TSTP Solution File: SEU340+1 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SEU340+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n024.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 : Sun May 5 09:34:08 EDT 2024
% Result : Theorem 7.22s 1.42s
% Output : Refutation 7.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 1151
% Syntax : Number of formulae : 3861 ( 100 unt; 0 def)
% Number of atoms : 17622 ( 81 equ)
% Maximal formula atoms : 17 ( 4 avg)
% Number of connectives : 22428 (8667 ~;12487 |; 120 &)
% (1114 <=>; 40 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 7 avg)
% Maximal term depth : 12 ( 2 avg)
% Number of predicates : 1117 (1115 usr;1103 prp; 0-3 aty)
% Number of functors : 23 ( 23 usr; 8 con; 0-2 aty)
% Number of variables : 7368 (7318 !; 50 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f15314,plain,
$false,
inference(avatar_sat_refutation,[],[f182,f187,f192,f197,f202,f207,f212,f217,f222,f227,f232,f237,f241,f245,f249,f253,f257,f261,f265,f269,f273,f277,f281,f290,f294,f298,f302,f306,f310,f315,f319,f323,f333,f337,f341,f345,f349,f353,f357,f361,f365,f369,f373,f403,f407,f411,f420,f424,f437,f441,f454,f461,f469,f480,f486,f492,f498,f502,f506,f516,f521,f526,f530,f544,f548,f555,f564,f569,f573,f580,f585,f586,f587,f588,f608,f631,f635,f645,f649,f653,f657,f661,f670,f680,f684,f688,f703,f707,f711,f715,f719,f723,f727,f731,f735,f759,f763,f767,f771,f786,f790,f794,f807,f811,f815,f825,f829,f844,f852,f861,f866,f875,f879,f883,f884,f888,f898,f928,f932,f936,f940,f944,f958,f963,f967,f971,f975,f1002,f1016,f1021,f1030,f1041,f1046,f1050,f1057,f1064,f1068,f1072,f1076,f1080,f1089,f1096,f1101,f1105,f1109,f1116,f1120,f1124,f1128,f1140,f1141,f1145,f1149,f1153,f1157,f1161,f1165,f1193,f1197,f1201,f1205,f1209,f1213,f1217,f1222,f1226,f1230,f1234,f1238,f1242,f1246,f1343,f1347,f1351,f1355,f1359,f1363,f1367,f1393,f1409,f1415,f1419,f1428,f1432,f1442,f1446,f1450,f1454,f1458,f1462,f1486,f1505,f1509,f1513,f1537,f1541,f1553,f1557,f1563,f1567,f1571,f1579,f1583,f1599,f1612,f1626,f1630,f1648,f1652,f1670,f1674,f1684,f1688,f1708,f1712,f1731,f1735,f1739,f1743,f1751,f1755,f1759,f1771,f1775,f1779,f1783,f1798,f1802,f1806,f1810,f1839,f1843,f1847,f1851,f1887,f1891,f1895,f1899,f1903,f1907,f1911,f1915,f1919,f1923,f1927,f1931,f1935,f1939,f1943,f1947,f1951,f1955,f1959,f1963,f1967,f1971,f1975,f2092,f2096,f2100,f2104,f2108,f2112,f2116,f2120,f2124,f2128,f2132,f2136,f2141,f2145,f2149,f2170,f2238,f2242,f2246,f2291,f2295,f2299,f2303,f2307,f2311,f2315,f2361,f2391,f2395,f2399,f2403,f2407,f2411,f2417,f2421,f2425,f2488,f2520,f2524,f2528,f2532,f2536,f2540,f2544,f2548,f2552,f2556,f2560,f2564,f2568,f2619,f2655,f2659,f2694,f2698,f2702,f2709,f2713,f2717,f2728,f2732,f2834,f2838,f2851,f2855,f2859,f2863,f2867,f2871,f2875,f2984,f2988,f2992,f2996,f3036,f3040,f3044,f3048,f3052,f3128,f3132,f3174,f3178,f3182,f3186,f3190,f3194,f3237,f3241,f3245,f3268,f3272,f3276,f3280,f3304,f3308,f3312,f3324,f3346,f3350,f3381,f3385,f3389,f3393,f3397,f3401,f3405,f3409,f3443,f3447,f3451,f3461,f3465,f3469,f3511,f3515,f3525,f3535,f3539,f3543,f3547,f3557,f3563,f3567,f3571,f3575,f3587,f3617,f3621,f3663,f3667,f3674,f3683,f3687,f3694,f3698,f3706,f3710,f3714,f3718,f3738,f3748,f3769,f3774,f3779,f3787,f3793,f3798,f3803,f3807,f3811,f3830,f3834,f3845,f3849,f3853,f3857,f3861,f3865,f3889,f3893,f3897,f3901,f3905,f3909,f3913,f3917,f3921,f3929,f4085,f4089,f4093,f4097,f4101,f4105,f4109,f4113,f4157,f4161,f4166,f4170,f4174,f4178,f4182,f4186,f4190,f4194,f4198,f4202,f4206,f4210,f4214,f4218,f4402,f4406,f4410,f4414,f4418,f4422,f4426,f4430,f4434,f4438,f4442,f4446,f4450,f4454,f4459,f4463,f4467,f4471,f4523,f4527,f4531,f4535,f4539,f4543,f4547,f4551,f4555,f4559,f4563,f4593,f4597,f4601,f4605,f4609,f4613,f4617,f4621,f4625,f4629,f4630,f4680,f4978,f4982,f4986,f4990,f4994,f4998,f5002,f5038,f5042,f5046,f5050,f5054,f5087,f5091,f5095,f5099,f5103,f5107,f5111,f5115,f5119,f5123,f5124,f5128,f5132,f5136,f5140,f5144,f5148,f5152,f5156,f5160,f5164,f5193,f5197,f5209,f5769,f5774,f5778,f5782,f5786,f5790,f5794,f5798,f5802,f5806,f5810,f5814,f5818,f5822,f5932,f6017,f6021,f6025,f6029,f6033,f6037,f6041,f6045,f6049,f6053,f6057,f6061,f6065,f6069,f6073,f6077,f6081,f6236,f6240,f6244,f6248,f6252,f6257,f6261,f6265,f6269,f6273,f6277,f6281,f6285,f6289,f6293,f6579,f6661,f6665,f6669,f6673,f6677,f6681,f6685,f6689,f6693,f6697,f6701,f6705,f6709,f6713,f6717,f6721,f6725,f6729,f6733,f6737,f6741,f6745,f6749,f6753,f6757,f6761,f6765,f6769,f6773,f6777,f6781,f6785,f7039,f7233,f7237,f7241,f7245,f7249,f7284,f7288,f7292,f7296,f7300,f7304,f7308,f7312,f7377,f7381,f7385,f7389,f7393,f7397,f7401,f7405,f7409,f7413,f7418,f7437,f7441,f7445,f7449,f7453,f7457,f7461,f7465,f7469,f7473,f7477,f7481,f7521,f7542,f7546,f7550,f7554,f7558,f7562,f7628,f7632,f7636,f7640,f7644,f7648,f7652,f7690,f7694,f7698,f7702,f7706,f7710,f7714,f7718,f7722,f7726,f7730,f7744,f7794,f7798,f7802,f7806,f7810,f7814,f7818,f7822,f7826,f7830,f7834,f7932,f7936,f7940,f7956,f7960,f7964,f7968,f7972,f7976,f7980,f7984,f7988,f8064,f8073,f8077,f8081,f8085,f8089,f8093,f8097,f8101,f8105,f8109,f8113,f8117,f8121,f8125,f8129,f8209,f8213,f8217,f8221,f8225,f8229,f8233,f8237,f8241,f8245,f8249,f8253,f8315,f8325,f8329,f8333,f8337,f8341,f8345,f8349,f8353,f8357,f8363,f8367,f8371,f8375,f8379,f8383,f8387,f8391,f8395,f8399,f8420,f8469,f9065,f9069,f9073,f9077,f9091,f9104,f9108,f9112,f9116,f9132,f9136,f9140,f9155,f9177,f9199,f9203,f9207,f9211,f9215,f9251,f9293,f9297,f9301,f9302,f9306,f9310,f9314,f9318,f9322,f9724,f9728,f9732,f9736,f9740,f9744,f9748,f9753,f9757,f9761,f9765,f9769,f9773,f9777,f9797,f10098,f10102,f10106,f10110,f10114,f10118,f10122,f10126,f10130,f10134,f10138,f10142,f10146,f10150,f10154,f10643,f10652,f10656,f10660,f10664,f10668,f10672,f10676,f10680,f10684,f10688,f10762,f10766,f10770,f10784,f10788,f10792,f10796,f10800,f10804,f10808,f10812,f10816,f10820,f10824,f10925,f10971,f10975,f10979,f10983,f10987,f10991,f10995,f11000,f11114,f11119,f11123,f11127,f11131,f11135,f11207,f11263,f11267,f11271,f11275,f11279,f11283,f11287,f11291,f11295,f11299,f11303,f11307,f11311,f11643,f11647,f11651,f11655,f11659,f11663,f11667,f11671,f11675,f11679,f11683,f11687,f11691,f11695,f11699,f11703,f11715,f11900,f12068,f12072,f12076,f12081,f12091,f12134,f12138,f12139,f12143,f12147,f12151,f12155,f12159,f12176,f12243,f12247,f12251,f12255,f12259,f12263,f12267,f12325,f12329,f12333,f12337,f12341,f12345,f12431,f12435,f12439,f12443,f12447,f12451,f12455,f12459,f12463,f12467,f12471,f12475,f12479,f12483,f12487,f12491,f12553,f12557,f12561,f12565,f12569,f12573,f12577,f12581,f12585,f12589,f12593,f12630,f12634,f12642,f12654,f12658,f12662,f12666,f12758,f12762,f12766,f12770,f12774,f12778,f12782,f12786,f12790,f12794,f12798,f12802,f12806,f12810,f12814,f12818,f12822,f12880,f12886,f12890,f12894,f12898,f12943,f12947,f12951,f12955,f12959,f12963,f12967,f12971,f12975,f12979,f12983,f12987,f12991,f12995,f12999,f13032,f13094,f13098,f13102,f13106,f13118,f13122,f13129,f13133,f13137,f13141,f13249,f13253,f13257,f13265,f13269,f13276,f13280,f13284,f13288,f13292,f13296,f13300,f13304,f13324,f13434,f13438,f13445,f13449,f13453,f13457,f13461,f13465,f13469,f13473,f13477,f13481,f13485,f13489,f13493,f13501,f13589,f13593,f13597,f13601,f13605,f13609,f13613,f13633,f13645,f13649,f13656,f13660,f13664,f13668,f13672,f13676,f13680,f13684,f13688,f13715,f13719,f13723,f13727,f13731,f13735,f13739,f13743,f13781,f13785,f13834,f13838,f14362,f14366,f14370,f14374,f14381,f14385,f14413,f14417,f14423,f14427,f14439,f14443,f14447,f14451,f14508,f14512,f14516,f14520,f14636,f14752,f14756,f14760,f14764,f14768,f14772,f14776,f14780,f14784,f15028,f15032,f15036,f15040,f15044,f15064,f15068,f15072,f15076,f15080,f15100,f15104,f15108,f15112,f15135,f15139,f15143,f15147,f15157,f15161,f15165,f15169,f15189,f15193,f15200,f15204,f15224,f15228,f15232,f15236,f15258,f15262,f15266,f15270,f15282,f15295,f15299,f15304,f15308,f15312,f15313]) ).
fof(f15313,plain,
( ~ spl17_5
| ~ spl17_107
| spl17_8
| ~ spl17_7
| ~ spl17_1097 ),
inference(avatar_split_clause,[],[f15291,f15280,f209,f214,f858,f199]) ).
fof(f199,plain,
( spl17_5
<=> element(sK5,the_carrier(sK2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_5])]) ).
fof(f858,plain,
( spl17_107
<=> in(sK5,the_carrier(sK2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_107])]) ).
fof(f214,plain,
( spl17_8
<=> related(sK2,sK3,sK5) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_8])]) ).
fof(f209,plain,
( spl17_7
<=> related(sK2,sK4,sK5) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_7])]) ).
fof(f15280,plain,
( spl17_1097
<=> ! [X0] :
( ~ in(X0,the_carrier(sK2))
| related(sK2,sK3,X0)
| ~ related(sK2,sK4,X0)
| ~ element(X0,the_carrier(sK2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1097])]) ).
fof(f15291,plain,
( related(sK2,sK3,sK5)
| ~ in(sK5,the_carrier(sK2))
| ~ element(sK5,the_carrier(sK2))
| ~ spl17_7
| ~ spl17_1097 ),
inference(resolution,[],[f15281,f211]) ).
fof(f211,plain,
( related(sK2,sK4,sK5)
| ~ spl17_7 ),
inference(avatar_component_clause,[],[f209]) ).
fof(f15281,plain,
( ! [X0] :
( ~ related(sK2,sK4,X0)
| related(sK2,sK3,X0)
| ~ in(X0,the_carrier(sK2))
| ~ element(X0,the_carrier(sK2)) )
| ~ spl17_1097 ),
inference(avatar_component_clause,[],[f15280]) ).
fof(f15312,plain,
( spl17_1102
| ~ spl17_19
| ~ spl17_650 ),
inference(avatar_split_clause,[],[f7673,f7646,f263,f15310]) ).
fof(f15310,plain,
( spl17_1102
<=> ! [X0,X1] :
( ~ empty(X0)
| empty(powerset(X0))
| sP0(sK6(powerset(X0)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1102])]) ).
fof(f263,plain,
( spl17_19
<=> ! [X0,X1] : ~ empty(unordered_pair(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_19])]) ).
fof(f7646,plain,
( spl17_650
<=> ! [X0,X1] :
( sP0(sK6(powerset(X0)),X1)
| ~ empty(X0)
| empty(powerset(X0))
| empty(unordered_pair(singleton(sK8(sK6(powerset(X0)),X1)),unordered_pair(sK9(sK6(powerset(X0)),X1),sK8(sK6(powerset(X0)),X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_650])]) ).
fof(f7673,plain,
( ! [X0,X1] :
( ~ empty(X0)
| empty(powerset(X0))
| sP0(sK6(powerset(X0)),X1) )
| ~ spl17_19
| ~ spl17_650 ),
inference(resolution,[],[f7647,f264]) ).
fof(f264,plain,
( ! [X0,X1] : ~ empty(unordered_pair(X0,X1))
| ~ spl17_19 ),
inference(avatar_component_clause,[],[f263]) ).
fof(f7647,plain,
( ! [X0,X1] :
( empty(unordered_pair(singleton(sK8(sK6(powerset(X0)),X1)),unordered_pair(sK9(sK6(powerset(X0)),X1),sK8(sK6(powerset(X0)),X1))))
| ~ empty(X0)
| empty(powerset(X0))
| sP0(sK6(powerset(X0)),X1) )
| ~ spl17_650 ),
inference(avatar_component_clause,[],[f7646]) ).
fof(f15308,plain,
( spl17_1101
| ~ spl17_72
| ~ spl17_482 ),
inference(avatar_split_clause,[],[f4892,f4619,f578,f15306]) ).
fof(f15306,plain,
( spl17_1101
<=> ! [X0,X1] :
( empty(cartesian_product2(X0,sK16))
| sP0(sK6(cartesian_product2(X0,sK16)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1101])]) ).
fof(f578,plain,
( spl17_72
<=> ! [X1] : ~ in(X1,sK16) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_72])]) ).
fof(f4619,plain,
( spl17_482
<=> ! [X2,X0,X1] :
( sP0(sK6(cartesian_product2(X0,X1)),X2)
| empty(cartesian_product2(X0,X1))
| in(sK9(sK6(cartesian_product2(X0,X1)),X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_482])]) ).
fof(f4892,plain,
( ! [X0,X1] :
( empty(cartesian_product2(X0,sK16))
| sP0(sK6(cartesian_product2(X0,sK16)),X1) )
| ~ spl17_72
| ~ spl17_482 ),
inference(resolution,[],[f4620,f579]) ).
fof(f579,plain,
( ! [X1] : ~ in(X1,sK16)
| ~ spl17_72 ),
inference(avatar_component_clause,[],[f578]) ).
fof(f4620,plain,
( ! [X2,X0,X1] :
( in(sK9(sK6(cartesian_product2(X0,X1)),X2),X1)
| empty(cartesian_product2(X0,X1))
| sP0(sK6(cartesian_product2(X0,X1)),X2) )
| ~ spl17_482 ),
inference(avatar_component_clause,[],[f4619]) ).
fof(f15304,plain,
( spl17_1100
| ~ spl17_72
| ~ spl17_481 ),
inference(avatar_split_clause,[],[f4851,f4615,f578,f15302]) ).
fof(f15302,plain,
( spl17_1100
<=> ! [X0,X1] :
( empty(cartesian_product2(sK16,X0))
| sP0(sK6(cartesian_product2(sK16,X0)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1100])]) ).
fof(f4615,plain,
( spl17_481
<=> ! [X2,X0,X1] :
( sP0(sK6(cartesian_product2(X0,X1)),X2)
| empty(cartesian_product2(X0,X1))
| in(sK8(sK6(cartesian_product2(X0,X1)),X2),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_481])]) ).
fof(f4851,plain,
( ! [X0,X1] :
( empty(cartesian_product2(sK16,X0))
| sP0(sK6(cartesian_product2(sK16,X0)),X1) )
| ~ spl17_72
| ~ spl17_481 ),
inference(resolution,[],[f4616,f579]) ).
fof(f4616,plain,
( ! [X2,X0,X1] :
( in(sK8(sK6(cartesian_product2(X0,X1)),X2),X0)
| empty(cartesian_product2(X0,X1))
| sP0(sK6(cartesian_product2(X0,X1)),X2) )
| ~ spl17_481 ),
inference(avatar_component_clause,[],[f4615]) ).
fof(f15299,plain,
( spl17_1099
| ~ spl17_19
| ~ spl17_661 ),
inference(avatar_split_clause,[],[f7777,f7724,f263,f15297]) ).
fof(f15297,plain,
( spl17_1099
<=> ! [X0,X1] :
( sP0(sK10(powerset(powerset(X0))),X1)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1099])]) ).
fof(f7724,plain,
( spl17_661
<=> ! [X0,X1] :
( ~ empty(X0)
| sP0(sK10(powerset(powerset(X0))),X1)
| empty(unordered_pair(singleton(sK8(sK10(powerset(powerset(X0))),X1)),unordered_pair(sK9(sK10(powerset(powerset(X0))),X1),sK8(sK10(powerset(powerset(X0))),X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_661])]) ).
fof(f7777,plain,
( ! [X0,X1] :
( sP0(sK10(powerset(powerset(X0))),X1)
| ~ empty(X0) )
| ~ spl17_19
| ~ spl17_661 ),
inference(resolution,[],[f7725,f264]) ).
fof(f7725,plain,
( ! [X0,X1] :
( empty(unordered_pair(singleton(sK8(sK10(powerset(powerset(X0))),X1)),unordered_pair(sK9(sK10(powerset(powerset(X0))),X1),sK8(sK10(powerset(powerset(X0))),X1))))
| sP0(sK10(powerset(powerset(X0))),X1)
| ~ empty(X0) )
| ~ spl17_661 ),
inference(avatar_component_clause,[],[f7724]) ).
fof(f15295,plain,
( ~ spl17_2
| ~ spl17_4
| spl17_1098
| ~ spl17_63
| ~ spl17_393 ),
inference(avatar_split_clause,[],[f12129,f3736,f524,f15293,f194,f184]) ).
fof(f184,plain,
( spl17_2
<=> rel_str(sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_2])]) ).
fof(f194,plain,
( spl17_4
<=> element(sK4,the_carrier(sK2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_4])]) ).
fof(f15293,plain,
( spl17_1098
<=> ! [X0] :
( ~ in(X0,the_carrier(sK2))
| related(sK2,sK4,X0)
| ~ related(sK2,sK5,X0)
| ~ element(X0,the_carrier(sK2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1098])]) ).
fof(f524,plain,
( spl17_63
<=> ! [X2,X0,X1] :
( ~ in(unordered_pair(singleton(X1),unordered_pair(X1,X2)),the_InternalRel(X0))
| related(X0,X1,X2)
| ~ element(X2,the_carrier(X0))
| ~ element(X1,the_carrier(X0))
| ~ rel_str(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_63])]) ).
fof(f3736,plain,
( spl17_393
<=> ! [X0] :
( in(unordered_pair(singleton(sK4),unordered_pair(sK4,X0)),the_InternalRel(sK2))
| ~ in(X0,the_carrier(sK2))
| ~ element(X0,the_carrier(sK2))
| ~ related(sK2,sK5,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_393])]) ).
fof(f12129,plain,
( ! [X0] :
( ~ in(X0,the_carrier(sK2))
| ~ element(X0,the_carrier(sK2))
| ~ related(sK2,sK5,X0)
| related(sK2,sK4,X0)
| ~ element(sK4,the_carrier(sK2))
| ~ rel_str(sK2) )
| ~ spl17_63
| ~ spl17_393 ),
inference(duplicate_literal_removal,[],[f12099]) ).
fof(f12099,plain,
( ! [X0] :
( ~ in(X0,the_carrier(sK2))
| ~ element(X0,the_carrier(sK2))
| ~ related(sK2,sK5,X0)
| related(sK2,sK4,X0)
| ~ element(X0,the_carrier(sK2))
| ~ element(sK4,the_carrier(sK2))
| ~ rel_str(sK2) )
| ~ spl17_63
| ~ spl17_393 ),
inference(resolution,[],[f3737,f525]) ).
fof(f525,plain,
( ! [X2,X0,X1] :
( ~ in(unordered_pair(singleton(X1),unordered_pair(X1,X2)),the_InternalRel(X0))
| related(X0,X1,X2)
| ~ element(X2,the_carrier(X0))
| ~ element(X1,the_carrier(X0))
| ~ rel_str(X0) )
| ~ spl17_63 ),
inference(avatar_component_clause,[],[f524]) ).
fof(f3737,plain,
( ! [X0] :
( in(unordered_pair(singleton(sK4),unordered_pair(sK4,X0)),the_InternalRel(sK2))
| ~ in(X0,the_carrier(sK2))
| ~ element(X0,the_carrier(sK2))
| ~ related(sK2,sK5,X0) )
| ~ spl17_393 ),
inference(avatar_component_clause,[],[f3736]) ).
fof(f15282,plain,
( ~ spl17_2
| ~ spl17_3
| spl17_1097
| ~ spl17_63
| ~ spl17_373 ),
inference(avatar_split_clause,[],[f3612,f3555,f524,f15280,f189,f184]) ).
fof(f189,plain,
( spl17_3
<=> element(sK3,the_carrier(sK2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_3])]) ).
fof(f3555,plain,
( spl17_373
<=> ! [X0] :
( in(unordered_pair(singleton(sK3),unordered_pair(sK3,X0)),the_InternalRel(sK2))
| ~ in(X0,the_carrier(sK2))
| ~ element(X0,the_carrier(sK2))
| ~ related(sK2,sK4,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_373])]) ).
fof(f3612,plain,
( ! [X0] :
( ~ in(X0,the_carrier(sK2))
| ~ element(X0,the_carrier(sK2))
| ~ related(sK2,sK4,X0)
| related(sK2,sK3,X0)
| ~ element(sK3,the_carrier(sK2))
| ~ rel_str(sK2) )
| ~ spl17_63
| ~ spl17_373 ),
inference(duplicate_literal_removal,[],[f3590]) ).
fof(f3590,plain,
( ! [X0] :
( ~ in(X0,the_carrier(sK2))
| ~ element(X0,the_carrier(sK2))
| ~ related(sK2,sK4,X0)
| related(sK2,sK3,X0)
| ~ element(X0,the_carrier(sK2))
| ~ element(sK3,the_carrier(sK2))
| ~ rel_str(sK2) )
| ~ spl17_63
| ~ spl17_373 ),
inference(resolution,[],[f3556,f525]) ).
fof(f3556,plain,
( ! [X0] :
( in(unordered_pair(singleton(sK3),unordered_pair(sK3,X0)),the_InternalRel(sK2))
| ~ in(X0,the_carrier(sK2))
| ~ element(X0,the_carrier(sK2))
| ~ related(sK2,sK4,X0) )
| ~ spl17_373 ),
inference(avatar_component_clause,[],[f3555]) ).
fof(f15270,plain,
( spl17_1096
| ~ spl17_321
| ~ spl17_332 ),
inference(avatar_split_clause,[],[f3158,f3130,f2873,f15268]) ).
fof(f15268,plain,
( spl17_1096
<=> ! [X2,X0,X1] :
( element(unordered_pair(singleton(sK7(sK10(powerset(unordered_pair(singleton(sK7(sK10(powerset(powerset(X0))),X1)),unordered_pair(sK8(sK10(powerset(powerset(X0))),X1),sK7(sK10(powerset(powerset(X0))),X1))))),X2)),unordered_pair(sK8(sK10(powerset(unordered_pair(singleton(sK7(sK10(powerset(powerset(X0))),X1)),unordered_pair(sK8(sK10(powerset(powerset(X0))),X1),sK7(sK10(powerset(powerset(X0))),X1))))),X2),sK7(sK10(powerset(unordered_pair(singleton(sK7(sK10(powerset(powerset(X0))),X1)),unordered_pair(sK8(sK10(powerset(powerset(X0))),X1),sK7(sK10(powerset(powerset(X0))),X1))))),X2))),X0)
| sP0(sK10(powerset(powerset(X0))),X1)
| empty(unordered_pair(singleton(sK7(sK10(powerset(powerset(X0))),X1)),unordered_pair(sK8(sK10(powerset(powerset(X0))),X1),sK7(sK10(powerset(powerset(X0))),X1))))
| sP0(sK10(powerset(unordered_pair(singleton(sK7(sK10(powerset(powerset(X0))),X1)),unordered_pair(sK8(sK10(powerset(powerset(X0))),X1),sK7(sK10(powerset(powerset(X0))),X1))))),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1096])]) ).
fof(f2873,plain,
( spl17_321
<=> ! [X0,X1] :
( sP0(sK10(powerset(X0)),X1)
| empty(X0)
| in(unordered_pair(singleton(sK7(sK10(powerset(X0)),X1)),unordered_pair(sK8(sK10(powerset(X0)),X1),sK7(sK10(powerset(X0)),X1))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_321])]) ).
fof(f3130,plain,
( spl17_332
<=> ! [X2,X0,X1] :
( sP0(sK10(powerset(powerset(X0))),X1)
| element(X2,X0)
| ~ in(X2,unordered_pair(singleton(sK7(sK10(powerset(powerset(X0))),X1)),unordered_pair(sK8(sK10(powerset(powerset(X0))),X1),sK7(sK10(powerset(powerset(X0))),X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_332])]) ).
fof(f3158,plain,
( ! [X2,X0,X1] :
( element(unordered_pair(singleton(sK7(sK10(powerset(unordered_pair(singleton(sK7(sK10(powerset(powerset(X0))),X1)),unordered_pair(sK8(sK10(powerset(powerset(X0))),X1),sK7(sK10(powerset(powerset(X0))),X1))))),X2)),unordered_pair(sK8(sK10(powerset(unordered_pair(singleton(sK7(sK10(powerset(powerset(X0))),X1)),unordered_pair(sK8(sK10(powerset(powerset(X0))),X1),sK7(sK10(powerset(powerset(X0))),X1))))),X2),sK7(sK10(powerset(unordered_pair(singleton(sK7(sK10(powerset(powerset(X0))),X1)),unordered_pair(sK8(sK10(powerset(powerset(X0))),X1),sK7(sK10(powerset(powerset(X0))),X1))))),X2))),X0)
| sP0(sK10(powerset(powerset(X0))),X1)
| empty(unordered_pair(singleton(sK7(sK10(powerset(powerset(X0))),X1)),unordered_pair(sK8(sK10(powerset(powerset(X0))),X1),sK7(sK10(powerset(powerset(X0))),X1))))
| sP0(sK10(powerset(unordered_pair(singleton(sK7(sK10(powerset(powerset(X0))),X1)),unordered_pair(sK8(sK10(powerset(powerset(X0))),X1),sK7(sK10(powerset(powerset(X0))),X1))))),X2) )
| ~ spl17_321
| ~ spl17_332 ),
inference(resolution,[],[f3131,f2874]) ).
fof(f2874,plain,
( ! [X0,X1] :
( in(unordered_pair(singleton(sK7(sK10(powerset(X0)),X1)),unordered_pair(sK8(sK10(powerset(X0)),X1),sK7(sK10(powerset(X0)),X1))),X0)
| empty(X0)
| sP0(sK10(powerset(X0)),X1) )
| ~ spl17_321 ),
inference(avatar_component_clause,[],[f2873]) ).
fof(f3131,plain,
( ! [X2,X0,X1] :
( ~ in(X2,unordered_pair(singleton(sK7(sK10(powerset(powerset(X0))),X1)),unordered_pair(sK8(sK10(powerset(powerset(X0))),X1),sK7(sK10(powerset(powerset(X0))),X1))))
| element(X2,X0)
| sP0(sK10(powerset(powerset(X0))),X1) )
| ~ spl17_332 ),
inference(avatar_component_clause,[],[f3130]) ).
fof(f15266,plain,
( spl17_1095
| ~ spl17_320
| ~ spl17_332 ),
inference(avatar_split_clause,[],[f3155,f3130,f2869,f15264]) ).
fof(f15264,plain,
( spl17_1095
<=> ! [X2,X0,X1] :
( element(unordered_pair(singleton(sK8(sK10(powerset(unordered_pair(singleton(sK7(sK10(powerset(powerset(X0))),X1)),unordered_pair(sK8(sK10(powerset(powerset(X0))),X1),sK7(sK10(powerset(powerset(X0))),X1))))),X2)),unordered_pair(sK9(sK10(powerset(unordered_pair(singleton(sK7(sK10(powerset(powerset(X0))),X1)),unordered_pair(sK8(sK10(powerset(powerset(X0))),X1),sK7(sK10(powerset(powerset(X0))),X1))))),X2),sK8(sK10(powerset(unordered_pair(singleton(sK7(sK10(powerset(powerset(X0))),X1)),unordered_pair(sK8(sK10(powerset(powerset(X0))),X1),sK7(sK10(powerset(powerset(X0))),X1))))),X2))),X0)
| sP0(sK10(powerset(powerset(X0))),X1)
| empty(unordered_pair(singleton(sK7(sK10(powerset(powerset(X0))),X1)),unordered_pair(sK8(sK10(powerset(powerset(X0))),X1),sK7(sK10(powerset(powerset(X0))),X1))))
| sP0(sK10(powerset(unordered_pair(singleton(sK7(sK10(powerset(powerset(X0))),X1)),unordered_pair(sK8(sK10(powerset(powerset(X0))),X1),sK7(sK10(powerset(powerset(X0))),X1))))),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1095])]) ).
fof(f2869,plain,
( spl17_320
<=> ! [X0,X1] :
( sP0(sK10(powerset(X0)),X1)
| empty(X0)
| in(unordered_pair(singleton(sK8(sK10(powerset(X0)),X1)),unordered_pair(sK9(sK10(powerset(X0)),X1),sK8(sK10(powerset(X0)),X1))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_320])]) ).
fof(f3155,plain,
( ! [X2,X0,X1] :
( element(unordered_pair(singleton(sK8(sK10(powerset(unordered_pair(singleton(sK7(sK10(powerset(powerset(X0))),X1)),unordered_pair(sK8(sK10(powerset(powerset(X0))),X1),sK7(sK10(powerset(powerset(X0))),X1))))),X2)),unordered_pair(sK9(sK10(powerset(unordered_pair(singleton(sK7(sK10(powerset(powerset(X0))),X1)),unordered_pair(sK8(sK10(powerset(powerset(X0))),X1),sK7(sK10(powerset(powerset(X0))),X1))))),X2),sK8(sK10(powerset(unordered_pair(singleton(sK7(sK10(powerset(powerset(X0))),X1)),unordered_pair(sK8(sK10(powerset(powerset(X0))),X1),sK7(sK10(powerset(powerset(X0))),X1))))),X2))),X0)
| sP0(sK10(powerset(powerset(X0))),X1)
| empty(unordered_pair(singleton(sK7(sK10(powerset(powerset(X0))),X1)),unordered_pair(sK8(sK10(powerset(powerset(X0))),X1),sK7(sK10(powerset(powerset(X0))),X1))))
| sP0(sK10(powerset(unordered_pair(singleton(sK7(sK10(powerset(powerset(X0))),X1)),unordered_pair(sK8(sK10(powerset(powerset(X0))),X1),sK7(sK10(powerset(powerset(X0))),X1))))),X2) )
| ~ spl17_320
| ~ spl17_332 ),
inference(resolution,[],[f3131,f2870]) ).
fof(f2870,plain,
( ! [X0,X1] :
( in(unordered_pair(singleton(sK8(sK10(powerset(X0)),X1)),unordered_pair(sK9(sK10(powerset(X0)),X1),sK8(sK10(powerset(X0)),X1))),X0)
| empty(X0)
| sP0(sK10(powerset(X0)),X1) )
| ~ spl17_320 ),
inference(avatar_component_clause,[],[f2869]) ).
fof(f15262,plain,
( spl17_1094
| ~ spl17_321
| ~ spl17_331 ),
inference(avatar_split_clause,[],[f3138,f3126,f2873,f15260]) ).
fof(f15260,plain,
( spl17_1094
<=> ! [X2,X0,X1] :
( element(unordered_pair(singleton(sK7(sK10(powerset(unordered_pair(singleton(sK8(sK10(powerset(powerset(X0))),X1)),unordered_pair(sK9(sK10(powerset(powerset(X0))),X1),sK8(sK10(powerset(powerset(X0))),X1))))),X2)),unordered_pair(sK8(sK10(powerset(unordered_pair(singleton(sK8(sK10(powerset(powerset(X0))),X1)),unordered_pair(sK9(sK10(powerset(powerset(X0))),X1),sK8(sK10(powerset(powerset(X0))),X1))))),X2),sK7(sK10(powerset(unordered_pair(singleton(sK8(sK10(powerset(powerset(X0))),X1)),unordered_pair(sK9(sK10(powerset(powerset(X0))),X1),sK8(sK10(powerset(powerset(X0))),X1))))),X2))),X0)
| sP0(sK10(powerset(powerset(X0))),X1)
| empty(unordered_pair(singleton(sK8(sK10(powerset(powerset(X0))),X1)),unordered_pair(sK9(sK10(powerset(powerset(X0))),X1),sK8(sK10(powerset(powerset(X0))),X1))))
| sP0(sK10(powerset(unordered_pair(singleton(sK8(sK10(powerset(powerset(X0))),X1)),unordered_pair(sK9(sK10(powerset(powerset(X0))),X1),sK8(sK10(powerset(powerset(X0))),X1))))),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1094])]) ).
fof(f3126,plain,
( spl17_331
<=> ! [X2,X0,X1] :
( sP0(sK10(powerset(powerset(X0))),X1)
| element(X2,X0)
| ~ in(X2,unordered_pair(singleton(sK8(sK10(powerset(powerset(X0))),X1)),unordered_pair(sK9(sK10(powerset(powerset(X0))),X1),sK8(sK10(powerset(powerset(X0))),X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_331])]) ).
fof(f3138,plain,
( ! [X2,X0,X1] :
( element(unordered_pair(singleton(sK7(sK10(powerset(unordered_pair(singleton(sK8(sK10(powerset(powerset(X0))),X1)),unordered_pair(sK9(sK10(powerset(powerset(X0))),X1),sK8(sK10(powerset(powerset(X0))),X1))))),X2)),unordered_pair(sK8(sK10(powerset(unordered_pair(singleton(sK8(sK10(powerset(powerset(X0))),X1)),unordered_pair(sK9(sK10(powerset(powerset(X0))),X1),sK8(sK10(powerset(powerset(X0))),X1))))),X2),sK7(sK10(powerset(unordered_pair(singleton(sK8(sK10(powerset(powerset(X0))),X1)),unordered_pair(sK9(sK10(powerset(powerset(X0))),X1),sK8(sK10(powerset(powerset(X0))),X1))))),X2))),X0)
| sP0(sK10(powerset(powerset(X0))),X1)
| empty(unordered_pair(singleton(sK8(sK10(powerset(powerset(X0))),X1)),unordered_pair(sK9(sK10(powerset(powerset(X0))),X1),sK8(sK10(powerset(powerset(X0))),X1))))
| sP0(sK10(powerset(unordered_pair(singleton(sK8(sK10(powerset(powerset(X0))),X1)),unordered_pair(sK9(sK10(powerset(powerset(X0))),X1),sK8(sK10(powerset(powerset(X0))),X1))))),X2) )
| ~ spl17_321
| ~ spl17_331 ),
inference(resolution,[],[f3127,f2874]) ).
fof(f3127,plain,
( ! [X2,X0,X1] :
( ~ in(X2,unordered_pair(singleton(sK8(sK10(powerset(powerset(X0))),X1)),unordered_pair(sK9(sK10(powerset(powerset(X0))),X1),sK8(sK10(powerset(powerset(X0))),X1))))
| element(X2,X0)
| sP0(sK10(powerset(powerset(X0))),X1) )
| ~ spl17_331 ),
inference(avatar_component_clause,[],[f3126]) ).
fof(f15258,plain,
( spl17_1093
| ~ spl17_320
| ~ spl17_331 ),
inference(avatar_split_clause,[],[f3135,f3126,f2869,f15256]) ).
fof(f15256,plain,
( spl17_1093
<=> ! [X2,X0,X1] :
( element(unordered_pair(singleton(sK8(sK10(powerset(unordered_pair(singleton(sK8(sK10(powerset(powerset(X0))),X1)),unordered_pair(sK9(sK10(powerset(powerset(X0))),X1),sK8(sK10(powerset(powerset(X0))),X1))))),X2)),unordered_pair(sK9(sK10(powerset(unordered_pair(singleton(sK8(sK10(powerset(powerset(X0))),X1)),unordered_pair(sK9(sK10(powerset(powerset(X0))),X1),sK8(sK10(powerset(powerset(X0))),X1))))),X2),sK8(sK10(powerset(unordered_pair(singleton(sK8(sK10(powerset(powerset(X0))),X1)),unordered_pair(sK9(sK10(powerset(powerset(X0))),X1),sK8(sK10(powerset(powerset(X0))),X1))))),X2))),X0)
| sP0(sK10(powerset(powerset(X0))),X1)
| empty(unordered_pair(singleton(sK8(sK10(powerset(powerset(X0))),X1)),unordered_pair(sK9(sK10(powerset(powerset(X0))),X1),sK8(sK10(powerset(powerset(X0))),X1))))
| sP0(sK10(powerset(unordered_pair(singleton(sK8(sK10(powerset(powerset(X0))),X1)),unordered_pair(sK9(sK10(powerset(powerset(X0))),X1),sK8(sK10(powerset(powerset(X0))),X1))))),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1093])]) ).
fof(f3135,plain,
( ! [X2,X0,X1] :
( element(unordered_pair(singleton(sK8(sK10(powerset(unordered_pair(singleton(sK8(sK10(powerset(powerset(X0))),X1)),unordered_pair(sK9(sK10(powerset(powerset(X0))),X1),sK8(sK10(powerset(powerset(X0))),X1))))),X2)),unordered_pair(sK9(sK10(powerset(unordered_pair(singleton(sK8(sK10(powerset(powerset(X0))),X1)),unordered_pair(sK9(sK10(powerset(powerset(X0))),X1),sK8(sK10(powerset(powerset(X0))),X1))))),X2),sK8(sK10(powerset(unordered_pair(singleton(sK8(sK10(powerset(powerset(X0))),X1)),unordered_pair(sK9(sK10(powerset(powerset(X0))),X1),sK8(sK10(powerset(powerset(X0))),X1))))),X2))),X0)
| sP0(sK10(powerset(powerset(X0))),X1)
| empty(unordered_pair(singleton(sK8(sK10(powerset(powerset(X0))),X1)),unordered_pair(sK9(sK10(powerset(powerset(X0))),X1),sK8(sK10(powerset(powerset(X0))),X1))))
| sP0(sK10(powerset(unordered_pair(singleton(sK8(sK10(powerset(powerset(X0))),X1)),unordered_pair(sK9(sK10(powerset(powerset(X0))),X1),sK8(sK10(powerset(powerset(X0))),X1))))),X2) )
| ~ spl17_320
| ~ spl17_331 ),
inference(resolution,[],[f3127,f2870]) ).
fof(f15236,plain,
( spl17_1092
| ~ spl17_312
| ~ spl17_332 ),
inference(avatar_split_clause,[],[f3157,f3130,f2730,f15234]) ).
fof(f15234,plain,
( spl17_1092
<=> ! [X2,X0,X1] :
( element(unordered_pair(singleton(sK7(sK6(unordered_pair(singleton(sK7(sK10(powerset(powerset(X0))),X1)),unordered_pair(sK8(sK10(powerset(powerset(X0))),X1),sK7(sK10(powerset(powerset(X0))),X1)))),X2)),unordered_pair(sK8(sK6(unordered_pair(singleton(sK7(sK10(powerset(powerset(X0))),X1)),unordered_pair(sK8(sK10(powerset(powerset(X0))),X1),sK7(sK10(powerset(powerset(X0))),X1)))),X2),sK7(sK6(unordered_pair(singleton(sK7(sK10(powerset(powerset(X0))),X1)),unordered_pair(sK8(sK10(powerset(powerset(X0))),X1),sK7(sK10(powerset(powerset(X0))),X1)))),X2))),X0)
| sP0(sK10(powerset(powerset(X0))),X1)
| sP0(sK6(unordered_pair(singleton(sK7(sK10(powerset(powerset(X0))),X1)),unordered_pair(sK8(sK10(powerset(powerset(X0))),X1),sK7(sK10(powerset(powerset(X0))),X1)))),X2)
| empty(unordered_pair(singleton(sK7(sK10(powerset(powerset(X0))),X1)),unordered_pair(sK8(sK10(powerset(powerset(X0))),X1),sK7(sK10(powerset(powerset(X0))),X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1092])]) ).
fof(f2730,plain,
( spl17_312
<=> ! [X0,X1] :
( empty(X0)
| sP0(sK6(X0),X1)
| in(unordered_pair(singleton(sK7(sK6(X0),X1)),unordered_pair(sK8(sK6(X0),X1),sK7(sK6(X0),X1))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_312])]) ).
fof(f3157,plain,
( ! [X2,X0,X1] :
( element(unordered_pair(singleton(sK7(sK6(unordered_pair(singleton(sK7(sK10(powerset(powerset(X0))),X1)),unordered_pair(sK8(sK10(powerset(powerset(X0))),X1),sK7(sK10(powerset(powerset(X0))),X1)))),X2)),unordered_pair(sK8(sK6(unordered_pair(singleton(sK7(sK10(powerset(powerset(X0))),X1)),unordered_pair(sK8(sK10(powerset(powerset(X0))),X1),sK7(sK10(powerset(powerset(X0))),X1)))),X2),sK7(sK6(unordered_pair(singleton(sK7(sK10(powerset(powerset(X0))),X1)),unordered_pair(sK8(sK10(powerset(powerset(X0))),X1),sK7(sK10(powerset(powerset(X0))),X1)))),X2))),X0)
| sP0(sK10(powerset(powerset(X0))),X1)
| sP0(sK6(unordered_pair(singleton(sK7(sK10(powerset(powerset(X0))),X1)),unordered_pair(sK8(sK10(powerset(powerset(X0))),X1),sK7(sK10(powerset(powerset(X0))),X1)))),X2)
| empty(unordered_pair(singleton(sK7(sK10(powerset(powerset(X0))),X1)),unordered_pair(sK8(sK10(powerset(powerset(X0))),X1),sK7(sK10(powerset(powerset(X0))),X1)))) )
| ~ spl17_312
| ~ spl17_332 ),
inference(resolution,[],[f3131,f2731]) ).
fof(f2731,plain,
( ! [X0,X1] :
( in(unordered_pair(singleton(sK7(sK6(X0),X1)),unordered_pair(sK8(sK6(X0),X1),sK7(sK6(X0),X1))),X0)
| sP0(sK6(X0),X1)
| empty(X0) )
| ~ spl17_312 ),
inference(avatar_component_clause,[],[f2730]) ).
fof(f15232,plain,
( spl17_1091
| ~ spl17_311
| ~ spl17_332 ),
inference(avatar_split_clause,[],[f3154,f3130,f2726,f15230]) ).
fof(f15230,plain,
( spl17_1091
<=> ! [X2,X0,X1] :
( element(unordered_pair(singleton(sK8(sK6(unordered_pair(singleton(sK7(sK10(powerset(powerset(X0))),X1)),unordered_pair(sK8(sK10(powerset(powerset(X0))),X1),sK7(sK10(powerset(powerset(X0))),X1)))),X2)),unordered_pair(sK9(sK6(unordered_pair(singleton(sK7(sK10(powerset(powerset(X0))),X1)),unordered_pair(sK8(sK10(powerset(powerset(X0))),X1),sK7(sK10(powerset(powerset(X0))),X1)))),X2),sK8(sK6(unordered_pair(singleton(sK7(sK10(powerset(powerset(X0))),X1)),unordered_pair(sK8(sK10(powerset(powerset(X0))),X1),sK7(sK10(powerset(powerset(X0))),X1)))),X2))),X0)
| sP0(sK10(powerset(powerset(X0))),X1)
| sP0(sK6(unordered_pair(singleton(sK7(sK10(powerset(powerset(X0))),X1)),unordered_pair(sK8(sK10(powerset(powerset(X0))),X1),sK7(sK10(powerset(powerset(X0))),X1)))),X2)
| empty(unordered_pair(singleton(sK7(sK10(powerset(powerset(X0))),X1)),unordered_pair(sK8(sK10(powerset(powerset(X0))),X1),sK7(sK10(powerset(powerset(X0))),X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1091])]) ).
fof(f2726,plain,
( spl17_311
<=> ! [X0,X1] :
( empty(X0)
| sP0(sK6(X0),X1)
| in(unordered_pair(singleton(sK8(sK6(X0),X1)),unordered_pair(sK9(sK6(X0),X1),sK8(sK6(X0),X1))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_311])]) ).
fof(f3154,plain,
( ! [X2,X0,X1] :
( element(unordered_pair(singleton(sK8(sK6(unordered_pair(singleton(sK7(sK10(powerset(powerset(X0))),X1)),unordered_pair(sK8(sK10(powerset(powerset(X0))),X1),sK7(sK10(powerset(powerset(X0))),X1)))),X2)),unordered_pair(sK9(sK6(unordered_pair(singleton(sK7(sK10(powerset(powerset(X0))),X1)),unordered_pair(sK8(sK10(powerset(powerset(X0))),X1),sK7(sK10(powerset(powerset(X0))),X1)))),X2),sK8(sK6(unordered_pair(singleton(sK7(sK10(powerset(powerset(X0))),X1)),unordered_pair(sK8(sK10(powerset(powerset(X0))),X1),sK7(sK10(powerset(powerset(X0))),X1)))),X2))),X0)
| sP0(sK10(powerset(powerset(X0))),X1)
| sP0(sK6(unordered_pair(singleton(sK7(sK10(powerset(powerset(X0))),X1)),unordered_pair(sK8(sK10(powerset(powerset(X0))),X1),sK7(sK10(powerset(powerset(X0))),X1)))),X2)
| empty(unordered_pair(singleton(sK7(sK10(powerset(powerset(X0))),X1)),unordered_pair(sK8(sK10(powerset(powerset(X0))),X1),sK7(sK10(powerset(powerset(X0))),X1)))) )
| ~ spl17_311
| ~ spl17_332 ),
inference(resolution,[],[f3131,f2727]) ).
fof(f2727,plain,
( ! [X0,X1] :
( in(unordered_pair(singleton(sK8(sK6(X0),X1)),unordered_pair(sK9(sK6(X0),X1),sK8(sK6(X0),X1))),X0)
| sP0(sK6(X0),X1)
| empty(X0) )
| ~ spl17_311 ),
inference(avatar_component_clause,[],[f2726]) ).
fof(f15228,plain,
( spl17_1090
| ~ spl17_312
| ~ spl17_331 ),
inference(avatar_split_clause,[],[f3137,f3126,f2730,f15226]) ).
fof(f15226,plain,
( spl17_1090
<=> ! [X2,X0,X1] :
( element(unordered_pair(singleton(sK7(sK6(unordered_pair(singleton(sK8(sK10(powerset(powerset(X0))),X1)),unordered_pair(sK9(sK10(powerset(powerset(X0))),X1),sK8(sK10(powerset(powerset(X0))),X1)))),X2)),unordered_pair(sK8(sK6(unordered_pair(singleton(sK8(sK10(powerset(powerset(X0))),X1)),unordered_pair(sK9(sK10(powerset(powerset(X0))),X1),sK8(sK10(powerset(powerset(X0))),X1)))),X2),sK7(sK6(unordered_pair(singleton(sK8(sK10(powerset(powerset(X0))),X1)),unordered_pair(sK9(sK10(powerset(powerset(X0))),X1),sK8(sK10(powerset(powerset(X0))),X1)))),X2))),X0)
| sP0(sK10(powerset(powerset(X0))),X1)
| sP0(sK6(unordered_pair(singleton(sK8(sK10(powerset(powerset(X0))),X1)),unordered_pair(sK9(sK10(powerset(powerset(X0))),X1),sK8(sK10(powerset(powerset(X0))),X1)))),X2)
| empty(unordered_pair(singleton(sK8(sK10(powerset(powerset(X0))),X1)),unordered_pair(sK9(sK10(powerset(powerset(X0))),X1),sK8(sK10(powerset(powerset(X0))),X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1090])]) ).
fof(f3137,plain,
( ! [X2,X0,X1] :
( element(unordered_pair(singleton(sK7(sK6(unordered_pair(singleton(sK8(sK10(powerset(powerset(X0))),X1)),unordered_pair(sK9(sK10(powerset(powerset(X0))),X1),sK8(sK10(powerset(powerset(X0))),X1)))),X2)),unordered_pair(sK8(sK6(unordered_pair(singleton(sK8(sK10(powerset(powerset(X0))),X1)),unordered_pair(sK9(sK10(powerset(powerset(X0))),X1),sK8(sK10(powerset(powerset(X0))),X1)))),X2),sK7(sK6(unordered_pair(singleton(sK8(sK10(powerset(powerset(X0))),X1)),unordered_pair(sK9(sK10(powerset(powerset(X0))),X1),sK8(sK10(powerset(powerset(X0))),X1)))),X2))),X0)
| sP0(sK10(powerset(powerset(X0))),X1)
| sP0(sK6(unordered_pair(singleton(sK8(sK10(powerset(powerset(X0))),X1)),unordered_pair(sK9(sK10(powerset(powerset(X0))),X1),sK8(sK10(powerset(powerset(X0))),X1)))),X2)
| empty(unordered_pair(singleton(sK8(sK10(powerset(powerset(X0))),X1)),unordered_pair(sK9(sK10(powerset(powerset(X0))),X1),sK8(sK10(powerset(powerset(X0))),X1)))) )
| ~ spl17_312
| ~ spl17_331 ),
inference(resolution,[],[f3127,f2731]) ).
fof(f15224,plain,
( spl17_1089
| ~ spl17_311
| ~ spl17_331 ),
inference(avatar_split_clause,[],[f3134,f3126,f2726,f15222]) ).
fof(f15222,plain,
( spl17_1089
<=> ! [X2,X0,X1] :
( element(unordered_pair(singleton(sK8(sK6(unordered_pair(singleton(sK8(sK10(powerset(powerset(X0))),X1)),unordered_pair(sK9(sK10(powerset(powerset(X0))),X1),sK8(sK10(powerset(powerset(X0))),X1)))),X2)),unordered_pair(sK9(sK6(unordered_pair(singleton(sK8(sK10(powerset(powerset(X0))),X1)),unordered_pair(sK9(sK10(powerset(powerset(X0))),X1),sK8(sK10(powerset(powerset(X0))),X1)))),X2),sK8(sK6(unordered_pair(singleton(sK8(sK10(powerset(powerset(X0))),X1)),unordered_pair(sK9(sK10(powerset(powerset(X0))),X1),sK8(sK10(powerset(powerset(X0))),X1)))),X2))),X0)
| sP0(sK10(powerset(powerset(X0))),X1)
| sP0(sK6(unordered_pair(singleton(sK8(sK10(powerset(powerset(X0))),X1)),unordered_pair(sK9(sK10(powerset(powerset(X0))),X1),sK8(sK10(powerset(powerset(X0))),X1)))),X2)
| empty(unordered_pair(singleton(sK8(sK10(powerset(powerset(X0))),X1)),unordered_pair(sK9(sK10(powerset(powerset(X0))),X1),sK8(sK10(powerset(powerset(X0))),X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1089])]) ).
fof(f3134,plain,
( ! [X2,X0,X1] :
( element(unordered_pair(singleton(sK8(sK6(unordered_pair(singleton(sK8(sK10(powerset(powerset(X0))),X1)),unordered_pair(sK9(sK10(powerset(powerset(X0))),X1),sK8(sK10(powerset(powerset(X0))),X1)))),X2)),unordered_pair(sK9(sK6(unordered_pair(singleton(sK8(sK10(powerset(powerset(X0))),X1)),unordered_pair(sK9(sK10(powerset(powerset(X0))),X1),sK8(sK10(powerset(powerset(X0))),X1)))),X2),sK8(sK6(unordered_pair(singleton(sK8(sK10(powerset(powerset(X0))),X1)),unordered_pair(sK9(sK10(powerset(powerset(X0))),X1),sK8(sK10(powerset(powerset(X0))),X1)))),X2))),X0)
| sP0(sK10(powerset(powerset(X0))),X1)
| sP0(sK6(unordered_pair(singleton(sK8(sK10(powerset(powerset(X0))),X1)),unordered_pair(sK9(sK10(powerset(powerset(X0))),X1),sK8(sK10(powerset(powerset(X0))),X1)))),X2)
| empty(unordered_pair(singleton(sK8(sK10(powerset(powerset(X0))),X1)),unordered_pair(sK9(sK10(powerset(powerset(X0))),X1),sK8(sK10(powerset(powerset(X0))),X1)))) )
| ~ spl17_311
| ~ spl17_331 ),
inference(resolution,[],[f3127,f2727]) ).
fof(f15204,plain,
( spl17_1088
| ~ spl17_321
| ~ spl17_328 ),
inference(avatar_split_clause,[],[f3076,f3042,f2873,f15202]) ).
fof(f15202,plain,
( spl17_1088
<=> ! [X2,X0,X1] :
( sP0(sK6(powerset(X0)),X1)
| element(unordered_pair(singleton(sK7(sK10(powerset(unordered_pair(singleton(sK7(sK6(powerset(X0)),X1)),unordered_pair(sK8(sK6(powerset(X0)),X1),sK7(sK6(powerset(X0)),X1))))),X2)),unordered_pair(sK8(sK10(powerset(unordered_pair(singleton(sK7(sK6(powerset(X0)),X1)),unordered_pair(sK8(sK6(powerset(X0)),X1),sK7(sK6(powerset(X0)),X1))))),X2),sK7(sK10(powerset(unordered_pair(singleton(sK7(sK6(powerset(X0)),X1)),unordered_pair(sK8(sK6(powerset(X0)),X1),sK7(sK6(powerset(X0)),X1))))),X2))),X0)
| empty(powerset(X0))
| empty(unordered_pair(singleton(sK7(sK6(powerset(X0)),X1)),unordered_pair(sK8(sK6(powerset(X0)),X1),sK7(sK6(powerset(X0)),X1))))
| sP0(sK10(powerset(unordered_pair(singleton(sK7(sK6(powerset(X0)),X1)),unordered_pair(sK8(sK6(powerset(X0)),X1),sK7(sK6(powerset(X0)),X1))))),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1088])]) ).
fof(f3042,plain,
( spl17_328
<=> ! [X2,X0,X1] :
( empty(powerset(X0))
| sP0(sK6(powerset(X0)),X1)
| element(X2,X0)
| ~ in(X2,unordered_pair(singleton(sK7(sK6(powerset(X0)),X1)),unordered_pair(sK8(sK6(powerset(X0)),X1),sK7(sK6(powerset(X0)),X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_328])]) ).
fof(f3076,plain,
( ! [X2,X0,X1] :
( sP0(sK6(powerset(X0)),X1)
| element(unordered_pair(singleton(sK7(sK10(powerset(unordered_pair(singleton(sK7(sK6(powerset(X0)),X1)),unordered_pair(sK8(sK6(powerset(X0)),X1),sK7(sK6(powerset(X0)),X1))))),X2)),unordered_pair(sK8(sK10(powerset(unordered_pair(singleton(sK7(sK6(powerset(X0)),X1)),unordered_pair(sK8(sK6(powerset(X0)),X1),sK7(sK6(powerset(X0)),X1))))),X2),sK7(sK10(powerset(unordered_pair(singleton(sK7(sK6(powerset(X0)),X1)),unordered_pair(sK8(sK6(powerset(X0)),X1),sK7(sK6(powerset(X0)),X1))))),X2))),X0)
| empty(powerset(X0))
| empty(unordered_pair(singleton(sK7(sK6(powerset(X0)),X1)),unordered_pair(sK8(sK6(powerset(X0)),X1),sK7(sK6(powerset(X0)),X1))))
| sP0(sK10(powerset(unordered_pair(singleton(sK7(sK6(powerset(X0)),X1)),unordered_pair(sK8(sK6(powerset(X0)),X1),sK7(sK6(powerset(X0)),X1))))),X2) )
| ~ spl17_321
| ~ spl17_328 ),
inference(resolution,[],[f3043,f2874]) ).
fof(f3043,plain,
( ! [X2,X0,X1] :
( ~ in(X2,unordered_pair(singleton(sK7(sK6(powerset(X0)),X1)),unordered_pair(sK8(sK6(powerset(X0)),X1),sK7(sK6(powerset(X0)),X1))))
| sP0(sK6(powerset(X0)),X1)
| element(X2,X0)
| empty(powerset(X0)) )
| ~ spl17_328 ),
inference(avatar_component_clause,[],[f3042]) ).
fof(f15200,plain,
( spl17_1087
| ~ spl17_320
| ~ spl17_328 ),
inference(avatar_split_clause,[],[f3073,f3042,f2869,f15198]) ).
fof(f15198,plain,
( spl17_1087
<=> ! [X2,X0,X1] :
( sP0(sK6(powerset(X0)),X1)
| element(unordered_pair(singleton(sK8(sK10(powerset(unordered_pair(singleton(sK7(sK6(powerset(X0)),X1)),unordered_pair(sK8(sK6(powerset(X0)),X1),sK7(sK6(powerset(X0)),X1))))),X2)),unordered_pair(sK9(sK10(powerset(unordered_pair(singleton(sK7(sK6(powerset(X0)),X1)),unordered_pair(sK8(sK6(powerset(X0)),X1),sK7(sK6(powerset(X0)),X1))))),X2),sK8(sK10(powerset(unordered_pair(singleton(sK7(sK6(powerset(X0)),X1)),unordered_pair(sK8(sK6(powerset(X0)),X1),sK7(sK6(powerset(X0)),X1))))),X2))),X0)
| empty(powerset(X0))
| empty(unordered_pair(singleton(sK7(sK6(powerset(X0)),X1)),unordered_pair(sK8(sK6(powerset(X0)),X1),sK7(sK6(powerset(X0)),X1))))
| sP0(sK10(powerset(unordered_pair(singleton(sK7(sK6(powerset(X0)),X1)),unordered_pair(sK8(sK6(powerset(X0)),X1),sK7(sK6(powerset(X0)),X1))))),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1087])]) ).
fof(f3073,plain,
( ! [X2,X0,X1] :
( sP0(sK6(powerset(X0)),X1)
| element(unordered_pair(singleton(sK8(sK10(powerset(unordered_pair(singleton(sK7(sK6(powerset(X0)),X1)),unordered_pair(sK8(sK6(powerset(X0)),X1),sK7(sK6(powerset(X0)),X1))))),X2)),unordered_pair(sK9(sK10(powerset(unordered_pair(singleton(sK7(sK6(powerset(X0)),X1)),unordered_pair(sK8(sK6(powerset(X0)),X1),sK7(sK6(powerset(X0)),X1))))),X2),sK8(sK10(powerset(unordered_pair(singleton(sK7(sK6(powerset(X0)),X1)),unordered_pair(sK8(sK6(powerset(X0)),X1),sK7(sK6(powerset(X0)),X1))))),X2))),X0)
| empty(powerset(X0))
| empty(unordered_pair(singleton(sK7(sK6(powerset(X0)),X1)),unordered_pair(sK8(sK6(powerset(X0)),X1),sK7(sK6(powerset(X0)),X1))))
| sP0(sK10(powerset(unordered_pair(singleton(sK7(sK6(powerset(X0)),X1)),unordered_pair(sK8(sK6(powerset(X0)),X1),sK7(sK6(powerset(X0)),X1))))),X2) )
| ~ spl17_320
| ~ spl17_328 ),
inference(resolution,[],[f3043,f2870]) ).
fof(f15193,plain,
( spl17_1086
| ~ spl17_321
| ~ spl17_326 ),
inference(avatar_split_clause,[],[f3058,f3034,f2873,f15191]) ).
fof(f15191,plain,
( spl17_1086
<=> ! [X2,X0,X1] :
( sP0(sK6(powerset(X0)),X1)
| element(unordered_pair(singleton(sK7(sK10(powerset(unordered_pair(singleton(sK8(sK6(powerset(X0)),X1)),unordered_pair(sK9(sK6(powerset(X0)),X1),sK8(sK6(powerset(X0)),X1))))),X2)),unordered_pair(sK8(sK10(powerset(unordered_pair(singleton(sK8(sK6(powerset(X0)),X1)),unordered_pair(sK9(sK6(powerset(X0)),X1),sK8(sK6(powerset(X0)),X1))))),X2),sK7(sK10(powerset(unordered_pair(singleton(sK8(sK6(powerset(X0)),X1)),unordered_pair(sK9(sK6(powerset(X0)),X1),sK8(sK6(powerset(X0)),X1))))),X2))),X0)
| empty(powerset(X0))
| empty(unordered_pair(singleton(sK8(sK6(powerset(X0)),X1)),unordered_pair(sK9(sK6(powerset(X0)),X1),sK8(sK6(powerset(X0)),X1))))
| sP0(sK10(powerset(unordered_pair(singleton(sK8(sK6(powerset(X0)),X1)),unordered_pair(sK9(sK6(powerset(X0)),X1),sK8(sK6(powerset(X0)),X1))))),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1086])]) ).
fof(f3034,plain,
( spl17_326
<=> ! [X2,X0,X1] :
( empty(powerset(X0))
| sP0(sK6(powerset(X0)),X1)
| element(X2,X0)
| ~ in(X2,unordered_pair(singleton(sK8(sK6(powerset(X0)),X1)),unordered_pair(sK9(sK6(powerset(X0)),X1),sK8(sK6(powerset(X0)),X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_326])]) ).
fof(f3058,plain,
( ! [X2,X0,X1] :
( sP0(sK6(powerset(X0)),X1)
| element(unordered_pair(singleton(sK7(sK10(powerset(unordered_pair(singleton(sK8(sK6(powerset(X0)),X1)),unordered_pair(sK9(sK6(powerset(X0)),X1),sK8(sK6(powerset(X0)),X1))))),X2)),unordered_pair(sK8(sK10(powerset(unordered_pair(singleton(sK8(sK6(powerset(X0)),X1)),unordered_pair(sK9(sK6(powerset(X0)),X1),sK8(sK6(powerset(X0)),X1))))),X2),sK7(sK10(powerset(unordered_pair(singleton(sK8(sK6(powerset(X0)),X1)),unordered_pair(sK9(sK6(powerset(X0)),X1),sK8(sK6(powerset(X0)),X1))))),X2))),X0)
| empty(powerset(X0))
| empty(unordered_pair(singleton(sK8(sK6(powerset(X0)),X1)),unordered_pair(sK9(sK6(powerset(X0)),X1),sK8(sK6(powerset(X0)),X1))))
| sP0(sK10(powerset(unordered_pair(singleton(sK8(sK6(powerset(X0)),X1)),unordered_pair(sK9(sK6(powerset(X0)),X1),sK8(sK6(powerset(X0)),X1))))),X2) )
| ~ spl17_321
| ~ spl17_326 ),
inference(resolution,[],[f3035,f2874]) ).
fof(f3035,plain,
( ! [X2,X0,X1] :
( ~ in(X2,unordered_pair(singleton(sK8(sK6(powerset(X0)),X1)),unordered_pair(sK9(sK6(powerset(X0)),X1),sK8(sK6(powerset(X0)),X1))))
| sP0(sK6(powerset(X0)),X1)
| element(X2,X0)
| empty(powerset(X0)) )
| ~ spl17_326 ),
inference(avatar_component_clause,[],[f3034]) ).
fof(f15189,plain,
( spl17_1085
| ~ spl17_320
| ~ spl17_326 ),
inference(avatar_split_clause,[],[f3055,f3034,f2869,f15187]) ).
fof(f15187,plain,
( spl17_1085
<=> ! [X2,X0,X1] :
( sP0(sK6(powerset(X0)),X1)
| element(unordered_pair(singleton(sK8(sK10(powerset(unordered_pair(singleton(sK8(sK6(powerset(X0)),X1)),unordered_pair(sK9(sK6(powerset(X0)),X1),sK8(sK6(powerset(X0)),X1))))),X2)),unordered_pair(sK9(sK10(powerset(unordered_pair(singleton(sK8(sK6(powerset(X0)),X1)),unordered_pair(sK9(sK6(powerset(X0)),X1),sK8(sK6(powerset(X0)),X1))))),X2),sK8(sK10(powerset(unordered_pair(singleton(sK8(sK6(powerset(X0)),X1)),unordered_pair(sK9(sK6(powerset(X0)),X1),sK8(sK6(powerset(X0)),X1))))),X2))),X0)
| empty(powerset(X0))
| empty(unordered_pair(singleton(sK8(sK6(powerset(X0)),X1)),unordered_pair(sK9(sK6(powerset(X0)),X1),sK8(sK6(powerset(X0)),X1))))
| sP0(sK10(powerset(unordered_pair(singleton(sK8(sK6(powerset(X0)),X1)),unordered_pair(sK9(sK6(powerset(X0)),X1),sK8(sK6(powerset(X0)),X1))))),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1085])]) ).
fof(f3055,plain,
( ! [X2,X0,X1] :
( sP0(sK6(powerset(X0)),X1)
| element(unordered_pair(singleton(sK8(sK10(powerset(unordered_pair(singleton(sK8(sK6(powerset(X0)),X1)),unordered_pair(sK9(sK6(powerset(X0)),X1),sK8(sK6(powerset(X0)),X1))))),X2)),unordered_pair(sK9(sK10(powerset(unordered_pair(singleton(sK8(sK6(powerset(X0)),X1)),unordered_pair(sK9(sK6(powerset(X0)),X1),sK8(sK6(powerset(X0)),X1))))),X2),sK8(sK10(powerset(unordered_pair(singleton(sK8(sK6(powerset(X0)),X1)),unordered_pair(sK9(sK6(powerset(X0)),X1),sK8(sK6(powerset(X0)),X1))))),X2))),X0)
| empty(powerset(X0))
| empty(unordered_pair(singleton(sK8(sK6(powerset(X0)),X1)),unordered_pair(sK9(sK6(powerset(X0)),X1),sK8(sK6(powerset(X0)),X1))))
| sP0(sK10(powerset(unordered_pair(singleton(sK8(sK6(powerset(X0)),X1)),unordered_pair(sK9(sK6(powerset(X0)),X1),sK8(sK6(powerset(X0)),X1))))),X2) )
| ~ spl17_320
| ~ spl17_326 ),
inference(resolution,[],[f3035,f2870]) ).
fof(f15169,plain,
( spl17_1084
| ~ spl17_312
| ~ spl17_328 ),
inference(avatar_split_clause,[],[f3075,f3042,f2730,f15167]) ).
fof(f15167,plain,
( spl17_1084
<=> ! [X2,X0,X1] :
( sP0(sK6(powerset(X0)),X1)
| element(unordered_pair(singleton(sK7(sK6(unordered_pair(singleton(sK7(sK6(powerset(X0)),X1)),unordered_pair(sK8(sK6(powerset(X0)),X1),sK7(sK6(powerset(X0)),X1)))),X2)),unordered_pair(sK8(sK6(unordered_pair(singleton(sK7(sK6(powerset(X0)),X1)),unordered_pair(sK8(sK6(powerset(X0)),X1),sK7(sK6(powerset(X0)),X1)))),X2),sK7(sK6(unordered_pair(singleton(sK7(sK6(powerset(X0)),X1)),unordered_pair(sK8(sK6(powerset(X0)),X1),sK7(sK6(powerset(X0)),X1)))),X2))),X0)
| empty(powerset(X0))
| sP0(sK6(unordered_pair(singleton(sK7(sK6(powerset(X0)),X1)),unordered_pair(sK8(sK6(powerset(X0)),X1),sK7(sK6(powerset(X0)),X1)))),X2)
| empty(unordered_pair(singleton(sK7(sK6(powerset(X0)),X1)),unordered_pair(sK8(sK6(powerset(X0)),X1),sK7(sK6(powerset(X0)),X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1084])]) ).
fof(f3075,plain,
( ! [X2,X0,X1] :
( sP0(sK6(powerset(X0)),X1)
| element(unordered_pair(singleton(sK7(sK6(unordered_pair(singleton(sK7(sK6(powerset(X0)),X1)),unordered_pair(sK8(sK6(powerset(X0)),X1),sK7(sK6(powerset(X0)),X1)))),X2)),unordered_pair(sK8(sK6(unordered_pair(singleton(sK7(sK6(powerset(X0)),X1)),unordered_pair(sK8(sK6(powerset(X0)),X1),sK7(sK6(powerset(X0)),X1)))),X2),sK7(sK6(unordered_pair(singleton(sK7(sK6(powerset(X0)),X1)),unordered_pair(sK8(sK6(powerset(X0)),X1),sK7(sK6(powerset(X0)),X1)))),X2))),X0)
| empty(powerset(X0))
| sP0(sK6(unordered_pair(singleton(sK7(sK6(powerset(X0)),X1)),unordered_pair(sK8(sK6(powerset(X0)),X1),sK7(sK6(powerset(X0)),X1)))),X2)
| empty(unordered_pair(singleton(sK7(sK6(powerset(X0)),X1)),unordered_pair(sK8(sK6(powerset(X0)),X1),sK7(sK6(powerset(X0)),X1)))) )
| ~ spl17_312
| ~ spl17_328 ),
inference(resolution,[],[f3043,f2731]) ).
fof(f15165,plain,
( spl17_1083
| ~ spl17_311
| ~ spl17_328 ),
inference(avatar_split_clause,[],[f3072,f3042,f2726,f15163]) ).
fof(f15163,plain,
( spl17_1083
<=> ! [X2,X0,X1] :
( sP0(sK6(powerset(X0)),X1)
| element(unordered_pair(singleton(sK8(sK6(unordered_pair(singleton(sK7(sK6(powerset(X0)),X1)),unordered_pair(sK8(sK6(powerset(X0)),X1),sK7(sK6(powerset(X0)),X1)))),X2)),unordered_pair(sK9(sK6(unordered_pair(singleton(sK7(sK6(powerset(X0)),X1)),unordered_pair(sK8(sK6(powerset(X0)),X1),sK7(sK6(powerset(X0)),X1)))),X2),sK8(sK6(unordered_pair(singleton(sK7(sK6(powerset(X0)),X1)),unordered_pair(sK8(sK6(powerset(X0)),X1),sK7(sK6(powerset(X0)),X1)))),X2))),X0)
| empty(powerset(X0))
| sP0(sK6(unordered_pair(singleton(sK7(sK6(powerset(X0)),X1)),unordered_pair(sK8(sK6(powerset(X0)),X1),sK7(sK6(powerset(X0)),X1)))),X2)
| empty(unordered_pair(singleton(sK7(sK6(powerset(X0)),X1)),unordered_pair(sK8(sK6(powerset(X0)),X1),sK7(sK6(powerset(X0)),X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1083])]) ).
fof(f3072,plain,
( ! [X2,X0,X1] :
( sP0(sK6(powerset(X0)),X1)
| element(unordered_pair(singleton(sK8(sK6(unordered_pair(singleton(sK7(sK6(powerset(X0)),X1)),unordered_pair(sK8(sK6(powerset(X0)),X1),sK7(sK6(powerset(X0)),X1)))),X2)),unordered_pair(sK9(sK6(unordered_pair(singleton(sK7(sK6(powerset(X0)),X1)),unordered_pair(sK8(sK6(powerset(X0)),X1),sK7(sK6(powerset(X0)),X1)))),X2),sK8(sK6(unordered_pair(singleton(sK7(sK6(powerset(X0)),X1)),unordered_pair(sK8(sK6(powerset(X0)),X1),sK7(sK6(powerset(X0)),X1)))),X2))),X0)
| empty(powerset(X0))
| sP0(sK6(unordered_pair(singleton(sK7(sK6(powerset(X0)),X1)),unordered_pair(sK8(sK6(powerset(X0)),X1),sK7(sK6(powerset(X0)),X1)))),X2)
| empty(unordered_pair(singleton(sK7(sK6(powerset(X0)),X1)),unordered_pair(sK8(sK6(powerset(X0)),X1),sK7(sK6(powerset(X0)),X1)))) )
| ~ spl17_311
| ~ spl17_328 ),
inference(resolution,[],[f3043,f2727]) ).
fof(f15161,plain,
( spl17_1082
| ~ spl17_312
| ~ spl17_326 ),
inference(avatar_split_clause,[],[f3057,f3034,f2730,f15159]) ).
fof(f15159,plain,
( spl17_1082
<=> ! [X2,X0,X1] :
( sP0(sK6(powerset(X0)),X1)
| element(unordered_pair(singleton(sK7(sK6(unordered_pair(singleton(sK8(sK6(powerset(X0)),X1)),unordered_pair(sK9(sK6(powerset(X0)),X1),sK8(sK6(powerset(X0)),X1)))),X2)),unordered_pair(sK8(sK6(unordered_pair(singleton(sK8(sK6(powerset(X0)),X1)),unordered_pair(sK9(sK6(powerset(X0)),X1),sK8(sK6(powerset(X0)),X1)))),X2),sK7(sK6(unordered_pair(singleton(sK8(sK6(powerset(X0)),X1)),unordered_pair(sK9(sK6(powerset(X0)),X1),sK8(sK6(powerset(X0)),X1)))),X2))),X0)
| empty(powerset(X0))
| sP0(sK6(unordered_pair(singleton(sK8(sK6(powerset(X0)),X1)),unordered_pair(sK9(sK6(powerset(X0)),X1),sK8(sK6(powerset(X0)),X1)))),X2)
| empty(unordered_pair(singleton(sK8(sK6(powerset(X0)),X1)),unordered_pair(sK9(sK6(powerset(X0)),X1),sK8(sK6(powerset(X0)),X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1082])]) ).
fof(f3057,plain,
( ! [X2,X0,X1] :
( sP0(sK6(powerset(X0)),X1)
| element(unordered_pair(singleton(sK7(sK6(unordered_pair(singleton(sK8(sK6(powerset(X0)),X1)),unordered_pair(sK9(sK6(powerset(X0)),X1),sK8(sK6(powerset(X0)),X1)))),X2)),unordered_pair(sK8(sK6(unordered_pair(singleton(sK8(sK6(powerset(X0)),X1)),unordered_pair(sK9(sK6(powerset(X0)),X1),sK8(sK6(powerset(X0)),X1)))),X2),sK7(sK6(unordered_pair(singleton(sK8(sK6(powerset(X0)),X1)),unordered_pair(sK9(sK6(powerset(X0)),X1),sK8(sK6(powerset(X0)),X1)))),X2))),X0)
| empty(powerset(X0))
| sP0(sK6(unordered_pair(singleton(sK8(sK6(powerset(X0)),X1)),unordered_pair(sK9(sK6(powerset(X0)),X1),sK8(sK6(powerset(X0)),X1)))),X2)
| empty(unordered_pair(singleton(sK8(sK6(powerset(X0)),X1)),unordered_pair(sK9(sK6(powerset(X0)),X1),sK8(sK6(powerset(X0)),X1)))) )
| ~ spl17_312
| ~ spl17_326 ),
inference(resolution,[],[f3035,f2731]) ).
fof(f15157,plain,
( spl17_1081
| ~ spl17_311
| ~ spl17_326 ),
inference(avatar_split_clause,[],[f3054,f3034,f2726,f15155]) ).
fof(f15155,plain,
( spl17_1081
<=> ! [X2,X0,X1] :
( sP0(sK6(powerset(X0)),X1)
| element(unordered_pair(singleton(sK8(sK6(unordered_pair(singleton(sK8(sK6(powerset(X0)),X1)),unordered_pair(sK9(sK6(powerset(X0)),X1),sK8(sK6(powerset(X0)),X1)))),X2)),unordered_pair(sK9(sK6(unordered_pair(singleton(sK8(sK6(powerset(X0)),X1)),unordered_pair(sK9(sK6(powerset(X0)),X1),sK8(sK6(powerset(X0)),X1)))),X2),sK8(sK6(unordered_pair(singleton(sK8(sK6(powerset(X0)),X1)),unordered_pair(sK9(sK6(powerset(X0)),X1),sK8(sK6(powerset(X0)),X1)))),X2))),X0)
| empty(powerset(X0))
| sP0(sK6(unordered_pair(singleton(sK8(sK6(powerset(X0)),X1)),unordered_pair(sK9(sK6(powerset(X0)),X1),sK8(sK6(powerset(X0)),X1)))),X2)
| empty(unordered_pair(singleton(sK8(sK6(powerset(X0)),X1)),unordered_pair(sK9(sK6(powerset(X0)),X1),sK8(sK6(powerset(X0)),X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1081])]) ).
fof(f3054,plain,
( ! [X2,X0,X1] :
( sP0(sK6(powerset(X0)),X1)
| element(unordered_pair(singleton(sK8(sK6(unordered_pair(singleton(sK8(sK6(powerset(X0)),X1)),unordered_pair(sK9(sK6(powerset(X0)),X1),sK8(sK6(powerset(X0)),X1)))),X2)),unordered_pair(sK9(sK6(unordered_pair(singleton(sK8(sK6(powerset(X0)),X1)),unordered_pair(sK9(sK6(powerset(X0)),X1),sK8(sK6(powerset(X0)),X1)))),X2),sK8(sK6(unordered_pair(singleton(sK8(sK6(powerset(X0)),X1)),unordered_pair(sK9(sK6(powerset(X0)),X1),sK8(sK6(powerset(X0)),X1)))),X2))),X0)
| empty(powerset(X0))
| sP0(sK6(unordered_pair(singleton(sK8(sK6(powerset(X0)),X1)),unordered_pair(sK9(sK6(powerset(X0)),X1),sK8(sK6(powerset(X0)),X1)))),X2)
| empty(unordered_pair(singleton(sK8(sK6(powerset(X0)),X1)),unordered_pair(sK9(sK6(powerset(X0)),X1),sK8(sK6(powerset(X0)),X1)))) )
| ~ spl17_311
| ~ spl17_326 ),
inference(resolution,[],[f3035,f2727]) ).
fof(f15147,plain,
( spl17_1080
| ~ spl17_41
| ~ spl17_392 ),
inference(avatar_split_clause,[],[f3732,f3716,f363,f15145]) ).
fof(f15145,plain,
( spl17_1080
<=> ! [X0,X3,X2,X1] :
( sP0(powerset(powerset(cartesian_product2(X0,X1))),X2)
| sP0(unordered_pair(singleton(sK7(powerset(powerset(cartesian_product2(X0,X1))),X2)),unordered_pair(sK8(powerset(powerset(cartesian_product2(X0,X1))),X2),sK7(powerset(powerset(cartesian_product2(X0,X1))),X2))),X3)
| relation(unordered_pair(singleton(sK7(unordered_pair(singleton(sK7(powerset(powerset(cartesian_product2(X0,X1))),X2)),unordered_pair(sK8(powerset(powerset(cartesian_product2(X0,X1))),X2),sK7(powerset(powerset(cartesian_product2(X0,X1))),X2))),X3)),unordered_pair(sK8(unordered_pair(singleton(sK7(powerset(powerset(cartesian_product2(X0,X1))),X2)),unordered_pair(sK8(powerset(powerset(cartesian_product2(X0,X1))),X2),sK7(powerset(powerset(cartesian_product2(X0,X1))),X2))),X3),sK7(unordered_pair(singleton(sK7(powerset(powerset(cartesian_product2(X0,X1))),X2)),unordered_pair(sK8(powerset(powerset(cartesian_product2(X0,X1))),X2),sK7(powerset(powerset(cartesian_product2(X0,X1))),X2))),X3)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1080])]) ).
fof(f363,plain,
( spl17_41
<=> ! [X2,X0,X1] :
( relation(X2)
| ~ element(X2,powerset(cartesian_product2(X0,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_41])]) ).
fof(f3716,plain,
( spl17_392
<=> ! [X2,X0,X1] :
( element(unordered_pair(singleton(sK7(unordered_pair(singleton(sK7(powerset(X0),X1)),unordered_pair(sK8(powerset(X0),X1),sK7(powerset(X0),X1))),X2)),unordered_pair(sK8(unordered_pair(singleton(sK7(powerset(X0),X1)),unordered_pair(sK8(powerset(X0),X1),sK7(powerset(X0),X1))),X2),sK7(unordered_pair(singleton(sK7(powerset(X0),X1)),unordered_pair(sK8(powerset(X0),X1),sK7(powerset(X0),X1))),X2))),X0)
| sP0(powerset(X0),X1)
| sP0(unordered_pair(singleton(sK7(powerset(X0),X1)),unordered_pair(sK8(powerset(X0),X1),sK7(powerset(X0),X1))),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_392])]) ).
fof(f3732,plain,
( ! [X2,X3,X0,X1] :
( sP0(powerset(powerset(cartesian_product2(X0,X1))),X2)
| sP0(unordered_pair(singleton(sK7(powerset(powerset(cartesian_product2(X0,X1))),X2)),unordered_pair(sK8(powerset(powerset(cartesian_product2(X0,X1))),X2),sK7(powerset(powerset(cartesian_product2(X0,X1))),X2))),X3)
| relation(unordered_pair(singleton(sK7(unordered_pair(singleton(sK7(powerset(powerset(cartesian_product2(X0,X1))),X2)),unordered_pair(sK8(powerset(powerset(cartesian_product2(X0,X1))),X2),sK7(powerset(powerset(cartesian_product2(X0,X1))),X2))),X3)),unordered_pair(sK8(unordered_pair(singleton(sK7(powerset(powerset(cartesian_product2(X0,X1))),X2)),unordered_pair(sK8(powerset(powerset(cartesian_product2(X0,X1))),X2),sK7(powerset(powerset(cartesian_product2(X0,X1))),X2))),X3),sK7(unordered_pair(singleton(sK7(powerset(powerset(cartesian_product2(X0,X1))),X2)),unordered_pair(sK8(powerset(powerset(cartesian_product2(X0,X1))),X2),sK7(powerset(powerset(cartesian_product2(X0,X1))),X2))),X3)))) )
| ~ spl17_41
| ~ spl17_392 ),
inference(resolution,[],[f3717,f364]) ).
fof(f364,plain,
( ! [X2,X0,X1] :
( ~ element(X2,powerset(cartesian_product2(X0,X1)))
| relation(X2) )
| ~ spl17_41 ),
inference(avatar_component_clause,[],[f363]) ).
fof(f3717,plain,
( ! [X2,X0,X1] :
( element(unordered_pair(singleton(sK7(unordered_pair(singleton(sK7(powerset(X0),X1)),unordered_pair(sK8(powerset(X0),X1),sK7(powerset(X0),X1))),X2)),unordered_pair(sK8(unordered_pair(singleton(sK7(powerset(X0),X1)),unordered_pair(sK8(powerset(X0),X1),sK7(powerset(X0),X1))),X2),sK7(unordered_pair(singleton(sK7(powerset(X0),X1)),unordered_pair(sK8(powerset(X0),X1),sK7(powerset(X0),X1))),X2))),X0)
| sP0(powerset(X0),X1)
| sP0(unordered_pair(singleton(sK7(powerset(X0),X1)),unordered_pair(sK8(powerset(X0),X1),sK7(powerset(X0),X1))),X2) )
| ~ spl17_392 ),
inference(avatar_component_clause,[],[f3716]) ).
fof(f15143,plain,
( spl17_1079
| ~ spl17_41
| ~ spl17_391 ),
inference(avatar_split_clause,[],[f3728,f3712,f363,f15141]) ).
fof(f15141,plain,
( spl17_1079
<=> ! [X0,X3,X2,X1] :
( sP0(powerset(powerset(cartesian_product2(X0,X1))),X2)
| sP0(unordered_pair(singleton(sK7(powerset(powerset(cartesian_product2(X0,X1))),X2)),unordered_pair(sK8(powerset(powerset(cartesian_product2(X0,X1))),X2),sK7(powerset(powerset(cartesian_product2(X0,X1))),X2))),X3)
| relation(unordered_pair(singleton(sK8(unordered_pair(singleton(sK7(powerset(powerset(cartesian_product2(X0,X1))),X2)),unordered_pair(sK8(powerset(powerset(cartesian_product2(X0,X1))),X2),sK7(powerset(powerset(cartesian_product2(X0,X1))),X2))),X3)),unordered_pair(sK9(unordered_pair(singleton(sK7(powerset(powerset(cartesian_product2(X0,X1))),X2)),unordered_pair(sK8(powerset(powerset(cartesian_product2(X0,X1))),X2),sK7(powerset(powerset(cartesian_product2(X0,X1))),X2))),X3),sK8(unordered_pair(singleton(sK7(powerset(powerset(cartesian_product2(X0,X1))),X2)),unordered_pair(sK8(powerset(powerset(cartesian_product2(X0,X1))),X2),sK7(powerset(powerset(cartesian_product2(X0,X1))),X2))),X3)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1079])]) ).
