TSTP Solution File: SEU395+1 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SEU395+1 : TPTP v8.1.2. Released v3.3.0.
% 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 : n001.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Sep 2 00:19:15 EDT 2023
% Result : Theorem 0.17s 0.65s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 1328
% Syntax : Number of formulae : 4294 ( 519 unt; 0 def)
% Number of atoms : 19186 ( 361 equ)
% Maximal formula atoms : 34 ( 4 avg)
% Number of connectives : 25455 (10563 ~;12108 |;1447 &)
% (1150 <=>; 184 =>; 0 <=; 3 <~>)
% Maximal formula depth : 22 ( 6 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 1208 (1206 usr;1140 prp; 0-3 aty)
% Number of functors : 63 ( 63 usr; 20 con; 0-4 aty)
% Number of variables : 4018 (;3852 !; 166 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f9243,plain,
$false,
inference(avatar_sat_refutation,[],[f895,f900,f905,f910,f915,f920,f925,f930,f935,f940,f945,f950,f955,f960,f965,f970,f975,f980,f985,f990,f995,f1000,f1005,f1010,f1015,f1020,f1025,f1030,f1035,f1040,f1045,f1050,f1055,f1060,f1065,f1070,f1075,f1080,f1085,f1090,f1095,f1100,f1105,f1110,f1115,f1120,f1125,f1130,f1135,f1140,f1145,f1150,f1155,f1160,f1165,f1170,f1175,f1180,f1185,f1190,f1195,f1200,f1205,f1210,f1215,f1220,f1225,f1230,f1235,f1240,f1245,f1250,f1255,f1260,f1265,f1270,f1275,f1280,f1285,f1290,f1295,f1300,f1305,f1310,f1315,f1320,f1325,f1330,f1335,f1340,f1345,f1350,f1355,f1360,f1365,f1370,f1375,f1380,f1385,f1390,f1395,f1400,f1405,f1410,f1414,f1418,f1422,f1426,f1430,f1434,f1438,f1442,f1446,f1450,f1454,f1458,f1462,f1466,f1470,f1474,f1478,f1482,f1486,f1490,f1494,f1498,f1502,f1506,f1510,f1519,f1523,f1527,f1531,f1535,f1539,f1543,f1547,f1551,f1555,f1559,f1563,f1567,f1571,f1575,f1579,f1583,f1587,f1591,f1595,f1599,f1603,f1607,f1611,f1615,f1619,f1623,f1627,f1631,f1657,f1662,f1674,f1679,f1683,f1687,f1691,f1695,f1699,f1703,f1707,f1711,f1715,f1719,f1723,f1727,f1731,f1735,f1739,f1743,f1747,f1751,f1755,f1759,f1764,f1768,f1772,f1776,f1780,f1784,f1788,f1792,f1796,f1800,f1804,f1808,f1812,f1816,f1820,f1824,f1828,f1835,f1851,f1860,f1865,f1869,f1873,f1877,f1881,f1886,f1890,f1894,f1898,f1902,f1906,f1910,f1914,f1918,f1922,f1926,f1931,f1935,f1939,f1943,f1947,f1951,f1955,f1959,f1963,f1967,f1971,f1976,f1980,f1984,f1988,f1992,f1996,f2000,f2004,f2008,f2012,f2016,f2021,f2025,f2029,f2038,f2059,f2066,f2070,f2074,f2078,f2082,f2086,f2090,f2094,f2098,f2102,f2106,f2110,f2115,f2119,f2123,f2127,f2140,f2165,f2169,f2173,f2178,f2182,f2186,f2190,f2194,f2198,f2202,f2206,f2210,f2214,f2218,f2222,f2226,f2230,f2234,f2238,f2242,f2246,f2250,f2254,f2258,f2263,f2267,f2271,f2275,f2279,f2283,f2287,f2291,f2295,f2299,f2303,f2308,f2312,f2316,f2361,f2414,f2418,f2422,f2431,f2435,f2439,f2443,f2447,f2451,f2455,f2459,f2490,f2494,f2498,f2503,f2507,f2511,f2515,f2519,f2523,f2527,f2531,f2535,f2539,f2543,f2555,f2559,f2563,f2567,f2571,f2575,f2656,f2660,f2664,f2673,f2679,f2683,f2687,f2691,f2695,f2699,f2703,f2707,f2739,f2766,f2770,f2774,f2778,f2782,f2786,f2790,f2801,f2808,f2812,f2816,f2820,f2824,f2828,f2832,f2836,f2840,f2968,f3005,f3009,f3013,f3026,f3030,f3034,f3041,f3133,f3141,f3145,f3150,f3156,f3160,f3164,f3168,f3203,f3207,f3215,f3219,f3224,f3228,f3236,f3242,f3246,f3250,f3254,f3258,f3262,f3266,f3356,f3360,f3418,f3423,f3430,f3449,f3454,f3459,f3464,f3470,f3480,f3490,f3494,f3498,f3502,f3507,f3514,f3518,f3531,f3538,f3542,f3546,f3556,f3560,f3564,f3568,f3588,f3592,f3596,f3601,f3605,f3609,f3613,f3617,f3621,f3626,f3630,f3634,f3638,f3642,f3646,f3650,f3654,f3658,f3662,f3669,f3676,f3677,f3678,f3713,f3938,f3942,f3947,f3959,f3963,f3968,f3972,f3976,f3980,f3985,f3992,f3999,f4006,f4014,f4021,f4026,f4031,f4036,f4041,f4046,f4051,f4056,f4060,f4064,f4068,f4072,f4077,f4081,f4085,f4089,f4093,f4104,f4120,f4124,f4128,f4145,f4149,f4153,f4157,f4161,f4165,f4169,f4173,f4177,f4181,f4186,f4190,f4194,f4198,f4202,f4206,f4210,f4214,f4218,f4222,f4226,f4250,f4288,f4304,f4308,f4312,f4316,f4320,f4329,f4333,f4337,f4341,f4345,f4349,f4354,f4359,f4369,f4374,f4379,f4384,f4389,f4395,f4401,f4407,f4412,f4416,f4423,f4431,f4438,f4445,f4451,f4460,f4465,f4500,f4504,f4508,f4512,f4516,f4520,f4524,f4528,f4532,f4537,f4541,f4545,f4549,f4553,f4557,f4561,f4565,f4569,f4573,f4577,f4581,f4585,f4589,f4593,f4597,f4601,f4606,f4615,f4624,f4629,f4638,f4647,f4656,f4664,f4668,f4672,f4681,f4756,f4761,f4768,f4772,f4776,f4780,f4784,f4788,f4792,f4796,f4800,f4804,f4808,f4812,f4816,f4820,f4824,f4828,f4832,f4836,f4840,f4845,f4854,f4858,f4862,f4900,f4975,f4979,f4983,f4987,f4991,f4995,f4999,f5003,f5007,f5011,f5015,f5019,f5023,f5027,f5032,f5036,f5040,f5044,f5048,f5052,f5056,f5060,f5064,f5068,f5147,f5161,f5165,f5169,f5173,f5177,f5181,f5185,f5189,f5194,f5198,f5202,f5206,f5210,f5214,f5218,f5222,f5226,f5235,f5240,f5250,f5260,f5265,f5270,f5275,f5280,f5285,f5289,f5293,f5297,f5312,f5357,f5372,f5376,f5380,f5384,f5389,f5393,f5397,f5401,f5405,f5409,f5413,f5417,f5421,f5425,f5429,f5434,f5438,f5442,f5446,f5450,f5454,f5458,f5462,f5466,f5470,f5474,f5478,f5482,f5486,f5721,f5725,f5729,f5733,f5737,f5741,f5745,f5749,f5753,f5757,f5761,f5765,f5769,f5773,f5777,f5781,f5785,f5789,f5793,f5798,f5807,f5818,f5891,f5895,f5899,f5903,f5907,f5911,f5933,f5937,f5941,f5945,f5949,f5953,f5957,f5961,f5965,f5974,f5983,f5992,f5997,f6012,f6026,f6030,f6034,f6038,f6042,f6046,f6084,f6089,f6093,f6097,f6101,f6105,f6109,f6113,f6186,f6190,f6194,f6198,f6202,f6206,f6210,f6215,f6219,f6223,f6227,f6231,f6235,f6239,f6243,f6247,f6251,f6255,f6259,f6263,f6267,f6271,f6275,f6279,f6283,f6287,f6296,f6329,f6333,f6337,f6342,f6346,f6350,f6354,f6358,f6362,f6366,f6370,f6382,f6386,f6390,f6394,f6428,f6432,f6436,f6440,f6444,f6448,f6452,f6456,f6460,f6464,f6468,f6492,f6498,f6504,f6508,f6512,f6567,f6571,f6575,f6579,f6583,f6587,f6591,f6595,f6599,f6603,f6607,f6611,f6687,f6693,f6697,f6707,f6712,f6716,f6720,f6724,f6728,f6732,f6736,f6746,f6750,f6754,f6758,f6848,f6852,f6862,f6866,f6876,f6880,f6884,f6888,f6998,f7002,f7010,f7018,f7022,f7026,f7030,f7034,f7038,f7042,f7046,f7050,f7054,f7059,f7063,f7067,f7071,f7075,f7079,f7083,f7087,f7097,f7101,f7105,f7109,f7113,f7117,f7123,f7127,f7131,f7135,f7139,f7143,f7147,f7151,f7155,f7160,f7195,f7217,f7221,f7225,f7229,f7233,f7237,f7241,f7247,f7251,f7255,f7259,f7263,f7267,f7271,f7275,f7284,f7288,f7292,f7296,f7300,f7304,f7308,f7312,f7316,f7320,f7324,f7328,f7354,f7376,f7380,f7384,f7388,f7392,f7396,f7400,f7404,f7408,f7412,f7416,f7420,f7424,f7429,f7436,f7440,f7444,f7448,f7452,f7456,f7460,f7464,f7468,f7472,f7476,f7480,f7484,f7488,f7492,f7531,f7535,f7539,f7543,f7547,f7571,f7575,f7579,f7583,f7587,f7591,f7597,f7601,f7605,f7610,f7630,f7634,f7638,f7646,f7650,f7664,f7673,f7681,f7685,f7689,f7693,f7698,f7702,f7714,f7723,f7727,f7731,f7741,f7745,f7752,f7762,f7767,f7775,f7780,f7784,f7801,f7805,f7819,f7823,f7828,f7832,f7837,f7878,f7882,f7886,f7893,f7897,f7901,f7905,f7909,f7913,f7920,f7939,f7941,f7943,f7954,f7958,f7964,f7974,f7978,f7982,f7986,f7990,f7994,f7998,f8002,f8006,f8010,f8014,f8018,f8022,f8026,f8030,f8035,f8040,f8174,f8178,f8182,f8186,f8190,f8194,f8198,f8252,f8256,f8260,f8264,f8268,f8272,f8276,f8280,f8284,f8288,f8292,f8298,f8302,f8306,f8310,f8314,f8318,f8322,f8326,f8330,f8334,f8340,f8344,f8348,f8434,f8481,f8528,f8537,f8546,f8550,f8554,f8558,f8562,f8566,f8570,f8574,f8578,f8582,f8587,f8591,f8595,f8599,f8603,f8607,f8611,f8619,f8633,f8656,f8664,f8668,f8669,f8673,f8677,f8681,f8685,f8689,f8693,f8697,f8701,f8705,f8710,f8714,f8718,f8722,f8726,f8730,f8755,f8774,f8789,f8793,f8797,f8801,f8805,f8809,f8833,f8837,f8841,f8845,f8849,f8853,f8857,f8861,f8865,f8869,f8874,f8878,f8882,f8886,f8890,f8894,f8898,f8902,f8906,f8910,f8914,f8929,f8933,f8937,f8995,f9143,f9147,f9151,f9155,f9159,f9163,f9167,f9171,f9172,f9179,f9184,f9190,f9195,f9201,f9205,f9209,f9213,f9217,f9221,f9225,f9229,f9233,f9237,f9241,f9242]) ).
fof(f9242,plain,
( spl61_131
| ~ spl61_5
| ~ spl61_130
| ~ spl61_1067 ),
inference(avatar_split_clause,[],[f9173,f8654,f1512,f912,f1516]) ).
fof(f1516,plain,
( spl61_131
<=> is_a_convergence_point_of_set(sK12,sK13,sK14) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_131])]) ).
fof(f912,plain,
( spl61_5
<=> element(sK14,the_carrier(sK12)) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_5])]) ).
fof(f1512,plain,
( spl61_130
<=> in(sK14,lim_points_of_net(sK12,net_of_bool_filter(sK12,cast_as_carrier_subset(sK12),sK13))) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_130])]) ).
fof(f8654,plain,
( spl61_1067
<=> ! [X0] :
( is_a_convergence_point_of_set(sK12,sK13,X0)
| ~ element(X0,the_carrier(sK12))
| ~ in(X0,lim_points_of_net(sK12,net_of_bool_filter(sK12,cast_as_carrier_subset(sK12),sK13))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_1067])]) ).
fof(f9173,plain,
( ~ element(sK14,the_carrier(sK12))
| is_a_convergence_point_of_set(sK12,sK13,sK14)
| ~ spl61_130
| ~ spl61_1067 ),
inference(resolution,[],[f1514,f8655]) ).
fof(f8655,plain,
( ! [X0] :
( ~ in(X0,lim_points_of_net(sK12,net_of_bool_filter(sK12,cast_as_carrier_subset(sK12),sK13)))
| ~ element(X0,the_carrier(sK12))
| is_a_convergence_point_of_set(sK12,sK13,X0) )
| ~ spl61_1067 ),
inference(avatar_component_clause,[],[f8654]) ).
fof(f1514,plain,
( in(sK14,lim_points_of_net(sK12,net_of_bool_filter(sK12,cast_as_carrier_subset(sK12),sK13)))
| ~ spl61_130 ),
inference(avatar_component_clause,[],[f1512]) ).
fof(f9241,plain,
( spl61_1139
| ~ spl61_240
| ~ spl61_691 ),
inference(avatar_split_clause,[],[f5838,f5739,f2010,f9239]) ).
fof(f9239,plain,
( spl61_1139
<=> ! [X2] :
( ~ topological_space(X2)
| empty(powerset(the_carrier(X2)))
| ~ top_str(X2)
| ~ in(powerset(the_carrier(X2)),sK36(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_1139])]) ).
fof(f2010,plain,
( spl61_240
<=> ! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_240])]) ).
fof(f5739,plain,
( spl61_691
<=> ! [X4] :
( ~ top_str(X4)
| ~ topological_space(X4)
| empty(powerset(the_carrier(X4)))
| in(sK36(X4),powerset(the_carrier(X4))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_691])]) ).
fof(f5838,plain,
( ! [X2] :
( ~ topological_space(X2)
| empty(powerset(the_carrier(X2)))
| ~ top_str(X2)
| ~ in(powerset(the_carrier(X2)),sK36(X2)) )
| ~ spl61_240
| ~ spl61_691 ),
inference(resolution,[],[f5740,f2011]) ).
fof(f2011,plain,
( ! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) )
| ~ spl61_240 ),
inference(avatar_component_clause,[],[f2010]) ).
fof(f5740,plain,
( ! [X4] :
( in(sK36(X4),powerset(the_carrier(X4)))
| ~ topological_space(X4)
| empty(powerset(the_carrier(X4)))
| ~ top_str(X4) )
| ~ spl61_691 ),
inference(avatar_component_clause,[],[f5739]) ).
fof(f9237,plain,
( spl61_1138
| ~ spl61_240
| ~ spl61_690 ),
inference(avatar_split_clause,[],[f5835,f5735,f2010,f9235]) ).
fof(f9235,plain,
( spl61_1138
<=> ! [X2] :
( ~ topological_space(X2)
| empty(powerset(the_carrier(X2)))
| ~ top_str(X2)
| ~ in(powerset(the_carrier(X2)),sK35(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_1138])]) ).
fof(f5735,plain,
( spl61_690
<=> ! [X4] :
( ~ top_str(X4)
| ~ topological_space(X4)
| empty(powerset(the_carrier(X4)))
| in(sK35(X4),powerset(the_carrier(X4))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_690])]) ).
fof(f5835,plain,
( ! [X2] :
( ~ topological_space(X2)
| empty(powerset(the_carrier(X2)))
| ~ top_str(X2)
| ~ in(powerset(the_carrier(X2)),sK35(X2)) )
| ~ spl61_240
| ~ spl61_690 ),
inference(resolution,[],[f5736,f2011]) ).
fof(f5736,plain,
( ! [X4] :
( in(sK35(X4),powerset(the_carrier(X4)))
| ~ topological_space(X4)
| empty(powerset(the_carrier(X4)))
| ~ top_str(X4) )
| ~ spl61_690 ),
inference(avatar_component_clause,[],[f5735]) ).
fof(f9233,plain,
( spl61_1137
| ~ spl61_240
| ~ spl61_689 ),
inference(avatar_split_clause,[],[f5832,f5731,f2010,f9231]) ).
fof(f9231,plain,
( spl61_1137
<=> ! [X2] :
( ~ topological_space(X2)
| empty(powerset(the_carrier(X2)))
| ~ top_str(X2)
| ~ in(powerset(the_carrier(X2)),sK34(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_1137])]) ).
fof(f5731,plain,
( spl61_689
<=> ! [X4] :
( ~ top_str(X4)
| ~ topological_space(X4)
| empty(powerset(the_carrier(X4)))
| in(sK34(X4),powerset(the_carrier(X4))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_689])]) ).
fof(f5832,plain,
( ! [X2] :
( ~ topological_space(X2)
| empty(powerset(the_carrier(X2)))
| ~ top_str(X2)
| ~ in(powerset(the_carrier(X2)),sK34(X2)) )
| ~ spl61_240
| ~ spl61_689 ),
inference(resolution,[],[f5732,f2011]) ).
fof(f5732,plain,
( ! [X4] :
( in(sK34(X4),powerset(the_carrier(X4)))
| ~ topological_space(X4)
| empty(powerset(the_carrier(X4)))
| ~ top_str(X4) )
| ~ spl61_689 ),
inference(avatar_component_clause,[],[f5731]) ).
fof(f9229,plain,
( spl61_1136
| ~ spl61_240
| ~ spl61_688 ),
inference(avatar_split_clause,[],[f5829,f5727,f2010,f9227]) ).
fof(f9227,plain,
( spl61_1136
<=> ! [X2] :
( empty_carrier(X2)
| empty(powerset(the_carrier(X2)))
| ~ rel_str(X2)
| ~ in(powerset(the_carrier(X2)),sK29(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_1136])]) ).
fof(f5727,plain,
( spl61_688
<=> ! [X4] :
( ~ rel_str(X4)
| empty_carrier(X4)
| empty(powerset(the_carrier(X4)))
| in(sK29(X4),powerset(the_carrier(X4))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_688])]) ).
fof(f5829,plain,
( ! [X2] :
( empty_carrier(X2)
| empty(powerset(the_carrier(X2)))
| ~ rel_str(X2)
| ~ in(powerset(the_carrier(X2)),sK29(X2)) )
| ~ spl61_240
| ~ spl61_688 ),
inference(resolution,[],[f5728,f2011]) ).
fof(f5728,plain,
( ! [X4] :
( in(sK29(X4),powerset(the_carrier(X4)))
| empty_carrier(X4)
| empty(powerset(the_carrier(X4)))
| ~ rel_str(X4) )
| ~ spl61_688 ),
inference(avatar_component_clause,[],[f5727]) ).
fof(f9225,plain,
( spl61_1135
| ~ spl61_240
| ~ spl61_687 ),
inference(avatar_split_clause,[],[f5826,f5723,f2010,f9223]) ).
fof(f9223,plain,
( spl61_1135
<=> ! [X2] :
( empty_carrier(X2)
| empty(powerset(the_carrier(X2)))
| ~ one_sorted_str(X2)
| ~ in(powerset(the_carrier(X2)),sK28(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_1135])]) ).
fof(f5723,plain,
( spl61_687
<=> ! [X4] :
( ~ one_sorted_str(X4)
| empty_carrier(X4)
| empty(powerset(the_carrier(X4)))
| in(sK28(X4),powerset(the_carrier(X4))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_687])]) ).
fof(f5826,plain,
( ! [X2] :
( empty_carrier(X2)
| empty(powerset(the_carrier(X2)))
| ~ one_sorted_str(X2)
| ~ in(powerset(the_carrier(X2)),sK28(X2)) )
| ~ spl61_240
| ~ spl61_687 ),
inference(resolution,[],[f5724,f2011]) ).
fof(f5724,plain,
( ! [X4] :
( in(sK28(X4),powerset(the_carrier(X4)))
| empty_carrier(X4)
| empty(powerset(the_carrier(X4)))
| ~ one_sorted_str(X4) )
| ~ spl61_687 ),
inference(avatar_component_clause,[],[f5723]) ).
fof(f9221,plain,
( spl61_1134
| ~ spl61_240
| ~ spl61_686 ),
inference(avatar_split_clause,[],[f5823,f5719,f2010,f9219]) ).
fof(f9219,plain,
( spl61_1134
<=> ! [X2] :
( empty(powerset(powerset(the_carrier(X2))))
| ~ one_sorted_str(X2)
| ~ in(powerset(powerset(the_carrier(X2))),sK22(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_1134])]) ).
fof(f5719,plain,
( spl61_686
<=> ! [X2] :
( ~ one_sorted_str(X2)
| empty(powerset(powerset(the_carrier(X2))))
| in(sK22(X2),powerset(powerset(the_carrier(X2)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_686])]) ).
fof(f5823,plain,
( ! [X2] :
( empty(powerset(powerset(the_carrier(X2))))
| ~ one_sorted_str(X2)
| ~ in(powerset(powerset(the_carrier(X2))),sK22(X2)) )
| ~ spl61_240
| ~ spl61_686 ),
inference(resolution,[],[f5720,f2011]) ).
fof(f5720,plain,
( ! [X2] :
( in(sK22(X2),powerset(powerset(the_carrier(X2))))
| empty(powerset(powerset(the_carrier(X2))))
| ~ one_sorted_str(X2) )
| ~ spl61_686 ),
inference(avatar_component_clause,[],[f5719]) ).
fof(f9217,plain,
( spl61_1133
| ~ spl61_501
| ~ spl61_667 ),
inference(avatar_split_clause,[],[f5613,f5411,f4220,f9215]) ).
fof(f9215,plain,
( spl61_1133
<=> ! [X73,X74] :
( element(sK41(X73,sK38(powerset(X74))),X73)
| sK38(powerset(X74)) = X73
| ~ empty(X74) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_1133])]) ).
fof(f4220,plain,
( spl61_501
<=> ! [X29,X28] :
( ~ empty(X28)
| ~ in(X29,sK38(powerset(X28))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_501])]) ).
fof(f5411,plain,
( spl61_667
<=> ! [X0,X1] :
( in(sK41(X0,X1),X1)
| X0 = X1
| element(sK41(X0,X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_667])]) ).
fof(f5613,plain,
( ! [X73,X74] :
( element(sK41(X73,sK38(powerset(X74))),X73)
| sK38(powerset(X74)) = X73
| ~ empty(X74) )
| ~ spl61_501
| ~ spl61_667 ),
inference(resolution,[],[f5412,f4221]) ).
fof(f4221,plain,
( ! [X28,X29] :
( ~ in(X29,sK38(powerset(X28)))
| ~ empty(X28) )
| ~ spl61_501 ),
inference(avatar_component_clause,[],[f4220]) ).
fof(f5412,plain,
( ! [X0,X1] :
( element(sK41(X0,X1),X0)
| in(sK41(X0,X1),X1)
| X0 = X1 )
| ~ spl61_667 ),
inference(avatar_component_clause,[],[f5411]) ).
fof(f9213,plain,
( spl61_1132
| ~ spl61_501
| ~ spl61_665 ),
inference(avatar_split_clause,[],[f5556,f5403,f4220,f9211]) ).
fof(f9211,plain,
( spl61_1132
<=> ! [X73,X72] :
( element(sK41(sK38(powerset(X72)),X73),X73)
| sK38(powerset(X72)) = X73
| ~ empty(X72) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_1132])]) ).
fof(f5403,plain,
( spl61_665
<=> ! [X0,X1] :
( in(sK41(X0,X1),X0)
| X0 = X1
| element(sK41(X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_665])]) ).
fof(f5556,plain,
( ! [X72,X73] :
( element(sK41(sK38(powerset(X72)),X73),X73)
| sK38(powerset(X72)) = X73
| ~ empty(X72) )
| ~ spl61_501
| ~ spl61_665 ),
inference(resolution,[],[f5404,f4221]) ).
fof(f5404,plain,
( ! [X0,X1] :
( element(sK41(X0,X1),X1)
| in(sK41(X0,X1),X0)
| X0 = X1 )
| ~ spl61_665 ),
inference(avatar_component_clause,[],[f5403]) ).
fof(f9209,plain,
( spl61_1131
| ~ spl61_528
| ~ spl61_598 ),
inference(avatar_split_clause,[],[f4967,f4860,f4410,f9207]) ).
fof(f9207,plain,
( spl61_1131
<=> ! [X50,X49] :
( sK38(powerset(X50)) = X49
| ~ empty(X49)
| element(sK41(X49,sK38(powerset(X50))),X50) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_1131])]) ).
fof(f4410,plain,
( spl61_528
<=> ! [X43,X42] :
( element(X42,X43)
| ~ in(X42,sK38(powerset(X43))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_528])]) ).
fof(f4860,plain,
( spl61_598
<=> ! [X4,X5] :
( in(sK41(X4,X5),X5)
| X4 = X5
| ~ empty(X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_598])]) ).
fof(f4967,plain,
( ! [X50,X49] :
( sK38(powerset(X50)) = X49
| ~ empty(X49)
| element(sK41(X49,sK38(powerset(X50))),X50) )
| ~ spl61_528
| ~ spl61_598 ),
inference(resolution,[],[f4861,f4411]) ).
fof(f4411,plain,
( ! [X42,X43] :
( ~ in(X42,sK38(powerset(X43)))
| element(X42,X43) )
| ~ spl61_528 ),
inference(avatar_component_clause,[],[f4410]) ).
fof(f4861,plain,
( ! [X4,X5] :
( in(sK41(X4,X5),X5)
| X4 = X5
| ~ empty(X4) )
| ~ spl61_598 ),
inference(avatar_component_clause,[],[f4860]) ).
fof(f9205,plain,
( spl61_1130
| ~ spl61_561
| ~ spl61_598 ),
inference(avatar_split_clause,[],[f4952,f4860,f4599,f9203]) ).
fof(f9203,plain,
( spl61_1130
<=> ! [X20,X19] :
( sK17(X20) = X19
| ~ empty(X19)
| element(sK41(X19,sK17(X20)),X20)
| empty(X20) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_1130])]) ).
fof(f4599,plain,
( spl61_561
<=> ! [X14,X15] :
( element(X14,X15)
| ~ in(X14,sK17(X15))
| empty(X15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_561])]) ).
fof(f4952,plain,
( ! [X19,X20] :
( sK17(X20) = X19
| ~ empty(X19)
| element(sK41(X19,sK17(X20)),X20)
| empty(X20) )
| ~ spl61_561
| ~ spl61_598 ),
inference(resolution,[],[f4861,f4600]) ).
fof(f4600,plain,
( ! [X14,X15] :
( ~ in(X14,sK17(X15))
| element(X14,X15)
| empty(X15) )
| ~ spl61_561 ),
inference(avatar_component_clause,[],[f4599]) ).
fof(f9201,plain,
( spl61_1129
| ~ spl61_132
| spl61_1126 ),
inference(avatar_split_clause,[],[f9185,f9181,f1521,f9198]) ).
fof(f9198,plain,
( spl61_1129
<=> sP0(lim_points_of_net(sK12,net_of_bool_filter(sK12,cast_as_carrier_subset(sK12),sK13))) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_1129])]) ).
fof(f1521,plain,
( spl61_132
<=> ! [X0] :
( sP0(X0)
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_132])]) ).
fof(f9181,plain,
( spl61_1126
<=> empty(lim_points_of_net(sK12,net_of_bool_filter(sK12,cast_as_carrier_subset(sK12),sK13))) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_1126])]) ).
fof(f9185,plain,
( sP0(lim_points_of_net(sK12,net_of_bool_filter(sK12,cast_as_carrier_subset(sK12),sK13)))
| ~ spl61_132
| spl61_1126 ),
inference(resolution,[],[f9183,f1522]) ).
fof(f1522,plain,
( ! [X0] :
( empty(X0)
| sP0(X0) )
| ~ spl61_132 ),
inference(avatar_component_clause,[],[f1521]) ).
fof(f9183,plain,
( ~ empty(lim_points_of_net(sK12,net_of_bool_filter(sK12,cast_as_carrier_subset(sK12),sK13)))
| spl61_1126 ),
inference(avatar_component_clause,[],[f9181]) ).
fof(f9195,plain,
( ~ spl61_1128
| ~ spl61_130
| ~ spl61_240 ),
inference(avatar_split_clause,[],[f9178,f2010,f1512,f9192]) ).
fof(f9192,plain,
( spl61_1128
<=> in(lim_points_of_net(sK12,net_of_bool_filter(sK12,cast_as_carrier_subset(sK12),sK13)),sK14) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_1128])]) ).
fof(f9178,plain,
( ~ in(lim_points_of_net(sK12,net_of_bool_filter(sK12,cast_as_carrier_subset(sK12),sK13)),sK14)
| ~ spl61_130
| ~ spl61_240 ),
inference(resolution,[],[f1514,f2011]) ).
fof(f9190,plain,
( spl61_1127
| ~ spl61_130
| ~ spl61_241 ),
inference(avatar_split_clause,[],[f9177,f2014,f1512,f9187]) ).
fof(f9187,plain,
( spl61_1127
<=> element(sK14,lim_points_of_net(sK12,net_of_bool_filter(sK12,cast_as_carrier_subset(sK12),sK13))) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_1127])]) ).
fof(f2014,plain,
( spl61_241
<=> ! [X0,X1] :
( element(X0,X1)
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_241])]) ).
fof(f9177,plain,
( element(sK14,lim_points_of_net(sK12,net_of_bool_filter(sK12,cast_as_carrier_subset(sK12),sK13)))
| ~ spl61_130
| ~ spl61_241 ),
inference(resolution,[],[f1514,f2015]) ).
fof(f2015,plain,
( ! [X0,X1] :
( ~ in(X0,X1)
| element(X0,X1) )
| ~ spl61_241 ),
inference(avatar_component_clause,[],[f2014]) ).
fof(f9184,plain,
( ~ spl61_1126
| ~ spl61_130
| ~ spl61_200 ),
inference(avatar_split_clause,[],[f9176,f1826,f1512,f9181]) ).
fof(f1826,plain,
( spl61_200
<=> ! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_200])]) ).
fof(f9176,plain,
( ~ empty(lim_points_of_net(sK12,net_of_bool_filter(sK12,cast_as_carrier_subset(sK12),sK13)))
| ~ spl61_130
| ~ spl61_200 ),
inference(resolution,[],[f1514,f1827]) ).
fof(f1827,plain,
( ! [X0,X1] :
( ~ in(X0,X1)
| ~ empty(X1) )
| ~ spl61_200 ),
inference(avatar_component_clause,[],[f1826]) ).
fof(f9179,plain,
( ~ spl61_130
| ~ spl61_131 ),
inference(avatar_split_clause,[],[f453,f1516,f1512]) ).
fof(f453,plain,
( ~ is_a_convergence_point_of_set(sK12,sK13,sK14)
| ~ in(sK14,lim_points_of_net(sK12,net_of_bool_filter(sK12,cast_as_carrier_subset(sK12),sK13))) ),
inference(cnf_transformation,[],[f331]) ).
fof(f331,plain,
( ( ~ is_a_convergence_point_of_set(sK12,sK13,sK14)
| ~ in(sK14,lim_points_of_net(sK12,net_of_bool_filter(sK12,cast_as_carrier_subset(sK12),sK13))) )
& ( is_a_convergence_point_of_set(sK12,sK13,sK14)
| in(sK14,lim_points_of_net(sK12,net_of_bool_filter(sK12,cast_as_carrier_subset(sK12),sK13))) )
& element(sK14,the_carrier(sK12))
& element(sK13,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(sK12)))))
& proper_element(sK13,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(sK12)))))
& upper_relstr_subset(sK13,boole_POSet(cast_as_carrier_subset(sK12)))
& filtered_subset(sK13,boole_POSet(cast_as_carrier_subset(sK12)))
& ~ empty(sK13)
& top_str(sK12)
& topological_space(sK12)
& ~ empty_carrier(sK12) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK12,sK13,sK14])],[f327,f330,f329,f328]) ).
fof(f328,plain,
( ? [X0] :
( ? [X1] :
( ? [X2] :
( ( ~ is_a_convergence_point_of_set(X0,X1,X2)
| ~ in(X2,lim_points_of_net(X0,net_of_bool_filter(X0,cast_as_carrier_subset(X0),X1))) )
& ( is_a_convergence_point_of_set(X0,X1,X2)
| in(X2,lim_points_of_net(X0,net_of_bool_filter(X0,cast_as_carrier_subset(X0),X1))) )
& element(X2,the_carrier(X0)) )
& element(X1,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(X0)))))
& proper_element(X1,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(X0)))))
& upper_relstr_subset(X1,boole_POSet(cast_as_carrier_subset(X0)))
& filtered_subset(X1,boole_POSet(cast_as_carrier_subset(X0)))
& ~ empty(X1) )
& top_str(X0)
& topological_space(X0)
& ~ empty_carrier(X0) )
=> ( ? [X1] :
( ? [X2] :
( ( ~ is_a_convergence_point_of_set(sK12,X1,X2)
| ~ in(X2,lim_points_of_net(sK12,net_of_bool_filter(sK12,cast_as_carrier_subset(sK12),X1))) )
& ( is_a_convergence_point_of_set(sK12,X1,X2)
| in(X2,lim_points_of_net(sK12,net_of_bool_filter(sK12,cast_as_carrier_subset(sK12),X1))) )
& element(X2,the_carrier(sK12)) )
& element(X1,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(sK12)))))
& proper_element(X1,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(sK12)))))
& upper_relstr_subset(X1,boole_POSet(cast_as_carrier_subset(sK12)))
& filtered_subset(X1,boole_POSet(cast_as_carrier_subset(sK12)))
& ~ empty(X1) )
& top_str(sK12)
& topological_space(sK12)
& ~ empty_carrier(sK12) ) ),
introduced(choice_axiom,[]) ).
fof(f329,plain,
( ? [X1] :
( ? [X2] :
( ( ~ is_a_convergence_point_of_set(sK12,X1,X2)
| ~ in(X2,lim_points_of_net(sK12,net_of_bool_filter(sK12,cast_as_carrier_subset(sK12),X1))) )
& ( is_a_convergence_point_of_set(sK12,X1,X2)
| in(X2,lim_points_of_net(sK12,net_of_bool_filter(sK12,cast_as_carrier_subset(sK12),X1))) )
& element(X2,the_carrier(sK12)) )
& element(X1,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(sK12)))))
& proper_element(X1,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(sK12)))))
& upper_relstr_subset(X1,boole_POSet(cast_as_carrier_subset(sK12)))
& filtered_subset(X1,boole_POSet(cast_as_carrier_subset(sK12)))
& ~ empty(X1) )
=> ( ? [X2] :
( ( ~ is_a_convergence_point_of_set(sK12,sK13,X2)
| ~ in(X2,lim_points_of_net(sK12,net_of_bool_filter(sK12,cast_as_carrier_subset(sK12),sK13))) )
& ( is_a_convergence_point_of_set(sK12,sK13,X2)
| in(X2,lim_points_of_net(sK12,net_of_bool_filter(sK12,cast_as_carrier_subset(sK12),sK13))) )
& element(X2,the_carrier(sK12)) )
& element(sK13,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(sK12)))))
& proper_element(sK13,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(sK12)))))
& upper_relstr_subset(sK13,boole_POSet(cast_as_carrier_subset(sK12)))
& filtered_subset(sK13,boole_POSet(cast_as_carrier_subset(sK12)))
& ~ empty(sK13) ) ),
introduced(choice_axiom,[]) ).
fof(f330,plain,
( ? [X2] :
( ( ~ is_a_convergence_point_of_set(sK12,sK13,X2)
| ~ in(X2,lim_points_of_net(sK12,net_of_bool_filter(sK12,cast_as_carrier_subset(sK12),sK13))) )
& ( is_a_convergence_point_of_set(sK12,sK13,X2)
| in(X2,lim_points_of_net(sK12,net_of_bool_filter(sK12,cast_as_carrier_subset(sK12),sK13))) )
& element(X2,the_carrier(sK12)) )
=> ( ( ~ is_a_convergence_point_of_set(sK12,sK13,sK14)
| ~ in(sK14,lim_points_of_net(sK12,net_of_bool_filter(sK12,cast_as_carrier_subset(sK12),sK13))) )
& ( is_a_convergence_point_of_set(sK12,sK13,sK14)
| in(sK14,lim_points_of_net(sK12,net_of_bool_filter(sK12,cast_as_carrier_subset(sK12),sK13))) )
& element(sK14,the_carrier(sK12)) ) ),
introduced(choice_axiom,[]) ).
fof(f327,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ( ~ is_a_convergence_point_of_set(X0,X1,X2)
| ~ in(X2,lim_points_of_net(X0,net_of_bool_filter(X0,cast_as_carrier_subset(X0),X1))) )
& ( is_a_convergence_point_of_set(X0,X1,X2)
| in(X2,lim_points_of_net(X0,net_of_bool_filter(X0,cast_as_carrier_subset(X0),X1))) )
& element(X2,the_carrier(X0)) )
& element(X1,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(X0)))))
& proper_element(X1,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(X0)))))
& upper_relstr_subset(X1,boole_POSet(cast_as_carrier_subset(X0)))
& filtered_subset(X1,boole_POSet(cast_as_carrier_subset(X0)))
& ~ empty(X1) )
& top_str(X0)
& topological_space(X0)
& ~ empty_carrier(X0) ),
inference(flattening,[],[f326]) ).
fof(f326,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ( ~ is_a_convergence_point_of_set(X0,X1,X2)
| ~ in(X2,lim_points_of_net(X0,net_of_bool_filter(X0,cast_as_carrier_subset(X0),X1))) )
& ( is_a_convergence_point_of_set(X0,X1,X2)
| in(X2,lim_points_of_net(X0,net_of_bool_filter(X0,cast_as_carrier_subset(X0),X1))) )
& element(X2,the_carrier(X0)) )
& element(X1,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(X0)))))
& proper_element(X1,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(X0)))))
& upper_relstr_subset(X1,boole_POSet(cast_as_carrier_subset(X0)))
& filtered_subset(X1,boole_POSet(cast_as_carrier_subset(X0)))
& ~ empty(X1) )
& top_str(X0)
& topological_space(X0)
& ~ empty_carrier(X0) ),
inference(nnf_transformation,[],[f140]) ).
fof(f140,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ( in(X2,lim_points_of_net(X0,net_of_bool_filter(X0,cast_as_carrier_subset(X0),X1)))
<~> is_a_convergence_point_of_set(X0,X1,X2) )
& element(X2,the_carrier(X0)) )
& element(X1,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(X0)))))
& proper_element(X1,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(X0)))))
& upper_relstr_subset(X1,boole_POSet(cast_as_carrier_subset(X0)))
& filtered_subset(X1,boole_POSet(cast_as_carrier_subset(X0)))
& ~ empty(X1) )
& top_str(X0)
& topological_space(X0)
& ~ empty_carrier(X0) ),
inference(flattening,[],[f139]) ).
fof(f139,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ( in(X2,lim_points_of_net(X0,net_of_bool_filter(X0,cast_as_carrier_subset(X0),X1)))
<~> is_a_convergence_point_of_set(X0,X1,X2) )
& element(X2,the_carrier(X0)) )
& element(X1,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(X0)))))
& proper_element(X1,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(X0)))))
& upper_relstr_subset(X1,boole_POSet(cast_as_carrier_subset(X0)))
& filtered_subset(X1,boole_POSet(cast_as_carrier_subset(X0)))
& ~ empty(X1) )
& top_str(X0)
& topological_space(X0)
& ~ empty_carrier(X0) ),
inference(ennf_transformation,[],[f128]) ).
fof(f128,negated_conjecture,
~ ! [X0] :
( ( top_str(X0)
& topological_space(X0)
& ~ empty_carrier(X0) )
=> ! [X1] :
( ( element(X1,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(X0)))))
& proper_element(X1,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(X0)))))
& upper_relstr_subset(X1,boole_POSet(cast_as_carrier_subset(X0)))
& filtered_subset(X1,boole_POSet(cast_as_carrier_subset(X0)))
& ~ empty(X1) )
=> ! [X2] :
( element(X2,the_carrier(X0))
=> ( in(X2,lim_points_of_net(X0,net_of_bool_filter(X0,cast_as_carrier_subset(X0),X1)))
<=> is_a_convergence_point_of_set(X0,X1,X2) ) ) ) ),
inference(negated_conjecture,[],[f127]) ).
fof(f127,conjecture,
! [X0] :
( ( top_str(X0)
& topological_space(X0)
& ~ empty_carrier(X0) )
=> ! [X1] :
( ( element(X1,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(X0)))))
& proper_element(X1,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(X0)))))
& upper_relstr_subset(X1,boole_POSet(cast_as_carrier_subset(X0)))
& filtered_subset(X1,boole_POSet(cast_as_carrier_subset(X0)))
& ~ empty(X1) )
=> ! [X2] :
( element(X2,the_carrier(X0))
=> ( in(X2,lim_points_of_net(X0,net_of_bool_filter(X0,cast_as_carrier_subset(X0),X1)))
<=> is_a_convergence_point_of_set(X0,X1,X2) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.XVCyggMQ11/Vampire---4.8_15325',t18_yellow19) ).
fof(f9172,plain,
( ~ spl61_131
| ~ spl61_5
| spl61_130
| ~ spl61_1085 ),
inference(avatar_split_clause,[],[f8783,f8772,f1512,f912,f1516]) ).
fof(f8772,plain,
( spl61_1085
<=> ! [X1] :
( ~ is_a_convergence_point_of_set(sK12,sK13,X1)
| ~ element(X1,the_carrier(sK12))
| in(X1,lim_points_of_net(sK12,net_of_bool_filter(sK12,cast_as_carrier_subset(sK12),sK13))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_1085])]) ).
fof(f8783,plain,
( ~ element(sK14,the_carrier(sK12))
| ~ is_a_convergence_point_of_set(sK12,sK13,sK14)
| spl61_130
| ~ spl61_1085 ),
inference(resolution,[],[f8773,f1513]) ).
fof(f1513,plain,
( ~ in(sK14,lim_points_of_net(sK12,net_of_bool_filter(sK12,cast_as_carrier_subset(sK12),sK13)))
| spl61_130 ),
inference(avatar_component_clause,[],[f1512]) ).
fof(f8773,plain,
( ! [X1] :
( in(X1,lim_points_of_net(sK12,net_of_bool_filter(sK12,cast_as_carrier_subset(sK12),sK13)))
| ~ element(X1,the_carrier(sK12))
| ~ is_a_convergence_point_of_set(sK12,sK13,X1) )
| ~ spl61_1085 ),
inference(avatar_component_clause,[],[f8772]) ).
fof(f9171,plain,
( spl61_1125
| ~ spl61_560
| ~ spl61_598 ),
inference(avatar_split_clause,[],[f4951,f4860,f4595,f9169]) ).
fof(f9169,plain,
( spl61_1125
<=> ! [X18,X17] :
( sK16(X18) = X17
| ~ empty(X17)
| element(sK41(X17,sK16(X18)),X18)
| empty(X18) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_1125])]) ).
fof(f4595,plain,
( spl61_560
<=> ! [X13,X12] :
( element(X12,X13)
| ~ in(X12,sK16(X13))
| empty(X13) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_560])]) ).
fof(f4951,plain,
( ! [X18,X17] :
( sK16(X18) = X17
| ~ empty(X17)
| element(sK41(X17,sK16(X18)),X18)
| empty(X18) )
| ~ spl61_560
| ~ spl61_598 ),
inference(resolution,[],[f4861,f4596]) ).
fof(f4596,plain,
( ! [X12,X13] :
( ~ in(X12,sK16(X13))
| element(X12,X13)
| empty(X13) )
| ~ spl61_560 ),
inference(avatar_component_clause,[],[f4595]) ).
fof(f9167,plain,
( spl61_1124
| ~ spl61_559
| ~ spl61_598 ),
inference(avatar_split_clause,[],[f4950,f4860,f4591,f9165]) ).
fof(f9165,plain,
( spl61_1124
<=> ! [X16,X15] :
( sK15(X16) = X15
| ~ empty(X15)
| element(sK41(X15,sK15(X16)),X16)
| empty(X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_1124])]) ).
fof(f4591,plain,
( spl61_559
<=> ! [X11,X10] :
( element(X10,X11)
| ~ in(X10,sK15(X11))
| empty(X11) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_559])]) ).
fof(f4950,plain,
( ! [X16,X15] :
( sK15(X16) = X15
| ~ empty(X15)
| element(sK41(X15,sK15(X16)),X16)
| empty(X16) )
| ~ spl61_559
| ~ spl61_598 ),
inference(resolution,[],[f4861,f4592]) ).
fof(f4592,plain,
( ! [X10,X11] :
( ~ in(X10,sK15(X11))
| element(X10,X11)
| empty(X11) )
| ~ spl61_559 ),
inference(avatar_component_clause,[],[f4591]) ).
fof(f9163,plain,
( spl61_1123
| ~ spl61_528
| ~ spl61_597 ),
inference(avatar_split_clause,[],[f4938,f4856,f4410,f9161]) ).
fof(f9161,plain,
( spl61_1123
<=> ! [X48,X49] :
( sK38(powerset(X48)) = X49
| ~ empty(X49)
| element(sK41(sK38(powerset(X48)),X49),X48) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_1123])]) ).
fof(f4856,plain,
( spl61_597
<=> ! [X4,X5] :
( in(sK41(X4,X5),X4)
| X4 = X5
| ~ empty(X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_597])]) ).
fof(f4938,plain,
( ! [X48,X49] :
( sK38(powerset(X48)) = X49
| ~ empty(X49)
| element(sK41(sK38(powerset(X48)),X49),X48) )
| ~ spl61_528
| ~ spl61_597 ),
inference(resolution,[],[f4857,f4411]) ).
fof(f4857,plain,
( ! [X4,X5] :
( in(sK41(X4,X5),X4)
| X4 = X5
| ~ empty(X5) )
| ~ spl61_597 ),
inference(avatar_component_clause,[],[f4856]) ).
fof(f9159,plain,
( spl61_1122
| ~ spl61_561
| ~ spl61_597 ),
inference(avatar_split_clause,[],[f4923,f4856,f4599,f9157]) ).
fof(f9157,plain,
( spl61_1122
<=> ! [X18,X19] :
( sK17(X18) = X19
| ~ empty(X19)
| element(sK41(sK17(X18),X19),X18)
| empty(X18) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_1122])]) ).
fof(f4923,plain,
( ! [X18,X19] :
( sK17(X18) = X19
| ~ empty(X19)
| element(sK41(sK17(X18),X19),X18)
| empty(X18) )
| ~ spl61_561
| ~ spl61_597 ),
inference(resolution,[],[f4857,f4600]) ).
fof(f9155,plain,
( spl61_1121
| ~ spl61_560
| ~ spl61_597 ),
inference(avatar_split_clause,[],[f4922,f4856,f4595,f9153]) ).
fof(f9153,plain,
( spl61_1121
<=> ! [X16,X17] :
( sK16(X16) = X17
| ~ empty(X17)
| element(sK41(sK16(X16),X17),X16)
| empty(X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_1121])]) ).
fof(f4922,plain,
( ! [X16,X17] :
( sK16(X16) = X17
| ~ empty(X17)
| element(sK41(sK16(X16),X17),X16)
| empty(X16) )
| ~ spl61_560
| ~ spl61_597 ),
inference(resolution,[],[f4857,f4596]) ).
fof(f9151,plain,
( spl61_1120
| ~ spl61_559
| ~ spl61_597 ),
inference(avatar_split_clause,[],[f4921,f4856,f4591,f9149]) ).
fof(f9149,plain,
( spl61_1120
<=> ! [X14,X15] :
( sK15(X14) = X15
| ~ empty(X15)
| element(sK41(sK15(X14),X15),X14)
| empty(X14) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_1120])]) ).
fof(f4921,plain,
( ! [X14,X15] :
( sK15(X14) = X15
| ~ empty(X15)
| element(sK41(sK15(X14),X15),X14)
| empty(X14) )
| ~ spl61_559
| ~ spl61_597 ),
inference(resolution,[],[f4857,f4592]) ).
fof(f9147,plain,
( spl61_1119
| ~ spl61_353
| ~ spl61_501 ),
inference(avatar_split_clause,[],[f4280,f4220,f2784,f9145]) ).
fof(f9145,plain,
( spl61_1119
<=> ! [X4,X3] :
( ~ empty(X3)
| in(sK41(sK38(powerset(X3)),X4),X4)
| sK38(powerset(X3)) = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_1119])]) ).
fof(f2784,plain,
( spl61_353
<=> ! [X0,X1] :
( X0 = X1
| in(sK41(X0,X1),X1)
| in(sK41(X0,X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_353])]) ).
fof(f4280,plain,
( ! [X3,X4] :
( ~ empty(X3)
| in(sK41(sK38(powerset(X3)),X4),X4)
| sK38(powerset(X3)) = X4 )
| ~ spl61_353
| ~ spl61_501 ),
inference(resolution,[],[f4221,f2785]) ).
fof(f2785,plain,
( ! [X0,X1] :
( in(sK41(X0,X1),X1)
| in(sK41(X0,X1),X0)
| X0 = X1 )
| ~ spl61_353 ),
inference(avatar_component_clause,[],[f2784]) ).
fof(f9143,plain,
( spl61_1118
| ~ spl61_353
| ~ spl61_501 ),
inference(avatar_split_clause,[],[f4279,f4220,f2784,f9141]) ).
fof(f9141,plain,
( spl61_1118
<=> ! [X2,X1] :
( ~ empty(X1)
| in(sK41(X2,sK38(powerset(X1))),X2)
| sK38(powerset(X1)) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_1118])]) ).
fof(f4279,plain,
( ! [X2,X1] :
( ~ empty(X1)
| in(sK41(X2,sK38(powerset(X1))),X2)
| sK38(powerset(X1)) = X2 )
| ~ spl61_353
| ~ spl61_501 ),
inference(resolution,[],[f4221,f2785]) ).
fof(f8995,plain,
( ~ spl61_1116
| spl61_1117
| ~ spl61_266
| ~ spl61_1079 ),
inference(avatar_split_clause,[],[f8826,f8707,f2171,f8992,f8988]) ).
fof(f8988,plain,
( spl61_1116
<=> finite(the_carrier(sK12)) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_1116])]) ).
fof(f8992,plain,
( spl61_1117
<=> finite(cast_as_carrier_subset(sK12)) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_1117])]) ).
fof(f2171,plain,
( spl61_266
<=> ! [X0,X1] :
( finite(X1)
| ~ element(X1,powerset(X0))
| ~ finite(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_266])]) ).
fof(f8707,plain,
( spl61_1079
<=> element(cast_as_carrier_subset(sK12),powerset(the_carrier(sK12))) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_1079])]) ).
fof(f8826,plain,
( finite(cast_as_carrier_subset(sK12))
| ~ finite(the_carrier(sK12))
| ~ spl61_266
| ~ spl61_1079 ),
inference(resolution,[],[f8708,f2172]) ).
fof(f2172,plain,
( ! [X0,X1] :
( ~ element(X1,powerset(X0))
| finite(X1)
| ~ finite(X0) )
| ~ spl61_266 ),
inference(avatar_component_clause,[],[f2171]) ).
fof(f8708,plain,
( element(cast_as_carrier_subset(sK12),powerset(the_carrier(sK12)))
| ~ spl61_1079 ),
inference(avatar_component_clause,[],[f8707]) ).
fof(f8937,plain,
( spl61_1115
| ~ spl61_240
| ~ spl61_667 ),
inference(avatar_split_clause,[],[f5580,f5411,f2010,f8935]) ).
fof(f8935,plain,
( spl61_1115
<=> ! [X6,X7] :
( element(sK41(X6,X7),X6)
| X6 = X7
| ~ in(X7,sK41(X6,X7)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_1115])]) ).
fof(f5580,plain,
( ! [X6,X7] :
( element(sK41(X6,X7),X6)
| X6 = X7
| ~ in(X7,sK41(X6,X7)) )
| ~ spl61_240
| ~ spl61_667 ),
inference(resolution,[],[f5412,f2011]) ).
fof(f8933,plain,
( spl61_1114
| ~ spl61_240
| ~ spl61_665 ),
inference(avatar_split_clause,[],[f5523,f5403,f2010,f8931]) ).
fof(f8931,plain,
( spl61_1114
<=> ! [X6,X5] :
( element(sK41(X5,X6),X6)
| X5 = X6
| ~ in(X5,sK41(X5,X6)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_1114])]) ).
fof(f5523,plain,
( ! [X6,X5] :
( element(sK41(X5,X6),X6)
| X5 = X6
| ~ in(X5,sK41(X5,X6)) )
| ~ spl61_240
| ~ spl61_665 ),
inference(resolution,[],[f5404,f2011]) ).
fof(f8929,plain,
( spl61_1113
| ~ spl61_241
| ~ spl61_665 ),
inference(avatar_split_clause,[],[f5522,f5403,f2014,f8927]) ).
fof(f8927,plain,
( spl61_1113
<=> ! [X4,X3] :
( element(sK41(X3,X4),X4)
| X3 = X4
| element(sK41(X3,X4),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_1113])]) ).
fof(f5522,plain,
( ! [X3,X4] :
( element(sK41(X3,X4),X4)
| X3 = X4
| element(sK41(X3,X4),X3) )
| ~ spl61_241
| ~ spl61_665 ),
inference(resolution,[],[f5404,f2015]) ).
fof(f8914,plain,
( spl61_1112
| ~ spl61_469
| ~ spl61_639 ),
inference(avatar_split_clause,[],[f5358,f5216,f4058,f8912]) ).
fof(f8912,plain,
( spl61_1112
<=> ! [X0] :
( element(sK38(sK36(X0)),the_carrier(X0))
| ~ top_str(X0)
| ~ topological_space(X0)
| empty(sK36(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_1112])]) ).
fof(f4058,plain,
( spl61_469
<=> ! [X13] :
( empty(X13)
| in(sK38(X13),X13) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_469])]) ).
fof(f5216,plain,
( spl61_639
<=> ! [X38,X39] :
( element(X38,the_carrier(X39))
| ~ in(X38,sK36(X39))
| ~ top_str(X39)
| ~ topological_space(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_639])]) ).
fof(f5358,plain,
( ! [X0] :
( element(sK38(sK36(X0)),the_carrier(X0))
| ~ top_str(X0)
| ~ topological_space(X0)
| empty(sK36(X0)) )
| ~ spl61_469
| ~ spl61_639 ),
inference(resolution,[],[f5217,f4059]) ).
fof(f4059,plain,
( ! [X13] :
( in(sK38(X13),X13)
| empty(X13) )
| ~ spl61_469 ),
inference(avatar_component_clause,[],[f4058]) ).
fof(f5217,plain,
( ! [X38,X39] :
( ~ in(X38,sK36(X39))
| element(X38,the_carrier(X39))
| ~ top_str(X39)
| ~ topological_space(X39) )
| ~ spl61_639 ),
inference(avatar_component_clause,[],[f5216]) ).
fof(f8910,plain,
( spl61_1111
| ~ spl61_469
| ~ spl61_638 ),
inference(avatar_split_clause,[],[f5348,f5212,f4058,f8908]) ).
fof(f8908,plain,
( spl61_1111
<=> ! [X0] :
( element(sK38(sK35(X0)),the_carrier(X0))
| ~ top_str(X0)
| ~ topological_space(X0)
| empty(sK35(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_1111])]) ).
fof(f5212,plain,
( spl61_638
<=> ! [X36,X37] :
( element(X36,the_carrier(X37))
| ~ in(X36,sK35(X37))
| ~ top_str(X37)
| ~ topological_space(X37) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_638])]) ).
fof(f5348,plain,
( ! [X0] :
( element(sK38(sK35(X0)),the_carrier(X0))
| ~ top_str(X0)
| ~ topological_space(X0)
| empty(sK35(X0)) )
| ~ spl61_469
| ~ spl61_638 ),
inference(resolution,[],[f5213,f4059]) ).
fof(f5213,plain,
( ! [X36,X37] :
( ~ in(X36,sK35(X37))
| element(X36,the_carrier(X37))
| ~ top_str(X37)
| ~ topological_space(X37) )
| ~ spl61_638 ),
inference(avatar_component_clause,[],[f5212]) ).
fof(f8906,plain,
( spl61_1110
| ~ spl61_469
| ~ spl61_637 ),
inference(avatar_split_clause,[],[f5343,f5208,f4058,f8904]) ).
fof(f8904,plain,
( spl61_1110
<=> ! [X0] :
( element(sK38(sK34(X0)),the_carrier(X0))
| ~ top_str(X0)
| ~ topological_space(X0)
| empty(sK34(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_1110])]) ).
fof(f5208,plain,
( spl61_637
<=> ! [X34,X35] :
( element(X34,the_carrier(X35))
| ~ in(X34,sK34(X35))
| ~ top_str(X35)
| ~ topological_space(X35) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_637])]) ).
fof(f5343,plain,
( ! [X0] :
( element(sK38(sK34(X0)),the_carrier(X0))
| ~ top_str(X0)
| ~ topological_space(X0)
| empty(sK34(X0)) )
| ~ spl61_469
| ~ spl61_637 ),
inference(resolution,[],[f5209,f4059]) ).
fof(f5209,plain,
( ! [X34,X35] :
( ~ in(X34,sK34(X35))
| element(X34,the_carrier(X35))
| ~ top_str(X35)
| ~ topological_space(X35) )
| ~ spl61_637 ),
inference(avatar_component_clause,[],[f5208]) ).
fof(f8902,plain,
( spl61_1109
| ~ spl61_469
| ~ spl61_636 ),
inference(avatar_split_clause,[],[f5338,f5204,f4058,f8900]) ).
fof(f8900,plain,
( spl61_1109
<=> ! [X0] :
( element(sK38(sK29(X0)),the_carrier(X0))
| ~ rel_str(X0)
| empty_carrier(X0)
| empty(sK29(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_1109])]) ).
fof(f5204,plain,
( spl61_636
<=> ! [X29,X28] :
( element(X28,the_carrier(X29))
| ~ in(X28,sK29(X29))
| ~ rel_str(X29)
| empty_carrier(X29) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_636])]) ).
fof(f5338,plain,
( ! [X0] :
( element(sK38(sK29(X0)),the_carrier(X0))
| ~ rel_str(X0)
| empty_carrier(X0)
| empty(sK29(X0)) )
| ~ spl61_469
| ~ spl61_636 ),
inference(resolution,[],[f5205,f4059]) ).
fof(f5205,plain,
( ! [X28,X29] :
( ~ in(X28,sK29(X29))
| element(X28,the_carrier(X29))
| ~ rel_str(X29)
| empty_carrier(X29) )
| ~ spl61_636 ),
inference(avatar_component_clause,[],[f5204]) ).
fof(f8898,plain,
( spl61_1108
| ~ spl61_469
| ~ spl61_635 ),
inference(avatar_split_clause,[],[f5333,f5200,f4058,f8896]) ).
fof(f8896,plain,
( spl61_1108
<=> ! [X0] :
( element(sK38(sK28(X0)),the_carrier(X0))
| ~ one_sorted_str(X0)
| empty_carrier(X0)
| empty(sK28(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_1108])]) ).
fof(f5200,plain,
( spl61_635
<=> ! [X27,X26] :
( element(X26,the_carrier(X27))
| ~ in(X26,sK28(X27))
| ~ one_sorted_str(X27)
| empty_carrier(X27) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_635])]) ).
fof(f5333,plain,
( ! [X0] :
( element(sK38(sK28(X0)),the_carrier(X0))
| ~ one_sorted_str(X0)
| empty_carrier(X0)
| empty(sK28(X0)) )
| ~ spl61_469
| ~ spl61_635 ),
inference(resolution,[],[f5201,f4059]) ).
fof(f5201,plain,
( ! [X26,X27] :
( ~ in(X26,sK28(X27))
| element(X26,the_carrier(X27))
| ~ one_sorted_str(X27)
| empty_carrier(X27) )
| ~ spl61_635 ),
inference(avatar_component_clause,[],[f5200]) ).
fof(f8894,plain,
( spl61_1107
| ~ spl61_305
| ~ spl61_634 ),
inference(avatar_split_clause,[],[f5329,f5196,f2416,f8892]) ).
fof(f8892,plain,
( spl61_1107
<=> ! [X0,X1] :
( ~ in(X0,the_InternalRel(X1))
| element(X0,cartesian_product2(the_carrier(X1),the_carrier(X1)))
| ~ rel_str(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_1107])]) ).
fof(f2416,plain,
( spl61_305
<=> ! [X0] :
( relation_of2_as_subset(the_InternalRel(X0),the_carrier(X0),the_carrier(X0))
| ~ rel_str(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_305])]) ).
fof(f5196,plain,
( spl61_634
<=> ! [X5,X4,X6,X3] :
( element(X3,cartesian_product2(X4,X5))
| ~ in(X3,X6)
| ~ relation_of2_as_subset(X6,X4,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_634])]) ).
fof(f5329,plain,
( ! [X0,X1] :
( ~ in(X0,the_InternalRel(X1))
| element(X0,cartesian_product2(the_carrier(X1),the_carrier(X1)))
| ~ rel_str(X1) )
| ~ spl61_305
| ~ spl61_634 ),
inference(resolution,[],[f5197,f2417]) ).
fof(f2417,plain,
( ! [X0] :
( relation_of2_as_subset(the_InternalRel(X0),the_carrier(X0),the_carrier(X0))
| ~ rel_str(X0) )
| ~ spl61_305 ),
inference(avatar_component_clause,[],[f2416]) ).
fof(f5197,plain,
( ! [X3,X6,X4,X5] :
( ~ relation_of2_as_subset(X6,X4,X5)
| ~ in(X3,X6)
| element(X3,cartesian_product2(X4,X5)) )
| ~ spl61_634 ),
inference(avatar_component_clause,[],[f5196]) ).
fof(f8890,plain,
( spl61_1106
| ~ spl61_335
| ~ spl61_606 ),
inference(avatar_split_clause,[],[f5108,f4997,f2573,f8888]) ).
fof(f8888,plain,
( spl61_1106
<=> ! [X34,X32,X33] :
( ~ in(X32,sK22(X33))
| ~ one_sorted_str(X33)
| element(X34,the_carrier(X33))
| ~ in(X34,X32) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_1106])]) ).
fof(f2573,plain,
( spl61_335
<=> ! [X2,X0,X1] :
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_335])]) ).
fof(f4997,plain,
( spl61_606
<=> ! [X18,X19] :
( element(X18,powerset(the_carrier(X19)))
| ~ in(X18,sK22(X19))
| ~ one_sorted_str(X19) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_606])]) ).
fof(f5108,plain,
( ! [X34,X32,X33] :
( ~ in(X32,sK22(X33))
| ~ one_sorted_str(X33)
| element(X34,the_carrier(X33))
| ~ in(X34,X32) )
| ~ spl61_335
| ~ spl61_606 ),
inference(resolution,[],[f4998,f2574]) ).
fof(f2574,plain,
( ! [X2,X0,X1] :
( ~ element(X1,powerset(X2))
| element(X0,X2)
| ~ in(X0,X1) )
| ~ spl61_335 ),
inference(avatar_component_clause,[],[f2573]) ).
fof(f4998,plain,
( ! [X18,X19] :
( element(X18,powerset(the_carrier(X19)))
| ~ in(X18,sK22(X19))
| ~ one_sorted_str(X19) )
| ~ spl61_606 ),
inference(avatar_component_clause,[],[f4997]) ).
fof(f8886,plain,
( spl61_1105
| ~ spl61_339
| ~ spl61_606 ),
inference(avatar_split_clause,[],[f5095,f4997,f2677,f8884]) ).
fof(f8884,plain,
( spl61_1105
<=> ! [X0,X1] :
( ~ in(X0,sK22(X1))
| ~ one_sorted_str(X1)
| ~ empty(X0)
| boundary_set(X0,X1)
| ~ top_str(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_1105])]) ).
fof(f2677,plain,
( spl61_339
<=> ! [X0,X1] :
( boundary_set(X1,X0)
| ~ empty(X1)
| ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_339])]) ).
fof(f5095,plain,
( ! [X0,X1] :
( ~ in(X0,sK22(X1))
| ~ one_sorted_str(X1)
| ~ empty(X0)
| boundary_set(X0,X1)
| ~ top_str(X1) )
| ~ spl61_339
| ~ spl61_606 ),
inference(resolution,[],[f4998,f2678]) ).
fof(f2678,plain,
( ! [X0,X1] :
( ~ element(X1,powerset(the_carrier(X0)))
| ~ empty(X1)
| boundary_set(X1,X0)
| ~ top_str(X0) )
| ~ spl61_339 ),
inference(avatar_component_clause,[],[f2677]) ).
fof(f8882,plain,
( spl61_1104
| ~ spl61_598
| ~ spl61_604 ),
inference(avatar_split_clause,[],[f5087,f4989,f4860,f8880]) ).
fof(f8880,plain,
( spl61_1104
<=> ! [X2,X1] :
( ~ topological_space(X1)
| ~ empty(the_carrier(X1))
| ~ top_str(X1)
| sK36(X1) = X2
| ~ empty(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_1104])]) ).
fof(f4989,plain,
( spl61_604
<=> ! [X0,X1] :
( ~ top_str(X0)
| ~ topological_space(X0)
| ~ empty(the_carrier(X0))
| ~ in(X1,sK36(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_604])]) ).
fof(f5087,plain,
( ! [X2,X1] :
( ~ topological_space(X1)
| ~ empty(the_carrier(X1))
| ~ top_str(X1)
| sK36(X1) = X2
| ~ empty(X2) )
| ~ spl61_598
| ~ spl61_604 ),
inference(resolution,[],[f4990,f4861]) ).
fof(f4990,plain,
( ! [X0,X1] :
( ~ in(X1,sK36(X0))
| ~ topological_space(X0)
| ~ empty(the_carrier(X0))
| ~ top_str(X0) )
| ~ spl61_604 ),
inference(avatar_component_clause,[],[f4989]) ).
fof(f8878,plain,
( spl61_1103
| ~ spl61_598
| ~ spl61_603 ),
inference(avatar_split_clause,[],[f5082,f4985,f4860,f8876]) ).
fof(f8876,plain,
( spl61_1103
<=> ! [X2,X1] :
( ~ topological_space(X1)
| ~ empty(the_carrier(X1))
| ~ top_str(X1)
| sK35(X1) = X2
| ~ empty(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_1103])]) ).
fof(f4985,plain,
( spl61_603
<=> ! [X0,X1] :
( ~ top_str(X0)
| ~ topological_space(X0)
| ~ empty(the_carrier(X0))
| ~ in(X1,sK35(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_603])]) ).
fof(f5082,plain,
( ! [X2,X1] :
( ~ topological_space(X1)
| ~ empty(the_carrier(X1))
| ~ top_str(X1)
| sK35(X1) = X2
| ~ empty(X2) )
| ~ spl61_598
| ~ spl61_603 ),
inference(resolution,[],[f4986,f4861]) ).
fof(f4986,plain,
( ! [X0,X1] :
( ~ in(X1,sK35(X0))
| ~ topological_space(X0)
| ~ empty(the_carrier(X0))
| ~ top_str(X0) )
| ~ spl61_603 ),
inference(avatar_component_clause,[],[f4985]) ).
fof(f8874,plain,
( spl61_1102
| ~ spl61_260
| ~ spl61_1079 ),
inference(avatar_split_clause,[],[f8827,f8707,f2117,f8871]) ).
fof(f8871,plain,
( spl61_1102
<=> subset(cast_as_carrier_subset(sK12),the_carrier(sK12)) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_1102])]) ).
fof(f2117,plain,
( spl61_260
<=> ! [X0,X1] :
( subset(X0,X1)
| ~ element(X0,powerset(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_260])]) ).
fof(f8827,plain,
( subset(cast_as_carrier_subset(sK12),the_carrier(sK12))
| ~ spl61_260
| ~ spl61_1079 ),
inference(resolution,[],[f8708,f2118]) ).
fof(f2118,plain,
( ! [X0,X1] :
( ~ element(X0,powerset(X1))
| subset(X0,X1) )
| ~ spl61_260 ),
inference(avatar_component_clause,[],[f2117]) ).
fof(f8869,plain,
( spl61_1101
| ~ spl61_598
| ~ spl61_602 ),
inference(avatar_split_clause,[],[f5077,f4981,f4860,f8867]) ).
fof(f8867,plain,
( spl61_1101
<=> ! [X2,X1] :
( ~ topological_space(X1)
| ~ empty(the_carrier(X1))
| ~ top_str(X1)
| sK34(X1) = X2
| ~ empty(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_1101])]) ).
fof(f4981,plain,
( spl61_602
<=> ! [X0,X1] :
( ~ top_str(X0)
| ~ topological_space(X0)
| ~ empty(the_carrier(X0))
| ~ in(X1,sK34(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_602])]) ).
fof(f5077,plain,
( ! [X2,X1] :
( ~ topological_space(X1)
| ~ empty(the_carrier(X1))
| ~ top_str(X1)
| sK34(X1) = X2
| ~ empty(X2) )
| ~ spl61_598
| ~ spl61_602 ),
inference(resolution,[],[f4982,f4861]) ).
fof(f4982,plain,
( ! [X0,X1] :
( ~ in(X1,sK34(X0))
| ~ topological_space(X0)
| ~ empty(the_carrier(X0))
| ~ top_str(X0) )
| ~ spl61_602 ),
inference(avatar_component_clause,[],[f4981]) ).
fof(f8865,plain,
( spl61_1100
| ~ spl61_598
| ~ spl61_601 ),
inference(avatar_split_clause,[],[f5072,f4977,f4860,f8863]) ).
fof(f8863,plain,
( spl61_1100
<=> ! [X2,X1] :
( empty_carrier(X1)
| ~ empty(the_carrier(X1))
| ~ rel_str(X1)
| sK29(X1) = X2
| ~ empty(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_1100])]) ).
fof(f4977,plain,
( spl61_601
<=> ! [X0,X1] :
( ~ rel_str(X0)
| empty_carrier(X0)
| ~ empty(the_carrier(X0))
| ~ in(X1,sK29(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_601])]) ).
fof(f5072,plain,
( ! [X2,X1] :
( empty_carrier(X1)
| ~ empty(the_carrier(X1))
| ~ rel_str(X1)
| sK29(X1) = X2
| ~ empty(X2) )
| ~ spl61_598
| ~ spl61_601 ),
inference(resolution,[],[f4978,f4861]) ).
fof(f4978,plain,
( ! [X0,X1] :
( ~ in(X1,sK29(X0))
| empty_carrier(X0)
| ~ empty(the_carrier(X0))
| ~ rel_str(X0) )
| ~ spl61_601 ),
inference(avatar_component_clause,[],[f4977]) ).
fof(f8861,plain,
( spl61_1099
| ~ spl61_529
| ~ spl61_598 ),
inference(avatar_split_clause,[],[f4969,f4860,f4414,f8859]) ).
fof(f8859,plain,
( spl61_1099
<=> ! [X54,X53] :
( sK40(X54) = X53
| ~ empty(X53)
| element(sK41(X53,sK40(X54)),powerset(X54)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_1099])]) ).
fof(f4414,plain,
( spl61_529
<=> ! [X46,X47] :
( element(X46,powerset(X47))
| ~ in(X46,sK40(X47)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_529])]) ).
fof(f4969,plain,
( ! [X54,X53] :
( sK40(X54) = X53
| ~ empty(X53)
| element(sK41(X53,sK40(X54)),powerset(X54)) )
| ~ spl61_529
| ~ spl61_598 ),
inference(resolution,[],[f4861,f4415]) ).
fof(f4415,plain,
( ! [X46,X47] :
( ~ in(X46,sK40(X47))
| element(X46,powerset(X47)) )
| ~ spl61_529 ),
inference(avatar_component_clause,[],[f4414]) ).
fof(f8857,plain,
( spl61_1098
| ~ spl61_529
| ~ spl61_597 ),
inference(avatar_split_clause,[],[f4940,f4856,f4414,f8855]) ).
fof(f8855,plain,
( spl61_1098
<=> ! [X52,X53] :
( sK40(X52) = X53
| ~ empty(X53)
| element(sK41(sK40(X52),X53),powerset(X52)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_1098])]) ).
fof(f4940,plain,
( ! [X52,X53] :
( sK40(X52) = X53
| ~ empty(X53)
| element(sK41(sK40(X52),X53),powerset(X52)) )
| ~ spl61_529
| ~ spl61_597 ),
inference(resolution,[],[f4857,f4415]) ).
fof(f8853,plain,
( spl61_1097
| ~ spl61_362
| ~ spl61_568 ),
inference(avatar_split_clause,[],[f4659,f4653,f2834,f8851]) ).
fof(f8851,plain,
( spl61_1097
<=> ! [X4,X5] :
( sK57 != rel_str_of(X4,X5)
| the_carrier(sK57) = X4
| ~ relation_of2(X5,X4,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_1097])]) ).
fof(f2834,plain,
( spl61_362
<=> ! [X0,X3,X2,X1] :
( X0 = X2
| rel_str_of(X0,X1) != rel_str_of(X2,X3)
| ~ relation_of2(X1,X0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_362])]) ).
fof(f4653,plain,
( spl61_568
<=> sK57 = rel_str_of(the_carrier(sK57),the_InternalRel(sK57)) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_568])]) ).
fof(f4659,plain,
( ! [X4,X5] :
( sK57 != rel_str_of(X4,X5)
| the_carrier(sK57) = X4
| ~ relation_of2(X5,X4,X4) )
| ~ spl61_362
| ~ spl61_568 ),
inference(superposition,[],[f2835,f4655]) ).
fof(f4655,plain,
( sK57 = rel_str_of(the_carrier(sK57),the_InternalRel(sK57))
| ~ spl61_568 ),
inference(avatar_component_clause,[],[f4653]) ).
fof(f2835,plain,
( ! [X2,X3,X0,X1] :
( rel_str_of(X0,X1) != rel_str_of(X2,X3)
| X0 = X2
| ~ relation_of2(X1,X0,X0) )
| ~ spl61_362 ),
inference(avatar_component_clause,[],[f2834]) ).
fof(f8849,plain,
( spl61_1096
| ~ spl61_363
| ~ spl61_568 ),
inference(avatar_split_clause,[],[f4657,f4653,f2838,f8847]) ).
fof(f8847,plain,
( spl61_1096
<=> ! [X0,X1] :
( rel_str_of(X0,X1) != sK57
| the_InternalRel(sK57) = X1
| ~ relation_of2(X1,X0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_1096])]) ).
fof(f2838,plain,
( spl61_363
<=> ! [X0,X3,X2,X1] :
( X1 = X3
| rel_str_of(X0,X1) != rel_str_of(X2,X3)
| ~ relation_of2(X1,X0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_363])]) ).
fof(f4657,plain,
( ! [X0,X1] :
( rel_str_of(X0,X1) != sK57
| the_InternalRel(sK57) = X1
| ~ relation_of2(X1,X0,X0) )
| ~ spl61_363
| ~ spl61_568 ),
inference(superposition,[],[f2839,f4655]) ).
fof(f2839,plain,
( ! [X2,X3,X0,X1] :
( rel_str_of(X0,X1) != rel_str_of(X2,X3)
| X1 = X3
| ~ relation_of2(X1,X0,X0) )
| ~ spl61_363 ),
inference(avatar_component_clause,[],[f2838]) ).
fof(f8845,plain,
( spl61_1095
| ~ spl61_362
| ~ spl61_567 ),
inference(avatar_split_clause,[],[f4650,f4644,f2834,f8843]) ).
fof(f8843,plain,
( spl61_1095
<=> ! [X4,X5] :
( sK56 != rel_str_of(X4,X5)
| the_carrier(sK56) = X4
| ~ relation_of2(X5,X4,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_1095])]) ).
fof(f4644,plain,
( spl61_567
<=> sK56 = rel_str_of(the_carrier(sK56),the_InternalRel(sK56)) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_567])]) ).
fof(f4650,plain,
( ! [X4,X5] :
( sK56 != rel_str_of(X4,X5)
| the_carrier(sK56) = X4
| ~ relation_of2(X5,X4,X4) )
| ~ spl61_362
| ~ spl61_567 ),
inference(superposition,[],[f2835,f4646]) ).
fof(f4646,plain,
( sK56 = rel_str_of(the_carrier(sK56),the_InternalRel(sK56))
| ~ spl61_567 ),
inference(avatar_component_clause,[],[f4644]) ).
fof(f8841,plain,
( spl61_1094
| ~ spl61_363
| ~ spl61_567 ),
inference(avatar_split_clause,[],[f4648,f4644,f2838,f8839]) ).
fof(f8839,plain,
( spl61_1094
<=> ! [X0,X1] :
( rel_str_of(X0,X1) != sK56
| the_InternalRel(sK56) = X1
| ~ relation_of2(X1,X0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_1094])]) ).
fof(f4648,plain,
( ! [X0,X1] :
( rel_str_of(X0,X1) != sK56
| the_InternalRel(sK56) = X1
| ~ relation_of2(X1,X0,X0) )
| ~ spl61_363
| ~ spl61_567 ),
inference(superposition,[],[f2839,f4646]) ).
fof(f8837,plain,
( spl61_1093
| ~ spl61_362
| ~ spl61_566 ),
inference(avatar_split_clause,[],[f4641,f4635,f2834,f8835]) ).
fof(f8835,plain,
( spl61_1093
<=> ! [X4,X5] :
( sK55 != rel_str_of(X4,X5)
| the_carrier(sK55) = X4
| ~ relation_of2(X5,X4,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_1093])]) ).
fof(f4635,plain,
( spl61_566
<=> sK55 = rel_str_of(the_carrier(sK55),the_InternalRel(sK55)) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_566])]) ).
fof(f4641,plain,
( ! [X4,X5] :
( sK55 != rel_str_of(X4,X5)
| the_carrier(sK55) = X4
| ~ relation_of2(X5,X4,X4) )
| ~ spl61_362
| ~ spl61_566 ),
inference(superposition,[],[f2835,f4637]) ).
fof(f4637,plain,
( sK55 = rel_str_of(the_carrier(sK55),the_InternalRel(sK55))
| ~ spl61_566 ),
inference(avatar_component_clause,[],[f4635]) ).
fof(f8833,plain,
( spl61_1092
| ~ spl61_363
| ~ spl61_566 ),
inference(avatar_split_clause,[],[f4639,f4635,f2838,f8831]) ).
fof(f8831,plain,
( spl61_1092
<=> ! [X0,X1] :
( rel_str_of(X0,X1) != sK55
| the_InternalRel(sK55) = X1
| ~ relation_of2(X1,X0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_1092])]) ).
fof(f4639,plain,
( ! [X0,X1] :
( rel_str_of(X0,X1) != sK55
| the_InternalRel(sK55) = X1
| ~ relation_of2(X1,X0,X0) )
| ~ spl61_363
| ~ spl61_566 ),
inference(superposition,[],[f2839,f4637]) ).
fof(f8809,plain,
( spl61_1091
| ~ spl61_362
| ~ spl61_565 ),
inference(avatar_split_clause,[],[f4632,f4626,f2834,f8807]) ).
fof(f8807,plain,
( spl61_1091
<=> ! [X4,X5] :
( sK54 != rel_str_of(X4,X5)
| the_carrier(sK54) = X4
| ~ relation_of2(X5,X4,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_1091])]) ).
fof(f4626,plain,
( spl61_565
<=> sK54 = rel_str_of(the_carrier(sK54),the_InternalRel(sK54)) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_565])]) ).
fof(f4632,plain,
( ! [X4,X5] :
( sK54 != rel_str_of(X4,X5)
| the_carrier(sK54) = X4
| ~ relation_of2(X5,X4,X4) )
| ~ spl61_362
| ~ spl61_565 ),
inference(superposition,[],[f2835,f4628]) ).
fof(f4628,plain,
( sK54 = rel_str_of(the_carrier(sK54),the_InternalRel(sK54))
| ~ spl61_565 ),
inference(avatar_component_clause,[],[f4626]) ).
fof(f8805,plain,
( spl61_1090
| ~ spl61_363
| ~ spl61_565 ),
inference(avatar_split_clause,[],[f4630,f4626,f2838,f8803]) ).
fof(f8803,plain,
( spl61_1090
<=> ! [X0,X1] :
( rel_str_of(X0,X1) != sK54
| the_InternalRel(sK54) = X1
| ~ relation_of2(X1,X0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_1090])]) ).
fof(f4630,plain,
( ! [X0,X1] :
( rel_str_of(X0,X1) != sK54
| the_InternalRel(sK54) = X1
| ~ relation_of2(X1,X0,X0) )
| ~ spl61_363
| ~ spl61_565 ),
inference(superposition,[],[f2839,f4628]) ).
fof(f8801,plain,
( spl61_1089
| ~ spl61_362
| ~ spl61_563 ),
inference(avatar_split_clause,[],[f4618,f4612,f2834,f8799]) ).
fof(f8799,plain,
( spl61_1089
<=> ! [X4,X5] :
( sK53 != rel_str_of(X4,X5)
| the_carrier(sK53) = X4
| ~ relation_of2(X5,X4,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_1089])]) ).
fof(f4612,plain,
( spl61_563
<=> sK53 = rel_str_of(the_carrier(sK53),the_InternalRel(sK53)) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_563])]) ).
fof(f4618,plain,
( ! [X4,X5] :
( sK53 != rel_str_of(X4,X5)
| the_carrier(sK53) = X4
| ~ relation_of2(X5,X4,X4) )
| ~ spl61_362
| ~ spl61_563 ),
inference(superposition,[],[f2835,f4614]) ).
fof(f4614,plain,
( sK53 = rel_str_of(the_carrier(sK53),the_InternalRel(sK53))
| ~ spl61_563 ),
inference(avatar_component_clause,[],[f4612]) ).
fof(f8797,plain,
( spl61_1088
| ~ spl61_363
| ~ spl61_563 ),
inference(avatar_split_clause,[],[f4616,f4612,f2838,f8795]) ).
fof(f8795,plain,
( spl61_1088
<=> ! [X0,X1] :
( rel_str_of(X0,X1) != sK53
| the_InternalRel(sK53) = X1
| ~ relation_of2(X1,X0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_1088])]) ).
fof(f4616,plain,
( ! [X0,X1] :
( rel_str_of(X0,X1) != sK53
| the_InternalRel(sK53) = X1
| ~ relation_of2(X1,X0,X0) )
| ~ spl61_363
| ~ spl61_563 ),
inference(superposition,[],[f2839,f4614]) ).
fof(f8793,plain,
( spl61_1087
| ~ spl61_362
| ~ spl61_562 ),
inference(avatar_split_clause,[],[f4609,f4603,f2834,f8791]) ).
fof(f8791,plain,
( spl61_1087
<=> ! [X4,X5] :
( sK52 != rel_str_of(X4,X5)
| the_carrier(sK52) = X4
| ~ relation_of2(X5,X4,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_1087])]) ).
fof(f4603,plain,
( spl61_562
<=> sK52 = rel_str_of(the_carrier(sK52),the_InternalRel(sK52)) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_562])]) ).
fof(f4609,plain,
( ! [X4,X5] :
( sK52 != rel_str_of(X4,X5)
| the_carrier(sK52) = X4
| ~ relation_of2(X5,X4,X4) )
| ~ spl61_362
| ~ spl61_562 ),
inference(superposition,[],[f2835,f4605]) ).
fof(f4605,plain,
( sK52 = rel_str_of(the_carrier(sK52),the_InternalRel(sK52))
| ~ spl61_562 ),
inference(avatar_component_clause,[],[f4603]) ).
fof(f8789,plain,
( spl61_1086
| ~ spl61_363
| ~ spl61_562 ),
inference(avatar_split_clause,[],[f4607,f4603,f2838,f8787]) ).
fof(f8787,plain,
( spl61_1086
<=> ! [X0,X1] :
( rel_str_of(X0,X1) != sK52
| the_InternalRel(sK52) = X1
| ~ relation_of2(X1,X0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_1086])]) ).
fof(f4607,plain,
( ! [X0,X1] :
( rel_str_of(X0,X1) != sK52
| the_InternalRel(sK52) = X1
| ~ relation_of2(X1,X0,X0) )
| ~ spl61_363
| ~ spl61_562 ),
inference(superposition,[],[f2839,f4605]) ).
fof(f8774,plain,
( spl61_1
| ~ spl61_2
| ~ spl61_3
| spl61_754
| ~ spl61_774
| ~ spl61_1065
| ~ spl61_1066
| spl61_1085
| ~ spl61_385
| ~ spl61_535 ),
inference(avatar_split_clause,[],[f4472,f4462,f3226,f8772,f8650,f8646,f6326,f6212,f902,f897,f892]) ).
fof(f892,plain,
( spl61_1
<=> empty_carrier(sK12) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_1])]) ).
fof(f897,plain,
( spl61_2
<=> topological_space(sK12) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_2])]) ).
fof(f902,plain,
( spl61_3
<=> top_str(sK12) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_3])]) ).
fof(f6212,plain,
( spl61_754
<=> empty_carrier(net_of_bool_filter(sK12,cast_as_carrier_subset(sK12),sK13)) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_754])]) ).
fof(f6326,plain,
( spl61_774
<=> transitive_relstr(net_of_bool_filter(sK12,cast_as_carrier_subset(sK12),sK13)) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_774])]) ).
fof(f8646,plain,
( spl61_1065
<=> directed_relstr(net_of_bool_filter(sK12,cast_as_carrier_subset(sK12),sK13)) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_1065])]) ).
fof(f8650,plain,
( spl61_1066
<=> net_str(net_of_bool_filter(sK12,cast_as_carrier_subset(sK12),sK13),sK12) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_1066])]) ).
fof(f3226,plain,
( spl61_385
<=> ! [X2,X0,X1] :
( in(X2,lim_points_of_net(X0,X1))
| ~ is_a_convergence_point_of_set(X0,filter_of_net_str(X0,X1),X2)
| ~ element(X2,the_carrier(X0))
| ~ net_str(X1,X0)
| ~ directed_relstr(X1)
| ~ transitive_relstr(X1)
| empty_carrier(X1)
| ~ top_str(X0)
| ~ topological_space(X0)
| empty_carrier(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_385])]) ).
fof(f4462,plain,
( spl61_535
<=> sK13 = filter_of_net_str(sK12,net_of_bool_filter(sK12,cast_as_carrier_subset(sK12),sK13)) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_535])]) ).
fof(f4472,plain,
( ! [X1] :
( ~ is_a_convergence_point_of_set(sK12,sK13,X1)
| in(X1,lim_points_of_net(sK12,net_of_bool_filter(sK12,cast_as_carrier_subset(sK12),sK13)))
| ~ element(X1,the_carrier(sK12))
| ~ net_str(net_of_bool_filter(sK12,cast_as_carrier_subset(sK12),sK13),sK12)
| ~ directed_relstr(net_of_bool_filter(sK12,cast_as_carrier_subset(sK12),sK13))
| ~ transitive_relstr(net_of_bool_filter(sK12,cast_as_carrier_subset(sK12),sK13))
| empty_carrier(net_of_bool_filter(sK12,cast_as_carrier_subset(sK12),sK13))
| ~ top_str(sK12)
| ~ topological_space(sK12)
| empty_carrier(sK12) )
| ~ spl61_385
| ~ spl61_535 ),
inference(superposition,[],[f3227,f4464]) ).
fof(f4464,plain,
( sK13 = filter_of_net_str(sK12,net_of_bool_filter(sK12,cast_as_carrier_subset(sK12),sK13))
| ~ spl61_535 ),
inference(avatar_component_clause,[],[f4462]) ).
fof(f3227,plain,
( ! [X2,X0,X1] :
( ~ is_a_convergence_point_of_set(X0,filter_of_net_str(X0,X1),X2)
| in(X2,lim_points_of_net(X0,X1))
| ~ element(X2,the_carrier(X0))
| ~ net_str(X1,X0)
| ~ directed_relstr(X1)
| ~ transitive_relstr(X1)
| empty_carrier(X1)
| ~ top_str(X0)
| ~ topological_space(X0)
| empty_carrier(X0) )
| ~ spl61_385 ),
inference(avatar_component_clause,[],[f3226]) ).
fof(f8755,plain,
( ~ spl61_161
| ~ spl61_265
| spl61_1079 ),
inference(avatar_split_clause,[],[f8745,f8707,f2167,f1659]) ).
fof(f1659,plain,
( spl61_161
<=> one_sorted_str(sK12) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_161])]) ).
fof(f2167,plain,
( spl61_265
<=> ! [X0] :
( element(cast_as_carrier_subset(X0),powerset(the_carrier(X0)))
| ~ one_sorted_str(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_265])]) ).
fof(f8745,plain,
( ~ one_sorted_str(sK12)
| ~ spl61_265
| spl61_1079 ),
inference(resolution,[],[f8709,f2168]) ).
fof(f2168,plain,
( ! [X0] :
( element(cast_as_carrier_subset(X0),powerset(the_carrier(X0)))
| ~ one_sorted_str(X0) )
| ~ spl61_265 ),
inference(avatar_component_clause,[],[f2167]) ).
fof(f8709,plain,
( ~ element(cast_as_carrier_subset(sK12),powerset(the_carrier(sK12)))
| spl61_1079 ),
inference(avatar_component_clause,[],[f8707]) ).
fof(f8730,plain,
( spl61_1084
| ~ spl61_129
| ~ spl61_696 ),
inference(avatar_split_clause,[],[f5853,f5759,f1508,f8728]) ).
fof(f8728,plain,
( spl61_1084
<=> ! [X0] :
( boundary_set(the_carrier(X0),X0)
| ~ top_str(X0)
| ~ topological_space(X0)
| ~ nowhere_dense(the_carrier(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_1084])]) ).
fof(f1508,plain,
( spl61_129
<=> ! [X0] : subset(X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_129])]) ).
fof(f5759,plain,
( spl61_696
<=> ! [X0,X1] :
( ~ nowhere_dense(X0,X1)
| boundary_set(X0,X1)
| ~ top_str(X1)
| ~ topological_space(X1)
| ~ subset(X0,the_carrier(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_696])]) ).
fof(f5853,plain,
( ! [X0] :
( boundary_set(the_carrier(X0),X0)
| ~ top_str(X0)
| ~ topological_space(X0)
| ~ nowhere_dense(the_carrier(X0),X0) )
| ~ spl61_129
| ~ spl61_696 ),
inference(resolution,[],[f5760,f1509]) ).
fof(f1509,plain,
( ! [X0] : subset(X0,X0)
| ~ spl61_129 ),
inference(avatar_component_clause,[],[f1508]) ).
fof(f5760,plain,
( ! [X0,X1] :
( ~ subset(X0,the_carrier(X1))
| boundary_set(X0,X1)
| ~ top_str(X1)
| ~ topological_space(X1)
| ~ nowhere_dense(X0,X1) )
| ~ spl61_696 ),
inference(avatar_component_clause,[],[f5759]) ).
fof(f8726,plain,
( spl61_1083
| ~ spl61_294
| ~ spl61_664 ),
inference(avatar_split_clause,[],[f5500,f5399,f2285,f8724]) ).
fof(f8724,plain,
( spl61_1083
<=> ! [X1] :
( ~ one_sorted_str(X1)
| ~ net_str(X1,X1)
| strict_rel_str(rel_str_of(the_carrier(X1),the_mapping(X1,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_1083])]) ).
fof(f2285,plain,
( spl61_294
<=> ! [X0,X1] :
( strict_rel_str(rel_str_of(X0,X1))
| ~ relation_of2(X1,X0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_294])]) ).
fof(f5399,plain,
( spl61_664
<=> ! [X0,X1] :
( ~ net_str(X0,X1)
| ~ one_sorted_str(X1)
| relation_of2(the_mapping(X1,X0),the_carrier(X0),the_carrier(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_664])]) ).
fof(f5500,plain,
( ! [X1] :
( ~ one_sorted_str(X1)
| ~ net_str(X1,X1)
| strict_rel_str(rel_str_of(the_carrier(X1),the_mapping(X1,X1))) )
| ~ spl61_294
| ~ spl61_664 ),
inference(resolution,[],[f5400,f2286]) ).
fof(f2286,plain,
( ! [X0,X1] :
( ~ relation_of2(X1,X0,X0)
| strict_rel_str(rel_str_of(X0,X1)) )
| ~ spl61_294 ),
inference(avatar_component_clause,[],[f2285]) ).
fof(f5400,plain,
( ! [X0,X1] :
( relation_of2(the_mapping(X1,X0),the_carrier(X0),the_carrier(X1))
| ~ one_sorted_str(X1)
| ~ net_str(X0,X1) )
| ~ spl61_664 ),
inference(avatar_component_clause,[],[f5399]) ).
fof(f8722,plain,
( spl61_1082
| ~ spl61_295
| ~ spl61_664 ),
inference(avatar_split_clause,[],[f5499,f5399,f2289,f8720]) ).
fof(f8720,plain,
( spl61_1082
<=> ! [X0] :
( ~ one_sorted_str(X0)
| ~ net_str(X0,X0)
| rel_str(rel_str_of(the_carrier(X0),the_mapping(X0,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_1082])]) ).
fof(f2289,plain,
( spl61_295
<=> ! [X0,X1] :
( rel_str(rel_str_of(X0,X1))
| ~ relation_of2(X1,X0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_295])]) ).
fof(f5499,plain,
( ! [X0] :
( ~ one_sorted_str(X0)
| ~ net_str(X0,X0)
| rel_str(rel_str_of(the_carrier(X0),the_mapping(X0,X0))) )
| ~ spl61_295
| ~ spl61_664 ),
inference(resolution,[],[f5400,f2290]) ).
fof(f2290,plain,
( ! [X0,X1] :
( ~ relation_of2(X1,X0,X0)
| rel_str(rel_str_of(X0,X1)) )
| ~ spl61_295 ),
inference(avatar_component_clause,[],[f2289]) ).
fof(f8718,plain,
( spl61_1081
| ~ spl61_469
| ~ spl61_660 ),
inference(avatar_split_clause,[],[f5493,f5382,f4058,f8716]) ).
fof(f8716,plain,
( spl61_1081
<=> ! [X0] :
( ~ topological_space(X0)
| empty_carrier(X0)
| ~ empty(the_carrier(X0))
| ~ top_str(X0)
| empty(sK27(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_1081])]) ).
fof(f5382,plain,
( spl61_660
<=> ! [X4,X3] :
( ~ top_str(X3)
| ~ topological_space(X3)
| empty_carrier(X3)
| ~ empty(the_carrier(X3))
| ~ in(X4,sK27(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_660])]) ).
fof(f5493,plain,
( ! [X0] :
( ~ topological_space(X0)
| empty_carrier(X0)
| ~ empty(the_carrier(X0))
| ~ top_str(X0)
| empty(sK27(X0)) )
| ~ spl61_469
| ~ spl61_660 ),
inference(resolution,[],[f5383,f4059]) ).
fof(f5383,plain,
( ! [X3,X4] :
( ~ in(X4,sK27(X3))
| ~ topological_space(X3)
| empty_carrier(X3)
| ~ empty(the_carrier(X3))
| ~ top_str(X3) )
| ~ spl61_660 ),
inference(avatar_component_clause,[],[f5382]) ).
fof(f8714,plain,
( spl61_1080
| ~ spl61_469
| ~ spl61_659 ),
inference(avatar_split_clause,[],[f5488,f5378,f4058,f8712]) ).
fof(f8712,plain,
( spl61_1080
<=> ! [X0] :
( ~ topological_space(X0)
| empty_carrier(X0)
| ~ empty(the_carrier(X0))
| ~ top_str(X0)
| empty(sK26(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_1080])]) ).
fof(f5378,plain,
( spl61_659
<=> ! [X4,X3] :
( ~ top_str(X3)
| ~ topological_space(X3)
| empty_carrier(X3)
| ~ empty(the_carrier(X3))
| ~ in(X4,sK26(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_659])]) ).
fof(f5488,plain,
( ! [X0] :
( ~ topological_space(X0)
| empty_carrier(X0)
| ~ empty(the_carrier(X0))
| ~ top_str(X0)
| empty(sK26(X0)) )
| ~ spl61_469
| ~ spl61_659 ),
inference(resolution,[],[f5379,f4059]) ).
fof(f5379,plain,
( ! [X3,X4] :
( ~ in(X4,sK26(X3))
| ~ topological_space(X3)
| empty_carrier(X3)
| ~ empty(the_carrier(X3))
| ~ top_str(X3) )
| ~ spl61_659 ),
inference(avatar_component_clause,[],[f5378]) ).
fof(f8710,plain,
( ~ spl61_1079
| ~ spl61_161
| spl61_1
| ~ spl61_533
| spl61_1066 ),
inference(avatar_split_clause,[],[f8658,f8650,f4449,f892,f1659,f8707]) ).
fof(f4449,plain,
( spl61_533
<=> ! [X11] :
( net_str(net_of_bool_filter(X11,cast_as_carrier_subset(sK12),sK13),X11)
| empty_carrier(X11)
| ~ one_sorted_str(X11)
| ~ element(cast_as_carrier_subset(sK12),powerset(the_carrier(X11))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_533])]) ).
fof(f8658,plain,
( empty_carrier(sK12)
| ~ one_sorted_str(sK12)
| ~ element(cast_as_carrier_subset(sK12),powerset(the_carrier(sK12)))
| ~ spl61_533
| spl61_1066 ),
inference(resolution,[],[f8652,f4450]) ).
fof(f4450,plain,
( ! [X11] :
( net_str(net_of_bool_filter(X11,cast_as_carrier_subset(sK12),sK13),X11)
| empty_carrier(X11)
| ~ one_sorted_str(X11)
| ~ element(cast_as_carrier_subset(sK12),powerset(the_carrier(X11))) )
| ~ spl61_533 ),
inference(avatar_component_clause,[],[f4449]) ).
fof(f8652,plain,
( ~ net_str(net_of_bool_filter(sK12,cast_as_carrier_subset(sK12),sK13),sK12)
| spl61_1066 ),
inference(avatar_component_clause,[],[f8650]) ).
fof(f8705,plain,
( spl61_1078
| ~ spl61_240
| ~ spl61_632 ),
inference(avatar_split_clause,[],[f5328,f5187,f2010,f8703]) ).
fof(f8703,plain,
( spl61_1078
<=> ! [X2] :
( empty(powerset(the_carrier(X2)))
| ~ sP10(X2)
| ~ in(powerset(the_carrier(X2)),sK37(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_1078])]) ).
fof(f5187,plain,
( spl61_632
<=> ! [X12] :
( empty(powerset(the_carrier(X12)))
| in(sK37(X12),powerset(the_carrier(X12)))
| ~ sP10(X12) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_632])]) ).
fof(f5328,plain,
( ! [X2] :
( empty(powerset(the_carrier(X2)))
| ~ sP10(X2)
| ~ in(powerset(the_carrier(X2)),sK37(X2)) )
| ~ spl61_240
| ~ spl61_632 ),
inference(resolution,[],[f5188,f2011]) ).
fof(f5188,plain,
( ! [X12] :
( in(sK37(X12),powerset(the_carrier(X12)))
| empty(powerset(the_carrier(X12)))
| ~ sP10(X12) )
| ~ spl61_632 ),
inference(avatar_component_clause,[],[f5187]) ).
fof(f8701,plain,
( spl61_1077
| ~ spl61_240
| ~ spl61_631 ),
inference(avatar_split_clause,[],[f5324,f5183,f2010,f8699]) ).
fof(f8699,plain,
( spl61_1077
<=> ! [X2] :
( empty(powerset(the_carrier(X2)))
| ~ sP9(X2)
| ~ in(powerset(the_carrier(X2)),sK33(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_1077])]) ).
fof(f5183,plain,
( spl61_631
<=> ! [X11] :
( empty(powerset(the_carrier(X11)))
| in(sK33(X11),powerset(the_carrier(X11)))
| ~ sP9(X11) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_631])]) ).
fof(f5324,plain,
( ! [X2] :
( empty(powerset(the_carrier(X2)))
| ~ sP9(X2)
| ~ in(powerset(the_carrier(X2)),sK33(X2)) )
| ~ spl61_240
| ~ spl61_631 ),
inference(resolution,[],[f5184,f2011]) ).
fof(f5184,plain,
( ! [X11] :
( in(sK33(X11),powerset(the_carrier(X11)))
| empty(powerset(the_carrier(X11)))
| ~ sP9(X11) )
| ~ spl61_631 ),
inference(avatar_component_clause,[],[f5183]) ).
fof(f8697,plain,
( spl61_1076
| ~ spl61_240
| ~ spl61_630 ),
inference(avatar_split_clause,[],[f5321,f5179,f2010,f8695]) ).
fof(f8695,plain,
( spl61_1076
<=> ! [X2] :
( empty(powerset(the_carrier(X2)))
| ~ sP7(X2)
| ~ in(powerset(the_carrier(X2)),sK30(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_1076])]) ).
fof(f5179,plain,
( spl61_630
<=> ! [X10] :
( empty(powerset(the_carrier(X10)))
| in(sK30(X10),powerset(the_carrier(X10)))
| ~ sP7(X10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_630])]) ).
fof(f5321,plain,
( ! [X2] :
( empty(powerset(the_carrier(X2)))
| ~ sP7(X2)
| ~ in(powerset(the_carrier(X2)),sK30(X2)) )
| ~ spl61_240
| ~ spl61_630 ),
inference(resolution,[],[f5180,f2011]) ).
fof(f5180,plain,
( ! [X10] :
( in(sK30(X10),powerset(the_carrier(X10)))
| empty(powerset(the_carrier(X10)))
| ~ sP7(X10) )
| ~ spl61_630 ),
inference(avatar_component_clause,[],[f5179]) ).
fof(f8693,plain,
( spl61_1075
| ~ spl61_240
| ~ spl61_629 ),
inference(avatar_split_clause,[],[f5318,f5175,f2010,f8691]) ).
fof(f8691,plain,
( spl61_1075
<=> ! [X2] :
( empty(powerset(the_carrier(X2)))
| ~ sP6(X2)
| ~ in(powerset(the_carrier(X2)),sK25(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_1075])]) ).
fof(f5175,plain,
( spl61_629
<=> ! [X9] :
( empty(powerset(the_carrier(X9)))
| in(sK25(X9),powerset(the_carrier(X9)))
| ~ sP6(X9) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_629])]) ).
fof(f5318,plain,
( ! [X2] :
( empty(powerset(the_carrier(X2)))
| ~ sP6(X2)
| ~ in(powerset(the_carrier(X2)),sK25(X2)) )
| ~ spl61_240
| ~ spl61_629 ),
inference(resolution,[],[f5176,f2011]) ).
fof(f5176,plain,
( ! [X9] :
( in(sK25(X9),powerset(the_carrier(X9)))
| empty(powerset(the_carrier(X9)))
| ~ sP6(X9) )
| ~ spl61_629 ),
inference(avatar_component_clause,[],[f5175]) ).
fof(f8689,plain,
( spl61_1074
| ~ spl61_240
| ~ spl61_628 ),
inference(avatar_split_clause,[],[f5315,f5171,f2010,f8687]) ).
fof(f8687,plain,
( spl61_1074
<=> ! [X2] :
( empty(powerset(the_carrier(X2)))
| ~ rel_str(X2)
| ~ in(powerset(the_carrier(X2)),sK24(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_1074])]) ).
fof(f5171,plain,
( spl61_628
<=> ! [X8] :
( empty(powerset(the_carrier(X8)))
| in(sK24(X8),powerset(the_carrier(X8)))
| ~ rel_str(X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_628])]) ).
fof(f5315,plain,
( ! [X2] :
( empty(powerset(the_carrier(X2)))
| ~ rel_str(X2)
| ~ in(powerset(the_carrier(X2)),sK24(X2)) )
| ~ spl61_240
| ~ spl61_628 ),
inference(resolution,[],[f5172,f2011]) ).
fof(f5172,plain,
( ! [X8] :
( in(sK24(X8),powerset(the_carrier(X8)))
| empty(powerset(the_carrier(X8)))
| ~ rel_str(X8) )
| ~ spl61_628 ),
inference(avatar_component_clause,[],[f5171]) ).
fof(f8685,plain,
( spl61_1073
| ~ spl61_240
| ~ spl61_627 ),
inference(avatar_split_clause,[],[f5307,f5167,f2010,f8683]) ).
fof(f8683,plain,
( spl61_1073
<=> ! [X2] :
( empty(powerset(the_carrier(X2)))
| ~ rel_str(X2)
| ~ in(powerset(the_carrier(X2)),sK23(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_1073])]) ).
fof(f5167,plain,
( spl61_627
<=> ! [X7] :
( empty(powerset(the_carrier(X7)))
| in(sK23(X7),powerset(the_carrier(X7)))
| ~ rel_str(X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_627])]) ).
fof(f5307,plain,
( ! [X2] :
( empty(powerset(the_carrier(X2)))
| ~ rel_str(X2)
| ~ in(powerset(the_carrier(X2)),sK23(X2)) )
| ~ spl61_240
| ~ spl61_627 ),
inference(resolution,[],[f5168,f2011]) ).
fof(f5168,plain,
( ! [X7] :
( in(sK23(X7),powerset(the_carrier(X7)))
| empty(powerset(the_carrier(X7)))
| ~ rel_str(X7) )
| ~ spl61_627 ),
inference(avatar_component_clause,[],[f5167]) ).
fof(f8681,plain,
( spl61_1072
| ~ spl61_240
| ~ spl61_626 ),
inference(avatar_split_clause,[],[f5303,f5163,f2010,f8679]) ).
fof(f8679,plain,
( spl61_1072
<=> ! [X2] :
( empty(powerset(the_carrier(X2)))
| ~ sP1(X2)
| ~ in(powerset(the_carrier(X2)),sK18(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_1072])]) ).
fof(f5163,plain,
( spl61_626
<=> ! [X6] :
( empty(powerset(the_carrier(X6)))
| in(sK18(X6),powerset(the_carrier(X6)))
| ~ sP1(X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_626])]) ).
fof(f5303,plain,
( ! [X2] :
( empty(powerset(the_carrier(X2)))
| ~ sP1(X2)
| ~ in(powerset(the_carrier(X2)),sK18(X2)) )
| ~ spl61_240
| ~ spl61_626 ),
inference(resolution,[],[f5164,f2011]) ).
fof(f5164,plain,
( ! [X6] :
( in(sK18(X6),powerset(the_carrier(X6)))
| empty(powerset(the_carrier(X6)))
| ~ sP1(X6) )
| ~ spl61_626 ),
inference(avatar_component_clause,[],[f5163]) ).
fof(f8677,plain,
( spl61_1071
| ~ spl61_240
| ~ spl61_625 ),
inference(avatar_split_clause,[],[f5300,f5159,f2010,f8675]) ).
fof(f8675,plain,
( spl61_1071
<=> ! [X2] :
( empty(powerset(the_carrier(X2)))
| ~ one_sorted_str(X2)
| ~ in(powerset(the_carrier(X2)),cast_as_carrier_subset(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_1071])]) ).
fof(f5159,plain,
( spl61_625
<=> ! [X2] :
( empty(powerset(the_carrier(X2)))
| in(cast_as_carrier_subset(X2),powerset(the_carrier(X2)))
| ~ one_sorted_str(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_625])]) ).
fof(f5300,plain,
( ! [X2] :
( empty(powerset(the_carrier(X2)))
| ~ one_sorted_str(X2)
| ~ in(powerset(the_carrier(X2)),cast_as_carrier_subset(X2)) )
| ~ spl61_240
| ~ spl61_625 ),
inference(resolution,[],[f5160,f2011]) ).
fof(f5160,plain,
( ! [X2] :
( in(cast_as_carrier_subset(X2),powerset(the_carrier(X2)))
| empty(powerset(the_carrier(X2)))
| ~ one_sorted_str(X2) )
| ~ spl61_625 ),
inference(avatar_component_clause,[],[f5159]) ).
fof(f8673,plain,
( spl61_1070
| ~ spl61_315
| ~ spl61_606 ),
inference(avatar_split_clause,[],[f5107,f4997,f2457,f8671]) ).
fof(f8671,plain,
( spl61_1070
<=> ! [X29,X30,X31] :
( ~ in(X29,sK22(X30))
| ~ one_sorted_str(X30)
| ~ empty(the_carrier(X30))
| ~ in(X31,X29) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_1070])]) ).
fof(f2457,plain,
( spl61_315
<=> ! [X2,X0,X1] :
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_315])]) ).
fof(f5107,plain,
( ! [X31,X29,X30] :
( ~ in(X29,sK22(X30))
| ~ one_sorted_str(X30)
| ~ empty(the_carrier(X30))
| ~ in(X31,X29) )
| ~ spl61_315
| ~ spl61_606 ),
inference(resolution,[],[f4998,f2458]) ).
fof(f2458,plain,
( ! [X2,X0,X1] :
( ~ element(X1,powerset(X2))
| ~ empty(X2)
| ~ in(X0,X1) )
| ~ spl61_315 ),
inference(avatar_component_clause,[],[f2457]) ).
fof(f8669,plain,
( ~ spl61_740
| ~ spl61_314
| spl61_1065 ),
inference(avatar_split_clause,[],[f8657,f8646,f2453,f6086]) ).
fof(f6086,plain,
( spl61_740
<=> sP11(sK13,cast_as_carrier_subset(sK12),sK12) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_740])]) ).
fof(f2453,plain,
( spl61_314
<=> ! [X2,X0,X1] :
( directed_relstr(net_of_bool_filter(X2,X1,X0))
| ~ sP11(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_314])]) ).
fof(f8657,plain,
( ~ sP11(sK13,cast_as_carrier_subset(sK12),sK12)
| ~ spl61_314
| spl61_1065 ),
inference(resolution,[],[f8648,f2454]) ).
fof(f2454,plain,
( ! [X2,X0,X1] :
( directed_relstr(net_of_bool_filter(X2,X1,X0))
| ~ sP11(X0,X1,X2) )
| ~ spl61_314 ),
inference(avatar_component_clause,[],[f2453]) ).
fof(f8648,plain,
( ~ directed_relstr(net_of_bool_filter(sK12,cast_as_carrier_subset(sK12),sK13))
| spl61_1065 ),
inference(avatar_component_clause,[],[f8646]) ).
fof(f8668,plain,
( spl61_1069
| ~ spl61_305
| ~ spl61_605 ),
inference(avatar_split_clause,[],[f5091,f4993,f2416,f8666]) ).
fof(f8666,plain,
( spl61_1069
<=> ! [X0,X1] :
( ~ empty(cartesian_product2(the_carrier(X0),the_carrier(X0)))
| ~ in(X1,the_InternalRel(X0))
| ~ rel_str(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_1069])]) ).
fof(f4993,plain,
( spl61_605
<=> ! [X6,X4,X5,X3] :
( ~ relation_of2_as_subset(X3,X4,X5)
| ~ empty(cartesian_product2(X4,X5))
| ~ in(X6,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_605])]) ).
fof(f5091,plain,
( ! [X0,X1] :
( ~ empty(cartesian_product2(the_carrier(X0),the_carrier(X0)))
| ~ in(X1,the_InternalRel(X0))
| ~ rel_str(X0) )
| ~ spl61_305
| ~ spl61_605 ),
inference(resolution,[],[f4994,f2417]) ).
fof(f4994,plain,
( ! [X3,X6,X4,X5] :
( ~ relation_of2_as_subset(X3,X4,X5)
| ~ empty(cartesian_product2(X4,X5))
| ~ in(X6,X3) )
| ~ spl61_605 ),
inference(avatar_component_clause,[],[f4993]) ).
fof(f8664,plain,
( ~ spl61_49
| ~ spl61_50
| ~ spl61_51
| ~ spl61_459
| spl61_1068
| ~ spl61_46
| ~ spl61_361
| ~ spl61_460 ),
inference(avatar_split_clause,[],[f4015,f4011,f2830,f1117,f8661,f4003,f1142,f1137,f1132]) ).
fof(f1132,plain,
( spl61_49
<=> reflexive_relstr(sK54) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_49])]) ).
fof(f1137,plain,
( spl61_50
<=> transitive_relstr(sK54) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_50])]) ).
fof(f1142,plain,
( spl61_51
<=> antisymmetric_relstr(sK54) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_51])]) ).
fof(f4003,plain,
( spl61_459
<=> with_suprema_relstr(sK54) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_459])]) ).
fof(f8661,plain,
( spl61_1068
<=> sP10(sK54) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_1068])]) ).
fof(f1117,plain,
( spl61_46
<=> rel_str(sK54) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_46])]) ).
fof(f2830,plain,
( spl61_361
<=> ! [X0] :
( sP10(X0)
| ~ rel_str(X0)
| ~ with_infima_relstr(X0)
| ~ with_suprema_relstr(X0)
| ~ antisymmetric_relstr(X0)
| ~ transitive_relstr(X0)
| ~ reflexive_relstr(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_361])]) ).
fof(f4011,plain,
( spl61_460
<=> with_infima_relstr(sK54) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_460])]) ).
fof(f4015,plain,
( ~ rel_str(sK54)
| sP10(sK54)
| ~ with_suprema_relstr(sK54)
| ~ antisymmetric_relstr(sK54)
| ~ transitive_relstr(sK54)
| ~ reflexive_relstr(sK54)
| ~ spl61_361
| ~ spl61_460 ),
inference(resolution,[],[f4013,f2831]) ).
fof(f2831,plain,
( ! [X0] :
( ~ with_infima_relstr(X0)
| ~ rel_str(X0)
| sP10(X0)
| ~ with_suprema_relstr(X0)
| ~ antisymmetric_relstr(X0)
| ~ transitive_relstr(X0)
| ~ reflexive_relstr(X0) )
| ~ spl61_361 ),
inference(avatar_component_clause,[],[f2830]) ).
fof(f4013,plain,
( with_infima_relstr(sK54)
| ~ spl61_460 ),
inference(avatar_component_clause,[],[f4011]) ).
fof(f8656,plain,
( spl61_1
| ~ spl61_2
| ~ spl61_3
| spl61_754
| ~ spl61_774
| ~ spl61_1065
| ~ spl61_1066
| spl61_1067
| ~ spl61_384
| ~ spl61_535 ),
inference(avatar_split_clause,[],[f4471,f4462,f3222,f8654,f8650,f8646,f6326,f6212,f902,f897,f892]) ).
fof(f3222,plain,
( spl61_384
<=> ! [X2,X0,X1] :
( is_a_convergence_point_of_set(X0,filter_of_net_str(X0,X1),X2)
| ~ in(X2,lim_points_of_net(X0,X1))
| ~ element(X2,the_carrier(X0))
| ~ net_str(X1,X0)
| ~ directed_relstr(X1)
| ~ transitive_relstr(X1)
| empty_carrier(X1)
| ~ top_str(X0)
| ~ topological_space(X0)
| empty_carrier(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_384])]) ).
fof(f4471,plain,
( ! [X0] :
( is_a_convergence_point_of_set(sK12,sK13,X0)
| ~ in(X0,lim_points_of_net(sK12,net_of_bool_filter(sK12,cast_as_carrier_subset(sK12),sK13)))
| ~ element(X0,the_carrier(sK12))
| ~ net_str(net_of_bool_filter(sK12,cast_as_carrier_subset(sK12),sK13),sK12)
| ~ directed_relstr(net_of_bool_filter(sK12,cast_as_carrier_subset(sK12),sK13))
| ~ transitive_relstr(net_of_bool_filter(sK12,cast_as_carrier_subset(sK12),sK13))
| empty_carrier(net_of_bool_filter(sK12,cast_as_carrier_subset(sK12),sK13))
| ~ top_str(sK12)
| ~ topological_space(sK12)
| empty_carrier(sK12) )
| ~ spl61_384
| ~ spl61_535 ),
inference(superposition,[],[f3223,f4464]) ).
fof(f3223,plain,
( ! [X2,X0,X1] :
( is_a_convergence_point_of_set(X0,filter_of_net_str(X0,X1),X2)
| ~ in(X2,lim_points_of_net(X0,X1))
| ~ element(X2,the_carrier(X0))
| ~ net_str(X1,X0)
| ~ directed_relstr(X1)
| ~ transitive_relstr(X1)
| empty_carrier(X1)
| ~ top_str(X0)
| ~ topological_space(X0)
| empty_carrier(X0) )
| ~ spl61_384 ),
inference(avatar_component_clause,[],[f3222]) ).
fof(f8633,plain,
( spl61_1064
| ~ spl61_135
| ~ spl61_1043 ),
inference(avatar_split_clause,[],[f8583,f8479,f1533,f8631]) ).
fof(f8631,plain,
( spl61_1064
<=> ! [X0] :
( ~ one_sorted_str(X0)
| ~ in(cast_as_carrier_subset(sK12),sK22(X0))
| empty_carrier(X0)
| sP2(net_of_bool_filter(X0,cast_as_carrier_subset(sK12),sK13)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_1064])]) ).
fof(f1533,plain,
( spl61_135
<=> ! [X0] :
( sP2(X0)
| ~ one_sorted_str(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_135])]) ).
fof(f8479,plain,
( spl61_1043
<=> ! [X1] :
( empty_carrier(X1)
| ~ one_sorted_str(X1)
| ~ in(cast_as_carrier_subset(sK12),sK22(X1))
| one_sorted_str(net_of_bool_filter(X1,cast_as_carrier_subset(sK12),sK13)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_1043])]) ).
fof(f8583,plain,
( ! [X0] :
( ~ one_sorted_str(X0)
| ~ in(cast_as_carrier_subset(sK12),sK22(X0))
| empty_carrier(X0)
| sP2(net_of_bool_filter(X0,cast_as_carrier_subset(sK12),sK13)) )
| ~ spl61_135
| ~ spl61_1043 ),
inference(resolution,[],[f8480,f1534]) ).
fof(f1534,plain,
( ! [X0] :
( ~ one_sorted_str(X0)
| sP2(X0) )
| ~ spl61_135 ),
inference(avatar_component_clause,[],[f1533]) ).
fof(f8480,plain,
( ! [X1] :
( one_sorted_str(net_of_bool_filter(X1,cast_as_carrier_subset(sK12),sK13))
| ~ one_sorted_str(X1)
| ~ in(cast_as_carrier_subset(sK12),sK22(X1))
| empty_carrier(X1) )
| ~ spl61_1043 ),
inference(avatar_component_clause,[],[f8479]) ).
fof(f8619,plain,
( spl61_1063
| ~ spl61_135
| ~ spl61_1042 ),
inference(avatar_split_clause,[],[f8542,f8432,f1533,f8617]) ).
fof(f8617,plain,
( spl61_1063
<=> ! [X0] :
( ~ one_sorted_str(X0)
| ~ subset(cast_as_carrier_subset(sK12),the_carrier(X0))
| empty_carrier(X0)
| sP2(net_of_bool_filter(X0,cast_as_carrier_subset(sK12),sK13)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_1063])]) ).
fof(f8432,plain,
( spl61_1042
<=> ! [X1] :
( empty_carrier(X1)
| ~ one_sorted_str(X1)
| ~ subset(cast_as_carrier_subset(sK12),the_carrier(X1))
| one_sorted_str(net_of_bool_filter(X1,cast_as_carrier_subset(sK12),sK13)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_1042])]) ).
fof(f8542,plain,
( ! [X0] :
( ~ one_sorted_str(X0)
| ~ subset(cast_as_carrier_subset(sK12),the_carrier(X0))
| empty_carrier(X0)
| sP2(net_of_bool_filter(X0,cast_as_carrier_subset(sK12),sK13)) )
| ~ spl61_135
| ~ spl61_1042 ),
inference(resolution,[],[f8433,f1534]) ).
fof(f8433,plain,
( ! [X1] :
( one_sorted_str(net_of_bool_filter(X1,cast_as_carrier_subset(sK12),sK13))
| ~ one_sorted_str(X1)
| ~ subset(cast_as_carrier_subset(sK12),the_carrier(X1))
| empty_carrier(X1) )
| ~ spl61_1042 ),
inference(avatar_component_clause,[],[f8432]) ).
fof(f8611,plain,
( spl61_1062
| ~ spl61_129
| ~ spl61_681 ),
inference(avatar_split_clause,[],[f5685,f5468,f1508,f8609]) ).
fof(f8609,plain,
( spl61_1062
<=> ! [X0] :
( closed_subset(the_carrier(X0),X0)
| ~ top_str(X0)
| ~ topological_space(X0)
| ~ empty(the_carrier(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_1062])]) ).
fof(f5468,plain,
( spl61_681
<=> ! [X0,X1] :
( ~ empty(X0)
| closed_subset(X0,X1)
| ~ top_str(X1)
| ~ topological_space(X1)
| ~ subset(X0,the_carrier(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_681])]) ).
fof(f5685,plain,
( ! [X0] :
( closed_subset(the_carrier(X0),X0)
| ~ top_str(X0)
| ~ topological_space(X0)
| ~ empty(the_carrier(X0)) )
| ~ spl61_129
| ~ spl61_681 ),
inference(resolution,[],[f5469,f1509]) ).
fof(f5469,plain,
( ! [X0,X1] :
( ~ subset(X0,the_carrier(X1))
| closed_subset(X0,X1)
| ~ top_str(X1)
| ~ topological_space(X1)
| ~ empty(X0) )
| ~ spl61_681 ),
inference(avatar_component_clause,[],[f5468]) ).
fof(f8607,plain,
( spl61_1061
| ~ spl61_129
| ~ spl61_677 ),
inference(avatar_split_clause,[],[f5655,f5452,f1508,f8605]) ).
fof(f8605,plain,
( spl61_1061
<=> ! [X0] :
( open_subset(the_carrier(X0),X0)
| ~ top_str(X0)
| ~ topological_space(X0)
| ~ empty(the_carrier(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_1061])]) ).
fof(f5452,plain,
( spl61_677
<=> ! [X0,X1] :
( ~ empty(X0)
| open_subset(X0,X1)
| ~ top_str(X1)
| ~ topological_space(X1)
| ~ subset(X0,the_carrier(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_677])]) ).
fof(f5655,plain,
( ! [X0] :
( open_subset(the_carrier(X0),X0)
| ~ top_str(X0)
| ~ topological_space(X0)
| ~ empty(the_carrier(X0)) )
| ~ spl61_129
| ~ spl61_677 ),
inference(resolution,[],[f5453,f1509]) ).
fof(f5453,plain,
( ! [X0,X1] :
( ~ subset(X0,the_carrier(X1))
| open_subset(X0,X1)
| ~ top_str(X1)
| ~ topological_space(X1)
| ~ empty(X0) )
| ~ spl61_677 ),
inference(avatar_component_clause,[],[f5452]) ).
fof(f8603,plain,
( spl61_1060
| ~ spl61_129
| ~ spl61_671 ),
inference(avatar_split_clause,[],[f5625,f5427,f1508,f8601]) ).
fof(f8601,plain,
( spl61_1060
<=> ! [X0] :
( nowhere_dense(the_carrier(X0),X0)
| ~ top_str(X0)
| ~ topological_space(X0)
| ~ empty(the_carrier(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_1060])]) ).
fof(f5427,plain,
( spl61_671
<=> ! [X0,X1] :
( ~ empty(X0)
| nowhere_dense(X0,X1)
| ~ top_str(X1)
| ~ topological_space(X1)
| ~ subset(X0,the_carrier(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_671])]) ).
fof(f5625,plain,
( ! [X0] :
( nowhere_dense(the_carrier(X0),X0)
| ~ top_str(X0)
| ~ topological_space(X0)
| ~ empty(the_carrier(X0)) )
| ~ spl61_129
| ~ spl61_671 ),
inference(resolution,[],[f5428,f1509]) ).
fof(f5428,plain,
( ! [X0,X1] :
( ~ subset(X0,the_carrier(X1))
| nowhere_dense(X0,X1)
| ~ top_str(X1)
| ~ topological_space(X1)
| ~ empty(X0) )
| ~ spl61_671 ),
inference(avatar_component_clause,[],[f5427]) ).
fof(f8599,plain,
( spl61_1059
| ~ spl61_266
| ~ spl61_606 ),
inference(avatar_split_clause,[],[f5109,f4997,f2171,f8597]) ).
fof(f8597,plain,
( spl61_1059
<=> ! [X36,X35] :
( ~ in(X35,sK22(X36))
| ~ one_sorted_str(X36)
| finite(X35)
| ~ finite(the_carrier(X36)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_1059])]) ).
fof(f5109,plain,
( ! [X36,X35] :
( ~ in(X35,sK22(X36))
| ~ one_sorted_str(X36)
| finite(X35)
| ~ finite(the_carrier(X36)) )
| ~ spl61_266
| ~ spl61_606 ),
inference(resolution,[],[f4998,f2172]) ).
fof(f8595,plain,
( spl61_1058
| ~ spl61_551
| ~ spl61_597 ),
inference(avatar_split_clause,[],[f4937,f4856,f4559,f8593]) ).
fof(f8593,plain,
( spl61_1058
<=> ! [X46,X47] :
( sK37(X46) = X47
| ~ empty(X47)
| ~ empty(the_carrier(X46))
| ~ sP10(X46) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_1058])]) ).
fof(f4559,plain,
( spl61_551
<=> ! [X27,X26] :
( ~ empty(the_carrier(X26))
| ~ in(X27,sK37(X26))
| ~ sP10(X26) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_551])]) ).
fof(f4937,plain,
( ! [X46,X47] :
( sK37(X46) = X47
| ~ empty(X47)
| ~ empty(the_carrier(X46))
| ~ sP10(X46) )
| ~ spl61_551
| ~ spl61_597 ),
inference(resolution,[],[f4857,f4560]) ).
fof(f4560,plain,
( ! [X26,X27] :
( ~ in(X27,sK37(X26))
| ~ empty(the_carrier(X26))
| ~ sP10(X26) )
| ~ spl61_551 ),
inference(avatar_component_clause,[],[f4559]) ).
fof(f8591,plain,
( spl61_1057
| ~ spl61_549
| ~ spl61_597 ),
inference(avatar_split_clause,[],[f4933,f4856,f4551,f8589]) ).
fof(f8589,plain,
( spl61_1057
<=> ! [X38,X39] :
( sK30(X38) = X39
| ~ empty(X39)
| ~ empty(the_carrier(X38))
| ~ sP7(X38) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_1057])]) ).
fof(f4551,plain,
( spl61_549
<=> ! [X22,X23] :
( ~ empty(the_carrier(X22))
| ~ in(X23,sK30(X22))
| ~ sP7(X22) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_549])]) ).
fof(f4933,plain,
( ! [X38,X39] :
( sK30(X38) = X39
| ~ empty(X39)
| ~ empty(the_carrier(X38))
| ~ sP7(X38) )
| ~ spl61_549
| ~ spl61_597 ),
inference(resolution,[],[f4857,f4552]) ).
fof(f4552,plain,
( ! [X22,X23] :
( ~ in(X23,sK30(X22))
| ~ empty(the_carrier(X22))
| ~ sP7(X22) )
| ~ spl61_549 ),
inference(avatar_component_clause,[],[f4551]) ).
fof(f8587,plain,
( spl61_1056
| ~ spl61_548
| ~ spl61_597 ),
inference(avatar_split_clause,[],[f4931,f4856,f4547,f8585]) ).
fof(f8585,plain,
( spl61_1056
<=> ! [X34,X35] :
( sK25(X34) = X35
| ~ empty(X35)
| ~ empty(the_carrier(X34))
| ~ sP6(X34) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_1056])]) ).
fof(f4547,plain,
( spl61_548
<=> ! [X20,X21] :
( ~ empty(the_carrier(X20))
| ~ in(X21,sK25(X20))
| ~ sP6(X20) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_548])]) ).
fof(f4931,plain,
( ! [X34,X35] :
( sK25(X34) = X35
| ~ empty(X35)
| ~ empty(the_carrier(X34))
| ~ sP6(X34) )
| ~ spl61_548
| ~ spl61_597 ),
inference(resolution,[],[f4857,f4548]) ).
fof(f4548,plain,
( ! [X21,X20] :
( ~ in(X21,sK25(X20))
| ~ empty(the_carrier(X20))
| ~ sP6(X20) )
| ~ spl61_548 ),
inference(avatar_component_clause,[],[f4547]) ).
fof(f8582,plain,
( spl61_1055
| ~ spl61_547
| ~ spl61_597 ),
inference(avatar_split_clause,[],[f4929,f4856,f4543,f8580]) ).
fof(f8580,plain,
( spl61_1055
<=> ! [X30,X31] :
( sK24(X30) = X31
| ~ empty(X31)
| ~ empty(the_carrier(X30))
| ~ rel_str(X30) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_1055])]) ).
fof(f4543,plain,
( spl61_547
<=> ! [X18,X19] :
( ~ empty(the_carrier(X18))
| ~ in(X19,sK24(X18))
| ~ rel_str(X18) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_547])]) ).
fof(f4929,plain,
( ! [X31,X30] :
( sK24(X30) = X31
| ~ empty(X31)
| ~ empty(the_carrier(X30))
| ~ rel_str(X30) )
| ~ spl61_547
| ~ spl61_597 ),
inference(resolution,[],[f4857,f4544]) ).
fof(f4544,plain,
( ! [X18,X19] :
( ~ in(X19,sK24(X18))
| ~ empty(the_carrier(X18))
| ~ rel_str(X18) )
| ~ spl61_547 ),
inference(avatar_component_clause,[],[f4543]) ).
fof(f8578,plain,
( spl61_1054
| ~ spl61_546
| ~ spl61_597 ),
inference(avatar_split_clause,[],[f4927,f4856,f4539,f8576]) ).
fof(f8576,plain,
( spl61_1054
<=> ! [X27,X26] :
( sK23(X26) = X27
| ~ empty(X27)
| ~ empty(the_carrier(X26))
| ~ rel_str(X26) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_1054])]) ).
fof(f4539,plain,
( spl61_546
<=> ! [X16,X17] :
( ~ empty(the_carrier(X16))
| ~ in(X17,sK23(X16))
| ~ rel_str(X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_546])]) ).
fof(f4927,plain,
( ! [X26,X27] :
( sK23(X26) = X27
| ~ empty(X27)
| ~ empty(the_carrier(X26))
| ~ rel_str(X26) )
| ~ spl61_546
| ~ spl61_597 ),
inference(resolution,[],[f4857,f4540]) ).
fof(f4540,plain,
( ! [X16,X17] :
( ~ in(X17,sK23(X16))
| ~ empty(the_carrier(X16))
| ~ rel_str(X16) )
| ~ spl61_546 ),
inference(avatar_component_clause,[],[f4539]) ).
fof(f8574,plain,
( spl61_1053
| ~ spl61_543
| ~ spl61_597 ),
inference(avatar_split_clause,[],[f4920,f4856,f4526,f8572]) ).
fof(f8572,plain,
( spl61_1053
<=> ! [X13,X12] :
( cast_as_carrier_subset(X12) = X13
| ~ empty(X13)
| ~ empty(the_carrier(X12))
| ~ one_sorted_str(X12) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_1053])]) ).
fof(f4526,plain,
( spl61_543
<=> ! [X4,X3] :
( ~ empty(the_carrier(X3))
| ~ in(X4,cast_as_carrier_subset(X3))
| ~ one_sorted_str(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_543])]) ).
fof(f4920,plain,
( ! [X12,X13] :
( cast_as_carrier_subset(X12) = X13
| ~ empty(X13)
| ~ empty(the_carrier(X12))
| ~ one_sorted_str(X12) )
| ~ spl61_543
| ~ spl61_597 ),
inference(resolution,[],[f4857,f4527]) ).
fof(f4527,plain,
( ! [X3,X4] :
( ~ in(X4,cast_as_carrier_subset(X3))
| ~ empty(the_carrier(X3))
| ~ one_sorted_str(X3) )
| ~ spl61_543 ),
inference(avatar_component_clause,[],[f4526]) ).
fof(f8570,plain,
( spl61_1052
| ~ spl61_469
| ~ spl61_593 ),
inference(avatar_split_clause,[],[f4911,f4838,f4058,f8568]) ).
fof(f8568,plain,
( spl61_1052
<=> ! [X0] :
( element(sK38(sK37(X0)),the_carrier(X0))
| ~ sP10(X0)
| empty(sK37(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_1052])]) ).
fof(f4838,plain,
( spl61_593
<=> ! [X41,X40] :
( element(X40,the_carrier(X41))
| ~ in(X40,sK37(X41))
| ~ sP10(X41) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_593])]) ).
fof(f4911,plain,
( ! [X0] :
( element(sK38(sK37(X0)),the_carrier(X0))
| ~ sP10(X0)
| empty(sK37(X0)) )
| ~ spl61_469
| ~ spl61_593 ),
inference(resolution,[],[f4839,f4059]) ).
fof(f4839,plain,
( ! [X40,X41] :
( ~ in(X40,sK37(X41))
| element(X40,the_carrier(X41))
| ~ sP10(X41) )
| ~ spl61_593 ),
inference(avatar_component_clause,[],[f4838]) ).
fof(f8566,plain,
( spl61_1051
| ~ spl61_469
| ~ spl61_591 ),
inference(avatar_split_clause,[],[f4904,f4830,f4058,f8564]) ).
fof(f8564,plain,
( spl61_1051
<=> ! [X0] :
( element(sK38(sK30(X0)),the_carrier(X0))
| ~ sP7(X0)
| empty(sK30(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_1051])]) ).
fof(f4830,plain,
( spl61_591
<=> ! [X30,X31] :
( element(X30,the_carrier(X31))
| ~ in(X30,sK30(X31))
| ~ sP7(X31) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_591])]) ).
fof(f4904,plain,
( ! [X0] :
( element(sK38(sK30(X0)),the_carrier(X0))
| ~ sP7(X0)
| empty(sK30(X0)) )
| ~ spl61_469
| ~ spl61_591 ),
inference(resolution,[],[f4831,f4059]) ).
fof(f4831,plain,
( ! [X31,X30] :
( ~ in(X30,sK30(X31))
| element(X30,the_carrier(X31))
| ~ sP7(X31) )
| ~ spl61_591 ),
inference(avatar_component_clause,[],[f4830]) ).
fof(f8562,plain,
( spl61_1050
| ~ spl61_469
| ~ spl61_590 ),
inference(avatar_split_clause,[],[f4901,f4826,f4058,f8560]) ).
fof(f8560,plain,
( spl61_1050
<=> ! [X0] :
( element(sK38(sK25(X0)),the_carrier(X0))
| ~ sP6(X0)
| empty(sK25(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_1050])]) ).
fof(f4826,plain,
( spl61_590
<=> ! [X25,X24] :
( element(X24,the_carrier(X25))
| ~ in(X24,sK25(X25))
| ~ sP6(X25) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_590])]) ).
fof(f4901,plain,
( ! [X0] :
( element(sK38(sK25(X0)),the_carrier(X0))
| ~ sP6(X0)
| empty(sK25(X0)) )
| ~ spl61_469
| ~ spl61_590 ),
inference(resolution,[],[f4827,f4059]) ).
fof(f4827,plain,
( ! [X24,X25] :
( ~ in(X24,sK25(X25))
| element(X24,the_carrier(X25))
| ~ sP6(X25) )
| ~ spl61_590 ),
inference(avatar_component_clause,[],[f4826]) ).
fof(f8558,plain,
( spl61_1049
| ~ spl61_469
| ~ spl61_589 ),
inference(avatar_split_clause,[],[f4893,f4822,f4058,f8556]) ).
fof(f8556,plain,
( spl61_1049
<=> ! [X0] :
( element(sK38(sK24(X0)),the_carrier(X0))
| ~ rel_str(X0)
| empty(sK24(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_1049])]) ).
fof(f4822,plain,
( spl61_589
<=> ! [X22,X23] :
( element(X22,the_carrier(X23))
| ~ in(X22,sK24(X23))
| ~ rel_str(X23) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_589])]) ).
fof(f4893,plain,
( ! [X0] :
( element(sK38(sK24(X0)),the_carrier(X0))
| ~ rel_str(X0)
| empty(sK24(X0)) )
| ~ spl61_469
| ~ spl61_589 ),
inference(resolution,[],[f4823,f4059]) ).
fof(f4823,plain,
( ! [X22,X23] :
( ~ in(X22,sK24(X23))
| element(X22,the_carrier(X23))
| ~ rel_str(X23) )
| ~ spl61_589 ),
inference(avatar_component_clause,[],[f4822]) ).
fof(f8554,plain,
( spl61_1048
| ~ spl61_469
| ~ spl61_588 ),
inference(avatar_split_clause,[],[f4890,f4818,f4058,f8552]) ).
fof(f8552,plain,
( spl61_1048
<=> ! [X0] :
( element(sK38(sK23(X0)),the_carrier(X0))
| ~ rel_str(X0)
| empty(sK23(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_1048])]) ).
fof(f4818,plain,
( spl61_588
<=> ! [X20,X21] :
( element(X20,the_carrier(X21))
| ~ in(X20,sK23(X21))
| ~ rel_str(X21) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_588])]) ).
fof(f4890,plain,
( ! [X0] :
( element(sK38(sK23(X0)),the_carrier(X0))
| ~ rel_str(X0)
| empty(sK23(X0)) )
| ~ spl61_469
| ~ spl61_588 ),
inference(resolution,[],[f4819,f4059]) ).
fof(f4819,plain,
( ! [X21,X20] :
( ~ in(X20,sK23(X21))
| element(X20,the_carrier(X21))
| ~ rel_str(X21) )
| ~ spl61_588 ),
inference(avatar_component_clause,[],[f4818]) ).
fof(f8550,plain,
( spl61_1047
| ~ spl61_469
| ~ spl61_586 ),
inference(avatar_split_clause,[],[f4883,f4810,f4058,f8548]) ).
fof(f8548,plain,
( spl61_1047
<=> ! [X0] :
( element(sK38(cast_as_carrier_subset(X0)),the_carrier(X0))
| ~ one_sorted_str(X0)
| empty(cast_as_carrier_subset(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_1047])]) ).
fof(f4810,plain,
( spl61_586
<=> ! [X8,X7] :
( element(X7,the_carrier(X8))
| ~ in(X7,cast_as_carrier_subset(X8))
| ~ one_sorted_str(X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_586])]) ).
fof(f4883,plain,
( ! [X0] :
( element(sK38(cast_as_carrier_subset(X0)),the_carrier(X0))
| ~ one_sorted_str(X0)
| empty(cast_as_carrier_subset(X0)) )
| ~ spl61_469
| ~ spl61_586 ),
inference(resolution,[],[f4811,f4059]) ).
fof(f4811,plain,
( ! [X8,X7] :
( ~ in(X7,cast_as_carrier_subset(X8))
| element(X7,the_carrier(X8))
| ~ one_sorted_str(X8) )
| ~ spl61_586 ),
inference(avatar_component_clause,[],[f4810]) ).
fof(f8546,plain,
( spl61_1046
| ~ spl61_305
| ~ spl61_585 ),
inference(avatar_split_clause,[],[f4879,f4806,f2416,f8544]) ).
fof(f8544,plain,
( spl61_1046
<=> ! [X0] :
( finite(the_InternalRel(X0))
| ~ finite(cartesian_product2(the_carrier(X0),the_carrier(X0)))
| ~ rel_str(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_1046])]) ).
fof(f4806,plain,
( spl61_585
<=> ! [X9,X8,X7] :
( ~ relation_of2_as_subset(X7,X8,X9)
| finite(X7)
| ~ finite(cartesian_product2(X8,X9)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_585])]) ).
fof(f4879,plain,
( ! [X0] :
( finite(the_InternalRel(X0))
| ~ finite(cartesian_product2(the_carrier(X0),the_carrier(X0)))
| ~ rel_str(X0) )
| ~ spl61_305
| ~ spl61_585 ),
inference(resolution,[],[f4807,f2417]) ).
fof(f4807,plain,
( ! [X8,X9,X7] :
( ~ relation_of2_as_subset(X7,X8,X9)
| finite(X7)
| ~ finite(cartesian_product2(X8,X9)) )
| ~ spl61_585 ),
inference(avatar_component_clause,[],[f4806]) ).
fof(f8537,plain,
( spl61_1045
| ~ spl61_372
| ~ spl61_532 ),
inference(avatar_split_clause,[],[f4447,f4443,f3131,f8535]) ).
fof(f8535,plain,
( spl61_1045
<=> ! [X0] :
( empty_carrier(X0)
| ~ one_sorted_str(X0)
| ~ element(cast_as_carrier_subset(sK12),powerset(the_carrier(X0)))
| net_of_bool_filter(X0,cast_as_carrier_subset(sK12),sK13) = net_str_of(X0,the_carrier(net_of_bool_filter(X0,cast_as_carrier_subset(sK12),sK13)),the_InternalRel(net_of_bool_filter(X0,cast_as_carrier_subset(sK12),sK13)),the_mapping(X0,net_of_bool_filter(X0,cast_as_carrier_subset(sK12),sK13)))
| ~ net_str(net_of_bool_filter(X0,cast_as_carrier_subset(sK12),sK13),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_1045])]) ).
fof(f3131,plain,
( spl61_372
<=> ! [X0,X1] :
( net_str_of(X0,the_carrier(X1),the_InternalRel(X1),the_mapping(X0,X1)) = X1
| ~ strict_net_str(X1,X0)
| ~ net_str(X1,X0)
| ~ one_sorted_str(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_372])]) ).
fof(f4443,plain,
( spl61_532
<=> ! [X11] :
( strict_net_str(net_of_bool_filter(X11,cast_as_carrier_subset(sK12),sK13),X11)
| empty_carrier(X11)
| ~ one_sorted_str(X11)
| ~ element(cast_as_carrier_subset(sK12),powerset(the_carrier(X11))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_532])]) ).
fof(f4447,plain,
( ! [X0] :
( empty_carrier(X0)
| ~ one_sorted_str(X0)
| ~ element(cast_as_carrier_subset(sK12),powerset(the_carrier(X0)))
| net_of_bool_filter(X0,cast_as_carrier_subset(sK12),sK13) = net_str_of(X0,the_carrier(net_of_bool_filter(X0,cast_as_carrier_subset(sK12),sK13)),the_InternalRel(net_of_bool_filter(X0,cast_as_carrier_subset(sK12),sK13)),the_mapping(X0,net_of_bool_filter(X0,cast_as_carrier_subset(sK12),sK13)))
| ~ net_str(net_of_bool_filter(X0,cast_as_carrier_subset(sK12),sK13),X0) )
| ~ spl61_372
| ~ spl61_532 ),
inference(duplicate_literal_removal,[],[f4446]) ).
fof(f4446,plain,
( ! [X0] :
( empty_carrier(X0)
| ~ one_sorted_str(X0)
| ~ element(cast_as_carrier_subset(sK12),powerset(the_carrier(X0)))
| net_of_bool_filter(X0,cast_as_carrier_subset(sK12),sK13) = net_str_of(X0,the_carrier(net_of_bool_filter(X0,cast_as_carrier_subset(sK12),sK13)),the_InternalRel(net_of_bool_filter(X0,cast_as_carrier_subset(sK12),sK13)),the_mapping(X0,net_of_bool_filter(X0,cast_as_carrier_subset(sK12),sK13)))
| ~ net_str(net_of_bool_filter(X0,cast_as_carrier_subset(sK12),sK13),X0)
| ~ one_sorted_str(X0) )
| ~ spl61_372
| ~ spl61_532 ),
inference(resolution,[],[f4444,f3132]) ).
