23,axiom,
! [X0,X1] :
( ~ empty(X0)
=> ~ empty(set_union2(X1,X0)) ),
file('/export/starexec/sandbox2/tmp/tmp.woznqBvrsC/Vampire---4.8_317',fc3_xboole_0) ).
fof(f502,plain,
spl19_50,
inference(avatar_split_clause,[],[f193,f500]) ).
fof(f193,plain,
! [X0,X1] :
( ~ empty(set_union2(X0,X1))
| empty(X0) ),
inference(cnf_transformation,[],[f81]) ).
fof(f81,plain,
! [X0,X1] :
( ~ empty(set_union2(X0,X1))
| empty(X0) ),
inference(ennf_transformation,[],[f21]) ).
fof(f21,axiom,
! [X0,X1] :
( ~ empty(X0)
=> ~ empty(set_union2(X0,X1)) ),
file('/export/starexec/sandbox2/tmp/tmp.woznqBvrsC/Vampire---4.8_317',fc2_xboole_0) ).
fof(f498,plain,
spl19_49,
inference(avatar_split_clause,[],[f188,f496]) ).
fof(f188,plain,
! [X0] :
( epsilon_transitive(X0)
| ~ subset(sK2(X0),X0) ),
inference(cnf_transformation,[],[f108]) ).
fof(f494,plain,
spl19_48,
inference(avatar_split_clause,[],[f187,f492]) ).
fof(f187,plain,
! [X0] :
( epsilon_transitive(X0)
| in(sK2(X0),X0) ),
inference(cnf_transformation,[],[f108]) ).
fof(f490,plain,
spl19_47,
inference(avatar_split_clause,[],[f183,f488]) ).
fof(f488,plain,
( spl19_47
<=> ! [X0] :
( ordinal(X0)
| ~ epsilon_connected(X0)
| ~ epsilon_transitive(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_47])]) ).
fof(f183,plain,
! [X0] :
( ordinal(X0)
| ~ epsilon_connected(X0)
| ~ epsilon_transitive(X0) ),
inference(cnf_transformation,[],[f77]) ).
fof(f77,plain,
! [X0] :
( ordinal(X0)
| ~ epsilon_connected(X0)
| ~ epsilon_transitive(X0) ),
inference(flattening,[],[f76]) ).
fof(f76,plain,
! [X0] :
( ordinal(X0)
| ~ epsilon_connected(X0)
| ~ epsilon_transitive(X0) ),
inference(ennf_transformation,[],[f6]) ).
fof(f6,axiom,
! [X0] :
( ( epsilon_connected(X0)
& epsilon_transitive(X0) )
=> ordinal(X0) ),
file('/export/starexec/sandbox2/tmp/tmp.woznqBvrsC/Vampire---4.8_317',cc2_ordinal1) ).
fof(f486,plain,
( spl19_46
| ~ spl19_5
| ~ spl19_41 ),
inference(avatar_split_clause,[],[f482,f447,f283,f484]) ).
fof(f482,plain,
( ! [X0] : ~ in(X0,empty_set)
| ~ spl19_5
| ~ spl19_41 ),
inference(resolution,[],[f448,f285]) ).
fof(f481,plain,
( spl19_45
| ~ spl19_24
| ~ spl19_39 ),
inference(avatar_split_clause,[],[f454,f439,f378,f478]) ).
fof(f478,plain,
( spl19_45
<=> empty_set = sK18 ),
introduced(avatar_definition,[new_symbols(naming,[spl19_45])]) ).
fof(f378,plain,
( spl19_24
<=> empty(sK18) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_24])]) ).
fof(f454,plain,
( empty_set = sK18
| ~ spl19_24
| ~ spl19_39 ),
inference(resolution,[],[f440,f380]) ).
fof(f380,plain,
( empty(sK18)
| ~ spl19_24 ),
inference(avatar_component_clause,[],[f378]) ).
fof(f476,plain,
( spl19_44
| ~ spl19_20
| ~ spl19_39 ),
inference(avatar_split_clause,[],[f453,f439,f358,f473]) ).
fof(f473,plain,
( spl19_44
<=> empty_set = sK17 ),
introduced(avatar_definition,[new_symbols(naming,[spl19_44])]) ).