fof(f3712,plain,
( spl17_391
<=> ! [X2,X0,X1] :
( element(unordered_pair(singleton(sK8(unordered_pair(singleton(sK7(powerset(X0),X1)),unordered_pair(sK8(powerset(X0),X1),sK7(powerset(X0),X1))),X2)),unordered_pair(sK9(unordered_pair(singleton(sK7(powerset(X0),X1)),unordered_pair(sK8(powerset(X0),X1),sK7(powerset(X0),X1))),X2),sK8(unordered_pair(singleton(sK7(powerset(X0),X1)),unordered_pair(sK8(powerset(X0),X1),sK7(powerset(X0),X1))),X2))),X0)
| sP0(powerset(X0),X1)
| sP0(unordered_pair(singleton(sK7(powerset(X0),X1)),unordered_pair(sK8(powerset(X0),X1),sK7(powerset(X0),X1))),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_391])]) ).
fof(f3728,plain,
( ! [X2,X3,X0,X1] :
( sP0(powerset(powerset(cartesian_product2(X0,X1))),X2)
| sP0(unordered_pair(singleton(sK7(powerset(powerset(cartesian_product2(X0,X1))),X2)),unordered_pair(sK8(powerset(powerset(cartesian_product2(X0,X1))),X2),sK7(powerset(powerset(cartesian_product2(X0,X1))),X2))),X3)
| relation(unordered_pair(singleton(sK8(unordered_pair(singleton(sK7(powerset(powerset(cartesian_product2(X0,X1))),X2)),unordered_pair(sK8(powerset(powerset(cartesian_product2(X0,X1))),X2),sK7(powerset(powerset(cartesian_product2(X0,X1))),X2))),X3)),unordered_pair(sK9(unordered_pair(singleton(sK7(powerset(powerset(cartesian_product2(X0,X1))),X2)),unordered_pair(sK8(powerset(powerset(cartesian_product2(X0,X1))),X2),sK7(powerset(powerset(cartesian_product2(X0,X1))),X2))),X3),sK8(unordered_pair(singleton(sK7(powerset(powerset(cartesian_product2(X0,X1))),X2)),unordered_pair(sK8(powerset(powerset(cartesian_product2(X0,X1))),X2),sK7(powerset(powerset(cartesian_product2(X0,X1))),X2))),X3)))) )
| ~ spl17_41
| ~ spl17_391 ),
inference(resolution,[],[f3713,f364]) ).
fof(f3713,plain,
( ! [X2,X0,X1] :
( element(unordered_pair(singleton(sK8(unordered_pair(singleton(sK7(powerset(X0),X1)),unordered_pair(sK8(powerset(X0),X1),sK7(powerset(X0),X1))),X2)),unordered_pair(sK9(unordered_pair(singleton(sK7(powerset(X0),X1)),unordered_pair(sK8(powerset(X0),X1),sK7(powerset(X0),X1))),X2),sK8(unordered_pair(singleton(sK7(powerset(X0),X1)),unordered_pair(sK8(powerset(X0),X1),sK7(powerset(X0),X1))),X2))),X0)
| sP0(powerset(X0),X1)
| sP0(unordered_pair(singleton(sK7(powerset(X0),X1)),unordered_pair(sK8(powerset(X0),X1),sK7(powerset(X0),X1))),X2) )
| ~ spl17_391 ),
inference(avatar_component_clause,[],[f3712]) ).
fof(f15139,plain,
( spl17_1078
| ~ spl17_41
| ~ spl17_390 ),
inference(avatar_split_clause,[],[f3724,f3708,f363,f15137]) ).
fof(f15137,plain,
( spl17_1078
<=> ! [X0,X3,X2,X1] :
( sP0(powerset(powerset(cartesian_product2(X0,X1))),X2)
| sP0(unordered_pair(singleton(sK8(powerset(powerset(cartesian_product2(X0,X1))),X2)),unordered_pair(sK9(powerset(powerset(cartesian_product2(X0,X1))),X2),sK8(powerset(powerset(cartesian_product2(X0,X1))),X2))),X3)
| relation(unordered_pair(singleton(sK7(unordered_pair(singleton(sK8(powerset(powerset(cartesian_product2(X0,X1))),X2)),unordered_pair(sK9(powerset(powerset(cartesian_product2(X0,X1))),X2),sK8(powerset(powerset(cartesian_product2(X0,X1))),X2))),X3)),unordered_pair(sK8(unordered_pair(singleton(sK8(powerset(powerset(cartesian_product2(X0,X1))),X2)),unordered_pair(sK9(powerset(powerset(cartesian_product2(X0,X1))),X2),sK8(powerset(powerset(cartesian_product2(X0,X1))),X2))),X3),sK7(unordered_pair(singleton(sK8(powerset(powerset(cartesian_product2(X0,X1))),X2)),unordered_pair(sK9(powerset(powerset(cartesian_product2(X0,X1))),X2),sK8(powerset(powerset(cartesian_product2(X0,X1))),X2))),X3)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1078])]) ).
fof(f3708,plain,
( spl17_390
<=> ! [X2,X0,X1] :
( element(unordered_pair(singleton(sK7(unordered_pair(singleton(sK8(powerset(X0),X1)),unordered_pair(sK9(powerset(X0),X1),sK8(powerset(X0),X1))),X2)),unordered_pair(sK8(unordered_pair(singleton(sK8(powerset(X0),X1)),unordered_pair(sK9(powerset(X0),X1),sK8(powerset(X0),X1))),X2),sK7(unordered_pair(singleton(sK8(powerset(X0),X1)),unordered_pair(sK9(powerset(X0),X1),sK8(powerset(X0),X1))),X2))),X0)
| sP0(powerset(X0),X1)
| sP0(unordered_pair(singleton(sK8(powerset(X0),X1)),unordered_pair(sK9(powerset(X0),X1),sK8(powerset(X0),X1))),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_390])]) ).
fof(f3724,plain,
( ! [X2,X3,X0,X1] :
( sP0(powerset(powerset(cartesian_product2(X0,X1))),X2)
| sP0(unordered_pair(singleton(sK8(powerset(powerset(cartesian_product2(X0,X1))),X2)),unordered_pair(sK9(powerset(powerset(cartesian_product2(X0,X1))),X2),sK8(powerset(powerset(cartesian_product2(X0,X1))),X2))),X3)
| relation(unordered_pair(singleton(sK7(unordered_pair(singleton(sK8(powerset(powerset(cartesian_product2(X0,X1))),X2)),unordered_pair(sK9(powerset(powerset(cartesian_product2(X0,X1))),X2),sK8(powerset(powerset(cartesian_product2(X0,X1))),X2))),X3)),unordered_pair(sK8(unordered_pair(singleton(sK8(powerset(powerset(cartesian_product2(X0,X1))),X2)),unordered_pair(sK9(powerset(powerset(cartesian_product2(X0,X1))),X2),sK8(powerset(powerset(cartesian_product2(X0,X1))),X2))),X3),sK7(unordered_pair(singleton(sK8(powerset(powerset(cartesian_product2(X0,X1))),X2)),unordered_pair(sK9(powerset(powerset(cartesian_product2(X0,X1))),X2),sK8(powerset(powerset(cartesian_product2(X0,X1))),X2))),X3)))) )
| ~ spl17_41
| ~ spl17_390 ),
inference(resolution,[],[f3709,f364]) ).
fof(f3709,plain,
( ! [X2,X0,X1] :
( element(unordered_pair(singleton(sK7(unordered_pair(singleton(sK8(powerset(X0),X1)),unordered_pair(sK9(powerset(X0),X1),sK8(powerset(X0),X1))),X2)),unordered_pair(sK8(unordered_pair(singleton(sK8(powerset(X0),X1)),unordered_pair(sK9(powerset(X0),X1),sK8(powerset(X0),X1))),X2),sK7(unordered_pair(singleton(sK8(powerset(X0),X1)),unordered_pair(sK9(powerset(X0),X1),sK8(powerset(X0),X1))),X2))),X0)
| sP0(powerset(X0),X1)
| sP0(unordered_pair(singleton(sK8(powerset(X0),X1)),unordered_pair(sK9(powerset(X0),X1),sK8(powerset(X0),X1))),X2) )
| ~ spl17_390 ),
inference(avatar_component_clause,[],[f3708]) ).
fof(f15135,plain,
( spl17_1077
| ~ spl17_41
| ~ spl17_389 ),
inference(avatar_split_clause,[],[f3720,f3704,f363,f15133]) ).
fof(f15133,plain,
( spl17_1077
<=> ! [X0,X3,X2,X1] :
( sP0(powerset(powerset(cartesian_product2(X0,X1))),X2)
| sP0(unordered_pair(singleton(sK8(powerset(powerset(cartesian_product2(X0,X1))),X2)),unordered_pair(sK9(powerset(powerset(cartesian_product2(X0,X1))),X2),sK8(powerset(powerset(cartesian_product2(X0,X1))),X2))),X3)
| relation(unordered_pair(singleton(sK8(unordered_pair(singleton(sK8(powerset(powerset(cartesian_product2(X0,X1))),X2)),unordered_pair(sK9(powerset(powerset(cartesian_product2(X0,X1))),X2),sK8(powerset(powerset(cartesian_product2(X0,X1))),X2))),X3)),unordered_pair(sK9(unordered_pair(singleton(sK8(powerset(powerset(cartesian_product2(X0,X1))),X2)),unordered_pair(sK9(powerset(powerset(cartesian_product2(X0,X1))),X2),sK8(powerset(powerset(cartesian_product2(X0,X1))),X2))),X3),sK8(unordered_pair(singleton(sK8(powerset(powerset(cartesian_product2(X0,X1))),X2)),unordered_pair(sK9(powerset(powerset(cartesian_product2(X0,X1))),X2),sK8(powerset(powerset(cartesian_product2(X0,X1))),X2))),X3)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1077])]) ).
fof(f3704,plain,
( spl17_389
<=> ! [X2,X0,X1] :
( element(unordered_pair(singleton(sK8(unordered_pair(singleton(sK8(powerset(X0),X1)),unordered_pair(sK9(powerset(X0),X1),sK8(powerset(X0),X1))),X2)),unordered_pair(sK9(unordered_pair(singleton(sK8(powerset(X0),X1)),unordered_pair(sK9(powerset(X0),X1),sK8(powerset(X0),X1))),X2),sK8(unordered_pair(singleton(sK8(powerset(X0),X1)),unordered_pair(sK9(powerset(X0),X1),sK8(powerset(X0),X1))),X2))),X0)
| sP0(powerset(X0),X1)
| sP0(unordered_pair(singleton(sK8(powerset(X0),X1)),unordered_pair(sK9(powerset(X0),X1),sK8(powerset(X0),X1))),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_389])]) ).
fof(f3720,plain,
( ! [X2,X3,X0,X1] :
( sP0(powerset(powerset(cartesian_product2(X0,X1))),X2)
| sP0(unordered_pair(singleton(sK8(powerset(powerset(cartesian_product2(X0,X1))),X2)),unordered_pair(sK9(powerset(powerset(cartesian_product2(X0,X1))),X2),sK8(powerset(powerset(cartesian_product2(X0,X1))),X2))),X3)
| relation(unordered_pair(singleton(sK8(unordered_pair(singleton(sK8(powerset(powerset(cartesian_product2(X0,X1))),X2)),unordered_pair(sK9(powerset(powerset(cartesian_product2(X0,X1))),X2),sK8(powerset(powerset(cartesian_product2(X0,X1))),X2))),X3)),unordered_pair(sK9(unordered_pair(singleton(sK8(powerset(powerset(cartesian_product2(X0,X1))),X2)),unordered_pair(sK9(powerset(powerset(cartesian_product2(X0,X1))),X2),sK8(powerset(powerset(cartesian_product2(X0,X1))),X2))),X3),sK8(unordered_pair(singleton(sK8(powerset(powerset(cartesian_product2(X0,X1))),X2)),unordered_pair(sK9(powerset(powerset(cartesian_product2(X0,X1))),X2),sK8(powerset(powerset(cartesian_product2(X0,X1))),X2))),X3)))) )
| ~ spl17_41
| ~ spl17_389 ),
inference(resolution,[],[f3705,f364]) ).
fof(f3705,plain,
( ! [X2,X0,X1] :
( element(unordered_pair(singleton(sK8(unordered_pair(singleton(sK8(powerset(X0),X1)),unordered_pair(sK9(powerset(X0),X1),sK8(powerset(X0),X1))),X2)),unordered_pair(sK9(unordered_pair(singleton(sK8(powerset(X0),X1)),unordered_pair(sK9(powerset(X0),X1),sK8(powerset(X0),X1))),X2),sK8(unordered_pair(singleton(sK8(powerset(X0),X1)),unordered_pair(sK9(powerset(X0),X1),sK8(powerset(X0),X1))),X2))),X0)
| sP0(powerset(X0),X1)
| sP0(unordered_pair(singleton(sK8(powerset(X0),X1)),unordered_pair(sK9(powerset(X0),X1),sK8(powerset(X0),X1))),X2) )
| ~ spl17_389 ),
inference(avatar_component_clause,[],[f3704]) ).
fof(f15112,plain,
( spl17_1076
| ~ spl17_60
| ~ spl17_332 ),
inference(avatar_split_clause,[],[f3156,f3130,f504,f15110]) ).
fof(f15110,plain,
( spl17_1076
<=> ! [X2,X0,X1] :
( element(unordered_pair(singleton(sK7(unordered_pair(singleton(sK7(sK10(powerset(powerset(X0))),X1)),unordered_pair(sK8(sK10(powerset(powerset(X0))),X1),sK7(sK10(powerset(powerset(X0))),X1))),X2)),unordered_pair(sK8(unordered_pair(singleton(sK7(sK10(powerset(powerset(X0))),X1)),unordered_pair(sK8(sK10(powerset(powerset(X0))),X1),sK7(sK10(powerset(powerset(X0))),X1))),X2),sK7(unordered_pair(singleton(sK7(sK10(powerset(powerset(X0))),X1)),unordered_pair(sK8(sK10(powerset(powerset(X0))),X1),sK7(sK10(powerset(powerset(X0))),X1))),X2))),X0)
| sP0(sK10(powerset(powerset(X0))),X1)
| sP0(unordered_pair(singleton(sK7(sK10(powerset(powerset(X0))),X1)),unordered_pair(sK8(sK10(powerset(powerset(X0))),X1),sK7(sK10(powerset(powerset(X0))),X1))),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1076])]) ).
fof(f504,plain,
( spl17_60
<=> ! [X0,X1] :
( in(unordered_pair(singleton(sK7(X0,X1)),unordered_pair(sK8(X0,X1),sK7(X0,X1))),X0)
| sP0(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_60])]) ).
fof(f3156,plain,
( ! [X2,X0,X1] :
( element(unordered_pair(singleton(sK7(unordered_pair(singleton(sK7(sK10(powerset(powerset(X0))),X1)),unordered_pair(sK8(sK10(powerset(powerset(X0))),X1),sK7(sK10(powerset(powerset(X0))),X1))),X2)),unordered_pair(sK8(unordered_pair(singleton(sK7(sK10(powerset(powerset(X0))),X1)),unordered_pair(sK8(sK10(powerset(powerset(X0))),X1),sK7(sK10(powerset(powerset(X0))),X1))),X2),sK7(unordered_pair(singleton(sK7(sK10(powerset(powerset(X0))),X1)),unordered_pair(sK8(sK10(powerset(powerset(X0))),X1),sK7(sK10(powerset(powerset(X0))),X1))),X2))),X0)
| sP0(sK10(powerset(powerset(X0))),X1)
| sP0(unordered_pair(singleton(sK7(sK10(powerset(powerset(X0))),X1)),unordered_pair(sK8(sK10(powerset(powerset(X0))),X1),sK7(sK10(powerset(powerset(X0))),X1))),X2) )
| ~ spl17_60
| ~ spl17_332 ),
inference(resolution,[],[f3131,f505]) ).
fof(f505,plain,
( ! [X0,X1] :
( in(unordered_pair(singleton(sK7(X0,X1)),unordered_pair(sK8(X0,X1),sK7(X0,X1))),X0)
| sP0(X0,X1) )
| ~ spl17_60 ),
inference(avatar_component_clause,[],[f504]) ).
fof(f15108,plain,
( spl17_1075
| ~ spl17_59
| ~ spl17_332 ),
inference(avatar_split_clause,[],[f3153,f3130,f500,f15106]) ).
fof(f15106,plain,
( spl17_1075
<=> ! [X2,X0,X1] :
( element(unordered_pair(singleton(sK8(unordered_pair(singleton(sK7(sK10(powerset(powerset(X0))),X1)),unordered_pair(sK8(sK10(powerset(powerset(X0))),X1),sK7(sK10(powerset(powerset(X0))),X1))),X2)),unordered_pair(sK9(unordered_pair(singleton(sK7(sK10(powerset(powerset(X0))),X1)),unordered_pair(sK8(sK10(powerset(powerset(X0))),X1),sK7(sK10(powerset(powerset(X0))),X1))),X2),sK8(unordered_pair(singleton(sK7(sK10(powerset(powerset(X0))),X1)),unordered_pair(sK8(sK10(powerset(powerset(X0))),X1),sK7(sK10(powerset(powerset(X0))),X1))),X2))),X0)
| sP0(sK10(powerset(powerset(X0))),X1)
| sP0(unordered_pair(singleton(sK7(sK10(powerset(powerset(X0))),X1)),unordered_pair(sK8(sK10(powerset(powerset(X0))),X1),sK7(sK10(powerset(powerset(X0))),X1))),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1075])]) ).
fof(f500,plain,
( spl17_59
<=> ! [X0,X1] :
( in(unordered_pair(singleton(sK8(X0,X1)),unordered_pair(sK9(X0,X1),sK8(X0,X1))),X0)
| sP0(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_59])]) ).
fof(f3153,plain,
( ! [X2,X0,X1] :
( element(unordered_pair(singleton(sK8(unordered_pair(singleton(sK7(sK10(powerset(powerset(X0))),X1)),unordered_pair(sK8(sK10(powerset(powerset(X0))),X1),sK7(sK10(powerset(powerset(X0))),X1))),X2)),unordered_pair(sK9(unordered_pair(singleton(sK7(sK10(powerset(powerset(X0))),X1)),unordered_pair(sK8(sK10(powerset(powerset(X0))),X1),sK7(sK10(powerset(powerset(X0))),X1))),X2),sK8(unordered_pair(singleton(sK7(sK10(powerset(powerset(X0))),X1)),unordered_pair(sK8(sK10(powerset(powerset(X0))),X1),sK7(sK10(powerset(powerset(X0))),X1))),X2))),X0)
| sP0(sK10(powerset(powerset(X0))),X1)
| sP0(unordered_pair(singleton(sK7(sK10(powerset(powerset(X0))),X1)),unordered_pair(sK8(sK10(powerset(powerset(X0))),X1),sK7(sK10(powerset(powerset(X0))),X1))),X2) )
| ~ spl17_59
| ~ spl17_332 ),
inference(resolution,[],[f3131,f501]) ).
fof(f501,plain,
( ! [X0,X1] :
( in(unordered_pair(singleton(sK8(X0,X1)),unordered_pair(sK9(X0,X1),sK8(X0,X1))),X0)
| sP0(X0,X1) )
| ~ spl17_59 ),
inference(avatar_component_clause,[],[f500]) ).
fof(f15104,plain,
( spl17_1074
| ~ spl17_60
| ~ spl17_331 ),
inference(avatar_split_clause,[],[f3136,f3126,f504,f15102]) ).
fof(f15102,plain,
( spl17_1074
<=> ! [X2,X0,X1] :
( element(unordered_pair(singleton(sK7(unordered_pair(singleton(sK8(sK10(powerset(powerset(X0))),X1)),unordered_pair(sK9(sK10(powerset(powerset(X0))),X1),sK8(sK10(powerset(powerset(X0))),X1))),X2)),unordered_pair(sK8(unordered_pair(singleton(sK8(sK10(powerset(powerset(X0))),X1)),unordered_pair(sK9(sK10(powerset(powerset(X0))),X1),sK8(sK10(powerset(powerset(X0))),X1))),X2),sK7(unordered_pair(singleton(sK8(sK10(powerset(powerset(X0))),X1)),unordered_pair(sK9(sK10(powerset(powerset(X0))),X1),sK8(sK10(powerset(powerset(X0))),X1))),X2))),X0)
| sP0(sK10(powerset(powerset(X0))),X1)
| sP0(unordered_pair(singleton(sK8(sK10(powerset(powerset(X0))),X1)),unordered_pair(sK9(sK10(powerset(powerset(X0))),X1),sK8(sK10(powerset(powerset(X0))),X1))),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1074])]) ).
fof(f3136,plain,
( ! [X2,X0,X1] :
( element(unordered_pair(singleton(sK7(unordered_pair(singleton(sK8(sK10(powerset(powerset(X0))),X1)),unordered_pair(sK9(sK10(powerset(powerset(X0))),X1),sK8(sK10(powerset(powerset(X0))),X1))),X2)),unordered_pair(sK8(unordered_pair(singleton(sK8(sK10(powerset(powerset(X0))),X1)),unordered_pair(sK9(sK10(powerset(powerset(X0))),X1),sK8(sK10(powerset(powerset(X0))),X1))),X2),sK7(unordered_pair(singleton(sK8(sK10(powerset(powerset(X0))),X1)),unordered_pair(sK9(sK10(powerset(powerset(X0))),X1),sK8(sK10(powerset(powerset(X0))),X1))),X2))),X0)
| sP0(sK10(powerset(powerset(X0))),X1)
| sP0(unordered_pair(singleton(sK8(sK10(powerset(powerset(X0))),X1)),unordered_pair(sK9(sK10(powerset(powerset(X0))),X1),sK8(sK10(powerset(powerset(X0))),X1))),X2) )
| ~ spl17_60
| ~ spl17_331 ),
inference(resolution,[],[f3127,f505]) ).
fof(f15100,plain,
( spl17_1073
| ~ spl17_59
| ~ spl17_331 ),
inference(avatar_split_clause,[],[f3133,f3126,f500,f15098]) ).
fof(f15098,plain,
( spl17_1073
<=> ! [X2,X0,X1] :
( element(unordered_pair(singleton(sK8(unordered_pair(singleton(sK8(sK10(powerset(powerset(X0))),X1)),unordered_pair(sK9(sK10(powerset(powerset(X0))),X1),sK8(sK10(powerset(powerset(X0))),X1))),X2)),unordered_pair(sK9(unordered_pair(singleton(sK8(sK10(powerset(powerset(X0))),X1)),unordered_pair(sK9(sK10(powerset(powerset(X0))),X1),sK8(sK10(powerset(powerset(X0))),X1))),X2),sK8(unordered_pair(singleton(sK8(sK10(powerset(powerset(X0))),X1)),unordered_pair(sK9(sK10(powerset(powerset(X0))),X1),sK8(sK10(powerset(powerset(X0))),X1))),X2))),X0)
| sP0(sK10(powerset(powerset(X0))),X1)
| sP0(unordered_pair(singleton(sK8(sK10(powerset(powerset(X0))),X1)),unordered_pair(sK9(sK10(powerset(powerset(X0))),X1),sK8(sK10(powerset(powerset(X0))),X1))),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1073])]) ).
fof(f3133,plain,
( ! [X2,X0,X1] :
( element(unordered_pair(singleton(sK8(unordered_pair(singleton(sK8(sK10(powerset(powerset(X0))),X1)),unordered_pair(sK9(sK10(powerset(powerset(X0))),X1),sK8(sK10(powerset(powerset(X0))),X1))),X2)),unordered_pair(sK9(unordered_pair(singleton(sK8(sK10(powerset(powerset(X0))),X1)),unordered_pair(sK9(sK10(powerset(powerset(X0))),X1),sK8(sK10(powerset(powerset(X0))),X1))),X2),sK8(unordered_pair(singleton(sK8(sK10(powerset(powerset(X0))),X1)),unordered_pair(sK9(sK10(powerset(powerset(X0))),X1),sK8(sK10(powerset(powerset(X0))),X1))),X2))),X0)
| sP0(sK10(powerset(powerset(X0))),X1)
| sP0(unordered_pair(singleton(sK8(sK10(powerset(powerset(X0))),X1)),unordered_pair(sK9(sK10(powerset(powerset(X0))),X1),sK8(sK10(powerset(powerset(X0))),X1))),X2) )
| ~ spl17_59
| ~ spl17_331 ),
inference(resolution,[],[f3127,f501]) ).
fof(f15080,plain,
( spl17_1072
| ~ spl17_30
| ~ spl17_1011 ),
inference(avatar_split_clause,[],[f14418,f13631,f313,f15078]) ).
fof(f15078,plain,
( spl17_1072
<=> ! [X0] :
( ~ in(the_InternalRel(sK2),unordered_pair(singleton(sK4),unordered_pair(X0,sK4)))
| ~ element(X0,the_carrier(sK2))
| ~ related(sK2,sK5,X0)
| ~ in(X0,the_carrier(sK2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1072])]) ).
fof(f313,plain,
( spl17_30
<=> ! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_30])]) ).
fof(f13631,plain,
( spl17_1011
<=> ! [X0] :
( ~ in(X0,the_carrier(sK2))
| ~ element(X0,the_carrier(sK2))
| ~ related(sK2,sK5,X0)
| ~ in(the_InternalRel(sK2),unordered_pair(singleton(sK4),unordered_pair(sK4,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1011])]) ).
fof(f14418,plain,
( ! [X0] :
( ~ in(the_InternalRel(sK2),unordered_pair(singleton(sK4),unordered_pair(X0,sK4)))
| ~ element(X0,the_carrier(sK2))
| ~ related(sK2,sK5,X0)
| ~ in(X0,the_carrier(sK2)) )
| ~ spl17_30
| ~ spl17_1011 ),
inference(superposition,[],[f13632,f314]) ).
fof(f314,plain,
( ! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0)
| ~ spl17_30 ),
inference(avatar_component_clause,[],[f313]) ).
fof(f13632,plain,
( ! [X0] :
( ~ in(the_InternalRel(sK2),unordered_pair(singleton(sK4),unordered_pair(sK4,X0)))
| ~ element(X0,the_carrier(sK2))
| ~ related(sK2,sK5,X0)
| ~ in(X0,the_carrier(sK2)) )
| ~ spl17_1011 ),
inference(avatar_component_clause,[],[f13631]) ).
fof(f15076,plain,
( spl17_1071
| ~ spl17_188
| ~ spl17_321 ),
inference(avatar_split_clause,[],[f2947,f2873,f1511,f15074]) ).
fof(f15074,plain,
( spl17_1071
<=> ! [X2,X0,X1] :
( empty(unordered_pair(singleton(sK7(powerset(X0),X1)),unordered_pair(sK8(powerset(X0),X1),sK7(powerset(X0),X1))))
| sP0(sK10(powerset(unordered_pair(singleton(sK7(powerset(X0),X1)),unordered_pair(sK8(powerset(X0),X1),sK7(powerset(X0),X1))))),X2)
| element(unordered_pair(singleton(sK7(sK10(powerset(unordered_pair(singleton(sK7(powerset(X0),X1)),unordered_pair(sK8(powerset(X0),X1),sK7(powerset(X0),X1))))),X2)),unordered_pair(sK8(sK10(powerset(unordered_pair(singleton(sK7(powerset(X0),X1)),unordered_pair(sK8(powerset(X0),X1),sK7(powerset(X0),X1))))),X2),sK7(sK10(powerset(unordered_pair(singleton(sK7(powerset(X0),X1)),unordered_pair(sK8(powerset(X0),X1),sK7(powerset(X0),X1))))),X2))),X0)
| sP0(powerset(X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1071])]) ).
fof(f1511,plain,
( spl17_188
<=> ! [X2,X0,X1] :
( sP0(powerset(X0),X1)
| element(X2,X0)
| ~ in(X2,unordered_pair(singleton(sK7(powerset(X0),X1)),unordered_pair(sK8(powerset(X0),X1),sK7(powerset(X0),X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_188])]) ).
fof(f2947,plain,
( ! [X2,X0,X1] :
( empty(unordered_pair(singleton(sK7(powerset(X0),X1)),unordered_pair(sK8(powerset(X0),X1),sK7(powerset(X0),X1))))
| sP0(sK10(powerset(unordered_pair(singleton(sK7(powerset(X0),X1)),unordered_pair(sK8(powerset(X0),X1),sK7(powerset(X0),X1))))),X2)
| element(unordered_pair(singleton(sK7(sK10(powerset(unordered_pair(singleton(sK7(powerset(X0),X1)),unordered_pair(sK8(powerset(X0),X1),sK7(powerset(X0),X1))))),X2)),unordered_pair(sK8(sK10(powerset(unordered_pair(singleton(sK7(powerset(X0),X1)),unordered_pair(sK8(powerset(X0),X1),sK7(powerset(X0),X1))))),X2),sK7(sK10(powerset(unordered_pair(singleton(sK7(powerset(X0),X1)),unordered_pair(sK8(powerset(X0),X1),sK7(powerset(X0),X1))))),X2))),X0)
| sP0(powerset(X0),X1) )
| ~ spl17_188
| ~ spl17_321 ),
inference(resolution,[],[f2874,f1512]) ).
fof(f1512,plain,
( ! [X2,X0,X1] :
( ~ in(X2,unordered_pair(singleton(sK7(powerset(X0),X1)),unordered_pair(sK8(powerset(X0),X1),sK7(powerset(X0),X1))))
| element(X2,X0)
| sP0(powerset(X0),X1) )
| ~ spl17_188 ),
inference(avatar_component_clause,[],[f1511]) ).
fof(f15072,plain,
( spl17_1070
| ~ spl17_187
| ~ spl17_321 ),
inference(avatar_split_clause,[],[f2946,f2873,f1507,f15070]) ).
fof(f15070,plain,
( spl17_1070
<=> ! [X2,X0,X1] :
( empty(unordered_pair(singleton(sK8(powerset(X0),X1)),unordered_pair(sK9(powerset(X0),X1),sK8(powerset(X0),X1))))
| sP0(sK10(powerset(unordered_pair(singleton(sK8(powerset(X0),X1)),unordered_pair(sK9(powerset(X0),X1),sK8(powerset(X0),X1))))),X2)
| element(unordered_pair(singleton(sK7(sK10(powerset(unordered_pair(singleton(sK8(powerset(X0),X1)),unordered_pair(sK9(powerset(X0),X1),sK8(powerset(X0),X1))))),X2)),unordered_pair(sK8(sK10(powerset(unordered_pair(singleton(sK8(powerset(X0),X1)),unordered_pair(sK9(powerset(X0),X1),sK8(powerset(X0),X1))))),X2),sK7(sK10(powerset(unordered_pair(singleton(sK8(powerset(X0),X1)),unordered_pair(sK9(powerset(X0),X1),sK8(powerset(X0),X1))))),X2))),X0)
| sP0(powerset(X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1070])]) ).
fof(f1507,plain,
( spl17_187
<=> ! [X2,X0,X1] :
( sP0(powerset(X0),X1)
| element(X2,X0)
| ~ in(X2,unordered_pair(singleton(sK8(powerset(X0),X1)),unordered_pair(sK9(powerset(X0),X1),sK8(powerset(X0),X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_187])]) ).
fof(f2946,plain,
( ! [X2,X0,X1] :
( empty(unordered_pair(singleton(sK8(powerset(X0),X1)),unordered_pair(sK9(powerset(X0),X1),sK8(powerset(X0),X1))))
| sP0(sK10(powerset(unordered_pair(singleton(sK8(powerset(X0),X1)),unordered_pair(sK9(powerset(X0),X1),sK8(powerset(X0),X1))))),X2)
| element(unordered_pair(singleton(sK7(sK10(powerset(unordered_pair(singleton(sK8(powerset(X0),X1)),unordered_pair(sK9(powerset(X0),X1),sK8(powerset(X0),X1))))),X2)),unordered_pair(sK8(sK10(powerset(unordered_pair(singleton(sK8(powerset(X0),X1)),unordered_pair(sK9(powerset(X0),X1),sK8(powerset(X0),X1))))),X2),sK7(sK10(powerset(unordered_pair(singleton(sK8(powerset(X0),X1)),unordered_pair(sK9(powerset(X0),X1),sK8(powerset(X0),X1))))),X2))),X0)
| sP0(powerset(X0),X1) )
| ~ spl17_187
| ~ spl17_321 ),
inference(resolution,[],[f2874,f1508]) ).
fof(f1508,plain,
( ! [X2,X0,X1] :
( ~ in(X2,unordered_pair(singleton(sK8(powerset(X0),X1)),unordered_pair(sK9(powerset(X0),X1),sK8(powerset(X0),X1))))
| element(X2,X0)
| sP0(powerset(X0),X1) )
| ~ spl17_187 ),
inference(avatar_component_clause,[],[f1507]) ).
fof(f15068,plain,
( spl17_1069
| ~ spl17_188
| ~ spl17_320 ),
inference(avatar_split_clause,[],[f2896,f2869,f1511,f15066]) ).
fof(f15066,plain,
( spl17_1069
<=> ! [X2,X0,X1] :
( empty(unordered_pair(singleton(sK7(powerset(X0),X1)),unordered_pair(sK8(powerset(X0),X1),sK7(powerset(X0),X1))))
| sP0(sK10(powerset(unordered_pair(singleton(sK7(powerset(X0),X1)),unordered_pair(sK8(powerset(X0),X1),sK7(powerset(X0),X1))))),X2)
| element(unordered_pair(singleton(sK8(sK10(powerset(unordered_pair(singleton(sK7(powerset(X0),X1)),unordered_pair(sK8(powerset(X0),X1),sK7(powerset(X0),X1))))),X2)),unordered_pair(sK9(sK10(powerset(unordered_pair(singleton(sK7(powerset(X0),X1)),unordered_pair(sK8(powerset(X0),X1),sK7(powerset(X0),X1))))),X2),sK8(sK10(powerset(unordered_pair(singleton(sK7(powerset(X0),X1)),unordered_pair(sK8(powerset(X0),X1),sK7(powerset(X0),X1))))),X2))),X0)
| sP0(powerset(X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1069])]) ).
fof(f2896,plain,
( ! [X2,X0,X1] :
( empty(unordered_pair(singleton(sK7(powerset(X0),X1)),unordered_pair(sK8(powerset(X0),X1),sK7(powerset(X0),X1))))
| sP0(sK10(powerset(unordered_pair(singleton(sK7(powerset(X0),X1)),unordered_pair(sK8(powerset(X0),X1),sK7(powerset(X0),X1))))),X2)
| element(unordered_pair(singleton(sK8(sK10(powerset(unordered_pair(singleton(sK7(powerset(X0),X1)),unordered_pair(sK8(powerset(X0),X1),sK7(powerset(X0),X1))))),X2)),unordered_pair(sK9(sK10(powerset(unordered_pair(singleton(sK7(powerset(X0),X1)),unordered_pair(sK8(powerset(X0),X1),sK7(powerset(X0),X1))))),X2),sK8(sK10(powerset(unordered_pair(singleton(sK7(powerset(X0),X1)),unordered_pair(sK8(powerset(X0),X1),sK7(powerset(X0),X1))))),X2))),X0)
| sP0(powerset(X0),X1) )
| ~ spl17_188
| ~ spl17_320 ),
inference(resolution,[],[f2870,f1512]) ).
fof(f15064,plain,
( spl17_1068
| ~ spl17_187
| ~ spl17_320 ),
inference(avatar_split_clause,[],[f2895,f2869,f1507,f15062]) ).
fof(f15062,plain,
( spl17_1068
<=> ! [X2,X0,X1] :
( empty(unordered_pair(singleton(sK8(powerset(X0),X1)),unordered_pair(sK9(powerset(X0),X1),sK8(powerset(X0),X1))))
| sP0(sK10(powerset(unordered_pair(singleton(sK8(powerset(X0),X1)),unordered_pair(sK9(powerset(X0),X1),sK8(powerset(X0),X1))))),X2)
| element(unordered_pair(singleton(sK8(sK10(powerset(unordered_pair(singleton(sK8(powerset(X0),X1)),unordered_pair(sK9(powerset(X0),X1),sK8(powerset(X0),X1))))),X2)),unordered_pair(sK9(sK10(powerset(unordered_pair(singleton(sK8(powerset(X0),X1)),unordered_pair(sK9(powerset(X0),X1),sK8(powerset(X0),X1))))),X2),sK8(sK10(powerset(unordered_pair(singleton(sK8(powerset(X0),X1)),unordered_pair(sK9(powerset(X0),X1),sK8(powerset(X0),X1))))),X2))),X0)
| sP0(powerset(X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1068])]) ).
fof(f2895,plain,
( ! [X2,X0,X1] :
( empty(unordered_pair(singleton(sK8(powerset(X0),X1)),unordered_pair(sK9(powerset(X0),X1),sK8(powerset(X0),X1))))
| sP0(sK10(powerset(unordered_pair(singleton(sK8(powerset(X0),X1)),unordered_pair(sK9(powerset(X0),X1),sK8(powerset(X0),X1))))),X2)
| element(unordered_pair(singleton(sK8(sK10(powerset(unordered_pair(singleton(sK8(powerset(X0),X1)),unordered_pair(sK9(powerset(X0),X1),sK8(powerset(X0),X1))))),X2)),unordered_pair(sK9(sK10(powerset(unordered_pair(singleton(sK8(powerset(X0),X1)),unordered_pair(sK9(powerset(X0),X1),sK8(powerset(X0),X1))))),X2),sK8(sK10(powerset(unordered_pair(singleton(sK8(powerset(X0),X1)),unordered_pair(sK9(powerset(X0),X1),sK8(powerset(X0),X1))))),X2))),X0)
| sP0(powerset(X0),X1) )
| ~ spl17_187
| ~ spl17_320 ),
inference(resolution,[],[f2870,f1508]) ).
fof(f15044,plain,
( spl17_1067
| ~ spl17_188
| ~ spl17_312 ),
inference(avatar_split_clause,[],[f2798,f2730,f1511,f15042]) ).
fof(f15042,plain,
( spl17_1067
<=> ! [X2,X0,X1] :
( sP0(sK6(unordered_pair(singleton(sK7(powerset(X0),X1)),unordered_pair(sK8(powerset(X0),X1),sK7(powerset(X0),X1)))),X2)
| empty(unordered_pair(singleton(sK7(powerset(X0),X1)),unordered_pair(sK8(powerset(X0),X1),sK7(powerset(X0),X1))))
| element(unordered_pair(singleton(sK7(sK6(unordered_pair(singleton(sK7(powerset(X0),X1)),unordered_pair(sK8(powerset(X0),X1),sK7(powerset(X0),X1)))),X2)),unordered_pair(sK8(sK6(unordered_pair(singleton(sK7(powerset(X0),X1)),unordered_pair(sK8(powerset(X0),X1),sK7(powerset(X0),X1)))),X2),sK7(sK6(unordered_pair(singleton(sK7(powerset(X0),X1)),unordered_pair(sK8(powerset(X0),X1),sK7(powerset(X0),X1)))),X2))),X0)
| sP0(powerset(X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1067])]) ).
fof(f2798,plain,
( ! [X2,X0,X1] :
( sP0(sK6(unordered_pair(singleton(sK7(powerset(X0),X1)),unordered_pair(sK8(powerset(X0),X1),sK7(powerset(X0),X1)))),X2)
| empty(unordered_pair(singleton(sK7(powerset(X0),X1)),unordered_pair(sK8(powerset(X0),X1),sK7(powerset(X0),X1))))
| element(unordered_pair(singleton(sK7(sK6(unordered_pair(singleton(sK7(powerset(X0),X1)),unordered_pair(sK8(powerset(X0),X1),sK7(powerset(X0),X1)))),X2)),unordered_pair(sK8(sK6(unordered_pair(singleton(sK7(powerset(X0),X1)),unordered_pair(sK8(powerset(X0),X1),sK7(powerset(X0),X1)))),X2),sK7(sK6(unordered_pair(singleton(sK7(powerset(X0),X1)),unordered_pair(sK8(powerset(X0),X1),sK7(powerset(X0),X1)))),X2))),X0)
| sP0(powerset(X0),X1) )
| ~ spl17_188
| ~ spl17_312 ),
inference(resolution,[],[f2731,f1512]) ).
fof(f15040,plain,
( spl17_1066
| ~ spl17_187
| ~ spl17_312 ),
inference(avatar_split_clause,[],[f2797,f2730,f1507,f15038]) ).
fof(f15038,plain,
( spl17_1066
<=> ! [X2,X0,X1] :
( sP0(sK6(unordered_pair(singleton(sK8(powerset(X0),X1)),unordered_pair(sK9(powerset(X0),X1),sK8(powerset(X0),X1)))),X2)
| empty(unordered_pair(singleton(sK8(powerset(X0),X1)),unordered_pair(sK9(powerset(X0),X1),sK8(powerset(X0),X1))))
| element(unordered_pair(singleton(sK7(sK6(unordered_pair(singleton(sK8(powerset(X0),X1)),unordered_pair(sK9(powerset(X0),X1),sK8(powerset(X0),X1)))),X2)),unordered_pair(sK8(sK6(unordered_pair(singleton(sK8(powerset(X0),X1)),unordered_pair(sK9(powerset(X0),X1),sK8(powerset(X0),X1)))),X2),sK7(sK6(unordered_pair(singleton(sK8(powerset(X0),X1)),unordered_pair(sK9(powerset(X0),X1),sK8(powerset(X0),X1)))),X2))),X0)
| sP0(powerset(X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1066])]) ).
fof(f2797,plain,
( ! [X2,X0,X1] :
( sP0(sK6(unordered_pair(singleton(sK8(powerset(X0),X1)),unordered_pair(sK9(powerset(X0),X1),sK8(powerset(X0),X1)))),X2)
| empty(unordered_pair(singleton(sK8(powerset(X0),X1)),unordered_pair(sK9(powerset(X0),X1),sK8(powerset(X0),X1))))
| element(unordered_pair(singleton(sK7(sK6(unordered_pair(singleton(sK8(powerset(X0),X1)),unordered_pair(sK9(powerset(X0),X1),sK8(powerset(X0),X1)))),X2)),unordered_pair(sK8(sK6(unordered_pair(singleton(sK8(powerset(X0),X1)),unordered_pair(sK9(powerset(X0),X1),sK8(powerset(X0),X1)))),X2),sK7(sK6(unordered_pair(singleton(sK8(powerset(X0),X1)),unordered_pair(sK9(powerset(X0),X1),sK8(powerset(X0),X1)))),X2))),X0)
| sP0(powerset(X0),X1) )
| ~ spl17_187
| ~ spl17_312 ),
inference(resolution,[],[f2731,f1508]) ).
fof(f15036,plain,
( spl17_1065
| ~ spl17_30
| ~ spl17_1004 ),
inference(avatar_split_clause,[],[f14376,f13587,f313,f15034]) ).
fof(f15034,plain,
( spl17_1065
<=> ! [X0] :
( element(unordered_pair(singleton(sK4),unordered_pair(X0,sK4)),the_InternalRel(sK2))
| ~ element(X0,the_carrier(sK2))
| ~ related(sK2,sK5,X0)
| ~ in(X0,the_carrier(sK2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1065])]) ).
fof(f13587,plain,
( spl17_1004
<=> ! [X0] :
( ~ in(X0,the_carrier(sK2))
| ~ element(X0,the_carrier(sK2))
| ~ related(sK2,sK5,X0)
| element(unordered_pair(singleton(sK4),unordered_pair(sK4,X0)),the_InternalRel(sK2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1004])]) ).
fof(f14376,plain,
( ! [X0] :
( element(unordered_pair(singleton(sK4),unordered_pair(X0,sK4)),the_InternalRel(sK2))
| ~ element(X0,the_carrier(sK2))
| ~ related(sK2,sK5,X0)
| ~ in(X0,the_carrier(sK2)) )
| ~ spl17_30
| ~ spl17_1004 ),
inference(superposition,[],[f13588,f314]) ).
fof(f13588,plain,
( ! [X0] :
( element(unordered_pair(singleton(sK4),unordered_pair(sK4,X0)),the_InternalRel(sK2))
| ~ element(X0,the_carrier(sK2))
| ~ related(sK2,sK5,X0)
| ~ in(X0,the_carrier(sK2)) )
| ~ spl17_1004 ),
inference(avatar_component_clause,[],[f13587]) ).
fof(f15032,plain,
( spl17_1064
| ~ spl17_188
| ~ spl17_311 ),
inference(avatar_split_clause,[],[f2749,f2726,f1511,f15030]) ).
fof(f15030,plain,
( spl17_1064
<=> ! [X2,X0,X1] :
( sP0(sK6(unordered_pair(singleton(sK7(powerset(X0),X1)),unordered_pair(sK8(powerset(X0),X1),sK7(powerset(X0),X1)))),X2)
| empty(unordered_pair(singleton(sK7(powerset(X0),X1)),unordered_pair(sK8(powerset(X0),X1),sK7(powerset(X0),X1))))
| element(unordered_pair(singleton(sK8(sK6(unordered_pair(singleton(sK7(powerset(X0),X1)),unordered_pair(sK8(powerset(X0),X1),sK7(powerset(X0),X1)))),X2)),unordered_pair(sK9(sK6(unordered_pair(singleton(sK7(powerset(X0),X1)),unordered_pair(sK8(powerset(X0),X1),sK7(powerset(X0),X1)))),X2),sK8(sK6(unordered_pair(singleton(sK7(powerset(X0),X1)),unordered_pair(sK8(powerset(X0),X1),sK7(powerset(X0),X1)))),X2))),X0)
| sP0(powerset(X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1064])]) ).
fof(f2749,plain,
( ! [X2,X0,X1] :
( sP0(sK6(unordered_pair(singleton(sK7(powerset(X0),X1)),unordered_pair(sK8(powerset(X0),X1),sK7(powerset(X0),X1)))),X2)
| empty(unordered_pair(singleton(sK7(powerset(X0),X1)),unordered_pair(sK8(powerset(X0),X1),sK7(powerset(X0),X1))))
| element(unordered_pair(singleton(sK8(sK6(unordered_pair(singleton(sK7(powerset(X0),X1)),unordered_pair(sK8(powerset(X0),X1),sK7(powerset(X0),X1)))),X2)),unordered_pair(sK9(sK6(unordered_pair(singleton(sK7(powerset(X0),X1)),unordered_pair(sK8(powerset(X0),X1),sK7(powerset(X0),X1)))),X2),sK8(sK6(unordered_pair(singleton(sK7(powerset(X0),X1)),unordered_pair(sK8(powerset(X0),X1),sK7(powerset(X0),X1)))),X2))),X0)
| sP0(powerset(X0),X1) )
| ~ spl17_188
| ~ spl17_311 ),
inference(resolution,[],[f2727,f1512]) ).
fof(f15028,plain,
( spl17_1063
| ~ spl17_187
| ~ spl17_311 ),
inference(avatar_split_clause,[],[f2748,f2726,f1507,f15026]) ).
fof(f15026,plain,
( spl17_1063
<=> ! [X2,X0,X1] :
( sP0(sK6(unordered_pair(singleton(sK8(powerset(X0),X1)),unordered_pair(sK9(powerset(X0),X1),sK8(powerset(X0),X1)))),X2)
| empty(unordered_pair(singleton(sK8(powerset(X0),X1)),unordered_pair(sK9(powerset(X0),X1),sK8(powerset(X0),X1))))
| element(unordered_pair(singleton(sK8(sK6(unordered_pair(singleton(sK8(powerset(X0),X1)),unordered_pair(sK9(powerset(X0),X1),sK8(powerset(X0),X1)))),X2)),unordered_pair(sK9(sK6(unordered_pair(singleton(sK8(powerset(X0),X1)),unordered_pair(sK9(powerset(X0),X1),sK8(powerset(X0),X1)))),X2),sK8(sK6(unordered_pair(singleton(sK8(powerset(X0),X1)),unordered_pair(sK9(powerset(X0),X1),sK8(powerset(X0),X1)))),X2))),X0)
| sP0(powerset(X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1063])]) ).
fof(f2748,plain,
( ! [X2,X0,X1] :
( sP0(sK6(unordered_pair(singleton(sK8(powerset(X0),X1)),unordered_pair(sK9(powerset(X0),X1),sK8(powerset(X0),X1)))),X2)
| empty(unordered_pair(singleton(sK8(powerset(X0),X1)),unordered_pair(sK9(powerset(X0),X1),sK8(powerset(X0),X1))))
| element(unordered_pair(singleton(sK8(sK6(unordered_pair(singleton(sK8(powerset(X0),X1)),unordered_pair(sK9(powerset(X0),X1),sK8(powerset(X0),X1)))),X2)),unordered_pair(sK9(sK6(unordered_pair(singleton(sK8(powerset(X0),X1)),unordered_pair(sK9(powerset(X0),X1),sK8(powerset(X0),X1)))),X2),sK8(sK6(unordered_pair(singleton(sK8(powerset(X0),X1)),unordered_pair(sK9(powerset(X0),X1),sK8(powerset(X0),X1)))),X2))),X0)
| sP0(powerset(X0),X1) )
| ~ spl17_187
| ~ spl17_311 ),
inference(resolution,[],[f2727,f1508]) ).
fof(f14784,plain,
( spl17_1062
| ~ spl17_30
| ~ spl17_994 ),
inference(avatar_split_clause,[],[f13744,f13459,f313,f14782]) ).
fof(f14782,plain,
( spl17_1062
<=> ! [X0] :
( ~ in(the_InternalRel(sK2),unordered_pair(singleton(sK3),unordered_pair(X0,sK3)))
| ~ element(X0,the_carrier(sK2))
| ~ related(sK2,sK4,X0)
| ~ in(X0,the_carrier(sK2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1062])]) ).
fof(f13459,plain,
( spl17_994
<=> ! [X0] :
( ~ in(X0,the_carrier(sK2))
| ~ element(X0,the_carrier(sK2))
| ~ related(sK2,sK4,X0)
| ~ in(the_InternalRel(sK2),unordered_pair(singleton(sK3),unordered_pair(sK3,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_994])]) ).
fof(f13744,plain,
( ! [X0] :
( ~ in(the_InternalRel(sK2),unordered_pair(singleton(sK3),unordered_pair(X0,sK3)))
| ~ element(X0,the_carrier(sK2))
| ~ related(sK2,sK4,X0)
| ~ in(X0,the_carrier(sK2)) )
| ~ spl17_30
| ~ spl17_994 ),
inference(superposition,[],[f13460,f314]) ).
fof(f13460,plain,
( ! [X0] :
( ~ in(the_InternalRel(sK2),unordered_pair(singleton(sK3),unordered_pair(sK3,X0)))
| ~ element(X0,the_carrier(sK2))
| ~ related(sK2,sK4,X0)
| ~ in(X0,the_carrier(sK2)) )
| ~ spl17_994 ),
inference(avatar_component_clause,[],[f13459]) ).
fof(f14780,plain,
( spl17_1061
| ~ spl17_51
| ~ spl17_392 ),
inference(avatar_split_clause,[],[f3734,f3716,f439,f14778]) ).
fof(f14778,plain,
( spl17_1061
<=> ! [X0,X3,X2,X1] :
( sP0(powerset(powerset(X0)),X1)
| sP0(unordered_pair(singleton(sK7(powerset(powerset(X0)),X1)),unordered_pair(sK8(powerset(powerset(X0)),X1),sK7(powerset(powerset(X0)),X1))),X2)
| element(X3,X0)
| ~ in(X3,unordered_pair(singleton(sK7(unordered_pair(singleton(sK7(powerset(powerset(X0)),X1)),unordered_pair(sK8(powerset(powerset(X0)),X1),sK7(powerset(powerset(X0)),X1))),X2)),unordered_pair(sK8(unordered_pair(singleton(sK7(powerset(powerset(X0)),X1)),unordered_pair(sK8(powerset(powerset(X0)),X1),sK7(powerset(powerset(X0)),X1))),X2),sK7(unordered_pair(singleton(sK7(powerset(powerset(X0)),X1)),unordered_pair(sK8(powerset(powerset(X0)),X1),sK7(powerset(powerset(X0)),X1))),X2)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1061])]) ).
fof(f439,plain,
( spl17_51
<=> ! [X2,X0,X1] :
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_51])]) ).
fof(f3734,plain,
( ! [X2,X3,X0,X1] :
( sP0(powerset(powerset(X0)),X1)
| sP0(unordered_pair(singleton(sK7(powerset(powerset(X0)),X1)),unordered_pair(sK8(powerset(powerset(X0)),X1),sK7(powerset(powerset(X0)),X1))),X2)
| element(X3,X0)
| ~ in(X3,unordered_pair(singleton(sK7(unordered_pair(singleton(sK7(powerset(powerset(X0)),X1)),unordered_pair(sK8(powerset(powerset(X0)),X1),sK7(powerset(powerset(X0)),X1))),X2)),unordered_pair(sK8(unordered_pair(singleton(sK7(powerset(powerset(X0)),X1)),unordered_pair(sK8(powerset(powerset(X0)),X1),sK7(powerset(powerset(X0)),X1))),X2),sK7(unordered_pair(singleton(sK7(powerset(powerset(X0)),X1)),unordered_pair(sK8(powerset(powerset(X0)),X1),sK7(powerset(powerset(X0)),X1))),X2)))) )
| ~ spl17_51
| ~ spl17_392 ),
inference(resolution,[],[f3717,f440]) ).
fof(f440,plain,
( ! [X2,X0,X1] :
( ~ element(X1,powerset(X2))
| element(X0,X2)
| ~ in(X0,X1) )
| ~ spl17_51 ),
inference(avatar_component_clause,[],[f439]) ).
fof(f14776,plain,
( spl17_1060
| ~ spl17_51
| ~ spl17_391 ),
inference(avatar_split_clause,[],[f3730,f3712,f439,f14774]) ).
fof(f14774,plain,
( spl17_1060
<=> ! [X0,X3,X2,X1] :
( sP0(powerset(powerset(X0)),X1)
| sP0(unordered_pair(singleton(sK7(powerset(powerset(X0)),X1)),unordered_pair(sK8(powerset(powerset(X0)),X1),sK7(powerset(powerset(X0)),X1))),X2)
| element(X3,X0)
| ~ in(X3,unordered_pair(singleton(sK8(unordered_pair(singleton(sK7(powerset(powerset(X0)),X1)),unordered_pair(sK8(powerset(powerset(X0)),X1),sK7(powerset(powerset(X0)),X1))),X2)),unordered_pair(sK9(unordered_pair(singleton(sK7(powerset(powerset(X0)),X1)),unordered_pair(sK8(powerset(powerset(X0)),X1),sK7(powerset(powerset(X0)),X1))),X2),sK8(unordered_pair(singleton(sK7(powerset(powerset(X0)),X1)),unordered_pair(sK8(powerset(powerset(X0)),X1),sK7(powerset(powerset(X0)),X1))),X2)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1060])]) ).
fof(f3730,plain,
( ! [X2,X3,X0,X1] :
( sP0(powerset(powerset(X0)),X1)
| sP0(unordered_pair(singleton(sK7(powerset(powerset(X0)),X1)),unordered_pair(sK8(powerset(powerset(X0)),X1),sK7(powerset(powerset(X0)),X1))),X2)
| element(X3,X0)
| ~ in(X3,unordered_pair(singleton(sK8(unordered_pair(singleton(sK7(powerset(powerset(X0)),X1)),unordered_pair(sK8(powerset(powerset(X0)),X1),sK7(powerset(powerset(X0)),X1))),X2)),unordered_pair(sK9(unordered_pair(singleton(sK7(powerset(powerset(X0)),X1)),unordered_pair(sK8(powerset(powerset(X0)),X1),sK7(powerset(powerset(X0)),X1))),X2),sK8(unordered_pair(singleton(sK7(powerset(powerset(X0)),X1)),unordered_pair(sK8(powerset(powerset(X0)),X1),sK7(powerset(powerset(X0)),X1))),X2)))) )
| ~ spl17_51
| ~ spl17_391 ),
inference(resolution,[],[f3713,f440]) ).
fof(f14772,plain,
( spl17_1059
| ~ spl17_51
| ~ spl17_390 ),
inference(avatar_split_clause,[],[f3726,f3708,f439,f14770]) ).
fof(f14770,plain,
( spl17_1059
<=> ! [X0,X3,X2,X1] :
( sP0(powerset(powerset(X0)),X1)
| sP0(unordered_pair(singleton(sK8(powerset(powerset(X0)),X1)),unordered_pair(sK9(powerset(powerset(X0)),X1),sK8(powerset(powerset(X0)),X1))),X2)
| element(X3,X0)
| ~ in(X3,unordered_pair(singleton(sK7(unordered_pair(singleton(sK8(powerset(powerset(X0)),X1)),unordered_pair(sK9(powerset(powerset(X0)),X1),sK8(powerset(powerset(X0)),X1))),X2)),unordered_pair(sK8(unordered_pair(singleton(sK8(powerset(powerset(X0)),X1)),unordered_pair(sK9(powerset(powerset(X0)),X1),sK8(powerset(powerset(X0)),X1))),X2),sK7(unordered_pair(singleton(sK8(powerset(powerset(X0)),X1)),unordered_pair(sK9(powerset(powerset(X0)),X1),sK8(powerset(powerset(X0)),X1))),X2)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1059])]) ).
fof(f3726,plain,
( ! [X2,X3,X0,X1] :
( sP0(powerset(powerset(X0)),X1)
| sP0(unordered_pair(singleton(sK8(powerset(powerset(X0)),X1)),unordered_pair(sK9(powerset(powerset(X0)),X1),sK8(powerset(powerset(X0)),X1))),X2)
| element(X3,X0)
| ~ in(X3,unordered_pair(singleton(sK7(unordered_pair(singleton(sK8(powerset(powerset(X0)),X1)),unordered_pair(sK9(powerset(powerset(X0)),X1),sK8(powerset(powerset(X0)),X1))),X2)),unordered_pair(sK8(unordered_pair(singleton(sK8(powerset(powerset(X0)),X1)),unordered_pair(sK9(powerset(powerset(X0)),X1),sK8(powerset(powerset(X0)),X1))),X2),sK7(unordered_pair(singleton(sK8(powerset(powerset(X0)),X1)),unordered_pair(sK9(powerset(powerset(X0)),X1),sK8(powerset(powerset(X0)),X1))),X2)))) )
| ~ spl17_51
| ~ spl17_390 ),
inference(resolution,[],[f3709,f440]) ).
fof(f14768,plain,
( spl17_1058
| ~ spl17_51
| ~ spl17_389 ),
inference(avatar_split_clause,[],[f3722,f3704,f439,f14766]) ).
fof(f14766,plain,
( spl17_1058
<=> ! [X0,X3,X2,X1] :
( sP0(powerset(powerset(X0)),X1)
| sP0(unordered_pair(singleton(sK8(powerset(powerset(X0)),X1)),unordered_pair(sK9(powerset(powerset(X0)),X1),sK8(powerset(powerset(X0)),X1))),X2)
| element(X3,X0)
| ~ in(X3,unordered_pair(singleton(sK8(unordered_pair(singleton(sK8(powerset(powerset(X0)),X1)),unordered_pair(sK9(powerset(powerset(X0)),X1),sK8(powerset(powerset(X0)),X1))),X2)),unordered_pair(sK9(unordered_pair(singleton(sK8(powerset(powerset(X0)),X1)),unordered_pair(sK9(powerset(powerset(X0)),X1),sK8(powerset(powerset(X0)),X1))),X2),sK8(unordered_pair(singleton(sK8(powerset(powerset(X0)),X1)),unordered_pair(sK9(powerset(powerset(X0)),X1),sK8(powerset(powerset(X0)),X1))),X2)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1058])]) ).
fof(f3722,plain,
( ! [X2,X3,X0,X1] :
( sP0(powerset(powerset(X0)),X1)
| sP0(unordered_pair(singleton(sK8(powerset(powerset(X0)),X1)),unordered_pair(sK9(powerset(powerset(X0)),X1),sK8(powerset(powerset(X0)),X1))),X2)
| element(X3,X0)
| ~ in(X3,unordered_pair(singleton(sK8(unordered_pair(singleton(sK8(powerset(powerset(X0)),X1)),unordered_pair(sK9(powerset(powerset(X0)),X1),sK8(powerset(powerset(X0)),X1))),X2)),unordered_pair(sK9(unordered_pair(singleton(sK8(powerset(powerset(X0)),X1)),unordered_pair(sK9(powerset(powerset(X0)),X1),sK8(powerset(powerset(X0)),X1))),X2),sK8(unordered_pair(singleton(sK8(powerset(powerset(X0)),X1)),unordered_pair(sK9(powerset(powerset(X0)),X1),sK8(powerset(powerset(X0)),X1))),X2)))) )
| ~ spl17_51
| ~ spl17_389 ),
inference(resolution,[],[f3705,f440]) ).
fof(f14764,plain,
( spl17_1057
| ~ spl17_60
| ~ spl17_328 ),
inference(avatar_split_clause,[],[f3074,f3042,f504,f14762]) ).
fof(f14762,plain,
( spl17_1057
<=> ! [X2,X0,X1] :
( sP0(sK6(powerset(X0)),X1)
| element(unordered_pair(singleton(sK7(unordered_pair(singleton(sK7(sK6(powerset(X0)),X1)),unordered_pair(sK8(sK6(powerset(X0)),X1),sK7(sK6(powerset(X0)),X1))),X2)),unordered_pair(sK8(unordered_pair(singleton(sK7(sK6(powerset(X0)),X1)),unordered_pair(sK8(sK6(powerset(X0)),X1),sK7(sK6(powerset(X0)),X1))),X2),sK7(unordered_pair(singleton(sK7(sK6(powerset(X0)),X1)),unordered_pair(sK8(sK6(powerset(X0)),X1),sK7(sK6(powerset(X0)),X1))),X2))),X0)
| empty(powerset(X0))
| sP0(unordered_pair(singleton(sK7(sK6(powerset(X0)),X1)),unordered_pair(sK8(sK6(powerset(X0)),X1),sK7(sK6(powerset(X0)),X1))),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1057])]) ).
fof(f3074,plain,
( ! [X2,X0,X1] :
( sP0(sK6(powerset(X0)),X1)
| element(unordered_pair(singleton(sK7(unordered_pair(singleton(sK7(sK6(powerset(X0)),X1)),unordered_pair(sK8(sK6(powerset(X0)),X1),sK7(sK6(powerset(X0)),X1))),X2)),unordered_pair(sK8(unordered_pair(singleton(sK7(sK6(powerset(X0)),X1)),unordered_pair(sK8(sK6(powerset(X0)),X1),sK7(sK6(powerset(X0)),X1))),X2),sK7(unordered_pair(singleton(sK7(sK6(powerset(X0)),X1)),unordered_pair(sK8(sK6(powerset(X0)),X1),sK7(sK6(powerset(X0)),X1))),X2))),X0)
| empty(powerset(X0))
| sP0(unordered_pair(singleton(sK7(sK6(powerset(X0)),X1)),unordered_pair(sK8(sK6(powerset(X0)),X1),sK7(sK6(powerset(X0)),X1))),X2) )
| ~ spl17_60
| ~ spl17_328 ),
inference(resolution,[],[f3043,f505]) ).
fof(f14760,plain,
( spl17_1056
| ~ spl17_59
| ~ spl17_328 ),
inference(avatar_split_clause,[],[f3071,f3042,f500,f14758]) ).
fof(f14758,plain,
( spl17_1056
<=> ! [X2,X0,X1] :
( sP0(sK6(powerset(X0)),X1)
| element(unordered_pair(singleton(sK8(unordered_pair(singleton(sK7(sK6(powerset(X0)),X1)),unordered_pair(sK8(sK6(powerset(X0)),X1),sK7(sK6(powerset(X0)),X1))),X2)),unordered_pair(sK9(unordered_pair(singleton(sK7(sK6(powerset(X0)),X1)),unordered_pair(sK8(sK6(powerset(X0)),X1),sK7(sK6(powerset(X0)),X1))),X2),sK8(unordered_pair(singleton(sK7(sK6(powerset(X0)),X1)),unordered_pair(sK8(sK6(powerset(X0)),X1),sK7(sK6(powerset(X0)),X1))),X2))),X0)
| empty(powerset(X0))
| sP0(unordered_pair(singleton(sK7(sK6(powerset(X0)),X1)),unordered_pair(sK8(sK6(powerset(X0)),X1),sK7(sK6(powerset(X0)),X1))),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1056])]) ).
fof(f3071,plain,
( ! [X2,X0,X1] :
( sP0(sK6(powerset(X0)),X1)
| element(unordered_pair(singleton(sK8(unordered_pair(singleton(sK7(sK6(powerset(X0)),X1)),unordered_pair(sK8(sK6(powerset(X0)),X1),sK7(sK6(powerset(X0)),X1))),X2)),unordered_pair(sK9(unordered_pair(singleton(sK7(sK6(powerset(X0)),X1)),unordered_pair(sK8(sK6(powerset(X0)),X1),sK7(sK6(powerset(X0)),X1))),X2),sK8(unordered_pair(singleton(sK7(sK6(powerset(X0)),X1)),unordered_pair(sK8(sK6(powerset(X0)),X1),sK7(sK6(powerset(X0)),X1))),X2))),X0)
| empty(powerset(X0))
| sP0(unordered_pair(singleton(sK7(sK6(powerset(X0)),X1)),unordered_pair(sK8(sK6(powerset(X0)),X1),sK7(sK6(powerset(X0)),X1))),X2) )
| ~ spl17_59
| ~ spl17_328 ),
inference(resolution,[],[f3043,f501]) ).
fof(f14756,plain,
( spl17_1055
| ~ spl17_60
| ~ spl17_326 ),
inference(avatar_split_clause,[],[f3056,f3034,f504,f14754]) ).
fof(f14754,plain,
( spl17_1055
<=> ! [X2,X0,X1] :
( sP0(sK6(powerset(X0)),X1)
| element(unordered_pair(singleton(sK7(unordered_pair(singleton(sK8(sK6(powerset(X0)),X1)),unordered_pair(sK9(sK6(powerset(X0)),X1),sK8(sK6(powerset(X0)),X1))),X2)),unordered_pair(sK8(unordered_pair(singleton(sK8(sK6(powerset(X0)),X1)),unordered_pair(sK9(sK6(powerset(X0)),X1),sK8(sK6(powerset(X0)),X1))),X2),sK7(unordered_pair(singleton(sK8(sK6(powerset(X0)),X1)),unordered_pair(sK9(sK6(powerset(X0)),X1),sK8(sK6(powerset(X0)),X1))),X2))),X0)
| empty(powerset(X0))
| sP0(unordered_pair(singleton(sK8(sK6(powerset(X0)),X1)),unordered_pair(sK9(sK6(powerset(X0)),X1),sK8(sK6(powerset(X0)),X1))),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1055])]) ).
fof(f3056,plain,
( ! [X2,X0,X1] :
( sP0(sK6(powerset(X0)),X1)
| element(unordered_pair(singleton(sK7(unordered_pair(singleton(sK8(sK6(powerset(X0)),X1)),unordered_pair(sK9(sK6(powerset(X0)),X1),sK8(sK6(powerset(X0)),X1))),X2)),unordered_pair(sK8(unordered_pair(singleton(sK8(sK6(powerset(X0)),X1)),unordered_pair(sK9(sK6(powerset(X0)),X1),sK8(sK6(powerset(X0)),X1))),X2),sK7(unordered_pair(singleton(sK8(sK6(powerset(X0)),X1)),unordered_pair(sK9(sK6(powerset(X0)),X1),sK8(sK6(powerset(X0)),X1))),X2))),X0)
| empty(powerset(X0))
| sP0(unordered_pair(singleton(sK8(sK6(powerset(X0)),X1)),unordered_pair(sK9(sK6(powerset(X0)),X1),sK8(sK6(powerset(X0)),X1))),X2) )
| ~ spl17_60
| ~ spl17_326 ),
inference(resolution,[],[f3035,f505]) ).
fof(f14752,plain,
( spl17_1054
| ~ spl17_59
| ~ spl17_326 ),
inference(avatar_split_clause,[],[f3053,f3034,f500,f14750]) ).
fof(f14750,plain,
( spl17_1054
<=> ! [X2,X0,X1] :
( sP0(sK6(powerset(X0)),X1)
| element(unordered_pair(singleton(sK8(unordered_pair(singleton(sK8(sK6(powerset(X0)),X1)),unordered_pair(sK9(sK6(powerset(X0)),X1),sK8(sK6(powerset(X0)),X1))),X2)),unordered_pair(sK9(unordered_pair(singleton(sK8(sK6(powerset(X0)),X1)),unordered_pair(sK9(sK6(powerset(X0)),X1),sK8(sK6(powerset(X0)),X1))),X2),sK8(unordered_pair(singleton(sK8(sK6(powerset(X0)),X1)),unordered_pair(sK9(sK6(powerset(X0)),X1),sK8(sK6(powerset(X0)),X1))),X2))),X0)
| empty(powerset(X0))
| sP0(unordered_pair(singleton(sK8(sK6(powerset(X0)),X1)),unordered_pair(sK9(sK6(powerset(X0)),X1),sK8(sK6(powerset(X0)),X1))),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1054])]) ).
fof(f3053,plain,
( ! [X2,X0,X1] :
( sP0(sK6(powerset(X0)),X1)
| element(unordered_pair(singleton(sK8(unordered_pair(singleton(sK8(sK6(powerset(X0)),X1)),unordered_pair(sK9(sK6(powerset(X0)),X1),sK8(sK6(powerset(X0)),X1))),X2)),unordered_pair(sK9(unordered_pair(singleton(sK8(sK6(powerset(X0)),X1)),unordered_pair(sK9(sK6(powerset(X0)),X1),sK8(sK6(powerset(X0)),X1))),X2),sK8(unordered_pair(singleton(sK8(sK6(powerset(X0)),X1)),unordered_pair(sK9(sK6(powerset(X0)),X1),sK8(sK6(powerset(X0)),X1))),X2))),X0)
| empty(powerset(X0))
| sP0(unordered_pair(singleton(sK8(sK6(powerset(X0)),X1)),unordered_pair(sK9(sK6(powerset(X0)),X1),sK8(sK6(powerset(X0)),X1))),X2) )
| ~ spl17_59
| ~ spl17_326 ),
inference(resolution,[],[f3035,f501]) ).
fof(f14636,plain,
( spl17_1053
| ~ spl17_30
| ~ spl17_987 ),
inference(avatar_split_clause,[],[f13706,f13322,f313,f14634]) ).
fof(f14634,plain,
( spl17_1053
<=> ! [X0] :
( element(unordered_pair(singleton(sK3),unordered_pair(X0,sK3)),the_InternalRel(sK2))
| ~ element(X0,the_carrier(sK2))
| ~ related(sK2,sK4,X0)
| ~ in(X0,the_carrier(sK2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1053])]) ).
fof(f13322,plain,
( spl17_987
<=> ! [X0] :
( ~ in(X0,the_carrier(sK2))
| ~ element(X0,the_carrier(sK2))
| ~ related(sK2,sK4,X0)
| element(unordered_pair(singleton(sK3),unordered_pair(sK3,X0)),the_InternalRel(sK2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_987])]) ).
fof(f13706,plain,
( ! [X0] :
( element(unordered_pair(singleton(sK3),unordered_pair(X0,sK3)),the_InternalRel(sK2))
| ~ element(X0,the_carrier(sK2))
| ~ related(sK2,sK4,X0)
| ~ in(X0,the_carrier(sK2)) )
| ~ spl17_30
| ~ spl17_987 ),
inference(superposition,[],[f13323,f314]) ).
fof(f13323,plain,
( ! [X0] :
( element(unordered_pair(singleton(sK3),unordered_pair(sK3,X0)),the_InternalRel(sK2))
| ~ element(X0,the_carrier(sK2))
| ~ related(sK2,sK4,X0)
| ~ in(X0,the_carrier(sK2)) )
| ~ spl17_987 ),
inference(avatar_component_clause,[],[f13322]) ).
fof(f14520,plain,
( spl17_1052
| ~ spl17_49
| ~ spl17_392 ),
inference(avatar_split_clause,[],[f3733,f3716,f422,f14518]) ).
fof(f14518,plain,
( spl17_1052
<=> ! [X2,X0,X1,X3] :
( sP0(powerset(powerset(X0)),X1)
| sP0(unordered_pair(singleton(sK7(powerset(powerset(X0)),X1)),unordered_pair(sK8(powerset(powerset(X0)),X1),sK7(powerset(powerset(X0)),X1))),X2)
| ~ empty(X0)
| ~ in(X3,unordered_pair(singleton(sK7(unordered_pair(singleton(sK7(powerset(powerset(X0)),X1)),unordered_pair(sK8(powerset(powerset(X0)),X1),sK7(powerset(powerset(X0)),X1))),X2)),unordered_pair(sK8(unordered_pair(singleton(sK7(powerset(powerset(X0)),X1)),unordered_pair(sK8(powerset(powerset(X0)),X1),sK7(powerset(powerset(X0)),X1))),X2),sK7(unordered_pair(singleton(sK7(powerset(powerset(X0)),X1)),unordered_pair(sK8(powerset(powerset(X0)),X1),sK7(powerset(powerset(X0)),X1))),X2)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1052])]) ).
fof(f422,plain,
( spl17_49
<=> ! [X2,X0,X1] :
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_49])]) ).
fof(f3733,plain,
( ! [X2,X3,X0,X1] :
( sP0(powerset(powerset(X0)),X1)
| sP0(unordered_pair(singleton(sK7(powerset(powerset(X0)),X1)),unordered_pair(sK8(powerset(powerset(X0)),X1),sK7(powerset(powerset(X0)),X1))),X2)
| ~ empty(X0)
| ~ in(X3,unordered_pair(singleton(sK7(unordered_pair(singleton(sK7(powerset(powerset(X0)),X1)),unordered_pair(sK8(powerset(powerset(X0)),X1),sK7(powerset(powerset(X0)),X1))),X2)),unordered_pair(sK8(unordered_pair(singleton(sK7(powerset(powerset(X0)),X1)),unordered_pair(sK8(powerset(powerset(X0)),X1),sK7(powerset(powerset(X0)),X1))),X2),sK7(unordered_pair(singleton(sK7(powerset(powerset(X0)),X1)),unordered_pair(sK8(powerset(powerset(X0)),X1),sK7(powerset(powerset(X0)),X1))),X2)))) )
| ~ spl17_49
| ~ spl17_392 ),
inference(resolution,[],[f3717,f423]) ).
fof(f423,plain,
( ! [X2,X0,X1] :
( ~ element(X1,powerset(X2))
| ~ empty(X2)
| ~ in(X0,X1) )
| ~ spl17_49 ),
inference(avatar_component_clause,[],[f422]) ).
fof(f14516,plain,
( spl17_1051
| ~ spl17_49
| ~ spl17_391 ),
inference(avatar_split_clause,[],[f3729,f3712,f422,f14514]) ).
fof(f14514,plain,
( spl17_1051
<=> ! [X2,X0,X1,X3] :
( sP0(powerset(powerset(X0)),X1)
| sP0(unordered_pair(singleton(sK7(powerset(powerset(X0)),X1)),unordered_pair(sK8(powerset(powerset(X0)),X1),sK7(powerset(powerset(X0)),X1))),X2)
| ~ empty(X0)
| ~ in(X3,unordered_pair(singleton(sK8(unordered_pair(singleton(sK7(powerset(powerset(X0)),X1)),unordered_pair(sK8(powerset(powerset(X0)),X1),sK7(powerset(powerset(X0)),X1))),X2)),unordered_pair(sK9(unordered_pair(singleton(sK7(powerset(powerset(X0)),X1)),unordered_pair(sK8(powerset(powerset(X0)),X1),sK7(powerset(powerset(X0)),X1))),X2),sK8(unordered_pair(singleton(sK7(powerset(powerset(X0)),X1)),unordered_pair(sK8(powerset(powerset(X0)),X1),sK7(powerset(powerset(X0)),X1))),X2)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1051])]) ).
fof(f3729,plain,
( ! [X2,X3,X0,X1] :
( sP0(powerset(powerset(X0)),X1)
| sP0(unordered_pair(singleton(sK7(powerset(powerset(X0)),X1)),unordered_pair(sK8(powerset(powerset(X0)),X1),sK7(powerset(powerset(X0)),X1))),X2)
| ~ empty(X0)
| ~ in(X3,unordered_pair(singleton(sK8(unordered_pair(singleton(sK7(powerset(powerset(X0)),X1)),unordered_pair(sK8(powerset(powerset(X0)),X1),sK7(powerset(powerset(X0)),X1))),X2)),unordered_pair(sK9(unordered_pair(singleton(sK7(powerset(powerset(X0)),X1)),unordered_pair(sK8(powerset(powerset(X0)),X1),sK7(powerset(powerset(X0)),X1))),X2),sK8(unordered_pair(singleton(sK7(powerset(powerset(X0)),X1)),unordered_pair(sK8(powerset(powerset(X0)),X1),sK7(powerset(powerset(X0)),X1))),X2)))) )
| ~ spl17_49
| ~ spl17_391 ),
inference(resolution,[],[f3713,f423]) ).
fof(f14512,plain,
( spl17_1050
| ~ spl17_49
| ~ spl17_390 ),
inference(avatar_split_clause,[],[f3725,f3708,f422,f14510]) ).
fof(f14510,plain,
( spl17_1050
<=> ! [X2,X0,X1,X3] :
( sP0(powerset(powerset(X0)),X1)
| sP0(unordered_pair(singleton(sK8(powerset(powerset(X0)),X1)),unordered_pair(sK9(powerset(powerset(X0)),X1),sK8(powerset(powerset(X0)),X1))),X2)
| ~ empty(X0)
| ~ in(X3,unordered_pair(singleton(sK7(unordered_pair(singleton(sK8(powerset(powerset(X0)),X1)),unordered_pair(sK9(powerset(powerset(X0)),X1),sK8(powerset(powerset(X0)),X1))),X2)),unordered_pair(sK8(unordered_pair(singleton(sK8(powerset(powerset(X0)),X1)),unordered_pair(sK9(powerset(powerset(X0)),X1),sK8(powerset(powerset(X0)),X1))),X2),sK7(unordered_pair(singleton(sK8(powerset(powerset(X0)),X1)),unordered_pair(sK9(powerset(powerset(X0)),X1),sK8(powerset(powerset(X0)),X1))),X2)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1050])]) ).
fof(f3725,plain,
( ! [X2,X3,X0,X1] :
( sP0(powerset(powerset(X0)),X1)
| sP0(unordered_pair(singleton(sK8(powerset(powerset(X0)),X1)),unordered_pair(sK9(powerset(powerset(X0)),X1),sK8(powerset(powerset(X0)),X1))),X2)
| ~ empty(X0)
| ~ in(X3,unordered_pair(singleton(sK7(unordered_pair(singleton(sK8(powerset(powerset(X0)),X1)),unordered_pair(sK9(powerset(powerset(X0)),X1),sK8(powerset(powerset(X0)),X1))),X2)),unordered_pair(sK8(unordered_pair(singleton(sK8(powerset(powerset(X0)),X1)),unordered_pair(sK9(powerset(powerset(X0)),X1),sK8(powerset(powerset(X0)),X1))),X2),sK7(unordered_pair(singleton(sK8(powerset(powerset(X0)),X1)),unordered_pair(sK9(powerset(powerset(X0)),X1),sK8(powerset(powerset(X0)),X1))),X2)))) )
| ~ spl17_49
| ~ spl17_390 ),
inference(resolution,[],[f3709,f423]) ).
fof(f14508,plain,
( spl17_1049
| ~ spl17_49
| ~ spl17_389 ),
inference(avatar_split_clause,[],[f3721,f3704,f422,f14506]) ).
fof(f14506,plain,
( spl17_1049
<=> ! [X2,X0,X1,X3] :
( sP0(powerset(powerset(X0)),X1)
| sP0(unordered_pair(singleton(sK8(powerset(powerset(X0)),X1)),unordered_pair(sK9(powerset(powerset(X0)),X1),sK8(powerset(powerset(X0)),X1))),X2)
| ~ empty(X0)
| ~ in(X3,unordered_pair(singleton(sK8(unordered_pair(singleton(sK8(powerset(powerset(X0)),X1)),unordered_pair(sK9(powerset(powerset(X0)),X1),sK8(powerset(powerset(X0)),X1))),X2)),unordered_pair(sK9(unordered_pair(singleton(sK8(powerset(powerset(X0)),X1)),unordered_pair(sK9(powerset(powerset(X0)),X1),sK8(powerset(powerset(X0)),X1))),X2),sK8(unordered_pair(singleton(sK8(powerset(powerset(X0)),X1)),unordered_pair(sK9(powerset(powerset(X0)),X1),sK8(powerset(powerset(X0)),X1))),X2)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1049])]) ).
fof(f3721,plain,
( ! [X2,X3,X0,X1] :
( sP0(powerset(powerset(X0)),X1)
| sP0(unordered_pair(singleton(sK8(powerset(powerset(X0)),X1)),unordered_pair(sK9(powerset(powerset(X0)),X1),sK8(powerset(powerset(X0)),X1))),X2)
| ~ empty(X0)
| ~ in(X3,unordered_pair(singleton(sK8(unordered_pair(singleton(sK8(powerset(powerset(X0)),X1)),unordered_pair(sK9(powerset(powerset(X0)),X1),sK8(powerset(powerset(X0)),X1))),X2)),unordered_pair(sK9(unordered_pair(singleton(sK8(powerset(powerset(X0)),X1)),unordered_pair(sK9(powerset(powerset(X0)),X1),sK8(powerset(powerset(X0)),X1))),X2),sK8(unordered_pair(singleton(sK8(powerset(powerset(X0)),X1)),unordered_pair(sK9(powerset(powerset(X0)),X1),sK8(powerset(powerset(X0)),X1))),X2)))) )
| ~ spl17_49
| ~ spl17_389 ),
inference(resolution,[],[f3705,f423]) ).
fof(f14451,plain,
( spl17_1048
| ~ spl17_320
| ~ spl17_379 ),
inference(avatar_split_clause,[],[f3650,f3615,f2869,f14449]) ).
fof(f14449,plain,
( spl17_1048
<=> ! [X4,X0,X3,X2,X1] :
( ~ relation_of2_as_subset(unordered_pair(singleton(sK9(sK10(powerset(powerset(cartesian_product2(X0,X1)))),X2)),unordered_pair(sK9(sK10(powerset(powerset(cartesian_product2(X0,X1)))),X2),X3)),X0,X1)
| empty(powerset(cartesian_product2(X0,X1)))
| in(unordered_pair(singleton(sK8(sK10(powerset(powerset(cartesian_product2(X0,X1)))),X2)),unordered_pair(sK8(sK10(powerset(powerset(cartesian_product2(X0,X1)))),X2),X3)),powerset(cartesian_product2(X0,X1)))
| ~ in(X3,X4)
| ~ in(sK9(sK10(powerset(powerset(cartesian_product2(X0,X1)))),X2),X4)
| ~ in(sK8(sK10(powerset(powerset(cartesian_product2(X0,X1)))),X2),X4)
| ~ sP0(powerset(cartesian_product2(X0,X1)),X4)
| sP0(sK10(powerset(powerset(cartesian_product2(X0,X1)))),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1048])]) ).
fof(f3615,plain,
( spl17_379
<=> ! [X5,X4,X0,X3,X2,X1] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X1,X0)),powerset(cartesian_product2(X2,X3)))
| ~ relation_of2_as_subset(unordered_pair(singleton(X1),unordered_pair(X1,X4)),X2,X3)
| empty(powerset(cartesian_product2(X2,X3)))
| in(unordered_pair(singleton(X0),unordered_pair(X0,X4)),powerset(cartesian_product2(X2,X3)))
| ~ in(X4,X5)
| ~ in(X1,X5)
| ~ in(X0,X5)
| ~ sP0(powerset(cartesian_product2(X2,X3)),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_379])]) ).
fof(f3650,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ relation_of2_as_subset(unordered_pair(singleton(sK9(sK10(powerset(powerset(cartesian_product2(X0,X1)))),X2)),unordered_pair(sK9(sK10(powerset(powerset(cartesian_product2(X0,X1)))),X2),X3)),X0,X1)
| empty(powerset(cartesian_product2(X0,X1)))
| in(unordered_pair(singleton(sK8(sK10(powerset(powerset(cartesian_product2(X0,X1)))),X2)),unordered_pair(sK8(sK10(powerset(powerset(cartesian_product2(X0,X1)))),X2),X3)),powerset(cartesian_product2(X0,X1)))
| ~ in(X3,X4)
| ~ in(sK9(sK10(powerset(powerset(cartesian_product2(X0,X1)))),X2),X4)
| ~ in(sK8(sK10(powerset(powerset(cartesian_product2(X0,X1)))),X2),X4)
| ~ sP0(powerset(cartesian_product2(X0,X1)),X4)
| sP0(sK10(powerset(powerset(cartesian_product2(X0,X1)))),X2) )
| ~ spl17_320
| ~ spl17_379 ),
inference(duplicate_literal_removal,[],[f3642]) ).