fof(f3132,plain,
( ! [X0,X1] :
( ~ strict_net_str(X1,X0)
| net_str_of(X0,the_carrier(X1),the_InternalRel(X1),the_mapping(X0,X1)) = X1
| ~ net_str(X1,X0)
| ~ one_sorted_str(X0) )
| ~ spl61_372 ),
inference(avatar_component_clause,[],[f3131]) ).
fof(f4444,plain,
( ! [X11] :
( strict_net_str(net_of_bool_filter(X11,cast_as_carrier_subset(sK12),sK13),X11)
| empty_carrier(X11)
| ~ one_sorted_str(X11)
| ~ element(cast_as_carrier_subset(sK12),powerset(the_carrier(X11))) )
| ~ spl61_532 ),
inference(avatar_component_clause,[],[f4443]) ).
fof(f8528,plain,
( spl61_1044
| ~ spl61_533
| ~ spl61_834 ),
inference(avatar_split_clause,[],[f6892,f6874,f4449,f8526]) ).
fof(f8526,plain,
( spl61_1044
<=> ! [X0] :
( net_of_bool_filter(X0,cast_as_carrier_subset(sK12),sK13) = net_str_of(X0,the_carrier(net_of_bool_filter(X0,cast_as_carrier_subset(sK12),sK13)),the_InternalRel(net_of_bool_filter(X0,cast_as_carrier_subset(sK12),sK13)),the_mapping(X0,net_of_bool_filter(X0,cast_as_carrier_subset(sK12),sK13)))
| ~ one_sorted_str(X0)
| ~ sP11(sK13,cast_as_carrier_subset(sK12),X0)
| empty_carrier(X0)
| ~ element(cast_as_carrier_subset(sK12),powerset(the_carrier(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_1044])]) ).
fof(f6874,plain,
( spl61_834
<=> ! [X4,X2,X3] :
( net_of_bool_filter(X2,X3,X4) = net_str_of(X2,the_carrier(net_of_bool_filter(X2,X3,X4)),the_InternalRel(net_of_bool_filter(X2,X3,X4)),the_mapping(X2,net_of_bool_filter(X2,X3,X4)))
| ~ net_str(net_of_bool_filter(X2,X3,X4),X2)
| ~ one_sorted_str(X2)
| ~ sP11(X4,X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_834])]) ).
fof(f6892,plain,
( ! [X0] :
( net_of_bool_filter(X0,cast_as_carrier_subset(sK12),sK13) = net_str_of(X0,the_carrier(net_of_bool_filter(X0,cast_as_carrier_subset(sK12),sK13)),the_InternalRel(net_of_bool_filter(X0,cast_as_carrier_subset(sK12),sK13)),the_mapping(X0,net_of_bool_filter(X0,cast_as_carrier_subset(sK12),sK13)))
| ~ one_sorted_str(X0)
| ~ sP11(sK13,cast_as_carrier_subset(sK12),X0)
| empty_carrier(X0)
| ~ element(cast_as_carrier_subset(sK12),powerset(the_carrier(X0))) )
| ~ spl61_533
| ~ spl61_834 ),
inference(duplicate_literal_removal,[],[f6889]) ).
fof(f6889,plain,
( ! [X0] :
( net_of_bool_filter(X0,cast_as_carrier_subset(sK12),sK13) = net_str_of(X0,the_carrier(net_of_bool_filter(X0,cast_as_carrier_subset(sK12),sK13)),the_InternalRel(net_of_bool_filter(X0,cast_as_carrier_subset(sK12),sK13)),the_mapping(X0,net_of_bool_filter(X0,cast_as_carrier_subset(sK12),sK13)))
| ~ one_sorted_str(X0)
| ~ sP11(sK13,cast_as_carrier_subset(sK12),X0)
| empty_carrier(X0)
| ~ one_sorted_str(X0)
| ~ element(cast_as_carrier_subset(sK12),powerset(the_carrier(X0))) )
| ~ spl61_533
| ~ spl61_834 ),
inference(resolution,[],[f6875,f4450]) ).
fof(f6875,plain,
( ! [X2,X3,X4] :
( ~ net_str(net_of_bool_filter(X2,X3,X4),X2)
| net_of_bool_filter(X2,X3,X4) = net_str_of(X2,the_carrier(net_of_bool_filter(X2,X3,X4)),the_InternalRel(net_of_bool_filter(X2,X3,X4)),the_mapping(X2,net_of_bool_filter(X2,X3,X4)))
| ~ one_sorted_str(X2)
| ~ sP11(X4,X3,X2) )
| ~ spl61_834 ),
inference(avatar_component_clause,[],[f6874]) ).
fof(f8481,plain,
( spl61_1043
| ~ spl61_136
| ~ spl61_1018 ),
inference(avatar_split_clause,[],[f8336,f8250,f1537,f8479]) ).
fof(f1537,plain,
( spl61_136
<=> ! [X0] :
( one_sorted_str(X0)
| ~ rel_str(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_136])]) ).
fof(f8250,plain,
( spl61_1018
<=> ! [X0] :
( ~ one_sorted_str(X0)
| empty_carrier(X0)
| rel_str(net_of_bool_filter(X0,cast_as_carrier_subset(sK12),sK13))
| ~ in(cast_as_carrier_subset(sK12),sK22(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_1018])]) ).
fof(f8336,plain,
( ! [X1] :
( empty_carrier(X1)
| ~ one_sorted_str(X1)
| ~ in(cast_as_carrier_subset(sK12),sK22(X1))
| one_sorted_str(net_of_bool_filter(X1,cast_as_carrier_subset(sK12),sK13)) )
| ~ spl61_136
| ~ spl61_1018 ),
inference(resolution,[],[f8251,f1538]) ).
fof(f1538,plain,
( ! [X0] :
( ~ rel_str(X0)
| one_sorted_str(X0) )
| ~ spl61_136 ),
inference(avatar_component_clause,[],[f1537]) ).
fof(f8251,plain,
( ! [X0] :
( rel_str(net_of_bool_filter(X0,cast_as_carrier_subset(sK12),sK13))
| empty_carrier(X0)
| ~ one_sorted_str(X0)
| ~ in(cast_as_carrier_subset(sK12),sK22(X0)) )
| ~ spl61_1018 ),
inference(avatar_component_clause,[],[f8250]) ).
fof(f8434,plain,
( spl61_1042
| ~ spl61_136
| ~ spl61_1013 ),
inference(avatar_split_clause,[],[f8294,f8180,f1537,f8432]) ).
fof(f8180,plain,
( spl61_1013
<=> ! [X1] :
( ~ one_sorted_str(X1)
| empty_carrier(X1)
| rel_str(net_of_bool_filter(X1,cast_as_carrier_subset(sK12),sK13))
| ~ subset(cast_as_carrier_subset(sK12),the_carrier(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_1013])]) ).
fof(f8294,plain,
( ! [X1] :
( empty_carrier(X1)
| ~ one_sorted_str(X1)
| ~ subset(cast_as_carrier_subset(sK12),the_carrier(X1))
| one_sorted_str(net_of_bool_filter(X1,cast_as_carrier_subset(sK12),sK13)) )
| ~ spl61_136
| ~ spl61_1013 ),
inference(resolution,[],[f8181,f1538]) ).
fof(f8181,plain,
( ! [X1] :
( rel_str(net_of_bool_filter(X1,cast_as_carrier_subset(sK12),sK13))
| empty_carrier(X1)
| ~ one_sorted_str(X1)
| ~ subset(cast_as_carrier_subset(sK12),the_carrier(X1)) )
| ~ spl61_1013 ),
inference(avatar_component_clause,[],[f8180]) ).
fof(f8348,plain,
( spl61_1041
| ~ spl61_569
| ~ spl61_685 ),
inference(avatar_split_clause,[],[f5717,f5484,f4662,f8346]) ).
fof(f8346,plain,
( spl61_1041
<=> ! [X0] :
( ~ open_subset(sK60,X0)
| sP8(X0,sK60)
| ~ top_str(X0)
| ~ topological_space(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_1041])]) ).
fof(f4662,plain,
( spl61_569
<=> ! [X23] :
( nowhere_dense(sK60,X23)
| ~ topological_space(X23)
| ~ top_str(X23) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_569])]) ).
fof(f5484,plain,
( spl61_685
<=> ! [X23] :
( sP8(X23,sK60)
| ~ open_subset(sK60,X23)
| ~ nowhere_dense(sK60,X23)
| ~ top_str(X23)
| ~ topological_space(X23) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_685])]) ).
fof(f5717,plain,
( ! [X0] :
( ~ open_subset(sK60,X0)
| sP8(X0,sK60)
| ~ top_str(X0)
| ~ topological_space(X0) )
| ~ spl61_569
| ~ spl61_685 ),
inference(duplicate_literal_removal,[],[f5715]) ).
fof(f5715,plain,
( ! [X0] :
( ~ open_subset(sK60,X0)
| sP8(X0,sK60)
| ~ top_str(X0)
| ~ topological_space(X0)
| ~ topological_space(X0)
| ~ top_str(X0) )
| ~ spl61_569
| ~ spl61_685 ),
inference(resolution,[],[f5485,f4663]) ).
fof(f4663,plain,
( ! [X23] :
( nowhere_dense(sK60,X23)
| ~ topological_space(X23)
| ~ top_str(X23) )
| ~ spl61_569 ),
inference(avatar_component_clause,[],[f4662]) ).
fof(f5485,plain,
( ! [X23] :
( ~ nowhere_dense(sK60,X23)
| ~ open_subset(sK60,X23)
| sP8(X23,sK60)
| ~ top_str(X23)
| ~ topological_space(X23) )
| ~ spl61_685 ),
inference(avatar_component_clause,[],[f5484]) ).
fof(f8344,plain,
( spl61_1040
| ~ spl61_125
| ~ spl61_657 ),
inference(avatar_split_clause,[],[f5487,f5370,f1492,f8342]) ).
fof(f8342,plain,
( spl61_1040
<=> ! [X0] : boole_POSet(X0) = rel_str_of(the_carrier(boole_POSet(X0)),the_InternalRel(boole_POSet(X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_1040])]) ).
fof(f1492,plain,
( spl61_125
<=> ! [X0] : rel_str(boole_POSet(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_125])]) ).
fof(f5370,plain,
( spl61_657
<=> ! [X0] :
( boole_POSet(X0) = rel_str_of(the_carrier(boole_POSet(X0)),the_InternalRel(boole_POSet(X0)))
| ~ rel_str(boole_POSet(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_657])]) ).
fof(f5487,plain,
( ! [X0] : boole_POSet(X0) = rel_str_of(the_carrier(boole_POSet(X0)),the_InternalRel(boole_POSet(X0)))
| ~ spl61_125
| ~ spl61_657 ),
inference(resolution,[],[f5371,f1493]) ).
fof(f1493,plain,
( ! [X0] : rel_str(boole_POSet(X0))
| ~ spl61_125 ),
inference(avatar_component_clause,[],[f1492]) ).
fof(f5371,plain,
( ! [X0] :
( ~ rel_str(boole_POSet(X0))
| boole_POSet(X0) = rel_str_of(the_carrier(boole_POSet(X0)),the_InternalRel(boole_POSet(X0))) )
| ~ spl61_657 ),
inference(avatar_component_clause,[],[f5370]) ).
fof(f8340,plain,
( spl61_1039
| ~ spl61_244
| ~ spl61_634 ),
inference(avatar_split_clause,[],[f5332,f5196,f2027,f8338]) ).
fof(f8338,plain,
( spl61_1039
<=> ! [X9,X8,X10] :
( ~ in(X8,sK43(X9,X10))
| element(X8,cartesian_product2(X9,X10)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_1039])]) ).
fof(f2027,plain,
( spl61_244
<=> ! [X0,X1] : relation_of2_as_subset(sK43(X0,X1),X0,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_244])]) ).
fof(f5332,plain,
( ! [X10,X8,X9] :
( ~ in(X8,sK43(X9,X10))
| element(X8,cartesian_product2(X9,X10)) )
| ~ spl61_244
| ~ spl61_634 ),
inference(resolution,[],[f5197,f2028]) ).
fof(f2028,plain,
( ! [X0,X1] : relation_of2_as_subset(sK43(X0,X1),X0,X1)
| ~ spl61_244 ),
inference(avatar_component_clause,[],[f2027]) ).
fof(f8334,plain,
( spl61_1038
| ~ spl61_475
| ~ spl61_634 ),
inference(avatar_split_clause,[],[f5331,f5196,f4083,f8332]) ).
fof(f8332,plain,
( spl61_1038
<=> ! [X6,X5,X7] :
( ~ in(X5,sK42(X6,X7))
| element(X5,cartesian_product2(X6,X7)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_1038])]) ).
fof(f4083,plain,
( spl61_475
<=> ! [X0,X1] : relation_of2_as_subset(sK42(X0,X1),X0,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_475])]) ).
fof(f5331,plain,
( ! [X6,X7,X5] :
( ~ in(X5,sK42(X6,X7))
| element(X5,cartesian_product2(X6,X7)) )
| ~ spl61_475
| ~ spl61_634 ),
inference(resolution,[],[f5197,f4084]) ).
fof(f4084,plain,
( ! [X0,X1] : relation_of2_as_subset(sK42(X0,X1),X0,X1)
| ~ spl61_475 ),
inference(avatar_component_clause,[],[f4083]) ).
fof(f8330,plain,
( spl61_1037
| ~ spl61_260
| ~ spl61_606 ),
inference(avatar_split_clause,[],[f5110,f4997,f2117,f8328]) ).
fof(f8328,plain,
( spl61_1037
<=> ! [X38,X37] :
( ~ in(X37,sK22(X38))
| ~ one_sorted_str(X38)
| subset(X37,the_carrier(X38)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_1037])]) ).
fof(f5110,plain,
( ! [X38,X37] :
( ~ in(X37,sK22(X38))
| ~ one_sorted_str(X38)
| subset(X37,the_carrier(X38)) )
| ~ spl61_260
| ~ spl61_606 ),
inference(resolution,[],[f4998,f2118]) ).
fof(f8326,plain,
( spl61_1036
| ~ spl61_469
| ~ spl61_604 ),
inference(avatar_split_clause,[],[f5086,f4989,f4058,f8324]) ).
fof(f8324,plain,
( spl61_1036
<=> ! [X0] :
( ~ topological_space(X0)
| ~ empty(the_carrier(X0))
| ~ top_str(X0)
| empty(sK36(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_1036])]) ).
fof(f5086,plain,
( ! [X0] :
( ~ topological_space(X0)
| ~ empty(the_carrier(X0))
| ~ top_str(X0)
| empty(sK36(X0)) )
| ~ spl61_469
| ~ spl61_604 ),
inference(resolution,[],[f4990,f4059]) ).
fof(f8322,plain,
( spl61_1035
| ~ spl61_469
| ~ spl61_603 ),
inference(avatar_split_clause,[],[f5081,f4985,f4058,f8320]) ).
fof(f8320,plain,
( spl61_1035
<=> ! [X0] :
( ~ topological_space(X0)
| ~ empty(the_carrier(X0))
| ~ top_str(X0)
| empty(sK35(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_1035])]) ).
fof(f5081,plain,
( ! [X0] :
( ~ topological_space(X0)
| ~ empty(the_carrier(X0))
| ~ top_str(X0)
| empty(sK35(X0)) )
| ~ spl61_469
| ~ spl61_603 ),
inference(resolution,[],[f4986,f4059]) ).
fof(f8318,plain,
( spl61_1034
| ~ spl61_469
| ~ spl61_602 ),
inference(avatar_split_clause,[],[f5076,f4981,f4058,f8316]) ).
fof(f8316,plain,
( spl61_1034
<=> ! [X0] :
( ~ topological_space(X0)
| ~ empty(the_carrier(X0))
| ~ top_str(X0)
| empty(sK34(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_1034])]) ).
fof(f5076,plain,
( ! [X0] :
( ~ topological_space(X0)
| ~ empty(the_carrier(X0))
| ~ top_str(X0)
| empty(sK34(X0)) )
| ~ spl61_469
| ~ spl61_602 ),
inference(resolution,[],[f4982,f4059]) ).
fof(f8314,plain,
( spl61_1033
| ~ spl61_469
| ~ spl61_601 ),
inference(avatar_split_clause,[],[f5071,f4977,f4058,f8312]) ).
fof(f8312,plain,
( spl61_1033
<=> ! [X0] :
( empty_carrier(X0)
| ~ empty(the_carrier(X0))
| ~ rel_str(X0)
| empty(sK29(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_1033])]) ).
fof(f5071,plain,
( ! [X0] :
( empty_carrier(X0)
| ~ empty(the_carrier(X0))
| ~ rel_str(X0)
| empty(sK29(X0)) )
| ~ spl61_469
| ~ spl61_601 ),
inference(resolution,[],[f4978,f4059]) ).
fof(f8310,plain,
( spl61_1032
| ~ spl61_479
| ~ spl61_600 ),
inference(avatar_split_clause,[],[f5070,f4973,f4118,f8308]) ).
fof(f8308,plain,
( spl61_1032
<=> ! [X0] :
( sP7(sK20(X0))
| empty_carrier(sK20(X0))
| ~ sP2(X0)
| ~ one_sorted_str(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_1032])]) ).
fof(f4118,plain,
( spl61_479
<=> ! [X1] :
( rel_str(sK20(X1))
| ~ one_sorted_str(X1)
| ~ sP2(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_479])]) ).
fof(f4973,plain,
( spl61_600
<=> ! [X1] :
( ~ rel_str(sK20(X1))
| sP7(sK20(X1))
| empty_carrier(sK20(X1))
| ~ sP2(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_600])]) ).
fof(f5070,plain,
( ! [X0] :
( sP7(sK20(X0))
| empty_carrier(sK20(X0))
| ~ sP2(X0)
| ~ one_sorted_str(X0) )
| ~ spl61_479
| ~ spl61_600 ),
inference(duplicate_literal_removal,[],[f5069]) ).
fof(f5069,plain,
( ! [X0] :
( sP7(sK20(X0))
| empty_carrier(sK20(X0))
| ~ sP2(X0)
| ~ one_sorted_str(X0)
| ~ sP2(X0) )
| ~ spl61_479
| ~ spl61_600 ),
inference(resolution,[],[f4974,f4119]) ).
fof(f4119,plain,
( ! [X1] :
( rel_str(sK20(X1))
| ~ one_sorted_str(X1)
| ~ sP2(X1) )
| ~ spl61_479 ),
inference(avatar_component_clause,[],[f4118]) ).
fof(f4974,plain,
( ! [X1] :
( ~ rel_str(sK20(X1))
| sP7(sK20(X1))
| empty_carrier(sK20(X1))
| ~ sP2(X1) )
| ~ spl61_600 ),
inference(avatar_component_clause,[],[f4973]) ).
fof(f8306,plain,
( spl61_1031
| ~ spl61_240
| ~ spl61_598 ),
inference(avatar_split_clause,[],[f4946,f4860,f2010,f8304]) ).
fof(f8304,plain,
( spl61_1031
<=> ! [X6,X7] :
( X6 = X7
| ~ empty(X6)
| ~ in(X7,sK41(X6,X7)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_1031])]) ).
fof(f4946,plain,
( ! [X6,X7] :
( X6 = X7
| ~ empty(X6)
| ~ in(X7,sK41(X6,X7)) )
| ~ spl61_240
| ~ spl61_598 ),
inference(resolution,[],[f4861,f2011]) ).
fof(f8302,plain,
( spl61_1030
| ~ spl61_241
| ~ spl61_598 ),
inference(avatar_split_clause,[],[f4945,f4860,f2014,f8300]) ).
fof(f8300,plain,
( spl61_1030
<=> ! [X4,X5] :
( X4 = X5
| ~ empty(X4)
| element(sK41(X4,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_1030])]) ).
fof(f4945,plain,
( ! [X4,X5] :
( X4 = X5
| ~ empty(X4)
| element(sK41(X4,X5),X5) )
| ~ spl61_241
| ~ spl61_598 ),
inference(resolution,[],[f4861,f2015]) ).
fof(f8298,plain,
( spl61_1029
| ~ spl61_240
| ~ spl61_597 ),
inference(avatar_split_clause,[],[f4917,f4856,f2010,f8296]) ).
fof(f8296,plain,
( spl61_1029
<=> ! [X6,X5] :
( X5 = X6
| ~ empty(X6)
| ~ in(X5,sK41(X5,X6)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_1029])]) ).
fof(f4917,plain,
( ! [X6,X5] :
( X5 = X6
| ~ empty(X6)
| ~ in(X5,sK41(X5,X6)) )
| ~ spl61_240
| ~ spl61_597 ),
inference(resolution,[],[f4857,f2011]) ).
fof(f8292,plain,
( spl61_1028
| ~ spl61_241
| ~ spl61_597 ),
inference(avatar_split_clause,[],[f4916,f4856,f2014,f8290]) ).
fof(f8290,plain,
( spl61_1028
<=> ! [X4,X3] :
( X3 = X4
| ~ empty(X4)
| element(sK41(X3,X4),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_1028])]) ).
fof(f4916,plain,
( ! [X3,X4] :
( X3 = X4
| ~ empty(X4)
| element(sK41(X3,X4),X3) )
| ~ spl61_241
| ~ spl61_597 ),
inference(resolution,[],[f4857,f2015]) ).
fof(f8288,plain,
( spl61_1027
| ~ spl61_240
| ~ spl61_579 ),
inference(avatar_split_clause,[],[f4878,f4782,f2010,f8286]) ).
fof(f8286,plain,
( spl61_1027
<=> ! [X2] :
( empty(powerset(powerset(X2)))
| ~ in(powerset(powerset(X2)),sK40(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_1027])]) ).
fof(f4782,plain,
( spl61_579
<=> ! [X15] :
( empty(powerset(powerset(X15)))
| in(sK40(X15),powerset(powerset(X15))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_579])]) ).
fof(f4878,plain,
( ! [X2] :
( empty(powerset(powerset(X2)))
| ~ in(powerset(powerset(X2)),sK40(X2)) )
| ~ spl61_240
| ~ spl61_579 ),
inference(resolution,[],[f4783,f2011]) ).
fof(f4783,plain,
( ! [X15] :
( in(sK40(X15),powerset(powerset(X15)))
| empty(powerset(powerset(X15))) )
| ~ spl61_579 ),
inference(avatar_component_clause,[],[f4782]) ).
fof(f8284,plain,
( spl61_1026
| ~ spl61_240
| ~ spl61_578 ),
inference(avatar_split_clause,[],[f4875,f4778,f2010,f8282]) ).
fof(f8282,plain,
( spl61_1026
<=> ! [X2] :
( empty(powerset(X2))
| empty(X2)
| ~ in(powerset(X2),sK17(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_1026])]) ).
fof(f4778,plain,
( spl61_578
<=> ! [X5] :
( empty(powerset(X5))
| in(sK17(X5),powerset(X5))
| empty(X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_578])]) ).
fof(f4875,plain,
( ! [X2] :
( empty(powerset(X2))
| empty(X2)
| ~ in(powerset(X2),sK17(X2)) )
| ~ spl61_240
| ~ spl61_578 ),
inference(resolution,[],[f4779,f2011]) ).
fof(f4779,plain,
( ! [X5] :
( in(sK17(X5),powerset(X5))
| empty(powerset(X5))
| empty(X5) )
| ~ spl61_578 ),
inference(avatar_component_clause,[],[f4778]) ).
fof(f8280,plain,
( spl61_1025
| ~ spl61_240
| ~ spl61_577 ),
inference(avatar_split_clause,[],[f4872,f4774,f2010,f8278]) ).
fof(f8278,plain,
( spl61_1025
<=> ! [X2] :
( empty(powerset(X2))
| empty(X2)
| ~ in(powerset(X2),sK16(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_1025])]) ).
fof(f4774,plain,
( spl61_577
<=> ! [X4] :
( empty(powerset(X4))
| in(sK16(X4),powerset(X4))
| empty(X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_577])]) ).
fof(f4872,plain,
( ! [X2] :
( empty(powerset(X2))
| empty(X2)
| ~ in(powerset(X2),sK16(X2)) )
| ~ spl61_240
| ~ spl61_577 ),
inference(resolution,[],[f4775,f2011]) ).
fof(f4775,plain,
( ! [X4] :
( in(sK16(X4),powerset(X4))
| empty(powerset(X4))
| empty(X4) )
| ~ spl61_577 ),
inference(avatar_component_clause,[],[f4774]) ).
fof(f8276,plain,
( spl61_1024
| ~ spl61_240
| ~ spl61_576 ),
inference(avatar_split_clause,[],[f4869,f4770,f2010,f8274]) ).
fof(f8274,plain,
( spl61_1024
<=> ! [X2] :
( empty(powerset(X2))
| empty(X2)
| ~ in(powerset(X2),sK15(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_1024])]) ).
fof(f4770,plain,
( spl61_576
<=> ! [X3] :
( empty(powerset(X3))
| in(sK15(X3),powerset(X3))
| empty(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_576])]) ).
fof(f4869,plain,
( ! [X2] :
( empty(powerset(X2))
| empty(X2)
| ~ in(powerset(X2),sK15(X2)) )
| ~ spl61_240
| ~ spl61_576 ),
inference(resolution,[],[f4771,f2011]) ).
fof(f4771,plain,
( ! [X3] :
( in(sK15(X3),powerset(X3))
| empty(powerset(X3))
| empty(X3) )
| ~ spl61_576 ),
inference(avatar_component_clause,[],[f4770]) ).
fof(f8272,plain,
( spl61_1023
| ~ spl61_240
| ~ spl61_575 ),
inference(avatar_split_clause,[],[f4865,f4766,f2010,f8270]) ).
fof(f8270,plain,
( spl61_1023
<=> ! [X4,X5] :
( empty(powerset(X4))
| ~ subset(X5,X4)
| ~ in(powerset(X4),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_1023])]) ).
fof(f4766,plain,
( spl61_575
<=> ! [X0,X1] :
( empty(powerset(X0))
| in(X1,powerset(X0))
| ~ subset(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_575])]) ).
fof(f4865,plain,
( ! [X4,X5] :
( empty(powerset(X4))
| ~ subset(X5,X4)
| ~ in(powerset(X4),X5) )
| ~ spl61_240
| ~ spl61_575 ),
inference(resolution,[],[f4767,f2011]) ).
fof(f4767,plain,
( ! [X0,X1] :
( in(X1,powerset(X0))
| empty(powerset(X0))
| ~ subset(X1,X0) )
| ~ spl61_575 ),
inference(avatar_component_clause,[],[f4766]) ).
fof(f8268,plain,
( spl61_1022
| ~ spl61_469
| ~ spl61_561 ),
inference(avatar_split_clause,[],[f4750,f4599,f4058,f8266]) ).
fof(f8266,plain,
( spl61_1022
<=> ! [X0] :
( element(sK38(sK17(X0)),X0)
| empty(X0)
| empty(sK17(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_1022])]) ).
fof(f4750,plain,
( ! [X0] :
( element(sK38(sK17(X0)),X0)
| empty(X0)
| empty(sK17(X0)) )
| ~ spl61_469
| ~ spl61_561 ),
inference(resolution,[],[f4600,f4059]) ).
fof(f8264,plain,
( spl61_1021
| ~ spl61_469
| ~ spl61_560 ),
inference(avatar_split_clause,[],[f4747,f4595,f4058,f8262]) ).
fof(f8262,plain,
( spl61_1021
<=> ! [X0] :
( element(sK38(sK16(X0)),X0)
| empty(X0)
| empty(sK16(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_1021])]) ).
fof(f4747,plain,
( ! [X0] :
( element(sK38(sK16(X0)),X0)
| empty(X0)
| empty(sK16(X0)) )
| ~ spl61_469
| ~ spl61_560 ),
inference(resolution,[],[f4596,f4059]) ).
fof(f8260,plain,
( spl61_1020
| ~ spl61_469
| ~ spl61_559 ),
inference(avatar_split_clause,[],[f4744,f4591,f4058,f8258]) ).
fof(f8258,plain,
( spl61_1020
<=> ! [X0] :
( element(sK38(sK15(X0)),X0)
| empty(X0)
| empty(sK15(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_1020])]) ).
fof(f4744,plain,
( ! [X0] :
( element(sK38(sK15(X0)),X0)
| empty(X0)
| empty(sK15(X0)) )
| ~ spl61_469
| ~ spl61_559 ),
inference(resolution,[],[f4592,f4059]) ).
fof(f8256,plain,
( spl61_1019
| ~ spl61_469
| ~ spl61_528 ),
inference(avatar_split_clause,[],[f4491,f4410,f4058,f8254]) ).
fof(f8254,plain,
( spl61_1019
<=> ! [X0] :
( element(sK38(sK38(powerset(X0))),X0)
| empty(sK38(powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_1019])]) ).
fof(f4491,plain,
( ! [X0] :
( element(sK38(sK38(powerset(X0))),X0)
| empty(sK38(powerset(X0))) )
| ~ spl61_469
| ~ spl61_528 ),
inference(resolution,[],[f4411,f4059]) ).
fof(f8252,plain,
( spl61_1018
| ~ spl61_606
| ~ spl61_956 ),
inference(avatar_split_clause,[],[f7718,f7683,f4997,f8250]) ).
fof(f7683,plain,
( spl61_956
<=> ! [X1] :
( empty_carrier(X1)
| ~ one_sorted_str(X1)
| ~ element(cast_as_carrier_subset(sK12),powerset(the_carrier(X1)))
| rel_str(net_of_bool_filter(X1,cast_as_carrier_subset(sK12),sK13)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_956])]) ).
fof(f7718,plain,
( ! [X0] :
( ~ one_sorted_str(X0)
| empty_carrier(X0)
| rel_str(net_of_bool_filter(X0,cast_as_carrier_subset(sK12),sK13))
| ~ in(cast_as_carrier_subset(sK12),sK22(X0)) )
| ~ spl61_606
| ~ spl61_956 ),
inference(duplicate_literal_removal,[],[f7716]) ).
fof(f7716,plain,
( ! [X0] :
( ~ one_sorted_str(X0)
| empty_carrier(X0)
| rel_str(net_of_bool_filter(X0,cast_as_carrier_subset(sK12),sK13))
| ~ in(cast_as_carrier_subset(sK12),sK22(X0))
| ~ one_sorted_str(X0) )
| ~ spl61_606
| ~ spl61_956 ),
inference(resolution,[],[f7684,f4998]) ).
fof(f7684,plain,
( ! [X1] :
( ~ element(cast_as_carrier_subset(sK12),powerset(the_carrier(X1)))
| ~ one_sorted_str(X1)
| empty_carrier(X1)
| rel_str(net_of_bool_filter(X1,cast_as_carrier_subset(sK12),sK13)) )
| ~ spl61_956 ),
inference(avatar_component_clause,[],[f7683]) ).
fof(f8198,plain,
( spl61_1017
| ~ spl61_129
| ~ spl61_609 ),
inference(avatar_split_clause,[],[f5120,f5009,f1508,f8196]) ).
fof(f8196,plain,
( spl61_1017
<=> ! [X0] :
( boundary_set(the_carrier(X0),X0)
| ~ top_str(X0)
| ~ empty(the_carrier(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_1017])]) ).
fof(f5009,plain,
( spl61_609
<=> ! [X0,X1] :
( ~ empty(X0)
| boundary_set(X0,X1)
| ~ top_str(X1)
| ~ subset(X0,the_carrier(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_609])]) ).
fof(f5120,plain,
( ! [X0] :
( boundary_set(the_carrier(X0),X0)
| ~ top_str(X0)
| ~ empty(the_carrier(X0)) )
| ~ spl61_129
| ~ spl61_609 ),
inference(resolution,[],[f5010,f1509]) ).
fof(f5010,plain,
( ! [X0,X1] :
( ~ subset(X0,the_carrier(X1))
| boundary_set(X0,X1)
| ~ top_str(X1)
| ~ empty(X0) )
| ~ spl61_609 ),
inference(avatar_component_clause,[],[f5009]) ).
fof(f8194,plain,
( spl61_1016
| ~ spl61_244
| ~ spl61_605 ),
inference(avatar_split_clause,[],[f5094,f4993,f2027,f8192]) ).
fof(f8192,plain,
( spl61_1016
<=> ! [X9,X8,X10] :
( ~ empty(cartesian_product2(X8,X9))
| ~ in(X10,sK43(X8,X9)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_1016])]) ).
fof(f5094,plain,
( ! [X10,X8,X9] :
( ~ empty(cartesian_product2(X8,X9))
| ~ in(X10,sK43(X8,X9)) )
| ~ spl61_244
| ~ spl61_605 ),
inference(resolution,[],[f4994,f2028]) ).
fof(f8190,plain,
( spl61_1015
| ~ spl61_475
| ~ spl61_605 ),
inference(avatar_split_clause,[],[f5093,f4993,f4083,f8188]) ).
fof(f8188,plain,
( spl61_1015
<=> ! [X6,X5,X7] :
( ~ empty(cartesian_product2(X5,X6))
| ~ in(X7,sK42(X5,X6)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_1015])]) ).
fof(f5093,plain,
( ! [X6,X7,X5] :
( ~ empty(cartesian_product2(X5,X6))
| ~ in(X7,sK42(X5,X6)) )
| ~ spl61_475
| ~ spl61_605 ),
inference(resolution,[],[f4994,f4084]) ).
fof(f8186,plain,
( spl61_1014
| ~ spl61_501
| ~ spl61_597 ),
inference(avatar_split_clause,[],[f4939,f4856,f4220,f8184]) ).
fof(f8184,plain,
( spl61_1014
<=> ! [X50,X51] :
( sK38(powerset(X50)) = X51
| ~ empty(X51)
| ~ empty(X50) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_1014])]) ).
fof(f4939,plain,
( ! [X50,X51] :
( sK38(powerset(X50)) = X51
| ~ empty(X51)
| ~ empty(X50) )
| ~ spl61_501
| ~ spl61_597 ),
inference(resolution,[],[f4857,f4221]) ).
fof(f8182,plain,
( spl61_1013
| ~ spl61_261
| ~ spl61_956 ),
inference(avatar_split_clause,[],[f7717,f7683,f2121,f8180]) ).
fof(f2121,plain,
( spl61_261
<=> ! [X0,X1] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_261])]) ).
fof(f7717,plain,
( ! [X1] :
( ~ one_sorted_str(X1)
| empty_carrier(X1)
| rel_str(net_of_bool_filter(X1,cast_as_carrier_subset(sK12),sK13))
| ~ subset(cast_as_carrier_subset(sK12),the_carrier(X1)) )
| ~ spl61_261
| ~ spl61_956 ),
inference(resolution,[],[f7684,f2122]) ).
fof(f2122,plain,
( ! [X0,X1] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) )
| ~ spl61_261 ),
inference(avatar_component_clause,[],[f2121]) ).
fof(f8178,plain,
( spl61_1012
| ~ spl61_469
| ~ spl61_529 ),
inference(avatar_split_clause,[],[f4494,f4414,f4058,f8176]) ).
fof(f8176,plain,
( spl61_1012
<=> ! [X0] :
( element(sK38(sK40(X0)),powerset(X0))
| empty(sK40(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_1012])]) ).
fof(f4494,plain,
( ! [X0] :
( element(sK38(sK40(X0)),powerset(X0))
| empty(sK40(X0)) )
| ~ spl61_469
| ~ spl61_529 ),
inference(resolution,[],[f4415,f4059]) ).
fof(f8174,plain,
( spl61_1011
| ~ spl61_352
| ~ spl61_476 ),
inference(avatar_split_clause,[],[f4112,f4087,f2780,f8172]) ).
fof(f8172,plain,
( spl61_1011
<=> ! [X2,X1] :
( relation(the_mapping(X1,X2))
| ~ net_str(X2,X1)
| ~ one_sorted_str(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_1011])]) ).
fof(f2780,plain,
( spl61_352
<=> ! [X0,X1] :
( relation_of2_as_subset(the_mapping(X0,X1),the_carrier(X1),the_carrier(X0))
| ~ net_str(X1,X0)
| ~ one_sorted_str(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_352])]) ).
fof(f4087,plain,
( spl61_476
<=> ! [X2,X0,X1] :
( ~ relation_of2_as_subset(X0,X1,X2)
| relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_476])]) ).
fof(f4112,plain,
( ! [X2,X1] :
( relation(the_mapping(X1,X2))
| ~ net_str(X2,X1)
| ~ one_sorted_str(X1) )
| ~ spl61_352
| ~ spl61_476 ),
inference(resolution,[],[f4088,f2781]) ).
fof(f2781,plain,
( ! [X0,X1] :
( relation_of2_as_subset(the_mapping(X0,X1),the_carrier(X1),the_carrier(X0))
| ~ net_str(X1,X0)
| ~ one_sorted_str(X0) )
| ~ spl61_352 ),
inference(avatar_component_clause,[],[f2780]) ).
fof(f4088,plain,
( ! [X2,X0,X1] :
( ~ relation_of2_as_subset(X0,X1,X2)
| relation(X0) )
| ~ spl61_476 ),
inference(avatar_component_clause,[],[f4087]) ).
fof(f8040,plain,
( ~ spl61_92
| spl61_93
| ~ spl61_94
| spl61_1010
| ~ spl61_317
| ~ spl61_708 ),
inference(avatar_split_clause,[],[f5819,f5811,f2492,f8037,f1357,f1352,f1347]) ).
fof(f1347,plain,
( spl61_92
<=> rel_str(sK59) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_92])]) ).
fof(f1352,plain,
( spl61_93
<=> empty_carrier(sK59) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_93])]) ).
fof(f1357,plain,
( spl61_94
<=> reflexive_relstr(sK59) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_94])]) ).
fof(f8037,plain,
( spl61_1010
<=> sP3(sK59) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_1010])]) ).
fof(f2492,plain,
( spl61_317
<=> ! [X0] :
( sP3(X0)
| ~ trivial_carrier(X0)
| ~ reflexive_relstr(X0)
| empty_carrier(X0)
| ~ rel_str(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_317])]) ).
fof(f5811,plain,
( spl61_708
<=> trivial_carrier(sK59) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_708])]) ).
fof(f5819,plain,
( sP3(sK59)
| ~ reflexive_relstr(sK59)
| empty_carrier(sK59)
| ~ rel_str(sK59)
| ~ spl61_317
| ~ spl61_708 ),
inference(resolution,[],[f5813,f2493]) ).
fof(f2493,plain,
( ! [X0] :
( ~ trivial_carrier(X0)
| sP3(X0)
| ~ reflexive_relstr(X0)
| empty_carrier(X0)
| ~ rel_str(X0) )
| ~ spl61_317 ),
inference(avatar_component_clause,[],[f2492]) ).
fof(f5813,plain,
( trivial_carrier(sK59)
| ~ spl61_708 ),
inference(avatar_component_clause,[],[f5811]) ).
fof(f8035,plain,
( ~ spl61_72
| spl61_73
| ~ spl61_75
| spl61_1009
| ~ spl61_317
| ~ spl61_706 ),
inference(avatar_split_clause,[],[f5808,f5800,f2492,f8032,f1262,f1252,f1247]) ).
fof(f1247,plain,
( spl61_72
<=> rel_str(sK57) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_72])]) ).
fof(f1252,plain,
( spl61_73
<=> empty_carrier(sK57) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_73])]) ).
fof(f1262,plain,
( spl61_75
<=> reflexive_relstr(sK57) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_75])]) ).
fof(f8032,plain,
( spl61_1009
<=> sP3(sK57) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_1009])]) ).
fof(f5800,plain,
( spl61_706
<=> trivial_carrier(sK57) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_706])]) ).
fof(f5808,plain,
( sP3(sK57)
| ~ reflexive_relstr(sK57)
| empty_carrier(sK57)
| ~ rel_str(sK57)
| ~ spl61_317
| ~ spl61_706 ),
inference(resolution,[],[f5802,f2493]) ).
fof(f5802,plain,
( trivial_carrier(sK57)
| ~ spl61_706 ),
inference(avatar_component_clause,[],[f5800]) ).
fof(f8030,plain,
( spl61_1008
| ~ spl61_244
| ~ spl61_585 ),
inference(avatar_split_clause,[],[f4882,f4806,f2027,f8028]) ).
fof(f8028,plain,
( spl61_1008
<=> ! [X6,X5] :
( finite(sK43(X5,X6))
| ~ finite(cartesian_product2(X5,X6)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_1008])]) ).
fof(f4882,plain,
( ! [X6,X5] :
( finite(sK43(X5,X6))
| ~ finite(cartesian_product2(X5,X6)) )
| ~ spl61_244
| ~ spl61_585 ),
inference(resolution,[],[f4807,f2028]) ).
fof(f8026,plain,
( spl61_1007
| ~ spl61_475
| ~ spl61_585 ),
inference(avatar_split_clause,[],[f4881,f4806,f4083,f8024]) ).
fof(f8024,plain,
( spl61_1007
<=> ! [X4,X3] :
( finite(sK42(X3,X4))
| ~ finite(cartesian_product2(X3,X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_1007])]) ).
fof(f4881,plain,
( ! [X3,X4] :
( finite(sK42(X3,X4))
| ~ finite(cartesian_product2(X3,X4)) )
| ~ spl61_475
| ~ spl61_585 ),
inference(resolution,[],[f4807,f4084]) ).
fof(f8022,plain,
( spl61_1006
| ~ spl61_469
| ~ spl61_551 ),
inference(avatar_split_clause,[],[f4705,f4559,f4058,f8020]) ).
fof(f8020,plain,
( spl61_1006
<=> ! [X0] :
( ~ empty(the_carrier(X0))
| ~ sP10(X0)
| empty(sK37(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_1006])]) ).
fof(f4705,plain,
( ! [X0] :
( ~ empty(the_carrier(X0))
| ~ sP10(X0)
| empty(sK37(X0)) )
| ~ spl61_469
| ~ spl61_551 ),
inference(resolution,[],[f4560,f4059]) ).
fof(f8018,plain,
( spl61_1005
| ~ spl61_469
| ~ spl61_549 ),
inference(avatar_split_clause,[],[f4698,f4551,f4058,f8016]) ).
fof(f8016,plain,
( spl61_1005
<=> ! [X0] :
( ~ empty(the_carrier(X0))
| ~ sP7(X0)
| empty(sK30(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_1005])]) ).
fof(f4698,plain,
( ! [X0] :
( ~ empty(the_carrier(X0))
| ~ sP7(X0)
| empty(sK30(X0)) )
| ~ spl61_469
| ~ spl61_549 ),
inference(resolution,[],[f4552,f4059]) ).
fof(f8014,plain,
( spl61_1004
| ~ spl61_469
| ~ spl61_548 ),
inference(avatar_split_clause,[],[f4695,f4547,f4058,f8012]) ).
fof(f8012,plain,
( spl61_1004
<=> ! [X0] :
( ~ empty(the_carrier(X0))
| ~ sP6(X0)
| empty(sK25(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_1004])]) ).
fof(f4695,plain,
( ! [X0] :
( ~ empty(the_carrier(X0))
| ~ sP6(X0)
| empty(sK25(X0)) )
| ~ spl61_469
| ~ spl61_548 ),
inference(resolution,[],[f4548,f4059]) ).
fof(f8010,plain,
( spl61_1003
| ~ spl61_469
| ~ spl61_547 ),
inference(avatar_split_clause,[],[f4692,f4543,f4058,f8008]) ).
fof(f8008,plain,
( spl61_1003
<=> ! [X0] :
( ~ empty(the_carrier(X0))
| ~ rel_str(X0)
| empty(sK24(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_1003])]) ).
fof(f4692,plain,
( ! [X0] :
( ~ empty(the_carrier(X0))
| ~ rel_str(X0)
| empty(sK24(X0)) )
| ~ spl61_469
| ~ spl61_547 ),
inference(resolution,[],[f4544,f4059]) ).
fof(f8006,plain,
( spl61_1002
| ~ spl61_469
| ~ spl61_546 ),
inference(avatar_split_clause,[],[f4689,f4539,f4058,f8004]) ).
fof(f8004,plain,
( spl61_1002
<=> ! [X0] :
( ~ empty(the_carrier(X0))
| ~ rel_str(X0)
| empty(sK23(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_1002])]) ).
fof(f4689,plain,
( ! [X0] :
( ~ empty(the_carrier(X0))
| ~ rel_str(X0)
| empty(sK23(X0)) )
| ~ spl61_469
| ~ spl61_546 ),
inference(resolution,[],[f4540,f4059]) ).
fof(f8002,plain,
( spl61_1001
| ~ spl61_106
| ~ spl61_986 ),
inference(avatar_split_clause,[],[f7927,f7911,f1416,f8000]) ).
fof(f8000,plain,
( spl61_1001
<=> ! [X0] : sP7(boole_POSet(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_1001])]) ).
fof(f1416,plain,
( spl61_106
<=> ! [X0] : ~ empty_carrier(boole_POSet(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_106])]) ).
fof(f7911,plain,
( spl61_986
<=> ! [X0] :
( sP7(boole_POSet(X0))
| empty_carrier(boole_POSet(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_986])]) ).
fof(f7927,plain,
( ! [X0] : sP7(boole_POSet(X0))
| ~ spl61_106
| ~ spl61_986 ),
inference(resolution,[],[f7912,f1417]) ).
fof(f1417,plain,
( ! [X0] : ~ empty_carrier(boole_POSet(X0))
| ~ spl61_106 ),
inference(avatar_component_clause,[],[f1416]) ).
fof(f7912,plain,
( ! [X0] :
( empty_carrier(boole_POSet(X0))
| sP7(boole_POSet(X0)) )
| ~ spl61_986 ),
inference(avatar_component_clause,[],[f7911]) ).
fof(f7998,plain,
( spl61_1000
| ~ spl61_469
| ~ spl61_543 ),
inference(avatar_split_clause,[],[f4682,f4526,f4058,f7996]) ).
fof(f7996,plain,
( spl61_1000
<=> ! [X0] :
( ~ empty(the_carrier(X0))
| ~ one_sorted_str(X0)
| empty(cast_as_carrier_subset(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_1000])]) ).
fof(f4682,plain,
( ! [X0] :
( ~ empty(the_carrier(X0))
| ~ one_sorted_str(X0)
| empty(cast_as_carrier_subset(X0)) )
| ~ spl61_469
| ~ spl61_543 ),
inference(resolution,[],[f4527,f4059]) ).
fof(f7994,plain,
( spl61_999
| ~ spl61_294
| ~ spl61_540 ),
inference(avatar_split_clause,[],[f4675,f4514,f2285,f7992]) ).
fof(f7992,plain,
( spl61_999
<=> ! [X1] :
( ~ rel_str(X1)
| strict_rel_str(rel_str_of(the_carrier(X1),the_InternalRel(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_999])]) ).
fof(f4514,plain,
( spl61_540
<=> ! [X0] :
( ~ rel_str(X0)
| relation_of2(the_InternalRel(X0),the_carrier(X0),the_carrier(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_540])]) ).
fof(f4675,plain,
( ! [X1] :
( ~ rel_str(X1)
| strict_rel_str(rel_str_of(the_carrier(X1),the_InternalRel(X1))) )
| ~ spl61_294
| ~ spl61_540 ),
inference(resolution,[],[f4515,f2286]) ).
fof(f4515,plain,
( ! [X0] :
( relation_of2(the_InternalRel(X0),the_carrier(X0),the_carrier(X0))
| ~ rel_str(X0) )
| ~ spl61_540 ),
inference(avatar_component_clause,[],[f4514]) ).
fof(f7990,plain,
( spl61_998
| ~ spl61_295
| ~ spl61_540 ),
inference(avatar_split_clause,[],[f4674,f4514,f2289,f7988]) ).
fof(f7988,plain,
( spl61_998
<=> ! [X0] :
( ~ rel_str(X0)
| rel_str(rel_str_of(the_carrier(X0),the_InternalRel(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_998])]) ).
fof(f4674,plain,
( ! [X0] :
( ~ rel_str(X0)
| rel_str(rel_str_of(the_carrier(X0),the_InternalRel(X0))) )
| ~ spl61_295
| ~ spl61_540 ),
inference(resolution,[],[f4515,f2290]) ).
fof(f7986,plain,
( spl61_997
| ~ spl61_192
| ~ spl61_487 ),
inference(avatar_split_clause,[],[f4241,f4163,f1794,f7984]) ).
fof(f7984,plain,
( spl61_997
<=> ! [X6,X5] :
( sK33(X5) = X6
| sP0(X6)
| ~ sP9(X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_997])]) ).
fof(f1794,plain,
( spl61_192
<=> ! [X0] :
( empty(sK33(X0))
| ~ sP9(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_192])]) ).
fof(f4163,plain,
( spl61_487
<=> ! [X0,X1] :
( X0 = X1
| ~ empty(X0)
| sP0(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_487])]) ).
fof(f4241,plain,
( ! [X6,X5] :
( sK33(X5) = X6
| sP0(X6)
| ~ sP9(X5) )
| ~ spl61_192
| ~ spl61_487 ),
inference(resolution,[],[f4164,f1795]) ).
fof(f1795,plain,
( ! [X0] :
( empty(sK33(X0))
| ~ sP9(X0) )
| ~ spl61_192 ),
inference(avatar_component_clause,[],[f1794]) ).
fof(f4164,plain,
( ! [X0,X1] :
( ~ empty(X0)
| X0 = X1
| sP0(X1) )
| ~ spl61_487 ),
inference(avatar_component_clause,[],[f4163]) ).
fof(f7982,plain,
( spl61_996
| ~ spl61_169
| ~ spl61_487 ),
inference(avatar_split_clause,[],[f4240,f4163,f1701,f7980]) ).
fof(f7980,plain,
( spl61_996
<=> ! [X4,X3] :
( sK18(X3) = X4
| sP0(X4)
| ~ sP1(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_996])]) ).
fof(f1701,plain,
( spl61_169
<=> ! [X0] :
( empty(sK18(X0))
| ~ sP1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_169])]) ).
fof(f4240,plain,
( ! [X3,X4] :
( sK18(X3) = X4
| sP0(X4)
| ~ sP1(X3) )
| ~ spl61_169
| ~ spl61_487 ),
inference(resolution,[],[f4164,f1702]) ).
fof(f1702,plain,
( ! [X0] :
( empty(sK18(X0))
| ~ sP1(X0) )
| ~ spl61_169 ),
inference(avatar_component_clause,[],[f1701]) ).
fof(f7978,plain,
( spl61_995
| ~ spl61_353
| ~ spl61_446 ),
inference(avatar_split_clause,[],[f3933,f3667,f2784,f7976]) ).
fof(f7976,plain,
( spl61_995
<=> ! [X1] :
( in(sK41(sK60,X1),X1)
| sK60 = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_995])]) ).
fof(f3667,plain,
( spl61_446
<=> ! [X31] : ~ in(X31,sK60) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_446])]) ).
fof(f3933,plain,
( ! [X1] :
( in(sK41(sK60,X1),X1)
| sK60 = X1 )
| ~ spl61_353
| ~ spl61_446 ),
inference(resolution,[],[f3668,f2785]) ).
fof(f3668,plain,
( ! [X31] : ~ in(X31,sK60)
| ~ spl61_446 ),
inference(avatar_component_clause,[],[f3667]) ).
fof(f7974,plain,
( spl61_994
| ~ spl61_353
| ~ spl61_446 ),
inference(avatar_split_clause,[],[f3932,f3667,f2784,f7972]) ).
fof(f7972,plain,
( spl61_994
<=> ! [X0] :
( in(sK41(X0,sK60),X0)
| sK60 = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_994])]) ).
fof(f3932,plain,
( ! [X0] :
( in(sK41(X0,sK60),X0)
| sK60 = X0 )
| ~ spl61_353
| ~ spl61_446 ),
inference(resolution,[],[f3668,f2785]) ).
fof(f7964,plain,
( spl61_993
| ~ spl61_366
| ~ spl61_533 ),
inference(avatar_split_clause,[],[f4455,f4449,f3007,f7962]) ).
fof(f7962,plain,
( spl61_993
<=> ! [X0] :
( empty_carrier(X0)
| ~ one_sorted_str(X0)
| ~ element(cast_as_carrier_subset(sK12),powerset(the_carrier(X0)))
| filter_of_net_str(X0,net_of_bool_filter(X0,cast_as_carrier_subset(sK12),sK13)) = a_2_1_yellow19(X0,net_of_bool_filter(X0,cast_as_carrier_subset(sK12),sK13))
| empty_carrier(net_of_bool_filter(X0,cast_as_carrier_subset(sK12),sK13)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_993])]) ).
fof(f3007,plain,
( spl61_366
<=> ! [X0,X1] :
( filter_of_net_str(X0,X1) = a_2_1_yellow19(X0,X1)
| ~ net_str(X1,X0)
| empty_carrier(X1)
| ~ one_sorted_str(X0)
| empty_carrier(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_366])]) ).
fof(f4455,plain,
( ! [X0] :
( empty_carrier(X0)
| ~ one_sorted_str(X0)
| ~ element(cast_as_carrier_subset(sK12),powerset(the_carrier(X0)))
| filter_of_net_str(X0,net_of_bool_filter(X0,cast_as_carrier_subset(sK12),sK13)) = a_2_1_yellow19(X0,net_of_bool_filter(X0,cast_as_carrier_subset(sK12),sK13))
| empty_carrier(net_of_bool_filter(X0,cast_as_carrier_subset(sK12),sK13)) )
| ~ spl61_366
| ~ spl61_533 ),
inference(duplicate_literal_removal,[],[f4452]) ).
fof(f4452,plain,
( ! [X0] :
( empty_carrier(X0)
| ~ one_sorted_str(X0)
| ~ element(cast_as_carrier_subset(sK12),powerset(the_carrier(X0)))
| filter_of_net_str(X0,net_of_bool_filter(X0,cast_as_carrier_subset(sK12),sK13)) = a_2_1_yellow19(X0,net_of_bool_filter(X0,cast_as_carrier_subset(sK12),sK13))
| empty_carrier(net_of_bool_filter(X0,cast_as_carrier_subset(sK12),sK13))
| ~ one_sorted_str(X0)
| empty_carrier(X0) )
| ~ spl61_366
| ~ spl61_533 ),
inference(resolution,[],[f4450,f3008]) ).
fof(f3008,plain,
( ! [X0,X1] :
( ~ net_str(X1,X0)
| filter_of_net_str(X0,X1) = a_2_1_yellow19(X0,X1)
| empty_carrier(X1)
| ~ one_sorted_str(X0)
| empty_carrier(X0) )
| ~ spl61_366 ),
inference(avatar_component_clause,[],[f3007]) ).
fof(f7958,plain,
( spl61_992
| ~ spl61_132
| ~ spl61_487 ),
inference(avatar_split_clause,[],[f4238,f4163,f1521,f7956]) ).
fof(f7956,plain,
( spl61_992
<=> ! [X0,X1] :
( X0 = X1
| sP0(X1)
| sP0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_992])]) ).
fof(f4238,plain,
( ! [X0,X1] :
( X0 = X1
| sP0(X1)
| sP0(X0) )
| ~ spl61_132
| ~ spl61_487 ),
inference(resolution,[],[f4164,f1522]) ).
fof(f7954,plain,
( spl61_991
| ~ spl61_136
| ~ spl61_479 ),
inference(avatar_split_clause,[],[f4237,f4118,f1537,f7952]) ).
fof(f7952,plain,
( spl61_991
<=> ! [X0] :
( ~ one_sorted_str(X0)
| ~ sP2(X0)
| one_sorted_str(sK20(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_991])]) ).
fof(f4237,plain,
( ! [X0] :
( ~ one_sorted_str(X0)
| ~ sP2(X0)
| one_sorted_str(sK20(X0)) )
| ~ spl61_136
| ~ spl61_479 ),
inference(resolution,[],[f4119,f1538]) ).
fof(f7943,plain,
( ~ spl61_106
| ~ spl61_988 ),
inference(avatar_contradiction_clause,[],[f7942]) ).
fof(f7942,plain,
( $false
| ~ spl61_106
| ~ spl61_988 ),
inference(resolution,[],[f7931,f1417]) ).
fof(f7931,plain,
( empty_carrier(boole_POSet(cast_as_carrier_subset(sK12)))
| ~ spl61_988 ),
inference(avatar_component_clause,[],[f7929]) ).
fof(f7929,plain,
( spl61_988
<=> empty_carrier(boole_POSet(cast_as_carrier_subset(sK12))) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_988])]) ).
fof(f7941,plain,
( ~ spl61_408
| spl61_989 ),
inference(avatar_contradiction_clause,[],[f7940]) ).
fof(f7940,plain,
( $false
| ~ spl61_408
| spl61_989 ),
inference(resolution,[],[f7935,f3497]) ).
fof(f3497,plain,
( ! [X0] : one_sorted_str(boole_POSet(X0))
| ~ spl61_408 ),
inference(avatar_component_clause,[],[f3496]) ).
fof(f3496,plain,
( spl61_408
<=> ! [X0] : one_sorted_str(boole_POSet(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_408])]) ).
fof(f7935,plain,
( ~ one_sorted_str(boole_POSet(cast_as_carrier_subset(sK12)))
| spl61_989 ),
inference(avatar_component_clause,[],[f7933]) ).
fof(f7933,plain,
( spl61_989
<=> one_sorted_str(boole_POSet(cast_as_carrier_subset(sK12))) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_989])]) ).
fof(f7939,plain,
( spl61_988
| ~ spl61_989
| spl61_990
| ~ spl61_9
| ~ spl61_802 ),
inference(avatar_split_clause,[],[f6527,f6510,f932,f7937,f7933,f7929]) ).
fof(f7937,plain,
( spl61_990
<=> ! [X14] :
( in(sK13,a_2_1_yellow19(boole_POSet(cast_as_carrier_subset(sK12)),X14))
| empty_carrier(X14)
| ~ net_str(X14,boole_POSet(cast_as_carrier_subset(sK12)))
| ~ is_eventually_in(boole_POSet(cast_as_carrier_subset(sK12)),X14,sK13) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_990])]) ).
fof(f932,plain,
( spl61_9
<=> element(sK13,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(sK12))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_9])]) ).
fof(f6510,plain,
( spl61_802
<=> ! [X2,X0,X1] :
( ~ is_eventually_in(X0,X1,X2)
| in(X2,a_2_1_yellow19(X0,X1))
| ~ element(X2,powerset(the_carrier(X0)))
| ~ net_str(X1,X0)
| empty_carrier(X1)
| ~ one_sorted_str(X0)
| empty_carrier(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_802])]) ).
fof(f6527,plain,
( ! [X14] :
( in(sK13,a_2_1_yellow19(boole_POSet(cast_as_carrier_subset(sK12)),X14))
| ~ is_eventually_in(boole_POSet(cast_as_carrier_subset(sK12)),X14,sK13)
| ~ net_str(X14,boole_POSet(cast_as_carrier_subset(sK12)))
| empty_carrier(X14)
| ~ one_sorted_str(boole_POSet(cast_as_carrier_subset(sK12)))
| empty_carrier(boole_POSet(cast_as_carrier_subset(sK12))) )
| ~ spl61_9
| ~ spl61_802 ),
inference(resolution,[],[f6511,f934]) ).
fof(f934,plain,
( element(sK13,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(sK12)))))
| ~ spl61_9 ),
inference(avatar_component_clause,[],[f932]) ).
fof(f6511,plain,
( ! [X2,X0,X1] :
( ~ element(X2,powerset(the_carrier(X0)))
| in(X2,a_2_1_yellow19(X0,X1))
| ~ is_eventually_in(X0,X1,X2)
| ~ net_str(X1,X0)
| empty_carrier(X1)
| ~ one_sorted_str(X0)
| empty_carrier(X0) )
| ~ spl61_802 ),
inference(avatar_component_clause,[],[f6510]) ).
fof(f7920,plain,
( spl61_987
| ~ spl61_135
| ~ spl61_977 ),
inference(avatar_split_clause,[],[f7889,f7834,f1533,f7917]) ).
fof(f7917,plain,
( spl61_987
<=> sP2(net_of_bool_filter(sK12,cast_as_carrier_subset(sK12),sK13)) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_987])]) ).
fof(f7834,plain,
( spl61_977
<=> one_sorted_str(net_of_bool_filter(sK12,cast_as_carrier_subset(sK12),sK13)) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_977])]) ).
fof(f7889,plain,
( sP2(net_of_bool_filter(sK12,cast_as_carrier_subset(sK12),sK13))
| ~ spl61_135
| ~ spl61_977 ),
inference(resolution,[],[f7836,f1534]) ).
fof(f7836,plain,
( one_sorted_str(net_of_bool_filter(sK12,cast_as_carrier_subset(sK12),sK13))
| ~ spl61_977 ),
inference(avatar_component_clause,[],[f7834]) ).
fof(f7913,plain,
( spl61_986
| ~ spl61_125
| ~ spl61_536 ),
inference(avatar_split_clause,[],[f4673,f4498,f1492,f7911]) ).
fof(f4498,plain,
( spl61_536
<=> ! [X0] :
( ~ rel_str(boole_POSet(X0))
| sP7(boole_POSet(X0))
| empty_carrier(boole_POSet(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_536])]) ).
fof(f4673,plain,
( ! [X0] :
( sP7(boole_POSet(X0))
| empty_carrier(boole_POSet(X0)) )
| ~ spl61_125
| ~ spl61_536 ),
inference(resolution,[],[f4499,f1493]) ).
fof(f4499,plain,
( ! [X0] :
( ~ rel_str(boole_POSet(X0))
| sP7(boole_POSet(X0))
| empty_carrier(boole_POSet(X0)) )
| ~ spl61_536 ),
inference(avatar_component_clause,[],[f4498]) ).
fof(f7909,plain,
( spl61_985
| ~ spl61_469
| ~ spl61_501 ),
inference(avatar_split_clause,[],[f4278,f4220,f4058,f7907]) ).
fof(f7907,plain,
( spl61_985
<=> ! [X0] :
( ~ empty(X0)
| empty(sK38(powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_985])]) ).
fof(f4278,plain,
( ! [X0] :
( ~ empty(X0)
| empty(sK38(powerset(X0))) )
| ~ spl61_469
| ~ spl61_501 ),
inference(resolution,[],[f4221,f4059]) ).
fof(f7905,plain,
( spl61_984
| ~ spl61_294
| ~ spl61_474 ),
inference(avatar_split_clause,[],[f4108,f4079,f2285,f7903]) ).
fof(f7903,plain,
( spl61_984
<=> ! [X1] : strict_rel_str(rel_str_of(X1,sK43(X1,X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_984])]) ).
fof(f4079,plain,
( spl61_474
<=> ! [X0,X1] : relation_of2(sK43(X0,X1),X0,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_474])]) ).
fof(f4108,plain,
( ! [X1] : strict_rel_str(rel_str_of(X1,sK43(X1,X1)))
| ~ spl61_294
| ~ spl61_474 ),
inference(resolution,[],[f4080,f2286]) ).
fof(f4080,plain,
( ! [X0,X1] : relation_of2(sK43(X0,X1),X0,X1)
| ~ spl61_474 ),
inference(avatar_component_clause,[],[f4079]) ).
fof(f7901,plain,
( spl61_983
| ~ spl61_295
| ~ spl61_474 ),
inference(avatar_split_clause,[],[f4107,f4079,f2289,f7899]) ).
fof(f7899,plain,
( spl61_983
<=> ! [X0] : rel_str(rel_str_of(X0,sK43(X0,X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_983])]) ).
fof(f4107,plain,
( ! [X0] : rel_str(rel_str_of(X0,sK43(X0,X0)))
| ~ spl61_295
| ~ spl61_474 ),
inference(resolution,[],[f4080,f2290]) ).
fof(f7897,plain,
( spl61_982
| ~ spl61_136
| ~ spl61_471 ),
inference(avatar_split_clause,[],[f4106,f4066,f1537,f7895]) ).
fof(f7895,plain,
( spl61_982
<=> ! [X0] : one_sorted_str(rel_str_of(X0,sK42(X0,X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_982])]) ).
fof(f4066,plain,
( spl61_471
<=> ! [X0] : rel_str(rel_str_of(X0,sK42(X0,X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_471])]) ).
fof(f4106,plain,
( ! [X0] : one_sorted_str(rel_str_of(X0,sK42(X0,X0)))
| ~ spl61_136
| ~ spl61_471 ),
inference(resolution,[],[f4067,f1538]) ).
fof(f4067,plain,
( ! [X0] : rel_str(rel_str_of(X0,sK42(X0,X0)))
| ~ spl61_471 ),
inference(avatar_component_clause,[],[f4066]) ).
fof(f7893,plain,
( spl61_981
| ~ spl61_240
| ~ spl61_469 ),
inference(avatar_split_clause,[],[f4097,f4058,f2010,f7891]) ).
fof(f7891,plain,
( spl61_981
<=> ! [X2] :
( empty(X2)
| ~ in(X2,sK38(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_981])]) ).
fof(f4097,plain,
( ! [X2] :
( empty(X2)
| ~ in(X2,sK38(X2)) )
| ~ spl61_240
| ~ spl61_469 ),
inference(resolution,[],[f4059,f2011]) ).
fof(f7886,plain,
( spl61_980
| ~ spl61_305
| ~ spl61_476 ),
inference(avatar_split_clause,[],[f4111,f4087,f2416,f7884]) ).
fof(f7884,plain,
( spl61_980
<=> ! [X0] :
( relation(the_InternalRel(X0))
| ~ rel_str(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_980])]) ).
fof(f4111,plain,
( ! [X0] :
( relation(the_InternalRel(X0))
| ~ rel_str(X0) )
| ~ spl61_305
| ~ spl61_476 ),
inference(resolution,[],[f4088,f2417]) ).
fof(f7882,plain,
( spl61_979
| ~ spl61_136
| ~ spl61_441 ),
inference(avatar_split_clause,[],[f3949,f3648,f1537,f7880]) ).
fof(f7880,plain,
( spl61_979
<=> ! [X0] :
( ~ one_sorted_str(X0)
| one_sorted_str(sK19(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_979])]) ).
fof(f3648,plain,
( spl61_441
<=> ! [X0] :
( rel_str(sK19(X0))
| ~ one_sorted_str(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_441])]) ).
fof(f3949,plain,
( ! [X0] :
( ~ one_sorted_str(X0)
| one_sorted_str(sK19(X0)) )
| ~ spl61_136
| ~ spl61_441 ),
inference(resolution,[],[f3649,f1538]) ).
fof(f3649,plain,
( ! [X0] :
( rel_str(sK19(X0))
| ~ one_sorted_str(X0) )
| ~ spl61_441 ),
inference(avatar_component_clause,[],[f3648]) ).
fof(f7878,plain,
( spl61_978
| ~ spl61_136
| ~ spl61_440 ),
inference(avatar_split_clause,[],[f3948,f3644,f1537,f7876]) ).
fof(f7876,plain,
( spl61_978
<=> ! [X0] :
( ~ one_sorted_str(X0)
| one_sorted_str(sK21(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_978])]) ).
fof(f3644,plain,
( spl61_440
<=> ! [X2] :
( rel_str(sK21(X2))
| ~ one_sorted_str(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_440])]) ).
fof(f3948,plain,
( ! [X0] :
( ~ one_sorted_str(X0)
| one_sorted_str(sK21(X0)) )
| ~ spl61_136
| ~ spl61_440 ),
inference(resolution,[],[f3645,f1538]) ).
fof(f3645,plain,
( ! [X2] :
( rel_str(sK21(X2))
| ~ one_sorted_str(X2) )
| ~ spl61_440 ),
inference(avatar_component_clause,[],[f3644]) ).
fof(f7837,plain,
( spl61_977
| ~ spl61_136
| ~ spl61_967 ),
inference(avatar_split_clause,[],[f7796,f7749,f1537,f7834]) ).
fof(f7749,plain,
( spl61_967
<=> rel_str(net_of_bool_filter(sK12,cast_as_carrier_subset(sK12),sK13)) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_967])]) ).
fof(f7796,plain,
( one_sorted_str(net_of_bool_filter(sK12,cast_as_carrier_subset(sK12),sK13))
| ~ spl61_136
| ~ spl61_967 ),
inference(resolution,[],[f7751,f1538]) ).
fof(f7751,plain,
( rel_str(net_of_bool_filter(sK12,cast_as_carrier_subset(sK12),sK13))
| ~ spl61_967 ),
inference(avatar_component_clause,[],[f7749]) ).
fof(f7832,plain,
( spl61_976
| ~ spl61_129
| ~ spl61_500 ),
inference(avatar_split_clause,[],[f4272,f4216,f1508,f7830]) ).
fof(f7830,plain,
( spl61_976
<=> ! [X0,X1] : relation(cartesian_product2(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_976])]) ).
fof(f4216,plain,
( spl61_500
<=> ! [X2,X0,X1] :
( relation(X0)
| ~ subset(X0,cartesian_product2(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_500])]) ).
fof(f4272,plain,
( ! [X0,X1] : relation(cartesian_product2(X0,X1))
| ~ spl61_129
| ~ spl61_500 ),
inference(resolution,[],[f4217,f1509]) ).
fof(f4217,plain,
( ! [X2,X0,X1] :
( ~ subset(X0,cartesian_product2(X1,X2))
| relation(X0) )
| ~ spl61_500 ),
inference(avatar_component_clause,[],[f4216]) ).
fof(f7828,plain,
( spl61_975
| ~ spl61_220
| ~ spl61_477 ),
inference(avatar_split_clause,[],[f4116,f4091,f1928,f7825]) ).
fof(f7825,plain,
( spl61_975
<=> sK60 = sK18(sK45) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_975])]) ).
fof(f1928,plain,
( spl61_220
<=> sP1(sK45) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_220])]) ).
fof(f4091,plain,
( spl61_477
<=> ! [X1] :
( sK60 = sK18(X1)
| ~ sP1(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_477])]) ).
fof(f4116,plain,
( sK60 = sK18(sK45)
| ~ spl61_220
| ~ spl61_477 ),
inference(resolution,[],[f4092,f1930]) ).
fof(f1930,plain,
( sP1(sK45)
| ~ spl61_220 ),
inference(avatar_component_clause,[],[f1928]) ).
fof(f4092,plain,
( ! [X1] :
( ~ sP1(X1)
| sK60 = sK18(X1) )
| ~ spl61_477 ),
inference(avatar_component_clause,[],[f4091]) ).
fof(f7823,plain,
( spl61_974
| ~ spl61_244
| ~ spl61_476 ),
inference(avatar_split_clause,[],[f4114,f4087,f2027,f7821]) ).
fof(f7821,plain,
( spl61_974
<=> ! [X6,X5] : relation(sK43(X5,X6)) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_974])]) ).
fof(f4114,plain,
( ! [X6,X5] : relation(sK43(X5,X6))
| ~ spl61_244
| ~ spl61_476 ),
inference(resolution,[],[f4088,f2028]) ).
fof(f7819,plain,
( spl61_973
| ~ spl61_475
| ~ spl61_476 ),
inference(avatar_split_clause,[],[f4113,f4087,f4083,f7817]) ).
fof(f7817,plain,
( spl61_973
<=> ! [X4,X3] : relation(sK42(X3,X4)) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_973])]) ).
fof(f4113,plain,
( ! [X3,X4] : relation(sK42(X3,X4))
| ~ spl61_475
| ~ spl61_476 ),
inference(resolution,[],[f4088,f4084]) ).
fof(f7805,plain,
( ~ spl61_62
| spl61_730
| ~ spl61_212
| ~ spl61_458 ),
inference(avatar_split_clause,[],[f4001,f3996,f1896,f5989,f1197]) ).
fof(f1197,plain,
( spl61_62
<=> rel_str(sK56) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_62])]) ).
fof(f5989,plain,
( spl61_730
<=> lower_bounded_relstr(sK56) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_730])]) ).
fof(f1896,plain,
( spl61_212
<=> ! [X0] :
( lower_bounded_relstr(X0)
| ~ bounded_relstr(X0)
| ~ rel_str(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_212])]) ).
fof(f3996,plain,
( spl61_458
<=> bounded_relstr(sK56) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_458])]) ).
fof(f4001,plain,
( lower_bounded_relstr(sK56)
| ~ rel_str(sK56)
| ~ spl61_212
| ~ spl61_458 ),
inference(resolution,[],[f3998,f1897]) ).
fof(f1897,plain,
( ! [X0] :
( ~ bounded_relstr(X0)
| lower_bounded_relstr(X0)
| ~ rel_str(X0) )
| ~ spl61_212 ),
inference(avatar_component_clause,[],[f1896]) ).
fof(f3998,plain,
( bounded_relstr(sK56)
| ~ spl61_458 ),
inference(avatar_component_clause,[],[f3996]) ).
fof(f7801,plain,
( ~ spl61_62
| spl61_972
| ~ spl61_213
| ~ spl61_458 ),
inference(avatar_split_clause,[],[f4000,f3996,f1900,f7798,f1197]) ).
fof(f7798,plain,
( spl61_972
<=> upper_bounded_relstr(sK56) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_972])]) ).
fof(f1900,plain,
( spl61_213
<=> ! [X0] :
( upper_bounded_relstr(X0)
| ~ bounded_relstr(X0)
| ~ rel_str(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_213])]) ).
fof(f4000,plain,
( upper_bounded_relstr(sK56)
| ~ rel_str(sK56)
| ~ spl61_213
| ~ spl61_458 ),
inference(resolution,[],[f3998,f1901]) ).
fof(f1901,plain,
( ! [X0] :
( ~ bounded_relstr(X0)
| upper_bounded_relstr(X0)
| ~ rel_str(X0) )
| ~ spl61_213 ),
inference(avatar_component_clause,[],[f1900]) ).
fof(f7784,plain,
( ~ spl61_53
| spl61_728
| ~ spl61_212
| ~ spl61_457 ),
inference(avatar_split_clause,[],[f3994,f3989,f1896,f5980,f1152]) ).
fof(f1152,plain,
( spl61_53
<=> rel_str(sK55) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_53])]) ).
fof(f5980,plain,
( spl61_728
<=> lower_bounded_relstr(sK55) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_728])]) ).
fof(f3989,plain,
( spl61_457
<=> bounded_relstr(sK55) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_457])]) ).
fof(f3994,plain,
( lower_bounded_relstr(sK55)
| ~ rel_str(sK55)
| ~ spl61_212
| ~ spl61_457 ),
inference(resolution,[],[f3991,f1897]) ).
fof(f3991,plain,
( bounded_relstr(sK55)
| ~ spl61_457 ),
inference(avatar_component_clause,[],[f3989]) ).
fof(f7780,plain,
( ~ spl61_53
| spl61_971
| ~ spl61_213
| ~ spl61_457 ),
inference(avatar_split_clause,[],[f3993,f3989,f1900,f7777,f1152]) ).
fof(f7777,plain,
( spl61_971
<=> upper_bounded_relstr(sK55) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_971])]) ).
fof(f3993,plain,
( upper_bounded_relstr(sK55)
| ~ rel_str(sK55)
| ~ spl61_213
| ~ spl61_457 ),
inference(resolution,[],[f3991,f1901]) ).
fof(f7775,plain,
( ~ spl61_46
| spl61_970
| ~ spl61_212
| ~ spl61_456 ),
inference(avatar_split_clause,[],[f3987,f3982,f1896,f7772,f1117]) ).
fof(f7772,plain,
( spl61_970
<=> lower_bounded_relstr(sK54) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_970])]) ).
fof(f3982,plain,
( spl61_456
<=> bounded_relstr(sK54) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_456])]) ).
fof(f3987,plain,
( lower_bounded_relstr(sK54)
| ~ rel_str(sK54)
| ~ spl61_212
| ~ spl61_456 ),
inference(resolution,[],[f3984,f1897]) ).
fof(f3984,plain,
( bounded_relstr(sK54)
| ~ spl61_456 ),
inference(avatar_component_clause,[],[f3982]) ).
fof(f7767,plain,
( ~ spl61_46
| spl61_969
| ~ spl61_213
| ~ spl61_456 ),
inference(avatar_split_clause,[],[f3986,f3982,f1900,f7764,f1117]) ).
fof(f7764,plain,
( spl61_969
<=> upper_bounded_relstr(sK54) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_969])]) ).
fof(f3986,plain,
( upper_bounded_relstr(sK54)
| ~ rel_str(sK54)
| ~ spl61_213
| ~ spl61_456 ),
inference(resolution,[],[f3984,f1901]) ).
fof(f7762,plain,
( spl61_968
| ~ spl61_199
| ~ spl61_420 ),
inference(avatar_split_clause,[],[f3570,f3558,f1822,f7760]) ).
fof(f7760,plain,
( spl61_968
<=> ! [X0] : element(sK60,powerset(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_968])]) ).
fof(f1822,plain,
( spl61_199
<=> ! [X0] : element(sK39(X0),powerset(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_199])]) ).
fof(f3558,plain,
( spl61_420
<=> ! [X2] : sK60 = sK39(X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_420])]) ).
fof(f3570,plain,
( ! [X0] : element(sK60,powerset(X0))
| ~ spl61_199
| ~ spl61_420 ),
inference(superposition,[],[f1823,f3559]) ).
fof(f3559,plain,
( ! [X2] : sK60 = sK39(X2)
| ~ spl61_420 ),
inference(avatar_component_clause,[],[f3558]) ).
fof(f1823,plain,
( ! [X0] : element(sK39(X0),powerset(X0))
| ~ spl61_199 ),
inference(avatar_component_clause,[],[f1822]) ).
fof(f7752,plain,
( spl61_967
| spl61_1
| ~ spl61_161
| ~ spl61_265
| ~ spl61_956 ),
inference(avatar_split_clause,[],[f7719,f7683,f2167,f1659,f892,f7749]) ).
fof(f7719,plain,
( ~ one_sorted_str(sK12)
| empty_carrier(sK12)
| rel_str(net_of_bool_filter(sK12,cast_as_carrier_subset(sK12),sK13))
| ~ spl61_265
| ~ spl61_956 ),
inference(duplicate_literal_removal,[],[f7715]) ).
fof(f7715,plain,
( ~ one_sorted_str(sK12)
| empty_carrier(sK12)
| rel_str(net_of_bool_filter(sK12,cast_as_carrier_subset(sK12),sK13))
| ~ one_sorted_str(sK12)
| ~ spl61_265
| ~ spl61_956 ),
inference(resolution,[],[f7684,f2168]) ).
fof(f7745,plain,
( spl61_966
| ~ spl61_379
| ~ spl61_396 ),
inference(avatar_split_clause,[],[f3414,f3358,f3166,f7743]) ).
fof(f7743,plain,
( spl61_966
<=> ! [X55,X54,X56,X57] :
( net_str(net_of_bool_filter(X54,X55,sK44(X56,boole_POSet(X55),X57)),X54)
| ~ upper_relstr_subset(sK44(X56,boole_POSet(X55),X57),boole_POSet(X55))
| ~ filtered_subset(sK44(X56,boole_POSet(X55),X57),boole_POSet(X55))
| empty(sK44(X56,boole_POSet(X55),X57))
| ~ element(X55,powerset(the_carrier(X54)))
| empty(X55)
| ~ one_sorted_str(X54)
| empty_carrier(X54)
| ~ in(X56,a_2_1_yellow19(boole_POSet(X55),X57))
| ~ net_str(X57,boole_POSet(X55))
| empty_carrier(X57)
| ~ one_sorted_str(boole_POSet(X55))
| empty_carrier(boole_POSet(X55)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_966])]) ).
fof(f3166,plain,
( spl61_379
<=> ! [X2,X0,X1] :
( element(sK44(X0,X1,X2),powerset(the_carrier(X1)))
| ~ in(X0,a_2_1_yellow19(X1,X2))
| ~ net_str(X2,X1)
| empty_carrier(X2)
| ~ one_sorted_str(X1)
| empty_carrier(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_379])]) ).
fof(f3358,plain,
( spl61_396
<=> ! [X2,X0,X1] :
( net_str(net_of_bool_filter(X0,X1,X2),X0)
| ~ element(X2,powerset(the_carrier(boole_POSet(X1))))
| ~ upper_relstr_subset(X2,boole_POSet(X1))
| ~ filtered_subset(X2,boole_POSet(X1))
| empty(X2)
| ~ element(X1,powerset(the_carrier(X0)))
| empty(X1)
| ~ one_sorted_str(X0)
| empty_carrier(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_396])]) ).
fof(f3414,plain,
( ! [X56,X54,X57,X55] :
( net_str(net_of_bool_filter(X54,X55,sK44(X56,boole_POSet(X55),X57)),X54)
| ~ upper_relstr_subset(sK44(X56,boole_POSet(X55),X57),boole_POSet(X55))
| ~ filtered_subset(sK44(X56,boole_POSet(X55),X57),boole_POSet(X55))
| empty(sK44(X56,boole_POSet(X55),X57))
| ~ element(X55,powerset(the_carrier(X54)))
| empty(X55)
| ~ one_sorted_str(X54)
| empty_carrier(X54)
| ~ in(X56,a_2_1_yellow19(boole_POSet(X55),X57))
| ~ net_str(X57,boole_POSet(X55))
| empty_carrier(X57)
| ~ one_sorted_str(boole_POSet(X55))
| empty_carrier(boole_POSet(X55)) )
| ~ spl61_379
| ~ spl61_396 ),
inference(resolution,[],[f3359,f3167]) ).
fof(f3167,plain,
( ! [X2,X0,X1] :
( element(sK44(X0,X1,X2),powerset(the_carrier(X1)))
| ~ in(X0,a_2_1_yellow19(X1,X2))
| ~ net_str(X2,X1)
| empty_carrier(X2)
| ~ one_sorted_str(X1)
| empty_carrier(X1) )
| ~ spl61_379 ),
inference(avatar_component_clause,[],[f3166]) ).
fof(f3359,plain,
( ! [X2,X0,X1] :
( ~ element(X2,powerset(the_carrier(boole_POSet(X1))))
| net_str(net_of_bool_filter(X0,X1,X2),X0)
| ~ upper_relstr_subset(X2,boole_POSet(X1))
| ~ filtered_subset(X2,boole_POSet(X1))
| empty(X2)
| ~ element(X1,powerset(the_carrier(X0)))
| empty(X1)
| ~ one_sorted_str(X0)
| empty_carrier(X0) )
| ~ spl61_396 ),
inference(avatar_component_clause,[],[f3358]) ).
fof(f7741,plain,
( spl61_965
| ~ spl61_379
| ~ spl61_395 ),
inference(avatar_split_clause,[],[f3387,f3354,f3166,f7739]) ).
fof(f7739,plain,
( spl61_965
<=> ! [X55,X54,X56,X57] :
( strict_net_str(net_of_bool_filter(X54,X55,sK44(X56,boole_POSet(X55),X57)),X54)
| ~ upper_relstr_subset(sK44(X56,boole_POSet(X55),X57),boole_POSet(X55))
| ~ filtered_subset(sK44(X56,boole_POSet(X55),X57),boole_POSet(X55))
| empty(sK44(X56,boole_POSet(X55),X57))
| ~ element(X55,powerset(the_carrier(X54)))
| empty(X55)
| ~ one_sorted_str(X54)
| empty_carrier(X54)
| ~ in(X56,a_2_1_yellow19(boole_POSet(X55),X57))
| ~ net_str(X57,boole_POSet(X55))
| empty_carrier(X57)
| ~ one_sorted_str(boole_POSet(X55))
| empty_carrier(boole_POSet(X55)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_965])]) ).
fof(f3354,plain,
( spl61_395
<=> ! [X2,X0,X1] :
( strict_net_str(net_of_bool_filter(X0,X1,X2),X0)
| ~ element(X2,powerset(the_carrier(boole_POSet(X1))))
| ~ upper_relstr_subset(X2,boole_POSet(X1))
| ~ filtered_subset(X2,boole_POSet(X1))
| empty(X2)
| ~ element(X1,powerset(the_carrier(X0)))
| empty(X1)
| ~ one_sorted_str(X0)
| empty_carrier(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_395])]) ).
fof(f3387,plain,
( ! [X56,X54,X57,X55] :
( strict_net_str(net_of_bool_filter(X54,X55,sK44(X56,boole_POSet(X55),X57)),X54)
| ~ upper_relstr_subset(sK44(X56,boole_POSet(X55),X57),boole_POSet(X55))
| ~ filtered_subset(sK44(X56,boole_POSet(X55),X57),boole_POSet(X55))
| empty(sK44(X56,boole_POSet(X55),X57))
| ~ element(X55,powerset(the_carrier(X54)))
| empty(X55)
| ~ one_sorted_str(X54)
| empty_carrier(X54)
| ~ in(X56,a_2_1_yellow19(boole_POSet(X55),X57))
| ~ net_str(X57,boole_POSet(X55))
| empty_carrier(X57)
| ~ one_sorted_str(boole_POSet(X55))
| empty_carrier(boole_POSet(X55)) )
| ~ spl61_379
| ~ spl61_395 ),
inference(resolution,[],[f3355,f3167]) ).
fof(f3355,plain,
( ! [X2,X0,X1] :
( ~ element(X2,powerset(the_carrier(boole_POSet(X1))))
| strict_net_str(net_of_bool_filter(X0,X1,X2),X0)
| ~ upper_relstr_subset(X2,boole_POSet(X1))
| ~ filtered_subset(X2,boole_POSet(X1))
| empty(X2)
| ~ element(X1,powerset(the_carrier(X0)))
| empty(X1)
| ~ one_sorted_str(X0)
| empty_carrier(X0) )
| ~ spl61_395 ),
inference(avatar_component_clause,[],[f3354]) ).
fof(f7731,plain,
( spl61_964
| ~ spl61_378
| ~ spl61_397 ),
inference(avatar_split_clause,[],[f3426,f3416,f3162,f7729]) ).
fof(f7729,plain,
( spl61_964
<=> ! [X4,X5,X3] :
( ~ element(filter_of_net_str(X3,X4),powerset(the_carrier(boole_POSet(cast_as_carrier_subset(X3)))))
| sP11(filter_of_net_str(X3,X4),cast_as_carrier_subset(X3),X5)
| ~ upper_relstr_subset(filter_of_net_str(X3,X4),boole_POSet(cast_as_carrier_subset(X3)))
| ~ filtered_subset(filter_of_net_str(X3,X4),boole_POSet(cast_as_carrier_subset(X3)))
| empty(filter_of_net_str(X3,X4))
| ~ element(cast_as_carrier_subset(X3),powerset(the_carrier(X5)))
| empty(cast_as_carrier_subset(X3))
| ~ one_sorted_str(X5)
| empty_carrier(X5)
| ~ net_str(X4,X3)
| ~ directed_relstr(X4)
| ~ transitive_relstr(X4)
| empty_carrier(X4)
| ~ one_sorted_str(X3)
| empty_carrier(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_964])]) ).
fof(f3162,plain,
( spl61_378
<=> ! [X0,X1] :
( proper_element(filter_of_net_str(X0,X1),powerset(the_carrier(boole_POSet(cast_as_carrier_subset(X0)))))
| ~ net_str(X1,X0)
| ~ directed_relstr(X1)
| ~ transitive_relstr(X1)
| empty_carrier(X1)
| ~ one_sorted_str(X0)
| empty_carrier(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_378])]) ).
fof(f3416,plain,
( spl61_397
<=> ! [X2,X0,X1] :
( sP11(X2,X1,X0)
| ~ element(X2,powerset(the_carrier(boole_POSet(X1))))
| ~ proper_element(X2,powerset(the_carrier(boole_POSet(X1))))
| ~ upper_relstr_subset(X2,boole_POSet(X1))
| ~ filtered_subset(X2,boole_POSet(X1))
| empty(X2)
| ~ element(X1,powerset(the_carrier(X0)))
| empty(X1)
| ~ one_sorted_str(X0)
| empty_carrier(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_397])]) ).
fof(f3426,plain,
( ! [X3,X4,X5] :
( ~ element(filter_of_net_str(X3,X4),powerset(the_carrier(boole_POSet(cast_as_carrier_subset(X3)))))
| sP11(filter_of_net_str(X3,X4),cast_as_carrier_subset(X3),X5)
| ~ upper_relstr_subset(filter_of_net_str(X3,X4),boole_POSet(cast_as_carrier_subset(X3)))
| ~ filtered_subset(filter_of_net_str(X3,X4),boole_POSet(cast_as_carrier_subset(X3)))
| empty(filter_of_net_str(X3,X4))
| ~ element(cast_as_carrier_subset(X3),powerset(the_carrier(X5)))
| empty(cast_as_carrier_subset(X3))
| ~ one_sorted_str(X5)
| empty_carrier(X5)
| ~ net_str(X4,X3)
| ~ directed_relstr(X4)
| ~ transitive_relstr(X4)
| empty_carrier(X4)
| ~ one_sorted_str(X3)
| empty_carrier(X3) )
| ~ spl61_378
| ~ spl61_397 ),
inference(resolution,[],[f3417,f3163]) ).
fof(f3163,plain,
( ! [X0,X1] :
( proper_element(filter_of_net_str(X0,X1),powerset(the_carrier(boole_POSet(cast_as_carrier_subset(X0)))))
| ~ net_str(X1,X0)
| ~ directed_relstr(X1)
| ~ transitive_relstr(X1)
| empty_carrier(X1)
| ~ one_sorted_str(X0)
| empty_carrier(X0) )
| ~ spl61_378 ),
inference(avatar_component_clause,[],[f3162]) ).
fof(f3417,plain,
( ! [X2,X0,X1] :
( ~ proper_element(X2,powerset(the_carrier(boole_POSet(X1))))
| ~ element(X2,powerset(the_carrier(boole_POSet(X1))))
| sP11(X2,X1,X0)
| ~ upper_relstr_subset(X2,boole_POSet(X1))
| ~ filtered_subset(X2,boole_POSet(X1))
| empty(X2)
| ~ element(X1,powerset(the_carrier(X0)))
| empty(X1)
| ~ one_sorted_str(X0)
| empty_carrier(X0) )
| ~ spl61_397 ),
inference(avatar_component_clause,[],[f3416]) ).
fof(f7727,plain,
( spl61_963
| ~ spl61_379
| ~ spl61_390 ),
inference(avatar_split_clause,[],[f3348,f3248,f3166,f7725]) ).
fof(f7725,plain,
( spl61_963
<=> ! [X55,X54,X56,X57] :
( transitive_relstr(net_of_bool_filter(X54,X55,sK44(X56,boole_POSet(X55),X57)))
| ~ upper_relstr_subset(sK44(X56,boole_POSet(X55),X57),boole_POSet(X55))
| ~ filtered_subset(sK44(X56,boole_POSet(X55),X57),boole_POSet(X55))
| empty(sK44(X56,boole_POSet(X55),X57))
| ~ element(X55,powerset(the_carrier(X54)))
| empty(X55)
| ~ one_sorted_str(X54)
| empty_carrier(X54)
| ~ in(X56,a_2_1_yellow19(boole_POSet(X55),X57))
| ~ net_str(X57,boole_POSet(X55))
| empty_carrier(X57)
| ~ one_sorted_str(boole_POSet(X55))
| empty_carrier(boole_POSet(X55)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_963])]) ).
fof(f3248,plain,
( spl61_390
<=> ! [X2,X0,X1] :
( transitive_relstr(net_of_bool_filter(X0,X1,X2))
| ~ element(X2,powerset(the_carrier(boole_POSet(X1))))
| ~ upper_relstr_subset(X2,boole_POSet(X1))
| ~ filtered_subset(X2,boole_POSet(X1))
| empty(X2)
| ~ element(X1,powerset(the_carrier(X0)))
| empty(X1)
| ~ one_sorted_str(X0)
| empty_carrier(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_390])]) ).
fof(f3348,plain,
( ! [X56,X54,X57,X55] :
( transitive_relstr(net_of_bool_filter(X54,X55,sK44(X56,boole_POSet(X55),X57)))
| ~ upper_relstr_subset(sK44(X56,boole_POSet(X55),X57),boole_POSet(X55))
| ~ filtered_subset(sK44(X56,boole_POSet(X55),X57),boole_POSet(X55))
| empty(sK44(X56,boole_POSet(X55),X57))
| ~ element(X55,powerset(the_carrier(X54)))
| empty(X55)
| ~ one_sorted_str(X54)
| empty_carrier(X54)
| ~ in(X56,a_2_1_yellow19(boole_POSet(X55),X57))
| ~ net_str(X57,boole_POSet(X55))
| empty_carrier(X57)
| ~ one_sorted_str(boole_POSet(X55))
| empty_carrier(boole_POSet(X55)) )
| ~ spl61_379
| ~ spl61_390 ),
inference(resolution,[],[f3249,f3167]) ).
fof(f3249,plain,
( ! [X2,X0,X1] :
( ~ element(X2,powerset(the_carrier(boole_POSet(X1))))
| transitive_relstr(net_of_bool_filter(X0,X1,X2))
| ~ upper_relstr_subset(X2,boole_POSet(X1))
| ~ filtered_subset(X2,boole_POSet(X1))
| empty(X2)
| ~ element(X1,powerset(the_carrier(X0)))
| empty(X1)
| ~ one_sorted_str(X0)
| empty_carrier(X0) )
| ~ spl61_390 ),
inference(avatar_component_clause,[],[f3248]) ).
fof(f7723,plain,
( spl61_962
| ~ spl61_379
| ~ spl61_389 ),
inference(avatar_split_clause,[],[f3320,f3244,f3166,f7721]) ).
fof(f7721,plain,
( spl61_962
<=> ! [X55,X54,X56,X57] :
( reflexive_relstr(net_of_bool_filter(X54,X55,sK44(X56,boole_POSet(X55),X57)))
| ~ upper_relstr_subset(sK44(X56,boole_POSet(X55),X57),boole_POSet(X55))
| ~ filtered_subset(sK44(X56,boole_POSet(X55),X57),boole_POSet(X55))
| empty(sK44(X56,boole_POSet(X55),X57))
| ~ element(X55,powerset(the_carrier(X54)))
| empty(X55)
| ~ one_sorted_str(X54)
| empty_carrier(X54)
| ~ in(X56,a_2_1_yellow19(boole_POSet(X55),X57))
| ~ net_str(X57,boole_POSet(X55))
| empty_carrier(X57)
| ~ one_sorted_str(boole_POSet(X55))
| empty_carrier(boole_POSet(X55)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_962])]) ).
fof(f3244,plain,
( spl61_389
<=> ! [X2,X0,X1] :
( reflexive_relstr(net_of_bool_filter(X0,X1,X2))
| ~ element(X2,powerset(the_carrier(boole_POSet(X1))))
| ~ upper_relstr_subset(X2,boole_POSet(X1))
| ~ filtered_subset(X2,boole_POSet(X1))
| empty(X2)
| ~ element(X1,powerset(the_carrier(X0)))
| empty(X1)
| ~ one_sorted_str(X0)
| empty_carrier(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_389])]) ).
fof(f3320,plain,
( ! [X56,X54,X57,X55] :
( reflexive_relstr(net_of_bool_filter(X54,X55,sK44(X56,boole_POSet(X55),X57)))
| ~ upper_relstr_subset(sK44(X56,boole_POSet(X55),X57),boole_POSet(X55))
| ~ filtered_subset(sK44(X56,boole_POSet(X55),X57),boole_POSet(X55))
| empty(sK44(X56,boole_POSet(X55),X57))
| ~ element(X55,powerset(the_carrier(X54)))
| empty(X55)
| ~ one_sorted_str(X54)
| empty_carrier(X54)
| ~ in(X56,a_2_1_yellow19(boole_POSet(X55),X57))
| ~ net_str(X57,boole_POSet(X55))
| empty_carrier(X57)
| ~ one_sorted_str(boole_POSet(X55))
| empty_carrier(boole_POSet(X55)) )
| ~ spl61_379
| ~ spl61_389 ),
inference(resolution,[],[f3245,f3167]) ).
fof(f3245,plain,
( ! [X2,X0,X1] :
( ~ element(X2,powerset(the_carrier(boole_POSet(X1))))
| reflexive_relstr(net_of_bool_filter(X0,X1,X2))
| ~ upper_relstr_subset(X2,boole_POSet(X1))
| ~ filtered_subset(X2,boole_POSet(X1))
| empty(X2)
| ~ element(X1,powerset(the_carrier(X0)))
| empty(X1)
| ~ one_sorted_str(X0)
| empty_carrier(X0) )
| ~ spl61_389 ),
inference(avatar_component_clause,[],[f3244]) ).
fof(f7714,plain,
( spl61_961
| ~ spl61_379
| ~ spl61_388 ),
inference(avatar_split_clause,[],[f3293,f3240,f3166,f7712]) ).
fof(f7712,plain,
( spl61_961
<=> ! [X55,X54,X56,X57] :
( ~ empty_carrier(net_of_bool_filter(X54,X55,sK44(X56,boole_POSet(X55),X57)))
| ~ upper_relstr_subset(sK44(X56,boole_POSet(X55),X57),boole_POSet(X55))
| ~ filtered_subset(sK44(X56,boole_POSet(X55),X57),boole_POSet(X55))
| empty(sK44(X56,boole_POSet(X55),X57))
| ~ element(X55,powerset(the_carrier(X54)))
| empty(X55)
| ~ one_sorted_str(X54)
| empty_carrier(X54)
| ~ in(X56,a_2_1_yellow19(boole_POSet(X55),X57))
| ~ net_str(X57,boole_POSet(X55))
| empty_carrier(X57)
| ~ one_sorted_str(boole_POSet(X55))
| empty_carrier(boole_POSet(X55)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_961])]) ).
fof(f3240,plain,
( spl61_388
<=> ! [X2,X0,X1] :
( ~ empty_carrier(net_of_bool_filter(X0,X1,X2))
| ~ element(X2,powerset(the_carrier(boole_POSet(X1))))
| ~ upper_relstr_subset(X2,boole_POSet(X1))
| ~ filtered_subset(X2,boole_POSet(X1))
| empty(X2)
| ~ element(X1,powerset(the_carrier(X0)))
| empty(X1)
| ~ one_sorted_str(X0)
| empty_carrier(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_388])]) ).
fof(f3293,plain,
( ! [X56,X54,X57,X55] :
( ~ empty_carrier(net_of_bool_filter(X54,X55,sK44(X56,boole_POSet(X55),X57)))
| ~ upper_relstr_subset(sK44(X56,boole_POSet(X55),X57),boole_POSet(X55))
| ~ filtered_subset(sK44(X56,boole_POSet(X55),X57),boole_POSet(X55))
| empty(sK44(X56,boole_POSet(X55),X57))
| ~ element(X55,powerset(the_carrier(X54)))
| empty(X55)
| ~ one_sorted_str(X54)
| empty_carrier(X54)
| ~ in(X56,a_2_1_yellow19(boole_POSet(X55),X57))
| ~ net_str(X57,boole_POSet(X55))
| empty_carrier(X57)
| ~ one_sorted_str(boole_POSet(X55))
| empty_carrier(boole_POSet(X55)) )
| ~ spl61_379
| ~ spl61_388 ),
inference(resolution,[],[f3241,f3167]) ).
fof(f3241,plain,
( ! [X2,X0,X1] :
( ~ element(X2,powerset(the_carrier(boole_POSet(X1))))
| ~ empty_carrier(net_of_bool_filter(X0,X1,X2))
| ~ upper_relstr_subset(X2,boole_POSet(X1))
| ~ filtered_subset(X2,boole_POSet(X1))
| empty(X2)
| ~ element(X1,powerset(the_carrier(X0)))
| empty(X1)
| ~ one_sorted_str(X0)
| empty_carrier(X0) )
| ~ spl61_388 ),
inference(avatar_component_clause,[],[f3240]) ).
fof(f7702,plain,
( spl61_960
| ~ spl61_377
| ~ spl61_396 ),
inference(avatar_split_clause,[],[f3390,f3358,f3158,f7700]) ).
fof(f7700,plain,
( spl61_960
<=> ! [X6,X8,X7] :
( net_str(net_of_bool_filter(X6,X7,lim_points_of_net(boole_POSet(X7),X8)),X6)
| ~ upper_relstr_subset(lim_points_of_net(boole_POSet(X7),X8),boole_POSet(X7))
| ~ filtered_subset(lim_points_of_net(boole_POSet(X7),X8),boole_POSet(X7))
| empty(lim_points_of_net(boole_POSet(X7),X8))
| ~ element(X7,powerset(the_carrier(X6)))
| empty(X7)
| ~ one_sorted_str(X6)
| empty_carrier(X6)
| ~ net_str(X8,boole_POSet(X7))
| ~ directed_relstr(X8)
| ~ transitive_relstr(X8)
| empty_carrier(X8)
| ~ top_str(boole_POSet(X7))
| ~ topological_space(boole_POSet(X7))
| empty_carrier(boole_POSet(X7)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_960])]) ).
fof(f3158,plain,
( spl61_377
<=> ! [X0,X1] :
( element(lim_points_of_net(X0,X1),powerset(the_carrier(X0)))
| ~ net_str(X1,X0)
| ~ directed_relstr(X1)
| ~ transitive_relstr(X1)
| empty_carrier(X1)
| ~ top_str(X0)
| ~ topological_space(X0)
| empty_carrier(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_377])]) ).
fof(f3390,plain,
( ! [X8,X6,X7] :
( net_str(net_of_bool_filter(X6,X7,lim_points_of_net(boole_POSet(X7),X8)),X6)
| ~ upper_relstr_subset(lim_points_of_net(boole_POSet(X7),X8),boole_POSet(X7))
| ~ filtered_subset(lim_points_of_net(boole_POSet(X7),X8),boole_POSet(X7))
| empty(lim_points_of_net(boole_POSet(X7),X8))
| ~ element(X7,powerset(the_carrier(X6)))
| empty(X7)
| ~ one_sorted_str(X6)
| empty_carrier(X6)
| ~ net_str(X8,boole_POSet(X7))
| ~ directed_relstr(X8)
| ~ transitive_relstr(X8)
| empty_carrier(X8)
| ~ top_str(boole_POSet(X7))
| ~ topological_space(boole_POSet(X7))
| empty_carrier(boole_POSet(X7)) )
| ~ spl61_377
| ~ spl61_396 ),
inference(resolution,[],[f3359,f3159]) ).
fof(f3159,plain,
( ! [X0,X1] :
( element(lim_points_of_net(X0,X1),powerset(the_carrier(X0)))
| ~ net_str(X1,X0)
| ~ directed_relstr(X1)
| ~ transitive_relstr(X1)
| empty_carrier(X1)
| ~ top_str(X0)
| ~ topological_space(X0)
| empty_carrier(X0) )
| ~ spl61_377 ),
inference(avatar_component_clause,[],[f3158]) ).
fof(f7698,plain,
( spl61_959
| ~ spl61_377
| ~ spl61_395 ),
inference(avatar_split_clause,[],[f3363,f3354,f3158,f7696]) ).
fof(f7696,plain,
( spl61_959
<=> ! [X6,X8,X7] :
( strict_net_str(net_of_bool_filter(X6,X7,lim_points_of_net(boole_POSet(X7),X8)),X6)
| ~ upper_relstr_subset(lim_points_of_net(boole_POSet(X7),X8),boole_POSet(X7))
| ~ filtered_subset(lim_points_of_net(boole_POSet(X7),X8),boole_POSet(X7))
| empty(lim_points_of_net(boole_POSet(X7),X8))
| ~ element(X7,powerset(the_carrier(X6)))
| empty(X7)
| ~ one_sorted_str(X6)
| empty_carrier(X6)
| ~ net_str(X8,boole_POSet(X7))
| ~ directed_relstr(X8)
| ~ transitive_relstr(X8)
| empty_carrier(X8)
| ~ top_str(boole_POSet(X7))
| ~ topological_space(boole_POSet(X7))
| empty_carrier(boole_POSet(X7)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_959])]) ).
fof(f3363,plain,
( ! [X8,X6,X7] :
( strict_net_str(net_of_bool_filter(X6,X7,lim_points_of_net(boole_POSet(X7),X8)),X6)
| ~ upper_relstr_subset(lim_points_of_net(boole_POSet(X7),X8),boole_POSet(X7))
| ~ filtered_subset(lim_points_of_net(boole_POSet(X7),X8),boole_POSet(X7))
| empty(lim_points_of_net(boole_POSet(X7),X8))
| ~ element(X7,powerset(the_carrier(X6)))
| empty(X7)
| ~ one_sorted_str(X6)
| empty_carrier(X6)
| ~ net_str(X8,boole_POSet(X7))
| ~ directed_relstr(X8)
| ~ transitive_relstr(X8)
| empty_carrier(X8)
| ~ top_str(boole_POSet(X7))
| ~ topological_space(boole_POSet(X7))
| empty_carrier(boole_POSet(X7)) )
| ~ spl61_377
| ~ spl61_395 ),
inference(resolution,[],[f3355,f3159]) ).
fof(f7693,plain,
( spl61_958
| ~ spl61_377
| ~ spl61_390 ),
inference(avatar_split_clause,[],[f3324,f3248,f3158,f7691]) ).
fof(f7691,plain,
( spl61_958
<=> ! [X6,X8,X7] :
( transitive_relstr(net_of_bool_filter(X6,X7,lim_points_of_net(boole_POSet(X7),X8)))
| ~ upper_relstr_subset(lim_points_of_net(boole_POSet(X7),X8),boole_POSet(X7))
| ~ filtered_subset(lim_points_of_net(boole_POSet(X7),X8),boole_POSet(X7))
| empty(lim_points_of_net(boole_POSet(X7),X8))
| ~ element(X7,powerset(the_carrier(X6)))
| empty(X7)
| ~ one_sorted_str(X6)
| empty_carrier(X6)
| ~ net_str(X8,boole_POSet(X7))
| ~ directed_relstr(X8)
| ~ transitive_relstr(X8)
| empty_carrier(X8)
| ~ top_str(boole_POSet(X7))
| ~ topological_space(boole_POSet(X7))
| empty_carrier(boole_POSet(X7)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_958])]) ).
fof(f3324,plain,
( ! [X8,X6,X7] :
( transitive_relstr(net_of_bool_filter(X6,X7,lim_points_of_net(boole_POSet(X7),X8)))
| ~ upper_relstr_subset(lim_points_of_net(boole_POSet(X7),X8),boole_POSet(X7))
| ~ filtered_subset(lim_points_of_net(boole_POSet(X7),X8),boole_POSet(X7))
| empty(lim_points_of_net(boole_POSet(X7),X8))
| ~ element(X7,powerset(the_carrier(X6)))
| empty(X7)
| ~ one_sorted_str(X6)
| empty_carrier(X6)
| ~ net_str(X8,boole_POSet(X7))
| ~ directed_relstr(X8)
| ~ transitive_relstr(X8)
| empty_carrier(X8)
| ~ top_str(boole_POSet(X7))
| ~ topological_space(boole_POSet(X7))
| empty_carrier(boole_POSet(X7)) )
| ~ spl61_377
| ~ spl61_390 ),
inference(resolution,[],[f3249,f3159]) ).
fof(f7689,plain,
( spl61_957
| ~ spl61_377
| ~ spl61_389 ),
inference(avatar_split_clause,[],[f3296,f3244,f3158,f7687]) ).
fof(f7687,plain,
( spl61_957
<=> ! [X6,X8,X7] :
( reflexive_relstr(net_of_bool_filter(X6,X7,lim_points_of_net(boole_POSet(X7),X8)))
| ~ upper_relstr_subset(lim_points_of_net(boole_POSet(X7),X8),boole_POSet(X7))
| ~ filtered_subset(lim_points_of_net(boole_POSet(X7),X8),boole_POSet(X7))
| empty(lim_points_of_net(boole_POSet(X7),X8))
| ~ element(X7,powerset(the_carrier(X6)))
| empty(X7)
| ~ one_sorted_str(X6)
| empty_carrier(X6)
| ~ net_str(X8,boole_POSet(X7))
| ~ directed_relstr(X8)
| ~ transitive_relstr(X8)
| empty_carrier(X8)
| ~ top_str(boole_POSet(X7))
| ~ topological_space(boole_POSet(X7))
| empty_carrier(boole_POSet(X7)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_957])]) ).
fof(f3296,plain,
( ! [X8,X6,X7] :
( reflexive_relstr(net_of_bool_filter(X6,X7,lim_points_of_net(boole_POSet(X7),X8)))
| ~ upper_relstr_subset(lim_points_of_net(boole_POSet(X7),X8),boole_POSet(X7))
| ~ filtered_subset(lim_points_of_net(boole_POSet(X7),X8),boole_POSet(X7))
| empty(lim_points_of_net(boole_POSet(X7),X8))
| ~ element(X7,powerset(the_carrier(X6)))
| empty(X7)
| ~ one_sorted_str(X6)
| empty_carrier(X6)
| ~ net_str(X8,boole_POSet(X7))
| ~ directed_relstr(X8)
| ~ transitive_relstr(X8)
| empty_carrier(X8)
| ~ top_str(boole_POSet(X7))
| ~ topological_space(boole_POSet(X7))
| empty_carrier(boole_POSet(X7)) )
| ~ spl61_377
| ~ spl61_389 ),
inference(resolution,[],[f3245,f3159]) ).
fof(f7685,plain,
( spl61_956
| ~ spl61_251
| ~ spl61_533 ),
inference(avatar_split_clause,[],[f4454,f4449,f2080,f7683]) ).
fof(f2080,plain,
( spl61_251
<=> ! [X0,X1] :
( rel_str(X1)
| ~ net_str(X1,X0)
| ~ one_sorted_str(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_251])]) ).
fof(f4454,plain,
( ! [X1] :
( empty_carrier(X1)
| ~ one_sorted_str(X1)
| ~ element(cast_as_carrier_subset(sK12),powerset(the_carrier(X1)))
| rel_str(net_of_bool_filter(X1,cast_as_carrier_subset(sK12),sK13)) )
| ~ spl61_251
| ~ spl61_533 ),
inference(duplicate_literal_removal,[],[f4453]) ).
fof(f4453,plain,
( ! [X1] :
( empty_carrier(X1)
| ~ one_sorted_str(X1)
| ~ element(cast_as_carrier_subset(sK12),powerset(the_carrier(X1)))
| rel_str(net_of_bool_filter(X1,cast_as_carrier_subset(sK12),sK13))
| ~ one_sorted_str(X1) )
| ~ spl61_251
| ~ spl61_533 ),
inference(resolution,[],[f4450,f2081]) ).
fof(f2081,plain,
( ! [X0,X1] :
( ~ net_str(X1,X0)
| rel_str(X1)
| ~ one_sorted_str(X0) )
| ~ spl61_251 ),
inference(avatar_component_clause,[],[f2080]) ).
fof(f7681,plain,
( spl61_955
| ~ spl61_377
| ~ spl61_388 ),
inference(avatar_split_clause,[],[f3269,f3240,f3158,f7679]) ).
fof(f7679,plain,
( spl61_955
<=> ! [X6,X8,X7] :
( ~ empty_carrier(net_of_bool_filter(X6,X7,lim_points_of_net(boole_POSet(X7),X8)))
| ~ upper_relstr_subset(lim_points_of_net(boole_POSet(X7),X8),boole_POSet(X7))
| ~ filtered_subset(lim_points_of_net(boole_POSet(X7),X8),boole_POSet(X7))
| empty(lim_points_of_net(boole_POSet(X7),X8))
| ~ element(X7,powerset(the_carrier(X6)))
| empty(X7)
| ~ one_sorted_str(X6)
| empty_carrier(X6)
| ~ net_str(X8,boole_POSet(X7))
| ~ directed_relstr(X8)
| ~ transitive_relstr(X8)
| empty_carrier(X8)
| ~ top_str(boole_POSet(X7))
| ~ topological_space(boole_POSet(X7))
| empty_carrier(boole_POSet(X7)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_955])]) ).
fof(f3269,plain,
( ! [X8,X6,X7] :
( ~ empty_carrier(net_of_bool_filter(X6,X7,lim_points_of_net(boole_POSet(X7),X8)))
| ~ upper_relstr_subset(lim_points_of_net(boole_POSet(X7),X8),boole_POSet(X7))
| ~ filtered_subset(lim_points_of_net(boole_POSet(X7),X8),boole_POSet(X7))
| empty(lim_points_of_net(boole_POSet(X7),X8))
| ~ element(X7,powerset(the_carrier(X6)))
| empty(X7)
| ~ one_sorted_str(X6)
| empty_carrier(X6)
| ~ net_str(X8,boole_POSet(X7))
| ~ directed_relstr(X8)
| ~ transitive_relstr(X8)
| empty_carrier(X8)
| ~ top_str(boole_POSet(X7))
| ~ topological_space(boole_POSet(X7))
| empty_carrier(boole_POSet(X7)) )
| ~ spl61_377
| ~ spl61_388 ),
inference(resolution,[],[f3241,f3159]) ).
fof(f7673,plain,
( spl61_954
| ~ spl61_275
| ~ spl61_399 ),
inference(avatar_split_clause,[],[f3432,f3428,f2208,f7671]) ).
fof(f7671,plain,
( spl61_954
<=> ! [X0] :
( ~ element(sK25(boole_POSet(cast_as_carrier_subset(X0))),powerset(the_carrier(boole_POSet(cast_as_carrier_subset(X0)))))
| sK25(boole_POSet(cast_as_carrier_subset(X0))) = filter_of_net_str(X0,net_of_bool_filter(X0,cast_as_carrier_subset(X0),sK25(boole_POSet(cast_as_carrier_subset(X0)))))
| ~ upper_relstr_subset(sK25(boole_POSet(cast_as_carrier_subset(X0))),boole_POSet(cast_as_carrier_subset(X0)))
| ~ filtered_subset(sK25(boole_POSet(cast_as_carrier_subset(X0))),boole_POSet(cast_as_carrier_subset(X0)))
| empty(sK25(boole_POSet(cast_as_carrier_subset(X0))))
| ~ one_sorted_str(X0)
| empty_carrier(X0)
| ~ sP6(boole_POSet(cast_as_carrier_subset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_954])]) ).
fof(f2208,plain,
( spl61_275
<=> ! [X0] :
( proper_element(sK25(X0),powerset(the_carrier(X0)))
| ~ sP6(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_275])]) ).
fof(f3428,plain,
( spl61_399
<=> ! [X0,X1] :
( filter_of_net_str(X0,net_of_bool_filter(X0,cast_as_carrier_subset(X0),X1)) = X1
| ~ element(X1,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(X0)))))
| ~ proper_element(X1,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(X0)))))
| ~ upper_relstr_subset(X1,boole_POSet(cast_as_carrier_subset(X0)))
| ~ filtered_subset(X1,boole_POSet(cast_as_carrier_subset(X0)))
| empty(X1)
| ~ one_sorted_str(X0)
| empty_carrier(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_399])]) ).
fof(f3432,plain,
( ! [X0] :
( ~ element(sK25(boole_POSet(cast_as_carrier_subset(X0))),powerset(the_carrier(boole_POSet(cast_as_carrier_subset(X0)))))
| sK25(boole_POSet(cast_as_carrier_subset(X0))) = filter_of_net_str(X0,net_of_bool_filter(X0,cast_as_carrier_subset(X0),sK25(boole_POSet(cast_as_carrier_subset(X0)))))
| ~ upper_relstr_subset(sK25(boole_POSet(cast_as_carrier_subset(X0))),boole_POSet(cast_as_carrier_subset(X0)))
| ~ filtered_subset(sK25(boole_POSet(cast_as_carrier_subset(X0))),boole_POSet(cast_as_carrier_subset(X0)))
| empty(sK25(boole_POSet(cast_as_carrier_subset(X0))))
| ~ one_sorted_str(X0)
| empty_carrier(X0)
| ~ sP6(boole_POSet(cast_as_carrier_subset(X0))) )
| ~ spl61_275
| ~ spl61_399 ),
inference(resolution,[],[f3429,f2209]) ).
fof(f2209,plain,
( ! [X0] :
( proper_element(sK25(X0),powerset(the_carrier(X0)))
| ~ sP6(X0) )
| ~ spl61_275 ),
inference(avatar_component_clause,[],[f2208]) ).
fof(f3429,plain,
( ! [X0,X1] :
( ~ proper_element(X1,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(X0)))))
| ~ element(X1,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(X0)))))
| filter_of_net_str(X0,net_of_bool_filter(X0,cast_as_carrier_subset(X0),X1)) = X1
| ~ upper_relstr_subset(X1,boole_POSet(cast_as_carrier_subset(X0)))
| ~ filtered_subset(X1,boole_POSet(cast_as_carrier_subset(X0)))
| empty(X1)
| ~ one_sorted_str(X0)
| empty_carrier(X0) )
| ~ spl61_399 ),
inference(avatar_component_clause,[],[f3428]) ).
fof(f7664,plain,
( spl61_953
| ~ spl61_378
| ~ spl61_399 ),
inference(avatar_split_clause,[],[f3434,f3428,f3162,f7662]) ).
fof(f7662,plain,
( spl61_953
<=> ! [X2,X1] :
( ~ element(filter_of_net_str(X1,X2),powerset(the_carrier(boole_POSet(cast_as_carrier_subset(X1)))))
| filter_of_net_str(X1,X2) = filter_of_net_str(X1,net_of_bool_filter(X1,cast_as_carrier_subset(X1),filter_of_net_str(X1,X2)))
| ~ upper_relstr_subset(filter_of_net_str(X1,X2),boole_POSet(cast_as_carrier_subset(X1)))
| ~ filtered_subset(filter_of_net_str(X1,X2),boole_POSet(cast_as_carrier_subset(X1)))
| empty(filter_of_net_str(X1,X2))
| ~ one_sorted_str(X1)
| empty_carrier(X1)
| ~ net_str(X2,X1)
| ~ directed_relstr(X2)
| ~ transitive_relstr(X2)
| empty_carrier(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_953])]) ).
fof(f3434,plain,
( ! [X2,X1] :
( ~ element(filter_of_net_str(X1,X2),powerset(the_carrier(boole_POSet(cast_as_carrier_subset(X1)))))
| filter_of_net_str(X1,X2) = filter_of_net_str(X1,net_of_bool_filter(X1,cast_as_carrier_subset(X1),filter_of_net_str(X1,X2)))
| ~ upper_relstr_subset(filter_of_net_str(X1,X2),boole_POSet(cast_as_carrier_subset(X1)))
| ~ filtered_subset(filter_of_net_str(X1,X2),boole_POSet(cast_as_carrier_subset(X1)))
| empty(filter_of_net_str(X1,X2))
| ~ one_sorted_str(X1)
| empty_carrier(X1)
| ~ net_str(X2,X1)
| ~ directed_relstr(X2)
| ~ transitive_relstr(X2)
| empty_carrier(X2) )
| ~ spl61_378
| ~ spl61_399 ),
inference(duplicate_literal_removal,[],[f3433]) ).
fof(f3433,plain,
( ! [X2,X1] :
( ~ element(filter_of_net_str(X1,X2),powerset(the_carrier(boole_POSet(cast_as_carrier_subset(X1)))))
| filter_of_net_str(X1,X2) = filter_of_net_str(X1,net_of_bool_filter(X1,cast_as_carrier_subset(X1),filter_of_net_str(X1,X2)))
| ~ upper_relstr_subset(filter_of_net_str(X1,X2),boole_POSet(cast_as_carrier_subset(X1)))
| ~ filtered_subset(filter_of_net_str(X1,X2),boole_POSet(cast_as_carrier_subset(X1)))
| empty(filter_of_net_str(X1,X2))
| ~ one_sorted_str(X1)
| empty_carrier(X1)
| ~ net_str(X2,X1)
| ~ directed_relstr(X2)
| ~ transitive_relstr(X2)
| empty_carrier(X2)
| ~ one_sorted_str(X1)
| empty_carrier(X1) )
| ~ spl61_378
| ~ spl61_399 ),
inference(resolution,[],[f3429,f3163]) ).
fof(f7650,plain,
( spl61_952
| ~ spl61_371
| ~ spl61_396 ),
inference(avatar_split_clause,[],[f3389,f3358,f3039,f7648]) ).
fof(f7648,plain,
( spl61_952
<=> ! [X4,X5,X3] :
( net_str(net_of_bool_filter(X3,cast_as_carrier_subset(X4),filter_of_net_str(X4,X5)),X3)
| ~ upper_relstr_subset(filter_of_net_str(X4,X5),boole_POSet(cast_as_carrier_subset(X4)))
| ~ filtered_subset(filter_of_net_str(X4,X5),boole_POSet(cast_as_carrier_subset(X4)))
| empty(filter_of_net_str(X4,X5))
| ~ element(cast_as_carrier_subset(X4),powerset(the_carrier(X3)))
| empty(cast_as_carrier_subset(X4))
| ~ one_sorted_str(X3)
| empty_carrier(X3)
| ~ net_str(X5,X4)
| empty_carrier(X5)
| ~ one_sorted_str(X4)
| empty_carrier(X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_952])]) ).
fof(f3039,plain,
( spl61_371
<=> ! [X0,X1] :
( element(filter_of_net_str(X0,X1),powerset(the_carrier(boole_POSet(cast_as_carrier_subset(X0)))))
| ~ net_str(X1,X0)
| empty_carrier(X1)
| ~ one_sorted_str(X0)
| empty_carrier(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_371])]) ).
fof(f3389,plain,
( ! [X3,X4,X5] :
( net_str(net_of_bool_filter(X3,cast_as_carrier_subset(X4),filter_of_net_str(X4,X5)),X3)
| ~ upper_relstr_subset(filter_of_net_str(X4,X5),boole_POSet(cast_as_carrier_subset(X4)))
| ~ filtered_subset(filter_of_net_str(X4,X5),boole_POSet(cast_as_carrier_subset(X4)))
| empty(filter_of_net_str(X4,X5))
| ~ element(cast_as_carrier_subset(X4),powerset(the_carrier(X3)))
| empty(cast_as_carrier_subset(X4))
| ~ one_sorted_str(X3)
| empty_carrier(X3)
| ~ net_str(X5,X4)
| empty_carrier(X5)
| ~ one_sorted_str(X4)
| empty_carrier(X4) )
| ~ spl61_371
| ~ spl61_396 ),
inference(resolution,[],[f3359,f3040]) ).
fof(f3040,plain,
( ! [X0,X1] :
( element(filter_of_net_str(X0,X1),powerset(the_carrier(boole_POSet(cast_as_carrier_subset(X0)))))
| ~ net_str(X1,X0)
| empty_carrier(X1)
| ~ one_sorted_str(X0)
| empty_carrier(X0) )
| ~ spl61_371 ),
inference(avatar_component_clause,[],[f3039]) ).
fof(f7646,plain,
( spl61_951
| ~ spl61_371
| ~ spl61_395 ),
inference(avatar_split_clause,[],[f3362,f3354,f3039,f7644]) ).
fof(f7644,plain,
( spl61_951
<=> ! [X4,X5,X3] :
( strict_net_str(net_of_bool_filter(X3,cast_as_carrier_subset(X4),filter_of_net_str(X4,X5)),X3)
| ~ upper_relstr_subset(filter_of_net_str(X4,X5),boole_POSet(cast_as_carrier_subset(X4)))
| ~ filtered_subset(filter_of_net_str(X4,X5),boole_POSet(cast_as_carrier_subset(X4)))
| empty(filter_of_net_str(X4,X5))
| ~ element(cast_as_carrier_subset(X4),powerset(the_carrier(X3)))
| empty(cast_as_carrier_subset(X4))
| ~ one_sorted_str(X3)
| empty_carrier(X3)
| ~ net_str(X5,X4)
| empty_carrier(X5)
| ~ one_sorted_str(X4)
| empty_carrier(X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_951])]) ).
fof(f3362,plain,
( ! [X3,X4,X5] :
( strict_net_str(net_of_bool_filter(X3,cast_as_carrier_subset(X4),filter_of_net_str(X4,X5)),X3)
| ~ upper_relstr_subset(filter_of_net_str(X4,X5),boole_POSet(cast_as_carrier_subset(X4)))
| ~ filtered_subset(filter_of_net_str(X4,X5),boole_POSet(cast_as_carrier_subset(X4)))
| empty(filter_of_net_str(X4,X5))
| ~ element(cast_as_carrier_subset(X4),powerset(the_carrier(X3)))
| empty(cast_as_carrier_subset(X4))
| ~ one_sorted_str(X3)
| empty_carrier(X3)
| ~ net_str(X5,X4)
| empty_carrier(X5)
| ~ one_sorted_str(X4)
| empty_carrier(X4) )
| ~ spl61_371
| ~ spl61_395 ),
inference(resolution,[],[f3355,f3040]) ).
fof(f7638,plain,
( spl61_950
| ~ spl61_371
| ~ spl61_390 ),
inference(avatar_split_clause,[],[f3323,f3248,f3039,f7636]) ).
fof(f7636,plain,
( spl61_950
<=> ! [X4,X5,X3] :
( transitive_relstr(net_of_bool_filter(X3,cast_as_carrier_subset(X4),filter_of_net_str(X4,X5)))
| ~ upper_relstr_subset(filter_of_net_str(X4,X5),boole_POSet(cast_as_carrier_subset(X4)))
| ~ filtered_subset(filter_of_net_str(X4,X5),boole_POSet(cast_as_carrier_subset(X4)))
| empty(filter_of_net_str(X4,X5))
| ~ element(cast_as_carrier_subset(X4),powerset(the_carrier(X3)))
| empty(cast_as_carrier_subset(X4))
| ~ one_sorted_str(X3)
| empty_carrier(X3)
| ~ net_str(X5,X4)
| empty_carrier(X5)
| ~ one_sorted_str(X4)
| empty_carrier(X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_950])]) ).
fof(f3323,plain,
( ! [X3,X4,X5] :
( transitive_relstr(net_of_bool_filter(X3,cast_as_carrier_subset(X4),filter_of_net_str(X4,X5)))
| ~ upper_relstr_subset(filter_of_net_str(X4,X5),boole_POSet(cast_as_carrier_subset(X4)))
| ~ filtered_subset(filter_of_net_str(X4,X5),boole_POSet(cast_as_carrier_subset(X4)))
| empty(filter_of_net_str(X4,X5))
| ~ element(cast_as_carrier_subset(X4),powerset(the_carrier(X3)))
| empty(cast_as_carrier_subset(X4))
| ~ one_sorted_str(X3)
| empty_carrier(X3)
| ~ net_str(X5,X4)
| empty_carrier(X5)
| ~ one_sorted_str(X4)
| empty_carrier(X4) )
| ~ spl61_371
| ~ spl61_390 ),
inference(resolution,[],[f3249,f3040]) ).
fof(f7634,plain,
( spl61_949
| ~ spl61_371
| ~ spl61_389 ),
inference(avatar_split_clause,[],[f3295,f3244,f3039,f7632]) ).
fof(f7632,plain,
( spl61_949
<=> ! [X4,X5,X3] :
( reflexive_relstr(net_of_bool_filter(X3,cast_as_carrier_subset(X4),filter_of_net_str(X4,X5)))
| ~ upper_relstr_subset(filter_of_net_str(X4,X5),boole_POSet(cast_as_carrier_subset(X4)))
| ~ filtered_subset(filter_of_net_str(X4,X5),boole_POSet(cast_as_carrier_subset(X4)))
| empty(filter_of_net_str(X4,X5))
| ~ element(cast_as_carrier_subset(X4),powerset(the_carrier(X3)))
| empty(cast_as_carrier_subset(X4))
| ~ one_sorted_str(X3)
| empty_carrier(X3)
| ~ net_str(X5,X4)
| empty_carrier(X5)
| ~ one_sorted_str(X4)
| empty_carrier(X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_949])]) ).
fof(f3295,plain,
( ! [X3,X4,X5] :
( reflexive_relstr(net_of_bool_filter(X3,cast_as_carrier_subset(X4),filter_of_net_str(X4,X5)))
| ~ upper_relstr_subset(filter_of_net_str(X4,X5),boole_POSet(cast_as_carrier_subset(X4)))
| ~ filtered_subset(filter_of_net_str(X4,X5),boole_POSet(cast_as_carrier_subset(X4)))
| empty(filter_of_net_str(X4,X5))
| ~ element(cast_as_carrier_subset(X4),powerset(the_carrier(X3)))
| empty(cast_as_carrier_subset(X4))
| ~ one_sorted_str(X3)
| empty_carrier(X3)
| ~ net_str(X5,X4)
| empty_carrier(X5)
| ~ one_sorted_str(X4)
| empty_carrier(X4) )
| ~ spl61_371
| ~ spl61_389 ),
inference(resolution,[],[f3245,f3040]) ).
fof(f7630,plain,
( spl61_948
| ~ spl61_371
| ~ spl61_388 ),
inference(avatar_split_clause,[],[f3268,f3240,f3039,f7628]) ).
fof(f7628,plain,
( spl61_948
<=> ! [X4,X5,X3] :
( ~ empty_carrier(net_of_bool_filter(X3,cast_as_carrier_subset(X4),filter_of_net_str(X4,X5)))
| ~ upper_relstr_subset(filter_of_net_str(X4,X5),boole_POSet(cast_as_carrier_subset(X4)))
| ~ filtered_subset(filter_of_net_str(X4,X5),boole_POSet(cast_as_carrier_subset(X4)))
| empty(filter_of_net_str(X4,X5))
| ~ element(cast_as_carrier_subset(X4),powerset(the_carrier(X3)))
| empty(cast_as_carrier_subset(X4))
| ~ one_sorted_str(X3)
| empty_carrier(X3)
| ~ net_str(X5,X4)
| empty_carrier(X5)
| ~ one_sorted_str(X4)
| empty_carrier(X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_948])]) ).
fof(f3268,plain,
( ! [X3,X4,X5] :
( ~ empty_carrier(net_of_bool_filter(X3,cast_as_carrier_subset(X4),filter_of_net_str(X4,X5)))
| ~ upper_relstr_subset(filter_of_net_str(X4,X5),boole_POSet(cast_as_carrier_subset(X4)))
| ~ filtered_subset(filter_of_net_str(X4,X5),boole_POSet(cast_as_carrier_subset(X4)))
| empty(filter_of_net_str(X4,X5))
| ~ element(cast_as_carrier_subset(X4),powerset(the_carrier(X3)))
| empty(cast_as_carrier_subset(X4))
| ~ one_sorted_str(X3)
| empty_carrier(X3)
| ~ net_str(X5,X4)
| empty_carrier(X5)
| ~ one_sorted_str(X4)
| empty_carrier(X4) )
| ~ spl61_371
| ~ spl61_388 ),
inference(resolution,[],[f3241,f3040]) ).
fof(f7610,plain,
( spl61_947
| ~ spl61_357
| ~ spl61_396 ),
inference(avatar_split_clause,[],[f3406,f3358,f2814,f7608]) ).
fof(f7608,plain,
( spl61_947
<=> ! [X38,X39] :
( net_str(net_of_bool_filter(X38,X39,sK32(boole_POSet(X39))),X38)
| ~ upper_relstr_subset(sK32(boole_POSet(X39)),boole_POSet(X39))
| ~ filtered_subset(sK32(boole_POSet(X39)),boole_POSet(X39))
| empty(sK32(boole_POSet(X39)))
| ~ element(X39,powerset(the_carrier(X38)))
| empty(X39)
| ~ one_sorted_str(X38)
| empty_carrier(X38)
| ~ rel_str(boole_POSet(X39))
| ~ transitive_relstr(boole_POSet(X39))
| ~ reflexive_relstr(boole_POSet(X39))
| empty_carrier(boole_POSet(X39)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_947])]) ).
fof(f2814,plain,
( spl61_357
<=> ! [X0] :
( element(sK32(X0),powerset(the_carrier(X0)))
| ~ rel_str(X0)
| ~ transitive_relstr(X0)
| ~ reflexive_relstr(X0)
| empty_carrier(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_357])]) ).
fof(f3406,plain,
( ! [X38,X39] :
( net_str(net_of_bool_filter(X38,X39,sK32(boole_POSet(X39))),X38)
| ~ upper_relstr_subset(sK32(boole_POSet(X39)),boole_POSet(X39))
| ~ filtered_subset(sK32(boole_POSet(X39)),boole_POSet(X39))
| empty(sK32(boole_POSet(X39)))
| ~ element(X39,powerset(the_carrier(X38)))
| empty(X39)
| ~ one_sorted_str(X38)
| empty_carrier(X38)
| ~ rel_str(boole_POSet(X39))
| ~ transitive_relstr(boole_POSet(X39))
| ~ reflexive_relstr(boole_POSet(X39))
| empty_carrier(boole_POSet(X39)) )
| ~ spl61_357
| ~ spl61_396 ),
inference(resolution,[],[f3359,f2815]) ).
fof(f2815,plain,
( ! [X0] :
( element(sK32(X0),powerset(the_carrier(X0)))
| ~ rel_str(X0)
| ~ transitive_relstr(X0)
| ~ reflexive_relstr(X0)
| empty_carrier(X0) )
| ~ spl61_357 ),
inference(avatar_component_clause,[],[f2814]) ).
fof(f7605,plain,
( spl61_946
| ~ spl61_356
| ~ spl61_396 ),
inference(avatar_split_clause,[],[f3405,f3358,f2810,f7603]) ).
fof(f7603,plain,
( spl61_946
<=> ! [X36,X37] :
( net_str(net_of_bool_filter(X36,X37,sK31(boole_POSet(X37))),X36)
| ~ upper_relstr_subset(sK31(boole_POSet(X37)),boole_POSet(X37))
| ~ filtered_subset(sK31(boole_POSet(X37)),boole_POSet(X37))
| empty(sK31(boole_POSet(X37)))
| ~ element(X37,powerset(the_carrier(X36)))
| empty(X37)
| ~ one_sorted_str(X36)
| empty_carrier(X36)
| ~ rel_str(boole_POSet(X37))
| ~ transitive_relstr(boole_POSet(X37))
| ~ reflexive_relstr(boole_POSet(X37))
| empty_carrier(boole_POSet(X37)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_946])]) ).
fof(f2810,plain,
( spl61_356
<=> ! [X0] :
( element(sK31(X0),powerset(the_carrier(X0)))
| ~ rel_str(X0)
| ~ transitive_relstr(X0)
| ~ reflexive_relstr(X0)
| empty_carrier(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_356])]) ).
fof(f3405,plain,
( ! [X36,X37] :
( net_str(net_of_bool_filter(X36,X37,sK31(boole_POSet(X37))),X36)
| ~ upper_relstr_subset(sK31(boole_POSet(X37)),boole_POSet(X37))
| ~ filtered_subset(sK31(boole_POSet(X37)),boole_POSet(X37))
| empty(sK31(boole_POSet(X37)))
| ~ element(X37,powerset(the_carrier(X36)))
| empty(X37)
| ~ one_sorted_str(X36)
| empty_carrier(X36)
| ~ rel_str(boole_POSet(X37))
| ~ transitive_relstr(boole_POSet(X37))
| ~ reflexive_relstr(boole_POSet(X37))
| empty_carrier(boole_POSet(X37)) )
| ~ spl61_356
| ~ spl61_396 ),
inference(resolution,[],[f3359,f2811]) ).
fof(f2811,plain,
( ! [X0] :
( element(sK31(X0),powerset(the_carrier(X0)))
| ~ rel_str(X0)
| ~ transitive_relstr(X0)
| ~ reflexive_relstr(X0)
| empty_carrier(X0) )
| ~ spl61_356 ),
inference(avatar_component_clause,[],[f2810]) ).
fof(f7601,plain,
( spl61_945
| ~ spl61_357
| ~ spl61_395 ),
inference(avatar_split_clause,[],[f3379,f3354,f2814,f7599]) ).
fof(f7599,plain,
( spl61_945
<=> ! [X38,X39] :
( strict_net_str(net_of_bool_filter(X38,X39,sK32(boole_POSet(X39))),X38)
| ~ upper_relstr_subset(sK32(boole_POSet(X39)),boole_POSet(X39))
| ~ filtered_subset(sK32(boole_POSet(X39)),boole_POSet(X39))
| empty(sK32(boole_POSet(X39)))
| ~ element(X39,powerset(the_carrier(X38)))
| empty(X39)
| ~ one_sorted_str(X38)
| empty_carrier(X38)
| ~ rel_str(boole_POSet(X39))
| ~ transitive_relstr(boole_POSet(X39))
| ~ reflexive_relstr(boole_POSet(X39))
| empty_carrier(boole_POSet(X39)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_945])]) ).
fof(f3379,plain,
( ! [X38,X39] :
( strict_net_str(net_of_bool_filter(X38,X39,sK32(boole_POSet(X39))),X38)
| ~ upper_relstr_subset(sK32(boole_POSet(X39)),boole_POSet(X39))
| ~ filtered_subset(sK32(boole_POSet(X39)),boole_POSet(X39))
| empty(sK32(boole_POSet(X39)))
| ~ element(X39,powerset(the_carrier(X38)))
| empty(X39)
| ~ one_sorted_str(X38)
| empty_carrier(X38)
| ~ rel_str(boole_POSet(X39))
| ~ transitive_relstr(boole_POSet(X39))
| ~ reflexive_relstr(boole_POSet(X39))
| empty_carrier(boole_POSet(X39)) )
| ~ spl61_357
| ~ spl61_395 ),
inference(resolution,[],[f3355,f2815]) ).
fof(f7597,plain,
( spl61_944
| ~ spl61_356
| ~ spl61_395 ),
inference(avatar_split_clause,[],[f3378,f3354,f2810,f7595]) ).
fof(f7595,plain,
( spl61_944
<=> ! [X36,X37] :
( strict_net_str(net_of_bool_filter(X36,X37,sK31(boole_POSet(X37))),X36)
| ~ upper_relstr_subset(sK31(boole_POSet(X37)),boole_POSet(X37))
| ~ filtered_subset(sK31(boole_POSet(X37)),boole_POSet(X37))
| empty(sK31(boole_POSet(X37)))
| ~ element(X37,powerset(the_carrier(X36)))
| empty(X37)
| ~ one_sorted_str(X36)
| empty_carrier(X36)
| ~ rel_str(boole_POSet(X37))
| ~ transitive_relstr(boole_POSet(X37))
| ~ reflexive_relstr(boole_POSet(X37))
| empty_carrier(boole_POSet(X37)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_944])]) ).
fof(f3378,plain,
( ! [X36,X37] :
( strict_net_str(net_of_bool_filter(X36,X37,sK31(boole_POSet(X37))),X36)
| ~ upper_relstr_subset(sK31(boole_POSet(X37)),boole_POSet(X37))
| ~ filtered_subset(sK31(boole_POSet(X37)),boole_POSet(X37))
| empty(sK31(boole_POSet(X37)))
| ~ element(X37,powerset(the_carrier(X36)))
| empty(X37)
| ~ one_sorted_str(X36)
| empty_carrier(X36)
| ~ rel_str(boole_POSet(X37))
| ~ transitive_relstr(boole_POSet(X37))
| ~ reflexive_relstr(boole_POSet(X37))
| empty_carrier(boole_POSet(X37)) )
| ~ spl61_356
| ~ spl61_395 ),
inference(resolution,[],[f3355,f2811]) ).
fof(f7591,plain,
( spl61_943
| ~ spl61_357
| ~ spl61_390 ),
inference(avatar_split_clause,[],[f3340,f3248,f2814,f7589]) ).
fof(f7589,plain,
( spl61_943
<=> ! [X38,X39] :
( transitive_relstr(net_of_bool_filter(X38,X39,sK32(boole_POSet(X39))))
| ~ upper_relstr_subset(sK32(boole_POSet(X39)),boole_POSet(X39))
| ~ filtered_subset(sK32(boole_POSet(X39)),boole_POSet(X39))
| empty(sK32(boole_POSet(X39)))
| ~ element(X39,powerset(the_carrier(X38)))
| empty(X39)
| ~ one_sorted_str(X38)
| empty_carrier(X38)
| ~ rel_str(boole_POSet(X39))
| ~ transitive_relstr(boole_POSet(X39))
| ~ reflexive_relstr(boole_POSet(X39))
| empty_carrier(boole_POSet(X39)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_943])]) ).
fof(f3340,plain,
( ! [X38,X39] :
( transitive_relstr(net_of_bool_filter(X38,X39,sK32(boole_POSet(X39))))
| ~ upper_relstr_subset(sK32(boole_POSet(X39)),boole_POSet(X39))
| ~ filtered_subset(sK32(boole_POSet(X39)),boole_POSet(X39))
| empty(sK32(boole_POSet(X39)))
| ~ element(X39,powerset(the_carrier(X38)))
| empty(X39)
| ~ one_sorted_str(X38)
| empty_carrier(X38)
| ~ rel_str(boole_POSet(X39))
| ~ transitive_relstr(boole_POSet(X39))
| ~ reflexive_relstr(boole_POSet(X39))
| empty_carrier(boole_POSet(X39)) )
| ~ spl61_357
| ~ spl61_390 ),
inference(resolution,[],[f3249,f2815]) ).
fof(f7587,plain,
( spl61_942
| ~ spl61_356
| ~ spl61_390 ),
inference(avatar_split_clause,[],[f3339,f3248,f2810,f7585]) ).
fof(f7585,plain,
( spl61_942
<=> ! [X36,X37] :
( transitive_relstr(net_of_bool_filter(X36,X37,sK31(boole_POSet(X37))))
| ~ upper_relstr_subset(sK31(boole_POSet(X37)),boole_POSet(X37))
| ~ filtered_subset(sK31(boole_POSet(X37)),boole_POSet(X37))
| empty(sK31(boole_POSet(X37)))
| ~ element(X37,powerset(the_carrier(X36)))
| empty(X37)
| ~ one_sorted_str(X36)
| empty_carrier(X36)
| ~ rel_str(boole_POSet(X37))
| ~ transitive_relstr(boole_POSet(X37))
| ~ reflexive_relstr(boole_POSet(X37))
| empty_carrier(boole_POSet(X37)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_942])]) ).
fof(f3339,plain,
( ! [X36,X37] :
( transitive_relstr(net_of_bool_filter(X36,X37,sK31(boole_POSet(X37))))
| ~ upper_relstr_subset(sK31(boole_POSet(X37)),boole_POSet(X37))
| ~ filtered_subset(sK31(boole_POSet(X37)),boole_POSet(X37))
| empty(sK31(boole_POSet(X37)))
| ~ element(X37,powerset(the_carrier(X36)))
| empty(X37)
| ~ one_sorted_str(X36)
| empty_carrier(X36)
| ~ rel_str(boole_POSet(X37))
| ~ transitive_relstr(boole_POSet(X37))
| ~ reflexive_relstr(boole_POSet(X37))
| empty_carrier(boole_POSet(X37)) )
| ~ spl61_356
| ~ spl61_390 ),
inference(resolution,[],[f3249,f2811]) ).
fof(f7583,plain,
( spl61_941
| ~ spl61_357
| ~ spl61_389 ),
inference(avatar_split_clause,[],[f3312,f3244,f2814,f7581]) ).
fof(f7581,plain,
( spl61_941
<=> ! [X38,X39] :
( reflexive_relstr(net_of_bool_filter(X38,X39,sK32(boole_POSet(X39))))
| ~ upper_relstr_subset(sK32(boole_POSet(X39)),boole_POSet(X39))
| ~ filtered_subset(sK32(boole_POSet(X39)),boole_POSet(X39))
| empty(sK32(boole_POSet(X39)))
| ~ element(X39,powerset(the_carrier(X38)))
| empty(X39)
| ~ one_sorted_str(X38)
| empty_carrier(X38)
| ~ rel_str(boole_POSet(X39))
| ~ transitive_relstr(boole_POSet(X39))
| ~ reflexive_relstr(boole_POSet(X39))
| empty_carrier(boole_POSet(X39)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_941])]) ).