fof(f358,plain,
( spl19_20
<=> empty(sK17) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_20])]) ).
fof(f453,plain,
( empty_set = sK17
| ~ spl19_20
| ~ spl19_39 ),
inference(resolution,[],[f440,f360]) ).
fof(f360,plain,
( empty(sK17)
| ~ spl19_20 ),
inference(avatar_component_clause,[],[f358]) ).
fof(f471,plain,
( spl19_43
| ~ spl19_19
| ~ spl19_39 ),
inference(avatar_split_clause,[],[f452,f439,f353,f468]) ).
fof(f468,plain,
( spl19_43
<=> empty_set = sK11 ),
introduced(avatar_definition,[new_symbols(naming,[spl19_43])]) ).
fof(f353,plain,
( spl19_19
<=> empty(sK11) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_19])]) ).
fof(f452,plain,
( empty_set = sK11
| ~ spl19_19
| ~ spl19_39 ),
inference(resolution,[],[f440,f355]) ).
fof(f355,plain,
( empty(sK11)
| ~ spl19_19 ),
inference(avatar_component_clause,[],[f353]) ).
fof(f466,plain,
( spl19_42
| ~ spl19_10
| ~ spl19_39 ),
inference(avatar_split_clause,[],[f451,f439,f308,f463]) ).
fof(f463,plain,
( spl19_42
<=> empty_set = sK7 ),
introduced(avatar_definition,[new_symbols(naming,[spl19_42])]) ).
fof(f308,plain,
( spl19_10
<=> empty(sK7) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_10])]) ).
fof(f451,plain,
( empty_set = sK7
| ~ spl19_10
| ~ spl19_39 ),
inference(resolution,[],[f440,f310]) ).
fof(f310,plain,
( empty(sK7)
| ~ spl19_10 ),
inference(avatar_component_clause,[],[f308]) ).
fof(f449,plain,
spl19_41,
inference(avatar_split_clause,[],[f213,f447]) ).
fof(f213,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f96]) ).
fof(f96,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f54]) ).
fof(f54,axiom,
! [X0,X1] :
~ ( empty(X1)
& in(X0,X1) ),
file('/export/starexec/sandbox2/tmp/tmp.woznqBvrsC/Vampire---4.8_317',t7_boole) ).
fof(f445,plain,
spl19_40,
inference(avatar_split_clause,[],[f191,f443]) ).
fof(f191,plain,
! [X0] : set_union2(X0,X0) = X0,
inference(cnf_transformation,[],[f57]) ).
fof(f57,plain,
! [X0] : set_union2(X0,X0) = X0,
inference(rectify,[],[f25]) ).
fof(f25,axiom,
! [X0,X1] : set_union2(X0,X0) = X0,
file('/export/starexec/sandbox2/tmp/tmp.woznqBvrsC/Vampire---4.8_317',idempotence_k2_xboole_0) ).
fof(f441,plain,
spl19_39,
inference(avatar_split_clause,[],[f179,f439]) ).
fof(f179,plain,
! [X0] :
( empty_set = X0
| ~ empty(X0) ),
inference(cnf_transformation,[],[f74]) ).
fof(f74,plain,
! [X0] :
( empty_set = X0
| ~ empty(X0) ),
inference(ennf_transformation,[],[f53]) ).
fof(f53,axiom,
! [X0] :
( empty(X0)
=> empty_set = X0 ),
file('/export/starexec/sandbox2/tmp/tmp.woznqBvrsC/Vampire---4.8_317',t6_boole) ).
fof(f437,plain,
spl19_38,
inference(avatar_split_clause,[],[f175,f435]) ).
fof(f175,plain,
! [X0] :
( ordinal(succ(X0))
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f69]) ).
fof(f69,plain,
! [X0] :
( ( ordinal(succ(X0))
& epsilon_connected(succ(X0))
& epsilon_transitive(succ(X0))
& ~ empty(succ(X0)) )
| ~ ordinal(X0) ),
inference(ennf_transformation,[],[f22]) ).