fof(f3642,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ relation_of2_as_subset(unordered_pair(singleton(sK9(sK10(powerset(powerset(cartesian_product2(X0,X1)))),X2)),unordered_pair(sK9(sK10(powerset(powerset(cartesian_product2(X0,X1)))),X2),X3)),X0,X1)
| empty(powerset(cartesian_product2(X0,X1)))
| in(unordered_pair(singleton(sK8(sK10(powerset(powerset(cartesian_product2(X0,X1)))),X2)),unordered_pair(sK8(sK10(powerset(powerset(cartesian_product2(X0,X1)))),X2),X3)),powerset(cartesian_product2(X0,X1)))
| ~ in(X3,X4)
| ~ in(sK9(sK10(powerset(powerset(cartesian_product2(X0,X1)))),X2),X4)
| ~ in(sK8(sK10(powerset(powerset(cartesian_product2(X0,X1)))),X2),X4)
| ~ sP0(powerset(cartesian_product2(X0,X1)),X4)
| empty(powerset(cartesian_product2(X0,X1)))
| sP0(sK10(powerset(powerset(cartesian_product2(X0,X1)))),X2) )
| ~ spl17_320
| ~ spl17_379 ),
inference(resolution,[],[f3616,f2870]) ).
fof(f3616,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X1,X0)),powerset(cartesian_product2(X2,X3)))
| ~ relation_of2_as_subset(unordered_pair(singleton(X1),unordered_pair(X1,X4)),X2,X3)
| empty(powerset(cartesian_product2(X2,X3)))
| in(unordered_pair(singleton(X0),unordered_pair(X0,X4)),powerset(cartesian_product2(X2,X3)))
| ~ in(X4,X5)
| ~ in(X1,X5)
| ~ in(X0,X5)
| ~ sP0(powerset(cartesian_product2(X2,X3)),X5) )
| ~ spl17_379 ),
inference(avatar_component_clause,[],[f3615]) ).
fof(f14447,plain,
( spl17_1047
| ~ spl17_321
| ~ spl17_379 ),
inference(avatar_split_clause,[],[f3648,f3615,f2873,f14445]) ).
fof(f14445,plain,
( spl17_1047
<=> ! [X4,X0,X3,X2,X1] :
( ~ relation_of2_as_subset(unordered_pair(singleton(sK8(sK10(powerset(powerset(cartesian_product2(X0,X1)))),X2)),unordered_pair(sK8(sK10(powerset(powerset(cartesian_product2(X0,X1)))),X2),X3)),X0,X1)
| empty(powerset(cartesian_product2(X0,X1)))
| in(unordered_pair(singleton(sK7(sK10(powerset(powerset(cartesian_product2(X0,X1)))),X2)),unordered_pair(sK7(sK10(powerset(powerset(cartesian_product2(X0,X1)))),X2),X3)),powerset(cartesian_product2(X0,X1)))
| ~ in(X3,X4)
| ~ in(sK8(sK10(powerset(powerset(cartesian_product2(X0,X1)))),X2),X4)
| ~ in(sK7(sK10(powerset(powerset(cartesian_product2(X0,X1)))),X2),X4)
| ~ sP0(powerset(cartesian_product2(X0,X1)),X4)
| sP0(sK10(powerset(powerset(cartesian_product2(X0,X1)))),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1047])]) ).
fof(f3648,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ relation_of2_as_subset(unordered_pair(singleton(sK8(sK10(powerset(powerset(cartesian_product2(X0,X1)))),X2)),unordered_pair(sK8(sK10(powerset(powerset(cartesian_product2(X0,X1)))),X2),X3)),X0,X1)
| empty(powerset(cartesian_product2(X0,X1)))
| in(unordered_pair(singleton(sK7(sK10(powerset(powerset(cartesian_product2(X0,X1)))),X2)),unordered_pair(sK7(sK10(powerset(powerset(cartesian_product2(X0,X1)))),X2),X3)),powerset(cartesian_product2(X0,X1)))
| ~ in(X3,X4)
| ~ in(sK8(sK10(powerset(powerset(cartesian_product2(X0,X1)))),X2),X4)
| ~ in(sK7(sK10(powerset(powerset(cartesian_product2(X0,X1)))),X2),X4)
| ~ sP0(powerset(cartesian_product2(X0,X1)),X4)
| sP0(sK10(powerset(powerset(cartesian_product2(X0,X1)))),X2) )
| ~ spl17_321
| ~ spl17_379 ),
inference(duplicate_literal_removal,[],[f3645]) ).
fof(f3645,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ relation_of2_as_subset(unordered_pair(singleton(sK8(sK10(powerset(powerset(cartesian_product2(X0,X1)))),X2)),unordered_pair(sK8(sK10(powerset(powerset(cartesian_product2(X0,X1)))),X2),X3)),X0,X1)
| empty(powerset(cartesian_product2(X0,X1)))
| in(unordered_pair(singleton(sK7(sK10(powerset(powerset(cartesian_product2(X0,X1)))),X2)),unordered_pair(sK7(sK10(powerset(powerset(cartesian_product2(X0,X1)))),X2),X3)),powerset(cartesian_product2(X0,X1)))
| ~ in(X3,X4)
| ~ in(sK8(sK10(powerset(powerset(cartesian_product2(X0,X1)))),X2),X4)
| ~ in(sK7(sK10(powerset(powerset(cartesian_product2(X0,X1)))),X2),X4)
| ~ sP0(powerset(cartesian_product2(X0,X1)),X4)
| empty(powerset(cartesian_product2(X0,X1)))
| sP0(sK10(powerset(powerset(cartesian_product2(X0,X1)))),X2) )
| ~ spl17_321
| ~ spl17_379 ),
inference(resolution,[],[f3616,f2874]) ).
fof(f14443,plain,
( spl17_1046
| ~ spl17_320
| ~ spl17_378 ),
inference(avatar_split_clause,[],[f3634,f3585,f2869,f14441]) ).
fof(f14441,plain,
( spl17_1046
<=> ! [X4,X0,X3,X2,X1] :
( in(unordered_pair(singleton(sK8(sK10(powerset(powerset(cartesian_product2(X0,X1)))),X2)),unordered_pair(sK8(sK10(powerset(powerset(cartesian_product2(X0,X1)))),X2),X3)),powerset(cartesian_product2(X0,X1)))
| ~ in(X3,X4)
| ~ in(sK9(sK10(powerset(powerset(cartesian_product2(X0,X1)))),X2),X4)
| ~ in(sK8(sK10(powerset(powerset(cartesian_product2(X0,X1)))),X2),X4)
| ~ sP0(powerset(cartesian_product2(X0,X1)),X4)
| empty(powerset(cartesian_product2(X0,X1)))
| ~ relation_of2_as_subset(unordered_pair(singleton(sK9(sK10(powerset(powerset(cartesian_product2(X0,X1)))),X2)),unordered_pair(X3,sK9(sK10(powerset(powerset(cartesian_product2(X0,X1)))),X2))),X0,X1)
| sP0(sK10(powerset(powerset(cartesian_product2(X0,X1)))),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1046])]) ).
fof(f3585,plain,
( spl17_378
<=> ! [X5,X4,X0,X3,X2,X1] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X1,X0)),powerset(cartesian_product2(X2,X3)))
| in(unordered_pair(singleton(X0),unordered_pair(X0,X4)),powerset(cartesian_product2(X2,X3)))
| ~ in(X4,X5)
| ~ in(X1,X5)
| ~ in(X0,X5)
| ~ sP0(powerset(cartesian_product2(X2,X3)),X5)
| empty(powerset(cartesian_product2(X2,X3)))
| ~ relation_of2_as_subset(unordered_pair(singleton(X1),unordered_pair(X4,X1)),X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_378])]) ).
fof(f3634,plain,
( ! [X2,X3,X0,X1,X4] :
( in(unordered_pair(singleton(sK8(sK10(powerset(powerset(cartesian_product2(X0,X1)))),X2)),unordered_pair(sK8(sK10(powerset(powerset(cartesian_product2(X0,X1)))),X2),X3)),powerset(cartesian_product2(X0,X1)))
| ~ in(X3,X4)
| ~ in(sK9(sK10(powerset(powerset(cartesian_product2(X0,X1)))),X2),X4)
| ~ in(sK8(sK10(powerset(powerset(cartesian_product2(X0,X1)))),X2),X4)
| ~ sP0(powerset(cartesian_product2(X0,X1)),X4)
| empty(powerset(cartesian_product2(X0,X1)))
| ~ relation_of2_as_subset(unordered_pair(singleton(sK9(sK10(powerset(powerset(cartesian_product2(X0,X1)))),X2)),unordered_pair(X3,sK9(sK10(powerset(powerset(cartesian_product2(X0,X1)))),X2))),X0,X1)
| sP0(sK10(powerset(powerset(cartesian_product2(X0,X1)))),X2) )
| ~ spl17_320
| ~ spl17_378 ),
inference(duplicate_literal_removal,[],[f3626]) ).
fof(f3626,plain,
( ! [X2,X3,X0,X1,X4] :
( in(unordered_pair(singleton(sK8(sK10(powerset(powerset(cartesian_product2(X0,X1)))),X2)),unordered_pair(sK8(sK10(powerset(powerset(cartesian_product2(X0,X1)))),X2),X3)),powerset(cartesian_product2(X0,X1)))
| ~ in(X3,X4)
| ~ in(sK9(sK10(powerset(powerset(cartesian_product2(X0,X1)))),X2),X4)
| ~ in(sK8(sK10(powerset(powerset(cartesian_product2(X0,X1)))),X2),X4)
| ~ sP0(powerset(cartesian_product2(X0,X1)),X4)
| empty(powerset(cartesian_product2(X0,X1)))
| ~ relation_of2_as_subset(unordered_pair(singleton(sK9(sK10(powerset(powerset(cartesian_product2(X0,X1)))),X2)),unordered_pair(X3,sK9(sK10(powerset(powerset(cartesian_product2(X0,X1)))),X2))),X0,X1)
| empty(powerset(cartesian_product2(X0,X1)))
| sP0(sK10(powerset(powerset(cartesian_product2(X0,X1)))),X2) )
| ~ spl17_320
| ~ spl17_378 ),
inference(resolution,[],[f3586,f2870]) ).
fof(f3586,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X1,X0)),powerset(cartesian_product2(X2,X3)))
| in(unordered_pair(singleton(X0),unordered_pair(X0,X4)),powerset(cartesian_product2(X2,X3)))
| ~ in(X4,X5)
| ~ in(X1,X5)
| ~ in(X0,X5)
| ~ sP0(powerset(cartesian_product2(X2,X3)),X5)
| empty(powerset(cartesian_product2(X2,X3)))
| ~ relation_of2_as_subset(unordered_pair(singleton(X1),unordered_pair(X4,X1)),X2,X3) )
| ~ spl17_378 ),
inference(avatar_component_clause,[],[f3585]) ).
fof(f14439,plain,
( spl17_1045
| ~ spl17_321
| ~ spl17_378 ),
inference(avatar_split_clause,[],[f3632,f3585,f2873,f14437]) ).
fof(f14437,plain,
( spl17_1045
<=> ! [X4,X0,X3,X2,X1] :
( in(unordered_pair(singleton(sK7(sK10(powerset(powerset(cartesian_product2(X0,X1)))),X2)),unordered_pair(sK7(sK10(powerset(powerset(cartesian_product2(X0,X1)))),X2),X3)),powerset(cartesian_product2(X0,X1)))
| ~ in(X3,X4)
| ~ in(sK8(sK10(powerset(powerset(cartesian_product2(X0,X1)))),X2),X4)
| ~ in(sK7(sK10(powerset(powerset(cartesian_product2(X0,X1)))),X2),X4)
| ~ sP0(powerset(cartesian_product2(X0,X1)),X4)
| empty(powerset(cartesian_product2(X0,X1)))
| ~ relation_of2_as_subset(unordered_pair(singleton(sK8(sK10(powerset(powerset(cartesian_product2(X0,X1)))),X2)),unordered_pair(X3,sK8(sK10(powerset(powerset(cartesian_product2(X0,X1)))),X2))),X0,X1)
| sP0(sK10(powerset(powerset(cartesian_product2(X0,X1)))),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1045])]) ).
fof(f3632,plain,
( ! [X2,X3,X0,X1,X4] :
( in(unordered_pair(singleton(sK7(sK10(powerset(powerset(cartesian_product2(X0,X1)))),X2)),unordered_pair(sK7(sK10(powerset(powerset(cartesian_product2(X0,X1)))),X2),X3)),powerset(cartesian_product2(X0,X1)))
| ~ in(X3,X4)
| ~ in(sK8(sK10(powerset(powerset(cartesian_product2(X0,X1)))),X2),X4)
| ~ in(sK7(sK10(powerset(powerset(cartesian_product2(X0,X1)))),X2),X4)
| ~ sP0(powerset(cartesian_product2(X0,X1)),X4)
| empty(powerset(cartesian_product2(X0,X1)))
| ~ relation_of2_as_subset(unordered_pair(singleton(sK8(sK10(powerset(powerset(cartesian_product2(X0,X1)))),X2)),unordered_pair(X3,sK8(sK10(powerset(powerset(cartesian_product2(X0,X1)))),X2))),X0,X1)
| sP0(sK10(powerset(powerset(cartesian_product2(X0,X1)))),X2) )
| ~ spl17_321
| ~ spl17_378 ),
inference(duplicate_literal_removal,[],[f3629]) ).
fof(f3629,plain,
( ! [X2,X3,X0,X1,X4] :
( in(unordered_pair(singleton(sK7(sK10(powerset(powerset(cartesian_product2(X0,X1)))),X2)),unordered_pair(sK7(sK10(powerset(powerset(cartesian_product2(X0,X1)))),X2),X3)),powerset(cartesian_product2(X0,X1)))
| ~ in(X3,X4)
| ~ in(sK8(sK10(powerset(powerset(cartesian_product2(X0,X1)))),X2),X4)
| ~ in(sK7(sK10(powerset(powerset(cartesian_product2(X0,X1)))),X2),X4)
| ~ sP0(powerset(cartesian_product2(X0,X1)),X4)
| empty(powerset(cartesian_product2(X0,X1)))
| ~ relation_of2_as_subset(unordered_pair(singleton(sK8(sK10(powerset(powerset(cartesian_product2(X0,X1)))),X2)),unordered_pair(X3,sK8(sK10(powerset(powerset(cartesian_product2(X0,X1)))),X2))),X0,X1)
| empty(powerset(cartesian_product2(X0,X1)))
| sP0(sK10(powerset(powerset(cartesian_product2(X0,X1)))),X2) )
| ~ spl17_321
| ~ spl17_378 ),
inference(resolution,[],[f3586,f2874]) ).
fof(f14427,plain,
( spl17_1044
| ~ spl17_311
| ~ spl17_379 ),
inference(avatar_split_clause,[],[f3651,f3615,f2726,f14425]) ).
fof(f14425,plain,
( spl17_1044
<=> ! [X4,X0,X3,X2,X1] :
( ~ relation_of2_as_subset(unordered_pair(singleton(sK9(sK6(powerset(cartesian_product2(X0,X1))),X2)),unordered_pair(sK9(sK6(powerset(cartesian_product2(X0,X1))),X2),X3)),X0,X1)
| empty(powerset(cartesian_product2(X0,X1)))
| in(unordered_pair(singleton(sK8(sK6(powerset(cartesian_product2(X0,X1))),X2)),unordered_pair(sK8(sK6(powerset(cartesian_product2(X0,X1))),X2),X3)),powerset(cartesian_product2(X0,X1)))
| ~ in(X3,X4)
| ~ in(sK9(sK6(powerset(cartesian_product2(X0,X1))),X2),X4)
| ~ in(sK8(sK6(powerset(cartesian_product2(X0,X1))),X2),X4)
| ~ sP0(powerset(cartesian_product2(X0,X1)),X4)
| sP0(sK6(powerset(cartesian_product2(X0,X1))),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1044])]) ).
fof(f3651,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ relation_of2_as_subset(unordered_pair(singleton(sK9(sK6(powerset(cartesian_product2(X0,X1))),X2)),unordered_pair(sK9(sK6(powerset(cartesian_product2(X0,X1))),X2),X3)),X0,X1)
| empty(powerset(cartesian_product2(X0,X1)))
| in(unordered_pair(singleton(sK8(sK6(powerset(cartesian_product2(X0,X1))),X2)),unordered_pair(sK8(sK6(powerset(cartesian_product2(X0,X1))),X2),X3)),powerset(cartesian_product2(X0,X1)))
| ~ in(X3,X4)
| ~ in(sK9(sK6(powerset(cartesian_product2(X0,X1))),X2),X4)
| ~ in(sK8(sK6(powerset(cartesian_product2(X0,X1))),X2),X4)
| ~ sP0(powerset(cartesian_product2(X0,X1)),X4)
| sP0(sK6(powerset(cartesian_product2(X0,X1))),X2) )
| ~ spl17_311
| ~ spl17_379 ),
inference(duplicate_literal_removal,[],[f3641]) ).
fof(f3641,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ relation_of2_as_subset(unordered_pair(singleton(sK9(sK6(powerset(cartesian_product2(X0,X1))),X2)),unordered_pair(sK9(sK6(powerset(cartesian_product2(X0,X1))),X2),X3)),X0,X1)
| empty(powerset(cartesian_product2(X0,X1)))
| in(unordered_pair(singleton(sK8(sK6(powerset(cartesian_product2(X0,X1))),X2)),unordered_pair(sK8(sK6(powerset(cartesian_product2(X0,X1))),X2),X3)),powerset(cartesian_product2(X0,X1)))
| ~ in(X3,X4)
| ~ in(sK9(sK6(powerset(cartesian_product2(X0,X1))),X2),X4)
| ~ in(sK8(sK6(powerset(cartesian_product2(X0,X1))),X2),X4)
| ~ sP0(powerset(cartesian_product2(X0,X1)),X4)
| sP0(sK6(powerset(cartesian_product2(X0,X1))),X2)
| empty(powerset(cartesian_product2(X0,X1))) )
| ~ spl17_311
| ~ spl17_379 ),
inference(resolution,[],[f3616,f2727]) ).
fof(f14423,plain,
( spl17_1043
| ~ spl17_312
| ~ spl17_379 ),
inference(avatar_split_clause,[],[f3649,f3615,f2730,f14421]) ).
fof(f14421,plain,
( spl17_1043
<=> ! [X4,X0,X3,X2,X1] :
( ~ relation_of2_as_subset(unordered_pair(singleton(sK8(sK6(powerset(cartesian_product2(X0,X1))),X2)),unordered_pair(sK8(sK6(powerset(cartesian_product2(X0,X1))),X2),X3)),X0,X1)
| empty(powerset(cartesian_product2(X0,X1)))
| in(unordered_pair(singleton(sK7(sK6(powerset(cartesian_product2(X0,X1))),X2)),unordered_pair(sK7(sK6(powerset(cartesian_product2(X0,X1))),X2),X3)),powerset(cartesian_product2(X0,X1)))
| ~ in(X3,X4)
| ~ in(sK8(sK6(powerset(cartesian_product2(X0,X1))),X2),X4)
| ~ in(sK7(sK6(powerset(cartesian_product2(X0,X1))),X2),X4)
| ~ sP0(powerset(cartesian_product2(X0,X1)),X4)
| sP0(sK6(powerset(cartesian_product2(X0,X1))),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1043])]) ).
fof(f3649,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ relation_of2_as_subset(unordered_pair(singleton(sK8(sK6(powerset(cartesian_product2(X0,X1))),X2)),unordered_pair(sK8(sK6(powerset(cartesian_product2(X0,X1))),X2),X3)),X0,X1)
| empty(powerset(cartesian_product2(X0,X1)))
| in(unordered_pair(singleton(sK7(sK6(powerset(cartesian_product2(X0,X1))),X2)),unordered_pair(sK7(sK6(powerset(cartesian_product2(X0,X1))),X2),X3)),powerset(cartesian_product2(X0,X1)))
| ~ in(X3,X4)
| ~ in(sK8(sK6(powerset(cartesian_product2(X0,X1))),X2),X4)
| ~ in(sK7(sK6(powerset(cartesian_product2(X0,X1))),X2),X4)
| ~ sP0(powerset(cartesian_product2(X0,X1)),X4)
| sP0(sK6(powerset(cartesian_product2(X0,X1))),X2) )
| ~ spl17_312
| ~ spl17_379 ),
inference(duplicate_literal_removal,[],[f3644]) ).
fof(f3644,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ relation_of2_as_subset(unordered_pair(singleton(sK8(sK6(powerset(cartesian_product2(X0,X1))),X2)),unordered_pair(sK8(sK6(powerset(cartesian_product2(X0,X1))),X2),X3)),X0,X1)
| empty(powerset(cartesian_product2(X0,X1)))
| in(unordered_pair(singleton(sK7(sK6(powerset(cartesian_product2(X0,X1))),X2)),unordered_pair(sK7(sK6(powerset(cartesian_product2(X0,X1))),X2),X3)),powerset(cartesian_product2(X0,X1)))
| ~ in(X3,X4)
| ~ in(sK8(sK6(powerset(cartesian_product2(X0,X1))),X2),X4)
| ~ in(sK7(sK6(powerset(cartesian_product2(X0,X1))),X2),X4)
| ~ sP0(powerset(cartesian_product2(X0,X1)),X4)
| sP0(sK6(powerset(cartesian_product2(X0,X1))),X2)
| empty(powerset(cartesian_product2(X0,X1))) )
| ~ spl17_312
| ~ spl17_379 ),
inference(resolution,[],[f3616,f2731]) ).
fof(f14417,plain,
( spl17_1042
| ~ spl17_311
| ~ spl17_378 ),
inference(avatar_split_clause,[],[f3635,f3585,f2726,f14415]) ).
fof(f14415,plain,
( spl17_1042
<=> ! [X4,X0,X3,X2,X1] :
( in(unordered_pair(singleton(sK8(sK6(powerset(cartesian_product2(X0,X1))),X2)),unordered_pair(sK8(sK6(powerset(cartesian_product2(X0,X1))),X2),X3)),powerset(cartesian_product2(X0,X1)))
| ~ in(X3,X4)
| ~ in(sK9(sK6(powerset(cartesian_product2(X0,X1))),X2),X4)
| ~ in(sK8(sK6(powerset(cartesian_product2(X0,X1))),X2),X4)
| ~ sP0(powerset(cartesian_product2(X0,X1)),X4)
| empty(powerset(cartesian_product2(X0,X1)))
| ~ relation_of2_as_subset(unordered_pair(singleton(sK9(sK6(powerset(cartesian_product2(X0,X1))),X2)),unordered_pair(X3,sK9(sK6(powerset(cartesian_product2(X0,X1))),X2))),X0,X1)
| sP0(sK6(powerset(cartesian_product2(X0,X1))),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1042])]) ).
fof(f3635,plain,
( ! [X2,X3,X0,X1,X4] :
( in(unordered_pair(singleton(sK8(sK6(powerset(cartesian_product2(X0,X1))),X2)),unordered_pair(sK8(sK6(powerset(cartesian_product2(X0,X1))),X2),X3)),powerset(cartesian_product2(X0,X1)))
| ~ in(X3,X4)
| ~ in(sK9(sK6(powerset(cartesian_product2(X0,X1))),X2),X4)
| ~ in(sK8(sK6(powerset(cartesian_product2(X0,X1))),X2),X4)
| ~ sP0(powerset(cartesian_product2(X0,X1)),X4)
| empty(powerset(cartesian_product2(X0,X1)))
| ~ relation_of2_as_subset(unordered_pair(singleton(sK9(sK6(powerset(cartesian_product2(X0,X1))),X2)),unordered_pair(X3,sK9(sK6(powerset(cartesian_product2(X0,X1))),X2))),X0,X1)
| sP0(sK6(powerset(cartesian_product2(X0,X1))),X2) )
| ~ spl17_311
| ~ spl17_378 ),
inference(duplicate_literal_removal,[],[f3625]) ).
fof(f3625,plain,
( ! [X2,X3,X0,X1,X4] :
( in(unordered_pair(singleton(sK8(sK6(powerset(cartesian_product2(X0,X1))),X2)),unordered_pair(sK8(sK6(powerset(cartesian_product2(X0,X1))),X2),X3)),powerset(cartesian_product2(X0,X1)))
| ~ in(X3,X4)
| ~ in(sK9(sK6(powerset(cartesian_product2(X0,X1))),X2),X4)
| ~ in(sK8(sK6(powerset(cartesian_product2(X0,X1))),X2),X4)
| ~ sP0(powerset(cartesian_product2(X0,X1)),X4)
| empty(powerset(cartesian_product2(X0,X1)))
| ~ relation_of2_as_subset(unordered_pair(singleton(sK9(sK6(powerset(cartesian_product2(X0,X1))),X2)),unordered_pair(X3,sK9(sK6(powerset(cartesian_product2(X0,X1))),X2))),X0,X1)
| sP0(sK6(powerset(cartesian_product2(X0,X1))),X2)
| empty(powerset(cartesian_product2(X0,X1))) )
| ~ spl17_311
| ~ spl17_378 ),
inference(resolution,[],[f3586,f2727]) ).
fof(f14413,plain,
( spl17_1041
| ~ spl17_312
| ~ spl17_378 ),
inference(avatar_split_clause,[],[f3633,f3585,f2730,f14411]) ).
fof(f14411,plain,
( spl17_1041
<=> ! [X4,X0,X3,X2,X1] :
( in(unordered_pair(singleton(sK7(sK6(powerset(cartesian_product2(X0,X1))),X2)),unordered_pair(sK7(sK6(powerset(cartesian_product2(X0,X1))),X2),X3)),powerset(cartesian_product2(X0,X1)))
| ~ in(X3,X4)
| ~ in(sK8(sK6(powerset(cartesian_product2(X0,X1))),X2),X4)
| ~ in(sK7(sK6(powerset(cartesian_product2(X0,X1))),X2),X4)
| ~ sP0(powerset(cartesian_product2(X0,X1)),X4)
| empty(powerset(cartesian_product2(X0,X1)))
| ~ relation_of2_as_subset(unordered_pair(singleton(sK8(sK6(powerset(cartesian_product2(X0,X1))),X2)),unordered_pair(X3,sK8(sK6(powerset(cartesian_product2(X0,X1))),X2))),X0,X1)
| sP0(sK6(powerset(cartesian_product2(X0,X1))),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1041])]) ).
fof(f3633,plain,
( ! [X2,X3,X0,X1,X4] :
( in(unordered_pair(singleton(sK7(sK6(powerset(cartesian_product2(X0,X1))),X2)),unordered_pair(sK7(sK6(powerset(cartesian_product2(X0,X1))),X2),X3)),powerset(cartesian_product2(X0,X1)))
| ~ in(X3,X4)
| ~ in(sK8(sK6(powerset(cartesian_product2(X0,X1))),X2),X4)
| ~ in(sK7(sK6(powerset(cartesian_product2(X0,X1))),X2),X4)
| ~ sP0(powerset(cartesian_product2(X0,X1)),X4)
| empty(powerset(cartesian_product2(X0,X1)))
| ~ relation_of2_as_subset(unordered_pair(singleton(sK8(sK6(powerset(cartesian_product2(X0,X1))),X2)),unordered_pair(X3,sK8(sK6(powerset(cartesian_product2(X0,X1))),X2))),X0,X1)
| sP0(sK6(powerset(cartesian_product2(X0,X1))),X2) )
| ~ spl17_312
| ~ spl17_378 ),
inference(duplicate_literal_removal,[],[f3628]) ).
fof(f3628,plain,
( ! [X2,X3,X0,X1,X4] :
( in(unordered_pair(singleton(sK7(sK6(powerset(cartesian_product2(X0,X1))),X2)),unordered_pair(sK7(sK6(powerset(cartesian_product2(X0,X1))),X2),X3)),powerset(cartesian_product2(X0,X1)))
| ~ in(X3,X4)
| ~ in(sK8(sK6(powerset(cartesian_product2(X0,X1))),X2),X4)
| ~ in(sK7(sK6(powerset(cartesian_product2(X0,X1))),X2),X4)
| ~ sP0(powerset(cartesian_product2(X0,X1)),X4)
| empty(powerset(cartesian_product2(X0,X1)))
| ~ relation_of2_as_subset(unordered_pair(singleton(sK8(sK6(powerset(cartesian_product2(X0,X1))),X2)),unordered_pair(X3,sK8(sK6(powerset(cartesian_product2(X0,X1))),X2))),X0,X1)
| sP0(sK6(powerset(cartesian_product2(X0,X1))),X2)
| empty(powerset(cartesian_product2(X0,X1))) )
| ~ spl17_312
| ~ spl17_378 ),
inference(resolution,[],[f3586,f2731]) ).
fof(f14385,plain,
( spl17_1040
| ~ spl17_266
| ~ spl17_332 ),
inference(avatar_split_clause,[],[f3170,f3130,f2147,f14383]) ).
fof(f14383,plain,
( spl17_1040
<=> ! [X2,X0,X1] :
( element(sK9(X0,sK10(powerset(unordered_pair(singleton(sK7(sK10(powerset(powerset(X1))),X2)),unordered_pair(sK8(sK10(powerset(powerset(X1))),X2),sK7(sK10(powerset(powerset(X1))),X2)))))),X1)
| sP0(sK10(powerset(powerset(X1))),X2)
| empty(unordered_pair(singleton(sK7(sK10(powerset(powerset(X1))),X2)),unordered_pair(sK8(sK10(powerset(powerset(X1))),X2),sK7(sK10(powerset(powerset(X1))),X2))))
| sP0(X0,sK10(powerset(unordered_pair(singleton(sK7(sK10(powerset(powerset(X1))),X2)),unordered_pair(sK8(sK10(powerset(powerset(X1))),X2),sK7(sK10(powerset(powerset(X1))),X2)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1040])]) ).
fof(f2147,plain,
( spl17_266
<=> ! [X0,X1] :
( sP0(X0,sK10(powerset(X1)))
| empty(X1)
| in(sK9(X0,sK10(powerset(X1))),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_266])]) ).
fof(f3170,plain,
( ! [X2,X0,X1] :
( element(sK9(X0,sK10(powerset(unordered_pair(singleton(sK7(sK10(powerset(powerset(X1))),X2)),unordered_pair(sK8(sK10(powerset(powerset(X1))),X2),sK7(sK10(powerset(powerset(X1))),X2)))))),X1)
| sP0(sK10(powerset(powerset(X1))),X2)
| empty(unordered_pair(singleton(sK7(sK10(powerset(powerset(X1))),X2)),unordered_pair(sK8(sK10(powerset(powerset(X1))),X2),sK7(sK10(powerset(powerset(X1))),X2))))
| sP0(X0,sK10(powerset(unordered_pair(singleton(sK7(sK10(powerset(powerset(X1))),X2)),unordered_pair(sK8(sK10(powerset(powerset(X1))),X2),sK7(sK10(powerset(powerset(X1))),X2)))))) )
| ~ spl17_266
| ~ spl17_332 ),
inference(resolution,[],[f3131,f2148]) ).
fof(f2148,plain,
( ! [X0,X1] :
( in(sK9(X0,sK10(powerset(X1))),X1)
| empty(X1)
| sP0(X0,sK10(powerset(X1))) )
| ~ spl17_266 ),
inference(avatar_component_clause,[],[f2147]) ).
fof(f14381,plain,
( spl17_1039
| ~ spl17_265
| ~ spl17_332 ),
inference(avatar_split_clause,[],[f3167,f3130,f2143,f14379]) ).
fof(f14379,plain,
( spl17_1039
<=> ! [X2,X0,X1] :
( element(sK8(X0,sK10(powerset(unordered_pair(singleton(sK7(sK10(powerset(powerset(X1))),X2)),unordered_pair(sK8(sK10(powerset(powerset(X1))),X2),sK7(sK10(powerset(powerset(X1))),X2)))))),X1)
| sP0(sK10(powerset(powerset(X1))),X2)
| empty(unordered_pair(singleton(sK7(sK10(powerset(powerset(X1))),X2)),unordered_pair(sK8(sK10(powerset(powerset(X1))),X2),sK7(sK10(powerset(powerset(X1))),X2))))
| sP0(X0,sK10(powerset(unordered_pair(singleton(sK7(sK10(powerset(powerset(X1))),X2)),unordered_pair(sK8(sK10(powerset(powerset(X1))),X2),sK7(sK10(powerset(powerset(X1))),X2)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1039])]) ).
fof(f2143,plain,
( spl17_265
<=> ! [X0,X1] :
( sP0(X0,sK10(powerset(X1)))
| empty(X1)
| in(sK8(X0,sK10(powerset(X1))),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_265])]) ).
fof(f3167,plain,
( ! [X2,X0,X1] :
( element(sK8(X0,sK10(powerset(unordered_pair(singleton(sK7(sK10(powerset(powerset(X1))),X2)),unordered_pair(sK8(sK10(powerset(powerset(X1))),X2),sK7(sK10(powerset(powerset(X1))),X2)))))),X1)
| sP0(sK10(powerset(powerset(X1))),X2)
| empty(unordered_pair(singleton(sK7(sK10(powerset(powerset(X1))),X2)),unordered_pair(sK8(sK10(powerset(powerset(X1))),X2),sK7(sK10(powerset(powerset(X1))),X2))))
| sP0(X0,sK10(powerset(unordered_pair(singleton(sK7(sK10(powerset(powerset(X1))),X2)),unordered_pair(sK8(sK10(powerset(powerset(X1))),X2),sK7(sK10(powerset(powerset(X1))),X2)))))) )
| ~ spl17_265
| ~ spl17_332 ),
inference(resolution,[],[f3131,f2144]) ).
fof(f2144,plain,
( ! [X0,X1] :
( in(sK8(X0,sK10(powerset(X1))),X1)
| empty(X1)
| sP0(X0,sK10(powerset(X1))) )
| ~ spl17_265 ),
inference(avatar_component_clause,[],[f2143]) ).
fof(f14374,plain,
( spl17_1038
| ~ spl17_264
| ~ spl17_332 ),
inference(avatar_split_clause,[],[f3164,f3130,f2139,f14372]) ).
fof(f14372,plain,
( spl17_1038
<=> ! [X2,X0,X1] :
( element(sK7(X0,sK10(powerset(unordered_pair(singleton(sK7(sK10(powerset(powerset(X1))),X2)),unordered_pair(sK8(sK10(powerset(powerset(X1))),X2),sK7(sK10(powerset(powerset(X1))),X2)))))),X1)
| sP0(sK10(powerset(powerset(X1))),X2)
| empty(unordered_pair(singleton(sK7(sK10(powerset(powerset(X1))),X2)),unordered_pair(sK8(sK10(powerset(powerset(X1))),X2),sK7(sK10(powerset(powerset(X1))),X2))))
| sP0(X0,sK10(powerset(unordered_pair(singleton(sK7(sK10(powerset(powerset(X1))),X2)),unordered_pair(sK8(sK10(powerset(powerset(X1))),X2),sK7(sK10(powerset(powerset(X1))),X2)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1038])]) ).
fof(f2139,plain,
( spl17_264
<=> ! [X0,X1] :
( sP0(X0,sK10(powerset(X1)))
| empty(X1)
| in(sK7(X0,sK10(powerset(X1))),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_264])]) ).
fof(f3164,plain,
( ! [X2,X0,X1] :
( element(sK7(X0,sK10(powerset(unordered_pair(singleton(sK7(sK10(powerset(powerset(X1))),X2)),unordered_pair(sK8(sK10(powerset(powerset(X1))),X2),sK7(sK10(powerset(powerset(X1))),X2)))))),X1)
| sP0(sK10(powerset(powerset(X1))),X2)
| empty(unordered_pair(singleton(sK7(sK10(powerset(powerset(X1))),X2)),unordered_pair(sK8(sK10(powerset(powerset(X1))),X2),sK7(sK10(powerset(powerset(X1))),X2))))
| sP0(X0,sK10(powerset(unordered_pair(singleton(sK7(sK10(powerset(powerset(X1))),X2)),unordered_pair(sK8(sK10(powerset(powerset(X1))),X2),sK7(sK10(powerset(powerset(X1))),X2)))))) )
| ~ spl17_264
| ~ spl17_332 ),
inference(resolution,[],[f3131,f2140]) ).
fof(f2140,plain,
( ! [X0,X1] :
( in(sK7(X0,sK10(powerset(X1))),X1)
| empty(X1)
| sP0(X0,sK10(powerset(X1))) )
| ~ spl17_264 ),
inference(avatar_component_clause,[],[f2139]) ).
fof(f14370,plain,
( spl17_1037
| ~ spl17_266
| ~ spl17_331 ),
inference(avatar_split_clause,[],[f3150,f3126,f2147,f14368]) ).
fof(f14368,plain,
( spl17_1037
<=> ! [X2,X0,X1] :
( element(sK9(X0,sK10(powerset(unordered_pair(singleton(sK8(sK10(powerset(powerset(X1))),X2)),unordered_pair(sK9(sK10(powerset(powerset(X1))),X2),sK8(sK10(powerset(powerset(X1))),X2)))))),X1)
| sP0(sK10(powerset(powerset(X1))),X2)
| empty(unordered_pair(singleton(sK8(sK10(powerset(powerset(X1))),X2)),unordered_pair(sK9(sK10(powerset(powerset(X1))),X2),sK8(sK10(powerset(powerset(X1))),X2))))
| sP0(X0,sK10(powerset(unordered_pair(singleton(sK8(sK10(powerset(powerset(X1))),X2)),unordered_pair(sK9(sK10(powerset(powerset(X1))),X2),sK8(sK10(powerset(powerset(X1))),X2)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1037])]) ).
fof(f3150,plain,
( ! [X2,X0,X1] :
( element(sK9(X0,sK10(powerset(unordered_pair(singleton(sK8(sK10(powerset(powerset(X1))),X2)),unordered_pair(sK9(sK10(powerset(powerset(X1))),X2),sK8(sK10(powerset(powerset(X1))),X2)))))),X1)
| sP0(sK10(powerset(powerset(X1))),X2)
| empty(unordered_pair(singleton(sK8(sK10(powerset(powerset(X1))),X2)),unordered_pair(sK9(sK10(powerset(powerset(X1))),X2),sK8(sK10(powerset(powerset(X1))),X2))))
| sP0(X0,sK10(powerset(unordered_pair(singleton(sK8(sK10(powerset(powerset(X1))),X2)),unordered_pair(sK9(sK10(powerset(powerset(X1))),X2),sK8(sK10(powerset(powerset(X1))),X2)))))) )
| ~ spl17_266
| ~ spl17_331 ),
inference(resolution,[],[f3127,f2148]) ).
fof(f14366,plain,
( spl17_1036
| ~ spl17_265
| ~ spl17_331 ),
inference(avatar_split_clause,[],[f3147,f3126,f2143,f14364]) ).
fof(f14364,plain,
( spl17_1036
<=> ! [X2,X0,X1] :
( element(sK8(X0,sK10(powerset(unordered_pair(singleton(sK8(sK10(powerset(powerset(X1))),X2)),unordered_pair(sK9(sK10(powerset(powerset(X1))),X2),sK8(sK10(powerset(powerset(X1))),X2)))))),X1)
| sP0(sK10(powerset(powerset(X1))),X2)
| empty(unordered_pair(singleton(sK8(sK10(powerset(powerset(X1))),X2)),unordered_pair(sK9(sK10(powerset(powerset(X1))),X2),sK8(sK10(powerset(powerset(X1))),X2))))
| sP0(X0,sK10(powerset(unordered_pair(singleton(sK8(sK10(powerset(powerset(X1))),X2)),unordered_pair(sK9(sK10(powerset(powerset(X1))),X2),sK8(sK10(powerset(powerset(X1))),X2)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1036])]) ).
fof(f3147,plain,
( ! [X2,X0,X1] :
( element(sK8(X0,sK10(powerset(unordered_pair(singleton(sK8(sK10(powerset(powerset(X1))),X2)),unordered_pair(sK9(sK10(powerset(powerset(X1))),X2),sK8(sK10(powerset(powerset(X1))),X2)))))),X1)
| sP0(sK10(powerset(powerset(X1))),X2)
| empty(unordered_pair(singleton(sK8(sK10(powerset(powerset(X1))),X2)),unordered_pair(sK9(sK10(powerset(powerset(X1))),X2),sK8(sK10(powerset(powerset(X1))),X2))))
| sP0(X0,sK10(powerset(unordered_pair(singleton(sK8(sK10(powerset(powerset(X1))),X2)),unordered_pair(sK9(sK10(powerset(powerset(X1))),X2),sK8(sK10(powerset(powerset(X1))),X2)))))) )
| ~ spl17_265
| ~ spl17_331 ),
inference(resolution,[],[f3127,f2144]) ).
fof(f14362,plain,
( spl17_1035
| ~ spl17_264
| ~ spl17_331 ),
inference(avatar_split_clause,[],[f3144,f3126,f2139,f14360]) ).
fof(f14360,plain,
( spl17_1035
<=> ! [X2,X0,X1] :
( element(sK7(X0,sK10(powerset(unordered_pair(singleton(sK8(sK10(powerset(powerset(X1))),X2)),unordered_pair(sK9(sK10(powerset(powerset(X1))),X2),sK8(sK10(powerset(powerset(X1))),X2)))))),X1)
| sP0(sK10(powerset(powerset(X1))),X2)
| empty(unordered_pair(singleton(sK8(sK10(powerset(powerset(X1))),X2)),unordered_pair(sK9(sK10(powerset(powerset(X1))),X2),sK8(sK10(powerset(powerset(X1))),X2))))
| sP0(X0,sK10(powerset(unordered_pair(singleton(sK8(sK10(powerset(powerset(X1))),X2)),unordered_pair(sK9(sK10(powerset(powerset(X1))),X2),sK8(sK10(powerset(powerset(X1))),X2)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1035])]) ).
fof(f3144,plain,
( ! [X2,X0,X1] :
( element(sK7(X0,sK10(powerset(unordered_pair(singleton(sK8(sK10(powerset(powerset(X1))),X2)),unordered_pair(sK9(sK10(powerset(powerset(X1))),X2),sK8(sK10(powerset(powerset(X1))),X2)))))),X1)
| sP0(sK10(powerset(powerset(X1))),X2)
| empty(unordered_pair(singleton(sK8(sK10(powerset(powerset(X1))),X2)),unordered_pair(sK9(sK10(powerset(powerset(X1))),X2),sK8(sK10(powerset(powerset(X1))),X2))))
| sP0(X0,sK10(powerset(unordered_pair(singleton(sK8(sK10(powerset(powerset(X1))),X2)),unordered_pair(sK9(sK10(powerset(powerset(X1))),X2),sK8(sK10(powerset(powerset(X1))),X2)))))) )
| ~ spl17_264
| ~ spl17_331 ),
inference(resolution,[],[f3127,f2140]) ).
fof(f13838,plain,
( spl17_1034
| ~ spl17_39
| ~ spl17_392 ),
inference(avatar_split_clause,[],[f3731,f3716,f355,f13836]) ).
fof(f13836,plain,
( spl17_1034
<=> ! [X2,X0,X1] :
( sP0(powerset(X0),X1)
| sP0(unordered_pair(singleton(sK7(powerset(X0),X1)),unordered_pair(sK8(powerset(X0),X1),sK7(powerset(X0),X1))),X2)
| empty(X0)
| in(unordered_pair(singleton(sK7(unordered_pair(singleton(sK7(powerset(X0),X1)),unordered_pair(sK8(powerset(X0),X1),sK7(powerset(X0),X1))),X2)),unordered_pair(sK8(unordered_pair(singleton(sK7(powerset(X0),X1)),unordered_pair(sK8(powerset(X0),X1),sK7(powerset(X0),X1))),X2),sK7(unordered_pair(singleton(sK7(powerset(X0),X1)),unordered_pair(sK8(powerset(X0),X1),sK7(powerset(X0),X1))),X2))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1034])]) ).
fof(f355,plain,
( spl17_39
<=> ! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_39])]) ).
fof(f3731,plain,
( ! [X2,X0,X1] :
( sP0(powerset(X0),X1)
| sP0(unordered_pair(singleton(sK7(powerset(X0),X1)),unordered_pair(sK8(powerset(X0),X1),sK7(powerset(X0),X1))),X2)
| empty(X0)
| in(unordered_pair(singleton(sK7(unordered_pair(singleton(sK7(powerset(X0),X1)),unordered_pair(sK8(powerset(X0),X1),sK7(powerset(X0),X1))),X2)),unordered_pair(sK8(unordered_pair(singleton(sK7(powerset(X0),X1)),unordered_pair(sK8(powerset(X0),X1),sK7(powerset(X0),X1))),X2),sK7(unordered_pair(singleton(sK7(powerset(X0),X1)),unordered_pair(sK8(powerset(X0),X1),sK7(powerset(X0),X1))),X2))),X0) )
| ~ spl17_39
| ~ spl17_392 ),
inference(resolution,[],[f3717,f356]) ).
fof(f356,plain,
( ! [X0,X1] :
( ~ element(X0,X1)
| empty(X1)
| in(X0,X1) )
| ~ spl17_39 ),
inference(avatar_component_clause,[],[f355]) ).
fof(f13834,plain,
( spl17_1033
| ~ spl17_39
| ~ spl17_391 ),
inference(avatar_split_clause,[],[f3727,f3712,f355,f13832]) ).
fof(f13832,plain,
( spl17_1033
<=> ! [X2,X0,X1] :
( sP0(powerset(X0),X1)
| sP0(unordered_pair(singleton(sK7(powerset(X0),X1)),unordered_pair(sK8(powerset(X0),X1),sK7(powerset(X0),X1))),X2)
| empty(X0)
| in(unordered_pair(singleton(sK8(unordered_pair(singleton(sK7(powerset(X0),X1)),unordered_pair(sK8(powerset(X0),X1),sK7(powerset(X0),X1))),X2)),unordered_pair(sK9(unordered_pair(singleton(sK7(powerset(X0),X1)),unordered_pair(sK8(powerset(X0),X1),sK7(powerset(X0),X1))),X2),sK8(unordered_pair(singleton(sK7(powerset(X0),X1)),unordered_pair(sK8(powerset(X0),X1),sK7(powerset(X0),X1))),X2))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1033])]) ).
fof(f3727,plain,
( ! [X2,X0,X1] :
( sP0(powerset(X0),X1)
| sP0(unordered_pair(singleton(sK7(powerset(X0),X1)),unordered_pair(sK8(powerset(X0),X1),sK7(powerset(X0),X1))),X2)
| empty(X0)
| in(unordered_pair(singleton(sK8(unordered_pair(singleton(sK7(powerset(X0),X1)),unordered_pair(sK8(powerset(X0),X1),sK7(powerset(X0),X1))),X2)),unordered_pair(sK9(unordered_pair(singleton(sK7(powerset(X0),X1)),unordered_pair(sK8(powerset(X0),X1),sK7(powerset(X0),X1))),X2),sK8(unordered_pair(singleton(sK7(powerset(X0),X1)),unordered_pair(sK8(powerset(X0),X1),sK7(powerset(X0),X1))),X2))),X0) )
| ~ spl17_39
| ~ spl17_391 ),
inference(resolution,[],[f3713,f356]) ).
fof(f13785,plain,
( spl17_1032
| ~ spl17_39
| ~ spl17_390 ),
inference(avatar_split_clause,[],[f3723,f3708,f355,f13783]) ).
fof(f13783,plain,
( spl17_1032
<=> ! [X2,X0,X1] :
( sP0(powerset(X0),X1)
| sP0(unordered_pair(singleton(sK8(powerset(X0),X1)),unordered_pair(sK9(powerset(X0),X1),sK8(powerset(X0),X1))),X2)
| empty(X0)
| in(unordered_pair(singleton(sK7(unordered_pair(singleton(sK8(powerset(X0),X1)),unordered_pair(sK9(powerset(X0),X1),sK8(powerset(X0),X1))),X2)),unordered_pair(sK8(unordered_pair(singleton(sK8(powerset(X0),X1)),unordered_pair(sK9(powerset(X0),X1),sK8(powerset(X0),X1))),X2),sK7(unordered_pair(singleton(sK8(powerset(X0),X1)),unordered_pair(sK9(powerset(X0),X1),sK8(powerset(X0),X1))),X2))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1032])]) ).
fof(f3723,plain,
( ! [X2,X0,X1] :
( sP0(powerset(X0),X1)
| sP0(unordered_pair(singleton(sK8(powerset(X0),X1)),unordered_pair(sK9(powerset(X0),X1),sK8(powerset(X0),X1))),X2)
| empty(X0)
| in(unordered_pair(singleton(sK7(unordered_pair(singleton(sK8(powerset(X0),X1)),unordered_pair(sK9(powerset(X0),X1),sK8(powerset(X0),X1))),X2)),unordered_pair(sK8(unordered_pair(singleton(sK8(powerset(X0),X1)),unordered_pair(sK9(powerset(X0),X1),sK8(powerset(X0),X1))),X2),sK7(unordered_pair(singleton(sK8(powerset(X0),X1)),unordered_pair(sK9(powerset(X0),X1),sK8(powerset(X0),X1))),X2))),X0) )
| ~ spl17_39
| ~ spl17_390 ),
inference(resolution,[],[f3709,f356]) ).
fof(f13781,plain,
( spl17_1031
| ~ spl17_39
| ~ spl17_389 ),
inference(avatar_split_clause,[],[f3719,f3704,f355,f13779]) ).
fof(f13779,plain,
( spl17_1031
<=> ! [X2,X0,X1] :
( sP0(powerset(X0),X1)
| sP0(unordered_pair(singleton(sK8(powerset(X0),X1)),unordered_pair(sK9(powerset(X0),X1),sK8(powerset(X0),X1))),X2)
| empty(X0)
| in(unordered_pair(singleton(sK8(unordered_pair(singleton(sK8(powerset(X0),X1)),unordered_pair(sK9(powerset(X0),X1),sK8(powerset(X0),X1))),X2)),unordered_pair(sK9(unordered_pair(singleton(sK8(powerset(X0),X1)),unordered_pair(sK9(powerset(X0),X1),sK8(powerset(X0),X1))),X2),sK8(unordered_pair(singleton(sK8(powerset(X0),X1)),unordered_pair(sK9(powerset(X0),X1),sK8(powerset(X0),X1))),X2))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1031])]) ).
fof(f3719,plain,
( ! [X2,X0,X1] :
( sP0(powerset(X0),X1)
| sP0(unordered_pair(singleton(sK8(powerset(X0),X1)),unordered_pair(sK9(powerset(X0),X1),sK8(powerset(X0),X1))),X2)
| empty(X0)
| in(unordered_pair(singleton(sK8(unordered_pair(singleton(sK8(powerset(X0),X1)),unordered_pair(sK9(powerset(X0),X1),sK8(powerset(X0),X1))),X2)),unordered_pair(sK9(unordered_pair(singleton(sK8(powerset(X0),X1)),unordered_pair(sK9(powerset(X0),X1),sK8(powerset(X0),X1))),X2),sK8(unordered_pair(singleton(sK8(powerset(X0),X1)),unordered_pair(sK9(powerset(X0),X1),sK8(powerset(X0),X1))),X2))),X0) )
| ~ spl17_39
| ~ spl17_389 ),
inference(resolution,[],[f3705,f356]) ).
fof(f13743,plain,
( spl17_1030
| ~ spl17_241
| ~ spl17_332 ),
inference(avatar_split_clause,[],[f3169,f3130,f1933,f13741]) ).
fof(f13741,plain,
( spl17_1030
<=> ! [X2,X0,X1] :
( element(sK9(X0,sK6(unordered_pair(singleton(sK7(sK10(powerset(powerset(X1))),X2)),unordered_pair(sK8(sK10(powerset(powerset(X1))),X2),sK7(sK10(powerset(powerset(X1))),X2))))),X1)
| sP0(sK10(powerset(powerset(X1))),X2)
| sP0(X0,sK6(unordered_pair(singleton(sK7(sK10(powerset(powerset(X1))),X2)),unordered_pair(sK8(sK10(powerset(powerset(X1))),X2),sK7(sK10(powerset(powerset(X1))),X2)))))
| empty(unordered_pair(singleton(sK7(sK10(powerset(powerset(X1))),X2)),unordered_pair(sK8(sK10(powerset(powerset(X1))),X2),sK7(sK10(powerset(powerset(X1))),X2)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1030])]) ).
fof(f1933,plain,
( spl17_241
<=> ! [X0,X1] :
( empty(X0)
| sP0(X1,sK6(X0))
| in(sK9(X1,sK6(X0)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_241])]) ).
fof(f3169,plain,
( ! [X2,X0,X1] :
( element(sK9(X0,sK6(unordered_pair(singleton(sK7(sK10(powerset(powerset(X1))),X2)),unordered_pair(sK8(sK10(powerset(powerset(X1))),X2),sK7(sK10(powerset(powerset(X1))),X2))))),X1)
| sP0(sK10(powerset(powerset(X1))),X2)
| sP0(X0,sK6(unordered_pair(singleton(sK7(sK10(powerset(powerset(X1))),X2)),unordered_pair(sK8(sK10(powerset(powerset(X1))),X2),sK7(sK10(powerset(powerset(X1))),X2)))))
| empty(unordered_pair(singleton(sK7(sK10(powerset(powerset(X1))),X2)),unordered_pair(sK8(sK10(powerset(powerset(X1))),X2),sK7(sK10(powerset(powerset(X1))),X2)))) )
| ~ spl17_241
| ~ spl17_332 ),
inference(resolution,[],[f3131,f1934]) ).
fof(f1934,plain,
( ! [X0,X1] :
( in(sK9(X1,sK6(X0)),X0)
| sP0(X1,sK6(X0))
| empty(X0) )
| ~ spl17_241 ),
inference(avatar_component_clause,[],[f1933]) ).
fof(f13739,plain,
( spl17_1029
| ~ spl17_240
| ~ spl17_332 ),
inference(avatar_split_clause,[],[f3166,f3130,f1929,f13737]) ).
fof(f13737,plain,
( spl17_1029
<=> ! [X2,X0,X1] :
( element(sK8(X0,sK6(unordered_pair(singleton(sK7(sK10(powerset(powerset(X1))),X2)),unordered_pair(sK8(sK10(powerset(powerset(X1))),X2),sK7(sK10(powerset(powerset(X1))),X2))))),X1)
| sP0(sK10(powerset(powerset(X1))),X2)
| sP0(X0,sK6(unordered_pair(singleton(sK7(sK10(powerset(powerset(X1))),X2)),unordered_pair(sK8(sK10(powerset(powerset(X1))),X2),sK7(sK10(powerset(powerset(X1))),X2)))))
| empty(unordered_pair(singleton(sK7(sK10(powerset(powerset(X1))),X2)),unordered_pair(sK8(sK10(powerset(powerset(X1))),X2),sK7(sK10(powerset(powerset(X1))),X2)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1029])]) ).
fof(f1929,plain,
( spl17_240
<=> ! [X0,X1] :
( empty(X0)
| sP0(X1,sK6(X0))
| in(sK8(X1,sK6(X0)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_240])]) ).
fof(f3166,plain,
( ! [X2,X0,X1] :
( element(sK8(X0,sK6(unordered_pair(singleton(sK7(sK10(powerset(powerset(X1))),X2)),unordered_pair(sK8(sK10(powerset(powerset(X1))),X2),sK7(sK10(powerset(powerset(X1))),X2))))),X1)
| sP0(sK10(powerset(powerset(X1))),X2)
| sP0(X0,sK6(unordered_pair(singleton(sK7(sK10(powerset(powerset(X1))),X2)),unordered_pair(sK8(sK10(powerset(powerset(X1))),X2),sK7(sK10(powerset(powerset(X1))),X2)))))
| empty(unordered_pair(singleton(sK7(sK10(powerset(powerset(X1))),X2)),unordered_pair(sK8(sK10(powerset(powerset(X1))),X2),sK7(sK10(powerset(powerset(X1))),X2)))) )
| ~ spl17_240
| ~ spl17_332 ),
inference(resolution,[],[f3131,f1930]) ).
fof(f1930,plain,
( ! [X0,X1] :
( in(sK8(X1,sK6(X0)),X0)
| sP0(X1,sK6(X0))
| empty(X0) )
| ~ spl17_240 ),
inference(avatar_component_clause,[],[f1929]) ).
fof(f13735,plain,
( spl17_1028
| ~ spl17_239
| ~ spl17_332 ),
inference(avatar_split_clause,[],[f3163,f3130,f1925,f13733]) ).
fof(f13733,plain,
( spl17_1028
<=> ! [X2,X0,X1] :
( element(sK7(X0,sK6(unordered_pair(singleton(sK7(sK10(powerset(powerset(X1))),X2)),unordered_pair(sK8(sK10(powerset(powerset(X1))),X2),sK7(sK10(powerset(powerset(X1))),X2))))),X1)
| sP0(sK10(powerset(powerset(X1))),X2)
| sP0(X0,sK6(unordered_pair(singleton(sK7(sK10(powerset(powerset(X1))),X2)),unordered_pair(sK8(sK10(powerset(powerset(X1))),X2),sK7(sK10(powerset(powerset(X1))),X2)))))
| empty(unordered_pair(singleton(sK7(sK10(powerset(powerset(X1))),X2)),unordered_pair(sK8(sK10(powerset(powerset(X1))),X2),sK7(sK10(powerset(powerset(X1))),X2)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1028])]) ).
fof(f1925,plain,
( spl17_239
<=> ! [X0,X1] :
( empty(X0)
| sP0(X1,sK6(X0))
| in(sK7(X1,sK6(X0)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_239])]) ).
fof(f3163,plain,
( ! [X2,X0,X1] :
( element(sK7(X0,sK6(unordered_pair(singleton(sK7(sK10(powerset(powerset(X1))),X2)),unordered_pair(sK8(sK10(powerset(powerset(X1))),X2),sK7(sK10(powerset(powerset(X1))),X2))))),X1)
| sP0(sK10(powerset(powerset(X1))),X2)
| sP0(X0,sK6(unordered_pair(singleton(sK7(sK10(powerset(powerset(X1))),X2)),unordered_pair(sK8(sK10(powerset(powerset(X1))),X2),sK7(sK10(powerset(powerset(X1))),X2)))))
| empty(unordered_pair(singleton(sK7(sK10(powerset(powerset(X1))),X2)),unordered_pair(sK8(sK10(powerset(powerset(X1))),X2),sK7(sK10(powerset(powerset(X1))),X2)))) )
| ~ spl17_239
| ~ spl17_332 ),
inference(resolution,[],[f3131,f1926]) ).
fof(f1926,plain,
( ! [X0,X1] :
( in(sK7(X1,sK6(X0)),X0)
| sP0(X1,sK6(X0))
| empty(X0) )
| ~ spl17_239 ),
inference(avatar_component_clause,[],[f1925]) ).
fof(f13731,plain,
( spl17_1027
| ~ spl17_229
| ~ spl17_332 ),
inference(avatar_split_clause,[],[f3161,f3130,f1885,f13729]) ).
fof(f13729,plain,
( spl17_1027
<=> ! [X0,X1] :
( element(sK10(sK10(powerset(unordered_pair(singleton(sK7(sK10(powerset(powerset(X0))),X1)),unordered_pair(sK8(sK10(powerset(powerset(X0))),X1),sK7(sK10(powerset(powerset(X0))),X1)))))),X0)
| sP0(sK10(powerset(powerset(X0))),X1)
| empty(unordered_pair(singleton(sK7(sK10(powerset(powerset(X0))),X1)),unordered_pair(sK8(sK10(powerset(powerset(X0))),X1),sK7(sK10(powerset(powerset(X0))),X1))))
| empty(sK10(powerset(unordered_pair(singleton(sK7(sK10(powerset(powerset(X0))),X1)),unordered_pair(sK8(sK10(powerset(powerset(X0))),X1),sK7(sK10(powerset(powerset(X0))),X1)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1027])]) ).
fof(f1885,plain,
( spl17_229
<=> ! [X0] :
( empty(sK10(powerset(X0)))
| empty(X0)
| in(sK10(sK10(powerset(X0))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_229])]) ).
fof(f3161,plain,
( ! [X0,X1] :
( element(sK10(sK10(powerset(unordered_pair(singleton(sK7(sK10(powerset(powerset(X0))),X1)),unordered_pair(sK8(sK10(powerset(powerset(X0))),X1),sK7(sK10(powerset(powerset(X0))),X1)))))),X0)
| sP0(sK10(powerset(powerset(X0))),X1)
| empty(unordered_pair(singleton(sK7(sK10(powerset(powerset(X0))),X1)),unordered_pair(sK8(sK10(powerset(powerset(X0))),X1),sK7(sK10(powerset(powerset(X0))),X1))))
| empty(sK10(powerset(unordered_pair(singleton(sK7(sK10(powerset(powerset(X0))),X1)),unordered_pair(sK8(sK10(powerset(powerset(X0))),X1),sK7(sK10(powerset(powerset(X0))),X1)))))) )
| ~ spl17_229
| ~ spl17_332 ),
inference(resolution,[],[f3131,f1886]) ).
fof(f1886,plain,
( ! [X0] :
( in(sK10(sK10(powerset(X0))),X0)
| empty(X0)
| empty(sK10(powerset(X0))) )
| ~ spl17_229 ),
inference(avatar_component_clause,[],[f1885]) ).
fof(f13727,plain,
( spl17_1026
| ~ spl17_241
| ~ spl17_331 ),
inference(avatar_split_clause,[],[f3149,f3126,f1933,f13725]) ).
fof(f13725,plain,
( spl17_1026
<=> ! [X2,X0,X1] :
( element(sK9(X0,sK6(unordered_pair(singleton(sK8(sK10(powerset(powerset(X1))),X2)),unordered_pair(sK9(sK10(powerset(powerset(X1))),X2),sK8(sK10(powerset(powerset(X1))),X2))))),X1)
| sP0(sK10(powerset(powerset(X1))),X2)
| sP0(X0,sK6(unordered_pair(singleton(sK8(sK10(powerset(powerset(X1))),X2)),unordered_pair(sK9(sK10(powerset(powerset(X1))),X2),sK8(sK10(powerset(powerset(X1))),X2)))))
| empty(unordered_pair(singleton(sK8(sK10(powerset(powerset(X1))),X2)),unordered_pair(sK9(sK10(powerset(powerset(X1))),X2),sK8(sK10(powerset(powerset(X1))),X2)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1026])]) ).
fof(f3149,plain,
( ! [X2,X0,X1] :
( element(sK9(X0,sK6(unordered_pair(singleton(sK8(sK10(powerset(powerset(X1))),X2)),unordered_pair(sK9(sK10(powerset(powerset(X1))),X2),sK8(sK10(powerset(powerset(X1))),X2))))),X1)
| sP0(sK10(powerset(powerset(X1))),X2)
| sP0(X0,sK6(unordered_pair(singleton(sK8(sK10(powerset(powerset(X1))),X2)),unordered_pair(sK9(sK10(powerset(powerset(X1))),X2),sK8(sK10(powerset(powerset(X1))),X2)))))
| empty(unordered_pair(singleton(sK8(sK10(powerset(powerset(X1))),X2)),unordered_pair(sK9(sK10(powerset(powerset(X1))),X2),sK8(sK10(powerset(powerset(X1))),X2)))) )
| ~ spl17_241
| ~ spl17_331 ),
inference(resolution,[],[f3127,f1934]) ).
fof(f13723,plain,
( spl17_1025
| ~ spl17_240
| ~ spl17_331 ),
inference(avatar_split_clause,[],[f3146,f3126,f1929,f13721]) ).
fof(f13721,plain,
( spl17_1025
<=> ! [X2,X0,X1] :
( element(sK8(X0,sK6(unordered_pair(singleton(sK8(sK10(powerset(powerset(X1))),X2)),unordered_pair(sK9(sK10(powerset(powerset(X1))),X2),sK8(sK10(powerset(powerset(X1))),X2))))),X1)
| sP0(sK10(powerset(powerset(X1))),X2)
| sP0(X0,sK6(unordered_pair(singleton(sK8(sK10(powerset(powerset(X1))),X2)),unordered_pair(sK9(sK10(powerset(powerset(X1))),X2),sK8(sK10(powerset(powerset(X1))),X2)))))
| empty(unordered_pair(singleton(sK8(sK10(powerset(powerset(X1))),X2)),unordered_pair(sK9(sK10(powerset(powerset(X1))),X2),sK8(sK10(powerset(powerset(X1))),X2)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1025])]) ).
fof(f3146,plain,
( ! [X2,X0,X1] :
( element(sK8(X0,sK6(unordered_pair(singleton(sK8(sK10(powerset(powerset(X1))),X2)),unordered_pair(sK9(sK10(powerset(powerset(X1))),X2),sK8(sK10(powerset(powerset(X1))),X2))))),X1)
| sP0(sK10(powerset(powerset(X1))),X2)
| sP0(X0,sK6(unordered_pair(singleton(sK8(sK10(powerset(powerset(X1))),X2)),unordered_pair(sK9(sK10(powerset(powerset(X1))),X2),sK8(sK10(powerset(powerset(X1))),X2)))))
| empty(unordered_pair(singleton(sK8(sK10(powerset(powerset(X1))),X2)),unordered_pair(sK9(sK10(powerset(powerset(X1))),X2),sK8(sK10(powerset(powerset(X1))),X2)))) )
| ~ spl17_240
| ~ spl17_331 ),
inference(resolution,[],[f3127,f1930]) ).
fof(f13719,plain,
( spl17_1024
| ~ spl17_239
| ~ spl17_331 ),
inference(avatar_split_clause,[],[f3143,f3126,f1925,f13717]) ).
fof(f13717,plain,
( spl17_1024
<=> ! [X2,X0,X1] :
( element(sK7(X0,sK6(unordered_pair(singleton(sK8(sK10(powerset(powerset(X1))),X2)),unordered_pair(sK9(sK10(powerset(powerset(X1))),X2),sK8(sK10(powerset(powerset(X1))),X2))))),X1)
| sP0(sK10(powerset(powerset(X1))),X2)
| sP0(X0,sK6(unordered_pair(singleton(sK8(sK10(powerset(powerset(X1))),X2)),unordered_pair(sK9(sK10(powerset(powerset(X1))),X2),sK8(sK10(powerset(powerset(X1))),X2)))))
| empty(unordered_pair(singleton(sK8(sK10(powerset(powerset(X1))),X2)),unordered_pair(sK9(sK10(powerset(powerset(X1))),X2),sK8(sK10(powerset(powerset(X1))),X2)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1024])]) ).
fof(f3143,plain,
( ! [X2,X0,X1] :
( element(sK7(X0,sK6(unordered_pair(singleton(sK8(sK10(powerset(powerset(X1))),X2)),unordered_pair(sK9(sK10(powerset(powerset(X1))),X2),sK8(sK10(powerset(powerset(X1))),X2))))),X1)
| sP0(sK10(powerset(powerset(X1))),X2)
| sP0(X0,sK6(unordered_pair(singleton(sK8(sK10(powerset(powerset(X1))),X2)),unordered_pair(sK9(sK10(powerset(powerset(X1))),X2),sK8(sK10(powerset(powerset(X1))),X2)))))
| empty(unordered_pair(singleton(sK8(sK10(powerset(powerset(X1))),X2)),unordered_pair(sK9(sK10(powerset(powerset(X1))),X2),sK8(sK10(powerset(powerset(X1))),X2)))) )
| ~ spl17_239
| ~ spl17_331 ),
inference(resolution,[],[f3127,f1926]) ).
fof(f13715,plain,
( spl17_1023
| ~ spl17_229
| ~ spl17_331 ),
inference(avatar_split_clause,[],[f3141,f3126,f1885,f13713]) ).
fof(f13713,plain,
( spl17_1023
<=> ! [X0,X1] :
( element(sK10(sK10(powerset(unordered_pair(singleton(sK8(sK10(powerset(powerset(X0))),X1)),unordered_pair(sK9(sK10(powerset(powerset(X0))),X1),sK8(sK10(powerset(powerset(X0))),X1)))))),X0)
| sP0(sK10(powerset(powerset(X0))),X1)
| empty(unordered_pair(singleton(sK8(sK10(powerset(powerset(X0))),X1)),unordered_pair(sK9(sK10(powerset(powerset(X0))),X1),sK8(sK10(powerset(powerset(X0))),X1))))
| empty(sK10(powerset(unordered_pair(singleton(sK8(sK10(powerset(powerset(X0))),X1)),unordered_pair(sK9(sK10(powerset(powerset(X0))),X1),sK8(sK10(powerset(powerset(X0))),X1)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1023])]) ).
fof(f3141,plain,
( ! [X0,X1] :
( element(sK10(sK10(powerset(unordered_pair(singleton(sK8(sK10(powerset(powerset(X0))),X1)),unordered_pair(sK9(sK10(powerset(powerset(X0))),X1),sK8(sK10(powerset(powerset(X0))),X1)))))),X0)
| sP0(sK10(powerset(powerset(X0))),X1)
| empty(unordered_pair(singleton(sK8(sK10(powerset(powerset(X0))),X1)),unordered_pair(sK9(sK10(powerset(powerset(X0))),X1),sK8(sK10(powerset(powerset(X0))),X1))))
| empty(sK10(powerset(unordered_pair(singleton(sK8(sK10(powerset(powerset(X0))),X1)),unordered_pair(sK9(sK10(powerset(powerset(X0))),X1),sK8(sK10(powerset(powerset(X0))),X1)))))) )
| ~ spl17_229
| ~ spl17_331 ),
inference(resolution,[],[f3127,f1886]) ).
fof(f13688,plain,
( spl17_1022
| ~ spl17_60
| ~ spl17_379 ),
inference(avatar_split_clause,[],[f3643,f3615,f504,f13686]) ).
fof(f13686,plain,
( spl17_1022
<=> ! [X4,X0,X3,X2,X1] :
( ~ relation_of2_as_subset(unordered_pair(singleton(sK8(powerset(cartesian_product2(X0,X1)),X2)),unordered_pair(sK8(powerset(cartesian_product2(X0,X1)),X2),X3)),X0,X1)
| empty(powerset(cartesian_product2(X0,X1)))
| in(unordered_pair(singleton(sK7(powerset(cartesian_product2(X0,X1)),X2)),unordered_pair(sK7(powerset(cartesian_product2(X0,X1)),X2),X3)),powerset(cartesian_product2(X0,X1)))
| ~ in(X3,X4)
| ~ in(sK8(powerset(cartesian_product2(X0,X1)),X2),X4)
| ~ in(sK7(powerset(cartesian_product2(X0,X1)),X2),X4)
| ~ sP0(powerset(cartesian_product2(X0,X1)),X4)
| sP0(powerset(cartesian_product2(X0,X1)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1022])]) ).
fof(f3643,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ relation_of2_as_subset(unordered_pair(singleton(sK8(powerset(cartesian_product2(X0,X1)),X2)),unordered_pair(sK8(powerset(cartesian_product2(X0,X1)),X2),X3)),X0,X1)
| empty(powerset(cartesian_product2(X0,X1)))
| in(unordered_pair(singleton(sK7(powerset(cartesian_product2(X0,X1)),X2)),unordered_pair(sK7(powerset(cartesian_product2(X0,X1)),X2),X3)),powerset(cartesian_product2(X0,X1)))
| ~ in(X3,X4)
| ~ in(sK8(powerset(cartesian_product2(X0,X1)),X2),X4)
| ~ in(sK7(powerset(cartesian_product2(X0,X1)),X2),X4)
| ~ sP0(powerset(cartesian_product2(X0,X1)),X4)
| sP0(powerset(cartesian_product2(X0,X1)),X2) )
| ~ spl17_60
| ~ spl17_379 ),
inference(resolution,[],[f3616,f505]) ).
fof(f13684,plain,
( spl17_1021
| ~ spl17_59
| ~ spl17_379 ),
inference(avatar_split_clause,[],[f3640,f3615,f500,f13682]) ).
fof(f13682,plain,
( spl17_1021
<=> ! [X4,X0,X3,X2,X1] :
( ~ relation_of2_as_subset(unordered_pair(singleton(sK9(powerset(cartesian_product2(X0,X1)),X2)),unordered_pair(sK9(powerset(cartesian_product2(X0,X1)),X2),X3)),X0,X1)
| empty(powerset(cartesian_product2(X0,X1)))
| in(unordered_pair(singleton(sK8(powerset(cartesian_product2(X0,X1)),X2)),unordered_pair(sK8(powerset(cartesian_product2(X0,X1)),X2),X3)),powerset(cartesian_product2(X0,X1)))
| ~ in(X3,X4)
| ~ in(sK9(powerset(cartesian_product2(X0,X1)),X2),X4)
| ~ in(sK8(powerset(cartesian_product2(X0,X1)),X2),X4)
| ~ sP0(powerset(cartesian_product2(X0,X1)),X4)
| sP0(powerset(cartesian_product2(X0,X1)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1021])]) ).
fof(f3640,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ relation_of2_as_subset(unordered_pair(singleton(sK9(powerset(cartesian_product2(X0,X1)),X2)),unordered_pair(sK9(powerset(cartesian_product2(X0,X1)),X2),X3)),X0,X1)
| empty(powerset(cartesian_product2(X0,X1)))
| in(unordered_pair(singleton(sK8(powerset(cartesian_product2(X0,X1)),X2)),unordered_pair(sK8(powerset(cartesian_product2(X0,X1)),X2),X3)),powerset(cartesian_product2(X0,X1)))
| ~ in(X3,X4)
| ~ in(sK9(powerset(cartesian_product2(X0,X1)),X2),X4)
| ~ in(sK8(powerset(cartesian_product2(X0,X1)),X2),X4)
| ~ sP0(powerset(cartesian_product2(X0,X1)),X4)
| sP0(powerset(cartesian_product2(X0,X1)),X2) )
| ~ spl17_59
| ~ spl17_379 ),
inference(resolution,[],[f3616,f501]) ).
fof(f13680,plain,
( spl17_1020
| ~ spl17_60
| ~ spl17_378 ),
inference(avatar_split_clause,[],[f3627,f3585,f504,f13678]) ).
fof(f13678,plain,
( spl17_1020
<=> ! [X4,X0,X3,X2,X1] :
( in(unordered_pair(singleton(sK7(powerset(cartesian_product2(X0,X1)),X2)),unordered_pair(sK7(powerset(cartesian_product2(X0,X1)),X2),X3)),powerset(cartesian_product2(X0,X1)))
| ~ in(X3,X4)
| ~ in(sK8(powerset(cartesian_product2(X0,X1)),X2),X4)
| ~ in(sK7(powerset(cartesian_product2(X0,X1)),X2),X4)
| ~ sP0(powerset(cartesian_product2(X0,X1)),X4)
| empty(powerset(cartesian_product2(X0,X1)))
| ~ relation_of2_as_subset(unordered_pair(singleton(sK8(powerset(cartesian_product2(X0,X1)),X2)),unordered_pair(X3,sK8(powerset(cartesian_product2(X0,X1)),X2))),X0,X1)
| sP0(powerset(cartesian_product2(X0,X1)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1020])]) ).
fof(f3627,plain,
( ! [X2,X3,X0,X1,X4] :
( in(unordered_pair(singleton(sK7(powerset(cartesian_product2(X0,X1)),X2)),unordered_pair(sK7(powerset(cartesian_product2(X0,X1)),X2),X3)),powerset(cartesian_product2(X0,X1)))
| ~ in(X3,X4)
| ~ in(sK8(powerset(cartesian_product2(X0,X1)),X2),X4)
| ~ in(sK7(powerset(cartesian_product2(X0,X1)),X2),X4)
| ~ sP0(powerset(cartesian_product2(X0,X1)),X4)
| empty(powerset(cartesian_product2(X0,X1)))
| ~ relation_of2_as_subset(unordered_pair(singleton(sK8(powerset(cartesian_product2(X0,X1)),X2)),unordered_pair(X3,sK8(powerset(cartesian_product2(X0,X1)),X2))),X0,X1)
| sP0(powerset(cartesian_product2(X0,X1)),X2) )
| ~ spl17_60
| ~ spl17_378 ),
inference(resolution,[],[f3586,f505]) ).
fof(f13676,plain,
( spl17_1019
| ~ spl17_59
| ~ spl17_378 ),
inference(avatar_split_clause,[],[f3624,f3585,f500,f13674]) ).
fof(f13674,plain,
( spl17_1019
<=> ! [X4,X0,X3,X2,X1] :
( in(unordered_pair(singleton(sK8(powerset(cartesian_product2(X0,X1)),X2)),unordered_pair(sK8(powerset(cartesian_product2(X0,X1)),X2),X3)),powerset(cartesian_product2(X0,X1)))
| ~ in(X3,X4)
| ~ in(sK9(powerset(cartesian_product2(X0,X1)),X2),X4)
| ~ in(sK8(powerset(cartesian_product2(X0,X1)),X2),X4)
| ~ sP0(powerset(cartesian_product2(X0,X1)),X4)
| empty(powerset(cartesian_product2(X0,X1)))
| ~ relation_of2_as_subset(unordered_pair(singleton(sK9(powerset(cartesian_product2(X0,X1)),X2)),unordered_pair(X3,sK9(powerset(cartesian_product2(X0,X1)),X2))),X0,X1)
| sP0(powerset(cartesian_product2(X0,X1)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1019])]) ).
fof(f3624,plain,
( ! [X2,X3,X0,X1,X4] :
( in(unordered_pair(singleton(sK8(powerset(cartesian_product2(X0,X1)),X2)),unordered_pair(sK8(powerset(cartesian_product2(X0,X1)),X2),X3)),powerset(cartesian_product2(X0,X1)))
| ~ in(X3,X4)
| ~ in(sK9(powerset(cartesian_product2(X0,X1)),X2),X4)
| ~ in(sK8(powerset(cartesian_product2(X0,X1)),X2),X4)
| ~ sP0(powerset(cartesian_product2(X0,X1)),X4)
| empty(powerset(cartesian_product2(X0,X1)))
| ~ relation_of2_as_subset(unordered_pair(singleton(sK9(powerset(cartesian_product2(X0,X1)),X2)),unordered_pair(X3,sK9(powerset(cartesian_product2(X0,X1)),X2))),X0,X1)
| sP0(powerset(cartesian_product2(X0,X1)),X2) )
| ~ spl17_59
| ~ spl17_378 ),
inference(resolution,[],[f3586,f501]) ).
fof(f13672,plain,
( spl17_1018
| ~ spl17_30
| ~ spl17_393 ),
inference(avatar_split_clause,[],[f12118,f3736,f313,f13670]) ).
fof(f13670,plain,
( spl17_1018
<=> ! [X0] :
( in(unordered_pair(singleton(sK4),unordered_pair(X0,sK4)),the_InternalRel(sK2))
| ~ in(X0,the_carrier(sK2))
| ~ element(X0,the_carrier(sK2))
| ~ related(sK2,sK5,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1018])]) ).
fof(f12118,plain,
( ! [X0] :
( in(unordered_pair(singleton(sK4),unordered_pair(X0,sK4)),the_InternalRel(sK2))
| ~ in(X0,the_carrier(sK2))
| ~ element(X0,the_carrier(sK2))
| ~ related(sK2,sK5,X0) )
| ~ spl17_30
| ~ spl17_393 ),
inference(superposition,[],[f3737,f314]) ).
fof(f13668,plain,
( spl17_1017
| ~ spl17_224
| ~ spl17_332 ),
inference(avatar_split_clause,[],[f3160,f3130,f1808,f13666]) ).
fof(f13666,plain,
( spl17_1017
<=> ! [X0,X1] :
( element(sK10(sK6(unordered_pair(singleton(sK7(sK10(powerset(powerset(X0))),X1)),unordered_pair(sK8(sK10(powerset(powerset(X0))),X1),sK7(sK10(powerset(powerset(X0))),X1))))),X0)
| sP0(sK10(powerset(powerset(X0))),X1)
| empty(sK6(unordered_pair(singleton(sK7(sK10(powerset(powerset(X0))),X1)),unordered_pair(sK8(sK10(powerset(powerset(X0))),X1),sK7(sK10(powerset(powerset(X0))),X1)))))
| empty(unordered_pair(singleton(sK7(sK10(powerset(powerset(X0))),X1)),unordered_pair(sK8(sK10(powerset(powerset(X0))),X1),sK7(sK10(powerset(powerset(X0))),X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1017])]) ).
fof(f1808,plain,
( spl17_224
<=> ! [X0] :
( empty(X0)
| empty(sK6(X0))
| in(sK10(sK6(X0)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_224])]) ).
fof(f3160,plain,
( ! [X0,X1] :
( element(sK10(sK6(unordered_pair(singleton(sK7(sK10(powerset(powerset(X0))),X1)),unordered_pair(sK8(sK10(powerset(powerset(X0))),X1),sK7(sK10(powerset(powerset(X0))),X1))))),X0)
| sP0(sK10(powerset(powerset(X0))),X1)
| empty(sK6(unordered_pair(singleton(sK7(sK10(powerset(powerset(X0))),X1)),unordered_pair(sK8(sK10(powerset(powerset(X0))),X1),sK7(sK10(powerset(powerset(X0))),X1)))))
| empty(unordered_pair(singleton(sK7(sK10(powerset(powerset(X0))),X1)),unordered_pair(sK8(sK10(powerset(powerset(X0))),X1),sK7(sK10(powerset(powerset(X0))),X1)))) )
| ~ spl17_224
| ~ spl17_332 ),
inference(resolution,[],[f3131,f1809]) ).
fof(f1809,plain,
( ! [X0] :
( in(sK10(sK6(X0)),X0)
| empty(sK6(X0))
| empty(X0) )
| ~ spl17_224 ),
inference(avatar_component_clause,[],[f1808]) ).
fof(f13664,plain,
( spl17_1016
| ~ spl17_224
| ~ spl17_331 ),
inference(avatar_split_clause,[],[f3140,f3126,f1808,f13662]) ).
fof(f13662,plain,
( spl17_1016
<=> ! [X0,X1] :
( element(sK10(sK6(unordered_pair(singleton(sK8(sK10(powerset(powerset(X0))),X1)),unordered_pair(sK9(sK10(powerset(powerset(X0))),X1),sK8(sK10(powerset(powerset(X0))),X1))))),X0)
| sP0(sK10(powerset(powerset(X0))),X1)
| empty(sK6(unordered_pair(singleton(sK8(sK10(powerset(powerset(X0))),X1)),unordered_pair(sK9(sK10(powerset(powerset(X0))),X1),sK8(sK10(powerset(powerset(X0))),X1)))))
| empty(unordered_pair(singleton(sK8(sK10(powerset(powerset(X0))),X1)),unordered_pair(sK9(sK10(powerset(powerset(X0))),X1),sK8(sK10(powerset(powerset(X0))),X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1016])]) ).
fof(f3140,plain,
( ! [X0,X1] :
( element(sK10(sK6(unordered_pair(singleton(sK8(sK10(powerset(powerset(X0))),X1)),unordered_pair(sK9(sK10(powerset(powerset(X0))),X1),sK8(sK10(powerset(powerset(X0))),X1))))),X0)
| sP0(sK10(powerset(powerset(X0))),X1)
| empty(sK6(unordered_pair(singleton(sK8(sK10(powerset(powerset(X0))),X1)),unordered_pair(sK9(sK10(powerset(powerset(X0))),X1),sK8(sK10(powerset(powerset(X0))),X1)))))
| empty(unordered_pair(singleton(sK8(sK10(powerset(powerset(X0))),X1)),unordered_pair(sK9(sK10(powerset(powerset(X0))),X1),sK8(sK10(powerset(powerset(X0))),X1)))) )
| ~ spl17_224
| ~ spl17_331 ),
inference(resolution,[],[f3127,f1809]) ).
fof(f13660,plain,
( spl17_1015
| ~ spl17_209
| ~ spl17_321 ),
inference(avatar_split_clause,[],[f2977,f2873,f1710,f13658]) ).
fof(f13658,plain,
( spl17_1015
<=> ! [X4,X0,X3,X2,X1] :
( empty(powerset(cartesian_product2(X0,X1)))
| sP0(sK10(powerset(powerset(cartesian_product2(X0,X1)))),X2)
| in(unordered_pair(singleton(X3),unordered_pair(X3,sK8(sK10(powerset(powerset(cartesian_product2(X0,X1)))),X2))),powerset(cartesian_product2(X0,X1)))
| ~ in(sK8(sK10(powerset(powerset(cartesian_product2(X0,X1)))),X2),X4)
| ~ in(sK7(sK10(powerset(powerset(cartesian_product2(X0,X1)))),X2),X4)
| ~ in(X3,X4)
| ~ sP0(powerset(cartesian_product2(X0,X1)),X4)
| ~ relation_of2_as_subset(unordered_pair(singleton(X3),unordered_pair(X3,sK7(sK10(powerset(powerset(cartesian_product2(X0,X1)))),X2))),X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1015])]) ).
fof(f1710,plain,
( spl17_209
<=> ! [X5,X4,X0,X3,X2,X1] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X1,X0)),powerset(cartesian_product2(X2,X3)))
| in(unordered_pair(singleton(X4),unordered_pair(X4,X1)),powerset(cartesian_product2(X2,X3)))
| ~ in(X1,X5)
| ~ in(X0,X5)
| ~ in(X4,X5)
| ~ sP0(powerset(cartesian_product2(X2,X3)),X5)
| empty(powerset(cartesian_product2(X2,X3)))
| ~ relation_of2_as_subset(unordered_pair(singleton(X4),unordered_pair(X4,X0)),X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_209])]) ).
fof(f2977,plain,
( ! [X2,X3,X0,X1,X4] :
( empty(powerset(cartesian_product2(X0,X1)))
| sP0(sK10(powerset(powerset(cartesian_product2(X0,X1)))),X2)
| in(unordered_pair(singleton(X3),unordered_pair(X3,sK8(sK10(powerset(powerset(cartesian_product2(X0,X1)))),X2))),powerset(cartesian_product2(X0,X1)))
| ~ in(sK8(sK10(powerset(powerset(cartesian_product2(X0,X1)))),X2),X4)
| ~ in(sK7(sK10(powerset(powerset(cartesian_product2(X0,X1)))),X2),X4)
| ~ in(X3,X4)
| ~ sP0(powerset(cartesian_product2(X0,X1)),X4)
| ~ relation_of2_as_subset(unordered_pair(singleton(X3),unordered_pair(X3,sK7(sK10(powerset(powerset(cartesian_product2(X0,X1)))),X2))),X0,X1) )
| ~ spl17_209
| ~ spl17_321 ),
inference(duplicate_literal_removal,[],[f2938]) ).