fof(f3312,plain,
( ! [X38,X39] :
( reflexive_relstr(net_of_bool_filter(X38,X39,sK32(boole_POSet(X39))))
| ~ upper_relstr_subset(sK32(boole_POSet(X39)),boole_POSet(X39))
| ~ filtered_subset(sK32(boole_POSet(X39)),boole_POSet(X39))
| empty(sK32(boole_POSet(X39)))
| ~ element(X39,powerset(the_carrier(X38)))
| empty(X39)
| ~ one_sorted_str(X38)
| empty_carrier(X38)
| ~ rel_str(boole_POSet(X39))
| ~ transitive_relstr(boole_POSet(X39))
| ~ reflexive_relstr(boole_POSet(X39))
| empty_carrier(boole_POSet(X39)) )
| ~ spl61_357
| ~ spl61_389 ),
inference(resolution,[],[f3245,f2815]) ).
fof(f7579,plain,
( spl61_940
| ~ spl61_356
| ~ spl61_389 ),
inference(avatar_split_clause,[],[f3311,f3244,f2810,f7577]) ).
fof(f7577,plain,
( spl61_940
<=> ! [X36,X37] :
( reflexive_relstr(net_of_bool_filter(X36,X37,sK31(boole_POSet(X37))))
| ~ upper_relstr_subset(sK31(boole_POSet(X37)),boole_POSet(X37))
| ~ filtered_subset(sK31(boole_POSet(X37)),boole_POSet(X37))
| empty(sK31(boole_POSet(X37)))
| ~ element(X37,powerset(the_carrier(X36)))
| empty(X37)
| ~ one_sorted_str(X36)
| empty_carrier(X36)
| ~ rel_str(boole_POSet(X37))
| ~ transitive_relstr(boole_POSet(X37))
| ~ reflexive_relstr(boole_POSet(X37))
| empty_carrier(boole_POSet(X37)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_940])]) ).
fof(f3311,plain,
( ! [X36,X37] :
( reflexive_relstr(net_of_bool_filter(X36,X37,sK31(boole_POSet(X37))))
| ~ upper_relstr_subset(sK31(boole_POSet(X37)),boole_POSet(X37))
| ~ filtered_subset(sK31(boole_POSet(X37)),boole_POSet(X37))
| empty(sK31(boole_POSet(X37)))
| ~ element(X37,powerset(the_carrier(X36)))
| empty(X37)
| ~ one_sorted_str(X36)
| empty_carrier(X36)
| ~ rel_str(boole_POSet(X37))
| ~ transitive_relstr(boole_POSet(X37))
| ~ reflexive_relstr(boole_POSet(X37))
| empty_carrier(boole_POSet(X37)) )
| ~ spl61_356
| ~ spl61_389 ),
inference(resolution,[],[f3245,f2811]) ).
fof(f7575,plain,
( spl61_939
| ~ spl61_357
| ~ spl61_388 ),
inference(avatar_split_clause,[],[f3285,f3240,f2814,f7573]) ).
fof(f7573,plain,
( spl61_939
<=> ! [X38,X39] :
( ~ empty_carrier(net_of_bool_filter(X38,X39,sK32(boole_POSet(X39))))
| ~ upper_relstr_subset(sK32(boole_POSet(X39)),boole_POSet(X39))
| ~ filtered_subset(sK32(boole_POSet(X39)),boole_POSet(X39))
| empty(sK32(boole_POSet(X39)))
| ~ element(X39,powerset(the_carrier(X38)))
| empty(X39)
| ~ one_sorted_str(X38)
| empty_carrier(X38)
| ~ rel_str(boole_POSet(X39))
| ~ transitive_relstr(boole_POSet(X39))
| ~ reflexive_relstr(boole_POSet(X39))
| empty_carrier(boole_POSet(X39)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_939])]) ).
fof(f3285,plain,
( ! [X38,X39] :
( ~ empty_carrier(net_of_bool_filter(X38,X39,sK32(boole_POSet(X39))))
| ~ upper_relstr_subset(sK32(boole_POSet(X39)),boole_POSet(X39))
| ~ filtered_subset(sK32(boole_POSet(X39)),boole_POSet(X39))
| empty(sK32(boole_POSet(X39)))
| ~ element(X39,powerset(the_carrier(X38)))
| empty(X39)
| ~ one_sorted_str(X38)
| empty_carrier(X38)
| ~ rel_str(boole_POSet(X39))
| ~ transitive_relstr(boole_POSet(X39))
| ~ reflexive_relstr(boole_POSet(X39))
| empty_carrier(boole_POSet(X39)) )
| ~ spl61_357
| ~ spl61_388 ),
inference(resolution,[],[f3241,f2815]) ).
fof(f7571,plain,
( spl61_938
| ~ spl61_356
| ~ spl61_388 ),
inference(avatar_split_clause,[],[f3284,f3240,f2810,f7569]) ).
fof(f7569,plain,
( spl61_938
<=> ! [X36,X37] :
( ~ empty_carrier(net_of_bool_filter(X36,X37,sK31(boole_POSet(X37))))
| ~ upper_relstr_subset(sK31(boole_POSet(X37)),boole_POSet(X37))
| ~ filtered_subset(sK31(boole_POSet(X37)),boole_POSet(X37))
| empty(sK31(boole_POSet(X37)))
| ~ element(X37,powerset(the_carrier(X36)))
| empty(X37)
| ~ one_sorted_str(X36)
| empty_carrier(X36)
| ~ rel_str(boole_POSet(X37))
| ~ transitive_relstr(boole_POSet(X37))
| ~ reflexive_relstr(boole_POSet(X37))
| empty_carrier(boole_POSet(X37)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_938])]) ).
fof(f3284,plain,
( ! [X36,X37] :
( ~ empty_carrier(net_of_bool_filter(X36,X37,sK31(boole_POSet(X37))))
| ~ upper_relstr_subset(sK31(boole_POSet(X37)),boole_POSet(X37))
| ~ filtered_subset(sK31(boole_POSet(X37)),boole_POSet(X37))
| empty(sK31(boole_POSet(X37)))
| ~ element(X37,powerset(the_carrier(X36)))
| empty(X37)
| ~ one_sorted_str(X36)
| empty_carrier(X36)
| ~ rel_str(boole_POSet(X37))
| ~ transitive_relstr(boole_POSet(X37))
| ~ reflexive_relstr(boole_POSet(X37))
| empty_carrier(boole_POSet(X37)) )
| ~ spl61_356
| ~ spl61_388 ),
inference(resolution,[],[f3241,f2811]) ).
fof(f7547,plain,
( spl61_937
| ~ spl61_275
| ~ spl61_397 ),
inference(avatar_split_clause,[],[f3425,f3416,f2208,f7545]) ).
fof(f7545,plain,
( spl61_937
<=> ! [X2,X1] :
( ~ element(sK25(boole_POSet(X1)),powerset(the_carrier(boole_POSet(X1))))
| sP11(sK25(boole_POSet(X1)),X1,X2)
| ~ upper_relstr_subset(sK25(boole_POSet(X1)),boole_POSet(X1))
| ~ filtered_subset(sK25(boole_POSet(X1)),boole_POSet(X1))
| empty(sK25(boole_POSet(X1)))
| ~ element(X1,powerset(the_carrier(X2)))
| empty(X1)
| ~ one_sorted_str(X2)
| empty_carrier(X2)
| ~ sP6(boole_POSet(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_937])]) ).
fof(f3425,plain,
( ! [X2,X1] :
( ~ element(sK25(boole_POSet(X1)),powerset(the_carrier(boole_POSet(X1))))
| sP11(sK25(boole_POSet(X1)),X1,X2)
| ~ upper_relstr_subset(sK25(boole_POSet(X1)),boole_POSet(X1))
| ~ filtered_subset(sK25(boole_POSet(X1)),boole_POSet(X1))
| empty(sK25(boole_POSet(X1)))
| ~ element(X1,powerset(the_carrier(X2)))
| empty(X1)
| ~ one_sorted_str(X2)
| empty_carrier(X2)
| ~ sP6(boole_POSet(X1)) )
| ~ spl61_275
| ~ spl61_397 ),
inference(resolution,[],[f3417,f2209]) ).
fof(f7543,plain,
( spl61_936
| ~ spl61_342
| ~ spl61_396 ),
inference(avatar_split_clause,[],[f3401,f3358,f2689,f7541]) ).
fof(f7541,plain,
( spl61_936
<=> ! [X29,X28] :
( net_str(net_of_bool_filter(X28,X29,sK27(boole_POSet(X29))),X28)
| ~ upper_relstr_subset(sK27(boole_POSet(X29)),boole_POSet(X29))
| ~ filtered_subset(sK27(boole_POSet(X29)),boole_POSet(X29))
| empty(sK27(boole_POSet(X29)))
| ~ element(X29,powerset(the_carrier(X28)))
| empty(X29)
| ~ one_sorted_str(X28)
| empty_carrier(X28)
| ~ top_str(boole_POSet(X29))
| ~ topological_space(boole_POSet(X29))
| empty_carrier(boole_POSet(X29)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_936])]) ).
fof(f2689,plain,
( spl61_342
<=> ! [X0] :
( element(sK27(X0),powerset(the_carrier(X0)))
| ~ top_str(X0)
| ~ topological_space(X0)
| empty_carrier(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_342])]) ).
fof(f3401,plain,
( ! [X28,X29] :
( net_str(net_of_bool_filter(X28,X29,sK27(boole_POSet(X29))),X28)
| ~ upper_relstr_subset(sK27(boole_POSet(X29)),boole_POSet(X29))
| ~ filtered_subset(sK27(boole_POSet(X29)),boole_POSet(X29))
| empty(sK27(boole_POSet(X29)))
| ~ element(X29,powerset(the_carrier(X28)))
| empty(X29)
| ~ one_sorted_str(X28)
| empty_carrier(X28)
| ~ top_str(boole_POSet(X29))
| ~ topological_space(boole_POSet(X29))
| empty_carrier(boole_POSet(X29)) )
| ~ spl61_342
| ~ spl61_396 ),
inference(resolution,[],[f3359,f2690]) ).
fof(f2690,plain,
( ! [X0] :
( element(sK27(X0),powerset(the_carrier(X0)))
| ~ top_str(X0)
| ~ topological_space(X0)
| empty_carrier(X0) )
| ~ spl61_342 ),
inference(avatar_component_clause,[],[f2689]) ).
fof(f7539,plain,
( spl61_935
| ~ spl61_341
| ~ spl61_396 ),
inference(avatar_split_clause,[],[f3400,f3358,f2685,f7537]) ).
fof(f7537,plain,
( spl61_935
<=> ! [X27,X26] :
( net_str(net_of_bool_filter(X26,X27,sK26(boole_POSet(X27))),X26)
| ~ upper_relstr_subset(sK26(boole_POSet(X27)),boole_POSet(X27))
| ~ filtered_subset(sK26(boole_POSet(X27)),boole_POSet(X27))
| empty(sK26(boole_POSet(X27)))
| ~ element(X27,powerset(the_carrier(X26)))
| empty(X27)
| ~ one_sorted_str(X26)
| empty_carrier(X26)
| ~ top_str(boole_POSet(X27))
| ~ topological_space(boole_POSet(X27))
| empty_carrier(boole_POSet(X27)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_935])]) ).
fof(f2685,plain,
( spl61_341
<=> ! [X0] :
( element(sK26(X0),powerset(the_carrier(X0)))
| ~ top_str(X0)
| ~ topological_space(X0)
| empty_carrier(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_341])]) ).
fof(f3400,plain,
( ! [X26,X27] :
( net_str(net_of_bool_filter(X26,X27,sK26(boole_POSet(X27))),X26)
| ~ upper_relstr_subset(sK26(boole_POSet(X27)),boole_POSet(X27))
| ~ filtered_subset(sK26(boole_POSet(X27)),boole_POSet(X27))
| empty(sK26(boole_POSet(X27)))
| ~ element(X27,powerset(the_carrier(X26)))
| empty(X27)
| ~ one_sorted_str(X26)
| empty_carrier(X26)
| ~ top_str(boole_POSet(X27))
| ~ topological_space(boole_POSet(X27))
| empty_carrier(boole_POSet(X27)) )
| ~ spl61_341
| ~ spl61_396 ),
inference(resolution,[],[f3359,f2686]) ).
fof(f2686,plain,
( ! [X0] :
( element(sK26(X0),powerset(the_carrier(X0)))
| ~ top_str(X0)
| ~ topological_space(X0)
| empty_carrier(X0) )
| ~ spl61_341 ),
inference(avatar_component_clause,[],[f2685]) ).
fof(f7535,plain,
( spl61_934
| ~ spl61_342
| ~ spl61_395 ),
inference(avatar_split_clause,[],[f3374,f3354,f2689,f7533]) ).
fof(f7533,plain,
( spl61_934
<=> ! [X29,X28] :
( strict_net_str(net_of_bool_filter(X28,X29,sK27(boole_POSet(X29))),X28)
| ~ upper_relstr_subset(sK27(boole_POSet(X29)),boole_POSet(X29))
| ~ filtered_subset(sK27(boole_POSet(X29)),boole_POSet(X29))
| empty(sK27(boole_POSet(X29)))
| ~ element(X29,powerset(the_carrier(X28)))
| empty(X29)
| ~ one_sorted_str(X28)
| empty_carrier(X28)
| ~ top_str(boole_POSet(X29))
| ~ topological_space(boole_POSet(X29))
| empty_carrier(boole_POSet(X29)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_934])]) ).
fof(f3374,plain,
( ! [X28,X29] :
( strict_net_str(net_of_bool_filter(X28,X29,sK27(boole_POSet(X29))),X28)
| ~ upper_relstr_subset(sK27(boole_POSet(X29)),boole_POSet(X29))
| ~ filtered_subset(sK27(boole_POSet(X29)),boole_POSet(X29))
| empty(sK27(boole_POSet(X29)))
| ~ element(X29,powerset(the_carrier(X28)))
| empty(X29)
| ~ one_sorted_str(X28)
| empty_carrier(X28)
| ~ top_str(boole_POSet(X29))
| ~ topological_space(boole_POSet(X29))
| empty_carrier(boole_POSet(X29)) )
| ~ spl61_342
| ~ spl61_395 ),
inference(resolution,[],[f3355,f2690]) ).
fof(f7531,plain,
( spl61_933
| ~ spl61_341
| ~ spl61_395 ),
inference(avatar_split_clause,[],[f3373,f3354,f2685,f7529]) ).
fof(f7529,plain,
( spl61_933
<=> ! [X27,X26] :
( strict_net_str(net_of_bool_filter(X26,X27,sK26(boole_POSet(X27))),X26)
| ~ upper_relstr_subset(sK26(boole_POSet(X27)),boole_POSet(X27))
| ~ filtered_subset(sK26(boole_POSet(X27)),boole_POSet(X27))
| empty(sK26(boole_POSet(X27)))
| ~ element(X27,powerset(the_carrier(X26)))
| empty(X27)
| ~ one_sorted_str(X26)
| empty_carrier(X26)
| ~ top_str(boole_POSet(X27))
| ~ topological_space(boole_POSet(X27))
| empty_carrier(boole_POSet(X27)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_933])]) ).
fof(f3373,plain,
( ! [X26,X27] :
( strict_net_str(net_of_bool_filter(X26,X27,sK26(boole_POSet(X27))),X26)
| ~ upper_relstr_subset(sK26(boole_POSet(X27)),boole_POSet(X27))
| ~ filtered_subset(sK26(boole_POSet(X27)),boole_POSet(X27))
| empty(sK26(boole_POSet(X27)))
| ~ element(X27,powerset(the_carrier(X26)))
| empty(X27)
| ~ one_sorted_str(X26)
| empty_carrier(X26)
| ~ top_str(boole_POSet(X27))
| ~ topological_space(boole_POSet(X27))
| empty_carrier(boole_POSet(X27)) )
| ~ spl61_341
| ~ spl61_395 ),
inference(resolution,[],[f3355,f2686]) ).
fof(f7492,plain,
( spl61_932
| ~ spl61_159
| ~ spl61_396 ),
inference(avatar_split_clause,[],[f3412,f3358,f1629,f7490]) ).
fof(f7490,plain,
( spl61_932
<=> ! [X50,X51] :
( net_str(net_of_bool_filter(X50,X51,sK38(powerset(the_carrier(boole_POSet(X51))))),X50)
| ~ upper_relstr_subset(sK38(powerset(the_carrier(boole_POSet(X51)))),boole_POSet(X51))
| ~ filtered_subset(sK38(powerset(the_carrier(boole_POSet(X51)))),boole_POSet(X51))
| empty(sK38(powerset(the_carrier(boole_POSet(X51)))))
| ~ element(X51,powerset(the_carrier(X50)))
| empty(X51)
| ~ one_sorted_str(X50)
| empty_carrier(X50) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_932])]) ).
fof(f1629,plain,
( spl61_159
<=> ! [X0] : element(sK38(X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_159])]) ).
fof(f3412,plain,
( ! [X50,X51] :
( net_str(net_of_bool_filter(X50,X51,sK38(powerset(the_carrier(boole_POSet(X51))))),X50)
| ~ upper_relstr_subset(sK38(powerset(the_carrier(boole_POSet(X51)))),boole_POSet(X51))
| ~ filtered_subset(sK38(powerset(the_carrier(boole_POSet(X51)))),boole_POSet(X51))
| empty(sK38(powerset(the_carrier(boole_POSet(X51)))))
| ~ element(X51,powerset(the_carrier(X50)))
| empty(X51)
| ~ one_sorted_str(X50)
| empty_carrier(X50) )
| ~ spl61_159
| ~ spl61_396 ),
inference(resolution,[],[f3359,f1630]) ).
fof(f1630,plain,
( ! [X0] : element(sK38(X0),X0)
| ~ spl61_159 ),
inference(avatar_component_clause,[],[f1629]) ).
fof(f7488,plain,
( spl61_931
| ~ spl61_250
| ~ spl61_396 ),
inference(avatar_split_clause,[],[f3395,f3358,f2076,f7486]) ).
fof(f7486,plain,
( spl61_931
<=> ! [X16,X17] :
( net_str(net_of_bool_filter(X16,X17,sK17(the_carrier(boole_POSet(X17)))),X16)
| ~ upper_relstr_subset(sK17(the_carrier(boole_POSet(X17))),boole_POSet(X17))
| ~ filtered_subset(sK17(the_carrier(boole_POSet(X17))),boole_POSet(X17))
| empty(sK17(the_carrier(boole_POSet(X17))))
| ~ element(X17,powerset(the_carrier(X16)))
| empty(X17)
| ~ one_sorted_str(X16)
| empty_carrier(X16)
| empty(the_carrier(boole_POSet(X17))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_931])]) ).
fof(f2076,plain,
( spl61_250
<=> ! [X0] :
( element(sK17(X0),powerset(X0))
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_250])]) ).
fof(f3395,plain,
( ! [X16,X17] :
( net_str(net_of_bool_filter(X16,X17,sK17(the_carrier(boole_POSet(X17)))),X16)
| ~ upper_relstr_subset(sK17(the_carrier(boole_POSet(X17))),boole_POSet(X17))
| ~ filtered_subset(sK17(the_carrier(boole_POSet(X17))),boole_POSet(X17))
| empty(sK17(the_carrier(boole_POSet(X17))))
| ~ element(X17,powerset(the_carrier(X16)))
| empty(X17)
| ~ one_sorted_str(X16)
| empty_carrier(X16)
| empty(the_carrier(boole_POSet(X17))) )
| ~ spl61_250
| ~ spl61_396 ),
inference(resolution,[],[f3359,f2077]) ).
fof(f2077,plain,
( ! [X0] :
( element(sK17(X0),powerset(X0))
| empty(X0) )
| ~ spl61_250 ),
inference(avatar_component_clause,[],[f2076]) ).
fof(f7484,plain,
( spl61_930
| ~ spl61_249
| ~ spl61_396 ),
inference(avatar_split_clause,[],[f3394,f3358,f2072,f7482]) ).
fof(f7482,plain,
( spl61_930
<=> ! [X14,X15] :
( net_str(net_of_bool_filter(X14,X15,sK16(the_carrier(boole_POSet(X15)))),X14)
| ~ upper_relstr_subset(sK16(the_carrier(boole_POSet(X15))),boole_POSet(X15))
| ~ filtered_subset(sK16(the_carrier(boole_POSet(X15))),boole_POSet(X15))
| empty(sK16(the_carrier(boole_POSet(X15))))
| ~ element(X15,powerset(the_carrier(X14)))
| empty(X15)
| ~ one_sorted_str(X14)
| empty_carrier(X14)
| empty(the_carrier(boole_POSet(X15))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_930])]) ).
fof(f2072,plain,
( spl61_249
<=> ! [X0] :
( element(sK16(X0),powerset(X0))
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_249])]) ).
fof(f3394,plain,
( ! [X14,X15] :
( net_str(net_of_bool_filter(X14,X15,sK16(the_carrier(boole_POSet(X15)))),X14)
| ~ upper_relstr_subset(sK16(the_carrier(boole_POSet(X15))),boole_POSet(X15))
| ~ filtered_subset(sK16(the_carrier(boole_POSet(X15))),boole_POSet(X15))
| empty(sK16(the_carrier(boole_POSet(X15))))
| ~ element(X15,powerset(the_carrier(X14)))
| empty(X15)
| ~ one_sorted_str(X14)
| empty_carrier(X14)
| empty(the_carrier(boole_POSet(X15))) )
| ~ spl61_249
| ~ spl61_396 ),
inference(resolution,[],[f3359,f2073]) ).
fof(f2073,plain,
( ! [X0] :
( element(sK16(X0),powerset(X0))
| empty(X0) )
| ~ spl61_249 ),
inference(avatar_component_clause,[],[f2072]) ).
fof(f7480,plain,
( spl61_929
| ~ spl61_248
| ~ spl61_396 ),
inference(avatar_split_clause,[],[f3393,f3358,f2068,f7478]) ).
fof(f7478,plain,
( spl61_929
<=> ! [X13,X12] :
( net_str(net_of_bool_filter(X12,X13,sK15(the_carrier(boole_POSet(X13)))),X12)
| ~ upper_relstr_subset(sK15(the_carrier(boole_POSet(X13))),boole_POSet(X13))
| ~ filtered_subset(sK15(the_carrier(boole_POSet(X13))),boole_POSet(X13))
| empty(sK15(the_carrier(boole_POSet(X13))))
| ~ element(X13,powerset(the_carrier(X12)))
| empty(X13)
| ~ one_sorted_str(X12)
| empty_carrier(X12)
| empty(the_carrier(boole_POSet(X13))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_929])]) ).
fof(f2068,plain,
( spl61_248
<=> ! [X0] :
( element(sK15(X0),powerset(X0))
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_248])]) ).
fof(f3393,plain,
( ! [X12,X13] :
( net_str(net_of_bool_filter(X12,X13,sK15(the_carrier(boole_POSet(X13)))),X12)
| ~ upper_relstr_subset(sK15(the_carrier(boole_POSet(X13))),boole_POSet(X13))
| ~ filtered_subset(sK15(the_carrier(boole_POSet(X13))),boole_POSet(X13))
| empty(sK15(the_carrier(boole_POSet(X13))))
| ~ element(X13,powerset(the_carrier(X12)))
| empty(X13)
| ~ one_sorted_str(X12)
| empty_carrier(X12)
| empty(the_carrier(boole_POSet(X13))) )
| ~ spl61_248
| ~ spl61_396 ),
inference(resolution,[],[f3359,f2069]) ).
fof(f2069,plain,
( ! [X0] :
( element(sK15(X0),powerset(X0))
| empty(X0) )
| ~ spl61_248 ),
inference(avatar_component_clause,[],[f2068]) ).
fof(f7476,plain,
( spl61_928
| ~ spl61_159
| ~ spl61_395 ),
inference(avatar_split_clause,[],[f3385,f3354,f1629,f7474]) ).
fof(f7474,plain,
( spl61_928
<=> ! [X50,X51] :
( strict_net_str(net_of_bool_filter(X50,X51,sK38(powerset(the_carrier(boole_POSet(X51))))),X50)
| ~ upper_relstr_subset(sK38(powerset(the_carrier(boole_POSet(X51)))),boole_POSet(X51))
| ~ filtered_subset(sK38(powerset(the_carrier(boole_POSet(X51)))),boole_POSet(X51))
| empty(sK38(powerset(the_carrier(boole_POSet(X51)))))
| ~ element(X51,powerset(the_carrier(X50)))
| empty(X51)
| ~ one_sorted_str(X50)
| empty_carrier(X50) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_928])]) ).
fof(f3385,plain,
( ! [X50,X51] :
( strict_net_str(net_of_bool_filter(X50,X51,sK38(powerset(the_carrier(boole_POSet(X51))))),X50)
| ~ upper_relstr_subset(sK38(powerset(the_carrier(boole_POSet(X51)))),boole_POSet(X51))
| ~ filtered_subset(sK38(powerset(the_carrier(boole_POSet(X51)))),boole_POSet(X51))
| empty(sK38(powerset(the_carrier(boole_POSet(X51)))))
| ~ element(X51,powerset(the_carrier(X50)))
| empty(X51)
| ~ one_sorted_str(X50)
| empty_carrier(X50) )
| ~ spl61_159
| ~ spl61_395 ),
inference(resolution,[],[f3355,f1630]) ).
fof(f7472,plain,
( spl61_927
| ~ spl61_250
| ~ spl61_395 ),
inference(avatar_split_clause,[],[f3368,f3354,f2076,f7470]) ).
fof(f7470,plain,
( spl61_927
<=> ! [X16,X17] :
( strict_net_str(net_of_bool_filter(X16,X17,sK17(the_carrier(boole_POSet(X17)))),X16)
| ~ upper_relstr_subset(sK17(the_carrier(boole_POSet(X17))),boole_POSet(X17))
| ~ filtered_subset(sK17(the_carrier(boole_POSet(X17))),boole_POSet(X17))
| empty(sK17(the_carrier(boole_POSet(X17))))
| ~ element(X17,powerset(the_carrier(X16)))
| empty(X17)
| ~ one_sorted_str(X16)
| empty_carrier(X16)
| empty(the_carrier(boole_POSet(X17))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_927])]) ).
fof(f3368,plain,
( ! [X16,X17] :
( strict_net_str(net_of_bool_filter(X16,X17,sK17(the_carrier(boole_POSet(X17)))),X16)
| ~ upper_relstr_subset(sK17(the_carrier(boole_POSet(X17))),boole_POSet(X17))
| ~ filtered_subset(sK17(the_carrier(boole_POSet(X17))),boole_POSet(X17))
| empty(sK17(the_carrier(boole_POSet(X17))))
| ~ element(X17,powerset(the_carrier(X16)))
| empty(X17)
| ~ one_sorted_str(X16)
| empty_carrier(X16)
| empty(the_carrier(boole_POSet(X17))) )
| ~ spl61_250
| ~ spl61_395 ),
inference(resolution,[],[f3355,f2077]) ).
fof(f7468,plain,
( spl61_926
| ~ spl61_249
| ~ spl61_395 ),
inference(avatar_split_clause,[],[f3367,f3354,f2072,f7466]) ).
fof(f7466,plain,
( spl61_926
<=> ! [X14,X15] :
( strict_net_str(net_of_bool_filter(X14,X15,sK16(the_carrier(boole_POSet(X15)))),X14)
| ~ upper_relstr_subset(sK16(the_carrier(boole_POSet(X15))),boole_POSet(X15))
| ~ filtered_subset(sK16(the_carrier(boole_POSet(X15))),boole_POSet(X15))
| empty(sK16(the_carrier(boole_POSet(X15))))
| ~ element(X15,powerset(the_carrier(X14)))
| empty(X15)
| ~ one_sorted_str(X14)
| empty_carrier(X14)
| empty(the_carrier(boole_POSet(X15))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_926])]) ).
fof(f3367,plain,
( ! [X14,X15] :
( strict_net_str(net_of_bool_filter(X14,X15,sK16(the_carrier(boole_POSet(X15)))),X14)
| ~ upper_relstr_subset(sK16(the_carrier(boole_POSet(X15))),boole_POSet(X15))
| ~ filtered_subset(sK16(the_carrier(boole_POSet(X15))),boole_POSet(X15))
| empty(sK16(the_carrier(boole_POSet(X15))))
| ~ element(X15,powerset(the_carrier(X14)))
| empty(X15)
| ~ one_sorted_str(X14)
| empty_carrier(X14)
| empty(the_carrier(boole_POSet(X15))) )
| ~ spl61_249
| ~ spl61_395 ),
inference(resolution,[],[f3355,f2073]) ).
fof(f7464,plain,
( spl61_925
| ~ spl61_248
| ~ spl61_395 ),
inference(avatar_split_clause,[],[f3366,f3354,f2068,f7462]) ).
fof(f7462,plain,
( spl61_925
<=> ! [X13,X12] :
( strict_net_str(net_of_bool_filter(X12,X13,sK15(the_carrier(boole_POSet(X13)))),X12)
| ~ upper_relstr_subset(sK15(the_carrier(boole_POSet(X13))),boole_POSet(X13))
| ~ filtered_subset(sK15(the_carrier(boole_POSet(X13))),boole_POSet(X13))
| empty(sK15(the_carrier(boole_POSet(X13))))
| ~ element(X13,powerset(the_carrier(X12)))
| empty(X13)
| ~ one_sorted_str(X12)
| empty_carrier(X12)
| empty(the_carrier(boole_POSet(X13))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_925])]) ).
fof(f3366,plain,
( ! [X12,X13] :
( strict_net_str(net_of_bool_filter(X12,X13,sK15(the_carrier(boole_POSet(X13)))),X12)
| ~ upper_relstr_subset(sK15(the_carrier(boole_POSet(X13))),boole_POSet(X13))
| ~ filtered_subset(sK15(the_carrier(boole_POSet(X13))),boole_POSet(X13))
| empty(sK15(the_carrier(boole_POSet(X13))))
| ~ element(X13,powerset(the_carrier(X12)))
| empty(X13)
| ~ one_sorted_str(X12)
| empty_carrier(X12)
| empty(the_carrier(boole_POSet(X13))) )
| ~ spl61_248
| ~ spl61_395 ),
inference(resolution,[],[f3355,f2069]) ).
fof(f7460,plain,
( spl61_924
| ~ spl61_342
| ~ spl61_390 ),
inference(avatar_split_clause,[],[f3335,f3248,f2689,f7458]) ).
fof(f7458,plain,
( spl61_924
<=> ! [X29,X28] :
( transitive_relstr(net_of_bool_filter(X28,X29,sK27(boole_POSet(X29))))
| ~ upper_relstr_subset(sK27(boole_POSet(X29)),boole_POSet(X29))
| ~ filtered_subset(sK27(boole_POSet(X29)),boole_POSet(X29))
| empty(sK27(boole_POSet(X29)))
| ~ element(X29,powerset(the_carrier(X28)))
| empty(X29)
| ~ one_sorted_str(X28)
| empty_carrier(X28)
| ~ top_str(boole_POSet(X29))
| ~ topological_space(boole_POSet(X29))
| empty_carrier(boole_POSet(X29)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_924])]) ).
fof(f3335,plain,
( ! [X28,X29] :
( transitive_relstr(net_of_bool_filter(X28,X29,sK27(boole_POSet(X29))))
| ~ upper_relstr_subset(sK27(boole_POSet(X29)),boole_POSet(X29))
| ~ filtered_subset(sK27(boole_POSet(X29)),boole_POSet(X29))
| empty(sK27(boole_POSet(X29)))
| ~ element(X29,powerset(the_carrier(X28)))
| empty(X29)
| ~ one_sorted_str(X28)
| empty_carrier(X28)
| ~ top_str(boole_POSet(X29))
| ~ topological_space(boole_POSet(X29))
| empty_carrier(boole_POSet(X29)) )
| ~ spl61_342
| ~ spl61_390 ),
inference(resolution,[],[f3249,f2690]) ).
fof(f7456,plain,
( spl61_923
| ~ spl61_341
| ~ spl61_390 ),
inference(avatar_split_clause,[],[f3334,f3248,f2685,f7454]) ).
fof(f7454,plain,
( spl61_923
<=> ! [X27,X26] :
( transitive_relstr(net_of_bool_filter(X26,X27,sK26(boole_POSet(X27))))
| ~ upper_relstr_subset(sK26(boole_POSet(X27)),boole_POSet(X27))
| ~ filtered_subset(sK26(boole_POSet(X27)),boole_POSet(X27))
| empty(sK26(boole_POSet(X27)))
| ~ element(X27,powerset(the_carrier(X26)))
| empty(X27)
| ~ one_sorted_str(X26)
| empty_carrier(X26)
| ~ top_str(boole_POSet(X27))
| ~ topological_space(boole_POSet(X27))
| empty_carrier(boole_POSet(X27)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_923])]) ).
fof(f3334,plain,
( ! [X26,X27] :
( transitive_relstr(net_of_bool_filter(X26,X27,sK26(boole_POSet(X27))))
| ~ upper_relstr_subset(sK26(boole_POSet(X27)),boole_POSet(X27))
| ~ filtered_subset(sK26(boole_POSet(X27)),boole_POSet(X27))
| empty(sK26(boole_POSet(X27)))
| ~ element(X27,powerset(the_carrier(X26)))
| empty(X27)
| ~ one_sorted_str(X26)
| empty_carrier(X26)
| ~ top_str(boole_POSet(X27))
| ~ topological_space(boole_POSet(X27))
| empty_carrier(boole_POSet(X27)) )
| ~ spl61_341
| ~ spl61_390 ),
inference(resolution,[],[f3249,f2686]) ).
fof(f7452,plain,
( spl61_922
| ~ spl61_342
| ~ spl61_389 ),
inference(avatar_split_clause,[],[f3307,f3244,f2689,f7450]) ).
fof(f7450,plain,
( spl61_922
<=> ! [X29,X28] :
( reflexive_relstr(net_of_bool_filter(X28,X29,sK27(boole_POSet(X29))))
| ~ upper_relstr_subset(sK27(boole_POSet(X29)),boole_POSet(X29))
| ~ filtered_subset(sK27(boole_POSet(X29)),boole_POSet(X29))
| empty(sK27(boole_POSet(X29)))
| ~ element(X29,powerset(the_carrier(X28)))
| empty(X29)
| ~ one_sorted_str(X28)
| empty_carrier(X28)
| ~ top_str(boole_POSet(X29))
| ~ topological_space(boole_POSet(X29))
| empty_carrier(boole_POSet(X29)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_922])]) ).
fof(f3307,plain,
( ! [X28,X29] :
( reflexive_relstr(net_of_bool_filter(X28,X29,sK27(boole_POSet(X29))))
| ~ upper_relstr_subset(sK27(boole_POSet(X29)),boole_POSet(X29))
| ~ filtered_subset(sK27(boole_POSet(X29)),boole_POSet(X29))
| empty(sK27(boole_POSet(X29)))
| ~ element(X29,powerset(the_carrier(X28)))
| empty(X29)
| ~ one_sorted_str(X28)
| empty_carrier(X28)
| ~ top_str(boole_POSet(X29))
| ~ topological_space(boole_POSet(X29))
| empty_carrier(boole_POSet(X29)) )
| ~ spl61_342
| ~ spl61_389 ),
inference(resolution,[],[f3245,f2690]) ).
fof(f7448,plain,
( spl61_921
| ~ spl61_531
| ~ spl61_606 ),
inference(avatar_split_clause,[],[f5118,f4997,f4436,f7446]) ).
fof(f7446,plain,
( spl61_921
<=> ! [X42] :
( ~ in(cast_as_carrier_subset(sK12),sK22(X42))
| ~ one_sorted_str(X42)
| empty_carrier(X42)
| transitive_relstr(net_of_bool_filter(X42,cast_as_carrier_subset(sK12),sK13)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_921])]) ).
fof(f4436,plain,
( spl61_531
<=> ! [X11] :
( transitive_relstr(net_of_bool_filter(X11,cast_as_carrier_subset(sK12),sK13))
| empty_carrier(X11)
| ~ one_sorted_str(X11)
| ~ element(cast_as_carrier_subset(sK12),powerset(the_carrier(X11))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_531])]) ).
fof(f5118,plain,
( ! [X42] :
( ~ in(cast_as_carrier_subset(sK12),sK22(X42))
| ~ one_sorted_str(X42)
| empty_carrier(X42)
| transitive_relstr(net_of_bool_filter(X42,cast_as_carrier_subset(sK12),sK13)) )
| ~ spl61_531
| ~ spl61_606 ),
inference(duplicate_literal_removal,[],[f5113]) ).
fof(f5113,plain,
( ! [X42] :
( ~ in(cast_as_carrier_subset(sK12),sK22(X42))
| ~ one_sorted_str(X42)
| empty_carrier(X42)
| ~ one_sorted_str(X42)
| transitive_relstr(net_of_bool_filter(X42,cast_as_carrier_subset(sK12),sK13)) )
| ~ spl61_531
| ~ spl61_606 ),
inference(resolution,[],[f4998,f4437]) ).
fof(f4437,plain,
( ! [X11] :
( ~ element(cast_as_carrier_subset(sK12),powerset(the_carrier(X11)))
| empty_carrier(X11)
| ~ one_sorted_str(X11)
| transitive_relstr(net_of_bool_filter(X11,cast_as_carrier_subset(sK12),sK13)) )
| ~ spl61_531 ),
inference(avatar_component_clause,[],[f4436]) ).
fof(f7444,plain,
( spl61_920
| ~ spl61_341
| ~ spl61_389 ),
inference(avatar_split_clause,[],[f3306,f3244,f2685,f7442]) ).
fof(f7442,plain,
( spl61_920
<=> ! [X27,X26] :
( reflexive_relstr(net_of_bool_filter(X26,X27,sK26(boole_POSet(X27))))
| ~ upper_relstr_subset(sK26(boole_POSet(X27)),boole_POSet(X27))
| ~ filtered_subset(sK26(boole_POSet(X27)),boole_POSet(X27))
| empty(sK26(boole_POSet(X27)))
| ~ element(X27,powerset(the_carrier(X26)))
| empty(X27)
| ~ one_sorted_str(X26)
| empty_carrier(X26)
| ~ top_str(boole_POSet(X27))
| ~ topological_space(boole_POSet(X27))
| empty_carrier(boole_POSet(X27)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_920])]) ).
fof(f3306,plain,
( ! [X26,X27] :
( reflexive_relstr(net_of_bool_filter(X26,X27,sK26(boole_POSet(X27))))
| ~ upper_relstr_subset(sK26(boole_POSet(X27)),boole_POSet(X27))
| ~ filtered_subset(sK26(boole_POSet(X27)),boole_POSet(X27))
| empty(sK26(boole_POSet(X27)))
| ~ element(X27,powerset(the_carrier(X26)))
| empty(X27)
| ~ one_sorted_str(X26)
| empty_carrier(X26)
| ~ top_str(boole_POSet(X27))
| ~ topological_space(boole_POSet(X27))
| empty_carrier(boole_POSet(X27)) )
| ~ spl61_341
| ~ spl61_389 ),
inference(resolution,[],[f3245,f2686]) ).
fof(f7440,plain,
( spl61_919
| ~ spl61_342
| ~ spl61_388 ),
inference(avatar_split_clause,[],[f3280,f3240,f2689,f7438]) ).
fof(f7438,plain,
( spl61_919
<=> ! [X29,X28] :
( ~ empty_carrier(net_of_bool_filter(X28,X29,sK27(boole_POSet(X29))))
| ~ upper_relstr_subset(sK27(boole_POSet(X29)),boole_POSet(X29))
| ~ filtered_subset(sK27(boole_POSet(X29)),boole_POSet(X29))
| empty(sK27(boole_POSet(X29)))
| ~ element(X29,powerset(the_carrier(X28)))
| empty(X29)
| ~ one_sorted_str(X28)
| empty_carrier(X28)
| ~ top_str(boole_POSet(X29))
| ~ topological_space(boole_POSet(X29))
| empty_carrier(boole_POSet(X29)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_919])]) ).
fof(f3280,plain,
( ! [X28,X29] :
( ~ empty_carrier(net_of_bool_filter(X28,X29,sK27(boole_POSet(X29))))
| ~ upper_relstr_subset(sK27(boole_POSet(X29)),boole_POSet(X29))
| ~ filtered_subset(sK27(boole_POSet(X29)),boole_POSet(X29))
| empty(sK27(boole_POSet(X29)))
| ~ element(X29,powerset(the_carrier(X28)))
| empty(X29)
| ~ one_sorted_str(X28)
| empty_carrier(X28)
| ~ top_str(boole_POSet(X29))
| ~ topological_space(boole_POSet(X29))
| empty_carrier(boole_POSet(X29)) )
| ~ spl61_342
| ~ spl61_388 ),
inference(resolution,[],[f3241,f2690]) ).
fof(f7436,plain,
( spl61_918
| ~ spl61_341
| ~ spl61_388 ),
inference(avatar_split_clause,[],[f3279,f3240,f2685,f7434]) ).
fof(f7434,plain,
( spl61_918
<=> ! [X27,X26] :
( ~ empty_carrier(net_of_bool_filter(X26,X27,sK26(boole_POSet(X27))))
| ~ upper_relstr_subset(sK26(boole_POSet(X27)),boole_POSet(X27))
| ~ filtered_subset(sK26(boole_POSet(X27)),boole_POSet(X27))
| empty(sK26(boole_POSet(X27)))
| ~ element(X27,powerset(the_carrier(X26)))
| empty(X27)
| ~ one_sorted_str(X26)
| empty_carrier(X26)
| ~ top_str(boole_POSet(X27))
| ~ topological_space(boole_POSet(X27))
| empty_carrier(boole_POSet(X27)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_918])]) ).
fof(f3279,plain,
( ! [X26,X27] :
( ~ empty_carrier(net_of_bool_filter(X26,X27,sK26(boole_POSet(X27))))
| ~ upper_relstr_subset(sK26(boole_POSet(X27)),boole_POSet(X27))
| ~ filtered_subset(sK26(boole_POSet(X27)),boole_POSet(X27))
| empty(sK26(boole_POSet(X27)))
| ~ element(X27,powerset(the_carrier(X26)))
| empty(X27)
| ~ one_sorted_str(X26)
| empty_carrier(X26)
| ~ top_str(boole_POSet(X27))
| ~ topological_space(boole_POSet(X27))
| empty_carrier(boole_POSet(X27)) )
| ~ spl61_341
| ~ spl61_388 ),
inference(resolution,[],[f3241,f2686]) ).
fof(f7429,plain,
( spl61_917
| ~ spl61_530
| ~ spl61_606 ),
inference(avatar_split_clause,[],[f5117,f4997,f4429,f7427]) ).
fof(f7427,plain,
( spl61_917
<=> ! [X43] :
( ~ in(cast_as_carrier_subset(sK12),sK22(X43))
| ~ one_sorted_str(X43)
| empty_carrier(X43)
| reflexive_relstr(net_of_bool_filter(X43,cast_as_carrier_subset(sK12),sK13)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_917])]) ).
fof(f4429,plain,
( spl61_530
<=> ! [X11] :
( reflexive_relstr(net_of_bool_filter(X11,cast_as_carrier_subset(sK12),sK13))
| empty_carrier(X11)
| ~ one_sorted_str(X11)
| ~ element(cast_as_carrier_subset(sK12),powerset(the_carrier(X11))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_530])]) ).
fof(f5117,plain,
( ! [X43] :
( ~ in(cast_as_carrier_subset(sK12),sK22(X43))
| ~ one_sorted_str(X43)
| empty_carrier(X43)
| reflexive_relstr(net_of_bool_filter(X43,cast_as_carrier_subset(sK12),sK13)) )
| ~ spl61_530
| ~ spl61_606 ),
inference(duplicate_literal_removal,[],[f5114]) ).
fof(f5114,plain,
( ! [X43] :
( ~ in(cast_as_carrier_subset(sK12),sK22(X43))
| ~ one_sorted_str(X43)
| empty_carrier(X43)
| ~ one_sorted_str(X43)
| reflexive_relstr(net_of_bool_filter(X43,cast_as_carrier_subset(sK12),sK13)) )
| ~ spl61_530
| ~ spl61_606 ),
inference(resolution,[],[f4998,f4430]) ).
fof(f4430,plain,
( ! [X11] :
( ~ element(cast_as_carrier_subset(sK12),powerset(the_carrier(X11)))
| empty_carrier(X11)
| ~ one_sorted_str(X11)
| reflexive_relstr(net_of_bool_filter(X11,cast_as_carrier_subset(sK12),sK13)) )
| ~ spl61_530 ),
inference(avatar_component_clause,[],[f4429]) ).
fof(f7424,plain,
( spl61_916
| ~ spl61_159
| ~ spl61_390 ),
inference(avatar_split_clause,[],[f3346,f3248,f1629,f7422]) ).
fof(f7422,plain,
( spl61_916
<=> ! [X50,X51] :
( transitive_relstr(net_of_bool_filter(X50,X51,sK38(powerset(the_carrier(boole_POSet(X51))))))
| ~ upper_relstr_subset(sK38(powerset(the_carrier(boole_POSet(X51)))),boole_POSet(X51))
| ~ filtered_subset(sK38(powerset(the_carrier(boole_POSet(X51)))),boole_POSet(X51))
| empty(sK38(powerset(the_carrier(boole_POSet(X51)))))
| ~ element(X51,powerset(the_carrier(X50)))
| empty(X51)
| ~ one_sorted_str(X50)
| empty_carrier(X50) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_916])]) ).
fof(f3346,plain,
( ! [X50,X51] :
( transitive_relstr(net_of_bool_filter(X50,X51,sK38(powerset(the_carrier(boole_POSet(X51))))))
| ~ upper_relstr_subset(sK38(powerset(the_carrier(boole_POSet(X51)))),boole_POSet(X51))
| ~ filtered_subset(sK38(powerset(the_carrier(boole_POSet(X51)))),boole_POSet(X51))
| empty(sK38(powerset(the_carrier(boole_POSet(X51)))))
| ~ element(X51,powerset(the_carrier(X50)))
| empty(X51)
| ~ one_sorted_str(X50)
| empty_carrier(X50) )
| ~ spl61_159
| ~ spl61_390 ),
inference(resolution,[],[f3249,f1630]) ).
fof(f7420,plain,
( spl61_915
| ~ spl61_250
| ~ spl61_390 ),
inference(avatar_split_clause,[],[f3329,f3248,f2076,f7418]) ).
fof(f7418,plain,
( spl61_915
<=> ! [X16,X17] :
( transitive_relstr(net_of_bool_filter(X16,X17,sK17(the_carrier(boole_POSet(X17)))))
| ~ upper_relstr_subset(sK17(the_carrier(boole_POSet(X17))),boole_POSet(X17))
| ~ filtered_subset(sK17(the_carrier(boole_POSet(X17))),boole_POSet(X17))
| empty(sK17(the_carrier(boole_POSet(X17))))
| ~ element(X17,powerset(the_carrier(X16)))
| empty(X17)
| ~ one_sorted_str(X16)
| empty_carrier(X16)
| empty(the_carrier(boole_POSet(X17))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_915])]) ).
fof(f3329,plain,
( ! [X16,X17] :
( transitive_relstr(net_of_bool_filter(X16,X17,sK17(the_carrier(boole_POSet(X17)))))
| ~ upper_relstr_subset(sK17(the_carrier(boole_POSet(X17))),boole_POSet(X17))
| ~ filtered_subset(sK17(the_carrier(boole_POSet(X17))),boole_POSet(X17))
| empty(sK17(the_carrier(boole_POSet(X17))))
| ~ element(X17,powerset(the_carrier(X16)))
| empty(X17)
| ~ one_sorted_str(X16)
| empty_carrier(X16)
| empty(the_carrier(boole_POSet(X17))) )
| ~ spl61_250
| ~ spl61_390 ),
inference(resolution,[],[f3249,f2077]) ).
fof(f7416,plain,
( spl61_914
| ~ spl61_249
| ~ spl61_390 ),
inference(avatar_split_clause,[],[f3328,f3248,f2072,f7414]) ).
fof(f7414,plain,
( spl61_914
<=> ! [X14,X15] :
( transitive_relstr(net_of_bool_filter(X14,X15,sK16(the_carrier(boole_POSet(X15)))))
| ~ upper_relstr_subset(sK16(the_carrier(boole_POSet(X15))),boole_POSet(X15))
| ~ filtered_subset(sK16(the_carrier(boole_POSet(X15))),boole_POSet(X15))
| empty(sK16(the_carrier(boole_POSet(X15))))
| ~ element(X15,powerset(the_carrier(X14)))
| empty(X15)
| ~ one_sorted_str(X14)
| empty_carrier(X14)
| empty(the_carrier(boole_POSet(X15))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_914])]) ).
fof(f3328,plain,
( ! [X14,X15] :
( transitive_relstr(net_of_bool_filter(X14,X15,sK16(the_carrier(boole_POSet(X15)))))
| ~ upper_relstr_subset(sK16(the_carrier(boole_POSet(X15))),boole_POSet(X15))
| ~ filtered_subset(sK16(the_carrier(boole_POSet(X15))),boole_POSet(X15))
| empty(sK16(the_carrier(boole_POSet(X15))))
| ~ element(X15,powerset(the_carrier(X14)))
| empty(X15)
| ~ one_sorted_str(X14)
| empty_carrier(X14)
| empty(the_carrier(boole_POSet(X15))) )
| ~ spl61_249
| ~ spl61_390 ),
inference(resolution,[],[f3249,f2073]) ).
fof(f7412,plain,
( spl61_913
| ~ spl61_248
| ~ spl61_390 ),
inference(avatar_split_clause,[],[f3327,f3248,f2068,f7410]) ).
fof(f7410,plain,
( spl61_913
<=> ! [X13,X12] :
( transitive_relstr(net_of_bool_filter(X12,X13,sK15(the_carrier(boole_POSet(X13)))))
| ~ upper_relstr_subset(sK15(the_carrier(boole_POSet(X13))),boole_POSet(X13))
| ~ filtered_subset(sK15(the_carrier(boole_POSet(X13))),boole_POSet(X13))
| empty(sK15(the_carrier(boole_POSet(X13))))
| ~ element(X13,powerset(the_carrier(X12)))
| empty(X13)
| ~ one_sorted_str(X12)
| empty_carrier(X12)
| empty(the_carrier(boole_POSet(X13))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_913])]) ).
fof(f3327,plain,
( ! [X12,X13] :
( transitive_relstr(net_of_bool_filter(X12,X13,sK15(the_carrier(boole_POSet(X13)))))
| ~ upper_relstr_subset(sK15(the_carrier(boole_POSet(X13))),boole_POSet(X13))
| ~ filtered_subset(sK15(the_carrier(boole_POSet(X13))),boole_POSet(X13))
| empty(sK15(the_carrier(boole_POSet(X13))))
| ~ element(X13,powerset(the_carrier(X12)))
| empty(X13)
| ~ one_sorted_str(X12)
| empty_carrier(X12)
| empty(the_carrier(boole_POSet(X13))) )
| ~ spl61_248
| ~ spl61_390 ),
inference(resolution,[],[f3249,f2069]) ).
fof(f7408,plain,
( spl61_912
| ~ spl61_159
| ~ spl61_389 ),
inference(avatar_split_clause,[],[f3318,f3244,f1629,f7406]) ).
fof(f7406,plain,
( spl61_912
<=> ! [X50,X51] :
( reflexive_relstr(net_of_bool_filter(X50,X51,sK38(powerset(the_carrier(boole_POSet(X51))))))
| ~ upper_relstr_subset(sK38(powerset(the_carrier(boole_POSet(X51)))),boole_POSet(X51))
| ~ filtered_subset(sK38(powerset(the_carrier(boole_POSet(X51)))),boole_POSet(X51))
| empty(sK38(powerset(the_carrier(boole_POSet(X51)))))
| ~ element(X51,powerset(the_carrier(X50)))
| empty(X51)
| ~ one_sorted_str(X50)
| empty_carrier(X50) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_912])]) ).
fof(f3318,plain,
( ! [X50,X51] :
( reflexive_relstr(net_of_bool_filter(X50,X51,sK38(powerset(the_carrier(boole_POSet(X51))))))
| ~ upper_relstr_subset(sK38(powerset(the_carrier(boole_POSet(X51)))),boole_POSet(X51))
| ~ filtered_subset(sK38(powerset(the_carrier(boole_POSet(X51)))),boole_POSet(X51))
| empty(sK38(powerset(the_carrier(boole_POSet(X51)))))
| ~ element(X51,powerset(the_carrier(X50)))
| empty(X51)
| ~ one_sorted_str(X50)
| empty_carrier(X50) )
| ~ spl61_159
| ~ spl61_389 ),
inference(resolution,[],[f3245,f1630]) ).
fof(f7404,plain,
( spl61_911
| ~ spl61_505
| ~ spl61_606 ),
inference(avatar_split_clause,[],[f5116,f4997,f4286,f7402]) ).
fof(f7402,plain,
( spl61_911
<=> ! [X44] :
( ~ in(cast_as_carrier_subset(sK12),sK22(X44))
| ~ one_sorted_str(X44)
| empty_carrier(X44)
| ~ empty_carrier(net_of_bool_filter(X44,cast_as_carrier_subset(sK12),sK13)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_911])]) ).
fof(f4286,plain,
( spl61_505
<=> ! [X11] :
( ~ empty_carrier(net_of_bool_filter(X11,cast_as_carrier_subset(sK12),sK13))
| empty_carrier(X11)
| ~ one_sorted_str(X11)
| ~ element(cast_as_carrier_subset(sK12),powerset(the_carrier(X11))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_505])]) ).
fof(f5116,plain,
( ! [X44] :
( ~ in(cast_as_carrier_subset(sK12),sK22(X44))
| ~ one_sorted_str(X44)
| empty_carrier(X44)
| ~ empty_carrier(net_of_bool_filter(X44,cast_as_carrier_subset(sK12),sK13)) )
| ~ spl61_505
| ~ spl61_606 ),
inference(duplicate_literal_removal,[],[f5115]) ).
fof(f5115,plain,
( ! [X44] :
( ~ in(cast_as_carrier_subset(sK12),sK22(X44))
| ~ one_sorted_str(X44)
| empty_carrier(X44)
| ~ one_sorted_str(X44)
| ~ empty_carrier(net_of_bool_filter(X44,cast_as_carrier_subset(sK12),sK13)) )
| ~ spl61_505
| ~ spl61_606 ),
inference(resolution,[],[f4998,f4287]) ).
fof(f4287,plain,
( ! [X11] :
( ~ element(cast_as_carrier_subset(sK12),powerset(the_carrier(X11)))
| empty_carrier(X11)
| ~ one_sorted_str(X11)
| ~ empty_carrier(net_of_bool_filter(X11,cast_as_carrier_subset(sK12),sK13)) )
| ~ spl61_505 ),
inference(avatar_component_clause,[],[f4286]) ).
fof(f7400,plain,
( spl61_910
| ~ spl61_250
| ~ spl61_389 ),
inference(avatar_split_clause,[],[f3301,f3244,f2076,f7398]) ).
fof(f7398,plain,
( spl61_910
<=> ! [X16,X17] :
( reflexive_relstr(net_of_bool_filter(X16,X17,sK17(the_carrier(boole_POSet(X17)))))
| ~ upper_relstr_subset(sK17(the_carrier(boole_POSet(X17))),boole_POSet(X17))
| ~ filtered_subset(sK17(the_carrier(boole_POSet(X17))),boole_POSet(X17))
| empty(sK17(the_carrier(boole_POSet(X17))))
| ~ element(X17,powerset(the_carrier(X16)))
| empty(X17)
| ~ one_sorted_str(X16)
| empty_carrier(X16)
| empty(the_carrier(boole_POSet(X17))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_910])]) ).
fof(f3301,plain,
( ! [X16,X17] :
( reflexive_relstr(net_of_bool_filter(X16,X17,sK17(the_carrier(boole_POSet(X17)))))
| ~ upper_relstr_subset(sK17(the_carrier(boole_POSet(X17))),boole_POSet(X17))
| ~ filtered_subset(sK17(the_carrier(boole_POSet(X17))),boole_POSet(X17))
| empty(sK17(the_carrier(boole_POSet(X17))))
| ~ element(X17,powerset(the_carrier(X16)))
| empty(X17)
| ~ one_sorted_str(X16)
| empty_carrier(X16)
| empty(the_carrier(boole_POSet(X17))) )
| ~ spl61_250
| ~ spl61_389 ),
inference(resolution,[],[f3245,f2077]) ).
fof(f7396,plain,
( spl61_909
| ~ spl61_249
| ~ spl61_389 ),
inference(avatar_split_clause,[],[f3300,f3244,f2072,f7394]) ).
fof(f7394,plain,
( spl61_909
<=> ! [X14,X15] :
( reflexive_relstr(net_of_bool_filter(X14,X15,sK16(the_carrier(boole_POSet(X15)))))
| ~ upper_relstr_subset(sK16(the_carrier(boole_POSet(X15))),boole_POSet(X15))
| ~ filtered_subset(sK16(the_carrier(boole_POSet(X15))),boole_POSet(X15))
| empty(sK16(the_carrier(boole_POSet(X15))))
| ~ element(X15,powerset(the_carrier(X14)))
| empty(X15)
| ~ one_sorted_str(X14)
| empty_carrier(X14)
| empty(the_carrier(boole_POSet(X15))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_909])]) ).
fof(f3300,plain,
( ! [X14,X15] :
( reflexive_relstr(net_of_bool_filter(X14,X15,sK16(the_carrier(boole_POSet(X15)))))
| ~ upper_relstr_subset(sK16(the_carrier(boole_POSet(X15))),boole_POSet(X15))
| ~ filtered_subset(sK16(the_carrier(boole_POSet(X15))),boole_POSet(X15))
| empty(sK16(the_carrier(boole_POSet(X15))))
| ~ element(X15,powerset(the_carrier(X14)))
| empty(X15)
| ~ one_sorted_str(X14)
| empty_carrier(X14)
| empty(the_carrier(boole_POSet(X15))) )
| ~ spl61_249
| ~ spl61_389 ),
inference(resolution,[],[f3245,f2073]) ).
fof(f7392,plain,
( spl61_908
| ~ spl61_248
| ~ spl61_389 ),
inference(avatar_split_clause,[],[f3299,f3244,f2068,f7390]) ).
fof(f7390,plain,
( spl61_908
<=> ! [X13,X12] :
( reflexive_relstr(net_of_bool_filter(X12,X13,sK15(the_carrier(boole_POSet(X13)))))
| ~ upper_relstr_subset(sK15(the_carrier(boole_POSet(X13))),boole_POSet(X13))
| ~ filtered_subset(sK15(the_carrier(boole_POSet(X13))),boole_POSet(X13))
| empty(sK15(the_carrier(boole_POSet(X13))))
| ~ element(X13,powerset(the_carrier(X12)))
| empty(X13)
| ~ one_sorted_str(X12)
| empty_carrier(X12)
| empty(the_carrier(boole_POSet(X13))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_908])]) ).
fof(f3299,plain,
( ! [X12,X13] :
( reflexive_relstr(net_of_bool_filter(X12,X13,sK15(the_carrier(boole_POSet(X13)))))
| ~ upper_relstr_subset(sK15(the_carrier(boole_POSet(X13))),boole_POSet(X13))
| ~ filtered_subset(sK15(the_carrier(boole_POSet(X13))),boole_POSet(X13))
| empty(sK15(the_carrier(boole_POSet(X13))))
| ~ element(X13,powerset(the_carrier(X12)))
| empty(X13)
| ~ one_sorted_str(X12)
| empty_carrier(X12)
| empty(the_carrier(boole_POSet(X13))) )
| ~ spl61_248
| ~ spl61_389 ),
inference(resolution,[],[f3245,f2069]) ).
fof(f7388,plain,
( spl61_907
| ~ spl61_159
| ~ spl61_388 ),
inference(avatar_split_clause,[],[f3291,f3240,f1629,f7386]) ).
fof(f7386,plain,
( spl61_907
<=> ! [X50,X51] :
( ~ empty_carrier(net_of_bool_filter(X50,X51,sK38(powerset(the_carrier(boole_POSet(X51))))))
| ~ upper_relstr_subset(sK38(powerset(the_carrier(boole_POSet(X51)))),boole_POSet(X51))
| ~ filtered_subset(sK38(powerset(the_carrier(boole_POSet(X51)))),boole_POSet(X51))
| empty(sK38(powerset(the_carrier(boole_POSet(X51)))))
| ~ element(X51,powerset(the_carrier(X50)))
| empty(X51)
| ~ one_sorted_str(X50)
| empty_carrier(X50) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_907])]) ).
fof(f3291,plain,
( ! [X50,X51] :
( ~ empty_carrier(net_of_bool_filter(X50,X51,sK38(powerset(the_carrier(boole_POSet(X51))))))
| ~ upper_relstr_subset(sK38(powerset(the_carrier(boole_POSet(X51)))),boole_POSet(X51))
| ~ filtered_subset(sK38(powerset(the_carrier(boole_POSet(X51)))),boole_POSet(X51))
| empty(sK38(powerset(the_carrier(boole_POSet(X51)))))
| ~ element(X51,powerset(the_carrier(X50)))
| empty(X51)
| ~ one_sorted_str(X50)
| empty_carrier(X50) )
| ~ spl61_159
| ~ spl61_388 ),
inference(resolution,[],[f3241,f1630]) ).
fof(f7384,plain,
( spl61_906
| ~ spl61_250
| ~ spl61_388 ),
inference(avatar_split_clause,[],[f3274,f3240,f2076,f7382]) ).
fof(f7382,plain,
( spl61_906
<=> ! [X16,X17] :
( ~ empty_carrier(net_of_bool_filter(X16,X17,sK17(the_carrier(boole_POSet(X17)))))
| ~ upper_relstr_subset(sK17(the_carrier(boole_POSet(X17))),boole_POSet(X17))
| ~ filtered_subset(sK17(the_carrier(boole_POSet(X17))),boole_POSet(X17))
| empty(sK17(the_carrier(boole_POSet(X17))))
| ~ element(X17,powerset(the_carrier(X16)))
| empty(X17)
| ~ one_sorted_str(X16)
| empty_carrier(X16)
| empty(the_carrier(boole_POSet(X17))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_906])]) ).
fof(f3274,plain,
( ! [X16,X17] :
( ~ empty_carrier(net_of_bool_filter(X16,X17,sK17(the_carrier(boole_POSet(X17)))))
| ~ upper_relstr_subset(sK17(the_carrier(boole_POSet(X17))),boole_POSet(X17))
| ~ filtered_subset(sK17(the_carrier(boole_POSet(X17))),boole_POSet(X17))
| empty(sK17(the_carrier(boole_POSet(X17))))
| ~ element(X17,powerset(the_carrier(X16)))
| empty(X17)
| ~ one_sorted_str(X16)
| empty_carrier(X16)
| empty(the_carrier(boole_POSet(X17))) )
| ~ spl61_250
| ~ spl61_388 ),
inference(resolution,[],[f3241,f2077]) ).
fof(f7380,plain,
( spl61_905
| ~ spl61_249
| ~ spl61_388 ),
inference(avatar_split_clause,[],[f3273,f3240,f2072,f7378]) ).
fof(f7378,plain,
( spl61_905
<=> ! [X14,X15] :
( ~ empty_carrier(net_of_bool_filter(X14,X15,sK16(the_carrier(boole_POSet(X15)))))
| ~ upper_relstr_subset(sK16(the_carrier(boole_POSet(X15))),boole_POSet(X15))
| ~ filtered_subset(sK16(the_carrier(boole_POSet(X15))),boole_POSet(X15))
| empty(sK16(the_carrier(boole_POSet(X15))))
| ~ element(X15,powerset(the_carrier(X14)))
| empty(X15)
| ~ one_sorted_str(X14)
| empty_carrier(X14)
| empty(the_carrier(boole_POSet(X15))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_905])]) ).
fof(f3273,plain,
( ! [X14,X15] :
( ~ empty_carrier(net_of_bool_filter(X14,X15,sK16(the_carrier(boole_POSet(X15)))))
| ~ upper_relstr_subset(sK16(the_carrier(boole_POSet(X15))),boole_POSet(X15))
| ~ filtered_subset(sK16(the_carrier(boole_POSet(X15))),boole_POSet(X15))
| empty(sK16(the_carrier(boole_POSet(X15))))
| ~ element(X15,powerset(the_carrier(X14)))
| empty(X15)
| ~ one_sorted_str(X14)
| empty_carrier(X14)
| empty(the_carrier(boole_POSet(X15))) )
| ~ spl61_249
| ~ spl61_388 ),
inference(resolution,[],[f3241,f2073]) ).
fof(f7376,plain,
( spl61_904
| ~ spl61_248
| ~ spl61_388 ),
inference(avatar_split_clause,[],[f3272,f3240,f2068,f7374]) ).
fof(f7374,plain,
( spl61_904
<=> ! [X13,X12] :
( ~ empty_carrier(net_of_bool_filter(X12,X13,sK15(the_carrier(boole_POSet(X13)))))
| ~ upper_relstr_subset(sK15(the_carrier(boole_POSet(X13))),boole_POSet(X13))
| ~ filtered_subset(sK15(the_carrier(boole_POSet(X13))),boole_POSet(X13))
| empty(sK15(the_carrier(boole_POSet(X13))))
| ~ element(X13,powerset(the_carrier(X12)))
| empty(X13)
| ~ one_sorted_str(X12)
| empty_carrier(X12)
| empty(the_carrier(boole_POSet(X13))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_904])]) ).
fof(f3272,plain,
( ! [X12,X13] :
( ~ empty_carrier(net_of_bool_filter(X12,X13,sK15(the_carrier(boole_POSet(X13)))))
| ~ upper_relstr_subset(sK15(the_carrier(boole_POSet(X13))),boole_POSet(X13))
| ~ filtered_subset(sK15(the_carrier(boole_POSet(X13))),boole_POSet(X13))
| empty(sK15(the_carrier(boole_POSet(X13))))
| ~ element(X13,powerset(the_carrier(X12)))
| empty(X13)
| ~ one_sorted_str(X12)
| empty_carrier(X12)
| empty(the_carrier(boole_POSet(X13))) )
| ~ spl61_248
| ~ spl61_388 ),
inference(resolution,[],[f3241,f2069]) ).
fof(f7354,plain,
( spl61_903
| ~ spl61_261
| ~ spl61_531 ),
inference(avatar_split_clause,[],[f4440,f4436,f2121,f7352]) ).
fof(f7352,plain,
( spl61_903
<=> ! [X0] :
( empty_carrier(X0)
| ~ one_sorted_str(X0)
| transitive_relstr(net_of_bool_filter(X0,cast_as_carrier_subset(sK12),sK13))
| ~ subset(cast_as_carrier_subset(sK12),the_carrier(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_903])]) ).
fof(f4440,plain,
( ! [X0] :
( empty_carrier(X0)
| ~ one_sorted_str(X0)
| transitive_relstr(net_of_bool_filter(X0,cast_as_carrier_subset(sK12),sK13))
| ~ subset(cast_as_carrier_subset(sK12),the_carrier(X0)) )
| ~ spl61_261
| ~ spl61_531 ),
inference(resolution,[],[f4437,f2122]) ).
fof(f7328,plain,
( spl61_902
| ~ spl61_332
| ~ spl61_396 ),
inference(avatar_split_clause,[],[f3410,f3358,f2561,f7326]) ).
fof(f7326,plain,
( spl61_902
<=> ! [X46,X47] :
( net_str(net_of_bool_filter(X46,X47,sK36(boole_POSet(X47))),X46)
| ~ upper_relstr_subset(sK36(boole_POSet(X47)),boole_POSet(X47))
| ~ filtered_subset(sK36(boole_POSet(X47)),boole_POSet(X47))
| empty(sK36(boole_POSet(X47)))
| ~ element(X47,powerset(the_carrier(X46)))
| empty(X47)
| ~ one_sorted_str(X46)
| empty_carrier(X46)
| ~ top_str(boole_POSet(X47))
| ~ topological_space(boole_POSet(X47)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_902])]) ).
fof(f2561,plain,
( spl61_332
<=> ! [X0] :
( element(sK36(X0),powerset(the_carrier(X0)))
| ~ top_str(X0)
| ~ topological_space(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_332])]) ).
fof(f3410,plain,
( ! [X46,X47] :
( net_str(net_of_bool_filter(X46,X47,sK36(boole_POSet(X47))),X46)
| ~ upper_relstr_subset(sK36(boole_POSet(X47)),boole_POSet(X47))
| ~ filtered_subset(sK36(boole_POSet(X47)),boole_POSet(X47))
| empty(sK36(boole_POSet(X47)))
| ~ element(X47,powerset(the_carrier(X46)))
| empty(X47)
| ~ one_sorted_str(X46)
| empty_carrier(X46)
| ~ top_str(boole_POSet(X47))
| ~ topological_space(boole_POSet(X47)) )
| ~ spl61_332
| ~ spl61_396 ),
inference(resolution,[],[f3359,f2562]) ).
fof(f2562,plain,
( ! [X0] :
( element(sK36(X0),powerset(the_carrier(X0)))
| ~ top_str(X0)
| ~ topological_space(X0) )
| ~ spl61_332 ),
inference(avatar_component_clause,[],[f2561]) ).
fof(f7324,plain,
( spl61_901
| ~ spl61_331
| ~ spl61_396 ),
inference(avatar_split_clause,[],[f3409,f3358,f2557,f7322]) ).
fof(f7322,plain,
( spl61_901
<=> ! [X45,X44] :
( net_str(net_of_bool_filter(X44,X45,sK35(boole_POSet(X45))),X44)
| ~ upper_relstr_subset(sK35(boole_POSet(X45)),boole_POSet(X45))
| ~ filtered_subset(sK35(boole_POSet(X45)),boole_POSet(X45))
| empty(sK35(boole_POSet(X45)))
| ~ element(X45,powerset(the_carrier(X44)))
| empty(X45)
| ~ one_sorted_str(X44)
| empty_carrier(X44)
| ~ top_str(boole_POSet(X45))
| ~ topological_space(boole_POSet(X45)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_901])]) ).
fof(f2557,plain,
( spl61_331
<=> ! [X0] :
( element(sK35(X0),powerset(the_carrier(X0)))
| ~ top_str(X0)
| ~ topological_space(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_331])]) ).
fof(f3409,plain,
( ! [X44,X45] :
( net_str(net_of_bool_filter(X44,X45,sK35(boole_POSet(X45))),X44)
| ~ upper_relstr_subset(sK35(boole_POSet(X45)),boole_POSet(X45))
| ~ filtered_subset(sK35(boole_POSet(X45)),boole_POSet(X45))
| empty(sK35(boole_POSet(X45)))
| ~ element(X45,powerset(the_carrier(X44)))
| empty(X45)
| ~ one_sorted_str(X44)
| empty_carrier(X44)
| ~ top_str(boole_POSet(X45))
| ~ topological_space(boole_POSet(X45)) )
| ~ spl61_331
| ~ spl61_396 ),
inference(resolution,[],[f3359,f2558]) ).
fof(f2558,plain,
( ! [X0] :
( element(sK35(X0),powerset(the_carrier(X0)))
| ~ top_str(X0)
| ~ topological_space(X0) )
| ~ spl61_331 ),
inference(avatar_component_clause,[],[f2557]) ).
fof(f7320,plain,
( spl61_900
| ~ spl61_330
| ~ spl61_396 ),
inference(avatar_split_clause,[],[f3408,f3358,f2553,f7318]) ).
fof(f7318,plain,
( spl61_900
<=> ! [X43,X42] :
( net_str(net_of_bool_filter(X42,X43,sK34(boole_POSet(X43))),X42)
| ~ upper_relstr_subset(sK34(boole_POSet(X43)),boole_POSet(X43))
| ~ filtered_subset(sK34(boole_POSet(X43)),boole_POSet(X43))
| empty(sK34(boole_POSet(X43)))
| ~ element(X43,powerset(the_carrier(X42)))
| empty(X43)
| ~ one_sorted_str(X42)
| empty_carrier(X42)
| ~ top_str(boole_POSet(X43))
| ~ topological_space(boole_POSet(X43)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_900])]) ).
fof(f2553,plain,
( spl61_330
<=> ! [X0] :
( element(sK34(X0),powerset(the_carrier(X0)))
| ~ top_str(X0)
| ~ topological_space(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_330])]) ).
fof(f3408,plain,
( ! [X42,X43] :
( net_str(net_of_bool_filter(X42,X43,sK34(boole_POSet(X43))),X42)
| ~ upper_relstr_subset(sK34(boole_POSet(X43)),boole_POSet(X43))
| ~ filtered_subset(sK34(boole_POSet(X43)),boole_POSet(X43))
| empty(sK34(boole_POSet(X43)))
| ~ element(X43,powerset(the_carrier(X42)))
| empty(X43)
| ~ one_sorted_str(X42)
| empty_carrier(X42)
| ~ top_str(boole_POSet(X43))
| ~ topological_space(boole_POSet(X43)) )
| ~ spl61_330
| ~ spl61_396 ),
inference(resolution,[],[f3359,f2554]) ).
fof(f2554,plain,
( ! [X0] :
( element(sK34(X0),powerset(the_carrier(X0)))
| ~ top_str(X0)
| ~ topological_space(X0) )
| ~ spl61_330 ),
inference(avatar_component_clause,[],[f2553]) ).
fof(f7316,plain,
( spl61_899
| ~ spl61_261
| ~ spl61_530 ),
inference(avatar_split_clause,[],[f4433,f4429,f2121,f7314]) ).
fof(f7314,plain,
( spl61_899
<=> ! [X0] :
( empty_carrier(X0)
| ~ one_sorted_str(X0)
| reflexive_relstr(net_of_bool_filter(X0,cast_as_carrier_subset(sK12),sK13))
| ~ subset(cast_as_carrier_subset(sK12),the_carrier(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_899])]) ).
fof(f4433,plain,
( ! [X0] :
( empty_carrier(X0)
| ~ one_sorted_str(X0)
| reflexive_relstr(net_of_bool_filter(X0,cast_as_carrier_subset(sK12),sK13))
| ~ subset(cast_as_carrier_subset(sK12),the_carrier(X0)) )
| ~ spl61_261
| ~ spl61_530 ),
inference(resolution,[],[f4430,f2122]) ).
fof(f7312,plain,
( spl61_898
| ~ spl61_329
| ~ spl61_396 ),
inference(avatar_split_clause,[],[f3403,f3358,f2541,f7310]) ).
fof(f7310,plain,
( spl61_898
<=> ! [X32,X33] :
( net_str(net_of_bool_filter(X32,X33,sK29(boole_POSet(X33))),X32)
| ~ upper_relstr_subset(sK29(boole_POSet(X33)),boole_POSet(X33))
| ~ filtered_subset(sK29(boole_POSet(X33)),boole_POSet(X33))
| empty(sK29(boole_POSet(X33)))
| ~ element(X33,powerset(the_carrier(X32)))
| empty(X33)
| ~ one_sorted_str(X32)
| empty_carrier(X32)
| ~ rel_str(boole_POSet(X33))
| empty_carrier(boole_POSet(X33)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_898])]) ).
fof(f2541,plain,
( spl61_329
<=> ! [X0] :
( element(sK29(X0),powerset(the_carrier(X0)))
| ~ rel_str(X0)
| empty_carrier(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_329])]) ).
fof(f3403,plain,
( ! [X32,X33] :
( net_str(net_of_bool_filter(X32,X33,sK29(boole_POSet(X33))),X32)
| ~ upper_relstr_subset(sK29(boole_POSet(X33)),boole_POSet(X33))
| ~ filtered_subset(sK29(boole_POSet(X33)),boole_POSet(X33))
| empty(sK29(boole_POSet(X33)))
| ~ element(X33,powerset(the_carrier(X32)))
| empty(X33)
| ~ one_sorted_str(X32)
| empty_carrier(X32)
| ~ rel_str(boole_POSet(X33))
| empty_carrier(boole_POSet(X33)) )
| ~ spl61_329
| ~ spl61_396 ),
inference(resolution,[],[f3359,f2542]) ).
fof(f2542,plain,
( ! [X0] :
( element(sK29(X0),powerset(the_carrier(X0)))
| ~ rel_str(X0)
| empty_carrier(X0) )
| ~ spl61_329 ),
inference(avatar_component_clause,[],[f2541]) ).
fof(f7308,plain,
( spl61_897
| ~ spl61_326
| ~ spl61_396 ),
inference(avatar_split_clause,[],[f3402,f3358,f2529,f7306]) ).
fof(f7306,plain,
( spl61_897
<=> ! [X30,X31] :
( net_str(net_of_bool_filter(X30,X31,sK28(boole_POSet(X31))),X30)
| ~ upper_relstr_subset(sK28(boole_POSet(X31)),boole_POSet(X31))
| ~ filtered_subset(sK28(boole_POSet(X31)),boole_POSet(X31))
| empty(sK28(boole_POSet(X31)))
| ~ element(X31,powerset(the_carrier(X30)))
| empty(X31)
| ~ one_sorted_str(X30)
| empty_carrier(X30)
| ~ one_sorted_str(boole_POSet(X31))
| empty_carrier(boole_POSet(X31)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_897])]) ).
fof(f2529,plain,
( spl61_326
<=> ! [X0] :
( element(sK28(X0),powerset(the_carrier(X0)))
| ~ one_sorted_str(X0)
| empty_carrier(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_326])]) ).
fof(f3402,plain,
( ! [X31,X30] :
( net_str(net_of_bool_filter(X30,X31,sK28(boole_POSet(X31))),X30)
| ~ upper_relstr_subset(sK28(boole_POSet(X31)),boole_POSet(X31))
| ~ filtered_subset(sK28(boole_POSet(X31)),boole_POSet(X31))
| empty(sK28(boole_POSet(X31)))
| ~ element(X31,powerset(the_carrier(X30)))
| empty(X31)
| ~ one_sorted_str(X30)
| empty_carrier(X30)
| ~ one_sorted_str(boole_POSet(X31))
| empty_carrier(boole_POSet(X31)) )
| ~ spl61_326
| ~ spl61_396 ),
inference(resolution,[],[f3359,f2530]) ).
fof(f2530,plain,
( ! [X0] :
( element(sK28(X0),powerset(the_carrier(X0)))
| ~ one_sorted_str(X0)
| empty_carrier(X0) )
| ~ spl61_326 ),
inference(avatar_component_clause,[],[f2529]) ).
fof(f7304,plain,
( spl61_896
| ~ spl61_332
| ~ spl61_395 ),
inference(avatar_split_clause,[],[f3383,f3354,f2561,f7302]) ).
fof(f7302,plain,
( spl61_896
<=> ! [X46,X47] :
( strict_net_str(net_of_bool_filter(X46,X47,sK36(boole_POSet(X47))),X46)
| ~ upper_relstr_subset(sK36(boole_POSet(X47)),boole_POSet(X47))
| ~ filtered_subset(sK36(boole_POSet(X47)),boole_POSet(X47))
| empty(sK36(boole_POSet(X47)))
| ~ element(X47,powerset(the_carrier(X46)))
| empty(X47)
| ~ one_sorted_str(X46)
| empty_carrier(X46)
| ~ top_str(boole_POSet(X47))
| ~ topological_space(boole_POSet(X47)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_896])]) ).
fof(f3383,plain,
( ! [X46,X47] :
( strict_net_str(net_of_bool_filter(X46,X47,sK36(boole_POSet(X47))),X46)
| ~ upper_relstr_subset(sK36(boole_POSet(X47)),boole_POSet(X47))
| ~ filtered_subset(sK36(boole_POSet(X47)),boole_POSet(X47))
| empty(sK36(boole_POSet(X47)))
| ~ element(X47,powerset(the_carrier(X46)))
| empty(X47)
| ~ one_sorted_str(X46)
| empty_carrier(X46)
| ~ top_str(boole_POSet(X47))
| ~ topological_space(boole_POSet(X47)) )
| ~ spl61_332
| ~ spl61_395 ),
inference(resolution,[],[f3355,f2562]) ).
fof(f7300,plain,
( spl61_895
| ~ spl61_331
| ~ spl61_395 ),
inference(avatar_split_clause,[],[f3382,f3354,f2557,f7298]) ).
fof(f7298,plain,
( spl61_895
<=> ! [X45,X44] :
( strict_net_str(net_of_bool_filter(X44,X45,sK35(boole_POSet(X45))),X44)
| ~ upper_relstr_subset(sK35(boole_POSet(X45)),boole_POSet(X45))
| ~ filtered_subset(sK35(boole_POSet(X45)),boole_POSet(X45))
| empty(sK35(boole_POSet(X45)))
| ~ element(X45,powerset(the_carrier(X44)))
| empty(X45)
| ~ one_sorted_str(X44)
| empty_carrier(X44)
| ~ top_str(boole_POSet(X45))
| ~ topological_space(boole_POSet(X45)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_895])]) ).
fof(f3382,plain,
( ! [X44,X45] :
( strict_net_str(net_of_bool_filter(X44,X45,sK35(boole_POSet(X45))),X44)
| ~ upper_relstr_subset(sK35(boole_POSet(X45)),boole_POSet(X45))
| ~ filtered_subset(sK35(boole_POSet(X45)),boole_POSet(X45))
| empty(sK35(boole_POSet(X45)))
| ~ element(X45,powerset(the_carrier(X44)))
| empty(X45)
| ~ one_sorted_str(X44)
| empty_carrier(X44)
| ~ top_str(boole_POSet(X45))
| ~ topological_space(boole_POSet(X45)) )
| ~ spl61_331
| ~ spl61_395 ),
inference(resolution,[],[f3355,f2558]) ).
fof(f7296,plain,
( spl61_894
| ~ spl61_330
| ~ spl61_395 ),
inference(avatar_split_clause,[],[f3381,f3354,f2553,f7294]) ).
fof(f7294,plain,
( spl61_894
<=> ! [X43,X42] :
( strict_net_str(net_of_bool_filter(X42,X43,sK34(boole_POSet(X43))),X42)
| ~ upper_relstr_subset(sK34(boole_POSet(X43)),boole_POSet(X43))
| ~ filtered_subset(sK34(boole_POSet(X43)),boole_POSet(X43))
| empty(sK34(boole_POSet(X43)))
| ~ element(X43,powerset(the_carrier(X42)))
| empty(X43)
| ~ one_sorted_str(X42)
| empty_carrier(X42)
| ~ top_str(boole_POSet(X43))
| ~ topological_space(boole_POSet(X43)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_894])]) ).
fof(f3381,plain,
( ! [X42,X43] :
( strict_net_str(net_of_bool_filter(X42,X43,sK34(boole_POSet(X43))),X42)
| ~ upper_relstr_subset(sK34(boole_POSet(X43)),boole_POSet(X43))
| ~ filtered_subset(sK34(boole_POSet(X43)),boole_POSet(X43))
| empty(sK34(boole_POSet(X43)))
| ~ element(X43,powerset(the_carrier(X42)))
| empty(X43)
| ~ one_sorted_str(X42)
| empty_carrier(X42)
| ~ top_str(boole_POSet(X43))
| ~ topological_space(boole_POSet(X43)) )
| ~ spl61_330
| ~ spl61_395 ),
inference(resolution,[],[f3355,f2554]) ).
fof(f7292,plain,
( spl61_893
| ~ spl61_329
| ~ spl61_395 ),
inference(avatar_split_clause,[],[f3376,f3354,f2541,f7290]) ).
fof(f7290,plain,
( spl61_893
<=> ! [X32,X33] :
( strict_net_str(net_of_bool_filter(X32,X33,sK29(boole_POSet(X33))),X32)
| ~ upper_relstr_subset(sK29(boole_POSet(X33)),boole_POSet(X33))
| ~ filtered_subset(sK29(boole_POSet(X33)),boole_POSet(X33))
| empty(sK29(boole_POSet(X33)))
| ~ element(X33,powerset(the_carrier(X32)))
| empty(X33)
| ~ one_sorted_str(X32)
| empty_carrier(X32)
| ~ rel_str(boole_POSet(X33))
| empty_carrier(boole_POSet(X33)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_893])]) ).
fof(f3376,plain,
( ! [X32,X33] :
( strict_net_str(net_of_bool_filter(X32,X33,sK29(boole_POSet(X33))),X32)
| ~ upper_relstr_subset(sK29(boole_POSet(X33)),boole_POSet(X33))
| ~ filtered_subset(sK29(boole_POSet(X33)),boole_POSet(X33))
| empty(sK29(boole_POSet(X33)))
| ~ element(X33,powerset(the_carrier(X32)))
| empty(X33)
| ~ one_sorted_str(X32)
| empty_carrier(X32)
| ~ rel_str(boole_POSet(X33))
| empty_carrier(boole_POSet(X33)) )
| ~ spl61_329
| ~ spl61_395 ),
inference(resolution,[],[f3355,f2542]) ).
fof(f7288,plain,
( spl61_892
| ~ spl61_326
| ~ spl61_395 ),
inference(avatar_split_clause,[],[f3375,f3354,f2529,f7286]) ).
fof(f7286,plain,
( spl61_892
<=> ! [X30,X31] :
( strict_net_str(net_of_bool_filter(X30,X31,sK28(boole_POSet(X31))),X30)
| ~ upper_relstr_subset(sK28(boole_POSet(X31)),boole_POSet(X31))
| ~ filtered_subset(sK28(boole_POSet(X31)),boole_POSet(X31))
| empty(sK28(boole_POSet(X31)))
| ~ element(X31,powerset(the_carrier(X30)))
| empty(X31)
| ~ one_sorted_str(X30)
| empty_carrier(X30)
| ~ one_sorted_str(boole_POSet(X31))
| empty_carrier(boole_POSet(X31)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_892])]) ).
fof(f3375,plain,
( ! [X31,X30] :
( strict_net_str(net_of_bool_filter(X30,X31,sK28(boole_POSet(X31))),X30)
| ~ upper_relstr_subset(sK28(boole_POSet(X31)),boole_POSet(X31))
| ~ filtered_subset(sK28(boole_POSet(X31)),boole_POSet(X31))
| empty(sK28(boole_POSet(X31)))
| ~ element(X31,powerset(the_carrier(X30)))
| empty(X31)
| ~ one_sorted_str(X30)
| empty_carrier(X30)
| ~ one_sorted_str(boole_POSet(X31))
| empty_carrier(boole_POSet(X31)) )
| ~ spl61_326
| ~ spl61_395 ),
inference(resolution,[],[f3355,f2530]) ).
fof(f7284,plain,
( spl61_891
| ~ spl61_261
| ~ spl61_505 ),
inference(avatar_split_clause,[],[f4426,f4286,f2121,f7282]) ).
fof(f7282,plain,
( spl61_891
<=> ! [X0] :
( empty_carrier(X0)
| ~ one_sorted_str(X0)
| ~ empty_carrier(net_of_bool_filter(X0,cast_as_carrier_subset(sK12),sK13))
| ~ subset(cast_as_carrier_subset(sK12),the_carrier(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_891])]) ).
fof(f4426,plain,
( ! [X0] :
( empty_carrier(X0)
| ~ one_sorted_str(X0)
| ~ empty_carrier(net_of_bool_filter(X0,cast_as_carrier_subset(sK12),sK13))
| ~ subset(cast_as_carrier_subset(sK12),the_carrier(X0)) )
| ~ spl61_261
| ~ spl61_505 ),
inference(resolution,[],[f4287,f2122]) ).
fof(f7275,plain,
( spl61_890
| ~ spl61_332
| ~ spl61_390 ),
inference(avatar_split_clause,[],[f3344,f3248,f2561,f7273]) ).
fof(f7273,plain,
( spl61_890
<=> ! [X46,X47] :
( transitive_relstr(net_of_bool_filter(X46,X47,sK36(boole_POSet(X47))))
| ~ upper_relstr_subset(sK36(boole_POSet(X47)),boole_POSet(X47))
| ~ filtered_subset(sK36(boole_POSet(X47)),boole_POSet(X47))
| empty(sK36(boole_POSet(X47)))
| ~ element(X47,powerset(the_carrier(X46)))
| empty(X47)
| ~ one_sorted_str(X46)
| empty_carrier(X46)
| ~ top_str(boole_POSet(X47))
| ~ topological_space(boole_POSet(X47)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_890])]) ).
fof(f3344,plain,
( ! [X46,X47] :
( transitive_relstr(net_of_bool_filter(X46,X47,sK36(boole_POSet(X47))))
| ~ upper_relstr_subset(sK36(boole_POSet(X47)),boole_POSet(X47))
| ~ filtered_subset(sK36(boole_POSet(X47)),boole_POSet(X47))
| empty(sK36(boole_POSet(X47)))
| ~ element(X47,powerset(the_carrier(X46)))
| empty(X47)
| ~ one_sorted_str(X46)
| empty_carrier(X46)
| ~ top_str(boole_POSet(X47))
| ~ topological_space(boole_POSet(X47)) )
| ~ spl61_332
| ~ spl61_390 ),
inference(resolution,[],[f3249,f2562]) ).
fof(f7271,plain,
( spl61_889
| ~ spl61_331
| ~ spl61_390 ),
inference(avatar_split_clause,[],[f3343,f3248,f2557,f7269]) ).
fof(f7269,plain,
( spl61_889
<=> ! [X45,X44] :
( transitive_relstr(net_of_bool_filter(X44,X45,sK35(boole_POSet(X45))))
| ~ upper_relstr_subset(sK35(boole_POSet(X45)),boole_POSet(X45))
| ~ filtered_subset(sK35(boole_POSet(X45)),boole_POSet(X45))
| empty(sK35(boole_POSet(X45)))
| ~ element(X45,powerset(the_carrier(X44)))
| empty(X45)
| ~ one_sorted_str(X44)
| empty_carrier(X44)
| ~ top_str(boole_POSet(X45))
| ~ topological_space(boole_POSet(X45)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_889])]) ).
fof(f3343,plain,
( ! [X44,X45] :
( transitive_relstr(net_of_bool_filter(X44,X45,sK35(boole_POSet(X45))))
| ~ upper_relstr_subset(sK35(boole_POSet(X45)),boole_POSet(X45))
| ~ filtered_subset(sK35(boole_POSet(X45)),boole_POSet(X45))
| empty(sK35(boole_POSet(X45)))
| ~ element(X45,powerset(the_carrier(X44)))
| empty(X45)
| ~ one_sorted_str(X44)
| empty_carrier(X44)
| ~ top_str(boole_POSet(X45))
| ~ topological_space(boole_POSet(X45)) )
| ~ spl61_331
| ~ spl61_390 ),
inference(resolution,[],[f3249,f2558]) ).
fof(f7267,plain,
( spl61_888
| ~ spl61_330
| ~ spl61_390 ),
inference(avatar_split_clause,[],[f3342,f3248,f2553,f7265]) ).
fof(f7265,plain,
( spl61_888
<=> ! [X43,X42] :
( transitive_relstr(net_of_bool_filter(X42,X43,sK34(boole_POSet(X43))))
| ~ upper_relstr_subset(sK34(boole_POSet(X43)),boole_POSet(X43))
| ~ filtered_subset(sK34(boole_POSet(X43)),boole_POSet(X43))
| empty(sK34(boole_POSet(X43)))
| ~ element(X43,powerset(the_carrier(X42)))
| empty(X43)
| ~ one_sorted_str(X42)
| empty_carrier(X42)
| ~ top_str(boole_POSet(X43))
| ~ topological_space(boole_POSet(X43)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_888])]) ).
fof(f3342,plain,
( ! [X42,X43] :
( transitive_relstr(net_of_bool_filter(X42,X43,sK34(boole_POSet(X43))))
| ~ upper_relstr_subset(sK34(boole_POSet(X43)),boole_POSet(X43))
| ~ filtered_subset(sK34(boole_POSet(X43)),boole_POSet(X43))
| empty(sK34(boole_POSet(X43)))
| ~ element(X43,powerset(the_carrier(X42)))
| empty(X43)
| ~ one_sorted_str(X42)
| empty_carrier(X42)
| ~ top_str(boole_POSet(X43))
| ~ topological_space(boole_POSet(X43)) )
| ~ spl61_330
| ~ spl61_390 ),
inference(resolution,[],[f3249,f2554]) ).
fof(f7263,plain,
( spl61_887
| ~ spl61_329
| ~ spl61_390 ),
inference(avatar_split_clause,[],[f3337,f3248,f2541,f7261]) ).
fof(f7261,plain,
( spl61_887
<=> ! [X32,X33] :
( transitive_relstr(net_of_bool_filter(X32,X33,sK29(boole_POSet(X33))))
| ~ upper_relstr_subset(sK29(boole_POSet(X33)),boole_POSet(X33))
| ~ filtered_subset(sK29(boole_POSet(X33)),boole_POSet(X33))
| empty(sK29(boole_POSet(X33)))
| ~ element(X33,powerset(the_carrier(X32)))
| empty(X33)
| ~ one_sorted_str(X32)
| empty_carrier(X32)
| ~ rel_str(boole_POSet(X33))
| empty_carrier(boole_POSet(X33)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_887])]) ).
fof(f3337,plain,
( ! [X32,X33] :
( transitive_relstr(net_of_bool_filter(X32,X33,sK29(boole_POSet(X33))))
| ~ upper_relstr_subset(sK29(boole_POSet(X33)),boole_POSet(X33))
| ~ filtered_subset(sK29(boole_POSet(X33)),boole_POSet(X33))
| empty(sK29(boole_POSet(X33)))
| ~ element(X33,powerset(the_carrier(X32)))
| empty(X33)
| ~ one_sorted_str(X32)
| empty_carrier(X32)
| ~ rel_str(boole_POSet(X33))
| empty_carrier(boole_POSet(X33)) )
| ~ spl61_329
| ~ spl61_390 ),
inference(resolution,[],[f3249,f2542]) ).
fof(f7259,plain,
( spl61_886
| ~ spl61_326
| ~ spl61_390 ),
inference(avatar_split_clause,[],[f3336,f3248,f2529,f7257]) ).
fof(f7257,plain,
( spl61_886
<=> ! [X30,X31] :
( transitive_relstr(net_of_bool_filter(X30,X31,sK28(boole_POSet(X31))))
| ~ upper_relstr_subset(sK28(boole_POSet(X31)),boole_POSet(X31))
| ~ filtered_subset(sK28(boole_POSet(X31)),boole_POSet(X31))
| empty(sK28(boole_POSet(X31)))
| ~ element(X31,powerset(the_carrier(X30)))
| empty(X31)
| ~ one_sorted_str(X30)
| empty_carrier(X30)
| ~ one_sorted_str(boole_POSet(X31))
| empty_carrier(boole_POSet(X31)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_886])]) ).
fof(f3336,plain,
( ! [X31,X30] :
( transitive_relstr(net_of_bool_filter(X30,X31,sK28(boole_POSet(X31))))
| ~ upper_relstr_subset(sK28(boole_POSet(X31)),boole_POSet(X31))
| ~ filtered_subset(sK28(boole_POSet(X31)),boole_POSet(X31))
| empty(sK28(boole_POSet(X31)))
| ~ element(X31,powerset(the_carrier(X30)))
| empty(X31)
| ~ one_sorted_str(X30)
| empty_carrier(X30)
| ~ one_sorted_str(boole_POSet(X31))
| empty_carrier(boole_POSet(X31)) )
| ~ spl61_326
| ~ spl61_390 ),
inference(resolution,[],[f3249,f2530]) ).
fof(f7255,plain,
( spl61_885
| ~ spl61_332
| ~ spl61_389 ),
inference(avatar_split_clause,[],[f3316,f3244,f2561,f7253]) ).
fof(f7253,plain,
( spl61_885
<=> ! [X46,X47] :
( reflexive_relstr(net_of_bool_filter(X46,X47,sK36(boole_POSet(X47))))
| ~ upper_relstr_subset(sK36(boole_POSet(X47)),boole_POSet(X47))
| ~ filtered_subset(sK36(boole_POSet(X47)),boole_POSet(X47))
| empty(sK36(boole_POSet(X47)))
| ~ element(X47,powerset(the_carrier(X46)))
| empty(X47)
| ~ one_sorted_str(X46)
| empty_carrier(X46)
| ~ top_str(boole_POSet(X47))
| ~ topological_space(boole_POSet(X47)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_885])]) ).
fof(f3316,plain,
( ! [X46,X47] :
( reflexive_relstr(net_of_bool_filter(X46,X47,sK36(boole_POSet(X47))))
| ~ upper_relstr_subset(sK36(boole_POSet(X47)),boole_POSet(X47))
| ~ filtered_subset(sK36(boole_POSet(X47)),boole_POSet(X47))
| empty(sK36(boole_POSet(X47)))
| ~ element(X47,powerset(the_carrier(X46)))
| empty(X47)
| ~ one_sorted_str(X46)
| empty_carrier(X46)
| ~ top_str(boole_POSet(X47))
| ~ topological_space(boole_POSet(X47)) )
| ~ spl61_332
| ~ spl61_389 ),
inference(resolution,[],[f3245,f2562]) ).
fof(f7251,plain,
( spl61_884
| ~ spl61_331
| ~ spl61_389 ),
inference(avatar_split_clause,[],[f3315,f3244,f2557,f7249]) ).
fof(f7249,plain,
( spl61_884
<=> ! [X45,X44] :
( reflexive_relstr(net_of_bool_filter(X44,X45,sK35(boole_POSet(X45))))
| ~ upper_relstr_subset(sK35(boole_POSet(X45)),boole_POSet(X45))
| ~ filtered_subset(sK35(boole_POSet(X45)),boole_POSet(X45))
| empty(sK35(boole_POSet(X45)))
| ~ element(X45,powerset(the_carrier(X44)))
| empty(X45)
| ~ one_sorted_str(X44)
| empty_carrier(X44)
| ~ top_str(boole_POSet(X45))
| ~ topological_space(boole_POSet(X45)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_884])]) ).
fof(f3315,plain,
( ! [X44,X45] :
( reflexive_relstr(net_of_bool_filter(X44,X45,sK35(boole_POSet(X45))))
| ~ upper_relstr_subset(sK35(boole_POSet(X45)),boole_POSet(X45))
| ~ filtered_subset(sK35(boole_POSet(X45)),boole_POSet(X45))
| empty(sK35(boole_POSet(X45)))
| ~ element(X45,powerset(the_carrier(X44)))
| empty(X45)
| ~ one_sorted_str(X44)
| empty_carrier(X44)
| ~ top_str(boole_POSet(X45))
| ~ topological_space(boole_POSet(X45)) )
| ~ spl61_331
| ~ spl61_389 ),
inference(resolution,[],[f3245,f2558]) ).
fof(f7247,plain,
( spl61_883
| ~ spl61_330
| ~ spl61_389 ),
inference(avatar_split_clause,[],[f3314,f3244,f2553,f7245]) ).
fof(f7245,plain,
( spl61_883
<=> ! [X43,X42] :
( reflexive_relstr(net_of_bool_filter(X42,X43,sK34(boole_POSet(X43))))
| ~ upper_relstr_subset(sK34(boole_POSet(X43)),boole_POSet(X43))
| ~ filtered_subset(sK34(boole_POSet(X43)),boole_POSet(X43))
| empty(sK34(boole_POSet(X43)))
| ~ element(X43,powerset(the_carrier(X42)))
| empty(X43)
| ~ one_sorted_str(X42)
| empty_carrier(X42)
| ~ top_str(boole_POSet(X43))
| ~ topological_space(boole_POSet(X43)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_883])]) ).
fof(f3314,plain,
( ! [X42,X43] :
( reflexive_relstr(net_of_bool_filter(X42,X43,sK34(boole_POSet(X43))))
| ~ upper_relstr_subset(sK34(boole_POSet(X43)),boole_POSet(X43))
| ~ filtered_subset(sK34(boole_POSet(X43)),boole_POSet(X43))
| empty(sK34(boole_POSet(X43)))
| ~ element(X43,powerset(the_carrier(X42)))
| empty(X43)
| ~ one_sorted_str(X42)
| empty_carrier(X42)
| ~ top_str(boole_POSet(X43))
| ~ topological_space(boole_POSet(X43)) )
| ~ spl61_330
| ~ spl61_389 ),
inference(resolution,[],[f3245,f2554]) ).
fof(f7241,plain,
( spl61_882
| ~ spl61_329
| ~ spl61_389 ),
inference(avatar_split_clause,[],[f3309,f3244,f2541,f7239]) ).
fof(f7239,plain,
( spl61_882
<=> ! [X32,X33] :
( reflexive_relstr(net_of_bool_filter(X32,X33,sK29(boole_POSet(X33))))
| ~ upper_relstr_subset(sK29(boole_POSet(X33)),boole_POSet(X33))
| ~ filtered_subset(sK29(boole_POSet(X33)),boole_POSet(X33))
| empty(sK29(boole_POSet(X33)))
| ~ element(X33,powerset(the_carrier(X32)))
| empty(X33)
| ~ one_sorted_str(X32)
| empty_carrier(X32)
| ~ rel_str(boole_POSet(X33))
| empty_carrier(boole_POSet(X33)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_882])]) ).
fof(f3309,plain,
( ! [X32,X33] :
( reflexive_relstr(net_of_bool_filter(X32,X33,sK29(boole_POSet(X33))))
| ~ upper_relstr_subset(sK29(boole_POSet(X33)),boole_POSet(X33))
| ~ filtered_subset(sK29(boole_POSet(X33)),boole_POSet(X33))
| empty(sK29(boole_POSet(X33)))
| ~ element(X33,powerset(the_carrier(X32)))
| empty(X33)
| ~ one_sorted_str(X32)
| empty_carrier(X32)
| ~ rel_str(boole_POSet(X33))
| empty_carrier(boole_POSet(X33)) )
| ~ spl61_329
| ~ spl61_389 ),
inference(resolution,[],[f3245,f2542]) ).
fof(f7237,plain,
( spl61_881
| ~ spl61_326
| ~ spl61_389 ),
inference(avatar_split_clause,[],[f3308,f3244,f2529,f7235]) ).
fof(f7235,plain,
( spl61_881
<=> ! [X30,X31] :
( reflexive_relstr(net_of_bool_filter(X30,X31,sK28(boole_POSet(X31))))
| ~ upper_relstr_subset(sK28(boole_POSet(X31)),boole_POSet(X31))
| ~ filtered_subset(sK28(boole_POSet(X31)),boole_POSet(X31))
| empty(sK28(boole_POSet(X31)))
| ~ element(X31,powerset(the_carrier(X30)))
| empty(X31)
| ~ one_sorted_str(X30)
| empty_carrier(X30)
| ~ one_sorted_str(boole_POSet(X31))
| empty_carrier(boole_POSet(X31)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_881])]) ).
fof(f3308,plain,
( ! [X31,X30] :
( reflexive_relstr(net_of_bool_filter(X30,X31,sK28(boole_POSet(X31))))
| ~ upper_relstr_subset(sK28(boole_POSet(X31)),boole_POSet(X31))
| ~ filtered_subset(sK28(boole_POSet(X31)),boole_POSet(X31))
| empty(sK28(boole_POSet(X31)))
| ~ element(X31,powerset(the_carrier(X30)))
| empty(X31)
| ~ one_sorted_str(X30)
| empty_carrier(X30)
| ~ one_sorted_str(boole_POSet(X31))
| empty_carrier(boole_POSet(X31)) )
| ~ spl61_326
| ~ spl61_389 ),
inference(resolution,[],[f3245,f2530]) ).
fof(f7233,plain,
( spl61_880
| ~ spl61_332
| ~ spl61_388 ),
inference(avatar_split_clause,[],[f3289,f3240,f2561,f7231]) ).
fof(f7231,plain,
( spl61_880
<=> ! [X46,X47] :
( ~ empty_carrier(net_of_bool_filter(X46,X47,sK36(boole_POSet(X47))))
| ~ upper_relstr_subset(sK36(boole_POSet(X47)),boole_POSet(X47))
| ~ filtered_subset(sK36(boole_POSet(X47)),boole_POSet(X47))
| empty(sK36(boole_POSet(X47)))
| ~ element(X47,powerset(the_carrier(X46)))
| empty(X47)
| ~ one_sorted_str(X46)
| empty_carrier(X46)
| ~ top_str(boole_POSet(X47))
| ~ topological_space(boole_POSet(X47)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_880])]) ).
fof(f3289,plain,
( ! [X46,X47] :
( ~ empty_carrier(net_of_bool_filter(X46,X47,sK36(boole_POSet(X47))))
| ~ upper_relstr_subset(sK36(boole_POSet(X47)),boole_POSet(X47))
| ~ filtered_subset(sK36(boole_POSet(X47)),boole_POSet(X47))
| empty(sK36(boole_POSet(X47)))
| ~ element(X47,powerset(the_carrier(X46)))
| empty(X47)
| ~ one_sorted_str(X46)
| empty_carrier(X46)
| ~ top_str(boole_POSet(X47))
| ~ topological_space(boole_POSet(X47)) )
| ~ spl61_332
| ~ spl61_388 ),
inference(resolution,[],[f3241,f2562]) ).
fof(f7229,plain,
( spl61_879
| ~ spl61_331
| ~ spl61_388 ),
inference(avatar_split_clause,[],[f3288,f3240,f2557,f7227]) ).
fof(f7227,plain,
( spl61_879
<=> ! [X45,X44] :
( ~ empty_carrier(net_of_bool_filter(X44,X45,sK35(boole_POSet(X45))))
| ~ upper_relstr_subset(sK35(boole_POSet(X45)),boole_POSet(X45))
| ~ filtered_subset(sK35(boole_POSet(X45)),boole_POSet(X45))
| empty(sK35(boole_POSet(X45)))
| ~ element(X45,powerset(the_carrier(X44)))
| empty(X45)
| ~ one_sorted_str(X44)
| empty_carrier(X44)
| ~ top_str(boole_POSet(X45))
| ~ topological_space(boole_POSet(X45)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_879])]) ).
fof(f3288,plain,
( ! [X44,X45] :
( ~ empty_carrier(net_of_bool_filter(X44,X45,sK35(boole_POSet(X45))))
| ~ upper_relstr_subset(sK35(boole_POSet(X45)),boole_POSet(X45))
| ~ filtered_subset(sK35(boole_POSet(X45)),boole_POSet(X45))
| empty(sK35(boole_POSet(X45)))
| ~ element(X45,powerset(the_carrier(X44)))
| empty(X45)
| ~ one_sorted_str(X44)
| empty_carrier(X44)
| ~ top_str(boole_POSet(X45))
| ~ topological_space(boole_POSet(X45)) )
| ~ spl61_331
| ~ spl61_388 ),
inference(resolution,[],[f3241,f2558]) ).
fof(f7225,plain,
( spl61_878
| ~ spl61_330
| ~ spl61_388 ),
inference(avatar_split_clause,[],[f3287,f3240,f2553,f7223]) ).
fof(f7223,plain,
( spl61_878
<=> ! [X43,X42] :
( ~ empty_carrier(net_of_bool_filter(X42,X43,sK34(boole_POSet(X43))))
| ~ upper_relstr_subset(sK34(boole_POSet(X43)),boole_POSet(X43))
| ~ filtered_subset(sK34(boole_POSet(X43)),boole_POSet(X43))
| empty(sK34(boole_POSet(X43)))
| ~ element(X43,powerset(the_carrier(X42)))
| empty(X43)
| ~ one_sorted_str(X42)
| empty_carrier(X42)
| ~ top_str(boole_POSet(X43))
| ~ topological_space(boole_POSet(X43)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_878])]) ).
fof(f3287,plain,
( ! [X42,X43] :
( ~ empty_carrier(net_of_bool_filter(X42,X43,sK34(boole_POSet(X43))))
| ~ upper_relstr_subset(sK34(boole_POSet(X43)),boole_POSet(X43))
| ~ filtered_subset(sK34(boole_POSet(X43)),boole_POSet(X43))
| empty(sK34(boole_POSet(X43)))
| ~ element(X43,powerset(the_carrier(X42)))
| empty(X43)
| ~ one_sorted_str(X42)
| empty_carrier(X42)
| ~ top_str(boole_POSet(X43))
| ~ topological_space(boole_POSet(X43)) )
| ~ spl61_330
| ~ spl61_388 ),
inference(resolution,[],[f3241,f2554]) ).
fof(f7221,plain,
( spl61_877
| ~ spl61_329
| ~ spl61_388 ),
inference(avatar_split_clause,[],[f3282,f3240,f2541,f7219]) ).
fof(f7219,plain,
( spl61_877
<=> ! [X32,X33] :
( ~ empty_carrier(net_of_bool_filter(X32,X33,sK29(boole_POSet(X33))))
| ~ upper_relstr_subset(sK29(boole_POSet(X33)),boole_POSet(X33))
| ~ filtered_subset(sK29(boole_POSet(X33)),boole_POSet(X33))
| empty(sK29(boole_POSet(X33)))
| ~ element(X33,powerset(the_carrier(X32)))
| empty(X33)
| ~ one_sorted_str(X32)
| empty_carrier(X32)
| ~ rel_str(boole_POSet(X33))
| empty_carrier(boole_POSet(X33)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_877])]) ).
fof(f3282,plain,
( ! [X32,X33] :
( ~ empty_carrier(net_of_bool_filter(X32,X33,sK29(boole_POSet(X33))))
| ~ upper_relstr_subset(sK29(boole_POSet(X33)),boole_POSet(X33))
| ~ filtered_subset(sK29(boole_POSet(X33)),boole_POSet(X33))
| empty(sK29(boole_POSet(X33)))
| ~ element(X33,powerset(the_carrier(X32)))
| empty(X33)
| ~ one_sorted_str(X32)
| empty_carrier(X32)
| ~ rel_str(boole_POSet(X33))
| empty_carrier(boole_POSet(X33)) )
| ~ spl61_329
| ~ spl61_388 ),
inference(resolution,[],[f3241,f2542]) ).
fof(f7217,plain,
( spl61_876
| ~ spl61_326
| ~ spl61_388 ),
inference(avatar_split_clause,[],[f3281,f3240,f2529,f7215]) ).
fof(f7215,plain,
( spl61_876
<=> ! [X30,X31] :
( ~ empty_carrier(net_of_bool_filter(X30,X31,sK28(boole_POSet(X31))))
| ~ upper_relstr_subset(sK28(boole_POSet(X31)),boole_POSet(X31))
| ~ filtered_subset(sK28(boole_POSet(X31)),boole_POSet(X31))
| empty(sK28(boole_POSet(X31)))
| ~ element(X31,powerset(the_carrier(X30)))
| empty(X31)
| ~ one_sorted_str(X30)
| empty_carrier(X30)
| ~ one_sorted_str(boole_POSet(X31))
| empty_carrier(boole_POSet(X31)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_876])]) ).
fof(f3281,plain,
( ! [X31,X30] :
( ~ empty_carrier(net_of_bool_filter(X30,X31,sK28(boole_POSet(X31))))
| ~ upper_relstr_subset(sK28(boole_POSet(X31)),boole_POSet(X31))
| ~ filtered_subset(sK28(boole_POSet(X31)),boole_POSet(X31))
| empty(sK28(boole_POSet(X31)))
| ~ element(X31,powerset(the_carrier(X30)))
| empty(X31)
| ~ one_sorted_str(X30)
| empty_carrier(X30)
| ~ one_sorted_str(boole_POSet(X31))
| empty_carrier(boole_POSet(X31)) )
| ~ spl61_326
| ~ spl61_388 ),
inference(resolution,[],[f3241,f2530]) ).
fof(f7195,plain,
( spl61_875
| ~ spl61_573
| ~ spl61_606 ),
inference(avatar_split_clause,[],[f5119,f4997,f4754,f7193]) ).
fof(f7193,plain,
( spl61_875
<=> ! [X41] :
( ~ in(cast_as_carrier_subset(sK12),sK22(X41))
| ~ one_sorted_str(X41)
| empty_carrier(X41)
| sP11(sK13,cast_as_carrier_subset(sK12),X41) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_875])]) ).
fof(f4754,plain,
( spl61_573
<=> ! [X0] :
( sP11(sK13,cast_as_carrier_subset(sK12),X0)
| empty_carrier(X0)
| ~ one_sorted_str(X0)
| ~ element(cast_as_carrier_subset(sK12),powerset(the_carrier(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_573])]) ).
fof(f5119,plain,
( ! [X41] :
( ~ in(cast_as_carrier_subset(sK12),sK22(X41))
| ~ one_sorted_str(X41)
| empty_carrier(X41)
| sP11(sK13,cast_as_carrier_subset(sK12),X41) )
| ~ spl61_573
| ~ spl61_606 ),
inference(duplicate_literal_removal,[],[f5112]) ).
fof(f5112,plain,
( ! [X41] :
( ~ in(cast_as_carrier_subset(sK12),sK22(X41))
| ~ one_sorted_str(X41)
| empty_carrier(X41)
| ~ one_sorted_str(X41)
| sP11(sK13,cast_as_carrier_subset(sK12),X41) )
| ~ spl61_573
| ~ spl61_606 ),
inference(resolution,[],[f4998,f4755]) ).
fof(f4755,plain,
( ! [X0] :
( ~ element(cast_as_carrier_subset(sK12),powerset(the_carrier(X0)))
| empty_carrier(X0)
| ~ one_sorted_str(X0)
| sP11(sK13,cast_as_carrier_subset(sK12),X0) )
| ~ spl61_573 ),
inference(avatar_component_clause,[],[f4754]) ).
fof(f7160,plain,
( spl61_874
| ~ spl61_261
| ~ spl61_573 ),
inference(avatar_split_clause,[],[f4763,f4754,f2121,f7158]) ).
fof(f7158,plain,
( spl61_874
<=> ! [X0] :
( empty_carrier(X0)
| ~ one_sorted_str(X0)
| sP11(sK13,cast_as_carrier_subset(sK12),X0)
| ~ subset(cast_as_carrier_subset(sK12),the_carrier(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_874])]) ).
fof(f4763,plain,
( ! [X0] :
( empty_carrier(X0)
| ~ one_sorted_str(X0)
| sP11(sK13,cast_as_carrier_subset(sK12),X0)
| ~ subset(cast_as_carrier_subset(sK12),the_carrier(X0)) )
| ~ spl61_261
| ~ spl61_573 ),
inference(resolution,[],[f4755,f2122]) ).
fof(f7155,plain,
( spl61_873
| ~ spl61_292
| ~ spl61_396 ),
inference(avatar_split_clause,[],[f3411,f3358,f2277,f7153]) ).
fof(f7153,plain,
( spl61_873
<=> ! [X48,X49] :
( net_str(net_of_bool_filter(X48,X49,sK37(boole_POSet(X49))),X48)
| ~ upper_relstr_subset(sK37(boole_POSet(X49)),boole_POSet(X49))
| ~ filtered_subset(sK37(boole_POSet(X49)),boole_POSet(X49))
| empty(sK37(boole_POSet(X49)))
| ~ element(X49,powerset(the_carrier(X48)))
| empty(X49)
| ~ one_sorted_str(X48)
| empty_carrier(X48)
| ~ sP10(boole_POSet(X49)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_873])]) ).
fof(f2277,plain,
( spl61_292
<=> ! [X0] :
( element(sK37(X0),powerset(the_carrier(X0)))
| ~ sP10(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_292])]) ).
fof(f3411,plain,
( ! [X48,X49] :
( net_str(net_of_bool_filter(X48,X49,sK37(boole_POSet(X49))),X48)
| ~ upper_relstr_subset(sK37(boole_POSet(X49)),boole_POSet(X49))
| ~ filtered_subset(sK37(boole_POSet(X49)),boole_POSet(X49))
| empty(sK37(boole_POSet(X49)))
| ~ element(X49,powerset(the_carrier(X48)))
| empty(X49)
| ~ one_sorted_str(X48)
| empty_carrier(X48)
| ~ sP10(boole_POSet(X49)) )
| ~ spl61_292
| ~ spl61_396 ),
inference(resolution,[],[f3359,f2278]) ).
fof(f2278,plain,
( ! [X0] :
( element(sK37(X0),powerset(the_carrier(X0)))
| ~ sP10(X0) )
| ~ spl61_292 ),
inference(avatar_component_clause,[],[f2277]) ).
fof(f7151,plain,
( spl61_872
| ~ spl61_280
| ~ spl61_396 ),
inference(avatar_split_clause,[],[f3404,f3358,f2228,f7149]) ).
fof(f7149,plain,
( spl61_872
<=> ! [X34,X35] :
( net_str(net_of_bool_filter(X34,X35,sK30(boole_POSet(X35))),X34)
| ~ upper_relstr_subset(sK30(boole_POSet(X35)),boole_POSet(X35))
| ~ filtered_subset(sK30(boole_POSet(X35)),boole_POSet(X35))
| empty(sK30(boole_POSet(X35)))
| ~ element(X35,powerset(the_carrier(X34)))
| empty(X35)
| ~ one_sorted_str(X34)
| empty_carrier(X34)
| ~ sP7(boole_POSet(X35)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_872])]) ).
fof(f2228,plain,
( spl61_280
<=> ! [X0] :
( element(sK30(X0),powerset(the_carrier(X0)))
| ~ sP7(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_280])]) ).
fof(f3404,plain,
( ! [X34,X35] :
( net_str(net_of_bool_filter(X34,X35,sK30(boole_POSet(X35))),X34)
| ~ upper_relstr_subset(sK30(boole_POSet(X35)),boole_POSet(X35))
| ~ filtered_subset(sK30(boole_POSet(X35)),boole_POSet(X35))
| empty(sK30(boole_POSet(X35)))
| ~ element(X35,powerset(the_carrier(X34)))
| empty(X35)
| ~ one_sorted_str(X34)
| empty_carrier(X34)
| ~ sP7(boole_POSet(X35)) )
| ~ spl61_280
| ~ spl61_396 ),
inference(resolution,[],[f3359,f2229]) ).
fof(f2229,plain,
( ! [X0] :
( element(sK30(X0),powerset(the_carrier(X0)))
| ~ sP7(X0) )
| ~ spl61_280 ),
inference(avatar_component_clause,[],[f2228]) ).
fof(f7147,plain,
( spl61_871
| ~ spl61_274
| ~ spl61_396 ),
inference(avatar_split_clause,[],[f3399,f3358,f2204,f7145]) ).
fof(f7145,plain,
( spl61_871
<=> ! [X25,X24] :
( net_str(net_of_bool_filter(X24,X25,sK25(boole_POSet(X25))),X24)
| ~ upper_relstr_subset(sK25(boole_POSet(X25)),boole_POSet(X25))
| ~ filtered_subset(sK25(boole_POSet(X25)),boole_POSet(X25))
| empty(sK25(boole_POSet(X25)))
| ~ element(X25,powerset(the_carrier(X24)))
| empty(X25)
| ~ one_sorted_str(X24)
| empty_carrier(X24)
| ~ sP6(boole_POSet(X25)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_871])]) ).
fof(f2204,plain,
( spl61_274
<=> ! [X0] :
( element(sK25(X0),powerset(the_carrier(X0)))
| ~ sP6(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_274])]) ).
fof(f3399,plain,
( ! [X24,X25] :
( net_str(net_of_bool_filter(X24,X25,sK25(boole_POSet(X25))),X24)
| ~ upper_relstr_subset(sK25(boole_POSet(X25)),boole_POSet(X25))
| ~ filtered_subset(sK25(boole_POSet(X25)),boole_POSet(X25))
| empty(sK25(boole_POSet(X25)))
| ~ element(X25,powerset(the_carrier(X24)))
| empty(X25)
| ~ one_sorted_str(X24)
| empty_carrier(X24)
| ~ sP6(boole_POSet(X25)) )
| ~ spl61_274
| ~ spl61_396 ),
inference(resolution,[],[f3359,f2205]) ).
fof(f2205,plain,
( ! [X0] :
( element(sK25(X0),powerset(the_carrier(X0)))
| ~ sP6(X0) )
| ~ spl61_274 ),
inference(avatar_component_clause,[],[f2204]) ).
fof(f7143,plain,
( spl61_870
| ~ spl61_273
| ~ spl61_396 ),
inference(avatar_split_clause,[],[f3398,f3358,f2200,f7141]) ).
fof(f7141,plain,
( spl61_870
<=> ! [X22,X23] :
( net_str(net_of_bool_filter(X22,X23,sK24(boole_POSet(X23))),X22)
| ~ upper_relstr_subset(sK24(boole_POSet(X23)),boole_POSet(X23))
| ~ filtered_subset(sK24(boole_POSet(X23)),boole_POSet(X23))
| empty(sK24(boole_POSet(X23)))
| ~ element(X23,powerset(the_carrier(X22)))
| empty(X23)
| ~ one_sorted_str(X22)
| empty_carrier(X22)
| ~ rel_str(boole_POSet(X23)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_870])]) ).
fof(f2200,plain,
( spl61_273
<=> ! [X0] :
( element(sK24(X0),powerset(the_carrier(X0)))
| ~ rel_str(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_273])]) ).
fof(f3398,plain,
( ! [X22,X23] :
( net_str(net_of_bool_filter(X22,X23,sK24(boole_POSet(X23))),X22)
| ~ upper_relstr_subset(sK24(boole_POSet(X23)),boole_POSet(X23))
| ~ filtered_subset(sK24(boole_POSet(X23)),boole_POSet(X23))
| empty(sK24(boole_POSet(X23)))
| ~ element(X23,powerset(the_carrier(X22)))
| empty(X23)
| ~ one_sorted_str(X22)
| empty_carrier(X22)
| ~ rel_str(boole_POSet(X23)) )
| ~ spl61_273
| ~ spl61_396 ),
inference(resolution,[],[f3359,f2201]) ).
fof(f2201,plain,
( ! [X0] :
( element(sK24(X0),powerset(the_carrier(X0)))
| ~ rel_str(X0) )
| ~ spl61_273 ),
inference(avatar_component_clause,[],[f2200]) ).
fof(f7139,plain,
( spl61_869
| ~ spl61_272
| ~ spl61_396 ),
inference(avatar_split_clause,[],[f3397,f3358,f2196,f7137]) ).
fof(f7137,plain,
( spl61_869
<=> ! [X20,X21] :
( net_str(net_of_bool_filter(X20,X21,sK23(boole_POSet(X21))),X20)
| ~ upper_relstr_subset(sK23(boole_POSet(X21)),boole_POSet(X21))
| ~ filtered_subset(sK23(boole_POSet(X21)),boole_POSet(X21))
| empty(sK23(boole_POSet(X21)))
| ~ element(X21,powerset(the_carrier(X20)))
| empty(X21)
| ~ one_sorted_str(X20)
| empty_carrier(X20)
| ~ rel_str(boole_POSet(X21)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_869])]) ).
fof(f2196,plain,
( spl61_272
<=> ! [X0] :
( element(sK23(X0),powerset(the_carrier(X0)))
| ~ rel_str(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_272])]) ).
fof(f3397,plain,
( ! [X21,X20] :
( net_str(net_of_bool_filter(X20,X21,sK23(boole_POSet(X21))),X20)
| ~ upper_relstr_subset(sK23(boole_POSet(X21)),boole_POSet(X21))
| ~ filtered_subset(sK23(boole_POSet(X21)),boole_POSet(X21))
| empty(sK23(boole_POSet(X21)))
| ~ element(X21,powerset(the_carrier(X20)))
| empty(X21)
| ~ one_sorted_str(X20)
| empty_carrier(X20)
| ~ rel_str(boole_POSet(X21)) )
| ~ spl61_272
| ~ spl61_396 ),
inference(resolution,[],[f3359,f2197]) ).
fof(f2197,plain,
( ! [X0] :
( element(sK23(X0),powerset(the_carrier(X0)))
| ~ rel_str(X0) )
| ~ spl61_272 ),
inference(avatar_component_clause,[],[f2196]) ).
fof(f7135,plain,
( spl61_868
| ~ spl61_265
| ~ spl61_396 ),
inference(avatar_split_clause,[],[f3391,f3358,f2167,f7133]) ).
fof(f7133,plain,
( spl61_868
<=> ! [X9,X10] :
( net_str(net_of_bool_filter(X9,X10,cast_as_carrier_subset(boole_POSet(X10))),X9)
| ~ upper_relstr_subset(cast_as_carrier_subset(boole_POSet(X10)),boole_POSet(X10))
| ~ filtered_subset(cast_as_carrier_subset(boole_POSet(X10)),boole_POSet(X10))
| empty(cast_as_carrier_subset(boole_POSet(X10)))
| ~ element(X10,powerset(the_carrier(X9)))
| empty(X10)
| ~ one_sorted_str(X9)
| empty_carrier(X9)
| ~ one_sorted_str(boole_POSet(X10)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_868])]) ).
fof(f3391,plain,
( ! [X10,X9] :
( net_str(net_of_bool_filter(X9,X10,cast_as_carrier_subset(boole_POSet(X10))),X9)
| ~ upper_relstr_subset(cast_as_carrier_subset(boole_POSet(X10)),boole_POSet(X10))
| ~ filtered_subset(cast_as_carrier_subset(boole_POSet(X10)),boole_POSet(X10))
| empty(cast_as_carrier_subset(boole_POSet(X10)))
| ~ element(X10,powerset(the_carrier(X9)))
| empty(X10)
| ~ one_sorted_str(X9)
| empty_carrier(X9)
| ~ one_sorted_str(boole_POSet(X10)) )
| ~ spl61_265
| ~ spl61_396 ),
inference(resolution,[],[f3359,f2168]) ).
fof(f7131,plain,
( spl61_867
| ~ spl61_292
| ~ spl61_395 ),
inference(avatar_split_clause,[],[f3384,f3354,f2277,f7129]) ).
fof(f7129,plain,
( spl61_867
<=> ! [X48,X49] :
( strict_net_str(net_of_bool_filter(X48,X49,sK37(boole_POSet(X49))),X48)
| ~ upper_relstr_subset(sK37(boole_POSet(X49)),boole_POSet(X49))
| ~ filtered_subset(sK37(boole_POSet(X49)),boole_POSet(X49))
| empty(sK37(boole_POSet(X49)))
| ~ element(X49,powerset(the_carrier(X48)))
| empty(X49)
| ~ one_sorted_str(X48)
| empty_carrier(X48)
| ~ sP10(boole_POSet(X49)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_867])]) ).
fof(f3384,plain,
( ! [X48,X49] :
( strict_net_str(net_of_bool_filter(X48,X49,sK37(boole_POSet(X49))),X48)
| ~ upper_relstr_subset(sK37(boole_POSet(X49)),boole_POSet(X49))
| ~ filtered_subset(sK37(boole_POSet(X49)),boole_POSet(X49))
| empty(sK37(boole_POSet(X49)))
| ~ element(X49,powerset(the_carrier(X48)))
| empty(X49)
| ~ one_sorted_str(X48)
| empty_carrier(X48)
| ~ sP10(boole_POSet(X49)) )
| ~ spl61_292
| ~ spl61_395 ),
inference(resolution,[],[f3355,f2278]) ).
fof(f7127,plain,
( spl61_866
| ~ spl61_280
| ~ spl61_395 ),
inference(avatar_split_clause,[],[f3377,f3354,f2228,f7125]) ).
fof(f7125,plain,
( spl61_866
<=> ! [X34,X35] :
( strict_net_str(net_of_bool_filter(X34,X35,sK30(boole_POSet(X35))),X34)
| ~ upper_relstr_subset(sK30(boole_POSet(X35)),boole_POSet(X35))
| ~ filtered_subset(sK30(boole_POSet(X35)),boole_POSet(X35))
| empty(sK30(boole_POSet(X35)))
| ~ element(X35,powerset(the_carrier(X34)))
| empty(X35)
| ~ one_sorted_str(X34)
| empty_carrier(X34)
| ~ sP7(boole_POSet(X35)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_866])]) ).
fof(f3377,plain,
( ! [X34,X35] :
( strict_net_str(net_of_bool_filter(X34,X35,sK30(boole_POSet(X35))),X34)
| ~ upper_relstr_subset(sK30(boole_POSet(X35)),boole_POSet(X35))
| ~ filtered_subset(sK30(boole_POSet(X35)),boole_POSet(X35))
| empty(sK30(boole_POSet(X35)))
| ~ element(X35,powerset(the_carrier(X34)))
| empty(X35)
| ~ one_sorted_str(X34)
| empty_carrier(X34)
| ~ sP7(boole_POSet(X35)) )
| ~ spl61_280
| ~ spl61_395 ),
inference(resolution,[],[f3355,f2229]) ).
fof(f7123,plain,
( spl61_865
| ~ spl61_274
| ~ spl61_395 ),
inference(avatar_split_clause,[],[f3372,f3354,f2204,f7121]) ).
fof(f7121,plain,
( spl61_865
<=> ! [X25,X24] :
( strict_net_str(net_of_bool_filter(X24,X25,sK25(boole_POSet(X25))),X24)
| ~ upper_relstr_subset(sK25(boole_POSet(X25)),boole_POSet(X25))
| ~ filtered_subset(sK25(boole_POSet(X25)),boole_POSet(X25))
| empty(sK25(boole_POSet(X25)))
| ~ element(X25,powerset(the_carrier(X24)))
| empty(X25)
| ~ one_sorted_str(X24)
| empty_carrier(X24)
| ~ sP6(boole_POSet(X25)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_865])]) ).
fof(f3372,plain,
( ! [X24,X25] :
( strict_net_str(net_of_bool_filter(X24,X25,sK25(boole_POSet(X25))),X24)
| ~ upper_relstr_subset(sK25(boole_POSet(X25)),boole_POSet(X25))
| ~ filtered_subset(sK25(boole_POSet(X25)),boole_POSet(X25))
| empty(sK25(boole_POSet(X25)))
| ~ element(X25,powerset(the_carrier(X24)))
| empty(X25)
| ~ one_sorted_str(X24)
| empty_carrier(X24)
| ~ sP6(boole_POSet(X25)) )
| ~ spl61_274
| ~ spl61_395 ),
inference(resolution,[],[f3355,f2205]) ).
fof(f7117,plain,
( spl61_864
| ~ spl61_273
| ~ spl61_395 ),
inference(avatar_split_clause,[],[f3371,f3354,f2200,f7115]) ).
fof(f7115,plain,
( spl61_864
<=> ! [X22,X23] :
( strict_net_str(net_of_bool_filter(X22,X23,sK24(boole_POSet(X23))),X22)
| ~ upper_relstr_subset(sK24(boole_POSet(X23)),boole_POSet(X23))
| ~ filtered_subset(sK24(boole_POSet(X23)),boole_POSet(X23))
| empty(sK24(boole_POSet(X23)))
| ~ element(X23,powerset(the_carrier(X22)))
| empty(X23)
| ~ one_sorted_str(X22)
| empty_carrier(X22)
| ~ rel_str(boole_POSet(X23)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_864])]) ).
fof(f3371,plain,
( ! [X22,X23] :
( strict_net_str(net_of_bool_filter(X22,X23,sK24(boole_POSet(X23))),X22)
| ~ upper_relstr_subset(sK24(boole_POSet(X23)),boole_POSet(X23))
| ~ filtered_subset(sK24(boole_POSet(X23)),boole_POSet(X23))
| empty(sK24(boole_POSet(X23)))
| ~ element(X23,powerset(the_carrier(X22)))
| empty(X23)
| ~ one_sorted_str(X22)
| empty_carrier(X22)
| ~ rel_str(boole_POSet(X23)) )
| ~ spl61_273
| ~ spl61_395 ),
inference(resolution,[],[f3355,f2201]) ).
fof(f7113,plain,
( spl61_863
| ~ spl61_272
| ~ spl61_395 ),
inference(avatar_split_clause,[],[f3370,f3354,f2196,f7111]) ).
fof(f7111,plain,
( spl61_863
<=> ! [X20,X21] :
( strict_net_str(net_of_bool_filter(X20,X21,sK23(boole_POSet(X21))),X20)
| ~ upper_relstr_subset(sK23(boole_POSet(X21)),boole_POSet(X21))
| ~ filtered_subset(sK23(boole_POSet(X21)),boole_POSet(X21))
| empty(sK23(boole_POSet(X21)))
| ~ element(X21,powerset(the_carrier(X20)))
| empty(X21)
| ~ one_sorted_str(X20)
| empty_carrier(X20)
| ~ rel_str(boole_POSet(X21)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_863])]) ).
fof(f3370,plain,
( ! [X21,X20] :
( strict_net_str(net_of_bool_filter(X20,X21,sK23(boole_POSet(X21))),X20)
| ~ upper_relstr_subset(sK23(boole_POSet(X21)),boole_POSet(X21))
| ~ filtered_subset(sK23(boole_POSet(X21)),boole_POSet(X21))
| empty(sK23(boole_POSet(X21)))
| ~ element(X21,powerset(the_carrier(X20)))
| empty(X21)
| ~ one_sorted_str(X20)
| empty_carrier(X20)
| ~ rel_str(boole_POSet(X21)) )
| ~ spl61_272
| ~ spl61_395 ),
inference(resolution,[],[f3355,f2197]) ).
fof(f7109,plain,
( spl61_862
| ~ spl61_265
| ~ spl61_395 ),
inference(avatar_split_clause,[],[f3364,f3354,f2167,f7107]) ).
fof(f7107,plain,
( spl61_862
<=> ! [X9,X10] :
( strict_net_str(net_of_bool_filter(X9,X10,cast_as_carrier_subset(boole_POSet(X10))),X9)
| ~ upper_relstr_subset(cast_as_carrier_subset(boole_POSet(X10)),boole_POSet(X10))
| ~ filtered_subset(cast_as_carrier_subset(boole_POSet(X10)),boole_POSet(X10))
| empty(cast_as_carrier_subset(boole_POSet(X10)))
| ~ element(X10,powerset(the_carrier(X9)))
| empty(X10)
| ~ one_sorted_str(X9)
| empty_carrier(X9)
| ~ one_sorted_str(boole_POSet(X10)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_862])]) ).
fof(f3364,plain,
( ! [X10,X9] :
( strict_net_str(net_of_bool_filter(X9,X10,cast_as_carrier_subset(boole_POSet(X10))),X9)
| ~ upper_relstr_subset(cast_as_carrier_subset(boole_POSet(X10)),boole_POSet(X10))
| ~ filtered_subset(cast_as_carrier_subset(boole_POSet(X10)),boole_POSet(X10))
| empty(cast_as_carrier_subset(boole_POSet(X10)))
| ~ element(X10,powerset(the_carrier(X9)))
| empty(X10)
| ~ one_sorted_str(X9)
| empty_carrier(X9)
| ~ one_sorted_str(boole_POSet(X10)) )
| ~ spl61_265
| ~ spl61_395 ),
inference(resolution,[],[f3355,f2168]) ).
fof(f7105,plain,
( spl61_861
| ~ spl61_370
| ~ spl61_371 ),
inference(avatar_split_clause,[],[f3124,f3039,f3032,f7103]) ).
fof(f7103,plain,
( spl61_861
<=> ! [X13,X12] :
( ~ net_str(X12,X13)
| empty_carrier(X12)
| ~ one_sorted_str(X13)
| empty_carrier(X13)
| ~ boundary_set(filter_of_net_str(X13,X12),boole_POSet(cast_as_carrier_subset(X13)))
| ~ closed_subset(filter_of_net_str(X13,X12),boole_POSet(cast_as_carrier_subset(X13)))
| nowhere_dense(filter_of_net_str(X13,X12),boole_POSet(cast_as_carrier_subset(X13)))
| ~ top_str(boole_POSet(cast_as_carrier_subset(X13)))
| ~ topological_space(boole_POSet(cast_as_carrier_subset(X13))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_861])]) ).
fof(f3032,plain,
( spl61_370
<=> ! [X0,X1] :
( nowhere_dense(X1,X0)
| ~ boundary_set(X1,X0)
| ~ closed_subset(X1,X0)
| ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0)
| ~ topological_space(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_370])]) ).
fof(f3124,plain,
( ! [X12,X13] :
( ~ net_str(X12,X13)
| empty_carrier(X12)
| ~ one_sorted_str(X13)
| empty_carrier(X13)
| ~ boundary_set(filter_of_net_str(X13,X12),boole_POSet(cast_as_carrier_subset(X13)))
| ~ closed_subset(filter_of_net_str(X13,X12),boole_POSet(cast_as_carrier_subset(X13)))
| nowhere_dense(filter_of_net_str(X13,X12),boole_POSet(cast_as_carrier_subset(X13)))
| ~ top_str(boole_POSet(cast_as_carrier_subset(X13)))
| ~ topological_space(boole_POSet(cast_as_carrier_subset(X13))) )
| ~ spl61_370
| ~ spl61_371 ),
inference(resolution,[],[f3040,f3033]) ).
fof(f3033,plain,
( ! [X0,X1] :
( ~ element(X1,powerset(the_carrier(X0)))
| ~ boundary_set(X1,X0)
| ~ closed_subset(X1,X0)
| nowhere_dense(X1,X0)
| ~ top_str(X0)
| ~ topological_space(X0) )
| ~ spl61_370 ),
inference(avatar_component_clause,[],[f3032]) ).
fof(f7101,plain,
( spl61_860
| ~ spl61_369
| ~ spl61_371 ),
inference(avatar_split_clause,[],[f3123,f3039,f3028,f7099]) ).
fof(f7099,plain,
( spl61_860
<=> ! [X11,X10] :
( ~ net_str(X10,X11)
| empty_carrier(X10)
| ~ one_sorted_str(X11)
| empty_carrier(X11)
| ~ nowhere_dense(filter_of_net_str(X11,X10),boole_POSet(cast_as_carrier_subset(X11)))
| ~ open_subset(filter_of_net_str(X11,X10),boole_POSet(cast_as_carrier_subset(X11)))
| sP8(boole_POSet(cast_as_carrier_subset(X11)),filter_of_net_str(X11,X10))
| ~ top_str(boole_POSet(cast_as_carrier_subset(X11)))
| ~ topological_space(boole_POSet(cast_as_carrier_subset(X11))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_860])]) ).
fof(f3028,plain,
( spl61_369
<=> ! [X0,X1] :
( sP8(X0,X1)
| ~ nowhere_dense(X1,X0)
| ~ open_subset(X1,X0)
| ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0)
| ~ topological_space(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_369])]) ).
fof(f3123,plain,
( ! [X10,X11] :
( ~ net_str(X10,X11)
| empty_carrier(X10)
| ~ one_sorted_str(X11)
| empty_carrier(X11)
| ~ nowhere_dense(filter_of_net_str(X11,X10),boole_POSet(cast_as_carrier_subset(X11)))
| ~ open_subset(filter_of_net_str(X11,X10),boole_POSet(cast_as_carrier_subset(X11)))
| sP8(boole_POSet(cast_as_carrier_subset(X11)),filter_of_net_str(X11,X10))
| ~ top_str(boole_POSet(cast_as_carrier_subset(X11)))
| ~ topological_space(boole_POSet(cast_as_carrier_subset(X11))) )
| ~ spl61_369
| ~ spl61_371 ),
inference(resolution,[],[f3040,f3029]) ).
fof(f3029,plain,
( ! [X0,X1] :
( ~ element(X1,powerset(the_carrier(X0)))
| ~ nowhere_dense(X1,X0)
| ~ open_subset(X1,X0)
| sP8(X0,X1)
| ~ top_str(X0)
| ~ topological_space(X0) )
| ~ spl61_369 ),
inference(avatar_component_clause,[],[f3028]) ).
fof(f7097,plain,
( spl61_859
| ~ spl61_575
| ~ spl61_835 ),
inference(avatar_split_clause,[],[f7011,f6878,f4766,f7095]) ).
fof(f7095,plain,
( spl61_859
<=> ! [X0] :
( ~ in(powerset(X0),sK13)
| empty(powerset(X0))
| ~ subset(the_carrier(boole_POSet(cast_as_carrier_subset(sK12))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_859])]) ).
fof(f6878,plain,
( spl61_835
<=> ! [X2] :
( ~ in(X2,sK13)
| ~ in(the_carrier(boole_POSet(cast_as_carrier_subset(sK12))),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_835])]) ).
fof(f7011,plain,
( ! [X0] :
( ~ in(powerset(X0),sK13)
| empty(powerset(X0))
| ~ subset(the_carrier(boole_POSet(cast_as_carrier_subset(sK12))),X0) )
| ~ spl61_575
| ~ spl61_835 ),
inference(resolution,[],[f6879,f4767]) ).
fof(f6879,plain,
( ! [X2] :
( ~ in(the_carrier(boole_POSet(cast_as_carrier_subset(sK12))),X2)
| ~ in(X2,sK13) )
| ~ spl61_835 ),
inference(avatar_component_clause,[],[f6878]) ).
fof(f7087,plain,
( spl61_858
| ~ spl61_292
| ~ spl61_390 ),
inference(avatar_split_clause,[],[f3345,f3248,f2277,f7085]) ).
fof(f7085,plain,
( spl61_858
<=> ! [X48,X49] :
( transitive_relstr(net_of_bool_filter(X48,X49,sK37(boole_POSet(X49))))
| ~ upper_relstr_subset(sK37(boole_POSet(X49)),boole_POSet(X49))
| ~ filtered_subset(sK37(boole_POSet(X49)),boole_POSet(X49))
| empty(sK37(boole_POSet(X49)))
| ~ element(X49,powerset(the_carrier(X48)))
| empty(X49)
| ~ one_sorted_str(X48)
| empty_carrier(X48)
| ~ sP10(boole_POSet(X49)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_858])]) ).
fof(f3345,plain,
( ! [X48,X49] :
( transitive_relstr(net_of_bool_filter(X48,X49,sK37(boole_POSet(X49))))
| ~ upper_relstr_subset(sK37(boole_POSet(X49)),boole_POSet(X49))
| ~ filtered_subset(sK37(boole_POSet(X49)),boole_POSet(X49))
| empty(sK37(boole_POSet(X49)))
| ~ element(X49,powerset(the_carrier(X48)))
| empty(X49)
| ~ one_sorted_str(X48)
| empty_carrier(X48)
| ~ sP10(boole_POSet(X49)) )
| ~ spl61_292
| ~ spl61_390 ),
inference(resolution,[],[f3249,f2278]) ).
fof(f7083,plain,
( spl61_857
| ~ spl61_280
| ~ spl61_390 ),
inference(avatar_split_clause,[],[f3338,f3248,f2228,f7081]) ).
fof(f7081,plain,
( spl61_857
<=> ! [X34,X35] :
( transitive_relstr(net_of_bool_filter(X34,X35,sK30(boole_POSet(X35))))
| ~ upper_relstr_subset(sK30(boole_POSet(X35)),boole_POSet(X35))
| ~ filtered_subset(sK30(boole_POSet(X35)),boole_POSet(X35))
| empty(sK30(boole_POSet(X35)))
| ~ element(X35,powerset(the_carrier(X34)))
| empty(X35)
| ~ one_sorted_str(X34)
| empty_carrier(X34)
| ~ sP7(boole_POSet(X35)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_857])]) ).
fof(f3338,plain,
( ! [X34,X35] :
( transitive_relstr(net_of_bool_filter(X34,X35,sK30(boole_POSet(X35))))
| ~ upper_relstr_subset(sK30(boole_POSet(X35)),boole_POSet(X35))
| ~ filtered_subset(sK30(boole_POSet(X35)),boole_POSet(X35))
| empty(sK30(boole_POSet(X35)))
| ~ element(X35,powerset(the_carrier(X34)))
| empty(X35)
| ~ one_sorted_str(X34)
| empty_carrier(X34)
| ~ sP7(boole_POSet(X35)) )
| ~ spl61_280
| ~ spl61_390 ),
inference(resolution,[],[f3249,f2229]) ).