fof(f22,axiom,
! [X0] :
( ordinal(X0)
=> ( ordinal(succ(X0))
& epsilon_connected(succ(X0))
& epsilon_transitive(succ(X0))
& ~ empty(succ(X0)) ) ),
file('/export/starexec/sandbox2/tmp/tmp.woznqBvrsC/Vampire---4.8_317',fc3_ordinal1) ).
fof(f433,plain,
spl19_37,
inference(avatar_split_clause,[],[f174,f431]) ).
fof(f431,plain,
( spl19_37
<=> ! [X0] :
( epsilon_connected(succ(X0))
| ~ ordinal(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_37])]) ).
fof(f174,plain,
! [X0] :
( epsilon_connected(succ(X0))
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f69]) ).
fof(f429,plain,
spl19_36,
inference(avatar_split_clause,[],[f173,f427]) ).
fof(f173,plain,
! [X0] :
( epsilon_transitive(succ(X0))
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f69]) ).
fof(f425,plain,
spl19_35,
inference(avatar_split_clause,[],[f168,f423]) ).
fof(f168,plain,
! [X0] : set_union2(X0,empty_set) = X0,
inference(cnf_transformation,[],[f44]) ).
fof(f44,axiom,
! [X0] : set_union2(X0,empty_set) = X0,
file('/export/starexec/sandbox2/tmp/tmp.woznqBvrsC/Vampire---4.8_317',t1_boole) ).
fof(f421,plain,
spl19_34,
inference(avatar_split_clause,[],[f256,f419]) ).
fof(f256,plain,
! [X3] : in(X3,singleton(X3)),
inference(equality_resolution,[],[f255]) ).
fof(f255,plain,
! [X3,X1] :
( in(X3,X1)
| singleton(X3) != X1 ),
inference(equality_resolution,[],[f207]) ).
fof(f207,plain,
! [X3,X0,X1] :
( in(X3,X1)
| X0 != X3
| singleton(X0) != X1 ),
inference(cnf_transformation,[],[f117]) ).
fof(f417,plain,
spl19_33,
inference(avatar_split_clause,[],[f189,f415]) ).
fof(f189,plain,
! [X0] : element(sK3(X0),X0),
inference(cnf_transformation,[],[f110]) ).
fof(f110,plain,
! [X0] : element(sK3(X0),X0),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f15,f109]) ).
fof(f109,plain,
! [X0] :
( ? [X1] : element(X1,X0)
=> element(sK3(X0),X0) ),
introduced(choice_axiom,[]) ).
fof(f15,axiom,
! [X0] :
? [X1] : element(X1,X0),
file('/export/starexec/sandbox2/tmp/tmp.woznqBvrsC/Vampire---4.8_317',existence_m1_subset_1) ).
fof(f413,plain,
spl19_32,
inference(avatar_split_clause,[],[f182,f411]) ).
fof(f182,plain,
! [X0] :
( ordinal(X0)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f75]) ).
fof(f75,plain,
! [X0] :
( ( ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0) )
| ~ empty(X0) ),
inference(ennf_transformation,[],[f7]) ).
fof(f7,axiom,
! [X0] :
( empty(X0)
=> ( ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0) ) ),
file('/export/starexec/sandbox2/tmp/tmp.woznqBvrsC/Vampire---4.8_317',cc3_ordinal1) ).
fof(f409,plain,
spl19_31,
inference(avatar_split_clause,[],[f181,f407]) ).
fof(f407,plain,
( spl19_31
<=> ! [X0] :
( epsilon_connected(X0)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_31])]) ).
fof(f181,plain,
! [X0] :
( epsilon_connected(X0)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f75]) ).
fof(f405,plain,
spl19_30,
inference(avatar_split_clause,[],[f180,f403]) ).
fof(f180,plain,
! [X0] :
( epsilon_transitive(X0)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f75]) ).
fof(f401,plain,
spl19_29,
inference(avatar_split_clause,[],[f170,f399]) ).
fof(f170,plain,
! [X0] :
( epsilon_transitive(X0)
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f68]) ).
fof(f68,plain,
! [X0] :
( ( epsilon_connected(X0)
& epsilon_transitive(X0) )
| ~ ordinal(X0) ),
inference(ennf_transformation,[],[f3]) ).