fof(f2938,plain,
( ! [X2,X3,X0,X1,X4] :
( empty(powerset(cartesian_product2(X0,X1)))
| sP0(sK10(powerset(powerset(cartesian_product2(X0,X1)))),X2)
| in(unordered_pair(singleton(X3),unordered_pair(X3,sK8(sK10(powerset(powerset(cartesian_product2(X0,X1)))),X2))),powerset(cartesian_product2(X0,X1)))
| ~ in(sK8(sK10(powerset(powerset(cartesian_product2(X0,X1)))),X2),X4)
| ~ in(sK7(sK10(powerset(powerset(cartesian_product2(X0,X1)))),X2),X4)
| ~ in(X3,X4)
| ~ sP0(powerset(cartesian_product2(X0,X1)),X4)
| empty(powerset(cartesian_product2(X0,X1)))
| ~ relation_of2_as_subset(unordered_pair(singleton(X3),unordered_pair(X3,sK7(sK10(powerset(powerset(cartesian_product2(X0,X1)))),X2))),X0,X1) )
| ~ spl17_209
| ~ spl17_321 ),
inference(resolution,[],[f2874,f1711]) ).
fof(f1711,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X1,X0)),powerset(cartesian_product2(X2,X3)))
| in(unordered_pair(singleton(X4),unordered_pair(X4,X1)),powerset(cartesian_product2(X2,X3)))
| ~ in(X1,X5)
| ~ in(X0,X5)
| ~ in(X4,X5)
| ~ sP0(powerset(cartesian_product2(X2,X3)),X5)
| empty(powerset(cartesian_product2(X2,X3)))
| ~ relation_of2_as_subset(unordered_pair(singleton(X4),unordered_pair(X4,X0)),X2,X3) )
| ~ spl17_209 ),
inference(avatar_component_clause,[],[f1710]) ).
fof(f13656,plain,
( spl17_1014
| ~ spl17_209
| ~ spl17_320 ),
inference(avatar_split_clause,[],[f2926,f2869,f1710,f13654]) ).
fof(f13654,plain,
( spl17_1014
<=> ! [X4,X0,X3,X2,X1] :
( empty(powerset(cartesian_product2(X0,X1)))
| sP0(sK10(powerset(powerset(cartesian_product2(X0,X1)))),X2)
| in(unordered_pair(singleton(X3),unordered_pair(X3,sK9(sK10(powerset(powerset(cartesian_product2(X0,X1)))),X2))),powerset(cartesian_product2(X0,X1)))
| ~ in(sK9(sK10(powerset(powerset(cartesian_product2(X0,X1)))),X2),X4)
| ~ in(sK8(sK10(powerset(powerset(cartesian_product2(X0,X1)))),X2),X4)
| ~ in(X3,X4)
| ~ sP0(powerset(cartesian_product2(X0,X1)),X4)
| ~ relation_of2_as_subset(unordered_pair(singleton(X3),unordered_pair(X3,sK8(sK10(powerset(powerset(cartesian_product2(X0,X1)))),X2))),X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1014])]) ).
fof(f2926,plain,
( ! [X2,X3,X0,X1,X4] :
( empty(powerset(cartesian_product2(X0,X1)))
| sP0(sK10(powerset(powerset(cartesian_product2(X0,X1)))),X2)
| in(unordered_pair(singleton(X3),unordered_pair(X3,sK9(sK10(powerset(powerset(cartesian_product2(X0,X1)))),X2))),powerset(cartesian_product2(X0,X1)))
| ~ in(sK9(sK10(powerset(powerset(cartesian_product2(X0,X1)))),X2),X4)
| ~ in(sK8(sK10(powerset(powerset(cartesian_product2(X0,X1)))),X2),X4)
| ~ in(X3,X4)
| ~ sP0(powerset(cartesian_product2(X0,X1)),X4)
| ~ relation_of2_as_subset(unordered_pair(singleton(X3),unordered_pair(X3,sK8(sK10(powerset(powerset(cartesian_product2(X0,X1)))),X2))),X0,X1) )
| ~ spl17_209
| ~ spl17_320 ),
inference(duplicate_literal_removal,[],[f2887]) ).
fof(f2887,plain,
( ! [X2,X3,X0,X1,X4] :
( empty(powerset(cartesian_product2(X0,X1)))
| sP0(sK10(powerset(powerset(cartesian_product2(X0,X1)))),X2)
| in(unordered_pair(singleton(X3),unordered_pair(X3,sK9(sK10(powerset(powerset(cartesian_product2(X0,X1)))),X2))),powerset(cartesian_product2(X0,X1)))
| ~ in(sK9(sK10(powerset(powerset(cartesian_product2(X0,X1)))),X2),X4)
| ~ in(sK8(sK10(powerset(powerset(cartesian_product2(X0,X1)))),X2),X4)
| ~ in(X3,X4)
| ~ sP0(powerset(cartesian_product2(X0,X1)),X4)
| empty(powerset(cartesian_product2(X0,X1)))
| ~ relation_of2_as_subset(unordered_pair(singleton(X3),unordered_pair(X3,sK8(sK10(powerset(powerset(cartesian_product2(X0,X1)))),X2))),X0,X1) )
| ~ spl17_209
| ~ spl17_320 ),
inference(resolution,[],[f2870,f1711]) ).
fof(f13649,plain,
( spl17_1013
| ~ spl17_207
| ~ spl17_321 ),
inference(avatar_split_clause,[],[f2939,f2873,f1686,f13647]) ).
fof(f13647,plain,
( spl17_1013
<=> ! [X0,X3,X2,X1] :
( empty(the_InternalRel(X0))
| sP0(sK10(powerset(the_InternalRel(X0))),X1)
| in(unordered_pair(singleton(sK7(sK10(powerset(the_InternalRel(X0))),X1)),unordered_pair(sK7(sK10(powerset(the_InternalRel(X0))),X1),X2)),the_InternalRel(X0))
| ~ in(X2,X3)
| ~ in(sK8(sK10(powerset(the_InternalRel(X0))),X1),X3)
| ~ in(sK7(sK10(powerset(the_InternalRel(X0))),X1),X3)
| ~ sP0(the_InternalRel(X0),X3)
| ~ related(X0,sK8(sK10(powerset(the_InternalRel(X0))),X1),X2)
| ~ element(X2,the_carrier(X0))
| ~ element(sK8(sK10(powerset(the_InternalRel(X0))),X1),the_carrier(X0))
| ~ rel_str(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1013])]) ).
fof(f1686,plain,
( spl17_207
<=> ! [X4,X0,X3,X2,X1] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X1,X0)),the_InternalRel(X2))
| in(unordered_pair(singleton(X0),unordered_pair(X0,X3)),the_InternalRel(X2))
| ~ in(X3,X4)
| ~ in(X1,X4)
| ~ in(X0,X4)
| ~ sP0(the_InternalRel(X2),X4)
| ~ related(X2,X1,X3)
| ~ element(X3,the_carrier(X2))
| ~ element(X1,the_carrier(X2))
| ~ rel_str(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_207])]) ).
fof(f2939,plain,
( ! [X2,X3,X0,X1] :
( empty(the_InternalRel(X0))
| sP0(sK10(powerset(the_InternalRel(X0))),X1)
| in(unordered_pair(singleton(sK7(sK10(powerset(the_InternalRel(X0))),X1)),unordered_pair(sK7(sK10(powerset(the_InternalRel(X0))),X1),X2)),the_InternalRel(X0))
| ~ in(X2,X3)
| ~ in(sK8(sK10(powerset(the_InternalRel(X0))),X1),X3)
| ~ in(sK7(sK10(powerset(the_InternalRel(X0))),X1),X3)
| ~ sP0(the_InternalRel(X0),X3)
| ~ related(X0,sK8(sK10(powerset(the_InternalRel(X0))),X1),X2)
| ~ element(X2,the_carrier(X0))
| ~ element(sK8(sK10(powerset(the_InternalRel(X0))),X1),the_carrier(X0))
| ~ rel_str(X0) )
| ~ spl17_207
| ~ spl17_321 ),
inference(resolution,[],[f2874,f1687]) ).
fof(f1687,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X1,X0)),the_InternalRel(X2))
| in(unordered_pair(singleton(X0),unordered_pair(X0,X3)),the_InternalRel(X2))
| ~ in(X3,X4)
| ~ in(X1,X4)
| ~ in(X0,X4)
| ~ sP0(the_InternalRel(X2),X4)
| ~ related(X2,X1,X3)
| ~ element(X3,the_carrier(X2))
| ~ element(X1,the_carrier(X2))
| ~ rel_str(X2) )
| ~ spl17_207 ),
inference(avatar_component_clause,[],[f1686]) ).
fof(f13645,plain,
( spl17_1012
| ~ spl17_207
| ~ spl17_320 ),
inference(avatar_split_clause,[],[f2888,f2869,f1686,f13643]) ).
fof(f13643,plain,
( spl17_1012
<=> ! [X0,X3,X2,X1] :
( empty(the_InternalRel(X0))
| sP0(sK10(powerset(the_InternalRel(X0))),X1)
| in(unordered_pair(singleton(sK8(sK10(powerset(the_InternalRel(X0))),X1)),unordered_pair(sK8(sK10(powerset(the_InternalRel(X0))),X1),X2)),the_InternalRel(X0))
| ~ in(X2,X3)
| ~ in(sK9(sK10(powerset(the_InternalRel(X0))),X1),X3)
| ~ in(sK8(sK10(powerset(the_InternalRel(X0))),X1),X3)
| ~ sP0(the_InternalRel(X0),X3)
| ~ related(X0,sK9(sK10(powerset(the_InternalRel(X0))),X1),X2)
| ~ element(X2,the_carrier(X0))
| ~ element(sK9(sK10(powerset(the_InternalRel(X0))),X1),the_carrier(X0))
| ~ rel_str(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1012])]) ).
fof(f2888,plain,
( ! [X2,X3,X0,X1] :
( empty(the_InternalRel(X0))
| sP0(sK10(powerset(the_InternalRel(X0))),X1)
| in(unordered_pair(singleton(sK8(sK10(powerset(the_InternalRel(X0))),X1)),unordered_pair(sK8(sK10(powerset(the_InternalRel(X0))),X1),X2)),the_InternalRel(X0))
| ~ in(X2,X3)
| ~ in(sK9(sK10(powerset(the_InternalRel(X0))),X1),X3)
| ~ in(sK8(sK10(powerset(the_InternalRel(X0))),X1),X3)
| ~ sP0(the_InternalRel(X0),X3)
| ~ related(X0,sK9(sK10(powerset(the_InternalRel(X0))),X1),X2)
| ~ element(X2,the_carrier(X0))
| ~ element(sK9(sK10(powerset(the_InternalRel(X0))),X1),the_carrier(X0))
| ~ rel_str(X0) )
| ~ spl17_207
| ~ spl17_320 ),
inference(resolution,[],[f2870,f1687]) ).
fof(f13633,plain,
( spl17_1011
| ~ spl17_25
| ~ spl17_393 ),
inference(avatar_split_clause,[],[f12117,f3736,f292,f13631]) ).
fof(f292,plain,
( spl17_25
<=> ! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_25])]) ).
fof(f12117,plain,
( ! [X0] :
( ~ in(X0,the_carrier(sK2))
| ~ element(X0,the_carrier(sK2))
| ~ related(sK2,sK5,X0)
| ~ in(the_InternalRel(sK2),unordered_pair(singleton(sK4),unordered_pair(sK4,X0))) )
| ~ spl17_25
| ~ spl17_393 ),
inference(resolution,[],[f3737,f293]) ).
fof(f293,plain,
( ! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) )
| ~ spl17_25 ),
inference(avatar_component_clause,[],[f292]) ).
fof(f13613,plain,
( spl17_1010
| ~ spl17_266
| ~ spl17_328 ),
inference(avatar_split_clause,[],[f3088,f3042,f2147,f13611]) ).
fof(f13611,plain,
( spl17_1010
<=> ! [X2,X0,X1] :
( sP0(sK6(powerset(X0)),X1)
| element(sK9(X2,sK10(powerset(unordered_pair(singleton(sK7(sK6(powerset(X0)),X1)),unordered_pair(sK8(sK6(powerset(X0)),X1),sK7(sK6(powerset(X0)),X1)))))),X0)
| empty(powerset(X0))
| empty(unordered_pair(singleton(sK7(sK6(powerset(X0)),X1)),unordered_pair(sK8(sK6(powerset(X0)),X1),sK7(sK6(powerset(X0)),X1))))
| sP0(X2,sK10(powerset(unordered_pair(singleton(sK7(sK6(powerset(X0)),X1)),unordered_pair(sK8(sK6(powerset(X0)),X1),sK7(sK6(powerset(X0)),X1)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1010])]) ).
fof(f3088,plain,
( ! [X2,X0,X1] :
( sP0(sK6(powerset(X0)),X1)
| element(sK9(X2,sK10(powerset(unordered_pair(singleton(sK7(sK6(powerset(X0)),X1)),unordered_pair(sK8(sK6(powerset(X0)),X1),sK7(sK6(powerset(X0)),X1)))))),X0)
| empty(powerset(X0))
| empty(unordered_pair(singleton(sK7(sK6(powerset(X0)),X1)),unordered_pair(sK8(sK6(powerset(X0)),X1),sK7(sK6(powerset(X0)),X1))))
| sP0(X2,sK10(powerset(unordered_pair(singleton(sK7(sK6(powerset(X0)),X1)),unordered_pair(sK8(sK6(powerset(X0)),X1),sK7(sK6(powerset(X0)),X1)))))) )
| ~ spl17_266
| ~ spl17_328 ),
inference(resolution,[],[f3043,f2148]) ).
fof(f13609,plain,
( spl17_1009
| ~ spl17_265
| ~ spl17_328 ),
inference(avatar_split_clause,[],[f3085,f3042,f2143,f13607]) ).
fof(f13607,plain,
( spl17_1009
<=> ! [X2,X0,X1] :
( sP0(sK6(powerset(X0)),X1)
| element(sK8(X2,sK10(powerset(unordered_pair(singleton(sK7(sK6(powerset(X0)),X1)),unordered_pair(sK8(sK6(powerset(X0)),X1),sK7(sK6(powerset(X0)),X1)))))),X0)
| empty(powerset(X0))
| empty(unordered_pair(singleton(sK7(sK6(powerset(X0)),X1)),unordered_pair(sK8(sK6(powerset(X0)),X1),sK7(sK6(powerset(X0)),X1))))
| sP0(X2,sK10(powerset(unordered_pair(singleton(sK7(sK6(powerset(X0)),X1)),unordered_pair(sK8(sK6(powerset(X0)),X1),sK7(sK6(powerset(X0)),X1)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1009])]) ).
fof(f3085,plain,
( ! [X2,X0,X1] :
( sP0(sK6(powerset(X0)),X1)
| element(sK8(X2,sK10(powerset(unordered_pair(singleton(sK7(sK6(powerset(X0)),X1)),unordered_pair(sK8(sK6(powerset(X0)),X1),sK7(sK6(powerset(X0)),X1)))))),X0)
| empty(powerset(X0))
| empty(unordered_pair(singleton(sK7(sK6(powerset(X0)),X1)),unordered_pair(sK8(sK6(powerset(X0)),X1),sK7(sK6(powerset(X0)),X1))))
| sP0(X2,sK10(powerset(unordered_pair(singleton(sK7(sK6(powerset(X0)),X1)),unordered_pair(sK8(sK6(powerset(X0)),X1),sK7(sK6(powerset(X0)),X1)))))) )
| ~ spl17_265
| ~ spl17_328 ),
inference(resolution,[],[f3043,f2144]) ).
fof(f13605,plain,
( spl17_1008
| ~ spl17_264
| ~ spl17_328 ),
inference(avatar_split_clause,[],[f3082,f3042,f2139,f13603]) ).
fof(f13603,plain,
( spl17_1008
<=> ! [X2,X0,X1] :
( sP0(sK6(powerset(X0)),X1)
| element(sK7(X2,sK10(powerset(unordered_pair(singleton(sK7(sK6(powerset(X0)),X1)),unordered_pair(sK8(sK6(powerset(X0)),X1),sK7(sK6(powerset(X0)),X1)))))),X0)
| empty(powerset(X0))
| empty(unordered_pair(singleton(sK7(sK6(powerset(X0)),X1)),unordered_pair(sK8(sK6(powerset(X0)),X1),sK7(sK6(powerset(X0)),X1))))
| sP0(X2,sK10(powerset(unordered_pair(singleton(sK7(sK6(powerset(X0)),X1)),unordered_pair(sK8(sK6(powerset(X0)),X1),sK7(sK6(powerset(X0)),X1)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1008])]) ).
fof(f3082,plain,
( ! [X2,X0,X1] :
( sP0(sK6(powerset(X0)),X1)
| element(sK7(X2,sK10(powerset(unordered_pair(singleton(sK7(sK6(powerset(X0)),X1)),unordered_pair(sK8(sK6(powerset(X0)),X1),sK7(sK6(powerset(X0)),X1)))))),X0)
| empty(powerset(X0))
| empty(unordered_pair(singleton(sK7(sK6(powerset(X0)),X1)),unordered_pair(sK8(sK6(powerset(X0)),X1),sK7(sK6(powerset(X0)),X1))))
| sP0(X2,sK10(powerset(unordered_pair(singleton(sK7(sK6(powerset(X0)),X1)),unordered_pair(sK8(sK6(powerset(X0)),X1),sK7(sK6(powerset(X0)),X1)))))) )
| ~ spl17_264
| ~ spl17_328 ),
inference(resolution,[],[f3043,f2140]) ).
fof(f13601,plain,
( spl17_1007
| ~ spl17_266
| ~ spl17_326 ),
inference(avatar_split_clause,[],[f3070,f3034,f2147,f13599]) ).
fof(f13599,plain,
( spl17_1007
<=> ! [X2,X0,X1] :
( sP0(sK6(powerset(X0)),X1)
| element(sK9(X2,sK10(powerset(unordered_pair(singleton(sK8(sK6(powerset(X0)),X1)),unordered_pair(sK9(sK6(powerset(X0)),X1),sK8(sK6(powerset(X0)),X1)))))),X0)
| empty(powerset(X0))
| empty(unordered_pair(singleton(sK8(sK6(powerset(X0)),X1)),unordered_pair(sK9(sK6(powerset(X0)),X1),sK8(sK6(powerset(X0)),X1))))
| sP0(X2,sK10(powerset(unordered_pair(singleton(sK8(sK6(powerset(X0)),X1)),unordered_pair(sK9(sK6(powerset(X0)),X1),sK8(sK6(powerset(X0)),X1)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1007])]) ).
fof(f3070,plain,
( ! [X2,X0,X1] :
( sP0(sK6(powerset(X0)),X1)
| element(sK9(X2,sK10(powerset(unordered_pair(singleton(sK8(sK6(powerset(X0)),X1)),unordered_pair(sK9(sK6(powerset(X0)),X1),sK8(sK6(powerset(X0)),X1)))))),X0)
| empty(powerset(X0))
| empty(unordered_pair(singleton(sK8(sK6(powerset(X0)),X1)),unordered_pair(sK9(sK6(powerset(X0)),X1),sK8(sK6(powerset(X0)),X1))))
| sP0(X2,sK10(powerset(unordered_pair(singleton(sK8(sK6(powerset(X0)),X1)),unordered_pair(sK9(sK6(powerset(X0)),X1),sK8(sK6(powerset(X0)),X1)))))) )
| ~ spl17_266
| ~ spl17_326 ),
inference(resolution,[],[f3035,f2148]) ).
fof(f13597,plain,
( spl17_1006
| ~ spl17_265
| ~ spl17_326 ),
inference(avatar_split_clause,[],[f3067,f3034,f2143,f13595]) ).
fof(f13595,plain,
( spl17_1006
<=> ! [X2,X0,X1] :
( sP0(sK6(powerset(X0)),X1)
| element(sK8(X2,sK10(powerset(unordered_pair(singleton(sK8(sK6(powerset(X0)),X1)),unordered_pair(sK9(sK6(powerset(X0)),X1),sK8(sK6(powerset(X0)),X1)))))),X0)
| empty(powerset(X0))
| empty(unordered_pair(singleton(sK8(sK6(powerset(X0)),X1)),unordered_pair(sK9(sK6(powerset(X0)),X1),sK8(sK6(powerset(X0)),X1))))
| sP0(X2,sK10(powerset(unordered_pair(singleton(sK8(sK6(powerset(X0)),X1)),unordered_pair(sK9(sK6(powerset(X0)),X1),sK8(sK6(powerset(X0)),X1)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1006])]) ).
fof(f3067,plain,
( ! [X2,X0,X1] :
( sP0(sK6(powerset(X0)),X1)
| element(sK8(X2,sK10(powerset(unordered_pair(singleton(sK8(sK6(powerset(X0)),X1)),unordered_pair(sK9(sK6(powerset(X0)),X1),sK8(sK6(powerset(X0)),X1)))))),X0)
| empty(powerset(X0))
| empty(unordered_pair(singleton(sK8(sK6(powerset(X0)),X1)),unordered_pair(sK9(sK6(powerset(X0)),X1),sK8(sK6(powerset(X0)),X1))))
| sP0(X2,sK10(powerset(unordered_pair(singleton(sK8(sK6(powerset(X0)),X1)),unordered_pair(sK9(sK6(powerset(X0)),X1),sK8(sK6(powerset(X0)),X1)))))) )
| ~ spl17_265
| ~ spl17_326 ),
inference(resolution,[],[f3035,f2144]) ).
fof(f13593,plain,
( spl17_1005
| ~ spl17_264
| ~ spl17_326 ),
inference(avatar_split_clause,[],[f3064,f3034,f2139,f13591]) ).
fof(f13591,plain,
( spl17_1005
<=> ! [X2,X0,X1] :
( sP0(sK6(powerset(X0)),X1)
| element(sK7(X2,sK10(powerset(unordered_pair(singleton(sK8(sK6(powerset(X0)),X1)),unordered_pair(sK9(sK6(powerset(X0)),X1),sK8(sK6(powerset(X0)),X1)))))),X0)
| empty(powerset(X0))
| empty(unordered_pair(singleton(sK8(sK6(powerset(X0)),X1)),unordered_pair(sK9(sK6(powerset(X0)),X1),sK8(sK6(powerset(X0)),X1))))
| sP0(X2,sK10(powerset(unordered_pair(singleton(sK8(sK6(powerset(X0)),X1)),unordered_pair(sK9(sK6(powerset(X0)),X1),sK8(sK6(powerset(X0)),X1)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1005])]) ).
fof(f3064,plain,
( ! [X2,X0,X1] :
( sP0(sK6(powerset(X0)),X1)
| element(sK7(X2,sK10(powerset(unordered_pair(singleton(sK8(sK6(powerset(X0)),X1)),unordered_pair(sK9(sK6(powerset(X0)),X1),sK8(sK6(powerset(X0)),X1)))))),X0)
| empty(powerset(X0))
| empty(unordered_pair(singleton(sK8(sK6(powerset(X0)),X1)),unordered_pair(sK9(sK6(powerset(X0)),X1),sK8(sK6(powerset(X0)),X1))))
| sP0(X2,sK10(powerset(unordered_pair(singleton(sK8(sK6(powerset(X0)),X1)),unordered_pair(sK9(sK6(powerset(X0)),X1),sK8(sK6(powerset(X0)),X1)))))) )
| ~ spl17_264
| ~ spl17_326 ),
inference(resolution,[],[f3035,f2140]) ).
fof(f13589,plain,
( spl17_1004
| ~ spl17_26
| ~ spl17_393 ),
inference(avatar_split_clause,[],[f12116,f3736,f296,f13587]) ).
fof(f296,plain,
( spl17_26
<=> ! [X0,X1] :
( element(X0,X1)
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_26])]) ).
fof(f12116,plain,
( ! [X0] :
( ~ in(X0,the_carrier(sK2))
| ~ element(X0,the_carrier(sK2))
| ~ related(sK2,sK5,X0)
| element(unordered_pair(singleton(sK4),unordered_pair(sK4,X0)),the_InternalRel(sK2)) )
| ~ spl17_26
| ~ spl17_393 ),
inference(resolution,[],[f3737,f297]) ).
fof(f297,plain,
( ! [X0,X1] :
( ~ in(X0,X1)
| element(X0,X1) )
| ~ spl17_26 ),
inference(avatar_component_clause,[],[f296]) ).
fof(f13501,plain,
( spl17_1003
| ~ spl17_30
| ~ spl17_373 ),
inference(avatar_split_clause,[],[f3603,f3555,f313,f13499]) ).
fof(f13499,plain,
( spl17_1003
<=> ! [X0] :
( in(unordered_pair(singleton(sK3),unordered_pair(X0,sK3)),the_InternalRel(sK2))
| ~ in(X0,the_carrier(sK2))
| ~ element(X0,the_carrier(sK2))
| ~ related(sK2,sK4,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1003])]) ).
fof(f3603,plain,
( ! [X0] :
( in(unordered_pair(singleton(sK3),unordered_pair(X0,sK3)),the_InternalRel(sK2))
| ~ in(X0,the_carrier(sK2))
| ~ element(X0,the_carrier(sK2))
| ~ related(sK2,sK4,X0) )
| ~ spl17_30
| ~ spl17_373 ),
inference(superposition,[],[f3556,f314]) ).
fof(f13493,plain,
( spl17_1002
| ~ spl17_241
| ~ spl17_328 ),
inference(avatar_split_clause,[],[f3087,f3042,f1933,f13491]) ).
fof(f13491,plain,
( spl17_1002
<=> ! [X2,X0,X1] :
( sP0(sK6(powerset(X0)),X1)
| element(sK9(X2,sK6(unordered_pair(singleton(sK7(sK6(powerset(X0)),X1)),unordered_pair(sK8(sK6(powerset(X0)),X1),sK7(sK6(powerset(X0)),X1))))),X0)
| empty(powerset(X0))
| sP0(X2,sK6(unordered_pair(singleton(sK7(sK6(powerset(X0)),X1)),unordered_pair(sK8(sK6(powerset(X0)),X1),sK7(sK6(powerset(X0)),X1)))))
| empty(unordered_pair(singleton(sK7(sK6(powerset(X0)),X1)),unordered_pair(sK8(sK6(powerset(X0)),X1),sK7(sK6(powerset(X0)),X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1002])]) ).
fof(f3087,plain,
( ! [X2,X0,X1] :
( sP0(sK6(powerset(X0)),X1)
| element(sK9(X2,sK6(unordered_pair(singleton(sK7(sK6(powerset(X0)),X1)),unordered_pair(sK8(sK6(powerset(X0)),X1),sK7(sK6(powerset(X0)),X1))))),X0)
| empty(powerset(X0))
| sP0(X2,sK6(unordered_pair(singleton(sK7(sK6(powerset(X0)),X1)),unordered_pair(sK8(sK6(powerset(X0)),X1),sK7(sK6(powerset(X0)),X1)))))
| empty(unordered_pair(singleton(sK7(sK6(powerset(X0)),X1)),unordered_pair(sK8(sK6(powerset(X0)),X1),sK7(sK6(powerset(X0)),X1)))) )
| ~ spl17_241
| ~ spl17_328 ),
inference(resolution,[],[f3043,f1934]) ).
fof(f13489,plain,
( spl17_1001
| ~ spl17_240
| ~ spl17_328 ),
inference(avatar_split_clause,[],[f3084,f3042,f1929,f13487]) ).
fof(f13487,plain,
( spl17_1001
<=> ! [X2,X0,X1] :
( sP0(sK6(powerset(X0)),X1)
| element(sK8(X2,sK6(unordered_pair(singleton(sK7(sK6(powerset(X0)),X1)),unordered_pair(sK8(sK6(powerset(X0)),X1),sK7(sK6(powerset(X0)),X1))))),X0)
| empty(powerset(X0))
| sP0(X2,sK6(unordered_pair(singleton(sK7(sK6(powerset(X0)),X1)),unordered_pair(sK8(sK6(powerset(X0)),X1),sK7(sK6(powerset(X0)),X1)))))
| empty(unordered_pair(singleton(sK7(sK6(powerset(X0)),X1)),unordered_pair(sK8(sK6(powerset(X0)),X1),sK7(sK6(powerset(X0)),X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1001])]) ).
fof(f3084,plain,
( ! [X2,X0,X1] :
( sP0(sK6(powerset(X0)),X1)
| element(sK8(X2,sK6(unordered_pair(singleton(sK7(sK6(powerset(X0)),X1)),unordered_pair(sK8(sK6(powerset(X0)),X1),sK7(sK6(powerset(X0)),X1))))),X0)
| empty(powerset(X0))
| sP0(X2,sK6(unordered_pair(singleton(sK7(sK6(powerset(X0)),X1)),unordered_pair(sK8(sK6(powerset(X0)),X1),sK7(sK6(powerset(X0)),X1)))))
| empty(unordered_pair(singleton(sK7(sK6(powerset(X0)),X1)),unordered_pair(sK8(sK6(powerset(X0)),X1),sK7(sK6(powerset(X0)),X1)))) )
| ~ spl17_240
| ~ spl17_328 ),
inference(resolution,[],[f3043,f1930]) ).
fof(f13485,plain,
( spl17_1000
| ~ spl17_239
| ~ spl17_328 ),
inference(avatar_split_clause,[],[f3081,f3042,f1925,f13483]) ).
fof(f13483,plain,
( spl17_1000
<=> ! [X2,X0,X1] :
( sP0(sK6(powerset(X0)),X1)
| element(sK7(X2,sK6(unordered_pair(singleton(sK7(sK6(powerset(X0)),X1)),unordered_pair(sK8(sK6(powerset(X0)),X1),sK7(sK6(powerset(X0)),X1))))),X0)
| empty(powerset(X0))
| sP0(X2,sK6(unordered_pair(singleton(sK7(sK6(powerset(X0)),X1)),unordered_pair(sK8(sK6(powerset(X0)),X1),sK7(sK6(powerset(X0)),X1)))))
| empty(unordered_pair(singleton(sK7(sK6(powerset(X0)),X1)),unordered_pair(sK8(sK6(powerset(X0)),X1),sK7(sK6(powerset(X0)),X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1000])]) ).
fof(f3081,plain,
( ! [X2,X0,X1] :
( sP0(sK6(powerset(X0)),X1)
| element(sK7(X2,sK6(unordered_pair(singleton(sK7(sK6(powerset(X0)),X1)),unordered_pair(sK8(sK6(powerset(X0)),X1),sK7(sK6(powerset(X0)),X1))))),X0)
| empty(powerset(X0))
| sP0(X2,sK6(unordered_pair(singleton(sK7(sK6(powerset(X0)),X1)),unordered_pair(sK8(sK6(powerset(X0)),X1),sK7(sK6(powerset(X0)),X1)))))
| empty(unordered_pair(singleton(sK7(sK6(powerset(X0)),X1)),unordered_pair(sK8(sK6(powerset(X0)),X1),sK7(sK6(powerset(X0)),X1)))) )
| ~ spl17_239
| ~ spl17_328 ),
inference(resolution,[],[f3043,f1926]) ).
fof(f13481,plain,
( spl17_999
| ~ spl17_229
| ~ spl17_328 ),
inference(avatar_split_clause,[],[f3079,f3042,f1885,f13479]) ).
fof(f13479,plain,
( spl17_999
<=> ! [X0,X1] :
( sP0(sK6(powerset(X0)),X1)
| element(sK10(sK10(powerset(unordered_pair(singleton(sK7(sK6(powerset(X0)),X1)),unordered_pair(sK8(sK6(powerset(X0)),X1),sK7(sK6(powerset(X0)),X1)))))),X0)
| empty(powerset(X0))
| empty(unordered_pair(singleton(sK7(sK6(powerset(X0)),X1)),unordered_pair(sK8(sK6(powerset(X0)),X1),sK7(sK6(powerset(X0)),X1))))
| empty(sK10(powerset(unordered_pair(singleton(sK7(sK6(powerset(X0)),X1)),unordered_pair(sK8(sK6(powerset(X0)),X1),sK7(sK6(powerset(X0)),X1)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_999])]) ).
fof(f3079,plain,
( ! [X0,X1] :
( sP0(sK6(powerset(X0)),X1)
| element(sK10(sK10(powerset(unordered_pair(singleton(sK7(sK6(powerset(X0)),X1)),unordered_pair(sK8(sK6(powerset(X0)),X1),sK7(sK6(powerset(X0)),X1)))))),X0)
| empty(powerset(X0))
| empty(unordered_pair(singleton(sK7(sK6(powerset(X0)),X1)),unordered_pair(sK8(sK6(powerset(X0)),X1),sK7(sK6(powerset(X0)),X1))))
| empty(sK10(powerset(unordered_pair(singleton(sK7(sK6(powerset(X0)),X1)),unordered_pair(sK8(sK6(powerset(X0)),X1),sK7(sK6(powerset(X0)),X1)))))) )
| ~ spl17_229
| ~ spl17_328 ),
inference(resolution,[],[f3043,f1886]) ).
fof(f13477,plain,
( spl17_998
| ~ spl17_241
| ~ spl17_326 ),
inference(avatar_split_clause,[],[f3069,f3034,f1933,f13475]) ).
fof(f13475,plain,
( spl17_998
<=> ! [X2,X0,X1] :
( sP0(sK6(powerset(X0)),X1)
| element(sK9(X2,sK6(unordered_pair(singleton(sK8(sK6(powerset(X0)),X1)),unordered_pair(sK9(sK6(powerset(X0)),X1),sK8(sK6(powerset(X0)),X1))))),X0)
| empty(powerset(X0))
| sP0(X2,sK6(unordered_pair(singleton(sK8(sK6(powerset(X0)),X1)),unordered_pair(sK9(sK6(powerset(X0)),X1),sK8(sK6(powerset(X0)),X1)))))
| empty(unordered_pair(singleton(sK8(sK6(powerset(X0)),X1)),unordered_pair(sK9(sK6(powerset(X0)),X1),sK8(sK6(powerset(X0)),X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_998])]) ).
fof(f3069,plain,
( ! [X2,X0,X1] :
( sP0(sK6(powerset(X0)),X1)
| element(sK9(X2,sK6(unordered_pair(singleton(sK8(sK6(powerset(X0)),X1)),unordered_pair(sK9(sK6(powerset(X0)),X1),sK8(sK6(powerset(X0)),X1))))),X0)
| empty(powerset(X0))
| sP0(X2,sK6(unordered_pair(singleton(sK8(sK6(powerset(X0)),X1)),unordered_pair(sK9(sK6(powerset(X0)),X1),sK8(sK6(powerset(X0)),X1)))))
| empty(unordered_pair(singleton(sK8(sK6(powerset(X0)),X1)),unordered_pair(sK9(sK6(powerset(X0)),X1),sK8(sK6(powerset(X0)),X1)))) )
| ~ spl17_241
| ~ spl17_326 ),
inference(resolution,[],[f3035,f1934]) ).
fof(f13473,plain,
( spl17_997
| ~ spl17_240
| ~ spl17_326 ),
inference(avatar_split_clause,[],[f3066,f3034,f1929,f13471]) ).
fof(f13471,plain,
( spl17_997
<=> ! [X2,X0,X1] :
( sP0(sK6(powerset(X0)),X1)
| element(sK8(X2,sK6(unordered_pair(singleton(sK8(sK6(powerset(X0)),X1)),unordered_pair(sK9(sK6(powerset(X0)),X1),sK8(sK6(powerset(X0)),X1))))),X0)
| empty(powerset(X0))
| sP0(X2,sK6(unordered_pair(singleton(sK8(sK6(powerset(X0)),X1)),unordered_pair(sK9(sK6(powerset(X0)),X1),sK8(sK6(powerset(X0)),X1)))))
| empty(unordered_pair(singleton(sK8(sK6(powerset(X0)),X1)),unordered_pair(sK9(sK6(powerset(X0)),X1),sK8(sK6(powerset(X0)),X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_997])]) ).
fof(f3066,plain,
( ! [X2,X0,X1] :
( sP0(sK6(powerset(X0)),X1)
| element(sK8(X2,sK6(unordered_pair(singleton(sK8(sK6(powerset(X0)),X1)),unordered_pair(sK9(sK6(powerset(X0)),X1),sK8(sK6(powerset(X0)),X1))))),X0)
| empty(powerset(X0))
| sP0(X2,sK6(unordered_pair(singleton(sK8(sK6(powerset(X0)),X1)),unordered_pair(sK9(sK6(powerset(X0)),X1),sK8(sK6(powerset(X0)),X1)))))
| empty(unordered_pair(singleton(sK8(sK6(powerset(X0)),X1)),unordered_pair(sK9(sK6(powerset(X0)),X1),sK8(sK6(powerset(X0)),X1)))) )
| ~ spl17_240
| ~ spl17_326 ),
inference(resolution,[],[f3035,f1930]) ).
fof(f13469,plain,
( spl17_996
| ~ spl17_239
| ~ spl17_326 ),
inference(avatar_split_clause,[],[f3063,f3034,f1925,f13467]) ).
fof(f13467,plain,
( spl17_996
<=> ! [X2,X0,X1] :
( sP0(sK6(powerset(X0)),X1)
| element(sK7(X2,sK6(unordered_pair(singleton(sK8(sK6(powerset(X0)),X1)),unordered_pair(sK9(sK6(powerset(X0)),X1),sK8(sK6(powerset(X0)),X1))))),X0)
| empty(powerset(X0))
| sP0(X2,sK6(unordered_pair(singleton(sK8(sK6(powerset(X0)),X1)),unordered_pair(sK9(sK6(powerset(X0)),X1),sK8(sK6(powerset(X0)),X1)))))
| empty(unordered_pair(singleton(sK8(sK6(powerset(X0)),X1)),unordered_pair(sK9(sK6(powerset(X0)),X1),sK8(sK6(powerset(X0)),X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_996])]) ).
fof(f3063,plain,
( ! [X2,X0,X1] :
( sP0(sK6(powerset(X0)),X1)
| element(sK7(X2,sK6(unordered_pair(singleton(sK8(sK6(powerset(X0)),X1)),unordered_pair(sK9(sK6(powerset(X0)),X1),sK8(sK6(powerset(X0)),X1))))),X0)
| empty(powerset(X0))
| sP0(X2,sK6(unordered_pair(singleton(sK8(sK6(powerset(X0)),X1)),unordered_pair(sK9(sK6(powerset(X0)),X1),sK8(sK6(powerset(X0)),X1)))))
| empty(unordered_pair(singleton(sK8(sK6(powerset(X0)),X1)),unordered_pair(sK9(sK6(powerset(X0)),X1),sK8(sK6(powerset(X0)),X1)))) )
| ~ spl17_239
| ~ spl17_326 ),
inference(resolution,[],[f3035,f1926]) ).
fof(f13465,plain,
( spl17_995
| ~ spl17_229
| ~ spl17_326 ),
inference(avatar_split_clause,[],[f3061,f3034,f1885,f13463]) ).
fof(f13463,plain,
( spl17_995
<=> ! [X0,X1] :
( sP0(sK6(powerset(X0)),X1)
| element(sK10(sK10(powerset(unordered_pair(singleton(sK8(sK6(powerset(X0)),X1)),unordered_pair(sK9(sK6(powerset(X0)),X1),sK8(sK6(powerset(X0)),X1)))))),X0)
| empty(powerset(X0))
| empty(unordered_pair(singleton(sK8(sK6(powerset(X0)),X1)),unordered_pair(sK9(sK6(powerset(X0)),X1),sK8(sK6(powerset(X0)),X1))))
| empty(sK10(powerset(unordered_pair(singleton(sK8(sK6(powerset(X0)),X1)),unordered_pair(sK9(sK6(powerset(X0)),X1),sK8(sK6(powerset(X0)),X1)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_995])]) ).
fof(f3061,plain,
( ! [X0,X1] :
( sP0(sK6(powerset(X0)),X1)
| element(sK10(sK10(powerset(unordered_pair(singleton(sK8(sK6(powerset(X0)),X1)),unordered_pair(sK9(sK6(powerset(X0)),X1),sK8(sK6(powerset(X0)),X1)))))),X0)
| empty(powerset(X0))
| empty(unordered_pair(singleton(sK8(sK6(powerset(X0)),X1)),unordered_pair(sK9(sK6(powerset(X0)),X1),sK8(sK6(powerset(X0)),X1))))
| empty(sK10(powerset(unordered_pair(singleton(sK8(sK6(powerset(X0)),X1)),unordered_pair(sK9(sK6(powerset(X0)),X1),sK8(sK6(powerset(X0)),X1)))))) )
| ~ spl17_229
| ~ spl17_326 ),
inference(resolution,[],[f3035,f1886]) ).
fof(f13461,plain,
( spl17_994
| ~ spl17_25
| ~ spl17_373 ),
inference(avatar_split_clause,[],[f3602,f3555,f292,f13459]) ).
fof(f3602,plain,
( ! [X0] :
( ~ in(X0,the_carrier(sK2))
| ~ element(X0,the_carrier(sK2))
| ~ related(sK2,sK4,X0)
| ~ in(the_InternalRel(sK2),unordered_pair(singleton(sK3),unordered_pair(sK3,X0))) )
| ~ spl17_25
| ~ spl17_373 ),
inference(resolution,[],[f3556,f293]) ).
fof(f13457,plain,
( spl17_993
| ~ spl17_201
| ~ spl17_321 ),
inference(avatar_split_clause,[],[f2932,f2873,f1628,f13455]) ).
fof(f13455,plain,
( spl17_993
<=> ! [X4,X0,X3,X2,X1] :
( empty(cartesian_product2(X0,X1))
| sP0(sK10(powerset(cartesian_product2(X0,X1))),X2)
| in(unordered_pair(singleton(sK7(sK10(powerset(cartesian_product2(X0,X1))),X2)),unordered_pair(sK7(sK10(powerset(cartesian_product2(X0,X1))),X2),X3)),cartesian_product2(X0,X1))
| ~ in(X3,X4)
| ~ in(sK8(sK10(powerset(cartesian_product2(X0,X1))),X2),X4)
| ~ in(sK7(sK10(powerset(cartesian_product2(X0,X1))),X2),X4)
| ~ sP0(cartesian_product2(X0,X1),X4)
| ~ in(X3,X1)
| ~ in(sK8(sK10(powerset(cartesian_product2(X0,X1))),X2),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_993])]) ).
fof(f1628,plain,
( spl17_201
<=> ! [X5,X4,X0,X3,X2,X1] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X1,X0)),cartesian_product2(X2,X3))
| in(unordered_pair(singleton(X0),unordered_pair(X0,X4)),cartesian_product2(X2,X3))
| ~ in(X4,X5)
| ~ in(X1,X5)
| ~ in(X0,X5)
| ~ sP0(cartesian_product2(X2,X3),X5)
| ~ in(X4,X3)
| ~ in(X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_201])]) ).
fof(f2932,plain,
( ! [X2,X3,X0,X1,X4] :
( empty(cartesian_product2(X0,X1))
| sP0(sK10(powerset(cartesian_product2(X0,X1))),X2)
| in(unordered_pair(singleton(sK7(sK10(powerset(cartesian_product2(X0,X1))),X2)),unordered_pair(sK7(sK10(powerset(cartesian_product2(X0,X1))),X2),X3)),cartesian_product2(X0,X1))
| ~ in(X3,X4)
| ~ in(sK8(sK10(powerset(cartesian_product2(X0,X1))),X2),X4)
| ~ in(sK7(sK10(powerset(cartesian_product2(X0,X1))),X2),X4)
| ~ sP0(cartesian_product2(X0,X1),X4)
| ~ in(X3,X1)
| ~ in(sK8(sK10(powerset(cartesian_product2(X0,X1))),X2),X0) )
| ~ spl17_201
| ~ spl17_321 ),
inference(resolution,[],[f2874,f1629]) ).
fof(f1629,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X1,X0)),cartesian_product2(X2,X3))
| in(unordered_pair(singleton(X0),unordered_pair(X0,X4)),cartesian_product2(X2,X3))
| ~ in(X4,X5)
| ~ in(X1,X5)
| ~ in(X0,X5)
| ~ sP0(cartesian_product2(X2,X3),X5)
| ~ in(X4,X3)
| ~ in(X1,X2) )
| ~ spl17_201 ),
inference(avatar_component_clause,[],[f1628]) ).
fof(f13453,plain,
( spl17_992
| ~ spl17_201
| ~ spl17_320 ),
inference(avatar_split_clause,[],[f2881,f2869,f1628,f13451]) ).
fof(f13451,plain,
( spl17_992
<=> ! [X4,X0,X3,X2,X1] :
( empty(cartesian_product2(X0,X1))
| sP0(sK10(powerset(cartesian_product2(X0,X1))),X2)
| in(unordered_pair(singleton(sK8(sK10(powerset(cartesian_product2(X0,X1))),X2)),unordered_pair(sK8(sK10(powerset(cartesian_product2(X0,X1))),X2),X3)),cartesian_product2(X0,X1))
| ~ in(X3,X4)
| ~ in(sK9(sK10(powerset(cartesian_product2(X0,X1))),X2),X4)
| ~ in(sK8(sK10(powerset(cartesian_product2(X0,X1))),X2),X4)
| ~ sP0(cartesian_product2(X0,X1),X4)
| ~ in(X3,X1)
| ~ in(sK9(sK10(powerset(cartesian_product2(X0,X1))),X2),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_992])]) ).
fof(f2881,plain,
( ! [X2,X3,X0,X1,X4] :
( empty(cartesian_product2(X0,X1))
| sP0(sK10(powerset(cartesian_product2(X0,X1))),X2)
| in(unordered_pair(singleton(sK8(sK10(powerset(cartesian_product2(X0,X1))),X2)),unordered_pair(sK8(sK10(powerset(cartesian_product2(X0,X1))),X2),X3)),cartesian_product2(X0,X1))
| ~ in(X3,X4)
| ~ in(sK9(sK10(powerset(cartesian_product2(X0,X1))),X2),X4)
| ~ in(sK8(sK10(powerset(cartesian_product2(X0,X1))),X2),X4)
| ~ sP0(cartesian_product2(X0,X1),X4)
| ~ in(X3,X1)
| ~ in(sK9(sK10(powerset(cartesian_product2(X0,X1))),X2),X0) )
| ~ spl17_201
| ~ spl17_320 ),
inference(resolution,[],[f2870,f1629]) ).
fof(f13449,plain,
( spl17_991
| ~ spl17_209
| ~ spl17_312 ),
inference(avatar_split_clause,[],[f2827,f2730,f1710,f13447]) ).
fof(f13447,plain,
( spl17_991
<=> ! [X4,X0,X3,X2,X1] :
( sP0(sK6(powerset(cartesian_product2(X0,X1))),X2)
| empty(powerset(cartesian_product2(X0,X1)))
| in(unordered_pair(singleton(X3),unordered_pair(X3,sK8(sK6(powerset(cartesian_product2(X0,X1))),X2))),powerset(cartesian_product2(X0,X1)))
| ~ in(sK8(sK6(powerset(cartesian_product2(X0,X1))),X2),X4)
| ~ in(sK7(sK6(powerset(cartesian_product2(X0,X1))),X2),X4)
| ~ in(X3,X4)
| ~ sP0(powerset(cartesian_product2(X0,X1)),X4)
| ~ relation_of2_as_subset(unordered_pair(singleton(X3),unordered_pair(X3,sK7(sK6(powerset(cartesian_product2(X0,X1))),X2))),X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_991])]) ).
fof(f2827,plain,
( ! [X2,X3,X0,X1,X4] :
( sP0(sK6(powerset(cartesian_product2(X0,X1))),X2)
| empty(powerset(cartesian_product2(X0,X1)))
| in(unordered_pair(singleton(X3),unordered_pair(X3,sK8(sK6(powerset(cartesian_product2(X0,X1))),X2))),powerset(cartesian_product2(X0,X1)))
| ~ in(sK8(sK6(powerset(cartesian_product2(X0,X1))),X2),X4)
| ~ in(sK7(sK6(powerset(cartesian_product2(X0,X1))),X2),X4)
| ~ in(X3,X4)
| ~ sP0(powerset(cartesian_product2(X0,X1)),X4)
| ~ relation_of2_as_subset(unordered_pair(singleton(X3),unordered_pair(X3,sK7(sK6(powerset(cartesian_product2(X0,X1))),X2))),X0,X1) )
| ~ spl17_209
| ~ spl17_312 ),
inference(duplicate_literal_removal,[],[f2789]) ).
fof(f2789,plain,
( ! [X2,X3,X0,X1,X4] :
( sP0(sK6(powerset(cartesian_product2(X0,X1))),X2)
| empty(powerset(cartesian_product2(X0,X1)))
| in(unordered_pair(singleton(X3),unordered_pair(X3,sK8(sK6(powerset(cartesian_product2(X0,X1))),X2))),powerset(cartesian_product2(X0,X1)))
| ~ in(sK8(sK6(powerset(cartesian_product2(X0,X1))),X2),X4)
| ~ in(sK7(sK6(powerset(cartesian_product2(X0,X1))),X2),X4)
| ~ in(X3,X4)
| ~ sP0(powerset(cartesian_product2(X0,X1)),X4)
| empty(powerset(cartesian_product2(X0,X1)))
| ~ relation_of2_as_subset(unordered_pair(singleton(X3),unordered_pair(X3,sK7(sK6(powerset(cartesian_product2(X0,X1))),X2))),X0,X1) )
| ~ spl17_209
| ~ spl17_312 ),
inference(resolution,[],[f2731,f1711]) ).
fof(f13445,plain,
( spl17_990
| ~ spl17_209
| ~ spl17_311 ),
inference(avatar_split_clause,[],[f2778,f2726,f1710,f13443]) ).
fof(f13443,plain,
( spl17_990
<=> ! [X4,X0,X3,X2,X1] :
( sP0(sK6(powerset(cartesian_product2(X0,X1))),X2)
| empty(powerset(cartesian_product2(X0,X1)))
| in(unordered_pair(singleton(X3),unordered_pair(X3,sK9(sK6(powerset(cartesian_product2(X0,X1))),X2))),powerset(cartesian_product2(X0,X1)))
| ~ in(sK9(sK6(powerset(cartesian_product2(X0,X1))),X2),X4)
| ~ in(sK8(sK6(powerset(cartesian_product2(X0,X1))),X2),X4)
| ~ in(X3,X4)
| ~ sP0(powerset(cartesian_product2(X0,X1)),X4)
| ~ relation_of2_as_subset(unordered_pair(singleton(X3),unordered_pair(X3,sK8(sK6(powerset(cartesian_product2(X0,X1))),X2))),X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_990])]) ).
fof(f2778,plain,
( ! [X2,X3,X0,X1,X4] :
( sP0(sK6(powerset(cartesian_product2(X0,X1))),X2)
| empty(powerset(cartesian_product2(X0,X1)))
| in(unordered_pair(singleton(X3),unordered_pair(X3,sK9(sK6(powerset(cartesian_product2(X0,X1))),X2))),powerset(cartesian_product2(X0,X1)))
| ~ in(sK9(sK6(powerset(cartesian_product2(X0,X1))),X2),X4)
| ~ in(sK8(sK6(powerset(cartesian_product2(X0,X1))),X2),X4)
| ~ in(X3,X4)
| ~ sP0(powerset(cartesian_product2(X0,X1)),X4)
| ~ relation_of2_as_subset(unordered_pair(singleton(X3),unordered_pair(X3,sK8(sK6(powerset(cartesian_product2(X0,X1))),X2))),X0,X1) )
| ~ spl17_209
| ~ spl17_311 ),
inference(duplicate_literal_removal,[],[f2740]) ).
fof(f2740,plain,
( ! [X2,X3,X0,X1,X4] :
( sP0(sK6(powerset(cartesian_product2(X0,X1))),X2)
| empty(powerset(cartesian_product2(X0,X1)))
| in(unordered_pair(singleton(X3),unordered_pair(X3,sK9(sK6(powerset(cartesian_product2(X0,X1))),X2))),powerset(cartesian_product2(X0,X1)))
| ~ in(sK9(sK6(powerset(cartesian_product2(X0,X1))),X2),X4)
| ~ in(sK8(sK6(powerset(cartesian_product2(X0,X1))),X2),X4)
| ~ in(X3,X4)
| ~ sP0(powerset(cartesian_product2(X0,X1)),X4)
| empty(powerset(cartesian_product2(X0,X1)))
| ~ relation_of2_as_subset(unordered_pair(singleton(X3),unordered_pair(X3,sK8(sK6(powerset(cartesian_product2(X0,X1))),X2))),X0,X1) )
| ~ spl17_209
| ~ spl17_311 ),
inference(resolution,[],[f2727,f1711]) ).
fof(f13438,plain,
( spl17_989
| ~ spl17_206
| ~ spl17_321 ),
inference(avatar_split_clause,[],[f2940,f2873,f1682,f13436]) ).
fof(f13436,plain,
( spl17_989
<=> ! [X0,X3,X2,X1] :
( empty(the_InternalRel(X0))
| sP0(sK10(powerset(the_InternalRel(X0))),X1)
| in(unordered_pair(singleton(X2),unordered_pair(X2,sK8(sK10(powerset(the_InternalRel(X0))),X1))),the_InternalRel(X0))
| ~ in(sK8(sK10(powerset(the_InternalRel(X0))),X1),X3)
| ~ in(sK7(sK10(powerset(the_InternalRel(X0))),X1),X3)
| ~ in(X2,X3)
| ~ sP0(the_InternalRel(X0),X3)
| ~ related(X0,X2,sK7(sK10(powerset(the_InternalRel(X0))),X1))
| ~ element(sK7(sK10(powerset(the_InternalRel(X0))),X1),the_carrier(X0))
| ~ element(X2,the_carrier(X0))
| ~ rel_str(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_989])]) ).
fof(f1682,plain,
( spl17_206
<=> ! [X4,X0,X3,X2,X1] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X1,X0)),the_InternalRel(X2))
| in(unordered_pair(singleton(X3),unordered_pair(X3,X1)),the_InternalRel(X2))
| ~ in(X1,X4)
| ~ in(X0,X4)
| ~ in(X3,X4)
| ~ sP0(the_InternalRel(X2),X4)
| ~ related(X2,X3,X0)
| ~ element(X0,the_carrier(X2))
| ~ element(X3,the_carrier(X2))
| ~ rel_str(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_206])]) ).
fof(f2940,plain,
( ! [X2,X3,X0,X1] :
( empty(the_InternalRel(X0))
| sP0(sK10(powerset(the_InternalRel(X0))),X1)
| in(unordered_pair(singleton(X2),unordered_pair(X2,sK8(sK10(powerset(the_InternalRel(X0))),X1))),the_InternalRel(X0))
| ~ in(sK8(sK10(powerset(the_InternalRel(X0))),X1),X3)
| ~ in(sK7(sK10(powerset(the_InternalRel(X0))),X1),X3)
| ~ in(X2,X3)
| ~ sP0(the_InternalRel(X0),X3)
| ~ related(X0,X2,sK7(sK10(powerset(the_InternalRel(X0))),X1))
| ~ element(sK7(sK10(powerset(the_InternalRel(X0))),X1),the_carrier(X0))
| ~ element(X2,the_carrier(X0))
| ~ rel_str(X0) )
| ~ spl17_206
| ~ spl17_321 ),
inference(resolution,[],[f2874,f1683]) ).
fof(f1683,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X1,X0)),the_InternalRel(X2))
| in(unordered_pair(singleton(X3),unordered_pair(X3,X1)),the_InternalRel(X2))
| ~ in(X1,X4)
| ~ in(X0,X4)
| ~ in(X3,X4)
| ~ sP0(the_InternalRel(X2),X4)
| ~ related(X2,X3,X0)
| ~ element(X0,the_carrier(X2))
| ~ element(X3,the_carrier(X2))
| ~ rel_str(X2) )
| ~ spl17_206 ),
inference(avatar_component_clause,[],[f1682]) ).
fof(f13434,plain,
( spl17_988
| ~ spl17_206
| ~ spl17_320 ),
inference(avatar_split_clause,[],[f2889,f2869,f1682,f13432]) ).
fof(f13432,plain,
( spl17_988
<=> ! [X0,X3,X2,X1] :
( empty(the_InternalRel(X0))
| sP0(sK10(powerset(the_InternalRel(X0))),X1)
| in(unordered_pair(singleton(X2),unordered_pair(X2,sK9(sK10(powerset(the_InternalRel(X0))),X1))),the_InternalRel(X0))
| ~ in(sK9(sK10(powerset(the_InternalRel(X0))),X1),X3)
| ~ in(sK8(sK10(powerset(the_InternalRel(X0))),X1),X3)
| ~ in(X2,X3)
| ~ sP0(the_InternalRel(X0),X3)
| ~ related(X0,X2,sK8(sK10(powerset(the_InternalRel(X0))),X1))
| ~ element(sK8(sK10(powerset(the_InternalRel(X0))),X1),the_carrier(X0))
| ~ element(X2,the_carrier(X0))
| ~ rel_str(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_988])]) ).
fof(f2889,plain,
( ! [X2,X3,X0,X1] :
( empty(the_InternalRel(X0))
| sP0(sK10(powerset(the_InternalRel(X0))),X1)
| in(unordered_pair(singleton(X2),unordered_pair(X2,sK9(sK10(powerset(the_InternalRel(X0))),X1))),the_InternalRel(X0))
| ~ in(sK9(sK10(powerset(the_InternalRel(X0))),X1),X3)
| ~ in(sK8(sK10(powerset(the_InternalRel(X0))),X1),X3)
| ~ in(X2,X3)
| ~ sP0(the_InternalRel(X0),X3)
| ~ related(X0,X2,sK8(sK10(powerset(the_InternalRel(X0))),X1))
| ~ element(sK8(sK10(powerset(the_InternalRel(X0))),X1),the_carrier(X0))
| ~ element(X2,the_carrier(X0))
| ~ rel_str(X0) )
| ~ spl17_206
| ~ spl17_320 ),
inference(resolution,[],[f2870,f1683]) ).
fof(f13324,plain,
( spl17_987
| ~ spl17_26
| ~ spl17_373 ),
inference(avatar_split_clause,[],[f3601,f3555,f296,f13322]) ).
fof(f3601,plain,
( ! [X0] :
( ~ in(X0,the_carrier(sK2))
| ~ element(X0,the_carrier(sK2))
| ~ related(sK2,sK4,X0)
| element(unordered_pair(singleton(sK3),unordered_pair(sK3,X0)),the_InternalRel(sK2)) )
| ~ spl17_26
| ~ spl17_373 ),
inference(resolution,[],[f3556,f297]) ).
fof(f13304,plain,
( spl17_986
| ~ spl17_193
| ~ spl17_368 ),
inference(avatar_split_clause,[],[f3531,f3523,f1561,f13302]) ).
fof(f13302,plain,
( spl17_986
<=> ! [X2,X0,X1] :
( ~ in(sK9(the_InternalRel(X0),X1),the_carrier(X0))
| ~ in(sK8(the_InternalRel(X0),X1),the_carrier(X0))
| in(unordered_pair(singleton(sK8(the_InternalRel(X0),X1)),unordered_pair(sK8(the_InternalRel(X0),X1),X2)),the_InternalRel(X0))
| ~ related(X0,sK9(the_InternalRel(X0),X1),X2)
| ~ element(X2,the_carrier(X0))
| ~ element(sK9(the_InternalRel(X0),X1),the_carrier(X0))
| ~ rel_str(X0)
| ~ in(X2,the_carrier(X0))
| ~ element(sK8(the_InternalRel(X0),X1),the_carrier(X0))
| ~ transitive_relstr(X0)
| ~ sP1(the_InternalRel(X0))
| sP0(the_InternalRel(X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_986])]) ).
fof(f1561,plain,
( spl17_193
<=> ! [X0,X1] :
( related(X0,sK8(the_InternalRel(X0),X1),sK9(the_InternalRel(X0),X1))
| ~ element(sK9(the_InternalRel(X0),X1),the_carrier(X0))
| ~ element(sK8(the_InternalRel(X0),X1),the_carrier(X0))
| ~ rel_str(X0)
| sP0(the_InternalRel(X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_193])]) ).
fof(f3523,plain,
( spl17_368
<=> ! [X0,X3,X2,X1] :
( ~ in(X0,the_carrier(X1))
| ~ in(X2,the_carrier(X1))
| ~ in(X3,the_carrier(X1))
| in(unordered_pair(singleton(X3),unordered_pair(X3,X0)),the_InternalRel(X1))
| ~ related(X1,X2,X0)
| ~ element(X0,the_carrier(X1))
| ~ element(X2,the_carrier(X1))
| ~ rel_str(X1)
| ~ related(X1,X3,X2)
| ~ element(X3,the_carrier(X1))
| ~ transitive_relstr(X1)
| ~ sP1(the_InternalRel(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_368])]) ).
fof(f3531,plain,
( ! [X2,X0,X1] :
( ~ in(sK9(the_InternalRel(X0),X1),the_carrier(X0))
| ~ in(sK8(the_InternalRel(X0),X1),the_carrier(X0))
| in(unordered_pair(singleton(sK8(the_InternalRel(X0),X1)),unordered_pair(sK8(the_InternalRel(X0),X1),X2)),the_InternalRel(X0))
| ~ related(X0,sK9(the_InternalRel(X0),X1),X2)
| ~ element(X2,the_carrier(X0))
| ~ element(sK9(the_InternalRel(X0),X1),the_carrier(X0))
| ~ rel_str(X0)
| ~ in(X2,the_carrier(X0))
| ~ element(sK8(the_InternalRel(X0),X1),the_carrier(X0))
| ~ transitive_relstr(X0)
| ~ sP1(the_InternalRel(X0))
| sP0(the_InternalRel(X0),X1) )
| ~ spl17_193
| ~ spl17_368 ),
inference(duplicate_literal_removal,[],[f3528]) ).
fof(f3528,plain,
( ! [X2,X0,X1] :
( ~ in(sK9(the_InternalRel(X0),X1),the_carrier(X0))
| ~ in(sK8(the_InternalRel(X0),X1),the_carrier(X0))
| in(unordered_pair(singleton(sK8(the_InternalRel(X0),X1)),unordered_pair(sK8(the_InternalRel(X0),X1),X2)),the_InternalRel(X0))
| ~ related(X0,sK9(the_InternalRel(X0),X1),X2)
| ~ element(X2,the_carrier(X0))
| ~ element(sK9(the_InternalRel(X0),X1),the_carrier(X0))
| ~ rel_str(X0)
| ~ in(X2,the_carrier(X0))
| ~ element(sK8(the_InternalRel(X0),X1),the_carrier(X0))
| ~ transitive_relstr(X0)
| ~ sP1(the_InternalRel(X0))
| ~ element(sK9(the_InternalRel(X0),X1),the_carrier(X0))
| ~ element(sK8(the_InternalRel(X0),X1),the_carrier(X0))
| ~ rel_str(X0)
| sP0(the_InternalRel(X0),X1) )
| ~ spl17_193
| ~ spl17_368 ),
inference(resolution,[],[f3524,f1562]) ).
fof(f1562,plain,
( ! [X0,X1] :
( related(X0,sK8(the_InternalRel(X0),X1),sK9(the_InternalRel(X0),X1))
| ~ element(sK9(the_InternalRel(X0),X1),the_carrier(X0))
| ~ element(sK8(the_InternalRel(X0),X1),the_carrier(X0))
| ~ rel_str(X0)
| sP0(the_InternalRel(X0),X1) )
| ~ spl17_193 ),
inference(avatar_component_clause,[],[f1561]) ).
fof(f3524,plain,
( ! [X2,X3,X0,X1] :
( ~ related(X1,X3,X2)
| ~ in(X2,the_carrier(X1))
| ~ in(X3,the_carrier(X1))
| in(unordered_pair(singleton(X3),unordered_pair(X3,X0)),the_InternalRel(X1))
| ~ related(X1,X2,X0)
| ~ element(X0,the_carrier(X1))
| ~ element(X2,the_carrier(X1))
| ~ rel_str(X1)
| ~ in(X0,the_carrier(X1))
| ~ element(X3,the_carrier(X1))
| ~ transitive_relstr(X1)
| ~ sP1(the_InternalRel(X1)) )
| ~ spl17_368 ),
inference(avatar_component_clause,[],[f3523]) ).
fof(f13300,plain,
( spl17_985
| ~ spl17_194
| ~ spl17_368 ),
inference(avatar_split_clause,[],[f3530,f3523,f1565,f13298]) ).
fof(f13298,plain,
( spl17_985
<=> ! [X2,X0,X1] :
( ~ in(sK8(the_InternalRel(X0),X1),the_carrier(X0))
| ~ in(sK7(the_InternalRel(X0),X1),the_carrier(X0))
| in(unordered_pair(singleton(sK7(the_InternalRel(X0),X1)),unordered_pair(sK7(the_InternalRel(X0),X1),X2)),the_InternalRel(X0))
| ~ related(X0,sK8(the_InternalRel(X0),X1),X2)
| ~ element(X2,the_carrier(X0))
| ~ element(sK8(the_InternalRel(X0),X1),the_carrier(X0))
| ~ rel_str(X0)
| ~ in(X2,the_carrier(X0))
| ~ element(sK7(the_InternalRel(X0),X1),the_carrier(X0))
| ~ transitive_relstr(X0)
| ~ sP1(the_InternalRel(X0))
| sP0(the_InternalRel(X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_985])]) ).
fof(f1565,plain,
( spl17_194
<=> ! [X0,X1] :
( related(X0,sK7(the_InternalRel(X0),X1),sK8(the_InternalRel(X0),X1))
| ~ element(sK8(the_InternalRel(X0),X1),the_carrier(X0))
| ~ element(sK7(the_InternalRel(X0),X1),the_carrier(X0))
| ~ rel_str(X0)
| sP0(the_InternalRel(X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_194])]) ).
fof(f3530,plain,
( ! [X2,X0,X1] :
( ~ in(sK8(the_InternalRel(X0),X1),the_carrier(X0))
| ~ in(sK7(the_InternalRel(X0),X1),the_carrier(X0))
| in(unordered_pair(singleton(sK7(the_InternalRel(X0),X1)),unordered_pair(sK7(the_InternalRel(X0),X1),X2)),the_InternalRel(X0))
| ~ related(X0,sK8(the_InternalRel(X0),X1),X2)
| ~ element(X2,the_carrier(X0))
| ~ element(sK8(the_InternalRel(X0),X1),the_carrier(X0))
| ~ rel_str(X0)
| ~ in(X2,the_carrier(X0))
| ~ element(sK7(the_InternalRel(X0),X1),the_carrier(X0))
| ~ transitive_relstr(X0)
| ~ sP1(the_InternalRel(X0))
| sP0(the_InternalRel(X0),X1) )
| ~ spl17_194
| ~ spl17_368 ),
inference(duplicate_literal_removal,[],[f3529]) ).
fof(f3529,plain,
( ! [X2,X0,X1] :
( ~ in(sK8(the_InternalRel(X0),X1),the_carrier(X0))
| ~ in(sK7(the_InternalRel(X0),X1),the_carrier(X0))
| in(unordered_pair(singleton(sK7(the_InternalRel(X0),X1)),unordered_pair(sK7(the_InternalRel(X0),X1),X2)),the_InternalRel(X0))
| ~ related(X0,sK8(the_InternalRel(X0),X1),X2)
| ~ element(X2,the_carrier(X0))
| ~ element(sK8(the_InternalRel(X0),X1),the_carrier(X0))
| ~ rel_str(X0)
| ~ in(X2,the_carrier(X0))
| ~ element(sK7(the_InternalRel(X0),X1),the_carrier(X0))
| ~ transitive_relstr(X0)
| ~ sP1(the_InternalRel(X0))
| ~ element(sK8(the_InternalRel(X0),X1),the_carrier(X0))
| ~ element(sK7(the_InternalRel(X0),X1),the_carrier(X0))
| ~ rel_str(X0)
| sP0(the_InternalRel(X0),X1) )
| ~ spl17_194
| ~ spl17_368 ),
inference(resolution,[],[f3524,f1566]) ).
fof(f1566,plain,
( ! [X0,X1] :
( related(X0,sK7(the_InternalRel(X0),X1),sK8(the_InternalRel(X0),X1))
| ~ element(sK8(the_InternalRel(X0),X1),the_carrier(X0))
| ~ element(sK7(the_InternalRel(X0),X1),the_carrier(X0))
| ~ rel_str(X0)
| sP0(the_InternalRel(X0),X1) )
| ~ spl17_194 ),
inference(avatar_component_clause,[],[f1565]) ).
fof(f13296,plain,
( spl17_984
| ~ spl17_320
| ~ spl17_364 ),
inference(avatar_split_clause,[],[f3498,f3463,f2869,f13294]) ).
fof(f13294,plain,
( spl17_984
<=> ! [X0,X3,X2,X1] :
( ~ subset(unordered_pair(singleton(sK9(sK10(powerset(powerset(X0))),X1)),unordered_pair(sK9(sK10(powerset(powerset(X0))),X1),X2)),X0)
| empty(powerset(X0))
| in(unordered_pair(singleton(sK8(sK10(powerset(powerset(X0))),X1)),unordered_pair(sK8(sK10(powerset(powerset(X0))),X1),X2)),powerset(X0))
| ~ in(X2,X3)
| ~ in(sK9(sK10(powerset(powerset(X0))),X1),X3)
| ~ in(sK8(sK10(powerset(powerset(X0))),X1),X3)
| ~ sP0(powerset(X0),X3)
| sP0(sK10(powerset(powerset(X0))),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_984])]) ).
fof(f3463,plain,
( spl17_364
<=> ! [X4,X0,X3,X2,X1] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X1,X0)),powerset(X2))
| ~ subset(unordered_pair(singleton(X1),unordered_pair(X1,X3)),X2)
| empty(powerset(X2))
| in(unordered_pair(singleton(X0),unordered_pair(X0,X3)),powerset(X2))
| ~ in(X3,X4)
| ~ in(X1,X4)
| ~ in(X0,X4)
| ~ sP0(powerset(X2),X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_364])]) ).
fof(f3498,plain,
( ! [X2,X3,X0,X1] :
( ~ subset(unordered_pair(singleton(sK9(sK10(powerset(powerset(X0))),X1)),unordered_pair(sK9(sK10(powerset(powerset(X0))),X1),X2)),X0)
| empty(powerset(X0))
| in(unordered_pair(singleton(sK8(sK10(powerset(powerset(X0))),X1)),unordered_pair(sK8(sK10(powerset(powerset(X0))),X1),X2)),powerset(X0))
| ~ in(X2,X3)
| ~ in(sK9(sK10(powerset(powerset(X0))),X1),X3)
| ~ in(sK8(sK10(powerset(powerset(X0))),X1),X3)
| ~ sP0(powerset(X0),X3)
| sP0(sK10(powerset(powerset(X0))),X1) )
| ~ spl17_320
| ~ spl17_364 ),
inference(duplicate_literal_removal,[],[f3490]) ).
fof(f3490,plain,
( ! [X2,X3,X0,X1] :
( ~ subset(unordered_pair(singleton(sK9(sK10(powerset(powerset(X0))),X1)),unordered_pair(sK9(sK10(powerset(powerset(X0))),X1),X2)),X0)
| empty(powerset(X0))
| in(unordered_pair(singleton(sK8(sK10(powerset(powerset(X0))),X1)),unordered_pair(sK8(sK10(powerset(powerset(X0))),X1),X2)),powerset(X0))
| ~ in(X2,X3)
| ~ in(sK9(sK10(powerset(powerset(X0))),X1),X3)
| ~ in(sK8(sK10(powerset(powerset(X0))),X1),X3)
| ~ sP0(powerset(X0),X3)
| empty(powerset(X0))
| sP0(sK10(powerset(powerset(X0))),X1) )
| ~ spl17_320
| ~ spl17_364 ),
inference(resolution,[],[f3464,f2870]) ).
fof(f3464,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X1,X0)),powerset(X2))
| ~ subset(unordered_pair(singleton(X1),unordered_pair(X1,X3)),X2)
| empty(powerset(X2))
| in(unordered_pair(singleton(X0),unordered_pair(X0,X3)),powerset(X2))
| ~ in(X3,X4)
| ~ in(X1,X4)
| ~ in(X0,X4)
| ~ sP0(powerset(X2),X4) )
| ~ spl17_364 ),
inference(avatar_component_clause,[],[f3463]) ).
fof(f13292,plain,
( spl17_983
| ~ spl17_321
| ~ spl17_364 ),
inference(avatar_split_clause,[],[f3496,f3463,f2873,f13290]) ).
fof(f13290,plain,
( spl17_983
<=> ! [X0,X3,X2,X1] :
( ~ subset(unordered_pair(singleton(sK8(sK10(powerset(powerset(X0))),X1)),unordered_pair(sK8(sK10(powerset(powerset(X0))),X1),X2)),X0)
| empty(powerset(X0))
| in(unordered_pair(singleton(sK7(sK10(powerset(powerset(X0))),X1)),unordered_pair(sK7(sK10(powerset(powerset(X0))),X1),X2)),powerset(X0))
| ~ in(X2,X3)
| ~ in(sK8(sK10(powerset(powerset(X0))),X1),X3)
| ~ in(sK7(sK10(powerset(powerset(X0))),X1),X3)
| ~ sP0(powerset(X0),X3)
| sP0(sK10(powerset(powerset(X0))),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_983])]) ).
fof(f3496,plain,
( ! [X2,X3,X0,X1] :
( ~ subset(unordered_pair(singleton(sK8(sK10(powerset(powerset(X0))),X1)),unordered_pair(sK8(sK10(powerset(powerset(X0))),X1),X2)),X0)
| empty(powerset(X0))
| in(unordered_pair(singleton(sK7(sK10(powerset(powerset(X0))),X1)),unordered_pair(sK7(sK10(powerset(powerset(X0))),X1),X2)),powerset(X0))
| ~ in(X2,X3)
| ~ in(sK8(sK10(powerset(powerset(X0))),X1),X3)
| ~ in(sK7(sK10(powerset(powerset(X0))),X1),X3)
| ~ sP0(powerset(X0),X3)
| sP0(sK10(powerset(powerset(X0))),X1) )
| ~ spl17_321
| ~ spl17_364 ),
inference(duplicate_literal_removal,[],[f3493]) ).
fof(f3493,plain,
( ! [X2,X3,X0,X1] :
( ~ subset(unordered_pair(singleton(sK8(sK10(powerset(powerset(X0))),X1)),unordered_pair(sK8(sK10(powerset(powerset(X0))),X1),X2)),X0)
| empty(powerset(X0))
| in(unordered_pair(singleton(sK7(sK10(powerset(powerset(X0))),X1)),unordered_pair(sK7(sK10(powerset(powerset(X0))),X1),X2)),powerset(X0))
| ~ in(X2,X3)
| ~ in(sK8(sK10(powerset(powerset(X0))),X1),X3)
| ~ in(sK7(sK10(powerset(powerset(X0))),X1),X3)
| ~ sP0(powerset(X0),X3)
| empty(powerset(X0))
| sP0(sK10(powerset(powerset(X0))),X1) )
| ~ spl17_321
| ~ spl17_364 ),
inference(resolution,[],[f3464,f2874]) ).
fof(f13288,plain,
( spl17_982
| ~ spl17_320
| ~ spl17_363 ),
inference(avatar_split_clause,[],[f3482,f3459,f2869,f13286]) ).
fof(f13286,plain,
( spl17_982
<=> ! [X0,X3,X2,X1] :
( in(unordered_pair(singleton(sK8(sK10(powerset(powerset(X0))),X1)),unordered_pair(sK8(sK10(powerset(powerset(X0))),X1),X2)),powerset(X0))
| ~ in(X2,X3)
| ~ in(sK9(sK10(powerset(powerset(X0))),X1),X3)
| ~ in(sK8(sK10(powerset(powerset(X0))),X1),X3)
| ~ sP0(powerset(X0),X3)
| empty(powerset(X0))
| ~ subset(unordered_pair(singleton(sK9(sK10(powerset(powerset(X0))),X1)),unordered_pair(X2,sK9(sK10(powerset(powerset(X0))),X1))),X0)
| sP0(sK10(powerset(powerset(X0))),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_982])]) ).
fof(f3459,plain,
( spl17_363
<=> ! [X4,X0,X3,X2,X1] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X1,X0)),powerset(X2))
| in(unordered_pair(singleton(X0),unordered_pair(X0,X3)),powerset(X2))
| ~ in(X3,X4)
| ~ in(X1,X4)
| ~ in(X0,X4)
| ~ sP0(powerset(X2),X4)
| empty(powerset(X2))
| ~ subset(unordered_pair(singleton(X1),unordered_pair(X3,X1)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_363])]) ).
fof(f3482,plain,
( ! [X2,X3,X0,X1] :
( in(unordered_pair(singleton(sK8(sK10(powerset(powerset(X0))),X1)),unordered_pair(sK8(sK10(powerset(powerset(X0))),X1),X2)),powerset(X0))
| ~ in(X2,X3)
| ~ in(sK9(sK10(powerset(powerset(X0))),X1),X3)
| ~ in(sK8(sK10(powerset(powerset(X0))),X1),X3)
| ~ sP0(powerset(X0),X3)
| empty(powerset(X0))
| ~ subset(unordered_pair(singleton(sK9(sK10(powerset(powerset(X0))),X1)),unordered_pair(X2,sK9(sK10(powerset(powerset(X0))),X1))),X0)
| sP0(sK10(powerset(powerset(X0))),X1) )
| ~ spl17_320
| ~ spl17_363 ),
inference(duplicate_literal_removal,[],[f3474]) ).
fof(f3474,plain,
( ! [X2,X3,X0,X1] :
( in(unordered_pair(singleton(sK8(sK10(powerset(powerset(X0))),X1)),unordered_pair(sK8(sK10(powerset(powerset(X0))),X1),X2)),powerset(X0))
| ~ in(X2,X3)
| ~ in(sK9(sK10(powerset(powerset(X0))),X1),X3)
| ~ in(sK8(sK10(powerset(powerset(X0))),X1),X3)
| ~ sP0(powerset(X0),X3)
| empty(powerset(X0))
| ~ subset(unordered_pair(singleton(sK9(sK10(powerset(powerset(X0))),X1)),unordered_pair(X2,sK9(sK10(powerset(powerset(X0))),X1))),X0)
| empty(powerset(X0))
| sP0(sK10(powerset(powerset(X0))),X1) )
| ~ spl17_320
| ~ spl17_363 ),
inference(resolution,[],[f3460,f2870]) ).
fof(f3460,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X1,X0)),powerset(X2))
| in(unordered_pair(singleton(X0),unordered_pair(X0,X3)),powerset(X2))
| ~ in(X3,X4)
| ~ in(X1,X4)
| ~ in(X0,X4)
| ~ sP0(powerset(X2),X4)
| empty(powerset(X2))
| ~ subset(unordered_pair(singleton(X1),unordered_pair(X3,X1)),X2) )
| ~ spl17_363 ),
inference(avatar_component_clause,[],[f3459]) ).
fof(f13284,plain,
( spl17_981
| ~ spl17_321
| ~ spl17_363 ),
inference(avatar_split_clause,[],[f3480,f3459,f2873,f13282]) ).
fof(f13282,plain,
( spl17_981
<=> ! [X0,X3,X2,X1] :
( in(unordered_pair(singleton(sK7(sK10(powerset(powerset(X0))),X1)),unordered_pair(sK7(sK10(powerset(powerset(X0))),X1),X2)),powerset(X0))
| ~ in(X2,X3)
| ~ in(sK8(sK10(powerset(powerset(X0))),X1),X3)
| ~ in(sK7(sK10(powerset(powerset(X0))),X1),X3)
| ~ sP0(powerset(X0),X3)
| empty(powerset(X0))
| ~ subset(unordered_pair(singleton(sK8(sK10(powerset(powerset(X0))),X1)),unordered_pair(X2,sK8(sK10(powerset(powerset(X0))),X1))),X0)
| sP0(sK10(powerset(powerset(X0))),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_981])]) ).
fof(f3480,plain,
( ! [X2,X3,X0,X1] :
( in(unordered_pair(singleton(sK7(sK10(powerset(powerset(X0))),X1)),unordered_pair(sK7(sK10(powerset(powerset(X0))),X1),X2)),powerset(X0))
| ~ in(X2,X3)
| ~ in(sK8(sK10(powerset(powerset(X0))),X1),X3)
| ~ in(sK7(sK10(powerset(powerset(X0))),X1),X3)
| ~ sP0(powerset(X0),X3)
| empty(powerset(X0))
| ~ subset(unordered_pair(singleton(sK8(sK10(powerset(powerset(X0))),X1)),unordered_pair(X2,sK8(sK10(powerset(powerset(X0))),X1))),X0)
| sP0(sK10(powerset(powerset(X0))),X1) )
| ~ spl17_321
| ~ spl17_363 ),
inference(duplicate_literal_removal,[],[f3477]) ).
fof(f3477,plain,
( ! [X2,X3,X0,X1] :
( in(unordered_pair(singleton(sK7(sK10(powerset(powerset(X0))),X1)),unordered_pair(sK7(sK10(powerset(powerset(X0))),X1),X2)),powerset(X0))
| ~ in(X2,X3)
| ~ in(sK8(sK10(powerset(powerset(X0))),X1),X3)
| ~ in(sK7(sK10(powerset(powerset(X0))),X1),X3)
| ~ sP0(powerset(X0),X3)
| empty(powerset(X0))
| ~ subset(unordered_pair(singleton(sK8(sK10(powerset(powerset(X0))),X1)),unordered_pair(X2,sK8(sK10(powerset(powerset(X0))),X1))),X0)
| empty(powerset(X0))
| sP0(sK10(powerset(powerset(X0))),X1) )
| ~ spl17_321
| ~ spl17_363 ),
inference(resolution,[],[f3460,f2874]) ).
fof(f13280,plain,
( spl17_980
| ~ spl17_224
| ~ spl17_328 ),
inference(avatar_split_clause,[],[f3078,f3042,f1808,f13278]) ).
fof(f13278,plain,
( spl17_980
<=> ! [X0,X1] :
( sP0(sK6(powerset(X0)),X1)
| element(sK10(sK6(unordered_pair(singleton(sK7(sK6(powerset(X0)),X1)),unordered_pair(sK8(sK6(powerset(X0)),X1),sK7(sK6(powerset(X0)),X1))))),X0)
| empty(powerset(X0))
| empty(sK6(unordered_pair(singleton(sK7(sK6(powerset(X0)),X1)),unordered_pair(sK8(sK6(powerset(X0)),X1),sK7(sK6(powerset(X0)),X1)))))
| empty(unordered_pair(singleton(sK7(sK6(powerset(X0)),X1)),unordered_pair(sK8(sK6(powerset(X0)),X1),sK7(sK6(powerset(X0)),X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_980])]) ).
fof(f3078,plain,
( ! [X0,X1] :
( sP0(sK6(powerset(X0)),X1)
| element(sK10(sK6(unordered_pair(singleton(sK7(sK6(powerset(X0)),X1)),unordered_pair(sK8(sK6(powerset(X0)),X1),sK7(sK6(powerset(X0)),X1))))),X0)
| empty(powerset(X0))
| empty(sK6(unordered_pair(singleton(sK7(sK6(powerset(X0)),X1)),unordered_pair(sK8(sK6(powerset(X0)),X1),sK7(sK6(powerset(X0)),X1)))))
| empty(unordered_pair(singleton(sK7(sK6(powerset(X0)),X1)),unordered_pair(sK8(sK6(powerset(X0)),X1),sK7(sK6(powerset(X0)),X1)))) )
| ~ spl17_224
| ~ spl17_328 ),
inference(resolution,[],[f3043,f1809]) ).
fof(f13276,plain,
( spl17_979
| ~ spl17_224
| ~ spl17_326 ),
inference(avatar_split_clause,[],[f3060,f3034,f1808,f13274]) ).
fof(f13274,plain,
( spl17_979
<=> ! [X0,X1] :
( sP0(sK6(powerset(X0)),X1)
| element(sK10(sK6(unordered_pair(singleton(sK8(sK6(powerset(X0)),X1)),unordered_pair(sK9(sK6(powerset(X0)),X1),sK8(sK6(powerset(X0)),X1))))),X0)
| empty(powerset(X0))
| empty(sK6(unordered_pair(singleton(sK8(sK6(powerset(X0)),X1)),unordered_pair(sK9(sK6(powerset(X0)),X1),sK8(sK6(powerset(X0)),X1)))))
| empty(unordered_pair(singleton(sK8(sK6(powerset(X0)),X1)),unordered_pair(sK9(sK6(powerset(X0)),X1),sK8(sK6(powerset(X0)),X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_979])]) ).
fof(f3060,plain,
( ! [X0,X1] :
( sP0(sK6(powerset(X0)),X1)
| element(sK10(sK6(unordered_pair(singleton(sK8(sK6(powerset(X0)),X1)),unordered_pair(sK9(sK6(powerset(X0)),X1),sK8(sK6(powerset(X0)),X1))))),X0)
| empty(powerset(X0))
| empty(sK6(unordered_pair(singleton(sK8(sK6(powerset(X0)),X1)),unordered_pair(sK9(sK6(powerset(X0)),X1),sK8(sK6(powerset(X0)),X1)))))
| empty(unordered_pair(singleton(sK8(sK6(powerset(X0)),X1)),unordered_pair(sK9(sK6(powerset(X0)),X1),sK8(sK6(powerset(X0)),X1)))) )
| ~ spl17_224
| ~ spl17_326 ),
inference(resolution,[],[f3035,f1809]) ).