fof(f7079,plain,
( spl61_856
| ~ spl61_274
| ~ spl61_390 ),
inference(avatar_split_clause,[],[f3333,f3248,f2204,f7077]) ).
fof(f7077,plain,
( spl61_856
<=> ! [X25,X24] :
( transitive_relstr(net_of_bool_filter(X24,X25,sK25(boole_POSet(X25))))
| ~ upper_relstr_subset(sK25(boole_POSet(X25)),boole_POSet(X25))
| ~ filtered_subset(sK25(boole_POSet(X25)),boole_POSet(X25))
| empty(sK25(boole_POSet(X25)))
| ~ element(X25,powerset(the_carrier(X24)))
| empty(X25)
| ~ one_sorted_str(X24)
| empty_carrier(X24)
| ~ sP6(boole_POSet(X25)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_856])]) ).
fof(f3333,plain,
( ! [X24,X25] :
( transitive_relstr(net_of_bool_filter(X24,X25,sK25(boole_POSet(X25))))
| ~ upper_relstr_subset(sK25(boole_POSet(X25)),boole_POSet(X25))
| ~ filtered_subset(sK25(boole_POSet(X25)),boole_POSet(X25))
| empty(sK25(boole_POSet(X25)))
| ~ element(X25,powerset(the_carrier(X24)))
| empty(X25)
| ~ one_sorted_str(X24)
| empty_carrier(X24)
| ~ sP6(boole_POSet(X25)) )
| ~ spl61_274
| ~ spl61_390 ),
inference(resolution,[],[f3249,f2205]) ).
fof(f7075,plain,
( spl61_855
| ~ spl61_273
| ~ spl61_390 ),
inference(avatar_split_clause,[],[f3332,f3248,f2200,f7073]) ).
fof(f7073,plain,
( spl61_855
<=> ! [X22,X23] :
( transitive_relstr(net_of_bool_filter(X22,X23,sK24(boole_POSet(X23))))
| ~ upper_relstr_subset(sK24(boole_POSet(X23)),boole_POSet(X23))
| ~ filtered_subset(sK24(boole_POSet(X23)),boole_POSet(X23))
| empty(sK24(boole_POSet(X23)))
| ~ element(X23,powerset(the_carrier(X22)))
| empty(X23)
| ~ one_sorted_str(X22)
| empty_carrier(X22)
| ~ rel_str(boole_POSet(X23)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_855])]) ).
fof(f3332,plain,
( ! [X22,X23] :
( transitive_relstr(net_of_bool_filter(X22,X23,sK24(boole_POSet(X23))))
| ~ upper_relstr_subset(sK24(boole_POSet(X23)),boole_POSet(X23))
| ~ filtered_subset(sK24(boole_POSet(X23)),boole_POSet(X23))
| empty(sK24(boole_POSet(X23)))
| ~ element(X23,powerset(the_carrier(X22)))
| empty(X23)
| ~ one_sorted_str(X22)
| empty_carrier(X22)
| ~ rel_str(boole_POSet(X23)) )
| ~ spl61_273
| ~ spl61_390 ),
inference(resolution,[],[f3249,f2201]) ).
fof(f7071,plain,
( spl61_854
| ~ spl61_272
| ~ spl61_390 ),
inference(avatar_split_clause,[],[f3331,f3248,f2196,f7069]) ).
fof(f7069,plain,
( spl61_854
<=> ! [X20,X21] :
( transitive_relstr(net_of_bool_filter(X20,X21,sK23(boole_POSet(X21))))
| ~ upper_relstr_subset(sK23(boole_POSet(X21)),boole_POSet(X21))
| ~ filtered_subset(sK23(boole_POSet(X21)),boole_POSet(X21))
| empty(sK23(boole_POSet(X21)))
| ~ element(X21,powerset(the_carrier(X20)))
| empty(X21)
| ~ one_sorted_str(X20)
| empty_carrier(X20)
| ~ rel_str(boole_POSet(X21)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_854])]) ).
fof(f3331,plain,
( ! [X21,X20] :
( transitive_relstr(net_of_bool_filter(X20,X21,sK23(boole_POSet(X21))))
| ~ upper_relstr_subset(sK23(boole_POSet(X21)),boole_POSet(X21))
| ~ filtered_subset(sK23(boole_POSet(X21)),boole_POSet(X21))
| empty(sK23(boole_POSet(X21)))
| ~ element(X21,powerset(the_carrier(X20)))
| empty(X21)
| ~ one_sorted_str(X20)
| empty_carrier(X20)
| ~ rel_str(boole_POSet(X21)) )
| ~ spl61_272
| ~ spl61_390 ),
inference(resolution,[],[f3249,f2197]) ).
fof(f7067,plain,
( spl61_853
| ~ spl61_265
| ~ spl61_390 ),
inference(avatar_split_clause,[],[f3325,f3248,f2167,f7065]) ).
fof(f7065,plain,
( spl61_853
<=> ! [X9,X10] :
( transitive_relstr(net_of_bool_filter(X9,X10,cast_as_carrier_subset(boole_POSet(X10))))
| ~ upper_relstr_subset(cast_as_carrier_subset(boole_POSet(X10)),boole_POSet(X10))
| ~ filtered_subset(cast_as_carrier_subset(boole_POSet(X10)),boole_POSet(X10))
| empty(cast_as_carrier_subset(boole_POSet(X10)))
| ~ element(X10,powerset(the_carrier(X9)))
| empty(X10)
| ~ one_sorted_str(X9)
| empty_carrier(X9)
| ~ one_sorted_str(boole_POSet(X10)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_853])]) ).
fof(f3325,plain,
( ! [X10,X9] :
( transitive_relstr(net_of_bool_filter(X9,X10,cast_as_carrier_subset(boole_POSet(X10))))
| ~ upper_relstr_subset(cast_as_carrier_subset(boole_POSet(X10)),boole_POSet(X10))
| ~ filtered_subset(cast_as_carrier_subset(boole_POSet(X10)),boole_POSet(X10))
| empty(cast_as_carrier_subset(boole_POSet(X10)))
| ~ element(X10,powerset(the_carrier(X9)))
| empty(X10)
| ~ one_sorted_str(X9)
| empty_carrier(X9)
| ~ one_sorted_str(boole_POSet(X10)) )
| ~ spl61_265
| ~ spl61_390 ),
inference(resolution,[],[f3249,f2168]) ).
fof(f7063,plain,
( spl61_852
| ~ spl61_292
| ~ spl61_389 ),
inference(avatar_split_clause,[],[f3317,f3244,f2277,f7061]) ).
fof(f7061,plain,
( spl61_852
<=> ! [X48,X49] :
( reflexive_relstr(net_of_bool_filter(X48,X49,sK37(boole_POSet(X49))))
| ~ upper_relstr_subset(sK37(boole_POSet(X49)),boole_POSet(X49))
| ~ filtered_subset(sK37(boole_POSet(X49)),boole_POSet(X49))
| empty(sK37(boole_POSet(X49)))
| ~ element(X49,powerset(the_carrier(X48)))
| empty(X49)
| ~ one_sorted_str(X48)
| empty_carrier(X48)
| ~ sP10(boole_POSet(X49)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_852])]) ).
fof(f3317,plain,
( ! [X48,X49] :
( reflexive_relstr(net_of_bool_filter(X48,X49,sK37(boole_POSet(X49))))
| ~ upper_relstr_subset(sK37(boole_POSet(X49)),boole_POSet(X49))
| ~ filtered_subset(sK37(boole_POSet(X49)),boole_POSet(X49))
| empty(sK37(boole_POSet(X49)))
| ~ element(X49,powerset(the_carrier(X48)))
| empty(X49)
| ~ one_sorted_str(X48)
| empty_carrier(X48)
| ~ sP10(boole_POSet(X49)) )
| ~ spl61_292
| ~ spl61_389 ),
inference(resolution,[],[f3245,f2278]) ).
fof(f7059,plain,
( ~ spl61_851
| ~ spl61_799
| ~ spl61_835 ),
inference(avatar_split_clause,[],[f7014,f6878,f6466,f7056]) ).
fof(f7056,plain,
( spl61_851
<=> in(the_carrier(boole_POSet(cast_as_carrier_subset(sK12))),sK13) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_851])]) ).
fof(f6466,plain,
( spl61_799
<=> ! [X0] :
( ~ in(X0,sK13)
| in(X0,the_carrier(boole_POSet(cast_as_carrier_subset(sK12)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_799])]) ).
fof(f7014,plain,
( ~ in(the_carrier(boole_POSet(cast_as_carrier_subset(sK12))),sK13)
| ~ spl61_799
| ~ spl61_835 ),
inference(duplicate_literal_removal,[],[f7013]) ).
fof(f7013,plain,
( ~ in(the_carrier(boole_POSet(cast_as_carrier_subset(sK12))),sK13)
| ~ in(the_carrier(boole_POSet(cast_as_carrier_subset(sK12))),sK13)
| ~ spl61_799
| ~ spl61_835 ),
inference(resolution,[],[f6879,f6467]) ).
fof(f6467,plain,
( ! [X0] :
( in(X0,the_carrier(boole_POSet(cast_as_carrier_subset(sK12))))
| ~ in(X0,sK13) )
| ~ spl61_799 ),
inference(avatar_component_clause,[],[f6466]) ).
fof(f7054,plain,
( spl61_850
| ~ spl61_280
| ~ spl61_389 ),
inference(avatar_split_clause,[],[f3310,f3244,f2228,f7052]) ).
fof(f7052,plain,
( spl61_850
<=> ! [X34,X35] :
( reflexive_relstr(net_of_bool_filter(X34,X35,sK30(boole_POSet(X35))))
| ~ upper_relstr_subset(sK30(boole_POSet(X35)),boole_POSet(X35))
| ~ filtered_subset(sK30(boole_POSet(X35)),boole_POSet(X35))
| empty(sK30(boole_POSet(X35)))
| ~ element(X35,powerset(the_carrier(X34)))
| empty(X35)
| ~ one_sorted_str(X34)
| empty_carrier(X34)
| ~ sP7(boole_POSet(X35)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_850])]) ).
fof(f3310,plain,
( ! [X34,X35] :
( reflexive_relstr(net_of_bool_filter(X34,X35,sK30(boole_POSet(X35))))
| ~ upper_relstr_subset(sK30(boole_POSet(X35)),boole_POSet(X35))
| ~ filtered_subset(sK30(boole_POSet(X35)),boole_POSet(X35))
| empty(sK30(boole_POSet(X35)))
| ~ element(X35,powerset(the_carrier(X34)))
| empty(X35)
| ~ one_sorted_str(X34)
| empty_carrier(X34)
| ~ sP7(boole_POSet(X35)) )
| ~ spl61_280
| ~ spl61_389 ),
inference(resolution,[],[f3245,f2229]) ).
fof(f7050,plain,
( spl61_849
| ~ spl61_274
| ~ spl61_389 ),
inference(avatar_split_clause,[],[f3305,f3244,f2204,f7048]) ).
fof(f7048,plain,
( spl61_849
<=> ! [X25,X24] :
( reflexive_relstr(net_of_bool_filter(X24,X25,sK25(boole_POSet(X25))))
| ~ upper_relstr_subset(sK25(boole_POSet(X25)),boole_POSet(X25))
| ~ filtered_subset(sK25(boole_POSet(X25)),boole_POSet(X25))
| empty(sK25(boole_POSet(X25)))
| ~ element(X25,powerset(the_carrier(X24)))
| empty(X25)
| ~ one_sorted_str(X24)
| empty_carrier(X24)
| ~ sP6(boole_POSet(X25)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_849])]) ).
fof(f3305,plain,
( ! [X24,X25] :
( reflexive_relstr(net_of_bool_filter(X24,X25,sK25(boole_POSet(X25))))
| ~ upper_relstr_subset(sK25(boole_POSet(X25)),boole_POSet(X25))
| ~ filtered_subset(sK25(boole_POSet(X25)),boole_POSet(X25))
| empty(sK25(boole_POSet(X25)))
| ~ element(X25,powerset(the_carrier(X24)))
| empty(X25)
| ~ one_sorted_str(X24)
| empty_carrier(X24)
| ~ sP6(boole_POSet(X25)) )
| ~ spl61_274
| ~ spl61_389 ),
inference(resolution,[],[f3245,f2205]) ).
fof(f7046,plain,
( spl61_848
| ~ spl61_273
| ~ spl61_389 ),
inference(avatar_split_clause,[],[f3304,f3244,f2200,f7044]) ).
fof(f7044,plain,
( spl61_848
<=> ! [X22,X23] :
( reflexive_relstr(net_of_bool_filter(X22,X23,sK24(boole_POSet(X23))))
| ~ upper_relstr_subset(sK24(boole_POSet(X23)),boole_POSet(X23))
| ~ filtered_subset(sK24(boole_POSet(X23)),boole_POSet(X23))
| empty(sK24(boole_POSet(X23)))
| ~ element(X23,powerset(the_carrier(X22)))
| empty(X23)
| ~ one_sorted_str(X22)
| empty_carrier(X22)
| ~ rel_str(boole_POSet(X23)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_848])]) ).
fof(f3304,plain,
( ! [X22,X23] :
( reflexive_relstr(net_of_bool_filter(X22,X23,sK24(boole_POSet(X23))))
| ~ upper_relstr_subset(sK24(boole_POSet(X23)),boole_POSet(X23))
| ~ filtered_subset(sK24(boole_POSet(X23)),boole_POSet(X23))
| empty(sK24(boole_POSet(X23)))
| ~ element(X23,powerset(the_carrier(X22)))
| empty(X23)
| ~ one_sorted_str(X22)
| empty_carrier(X22)
| ~ rel_str(boole_POSet(X23)) )
| ~ spl61_273
| ~ spl61_389 ),
inference(resolution,[],[f3245,f2201]) ).
fof(f7042,plain,
( spl61_847
| ~ spl61_272
| ~ spl61_389 ),
inference(avatar_split_clause,[],[f3303,f3244,f2196,f7040]) ).
fof(f7040,plain,
( spl61_847
<=> ! [X20,X21] :
( reflexive_relstr(net_of_bool_filter(X20,X21,sK23(boole_POSet(X21))))
| ~ upper_relstr_subset(sK23(boole_POSet(X21)),boole_POSet(X21))
| ~ filtered_subset(sK23(boole_POSet(X21)),boole_POSet(X21))
| empty(sK23(boole_POSet(X21)))
| ~ element(X21,powerset(the_carrier(X20)))
| empty(X21)
| ~ one_sorted_str(X20)
| empty_carrier(X20)
| ~ rel_str(boole_POSet(X21)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_847])]) ).
fof(f3303,plain,
( ! [X21,X20] :
( reflexive_relstr(net_of_bool_filter(X20,X21,sK23(boole_POSet(X21))))
| ~ upper_relstr_subset(sK23(boole_POSet(X21)),boole_POSet(X21))
| ~ filtered_subset(sK23(boole_POSet(X21)),boole_POSet(X21))
| empty(sK23(boole_POSet(X21)))
| ~ element(X21,powerset(the_carrier(X20)))
| empty(X21)
| ~ one_sorted_str(X20)
| empty_carrier(X20)
| ~ rel_str(boole_POSet(X21)) )
| ~ spl61_272
| ~ spl61_389 ),
inference(resolution,[],[f3245,f2197]) ).
fof(f7038,plain,
( spl61_846
| ~ spl61_265
| ~ spl61_389 ),
inference(avatar_split_clause,[],[f3297,f3244,f2167,f7036]) ).
fof(f7036,plain,
( spl61_846
<=> ! [X9,X10] :
( reflexive_relstr(net_of_bool_filter(X9,X10,cast_as_carrier_subset(boole_POSet(X10))))
| ~ upper_relstr_subset(cast_as_carrier_subset(boole_POSet(X10)),boole_POSet(X10))
| ~ filtered_subset(cast_as_carrier_subset(boole_POSet(X10)),boole_POSet(X10))
| empty(cast_as_carrier_subset(boole_POSet(X10)))
| ~ element(X10,powerset(the_carrier(X9)))
| empty(X10)
| ~ one_sorted_str(X9)
| empty_carrier(X9)
| ~ one_sorted_str(boole_POSet(X10)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_846])]) ).
fof(f3297,plain,
( ! [X10,X9] :
( reflexive_relstr(net_of_bool_filter(X9,X10,cast_as_carrier_subset(boole_POSet(X10))))
| ~ upper_relstr_subset(cast_as_carrier_subset(boole_POSet(X10)),boole_POSet(X10))
| ~ filtered_subset(cast_as_carrier_subset(boole_POSet(X10)),boole_POSet(X10))
| empty(cast_as_carrier_subset(boole_POSet(X10)))
| ~ element(X10,powerset(the_carrier(X9)))
| empty(X10)
| ~ one_sorted_str(X9)
| empty_carrier(X9)
| ~ one_sorted_str(boole_POSet(X10)) )
| ~ spl61_265
| ~ spl61_389 ),
inference(resolution,[],[f3245,f2168]) ).
fof(f7034,plain,
( spl61_845
| ~ spl61_292
| ~ spl61_388 ),
inference(avatar_split_clause,[],[f3290,f3240,f2277,f7032]) ).
fof(f7032,plain,
( spl61_845
<=> ! [X48,X49] :
( ~ empty_carrier(net_of_bool_filter(X48,X49,sK37(boole_POSet(X49))))
| ~ upper_relstr_subset(sK37(boole_POSet(X49)),boole_POSet(X49))
| ~ filtered_subset(sK37(boole_POSet(X49)),boole_POSet(X49))
| empty(sK37(boole_POSet(X49)))
| ~ element(X49,powerset(the_carrier(X48)))
| empty(X49)
| ~ one_sorted_str(X48)
| empty_carrier(X48)
| ~ sP10(boole_POSet(X49)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_845])]) ).
fof(f3290,plain,
( ! [X48,X49] :
( ~ empty_carrier(net_of_bool_filter(X48,X49,sK37(boole_POSet(X49))))
| ~ upper_relstr_subset(sK37(boole_POSet(X49)),boole_POSet(X49))
| ~ filtered_subset(sK37(boole_POSet(X49)),boole_POSet(X49))
| empty(sK37(boole_POSet(X49)))
| ~ element(X49,powerset(the_carrier(X48)))
| empty(X49)
| ~ one_sorted_str(X48)
| empty_carrier(X48)
| ~ sP10(boole_POSet(X49)) )
| ~ spl61_292
| ~ spl61_388 ),
inference(resolution,[],[f3241,f2278]) ).
fof(f7030,plain,
( spl61_844
| ~ spl61_280
| ~ spl61_388 ),
inference(avatar_split_clause,[],[f3283,f3240,f2228,f7028]) ).
fof(f7028,plain,
( spl61_844
<=> ! [X34,X35] :
( ~ empty_carrier(net_of_bool_filter(X34,X35,sK30(boole_POSet(X35))))
| ~ upper_relstr_subset(sK30(boole_POSet(X35)),boole_POSet(X35))
| ~ filtered_subset(sK30(boole_POSet(X35)),boole_POSet(X35))
| empty(sK30(boole_POSet(X35)))
| ~ element(X35,powerset(the_carrier(X34)))
| empty(X35)
| ~ one_sorted_str(X34)
| empty_carrier(X34)
| ~ sP7(boole_POSet(X35)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_844])]) ).
fof(f3283,plain,
( ! [X34,X35] :
( ~ empty_carrier(net_of_bool_filter(X34,X35,sK30(boole_POSet(X35))))
| ~ upper_relstr_subset(sK30(boole_POSet(X35)),boole_POSet(X35))
| ~ filtered_subset(sK30(boole_POSet(X35)),boole_POSet(X35))
| empty(sK30(boole_POSet(X35)))
| ~ element(X35,powerset(the_carrier(X34)))
| empty(X35)
| ~ one_sorted_str(X34)
| empty_carrier(X34)
| ~ sP7(boole_POSet(X35)) )
| ~ spl61_280
| ~ spl61_388 ),
inference(resolution,[],[f3241,f2229]) ).
fof(f7026,plain,
( spl61_843
| ~ spl61_274
| ~ spl61_388 ),
inference(avatar_split_clause,[],[f3278,f3240,f2204,f7024]) ).
fof(f7024,plain,
( spl61_843
<=> ! [X25,X24] :
( ~ empty_carrier(net_of_bool_filter(X24,X25,sK25(boole_POSet(X25))))
| ~ upper_relstr_subset(sK25(boole_POSet(X25)),boole_POSet(X25))
| ~ filtered_subset(sK25(boole_POSet(X25)),boole_POSet(X25))
| empty(sK25(boole_POSet(X25)))
| ~ element(X25,powerset(the_carrier(X24)))
| empty(X25)
| ~ one_sorted_str(X24)
| empty_carrier(X24)
| ~ sP6(boole_POSet(X25)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_843])]) ).
fof(f3278,plain,
( ! [X24,X25] :
( ~ empty_carrier(net_of_bool_filter(X24,X25,sK25(boole_POSet(X25))))
| ~ upper_relstr_subset(sK25(boole_POSet(X25)),boole_POSet(X25))
| ~ filtered_subset(sK25(boole_POSet(X25)),boole_POSet(X25))
| empty(sK25(boole_POSet(X25)))
| ~ element(X25,powerset(the_carrier(X24)))
| empty(X25)
| ~ one_sorted_str(X24)
| empty_carrier(X24)
| ~ sP6(boole_POSet(X25)) )
| ~ spl61_274
| ~ spl61_388 ),
inference(resolution,[],[f3241,f2205]) ).
fof(f7022,plain,
( spl61_842
| ~ spl61_273
| ~ spl61_388 ),
inference(avatar_split_clause,[],[f3277,f3240,f2200,f7020]) ).
fof(f7020,plain,
( spl61_842
<=> ! [X22,X23] :
( ~ empty_carrier(net_of_bool_filter(X22,X23,sK24(boole_POSet(X23))))
| ~ upper_relstr_subset(sK24(boole_POSet(X23)),boole_POSet(X23))
| ~ filtered_subset(sK24(boole_POSet(X23)),boole_POSet(X23))
| empty(sK24(boole_POSet(X23)))
| ~ element(X23,powerset(the_carrier(X22)))
| empty(X23)
| ~ one_sorted_str(X22)
| empty_carrier(X22)
| ~ rel_str(boole_POSet(X23)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_842])]) ).
fof(f3277,plain,
( ! [X22,X23] :
( ~ empty_carrier(net_of_bool_filter(X22,X23,sK24(boole_POSet(X23))))
| ~ upper_relstr_subset(sK24(boole_POSet(X23)),boole_POSet(X23))
| ~ filtered_subset(sK24(boole_POSet(X23)),boole_POSet(X23))
| empty(sK24(boole_POSet(X23)))
| ~ element(X23,powerset(the_carrier(X22)))
| empty(X23)
| ~ one_sorted_str(X22)
| empty_carrier(X22)
| ~ rel_str(boole_POSet(X23)) )
| ~ spl61_273
| ~ spl61_388 ),
inference(resolution,[],[f3241,f2201]) ).
fof(f7018,plain,
( spl61_841
| ~ spl61_272
| ~ spl61_388 ),
inference(avatar_split_clause,[],[f3276,f3240,f2196,f7016]) ).
fof(f7016,plain,
( spl61_841
<=> ! [X20,X21] :
( ~ empty_carrier(net_of_bool_filter(X20,X21,sK23(boole_POSet(X21))))
| ~ upper_relstr_subset(sK23(boole_POSet(X21)),boole_POSet(X21))
| ~ filtered_subset(sK23(boole_POSet(X21)),boole_POSet(X21))
| empty(sK23(boole_POSet(X21)))
| ~ element(X21,powerset(the_carrier(X20)))
| empty(X21)
| ~ one_sorted_str(X20)
| empty_carrier(X20)
| ~ rel_str(boole_POSet(X21)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_841])]) ).
fof(f3276,plain,
( ! [X21,X20] :
( ~ empty_carrier(net_of_bool_filter(X20,X21,sK23(boole_POSet(X21))))
| ~ upper_relstr_subset(sK23(boole_POSet(X21)),boole_POSet(X21))
| ~ filtered_subset(sK23(boole_POSet(X21)),boole_POSet(X21))
| empty(sK23(boole_POSet(X21)))
| ~ element(X21,powerset(the_carrier(X20)))
| empty(X21)
| ~ one_sorted_str(X20)
| empty_carrier(X20)
| ~ rel_str(boole_POSet(X21)) )
| ~ spl61_272
| ~ spl61_388 ),
inference(resolution,[],[f3241,f2197]) ).
fof(f7010,plain,
( spl61_840
| ~ spl61_265
| ~ spl61_388 ),
inference(avatar_split_clause,[],[f3270,f3240,f2167,f7008]) ).
fof(f7008,plain,
( spl61_840
<=> ! [X9,X10] :
( ~ empty_carrier(net_of_bool_filter(X9,X10,cast_as_carrier_subset(boole_POSet(X10))))
| ~ upper_relstr_subset(cast_as_carrier_subset(boole_POSet(X10)),boole_POSet(X10))
| ~ filtered_subset(cast_as_carrier_subset(boole_POSet(X10)),boole_POSet(X10))
| empty(cast_as_carrier_subset(boole_POSet(X10)))
| ~ element(X10,powerset(the_carrier(X9)))
| empty(X10)
| ~ one_sorted_str(X9)
| empty_carrier(X9)
| ~ one_sorted_str(boole_POSet(X10)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_840])]) ).
fof(f3270,plain,
( ! [X10,X9] :
( ~ empty_carrier(net_of_bool_filter(X9,X10,cast_as_carrier_subset(boole_POSet(X10))))
| ~ upper_relstr_subset(cast_as_carrier_subset(boole_POSet(X10)),boole_POSet(X10))
| ~ filtered_subset(cast_as_carrier_subset(boole_POSet(X10)),boole_POSet(X10))
| empty(cast_as_carrier_subset(boole_POSet(X10)))
| ~ element(X10,powerset(the_carrier(X9)))
| empty(X10)
| ~ one_sorted_str(X9)
| empty_carrier(X9)
| ~ one_sorted_str(boole_POSet(X10)) )
| ~ spl61_265
| ~ spl61_388 ),
inference(resolution,[],[f3241,f2168]) ).
fof(f7002,plain,
( spl61_839
| ~ spl61_370
| ~ spl61_379 ),
inference(avatar_split_clause,[],[f3194,f3166,f3032,f7000]) ).
fof(f7000,plain,
( spl61_839
<=> ! [X20,X18,X19] :
( ~ in(X18,a_2_1_yellow19(X19,X20))
| ~ net_str(X20,X19)
| empty_carrier(X20)
| ~ one_sorted_str(X19)
| empty_carrier(X19)
| ~ boundary_set(sK44(X18,X19,X20),X19)
| ~ closed_subset(sK44(X18,X19,X20),X19)
| nowhere_dense(sK44(X18,X19,X20),X19)
| ~ top_str(X19)
| ~ topological_space(X19) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_839])]) ).
fof(f3194,plain,
( ! [X18,X19,X20] :
( ~ in(X18,a_2_1_yellow19(X19,X20))
| ~ net_str(X20,X19)
| empty_carrier(X20)
| ~ one_sorted_str(X19)
| empty_carrier(X19)
| ~ boundary_set(sK44(X18,X19,X20),X19)
| ~ closed_subset(sK44(X18,X19,X20),X19)
| nowhere_dense(sK44(X18,X19,X20),X19)
| ~ top_str(X19)
| ~ topological_space(X19) )
| ~ spl61_370
| ~ spl61_379 ),
inference(resolution,[],[f3167,f3033]) ).
fof(f6998,plain,
( spl61_838
| ~ spl61_369
| ~ spl61_379 ),
inference(avatar_split_clause,[],[f3193,f3166,f3028,f6996]) ).
fof(f6996,plain,
( spl61_838
<=> ! [X16,X17,X15] :
( ~ in(X15,a_2_1_yellow19(X16,X17))
| ~ net_str(X17,X16)
| empty_carrier(X17)
| ~ one_sorted_str(X16)
| empty_carrier(X16)
| ~ nowhere_dense(sK44(X15,X16,X17),X16)
| ~ open_subset(sK44(X15,X16,X17),X16)
| sP8(X16,sK44(X15,X16,X17))
| ~ top_str(X16)
| ~ topological_space(X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_838])]) ).
fof(f3193,plain,
( ! [X16,X17,X15] :
( ~ in(X15,a_2_1_yellow19(X16,X17))
| ~ net_str(X17,X16)
| empty_carrier(X17)
| ~ one_sorted_str(X16)
| empty_carrier(X16)
| ~ nowhere_dense(sK44(X15,X16,X17),X16)
| ~ open_subset(sK44(X15,X16,X17),X16)
| sP8(X16,sK44(X15,X16,X17))
| ~ top_str(X16)
| ~ topological_space(X16) )
| ~ spl61_369
| ~ spl61_379 ),
inference(resolution,[],[f3167,f3029]) ).
fof(f6888,plain,
( spl61_837
| ~ spl61_353
| ~ spl61_374 ),
inference(avatar_split_clause,[],[f3152,f3143,f2784,f6886]) ).
fof(f6886,plain,
( spl61_837
<=> ! [X4,X5,X3] :
( sK41(a_2_1_yellow19(X3,X4),X5) = sK44(sK41(a_2_1_yellow19(X3,X4),X5),X3,X4)
| ~ net_str(X4,X3)
| empty_carrier(X4)
| ~ one_sorted_str(X3)
| empty_carrier(X3)
| in(sK41(a_2_1_yellow19(X3,X4),X5),X5)
| a_2_1_yellow19(X3,X4) = X5 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_837])]) ).
fof(f3143,plain,
( spl61_374
<=> ! [X2,X0,X1] :
( sK44(X0,X1,X2) = X0
| ~ in(X0,a_2_1_yellow19(X1,X2))
| ~ net_str(X2,X1)
| empty_carrier(X2)
| ~ one_sorted_str(X1)
| empty_carrier(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_374])]) ).
fof(f3152,plain,
( ! [X3,X4,X5] :
( sK41(a_2_1_yellow19(X3,X4),X5) = sK44(sK41(a_2_1_yellow19(X3,X4),X5),X3,X4)
| ~ net_str(X4,X3)
| empty_carrier(X4)
| ~ one_sorted_str(X3)
| empty_carrier(X3)
| in(sK41(a_2_1_yellow19(X3,X4),X5),X5)
| a_2_1_yellow19(X3,X4) = X5 )
| ~ spl61_353
| ~ spl61_374 ),
inference(resolution,[],[f3144,f2785]) ).
fof(f3144,plain,
( ! [X2,X0,X1] :
( ~ in(X0,a_2_1_yellow19(X1,X2))
| sK44(X0,X1,X2) = X0
| ~ net_str(X2,X1)
| empty_carrier(X2)
| ~ one_sorted_str(X1)
| empty_carrier(X1) )
| ~ spl61_374 ),
inference(avatar_component_clause,[],[f3143]) ).
fof(f6884,plain,
( spl61_836
| ~ spl61_353
| ~ spl61_374 ),
inference(avatar_split_clause,[],[f3151,f3143,f2784,f6882]) ).
fof(f6882,plain,
( spl61_836
<=> ! [X2,X0,X1] :
( sK41(X0,a_2_1_yellow19(X1,X2)) = sK44(sK41(X0,a_2_1_yellow19(X1,X2)),X1,X2)
| ~ net_str(X2,X1)
| empty_carrier(X2)
| ~ one_sorted_str(X1)
| empty_carrier(X1)
| in(sK41(X0,a_2_1_yellow19(X1,X2)),X0)
| a_2_1_yellow19(X1,X2) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_836])]) ).
fof(f3151,plain,
( ! [X2,X0,X1] :
( sK41(X0,a_2_1_yellow19(X1,X2)) = sK44(sK41(X0,a_2_1_yellow19(X1,X2)),X1,X2)
| ~ net_str(X2,X1)
| empty_carrier(X2)
| ~ one_sorted_str(X1)
| empty_carrier(X1)
| in(sK41(X0,a_2_1_yellow19(X1,X2)),X0)
| a_2_1_yellow19(X1,X2) = X0 )
| ~ spl61_353
| ~ spl61_374 ),
inference(resolution,[],[f3144,f2785]) ).
fof(f6880,plain,
( spl61_835
| ~ spl61_240
| ~ spl61_799 ),
inference(avatar_split_clause,[],[f6816,f6466,f2010,f6878]) ).
fof(f6816,plain,
( ! [X2] :
( ~ in(X2,sK13)
| ~ in(the_carrier(boole_POSet(cast_as_carrier_subset(sK12))),X2) )
| ~ spl61_240
| ~ spl61_799 ),
inference(resolution,[],[f6467,f2011]) ).
fof(f6876,plain,
( spl61_834
| ~ spl61_334
| ~ spl61_372 ),
inference(avatar_split_clause,[],[f3136,f3131,f2569,f6874]) ).
fof(f2569,plain,
( spl61_334
<=> ! [X2,X0,X1] :
( strict_net_str(net_of_bool_filter(X2,X1,X0),X2)
| ~ sP11(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_334])]) ).
fof(f3136,plain,
( ! [X2,X3,X4] :
( net_of_bool_filter(X2,X3,X4) = net_str_of(X2,the_carrier(net_of_bool_filter(X2,X3,X4)),the_InternalRel(net_of_bool_filter(X2,X3,X4)),the_mapping(X2,net_of_bool_filter(X2,X3,X4)))
| ~ net_str(net_of_bool_filter(X2,X3,X4),X2)
| ~ one_sorted_str(X2)
| ~ sP11(X4,X3,X2) )
| ~ spl61_334
| ~ spl61_372 ),
inference(resolution,[],[f3132,f2570]) ).
fof(f2570,plain,
( ! [X2,X0,X1] :
( strict_net_str(net_of_bool_filter(X2,X1,X0),X2)
| ~ sP11(X0,X1,X2) )
| ~ spl61_334 ),
inference(avatar_component_clause,[],[f2569]) ).
fof(f6866,plain,
( spl61_833
| ~ spl61_351
| ~ spl61_381 ),
inference(avatar_split_clause,[],[f3211,f3205,f2776,f6864]) ).
fof(f6864,plain,
( spl61_833
<=> ! [X2,X0,X1] :
( ~ relation_of2(the_mapping(X0,X1),the_carrier(X1),the_carrier(X0))
| net_str(net_str_of(X0,the_carrier(X1),X2,the_mapping(X0,X1)),X0)
| ~ function(the_mapping(X0,X1))
| ~ relation_of2(X2,the_carrier(X1),the_carrier(X1))
| ~ one_sorted_str(X0)
| ~ net_str(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_833])]) ).
fof(f2776,plain,
( spl61_351
<=> ! [X0,X1] :
( quasi_total(the_mapping(X0,X1),the_carrier(X1),the_carrier(X0))
| ~ net_str(X1,X0)
| ~ one_sorted_str(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_351])]) ).
fof(f3205,plain,
( spl61_381
<=> ! [X0,X3,X2,X1] :
( net_str(net_str_of(X0,X1,X2,X3),X0)
| ~ relation_of2(X3,X1,the_carrier(X0))
| ~ quasi_total(X3,X1,the_carrier(X0))
| ~ function(X3)
| ~ relation_of2(X2,X1,X1)
| ~ one_sorted_str(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_381])]) ).
fof(f3211,plain,
( ! [X2,X0,X1] :
( ~ relation_of2(the_mapping(X0,X1),the_carrier(X1),the_carrier(X0))
| net_str(net_str_of(X0,the_carrier(X1),X2,the_mapping(X0,X1)),X0)
| ~ function(the_mapping(X0,X1))
| ~ relation_of2(X2,the_carrier(X1),the_carrier(X1))
| ~ one_sorted_str(X0)
| ~ net_str(X1,X0) )
| ~ spl61_351
| ~ spl61_381 ),
inference(duplicate_literal_removal,[],[f3210]) ).
fof(f3210,plain,
( ! [X2,X0,X1] :
( ~ relation_of2(the_mapping(X0,X1),the_carrier(X1),the_carrier(X0))
| net_str(net_str_of(X0,the_carrier(X1),X2,the_mapping(X0,X1)),X0)
| ~ function(the_mapping(X0,X1))
| ~ relation_of2(X2,the_carrier(X1),the_carrier(X1))
| ~ one_sorted_str(X0)
| ~ net_str(X1,X0)
| ~ one_sorted_str(X0) )
| ~ spl61_351
| ~ spl61_381 ),
inference(resolution,[],[f3206,f2777]) ).
fof(f2777,plain,
( ! [X0,X1] :
( quasi_total(the_mapping(X0,X1),the_carrier(X1),the_carrier(X0))
| ~ net_str(X1,X0)
| ~ one_sorted_str(X0) )
| ~ spl61_351 ),
inference(avatar_component_clause,[],[f2776]) ).
fof(f3206,plain,
( ! [X2,X3,X0,X1] :
( ~ quasi_total(X3,X1,the_carrier(X0))
| ~ relation_of2(X3,X1,the_carrier(X0))
| net_str(net_str_of(X0,X1,X2,X3),X0)
| ~ function(X3)
| ~ relation_of2(X2,X1,X1)
| ~ one_sorted_str(X0) )
| ~ spl61_381 ),
inference(avatar_component_clause,[],[f3205]) ).
fof(f6862,plain,
( spl61_832
| ~ spl61_351
| ~ spl61_380 ),
inference(avatar_split_clause,[],[f3209,f3201,f2776,f6860]) ).
fof(f6860,plain,
( spl61_832
<=> ! [X2,X0,X1] :
( ~ relation_of2(the_mapping(X0,X1),the_carrier(X1),the_carrier(X0))
| strict_net_str(net_str_of(X0,the_carrier(X1),X2,the_mapping(X0,X1)),X0)
| ~ function(the_mapping(X0,X1))
| ~ relation_of2(X2,the_carrier(X1),the_carrier(X1))
| ~ one_sorted_str(X0)
| ~ net_str(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_832])]) ).
fof(f3201,plain,
( spl61_380
<=> ! [X0,X3,X2,X1] :
( strict_net_str(net_str_of(X0,X1,X2,X3),X0)
| ~ relation_of2(X3,X1,the_carrier(X0))
| ~ quasi_total(X3,X1,the_carrier(X0))
| ~ function(X3)
| ~ relation_of2(X2,X1,X1)
| ~ one_sorted_str(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_380])]) ).
fof(f3209,plain,
( ! [X2,X0,X1] :
( ~ relation_of2(the_mapping(X0,X1),the_carrier(X1),the_carrier(X0))
| strict_net_str(net_str_of(X0,the_carrier(X1),X2,the_mapping(X0,X1)),X0)
| ~ function(the_mapping(X0,X1))
| ~ relation_of2(X2,the_carrier(X1),the_carrier(X1))
| ~ one_sorted_str(X0)
| ~ net_str(X1,X0) )
| ~ spl61_351
| ~ spl61_380 ),
inference(duplicate_literal_removal,[],[f3208]) ).
fof(f3208,plain,
( ! [X2,X0,X1] :
( ~ relation_of2(the_mapping(X0,X1),the_carrier(X1),the_carrier(X0))
| strict_net_str(net_str_of(X0,the_carrier(X1),X2,the_mapping(X0,X1)),X0)
| ~ function(the_mapping(X0,X1))
| ~ relation_of2(X2,the_carrier(X1),the_carrier(X1))
| ~ one_sorted_str(X0)
| ~ net_str(X1,X0)
| ~ one_sorted_str(X0) )
| ~ spl61_351
| ~ spl61_380 ),
inference(resolution,[],[f3202,f2777]) ).
fof(f3202,plain,
( ! [X2,X3,X0,X1] :
( ~ quasi_total(X3,X1,the_carrier(X0))
| ~ relation_of2(X3,X1,the_carrier(X0))
| strict_net_str(net_str_of(X0,X1,X2,X3),X0)
| ~ function(X3)
| ~ relation_of2(X2,X1,X1)
| ~ one_sorted_str(X0) )
| ~ spl61_380 ),
inference(avatar_component_clause,[],[f3201]) ).
fof(f6852,plain,
( spl61_831
| ~ spl61_261
| ~ spl61_396 ),
inference(avatar_split_clause,[],[f3388,f3358,f2121,f6850]) ).
fof(f6850,plain,
( spl61_831
<=> ! [X2,X0,X1] :
( net_str(net_of_bool_filter(X0,X1,X2),X0)
| ~ upper_relstr_subset(X2,boole_POSet(X1))
| ~ filtered_subset(X2,boole_POSet(X1))
| empty(X2)
| ~ element(X1,powerset(the_carrier(X0)))
| empty(X1)
| ~ one_sorted_str(X0)
| empty_carrier(X0)
| ~ subset(X2,the_carrier(boole_POSet(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_831])]) ).
fof(f3388,plain,
( ! [X2,X0,X1] :
( net_str(net_of_bool_filter(X0,X1,X2),X0)
| ~ upper_relstr_subset(X2,boole_POSet(X1))
| ~ filtered_subset(X2,boole_POSet(X1))
| empty(X2)
| ~ element(X1,powerset(the_carrier(X0)))
| empty(X1)
| ~ one_sorted_str(X0)
| empty_carrier(X0)
| ~ subset(X2,the_carrier(boole_POSet(X1))) )
| ~ spl61_261
| ~ spl61_396 ),
inference(resolution,[],[f3359,f2122]) ).
fof(f6848,plain,
( spl61_830
| ~ spl61_261
| ~ spl61_395 ),
inference(avatar_split_clause,[],[f3361,f3354,f2121,f6846]) ).
fof(f6846,plain,
( spl61_830
<=> ! [X2,X0,X1] :
( strict_net_str(net_of_bool_filter(X0,X1,X2),X0)
| ~ upper_relstr_subset(X2,boole_POSet(X1))
| ~ filtered_subset(X2,boole_POSet(X1))
| empty(X2)
| ~ element(X1,powerset(the_carrier(X0)))
| empty(X1)
| ~ one_sorted_str(X0)
| empty_carrier(X0)
| ~ subset(X2,the_carrier(boole_POSet(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_830])]) ).
fof(f3361,plain,
( ! [X2,X0,X1] :
( strict_net_str(net_of_bool_filter(X0,X1,X2),X0)
| ~ upper_relstr_subset(X2,boole_POSet(X1))
| ~ filtered_subset(X2,boole_POSet(X1))
| empty(X2)
| ~ element(X1,powerset(the_carrier(X0)))
| empty(X1)
| ~ one_sorted_str(X0)
| empty_carrier(X0)
| ~ subset(X2,the_carrier(boole_POSet(X1))) )
| ~ spl61_261
| ~ spl61_395 ),
inference(resolution,[],[f3355,f2122]) ).
fof(f6758,plain,
( spl61_829
| ~ spl61_261
| ~ spl61_390 ),
inference(avatar_split_clause,[],[f3322,f3248,f2121,f6756]) ).
fof(f6756,plain,
( spl61_829
<=> ! [X2,X0,X1] :
( transitive_relstr(net_of_bool_filter(X0,X1,X2))
| ~ upper_relstr_subset(X2,boole_POSet(X1))
| ~ filtered_subset(X2,boole_POSet(X1))
| empty(X2)
| ~ element(X1,powerset(the_carrier(X0)))
| empty(X1)
| ~ one_sorted_str(X0)
| empty_carrier(X0)
| ~ subset(X2,the_carrier(boole_POSet(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_829])]) ).
fof(f3322,plain,
( ! [X2,X0,X1] :
( transitive_relstr(net_of_bool_filter(X0,X1,X2))
| ~ upper_relstr_subset(X2,boole_POSet(X1))
| ~ filtered_subset(X2,boole_POSet(X1))
| empty(X2)
| ~ element(X1,powerset(the_carrier(X0)))
| empty(X1)
| ~ one_sorted_str(X0)
| empty_carrier(X0)
| ~ subset(X2,the_carrier(boole_POSet(X1))) )
| ~ spl61_261
| ~ spl61_390 ),
inference(resolution,[],[f3249,f2122]) ).
fof(f6754,plain,
( spl61_828
| ~ spl61_261
| ~ spl61_389 ),
inference(avatar_split_clause,[],[f3294,f3244,f2121,f6752]) ).
fof(f6752,plain,
( spl61_828
<=> ! [X2,X0,X1] :
( reflexive_relstr(net_of_bool_filter(X0,X1,X2))
| ~ upper_relstr_subset(X2,boole_POSet(X1))
| ~ filtered_subset(X2,boole_POSet(X1))
| empty(X2)
| ~ element(X1,powerset(the_carrier(X0)))
| empty(X1)
| ~ one_sorted_str(X0)
| empty_carrier(X0)
| ~ subset(X2,the_carrier(boole_POSet(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_828])]) ).
fof(f3294,plain,
( ! [X2,X0,X1] :
( reflexive_relstr(net_of_bool_filter(X0,X1,X2))
| ~ upper_relstr_subset(X2,boole_POSet(X1))
| ~ filtered_subset(X2,boole_POSet(X1))
| empty(X2)
| ~ element(X1,powerset(the_carrier(X0)))
| empty(X1)
| ~ one_sorted_str(X0)
| empty_carrier(X0)
| ~ subset(X2,the_carrier(boole_POSet(X1))) )
| ~ spl61_261
| ~ spl61_389 ),
inference(resolution,[],[f3245,f2122]) ).
fof(f6750,plain,
( spl61_827
| ~ spl61_261
| ~ spl61_388 ),
inference(avatar_split_clause,[],[f3267,f3240,f2121,f6748]) ).
fof(f6748,plain,
( spl61_827
<=> ! [X2,X0,X1] :
( ~ empty_carrier(net_of_bool_filter(X0,X1,X2))
| ~ upper_relstr_subset(X2,boole_POSet(X1))
| ~ filtered_subset(X2,boole_POSet(X1))
| empty(X2)
| ~ element(X1,powerset(the_carrier(X0)))
| empty(X1)
| ~ one_sorted_str(X0)
| empty_carrier(X0)
| ~ subset(X2,the_carrier(boole_POSet(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_827])]) ).
fof(f3267,plain,
( ! [X2,X0,X1] :
( ~ empty_carrier(net_of_bool_filter(X0,X1,X2))
| ~ upper_relstr_subset(X2,boole_POSet(X1))
| ~ filtered_subset(X2,boole_POSet(X1))
| empty(X2)
| ~ element(X1,powerset(the_carrier(X0)))
| empty(X1)
| ~ one_sorted_str(X0)
| empty_carrier(X0)
| ~ subset(X2,the_carrier(boole_POSet(X1))) )
| ~ spl61_261
| ~ spl61_388 ),
inference(resolution,[],[f3241,f2122]) ).
fof(f6746,plain,
( spl61_826
| ~ spl61_364
| ~ spl61_371 ),
inference(avatar_split_clause,[],[f3122,f3039,f2966,f6744]) ).
fof(f6744,plain,
( spl61_826
<=> ! [X9,X8] :
( ~ net_str(X8,X9)
| empty_carrier(X8)
| ~ one_sorted_str(X9)
| empty_carrier(X9)
| ~ nowhere_dense(filter_of_net_str(X9,X8),boole_POSet(cast_as_carrier_subset(X9)))
| boundary_set(filter_of_net_str(X9,X8),boole_POSet(cast_as_carrier_subset(X9)))
| ~ top_str(boole_POSet(cast_as_carrier_subset(X9)))
| ~ topological_space(boole_POSet(cast_as_carrier_subset(X9))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_826])]) ).
fof(f2966,plain,
( spl61_364
<=> ! [X0,X1] :
( boundary_set(X1,X0)
| ~ nowhere_dense(X1,X0)
| ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0)
| ~ topological_space(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_364])]) ).
fof(f3122,plain,
( ! [X8,X9] :
( ~ net_str(X8,X9)
| empty_carrier(X8)
| ~ one_sorted_str(X9)
| empty_carrier(X9)
| ~ nowhere_dense(filter_of_net_str(X9,X8),boole_POSet(cast_as_carrier_subset(X9)))
| boundary_set(filter_of_net_str(X9,X8),boole_POSet(cast_as_carrier_subset(X9)))
| ~ top_str(boole_POSet(cast_as_carrier_subset(X9)))
| ~ topological_space(boole_POSet(cast_as_carrier_subset(X9))) )
| ~ spl61_364
| ~ spl61_371 ),
inference(resolution,[],[f3040,f2967]) ).
fof(f2967,plain,
( ! [X0,X1] :
( ~ element(X1,powerset(the_carrier(X0)))
| ~ nowhere_dense(X1,X0)
| boundary_set(X1,X0)
| ~ top_str(X0)
| ~ topological_space(X0) )
| ~ spl61_364 ),
inference(avatar_component_clause,[],[f2966]) ).
fof(f6736,plain,
( spl61_825
| ~ spl61_364
| ~ spl61_379 ),
inference(avatar_split_clause,[],[f3192,f3166,f2966,f6734]) ).
fof(f6734,plain,
( spl61_825
<=> ! [X13,X12,X14] :
( ~ in(X12,a_2_1_yellow19(X13,X14))
| ~ net_str(X14,X13)
| empty_carrier(X14)
| ~ one_sorted_str(X13)
| empty_carrier(X13)
| ~ nowhere_dense(sK44(X12,X13,X14),X13)
| boundary_set(sK44(X12,X13,X14),X13)
| ~ top_str(X13)
| ~ topological_space(X13) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_825])]) ).
fof(f3192,plain,
( ! [X14,X12,X13] :
( ~ in(X12,a_2_1_yellow19(X13,X14))
| ~ net_str(X14,X13)
| empty_carrier(X14)
| ~ one_sorted_str(X13)
| empty_carrier(X13)
| ~ nowhere_dense(sK44(X12,X13,X14),X13)
| boundary_set(sK44(X12,X13,X14),X13)
| ~ top_str(X13)
| ~ topological_space(X13) )
| ~ spl61_364
| ~ spl61_379 ),
inference(resolution,[],[f3167,f2967]) ).
fof(f6732,plain,
( spl61_824
| ~ spl61_369
| ~ spl61_377 ),
inference(avatar_split_clause,[],[f3182,f3158,f3028,f6730]) ).
fof(f6730,plain,
( spl61_824
<=> ! [X11,X10] :
( ~ net_str(X10,X11)
| ~ directed_relstr(X10)
| ~ transitive_relstr(X10)
| empty_carrier(X10)
| ~ top_str(X11)
| ~ topological_space(X11)
| empty_carrier(X11)
| ~ nowhere_dense(lim_points_of_net(X11,X10),X11)
| ~ open_subset(lim_points_of_net(X11,X10),X11)
| sP8(X11,lim_points_of_net(X11,X10)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_824])]) ).
fof(f3182,plain,
( ! [X10,X11] :
( ~ net_str(X10,X11)
| ~ directed_relstr(X10)
| ~ transitive_relstr(X10)
| empty_carrier(X10)
| ~ top_str(X11)
| ~ topological_space(X11)
| empty_carrier(X11)
| ~ nowhere_dense(lim_points_of_net(X11,X10),X11)
| ~ open_subset(lim_points_of_net(X11,X10),X11)
| sP8(X11,lim_points_of_net(X11,X10)) )
| ~ spl61_369
| ~ spl61_377 ),
inference(duplicate_literal_removal,[],[f3174]) ).
fof(f3174,plain,
( ! [X10,X11] :
( ~ net_str(X10,X11)
| ~ directed_relstr(X10)
| ~ transitive_relstr(X10)
| empty_carrier(X10)
| ~ top_str(X11)
| ~ topological_space(X11)
| empty_carrier(X11)
| ~ nowhere_dense(lim_points_of_net(X11,X10),X11)
| ~ open_subset(lim_points_of_net(X11,X10),X11)
| sP8(X11,lim_points_of_net(X11,X10))
| ~ top_str(X11)
| ~ topological_space(X11) )
| ~ spl61_369
| ~ spl61_377 ),
inference(resolution,[],[f3159,f3029]) ).
fof(f6728,plain,
( spl61_823
| ~ spl61_370
| ~ spl61_377 ),
inference(avatar_split_clause,[],[f3181,f3158,f3032,f6726]) ).
fof(f6726,plain,
( spl61_823
<=> ! [X13,X12] :
( ~ net_str(X12,X13)
| ~ directed_relstr(X12)
| ~ transitive_relstr(X12)
| empty_carrier(X12)
| ~ top_str(X13)
| ~ topological_space(X13)
| empty_carrier(X13)
| ~ boundary_set(lim_points_of_net(X13,X12),X13)
| ~ closed_subset(lim_points_of_net(X13,X12),X13)
| nowhere_dense(lim_points_of_net(X13,X12),X13) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_823])]) ).
fof(f3181,plain,
( ! [X12,X13] :
( ~ net_str(X12,X13)
| ~ directed_relstr(X12)
| ~ transitive_relstr(X12)
| empty_carrier(X12)
| ~ top_str(X13)
| ~ topological_space(X13)
| empty_carrier(X13)
| ~ boundary_set(lim_points_of_net(X13,X12),X13)
| ~ closed_subset(lim_points_of_net(X13,X12),X13)
| nowhere_dense(lim_points_of_net(X13,X12),X13) )
| ~ spl61_370
| ~ spl61_377 ),
inference(duplicate_literal_removal,[],[f3175]) ).
fof(f3175,plain,
( ! [X12,X13] :
( ~ net_str(X12,X13)
| ~ directed_relstr(X12)
| ~ transitive_relstr(X12)
| empty_carrier(X12)
| ~ top_str(X13)
| ~ topological_space(X13)
| empty_carrier(X13)
| ~ boundary_set(lim_points_of_net(X13,X12),X13)
| ~ closed_subset(lim_points_of_net(X13,X12),X13)
| nowhere_dense(lim_points_of_net(X13,X12),X13)
| ~ top_str(X13)
| ~ topological_space(X13) )
| ~ spl61_370
| ~ spl61_377 ),
inference(resolution,[],[f3159,f3033]) ).
fof(f6724,plain,
( spl61_822
| ~ spl61_360
| ~ spl61_379 ),
inference(avatar_split_clause,[],[f3191,f3166,f2826,f6722]) ).
fof(f6722,plain,
( spl61_822
<=> ! [X9,X11,X10] :
( ~ in(X9,a_2_1_yellow19(X10,X11))
| ~ net_str(X11,X10)
| empty_carrier(X11)
| ~ one_sorted_str(X10)
| empty_carrier(X10)
| ~ empty(sK44(X9,X10,X11))
| closed_subset(sK44(X9,X10,X11),X10)
| ~ top_str(X10)
| ~ topological_space(X10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_822])]) ).
fof(f2826,plain,
( spl61_360
<=> ! [X0,X1] :
( closed_subset(X1,X0)
| ~ empty(X1)
| ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0)
| ~ topological_space(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_360])]) ).
fof(f3191,plain,
( ! [X10,X11,X9] :
( ~ in(X9,a_2_1_yellow19(X10,X11))
| ~ net_str(X11,X10)
| empty_carrier(X11)
| ~ one_sorted_str(X10)
| empty_carrier(X10)
| ~ empty(sK44(X9,X10,X11))
| closed_subset(sK44(X9,X10,X11),X10)
| ~ top_str(X10)
| ~ topological_space(X10) )
| ~ spl61_360
| ~ spl61_379 ),
inference(resolution,[],[f3167,f2827]) ).
fof(f2827,plain,
( ! [X0,X1] :
( ~ element(X1,powerset(the_carrier(X0)))
| ~ empty(X1)
| closed_subset(X1,X0)
| ~ top_str(X0)
| ~ topological_space(X0) )
| ~ spl61_360 ),
inference(avatar_component_clause,[],[f2826]) ).
fof(f6720,plain,
( spl61_821
| ~ spl61_359
| ~ spl61_379 ),
inference(avatar_split_clause,[],[f3190,f3166,f2822,f6718]) ).
fof(f6718,plain,
( spl61_821
<=> ! [X6,X8,X7] :
( ~ in(X6,a_2_1_yellow19(X7,X8))
| ~ net_str(X8,X7)
| empty_carrier(X8)
| ~ one_sorted_str(X7)
| empty_carrier(X7)
| ~ empty(sK44(X6,X7,X8))
| open_subset(sK44(X6,X7,X8),X7)
| ~ top_str(X7)
| ~ topological_space(X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_821])]) ).
fof(f2822,plain,
( spl61_359
<=> ! [X0,X1] :
( open_subset(X1,X0)
| ~ empty(X1)
| ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0)
| ~ topological_space(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_359])]) ).
fof(f3190,plain,
( ! [X8,X6,X7] :
( ~ in(X6,a_2_1_yellow19(X7,X8))
| ~ net_str(X8,X7)
| empty_carrier(X8)
| ~ one_sorted_str(X7)
| empty_carrier(X7)
| ~ empty(sK44(X6,X7,X8))
| open_subset(sK44(X6,X7,X8),X7)
| ~ top_str(X7)
| ~ topological_space(X7) )
| ~ spl61_359
| ~ spl61_379 ),
inference(resolution,[],[f3167,f2823]) ).
fof(f2823,plain,
( ! [X0,X1] :
( ~ element(X1,powerset(the_carrier(X0)))
| ~ empty(X1)
| open_subset(X1,X0)
| ~ top_str(X0)
| ~ topological_space(X0) )
| ~ spl61_359 ),
inference(avatar_component_clause,[],[f2822]) ).
fof(f6716,plain,
( spl61_820
| ~ spl61_358
| ~ spl61_379 ),
inference(avatar_split_clause,[],[f3189,f3166,f2818,f6714]) ).
fof(f6714,plain,
( spl61_820
<=> ! [X4,X5,X3] :
( ~ in(X3,a_2_1_yellow19(X4,X5))
| ~ net_str(X5,X4)
| empty_carrier(X5)
| ~ one_sorted_str(X4)
| empty_carrier(X4)
| ~ empty(sK44(X3,X4,X5))
| nowhere_dense(sK44(X3,X4,X5),X4)
| ~ top_str(X4)
| ~ topological_space(X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_820])]) ).
fof(f2818,plain,
( spl61_358
<=> ! [X0,X1] :
( nowhere_dense(X1,X0)
| ~ empty(X1)
| ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0)
| ~ topological_space(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_358])]) ).
fof(f3189,plain,
( ! [X3,X4,X5] :
( ~ in(X3,a_2_1_yellow19(X4,X5))
| ~ net_str(X5,X4)
| empty_carrier(X5)
| ~ one_sorted_str(X4)
| empty_carrier(X4)
| ~ empty(sK44(X3,X4,X5))
| nowhere_dense(sK44(X3,X4,X5),X4)
| ~ top_str(X4)
| ~ topological_space(X4) )
| ~ spl61_358
| ~ spl61_379 ),
inference(resolution,[],[f3167,f2819]) ).
fof(f2819,plain,
( ! [X0,X1] :
( ~ element(X1,powerset(the_carrier(X0)))
| ~ empty(X1)
| nowhere_dense(X1,X0)
| ~ top_str(X0)
| ~ topological_space(X0) )
| ~ spl61_358 ),
inference(avatar_component_clause,[],[f2818]) ).
fof(f6712,plain,
( spl61_819
| ~ spl61_421
| ~ spl61_446 ),
inference(avatar_split_clause,[],[f6672,f3667,f3562,f6709]) ).
fof(f6709,plain,
( spl61_819
<=> sK13 = sK60 ),
introduced(avatar_definition,[new_symbols(naming,[spl61_819])]) ).
fof(f3562,plain,
( spl61_421
<=> ! [X0] :
( in(sK41(X0,sK13),X0)
| sK13 = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_421])]) ).
fof(f6672,plain,
( sK13 = sK60
| ~ spl61_421
| ~ spl61_446 ),
inference(resolution,[],[f3563,f3668]) ).
fof(f3563,plain,
( ! [X0] :
( in(sK41(X0,sK13),X0)
| sK13 = X0 )
| ~ spl61_421 ),
inference(avatar_component_clause,[],[f3562]) ).
fof(f6707,plain,
( spl61_818
| ~ spl61_339
| ~ spl61_379 ),
inference(avatar_split_clause,[],[f3188,f3166,f2677,f6705]) ).
fof(f6705,plain,
( spl61_818
<=> ! [X2,X0,X1] :
( ~ in(X0,a_2_1_yellow19(X1,X2))
| ~ net_str(X2,X1)
| empty_carrier(X2)
| ~ one_sorted_str(X1)
| empty_carrier(X1)
| ~ empty(sK44(X0,X1,X2))
| boundary_set(sK44(X0,X1,X2),X1)
| ~ top_str(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_818])]) ).
fof(f3188,plain,
( ! [X2,X0,X1] :
( ~ in(X0,a_2_1_yellow19(X1,X2))
| ~ net_str(X2,X1)
| empty_carrier(X2)
| ~ one_sorted_str(X1)
| empty_carrier(X1)
| ~ empty(sK44(X0,X1,X2))
| boundary_set(sK44(X0,X1,X2),X1)
| ~ top_str(X1) )
| ~ spl61_339
| ~ spl61_379 ),
inference(resolution,[],[f3167,f2678]) ).
fof(f6697,plain,
( spl61_817
| ~ spl61_293
| ~ spl61_379 ),
inference(avatar_split_clause,[],[f3199,f3166,f2281,f6695]) ).
fof(f6695,plain,
( spl61_817
<=> ! [X36,X37,X35] :
( ~ in(X35,a_2_1_yellow19(X36,X37))
| ~ net_str(X37,X36)
| empty_carrier(X37)
| ~ one_sorted_str(X36)
| empty_carrier(X36)
| empty(powerset(the_carrier(X36)))
| in(sK44(X35,X36,X37),powerset(the_carrier(X36))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_817])]) ).
fof(f2281,plain,
( spl61_293
<=> ! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_293])]) ).
fof(f3199,plain,
( ! [X36,X37,X35] :
( ~ in(X35,a_2_1_yellow19(X36,X37))
| ~ net_str(X37,X36)
| empty_carrier(X37)
| ~ one_sorted_str(X36)
| empty_carrier(X36)
| empty(powerset(the_carrier(X36)))
| in(sK44(X35,X36,X37),powerset(the_carrier(X36))) )
| ~ spl61_293
| ~ spl61_379 ),
inference(resolution,[],[f3167,f2282]) ).
fof(f2282,plain,
( ! [X0,X1] :
( ~ element(X0,X1)
| empty(X1)
| in(X0,X1) )
| ~ spl61_293 ),
inference(avatar_component_clause,[],[f2281]) ).
fof(f6693,plain,
( spl61_816
| ~ spl61_293
| ~ spl61_377 ),
inference(avatar_split_clause,[],[f3180,f3158,f2281,f6691]) ).
fof(f6691,plain,
( spl61_816
<=> ! [X25,X24] :
( ~ net_str(X24,X25)
| ~ directed_relstr(X24)
| ~ transitive_relstr(X24)
| empty_carrier(X24)
| ~ top_str(X25)
| ~ topological_space(X25)
| empty_carrier(X25)
| empty(powerset(the_carrier(X25)))
| in(lim_points_of_net(X25,X24),powerset(the_carrier(X25))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_816])]) ).
fof(f3180,plain,
( ! [X24,X25] :
( ~ net_str(X24,X25)
| ~ directed_relstr(X24)
| ~ transitive_relstr(X24)
| empty_carrier(X24)
| ~ top_str(X25)
| ~ topological_space(X25)
| empty_carrier(X25)
| empty(powerset(the_carrier(X25)))
| in(lim_points_of_net(X25,X24),powerset(the_carrier(X25))) )
| ~ spl61_293
| ~ spl61_377 ),
inference(resolution,[],[f3159,f2282]) ).
fof(f6687,plain,
( spl61_815
| ~ spl61_364
| ~ spl61_377 ),
inference(avatar_split_clause,[],[f3183,f3158,f2966,f6685]) ).
fof(f6685,plain,
( spl61_815
<=> ! [X9,X8] :
( ~ net_str(X8,X9)
| ~ directed_relstr(X8)
| ~ transitive_relstr(X8)
| empty_carrier(X8)
| ~ top_str(X9)
| ~ topological_space(X9)
| empty_carrier(X9)
| ~ nowhere_dense(lim_points_of_net(X9,X8),X9)
| boundary_set(lim_points_of_net(X9,X8),X9) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_815])]) ).
fof(f3183,plain,
( ! [X8,X9] :
( ~ net_str(X8,X9)
| ~ directed_relstr(X8)
| ~ transitive_relstr(X8)
| empty_carrier(X8)
| ~ top_str(X9)
| ~ topological_space(X9)
| empty_carrier(X9)
| ~ nowhere_dense(lim_points_of_net(X9,X8),X9)
| boundary_set(lim_points_of_net(X9,X8),X9) )
| ~ spl61_364
| ~ spl61_377 ),
inference(duplicate_literal_removal,[],[f3173]) ).
fof(f3173,plain,
( ! [X8,X9] :
( ~ net_str(X8,X9)
| ~ directed_relstr(X8)
| ~ transitive_relstr(X8)
| empty_carrier(X8)
| ~ top_str(X9)
| ~ topological_space(X9)
| empty_carrier(X9)
| ~ nowhere_dense(lim_points_of_net(X9,X8),X9)
| boundary_set(lim_points_of_net(X9,X8),X9)
| ~ top_str(X9)
| ~ topological_space(X9) )
| ~ spl61_364
| ~ spl61_377 ),
inference(resolution,[],[f3159,f2967]) ).
fof(f6611,plain,
( spl61_814
| ~ spl61_335
| ~ spl61_379 ),
inference(avatar_split_clause,[],[f3195,f3166,f2573,f6609]) ).
fof(f6609,plain,
( spl61_814
<=> ! [X24,X21,X23,X22] :
( ~ in(X21,a_2_1_yellow19(X22,X23))
| ~ net_str(X23,X22)
| empty_carrier(X23)
| ~ one_sorted_str(X22)
| empty_carrier(X22)
| element(X24,the_carrier(X22))
| ~ in(X24,sK44(X21,X22,X23)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_814])]) ).
fof(f3195,plain,
( ! [X21,X24,X22,X23] :
( ~ in(X21,a_2_1_yellow19(X22,X23))
| ~ net_str(X23,X22)
| empty_carrier(X23)
| ~ one_sorted_str(X22)
| empty_carrier(X22)
| element(X24,the_carrier(X22))
| ~ in(X24,sK44(X21,X22,X23)) )
| ~ spl61_335
| ~ spl61_379 ),
inference(resolution,[],[f3167,f2574]) ).
fof(f6607,plain,
( spl61_813
| ~ spl61_339
| ~ spl61_377 ),
inference(avatar_split_clause,[],[f3187,f3158,f2677,f6605]) ).
fof(f6605,plain,
( spl61_813
<=> ! [X0,X1] :
( ~ net_str(X0,X1)
| ~ directed_relstr(X0)
| ~ transitive_relstr(X0)
| empty_carrier(X0)
| ~ top_str(X1)
| ~ topological_space(X1)
| empty_carrier(X1)
| ~ empty(lim_points_of_net(X1,X0))
| boundary_set(lim_points_of_net(X1,X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_813])]) ).
fof(f3187,plain,
( ! [X0,X1] :
( ~ net_str(X0,X1)
| ~ directed_relstr(X0)
| ~ transitive_relstr(X0)
| empty_carrier(X0)
| ~ top_str(X1)
| ~ topological_space(X1)
| empty_carrier(X1)
| ~ empty(lim_points_of_net(X1,X0))
| boundary_set(lim_points_of_net(X1,X0),X1) )
| ~ spl61_339
| ~ spl61_377 ),
inference(duplicate_literal_removal,[],[f3169]) ).
fof(f3169,plain,
( ! [X0,X1] :
( ~ net_str(X0,X1)
| ~ directed_relstr(X0)
| ~ transitive_relstr(X0)
| empty_carrier(X0)
| ~ top_str(X1)
| ~ topological_space(X1)
| empty_carrier(X1)
| ~ empty(lim_points_of_net(X1,X0))
| boundary_set(lim_points_of_net(X1,X0),X1)
| ~ top_str(X1) )
| ~ spl61_339
| ~ spl61_377 ),
inference(resolution,[],[f3159,f2678]) ).
fof(f6603,plain,
( spl61_812
| ~ spl61_358
| ~ spl61_377 ),
inference(avatar_split_clause,[],[f3186,f3158,f2818,f6601]) ).
fof(f6601,plain,
( spl61_812
<=> ! [X2,X3] :
( ~ net_str(X2,X3)
| ~ directed_relstr(X2)
| ~ transitive_relstr(X2)
| empty_carrier(X2)
| ~ top_str(X3)
| ~ topological_space(X3)
| empty_carrier(X3)
| ~ empty(lim_points_of_net(X3,X2))
| nowhere_dense(lim_points_of_net(X3,X2),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_812])]) ).
fof(f3186,plain,
( ! [X2,X3] :
( ~ net_str(X2,X3)
| ~ directed_relstr(X2)
| ~ transitive_relstr(X2)
| empty_carrier(X2)
| ~ top_str(X3)
| ~ topological_space(X3)
| empty_carrier(X3)
| ~ empty(lim_points_of_net(X3,X2))
| nowhere_dense(lim_points_of_net(X3,X2),X3) )
| ~ spl61_358
| ~ spl61_377 ),
inference(duplicate_literal_removal,[],[f3170]) ).
fof(f3170,plain,
( ! [X2,X3] :
( ~ net_str(X2,X3)
| ~ directed_relstr(X2)
| ~ transitive_relstr(X2)
| empty_carrier(X2)
| ~ top_str(X3)
| ~ topological_space(X3)
| empty_carrier(X3)
| ~ empty(lim_points_of_net(X3,X2))
| nowhere_dense(lim_points_of_net(X3,X2),X3)
| ~ top_str(X3)
| ~ topological_space(X3) )
| ~ spl61_358
| ~ spl61_377 ),
inference(resolution,[],[f3159,f2819]) ).
fof(f6599,plain,
( spl61_811
| ~ spl61_359
| ~ spl61_377 ),
inference(avatar_split_clause,[],[f3185,f3158,f2822,f6597]) ).
fof(f6597,plain,
( spl61_811
<=> ! [X4,X5] :
( ~ net_str(X4,X5)
| ~ directed_relstr(X4)
| ~ transitive_relstr(X4)
| empty_carrier(X4)
| ~ top_str(X5)
| ~ topological_space(X5)
| empty_carrier(X5)
| ~ empty(lim_points_of_net(X5,X4))
| open_subset(lim_points_of_net(X5,X4),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_811])]) ).
fof(f3185,plain,
( ! [X4,X5] :
( ~ net_str(X4,X5)
| ~ directed_relstr(X4)
| ~ transitive_relstr(X4)
| empty_carrier(X4)
| ~ top_str(X5)
| ~ topological_space(X5)
| empty_carrier(X5)
| ~ empty(lim_points_of_net(X5,X4))
| open_subset(lim_points_of_net(X5,X4),X5) )
| ~ spl61_359
| ~ spl61_377 ),
inference(duplicate_literal_removal,[],[f3171]) ).
fof(f3171,plain,
( ! [X4,X5] :
( ~ net_str(X4,X5)
| ~ directed_relstr(X4)
| ~ transitive_relstr(X4)
| empty_carrier(X4)
| ~ top_str(X5)
| ~ topological_space(X5)
| empty_carrier(X5)
| ~ empty(lim_points_of_net(X5,X4))
| open_subset(lim_points_of_net(X5,X4),X5)
| ~ top_str(X5)
| ~ topological_space(X5) )
| ~ spl61_359
| ~ spl61_377 ),
inference(resolution,[],[f3159,f2823]) ).
fof(f6595,plain,
( spl61_810
| ~ spl61_360
| ~ spl61_377 ),
inference(avatar_split_clause,[],[f3184,f3158,f2826,f6593]) ).
fof(f6593,plain,
( spl61_810
<=> ! [X6,X7] :
( ~ net_str(X6,X7)
| ~ directed_relstr(X6)
| ~ transitive_relstr(X6)
| empty_carrier(X6)
| ~ top_str(X7)
| ~ topological_space(X7)
| empty_carrier(X7)
| ~ empty(lim_points_of_net(X7,X6))
| closed_subset(lim_points_of_net(X7,X6),X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_810])]) ).
fof(f3184,plain,
( ! [X6,X7] :
( ~ net_str(X6,X7)
| ~ directed_relstr(X6)
| ~ transitive_relstr(X6)
| empty_carrier(X6)
| ~ top_str(X7)
| ~ topological_space(X7)
| empty_carrier(X7)
| ~ empty(lim_points_of_net(X7,X6))
| closed_subset(lim_points_of_net(X7,X6),X7) )
| ~ spl61_360
| ~ spl61_377 ),
inference(duplicate_literal_removal,[],[f3172]) ).
fof(f3172,plain,
( ! [X6,X7] :
( ~ net_str(X6,X7)
| ~ directed_relstr(X6)
| ~ transitive_relstr(X6)
| empty_carrier(X6)
| ~ top_str(X7)
| ~ topological_space(X7)
| empty_carrier(X7)
| ~ empty(lim_points_of_net(X7,X6))
| closed_subset(lim_points_of_net(X7,X6),X7)
| ~ top_str(X7)
| ~ topological_space(X7) )
| ~ spl61_360
| ~ spl61_377 ),
inference(resolution,[],[f3159,f2827]) ).
fof(f6591,plain,
( spl61_809
| ~ spl61_335
| ~ spl61_377 ),
inference(avatar_split_clause,[],[f3176,f3158,f2573,f6589]) ).
fof(f6589,plain,
( spl61_809
<=> ! [X16,X14,X15] :
( ~ net_str(X14,X15)
| ~ directed_relstr(X14)
| ~ transitive_relstr(X14)
| empty_carrier(X14)
| ~ top_str(X15)
| ~ topological_space(X15)
| empty_carrier(X15)
| element(X16,the_carrier(X15))
| ~ in(X16,lim_points_of_net(X15,X14)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_809])]) ).
fof(f3176,plain,
( ! [X16,X14,X15] :
( ~ net_str(X14,X15)
| ~ directed_relstr(X14)
| ~ transitive_relstr(X14)
| empty_carrier(X14)
| ~ top_str(X15)
| ~ topological_space(X15)
| empty_carrier(X15)
| element(X16,the_carrier(X15))
| ~ in(X16,lim_points_of_net(X15,X14)) )
| ~ spl61_335
| ~ spl61_377 ),
inference(resolution,[],[f3159,f2574]) ).
fof(f6587,plain,
( spl61_808
| ~ spl61_293
| ~ spl61_371 ),
inference(avatar_split_clause,[],[f3129,f3039,f2281,f6585]) ).
fof(f6585,plain,
( spl61_808
<=> ! [X25,X24] :
( ~ net_str(X24,X25)
| empty_carrier(X24)
| ~ one_sorted_str(X25)
| empty_carrier(X25)
| empty(powerset(the_carrier(boole_POSet(cast_as_carrier_subset(X25)))))
| in(filter_of_net_str(X25,X24),powerset(the_carrier(boole_POSet(cast_as_carrier_subset(X25))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_808])]) ).
fof(f3129,plain,
( ! [X24,X25] :
( ~ net_str(X24,X25)
| empty_carrier(X24)
| ~ one_sorted_str(X25)
| empty_carrier(X25)
| empty(powerset(the_carrier(boole_POSet(cast_as_carrier_subset(X25)))))
| in(filter_of_net_str(X25,X24),powerset(the_carrier(boole_POSet(cast_as_carrier_subset(X25))))) )
| ~ spl61_293
| ~ spl61_371 ),
inference(resolution,[],[f3040,f2282]) ).
fof(f6583,plain,
( spl61_807
| ~ spl61_357
| ~ spl61_370 ),
inference(avatar_split_clause,[],[f3099,f3032,f2814,f6581]) ).
fof(f6581,plain,
( spl61_807
<=> ! [X16] :
( ~ boundary_set(sK32(X16),X16)
| ~ closed_subset(sK32(X16),X16)
| nowhere_dense(sK32(X16),X16)
| ~ top_str(X16)
| ~ topological_space(X16)
| ~ rel_str(X16)
| ~ transitive_relstr(X16)
| ~ reflexive_relstr(X16)
| empty_carrier(X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_807])]) ).
fof(f3099,plain,
( ! [X16] :
( ~ boundary_set(sK32(X16),X16)
| ~ closed_subset(sK32(X16),X16)
| nowhere_dense(sK32(X16),X16)
| ~ top_str(X16)
| ~ topological_space(X16)
| ~ rel_str(X16)
| ~ transitive_relstr(X16)
| ~ reflexive_relstr(X16)
| empty_carrier(X16) )
| ~ spl61_357
| ~ spl61_370 ),
inference(resolution,[],[f3033,f2815]) ).
fof(f6579,plain,
( spl61_806
| ~ spl61_356
| ~ spl61_370 ),
inference(avatar_split_clause,[],[f3098,f3032,f2810,f6577]) ).
fof(f6577,plain,
( spl61_806
<=> ! [X15] :
( ~ boundary_set(sK31(X15),X15)
| ~ closed_subset(sK31(X15),X15)
| nowhere_dense(sK31(X15),X15)
| ~ top_str(X15)
| ~ topological_space(X15)
| ~ rel_str(X15)
| ~ transitive_relstr(X15)
| ~ reflexive_relstr(X15)
| empty_carrier(X15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_806])]) ).
fof(f3098,plain,
( ! [X15] :
( ~ boundary_set(sK31(X15),X15)
| ~ closed_subset(sK31(X15),X15)
| nowhere_dense(sK31(X15),X15)
| ~ top_str(X15)
| ~ topological_space(X15)
| ~ rel_str(X15)
| ~ transitive_relstr(X15)
| ~ reflexive_relstr(X15)
| empty_carrier(X15) )
| ~ spl61_356
| ~ spl61_370 ),
inference(resolution,[],[f3033,f2811]) ).
fof(f6575,plain,
( spl61_805
| ~ spl61_357
| ~ spl61_369 ),
inference(avatar_split_clause,[],[f3064,f3028,f2814,f6573]) ).
fof(f6573,plain,
( spl61_805
<=> ! [X16] :
( ~ nowhere_dense(sK32(X16),X16)
| ~ open_subset(sK32(X16),X16)
| sP8(X16,sK32(X16))
| ~ top_str(X16)
| ~ topological_space(X16)
| ~ rel_str(X16)
| ~ transitive_relstr(X16)
| ~ reflexive_relstr(X16)
| empty_carrier(X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_805])]) ).
fof(f3064,plain,
( ! [X16] :
( ~ nowhere_dense(sK32(X16),X16)
| ~ open_subset(sK32(X16),X16)
| sP8(X16,sK32(X16))
| ~ top_str(X16)
| ~ topological_space(X16)
| ~ rel_str(X16)
| ~ transitive_relstr(X16)
| ~ reflexive_relstr(X16)
| empty_carrier(X16) )
| ~ spl61_357
| ~ spl61_369 ),
inference(resolution,[],[f3029,f2815]) ).
fof(f6571,plain,
( spl61_804
| ~ spl61_356
| ~ spl61_369 ),
inference(avatar_split_clause,[],[f3063,f3028,f2810,f6569]) ).
fof(f6569,plain,
( spl61_804
<=> ! [X15] :
( ~ nowhere_dense(sK31(X15),X15)
| ~ open_subset(sK31(X15),X15)
| sP8(X15,sK31(X15))
| ~ top_str(X15)
| ~ topological_space(X15)
| ~ rel_str(X15)
| ~ transitive_relstr(X15)
| ~ reflexive_relstr(X15)
| empty_carrier(X15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_804])]) ).
fof(f3063,plain,
( ! [X15] :
( ~ nowhere_dense(sK31(X15),X15)
| ~ open_subset(sK31(X15),X15)
| sP8(X15,sK31(X15))
| ~ top_str(X15)
| ~ topological_space(X15)
| ~ rel_str(X15)
| ~ transitive_relstr(X15)
| ~ reflexive_relstr(X15)
| empty_carrier(X15) )
| ~ spl61_356
| ~ spl61_369 ),
inference(resolution,[],[f3029,f2811]) ).
fof(f6567,plain,
( spl61_803
| ~ spl61_118
| ~ spl61_368 ),
inference(avatar_split_clause,[],[f3042,f3024,f1464,f6565]) ).
fof(f6565,plain,
( spl61_803
<=> ! [X0] :
( ~ up_complete_relstr(boole_POSet(X0))
| ~ lower_bounded_relstr(boole_POSet(X0))
| sP5(boole_POSet(X0))
| ~ antisymmetric_relstr(boole_POSet(X0))
| ~ transitive_relstr(boole_POSet(X0))
| ~ reflexive_relstr(boole_POSet(X0))
| empty_carrier(boole_POSet(X0))
| ~ rel_str(boole_POSet(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_803])]) ).
fof(f1464,plain,
( spl61_118
<=> ! [X0] : with_suprema_relstr(boole_POSet(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_118])]) ).
fof(f3024,plain,
( spl61_368
<=> ! [X0] :
( sP5(X0)
| ~ up_complete_relstr(X0)
| ~ lower_bounded_relstr(X0)
| ~ with_suprema_relstr(X0)
| ~ antisymmetric_relstr(X0)
| ~ transitive_relstr(X0)
| ~ reflexive_relstr(X0)
| empty_carrier(X0)
| ~ rel_str(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_368])]) ).
fof(f3042,plain,
( ! [X0] :
( ~ up_complete_relstr(boole_POSet(X0))
| ~ lower_bounded_relstr(boole_POSet(X0))
| sP5(boole_POSet(X0))
| ~ antisymmetric_relstr(boole_POSet(X0))
| ~ transitive_relstr(boole_POSet(X0))
| ~ reflexive_relstr(boole_POSet(X0))
| empty_carrier(boole_POSet(X0))
| ~ rel_str(boole_POSet(X0)) )
| ~ spl61_118
| ~ spl61_368 ),
inference(resolution,[],[f3025,f1465]) ).
fof(f1465,plain,
( ! [X0] : with_suprema_relstr(boole_POSet(X0))
| ~ spl61_118 ),
inference(avatar_component_clause,[],[f1464]) ).
fof(f3025,plain,
( ! [X0] :
( ~ with_suprema_relstr(X0)
| ~ up_complete_relstr(X0)
| ~ lower_bounded_relstr(X0)
| sP5(X0)
| ~ antisymmetric_relstr(X0)
| ~ transitive_relstr(X0)
| ~ reflexive_relstr(X0)
| empty_carrier(X0)
| ~ rel_str(X0) )
| ~ spl61_368 ),
inference(avatar_component_clause,[],[f3024]) ).
fof(f6512,plain,
( spl61_802
| ~ spl61_382 ),
inference(avatar_split_clause,[],[f3220,f3213,f6510]) ).
fof(f3213,plain,
( spl61_382
<=> ! [X0,X3,X2,X1] :
( in(X0,a_2_1_yellow19(X1,X2))
| ~ is_eventually_in(X1,X2,X3)
| X0 != X3
| ~ element(X3,powerset(the_carrier(X1)))
| ~ net_str(X2,X1)
| empty_carrier(X2)
| ~ one_sorted_str(X1)
| empty_carrier(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_382])]) ).
fof(f3220,plain,
( ! [X2,X0,X1] :
( ~ is_eventually_in(X0,X1,X2)
| in(X2,a_2_1_yellow19(X0,X1))
| ~ element(X2,powerset(the_carrier(X0)))
| ~ net_str(X1,X0)
| empty_carrier(X1)
| ~ one_sorted_str(X0)
| empty_carrier(X0) )
| ~ spl61_382 ),
inference(equality_resolution,[],[f3214]) ).
fof(f3214,plain,
( ! [X2,X3,X0,X1] :
( X0 != X3
| ~ is_eventually_in(X1,X2,X3)
| in(X0,a_2_1_yellow19(X1,X2))
| ~ element(X3,powerset(the_carrier(X1)))
| ~ net_str(X2,X1)
| empty_carrier(X2)
| ~ one_sorted_str(X1)
| empty_carrier(X1) )
| ~ spl61_382 ),
inference(avatar_component_clause,[],[f3213]) ).
fof(f6508,plain,
( spl61_801
| ~ spl61_315
| ~ spl61_377 ),
inference(avatar_split_clause,[],[f3177,f3158,f2457,f6506]) ).
fof(f6506,plain,
( spl61_801
<=> ! [X18,X17,X19] :
( ~ net_str(X17,X18)
| ~ directed_relstr(X17)
| ~ transitive_relstr(X17)
| empty_carrier(X17)
| ~ top_str(X18)
| ~ topological_space(X18)
| empty_carrier(X18)
| ~ empty(the_carrier(X18))
| ~ in(X19,lim_points_of_net(X18,X17)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_801])]) ).
fof(f3177,plain,
( ! [X18,X19,X17] :
( ~ net_str(X17,X18)
| ~ directed_relstr(X17)
| ~ transitive_relstr(X17)
| empty_carrier(X17)
| ~ top_str(X18)
| ~ topological_space(X18)
| empty_carrier(X18)
| ~ empty(the_carrier(X18))
| ~ in(X19,lim_points_of_net(X18,X17)) )
| ~ spl61_315
| ~ spl61_377 ),
inference(resolution,[],[f3159,f2458]) ).
fof(f6504,plain,
( spl61_800
| ~ spl61_208
| ~ spl61_372 ),
inference(avatar_split_clause,[],[f3134,f3131,f1879,f6502]) ).
fof(f6502,plain,
( spl61_800
<=> ! [X0] :
( sK20(X0) = net_str_of(X0,the_carrier(sK20(X0)),the_InternalRel(sK20(X0)),the_mapping(X0,sK20(X0)))
| ~ net_str(sK20(X0),X0)
| ~ one_sorted_str(X0)
| ~ sP2(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_800])]) ).
fof(f1879,plain,
( spl61_208
<=> ! [X0] :
( strict_net_str(sK20(X0),X0)
| ~ sP2(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_208])]) ).
fof(f3134,plain,
( ! [X0] :
( sK20(X0) = net_str_of(X0,the_carrier(sK20(X0)),the_InternalRel(sK20(X0)),the_mapping(X0,sK20(X0)))
| ~ net_str(sK20(X0),X0)
| ~ one_sorted_str(X0)
| ~ sP2(X0) )
| ~ spl61_208
| ~ spl61_372 ),
inference(resolution,[],[f3132,f1880]) ).
fof(f1880,plain,
( ! [X0] :
( strict_net_str(sK20(X0),X0)
| ~ sP2(X0) )
| ~ spl61_208 ),
inference(avatar_component_clause,[],[f1879]) ).
fof(f6498,plain,
( ~ spl61_103
| spl61_387
| ~ spl61_405 ),
inference(avatar_split_clause,[],[f6497,f3477,f3233,f1402]) ).
fof(f1402,plain,
( spl61_103
<=> empty(sK60) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_103])]) ).
fof(f3233,plain,
( spl61_387
<=> empty(the_carrier(boole_POSet(cast_as_carrier_subset(sK12)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_387])]) ).
fof(f3477,plain,
( spl61_405
<=> the_carrier(boole_POSet(cast_as_carrier_subset(sK12))) = sK60 ),
introduced(avatar_definition,[new_symbols(naming,[spl61_405])]) ).
fof(f6497,plain,
( ~ empty(sK60)
| spl61_387
| ~ spl61_405 ),
inference(forward_demodulation,[],[f3235,f3479]) ).
fof(f3479,plain,
( the_carrier(boole_POSet(cast_as_carrier_subset(sK12))) = sK60
| ~ spl61_405 ),
inference(avatar_component_clause,[],[f3477]) ).
fof(f3235,plain,
( ~ empty(the_carrier(boole_POSet(cast_as_carrier_subset(sK12))))
| spl61_387 ),
inference(avatar_component_clause,[],[f3233]) ).
fof(f6492,plain,
( spl61_4
| ~ spl61_386
| ~ spl61_469 ),
inference(avatar_split_clause,[],[f6474,f4058,f3230,f907]) ).
fof(f907,plain,
( spl61_4
<=> empty(sK13) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_4])]) ).
fof(f3230,plain,
( spl61_386
<=> ! [X5] : ~ in(X5,sK13) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_386])]) ).
fof(f6474,plain,
( empty(sK13)
| ~ spl61_386
| ~ spl61_469 ),
inference(resolution,[],[f3231,f4059]) ).
fof(f3231,plain,
( ! [X5] : ~ in(X5,sK13)
| ~ spl61_386 ),
inference(avatar_component_clause,[],[f3230]) ).
fof(f6468,plain,
( spl61_387
| spl61_799
| ~ spl61_293
| ~ spl61_422 ),
inference(avatar_split_clause,[],[f3569,f3566,f2281,f6466,f3233]) ).
fof(f3566,plain,
( spl61_422
<=> ! [X9] :
( element(X9,the_carrier(boole_POSet(cast_as_carrier_subset(sK12))))
| ~ in(X9,sK13) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_422])]) ).
fof(f3569,plain,
( ! [X0] :
( ~ in(X0,sK13)
| empty(the_carrier(boole_POSet(cast_as_carrier_subset(sK12))))
| in(X0,the_carrier(boole_POSet(cast_as_carrier_subset(sK12)))) )
| ~ spl61_293
| ~ spl61_422 ),
inference(resolution,[],[f3567,f2282]) ).
fof(f3567,plain,
( ! [X9] :
( element(X9,the_carrier(boole_POSet(cast_as_carrier_subset(sK12))))
| ~ in(X9,sK13) )
| ~ spl61_422 ),
inference(avatar_component_clause,[],[f3566]) ).
fof(f6464,plain,
( spl61_798
| ~ spl61_266
| ~ spl61_379 ),
inference(avatar_split_clause,[],[f3197,f3166,f2171,f6462]) ).
fof(f6462,plain,
( spl61_798
<=> ! [X29,X30,X31] :
( ~ in(X29,a_2_1_yellow19(X30,X31))
| ~ net_str(X31,X30)
| empty_carrier(X31)
| ~ one_sorted_str(X30)
| empty_carrier(X30)
| finite(sK44(X29,X30,X31))
| ~ finite(the_carrier(X30)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_798])]) ).
fof(f3197,plain,
( ! [X31,X29,X30] :
( ~ in(X29,a_2_1_yellow19(X30,X31))
| ~ net_str(X31,X30)
| empty_carrier(X31)
| ~ one_sorted_str(X30)
| empty_carrier(X30)
| finite(sK44(X29,X30,X31))
| ~ finite(the_carrier(X30)) )
| ~ spl61_266
| ~ spl61_379 ),
inference(resolution,[],[f3167,f2172]) ).
fof(f6460,plain,
( spl61_797
| ~ spl61_266
| ~ spl61_377 ),
inference(avatar_split_clause,[],[f3178,f3158,f2171,f6458]) ).
fof(f6458,plain,
( spl61_797
<=> ! [X20,X21] :
( ~ net_str(X20,X21)
| ~ directed_relstr(X20)
| ~ transitive_relstr(X20)
| empty_carrier(X20)
| ~ top_str(X21)
| ~ topological_space(X21)
| empty_carrier(X21)
| finite(lim_points_of_net(X21,X20))
| ~ finite(the_carrier(X21)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_797])]) ).
fof(f3178,plain,
( ! [X21,X20] :
( ~ net_str(X20,X21)
| ~ directed_relstr(X20)
| ~ transitive_relstr(X20)
| empty_carrier(X20)
| ~ top_str(X21)
| ~ topological_space(X21)
| empty_carrier(X21)
| finite(lim_points_of_net(X21,X20))
| ~ finite(the_carrier(X21)) )
| ~ spl61_266
| ~ spl61_377 ),
inference(resolution,[],[f3159,f2172]) ).
fof(f6456,plain,
( spl61_796
| ~ spl61_159
| ~ spl61_370 ),
inference(avatar_split_clause,[],[f3105,f3032,f1629,f6454]) ).
fof(f6454,plain,
( spl61_796
<=> ! [X22] :
( ~ boundary_set(sK38(powerset(the_carrier(X22))),X22)
| ~ closed_subset(sK38(powerset(the_carrier(X22))),X22)
| nowhere_dense(sK38(powerset(the_carrier(X22))),X22)
| ~ top_str(X22)
| ~ topological_space(X22) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_796])]) ).
fof(f3105,plain,
( ! [X22] :
( ~ boundary_set(sK38(powerset(the_carrier(X22))),X22)
| ~ closed_subset(sK38(powerset(the_carrier(X22))),X22)
| nowhere_dense(sK38(powerset(the_carrier(X22))),X22)
| ~ top_str(X22)
| ~ topological_space(X22) )
| ~ spl61_159
| ~ spl61_370 ),
inference(resolution,[],[f3033,f1630]) ).
fof(f6452,plain,
( spl61_795
| ~ spl61_250
| ~ spl61_370 ),
inference(avatar_split_clause,[],[f3088,f3032,f2076,f6450]) ).
fof(f6450,plain,
( spl61_795
<=> ! [X5] :
( ~ boundary_set(sK17(the_carrier(X5)),X5)
| ~ closed_subset(sK17(the_carrier(X5)),X5)
| nowhere_dense(sK17(the_carrier(X5)),X5)
| ~ top_str(X5)
| ~ topological_space(X5)
| empty(the_carrier(X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_795])]) ).
fof(f3088,plain,
( ! [X5] :
( ~ boundary_set(sK17(the_carrier(X5)),X5)
| ~ closed_subset(sK17(the_carrier(X5)),X5)
| nowhere_dense(sK17(the_carrier(X5)),X5)
| ~ top_str(X5)
| ~ topological_space(X5)
| empty(the_carrier(X5)) )
| ~ spl61_250
| ~ spl61_370 ),
inference(resolution,[],[f3033,f2077]) ).
fof(f6448,plain,
( spl61_794
| ~ spl61_249
| ~ spl61_370 ),
inference(avatar_split_clause,[],[f3087,f3032,f2072,f6446]) ).
fof(f6446,plain,
( spl61_794
<=> ! [X4] :
( ~ boundary_set(sK16(the_carrier(X4)),X4)
| ~ closed_subset(sK16(the_carrier(X4)),X4)
| nowhere_dense(sK16(the_carrier(X4)),X4)
| ~ top_str(X4)
| ~ topological_space(X4)
| empty(the_carrier(X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_794])]) ).
fof(f3087,plain,
( ! [X4] :
( ~ boundary_set(sK16(the_carrier(X4)),X4)
| ~ closed_subset(sK16(the_carrier(X4)),X4)
| nowhere_dense(sK16(the_carrier(X4)),X4)
| ~ top_str(X4)
| ~ topological_space(X4)
| empty(the_carrier(X4)) )
| ~ spl61_249
| ~ spl61_370 ),
inference(resolution,[],[f3033,f2073]) ).
fof(f6444,plain,
( spl61_793
| ~ spl61_248
| ~ spl61_370 ),
inference(avatar_split_clause,[],[f3086,f3032,f2068,f6442]) ).
fof(f6442,plain,
( spl61_793
<=> ! [X3] :
( ~ boundary_set(sK15(the_carrier(X3)),X3)
| ~ closed_subset(sK15(the_carrier(X3)),X3)
| nowhere_dense(sK15(the_carrier(X3)),X3)
| ~ top_str(X3)
| ~ topological_space(X3)
| empty(the_carrier(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_793])]) ).
fof(f3086,plain,
( ! [X3] :
( ~ boundary_set(sK15(the_carrier(X3)),X3)
| ~ closed_subset(sK15(the_carrier(X3)),X3)
| nowhere_dense(sK15(the_carrier(X3)),X3)
| ~ top_str(X3)
| ~ topological_space(X3)
| empty(the_carrier(X3)) )
| ~ spl61_248
| ~ spl61_370 ),
inference(resolution,[],[f3033,f2069]) ).
fof(f6440,plain,
( spl61_792
| ~ spl61_159
| ~ spl61_369 ),
inference(avatar_split_clause,[],[f3070,f3028,f1629,f6438]) ).
fof(f6438,plain,
( spl61_792
<=> ! [X22] :
( ~ nowhere_dense(sK38(powerset(the_carrier(X22))),X22)
| ~ open_subset(sK38(powerset(the_carrier(X22))),X22)
| sP8(X22,sK38(powerset(the_carrier(X22))))
| ~ top_str(X22)
| ~ topological_space(X22) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_792])]) ).
fof(f3070,plain,
( ! [X22] :
( ~ nowhere_dense(sK38(powerset(the_carrier(X22))),X22)
| ~ open_subset(sK38(powerset(the_carrier(X22))),X22)
| sP8(X22,sK38(powerset(the_carrier(X22))))
| ~ top_str(X22)
| ~ topological_space(X22) )
| ~ spl61_159
| ~ spl61_369 ),
inference(resolution,[],[f3029,f1630]) ).
fof(f6436,plain,
( spl61_791
| ~ spl61_250
| ~ spl61_369 ),
inference(avatar_split_clause,[],[f3053,f3028,f2076,f6434]) ).
fof(f6434,plain,
( spl61_791
<=> ! [X5] :
( ~ nowhere_dense(sK17(the_carrier(X5)),X5)
| ~ open_subset(sK17(the_carrier(X5)),X5)
| sP8(X5,sK17(the_carrier(X5)))
| ~ top_str(X5)
| ~ topological_space(X5)
| empty(the_carrier(X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_791])]) ).
fof(f3053,plain,
( ! [X5] :
( ~ nowhere_dense(sK17(the_carrier(X5)),X5)
| ~ open_subset(sK17(the_carrier(X5)),X5)
| sP8(X5,sK17(the_carrier(X5)))
| ~ top_str(X5)
| ~ topological_space(X5)
| empty(the_carrier(X5)) )
| ~ spl61_250
| ~ spl61_369 ),
inference(resolution,[],[f3029,f2077]) ).
fof(f6432,plain,
( spl61_790
| ~ spl61_249
| ~ spl61_369 ),
inference(avatar_split_clause,[],[f3052,f3028,f2072,f6430]) ).
fof(f6430,plain,
( spl61_790
<=> ! [X4] :
( ~ nowhere_dense(sK16(the_carrier(X4)),X4)
| ~ open_subset(sK16(the_carrier(X4)),X4)
| sP8(X4,sK16(the_carrier(X4)))
| ~ top_str(X4)
| ~ topological_space(X4)
| empty(the_carrier(X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_790])]) ).
fof(f3052,plain,
( ! [X4] :
( ~ nowhere_dense(sK16(the_carrier(X4)),X4)
| ~ open_subset(sK16(the_carrier(X4)),X4)
| sP8(X4,sK16(the_carrier(X4)))
| ~ top_str(X4)
| ~ topological_space(X4)
| empty(the_carrier(X4)) )
| ~ spl61_249
| ~ spl61_369 ),
inference(resolution,[],[f3029,f2073]) ).
fof(f6428,plain,
( spl61_789
| ~ spl61_248
| ~ spl61_369 ),
inference(avatar_split_clause,[],[f3051,f3028,f2068,f6426]) ).
fof(f6426,plain,
( spl61_789
<=> ! [X3] :
( ~ nowhere_dense(sK15(the_carrier(X3)),X3)
| ~ open_subset(sK15(the_carrier(X3)),X3)
| sP8(X3,sK15(the_carrier(X3)))
| ~ top_str(X3)
| ~ topological_space(X3)
| empty(the_carrier(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_789])]) ).
fof(f3051,plain,
( ! [X3] :
( ~ nowhere_dense(sK15(the_carrier(X3)),X3)
| ~ open_subset(sK15(the_carrier(X3)),X3)
| sP8(X3,sK15(the_carrier(X3)))
| ~ top_str(X3)
| ~ topological_space(X3)
| empty(the_carrier(X3)) )
| ~ spl61_248
| ~ spl61_369 ),
inference(resolution,[],[f3029,f2069]) ).
fof(f6394,plain,
( spl61_788
| ~ spl61_260
| ~ spl61_379 ),
inference(avatar_split_clause,[],[f3198,f3166,f2117,f6392]) ).
fof(f6392,plain,
( spl61_788
<=> ! [X34,X32,X33] :
( ~ in(X32,a_2_1_yellow19(X33,X34))
| ~ net_str(X34,X33)
| empty_carrier(X34)
| ~ one_sorted_str(X33)
| empty_carrier(X33)
| subset(sK44(X32,X33,X34),the_carrier(X33)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_788])]) ).
fof(f3198,plain,
( ! [X34,X32,X33] :
( ~ in(X32,a_2_1_yellow19(X33,X34))
| ~ net_str(X34,X33)
| empty_carrier(X34)
| ~ one_sorted_str(X33)
| empty_carrier(X33)
| subset(sK44(X32,X33,X34),the_carrier(X33)) )
| ~ spl61_260
| ~ spl61_379 ),
inference(resolution,[],[f3167,f2118]) ).
fof(f6390,plain,
( spl61_787
| ~ spl61_260
| ~ spl61_377 ),
inference(avatar_split_clause,[],[f3179,f3158,f2117,f6388]) ).
fof(f6388,plain,
( spl61_787
<=> ! [X22,X23] :
( ~ net_str(X22,X23)
| ~ directed_relstr(X22)
| ~ transitive_relstr(X22)
| empty_carrier(X22)
| ~ top_str(X23)
| ~ topological_space(X23)
| empty_carrier(X23)
| subset(lim_points_of_net(X23,X22),the_carrier(X23)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_787])]) ).
fof(f3179,plain,
( ! [X22,X23] :
( ~ net_str(X22,X23)
| ~ directed_relstr(X22)
| ~ transitive_relstr(X22)
| empty_carrier(X22)
| ~ top_str(X23)
| ~ topological_space(X23)
| empty_carrier(X23)
| subset(lim_points_of_net(X23,X22),the_carrier(X23)) )
| ~ spl61_260
| ~ spl61_377 ),
inference(resolution,[],[f3159,f2118]) ).
fof(f6386,plain,
( spl61_786
| ~ spl61_211
| ~ spl61_372 ),
inference(avatar_split_clause,[],[f3137,f3131,f1892,f6384]) ).
fof(f6384,plain,
( spl61_786
<=> ! [X1] :
( sK21(X1) = net_str_of(X1,the_carrier(sK21(X1)),the_InternalRel(sK21(X1)),the_mapping(X1,sK21(X1)))
| ~ net_str(sK21(X1),X1)
| ~ one_sorted_str(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_786])]) ).
fof(f1892,plain,
( spl61_211
<=> ! [X0] :
( strict_net_str(sK21(X0),X0)
| ~ one_sorted_str(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_211])]) ).
fof(f3137,plain,
( ! [X1] :
( sK21(X1) = net_str_of(X1,the_carrier(sK21(X1)),the_InternalRel(sK21(X1)),the_mapping(X1,sK21(X1)))
| ~ net_str(sK21(X1),X1)
| ~ one_sorted_str(X1) )
| ~ spl61_211
| ~ spl61_372 ),
inference(duplicate_literal_removal,[],[f3135]) ).
fof(f3135,plain,
( ! [X1] :
( sK21(X1) = net_str_of(X1,the_carrier(sK21(X1)),the_InternalRel(sK21(X1)),the_mapping(X1,sK21(X1)))
| ~ net_str(sK21(X1),X1)
| ~ one_sorted_str(X1)
| ~ one_sorted_str(X1) )
| ~ spl61_211
| ~ spl61_372 ),
inference(resolution,[],[f3132,f1893]) ).
fof(f1893,plain,
( ! [X0] :
( strict_net_str(sK21(X0),X0)
| ~ one_sorted_str(X0) )
| ~ spl61_211 ),
inference(avatar_component_clause,[],[f1892]) ).
fof(f6382,plain,
( spl61_785
| ~ spl61_112
| ~ spl61_365 ),
inference(avatar_split_clause,[],[f3014,f3003,f1440,f6380]) ).
fof(f6380,plain,
( spl61_785
<=> ! [X0] :
( ~ rel_str(boole_POSet(X0))
| sP6(boole_POSet(X0))
| ~ antisymmetric_relstr(boole_POSet(X0))
| ~ transitive_relstr(boole_POSet(X0))
| ~ reflexive_relstr(boole_POSet(X0))
| trivial_carrier(boole_POSet(X0))
| empty_carrier(boole_POSet(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_785])]) ).
fof(f1440,plain,
( spl61_112
<=> ! [X0] : upper_bounded_relstr(boole_POSet(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_112])]) ).
fof(f3003,plain,
( spl61_365
<=> ! [X0] :
( sP6(X0)
| ~ rel_str(X0)
| ~ upper_bounded_relstr(X0)
| ~ antisymmetric_relstr(X0)
| ~ transitive_relstr(X0)
| ~ reflexive_relstr(X0)
| trivial_carrier(X0)
| empty_carrier(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_365])]) ).
fof(f3014,plain,
( ! [X0] :
( ~ rel_str(boole_POSet(X0))
| sP6(boole_POSet(X0))
| ~ antisymmetric_relstr(boole_POSet(X0))
| ~ transitive_relstr(boole_POSet(X0))
| ~ reflexive_relstr(boole_POSet(X0))
| trivial_carrier(boole_POSet(X0))
| empty_carrier(boole_POSet(X0)) )
| ~ spl61_112
| ~ spl61_365 ),
inference(resolution,[],[f3004,f1441]) ).
fof(f1441,plain,
( ! [X0] : upper_bounded_relstr(boole_POSet(X0))
| ~ spl61_112 ),
inference(avatar_component_clause,[],[f1440]) ).
fof(f3004,plain,
( ! [X0] :
( ~ upper_bounded_relstr(X0)
| ~ rel_str(X0)
| sP6(X0)
| ~ antisymmetric_relstr(X0)
| ~ transitive_relstr(X0)
| ~ reflexive_relstr(X0)
| trivial_carrier(X0)
| empty_carrier(X0) )
| ~ spl61_365 ),
inference(avatar_component_clause,[],[f3003]) ).
fof(f6370,plain,
( spl61_784
| ~ spl61_135
| ~ spl61_408 ),
inference(avatar_split_clause,[],[f3519,f3496,f1533,f6368]) ).
fof(f6368,plain,
( spl61_784
<=> ! [X0] : sP2(boole_POSet(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_784])]) ).
fof(f3519,plain,
( ! [X0] : sP2(boole_POSet(X0))
| ~ spl61_135
| ~ spl61_408 ),
inference(resolution,[],[f3497,f1534]) ).
fof(f6366,plain,
( spl61_783
| ~ spl61_335
| ~ spl61_371 ),
inference(avatar_split_clause,[],[f3125,f3039,f2573,f6364]) ).
fof(f6364,plain,
( spl61_783
<=> ! [X16,X14,X15] :
( ~ net_str(X14,X15)
| empty_carrier(X14)
| ~ one_sorted_str(X15)
| empty_carrier(X15)
| element(X16,the_carrier(boole_POSet(cast_as_carrier_subset(X15))))
| ~ in(X16,filter_of_net_str(X15,X14)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_783])]) ).
fof(f3125,plain,
( ! [X16,X14,X15] :
( ~ net_str(X14,X15)
| empty_carrier(X14)
| ~ one_sorted_str(X15)
| empty_carrier(X15)
| element(X16,the_carrier(boole_POSet(cast_as_carrier_subset(X15))))
| ~ in(X16,filter_of_net_str(X15,X14)) )
| ~ spl61_335
| ~ spl61_371 ),
inference(resolution,[],[f3040,f2574]) ).
fof(f6362,plain,
( spl61_782
| ~ spl61_329
| ~ spl61_370 ),
inference(avatar_split_clause,[],[f3096,f3032,f2541,f6360]) ).
fof(f6360,plain,
( spl61_782
<=> ! [X13] :
( ~ boundary_set(sK29(X13),X13)
| ~ closed_subset(sK29(X13),X13)
| nowhere_dense(sK29(X13),X13)
| ~ top_str(X13)
| ~ topological_space(X13)
| ~ rel_str(X13)
| empty_carrier(X13) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_782])]) ).
fof(f3096,plain,
( ! [X13] :
( ~ boundary_set(sK29(X13),X13)
| ~ closed_subset(sK29(X13),X13)
| nowhere_dense(sK29(X13),X13)
| ~ top_str(X13)
| ~ topological_space(X13)
| ~ rel_str(X13)
| empty_carrier(X13) )
| ~ spl61_329
| ~ spl61_370 ),
inference(resolution,[],[f3033,f2542]) ).
fof(f6358,plain,
( spl61_781
| ~ spl61_326
| ~ spl61_370 ),
inference(avatar_split_clause,[],[f3095,f3032,f2529,f6356]) ).
fof(f6356,plain,
( spl61_781
<=> ! [X12] :
( ~ boundary_set(sK28(X12),X12)
| ~ closed_subset(sK28(X12),X12)
| nowhere_dense(sK28(X12),X12)
| ~ top_str(X12)
| ~ topological_space(X12)
| ~ one_sorted_str(X12)
| empty_carrier(X12) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_781])]) ).
fof(f3095,plain,
( ! [X12] :
( ~ boundary_set(sK28(X12),X12)
| ~ closed_subset(sK28(X12),X12)
| nowhere_dense(sK28(X12),X12)
| ~ top_str(X12)
| ~ topological_space(X12)
| ~ one_sorted_str(X12)
| empty_carrier(X12) )
| ~ spl61_326
| ~ spl61_370 ),
inference(resolution,[],[f3033,f2530]) ).
fof(f6354,plain,
( spl61_780
| ~ spl61_329
| ~ spl61_369 ),
inference(avatar_split_clause,[],[f3061,f3028,f2541,f6352]) ).
fof(f6352,plain,
( spl61_780
<=> ! [X13] :
( ~ nowhere_dense(sK29(X13),X13)
| ~ open_subset(sK29(X13),X13)
| sP8(X13,sK29(X13))
| ~ top_str(X13)
| ~ topological_space(X13)
| ~ rel_str(X13)
| empty_carrier(X13) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_780])]) ).
fof(f3061,plain,
( ! [X13] :
( ~ nowhere_dense(sK29(X13),X13)
| ~ open_subset(sK29(X13),X13)
| sP8(X13,sK29(X13))
| ~ top_str(X13)
| ~ topological_space(X13)
| ~ rel_str(X13)
| empty_carrier(X13) )
| ~ spl61_329
| ~ spl61_369 ),
inference(resolution,[],[f3029,f2542]) ).
fof(f6350,plain,
( spl61_779
| ~ spl61_326
| ~ spl61_369 ),
inference(avatar_split_clause,[],[f3060,f3028,f2529,f6348]) ).
fof(f6348,plain,
( spl61_779
<=> ! [X12] :
( ~ nowhere_dense(sK28(X12),X12)
| ~ open_subset(sK28(X12),X12)
| sP8(X12,sK28(X12))
| ~ top_str(X12)
| ~ topological_space(X12)
| ~ one_sorted_str(X12)
| empty_carrier(X12) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_779])]) ).
fof(f3060,plain,
( ! [X12] :
( ~ nowhere_dense(sK28(X12),X12)
| ~ open_subset(sK28(X12),X12)
| sP8(X12,sK28(X12))
| ~ top_str(X12)
| ~ topological_space(X12)
| ~ one_sorted_str(X12)
| empty_carrier(X12) )
| ~ spl61_326
| ~ spl61_369 ),
inference(resolution,[],[f3029,f2530]) ).
fof(f6346,plain,
( spl61_778
| ~ spl61_357
| ~ spl61_364 ),
inference(avatar_split_clause,[],[f2985,f2966,f2814,f6344]) ).
fof(f6344,plain,
( spl61_778
<=> ! [X16] :
( ~ nowhere_dense(sK32(X16),X16)
| boundary_set(sK32(X16),X16)
| ~ top_str(X16)
| ~ topological_space(X16)
| ~ rel_str(X16)
| ~ transitive_relstr(X16)
| ~ reflexive_relstr(X16)
| empty_carrier(X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_778])]) ).
fof(f2985,plain,
( ! [X16] :
( ~ nowhere_dense(sK32(X16),X16)
| boundary_set(sK32(X16),X16)
| ~ top_str(X16)
| ~ topological_space(X16)
| ~ rel_str(X16)
| ~ transitive_relstr(X16)
| ~ reflexive_relstr(X16)
| empty_carrier(X16) )
| ~ spl61_357
| ~ spl61_364 ),
inference(resolution,[],[f2967,f2815]) ).
fof(f6342,plain,
( spl61_777
| ~ spl61_356
| ~ spl61_364 ),
inference(avatar_split_clause,[],[f2984,f2966,f2810,f6340]) ).
fof(f6340,plain,
( spl61_777
<=> ! [X15] :
( ~ nowhere_dense(sK31(X15),X15)
| boundary_set(sK31(X15),X15)
| ~ top_str(X15)
| ~ topological_space(X15)
| ~ rel_str(X15)
| ~ transitive_relstr(X15)
| ~ reflexive_relstr(X15)
| empty_carrier(X15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_777])]) ).
fof(f2984,plain,
( ! [X15] :
( ~ nowhere_dense(sK31(X15),X15)
| boundary_set(sK31(X15),X15)
| ~ top_str(X15)
| ~ topological_space(X15)
| ~ rel_str(X15)
| ~ transitive_relstr(X15)
| ~ reflexive_relstr(X15)
| empty_carrier(X15) )
| ~ spl61_356
| ~ spl61_364 ),
inference(resolution,[],[f2967,f2811]) ).
fof(f6337,plain,
( spl61_776
| ~ spl61_315
| ~ spl61_371 ),
inference(avatar_split_clause,[],[f3126,f3039,f2457,f6335]) ).
fof(f6335,plain,
( spl61_776
<=> ! [X18,X17,X19] :
( ~ net_str(X17,X18)
| empty_carrier(X17)
| ~ one_sorted_str(X18)
| empty_carrier(X18)
| ~ empty(the_carrier(boole_POSet(cast_as_carrier_subset(X18))))
| ~ in(X19,filter_of_net_str(X18,X17)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_776])]) ).
fof(f3126,plain,
( ! [X18,X19,X17] :
( ~ net_str(X17,X18)
| empty_carrier(X17)
| ~ one_sorted_str(X18)
| empty_carrier(X18)
| ~ empty(the_carrier(boole_POSet(cast_as_carrier_subset(X18))))
| ~ in(X19,filter_of_net_str(X18,X17)) )
| ~ spl61_315
| ~ spl61_371 ),
inference(resolution,[],[f3040,f2458]) ).
fof(f6333,plain,
( spl61_775
| ~ spl61_281
| ~ spl61_312 ),
inference(avatar_split_clause,[],[f2467,f2445,f2232,f6331]) ).
fof(f6331,plain,
( spl61_775
<=> ! [X2,X0,X1] :
( ~ sP11(X0,X1,X2)
| ~ rel_str(net_of_bool_filter(X2,X1,X0))
| sP7(net_of_bool_filter(X2,X1,X0))
| empty_carrier(net_of_bool_filter(X2,X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_775])]) ).
fof(f2232,plain,
( spl61_281
<=> ! [X0] :
( sP7(X0)
| ~ rel_str(X0)
| ~ reflexive_relstr(X0)
| empty_carrier(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_281])]) ).
fof(f2445,plain,
( spl61_312
<=> ! [X2,X0,X1] :
( reflexive_relstr(net_of_bool_filter(X2,X1,X0))
| ~ sP11(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_312])]) ).
fof(f2467,plain,
( ! [X2,X0,X1] :
( ~ sP11(X0,X1,X2)
| ~ rel_str(net_of_bool_filter(X2,X1,X0))
| sP7(net_of_bool_filter(X2,X1,X0))
| empty_carrier(net_of_bool_filter(X2,X1,X0)) )
| ~ spl61_281
| ~ spl61_312 ),
inference(resolution,[],[f2446,f2233]) ).
fof(f2233,plain,
( ! [X0] :
( ~ reflexive_relstr(X0)
| ~ rel_str(X0)
| sP7(X0)
| empty_carrier(X0) )
| ~ spl61_281 ),
inference(avatar_component_clause,[],[f2232]) ).
fof(f2446,plain,
( ! [X2,X0,X1] :
( reflexive_relstr(net_of_bool_filter(X2,X1,X0))
| ~ sP11(X0,X1,X2) )
| ~ spl61_312 ),
inference(avatar_component_clause,[],[f2445]) ).
fof(f6329,plain,
( spl61_774
| ~ spl61_161
| spl61_1
| ~ spl61_265
| ~ spl61_531 ),
inference(avatar_split_clause,[],[f4441,f4436,f2167,f892,f1659,f6326]) ).
fof(f4441,plain,
( empty_carrier(sK12)
| ~ one_sorted_str(sK12)
| transitive_relstr(net_of_bool_filter(sK12,cast_as_carrier_subset(sK12),sK13))
| ~ spl61_265
| ~ spl61_531 ),
inference(duplicate_literal_removal,[],[f4439]) ).
fof(f4439,plain,
( empty_carrier(sK12)
| ~ one_sorted_str(sK12)
| transitive_relstr(net_of_bool_filter(sK12,cast_as_carrier_subset(sK12),sK13))
| ~ one_sorted_str(sK12)
| ~ spl61_265
| ~ spl61_531 ),
inference(resolution,[],[f4437,f2168]) ).
fof(f6296,plain,
( spl61_773
| ~ spl61_161
| spl61_1
| ~ spl61_265
| ~ spl61_530 ),
inference(avatar_split_clause,[],[f4434,f4429,f2167,f892,f1659,f6293]) ).
fof(f6293,plain,
( spl61_773
<=> reflexive_relstr(net_of_bool_filter(sK12,cast_as_carrier_subset(sK12),sK13)) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_773])]) ).
fof(f4434,plain,
( empty_carrier(sK12)
| ~ one_sorted_str(sK12)
| reflexive_relstr(net_of_bool_filter(sK12,cast_as_carrier_subset(sK12),sK13))
| ~ spl61_265
| ~ spl61_530 ),
inference(duplicate_literal_removal,[],[f4432]) ).
fof(f4432,plain,
( empty_carrier(sK12)
| ~ one_sorted_str(sK12)
| reflexive_relstr(net_of_bool_filter(sK12,cast_as_carrier_subset(sK12),sK13))
| ~ one_sorted_str(sK12)
| ~ spl61_265
| ~ spl61_530 ),
inference(resolution,[],[f4430,f2168]) ).
fof(f6287,plain,
( spl61_772
| ~ spl61_266
| ~ spl61_371 ),
inference(avatar_split_clause,[],[f3127,f3039,f2171,f6285]) ).
fof(f6285,plain,
( spl61_772
<=> ! [X20,X21] :
( ~ net_str(X20,X21)
| empty_carrier(X20)
| ~ one_sorted_str(X21)
| empty_carrier(X21)
| finite(filter_of_net_str(X21,X20))
| ~ finite(the_carrier(boole_POSet(cast_as_carrier_subset(X21)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_772])]) ).
fof(f3127,plain,
( ! [X21,X20] :
( ~ net_str(X20,X21)
| empty_carrier(X20)
| ~ one_sorted_str(X21)
| empty_carrier(X21)
| finite(filter_of_net_str(X21,X20))
| ~ finite(the_carrier(boole_POSet(cast_as_carrier_subset(X21)))) )
| ~ spl61_266
| ~ spl61_371 ),
inference(resolution,[],[f3040,f2172]) ).
fof(f6283,plain,
( spl61_771
| ~ spl61_341
| ~ spl61_370 ),
inference(avatar_split_clause,[],[f3111,f3032,f2685,f6281]) ).
fof(f6281,plain,
( spl61_771
<=> ! [X10] :
( ~ boundary_set(sK26(X10),X10)
| ~ closed_subset(sK26(X10),X10)
| nowhere_dense(sK26(X10),X10)
| ~ top_str(X10)
| ~ topological_space(X10)
| empty_carrier(X10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_771])]) ).
fof(f3111,plain,
( ! [X10] :
( ~ boundary_set(sK26(X10),X10)
| ~ closed_subset(sK26(X10),X10)
| nowhere_dense(sK26(X10),X10)
| ~ top_str(X10)
| ~ topological_space(X10)
| empty_carrier(X10) )
| ~ spl61_341
| ~ spl61_370 ),
inference(duplicate_literal_removal,[],[f3093]) ).
fof(f3093,plain,
( ! [X10] :
( ~ boundary_set(sK26(X10),X10)
| ~ closed_subset(sK26(X10),X10)
| nowhere_dense(sK26(X10),X10)
| ~ top_str(X10)
| ~ topological_space(X10)
| ~ top_str(X10)
| ~ topological_space(X10)
| empty_carrier(X10) )
| ~ spl61_341
| ~ spl61_370 ),
inference(resolution,[],[f3033,f2686]) ).
fof(f6279,plain,
( spl61_770
| ~ spl61_342
| ~ spl61_370 ),
inference(avatar_split_clause,[],[f3110,f3032,f2689,f6277]) ).
fof(f6277,plain,
( spl61_770
<=> ! [X11] :
( ~ boundary_set(sK27(X11),X11)
| ~ closed_subset(sK27(X11),X11)
| nowhere_dense(sK27(X11),X11)
| ~ top_str(X11)
| ~ topological_space(X11)
| empty_carrier(X11) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_770])]) ).
fof(f3110,plain,
( ! [X11] :
( ~ boundary_set(sK27(X11),X11)
| ~ closed_subset(sK27(X11),X11)
| nowhere_dense(sK27(X11),X11)
| ~ top_str(X11)
| ~ topological_space(X11)
| empty_carrier(X11) )
| ~ spl61_342
| ~ spl61_370 ),
inference(duplicate_literal_removal,[],[f3094]) ).
fof(f3094,plain,
( ! [X11] :
( ~ boundary_set(sK27(X11),X11)
| ~ closed_subset(sK27(X11),X11)
| nowhere_dense(sK27(X11),X11)
| ~ top_str(X11)
| ~ topological_space(X11)
| ~ top_str(X11)
| ~ topological_space(X11)
| empty_carrier(X11) )
| ~ spl61_342
| ~ spl61_370 ),
inference(resolution,[],[f3033,f2690]) ).
fof(f6275,plain,
( spl61_769
| ~ spl61_292
| ~ spl61_370 ),
inference(avatar_split_clause,[],[f3104,f3032,f2277,f6273]) ).
fof(f6273,plain,
( spl61_769
<=> ! [X21] :
( ~ boundary_set(sK37(X21),X21)
| ~ closed_subset(sK37(X21),X21)
| nowhere_dense(sK37(X21),X21)
| ~ top_str(X21)
| ~ topological_space(X21)
| ~ sP10(X21) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_769])]) ).
fof(f3104,plain,
( ! [X21] :
( ~ boundary_set(sK37(X21),X21)
| ~ closed_subset(sK37(X21),X21)
| nowhere_dense(sK37(X21),X21)
| ~ top_str(X21)
| ~ topological_space(X21)
| ~ sP10(X21) )
| ~ spl61_292
| ~ spl61_370 ),
inference(resolution,[],[f3033,f2278]) ).
fof(f6271,plain,
( spl61_768
| ~ spl61_280
| ~ spl61_370 ),
inference(avatar_split_clause,[],[f3097,f3032,f2228,f6269]) ).
fof(f6269,plain,
( spl61_768
<=> ! [X14] :
( ~ boundary_set(sK30(X14),X14)
| ~ closed_subset(sK30(X14),X14)
| nowhere_dense(sK30(X14),X14)
| ~ top_str(X14)
| ~ topological_space(X14)
| ~ sP7(X14) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_768])]) ).
fof(f3097,plain,
( ! [X14] :
( ~ boundary_set(sK30(X14),X14)
| ~ closed_subset(sK30(X14),X14)
| nowhere_dense(sK30(X14),X14)
| ~ top_str(X14)
| ~ topological_space(X14)
| ~ sP7(X14) )
| ~ spl61_280
| ~ spl61_370 ),
inference(resolution,[],[f3033,f2229]) ).
fof(f6267,plain,
( spl61_767
| ~ spl61_274
| ~ spl61_370 ),
inference(avatar_split_clause,[],[f3092,f3032,f2204,f6265]) ).
fof(f6265,plain,
( spl61_767
<=> ! [X9] :
( ~ boundary_set(sK25(X9),X9)
| ~ closed_subset(sK25(X9),X9)
| nowhere_dense(sK25(X9),X9)
| ~ top_str(X9)
| ~ topological_space(X9)
| ~ sP6(X9) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_767])]) ).
fof(f3092,plain,
( ! [X9] :
( ~ boundary_set(sK25(X9),X9)
| ~ closed_subset(sK25(X9),X9)
| nowhere_dense(sK25(X9),X9)
| ~ top_str(X9)
| ~ topological_space(X9)
| ~ sP6(X9) )
| ~ spl61_274
| ~ spl61_370 ),
inference(resolution,[],[f3033,f2205]) ).
fof(f6263,plain,
( spl61_766
| ~ spl61_273
| ~ spl61_370 ),
inference(avatar_split_clause,[],[f3091,f3032,f2200,f6261]) ).
fof(f6261,plain,
( spl61_766
<=> ! [X8] :
( ~ boundary_set(sK24(X8),X8)
| ~ closed_subset(sK24(X8),X8)
| nowhere_dense(sK24(X8),X8)
| ~ top_str(X8)
| ~ topological_space(X8)
| ~ rel_str(X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_766])]) ).
fof(f3091,plain,
( ! [X8] :
( ~ boundary_set(sK24(X8),X8)
| ~ closed_subset(sK24(X8),X8)
| nowhere_dense(sK24(X8),X8)
| ~ top_str(X8)
| ~ topological_space(X8)
| ~ rel_str(X8) )
| ~ spl61_273
| ~ spl61_370 ),
inference(resolution,[],[f3033,f2201]) ).
fof(f6259,plain,
( spl61_765
| ~ spl61_272
| ~ spl61_370 ),
inference(avatar_split_clause,[],[f3090,f3032,f2196,f6257]) ).
fof(f6257,plain,
( spl61_765
<=> ! [X7] :
( ~ boundary_set(sK23(X7),X7)
| ~ closed_subset(sK23(X7),X7)
| nowhere_dense(sK23(X7),X7)
| ~ top_str(X7)
| ~ topological_space(X7)
| ~ rel_str(X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_765])]) ).
fof(f3090,plain,
( ! [X7] :
( ~ boundary_set(sK23(X7),X7)
| ~ closed_subset(sK23(X7),X7)
| nowhere_dense(sK23(X7),X7)
| ~ top_str(X7)
| ~ topological_space(X7)
| ~ rel_str(X7) )
| ~ spl61_272
| ~ spl61_370 ),
inference(resolution,[],[f3033,f2197]) ).
fof(f6255,plain,
( spl61_764
| ~ spl61_264
| ~ spl61_370 ),
inference(avatar_split_clause,[],[f3089,f3032,f2163,f6253]) ).
fof(f6253,plain,
( spl61_764
<=> ! [X6] :
( ~ boundary_set(sK18(X6),X6)
| ~ closed_subset(sK18(X6),X6)
| nowhere_dense(sK18(X6),X6)
| ~ top_str(X6)
| ~ topological_space(X6)
| ~ sP1(X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_764])]) ).
fof(f2163,plain,
( spl61_264
<=> ! [X0] :
( element(sK18(X0),powerset(the_carrier(X0)))
| ~ sP1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_264])]) ).
fof(f3089,plain,
( ! [X6] :
( ~ boundary_set(sK18(X6),X6)
| ~ closed_subset(sK18(X6),X6)
| nowhere_dense(sK18(X6),X6)
| ~ top_str(X6)
| ~ topological_space(X6)
| ~ sP1(X6) )
| ~ spl61_264
| ~ spl61_370 ),
inference(resolution,[],[f3033,f2164]) ).
fof(f2164,plain,
( ! [X0] :
( element(sK18(X0),powerset(the_carrier(X0)))
| ~ sP1(X0) )
| ~ spl61_264 ),
inference(avatar_component_clause,[],[f2163]) ).
fof(f6251,plain,
( spl61_763
| ~ spl61_265
| ~ spl61_370 ),
inference(avatar_split_clause,[],[f3084,f3032,f2167,f6249]) ).
fof(f6249,plain,
( spl61_763
<=> ! [X2] :
( ~ boundary_set(cast_as_carrier_subset(X2),X2)
| ~ closed_subset(cast_as_carrier_subset(X2),X2)
| nowhere_dense(cast_as_carrier_subset(X2),X2)
| ~ top_str(X2)
| ~ topological_space(X2)
| ~ one_sorted_str(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_763])]) ).
fof(f3084,plain,
( ! [X2] :
( ~ boundary_set(cast_as_carrier_subset(X2),X2)
| ~ closed_subset(cast_as_carrier_subset(X2),X2)
| nowhere_dense(cast_as_carrier_subset(X2),X2)
| ~ top_str(X2)
| ~ topological_space(X2)
| ~ one_sorted_str(X2) )
| ~ spl61_265
| ~ spl61_370 ),
inference(resolution,[],[f3033,f2168]) ).
fof(f6247,plain,
( spl61_762
| ~ spl61_341
| ~ spl61_369 ),
inference(avatar_split_clause,[],[f3076,f3028,f2685,f6245]) ).
fof(f6245,plain,
( spl61_762
<=> ! [X10] :
( ~ nowhere_dense(sK26(X10),X10)
| ~ open_subset(sK26(X10),X10)
| sP8(X10,sK26(X10))
| ~ top_str(X10)
| ~ topological_space(X10)
| empty_carrier(X10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_762])]) ).
fof(f3076,plain,
( ! [X10] :
( ~ nowhere_dense(sK26(X10),X10)
| ~ open_subset(sK26(X10),X10)
| sP8(X10,sK26(X10))
| ~ top_str(X10)
| ~ topological_space(X10)
| empty_carrier(X10) )
| ~ spl61_341
| ~ spl61_369 ),
inference(duplicate_literal_removal,[],[f3058]) ).
fof(f3058,plain,
( ! [X10] :
( ~ nowhere_dense(sK26(X10),X10)
| ~ open_subset(sK26(X10),X10)
| sP8(X10,sK26(X10))
| ~ top_str(X10)
| ~ topological_space(X10)
| ~ top_str(X10)
| ~ topological_space(X10)
| empty_carrier(X10) )
| ~ spl61_341
| ~ spl61_369 ),
inference(resolution,[],[f3029,f2686]) ).
fof(f6243,plain,
( spl61_761
| ~ spl61_342
| ~ spl61_369 ),
inference(avatar_split_clause,[],[f3075,f3028,f2689,f6241]) ).
fof(f6241,plain,
( spl61_761
<=> ! [X11] :
( ~ nowhere_dense(sK27(X11),X11)
| ~ open_subset(sK27(X11),X11)
| sP8(X11,sK27(X11))
| ~ top_str(X11)
| ~ topological_space(X11)
| empty_carrier(X11) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_761])]) ).
fof(f3075,plain,
( ! [X11] :
( ~ nowhere_dense(sK27(X11),X11)
| ~ open_subset(sK27(X11),X11)
| sP8(X11,sK27(X11))
| ~ top_str(X11)
| ~ topological_space(X11)
| empty_carrier(X11) )
| ~ spl61_342
| ~ spl61_369 ),
inference(duplicate_literal_removal,[],[f3059]) ).
fof(f3059,plain,
( ! [X11] :
( ~ nowhere_dense(sK27(X11),X11)
| ~ open_subset(sK27(X11),X11)
| sP8(X11,sK27(X11))
| ~ top_str(X11)
| ~ topological_space(X11)
| ~ top_str(X11)
| ~ topological_space(X11)
| empty_carrier(X11) )
| ~ spl61_342
| ~ spl61_369 ),
inference(resolution,[],[f3029,f2690]) ).
fof(f6239,plain,
( spl61_760
| ~ spl61_292
| ~ spl61_369 ),
inference(avatar_split_clause,[],[f3069,f3028,f2277,f6237]) ).
fof(f6237,plain,
( spl61_760
<=> ! [X21] :
( ~ nowhere_dense(sK37(X21),X21)
| ~ open_subset(sK37(X21),X21)
| sP8(X21,sK37(X21))
| ~ top_str(X21)
| ~ topological_space(X21)
| ~ sP10(X21) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_760])]) ).
fof(f3069,plain,
( ! [X21] :
( ~ nowhere_dense(sK37(X21),X21)
| ~ open_subset(sK37(X21),X21)
| sP8(X21,sK37(X21))
| ~ top_str(X21)
| ~ topological_space(X21)
| ~ sP10(X21) )
| ~ spl61_292
| ~ spl61_369 ),
inference(resolution,[],[f3029,f2278]) ).
fof(f6235,plain,
( spl61_759
| ~ spl61_284
| ~ spl61_369 ),
inference(avatar_split_clause,[],[f3065,f3028,f2244,f6233]) ).
fof(f6233,plain,
( spl61_759
<=> ! [X17] :
( ~ nowhere_dense(sK33(X17),X17)
| ~ open_subset(sK33(X17),X17)
| sP8(X17,sK33(X17))
| ~ top_str(X17)
| ~ topological_space(X17)
| ~ sP9(X17) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_759])]) ).
fof(f2244,plain,
( spl61_284
<=> ! [X0] :
( element(sK33(X0),powerset(the_carrier(X0)))
| ~ sP9(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_284])]) ).
fof(f3065,plain,
( ! [X17] :
( ~ nowhere_dense(sK33(X17),X17)
| ~ open_subset(sK33(X17),X17)
| sP8(X17,sK33(X17))
| ~ top_str(X17)
| ~ topological_space(X17)
| ~ sP9(X17) )
| ~ spl61_284
| ~ spl61_369 ),
inference(resolution,[],[f3029,f2245]) ).
fof(f2245,plain,
( ! [X0] :
( element(sK33(X0),powerset(the_carrier(X0)))
| ~ sP9(X0) )
| ~ spl61_284 ),
inference(avatar_component_clause,[],[f2244]) ).
fof(f6231,plain,
( spl61_758
| ~ spl61_280
| ~ spl61_369 ),
inference(avatar_split_clause,[],[f3062,f3028,f2228,f6229]) ).
fof(f6229,plain,
( spl61_758
<=> ! [X14] :
( ~ nowhere_dense(sK30(X14),X14)
| ~ open_subset(sK30(X14),X14)
| sP8(X14,sK30(X14))
| ~ top_str(X14)
| ~ topological_space(X14)
| ~ sP7(X14) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_758])]) ).
fof(f3062,plain,
( ! [X14] :
( ~ nowhere_dense(sK30(X14),X14)
| ~ open_subset(sK30(X14),X14)
| sP8(X14,sK30(X14))
| ~ top_str(X14)
| ~ topological_space(X14)
| ~ sP7(X14) )
| ~ spl61_280
| ~ spl61_369 ),
inference(resolution,[],[f3029,f2229]) ).
fof(f6227,plain,
( spl61_757
| ~ spl61_274
| ~ spl61_369 ),
inference(avatar_split_clause,[],[f3057,f3028,f2204,f6225]) ).
fof(f6225,plain,
( spl61_757
<=> ! [X9] :
( ~ nowhere_dense(sK25(X9),X9)
| ~ open_subset(sK25(X9),X9)
| sP8(X9,sK25(X9))
| ~ top_str(X9)
| ~ topological_space(X9)
| ~ sP6(X9) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_757])]) ).
fof(f3057,plain,
( ! [X9] :
( ~ nowhere_dense(sK25(X9),X9)
| ~ open_subset(sK25(X9),X9)
| sP8(X9,sK25(X9))
| ~ top_str(X9)
| ~ topological_space(X9)
| ~ sP6(X9) )
| ~ spl61_274
| ~ spl61_369 ),
inference(resolution,[],[f3029,f2205]) ).
fof(f6223,plain,
( spl61_756
| ~ spl61_273
| ~ spl61_369 ),
inference(avatar_split_clause,[],[f3056,f3028,f2200,f6221]) ).
fof(f6221,plain,
( spl61_756
<=> ! [X8] :
( ~ nowhere_dense(sK24(X8),X8)
| ~ open_subset(sK24(X8),X8)
| sP8(X8,sK24(X8))
| ~ top_str(X8)
| ~ topological_space(X8)
| ~ rel_str(X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_756])]) ).
fof(f3056,plain,
( ! [X8] :
( ~ nowhere_dense(sK24(X8),X8)
| ~ open_subset(sK24(X8),X8)
| sP8(X8,sK24(X8))
| ~ top_str(X8)
| ~ topological_space(X8)
| ~ rel_str(X8) )
| ~ spl61_273
| ~ spl61_369 ),
inference(resolution,[],[f3029,f2201]) ).
fof(f6219,plain,
( spl61_755
| ~ spl61_272
| ~ spl61_369 ),
inference(avatar_split_clause,[],[f3055,f3028,f2196,f6217]) ).
fof(f6217,plain,
( spl61_755
<=> ! [X7] :
( ~ nowhere_dense(sK23(X7),X7)
| ~ open_subset(sK23(X7),X7)
| sP8(X7,sK23(X7))
| ~ top_str(X7)
| ~ topological_space(X7)
| ~ rel_str(X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_755])]) ).
fof(f3055,plain,
( ! [X7] :
( ~ nowhere_dense(sK23(X7),X7)
| ~ open_subset(sK23(X7),X7)
| sP8(X7,sK23(X7))
| ~ top_str(X7)
| ~ topological_space(X7)
| ~ rel_str(X7) )
| ~ spl61_272
| ~ spl61_369 ),
inference(resolution,[],[f3029,f2197]) ).
fof(f6215,plain,
( ~ spl61_754
| ~ spl61_161
| spl61_1
| ~ spl61_265
| ~ spl61_505 ),
inference(avatar_split_clause,[],[f4427,f4286,f2167,f892,f1659,f6212]) ).
fof(f4427,plain,
( empty_carrier(sK12)
| ~ one_sorted_str(sK12)
| ~ empty_carrier(net_of_bool_filter(sK12,cast_as_carrier_subset(sK12),sK13))
| ~ spl61_265
| ~ spl61_505 ),
inference(duplicate_literal_removal,[],[f4425]) ).
fof(f4425,plain,
( empty_carrier(sK12)
| ~ one_sorted_str(sK12)
| ~ empty_carrier(net_of_bool_filter(sK12,cast_as_carrier_subset(sK12),sK13))
| ~ one_sorted_str(sK12)
| ~ spl61_265
| ~ spl61_505 ),
inference(resolution,[],[f4287,f2168]) ).
fof(f6210,plain,
( spl61_753
| ~ spl61_264
| ~ spl61_369 ),
inference(avatar_split_clause,[],[f3054,f3028,f2163,f6208]) ).
fof(f6208,plain,
( spl61_753
<=> ! [X6] :
( ~ nowhere_dense(sK18(X6),X6)
| ~ open_subset(sK18(X6),X6)
| sP8(X6,sK18(X6))
| ~ top_str(X6)
| ~ topological_space(X6)
| ~ sP1(X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_753])]) ).
fof(f3054,plain,
( ! [X6] :
( ~ nowhere_dense(sK18(X6),X6)
| ~ open_subset(sK18(X6),X6)
| sP8(X6,sK18(X6))
| ~ top_str(X6)
| ~ topological_space(X6)
| ~ sP1(X6) )
| ~ spl61_264
| ~ spl61_369 ),
inference(resolution,[],[f3029,f2164]) ).
fof(f6206,plain,
( spl61_752
| ~ spl61_265
| ~ spl61_369 ),
inference(avatar_split_clause,[],[f3049,f3028,f2167,f6204]) ).
fof(f6204,plain,
( spl61_752
<=> ! [X2] :
( ~ nowhere_dense(cast_as_carrier_subset(X2),X2)
| ~ open_subset(cast_as_carrier_subset(X2),X2)
| sP8(X2,cast_as_carrier_subset(X2))
| ~ top_str(X2)
| ~ topological_space(X2)
| ~ one_sorted_str(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_752])]) ).
fof(f3049,plain,
( ! [X2] :
( ~ nowhere_dense(cast_as_carrier_subset(X2),X2)
| ~ open_subset(cast_as_carrier_subset(X2),X2)
| sP8(X2,cast_as_carrier_subset(X2))
| ~ top_str(X2)
| ~ topological_space(X2)
| ~ one_sorted_str(X2) )
| ~ spl61_265
| ~ spl61_369 ),
inference(resolution,[],[f3029,f2168]) ).
fof(f6202,plain,
( spl61_751
| ~ spl61_207
| ~ spl61_366 ),
inference(avatar_split_clause,[],[f3019,f3007,f1875,f6200]) ).
fof(f6200,plain,
( spl61_751
<=> ! [X1] :
( filter_of_net_str(X1,sK20(X1)) = a_2_1_yellow19(X1,sK20(X1))
| empty_carrier(sK20(X1))
| ~ one_sorted_str(X1)
| empty_carrier(X1)
| ~ sP2(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_751])]) ).
fof(f1875,plain,
( spl61_207
<=> ! [X0] :
( net_str(sK20(X0),X0)
| ~ sP2(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_207])]) ).
fof(f3019,plain,
( ! [X1] :
( filter_of_net_str(X1,sK20(X1)) = a_2_1_yellow19(X1,sK20(X1))
| empty_carrier(sK20(X1))
| ~ one_sorted_str(X1)
| empty_carrier(X1)
| ~ sP2(X1) )
| ~ spl61_207
| ~ spl61_366 ),
inference(resolution,[],[f3008,f1876]) ).
fof(f1876,plain,
( ! [X0] :
( net_str(sK20(X0),X0)
| ~ sP2(X0) )
| ~ spl61_207 ),
inference(avatar_component_clause,[],[f1875]) ).
fof(f6198,plain,
( spl61_750
| ~ spl61_119
| ~ spl61_361 ),
inference(avatar_split_clause,[],[f2957,f2830,f1468,f6196]) ).
fof(f6196,plain,
( spl61_750
<=> ! [X0] :
( ~ rel_str(boole_POSet(X0))
| sP10(boole_POSet(X0))
| ~ with_suprema_relstr(boole_POSet(X0))
| ~ antisymmetric_relstr(boole_POSet(X0))
| ~ transitive_relstr(boole_POSet(X0))
| ~ reflexive_relstr(boole_POSet(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_750])]) ).
fof(f1468,plain,
( spl61_119
<=> ! [X0] : with_infima_relstr(boole_POSet(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_119])]) ).
fof(f2957,plain,
( ! [X0] :
( ~ rel_str(boole_POSet(X0))
| sP10(boole_POSet(X0))
| ~ with_suprema_relstr(boole_POSet(X0))
| ~ antisymmetric_relstr(boole_POSet(X0))
| ~ transitive_relstr(boole_POSet(X0))
| ~ reflexive_relstr(boole_POSet(X0)) )
| ~ spl61_119
| ~ spl61_361 ),
inference(resolution,[],[f2831,f1469]) ).
fof(f1469,plain,
( ! [X0] : with_infima_relstr(boole_POSet(X0))
| ~ spl61_119 ),
inference(avatar_component_clause,[],[f1468]) ).
fof(f6194,plain,
( spl61_749
| ~ spl61_293
| ~ spl61_357 ),
inference(avatar_split_clause,[],[f2857,f2814,f2281,f6192]) ).
fof(f6192,plain,
( spl61_749
<=> ! [X7] :
( ~ rel_str(X7)
| ~ transitive_relstr(X7)
| ~ reflexive_relstr(X7)
| empty_carrier(X7)
| empty(powerset(the_carrier(X7)))
| in(sK32(X7),powerset(the_carrier(X7))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_749])]) ).
fof(f2857,plain,
( ! [X7] :
( ~ rel_str(X7)
| ~ transitive_relstr(X7)
| ~ reflexive_relstr(X7)
| empty_carrier(X7)
| empty(powerset(the_carrier(X7)))
| in(sK32(X7),powerset(the_carrier(X7))) )
| ~ spl61_293
| ~ spl61_357 ),
inference(resolution,[],[f2815,f2282]) ).