fof(f3,axiom,
! [X0] :
( ordinal(X0)
=> ( epsilon_connected(X0)
& epsilon_transitive(X0) ) ),
file('/export/starexec/sandbox2/tmp/tmp.woznqBvrsC/Vampire---4.8_317',cc1_ordinal1) ).
fof(f397,plain,
spl19_28,
inference(avatar_split_clause,[],[f167,f395]) ).
fof(f167,plain,
! [X0] : in(X0,succ(X0)),
inference(cnf_transformation,[],[f42]) ).
fof(f42,axiom,
! [X0] : in(X0,succ(X0)),
file('/export/starexec/sandbox2/tmp/tmp.woznqBvrsC/Vampire---4.8_317',t10_ordinal1) ).
fof(f393,plain,
spl19_27,
inference(avatar_split_clause,[],[f166,f391]) ).
fof(f166,plain,
! [X0] : succ(X0) != X0,
inference(cnf_transformation,[],[f43]) ).
fof(f43,axiom,
! [X0] : succ(X0) != X0,
file('/export/starexec/sandbox2/tmp/tmp.woznqBvrsC/Vampire---4.8_317',t14_ordinal1) ).
fof(f389,plain,
spl19_26,
inference(avatar_split_clause,[],[f190,f387]) ).
fof(f190,plain,
! [X0] : subset(X0,X0),
inference(cnf_transformation,[],[f56]) ).
fof(f56,plain,
! [X0] : subset(X0,X0),
inference(rectify,[],[f41]) ).
fof(f41,axiom,
! [X0,X1] : subset(X0,X0),
file('/export/starexec/sandbox2/tmp/tmp.woznqBvrsC/Vampire---4.8_317',reflexivity_r1_tarski) ).
fof(f385,plain,
spl19_25,
inference(avatar_split_clause,[],[f165,f383]) ).
fof(f165,plain,
! [X0] : ~ empty(succ(X0)),
inference(cnf_transformation,[],[f17]) ).
fof(f17,axiom,
! [X0] : ~ empty(succ(X0)),
file('/export/starexec/sandbox2/tmp/tmp.woznqBvrsC/Vampire---4.8_317',fc1_ordinal1) ).
fof(f381,plain,
spl19_24,
inference(avatar_split_clause,[],[f251,f378]) ).
fof(f251,plain,
empty(sK18),
inference(cnf_transformation,[],[f149]) ).
fof(f149,plain,
( function(sK18)
& empty(sK18)
& relation(sK18) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK18])],[f30,f148]) ).
fof(f148,plain,
( ? [X0] :
( function(X0)
& empty(X0)
& relation(X0) )
=> ( function(sK18)
& empty(sK18)
& relation(sK18) ) ),
introduced(choice_axiom,[]) ).
fof(f30,axiom,
? [X0] :
( function(X0)
& empty(X0)
& relation(X0) ),
file('/export/starexec/sandbox2/tmp/tmp.woznqBvrsC/Vampire---4.8_317',rc2_funct_1) ).
fof(f376,plain,
spl19_23,
inference(avatar_split_clause,[],[f249,f373]) ).
fof(f373,plain,
( spl19_23
<=> ordinal(sK17) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_23])]) ).
fof(f249,plain,
ordinal(sK17),
inference(cnf_transformation,[],[f147]) ).
fof(f147,plain,
( ordinal(sK17)
& epsilon_connected(sK17)
& epsilon_transitive(sK17)
& empty(sK17)
& function(sK17)
& relation(sK17) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK17])],[f63,f146]) ).
fof(f146,plain,
( ? [X0] :
( ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0)
& empty(X0)
& function(X0)
& relation(X0) )
=> ( ordinal(sK17)
& epsilon_connected(sK17)
& epsilon_transitive(sK17)
& empty(sK17)
& function(sK17)
& relation(sK17) ) ),
introduced(choice_axiom,[]) ).
fof(f63,plain,
? [X0] :
( ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0)
& empty(X0)
& function(X0)
& relation(X0) ),
inference(pure_predicate_removal,[],[f31]) ).