fof(f13269,plain,
( spl17_978
| ~ spl17_207
| ~ spl17_312 ),
inference(avatar_split_clause,[],[f2790,f2730,f1686,f13267]) ).
fof(f13267,plain,
( spl17_978
<=> ! [X0,X3,X2,X1] :
( sP0(sK6(the_InternalRel(X0)),X1)
| empty(the_InternalRel(X0))
| in(unordered_pair(singleton(sK7(sK6(the_InternalRel(X0)),X1)),unordered_pair(sK7(sK6(the_InternalRel(X0)),X1),X2)),the_InternalRel(X0))
| ~ in(X2,X3)
| ~ in(sK8(sK6(the_InternalRel(X0)),X1),X3)
| ~ in(sK7(sK6(the_InternalRel(X0)),X1),X3)
| ~ sP0(the_InternalRel(X0),X3)
| ~ related(X0,sK8(sK6(the_InternalRel(X0)),X1),X2)
| ~ element(X2,the_carrier(X0))
| ~ element(sK8(sK6(the_InternalRel(X0)),X1),the_carrier(X0))
| ~ rel_str(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_978])]) ).
fof(f2790,plain,
( ! [X2,X3,X0,X1] :
( sP0(sK6(the_InternalRel(X0)),X1)
| empty(the_InternalRel(X0))
| in(unordered_pair(singleton(sK7(sK6(the_InternalRel(X0)),X1)),unordered_pair(sK7(sK6(the_InternalRel(X0)),X1),X2)),the_InternalRel(X0))
| ~ in(X2,X3)
| ~ in(sK8(sK6(the_InternalRel(X0)),X1),X3)
| ~ in(sK7(sK6(the_InternalRel(X0)),X1),X3)
| ~ sP0(the_InternalRel(X0),X3)
| ~ related(X0,sK8(sK6(the_InternalRel(X0)),X1),X2)
| ~ element(X2,the_carrier(X0))
| ~ element(sK8(sK6(the_InternalRel(X0)),X1),the_carrier(X0))
| ~ rel_str(X0) )
| ~ spl17_207
| ~ spl17_312 ),
inference(resolution,[],[f2731,f1687]) ).
fof(f13265,plain,
( spl17_977
| ~ spl17_207
| ~ spl17_311 ),
inference(avatar_split_clause,[],[f2741,f2726,f1686,f13263]) ).
fof(f13263,plain,
( spl17_977
<=> ! [X0,X3,X2,X1] :
( sP0(sK6(the_InternalRel(X0)),X1)
| empty(the_InternalRel(X0))
| in(unordered_pair(singleton(sK8(sK6(the_InternalRel(X0)),X1)),unordered_pair(sK8(sK6(the_InternalRel(X0)),X1),X2)),the_InternalRel(X0))
| ~ in(X2,X3)
| ~ in(sK9(sK6(the_InternalRel(X0)),X1),X3)
| ~ in(sK8(sK6(the_InternalRel(X0)),X1),X3)
| ~ sP0(the_InternalRel(X0),X3)
| ~ related(X0,sK9(sK6(the_InternalRel(X0)),X1),X2)
| ~ element(X2,the_carrier(X0))
| ~ element(sK9(sK6(the_InternalRel(X0)),X1),the_carrier(X0))
| ~ rel_str(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_977])]) ).
fof(f2741,plain,
( ! [X2,X3,X0,X1] :
( sP0(sK6(the_InternalRel(X0)),X1)
| empty(the_InternalRel(X0))
| in(unordered_pair(singleton(sK8(sK6(the_InternalRel(X0)),X1)),unordered_pair(sK8(sK6(the_InternalRel(X0)),X1),X2)),the_InternalRel(X0))
| ~ in(X2,X3)
| ~ in(sK9(sK6(the_InternalRel(X0)),X1),X3)
| ~ in(sK8(sK6(the_InternalRel(X0)),X1),X3)
| ~ sP0(the_InternalRel(X0),X3)
| ~ related(X0,sK9(sK6(the_InternalRel(X0)),X1),X2)
| ~ element(X2,the_carrier(X0))
| ~ element(sK9(sK6(the_InternalRel(X0)),X1),the_carrier(X0))
| ~ rel_str(X0) )
| ~ spl17_207
| ~ spl17_311 ),
inference(resolution,[],[f2727,f1687]) ).
fof(f13257,plain,
( spl17_976
| ~ spl17_108
| ~ spl17_519 ),
inference(avatar_split_clause,[],[f5518,f5207,f864,f13255]) ).
fof(f13255,plain,
( spl17_976
<=> ! [X0,X1] :
( ~ in(powerset(cartesian_product2(X0,X1)),the_InternalRel(sK2))
| empty(powerset(cartesian_product2(X0,X1)))
| ~ relation_of2_as_subset(cartesian_product2(sK16,sK16),X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_976])]) ).
fof(f864,plain,
( spl17_108
<=> ! [X2,X0,X1] :
( ~ relation_of2_as_subset(X0,X1,X2)
| empty(powerset(cartesian_product2(X1,X2)))
| in(X0,powerset(cartesian_product2(X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_108])]) ).
fof(f5207,plain,
( spl17_519
<=> ! [X0] :
( ~ in(X0,the_InternalRel(sK2))
| ~ in(cartesian_product2(sK16,sK16),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_519])]) ).
fof(f5518,plain,
( ! [X0,X1] :
( ~ in(powerset(cartesian_product2(X0,X1)),the_InternalRel(sK2))
| empty(powerset(cartesian_product2(X0,X1)))
| ~ relation_of2_as_subset(cartesian_product2(sK16,sK16),X0,X1) )
| ~ spl17_108
| ~ spl17_519 ),
inference(resolution,[],[f5208,f865]) ).
fof(f865,plain,
( ! [X2,X0,X1] :
( in(X0,powerset(cartesian_product2(X1,X2)))
| empty(powerset(cartesian_product2(X1,X2)))
| ~ relation_of2_as_subset(X0,X1,X2) )
| ~ spl17_108 ),
inference(avatar_component_clause,[],[f864]) ).
fof(f5208,plain,
( ! [X0] :
( ~ in(cartesian_product2(sK16,sK16),X0)
| ~ in(X0,the_InternalRel(sK2)) )
| ~ spl17_519 ),
inference(avatar_component_clause,[],[f5207]) ).
fof(f13253,plain,
( spl17_975
| ~ spl17_108
| ~ spl17_351 ),
inference(avatar_split_clause,[],[f3370,f3348,f864,f13251]) ).
fof(f13251,plain,
( spl17_975
<=> ! [X4,X0,X3,X2,X1] :
( in(unordered_pair(singleton(X0),unordered_pair(X0,sK8(powerset(cartesian_product2(X1,X2)),X3))),powerset(cartesian_product2(X1,X2)))
| ~ in(sK8(powerset(cartesian_product2(X1,X2)),X3),X4)
| ~ in(sK7(powerset(cartesian_product2(X1,X2)),X3),X4)
| ~ in(X0,X4)
| ~ sP0(powerset(cartesian_product2(X1,X2)),X4)
| sP0(powerset(cartesian_product2(X1,X2)),X3)
| empty(powerset(cartesian_product2(X1,X2)))
| ~ relation_of2_as_subset(unordered_pair(singleton(X0),unordered_pair(sK7(powerset(cartesian_product2(X1,X2)),X3),X0)),X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_975])]) ).
fof(f3348,plain,
( spl17_351
<=> ! [X0,X3,X2,X1] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(sK7(X1,X2),X0)),X1)
| in(unordered_pair(singleton(X0),unordered_pair(X0,sK8(X1,X2))),X1)
| ~ in(sK8(X1,X2),X3)
| ~ in(sK7(X1,X2),X3)
| ~ in(X0,X3)
| ~ sP0(X1,X3)
| sP0(X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_351])]) ).
fof(f3370,plain,
( ! [X2,X3,X0,X1,X4] :
( in(unordered_pair(singleton(X0),unordered_pair(X0,sK8(powerset(cartesian_product2(X1,X2)),X3))),powerset(cartesian_product2(X1,X2)))
| ~ in(sK8(powerset(cartesian_product2(X1,X2)),X3),X4)
| ~ in(sK7(powerset(cartesian_product2(X1,X2)),X3),X4)
| ~ in(X0,X4)
| ~ sP0(powerset(cartesian_product2(X1,X2)),X4)
| sP0(powerset(cartesian_product2(X1,X2)),X3)
| empty(powerset(cartesian_product2(X1,X2)))
| ~ relation_of2_as_subset(unordered_pair(singleton(X0),unordered_pair(sK7(powerset(cartesian_product2(X1,X2)),X3),X0)),X1,X2) )
| ~ spl17_108
| ~ spl17_351 ),
inference(resolution,[],[f3349,f865]) ).
fof(f3349,plain,
( ! [X2,X3,X0,X1] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(sK7(X1,X2),X0)),X1)
| in(unordered_pair(singleton(X0),unordered_pair(X0,sK8(X1,X2))),X1)
| ~ in(sK8(X1,X2),X3)
| ~ in(sK7(X1,X2),X3)
| ~ in(X0,X3)
| ~ sP0(X1,X3)
| sP0(X1,X2) )
| ~ spl17_351 ),
inference(avatar_component_clause,[],[f3348]) ).
fof(f13249,plain,
( spl17_974
| ~ spl17_108
| ~ spl17_350 ),
inference(avatar_split_clause,[],[f3356,f3344,f864,f13247]) ).
fof(f13247,plain,
( spl17_974
<=> ! [X4,X0,X3,X2,X1] :
( in(unordered_pair(singleton(X0),unordered_pair(X0,sK9(powerset(cartesian_product2(X1,X2)),X3))),powerset(cartesian_product2(X1,X2)))
| ~ in(sK9(powerset(cartesian_product2(X1,X2)),X3),X4)
| ~ in(sK8(powerset(cartesian_product2(X1,X2)),X3),X4)
| ~ in(X0,X4)
| ~ sP0(powerset(cartesian_product2(X1,X2)),X4)
| sP0(powerset(cartesian_product2(X1,X2)),X3)
| empty(powerset(cartesian_product2(X1,X2)))
| ~ relation_of2_as_subset(unordered_pair(singleton(X0),unordered_pair(sK8(powerset(cartesian_product2(X1,X2)),X3),X0)),X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_974])]) ).
fof(f3344,plain,
( spl17_350
<=> ! [X0,X3,X2,X1] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(sK8(X1,X2),X0)),X1)
| in(unordered_pair(singleton(X0),unordered_pair(X0,sK9(X1,X2))),X1)
| ~ in(sK9(X1,X2),X3)
| ~ in(sK8(X1,X2),X3)
| ~ in(X0,X3)
| ~ sP0(X1,X3)
| sP0(X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_350])]) ).
fof(f3356,plain,
( ! [X2,X3,X0,X1,X4] :
( in(unordered_pair(singleton(X0),unordered_pair(X0,sK9(powerset(cartesian_product2(X1,X2)),X3))),powerset(cartesian_product2(X1,X2)))
| ~ in(sK9(powerset(cartesian_product2(X1,X2)),X3),X4)
| ~ in(sK8(powerset(cartesian_product2(X1,X2)),X3),X4)
| ~ in(X0,X4)
| ~ sP0(powerset(cartesian_product2(X1,X2)),X4)
| sP0(powerset(cartesian_product2(X1,X2)),X3)
| empty(powerset(cartesian_product2(X1,X2)))
| ~ relation_of2_as_subset(unordered_pair(singleton(X0),unordered_pair(sK8(powerset(cartesian_product2(X1,X2)),X3),X0)),X1,X2) )
| ~ spl17_108
| ~ spl17_350 ),
inference(resolution,[],[f3345,f865]) ).
fof(f3345,plain,
( ! [X2,X3,X0,X1] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(sK8(X1,X2),X0)),X1)
| in(unordered_pair(singleton(X0),unordered_pair(X0,sK9(X1,X2))),X1)
| ~ in(sK9(X1,X2),X3)
| ~ in(sK8(X1,X2),X3)
| ~ in(X0,X3)
| ~ sP0(X1,X3)
| sP0(X1,X2) )
| ~ spl17_350 ),
inference(avatar_component_clause,[],[f3344]) ).
fof(f13141,plain,
( spl17_973
| ~ spl17_200
| ~ spl17_321 ),
inference(avatar_split_clause,[],[f2933,f2873,f1624,f13139]) ).
fof(f13139,plain,
( spl17_973
<=> ! [X4,X0,X3,X2,X1] :
( empty(cartesian_product2(X0,X1))
| sP0(sK10(powerset(cartesian_product2(X0,X1))),X2)
| in(unordered_pair(singleton(X3),unordered_pair(X3,sK8(sK10(powerset(cartesian_product2(X0,X1))),X2))),cartesian_product2(X0,X1))
| ~ in(sK8(sK10(powerset(cartesian_product2(X0,X1))),X2),X4)
| ~ in(sK7(sK10(powerset(cartesian_product2(X0,X1))),X2),X4)
| ~ in(X3,X4)
| ~ sP0(cartesian_product2(X0,X1),X4)
| ~ in(sK7(sK10(powerset(cartesian_product2(X0,X1))),X2),X1)
| ~ in(X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_973])]) ).
fof(f1624,plain,
( spl17_200
<=> ! [X5,X4,X0,X3,X2,X1] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X1,X0)),cartesian_product2(X2,X3))
| in(unordered_pair(singleton(X4),unordered_pair(X4,X1)),cartesian_product2(X2,X3))
| ~ in(X1,X5)
| ~ in(X0,X5)
| ~ in(X4,X5)
| ~ sP0(cartesian_product2(X2,X3),X5)
| ~ in(X0,X3)
| ~ in(X4,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_200])]) ).
fof(f2933,plain,
( ! [X2,X3,X0,X1,X4] :
( empty(cartesian_product2(X0,X1))
| sP0(sK10(powerset(cartesian_product2(X0,X1))),X2)
| in(unordered_pair(singleton(X3),unordered_pair(X3,sK8(sK10(powerset(cartesian_product2(X0,X1))),X2))),cartesian_product2(X0,X1))
| ~ in(sK8(sK10(powerset(cartesian_product2(X0,X1))),X2),X4)
| ~ in(sK7(sK10(powerset(cartesian_product2(X0,X1))),X2),X4)
| ~ in(X3,X4)
| ~ sP0(cartesian_product2(X0,X1),X4)
| ~ in(sK7(sK10(powerset(cartesian_product2(X0,X1))),X2),X1)
| ~ in(X3,X0) )
| ~ spl17_200
| ~ spl17_321 ),
inference(resolution,[],[f2874,f1625]) ).
fof(f1625,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X1,X0)),cartesian_product2(X2,X3))
| in(unordered_pair(singleton(X4),unordered_pair(X4,X1)),cartesian_product2(X2,X3))
| ~ in(X1,X5)
| ~ in(X0,X5)
| ~ in(X4,X5)
| ~ sP0(cartesian_product2(X2,X3),X5)
| ~ in(X0,X3)
| ~ in(X4,X2) )
| ~ spl17_200 ),
inference(avatar_component_clause,[],[f1624]) ).
fof(f13137,plain,
( spl17_972
| ~ spl17_200
| ~ spl17_320 ),
inference(avatar_split_clause,[],[f2882,f2869,f1624,f13135]) ).
fof(f13135,plain,
( spl17_972
<=> ! [X4,X0,X3,X2,X1] :
( empty(cartesian_product2(X0,X1))
| sP0(sK10(powerset(cartesian_product2(X0,X1))),X2)
| in(unordered_pair(singleton(X3),unordered_pair(X3,sK9(sK10(powerset(cartesian_product2(X0,X1))),X2))),cartesian_product2(X0,X1))
| ~ in(sK9(sK10(powerset(cartesian_product2(X0,X1))),X2),X4)
| ~ in(sK8(sK10(powerset(cartesian_product2(X0,X1))),X2),X4)
| ~ in(X3,X4)
| ~ sP0(cartesian_product2(X0,X1),X4)
| ~ in(sK8(sK10(powerset(cartesian_product2(X0,X1))),X2),X1)
| ~ in(X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_972])]) ).
fof(f2882,plain,
( ! [X2,X3,X0,X1,X4] :
( empty(cartesian_product2(X0,X1))
| sP0(sK10(powerset(cartesian_product2(X0,X1))),X2)
| in(unordered_pair(singleton(X3),unordered_pair(X3,sK9(sK10(powerset(cartesian_product2(X0,X1))),X2))),cartesian_product2(X0,X1))
| ~ in(sK9(sK10(powerset(cartesian_product2(X0,X1))),X2),X4)
| ~ in(sK8(sK10(powerset(cartesian_product2(X0,X1))),X2),X4)
| ~ in(X3,X4)
| ~ sP0(cartesian_product2(X0,X1),X4)
| ~ in(sK8(sK10(powerset(cartesian_product2(X0,X1))),X2),X1)
| ~ in(X3,X0) )
| ~ spl17_200
| ~ spl17_320 ),
inference(resolution,[],[f2870,f1625]) ).
fof(f13133,plain,
( spl17_971
| ~ spl17_201
| ~ spl17_312 ),
inference(avatar_split_clause,[],[f2783,f2730,f1628,f13131]) ).
fof(f13131,plain,
( spl17_971
<=> ! [X4,X0,X3,X2,X1] :
( sP0(sK6(cartesian_product2(X0,X1)),X2)
| empty(cartesian_product2(X0,X1))
| in(unordered_pair(singleton(sK7(sK6(cartesian_product2(X0,X1)),X2)),unordered_pair(sK7(sK6(cartesian_product2(X0,X1)),X2),X3)),cartesian_product2(X0,X1))
| ~ in(X3,X4)
| ~ in(sK8(sK6(cartesian_product2(X0,X1)),X2),X4)
| ~ in(sK7(sK6(cartesian_product2(X0,X1)),X2),X4)
| ~ sP0(cartesian_product2(X0,X1),X4)
| ~ in(X3,X1)
| ~ in(sK8(sK6(cartesian_product2(X0,X1)),X2),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_971])]) ).
fof(f2783,plain,
( ! [X2,X3,X0,X1,X4] :
( sP0(sK6(cartesian_product2(X0,X1)),X2)
| empty(cartesian_product2(X0,X1))
| in(unordered_pair(singleton(sK7(sK6(cartesian_product2(X0,X1)),X2)),unordered_pair(sK7(sK6(cartesian_product2(X0,X1)),X2),X3)),cartesian_product2(X0,X1))
| ~ in(X3,X4)
| ~ in(sK8(sK6(cartesian_product2(X0,X1)),X2),X4)
| ~ in(sK7(sK6(cartesian_product2(X0,X1)),X2),X4)
| ~ sP0(cartesian_product2(X0,X1),X4)
| ~ in(X3,X1)
| ~ in(sK8(sK6(cartesian_product2(X0,X1)),X2),X0) )
| ~ spl17_201
| ~ spl17_312 ),
inference(resolution,[],[f2731,f1629]) ).
fof(f13129,plain,
( spl17_970
| ~ spl17_201
| ~ spl17_311 ),
inference(avatar_split_clause,[],[f2734,f2726,f1628,f13127]) ).
fof(f13127,plain,
( spl17_970
<=> ! [X4,X0,X3,X2,X1] :
( sP0(sK6(cartesian_product2(X0,X1)),X2)
| empty(cartesian_product2(X0,X1))
| in(unordered_pair(singleton(sK8(sK6(cartesian_product2(X0,X1)),X2)),unordered_pair(sK8(sK6(cartesian_product2(X0,X1)),X2),X3)),cartesian_product2(X0,X1))
| ~ in(X3,X4)
| ~ in(sK9(sK6(cartesian_product2(X0,X1)),X2),X4)
| ~ in(sK8(sK6(cartesian_product2(X0,X1)),X2),X4)
| ~ sP0(cartesian_product2(X0,X1),X4)
| ~ in(X3,X1)
| ~ in(sK9(sK6(cartesian_product2(X0,X1)),X2),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_970])]) ).
fof(f2734,plain,
( ! [X2,X3,X0,X1,X4] :
( sP0(sK6(cartesian_product2(X0,X1)),X2)
| empty(cartesian_product2(X0,X1))
| in(unordered_pair(singleton(sK8(sK6(cartesian_product2(X0,X1)),X2)),unordered_pair(sK8(sK6(cartesian_product2(X0,X1)),X2),X3)),cartesian_product2(X0,X1))
| ~ in(X3,X4)
| ~ in(sK9(sK6(cartesian_product2(X0,X1)),X2),X4)
| ~ in(sK8(sK6(cartesian_product2(X0,X1)),X2),X4)
| ~ sP0(cartesian_product2(X0,X1),X4)
| ~ in(X3,X1)
| ~ in(sK9(sK6(cartesian_product2(X0,X1)),X2),X0) )
| ~ spl17_201
| ~ spl17_311 ),
inference(resolution,[],[f2727,f1629]) ).
fof(f13122,plain,
( spl17_969
| ~ spl17_206
| ~ spl17_312 ),
inference(avatar_split_clause,[],[f2791,f2730,f1682,f13120]) ).
fof(f13120,plain,
( spl17_969
<=> ! [X0,X3,X2,X1] :
( sP0(sK6(the_InternalRel(X0)),X1)
| empty(the_InternalRel(X0))
| in(unordered_pair(singleton(X2),unordered_pair(X2,sK8(sK6(the_InternalRel(X0)),X1))),the_InternalRel(X0))
| ~ in(sK8(sK6(the_InternalRel(X0)),X1),X3)
| ~ in(sK7(sK6(the_InternalRel(X0)),X1),X3)
| ~ in(X2,X3)
| ~ sP0(the_InternalRel(X0),X3)
| ~ related(X0,X2,sK7(sK6(the_InternalRel(X0)),X1))
| ~ element(sK7(sK6(the_InternalRel(X0)),X1),the_carrier(X0))
| ~ element(X2,the_carrier(X0))
| ~ rel_str(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_969])]) ).
fof(f2791,plain,
( ! [X2,X3,X0,X1] :
( sP0(sK6(the_InternalRel(X0)),X1)
| empty(the_InternalRel(X0))
| in(unordered_pair(singleton(X2),unordered_pair(X2,sK8(sK6(the_InternalRel(X0)),X1))),the_InternalRel(X0))
| ~ in(sK8(sK6(the_InternalRel(X0)),X1),X3)
| ~ in(sK7(sK6(the_InternalRel(X0)),X1),X3)
| ~ in(X2,X3)
| ~ sP0(the_InternalRel(X0),X3)
| ~ related(X0,X2,sK7(sK6(the_InternalRel(X0)),X1))
| ~ element(sK7(sK6(the_InternalRel(X0)),X1),the_carrier(X0))
| ~ element(X2,the_carrier(X0))
| ~ rel_str(X0) )
| ~ spl17_206
| ~ spl17_312 ),
inference(resolution,[],[f2731,f1683]) ).
fof(f13118,plain,
( spl17_968
| ~ spl17_206
| ~ spl17_311 ),
inference(avatar_split_clause,[],[f2742,f2726,f1682,f13116]) ).
fof(f13116,plain,
( spl17_968
<=> ! [X0,X3,X2,X1] :
( sP0(sK6(the_InternalRel(X0)),X1)
| empty(the_InternalRel(X0))
| in(unordered_pair(singleton(X2),unordered_pair(X2,sK9(sK6(the_InternalRel(X0)),X1))),the_InternalRel(X0))
| ~ in(sK9(sK6(the_InternalRel(X0)),X1),X3)
| ~ in(sK8(sK6(the_InternalRel(X0)),X1),X3)
| ~ in(X2,X3)
| ~ sP0(the_InternalRel(X0),X3)
| ~ related(X0,X2,sK8(sK6(the_InternalRel(X0)),X1))
| ~ element(sK8(sK6(the_InternalRel(X0)),X1),the_carrier(X0))
| ~ element(X2,the_carrier(X0))
| ~ rel_str(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_968])]) ).
fof(f2742,plain,
( ! [X2,X3,X0,X1] :
( sP0(sK6(the_InternalRel(X0)),X1)
| empty(the_InternalRel(X0))
| in(unordered_pair(singleton(X2),unordered_pair(X2,sK9(sK6(the_InternalRel(X0)),X1))),the_InternalRel(X0))
| ~ in(sK9(sK6(the_InternalRel(X0)),X1),X3)
| ~ in(sK8(sK6(the_InternalRel(X0)),X1),X3)
| ~ in(X2,X3)
| ~ sP0(the_InternalRel(X0),X3)
| ~ related(X0,X2,sK8(sK6(the_InternalRel(X0)),X1))
| ~ element(sK8(sK6(the_InternalRel(X0)),X1),the_carrier(X0))
| ~ element(X2,the_carrier(X0))
| ~ rel_str(X0) )
| ~ spl17_206
| ~ spl17_311 ),
inference(resolution,[],[f2727,f1683]) ).
fof(f13106,plain,
( spl17_967
| ~ spl17_311
| ~ spl17_364 ),
inference(avatar_split_clause,[],[f3499,f3463,f2726,f13104]) ).
fof(f13104,plain,
( spl17_967
<=> ! [X0,X3,X2,X1] :
( ~ subset(unordered_pair(singleton(sK9(sK6(powerset(X0)),X1)),unordered_pair(sK9(sK6(powerset(X0)),X1),X2)),X0)
| empty(powerset(X0))
| in(unordered_pair(singleton(sK8(sK6(powerset(X0)),X1)),unordered_pair(sK8(sK6(powerset(X0)),X1),X2)),powerset(X0))
| ~ in(X2,X3)
| ~ in(sK9(sK6(powerset(X0)),X1),X3)
| ~ in(sK8(sK6(powerset(X0)),X1),X3)
| ~ sP0(powerset(X0),X3)
| sP0(sK6(powerset(X0)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_967])]) ).
fof(f3499,plain,
( ! [X2,X3,X0,X1] :
( ~ subset(unordered_pair(singleton(sK9(sK6(powerset(X0)),X1)),unordered_pair(sK9(sK6(powerset(X0)),X1),X2)),X0)
| empty(powerset(X0))
| in(unordered_pair(singleton(sK8(sK6(powerset(X0)),X1)),unordered_pair(sK8(sK6(powerset(X0)),X1),X2)),powerset(X0))
| ~ in(X2,X3)
| ~ in(sK9(sK6(powerset(X0)),X1),X3)
| ~ in(sK8(sK6(powerset(X0)),X1),X3)
| ~ sP0(powerset(X0),X3)
| sP0(sK6(powerset(X0)),X1) )
| ~ spl17_311
| ~ spl17_364 ),
inference(duplicate_literal_removal,[],[f3489]) ).
fof(f3489,plain,
( ! [X2,X3,X0,X1] :
( ~ subset(unordered_pair(singleton(sK9(sK6(powerset(X0)),X1)),unordered_pair(sK9(sK6(powerset(X0)),X1),X2)),X0)
| empty(powerset(X0))
| in(unordered_pair(singleton(sK8(sK6(powerset(X0)),X1)),unordered_pair(sK8(sK6(powerset(X0)),X1),X2)),powerset(X0))
| ~ in(X2,X3)
| ~ in(sK9(sK6(powerset(X0)),X1),X3)
| ~ in(sK8(sK6(powerset(X0)),X1),X3)
| ~ sP0(powerset(X0),X3)
| sP0(sK6(powerset(X0)),X1)
| empty(powerset(X0)) )
| ~ spl17_311
| ~ spl17_364 ),
inference(resolution,[],[f3464,f2727]) ).
fof(f13102,plain,
( spl17_966
| ~ spl17_312
| ~ spl17_364 ),
inference(avatar_split_clause,[],[f3497,f3463,f2730,f13100]) ).
fof(f13100,plain,
( spl17_966
<=> ! [X0,X3,X2,X1] :
( ~ subset(unordered_pair(singleton(sK8(sK6(powerset(X0)),X1)),unordered_pair(sK8(sK6(powerset(X0)),X1),X2)),X0)
| empty(powerset(X0))
| in(unordered_pair(singleton(sK7(sK6(powerset(X0)),X1)),unordered_pair(sK7(sK6(powerset(X0)),X1),X2)),powerset(X0))
| ~ in(X2,X3)
| ~ in(sK8(sK6(powerset(X0)),X1),X3)
| ~ in(sK7(sK6(powerset(X0)),X1),X3)
| ~ sP0(powerset(X0),X3)
| sP0(sK6(powerset(X0)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_966])]) ).
fof(f3497,plain,
( ! [X2,X3,X0,X1] :
( ~ subset(unordered_pair(singleton(sK8(sK6(powerset(X0)),X1)),unordered_pair(sK8(sK6(powerset(X0)),X1),X2)),X0)
| empty(powerset(X0))
| in(unordered_pair(singleton(sK7(sK6(powerset(X0)),X1)),unordered_pair(sK7(sK6(powerset(X0)),X1),X2)),powerset(X0))
| ~ in(X2,X3)
| ~ in(sK8(sK6(powerset(X0)),X1),X3)
| ~ in(sK7(sK6(powerset(X0)),X1),X3)
| ~ sP0(powerset(X0),X3)
| sP0(sK6(powerset(X0)),X1) )
| ~ spl17_312
| ~ spl17_364 ),
inference(duplicate_literal_removal,[],[f3492]) ).
fof(f3492,plain,
( ! [X2,X3,X0,X1] :
( ~ subset(unordered_pair(singleton(sK8(sK6(powerset(X0)),X1)),unordered_pair(sK8(sK6(powerset(X0)),X1),X2)),X0)
| empty(powerset(X0))
| in(unordered_pair(singleton(sK7(sK6(powerset(X0)),X1)),unordered_pair(sK7(sK6(powerset(X0)),X1),X2)),powerset(X0))
| ~ in(X2,X3)
| ~ in(sK8(sK6(powerset(X0)),X1),X3)
| ~ in(sK7(sK6(powerset(X0)),X1),X3)
| ~ sP0(powerset(X0),X3)
| sP0(sK6(powerset(X0)),X1)
| empty(powerset(X0)) )
| ~ spl17_312
| ~ spl17_364 ),
inference(resolution,[],[f3464,f2731]) ).
fof(f13098,plain,
( spl17_965
| ~ spl17_311
| ~ spl17_363 ),
inference(avatar_split_clause,[],[f3483,f3459,f2726,f13096]) ).
fof(f13096,plain,
( spl17_965
<=> ! [X0,X3,X2,X1] :
( in(unordered_pair(singleton(sK8(sK6(powerset(X0)),X1)),unordered_pair(sK8(sK6(powerset(X0)),X1),X2)),powerset(X0))
| ~ in(X2,X3)
| ~ in(sK9(sK6(powerset(X0)),X1),X3)
| ~ in(sK8(sK6(powerset(X0)),X1),X3)
| ~ sP0(powerset(X0),X3)
| empty(powerset(X0))
| ~ subset(unordered_pair(singleton(sK9(sK6(powerset(X0)),X1)),unordered_pair(X2,sK9(sK6(powerset(X0)),X1))),X0)
| sP0(sK6(powerset(X0)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_965])]) ).
fof(f3483,plain,
( ! [X2,X3,X0,X1] :
( in(unordered_pair(singleton(sK8(sK6(powerset(X0)),X1)),unordered_pair(sK8(sK6(powerset(X0)),X1),X2)),powerset(X0))
| ~ in(X2,X3)
| ~ in(sK9(sK6(powerset(X0)),X1),X3)
| ~ in(sK8(sK6(powerset(X0)),X1),X3)
| ~ sP0(powerset(X0),X3)
| empty(powerset(X0))
| ~ subset(unordered_pair(singleton(sK9(sK6(powerset(X0)),X1)),unordered_pair(X2,sK9(sK6(powerset(X0)),X1))),X0)
| sP0(sK6(powerset(X0)),X1) )
| ~ spl17_311
| ~ spl17_363 ),
inference(duplicate_literal_removal,[],[f3473]) ).
fof(f3473,plain,
( ! [X2,X3,X0,X1] :
( in(unordered_pair(singleton(sK8(sK6(powerset(X0)),X1)),unordered_pair(sK8(sK6(powerset(X0)),X1),X2)),powerset(X0))
| ~ in(X2,X3)
| ~ in(sK9(sK6(powerset(X0)),X1),X3)
| ~ in(sK8(sK6(powerset(X0)),X1),X3)
| ~ sP0(powerset(X0),X3)
| empty(powerset(X0))
| ~ subset(unordered_pair(singleton(sK9(sK6(powerset(X0)),X1)),unordered_pair(X2,sK9(sK6(powerset(X0)),X1))),X0)
| sP0(sK6(powerset(X0)),X1)
| empty(powerset(X0)) )
| ~ spl17_311
| ~ spl17_363 ),
inference(resolution,[],[f3460,f2727]) ).
fof(f13094,plain,
( spl17_964
| ~ spl17_312
| ~ spl17_363 ),
inference(avatar_split_clause,[],[f3481,f3459,f2730,f13092]) ).
fof(f13092,plain,
( spl17_964
<=> ! [X0,X3,X2,X1] :
( in(unordered_pair(singleton(sK7(sK6(powerset(X0)),X1)),unordered_pair(sK7(sK6(powerset(X0)),X1),X2)),powerset(X0))
| ~ in(X2,X3)
| ~ in(sK8(sK6(powerset(X0)),X1),X3)
| ~ in(sK7(sK6(powerset(X0)),X1),X3)
| ~ sP0(powerset(X0),X3)
| empty(powerset(X0))
| ~ subset(unordered_pair(singleton(sK8(sK6(powerset(X0)),X1)),unordered_pair(X2,sK8(sK6(powerset(X0)),X1))),X0)
| sP0(sK6(powerset(X0)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_964])]) ).
fof(f3481,plain,
( ! [X2,X3,X0,X1] :
( in(unordered_pair(singleton(sK7(sK6(powerset(X0)),X1)),unordered_pair(sK7(sK6(powerset(X0)),X1),X2)),powerset(X0))
| ~ in(X2,X3)
| ~ in(sK8(sK6(powerset(X0)),X1),X3)
| ~ in(sK7(sK6(powerset(X0)),X1),X3)
| ~ sP0(powerset(X0),X3)
| empty(powerset(X0))
| ~ subset(unordered_pair(singleton(sK8(sK6(powerset(X0)),X1)),unordered_pair(X2,sK8(sK6(powerset(X0)),X1))),X0)
| sP0(sK6(powerset(X0)),X1) )
| ~ spl17_312
| ~ spl17_363 ),
inference(duplicate_literal_removal,[],[f3476]) ).
fof(f3476,plain,
( ! [X2,X3,X0,X1] :
( in(unordered_pair(singleton(sK7(sK6(powerset(X0)),X1)),unordered_pair(sK7(sK6(powerset(X0)),X1),X2)),powerset(X0))
| ~ in(X2,X3)
| ~ in(sK8(sK6(powerset(X0)),X1),X3)
| ~ in(sK7(sK6(powerset(X0)),X1),X3)
| ~ sP0(powerset(X0),X3)
| empty(powerset(X0))
| ~ subset(unordered_pair(singleton(sK8(sK6(powerset(X0)),X1)),unordered_pair(X2,sK8(sK6(powerset(X0)),X1))),X0)
| sP0(sK6(powerset(X0)),X1)
| empty(powerset(X0)) )
| ~ spl17_312
| ~ spl17_363 ),
inference(resolution,[],[f3460,f2731]) ).
fof(f13032,plain,
( ~ spl17_2
| spl17_962
| ~ spl17_963
| ~ spl17_4
| ~ spl17_106
| ~ spl17_118
| ~ spl17_393 ),
inference(avatar_split_clause,[],[f12128,f3736,f956,f849,f194,f13029,f13025,f184]) ).
fof(f13025,plain,
( spl17_962
<=> related(sK2,sK4,sK4) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_962])]) ).
fof(f13029,plain,
( spl17_963
<=> related(sK2,sK5,sK4) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_963])]) ).
fof(f849,plain,
( spl17_106
<=> in(sK4,the_carrier(sK2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_106])]) ).
fof(f956,plain,
( spl17_118
<=> ! [X2,X0,X1] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X1,X0)),the_InternalRel(X2))
| related(X2,X0,X1)
| ~ element(X1,the_carrier(X2))
| ~ element(X0,the_carrier(X2))
| ~ rel_str(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_118])]) ).
fof(f12128,plain,
( ~ in(sK4,the_carrier(sK2))
| ~ element(sK4,the_carrier(sK2))
| ~ related(sK2,sK5,sK4)
| related(sK2,sK4,sK4)
| ~ rel_str(sK2)
| ~ spl17_118
| ~ spl17_393 ),
inference(duplicate_literal_removal,[],[f12100]) ).
fof(f12100,plain,
( ~ in(sK4,the_carrier(sK2))
| ~ element(sK4,the_carrier(sK2))
| ~ related(sK2,sK5,sK4)
| related(sK2,sK4,sK4)
| ~ element(sK4,the_carrier(sK2))
| ~ element(sK4,the_carrier(sK2))
| ~ rel_str(sK2)
| ~ spl17_118
| ~ spl17_393 ),
inference(resolution,[],[f3737,f957]) ).
fof(f957,plain,
( ! [X2,X0,X1] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X1,X0)),the_InternalRel(X2))
| related(X2,X0,X1)
| ~ element(X1,the_carrier(X2))
| ~ element(X0,the_carrier(X2))
| ~ rel_str(X2) )
| ~ spl17_118 ),
inference(avatar_component_clause,[],[f956]) ).
fof(f12999,plain,
( spl17_961
| ~ spl17_41
| ~ spl17_358 ),
inference(avatar_split_clause,[],[f3431,f3403,f363,f12997]) ).
fof(f12997,plain,
( spl17_961
<=> ! [X0,X3,X2,X1] :
( sP0(powerset(powerset(cartesian_product2(X0,X1))),X2)
| sP0(X3,unordered_pair(singleton(sK7(powerset(powerset(cartesian_product2(X0,X1))),X2)),unordered_pair(sK8(powerset(powerset(cartesian_product2(X0,X1))),X2),sK7(powerset(powerset(cartesian_product2(X0,X1))),X2))))
| relation(sK9(X3,unordered_pair(singleton(sK7(powerset(powerset(cartesian_product2(X0,X1))),X2)),unordered_pair(sK8(powerset(powerset(cartesian_product2(X0,X1))),X2),sK7(powerset(powerset(cartesian_product2(X0,X1))),X2))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_961])]) ).
fof(f3403,plain,
( spl17_358
<=> ! [X2,X0,X1] :
( element(sK9(X0,unordered_pair(singleton(sK7(powerset(X1),X2)),unordered_pair(sK8(powerset(X1),X2),sK7(powerset(X1),X2)))),X1)
| sP0(powerset(X1),X2)
| sP0(X0,unordered_pair(singleton(sK7(powerset(X1),X2)),unordered_pair(sK8(powerset(X1),X2),sK7(powerset(X1),X2)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_358])]) ).
fof(f3431,plain,
( ! [X2,X3,X0,X1] :
( sP0(powerset(powerset(cartesian_product2(X0,X1))),X2)
| sP0(X3,unordered_pair(singleton(sK7(powerset(powerset(cartesian_product2(X0,X1))),X2)),unordered_pair(sK8(powerset(powerset(cartesian_product2(X0,X1))),X2),sK7(powerset(powerset(cartesian_product2(X0,X1))),X2))))
| relation(sK9(X3,unordered_pair(singleton(sK7(powerset(powerset(cartesian_product2(X0,X1))),X2)),unordered_pair(sK8(powerset(powerset(cartesian_product2(X0,X1))),X2),sK7(powerset(powerset(cartesian_product2(X0,X1))),X2))))) )
| ~ spl17_41
| ~ spl17_358 ),
inference(resolution,[],[f3404,f364]) ).
fof(f3404,plain,
( ! [X2,X0,X1] :
( element(sK9(X0,unordered_pair(singleton(sK7(powerset(X1),X2)),unordered_pair(sK8(powerset(X1),X2),sK7(powerset(X1),X2)))),X1)
| sP0(powerset(X1),X2)
| sP0(X0,unordered_pair(singleton(sK7(powerset(X1),X2)),unordered_pair(sK8(powerset(X1),X2),sK7(powerset(X1),X2)))) )
| ~ spl17_358 ),
inference(avatar_component_clause,[],[f3403]) ).
fof(f12995,plain,
( spl17_960
| ~ spl17_41
| ~ spl17_356 ),
inference(avatar_split_clause,[],[f3427,f3395,f363,f12993]) ).
fof(f12993,plain,
( spl17_960
<=> ! [X0,X3,X2,X1] :
( sP0(powerset(powerset(cartesian_product2(X0,X1))),X2)
| sP0(X3,unordered_pair(singleton(sK7(powerset(powerset(cartesian_product2(X0,X1))),X2)),unordered_pair(sK8(powerset(powerset(cartesian_product2(X0,X1))),X2),sK7(powerset(powerset(cartesian_product2(X0,X1))),X2))))
| relation(sK8(X3,unordered_pair(singleton(sK7(powerset(powerset(cartesian_product2(X0,X1))),X2)),unordered_pair(sK8(powerset(powerset(cartesian_product2(X0,X1))),X2),sK7(powerset(powerset(cartesian_product2(X0,X1))),X2))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_960])]) ).
fof(f3395,plain,
( spl17_356
<=> ! [X2,X0,X1] :
( element(sK8(X0,unordered_pair(singleton(sK7(powerset(X1),X2)),unordered_pair(sK8(powerset(X1),X2),sK7(powerset(X1),X2)))),X1)
| sP0(powerset(X1),X2)
| sP0(X0,unordered_pair(singleton(sK7(powerset(X1),X2)),unordered_pair(sK8(powerset(X1),X2),sK7(powerset(X1),X2)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_356])]) ).
fof(f3427,plain,
( ! [X2,X3,X0,X1] :
( sP0(powerset(powerset(cartesian_product2(X0,X1))),X2)
| sP0(X3,unordered_pair(singleton(sK7(powerset(powerset(cartesian_product2(X0,X1))),X2)),unordered_pair(sK8(powerset(powerset(cartesian_product2(X0,X1))),X2),sK7(powerset(powerset(cartesian_product2(X0,X1))),X2))))
| relation(sK8(X3,unordered_pair(singleton(sK7(powerset(powerset(cartesian_product2(X0,X1))),X2)),unordered_pair(sK8(powerset(powerset(cartesian_product2(X0,X1))),X2),sK7(powerset(powerset(cartesian_product2(X0,X1))),X2))))) )
| ~ spl17_41
| ~ spl17_356 ),
inference(resolution,[],[f3396,f364]) ).
fof(f3396,plain,
( ! [X2,X0,X1] :
( element(sK8(X0,unordered_pair(singleton(sK7(powerset(X1),X2)),unordered_pair(sK8(powerset(X1),X2),sK7(powerset(X1),X2)))),X1)
| sP0(powerset(X1),X2)
| sP0(X0,unordered_pair(singleton(sK7(powerset(X1),X2)),unordered_pair(sK8(powerset(X1),X2),sK7(powerset(X1),X2)))) )
| ~ spl17_356 ),
inference(avatar_component_clause,[],[f3395]) ).
fof(f12991,plain,
( spl17_959
| ~ spl17_41
| ~ spl17_355 ),
inference(avatar_split_clause,[],[f3423,f3391,f363,f12989]) ).
fof(f12989,plain,
( spl17_959
<=> ! [X0,X3,X2,X1] :
( sP0(powerset(powerset(cartesian_product2(X0,X1))),X2)
| sP0(X3,unordered_pair(singleton(sK7(powerset(powerset(cartesian_product2(X0,X1))),X2)),unordered_pair(sK8(powerset(powerset(cartesian_product2(X0,X1))),X2),sK7(powerset(powerset(cartesian_product2(X0,X1))),X2))))
| relation(sK7(X3,unordered_pair(singleton(sK7(powerset(powerset(cartesian_product2(X0,X1))),X2)),unordered_pair(sK8(powerset(powerset(cartesian_product2(X0,X1))),X2),sK7(powerset(powerset(cartesian_product2(X0,X1))),X2))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_959])]) ).
fof(f3391,plain,
( spl17_355
<=> ! [X2,X0,X1] :
( element(sK7(X0,unordered_pair(singleton(sK7(powerset(X1),X2)),unordered_pair(sK8(powerset(X1),X2),sK7(powerset(X1),X2)))),X1)
| sP0(powerset(X1),X2)
| sP0(X0,unordered_pair(singleton(sK7(powerset(X1),X2)),unordered_pair(sK8(powerset(X1),X2),sK7(powerset(X1),X2)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_355])]) ).
fof(f3423,plain,
( ! [X2,X3,X0,X1] :
( sP0(powerset(powerset(cartesian_product2(X0,X1))),X2)
| sP0(X3,unordered_pair(singleton(sK7(powerset(powerset(cartesian_product2(X0,X1))),X2)),unordered_pair(sK8(powerset(powerset(cartesian_product2(X0,X1))),X2),sK7(powerset(powerset(cartesian_product2(X0,X1))),X2))))
| relation(sK7(X3,unordered_pair(singleton(sK7(powerset(powerset(cartesian_product2(X0,X1))),X2)),unordered_pair(sK8(powerset(powerset(cartesian_product2(X0,X1))),X2),sK7(powerset(powerset(cartesian_product2(X0,X1))),X2))))) )
| ~ spl17_41
| ~ spl17_355 ),
inference(resolution,[],[f3392,f364]) ).
fof(f3392,plain,
( ! [X2,X0,X1] :
( element(sK7(X0,unordered_pair(singleton(sK7(powerset(X1),X2)),unordered_pair(sK8(powerset(X1),X2),sK7(powerset(X1),X2)))),X1)
| sP0(powerset(X1),X2)
| sP0(X0,unordered_pair(singleton(sK7(powerset(X1),X2)),unordered_pair(sK8(powerset(X1),X2),sK7(powerset(X1),X2)))) )
| ~ spl17_355 ),
inference(avatar_component_clause,[],[f3391]) ).
fof(f12987,plain,
( spl17_958
| ~ spl17_41
| ~ spl17_354 ),
inference(avatar_split_clause,[],[f3419,f3387,f363,f12985]) ).
fof(f12985,plain,
( spl17_958
<=> ! [X0,X3,X2,X1] :
( sP0(powerset(powerset(cartesian_product2(X0,X1))),X2)
| sP0(X3,unordered_pair(singleton(sK8(powerset(powerset(cartesian_product2(X0,X1))),X2)),unordered_pair(sK9(powerset(powerset(cartesian_product2(X0,X1))),X2),sK8(powerset(powerset(cartesian_product2(X0,X1))),X2))))
| relation(sK9(X3,unordered_pair(singleton(sK8(powerset(powerset(cartesian_product2(X0,X1))),X2)),unordered_pair(sK9(powerset(powerset(cartesian_product2(X0,X1))),X2),sK8(powerset(powerset(cartesian_product2(X0,X1))),X2))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_958])]) ).
fof(f3387,plain,
( spl17_354
<=> ! [X2,X0,X1] :
( element(sK9(X0,unordered_pair(singleton(sK8(powerset(X1),X2)),unordered_pair(sK9(powerset(X1),X2),sK8(powerset(X1),X2)))),X1)
| sP0(powerset(X1),X2)
| sP0(X0,unordered_pair(singleton(sK8(powerset(X1),X2)),unordered_pair(sK9(powerset(X1),X2),sK8(powerset(X1),X2)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_354])]) ).
fof(f3419,plain,
( ! [X2,X3,X0,X1] :
( sP0(powerset(powerset(cartesian_product2(X0,X1))),X2)
| sP0(X3,unordered_pair(singleton(sK8(powerset(powerset(cartesian_product2(X0,X1))),X2)),unordered_pair(sK9(powerset(powerset(cartesian_product2(X0,X1))),X2),sK8(powerset(powerset(cartesian_product2(X0,X1))),X2))))
| relation(sK9(X3,unordered_pair(singleton(sK8(powerset(powerset(cartesian_product2(X0,X1))),X2)),unordered_pair(sK9(powerset(powerset(cartesian_product2(X0,X1))),X2),sK8(powerset(powerset(cartesian_product2(X0,X1))),X2))))) )
| ~ spl17_41
| ~ spl17_354 ),
inference(resolution,[],[f3388,f364]) ).
fof(f3388,plain,
( ! [X2,X0,X1] :
( element(sK9(X0,unordered_pair(singleton(sK8(powerset(X1),X2)),unordered_pair(sK9(powerset(X1),X2),sK8(powerset(X1),X2)))),X1)
| sP0(powerset(X1),X2)
| sP0(X0,unordered_pair(singleton(sK8(powerset(X1),X2)),unordered_pair(sK9(powerset(X1),X2),sK8(powerset(X1),X2)))) )
| ~ spl17_354 ),
inference(avatar_component_clause,[],[f3387]) ).
fof(f12983,plain,
( spl17_957
| ~ spl17_41
| ~ spl17_353 ),
inference(avatar_split_clause,[],[f3415,f3383,f363,f12981]) ).
fof(f12981,plain,
( spl17_957
<=> ! [X0,X3,X2,X1] :
( sP0(powerset(powerset(cartesian_product2(X0,X1))),X2)
| sP0(X3,unordered_pair(singleton(sK8(powerset(powerset(cartesian_product2(X0,X1))),X2)),unordered_pair(sK9(powerset(powerset(cartesian_product2(X0,X1))),X2),sK8(powerset(powerset(cartesian_product2(X0,X1))),X2))))
| relation(sK8(X3,unordered_pair(singleton(sK8(powerset(powerset(cartesian_product2(X0,X1))),X2)),unordered_pair(sK9(powerset(powerset(cartesian_product2(X0,X1))),X2),sK8(powerset(powerset(cartesian_product2(X0,X1))),X2))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_957])]) ).
fof(f3383,plain,
( spl17_353
<=> ! [X2,X0,X1] :
( element(sK8(X0,unordered_pair(singleton(sK8(powerset(X1),X2)),unordered_pair(sK9(powerset(X1),X2),sK8(powerset(X1),X2)))),X1)
| sP0(powerset(X1),X2)
| sP0(X0,unordered_pair(singleton(sK8(powerset(X1),X2)),unordered_pair(sK9(powerset(X1),X2),sK8(powerset(X1),X2)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_353])]) ).
fof(f3415,plain,
( ! [X2,X3,X0,X1] :
( sP0(powerset(powerset(cartesian_product2(X0,X1))),X2)
| sP0(X3,unordered_pair(singleton(sK8(powerset(powerset(cartesian_product2(X0,X1))),X2)),unordered_pair(sK9(powerset(powerset(cartesian_product2(X0,X1))),X2),sK8(powerset(powerset(cartesian_product2(X0,X1))),X2))))
| relation(sK8(X3,unordered_pair(singleton(sK8(powerset(powerset(cartesian_product2(X0,X1))),X2)),unordered_pair(sK9(powerset(powerset(cartesian_product2(X0,X1))),X2),sK8(powerset(powerset(cartesian_product2(X0,X1))),X2))))) )
| ~ spl17_41
| ~ spl17_353 ),
inference(resolution,[],[f3384,f364]) ).
fof(f3384,plain,
( ! [X2,X0,X1] :
( element(sK8(X0,unordered_pair(singleton(sK8(powerset(X1),X2)),unordered_pair(sK9(powerset(X1),X2),sK8(powerset(X1),X2)))),X1)
| sP0(powerset(X1),X2)
| sP0(X0,unordered_pair(singleton(sK8(powerset(X1),X2)),unordered_pair(sK9(powerset(X1),X2),sK8(powerset(X1),X2)))) )
| ~ spl17_353 ),
inference(avatar_component_clause,[],[f3383]) ).
fof(f12979,plain,
( spl17_956
| ~ spl17_41
| ~ spl17_352 ),
inference(avatar_split_clause,[],[f3411,f3379,f363,f12977]) ).
fof(f12977,plain,
( spl17_956
<=> ! [X0,X3,X2,X1] :
( sP0(powerset(powerset(cartesian_product2(X0,X1))),X2)
| sP0(X3,unordered_pair(singleton(sK8(powerset(powerset(cartesian_product2(X0,X1))),X2)),unordered_pair(sK9(powerset(powerset(cartesian_product2(X0,X1))),X2),sK8(powerset(powerset(cartesian_product2(X0,X1))),X2))))
| relation(sK7(X3,unordered_pair(singleton(sK8(powerset(powerset(cartesian_product2(X0,X1))),X2)),unordered_pair(sK9(powerset(powerset(cartesian_product2(X0,X1))),X2),sK8(powerset(powerset(cartesian_product2(X0,X1))),X2))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_956])]) ).
fof(f3379,plain,
( spl17_352
<=> ! [X2,X0,X1] :
( element(sK7(X0,unordered_pair(singleton(sK8(powerset(X1),X2)),unordered_pair(sK9(powerset(X1),X2),sK8(powerset(X1),X2)))),X1)
| sP0(powerset(X1),X2)
| sP0(X0,unordered_pair(singleton(sK8(powerset(X1),X2)),unordered_pair(sK9(powerset(X1),X2),sK8(powerset(X1),X2)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_352])]) ).
fof(f3411,plain,
( ! [X2,X3,X0,X1] :
( sP0(powerset(powerset(cartesian_product2(X0,X1))),X2)
| sP0(X3,unordered_pair(singleton(sK8(powerset(powerset(cartesian_product2(X0,X1))),X2)),unordered_pair(sK9(powerset(powerset(cartesian_product2(X0,X1))),X2),sK8(powerset(powerset(cartesian_product2(X0,X1))),X2))))
| relation(sK7(X3,unordered_pair(singleton(sK8(powerset(powerset(cartesian_product2(X0,X1))),X2)),unordered_pair(sK9(powerset(powerset(cartesian_product2(X0,X1))),X2),sK8(powerset(powerset(cartesian_product2(X0,X1))),X2))))) )
| ~ spl17_41
| ~ spl17_352 ),
inference(resolution,[],[f3380,f364]) ).
fof(f3380,plain,
( ! [X2,X0,X1] :
( element(sK7(X0,unordered_pair(singleton(sK8(powerset(X1),X2)),unordered_pair(sK9(powerset(X1),X2),sK8(powerset(X1),X2)))),X1)
| sP0(powerset(X1),X2)
| sP0(X0,unordered_pair(singleton(sK8(powerset(X1),X2)),unordered_pair(sK9(powerset(X1),X2),sK8(powerset(X1),X2)))) )
| ~ spl17_352 ),
inference(avatar_component_clause,[],[f3379]) ).
fof(f12975,plain,
( spl17_955
| ~ spl17_200
| ~ spl17_312 ),
inference(avatar_split_clause,[],[f2784,f2730,f1624,f12973]) ).
fof(f12973,plain,
( spl17_955
<=> ! [X4,X0,X3,X2,X1] :
( sP0(sK6(cartesian_product2(X0,X1)),X2)
| empty(cartesian_product2(X0,X1))
| in(unordered_pair(singleton(X3),unordered_pair(X3,sK8(sK6(cartesian_product2(X0,X1)),X2))),cartesian_product2(X0,X1))
| ~ in(sK8(sK6(cartesian_product2(X0,X1)),X2),X4)
| ~ in(sK7(sK6(cartesian_product2(X0,X1)),X2),X4)
| ~ in(X3,X4)
| ~ sP0(cartesian_product2(X0,X1),X4)
| ~ in(sK7(sK6(cartesian_product2(X0,X1)),X2),X1)
| ~ in(X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_955])]) ).
fof(f2784,plain,
( ! [X2,X3,X0,X1,X4] :
( sP0(sK6(cartesian_product2(X0,X1)),X2)
| empty(cartesian_product2(X0,X1))
| in(unordered_pair(singleton(X3),unordered_pair(X3,sK8(sK6(cartesian_product2(X0,X1)),X2))),cartesian_product2(X0,X1))
| ~ in(sK8(sK6(cartesian_product2(X0,X1)),X2),X4)
| ~ in(sK7(sK6(cartesian_product2(X0,X1)),X2),X4)
| ~ in(X3,X4)
| ~ sP0(cartesian_product2(X0,X1),X4)
| ~ in(sK7(sK6(cartesian_product2(X0,X1)),X2),X1)
| ~ in(X3,X0) )
| ~ spl17_200
| ~ spl17_312 ),
inference(resolution,[],[f2731,f1625]) ).
fof(f12971,plain,
( spl17_954
| ~ spl17_200
| ~ spl17_311 ),
inference(avatar_split_clause,[],[f2735,f2726,f1624,f12969]) ).
fof(f12969,plain,
( spl17_954
<=> ! [X4,X0,X3,X2,X1] :
( sP0(sK6(cartesian_product2(X0,X1)),X2)
| empty(cartesian_product2(X0,X1))
| in(unordered_pair(singleton(X3),unordered_pair(X3,sK9(sK6(cartesian_product2(X0,X1)),X2))),cartesian_product2(X0,X1))
| ~ in(sK9(sK6(cartesian_product2(X0,X1)),X2),X4)
| ~ in(sK8(sK6(cartesian_product2(X0,X1)),X2),X4)
| ~ in(X3,X4)
| ~ sP0(cartesian_product2(X0,X1),X4)
| ~ in(sK8(sK6(cartesian_product2(X0,X1)),X2),X1)
| ~ in(X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_954])]) ).
fof(f2735,plain,
( ! [X2,X3,X0,X1,X4] :
( sP0(sK6(cartesian_product2(X0,X1)),X2)
| empty(cartesian_product2(X0,X1))
| in(unordered_pair(singleton(X3),unordered_pair(X3,sK9(sK6(cartesian_product2(X0,X1)),X2))),cartesian_product2(X0,X1))
| ~ in(sK9(sK6(cartesian_product2(X0,X1)),X2),X4)
| ~ in(sK8(sK6(cartesian_product2(X0,X1)),X2),X4)
| ~ in(X3,X4)
| ~ sP0(cartesian_product2(X0,X1),X4)
| ~ in(sK8(sK6(cartesian_product2(X0,X1)),X2),X1)
| ~ in(X3,X0) )
| ~ spl17_200
| ~ spl17_311 ),
inference(resolution,[],[f2727,f1625]) ).
fof(f12967,plain,
( spl17_953
| ~ spl17_188
| ~ spl17_266 ),
inference(avatar_split_clause,[],[f2219,f2147,f1511,f12965]) ).
fof(f12965,plain,
( spl17_953
<=> ! [X2,X0,X1] :
( empty(unordered_pair(singleton(sK7(powerset(X0),X1)),unordered_pair(sK8(powerset(X0),X1),sK7(powerset(X0),X1))))
| sP0(X2,sK10(powerset(unordered_pair(singleton(sK7(powerset(X0),X1)),unordered_pair(sK8(powerset(X0),X1),sK7(powerset(X0),X1))))))
| element(sK9(X2,sK10(powerset(unordered_pair(singleton(sK7(powerset(X0),X1)),unordered_pair(sK8(powerset(X0),X1),sK7(powerset(X0),X1)))))),X0)
| sP0(powerset(X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_953])]) ).
fof(f2219,plain,
( ! [X2,X0,X1] :
( empty(unordered_pair(singleton(sK7(powerset(X0),X1)),unordered_pair(sK8(powerset(X0),X1),sK7(powerset(X0),X1))))
| sP0(X2,sK10(powerset(unordered_pair(singleton(sK7(powerset(X0),X1)),unordered_pair(sK8(powerset(X0),X1),sK7(powerset(X0),X1))))))
| element(sK9(X2,sK10(powerset(unordered_pair(singleton(sK7(powerset(X0),X1)),unordered_pair(sK8(powerset(X0),X1),sK7(powerset(X0),X1)))))),X0)
| sP0(powerset(X0),X1) )
| ~ spl17_188
| ~ spl17_266 ),
inference(resolution,[],[f2148,f1512]) ).
fof(f12963,plain,
( spl17_952
| ~ spl17_187
| ~ spl17_266 ),
inference(avatar_split_clause,[],[f2217,f2147,f1507,f12961]) ).
fof(f12961,plain,
( spl17_952
<=> ! [X2,X0,X1] :
( empty(unordered_pair(singleton(sK8(powerset(X0),X1)),unordered_pair(sK9(powerset(X0),X1),sK8(powerset(X0),X1))))
| sP0(X2,sK10(powerset(unordered_pair(singleton(sK8(powerset(X0),X1)),unordered_pair(sK9(powerset(X0),X1),sK8(powerset(X0),X1))))))
| element(sK9(X2,sK10(powerset(unordered_pair(singleton(sK8(powerset(X0),X1)),unordered_pair(sK9(powerset(X0),X1),sK8(powerset(X0),X1)))))),X0)
| sP0(powerset(X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_952])]) ).
fof(f2217,plain,
( ! [X2,X0,X1] :
( empty(unordered_pair(singleton(sK8(powerset(X0),X1)),unordered_pair(sK9(powerset(X0),X1),sK8(powerset(X0),X1))))
| sP0(X2,sK10(powerset(unordered_pair(singleton(sK8(powerset(X0),X1)),unordered_pair(sK9(powerset(X0),X1),sK8(powerset(X0),X1))))))
| element(sK9(X2,sK10(powerset(unordered_pair(singleton(sK8(powerset(X0),X1)),unordered_pair(sK9(powerset(X0),X1),sK8(powerset(X0),X1)))))),X0)
| sP0(powerset(X0),X1) )
| ~ spl17_187
| ~ spl17_266 ),
inference(resolution,[],[f2148,f1508]) ).
fof(f12959,plain,
( spl17_951
| ~ spl17_188
| ~ spl17_265 ),
inference(avatar_split_clause,[],[f2198,f2143,f1511,f12957]) ).
fof(f12957,plain,
( spl17_951
<=> ! [X2,X0,X1] :
( empty(unordered_pair(singleton(sK7(powerset(X0),X1)),unordered_pair(sK8(powerset(X0),X1),sK7(powerset(X0),X1))))
| sP0(X2,sK10(powerset(unordered_pair(singleton(sK7(powerset(X0),X1)),unordered_pair(sK8(powerset(X0),X1),sK7(powerset(X0),X1))))))
| element(sK8(X2,sK10(powerset(unordered_pair(singleton(sK7(powerset(X0),X1)),unordered_pair(sK8(powerset(X0),X1),sK7(powerset(X0),X1)))))),X0)
| sP0(powerset(X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_951])]) ).
fof(f2198,plain,
( ! [X2,X0,X1] :
( empty(unordered_pair(singleton(sK7(powerset(X0),X1)),unordered_pair(sK8(powerset(X0),X1),sK7(powerset(X0),X1))))
| sP0(X2,sK10(powerset(unordered_pair(singleton(sK7(powerset(X0),X1)),unordered_pair(sK8(powerset(X0),X1),sK7(powerset(X0),X1))))))
| element(sK8(X2,sK10(powerset(unordered_pair(singleton(sK7(powerset(X0),X1)),unordered_pair(sK8(powerset(X0),X1),sK7(powerset(X0),X1)))))),X0)
| sP0(powerset(X0),X1) )
| ~ spl17_188
| ~ spl17_265 ),
inference(resolution,[],[f2144,f1512]) ).
fof(f12955,plain,
( spl17_950
| ~ spl17_187
| ~ spl17_265 ),
inference(avatar_split_clause,[],[f2196,f2143,f1507,f12953]) ).
fof(f12953,plain,
( spl17_950
<=> ! [X2,X0,X1] :
( empty(unordered_pair(singleton(sK8(powerset(X0),X1)),unordered_pair(sK9(powerset(X0),X1),sK8(powerset(X0),X1))))
| sP0(X2,sK10(powerset(unordered_pair(singleton(sK8(powerset(X0),X1)),unordered_pair(sK9(powerset(X0),X1),sK8(powerset(X0),X1))))))
| element(sK8(X2,sK10(powerset(unordered_pair(singleton(sK8(powerset(X0),X1)),unordered_pair(sK9(powerset(X0),X1),sK8(powerset(X0),X1)))))),X0)
| sP0(powerset(X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_950])]) ).
fof(f2196,plain,
( ! [X2,X0,X1] :
( empty(unordered_pair(singleton(sK8(powerset(X0),X1)),unordered_pair(sK9(powerset(X0),X1),sK8(powerset(X0),X1))))
| sP0(X2,sK10(powerset(unordered_pair(singleton(sK8(powerset(X0),X1)),unordered_pair(sK9(powerset(X0),X1),sK8(powerset(X0),X1))))))
| element(sK8(X2,sK10(powerset(unordered_pair(singleton(sK8(powerset(X0),X1)),unordered_pair(sK9(powerset(X0),X1),sK8(powerset(X0),X1)))))),X0)
| sP0(powerset(X0),X1) )
| ~ spl17_187
| ~ spl17_265 ),
inference(resolution,[],[f2144,f1508]) ).
fof(f12951,plain,
( spl17_949
| ~ spl17_188
| ~ spl17_264 ),
inference(avatar_split_clause,[],[f2177,f2139,f1511,f12949]) ).
fof(f12949,plain,
( spl17_949
<=> ! [X2,X0,X1] :
( empty(unordered_pair(singleton(sK7(powerset(X0),X1)),unordered_pair(sK8(powerset(X0),X1),sK7(powerset(X0),X1))))
| sP0(X2,sK10(powerset(unordered_pair(singleton(sK7(powerset(X0),X1)),unordered_pair(sK8(powerset(X0),X1),sK7(powerset(X0),X1))))))
| element(sK7(X2,sK10(powerset(unordered_pair(singleton(sK7(powerset(X0),X1)),unordered_pair(sK8(powerset(X0),X1),sK7(powerset(X0),X1)))))),X0)
| sP0(powerset(X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_949])]) ).
fof(f2177,plain,
( ! [X2,X0,X1] :
( empty(unordered_pair(singleton(sK7(powerset(X0),X1)),unordered_pair(sK8(powerset(X0),X1),sK7(powerset(X0),X1))))
| sP0(X2,sK10(powerset(unordered_pair(singleton(sK7(powerset(X0),X1)),unordered_pair(sK8(powerset(X0),X1),sK7(powerset(X0),X1))))))
| element(sK7(X2,sK10(powerset(unordered_pair(singleton(sK7(powerset(X0),X1)),unordered_pair(sK8(powerset(X0),X1),sK7(powerset(X0),X1)))))),X0)
| sP0(powerset(X0),X1) )
| ~ spl17_188
| ~ spl17_264 ),
inference(resolution,[],[f2140,f1512]) ).
fof(f12947,plain,
( spl17_948
| ~ spl17_187
| ~ spl17_264 ),
inference(avatar_split_clause,[],[f2175,f2139,f1507,f12945]) ).
fof(f12945,plain,
( spl17_948
<=> ! [X2,X0,X1] :
( empty(unordered_pair(singleton(sK8(powerset(X0),X1)),unordered_pair(sK9(powerset(X0),X1),sK8(powerset(X0),X1))))
| sP0(X2,sK10(powerset(unordered_pair(singleton(sK8(powerset(X0),X1)),unordered_pair(sK9(powerset(X0),X1),sK8(powerset(X0),X1))))))
| element(sK7(X2,sK10(powerset(unordered_pair(singleton(sK8(powerset(X0),X1)),unordered_pair(sK9(powerset(X0),X1),sK8(powerset(X0),X1)))))),X0)
| sP0(powerset(X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_948])]) ).
fof(f2175,plain,
( ! [X2,X0,X1] :
( empty(unordered_pair(singleton(sK8(powerset(X0),X1)),unordered_pair(sK9(powerset(X0),X1),sK8(powerset(X0),X1))))
| sP0(X2,sK10(powerset(unordered_pair(singleton(sK8(powerset(X0),X1)),unordered_pair(sK9(powerset(X0),X1),sK8(powerset(X0),X1))))))
| element(sK7(X2,sK10(powerset(unordered_pair(singleton(sK8(powerset(X0),X1)),unordered_pair(sK9(powerset(X0),X1),sK8(powerset(X0),X1)))))),X0)
| sP0(powerset(X0),X1) )
| ~ spl17_187
| ~ spl17_264 ),
inference(resolution,[],[f2140,f1508]) ).
fof(f12943,plain,
( spl17_654
| ~ spl17_30
| ~ spl17_667 ),
inference(avatar_split_clause,[],[f8411,f7804,f313,f7696]) ).
fof(f7696,plain,
( spl17_654
<=> ! [X0,X1] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),the_InternalRel(sK2))
| in(X1,sK16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_654])]) ).
fof(f7804,plain,
( spl17_667
<=> ! [X0,X1] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X1,X0)),the_InternalRel(sK2))
| in(X1,sK16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_667])]) ).
fof(f8411,plain,
( ! [X0,X1] :
( ~ in(unordered_pair(singleton(X1),unordered_pair(X1,X0)),the_InternalRel(sK2))
| in(X0,sK16) )
| ~ spl17_30
| ~ spl17_667 ),
inference(superposition,[],[f7805,f314]) ).
fof(f7805,plain,
( ! [X0,X1] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X1,X0)),the_InternalRel(sK2))
| in(X1,sK16) )
| ~ spl17_667 ),
inference(avatar_component_clause,[],[f7804]) ).
fof(f12898,plain,
( spl17_947
| ~ spl17_321
| ~ spl17_341 ),
inference(avatar_split_clause,[],[f3253,f3243,f2873,f12896]) ).
fof(f12896,plain,
( spl17_947
<=> ! [X0,X3,X2,X1] :
( ~ in(unordered_pair(singleton(sK8(sK10(powerset(X0)),X1)),unordered_pair(sK8(sK10(powerset(X0)),X1),X2)),X0)
| in(unordered_pair(singleton(sK7(sK10(powerset(X0)),X1)),unordered_pair(sK7(sK10(powerset(X0)),X1),X2)),X0)
| ~ in(X2,X3)
| ~ in(sK8(sK10(powerset(X0)),X1),X3)
| ~ in(sK7(sK10(powerset(X0)),X1),X3)
| ~ sP0(X0,X3)
| empty(X0)
| sP0(sK10(powerset(X0)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_947])]) ).
fof(f3243,plain,
( spl17_341
<=> ! [X4,X0,X3,X2,X1] :
( ~ in(unordered_pair(singleton(X1),unordered_pair(X1,X0)),X2)
| ~ in(unordered_pair(singleton(X3),unordered_pair(X1,X3)),X2)
| in(unordered_pair(singleton(X3),unordered_pair(X3,X0)),X2)
| ~ in(X0,X4)
| ~ in(X1,X4)
| ~ in(X3,X4)
| ~ sP0(X2,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_341])]) ).
fof(f3253,plain,
( ! [X2,X3,X0,X1] :
( ~ in(unordered_pair(singleton(sK8(sK10(powerset(X0)),X1)),unordered_pair(sK8(sK10(powerset(X0)),X1),X2)),X0)
| in(unordered_pair(singleton(sK7(sK10(powerset(X0)),X1)),unordered_pair(sK7(sK10(powerset(X0)),X1),X2)),X0)
| ~ in(X2,X3)
| ~ in(sK8(sK10(powerset(X0)),X1),X3)
| ~ in(sK7(sK10(powerset(X0)),X1),X3)
| ~ sP0(X0,X3)
| empty(X0)
| sP0(sK10(powerset(X0)),X1) )
| ~ spl17_321
| ~ spl17_341 ),
inference(resolution,[],[f3244,f2874]) ).
fof(f3244,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ in(unordered_pair(singleton(X3),unordered_pair(X1,X3)),X2)
| ~ in(unordered_pair(singleton(X1),unordered_pair(X1,X0)),X2)
| in(unordered_pair(singleton(X3),unordered_pair(X3,X0)),X2)
| ~ in(X0,X4)
| ~ in(X1,X4)
| ~ in(X3,X4)
| ~ sP0(X2,X4) )
| ~ spl17_341 ),
inference(avatar_component_clause,[],[f3243]) ).
fof(f12894,plain,
( spl17_946
| ~ spl17_320
| ~ spl17_341 ),
inference(avatar_split_clause,[],[f3250,f3243,f2869,f12892]) ).
fof(f12892,plain,
( spl17_946
<=> ! [X0,X3,X2,X1] :
( ~ in(unordered_pair(singleton(sK9(sK10(powerset(X0)),X1)),unordered_pair(sK9(sK10(powerset(X0)),X1),X2)),X0)
| in(unordered_pair(singleton(sK8(sK10(powerset(X0)),X1)),unordered_pair(sK8(sK10(powerset(X0)),X1),X2)),X0)
| ~ in(X2,X3)
| ~ in(sK9(sK10(powerset(X0)),X1),X3)
| ~ in(sK8(sK10(powerset(X0)),X1),X3)
| ~ sP0(X0,X3)
| empty(X0)
| sP0(sK10(powerset(X0)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_946])]) ).
fof(f3250,plain,
( ! [X2,X3,X0,X1] :
( ~ in(unordered_pair(singleton(sK9(sK10(powerset(X0)),X1)),unordered_pair(sK9(sK10(powerset(X0)),X1),X2)),X0)
| in(unordered_pair(singleton(sK8(sK10(powerset(X0)),X1)),unordered_pair(sK8(sK10(powerset(X0)),X1),X2)),X0)
| ~ in(X2,X3)
| ~ in(sK9(sK10(powerset(X0)),X1),X3)
| ~ in(sK8(sK10(powerset(X0)),X1),X3)
| ~ sP0(X0,X3)
| empty(X0)
| sP0(sK10(powerset(X0)),X1) )
| ~ spl17_320
| ~ spl17_341 ),
inference(resolution,[],[f3244,f2870]) ).
fof(f12890,plain,
( spl17_945
| ~ spl17_203
| ~ spl17_321 ),
inference(avatar_split_clause,[],[f2978,f2873,f1650,f12888]) ).
fof(f12888,plain,
( spl17_945
<=> ! [X0,X3,X2,X1] :
( empty(powerset(X0))
| sP0(sK10(powerset(powerset(X0))),X1)
| in(unordered_pair(singleton(X2),unordered_pair(X2,sK8(sK10(powerset(powerset(X0))),X1))),powerset(X0))
| ~ in(sK8(sK10(powerset(powerset(X0))),X1),X3)
| ~ in(sK7(sK10(powerset(powerset(X0))),X1),X3)
| ~ in(X2,X3)
| ~ sP0(powerset(X0),X3)
| ~ subset(unordered_pair(singleton(X2),unordered_pair(X2,sK7(sK10(powerset(powerset(X0))),X1))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_945])]) ).
fof(f1650,plain,
( spl17_203
<=> ! [X4,X0,X3,X2,X1] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X1,X0)),powerset(X2))
| in(unordered_pair(singleton(X3),unordered_pair(X3,X1)),powerset(X2))
| ~ in(X1,X4)
| ~ in(X0,X4)
| ~ in(X3,X4)
| ~ sP0(powerset(X2),X4)
| empty(powerset(X2))
| ~ subset(unordered_pair(singleton(X3),unordered_pair(X3,X0)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_203])]) ).
fof(f2978,plain,
( ! [X2,X3,X0,X1] :
( empty(powerset(X0))
| sP0(sK10(powerset(powerset(X0))),X1)
| in(unordered_pair(singleton(X2),unordered_pair(X2,sK8(sK10(powerset(powerset(X0))),X1))),powerset(X0))
| ~ in(sK8(sK10(powerset(powerset(X0))),X1),X3)
| ~ in(sK7(sK10(powerset(powerset(X0))),X1),X3)
| ~ in(X2,X3)
| ~ sP0(powerset(X0),X3)
| ~ subset(unordered_pair(singleton(X2),unordered_pair(X2,sK7(sK10(powerset(powerset(X0))),X1))),X0) )
| ~ spl17_203
| ~ spl17_321 ),
inference(duplicate_literal_removal,[],[f2937]) ).
fof(f2937,plain,
( ! [X2,X3,X0,X1] :
( empty(powerset(X0))
| sP0(sK10(powerset(powerset(X0))),X1)
| in(unordered_pair(singleton(X2),unordered_pair(X2,sK8(sK10(powerset(powerset(X0))),X1))),powerset(X0))
| ~ in(sK8(sK10(powerset(powerset(X0))),X1),X3)
| ~ in(sK7(sK10(powerset(powerset(X0))),X1),X3)
| ~ in(X2,X3)
| ~ sP0(powerset(X0),X3)
| empty(powerset(X0))
| ~ subset(unordered_pair(singleton(X2),unordered_pair(X2,sK7(sK10(powerset(powerset(X0))),X1))),X0) )
| ~ spl17_203
| ~ spl17_321 ),
inference(resolution,[],[f2874,f1651]) ).
fof(f1651,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X1,X0)),powerset(X2))
| in(unordered_pair(singleton(X3),unordered_pair(X3,X1)),powerset(X2))
| ~ in(X1,X4)
| ~ in(X0,X4)
| ~ in(X3,X4)
| ~ sP0(powerset(X2),X4)
| empty(powerset(X2))
| ~ subset(unordered_pair(singleton(X3),unordered_pair(X3,X0)),X2) )
| ~ spl17_203 ),
inference(avatar_component_clause,[],[f1650]) ).
fof(f12886,plain,
( spl17_944
| ~ spl17_203
| ~ spl17_320 ),
inference(avatar_split_clause,[],[f2927,f2869,f1650,f12884]) ).
fof(f12884,plain,
( spl17_944
<=> ! [X0,X3,X2,X1] :
( empty(powerset(X0))
| sP0(sK10(powerset(powerset(X0))),X1)
| in(unordered_pair(singleton(X2),unordered_pair(X2,sK9(sK10(powerset(powerset(X0))),X1))),powerset(X0))
| ~ in(sK9(sK10(powerset(powerset(X0))),X1),X3)
| ~ in(sK8(sK10(powerset(powerset(X0))),X1),X3)
| ~ in(X2,X3)
| ~ sP0(powerset(X0),X3)
| ~ subset(unordered_pair(singleton(X2),unordered_pair(X2,sK8(sK10(powerset(powerset(X0))),X1))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_944])]) ).
fof(f2927,plain,
( ! [X2,X3,X0,X1] :
( empty(powerset(X0))
| sP0(sK10(powerset(powerset(X0))),X1)
| in(unordered_pair(singleton(X2),unordered_pair(X2,sK9(sK10(powerset(powerset(X0))),X1))),powerset(X0))
| ~ in(sK9(sK10(powerset(powerset(X0))),X1),X3)
| ~ in(sK8(sK10(powerset(powerset(X0))),X1),X3)
| ~ in(X2,X3)
| ~ sP0(powerset(X0),X3)
| ~ subset(unordered_pair(singleton(X2),unordered_pair(X2,sK8(sK10(powerset(powerset(X0))),X1))),X0) )
| ~ spl17_203
| ~ spl17_320 ),
inference(duplicate_literal_removal,[],[f2886]) ).
fof(f2886,plain,
( ! [X2,X3,X0,X1] :
( empty(powerset(X0))
| sP0(sK10(powerset(powerset(X0))),X1)
| in(unordered_pair(singleton(X2),unordered_pair(X2,sK9(sK10(powerset(powerset(X0))),X1))),powerset(X0))
| ~ in(sK9(sK10(powerset(powerset(X0))),X1),X3)
| ~ in(sK8(sK10(powerset(powerset(X0))),X1),X3)
| ~ in(X2,X3)
| ~ sP0(powerset(X0),X3)
| empty(powerset(X0))
| ~ subset(unordered_pair(singleton(X2),unordered_pair(X2,sK8(sK10(powerset(powerset(X0))),X1))),X0) )
| ~ spl17_203
| ~ spl17_320 ),
inference(resolution,[],[f2870,f1651]) ).
fof(f12880,plain,
( spl17_112
| ~ spl17_5
| ~ spl17_107
| ~ spl17_7
| ~ spl17_892 ),
inference(avatar_split_clause,[],[f12839,f12429,f209,f858,f199,f895]) ).
fof(f895,plain,
( spl17_112
<=> in(sK5,sK16) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_112])]) ).
fof(f12429,plain,
( spl17_892
<=> ! [X0] :
( in(X0,sK16)
| ~ in(X0,the_carrier(sK2))
| ~ element(X0,the_carrier(sK2))
| ~ related(sK2,sK4,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_892])]) ).
fof(f12839,plain,
( ~ in(sK5,the_carrier(sK2))
| ~ element(sK5,the_carrier(sK2))
| in(sK5,sK16)
| ~ spl17_7
| ~ spl17_892 ),
inference(resolution,[],[f12430,f211]) ).
fof(f12430,plain,
( ! [X0] :
( ~ related(sK2,sK4,X0)
| ~ in(X0,the_carrier(sK2))
| ~ element(X0,the_carrier(sK2))
| in(X0,sK16) )
| ~ spl17_892 ),
inference(avatar_component_clause,[],[f12429]) ).
fof(f12822,plain,
( spl17_943
| ~ spl17_41
| ~ spl17_347 ),
inference(avatar_split_clause,[],[f3318,f3306,f363,f12820]) ).
fof(f12820,plain,
( spl17_943
<=> ! [X2,X0,X1] :
( sP0(powerset(powerset(cartesian_product2(X0,X1))),X2)
| empty(unordered_pair(singleton(sK7(powerset(powerset(cartesian_product2(X0,X1))),X2)),unordered_pair(sK8(powerset(powerset(cartesian_product2(X0,X1))),X2),sK7(powerset(powerset(cartesian_product2(X0,X1))),X2))))
| relation(sK10(unordered_pair(singleton(sK7(powerset(powerset(cartesian_product2(X0,X1))),X2)),unordered_pair(sK8(powerset(powerset(cartesian_product2(X0,X1))),X2),sK7(powerset(powerset(cartesian_product2(X0,X1))),X2))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_943])]) ).
fof(f3306,plain,
( spl17_347
<=> ! [X0,X1] :
( element(sK10(unordered_pair(singleton(sK7(powerset(X0),X1)),unordered_pair(sK8(powerset(X0),X1),sK7(powerset(X0),X1)))),X0)
| sP0(powerset(X0),X1)
| empty(unordered_pair(singleton(sK7(powerset(X0),X1)),unordered_pair(sK8(powerset(X0),X1),sK7(powerset(X0),X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_347])]) ).
fof(f3318,plain,
( ! [X2,X0,X1] :
( sP0(powerset(powerset(cartesian_product2(X0,X1))),X2)
| empty(unordered_pair(singleton(sK7(powerset(powerset(cartesian_product2(X0,X1))),X2)),unordered_pair(sK8(powerset(powerset(cartesian_product2(X0,X1))),X2),sK7(powerset(powerset(cartesian_product2(X0,X1))),X2))))
| relation(sK10(unordered_pair(singleton(sK7(powerset(powerset(cartesian_product2(X0,X1))),X2)),unordered_pair(sK8(powerset(powerset(cartesian_product2(X0,X1))),X2),sK7(powerset(powerset(cartesian_product2(X0,X1))),X2))))) )
| ~ spl17_41
| ~ spl17_347 ),
inference(resolution,[],[f3307,f364]) ).
fof(f3307,plain,
( ! [X0,X1] :
( element(sK10(unordered_pair(singleton(sK7(powerset(X0),X1)),unordered_pair(sK8(powerset(X0),X1),sK7(powerset(X0),X1)))),X0)
| sP0(powerset(X0),X1)
| empty(unordered_pair(singleton(sK7(powerset(X0),X1)),unordered_pair(sK8(powerset(X0),X1),sK7(powerset(X0),X1)))) )
| ~ spl17_347 ),
inference(avatar_component_clause,[],[f3306]) ).
fof(f12818,plain,
( spl17_942
| ~ spl17_41
| ~ spl17_346 ),
inference(avatar_split_clause,[],[f3314,f3302,f363,f12816]) ).
fof(f12816,plain,
( spl17_942
<=> ! [X2,X0,X1] :
( sP0(powerset(powerset(cartesian_product2(X0,X1))),X2)
| empty(unordered_pair(singleton(sK8(powerset(powerset(cartesian_product2(X0,X1))),X2)),unordered_pair(sK9(powerset(powerset(cartesian_product2(X0,X1))),X2),sK8(powerset(powerset(cartesian_product2(X0,X1))),X2))))
| relation(sK10(unordered_pair(singleton(sK8(powerset(powerset(cartesian_product2(X0,X1))),X2)),unordered_pair(sK9(powerset(powerset(cartesian_product2(X0,X1))),X2),sK8(powerset(powerset(cartesian_product2(X0,X1))),X2))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_942])]) ).
fof(f3302,plain,
( spl17_346
<=> ! [X0,X1] :
( element(sK10(unordered_pair(singleton(sK8(powerset(X0),X1)),unordered_pair(sK9(powerset(X0),X1),sK8(powerset(X0),X1)))),X0)
| sP0(powerset(X0),X1)
| empty(unordered_pair(singleton(sK8(powerset(X0),X1)),unordered_pair(sK9(powerset(X0),X1),sK8(powerset(X0),X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_346])]) ).
fof(f3314,plain,
( ! [X2,X0,X1] :
( sP0(powerset(powerset(cartesian_product2(X0,X1))),X2)
| empty(unordered_pair(singleton(sK8(powerset(powerset(cartesian_product2(X0,X1))),X2)),unordered_pair(sK9(powerset(powerset(cartesian_product2(X0,X1))),X2),sK8(powerset(powerset(cartesian_product2(X0,X1))),X2))))
| relation(sK10(unordered_pair(singleton(sK8(powerset(powerset(cartesian_product2(X0,X1))),X2)),unordered_pair(sK9(powerset(powerset(cartesian_product2(X0,X1))),X2),sK8(powerset(powerset(cartesian_product2(X0,X1))),X2))))) )
| ~ spl17_41
| ~ spl17_346 ),
inference(resolution,[],[f3303,f364]) ).
fof(f3303,plain,
( ! [X0,X1] :
( element(sK10(unordered_pair(singleton(sK8(powerset(X0),X1)),unordered_pair(sK9(powerset(X0),X1),sK8(powerset(X0),X1)))),X0)
| sP0(powerset(X0),X1)
| empty(unordered_pair(singleton(sK8(powerset(X0),X1)),unordered_pair(sK9(powerset(X0),X1),sK8(powerset(X0),X1)))) )
| ~ spl17_346 ),
inference(avatar_component_clause,[],[f3302]) ).