fof(f6190,plain,
( spl61_748
| ~ spl61_293
| ~ spl61_356 ),
inference(avatar_split_clause,[],[f2851,f2810,f2281,f6188]) ).
fof(f6188,plain,
( spl61_748
<=> ! [X7] :
( ~ rel_str(X7)
| ~ transitive_relstr(X7)
| ~ reflexive_relstr(X7)
| empty_carrier(X7)
| empty(powerset(the_carrier(X7)))
| in(sK31(X7),powerset(the_carrier(X7))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_748])]) ).
fof(f2851,plain,
( ! [X7] :
( ~ rel_str(X7)
| ~ transitive_relstr(X7)
| ~ reflexive_relstr(X7)
| empty_carrier(X7)
| empty(powerset(the_carrier(X7)))
| in(sK31(X7),powerset(the_carrier(X7))) )
| ~ spl61_293
| ~ spl61_356 ),
inference(resolution,[],[f2811,f2282]) ).
fof(f6186,plain,
( spl61_747
| ~ spl61_112
| ~ spl61_355 ),
inference(avatar_split_clause,[],[f2842,f2806,f1440,f6184]) ).
fof(f6184,plain,
( spl61_747
<=> ! [X0] :
( ~ join_complete_relstr(boole_POSet(X0))
| sP4(boole_POSet(X0))
| ~ antisymmetric_relstr(boole_POSet(X0))
| ~ reflexive_relstr(boole_POSet(X0))
| empty_carrier(boole_POSet(X0))
| ~ rel_str(boole_POSet(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_747])]) ).
fof(f2806,plain,
( spl61_355
<=> ! [X0] :
( sP4(X0)
| ~ join_complete_relstr(X0)
| ~ upper_bounded_relstr(X0)
| ~ antisymmetric_relstr(X0)
| ~ reflexive_relstr(X0)
| empty_carrier(X0)
| ~ rel_str(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_355])]) ).
fof(f2842,plain,
( ! [X0] :
( ~ join_complete_relstr(boole_POSet(X0))
| sP4(boole_POSet(X0))
| ~ antisymmetric_relstr(boole_POSet(X0))
| ~ reflexive_relstr(boole_POSet(X0))
| empty_carrier(boole_POSet(X0))
| ~ rel_str(boole_POSet(X0)) )
| ~ spl61_112
| ~ spl61_355 ),
inference(resolution,[],[f2807,f1441]) ).
fof(f2807,plain,
( ! [X0] :
( ~ upper_bounded_relstr(X0)
| ~ join_complete_relstr(X0)
| sP4(X0)
| ~ antisymmetric_relstr(X0)
| ~ reflexive_relstr(X0)
| empty_carrier(X0)
| ~ rel_str(X0) )
| ~ spl61_355 ),
inference(avatar_component_clause,[],[f2806]) ).
fof(f6113,plain,
( spl61_746
| ~ spl61_260
| ~ spl61_371 ),
inference(avatar_split_clause,[],[f3128,f3039,f2117,f6111]) ).
fof(f6111,plain,
( spl61_746
<=> ! [X22,X23] :
( ~ net_str(X22,X23)
| empty_carrier(X22)
| ~ one_sorted_str(X23)
| empty_carrier(X23)
| subset(filter_of_net_str(X23,X22),the_carrier(boole_POSet(cast_as_carrier_subset(X23)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_746])]) ).
fof(f3128,plain,
( ! [X22,X23] :
( ~ net_str(X22,X23)
| empty_carrier(X22)
| ~ one_sorted_str(X23)
| empty_carrier(X23)
| subset(filter_of_net_str(X23,X22),the_carrier(boole_POSet(cast_as_carrier_subset(X23)))) )
| ~ spl61_260
| ~ spl61_371 ),
inference(resolution,[],[f3040,f2118]) ).
fof(f6109,plain,
( spl61_745
| ~ spl61_261
| ~ spl61_370 ),
inference(avatar_split_clause,[],[f3083,f3032,f2121,f6107]) ).
fof(f6107,plain,
( spl61_745
<=> ! [X0,X1] :
( ~ boundary_set(X0,X1)
| ~ closed_subset(X0,X1)
| nowhere_dense(X0,X1)
| ~ top_str(X1)
| ~ topological_space(X1)
| ~ subset(X0,the_carrier(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_745])]) ).
fof(f3083,plain,
( ! [X0,X1] :
( ~ boundary_set(X0,X1)
| ~ closed_subset(X0,X1)
| nowhere_dense(X0,X1)
| ~ top_str(X1)
| ~ topological_space(X1)
| ~ subset(X0,the_carrier(X1)) )
| ~ spl61_261
| ~ spl61_370 ),
inference(resolution,[],[f3033,f2122]) ).
fof(f6105,plain,
( spl61_744
| ~ spl61_261
| ~ spl61_369 ),
inference(avatar_split_clause,[],[f3048,f3028,f2121,f6103]) ).
fof(f6103,plain,
( spl61_744
<=> ! [X0,X1] :
( ~ nowhere_dense(X0,X1)
| ~ open_subset(X0,X1)
| sP8(X1,X0)
| ~ top_str(X1)
| ~ topological_space(X1)
| ~ subset(X0,the_carrier(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_744])]) ).
fof(f3048,plain,
( ! [X0,X1] :
( ~ nowhere_dense(X0,X1)
| ~ open_subset(X0,X1)
| sP8(X1,X0)
| ~ top_str(X1)
| ~ topological_space(X1)
| ~ subset(X0,the_carrier(X1)) )
| ~ spl61_261
| ~ spl61_369 ),
inference(resolution,[],[f3029,f2122]) ).
fof(f6101,plain,
( spl61_743
| ~ spl61_250
| ~ spl61_364 ),
inference(avatar_split_clause,[],[f2974,f2966,f2076,f6099]) ).
fof(f6099,plain,
( spl61_743
<=> ! [X5] :
( ~ nowhere_dense(sK17(the_carrier(X5)),X5)
| boundary_set(sK17(the_carrier(X5)),X5)
| ~ top_str(X5)
| ~ topological_space(X5)
| empty(the_carrier(X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_743])]) ).
fof(f2974,plain,
( ! [X5] :
( ~ nowhere_dense(sK17(the_carrier(X5)),X5)
| boundary_set(sK17(the_carrier(X5)),X5)
| ~ top_str(X5)
| ~ topological_space(X5)
| empty(the_carrier(X5)) )
| ~ spl61_250
| ~ spl61_364 ),
inference(resolution,[],[f2967,f2077]) ).
fof(f6097,plain,
( spl61_742
| ~ spl61_249
| ~ spl61_364 ),
inference(avatar_split_clause,[],[f2973,f2966,f2072,f6095]) ).
fof(f6095,plain,
( spl61_742
<=> ! [X4] :
( ~ nowhere_dense(sK16(the_carrier(X4)),X4)
| boundary_set(sK16(the_carrier(X4)),X4)
| ~ top_str(X4)
| ~ topological_space(X4)
| empty(the_carrier(X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_742])]) ).
fof(f2973,plain,
( ! [X4] :
( ~ nowhere_dense(sK16(the_carrier(X4)),X4)
| boundary_set(sK16(the_carrier(X4)),X4)
| ~ top_str(X4)
| ~ topological_space(X4)
| empty(the_carrier(X4)) )
| ~ spl61_249
| ~ spl61_364 ),
inference(resolution,[],[f2967,f2073]) ).
fof(f6093,plain,
( spl61_741
| ~ spl61_248
| ~ spl61_364 ),
inference(avatar_split_clause,[],[f2972,f2966,f2068,f6091]) ).
fof(f6091,plain,
( spl61_741
<=> ! [X3] :
( ~ nowhere_dense(sK15(the_carrier(X3)),X3)
| boundary_set(sK15(the_carrier(X3)),X3)
| ~ top_str(X3)
| ~ topological_space(X3)
| empty(the_carrier(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_741])]) ).
fof(f2972,plain,
( ! [X3] :
( ~ nowhere_dense(sK15(the_carrier(X3)),X3)
| boundary_set(sK15(the_carrier(X3)),X3)
| ~ top_str(X3)
| ~ topological_space(X3)
| empty(the_carrier(X3)) )
| ~ spl61_248
| ~ spl61_364 ),
inference(resolution,[],[f2967,f2069]) ).
fof(f6089,plain,
( spl61_740
| ~ spl61_161
| spl61_1
| ~ spl61_265
| ~ spl61_573 ),
inference(avatar_split_clause,[],[f4764,f4754,f2167,f892,f1659,f6086]) ).
fof(f4764,plain,
( empty_carrier(sK12)
| ~ one_sorted_str(sK12)
| sP11(sK13,cast_as_carrier_subset(sK12),sK12)
| ~ spl61_265
| ~ spl61_573 ),
inference(duplicate_literal_removal,[],[f4762]) ).
fof(f4762,plain,
( empty_carrier(sK12)
| ~ one_sorted_str(sK12)
| sP11(sK13,cast_as_carrier_subset(sK12),sK12)
| ~ one_sorted_str(sK12)
| ~ spl61_265
| ~ spl61_573 ),
inference(resolution,[],[f4755,f2168]) ).
fof(f6084,plain,
( spl61_739
| ~ spl61_178
| ~ spl61_340 ),
inference(avatar_split_clause,[],[f2741,f2681,f1737,f6082]) ).
fof(f6082,plain,
( spl61_739
<=> ! [X1] :
( ~ join_complete_relstr(sK20(X1))
| with_infima_relstr(sK20(X1))
| ~ reflexive_relstr(sK20(X1))
| empty_carrier(sK20(X1))
| ~ rel_str(sK20(X1))
| ~ sP2(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_739])]) ).
fof(f1737,plain,
( spl61_178
<=> ! [X0] :
( antisymmetric_relstr(sK20(X0))
| ~ sP2(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_178])]) ).
fof(f2681,plain,
( spl61_340
<=> ! [X0] :
( with_infima_relstr(X0)
| ~ join_complete_relstr(X0)
| ~ antisymmetric_relstr(X0)
| ~ reflexive_relstr(X0)
| empty_carrier(X0)
| ~ rel_str(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_340])]) ).
fof(f2741,plain,
( ! [X1] :
( ~ join_complete_relstr(sK20(X1))
| with_infima_relstr(sK20(X1))
| ~ reflexive_relstr(sK20(X1))
| empty_carrier(sK20(X1))
| ~ rel_str(sK20(X1))
| ~ sP2(X1) )
| ~ spl61_178
| ~ spl61_340 ),
inference(resolution,[],[f2682,f1738]) ).
fof(f1738,plain,
( ! [X0] :
( antisymmetric_relstr(sK20(X0))
| ~ sP2(X0) )
| ~ spl61_178 ),
inference(avatar_component_clause,[],[f1737]) ).
fof(f2682,plain,
( ! [X0] :
( ~ antisymmetric_relstr(X0)
| ~ join_complete_relstr(X0)
| with_infima_relstr(X0)
| ~ reflexive_relstr(X0)
| empty_carrier(X0)
| ~ rel_str(X0) )
| ~ spl61_340 ),
inference(avatar_component_clause,[],[f2681]) ).
fof(f6046,plain,
( spl61_738
| ~ spl61_330
| ~ spl61_370 ),
inference(avatar_split_clause,[],[f3109,f3032,f2553,f6044]) ).
fof(f6044,plain,
( spl61_738
<=> ! [X18] :
( ~ boundary_set(sK34(X18),X18)
| ~ closed_subset(sK34(X18),X18)
| nowhere_dense(sK34(X18),X18)
| ~ top_str(X18)
| ~ topological_space(X18) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_738])]) ).
fof(f3109,plain,
( ! [X18] :
( ~ boundary_set(sK34(X18),X18)
| ~ closed_subset(sK34(X18),X18)
| nowhere_dense(sK34(X18),X18)
| ~ top_str(X18)
| ~ topological_space(X18) )
| ~ spl61_330
| ~ spl61_370 ),
inference(duplicate_literal_removal,[],[f3101]) ).
fof(f3101,plain,
( ! [X18] :
( ~ boundary_set(sK34(X18),X18)
| ~ closed_subset(sK34(X18),X18)
| nowhere_dense(sK34(X18),X18)
| ~ top_str(X18)
| ~ topological_space(X18)
| ~ top_str(X18)
| ~ topological_space(X18) )
| ~ spl61_330
| ~ spl61_370 ),
inference(resolution,[],[f3033,f2554]) ).
fof(f6042,plain,
( spl61_737
| ~ spl61_331
| ~ spl61_370 ),
inference(avatar_split_clause,[],[f3108,f3032,f2557,f6040]) ).
fof(f6040,plain,
( spl61_737
<=> ! [X19] :
( ~ boundary_set(sK35(X19),X19)
| ~ closed_subset(sK35(X19),X19)
| nowhere_dense(sK35(X19),X19)
| ~ top_str(X19)
| ~ topological_space(X19) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_737])]) ).
fof(f3108,plain,
( ! [X19] :
( ~ boundary_set(sK35(X19),X19)
| ~ closed_subset(sK35(X19),X19)
| nowhere_dense(sK35(X19),X19)
| ~ top_str(X19)
| ~ topological_space(X19) )
| ~ spl61_331
| ~ spl61_370 ),
inference(duplicate_literal_removal,[],[f3102]) ).
fof(f3102,plain,
( ! [X19] :
( ~ boundary_set(sK35(X19),X19)
| ~ closed_subset(sK35(X19),X19)
| nowhere_dense(sK35(X19),X19)
| ~ top_str(X19)
| ~ topological_space(X19)
| ~ top_str(X19)
| ~ topological_space(X19) )
| ~ spl61_331
| ~ spl61_370 ),
inference(resolution,[],[f3033,f2558]) ).
fof(f6038,plain,
( spl61_736
| ~ spl61_332
| ~ spl61_370 ),
inference(avatar_split_clause,[],[f3107,f3032,f2561,f6036]) ).
fof(f6036,plain,
( spl61_736
<=> ! [X20] :
( ~ boundary_set(sK36(X20),X20)
| ~ closed_subset(sK36(X20),X20)
| nowhere_dense(sK36(X20),X20)
| ~ top_str(X20)
| ~ topological_space(X20) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_736])]) ).
fof(f3107,plain,
( ! [X20] :
( ~ boundary_set(sK36(X20),X20)
| ~ closed_subset(sK36(X20),X20)
| nowhere_dense(sK36(X20),X20)
| ~ top_str(X20)
| ~ topological_space(X20) )
| ~ spl61_332
| ~ spl61_370 ),
inference(duplicate_literal_removal,[],[f3103]) ).
fof(f3103,plain,
( ! [X20] :
( ~ boundary_set(sK36(X20),X20)
| ~ closed_subset(sK36(X20),X20)
| nowhere_dense(sK36(X20),X20)
| ~ top_str(X20)
| ~ topological_space(X20)
| ~ top_str(X20)
| ~ topological_space(X20) )
| ~ spl61_332
| ~ spl61_370 ),
inference(resolution,[],[f3033,f2562]) ).
fof(f6034,plain,
( spl61_735
| ~ spl61_330
| ~ spl61_369 ),
inference(avatar_split_clause,[],[f3074,f3028,f2553,f6032]) ).
fof(f6032,plain,
( spl61_735
<=> ! [X18] :
( ~ nowhere_dense(sK34(X18),X18)
| ~ open_subset(sK34(X18),X18)
| sP8(X18,sK34(X18))
| ~ top_str(X18)
| ~ topological_space(X18) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_735])]) ).
fof(f3074,plain,
( ! [X18] :
( ~ nowhere_dense(sK34(X18),X18)
| ~ open_subset(sK34(X18),X18)
| sP8(X18,sK34(X18))
| ~ top_str(X18)
| ~ topological_space(X18) )
| ~ spl61_330
| ~ spl61_369 ),
inference(duplicate_literal_removal,[],[f3066]) ).
fof(f3066,plain,
( ! [X18] :
( ~ nowhere_dense(sK34(X18),X18)
| ~ open_subset(sK34(X18),X18)
| sP8(X18,sK34(X18))
| ~ top_str(X18)
| ~ topological_space(X18)
| ~ top_str(X18)
| ~ topological_space(X18) )
| ~ spl61_330
| ~ spl61_369 ),
inference(resolution,[],[f3029,f2554]) ).
fof(f6030,plain,
( spl61_734
| ~ spl61_331
| ~ spl61_369 ),
inference(avatar_split_clause,[],[f3073,f3028,f2557,f6028]) ).
fof(f6028,plain,
( spl61_734
<=> ! [X19] :
( ~ nowhere_dense(sK35(X19),X19)
| ~ open_subset(sK35(X19),X19)
| sP8(X19,sK35(X19))
| ~ top_str(X19)
| ~ topological_space(X19) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_734])]) ).
fof(f3073,plain,
( ! [X19] :
( ~ nowhere_dense(sK35(X19),X19)
| ~ open_subset(sK35(X19),X19)
| sP8(X19,sK35(X19))
| ~ top_str(X19)
| ~ topological_space(X19) )
| ~ spl61_331
| ~ spl61_369 ),
inference(duplicate_literal_removal,[],[f3067]) ).
fof(f3067,plain,
( ! [X19] :
( ~ nowhere_dense(sK35(X19),X19)
| ~ open_subset(sK35(X19),X19)
| sP8(X19,sK35(X19))
| ~ top_str(X19)
| ~ topological_space(X19)
| ~ top_str(X19)
| ~ topological_space(X19) )
| ~ spl61_331
| ~ spl61_369 ),
inference(resolution,[],[f3029,f2558]) ).
fof(f6026,plain,
( spl61_733
| ~ spl61_332
| ~ spl61_369 ),
inference(avatar_split_clause,[],[f3072,f3028,f2561,f6024]) ).
fof(f6024,plain,
( spl61_733
<=> ! [X20] :
( ~ nowhere_dense(sK36(X20),X20)
| ~ open_subset(sK36(X20),X20)
| sP8(X20,sK36(X20))
| ~ top_str(X20)
| ~ topological_space(X20) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_733])]) ).
fof(f3072,plain,
( ! [X20] :
( ~ nowhere_dense(sK36(X20),X20)
| ~ open_subset(sK36(X20),X20)
| sP8(X20,sK36(X20))
| ~ top_str(X20)
| ~ topological_space(X20) )
| ~ spl61_332
| ~ spl61_369 ),
inference(duplicate_literal_removal,[],[f3068]) ).
fof(f3068,plain,
( ! [X20] :
( ~ nowhere_dense(sK36(X20),X20)
| ~ open_subset(sK36(X20),X20)
| sP8(X20,sK36(X20))
| ~ top_str(X20)
| ~ topological_space(X20)
| ~ top_str(X20)
| ~ topological_space(X20) )
| ~ spl61_332
| ~ spl61_369 ),
inference(resolution,[],[f3029,f2562]) ).
fof(f6012,plain,
( ~ spl61_92
| spl61_93
| ~ spl61_94
| ~ spl61_95
| ~ spl61_96
| spl61_732
| ~ spl61_100
| ~ spl61_523
| ~ spl61_97
| ~ spl61_368 ),
inference(avatar_split_clause,[],[f3047,f3024,f1372,f4381,f1387,f6009,f1367,f1362,f1357,f1352,f1347]) ).
fof(f1362,plain,
( spl61_95
<=> transitive_relstr(sK59) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_95])]) ).
fof(f1367,plain,
( spl61_96
<=> antisymmetric_relstr(sK59) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_96])]) ).
fof(f6009,plain,
( spl61_732
<=> sP5(sK59) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_732])]) ).
fof(f1387,plain,
( spl61_100
<=> lower_bounded_relstr(sK59) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_100])]) ).
fof(f4381,plain,
( spl61_523
<=> up_complete_relstr(sK59) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_523])]) ).
fof(f1372,plain,
( spl61_97
<=> with_suprema_relstr(sK59) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_97])]) ).
fof(f3047,plain,
( ~ up_complete_relstr(sK59)
| ~ lower_bounded_relstr(sK59)
| sP5(sK59)
| ~ antisymmetric_relstr(sK59)
| ~ transitive_relstr(sK59)
| ~ reflexive_relstr(sK59)
| empty_carrier(sK59)
| ~ rel_str(sK59)
| ~ spl61_97
| ~ spl61_368 ),
inference(resolution,[],[f3025,f1374]) ).
fof(f1374,plain,
( with_suprema_relstr(sK59)
| ~ spl61_97 ),
inference(avatar_component_clause,[],[f1372]) ).
fof(f5997,plain,
( ~ spl61_72
| spl61_73
| ~ spl61_75
| ~ spl61_76
| ~ spl61_77
| spl61_731
| ~ spl61_81
| ~ spl61_84
| ~ spl61_78
| ~ spl61_368 ),
inference(avatar_split_clause,[],[f3046,f3024,f1277,f1307,f1292,f5994,f1272,f1267,f1262,f1252,f1247]) ).
fof(f1267,plain,
( spl61_76
<=> transitive_relstr(sK57) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_76])]) ).
fof(f1272,plain,
( spl61_77
<=> antisymmetric_relstr(sK57) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_77])]) ).
fof(f5994,plain,
( spl61_731
<=> sP5(sK57) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_731])]) ).
fof(f1292,plain,
( spl61_81
<=> lower_bounded_relstr(sK57) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_81])]) ).
fof(f1307,plain,
( spl61_84
<=> up_complete_relstr(sK57) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_84])]) ).
fof(f1277,plain,
( spl61_78
<=> with_suprema_relstr(sK57) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_78])]) ).
fof(f3046,plain,
( ~ up_complete_relstr(sK57)
| ~ lower_bounded_relstr(sK57)
| sP5(sK57)
| ~ antisymmetric_relstr(sK57)
| ~ transitive_relstr(sK57)
| ~ reflexive_relstr(sK57)
| empty_carrier(sK57)
| ~ rel_str(sK57)
| ~ spl61_78
| ~ spl61_368 ),
inference(resolution,[],[f3025,f1279]) ).
fof(f1279,plain,
( with_suprema_relstr(sK57)
| ~ spl61_78 ),
inference(avatar_component_clause,[],[f1277]) ).
fof(f5992,plain,
( ~ spl61_62
| spl61_63
| ~ spl61_65
| ~ spl61_66
| ~ spl61_67
| spl61_729
| ~ spl61_730
| ~ spl61_522
| ~ spl61_68
| ~ spl61_368 ),
inference(avatar_split_clause,[],[f3045,f3024,f1227,f4376,f5989,f5985,f1222,f1217,f1212,f1202,f1197]) ).
fof(f1202,plain,
( spl61_63
<=> empty_carrier(sK56) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_63])]) ).
fof(f1212,plain,
( spl61_65
<=> reflexive_relstr(sK56) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_65])]) ).
fof(f1217,plain,
( spl61_66
<=> transitive_relstr(sK56) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_66])]) ).
fof(f1222,plain,
( spl61_67
<=> antisymmetric_relstr(sK56) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_67])]) ).
fof(f5985,plain,
( spl61_729
<=> sP5(sK56) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_729])]) ).
fof(f4376,plain,
( spl61_522
<=> up_complete_relstr(sK56) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_522])]) ).
fof(f1227,plain,
( spl61_68
<=> with_suprema_relstr(sK56) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_68])]) ).
fof(f3045,plain,
( ~ up_complete_relstr(sK56)
| ~ lower_bounded_relstr(sK56)
| sP5(sK56)
| ~ antisymmetric_relstr(sK56)
| ~ transitive_relstr(sK56)
| ~ reflexive_relstr(sK56)
| empty_carrier(sK56)
| ~ rel_str(sK56)
| ~ spl61_68
| ~ spl61_368 ),
inference(resolution,[],[f3025,f1229]) ).
fof(f1229,plain,
( with_suprema_relstr(sK56)
| ~ spl61_68 ),
inference(avatar_component_clause,[],[f1227]) ).
fof(f5983,plain,
( ~ spl61_53
| spl61_54
| ~ spl61_56
| ~ spl61_57
| ~ spl61_58
| spl61_727
| ~ spl61_728
| ~ spl61_521
| ~ spl61_59
| ~ spl61_368 ),
inference(avatar_split_clause,[],[f3044,f3024,f1182,f4371,f5980,f5976,f1177,f1172,f1167,f1157,f1152]) ).
fof(f1157,plain,
( spl61_54
<=> empty_carrier(sK55) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_54])]) ).
fof(f1167,plain,
( spl61_56
<=> reflexive_relstr(sK55) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_56])]) ).
fof(f1172,plain,
( spl61_57
<=> transitive_relstr(sK55) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_57])]) ).
fof(f1177,plain,
( spl61_58
<=> antisymmetric_relstr(sK55) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_58])]) ).
fof(f5976,plain,
( spl61_727
<=> sP5(sK55) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_727])]) ).
fof(f4371,plain,
( spl61_521
<=> up_complete_relstr(sK55) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_521])]) ).
fof(f1182,plain,
( spl61_59
<=> with_suprema_relstr(sK55) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_59])]) ).
fof(f3044,plain,
( ~ up_complete_relstr(sK55)
| ~ lower_bounded_relstr(sK55)
| sP5(sK55)
| ~ antisymmetric_relstr(sK55)
| ~ transitive_relstr(sK55)
| ~ reflexive_relstr(sK55)
| empty_carrier(sK55)
| ~ rel_str(sK55)
| ~ spl61_59
| ~ spl61_368 ),
inference(resolution,[],[f3025,f1184]) ).
fof(f1184,plain,
( with_suprema_relstr(sK55)
| ~ spl61_59 ),
inference(avatar_component_clause,[],[f1182]) ).
fof(f5974,plain,
( ~ spl61_24
| spl61_25
| ~ spl61_28
| ~ spl61_29
| ~ spl61_30
| spl61_725
| ~ spl61_31
| ~ spl61_726
| ~ spl61_39
| ~ spl61_368 ),
inference(avatar_split_clause,[],[f3043,f3024,f1082,f5971,f1042,f5967,f1037,f1032,f1027,f1012,f1007]) ).
fof(f1007,plain,
( spl61_24
<=> rel_str(sK52) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_24])]) ).
fof(f1012,plain,
( spl61_25
<=> empty_carrier(sK52) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_25])]) ).
fof(f1027,plain,
( spl61_28
<=> reflexive_relstr(sK52) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_28])]) ).
fof(f1032,plain,
( spl61_29
<=> transitive_relstr(sK52) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_29])]) ).
fof(f1037,plain,
( spl61_30
<=> antisymmetric_relstr(sK52) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_30])]) ).
fof(f5967,plain,
( spl61_725
<=> sP5(sK52) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_725])]) ).
fof(f1042,plain,
( spl61_31
<=> lower_bounded_relstr(sK52) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_31])]) ).
fof(f5971,plain,
( spl61_726
<=> up_complete_relstr(sK52) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_726])]) ).
fof(f1082,plain,
( spl61_39
<=> with_suprema_relstr(sK52) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_39])]) ).
fof(f3043,plain,
( ~ up_complete_relstr(sK52)
| ~ lower_bounded_relstr(sK52)
| sP5(sK52)
| ~ antisymmetric_relstr(sK52)
| ~ transitive_relstr(sK52)
| ~ reflexive_relstr(sK52)
| empty_carrier(sK52)
| ~ rel_str(sK52)
| ~ spl61_39
| ~ spl61_368 ),
inference(resolution,[],[f3025,f1084]) ).
fof(f1084,plain,
( with_suprema_relstr(sK52)
| ~ spl61_39 ),
inference(avatar_component_clause,[],[f1082]) ).
fof(f5965,plain,
( spl61_724
| ~ spl61_206
| ~ spl61_366 ),
inference(avatar_split_clause,[],[f3022,f3007,f1871,f5963]) ).
fof(f5963,plain,
( spl61_724
<=> ! [X0] :
( filter_of_net_str(X0,sK19(X0)) = a_2_1_yellow19(X0,sK19(X0))
| empty_carrier(sK19(X0))
| ~ one_sorted_str(X0)
| empty_carrier(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_724])]) ).
fof(f1871,plain,
( spl61_206
<=> ! [X0] :
( net_str(sK19(X0),X0)
| ~ one_sorted_str(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_206])]) ).
fof(f3022,plain,
( ! [X0] :
( filter_of_net_str(X0,sK19(X0)) = a_2_1_yellow19(X0,sK19(X0))
| empty_carrier(sK19(X0))
| ~ one_sorted_str(X0)
| empty_carrier(X0) )
| ~ spl61_206
| ~ spl61_366 ),
inference(duplicate_literal_removal,[],[f3018]) ).
fof(f3018,plain,
( ! [X0] :
( filter_of_net_str(X0,sK19(X0)) = a_2_1_yellow19(X0,sK19(X0))
| empty_carrier(sK19(X0))
| ~ one_sorted_str(X0)
| empty_carrier(X0)
| ~ one_sorted_str(X0) )
| ~ spl61_206
| ~ spl61_366 ),
inference(resolution,[],[f3008,f1872]) ).
fof(f1872,plain,
( ! [X0] :
( net_str(sK19(X0),X0)
| ~ one_sorted_str(X0) )
| ~ spl61_206 ),
inference(avatar_component_clause,[],[f1871]) ).
fof(f5961,plain,
( spl61_723
| ~ spl61_210
| ~ spl61_366 ),
inference(avatar_split_clause,[],[f3021,f3007,f1888,f5959]) ).
fof(f5959,plain,
( spl61_723
<=> ! [X2] :
( filter_of_net_str(X2,sK21(X2)) = a_2_1_yellow19(X2,sK21(X2))
| empty_carrier(sK21(X2))
| ~ one_sorted_str(X2)
| empty_carrier(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_723])]) ).
fof(f1888,plain,
( spl61_210
<=> ! [X0] :
( net_str(sK21(X0),X0)
| ~ one_sorted_str(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_210])]) ).
fof(f3021,plain,
( ! [X2] :
( filter_of_net_str(X2,sK21(X2)) = a_2_1_yellow19(X2,sK21(X2))
| empty_carrier(sK21(X2))
| ~ one_sorted_str(X2)
| empty_carrier(X2) )
| ~ spl61_210
| ~ spl61_366 ),
inference(duplicate_literal_removal,[],[f3020]) ).
fof(f3020,plain,
( ! [X2] :
( filter_of_net_str(X2,sK21(X2)) = a_2_1_yellow19(X2,sK21(X2))
| empty_carrier(sK21(X2))
| ~ one_sorted_str(X2)
| empty_carrier(X2)
| ~ one_sorted_str(X2) )
| ~ spl61_210
| ~ spl61_366 ),
inference(resolution,[],[f3008,f1889]) ).
fof(f1889,plain,
( ! [X0] :
( net_str(sK21(X0),X0)
| ~ one_sorted_str(X0) )
| ~ spl61_210 ),
inference(avatar_component_clause,[],[f1888]) ).
fof(f5957,plain,
( spl61_722
| ~ spl61_159
| ~ spl61_364 ),
inference(avatar_split_clause,[],[f2991,f2966,f1629,f5955]) ).
fof(f5955,plain,
( spl61_722
<=> ! [X22] :
( ~ nowhere_dense(sK38(powerset(the_carrier(X22))),X22)
| boundary_set(sK38(powerset(the_carrier(X22))),X22)
| ~ top_str(X22)
| ~ topological_space(X22) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_722])]) ).
fof(f2991,plain,
( ! [X22] :
( ~ nowhere_dense(sK38(powerset(the_carrier(X22))),X22)
| boundary_set(sK38(powerset(the_carrier(X22))),X22)
| ~ top_str(X22)
| ~ topological_space(X22) )
| ~ spl61_159
| ~ spl61_364 ),
inference(resolution,[],[f2967,f1630]) ).
fof(f5953,plain,
( spl61_721
| ~ spl61_329
| ~ spl61_364 ),
inference(avatar_split_clause,[],[f2982,f2966,f2541,f5951]) ).
fof(f5951,plain,
( spl61_721
<=> ! [X13] :
( ~ nowhere_dense(sK29(X13),X13)
| boundary_set(sK29(X13),X13)
| ~ top_str(X13)
| ~ topological_space(X13)
| ~ rel_str(X13)
| empty_carrier(X13) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_721])]) ).
fof(f2982,plain,
( ! [X13] :
( ~ nowhere_dense(sK29(X13),X13)
| boundary_set(sK29(X13),X13)
| ~ top_str(X13)
| ~ topological_space(X13)
| ~ rel_str(X13)
| empty_carrier(X13) )
| ~ spl61_329
| ~ spl61_364 ),
inference(resolution,[],[f2967,f2542]) ).
fof(f5949,plain,
( spl61_720
| ~ spl61_326
| ~ spl61_364 ),
inference(avatar_split_clause,[],[f2981,f2966,f2529,f5947]) ).
fof(f5947,plain,
( spl61_720
<=> ! [X12] :
( ~ nowhere_dense(sK28(X12),X12)
| boundary_set(sK28(X12),X12)
| ~ top_str(X12)
| ~ topological_space(X12)
| ~ one_sorted_str(X12)
| empty_carrier(X12) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_720])]) ).
fof(f2981,plain,
( ! [X12] :
( ~ nowhere_dense(sK28(X12),X12)
| boundary_set(sK28(X12),X12)
| ~ top_str(X12)
| ~ topological_space(X12)
| ~ one_sorted_str(X12)
| empty_carrier(X12) )
| ~ spl61_326
| ~ spl61_364 ),
inference(resolution,[],[f2967,f2530]) ).
fof(f5945,plain,
( spl61_719
| ~ spl61_335
| ~ spl61_357 ),
inference(avatar_split_clause,[],[f2853,f2814,f2573,f5943]) ).
fof(f5943,plain,
( spl61_719
<=> ! [X2,X1] :
( ~ rel_str(X1)
| ~ transitive_relstr(X1)
| ~ reflexive_relstr(X1)
| empty_carrier(X1)
| element(X2,the_carrier(X1))
| ~ in(X2,sK32(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_719])]) ).
fof(f2853,plain,
( ! [X2,X1] :
( ~ rel_str(X1)
| ~ transitive_relstr(X1)
| ~ reflexive_relstr(X1)
| empty_carrier(X1)
| element(X2,the_carrier(X1))
| ~ in(X2,sK32(X1)) )
| ~ spl61_335
| ~ spl61_357 ),
inference(resolution,[],[f2815,f2574]) ).
fof(f5941,plain,
( spl61_718
| ~ spl61_335
| ~ spl61_356 ),
inference(avatar_split_clause,[],[f2847,f2810,f2573,f5939]) ).
fof(f5939,plain,
( spl61_718
<=> ! [X2,X1] :
( ~ rel_str(X1)
| ~ transitive_relstr(X1)
| ~ reflexive_relstr(X1)
| empty_carrier(X1)
| element(X2,the_carrier(X1))
| ~ in(X2,sK31(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_718])]) ).
fof(f2847,plain,
( ! [X2,X1] :
( ~ rel_str(X1)
| ~ transitive_relstr(X1)
| ~ reflexive_relstr(X1)
| empty_carrier(X1)
| element(X2,the_carrier(X1))
| ~ in(X2,sK31(X1)) )
| ~ spl61_335
| ~ spl61_356 ),
inference(resolution,[],[f2811,f2574]) ).
fof(f5937,plain,
( spl61_717
| ~ spl61_293
| ~ spl61_342 ),
inference(avatar_split_clause,[],[f2761,f2689,f2281,f5935]) ).
fof(f5935,plain,
( spl61_717
<=> ! [X7] :
( ~ top_str(X7)
| ~ topological_space(X7)
| empty_carrier(X7)
| empty(powerset(the_carrier(X7)))
| in(sK27(X7),powerset(the_carrier(X7))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_717])]) ).
fof(f2761,plain,
( ! [X7] :
( ~ top_str(X7)
| ~ topological_space(X7)
| empty_carrier(X7)
| empty(powerset(the_carrier(X7)))
| in(sK27(X7),powerset(the_carrier(X7))) )
| ~ spl61_293
| ~ spl61_342 ),
inference(resolution,[],[f2690,f2282]) ).
fof(f5933,plain,
( spl61_716
| ~ spl61_293
| ~ spl61_341 ),
inference(avatar_split_clause,[],[f2754,f2685,f2281,f5931]) ).
fof(f5931,plain,
( spl61_716
<=> ! [X7] :
( ~ top_str(X7)
| ~ topological_space(X7)
| empty_carrier(X7)
| empty(powerset(the_carrier(X7)))
| in(sK26(X7),powerset(the_carrier(X7))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_716])]) ).
fof(f2754,plain,
( ! [X7] :
( ~ top_str(X7)
| ~ topological_space(X7)
| empty_carrier(X7)
| empty(powerset(the_carrier(X7)))
| in(sK26(X7),powerset(the_carrier(X7))) )
| ~ spl61_293
| ~ spl61_341 ),
inference(resolution,[],[f2686,f2282]) ).
fof(f5911,plain,
( spl61_715
| ~ spl61_159
| ~ spl61_360 ),
inference(avatar_split_clause,[],[f2946,f2826,f1629,f5909]) ).
fof(f5909,plain,
( spl61_715
<=> ! [X22] :
( ~ empty(sK38(powerset(the_carrier(X22))))
| closed_subset(sK38(powerset(the_carrier(X22))),X22)
| ~ top_str(X22)
| ~ topological_space(X22) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_715])]) ).
fof(f2946,plain,
( ! [X22] :
( ~ empty(sK38(powerset(the_carrier(X22))))
| closed_subset(sK38(powerset(the_carrier(X22))),X22)
| ~ top_str(X22)
| ~ topological_space(X22) )
| ~ spl61_159
| ~ spl61_360 ),
inference(resolution,[],[f2827,f1630]) ).
fof(f5907,plain,
( spl61_714
| ~ spl61_159
| ~ spl61_359 ),
inference(avatar_split_clause,[],[f2913,f2822,f1629,f5905]) ).
fof(f5905,plain,
( spl61_714
<=> ! [X22] :
( ~ empty(sK38(powerset(the_carrier(X22))))
| open_subset(sK38(powerset(the_carrier(X22))),X22)
| ~ top_str(X22)
| ~ topological_space(X22) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_714])]) ).
fof(f2913,plain,
( ! [X22] :
( ~ empty(sK38(powerset(the_carrier(X22))))
| open_subset(sK38(powerset(the_carrier(X22))),X22)
| ~ top_str(X22)
| ~ topological_space(X22) )
| ~ spl61_159
| ~ spl61_359 ),
inference(resolution,[],[f2823,f1630]) ).
fof(f5903,plain,
( spl61_713
| ~ spl61_159
| ~ spl61_358 ),
inference(avatar_split_clause,[],[f2880,f2818,f1629,f5901]) ).
fof(f5901,plain,
( spl61_713
<=> ! [X22] :
( ~ empty(sK38(powerset(the_carrier(X22))))
| nowhere_dense(sK38(powerset(the_carrier(X22))),X22)
| ~ top_str(X22)
| ~ topological_space(X22) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_713])]) ).
fof(f2880,plain,
( ! [X22] :
( ~ empty(sK38(powerset(the_carrier(X22))))
| nowhere_dense(sK38(powerset(the_carrier(X22))),X22)
| ~ top_str(X22)
| ~ topological_space(X22) )
| ~ spl61_159
| ~ spl61_358 ),
inference(resolution,[],[f2819,f1630]) ).
fof(f5899,plain,
( spl61_712
| ~ spl61_315
| ~ spl61_357 ),
inference(avatar_split_clause,[],[f2854,f2814,f2457,f5897]) ).
fof(f5897,plain,
( spl61_712
<=> ! [X4,X3] :
( ~ rel_str(X3)
| ~ transitive_relstr(X3)
| ~ reflexive_relstr(X3)
| empty_carrier(X3)
| ~ empty(the_carrier(X3))
| ~ in(X4,sK32(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_712])]) ).
fof(f2854,plain,
( ! [X3,X4] :
( ~ rel_str(X3)
| ~ transitive_relstr(X3)
| ~ reflexive_relstr(X3)
| empty_carrier(X3)
| ~ empty(the_carrier(X3))
| ~ in(X4,sK32(X3)) )
| ~ spl61_315
| ~ spl61_357 ),
inference(resolution,[],[f2815,f2458]) ).
fof(f5895,plain,
( spl61_711
| ~ spl61_315
| ~ spl61_356 ),
inference(avatar_split_clause,[],[f2848,f2810,f2457,f5893]) ).
fof(f5893,plain,
( spl61_711
<=> ! [X4,X3] :
( ~ rel_str(X3)
| ~ transitive_relstr(X3)
| ~ reflexive_relstr(X3)
| empty_carrier(X3)
| ~ empty(the_carrier(X3))
| ~ in(X4,sK31(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_711])]) ).
fof(f2848,plain,
( ! [X3,X4] :
( ~ rel_str(X3)
| ~ transitive_relstr(X3)
| ~ reflexive_relstr(X3)
| empty_carrier(X3)
| ~ empty(the_carrier(X3))
| ~ in(X4,sK31(X3)) )
| ~ spl61_315
| ~ spl61_356 ),
inference(resolution,[],[f2811,f2458]) ).
fof(f5891,plain,
( spl61_710
| ~ spl61_293
| ~ spl61_333 ),
inference(avatar_split_clause,[],[f2627,f2565,f2281,f5889]) ).
fof(f5889,plain,
( spl61_710
<=> ! [X13,X14,X15] :
( ~ relation_of2_as_subset(X13,X14,X15)
| empty(powerset(cartesian_product2(X14,X15)))
| in(X13,powerset(cartesian_product2(X14,X15))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_710])]) ).
fof(f2565,plain,
( spl61_333
<=> ! [X2,X0,X1] :
( element(X2,powerset(cartesian_product2(X0,X1)))
| ~ relation_of2_as_subset(X2,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_333])]) ).
fof(f2627,plain,
( ! [X14,X15,X13] :
( ~ relation_of2_as_subset(X13,X14,X15)
| empty(powerset(cartesian_product2(X14,X15)))
| in(X13,powerset(cartesian_product2(X14,X15))) )
| ~ spl61_293
| ~ spl61_333 ),
inference(resolution,[],[f2566,f2282]) ).
fof(f2566,plain,
( ! [X2,X0,X1] :
( element(X2,powerset(cartesian_product2(X0,X1)))
| ~ relation_of2_as_subset(X2,X0,X1) )
| ~ spl61_333 ),
inference(avatar_component_clause,[],[f2565]) ).
fof(f5818,plain,
( spl61_93
| spl61_708
| ~ spl61_94
| ~ spl61_95
| ~ spl61_96
| spl61_709
| ~ spl61_92
| ~ spl61_101
| ~ spl61_365 ),
inference(avatar_split_clause,[],[f3017,f3003,f1392,f1347,f5815,f1367,f1362,f1357,f5811,f1352]) ).
fof(f5815,plain,
( spl61_709
<=> sP6(sK59) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_709])]) ).
fof(f1392,plain,
( spl61_101
<=> upper_bounded_relstr(sK59) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_101])]) ).
fof(f3017,plain,
( ~ rel_str(sK59)
| sP6(sK59)
| ~ antisymmetric_relstr(sK59)
| ~ transitive_relstr(sK59)
| ~ reflexive_relstr(sK59)
| trivial_carrier(sK59)
| empty_carrier(sK59)
| ~ spl61_101
| ~ spl61_365 ),
inference(resolution,[],[f3004,f1394]) ).
fof(f1394,plain,
( upper_bounded_relstr(sK59)
| ~ spl61_101 ),
inference(avatar_component_clause,[],[f1392]) ).
fof(f5807,plain,
( spl61_73
| spl61_706
| ~ spl61_75
| ~ spl61_76
| ~ spl61_77
| spl61_707
| ~ spl61_72
| ~ spl61_82
| ~ spl61_365 ),
inference(avatar_split_clause,[],[f3016,f3003,f1297,f1247,f5804,f1272,f1267,f1262,f5800,f1252]) ).
fof(f5804,plain,
( spl61_707
<=> sP6(sK57) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_707])]) ).
fof(f1297,plain,
( spl61_82
<=> upper_bounded_relstr(sK57) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_82])]) ).
fof(f3016,plain,
( ~ rel_str(sK57)
| sP6(sK57)
| ~ antisymmetric_relstr(sK57)
| ~ transitive_relstr(sK57)
| ~ reflexive_relstr(sK57)
| trivial_carrier(sK57)
| empty_carrier(sK57)
| ~ spl61_82
| ~ spl61_365 ),
inference(resolution,[],[f3004,f1299]) ).
fof(f1299,plain,
( upper_bounded_relstr(sK57)
| ~ spl61_82 ),
inference(avatar_component_clause,[],[f1297]) ).
fof(f5798,plain,
( spl61_25
| spl61_26
| ~ spl61_28
| ~ spl61_29
| ~ spl61_30
| spl61_705
| ~ spl61_24
| ~ spl61_32
| ~ spl61_365 ),
inference(avatar_split_clause,[],[f3015,f3003,f1047,f1007,f5795,f1037,f1032,f1027,f1017,f1012]) ).
fof(f1017,plain,
( spl61_26
<=> trivial_carrier(sK52) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_26])]) ).
fof(f5795,plain,
( spl61_705
<=> sP6(sK52) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_705])]) ).
fof(f1047,plain,
( spl61_32
<=> upper_bounded_relstr(sK52) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_32])]) ).
fof(f3015,plain,
( ~ rel_str(sK52)
| sP6(sK52)
| ~ antisymmetric_relstr(sK52)
| ~ transitive_relstr(sK52)
| ~ reflexive_relstr(sK52)
| trivial_carrier(sK52)
| empty_carrier(sK52)
| ~ spl61_32
| ~ spl61_365 ),
inference(resolution,[],[f3004,f1049]) ).
fof(f1049,plain,
( upper_bounded_relstr(sK52)
| ~ spl61_32 ),
inference(avatar_component_clause,[],[f1047]) ).
fof(f5793,plain,
( spl61_704
| ~ spl61_341
| ~ spl61_364 ),
inference(avatar_split_clause,[],[f2997,f2966,f2685,f5791]) ).
fof(f5791,plain,
( spl61_704
<=> ! [X10] :
( ~ nowhere_dense(sK26(X10),X10)
| boundary_set(sK26(X10),X10)
| ~ top_str(X10)
| ~ topological_space(X10)
| empty_carrier(X10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_704])]) ).
fof(f2997,plain,
( ! [X10] :
( ~ nowhere_dense(sK26(X10),X10)
| boundary_set(sK26(X10),X10)
| ~ top_str(X10)
| ~ topological_space(X10)
| empty_carrier(X10) )
| ~ spl61_341
| ~ spl61_364 ),
inference(duplicate_literal_removal,[],[f2979]) ).
fof(f2979,plain,
( ! [X10] :
( ~ nowhere_dense(sK26(X10),X10)
| boundary_set(sK26(X10),X10)
| ~ top_str(X10)
| ~ topological_space(X10)
| ~ top_str(X10)
| ~ topological_space(X10)
| empty_carrier(X10) )
| ~ spl61_341
| ~ spl61_364 ),
inference(resolution,[],[f2967,f2686]) ).
fof(f5789,plain,
( spl61_703
| ~ spl61_342
| ~ spl61_364 ),
inference(avatar_split_clause,[],[f2996,f2966,f2689,f5787]) ).
fof(f5787,plain,
( spl61_703
<=> ! [X11] :
( ~ nowhere_dense(sK27(X11),X11)
| boundary_set(sK27(X11),X11)
| ~ top_str(X11)
| ~ topological_space(X11)
| empty_carrier(X11) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_703])]) ).
fof(f2996,plain,
( ! [X11] :
( ~ nowhere_dense(sK27(X11),X11)
| boundary_set(sK27(X11),X11)
| ~ top_str(X11)
| ~ topological_space(X11)
| empty_carrier(X11) )
| ~ spl61_342
| ~ spl61_364 ),
inference(duplicate_literal_removal,[],[f2980]) ).
fof(f2980,plain,
( ! [X11] :
( ~ nowhere_dense(sK27(X11),X11)
| boundary_set(sK27(X11),X11)
| ~ top_str(X11)
| ~ topological_space(X11)
| ~ top_str(X11)
| ~ topological_space(X11)
| empty_carrier(X11) )
| ~ spl61_342
| ~ spl61_364 ),
inference(resolution,[],[f2967,f2690]) ).
fof(f5785,plain,
( spl61_702
| ~ spl61_292
| ~ spl61_364 ),
inference(avatar_split_clause,[],[f2990,f2966,f2277,f5783]) ).
fof(f5783,plain,
( spl61_702
<=> ! [X21] :
( ~ nowhere_dense(sK37(X21),X21)
| boundary_set(sK37(X21),X21)
| ~ top_str(X21)
| ~ topological_space(X21)
| ~ sP10(X21) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_702])]) ).
fof(f2990,plain,
( ! [X21] :
( ~ nowhere_dense(sK37(X21),X21)
| boundary_set(sK37(X21),X21)
| ~ top_str(X21)
| ~ topological_space(X21)
| ~ sP10(X21) )
| ~ spl61_292
| ~ spl61_364 ),
inference(resolution,[],[f2967,f2278]) ).
fof(f5781,plain,
( spl61_701
| ~ spl61_280
| ~ spl61_364 ),
inference(avatar_split_clause,[],[f2983,f2966,f2228,f5779]) ).
fof(f5779,plain,
( spl61_701
<=> ! [X14] :
( ~ nowhere_dense(sK30(X14),X14)
| boundary_set(sK30(X14),X14)
| ~ top_str(X14)
| ~ topological_space(X14)
| ~ sP7(X14) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_701])]) ).
fof(f2983,plain,
( ! [X14] :
( ~ nowhere_dense(sK30(X14),X14)
| boundary_set(sK30(X14),X14)
| ~ top_str(X14)
| ~ topological_space(X14)
| ~ sP7(X14) )
| ~ spl61_280
| ~ spl61_364 ),
inference(resolution,[],[f2967,f2229]) ).
fof(f5777,plain,
( spl61_700
| ~ spl61_274
| ~ spl61_364 ),
inference(avatar_split_clause,[],[f2978,f2966,f2204,f5775]) ).
fof(f5775,plain,
( spl61_700
<=> ! [X9] :
( ~ nowhere_dense(sK25(X9),X9)
| boundary_set(sK25(X9),X9)
| ~ top_str(X9)
| ~ topological_space(X9)
| ~ sP6(X9) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_700])]) ).
fof(f2978,plain,
( ! [X9] :
( ~ nowhere_dense(sK25(X9),X9)
| boundary_set(sK25(X9),X9)
| ~ top_str(X9)
| ~ topological_space(X9)
| ~ sP6(X9) )
| ~ spl61_274
| ~ spl61_364 ),
inference(resolution,[],[f2967,f2205]) ).
fof(f5773,plain,
( spl61_699
| ~ spl61_273
| ~ spl61_364 ),
inference(avatar_split_clause,[],[f2977,f2966,f2200,f5771]) ).
fof(f5771,plain,
( spl61_699
<=> ! [X8] :
( ~ nowhere_dense(sK24(X8),X8)
| boundary_set(sK24(X8),X8)
| ~ top_str(X8)
| ~ topological_space(X8)
| ~ rel_str(X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_699])]) ).
fof(f2977,plain,
( ! [X8] :
( ~ nowhere_dense(sK24(X8),X8)
| boundary_set(sK24(X8),X8)
| ~ top_str(X8)
| ~ topological_space(X8)
| ~ rel_str(X8) )
| ~ spl61_273
| ~ spl61_364 ),
inference(resolution,[],[f2967,f2201]) ).
fof(f5769,plain,
( spl61_698
| ~ spl61_272
| ~ spl61_364 ),
inference(avatar_split_clause,[],[f2976,f2966,f2196,f5767]) ).
fof(f5767,plain,
( spl61_698
<=> ! [X7] :
( ~ nowhere_dense(sK23(X7),X7)
| boundary_set(sK23(X7),X7)
| ~ top_str(X7)
| ~ topological_space(X7)
| ~ rel_str(X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_698])]) ).
fof(f2976,plain,
( ! [X7] :
( ~ nowhere_dense(sK23(X7),X7)
| boundary_set(sK23(X7),X7)
| ~ top_str(X7)
| ~ topological_space(X7)
| ~ rel_str(X7) )
| ~ spl61_272
| ~ spl61_364 ),
inference(resolution,[],[f2967,f2197]) ).
fof(f5765,plain,
( spl61_697
| ~ spl61_265
| ~ spl61_364 ),
inference(avatar_split_clause,[],[f2970,f2966,f2167,f5763]) ).
fof(f5763,plain,
( spl61_697
<=> ! [X2] :
( ~ nowhere_dense(cast_as_carrier_subset(X2),X2)
| boundary_set(cast_as_carrier_subset(X2),X2)
| ~ top_str(X2)
| ~ topological_space(X2)
| ~ one_sorted_str(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_697])]) ).
fof(f2970,plain,
( ! [X2] :
( ~ nowhere_dense(cast_as_carrier_subset(X2),X2)
| boundary_set(cast_as_carrier_subset(X2),X2)
| ~ top_str(X2)
| ~ topological_space(X2)
| ~ one_sorted_str(X2) )
| ~ spl61_265
| ~ spl61_364 ),
inference(resolution,[],[f2967,f2168]) ).
fof(f5761,plain,
( spl61_696
| ~ spl61_261
| ~ spl61_364 ),
inference(avatar_split_clause,[],[f2969,f2966,f2121,f5759]) ).
fof(f2969,plain,
( ! [X0,X1] :
( ~ nowhere_dense(X0,X1)
| boundary_set(X0,X1)
| ~ top_str(X1)
| ~ topological_space(X1)
| ~ subset(X0,the_carrier(X1)) )
| ~ spl61_261
| ~ spl61_364 ),
inference(resolution,[],[f2967,f2122]) ).
fof(f5757,plain,
( spl61_695
| ~ spl61_266
| ~ spl61_357 ),
inference(avatar_split_clause,[],[f2855,f2814,f2171,f5755]) ).
fof(f5755,plain,
( spl61_695
<=> ! [X5] :
( ~ rel_str(X5)
| ~ transitive_relstr(X5)
| ~ reflexive_relstr(X5)
| empty_carrier(X5)
| finite(sK32(X5))
| ~ finite(the_carrier(X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_695])]) ).
fof(f2855,plain,
( ! [X5] :
( ~ rel_str(X5)
| ~ transitive_relstr(X5)
| ~ reflexive_relstr(X5)
| empty_carrier(X5)
| finite(sK32(X5))
| ~ finite(the_carrier(X5)) )
| ~ spl61_266
| ~ spl61_357 ),
inference(resolution,[],[f2815,f2172]) ).
fof(f5753,plain,
( spl61_694
| ~ spl61_266
| ~ spl61_356 ),
inference(avatar_split_clause,[],[f2849,f2810,f2171,f5751]) ).
fof(f5751,plain,
( spl61_694
<=> ! [X5] :
( ~ rel_str(X5)
| ~ transitive_relstr(X5)
| ~ reflexive_relstr(X5)
| empty_carrier(X5)
| finite(sK31(X5))
| ~ finite(the_carrier(X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_694])]) ).
fof(f2849,plain,
( ! [X5] :
( ~ rel_str(X5)
| ~ transitive_relstr(X5)
| ~ reflexive_relstr(X5)
| empty_carrier(X5)
| finite(sK31(X5))
| ~ finite(the_carrier(X5)) )
| ~ spl61_266
| ~ spl61_356 ),
inference(resolution,[],[f2811,f2172]) ).
fof(f5749,plain,
( spl61_693
| ~ spl61_335
| ~ spl61_342 ),
inference(avatar_split_clause,[],[f2757,f2689,f2573,f5747]) ).
fof(f5747,plain,
( spl61_693
<=> ! [X2,X1] :
( ~ top_str(X1)
| ~ topological_space(X1)
| empty_carrier(X1)
| element(X2,the_carrier(X1))
| ~ in(X2,sK27(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_693])]) ).
fof(f2757,plain,
( ! [X2,X1] :
( ~ top_str(X1)
| ~ topological_space(X1)
| empty_carrier(X1)
| element(X2,the_carrier(X1))
| ~ in(X2,sK27(X1)) )
| ~ spl61_335
| ~ spl61_342 ),
inference(resolution,[],[f2690,f2574]) ).
fof(f5745,plain,
( spl61_692
| ~ spl61_335
| ~ spl61_341 ),
inference(avatar_split_clause,[],[f2750,f2685,f2573,f5743]) ).
fof(f5743,plain,
( spl61_692
<=> ! [X2,X1] :
( ~ top_str(X1)
| ~ topological_space(X1)
| empty_carrier(X1)
| element(X2,the_carrier(X1))
| ~ in(X2,sK26(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_692])]) ).
fof(f2750,plain,
( ! [X2,X1] :
( ~ top_str(X1)
| ~ topological_space(X1)
| empty_carrier(X1)
| element(X2,the_carrier(X1))
| ~ in(X2,sK26(X1)) )
| ~ spl61_335
| ~ spl61_341 ),
inference(resolution,[],[f2686,f2574]) ).
fof(f5741,plain,
( spl61_691
| ~ spl61_293
| ~ spl61_332 ),
inference(avatar_split_clause,[],[f2622,f2561,f2281,f5739]) ).
fof(f2622,plain,
( ! [X4] :
( ~ top_str(X4)
| ~ topological_space(X4)
| empty(powerset(the_carrier(X4)))
| in(sK36(X4),powerset(the_carrier(X4))) )
| ~ spl61_293
| ~ spl61_332 ),
inference(resolution,[],[f2562,f2282]) ).
fof(f5737,plain,
( spl61_690
| ~ spl61_293
| ~ spl61_331 ),
inference(avatar_split_clause,[],[f2618,f2557,f2281,f5735]) ).
fof(f2618,plain,
( ! [X4] :
( ~ top_str(X4)
| ~ topological_space(X4)
| empty(powerset(the_carrier(X4)))
| in(sK35(X4),powerset(the_carrier(X4))) )
| ~ spl61_293
| ~ spl61_331 ),
inference(resolution,[],[f2558,f2282]) ).
fof(f5733,plain,
( spl61_689
| ~ spl61_293
| ~ spl61_330 ),
inference(avatar_split_clause,[],[f2609,f2553,f2281,f5731]) ).
fof(f2609,plain,
( ! [X4] :
( ~ top_str(X4)
| ~ topological_space(X4)
| empty(powerset(the_carrier(X4)))
| in(sK34(X4),powerset(the_carrier(X4))) )
| ~ spl61_293
| ~ spl61_330 ),
inference(resolution,[],[f2554,f2282]) ).
fof(f5729,plain,
( spl61_688
| ~ spl61_293
| ~ spl61_329 ),
inference(avatar_split_clause,[],[f2605,f2541,f2281,f5727]) ).
fof(f2605,plain,
( ! [X4] :
( ~ rel_str(X4)
| empty_carrier(X4)
| empty(powerset(the_carrier(X4)))
| in(sK29(X4),powerset(the_carrier(X4))) )
| ~ spl61_293
| ~ spl61_329 ),
inference(resolution,[],[f2542,f2282]) ).
fof(f5725,plain,
( spl61_687
| ~ spl61_293
| ~ spl61_326 ),
inference(avatar_split_clause,[],[f2601,f2529,f2281,f5723]) ).
fof(f2601,plain,
( ! [X4] :
( ~ one_sorted_str(X4)
| empty_carrier(X4)
| empty(powerset(the_carrier(X4)))
| in(sK28(X4),powerset(the_carrier(X4))) )
| ~ spl61_293
| ~ spl61_326 ),
inference(resolution,[],[f2530,f2282]) ).
fof(f5721,plain,
( spl61_686
| ~ spl61_293
| ~ spl61_304 ),
inference(avatar_split_clause,[],[f2462,f2412,f2281,f5719]) ).
fof(f2412,plain,
( spl61_304
<=> ! [X0] :
( element(sK22(X0),powerset(powerset(the_carrier(X0))))
| ~ one_sorted_str(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_304])]) ).
fof(f2462,plain,
( ! [X2] :
( ~ one_sorted_str(X2)
| empty(powerset(powerset(the_carrier(X2))))
| in(sK22(X2),powerset(powerset(the_carrier(X2)))) )
| ~ spl61_293
| ~ spl61_304 ),
inference(resolution,[],[f2413,f2282]) ).
fof(f2413,plain,
( ! [X0] :
( element(sK22(X0),powerset(powerset(the_carrier(X0))))
| ~ one_sorted_str(X0) )
| ~ spl61_304 ),
inference(avatar_component_clause,[],[f2412]) ).
fof(f5486,plain,
( spl61_685
| ~ spl61_103
| ~ spl61_126
| ~ spl61_182
| ~ spl61_199
| ~ spl61_369 ),
inference(avatar_split_clause,[],[f3082,f3028,f1822,f1753,f1496,f1402,f5484]) ).
fof(f1496,plain,
( spl61_126
<=> ! [X0] : empty(sK39(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_126])]) ).
fof(f1753,plain,
( spl61_182
<=> ! [X0] :
( empty_set = X0
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_182])]) ).
fof(f3082,plain,
( ! [X23] :
( sP8(X23,sK60)
| ~ open_subset(sK60,X23)
| ~ nowhere_dense(sK60,X23)
| ~ top_str(X23)
| ~ topological_space(X23) )
| ~ spl61_103
| ~ spl61_126
| ~ spl61_182
| ~ spl61_199
| ~ spl61_369 ),
inference(forward_demodulation,[],[f3081,f1844]) ).
fof(f1844,plain,
( empty_set = sK60
| ~ spl61_103
| ~ spl61_182 ),
inference(resolution,[],[f1754,f1404]) ).
fof(f1404,plain,
( empty(sK60)
| ~ spl61_103 ),
inference(avatar_component_clause,[],[f1402]) ).
fof(f1754,plain,
( ! [X0] :
( ~ empty(X0)
| empty_set = X0 )
| ~ spl61_182 ),
inference(avatar_component_clause,[],[f1753]) ).
fof(f3081,plain,
( ! [X23] :
( sP8(X23,empty_set)
| ~ open_subset(sK60,X23)
| ~ nowhere_dense(sK60,X23)
| ~ top_str(X23)
| ~ topological_space(X23) )
| ~ spl61_103
| ~ spl61_126
| ~ spl61_182
| ~ spl61_199
| ~ spl61_369 ),
inference(forward_demodulation,[],[f3080,f1843]) ).
fof(f1843,plain,
( ! [X2] : empty_set = sK39(X2)
| ~ spl61_126
| ~ spl61_182 ),
inference(resolution,[],[f1754,f1497]) ).
fof(f1497,plain,
( ! [X0] : empty(sK39(X0))
| ~ spl61_126 ),
inference(avatar_component_clause,[],[f1496]) ).
fof(f3080,plain,
( ! [X23] :
( ~ open_subset(sK60,X23)
| ~ nowhere_dense(sK60,X23)
| sP8(X23,sK39(the_carrier(X23)))
| ~ top_str(X23)
| ~ topological_space(X23) )
| ~ spl61_103
| ~ spl61_126
| ~ spl61_182
| ~ spl61_199
| ~ spl61_369 ),
inference(forward_demodulation,[],[f3079,f1844]) ).
fof(f3079,plain,
( ! [X23] :
( ~ open_subset(empty_set,X23)
| ~ nowhere_dense(sK60,X23)
| sP8(X23,sK39(the_carrier(X23)))
| ~ top_str(X23)
| ~ topological_space(X23) )
| ~ spl61_103
| ~ spl61_126
| ~ spl61_182
| ~ spl61_199
| ~ spl61_369 ),
inference(forward_demodulation,[],[f3078,f1843]) ).
fof(f3078,plain,
( ! [X23] :
( ~ nowhere_dense(sK60,X23)
| ~ open_subset(sK39(the_carrier(X23)),X23)
| sP8(X23,sK39(the_carrier(X23)))
| ~ top_str(X23)
| ~ topological_space(X23) )
| ~ spl61_103
| ~ spl61_126
| ~ spl61_182
| ~ spl61_199
| ~ spl61_369 ),
inference(forward_demodulation,[],[f3077,f1844]) ).
fof(f3077,plain,
( ! [X23] :
( ~ nowhere_dense(empty_set,X23)
| ~ open_subset(sK39(the_carrier(X23)),X23)
| sP8(X23,sK39(the_carrier(X23)))
| ~ top_str(X23)
| ~ topological_space(X23) )
| ~ spl61_126
| ~ spl61_182
| ~ spl61_199
| ~ spl61_369 ),
inference(forward_demodulation,[],[f3071,f1843]) ).
fof(f3071,plain,
( ! [X23] :
( ~ nowhere_dense(sK39(the_carrier(X23)),X23)
| ~ open_subset(sK39(the_carrier(X23)),X23)
| sP8(X23,sK39(the_carrier(X23)))
| ~ top_str(X23)
| ~ topological_space(X23) )
| ~ spl61_199
| ~ spl61_369 ),
inference(resolution,[],[f3029,f1823]) ).
fof(f5482,plain,
( spl61_684
| ~ spl61_273
| ~ spl61_360 ),
inference(avatar_split_clause,[],[f2932,f2826,f2200,f5480]) ).
fof(f5480,plain,
( spl61_684
<=> ! [X8] :
( ~ empty(sK24(X8))
| closed_subset(sK24(X8),X8)
| ~ top_str(X8)
| ~ topological_space(X8)
| ~ rel_str(X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_684])]) ).
fof(f2932,plain,
( ! [X8] :
( ~ empty(sK24(X8))
| closed_subset(sK24(X8),X8)
| ~ top_str(X8)
| ~ topological_space(X8)
| ~ rel_str(X8) )
| ~ spl61_273
| ~ spl61_360 ),
inference(resolution,[],[f2827,f2201]) ).
fof(f5478,plain,
( spl61_683
| ~ spl61_272
| ~ spl61_360 ),
inference(avatar_split_clause,[],[f2931,f2826,f2196,f5476]) ).
fof(f5476,plain,
( spl61_683
<=> ! [X7] :
( ~ empty(sK23(X7))
| closed_subset(sK23(X7),X7)
| ~ top_str(X7)
| ~ topological_space(X7)
| ~ rel_str(X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_683])]) ).
fof(f2931,plain,
( ! [X7] :
( ~ empty(sK23(X7))
| closed_subset(sK23(X7),X7)
| ~ top_str(X7)
| ~ topological_space(X7)
| ~ rel_str(X7) )
| ~ spl61_272
| ~ spl61_360 ),
inference(resolution,[],[f2827,f2197]) ).
fof(f5474,plain,
( spl61_682
| ~ spl61_264
| ~ spl61_360 ),
inference(avatar_split_clause,[],[f2930,f2826,f2163,f5472]) ).
fof(f5472,plain,
( spl61_682
<=> ! [X6] :
( ~ empty(sK18(X6))
| closed_subset(sK18(X6),X6)
| ~ top_str(X6)
| ~ topological_space(X6)
| ~ sP1(X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_682])]) ).
fof(f2930,plain,
( ! [X6] :
( ~ empty(sK18(X6))
| closed_subset(sK18(X6),X6)
| ~ top_str(X6)
| ~ topological_space(X6)
| ~ sP1(X6) )
| ~ spl61_264
| ~ spl61_360 ),
inference(resolution,[],[f2827,f2164]) ).
fof(f5470,plain,
( spl61_681
| ~ spl61_261
| ~ spl61_360 ),
inference(avatar_split_clause,[],[f2924,f2826,f2121,f5468]) ).
fof(f2924,plain,
( ! [X0,X1] :
( ~ empty(X0)
| closed_subset(X0,X1)
| ~ top_str(X1)
| ~ topological_space(X1)
| ~ subset(X0,the_carrier(X1)) )
| ~ spl61_261
| ~ spl61_360 ),
inference(resolution,[],[f2827,f2122]) ).
fof(f5466,plain,
( spl61_680
| ~ spl61_273
| ~ spl61_359 ),
inference(avatar_split_clause,[],[f2899,f2822,f2200,f5464]) ).
fof(f5464,plain,
( spl61_680
<=> ! [X8] :
( ~ empty(sK24(X8))
| open_subset(sK24(X8),X8)
| ~ top_str(X8)
| ~ topological_space(X8)
| ~ rel_str(X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_680])]) ).
fof(f2899,plain,
( ! [X8] :
( ~ empty(sK24(X8))
| open_subset(sK24(X8),X8)
| ~ top_str(X8)
| ~ topological_space(X8)
| ~ rel_str(X8) )
| ~ spl61_273
| ~ spl61_359 ),
inference(resolution,[],[f2823,f2201]) ).
fof(f5462,plain,
( spl61_679
| ~ spl61_272
| ~ spl61_359 ),
inference(avatar_split_clause,[],[f2898,f2822,f2196,f5460]) ).
fof(f5460,plain,
( spl61_679
<=> ! [X7] :
( ~ empty(sK23(X7))
| open_subset(sK23(X7),X7)
| ~ top_str(X7)
| ~ topological_space(X7)
| ~ rel_str(X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_679])]) ).
fof(f2898,plain,
( ! [X7] :
( ~ empty(sK23(X7))
| open_subset(sK23(X7),X7)
| ~ top_str(X7)
| ~ topological_space(X7)
| ~ rel_str(X7) )
| ~ spl61_272
| ~ spl61_359 ),
inference(resolution,[],[f2823,f2197]) ).
fof(f5458,plain,
( spl61_678
| ~ spl61_264
| ~ spl61_359 ),
inference(avatar_split_clause,[],[f2897,f2822,f2163,f5456]) ).
fof(f5456,plain,
( spl61_678
<=> ! [X6] :
( ~ empty(sK18(X6))
| open_subset(sK18(X6),X6)
| ~ top_str(X6)
| ~ topological_space(X6)
| ~ sP1(X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_678])]) ).
fof(f2897,plain,
( ! [X6] :
( ~ empty(sK18(X6))
| open_subset(sK18(X6),X6)
| ~ top_str(X6)
| ~ topological_space(X6)
| ~ sP1(X6) )
| ~ spl61_264
| ~ spl61_359 ),
inference(resolution,[],[f2823,f2164]) ).
fof(f5454,plain,
( spl61_677
| ~ spl61_261
| ~ spl61_359 ),
inference(avatar_split_clause,[],[f2891,f2822,f2121,f5452]) ).
fof(f2891,plain,
( ! [X0,X1] :
( ~ empty(X0)
| open_subset(X0,X1)
| ~ top_str(X1)
| ~ topological_space(X1)
| ~ subset(X0,the_carrier(X1)) )
| ~ spl61_261
| ~ spl61_359 ),
inference(resolution,[],[f2823,f2122]) ).
fof(f5450,plain,
( spl61_676
| ~ spl61_273
| ~ spl61_358 ),
inference(avatar_split_clause,[],[f2866,f2818,f2200,f5448]) ).
fof(f5448,plain,
( spl61_676
<=> ! [X8] :
( ~ empty(sK24(X8))
| nowhere_dense(sK24(X8),X8)
| ~ top_str(X8)
| ~ topological_space(X8)
| ~ rel_str(X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_676])]) ).
fof(f2866,plain,
( ! [X8] :
( ~ empty(sK24(X8))
| nowhere_dense(sK24(X8),X8)
| ~ top_str(X8)
| ~ topological_space(X8)
| ~ rel_str(X8) )
| ~ spl61_273
| ~ spl61_358 ),
inference(resolution,[],[f2819,f2201]) ).
fof(f5446,plain,
( spl61_675
| ~ spl61_272
| ~ spl61_358 ),
inference(avatar_split_clause,[],[f2865,f2818,f2196,f5444]) ).
fof(f5444,plain,
( spl61_675
<=> ! [X7] :
( ~ empty(sK23(X7))
| nowhere_dense(sK23(X7),X7)
| ~ top_str(X7)
| ~ topological_space(X7)
| ~ rel_str(X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_675])]) ).
fof(f2865,plain,
( ! [X7] :
( ~ empty(sK23(X7))
| nowhere_dense(sK23(X7),X7)
| ~ top_str(X7)
| ~ topological_space(X7)
| ~ rel_str(X7) )
| ~ spl61_272
| ~ spl61_358 ),
inference(resolution,[],[f2819,f2197]) ).
fof(f5442,plain,
( spl61_674
| ~ spl61_264
| ~ spl61_358 ),
inference(avatar_split_clause,[],[f2864,f2818,f2163,f5440]) ).
fof(f5440,plain,
( spl61_674
<=> ! [X6] :
( ~ empty(sK18(X6))
| nowhere_dense(sK18(X6),X6)
| ~ top_str(X6)
| ~ topological_space(X6)
| ~ sP1(X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_674])]) ).
fof(f2864,plain,
( ! [X6] :
( ~ empty(sK18(X6))
| nowhere_dense(sK18(X6),X6)
| ~ top_str(X6)
| ~ topological_space(X6)
| ~ sP1(X6) )
| ~ spl61_264
| ~ spl61_358 ),
inference(resolution,[],[f2819,f2164]) ).
fof(f5438,plain,
( spl61_673
| ~ spl61_265
| ~ spl61_358 ),
inference(avatar_split_clause,[],[f2859,f2818,f2167,f5436]) ).
fof(f5436,plain,
( spl61_673
<=> ! [X2] :
( ~ empty(cast_as_carrier_subset(X2))
| nowhere_dense(cast_as_carrier_subset(X2),X2)
| ~ top_str(X2)
| ~ topological_space(X2)
| ~ one_sorted_str(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_673])]) ).
fof(f2859,plain,
( ! [X2] :
( ~ empty(cast_as_carrier_subset(X2))
| nowhere_dense(cast_as_carrier_subset(X2),X2)
| ~ top_str(X2)
| ~ topological_space(X2)
| ~ one_sorted_str(X2) )
| ~ spl61_265
| ~ spl61_358 ),
inference(resolution,[],[f2819,f2168]) ).
fof(f5434,plain,
( spl61_672
| ~ spl61_12
| ~ spl61_411 ),
inference(avatar_split_clause,[],[f3520,f3511,f947,f5431]) ).
fof(f5431,plain,
( spl61_672
<=> relation_empty_yielding(sK60) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_672])]) ).
fof(f947,plain,
( spl61_12
<=> relation_empty_yielding(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_12])]) ).
fof(f3511,plain,
( spl61_411
<=> empty_set = sK60 ),
introduced(avatar_definition,[new_symbols(naming,[spl61_411])]) ).
fof(f3520,plain,
( relation_empty_yielding(sK60)
| ~ spl61_12
| ~ spl61_411 ),
inference(superposition,[],[f949,f3513]) ).
fof(f3513,plain,
( empty_set = sK60
| ~ spl61_411 ),
inference(avatar_component_clause,[],[f3511]) ).
fof(f949,plain,
( relation_empty_yielding(empty_set)
| ~ spl61_12 ),
inference(avatar_component_clause,[],[f947]) ).
fof(f5429,plain,
( spl61_671
| ~ spl61_261
| ~ spl61_358 ),
inference(avatar_split_clause,[],[f2858,f2818,f2121,f5427]) ).
fof(f2858,plain,
( ! [X0,X1] :
( ~ empty(X0)
| nowhere_dense(X0,X1)
| ~ top_str(X1)
| ~ topological_space(X1)
| ~ subset(X0,the_carrier(X1)) )
| ~ spl61_261
| ~ spl61_358 ),
inference(resolution,[],[f2819,f2122]) ).
fof(f5425,plain,
( spl61_670
| ~ spl61_260
| ~ spl61_357 ),
inference(avatar_split_clause,[],[f2856,f2814,f2117,f5423]) ).
fof(f5423,plain,
( spl61_670
<=> ! [X6] :
( ~ rel_str(X6)
| ~ transitive_relstr(X6)
| ~ reflexive_relstr(X6)
| empty_carrier(X6)
| subset(sK32(X6),the_carrier(X6)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_670])]) ).
fof(f2856,plain,
( ! [X6] :
( ~ rel_str(X6)
| ~ transitive_relstr(X6)
| ~ reflexive_relstr(X6)
| empty_carrier(X6)
| subset(sK32(X6),the_carrier(X6)) )
| ~ spl61_260
| ~ spl61_357 ),
inference(resolution,[],[f2815,f2118]) ).
fof(f5421,plain,
( spl61_669
| ~ spl61_260
| ~ spl61_356 ),
inference(avatar_split_clause,[],[f2850,f2810,f2117,f5419]) ).
fof(f5419,plain,
( spl61_669
<=> ! [X6] :
( ~ rel_str(X6)
| ~ transitive_relstr(X6)
| ~ reflexive_relstr(X6)
| empty_carrier(X6)
| subset(sK31(X6),the_carrier(X6)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_669])]) ).
fof(f2850,plain,
( ! [X6] :
( ~ rel_str(X6)
| ~ transitive_relstr(X6)
| ~ reflexive_relstr(X6)
| empty_carrier(X6)
| subset(sK31(X6),the_carrier(X6)) )
| ~ spl61_260
| ~ spl61_356 ),
inference(resolution,[],[f2811,f2118]) ).
fof(f5417,plain,
( spl61_668
| ~ spl61_240
| ~ spl61_353 ),
inference(avatar_split_clause,[],[f2798,f2784,f2010,f5415]) ).
fof(f5415,plain,
( spl61_668
<=> ! [X2,X3] :
( in(sK41(X2,X3),X3)
| X2 = X3
| ~ in(X2,sK41(X2,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_668])]) ).
fof(f2798,plain,
( ! [X2,X3] :
( in(sK41(X2,X3),X3)
| X2 = X3
| ~ in(X2,sK41(X2,X3)) )
| ~ spl61_240
| ~ spl61_353 ),
inference(resolution,[],[f2785,f2011]) ).
fof(f5413,plain,
( spl61_667
| ~ spl61_241
| ~ spl61_353 ),
inference(avatar_split_clause,[],[f2797,f2784,f2014,f5411]) ).
fof(f2797,plain,
( ! [X0,X1] :
( in(sK41(X0,X1),X1)
| X0 = X1
| element(sK41(X0,X1),X0) )
| ~ spl61_241
| ~ spl61_353 ),
inference(resolution,[],[f2785,f2015]) ).
fof(f5409,plain,
( spl61_666
| ~ spl61_240
| ~ spl61_353 ),
inference(avatar_split_clause,[],[f2795,f2784,f2010,f5407]) ).
fof(f5407,plain,
( spl61_666
<=> ! [X2,X3] :
( in(sK41(X2,X3),X2)
| X2 = X3
| ~ in(X3,sK41(X2,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_666])]) ).
fof(f2795,plain,
( ! [X2,X3] :
( in(sK41(X2,X3),X2)
| X2 = X3
| ~ in(X3,sK41(X2,X3)) )
| ~ spl61_240
| ~ spl61_353 ),
inference(resolution,[],[f2785,f2011]) ).
fof(f5405,plain,
( spl61_665
| ~ spl61_241
| ~ spl61_353 ),
inference(avatar_split_clause,[],[f2794,f2784,f2014,f5403]) ).
fof(f2794,plain,
( ! [X0,X1] :
( in(sK41(X0,X1),X0)
| X0 = X1
| element(sK41(X0,X1),X1) )
| ~ spl61_241
| ~ spl61_353 ),
inference(resolution,[],[f2785,f2015]) ).
fof(f5401,plain,
( spl61_664
| ~ spl61_300
| ~ spl61_352 ),
inference(avatar_split_clause,[],[f2793,f2780,f2310,f5399]) ).
fof(f2310,plain,
( spl61_300
<=> ! [X2,X0,X1] :
( relation_of2(X2,X0,X1)
| ~ relation_of2_as_subset(X2,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_300])]) ).
fof(f2793,plain,
( ! [X0,X1] :
( ~ net_str(X0,X1)
| ~ one_sorted_str(X1)
| relation_of2(the_mapping(X1,X0),the_carrier(X0),the_carrier(X1)) )
| ~ spl61_300
| ~ spl61_352 ),
inference(resolution,[],[f2781,f2311]) ).
fof(f2311,plain,
( ! [X2,X0,X1] :
( ~ relation_of2_as_subset(X2,X0,X1)
| relation_of2(X2,X0,X1) )
| ~ spl61_300 ),
inference(avatar_component_clause,[],[f2310]) ).
fof(f5397,plain,
( spl61_663
| ~ spl61_132
| ~ spl61_350 ),
inference(avatar_split_clause,[],[f2792,f2772,f1521,f5395]) ).
fof(f5395,plain,
( spl61_663
<=> ! [X0,X1] :
( ~ net_str(X0,X1)
| empty_carrier(X0)
| ~ one_sorted_str(X1)
| empty_carrier(X1)
| sP0(filter_of_net_str(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_663])]) ).
fof(f2772,plain,
( spl61_350
<=> ! [X0,X1] :
( ~ empty(filter_of_net_str(X0,X1))
| ~ net_str(X1,X0)
| empty_carrier(X1)
| ~ one_sorted_str(X0)
| empty_carrier(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_350])]) ).
fof(f2792,plain,
( ! [X0,X1] :
( ~ net_str(X0,X1)
| empty_carrier(X0)
| ~ one_sorted_str(X1)
| empty_carrier(X1)
| sP0(filter_of_net_str(X1,X0)) )
| ~ spl61_132
| ~ spl61_350 ),
inference(resolution,[],[f2773,f1522]) ).
fof(f2773,plain,
( ! [X0,X1] :
( ~ empty(filter_of_net_str(X0,X1))
| ~ net_str(X1,X0)
| empty_carrier(X1)
| ~ one_sorted_str(X0)
| empty_carrier(X0) )
| ~ spl61_350 ),
inference(avatar_component_clause,[],[f2772]) ).
fof(f5393,plain,
( spl61_662
| ~ spl61_132
| ~ spl61_348 ),
inference(avatar_split_clause,[],[f2791,f2764,f1521,f5391]) ).
fof(f5391,plain,
( spl61_662
<=> ! [X0,X1] :
( ~ net_str(X0,X1)
| empty_carrier(X0)
| ~ one_sorted_str(X1)
| empty_carrier(X1)
| sP0(the_mapping(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_662])]) ).
fof(f2764,plain,
( spl61_348
<=> ! [X0,X1] :
( ~ empty(the_mapping(X0,X1))
| ~ net_str(X1,X0)
| empty_carrier(X1)
| ~ one_sorted_str(X0)
| empty_carrier(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_348])]) ).
fof(f2791,plain,
( ! [X0,X1] :
( ~ net_str(X0,X1)
| empty_carrier(X0)
| ~ one_sorted_str(X1)
| empty_carrier(X1)
| sP0(the_mapping(X1,X0)) )
| ~ spl61_132
| ~ spl61_348 ),
inference(resolution,[],[f2765,f1522]) ).
fof(f2765,plain,
( ! [X0,X1] :
( ~ empty(the_mapping(X0,X1))
| ~ net_str(X1,X0)
| empty_carrier(X1)
| ~ one_sorted_str(X0)
| empty_carrier(X0) )
| ~ spl61_348 ),
inference(avatar_component_clause,[],[f2764]) ).
fof(f5389,plain,
( spl61_661
| ~ spl61_135
| ~ spl61_402 ),
inference(avatar_split_clause,[],[f3486,f3456,f1533,f5386]) ).
fof(f5386,plain,
( spl61_661
<=> sP2(sK59) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_661])]) ).
fof(f3456,plain,
( spl61_402
<=> one_sorted_str(sK59) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_402])]) ).
fof(f3486,plain,
( sP2(sK59)
| ~ spl61_135
| ~ spl61_402 ),
inference(resolution,[],[f3458,f1534]) ).
fof(f3458,plain,
( one_sorted_str(sK59)
| ~ spl61_402 ),
inference(avatar_component_clause,[],[f3456]) ).
fof(f5384,plain,
( spl61_660
| ~ spl61_315
| ~ spl61_342 ),
inference(avatar_split_clause,[],[f2758,f2689,f2457,f5382]) ).
fof(f2758,plain,
( ! [X3,X4] :
( ~ top_str(X3)
| ~ topological_space(X3)
| empty_carrier(X3)
| ~ empty(the_carrier(X3))
| ~ in(X4,sK27(X3)) )
| ~ spl61_315
| ~ spl61_342 ),
inference(resolution,[],[f2690,f2458]) ).
fof(f5380,plain,
( spl61_659
| ~ spl61_315
| ~ spl61_341 ),
inference(avatar_split_clause,[],[f2751,f2685,f2457,f5378]) ).
fof(f2751,plain,
( ! [X3,X4] :
( ~ top_str(X3)
| ~ topological_space(X3)
| empty_carrier(X3)
| ~ empty(the_carrier(X3))
| ~ in(X4,sK26(X3)) )
| ~ spl61_315
| ~ spl61_341 ),
inference(resolution,[],[f2686,f2458]) ).
fof(f5376,plain,
( spl61_658
| ~ spl61_159
| ~ spl61_339 ),
inference(avatar_split_clause,[],[f2726,f2677,f1629,f5374]) ).
fof(f5374,plain,
( spl61_658
<=> ! [X18] :
( ~ empty(sK38(powerset(the_carrier(X18))))
| boundary_set(sK38(powerset(the_carrier(X18))),X18)
| ~ top_str(X18) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_658])]) ).
fof(f2726,plain,
( ! [X18] :
( ~ empty(sK38(powerset(the_carrier(X18))))
| boundary_set(sK38(powerset(the_carrier(X18))),X18)
| ~ top_str(X18) )
| ~ spl61_159
| ~ spl61_339 ),
inference(resolution,[],[f2678,f1630]) ).
fof(f5372,plain,
( spl61_657
| ~ spl61_107
| ~ spl61_336 ),
inference(avatar_split_clause,[],[f2665,f2654,f1420,f5370]) ).
fof(f1420,plain,
( spl61_107
<=> ! [X0] : strict_rel_str(boole_POSet(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_107])]) ).
fof(f2654,plain,
( spl61_336
<=> ! [X0] :
( rel_str_of(the_carrier(X0),the_InternalRel(X0)) = X0
| ~ strict_rel_str(X0)
| ~ rel_str(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_336])]) ).
fof(f2665,plain,
( ! [X0] :
( boole_POSet(X0) = rel_str_of(the_carrier(boole_POSet(X0)),the_InternalRel(boole_POSet(X0)))
| ~ rel_str(boole_POSet(X0)) )
| ~ spl61_107
| ~ spl61_336 ),
inference(resolution,[],[f2655,f1421]) ).
fof(f1421,plain,
( ! [X0] : strict_rel_str(boole_POSet(X0))
| ~ spl61_107 ),
inference(avatar_component_clause,[],[f1420]) ).
fof(f2655,plain,
( ! [X0] :
( ~ strict_rel_str(X0)
| rel_str_of(the_carrier(X0),the_InternalRel(X0)) = X0
| ~ rel_str(X0) )
| ~ spl61_336 ),
inference(avatar_component_clause,[],[f2654]) ).
fof(f5357,plain,
( spl61_656
| ~ spl61_135
| ~ spl61_401 ),
inference(avatar_split_clause,[],[f3485,f3451,f1533,f5354]) ).
fof(f5354,plain,
( spl61_656
<=> sP2(sK58) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_656])]) ).
fof(f3451,plain,
( spl61_401
<=> one_sorted_str(sK58) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_401])]) ).
fof(f3485,plain,
( sP2(sK58)
| ~ spl61_135
| ~ spl61_401 ),
inference(resolution,[],[f3453,f1534]) ).
fof(f3453,plain,
( one_sorted_str(sK58)
| ~ spl61_401 ),
inference(avatar_component_clause,[],[f3451]) ).
fof(f5312,plain,
( spl61_655
| ~ spl61_135
| ~ spl61_400 ),
inference(avatar_split_clause,[],[f3484,f3446,f1533,f5309]) ).
fof(f5309,plain,
( spl61_655
<=> sP2(sK57) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_655])]) ).
fof(f3446,plain,
( spl61_400
<=> one_sorted_str(sK57) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_400])]) ).
fof(f3484,plain,
( sP2(sK57)
| ~ spl61_135
| ~ spl61_400 ),
inference(resolution,[],[f3448,f1534]) ).
fof(f3448,plain,
( one_sorted_str(sK57)
| ~ spl61_400 ),
inference(avatar_component_clause,[],[f3446]) ).
fof(f5297,plain,
( spl61_654
| ~ spl61_330
| ~ spl61_364 ),
inference(avatar_split_clause,[],[f2995,f2966,f2553,f5295]) ).
fof(f5295,plain,
( spl61_654
<=> ! [X18] :
( ~ nowhere_dense(sK34(X18),X18)
| boundary_set(sK34(X18),X18)
| ~ top_str(X18)
| ~ topological_space(X18) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_654])]) ).
fof(f2995,plain,
( ! [X18] :
( ~ nowhere_dense(sK34(X18),X18)
| boundary_set(sK34(X18),X18)
| ~ top_str(X18)
| ~ topological_space(X18) )
| ~ spl61_330
| ~ spl61_364 ),
inference(duplicate_literal_removal,[],[f2987]) ).
fof(f2987,plain,
( ! [X18] :
( ~ nowhere_dense(sK34(X18),X18)
| boundary_set(sK34(X18),X18)
| ~ top_str(X18)
| ~ topological_space(X18)
| ~ top_str(X18)
| ~ topological_space(X18) )
| ~ spl61_330
| ~ spl61_364 ),
inference(resolution,[],[f2967,f2554]) ).
fof(f5293,plain,
( spl61_653
| ~ spl61_331
| ~ spl61_364 ),
inference(avatar_split_clause,[],[f2994,f2966,f2557,f5291]) ).
fof(f5291,plain,
( spl61_653
<=> ! [X19] :
( ~ nowhere_dense(sK35(X19),X19)
| boundary_set(sK35(X19),X19)
| ~ top_str(X19)
| ~ topological_space(X19) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_653])]) ).
fof(f2994,plain,
( ! [X19] :
( ~ nowhere_dense(sK35(X19),X19)
| boundary_set(sK35(X19),X19)
| ~ top_str(X19)
| ~ topological_space(X19) )
| ~ spl61_331
| ~ spl61_364 ),
inference(duplicate_literal_removal,[],[f2988]) ).
fof(f2988,plain,
( ! [X19] :
( ~ nowhere_dense(sK35(X19),X19)
| boundary_set(sK35(X19),X19)
| ~ top_str(X19)
| ~ topological_space(X19)
| ~ top_str(X19)
| ~ topological_space(X19) )
| ~ spl61_331
| ~ spl61_364 ),
inference(resolution,[],[f2967,f2558]) ).
fof(f5289,plain,
( spl61_652
| ~ spl61_332
| ~ spl61_364 ),
inference(avatar_split_clause,[],[f2993,f2966,f2561,f5287]) ).
fof(f5287,plain,
( spl61_652
<=> ! [X20] :
( ~ nowhere_dense(sK36(X20),X20)
| boundary_set(sK36(X20),X20)
| ~ top_str(X20)
| ~ topological_space(X20) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_652])]) ).
fof(f2993,plain,
( ! [X20] :
( ~ nowhere_dense(sK36(X20),X20)
| boundary_set(sK36(X20),X20)
| ~ top_str(X20)
| ~ topological_space(X20) )
| ~ spl61_332
| ~ spl61_364 ),
inference(duplicate_literal_removal,[],[f2989]) ).
fof(f2989,plain,
( ! [X20] :
( ~ nowhere_dense(sK36(X20),X20)
| boundary_set(sK36(X20),X20)
| ~ top_str(X20)
| ~ topological_space(X20)
| ~ top_str(X20)
| ~ topological_space(X20) )
| ~ spl61_332
| ~ spl61_364 ),
inference(resolution,[],[f2967,f2562]) ).
fof(f5285,plain,
( ~ spl61_94
| ~ spl61_95
| ~ spl61_96
| ~ spl61_97
| spl61_651
| ~ spl61_92
| ~ spl61_98
| ~ spl61_361 ),
inference(avatar_split_clause,[],[f2962,f2830,f1377,f1347,f5282,f1372,f1367,f1362,f1357]) ).
fof(f5282,plain,
( spl61_651
<=> sP10(sK59) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_651])]) ).
fof(f1377,plain,
( spl61_98
<=> with_infima_relstr(sK59) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_98])]) ).
fof(f2962,plain,
( ~ rel_str(sK59)
| sP10(sK59)
| ~ with_suprema_relstr(sK59)
| ~ antisymmetric_relstr(sK59)
| ~ transitive_relstr(sK59)
| ~ reflexive_relstr(sK59)
| ~ spl61_98
| ~ spl61_361 ),
inference(resolution,[],[f2831,f1379]) ).
fof(f1379,plain,
( with_infima_relstr(sK59)
| ~ spl61_98 ),
inference(avatar_component_clause,[],[f1377]) ).
fof(f5280,plain,
( ~ spl61_75
| ~ spl61_76
| ~ spl61_77
| ~ spl61_78
| spl61_650
| ~ spl61_72
| ~ spl61_79
| ~ spl61_361 ),
inference(avatar_split_clause,[],[f2961,f2830,f1282,f1247,f5277,f1277,f1272,f1267,f1262]) ).
fof(f5277,plain,
( spl61_650
<=> sP10(sK57) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_650])]) ).
fof(f1282,plain,
( spl61_79
<=> with_infima_relstr(sK57) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_79])]) ).
fof(f2961,plain,
( ~ rel_str(sK57)
| sP10(sK57)
| ~ with_suprema_relstr(sK57)
| ~ antisymmetric_relstr(sK57)
| ~ transitive_relstr(sK57)
| ~ reflexive_relstr(sK57)
| ~ spl61_79
| ~ spl61_361 ),
inference(resolution,[],[f2831,f1284]) ).
fof(f1284,plain,
( with_infima_relstr(sK57)
| ~ spl61_79 ),
inference(avatar_component_clause,[],[f1282]) ).
fof(f5275,plain,
( spl61_649
| ~ spl61_135
| ~ spl61_299 ),
inference(avatar_split_clause,[],[f3483,f2305,f1533,f5272]) ).
fof(f5272,plain,
( spl61_649
<=> sP2(sK56) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_649])]) ).
fof(f2305,plain,
( spl61_299
<=> one_sorted_str(sK56) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_299])]) ).
fof(f3483,plain,
( sP2(sK56)
| ~ spl61_135
| ~ spl61_299 ),
inference(resolution,[],[f2307,f1534]) ).
fof(f2307,plain,
( one_sorted_str(sK56)
| ~ spl61_299 ),
inference(avatar_component_clause,[],[f2305]) ).
fof(f5270,plain,
( ~ spl61_65
| ~ spl61_66
| ~ spl61_67
| ~ spl61_68
| spl61_648
| ~ spl61_62
| ~ spl61_69
| ~ spl61_361 ),
inference(avatar_split_clause,[],[f2960,f2830,f1232,f1197,f5267,f1227,f1222,f1217,f1212]) ).
fof(f5267,plain,
( spl61_648
<=> sP10(sK56) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_648])]) ).
fof(f1232,plain,
( spl61_69
<=> with_infima_relstr(sK56) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_69])]) ).
fof(f2960,plain,
( ~ rel_str(sK56)
| sP10(sK56)
| ~ with_suprema_relstr(sK56)
| ~ antisymmetric_relstr(sK56)
| ~ transitive_relstr(sK56)
| ~ reflexive_relstr(sK56)
| ~ spl61_69
| ~ spl61_361 ),
inference(resolution,[],[f2831,f1234]) ).
fof(f1234,plain,
( with_infima_relstr(sK56)
| ~ spl61_69 ),
inference(avatar_component_clause,[],[f1232]) ).
fof(f5265,plain,
( ~ spl61_56
| ~ spl61_57
| ~ spl61_58
| ~ spl61_59
| spl61_647
| ~ spl61_53
| ~ spl61_60
| ~ spl61_361 ),
inference(avatar_split_clause,[],[f2959,f2830,f1187,f1152,f5262,f1182,f1177,f1172,f1167]) ).
fof(f5262,plain,
( spl61_647
<=> sP10(sK55) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_647])]) ).
fof(f1187,plain,
( spl61_60
<=> with_infima_relstr(sK55) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_60])]) ).
fof(f2959,plain,
( ~ rel_str(sK55)
| sP10(sK55)
| ~ with_suprema_relstr(sK55)
| ~ antisymmetric_relstr(sK55)
| ~ transitive_relstr(sK55)
| ~ reflexive_relstr(sK55)
| ~ spl61_60
| ~ spl61_361 ),
inference(resolution,[],[f2831,f1189]) ).
fof(f1189,plain,
( with_infima_relstr(sK55)
| ~ spl61_60 ),
inference(avatar_component_clause,[],[f1187]) ).
fof(f5260,plain,
( ~ spl61_28
| ~ spl61_29
| ~ spl61_30
| ~ spl61_39
| spl61_646
| ~ spl61_24
| ~ spl61_40
| ~ spl61_361 ),
inference(avatar_split_clause,[],[f2958,f2830,f1087,f1007,f5257,f1082,f1037,f1032,f1027]) ).
fof(f5257,plain,
( spl61_646
<=> sP10(sK52) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_646])]) ).
fof(f1087,plain,
( spl61_40
<=> with_infima_relstr(sK52) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_40])]) ).
fof(f2958,plain,
( ~ rel_str(sK52)
| sP10(sK52)
| ~ with_suprema_relstr(sK52)
| ~ antisymmetric_relstr(sK52)
| ~ transitive_relstr(sK52)
| ~ reflexive_relstr(sK52)
| ~ spl61_40
| ~ spl61_361 ),
inference(resolution,[],[f2831,f1089]) ).
fof(f1089,plain,
( with_infima_relstr(sK52)
| ~ spl61_40 ),
inference(avatar_component_clause,[],[f1087]) ).
fof(f5250,plain,
( ~ spl61_92
| spl61_93
| ~ spl61_94
| ~ spl61_96
| spl61_645
| ~ spl61_527
| ~ spl61_101
| ~ spl61_355 ),
inference(avatar_split_clause,[],[f2845,f2806,f1392,f4404,f5247,f1367,f1357,f1352,f1347]) ).
fof(f5247,plain,
( spl61_645
<=> sP4(sK59) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_645])]) ).
fof(f4404,plain,
( spl61_527
<=> join_complete_relstr(sK59) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_527])]) ).
fof(f2845,plain,
( ~ join_complete_relstr(sK59)
| sP4(sK59)
| ~ antisymmetric_relstr(sK59)
| ~ reflexive_relstr(sK59)
| empty_carrier(sK59)
| ~ rel_str(sK59)
| ~ spl61_101
| ~ spl61_355 ),
inference(resolution,[],[f2807,f1394]) ).
fof(f5240,plain,
( ~ spl61_72
| spl61_73
| ~ spl61_75
| ~ spl61_77
| spl61_644
| ~ spl61_85
| ~ spl61_82
| ~ spl61_355 ),
inference(avatar_split_clause,[],[f2844,f2806,f1297,f1312,f5237,f1272,f1262,f1252,f1247]) ).
fof(f5237,plain,
( spl61_644
<=> sP4(sK57) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_644])]) ).
fof(f1312,plain,
( spl61_85
<=> join_complete_relstr(sK57) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_85])]) ).
fof(f2844,plain,
( ~ join_complete_relstr(sK57)
| sP4(sK57)
| ~ antisymmetric_relstr(sK57)
| ~ reflexive_relstr(sK57)
| empty_carrier(sK57)
| ~ rel_str(sK57)
| ~ spl61_82
| ~ spl61_355 ),
inference(resolution,[],[f2807,f1299]) ).
fof(f5235,plain,
( ~ spl61_24
| spl61_25
| ~ spl61_28
| ~ spl61_30
| spl61_642
| ~ spl61_643
| ~ spl61_32
| ~ spl61_355 ),
inference(avatar_split_clause,[],[f2843,f2806,f1047,f5232,f5228,f1037,f1027,f1012,f1007]) ).
fof(f5228,plain,
( spl61_642
<=> sP4(sK52) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_642])]) ).
fof(f5232,plain,
( spl61_643
<=> join_complete_relstr(sK52) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_643])]) ).
fof(f2843,plain,
( ~ join_complete_relstr(sK52)
| sP4(sK52)
| ~ antisymmetric_relstr(sK52)
| ~ reflexive_relstr(sK52)
| empty_carrier(sK52)
| ~ rel_str(sK52)
| ~ spl61_32
| ~ spl61_355 ),
inference(resolution,[],[f2807,f1049]) ).
fof(f5226,plain,
( spl61_641
| ~ spl61_266
| ~ spl61_342 ),
inference(avatar_split_clause,[],[f2759,f2689,f2171,f5224]) ).
fof(f5224,plain,
( spl61_641
<=> ! [X5] :
( ~ top_str(X5)
| ~ topological_space(X5)
| empty_carrier(X5)
| finite(sK27(X5))
| ~ finite(the_carrier(X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_641])]) ).
fof(f2759,plain,
( ! [X5] :
( ~ top_str(X5)
| ~ topological_space(X5)
| empty_carrier(X5)
| finite(sK27(X5))
| ~ finite(the_carrier(X5)) )
| ~ spl61_266
| ~ spl61_342 ),
inference(resolution,[],[f2690,f2172]) ).
fof(f5222,plain,
( spl61_640
| ~ spl61_266
| ~ spl61_341 ),
inference(avatar_split_clause,[],[f2752,f2685,f2171,f5220]) ).
fof(f5220,plain,
( spl61_640
<=> ! [X5] :
( ~ top_str(X5)
| ~ topological_space(X5)
| empty_carrier(X5)
| finite(sK26(X5))
| ~ finite(the_carrier(X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_640])]) ).
fof(f2752,plain,
( ! [X5] :
( ~ top_str(X5)
| ~ topological_space(X5)
| empty_carrier(X5)
| finite(sK26(X5))
| ~ finite(the_carrier(X5)) )
| ~ spl61_266
| ~ spl61_341 ),
inference(resolution,[],[f2686,f2172]) ).
fof(f5218,plain,
( spl61_639
| ~ spl61_332
| ~ spl61_335 ),
inference(avatar_split_clause,[],[f2646,f2573,f2561,f5216]) ).
fof(f2646,plain,
( ! [X38,X39] :
( element(X38,the_carrier(X39))
| ~ in(X38,sK36(X39))
| ~ top_str(X39)
| ~ topological_space(X39) )
| ~ spl61_332
| ~ spl61_335 ),
inference(resolution,[],[f2574,f2562]) ).
fof(f5214,plain,
( spl61_638
| ~ spl61_331
| ~ spl61_335 ),
inference(avatar_split_clause,[],[f2645,f2573,f2557,f5212]) ).
fof(f2645,plain,
( ! [X36,X37] :
( element(X36,the_carrier(X37))
| ~ in(X36,sK35(X37))
| ~ top_str(X37)
| ~ topological_space(X37) )
| ~ spl61_331
| ~ spl61_335 ),
inference(resolution,[],[f2574,f2558]) ).
fof(f5210,plain,
( spl61_637
| ~ spl61_330
| ~ spl61_335 ),
inference(avatar_split_clause,[],[f2644,f2573,f2553,f5208]) ).
fof(f2644,plain,
( ! [X34,X35] :
( element(X34,the_carrier(X35))
| ~ in(X34,sK34(X35))
| ~ top_str(X35)
| ~ topological_space(X35) )
| ~ spl61_330
| ~ spl61_335 ),
inference(resolution,[],[f2574,f2554]) ).
fof(f5206,plain,
( spl61_636
| ~ spl61_329
| ~ spl61_335 ),
inference(avatar_split_clause,[],[f2641,f2573,f2541,f5204]) ).
fof(f2641,plain,
( ! [X28,X29] :
( element(X28,the_carrier(X29))
| ~ in(X28,sK29(X29))
| ~ rel_str(X29)
| empty_carrier(X29) )
| ~ spl61_329
| ~ spl61_335 ),
inference(resolution,[],[f2574,f2542]) ).
fof(f5202,plain,
( spl61_635
| ~ spl61_326
| ~ spl61_335 ),
inference(avatar_split_clause,[],[f2640,f2573,f2529,f5200]) ).
fof(f2640,plain,
( ! [X26,X27] :
( element(X26,the_carrier(X27))
| ~ in(X26,sK28(X27))
| ~ one_sorted_str(X27)
| empty_carrier(X27) )
| ~ spl61_326
| ~ spl61_335 ),
inference(resolution,[],[f2574,f2530]) ).
fof(f5198,plain,
( spl61_634
| ~ spl61_333
| ~ spl61_335 ),
inference(avatar_split_clause,[],[f2629,f2573,f2565,f5196]) ).
fof(f2629,plain,
( ! [X3,X6,X4,X5] :
( element(X3,cartesian_product2(X4,X5))
| ~ in(X3,X6)
| ~ relation_of2_as_subset(X6,X4,X5) )
| ~ spl61_333
| ~ spl61_335 ),
inference(resolution,[],[f2574,f2566]) ).
fof(f5194,plain,
( spl61_633
| ~ spl61_135
| ~ spl61_288 ),
inference(avatar_split_clause,[],[f3482,f2260,f1533,f5191]) ).
fof(f5191,plain,
( spl61_633
<=> sP2(sK55) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_633])]) ).
fof(f2260,plain,
( spl61_288
<=> one_sorted_str(sK55) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_288])]) ).
fof(f3482,plain,
( sP2(sK55)
| ~ spl61_135
| ~ spl61_288 ),
inference(resolution,[],[f2262,f1534]) ).
fof(f2262,plain,
( one_sorted_str(sK55)
| ~ spl61_288 ),
inference(avatar_component_clause,[],[f2260]) ).
fof(f5189,plain,
( spl61_632
| ~ spl61_292
| ~ spl61_293 ),
inference(avatar_split_clause,[],[f2394,f2281,f2277,f5187]) ).
fof(f2394,plain,
( ! [X12] :
( empty(powerset(the_carrier(X12)))
| in(sK37(X12),powerset(the_carrier(X12)))
| ~ sP10(X12) )
| ~ spl61_292
| ~ spl61_293 ),
inference(resolution,[],[f2282,f2278]) ).
fof(f5185,plain,
( spl61_631
| ~ spl61_284
| ~ spl61_293 ),
inference(avatar_split_clause,[],[f2393,f2281,f2244,f5183]) ).
fof(f2393,plain,
( ! [X11] :
( empty(powerset(the_carrier(X11)))
| in(sK33(X11),powerset(the_carrier(X11)))
| ~ sP9(X11) )
| ~ spl61_284
| ~ spl61_293 ),
inference(resolution,[],[f2282,f2245]) ).
fof(f5181,plain,
( spl61_630
| ~ spl61_280
| ~ spl61_293 ),
inference(avatar_split_clause,[],[f2392,f2281,f2228,f5179]) ).
fof(f2392,plain,
( ! [X10] :
( empty(powerset(the_carrier(X10)))
| in(sK30(X10),powerset(the_carrier(X10)))
| ~ sP7(X10) )
| ~ spl61_280
| ~ spl61_293 ),
inference(resolution,[],[f2282,f2229]) ).
fof(f5177,plain,
( spl61_629
| ~ spl61_274
| ~ spl61_293 ),
inference(avatar_split_clause,[],[f2391,f2281,f2204,f5175]) ).
fof(f2391,plain,
( ! [X9] :
( empty(powerset(the_carrier(X9)))
| in(sK25(X9),powerset(the_carrier(X9)))
| ~ sP6(X9) )
| ~ spl61_274
| ~ spl61_293 ),
inference(resolution,[],[f2282,f2205]) ).
fof(f5173,plain,
( spl61_628
| ~ spl61_273
| ~ spl61_293 ),
inference(avatar_split_clause,[],[f2390,f2281,f2200,f5171]) ).
fof(f2390,plain,
( ! [X8] :
( empty(powerset(the_carrier(X8)))
| in(sK24(X8),powerset(the_carrier(X8)))
| ~ rel_str(X8) )
| ~ spl61_273
| ~ spl61_293 ),
inference(resolution,[],[f2282,f2201]) ).
fof(f5169,plain,
( spl61_627
| ~ spl61_272
| ~ spl61_293 ),
inference(avatar_split_clause,[],[f2389,f2281,f2196,f5167]) ).
fof(f2389,plain,
( ! [X7] :
( empty(powerset(the_carrier(X7)))
| in(sK23(X7),powerset(the_carrier(X7)))
| ~ rel_str(X7) )
| ~ spl61_272
| ~ spl61_293 ),
inference(resolution,[],[f2282,f2197]) ).
fof(f5165,plain,
( spl61_626
| ~ spl61_264
| ~ spl61_293 ),
inference(avatar_split_clause,[],[f2388,f2281,f2163,f5163]) ).
fof(f2388,plain,
( ! [X6] :
( empty(powerset(the_carrier(X6)))
| in(sK18(X6),powerset(the_carrier(X6)))
| ~ sP1(X6) )
| ~ spl61_264
| ~ spl61_293 ),
inference(resolution,[],[f2282,f2164]) ).
fof(f5161,plain,
( spl61_625
| ~ spl61_265
| ~ spl61_293 ),
inference(avatar_split_clause,[],[f2382,f2281,f2167,f5159]) ).
fof(f2382,plain,
( ! [X2] :
( empty(powerset(the_carrier(X2)))
| in(cast_as_carrier_subset(X2),powerset(the_carrier(X2)))
| ~ one_sorted_str(X2) )
| ~ spl61_265
| ~ spl61_293 ),
inference(resolution,[],[f2282,f2168]) ).
fof(f5147,plain,
( ~ spl61_247
| spl61_624
| ~ spl61_233
| ~ spl61_478 ),
inference(avatar_split_clause,[],[f4138,f4101,f1982,f5144,f2063]) ).
fof(f2063,plain,
( spl61_247
<=> sP9(sK12) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_247])]) ).
fof(f5144,plain,
( spl61_624
<=> nowhere_dense(sK60,sK12) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_624])]) ).
fof(f1982,plain,
( spl61_233
<=> ! [X0] :
( nowhere_dense(sK33(X0),X0)
| ~ sP9(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_233])]) ).
fof(f4101,plain,
( spl61_478
<=> sK60 = sK33(sK12) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_478])]) ).
fof(f4138,plain,
( nowhere_dense(sK60,sK12)
| ~ sP9(sK12)
| ~ spl61_233
| ~ spl61_478 ),
inference(superposition,[],[f1983,f4103]) ).
fof(f4103,plain,
( sK60 = sK33(sK12)
| ~ spl61_478 ),
inference(avatar_component_clause,[],[f4101]) ).
fof(f1983,plain,
( ! [X0] :
( nowhere_dense(sK33(X0),X0)
| ~ sP9(X0) )
| ~ spl61_233 ),
inference(avatar_component_clause,[],[f1982]) ).
fof(f5068,plain,
( spl61_623
| ~ spl61_330
| ~ spl61_360 ),
inference(avatar_split_clause,[],[f2950,f2826,f2553,f5066]) ).
fof(f5066,plain,
( spl61_623
<=> ! [X18] :
( ~ empty(sK34(X18))
| closed_subset(sK34(X18),X18)
| ~ top_str(X18)
| ~ topological_space(X18) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_623])]) ).
fof(f2950,plain,
( ! [X18] :
( ~ empty(sK34(X18))
| closed_subset(sK34(X18),X18)
| ~ top_str(X18)
| ~ topological_space(X18) )
| ~ spl61_330
| ~ spl61_360 ),
inference(duplicate_literal_removal,[],[f2942]) ).
fof(f2942,plain,
( ! [X18] :
( ~ empty(sK34(X18))
| closed_subset(sK34(X18),X18)
| ~ top_str(X18)
| ~ topological_space(X18)
| ~ top_str(X18)
| ~ topological_space(X18) )
| ~ spl61_330
| ~ spl61_360 ),
inference(resolution,[],[f2827,f2554]) ).
fof(f5064,plain,
( spl61_622
| ~ spl61_332
| ~ spl61_359 ),
inference(avatar_split_clause,[],[f2915,f2822,f2561,f5062]) ).
fof(f5062,plain,
( spl61_622
<=> ! [X20] :
( ~ empty(sK36(X20))
| open_subset(sK36(X20),X20)
| ~ top_str(X20)
| ~ topological_space(X20) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_622])]) ).
fof(f2915,plain,
( ! [X20] :
( ~ empty(sK36(X20))
| open_subset(sK36(X20),X20)
| ~ top_str(X20)
| ~ topological_space(X20) )
| ~ spl61_332
| ~ spl61_359 ),
inference(duplicate_literal_removal,[],[f2911]) ).
fof(f2911,plain,
( ! [X20] :
( ~ empty(sK36(X20))
| open_subset(sK36(X20),X20)
| ~ top_str(X20)
| ~ topological_space(X20)
| ~ top_str(X20)
| ~ topological_space(X20) )
| ~ spl61_332
| ~ spl61_359 ),
inference(resolution,[],[f2823,f2562]) ).
fof(f5060,plain,
( spl61_621
| ~ spl61_330
| ~ spl61_358 ),
inference(avatar_split_clause,[],[f2884,f2818,f2553,f5058]) ).
fof(f5058,plain,
( spl61_621
<=> ! [X18] :
( ~ empty(sK34(X18))
| nowhere_dense(sK34(X18),X18)
| ~ top_str(X18)
| ~ topological_space(X18) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_621])]) ).
fof(f2884,plain,
( ! [X18] :
( ~ empty(sK34(X18))
| nowhere_dense(sK34(X18),X18)
| ~ top_str(X18)
| ~ topological_space(X18) )
| ~ spl61_330
| ~ spl61_358 ),
inference(duplicate_literal_removal,[],[f2876]) ).
fof(f2876,plain,
( ! [X18] :
( ~ empty(sK34(X18))
| nowhere_dense(sK34(X18),X18)
| ~ top_str(X18)
| ~ topological_space(X18)
| ~ top_str(X18)
| ~ topological_space(X18) )
| ~ spl61_330
| ~ spl61_358 ),
inference(resolution,[],[f2819,f2554]) ).
fof(f5056,plain,
( spl61_620
| ~ spl61_331
| ~ spl61_358 ),
inference(avatar_split_clause,[],[f2883,f2818,f2557,f5054]) ).
fof(f5054,plain,
( spl61_620
<=> ! [X19] :
( ~ empty(sK35(X19))
| nowhere_dense(sK35(X19),X19)
| ~ top_str(X19)
| ~ topological_space(X19) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_620])]) ).
fof(f2883,plain,
( ! [X19] :
( ~ empty(sK35(X19))
| nowhere_dense(sK35(X19),X19)
| ~ top_str(X19)
| ~ topological_space(X19) )
| ~ spl61_331
| ~ spl61_358 ),
inference(duplicate_literal_removal,[],[f2877]) ).
fof(f2877,plain,
( ! [X19] :
( ~ empty(sK35(X19))
| nowhere_dense(sK35(X19),X19)
| ~ top_str(X19)
| ~ topological_space(X19)
| ~ top_str(X19)
| ~ topological_space(X19) )
| ~ spl61_331
| ~ spl61_358 ),
inference(resolution,[],[f2819,f2558]) ).
fof(f5052,plain,
( spl61_619
| ~ spl61_332
| ~ spl61_358 ),
inference(avatar_split_clause,[],[f2882,f2818,f2561,f5050]) ).
fof(f5050,plain,
( spl61_619
<=> ! [X20] :
( ~ empty(sK36(X20))
| nowhere_dense(sK36(X20),X20)
| ~ top_str(X20)
| ~ topological_space(X20) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_619])]) ).
fof(f2882,plain,
( ! [X20] :
( ~ empty(sK36(X20))
| nowhere_dense(sK36(X20),X20)
| ~ top_str(X20)
| ~ topological_space(X20) )
| ~ spl61_332
| ~ spl61_358 ),
inference(duplicate_literal_removal,[],[f2878]) ).
fof(f2878,plain,
( ! [X20] :
( ~ empty(sK36(X20))
| nowhere_dense(sK36(X20),X20)
| ~ top_str(X20)
| ~ topological_space(X20)
| ~ top_str(X20)
| ~ topological_space(X20) )
| ~ spl61_332
| ~ spl61_358 ),
inference(resolution,[],[f2819,f2562]) ).
fof(f5048,plain,
( spl61_618
| ~ spl61_260
| ~ spl61_342 ),
inference(avatar_split_clause,[],[f2760,f2689,f2117,f5046]) ).
fof(f5046,plain,
( spl61_618
<=> ! [X6] :
( ~ top_str(X6)
| ~ topological_space(X6)
| empty_carrier(X6)
| subset(sK27(X6),the_carrier(X6)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_618])]) ).
fof(f2760,plain,
( ! [X6] :
( ~ top_str(X6)
| ~ topological_space(X6)
| empty_carrier(X6)
| subset(sK27(X6),the_carrier(X6)) )
| ~ spl61_260
| ~ spl61_342 ),
inference(resolution,[],[f2690,f2118]) ).
fof(f5044,plain,
( spl61_617
| ~ spl61_260
| ~ spl61_341 ),
inference(avatar_split_clause,[],[f2753,f2685,f2117,f5042]) ).
fof(f5042,plain,
( spl61_617
<=> ! [X6] :
( ~ top_str(X6)
| ~ topological_space(X6)
| empty_carrier(X6)
| subset(sK26(X6),the_carrier(X6)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_617])]) ).
fof(f2753,plain,
( ! [X6] :
( ~ top_str(X6)
| ~ topological_space(X6)
| empty_carrier(X6)
| subset(sK26(X6),the_carrier(X6)) )
| ~ spl61_260
| ~ spl61_341 ),
inference(resolution,[],[f2686,f2118]) ).
fof(f5040,plain,
( spl61_616
| ~ spl61_330
| ~ spl61_339 ),
inference(avatar_split_clause,[],[f2730,f2677,f2553,f5038]) ).
fof(f5038,plain,
( spl61_616
<=> ! [X14] :
( ~ empty(sK34(X14))
| boundary_set(sK34(X14),X14)
| ~ top_str(X14)
| ~ topological_space(X14) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_616])]) ).
fof(f2730,plain,
( ! [X14] :
( ~ empty(sK34(X14))
| boundary_set(sK34(X14),X14)
| ~ top_str(X14)
| ~ topological_space(X14) )
| ~ spl61_330
| ~ spl61_339 ),
inference(duplicate_literal_removal,[],[f2722]) ).
fof(f2722,plain,
( ! [X14] :
( ~ empty(sK34(X14))
| boundary_set(sK34(X14),X14)
| ~ top_str(X14)
| ~ top_str(X14)
| ~ topological_space(X14) )
| ~ spl61_330
| ~ spl61_339 ),
inference(resolution,[],[f2678,f2554]) ).
fof(f5036,plain,
( spl61_615
| ~ spl61_331
| ~ spl61_339 ),
inference(avatar_split_clause,[],[f2729,f2677,f2557,f5034]) ).
fof(f5034,plain,
( spl61_615
<=> ! [X15] :
( ~ empty(sK35(X15))
| boundary_set(sK35(X15),X15)
| ~ top_str(X15)
| ~ topological_space(X15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_615])]) ).
fof(f2729,plain,
( ! [X15] :
( ~ empty(sK35(X15))
| boundary_set(sK35(X15),X15)
| ~ top_str(X15)
| ~ topological_space(X15) )
| ~ spl61_331
| ~ spl61_339 ),
inference(duplicate_literal_removal,[],[f2723]) ).
fof(f2723,plain,
( ! [X15] :
( ~ empty(sK35(X15))
| boundary_set(sK35(X15),X15)
| ~ top_str(X15)
| ~ top_str(X15)
| ~ topological_space(X15) )
| ~ spl61_331
| ~ spl61_339 ),
inference(resolution,[],[f2678,f2558]) ).
fof(f5032,plain,
( ~ spl61_247
| spl61_614
| ~ spl61_232
| ~ spl61_478 ),
inference(avatar_split_clause,[],[f4137,f4101,f1978,f5029,f2063]) ).
fof(f5029,plain,
( spl61_614
<=> boundary_set(sK60,sK12) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_614])]) ).
fof(f1978,plain,
( spl61_232
<=> ! [X0] :
( boundary_set(sK33(X0),X0)
| ~ sP9(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_232])]) ).
fof(f4137,plain,
( boundary_set(sK60,sK12)
| ~ sP9(sK12)
| ~ spl61_232
| ~ spl61_478 ),
inference(superposition,[],[f1979,f4103]) ).
fof(f1979,plain,
( ! [X0] :
( boundary_set(sK33(X0),X0)
| ~ sP9(X0) )
| ~ spl61_232 ),
inference(avatar_component_clause,[],[f1978]) ).
fof(f5027,plain,
( spl61_613
| ~ spl61_332
| ~ spl61_339 ),
inference(avatar_split_clause,[],[f2728,f2677,f2561,f5025]) ).
fof(f5025,plain,
( spl61_613
<=> ! [X16] :
( ~ empty(sK36(X16))
| boundary_set(sK36(X16),X16)
| ~ top_str(X16)
| ~ topological_space(X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_613])]) ).
fof(f2728,plain,
( ! [X16] :
( ~ empty(sK36(X16))
| boundary_set(sK36(X16),X16)
| ~ top_str(X16)
| ~ topological_space(X16) )
| ~ spl61_332
| ~ spl61_339 ),
inference(duplicate_literal_removal,[],[f2724]) ).
fof(f2724,plain,
( ! [X16] :
( ~ empty(sK36(X16))
| boundary_set(sK36(X16),X16)
| ~ top_str(X16)
| ~ top_str(X16)
| ~ topological_space(X16) )
| ~ spl61_332
| ~ spl61_339 ),
inference(resolution,[],[f2678,f2562]) ).
fof(f5023,plain,
( spl61_612
| ~ spl61_273
| ~ spl61_339 ),
inference(avatar_split_clause,[],[f2716,f2677,f2200,f5021]) ).
fof(f5021,plain,
( spl61_612
<=> ! [X8] :
( ~ empty(sK24(X8))
| boundary_set(sK24(X8),X8)
| ~ top_str(X8)
| ~ rel_str(X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_612])]) ).
fof(f2716,plain,
( ! [X8] :
( ~ empty(sK24(X8))
| boundary_set(sK24(X8),X8)
| ~ top_str(X8)
| ~ rel_str(X8) )
| ~ spl61_273
| ~ spl61_339 ),
inference(resolution,[],[f2678,f2201]) ).
fof(f5019,plain,
( spl61_611
| ~ spl61_272
| ~ spl61_339 ),
inference(avatar_split_clause,[],[f2715,f2677,f2196,f5017]) ).
fof(f5017,plain,
( spl61_611
<=> ! [X7] :
( ~ empty(sK23(X7))
| boundary_set(sK23(X7),X7)
| ~ top_str(X7)
| ~ rel_str(X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_611])]) ).
fof(f2715,plain,
( ! [X7] :
( ~ empty(sK23(X7))
| boundary_set(sK23(X7),X7)
| ~ top_str(X7)
| ~ rel_str(X7) )
| ~ spl61_272
| ~ spl61_339 ),
inference(resolution,[],[f2678,f2197]) ).
fof(f5015,plain,
( spl61_610
| ~ spl61_265
| ~ spl61_339 ),
inference(avatar_split_clause,[],[f2709,f2677,f2167,f5013]) ).
fof(f5013,plain,
( spl61_610
<=> ! [X2] :
( ~ empty(cast_as_carrier_subset(X2))
| boundary_set(cast_as_carrier_subset(X2),X2)
| ~ top_str(X2)
| ~ one_sorted_str(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_610])]) ).
fof(f2709,plain,
( ! [X2] :
( ~ empty(cast_as_carrier_subset(X2))
| boundary_set(cast_as_carrier_subset(X2),X2)
| ~ top_str(X2)
| ~ one_sorted_str(X2) )
| ~ spl61_265
| ~ spl61_339 ),
inference(resolution,[],[f2678,f2168]) ).
fof(f5011,plain,
( spl61_609
| ~ spl61_261
| ~ spl61_339 ),
inference(avatar_split_clause,[],[f2708,f2677,f2121,f5009]) ).
fof(f2708,plain,
( ! [X0,X1] :
( ~ empty(X0)
| boundary_set(X0,X1)
| ~ top_str(X1)
| ~ subset(X0,the_carrier(X1)) )
| ~ spl61_261
| ~ spl61_339 ),
inference(resolution,[],[f2678,f2122]) ).
fof(f5007,plain,
( spl61_608
| ~ spl61_132
| ~ spl61_338 ),
inference(avatar_split_clause,[],[f2675,f2662,f1521,f5005]) ).
fof(f5005,plain,
( spl61_608
<=> ! [X0] :
( ~ rel_str(X0)
| ~ transitive_relstr(X0)
| ~ reflexive_relstr(X0)
| empty_carrier(X0)
| sP0(sK32(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_608])]) ).
fof(f2662,plain,
( spl61_338
<=> ! [X0] :
( ~ empty(sK32(X0))
| ~ rel_str(X0)
| ~ transitive_relstr(X0)
| ~ reflexive_relstr(X0)
| empty_carrier(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_338])]) ).
fof(f2675,plain,
( ! [X0] :
( ~ rel_str(X0)
| ~ transitive_relstr(X0)
| ~ reflexive_relstr(X0)
| empty_carrier(X0)
| sP0(sK32(X0)) )
| ~ spl61_132
| ~ spl61_338 ),
inference(resolution,[],[f2663,f1522]) ).
fof(f2663,plain,
( ! [X0] :
( ~ empty(sK32(X0))
| ~ rel_str(X0)
| ~ transitive_relstr(X0)
| ~ reflexive_relstr(X0)
| empty_carrier(X0) )
| ~ spl61_338 ),
inference(avatar_component_clause,[],[f2662]) ).
fof(f5003,plain,
( spl61_607
| ~ spl61_132
| ~ spl61_337 ),
inference(avatar_split_clause,[],[f2672,f2658,f1521,f5001]) ).
fof(f5001,plain,
( spl61_607
<=> ! [X0] :
( ~ rel_str(X0)
| ~ transitive_relstr(X0)
| ~ reflexive_relstr(X0)
| empty_carrier(X0)
| sP0(sK31(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_607])]) ).
fof(f2658,plain,
( spl61_337
<=> ! [X0] :
( ~ empty(sK31(X0))
| ~ rel_str(X0)
| ~ transitive_relstr(X0)
| ~ reflexive_relstr(X0)
| empty_carrier(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_337])]) ).
fof(f2672,plain,
( ! [X0] :
( ~ rel_str(X0)
| ~ transitive_relstr(X0)
| ~ reflexive_relstr(X0)
| empty_carrier(X0)
| sP0(sK31(X0)) )
| ~ spl61_132
| ~ spl61_337 ),
inference(resolution,[],[f2659,f1522]) ).
fof(f2659,plain,
( ! [X0] :
( ~ empty(sK31(X0))
| ~ rel_str(X0)
| ~ transitive_relstr(X0)
| ~ reflexive_relstr(X0)
| empty_carrier(X0) )
| ~ spl61_337 ),
inference(avatar_component_clause,[],[f2658]) ).
fof(f4999,plain,
( spl61_606
| ~ spl61_304
| ~ spl61_335 ),
inference(avatar_split_clause,[],[f2636,f2573,f2412,f4997]) ).
fof(f2636,plain,
( ! [X18,X19] :
( element(X18,powerset(the_carrier(X19)))
| ~ in(X18,sK22(X19))
| ~ one_sorted_str(X19) )
| ~ spl61_304
| ~ spl61_335 ),
inference(resolution,[],[f2574,f2413]) ).
fof(f4995,plain,
( spl61_605
| ~ spl61_315
| ~ spl61_333 ),
inference(avatar_split_clause,[],[f2624,f2565,f2457,f4993]) ).
fof(f2624,plain,
( ! [X3,X6,X4,X5] :
( ~ relation_of2_as_subset(X3,X4,X5)
| ~ empty(cartesian_product2(X4,X5))
| ~ in(X6,X3) )
| ~ spl61_315
| ~ spl61_333 ),
inference(resolution,[],[f2566,f2458]) ).
fof(f4991,plain,
( spl61_604
| ~ spl61_315
| ~ spl61_332 ),
inference(avatar_split_clause,[],[f2619,f2561,f2457,f4989]) ).
fof(f2619,plain,
( ! [X0,X1] :
( ~ top_str(X0)
| ~ topological_space(X0)
| ~ empty(the_carrier(X0))
| ~ in(X1,sK36(X0)) )
| ~ spl61_315
| ~ spl61_332 ),
inference(resolution,[],[f2562,f2458]) ).
fof(f4987,plain,
( spl61_603
| ~ spl61_315
| ~ spl61_331 ),
inference(avatar_split_clause,[],[f2615,f2557,f2457,f4985]) ).
fof(f2615,plain,
( ! [X0,X1] :
( ~ top_str(X0)
| ~ topological_space(X0)
| ~ empty(the_carrier(X0))
| ~ in(X1,sK35(X0)) )
| ~ spl61_315
| ~ spl61_331 ),
inference(resolution,[],[f2558,f2458]) ).
fof(f4983,plain,
( spl61_602
| ~ spl61_315
| ~ spl61_330 ),
inference(avatar_split_clause,[],[f2606,f2553,f2457,f4981]) ).
fof(f2606,plain,
( ! [X0,X1] :
( ~ top_str(X0)
| ~ topological_space(X0)
| ~ empty(the_carrier(X0))
| ~ in(X1,sK34(X0)) )
| ~ spl61_315
| ~ spl61_330 ),
inference(resolution,[],[f2554,f2458]) ).
fof(f4979,plain,
( spl61_601
| ~ spl61_315
| ~ spl61_329 ),
inference(avatar_split_clause,[],[f2602,f2541,f2457,f4977]) ).
fof(f2602,plain,
( ! [X0,X1] :
( ~ rel_str(X0)
| empty_carrier(X0)
| ~ empty(the_carrier(X0))
| ~ in(X1,sK29(X0)) )
| ~ spl61_315
| ~ spl61_329 ),
inference(resolution,[],[f2542,f2458]) ).
fof(f4975,plain,
( spl61_600
| ~ spl61_176
| ~ spl61_281 ),
inference(avatar_split_clause,[],[f2369,f2232,f1729,f4973]) ).
fof(f1729,plain,
( spl61_176
<=> ! [X0] :
( reflexive_relstr(sK20(X0))
| ~ sP2(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_176])]) ).
fof(f2369,plain,
( ! [X1] :
( ~ rel_str(sK20(X1))
| sP7(sK20(X1))
| empty_carrier(sK20(X1))
| ~ sP2(X1) )
| ~ spl61_176
| ~ spl61_281 ),
inference(resolution,[],[f2233,f1730]) ).
fof(f1730,plain,
( ! [X0] :
( reflexive_relstr(sK20(X0))
| ~ sP2(X0) )
| ~ spl61_176 ),
inference(avatar_component_clause,[],[f1729]) ).
fof(f4900,plain,
( ~ spl61_247
| spl61_599
| ~ spl61_230
| ~ spl61_478 ),
inference(avatar_split_clause,[],[f4136,f4101,f1969,f4897,f2063]) ).
fof(f4897,plain,
( spl61_599
<=> closed_subset(sK60,sK12) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_599])]) ).
fof(f1969,plain,
( spl61_230
<=> ! [X0] :
( closed_subset(sK33(X0),X0)
| ~ sP9(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_230])]) ).
fof(f4136,plain,
( closed_subset(sK60,sK12)
| ~ sP9(sK12)
| ~ spl61_230
| ~ spl61_478 ),
inference(superposition,[],[f1970,f4103]) ).
fof(f1970,plain,
( ! [X0] :
( closed_subset(sK33(X0),X0)
| ~ sP9(X0) )
| ~ spl61_230 ),
inference(avatar_component_clause,[],[f1969]) ).
fof(f4862,plain,
( spl61_598
| ~ spl61_200
| ~ spl61_353 ),
inference(avatar_split_clause,[],[f2799,f2784,f1826,f4860]) ).
fof(f2799,plain,
( ! [X4,X5] :
( in(sK41(X4,X5),X5)
| X4 = X5
| ~ empty(X4) )
| ~ spl61_200
| ~ spl61_353 ),
inference(resolution,[],[f2785,f1827]) ).
fof(f4858,plain,
( spl61_597
| ~ spl61_200
| ~ spl61_353 ),
inference(avatar_split_clause,[],[f2796,f2784,f1826,f4856]) ).
fof(f2796,plain,
( ! [X4,X5] :
( in(sK41(X4,X5),X4)
| X4 = X5
| ~ empty(X5) )
| ~ spl61_200
| ~ spl61_353 ),
inference(resolution,[],[f2785,f1827]) ).
fof(f4854,plain,
( ~ spl61_86
| spl61_87
| ~ spl61_88
| spl61_595
| ~ spl61_596
| ~ spl61_90
| ~ spl61_340 ),
inference(avatar_split_clause,[],[f2747,f2681,f1337,f4851,f4847,f1327,f1322,f1317]) ).
fof(f1317,plain,
( spl61_86
<=> rel_str(sK58) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_86])]) ).
fof(f1322,plain,
( spl61_87
<=> empty_carrier(sK58) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_87])]) ).
fof(f1327,plain,
( spl61_88
<=> reflexive_relstr(sK58) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_88])]) ).
fof(f4847,plain,
( spl61_595
<=> with_infima_relstr(sK58) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_595])]) ).
fof(f4851,plain,
( spl61_596
<=> join_complete_relstr(sK58) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_596])]) ).
fof(f1337,plain,
( spl61_90
<=> antisymmetric_relstr(sK58) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_90])]) ).
fof(f2747,plain,
( ~ join_complete_relstr(sK58)
| with_infima_relstr(sK58)
| ~ reflexive_relstr(sK58)
| empty_carrier(sK58)
| ~ rel_str(sK58)
| ~ spl61_90
| ~ spl61_340 ),
inference(resolution,[],[f2682,f1339]) ).
fof(f1339,plain,
( antisymmetric_relstr(sK58)
| ~ spl61_90 ),
inference(avatar_component_clause,[],[f1337]) ).
fof(f4845,plain,
( ~ spl61_247
| spl61_594
| ~ spl61_229
| ~ spl61_478 ),
inference(avatar_split_clause,[],[f4135,f4101,f1965,f4842,f2063]) ).
fof(f4842,plain,
( spl61_594
<=> open_subset(sK60,sK12) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_594])]) ).
fof(f1965,plain,
( spl61_229
<=> ! [X0] :
( open_subset(sK33(X0),X0)
| ~ sP9(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_229])]) ).
fof(f4135,plain,
( open_subset(sK60,sK12)
| ~ sP9(sK12)
| ~ spl61_229
| ~ spl61_478 ),
inference(superposition,[],[f1966,f4103]) ).
fof(f1966,plain,
( ! [X0] :
( open_subset(sK33(X0),X0)
| ~ sP9(X0) )
| ~ spl61_229 ),
inference(avatar_component_clause,[],[f1965]) ).
fof(f4840,plain,
( spl61_593
| ~ spl61_292
| ~ spl61_335 ),
inference(avatar_split_clause,[],[f2647,f2573,f2277,f4838]) ).
fof(f2647,plain,
( ! [X40,X41] :
( element(X40,the_carrier(X41))
| ~ in(X40,sK37(X41))
| ~ sP10(X41) )
| ~ spl61_292
| ~ spl61_335 ),
inference(resolution,[],[f2574,f2278]) ).
fof(f4836,plain,
( spl61_592
| ~ spl61_284
| ~ spl61_335 ),
inference(avatar_split_clause,[],[f2643,f2573,f2244,f4834]) ).
fof(f4834,plain,
( spl61_592
<=> ! [X32,X33] :
( element(X32,the_carrier(X33))
| ~ in(X32,sK33(X33))
| ~ sP9(X33) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_592])]) ).
fof(f2643,plain,
( ! [X32,X33] :
( element(X32,the_carrier(X33))
| ~ in(X32,sK33(X33))
| ~ sP9(X33) )
| ~ spl61_284
| ~ spl61_335 ),
inference(resolution,[],[f2574,f2245]) ).
fof(f4832,plain,
( spl61_591
| ~ spl61_280
| ~ spl61_335 ),
inference(avatar_split_clause,[],[f2642,f2573,f2228,f4830]) ).
fof(f2642,plain,
( ! [X31,X30] :
( element(X30,the_carrier(X31))
| ~ in(X30,sK30(X31))
| ~ sP7(X31) )
| ~ spl61_280
| ~ spl61_335 ),
inference(resolution,[],[f2574,f2229]) ).
fof(f4828,plain,
( spl61_590
| ~ spl61_274
| ~ spl61_335 ),
inference(avatar_split_clause,[],[f2639,f2573,f2204,f4826]) ).
fof(f2639,plain,
( ! [X24,X25] :
( element(X24,the_carrier(X25))
| ~ in(X24,sK25(X25))
| ~ sP6(X25) )
| ~ spl61_274
| ~ spl61_335 ),
inference(resolution,[],[f2574,f2205]) ).
fof(f4824,plain,
( spl61_589
| ~ spl61_273
| ~ spl61_335 ),
inference(avatar_split_clause,[],[f2638,f2573,f2200,f4822]) ).
fof(f2638,plain,
( ! [X22,X23] :
( element(X22,the_carrier(X23))
| ~ in(X22,sK24(X23))
| ~ rel_str(X23) )
| ~ spl61_273
| ~ spl61_335 ),
inference(resolution,[],[f2574,f2201]) ).
fof(f4820,plain,
( spl61_588
| ~ spl61_272
| ~ spl61_335 ),
inference(avatar_split_clause,[],[f2637,f2573,f2196,f4818]) ).
fof(f2637,plain,
( ! [X21,X20] :
( element(X20,the_carrier(X21))
| ~ in(X20,sK23(X21))
| ~ rel_str(X21) )
| ~ spl61_272
| ~ spl61_335 ),
inference(resolution,[],[f2574,f2197]) ).
fof(f4816,plain,
( spl61_587
| ~ spl61_264
| ~ spl61_335 ),
inference(avatar_split_clause,[],[f2635,f2573,f2163,f4814]) ).
fof(f4814,plain,
( spl61_587
<=> ! [X16,X17] :
( element(X16,the_carrier(X17))
| ~ in(X16,sK18(X17))
| ~ sP1(X17) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_587])]) ).
fof(f2635,plain,
( ! [X16,X17] :
( element(X16,the_carrier(X17))
| ~ in(X16,sK18(X17))
| ~ sP1(X17) )
| ~ spl61_264
| ~ spl61_335 ),
inference(resolution,[],[f2574,f2164]) ).
fof(f4812,plain,
( spl61_586
| ~ spl61_265
| ~ spl61_335 ),
inference(avatar_split_clause,[],[f2630,f2573,f2167,f4810]) ).
fof(f2630,plain,
( ! [X8,X7] :
( element(X7,the_carrier(X8))
| ~ in(X7,cast_as_carrier_subset(X8))
| ~ one_sorted_str(X8) )
| ~ spl61_265
| ~ spl61_335 ),
inference(resolution,[],[f2574,f2168]) ).
fof(f4808,plain,
( spl61_585
| ~ spl61_266
| ~ spl61_333 ),
inference(avatar_split_clause,[],[f2625,f2565,f2171,f4806]) ).
fof(f2625,plain,
( ! [X8,X9,X7] :
( ~ relation_of2_as_subset(X7,X8,X9)
| finite(X7)
| ~ finite(cartesian_product2(X8,X9)) )
| ~ spl61_266
| ~ spl61_333 ),
inference(resolution,[],[f2566,f2172]) ).
fof(f4804,plain,
( spl61_584
| ~ spl61_266
| ~ spl61_332 ),
inference(avatar_split_clause,[],[f2620,f2561,f2171,f4802]) ).
fof(f4802,plain,
( spl61_584
<=> ! [X2] :
( ~ top_str(X2)
| ~ topological_space(X2)
| finite(sK36(X2))
| ~ finite(the_carrier(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_584])]) ).
fof(f2620,plain,
( ! [X2] :
( ~ top_str(X2)
| ~ topological_space(X2)
| finite(sK36(X2))
| ~ finite(the_carrier(X2)) )
| ~ spl61_266
| ~ spl61_332 ),
inference(resolution,[],[f2562,f2172]) ).
fof(f4800,plain,
( spl61_583
| ~ spl61_266
| ~ spl61_331 ),
inference(avatar_split_clause,[],[f2616,f2557,f2171,f4798]) ).
fof(f4798,plain,
( spl61_583
<=> ! [X2] :
( ~ top_str(X2)
| ~ topological_space(X2)
| finite(sK35(X2))
| ~ finite(the_carrier(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_583])]) ).
fof(f2616,plain,
( ! [X2] :
( ~ top_str(X2)
| ~ topological_space(X2)
| finite(sK35(X2))
| ~ finite(the_carrier(X2)) )
| ~ spl61_266
| ~ spl61_331 ),
inference(resolution,[],[f2558,f2172]) ).
fof(f4796,plain,
( spl61_582
| ~ spl61_266
| ~ spl61_330 ),
inference(avatar_split_clause,[],[f2607,f2553,f2171,f4794]) ).
fof(f4794,plain,
( spl61_582
<=> ! [X2] :
( ~ top_str(X2)
| ~ topological_space(X2)
| finite(sK34(X2))
| ~ finite(the_carrier(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_582])]) ).
fof(f2607,plain,
( ! [X2] :
( ~ top_str(X2)
| ~ topological_space(X2)
| finite(sK34(X2))
| ~ finite(the_carrier(X2)) )
| ~ spl61_266
| ~ spl61_330 ),
inference(resolution,[],[f2554,f2172]) ).
fof(f4792,plain,
( spl61_581
| ~ spl61_266
| ~ spl61_329 ),
inference(avatar_split_clause,[],[f2603,f2541,f2171,f4790]) ).
fof(f4790,plain,
( spl61_581
<=> ! [X2] :
( ~ rel_str(X2)
| empty_carrier(X2)
| finite(sK29(X2))
| ~ finite(the_carrier(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_581])]) ).
fof(f2603,plain,
( ! [X2] :
( ~ rel_str(X2)
| empty_carrier(X2)
| finite(sK29(X2))
| ~ finite(the_carrier(X2)) )
| ~ spl61_266
| ~ spl61_329 ),
inference(resolution,[],[f2542,f2172]) ).
fof(f4788,plain,
( spl61_580
| ~ spl61_266
| ~ spl61_326 ),
inference(avatar_split_clause,[],[f2599,f2529,f2171,f4786]) ).
fof(f4786,plain,
( spl61_580
<=> ! [X2] :
( ~ one_sorted_str(X2)
| empty_carrier(X2)
| finite(sK28(X2))
| ~ finite(the_carrier(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_580])]) ).
fof(f2599,plain,
( ! [X2] :
( ~ one_sorted_str(X2)
| empty_carrier(X2)
| finite(sK28(X2))
| ~ finite(the_carrier(X2)) )
| ~ spl61_266
| ~ spl61_326 ),
inference(resolution,[],[f2530,f2172]) ).
fof(f4784,plain,
( spl61_579
| ~ spl61_239
| ~ spl61_293 ),
inference(avatar_split_clause,[],[f2397,f2281,f2006,f4782]) ).
fof(f2006,plain,
( spl61_239
<=> ! [X0] : element(sK40(X0),powerset(powerset(X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_239])]) ).
fof(f2397,plain,
( ! [X15] :
( empty(powerset(powerset(X15)))
| in(sK40(X15),powerset(powerset(X15))) )
| ~ spl61_239
| ~ spl61_293 ),
inference(resolution,[],[f2282,f2007]) ).
fof(f2007,plain,
( ! [X0] : element(sK40(X0),powerset(powerset(X0)))
| ~ spl61_239 ),
inference(avatar_component_clause,[],[f2006]) ).
fof(f4780,plain,
( spl61_578
| ~ spl61_250
| ~ spl61_293 ),
inference(avatar_split_clause,[],[f2387,f2281,f2076,f4778]) ).