fof(f31,axiom,
? [X0] :
( ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0)
& empty(X0)
& one_to_one(X0)
& function(X0)
& relation(X0) ),
file('/export/starexec/sandbox2/tmp/tmp.woznqBvrsC/Vampire---4.8_317',rc2_ordinal1) ).
fof(f371,plain,
spl19_22,
inference(avatar_split_clause,[],[f248,f368]) ).
fof(f368,plain,
( spl19_22
<=> epsilon_connected(sK17) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_22])]) ).
fof(f248,plain,
epsilon_connected(sK17),
inference(cnf_transformation,[],[f147]) ).
fof(f366,plain,
spl19_21,
inference(avatar_split_clause,[],[f247,f363]) ).
fof(f363,plain,
( spl19_21
<=> epsilon_transitive(sK17) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_21])]) ).
fof(f247,plain,
epsilon_transitive(sK17),
inference(cnf_transformation,[],[f147]) ).
fof(f361,plain,
spl19_20,
inference(avatar_split_clause,[],[f246,f358]) ).
fof(f246,plain,
empty(sK17),
inference(cnf_transformation,[],[f147]) ).
fof(f356,plain,
spl19_19,
inference(avatar_split_clause,[],[f233,f353]) ).
fof(f233,plain,
empty(sK11),
inference(cnf_transformation,[],[f135]) ).
fof(f135,plain,
( relation(sK11)
& empty(sK11) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK11])],[f28,f134]) ).
fof(f134,plain,
( ? [X0] :
( relation(X0)
& empty(X0) )
=> ( relation(sK11)
& empty(sK11) ) ),
introduced(choice_axiom,[]) ).
fof(f28,axiom,
? [X0] :
( relation(X0)
& empty(X0) ),
file('/export/starexec/sandbox2/tmp/tmp.woznqBvrsC/Vampire---4.8_317',rc1_relat_1) ).
fof(f351,plain,
spl19_18,
inference(avatar_split_clause,[],[f232,f348]) ).
fof(f232,plain,
ordinal(sK10),
inference(cnf_transformation,[],[f133]) ).
fof(f133,plain,
( ordinal(sK10)
& epsilon_connected(sK10)
& epsilon_transitive(sK10) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK10])],[f27,f132]) ).
fof(f132,plain,
( ? [X0] :
( ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0) )
=> ( ordinal(sK10)
& epsilon_connected(sK10)
& epsilon_transitive(sK10) ) ),
introduced(choice_axiom,[]) ).
fof(f27,axiom,
? [X0] :
( ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0) ),
file('/export/starexec/sandbox2/tmp/tmp.woznqBvrsC/Vampire---4.8_317',rc1_ordinal1) ).
fof(f346,plain,
spl19_17,
inference(avatar_split_clause,[],[f231,f343]) ).
fof(f343,plain,
( spl19_17
<=> epsilon_connected(sK10) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_17])]) ).
fof(f231,plain,
epsilon_connected(sK10),
inference(cnf_transformation,[],[f133]) ).
fof(f341,plain,
spl19_16,
inference(avatar_split_clause,[],[f230,f338]) ).
fof(f230,plain,
epsilon_transitive(sK10),
inference(cnf_transformation,[],[f133]) ).
fof(f336,plain,
~ spl19_15,
inference(avatar_split_clause,[],[f228,f333]) ).
fof(f333,plain,
( spl19_15
<=> empty(sK9) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_15])]) ).
fof(f228,plain,
~ empty(sK9),
inference(cnf_transformation,[],[f131]) ).
fof(f131,plain,
( relation(sK9)
& ~ empty(sK9) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK9])],[f32,f130]) ).
fof(f130,plain,
( ? [X0] :
( relation(X0)
& ~ empty(X0) )
=> ( relation(sK9)
& ~ empty(sK9) ) ),
introduced(choice_axiom,[]) ).
fof(f32,axiom,
? [X0] :
( relation(X0)
& ~ empty(X0) ),
file('/export/starexec/sandbox2/tmp/tmp.woznqBvrsC/Vampire---4.8_317',rc2_relat_1) ).
fof(f331,plain,
spl19_14,
inference(avatar_split_clause,[],[f227,f328]) ).
fof(f227,plain,
ordinal(sK8),
inference(cnf_transformation,[],[f129]) ).