fof(f12814,plain,
( spl17_941
| ~ spl17_284
| ~ spl17_321 ),
inference(avatar_split_clause,[],[f2965,f2873,f2409,f12812]) ).
fof(f12812,plain,
( spl17_941
<=> ! [X2,X0,X1] :
( empty(sK9(X0,sK10(powerset(powerset(X1)))))
| sP0(sK10(powerset(sK9(X0,sK10(powerset(powerset(X1)))))),X2)
| element(unordered_pair(singleton(sK7(sK10(powerset(sK9(X0,sK10(powerset(powerset(X1)))))),X2)),unordered_pair(sK8(sK10(powerset(sK9(X0,sK10(powerset(powerset(X1)))))),X2),sK7(sK10(powerset(sK9(X0,sK10(powerset(powerset(X1)))))),X2))),X1)
| sP0(X0,sK10(powerset(powerset(X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_941])]) ).
fof(f2409,plain,
( spl17_284
<=> ! [X2,X0,X1] :
( sP0(X0,sK10(powerset(powerset(X1))))
| element(X2,X1)
| ~ in(X2,sK9(X0,sK10(powerset(powerset(X1))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_284])]) ).
fof(f2965,plain,
( ! [X2,X0,X1] :
( empty(sK9(X0,sK10(powerset(powerset(X1)))))
| sP0(sK10(powerset(sK9(X0,sK10(powerset(powerset(X1)))))),X2)
| element(unordered_pair(singleton(sK7(sK10(powerset(sK9(X0,sK10(powerset(powerset(X1)))))),X2)),unordered_pair(sK8(sK10(powerset(sK9(X0,sK10(powerset(powerset(X1)))))),X2),sK7(sK10(powerset(sK9(X0,sK10(powerset(powerset(X1)))))),X2))),X1)
| sP0(X0,sK10(powerset(powerset(X1)))) )
| ~ spl17_284
| ~ spl17_321 ),
inference(resolution,[],[f2874,f2410]) ).
fof(f2410,plain,
( ! [X2,X0,X1] :
( ~ in(X2,sK9(X0,sK10(powerset(powerset(X1)))))
| element(X2,X1)
| sP0(X0,sK10(powerset(powerset(X1)))) )
| ~ spl17_284 ),
inference(avatar_component_clause,[],[f2409]) ).
fof(f12810,plain,
( spl17_940
| ~ spl17_282
| ~ spl17_321 ),
inference(avatar_split_clause,[],[f2959,f2873,f2401,f12808]) ).
fof(f12808,plain,
( spl17_940
<=> ! [X2,X0,X1] :
( empty(sK8(X0,sK10(powerset(powerset(X1)))))
| sP0(sK10(powerset(sK8(X0,sK10(powerset(powerset(X1)))))),X2)
| element(unordered_pair(singleton(sK7(sK10(powerset(sK8(X0,sK10(powerset(powerset(X1)))))),X2)),unordered_pair(sK8(sK10(powerset(sK8(X0,sK10(powerset(powerset(X1)))))),X2),sK7(sK10(powerset(sK8(X0,sK10(powerset(powerset(X1)))))),X2))),X1)
| sP0(X0,sK10(powerset(powerset(X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_940])]) ).
fof(f2401,plain,
( spl17_282
<=> ! [X2,X0,X1] :
( sP0(X0,sK10(powerset(powerset(X1))))
| element(X2,X1)
| ~ in(X2,sK8(X0,sK10(powerset(powerset(X1))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_282])]) ).
fof(f2959,plain,
( ! [X2,X0,X1] :
( empty(sK8(X0,sK10(powerset(powerset(X1)))))
| sP0(sK10(powerset(sK8(X0,sK10(powerset(powerset(X1)))))),X2)
| element(unordered_pair(singleton(sK7(sK10(powerset(sK8(X0,sK10(powerset(powerset(X1)))))),X2)),unordered_pair(sK8(sK10(powerset(sK8(X0,sK10(powerset(powerset(X1)))))),X2),sK7(sK10(powerset(sK8(X0,sK10(powerset(powerset(X1)))))),X2))),X1)
| sP0(X0,sK10(powerset(powerset(X1)))) )
| ~ spl17_282
| ~ spl17_321 ),
inference(resolution,[],[f2874,f2402]) ).
fof(f2402,plain,
( ! [X2,X0,X1] :
( ~ in(X2,sK8(X0,sK10(powerset(powerset(X1)))))
| element(X2,X1)
| sP0(X0,sK10(powerset(powerset(X1)))) )
| ~ spl17_282 ),
inference(avatar_component_clause,[],[f2401]) ).
fof(f12806,plain,
( spl17_939
| ~ spl17_280
| ~ spl17_321 ),
inference(avatar_split_clause,[],[f2953,f2873,f2393,f12804]) ).
fof(f12804,plain,
( spl17_939
<=> ! [X2,X0,X1] :
( empty(sK7(X0,sK10(powerset(powerset(X1)))))
| sP0(sK10(powerset(sK7(X0,sK10(powerset(powerset(X1)))))),X2)
| element(unordered_pair(singleton(sK7(sK10(powerset(sK7(X0,sK10(powerset(powerset(X1)))))),X2)),unordered_pair(sK8(sK10(powerset(sK7(X0,sK10(powerset(powerset(X1)))))),X2),sK7(sK10(powerset(sK7(X0,sK10(powerset(powerset(X1)))))),X2))),X1)
| sP0(X0,sK10(powerset(powerset(X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_939])]) ).
fof(f2393,plain,
( spl17_280
<=> ! [X2,X0,X1] :
( sP0(X0,sK10(powerset(powerset(X1))))
| element(X2,X1)
| ~ in(X2,sK7(X0,sK10(powerset(powerset(X1))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_280])]) ).
fof(f2953,plain,
( ! [X2,X0,X1] :
( empty(sK7(X0,sK10(powerset(powerset(X1)))))
| sP0(sK10(powerset(sK7(X0,sK10(powerset(powerset(X1)))))),X2)
| element(unordered_pair(singleton(sK7(sK10(powerset(sK7(X0,sK10(powerset(powerset(X1)))))),X2)),unordered_pair(sK8(sK10(powerset(sK7(X0,sK10(powerset(powerset(X1)))))),X2),sK7(sK10(powerset(sK7(X0,sK10(powerset(powerset(X1)))))),X2))),X1)
| sP0(X0,sK10(powerset(powerset(X1)))) )
| ~ spl17_280
| ~ spl17_321 ),
inference(resolution,[],[f2874,f2394]) ).
fof(f2394,plain,
( ! [X2,X0,X1] :
( ~ in(X2,sK7(X0,sK10(powerset(powerset(X1)))))
| element(X2,X1)
| sP0(X0,sK10(powerset(powerset(X1)))) )
| ~ spl17_280 ),
inference(avatar_component_clause,[],[f2393]) ).
fof(f12802,plain,
( spl17_938
| ~ spl17_284
| ~ spl17_320 ),
inference(avatar_split_clause,[],[f2914,f2869,f2409,f12800]) ).
fof(f12800,plain,
( spl17_938
<=> ! [X2,X0,X1] :
( empty(sK9(X0,sK10(powerset(powerset(X1)))))
| sP0(sK10(powerset(sK9(X0,sK10(powerset(powerset(X1)))))),X2)
| element(unordered_pair(singleton(sK8(sK10(powerset(sK9(X0,sK10(powerset(powerset(X1)))))),X2)),unordered_pair(sK9(sK10(powerset(sK9(X0,sK10(powerset(powerset(X1)))))),X2),sK8(sK10(powerset(sK9(X0,sK10(powerset(powerset(X1)))))),X2))),X1)
| sP0(X0,sK10(powerset(powerset(X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_938])]) ).
fof(f2914,plain,
( ! [X2,X0,X1] :
( empty(sK9(X0,sK10(powerset(powerset(X1)))))
| sP0(sK10(powerset(sK9(X0,sK10(powerset(powerset(X1)))))),X2)
| element(unordered_pair(singleton(sK8(sK10(powerset(sK9(X0,sK10(powerset(powerset(X1)))))),X2)),unordered_pair(sK9(sK10(powerset(sK9(X0,sK10(powerset(powerset(X1)))))),X2),sK8(sK10(powerset(sK9(X0,sK10(powerset(powerset(X1)))))),X2))),X1)
| sP0(X0,sK10(powerset(powerset(X1)))) )
| ~ spl17_284
| ~ spl17_320 ),
inference(resolution,[],[f2870,f2410]) ).
fof(f12798,plain,
( spl17_937
| ~ spl17_393
| ~ spl17_654 ),
inference(avatar_split_clause,[],[f12092,f7696,f3736,f12796]) ).
fof(f12796,plain,
( spl17_937
<=> ! [X0] :
( ~ in(X0,the_carrier(sK2))
| ~ element(X0,the_carrier(sK2))
| ~ related(sK2,sK5,X0)
| in(X0,sK16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_937])]) ).
fof(f12092,plain,
( ! [X0] :
( ~ in(X0,the_carrier(sK2))
| ~ element(X0,the_carrier(sK2))
| ~ related(sK2,sK5,X0)
| in(X0,sK16) )
| ~ spl17_393
| ~ spl17_654 ),
inference(resolution,[],[f3737,f7697]) ).
fof(f7697,plain,
( ! [X0,X1] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),the_InternalRel(sK2))
| in(X1,sK16) )
| ~ spl17_654 ),
inference(avatar_component_clause,[],[f7696]) ).
fof(f12794,plain,
( spl17_936
| ~ spl17_282
| ~ spl17_320 ),
inference(avatar_split_clause,[],[f2908,f2869,f2401,f12792]) ).
fof(f12792,plain,
( spl17_936
<=> ! [X2,X0,X1] :
( empty(sK8(X0,sK10(powerset(powerset(X1)))))
| sP0(sK10(powerset(sK8(X0,sK10(powerset(powerset(X1)))))),X2)
| element(unordered_pair(singleton(sK8(sK10(powerset(sK8(X0,sK10(powerset(powerset(X1)))))),X2)),unordered_pair(sK9(sK10(powerset(sK8(X0,sK10(powerset(powerset(X1)))))),X2),sK8(sK10(powerset(sK8(X0,sK10(powerset(powerset(X1)))))),X2))),X1)
| sP0(X0,sK10(powerset(powerset(X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_936])]) ).
fof(f2908,plain,
( ! [X2,X0,X1] :
( empty(sK8(X0,sK10(powerset(powerset(X1)))))
| sP0(sK10(powerset(sK8(X0,sK10(powerset(powerset(X1)))))),X2)
| element(unordered_pair(singleton(sK8(sK10(powerset(sK8(X0,sK10(powerset(powerset(X1)))))),X2)),unordered_pair(sK9(sK10(powerset(sK8(X0,sK10(powerset(powerset(X1)))))),X2),sK8(sK10(powerset(sK8(X0,sK10(powerset(powerset(X1)))))),X2))),X1)
| sP0(X0,sK10(powerset(powerset(X1)))) )
| ~ spl17_282
| ~ spl17_320 ),
inference(resolution,[],[f2870,f2402]) ).
fof(f12790,plain,
( spl17_935
| ~ spl17_280
| ~ spl17_320 ),
inference(avatar_split_clause,[],[f2902,f2869,f2393,f12788]) ).
fof(f12788,plain,
( spl17_935
<=> ! [X2,X0,X1] :
( empty(sK7(X0,sK10(powerset(powerset(X1)))))
| sP0(sK10(powerset(sK7(X0,sK10(powerset(powerset(X1)))))),X2)
| element(unordered_pair(singleton(sK8(sK10(powerset(sK7(X0,sK10(powerset(powerset(X1)))))),X2)),unordered_pair(sK9(sK10(powerset(sK7(X0,sK10(powerset(powerset(X1)))))),X2),sK8(sK10(powerset(sK7(X0,sK10(powerset(powerset(X1)))))),X2))),X1)
| sP0(X0,sK10(powerset(powerset(X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_935])]) ).
fof(f2902,plain,
( ! [X2,X0,X1] :
( empty(sK7(X0,sK10(powerset(powerset(X1)))))
| sP0(sK10(powerset(sK7(X0,sK10(powerset(powerset(X1)))))),X2)
| element(unordered_pair(singleton(sK8(sK10(powerset(sK7(X0,sK10(powerset(powerset(X1)))))),X2)),unordered_pair(sK9(sK10(powerset(sK7(X0,sK10(powerset(powerset(X1)))))),X2),sK8(sK10(powerset(sK7(X0,sK10(powerset(powerset(X1)))))),X2))),X1)
| sP0(X0,sK10(powerset(powerset(X1)))) )
| ~ spl17_280
| ~ spl17_320 ),
inference(resolution,[],[f2870,f2394]) ).
fof(f12786,plain,
( spl17_934
| ~ spl17_188
| ~ spl17_241 ),
inference(avatar_split_clause,[],[f2051,f1933,f1511,f12784]) ).
fof(f12784,plain,
( spl17_934
<=> ! [X2,X0,X1] :
( sP0(X0,sK6(unordered_pair(singleton(sK7(powerset(X1),X2)),unordered_pair(sK8(powerset(X1),X2),sK7(powerset(X1),X2)))))
| empty(unordered_pair(singleton(sK7(powerset(X1),X2)),unordered_pair(sK8(powerset(X1),X2),sK7(powerset(X1),X2))))
| element(sK9(X0,sK6(unordered_pair(singleton(sK7(powerset(X1),X2)),unordered_pair(sK8(powerset(X1),X2),sK7(powerset(X1),X2))))),X1)
| sP0(powerset(X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_934])]) ).
fof(f2051,plain,
( ! [X2,X0,X1] :
( sP0(X0,sK6(unordered_pair(singleton(sK7(powerset(X1),X2)),unordered_pair(sK8(powerset(X1),X2),sK7(powerset(X1),X2)))))
| empty(unordered_pair(singleton(sK7(powerset(X1),X2)),unordered_pair(sK8(powerset(X1),X2),sK7(powerset(X1),X2))))
| element(sK9(X0,sK6(unordered_pair(singleton(sK7(powerset(X1),X2)),unordered_pair(sK8(powerset(X1),X2),sK7(powerset(X1),X2))))),X1)
| sP0(powerset(X1),X2) )
| ~ spl17_188
| ~ spl17_241 ),
inference(resolution,[],[f1934,f1512]) ).
fof(f12782,plain,
( spl17_933
| ~ spl17_187
| ~ spl17_241 ),
inference(avatar_split_clause,[],[f2049,f1933,f1507,f12780]) ).
fof(f12780,plain,
( spl17_933
<=> ! [X2,X0,X1] :
( sP0(X0,sK6(unordered_pair(singleton(sK8(powerset(X1),X2)),unordered_pair(sK9(powerset(X1),X2),sK8(powerset(X1),X2)))))
| empty(unordered_pair(singleton(sK8(powerset(X1),X2)),unordered_pair(sK9(powerset(X1),X2),sK8(powerset(X1),X2))))
| element(sK9(X0,sK6(unordered_pair(singleton(sK8(powerset(X1),X2)),unordered_pair(sK9(powerset(X1),X2),sK8(powerset(X1),X2))))),X1)
| sP0(powerset(X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_933])]) ).
fof(f2049,plain,
( ! [X2,X0,X1] :
( sP0(X0,sK6(unordered_pair(singleton(sK8(powerset(X1),X2)),unordered_pair(sK9(powerset(X1),X2),sK8(powerset(X1),X2)))))
| empty(unordered_pair(singleton(sK8(powerset(X1),X2)),unordered_pair(sK9(powerset(X1),X2),sK8(powerset(X1),X2))))
| element(sK9(X0,sK6(unordered_pair(singleton(sK8(powerset(X1),X2)),unordered_pair(sK9(powerset(X1),X2),sK8(powerset(X1),X2))))),X1)
| sP0(powerset(X1),X2) )
| ~ spl17_187
| ~ spl17_241 ),
inference(resolution,[],[f1934,f1508]) ).
fof(f12778,plain,
( spl17_932
| ~ spl17_188
| ~ spl17_240 ),
inference(avatar_split_clause,[],[f2032,f1929,f1511,f12776]) ).
fof(f12776,plain,
( spl17_932
<=> ! [X2,X0,X1] :
( sP0(X0,sK6(unordered_pair(singleton(sK7(powerset(X1),X2)),unordered_pair(sK8(powerset(X1),X2),sK7(powerset(X1),X2)))))
| empty(unordered_pair(singleton(sK7(powerset(X1),X2)),unordered_pair(sK8(powerset(X1),X2),sK7(powerset(X1),X2))))
| element(sK8(X0,sK6(unordered_pair(singleton(sK7(powerset(X1),X2)),unordered_pair(sK8(powerset(X1),X2),sK7(powerset(X1),X2))))),X1)
| sP0(powerset(X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_932])]) ).
fof(f2032,plain,
( ! [X2,X0,X1] :
( sP0(X0,sK6(unordered_pair(singleton(sK7(powerset(X1),X2)),unordered_pair(sK8(powerset(X1),X2),sK7(powerset(X1),X2)))))
| empty(unordered_pair(singleton(sK7(powerset(X1),X2)),unordered_pair(sK8(powerset(X1),X2),sK7(powerset(X1),X2))))
| element(sK8(X0,sK6(unordered_pair(singleton(sK7(powerset(X1),X2)),unordered_pair(sK8(powerset(X1),X2),sK7(powerset(X1),X2))))),X1)
| sP0(powerset(X1),X2) )
| ~ spl17_188
| ~ spl17_240 ),
inference(resolution,[],[f1930,f1512]) ).
fof(f12774,plain,
( spl17_931
| ~ spl17_187
| ~ spl17_240 ),
inference(avatar_split_clause,[],[f2030,f1929,f1507,f12772]) ).
fof(f12772,plain,
( spl17_931
<=> ! [X2,X0,X1] :
( sP0(X0,sK6(unordered_pair(singleton(sK8(powerset(X1),X2)),unordered_pair(sK9(powerset(X1),X2),sK8(powerset(X1),X2)))))
| empty(unordered_pair(singleton(sK8(powerset(X1),X2)),unordered_pair(sK9(powerset(X1),X2),sK8(powerset(X1),X2))))
| element(sK8(X0,sK6(unordered_pair(singleton(sK8(powerset(X1),X2)),unordered_pair(sK9(powerset(X1),X2),sK8(powerset(X1),X2))))),X1)
| sP0(powerset(X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_931])]) ).
fof(f2030,plain,
( ! [X2,X0,X1] :
( sP0(X0,sK6(unordered_pair(singleton(sK8(powerset(X1),X2)),unordered_pair(sK9(powerset(X1),X2),sK8(powerset(X1),X2)))))
| empty(unordered_pair(singleton(sK8(powerset(X1),X2)),unordered_pair(sK9(powerset(X1),X2),sK8(powerset(X1),X2))))
| element(sK8(X0,sK6(unordered_pair(singleton(sK8(powerset(X1),X2)),unordered_pair(sK9(powerset(X1),X2),sK8(powerset(X1),X2))))),X1)
| sP0(powerset(X1),X2) )
| ~ spl17_187
| ~ spl17_240 ),
inference(resolution,[],[f1930,f1508]) ).
fof(f12770,plain,
( spl17_930
| ~ spl17_188
| ~ spl17_239 ),
inference(avatar_split_clause,[],[f2013,f1925,f1511,f12768]) ).
fof(f12768,plain,
( spl17_930
<=> ! [X2,X0,X1] :
( sP0(X0,sK6(unordered_pair(singleton(sK7(powerset(X1),X2)),unordered_pair(sK8(powerset(X1),X2),sK7(powerset(X1),X2)))))
| empty(unordered_pair(singleton(sK7(powerset(X1),X2)),unordered_pair(sK8(powerset(X1),X2),sK7(powerset(X1),X2))))
| element(sK7(X0,sK6(unordered_pair(singleton(sK7(powerset(X1),X2)),unordered_pair(sK8(powerset(X1),X2),sK7(powerset(X1),X2))))),X1)
| sP0(powerset(X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_930])]) ).
fof(f2013,plain,
( ! [X2,X0,X1] :
( sP0(X0,sK6(unordered_pair(singleton(sK7(powerset(X1),X2)),unordered_pair(sK8(powerset(X1),X2),sK7(powerset(X1),X2)))))
| empty(unordered_pair(singleton(sK7(powerset(X1),X2)),unordered_pair(sK8(powerset(X1),X2),sK7(powerset(X1),X2))))
| element(sK7(X0,sK6(unordered_pair(singleton(sK7(powerset(X1),X2)),unordered_pair(sK8(powerset(X1),X2),sK7(powerset(X1),X2))))),X1)
| sP0(powerset(X1),X2) )
| ~ spl17_188
| ~ spl17_239 ),
inference(resolution,[],[f1926,f1512]) ).
fof(f12766,plain,
( spl17_929
| ~ spl17_187
| ~ spl17_239 ),
inference(avatar_split_clause,[],[f2011,f1925,f1507,f12764]) ).
fof(f12764,plain,
( spl17_929
<=> ! [X2,X0,X1] :
( sP0(X0,sK6(unordered_pair(singleton(sK8(powerset(X1),X2)),unordered_pair(sK9(powerset(X1),X2),sK8(powerset(X1),X2)))))
| empty(unordered_pair(singleton(sK8(powerset(X1),X2)),unordered_pair(sK9(powerset(X1),X2),sK8(powerset(X1),X2))))
| element(sK7(X0,sK6(unordered_pair(singleton(sK8(powerset(X1),X2)),unordered_pair(sK9(powerset(X1),X2),sK8(powerset(X1),X2))))),X1)
| sP0(powerset(X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_929])]) ).
fof(f2011,plain,
( ! [X2,X0,X1] :
( sP0(X0,sK6(unordered_pair(singleton(sK8(powerset(X1),X2)),unordered_pair(sK9(powerset(X1),X2),sK8(powerset(X1),X2)))))
| empty(unordered_pair(singleton(sK8(powerset(X1),X2)),unordered_pair(sK9(powerset(X1),X2),sK8(powerset(X1),X2))))
| element(sK7(X0,sK6(unordered_pair(singleton(sK8(powerset(X1),X2)),unordered_pair(sK9(powerset(X1),X2),sK8(powerset(X1),X2))))),X1)
| sP0(powerset(X1),X2) )
| ~ spl17_187
| ~ spl17_239 ),
inference(resolution,[],[f1926,f1508]) ).
fof(f12762,plain,
( spl17_928
| ~ spl17_188
| ~ spl17_229 ),
inference(avatar_split_clause,[],[f1981,f1885,f1511,f12760]) ).
fof(f12760,plain,
( spl17_928
<=> ! [X0,X1] :
( empty(unordered_pair(singleton(sK7(powerset(X0),X1)),unordered_pair(sK8(powerset(X0),X1),sK7(powerset(X0),X1))))
| empty(sK10(powerset(unordered_pair(singleton(sK7(powerset(X0),X1)),unordered_pair(sK8(powerset(X0),X1),sK7(powerset(X0),X1))))))
| element(sK10(sK10(powerset(unordered_pair(singleton(sK7(powerset(X0),X1)),unordered_pair(sK8(powerset(X0),X1),sK7(powerset(X0),X1)))))),X0)
| sP0(powerset(X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_928])]) ).
fof(f1981,plain,
( ! [X0,X1] :
( empty(unordered_pair(singleton(sK7(powerset(X0),X1)),unordered_pair(sK8(powerset(X0),X1),sK7(powerset(X0),X1))))
| empty(sK10(powerset(unordered_pair(singleton(sK7(powerset(X0),X1)),unordered_pair(sK8(powerset(X0),X1),sK7(powerset(X0),X1))))))
| element(sK10(sK10(powerset(unordered_pair(singleton(sK7(powerset(X0),X1)),unordered_pair(sK8(powerset(X0),X1),sK7(powerset(X0),X1)))))),X0)
| sP0(powerset(X0),X1) )
| ~ spl17_188
| ~ spl17_229 ),
inference(resolution,[],[f1886,f1512]) ).
fof(f12758,plain,
( spl17_927
| ~ spl17_187
| ~ spl17_229 ),
inference(avatar_split_clause,[],[f1979,f1885,f1507,f12756]) ).
fof(f12756,plain,
( spl17_927
<=> ! [X0,X1] :
( empty(unordered_pair(singleton(sK8(powerset(X0),X1)),unordered_pair(sK9(powerset(X0),X1),sK8(powerset(X0),X1))))
| empty(sK10(powerset(unordered_pair(singleton(sK8(powerset(X0),X1)),unordered_pair(sK9(powerset(X0),X1),sK8(powerset(X0),X1))))))
| element(sK10(sK10(powerset(unordered_pair(singleton(sK8(powerset(X0),X1)),unordered_pair(sK9(powerset(X0),X1),sK8(powerset(X0),X1)))))),X0)
| sP0(powerset(X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_927])]) ).
fof(f1979,plain,
( ! [X0,X1] :
( empty(unordered_pair(singleton(sK8(powerset(X0),X1)),unordered_pair(sK9(powerset(X0),X1),sK8(powerset(X0),X1))))
| empty(sK10(powerset(unordered_pair(singleton(sK8(powerset(X0),X1)),unordered_pair(sK9(powerset(X0),X1),sK8(powerset(X0),X1))))))
| element(sK10(sK10(powerset(unordered_pair(singleton(sK8(powerset(X0),X1)),unordered_pair(sK9(powerset(X0),X1),sK8(powerset(X0),X1)))))),X0)
| sP0(powerset(X0),X1) )
| ~ spl17_187
| ~ spl17_229 ),
inference(resolution,[],[f1886,f1508]) ).
fof(f12666,plain,
( spl17_926
| ~ spl17_304
| ~ spl17_341 ),
inference(avatar_split_clause,[],[f3256,f3243,f2657,f12664]) ).
fof(f12664,plain,
( spl17_926
<=> ! [X4,X0,X3,X2,X1] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),cartesian_product2(the_carrier(X2),the_carrier(X2)))
| in(unordered_pair(singleton(X3),unordered_pair(X3,X1)),cartesian_product2(the_carrier(X2),the_carrier(X2)))
| ~ in(X1,X4)
| ~ in(X0,X4)
| ~ in(X3,X4)
| ~ sP0(cartesian_product2(the_carrier(X2),the_carrier(X2)),X4)
| ~ rel_str(X2)
| empty(cartesian_product2(the_carrier(X2),the_carrier(X2)))
| ~ in(unordered_pair(singleton(X3),unordered_pair(X0,X3)),the_InternalRel(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_926])]) ).
fof(f2657,plain,
( spl17_304
<=> ! [X0,X1] :
( ~ in(X0,the_InternalRel(X1))
| ~ rel_str(X1)
| empty(cartesian_product2(the_carrier(X1),the_carrier(X1)))
| in(X0,cartesian_product2(the_carrier(X1),the_carrier(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_304])]) ).
fof(f3256,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),cartesian_product2(the_carrier(X2),the_carrier(X2)))
| in(unordered_pair(singleton(X3),unordered_pair(X3,X1)),cartesian_product2(the_carrier(X2),the_carrier(X2)))
| ~ in(X1,X4)
| ~ in(X0,X4)
| ~ in(X3,X4)
| ~ sP0(cartesian_product2(the_carrier(X2),the_carrier(X2)),X4)
| ~ rel_str(X2)
| empty(cartesian_product2(the_carrier(X2),the_carrier(X2)))
| ~ in(unordered_pair(singleton(X3),unordered_pair(X0,X3)),the_InternalRel(X2)) )
| ~ spl17_304
| ~ spl17_341 ),
inference(resolution,[],[f3244,f2658]) ).
fof(f2658,plain,
( ! [X0,X1] :
( in(X0,cartesian_product2(the_carrier(X1),the_carrier(X1)))
| ~ rel_str(X1)
| empty(cartesian_product2(the_carrier(X1),the_carrier(X1)))
| ~ in(X0,the_InternalRel(X1)) )
| ~ spl17_304 ),
inference(avatar_component_clause,[],[f2657]) ).
fof(f12662,plain,
( spl17_925
| ~ spl17_197
| ~ spl17_304 ),
inference(avatar_split_clause,[],[f2689,f2657,f1581,f12660]) ).
fof(f12660,plain,
( spl17_925
<=> ! [X4,X0,X3,X2,X1] :
( ~ rel_str(X0)
| empty(cartesian_product2(the_carrier(X0),the_carrier(X0)))
| ~ in(unordered_pair(singleton(X1),unordered_pair(X2,X1)),the_InternalRel(X0))
| ~ in(unordered_pair(singleton(X3),unordered_pair(X1,X3)),cartesian_product2(the_carrier(X0),the_carrier(X0)))
| in(unordered_pair(singleton(X3),unordered_pair(X3,X2)),cartesian_product2(the_carrier(X0),the_carrier(X0)))
| ~ in(X2,X4)
| ~ in(X1,X4)
| ~ in(X3,X4)
| ~ sP0(cartesian_product2(the_carrier(X0),the_carrier(X0)),X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_925])]) ).
fof(f1581,plain,
( spl17_197
<=> ! [X4,X0,X3,X2,X1] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X1,X0)),X2)
| ~ in(unordered_pair(singleton(X1),unordered_pair(X3,X1)),X2)
| in(unordered_pair(singleton(X0),unordered_pair(X0,X3)),X2)
| ~ in(X3,X4)
| ~ in(X1,X4)
| ~ in(X0,X4)
| ~ sP0(X2,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_197])]) ).
fof(f2689,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ rel_str(X0)
| empty(cartesian_product2(the_carrier(X0),the_carrier(X0)))
| ~ in(unordered_pair(singleton(X1),unordered_pair(X2,X1)),the_InternalRel(X0))
| ~ in(unordered_pair(singleton(X3),unordered_pair(X1,X3)),cartesian_product2(the_carrier(X0),the_carrier(X0)))
| in(unordered_pair(singleton(X3),unordered_pair(X3,X2)),cartesian_product2(the_carrier(X0),the_carrier(X0)))
| ~ in(X2,X4)
| ~ in(X1,X4)
| ~ in(X3,X4)
| ~ sP0(cartesian_product2(the_carrier(X0),the_carrier(X0)),X4) )
| ~ spl17_197
| ~ spl17_304 ),
inference(resolution,[],[f2658,f1582]) ).
fof(f1582,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ in(unordered_pair(singleton(X1),unordered_pair(X3,X1)),X2)
| ~ in(unordered_pair(singleton(X0),unordered_pair(X1,X0)),X2)
| in(unordered_pair(singleton(X0),unordered_pair(X0,X3)),X2)
| ~ in(X3,X4)
| ~ in(X1,X4)
| ~ in(X0,X4)
| ~ sP0(X2,X4) )
| ~ spl17_197 ),
inference(avatar_component_clause,[],[f1581]) ).
fof(f12658,plain,
( spl17_924
| ~ spl17_67
| ~ spl17_304 ),
inference(avatar_split_clause,[],[f2688,f2657,f553,f12656]) ).
fof(f12656,plain,
( spl17_924
<=> ! [X4,X0,X3,X2,X1] :
( ~ rel_str(X0)
| empty(cartesian_product2(the_carrier(X0),the_carrier(X0)))
| ~ in(unordered_pair(singleton(X1),unordered_pair(X1,X2)),the_InternalRel(X0))
| ~ in(unordered_pair(singleton(X3),unordered_pair(X3,X1)),cartesian_product2(the_carrier(X0),the_carrier(X0)))
| in(unordered_pair(singleton(X3),unordered_pair(X3,X2)),cartesian_product2(the_carrier(X0),the_carrier(X0)))
| ~ in(X2,X4)
| ~ in(X1,X4)
| ~ in(X3,X4)
| ~ sP0(cartesian_product2(the_carrier(X0),the_carrier(X0)),X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_924])]) ).
fof(f553,plain,
( spl17_67
<=> ! [X5,X0,X6,X1,X7] :
( ~ in(unordered_pair(singleton(X5),unordered_pair(X5,X6)),X0)
| ~ in(unordered_pair(singleton(X6),unordered_pair(X6,X7)),X0)
| in(unordered_pair(singleton(X5),unordered_pair(X5,X7)),X0)
| ~ in(X7,X1)
| ~ in(X6,X1)
| ~ in(X5,X1)
| ~ sP0(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_67])]) ).
fof(f2688,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ rel_str(X0)
| empty(cartesian_product2(the_carrier(X0),the_carrier(X0)))
| ~ in(unordered_pair(singleton(X1),unordered_pair(X1,X2)),the_InternalRel(X0))
| ~ in(unordered_pair(singleton(X3),unordered_pair(X3,X1)),cartesian_product2(the_carrier(X0),the_carrier(X0)))
| in(unordered_pair(singleton(X3),unordered_pair(X3,X2)),cartesian_product2(the_carrier(X0),the_carrier(X0)))
| ~ in(X2,X4)
| ~ in(X1,X4)
| ~ in(X3,X4)
| ~ sP0(cartesian_product2(the_carrier(X0),the_carrier(X0)),X4) )
| ~ spl17_67
| ~ spl17_304 ),
inference(resolution,[],[f2658,f554]) ).
fof(f554,plain,
( ! [X0,X1,X6,X7,X5] :
( ~ in(unordered_pair(singleton(X6),unordered_pair(X6,X7)),X0)
| ~ in(unordered_pair(singleton(X5),unordered_pair(X5,X6)),X0)
| in(unordered_pair(singleton(X5),unordered_pair(X5,X7)),X0)
| ~ in(X7,X1)
| ~ in(X6,X1)
| ~ in(X5,X1)
| ~ sP0(X0,X1) )
| ~ spl17_67 ),
inference(avatar_component_clause,[],[f553]) ).
fof(f12654,plain,
( spl17_923
| ~ spl17_123
| ~ spl17_304 ),
inference(avatar_split_clause,[],[f2687,f2657,f1000,f12652]) ).
fof(f12652,plain,
( spl17_923
<=> ! [X4,X0,X3,X2,X1] :
( ~ rel_str(X0)
| empty(cartesian_product2(the_carrier(X0),the_carrier(X0)))
| ~ in(unordered_pair(singleton(X1),unordered_pair(X1,X2)),the_InternalRel(X0))
| ~ in(unordered_pair(singleton(X2),unordered_pair(X3,X2)),cartesian_product2(the_carrier(X0),the_carrier(X0)))
| in(unordered_pair(singleton(X1),unordered_pair(X1,X3)),cartesian_product2(the_carrier(X0),the_carrier(X0)))
| ~ in(X3,X4)
| ~ in(X2,X4)
| ~ in(X1,X4)
| ~ sP0(cartesian_product2(the_carrier(X0),the_carrier(X0)),X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_923])]) ).
fof(f1000,plain,
( spl17_123
<=> ! [X4,X0,X3,X2,X1] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X1,X0)),X2)
| ~ in(unordered_pair(singleton(X3),unordered_pair(X3,X0)),X2)
| in(unordered_pair(singleton(X3),unordered_pair(X3,X1)),X2)
| ~ in(X1,X4)
| ~ in(X0,X4)
| ~ in(X3,X4)
| ~ sP0(X2,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_123])]) ).
fof(f2687,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ rel_str(X0)
| empty(cartesian_product2(the_carrier(X0),the_carrier(X0)))
| ~ in(unordered_pair(singleton(X1),unordered_pair(X1,X2)),the_InternalRel(X0))
| ~ in(unordered_pair(singleton(X2),unordered_pair(X3,X2)),cartesian_product2(the_carrier(X0),the_carrier(X0)))
| in(unordered_pair(singleton(X1),unordered_pair(X1,X3)),cartesian_product2(the_carrier(X0),the_carrier(X0)))
| ~ in(X3,X4)
| ~ in(X2,X4)
| ~ in(X1,X4)
| ~ sP0(cartesian_product2(the_carrier(X0),the_carrier(X0)),X4) )
| ~ spl17_123
| ~ spl17_304 ),
inference(resolution,[],[f2658,f1001]) ).
fof(f1001,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ in(unordered_pair(singleton(X3),unordered_pair(X3,X0)),X2)
| ~ in(unordered_pair(singleton(X0),unordered_pair(X1,X0)),X2)
| in(unordered_pair(singleton(X3),unordered_pair(X3,X1)),X2)
| ~ in(X1,X4)
| ~ in(X0,X4)
| ~ in(X3,X4)
| ~ sP0(X2,X4) )
| ~ spl17_123 ),
inference(avatar_component_clause,[],[f1000]) ).
fof(f12642,plain,
( ~ spl17_921
| spl17_922
| ~ spl17_34
| ~ spl17_910 ),
inference(avatar_split_clause,[],[f12602,f12559,f335,f12640,f12636]) ).
fof(f12636,plain,
( spl17_921
<=> sP1(sK6(the_InternalRel(sK2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_921])]) ).
fof(f12640,plain,
( spl17_922
<=> ! [X0] : is_transitive_in(sK6(the_InternalRel(sK2)),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_922])]) ).
fof(f335,plain,
( spl17_34
<=> ! [X0,X1] :
( is_transitive_in(X0,X1)
| ~ sP0(X0,X1)
| ~ sP1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_34])]) ).
fof(f12559,plain,
( spl17_910
<=> ! [X0] : sP0(sK6(the_InternalRel(sK2)),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_910])]) ).
fof(f12602,plain,
( ! [X0] :
( is_transitive_in(sK6(the_InternalRel(sK2)),X0)
| ~ sP1(sK6(the_InternalRel(sK2))) )
| ~ spl17_34
| ~ spl17_910 ),
inference(resolution,[],[f12560,f336]) ).
fof(f336,plain,
( ! [X0,X1] :
( ~ sP0(X0,X1)
| is_transitive_in(X0,X1)
| ~ sP1(X0) )
| ~ spl17_34 ),
inference(avatar_component_clause,[],[f335]) ).
fof(f12560,plain,
( ! [X0] : sP0(sK6(the_InternalRel(sK2)),X0)
| ~ spl17_910 ),
inference(avatar_component_clause,[],[f12559]) ).
fof(f12634,plain,
( spl17_920
| ~ spl17_188
| ~ spl17_224 ),
inference(avatar_split_clause,[],[f1822,f1808,f1511,f12632]) ).
fof(f12632,plain,
( spl17_920
<=> ! [X0,X1] :
( empty(sK6(unordered_pair(singleton(sK7(powerset(X0),X1)),unordered_pair(sK8(powerset(X0),X1),sK7(powerset(X0),X1)))))
| empty(unordered_pair(singleton(sK7(powerset(X0),X1)),unordered_pair(sK8(powerset(X0),X1),sK7(powerset(X0),X1))))
| element(sK10(sK6(unordered_pair(singleton(sK7(powerset(X0),X1)),unordered_pair(sK8(powerset(X0),X1),sK7(powerset(X0),X1))))),X0)
| sP0(powerset(X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_920])]) ).
fof(f1822,plain,
( ! [X0,X1] :
( empty(sK6(unordered_pair(singleton(sK7(powerset(X0),X1)),unordered_pair(sK8(powerset(X0),X1),sK7(powerset(X0),X1)))))
| empty(unordered_pair(singleton(sK7(powerset(X0),X1)),unordered_pair(sK8(powerset(X0),X1),sK7(powerset(X0),X1))))
| element(sK10(sK6(unordered_pair(singleton(sK7(powerset(X0),X1)),unordered_pair(sK8(powerset(X0),X1),sK7(powerset(X0),X1))))),X0)
| sP0(powerset(X0),X1) )
| ~ spl17_188
| ~ spl17_224 ),
inference(resolution,[],[f1809,f1512]) ).
fof(f12630,plain,
( spl17_919
| ~ spl17_187
| ~ spl17_224 ),
inference(avatar_split_clause,[],[f1820,f1808,f1507,f12628]) ).
fof(f12628,plain,
( spl17_919
<=> ! [X0,X1] :
( empty(sK6(unordered_pair(singleton(sK8(powerset(X0),X1)),unordered_pair(sK9(powerset(X0),X1),sK8(powerset(X0),X1)))))
| empty(unordered_pair(singleton(sK8(powerset(X0),X1)),unordered_pair(sK9(powerset(X0),X1),sK8(powerset(X0),X1))))
| element(sK10(sK6(unordered_pair(singleton(sK8(powerset(X0),X1)),unordered_pair(sK9(powerset(X0),X1),sK8(powerset(X0),X1))))),X0)
| sP0(powerset(X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_919])]) ).
fof(f1820,plain,
( ! [X0,X1] :
( empty(sK6(unordered_pair(singleton(sK8(powerset(X0),X1)),unordered_pair(sK9(powerset(X0),X1),sK8(powerset(X0),X1)))))
| empty(unordered_pair(singleton(sK8(powerset(X0),X1)),unordered_pair(sK9(powerset(X0),X1),sK8(powerset(X0),X1))))
| element(sK10(sK6(unordered_pair(singleton(sK8(powerset(X0),X1)),unordered_pair(sK9(powerset(X0),X1),sK8(powerset(X0),X1))))),X0)
| sP0(powerset(X0),X1) )
| ~ spl17_187
| ~ spl17_224 ),
inference(resolution,[],[f1809,f1508]) ).
fof(f12593,plain,
( spl17_918
| ~ spl17_60
| ~ spl17_364 ),
inference(avatar_split_clause,[],[f3491,f3463,f504,f12591]) ).
fof(f12591,plain,
( spl17_918
<=> ! [X0,X3,X2,X1] :
( ~ subset(unordered_pair(singleton(sK8(powerset(X0),X1)),unordered_pair(sK8(powerset(X0),X1),X2)),X0)
| empty(powerset(X0))
| in(unordered_pair(singleton(sK7(powerset(X0),X1)),unordered_pair(sK7(powerset(X0),X1),X2)),powerset(X0))
| ~ in(X2,X3)
| ~ in(sK8(powerset(X0),X1),X3)
| ~ in(sK7(powerset(X0),X1),X3)
| ~ sP0(powerset(X0),X3)
| sP0(powerset(X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_918])]) ).
fof(f3491,plain,
( ! [X2,X3,X0,X1] :
( ~ subset(unordered_pair(singleton(sK8(powerset(X0),X1)),unordered_pair(sK8(powerset(X0),X1),X2)),X0)
| empty(powerset(X0))
| in(unordered_pair(singleton(sK7(powerset(X0),X1)),unordered_pair(sK7(powerset(X0),X1),X2)),powerset(X0))
| ~ in(X2,X3)
| ~ in(sK8(powerset(X0),X1),X3)
| ~ in(sK7(powerset(X0),X1),X3)
| ~ sP0(powerset(X0),X3)
| sP0(powerset(X0),X1) )
| ~ spl17_60
| ~ spl17_364 ),
inference(resolution,[],[f3464,f505]) ).
fof(f12589,plain,
( spl17_917
| ~ spl17_59
| ~ spl17_364 ),
inference(avatar_split_clause,[],[f3488,f3463,f500,f12587]) ).
fof(f12587,plain,
( spl17_917
<=> ! [X0,X3,X2,X1] :
( ~ subset(unordered_pair(singleton(sK9(powerset(X0),X1)),unordered_pair(sK9(powerset(X0),X1),X2)),X0)
| empty(powerset(X0))
| in(unordered_pair(singleton(sK8(powerset(X0),X1)),unordered_pair(sK8(powerset(X0),X1),X2)),powerset(X0))
| ~ in(X2,X3)
| ~ in(sK9(powerset(X0),X1),X3)
| ~ in(sK8(powerset(X0),X1),X3)
| ~ sP0(powerset(X0),X3)
| sP0(powerset(X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_917])]) ).
fof(f3488,plain,
( ! [X2,X3,X0,X1] :
( ~ subset(unordered_pair(singleton(sK9(powerset(X0),X1)),unordered_pair(sK9(powerset(X0),X1),X2)),X0)
| empty(powerset(X0))
| in(unordered_pair(singleton(sK8(powerset(X0),X1)),unordered_pair(sK8(powerset(X0),X1),X2)),powerset(X0))
| ~ in(X2,X3)
| ~ in(sK9(powerset(X0),X1),X3)
| ~ in(sK8(powerset(X0),X1),X3)
| ~ sP0(powerset(X0),X3)
| sP0(powerset(X0),X1) )
| ~ spl17_59
| ~ spl17_364 ),
inference(resolution,[],[f3464,f501]) ).
fof(f12585,plain,
( spl17_916
| ~ spl17_60
| ~ spl17_363 ),
inference(avatar_split_clause,[],[f3475,f3459,f504,f12583]) ).
fof(f12583,plain,
( spl17_916
<=> ! [X0,X3,X2,X1] :
( in(unordered_pair(singleton(sK7(powerset(X0),X1)),unordered_pair(sK7(powerset(X0),X1),X2)),powerset(X0))
| ~ in(X2,X3)
| ~ in(sK8(powerset(X0),X1),X3)
| ~ in(sK7(powerset(X0),X1),X3)
| ~ sP0(powerset(X0),X3)
| empty(powerset(X0))
| ~ subset(unordered_pair(singleton(sK8(powerset(X0),X1)),unordered_pair(X2,sK8(powerset(X0),X1))),X0)
| sP0(powerset(X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_916])]) ).
fof(f3475,plain,
( ! [X2,X3,X0,X1] :
( in(unordered_pair(singleton(sK7(powerset(X0),X1)),unordered_pair(sK7(powerset(X0),X1),X2)),powerset(X0))
| ~ in(X2,X3)
| ~ in(sK8(powerset(X0),X1),X3)
| ~ in(sK7(powerset(X0),X1),X3)
| ~ sP0(powerset(X0),X3)
| empty(powerset(X0))
| ~ subset(unordered_pair(singleton(sK8(powerset(X0),X1)),unordered_pair(X2,sK8(powerset(X0),X1))),X0)
| sP0(powerset(X0),X1) )
| ~ spl17_60
| ~ spl17_363 ),
inference(resolution,[],[f3460,f505]) ).
fof(f12581,plain,
( spl17_915
| ~ spl17_59
| ~ spl17_363 ),
inference(avatar_split_clause,[],[f3472,f3459,f500,f12579]) ).
fof(f12579,plain,
( spl17_915
<=> ! [X0,X3,X2,X1] :
( in(unordered_pair(singleton(sK8(powerset(X0),X1)),unordered_pair(sK8(powerset(X0),X1),X2)),powerset(X0))
| ~ in(X2,X3)
| ~ in(sK9(powerset(X0),X1),X3)
| ~ in(sK8(powerset(X0),X1),X3)
| ~ sP0(powerset(X0),X3)
| empty(powerset(X0))
| ~ subset(unordered_pair(singleton(sK9(powerset(X0),X1)),unordered_pair(X2,sK9(powerset(X0),X1))),X0)
| sP0(powerset(X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_915])]) ).
fof(f3472,plain,
( ! [X2,X3,X0,X1] :
( in(unordered_pair(singleton(sK8(powerset(X0),X1)),unordered_pair(sK8(powerset(X0),X1),X2)),powerset(X0))
| ~ in(X2,X3)
| ~ in(sK9(powerset(X0),X1),X3)
| ~ in(sK8(powerset(X0),X1),X3)
| ~ sP0(powerset(X0),X3)
| empty(powerset(X0))
| ~ subset(unordered_pair(singleton(sK9(powerset(X0),X1)),unordered_pair(X2,sK9(powerset(X0),X1))),X0)
| sP0(powerset(X0),X1) )
| ~ spl17_59
| ~ spl17_363 ),
inference(resolution,[],[f3460,f501]) ).
fof(f12577,plain,
( spl17_914
| ~ spl17_292
| ~ spl17_321 ),
inference(avatar_split_clause,[],[f2963,f2873,f2530,f12575]) ).
fof(f12575,plain,
( spl17_914
<=> ! [X2,X0,X1] :
( empty(sK9(X0,sK6(powerset(X1))))
| sP0(sK10(powerset(sK9(X0,sK6(powerset(X1))))),X2)
| sP0(X0,sK6(powerset(X1)))
| element(unordered_pair(singleton(sK7(sK10(powerset(sK9(X0,sK6(powerset(X1))))),X2)),unordered_pair(sK8(sK10(powerset(sK9(X0,sK6(powerset(X1))))),X2),sK7(sK10(powerset(sK9(X0,sK6(powerset(X1))))),X2))),X1)
| empty(powerset(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_914])]) ).
fof(f2530,plain,
( spl17_292
<=> ! [X2,X0,X1] :
( empty(powerset(X0))
| sP0(X1,sK6(powerset(X0)))
| element(X2,X0)
| ~ in(X2,sK9(X1,sK6(powerset(X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_292])]) ).
fof(f2963,plain,
( ! [X2,X0,X1] :
( empty(sK9(X0,sK6(powerset(X1))))
| sP0(sK10(powerset(sK9(X0,sK6(powerset(X1))))),X2)
| sP0(X0,sK6(powerset(X1)))
| element(unordered_pair(singleton(sK7(sK10(powerset(sK9(X0,sK6(powerset(X1))))),X2)),unordered_pair(sK8(sK10(powerset(sK9(X0,sK6(powerset(X1))))),X2),sK7(sK10(powerset(sK9(X0,sK6(powerset(X1))))),X2))),X1)
| empty(powerset(X1)) )
| ~ spl17_292
| ~ spl17_321 ),
inference(resolution,[],[f2874,f2531]) ).
fof(f2531,plain,
( ! [X2,X0,X1] :
( ~ in(X2,sK9(X1,sK6(powerset(X0))))
| sP0(X1,sK6(powerset(X0)))
| element(X2,X0)
| empty(powerset(X0)) )
| ~ spl17_292 ),
inference(avatar_component_clause,[],[f2530]) ).
fof(f12573,plain,
( spl17_913
| ~ spl17_291
| ~ spl17_321 ),
inference(avatar_split_clause,[],[f2957,f2873,f2526,f12571]) ).
fof(f12571,plain,
( spl17_913
<=> ! [X2,X0,X1] :
( empty(sK8(X0,sK6(powerset(X1))))
| sP0(sK10(powerset(sK8(X0,sK6(powerset(X1))))),X2)
| sP0(X0,sK6(powerset(X1)))
| element(unordered_pair(singleton(sK7(sK10(powerset(sK8(X0,sK6(powerset(X1))))),X2)),unordered_pair(sK8(sK10(powerset(sK8(X0,sK6(powerset(X1))))),X2),sK7(sK10(powerset(sK8(X0,sK6(powerset(X1))))),X2))),X1)
| empty(powerset(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_913])]) ).
fof(f2526,plain,
( spl17_291
<=> ! [X2,X0,X1] :
( empty(powerset(X0))
| sP0(X1,sK6(powerset(X0)))
| element(X2,X0)
| ~ in(X2,sK8(X1,sK6(powerset(X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_291])]) ).
fof(f2957,plain,
( ! [X2,X0,X1] :
( empty(sK8(X0,sK6(powerset(X1))))
| sP0(sK10(powerset(sK8(X0,sK6(powerset(X1))))),X2)
| sP0(X0,sK6(powerset(X1)))
| element(unordered_pair(singleton(sK7(sK10(powerset(sK8(X0,sK6(powerset(X1))))),X2)),unordered_pair(sK8(sK10(powerset(sK8(X0,sK6(powerset(X1))))),X2),sK7(sK10(powerset(sK8(X0,sK6(powerset(X1))))),X2))),X1)
| empty(powerset(X1)) )
| ~ spl17_291
| ~ spl17_321 ),
inference(resolution,[],[f2874,f2527]) ).
fof(f2527,plain,
( ! [X2,X0,X1] :
( ~ in(X2,sK8(X1,sK6(powerset(X0))))
| sP0(X1,sK6(powerset(X0)))
| element(X2,X0)
| empty(powerset(X0)) )
| ~ spl17_291 ),
inference(avatar_component_clause,[],[f2526]) ).
fof(f12569,plain,
( spl17_912
| ~ spl17_290
| ~ spl17_321 ),
inference(avatar_split_clause,[],[f2951,f2873,f2522,f12567]) ).
fof(f12567,plain,
( spl17_912
<=> ! [X2,X0,X1] :
( empty(sK7(X0,sK6(powerset(X1))))
| sP0(sK10(powerset(sK7(X0,sK6(powerset(X1))))),X2)
| sP0(X0,sK6(powerset(X1)))
| element(unordered_pair(singleton(sK7(sK10(powerset(sK7(X0,sK6(powerset(X1))))),X2)),unordered_pair(sK8(sK10(powerset(sK7(X0,sK6(powerset(X1))))),X2),sK7(sK10(powerset(sK7(X0,sK6(powerset(X1))))),X2))),X1)
| empty(powerset(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_912])]) ).
fof(f2522,plain,
( spl17_290
<=> ! [X2,X0,X1] :
( empty(powerset(X0))
| sP0(X1,sK6(powerset(X0)))
| element(X2,X0)
| ~ in(X2,sK7(X1,sK6(powerset(X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_290])]) ).
fof(f2951,plain,
( ! [X2,X0,X1] :
( empty(sK7(X0,sK6(powerset(X1))))
| sP0(sK10(powerset(sK7(X0,sK6(powerset(X1))))),X2)
| sP0(X0,sK6(powerset(X1)))
| element(unordered_pair(singleton(sK7(sK10(powerset(sK7(X0,sK6(powerset(X1))))),X2)),unordered_pair(sK8(sK10(powerset(sK7(X0,sK6(powerset(X1))))),X2),sK7(sK10(powerset(sK7(X0,sK6(powerset(X1))))),X2))),X1)
| empty(powerset(X1)) )
| ~ spl17_290
| ~ spl17_321 ),
inference(resolution,[],[f2874,f2523]) ).
fof(f2523,plain,
( ! [X2,X0,X1] :
( ~ in(X2,sK7(X1,sK6(powerset(X0))))
| sP0(X1,sK6(powerset(X0)))
| element(X2,X0)
| empty(powerset(X0)) )
| ~ spl17_290 ),
inference(avatar_component_clause,[],[f2522]) ).
fof(f12565,plain,
( spl17_911
| ~ spl17_292
| ~ spl17_320 ),
inference(avatar_split_clause,[],[f2912,f2869,f2530,f12563]) ).
fof(f12563,plain,
( spl17_911
<=> ! [X2,X0,X1] :
( empty(sK9(X0,sK6(powerset(X1))))
| sP0(sK10(powerset(sK9(X0,sK6(powerset(X1))))),X2)
| sP0(X0,sK6(powerset(X1)))
| element(unordered_pair(singleton(sK8(sK10(powerset(sK9(X0,sK6(powerset(X1))))),X2)),unordered_pair(sK9(sK10(powerset(sK9(X0,sK6(powerset(X1))))),X2),sK8(sK10(powerset(sK9(X0,sK6(powerset(X1))))),X2))),X1)
| empty(powerset(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_911])]) ).
fof(f2912,plain,
( ! [X2,X0,X1] :
( empty(sK9(X0,sK6(powerset(X1))))
| sP0(sK10(powerset(sK9(X0,sK6(powerset(X1))))),X2)
| sP0(X0,sK6(powerset(X1)))
| element(unordered_pair(singleton(sK8(sK10(powerset(sK9(X0,sK6(powerset(X1))))),X2)),unordered_pair(sK9(sK10(powerset(sK9(X0,sK6(powerset(X1))))),X2),sK8(sK10(powerset(sK9(X0,sK6(powerset(X1))))),X2))),X1)
| empty(powerset(X1)) )
| ~ spl17_292
| ~ spl17_320 ),
inference(resolution,[],[f2870,f2531]) ).
fof(f12561,plain,
( spl17_910
| ~ spl17_72
| ~ spl17_903 ),
inference(avatar_split_clause,[],[f12515,f12473,f578,f12559]) ).
fof(f12473,plain,
( spl17_903
<=> ! [X0] :
( in(sK9(sK6(the_InternalRel(sK2)),X0),sK16)
| sP0(sK6(the_InternalRel(sK2)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_903])]) ).
fof(f12515,plain,
( ! [X0] : sP0(sK6(the_InternalRel(sK2)),X0)
| ~ spl17_72
| ~ spl17_903 ),
inference(resolution,[],[f12474,f579]) ).
fof(f12474,plain,
( ! [X0] :
( in(sK9(sK6(the_InternalRel(sK2)),X0),sK16)
| sP0(sK6(the_InternalRel(sK2)),X0) )
| ~ spl17_903 ),
inference(avatar_component_clause,[],[f12473]) ).
fof(f12557,plain,
( spl17_909
| ~ spl17_291
| ~ spl17_320 ),
inference(avatar_split_clause,[],[f2906,f2869,f2526,f12555]) ).
fof(f12555,plain,
( spl17_909
<=> ! [X2,X0,X1] :
( empty(sK8(X0,sK6(powerset(X1))))
| sP0(sK10(powerset(sK8(X0,sK6(powerset(X1))))),X2)
| sP0(X0,sK6(powerset(X1)))
| element(unordered_pair(singleton(sK8(sK10(powerset(sK8(X0,sK6(powerset(X1))))),X2)),unordered_pair(sK9(sK10(powerset(sK8(X0,sK6(powerset(X1))))),X2),sK8(sK10(powerset(sK8(X0,sK6(powerset(X1))))),X2))),X1)
| empty(powerset(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_909])]) ).
fof(f2906,plain,
( ! [X2,X0,X1] :
( empty(sK8(X0,sK6(powerset(X1))))
| sP0(sK10(powerset(sK8(X0,sK6(powerset(X1))))),X2)
| sP0(X0,sK6(powerset(X1)))
| element(unordered_pair(singleton(sK8(sK10(powerset(sK8(X0,sK6(powerset(X1))))),X2)),unordered_pair(sK9(sK10(powerset(sK8(X0,sK6(powerset(X1))))),X2),sK8(sK10(powerset(sK8(X0,sK6(powerset(X1))))),X2))),X1)
| empty(powerset(X1)) )
| ~ spl17_291
| ~ spl17_320 ),
inference(resolution,[],[f2870,f2527]) ).
fof(f12553,plain,
( spl17_908
| ~ spl17_290
| ~ spl17_320 ),
inference(avatar_split_clause,[],[f2900,f2869,f2522,f12551]) ).
fof(f12551,plain,
( spl17_908
<=> ! [X2,X0,X1] :
( empty(sK7(X0,sK6(powerset(X1))))
| sP0(sK10(powerset(sK7(X0,sK6(powerset(X1))))),X2)
| sP0(X0,sK6(powerset(X1)))
| element(unordered_pair(singleton(sK8(sK10(powerset(sK7(X0,sK6(powerset(X1))))),X2)),unordered_pair(sK9(sK10(powerset(sK7(X0,sK6(powerset(X1))))),X2),sK8(sK10(powerset(sK7(X0,sK6(powerset(X1))))),X2))),X1)
| empty(powerset(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_908])]) ).
fof(f2900,plain,
( ! [X2,X0,X1] :
( empty(sK7(X0,sK6(powerset(X1))))
| sP0(sK10(powerset(sK7(X0,sK6(powerset(X1))))),X2)
| sP0(X0,sK6(powerset(X1)))
| element(unordered_pair(singleton(sK8(sK10(powerset(sK7(X0,sK6(powerset(X1))))),X2)),unordered_pair(sK9(sK10(powerset(sK7(X0,sK6(powerset(X1))))),X2),sK8(sK10(powerset(sK7(X0,sK6(powerset(X1))))),X2))),X1)
| empty(powerset(X1)) )
| ~ spl17_290
| ~ spl17_320 ),
inference(resolution,[],[f2870,f2523]) ).
fof(f12491,plain,
( spl17_907
| ~ spl17_38
| ~ spl17_332 ),
inference(avatar_split_clause,[],[f3168,f3130,f351,f12489]) ).
fof(f12489,plain,
( spl17_907
<=> ! [X2,X0,X1] :
( element(sK9(X0,unordered_pair(singleton(sK7(sK10(powerset(powerset(X1))),X2)),unordered_pair(sK8(sK10(powerset(powerset(X1))),X2),sK7(sK10(powerset(powerset(X1))),X2)))),X1)
| sP0(sK10(powerset(powerset(X1))),X2)
| sP0(X0,unordered_pair(singleton(sK7(sK10(powerset(powerset(X1))),X2)),unordered_pair(sK8(sK10(powerset(powerset(X1))),X2),sK7(sK10(powerset(powerset(X1))),X2)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_907])]) ).
fof(f351,plain,
( spl17_38
<=> ! [X0,X1] :
( sP0(X0,X1)
| in(sK9(X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_38])]) ).
fof(f3168,plain,
( ! [X2,X0,X1] :
( element(sK9(X0,unordered_pair(singleton(sK7(sK10(powerset(powerset(X1))),X2)),unordered_pair(sK8(sK10(powerset(powerset(X1))),X2),sK7(sK10(powerset(powerset(X1))),X2)))),X1)
| sP0(sK10(powerset(powerset(X1))),X2)
| sP0(X0,unordered_pair(singleton(sK7(sK10(powerset(powerset(X1))),X2)),unordered_pair(sK8(sK10(powerset(powerset(X1))),X2),sK7(sK10(powerset(powerset(X1))),X2)))) )
| ~ spl17_38
| ~ spl17_332 ),
inference(resolution,[],[f3131,f352]) ).
fof(f352,plain,
( ! [X0,X1] :
( in(sK9(X0,X1),X1)
| sP0(X0,X1) )
| ~ spl17_38 ),
inference(avatar_component_clause,[],[f351]) ).
fof(f12487,plain,
( spl17_906
| ~ spl17_37
| ~ spl17_332 ),
inference(avatar_split_clause,[],[f3165,f3130,f347,f12485]) ).
fof(f12485,plain,
( spl17_906
<=> ! [X2,X0,X1] :
( element(sK8(X0,unordered_pair(singleton(sK7(sK10(powerset(powerset(X1))),X2)),unordered_pair(sK8(sK10(powerset(powerset(X1))),X2),sK7(sK10(powerset(powerset(X1))),X2)))),X1)
| sP0(sK10(powerset(powerset(X1))),X2)
| sP0(X0,unordered_pair(singleton(sK7(sK10(powerset(powerset(X1))),X2)),unordered_pair(sK8(sK10(powerset(powerset(X1))),X2),sK7(sK10(powerset(powerset(X1))),X2)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_906])]) ).
fof(f347,plain,
( spl17_37
<=> ! [X0,X1] :
( sP0(X0,X1)
| in(sK8(X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_37])]) ).
fof(f3165,plain,
( ! [X2,X0,X1] :
( element(sK8(X0,unordered_pair(singleton(sK7(sK10(powerset(powerset(X1))),X2)),unordered_pair(sK8(sK10(powerset(powerset(X1))),X2),sK7(sK10(powerset(powerset(X1))),X2)))),X1)
| sP0(sK10(powerset(powerset(X1))),X2)
| sP0(X0,unordered_pair(singleton(sK7(sK10(powerset(powerset(X1))),X2)),unordered_pair(sK8(sK10(powerset(powerset(X1))),X2),sK7(sK10(powerset(powerset(X1))),X2)))) )
| ~ spl17_37
| ~ spl17_332 ),
inference(resolution,[],[f3131,f348]) ).
fof(f348,plain,
( ! [X0,X1] :
( in(sK8(X0,X1),X1)
| sP0(X0,X1) )
| ~ spl17_37 ),
inference(avatar_component_clause,[],[f347]) ).
fof(f12483,plain,
( spl17_905
| ~ spl17_35
| ~ spl17_332 ),
inference(avatar_split_clause,[],[f3162,f3130,f339,f12481]) ).
fof(f12481,plain,
( spl17_905
<=> ! [X2,X0,X1] :
( element(sK7(X0,unordered_pair(singleton(sK7(sK10(powerset(powerset(X1))),X2)),unordered_pair(sK8(sK10(powerset(powerset(X1))),X2),sK7(sK10(powerset(powerset(X1))),X2)))),X1)
| sP0(sK10(powerset(powerset(X1))),X2)
| sP0(X0,unordered_pair(singleton(sK7(sK10(powerset(powerset(X1))),X2)),unordered_pair(sK8(sK10(powerset(powerset(X1))),X2),sK7(sK10(powerset(powerset(X1))),X2)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_905])]) ).
fof(f339,plain,
( spl17_35
<=> ! [X0,X1] :
( sP0(X0,X1)
| in(sK7(X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_35])]) ).
fof(f3162,plain,
( ! [X2,X0,X1] :
( element(sK7(X0,unordered_pair(singleton(sK7(sK10(powerset(powerset(X1))),X2)),unordered_pair(sK8(sK10(powerset(powerset(X1))),X2),sK7(sK10(powerset(powerset(X1))),X2)))),X1)
| sP0(sK10(powerset(powerset(X1))),X2)
| sP0(X0,unordered_pair(singleton(sK7(sK10(powerset(powerset(X1))),X2)),unordered_pair(sK8(sK10(powerset(powerset(X1))),X2),sK7(sK10(powerset(powerset(X1))),X2)))) )
| ~ spl17_35
| ~ spl17_332 ),
inference(resolution,[],[f3131,f340]) ).
fof(f340,plain,
( ! [X0,X1] :
( in(sK7(X0,X1),X1)
| sP0(X0,X1) )
| ~ spl17_35 ),
inference(avatar_component_clause,[],[f339]) ).
fof(f12479,plain,
( spl17_904
| ~ spl17_38
| ~ spl17_331 ),
inference(avatar_split_clause,[],[f3148,f3126,f351,f12477]) ).
fof(f12477,plain,
( spl17_904
<=> ! [X2,X0,X1] :
( element(sK9(X0,unordered_pair(singleton(sK8(sK10(powerset(powerset(X1))),X2)),unordered_pair(sK9(sK10(powerset(powerset(X1))),X2),sK8(sK10(powerset(powerset(X1))),X2)))),X1)
| sP0(sK10(powerset(powerset(X1))),X2)
| sP0(X0,unordered_pair(singleton(sK8(sK10(powerset(powerset(X1))),X2)),unordered_pair(sK9(sK10(powerset(powerset(X1))),X2),sK8(sK10(powerset(powerset(X1))),X2)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_904])]) ).
fof(f3148,plain,
( ! [X2,X0,X1] :
( element(sK9(X0,unordered_pair(singleton(sK8(sK10(powerset(powerset(X1))),X2)),unordered_pair(sK9(sK10(powerset(powerset(X1))),X2),sK8(sK10(powerset(powerset(X1))),X2)))),X1)
| sP0(sK10(powerset(powerset(X1))),X2)
| sP0(X0,unordered_pair(singleton(sK8(sK10(powerset(powerset(X1))),X2)),unordered_pair(sK9(sK10(powerset(powerset(X1))),X2),sK8(sK10(powerset(powerset(X1))),X2)))) )
| ~ spl17_38
| ~ spl17_331 ),
inference(resolution,[],[f3127,f352]) ).
fof(f12475,plain,
( spl17_131
| spl17_903
| ~ spl17_311
| ~ spl17_667 ),
inference(avatar_split_clause,[],[f8405,f7804,f2726,f12473,f1061]) ).
fof(f1061,plain,
( spl17_131
<=> empty(the_InternalRel(sK2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_131])]) ).
fof(f8405,plain,
( ! [X0] :
( in(sK9(sK6(the_InternalRel(sK2)),X0),sK16)
| sP0(sK6(the_InternalRel(sK2)),X0)
| empty(the_InternalRel(sK2)) )
| ~ spl17_311
| ~ spl17_667 ),
inference(resolution,[],[f7805,f2727]) ).
fof(f12471,plain,
( spl17_902
| ~ spl17_37
| ~ spl17_331 ),
inference(avatar_split_clause,[],[f3145,f3126,f347,f12469]) ).
fof(f12469,plain,
( spl17_902
<=> ! [X2,X0,X1] :
( element(sK8(X0,unordered_pair(singleton(sK8(sK10(powerset(powerset(X1))),X2)),unordered_pair(sK9(sK10(powerset(powerset(X1))),X2),sK8(sK10(powerset(powerset(X1))),X2)))),X1)
| sP0(sK10(powerset(powerset(X1))),X2)
| sP0(X0,unordered_pair(singleton(sK8(sK10(powerset(powerset(X1))),X2)),unordered_pair(sK9(sK10(powerset(powerset(X1))),X2),sK8(sK10(powerset(powerset(X1))),X2)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_902])]) ).
fof(f3145,plain,
( ! [X2,X0,X1] :
( element(sK8(X0,unordered_pair(singleton(sK8(sK10(powerset(powerset(X1))),X2)),unordered_pair(sK9(sK10(powerset(powerset(X1))),X2),sK8(sK10(powerset(powerset(X1))),X2)))),X1)
| sP0(sK10(powerset(powerset(X1))),X2)
| sP0(X0,unordered_pair(singleton(sK8(sK10(powerset(powerset(X1))),X2)),unordered_pair(sK9(sK10(powerset(powerset(X1))),X2),sK8(sK10(powerset(powerset(X1))),X2)))) )
| ~ spl17_37
| ~ spl17_331 ),
inference(resolution,[],[f3127,f348]) ).
fof(f12467,plain,
( spl17_901
| ~ spl17_35
| ~ spl17_331 ),
inference(avatar_split_clause,[],[f3142,f3126,f339,f12465]) ).
fof(f12465,plain,
( spl17_901
<=> ! [X2,X0,X1] :
( element(sK7(X0,unordered_pair(singleton(sK8(sK10(powerset(powerset(X1))),X2)),unordered_pair(sK9(sK10(powerset(powerset(X1))),X2),sK8(sK10(powerset(powerset(X1))),X2)))),X1)
| sP0(sK10(powerset(powerset(X1))),X2)
| sP0(X0,unordered_pair(singleton(sK8(sK10(powerset(powerset(X1))),X2)),unordered_pair(sK9(sK10(powerset(powerset(X1))),X2),sK8(sK10(powerset(powerset(X1))),X2)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_901])]) ).
fof(f3142,plain,
( ! [X2,X0,X1] :
( element(sK7(X0,unordered_pair(singleton(sK8(sK10(powerset(powerset(X1))),X2)),unordered_pair(sK9(sK10(powerset(powerset(X1))),X2),sK8(sK10(powerset(powerset(X1))),X2)))),X1)
| sP0(sK10(powerset(powerset(X1))),X2)
| sP0(X0,unordered_pair(singleton(sK8(sK10(powerset(powerset(X1))),X2)),unordered_pair(sK9(sK10(powerset(powerset(X1))),X2),sK8(sK10(powerset(powerset(X1))),X2)))) )
| ~ spl17_35
| ~ spl17_331 ),
inference(resolution,[],[f3127,f340]) ).
fof(f12463,plain,
( spl17_900
| ~ spl17_203
| ~ spl17_312 ),
inference(avatar_split_clause,[],[f2828,f2730,f1650,f12461]) ).
fof(f12461,plain,
( spl17_900
<=> ! [X0,X3,X2,X1] :
( sP0(sK6(powerset(X0)),X1)
| empty(powerset(X0))
| in(unordered_pair(singleton(X2),unordered_pair(X2,sK8(sK6(powerset(X0)),X1))),powerset(X0))
| ~ in(sK8(sK6(powerset(X0)),X1),X3)
| ~ in(sK7(sK6(powerset(X0)),X1),X3)
| ~ in(X2,X3)
| ~ sP0(powerset(X0),X3)
| ~ subset(unordered_pair(singleton(X2),unordered_pair(X2,sK7(sK6(powerset(X0)),X1))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_900])]) ).
fof(f2828,plain,
( ! [X2,X3,X0,X1] :
( sP0(sK6(powerset(X0)),X1)
| empty(powerset(X0))
| in(unordered_pair(singleton(X2),unordered_pair(X2,sK8(sK6(powerset(X0)),X1))),powerset(X0))
| ~ in(sK8(sK6(powerset(X0)),X1),X3)
| ~ in(sK7(sK6(powerset(X0)),X1),X3)
| ~ in(X2,X3)
| ~ sP0(powerset(X0),X3)
| ~ subset(unordered_pair(singleton(X2),unordered_pair(X2,sK7(sK6(powerset(X0)),X1))),X0) )
| ~ spl17_203
| ~ spl17_312 ),
inference(duplicate_literal_removal,[],[f2788]) ).
fof(f2788,plain,
( ! [X2,X3,X0,X1] :
( sP0(sK6(powerset(X0)),X1)
| empty(powerset(X0))
| in(unordered_pair(singleton(X2),unordered_pair(X2,sK8(sK6(powerset(X0)),X1))),powerset(X0))
| ~ in(sK8(sK6(powerset(X0)),X1),X3)
| ~ in(sK7(sK6(powerset(X0)),X1),X3)
| ~ in(X2,X3)
| ~ sP0(powerset(X0),X3)
| empty(powerset(X0))
| ~ subset(unordered_pair(singleton(X2),unordered_pair(X2,sK7(sK6(powerset(X0)),X1))),X0) )
| ~ spl17_203
| ~ spl17_312 ),
inference(resolution,[],[f2731,f1651]) ).
fof(f12459,plain,
( spl17_899
| ~ spl17_284
| ~ spl17_312 ),
inference(avatar_split_clause,[],[f2816,f2730,f2409,f12457]) ).
fof(f12457,plain,
( spl17_899
<=> ! [X2,X0,X1] :
( sP0(sK6(sK9(X0,sK10(powerset(powerset(X1))))),X2)
| empty(sK9(X0,sK10(powerset(powerset(X1)))))
| element(unordered_pair(singleton(sK7(sK6(sK9(X0,sK10(powerset(powerset(X1))))),X2)),unordered_pair(sK8(sK6(sK9(X0,sK10(powerset(powerset(X1))))),X2),sK7(sK6(sK9(X0,sK10(powerset(powerset(X1))))),X2))),X1)
| sP0(X0,sK10(powerset(powerset(X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_899])]) ).
fof(f2816,plain,
( ! [X2,X0,X1] :
( sP0(sK6(sK9(X0,sK10(powerset(powerset(X1))))),X2)
| empty(sK9(X0,sK10(powerset(powerset(X1)))))
| element(unordered_pair(singleton(sK7(sK6(sK9(X0,sK10(powerset(powerset(X1))))),X2)),unordered_pair(sK8(sK6(sK9(X0,sK10(powerset(powerset(X1))))),X2),sK7(sK6(sK9(X0,sK10(powerset(powerset(X1))))),X2))),X1)
| sP0(X0,sK10(powerset(powerset(X1)))) )
| ~ spl17_284
| ~ spl17_312 ),
inference(resolution,[],[f2731,f2410]) ).
fof(f12455,plain,
( spl17_898
| ~ spl17_282
| ~ spl17_312 ),
inference(avatar_split_clause,[],[f2810,f2730,f2401,f12453]) ).
fof(f12453,plain,
( spl17_898
<=> ! [X2,X0,X1] :
( sP0(sK6(sK8(X0,sK10(powerset(powerset(X1))))),X2)
| empty(sK8(X0,sK10(powerset(powerset(X1)))))
| element(unordered_pair(singleton(sK7(sK6(sK8(X0,sK10(powerset(powerset(X1))))),X2)),unordered_pair(sK8(sK6(sK8(X0,sK10(powerset(powerset(X1))))),X2),sK7(sK6(sK8(X0,sK10(powerset(powerset(X1))))),X2))),X1)
| sP0(X0,sK10(powerset(powerset(X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_898])]) ).
fof(f2810,plain,
( ! [X2,X0,X1] :
( sP0(sK6(sK8(X0,sK10(powerset(powerset(X1))))),X2)
| empty(sK8(X0,sK10(powerset(powerset(X1)))))
| element(unordered_pair(singleton(sK7(sK6(sK8(X0,sK10(powerset(powerset(X1))))),X2)),unordered_pair(sK8(sK6(sK8(X0,sK10(powerset(powerset(X1))))),X2),sK7(sK6(sK8(X0,sK10(powerset(powerset(X1))))),X2))),X1)
| sP0(X0,sK10(powerset(powerset(X1)))) )
| ~ spl17_282
| ~ spl17_312 ),
inference(resolution,[],[f2731,f2402]) ).
fof(f12451,plain,
( spl17_897
| ~ spl17_280
| ~ spl17_312 ),
inference(avatar_split_clause,[],[f2804,f2730,f2393,f12449]) ).
fof(f12449,plain,
( spl17_897
<=> ! [X2,X0,X1] :
( sP0(sK6(sK7(X0,sK10(powerset(powerset(X1))))),X2)
| empty(sK7(X0,sK10(powerset(powerset(X1)))))
| element(unordered_pair(singleton(sK7(sK6(sK7(X0,sK10(powerset(powerset(X1))))),X2)),unordered_pair(sK8(sK6(sK7(X0,sK10(powerset(powerset(X1))))),X2),sK7(sK6(sK7(X0,sK10(powerset(powerset(X1))))),X2))),X1)
| sP0(X0,sK10(powerset(powerset(X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_897])]) ).
fof(f2804,plain,
( ! [X2,X0,X1] :
( sP0(sK6(sK7(X0,sK10(powerset(powerset(X1))))),X2)
| empty(sK7(X0,sK10(powerset(powerset(X1)))))
| element(unordered_pair(singleton(sK7(sK6(sK7(X0,sK10(powerset(powerset(X1))))),X2)),unordered_pair(sK8(sK6(sK7(X0,sK10(powerset(powerset(X1))))),X2),sK7(sK6(sK7(X0,sK10(powerset(powerset(X1))))),X2))),X1)
| sP0(X0,sK10(powerset(powerset(X1)))) )
| ~ spl17_280
| ~ spl17_312 ),
inference(resolution,[],[f2731,f2394]) ).
fof(f12447,plain,
( spl17_896
| ~ spl17_203
| ~ spl17_311 ),
inference(avatar_split_clause,[],[f2779,f2726,f1650,f12445]) ).
fof(f12445,plain,
( spl17_896
<=> ! [X0,X3,X2,X1] :
( sP0(sK6(powerset(X0)),X1)
| empty(powerset(X0))
| in(unordered_pair(singleton(X2),unordered_pair(X2,sK9(sK6(powerset(X0)),X1))),powerset(X0))
| ~ in(sK9(sK6(powerset(X0)),X1),X3)
| ~ in(sK8(sK6(powerset(X0)),X1),X3)
| ~ in(X2,X3)
| ~ sP0(powerset(X0),X3)
| ~ subset(unordered_pair(singleton(X2),unordered_pair(X2,sK8(sK6(powerset(X0)),X1))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_896])]) ).
fof(f2779,plain,
( ! [X2,X3,X0,X1] :
( sP0(sK6(powerset(X0)),X1)
| empty(powerset(X0))
| in(unordered_pair(singleton(X2),unordered_pair(X2,sK9(sK6(powerset(X0)),X1))),powerset(X0))
| ~ in(sK9(sK6(powerset(X0)),X1),X3)
| ~ in(sK8(sK6(powerset(X0)),X1),X3)
| ~ in(X2,X3)
| ~ sP0(powerset(X0),X3)
| ~ subset(unordered_pair(singleton(X2),unordered_pair(X2,sK8(sK6(powerset(X0)),X1))),X0) )
| ~ spl17_203
| ~ spl17_311 ),
inference(duplicate_literal_removal,[],[f2739]) ).
fof(f2739,plain,
( ! [X2,X3,X0,X1] :
( sP0(sK6(powerset(X0)),X1)
| empty(powerset(X0))
| in(unordered_pair(singleton(X2),unordered_pair(X2,sK9(sK6(powerset(X0)),X1))),powerset(X0))
| ~ in(sK9(sK6(powerset(X0)),X1),X3)
| ~ in(sK8(sK6(powerset(X0)),X1),X3)
| ~ in(X2,X3)
| ~ sP0(powerset(X0),X3)
| empty(powerset(X0))
| ~ subset(unordered_pair(singleton(X2),unordered_pair(X2,sK8(sK6(powerset(X0)),X1))),X0) )
| ~ spl17_203
| ~ spl17_311 ),
inference(resolution,[],[f2727,f1651]) ).
fof(f12443,plain,
( spl17_895
| ~ spl17_284
| ~ spl17_311 ),
inference(avatar_split_clause,[],[f2767,f2726,f2409,f12441]) ).
fof(f12441,plain,
( spl17_895
<=> ! [X2,X0,X1] :
( sP0(sK6(sK9(X0,sK10(powerset(powerset(X1))))),X2)
| empty(sK9(X0,sK10(powerset(powerset(X1)))))
| element(unordered_pair(singleton(sK8(sK6(sK9(X0,sK10(powerset(powerset(X1))))),X2)),unordered_pair(sK9(sK6(sK9(X0,sK10(powerset(powerset(X1))))),X2),sK8(sK6(sK9(X0,sK10(powerset(powerset(X1))))),X2))),X1)
| sP0(X0,sK10(powerset(powerset(X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_895])]) ).
fof(f2767,plain,
( ! [X2,X0,X1] :
( sP0(sK6(sK9(X0,sK10(powerset(powerset(X1))))),X2)
| empty(sK9(X0,sK10(powerset(powerset(X1)))))
| element(unordered_pair(singleton(sK8(sK6(sK9(X0,sK10(powerset(powerset(X1))))),X2)),unordered_pair(sK9(sK6(sK9(X0,sK10(powerset(powerset(X1))))),X2),sK8(sK6(sK9(X0,sK10(powerset(powerset(X1))))),X2))),X1)
| sP0(X0,sK10(powerset(powerset(X1)))) )
| ~ spl17_284
| ~ spl17_311 ),
inference(resolution,[],[f2727,f2410]) ).
fof(f12439,plain,
( spl17_894
| ~ spl17_282
| ~ spl17_311 ),
inference(avatar_split_clause,[],[f2761,f2726,f2401,f12437]) ).
fof(f12437,plain,
( spl17_894
<=> ! [X2,X0,X1] :
( sP0(sK6(sK8(X0,sK10(powerset(powerset(X1))))),X2)
| empty(sK8(X0,sK10(powerset(powerset(X1)))))
| element(unordered_pair(singleton(sK8(sK6(sK8(X0,sK10(powerset(powerset(X1))))),X2)),unordered_pair(sK9(sK6(sK8(X0,sK10(powerset(powerset(X1))))),X2),sK8(sK6(sK8(X0,sK10(powerset(powerset(X1))))),X2))),X1)
| sP0(X0,sK10(powerset(powerset(X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_894])]) ).
fof(f2761,plain,
( ! [X2,X0,X1] :
( sP0(sK6(sK8(X0,sK10(powerset(powerset(X1))))),X2)
| empty(sK8(X0,sK10(powerset(powerset(X1)))))
| element(unordered_pair(singleton(sK8(sK6(sK8(X0,sK10(powerset(powerset(X1))))),X2)),unordered_pair(sK9(sK6(sK8(X0,sK10(powerset(powerset(X1))))),X2),sK8(sK6(sK8(X0,sK10(powerset(powerset(X1))))),X2))),X1)
| sP0(X0,sK10(powerset(powerset(X1)))) )
| ~ spl17_282
| ~ spl17_311 ),
inference(resolution,[],[f2727,f2402]) ).
fof(f12435,plain,
( spl17_893
| ~ spl17_280
| ~ spl17_311 ),
inference(avatar_split_clause,[],[f2755,f2726,f2393,f12433]) ).
fof(f12433,plain,
( spl17_893
<=> ! [X2,X0,X1] :
( sP0(sK6(sK7(X0,sK10(powerset(powerset(X1))))),X2)
| empty(sK7(X0,sK10(powerset(powerset(X1)))))
| element(unordered_pair(singleton(sK8(sK6(sK7(X0,sK10(powerset(powerset(X1))))),X2)),unordered_pair(sK9(sK6(sK7(X0,sK10(powerset(powerset(X1))))),X2),sK8(sK6(sK7(X0,sK10(powerset(powerset(X1))))),X2))),X1)
| sP0(X0,sK10(powerset(powerset(X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_893])]) ).
fof(f2755,plain,
( ! [X2,X0,X1] :
( sP0(sK6(sK7(X0,sK10(powerset(powerset(X1))))),X2)
| empty(sK7(X0,sK10(powerset(powerset(X1)))))
| element(unordered_pair(singleton(sK8(sK6(sK7(X0,sK10(powerset(powerset(X1))))),X2)),unordered_pair(sK9(sK6(sK7(X0,sK10(powerset(powerset(X1))))),X2),sK8(sK6(sK7(X0,sK10(powerset(powerset(X1))))),X2))),X1)
| sP0(X0,sK10(powerset(powerset(X1)))) )
| ~ spl17_280
| ~ spl17_311 ),
inference(resolution,[],[f2727,f2394]) ).
fof(f12431,plain,
( spl17_892
| ~ spl17_373
| ~ spl17_654 ),
inference(avatar_split_clause,[],[f7941,f7696,f3555,f12429]) ).
fof(f7941,plain,
( ! [X0] :
( in(X0,sK16)
| ~ in(X0,the_carrier(sK2))
| ~ element(X0,the_carrier(sK2))
| ~ related(sK2,sK4,X0) )
| ~ spl17_373
| ~ spl17_654 ),
inference(resolution,[],[f7697,f3556]) ).
fof(f12345,plain,
( spl17_891
| ~ spl17_16
| ~ spl17_362 ),
inference(avatar_split_clause,[],[f3455,f3449,f251,f12343]) ).
fof(f12343,plain,
( spl17_891
<=> ! [X0,X3,X2,X1] :
( ~ in(X0,X1)
| ~ in(X2,X1)
| ~ in(X3,X1)
| ~ sP0(powerset(unordered_pair(singleton(X2),unordered_pair(X0,X2))),X1)
| empty(powerset(unordered_pair(singleton(X2),unordered_pair(X0,X2))))
| ~ subset(unordered_pair(singleton(X3),unordered_pair(X3,X2)),unordered_pair(singleton(X2),unordered_pair(X0,X2)))
| in(unordered_pair(singleton(X3),unordered_pair(X3,X0)),powerset(unordered_pair(singleton(X2),unordered_pair(X0,X2)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_891])]) ).