fof(f2387,plain,
( ! [X5] :
( empty(powerset(X5))
| in(sK17(X5),powerset(X5))
| empty(X5) )
| ~ spl61_250
| ~ spl61_293 ),
inference(resolution,[],[f2282,f2077]) ).
fof(f4776,plain,
( spl61_577
| ~ spl61_249
| ~ spl61_293 ),
inference(avatar_split_clause,[],[f2386,f2281,f2072,f4774]) ).
fof(f2386,plain,
( ! [X4] :
( empty(powerset(X4))
| in(sK16(X4),powerset(X4))
| empty(X4) )
| ~ spl61_249
| ~ spl61_293 ),
inference(resolution,[],[f2282,f2073]) ).
fof(f4772,plain,
( spl61_576
| ~ spl61_248
| ~ spl61_293 ),
inference(avatar_split_clause,[],[f2385,f2281,f2068,f4770]) ).
fof(f2385,plain,
( ! [X3] :
( empty(powerset(X3))
| in(sK15(X3),powerset(X3))
| empty(X3) )
| ~ spl61_248
| ~ spl61_293 ),
inference(resolution,[],[f2282,f2069]) ).
fof(f4768,plain,
( spl61_575
| ~ spl61_261
| ~ spl61_293 ),
inference(avatar_split_clause,[],[f2381,f2281,f2121,f4766]) ).
fof(f2381,plain,
( ! [X0,X1] :
( empty(powerset(X0))
| in(X1,powerset(X0))
| ~ subset(X1,X0) )
| ~ spl61_261
| ~ spl61_293 ),
inference(resolution,[],[f2282,f2122]) ).
fof(f4761,plain,
( ~ spl61_247
| spl61_574
| ~ spl61_197
| ~ spl61_478 ),
inference(avatar_split_clause,[],[f4134,f4101,f1814,f4758,f2063]) ).
fof(f4758,plain,
( spl61_574
<=> v5_membered(sK60) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_574])]) ).
fof(f1814,plain,
( spl61_197
<=> ! [X0] :
( v5_membered(sK33(X0))
| ~ sP9(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_197])]) ).
fof(f4134,plain,
( v5_membered(sK60)
| ~ sP9(sK12)
| ~ spl61_197
| ~ spl61_478 ),
inference(superposition,[],[f1815,f4103]) ).
fof(f1815,plain,
( ! [X0] :
( v5_membered(sK33(X0))
| ~ sP9(X0) )
| ~ spl61_197 ),
inference(avatar_component_clause,[],[f1814]) ).
fof(f4756,plain,
( spl61_504
| spl61_4
| ~ spl61_6
| ~ spl61_7
| spl61_573
| ~ spl61_9
| ~ spl61_8
| ~ spl61_397 ),
inference(avatar_split_clause,[],[f3424,f3416,f927,f932,f4754,f922,f917,f907,f4282]) ).
fof(f4282,plain,
( spl61_504
<=> empty(cast_as_carrier_subset(sK12)) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_504])]) ).
fof(f917,plain,
( spl61_6
<=> filtered_subset(sK13,boole_POSet(cast_as_carrier_subset(sK12))) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_6])]) ).
fof(f922,plain,
( spl61_7
<=> upper_relstr_subset(sK13,boole_POSet(cast_as_carrier_subset(sK12))) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_7])]) ).
fof(f927,plain,
( spl61_8
<=> proper_element(sK13,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(sK12))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_8])]) ).
fof(f3424,plain,
( ! [X0] :
( ~ element(sK13,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(sK12)))))
| sP11(sK13,cast_as_carrier_subset(sK12),X0)
| ~ upper_relstr_subset(sK13,boole_POSet(cast_as_carrier_subset(sK12)))
| ~ filtered_subset(sK13,boole_POSet(cast_as_carrier_subset(sK12)))
| empty(sK13)
| ~ element(cast_as_carrier_subset(sK12),powerset(the_carrier(X0)))
| empty(cast_as_carrier_subset(sK12))
| ~ one_sorted_str(X0)
| empty_carrier(X0) )
| ~ spl61_8
| ~ spl61_397 ),
inference(resolution,[],[f3417,f929]) ).
fof(f929,plain,
( proper_element(sK13,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(sK12)))))
| ~ spl61_8 ),
inference(avatar_component_clause,[],[f927]) ).
fof(f4681,plain,
( ~ spl61_247
| spl61_572
| ~ spl61_196
| ~ spl61_478 ),
inference(avatar_split_clause,[],[f4133,f4101,f1810,f4678,f2063]) ).
fof(f4678,plain,
( spl61_572
<=> v4_membered(sK60) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_572])]) ).
fof(f1810,plain,
( spl61_196
<=> ! [X0] :
( v4_membered(sK33(X0))
| ~ sP9(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_196])]) ).
fof(f4133,plain,
( v4_membered(sK60)
| ~ sP9(sK12)
| ~ spl61_196
| ~ spl61_478 ),
inference(superposition,[],[f1811,f4103]) ).
fof(f1811,plain,
( ! [X0] :
( v4_membered(sK33(X0))
| ~ sP9(X0) )
| ~ spl61_196 ),
inference(avatar_component_clause,[],[f1810]) ).
fof(f4672,plain,
( ~ spl61_103
| spl61_571
| ~ spl61_103
| ~ spl61_126
| ~ spl61_182
| ~ spl61_199
| ~ spl61_360 ),
inference(avatar_split_clause,[],[f2956,f2826,f1822,f1753,f1496,f1402,f4670,f1402]) ).
fof(f4670,plain,
( spl61_571
<=> ! [X23] :
( closed_subset(sK60,X23)
| ~ topological_space(X23)
| ~ top_str(X23) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_571])]) ).
fof(f2956,plain,
( ! [X23] :
( closed_subset(sK60,X23)
| ~ empty(sK60)
| ~ top_str(X23)
| ~ topological_space(X23) )
| ~ spl61_103
| ~ spl61_126
| ~ spl61_182
| ~ spl61_199
| ~ spl61_360 ),
inference(forward_demodulation,[],[f2955,f1844]) ).
fof(f2955,plain,
( ! [X23] :
( closed_subset(empty_set,X23)
| ~ empty(sK60)
| ~ top_str(X23)
| ~ topological_space(X23) )
| ~ spl61_103
| ~ spl61_126
| ~ spl61_182
| ~ spl61_199
| ~ spl61_360 ),
inference(forward_demodulation,[],[f2954,f1843]) ).
fof(f2954,plain,
( ! [X23] :
( ~ empty(sK60)
| closed_subset(sK39(the_carrier(X23)),X23)
| ~ top_str(X23)
| ~ topological_space(X23) )
| ~ spl61_103
| ~ spl61_126
| ~ spl61_182
| ~ spl61_199
| ~ spl61_360 ),
inference(forward_demodulation,[],[f2953,f1844]) ).
fof(f2953,plain,
( ! [X23] :
( ~ empty(empty_set)
| closed_subset(sK39(the_carrier(X23)),X23)
| ~ top_str(X23)
| ~ topological_space(X23) )
| ~ spl61_126
| ~ spl61_182
| ~ spl61_199
| ~ spl61_360 ),
inference(forward_demodulation,[],[f2947,f1843]) ).
fof(f2947,plain,
( ! [X23] :
( ~ empty(sK39(the_carrier(X23)))
| closed_subset(sK39(the_carrier(X23)),X23)
| ~ top_str(X23)
| ~ topological_space(X23) )
| ~ spl61_199
| ~ spl61_360 ),
inference(resolution,[],[f2827,f1823]) ).
fof(f4668,plain,
( ~ spl61_103
| spl61_570
| ~ spl61_103
| ~ spl61_126
| ~ spl61_182
| ~ spl61_199
| ~ spl61_359 ),
inference(avatar_split_clause,[],[f2923,f2822,f1822,f1753,f1496,f1402,f4666,f1402]) ).
fof(f4666,plain,
( spl61_570
<=> ! [X23] :
( open_subset(sK60,X23)
| ~ topological_space(X23)
| ~ top_str(X23) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_570])]) ).
fof(f2923,plain,
( ! [X23] :
( open_subset(sK60,X23)
| ~ empty(sK60)
| ~ top_str(X23)
| ~ topological_space(X23) )
| ~ spl61_103
| ~ spl61_126
| ~ spl61_182
| ~ spl61_199
| ~ spl61_359 ),
inference(forward_demodulation,[],[f2922,f1844]) ).
fof(f2922,plain,
( ! [X23] :
( open_subset(empty_set,X23)
| ~ empty(sK60)
| ~ top_str(X23)
| ~ topological_space(X23) )
| ~ spl61_103
| ~ spl61_126
| ~ spl61_182
| ~ spl61_199
| ~ spl61_359 ),
inference(forward_demodulation,[],[f2921,f1843]) ).
fof(f2921,plain,
( ! [X23] :
( ~ empty(sK60)
| open_subset(sK39(the_carrier(X23)),X23)
| ~ top_str(X23)
| ~ topological_space(X23) )
| ~ spl61_103
| ~ spl61_126
| ~ spl61_182
| ~ spl61_199
| ~ spl61_359 ),
inference(forward_demodulation,[],[f2920,f1844]) ).
fof(f2920,plain,
( ! [X23] :
( ~ empty(empty_set)
| open_subset(sK39(the_carrier(X23)),X23)
| ~ top_str(X23)
| ~ topological_space(X23) )
| ~ spl61_126
| ~ spl61_182
| ~ spl61_199
| ~ spl61_359 ),
inference(forward_demodulation,[],[f2914,f1843]) ).
fof(f2914,plain,
( ! [X23] :
( ~ empty(sK39(the_carrier(X23)))
| open_subset(sK39(the_carrier(X23)),X23)
| ~ top_str(X23)
| ~ topological_space(X23) )
| ~ spl61_199
| ~ spl61_359 ),
inference(resolution,[],[f2823,f1823]) ).
fof(f4664,plain,
( ~ spl61_103
| spl61_569
| ~ spl61_103
| ~ spl61_126
| ~ spl61_182
| ~ spl61_199
| ~ spl61_358 ),
inference(avatar_split_clause,[],[f2890,f2818,f1822,f1753,f1496,f1402,f4662,f1402]) ).
fof(f2890,plain,
( ! [X23] :
( nowhere_dense(sK60,X23)
| ~ empty(sK60)
| ~ top_str(X23)
| ~ topological_space(X23) )
| ~ spl61_103
| ~ spl61_126
| ~ spl61_182
| ~ spl61_199
| ~ spl61_358 ),
inference(forward_demodulation,[],[f2889,f1844]) ).
fof(f2889,plain,
( ! [X23] :
( nowhere_dense(empty_set,X23)
| ~ empty(sK60)
| ~ top_str(X23)
| ~ topological_space(X23) )
| ~ spl61_103
| ~ spl61_126
| ~ spl61_182
| ~ spl61_199
| ~ spl61_358 ),
inference(forward_demodulation,[],[f2888,f1843]) ).
fof(f2888,plain,
( ! [X23] :
( ~ empty(sK60)
| nowhere_dense(sK39(the_carrier(X23)),X23)
| ~ top_str(X23)
| ~ topological_space(X23) )
| ~ spl61_103
| ~ spl61_126
| ~ spl61_182
| ~ spl61_199
| ~ spl61_358 ),
inference(forward_demodulation,[],[f2887,f1844]) ).
fof(f2887,plain,
( ! [X23] :
( ~ empty(empty_set)
| nowhere_dense(sK39(the_carrier(X23)),X23)
| ~ top_str(X23)
| ~ topological_space(X23) )
| ~ spl61_126
| ~ spl61_182
| ~ spl61_199
| ~ spl61_358 ),
inference(forward_demodulation,[],[f2881,f1843]) ).
fof(f2881,plain,
( ! [X23] :
( ~ empty(sK39(the_carrier(X23)))
| nowhere_dense(sK39(the_carrier(X23)),X23)
| ~ top_str(X23)
| ~ topological_space(X23) )
| ~ spl61_199
| ~ spl61_358 ),
inference(resolution,[],[f2819,f1823]) ).
fof(f4656,plain,
( ~ spl61_72
| spl61_568
| ~ spl61_74
| ~ spl61_336 ),
inference(avatar_split_clause,[],[f2671,f2654,f1257,f4653,f1247]) ).
fof(f1257,plain,
( spl61_74
<=> strict_rel_str(sK57) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_74])]) ).
fof(f2671,plain,
( sK57 = rel_str_of(the_carrier(sK57),the_InternalRel(sK57))
| ~ rel_str(sK57)
| ~ spl61_74
| ~ spl61_336 ),
inference(resolution,[],[f2655,f1259]) ).
fof(f1259,plain,
( strict_rel_str(sK57)
| ~ spl61_74 ),
inference(avatar_component_clause,[],[f1257]) ).
fof(f4647,plain,
( ~ spl61_62
| spl61_567
| ~ spl61_64
| ~ spl61_336 ),
inference(avatar_split_clause,[],[f2670,f2654,f1207,f4644,f1197]) ).
fof(f1207,plain,
( spl61_64
<=> strict_rel_str(sK56) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_64])]) ).
fof(f2670,plain,
( sK56 = rel_str_of(the_carrier(sK56),the_InternalRel(sK56))
| ~ rel_str(sK56)
| ~ spl61_64
| ~ spl61_336 ),
inference(resolution,[],[f2655,f1209]) ).
fof(f1209,plain,
( strict_rel_str(sK56)
| ~ spl61_64 ),
inference(avatar_component_clause,[],[f1207]) ).
fof(f4638,plain,
( ~ spl61_53
| spl61_566
| ~ spl61_55
| ~ spl61_336 ),
inference(avatar_split_clause,[],[f2669,f2654,f1162,f4635,f1152]) ).
fof(f1162,plain,
( spl61_55
<=> strict_rel_str(sK55) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_55])]) ).
fof(f2669,plain,
( sK55 = rel_str_of(the_carrier(sK55),the_InternalRel(sK55))
| ~ rel_str(sK55)
| ~ spl61_55
| ~ spl61_336 ),
inference(resolution,[],[f2655,f1164]) ).
fof(f1164,plain,
( strict_rel_str(sK55)
| ~ spl61_55 ),
inference(avatar_component_clause,[],[f1162]) ).
fof(f4629,plain,
( ~ spl61_46
| spl61_565
| ~ spl61_48
| ~ spl61_336 ),
inference(avatar_split_clause,[],[f2668,f2654,f1127,f4626,f1117]) ).
fof(f1127,plain,
( spl61_48
<=> strict_rel_str(sK54) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_48])]) ).
fof(f2668,plain,
( sK54 = rel_str_of(the_carrier(sK54),the_InternalRel(sK54))
| ~ rel_str(sK54)
| ~ spl61_48
| ~ spl61_336 ),
inference(resolution,[],[f2655,f1129]) ).
fof(f1129,plain,
( strict_rel_str(sK54)
| ~ spl61_48 ),
inference(avatar_component_clause,[],[f1127]) ).
fof(f4624,plain,
( ~ spl61_247
| spl61_564
| ~ spl61_195
| ~ spl61_478 ),
inference(avatar_split_clause,[],[f4132,f4101,f1806,f4621,f2063]) ).
fof(f4621,plain,
( spl61_564
<=> v3_membered(sK60) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_564])]) ).
fof(f1806,plain,
( spl61_195
<=> ! [X0] :
( v3_membered(sK33(X0))
| ~ sP9(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_195])]) ).
fof(f4132,plain,
( v3_membered(sK60)
| ~ sP9(sK12)
| ~ spl61_195
| ~ spl61_478 ),
inference(superposition,[],[f1807,f4103]) ).
fof(f1807,plain,
( ! [X0] :
( v3_membered(sK33(X0))
| ~ sP9(X0) )
| ~ spl61_195 ),
inference(avatar_component_clause,[],[f1806]) ).
fof(f4615,plain,
( ~ spl61_41
| spl61_563
| ~ spl61_43
| ~ spl61_336 ),
inference(avatar_split_clause,[],[f2667,f2654,f1102,f4612,f1092]) ).
fof(f1092,plain,
( spl61_41
<=> rel_str(sK53) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_41])]) ).
fof(f1102,plain,
( spl61_43
<=> strict_rel_str(sK53) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_43])]) ).
fof(f2667,plain,
( sK53 = rel_str_of(the_carrier(sK53),the_InternalRel(sK53))
| ~ rel_str(sK53)
| ~ spl61_43
| ~ spl61_336 ),
inference(resolution,[],[f2655,f1104]) ).
fof(f1104,plain,
( strict_rel_str(sK53)
| ~ spl61_43 ),
inference(avatar_component_clause,[],[f1102]) ).
fof(f4606,plain,
( ~ spl61_24
| spl61_562
| ~ spl61_27
| ~ spl61_336 ),
inference(avatar_split_clause,[],[f2666,f2654,f1022,f4603,f1007]) ).
fof(f1022,plain,
( spl61_27
<=> strict_rel_str(sK52) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_27])]) ).
fof(f2666,plain,
( sK52 = rel_str_of(the_carrier(sK52),the_InternalRel(sK52))
| ~ rel_str(sK52)
| ~ spl61_27
| ~ spl61_336 ),
inference(resolution,[],[f2655,f1024]) ).
fof(f1024,plain,
( strict_rel_str(sK52)
| ~ spl61_27 ),
inference(avatar_component_clause,[],[f1022]) ).
fof(f4601,plain,
( spl61_561
| ~ spl61_250
| ~ spl61_335 ),
inference(avatar_split_clause,[],[f2634,f2573,f2076,f4599]) ).
fof(f2634,plain,
( ! [X14,X15] :
( element(X14,X15)
| ~ in(X14,sK17(X15))
| empty(X15) )
| ~ spl61_250
| ~ spl61_335 ),
inference(resolution,[],[f2574,f2077]) ).
fof(f4597,plain,
( spl61_560
| ~ spl61_249
| ~ spl61_335 ),
inference(avatar_split_clause,[],[f2633,f2573,f2072,f4595]) ).
fof(f2633,plain,
( ! [X12,X13] :
( element(X12,X13)
| ~ in(X12,sK16(X13))
| empty(X13) )
| ~ spl61_249
| ~ spl61_335 ),
inference(resolution,[],[f2574,f2073]) ).
fof(f4593,plain,
( spl61_559
| ~ spl61_248
| ~ spl61_335 ),
inference(avatar_split_clause,[],[f2632,f2573,f2068,f4591]) ).
fof(f2632,plain,
( ! [X10,X11] :
( element(X10,X11)
| ~ in(X10,sK15(X11))
| empty(X11) )
| ~ spl61_248
| ~ spl61_335 ),
inference(resolution,[],[f2574,f2069]) ).
fof(f4589,plain,
( spl61_558
| ~ spl61_261
| ~ spl61_335 ),
inference(avatar_split_clause,[],[f2628,f2573,f2121,f4587]) ).
fof(f4587,plain,
( spl61_558
<=> ! [X2,X0,X1] :
( element(X0,X1)
| ~ in(X0,X2)
| ~ subset(X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_558])]) ).
fof(f2628,plain,
( ! [X2,X0,X1] :
( element(X0,X1)
| ~ in(X0,X2)
| ~ subset(X2,X1) )
| ~ spl61_261
| ~ spl61_335 ),
inference(resolution,[],[f2574,f2122]) ).
fof(f4585,plain,
( spl61_557
| ~ spl61_260
| ~ spl61_333 ),
inference(avatar_split_clause,[],[f2626,f2565,f2117,f4583]) ).
fof(f4583,plain,
( spl61_557
<=> ! [X11,X12,X10] :
( ~ relation_of2_as_subset(X10,X11,X12)
| subset(X10,cartesian_product2(X11,X12)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_557])]) ).
fof(f2626,plain,
( ! [X10,X11,X12] :
( ~ relation_of2_as_subset(X10,X11,X12)
| subset(X10,cartesian_product2(X11,X12)) )
| ~ spl61_260
| ~ spl61_333 ),
inference(resolution,[],[f2566,f2118]) ).
fof(f4581,plain,
( spl61_556
| ~ spl61_260
| ~ spl61_332 ),
inference(avatar_split_clause,[],[f2621,f2561,f2117,f4579]) ).
fof(f4579,plain,
( spl61_556
<=> ! [X3] :
( ~ top_str(X3)
| ~ topological_space(X3)
| subset(sK36(X3),the_carrier(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_556])]) ).
fof(f2621,plain,
( ! [X3] :
( ~ top_str(X3)
| ~ topological_space(X3)
| subset(sK36(X3),the_carrier(X3)) )
| ~ spl61_260
| ~ spl61_332 ),
inference(resolution,[],[f2562,f2118]) ).
fof(f4577,plain,
( spl61_555
| ~ spl61_260
| ~ spl61_331 ),
inference(avatar_split_clause,[],[f2617,f2557,f2117,f4575]) ).
fof(f4575,plain,
( spl61_555
<=> ! [X3] :
( ~ top_str(X3)
| ~ topological_space(X3)
| subset(sK35(X3),the_carrier(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_555])]) ).
fof(f2617,plain,
( ! [X3] :
( ~ top_str(X3)
| ~ topological_space(X3)
| subset(sK35(X3),the_carrier(X3)) )
| ~ spl61_260
| ~ spl61_331 ),
inference(resolution,[],[f2558,f2118]) ).
fof(f4573,plain,
( spl61_554
| ~ spl61_260
| ~ spl61_330 ),
inference(avatar_split_clause,[],[f2608,f2553,f2117,f4571]) ).
fof(f4571,plain,
( spl61_554
<=> ! [X3] :
( ~ top_str(X3)
| ~ topological_space(X3)
| subset(sK34(X3),the_carrier(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_554])]) ).
fof(f2608,plain,
( ! [X3] :
( ~ top_str(X3)
| ~ topological_space(X3)
| subset(sK34(X3),the_carrier(X3)) )
| ~ spl61_260
| ~ spl61_330 ),
inference(resolution,[],[f2554,f2118]) ).
fof(f4569,plain,
( spl61_553
| ~ spl61_260
| ~ spl61_329 ),
inference(avatar_split_clause,[],[f2604,f2541,f2117,f4567]) ).
fof(f4567,plain,
( spl61_553
<=> ! [X3] :
( ~ rel_str(X3)
| empty_carrier(X3)
| subset(sK29(X3),the_carrier(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_553])]) ).
fof(f2604,plain,
( ! [X3] :
( ~ rel_str(X3)
| empty_carrier(X3)
| subset(sK29(X3),the_carrier(X3)) )
| ~ spl61_260
| ~ spl61_329 ),
inference(resolution,[],[f2542,f2118]) ).
fof(f4565,plain,
( spl61_552
| ~ spl61_260
| ~ spl61_326 ),
inference(avatar_split_clause,[],[f2600,f2529,f2117,f4563]) ).
fof(f4563,plain,
( spl61_552
<=> ! [X3] :
( ~ one_sorted_str(X3)
| empty_carrier(X3)
| subset(sK28(X3),the_carrier(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_552])]) ).
fof(f2600,plain,
( ! [X3] :
( ~ one_sorted_str(X3)
| empty_carrier(X3)
| subset(sK28(X3),the_carrier(X3)) )
| ~ spl61_260
| ~ spl61_326 ),
inference(resolution,[],[f2530,f2118]) ).
fof(f4561,plain,
( spl61_551
| ~ spl61_292
| ~ spl61_315 ),
inference(avatar_split_clause,[],[f2481,f2457,f2277,f4559]) ).
fof(f2481,plain,
( ! [X26,X27] :
( ~ empty(the_carrier(X26))
| ~ in(X27,sK37(X26))
| ~ sP10(X26) )
| ~ spl61_292
| ~ spl61_315 ),
inference(resolution,[],[f2458,f2278]) ).
fof(f4557,plain,
( spl61_550
| ~ spl61_284
| ~ spl61_315 ),
inference(avatar_split_clause,[],[f2480,f2457,f2244,f4555]) ).
fof(f4555,plain,
( spl61_550
<=> ! [X25,X24] :
( ~ empty(the_carrier(X24))
| ~ in(X25,sK33(X24))
| ~ sP9(X24) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_550])]) ).
fof(f2480,plain,
( ! [X24,X25] :
( ~ empty(the_carrier(X24))
| ~ in(X25,sK33(X24))
| ~ sP9(X24) )
| ~ spl61_284
| ~ spl61_315 ),
inference(resolution,[],[f2458,f2245]) ).
fof(f4553,plain,
( spl61_549
| ~ spl61_280
| ~ spl61_315 ),
inference(avatar_split_clause,[],[f2479,f2457,f2228,f4551]) ).
fof(f2479,plain,
( ! [X22,X23] :
( ~ empty(the_carrier(X22))
| ~ in(X23,sK30(X22))
| ~ sP7(X22) )
| ~ spl61_280
| ~ spl61_315 ),
inference(resolution,[],[f2458,f2229]) ).
fof(f4549,plain,
( spl61_548
| ~ spl61_274
| ~ spl61_315 ),
inference(avatar_split_clause,[],[f2478,f2457,f2204,f4547]) ).
fof(f2478,plain,
( ! [X21,X20] :
( ~ empty(the_carrier(X20))
| ~ in(X21,sK25(X20))
| ~ sP6(X20) )
| ~ spl61_274
| ~ spl61_315 ),
inference(resolution,[],[f2458,f2205]) ).
fof(f4545,plain,
( spl61_547
| ~ spl61_273
| ~ spl61_315 ),
inference(avatar_split_clause,[],[f2477,f2457,f2200,f4543]) ).
fof(f2477,plain,
( ! [X18,X19] :
( ~ empty(the_carrier(X18))
| ~ in(X19,sK24(X18))
| ~ rel_str(X18) )
| ~ spl61_273
| ~ spl61_315 ),
inference(resolution,[],[f2458,f2201]) ).
fof(f4541,plain,
( spl61_546
| ~ spl61_272
| ~ spl61_315 ),
inference(avatar_split_clause,[],[f2476,f2457,f2196,f4539]) ).
fof(f2476,plain,
( ! [X16,X17] :
( ~ empty(the_carrier(X16))
| ~ in(X17,sK23(X16))
| ~ rel_str(X16) )
| ~ spl61_272
| ~ spl61_315 ),
inference(resolution,[],[f2458,f2197]) ).
fof(f4537,plain,
( ~ spl61_247
| spl61_545
| ~ spl61_194
| ~ spl61_478 ),
inference(avatar_split_clause,[],[f4131,f4101,f1802,f4534,f2063]) ).
fof(f4534,plain,
( spl61_545
<=> v2_membered(sK60) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_545])]) ).
fof(f1802,plain,
( spl61_194
<=> ! [X0] :
( v2_membered(sK33(X0))
| ~ sP9(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_194])]) ).
fof(f4131,plain,
( v2_membered(sK60)
| ~ sP9(sK12)
| ~ spl61_194
| ~ spl61_478 ),
inference(superposition,[],[f1803,f4103]) ).
fof(f1803,plain,
( ! [X0] :
( v2_membered(sK33(X0))
| ~ sP9(X0) )
| ~ spl61_194 ),
inference(avatar_component_clause,[],[f1802]) ).
fof(f4532,plain,
( spl61_544
| ~ spl61_264
| ~ spl61_315 ),
inference(avatar_split_clause,[],[f2474,f2457,f2163,f4530]) ).
fof(f4530,plain,
( spl61_544
<=> ! [X13,X12] :
( ~ empty(the_carrier(X12))
| ~ in(X13,sK18(X12))
| ~ sP1(X12) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_544])]) ).
fof(f2474,plain,
( ! [X12,X13] :
( ~ empty(the_carrier(X12))
| ~ in(X13,sK18(X12))
| ~ sP1(X12) )
| ~ spl61_264
| ~ spl61_315 ),
inference(resolution,[],[f2458,f2164]) ).
fof(f4528,plain,
( spl61_543
| ~ spl61_265
| ~ spl61_315 ),
inference(avatar_split_clause,[],[f2469,f2457,f2167,f4526]) ).
fof(f2469,plain,
( ! [X3,X4] :
( ~ empty(the_carrier(X3))
| ~ in(X4,cast_as_carrier_subset(X3))
| ~ one_sorted_str(X3) )
| ~ spl61_265
| ~ spl61_315 ),
inference(resolution,[],[f2458,f2168]) ).
fof(f4524,plain,
( spl61_542
| ~ spl61_132
| ~ spl61_309 ),
inference(avatar_split_clause,[],[f2466,f2433,f1521,f4522]) ).
fof(f4522,plain,
( spl61_542
<=> ! [X0] :
( ~ top_str(X0)
| ~ topological_space(X0)
| empty_carrier(X0)
| sP0(sK27(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_542])]) ).
fof(f2433,plain,
( spl61_309
<=> ! [X0] :
( ~ empty(sK27(X0))
| ~ top_str(X0)
| ~ topological_space(X0)
| empty_carrier(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_309])]) ).
fof(f2466,plain,
( ! [X0] :
( ~ top_str(X0)
| ~ topological_space(X0)
| empty_carrier(X0)
| sP0(sK27(X0)) )
| ~ spl61_132
| ~ spl61_309 ),
inference(resolution,[],[f2434,f1522]) ).
fof(f2434,plain,
( ! [X0] :
( ~ empty(sK27(X0))
| ~ top_str(X0)
| ~ topological_space(X0)
| empty_carrier(X0) )
| ~ spl61_309 ),
inference(avatar_component_clause,[],[f2433]) ).
fof(f4520,plain,
( spl61_541
| ~ spl61_132
| ~ spl61_306 ),
inference(avatar_split_clause,[],[f2464,f2420,f1521,f4518]) ).
fof(f4518,plain,
( spl61_541
<=> ! [X0] :
( ~ top_str(X0)
| ~ topological_space(X0)
| empty_carrier(X0)
| sP0(sK26(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_541])]) ).
fof(f2420,plain,
( spl61_306
<=> ! [X0] :
( ~ empty(sK26(X0))
| ~ top_str(X0)
| ~ topological_space(X0)
| empty_carrier(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_306])]) ).
fof(f2464,plain,
( ! [X0] :
( ~ top_str(X0)
| ~ topological_space(X0)
| empty_carrier(X0)
| sP0(sK26(X0)) )
| ~ spl61_132
| ~ spl61_306 ),
inference(resolution,[],[f2421,f1522]) ).
fof(f2421,plain,
( ! [X0] :
( ~ empty(sK26(X0))
| ~ top_str(X0)
| ~ topological_space(X0)
| empty_carrier(X0) )
| ~ spl61_306 ),
inference(avatar_component_clause,[],[f2420]) ).
fof(f4516,plain,
( spl61_540
| ~ spl61_300
| ~ spl61_305 ),
inference(avatar_split_clause,[],[f2463,f2416,f2310,f4514]) ).
fof(f2463,plain,
( ! [X0] :
( ~ rel_str(X0)
| relation_of2(the_InternalRel(X0),the_carrier(X0),the_carrier(X0)) )
| ~ spl61_300
| ~ spl61_305 ),
inference(resolution,[],[f2417,f2311]) ).
fof(f4512,plain,
( spl61_539
| ~ spl61_250
| ~ spl61_298 ),
inference(avatar_split_clause,[],[f2406,f2301,f2076,f4510]) ).
fof(f4510,plain,
( spl61_539
<=> ! [X8,X7] :
( relation(sK17(cartesian_product2(X7,X8)))
| empty(cartesian_product2(X7,X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_539])]) ).
fof(f2301,plain,
( spl61_298
<=> ! [X2,X0,X1] :
( relation(X2)
| ~ element(X2,powerset(cartesian_product2(X0,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_298])]) ).
fof(f2406,plain,
( ! [X8,X7] :
( relation(sK17(cartesian_product2(X7,X8)))
| empty(cartesian_product2(X7,X8)) )
| ~ spl61_250
| ~ spl61_298 ),
inference(resolution,[],[f2302,f2077]) ).
fof(f2302,plain,
( ! [X2,X0,X1] :
( ~ element(X2,powerset(cartesian_product2(X0,X1)))
| relation(X2) )
| ~ spl61_298 ),
inference(avatar_component_clause,[],[f2301]) ).
fof(f4508,plain,
( spl61_538
| ~ spl61_249
| ~ spl61_298 ),
inference(avatar_split_clause,[],[f2405,f2301,f2072,f4506]) ).
fof(f4506,plain,
( spl61_538
<=> ! [X6,X5] :
( relation(sK16(cartesian_product2(X5,X6)))
| empty(cartesian_product2(X5,X6)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_538])]) ).
fof(f2405,plain,
( ! [X6,X5] :
( relation(sK16(cartesian_product2(X5,X6)))
| empty(cartesian_product2(X5,X6)) )
| ~ spl61_249
| ~ spl61_298 ),
inference(resolution,[],[f2302,f2073]) ).
fof(f4504,plain,
( spl61_537
| ~ spl61_248
| ~ spl61_298 ),
inference(avatar_split_clause,[],[f2404,f2301,f2068,f4502]) ).
fof(f4502,plain,
( spl61_537
<=> ! [X4,X3] :
( relation(sK15(cartesian_product2(X3,X4)))
| empty(cartesian_product2(X3,X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_537])]) ).
fof(f2404,plain,
( ! [X3,X4] :
( relation(sK15(cartesian_product2(X3,X4)))
| empty(cartesian_product2(X3,X4)) )
| ~ spl61_248
| ~ spl61_298 ),
inference(resolution,[],[f2302,f2069]) ).
fof(f4500,plain,
( spl61_536
| ~ spl61_108
| ~ spl61_281 ),
inference(avatar_split_clause,[],[f2368,f2232,f1424,f4498]) ).
fof(f1424,plain,
( spl61_108
<=> ! [X0] : reflexive_relstr(boole_POSet(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_108])]) ).
fof(f2368,plain,
( ! [X0] :
( ~ rel_str(boole_POSet(X0))
| sP7(boole_POSet(X0))
| empty_carrier(boole_POSet(X0)) )
| ~ spl61_108
| ~ spl61_281 ),
inference(resolution,[],[f2233,f1425]) ).
fof(f1425,plain,
( ! [X0] : reflexive_relstr(boole_POSet(X0))
| ~ spl61_108 ),
inference(avatar_component_clause,[],[f1424]) ).
fof(f4465,plain,
( spl61_1
| ~ spl61_161
| spl61_4
| ~ spl61_6
| ~ spl61_7
| spl61_535
| ~ spl61_9
| ~ spl61_8
| ~ spl61_399 ),
inference(avatar_split_clause,[],[f3431,f3428,f927,f932,f4462,f922,f917,f907,f1659,f892]) ).
fof(f3431,plain,
( ~ element(sK13,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(sK12)))))
| sK13 = filter_of_net_str(sK12,net_of_bool_filter(sK12,cast_as_carrier_subset(sK12),sK13))
| ~ upper_relstr_subset(sK13,boole_POSet(cast_as_carrier_subset(sK12)))
| ~ filtered_subset(sK13,boole_POSet(cast_as_carrier_subset(sK12)))
| empty(sK13)
| ~ one_sorted_str(sK12)
| empty_carrier(sK12)
| ~ spl61_8
| ~ spl61_399 ),
inference(resolution,[],[f3429,f929]) ).
fof(f4460,plain,
( spl61_534
| ~ spl61_132
| spl61_504 ),
inference(avatar_split_clause,[],[f4424,f4282,f1521,f4457]) ).
fof(f4457,plain,
( spl61_534
<=> sP0(cast_as_carrier_subset(sK12)) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_534])]) ).
fof(f4424,plain,
( sP0(cast_as_carrier_subset(sK12))
| ~ spl61_132
| spl61_504 ),
inference(resolution,[],[f4283,f1522]) ).
fof(f4283,plain,
( ~ empty(cast_as_carrier_subset(sK12))
| spl61_504 ),
inference(avatar_component_clause,[],[f4282]) ).
fof(f4451,plain,
( spl61_504
| spl61_4
| ~ spl61_6
| ~ spl61_7
| spl61_533
| ~ spl61_9
| ~ spl61_396 ),
inference(avatar_split_clause,[],[f3392,f3358,f932,f4449,f922,f917,f907,f4282]) ).
fof(f3392,plain,
( ! [X11] :
( net_str(net_of_bool_filter(X11,cast_as_carrier_subset(sK12),sK13),X11)
| ~ upper_relstr_subset(sK13,boole_POSet(cast_as_carrier_subset(sK12)))
| ~ filtered_subset(sK13,boole_POSet(cast_as_carrier_subset(sK12)))
| empty(sK13)
| ~ element(cast_as_carrier_subset(sK12),powerset(the_carrier(X11)))
| empty(cast_as_carrier_subset(sK12))
| ~ one_sorted_str(X11)
| empty_carrier(X11) )
| ~ spl61_9
| ~ spl61_396 ),
inference(resolution,[],[f3359,f934]) ).
fof(f4445,plain,
( spl61_504
| spl61_4
| ~ spl61_6
| ~ spl61_7
| spl61_532
| ~ spl61_9
| ~ spl61_395 ),
inference(avatar_split_clause,[],[f3365,f3354,f932,f4443,f922,f917,f907,f4282]) ).
fof(f3365,plain,
( ! [X11] :
( strict_net_str(net_of_bool_filter(X11,cast_as_carrier_subset(sK12),sK13),X11)
| ~ upper_relstr_subset(sK13,boole_POSet(cast_as_carrier_subset(sK12)))
| ~ filtered_subset(sK13,boole_POSet(cast_as_carrier_subset(sK12)))
| empty(sK13)
| ~ element(cast_as_carrier_subset(sK12),powerset(the_carrier(X11)))
| empty(cast_as_carrier_subset(sK12))
| ~ one_sorted_str(X11)
| empty_carrier(X11) )
| ~ spl61_9
| ~ spl61_395 ),
inference(resolution,[],[f3355,f934]) ).
fof(f4438,plain,
( spl61_504
| spl61_4
| ~ spl61_6
| ~ spl61_7
| spl61_531
| ~ spl61_9
| ~ spl61_390 ),
inference(avatar_split_clause,[],[f3326,f3248,f932,f4436,f922,f917,f907,f4282]) ).
fof(f3326,plain,
( ! [X11] :
( transitive_relstr(net_of_bool_filter(X11,cast_as_carrier_subset(sK12),sK13))
| ~ upper_relstr_subset(sK13,boole_POSet(cast_as_carrier_subset(sK12)))
| ~ filtered_subset(sK13,boole_POSet(cast_as_carrier_subset(sK12)))
| empty(sK13)
| ~ element(cast_as_carrier_subset(sK12),powerset(the_carrier(X11)))
| empty(cast_as_carrier_subset(sK12))
| ~ one_sorted_str(X11)
| empty_carrier(X11) )
| ~ spl61_9
| ~ spl61_390 ),
inference(resolution,[],[f3249,f934]) ).
fof(f4431,plain,
( spl61_504
| spl61_4
| ~ spl61_6
| ~ spl61_7
| spl61_530
| ~ spl61_9
| ~ spl61_389 ),
inference(avatar_split_clause,[],[f3298,f3244,f932,f4429,f922,f917,f907,f4282]) ).
fof(f3298,plain,
( ! [X11] :
( reflexive_relstr(net_of_bool_filter(X11,cast_as_carrier_subset(sK12),sK13))
| ~ upper_relstr_subset(sK13,boole_POSet(cast_as_carrier_subset(sK12)))
| ~ filtered_subset(sK13,boole_POSet(cast_as_carrier_subset(sK12)))
| empty(sK13)
| ~ element(cast_as_carrier_subset(sK12),powerset(the_carrier(X11)))
| empty(cast_as_carrier_subset(sK12))
| ~ one_sorted_str(X11)
| empty_carrier(X11) )
| ~ spl61_9
| ~ spl61_389 ),
inference(resolution,[],[f3245,f934]) ).
fof(f4423,plain,
( spl61_1
| ~ spl61_161
| ~ spl61_252
| ~ spl61_504 ),
inference(avatar_split_clause,[],[f4292,f4282,f2084,f1659,f892]) ).
fof(f2084,plain,
( spl61_252
<=> ! [X0] :
( ~ empty(cast_as_carrier_subset(X0))
| ~ one_sorted_str(X0)
| empty_carrier(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_252])]) ).
fof(f4292,plain,
( ~ one_sorted_str(sK12)
| empty_carrier(sK12)
| ~ spl61_252
| ~ spl61_504 ),
inference(resolution,[],[f4284,f2085]) ).
fof(f2085,plain,
( ! [X0] :
( ~ empty(cast_as_carrier_subset(X0))
| ~ one_sorted_str(X0)
| empty_carrier(X0) )
| ~ spl61_252 ),
inference(avatar_component_clause,[],[f2084]) ).
fof(f4284,plain,
( empty(cast_as_carrier_subset(sK12))
| ~ spl61_504 ),
inference(avatar_component_clause,[],[f4282]) ).
fof(f4416,plain,
( spl61_529
| ~ spl61_239
| ~ spl61_335 ),
inference(avatar_split_clause,[],[f2650,f2573,f2006,f4414]) ).
fof(f2650,plain,
( ! [X46,X47] :
( element(X46,powerset(X47))
| ~ in(X46,sK40(X47)) )
| ~ spl61_239
| ~ spl61_335 ),
inference(resolution,[],[f2574,f2007]) ).
fof(f4412,plain,
( spl61_528
| ~ spl61_159
| ~ spl61_335 ),
inference(avatar_split_clause,[],[f2648,f2573,f1629,f4410]) ).
fof(f2648,plain,
( ! [X42,X43] :
( element(X42,X43)
| ~ in(X42,sK38(powerset(X43))) )
| ~ spl61_159
| ~ spl61_335 ),
inference(resolution,[],[f2574,f1630]) ).
fof(f4407,plain,
( ~ spl61_92
| spl61_93
| ~ spl61_94
| spl61_527
| ~ spl61_99
| ~ spl61_321 ),
inference(avatar_split_clause,[],[f2591,f2509,f1382,f4404,f1357,f1352,f1347]) ).
fof(f1382,plain,
( spl61_99
<=> complete_relstr(sK59) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_99])]) ).
fof(f2509,plain,
( spl61_321
<=> ! [X0] :
( join_complete_relstr(X0)
| ~ complete_relstr(X0)
| ~ reflexive_relstr(X0)
| empty_carrier(X0)
| ~ rel_str(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_321])]) ).
fof(f2591,plain,
( join_complete_relstr(sK59)
| ~ reflexive_relstr(sK59)
| empty_carrier(sK59)
| ~ rel_str(sK59)
| ~ spl61_99
| ~ spl61_321 ),
inference(resolution,[],[f2510,f1384]) ).
fof(f1384,plain,
( complete_relstr(sK59)
| ~ spl61_99 ),
inference(avatar_component_clause,[],[f1382]) ).
fof(f2510,plain,
( ! [X0] :
( ~ complete_relstr(X0)
| join_complete_relstr(X0)
| ~ reflexive_relstr(X0)
| empty_carrier(X0)
| ~ rel_str(X0) )
| ~ spl61_321 ),
inference(avatar_component_clause,[],[f2509]) ).
fof(f4401,plain,
( ~ spl61_62
| spl61_63
| ~ spl61_65
| spl61_526
| ~ spl61_70
| ~ spl61_321 ),
inference(avatar_split_clause,[],[f2589,f2509,f1237,f4398,f1212,f1202,f1197]) ).
fof(f4398,plain,
( spl61_526
<=> join_complete_relstr(sK56) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_526])]) ).
fof(f1237,plain,
( spl61_70
<=> complete_relstr(sK56) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_70])]) ).
fof(f2589,plain,
( join_complete_relstr(sK56)
| ~ reflexive_relstr(sK56)
| empty_carrier(sK56)
| ~ rel_str(sK56)
| ~ spl61_70
| ~ spl61_321 ),
inference(resolution,[],[f2510,f1239]) ).
fof(f1239,plain,
( complete_relstr(sK56)
| ~ spl61_70 ),
inference(avatar_component_clause,[],[f1237]) ).
fof(f4395,plain,
( ~ spl61_53
| spl61_54
| ~ spl61_56
| spl61_525
| ~ spl61_61
| ~ spl61_321 ),
inference(avatar_split_clause,[],[f2588,f2509,f1192,f4392,f1167,f1157,f1152]) ).
fof(f4392,plain,
( spl61_525
<=> join_complete_relstr(sK55) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_525])]) ).
fof(f1192,plain,
( spl61_61
<=> complete_relstr(sK55) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_61])]) ).
fof(f2588,plain,
( join_complete_relstr(sK55)
| ~ reflexive_relstr(sK55)
| empty_carrier(sK55)
| ~ rel_str(sK55)
| ~ spl61_61
| ~ spl61_321 ),
inference(resolution,[],[f2510,f1194]) ).
fof(f1194,plain,
( complete_relstr(sK55)
| ~ spl61_61 ),
inference(avatar_component_clause,[],[f1192]) ).
fof(f4389,plain,
( ~ spl61_46
| spl61_47
| ~ spl61_49
| spl61_524
| ~ spl61_52
| ~ spl61_321 ),
inference(avatar_split_clause,[],[f2587,f2509,f1147,f4386,f1132,f1122,f1117]) ).
fof(f1122,plain,
( spl61_47
<=> empty_carrier(sK54) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_47])]) ).
fof(f4386,plain,
( spl61_524
<=> join_complete_relstr(sK54) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_524])]) ).
fof(f1147,plain,
( spl61_52
<=> complete_relstr(sK54) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_52])]) ).
fof(f2587,plain,
( join_complete_relstr(sK54)
| ~ reflexive_relstr(sK54)
| empty_carrier(sK54)
| ~ rel_str(sK54)
| ~ spl61_52
| ~ spl61_321 ),
inference(resolution,[],[f2510,f1149]) ).
fof(f1149,plain,
( complete_relstr(sK54)
| ~ spl61_52 ),
inference(avatar_component_clause,[],[f1147]) ).
fof(f4384,plain,
( ~ spl61_92
| spl61_93
| ~ spl61_94
| spl61_523
| ~ spl61_99
| ~ spl61_320 ),
inference(avatar_split_clause,[],[f2585,f2505,f1382,f4381,f1357,f1352,f1347]) ).
fof(f2505,plain,
( spl61_320
<=> ! [X0] :
( up_complete_relstr(X0)
| ~ complete_relstr(X0)
| ~ reflexive_relstr(X0)
| empty_carrier(X0)
| ~ rel_str(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_320])]) ).
fof(f2585,plain,
( up_complete_relstr(sK59)
| ~ reflexive_relstr(sK59)
| empty_carrier(sK59)
| ~ rel_str(sK59)
| ~ spl61_99
| ~ spl61_320 ),
inference(resolution,[],[f2506,f1384]) ).
fof(f2506,plain,
( ! [X0] :
( ~ complete_relstr(X0)
| up_complete_relstr(X0)
| ~ reflexive_relstr(X0)
| empty_carrier(X0)
| ~ rel_str(X0) )
| ~ spl61_320 ),
inference(avatar_component_clause,[],[f2505]) ).
fof(f4379,plain,
( ~ spl61_62
| spl61_63
| ~ spl61_65
| spl61_522
| ~ spl61_70
| ~ spl61_320 ),
inference(avatar_split_clause,[],[f2583,f2505,f1237,f4376,f1212,f1202,f1197]) ).
fof(f2583,plain,
( up_complete_relstr(sK56)
| ~ reflexive_relstr(sK56)
| empty_carrier(sK56)
| ~ rel_str(sK56)
| ~ spl61_70
| ~ spl61_320 ),
inference(resolution,[],[f2506,f1239]) ).
fof(f4374,plain,
( ~ spl61_53
| spl61_54
| ~ spl61_56
| spl61_521
| ~ spl61_61
| ~ spl61_320 ),
inference(avatar_split_clause,[],[f2582,f2505,f1192,f4371,f1167,f1157,f1152]) ).
fof(f2582,plain,
( up_complete_relstr(sK55)
| ~ reflexive_relstr(sK55)
| empty_carrier(sK55)
| ~ rel_str(sK55)
| ~ spl61_61
| ~ spl61_320 ),
inference(resolution,[],[f2506,f1194]) ).
fof(f4369,plain,
( ~ spl61_46
| spl61_47
| ~ spl61_49
| spl61_520
| ~ spl61_52
| ~ spl61_320 ),
inference(avatar_split_clause,[],[f2581,f2505,f1147,f4366,f1132,f1122,f1117]) ).
fof(f4366,plain,
( spl61_520
<=> up_complete_relstr(sK54) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_520])]) ).
fof(f2581,plain,
( up_complete_relstr(sK54)
| ~ reflexive_relstr(sK54)
| empty_carrier(sK54)
| ~ rel_str(sK54)
| ~ spl61_52
| ~ spl61_320 ),
inference(resolution,[],[f2506,f1149]) ).
fof(f4359,plain,
( ~ spl61_62
| spl61_63
| ~ spl61_65
| spl61_519
| ~ spl61_71
| ~ spl61_317 ),
inference(avatar_split_clause,[],[f2577,f2492,f1242,f4356,f1212,f1202,f1197]) ).
fof(f4356,plain,
( spl61_519
<=> sP3(sK56) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_519])]) ).
fof(f1242,plain,
( spl61_71
<=> trivial_carrier(sK56) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_71])]) ).
fof(f2577,plain,
( sP3(sK56)
| ~ reflexive_relstr(sK56)
| empty_carrier(sK56)
| ~ rel_str(sK56)
| ~ spl61_71
| ~ spl61_317 ),
inference(resolution,[],[f2493,f1244]) ).
fof(f1244,plain,
( trivial_carrier(sK56)
| ~ spl61_71 ),
inference(avatar_component_clause,[],[f1242]) ).
fof(f4354,plain,
( ~ spl61_62
| spl61_63
| ~ spl61_65
| spl61_518
| ~ spl61_71
| ~ spl61_316 ),
inference(avatar_split_clause,[],[f2576,f2488,f1242,f4351,f1212,f1202,f1197]) ).
fof(f4351,plain,
( spl61_518
<=> connected_relstr(sK56) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_518])]) ).
fof(f2488,plain,
( spl61_316
<=> ! [X0] :
( connected_relstr(X0)
| ~ trivial_carrier(X0)
| ~ reflexive_relstr(X0)
| empty_carrier(X0)
| ~ rel_str(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_316])]) ).
fof(f2576,plain,
( connected_relstr(sK56)
| ~ reflexive_relstr(sK56)
| empty_carrier(sK56)
| ~ rel_str(sK56)
| ~ spl61_71
| ~ spl61_316 ),
inference(resolution,[],[f2489,f1244]) ).
fof(f2489,plain,
( ! [X0] :
( ~ trivial_carrier(X0)
| connected_relstr(X0)
| ~ reflexive_relstr(X0)
| empty_carrier(X0)
| ~ rel_str(X0) )
| ~ spl61_316 ),
inference(avatar_component_clause,[],[f2488]) ).
fof(f4349,plain,
( spl61_517
| ~ spl61_261
| ~ spl61_315 ),
inference(avatar_split_clause,[],[f2468,f2457,f2121,f4347]) ).
fof(f4347,plain,
( spl61_517
<=> ! [X2,X0,X1] :
( ~ empty(X0)
| ~ in(X1,X2)
| ~ subset(X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_517])]) ).
fof(f2468,plain,
( ! [X2,X0,X1] :
( ~ empty(X0)
| ~ in(X1,X2)
| ~ subset(X2,X0) )
| ~ spl61_261
| ~ spl61_315 ),
inference(resolution,[],[f2458,f2122]) ).
fof(f4345,plain,
( spl61_516
| ~ spl61_260
| ~ spl61_304 ),
inference(avatar_split_clause,[],[f2461,f2412,f2117,f4343]) ).
fof(f4343,plain,
( spl61_516
<=> ! [X1] :
( ~ one_sorted_str(X1)
| subset(sK22(X1),powerset(the_carrier(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_516])]) ).
fof(f2461,plain,
( ! [X1] :
( ~ one_sorted_str(X1)
| subset(sK22(X1),powerset(the_carrier(X1))) )
| ~ spl61_260
| ~ spl61_304 ),
inference(resolution,[],[f2413,f2118]) ).
fof(f4341,plain,
( spl61_515
| ~ spl61_132
| ~ spl61_296 ),
inference(avatar_split_clause,[],[f2402,f2293,f1521,f4339]) ).
fof(f4339,plain,
( spl61_515
<=> ! [X0,X1] :
( empty(X0)
| empty(X1)
| sP0(cartesian_product2(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_515])]) ).
fof(f2293,plain,
( spl61_296
<=> ! [X0,X1] :
( ~ empty(cartesian_product2(X0,X1))
| empty(X1)
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_296])]) ).
fof(f2402,plain,
( ! [X0,X1] :
( empty(X0)
| empty(X1)
| sP0(cartesian_product2(X1,X0)) )
| ~ spl61_132
| ~ spl61_296 ),
inference(resolution,[],[f2294,f1522]) ).
fof(f2294,plain,
( ! [X0,X1] :
( ~ empty(cartesian_product2(X0,X1))
| empty(X1)
| empty(X0) )
| ~ spl61_296 ),
inference(avatar_component_clause,[],[f2293]) ).
fof(f4337,plain,
( spl61_514
| ~ spl61_266
| ~ spl61_292 ),
inference(avatar_split_clause,[],[f2379,f2277,f2171,f4335]) ).
fof(f4335,plain,
( spl61_514
<=> ! [X0] :
( ~ sP10(X0)
| finite(sK37(X0))
| ~ finite(the_carrier(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_514])]) ).
fof(f2379,plain,
( ! [X0] :
( ~ sP10(X0)
| finite(sK37(X0))
| ~ finite(the_carrier(X0)) )
| ~ spl61_266
| ~ spl61_292 ),
inference(resolution,[],[f2278,f2172]) ).
fof(f4333,plain,
( spl61_513
| ~ spl61_266
| ~ spl61_274 ),
inference(avatar_split_clause,[],[f2364,f2204,f2171,f4331]) ).
fof(f4331,plain,
( spl61_513
<=> ! [X0] :
( ~ sP6(X0)
| finite(sK25(X0))
| ~ finite(the_carrier(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_513])]) ).
fof(f2364,plain,
( ! [X0] :
( ~ sP6(X0)
| finite(sK25(X0))
| ~ finite(the_carrier(X0)) )
| ~ spl61_266
| ~ spl61_274 ),
inference(resolution,[],[f2205,f2172]) ).
fof(f4329,plain,
( ~ spl61_511
| ~ spl61_512
| ~ spl61_258
| ~ spl61_504 ),
inference(avatar_split_clause,[],[f4289,f4282,f2108,f4326,f4322]) ).
fof(f4322,plain,
( spl61_511
<=> with_suprema_relstr(sK12) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_511])]) ).
fof(f4326,plain,
( spl61_512
<=> rel_str(sK12) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_512])]) ).
fof(f2108,plain,
( spl61_258
<=> ! [X0] :
( ~ empty(cast_as_carrier_subset(X0))
| ~ rel_str(X0)
| ~ with_suprema_relstr(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_258])]) ).
fof(f4289,plain,
( ~ rel_str(sK12)
| ~ with_suprema_relstr(sK12)
| ~ spl61_258
| ~ spl61_504 ),
inference(resolution,[],[f4284,f2109]) ).
fof(f2109,plain,
( ! [X0] :
( ~ empty(cast_as_carrier_subset(X0))
| ~ rel_str(X0)
| ~ with_suprema_relstr(X0) )
| ~ spl61_258 ),
inference(avatar_component_clause,[],[f2108]) ).
fof(f4320,plain,
( spl61_510
| ~ spl61_266
| ~ spl61_273 ),
inference(avatar_split_clause,[],[f2362,f2200,f2171,f4318]) ).
fof(f4318,plain,
( spl61_510
<=> ! [X0] :
( ~ rel_str(X0)
| finite(sK24(X0))
| ~ finite(the_carrier(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_510])]) ).
fof(f2362,plain,
( ! [X0] :
( ~ rel_str(X0)
| finite(sK24(X0))
| ~ finite(the_carrier(X0)) )
| ~ spl61_266
| ~ spl61_273 ),
inference(resolution,[],[f2201,f2172]) ).
fof(f4316,plain,
( spl61_509
| ~ spl61_266
| ~ spl61_272 ),
inference(avatar_split_clause,[],[f2351,f2196,f2171,f4314]) ).
fof(f4314,plain,
( spl61_509
<=> ! [X0] :
( ~ rel_str(X0)
| finite(sK23(X0))
| ~ finite(the_carrier(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_509])]) ).
fof(f2351,plain,
( ! [X0] :
( ~ rel_str(X0)
| finite(sK23(X0))
| ~ finite(the_carrier(X0)) )
| ~ spl61_266
| ~ spl61_272 ),
inference(resolution,[],[f2197,f2172]) ).
fof(f4312,plain,
( spl61_508
| ~ spl61_265
| ~ spl61_266 ),
inference(avatar_split_clause,[],[f2320,f2171,f2167,f4310]) ).
fof(f4310,plain,
( spl61_508
<=> ! [X2] :
( finite(cast_as_carrier_subset(X2))
| ~ finite(the_carrier(X2))
| ~ one_sorted_str(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_508])]) ).
fof(f2320,plain,
( ! [X2] :
( finite(cast_as_carrier_subset(X2))
| ~ finite(the_carrier(X2))
| ~ one_sorted_str(X2) )
| ~ spl61_265
| ~ spl61_266 ),
inference(resolution,[],[f2172,f2168]) ).
fof(f4308,plain,
( spl61_507
| ~ spl61_192
| ~ spl61_262 ),
inference(avatar_split_clause,[],[f2158,f2125,f1794,f4306]) ).
fof(f4306,plain,
( spl61_507
<=> ! [X6,X5] :
( sK33(X6) = X5
| ~ empty(X5)
| ~ sP9(X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_507])]) ).
fof(f2125,plain,
( spl61_262
<=> ! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_262])]) ).
fof(f2158,plain,
( ! [X6,X5] :
( sK33(X6) = X5
| ~ empty(X5)
| ~ sP9(X6) )
| ~ spl61_192
| ~ spl61_262 ),
inference(resolution,[],[f2126,f1795]) ).
fof(f2126,plain,
( ! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) )
| ~ spl61_262 ),
inference(avatar_component_clause,[],[f2125]) ).
fof(f4304,plain,
( spl61_506
| ~ spl61_169
| ~ spl61_262 ),
inference(avatar_split_clause,[],[f2157,f2125,f1701,f4302]) ).
fof(f4302,plain,
( spl61_506
<=> ! [X4,X3] :
( sK18(X4) = X3
| ~ empty(X3)
| ~ sP1(X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_506])]) ).
fof(f2157,plain,
( ! [X3,X4] :
( sK18(X4) = X3
| ~ empty(X3)
| ~ sP1(X4) )
| ~ spl61_169
| ~ spl61_262 ),
inference(resolution,[],[f2126,f1702]) ).
fof(f4288,plain,
( spl61_504
| spl61_4
| ~ spl61_6
| ~ spl61_7
| spl61_505
| ~ spl61_9
| ~ spl61_388 ),
inference(avatar_split_clause,[],[f3271,f3240,f932,f4286,f922,f917,f907,f4282]) ).
fof(f3271,plain,
( ! [X11] :
( ~ empty_carrier(net_of_bool_filter(X11,cast_as_carrier_subset(sK12),sK13))
| ~ upper_relstr_subset(sK13,boole_POSet(cast_as_carrier_subset(sK12)))
| ~ filtered_subset(sK13,boole_POSet(cast_as_carrier_subset(sK12)))
| empty(sK13)
| ~ element(cast_as_carrier_subset(sK12),powerset(the_carrier(X11)))
| empty(cast_as_carrier_subset(sK12))
| ~ one_sorted_str(X11)
| empty_carrier(X11) )
| ~ spl61_9
| ~ spl61_388 ),
inference(resolution,[],[f3241,f934]) ).
fof(f4250,plain,
( ~ spl61_247
| spl61_503
| ~ spl61_193
| ~ spl61_478 ),
inference(avatar_split_clause,[],[f4130,f4101,f1798,f4247,f2063]) ).
fof(f4247,plain,
( spl61_503
<=> v1_membered(sK60) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_503])]) ).
fof(f1798,plain,
( spl61_193
<=> ! [X0] :
( v1_membered(sK33(X0))
| ~ sP9(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_193])]) ).
fof(f4130,plain,
( v1_membered(sK60)
| ~ sP9(sK12)
| ~ spl61_193
| ~ spl61_478 ),
inference(superposition,[],[f1799,f4103]) ).
fof(f1799,plain,
( ! [X0] :
( v1_membered(sK33(X0))
| ~ sP9(X0) )
| ~ spl61_193 ),
inference(avatar_component_clause,[],[f1798]) ).
fof(f4226,plain,
( ~ spl61_103
| spl61_502
| ~ spl61_103
| ~ spl61_126
| ~ spl61_182
| ~ spl61_199
| ~ spl61_339 ),
inference(avatar_split_clause,[],[f2734,f2677,f1822,f1753,f1496,f1402,f4224,f1402]) ).
fof(f4224,plain,
( spl61_502
<=> ! [X19] :
( boundary_set(sK60,X19)
| ~ top_str(X19) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_502])]) ).
fof(f2734,plain,
( ! [X19] :
( boundary_set(sK60,X19)
| ~ empty(sK60)
| ~ top_str(X19) )
| ~ spl61_103
| ~ spl61_126
| ~ spl61_182
| ~ spl61_199
| ~ spl61_339 ),
inference(forward_demodulation,[],[f2733,f1844]) ).
fof(f2733,plain,
( ! [X19] :
( boundary_set(empty_set,X19)
| ~ empty(sK60)
| ~ top_str(X19) )
| ~ spl61_103
| ~ spl61_126
| ~ spl61_182
| ~ spl61_199
| ~ spl61_339 ),
inference(forward_demodulation,[],[f2732,f1843]) ).
fof(f2732,plain,
( ! [X19] :
( ~ empty(sK60)
| boundary_set(sK39(the_carrier(X19)),X19)
| ~ top_str(X19) )
| ~ spl61_103
| ~ spl61_126
| ~ spl61_182
| ~ spl61_199
| ~ spl61_339 ),
inference(forward_demodulation,[],[f2731,f1844]) ).
fof(f2731,plain,
( ! [X19] :
( ~ empty(empty_set)
| boundary_set(sK39(the_carrier(X19)),X19)
| ~ top_str(X19) )
| ~ spl61_126
| ~ spl61_182
| ~ spl61_199
| ~ spl61_339 ),
inference(forward_demodulation,[],[f2727,f1843]) ).
fof(f2727,plain,
( ! [X19] :
( ~ empty(sK39(the_carrier(X19)))
| boundary_set(sK39(the_carrier(X19)),X19)
| ~ top_str(X19) )
| ~ spl61_199
| ~ spl61_339 ),
inference(resolution,[],[f2678,f1823]) ).
fof(f4222,plain,
( spl61_501
| ~ spl61_159
| ~ spl61_315 ),
inference(avatar_split_clause,[],[f2482,f2457,f1629,f4220]) ).
fof(f2482,plain,
( ! [X28,X29] :
( ~ empty(X28)
| ~ in(X29,sK38(powerset(X28))) )
| ~ spl61_159
| ~ spl61_315 ),
inference(resolution,[],[f2458,f1630]) ).
fof(f4218,plain,
( spl61_500
| ~ spl61_261
| ~ spl61_298 ),
inference(avatar_split_clause,[],[f2403,f2301,f2121,f4216]) ).
fof(f2403,plain,
( ! [X2,X0,X1] :
( relation(X0)
| ~ subset(X0,cartesian_product2(X1,X2)) )
| ~ spl61_261
| ~ spl61_298 ),
inference(resolution,[],[f2302,f2122]) ).
fof(f4214,plain,
( spl61_499
| ~ spl61_103
| ~ spl61_126
| ~ spl61_182
| ~ spl61_199
| ~ spl61_293 ),
inference(avatar_split_clause,[],[f2399,f2281,f1822,f1753,f1496,f1402,f4212]) ).
fof(f4212,plain,
( spl61_499
<=> ! [X14] :
( in(sK60,powerset(X14))
| empty(powerset(X14)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_499])]) ).
fof(f2399,plain,
( ! [X14] :
( in(sK60,powerset(X14))
| empty(powerset(X14)) )
| ~ spl61_103
| ~ spl61_126
| ~ spl61_182
| ~ spl61_199
| ~ spl61_293 ),
inference(forward_demodulation,[],[f2398,f1844]) ).
fof(f2398,plain,
( ! [X14] :
( in(empty_set,powerset(X14))
| empty(powerset(X14)) )
| ~ spl61_126
| ~ spl61_182
| ~ spl61_199
| ~ spl61_293 ),
inference(forward_demodulation,[],[f2396,f1843]) ).
fof(f2396,plain,
( ! [X14] :
( empty(powerset(X14))
| in(sK39(X14),powerset(X14)) )
| ~ spl61_199
| ~ spl61_293 ),
inference(resolution,[],[f2282,f1823]) ).
fof(f4210,plain,
( spl61_498
| ~ spl61_260
| ~ spl61_292 ),
inference(avatar_split_clause,[],[f2380,f2277,f2117,f4208]) ).
fof(f4208,plain,
( spl61_498
<=> ! [X1] :
( ~ sP10(X1)
| subset(sK37(X1),the_carrier(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_498])]) ).
fof(f2380,plain,
( ! [X1] :
( ~ sP10(X1)
| subset(sK37(X1),the_carrier(X1)) )
| ~ spl61_260
| ~ spl61_292 ),
inference(resolution,[],[f2278,f2118]) ).
fof(f4206,plain,
( spl61_497
| ~ spl61_260
| ~ spl61_284 ),
inference(avatar_split_clause,[],[f2378,f2244,f2117,f4204]) ).
fof(f4204,plain,
( spl61_497
<=> ! [X1] :
( ~ sP9(X1)
| subset(sK33(X1),the_carrier(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_497])]) ).
fof(f2378,plain,
( ! [X1] :
( ~ sP9(X1)
| subset(sK33(X1),the_carrier(X1)) )
| ~ spl61_260
| ~ spl61_284 ),
inference(resolution,[],[f2245,f2118]) ).
fof(f4202,plain,
( spl61_496
| ~ spl61_260
| ~ spl61_280 ),
inference(avatar_split_clause,[],[f2367,f2228,f2117,f4200]) ).
fof(f4200,plain,
( spl61_496
<=> ! [X1] :
( ~ sP7(X1)
| subset(sK30(X1),the_carrier(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_496])]) ).
fof(f2367,plain,
( ! [X1] :
( ~ sP7(X1)
| subset(sK30(X1),the_carrier(X1)) )
| ~ spl61_260
| ~ spl61_280 ),
inference(resolution,[],[f2229,f2118]) ).
fof(f4198,plain,
( spl61_495
| ~ spl61_260
| ~ spl61_274 ),
inference(avatar_split_clause,[],[f2365,f2204,f2117,f4196]) ).
fof(f4196,plain,
( spl61_495
<=> ! [X1] :
( ~ sP6(X1)
| subset(sK25(X1),the_carrier(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_495])]) ).
fof(f2365,plain,
( ! [X1] :
( ~ sP6(X1)
| subset(sK25(X1),the_carrier(X1)) )
| ~ spl61_260
| ~ spl61_274 ),
inference(resolution,[],[f2205,f2118]) ).
fof(f4194,plain,
( spl61_494
| ~ spl61_260
| ~ spl61_273 ),
inference(avatar_split_clause,[],[f2363,f2200,f2117,f4192]) ).
fof(f4192,plain,
( spl61_494
<=> ! [X1] :
( ~ rel_str(X1)
| subset(sK24(X1),the_carrier(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_494])]) ).
fof(f2363,plain,
( ! [X1] :
( ~ rel_str(X1)
| subset(sK24(X1),the_carrier(X1)) )
| ~ spl61_260
| ~ spl61_273 ),
inference(resolution,[],[f2201,f2118]) ).
fof(f4190,plain,
( spl61_493
| ~ spl61_260
| ~ spl61_272 ),
inference(avatar_split_clause,[],[f2352,f2196,f2117,f4188]) ).
fof(f4188,plain,
( spl61_493
<=> ! [X1] :
( ~ rel_str(X1)
| subset(sK23(X1),the_carrier(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_493])]) ).
fof(f2352,plain,
( ! [X1] :
( ~ rel_str(X1)
| subset(sK23(X1),the_carrier(X1)) )
| ~ spl61_260
| ~ spl61_272 ),
inference(resolution,[],[f2197,f2118]) ).
fof(f4186,plain,
( spl61_492
| ~ spl61_163
| ~ spl61_477 ),
inference(avatar_split_clause,[],[f4115,f4091,f1676,f4183]) ).
fof(f4183,plain,
( spl61_492
<=> sK60 = sK18(sK12) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_492])]) ).
fof(f1676,plain,
( spl61_163
<=> sP1(sK12) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_163])]) ).
fof(f4115,plain,
( sK60 = sK18(sK12)
| ~ spl61_163
| ~ spl61_477 ),
inference(resolution,[],[f4092,f1678]) ).
fof(f1678,plain,
( sP1(sK12)
| ~ spl61_163 ),
inference(avatar_component_clause,[],[f1676]) ).
fof(f4181,plain,
( spl61_491
| ~ spl61_248
| ~ spl61_266 ),
inference(avatar_split_clause,[],[f2322,f2171,f2068,f4179]) ).
fof(f4179,plain,
( spl61_491
<=> ! [X3] :
( finite(sK15(X3))
| ~ finite(X3)
| empty(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_491])]) ).
fof(f2322,plain,
( ! [X3] :
( finite(sK15(X3))
| ~ finite(X3)
| empty(X3) )
| ~ spl61_248
| ~ spl61_266 ),
inference(resolution,[],[f2172,f2069]) ).
fof(f4177,plain,
( spl61_490
| ~ spl61_261
| ~ spl61_266 ),
inference(avatar_split_clause,[],[f2319,f2171,f2121,f4175]) ).
fof(f4175,plain,
( spl61_490
<=> ! [X0,X1] :
( finite(X0)
| ~ finite(X1)
| ~ subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_490])]) ).
fof(f2319,plain,
( ! [X0,X1] :
( finite(X0)
| ~ finite(X1)
| ~ subset(X0,X1) )
| ~ spl61_261
| ~ spl61_266 ),
inference(resolution,[],[f2172,f2122]) ).
fof(f4173,plain,
( spl61_489
| ~ spl61_260
| ~ spl61_265 ),
inference(avatar_split_clause,[],[f2318,f2167,f2117,f4171]) ).
fof(f4171,plain,
( spl61_489
<=> ! [X0] :
( ~ one_sorted_str(X0)
| subset(cast_as_carrier_subset(X0),the_carrier(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_489])]) ).
fof(f2318,plain,
( ! [X0] :
( ~ one_sorted_str(X0)
| subset(cast_as_carrier_subset(X0),the_carrier(X0)) )
| ~ spl61_260
| ~ spl61_265 ),
inference(resolution,[],[f2168,f2118]) ).
fof(f4169,plain,
( spl61_488
| ~ spl61_260
| ~ spl61_264 ),
inference(avatar_split_clause,[],[f2317,f2163,f2117,f4167]) ).
fof(f4167,plain,
( spl61_488
<=> ! [X0] :
( ~ sP1(X0)
| subset(sK18(X0),the_carrier(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_488])]) ).
fof(f2317,plain,
( ! [X0] :
( ~ sP1(X0)
| subset(sK18(X0),the_carrier(X0)) )
| ~ spl61_260
| ~ spl61_264 ),
inference(resolution,[],[f2164,f2118]) ).
fof(f4165,plain,
( spl61_487
| ~ spl61_132
| ~ spl61_262 ),
inference(avatar_split_clause,[],[f2155,f2125,f1521,f4163]) ).
fof(f2155,plain,
( ! [X0,X1] :
( X0 = X1
| ~ empty(X0)
| sP0(X1) )
| ~ spl61_132
| ~ spl61_262 ),
inference(resolution,[],[f2126,f1522]) ).
fof(f4161,plain,
( spl61_486
| ~ spl61_132
| ~ spl61_258 ),
inference(avatar_split_clause,[],[f2144,f2108,f1521,f4159]) ).
fof(f4159,plain,
( spl61_486
<=> ! [X0] :
( ~ rel_str(X0)
| ~ with_suprema_relstr(X0)
| sP0(cast_as_carrier_subset(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_486])]) ).
fof(f2144,plain,
( ! [X0] :
( ~ rel_str(X0)
| ~ with_suprema_relstr(X0)
| sP0(cast_as_carrier_subset(X0)) )
| ~ spl61_132
| ~ spl61_258 ),
inference(resolution,[],[f2109,f1522]) ).
fof(f4157,plain,
( spl61_485
| ~ spl61_132
| ~ spl61_257 ),
inference(avatar_split_clause,[],[f2143,f2104,f1521,f4155]) ).
fof(f4155,plain,
( spl61_485
<=> ! [X0] :
( ~ rel_str(X0)
| ~ with_infima_relstr(X0)
| sP0(cast_as_carrier_subset(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_485])]) ).
fof(f2104,plain,
( spl61_257
<=> ! [X0] :
( ~ empty(cast_as_carrier_subset(X0))
| ~ rel_str(X0)
| ~ with_infima_relstr(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_257])]) ).
fof(f2143,plain,
( ! [X0] :
( ~ rel_str(X0)
| ~ with_infima_relstr(X0)
| sP0(cast_as_carrier_subset(X0)) )
| ~ spl61_132
| ~ spl61_257 ),
inference(resolution,[],[f2105,f1522]) ).
fof(f2105,plain,
( ! [X0] :
( ~ empty(cast_as_carrier_subset(X0))
| ~ rel_str(X0)
| ~ with_infima_relstr(X0) )
| ~ spl61_257 ),
inference(avatar_component_clause,[],[f2104]) ).
fof(f4153,plain,
( spl61_484
| ~ spl61_132
| ~ spl61_256 ),
inference(avatar_split_clause,[],[f2142,f2100,f1521,f4151]) ).
fof(f4151,plain,
( spl61_484
<=> ! [X0] :
( ~ rel_str(X0)
| empty_carrier(X0)
| sP0(sK29(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_484])]) ).
fof(f2100,plain,
( spl61_256
<=> ! [X0] :
( ~ empty(sK29(X0))
| ~ rel_str(X0)
| empty_carrier(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_256])]) ).
fof(f2142,plain,
( ! [X0] :
( ~ rel_str(X0)
| empty_carrier(X0)
| sP0(sK29(X0)) )
| ~ spl61_132
| ~ spl61_256 ),
inference(resolution,[],[f2101,f1522]) ).
fof(f2101,plain,
( ! [X0] :
( ~ empty(sK29(X0))
| ~ rel_str(X0)
| empty_carrier(X0) )
| ~ spl61_256 ),
inference(avatar_component_clause,[],[f2100]) ).
fof(f4149,plain,
( spl61_483
| ~ spl61_132
| ~ spl61_255 ),
inference(avatar_split_clause,[],[f2141,f2096,f1521,f4147]) ).
fof(f4147,plain,
( spl61_483
<=> ! [X0] :
( ~ rel_str(X0)
| empty_carrier(X0)
| sP0(cast_as_carrier_subset(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_483])]) ).
fof(f2096,plain,
( spl61_255
<=> ! [X0] :
( ~ empty(cast_as_carrier_subset(X0))
| ~ rel_str(X0)
| empty_carrier(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_255])]) ).
fof(f2141,plain,
( ! [X0] :
( ~ rel_str(X0)
| empty_carrier(X0)
| sP0(cast_as_carrier_subset(X0)) )
| ~ spl61_132
| ~ spl61_255 ),
inference(resolution,[],[f2097,f1522]) ).
fof(f2097,plain,
( ! [X0] :
( ~ empty(cast_as_carrier_subset(X0))
| ~ rel_str(X0)
| empty_carrier(X0) )
| ~ spl61_255 ),
inference(avatar_component_clause,[],[f2096]) ).
fof(f4145,plain,
( spl61_482
| ~ spl61_132
| ~ spl61_254 ),
inference(avatar_split_clause,[],[f2135,f2092,f1521,f4143]) ).
fof(f4143,plain,
( spl61_482
<=> ! [X0] :
( ~ one_sorted_str(X0)
| empty_carrier(X0)
| sP0(sK28(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_482])]) ).
fof(f2092,plain,
( spl61_254
<=> ! [X0] :
( ~ empty(sK28(X0))
| ~ one_sorted_str(X0)
| empty_carrier(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_254])]) ).
fof(f2135,plain,
( ! [X0] :
( ~ one_sorted_str(X0)
| empty_carrier(X0)
| sP0(sK28(X0)) )
| ~ spl61_132
| ~ spl61_254 ),
inference(resolution,[],[f2093,f1522]) ).
fof(f2093,plain,
( ! [X0] :
( ~ empty(sK28(X0))
| ~ one_sorted_str(X0)
| empty_carrier(X0) )
| ~ spl61_254 ),
inference(avatar_component_clause,[],[f2092]) ).
fof(f4128,plain,
( spl61_481
| ~ spl61_132
| ~ spl61_253 ),
inference(avatar_split_clause,[],[f2134,f2088,f1521,f4126]) ).
fof(f4126,plain,
( spl61_481
<=> ! [X0] :
( ~ one_sorted_str(X0)
| empty_carrier(X0)
| sP0(the_carrier(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_481])]) ).
fof(f2088,plain,
( spl61_253
<=> ! [X0] :
( ~ empty(the_carrier(X0))
| ~ one_sorted_str(X0)
| empty_carrier(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_253])]) ).
fof(f2134,plain,
( ! [X0] :
( ~ one_sorted_str(X0)
| empty_carrier(X0)
| sP0(the_carrier(X0)) )
| ~ spl61_132
| ~ spl61_253 ),
inference(resolution,[],[f2089,f1522]) ).
fof(f2089,plain,
( ! [X0] :
( ~ empty(the_carrier(X0))
| ~ one_sorted_str(X0)
| empty_carrier(X0) )
| ~ spl61_253 ),
inference(avatar_component_clause,[],[f2088]) ).
fof(f4124,plain,
( spl61_480
| ~ spl61_132
| ~ spl61_252 ),
inference(avatar_split_clause,[],[f2133,f2084,f1521,f4122]) ).
fof(f4122,plain,
( spl61_480
<=> ! [X0] :
( ~ one_sorted_str(X0)
| empty_carrier(X0)
| sP0(cast_as_carrier_subset(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_480])]) ).
fof(f2133,plain,
( ! [X0] :
( ~ one_sorted_str(X0)
| empty_carrier(X0)
| sP0(cast_as_carrier_subset(X0)) )
| ~ spl61_132
| ~ spl61_252 ),
inference(resolution,[],[f2085,f1522]) ).
fof(f4120,plain,
( spl61_479
| ~ spl61_207
| ~ spl61_251 ),
inference(avatar_split_clause,[],[f2129,f2080,f1875,f4118]) ).
fof(f2129,plain,
( ! [X1] :
( rel_str(sK20(X1))
| ~ one_sorted_str(X1)
| ~ sP2(X1) )
| ~ spl61_207
| ~ spl61_251 ),
inference(resolution,[],[f2081,f1876]) ).
fof(f4104,plain,
( spl61_478
| ~ spl61_247
| ~ spl61_450 ),
inference(avatar_split_clause,[],[f4094,f3957,f2063,f4101]) ).
fof(f3957,plain,
( spl61_450
<=> ! [X0] :
( sK33(X0) = sK60
| ~ sP9(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_450])]) ).
fof(f4094,plain,
( sK60 = sK33(sK12)
| ~ spl61_247
| ~ spl61_450 ),
inference(resolution,[],[f3958,f2065]) ).
fof(f2065,plain,
( sP9(sK12)
| ~ spl61_247 ),
inference(avatar_component_clause,[],[f2063]) ).
fof(f3958,plain,
( ! [X0] :
( ~ sP9(X0)
| sK33(X0) = sK60 )
| ~ spl61_450 ),
inference(avatar_component_clause,[],[f3957]) ).
fof(f4093,plain,
( spl61_477
| ~ spl61_169
| ~ spl61_182
| ~ spl61_411 ),
inference(avatar_split_clause,[],[f3679,f3511,f1753,f1701,f4091]) ).
fof(f3679,plain,
( ! [X1] :
( sK60 = sK18(X1)
| ~ sP1(X1) )
| ~ spl61_169
| ~ spl61_182
| ~ spl61_411 ),
inference(forward_demodulation,[],[f1842,f3513]) ).
fof(f1842,plain,
( ! [X1] :
( empty_set = sK18(X1)
| ~ sP1(X1) )
| ~ spl61_169
| ~ spl61_182 ),
inference(resolution,[],[f1754,f1702]) ).
fof(f4089,plain,
( spl61_476
| ~ spl61_298
| ~ spl61_333 ),
inference(avatar_split_clause,[],[f2623,f2565,f2301,f4087]) ).
fof(f2623,plain,
( ! [X2,X0,X1] :
( ~ relation_of2_as_subset(X0,X1,X2)
| relation(X0) )
| ~ spl61_298
| ~ spl61_333 ),
inference(resolution,[],[f2566,f2302]) ).
fof(f4085,plain,
( spl61_475
| ~ spl61_243
| ~ spl61_301 ),
inference(avatar_split_clause,[],[f2410,f2314,f2023,f4083]) ).
fof(f2023,plain,
( spl61_243
<=> ! [X0,X1] : relation_of2(sK42(X0,X1),X0,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_243])]) ).
fof(f2314,plain,
( spl61_301
<=> ! [X2,X0,X1] :
( relation_of2_as_subset(X2,X0,X1)
| ~ relation_of2(X2,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_301])]) ).
fof(f2410,plain,
( ! [X0,X1] : relation_of2_as_subset(sK42(X0,X1),X0,X1)
| ~ spl61_243
| ~ spl61_301 ),
inference(resolution,[],[f2315,f2024]) ).
fof(f2024,plain,
( ! [X0,X1] : relation_of2(sK42(X0,X1),X0,X1)
| ~ spl61_243 ),
inference(avatar_component_clause,[],[f2023]) ).
fof(f2315,plain,
( ! [X2,X0,X1] :
( ~ relation_of2(X2,X0,X1)
| relation_of2_as_subset(X2,X0,X1) )
| ~ spl61_301 ),
inference(avatar_component_clause,[],[f2314]) ).
fof(f4081,plain,
( spl61_474
| ~ spl61_244
| ~ spl61_300 ),
inference(avatar_split_clause,[],[f2409,f2310,f2027,f4079]) ).
fof(f2409,plain,
( ! [X0,X1] : relation_of2(sK43(X0,X1),X0,X1)
| ~ spl61_244
| ~ spl61_300 ),
inference(resolution,[],[f2311,f2028]) ).
fof(f4077,plain,
( spl61_473
| ~ spl61_135
| ~ spl61_263 ),
inference(avatar_split_clause,[],[f3475,f2137,f1533,f4074]) ).
fof(f4074,plain,
( spl61_473
<=> sP2(sK54) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_473])]) ).
fof(f2137,plain,
( spl61_263
<=> one_sorted_str(sK54) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_263])]) ).
fof(f3475,plain,
( sP2(sK54)
| ~ spl61_135
| ~ spl61_263 ),
inference(resolution,[],[f2139,f1534]) ).
fof(f2139,plain,
( one_sorted_str(sK54)
| ~ spl61_263 ),
inference(avatar_component_clause,[],[f2137]) ).
fof(f4072,plain,
( spl61_472
| ~ spl61_159
| ~ spl61_298 ),
inference(avatar_split_clause,[],[f2407,f2301,f1629,f4070]) ).
fof(f4070,plain,
( spl61_472
<=> ! [X9,X10] : relation(sK38(powerset(cartesian_product2(X9,X10)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_472])]) ).
fof(f2407,plain,
( ! [X10,X9] : relation(sK38(powerset(cartesian_product2(X9,X10))))
| ~ spl61_159
| ~ spl61_298 ),
inference(resolution,[],[f2302,f1630]) ).
fof(f4068,plain,
( spl61_471
| ~ spl61_243
| ~ spl61_295 ),
inference(avatar_split_clause,[],[f2401,f2289,f2023,f4066]) ).
fof(f2401,plain,
( ! [X0] : rel_str(rel_str_of(X0,sK42(X0,X0)))
| ~ spl61_243
| ~ spl61_295 ),
inference(resolution,[],[f2290,f2024]) ).
fof(f4064,plain,
( spl61_470
| ~ spl61_243
| ~ spl61_294 ),
inference(avatar_split_clause,[],[f2400,f2285,f2023,f4062]) ).
fof(f4062,plain,
( spl61_470
<=> ! [X0] : strict_rel_str(rel_str_of(X0,sK42(X0,X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_470])]) ).
fof(f2400,plain,
( ! [X0] : strict_rel_str(rel_str_of(X0,sK42(X0,X0)))
| ~ spl61_243
| ~ spl61_294 ),
inference(resolution,[],[f2286,f2024]) ).
fof(f4060,plain,
( spl61_469
| ~ spl61_159
| ~ spl61_293 ),
inference(avatar_split_clause,[],[f2395,f2281,f1629,f4058]) ).
fof(f2395,plain,
( ! [X13] :
( empty(X13)
| in(sK38(X13),X13) )
| ~ spl61_159
| ~ spl61_293 ),
inference(resolution,[],[f2282,f1630]) ).
fof(f4056,plain,
( spl61_93
| spl61_468
| ~ spl61_92
| ~ spl61_94
| ~ spl61_281 ),
inference(avatar_split_clause,[],[f2376,f2232,f1357,f1347,f4053,f1352]) ).
fof(f4053,plain,
( spl61_468
<=> sP7(sK59) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_468])]) ).
fof(f2376,plain,
( ~ rel_str(sK59)
| sP7(sK59)
| empty_carrier(sK59)
| ~ spl61_94
| ~ spl61_281 ),
inference(resolution,[],[f2233,f1359]) ).
fof(f1359,plain,
( reflexive_relstr(sK59)
| ~ spl61_94 ),
inference(avatar_component_clause,[],[f1357]) ).
fof(f4051,plain,
( spl61_87
| spl61_467
| ~ spl61_86
| ~ spl61_88
| ~ spl61_281 ),
inference(avatar_split_clause,[],[f2375,f2232,f1327,f1317,f4048,f1322]) ).
fof(f4048,plain,
( spl61_467
<=> sP7(sK58) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_467])]) ).
fof(f2375,plain,
( ~ rel_str(sK58)
| sP7(sK58)
| empty_carrier(sK58)
| ~ spl61_88
| ~ spl61_281 ),
inference(resolution,[],[f2233,f1329]) ).
fof(f1329,plain,
( reflexive_relstr(sK58)
| ~ spl61_88 ),
inference(avatar_component_clause,[],[f1327]) ).
fof(f4046,plain,
( spl61_73
| spl61_466
| ~ spl61_72
| ~ spl61_75
| ~ spl61_281 ),
inference(avatar_split_clause,[],[f2374,f2232,f1262,f1247,f4043,f1252]) ).
fof(f4043,plain,
( spl61_466
<=> sP7(sK57) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_466])]) ).
fof(f2374,plain,
( ~ rel_str(sK57)
| sP7(sK57)
| empty_carrier(sK57)
| ~ spl61_75
| ~ spl61_281 ),
inference(resolution,[],[f2233,f1264]) ).
fof(f1264,plain,
( reflexive_relstr(sK57)
| ~ spl61_75 ),
inference(avatar_component_clause,[],[f1262]) ).
fof(f4041,plain,
( spl61_465
| ~ spl61_135
| ~ spl61_259 ),
inference(avatar_split_clause,[],[f3474,f2112,f1533,f4038]) ).
fof(f4038,plain,
( spl61_465
<=> sP2(sK53) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_465])]) ).
fof(f2112,plain,
( spl61_259
<=> one_sorted_str(sK53) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_259])]) ).
fof(f3474,plain,
( sP2(sK53)
| ~ spl61_135
| ~ spl61_259 ),
inference(resolution,[],[f2114,f1534]) ).
fof(f2114,plain,
( one_sorted_str(sK53)
| ~ spl61_259 ),
inference(avatar_component_clause,[],[f2112]) ).
fof(f4036,plain,
( spl61_63
| spl61_464
| ~ spl61_62
| ~ spl61_65
| ~ spl61_281 ),
inference(avatar_split_clause,[],[f2373,f2232,f1212,f1197,f4033,f1202]) ).
fof(f4033,plain,
( spl61_464
<=> sP7(sK56) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_464])]) ).
fof(f2373,plain,
( ~ rel_str(sK56)
| sP7(sK56)
| empty_carrier(sK56)
| ~ spl61_65
| ~ spl61_281 ),
inference(resolution,[],[f2233,f1214]) ).
fof(f1214,plain,
( reflexive_relstr(sK56)
| ~ spl61_65 ),
inference(avatar_component_clause,[],[f1212]) ).
fof(f4031,plain,
( spl61_54
| spl61_463
| ~ spl61_53
| ~ spl61_56
| ~ spl61_281 ),
inference(avatar_split_clause,[],[f2372,f2232,f1167,f1152,f4028,f1157]) ).
fof(f4028,plain,
( spl61_463
<=> sP7(sK55) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_463])]) ).
fof(f2372,plain,
( ~ rel_str(sK55)
| sP7(sK55)
| empty_carrier(sK55)
| ~ spl61_56
| ~ spl61_281 ),
inference(resolution,[],[f2233,f1169]) ).
fof(f1169,plain,
( reflexive_relstr(sK55)
| ~ spl61_56 ),
inference(avatar_component_clause,[],[f1167]) ).
fof(f4026,plain,
( spl61_47
| spl61_462
| ~ spl61_46
| ~ spl61_49
| ~ spl61_281 ),
inference(avatar_split_clause,[],[f2371,f2232,f1132,f1117,f4023,f1122]) ).
fof(f4023,plain,
( spl61_462
<=> sP7(sK54) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_462])]) ).
fof(f2371,plain,
( ~ rel_str(sK54)
| sP7(sK54)
| empty_carrier(sK54)
| ~ spl61_49
| ~ spl61_281 ),
inference(resolution,[],[f2233,f1134]) ).
fof(f1134,plain,
( reflexive_relstr(sK54)
| ~ spl61_49 ),
inference(avatar_component_clause,[],[f1132]) ).
fof(f4021,plain,
( spl61_25
| spl61_461
| ~ spl61_24
| ~ spl61_28
| ~ spl61_281 ),
inference(avatar_split_clause,[],[f2370,f2232,f1027,f1007,f4018,f1012]) ).
fof(f4018,plain,
( spl61_461
<=> sP7(sK52) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_461])]) ).
fof(f2370,plain,
( ~ rel_str(sK52)
| sP7(sK52)
| empty_carrier(sK52)
| ~ spl61_28
| ~ spl61_281 ),
inference(resolution,[],[f2233,f1029]) ).
fof(f1029,plain,
( reflexive_relstr(sK52)
| ~ spl61_28 ),
inference(avatar_component_clause,[],[f1027]) ).
fof(f4014,plain,
( ~ spl61_46
| spl61_47
| spl61_460
| ~ spl61_52
| ~ spl61_270 ),
inference(avatar_split_clause,[],[f2342,f2188,f1147,f4011,f1122,f1117]) ).
fof(f2188,plain,
( spl61_270
<=> ! [X0] :
( with_infima_relstr(X0)
| ~ complete_relstr(X0)
| empty_carrier(X0)
| ~ rel_str(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_270])]) ).
fof(f2342,plain,
( with_infima_relstr(sK54)
| empty_carrier(sK54)
| ~ rel_str(sK54)
| ~ spl61_52
| ~ spl61_270 ),
inference(resolution,[],[f2189,f1149]) ).
fof(f2189,plain,
( ! [X0] :
( ~ complete_relstr(X0)
| with_infima_relstr(X0)
| empty_carrier(X0)
| ~ rel_str(X0) )
| ~ spl61_270 ),
inference(avatar_component_clause,[],[f2188]) ).
fof(f4006,plain,
( ~ spl61_46
| spl61_47
| spl61_459
| ~ spl61_52
| ~ spl61_269 ),
inference(avatar_split_clause,[],[f2336,f2184,f1147,f4003,f1122,f1117]) ).
fof(f2184,plain,
( spl61_269
<=> ! [X0] :
( with_suprema_relstr(X0)
| ~ complete_relstr(X0)
| empty_carrier(X0)
| ~ rel_str(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_269])]) ).
fof(f2336,plain,
( with_suprema_relstr(sK54)
| empty_carrier(sK54)
| ~ rel_str(sK54)
| ~ spl61_52
| ~ spl61_269 ),
inference(resolution,[],[f2185,f1149]) ).
fof(f2185,plain,
( ! [X0] :
( ~ complete_relstr(X0)
| with_suprema_relstr(X0)
| empty_carrier(X0)
| ~ rel_str(X0) )
| ~ spl61_269 ),
inference(avatar_component_clause,[],[f2184]) ).
fof(f3999,plain,
( ~ spl61_62
| spl61_63
| spl61_458
| ~ spl61_70
| ~ spl61_268 ),
inference(avatar_split_clause,[],[f2332,f2180,f1237,f3996,f1202,f1197]) ).
fof(f2180,plain,
( spl61_268
<=> ! [X0] :
( bounded_relstr(X0)
| ~ complete_relstr(X0)
| empty_carrier(X0)
| ~ rel_str(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_268])]) ).
fof(f2332,plain,
( bounded_relstr(sK56)
| empty_carrier(sK56)
| ~ rel_str(sK56)
| ~ spl61_70
| ~ spl61_268 ),
inference(resolution,[],[f2181,f1239]) ).
fof(f2181,plain,
( ! [X0] :
( ~ complete_relstr(X0)
| bounded_relstr(X0)
| empty_carrier(X0)
| ~ rel_str(X0) )
| ~ spl61_268 ),
inference(avatar_component_clause,[],[f2180]) ).
fof(f3992,plain,
( ~ spl61_53
| spl61_54
| spl61_457
| ~ spl61_61
| ~ spl61_268 ),
inference(avatar_split_clause,[],[f2331,f2180,f1192,f3989,f1157,f1152]) ).
fof(f2331,plain,
( bounded_relstr(sK55)
| empty_carrier(sK55)
| ~ rel_str(sK55)
| ~ spl61_61
| ~ spl61_268 ),
inference(resolution,[],[f2181,f1194]) ).
fof(f3985,plain,
( ~ spl61_46
| spl61_47
| spl61_456
| ~ spl61_52
| ~ spl61_268 ),
inference(avatar_split_clause,[],[f2330,f2180,f1147,f3982,f1122,f1117]) ).
fof(f2330,plain,
( bounded_relstr(sK54)
| empty_carrier(sK54)
| ~ rel_str(sK54)
| ~ spl61_52
| ~ spl61_268 ),
inference(resolution,[],[f2181,f1149]) ).
fof(f3980,plain,
( spl61_455
| ~ spl61_159
| ~ spl61_266 ),
inference(avatar_split_clause,[],[f2326,f2171,f1629,f3978]) ).
fof(f3978,plain,
( spl61_455
<=> ! [X7] :
( finite(sK38(powerset(X7)))
| ~ finite(X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_455])]) ).
fof(f2326,plain,
( ! [X7] :
( finite(sK38(powerset(X7)))
| ~ finite(X7) )
| ~ spl61_159
| ~ spl61_266 ),
inference(resolution,[],[f2172,f1630]) ).
fof(f3976,plain,
( spl61_454
| ~ spl61_250
| ~ spl61_260 ),
inference(avatar_split_clause,[],[f2148,f2117,f2076,f3974]) ).
fof(f3974,plain,
( spl61_454
<=> ! [X2] :
( subset(sK17(X2),X2)
| empty(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_454])]) ).
fof(f2148,plain,
( ! [X2] :
( subset(sK17(X2),X2)
| empty(X2) )
| ~ spl61_250
| ~ spl61_260 ),
inference(resolution,[],[f2118,f2077]) ).
fof(f3972,plain,
( spl61_453
| ~ spl61_249
| ~ spl61_260 ),
inference(avatar_split_clause,[],[f2147,f2117,f2072,f3970]) ).
fof(f3970,plain,
( spl61_453
<=> ! [X1] :
( subset(sK16(X1),X1)
| empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_453])]) ).
fof(f2147,plain,
( ! [X1] :
( subset(sK16(X1),X1)
| empty(X1) )
| ~ spl61_249
| ~ spl61_260 ),
inference(resolution,[],[f2118,f2073]) ).
fof(f3968,plain,
( spl61_452
| ~ spl61_135
| ~ spl61_246 ),
inference(avatar_split_clause,[],[f3473,f2056,f1533,f3965]) ).
fof(f3965,plain,
( spl61_452
<=> sP2(sK52) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_452])]) ).
fof(f2056,plain,
( spl61_246
<=> one_sorted_str(sK52) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_246])]) ).
fof(f3473,plain,
( sP2(sK52)
| ~ spl61_135
| ~ spl61_246 ),
inference(resolution,[],[f2058,f1534]) ).
fof(f2058,plain,
( one_sorted_str(sK52)
| ~ spl61_246 ),
inference(avatar_component_clause,[],[f2056]) ).
fof(f3963,plain,
( spl61_451
| ~ spl61_248
| ~ spl61_260 ),
inference(avatar_split_clause,[],[f2146,f2117,f2068,f3961]) ).
fof(f3961,plain,
( spl61_451
<=> ! [X0] :
( subset(sK15(X0),X0)
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_451])]) ).
fof(f2146,plain,
( ! [X0] :
( subset(sK15(X0),X0)
| empty(X0) )
| ~ spl61_248
| ~ spl61_260 ),
inference(resolution,[],[f2118,f2069]) ).
fof(f3959,plain,
( spl61_450
| ~ spl61_103
| ~ spl61_182
| ~ spl61_192 ),
inference(avatar_split_clause,[],[f1855,f1794,f1753,f1402,f3957]) ).
fof(f1855,plain,
( ! [X0] :
( sK33(X0) = sK60
| ~ sP9(X0) )
| ~ spl61_103
| ~ spl61_182
| ~ spl61_192 ),
inference(forward_demodulation,[],[f1852,f1844]) ).
fof(f1852,plain,
( ! [X0] :
( ~ sP9(X0)
| empty_set = sK33(X0) )
| ~ spl61_182
| ~ spl61_192 ),
inference(resolution,[],[f1795,f1754]) ).
fof(f3947,plain,
( spl61_449
| ~ spl61_135
| ~ spl61_245 ),
inference(avatar_split_clause,[],[f3472,f2035,f1533,f3944]) ).
fof(f3944,plain,
( spl61_449
<=> sP2(sK47) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_449])]) ).
fof(f2035,plain,
( spl61_245
<=> one_sorted_str(sK47) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_245])]) ).
fof(f3472,plain,
( sP2(sK47)
| ~ spl61_135
| ~ spl61_245 ),
inference(resolution,[],[f2037,f1534]) ).
fof(f2037,plain,
( one_sorted_str(sK47)
| ~ spl61_245 ),
inference(avatar_component_clause,[],[f2035]) ).
fof(f3942,plain,
( spl61_448
| ~ spl61_411
| ~ spl61_434 ),
inference(avatar_split_clause,[],[f3622,f3619,f3511,f3940]) ).
fof(f3940,plain,
( spl61_448
<=> ! [X0] :
( sK60 = X0
| sP0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_448])]) ).
fof(f3619,plain,
( spl61_434
<=> ! [X0] :
( empty_set = X0
| sP0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_434])]) ).
fof(f3622,plain,
( ! [X0] :
( sK60 = X0
| sP0(X0) )
| ~ spl61_411
| ~ spl61_434 ),
inference(forward_demodulation,[],[f3620,f3513]) ).
fof(f3620,plain,
( ! [X0] :
( empty_set = X0
| sP0(X0) )
| ~ spl61_434 ),
inference(avatar_component_clause,[],[f3619]) ).
fof(f3938,plain,
( spl61_447
| ~ spl61_135
| ~ spl61_209 ),
inference(avatar_split_clause,[],[f3471,f1883,f1533,f3935]) ).
fof(f3935,plain,
( spl61_447
<=> sP2(sK45) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_447])]) ).
fof(f1883,plain,
( spl61_209
<=> one_sorted_str(sK45) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_209])]) ).
fof(f3471,plain,
( sP2(sK45)
| ~ spl61_135
| ~ spl61_209 ),
inference(resolution,[],[f1885,f1534]) ).
fof(f1885,plain,
( one_sorted_str(sK45)
| ~ spl61_209 ),
inference(avatar_component_clause,[],[f1883]) ).
fof(f3713,plain,
( spl61_444
| ~ spl61_182
| ~ spl61_411 ),
inference(avatar_split_clause,[],[f3680,f3511,f1753,f3660]) ).
fof(f3660,plain,
( spl61_444
<=> ! [X9] :
( sK60 = X9
| ~ empty(X9) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_444])]) ).
fof(f3680,plain,
( ! [X0] :
( sK60 = X0
| ~ empty(X0) )
| ~ spl61_182
| ~ spl61_411 ),
inference(forward_demodulation,[],[f1754,f3513]) ).
fof(f3678,plain,
( ~ spl61_10
| ~ spl61_445 ),
inference(avatar_contradiction_clause,[],[f3671]) ).
fof(f3671,plain,
( $false
| ~ spl61_10
| ~ spl61_445 ),
inference(resolution,[],[f3665,f939]) ).
fof(f939,plain,
( empty(empty_set)
| ~ spl61_10 ),
inference(avatar_component_clause,[],[f937]) ).
fof(f937,plain,
( spl61_10
<=> empty(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_10])]) ).
fof(f3665,plain,
( ! [X30] : ~ empty(X30)
| ~ spl61_445 ),
inference(avatar_component_clause,[],[f3664]) ).
fof(f3664,plain,
( spl61_445
<=> ! [X30] : ~ empty(X30) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_445])]) ).
fof(f3677,plain,
( ~ spl61_126
| ~ spl61_445 ),
inference(avatar_contradiction_clause,[],[f3674]) ).
fof(f3674,plain,
( $false
| ~ spl61_126
| ~ spl61_445 ),
inference(resolution,[],[f3665,f1497]) ).
fof(f3676,plain,
( ~ spl61_103
| ~ spl61_445 ),
inference(avatar_contradiction_clause,[],[f3675]) ).
fof(f3675,plain,
( $false
| ~ spl61_103
| ~ spl61_445 ),
inference(resolution,[],[f3665,f1404]) ).
fof(f3669,plain,
( spl61_445
| spl61_446
| ~ spl61_103
| ~ spl61_126
| ~ spl61_182
| ~ spl61_199
| ~ spl61_315 ),
inference(avatar_split_clause,[],[f2486,f2457,f1822,f1753,f1496,f1402,f3667,f3664]) ).
fof(f2486,plain,
( ! [X31,X30] :
( ~ in(X31,sK60)
| ~ empty(X30) )
| ~ spl61_103
| ~ spl61_126
| ~ spl61_182
| ~ spl61_199
| ~ spl61_315 ),
inference(forward_demodulation,[],[f2485,f1844]) ).
fof(f2485,plain,
( ! [X31,X30] :
( ~ in(X31,empty_set)
| ~ empty(X30) )
| ~ spl61_126
| ~ spl61_182
| ~ spl61_199
| ~ spl61_315 ),
inference(forward_demodulation,[],[f2483,f1843]) ).
fof(f2483,plain,
( ! [X31,X30] :
( ~ empty(X30)
| ~ in(X31,sK39(X30)) )
| ~ spl61_199
| ~ spl61_315 ),
inference(resolution,[],[f2458,f1823]) ).
fof(f3662,plain,
( spl61_444
| ~ spl61_103
| ~ spl61_262 ),
inference(avatar_split_clause,[],[f2160,f2125,f1402,f3660]) ).
fof(f2160,plain,
( ! [X9] :
( sK60 = X9
| ~ empty(X9) )
| ~ spl61_103
| ~ spl61_262 ),
inference(resolution,[],[f2126,f1404]) ).
fof(f3658,plain,
( spl61_443
| ~ spl61_239
| ~ spl61_260 ),
inference(avatar_split_clause,[],[f2151,f2117,f2006,f3656]) ).
fof(f3656,plain,
( spl61_443
<=> ! [X5] : subset(sK40(X5),powerset(X5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_443])]) ).
fof(f2151,plain,
( ! [X5] : subset(sK40(X5),powerset(X5))
| ~ spl61_239
| ~ spl61_260 ),
inference(resolution,[],[f2118,f2007]) ).
fof(f3654,plain,
( spl61_442
| ~ spl61_159
| ~ spl61_260 ),
inference(avatar_split_clause,[],[f2149,f2117,f1629,f3652]) ).
fof(f3652,plain,
( spl61_442
<=> ! [X3] : subset(sK38(powerset(X3)),X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_442])]) ).
fof(f2149,plain,
( ! [X3] : subset(sK38(powerset(X3)),X3)
| ~ spl61_159
| ~ spl61_260 ),
inference(resolution,[],[f2118,f1630]) ).
fof(f3650,plain,
( spl61_441
| ~ spl61_206
| ~ spl61_251 ),
inference(avatar_split_clause,[],[f2132,f2080,f1871,f3648]) ).
fof(f2132,plain,
( ! [X0] :
( rel_str(sK19(X0))
| ~ one_sorted_str(X0) )
| ~ spl61_206
| ~ spl61_251 ),
inference(duplicate_literal_removal,[],[f2128]) ).
fof(f2128,plain,
( ! [X0] :
( rel_str(sK19(X0))
| ~ one_sorted_str(X0)
| ~ one_sorted_str(X0) )
| ~ spl61_206
| ~ spl61_251 ),
inference(resolution,[],[f2081,f1872]) ).
fof(f3646,plain,
( spl61_440
| ~ spl61_210
| ~ spl61_251 ),
inference(avatar_split_clause,[],[f2131,f2080,f1888,f3644]) ).
fof(f2131,plain,
( ! [X2] :
( rel_str(sK21(X2))
| ~ one_sorted_str(X2) )
| ~ spl61_210
| ~ spl61_251 ),
inference(duplicate_literal_removal,[],[f2130]) ).
fof(f2130,plain,
( ! [X2] :
( rel_str(sK21(X2))
| ~ one_sorted_str(X2)
| ~ one_sorted_str(X2) )
| ~ spl61_210
| ~ spl61_251 ),
inference(resolution,[],[f2081,f1889]) ).
fof(f3642,plain,
( spl61_439
| ~ spl61_132
| ~ spl61_198 ),
inference(avatar_split_clause,[],[f1861,f1818,f1521,f3640]) ).
fof(f3640,plain,
( spl61_439
<=> ! [X0] :
( ~ sP10(X0)
| sP0(sK37(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_439])]) ).
fof(f1818,plain,
( spl61_198
<=> ! [X0] :
( ~ empty(sK37(X0))
| ~ sP10(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_198])]) ).
fof(f1861,plain,
( ! [X0] :
( ~ sP10(X0)
| sP0(sK37(X0)) )
| ~ spl61_132
| ~ spl61_198 ),
inference(resolution,[],[f1819,f1522]) ).
fof(f1819,plain,
( ! [X0] :
( ~ empty(sK37(X0))
| ~ sP10(X0) )
| ~ spl61_198 ),
inference(avatar_component_clause,[],[f1818]) ).
fof(f3638,plain,
( spl61_438
| ~ spl61_157
| ~ spl61_192 ),
inference(avatar_split_clause,[],[f1854,f1794,f1621,f3636]) ).
fof(f3636,plain,
( spl61_438
<=> ! [X2] :
( ~ sP9(X2)
| relation(sK33(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_438])]) ).
fof(f1621,plain,
( spl61_157
<=> ! [X0] :
( relation(X0)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_157])]) ).
fof(f1854,plain,
( ! [X2] :
( ~ sP9(X2)
| relation(sK33(X2)) )
| ~ spl61_157
| ~ spl61_192 ),
inference(resolution,[],[f1795,f1622]) ).
fof(f1622,plain,
( ! [X0] :
( ~ empty(X0)
| relation(X0) )
| ~ spl61_157 ),
inference(avatar_component_clause,[],[f1621]) ).
fof(f3634,plain,
( spl61_437
| ~ spl61_158
| ~ spl61_192 ),
inference(avatar_split_clause,[],[f1853,f1794,f1625,f3632]) ).
fof(f3632,plain,
( spl61_437
<=> ! [X1] :
( ~ sP9(X1)
| finite(sK33(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_437])]) ).
fof(f1625,plain,
( spl61_158
<=> ! [X0] :
( finite(X0)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_158])]) ).
fof(f1853,plain,
( ! [X1] :
( ~ sP9(X1)
| finite(sK33(X1)) )
| ~ spl61_158
| ~ spl61_192 ),
inference(resolution,[],[f1795,f1626]) ).
fof(f1626,plain,
( ! [X0] :
( ~ empty(X0)
| finite(X0) )
| ~ spl61_158 ),
inference(avatar_component_clause,[],[f1625]) ).
fof(f3630,plain,
( spl61_436
| ~ spl61_132
| ~ spl61_184 ),
inference(avatar_split_clause,[],[f1846,f1762,f1521,f3628]) ).
fof(f3628,plain,
( spl61_436
<=> ! [X0] :
( ~ sP7(X0)
| sP0(sK30(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_436])]) ).
fof(f1762,plain,
( spl61_184
<=> ! [X0] :
( ~ empty(sK30(X0))
| ~ sP7(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_184])]) ).
fof(f1846,plain,
( ! [X0] :
( ~ sP7(X0)
| sP0(sK30(X0)) )
| ~ spl61_132
| ~ spl61_184 ),
inference(resolution,[],[f1763,f1522]) ).
fof(f1763,plain,
( ! [X0] :
( ~ empty(sK30(X0))
| ~ sP7(X0) )
| ~ spl61_184 ),
inference(avatar_component_clause,[],[f1762]) ).
fof(f3626,plain,
( spl61_435
| ~ spl61_132
| ~ spl61_183 ),
inference(avatar_split_clause,[],[f1845,f1757,f1521,f3624]) ).
fof(f3624,plain,
( spl61_435
<=> ! [X0] :
( ~ sP6(X0)
| sP0(sK25(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_435])]) ).
fof(f1757,plain,
( spl61_183
<=> ! [X0] :
( ~ empty(sK25(X0))
| ~ sP6(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_183])]) ).
fof(f1845,plain,
( ! [X0] :
( ~ sP6(X0)
| sP0(sK25(X0)) )
| ~ spl61_132
| ~ spl61_183 ),
inference(resolution,[],[f1758,f1522]) ).
fof(f1758,plain,
( ! [X0] :
( ~ empty(sK25(X0))
| ~ sP6(X0) )
| ~ spl61_183 ),
inference(avatar_component_clause,[],[f1757]) ).
fof(f3621,plain,
( spl61_434
| ~ spl61_132
| ~ spl61_182 ),
inference(avatar_split_clause,[],[f1840,f1753,f1521,f3619]) ).
fof(f1840,plain,
( ! [X0] :
( empty_set = X0
| sP0(X0) )
| ~ spl61_132
| ~ spl61_182 ),
inference(resolution,[],[f1754,f1522]) ).
fof(f3617,plain,
( spl61_433
| ~ spl61_132
| ~ spl61_180 ),
inference(avatar_split_clause,[],[f1839,f1745,f1521,f3615]) ).
fof(f3615,plain,
( spl61_433
<=> ! [X0] :
( ~ one_sorted_str(X0)
| sP0(sK22(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_433])]) ).
fof(f1745,plain,
( spl61_180
<=> ! [X0] :
( ~ empty(sK22(X0))
| ~ one_sorted_str(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_180])]) ).
fof(f1839,plain,
( ! [X0] :
( ~ one_sorted_str(X0)
| sP0(sK22(X0)) )
| ~ spl61_132
| ~ spl61_180 ),
inference(resolution,[],[f1746,f1522]) ).
fof(f1746,plain,
( ! [X0] :
( ~ empty(sK22(X0))
| ~ one_sorted_str(X0) )
| ~ spl61_180 ),
inference(avatar_component_clause,[],[f1745]) ).
fof(f3613,plain,
( spl61_432
| ~ spl61_157
| ~ spl61_169 ),
inference(avatar_split_clause,[],[f1838,f1701,f1621,f3611]) ).
fof(f3611,plain,
( spl61_432
<=> ! [X1] :
( ~ sP1(X1)
| relation(sK18(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_432])]) ).
fof(f1838,plain,
( ! [X1] :
( ~ sP1(X1)
| relation(sK18(X1)) )
| ~ spl61_157
| ~ spl61_169 ),
inference(resolution,[],[f1702,f1622]) ).
fof(f3609,plain,
( spl61_431
| ~ spl61_158
| ~ spl61_169 ),
inference(avatar_split_clause,[],[f1837,f1701,f1625,f3607]) ).
fof(f3607,plain,
( spl61_431
<=> ! [X0] :
( ~ sP1(X0)
| finite(sK18(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_431])]) ).
fof(f1837,plain,
( ! [X0] :
( ~ sP1(X0)
| finite(sK18(X0)) )
| ~ spl61_158
| ~ spl61_169 ),
inference(resolution,[],[f1702,f1626]) ).
fof(f3605,plain,
( spl61_430
| ~ spl61_132
| ~ spl61_167 ),
inference(avatar_split_clause,[],[f1836,f1693,f1521,f3603]) ).
fof(f3603,plain,
( spl61_430
<=> ! [X0] :
( empty(X0)
| sP0(sK17(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_430])]) ).
fof(f1693,plain,
( spl61_167
<=> ! [X0] :
( ~ empty(sK17(X0))
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_167])]) ).
fof(f1836,plain,
( ! [X0] :
( empty(X0)
| sP0(sK17(X0)) )
| ~ spl61_132
| ~ spl61_167 ),
inference(resolution,[],[f1694,f1522]) ).
fof(f1694,plain,
( ! [X0] :
( ~ empty(sK17(X0))
| empty(X0) )
| ~ spl61_167 ),
inference(avatar_component_clause,[],[f1693]) ).
fof(f3601,plain,
( ~ spl61_429
| ~ spl61_240
| ~ spl61_413 ),
inference(avatar_split_clause,[],[f3533,f3524,f2010,f3598]) ).
fof(f3598,plain,
( spl61_429
<=> in(powerset(the_carrier(boole_POSet(cast_as_carrier_subset(sK12)))),sK13) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_429])]) ).
fof(f3524,plain,
( spl61_413
<=> in(sK13,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(sK12))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_413])]) ).
fof(f3533,plain,
( ~ in(powerset(the_carrier(boole_POSet(cast_as_carrier_subset(sK12)))),sK13)
| ~ spl61_240
| ~ spl61_413 ),
inference(resolution,[],[f3526,f2011]) ).
fof(f3526,plain,
( in(sK13,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(sK12)))))
| ~ spl61_413 ),
inference(avatar_component_clause,[],[f3524]) ).
fof(f3596,plain,
( spl61_428
| ~ spl61_132
| ~ spl61_165 ),
inference(avatar_split_clause,[],[f1830,f1685,f1521,f3594]) ).
fof(f3594,plain,
( spl61_428
<=> ! [X0] :
( empty(X0)
| sP0(sK16(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_428])]) ).
fof(f1685,plain,
( spl61_165
<=> ! [X0] :
( ~ empty(sK16(X0))
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_165])]) ).
fof(f1830,plain,
( ! [X0] :
( empty(X0)
| sP0(sK16(X0)) )
| ~ spl61_132
| ~ spl61_165 ),
inference(resolution,[],[f1686,f1522]) ).
fof(f1686,plain,
( ! [X0] :
( ~ empty(sK16(X0))
| empty(X0) )
| ~ spl61_165 ),
inference(avatar_component_clause,[],[f1685]) ).
fof(f3592,plain,
( spl61_427
| ~ spl61_132
| ~ spl61_164 ),
inference(avatar_split_clause,[],[f1829,f1681,f1521,f3590]) ).
fof(f3590,plain,
( spl61_427
<=> ! [X0] :
( empty(X0)
| sP0(sK15(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_427])]) ).
fof(f1681,plain,
( spl61_164
<=> ! [X0] :
( ~ empty(sK15(X0))
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_164])]) ).
fof(f1829,plain,
( ! [X0] :
( empty(X0)
| sP0(sK15(X0)) )
| ~ spl61_132
| ~ spl61_164 ),
inference(resolution,[],[f1682,f1522]) ).
fof(f1682,plain,
( ! [X0] :
( ~ empty(sK15(X0))
| empty(X0) )
| ~ spl61_164 ),
inference(avatar_component_clause,[],[f1681]) ).
fof(f3588,plain,
( ~ spl61_423
| ~ spl61_424
| spl61_425
| ~ spl61_426
| ~ spl61_9
| ~ spl61_364 ),
inference(avatar_split_clause,[],[f2971,f2966,f932,f3585,f3581,f3577,f3573]) ).
fof(f3573,plain,
( spl61_423
<=> topological_space(boole_POSet(cast_as_carrier_subset(sK12))) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_423])]) ).
fof(f3577,plain,
( spl61_424
<=> top_str(boole_POSet(cast_as_carrier_subset(sK12))) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_424])]) ).
fof(f3581,plain,
( spl61_425
<=> boundary_set(sK13,boole_POSet(cast_as_carrier_subset(sK12))) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_425])]) ).
fof(f3585,plain,
( spl61_426
<=> nowhere_dense(sK13,boole_POSet(cast_as_carrier_subset(sK12))) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_426])]) ).
fof(f2971,plain,
( ~ nowhere_dense(sK13,boole_POSet(cast_as_carrier_subset(sK12)))
| boundary_set(sK13,boole_POSet(cast_as_carrier_subset(sK12)))
| ~ top_str(boole_POSet(cast_as_carrier_subset(sK12)))
| ~ topological_space(boole_POSet(cast_as_carrier_subset(sK12)))
| ~ spl61_9
| ~ spl61_364 ),
inference(resolution,[],[f2967,f934]) ).
fof(f3568,plain,
( spl61_422
| ~ spl61_9
| ~ spl61_335 ),
inference(avatar_split_clause,[],[f2631,f2573,f932,f3566]) ).
fof(f2631,plain,
( ! [X9] :
( element(X9,the_carrier(boole_POSet(cast_as_carrier_subset(sK12))))
| ~ in(X9,sK13) )
| ~ spl61_9
| ~ spl61_335 ),
inference(resolution,[],[f2574,f934]) ).
fof(f3564,plain,
( spl61_421
| ~ spl61_353
| ~ spl61_386 ),
inference(avatar_split_clause,[],[f3435,f3230,f2784,f3562]) ).
fof(f3435,plain,
( ! [X0] :
( in(sK41(X0,sK13),X0)
| sK13 = X0 )
| ~ spl61_353
| ~ spl61_386 ),
inference(resolution,[],[f3231,f2785]) ).
fof(f3560,plain,
( spl61_420
| ~ spl61_411
| ~ spl61_417 ),
inference(avatar_split_clause,[],[f3547,f3544,f3511,f3558]) ).
fof(f3544,plain,
( spl61_417
<=> ! [X2] : empty_set = sK39(X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_417])]) ).
fof(f3547,plain,
( ! [X2] : sK60 = sK39(X2)
| ~ spl61_411
| ~ spl61_417 ),
inference(forward_demodulation,[],[f3545,f3513]) ).
fof(f3545,plain,
( ! [X2] : empty_set = sK39(X2)
| ~ spl61_417 ),
inference(avatar_component_clause,[],[f3544]) ).
fof(f3556,plain,
( ~ spl61_418
| spl61_419
| ~ spl61_13
| ~ spl61_234 ),
inference(avatar_split_clause,[],[f2061,f1986,f952,f3553,f3549]) ).
fof(f3549,plain,
( spl61_418
<=> topological_space(sK45) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_418])]) ).
fof(f3553,plain,
( spl61_419
<=> sP9(sK45) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_419])]) ).
fof(f952,plain,
( spl61_13
<=> top_str(sK45) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_13])]) ).
fof(f1986,plain,
( spl61_234
<=> ! [X0] :
( sP9(X0)
| ~ top_str(X0)
| ~ topological_space(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_234])]) ).
fof(f2061,plain,
( sP9(sK45)
| ~ topological_space(sK45)
| ~ spl61_13
| ~ spl61_234 ),
inference(resolution,[],[f1987,f954]) ).
fof(f954,plain,
( top_str(sK45)
| ~ spl61_13 ),
inference(avatar_component_clause,[],[f952]) ).
fof(f1987,plain,
( ! [X0] :
( ~ top_str(X0)
| sP9(X0)
| ~ topological_space(X0) )
| ~ spl61_234 ),
inference(avatar_component_clause,[],[f1986]) ).
fof(f3546,plain,
( spl61_417
| ~ spl61_126
| ~ spl61_182 ),
inference(avatar_split_clause,[],[f1843,f1753,f1496,f3544]) ).
fof(f3542,plain,
( spl61_416
| ~ spl61_132
| ~ spl61_158 ),
inference(avatar_split_clause,[],[f1667,f1625,f1521,f3540]) ).
fof(f3540,plain,
( spl61_416
<=> ! [X0] :
( finite(X0)
| sP0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_416])]) ).
fof(f1667,plain,
( ! [X0] :
( finite(X0)
| sP0(X0) )
| ~ spl61_132
| ~ spl61_158 ),
inference(resolution,[],[f1626,f1522]) ).
fof(f3538,plain,
( spl61_415
| ~ spl61_132
| ~ spl61_157 ),
inference(avatar_split_clause,[],[f1663,f1621,f1521,f3536]) ).
fof(f3536,plain,
( spl61_415
<=> ! [X0] :
( relation(X0)
| sP0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_415])]) ).
fof(f1663,plain,
( ! [X0] :
( relation(X0)
| sP0(X0) )
| ~ spl61_132
| ~ spl61_157 ),
inference(resolution,[],[f1622,f1522]) ).
fof(f3531,plain,
( spl61_413
| spl61_414
| ~ spl61_9
| ~ spl61_293 ),
inference(avatar_split_clause,[],[f2383,f2281,f932,f3528,f3524]) ).
fof(f3528,plain,
( spl61_414
<=> empty(powerset(the_carrier(boole_POSet(cast_as_carrier_subset(sK12))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_414])]) ).
fof(f2383,plain,
( empty(powerset(the_carrier(boole_POSet(cast_as_carrier_subset(sK12)))))
| in(sK13,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(sK12)))))
| ~ spl61_9
| ~ spl61_293 ),
inference(resolution,[],[f2282,f934]) ).
fof(f3518,plain,
( spl61_412
| ~ spl61_103
| ~ spl61_126
| ~ spl61_182
| ~ spl61_199
| ~ spl61_260 ),
inference(avatar_split_clause,[],[f2153,f2117,f1822,f1753,f1496,f1402,f3516]) ).
fof(f3516,plain,
( spl61_412
<=> ! [X4] : subset(sK60,X4) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_412])]) ).
fof(f2153,plain,
( ! [X4] : subset(sK60,X4)
| ~ spl61_103
| ~ spl61_126
| ~ spl61_182
| ~ spl61_199
| ~ spl61_260 ),
inference(forward_demodulation,[],[f2152,f1844]) ).
fof(f2152,plain,
( ! [X4] : subset(empty_set,X4)
| ~ spl61_126
| ~ spl61_182
| ~ spl61_199
| ~ spl61_260 ),
inference(forward_demodulation,[],[f2150,f1843]) ).
fof(f2150,plain,
( ! [X4] : subset(sK39(X4),X4)
| ~ spl61_199
| ~ spl61_260 ),
inference(resolution,[],[f2118,f1823]) ).
fof(f3514,plain,
( spl61_411
| ~ spl61_103
| ~ spl61_182 ),
inference(avatar_split_clause,[],[f1844,f1753,f1402,f3511]) ).
fof(f3507,plain,
( spl61_410
| ~ spl61_126
| ~ spl61_158 ),
inference(avatar_split_clause,[],[f1669,f1625,f1496,f3505]) ).
fof(f3505,plain,
( spl61_410
<=> ! [X1] : finite(sK39(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_410])]) ).
fof(f1669,plain,
( ! [X1] : finite(sK39(X1))
| ~ spl61_126
| ~ spl61_158 ),
inference(resolution,[],[f1626,f1497]) ).
fof(f3502,plain,
( spl61_409
| ~ spl61_126
| ~ spl61_157 ),
inference(avatar_split_clause,[],[f1665,f1621,f1496,f3500]) ).
fof(f3500,plain,
( spl61_409
<=> ! [X1] : relation(sK39(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_409])]) ).
fof(f1665,plain,
( ! [X1] : relation(sK39(X1))
| ~ spl61_126
| ~ spl61_157 ),
inference(resolution,[],[f1622,f1497]) ).
fof(f3498,plain,
( spl61_408
| ~ spl61_125
| ~ spl61_136 ),
inference(avatar_split_clause,[],[f1643,f1537,f1492,f3496]) ).
fof(f1643,plain,
( ! [X0] : one_sorted_str(boole_POSet(X0))
| ~ spl61_125
| ~ spl61_136 ),
inference(resolution,[],[f1538,f1493]) ).
fof(f3494,plain,
( spl61_407
| ~ spl61_127
| ~ spl61_132 ),
inference(avatar_split_clause,[],[f1634,f1521,f1500,f3492]) ).
fof(f3492,plain,
( spl61_407
<=> ! [X1] : sP0(sK40(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_407])]) ).
fof(f1500,plain,
( spl61_127
<=> ! [X0] : ~ empty(sK40(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_127])]) ).
fof(f1634,plain,
( ! [X1] : sP0(sK40(X1))
| ~ spl61_127
| ~ spl61_132 ),
inference(resolution,[],[f1522,f1501]) ).
fof(f1501,plain,
( ! [X0] : ~ empty(sK40(X0))
| ~ spl61_127 ),
inference(avatar_component_clause,[],[f1500]) ).
fof(f3490,plain,
( spl61_406
| ~ spl61_105
| ~ spl61_132 ),
inference(avatar_split_clause,[],[f1632,f1521,f1412,f3488]) ).
fof(f3488,plain,
( spl61_406
<=> ! [X0] : sP0(powerset(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_406])]) ).
fof(f1412,plain,
( spl61_105
<=> ! [X0] : ~ empty(powerset(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_105])]) ).
fof(f1632,plain,
( ! [X0] : sP0(powerset(X0))
| ~ spl61_105
| ~ spl61_132 ),
inference(resolution,[],[f1522,f1413]) ).
fof(f1413,plain,
( ! [X0] : ~ empty(powerset(X0))
| ~ spl61_105 ),
inference(avatar_component_clause,[],[f1412]) ).
fof(f3480,plain,
( spl61_405
| ~ spl61_103
| ~ spl61_182
| ~ spl61_387 ),
inference(avatar_split_clause,[],[f3442,f3233,f1753,f1402,f3477]) ).
fof(f3442,plain,
( the_carrier(boole_POSet(cast_as_carrier_subset(sK12))) = sK60
| ~ spl61_103
| ~ spl61_182
| ~ spl61_387 ),
inference(forward_demodulation,[],[f3439,f1844]) ).
fof(f3439,plain,
( empty_set = the_carrier(boole_POSet(cast_as_carrier_subset(sK12)))
| ~ spl61_182
| ~ spl61_387 ),
inference(resolution,[],[f3234,f1754]) ).
fof(f3234,plain,
( empty(the_carrier(boole_POSet(cast_as_carrier_subset(sK12))))
| ~ spl61_387 ),
inference(avatar_component_clause,[],[f3233]) ).
fof(f3470,plain,
( spl61_404
| ~ spl61_103
| ~ spl61_158 ),
inference(avatar_split_clause,[],[f1670,f1625,f1402,f3467]) ).
fof(f3467,plain,
( spl61_404
<=> finite(sK60) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_404])]) ).
fof(f1670,plain,
( finite(sK60)
| ~ spl61_103
| ~ spl61_158 ),
inference(resolution,[],[f1626,f1404]) ).
fof(f3464,plain,
( spl61_403
| ~ spl61_10
| ~ spl61_158 ),
inference(avatar_split_clause,[],[f1668,f1625,f937,f3461]) ).
fof(f3461,plain,
( spl61_403
<=> finite(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_403])]) ).
fof(f1668,plain,
( finite(empty_set)
| ~ spl61_10
| ~ spl61_158 ),
inference(resolution,[],[f1626,f939]) ).
fof(f3459,plain,
( spl61_402
| ~ spl61_92
| ~ spl61_136 ),
inference(avatar_split_clause,[],[f1652,f1537,f1347,f3456]) ).
fof(f1652,plain,
( one_sorted_str(sK59)
| ~ spl61_92
| ~ spl61_136 ),
inference(resolution,[],[f1538,f1349]) ).
fof(f1349,plain,
( rel_str(sK59)
| ~ spl61_92 ),
inference(avatar_component_clause,[],[f1347]) ).
fof(f3454,plain,
( spl61_401
| ~ spl61_86
| ~ spl61_136 ),
inference(avatar_split_clause,[],[f1651,f1537,f1317,f3451]) ).
fof(f1651,plain,
( one_sorted_str(sK58)
| ~ spl61_86
| ~ spl61_136 ),
inference(resolution,[],[f1538,f1319]) ).
fof(f1319,plain,
( rel_str(sK58)
| ~ spl61_86 ),
inference(avatar_component_clause,[],[f1317]) ).
fof(f3449,plain,
( spl61_400
| ~ spl61_72
| ~ spl61_136 ),
inference(avatar_split_clause,[],[f1650,f1537,f1247,f3446]) ).
fof(f1650,plain,
( one_sorted_str(sK57)
| ~ spl61_72
| ~ spl61_136 ),
inference(resolution,[],[f1538,f1249]) ).
fof(f1249,plain,
( rel_str(sK57)
| ~ spl61_72 ),
inference(avatar_component_clause,[],[f1247]) ).
fof(f3430,plain,
spl61_399,
inference(avatar_split_clause,[],[f648,f3428]) ).
fof(f648,plain,
! [X0,X1] :
( filter_of_net_str(X0,net_of_bool_filter(X0,cast_as_carrier_subset(X0),X1)) = X1
| ~ element(X1,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(X0)))))
| ~ proper_element(X1,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(X0)))))
| ~ upper_relstr_subset(X1,boole_POSet(cast_as_carrier_subset(X0)))
| ~ filtered_subset(X1,boole_POSet(cast_as_carrier_subset(X0)))
| empty(X1)
| ~ one_sorted_str(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f207]) ).
fof(f207,plain,
! [X0] :
( ! [X1] :
( filter_of_net_str(X0,net_of_bool_filter(X0,cast_as_carrier_subset(X0),X1)) = X1
| ~ element(X1,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(X0)))))
| ~ proper_element(X1,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(X0)))))
| ~ upper_relstr_subset(X1,boole_POSet(cast_as_carrier_subset(X0)))
| ~ filtered_subset(X1,boole_POSet(cast_as_carrier_subset(X0)))
| empty(X1) )
| ~ one_sorted_str(X0)
| empty_carrier(X0) ),
inference(flattening,[],[f206]) ).
fof(f206,plain,
! [X0] :
( ! [X1] :
( filter_of_net_str(X0,net_of_bool_filter(X0,cast_as_carrier_subset(X0),X1)) = X1
| ~ element(X1,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(X0)))))
| ~ proper_element(X1,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(X0)))))
| ~ upper_relstr_subset(X1,boole_POSet(cast_as_carrier_subset(X0)))
| ~ filtered_subset(X1,boole_POSet(cast_as_carrier_subset(X0)))
| empty(X1) )
| ~ one_sorted_str(X0)
| empty_carrier(X0) ),
inference(ennf_transformation,[],[f126]) ).
fof(f126,axiom,
! [X0] :
( ( one_sorted_str(X0)
& ~ empty_carrier(X0) )
=> ! [X1] :
( ( element(X1,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(X0)))))
& proper_element(X1,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(X0)))))
& upper_relstr_subset(X1,boole_POSet(cast_as_carrier_subset(X0)))
& filtered_subset(X1,boole_POSet(cast_as_carrier_subset(X0)))
& ~ empty(X1) )
=> filter_of_net_str(X0,net_of_bool_filter(X0,cast_as_carrier_subset(X0),X1)) = X1 ) ),
file('/export/starexec/sandbox2/tmp/tmp.XVCyggMQ11/Vampire---4.8_15325',t15_yellow19) ).
fof(f3423,plain,
( spl61_398
| ~ spl61_132
| spl61_387 ),
inference(avatar_split_clause,[],[f3321,f3233,f1521,f3420]) ).
fof(f3420,plain,
( spl61_398
<=> sP0(the_carrier(boole_POSet(cast_as_carrier_subset(sK12)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_398])]) ).
fof(f3321,plain,
( sP0(the_carrier(boole_POSet(cast_as_carrier_subset(sK12))))
| ~ spl61_132
| spl61_387 ),
inference(resolution,[],[f3235,f1522]) ).
fof(f3418,plain,
spl61_397,
inference(avatar_split_clause,[],[f775,f3416]) ).
fof(f775,plain,
! [X2,X0,X1] :
( sP11(X2,X1,X0)
| ~ element(X2,powerset(the_carrier(boole_POSet(X1))))
| ~ proper_element(X2,powerset(the_carrier(boole_POSet(X1))))
| ~ upper_relstr_subset(X2,boole_POSet(X1))
| ~ filtered_subset(X2,boole_POSet(X1))
| empty(X2)
| ~ element(X1,powerset(the_carrier(X0)))
| empty(X1)
| ~ one_sorted_str(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f325]) ).
fof(f325,plain,
! [X0,X1,X2] :
( sP11(X2,X1,X0)
| ~ element(X2,powerset(the_carrier(boole_POSet(X1))))
| ~ proper_element(X2,powerset(the_carrier(boole_POSet(X1))))
| ~ upper_relstr_subset(X2,boole_POSet(X1))
| ~ filtered_subset(X2,boole_POSet(X1))
| empty(X2)
| ~ element(X1,powerset(the_carrier(X0)))
| empty(X1)
| ~ one_sorted_str(X0)
| empty_carrier(X0) ),
inference(definition_folding,[],[f286,f324]) ).
fof(f324,plain,
! [X2,X1,X0] :
( ( directed_relstr(net_of_bool_filter(X0,X1,X2))
& strict_net_str(net_of_bool_filter(X0,X1,X2),X0)
& transitive_relstr(net_of_bool_filter(X0,X1,X2))
& reflexive_relstr(net_of_bool_filter(X0,X1,X2))
& ~ empty_carrier(net_of_bool_filter(X0,X1,X2)) )
| ~ sP11(X2,X1,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP11])]) ).
fof(f286,plain,
! [X0,X1,X2] :
( ( directed_relstr(net_of_bool_filter(X0,X1,X2))
& strict_net_str(net_of_bool_filter(X0,X1,X2),X0)
& transitive_relstr(net_of_bool_filter(X0,X1,X2))
& reflexive_relstr(net_of_bool_filter(X0,X1,X2))
& ~ empty_carrier(net_of_bool_filter(X0,X1,X2)) )
| ~ element(X2,powerset(the_carrier(boole_POSet(X1))))
| ~ proper_element(X2,powerset(the_carrier(boole_POSet(X1))))
| ~ upper_relstr_subset(X2,boole_POSet(X1))
| ~ filtered_subset(X2,boole_POSet(X1))
| empty(X2)
| ~ element(X1,powerset(the_carrier(X0)))
| empty(X1)
| ~ one_sorted_str(X0)
| empty_carrier(X0) ),
inference(flattening,[],[f285]) ).
fof(f285,plain,
! [X0,X1,X2] :
( ( directed_relstr(net_of_bool_filter(X0,X1,X2))
& strict_net_str(net_of_bool_filter(X0,X1,X2),X0)
& transitive_relstr(net_of_bool_filter(X0,X1,X2))
& reflexive_relstr(net_of_bool_filter(X0,X1,X2))
& ~ empty_carrier(net_of_bool_filter(X0,X1,X2)) )
| ~ element(X2,powerset(the_carrier(boole_POSet(X1))))
| ~ proper_element(X2,powerset(the_carrier(boole_POSet(X1))))
| ~ upper_relstr_subset(X2,boole_POSet(X1))
| ~ filtered_subset(X2,boole_POSet(X1))
| empty(X2)
| ~ element(X1,powerset(the_carrier(X0)))
| empty(X1)
| ~ one_sorted_str(X0)
| empty_carrier(X0) ),
inference(ennf_transformation,[],[f76]) ).
fof(f76,axiom,
! [X0,X1,X2] :
( ( element(X2,powerset(the_carrier(boole_POSet(X1))))
& proper_element(X2,powerset(the_carrier(boole_POSet(X1))))
& upper_relstr_subset(X2,boole_POSet(X1))
& filtered_subset(X2,boole_POSet(X1))
& ~ empty(X2)
& element(X1,powerset(the_carrier(X0)))
& ~ empty(X1)
& one_sorted_str(X0)
& ~ empty_carrier(X0) )
=> ( directed_relstr(net_of_bool_filter(X0,X1,X2))
& strict_net_str(net_of_bool_filter(X0,X1,X2),X0)
& transitive_relstr(net_of_bool_filter(X0,X1,X2))
& reflexive_relstr(net_of_bool_filter(X0,X1,X2))
& ~ empty_carrier(net_of_bool_filter(X0,X1,X2)) ) ),
file('/export/starexec/sandbox2/tmp/tmp.XVCyggMQ11/Vampire---4.8_15325',fc5_yellow19) ).
fof(f3360,plain,
spl61_396,
inference(avatar_split_clause,[],[f782,f3358]) ).
fof(f782,plain,
! [X2,X0,X1] :
( net_str(net_of_bool_filter(X0,X1,X2),X0)
| ~ element(X2,powerset(the_carrier(boole_POSet(X1))))
| ~ upper_relstr_subset(X2,boole_POSet(X1))
| ~ filtered_subset(X2,boole_POSet(X1))
| empty(X2)
| ~ element(X1,powerset(the_carrier(X0)))
| empty(X1)
| ~ one_sorted_str(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f290]) ).
fof(f290,plain,
! [X0,X1,X2] :
( ( net_str(net_of_bool_filter(X0,X1,X2),X0)
& strict_net_str(net_of_bool_filter(X0,X1,X2),X0)
& ~ empty_carrier(net_of_bool_filter(X0,X1,X2)) )
| ~ element(X2,powerset(the_carrier(boole_POSet(X1))))
| ~ upper_relstr_subset(X2,boole_POSet(X1))
| ~ filtered_subset(X2,boole_POSet(X1))
| empty(X2)
| ~ element(X1,powerset(the_carrier(X0)))
| empty(X1)
| ~ one_sorted_str(X0)
| empty_carrier(X0) ),
inference(flattening,[],[f289]) ).
fof(f289,plain,
! [X0,X1,X2] :
( ( net_str(net_of_bool_filter(X0,X1,X2),X0)
& strict_net_str(net_of_bool_filter(X0,X1,X2),X0)
& ~ empty_carrier(net_of_bool_filter(X0,X1,X2)) )
| ~ element(X2,powerset(the_carrier(boole_POSet(X1))))
| ~ upper_relstr_subset(X2,boole_POSet(X1))
| ~ filtered_subset(X2,boole_POSet(X1))
| empty(X2)
| ~ element(X1,powerset(the_carrier(X0)))
| empty(X1)
| ~ one_sorted_str(X0)
| empty_carrier(X0) ),
inference(ennf_transformation,[],[f37]) ).
fof(f37,axiom,
! [X0,X1,X2] :
( ( element(X2,powerset(the_carrier(boole_POSet(X1))))
& upper_relstr_subset(X2,boole_POSet(X1))
& filtered_subset(X2,boole_POSet(X1))
& ~ empty(X2)
& element(X1,powerset(the_carrier(X0)))
& ~ empty(X1)
& one_sorted_str(X0)
& ~ empty_carrier(X0) )
=> ( net_str(net_of_bool_filter(X0,X1,X2),X0)
& strict_net_str(net_of_bool_filter(X0,X1,X2),X0)
& ~ empty_carrier(net_of_bool_filter(X0,X1,X2)) ) ),
file('/export/starexec/sandbox2/tmp/tmp.XVCyggMQ11/Vampire---4.8_15325',dt_k3_yellow19) ).
fof(f3356,plain,
spl61_395,
inference(avatar_split_clause,[],[f779,f3354]) ).
fof(f779,plain,
! [X2,X0,X1] :
( strict_net_str(net_of_bool_filter(X0,X1,X2),X0)
| ~ element(X2,powerset(the_carrier(boole_POSet(X1))))
| ~ upper_relstr_subset(X2,boole_POSet(X1))
| ~ filtered_subset(X2,boole_POSet(X1))
| empty(X2)
| ~ element(X1,powerset(the_carrier(X0)))
| empty(X1)
| ~ one_sorted_str(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f288]) ).
fof(f288,plain,
! [X0,X1,X2] :
( ( strict_net_str(net_of_bool_filter(X0,X1,X2),X0)
& transitive_relstr(net_of_bool_filter(X0,X1,X2))
& reflexive_relstr(net_of_bool_filter(X0,X1,X2))
& ~ empty_carrier(net_of_bool_filter(X0,X1,X2)) )
| ~ element(X2,powerset(the_carrier(boole_POSet(X1))))
| ~ upper_relstr_subset(X2,boole_POSet(X1))
| ~ filtered_subset(X2,boole_POSet(X1))
| empty(X2)
| ~ element(X1,powerset(the_carrier(X0)))
| empty(X1)
| ~ one_sorted_str(X0)
| empty_carrier(X0) ),
inference(flattening,[],[f287]) ).
fof(f287,plain,
! [X0,X1,X2] :
( ( strict_net_str(net_of_bool_filter(X0,X1,X2),X0)
& transitive_relstr(net_of_bool_filter(X0,X1,X2))
& reflexive_relstr(net_of_bool_filter(X0,X1,X2))
& ~ empty_carrier(net_of_bool_filter(X0,X1,X2)) )
| ~ element(X2,powerset(the_carrier(boole_POSet(X1))))
| ~ upper_relstr_subset(X2,boole_POSet(X1))
| ~ filtered_subset(X2,boole_POSet(X1))
| empty(X2)
| ~ element(X1,powerset(the_carrier(X0)))
| empty(X1)
| ~ one_sorted_str(X0)
| empty_carrier(X0) ),
inference(ennf_transformation,[],[f73]) ).
fof(f73,axiom,
! [X0,X1,X2] :
( ( element(X2,powerset(the_carrier(boole_POSet(X1))))
& upper_relstr_subset(X2,boole_POSet(X1))
& filtered_subset(X2,boole_POSet(X1))
& ~ empty(X2)
& element(X1,powerset(the_carrier(X0)))
& ~ empty(X1)
& one_sorted_str(X0)
& ~ empty_carrier(X0) )
=> ( strict_net_str(net_of_bool_filter(X0,X1,X2),X0)
& transitive_relstr(net_of_bool_filter(X0,X1,X2))
& reflexive_relstr(net_of_bool_filter(X0,X1,X2))
& ~ empty_carrier(net_of_bool_filter(X0,X1,X2)) ) ),
file('/export/starexec/sandbox2/tmp/tmp.XVCyggMQ11/Vampire---4.8_15325',fc4_yellow19) ).
fof(f3266,plain,
spl61_394,
inference(avatar_split_clause,[],[f798,f3264]) ).
fof(f3264,plain,
( spl61_394
<=> ! [X5,X4,X2,X7,X0,X6,X3,X1] :
( X3 = X7
| net_str_of(X0,X1,X2,X3) != net_str_of(X4,X5,X6,X7)
| ~ relation_of2(X3,X1,the_carrier(X0))
| ~ quasi_total(X3,X1,the_carrier(X0))
| ~ function(X3)
| ~ relation_of2(X2,X1,X1)
| ~ one_sorted_str(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_394])]) ).