fof(f129,plain,
( ordinal(sK8)
& epsilon_connected(sK8)
& epsilon_transitive(sK8)
& ~ empty(sK8) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK8])],[f35,f128]) ).
fof(f128,plain,
( ? [X0] :
( ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0)
& ~ empty(X0) )
=> ( ordinal(sK8)
& epsilon_connected(sK8)
& epsilon_transitive(sK8)
& ~ empty(sK8) ) ),
introduced(choice_axiom,[]) ).
fof(f35,axiom,
? [X0] :
( ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0)
& ~ empty(X0) ),
file('/export/starexec/sandbox2/tmp/tmp.woznqBvrsC/Vampire---4.8_317',rc3_ordinal1) ).
fof(f326,plain,
spl19_13,
inference(avatar_split_clause,[],[f226,f323]) ).
fof(f323,plain,
( spl19_13
<=> epsilon_connected(sK8) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_13])]) ).
fof(f226,plain,
epsilon_connected(sK8),
inference(cnf_transformation,[],[f129]) ).
fof(f321,plain,
spl19_12,
inference(avatar_split_clause,[],[f225,f318]) ).
fof(f225,plain,
epsilon_transitive(sK8),
inference(cnf_transformation,[],[f129]) ).
fof(f316,plain,
~ spl19_11,
inference(avatar_split_clause,[],[f224,f313]) ).
fof(f224,plain,
~ empty(sK8),
inference(cnf_transformation,[],[f129]) ).
fof(f311,plain,
spl19_10,
inference(avatar_split_clause,[],[f223,f308]) ).
fof(f223,plain,
empty(sK7),
inference(cnf_transformation,[],[f127]) ).
fof(f127,plain,
empty(sK7),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK7])],[f29,f126]) ).
fof(f126,plain,
( ? [X0] : empty(X0)
=> empty(sK7) ),
introduced(choice_axiom,[]) ).
fof(f29,axiom,
? [X0] : empty(X0),
file('/export/starexec/sandbox2/tmp/tmp.woznqBvrsC/Vampire---4.8_317',rc1_xboole_0) ).
fof(f306,plain,
~ spl19_9,
inference(avatar_split_clause,[],[f222,f303]) ).
fof(f303,plain,
( spl19_9
<=> empty(sK6) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_9])]) ).
fof(f222,plain,
~ empty(sK6),
inference(cnf_transformation,[],[f125]) ).
fof(f125,plain,
~ empty(sK6),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6])],[f33,f124]) ).
fof(f124,plain,
( ? [X0] : ~ empty(X0)
=> ~ empty(sK6) ),
introduced(choice_axiom,[]) ).
fof(f33,axiom,
? [X0] : ~ empty(X0),
file('/export/starexec/sandbox2/tmp/tmp.woznqBvrsC/Vampire---4.8_317',rc2_xboole_0) ).
fof(f301,plain,
spl19_8,
inference(avatar_split_clause,[],[f164,f298]) ).
fof(f164,plain,
ordinal(empty_set),
inference(cnf_transformation,[],[f66]) ).
fof(f66,plain,
( ordinal(empty_set)
& epsilon_connected(empty_set)
& epsilon_transitive(empty_set)
& empty(empty_set)
& function(empty_set)
& relation(empty_set) ),
inference(pure_predicate_removal,[],[f61]) ).
fof(f61,plain,
( ordinal(empty_set)
& epsilon_connected(empty_set)
& epsilon_transitive(empty_set)
& empty(empty_set)
& one_to_one(empty_set)
& function(empty_set)
& relation(empty_set) ),
inference(pure_predicate_removal,[],[f19]) ).
fof(f19,axiom,
( ordinal(empty_set)
& epsilon_connected(empty_set)
& epsilon_transitive(empty_set)
& empty(empty_set)
& one_to_one(empty_set)
& function(empty_set)
& relation_empty_yielding(empty_set)
& relation(empty_set) ),
file('/export/starexec/sandbox2/tmp/tmp.woznqBvrsC/Vampire---4.8_317',fc2_ordinal1) ).
fof(f296,plain,
spl19_7,
inference(avatar_split_clause,[],[f163,f293]) ).