fof(f251,plain,
( spl17_16
<=> ! [X0] : subset(X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_16])]) ).
fof(f3449,plain,
( spl17_362
<=> ! [X4,X0,X3,X2,X1] :
( in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),powerset(X2))
| ~ in(X1,X3)
| ~ in(X4,X3)
| ~ in(X0,X3)
| ~ sP0(powerset(X2),X3)
| empty(powerset(X2))
| ~ subset(unordered_pair(singleton(X0),unordered_pair(X0,X4)),X2)
| ~ subset(unordered_pair(singleton(X4),unordered_pair(X1,X4)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_362])]) ).
fof(f3455,plain,
( ! [X2,X3,X0,X1] :
( ~ in(X0,X1)
| ~ in(X2,X1)
| ~ in(X3,X1)
| ~ sP0(powerset(unordered_pair(singleton(X2),unordered_pair(X0,X2))),X1)
| empty(powerset(unordered_pair(singleton(X2),unordered_pair(X0,X2))))
| ~ subset(unordered_pair(singleton(X3),unordered_pair(X3,X2)),unordered_pair(singleton(X2),unordered_pair(X0,X2)))
| in(unordered_pair(singleton(X3),unordered_pair(X3,X0)),powerset(unordered_pair(singleton(X2),unordered_pair(X0,X2)))) )
| ~ spl17_16
| ~ spl17_362 ),
inference(resolution,[],[f3450,f252]) ).
fof(f252,plain,
( ! [X0] : subset(X0,X0)
| ~ spl17_16 ),
inference(avatar_component_clause,[],[f251]) ).
fof(f3450,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ subset(unordered_pair(singleton(X4),unordered_pair(X1,X4)),X2)
| ~ in(X1,X3)
| ~ in(X4,X3)
| ~ in(X0,X3)
| ~ sP0(powerset(X2),X3)
| empty(powerset(X2))
| ~ subset(unordered_pair(singleton(X0),unordered_pair(X0,X4)),X2)
| in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),powerset(X2)) )
| ~ spl17_362 ),
inference(avatar_component_clause,[],[f3449]) ).
fof(f12341,plain,
( spl17_890
| ~ spl17_16
| ~ spl17_360 ),
inference(avatar_split_clause,[],[f3452,f3441,f251,f12339]) ).
fof(f12339,plain,
( spl17_890
<=> ! [X0,X3,X2,X1] :
( empty(powerset(unordered_pair(singleton(X0),unordered_pair(X0,X1))))
| in(unordered_pair(singleton(X0),unordered_pair(X0,X2)),powerset(unordered_pair(singleton(X0),unordered_pair(X0,X1))))
| ~ in(X2,X3)
| ~ in(X1,X3)
| ~ in(X0,X3)
| ~ sP0(powerset(unordered_pair(singleton(X0),unordered_pair(X0,X1))),X3)
| ~ subset(unordered_pair(singleton(X1),unordered_pair(X1,X2)),unordered_pair(singleton(X0),unordered_pair(X0,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_890])]) ).
fof(f3441,plain,
( spl17_360
<=> ! [X4,X0,X3,X2,X1] :
( ~ subset(unordered_pair(singleton(X0),unordered_pair(X0,X1)),X2)
| empty(powerset(X2))
| in(unordered_pair(singleton(X3),unordered_pair(X3,X1)),powerset(X2))
| ~ in(X1,X4)
| ~ in(X0,X4)
| ~ in(X3,X4)
| ~ sP0(powerset(X2),X4)
| ~ subset(unordered_pair(singleton(X3),unordered_pair(X3,X0)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_360])]) ).
fof(f3452,plain,
( ! [X2,X3,X0,X1] :
( empty(powerset(unordered_pair(singleton(X0),unordered_pair(X0,X1))))
| in(unordered_pair(singleton(X0),unordered_pair(X0,X2)),powerset(unordered_pair(singleton(X0),unordered_pair(X0,X1))))
| ~ in(X2,X3)
| ~ in(X1,X3)
| ~ in(X0,X3)
| ~ sP0(powerset(unordered_pair(singleton(X0),unordered_pair(X0,X1))),X3)
| ~ subset(unordered_pair(singleton(X1),unordered_pair(X1,X2)),unordered_pair(singleton(X0),unordered_pair(X0,X1))) )
| ~ spl17_16
| ~ spl17_360 ),
inference(resolution,[],[f3442,f252]) ).
fof(f3442,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ subset(unordered_pair(singleton(X3),unordered_pair(X3,X0)),X2)
| empty(powerset(X2))
| in(unordered_pair(singleton(X3),unordered_pair(X3,X1)),powerset(X2))
| ~ in(X1,X4)
| ~ in(X0,X4)
| ~ in(X3,X4)
| ~ sP0(powerset(X2),X4)
| ~ subset(unordered_pair(singleton(X0),unordered_pair(X0,X1)),X2) )
| ~ spl17_360 ),
inference(avatar_component_clause,[],[f3441]) ).
fof(f12337,plain,
( spl17_889
| ~ spl17_304
| ~ spl17_359 ),
inference(avatar_split_clause,[],[f3436,f3407,f2657,f12335]) ).
fof(f12335,plain,
( spl17_889
<=> ! [X4,X0,X3,X2,X1] :
( in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),cartesian_product2(the_carrier(X2),the_carrier(X2)))
| ~ in(X1,X3)
| ~ in(X4,X3)
| ~ in(X0,X3)
| ~ sP0(cartesian_product2(the_carrier(X2),the_carrier(X2)),X3)
| ~ in(X4,the_carrier(X2))
| ~ in(X0,the_carrier(X2))
| ~ rel_str(X2)
| empty(cartesian_product2(the_carrier(X2),the_carrier(X2)))
| ~ in(unordered_pair(singleton(X4),unordered_pair(X4,X1)),the_InternalRel(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_889])]) ).
fof(f3407,plain,
( spl17_359
<=> ! [X5,X4,X0,X3,X2,X1] :
( ~ in(unordered_pair(singleton(X1),unordered_pair(X1,X0)),cartesian_product2(X2,X3))
| in(unordered_pair(singleton(X4),unordered_pair(X4,X0)),cartesian_product2(X2,X3))
| ~ in(X0,X5)
| ~ in(X1,X5)
| ~ in(X4,X5)
| ~ sP0(cartesian_product2(X2,X3),X5)
| ~ in(X1,X3)
| ~ in(X4,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_359])]) ).
fof(f3436,plain,
( ! [X2,X3,X0,X1,X4] :
( in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),cartesian_product2(the_carrier(X2),the_carrier(X2)))
| ~ in(X1,X3)
| ~ in(X4,X3)
| ~ in(X0,X3)
| ~ sP0(cartesian_product2(the_carrier(X2),the_carrier(X2)),X3)
| ~ in(X4,the_carrier(X2))
| ~ in(X0,the_carrier(X2))
| ~ rel_str(X2)
| empty(cartesian_product2(the_carrier(X2),the_carrier(X2)))
| ~ in(unordered_pair(singleton(X4),unordered_pair(X4,X1)),the_InternalRel(X2)) )
| ~ spl17_304
| ~ spl17_359 ),
inference(resolution,[],[f3408,f2658]) ).
fof(f3408,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ in(unordered_pair(singleton(X1),unordered_pair(X1,X0)),cartesian_product2(X2,X3))
| in(unordered_pair(singleton(X4),unordered_pair(X4,X0)),cartesian_product2(X2,X3))
| ~ in(X0,X5)
| ~ in(X1,X5)
| ~ in(X4,X5)
| ~ sP0(cartesian_product2(X2,X3),X5)
| ~ in(X1,X3)
| ~ in(X4,X2) )
| ~ spl17_359 ),
inference(avatar_component_clause,[],[f3407]) ).
fof(f12333,plain,
( spl17_888
| ~ spl17_200
| ~ spl17_304 ),
inference(avatar_split_clause,[],[f2682,f2657,f1624,f12331]) ).
fof(f12331,plain,
( spl17_888
<=> ! [X4,X0,X3,X2,X1] :
( ~ rel_str(X0)
| empty(cartesian_product2(the_carrier(X0),the_carrier(X0)))
| ~ in(unordered_pair(singleton(X1),unordered_pair(X2,X1)),the_InternalRel(X0))
| in(unordered_pair(singleton(X3),unordered_pair(X3,X2)),cartesian_product2(the_carrier(X0),the_carrier(X0)))
| ~ in(X2,X4)
| ~ in(X1,X4)
| ~ in(X3,X4)
| ~ sP0(cartesian_product2(the_carrier(X0),the_carrier(X0)),X4)
| ~ in(X1,the_carrier(X0))
| ~ in(X3,the_carrier(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_888])]) ).
fof(f2682,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ rel_str(X0)
| empty(cartesian_product2(the_carrier(X0),the_carrier(X0)))
| ~ in(unordered_pair(singleton(X1),unordered_pair(X2,X1)),the_InternalRel(X0))
| in(unordered_pair(singleton(X3),unordered_pair(X3,X2)),cartesian_product2(the_carrier(X0),the_carrier(X0)))
| ~ in(X2,X4)
| ~ in(X1,X4)
| ~ in(X3,X4)
| ~ sP0(cartesian_product2(the_carrier(X0),the_carrier(X0)),X4)
| ~ in(X1,the_carrier(X0))
| ~ in(X3,the_carrier(X0)) )
| ~ spl17_200
| ~ spl17_304 ),
inference(resolution,[],[f2658,f1625]) ).
fof(f12329,plain,
( spl17_887
| ~ spl17_201
| ~ spl17_304 ),
inference(avatar_split_clause,[],[f2681,f2657,f1628,f12327]) ).
fof(f12327,plain,
( spl17_887
<=> ! [X4,X0,X3,X2,X1] :
( ~ rel_str(X0)
| empty(cartesian_product2(the_carrier(X0),the_carrier(X0)))
| ~ in(unordered_pair(singleton(X1),unordered_pair(X2,X1)),the_InternalRel(X0))
| in(unordered_pair(singleton(X1),unordered_pair(X1,X3)),cartesian_product2(the_carrier(X0),the_carrier(X0)))
| ~ in(X3,X4)
| ~ in(X2,X4)
| ~ in(X1,X4)
| ~ sP0(cartesian_product2(the_carrier(X0),the_carrier(X0)),X4)
| ~ in(X3,the_carrier(X0))
| ~ in(X2,the_carrier(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_887])]) ).
fof(f2681,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ rel_str(X0)
| empty(cartesian_product2(the_carrier(X0),the_carrier(X0)))
| ~ in(unordered_pair(singleton(X1),unordered_pair(X2,X1)),the_InternalRel(X0))
| in(unordered_pair(singleton(X1),unordered_pair(X1,X3)),cartesian_product2(the_carrier(X0),the_carrier(X0)))
| ~ in(X3,X4)
| ~ in(X2,X4)
| ~ in(X1,X4)
| ~ sP0(cartesian_product2(the_carrier(X0),the_carrier(X0)),X4)
| ~ in(X3,the_carrier(X0))
| ~ in(X2,the_carrier(X0)) )
| ~ spl17_201
| ~ spl17_304 ),
inference(resolution,[],[f2658,f1629]) ).
fof(f12325,plain,
( spl17_886
| ~ spl17_124
| ~ spl17_304 ),
inference(avatar_split_clause,[],[f2678,f2657,f1014,f12323]) ).
fof(f12323,plain,
( spl17_886
<=> ! [X4,X0,X3,X2,X1] :
( ~ rel_str(X0)
| empty(cartesian_product2(the_carrier(X0),the_carrier(X0)))
| ~ in(unordered_pair(singleton(X1),unordered_pair(X1,X2)),the_InternalRel(X0))
| in(unordered_pair(singleton(X1),unordered_pair(X1,X3)),cartesian_product2(the_carrier(X0),the_carrier(X0)))
| ~ in(X3,X4)
| ~ in(X2,X4)
| ~ in(X1,X4)
| ~ sP0(cartesian_product2(the_carrier(X0),the_carrier(X0)),X4)
| ~ in(X3,the_carrier(X0))
| ~ in(X2,the_carrier(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_886])]) ).
fof(f1014,plain,
( spl17_124
<=> ! [X5,X4,X0,X3,X2,X1] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),cartesian_product2(X2,X3))
| in(unordered_pair(singleton(X0),unordered_pair(X0,X4)),cartesian_product2(X2,X3))
| ~ in(X4,X5)
| ~ in(X1,X5)
| ~ in(X0,X5)
| ~ sP0(cartesian_product2(X2,X3),X5)
| ~ in(X4,X3)
| ~ in(X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_124])]) ).
fof(f2678,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ rel_str(X0)
| empty(cartesian_product2(the_carrier(X0),the_carrier(X0)))
| ~ in(unordered_pair(singleton(X1),unordered_pair(X1,X2)),the_InternalRel(X0))
| in(unordered_pair(singleton(X1),unordered_pair(X1,X3)),cartesian_product2(the_carrier(X0),the_carrier(X0)))
| ~ in(X3,X4)
| ~ in(X2,X4)
| ~ in(X1,X4)
| ~ sP0(cartesian_product2(the_carrier(X0),the_carrier(X0)),X4)
| ~ in(X3,the_carrier(X0))
| ~ in(X2,the_carrier(X0)) )
| ~ spl17_124
| ~ spl17_304 ),
inference(resolution,[],[f2658,f1015]) ).
fof(f1015,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),cartesian_product2(X2,X3))
| in(unordered_pair(singleton(X0),unordered_pair(X0,X4)),cartesian_product2(X2,X3))
| ~ in(X4,X5)
| ~ in(X1,X5)
| ~ in(X0,X5)
| ~ sP0(cartesian_product2(X2,X3),X5)
| ~ in(X4,X3)
| ~ in(X1,X2) )
| ~ spl17_124 ),
inference(avatar_component_clause,[],[f1014]) ).
fof(f12267,plain,
( spl17_885
| ~ spl17_312
| ~ spl17_341 ),
inference(avatar_split_clause,[],[f3252,f3243,f2730,f12265]) ).
fof(f12265,plain,
( spl17_885
<=> ! [X0,X3,X2,X1] :
( ~ in(unordered_pair(singleton(sK8(sK6(X0),X1)),unordered_pair(sK8(sK6(X0),X1),X2)),X0)
| in(unordered_pair(singleton(sK7(sK6(X0),X1)),unordered_pair(sK7(sK6(X0),X1),X2)),X0)
| ~ in(X2,X3)
| ~ in(sK8(sK6(X0),X1),X3)
| ~ in(sK7(sK6(X0),X1),X3)
| ~ sP0(X0,X3)
| sP0(sK6(X0),X1)
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_885])]) ).
fof(f3252,plain,
( ! [X2,X3,X0,X1] :
( ~ in(unordered_pair(singleton(sK8(sK6(X0),X1)),unordered_pair(sK8(sK6(X0),X1),X2)),X0)
| in(unordered_pair(singleton(sK7(sK6(X0),X1)),unordered_pair(sK7(sK6(X0),X1),X2)),X0)
| ~ in(X2,X3)
| ~ in(sK8(sK6(X0),X1),X3)
| ~ in(sK7(sK6(X0),X1),X3)
| ~ sP0(X0,X3)
| sP0(sK6(X0),X1)
| empty(X0) )
| ~ spl17_312
| ~ spl17_341 ),
inference(resolution,[],[f3244,f2731]) ).
fof(f12263,plain,
( spl17_884
| ~ spl17_311
| ~ spl17_341 ),
inference(avatar_split_clause,[],[f3249,f3243,f2726,f12261]) ).
fof(f12261,plain,
( spl17_884
<=> ! [X0,X3,X2,X1] :
( ~ in(unordered_pair(singleton(sK9(sK6(X0),X1)),unordered_pair(sK9(sK6(X0),X1),X2)),X0)
| in(unordered_pair(singleton(sK8(sK6(X0),X1)),unordered_pair(sK8(sK6(X0),X1),X2)),X0)
| ~ in(X2,X3)
| ~ in(sK9(sK6(X0),X1),X3)
| ~ in(sK8(sK6(X0),X1),X3)
| ~ sP0(X0,X3)
| sP0(sK6(X0),X1)
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_884])]) ).
fof(f3249,plain,
( ! [X2,X3,X0,X1] :
( ~ in(unordered_pair(singleton(sK9(sK6(X0),X1)),unordered_pair(sK9(sK6(X0),X1),X2)),X0)
| in(unordered_pair(singleton(sK8(sK6(X0),X1)),unordered_pair(sK8(sK6(X0),X1),X2)),X0)
| ~ in(X2,X3)
| ~ in(sK9(sK6(X0),X1),X3)
| ~ in(sK8(sK6(X0),X1),X3)
| ~ sP0(X0,X3)
| sP0(sK6(X0),X1)
| empty(X0) )
| ~ spl17_311
| ~ spl17_341 ),
inference(resolution,[],[f3244,f2727]) ).
fof(f12259,plain,
( ~ spl17_2
| spl17_883
| ~ spl17_64
| ~ spl17_667 ),
inference(avatar_split_clause,[],[f8412,f7804,f528,f12257,f184]) ).
fof(f12257,plain,
( spl17_883
<=> ! [X0] :
( in(X0,sK16)
| ~ element(X0,the_carrier(sK2))
| ~ related(sK2,X0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_883])]) ).
fof(f528,plain,
( spl17_64
<=> ! [X2,X0,X1] :
( in(unordered_pair(singleton(X1),unordered_pair(X1,X2)),the_InternalRel(X0))
| ~ related(X0,X1,X2)
| ~ element(X2,the_carrier(X0))
| ~ element(X1,the_carrier(X0))
| ~ rel_str(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_64])]) ).
fof(f8412,plain,
( ! [X0] :
( in(X0,sK16)
| ~ related(sK2,X0,X0)
| ~ element(X0,the_carrier(sK2))
| ~ rel_str(sK2) )
| ~ spl17_64
| ~ spl17_667 ),
inference(duplicate_literal_removal,[],[f8401]) ).
fof(f8401,plain,
( ! [X0] :
( in(X0,sK16)
| ~ related(sK2,X0,X0)
| ~ element(X0,the_carrier(sK2))
| ~ element(X0,the_carrier(sK2))
| ~ rel_str(sK2) )
| ~ spl17_64
| ~ spl17_667 ),
inference(resolution,[],[f7805,f529]) ).
fof(f529,plain,
( ! [X2,X0,X1] :
( in(unordered_pair(singleton(X1),unordered_pair(X1,X2)),the_InternalRel(X0))
| ~ related(X0,X1,X2)
| ~ element(X2,the_carrier(X0))
| ~ element(X1,the_carrier(X0))
| ~ rel_str(X0) )
| ~ spl17_64 ),
inference(avatar_component_clause,[],[f528]) ).
fof(f12255,plain,
( spl17_882
| ~ spl17_75
| ~ spl17_332 ),
inference(avatar_split_clause,[],[f3159,f3130,f643,f12253]) ).
fof(f12253,plain,
( spl17_882
<=> ! [X0,X1] :
( element(sK10(unordered_pair(singleton(sK7(sK10(powerset(powerset(X0))),X1)),unordered_pair(sK8(sK10(powerset(powerset(X0))),X1),sK7(sK10(powerset(powerset(X0))),X1)))),X0)
| sP0(sK10(powerset(powerset(X0))),X1)
| empty(unordered_pair(singleton(sK7(sK10(powerset(powerset(X0))),X1)),unordered_pair(sK8(sK10(powerset(powerset(X0))),X1),sK7(sK10(powerset(powerset(X0))),X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_882])]) ).
fof(f643,plain,
( spl17_75
<=> ! [X0] :
( empty(X0)
| in(sK10(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_75])]) ).
fof(f3159,plain,
( ! [X0,X1] :
( element(sK10(unordered_pair(singleton(sK7(sK10(powerset(powerset(X0))),X1)),unordered_pair(sK8(sK10(powerset(powerset(X0))),X1),sK7(sK10(powerset(powerset(X0))),X1)))),X0)
| sP0(sK10(powerset(powerset(X0))),X1)
| empty(unordered_pair(singleton(sK7(sK10(powerset(powerset(X0))),X1)),unordered_pair(sK8(sK10(powerset(powerset(X0))),X1),sK7(sK10(powerset(powerset(X0))),X1)))) )
| ~ spl17_75
| ~ spl17_332 ),
inference(resolution,[],[f3131,f644]) ).
fof(f644,plain,
( ! [X0] :
( in(sK10(X0),X0)
| empty(X0) )
| ~ spl17_75 ),
inference(avatar_component_clause,[],[f643]) ).
fof(f12251,plain,
( spl17_881
| ~ spl17_75
| ~ spl17_331 ),
inference(avatar_split_clause,[],[f3139,f3126,f643,f12249]) ).
fof(f12249,plain,
( spl17_881
<=> ! [X0,X1] :
( element(sK10(unordered_pair(singleton(sK8(sK10(powerset(powerset(X0))),X1)),unordered_pair(sK9(sK10(powerset(powerset(X0))),X1),sK8(sK10(powerset(powerset(X0))),X1)))),X0)
| sP0(sK10(powerset(powerset(X0))),X1)
| empty(unordered_pair(singleton(sK8(sK10(powerset(powerset(X0))),X1)),unordered_pair(sK9(sK10(powerset(powerset(X0))),X1),sK8(sK10(powerset(powerset(X0))),X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_881])]) ).
fof(f3139,plain,
( ! [X0,X1] :
( element(sK10(unordered_pair(singleton(sK8(sK10(powerset(powerset(X0))),X1)),unordered_pair(sK9(sK10(powerset(powerset(X0))),X1),sK8(sK10(powerset(powerset(X0))),X1)))),X0)
| sP0(sK10(powerset(powerset(X0))),X1)
| empty(unordered_pair(singleton(sK8(sK10(powerset(powerset(X0))),X1)),unordered_pair(sK9(sK10(powerset(powerset(X0))),X1),sK8(sK10(powerset(powerset(X0))),X1)))) )
| ~ spl17_75
| ~ spl17_331 ),
inference(resolution,[],[f3127,f644]) ).
fof(f12247,plain,
( spl17_880
| ~ spl17_269
| ~ spl17_321 ),
inference(avatar_split_clause,[],[f2971,f2873,f2240,f12245]) ).
fof(f12245,plain,
( spl17_880
<=> ! [X0,X1] :
( empty(sK10(sK10(powerset(powerset(X0)))))
| sP0(sK10(powerset(sK10(sK10(powerset(powerset(X0)))))),X1)
| element(unordered_pair(singleton(sK7(sK10(powerset(sK10(sK10(powerset(powerset(X0)))))),X1)),unordered_pair(sK8(sK10(powerset(sK10(sK10(powerset(powerset(X0)))))),X1),sK7(sK10(powerset(sK10(sK10(powerset(powerset(X0)))))),X1))),X0)
| empty(sK10(powerset(powerset(X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_880])]) ).
fof(f2240,plain,
( spl17_269
<=> ! [X0,X1] :
( empty(sK10(powerset(powerset(X0))))
| element(X1,X0)
| ~ in(X1,sK10(sK10(powerset(powerset(X0))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_269])]) ).
fof(f2971,plain,
( ! [X0,X1] :
( empty(sK10(sK10(powerset(powerset(X0)))))
| sP0(sK10(powerset(sK10(sK10(powerset(powerset(X0)))))),X1)
| element(unordered_pair(singleton(sK7(sK10(powerset(sK10(sK10(powerset(powerset(X0)))))),X1)),unordered_pair(sK8(sK10(powerset(sK10(sK10(powerset(powerset(X0)))))),X1),sK7(sK10(powerset(sK10(sK10(powerset(powerset(X0)))))),X1))),X0)
| empty(sK10(powerset(powerset(X0)))) )
| ~ spl17_269
| ~ spl17_321 ),
inference(resolution,[],[f2874,f2241]) ).
fof(f2241,plain,
( ! [X0,X1] :
( ~ in(X1,sK10(sK10(powerset(powerset(X0)))))
| element(X1,X0)
| empty(sK10(powerset(powerset(X0)))) )
| ~ spl17_269 ),
inference(avatar_component_clause,[],[f2240]) ).
fof(f12243,plain,
( spl17_879
| ~ spl17_269
| ~ spl17_320 ),
inference(avatar_split_clause,[],[f2920,f2869,f2240,f12241]) ).
fof(f12241,plain,
( spl17_879
<=> ! [X0,X1] :
( empty(sK10(sK10(powerset(powerset(X0)))))
| sP0(sK10(powerset(sK10(sK10(powerset(powerset(X0)))))),X1)
| element(unordered_pair(singleton(sK8(sK10(powerset(sK10(sK10(powerset(powerset(X0)))))),X1)),unordered_pair(sK9(sK10(powerset(sK10(sK10(powerset(powerset(X0)))))),X1),sK8(sK10(powerset(sK10(sK10(powerset(powerset(X0)))))),X1))),X0)
| empty(sK10(powerset(powerset(X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_879])]) ).
fof(f2920,plain,
( ! [X0,X1] :
( empty(sK10(sK10(powerset(powerset(X0)))))
| sP0(sK10(powerset(sK10(sK10(powerset(powerset(X0)))))),X1)
| element(unordered_pair(singleton(sK8(sK10(powerset(sK10(sK10(powerset(powerset(X0)))))),X1)),unordered_pair(sK9(sK10(powerset(sK10(sK10(powerset(powerset(X0)))))),X1),sK8(sK10(powerset(sK10(sK10(powerset(powerset(X0)))))),X1))),X0)
| empty(sK10(powerset(powerset(X0)))) )
| ~ spl17_269
| ~ spl17_320 ),
inference(resolution,[],[f2870,f2241]) ).
fof(f12176,plain,
( spl17_648
| ~ spl17_30
| ~ spl17_663 ),
inference(avatar_split_clause,[],[f8005,f7742,f313,f7638]) ).
fof(f7638,plain,
( spl17_648
<=> ! [X0,X1] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),the_InternalRel(sK2))
| in(X0,sK16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_648])]) ).
fof(f7742,plain,
( spl17_663
<=> ! [X0,X1] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X1,X0)),the_InternalRel(sK2))
| in(X0,sK16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_663])]) ).
fof(f8005,plain,
( ! [X0,X1] :
( ~ in(unordered_pair(singleton(X1),unordered_pair(X1,X0)),the_InternalRel(sK2))
| in(X1,sK16) )
| ~ spl17_30
| ~ spl17_663 ),
inference(superposition,[],[f7743,f314]) ).
fof(f7743,plain,
( ! [X0,X1] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X1,X0)),the_InternalRel(sK2))
| in(X0,sK16) )
| ~ spl17_663 ),
inference(avatar_component_clause,[],[f7742]) ).
fof(f12159,plain,
( spl17_878
| ~ spl17_30
| ~ spl17_378 ),
inference(avatar_split_clause,[],[f3630,f3585,f313,f12157]) ).
fof(f12157,plain,
( spl17_878
<=> ! [X5,X4,X0,X3,X2,X1] :
( ~ in(unordered_pair(singleton(X1),unordered_pair(X1,X0)),powerset(cartesian_product2(X2,X3)))
| in(unordered_pair(singleton(X1),unordered_pair(X1,X4)),powerset(cartesian_product2(X2,X3)))
| ~ in(X4,X5)
| ~ in(X0,X5)
| ~ in(X1,X5)
| ~ sP0(powerset(cartesian_product2(X2,X3)),X5)
| empty(powerset(cartesian_product2(X2,X3)))
| ~ relation_of2_as_subset(unordered_pair(singleton(X0),unordered_pair(X4,X0)),X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_878])]) ).
fof(f3630,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ in(unordered_pair(singleton(X1),unordered_pair(X1,X0)),powerset(cartesian_product2(X2,X3)))
| in(unordered_pair(singleton(X1),unordered_pair(X1,X4)),powerset(cartesian_product2(X2,X3)))
| ~ in(X4,X5)
| ~ in(X0,X5)
| ~ in(X1,X5)
| ~ sP0(powerset(cartesian_product2(X2,X3)),X5)
| empty(powerset(cartesian_product2(X2,X3)))
| ~ relation_of2_as_subset(unordered_pair(singleton(X0),unordered_pair(X4,X0)),X2,X3) )
| ~ spl17_30
| ~ spl17_378 ),
inference(superposition,[],[f3586,f314]) ).
fof(f12155,plain,
( spl17_877
| ~ spl17_108
| ~ spl17_341 ),
inference(avatar_split_clause,[],[f3258,f3243,f864,f12153]) ).
fof(f12153,plain,
( spl17_877
<=> ! [X5,X4,X0,X3,X2,X1] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),powerset(cartesian_product2(X2,X3)))
| in(unordered_pair(singleton(X4),unordered_pair(X4,X1)),powerset(cartesian_product2(X2,X3)))
| ~ in(X1,X5)
| ~ in(X0,X5)
| ~ in(X4,X5)
| ~ sP0(powerset(cartesian_product2(X2,X3)),X5)
| empty(powerset(cartesian_product2(X2,X3)))
| ~ relation_of2_as_subset(unordered_pair(singleton(X4),unordered_pair(X0,X4)),X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_877])]) ).
fof(f3258,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),powerset(cartesian_product2(X2,X3)))
| in(unordered_pair(singleton(X4),unordered_pair(X4,X1)),powerset(cartesian_product2(X2,X3)))
| ~ in(X1,X5)
| ~ in(X0,X5)
| ~ in(X4,X5)
| ~ sP0(powerset(cartesian_product2(X2,X3)),X5)
| empty(powerset(cartesian_product2(X2,X3)))
| ~ relation_of2_as_subset(unordered_pair(singleton(X4),unordered_pair(X0,X4)),X2,X3) )
| ~ spl17_108
| ~ spl17_341 ),
inference(resolution,[],[f3244,f865]) ).
fof(f12151,plain,
( spl17_876
| ~ spl17_197
| ~ spl17_321 ),
inference(avatar_split_clause,[],[f2931,f2873,f1581,f12149]) ).
fof(f12149,plain,
( spl17_876
<=> ! [X0,X3,X2,X1] :
( empty(X0)
| sP0(sK10(powerset(X0)),X1)
| ~ in(unordered_pair(singleton(X2),unordered_pair(sK7(sK10(powerset(X0)),X1),X2)),X0)
| in(unordered_pair(singleton(X2),unordered_pair(X2,sK8(sK10(powerset(X0)),X1))),X0)
| ~ in(sK8(sK10(powerset(X0)),X1),X3)
| ~ in(sK7(sK10(powerset(X0)),X1),X3)
| ~ in(X2,X3)
| ~ sP0(X0,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_876])]) ).
fof(f2931,plain,
( ! [X2,X3,X0,X1] :
( empty(X0)
| sP0(sK10(powerset(X0)),X1)
| ~ in(unordered_pair(singleton(X2),unordered_pair(sK7(sK10(powerset(X0)),X1),X2)),X0)
| in(unordered_pair(singleton(X2),unordered_pair(X2,sK8(sK10(powerset(X0)),X1))),X0)
| ~ in(sK8(sK10(powerset(X0)),X1),X3)
| ~ in(sK7(sK10(powerset(X0)),X1),X3)
| ~ in(X2,X3)
| ~ sP0(X0,X3) )
| ~ spl17_197
| ~ spl17_321 ),
inference(resolution,[],[f2874,f1582]) ).
fof(f12147,plain,
( spl17_875
| ~ spl17_197
| ~ spl17_320 ),
inference(avatar_split_clause,[],[f2880,f2869,f1581,f12145]) ).
fof(f12145,plain,
( spl17_875
<=> ! [X0,X3,X2,X1] :
( empty(X0)
| sP0(sK10(powerset(X0)),X1)
| ~ in(unordered_pair(singleton(X2),unordered_pair(sK8(sK10(powerset(X0)),X1),X2)),X0)
| in(unordered_pair(singleton(X2),unordered_pair(X2,sK9(sK10(powerset(X0)),X1))),X0)
| ~ in(sK9(sK10(powerset(X0)),X1),X3)
| ~ in(sK8(sK10(powerset(X0)),X1),X3)
| ~ in(X2,X3)
| ~ sP0(X0,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_875])]) ).
fof(f2880,plain,
( ! [X2,X3,X0,X1] :
( empty(X0)
| sP0(sK10(powerset(X0)),X1)
| ~ in(unordered_pair(singleton(X2),unordered_pair(sK8(sK10(powerset(X0)),X1),X2)),X0)
| in(unordered_pair(singleton(X2),unordered_pair(X2,sK9(sK10(powerset(X0)),X1))),X0)
| ~ in(sK9(sK10(powerset(X0)),X1),X3)
| ~ in(sK8(sK10(powerset(X0)),X1),X3)
| ~ in(X2,X3)
| ~ sP0(X0,X3) )
| ~ spl17_197
| ~ spl17_320 ),
inference(resolution,[],[f2870,f1582]) ).
fof(f12143,plain,
( spl17_874
| ~ spl17_292
| ~ spl17_312 ),
inference(avatar_split_clause,[],[f2814,f2730,f2530,f12141]) ).
fof(f12141,plain,
( spl17_874
<=> ! [X2,X0,X1] :
( sP0(sK6(sK9(X0,sK6(powerset(X1)))),X2)
| empty(sK9(X0,sK6(powerset(X1))))
| sP0(X0,sK6(powerset(X1)))
| element(unordered_pair(singleton(sK7(sK6(sK9(X0,sK6(powerset(X1)))),X2)),unordered_pair(sK8(sK6(sK9(X0,sK6(powerset(X1)))),X2),sK7(sK6(sK9(X0,sK6(powerset(X1)))),X2))),X1)
| empty(powerset(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_874])]) ).
fof(f2814,plain,
( ! [X2,X0,X1] :
( sP0(sK6(sK9(X0,sK6(powerset(X1)))),X2)
| empty(sK9(X0,sK6(powerset(X1))))
| sP0(X0,sK6(powerset(X1)))
| element(unordered_pair(singleton(sK7(sK6(sK9(X0,sK6(powerset(X1)))),X2)),unordered_pair(sK8(sK6(sK9(X0,sK6(powerset(X1)))),X2),sK7(sK6(sK9(X0,sK6(powerset(X1)))),X2))),X1)
| empty(powerset(X1)) )
| ~ spl17_292
| ~ spl17_312 ),
inference(resolution,[],[f2731,f2531]) ).
fof(f12139,plain,
( spl17_105
| ~ spl17_43
| ~ spl17_398 ),
inference(avatar_split_clause,[],[f3794,f3790,f371,f841]) ).
fof(f841,plain,
( spl17_105
<=> relation_of2_as_subset(the_InternalRel(sK2),sK16,sK16) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_105])]) ).
fof(f371,plain,
( spl17_43
<=> ! [X2,X0,X1] :
( relation_of2_as_subset(X2,X0,X1)
| ~ relation_of2(X2,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_43])]) ).
fof(f3790,plain,
( spl17_398
<=> relation_of2(the_InternalRel(sK2),sK16,sK16) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_398])]) ).
fof(f3794,plain,
( relation_of2_as_subset(the_InternalRel(sK2),sK16,sK16)
| ~ spl17_43
| ~ spl17_398 ),
inference(resolution,[],[f3792,f372]) ).
fof(f372,plain,
( ! [X2,X0,X1] :
( ~ relation_of2(X2,X0,X1)
| relation_of2_as_subset(X2,X0,X1) )
| ~ spl17_43 ),
inference(avatar_component_clause,[],[f371]) ).
fof(f3792,plain,
( relation_of2(the_InternalRel(sK2),sK16,sK16)
| ~ spl17_398 ),
inference(avatar_component_clause,[],[f3790]) ).
fof(f12138,plain,
( spl17_873
| ~ spl17_291
| ~ spl17_312 ),
inference(avatar_split_clause,[],[f2808,f2730,f2526,f12136]) ).
fof(f12136,plain,
( spl17_873
<=> ! [X2,X0,X1] :
( sP0(sK6(sK8(X0,sK6(powerset(X1)))),X2)
| empty(sK8(X0,sK6(powerset(X1))))
| sP0(X0,sK6(powerset(X1)))
| element(unordered_pair(singleton(sK7(sK6(sK8(X0,sK6(powerset(X1)))),X2)),unordered_pair(sK8(sK6(sK8(X0,sK6(powerset(X1)))),X2),sK7(sK6(sK8(X0,sK6(powerset(X1)))),X2))),X1)
| empty(powerset(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_873])]) ).
fof(f2808,plain,
( ! [X2,X0,X1] :
( sP0(sK6(sK8(X0,sK6(powerset(X1)))),X2)
| empty(sK8(X0,sK6(powerset(X1))))
| sP0(X0,sK6(powerset(X1)))
| element(unordered_pair(singleton(sK7(sK6(sK8(X0,sK6(powerset(X1)))),X2)),unordered_pair(sK8(sK6(sK8(X0,sK6(powerset(X1)))),X2),sK7(sK6(sK8(X0,sK6(powerset(X1)))),X2))),X1)
| empty(powerset(X1)) )
| ~ spl17_291
| ~ spl17_312 ),
inference(resolution,[],[f2731,f2527]) ).
fof(f12134,plain,
( spl17_872
| ~ spl17_290
| ~ spl17_312 ),
inference(avatar_split_clause,[],[f2802,f2730,f2522,f12132]) ).
fof(f12132,plain,
( spl17_872
<=> ! [X2,X0,X1] :
( sP0(sK6(sK7(X0,sK6(powerset(X1)))),X2)
| empty(sK7(X0,sK6(powerset(X1))))
| sP0(X0,sK6(powerset(X1)))
| element(unordered_pair(singleton(sK7(sK6(sK7(X0,sK6(powerset(X1)))),X2)),unordered_pair(sK8(sK6(sK7(X0,sK6(powerset(X1)))),X2),sK7(sK6(sK7(X0,sK6(powerset(X1)))),X2))),X1)
| empty(powerset(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_872])]) ).
fof(f2802,plain,
( ! [X2,X0,X1] :
( sP0(sK6(sK7(X0,sK6(powerset(X1)))),X2)
| empty(sK7(X0,sK6(powerset(X1))))
| sP0(X0,sK6(powerset(X1)))
| element(unordered_pair(singleton(sK7(sK6(sK7(X0,sK6(powerset(X1)))),X2)),unordered_pair(sK8(sK6(sK7(X0,sK6(powerset(X1)))),X2),sK7(sK6(sK7(X0,sK6(powerset(X1)))),X2))),X1)
| empty(powerset(X1)) )
| ~ spl17_290
| ~ spl17_312 ),
inference(resolution,[],[f2731,f2523]) ).
fof(f12091,plain,
( ~ spl17_48
| ~ spl17_23
| ~ spl17_107 ),
inference(avatar_split_clause,[],[f905,f858,f279,f417]) ).
fof(f417,plain,
( spl17_48
<=> empty(the_carrier(sK2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_48])]) ).
fof(f279,plain,
( spl17_23
<=> ! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_23])]) ).
fof(f905,plain,
( ~ empty(the_carrier(sK2))
| ~ spl17_23
| ~ spl17_107 ),
inference(resolution,[],[f860,f280]) ).
fof(f280,plain,
( ! [X0,X1] :
( ~ in(X0,X1)
| ~ empty(X1) )
| ~ spl17_23 ),
inference(avatar_component_clause,[],[f279]) ).
fof(f860,plain,
( in(sK5,the_carrier(sK2))
| ~ spl17_107 ),
inference(avatar_component_clause,[],[f858]) ).
fof(f12081,plain,
( ~ spl17_72
| ~ spl17_868 ),
inference(avatar_contradiction_clause,[],[f12077]) ).
fof(f12077,plain,
( $false
| ~ spl17_72
| ~ spl17_868 ),
inference(resolution,[],[f11899,f579]) ).
fof(f11899,plain,
( in(sK3,sK16)
| ~ spl17_868 ),
inference(avatar_component_clause,[],[f11897]) ).
fof(f11897,plain,
( spl17_868
<=> in(sK3,sK16) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_868])]) ).
fof(f12076,plain,
( spl17_871
| ~ spl17_292
| ~ spl17_311 ),
inference(avatar_split_clause,[],[f2765,f2726,f2530,f12074]) ).
fof(f12074,plain,
( spl17_871
<=> ! [X2,X0,X1] :
( sP0(sK6(sK9(X0,sK6(powerset(X1)))),X2)
| empty(sK9(X0,sK6(powerset(X1))))
| sP0(X0,sK6(powerset(X1)))
| element(unordered_pair(singleton(sK8(sK6(sK9(X0,sK6(powerset(X1)))),X2)),unordered_pair(sK9(sK6(sK9(X0,sK6(powerset(X1)))),X2),sK8(sK6(sK9(X0,sK6(powerset(X1)))),X2))),X1)
| empty(powerset(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_871])]) ).
fof(f2765,plain,
( ! [X2,X0,X1] :
( sP0(sK6(sK9(X0,sK6(powerset(X1)))),X2)
| empty(sK9(X0,sK6(powerset(X1))))
| sP0(X0,sK6(powerset(X1)))
| element(unordered_pair(singleton(sK8(sK6(sK9(X0,sK6(powerset(X1)))),X2)),unordered_pair(sK9(sK6(sK9(X0,sK6(powerset(X1)))),X2),sK8(sK6(sK9(X0,sK6(powerset(X1)))),X2))),X1)
| empty(powerset(X1)) )
| ~ spl17_292
| ~ spl17_311 ),
inference(resolution,[],[f2727,f2531]) ).
fof(f12072,plain,
( spl17_870
| ~ spl17_291
| ~ spl17_311 ),
inference(avatar_split_clause,[],[f2759,f2726,f2526,f12070]) ).
fof(f12070,plain,
( spl17_870
<=> ! [X2,X0,X1] :
( sP0(sK6(sK8(X0,sK6(powerset(X1)))),X2)
| empty(sK8(X0,sK6(powerset(X1))))
| sP0(X0,sK6(powerset(X1)))
| element(unordered_pair(singleton(sK8(sK6(sK8(X0,sK6(powerset(X1)))),X2)),unordered_pair(sK9(sK6(sK8(X0,sK6(powerset(X1)))),X2),sK8(sK6(sK8(X0,sK6(powerset(X1)))),X2))),X1)
| empty(powerset(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_870])]) ).
fof(f2759,plain,
( ! [X2,X0,X1] :
( sP0(sK6(sK8(X0,sK6(powerset(X1)))),X2)
| empty(sK8(X0,sK6(powerset(X1))))
| sP0(X0,sK6(powerset(X1)))
| element(unordered_pair(singleton(sK8(sK6(sK8(X0,sK6(powerset(X1)))),X2)),unordered_pair(sK9(sK6(sK8(X0,sK6(powerset(X1)))),X2),sK8(sK6(sK8(X0,sK6(powerset(X1)))),X2))),X1)
| empty(powerset(X1)) )
| ~ spl17_291
| ~ spl17_311 ),
inference(resolution,[],[f2727,f2527]) ).
fof(f12068,plain,
( spl17_869
| ~ spl17_290
| ~ spl17_311 ),
inference(avatar_split_clause,[],[f2753,f2726,f2522,f12066]) ).
fof(f12066,plain,
( spl17_869
<=> ! [X2,X0,X1] :
( sP0(sK6(sK7(X0,sK6(powerset(X1)))),X2)
| empty(sK7(X0,sK6(powerset(X1))))
| sP0(X0,sK6(powerset(X1)))
| element(unordered_pair(singleton(sK8(sK6(sK7(X0,sK6(powerset(X1)))),X2)),unordered_pair(sK9(sK6(sK7(X0,sK6(powerset(X1)))),X2),sK8(sK6(sK7(X0,sK6(powerset(X1)))),X2))),X1)
| empty(powerset(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_869])]) ).
fof(f2753,plain,
( ! [X2,X0,X1] :
( sP0(sK6(sK7(X0,sK6(powerset(X1)))),X2)
| empty(sK7(X0,sK6(powerset(X1))))
| sP0(X0,sK6(powerset(X1)))
| element(unordered_pair(singleton(sK8(sK6(sK7(X0,sK6(powerset(X1)))),X2)),unordered_pair(sK9(sK6(sK7(X0,sK6(powerset(X1)))),X2),sK8(sK6(sK7(X0,sK6(powerset(X1)))),X2))),X1)
| empty(powerset(X1)) )
| ~ spl17_290
| ~ spl17_311 ),
inference(resolution,[],[f2727,f2523]) ).
fof(f11900,plain,
( ~ spl17_80
| spl17_868
| ~ spl17_84
| ~ spl17_6
| ~ spl17_856 ),
inference(avatar_split_clause,[],[f11704,f11661,f204,f700,f11897,f667]) ).
fof(f667,plain,
( spl17_80
<=> element(sK4,sK16) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_80])]) ).
fof(f700,plain,
( spl17_84
<=> element(sK3,sK16) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_84])]) ).
fof(f204,plain,
( spl17_6
<=> related(sK2,sK3,sK4) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_6])]) ).
fof(f11661,plain,
( spl17_856
<=> ! [X0,X1] :
( ~ element(X0,sK16)
| ~ related(sK2,X0,X1)
| in(X0,sK16)
| ~ element(X1,sK16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_856])]) ).
fof(f11704,plain,
( ~ element(sK3,sK16)
| in(sK3,sK16)
| ~ element(sK4,sK16)
| ~ spl17_6
| ~ spl17_856 ),
inference(resolution,[],[f11662,f206]) ).
fof(f206,plain,
( related(sK2,sK3,sK4)
| ~ spl17_6 ),
inference(avatar_component_clause,[],[f204]) ).
fof(f11662,plain,
( ! [X0,X1] :
( ~ related(sK2,X0,X1)
| ~ element(X0,sK16)
| in(X0,sK16)
| ~ element(X1,sK16) )
| ~ spl17_856 ),
inference(avatar_component_clause,[],[f11661]) ).
fof(f11715,plain,
( spl17_867
| ~ spl17_30
| ~ spl17_376 ),
inference(avatar_split_clause,[],[f3580,f3569,f313,f11713]) ).
fof(f11713,plain,
( spl17_867
<=> ! [X5,X4,X0,X3,X2,X1] :
( ~ subset(unordered_pair(singleton(X0),unordered_pair(X1,X0)),cartesian_product2(X2,X3))
| empty(powerset(cartesian_product2(X2,X3)))
| in(unordered_pair(singleton(X0),unordered_pair(X0,X4)),powerset(cartesian_product2(X2,X3)))
| ~ in(X4,X5)
| ~ in(X1,X5)
| ~ in(X0,X5)
| ~ sP0(powerset(cartesian_product2(X2,X3)),X5)
| ~ relation_of2_as_subset(unordered_pair(singleton(X1),unordered_pair(X1,X4)),X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_867])]) ).
fof(f3569,plain,
( spl17_376
<=> ! [X5,X4,X0,X3,X2,X1] :
( ~ relation_of2_as_subset(unordered_pair(singleton(X0),unordered_pair(X0,X1)),X2,X3)
| empty(powerset(cartesian_product2(X2,X3)))
| in(unordered_pair(singleton(X4),unordered_pair(X4,X1)),powerset(cartesian_product2(X2,X3)))
| ~ in(X1,X5)
| ~ in(X0,X5)
| ~ in(X4,X5)
| ~ sP0(powerset(cartesian_product2(X2,X3)),X5)
| ~ subset(unordered_pair(singleton(X4),unordered_pair(X4,X0)),cartesian_product2(X2,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_376])]) ).
fof(f3580,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ subset(unordered_pair(singleton(X0),unordered_pair(X1,X0)),cartesian_product2(X2,X3))
| empty(powerset(cartesian_product2(X2,X3)))
| in(unordered_pair(singleton(X0),unordered_pair(X0,X4)),powerset(cartesian_product2(X2,X3)))
| ~ in(X4,X5)
| ~ in(X1,X5)
| ~ in(X0,X5)
| ~ sP0(powerset(cartesian_product2(X2,X3)),X5)
| ~ relation_of2_as_subset(unordered_pair(singleton(X1),unordered_pair(X1,X4)),X2,X3) )
| ~ spl17_30
| ~ spl17_376 ),
inference(superposition,[],[f3570,f314]) ).
fof(f3570,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ subset(unordered_pair(singleton(X4),unordered_pair(X4,X0)),cartesian_product2(X2,X3))
| empty(powerset(cartesian_product2(X2,X3)))
| in(unordered_pair(singleton(X4),unordered_pair(X4,X1)),powerset(cartesian_product2(X2,X3)))
| ~ in(X1,X5)
| ~ in(X0,X5)
| ~ in(X4,X5)
| ~ sP0(powerset(cartesian_product2(X2,X3)),X5)
| ~ relation_of2_as_subset(unordered_pair(singleton(X0),unordered_pair(X0,X1)),X2,X3) )
| ~ spl17_376 ),
inference(avatar_component_clause,[],[f3569]) ).
fof(f11703,plain,
( spl17_866
| ~ spl17_30
| ~ spl17_375 ),
inference(avatar_split_clause,[],[f3578,f3565,f313,f11701]) ).
fof(f11701,plain,
( spl17_866
<=> ! [X5,X4,X0,X3,X2,X1] :
( ~ subset(unordered_pair(singleton(X0),unordered_pair(X1,X0)),cartesian_product2(X2,X3))
| ~ in(X4,X5)
| ~ in(X1,X5)
| ~ in(X0,X5)
| ~ sP0(powerset(cartesian_product2(X2,X3)),X5)
| empty(powerset(cartesian_product2(X2,X3)))
| in(unordered_pair(singleton(X0),unordered_pair(X0,X4)),powerset(cartesian_product2(X2,X3)))
| ~ relation_of2_as_subset(unordered_pair(singleton(X1),unordered_pair(X4,X1)),X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_866])]) ).
fof(f3565,plain,
( spl17_375
<=> ! [X5,X4,X0,X3,X2,X1] :
( in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),powerset(cartesian_product2(X2,X3)))
| ~ in(X1,X4)
| ~ in(X5,X4)
| ~ in(X0,X4)
| ~ sP0(powerset(cartesian_product2(X2,X3)),X4)
| empty(powerset(cartesian_product2(X2,X3)))
| ~ subset(unordered_pair(singleton(X0),unordered_pair(X0,X5)),cartesian_product2(X2,X3))
| ~ relation_of2_as_subset(unordered_pair(singleton(X5),unordered_pair(X1,X5)),X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_375])]) ).
fof(f3578,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ subset(unordered_pair(singleton(X0),unordered_pair(X1,X0)),cartesian_product2(X2,X3))
| ~ in(X4,X5)
| ~ in(X1,X5)
| ~ in(X0,X5)
| ~ sP0(powerset(cartesian_product2(X2,X3)),X5)
| empty(powerset(cartesian_product2(X2,X3)))
| in(unordered_pair(singleton(X0),unordered_pair(X0,X4)),powerset(cartesian_product2(X2,X3)))
| ~ relation_of2_as_subset(unordered_pair(singleton(X1),unordered_pair(X4,X1)),X2,X3) )
| ~ spl17_30
| ~ spl17_375 ),
inference(superposition,[],[f3566,f314]) ).
fof(f3566,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ subset(unordered_pair(singleton(X0),unordered_pair(X0,X5)),cartesian_product2(X2,X3))
| ~ in(X1,X4)
| ~ in(X5,X4)
| ~ in(X0,X4)
| ~ sP0(powerset(cartesian_product2(X2,X3)),X4)
| empty(powerset(cartesian_product2(X2,X3)))
| in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),powerset(cartesian_product2(X2,X3)))
| ~ relation_of2_as_subset(unordered_pair(singleton(X5),unordered_pair(X1,X5)),X2,X3) )
| ~ spl17_375 ),
inference(avatar_component_clause,[],[f3565]) ).
fof(f11699,plain,
( spl17_865
| ~ spl17_108
| ~ spl17_364 ),
inference(avatar_split_clause,[],[f3500,f3463,f864,f11697]) ).
fof(f11697,plain,
( spl17_865
<=> ! [X5,X4,X0,X3,X2,X1] :
( ~ subset(unordered_pair(singleton(X0),unordered_pair(X0,X1)),cartesian_product2(X2,X3))
| empty(powerset(cartesian_product2(X2,X3)))
| in(unordered_pair(singleton(X4),unordered_pair(X4,X1)),powerset(cartesian_product2(X2,X3)))
| ~ in(X1,X5)
| ~ in(X0,X5)
| ~ in(X4,X5)
| ~ sP0(powerset(cartesian_product2(X2,X3)),X5)
| ~ relation_of2_as_subset(unordered_pair(singleton(X4),unordered_pair(X0,X4)),X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_865])]) ).
fof(f3500,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ subset(unordered_pair(singleton(X0),unordered_pair(X0,X1)),cartesian_product2(X2,X3))
| empty(powerset(cartesian_product2(X2,X3)))
| in(unordered_pair(singleton(X4),unordered_pair(X4,X1)),powerset(cartesian_product2(X2,X3)))
| ~ in(X1,X5)
| ~ in(X0,X5)
| ~ in(X4,X5)
| ~ sP0(powerset(cartesian_product2(X2,X3)),X5)
| ~ relation_of2_as_subset(unordered_pair(singleton(X4),unordered_pair(X0,X4)),X2,X3) )
| ~ spl17_108
| ~ spl17_364 ),
inference(duplicate_literal_removal,[],[f3487]) ).
fof(f3487,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ subset(unordered_pair(singleton(X0),unordered_pair(X0,X1)),cartesian_product2(X2,X3))
| empty(powerset(cartesian_product2(X2,X3)))
| in(unordered_pair(singleton(X4),unordered_pair(X4,X1)),powerset(cartesian_product2(X2,X3)))
| ~ in(X1,X5)
| ~ in(X0,X5)
| ~ in(X4,X5)
| ~ sP0(powerset(cartesian_product2(X2,X3)),X5)
| empty(powerset(cartesian_product2(X2,X3)))
| ~ relation_of2_as_subset(unordered_pair(singleton(X4),unordered_pair(X0,X4)),X2,X3) )
| ~ spl17_108
| ~ spl17_364 ),
inference(resolution,[],[f3464,f865]) ).
fof(f11695,plain,
( spl17_864
| ~ spl17_108
| ~ spl17_363 ),
inference(avatar_split_clause,[],[f3484,f3459,f864,f11693]) ).
fof(f11693,plain,
( spl17_864
<=> ! [X5,X4,X0,X3,X2,X1] :
( in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),powerset(cartesian_product2(X2,X3)))
| ~ in(X1,X4)
| ~ in(X5,X4)
| ~ in(X0,X4)
| ~ sP0(powerset(cartesian_product2(X2,X3)),X4)
| empty(powerset(cartesian_product2(X2,X3)))
| ~ subset(unordered_pair(singleton(X5),unordered_pair(X1,X5)),cartesian_product2(X2,X3))
| ~ relation_of2_as_subset(unordered_pair(singleton(X0),unordered_pair(X5,X0)),X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_864])]) ).
fof(f3484,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),powerset(cartesian_product2(X2,X3)))
| ~ in(X1,X4)
| ~ in(X5,X4)
| ~ in(X0,X4)
| ~ sP0(powerset(cartesian_product2(X2,X3)),X4)
| empty(powerset(cartesian_product2(X2,X3)))
| ~ subset(unordered_pair(singleton(X5),unordered_pair(X1,X5)),cartesian_product2(X2,X3))
| ~ relation_of2_as_subset(unordered_pair(singleton(X0),unordered_pair(X5,X0)),X2,X3) )
| ~ spl17_108
| ~ spl17_363 ),
inference(duplicate_literal_removal,[],[f3471]) ).
fof(f3471,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),powerset(cartesian_product2(X2,X3)))
| ~ in(X1,X4)
| ~ in(X5,X4)
| ~ in(X0,X4)
| ~ sP0(powerset(cartesian_product2(X2,X3)),X4)
| empty(powerset(cartesian_product2(X2,X3)))
| ~ subset(unordered_pair(singleton(X5),unordered_pair(X1,X5)),cartesian_product2(X2,X3))
| empty(powerset(cartesian_product2(X2,X3)))
| ~ relation_of2_as_subset(unordered_pair(singleton(X0),unordered_pair(X5,X0)),X2,X3) )
| ~ spl17_108
| ~ spl17_363 ),
inference(resolution,[],[f3460,f865]) ).
fof(f11691,plain,
( spl17_863
| ~ spl17_51
| ~ spl17_358 ),
inference(avatar_split_clause,[],[f3433,f3403,f439,f11689]) ).
fof(f11689,plain,
( spl17_863
<=> ! [X0,X3,X2,X1] :
( sP0(powerset(powerset(X0)),X1)
| sP0(X2,unordered_pair(singleton(sK7(powerset(powerset(X0)),X1)),unordered_pair(sK8(powerset(powerset(X0)),X1),sK7(powerset(powerset(X0)),X1))))
| element(X3,X0)
| ~ in(X3,sK9(X2,unordered_pair(singleton(sK7(powerset(powerset(X0)),X1)),unordered_pair(sK8(powerset(powerset(X0)),X1),sK7(powerset(powerset(X0)),X1))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_863])]) ).
fof(f3433,plain,
( ! [X2,X3,X0,X1] :
( sP0(powerset(powerset(X0)),X1)
| sP0(X2,unordered_pair(singleton(sK7(powerset(powerset(X0)),X1)),unordered_pair(sK8(powerset(powerset(X0)),X1),sK7(powerset(powerset(X0)),X1))))
| element(X3,X0)
| ~ in(X3,sK9(X2,unordered_pair(singleton(sK7(powerset(powerset(X0)),X1)),unordered_pair(sK8(powerset(powerset(X0)),X1),sK7(powerset(powerset(X0)),X1))))) )
| ~ spl17_51
| ~ spl17_358 ),
inference(resolution,[],[f3404,f440]) ).
fof(f11687,plain,
( spl17_862
| ~ spl17_51
| ~ spl17_356 ),
inference(avatar_split_clause,[],[f3429,f3395,f439,f11685]) ).
fof(f11685,plain,
( spl17_862
<=> ! [X0,X3,X2,X1] :
( sP0(powerset(powerset(X0)),X1)
| sP0(X2,unordered_pair(singleton(sK7(powerset(powerset(X0)),X1)),unordered_pair(sK8(powerset(powerset(X0)),X1),sK7(powerset(powerset(X0)),X1))))
| element(X3,X0)
| ~ in(X3,sK8(X2,unordered_pair(singleton(sK7(powerset(powerset(X0)),X1)),unordered_pair(sK8(powerset(powerset(X0)),X1),sK7(powerset(powerset(X0)),X1))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_862])]) ).
fof(f3429,plain,
( ! [X2,X3,X0,X1] :
( sP0(powerset(powerset(X0)),X1)
| sP0(X2,unordered_pair(singleton(sK7(powerset(powerset(X0)),X1)),unordered_pair(sK8(powerset(powerset(X0)),X1),sK7(powerset(powerset(X0)),X1))))
| element(X3,X0)
| ~ in(X3,sK8(X2,unordered_pair(singleton(sK7(powerset(powerset(X0)),X1)),unordered_pair(sK8(powerset(powerset(X0)),X1),sK7(powerset(powerset(X0)),X1))))) )
| ~ spl17_51
| ~ spl17_356 ),
inference(resolution,[],[f3396,f440]) ).
fof(f11683,plain,
( spl17_861
| ~ spl17_51
| ~ spl17_355 ),
inference(avatar_split_clause,[],[f3425,f3391,f439,f11681]) ).
fof(f11681,plain,
( spl17_861
<=> ! [X0,X3,X2,X1] :
( sP0(powerset(powerset(X0)),X1)
| sP0(X2,unordered_pair(singleton(sK7(powerset(powerset(X0)),X1)),unordered_pair(sK8(powerset(powerset(X0)),X1),sK7(powerset(powerset(X0)),X1))))
| element(X3,X0)
| ~ in(X3,sK7(X2,unordered_pair(singleton(sK7(powerset(powerset(X0)),X1)),unordered_pair(sK8(powerset(powerset(X0)),X1),sK7(powerset(powerset(X0)),X1))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_861])]) ).
fof(f3425,plain,
( ! [X2,X3,X0,X1] :
( sP0(powerset(powerset(X0)),X1)
| sP0(X2,unordered_pair(singleton(sK7(powerset(powerset(X0)),X1)),unordered_pair(sK8(powerset(powerset(X0)),X1),sK7(powerset(powerset(X0)),X1))))
| element(X3,X0)
| ~ in(X3,sK7(X2,unordered_pair(singleton(sK7(powerset(powerset(X0)),X1)),unordered_pair(sK8(powerset(powerset(X0)),X1),sK7(powerset(powerset(X0)),X1))))) )
| ~ spl17_51
| ~ spl17_355 ),
inference(resolution,[],[f3392,f440]) ).
fof(f11679,plain,
( spl17_860
| ~ spl17_51
| ~ spl17_354 ),
inference(avatar_split_clause,[],[f3421,f3387,f439,f11677]) ).
fof(f11677,plain,
( spl17_860
<=> ! [X0,X3,X2,X1] :
( sP0(powerset(powerset(X0)),X1)
| sP0(X2,unordered_pair(singleton(sK8(powerset(powerset(X0)),X1)),unordered_pair(sK9(powerset(powerset(X0)),X1),sK8(powerset(powerset(X0)),X1))))
| element(X3,X0)
| ~ in(X3,sK9(X2,unordered_pair(singleton(sK8(powerset(powerset(X0)),X1)),unordered_pair(sK9(powerset(powerset(X0)),X1),sK8(powerset(powerset(X0)),X1))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_860])]) ).
fof(f3421,plain,
( ! [X2,X3,X0,X1] :
( sP0(powerset(powerset(X0)),X1)
| sP0(X2,unordered_pair(singleton(sK8(powerset(powerset(X0)),X1)),unordered_pair(sK9(powerset(powerset(X0)),X1),sK8(powerset(powerset(X0)),X1))))
| element(X3,X0)
| ~ in(X3,sK9(X2,unordered_pair(singleton(sK8(powerset(powerset(X0)),X1)),unordered_pair(sK9(powerset(powerset(X0)),X1),sK8(powerset(powerset(X0)),X1))))) )
| ~ spl17_51
| ~ spl17_354 ),
inference(resolution,[],[f3388,f440]) ).
fof(f11675,plain,
( spl17_859
| ~ spl17_51
| ~ spl17_353 ),
inference(avatar_split_clause,[],[f3417,f3383,f439,f11673]) ).
fof(f11673,plain,
( spl17_859
<=> ! [X0,X3,X2,X1] :
( sP0(powerset(powerset(X0)),X1)
| sP0(X2,unordered_pair(singleton(sK8(powerset(powerset(X0)),X1)),unordered_pair(sK9(powerset(powerset(X0)),X1),sK8(powerset(powerset(X0)),X1))))
| element(X3,X0)
| ~ in(X3,sK8(X2,unordered_pair(singleton(sK8(powerset(powerset(X0)),X1)),unordered_pair(sK9(powerset(powerset(X0)),X1),sK8(powerset(powerset(X0)),X1))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_859])]) ).
fof(f3417,plain,
( ! [X2,X3,X0,X1] :
( sP0(powerset(powerset(X0)),X1)
| sP0(X2,unordered_pair(singleton(sK8(powerset(powerset(X0)),X1)),unordered_pair(sK9(powerset(powerset(X0)),X1),sK8(powerset(powerset(X0)),X1))))
| element(X3,X0)
| ~ in(X3,sK8(X2,unordered_pair(singleton(sK8(powerset(powerset(X0)),X1)),unordered_pair(sK9(powerset(powerset(X0)),X1),sK8(powerset(powerset(X0)),X1))))) )
| ~ spl17_51
| ~ spl17_353 ),
inference(resolution,[],[f3384,f440]) ).
fof(f11671,plain,
( spl17_858
| ~ spl17_51
| ~ spl17_352 ),
inference(avatar_split_clause,[],[f3413,f3379,f439,f11669]) ).
fof(f11669,plain,
( spl17_858
<=> ! [X0,X3,X2,X1] :
( sP0(powerset(powerset(X0)),X1)
| sP0(X2,unordered_pair(singleton(sK8(powerset(powerset(X0)),X1)),unordered_pair(sK9(powerset(powerset(X0)),X1),sK8(powerset(powerset(X0)),X1))))
| element(X3,X0)
| ~ in(X3,sK7(X2,unordered_pair(singleton(sK8(powerset(powerset(X0)),X1)),unordered_pair(sK9(powerset(powerset(X0)),X1),sK8(powerset(powerset(X0)),X1))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_858])]) ).
fof(f3413,plain,
( ! [X2,X3,X0,X1] :
( sP0(powerset(powerset(X0)),X1)
| sP0(X2,unordered_pair(singleton(sK8(powerset(powerset(X0)),X1)),unordered_pair(sK9(powerset(powerset(X0)),X1),sK8(powerset(powerset(X0)),X1))))
| element(X3,X0)
| ~ in(X3,sK7(X2,unordered_pair(singleton(sK8(powerset(powerset(X0)),X1)),unordered_pair(sK9(powerset(powerset(X0)),X1),sK8(powerset(powerset(X0)),X1))))) )
| ~ spl17_51
| ~ spl17_352 ),
inference(resolution,[],[f3380,f440]) ).
fof(f11667,plain,
( spl17_857
| ~ spl17_38
| ~ spl17_328 ),
inference(avatar_split_clause,[],[f3086,f3042,f351,f11665]) ).
fof(f11665,plain,
( spl17_857
<=> ! [X2,X0,X1] :
( sP0(sK6(powerset(X0)),X1)
| element(sK9(X2,unordered_pair(singleton(sK7(sK6(powerset(X0)),X1)),unordered_pair(sK8(sK6(powerset(X0)),X1),sK7(sK6(powerset(X0)),X1)))),X0)
| empty(powerset(X0))
| sP0(X2,unordered_pair(singleton(sK7(sK6(powerset(X0)),X1)),unordered_pair(sK8(sK6(powerset(X0)),X1),sK7(sK6(powerset(X0)),X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_857])]) ).
fof(f3086,plain,
( ! [X2,X0,X1] :
( sP0(sK6(powerset(X0)),X1)
| element(sK9(X2,unordered_pair(singleton(sK7(sK6(powerset(X0)),X1)),unordered_pair(sK8(sK6(powerset(X0)),X1),sK7(sK6(powerset(X0)),X1)))),X0)
| empty(powerset(X0))
| sP0(X2,unordered_pair(singleton(sK7(sK6(powerset(X0)),X1)),unordered_pair(sK8(sK6(powerset(X0)),X1),sK7(sK6(powerset(X0)),X1)))) )
| ~ spl17_38
| ~ spl17_328 ),
inference(resolution,[],[f3043,f352]) ).
fof(f11663,plain,
( ~ spl17_2
| spl17_856
| ~ spl17_64
| ~ spl17_65
| ~ spl17_648 ),
inference(avatar_split_clause,[],[f7859,f7638,f541,f528,f11661,f184]) ).
fof(f541,plain,
( spl17_65
<=> the_carrier(sK2) = sK16 ),
introduced(avatar_definition,[new_symbols(naming,[spl17_65])]) ).
fof(f7859,plain,
( ! [X0,X1] :
( ~ element(X0,sK16)
| ~ element(X1,sK16)
| in(X0,sK16)
| ~ related(sK2,X0,X1)
| ~ rel_str(sK2) )
| ~ spl17_64
| ~ spl17_65
| ~ spl17_648 ),
inference(forward_demodulation,[],[f7858,f543]) ).
fof(f543,plain,
( the_carrier(sK2) = sK16
| ~ spl17_65 ),
inference(avatar_component_clause,[],[f541]) ).
fof(f7858,plain,
( ! [X0,X1] :
( ~ element(X1,sK16)
| in(X0,sK16)
| ~ related(sK2,X0,X1)
| ~ element(X0,the_carrier(sK2))
| ~ rel_str(sK2) )
| ~ spl17_64
| ~ spl17_65
| ~ spl17_648 ),
inference(forward_demodulation,[],[f7851,f543]) ).
fof(f7851,plain,
( ! [X0,X1] :
( in(X0,sK16)
| ~ related(sK2,X0,X1)
| ~ element(X1,the_carrier(sK2))
| ~ element(X0,the_carrier(sK2))
| ~ rel_str(sK2) )
| ~ spl17_64
| ~ spl17_648 ),
inference(resolution,[],[f7639,f529]) ).
fof(f7639,plain,
( ! [X0,X1] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),the_InternalRel(sK2))
| in(X0,sK16) )
| ~ spl17_648 ),
inference(avatar_component_clause,[],[f7638]) ).
fof(f11659,plain,
( spl17_855
| ~ spl17_37
| ~ spl17_328 ),
inference(avatar_split_clause,[],[f3083,f3042,f347,f11657]) ).
fof(f11657,plain,
( spl17_855
<=> ! [X2,X0,X1] :
( sP0(sK6(powerset(X0)),X1)
| element(sK8(X2,unordered_pair(singleton(sK7(sK6(powerset(X0)),X1)),unordered_pair(sK8(sK6(powerset(X0)),X1),sK7(sK6(powerset(X0)),X1)))),X0)
| empty(powerset(X0))
| sP0(X2,unordered_pair(singleton(sK7(sK6(powerset(X0)),X1)),unordered_pair(sK8(sK6(powerset(X0)),X1),sK7(sK6(powerset(X0)),X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_855])]) ).
fof(f3083,plain,
( ! [X2,X0,X1] :
( sP0(sK6(powerset(X0)),X1)
| element(sK8(X2,unordered_pair(singleton(sK7(sK6(powerset(X0)),X1)),unordered_pair(sK8(sK6(powerset(X0)),X1),sK7(sK6(powerset(X0)),X1)))),X0)
| empty(powerset(X0))
| sP0(X2,unordered_pair(singleton(sK7(sK6(powerset(X0)),X1)),unordered_pair(sK8(sK6(powerset(X0)),X1),sK7(sK6(powerset(X0)),X1)))) )
| ~ spl17_37
| ~ spl17_328 ),
inference(resolution,[],[f3043,f348]) ).
fof(f11655,plain,
( spl17_854
| ~ spl17_35
| ~ spl17_328 ),
inference(avatar_split_clause,[],[f3080,f3042,f339,f11653]) ).
fof(f11653,plain,
( spl17_854
<=> ! [X2,X0,X1] :
( sP0(sK6(powerset(X0)),X1)
| element(sK7(X2,unordered_pair(singleton(sK7(sK6(powerset(X0)),X1)),unordered_pair(sK8(sK6(powerset(X0)),X1),sK7(sK6(powerset(X0)),X1)))),X0)
| empty(powerset(X0))
| sP0(X2,unordered_pair(singleton(sK7(sK6(powerset(X0)),X1)),unordered_pair(sK8(sK6(powerset(X0)),X1),sK7(sK6(powerset(X0)),X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_854])]) ).
fof(f3080,plain,
( ! [X2,X0,X1] :
( sP0(sK6(powerset(X0)),X1)
| element(sK7(X2,unordered_pair(singleton(sK7(sK6(powerset(X0)),X1)),unordered_pair(sK8(sK6(powerset(X0)),X1),sK7(sK6(powerset(X0)),X1)))),X0)
| empty(powerset(X0))
| sP0(X2,unordered_pair(singleton(sK7(sK6(powerset(X0)),X1)),unordered_pair(sK8(sK6(powerset(X0)),X1),sK7(sK6(powerset(X0)),X1)))) )
| ~ spl17_35
| ~ spl17_328 ),
inference(resolution,[],[f3043,f340]) ).
fof(f11651,plain,
( spl17_853
| ~ spl17_38
| ~ spl17_326 ),
inference(avatar_split_clause,[],[f3068,f3034,f351,f11649]) ).
fof(f11649,plain,
( spl17_853
<=> ! [X2,X0,X1] :
( sP0(sK6(powerset(X0)),X1)
| element(sK9(X2,unordered_pair(singleton(sK8(sK6(powerset(X0)),X1)),unordered_pair(sK9(sK6(powerset(X0)),X1),sK8(sK6(powerset(X0)),X1)))),X0)
| empty(powerset(X0))
| sP0(X2,unordered_pair(singleton(sK8(sK6(powerset(X0)),X1)),unordered_pair(sK9(sK6(powerset(X0)),X1),sK8(sK6(powerset(X0)),X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_853])]) ).
fof(f3068,plain,
( ! [X2,X0,X1] :
( sP0(sK6(powerset(X0)),X1)
| element(sK9(X2,unordered_pair(singleton(sK8(sK6(powerset(X0)),X1)),unordered_pair(sK9(sK6(powerset(X0)),X1),sK8(sK6(powerset(X0)),X1)))),X0)
| empty(powerset(X0))
| sP0(X2,unordered_pair(singleton(sK8(sK6(powerset(X0)),X1)),unordered_pair(sK9(sK6(powerset(X0)),X1),sK8(sK6(powerset(X0)),X1)))) )
| ~ spl17_38
| ~ spl17_326 ),
inference(resolution,[],[f3035,f352]) ).
fof(f11647,plain,
( spl17_852
| ~ spl17_37
| ~ spl17_326 ),
inference(avatar_split_clause,[],[f3065,f3034,f347,f11645]) ).
fof(f11645,plain,
( spl17_852
<=> ! [X2,X0,X1] :
( sP0(sK6(powerset(X0)),X1)
| element(sK8(X2,unordered_pair(singleton(sK8(sK6(powerset(X0)),X1)),unordered_pair(sK9(sK6(powerset(X0)),X1),sK8(sK6(powerset(X0)),X1)))),X0)
| empty(powerset(X0))
| sP0(X2,unordered_pair(singleton(sK8(sK6(powerset(X0)),X1)),unordered_pair(sK9(sK6(powerset(X0)),X1),sK8(sK6(powerset(X0)),X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_852])]) ).
fof(f3065,plain,
( ! [X2,X0,X1] :
( sP0(sK6(powerset(X0)),X1)
| element(sK8(X2,unordered_pair(singleton(sK8(sK6(powerset(X0)),X1)),unordered_pair(sK9(sK6(powerset(X0)),X1),sK8(sK6(powerset(X0)),X1)))),X0)
| empty(powerset(X0))
| sP0(X2,unordered_pair(singleton(sK8(sK6(powerset(X0)),X1)),unordered_pair(sK9(sK6(powerset(X0)),X1),sK8(sK6(powerset(X0)),X1)))) )
| ~ spl17_37
| ~ spl17_326 ),
inference(resolution,[],[f3035,f348]) ).
fof(f11643,plain,
( spl17_851
| ~ spl17_35
| ~ spl17_326 ),
inference(avatar_split_clause,[],[f3062,f3034,f339,f11641]) ).
fof(f11641,plain,
( spl17_851
<=> ! [X2,X0,X1] :
( sP0(sK6(powerset(X0)),X1)
| element(sK7(X2,unordered_pair(singleton(sK8(sK6(powerset(X0)),X1)),unordered_pair(sK9(sK6(powerset(X0)),X1),sK8(sK6(powerset(X0)),X1)))),X0)
| empty(powerset(X0))
| sP0(X2,unordered_pair(singleton(sK8(sK6(powerset(X0)),X1)),unordered_pair(sK9(sK6(powerset(X0)),X1),sK8(sK6(powerset(X0)),X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_851])]) ).
fof(f3062,plain,
( ! [X2,X0,X1] :
( sP0(sK6(powerset(X0)),X1)
| element(sK7(X2,unordered_pair(singleton(sK8(sK6(powerset(X0)),X1)),unordered_pair(sK9(sK6(powerset(X0)),X1),sK8(sK6(powerset(X0)),X1)))),X0)
| empty(powerset(X0))
| sP0(X2,unordered_pair(singleton(sK8(sK6(powerset(X0)),X1)),unordered_pair(sK9(sK6(powerset(X0)),X1),sK8(sK6(powerset(X0)),X1)))) )
| ~ spl17_35
| ~ spl17_326 ),
inference(resolution,[],[f3035,f340]) ).
fof(f11311,plain,
( spl17_850
| ~ spl17_108
| ~ spl17_378 ),
inference(avatar_split_clause,[],[f3637,f3585,f864,f11309]) ).
fof(f11309,plain,
( spl17_850
<=> ! [X5,X4,X0,X3,X2,X1] :
( in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),powerset(cartesian_product2(X2,X3)))
| ~ in(X1,X4)
| ~ in(X5,X4)
| ~ in(X0,X4)
| ~ sP0(powerset(cartesian_product2(X2,X3)),X4)
| empty(powerset(cartesian_product2(X2,X3)))
| ~ relation_of2_as_subset(unordered_pair(singleton(X5),unordered_pair(X1,X5)),X2,X3)
| ~ relation_of2_as_subset(unordered_pair(singleton(X0),unordered_pair(X5,X0)),X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_850])]) ).
fof(f3637,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),powerset(cartesian_product2(X2,X3)))
| ~ in(X1,X4)
| ~ in(X5,X4)
| ~ in(X0,X4)
| ~ sP0(powerset(cartesian_product2(X2,X3)),X4)
| empty(powerset(cartesian_product2(X2,X3)))
| ~ relation_of2_as_subset(unordered_pair(singleton(X5),unordered_pair(X1,X5)),X2,X3)
| ~ relation_of2_as_subset(unordered_pair(singleton(X0),unordered_pair(X5,X0)),X2,X3) )
| ~ spl17_108
| ~ spl17_378 ),
inference(duplicate_literal_removal,[],[f3622]) ).
fof(f3622,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),powerset(cartesian_product2(X2,X3)))
| ~ in(X1,X4)
| ~ in(X5,X4)
| ~ in(X0,X4)
| ~ sP0(powerset(cartesian_product2(X2,X3)),X4)
| empty(powerset(cartesian_product2(X2,X3)))
| ~ relation_of2_as_subset(unordered_pair(singleton(X5),unordered_pair(X1,X5)),X2,X3)
| empty(powerset(cartesian_product2(X2,X3)))
| ~ relation_of2_as_subset(unordered_pair(singleton(X0),unordered_pair(X5,X0)),X2,X3) )
| ~ spl17_108
| ~ spl17_378 ),
inference(resolution,[],[f3586,f865]) ).
fof(f11307,plain,
( spl17_849
| ~ spl17_30
| ~ spl17_371 ),
inference(avatar_split_clause,[],[f3552,f3541,f313,f11305]) ).
fof(f11305,plain,
( spl17_849
<=> ! [X5,X4,X0,X3,X2,X1] :
( ~ relation_of2_as_subset(unordered_pair(singleton(X0),unordered_pair(X1,X0)),X2,X3)
| empty(powerset(cartesian_product2(X2,X3)))
| in(unordered_pair(singleton(X0),unordered_pair(X0,X4)),powerset(cartesian_product2(X2,X3)))
| ~ in(X4,X5)
| ~ in(X1,X5)
| ~ in(X0,X5)
| ~ sP0(powerset(cartesian_product2(X2,X3)),X5)
| ~ relation_of2_as_subset(unordered_pair(singleton(X1),unordered_pair(X1,X4)),X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_849])]) ).
fof(f3541,plain,
( spl17_371
<=> ! [X5,X4,X0,X3,X2,X1] :
( ~ relation_of2_as_subset(unordered_pair(singleton(X0),unordered_pair(X0,X1)),X2,X3)
| empty(powerset(cartesian_product2(X2,X3)))
| in(unordered_pair(singleton(X4),unordered_pair(X4,X1)),powerset(cartesian_product2(X2,X3)))
| ~ in(X1,X5)
| ~ in(X0,X5)
| ~ in(X4,X5)
| ~ sP0(powerset(cartesian_product2(X2,X3)),X5)
| ~ relation_of2_as_subset(unordered_pair(singleton(X4),unordered_pair(X4,X0)),X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_371])]) ).
fof(f3552,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ relation_of2_as_subset(unordered_pair(singleton(X0),unordered_pair(X1,X0)),X2,X3)
| empty(powerset(cartesian_product2(X2,X3)))
| in(unordered_pair(singleton(X0),unordered_pair(X0,X4)),powerset(cartesian_product2(X2,X3)))
| ~ in(X4,X5)
| ~ in(X1,X5)
| ~ in(X0,X5)
| ~ sP0(powerset(cartesian_product2(X2,X3)),X5)
| ~ relation_of2_as_subset(unordered_pair(singleton(X1),unordered_pair(X1,X4)),X2,X3) )
| ~ spl17_30
| ~ spl17_371 ),
inference(superposition,[],[f3542,f314]) ).
fof(f3542,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ relation_of2_as_subset(unordered_pair(singleton(X4),unordered_pair(X4,X0)),X2,X3)
| empty(powerset(cartesian_product2(X2,X3)))
| in(unordered_pair(singleton(X4),unordered_pair(X4,X1)),powerset(cartesian_product2(X2,X3)))
| ~ in(X1,X5)
| ~ in(X0,X5)
| ~ in(X4,X5)
| ~ sP0(powerset(cartesian_product2(X2,X3)),X5)
| ~ relation_of2_as_subset(unordered_pair(singleton(X0),unordered_pair(X0,X1)),X2,X3) )
| ~ spl17_371 ),
inference(avatar_component_clause,[],[f3541]) ).
fof(f11303,plain,
( spl17_848
| ~ spl17_49
| ~ spl17_358 ),
inference(avatar_split_clause,[],[f3432,f3403,f422,f11301]) ).
fof(f11301,plain,
( spl17_848
<=> ! [X2,X0,X1,X3] :
( sP0(powerset(powerset(X0)),X1)
| sP0(X2,unordered_pair(singleton(sK7(powerset(powerset(X0)),X1)),unordered_pair(sK8(powerset(powerset(X0)),X1),sK7(powerset(powerset(X0)),X1))))
| ~ empty(X0)
| ~ in(X3,sK9(X2,unordered_pair(singleton(sK7(powerset(powerset(X0)),X1)),unordered_pair(sK8(powerset(powerset(X0)),X1),sK7(powerset(powerset(X0)),X1))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_848])]) ).
fof(f3432,plain,
( ! [X2,X3,X0,X1] :
( sP0(powerset(powerset(X0)),X1)
| sP0(X2,unordered_pair(singleton(sK7(powerset(powerset(X0)),X1)),unordered_pair(sK8(powerset(powerset(X0)),X1),sK7(powerset(powerset(X0)),X1))))
| ~ empty(X0)
| ~ in(X3,sK9(X2,unordered_pair(singleton(sK7(powerset(powerset(X0)),X1)),unordered_pair(sK8(powerset(powerset(X0)),X1),sK7(powerset(powerset(X0)),X1))))) )
| ~ spl17_49
| ~ spl17_358 ),
inference(resolution,[],[f3404,f423]) ).
fof(f11299,plain,
( spl17_847
| ~ spl17_17
| ~ spl17_818 ),
inference(avatar_split_clause,[],[f11115,f10810,f255,f11297]) ).
fof(f11297,plain,
( spl17_847
<=> ! [X0] :
( sP0(X0,sK10(powerset(powerset(sK16))))
| sP1(sK8(X0,sK10(powerset(powerset(sK16))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_847])]) ).
fof(f255,plain,
( spl17_17
<=> ! [X0] :
( sP1(X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_17])]) ).
fof(f10810,plain,
( spl17_818
<=> ! [X0] :
( relation(sK8(X0,sK10(powerset(powerset(sK16)))))
| sP0(X0,sK10(powerset(powerset(sK16)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_818])]) ).
fof(f11115,plain,
( ! [X0] :
( sP0(X0,sK10(powerset(powerset(sK16))))
| sP1(sK8(X0,sK10(powerset(powerset(sK16))))) )
| ~ spl17_17
| ~ spl17_818 ),
inference(resolution,[],[f10811,f256]) ).
fof(f256,plain,
( ! [X0] :
( ~ relation(X0)
| sP1(X0) )
| ~ spl17_17 ),
inference(avatar_component_clause,[],[f255]) ).
fof(f10811,plain,
( ! [X0] :
( relation(sK8(X0,sK10(powerset(powerset(sK16)))))
| sP0(X0,sK10(powerset(powerset(sK16)))) )
| ~ spl17_818 ),
inference(avatar_component_clause,[],[f10810]) ).
fof(f11295,plain,
( spl17_846
| ~ spl17_49
| ~ spl17_356 ),
inference(avatar_split_clause,[],[f3428,f3395,f422,f11293]) ).
fof(f11293,plain,
( spl17_846
<=> ! [X2,X0,X1,X3] :
( sP0(powerset(powerset(X0)),X1)
| sP0(X2,unordered_pair(singleton(sK7(powerset(powerset(X0)),X1)),unordered_pair(sK8(powerset(powerset(X0)),X1),sK7(powerset(powerset(X0)),X1))))
| ~ empty(X0)
| ~ in(X3,sK8(X2,unordered_pair(singleton(sK7(powerset(powerset(X0)),X1)),unordered_pair(sK8(powerset(powerset(X0)),X1),sK7(powerset(powerset(X0)),X1))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_846])]) ).
fof(f3428,plain,
( ! [X2,X3,X0,X1] :
( sP0(powerset(powerset(X0)),X1)
| sP0(X2,unordered_pair(singleton(sK7(powerset(powerset(X0)),X1)),unordered_pair(sK8(powerset(powerset(X0)),X1),sK7(powerset(powerset(X0)),X1))))
| ~ empty(X0)
| ~ in(X3,sK8(X2,unordered_pair(singleton(sK7(powerset(powerset(X0)),X1)),unordered_pair(sK8(powerset(powerset(X0)),X1),sK7(powerset(powerset(X0)),X1))))) )
| ~ spl17_49
| ~ spl17_356 ),
inference(resolution,[],[f3396,f423]) ).
fof(f11291,plain,
( spl17_845
| ~ spl17_49
| ~ spl17_355 ),
inference(avatar_split_clause,[],[f3424,f3391,f422,f11289]) ).