fof(f798,plain,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( X3 = X7
| net_str_of(X0,X1,X2,X3) != net_str_of(X4,X5,X6,X7)
| ~ relation_of2(X3,X1,the_carrier(X0))
| ~ quasi_total(X3,X1,the_carrier(X0))
| ~ function(X3)
| ~ relation_of2(X2,X1,X1)
| ~ one_sorted_str(X0) ),
inference(cnf_transformation,[],[f301]) ).
fof(f301,plain,
! [X0,X1,X2,X3] :
( ! [X4,X5,X6,X7] :
( ( X3 = X7
& X2 = X6
& X1 = X5
& X0 = X4 )
| net_str_of(X0,X1,X2,X3) != net_str_of(X4,X5,X6,X7) )
| ~ relation_of2(X3,X1,the_carrier(X0))
| ~ quasi_total(X3,X1,the_carrier(X0))
| ~ function(X3)
| ~ relation_of2(X2,X1,X1)
| ~ one_sorted_str(X0) ),
inference(flattening,[],[f300]) ).
fof(f300,plain,
! [X0,X1,X2,X3] :
( ! [X4,X5,X6,X7] :
( ( X3 = X7
& X2 = X6
& X1 = X5
& X0 = X4 )
| net_str_of(X0,X1,X2,X3) != net_str_of(X4,X5,X6,X7) )
| ~ relation_of2(X3,X1,the_carrier(X0))
| ~ quasi_total(X3,X1,the_carrier(X0))
| ~ function(X3)
| ~ relation_of2(X2,X1,X1)
| ~ one_sorted_str(X0) ),
inference(ennf_transformation,[],[f85]) ).
fof(f85,axiom,
! [X0,X1,X2,X3] :
( ( relation_of2(X3,X1,the_carrier(X0))
& quasi_total(X3,X1,the_carrier(X0))
& function(X3)
& relation_of2(X2,X1,X1)
& one_sorted_str(X0) )
=> ! [X4,X5,X6,X7] :
( net_str_of(X0,X1,X2,X3) = net_str_of(X4,X5,X6,X7)
=> ( X3 = X7
& X2 = X6
& X1 = X5
& X0 = X4 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.XVCyggMQ11/Vampire---4.8_15325',free_g1_waybel_0) ).
fof(f3262,plain,
spl61_393,
inference(avatar_split_clause,[],[f797,f3260]) ).
fof(f3260,plain,
( spl61_393
<=> ! [X5,X3,X4,X7,X0,X6,X2,X1] :
( X2 = X6
| net_str_of(X0,X1,X2,X3) != net_str_of(X4,X5,X6,X7)
| ~ relation_of2(X3,X1,the_carrier(X0))
| ~ quasi_total(X3,X1,the_carrier(X0))
| ~ function(X3)
| ~ relation_of2(X2,X1,X1)
| ~ one_sorted_str(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_393])]) ).
fof(f797,plain,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( X2 = X6
| net_str_of(X0,X1,X2,X3) != net_str_of(X4,X5,X6,X7)
| ~ relation_of2(X3,X1,the_carrier(X0))
| ~ quasi_total(X3,X1,the_carrier(X0))
| ~ function(X3)
| ~ relation_of2(X2,X1,X1)
| ~ one_sorted_str(X0) ),
inference(cnf_transformation,[],[f301]) ).
fof(f3258,plain,
spl61_392,
inference(avatar_split_clause,[],[f796,f3256]) ).
fof(f3256,plain,
( spl61_392
<=> ! [X5,X3,X4,X2,X7,X0,X6,X1] :
( X1 = X5
| net_str_of(X0,X1,X2,X3) != net_str_of(X4,X5,X6,X7)
| ~ relation_of2(X3,X1,the_carrier(X0))
| ~ quasi_total(X3,X1,the_carrier(X0))
| ~ function(X3)
| ~ relation_of2(X2,X1,X1)
| ~ one_sorted_str(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_392])]) ).
fof(f796,plain,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( X1 = X5
| net_str_of(X0,X1,X2,X3) != net_str_of(X4,X5,X6,X7)
| ~ relation_of2(X3,X1,the_carrier(X0))
| ~ quasi_total(X3,X1,the_carrier(X0))
| ~ function(X3)
| ~ relation_of2(X2,X1,X1)
| ~ one_sorted_str(X0) ),
inference(cnf_transformation,[],[f301]) ).
fof(f3254,plain,
spl61_391,
inference(avatar_split_clause,[],[f795,f3252]) ).
fof(f3252,plain,
( spl61_391
<=> ! [X5,X1,X4,X2,X0,X6,X3,X7] :
( X0 = X4
| net_str_of(X0,X1,X2,X3) != net_str_of(X4,X5,X6,X7)
| ~ relation_of2(X3,X1,the_carrier(X0))
| ~ quasi_total(X3,X1,the_carrier(X0))
| ~ function(X3)
| ~ relation_of2(X2,X1,X1)
| ~ one_sorted_str(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_391])]) ).
fof(f795,plain,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( X0 = X4
| net_str_of(X0,X1,X2,X3) != net_str_of(X4,X5,X6,X7)
| ~ relation_of2(X3,X1,the_carrier(X0))
| ~ quasi_total(X3,X1,the_carrier(X0))
| ~ function(X3)
| ~ relation_of2(X2,X1,X1)
| ~ one_sorted_str(X0) ),
inference(cnf_transformation,[],[f301]) ).
fof(f3250,plain,
spl61_390,
inference(avatar_split_clause,[],[f778,f3248]) ).
fof(f778,plain,
! [X2,X0,X1] :
( transitive_relstr(net_of_bool_filter(X0,X1,X2))
| ~ element(X2,powerset(the_carrier(boole_POSet(X1))))
| ~ upper_relstr_subset(X2,boole_POSet(X1))
| ~ filtered_subset(X2,boole_POSet(X1))
| empty(X2)
| ~ element(X1,powerset(the_carrier(X0)))
| empty(X1)
| ~ one_sorted_str(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f288]) ).
fof(f3246,plain,
spl61_389,
inference(avatar_split_clause,[],[f777,f3244]) ).
fof(f777,plain,
! [X2,X0,X1] :
( reflexive_relstr(net_of_bool_filter(X0,X1,X2))
| ~ element(X2,powerset(the_carrier(boole_POSet(X1))))
| ~ upper_relstr_subset(X2,boole_POSet(X1))
| ~ filtered_subset(X2,boole_POSet(X1))
| empty(X2)
| ~ element(X1,powerset(the_carrier(X0)))
| empty(X1)
| ~ one_sorted_str(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f288]) ).
fof(f3242,plain,
spl61_388,
inference(avatar_split_clause,[],[f776,f3240]) ).
fof(f776,plain,
! [X2,X0,X1] :
( ~ empty_carrier(net_of_bool_filter(X0,X1,X2))
| ~ element(X2,powerset(the_carrier(boole_POSet(X1))))
| ~ upper_relstr_subset(X2,boole_POSet(X1))
| ~ filtered_subset(X2,boole_POSet(X1))
| empty(X2)
| ~ element(X1,powerset(the_carrier(X0)))
| empty(X1)
| ~ one_sorted_str(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f288]) ).
fof(f3236,plain,
( spl61_386
| ~ spl61_387
| ~ spl61_9
| ~ spl61_315 ),
inference(avatar_split_clause,[],[f2470,f2457,f932,f3233,f3230]) ).
fof(f2470,plain,
( ! [X5] :
( ~ empty(the_carrier(boole_POSet(cast_as_carrier_subset(sK12))))
| ~ in(X5,sK13) )
| ~ spl61_9
| ~ spl61_315 ),
inference(resolution,[],[f2458,f934]) ).
fof(f3228,plain,
spl61_385,
inference(avatar_split_clause,[],[f638,f3226]) ).
fof(f638,plain,
! [X2,X0,X1] :
( in(X2,lim_points_of_net(X0,X1))
| ~ is_a_convergence_point_of_set(X0,filter_of_net_str(X0,X1),X2)
| ~ element(X2,the_carrier(X0))
| ~ net_str(X1,X0)
| ~ directed_relstr(X1)
| ~ transitive_relstr(X1)
| empty_carrier(X1)
| ~ top_str(X0)
| ~ topological_space(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f361]) ).
fof(f361,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( in(X2,lim_points_of_net(X0,X1))
| ~ is_a_convergence_point_of_set(X0,filter_of_net_str(X0,X1),X2) )
& ( is_a_convergence_point_of_set(X0,filter_of_net_str(X0,X1),X2)
| ~ in(X2,lim_points_of_net(X0,X1)) ) )
| ~ element(X2,the_carrier(X0)) )
| ~ net_str(X1,X0)
| ~ directed_relstr(X1)
| ~ transitive_relstr(X1)
| empty_carrier(X1) )
| ~ top_str(X0)
| ~ topological_space(X0)
| empty_carrier(X0) ),
inference(nnf_transformation,[],[f197]) ).
fof(f197,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( in(X2,lim_points_of_net(X0,X1))
<=> is_a_convergence_point_of_set(X0,filter_of_net_str(X0,X1),X2) )
| ~ element(X2,the_carrier(X0)) )
| ~ net_str(X1,X0)
| ~ directed_relstr(X1)
| ~ transitive_relstr(X1)
| empty_carrier(X1) )
| ~ top_str(X0)
| ~ topological_space(X0)
| empty_carrier(X0) ),
inference(flattening,[],[f196]) ).
fof(f196,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( in(X2,lim_points_of_net(X0,X1))
<=> is_a_convergence_point_of_set(X0,filter_of_net_str(X0,X1),X2) )
| ~ element(X2,the_carrier(X0)) )
| ~ net_str(X1,X0)
| ~ directed_relstr(X1)
| ~ transitive_relstr(X1)
| empty_carrier(X1) )
| ~ top_str(X0)
| ~ topological_space(X0)
| empty_carrier(X0) ),
inference(ennf_transformation,[],[f125]) ).
fof(f125,axiom,
! [X0] :
( ( top_str(X0)
& topological_space(X0)
& ~ empty_carrier(X0) )
=> ! [X1] :
( ( net_str(X1,X0)
& directed_relstr(X1)
& transitive_relstr(X1)
& ~ empty_carrier(X1) )
=> ! [X2] :
( element(X2,the_carrier(X0))
=> ( in(X2,lim_points_of_net(X0,X1))
<=> is_a_convergence_point_of_set(X0,filter_of_net_str(X0,X1),X2) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.XVCyggMQ11/Vampire---4.8_15325',t13_yellow19) ).
fof(f3224,plain,
spl61_384,
inference(avatar_split_clause,[],[f637,f3222]) ).
fof(f637,plain,
! [X2,X0,X1] :
( is_a_convergence_point_of_set(X0,filter_of_net_str(X0,X1),X2)
| ~ in(X2,lim_points_of_net(X0,X1))
| ~ element(X2,the_carrier(X0))
| ~ net_str(X1,X0)
| ~ directed_relstr(X1)
| ~ transitive_relstr(X1)
| empty_carrier(X1)
| ~ top_str(X0)
| ~ topological_space(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f361]) ).
fof(f3219,plain,
spl61_383,
inference(avatar_split_clause,[],[f791,f3217]) ).
fof(f3217,plain,
( spl61_383
<=> ! [X0,X3,X2,X1] :
( ~ empty_carrier(net_str_of(X0,X1,X2,X3))
| ~ relation_of2(X3,X1,the_carrier(X0))
| ~ quasi_total(X3,X1,the_carrier(X0))
| ~ function(X3)
| ~ relation_of2(X2,X1,X1)
| empty(X1)
| ~ one_sorted_str(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_383])]) ).
fof(f791,plain,
! [X2,X3,X0,X1] :
( ~ empty_carrier(net_str_of(X0,X1,X2,X3))
| ~ relation_of2(X3,X1,the_carrier(X0))
| ~ quasi_total(X3,X1,the_carrier(X0))
| ~ function(X3)
| ~ relation_of2(X2,X1,X1)
| empty(X1)
| ~ one_sorted_str(X0) ),
inference(cnf_transformation,[],[f297]) ).
fof(f297,plain,
! [X0,X1,X2,X3] :
( ( strict_net_str(net_str_of(X0,X1,X2,X3),X0)
& ~ empty_carrier(net_str_of(X0,X1,X2,X3)) )
| ~ relation_of2(X3,X1,the_carrier(X0))
| ~ quasi_total(X3,X1,the_carrier(X0))
| ~ function(X3)
| ~ relation_of2(X2,X1,X1)
| empty(X1)
| ~ one_sorted_str(X0) ),
inference(flattening,[],[f296]) ).
fof(f296,plain,
! [X0,X1,X2,X3] :
( ( strict_net_str(net_str_of(X0,X1,X2,X3),X0)
& ~ empty_carrier(net_str_of(X0,X1,X2,X3)) )
| ~ relation_of2(X3,X1,the_carrier(X0))
| ~ quasi_total(X3,X1,the_carrier(X0))
| ~ function(X3)
| ~ relation_of2(X2,X1,X1)
| empty(X1)
| ~ one_sorted_str(X0) ),
inference(ennf_transformation,[],[f77]) ).
fof(f77,axiom,
! [X0,X1,X2,X3] :
( ( relation_of2(X3,X1,the_carrier(X0))
& quasi_total(X3,X1,the_carrier(X0))
& function(X3)
& relation_of2(X2,X1,X1)
& ~ empty(X1)
& one_sorted_str(X0) )
=> ( strict_net_str(net_str_of(X0,X1,X2,X3),X0)
& ~ empty_carrier(net_str_of(X0,X1,X2,X3)) ) ),
file('/export/starexec/sandbox2/tmp/tmp.XVCyggMQ11/Vampire---4.8_15325',fc6_waybel_0) ).
fof(f3215,plain,
spl61_382,
inference(avatar_split_clause,[],[f786,f3213]) ).
fof(f786,plain,
! [X2,X3,X0,X1] :
( in(X0,a_2_1_yellow19(X1,X2))
| ~ is_eventually_in(X1,X2,X3)
| X0 != X3
| ~ element(X3,powerset(the_carrier(X1)))
| ~ net_str(X2,X1)
| empty_carrier(X2)
| ~ one_sorted_str(X1)
| empty_carrier(X1) ),
inference(cnf_transformation,[],[f409]) ).
fof(f409,plain,
! [X0,X1,X2] :
( ( ( in(X0,a_2_1_yellow19(X1,X2))
| ! [X3] :
( ~ is_eventually_in(X1,X2,X3)
| X0 != X3
| ~ element(X3,powerset(the_carrier(X1))) ) )
& ( ( is_eventually_in(X1,X2,sK44(X0,X1,X2))
& sK44(X0,X1,X2) = X0
& element(sK44(X0,X1,X2),powerset(the_carrier(X1))) )
| ~ in(X0,a_2_1_yellow19(X1,X2)) ) )
| ~ net_str(X2,X1)
| empty_carrier(X2)
| ~ one_sorted_str(X1)
| empty_carrier(X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK44])],[f407,f408]) ).
fof(f408,plain,
! [X0,X1,X2] :
( ? [X4] :
( is_eventually_in(X1,X2,X4)
& X0 = X4
& element(X4,powerset(the_carrier(X1))) )
=> ( is_eventually_in(X1,X2,sK44(X0,X1,X2))
& sK44(X0,X1,X2) = X0
& element(sK44(X0,X1,X2),powerset(the_carrier(X1))) ) ),
introduced(choice_axiom,[]) ).
fof(f407,plain,
! [X0,X1,X2] :
( ( ( in(X0,a_2_1_yellow19(X1,X2))
| ! [X3] :
( ~ is_eventually_in(X1,X2,X3)
| X0 != X3
| ~ element(X3,powerset(the_carrier(X1))) ) )
& ( ? [X4] :
( is_eventually_in(X1,X2,X4)
& X0 = X4
& element(X4,powerset(the_carrier(X1))) )
| ~ in(X0,a_2_1_yellow19(X1,X2)) ) )
| ~ net_str(X2,X1)
| empty_carrier(X2)
| ~ one_sorted_str(X1)
| empty_carrier(X1) ),
inference(rectify,[],[f406]) ).
fof(f406,plain,
! [X0,X1,X2] :
( ( ( in(X0,a_2_1_yellow19(X1,X2))
| ! [X3] :
( ~ is_eventually_in(X1,X2,X3)
| X0 != X3
| ~ element(X3,powerset(the_carrier(X1))) ) )
& ( ? [X3] :
( is_eventually_in(X1,X2,X3)
& X0 = X3
& element(X3,powerset(the_carrier(X1))) )
| ~ in(X0,a_2_1_yellow19(X1,X2)) ) )
| ~ net_str(X2,X1)
| empty_carrier(X2)
| ~ one_sorted_str(X1)
| empty_carrier(X1) ),
inference(nnf_transformation,[],[f292]) ).
fof(f292,plain,
! [X0,X1,X2] :
( ( in(X0,a_2_1_yellow19(X1,X2))
<=> ? [X3] :
( is_eventually_in(X1,X2,X3)
& X0 = X3
& element(X3,powerset(the_carrier(X1))) ) )
| ~ net_str(X2,X1)
| empty_carrier(X2)
| ~ one_sorted_str(X1)
| empty_carrier(X1) ),
inference(flattening,[],[f291]) ).
fof(f291,plain,
! [X0,X1,X2] :
( ( in(X0,a_2_1_yellow19(X1,X2))
<=> ? [X3] :
( is_eventually_in(X1,X2,X3)
& X0 = X3
& element(X3,powerset(the_carrier(X1))) ) )
| ~ net_str(X2,X1)
| empty_carrier(X2)
| ~ one_sorted_str(X1)
| empty_carrier(X1) ),
inference(ennf_transformation,[],[f83]) ).
fof(f83,axiom,
! [X0,X1,X2] :
( ( net_str(X2,X1)
& ~ empty_carrier(X2)
& one_sorted_str(X1)
& ~ empty_carrier(X1) )
=> ( in(X0,a_2_1_yellow19(X1,X2))
<=> ? [X3] :
( is_eventually_in(X1,X2,X3)
& X0 = X3
& element(X3,powerset(the_carrier(X1))) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.XVCyggMQ11/Vampire---4.8_15325',fraenkel_a_2_1_yellow19) ).
fof(f3207,plain,
spl61_381,
inference(avatar_split_clause,[],[f794,f3205]) ).
fof(f794,plain,
! [X2,X3,X0,X1] :
( net_str(net_str_of(X0,X1,X2,X3),X0)
| ~ relation_of2(X3,X1,the_carrier(X0))
| ~ quasi_total(X3,X1,the_carrier(X0))
| ~ function(X3)
| ~ relation_of2(X2,X1,X1)
| ~ one_sorted_str(X0) ),
inference(cnf_transformation,[],[f299]) ).
fof(f299,plain,
! [X0,X1,X2,X3] :
( ( net_str(net_str_of(X0,X1,X2,X3),X0)
& strict_net_str(net_str_of(X0,X1,X2,X3),X0) )
| ~ relation_of2(X3,X1,the_carrier(X0))
| ~ quasi_total(X3,X1,the_carrier(X0))
| ~ function(X3)
| ~ relation_of2(X2,X1,X1)
| ~ one_sorted_str(X0) ),
inference(flattening,[],[f298]) ).
fof(f298,plain,
! [X0,X1,X2,X3] :
( ( net_str(net_str_of(X0,X1,X2,X3),X0)
& strict_net_str(net_str_of(X0,X1,X2,X3),X0) )
| ~ relation_of2(X3,X1,the_carrier(X0))
| ~ quasi_total(X3,X1,the_carrier(X0))
| ~ function(X3)
| ~ relation_of2(X2,X1,X1)
| ~ one_sorted_str(X0) ),
inference(ennf_transformation,[],[f30]) ).
fof(f30,axiom,
! [X0,X1,X2,X3] :
( ( relation_of2(X3,X1,the_carrier(X0))
& quasi_total(X3,X1,the_carrier(X0))
& function(X3)
& relation_of2(X2,X1,X1)
& one_sorted_str(X0) )
=> ( net_str(net_str_of(X0,X1,X2,X3),X0)
& strict_net_str(net_str_of(X0,X1,X2,X3),X0) ) ),
file('/export/starexec/sandbox2/tmp/tmp.XVCyggMQ11/Vampire---4.8_15325',dt_g1_waybel_0) ).
fof(f3203,plain,
spl61_380,
inference(avatar_split_clause,[],[f793,f3201]) ).
fof(f793,plain,
! [X2,X3,X0,X1] :
( strict_net_str(net_str_of(X0,X1,X2,X3),X0)
| ~ relation_of2(X3,X1,the_carrier(X0))
| ~ quasi_total(X3,X1,the_carrier(X0))
| ~ function(X3)
| ~ relation_of2(X2,X1,X1)
| ~ one_sorted_str(X0) ),
inference(cnf_transformation,[],[f299]) ).
fof(f3168,plain,
spl61_379,
inference(avatar_split_clause,[],[f783,f3166]) ).
fof(f783,plain,
! [X2,X0,X1] :
( element(sK44(X0,X1,X2),powerset(the_carrier(X1)))
| ~ in(X0,a_2_1_yellow19(X1,X2))
| ~ net_str(X2,X1)
| empty_carrier(X2)
| ~ one_sorted_str(X1)
| empty_carrier(X1) ),
inference(cnf_transformation,[],[f409]) ).
fof(f3164,plain,
spl61_378,
inference(avatar_split_clause,[],[f747,f3162]) ).
fof(f747,plain,
! [X0,X1] :
( proper_element(filter_of_net_str(X0,X1),powerset(the_carrier(boole_POSet(cast_as_carrier_subset(X0)))))
| ~ net_str(X1,X0)
| ~ directed_relstr(X1)
| ~ transitive_relstr(X1)
| empty_carrier(X1)
| ~ one_sorted_str(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f267]) ).
fof(f267,plain,
! [X0,X1] :
( ( proper_element(filter_of_net_str(X0,X1),powerset(the_carrier(boole_POSet(cast_as_carrier_subset(X0)))))
& upper_relstr_subset(filter_of_net_str(X0,X1),boole_POSet(cast_as_carrier_subset(X0)))
& filtered_subset(filter_of_net_str(X0,X1),boole_POSet(cast_as_carrier_subset(X0)))
& ~ empty(filter_of_net_str(X0,X1)) )
| ~ net_str(X1,X0)
| ~ directed_relstr(X1)
| ~ transitive_relstr(X1)
| empty_carrier(X1)
| ~ one_sorted_str(X0)
| empty_carrier(X0) ),
inference(flattening,[],[f266]) ).
fof(f266,plain,
! [X0,X1] :
( ( proper_element(filter_of_net_str(X0,X1),powerset(the_carrier(boole_POSet(cast_as_carrier_subset(X0)))))
& upper_relstr_subset(filter_of_net_str(X0,X1),boole_POSet(cast_as_carrier_subset(X0)))
& filtered_subset(filter_of_net_str(X0,X1),boole_POSet(cast_as_carrier_subset(X0)))
& ~ empty(filter_of_net_str(X0,X1)) )
| ~ net_str(X1,X0)
| ~ directed_relstr(X1)
| ~ transitive_relstr(X1)
| empty_carrier(X1)
| ~ one_sorted_str(X0)
| empty_carrier(X0) ),
inference(ennf_transformation,[],[f69]) ).
fof(f69,axiom,
! [X0,X1] :
( ( net_str(X1,X0)
& directed_relstr(X1)
& transitive_relstr(X1)
& ~ empty_carrier(X1)
& one_sorted_str(X0)
& ~ empty_carrier(X0) )
=> ( proper_element(filter_of_net_str(X0,X1),powerset(the_carrier(boole_POSet(cast_as_carrier_subset(X0)))))
& upper_relstr_subset(filter_of_net_str(X0,X1),boole_POSet(cast_as_carrier_subset(X0)))
& filtered_subset(filter_of_net_str(X0,X1),boole_POSet(cast_as_carrier_subset(X0)))
& ~ empty(filter_of_net_str(X0,X1)) ) ),
file('/export/starexec/sandbox2/tmp/tmp.XVCyggMQ11/Vampire---4.8_15325',fc3_yellow19) ).
fof(f3160,plain,
spl61_377,
inference(avatar_split_clause,[],[f743,f3158]) ).
fof(f743,plain,
! [X0,X1] :
( element(lim_points_of_net(X0,X1),powerset(the_carrier(X0)))
| ~ net_str(X1,X0)
| ~ directed_relstr(X1)
| ~ transitive_relstr(X1)
| empty_carrier(X1)
| ~ top_str(X0)
| ~ topological_space(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f265]) ).
fof(f265,plain,
! [X0,X1] :
( element(lim_points_of_net(X0,X1),powerset(the_carrier(X0)))
| ~ net_str(X1,X0)
| ~ directed_relstr(X1)
| ~ transitive_relstr(X1)
| empty_carrier(X1)
| ~ top_str(X0)
| ~ topological_space(X0)
| empty_carrier(X0) ),
inference(flattening,[],[f264]) ).
fof(f264,plain,
! [X0,X1] :
( element(lim_points_of_net(X0,X1),powerset(the_carrier(X0)))
| ~ net_str(X1,X0)
| ~ directed_relstr(X1)
| ~ transitive_relstr(X1)
| empty_carrier(X1)
| ~ top_str(X0)
| ~ topological_space(X0)
| empty_carrier(X0) ),
inference(ennf_transformation,[],[f31]) ).
fof(f31,axiom,
! [X0,X1] :
( ( net_str(X1,X0)
& directed_relstr(X1)
& transitive_relstr(X1)
& ~ empty_carrier(X1)
& top_str(X0)
& topological_space(X0)
& ~ empty_carrier(X0) )
=> element(lim_points_of_net(X0,X1),powerset(the_carrier(X0))) ),
file('/export/starexec/sandbox2/tmp/tmp.XVCyggMQ11/Vampire---4.8_15325',dt_k11_yellow_6) ).
fof(f3156,plain,
spl61_376,
inference(avatar_split_clause,[],[f785,f3154]) ).
fof(f3154,plain,
( spl61_376
<=> ! [X2,X0,X1] :
( is_eventually_in(X1,X2,sK44(X0,X1,X2))
| ~ in(X0,a_2_1_yellow19(X1,X2))
| ~ net_str(X2,X1)
| empty_carrier(X2)
| ~ one_sorted_str(X1)
| empty_carrier(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_376])]) ).
fof(f785,plain,
! [X2,X0,X1] :
( is_eventually_in(X1,X2,sK44(X0,X1,X2))
| ~ in(X0,a_2_1_yellow19(X1,X2))
| ~ net_str(X2,X1)
| empty_carrier(X2)
| ~ one_sorted_str(X1)
| empty_carrier(X1) ),
inference(cnf_transformation,[],[f409]) ).
fof(f3150,plain,
( ~ spl61_375
| ~ spl61_240
| ~ spl61_307 ),
inference(avatar_split_clause,[],[f2611,f2424,f2010,f3147]) ).
fof(f3147,plain,
( spl61_375
<=> in(the_carrier(sK12),sK14) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_375])]) ).
fof(f2424,plain,
( spl61_307
<=> in(sK14,the_carrier(sK12)) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_307])]) ).
fof(f2611,plain,
( ~ in(the_carrier(sK12),sK14)
| ~ spl61_240
| ~ spl61_307 ),
inference(resolution,[],[f2426,f2011]) ).
fof(f2426,plain,
( in(sK14,the_carrier(sK12))
| ~ spl61_307 ),
inference(avatar_component_clause,[],[f2424]) ).
fof(f3145,plain,
spl61_374,
inference(avatar_split_clause,[],[f784,f3143]) ).
fof(f784,plain,
! [X2,X0,X1] :
( sK44(X0,X1,X2) = X0
| ~ in(X0,a_2_1_yellow19(X1,X2))
| ~ net_str(X2,X1)
| empty_carrier(X2)
| ~ one_sorted_str(X1)
| empty_carrier(X1) ),
inference(cnf_transformation,[],[f409]) ).
fof(f3141,plain,
spl61_373,
inference(avatar_split_clause,[],[f745,f3139]) ).
fof(f3139,plain,
( spl61_373
<=> ! [X0,X1] :
( filtered_subset(filter_of_net_str(X0,X1),boole_POSet(cast_as_carrier_subset(X0)))
| ~ net_str(X1,X0)
| ~ directed_relstr(X1)
| ~ transitive_relstr(X1)
| empty_carrier(X1)
| ~ one_sorted_str(X0)
| empty_carrier(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_373])]) ).
fof(f745,plain,
! [X0,X1] :
( filtered_subset(filter_of_net_str(X0,X1),boole_POSet(cast_as_carrier_subset(X0)))
| ~ net_str(X1,X0)
| ~ directed_relstr(X1)
| ~ transitive_relstr(X1)
| empty_carrier(X1)
| ~ one_sorted_str(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f267]) ).
fof(f3133,plain,
spl61_372,
inference(avatar_split_clause,[],[f758,f3131]) ).
fof(f758,plain,
! [X0,X1] :
( net_str_of(X0,the_carrier(X1),the_InternalRel(X1),the_mapping(X0,X1)) = X1
| ~ strict_net_str(X1,X0)
| ~ net_str(X1,X0)
| ~ one_sorted_str(X0) ),
inference(cnf_transformation,[],[f277]) ).
fof(f277,plain,
! [X0,X1] :
( net_str_of(X0,the_carrier(X1),the_InternalRel(X1),the_mapping(X0,X1)) = X1
| ~ strict_net_str(X1,X0)
| ~ net_str(X1,X0)
| ~ one_sorted_str(X0) ),
inference(flattening,[],[f276]) ).
fof(f276,plain,
! [X0,X1] :
( net_str_of(X0,the_carrier(X1),the_InternalRel(X1),the_mapping(X0,X1)) = X1
| ~ strict_net_str(X1,X0)
| ~ net_str(X1,X0)
| ~ one_sorted_str(X0) ),
inference(ennf_transformation,[],[f2]) ).
fof(f2,axiom,
! [X0,X1] :
( ( net_str(X1,X0)
& one_sorted_str(X0) )
=> ( strict_net_str(X1,X0)
=> net_str_of(X0,the_carrier(X1),the_InternalRel(X1),the_mapping(X0,X1)) = X1 ) ),
file('/export/starexec/sandbox2/tmp/tmp.XVCyggMQ11/Vampire---4.8_15325',abstractness_v6_waybel_0) ).
fof(f3041,plain,
spl61_371,
inference(avatar_split_clause,[],[f748,f3039]) ).
fof(f748,plain,
! [X0,X1] :
( element(filter_of_net_str(X0,X1),powerset(the_carrier(boole_POSet(cast_as_carrier_subset(X0)))))
| ~ net_str(X1,X0)
| empty_carrier(X1)
| ~ one_sorted_str(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f269]) ).
fof(f269,plain,
! [X0,X1] :
( element(filter_of_net_str(X0,X1),powerset(the_carrier(boole_POSet(cast_as_carrier_subset(X0)))))
| ~ net_str(X1,X0)
| empty_carrier(X1)
| ~ one_sorted_str(X0)
| empty_carrier(X0) ),
inference(flattening,[],[f268]) ).
fof(f268,plain,
! [X0,X1] :
( element(filter_of_net_str(X0,X1),powerset(the_carrier(boole_POSet(cast_as_carrier_subset(X0)))))
| ~ net_str(X1,X0)
| empty_carrier(X1)
| ~ one_sorted_str(X0)
| empty_carrier(X0) ),
inference(ennf_transformation,[],[f35]) ).
fof(f35,axiom,
! [X0,X1] :
( ( net_str(X1,X0)
& ~ empty_carrier(X1)
& one_sorted_str(X0)
& ~ empty_carrier(X0) )
=> element(filter_of_net_str(X0,X1),powerset(the_carrier(boole_POSet(cast_as_carrier_subset(X0))))) ),
file('/export/starexec/sandbox2/tmp/tmp.XVCyggMQ11/Vampire---4.8_15325',dt_k2_yellow19) ).
fof(f3034,plain,
spl61_370,
inference(avatar_split_clause,[],[f697,f3032]) ).
fof(f697,plain,
! [X0,X1] :
( nowhere_dense(X1,X0)
| ~ boundary_set(X1,X0)
| ~ closed_subset(X1,X0)
| ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(cnf_transformation,[],[f241]) ).
fof(f241,plain,
! [X0] :
( ! [X1] :
( ( nowhere_dense(X1,X0)
& boundary_set(X1,X0) )
| ~ boundary_set(X1,X0)
| ~ closed_subset(X1,X0)
| ~ element(X1,powerset(the_carrier(X0))) )
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(flattening,[],[f240]) ).
fof(f240,plain,
! [X0] :
( ! [X1] :
( ( nowhere_dense(X1,X0)
& boundary_set(X1,X0) )
| ~ boundary_set(X1,X0)
| ~ closed_subset(X1,X0)
| ~ element(X1,powerset(the_carrier(X0))) )
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(ennf_transformation,[],[f23]) ).
fof(f23,axiom,
! [X0] :
( ( top_str(X0)
& topological_space(X0) )
=> ! [X1] :
( element(X1,powerset(the_carrier(X0)))
=> ( ( boundary_set(X1,X0)
& closed_subset(X1,X0) )
=> ( nowhere_dense(X1,X0)
& boundary_set(X1,X0) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.XVCyggMQ11/Vampire---4.8_15325',cc5_tops_1) ).
fof(f3030,plain,
spl61_369,
inference(avatar_split_clause,[],[f695,f3028]) ).
fof(f695,plain,
! [X0,X1] :
( sP8(X0,X1)
| ~ nowhere_dense(X1,X0)
| ~ open_subset(X1,X0)
| ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(cnf_transformation,[],[f319]) ).
fof(f319,plain,
! [X0] :
( ! [X1] :
( sP8(X0,X1)
| ~ nowhere_dense(X1,X0)
| ~ open_subset(X1,X0)
| ~ element(X1,powerset(the_carrier(X0))) )
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(definition_folding,[],[f239,f318]) ).
fof(f318,plain,
! [X0,X1] :
( ( nowhere_dense(X1,X0)
& boundary_set(X1,X0)
& v5_membered(X1)
& v4_membered(X1)
& v3_membered(X1)
& v2_membered(X1)
& v1_membered(X1)
& closed_subset(X1,X0)
& open_subset(X1,X0)
& empty(X1) )
| ~ sP8(X0,X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP8])]) ).
fof(f239,plain,
! [X0] :
( ! [X1] :
( ( nowhere_dense(X1,X0)
& boundary_set(X1,X0)
& v5_membered(X1)
& v4_membered(X1)
& v3_membered(X1)
& v2_membered(X1)
& v1_membered(X1)
& closed_subset(X1,X0)
& open_subset(X1,X0)
& empty(X1) )
| ~ nowhere_dense(X1,X0)
| ~ open_subset(X1,X0)
| ~ element(X1,powerset(the_carrier(X0))) )
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(flattening,[],[f238]) ).
fof(f238,plain,
! [X0] :
( ! [X1] :
( ( nowhere_dense(X1,X0)
& boundary_set(X1,X0)
& v5_membered(X1)
& v4_membered(X1)
& v3_membered(X1)
& v2_membered(X1)
& v1_membered(X1)
& closed_subset(X1,X0)
& open_subset(X1,X0)
& empty(X1) )
| ~ nowhere_dense(X1,X0)
| ~ open_subset(X1,X0)
| ~ element(X1,powerset(the_carrier(X0))) )
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(ennf_transformation,[],[f26]) ).
fof(f26,axiom,
! [X0] :
( ( top_str(X0)
& topological_space(X0) )
=> ! [X1] :
( element(X1,powerset(the_carrier(X0)))
=> ( ( nowhere_dense(X1,X0)
& open_subset(X1,X0) )
=> ( nowhere_dense(X1,X0)
& boundary_set(X1,X0)
& v5_membered(X1)
& v4_membered(X1)
& v3_membered(X1)
& v2_membered(X1)
& v1_membered(X1)
& closed_subset(X1,X0)
& open_subset(X1,X0)
& empty(X1) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.XVCyggMQ11/Vampire---4.8_15325',cc6_tops_1) ).
fof(f3026,plain,
spl61_368,
inference(avatar_split_clause,[],[f616,f3024]) ).
fof(f616,plain,
! [X0] :
( sP5(X0)
| ~ up_complete_relstr(X0)
| ~ lower_bounded_relstr(X0)
| ~ with_suprema_relstr(X0)
| ~ antisymmetric_relstr(X0)
| ~ transitive_relstr(X0)
| ~ reflexive_relstr(X0)
| empty_carrier(X0)
| ~ rel_str(X0) ),
inference(cnf_transformation,[],[f313]) ).
fof(f313,plain,
! [X0] :
( sP5(X0)
| ~ up_complete_relstr(X0)
| ~ lower_bounded_relstr(X0)
| ~ with_suprema_relstr(X0)
| ~ antisymmetric_relstr(X0)
| ~ transitive_relstr(X0)
| ~ reflexive_relstr(X0)
| empty_carrier(X0)
| ~ rel_str(X0) ),
inference(definition_folding,[],[f184,f312]) ).
fof(f312,plain,
! [X0] :
( ( bounded_relstr(X0)
& upper_bounded_relstr(X0)
& lower_bounded_relstr(X0)
& complete_relstr(X0)
& with_infima_relstr(X0)
& with_suprema_relstr(X0)
& antisymmetric_relstr(X0)
& transitive_relstr(X0)
& reflexive_relstr(X0)
& ~ empty_carrier(X0) )
| ~ sP5(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP5])]) ).
fof(f184,plain,
! [X0] :
( ( bounded_relstr(X0)
& upper_bounded_relstr(X0)
& lower_bounded_relstr(X0)
& complete_relstr(X0)
& with_infima_relstr(X0)
& with_suprema_relstr(X0)
& antisymmetric_relstr(X0)
& transitive_relstr(X0)
& reflexive_relstr(X0)
& ~ empty_carrier(X0) )
| ~ up_complete_relstr(X0)
| ~ lower_bounded_relstr(X0)
| ~ with_suprema_relstr(X0)
| ~ antisymmetric_relstr(X0)
| ~ transitive_relstr(X0)
| ~ reflexive_relstr(X0)
| empty_carrier(X0)
| ~ rel_str(X0) ),
inference(flattening,[],[f183]) ).
fof(f183,plain,
! [X0] :
( ( bounded_relstr(X0)
& upper_bounded_relstr(X0)
& lower_bounded_relstr(X0)
& complete_relstr(X0)
& with_infima_relstr(X0)
& with_suprema_relstr(X0)
& antisymmetric_relstr(X0)
& transitive_relstr(X0)
& reflexive_relstr(X0)
& ~ empty_carrier(X0) )
| ~ up_complete_relstr(X0)
| ~ lower_bounded_relstr(X0)
| ~ with_suprema_relstr(X0)
| ~ antisymmetric_relstr(X0)
| ~ transitive_relstr(X0)
| ~ reflexive_relstr(X0)
| empty_carrier(X0)
| ~ rel_str(X0) ),
inference(ennf_transformation,[],[f6]) ).
fof(f6,axiom,
! [X0] :
( rel_str(X0)
=> ( ( up_complete_relstr(X0)
& lower_bounded_relstr(X0)
& with_suprema_relstr(X0)
& antisymmetric_relstr(X0)
& transitive_relstr(X0)
& reflexive_relstr(X0)
& ~ empty_carrier(X0) )
=> ( bounded_relstr(X0)
& upper_bounded_relstr(X0)
& lower_bounded_relstr(X0)
& complete_relstr(X0)
& with_infima_relstr(X0)
& with_suprema_relstr(X0)
& antisymmetric_relstr(X0)
& transitive_relstr(X0)
& reflexive_relstr(X0)
& ~ empty_carrier(X0) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.XVCyggMQ11/Vampire---4.8_15325',cc12_waybel_0) ).
fof(f3013,plain,
spl61_367,
inference(avatar_split_clause,[],[f754,f3011]) ).
fof(f3011,plain,
( spl61_367
<=> ! [X0,X1] :
( upper_relstr_subset(filter_of_net_str(X0,X1),boole_POSet(cast_as_carrier_subset(X0)))
| ~ net_str(X1,X0)
| empty_carrier(X1)
| ~ one_sorted_str(X0)
| empty_carrier(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_367])]) ).
fof(f754,plain,
! [X0,X1] :
( upper_relstr_subset(filter_of_net_str(X0,X1),boole_POSet(cast_as_carrier_subset(X0)))
| ~ net_str(X1,X0)
| empty_carrier(X1)
| ~ one_sorted_str(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f273]) ).
fof(f273,plain,
! [X0,X1] :
( ( upper_relstr_subset(filter_of_net_str(X0,X1),boole_POSet(cast_as_carrier_subset(X0)))
& ~ empty(filter_of_net_str(X0,X1)) )
| ~ net_str(X1,X0)
| empty_carrier(X1)
| ~ one_sorted_str(X0)
| empty_carrier(X0) ),
inference(flattening,[],[f272]) ).
fof(f272,plain,
! [X0,X1] :
( ( upper_relstr_subset(filter_of_net_str(X0,X1),boole_POSet(cast_as_carrier_subset(X0)))
& ~ empty(filter_of_net_str(X0,X1)) )
| ~ net_str(X1,X0)
| empty_carrier(X1)
| ~ one_sorted_str(X0)
| empty_carrier(X0) ),
inference(ennf_transformation,[],[f66]) ).
fof(f66,axiom,
! [X0,X1] :
( ( net_str(X1,X0)
& ~ empty_carrier(X1)
& one_sorted_str(X0)
& ~ empty_carrier(X0) )
=> ( upper_relstr_subset(filter_of_net_str(X0,X1),boole_POSet(cast_as_carrier_subset(X0)))
& ~ empty(filter_of_net_str(X0,X1)) ) ),
file('/export/starexec/sandbox2/tmp/tmp.XVCyggMQ11/Vampire---4.8_15325',fc2_yellow19) ).
fof(f3009,plain,
spl61_366,
inference(avatar_split_clause,[],[f649,f3007]) ).
fof(f649,plain,
! [X0,X1] :
( filter_of_net_str(X0,X1) = a_2_1_yellow19(X0,X1)
| ~ net_str(X1,X0)
| empty_carrier(X1)
| ~ one_sorted_str(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f209]) ).
fof(f209,plain,
! [X0] :
( ! [X1] :
( filter_of_net_str(X0,X1) = a_2_1_yellow19(X0,X1)
| ~ net_str(X1,X0)
| empty_carrier(X1) )
| ~ one_sorted_str(X0)
| empty_carrier(X0) ),
inference(flattening,[],[f208]) ).
fof(f208,plain,
! [X0] :
( ! [X1] :
( filter_of_net_str(X0,X1) = a_2_1_yellow19(X0,X1)
| ~ net_str(X1,X0)
| empty_carrier(X1) )
| ~ one_sorted_str(X0)
| empty_carrier(X0) ),
inference(ennf_transformation,[],[f28]) ).
fof(f28,axiom,
! [X0] :
( ( one_sorted_str(X0)
& ~ empty_carrier(X0) )
=> ! [X1] :
( ( net_str(X1,X0)
& ~ empty_carrier(X1) )
=> filter_of_net_str(X0,X1) = a_2_1_yellow19(X0,X1) ) ),
file('/export/starexec/sandbox2/tmp/tmp.XVCyggMQ11/Vampire---4.8_15325',d3_yellow19) ).
fof(f3005,plain,
spl61_365,
inference(avatar_split_clause,[],[f636,f3003]) ).
fof(f636,plain,
! [X0] :
( sP6(X0)
| ~ rel_str(X0)
| ~ upper_bounded_relstr(X0)
| ~ antisymmetric_relstr(X0)
| ~ transitive_relstr(X0)
| ~ reflexive_relstr(X0)
| trivial_carrier(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f315]) ).
fof(f315,plain,
! [X0] :
( sP6(X0)
| ~ rel_str(X0)
| ~ upper_bounded_relstr(X0)
| ~ antisymmetric_relstr(X0)
| ~ transitive_relstr(X0)
| ~ reflexive_relstr(X0)
| trivial_carrier(X0)
| empty_carrier(X0) ),
inference(definition_folding,[],[f195,f314]) ).
fof(f314,plain,
! [X0] :
( ? [X1] :
( upper_relstr_subset(X1,X0)
& filtered_subset(X1,X0)
& proper_element(X1,powerset(the_carrier(X0)))
& ~ empty(X1)
& element(X1,powerset(the_carrier(X0))) )
| ~ sP6(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP6])]) ).
fof(f195,plain,
! [X0] :
( ? [X1] :
( upper_relstr_subset(X1,X0)
& filtered_subset(X1,X0)
& proper_element(X1,powerset(the_carrier(X0)))
& ~ empty(X1)
& element(X1,powerset(the_carrier(X0))) )
| ~ rel_str(X0)
| ~ upper_bounded_relstr(X0)
| ~ antisymmetric_relstr(X0)
| ~ transitive_relstr(X0)
| ~ reflexive_relstr(X0)
| trivial_carrier(X0)
| empty_carrier(X0) ),
inference(flattening,[],[f194]) ).
fof(f194,plain,
! [X0] :
( ? [X1] :
( upper_relstr_subset(X1,X0)
& filtered_subset(X1,X0)
& proper_element(X1,powerset(the_carrier(X0)))
& ~ empty(X1)
& element(X1,powerset(the_carrier(X0))) )
| ~ rel_str(X0)
| ~ upper_bounded_relstr(X0)
| ~ antisymmetric_relstr(X0)
| ~ transitive_relstr(X0)
| ~ reflexive_relstr(X0)
| trivial_carrier(X0)
| empty_carrier(X0) ),
inference(ennf_transformation,[],[f113]) ).
fof(f113,axiom,
! [X0] :
( ( rel_str(X0)
& upper_bounded_relstr(X0)
& antisymmetric_relstr(X0)
& transitive_relstr(X0)
& reflexive_relstr(X0)
& ~ trivial_carrier(X0)
& ~ empty_carrier(X0) )
=> ? [X1] :
( upper_relstr_subset(X1,X0)
& filtered_subset(X1,X0)
& proper_element(X1,powerset(the_carrier(X0)))
& ~ empty(X1)
& element(X1,powerset(the_carrier(X0))) ) ),
file('/export/starexec/sandbox2/tmp/tmp.XVCyggMQ11/Vampire---4.8_15325',rc4_waybel_7) ).
fof(f2968,plain,
spl61_364,
inference(avatar_split_clause,[],[f684,f2966]) ).
fof(f684,plain,
! [X0,X1] :
( boundary_set(X1,X0)
| ~ nowhere_dense(X1,X0)
| ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(cnf_transformation,[],[f237]) ).
fof(f237,plain,
! [X0] :
( ! [X1] :
( boundary_set(X1,X0)
| ~ nowhere_dense(X1,X0)
| ~ element(X1,powerset(the_carrier(X0))) )
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(flattening,[],[f236]) ).
fof(f236,plain,
! [X0] :
( ! [X1] :
( boundary_set(X1,X0)
| ~ nowhere_dense(X1,X0)
| ~ element(X1,powerset(the_carrier(X0))) )
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(ennf_transformation,[],[f21]) ).
fof(f21,axiom,
! [X0] :
( ( top_str(X0)
& topological_space(X0) )
=> ! [X1] :
( element(X1,powerset(the_carrier(X0)))
=> ( nowhere_dense(X1,X0)
=> boundary_set(X1,X0) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.XVCyggMQ11/Vampire---4.8_15325',cc4_tops_1) ).
fof(f2840,plain,
spl61_363,
inference(avatar_split_clause,[],[f741,f2838]) ).
fof(f741,plain,
! [X2,X3,X0,X1] :
( X1 = X3
| rel_str_of(X0,X1) != rel_str_of(X2,X3)
| ~ relation_of2(X1,X0,X0) ),
inference(cnf_transformation,[],[f261]) ).
fof(f261,plain,
! [X0,X1] :
( ! [X2,X3] :
( ( X1 = X3
& X0 = X2 )
| rel_str_of(X0,X1) != rel_str_of(X2,X3) )
| ~ relation_of2(X1,X0,X0) ),
inference(ennf_transformation,[],[f84]) ).
fof(f84,axiom,
! [X0,X1] :
( relation_of2(X1,X0,X0)
=> ! [X2,X3] :
( rel_str_of(X0,X1) = rel_str_of(X2,X3)
=> ( X1 = X3
& X0 = X2 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.XVCyggMQ11/Vampire---4.8_15325',free_g1_orders_2) ).
fof(f2836,plain,
spl61_362,
inference(avatar_split_clause,[],[f740,f2834]) ).
fof(f740,plain,
! [X2,X3,X0,X1] :
( X0 = X2
| rel_str_of(X0,X1) != rel_str_of(X2,X3)
| ~ relation_of2(X1,X0,X0) ),
inference(cnf_transformation,[],[f261]) ).
fof(f2832,plain,
spl61_361,
inference(avatar_split_clause,[],[f727,f2830]) ).
fof(f727,plain,
! [X0] :
( sP10(X0)
| ~ rel_str(X0)
| ~ with_infima_relstr(X0)
| ~ with_suprema_relstr(X0)
| ~ antisymmetric_relstr(X0)
| ~ transitive_relstr(X0)
| ~ reflexive_relstr(X0) ),
inference(cnf_transformation,[],[f323]) ).
fof(f323,plain,
! [X0] :
( sP10(X0)
| ~ rel_str(X0)
| ~ with_infima_relstr(X0)
| ~ with_suprema_relstr(X0)
| ~ antisymmetric_relstr(X0)
| ~ transitive_relstr(X0)
| ~ reflexive_relstr(X0) ),
inference(definition_folding,[],[f255,f322]) ).
fof(f322,plain,
! [X0] :
( ? [X1] :
( upper_relstr_subset(X1,X0)
& lower_relstr_subset(X1,X0)
& filtered_subset(X1,X0)
& directed_subset(X1,X0)
& ~ empty(X1)
& element(X1,powerset(the_carrier(X0))) )
| ~ sP10(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP10])]) ).
fof(f255,plain,
! [X0] :
( ? [X1] :
( upper_relstr_subset(X1,X0)
& lower_relstr_subset(X1,X0)
& filtered_subset(X1,X0)
& directed_subset(X1,X0)
& ~ empty(X1)
& element(X1,powerset(the_carrier(X0))) )
| ~ rel_str(X0)
| ~ with_infima_relstr(X0)
| ~ with_suprema_relstr(X0)
| ~ antisymmetric_relstr(X0)
| ~ transitive_relstr(X0)
| ~ reflexive_relstr(X0) ),
inference(flattening,[],[f254]) ).
fof(f254,plain,
! [X0] :
( ? [X1] :
( upper_relstr_subset(X1,X0)
& lower_relstr_subset(X1,X0)
& filtered_subset(X1,X0)
& directed_subset(X1,X0)
& ~ empty(X1)
& element(X1,powerset(the_carrier(X0))) )
| ~ rel_str(X0)
| ~ with_infima_relstr(X0)
| ~ with_suprema_relstr(X0)
| ~ antisymmetric_relstr(X0)
| ~ transitive_relstr(X0)
| ~ reflexive_relstr(X0) ),
inference(ennf_transformation,[],[f87]) ).
fof(f87,axiom,
! [X0] :
( ( rel_str(X0)
& with_infima_relstr(X0)
& with_suprema_relstr(X0)
& antisymmetric_relstr(X0)
& transitive_relstr(X0)
& reflexive_relstr(X0) )
=> ? [X1] :
( upper_relstr_subset(X1,X0)
& lower_relstr_subset(X1,X0)
& filtered_subset(X1,X0)
& directed_subset(X1,X0)
& ~ empty(X1)
& element(X1,powerset(the_carrier(X0))) ) ),
file('/export/starexec/sandbox2/tmp/tmp.XVCyggMQ11/Vampire---4.8_15325',rc11_waybel_0) ).
fof(f2828,plain,
spl61_360,
inference(avatar_split_clause,[],[f683,f2826]) ).
fof(f683,plain,
! [X0,X1] :
( closed_subset(X1,X0)
| ~ empty(X1)
| ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(cnf_transformation,[],[f235]) ).
fof(f235,plain,
! [X0] :
( ! [X1] :
( ( closed_subset(X1,X0)
& open_subset(X1,X0) )
| ~ empty(X1)
| ~ element(X1,powerset(the_carrier(X0))) )
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(flattening,[],[f234]) ).
fof(f234,plain,
! [X0] :
( ! [X1] :
( ( closed_subset(X1,X0)
& open_subset(X1,X0) )
| ~ empty(X1)
| ~ element(X1,powerset(the_carrier(X0))) )
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(ennf_transformation,[],[f13]) ).
fof(f13,axiom,
! [X0] :
( ( top_str(X0)
& topological_space(X0) )
=> ! [X1] :
( element(X1,powerset(the_carrier(X0)))
=> ( empty(X1)
=> ( closed_subset(X1,X0)
& open_subset(X1,X0) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.XVCyggMQ11/Vampire---4.8_15325',cc1_tops_1) ).
fof(f2824,plain,
spl61_359,
inference(avatar_split_clause,[],[f682,f2822]) ).
fof(f682,plain,
! [X0,X1] :
( open_subset(X1,X0)
| ~ empty(X1)
| ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(cnf_transformation,[],[f235]) ).
fof(f2820,plain,
spl61_358,
inference(avatar_split_clause,[],[f681,f2818]) ).
fof(f681,plain,
! [X0,X1] :
( nowhere_dense(X1,X0)
| ~ empty(X1)
| ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(cnf_transformation,[],[f233]) ).
fof(f233,plain,
! [X0] :
( ! [X1] :
( nowhere_dense(X1,X0)
| ~ empty(X1)
| ~ element(X1,powerset(the_carrier(X0))) )
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(flattening,[],[f232]) ).
fof(f232,plain,
! [X0] :
( ! [X1] :
( nowhere_dense(X1,X0)
| ~ empty(X1)
| ~ element(X1,powerset(the_carrier(X0))) )
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(ennf_transformation,[],[f19]) ).
fof(f19,axiom,
! [X0] :
( ( top_str(X0)
& topological_space(X0) )
=> ! [X1] :
( element(X1,powerset(the_carrier(X0)))
=> ( empty(X1)
=> nowhere_dense(X1,X0) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.XVCyggMQ11/Vampire---4.8_15325',cc3_tops_1) ).
fof(f2816,plain,
spl61_357,
inference(avatar_split_clause,[],[f674,f2814]) ).
fof(f674,plain,
! [X0] :
( element(sK32(X0),powerset(the_carrier(X0)))
| ~ rel_str(X0)
| ~ transitive_relstr(X0)
| ~ reflexive_relstr(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f376]) ).
fof(f376,plain,
! [X0] :
( ( upper_relstr_subset(sK32(X0),X0)
& filtered_subset(sK32(X0),X0)
& ~ empty(sK32(X0))
& element(sK32(X0),powerset(the_carrier(X0))) )
| ~ rel_str(X0)
| ~ transitive_relstr(X0)
| ~ reflexive_relstr(X0)
| empty_carrier(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK32])],[f227,f375]) ).
fof(f375,plain,
! [X0] :
( ? [X1] :
( upper_relstr_subset(X1,X0)
& filtered_subset(X1,X0)
& ~ empty(X1)
& element(X1,powerset(the_carrier(X0))) )
=> ( upper_relstr_subset(sK32(X0),X0)
& filtered_subset(sK32(X0),X0)
& ~ empty(sK32(X0))
& element(sK32(X0),powerset(the_carrier(X0))) ) ),
introduced(choice_axiom,[]) ).
fof(f227,plain,
! [X0] :
( ? [X1] :
( upper_relstr_subset(X1,X0)
& filtered_subset(X1,X0)
& ~ empty(X1)
& element(X1,powerset(the_carrier(X0))) )
| ~ rel_str(X0)
| ~ transitive_relstr(X0)
| ~ reflexive_relstr(X0)
| empty_carrier(X0) ),
inference(flattening,[],[f226]) ).
fof(f226,plain,
! [X0] :
( ? [X1] :
( upper_relstr_subset(X1,X0)
& filtered_subset(X1,X0)
& ~ empty(X1)
& element(X1,powerset(the_carrier(X0))) )
| ~ rel_str(X0)
| ~ transitive_relstr(X0)
| ~ reflexive_relstr(X0)
| empty_carrier(X0) ),
inference(ennf_transformation,[],[f86]) ).
fof(f86,axiom,
! [X0] :
( ( rel_str(X0)
& transitive_relstr(X0)
& reflexive_relstr(X0)
& ~ empty_carrier(X0) )
=> ? [X1] :
( upper_relstr_subset(X1,X0)
& filtered_subset(X1,X0)
& ~ empty(X1)
& element(X1,powerset(the_carrier(X0))) ) ),
file('/export/starexec/sandbox2/tmp/tmp.XVCyggMQ11/Vampire---4.8_15325',rc10_waybel_0) ).
fof(f2812,plain,
spl61_356,
inference(avatar_split_clause,[],[f670,f2810]) ).
fof(f670,plain,
! [X0] :
( element(sK31(X0),powerset(the_carrier(X0)))
| ~ rel_str(X0)
| ~ transitive_relstr(X0)
| ~ reflexive_relstr(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f374]) ).
fof(f374,plain,
! [X0] :
( ( lower_relstr_subset(sK31(X0),X0)
& directed_subset(sK31(X0),X0)
& ~ empty(sK31(X0))
& element(sK31(X0),powerset(the_carrier(X0))) )
| ~ rel_str(X0)
| ~ transitive_relstr(X0)
| ~ reflexive_relstr(X0)
| empty_carrier(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK31])],[f225,f373]) ).
fof(f373,plain,
! [X0] :
( ? [X1] :
( lower_relstr_subset(X1,X0)
& directed_subset(X1,X0)
& ~ empty(X1)
& element(X1,powerset(the_carrier(X0))) )
=> ( lower_relstr_subset(sK31(X0),X0)
& directed_subset(sK31(X0),X0)
& ~ empty(sK31(X0))
& element(sK31(X0),powerset(the_carrier(X0))) ) ),
introduced(choice_axiom,[]) ).
fof(f225,plain,
! [X0] :
( ? [X1] :
( lower_relstr_subset(X1,X0)
& directed_subset(X1,X0)
& ~ empty(X1)
& element(X1,powerset(the_carrier(X0))) )
| ~ rel_str(X0)
| ~ transitive_relstr(X0)
| ~ reflexive_relstr(X0)
| empty_carrier(X0) ),
inference(flattening,[],[f224]) ).
fof(f224,plain,
! [X0] :
( ? [X1] :
( lower_relstr_subset(X1,X0)
& directed_subset(X1,X0)
& ~ empty(X1)
& element(X1,powerset(the_carrier(X0))) )
| ~ rel_str(X0)
| ~ transitive_relstr(X0)
| ~ reflexive_relstr(X0)
| empty_carrier(X0) ),
inference(ennf_transformation,[],[f122]) ).
fof(f122,axiom,
! [X0] :
( ( rel_str(X0)
& transitive_relstr(X0)
& reflexive_relstr(X0)
& ~ empty_carrier(X0) )
=> ? [X1] :
( lower_relstr_subset(X1,X0)
& directed_subset(X1,X0)
& ~ empty(X1)
& element(X1,powerset(the_carrier(X0))) ) ),
file('/export/starexec/sandbox2/tmp/tmp.XVCyggMQ11/Vampire---4.8_15325',rc9_waybel_0) ).
fof(f2808,plain,
spl61_355,
inference(avatar_split_clause,[],[f605,f2806]) ).
fof(f605,plain,
! [X0] :
( sP4(X0)
| ~ join_complete_relstr(X0)
| ~ upper_bounded_relstr(X0)
| ~ antisymmetric_relstr(X0)
| ~ reflexive_relstr(X0)
| empty_carrier(X0)
| ~ rel_str(X0) ),
inference(cnf_transformation,[],[f311]) ).
fof(f311,plain,
! [X0] :
( sP4(X0)
| ~ join_complete_relstr(X0)
| ~ upper_bounded_relstr(X0)
| ~ antisymmetric_relstr(X0)
| ~ reflexive_relstr(X0)
| empty_carrier(X0)
| ~ rel_str(X0) ),
inference(definition_folding,[],[f182,f310]) ).
fof(f310,plain,
! [X0] :
( ( upper_bounded_relstr(X0)
& with_suprema_relstr(X0)
& antisymmetric_relstr(X0)
& reflexive_relstr(X0)
& ~ empty_carrier(X0) )
| ~ sP4(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP4])]) ).
fof(f182,plain,
! [X0] :
( ( upper_bounded_relstr(X0)
& with_suprema_relstr(X0)
& antisymmetric_relstr(X0)
& reflexive_relstr(X0)
& ~ empty_carrier(X0) )
| ~ join_complete_relstr(X0)
| ~ upper_bounded_relstr(X0)
| ~ antisymmetric_relstr(X0)
| ~ reflexive_relstr(X0)
| empty_carrier(X0)
| ~ rel_str(X0) ),
inference(flattening,[],[f181]) ).
fof(f181,plain,
! [X0] :
( ( upper_bounded_relstr(X0)
& with_suprema_relstr(X0)
& antisymmetric_relstr(X0)
& reflexive_relstr(X0)
& ~ empty_carrier(X0) )
| ~ join_complete_relstr(X0)
| ~ upper_bounded_relstr(X0)
| ~ antisymmetric_relstr(X0)
| ~ reflexive_relstr(X0)
| empty_carrier(X0)
| ~ rel_str(X0) ),
inference(ennf_transformation,[],[f8]) ).
fof(f8,axiom,
! [X0] :
( rel_str(X0)
=> ( ( join_complete_relstr(X0)
& upper_bounded_relstr(X0)
& antisymmetric_relstr(X0)
& reflexive_relstr(X0)
& ~ empty_carrier(X0) )
=> ( upper_bounded_relstr(X0)
& with_suprema_relstr(X0)
& antisymmetric_relstr(X0)
& reflexive_relstr(X0)
& ~ empty_carrier(X0) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.XVCyggMQ11/Vampire---4.8_15325',cc14_waybel_0) ).
fof(f2801,plain,
( spl61_1
| ~ spl61_161
| ~ spl61_253
| ~ spl61_308 ),
inference(avatar_split_clause,[],[f2544,f2428,f2088,f1659,f892]) ).
fof(f2428,plain,
( spl61_308
<=> empty(the_carrier(sK12)) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_308])]) ).
fof(f2544,plain,
( ~ one_sorted_str(sK12)
| empty_carrier(sK12)
| ~ spl61_253
| ~ spl61_308 ),
inference(resolution,[],[f2430,f2089]) ).
fof(f2430,plain,
( empty(the_carrier(sK12))
| ~ spl61_308 ),
inference(avatar_component_clause,[],[f2428]) ).
fof(f2790,plain,
spl61_354,
inference(avatar_split_clause,[],[f761,f2788]) ).
fof(f2788,plain,
( spl61_354
<=> ! [X0,X1] :
( X0 = X1
| ~ in(sK41(X0,X1),X1)
| ~ in(sK41(X0,X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_354])]) ).
fof(f761,plain,
! [X0,X1] :
( X0 = X1
| ~ in(sK41(X0,X1),X1)
| ~ in(sK41(X0,X1),X0) ),
inference(cnf_transformation,[],[f398]) ).
fof(f398,plain,
! [X0,X1] :
( X0 = X1
| ( ( ~ in(sK41(X0,X1),X1)
| ~ in(sK41(X0,X1),X0) )
& ( in(sK41(X0,X1),X1)
| in(sK41(X0,X1),X0) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK41])],[f396,f397]) ).
fof(f397,plain,
! [X0,X1] :
( ? [X2] :
( ( ~ in(X2,X1)
| ~ in(X2,X0) )
& ( in(X2,X1)
| in(X2,X0) ) )
=> ( ( ~ in(sK41(X0,X1),X1)
| ~ in(sK41(X0,X1),X0) )
& ( in(sK41(X0,X1),X1)
| in(sK41(X0,X1),X0) ) ) ),
introduced(choice_axiom,[]) ).
fof(f396,plain,
! [X0,X1] :
( X0 = X1
| ? [X2] :
( ( ~ in(X2,X1)
| ~ in(X2,X0) )
& ( in(X2,X1)
| in(X2,X0) ) ) ),
inference(nnf_transformation,[],[f280]) ).
fof(f280,plain,
! [X0,X1] :
( X0 = X1
| ? [X2] :
( in(X2,X0)
<~> in(X2,X1) ) ),
inference(ennf_transformation,[],[f131]) ).
fof(f131,axiom,
! [X0,X1] :
( ! [X2] :
( in(X2,X0)
<=> in(X2,X1) )
=> X0 = X1 ),
file('/export/starexec/sandbox2/tmp/tmp.XVCyggMQ11/Vampire---4.8_15325',t2_tarski) ).
fof(f2786,plain,
spl61_353,
inference(avatar_split_clause,[],[f760,f2784]) ).
fof(f760,plain,
! [X0,X1] :
( X0 = X1
| in(sK41(X0,X1),X1)
| in(sK41(X0,X1),X0) ),
inference(cnf_transformation,[],[f398]) ).
fof(f2782,plain,
spl61_352,
inference(avatar_split_clause,[],[f757,f2780]) ).
fof(f757,plain,
! [X0,X1] :
( relation_of2_as_subset(the_mapping(X0,X1),the_carrier(X1),the_carrier(X0))
| ~ net_str(X1,X0)
| ~ one_sorted_str(X0) ),
inference(cnf_transformation,[],[f275]) ).
fof(f275,plain,
! [X0,X1] :
( ( relation_of2_as_subset(the_mapping(X0,X1),the_carrier(X1),the_carrier(X0))
& quasi_total(the_mapping(X0,X1),the_carrier(X1),the_carrier(X0))
& function(the_mapping(X0,X1)) )
| ~ net_str(X1,X0)
| ~ one_sorted_str(X0) ),
inference(flattening,[],[f274]) ).
fof(f274,plain,
! [X0,X1] :
( ( relation_of2_as_subset(the_mapping(X0,X1),the_carrier(X1),the_carrier(X0))
& quasi_total(the_mapping(X0,X1),the_carrier(X1),the_carrier(X0))
& function(the_mapping(X0,X1)) )
| ~ net_str(X1,X0)
| ~ one_sorted_str(X0) ),
inference(ennf_transformation,[],[f48]) ).
fof(f48,axiom,
! [X0,X1] :
( ( net_str(X1,X0)
& one_sorted_str(X0) )
=> ( relation_of2_as_subset(the_mapping(X0,X1),the_carrier(X1),the_carrier(X0))
& quasi_total(the_mapping(X0,X1),the_carrier(X1),the_carrier(X0))
& function(the_mapping(X0,X1)) ) ),
file('/export/starexec/sandbox2/tmp/tmp.XVCyggMQ11/Vampire---4.8_15325',dt_u1_waybel_0) ).
fof(f2778,plain,
spl61_351,
inference(avatar_split_clause,[],[f756,f2776]) ).
fof(f756,plain,
! [X0,X1] :
( quasi_total(the_mapping(X0,X1),the_carrier(X1),the_carrier(X0))
| ~ net_str(X1,X0)
| ~ one_sorted_str(X0) ),
inference(cnf_transformation,[],[f275]) ).
fof(f2774,plain,
spl61_350,
inference(avatar_split_clause,[],[f753,f2772]) ).
fof(f753,plain,
! [X0,X1] :
( ~ empty(filter_of_net_str(X0,X1))
| ~ net_str(X1,X0)
| empty_carrier(X1)
| ~ one_sorted_str(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f273]) ).
fof(f2770,plain,
spl61_349,
inference(avatar_split_clause,[],[f750,f2768]) ).
fof(f2768,plain,
( spl61_349
<=> ! [X0,X1] :
( relation(the_mapping(X0,X1))
| ~ net_str(X1,X0)
| empty_carrier(X1)
| ~ one_sorted_str(X0)
| empty_carrier(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_349])]) ).
fof(f750,plain,
! [X0,X1] :
( relation(the_mapping(X0,X1))
| ~ net_str(X1,X0)
| empty_carrier(X1)
| ~ one_sorted_str(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f271]) ).
fof(f271,plain,
! [X0,X1] :
( ( quasi_total(the_mapping(X0,X1),the_carrier(X1),the_carrier(X0))
& function(the_mapping(X0,X1))
& relation(the_mapping(X0,X1))
& ~ empty(the_mapping(X0,X1)) )
| ~ net_str(X1,X0)
| empty_carrier(X1)
| ~ one_sorted_str(X0)
| empty_carrier(X0) ),
inference(flattening,[],[f270]) ).
fof(f270,plain,
! [X0,X1] :
( ( quasi_total(the_mapping(X0,X1),the_carrier(X1),the_carrier(X0))
& function(the_mapping(X0,X1))
& relation(the_mapping(X0,X1))
& ~ empty(the_mapping(X0,X1)) )
| ~ net_str(X1,X0)
| empty_carrier(X1)
| ~ one_sorted_str(X0)
| empty_carrier(X0) ),
inference(ennf_transformation,[],[f59]) ).
fof(f59,axiom,
! [X0,X1] :
( ( net_str(X1,X0)
& ~ empty_carrier(X1)
& one_sorted_str(X0)
& ~ empty_carrier(X0) )
=> ( quasi_total(the_mapping(X0,X1),the_carrier(X1),the_carrier(X0))
& function(the_mapping(X0,X1))
& relation(the_mapping(X0,X1))
& ~ empty(the_mapping(X0,X1)) ) ),
file('/export/starexec/sandbox2/tmp/tmp.XVCyggMQ11/Vampire---4.8_15325',fc15_yellow_6) ).
fof(f2766,plain,
spl61_348,
inference(avatar_split_clause,[],[f749,f2764]) ).
fof(f749,plain,
! [X0,X1] :
( ~ empty(the_mapping(X0,X1))
| ~ net_str(X1,X0)
| empty_carrier(X1)
| ~ one_sorted_str(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f271]) ).
fof(f2739,plain,
( ~ spl61_347
| ~ spl61_103
| ~ spl61_182
| spl61_307
| ~ spl61_308 ),
inference(avatar_split_clause,[],[f2674,f2428,f2424,f1753,f1402,f2736]) ).
fof(f2736,plain,
( spl61_347
<=> in(sK14,sK60) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_347])]) ).
fof(f2674,plain,
( ~ in(sK14,sK60)
| ~ spl61_103
| ~ spl61_182
| spl61_307
| ~ spl61_308 ),
inference(forward_demodulation,[],[f2425,f2549]) ).
fof(f2549,plain,
( the_carrier(sK12) = sK60
| ~ spl61_103
| ~ spl61_182
| ~ spl61_308 ),
inference(forward_demodulation,[],[f2546,f1844]) ).
fof(f2546,plain,
( empty_set = the_carrier(sK12)
| ~ spl61_182
| ~ spl61_308 ),
inference(resolution,[],[f2430,f1754]) ).
fof(f2425,plain,
( ~ in(sK14,the_carrier(sK12))
| spl61_307 ),
inference(avatar_component_clause,[],[f2424]) ).
fof(f2707,plain,
spl61_346,
inference(avatar_split_clause,[],[f677,f2705]) ).
fof(f2705,plain,
( spl61_346
<=> ! [X0] :
( upper_relstr_subset(sK32(X0),X0)
| ~ rel_str(X0)
| ~ transitive_relstr(X0)
| ~ reflexive_relstr(X0)
| empty_carrier(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_346])]) ).
fof(f677,plain,
! [X0] :
( upper_relstr_subset(sK32(X0),X0)
| ~ rel_str(X0)
| ~ transitive_relstr(X0)
| ~ reflexive_relstr(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f376]) ).
fof(f2703,plain,
spl61_345,
inference(avatar_split_clause,[],[f676,f2701]) ).
fof(f2701,plain,
( spl61_345
<=> ! [X0] :
( filtered_subset(sK32(X0),X0)
| ~ rel_str(X0)
| ~ transitive_relstr(X0)
| ~ reflexive_relstr(X0)
| empty_carrier(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_345])]) ).
fof(f676,plain,
! [X0] :
( filtered_subset(sK32(X0),X0)
| ~ rel_str(X0)
| ~ transitive_relstr(X0)
| ~ reflexive_relstr(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f376]) ).
fof(f2699,plain,
spl61_344,
inference(avatar_split_clause,[],[f673,f2697]) ).
fof(f2697,plain,
( spl61_344
<=> ! [X0] :
( lower_relstr_subset(sK31(X0),X0)
| ~ rel_str(X0)
| ~ transitive_relstr(X0)
| ~ reflexive_relstr(X0)
| empty_carrier(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_344])]) ).
fof(f673,plain,
! [X0] :
( lower_relstr_subset(sK31(X0),X0)
| ~ rel_str(X0)
| ~ transitive_relstr(X0)
| ~ reflexive_relstr(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f374]) ).
fof(f2695,plain,
spl61_343,
inference(avatar_split_clause,[],[f672,f2693]) ).
fof(f2693,plain,
( spl61_343
<=> ! [X0] :
( directed_subset(sK31(X0),X0)
| ~ rel_str(X0)
| ~ transitive_relstr(X0)
| ~ reflexive_relstr(X0)
| empty_carrier(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_343])]) ).
fof(f672,plain,
! [X0] :
( directed_subset(sK31(X0),X0)
| ~ rel_str(X0)
| ~ transitive_relstr(X0)
| ~ reflexive_relstr(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f374]) ).
fof(f2691,plain,
spl61_342,
inference(avatar_split_clause,[],[f643,f2689]) ).
fof(f643,plain,
! [X0] :
( element(sK27(X0),powerset(the_carrier(X0)))
| ~ top_str(X0)
| ~ topological_space(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f365]) ).
fof(f365,plain,
! [X0] :
( ( closed_subset(sK27(X0),X0)
& ~ empty(sK27(X0))
& element(sK27(X0),powerset(the_carrier(X0))) )
| ~ top_str(X0)
| ~ topological_space(X0)
| empty_carrier(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK27])],[f201,f364]) ).
fof(f364,plain,
! [X0] :
( ? [X1] :
( closed_subset(X1,X0)
& ~ empty(X1)
& element(X1,powerset(the_carrier(X0))) )
=> ( closed_subset(sK27(X0),X0)
& ~ empty(sK27(X0))
& element(sK27(X0),powerset(the_carrier(X0))) ) ),
introduced(choice_axiom,[]) ).
fof(f201,plain,
! [X0] :
( ? [X1] :
( closed_subset(X1,X0)
& ~ empty(X1)
& element(X1,powerset(the_carrier(X0))) )
| ~ top_str(X0)
| ~ topological_space(X0)
| empty_carrier(X0) ),
inference(flattening,[],[f200]) ).
fof(f200,plain,
! [X0] :
( ? [X1] :
( closed_subset(X1,X0)
& ~ empty(X1)
& element(X1,powerset(the_carrier(X0))) )
| ~ top_str(X0)
| ~ topological_space(X0)
| empty_carrier(X0) ),
inference(ennf_transformation,[],[f119]) ).
fof(f119,axiom,
! [X0] :
( ( top_str(X0)
& topological_space(X0)
& ~ empty_carrier(X0) )
=> ? [X1] :
( closed_subset(X1,X0)
& ~ empty(X1)
& element(X1,powerset(the_carrier(X0))) ) ),
file('/export/starexec/sandbox2/tmp/tmp.XVCyggMQ11/Vampire---4.8_15325',rc7_pre_topc) ).
fof(f2687,plain,
spl61_341,
inference(avatar_split_clause,[],[f639,f2685]) ).
fof(f639,plain,
! [X0] :
( element(sK26(X0),powerset(the_carrier(X0)))
| ~ top_str(X0)
| ~ topological_space(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f363]) ).
fof(f363,plain,
! [X0] :
( ( closed_subset(sK26(X0),X0)
& open_subset(sK26(X0),X0)
& ~ empty(sK26(X0))
& element(sK26(X0),powerset(the_carrier(X0))) )
| ~ top_str(X0)
| ~ topological_space(X0)
| empty_carrier(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK26])],[f199,f362]) ).
fof(f362,plain,
! [X0] :
( ? [X1] :
( closed_subset(X1,X0)
& open_subset(X1,X0)
& ~ empty(X1)
& element(X1,powerset(the_carrier(X0))) )
=> ( closed_subset(sK26(X0),X0)
& open_subset(sK26(X0),X0)
& ~ empty(sK26(X0))
& element(sK26(X0),powerset(the_carrier(X0))) ) ),
introduced(choice_axiom,[]) ).
fof(f199,plain,
! [X0] :
( ? [X1] :
( closed_subset(X1,X0)
& open_subset(X1,X0)
& ~ empty(X1)
& element(X1,powerset(the_carrier(X0))) )
| ~ top_str(X0)
| ~ topological_space(X0)
| empty_carrier(X0) ),
inference(flattening,[],[f198]) ).
fof(f198,plain,
! [X0] :
( ? [X1] :
( closed_subset(X1,X0)
& open_subset(X1,X0)
& ~ empty(X1)
& element(X1,powerset(the_carrier(X0))) )
| ~ top_str(X0)
| ~ topological_space(X0)
| empty_carrier(X0) ),
inference(ennf_transformation,[],[f108]) ).
fof(f108,axiom,
! [X0] :
( ( top_str(X0)
& topological_space(X0)
& ~ empty_carrier(X0) )
=> ? [X1] :
( closed_subset(X1,X0)
& open_subset(X1,X0)
& ~ empty(X1)
& element(X1,powerset(the_carrier(X0))) ) ),
file('/export/starexec/sandbox2/tmp/tmp.XVCyggMQ11/Vampire---4.8_15325',rc3_tops_1) ).
fof(f2683,plain,
spl61_340,
inference(avatar_split_clause,[],[f599,f2681]) ).
fof(f599,plain,
! [X0] :
( with_infima_relstr(X0)
| ~ join_complete_relstr(X0)
| ~ antisymmetric_relstr(X0)
| ~ reflexive_relstr(X0)
| empty_carrier(X0)
| ~ rel_str(X0) ),
inference(cnf_transformation,[],[f180]) ).
fof(f180,plain,
! [X0] :
( ( with_infima_relstr(X0)
& antisymmetric_relstr(X0)
& reflexive_relstr(X0)
& ~ empty_carrier(X0) )
| ~ join_complete_relstr(X0)
| ~ antisymmetric_relstr(X0)
| ~ reflexive_relstr(X0)
| empty_carrier(X0)
| ~ rel_str(X0) ),
inference(flattening,[],[f179]) ).
fof(f179,plain,
! [X0] :
( ( with_infima_relstr(X0)
& antisymmetric_relstr(X0)
& reflexive_relstr(X0)
& ~ empty_carrier(X0) )
| ~ join_complete_relstr(X0)
| ~ antisymmetric_relstr(X0)
| ~ reflexive_relstr(X0)
| empty_carrier(X0)
| ~ rel_str(X0) ),
inference(ennf_transformation,[],[f7]) ).
fof(f7,axiom,
! [X0] :
( rel_str(X0)
=> ( ( join_complete_relstr(X0)
& antisymmetric_relstr(X0)
& reflexive_relstr(X0)
& ~ empty_carrier(X0) )
=> ( with_infima_relstr(X0)
& antisymmetric_relstr(X0)
& reflexive_relstr(X0)
& ~ empty_carrier(X0) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.XVCyggMQ11/Vampire---4.8_15325',cc13_waybel_0) ).
fof(f2679,plain,
spl61_339,
inference(avatar_split_clause,[],[f541,f2677]) ).
fof(f541,plain,
! [X0,X1] :
( boundary_set(X1,X0)
| ~ empty(X1)
| ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0) ),
inference(cnf_transformation,[],[f148]) ).
fof(f148,plain,
! [X0] :
( ! [X1] :
( boundary_set(X1,X0)
| ~ empty(X1)
| ~ element(X1,powerset(the_carrier(X0))) )
| ~ top_str(X0) ),
inference(flattening,[],[f147]) ).
fof(f147,plain,
! [X0] :
( ! [X1] :
( boundary_set(X1,X0)
| ~ empty(X1)
| ~ element(X1,powerset(the_carrier(X0))) )
| ~ top_str(X0) ),
inference(ennf_transformation,[],[f17]) ).
fof(f17,axiom,
! [X0] :
( top_str(X0)
=> ! [X1] :
( element(X1,powerset(the_carrier(X0)))
=> ( empty(X1)
=> boundary_set(X1,X0) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.XVCyggMQ11/Vampire---4.8_15325',cc2_tops_1) ).
fof(f2673,plain,
( ~ spl61_103
| ~ spl61_103
| ~ spl61_182
| ~ spl61_200
| ~ spl61_307
| ~ spl61_308 ),
inference(avatar_split_clause,[],[f2614,f2428,f2424,f1826,f1753,f1402,f1402]) ).
fof(f2614,plain,
( ~ empty(sK60)
| ~ spl61_103
| ~ spl61_182
| ~ spl61_200
| ~ spl61_307
| ~ spl61_308 ),
inference(forward_demodulation,[],[f2612,f2549]) ).
fof(f2612,plain,
( ~ empty(the_carrier(sK12))
| ~ spl61_200
| ~ spl61_307 ),
inference(resolution,[],[f2426,f1827]) ).
fof(f2664,plain,
spl61_338,
inference(avatar_split_clause,[],[f675,f2662]) ).
fof(f675,plain,
! [X0] :
( ~ empty(sK32(X0))
| ~ rel_str(X0)
| ~ transitive_relstr(X0)
| ~ reflexive_relstr(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f376]) ).
fof(f2660,plain,
spl61_337,
inference(avatar_split_clause,[],[f671,f2658]) ).
fof(f671,plain,
! [X0] :
( ~ empty(sK31(X0))
| ~ rel_str(X0)
| ~ transitive_relstr(X0)
| ~ reflexive_relstr(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f374]) ).
fof(f2656,plain,
spl61_336,
inference(avatar_split_clause,[],[f573,f2654]) ).
fof(f573,plain,
! [X0] :
( rel_str_of(the_carrier(X0),the_InternalRel(X0)) = X0
| ~ strict_rel_str(X0)
| ~ rel_str(X0) ),
inference(cnf_transformation,[],[f164]) ).
fof(f164,plain,
! [X0] :
( rel_str_of(the_carrier(X0),the_InternalRel(X0)) = X0
| ~ strict_rel_str(X0)
| ~ rel_str(X0) ),
inference(flattening,[],[f163]) ).
fof(f163,plain,
! [X0] :
( rel_str_of(the_carrier(X0),the_InternalRel(X0)) = X0
| ~ strict_rel_str(X0)
| ~ rel_str(X0) ),
inference(ennf_transformation,[],[f1]) ).
fof(f1,axiom,
! [X0] :
( rel_str(X0)
=> ( strict_rel_str(X0)
=> rel_str_of(the_carrier(X0),the_InternalRel(X0)) = X0 ) ),
file('/export/starexec/sandbox2/tmp/tmp.XVCyggMQ11/Vampire---4.8_15325',abstractness_v1_orders_2) ).
fof(f2575,plain,
spl61_335,
inference(avatar_split_clause,[],[f787,f2573]) ).
fof(f787,plain,
! [X2,X0,X1] :
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f294]) ).
fof(f294,plain,
! [X0,X1,X2] :
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(flattening,[],[f293]) ).
fof(f293,plain,
! [X0,X1,X2] :
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f133]) ).
fof(f133,axiom,
! [X0,X1,X2] :
( ( element(X1,powerset(X2))
& in(X0,X1) )
=> element(X0,X2) ),
file('/export/starexec/sandbox2/tmp/tmp.XVCyggMQ11/Vampire---4.8_15325',t4_subset) ).
fof(f2571,plain,
spl61_334,
inference(avatar_split_clause,[],[f773,f2569]) ).
fof(f773,plain,
! [X2,X0,X1] :
( strict_net_str(net_of_bool_filter(X2,X1,X0),X2)
| ~ sP11(X0,X1,X2) ),
inference(cnf_transformation,[],[f405]) ).
fof(f405,plain,
! [X0,X1,X2] :
( ( directed_relstr(net_of_bool_filter(X2,X1,X0))
& strict_net_str(net_of_bool_filter(X2,X1,X0),X2)
& transitive_relstr(net_of_bool_filter(X2,X1,X0))
& reflexive_relstr(net_of_bool_filter(X2,X1,X0))
& ~ empty_carrier(net_of_bool_filter(X2,X1,X0)) )
| ~ sP11(X0,X1,X2) ),
inference(rectify,[],[f404]) ).
fof(f404,plain,
! [X2,X1,X0] :
( ( directed_relstr(net_of_bool_filter(X0,X1,X2))
& strict_net_str(net_of_bool_filter(X0,X1,X2),X0)
& transitive_relstr(net_of_bool_filter(X0,X1,X2))
& reflexive_relstr(net_of_bool_filter(X0,X1,X2))
& ~ empty_carrier(net_of_bool_filter(X0,X1,X2)) )
| ~ sP11(X2,X1,X0) ),
inference(nnf_transformation,[],[f324]) ).
fof(f2567,plain,
spl61_333,
inference(avatar_split_clause,[],[f768,f2565]) ).
fof(f768,plain,
! [X2,X0,X1] :
( element(X2,powerset(cartesian_product2(X0,X1)))
| ~ relation_of2_as_subset(X2,X0,X1) ),
inference(cnf_transformation,[],[f283]) ).
fof(f283,plain,
! [X0,X1,X2] :
( element(X2,powerset(cartesian_product2(X0,X1)))
| ~ relation_of2_as_subset(X2,X0,X1) ),
inference(ennf_transformation,[],[f45]) ).
fof(f45,axiom,
! [X0,X1,X2] :
( relation_of2_as_subset(X2,X0,X1)
=> element(X2,powerset(cartesian_product2(X0,X1))) ),
file('/export/starexec/sandbox2/tmp/tmp.XVCyggMQ11/Vampire---4.8_15325',dt_m2_relset_1) ).
fof(f2563,plain,
spl61_332,
inference(avatar_split_clause,[],[f715,f2561]) ).
fof(f715,plain,
! [X0] :
( element(sK36(X0),powerset(the_carrier(X0)))
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(cnf_transformation,[],[f386]) ).
fof(f386,plain,
! [X0] :
( ( closed_subset(sK36(X0),X0)
& element(sK36(X0),powerset(the_carrier(X0))) )
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK36])],[f249,f385]) ).
fof(f385,plain,
! [X0] :
( ? [X1] :
( closed_subset(X1,X0)
& element(X1,powerset(the_carrier(X0))) )
=> ( closed_subset(sK36(X0),X0)
& element(sK36(X0),powerset(the_carrier(X0))) ) ),
introduced(choice_axiom,[]) ).
fof(f249,plain,
! [X0] :
( ? [X1] :
( closed_subset(X1,X0)
& element(X1,powerset(the_carrier(X0))) )
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(flattening,[],[f248]) ).
fof(f248,plain,
! [X0] :
( ? [X1] :
( closed_subset(X1,X0)
& element(X1,powerset(the_carrier(X0))) )
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(ennf_transformation,[],[f118]) ).
fof(f118,axiom,
! [X0] :
( ( top_str(X0)
& topological_space(X0) )
=> ? [X1] :
( closed_subset(X1,X0)
& element(X1,powerset(the_carrier(X0))) ) ),
file('/export/starexec/sandbox2/tmp/tmp.XVCyggMQ11/Vampire---4.8_15325',rc6_pre_topc) ).
fof(f2559,plain,
spl61_331,
inference(avatar_split_clause,[],[f712,f2557]) ).
fof(f712,plain,
! [X0] :
( element(sK35(X0),powerset(the_carrier(X0)))
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(cnf_transformation,[],[f384]) ).
fof(f384,plain,
! [X0] :
( ( closed_subset(sK35(X0),X0)
& open_subset(sK35(X0),X0)
& element(sK35(X0),powerset(the_carrier(X0))) )
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK35])],[f247,f383]) ).
fof(f383,plain,
! [X0] :
( ? [X1] :
( closed_subset(X1,X0)
& open_subset(X1,X0)
& element(X1,powerset(the_carrier(X0))) )
=> ( closed_subset(sK35(X0),X0)
& open_subset(sK35(X0),X0)
& element(sK35(X0),powerset(the_carrier(X0))) ) ),
introduced(choice_axiom,[]) ).
fof(f247,plain,
! [X0] :
( ? [X1] :
( closed_subset(X1,X0)
& open_subset(X1,X0)
& element(X1,powerset(the_carrier(X0))) )
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(flattening,[],[f246]) ).
fof(f246,plain,
! [X0] :
( ? [X1] :
( closed_subset(X1,X0)
& open_subset(X1,X0)
& element(X1,powerset(the_carrier(X0))) )
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(ennf_transformation,[],[f101]) ).
fof(f101,axiom,
! [X0] :
( ( top_str(X0)
& topological_space(X0) )
=> ? [X1] :
( closed_subset(X1,X0)
& open_subset(X1,X0)
& element(X1,powerset(the_carrier(X0))) ) ),
file('/export/starexec/sandbox2/tmp/tmp.XVCyggMQ11/Vampire---4.8_15325',rc2_tops_1) ).
fof(f2555,plain,
spl61_330,
inference(avatar_split_clause,[],[f710,f2553]) ).
fof(f710,plain,
! [X0] :
( element(sK34(X0),powerset(the_carrier(X0)))
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(cnf_transformation,[],[f382]) ).
fof(f382,plain,
! [X0] :
( ( open_subset(sK34(X0),X0)
& element(sK34(X0),powerset(the_carrier(X0))) )
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK34])],[f245,f381]) ).
fof(f381,plain,
! [X0] :
( ? [X1] :
( open_subset(X1,X0)
& element(X1,powerset(the_carrier(X0))) )
=> ( open_subset(sK34(X0),X0)
& element(sK34(X0),powerset(the_carrier(X0))) ) ),
introduced(choice_axiom,[]) ).
fof(f245,plain,
! [X0] :
( ? [X1] :
( open_subset(X1,X0)
& element(X1,powerset(the_carrier(X0))) )
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(flattening,[],[f244]) ).
fof(f244,plain,
! [X0] :
( ? [X1] :
( open_subset(X1,X0)
& element(X1,powerset(the_carrier(X0))) )
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(ennf_transformation,[],[f94]) ).
fof(f94,axiom,
! [X0] :
( ( top_str(X0)
& topological_space(X0) )
=> ? [X1] :
( open_subset(X1,X0)
& element(X1,powerset(the_carrier(X0))) ) ),
file('/export/starexec/sandbox2/tmp/tmp.XVCyggMQ11/Vampire---4.8_15325',rc1_tops_1) ).
fof(f2543,plain,
spl61_329,
inference(avatar_split_clause,[],[f660,f2541]) ).
fof(f660,plain,
! [X0] :
( element(sK29(X0),powerset(the_carrier(X0)))
| ~ rel_str(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f369]) ).
fof(f369,plain,
! [X0] :
( ( upper_relstr_subset(sK29(X0),X0)
& lower_relstr_subset(sK29(X0),X0)
& ~ empty(sK29(X0))
& element(sK29(X0),powerset(the_carrier(X0))) )
| ~ rel_str(X0)
| empty_carrier(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK29])],[f221,f368]) ).
fof(f368,plain,
! [X0] :
( ? [X1] :
( upper_relstr_subset(X1,X0)
& lower_relstr_subset(X1,X0)
& ~ empty(X1)
& element(X1,powerset(the_carrier(X0))) )
=> ( upper_relstr_subset(sK29(X0),X0)
& lower_relstr_subset(sK29(X0),X0)
& ~ empty(sK29(X0))
& element(sK29(X0),powerset(the_carrier(X0))) ) ),
introduced(choice_axiom,[]) ).
fof(f221,plain,
! [X0] :
( ? [X1] :
( upper_relstr_subset(X1,X0)
& lower_relstr_subset(X1,X0)
& ~ empty(X1)
& element(X1,powerset(the_carrier(X0))) )
| ~ rel_str(X0)
| empty_carrier(X0) ),
inference(flattening,[],[f220]) ).
fof(f220,plain,
! [X0] :
( ? [X1] :
( upper_relstr_subset(X1,X0)
& lower_relstr_subset(X1,X0)
& ~ empty(X1)
& element(X1,powerset(the_carrier(X0))) )
| ~ rel_str(X0)
| empty_carrier(X0) ),
inference(ennf_transformation,[],[f121]) ).
fof(f121,axiom,
! [X0] :
( ( rel_str(X0)
& ~ empty_carrier(X0) )
=> ? [X1] :
( upper_relstr_subset(X1,X0)
& lower_relstr_subset(X1,X0)
& ~ empty(X1)
& element(X1,powerset(the_carrier(X0))) ) ),
file('/export/starexec/sandbox2/tmp/tmp.XVCyggMQ11/Vampire---4.8_15325',rc8_waybel_0) ).
fof(f2539,plain,
spl61_328,
inference(avatar_split_clause,[],[f655,f2537]) ).
fof(f2537,plain,
( spl61_328
<=> ! [X0] :
( directed_subset(cast_as_carrier_subset(X0),X0)
| ~ rel_str(X0)
| ~ upper_bounded_relstr(X0)
| empty_carrier(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_328])]) ).
fof(f655,plain,
! [X0] :
( directed_subset(cast_as_carrier_subset(X0),X0)
| ~ rel_str(X0)
| ~ upper_bounded_relstr(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f215]) ).
fof(f215,plain,
! [X0] :
( ( directed_subset(cast_as_carrier_subset(X0),X0)
& ~ empty(cast_as_carrier_subset(X0)) )
| ~ rel_str(X0)
| ~ upper_bounded_relstr(X0)
| empty_carrier(X0) ),
inference(flattening,[],[f214]) ).
fof(f214,plain,
! [X0] :
( ( directed_subset(cast_as_carrier_subset(X0),X0)
& ~ empty(cast_as_carrier_subset(X0)) )
| ~ rel_str(X0)
| ~ upper_bounded_relstr(X0)
| empty_carrier(X0) ),
inference(ennf_transformation,[],[f68]) ).
fof(f68,axiom,
! [X0] :
( ( rel_str(X0)
& upper_bounded_relstr(X0)
& ~ empty_carrier(X0) )
=> ( directed_subset(cast_as_carrier_subset(X0),X0)
& ~ empty(cast_as_carrier_subset(X0)) ) ),
file('/export/starexec/sandbox2/tmp/tmp.XVCyggMQ11/Vampire---4.8_15325',fc3_waybel_0) ).
fof(f2535,plain,
spl61_327,
inference(avatar_split_clause,[],[f653,f2533]) ).
fof(f2533,plain,
( spl61_327
<=> ! [X0] :
( filtered_subset(cast_as_carrier_subset(X0),X0)
| ~ rel_str(X0)
| ~ lower_bounded_relstr(X0)
| empty_carrier(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_327])]) ).
fof(f653,plain,
! [X0] :
( filtered_subset(cast_as_carrier_subset(X0),X0)
| ~ rel_str(X0)
| ~ lower_bounded_relstr(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f213]) ).
fof(f213,plain,
! [X0] :
( ( filtered_subset(cast_as_carrier_subset(X0),X0)
& ~ empty(cast_as_carrier_subset(X0)) )
| ~ rel_str(X0)
| ~ lower_bounded_relstr(X0)
| empty_carrier(X0) ),
inference(flattening,[],[f212]) ).
fof(f212,plain,
! [X0] :
( ( filtered_subset(cast_as_carrier_subset(X0),X0)
& ~ empty(cast_as_carrier_subset(X0)) )
| ~ rel_str(X0)
| ~ lower_bounded_relstr(X0)
| empty_carrier(X0) ),
inference(ennf_transformation,[],[f75]) ).
fof(f75,axiom,
! [X0] :
( ( rel_str(X0)
& lower_bounded_relstr(X0)
& ~ empty_carrier(X0) )
=> ( filtered_subset(cast_as_carrier_subset(X0),X0)
& ~ empty(cast_as_carrier_subset(X0)) ) ),
file('/export/starexec/sandbox2/tmp/tmp.XVCyggMQ11/Vampire---4.8_15325',fc5_waybel_0) ).
fof(f2531,plain,
spl61_326,
inference(avatar_split_clause,[],[f650,f2529]) ).
fof(f650,plain,
! [X0] :
( element(sK28(X0),powerset(the_carrier(X0)))
| ~ one_sorted_str(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f367]) ).
fof(f367,plain,
! [X0] :
( ( ~ empty(sK28(X0))
& element(sK28(X0),powerset(the_carrier(X0))) )
| ~ one_sorted_str(X0)
| empty_carrier(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK28])],[f211,f366]) ).
fof(f366,plain,
! [X0] :
( ? [X1] :
( ~ empty(X1)
& element(X1,powerset(the_carrier(X0))) )
=> ( ~ empty(sK28(X0))
& element(sK28(X0),powerset(the_carrier(X0))) ) ),
introduced(choice_axiom,[]) ).
fof(f211,plain,
! [X0] :
( ? [X1] :
( ~ empty(X1)
& element(X1,powerset(the_carrier(X0))) )
| ~ one_sorted_str(X0)
| empty_carrier(X0) ),
inference(flattening,[],[f210]) ).
fof(f210,plain,
! [X0] :
( ? [X1] :
( ~ empty(X1)
& element(X1,powerset(the_carrier(X0))) )
| ~ one_sorted_str(X0)
| empty_carrier(X0) ),
inference(ennf_transformation,[],[f115]) ).
fof(f115,axiom,
! [X0] :
( ( one_sorted_str(X0)
& ~ empty_carrier(X0) )
=> ? [X1] :
( ~ empty(X1)
& element(X1,powerset(the_carrier(X0))) ) ),
file('/export/starexec/sandbox2/tmp/tmp.XVCyggMQ11/Vampire---4.8_15325',rc5_struct_0) ).
fof(f2527,plain,
spl61_325,
inference(avatar_split_clause,[],[f645,f2525]) ).
fof(f2525,plain,
( spl61_325
<=> ! [X0] :
( closed_subset(sK27(X0),X0)
| ~ top_str(X0)
| ~ topological_space(X0)
| empty_carrier(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_325])]) ).
fof(f645,plain,
! [X0] :
( closed_subset(sK27(X0),X0)
| ~ top_str(X0)
| ~ topological_space(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f365]) ).
fof(f2523,plain,
spl61_324,
inference(avatar_split_clause,[],[f642,f2521]) ).
fof(f2521,plain,
( spl61_324
<=> ! [X0] :
( closed_subset(sK26(X0),X0)
| ~ top_str(X0)
| ~ topological_space(X0)
| empty_carrier(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_324])]) ).
fof(f642,plain,
! [X0] :
( closed_subset(sK26(X0),X0)
| ~ top_str(X0)
| ~ topological_space(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f363]) ).
fof(f2519,plain,
spl61_323,
inference(avatar_split_clause,[],[f641,f2517]) ).
fof(f2517,plain,
( spl61_323
<=> ! [X0] :
( open_subset(sK26(X0),X0)
| ~ top_str(X0)
| ~ topological_space(X0)
| empty_carrier(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_323])]) ).
fof(f641,plain,
! [X0] :
( open_subset(sK26(X0),X0)
| ~ top_str(X0)
| ~ topological_space(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f363]) ).
fof(f2515,plain,
spl61_322,
inference(avatar_split_clause,[],[f621,f2513]) ).
fof(f2513,plain,
( spl61_322
<=> ! [X0] :
( upper_bounded_relstr(X0)
| ~ up_complete_relstr(X0)
| ~ with_suprema_relstr(X0)
| ~ reflexive_relstr(X0)
| ~ rel_str(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_322])]) ).
fof(f621,plain,
! [X0] :
( upper_bounded_relstr(X0)
| ~ up_complete_relstr(X0)
| ~ with_suprema_relstr(X0)
| ~ reflexive_relstr(X0)
| ~ rel_str(X0) ),
inference(cnf_transformation,[],[f188]) ).
fof(f188,plain,
! [X0] :
( ( upper_bounded_relstr(X0)
& with_suprema_relstr(X0)
& reflexive_relstr(X0)
& ~ empty_carrier(X0) )
| ~ up_complete_relstr(X0)
| ~ with_suprema_relstr(X0)
| ~ reflexive_relstr(X0)
| ~ rel_str(X0) ),
inference(flattening,[],[f187]) ).
fof(f187,plain,
! [X0] :
( ( upper_bounded_relstr(X0)
& with_suprema_relstr(X0)
& reflexive_relstr(X0)
& ~ empty_carrier(X0) )
| ~ up_complete_relstr(X0)
| ~ with_suprema_relstr(X0)
| ~ reflexive_relstr(X0)
| ~ rel_str(X0) ),
inference(ennf_transformation,[],[f27]) ).
fof(f27,axiom,
! [X0] :
( rel_str(X0)
=> ( ( up_complete_relstr(X0)
& with_suprema_relstr(X0)
& reflexive_relstr(X0) )
=> ( upper_bounded_relstr(X0)
& with_suprema_relstr(X0)
& reflexive_relstr(X0)
& ~ empty_carrier(X0) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.XVCyggMQ11/Vampire---4.8_15325',cc9_waybel_0) ).
fof(f2511,plain,
spl61_321,
inference(avatar_split_clause,[],[f595,f2509]) ).
fof(f595,plain,
! [X0] :
( join_complete_relstr(X0)
| ~ complete_relstr(X0)
| ~ reflexive_relstr(X0)
| empty_carrier(X0)
| ~ rel_str(X0) ),
inference(cnf_transformation,[],[f178]) ).
fof(f178,plain,
! [X0] :
( ( join_complete_relstr(X0)
& up_complete_relstr(X0)
& reflexive_relstr(X0)
& ~ empty_carrier(X0) )
| ~ complete_relstr(X0)
| ~ reflexive_relstr(X0)
| empty_carrier(X0)
| ~ rel_str(X0) ),
inference(flattening,[],[f177]) ).
fof(f177,plain,
! [X0] :
( ( join_complete_relstr(X0)
& up_complete_relstr(X0)
& reflexive_relstr(X0)
& ~ empty_carrier(X0) )
| ~ complete_relstr(X0)
| ~ reflexive_relstr(X0)
| empty_carrier(X0)
| ~ rel_str(X0) ),
inference(ennf_transformation,[],[f4]) ).
fof(f4,axiom,
! [X0] :
( rel_str(X0)
=> ( ( complete_relstr(X0)
& reflexive_relstr(X0)
& ~ empty_carrier(X0) )
=> ( join_complete_relstr(X0)
& up_complete_relstr(X0)
& reflexive_relstr(X0)
& ~ empty_carrier(X0) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.XVCyggMQ11/Vampire---4.8_15325',cc10_waybel_0) ).
fof(f2507,plain,
spl61_320,
inference(avatar_split_clause,[],[f594,f2505]) ).
fof(f594,plain,
! [X0] :
( up_complete_relstr(X0)
| ~ complete_relstr(X0)
| ~ reflexive_relstr(X0)
| empty_carrier(X0)
| ~ rel_str(X0) ),
inference(cnf_transformation,[],[f178]) ).
fof(f2503,plain,
( spl61_319
| ~ spl61_132
| spl61_308 ),
inference(avatar_split_clause,[],[f2465,f2428,f1521,f2500]) ).
fof(f2500,plain,
( spl61_319
<=> sP0(the_carrier(sK12)) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_319])]) ).
fof(f2465,plain,
( sP0(the_carrier(sK12))
| ~ spl61_132
| spl61_308 ),
inference(resolution,[],[f2429,f1522]) ).
fof(f2429,plain,
( ~ empty(the_carrier(sK12))
| spl61_308 ),
inference(avatar_component_clause,[],[f2428]) ).
fof(f2498,plain,
spl61_318,
inference(avatar_split_clause,[],[f591,f2496]) ).
fof(f2496,plain,
( spl61_318
<=> ! [X0] :
( lower_bounded_relstr(X0)
| ~ join_complete_relstr(X0)
| ~ reflexive_relstr(X0)
| empty_carrier(X0)
| ~ rel_str(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_318])]) ).
fof(f591,plain,
! [X0] :
( lower_bounded_relstr(X0)
| ~ join_complete_relstr(X0)
| ~ reflexive_relstr(X0)
| empty_carrier(X0)
| ~ rel_str(X0) ),
inference(cnf_transformation,[],[f176]) ).
fof(f176,plain,
! [X0] :
( ( lower_bounded_relstr(X0)
& reflexive_relstr(X0)
& ~ empty_carrier(X0) )
| ~ join_complete_relstr(X0)
| ~ reflexive_relstr(X0)
| empty_carrier(X0)
| ~ rel_str(X0) ),
inference(flattening,[],[f175]) ).
fof(f175,plain,
! [X0] :
( ( lower_bounded_relstr(X0)
& reflexive_relstr(X0)
& ~ empty_carrier(X0) )
| ~ join_complete_relstr(X0)
| ~ reflexive_relstr(X0)
| empty_carrier(X0)
| ~ rel_str(X0) ),
inference(ennf_transformation,[],[f5]) ).
fof(f5,axiom,
! [X0] :
( rel_str(X0)
=> ( ( join_complete_relstr(X0)
& reflexive_relstr(X0)
& ~ empty_carrier(X0) )
=> ( lower_bounded_relstr(X0)
& reflexive_relstr(X0)
& ~ empty_carrier(X0) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.XVCyggMQ11/Vampire---4.8_15325',cc11_waybel_0) ).
fof(f2494,plain,
spl61_317,
inference(avatar_split_clause,[],[f588,f2492]) ).
fof(f588,plain,
! [X0] :
( sP3(X0)
| ~ trivial_carrier(X0)
| ~ reflexive_relstr(X0)
| empty_carrier(X0)
| ~ rel_str(X0) ),
inference(cnf_transformation,[],[f309]) ).
fof(f309,plain,
! [X0] :
( sP3(X0)
| ~ trivial_carrier(X0)
| ~ reflexive_relstr(X0)
| empty_carrier(X0)
| ~ rel_str(X0) ),
inference(definition_folding,[],[f174,f308]) ).
fof(f308,plain,
! [X0] :
( ( complete_relstr(X0)
& antisymmetric_relstr(X0)
& transitive_relstr(X0)
& reflexive_relstr(X0)
& ~ empty_carrier(X0) )
| ~ sP3(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP3])]) ).
fof(f174,plain,
! [X0] :
( ( complete_relstr(X0)
& antisymmetric_relstr(X0)
& transitive_relstr(X0)
& reflexive_relstr(X0)
& ~ empty_carrier(X0) )
| ~ trivial_carrier(X0)
| ~ reflexive_relstr(X0)
| empty_carrier(X0)
| ~ rel_str(X0) ),
inference(flattening,[],[f173]) ).
fof(f173,plain,
! [X0] :
( ( complete_relstr(X0)
& antisymmetric_relstr(X0)
& transitive_relstr(X0)
& reflexive_relstr(X0)
& ~ empty_carrier(X0) )
| ~ trivial_carrier(X0)
| ~ reflexive_relstr(X0)
| empty_carrier(X0)
| ~ rel_str(X0) ),
inference(ennf_transformation,[],[f18]) ).
fof(f18,axiom,
! [X0] :
( rel_str(X0)
=> ( ( trivial_carrier(X0)
& reflexive_relstr(X0)
& ~ empty_carrier(X0) )
=> ( complete_relstr(X0)
& antisymmetric_relstr(X0)
& transitive_relstr(X0)
& reflexive_relstr(X0)
& ~ empty_carrier(X0) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.XVCyggMQ11/Vampire---4.8_15325',cc2_yellow_0) ).
fof(f2490,plain,
spl61_316,
inference(avatar_split_clause,[],[f582,f2488]) ).
fof(f582,plain,
! [X0] :
( connected_relstr(X0)
| ~ trivial_carrier(X0)
| ~ reflexive_relstr(X0)
| empty_carrier(X0)
| ~ rel_str(X0) ),
inference(cnf_transformation,[],[f172]) ).
fof(f172,plain,
! [X0] :
( ( connected_relstr(X0)
& reflexive_relstr(X0)
& ~ empty_carrier(X0) )
| ~ trivial_carrier(X0)
| ~ reflexive_relstr(X0)
| empty_carrier(X0)
| ~ rel_str(X0) ),
inference(flattening,[],[f171]) ).
fof(f171,plain,
! [X0] :
( ( connected_relstr(X0)
& reflexive_relstr(X0)
& ~ empty_carrier(X0) )
| ~ trivial_carrier(X0)
| ~ reflexive_relstr(X0)
| empty_carrier(X0)
| ~ rel_str(X0) ),
inference(ennf_transformation,[],[f24]) ).
fof(f24,axiom,
! [X0] :
( rel_str(X0)
=> ( ( trivial_carrier(X0)
& reflexive_relstr(X0)
& ~ empty_carrier(X0) )
=> ( connected_relstr(X0)
& reflexive_relstr(X0)
& ~ empty_carrier(X0) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.XVCyggMQ11/Vampire---4.8_15325',cc5_waybel_0) ).
fof(f2459,plain,
spl61_315,
inference(avatar_split_clause,[],[f790,f2457]) ).
fof(f790,plain,
! [X2,X0,X1] :
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f295]) ).
fof(f295,plain,
! [X0,X1,X2] :
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f134]) ).
fof(f134,axiom,
! [X0,X1,X2] :
~ ( empty(X2)
& element(X1,powerset(X2))
& in(X0,X1) ),
file('/export/starexec/sandbox2/tmp/tmp.XVCyggMQ11/Vampire---4.8_15325',t5_subset) ).
fof(f2455,plain,
spl61_314,
inference(avatar_split_clause,[],[f774,f2453]) ).
fof(f774,plain,
! [X2,X0,X1] :
( directed_relstr(net_of_bool_filter(X2,X1,X0))
| ~ sP11(X0,X1,X2) ),
inference(cnf_transformation,[],[f405]) ).
fof(f2451,plain,
spl61_313,
inference(avatar_split_clause,[],[f772,f2449]) ).
fof(f2449,plain,
( spl61_313
<=> ! [X2,X0,X1] :
( transitive_relstr(net_of_bool_filter(X2,X1,X0))
| ~ sP11(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_313])]) ).
fof(f772,plain,
! [X2,X0,X1] :
( transitive_relstr(net_of_bool_filter(X2,X1,X0))
| ~ sP11(X0,X1,X2) ),
inference(cnf_transformation,[],[f405]) ).
fof(f2447,plain,
spl61_312,
inference(avatar_split_clause,[],[f771,f2445]) ).
fof(f771,plain,
! [X2,X0,X1] :
( reflexive_relstr(net_of_bool_filter(X2,X1,X0))
| ~ sP11(X0,X1,X2) ),
inference(cnf_transformation,[],[f405]) ).
fof(f2443,plain,
spl61_311,
inference(avatar_split_clause,[],[f770,f2441]) ).
fof(f2441,plain,
( spl61_311
<=> ! [X2,X0,X1] :
( ~ empty_carrier(net_of_bool_filter(X2,X1,X0))
| ~ sP11(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_311])]) ).
fof(f770,plain,
! [X2,X0,X1] :
( ~ empty_carrier(net_of_bool_filter(X2,X1,X0))
| ~ sP11(X0,X1,X2) ),
inference(cnf_transformation,[],[f405]) ).
fof(f2439,plain,
spl61_310,
inference(avatar_split_clause,[],[f755,f2437]) ).
fof(f2437,plain,
( spl61_310
<=> ! [X0,X1] :
( function(the_mapping(X0,X1))
| ~ net_str(X1,X0)
| ~ one_sorted_str(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_310])]) ).
fof(f755,plain,
! [X0,X1] :
( function(the_mapping(X0,X1))
| ~ net_str(X1,X0)
| ~ one_sorted_str(X0) ),
inference(cnf_transformation,[],[f275]) ).
fof(f2435,plain,
spl61_309,
inference(avatar_split_clause,[],[f644,f2433]) ).
fof(f644,plain,
! [X0] :
( ~ empty(sK27(X0))
| ~ top_str(X0)
| ~ topological_space(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f365]) ).
fof(f2431,plain,
( spl61_307
| spl61_308
| ~ spl61_5
| ~ spl61_293 ),
inference(avatar_split_clause,[],[f2384,f2281,f912,f2428,f2424]) ).
fof(f2384,plain,
( empty(the_carrier(sK12))
| in(sK14,the_carrier(sK12))
| ~ spl61_5
| ~ spl61_293 ),
inference(resolution,[],[f2282,f914]) ).
fof(f914,plain,
( element(sK14,the_carrier(sK12))
| ~ spl61_5 ),
inference(avatar_component_clause,[],[f912]) ).
fof(f2422,plain,
spl61_306,
inference(avatar_split_clause,[],[f640,f2420]) ).
fof(f640,plain,
! [X0] :
( ~ empty(sK26(X0))
| ~ top_str(X0)
| ~ topological_space(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f363]) ).
fof(f2418,plain,
spl61_305,
inference(avatar_split_clause,[],[f569,f2416]) ).
fof(f569,plain,
! [X0] :
( relation_of2_as_subset(the_InternalRel(X0),the_carrier(X0),the_carrier(X0))
| ~ rel_str(X0) ),
inference(cnf_transformation,[],[f158]) ).
fof(f158,plain,
! [X0] :
( relation_of2_as_subset(the_InternalRel(X0),the_carrier(X0),the_carrier(X0))
| ~ rel_str(X0) ),
inference(ennf_transformation,[],[f46]) ).
fof(f46,axiom,
! [X0] :
( rel_str(X0)
=> relation_of2_as_subset(the_InternalRel(X0),the_carrier(X0),the_carrier(X0)) ),
file('/export/starexec/sandbox2/tmp/tmp.XVCyggMQ11/Vampire---4.8_15325',dt_u1_orders_2) ).
fof(f2414,plain,
spl61_304,
inference(avatar_split_clause,[],[f564,f2412]) ).
fof(f564,plain,
! [X0] :
( element(sK22(X0),powerset(powerset(the_carrier(X0))))
| ~ one_sorted_str(X0) ),
inference(cnf_transformation,[],[f350]) ).
fof(f350,plain,
! [X0] :
( ( finite(sK22(X0))
& ~ empty(sK22(X0))
& element(sK22(X0),powerset(powerset(the_carrier(X0)))) )
| ~ one_sorted_str(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK22])],[f155,f349]) ).
fof(f349,plain,
! [X0] :
( ? [X1] :
( finite(X1)
& ~ empty(X1)
& element(X1,powerset(powerset(the_carrier(X0)))) )
=> ( finite(sK22(X0))
& ~ empty(sK22(X0))
& element(sK22(X0),powerset(powerset(the_carrier(X0)))) ) ),
introduced(choice_axiom,[]) ).
fof(f155,plain,
! [X0] :
( ? [X1] :
( finite(X1)
& ~ empty(X1)
& element(X1,powerset(powerset(the_carrier(X0)))) )
| ~ one_sorted_str(X0) ),
inference(ennf_transformation,[],[f109]) ).
fof(f109,axiom,
! [X0] :
( one_sorted_str(X0)
=> ? [X1] :
( finite(X1)
& ~ empty(X1)
& element(X1,powerset(powerset(the_carrier(X0)))) ) ),
file('/export/starexec/sandbox2/tmp/tmp.XVCyggMQ11/Vampire---4.8_15325',rc3_waybel_7) ).
fof(f2361,plain,
( ~ spl61_302
| spl61_303
| ~ spl61_9
| ~ spl61_266 ),
inference(avatar_split_clause,[],[f2321,f2171,f932,f2358,f2354]) ).
fof(f2354,plain,
( spl61_302
<=> finite(the_carrier(boole_POSet(cast_as_carrier_subset(sK12)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_302])]) ).
fof(f2358,plain,
( spl61_303
<=> finite(sK13) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_303])]) ).
fof(f2321,plain,
( finite(sK13)
| ~ finite(the_carrier(boole_POSet(cast_as_carrier_subset(sK12))))
| ~ spl61_9
| ~ spl61_266 ),
inference(resolution,[],[f2172,f934]) ).
fof(f2316,plain,
spl61_301,
inference(avatar_split_clause,[],[f789,f2314]) ).
fof(f789,plain,
! [X2,X0,X1] :
( relation_of2_as_subset(X2,X0,X1)
| ~ relation_of2(X2,X0,X1) ),
inference(cnf_transformation,[],[f410]) ).
fof(f410,plain,
! [X0,X1,X2] :
( ( relation_of2_as_subset(X2,X0,X1)
| ~ relation_of2(X2,X0,X1) )
& ( relation_of2(X2,X0,X1)
| ~ relation_of2_as_subset(X2,X0,X1) ) ),
inference(nnf_transformation,[],[f123]) ).
fof(f123,axiom,
! [X0,X1,X2] :
( relation_of2_as_subset(X2,X0,X1)
<=> relation_of2(X2,X0,X1) ),
file('/export/starexec/sandbox2/tmp/tmp.XVCyggMQ11/Vampire---4.8_15325',redefinition_m2_relset_1) ).
fof(f2312,plain,
spl61_300,
inference(avatar_split_clause,[],[f788,f2310]) ).
fof(f788,plain,
! [X2,X0,X1] :
( relation_of2(X2,X0,X1)
| ~ relation_of2_as_subset(X2,X0,X1) ),
inference(cnf_transformation,[],[f410]) ).
fof(f2308,plain,
( spl61_299
| ~ spl61_62
| ~ spl61_136 ),
inference(avatar_split_clause,[],[f1649,f1537,f1197,f2305]) ).
fof(f1649,plain,
( one_sorted_str(sK56)
| ~ spl61_62
| ~ spl61_136 ),
inference(resolution,[],[f1538,f1199]) ).
fof(f1199,plain,
( rel_str(sK56)
| ~ spl61_62 ),
inference(avatar_component_clause,[],[f1197]) ).
fof(f2303,plain,
spl61_298,
inference(avatar_split_clause,[],[f769,f2301]) ).
fof(f769,plain,
! [X2,X0,X1] :
( relation(X2)
| ~ element(X2,powerset(cartesian_product2(X0,X1))) ),
inference(cnf_transformation,[],[f284]) ).
fof(f284,plain,
! [X0,X1,X2] :
( relation(X2)
| ~ element(X2,powerset(cartesian_product2(X0,X1))) ),
inference(ennf_transformation,[],[f12]) ).
fof(f12,axiom,
! [X0,X1,X2] :
( element(X2,powerset(cartesian_product2(X0,X1)))
=> relation(X2) ),
file('/export/starexec/sandbox2/tmp/tmp.XVCyggMQ11/Vampire---4.8_15325',cc1_relset_1) ).
fof(f2299,plain,
spl61_297,
inference(avatar_split_clause,[],[f759,f2297]) ).
fof(f2297,plain,
( spl61_297
<=> ! [X0,X1] :
( finite(cartesian_product2(X0,X1))
| ~ finite(X1)
| ~ finite(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_297])]) ).
fof(f759,plain,
! [X0,X1] :
( finite(cartesian_product2(X0,X1))
| ~ finite(X1)
| ~ finite(X0) ),
inference(cnf_transformation,[],[f279]) ).
fof(f279,plain,
! [X0,X1] :
( finite(cartesian_product2(X0,X1))
| ~ finite(X1)
| ~ finite(X0) ),
inference(flattening,[],[f278]) ).
fof(f278,plain,
! [X0,X1] :
( finite(cartesian_product2(X0,X1))
| ~ finite(X1)
| ~ finite(X0) ),
inference(ennf_transformation,[],[f57]) ).
fof(f57,axiom,
! [X0,X1] :
( ( finite(X1)
& finite(X0) )
=> finite(cartesian_product2(X0,X1)) ),
file('/export/starexec/sandbox2/tmp/tmp.XVCyggMQ11/Vampire---4.8_15325',fc14_finset_1) ).
fof(f2295,plain,
spl61_296,
inference(avatar_split_clause,[],[f742,f2293]) ).
fof(f742,plain,
! [X0,X1] :
( ~ empty(cartesian_product2(X0,X1))
| empty(X1)
| empty(X0) ),
inference(cnf_transformation,[],[f263]) ).
fof(f263,plain,
! [X0,X1] :
( ~ empty(cartesian_product2(X0,X1))
| empty(X1)
| empty(X0) ),
inference(flattening,[],[f262]) ).
fof(f262,plain,
! [X0,X1] :
( ~ empty(cartesian_product2(X0,X1))
| empty(X1)
| empty(X0) ),
inference(ennf_transformation,[],[f71]) ).
fof(f71,axiom,
! [X0,X1] :
( ( ~ empty(X1)
& ~ empty(X0) )
=> ~ empty(cartesian_product2(X0,X1)) ),
file('/export/starexec/sandbox2/tmp/tmp.XVCyggMQ11/Vampire---4.8_15325',fc4_subset_1) ).
fof(f2291,plain,
spl61_295,
inference(avatar_split_clause,[],[f739,f2289]) ).
fof(f739,plain,
! [X0,X1] :
( rel_str(rel_str_of(X0,X1))
| ~ relation_of2(X1,X0,X0) ),
inference(cnf_transformation,[],[f260]) ).
fof(f260,plain,
! [X0,X1] :
( ( rel_str(rel_str_of(X0,X1))
& strict_rel_str(rel_str_of(X0,X1)) )
| ~ relation_of2(X1,X0,X0) ),
inference(ennf_transformation,[],[f29]) ).
fof(f29,axiom,
! [X0,X1] :
( relation_of2(X1,X0,X0)
=> ( rel_str(rel_str_of(X0,X1))
& strict_rel_str(rel_str_of(X0,X1)) ) ),
file('/export/starexec/sandbox2/tmp/tmp.XVCyggMQ11/Vampire---4.8_15325',dt_g1_orders_2) ).
fof(f2287,plain,
spl61_294,
inference(avatar_split_clause,[],[f738,f2285]) ).
fof(f738,plain,
! [X0,X1] :
( strict_rel_str(rel_str_of(X0,X1))
| ~ relation_of2(X1,X0,X0) ),
inference(cnf_transformation,[],[f260]) ).
fof(f2283,plain,
spl61_293,
inference(avatar_split_clause,[],[f737,f2281]) ).
fof(f737,plain,
! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(cnf_transformation,[],[f259]) ).
fof(f259,plain,
! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(flattening,[],[f258]) ).
fof(f258,plain,
! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(ennf_transformation,[],[f130]) ).
fof(f130,axiom,
! [X0,X1] :
( element(X0,X1)
=> ( in(X0,X1)
| empty(X1) ) ),
file('/export/starexec/sandbox2/tmp/tmp.XVCyggMQ11/Vampire---4.8_15325',t2_subset) ).
fof(f2279,plain,
spl61_292,
inference(avatar_split_clause,[],[f721,f2277]) ).
fof(f721,plain,
! [X0] :
( element(sK37(X0),powerset(the_carrier(X0)))
| ~ sP10(X0) ),
inference(cnf_transformation,[],[f389]) ).
fof(f389,plain,
! [X0] :
( ( upper_relstr_subset(sK37(X0),X0)
& lower_relstr_subset(sK37(X0),X0)
& filtered_subset(sK37(X0),X0)
& directed_subset(sK37(X0),X0)
& ~ empty(sK37(X0))
& element(sK37(X0),powerset(the_carrier(X0))) )
| ~ sP10(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK37])],[f387,f388]) ).
fof(f388,plain,
! [X0] :
( ? [X1] :
( upper_relstr_subset(X1,X0)
& lower_relstr_subset(X1,X0)
& filtered_subset(X1,X0)
& directed_subset(X1,X0)
& ~ empty(X1)
& element(X1,powerset(the_carrier(X0))) )
=> ( upper_relstr_subset(sK37(X0),X0)
& lower_relstr_subset(sK37(X0),X0)
& filtered_subset(sK37(X0),X0)
& directed_subset(sK37(X0),X0)
& ~ empty(sK37(X0))
& element(sK37(X0),powerset(the_carrier(X0))) ) ),
introduced(choice_axiom,[]) ).
fof(f387,plain,
! [X0] :
( ? [X1] :
( upper_relstr_subset(X1,X0)
& lower_relstr_subset(X1,X0)
& filtered_subset(X1,X0)
& directed_subset(X1,X0)
& ~ empty(X1)
& element(X1,powerset(the_carrier(X0))) )
| ~ sP10(X0) ),
inference(nnf_transformation,[],[f322]) ).
fof(f2275,plain,
spl61_291,
inference(avatar_split_clause,[],[f720,f2273]) ).
fof(f2273,plain,
( spl61_291
<=> ! [X0] :
( directed_subset(cast_as_carrier_subset(X0),X0)
| ~ rel_str(X0)
| ~ with_suprema_relstr(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_291])]) ).
fof(f720,plain,
! [X0] :
( directed_subset(cast_as_carrier_subset(X0),X0)
| ~ rel_str(X0)
| ~ with_suprema_relstr(X0) ),
inference(cnf_transformation,[],[f253]) ).
fof(f253,plain,
! [X0] :
( ( directed_subset(cast_as_carrier_subset(X0),X0)
& ~ empty(cast_as_carrier_subset(X0)) )
| ~ rel_str(X0)
| ~ with_suprema_relstr(X0) ),
inference(flattening,[],[f252]) ).
fof(f252,plain,
! [X0] :
( ( directed_subset(cast_as_carrier_subset(X0),X0)
& ~ empty(cast_as_carrier_subset(X0)) )
| ~ rel_str(X0)
| ~ with_suprema_relstr(X0) ),
inference(ennf_transformation,[],[f64]) ).
fof(f64,axiom,
! [X0] :
( ( rel_str(X0)
& with_suprema_relstr(X0) )
=> ( directed_subset(cast_as_carrier_subset(X0),X0)
& ~ empty(cast_as_carrier_subset(X0)) ) ),
file('/export/starexec/sandbox2/tmp/tmp.XVCyggMQ11/Vampire---4.8_15325',fc2_waybel_0) ).
fof(f2271,plain,
spl61_290,
inference(avatar_split_clause,[],[f718,f2269]) ).
fof(f2269,plain,
( spl61_290
<=> ! [X0] :
( filtered_subset(cast_as_carrier_subset(X0),X0)
| ~ rel_str(X0)
| ~ with_infima_relstr(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_290])]) ).
fof(f718,plain,
! [X0] :
( filtered_subset(cast_as_carrier_subset(X0),X0)
| ~ rel_str(X0)
| ~ with_infima_relstr(X0) ),
inference(cnf_transformation,[],[f251]) ).
fof(f251,plain,
! [X0] :
( ( filtered_subset(cast_as_carrier_subset(X0),X0)
& ~ empty(cast_as_carrier_subset(X0)) )
| ~ rel_str(X0)
| ~ with_infima_relstr(X0) ),
inference(flattening,[],[f250]) ).
fof(f250,plain,
! [X0] :
( ( filtered_subset(cast_as_carrier_subset(X0),X0)
& ~ empty(cast_as_carrier_subset(X0)) )
| ~ rel_str(X0)
| ~ with_infima_relstr(X0) ),
inference(ennf_transformation,[],[f72]) ).
fof(f72,axiom,
! [X0] :
( ( rel_str(X0)
& with_infima_relstr(X0) )
=> ( filtered_subset(cast_as_carrier_subset(X0),X0)
& ~ empty(cast_as_carrier_subset(X0)) ) ),
file('/export/starexec/sandbox2/tmp/tmp.XVCyggMQ11/Vampire---4.8_15325',fc4_waybel_0) ).
fof(f2267,plain,
spl61_289,
inference(avatar_split_clause,[],[f716,f2265]) ).
fof(f2265,plain,
( spl61_289
<=> ! [X0] :
( closed_subset(sK36(X0),X0)
| ~ top_str(X0)
| ~ topological_space(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_289])]) ).
fof(f716,plain,
! [X0] :
( closed_subset(sK36(X0),X0)
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(cnf_transformation,[],[f386]) ).
fof(f2263,plain,
( spl61_288
| ~ spl61_53
| ~ spl61_136 ),
inference(avatar_split_clause,[],[f1648,f1537,f1152,f2260]) ).
fof(f1648,plain,
( one_sorted_str(sK55)
| ~ spl61_53
| ~ spl61_136 ),
inference(resolution,[],[f1538,f1154]) ).
fof(f1154,plain,
( rel_str(sK55)
| ~ spl61_53 ),
inference(avatar_component_clause,[],[f1152]) ).
fof(f2258,plain,
spl61_287,
inference(avatar_split_clause,[],[f714,f2256]) ).
fof(f2256,plain,
( spl61_287
<=> ! [X0] :
( closed_subset(sK35(X0),X0)
| ~ top_str(X0)
| ~ topological_space(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_287])]) ).
fof(f714,plain,
! [X0] :
( closed_subset(sK35(X0),X0)
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(cnf_transformation,[],[f384]) ).
fof(f2254,plain,
spl61_286,
inference(avatar_split_clause,[],[f713,f2252]) ).
fof(f2252,plain,
( spl61_286
<=> ! [X0] :
( open_subset(sK35(X0),X0)
| ~ top_str(X0)
| ~ topological_space(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_286])]) ).
fof(f713,plain,
! [X0] :
( open_subset(sK35(X0),X0)
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(cnf_transformation,[],[f384]) ).
fof(f2250,plain,
spl61_285,
inference(avatar_split_clause,[],[f711,f2248]) ).
fof(f2248,plain,
( spl61_285
<=> ! [X0] :
( open_subset(sK34(X0),X0)
| ~ top_str(X0)
| ~ topological_space(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_285])]) ).
fof(f711,plain,
! [X0] :
( open_subset(sK34(X0),X0)
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(cnf_transformation,[],[f382]) ).
fof(f2246,plain,
spl61_284,
inference(avatar_split_clause,[],[f698,f2244]) ).
fof(f698,plain,
! [X0] :
( element(sK33(X0),powerset(the_carrier(X0)))
| ~ sP9(X0) ),
inference(cnf_transformation,[],[f380]) ).
fof(f380,plain,
! [X0] :
( ( nowhere_dense(sK33(X0),X0)
& boundary_set(sK33(X0),X0)
& v5_membered(sK33(X0))
& v4_membered(sK33(X0))
& v3_membered(sK33(X0))
& v2_membered(sK33(X0))
& v1_membered(sK33(X0))
& closed_subset(sK33(X0),X0)
& open_subset(sK33(X0),X0)
& empty(sK33(X0))
& element(sK33(X0),powerset(the_carrier(X0))) )
| ~ sP9(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK33])],[f378,f379]) ).
fof(f379,plain,
! [X0] :
( ? [X1] :
( nowhere_dense(X1,X0)
& boundary_set(X1,X0)
& v5_membered(X1)
& v4_membered(X1)
& v3_membered(X1)
& v2_membered(X1)
& v1_membered(X1)
& closed_subset(X1,X0)
& open_subset(X1,X0)
& empty(X1)
& element(X1,powerset(the_carrier(X0))) )
=> ( nowhere_dense(sK33(X0),X0)
& boundary_set(sK33(X0),X0)
& v5_membered(sK33(X0))
& v4_membered(sK33(X0))
& v3_membered(sK33(X0))
& v2_membered(sK33(X0))
& v1_membered(sK33(X0))
& closed_subset(sK33(X0),X0)
& open_subset(sK33(X0),X0)
& empty(sK33(X0))
& element(sK33(X0),powerset(the_carrier(X0))) ) ),
introduced(choice_axiom,[]) ).
fof(f378,plain,
! [X0] :
( ? [X1] :
( nowhere_dense(X1,X0)
& boundary_set(X1,X0)
& v5_membered(X1)
& v4_membered(X1)
& v3_membered(X1)
& v2_membered(X1)
& v1_membered(X1)
& closed_subset(X1,X0)
& open_subset(X1,X0)
& empty(X1)
& element(X1,powerset(the_carrier(X0))) )
| ~ sP9(X0) ),
inference(nnf_transformation,[],[f320]) ).
fof(f320,plain,
! [X0] :
( ? [X1] :
( nowhere_dense(X1,X0)
& boundary_set(X1,X0)
& v5_membered(X1)
& v4_membered(X1)
& v3_membered(X1)
& v2_membered(X1)
& v1_membered(X1)
& closed_subset(X1,X0)
& open_subset(X1,X0)
& empty(X1)
& element(X1,powerset(the_carrier(X0))) )
| ~ sP9(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP9])]) ).
fof(f2242,plain,
spl61_283,
inference(avatar_split_clause,[],[f679,f2240]) ).
fof(f2240,plain,
( spl61_283
<=> ! [X0] :
( open_subset(cast_as_carrier_subset(X0),X0)
| ~ top_str(X0)
| ~ topological_space(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_283])]) ).
fof(f679,plain,
! [X0] :
( open_subset(cast_as_carrier_subset(X0),X0)
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(cnf_transformation,[],[f231]) ).
fof(f231,plain,
! [X0] :
( ( closed_subset(cast_as_carrier_subset(X0),X0)
& open_subset(cast_as_carrier_subset(X0),X0) )
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(flattening,[],[f230]) ).
fof(f230,plain,
! [X0] :
( ( closed_subset(cast_as_carrier_subset(X0),X0)
& open_subset(cast_as_carrier_subset(X0),X0) )
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(ennf_transformation,[],[f79]) ).
fof(f79,axiom,
! [X0] :
( ( top_str(X0)
& topological_space(X0) )
=> ( closed_subset(cast_as_carrier_subset(X0),X0)
& open_subset(cast_as_carrier_subset(X0),X0) ) ),
file('/export/starexec/sandbox2/tmp/tmp.XVCyggMQ11/Vampire---4.8_15325',fc8_tops_1) ).
fof(f2238,plain,
spl61_282,
inference(avatar_split_clause,[],[f678,f2236]) ).
fof(f2236,plain,
( spl61_282
<=> ! [X0] :
( closed_subset(cast_as_carrier_subset(X0),X0)
| ~ top_str(X0)
| ~ topological_space(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_282])]) ).
fof(f678,plain,
! [X0] :
( closed_subset(cast_as_carrier_subset(X0),X0)
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(cnf_transformation,[],[f229]) ).
fof(f229,plain,
! [X0] :
( closed_subset(cast_as_carrier_subset(X0),X0)
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(flattening,[],[f228]) ).
fof(f228,plain,
! [X0] :
( closed_subset(cast_as_carrier_subset(X0),X0)
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(ennf_transformation,[],[f74]) ).
fof(f74,axiom,
! [X0] :
( ( top_str(X0)
& topological_space(X0) )
=> closed_subset(cast_as_carrier_subset(X0),X0) ),
file('/export/starexec/sandbox2/tmp/tmp.XVCyggMQ11/Vampire---4.8_15325',fc5_pre_topc) ).
fof(f2234,plain,
spl61_281,
inference(avatar_split_clause,[],[f669,f2232]) ).
fof(f669,plain,
! [X0] :
( sP7(X0)
| ~ rel_str(X0)
| ~ reflexive_relstr(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f317]) ).
fof(f317,plain,
! [X0] :
( sP7(X0)
| ~ rel_str(X0)
| ~ reflexive_relstr(X0)
| empty_carrier(X0) ),
inference(definition_folding,[],[f223,f316]) ).
fof(f316,plain,
! [X0] :
( ? [X1] :
( filtered_subset(X1,X0)
& directed_subset(X1,X0)
& finite(X1)
& ~ empty(X1)
& element(X1,powerset(the_carrier(X0))) )
| ~ sP7(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP7])]) ).
fof(f223,plain,
! [X0] :
( ? [X1] :
( filtered_subset(X1,X0)
& directed_subset(X1,X0)
& finite(X1)
& ~ empty(X1)
& element(X1,powerset(the_carrier(X0))) )
| ~ rel_str(X0)
| ~ reflexive_relstr(X0)
| empty_carrier(X0) ),
inference(flattening,[],[f222]) ).
fof(f222,plain,
! [X0] :
( ? [X1] :
( filtered_subset(X1,X0)
& directed_subset(X1,X0)
& finite(X1)
& ~ empty(X1)
& element(X1,powerset(the_carrier(X0))) )
| ~ rel_str(X0)
| ~ reflexive_relstr(X0)
| empty_carrier(X0) ),
inference(ennf_transformation,[],[f102]) ).
fof(f102,axiom,
! [X0] :
( ( rel_str(X0)
& reflexive_relstr(X0)
& ~ empty_carrier(X0) )
=> ? [X1] :
( filtered_subset(X1,X0)
& directed_subset(X1,X0)
& finite(X1)
& ~ empty(X1)
& element(X1,powerset(the_carrier(X0))) ) ),
file('/export/starexec/sandbox2/tmp/tmp.XVCyggMQ11/Vampire---4.8_15325',rc2_waybel_0) ).
fof(f2230,plain,
spl61_280,
inference(avatar_split_clause,[],[f664,f2228]) ).
fof(f664,plain,
! [X0] :
( element(sK30(X0),powerset(the_carrier(X0)))
| ~ sP7(X0) ),
inference(cnf_transformation,[],[f372]) ).
fof(f372,plain,
! [X0] :
( ( filtered_subset(sK30(X0),X0)
& directed_subset(sK30(X0),X0)
& finite(sK30(X0))
& ~ empty(sK30(X0))
& element(sK30(X0),powerset(the_carrier(X0))) )
| ~ sP7(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK30])],[f370,f371]) ).
fof(f371,plain,
! [X0] :
( ? [X1] :
( filtered_subset(X1,X0)
& directed_subset(X1,X0)
& finite(X1)
& ~ empty(X1)
& element(X1,powerset(the_carrier(X0))) )
=> ( filtered_subset(sK30(X0),X0)
& directed_subset(sK30(X0),X0)
& finite(sK30(X0))
& ~ empty(sK30(X0))
& element(sK30(X0),powerset(the_carrier(X0))) ) ),
introduced(choice_axiom,[]) ).
fof(f370,plain,
! [X0] :
( ? [X1] :
( filtered_subset(X1,X0)
& directed_subset(X1,X0)
& finite(X1)
& ~ empty(X1)
& element(X1,powerset(the_carrier(X0))) )
| ~ sP7(X0) ),
inference(nnf_transformation,[],[f316]) ).
fof(f2226,plain,
spl61_279,
inference(avatar_split_clause,[],[f663,f2224]) ).
fof(f2224,plain,
( spl61_279
<=> ! [X0] :
( upper_relstr_subset(sK29(X0),X0)
| ~ rel_str(X0)
| empty_carrier(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_279])]) ).
fof(f663,plain,
! [X0] :
( upper_relstr_subset(sK29(X0),X0)
| ~ rel_str(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f369]) ).
fof(f2222,plain,
spl61_278,
inference(avatar_split_clause,[],[f662,f2220]) ).
fof(f2220,plain,
( spl61_278
<=> ! [X0] :
( lower_relstr_subset(sK29(X0),X0)
| ~ rel_str(X0)
| empty_carrier(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_278])]) ).
fof(f662,plain,
! [X0] :
( lower_relstr_subset(sK29(X0),X0)
| ~ rel_str(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f369]) ).
fof(f2218,plain,
spl61_277,
inference(avatar_split_clause,[],[f659,f2216]) ).
fof(f2216,plain,
( spl61_277
<=> ! [X0] :
( upper_relstr_subset(cast_as_carrier_subset(X0),X0)
| ~ rel_str(X0)
| empty_carrier(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_277])]) ).
fof(f659,plain,
! [X0] :
( upper_relstr_subset(cast_as_carrier_subset(X0),X0)
| ~ rel_str(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f219]) ).
fof(f219,plain,
! [X0] :
( ( upper_relstr_subset(cast_as_carrier_subset(X0),X0)
& lower_relstr_subset(cast_as_carrier_subset(X0),X0)
& ~ empty(cast_as_carrier_subset(X0)) )
| ~ rel_str(X0)
| empty_carrier(X0) ),
inference(flattening,[],[f218]) ).
fof(f218,plain,
! [X0] :
( ( upper_relstr_subset(cast_as_carrier_subset(X0),X0)
& lower_relstr_subset(cast_as_carrier_subset(X0),X0)
& ~ empty(cast_as_carrier_subset(X0)) )
| ~ rel_str(X0)
| empty_carrier(X0) ),
inference(ennf_transformation,[],[f58]) ).
fof(f58,axiom,
! [X0] :
( ( rel_str(X0)
& ~ empty_carrier(X0) )
=> ( upper_relstr_subset(cast_as_carrier_subset(X0),X0)
& lower_relstr_subset(cast_as_carrier_subset(X0),X0)
& ~ empty(cast_as_carrier_subset(X0)) ) ),
file('/export/starexec/sandbox2/tmp/tmp.XVCyggMQ11/Vampire---4.8_15325',fc15_waybel_0) ).
fof(f2214,plain,
spl61_276,
inference(avatar_split_clause,[],[f658,f2212]) ).
fof(f2212,plain,
( spl61_276
<=> ! [X0] :
( lower_relstr_subset(cast_as_carrier_subset(X0),X0)
| ~ rel_str(X0)
| empty_carrier(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_276])]) ).
fof(f658,plain,
! [X0] :
( lower_relstr_subset(cast_as_carrier_subset(X0),X0)
| ~ rel_str(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f219]) ).
fof(f2210,plain,
spl61_275,
inference(avatar_split_clause,[],[f633,f2208]) ).
fof(f633,plain,
! [X0] :
( proper_element(sK25(X0),powerset(the_carrier(X0)))
| ~ sP6(X0) ),
inference(cnf_transformation,[],[f360]) ).
fof(f360,plain,
! [X0] :
( ( upper_relstr_subset(sK25(X0),X0)
& filtered_subset(sK25(X0),X0)
& proper_element(sK25(X0),powerset(the_carrier(X0)))
& ~ empty(sK25(X0))
& element(sK25(X0),powerset(the_carrier(X0))) )
| ~ sP6(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK25])],[f358,f359]) ).
fof(f359,plain,
! [X0] :
( ? [X1] :
( upper_relstr_subset(X1,X0)
& filtered_subset(X1,X0)
& proper_element(X1,powerset(the_carrier(X0)))
& ~ empty(X1)
& element(X1,powerset(the_carrier(X0))) )
=> ( upper_relstr_subset(sK25(X0),X0)
& filtered_subset(sK25(X0),X0)
& proper_element(sK25(X0),powerset(the_carrier(X0)))
& ~ empty(sK25(X0))
& element(sK25(X0),powerset(the_carrier(X0))) ) ),
introduced(choice_axiom,[]) ).
fof(f358,plain,
! [X0] :
( ? [X1] :
( upper_relstr_subset(X1,X0)
& filtered_subset(X1,X0)
& proper_element(X1,powerset(the_carrier(X0)))
& ~ empty(X1)
& element(X1,powerset(the_carrier(X0))) )
| ~ sP6(X0) ),
inference(nnf_transformation,[],[f314]) ).
fof(f2206,plain,
spl61_274,
inference(avatar_split_clause,[],[f631,f2204]) ).
fof(f631,plain,
! [X0] :
( element(sK25(X0),powerset(the_carrier(X0)))
| ~ sP6(X0) ),
inference(cnf_transformation,[],[f360]) ).
fof(f2202,plain,
spl61_273,
inference(avatar_split_clause,[],[f625,f2200]) ).
fof(f625,plain,
! [X0] :
( element(sK24(X0),powerset(the_carrier(X0)))
| ~ rel_str(X0) ),
inference(cnf_transformation,[],[f357]) ).
fof(f357,plain,
! [X0] :
( ( filtered_subset(sK24(X0),X0)
& directed_subset(sK24(X0),X0)
& element(sK24(X0),powerset(the_carrier(X0))) )
| ~ rel_str(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK24])],[f190,f356]) ).