fof(f293,plain,
( spl19_7
<=> epsilon_connected(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_7])]) ).
fof(f163,plain,
epsilon_connected(empty_set),
inference(cnf_transformation,[],[f66]) ).
fof(f291,plain,
spl19_6,
inference(avatar_split_clause,[],[f162,f288]) ).
fof(f288,plain,
( spl19_6
<=> epsilon_transitive(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_6])]) ).
fof(f162,plain,
epsilon_transitive(empty_set),
inference(cnf_transformation,[],[f66]) ).
fof(f286,plain,
spl19_5,
inference(avatar_split_clause,[],[f154,f283]) ).
fof(f154,plain,
empty(empty_set),
inference(cnf_transformation,[],[f18]) ).
fof(f18,axiom,
empty(empty_set),
file('/export/starexec/sandbox2/tmp/tmp.woznqBvrsC/Vampire---4.8_317',fc1_xboole_0) ).
fof(f281,plain,
( ~ spl19_3
| ~ spl19_4 ),
inference(avatar_split_clause,[],[f153,f277,f273]) ).
fof(f153,plain,
( ~ ordinal_subset(sK0,sK1)
| ~ in(sK0,succ(sK1)) ),
inference(cnf_transformation,[],[f104]) ).
fof(f104,plain,
( ( ~ ordinal_subset(sK0,sK1)
| ~ in(sK0,succ(sK1)) )
& ( ordinal_subset(sK0,sK1)
| in(sK0,succ(sK1)) )
& ordinal(sK1)
& ordinal(sK0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f101,f103,f102]) ).
fof(f102,plain,
( ? [X0] :
( ? [X1] :
( ( ~ ordinal_subset(X0,X1)
| ~ in(X0,succ(X1)) )
& ( ordinal_subset(X0,X1)
| in(X0,succ(X1)) )
& ordinal(X1) )
& ordinal(X0) )
=> ( ? [X1] :
( ( ~ ordinal_subset(sK0,X1)
| ~ in(sK0,succ(X1)) )
& ( ordinal_subset(sK0,X1)
| in(sK0,succ(X1)) )
& ordinal(X1) )
& ordinal(sK0) ) ),
introduced(choice_axiom,[]) ).
fof(f103,plain,
( ? [X1] :
( ( ~ ordinal_subset(sK0,X1)
| ~ in(sK0,succ(X1)) )
& ( ordinal_subset(sK0,X1)
| in(sK0,succ(X1)) )
& ordinal(X1) )
=> ( ( ~ ordinal_subset(sK0,sK1)
| ~ in(sK0,succ(sK1)) )
& ( ordinal_subset(sK0,sK1)
| in(sK0,succ(sK1)) )
& ordinal(sK1) ) ),
introduced(choice_axiom,[]) ).
fof(f101,plain,
? [X0] :
( ? [X1] :
( ( ~ ordinal_subset(X0,X1)
| ~ in(X0,succ(X1)) )
& ( ordinal_subset(X0,X1)
| in(X0,succ(X1)) )
& ordinal(X1) )
& ordinal(X0) ),
inference(flattening,[],[f100]) ).
fof(f100,plain,
? [X0] :
( ? [X1] :
( ( ~ ordinal_subset(X0,X1)
| ~ in(X0,succ(X1)) )
& ( ordinal_subset(X0,X1)
| in(X0,succ(X1)) )
& ordinal(X1) )
& ordinal(X0) ),
inference(nnf_transformation,[],[f67]) ).
fof(f67,plain,
? [X0] :
( ? [X1] :
( ( in(X0,succ(X1))
<~> ordinal_subset(X0,X1) )
& ordinal(X1) )
& ordinal(X0) ),
inference(ennf_transformation,[],[f49]) ).
fof(f49,negated_conjecture,
~ ! [X0] :
( ordinal(X0)
=> ! [X1] :
( ordinal(X1)
=> ( in(X0,succ(X1))
<=> ordinal_subset(X0,X1) ) ) ),
inference(negated_conjecture,[],[f48]) ).
fof(f48,conjecture,
! [X0] :
( ordinal(X0)
=> ! [X1] :
( ordinal(X1)
=> ( in(X0,succ(X1))
<=> ordinal_subset(X0,X1) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.woznqBvrsC/Vampire---4.8_317',t34_ordinal1) ).
fof(f280,plain,
( spl19_3
| spl19_4 ),
inference(avatar_split_clause,[],[f152,f277,f273]) ).
fof(f152,plain,
( ordinal_subset(sK0,sK1)
| in(sK0,succ(sK1)) ),
inference(cnf_transformation,[],[f104]) ).
fof(f271,plain,
spl19_2,
inference(avatar_split_clause,[],[f151,f268]) ).
fof(f151,plain,
ordinal(sK1),
inference(cnf_transformation,[],[f104]) ).
fof(f266,plain,
spl19_1,
inference(avatar_split_clause,[],[f150,f263]) ).
fof(f150,plain,
ordinal(sK0),
inference(cnf_transformation,[],[f104]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : NUM401+1 : TPTP v8.1.2. Released v3.2.0.
% 0.12/0.14 % Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.15/0.35 % Computer : n015.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Fri Aug 25 15:48:37 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.15/0.36 This is a FOF_THM_RFO_SEQ problem
% 0.15/0.36 Running vampire_casc2023 --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/tmp/tmp.woznqBvrsC/Vampire---4.8_317
% 0.15/0.36 % (431)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.41 % (437)lrs-1010_2_av=off:bce=on:cond=on:er=filter:fde=unused:lcm=predicate:nm=2:nwc=3.0:sims=off:sp=frequency:urr=on:stl=188_520 on Vampire---4 for (520ds/0Mi)
% 0.23/0.42 % (433)ott+3_2:7_add=large:amm=off:anc=all:bce=on:drc=off:fsd=off:fde=unused:gs=on:irw=on:lcm=predicate:lma=on:msp=off:nwc=10.0:sac=on_598 on Vampire---4 for (598ds/0Mi)
% 0.23/0.42 % (435)lrs+2_5:4_anc=none:br=off:fde=unused:gsp=on:nm=32:nwc=1.3:sims=off:sos=all:urr=on:stl=62_558 on Vampire---4 for (558ds/0Mi)
% 0.23/0.43 % (438)ott+1010_1_aac=none:bce=on:ep=RS:fsd=off:nm=4:nwc=2.0:nicw=on:sas=z3:sims=off_453 on Vampire---4 for (453ds/0Mi)
% 0.23/0.43 % (436)lrs-1010_20_afr=on:anc=all_dependent:bs=on:bsr=on:cond=on:er=known:fde=none:nm=4:nwc=1.3:sims=off:sp=frequency:urr=on:stl=62_533 on Vampire---4 for (533ds/0Mi)
% 0.23/0.43 % (432)lrs+1010_20_av=off:bd=off:bs=on:bsr=on:bce=on:flr=on:fde=none:gsp=on:nwc=3.0:tgt=ground:urr=ec_only:stl=125_1192 on Vampire---4 for (1192ds/0Mi)
% 0.23/0.44 % (434)lrs+11_10:1_bs=unit_only:drc=off:fsd=off:fde=none:gs=on:msp=off:nm=16:nwc=2.0:nicw=on:sos=all:sac=on:sp=reverse_frequency:stl=62_575 on Vampire---4 for (575ds/0Mi)
% 2.65/0.76 % (433)First to succeed.
% 2.65/0.78 % (433)Refutation found. Thanks to Tanya!
% 2.65/0.78 % SZS status Theorem for Vampire---4
% 2.65/0.78 % SZS output start Proof for Vampire---4
% See solution above
% 2.65/0.80 % (433)------------------------------
% 2.65/0.80 % (433)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 2.65/0.80 % (433)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 2.65/0.80 % (433)Termination reason: Refutation
% 2.65/0.80
% 2.65/0.80 % (433)Memory used [KB]: 17142
% 2.65/0.80 % (433)Time elapsed: 0.352 s
% 2.65/0.80 % (433)------------------------------
% 2.65/0.80 % (433)------------------------------
% 2.65/0.80 % (431)Success in time 0.438 s
% 2.65/0.80 % Vampire---4.8 exiting
%------------------------------------------------------------------------------