fof(f356,plain,
! [X0] :
( ? [X1] :
( filtered_subset(X1,X0)
& directed_subset(X1,X0)
& element(X1,powerset(the_carrier(X0))) )
=> ( filtered_subset(sK24(X0),X0)
& directed_subset(sK24(X0),X0)
& element(sK24(X0),powerset(the_carrier(X0))) ) ),
introduced(choice_axiom,[]) ).
fof(f190,plain,
! [X0] :
( ? [X1] :
( filtered_subset(X1,X0)
& directed_subset(X1,X0)
& element(X1,powerset(the_carrier(X0))) )
| ~ rel_str(X0) ),
inference(ennf_transformation,[],[f95]) ).
fof(f95,axiom,
! [X0] :
( rel_str(X0)
=> ? [X1] :
( filtered_subset(X1,X0)
& directed_subset(X1,X0)
& element(X1,powerset(the_carrier(X0))) ) ),
file('/export/starexec/sandbox2/tmp/tmp.XVCyggMQ11/Vampire---4.8_15325',rc1_waybel_0) ).
fof(f2198,plain,
spl61_272,
inference(avatar_split_clause,[],[f622,f2196]) ).
fof(f622,plain,
! [X0] :
( element(sK23(X0),powerset(the_carrier(X0)))
| ~ rel_str(X0) ),
inference(cnf_transformation,[],[f355]) ).
fof(f355,plain,
! [X0] :
( ( upper_relstr_subset(sK23(X0),X0)
& lower_relstr_subset(sK23(X0),X0)
& element(sK23(X0),powerset(the_carrier(X0))) )
| ~ rel_str(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK23])],[f189,f354]) ).
fof(f354,plain,
! [X0] :
( ? [X1] :
( upper_relstr_subset(X1,X0)
& lower_relstr_subset(X1,X0)
& element(X1,powerset(the_carrier(X0))) )
=> ( upper_relstr_subset(sK23(X0),X0)
& lower_relstr_subset(sK23(X0),X0)
& element(sK23(X0),powerset(the_carrier(X0))) ) ),
introduced(choice_axiom,[]) ).
fof(f189,plain,
! [X0] :
( ? [X1] :
( upper_relstr_subset(X1,X0)
& lower_relstr_subset(X1,X0)
& element(X1,powerset(the_carrier(X0))) )
| ~ rel_str(X0) ),
inference(ennf_transformation,[],[f120]) ).
fof(f120,axiom,
! [X0] :
( rel_str(X0)
=> ? [X1] :
( upper_relstr_subset(X1,X0)
& lower_relstr_subset(X1,X0)
& element(X1,powerset(the_carrier(X0))) ) ),
file('/export/starexec/sandbox2/tmp/tmp.XVCyggMQ11/Vampire---4.8_15325',rc7_waybel_0) ).
fof(f2194,plain,
spl61_271,
inference(avatar_split_clause,[],[f617,f2192]) ).
fof(f2192,plain,
( spl61_271
<=> ! [X0] :
( bounded_relstr(X0)
| ~ upper_bounded_relstr(X0)
| ~ lower_bounded_relstr(X0)
| ~ rel_str(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_271])]) ).
fof(f617,plain,
! [X0] :
( bounded_relstr(X0)
| ~ upper_bounded_relstr(X0)
| ~ lower_bounded_relstr(X0)
| ~ rel_str(X0) ),
inference(cnf_transformation,[],[f186]) ).
fof(f186,plain,
! [X0] :
( bounded_relstr(X0)
| ~ upper_bounded_relstr(X0)
| ~ lower_bounded_relstr(X0)
| ~ rel_str(X0) ),
inference(flattening,[],[f185]) ).
fof(f185,plain,
! [X0] :
( bounded_relstr(X0)
| ~ upper_bounded_relstr(X0)
| ~ lower_bounded_relstr(X0)
| ~ rel_str(X0) ),
inference(ennf_transformation,[],[f25]) ).
fof(f25,axiom,
! [X0] :
( rel_str(X0)
=> ( ( upper_bounded_relstr(X0)
& lower_bounded_relstr(X0) )
=> bounded_relstr(X0) ) ),
file('/export/starexec/sandbox2/tmp/tmp.XVCyggMQ11/Vampire---4.8_15325',cc5_yellow_0) ).
fof(f2190,plain,
spl61_270,
inference(avatar_split_clause,[],[f579,f2188]) ).
fof(f579,plain,
! [X0] :
( with_infima_relstr(X0)
| ~ complete_relstr(X0)
| empty_carrier(X0)
| ~ rel_str(X0) ),
inference(cnf_transformation,[],[f170]) ).
fof(f170,plain,
! [X0] :
( ( with_infima_relstr(X0)
& with_suprema_relstr(X0)
& ~ empty_carrier(X0) )
| ~ complete_relstr(X0)
| empty_carrier(X0)
| ~ rel_str(X0) ),
inference(flattening,[],[f169]) ).
fof(f169,plain,
! [X0] :
( ( with_infima_relstr(X0)
& with_suprema_relstr(X0)
& ~ empty_carrier(X0) )
| ~ complete_relstr(X0)
| empty_carrier(X0)
| ~ rel_str(X0) ),
inference(ennf_transformation,[],[f14]) ).
fof(f14,axiom,
! [X0] :
( rel_str(X0)
=> ( ( complete_relstr(X0)
& ~ empty_carrier(X0) )
=> ( with_infima_relstr(X0)
& with_suprema_relstr(X0)
& ~ empty_carrier(X0) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.XVCyggMQ11/Vampire---4.8_15325',cc1_yellow_0) ).
fof(f2186,plain,
spl61_269,
inference(avatar_split_clause,[],[f578,f2184]) ).
fof(f578,plain,
! [X0] :
( with_suprema_relstr(X0)
| ~ complete_relstr(X0)
| empty_carrier(X0)
| ~ rel_str(X0) ),
inference(cnf_transformation,[],[f170]) ).
fof(f2182,plain,
spl61_268,
inference(avatar_split_clause,[],[f576,f2180]) ).
fof(f576,plain,
! [X0] :
( bounded_relstr(X0)
| ~ complete_relstr(X0)
| empty_carrier(X0)
| ~ rel_str(X0) ),
inference(cnf_transformation,[],[f168]) ).
fof(f168,plain,
! [X0] :
( ( bounded_relstr(X0)
& ~ empty_carrier(X0) )
| ~ complete_relstr(X0)
| empty_carrier(X0)
| ~ rel_str(X0) ),
inference(flattening,[],[f167]) ).
fof(f167,plain,
! [X0] :
( ( bounded_relstr(X0)
& ~ empty_carrier(X0) )
| ~ complete_relstr(X0)
| empty_carrier(X0)
| ~ rel_str(X0) ),
inference(ennf_transformation,[],[f20]) ).
fof(f20,axiom,
! [X0] :
( rel_str(X0)
=> ( ( complete_relstr(X0)
& ~ empty_carrier(X0) )
=> ( bounded_relstr(X0)
& ~ empty_carrier(X0) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.XVCyggMQ11/Vampire---4.8_15325',cc3_yellow_0) ).
fof(f2178,plain,
( spl61_267
| ~ spl61_9
| ~ spl61_260 ),
inference(avatar_split_clause,[],[f2145,f2117,f932,f2175]) ).
fof(f2175,plain,
( spl61_267
<=> subset(sK13,the_carrier(boole_POSet(cast_as_carrier_subset(sK12)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_267])]) ).
fof(f2145,plain,
( subset(sK13,the_carrier(boole_POSet(cast_as_carrier_subset(sK12))))
| ~ spl61_9
| ~ spl61_260 ),
inference(resolution,[],[f2118,f934]) ).
fof(f2173,plain,
spl61_266,
inference(avatar_split_clause,[],[f567,f2171]) ).
fof(f567,plain,
! [X0,X1] :
( finite(X1)
| ~ element(X1,powerset(X0))
| ~ finite(X0) ),
inference(cnf_transformation,[],[f156]) ).
fof(f156,plain,
! [X0] :
( ! [X1] :
( finite(X1)
| ~ element(X1,powerset(X0)) )
| ~ finite(X0) ),
inference(ennf_transformation,[],[f15]) ).
fof(f15,axiom,
! [X0] :
( finite(X0)
=> ! [X1] :
( element(X1,powerset(X0))
=> finite(X1) ) ),
file('/export/starexec/sandbox2/tmp/tmp.XVCyggMQ11/Vampire---4.8_15325',cc2_finset_1) ).
fof(f2169,plain,
spl61_265,
inference(avatar_split_clause,[],[f551,f2167]) ).
fof(f551,plain,
! [X0] :
( element(cast_as_carrier_subset(X0),powerset(the_carrier(X0)))
| ~ one_sorted_str(X0) ),
inference(cnf_transformation,[],[f150]) ).
fof(f150,plain,
! [X0] :
( element(cast_as_carrier_subset(X0),powerset(the_carrier(X0)))
| ~ one_sorted_str(X0) ),
inference(ennf_transformation,[],[f34]) ).
fof(f34,axiom,
! [X0] :
( one_sorted_str(X0)
=> element(cast_as_carrier_subset(X0),powerset(the_carrier(X0))) ),
file('/export/starexec/sandbox2/tmp/tmp.XVCyggMQ11/Vampire---4.8_15325',dt_k2_pre_topc) ).
fof(f2165,plain,
spl61_264,
inference(avatar_split_clause,[],[f542,f2163]) ).
fof(f542,plain,
! [X0] :
( element(sK18(X0),powerset(the_carrier(X0)))
| ~ sP1(X0) ),
inference(cnf_transformation,[],[f341]) ).
fof(f341,plain,
! [X0] :
( ( boundary_set(sK18(X0),X0)
& v5_membered(sK18(X0))
& v4_membered(sK18(X0))
& v3_membered(sK18(X0))
& v2_membered(sK18(X0))
& v1_membered(sK18(X0))
& empty(sK18(X0))
& element(sK18(X0),powerset(the_carrier(X0))) )
| ~ sP1(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK18])],[f339,f340]) ).
fof(f340,plain,
! [X0] :
( ? [X1] :
( boundary_set(X1,X0)
& v5_membered(X1)
& v4_membered(X1)
& v3_membered(X1)
& v2_membered(X1)
& v1_membered(X1)
& empty(X1)
& element(X1,powerset(the_carrier(X0))) )
=> ( boundary_set(sK18(X0),X0)
& v5_membered(sK18(X0))
& v4_membered(sK18(X0))
& v3_membered(sK18(X0))
& v2_membered(sK18(X0))
& v1_membered(sK18(X0))
& empty(sK18(X0))
& element(sK18(X0),powerset(the_carrier(X0))) ) ),
introduced(choice_axiom,[]) ).
fof(f339,plain,
! [X0] :
( ? [X1] :
( boundary_set(X1,X0)
& v5_membered(X1)
& v4_membered(X1)
& v3_membered(X1)
& v2_membered(X1)
& v1_membered(X1)
& empty(X1)
& element(X1,powerset(the_carrier(X0))) )
| ~ sP1(X0) ),
inference(nnf_transformation,[],[f304]) ).
fof(f304,plain,
! [X0] :
( ? [X1] :
( boundary_set(X1,X0)
& v5_membered(X1)
& v4_membered(X1)
& v3_membered(X1)
& v2_membered(X1)
& v1_membered(X1)
& empty(X1)
& element(X1,powerset(the_carrier(X0))) )
| ~ sP1(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).
fof(f2140,plain,
( spl61_263
| ~ spl61_46
| ~ spl61_136 ),
inference(avatar_split_clause,[],[f1647,f1537,f1117,f2137]) ).
fof(f1647,plain,
( one_sorted_str(sK54)
| ~ spl61_46
| ~ spl61_136 ),
inference(resolution,[],[f1538,f1119]) ).
fof(f1119,plain,
( rel_str(sK54)
| ~ spl61_46 ),
inference(avatar_component_clause,[],[f1117]) ).
fof(f2127,plain,
spl61_262,
inference(avatar_split_clause,[],[f764,f2125]) ).
fof(f764,plain,
! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) ),
inference(cnf_transformation,[],[f281]) ).
fof(f281,plain,
! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) ),
inference(ennf_transformation,[],[f137]) ).
fof(f137,axiom,
! [X0,X1] :
~ ( empty(X1)
& X0 != X1
& empty(X0) ),
file('/export/starexec/sandbox2/tmp/tmp.XVCyggMQ11/Vampire---4.8_15325',t8_boole) ).
fof(f2123,plain,
spl61_261,
inference(avatar_split_clause,[],[f763,f2121]) ).
fof(f763,plain,
! [X0,X1] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f399]) ).
fof(f399,plain,
! [X0,X1] :
( ( element(X0,powerset(X1))
| ~ subset(X0,X1) )
& ( subset(X0,X1)
| ~ element(X0,powerset(X1)) ) ),
inference(nnf_transformation,[],[f132]) ).
fof(f132,axiom,
! [X0,X1] :
( element(X0,powerset(X1))
<=> subset(X0,X1) ),
file('/export/starexec/sandbox2/tmp/tmp.XVCyggMQ11/Vampire---4.8_15325',t3_subset) ).
fof(f2119,plain,
spl61_260,
inference(avatar_split_clause,[],[f762,f2117]) ).
fof(f762,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f399]) ).
fof(f2115,plain,
( spl61_259
| ~ spl61_41
| ~ spl61_136 ),
inference(avatar_split_clause,[],[f1646,f1537,f1092,f2112]) ).
fof(f1646,plain,
( one_sorted_str(sK53)
| ~ spl61_41
| ~ spl61_136 ),
inference(resolution,[],[f1538,f1094]) ).
fof(f1094,plain,
( rel_str(sK53)
| ~ spl61_41 ),
inference(avatar_component_clause,[],[f1092]) ).
fof(f2110,plain,
spl61_258,
inference(avatar_split_clause,[],[f719,f2108]) ).
fof(f719,plain,
! [X0] :
( ~ empty(cast_as_carrier_subset(X0))
| ~ rel_str(X0)
| ~ with_suprema_relstr(X0) ),
inference(cnf_transformation,[],[f253]) ).
fof(f2106,plain,
spl61_257,
inference(avatar_split_clause,[],[f717,f2104]) ).
fof(f717,plain,
! [X0] :
( ~ empty(cast_as_carrier_subset(X0))
| ~ rel_str(X0)
| ~ with_infima_relstr(X0) ),
inference(cnf_transformation,[],[f251]) ).
fof(f2102,plain,
spl61_256,
inference(avatar_split_clause,[],[f661,f2100]) ).
fof(f661,plain,
! [X0] :
( ~ empty(sK29(X0))
| ~ rel_str(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f369]) ).
fof(f2098,plain,
spl61_255,
inference(avatar_split_clause,[],[f656,f2096]) ).
fof(f656,plain,
! [X0] :
( ~ empty(cast_as_carrier_subset(X0))
| ~ rel_str(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f217]) ).
fof(f217,plain,
! [X0] :
( ~ empty(cast_as_carrier_subset(X0))
| ~ rel_str(X0)
| empty_carrier(X0) ),
inference(flattening,[],[f216]) ).
fof(f216,plain,
! [X0] :
( ~ empty(cast_as_carrier_subset(X0))
| ~ rel_str(X0)
| empty_carrier(X0) ),
inference(ennf_transformation,[],[f67]) ).
fof(f67,axiom,
! [X0] :
( ( rel_str(X0)
& ~ empty_carrier(X0) )
=> ~ empty(cast_as_carrier_subset(X0)) ),
file('/export/starexec/sandbox2/tmp/tmp.XVCyggMQ11/Vampire---4.8_15325',fc2_yellow_0) ).
fof(f2094,plain,
spl61_254,
inference(avatar_split_clause,[],[f651,f2092]) ).
fof(f651,plain,
! [X0] :
( ~ empty(sK28(X0))
| ~ one_sorted_str(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f367]) ).
fof(f2090,plain,
spl61_253,
inference(avatar_split_clause,[],[f647,f2088]) ).
fof(f647,plain,
! [X0] :
( ~ empty(the_carrier(X0))
| ~ one_sorted_str(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f205]) ).
fof(f205,plain,
! [X0] :
( ~ empty(the_carrier(X0))
| ~ one_sorted_str(X0)
| empty_carrier(X0) ),
inference(flattening,[],[f204]) ).
fof(f204,plain,
! [X0] :
( ~ empty(the_carrier(X0))
| ~ one_sorted_str(X0)
| empty_carrier(X0) ),
inference(ennf_transformation,[],[f60]) ).
fof(f60,axiom,
! [X0] :
( ( one_sorted_str(X0)
& ~ empty_carrier(X0) )
=> ~ empty(the_carrier(X0)) ),
file('/export/starexec/sandbox2/tmp/tmp.XVCyggMQ11/Vampire---4.8_15325',fc1_struct_0) ).
fof(f2086,plain,
spl61_252,
inference(avatar_split_clause,[],[f646,f2084]) ).
fof(f646,plain,
! [X0] :
( ~ empty(cast_as_carrier_subset(X0))
| ~ one_sorted_str(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f203]) ).
fof(f203,plain,
! [X0] :
( ~ empty(cast_as_carrier_subset(X0))
| ~ one_sorted_str(X0)
| empty_carrier(X0) ),
inference(flattening,[],[f202]) ).
fof(f202,plain,
! [X0] :
( ~ empty(cast_as_carrier_subset(X0))
| ~ one_sorted_str(X0)
| empty_carrier(X0) ),
inference(ennf_transformation,[],[f63]) ).
fof(f63,axiom,
! [X0] :
( ( one_sorted_str(X0)
& ~ empty_carrier(X0) )
=> ~ empty(cast_as_carrier_subset(X0)) ),
file('/export/starexec/sandbox2/tmp/tmp.XVCyggMQ11/Vampire---4.8_15325',fc2_pre_topc) ).
fof(f2082,plain,
spl61_251,
inference(avatar_split_clause,[],[f552,f2080]) ).
fof(f552,plain,
! [X0,X1] :
( rel_str(X1)
| ~ net_str(X1,X0)
| ~ one_sorted_str(X0) ),
inference(cnf_transformation,[],[f151]) ).
fof(f151,plain,
! [X0] :
( ! [X1] :
( rel_str(X1)
| ~ net_str(X1,X0) )
| ~ one_sorted_str(X0) ),
inference(ennf_transformation,[],[f42]) ).
fof(f42,axiom,
! [X0] :
( one_sorted_str(X0)
=> ! [X1] :
( net_str(X1,X0)
=> rel_str(X1) ) ),
file('/export/starexec/sandbox2/tmp/tmp.XVCyggMQ11/Vampire---4.8_15325',dt_l1_waybel_0) ).
fof(f2078,plain,
spl61_250,
inference(avatar_split_clause,[],[f536,f2076]) ).
fof(f536,plain,
! [X0] :
( element(sK17(X0),powerset(X0))
| empty(X0) ),
inference(cnf_transformation,[],[f338]) ).
fof(f338,plain,
! [X0] :
( ( finite(sK17(X0))
& ~ empty(sK17(X0))
& element(sK17(X0),powerset(X0)) )
| empty(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK17])],[f144,f337]) ).
fof(f337,plain,
! [X0] :
( ? [X1] :
( finite(X1)
& ~ empty(X1)
& element(X1,powerset(X0)) )
=> ( finite(sK17(X0))
& ~ empty(sK17(X0))
& element(sK17(X0),powerset(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f144,plain,
! [X0] :
( ? [X1] :
( finite(X1)
& ~ empty(X1)
& element(X1,powerset(X0)) )
| empty(X0) ),
inference(ennf_transformation,[],[f105]) ).
fof(f105,axiom,
! [X0] :
( ~ empty(X0)
=> ? [X1] :
( finite(X1)
& ~ empty(X1)
& element(X1,powerset(X0)) ) ),
file('/export/starexec/sandbox2/tmp/tmp.XVCyggMQ11/Vampire---4.8_15325',rc3_finset_1) ).
fof(f2074,plain,
spl61_249,
inference(avatar_split_clause,[],[f533,f2072]) ).
fof(f533,plain,
! [X0] :
( element(sK16(X0),powerset(X0))
| empty(X0) ),
inference(cnf_transformation,[],[f336]) ).
fof(f336,plain,
! [X0] :
( ( finite(sK16(X0))
& ~ empty(sK16(X0))
& element(sK16(X0),powerset(X0)) )
| empty(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK16])],[f143,f335]) ).
fof(f335,plain,
! [X0] :
( ? [X1] :
( finite(X1)
& ~ empty(X1)
& element(X1,powerset(X0)) )
=> ( finite(sK16(X0))
& ~ empty(sK16(X0))
& element(sK16(X0),powerset(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f143,plain,
! [X0] :
( ? [X1] :
( finite(X1)
& ~ empty(X1)
& element(X1,powerset(X0)) )
| empty(X0) ),
inference(ennf_transformation,[],[f110]) ).
fof(f110,axiom,
! [X0] :
( ~ empty(X0)
=> ? [X1] :
( finite(X1)
& ~ empty(X1)
& element(X1,powerset(X0)) ) ),
file('/export/starexec/sandbox2/tmp/tmp.XVCyggMQ11/Vampire---4.8_15325',rc4_finset_1) ).
fof(f2070,plain,
spl61_248,
inference(avatar_split_clause,[],[f531,f2068]) ).
fof(f531,plain,
! [X0] :
( element(sK15(X0),powerset(X0))
| empty(X0) ),
inference(cnf_transformation,[],[f334]) ).
fof(f334,plain,
! [X0] :
( ( ~ empty(sK15(X0))
& element(sK15(X0),powerset(X0)) )
| empty(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK15])],[f142,f333]) ).
fof(f333,plain,
! [X0] :
( ? [X1] :
( ~ empty(X1)
& element(X1,powerset(X0)) )
=> ( ~ empty(sK15(X0))
& element(sK15(X0),powerset(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f142,plain,
! [X0] :
( ? [X1] :
( ~ empty(X1)
& element(X1,powerset(X0)) )
| empty(X0) ),
inference(ennf_transformation,[],[f93]) ).
fof(f93,axiom,
! [X0] :
( ~ empty(X0)
=> ? [X1] :
( ~ empty(X1)
& element(X1,powerset(X0)) ) ),
file('/export/starexec/sandbox2/tmp/tmp.XVCyggMQ11/Vampire---4.8_15325',rc1_subset_1) ).
fof(f2066,plain,
( ~ spl61_2
| spl61_247
| ~ spl61_3
| ~ spl61_234 ),
inference(avatar_split_clause,[],[f2060,f1986,f902,f2063,f897]) ).
fof(f2060,plain,
( sP9(sK12)
| ~ topological_space(sK12)
| ~ spl61_3
| ~ spl61_234 ),
inference(resolution,[],[f1987,f904]) ).
fof(f904,plain,
( top_str(sK12)
| ~ spl61_3 ),
inference(avatar_component_clause,[],[f902]) ).
fof(f2059,plain,
( spl61_246
| ~ spl61_24
| ~ spl61_136 ),
inference(avatar_split_clause,[],[f1645,f1537,f1007,f2056]) ).
fof(f1645,plain,
( one_sorted_str(sK52)
| ~ spl61_24
| ~ spl61_136 ),
inference(resolution,[],[f1538,f1009]) ).
fof(f1009,plain,
( rel_str(sK52)
| ~ spl61_24 ),
inference(avatar_component_clause,[],[f1007]) ).
fof(f2038,plain,
( spl61_245
| ~ spl61_15
| ~ spl61_136 ),
inference(avatar_split_clause,[],[f1644,f1537,f962,f2035]) ).
fof(f962,plain,
( spl61_15
<=> rel_str(sK47) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_15])]) ).
fof(f1644,plain,
( one_sorted_str(sK47)
| ~ spl61_15
| ~ spl61_136 ),
inference(resolution,[],[f1538,f964]) ).
fof(f964,plain,
( rel_str(sK47)
| ~ spl61_15 ),
inference(avatar_component_clause,[],[f962]) ).
fof(f2029,plain,
spl61_244,
inference(avatar_split_clause,[],[f767,f2027]) ).
fof(f767,plain,
! [X0,X1] : relation_of2_as_subset(sK43(X0,X1),X0,X1),
inference(cnf_transformation,[],[f403]) ).
fof(f403,plain,
! [X0,X1] : relation_of2_as_subset(sK43(X0,X1),X0,X1),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK43])],[f55,f402]) ).
fof(f402,plain,
! [X0,X1] :
( ? [X2] : relation_of2_as_subset(X2,X0,X1)
=> relation_of2_as_subset(sK43(X0,X1),X0,X1) ),
introduced(choice_axiom,[]) ).
fof(f55,axiom,
! [X0,X1] :
? [X2] : relation_of2_as_subset(X2,X0,X1),
file('/export/starexec/sandbox2/tmp/tmp.XVCyggMQ11/Vampire---4.8_15325',existence_m2_relset_1) ).
fof(f2025,plain,
spl61_243,
inference(avatar_split_clause,[],[f766,f2023]) ).
fof(f766,plain,
! [X0,X1] : relation_of2(sK42(X0,X1),X0,X1),
inference(cnf_transformation,[],[f401]) ).
fof(f401,plain,
! [X0,X1] : relation_of2(sK42(X0,X1),X0,X1),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK42])],[f53,f400]) ).
fof(f400,plain,
! [X0,X1] :
( ? [X2] : relation_of2(X2,X0,X1)
=> relation_of2(sK42(X0,X1),X0,X1) ),
introduced(choice_axiom,[]) ).
fof(f53,axiom,
! [X0,X1] :
? [X2] : relation_of2(X2,X0,X1),
file('/export/starexec/sandbox2/tmp/tmp.XVCyggMQ11/Vampire---4.8_15325',existence_m1_relset_1) ).
fof(f2021,plain,
( spl61_242
| ~ spl61_20
| ~ spl61_135 ),
inference(avatar_split_clause,[],[f1642,f1533,f987,f2018]) ).
fof(f2018,plain,
( spl61_242
<=> sP2(sK50) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_242])]) ).
fof(f987,plain,
( spl61_20
<=> one_sorted_str(sK50) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_20])]) ).
fof(f1642,plain,
( sP2(sK50)
| ~ spl61_20
| ~ spl61_135 ),
inference(resolution,[],[f1534,f989]) ).
fof(f989,plain,
( one_sorted_str(sK50)
| ~ spl61_20 ),
inference(avatar_component_clause,[],[f987]) ).
fof(f2016,plain,
spl61_241,
inference(avatar_split_clause,[],[f736,f2014]) ).
fof(f736,plain,
! [X0,X1] :
( element(X0,X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f257]) ).
fof(f257,plain,
! [X0,X1] :
( element(X0,X1)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f129]) ).
fof(f129,axiom,
! [X0,X1] :
( in(X0,X1)
=> element(X0,X1) ),
file('/export/starexec/sandbox2/tmp/tmp.XVCyggMQ11/Vampire---4.8_15325',t1_subset) ).
fof(f2012,plain,
spl61_240,
inference(avatar_split_clause,[],[f735,f2010]) ).
fof(f735,plain,
! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f256]) ).
fof(f256,plain,
! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f3]) ).
fof(f3,axiom,
! [X0,X1] :
( in(X0,X1)
=> ~ in(X1,X0) ),
file('/export/starexec/sandbox2/tmp/tmp.XVCyggMQ11/Vampire---4.8_15325',antisymmetry_r2_hidden) ).
fof(f2008,plain,
spl61_239,
inference(avatar_split_clause,[],[f731,f2006]) ).
fof(f731,plain,
! [X0] : element(sK40(X0),powerset(powerset(X0))),
inference(cnf_transformation,[],[f395]) ).
fof(f395,plain,
! [X0] :
( finite(sK40(X0))
& ~ empty(sK40(X0))
& element(sK40(X0),powerset(powerset(X0))) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK40])],[f103,f394]) ).
fof(f394,plain,
! [X0] :
( ? [X1] :
( finite(X1)
& ~ empty(X1)
& element(X1,powerset(powerset(X0))) )
=> ( finite(sK40(X0))
& ~ empty(sK40(X0))
& element(sK40(X0),powerset(powerset(X0))) ) ),
introduced(choice_axiom,[]) ).
fof(f103,axiom,
! [X0] :
? [X1] :
( finite(X1)
& ~ empty(X1)
& element(X1,powerset(powerset(X0))) ),
file('/export/starexec/sandbox2/tmp/tmp.XVCyggMQ11/Vampire---4.8_15325',rc2_waybel_7) ).
fof(f2004,plain,
spl61_238,
inference(avatar_split_clause,[],[f726,f2002]) ).
fof(f2002,plain,
( spl61_238
<=> ! [X0] :
( upper_relstr_subset(sK37(X0),X0)
| ~ sP10(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_238])]) ).
fof(f726,plain,
! [X0] :
( upper_relstr_subset(sK37(X0),X0)
| ~ sP10(X0) ),
inference(cnf_transformation,[],[f389]) ).
fof(f2000,plain,
spl61_237,
inference(avatar_split_clause,[],[f725,f1998]) ).
fof(f1998,plain,
( spl61_237
<=> ! [X0] :
( lower_relstr_subset(sK37(X0),X0)
| ~ sP10(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_237])]) ).
fof(f725,plain,
! [X0] :
( lower_relstr_subset(sK37(X0),X0)
| ~ sP10(X0) ),
inference(cnf_transformation,[],[f389]) ).
fof(f1996,plain,
spl61_236,
inference(avatar_split_clause,[],[f724,f1994]) ).
fof(f1994,plain,
( spl61_236
<=> ! [X0] :
( filtered_subset(sK37(X0),X0)
| ~ sP10(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_236])]) ).
fof(f724,plain,
! [X0] :
( filtered_subset(sK37(X0),X0)
| ~ sP10(X0) ),
inference(cnf_transformation,[],[f389]) ).
fof(f1992,plain,
spl61_235,
inference(avatar_split_clause,[],[f723,f1990]) ).
fof(f1990,plain,
( spl61_235
<=> ! [X0] :
( directed_subset(sK37(X0),X0)
| ~ sP10(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_235])]) ).
fof(f723,plain,
! [X0] :
( directed_subset(sK37(X0),X0)
| ~ sP10(X0) ),
inference(cnf_transformation,[],[f389]) ).
fof(f1988,plain,
spl61_234,
inference(avatar_split_clause,[],[f709,f1986]) ).
fof(f709,plain,
! [X0] :
( sP9(X0)
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(cnf_transformation,[],[f321]) ).
fof(f321,plain,
! [X0] :
( sP9(X0)
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(definition_folding,[],[f243,f320]) ).
fof(f243,plain,
! [X0] :
( ? [X1] :
( nowhere_dense(X1,X0)
& boundary_set(X1,X0)
& v5_membered(X1)
& v4_membered(X1)
& v3_membered(X1)
& v2_membered(X1)
& v1_membered(X1)
& closed_subset(X1,X0)
& open_subset(X1,X0)
& empty(X1)
& element(X1,powerset(the_carrier(X0))) )
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(flattening,[],[f242]) ).
fof(f242,plain,
! [X0] :
( ? [X1] :
( nowhere_dense(X1,X0)
& boundary_set(X1,X0)
& v5_membered(X1)
& v4_membered(X1)
& v3_membered(X1)
& v2_membered(X1)
& v1_membered(X1)
& closed_subset(X1,X0)
& open_subset(X1,X0)
& empty(X1)
& element(X1,powerset(the_carrier(X0))) )
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(ennf_transformation,[],[f116]) ).
fof(f116,axiom,
! [X0] :
( ( top_str(X0)
& topological_space(X0) )
=> ? [X1] :
( nowhere_dense(X1,X0)
& boundary_set(X1,X0)
& v5_membered(X1)
& v4_membered(X1)
& v3_membered(X1)
& v2_membered(X1)
& v1_membered(X1)
& closed_subset(X1,X0)
& open_subset(X1,X0)
& empty(X1)
& element(X1,powerset(the_carrier(X0))) ) ),
file('/export/starexec/sandbox2/tmp/tmp.XVCyggMQ11/Vampire---4.8_15325',rc5_tops_1) ).
fof(f1984,plain,
spl61_233,
inference(avatar_split_clause,[],[f708,f1982]) ).
fof(f708,plain,
! [X0] :
( nowhere_dense(sK33(X0),X0)
| ~ sP9(X0) ),
inference(cnf_transformation,[],[f380]) ).
fof(f1980,plain,
spl61_232,
inference(avatar_split_clause,[],[f707,f1978]) ).
fof(f707,plain,
! [X0] :
( boundary_set(sK33(X0),X0)
| ~ sP9(X0) ),
inference(cnf_transformation,[],[f380]) ).
fof(f1976,plain,
( spl61_231
| ~ spl61_14
| ~ spl61_135 ),
inference(avatar_split_clause,[],[f1641,f1533,f957,f1973]) ).
fof(f1973,plain,
( spl61_231
<=> sP2(sK46) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_231])]) ).
fof(f957,plain,
( spl61_14
<=> one_sorted_str(sK46) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_14])]) ).
fof(f1641,plain,
( sP2(sK46)
| ~ spl61_14
| ~ spl61_135 ),
inference(resolution,[],[f1534,f959]) ).
fof(f959,plain,
( one_sorted_str(sK46)
| ~ spl61_14 ),
inference(avatar_component_clause,[],[f957]) ).
fof(f1971,plain,
spl61_230,
inference(avatar_split_clause,[],[f701,f1969]) ).
fof(f701,plain,
! [X0] :
( closed_subset(sK33(X0),X0)
| ~ sP9(X0) ),
inference(cnf_transformation,[],[f380]) ).
fof(f1967,plain,
spl61_229,
inference(avatar_split_clause,[],[f700,f1965]) ).
fof(f700,plain,
! [X0] :
( open_subset(sK33(X0),X0)
| ~ sP9(X0) ),
inference(cnf_transformation,[],[f380]) ).
fof(f1963,plain,
spl61_228,
inference(avatar_split_clause,[],[f694,f1961]) ).
fof(f1961,plain,
( spl61_228
<=> ! [X0,X1] :
( nowhere_dense(X1,X0)
| ~ sP8(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_228])]) ).
fof(f694,plain,
! [X0,X1] :
( nowhere_dense(X1,X0)
| ~ sP8(X0,X1) ),
inference(cnf_transformation,[],[f377]) ).
fof(f377,plain,
! [X0,X1] :
( ( nowhere_dense(X1,X0)
& boundary_set(X1,X0)
& v5_membered(X1)
& v4_membered(X1)
& v3_membered(X1)
& v2_membered(X1)
& v1_membered(X1)
& closed_subset(X1,X0)
& open_subset(X1,X0)
& empty(X1) )
| ~ sP8(X0,X1) ),
inference(nnf_transformation,[],[f318]) ).
fof(f1959,plain,
spl61_227,
inference(avatar_split_clause,[],[f693,f1957]) ).
fof(f1957,plain,
( spl61_227
<=> ! [X0,X1] :
( boundary_set(X1,X0)
| ~ sP8(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_227])]) ).
fof(f693,plain,
! [X0,X1] :
( boundary_set(X1,X0)
| ~ sP8(X0,X1) ),
inference(cnf_transformation,[],[f377]) ).
fof(f1955,plain,
spl61_226,
inference(avatar_split_clause,[],[f687,f1953]) ).
fof(f1953,plain,
( spl61_226
<=> ! [X0,X1] :
( closed_subset(X1,X0)
| ~ sP8(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_226])]) ).
fof(f687,plain,
! [X0,X1] :
( closed_subset(X1,X0)
| ~ sP8(X0,X1) ),
inference(cnf_transformation,[],[f377]) ).
fof(f1951,plain,
spl61_225,
inference(avatar_split_clause,[],[f686,f1949]) ).
fof(f1949,plain,
( spl61_225
<=> ! [X0,X1] :
( open_subset(X1,X0)
| ~ sP8(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_225])]) ).
fof(f686,plain,
! [X0,X1] :
( open_subset(X1,X0)
| ~ sP8(X0,X1) ),
inference(cnf_transformation,[],[f377]) ).
fof(f1947,plain,
spl61_224,
inference(avatar_split_clause,[],[f668,f1945]) ).
fof(f1945,plain,
( spl61_224
<=> ! [X0] :
( filtered_subset(sK30(X0),X0)
| ~ sP7(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_224])]) ).
fof(f668,plain,
! [X0] :
( filtered_subset(sK30(X0),X0)
| ~ sP7(X0) ),
inference(cnf_transformation,[],[f372]) ).
fof(f1943,plain,
spl61_223,
inference(avatar_split_clause,[],[f667,f1941]) ).
fof(f1941,plain,
( spl61_223
<=> ! [X0] :
( directed_subset(sK30(X0),X0)
| ~ sP7(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_223])]) ).
fof(f667,plain,
! [X0] :
( directed_subset(sK30(X0),X0)
| ~ sP7(X0) ),
inference(cnf_transformation,[],[f372]) ).
fof(f1939,plain,
spl61_222,
inference(avatar_split_clause,[],[f635,f1937]) ).
fof(f1937,plain,
( spl61_222
<=> ! [X0] :
( upper_relstr_subset(sK25(X0),X0)
| ~ sP6(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_222])]) ).
fof(f635,plain,
! [X0] :
( upper_relstr_subset(sK25(X0),X0)
| ~ sP6(X0) ),
inference(cnf_transformation,[],[f360]) ).
fof(f1935,plain,
spl61_221,
inference(avatar_split_clause,[],[f634,f1933]) ).
fof(f1933,plain,
( spl61_221
<=> ! [X0] :
( filtered_subset(sK25(X0),X0)
| ~ sP6(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_221])]) ).
fof(f634,plain,
! [X0] :
( filtered_subset(sK25(X0),X0)
| ~ sP6(X0) ),
inference(cnf_transformation,[],[f360]) ).
fof(f1931,plain,
( spl61_220
| ~ spl61_13
| ~ spl61_134 ),
inference(avatar_split_clause,[],[f1640,f1529,f952,f1928]) ).
fof(f1529,plain,
( spl61_134
<=> ! [X0] :
( sP1(X0)
| ~ top_str(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_134])]) ).
fof(f1640,plain,
( sP1(sK45)
| ~ spl61_13
| ~ spl61_134 ),
inference(resolution,[],[f1530,f954]) ).
fof(f1530,plain,
( ! [X0] :
( ~ top_str(X0)
| sP1(X0) )
| ~ spl61_134 ),
inference(avatar_component_clause,[],[f1529]) ).
fof(f1926,plain,
spl61_219,
inference(avatar_split_clause,[],[f627,f1924]) ).
fof(f1924,plain,
( spl61_219
<=> ! [X0] :
( filtered_subset(sK24(X0),X0)
| ~ rel_str(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_219])]) ).
fof(f627,plain,
! [X0] :
( filtered_subset(sK24(X0),X0)
| ~ rel_str(X0) ),
inference(cnf_transformation,[],[f357]) ).
fof(f1922,plain,
spl61_218,
inference(avatar_split_clause,[],[f626,f1920]) ).
fof(f1920,plain,
( spl61_218
<=> ! [X0] :
( directed_subset(sK24(X0),X0)
| ~ rel_str(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_218])]) ).
fof(f626,plain,
! [X0] :
( directed_subset(sK24(X0),X0)
| ~ rel_str(X0) ),
inference(cnf_transformation,[],[f357]) ).
fof(f1918,plain,
spl61_217,
inference(avatar_split_clause,[],[f624,f1916]) ).
fof(f1916,plain,
( spl61_217
<=> ! [X0] :
( upper_relstr_subset(sK23(X0),X0)
| ~ rel_str(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_217])]) ).
fof(f624,plain,
! [X0] :
( upper_relstr_subset(sK23(X0),X0)
| ~ rel_str(X0) ),
inference(cnf_transformation,[],[f355]) ).
fof(f1914,plain,
spl61_216,
inference(avatar_split_clause,[],[f623,f1912]) ).
fof(f1912,plain,
( spl61_216
<=> ! [X0] :
( lower_relstr_subset(sK23(X0),X0)
| ~ rel_str(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_216])]) ).
fof(f623,plain,
! [X0] :
( lower_relstr_subset(sK23(X0),X0)
| ~ rel_str(X0) ),
inference(cnf_transformation,[],[f355]) ).
fof(f1910,plain,
spl61_215,
inference(avatar_split_clause,[],[f574,f1908]) ).
fof(f1908,plain,
( spl61_215
<=> ! [X0] :
( ~ empty_carrier(X0)
| ~ with_suprema_relstr(X0)
| ~ rel_str(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_215])]) ).
fof(f574,plain,
! [X0] :
( ~ empty_carrier(X0)
| ~ with_suprema_relstr(X0)
| ~ rel_str(X0) ),
inference(cnf_transformation,[],[f166]) ).
fof(f166,plain,
! [X0] :
( ~ empty_carrier(X0)
| ~ with_suprema_relstr(X0)
| ~ rel_str(X0) ),
inference(flattening,[],[f165]) ).
fof(f165,plain,
! [X0] :
( ~ empty_carrier(X0)
| ~ with_suprema_relstr(X0)
| ~ rel_str(X0) ),
inference(ennf_transformation,[],[f10]) ).
fof(f10,axiom,
! [X0] :
( rel_str(X0)
=> ( with_suprema_relstr(X0)
=> ~ empty_carrier(X0) ) ),
file('/export/starexec/sandbox2/tmp/tmp.XVCyggMQ11/Vampire---4.8_15325',cc1_lattice3) ).
fof(f1906,plain,
spl61_214,
inference(avatar_split_clause,[],[f572,f1904]) ).
fof(f1904,plain,
( spl61_214
<=> ! [X0] :
( ~ empty_carrier(X0)
| ~ with_infima_relstr(X0)
| ~ rel_str(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_214])]) ).
fof(f572,plain,
! [X0] :
( ~ empty_carrier(X0)
| ~ with_infima_relstr(X0)
| ~ rel_str(X0) ),
inference(cnf_transformation,[],[f162]) ).
fof(f162,plain,
! [X0] :
( ~ empty_carrier(X0)
| ~ with_infima_relstr(X0)
| ~ rel_str(X0) ),
inference(flattening,[],[f161]) ).
fof(f161,plain,
! [X0] :
( ~ empty_carrier(X0)
| ~ with_infima_relstr(X0)
| ~ rel_str(X0) ),
inference(ennf_transformation,[],[f16]) ).
fof(f16,axiom,
! [X0] :
( rel_str(X0)
=> ( with_infima_relstr(X0)
=> ~ empty_carrier(X0) ) ),
file('/export/starexec/sandbox2/tmp/tmp.XVCyggMQ11/Vampire---4.8_15325',cc2_lattice3) ).
fof(f1902,plain,
spl61_213,
inference(avatar_split_clause,[],[f571,f1900]) ).
fof(f571,plain,
! [X0] :
( upper_bounded_relstr(X0)
| ~ bounded_relstr(X0)
| ~ rel_str(X0) ),
inference(cnf_transformation,[],[f160]) ).
fof(f160,plain,
! [X0] :
( ( upper_bounded_relstr(X0)
& lower_bounded_relstr(X0) )
| ~ bounded_relstr(X0)
| ~ rel_str(X0) ),
inference(flattening,[],[f159]) ).
fof(f159,plain,
! [X0] :
( ( upper_bounded_relstr(X0)
& lower_bounded_relstr(X0) )
| ~ bounded_relstr(X0)
| ~ rel_str(X0) ),
inference(ennf_transformation,[],[f22]) ).
fof(f22,axiom,
! [X0] :
( rel_str(X0)
=> ( bounded_relstr(X0)
=> ( upper_bounded_relstr(X0)
& lower_bounded_relstr(X0) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.XVCyggMQ11/Vampire---4.8_15325',cc4_yellow_0) ).
fof(f1898,plain,
spl61_212,
inference(avatar_split_clause,[],[f570,f1896]) ).
fof(f570,plain,
! [X0] :
( lower_bounded_relstr(X0)
| ~ bounded_relstr(X0)
| ~ rel_str(X0) ),
inference(cnf_transformation,[],[f160]) ).
fof(f1894,plain,
spl61_211,
inference(avatar_split_clause,[],[f563,f1892]) ).
fof(f563,plain,
! [X0] :
( strict_net_str(sK21(X0),X0)
| ~ one_sorted_str(X0) ),
inference(cnf_transformation,[],[f348]) ).
fof(f348,plain,
! [X0] :
( ( strict_net_str(sK21(X0),X0)
& net_str(sK21(X0),X0) )
| ~ one_sorted_str(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK21])],[f154,f347]) ).
fof(f347,plain,
! [X0] :
( ? [X1] :
( strict_net_str(X1,X0)
& net_str(X1,X0) )
=> ( strict_net_str(sK21(X0),X0)
& net_str(sK21(X0),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f154,plain,
! [X0] :
( ? [X1] :
( strict_net_str(X1,X0)
& net_str(X1,X0) )
| ~ one_sorted_str(X0) ),
inference(ennf_transformation,[],[f112]) ).
fof(f112,axiom,
! [X0] :
( one_sorted_str(X0)
=> ? [X1] :
( strict_net_str(X1,X0)
& net_str(X1,X0) ) ),
file('/export/starexec/sandbox2/tmp/tmp.XVCyggMQ11/Vampire---4.8_15325',rc4_waybel_0) ).
fof(f1890,plain,
spl61_210,
inference(avatar_split_clause,[],[f562,f1888]) ).
fof(f562,plain,
! [X0] :
( net_str(sK21(X0),X0)
| ~ one_sorted_str(X0) ),
inference(cnf_transformation,[],[f348]) ).
fof(f1886,plain,
( spl61_209
| ~ spl61_13
| ~ spl61_133 ),
inference(avatar_split_clause,[],[f1638,f1525,f952,f1883]) ).
fof(f1525,plain,
( spl61_133
<=> ! [X0] :
( one_sorted_str(X0)
| ~ top_str(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_133])]) ).
fof(f1638,plain,
( one_sorted_str(sK45)
| ~ spl61_13
| ~ spl61_133 ),
inference(resolution,[],[f1526,f954]) ).
fof(f1526,plain,
( ! [X0] :
( ~ top_str(X0)
| one_sorted_str(X0) )
| ~ spl61_133 ),
inference(avatar_component_clause,[],[f1525]) ).
fof(f1881,plain,
spl61_208,
inference(avatar_split_clause,[],[f559,f1879]) ).
fof(f559,plain,
! [X0] :
( strict_net_str(sK20(X0),X0)
| ~ sP2(X0) ),
inference(cnf_transformation,[],[f346]) ).
fof(f346,plain,
! [X0] :
( ( directed_relstr(sK20(X0))
& strict_net_str(sK20(X0),X0)
& antisymmetric_relstr(sK20(X0))
& transitive_relstr(sK20(X0))
& reflexive_relstr(sK20(X0))
& ~ empty_carrier(sK20(X0))
& net_str(sK20(X0),X0) )
| ~ sP2(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK20])],[f344,f345]) ).
fof(f345,plain,
! [X0] :
( ? [X1] :
( directed_relstr(X1)
& strict_net_str(X1,X0)
& antisymmetric_relstr(X1)
& transitive_relstr(X1)
& reflexive_relstr(X1)
& ~ empty_carrier(X1)
& net_str(X1,X0) )
=> ( directed_relstr(sK20(X0))
& strict_net_str(sK20(X0),X0)
& antisymmetric_relstr(sK20(X0))
& transitive_relstr(sK20(X0))
& reflexive_relstr(sK20(X0))
& ~ empty_carrier(sK20(X0))
& net_str(sK20(X0),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f344,plain,
! [X0] :
( ? [X1] :
( directed_relstr(X1)
& strict_net_str(X1,X0)
& antisymmetric_relstr(X1)
& transitive_relstr(X1)
& reflexive_relstr(X1)
& ~ empty_carrier(X1)
& net_str(X1,X0) )
| ~ sP2(X0) ),
inference(nnf_transformation,[],[f306]) ).
fof(f306,plain,
! [X0] :
( ? [X1] :
( directed_relstr(X1)
& strict_net_str(X1,X0)
& antisymmetric_relstr(X1)
& transitive_relstr(X1)
& reflexive_relstr(X1)
& ~ empty_carrier(X1)
& net_str(X1,X0) )
| ~ sP2(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP2])]) ).
fof(f1877,plain,
spl61_207,
inference(avatar_split_clause,[],[f554,f1875]) ).
fof(f554,plain,
! [X0] :
( net_str(sK20(X0),X0)
| ~ sP2(X0) ),
inference(cnf_transformation,[],[f346]) ).
fof(f1873,plain,
spl61_206,
inference(avatar_split_clause,[],[f553,f1871]) ).
fof(f553,plain,
! [X0] :
( net_str(sK19(X0),X0)
| ~ one_sorted_str(X0) ),
inference(cnf_transformation,[],[f343]) ).
fof(f343,plain,
! [X0] :
( net_str(sK19(X0),X0)
| ~ one_sorted_str(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK19])],[f152,f342]) ).
fof(f342,plain,
! [X0] :
( ? [X1] : net_str(X1,X0)
=> net_str(sK19(X0),X0) ),
introduced(choice_axiom,[]) ).
fof(f152,plain,
! [X0] :
( ? [X1] : net_str(X1,X0)
| ~ one_sorted_str(X0) ),
inference(ennf_transformation,[],[f52]) ).
fof(f52,axiom,
! [X0] :
( one_sorted_str(X0)
=> ? [X1] : net_str(X1,X0) ),
file('/export/starexec/sandbox2/tmp/tmp.XVCyggMQ11/Vampire---4.8_15325',existence_l1_waybel_0) ).
fof(f1869,plain,
spl61_205,
inference(avatar_split_clause,[],[f549,f1867]) ).
fof(f1867,plain,
( spl61_205
<=> ! [X0] :
( boundary_set(sK18(X0),X0)
| ~ sP1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_205])]) ).
fof(f549,plain,
! [X0] :
( boundary_set(sK18(X0),X0)
| ~ sP1(X0) ),
inference(cnf_transformation,[],[f341]) ).
fof(f1865,plain,
spl61_204,
inference(avatar_split_clause,[],[f540,f1863]) ).
fof(f1863,plain,
( spl61_204
<=> ! [X0] :
( dense(cast_as_carrier_subset(X0),X0)
| ~ top_str(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_204])]) ).
fof(f540,plain,
! [X0] :
( dense(cast_as_carrier_subset(X0),X0)
| ~ top_str(X0) ),
inference(cnf_transformation,[],[f146]) ).
fof(f146,plain,
! [X0] :
( dense(cast_as_carrier_subset(X0),X0)
| ~ top_str(X0) ),
inference(ennf_transformation,[],[f82]) ).
fof(f82,axiom,
! [X0] :
( top_str(X0)
=> dense(cast_as_carrier_subset(X0),X0) ),
file('/export/starexec/sandbox2/tmp/tmp.XVCyggMQ11/Vampire---4.8_15325',fc9_tops_1) ).
fof(f1860,plain,
( spl61_203
| spl61_18
| ~ spl61_132 ),
inference(avatar_split_clause,[],[f1636,f1521,f977,f1857]) ).
fof(f1857,plain,
( spl61_203
<=> sP0(sK49) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_203])]) ).
fof(f977,plain,
( spl61_18
<=> empty(sK49) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_18])]) ).
fof(f1636,plain,
( sP0(sK49)
| spl61_18
| ~ spl61_132 ),
inference(resolution,[],[f1522,f979]) ).
fof(f979,plain,
( ~ empty(sK49)
| spl61_18 ),
inference(avatar_component_clause,[],[f977]) ).
fof(f1851,plain,
( spl61_202
| spl61_16
| ~ spl61_132 ),
inference(avatar_split_clause,[],[f1635,f1521,f967,f1848]) ).
fof(f1848,plain,
( spl61_202
<=> sP0(sK48) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_202])]) ).
fof(f967,plain,
( spl61_16
<=> empty(sK48) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_16])]) ).
fof(f1635,plain,
( sP0(sK48)
| spl61_16
| ~ spl61_132 ),
inference(resolution,[],[f1522,f969]) ).
fof(f969,plain,
( ~ empty(sK48)
| spl61_16 ),
inference(avatar_component_clause,[],[f967]) ).
fof(f1835,plain,
( spl61_201
| ~ spl61_135
| ~ spl61_161 ),
inference(avatar_split_clause,[],[f1760,f1659,f1533,f1832]) ).
fof(f1832,plain,
( spl61_201
<=> sP2(sK12) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_201])]) ).
fof(f1760,plain,
( sP2(sK12)
| ~ spl61_135
| ~ spl61_161 ),
inference(resolution,[],[f1661,f1534]) ).
fof(f1661,plain,
( one_sorted_str(sK12)
| ~ spl61_161 ),
inference(avatar_component_clause,[],[f1659]) ).
fof(f1828,plain,
spl61_200,
inference(avatar_split_clause,[],[f765,f1826]) ).
fof(f765,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f282]) ).
fof(f282,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f136]) ).
fof(f136,axiom,
! [X0,X1] :
~ ( empty(X1)
& in(X0,X1) ),
file('/export/starexec/sandbox2/tmp/tmp.XVCyggMQ11/Vampire---4.8_15325',t7_boole) ).
fof(f1824,plain,
spl61_199,
inference(avatar_split_clause,[],[f729,f1822]) ).
fof(f729,plain,
! [X0] : element(sK39(X0),powerset(X0)),
inference(cnf_transformation,[],[f393]) ).
fof(f393,plain,
! [X0] :
( empty(sK39(X0))
& element(sK39(X0),powerset(X0)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK39])],[f100,f392]) ).
fof(f392,plain,
! [X0] :
( ? [X1] :
( empty(X1)
& element(X1,powerset(X0)) )
=> ( empty(sK39(X0))
& element(sK39(X0),powerset(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f100,axiom,
! [X0] :
? [X1] :
( empty(X1)
& element(X1,powerset(X0)) ),
file('/export/starexec/sandbox2/tmp/tmp.XVCyggMQ11/Vampire---4.8_15325',rc2_subset_1) ).
fof(f1820,plain,
spl61_198,
inference(avatar_split_clause,[],[f722,f1818]) ).
fof(f722,plain,
! [X0] :
( ~ empty(sK37(X0))
| ~ sP10(X0) ),
inference(cnf_transformation,[],[f389]) ).
fof(f1816,plain,
spl61_197,
inference(avatar_split_clause,[],[f706,f1814]) ).
fof(f706,plain,
! [X0] :
( v5_membered(sK33(X0))
| ~ sP9(X0) ),
inference(cnf_transformation,[],[f380]) ).
fof(f1812,plain,
spl61_196,
inference(avatar_split_clause,[],[f705,f1810]) ).
fof(f705,plain,
! [X0] :
( v4_membered(sK33(X0))
| ~ sP9(X0) ),
inference(cnf_transformation,[],[f380]) ).
fof(f1808,plain,
spl61_195,
inference(avatar_split_clause,[],[f704,f1806]) ).
fof(f704,plain,
! [X0] :
( v3_membered(sK33(X0))
| ~ sP9(X0) ),
inference(cnf_transformation,[],[f380]) ).
fof(f1804,plain,
spl61_194,
inference(avatar_split_clause,[],[f703,f1802]) ).
fof(f703,plain,
! [X0] :
( v2_membered(sK33(X0))
| ~ sP9(X0) ),
inference(cnf_transformation,[],[f380]) ).
fof(f1800,plain,
spl61_193,
inference(avatar_split_clause,[],[f702,f1798]) ).
fof(f702,plain,
! [X0] :
( v1_membered(sK33(X0))
| ~ sP9(X0) ),
inference(cnf_transformation,[],[f380]) ).
fof(f1796,plain,
spl61_192,
inference(avatar_split_clause,[],[f699,f1794]) ).
fof(f699,plain,
! [X0] :
( empty(sK33(X0))
| ~ sP9(X0) ),
inference(cnf_transformation,[],[f380]) ).
fof(f1792,plain,
spl61_191,
inference(avatar_split_clause,[],[f692,f1790]) ).
fof(f1790,plain,
( spl61_191
<=> ! [X0,X1] :
( v5_membered(X1)
| ~ sP8(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_191])]) ).
fof(f692,plain,
! [X0,X1] :
( v5_membered(X1)
| ~ sP8(X0,X1) ),
inference(cnf_transformation,[],[f377]) ).
fof(f1788,plain,
spl61_190,
inference(avatar_split_clause,[],[f691,f1786]) ).
fof(f1786,plain,
( spl61_190
<=> ! [X0,X1] :
( v4_membered(X1)
| ~ sP8(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_190])]) ).
fof(f691,plain,
! [X0,X1] :
( v4_membered(X1)
| ~ sP8(X0,X1) ),
inference(cnf_transformation,[],[f377]) ).
fof(f1784,plain,
spl61_189,
inference(avatar_split_clause,[],[f690,f1782]) ).
fof(f1782,plain,
( spl61_189
<=> ! [X0,X1] :
( v3_membered(X1)
| ~ sP8(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_189])]) ).
fof(f690,plain,
! [X0,X1] :
( v3_membered(X1)
| ~ sP8(X0,X1) ),
inference(cnf_transformation,[],[f377]) ).
fof(f1780,plain,
spl61_188,
inference(avatar_split_clause,[],[f689,f1778]) ).
fof(f1778,plain,
( spl61_188
<=> ! [X0,X1] :
( v2_membered(X1)
| ~ sP8(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_188])]) ).
fof(f689,plain,
! [X0,X1] :
( v2_membered(X1)
| ~ sP8(X0,X1) ),
inference(cnf_transformation,[],[f377]) ).
fof(f1776,plain,
spl61_187,
inference(avatar_split_clause,[],[f688,f1774]) ).
fof(f1774,plain,
( spl61_187
<=> ! [X0,X1] :
( v1_membered(X1)
| ~ sP8(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_187])]) ).
fof(f688,plain,
! [X0,X1] :
( v1_membered(X1)
| ~ sP8(X0,X1) ),
inference(cnf_transformation,[],[f377]) ).
fof(f1772,plain,
spl61_186,
inference(avatar_split_clause,[],[f685,f1770]) ).
fof(f1770,plain,
( spl61_186
<=> ! [X0,X1] :
( empty(X1)
| ~ sP8(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_186])]) ).
fof(f685,plain,
! [X0,X1] :
( empty(X1)
| ~ sP8(X0,X1) ),
inference(cnf_transformation,[],[f377]) ).
fof(f1768,plain,
spl61_185,
inference(avatar_split_clause,[],[f666,f1766]) ).
fof(f1766,plain,
( spl61_185
<=> ! [X0] :
( finite(sK30(X0))
| ~ sP7(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_185])]) ).
fof(f666,plain,
! [X0] :
( finite(sK30(X0))
| ~ sP7(X0) ),
inference(cnf_transformation,[],[f372]) ).
fof(f1764,plain,
spl61_184,
inference(avatar_split_clause,[],[f665,f1762]) ).
fof(f665,plain,
! [X0] :
( ~ empty(sK30(X0))
| ~ sP7(X0) ),
inference(cnf_transformation,[],[f372]) ).
fof(f1759,plain,
spl61_183,
inference(avatar_split_clause,[],[f632,f1757]) ).
fof(f632,plain,
! [X0] :
( ~ empty(sK25(X0))
| ~ sP6(X0) ),
inference(cnf_transformation,[],[f360]) ).
fof(f1755,plain,
spl61_182,
inference(avatar_split_clause,[],[f630,f1753]) ).
fof(f630,plain,
! [X0] :
( empty_set = X0
| ~ empty(X0) ),
inference(cnf_transformation,[],[f193]) ).
fof(f193,plain,
! [X0] :
( empty_set = X0
| ~ empty(X0) ),
inference(ennf_transformation,[],[f135]) ).
fof(f135,axiom,
! [X0] :
( empty(X0)
=> empty_set = X0 ),
file('/export/starexec/sandbox2/tmp/tmp.XVCyggMQ11/Vampire---4.8_15325',t6_boole) ).
fof(f1751,plain,
spl61_181,
inference(avatar_split_clause,[],[f566,f1749]) ).
fof(f1749,plain,
( spl61_181
<=> ! [X0] :
( finite(sK22(X0))
| ~ one_sorted_str(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_181])]) ).
fof(f566,plain,
! [X0] :
( finite(sK22(X0))
| ~ one_sorted_str(X0) ),
inference(cnf_transformation,[],[f350]) ).
fof(f1747,plain,
spl61_180,
inference(avatar_split_clause,[],[f565,f1745]) ).
fof(f565,plain,
! [X0] :
( ~ empty(sK22(X0))
| ~ one_sorted_str(X0) ),
inference(cnf_transformation,[],[f350]) ).
fof(f1743,plain,
spl61_179,
inference(avatar_split_clause,[],[f560,f1741]) ).
fof(f1741,plain,
( spl61_179
<=> ! [X0] :
( directed_relstr(sK20(X0))
| ~ sP2(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_179])]) ).
fof(f560,plain,
! [X0] :
( directed_relstr(sK20(X0))
| ~ sP2(X0) ),
inference(cnf_transformation,[],[f346]) ).
fof(f1739,plain,
spl61_178,
inference(avatar_split_clause,[],[f558,f1737]) ).
fof(f558,plain,
! [X0] :
( antisymmetric_relstr(sK20(X0))
| ~ sP2(X0) ),
inference(cnf_transformation,[],[f346]) ).
fof(f1735,plain,
spl61_177,
inference(avatar_split_clause,[],[f557,f1733]) ).
fof(f1733,plain,
( spl61_177
<=> ! [X0] :
( transitive_relstr(sK20(X0))
| ~ sP2(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_177])]) ).
fof(f557,plain,
! [X0] :
( transitive_relstr(sK20(X0))
| ~ sP2(X0) ),
inference(cnf_transformation,[],[f346]) ).
fof(f1731,plain,
spl61_176,
inference(avatar_split_clause,[],[f556,f1729]) ).
fof(f556,plain,
! [X0] :
( reflexive_relstr(sK20(X0))
| ~ sP2(X0) ),
inference(cnf_transformation,[],[f346]) ).
fof(f1727,plain,
spl61_175,
inference(avatar_split_clause,[],[f555,f1725]) ).
fof(f1725,plain,
( spl61_175
<=> ! [X0] :
( ~ empty_carrier(sK20(X0))
| ~ sP2(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_175])]) ).
fof(f555,plain,
! [X0] :
( ~ empty_carrier(sK20(X0))
| ~ sP2(X0) ),
inference(cnf_transformation,[],[f346]) ).
fof(f1723,plain,
spl61_174,
inference(avatar_split_clause,[],[f548,f1721]) ).
fof(f1721,plain,
( spl61_174
<=> ! [X0] :
( v5_membered(sK18(X0))
| ~ sP1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_174])]) ).
fof(f548,plain,
! [X0] :
( v5_membered(sK18(X0))
| ~ sP1(X0) ),
inference(cnf_transformation,[],[f341]) ).
fof(f1719,plain,
spl61_173,
inference(avatar_split_clause,[],[f547,f1717]) ).
fof(f1717,plain,
( spl61_173
<=> ! [X0] :
( v4_membered(sK18(X0))
| ~ sP1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_173])]) ).
fof(f547,plain,
! [X0] :
( v4_membered(sK18(X0))
| ~ sP1(X0) ),
inference(cnf_transformation,[],[f341]) ).
fof(f1715,plain,
spl61_172,
inference(avatar_split_clause,[],[f546,f1713]) ).
fof(f1713,plain,
( spl61_172
<=> ! [X0] :
( v3_membered(sK18(X0))
| ~ sP1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_172])]) ).
fof(f546,plain,
! [X0] :
( v3_membered(sK18(X0))
| ~ sP1(X0) ),
inference(cnf_transformation,[],[f341]) ).
fof(f1711,plain,
spl61_171,
inference(avatar_split_clause,[],[f545,f1709]) ).
fof(f1709,plain,
( spl61_171
<=> ! [X0] :
( v2_membered(sK18(X0))
| ~ sP1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_171])]) ).
fof(f545,plain,
! [X0] :
( v2_membered(sK18(X0))
| ~ sP1(X0) ),
inference(cnf_transformation,[],[f341]) ).
fof(f1707,plain,
spl61_170,
inference(avatar_split_clause,[],[f544,f1705]) ).
fof(f1705,plain,
( spl61_170
<=> ! [X0] :
( v1_membered(sK18(X0))
| ~ sP1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_170])]) ).
fof(f544,plain,
! [X0] :
( v1_membered(sK18(X0))
| ~ sP1(X0) ),
inference(cnf_transformation,[],[f341]) ).
fof(f1703,plain,
spl61_169,
inference(avatar_split_clause,[],[f543,f1701]) ).
fof(f543,plain,
! [X0] :
( empty(sK18(X0))
| ~ sP1(X0) ),
inference(cnf_transformation,[],[f341]) ).
fof(f1699,plain,
spl61_168,
inference(avatar_split_clause,[],[f538,f1697]) ).
fof(f1697,plain,
( spl61_168
<=> ! [X0] :
( finite(sK17(X0))
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_168])]) ).
fof(f538,plain,
! [X0] :
( finite(sK17(X0))
| empty(X0) ),
inference(cnf_transformation,[],[f338]) ).
fof(f1695,plain,
spl61_167,
inference(avatar_split_clause,[],[f537,f1693]) ).
fof(f537,plain,
! [X0] :
( ~ empty(sK17(X0))
| empty(X0) ),
inference(cnf_transformation,[],[f338]) ).
fof(f1691,plain,
spl61_166,
inference(avatar_split_clause,[],[f535,f1689]) ).
fof(f1689,plain,
( spl61_166
<=> ! [X0] :
( finite(sK16(X0))
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_166])]) ).
fof(f535,plain,
! [X0] :
( finite(sK16(X0))
| empty(X0) ),
inference(cnf_transformation,[],[f336]) ).
fof(f1687,plain,
spl61_165,
inference(avatar_split_clause,[],[f534,f1685]) ).
fof(f534,plain,
! [X0] :
( ~ empty(sK16(X0))
| empty(X0) ),
inference(cnf_transformation,[],[f336]) ).
fof(f1683,plain,
spl61_164,
inference(avatar_split_clause,[],[f532,f1681]) ).
fof(f532,plain,
! [X0] :
( ~ empty(sK15(X0))
| empty(X0) ),
inference(cnf_transformation,[],[f334]) ).
fof(f1679,plain,
( spl61_163
| ~ spl61_3
| ~ spl61_134 ),
inference(avatar_split_clause,[],[f1639,f1529,f902,f1676]) ).
fof(f1639,plain,
( sP1(sK12)
| ~ spl61_3
| ~ spl61_134 ),
inference(resolution,[],[f1530,f904]) ).
fof(f1674,plain,
spl61_162,
inference(avatar_split_clause,[],[f512,f1672]) ).
fof(f1672,plain,
( spl61_162
<=> ! [X0] :
( ~ trivial_carrier(boole_POSet(X0))
| ~ sP0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_162])]) ).
fof(f512,plain,
! [X0] :
( ~ trivial_carrier(boole_POSet(X0))
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f332]) ).
fof(f332,plain,
! [X0] :
( ( complete_relstr(boole_POSet(X0))
& with_infima_relstr(boole_POSet(X0))
& with_suprema_relstr(boole_POSet(X0))
& boolean_relstr(boole_POSet(X0))
& complemented_relstr(boole_POSet(X0))
& heyting_relstr(boole_POSet(X0))
& distributive_relstr(boole_POSet(X0))
& ~ v1_yellow_3(boole_POSet(X0))
& join_complete_relstr(boole_POSet(X0))
& up_complete_relstr(boole_POSet(X0))
& bounded_relstr(boole_POSet(X0))
& upper_bounded_relstr(boole_POSet(X0))
& lower_bounded_relstr(boole_POSet(X0))
& antisymmetric_relstr(boole_POSet(X0))
& transitive_relstr(boole_POSet(X0))
& reflexive_relstr(boole_POSet(X0))
& strict_rel_str(boole_POSet(X0))
& ~ trivial_carrier(boole_POSet(X0))
& ~ empty_carrier(boole_POSet(X0)) )
| ~ sP0(X0) ),
inference(nnf_transformation,[],[f302]) ).
fof(f302,plain,
! [X0] :
( ( complete_relstr(boole_POSet(X0))
& with_infima_relstr(boole_POSet(X0))
& with_suprema_relstr(boole_POSet(X0))
& boolean_relstr(boole_POSet(X0))
& complemented_relstr(boole_POSet(X0))
& heyting_relstr(boole_POSet(X0))
& distributive_relstr(boole_POSet(X0))
& ~ v1_yellow_3(boole_POSet(X0))
& join_complete_relstr(boole_POSet(X0))
& up_complete_relstr(boole_POSet(X0))
& bounded_relstr(boole_POSet(X0))
& upper_bounded_relstr(boole_POSet(X0))
& lower_bounded_relstr(boole_POSet(X0))
& antisymmetric_relstr(boole_POSet(X0))
& transitive_relstr(boole_POSet(X0))
& reflexive_relstr(boole_POSet(X0))
& strict_rel_str(boole_POSet(X0))
& ~ trivial_carrier(boole_POSet(X0))
& ~ empty_carrier(boole_POSet(X0)) )
| ~ sP0(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f1662,plain,
( spl61_161
| ~ spl61_3
| ~ spl61_133 ),
inference(avatar_split_clause,[],[f1637,f1525,f902,f1659]) ).
fof(f1637,plain,
( one_sorted_str(sK12)
| ~ spl61_3
| ~ spl61_133 ),
inference(resolution,[],[f1526,f904]) ).
fof(f1657,plain,
( spl61_160
| spl61_4
| ~ spl61_132 ),
inference(avatar_split_clause,[],[f1633,f1521,f907,f1654]) ).
fof(f1654,plain,
( spl61_160
<=> sP0(sK13) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_160])]) ).
fof(f1633,plain,
( sP0(sK13)
| spl61_4
| ~ spl61_132 ),
inference(resolution,[],[f1522,f909]) ).
fof(f909,plain,
( ~ empty(sK13)
| spl61_4 ),
inference(avatar_component_clause,[],[f907]) ).
fof(f1631,plain,
spl61_159,
inference(avatar_split_clause,[],[f728,f1629]) ).
fof(f728,plain,
! [X0] : element(sK38(X0),X0),
inference(cnf_transformation,[],[f391]) ).
fof(f391,plain,
! [X0] : element(sK38(X0),X0),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK38])],[f54,f390]) ).
fof(f390,plain,
! [X0] :
( ? [X1] : element(X1,X0)
=> element(sK38(X0),X0) ),
introduced(choice_axiom,[]) ).
fof(f54,axiom,
! [X0] :
? [X1] : element(X1,X0),
file('/export/starexec/sandbox2/tmp/tmp.XVCyggMQ11/Vampire---4.8_15325',existence_m1_subset_1) ).
fof(f1627,plain,
spl61_158,
inference(avatar_split_clause,[],[f629,f1625]) ).
fof(f629,plain,
! [X0] :
( finite(X0)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f192]) ).
fof(f192,plain,
! [X0] :
( finite(X0)
| ~ empty(X0) ),
inference(ennf_transformation,[],[f9]) ).
fof(f9,axiom,
! [X0] :
( empty(X0)
=> finite(X0) ),
file('/export/starexec/sandbox2/tmp/tmp.XVCyggMQ11/Vampire---4.8_15325',cc1_finset_1) ).
fof(f1623,plain,
spl61_157,
inference(avatar_split_clause,[],[f628,f1621]) ).
fof(f628,plain,
! [X0] :
( relation(X0)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f191]) ).
fof(f191,plain,
! [X0] :
( relation(X0)
| ~ empty(X0) ),
inference(ennf_transformation,[],[f11]) ).
fof(f11,axiom,
! [X0] :
( empty(X0)
=> relation(X0) ),
file('/export/starexec/sandbox2/tmp/tmp.XVCyggMQ11/Vampire---4.8_15325',cc1_relat_1) ).
fof(f1619,plain,
spl61_156,
inference(avatar_split_clause,[],[f615,f1617]) ).
fof(f1617,plain,
( spl61_156
<=> ! [X0] :
( bounded_relstr(X0)
| ~ sP5(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_156])]) ).
fof(f615,plain,
! [X0] :
( bounded_relstr(X0)
| ~ sP5(X0) ),
inference(cnf_transformation,[],[f353]) ).
fof(f353,plain,
! [X0] :
( ( bounded_relstr(X0)
& upper_bounded_relstr(X0)
& lower_bounded_relstr(X0)
& complete_relstr(X0)
& with_infima_relstr(X0)
& with_suprema_relstr(X0)
& antisymmetric_relstr(X0)
& transitive_relstr(X0)
& reflexive_relstr(X0)
& ~ empty_carrier(X0) )
| ~ sP5(X0) ),
inference(nnf_transformation,[],[f312]) ).
fof(f1615,plain,
spl61_155,
inference(avatar_split_clause,[],[f614,f1613]) ).
fof(f1613,plain,
( spl61_155
<=> ! [X0] :
( upper_bounded_relstr(X0)
| ~ sP5(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_155])]) ).
fof(f614,plain,
! [X0] :
( upper_bounded_relstr(X0)
| ~ sP5(X0) ),
inference(cnf_transformation,[],[f353]) ).
fof(f1611,plain,
spl61_154,
inference(avatar_split_clause,[],[f613,f1609]) ).
fof(f1609,plain,
( spl61_154
<=> ! [X0] :
( lower_bounded_relstr(X0)
| ~ sP5(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_154])]) ).
fof(f613,plain,
! [X0] :
( lower_bounded_relstr(X0)
| ~ sP5(X0) ),
inference(cnf_transformation,[],[f353]) ).
fof(f1607,plain,
spl61_153,
inference(avatar_split_clause,[],[f612,f1605]) ).
fof(f1605,plain,
( spl61_153
<=> ! [X0] :
( complete_relstr(X0)
| ~ sP5(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_153])]) ).
fof(f612,plain,
! [X0] :
( complete_relstr(X0)
| ~ sP5(X0) ),
inference(cnf_transformation,[],[f353]) ).
fof(f1603,plain,
spl61_152,
inference(avatar_split_clause,[],[f611,f1601]) ).
fof(f1601,plain,
( spl61_152
<=> ! [X0] :
( with_infima_relstr(X0)
| ~ sP5(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_152])]) ).
fof(f611,plain,
! [X0] :
( with_infima_relstr(X0)
| ~ sP5(X0) ),
inference(cnf_transformation,[],[f353]) ).
fof(f1599,plain,
spl61_151,
inference(avatar_split_clause,[],[f610,f1597]) ).
fof(f1597,plain,
( spl61_151
<=> ! [X0] :
( with_suprema_relstr(X0)
| ~ sP5(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_151])]) ).
fof(f610,plain,
! [X0] :
( with_suprema_relstr(X0)
| ~ sP5(X0) ),
inference(cnf_transformation,[],[f353]) ).
fof(f1595,plain,
spl61_150,
inference(avatar_split_clause,[],[f609,f1593]) ).
fof(f1593,plain,
( spl61_150
<=> ! [X0] :
( antisymmetric_relstr(X0)
| ~ sP5(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_150])]) ).
fof(f609,plain,
! [X0] :
( antisymmetric_relstr(X0)
| ~ sP5(X0) ),
inference(cnf_transformation,[],[f353]) ).
fof(f1591,plain,
spl61_149,
inference(avatar_split_clause,[],[f608,f1589]) ).
fof(f1589,plain,
( spl61_149
<=> ! [X0] :
( transitive_relstr(X0)
| ~ sP5(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_149])]) ).
fof(f608,plain,
! [X0] :
( transitive_relstr(X0)
| ~ sP5(X0) ),
inference(cnf_transformation,[],[f353]) ).
fof(f1587,plain,
spl61_148,
inference(avatar_split_clause,[],[f607,f1585]) ).
fof(f1585,plain,
( spl61_148
<=> ! [X0] :
( reflexive_relstr(X0)
| ~ sP5(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_148])]) ).
fof(f607,plain,
! [X0] :
( reflexive_relstr(X0)
| ~ sP5(X0) ),
inference(cnf_transformation,[],[f353]) ).
fof(f1583,plain,
spl61_147,
inference(avatar_split_clause,[],[f606,f1581]) ).
fof(f1581,plain,
( spl61_147
<=> ! [X0] :
( ~ empty_carrier(X0)
| ~ sP5(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_147])]) ).
fof(f606,plain,
! [X0] :
( ~ empty_carrier(X0)
| ~ sP5(X0) ),
inference(cnf_transformation,[],[f353]) ).
fof(f1579,plain,
spl61_146,
inference(avatar_split_clause,[],[f604,f1577]) ).
fof(f1577,plain,
( spl61_146
<=> ! [X0] :
( upper_bounded_relstr(X0)
| ~ sP4(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_146])]) ).
fof(f604,plain,
! [X0] :
( upper_bounded_relstr(X0)
| ~ sP4(X0) ),
inference(cnf_transformation,[],[f352]) ).
fof(f352,plain,
! [X0] :
( ( upper_bounded_relstr(X0)
& with_suprema_relstr(X0)
& antisymmetric_relstr(X0)
& reflexive_relstr(X0)
& ~ empty_carrier(X0) )
| ~ sP4(X0) ),
inference(nnf_transformation,[],[f310]) ).
fof(f1575,plain,
spl61_145,
inference(avatar_split_clause,[],[f603,f1573]) ).
fof(f1573,plain,
( spl61_145
<=> ! [X0] :
( with_suprema_relstr(X0)
| ~ sP4(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_145])]) ).
fof(f603,plain,
! [X0] :
( with_suprema_relstr(X0)
| ~ sP4(X0) ),
inference(cnf_transformation,[],[f352]) ).
fof(f1571,plain,
spl61_144,
inference(avatar_split_clause,[],[f602,f1569]) ).
fof(f1569,plain,
( spl61_144
<=> ! [X0] :
( antisymmetric_relstr(X0)
| ~ sP4(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_144])]) ).
fof(f602,plain,
! [X0] :
( antisymmetric_relstr(X0)
| ~ sP4(X0) ),
inference(cnf_transformation,[],[f352]) ).
fof(f1567,plain,
spl61_143,
inference(avatar_split_clause,[],[f601,f1565]) ).
fof(f1565,plain,
( spl61_143
<=> ! [X0] :
( reflexive_relstr(X0)
| ~ sP4(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_143])]) ).
fof(f601,plain,
! [X0] :
( reflexive_relstr(X0)
| ~ sP4(X0) ),
inference(cnf_transformation,[],[f352]) ).
fof(f1563,plain,
spl61_142,
inference(avatar_split_clause,[],[f600,f1561]) ).
fof(f1561,plain,
( spl61_142
<=> ! [X0] :
( ~ empty_carrier(X0)
| ~ sP4(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_142])]) ).
fof(f600,plain,
! [X0] :
( ~ empty_carrier(X0)
| ~ sP4(X0) ),
inference(cnf_transformation,[],[f352]) ).
fof(f1559,plain,
spl61_141,
inference(avatar_split_clause,[],[f587,f1557]) ).
fof(f1557,plain,
( spl61_141
<=> ! [X0] :
( complete_relstr(X0)
| ~ sP3(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_141])]) ).
fof(f587,plain,
! [X0] :
( complete_relstr(X0)
| ~ sP3(X0) ),
inference(cnf_transformation,[],[f351]) ).
fof(f351,plain,
! [X0] :
( ( complete_relstr(X0)
& antisymmetric_relstr(X0)
& transitive_relstr(X0)
& reflexive_relstr(X0)
& ~ empty_carrier(X0) )
| ~ sP3(X0) ),
inference(nnf_transformation,[],[f308]) ).
fof(f1555,plain,
spl61_140,
inference(avatar_split_clause,[],[f586,f1553]) ).
fof(f1553,plain,
( spl61_140
<=> ! [X0] :
( antisymmetric_relstr(X0)
| ~ sP3(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_140])]) ).
fof(f586,plain,
! [X0] :
( antisymmetric_relstr(X0)
| ~ sP3(X0) ),
inference(cnf_transformation,[],[f351]) ).
fof(f1551,plain,
spl61_139,
inference(avatar_split_clause,[],[f585,f1549]) ).
fof(f1549,plain,
( spl61_139
<=> ! [X0] :
( transitive_relstr(X0)
| ~ sP3(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_139])]) ).
fof(f585,plain,
! [X0] :
( transitive_relstr(X0)
| ~ sP3(X0) ),
inference(cnf_transformation,[],[f351]) ).
fof(f1547,plain,
spl61_138,
inference(avatar_split_clause,[],[f584,f1545]) ).
fof(f1545,plain,
( spl61_138
<=> ! [X0] :
( reflexive_relstr(X0)
| ~ sP3(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_138])]) ).
fof(f584,plain,
! [X0] :
( reflexive_relstr(X0)
| ~ sP3(X0) ),
inference(cnf_transformation,[],[f351]) ).
fof(f1543,plain,
spl61_137,
inference(avatar_split_clause,[],[f583,f1541]) ).
fof(f1541,plain,
( spl61_137
<=> ! [X0] :
( ~ empty_carrier(X0)
| ~ sP3(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_137])]) ).
fof(f583,plain,
! [X0] :
( ~ empty_carrier(X0)
| ~ sP3(X0) ),
inference(cnf_transformation,[],[f351]) ).
fof(f1539,plain,
spl61_136,
inference(avatar_split_clause,[],[f568,f1537]) ).
fof(f568,plain,
! [X0] :
( one_sorted_str(X0)
| ~ rel_str(X0) ),
inference(cnf_transformation,[],[f157]) ).
fof(f157,plain,
! [X0] :
( one_sorted_str(X0)
| ~ rel_str(X0) ),
inference(ennf_transformation,[],[f39]) ).
fof(f39,axiom,
! [X0] :
( rel_str(X0)
=> one_sorted_str(X0) ),
file('/export/starexec/sandbox2/tmp/tmp.XVCyggMQ11/Vampire---4.8_15325',dt_l1_orders_2) ).
fof(f1535,plain,
spl61_135,
inference(avatar_split_clause,[],[f561,f1533]) ).
fof(f561,plain,
! [X0] :
( sP2(X0)
| ~ one_sorted_str(X0) ),
inference(cnf_transformation,[],[f307]) ).
fof(f307,plain,
! [X0] :
( sP2(X0)
| ~ one_sorted_str(X0) ),
inference(definition_folding,[],[f153,f306]) ).
fof(f153,plain,
! [X0] :
( ? [X1] :
( directed_relstr(X1)
& strict_net_str(X1,X0)
& antisymmetric_relstr(X1)
& transitive_relstr(X1)
& reflexive_relstr(X1)
& ~ empty_carrier(X1)
& net_str(X1,X0) )
| ~ one_sorted_str(X0) ),
inference(ennf_transformation,[],[f117]) ).
fof(f117,axiom,
! [X0] :
( one_sorted_str(X0)
=> ? [X1] :
( directed_relstr(X1)
& strict_net_str(X1,X0)
& antisymmetric_relstr(X1)
& transitive_relstr(X1)
& reflexive_relstr(X1)
& ~ empty_carrier(X1)
& net_str(X1,X0) ) ),
file('/export/starexec/sandbox2/tmp/tmp.XVCyggMQ11/Vampire---4.8_15325',rc5_waybel_0) ).
fof(f1531,plain,
spl61_134,
inference(avatar_split_clause,[],[f550,f1529]) ).
fof(f550,plain,
! [X0] :
( sP1(X0)
| ~ top_str(X0) ),
inference(cnf_transformation,[],[f305]) ).
fof(f305,plain,
! [X0] :
( sP1(X0)
| ~ top_str(X0) ),
inference(definition_folding,[],[f149,f304]) ).
fof(f149,plain,
! [X0] :
( ? [X1] :
( boundary_set(X1,X0)
& v5_membered(X1)
& v4_membered(X1)
& v3_membered(X1)
& v2_membered(X1)
& v1_membered(X1)
& empty(X1)
& element(X1,powerset(the_carrier(X0))) )
| ~ top_str(X0) ),
inference(ennf_transformation,[],[f111]) ).
fof(f111,axiom,
! [X0] :
( top_str(X0)
=> ? [X1] :
( boundary_set(X1,X0)
& v5_membered(X1)
& v4_membered(X1)
& v3_membered(X1)
& v2_membered(X1)
& v1_membered(X1)
& empty(X1)
& element(X1,powerset(the_carrier(X0))) ) ),
file('/export/starexec/sandbox2/tmp/tmp.XVCyggMQ11/Vampire---4.8_15325',rc4_tops_1) ).
fof(f1527,plain,
spl61_133,
inference(avatar_split_clause,[],[f539,f1525]) ).
fof(f539,plain,
! [X0] :
( one_sorted_str(X0)
| ~ top_str(X0) ),
inference(cnf_transformation,[],[f145]) ).
fof(f145,plain,
! [X0] :
( one_sorted_str(X0)
| ~ top_str(X0) ),
inference(ennf_transformation,[],[f40]) ).
fof(f40,axiom,
! [X0] :
( top_str(X0)
=> one_sorted_str(X0) ),
file('/export/starexec/sandbox2/tmp/tmp.XVCyggMQ11/Vampire---4.8_15325',dt_l1_pre_topc) ).
fof(f1523,plain,
spl61_132,
inference(avatar_split_clause,[],[f530,f1521]) ).
fof(f530,plain,
! [X0] :
( sP0(X0)
| empty(X0) ),
inference(cnf_transformation,[],[f303]) ).
fof(f303,plain,
! [X0] :
( sP0(X0)
| empty(X0) ),
inference(definition_folding,[],[f141,f302]) ).
fof(f141,plain,
! [X0] :
( ( complete_relstr(boole_POSet(X0))
& with_infima_relstr(boole_POSet(X0))
& with_suprema_relstr(boole_POSet(X0))
& boolean_relstr(boole_POSet(X0))
& complemented_relstr(boole_POSet(X0))
& heyting_relstr(boole_POSet(X0))
& distributive_relstr(boole_POSet(X0))
& ~ v1_yellow_3(boole_POSet(X0))
& join_complete_relstr(boole_POSet(X0))
& up_complete_relstr(boole_POSet(X0))
& bounded_relstr(boole_POSet(X0))
& upper_bounded_relstr(boole_POSet(X0))
& lower_bounded_relstr(boole_POSet(X0))
& antisymmetric_relstr(boole_POSet(X0))
& transitive_relstr(boole_POSet(X0))
& reflexive_relstr(boole_POSet(X0))
& strict_rel_str(boole_POSet(X0))
& ~ trivial_carrier(boole_POSet(X0))
& ~ empty_carrier(boole_POSet(X0)) )
| empty(X0) ),
inference(ennf_transformation,[],[f65]) ).
fof(f65,axiom,
! [X0] :
( ~ empty(X0)
=> ( complete_relstr(boole_POSet(X0))
& with_infima_relstr(boole_POSet(X0))
& with_suprema_relstr(boole_POSet(X0))
& boolean_relstr(boole_POSet(X0))
& complemented_relstr(boole_POSet(X0))
& heyting_relstr(boole_POSet(X0))
& distributive_relstr(boole_POSet(X0))
& ~ v1_yellow_3(boole_POSet(X0))
& join_complete_relstr(boole_POSet(X0))
& up_complete_relstr(boole_POSet(X0))
& bounded_relstr(boole_POSet(X0))
& upper_bounded_relstr(boole_POSet(X0))
& lower_bounded_relstr(boole_POSet(X0))
& antisymmetric_relstr(boole_POSet(X0))
& transitive_relstr(boole_POSet(X0))
& reflexive_relstr(boole_POSet(X0))
& strict_rel_str(boole_POSet(X0))
& ~ trivial_carrier(boole_POSet(X0))
& ~ empty_carrier(boole_POSet(X0)) ) ),
file('/export/starexec/sandbox2/tmp/tmp.XVCyggMQ11/Vampire---4.8_15325',fc2_waybel_7) ).
fof(f1519,plain,
( spl61_130
| spl61_131 ),
inference(avatar_split_clause,[],[f452,f1516,f1512]) ).
fof(f452,plain,
( is_a_convergence_point_of_set(sK12,sK13,sK14)
| in(sK14,lim_points_of_net(sK12,net_of_bool_filter(sK12,cast_as_carrier_subset(sK12),sK13))) ),
inference(cnf_transformation,[],[f331]) ).
fof(f1510,plain,
spl61_129,
inference(avatar_split_clause,[],[f734,f1508]) ).
fof(f734,plain,
! [X0] : subset(X0,X0),
inference(cnf_transformation,[],[f138]) ).
fof(f138,plain,
! [X0] : subset(X0,X0),
inference(rectify,[],[f124]) ).
fof(f124,axiom,
! [X0,X1] : subset(X0,X0),
file('/export/starexec/sandbox2/tmp/tmp.XVCyggMQ11/Vampire---4.8_15325',reflexivity_r1_tarski) ).
fof(f1506,plain,
spl61_128,
inference(avatar_split_clause,[],[f733,f1504]) ).
fof(f1504,plain,
( spl61_128
<=> ! [X0] : finite(sK40(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_128])]) ).
fof(f733,plain,
! [X0] : finite(sK40(X0)),
inference(cnf_transformation,[],[f395]) ).
fof(f1502,plain,
spl61_127,
inference(avatar_split_clause,[],[f732,f1500]) ).
fof(f732,plain,
! [X0] : ~ empty(sK40(X0)),
inference(cnf_transformation,[],[f395]) ).
fof(f1498,plain,
spl61_126,
inference(avatar_split_clause,[],[f730,f1496]) ).
fof(f730,plain,
! [X0] : empty(sK39(X0)),
inference(cnf_transformation,[],[f393]) ).
fof(f1494,plain,
spl61_125,
inference(avatar_split_clause,[],[f510,f1492]) ).
fof(f510,plain,
! [X0] : rel_str(boole_POSet(X0)),
inference(cnf_transformation,[],[f38]) ).
fof(f38,axiom,
! [X0] :
( rel_str(boole_POSet(X0))
& strict_rel_str(boole_POSet(X0)) ),
file('/export/starexec/sandbox2/tmp/tmp.XVCyggMQ11/Vampire---4.8_15325',dt_k3_yellow_1) ).
fof(f1490,plain,
spl61_124,
inference(avatar_split_clause,[],[f494,f1488]) ).
fof(f1488,plain,
( spl61_124
<=> ! [X0] : boolean_relstr(boole_POSet(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_124])]) ).
fof(f494,plain,
! [X0] : boolean_relstr(boole_POSet(X0)),
inference(cnf_transformation,[],[f62]) ).
fof(f62,axiom,
! [X0] :
( complete_relstr(boole_POSet(X0))
& with_infima_relstr(boole_POSet(X0))
& with_suprema_relstr(boole_POSet(X0))
& boolean_relstr(boole_POSet(X0))
& complemented_relstr(boole_POSet(X0))
& heyting_relstr(boole_POSet(X0))
& distributive_relstr(boole_POSet(X0))
& ~ v1_yellow_3(boole_POSet(X0))
& join_complete_relstr(boole_POSet(X0))
& up_complete_relstr(boole_POSet(X0))
& bounded_relstr(boole_POSet(X0))
& upper_bounded_relstr(boole_POSet(X0))
& lower_bounded_relstr(boole_POSet(X0))
& antisymmetric_relstr(boole_POSet(X0))
& transitive_relstr(boole_POSet(X0))
& reflexive_relstr(boole_POSet(X0))
& strict_rel_str(boole_POSet(X0))
& ~ empty_carrier(boole_POSet(X0)) ),
file('/export/starexec/sandbox2/tmp/tmp.XVCyggMQ11/Vampire---4.8_15325',fc1_waybel_7) ).
fof(f1486,plain,
spl61_123,
inference(avatar_split_clause,[],[f493,f1484]) ).
fof(f1484,plain,
( spl61_123
<=> ! [X0] : complemented_relstr(boole_POSet(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_123])]) ).
fof(f493,plain,
! [X0] : complemented_relstr(boole_POSet(X0)),
inference(cnf_transformation,[],[f62]) ).
fof(f1482,plain,
spl61_122,
inference(avatar_split_clause,[],[f492,f1480]) ).
fof(f1480,plain,
( spl61_122
<=> ! [X0] : heyting_relstr(boole_POSet(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_122])]) ).
fof(f492,plain,
! [X0] : heyting_relstr(boole_POSet(X0)),
inference(cnf_transformation,[],[f62]) ).
fof(f1478,plain,
spl61_121,
inference(avatar_split_clause,[],[f491,f1476]) ).
fof(f1476,plain,
( spl61_121
<=> ! [X0] : distributive_relstr(boole_POSet(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_121])]) ).
fof(f491,plain,
! [X0] : distributive_relstr(boole_POSet(X0)),
inference(cnf_transformation,[],[f62]) ).
fof(f1474,plain,
spl61_120,
inference(avatar_split_clause,[],[f479,f1472]) ).
fof(f1472,plain,
( spl61_120
<=> ! [X0] : complete_relstr(boole_POSet(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_120])]) ).
fof(f479,plain,
! [X0] : complete_relstr(boole_POSet(X0)),
inference(cnf_transformation,[],[f81]) ).
fof(f81,axiom,
! [X0] :
( complete_relstr(boole_POSet(X0))
& with_infima_relstr(boole_POSet(X0))
& with_suprema_relstr(boole_POSet(X0))
& ~ v1_yellow_3(boole_POSet(X0))
& join_complete_relstr(boole_POSet(X0))
& up_complete_relstr(boole_POSet(X0))
& directed_relstr(boole_POSet(X0))
& bounded_relstr(boole_POSet(X0))
& upper_bounded_relstr(boole_POSet(X0))
& lower_bounded_relstr(boole_POSet(X0))
& antisymmetric_relstr(boole_POSet(X0))
& transitive_relstr(boole_POSet(X0))
& reflexive_relstr(boole_POSet(X0))
& strict_rel_str(boole_POSet(X0))
& ~ empty_carrier(boole_POSet(X0)) ),
file('/export/starexec/sandbox2/tmp/tmp.XVCyggMQ11/Vampire---4.8_15325',fc8_yellow_6) ).
fof(f1470,plain,
spl61_119,
inference(avatar_split_clause,[],[f478,f1468]) ).
fof(f478,plain,
! [X0] : with_infima_relstr(boole_POSet(X0)),
inference(cnf_transformation,[],[f81]) ).
fof(f1466,plain,
spl61_118,
inference(avatar_split_clause,[],[f477,f1464]) ).
fof(f477,plain,
! [X0] : with_suprema_relstr(boole_POSet(X0)),
inference(cnf_transformation,[],[f81]) ).
fof(f1462,plain,
spl61_117,
inference(avatar_split_clause,[],[f476,f1460]) ).
fof(f1460,plain,
( spl61_117
<=> ! [X0] : ~ v1_yellow_3(boole_POSet(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_117])]) ).
fof(f476,plain,
! [X0] : ~ v1_yellow_3(boole_POSet(X0)),
inference(cnf_transformation,[],[f81]) ).
fof(f1458,plain,
spl61_116,
inference(avatar_split_clause,[],[f475,f1456]) ).
fof(f1456,plain,
( spl61_116
<=> ! [X0] : join_complete_relstr(boole_POSet(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_116])]) ).
fof(f475,plain,
! [X0] : join_complete_relstr(boole_POSet(X0)),
inference(cnf_transformation,[],[f81]) ).
fof(f1454,plain,
spl61_115,
inference(avatar_split_clause,[],[f474,f1452]) ).
fof(f1452,plain,
( spl61_115
<=> ! [X0] : up_complete_relstr(boole_POSet(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_115])]) ).
fof(f474,plain,
! [X0] : up_complete_relstr(boole_POSet(X0)),
inference(cnf_transformation,[],[f81]) ).
fof(f1450,plain,
spl61_114,
inference(avatar_split_clause,[],[f473,f1448]) ).
fof(f1448,plain,
( spl61_114
<=> ! [X0] : directed_relstr(boole_POSet(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_114])]) ).
fof(f473,plain,
! [X0] : directed_relstr(boole_POSet(X0)),
inference(cnf_transformation,[],[f81]) ).
fof(f1446,plain,
spl61_113,
inference(avatar_split_clause,[],[f472,f1444]) ).
fof(f1444,plain,
( spl61_113
<=> ! [X0] : bounded_relstr(boole_POSet(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_113])]) ).
fof(f472,plain,
! [X0] : bounded_relstr(boole_POSet(X0)),
inference(cnf_transformation,[],[f81]) ).
fof(f1442,plain,
spl61_112,
inference(avatar_split_clause,[],[f471,f1440]) ).
fof(f471,plain,
! [X0] : upper_bounded_relstr(boole_POSet(X0)),
inference(cnf_transformation,[],[f81]) ).
fof(f1438,plain,
spl61_111,
inference(avatar_split_clause,[],[f470,f1436]) ).
fof(f1436,plain,
( spl61_111
<=> ! [X0] : lower_bounded_relstr(boole_POSet(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_111])]) ).
fof(f470,plain,
! [X0] : lower_bounded_relstr(boole_POSet(X0)),
inference(cnf_transformation,[],[f81]) ).
fof(f1434,plain,
spl61_110,
inference(avatar_split_clause,[],[f464,f1432]) ).
fof(f1432,plain,
( spl61_110
<=> ! [X0] : antisymmetric_relstr(boole_POSet(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_110])]) ).
fof(f464,plain,
! [X0] : antisymmetric_relstr(boole_POSet(X0)),
inference(cnf_transformation,[],[f78]) ).
fof(f78,axiom,
! [X0] :
( antisymmetric_relstr(boole_POSet(X0))
& transitive_relstr(boole_POSet(X0))
& reflexive_relstr(boole_POSet(X0))
& strict_rel_str(boole_POSet(X0))
& ~ empty_carrier(boole_POSet(X0)) ),
file('/export/starexec/sandbox2/tmp/tmp.XVCyggMQ11/Vampire---4.8_15325',fc7_yellow_1) ).
fof(f1430,plain,
spl61_109,
inference(avatar_split_clause,[],[f463,f1428]) ).
fof(f1428,plain,
( spl61_109
<=> ! [X0] : transitive_relstr(boole_POSet(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_109])]) ).
fof(f463,plain,
! [X0] : transitive_relstr(boole_POSet(X0)),
inference(cnf_transformation,[],[f78]) ).
fof(f1426,plain,
spl61_108,
inference(avatar_split_clause,[],[f462,f1424]) ).
fof(f462,plain,
! [X0] : reflexive_relstr(boole_POSet(X0)),
inference(cnf_transformation,[],[f78]) ).
fof(f1422,plain,
spl61_107,
inference(avatar_split_clause,[],[f461,f1420]) ).
fof(f461,plain,
! [X0] : strict_rel_str(boole_POSet(X0)),
inference(cnf_transformation,[],[f78]) ).
fof(f1418,plain,
spl61_106,
inference(avatar_split_clause,[],[f460,f1416]) ).
fof(f460,plain,
! [X0] : ~ empty_carrier(boole_POSet(X0)),
inference(cnf_transformation,[],[f78]) ).
fof(f1414,plain,
spl61_105,
inference(avatar_split_clause,[],[f459,f1412]) ).
fof(f459,plain,
! [X0] : ~ empty(powerset(X0)),
inference(cnf_transformation,[],[f61]) ).
fof(f61,axiom,
! [X0] : ~ empty(powerset(X0)),
file('/export/starexec/sandbox2/tmp/tmp.XVCyggMQ11/Vampire---4.8_15325',fc1_subset_1) ).
fof(f1410,plain,
spl61_104,
inference(avatar_split_clause,[],[f890,f1407]) ).
fof(f1407,plain,
( spl61_104
<=> relation(sK60) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_104])]) ).
fof(f890,plain,
relation(sK60),
inference(cnf_transformation,[],[f442]) ).
fof(f442,plain,
( relation(sK60)
& empty(sK60) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK60])],[f92,f441]) ).
fof(f441,plain,
( ? [X0] :
( relation(X0)
& empty(X0) )
=> ( relation(sK60)
& empty(sK60) ) ),
introduced(choice_axiom,[]) ).
fof(f92,axiom,
? [X0] :
( relation(X0)
& empty(X0) ),
file('/export/starexec/sandbox2/tmp/tmp.XVCyggMQ11/Vampire---4.8_15325',rc1_relat_1) ).
fof(f1405,plain,
spl61_103,
inference(avatar_split_clause,[],[f889,f1402]) ).
fof(f889,plain,
empty(sK60),
inference(cnf_transformation,[],[f442]) ).
fof(f1400,plain,
spl61_102,
inference(avatar_split_clause,[],[f888,f1397]) ).
fof(f1397,plain,
( spl61_102
<=> bounded_relstr(sK59) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_102])]) ).
fof(f888,plain,
bounded_relstr(sK59),
inference(cnf_transformation,[],[f440]) ).
fof(f440,plain,
( bounded_relstr(sK59)
& upper_bounded_relstr(sK59)
& lower_bounded_relstr(sK59)
& complete_relstr(sK59)
& with_infima_relstr(sK59)
& with_suprema_relstr(sK59)
& antisymmetric_relstr(sK59)
& transitive_relstr(sK59)
& reflexive_relstr(sK59)
& ~ empty_carrier(sK59)
& rel_str(sK59) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK59])],[f104,f439]) ).
fof(f439,plain,
( ? [X0] :
( bounded_relstr(X0)
& upper_bounded_relstr(X0)
& lower_bounded_relstr(X0)
& complete_relstr(X0)
& with_infima_relstr(X0)
& with_suprema_relstr(X0)
& antisymmetric_relstr(X0)
& transitive_relstr(X0)
& reflexive_relstr(X0)
& ~ empty_carrier(X0)
& rel_str(X0) )
=> ( bounded_relstr(sK59)
& upper_bounded_relstr(sK59)
& lower_bounded_relstr(sK59)
& complete_relstr(sK59)
& with_infima_relstr(sK59)
& with_suprema_relstr(sK59)
& antisymmetric_relstr(sK59)
& transitive_relstr(sK59)
& reflexive_relstr(sK59)
& ~ empty_carrier(sK59)
& rel_str(sK59) ) ),
introduced(choice_axiom,[]) ).
fof(f104,axiom,
? [X0] :
( bounded_relstr(X0)
& upper_bounded_relstr(X0)
& lower_bounded_relstr(X0)
& complete_relstr(X0)
& with_infima_relstr(X0)
& with_suprema_relstr(X0)
& antisymmetric_relstr(X0)
& transitive_relstr(X0)
& reflexive_relstr(X0)
& ~ empty_carrier(X0)
& rel_str(X0) ),
file('/export/starexec/sandbox2/tmp/tmp.XVCyggMQ11/Vampire---4.8_15325',rc2_yellow_0) ).
fof(f1395,plain,
spl61_101,
inference(avatar_split_clause,[],[f887,f1392]) ).
fof(f887,plain,
upper_bounded_relstr(sK59),
inference(cnf_transformation,[],[f440]) ).
fof(f1390,plain,
spl61_100,
inference(avatar_split_clause,[],[f886,f1387]) ).
fof(f886,plain,
lower_bounded_relstr(sK59),
inference(cnf_transformation,[],[f440]) ).
fof(f1385,plain,
spl61_99,
inference(avatar_split_clause,[],[f885,f1382]) ).
fof(f885,plain,
complete_relstr(sK59),
inference(cnf_transformation,[],[f440]) ).
fof(f1380,plain,
spl61_98,
inference(avatar_split_clause,[],[f884,f1377]) ).
fof(f884,plain,
with_infima_relstr(sK59),
inference(cnf_transformation,[],[f440]) ).
fof(f1375,plain,
spl61_97,
inference(avatar_split_clause,[],[f883,f1372]) ).
fof(f883,plain,
with_suprema_relstr(sK59),
inference(cnf_transformation,[],[f440]) ).
fof(f1370,plain,
spl61_96,
inference(avatar_split_clause,[],[f882,f1367]) ).
fof(f882,plain,
antisymmetric_relstr(sK59),
inference(cnf_transformation,[],[f440]) ).
fof(f1365,plain,
spl61_95,
inference(avatar_split_clause,[],[f881,f1362]) ).
fof(f881,plain,
transitive_relstr(sK59),
inference(cnf_transformation,[],[f440]) ).
fof(f1360,plain,
spl61_94,
inference(avatar_split_clause,[],[f880,f1357]) ).
fof(f880,plain,
reflexive_relstr(sK59),
inference(cnf_transformation,[],[f440]) ).
fof(f1355,plain,
~ spl61_93,
inference(avatar_split_clause,[],[f879,f1352]) ).
fof(f879,plain,
~ empty_carrier(sK59),
inference(cnf_transformation,[],[f440]) ).
fof(f1350,plain,
spl61_92,
inference(avatar_split_clause,[],[f878,f1347]) ).
fof(f878,plain,
rel_str(sK59),
inference(cnf_transformation,[],[f440]) ).
fof(f1345,plain,
spl61_91,
inference(avatar_split_clause,[],[f877,f1342]) ).
fof(f1342,plain,
( spl61_91
<=> connected_relstr(sK58) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_91])]) ).
fof(f877,plain,
connected_relstr(sK58),
inference(cnf_transformation,[],[f438]) ).
fof(f438,plain,
( connected_relstr(sK58)
& antisymmetric_relstr(sK58)
& transitive_relstr(sK58)
& reflexive_relstr(sK58)
& ~ empty_carrier(sK58)
& rel_str(sK58) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK58])],[f88,f437]) ).
fof(f437,plain,
( ? [X0] :
( connected_relstr(X0)
& antisymmetric_relstr(X0)
& transitive_relstr(X0)
& reflexive_relstr(X0)
& ~ empty_carrier(X0)
& rel_str(X0) )
=> ( connected_relstr(sK58)
& antisymmetric_relstr(sK58)
& transitive_relstr(sK58)
& reflexive_relstr(sK58)
& ~ empty_carrier(sK58)
& rel_str(sK58) ) ),
introduced(choice_axiom,[]) ).
fof(f88,axiom,
? [X0] :
( connected_relstr(X0)
& antisymmetric_relstr(X0)
& transitive_relstr(X0)
& reflexive_relstr(X0)
& ~ empty_carrier(X0)
& rel_str(X0) ),
file('/export/starexec/sandbox2/tmp/tmp.XVCyggMQ11/Vampire---4.8_15325',rc12_waybel_0) ).
fof(f1340,plain,
spl61_90,
inference(avatar_split_clause,[],[f876,f1337]) ).
fof(f876,plain,
antisymmetric_relstr(sK58),
inference(cnf_transformation,[],[f438]) ).
fof(f1335,plain,
spl61_89,
inference(avatar_split_clause,[],[f875,f1332]) ).
fof(f1332,plain,
( spl61_89
<=> transitive_relstr(sK58) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_89])]) ).
fof(f875,plain,
transitive_relstr(sK58),
inference(cnf_transformation,[],[f438]) ).
fof(f1330,plain,
spl61_88,
inference(avatar_split_clause,[],[f874,f1327]) ).
fof(f874,plain,
reflexive_relstr(sK58),
inference(cnf_transformation,[],[f438]) ).
fof(f1325,plain,
~ spl61_87,
inference(avatar_split_clause,[],[f873,f1322]) ).
fof(f873,plain,
~ empty_carrier(sK58),
inference(cnf_transformation,[],[f438]) ).
fof(f1320,plain,
spl61_86,
inference(avatar_split_clause,[],[f872,f1317]) ).
fof(f872,plain,
rel_str(sK58),
inference(cnf_transformation,[],[f438]) ).
fof(f1315,plain,
spl61_85,
inference(avatar_split_clause,[],[f871,f1312]) ).
fof(f871,plain,
join_complete_relstr(sK57),
inference(cnf_transformation,[],[f436]) ).
fof(f436,plain,
( join_complete_relstr(sK57)
& up_complete_relstr(sK57)
& bounded_relstr(sK57)
& upper_bounded_relstr(sK57)
& lower_bounded_relstr(sK57)
& complete_relstr(sK57)
& with_infima_relstr(sK57)
& with_suprema_relstr(sK57)
& antisymmetric_relstr(sK57)
& transitive_relstr(sK57)
& reflexive_relstr(sK57)
& strict_rel_str(sK57)
& ~ empty_carrier(sK57)
& rel_str(sK57) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK57])],[f89,f435]) ).
fof(f435,plain,
( ? [X0] :
( join_complete_relstr(X0)
& up_complete_relstr(X0)
& bounded_relstr(X0)
& upper_bounded_relstr(X0)
& lower_bounded_relstr(X0)
& complete_relstr(X0)
& with_infima_relstr(X0)
& with_suprema_relstr(X0)
& antisymmetric_relstr(X0)
& transitive_relstr(X0)
& reflexive_relstr(X0)
& strict_rel_str(X0)
& ~ empty_carrier(X0)
& rel_str(X0) )
=> ( join_complete_relstr(sK57)
& up_complete_relstr(sK57)
& bounded_relstr(sK57)
& upper_bounded_relstr(sK57)
& lower_bounded_relstr(sK57)
& complete_relstr(sK57)
& with_infima_relstr(sK57)
& with_suprema_relstr(sK57)
& antisymmetric_relstr(sK57)
& transitive_relstr(sK57)
& reflexive_relstr(sK57)
& strict_rel_str(sK57)
& ~ empty_carrier(sK57)
& rel_str(sK57) ) ),
introduced(choice_axiom,[]) ).
fof(f89,axiom,
? [X0] :
( join_complete_relstr(X0)
& up_complete_relstr(X0)
& bounded_relstr(X0)
& upper_bounded_relstr(X0)
& lower_bounded_relstr(X0)
& complete_relstr(X0)
& with_infima_relstr(X0)
& with_suprema_relstr(X0)
& antisymmetric_relstr(X0)
& transitive_relstr(X0)
& reflexive_relstr(X0)
& strict_rel_str(X0)
& ~ empty_carrier(X0)
& rel_str(X0) ),
file('/export/starexec/sandbox2/tmp/tmp.XVCyggMQ11/Vampire---4.8_15325',rc13_waybel_0) ).
fof(f1310,plain,
spl61_84,
inference(avatar_split_clause,[],[f870,f1307]) ).
fof(f870,plain,
up_complete_relstr(sK57),
inference(cnf_transformation,[],[f436]) ).
fof(f1305,plain,
spl61_83,
inference(avatar_split_clause,[],[f869,f1302]) ).
fof(f1302,plain,
( spl61_83
<=> bounded_relstr(sK57) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_83])]) ).
fof(f869,plain,
bounded_relstr(sK57),
inference(cnf_transformation,[],[f436]) ).
fof(f1300,plain,
spl61_82,
inference(avatar_split_clause,[],[f868,f1297]) ).
fof(f868,plain,
upper_bounded_relstr(sK57),
inference(cnf_transformation,[],[f436]) ).
fof(f1295,plain,
spl61_81,
inference(avatar_split_clause,[],[f867,f1292]) ).
fof(f867,plain,
lower_bounded_relstr(sK57),
inference(cnf_transformation,[],[f436]) ).
fof(f1290,plain,
spl61_80,
inference(avatar_split_clause,[],[f866,f1287]) ).
fof(f1287,plain,
( spl61_80
<=> complete_relstr(sK57) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_80])]) ).
fof(f866,plain,
complete_relstr(sK57),
inference(cnf_transformation,[],[f436]) ).
fof(f1285,plain,
spl61_79,
inference(avatar_split_clause,[],[f865,f1282]) ).
fof(f865,plain,
with_infima_relstr(sK57),
inference(cnf_transformation,[],[f436]) ).
fof(f1280,plain,
spl61_78,
inference(avatar_split_clause,[],[f864,f1277]) ).
fof(f864,plain,
with_suprema_relstr(sK57),
inference(cnf_transformation,[],[f436]) ).
fof(f1275,plain,
spl61_77,
inference(avatar_split_clause,[],[f863,f1272]) ).
fof(f863,plain,
antisymmetric_relstr(sK57),
inference(cnf_transformation,[],[f436]) ).
fof(f1270,plain,
spl61_76,
inference(avatar_split_clause,[],[f862,f1267]) ).
fof(f862,plain,
transitive_relstr(sK57),
inference(cnf_transformation,[],[f436]) ).
fof(f1265,plain,
spl61_75,
inference(avatar_split_clause,[],[f861,f1262]) ).
fof(f861,plain,
reflexive_relstr(sK57),
inference(cnf_transformation,[],[f436]) ).
fof(f1260,plain,
spl61_74,
inference(avatar_split_clause,[],[f860,f1257]) ).
fof(f860,plain,
strict_rel_str(sK57),
inference(cnf_transformation,[],[f436]) ).
fof(f1255,plain,
~ spl61_73,
inference(avatar_split_clause,[],[f859,f1252]) ).
fof(f859,plain,
~ empty_carrier(sK57),
inference(cnf_transformation,[],[f436]) ).
fof(f1250,plain,
spl61_72,
inference(avatar_split_clause,[],[f858,f1247]) ).
fof(f858,plain,
rel_str(sK57),
inference(cnf_transformation,[],[f436]) ).
fof(f1245,plain,
spl61_71,
inference(avatar_split_clause,[],[f857,f1242]) ).
fof(f857,plain,
trivial_carrier(sK56),
inference(cnf_transformation,[],[f434]) ).
fof(f434,plain,
( trivial_carrier(sK56)
& complete_relstr(sK56)
& with_infima_relstr(sK56)
& with_suprema_relstr(sK56)
& antisymmetric_relstr(sK56)
& transitive_relstr(sK56)
& reflexive_relstr(sK56)
& strict_rel_str(sK56)
& ~ empty_carrier(sK56)
& rel_str(sK56) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK56])],[f97,f433]) ).
fof(f433,plain,
( ? [X0] :
( trivial_carrier(X0)
& complete_relstr(X0)
& with_infima_relstr(X0)
& with_suprema_relstr(X0)
& antisymmetric_relstr(X0)
& transitive_relstr(X0)
& reflexive_relstr(X0)
& strict_rel_str(X0)
& ~ empty_carrier(X0)
& rel_str(X0) )
=> ( trivial_carrier(sK56)
& complete_relstr(sK56)
& with_infima_relstr(sK56)
& with_suprema_relstr(sK56)
& antisymmetric_relstr(sK56)
& transitive_relstr(sK56)
& reflexive_relstr(sK56)
& strict_rel_str(sK56)
& ~ empty_carrier(sK56)
& rel_str(sK56) ) ),
introduced(choice_axiom,[]) ).
fof(f97,axiom,
? [X0] :
( trivial_carrier(X0)
& complete_relstr(X0)
& with_infima_relstr(X0)
& with_suprema_relstr(X0)
& antisymmetric_relstr(X0)
& transitive_relstr(X0)
& reflexive_relstr(X0)
& strict_rel_str(X0)
& ~ empty_carrier(X0)
& rel_str(X0) ),
file('/export/starexec/sandbox2/tmp/tmp.XVCyggMQ11/Vampire---4.8_15325',rc1_yellow_0) ).
fof(f1240,plain,
spl61_70,
inference(avatar_split_clause,[],[f856,f1237]) ).
fof(f856,plain,
complete_relstr(sK56),
inference(cnf_transformation,[],[f434]) ).
fof(f1235,plain,
spl61_69,
inference(avatar_split_clause,[],[f855,f1232]) ).
fof(f855,plain,
with_infima_relstr(sK56),
inference(cnf_transformation,[],[f434]) ).
fof(f1230,plain,
spl61_68,
inference(avatar_split_clause,[],[f854,f1227]) ).
fof(f854,plain,
with_suprema_relstr(sK56),
inference(cnf_transformation,[],[f434]) ).
fof(f1225,plain,
spl61_67,
inference(avatar_split_clause,[],[f853,f1222]) ).
fof(f853,plain,
antisymmetric_relstr(sK56),
inference(cnf_transformation,[],[f434]) ).
fof(f1220,plain,
spl61_66,
inference(avatar_split_clause,[],[f852,f1217]) ).
fof(f852,plain,
transitive_relstr(sK56),
inference(cnf_transformation,[],[f434]) ).
fof(f1215,plain,
spl61_65,
inference(avatar_split_clause,[],[f851,f1212]) ).
fof(f851,plain,
reflexive_relstr(sK56),
inference(cnf_transformation,[],[f434]) ).
fof(f1210,plain,
spl61_64,
inference(avatar_split_clause,[],[f850,f1207]) ).
fof(f850,plain,
strict_rel_str(sK56),
inference(cnf_transformation,[],[f434]) ).
fof(f1205,plain,
~ spl61_63,
inference(avatar_split_clause,[],[f849,f1202]) ).
fof(f849,plain,
~ empty_carrier(sK56),
inference(cnf_transformation,[],[f434]) ).
fof(f1200,plain,
spl61_62,
inference(avatar_split_clause,[],[f848,f1197]) ).
fof(f848,plain,
rel_str(sK56),
inference(cnf_transformation,[],[f434]) ).
fof(f1195,plain,
spl61_61,
inference(avatar_split_clause,[],[f847,f1192]) ).
fof(f847,plain,
complete_relstr(sK55),
inference(cnf_transformation,[],[f432]) ).
fof(f432,plain,
( complete_relstr(sK55)
& with_infima_relstr(sK55)
& with_suprema_relstr(sK55)
& antisymmetric_relstr(sK55)
& transitive_relstr(sK55)
& reflexive_relstr(sK55)
& strict_rel_str(sK55)
& ~ empty_carrier(sK55)
& rel_str(sK55) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK55])],[f98,f431]) ).
fof(f431,plain,
( ? [X0] :
( complete_relstr(X0)
& with_infima_relstr(X0)
& with_suprema_relstr(X0)
& antisymmetric_relstr(X0)
& transitive_relstr(X0)
& reflexive_relstr(X0)
& strict_rel_str(X0)
& ~ empty_carrier(X0)
& rel_str(X0) )
=> ( complete_relstr(sK55)
& with_infima_relstr(sK55)
& with_suprema_relstr(sK55)
& antisymmetric_relstr(sK55)
& transitive_relstr(sK55)
& reflexive_relstr(sK55)
& strict_rel_str(sK55)
& ~ empty_carrier(sK55)
& rel_str(sK55) ) ),
introduced(choice_axiom,[]) ).
fof(f98,axiom,
? [X0] :
( complete_relstr(X0)
& with_infima_relstr(X0)
& with_suprema_relstr(X0)
& antisymmetric_relstr(X0)
& transitive_relstr(X0)
& reflexive_relstr(X0)
& strict_rel_str(X0)
& ~ empty_carrier(X0)
& rel_str(X0) ),
file('/export/starexec/sandbox2/tmp/tmp.XVCyggMQ11/Vampire---4.8_15325',rc2_lattice3) ).
fof(f1190,plain,
spl61_60,
inference(avatar_split_clause,[],[f846,f1187]) ).
fof(f846,plain,
with_infima_relstr(sK55),
inference(cnf_transformation,[],[f432]) ).
fof(f1185,plain,
spl61_59,
inference(avatar_split_clause,[],[f845,f1182]) ).
fof(f845,plain,
with_suprema_relstr(sK55),
inference(cnf_transformation,[],[f432]) ).
fof(f1180,plain,
spl61_58,
inference(avatar_split_clause,[],[f844,f1177]) ).
fof(f844,plain,
antisymmetric_relstr(sK55),
inference(cnf_transformation,[],[f432]) ).
fof(f1175,plain,
spl61_57,
inference(avatar_split_clause,[],[f843,f1172]) ).
fof(f843,plain,
transitive_relstr(sK55),
inference(cnf_transformation,[],[f432]) ).
fof(f1170,plain,
spl61_56,
inference(avatar_split_clause,[],[f842,f1167]) ).
fof(f842,plain,
reflexive_relstr(sK55),
inference(cnf_transformation,[],[f432]) ).
fof(f1165,plain,
spl61_55,
inference(avatar_split_clause,[],[f841,f1162]) ).
fof(f841,plain,
strict_rel_str(sK55),
inference(cnf_transformation,[],[f432]) ).
fof(f1160,plain,
~ spl61_54,
inference(avatar_split_clause,[],[f840,f1157]) ).
fof(f840,plain,
~ empty_carrier(sK55),
inference(cnf_transformation,[],[f432]) ).
fof(f1155,plain,
spl61_53,
inference(avatar_split_clause,[],[f839,f1152]) ).
fof(f839,plain,
rel_str(sK55),
inference(cnf_transformation,[],[f432]) ).
fof(f1150,plain,
spl61_52,
inference(avatar_split_clause,[],[f838,f1147]) ).
fof(f838,plain,
complete_relstr(sK54),
inference(cnf_transformation,[],[f430]) ).
fof(f430,plain,
( complete_relstr(sK54)
& antisymmetric_relstr(sK54)
& transitive_relstr(sK54)
& reflexive_relstr(sK54)
& strict_rel_str(sK54)
& ~ empty_carrier(sK54)
& rel_str(sK54) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK54])],[f91,f429]) ).
fof(f429,plain,
( ? [X0] :
( complete_relstr(X0)
& antisymmetric_relstr(X0)
& transitive_relstr(X0)
& reflexive_relstr(X0)
& strict_rel_str(X0)
& ~ empty_carrier(X0)
& rel_str(X0) )
=> ( complete_relstr(sK54)
& antisymmetric_relstr(sK54)
& transitive_relstr(sK54)
& reflexive_relstr(sK54)
& strict_rel_str(sK54)
& ~ empty_carrier(sK54)
& rel_str(sK54) ) ),
introduced(choice_axiom,[]) ).
fof(f91,axiom,
? [X0] :
( complete_relstr(X0)
& antisymmetric_relstr(X0)
& transitive_relstr(X0)
& reflexive_relstr(X0)
& strict_rel_str(X0)
& ~ empty_carrier(X0)
& rel_str(X0) ),
file('/export/starexec/sandbox2/tmp/tmp.XVCyggMQ11/Vampire---4.8_15325',rc1_lattice3) ).
fof(f1145,plain,
spl61_51,
inference(avatar_split_clause,[],[f837,f1142]) ).
fof(f837,plain,
antisymmetric_relstr(sK54),
inference(cnf_transformation,[],[f430]) ).
fof(f1140,plain,
spl61_50,
inference(avatar_split_clause,[],[f836,f1137]) ).
fof(f836,plain,
transitive_relstr(sK54),
inference(cnf_transformation,[],[f430]) ).
fof(f1135,plain,
spl61_49,
inference(avatar_split_clause,[],[f835,f1132]) ).
fof(f835,plain,
reflexive_relstr(sK54),
inference(cnf_transformation,[],[f430]) ).
fof(f1130,plain,
spl61_48,
inference(avatar_split_clause,[],[f834,f1127]) ).
fof(f834,plain,
strict_rel_str(sK54),
inference(cnf_transformation,[],[f430]) ).
fof(f1125,plain,
~ spl61_47,
inference(avatar_split_clause,[],[f833,f1122]) ).
fof(f833,plain,
~ empty_carrier(sK54),
inference(cnf_transformation,[],[f430]) ).
fof(f1120,plain,
spl61_46,
inference(avatar_split_clause,[],[f832,f1117]) ).
fof(f832,plain,
rel_str(sK54),
inference(cnf_transformation,[],[f430]) ).
fof(f1115,plain,
spl61_45,
inference(avatar_split_clause,[],[f831,f1112]) ).
fof(f1112,plain,
( spl61_45
<=> directed_relstr(sK53) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_45])]) ).
fof(f831,plain,
directed_relstr(sK53),
inference(cnf_transformation,[],[f428]) ).
fof(f428,plain,
( directed_relstr(sK53)
& transitive_relstr(sK53)
& strict_rel_str(sK53)
& ~ empty_carrier(sK53)
& rel_str(sK53) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK53])],[f114,f427]) ).
fof(f427,plain,
( ? [X0] :
( directed_relstr(X0)
& transitive_relstr(X0)
& strict_rel_str(X0)
& ~ empty_carrier(X0)
& rel_str(X0) )
=> ( directed_relstr(sK53)
& transitive_relstr(sK53)
& strict_rel_str(sK53)
& ~ empty_carrier(sK53)
& rel_str(sK53) ) ),
introduced(choice_axiom,[]) ).
fof(f114,axiom,
? [X0] :
( directed_relstr(X0)
& transitive_relstr(X0)
& strict_rel_str(X0)
& ~ empty_carrier(X0)
& rel_str(X0) ),
file('/export/starexec/sandbox2/tmp/tmp.XVCyggMQ11/Vampire---4.8_15325',rc4_yellow_6) ).
fof(f1110,plain,
spl61_44,
inference(avatar_split_clause,[],[f830,f1107]) ).
fof(f1107,plain,
( spl61_44
<=> transitive_relstr(sK53) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_44])]) ).
fof(f830,plain,
transitive_relstr(sK53),
inference(cnf_transformation,[],[f428]) ).
fof(f1105,plain,
spl61_43,
inference(avatar_split_clause,[],[f829,f1102]) ).
fof(f829,plain,
strict_rel_str(sK53),
inference(cnf_transformation,[],[f428]) ).
fof(f1100,plain,
~ spl61_42,
inference(avatar_split_clause,[],[f828,f1097]) ).
fof(f1097,plain,
( spl61_42
<=> empty_carrier(sK53) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_42])]) ).
fof(f828,plain,
~ empty_carrier(sK53),
inference(cnf_transformation,[],[f428]) ).
fof(f1095,plain,
spl61_41,
inference(avatar_split_clause,[],[f827,f1092]) ).
fof(f827,plain,
rel_str(sK53),
inference(cnf_transformation,[],[f428]) ).
fof(f1090,plain,
spl61_40,
inference(avatar_split_clause,[],[f826,f1087]) ).
fof(f826,plain,
with_infima_relstr(sK52),
inference(cnf_transformation,[],[f426]) ).
fof(f426,plain,
( with_infima_relstr(sK52)
& with_suprema_relstr(sK52)
& boolean_relstr(sK52)
& complemented_relstr(sK52)
& heyting_relstr(sK52)
& distributive_relstr(sK52)
& ~ v1_yellow_3(sK52)
& bounded_relstr(sK52)
& upper_bounded_relstr(sK52)
& lower_bounded_relstr(sK52)
& antisymmetric_relstr(sK52)
& transitive_relstr(sK52)
& reflexive_relstr(sK52)
& strict_rel_str(sK52)
& ~ trivial_carrier(sK52)
& ~ empty_carrier(sK52)
& rel_str(sK52) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK52])],[f96,f425]) ).
fof(f425,plain,
( ? [X0] :
( with_infima_relstr(X0)
& with_suprema_relstr(X0)
& boolean_relstr(X0)
& complemented_relstr(X0)
& heyting_relstr(X0)
& distributive_relstr(X0)
& ~ v1_yellow_3(X0)
& bounded_relstr(X0)
& upper_bounded_relstr(X0)
& lower_bounded_relstr(X0)
& antisymmetric_relstr(X0)
& transitive_relstr(X0)
& reflexive_relstr(X0)
& strict_rel_str(X0)
& ~ trivial_carrier(X0)
& ~ empty_carrier(X0)
& rel_str(X0) )
=> ( with_infima_relstr(sK52)
& with_suprema_relstr(sK52)
& boolean_relstr(sK52)
& complemented_relstr(sK52)
& heyting_relstr(sK52)
& distributive_relstr(sK52)
& ~ v1_yellow_3(sK52)
& bounded_relstr(sK52)
& upper_bounded_relstr(sK52)
& lower_bounded_relstr(sK52)
& antisymmetric_relstr(sK52)
& transitive_relstr(sK52)
& reflexive_relstr(sK52)
& strict_rel_str(sK52)
& ~ trivial_carrier(sK52)
& ~ empty_carrier(sK52)
& rel_str(sK52) ) ),
introduced(choice_axiom,[]) ).
fof(f96,axiom,
? [X0] :
( with_infima_relstr(X0)
& with_suprema_relstr(X0)
& boolean_relstr(X0)
& complemented_relstr(X0)
& heyting_relstr(X0)
& distributive_relstr(X0)
& ~ v1_yellow_3(X0)
& bounded_relstr(X0)
& upper_bounded_relstr(X0)
& lower_bounded_relstr(X0)
& antisymmetric_relstr(X0)
& transitive_relstr(X0)
& reflexive_relstr(X0)
& strict_rel_str(X0)
& ~ trivial_carrier(X0)
& ~ empty_carrier(X0)
& rel_str(X0) ),
file('/export/starexec/sandbox2/tmp/tmp.XVCyggMQ11/Vampire---4.8_15325',rc1_waybel_7) ).
fof(f1085,plain,
spl61_39,
inference(avatar_split_clause,[],[f825,f1082]) ).
fof(f825,plain,
with_suprema_relstr(sK52),
inference(cnf_transformation,[],[f426]) ).
fof(f1080,plain,
spl61_38,
inference(avatar_split_clause,[],[f824,f1077]) ).
fof(f1077,plain,
( spl61_38
<=> boolean_relstr(sK52) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_38])]) ).
fof(f824,plain,
boolean_relstr(sK52),
inference(cnf_transformation,[],[f426]) ).
fof(f1075,plain,
spl61_37,
inference(avatar_split_clause,[],[f823,f1072]) ).
fof(f1072,plain,
( spl61_37
<=> complemented_relstr(sK52) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_37])]) ).
fof(f823,plain,
complemented_relstr(sK52),
inference(cnf_transformation,[],[f426]) ).
fof(f1070,plain,
spl61_36,
inference(avatar_split_clause,[],[f822,f1067]) ).
fof(f1067,plain,
( spl61_36
<=> heyting_relstr(sK52) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_36])]) ).
fof(f822,plain,
heyting_relstr(sK52),
inference(cnf_transformation,[],[f426]) ).
fof(f1065,plain,
spl61_35,
inference(avatar_split_clause,[],[f821,f1062]) ).
fof(f1062,plain,
( spl61_35
<=> distributive_relstr(sK52) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_35])]) ).
fof(f821,plain,
distributive_relstr(sK52),
inference(cnf_transformation,[],[f426]) ).
fof(f1060,plain,
~ spl61_34,
inference(avatar_split_clause,[],[f820,f1057]) ).
fof(f1057,plain,
( spl61_34
<=> v1_yellow_3(sK52) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_34])]) ).
fof(f820,plain,
~ v1_yellow_3(sK52),
inference(cnf_transformation,[],[f426]) ).
fof(f1055,plain,
spl61_33,
inference(avatar_split_clause,[],[f819,f1052]) ).
fof(f1052,plain,
( spl61_33
<=> bounded_relstr(sK52) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_33])]) ).
fof(f819,plain,
bounded_relstr(sK52),
inference(cnf_transformation,[],[f426]) ).
fof(f1050,plain,
spl61_32,
inference(avatar_split_clause,[],[f818,f1047]) ).
fof(f818,plain,
upper_bounded_relstr(sK52),
inference(cnf_transformation,[],[f426]) ).
fof(f1045,plain,
spl61_31,
inference(avatar_split_clause,[],[f817,f1042]) ).
fof(f817,plain,
lower_bounded_relstr(sK52),
inference(cnf_transformation,[],[f426]) ).
fof(f1040,plain,
spl61_30,
inference(avatar_split_clause,[],[f816,f1037]) ).
fof(f816,plain,
antisymmetric_relstr(sK52),
inference(cnf_transformation,[],[f426]) ).
fof(f1035,plain,
spl61_29,
inference(avatar_split_clause,[],[f815,f1032]) ).
fof(f815,plain,
transitive_relstr(sK52),
inference(cnf_transformation,[],[f426]) ).
fof(f1030,plain,
spl61_28,
inference(avatar_split_clause,[],[f814,f1027]) ).
fof(f814,plain,
reflexive_relstr(sK52),
inference(cnf_transformation,[],[f426]) ).
fof(f1025,plain,
spl61_27,
inference(avatar_split_clause,[],[f813,f1022]) ).
fof(f813,plain,
strict_rel_str(sK52),
inference(cnf_transformation,[],[f426]) ).
fof(f1020,plain,
~ spl61_26,
inference(avatar_split_clause,[],[f812,f1017]) ).
fof(f812,plain,
~ trivial_carrier(sK52),
inference(cnf_transformation,[],[f426]) ).
fof(f1015,plain,
~ spl61_25,
inference(avatar_split_clause,[],[f811,f1012]) ).
fof(f811,plain,
~ empty_carrier(sK52),
inference(cnf_transformation,[],[f426]) ).
fof(f1010,plain,
spl61_24,
inference(avatar_split_clause,[],[f810,f1007]) ).
fof(f810,plain,
rel_str(sK52),
inference(cnf_transformation,[],[f426]) ).
fof(f1005,plain,
spl61_23,
inference(avatar_split_clause,[],[f809,f1002]) ).
fof(f1002,plain,
( spl61_23
<=> relation_empty_yielding(sK51) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_23])]) ).
fof(f809,plain,
relation_empty_yielding(sK51),
inference(cnf_transformation,[],[f424]) ).
fof(f424,plain,
( relation_empty_yielding(sK51)
& relation(sK51) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK51])],[f106,f423]) ).
fof(f423,plain,
( ? [X0] :
( relation_empty_yielding(X0)
& relation(X0) )
=> ( relation_empty_yielding(sK51)
& relation(sK51) ) ),
introduced(choice_axiom,[]) ).
fof(f106,axiom,
? [X0] :
( relation_empty_yielding(X0)
& relation(X0) ),
file('/export/starexec/sandbox2/tmp/tmp.XVCyggMQ11/Vampire---4.8_15325',rc3_relat_1) ).
fof(f1000,plain,
spl61_22,
inference(avatar_split_clause,[],[f808,f997]) ).
fof(f997,plain,
( spl61_22
<=> relation(sK51) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_22])]) ).
fof(f808,plain,
relation(sK51),
inference(cnf_transformation,[],[f424]) ).
fof(f995,plain,
~ spl61_21,
inference(avatar_split_clause,[],[f807,f992]) ).
fof(f992,plain,
( spl61_21
<=> empty_carrier(sK50) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_21])]) ).
fof(f807,plain,
~ empty_carrier(sK50),
inference(cnf_transformation,[],[f422]) ).
fof(f422,plain,
( ~ empty_carrier(sK50)
& one_sorted_str(sK50) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK50])],[f107,f421]) ).
fof(f421,plain,
( ? [X0] :
( ~ empty_carrier(X0)
& one_sorted_str(X0) )
=> ( ~ empty_carrier(sK50)
& one_sorted_str(sK50) ) ),
introduced(choice_axiom,[]) ).
fof(f107,axiom,
? [X0] :
( ~ empty_carrier(X0)
& one_sorted_str(X0) ),
file('/export/starexec/sandbox2/tmp/tmp.XVCyggMQ11/Vampire---4.8_15325',rc3_struct_0) ).
fof(f990,plain,
spl61_20,
inference(avatar_split_clause,[],[f806,f987]) ).
fof(f806,plain,
one_sorted_str(sK50),
inference(cnf_transformation,[],[f422]) ).
fof(f985,plain,
spl61_19,
inference(avatar_split_clause,[],[f805,f982]) ).
fof(f982,plain,
( spl61_19
<=> finite(sK49) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_19])]) ).
fof(f805,plain,
finite(sK49),
inference(cnf_transformation,[],[f420]) ).
fof(f420,plain,
( finite(sK49)
& ~ empty(sK49) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK49])],[f90,f419]) ).
fof(f419,plain,
( ? [X0] :
( finite(X0)
& ~ empty(X0) )
=> ( finite(sK49)
& ~ empty(sK49) ) ),
introduced(choice_axiom,[]) ).
fof(f90,axiom,
? [X0] :
( finite(X0)
& ~ empty(X0) ),
file('/export/starexec/sandbox2/tmp/tmp.XVCyggMQ11/Vampire---4.8_15325',rc1_finset_1) ).
fof(f980,plain,
~ spl61_18,
inference(avatar_split_clause,[],[f804,f977]) ).
fof(f804,plain,
~ empty(sK49),
inference(cnf_transformation,[],[f420]) ).
fof(f975,plain,
spl61_17,
inference(avatar_split_clause,[],[f803,f972]) ).
fof(f972,plain,
( spl61_17
<=> relation(sK48) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_17])]) ).
fof(f803,plain,
relation(sK48),
inference(cnf_transformation,[],[f418]) ).
fof(f418,plain,
( relation(sK48)
& ~ empty(sK48) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK48])],[f99,f417]) ).
fof(f417,plain,
( ? [X0] :
( relation(X0)
& ~ empty(X0) )
=> ( relation(sK48)
& ~ empty(sK48) ) ),
introduced(choice_axiom,[]) ).
fof(f99,axiom,
? [X0] :
( relation(X0)
& ~ empty(X0) ),
file('/export/starexec/sandbox2/tmp/tmp.XVCyggMQ11/Vampire---4.8_15325',rc2_relat_1) ).
fof(f970,plain,
~ spl61_16,
inference(avatar_split_clause,[],[f802,f967]) ).
fof(f802,plain,
~ empty(sK48),
inference(cnf_transformation,[],[f418]) ).
fof(f965,plain,
spl61_15,
inference(avatar_split_clause,[],[f801,f962]) ).
fof(f801,plain,
rel_str(sK47),
inference(cnf_transformation,[],[f416]) ).
fof(f416,plain,
rel_str(sK47),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK47])],[f49,f415]) ).
fof(f415,plain,
( ? [X0] : rel_str(X0)
=> rel_str(sK47) ),
introduced(choice_axiom,[]) ).
fof(f49,axiom,
? [X0] : rel_str(X0),
file('/export/starexec/sandbox2/tmp/tmp.XVCyggMQ11/Vampire---4.8_15325',existence_l1_orders_2) ).
fof(f960,plain,
spl61_14,
inference(avatar_split_clause,[],[f800,f957]) ).
fof(f800,plain,
one_sorted_str(sK46),
inference(cnf_transformation,[],[f414]) ).
fof(f414,plain,
one_sorted_str(sK46),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK46])],[f51,f413]) ).
fof(f413,plain,
( ? [X0] : one_sorted_str(X0)
=> one_sorted_str(sK46) ),
introduced(choice_axiom,[]) ).
fof(f51,axiom,
? [X0] : one_sorted_str(X0),
file('/export/starexec/sandbox2/tmp/tmp.XVCyggMQ11/Vampire---4.8_15325',existence_l1_struct_0) ).
fof(f955,plain,
spl61_13,
inference(avatar_split_clause,[],[f799,f952]) ).
fof(f799,plain,
top_str(sK45),
inference(cnf_transformation,[],[f412]) ).
fof(f412,plain,
top_str(sK45),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK45])],[f50,f411]) ).
fof(f411,plain,
( ? [X0] : top_str(X0)
=> top_str(sK45) ),
introduced(choice_axiom,[]) ).
fof(f50,axiom,
? [X0] : top_str(X0),
file('/export/starexec/sandbox2/tmp/tmp.XVCyggMQ11/Vampire---4.8_15325',existence_l1_pre_topc) ).
fof(f950,plain,
spl61_12,
inference(avatar_split_clause,[],[f458,f947]) ).
fof(f458,plain,
relation_empty_yielding(empty_set),
inference(cnf_transformation,[],[f56]) ).
fof(f56,axiom,
( relation_empty_yielding(empty_set)
& relation(empty_set)
& empty(empty_set) ),
file('/export/starexec/sandbox2/tmp/tmp.XVCyggMQ11/Vampire---4.8_15325',fc12_relat_1) ).
fof(f945,plain,
spl61_11,
inference(avatar_split_clause,[],[f455,f942]) ).
fof(f942,plain,
( spl61_11
<=> relation(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_11])]) ).
fof(f455,plain,
relation(empty_set),
inference(cnf_transformation,[],[f70]) ).
fof(f70,axiom,
( relation(empty_set)
& empty(empty_set) ),
file('/export/starexec/sandbox2/tmp/tmp.XVCyggMQ11/Vampire---4.8_15325',fc4_relat_1) ).
fof(f940,plain,
spl61_10,
inference(avatar_split_clause,[],[f454,f937]) ).
fof(f454,plain,
empty(empty_set),
inference(cnf_transformation,[],[f70]) ).
fof(f935,plain,
spl61_9,
inference(avatar_split_clause,[],[f450,f932]) ).
fof(f450,plain,
element(sK13,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(sK12))))),
inference(cnf_transformation,[],[f331]) ).
fof(f930,plain,
spl61_8,
inference(avatar_split_clause,[],[f449,f927]) ).
fof(f449,plain,
proper_element(sK13,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(sK12))))),
inference(cnf_transformation,[],[f331]) ).
fof(f925,plain,
spl61_7,
inference(avatar_split_clause,[],[f448,f922]) ).
fof(f448,plain,
upper_relstr_subset(sK13,boole_POSet(cast_as_carrier_subset(sK12))),
inference(cnf_transformation,[],[f331]) ).
fof(f920,plain,
spl61_6,
inference(avatar_split_clause,[],[f447,f917]) ).
fof(f447,plain,
filtered_subset(sK13,boole_POSet(cast_as_carrier_subset(sK12))),
inference(cnf_transformation,[],[f331]) ).
fof(f915,plain,
spl61_5,
inference(avatar_split_clause,[],[f451,f912]) ).
fof(f451,plain,
element(sK14,the_carrier(sK12)),
inference(cnf_transformation,[],[f331]) ).
fof(f910,plain,
~ spl61_4,
inference(avatar_split_clause,[],[f446,f907]) ).
fof(f446,plain,
~ empty(sK13),
inference(cnf_transformation,[],[f331]) ).
fof(f905,plain,
spl61_3,
inference(avatar_split_clause,[],[f445,f902]) ).
fof(f445,plain,
top_str(sK12),
inference(cnf_transformation,[],[f331]) ).
fof(f900,plain,
spl61_2,
inference(avatar_split_clause,[],[f444,f897]) ).
fof(f444,plain,
topological_space(sK12),
inference(cnf_transformation,[],[f331]) ).
fof(f895,plain,
~ spl61_1,
inference(avatar_split_clause,[],[f443,f892]) ).
fof(f443,plain,
~ empty_carrier(sK12),
inference(cnf_transformation,[],[f331]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU395+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.13 % Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.12/0.33 % Computer : n001.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Wed Aug 30 14:43:39 EDT 2023
% 0.12/0.33 % CPUTime :
% 0.17/0.40 % (15440)Running in auto input_syntax mode. Trying TPTP
% 0.17/0.40 % (15442)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on Vampire---4 for (846ds/0Mi)
% 0.17/0.40 % (15443)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on Vampire---4 for (793ds/0Mi)
% 0.17/0.40 % (15446)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on Vampire---4 for (533ds/0Mi)
% 0.17/0.40 % (15449)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on Vampire---4 for (522ds/0Mi)
% 0.17/0.40 % (15448)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on Vampire---4 for (531ds/0Mi)
% 0.17/0.40 % (15444)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on Vampire---4 for (569ds/0Mi)
% 0.17/0.41 % (15450)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on Vampire---4 for (497ds/0Mi)
% 0.17/0.42 TRYING [1]
% 0.17/0.42 TRYING [2]
% 0.17/0.44 TRYING [3]
% 0.17/0.48 TRYING [1]
% 0.17/0.49 TRYING [2]
% 0.17/0.50 TRYING [4]
% 0.17/0.60 % (15448)First to succeed.
% 0.17/0.65 % (15448)Refutation found. Thanks to Tanya!
% 0.17/0.65 % SZS status Theorem for Vampire---4
% 0.17/0.65 % SZS output start Proof for Vampire---4
% See solution above
% 0.17/0.69 % (15448)------------------------------
% 0.17/0.69 % (15448)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.17/0.69 % (15448)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.17/0.69 % (15448)Termination reason: Refutation
% 0.17/0.69
% 0.17/0.69 % (15448)Memory used [KB]: 13560
% 0.17/0.69 % (15448)Time elapsed: 0.246 s
% 0.17/0.69 % (15448)------------------------------
% 0.17/0.69 % (15448)------------------------------
% 0.17/0.69 % (15440)Success in time 0.354 s
% 0.49/0.69 % Vampire---4.8 exiting
%------------------------------------------------------------------------------