fof(f11289,plain,
( spl17_845
<=> ! [X2,X0,X1,X3] :
( sP0(powerset(powerset(X0)),X1)
| sP0(X2,unordered_pair(singleton(sK7(powerset(powerset(X0)),X1)),unordered_pair(sK8(powerset(powerset(X0)),X1),sK7(powerset(powerset(X0)),X1))))
| ~ empty(X0)
| ~ in(X3,sK7(X2,unordered_pair(singleton(sK7(powerset(powerset(X0)),X1)),unordered_pair(sK8(powerset(powerset(X0)),X1),sK7(powerset(powerset(X0)),X1))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_845])]) ).
fof(f3424,plain,
( ! [X2,X3,X0,X1] :
( sP0(powerset(powerset(X0)),X1)
| sP0(X2,unordered_pair(singleton(sK7(powerset(powerset(X0)),X1)),unordered_pair(sK8(powerset(powerset(X0)),X1),sK7(powerset(powerset(X0)),X1))))
| ~ empty(X0)
| ~ in(X3,sK7(X2,unordered_pair(singleton(sK7(powerset(powerset(X0)),X1)),unordered_pair(sK8(powerset(powerset(X0)),X1),sK7(powerset(powerset(X0)),X1))))) )
| ~ spl17_49
| ~ spl17_355 ),
inference(resolution,[],[f3392,f423]) ).
fof(f11287,plain,
( spl17_844
| ~ spl17_49
| ~ spl17_354 ),
inference(avatar_split_clause,[],[f3420,f3387,f422,f11285]) ).
fof(f11285,plain,
( spl17_844
<=> ! [X2,X0,X1,X3] :
( sP0(powerset(powerset(X0)),X1)
| sP0(X2,unordered_pair(singleton(sK8(powerset(powerset(X0)),X1)),unordered_pair(sK9(powerset(powerset(X0)),X1),sK8(powerset(powerset(X0)),X1))))
| ~ empty(X0)
| ~ in(X3,sK9(X2,unordered_pair(singleton(sK8(powerset(powerset(X0)),X1)),unordered_pair(sK9(powerset(powerset(X0)),X1),sK8(powerset(powerset(X0)),X1))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_844])]) ).
fof(f3420,plain,
( ! [X2,X3,X0,X1] :
( sP0(powerset(powerset(X0)),X1)
| sP0(X2,unordered_pair(singleton(sK8(powerset(powerset(X0)),X1)),unordered_pair(sK9(powerset(powerset(X0)),X1),sK8(powerset(powerset(X0)),X1))))
| ~ empty(X0)
| ~ in(X3,sK9(X2,unordered_pair(singleton(sK8(powerset(powerset(X0)),X1)),unordered_pair(sK9(powerset(powerset(X0)),X1),sK8(powerset(powerset(X0)),X1))))) )
| ~ spl17_49
| ~ spl17_354 ),
inference(resolution,[],[f3388,f423]) ).
fof(f11283,plain,
( spl17_843
| ~ spl17_49
| ~ spl17_353 ),
inference(avatar_split_clause,[],[f3416,f3383,f422,f11281]) ).
fof(f11281,plain,
( spl17_843
<=> ! [X2,X0,X1,X3] :
( sP0(powerset(powerset(X0)),X1)
| sP0(X2,unordered_pair(singleton(sK8(powerset(powerset(X0)),X1)),unordered_pair(sK9(powerset(powerset(X0)),X1),sK8(powerset(powerset(X0)),X1))))
| ~ empty(X0)
| ~ in(X3,sK8(X2,unordered_pair(singleton(sK8(powerset(powerset(X0)),X1)),unordered_pair(sK9(powerset(powerset(X0)),X1),sK8(powerset(powerset(X0)),X1))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_843])]) ).
fof(f3416,plain,
( ! [X2,X3,X0,X1] :
( sP0(powerset(powerset(X0)),X1)
| sP0(X2,unordered_pair(singleton(sK8(powerset(powerset(X0)),X1)),unordered_pair(sK9(powerset(powerset(X0)),X1),sK8(powerset(powerset(X0)),X1))))
| ~ empty(X0)
| ~ in(X3,sK8(X2,unordered_pair(singleton(sK8(powerset(powerset(X0)),X1)),unordered_pair(sK9(powerset(powerset(X0)),X1),sK8(powerset(powerset(X0)),X1))))) )
| ~ spl17_49
| ~ spl17_353 ),
inference(resolution,[],[f3384,f423]) ).
fof(f11279,plain,
( spl17_842
| ~ spl17_49
| ~ spl17_352 ),
inference(avatar_split_clause,[],[f3412,f3379,f422,f11277]) ).
fof(f11277,plain,
( spl17_842
<=> ! [X2,X0,X1,X3] :
( sP0(powerset(powerset(X0)),X1)
| sP0(X2,unordered_pair(singleton(sK8(powerset(powerset(X0)),X1)),unordered_pair(sK9(powerset(powerset(X0)),X1),sK8(powerset(powerset(X0)),X1))))
| ~ empty(X0)
| ~ in(X3,sK7(X2,unordered_pair(singleton(sK8(powerset(powerset(X0)),X1)),unordered_pair(sK9(powerset(powerset(X0)),X1),sK8(powerset(powerset(X0)),X1))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_842])]) ).
fof(f3412,plain,
( ! [X2,X3,X0,X1] :
( sP0(powerset(powerset(X0)),X1)
| sP0(X2,unordered_pair(singleton(sK8(powerset(powerset(X0)),X1)),unordered_pair(sK9(powerset(powerset(X0)),X1),sK8(powerset(powerset(X0)),X1))))
| ~ empty(X0)
| ~ in(X3,sK7(X2,unordered_pair(singleton(sK8(powerset(powerset(X0)),X1)),unordered_pair(sK9(powerset(powerset(X0)),X1),sK8(powerset(powerset(X0)),X1))))) )
| ~ spl17_49
| ~ spl17_352 ),
inference(resolution,[],[f3380,f423]) ).
fof(f11275,plain,
( spl17_841
| ~ spl17_98
| ~ spl17_351 ),
inference(avatar_split_clause,[],[f3369,f3348,f788,f11273]) ).
fof(f11273,plain,
( spl17_841
<=> ! [X0,X3,X2,X1] :
( in(unordered_pair(singleton(X0),unordered_pair(X0,sK8(powerset(X1),X2))),powerset(X1))
| ~ in(sK8(powerset(X1),X2),X3)
| ~ in(sK7(powerset(X1),X2),X3)
| ~ in(X0,X3)
| ~ sP0(powerset(X1),X3)
| sP0(powerset(X1),X2)
| empty(powerset(X1))
| ~ subset(unordered_pair(singleton(X0),unordered_pair(sK7(powerset(X1),X2),X0)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_841])]) ).
fof(f788,plain,
( spl17_98
<=> ! [X0,X1] :
( empty(powerset(X0))
| in(X1,powerset(X0))
| ~ subset(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_98])]) ).
fof(f3369,plain,
( ! [X2,X3,X0,X1] :
( in(unordered_pair(singleton(X0),unordered_pair(X0,sK8(powerset(X1),X2))),powerset(X1))
| ~ in(sK8(powerset(X1),X2),X3)
| ~ in(sK7(powerset(X1),X2),X3)
| ~ in(X0,X3)
| ~ sP0(powerset(X1),X3)
| sP0(powerset(X1),X2)
| empty(powerset(X1))
| ~ subset(unordered_pair(singleton(X0),unordered_pair(sK7(powerset(X1),X2),X0)),X1) )
| ~ spl17_98
| ~ spl17_351 ),
inference(resolution,[],[f3349,f789]) ).
fof(f789,plain,
( ! [X0,X1] :
( in(X1,powerset(X0))
| empty(powerset(X0))
| ~ subset(X1,X0) )
| ~ spl17_98 ),
inference(avatar_component_clause,[],[f788]) ).
fof(f11271,plain,
( spl17_840
| ~ spl17_98
| ~ spl17_350 ),
inference(avatar_split_clause,[],[f3355,f3344,f788,f11269]) ).
fof(f11269,plain,
( spl17_840
<=> ! [X0,X3,X2,X1] :
( in(unordered_pair(singleton(X0),unordered_pair(X0,sK9(powerset(X1),X2))),powerset(X1))
| ~ in(sK9(powerset(X1),X2),X3)
| ~ in(sK8(powerset(X1),X2),X3)
| ~ in(X0,X3)
| ~ sP0(powerset(X1),X3)
| sP0(powerset(X1),X2)
| empty(powerset(X1))
| ~ subset(unordered_pair(singleton(X0),unordered_pair(sK8(powerset(X1),X2),X0)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_840])]) ).
fof(f3355,plain,
( ! [X2,X3,X0,X1] :
( in(unordered_pair(singleton(X0),unordered_pair(X0,sK9(powerset(X1),X2))),powerset(X1))
| ~ in(sK9(powerset(X1),X2),X3)
| ~ in(sK8(powerset(X1),X2),X3)
| ~ in(X0,X3)
| ~ sP0(powerset(X1),X3)
| sP0(powerset(X1),X2)
| empty(powerset(X1))
| ~ subset(unordered_pair(singleton(X0),unordered_pair(sK8(powerset(X1),X2),X0)),X1) )
| ~ spl17_98
| ~ spl17_350 ),
inference(resolution,[],[f3345,f789]) ).
fof(f11267,plain,
( spl17_839
| ~ spl17_271
| ~ spl17_321 ),
inference(avatar_split_clause,[],[f2969,f2873,f2289,f11265]) ).
fof(f11265,plain,
( spl17_839
<=> ! [X0,X1] :
( empty(sK10(sK6(powerset(X0))))
| sP0(sK10(powerset(sK10(sK6(powerset(X0))))),X1)
| empty(sK6(powerset(X0)))
| element(unordered_pair(singleton(sK7(sK10(powerset(sK10(sK6(powerset(X0))))),X1)),unordered_pair(sK8(sK10(powerset(sK10(sK6(powerset(X0))))),X1),sK7(sK10(powerset(sK10(sK6(powerset(X0))))),X1))),X0)
| empty(powerset(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_839])]) ).
fof(f2289,plain,
( spl17_271
<=> ! [X0,X1] :
( empty(powerset(X0))
| empty(sK6(powerset(X0)))
| element(X1,X0)
| ~ in(X1,sK10(sK6(powerset(X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_271])]) ).
fof(f2969,plain,
( ! [X0,X1] :
( empty(sK10(sK6(powerset(X0))))
| sP0(sK10(powerset(sK10(sK6(powerset(X0))))),X1)
| empty(sK6(powerset(X0)))
| element(unordered_pair(singleton(sK7(sK10(powerset(sK10(sK6(powerset(X0))))),X1)),unordered_pair(sK8(sK10(powerset(sK10(sK6(powerset(X0))))),X1),sK7(sK10(powerset(sK10(sK6(powerset(X0))))),X1))),X0)
| empty(powerset(X0)) )
| ~ spl17_271
| ~ spl17_321 ),
inference(resolution,[],[f2874,f2290]) ).
fof(f2290,plain,
( ! [X0,X1] :
( ~ in(X1,sK10(sK6(powerset(X0))))
| empty(sK6(powerset(X0)))
| element(X1,X0)
| empty(powerset(X0)) )
| ~ spl17_271 ),
inference(avatar_component_clause,[],[f2289]) ).
fof(f11263,plain,
( spl17_838
| ~ spl17_271
| ~ spl17_320 ),
inference(avatar_split_clause,[],[f2918,f2869,f2289,f11261]) ).
fof(f11261,plain,
( spl17_838
<=> ! [X0,X1] :
( empty(sK10(sK6(powerset(X0))))
| sP0(sK10(powerset(sK10(sK6(powerset(X0))))),X1)
| empty(sK6(powerset(X0)))
| element(unordered_pair(singleton(sK8(sK10(powerset(sK10(sK6(powerset(X0))))),X1)),unordered_pair(sK9(sK10(powerset(sK10(sK6(powerset(X0))))),X1),sK8(sK10(powerset(sK10(sK6(powerset(X0))))),X1))),X0)
| empty(powerset(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_838])]) ).
fof(f2918,plain,
( ! [X0,X1] :
( empty(sK10(sK6(powerset(X0))))
| sP0(sK10(powerset(sK10(sK6(powerset(X0))))),X1)
| empty(sK6(powerset(X0)))
| element(unordered_pair(singleton(sK8(sK10(powerset(sK10(sK6(powerset(X0))))),X1)),unordered_pair(sK9(sK10(powerset(sK10(sK6(powerset(X0))))),X1),sK8(sK10(powerset(sK10(sK6(powerset(X0))))),X1))),X0)
| empty(powerset(X0)) )
| ~ spl17_271
| ~ spl17_320 ),
inference(resolution,[],[f2870,f2290]) ).
fof(f11207,plain,
( spl17_837
| ~ spl17_17
| ~ spl17_809 ),
inference(avatar_split_clause,[],[f10996,f10764,f255,f11205]) ).
fof(f11205,plain,
( spl17_837
<=> ! [X0] :
( sP0(X0,sK10(powerset(powerset(sK16))))
| sP1(sK7(X0,sK10(powerset(powerset(sK16))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_837])]) ).
fof(f10764,plain,
( spl17_809
<=> ! [X0] :
( relation(sK7(X0,sK10(powerset(powerset(sK16)))))
| sP0(X0,sK10(powerset(powerset(sK16)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_809])]) ).
fof(f10996,plain,
( ! [X0] :
( sP0(X0,sK10(powerset(powerset(sK16))))
| sP1(sK7(X0,sK10(powerset(powerset(sK16))))) )
| ~ spl17_17
| ~ spl17_809 ),
inference(resolution,[],[f10765,f256]) ).
fof(f10765,plain,
( ! [X0] :
( relation(sK7(X0,sK10(powerset(powerset(sK16)))))
| sP0(X0,sK10(powerset(powerset(sK16)))) )
| ~ spl17_809 ),
inference(avatar_component_clause,[],[f10764]) ).
fof(f11135,plain,
( spl17_836
| ~ spl17_51
| ~ spl17_347 ),
inference(avatar_split_clause,[],[f3320,f3306,f439,f11133]) ).
fof(f11133,plain,
( spl17_836
<=> ! [X2,X0,X1] :
( sP0(powerset(powerset(X0)),X1)
| empty(unordered_pair(singleton(sK7(powerset(powerset(X0)),X1)),unordered_pair(sK8(powerset(powerset(X0)),X1),sK7(powerset(powerset(X0)),X1))))
| element(X2,X0)
| ~ in(X2,sK10(unordered_pair(singleton(sK7(powerset(powerset(X0)),X1)),unordered_pair(sK8(powerset(powerset(X0)),X1),sK7(powerset(powerset(X0)),X1))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_836])]) ).
fof(f3320,plain,
( ! [X2,X0,X1] :
( sP0(powerset(powerset(X0)),X1)
| empty(unordered_pair(singleton(sK7(powerset(powerset(X0)),X1)),unordered_pair(sK8(powerset(powerset(X0)),X1),sK7(powerset(powerset(X0)),X1))))
| element(X2,X0)
| ~ in(X2,sK10(unordered_pair(singleton(sK7(powerset(powerset(X0)),X1)),unordered_pair(sK8(powerset(powerset(X0)),X1),sK7(powerset(powerset(X0)),X1))))) )
| ~ spl17_51
| ~ spl17_347 ),
inference(resolution,[],[f3307,f440]) ).
fof(f11131,plain,
( spl17_835
| ~ spl17_51
| ~ spl17_346 ),
inference(avatar_split_clause,[],[f3316,f3302,f439,f11129]) ).
fof(f11129,plain,
( spl17_835
<=> ! [X2,X0,X1] :
( sP0(powerset(powerset(X0)),X1)
| empty(unordered_pair(singleton(sK8(powerset(powerset(X0)),X1)),unordered_pair(sK9(powerset(powerset(X0)),X1),sK8(powerset(powerset(X0)),X1))))
| element(X2,X0)
| ~ in(X2,sK10(unordered_pair(singleton(sK8(powerset(powerset(X0)),X1)),unordered_pair(sK9(powerset(powerset(X0)),X1),sK8(powerset(powerset(X0)),X1))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_835])]) ).
fof(f3316,plain,
( ! [X2,X0,X1] :
( sP0(powerset(powerset(X0)),X1)
| empty(unordered_pair(singleton(sK8(powerset(powerset(X0)),X1)),unordered_pair(sK9(powerset(powerset(X0)),X1),sK8(powerset(powerset(X0)),X1))))
| element(X2,X0)
| ~ in(X2,sK10(unordered_pair(singleton(sK8(powerset(powerset(X0)),X1)),unordered_pair(sK9(powerset(powerset(X0)),X1),sK8(powerset(powerset(X0)),X1))))) )
| ~ spl17_51
| ~ spl17_346 ),
inference(resolution,[],[f3303,f440]) ).
fof(f11127,plain,
( spl17_834
| ~ spl17_75
| ~ spl17_328 ),
inference(avatar_split_clause,[],[f3077,f3042,f643,f11125]) ).
fof(f11125,plain,
( spl17_834
<=> ! [X0,X1] :
( sP0(sK6(powerset(X0)),X1)
| element(sK10(unordered_pair(singleton(sK7(sK6(powerset(X0)),X1)),unordered_pair(sK8(sK6(powerset(X0)),X1),sK7(sK6(powerset(X0)),X1)))),X0)
| empty(powerset(X0))
| empty(unordered_pair(singleton(sK7(sK6(powerset(X0)),X1)),unordered_pair(sK8(sK6(powerset(X0)),X1),sK7(sK6(powerset(X0)),X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_834])]) ).
fof(f3077,plain,
( ! [X0,X1] :
( sP0(sK6(powerset(X0)),X1)
| element(sK10(unordered_pair(singleton(sK7(sK6(powerset(X0)),X1)),unordered_pair(sK8(sK6(powerset(X0)),X1),sK7(sK6(powerset(X0)),X1)))),X0)
| empty(powerset(X0))
| empty(unordered_pair(singleton(sK7(sK6(powerset(X0)),X1)),unordered_pair(sK8(sK6(powerset(X0)),X1),sK7(sK6(powerset(X0)),X1)))) )
| ~ spl17_75
| ~ spl17_328 ),
inference(resolution,[],[f3043,f644]) ).
fof(f11123,plain,
( spl17_833
| ~ spl17_75
| ~ spl17_326 ),
inference(avatar_split_clause,[],[f3059,f3034,f643,f11121]) ).
fof(f11121,plain,
( spl17_833
<=> ! [X0,X1] :
( sP0(sK6(powerset(X0)),X1)
| element(sK10(unordered_pair(singleton(sK8(sK6(powerset(X0)),X1)),unordered_pair(sK9(sK6(powerset(X0)),X1),sK8(sK6(powerset(X0)),X1)))),X0)
| empty(powerset(X0))
| empty(unordered_pair(singleton(sK8(sK6(powerset(X0)),X1)),unordered_pair(sK9(sK6(powerset(X0)),X1),sK8(sK6(powerset(X0)),X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_833])]) ).
fof(f3059,plain,
( ! [X0,X1] :
( sP0(sK6(powerset(X0)),X1)
| element(sK10(unordered_pair(singleton(sK8(sK6(powerset(X0)),X1)),unordered_pair(sK9(sK6(powerset(X0)),X1),sK8(sK6(powerset(X0)),X1)))),X0)
| empty(powerset(X0))
| empty(unordered_pair(singleton(sK8(sK6(powerset(X0)),X1)),unordered_pair(sK9(sK6(powerset(X0)),X1),sK8(sK6(powerset(X0)),X1)))) )
| ~ spl17_75
| ~ spl17_326 ),
inference(resolution,[],[f3035,f644]) ).
fof(f11119,plain,
( spl17_832
| ~ spl17_269
| ~ spl17_312 ),
inference(avatar_split_clause,[],[f2822,f2730,f2240,f11117]) ).
fof(f11117,plain,
( spl17_832
<=> ! [X0,X1] :
( sP0(sK6(sK10(sK10(powerset(powerset(X0))))),X1)
| empty(sK10(sK10(powerset(powerset(X0)))))
| element(unordered_pair(singleton(sK7(sK6(sK10(sK10(powerset(powerset(X0))))),X1)),unordered_pair(sK8(sK6(sK10(sK10(powerset(powerset(X0))))),X1),sK7(sK6(sK10(sK10(powerset(powerset(X0))))),X1))),X0)
| empty(sK10(powerset(powerset(X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_832])]) ).
fof(f2822,plain,
( ! [X0,X1] :
( sP0(sK6(sK10(sK10(powerset(powerset(X0))))),X1)
| empty(sK10(sK10(powerset(powerset(X0)))))
| element(unordered_pair(singleton(sK7(sK6(sK10(sK10(powerset(powerset(X0))))),X1)),unordered_pair(sK8(sK6(sK10(sK10(powerset(powerset(X0))))),X1),sK7(sK6(sK10(sK10(powerset(powerset(X0))))),X1))),X0)
| empty(sK10(powerset(powerset(X0)))) )
| ~ spl17_269
| ~ spl17_312 ),
inference(resolution,[],[f2731,f2241]) ).
fof(f11114,plain,
( spl17_831
| ~ spl17_269
| ~ spl17_311 ),
inference(avatar_split_clause,[],[f2773,f2726,f2240,f11112]) ).
fof(f11112,plain,
( spl17_831
<=> ! [X0,X1] :
( sP0(sK6(sK10(sK10(powerset(powerset(X0))))),X1)
| empty(sK10(sK10(powerset(powerset(X0)))))
| element(unordered_pair(singleton(sK8(sK6(sK10(sK10(powerset(powerset(X0))))),X1)),unordered_pair(sK9(sK6(sK10(sK10(powerset(powerset(X0))))),X1),sK8(sK6(sK10(sK10(powerset(powerset(X0))))),X1))),X0)
| empty(sK10(powerset(powerset(X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_831])]) ).
fof(f2773,plain,
( ! [X0,X1] :
( sP0(sK6(sK10(sK10(powerset(powerset(X0))))),X1)
| empty(sK10(sK10(powerset(powerset(X0)))))
| element(unordered_pair(singleton(sK8(sK6(sK10(sK10(powerset(powerset(X0))))),X1)),unordered_pair(sK9(sK6(sK10(sK10(powerset(powerset(X0))))),X1),sK8(sK6(sK10(sK10(powerset(powerset(X0))))),X1))),X0)
| empty(sK10(powerset(powerset(X0)))) )
| ~ spl17_269
| ~ spl17_311 ),
inference(resolution,[],[f2727,f2241]) ).
fof(f11000,plain,
( spl17_830
| ~ spl17_49
| ~ spl17_347 ),
inference(avatar_split_clause,[],[f3319,f3306,f422,f10998]) ).
fof(f10998,plain,
( spl17_830
<=> ! [X2,X0,X1] :
( sP0(powerset(powerset(X0)),X1)
| empty(unordered_pair(singleton(sK7(powerset(powerset(X0)),X1)),unordered_pair(sK8(powerset(powerset(X0)),X1),sK7(powerset(powerset(X0)),X1))))
| ~ empty(X0)
| ~ in(X2,sK10(unordered_pair(singleton(sK7(powerset(powerset(X0)),X1)),unordered_pair(sK8(powerset(powerset(X0)),X1),sK7(powerset(powerset(X0)),X1))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_830])]) ).
fof(f3319,plain,
( ! [X2,X0,X1] :
( sP0(powerset(powerset(X0)),X1)
| empty(unordered_pair(singleton(sK7(powerset(powerset(X0)),X1)),unordered_pair(sK8(powerset(powerset(X0)),X1),sK7(powerset(powerset(X0)),X1))))
| ~ empty(X0)
| ~ in(X2,sK10(unordered_pair(singleton(sK7(powerset(powerset(X0)),X1)),unordered_pair(sK8(powerset(powerset(X0)),X1),sK7(powerset(powerset(X0)),X1))))) )
| ~ spl17_49
| ~ spl17_347 ),
inference(resolution,[],[f3307,f423]) ).
fof(f10995,plain,
( spl17_829
| ~ spl17_49
| ~ spl17_346 ),
inference(avatar_split_clause,[],[f3315,f3302,f422,f10993]) ).
fof(f10993,plain,
( spl17_829
<=> ! [X2,X0,X1] :
( sP0(powerset(powerset(X0)),X1)
| empty(unordered_pair(singleton(sK8(powerset(powerset(X0)),X1)),unordered_pair(sK9(powerset(powerset(X0)),X1),sK8(powerset(powerset(X0)),X1))))
| ~ empty(X0)
| ~ in(X2,sK10(unordered_pair(singleton(sK8(powerset(powerset(X0)),X1)),unordered_pair(sK9(powerset(powerset(X0)),X1),sK8(powerset(powerset(X0)),X1))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_829])]) ).
fof(f3315,plain,
( ! [X2,X0,X1] :
( sP0(powerset(powerset(X0)),X1)
| empty(unordered_pair(singleton(sK8(powerset(powerset(X0)),X1)),unordered_pair(sK9(powerset(powerset(X0)),X1),sK8(powerset(powerset(X0)),X1))))
| ~ empty(X0)
| ~ in(X2,sK10(unordered_pair(singleton(sK8(powerset(powerset(X0)),X1)),unordered_pair(sK9(powerset(powerset(X0)),X1),sK8(powerset(powerset(X0)),X1))))) )
| ~ spl17_49
| ~ spl17_346 ),
inference(resolution,[],[f3303,f423]) ).
fof(f10991,plain,
( spl17_828
| ~ spl17_41
| ~ spl17_338 ),
inference(avatar_split_clause,[],[f3231,f3192,f363,f10989]) ).
fof(f10989,plain,
( spl17_828
<=> ! [X0,X3,X2,X1] :
( sP0(X0,powerset(powerset(cartesian_product2(X1,X2))))
| sP0(sK9(X0,powerset(powerset(cartesian_product2(X1,X2)))),X3)
| relation(unordered_pair(singleton(sK7(sK9(X0,powerset(powerset(cartesian_product2(X1,X2)))),X3)),unordered_pair(sK8(sK9(X0,powerset(powerset(cartesian_product2(X1,X2)))),X3),sK7(sK9(X0,powerset(powerset(cartesian_product2(X1,X2)))),X3)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_828])]) ).
fof(f3192,plain,
( spl17_338
<=> ! [X2,X0,X1] :
( element(unordered_pair(singleton(sK7(sK9(X0,powerset(X1)),X2)),unordered_pair(sK8(sK9(X0,powerset(X1)),X2),sK7(sK9(X0,powerset(X1)),X2))),X1)
| sP0(X0,powerset(X1))
| sP0(sK9(X0,powerset(X1)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_338])]) ).
fof(f3231,plain,
( ! [X2,X3,X0,X1] :
( sP0(X0,powerset(powerset(cartesian_product2(X1,X2))))
| sP0(sK9(X0,powerset(powerset(cartesian_product2(X1,X2)))),X3)
| relation(unordered_pair(singleton(sK7(sK9(X0,powerset(powerset(cartesian_product2(X1,X2)))),X3)),unordered_pair(sK8(sK9(X0,powerset(powerset(cartesian_product2(X1,X2)))),X3),sK7(sK9(X0,powerset(powerset(cartesian_product2(X1,X2)))),X3)))) )
| ~ spl17_41
| ~ spl17_338 ),
inference(resolution,[],[f3193,f364]) ).
fof(f3193,plain,
( ! [X2,X0,X1] :
( element(unordered_pair(singleton(sK7(sK9(X0,powerset(X1)),X2)),unordered_pair(sK8(sK9(X0,powerset(X1)),X2),sK7(sK9(X0,powerset(X1)),X2))),X1)
| sP0(X0,powerset(X1))
| sP0(sK9(X0,powerset(X1)),X2) )
| ~ spl17_338 ),
inference(avatar_component_clause,[],[f3192]) ).
fof(f10987,plain,
( spl17_827
| ~ spl17_41
| ~ spl17_337 ),
inference(avatar_split_clause,[],[f3227,f3188,f363,f10985]) ).
fof(f10985,plain,
( spl17_827
<=> ! [X0,X3,X2,X1] :
( sP0(X0,powerset(powerset(cartesian_product2(X1,X2))))
| sP0(sK9(X0,powerset(powerset(cartesian_product2(X1,X2)))),X3)
| relation(unordered_pair(singleton(sK8(sK9(X0,powerset(powerset(cartesian_product2(X1,X2)))),X3)),unordered_pair(sK9(sK9(X0,powerset(powerset(cartesian_product2(X1,X2)))),X3),sK8(sK9(X0,powerset(powerset(cartesian_product2(X1,X2)))),X3)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_827])]) ).
fof(f3188,plain,
( spl17_337
<=> ! [X2,X0,X1] :
( element(unordered_pair(singleton(sK8(sK9(X0,powerset(X1)),X2)),unordered_pair(sK9(sK9(X0,powerset(X1)),X2),sK8(sK9(X0,powerset(X1)),X2))),X1)
| sP0(X0,powerset(X1))
| sP0(sK9(X0,powerset(X1)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_337])]) ).
fof(f3227,plain,
( ! [X2,X3,X0,X1] :
( sP0(X0,powerset(powerset(cartesian_product2(X1,X2))))
| sP0(sK9(X0,powerset(powerset(cartesian_product2(X1,X2)))),X3)
| relation(unordered_pair(singleton(sK8(sK9(X0,powerset(powerset(cartesian_product2(X1,X2)))),X3)),unordered_pair(sK9(sK9(X0,powerset(powerset(cartesian_product2(X1,X2)))),X3),sK8(sK9(X0,powerset(powerset(cartesian_product2(X1,X2)))),X3)))) )
| ~ spl17_41
| ~ spl17_337 ),
inference(resolution,[],[f3189,f364]) ).
fof(f3189,plain,
( ! [X2,X0,X1] :
( element(unordered_pair(singleton(sK8(sK9(X0,powerset(X1)),X2)),unordered_pair(sK9(sK9(X0,powerset(X1)),X2),sK8(sK9(X0,powerset(X1)),X2))),X1)
| sP0(X0,powerset(X1))
| sP0(sK9(X0,powerset(X1)),X2) )
| ~ spl17_337 ),
inference(avatar_component_clause,[],[f3188]) ).
fof(f10983,plain,
( spl17_826
| ~ spl17_41
| ~ spl17_336 ),
inference(avatar_split_clause,[],[f3223,f3184,f363,f10981]) ).
fof(f10981,plain,
( spl17_826
<=> ! [X0,X3,X2,X1] :
( sP0(X0,powerset(powerset(cartesian_product2(X1,X2))))
| sP0(sK8(X0,powerset(powerset(cartesian_product2(X1,X2)))),X3)
| relation(unordered_pair(singleton(sK7(sK8(X0,powerset(powerset(cartesian_product2(X1,X2)))),X3)),unordered_pair(sK8(sK8(X0,powerset(powerset(cartesian_product2(X1,X2)))),X3),sK7(sK8(X0,powerset(powerset(cartesian_product2(X1,X2)))),X3)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_826])]) ).
fof(f3184,plain,
( spl17_336
<=> ! [X2,X0,X1] :
( element(unordered_pair(singleton(sK7(sK8(X0,powerset(X1)),X2)),unordered_pair(sK8(sK8(X0,powerset(X1)),X2),sK7(sK8(X0,powerset(X1)),X2))),X1)
| sP0(X0,powerset(X1))
| sP0(sK8(X0,powerset(X1)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_336])]) ).
fof(f3223,plain,
( ! [X2,X3,X0,X1] :
( sP0(X0,powerset(powerset(cartesian_product2(X1,X2))))
| sP0(sK8(X0,powerset(powerset(cartesian_product2(X1,X2)))),X3)
| relation(unordered_pair(singleton(sK7(sK8(X0,powerset(powerset(cartesian_product2(X1,X2)))),X3)),unordered_pair(sK8(sK8(X0,powerset(powerset(cartesian_product2(X1,X2)))),X3),sK7(sK8(X0,powerset(powerset(cartesian_product2(X1,X2)))),X3)))) )
| ~ spl17_41
| ~ spl17_336 ),
inference(resolution,[],[f3185,f364]) ).
fof(f3185,plain,
( ! [X2,X0,X1] :
( element(unordered_pair(singleton(sK7(sK8(X0,powerset(X1)),X2)),unordered_pair(sK8(sK8(X0,powerset(X1)),X2),sK7(sK8(X0,powerset(X1)),X2))),X1)
| sP0(X0,powerset(X1))
| sP0(sK8(X0,powerset(X1)),X2) )
| ~ spl17_336 ),
inference(avatar_component_clause,[],[f3184]) ).
fof(f10979,plain,
( spl17_825
| ~ spl17_41
| ~ spl17_335 ),
inference(avatar_split_clause,[],[f3204,f3180,f363,f10977]) ).
fof(f10977,plain,
( spl17_825
<=> ! [X0,X3,X2,X1] :
( sP0(X0,powerset(powerset(cartesian_product2(X1,X2))))
| sP0(sK8(X0,powerset(powerset(cartesian_product2(X1,X2)))),X3)
| relation(unordered_pair(singleton(sK8(sK8(X0,powerset(powerset(cartesian_product2(X1,X2)))),X3)),unordered_pair(sK9(sK8(X0,powerset(powerset(cartesian_product2(X1,X2)))),X3),sK8(sK8(X0,powerset(powerset(cartesian_product2(X1,X2)))),X3)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_825])]) ).
fof(f3180,plain,
( spl17_335
<=> ! [X2,X0,X1] :
( element(unordered_pair(singleton(sK8(sK8(X0,powerset(X1)),X2)),unordered_pair(sK9(sK8(X0,powerset(X1)),X2),sK8(sK8(X0,powerset(X1)),X2))),X1)
| sP0(X0,powerset(X1))
| sP0(sK8(X0,powerset(X1)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_335])]) ).
fof(f3204,plain,
( ! [X2,X3,X0,X1] :
( sP0(X0,powerset(powerset(cartesian_product2(X1,X2))))
| sP0(sK8(X0,powerset(powerset(cartesian_product2(X1,X2)))),X3)
| relation(unordered_pair(singleton(sK8(sK8(X0,powerset(powerset(cartesian_product2(X1,X2)))),X3)),unordered_pair(sK9(sK8(X0,powerset(powerset(cartesian_product2(X1,X2)))),X3),sK8(sK8(X0,powerset(powerset(cartesian_product2(X1,X2)))),X3)))) )
| ~ spl17_41
| ~ spl17_335 ),
inference(resolution,[],[f3181,f364]) ).
fof(f3181,plain,
( ! [X2,X0,X1] :
( element(unordered_pair(singleton(sK8(sK8(X0,powerset(X1)),X2)),unordered_pair(sK9(sK8(X0,powerset(X1)),X2),sK8(sK8(X0,powerset(X1)),X2))),X1)
| sP0(X0,powerset(X1))
| sP0(sK8(X0,powerset(X1)),X2) )
| ~ spl17_335 ),
inference(avatar_component_clause,[],[f3180]) ).
fof(f10975,plain,
( spl17_824
| ~ spl17_41
| ~ spl17_334 ),
inference(avatar_split_clause,[],[f3200,f3176,f363,f10973]) ).
fof(f10973,plain,
( spl17_824
<=> ! [X0,X3,X2,X1] :
( sP0(X0,powerset(powerset(cartesian_product2(X1,X2))))
| sP0(sK7(X0,powerset(powerset(cartesian_product2(X1,X2)))),X3)
| relation(unordered_pair(singleton(sK7(sK7(X0,powerset(powerset(cartesian_product2(X1,X2)))),X3)),unordered_pair(sK8(sK7(X0,powerset(powerset(cartesian_product2(X1,X2)))),X3),sK7(sK7(X0,powerset(powerset(cartesian_product2(X1,X2)))),X3)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_824])]) ).
fof(f3176,plain,
( spl17_334
<=> ! [X2,X0,X1] :
( element(unordered_pair(singleton(sK7(sK7(X0,powerset(X1)),X2)),unordered_pair(sK8(sK7(X0,powerset(X1)),X2),sK7(sK7(X0,powerset(X1)),X2))),X1)
| sP0(X0,powerset(X1))
| sP0(sK7(X0,powerset(X1)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_334])]) ).
fof(f3200,plain,
( ! [X2,X3,X0,X1] :
( sP0(X0,powerset(powerset(cartesian_product2(X1,X2))))
| sP0(sK7(X0,powerset(powerset(cartesian_product2(X1,X2)))),X3)
| relation(unordered_pair(singleton(sK7(sK7(X0,powerset(powerset(cartesian_product2(X1,X2)))),X3)),unordered_pair(sK8(sK7(X0,powerset(powerset(cartesian_product2(X1,X2)))),X3),sK7(sK7(X0,powerset(powerset(cartesian_product2(X1,X2)))),X3)))) )
| ~ spl17_41
| ~ spl17_334 ),
inference(resolution,[],[f3177,f364]) ).
fof(f3177,plain,
( ! [X2,X0,X1] :
( element(unordered_pair(singleton(sK7(sK7(X0,powerset(X1)),X2)),unordered_pair(sK8(sK7(X0,powerset(X1)),X2),sK7(sK7(X0,powerset(X1)),X2))),X1)
| sP0(X0,powerset(X1))
| sP0(sK7(X0,powerset(X1)),X2) )
| ~ spl17_334 ),
inference(avatar_component_clause,[],[f3176]) ).
fof(f10971,plain,
( spl17_823
| ~ spl17_41
| ~ spl17_333 ),
inference(avatar_split_clause,[],[f3196,f3172,f363,f10969]) ).
fof(f10969,plain,
( spl17_823
<=> ! [X0,X3,X2,X1] :
( sP0(X0,powerset(powerset(cartesian_product2(X1,X2))))
| sP0(sK7(X0,powerset(powerset(cartesian_product2(X1,X2)))),X3)
| relation(unordered_pair(singleton(sK8(sK7(X0,powerset(powerset(cartesian_product2(X1,X2)))),X3)),unordered_pair(sK9(sK7(X0,powerset(powerset(cartesian_product2(X1,X2)))),X3),sK8(sK7(X0,powerset(powerset(cartesian_product2(X1,X2)))),X3)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_823])]) ).
fof(f3172,plain,
( spl17_333
<=> ! [X2,X0,X1] :
( element(unordered_pair(singleton(sK8(sK7(X0,powerset(X1)),X2)),unordered_pair(sK9(sK7(X0,powerset(X1)),X2),sK8(sK7(X0,powerset(X1)),X2))),X1)
| sP0(X0,powerset(X1))
| sP0(sK7(X0,powerset(X1)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_333])]) ).
fof(f3196,plain,
( ! [X2,X3,X0,X1] :
( sP0(X0,powerset(powerset(cartesian_product2(X1,X2))))
| sP0(sK7(X0,powerset(powerset(cartesian_product2(X1,X2)))),X3)
| relation(unordered_pair(singleton(sK8(sK7(X0,powerset(powerset(cartesian_product2(X1,X2)))),X3)),unordered_pair(sK9(sK7(X0,powerset(powerset(cartesian_product2(X1,X2)))),X3),sK8(sK7(X0,powerset(powerset(cartesian_product2(X1,X2)))),X3)))) )
| ~ spl17_41
| ~ spl17_333 ),
inference(resolution,[],[f3173,f364]) ).
fof(f3173,plain,
( ! [X2,X0,X1] :
( element(unordered_pair(singleton(sK8(sK7(X0,powerset(X1)),X2)),unordered_pair(sK9(sK7(X0,powerset(X1)),X2),sK8(sK7(X0,powerset(X1)),X2))),X1)
| sP0(X0,powerset(X1))
| sP0(sK7(X0,powerset(X1)),X2) )
| ~ spl17_333 ),
inference(avatar_component_clause,[],[f3172]) ).
fof(f10925,plain,
( spl17_822
| ~ spl17_157
| ~ spl17_442 ),
inference(avatar_split_clause,[],[f4334,f4204,f1211,f10923]) ).
fof(f10923,plain,
( spl17_822
<=> ! [X0] :
( relation(sK9(X0,sK10(powerset(powerset(sK16)))))
| sP0(X0,sK10(powerset(powerset(sK16)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_822])]) ).
fof(f1211,plain,
( spl17_157
<=> ! [X0,X1] :
( element(sK9(X0,sK10(powerset(X1))),X1)
| sP0(X0,sK10(powerset(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_157])]) ).
fof(f4204,plain,
( spl17_442
<=> ! [X0] :
( ~ element(X0,powerset(sK16))
| relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_442])]) ).
fof(f4334,plain,
( ! [X0] :
( relation(sK9(X0,sK10(powerset(powerset(sK16)))))
| sP0(X0,sK10(powerset(powerset(sK16)))) )
| ~ spl17_157
| ~ spl17_442 ),
inference(resolution,[],[f4205,f1212]) ).
fof(f1212,plain,
( ! [X0,X1] :
( element(sK9(X0,sK10(powerset(X1))),X1)
| sP0(X0,sK10(powerset(X1))) )
| ~ spl17_157 ),
inference(avatar_component_clause,[],[f1211]) ).
fof(f4205,plain,
( ! [X0] :
( ~ element(X0,powerset(sK16))
| relation(X0) )
| ~ spl17_442 ),
inference(avatar_component_clause,[],[f4204]) ).
fof(f10824,plain,
( spl17_821
| ~ spl17_304
| ~ spl17_345 ),
inference(avatar_split_clause,[],[f3294,f3278,f2657,f10822]) ).
fof(f10822,plain,
( spl17_821
<=> ! [X0,X3,X2,X1] :
( in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),cartesian_product2(the_carrier(X2),the_carrier(X2)))
| ~ in(X1,X3)
| ~ in(X0,X3)
| ~ sP0(cartesian_product2(the_carrier(X2),the_carrier(X2)),X3)
| ~ in(X1,the_carrier(X2))
| ~ rel_str(X2)
| empty(cartesian_product2(the_carrier(X2),the_carrier(X2)))
| ~ in(unordered_pair(singleton(X0),unordered_pair(X1,X0)),the_InternalRel(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_821])]) ).
fof(f3278,plain,
( spl17_345
<=> ! [X4,X0,X3,X2,X1] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X1,X0)),cartesian_product2(X2,X3))
| in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),cartesian_product2(X2,X3))
| ~ in(X1,X4)
| ~ in(X0,X4)
| ~ sP0(cartesian_product2(X2,X3),X4)
| ~ in(X1,X3)
| ~ in(X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_345])]) ).
fof(f3294,plain,
( ! [X2,X3,X0,X1] :
( in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),cartesian_product2(the_carrier(X2),the_carrier(X2)))
| ~ in(X1,X3)
| ~ in(X0,X3)
| ~ sP0(cartesian_product2(the_carrier(X2),the_carrier(X2)),X3)
| ~ in(X1,the_carrier(X2))
| ~ rel_str(X2)
| empty(cartesian_product2(the_carrier(X2),the_carrier(X2)))
| ~ in(unordered_pair(singleton(X0),unordered_pair(X1,X0)),the_InternalRel(X2)) )
| ~ spl17_304
| ~ spl17_345 ),
inference(duplicate_literal_removal,[],[f3285]) ).
fof(f3285,plain,
( ! [X2,X3,X0,X1] :
( in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),cartesian_product2(the_carrier(X2),the_carrier(X2)))
| ~ in(X1,X3)
| ~ in(X0,X3)
| ~ sP0(cartesian_product2(the_carrier(X2),the_carrier(X2)),X3)
| ~ in(X1,the_carrier(X2))
| ~ in(X1,the_carrier(X2))
| ~ rel_str(X2)
| empty(cartesian_product2(the_carrier(X2),the_carrier(X2)))
| ~ in(unordered_pair(singleton(X0),unordered_pair(X1,X0)),the_InternalRel(X2)) )
| ~ spl17_304
| ~ spl17_345 ),
inference(resolution,[],[f3279,f2658]) ).
fof(f3279,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X1,X0)),cartesian_product2(X2,X3))
| in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),cartesian_product2(X2,X3))
| ~ in(X1,X4)
| ~ in(X0,X4)
| ~ sP0(cartesian_product2(X2,X3),X4)
| ~ in(X1,X3)
| ~ in(X1,X2) )
| ~ spl17_345 ),
inference(avatar_component_clause,[],[f3278]) ).
fof(f10820,plain,
( spl17_820
| ~ spl17_171
| ~ spl17_321 ),
inference(avatar_split_clause,[],[f2961,f2873,f1361,f10818]) ).
fof(f10818,plain,
( spl17_820
<=> ! [X2,X0,X1] :
( empty(sK9(X0,powerset(X1)))
| sP0(sK10(powerset(sK9(X0,powerset(X1)))),X2)
| element(unordered_pair(singleton(sK7(sK10(powerset(sK9(X0,powerset(X1)))),X2)),unordered_pair(sK8(sK10(powerset(sK9(X0,powerset(X1)))),X2),sK7(sK10(powerset(sK9(X0,powerset(X1)))),X2))),X1)
| sP0(X0,powerset(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_820])]) ).
fof(f1361,plain,
( spl17_171
<=> ! [X2,X0,X1] :
( sP0(X0,powerset(X1))
| element(X2,X1)
| ~ in(X2,sK9(X0,powerset(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_171])]) ).
fof(f2961,plain,
( ! [X2,X0,X1] :
( empty(sK9(X0,powerset(X1)))
| sP0(sK10(powerset(sK9(X0,powerset(X1)))),X2)
| element(unordered_pair(singleton(sK7(sK10(powerset(sK9(X0,powerset(X1)))),X2)),unordered_pair(sK8(sK10(powerset(sK9(X0,powerset(X1)))),X2),sK7(sK10(powerset(sK9(X0,powerset(X1)))),X2))),X1)
| sP0(X0,powerset(X1)) )
| ~ spl17_171
| ~ spl17_321 ),
inference(resolution,[],[f2874,f1362]) ).
fof(f1362,plain,
( ! [X2,X0,X1] :
( ~ in(X2,sK9(X0,powerset(X1)))
| element(X2,X1)
| sP0(X0,powerset(X1)) )
| ~ spl17_171 ),
inference(avatar_component_clause,[],[f1361]) ).
fof(f10816,plain,
( spl17_819
| ~ spl17_169
| ~ spl17_321 ),
inference(avatar_split_clause,[],[f2955,f2873,f1353,f10814]) ).
fof(f10814,plain,
( spl17_819
<=> ! [X2,X0,X1] :
( empty(sK8(X0,powerset(X1)))
| sP0(sK10(powerset(sK8(X0,powerset(X1)))),X2)
| element(unordered_pair(singleton(sK7(sK10(powerset(sK8(X0,powerset(X1)))),X2)),unordered_pair(sK8(sK10(powerset(sK8(X0,powerset(X1)))),X2),sK7(sK10(powerset(sK8(X0,powerset(X1)))),X2))),X1)
| sP0(X0,powerset(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_819])]) ).
fof(f1353,plain,
( spl17_169
<=> ! [X2,X0,X1] :
( sP0(X0,powerset(X1))
| element(X2,X1)
| ~ in(X2,sK8(X0,powerset(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_169])]) ).
fof(f2955,plain,
( ! [X2,X0,X1] :
( empty(sK8(X0,powerset(X1)))
| sP0(sK10(powerset(sK8(X0,powerset(X1)))),X2)
| element(unordered_pair(singleton(sK7(sK10(powerset(sK8(X0,powerset(X1)))),X2)),unordered_pair(sK8(sK10(powerset(sK8(X0,powerset(X1)))),X2),sK7(sK10(powerset(sK8(X0,powerset(X1)))),X2))),X1)
| sP0(X0,powerset(X1)) )
| ~ spl17_169
| ~ spl17_321 ),
inference(resolution,[],[f2874,f1354]) ).
fof(f1354,plain,
( ! [X2,X0,X1] :
( ~ in(X2,sK8(X0,powerset(X1)))
| element(X2,X1)
| sP0(X0,powerset(X1)) )
| ~ spl17_169 ),
inference(avatar_component_clause,[],[f1353]) ).
fof(f10812,plain,
( spl17_818
| ~ spl17_156
| ~ spl17_442 ),
inference(avatar_split_clause,[],[f4329,f4204,f1207,f10810]) ).
fof(f1207,plain,
( spl17_156
<=> ! [X0,X1] :
( element(sK8(X0,sK10(powerset(X1))),X1)
| sP0(X0,sK10(powerset(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_156])]) ).
fof(f4329,plain,
( ! [X0] :
( relation(sK8(X0,sK10(powerset(powerset(sK16)))))
| sP0(X0,sK10(powerset(powerset(sK16)))) )
| ~ spl17_156
| ~ spl17_442 ),
inference(resolution,[],[f4205,f1208]) ).
fof(f1208,plain,
( ! [X0,X1] :
( element(sK8(X0,sK10(powerset(X1))),X1)
| sP0(X0,sK10(powerset(X1))) )
| ~ spl17_156 ),
inference(avatar_component_clause,[],[f1207]) ).
fof(f10808,plain,
( spl17_817
| ~ spl17_167
| ~ spl17_321 ),
inference(avatar_split_clause,[],[f2949,f2873,f1345,f10806]) ).
fof(f10806,plain,
( spl17_817
<=> ! [X2,X0,X1] :
( empty(sK7(X0,powerset(X1)))
| sP0(sK10(powerset(sK7(X0,powerset(X1)))),X2)
| element(unordered_pair(singleton(sK7(sK10(powerset(sK7(X0,powerset(X1)))),X2)),unordered_pair(sK8(sK10(powerset(sK7(X0,powerset(X1)))),X2),sK7(sK10(powerset(sK7(X0,powerset(X1)))),X2))),X1)
| sP0(X0,powerset(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_817])]) ).
fof(f1345,plain,
( spl17_167
<=> ! [X2,X0,X1] :
( sP0(X0,powerset(X1))
| element(X2,X1)
| ~ in(X2,sK7(X0,powerset(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_167])]) ).
fof(f2949,plain,
( ! [X2,X0,X1] :
( empty(sK7(X0,powerset(X1)))
| sP0(sK10(powerset(sK7(X0,powerset(X1)))),X2)
| element(unordered_pair(singleton(sK7(sK10(powerset(sK7(X0,powerset(X1)))),X2)),unordered_pair(sK8(sK10(powerset(sK7(X0,powerset(X1)))),X2),sK7(sK10(powerset(sK7(X0,powerset(X1)))),X2))),X1)
| sP0(X0,powerset(X1)) )
| ~ spl17_167
| ~ spl17_321 ),
inference(resolution,[],[f2874,f1346]) ).
fof(f1346,plain,
( ! [X2,X0,X1] :
( ~ in(X2,sK7(X0,powerset(X1)))
| element(X2,X1)
| sP0(X0,powerset(X1)) )
| ~ spl17_167 ),
inference(avatar_component_clause,[],[f1345]) ).
fof(f10804,plain,
( spl17_816
| ~ spl17_171
| ~ spl17_320 ),
inference(avatar_split_clause,[],[f2910,f2869,f1361,f10802]) ).
fof(f10802,plain,
( spl17_816
<=> ! [X2,X0,X1] :
( empty(sK9(X0,powerset(X1)))
| sP0(sK10(powerset(sK9(X0,powerset(X1)))),X2)
| element(unordered_pair(singleton(sK8(sK10(powerset(sK9(X0,powerset(X1)))),X2)),unordered_pair(sK9(sK10(powerset(sK9(X0,powerset(X1)))),X2),sK8(sK10(powerset(sK9(X0,powerset(X1)))),X2))),X1)
| sP0(X0,powerset(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_816])]) ).
fof(f2910,plain,
( ! [X2,X0,X1] :
( empty(sK9(X0,powerset(X1)))
| sP0(sK10(powerset(sK9(X0,powerset(X1)))),X2)
| element(unordered_pair(singleton(sK8(sK10(powerset(sK9(X0,powerset(X1)))),X2)),unordered_pair(sK9(sK10(powerset(sK9(X0,powerset(X1)))),X2),sK8(sK10(powerset(sK9(X0,powerset(X1)))),X2))),X1)
| sP0(X0,powerset(X1)) )
| ~ spl17_171
| ~ spl17_320 ),
inference(resolution,[],[f2870,f1362]) ).
fof(f10800,plain,
( spl17_815
| ~ spl17_169
| ~ spl17_320 ),
inference(avatar_split_clause,[],[f2904,f2869,f1353,f10798]) ).
fof(f10798,plain,
( spl17_815
<=> ! [X2,X0,X1] :
( empty(sK8(X0,powerset(X1)))
| sP0(sK10(powerset(sK8(X0,powerset(X1)))),X2)
| element(unordered_pair(singleton(sK8(sK10(powerset(sK8(X0,powerset(X1)))),X2)),unordered_pair(sK9(sK10(powerset(sK8(X0,powerset(X1)))),X2),sK8(sK10(powerset(sK8(X0,powerset(X1)))),X2))),X1)
| sP0(X0,powerset(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_815])]) ).
fof(f2904,plain,
( ! [X2,X0,X1] :
( empty(sK8(X0,powerset(X1)))
| sP0(sK10(powerset(sK8(X0,powerset(X1)))),X2)
| element(unordered_pair(singleton(sK8(sK10(powerset(sK8(X0,powerset(X1)))),X2)),unordered_pair(sK9(sK10(powerset(sK8(X0,powerset(X1)))),X2),sK8(sK10(powerset(sK8(X0,powerset(X1)))),X2))),X1)
| sP0(X0,powerset(X1)) )
| ~ spl17_169
| ~ spl17_320 ),
inference(resolution,[],[f2870,f1354]) ).
fof(f10796,plain,
( spl17_814
| ~ spl17_167
| ~ spl17_320 ),
inference(avatar_split_clause,[],[f2898,f2869,f1345,f10794]) ).
fof(f10794,plain,
( spl17_814
<=> ! [X2,X0,X1] :
( empty(sK7(X0,powerset(X1)))
| sP0(sK10(powerset(sK7(X0,powerset(X1)))),X2)
| element(unordered_pair(singleton(sK8(sK10(powerset(sK7(X0,powerset(X1)))),X2)),unordered_pair(sK9(sK10(powerset(sK7(X0,powerset(X1)))),X2),sK8(sK10(powerset(sK7(X0,powerset(X1)))),X2))),X1)
| sP0(X0,powerset(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_814])]) ).
fof(f2898,plain,
( ! [X2,X0,X1] :
( empty(sK7(X0,powerset(X1)))
| sP0(sK10(powerset(sK7(X0,powerset(X1)))),X2)
| element(unordered_pair(singleton(sK8(sK10(powerset(sK7(X0,powerset(X1)))),X2)),unordered_pair(sK9(sK10(powerset(sK7(X0,powerset(X1)))),X2),sK8(sK10(powerset(sK7(X0,powerset(X1)))),X2))),X1)
| sP0(X0,powerset(X1)) )
| ~ spl17_167
| ~ spl17_320 ),
inference(resolution,[],[f2870,f1346]) ).
fof(f10792,plain,
( spl17_813
| ~ spl17_197
| ~ spl17_312 ),
inference(avatar_split_clause,[],[f2782,f2730,f1581,f10790]) ).
fof(f10790,plain,
( spl17_813
<=> ! [X0,X3,X2,X1] :
( sP0(sK6(X0),X1)
| empty(X0)
| ~ in(unordered_pair(singleton(X2),unordered_pair(sK7(sK6(X0),X1),X2)),X0)
| in(unordered_pair(singleton(X2),unordered_pair(X2,sK8(sK6(X0),X1))),X0)
| ~ in(sK8(sK6(X0),X1),X3)
| ~ in(sK7(sK6(X0),X1),X3)
| ~ in(X2,X3)
| ~ sP0(X0,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_813])]) ).
fof(f2782,plain,
( ! [X2,X3,X0,X1] :
( sP0(sK6(X0),X1)
| empty(X0)
| ~ in(unordered_pair(singleton(X2),unordered_pair(sK7(sK6(X0),X1),X2)),X0)
| in(unordered_pair(singleton(X2),unordered_pair(X2,sK8(sK6(X0),X1))),X0)
| ~ in(sK8(sK6(X0),X1),X3)
| ~ in(sK7(sK6(X0),X1),X3)
| ~ in(X2,X3)
| ~ sP0(X0,X3) )
| ~ spl17_197
| ~ spl17_312 ),
inference(resolution,[],[f2731,f1582]) ).
fof(f10788,plain,
( spl17_812
| ~ spl17_197
| ~ spl17_311 ),
inference(avatar_split_clause,[],[f2733,f2726,f1581,f10786]) ).
fof(f10786,plain,
( spl17_812
<=> ! [X0,X3,X2,X1] :
( sP0(sK6(X0),X1)
| empty(X0)
| ~ in(unordered_pair(singleton(X2),unordered_pair(sK8(sK6(X0),X1),X2)),X0)
| in(unordered_pair(singleton(X2),unordered_pair(X2,sK9(sK6(X0),X1))),X0)
| ~ in(sK9(sK6(X0),X1),X3)
| ~ in(sK8(sK6(X0),X1),X3)
| ~ in(X2,X3)
| ~ sP0(X0,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_812])]) ).
fof(f2733,plain,
( ! [X2,X3,X0,X1] :
( sP0(sK6(X0),X1)
| empty(X0)
| ~ in(unordered_pair(singleton(X2),unordered_pair(sK8(sK6(X0),X1),X2)),X0)
| in(unordered_pair(singleton(X2),unordered_pair(X2,sK9(sK6(X0),X1))),X0)
| ~ in(sK9(sK6(X0),X1),X3)
| ~ in(sK8(sK6(X0),X1),X3)
| ~ in(X2,X3)
| ~ sP0(X0,X3) )
| ~ spl17_197
| ~ spl17_311 ),
inference(resolution,[],[f2727,f1582]) ).
fof(f10784,plain,
( spl17_811
| ~ spl17_198
| ~ spl17_304 ),
inference(avatar_split_clause,[],[f2690,f2657,f1597,f10782]) ).
fof(f10782,plain,
( spl17_811
<=> ! [X0,X3,X2,X1] :
( ~ rel_str(X0)
| empty(cartesian_product2(the_carrier(X0),the_carrier(X0)))
| ~ in(unordered_pair(singleton(X1),unordered_pair(X2,X1)),the_InternalRel(X0))
| in(unordered_pair(singleton(X1),unordered_pair(X1,X2)),cartesian_product2(the_carrier(X0),the_carrier(X0)))
| ~ in(X2,X3)
| ~ in(X1,X3)
| ~ sP0(cartesian_product2(the_carrier(X0),the_carrier(X0)),X3)
| ~ in(X1,the_carrier(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_811])]) ).
fof(f1597,plain,
( spl17_198
<=> ! [X4,X0,X3,X2,X1] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X1,X0)),cartesian_product2(X2,X3))
| in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),cartesian_product2(X2,X3))
| ~ in(X1,X4)
| ~ in(X0,X4)
| ~ sP0(cartesian_product2(X2,X3),X4)
| ~ in(X0,X3)
| ~ in(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_198])]) ).
fof(f2690,plain,
( ! [X2,X3,X0,X1] :
( ~ rel_str(X0)
| empty(cartesian_product2(the_carrier(X0),the_carrier(X0)))
| ~ in(unordered_pair(singleton(X1),unordered_pair(X2,X1)),the_InternalRel(X0))
| in(unordered_pair(singleton(X1),unordered_pair(X1,X2)),cartesian_product2(the_carrier(X0),the_carrier(X0)))
| ~ in(X2,X3)
| ~ in(X1,X3)
| ~ sP0(cartesian_product2(the_carrier(X0),the_carrier(X0)),X3)
| ~ in(X1,the_carrier(X0)) )
| ~ spl17_198
| ~ spl17_304 ),
inference(duplicate_literal_removal,[],[f2683]) ).
fof(f2683,plain,
( ! [X2,X3,X0,X1] :
( ~ rel_str(X0)
| empty(cartesian_product2(the_carrier(X0),the_carrier(X0)))
| ~ in(unordered_pair(singleton(X1),unordered_pair(X2,X1)),the_InternalRel(X0))
| in(unordered_pair(singleton(X1),unordered_pair(X1,X2)),cartesian_product2(the_carrier(X0),the_carrier(X0)))
| ~ in(X2,X3)
| ~ in(X1,X3)
| ~ sP0(cartesian_product2(the_carrier(X0),the_carrier(X0)),X3)
| ~ in(X1,the_carrier(X0))
| ~ in(X1,the_carrier(X0)) )
| ~ spl17_198
| ~ spl17_304 ),
inference(resolution,[],[f2658,f1598]) ).
fof(f1598,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X1,X0)),cartesian_product2(X2,X3))
| in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),cartesian_product2(X2,X3))
| ~ in(X1,X4)
| ~ in(X0,X4)
| ~ sP0(cartesian_product2(X2,X3),X4)
| ~ in(X0,X3)
| ~ in(X0,X2) )
| ~ spl17_198 ),
inference(avatar_component_clause,[],[f1597]) ).
fof(f10770,plain,
( spl17_810
| ~ spl17_271
| ~ spl17_312 ),
inference(avatar_split_clause,[],[f2820,f2730,f2289,f10768]) ).
fof(f10768,plain,
( spl17_810
<=> ! [X0,X1] :
( sP0(sK6(sK10(sK6(powerset(X0)))),X1)
| empty(sK10(sK6(powerset(X0))))
| empty(sK6(powerset(X0)))
| element(unordered_pair(singleton(sK7(sK6(sK10(sK6(powerset(X0)))),X1)),unordered_pair(sK8(sK6(sK10(sK6(powerset(X0)))),X1),sK7(sK6(sK10(sK6(powerset(X0)))),X1))),X0)
| empty(powerset(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_810])]) ).
fof(f2820,plain,
( ! [X0,X1] :
( sP0(sK6(sK10(sK6(powerset(X0)))),X1)
| empty(sK10(sK6(powerset(X0))))
| empty(sK6(powerset(X0)))
| element(unordered_pair(singleton(sK7(sK6(sK10(sK6(powerset(X0)))),X1)),unordered_pair(sK8(sK6(sK10(sK6(powerset(X0)))),X1),sK7(sK6(sK10(sK6(powerset(X0)))),X1))),X0)
| empty(powerset(X0)) )
| ~ spl17_271
| ~ spl17_312 ),
inference(resolution,[],[f2731,f2290]) ).
fof(f10766,plain,
( spl17_809
| ~ spl17_155
| ~ spl17_442 ),
inference(avatar_split_clause,[],[f4324,f4204,f1203,f10764]) ).
fof(f1203,plain,
( spl17_155
<=> ! [X0,X1] :
( element(sK7(X0,sK10(powerset(X1))),X1)
| sP0(X0,sK10(powerset(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_155])]) ).
fof(f4324,plain,
( ! [X0] :
( relation(sK7(X0,sK10(powerset(powerset(sK16)))))
| sP0(X0,sK10(powerset(powerset(sK16)))) )
| ~ spl17_155
| ~ spl17_442 ),
inference(resolution,[],[f4205,f1204]) ).
fof(f1204,plain,
( ! [X0,X1] :
( element(sK7(X0,sK10(powerset(X1))),X1)
| sP0(X0,sK10(powerset(X1))) )
| ~ spl17_155 ),
inference(avatar_component_clause,[],[f1203]) ).
fof(f10762,plain,
( spl17_808
| ~ spl17_271
| ~ spl17_311 ),
inference(avatar_split_clause,[],[f2771,f2726,f2289,f10760]) ).
fof(f10760,plain,
( spl17_808
<=> ! [X0,X1] :
( sP0(sK6(sK10(sK6(powerset(X0)))),X1)
| empty(sK10(sK6(powerset(X0))))
| empty(sK6(powerset(X0)))
| element(unordered_pair(singleton(sK8(sK6(sK10(sK6(powerset(X0)))),X1)),unordered_pair(sK9(sK6(sK10(sK6(powerset(X0)))),X1),sK8(sK6(sK10(sK6(powerset(X0)))),X1))),X0)
| empty(powerset(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_808])]) ).
fof(f2771,plain,
( ! [X0,X1] :
( sP0(sK6(sK10(sK6(powerset(X0)))),X1)
| empty(sK10(sK6(powerset(X0))))
| empty(sK6(powerset(X0)))
| element(unordered_pair(singleton(sK8(sK6(sK10(sK6(powerset(X0)))),X1)),unordered_pair(sK9(sK6(sK10(sK6(powerset(X0)))),X1),sK8(sK6(sK10(sK6(powerset(X0)))),X1))),X0)
| empty(powerset(X0)) )
| ~ spl17_271
| ~ spl17_311 ),
inference(resolution,[],[f2727,f2290]) ).
fof(f10688,plain,
( spl17_807
| ~ spl17_60
| ~ spl17_341 ),
inference(avatar_split_clause,[],[f3251,f3243,f504,f10686]) ).
fof(f10686,plain,
( spl17_807
<=> ! [X0,X3,X2,X1] :
( ~ in(unordered_pair(singleton(sK8(X0,X1)),unordered_pair(sK8(X0,X1),X2)),X0)
| in(unordered_pair(singleton(sK7(X0,X1)),unordered_pair(sK7(X0,X1),X2)),X0)
| ~ in(X2,X3)
| ~ in(sK8(X0,X1),X3)
| ~ in(sK7(X0,X1),X3)
| ~ sP0(X0,X3)
| sP0(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_807])]) ).
fof(f3251,plain,
( ! [X2,X3,X0,X1] :
( ~ in(unordered_pair(singleton(sK8(X0,X1)),unordered_pair(sK8(X0,X1),X2)),X0)
| in(unordered_pair(singleton(sK7(X0,X1)),unordered_pair(sK7(X0,X1),X2)),X0)
| ~ in(X2,X3)
| ~ in(sK8(X0,X1),X3)
| ~ in(sK7(X0,X1),X3)
| ~ sP0(X0,X3)
| sP0(X0,X1) )
| ~ spl17_60
| ~ spl17_341 ),
inference(resolution,[],[f3244,f505]) ).
fof(f10684,plain,
( spl17_806
| ~ spl17_59
| ~ spl17_341 ),
inference(avatar_split_clause,[],[f3248,f3243,f500,f10682]) ).
fof(f10682,plain,
( spl17_806
<=> ! [X0,X3,X2,X1] :
( ~ in(unordered_pair(singleton(sK9(X0,X1)),unordered_pair(sK9(X0,X1),X2)),X0)
| in(unordered_pair(singleton(sK8(X0,X1)),unordered_pair(sK8(X0,X1),X2)),X0)
| ~ in(X2,X3)
| ~ in(sK9(X0,X1),X3)
| ~ in(sK8(X0,X1),X3)
| ~ sP0(X0,X3)
| sP0(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_806])]) ).
fof(f3248,plain,
( ! [X2,X3,X0,X1] :
( ~ in(unordered_pair(singleton(sK9(X0,X1)),unordered_pair(sK9(X0,X1),X2)),X0)
| in(unordered_pair(singleton(sK8(X0,X1)),unordered_pair(sK8(X0,X1),X2)),X0)
| ~ in(X2,X3)
| ~ in(sK9(X0,X1),X3)
| ~ in(sK8(X0,X1),X3)
| ~ sP0(X0,X3)
| sP0(X0,X1) )
| ~ spl17_59
| ~ spl17_341 ),
inference(resolution,[],[f3244,f501]) ).
fof(f10680,plain,
( spl17_805
| ~ spl17_118
| ~ spl17_321 ),
inference(avatar_split_clause,[],[f2942,f2873,f956,f10678]) ).
fof(f10678,plain,
( spl17_805
<=> ! [X0,X1] :
( empty(the_InternalRel(X0))
| sP0(sK10(powerset(the_InternalRel(X0))),X1)
| related(X0,sK7(sK10(powerset(the_InternalRel(X0))),X1),sK8(sK10(powerset(the_InternalRel(X0))),X1))
| ~ element(sK8(sK10(powerset(the_InternalRel(X0))),X1),the_carrier(X0))
| ~ element(sK7(sK10(powerset(the_InternalRel(X0))),X1),the_carrier(X0))
| ~ rel_str(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_805])]) ).
fof(f2942,plain,
( ! [X0,X1] :
( empty(the_InternalRel(X0))
| sP0(sK10(powerset(the_InternalRel(X0))),X1)
| related(X0,sK7(sK10(powerset(the_InternalRel(X0))),X1),sK8(sK10(powerset(the_InternalRel(X0))),X1))
| ~ element(sK8(sK10(powerset(the_InternalRel(X0))),X1),the_carrier(X0))
| ~ element(sK7(sK10(powerset(the_InternalRel(X0))),X1),the_carrier(X0))
| ~ rel_str(X0) )
| ~ spl17_118
| ~ spl17_321 ),
inference(resolution,[],[f2874,f957]) ).
fof(f10676,plain,
( spl17_804
| ~ spl17_118
| ~ spl17_320 ),
inference(avatar_split_clause,[],[f2891,f2869,f956,f10674]) ).
fof(f10674,plain,
( spl17_804
<=> ! [X0,X1] :
( empty(the_InternalRel(X0))
| sP0(sK10(powerset(the_InternalRel(X0))),X1)
| related(X0,sK8(sK10(powerset(the_InternalRel(X0))),X1),sK9(sK10(powerset(the_InternalRel(X0))),X1))
| ~ element(sK9(sK10(powerset(the_InternalRel(X0))),X1),the_carrier(X0))
| ~ element(sK8(sK10(powerset(the_InternalRel(X0))),X1),the_carrier(X0))
| ~ rel_str(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_804])]) ).
fof(f2891,plain,
( ! [X0,X1] :
( empty(the_InternalRel(X0))
| sP0(sK10(powerset(the_InternalRel(X0))),X1)
| related(X0,sK8(sK10(powerset(the_InternalRel(X0))),X1),sK9(sK10(powerset(the_InternalRel(X0))),X1))
| ~ element(sK9(sK10(powerset(the_InternalRel(X0))),X1),the_carrier(X0))
| ~ element(sK8(sK10(powerset(the_InternalRel(X0))),X1),the_carrier(X0))
| ~ rel_str(X0) )
| ~ spl17_118
| ~ spl17_320 ),
inference(resolution,[],[f2870,f957]) ).
fof(f10672,plain,
( spl17_803
| ~ spl17_60
| ~ spl17_284 ),
inference(avatar_split_clause,[],[f2458,f2409,f504,f10670]) ).
fof(f10670,plain,
( spl17_803
<=> ! [X2,X0,X1] :
( element(unordered_pair(singleton(sK7(sK9(X0,sK10(powerset(powerset(X1)))),X2)),unordered_pair(sK8(sK9(X0,sK10(powerset(powerset(X1)))),X2),sK7(sK9(X0,sK10(powerset(powerset(X1)))),X2))),X1)
| sP0(X0,sK10(powerset(powerset(X1))))
| sP0(sK9(X0,sK10(powerset(powerset(X1)))),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_803])]) ).
fof(f2458,plain,
( ! [X2,X0,X1] :
( element(unordered_pair(singleton(sK7(sK9(X0,sK10(powerset(powerset(X1)))),X2)),unordered_pair(sK8(sK9(X0,sK10(powerset(powerset(X1)))),X2),sK7(sK9(X0,sK10(powerset(powerset(X1)))),X2))),X1)
| sP0(X0,sK10(powerset(powerset(X1))))
| sP0(sK9(X0,sK10(powerset(powerset(X1)))),X2) )
| ~ spl17_60
| ~ spl17_284 ),
inference(resolution,[],[f2410,f505]) ).
fof(f10668,plain,
( spl17_802
| ~ spl17_59
| ~ spl17_284 ),
inference(avatar_split_clause,[],[f2457,f2409,f500,f10666]) ).
fof(f10666,plain,
( spl17_802
<=> ! [X2,X0,X1] :
( element(unordered_pair(singleton(sK8(sK9(X0,sK10(powerset(powerset(X1)))),X2)),unordered_pair(sK9(sK9(X0,sK10(powerset(powerset(X1)))),X2),sK8(sK9(X0,sK10(powerset(powerset(X1)))),X2))),X1)
| sP0(X0,sK10(powerset(powerset(X1))))
| sP0(sK9(X0,sK10(powerset(powerset(X1)))),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_802])]) ).
fof(f2457,plain,
( ! [X2,X0,X1] :
( element(unordered_pair(singleton(sK8(sK9(X0,sK10(powerset(powerset(X1)))),X2)),unordered_pair(sK9(sK9(X0,sK10(powerset(powerset(X1)))),X2),sK8(sK9(X0,sK10(powerset(powerset(X1)))),X2))),X1)
| sP0(X0,sK10(powerset(powerset(X1))))
| sP0(sK9(X0,sK10(powerset(powerset(X1)))),X2) )
| ~ spl17_59
| ~ spl17_284 ),
inference(resolution,[],[f2410,f501]) ).
fof(f10664,plain,
( spl17_801
| ~ spl17_60
| ~ spl17_282 ),
inference(avatar_split_clause,[],[f2443,f2401,f504,f10662]) ).
fof(f10662,plain,
( spl17_801
<=> ! [X2,X0,X1] :
( element(unordered_pair(singleton(sK7(sK8(X0,sK10(powerset(powerset(X1)))),X2)),unordered_pair(sK8(sK8(X0,sK10(powerset(powerset(X1)))),X2),sK7(sK8(X0,sK10(powerset(powerset(X1)))),X2))),X1)
| sP0(X0,sK10(powerset(powerset(X1))))
| sP0(sK8(X0,sK10(powerset(powerset(X1)))),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_801])]) ).
fof(f2443,plain,
( ! [X2,X0,X1] :
( element(unordered_pair(singleton(sK7(sK8(X0,sK10(powerset(powerset(X1)))),X2)),unordered_pair(sK8(sK8(X0,sK10(powerset(powerset(X1)))),X2),sK7(sK8(X0,sK10(powerset(powerset(X1)))),X2))),X1)
| sP0(X0,sK10(powerset(powerset(X1))))
| sP0(sK8(X0,sK10(powerset(powerset(X1)))),X2) )
| ~ spl17_60
| ~ spl17_282 ),
inference(resolution,[],[f2402,f505]) ).
fof(f10660,plain,
( spl17_800
| ~ spl17_59
| ~ spl17_282 ),
inference(avatar_split_clause,[],[f2442,f2401,f500,f10658]) ).
fof(f10658,plain,
( spl17_800
<=> ! [X2,X0,X1] :
( element(unordered_pair(singleton(sK8(sK8(X0,sK10(powerset(powerset(X1)))),X2)),unordered_pair(sK9(sK8(X0,sK10(powerset(powerset(X1)))),X2),sK8(sK8(X0,sK10(powerset(powerset(X1)))),X2))),X1)
| sP0(X0,sK10(powerset(powerset(X1))))
| sP0(sK8(X0,sK10(powerset(powerset(X1)))),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_800])]) ).
fof(f2442,plain,
( ! [X2,X0,X1] :
( element(unordered_pair(singleton(sK8(sK8(X0,sK10(powerset(powerset(X1)))),X2)),unordered_pair(sK9(sK8(X0,sK10(powerset(powerset(X1)))),X2),sK8(sK8(X0,sK10(powerset(powerset(X1)))),X2))),X1)
| sP0(X0,sK10(powerset(powerset(X1))))
| sP0(sK8(X0,sK10(powerset(powerset(X1)))),X2) )
| ~ spl17_59
| ~ spl17_282 ),
inference(resolution,[],[f2402,f501]) ).
fof(f10656,plain,
( spl17_799
| ~ spl17_60
| ~ spl17_280 ),
inference(avatar_split_clause,[],[f2428,f2393,f504,f10654]) ).
fof(f10654,plain,
( spl17_799
<=> ! [X2,X0,X1] :
( element(unordered_pair(singleton(sK7(sK7(X0,sK10(powerset(powerset(X1)))),X2)),unordered_pair(sK8(sK7(X0,sK10(powerset(powerset(X1)))),X2),sK7(sK7(X0,sK10(powerset(powerset(X1)))),X2))),X1)
| sP0(X0,sK10(powerset(powerset(X1))))
| sP0(sK7(X0,sK10(powerset(powerset(X1)))),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_799])]) ).
fof(f2428,plain,
( ! [X2,X0,X1] :
( element(unordered_pair(singleton(sK7(sK7(X0,sK10(powerset(powerset(X1)))),X2)),unordered_pair(sK8(sK7(X0,sK10(powerset(powerset(X1)))),X2),sK7(sK7(X0,sK10(powerset(powerset(X1)))),X2))),X1)
| sP0(X0,sK10(powerset(powerset(X1))))
| sP0(sK7(X0,sK10(powerset(powerset(X1)))),X2) )
| ~ spl17_60
| ~ spl17_280 ),
inference(resolution,[],[f2394,f505]) ).
fof(f10652,plain,
( spl17_797
| ~ spl17_798
| ~ spl17_16
| ~ spl17_790 ),
inference(avatar_split_clause,[],[f10180,f10132,f251,f10649,f10645]) ).
fof(f10645,plain,
( spl17_797
<=> empty(powerset(cartesian_product2(sK16,sK16))) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_797])]) ).
fof(f10649,plain,
( spl17_798
<=> in(powerset(cartesian_product2(sK16,sK16)),the_InternalRel(sK2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_798])]) ).
fof(f10132,plain,
( spl17_790
<=> ! [X0] :
( ~ in(powerset(X0),the_InternalRel(sK2))
| ~ subset(cartesian_product2(sK16,sK16),X0)
| empty(powerset(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_790])]) ).
fof(f10180,plain,
( ~ in(powerset(cartesian_product2(sK16,sK16)),the_InternalRel(sK2))
| empty(powerset(cartesian_product2(sK16,sK16)))
| ~ spl17_16
| ~ spl17_790 ),
inference(resolution,[],[f10133,f252]) ).
fof(f10133,plain,
( ! [X0] :
( ~ subset(cartesian_product2(sK16,sK16),X0)
| ~ in(powerset(X0),the_InternalRel(sK2))
| empty(powerset(X0)) )
| ~ spl17_790 ),
inference(avatar_component_clause,[],[f10132]) ).
fof(f10643,plain,
( spl17_796
| ~ spl17_59
| ~ spl17_280 ),
inference(avatar_split_clause,[],[f2427,f2393,f500,f10641]) ).
fof(f10641,plain,
( spl17_796
<=> ! [X2,X0,X1] :
( element(unordered_pair(singleton(sK8(sK7(X0,sK10(powerset(powerset(X1)))),X2)),unordered_pair(sK9(sK7(X0,sK10(powerset(powerset(X1)))),X2),sK8(sK7(X0,sK10(powerset(powerset(X1)))),X2))),X1)
| sP0(X0,sK10(powerset(powerset(X1))))
| sP0(sK7(X0,sK10(powerset(powerset(X1)))),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_796])]) ).
fof(f2427,plain,
( ! [X2,X0,X1] :
( element(unordered_pair(singleton(sK8(sK7(X0,sK10(powerset(powerset(X1)))),X2)),unordered_pair(sK9(sK7(X0,sK10(powerset(powerset(X1)))),X2),sK8(sK7(X0,sK10(powerset(powerset(X1)))),X2))),X1)
| sP0(X0,sK10(powerset(powerset(X1))))
| sP0(sK7(X0,sK10(powerset(powerset(X1)))),X2) )
| ~ spl17_59
| ~ spl17_280 ),
inference(resolution,[],[f2394,f501]) ).
fof(f10154,plain,
( spl17_795
| ~ spl17_30
| ~ spl17_363 ),
inference(avatar_split_clause,[],[f3478,f3459,f313,f10152]) ).
fof(f10152,plain,
( spl17_795
<=> ! [X4,X0,X3,X2,X1] :
( ~ in(unordered_pair(singleton(X1),unordered_pair(X1,X0)),powerset(X2))
| in(unordered_pair(singleton(X1),unordered_pair(X1,X3)),powerset(X2))
| ~ in(X3,X4)
| ~ in(X0,X4)
| ~ in(X1,X4)
| ~ sP0(powerset(X2),X4)
| empty(powerset(X2))
| ~ subset(unordered_pair(singleton(X0),unordered_pair(X3,X0)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_795])]) ).
fof(f3478,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ in(unordered_pair(singleton(X1),unordered_pair(X1,X0)),powerset(X2))
| in(unordered_pair(singleton(X1),unordered_pair(X1,X3)),powerset(X2))
| ~ in(X3,X4)
| ~ in(X0,X4)
| ~ in(X1,X4)
| ~ sP0(powerset(X2),X4)
| empty(powerset(X2))
| ~ subset(unordered_pair(singleton(X0),unordered_pair(X3,X0)),X2) )
| ~ spl17_30
| ~ spl17_363 ),
inference(superposition,[],[f3460,f314]) ).
fof(f10150,plain,
( spl17_794
| ~ spl17_39
| ~ spl17_358 ),
inference(avatar_split_clause,[],[f3430,f3403,f355,f10148]) ).
fof(f10148,plain,
( spl17_794
<=> ! [X2,X0,X1] :
( sP0(powerset(X0),X1)
| sP0(X2,unordered_pair(singleton(sK7(powerset(X0),X1)),unordered_pair(sK8(powerset(X0),X1),sK7(powerset(X0),X1))))
| empty(X0)
| in(sK9(X2,unordered_pair(singleton(sK7(powerset(X0),X1)),unordered_pair(sK8(powerset(X0),X1),sK7(powerset(X0),X1)))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_794])]) ).
fof(f3430,plain,
( ! [X2,X0,X1] :
( sP0(powerset(X0),X1)
| sP0(X2,unordered_pair(singleton(sK7(powerset(X0),X1)),unordered_pair(sK8(powerset(X0),X1),sK7(powerset(X0),X1))))
| empty(X0)
| in(sK9(X2,unordered_pair(singleton(sK7(powerset(X0),X1)),unordered_pair(sK8(powerset(X0),X1),sK7(powerset(X0),X1)))),X0) )
| ~ spl17_39
| ~ spl17_358 ),
inference(resolution,[],[f3404,f356]) ).
fof(f10146,plain,
( spl17_793
| ~ spl17_39
| ~ spl17_356 ),
inference(avatar_split_clause,[],[f3426,f3395,f355,f10144]) ).
fof(f10144,plain,
( spl17_793
<=> ! [X2,X0,X1] :
( sP0(powerset(X0),X1)
| sP0(X2,unordered_pair(singleton(sK7(powerset(X0),X1)),unordered_pair(sK8(powerset(X0),X1),sK7(powerset(X0),X1))))
| empty(X0)
| in(sK8(X2,unordered_pair(singleton(sK7(powerset(X0),X1)),unordered_pair(sK8(powerset(X0),X1),sK7(powerset(X0),X1)))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_793])]) ).
fof(f3426,plain,
( ! [X2,X0,X1] :
( sP0(powerset(X0),X1)
| sP0(X2,unordered_pair(singleton(sK7(powerset(X0),X1)),unordered_pair(sK8(powerset(X0),X1),sK7(powerset(X0),X1))))
| empty(X0)
| in(sK8(X2,unordered_pair(singleton(sK7(powerset(X0),X1)),unordered_pair(sK8(powerset(X0),X1),sK7(powerset(X0),X1)))),X0) )
| ~ spl17_39
| ~ spl17_356 ),
inference(resolution,[],[f3396,f356]) ).
fof(f10142,plain,
( spl17_792
| ~ spl17_39
| ~ spl17_355 ),
inference(avatar_split_clause,[],[f3422,f3391,f355,f10140]) ).
fof(f10140,plain,
( spl17_792
<=> ! [X2,X0,X1] :
( sP0(powerset(X0),X1)
| sP0(X2,unordered_pair(singleton(sK7(powerset(X0),X1)),unordered_pair(sK8(powerset(X0),X1),sK7(powerset(X0),X1))))
| empty(X0)
| in(sK7(X2,unordered_pair(singleton(sK7(powerset(X0),X1)),unordered_pair(sK8(powerset(X0),X1),sK7(powerset(X0),X1)))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_792])]) ).
fof(f3422,plain,
( ! [X2,X0,X1] :
( sP0(powerset(X0),X1)
| sP0(X2,unordered_pair(singleton(sK7(powerset(X0),X1)),unordered_pair(sK8(powerset(X0),X1),sK7(powerset(X0),X1))))
| empty(X0)
| in(sK7(X2,unordered_pair(singleton(sK7(powerset(X0),X1)),unordered_pair(sK8(powerset(X0),X1),sK7(powerset(X0),X1)))),X0) )
| ~ spl17_39
| ~ spl17_355 ),
inference(resolution,[],[f3392,f356]) ).
fof(f10138,plain,
( spl17_791
| ~ spl17_39
| ~ spl17_354 ),
inference(avatar_split_clause,[],[f3418,f3387,f355,f10136]) ).
fof(f10136,plain,
( spl17_791
<=> ! [X2,X0,X1] :
( sP0(powerset(X0),X1)
| sP0(X2,unordered_pair(singleton(sK8(powerset(X0),X1)),unordered_pair(sK9(powerset(X0),X1),sK8(powerset(X0),X1))))
| empty(X0)
| in(sK9(X2,unordered_pair(singleton(sK8(powerset(X0),X1)),unordered_pair(sK9(powerset(X0),X1),sK8(powerset(X0),X1)))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_791])]) ).
fof(f3418,plain,
( ! [X2,X0,X1] :
( sP0(powerset(X0),X1)
| sP0(X2,unordered_pair(singleton(sK8(powerset(X0),X1)),unordered_pair(sK9(powerset(X0),X1),sK8(powerset(X0),X1))))
| empty(X0)
| in(sK9(X2,unordered_pair(singleton(sK8(powerset(X0),X1)),unordered_pair(sK9(powerset(X0),X1),sK8(powerset(X0),X1)))),X0) )
| ~ spl17_39
| ~ spl17_354 ),
inference(resolution,[],[f3388,f356]) ).
fof(f10134,plain,
( spl17_790
| ~ spl17_149
| ~ spl17_404 ),
inference(avatar_split_clause,[],[f5169,f3828,f1155,f10132]) ).
fof(f1155,plain,
( spl17_149
<=> ! [X0,X1] :
( empty(powerset(X0))
| ~ subset(X1,X0)
| ~ in(powerset(X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_149])]) ).
fof(f3828,plain,
( spl17_404
<=> ! [X0] :
( ~ in(X0,the_InternalRel(sK2))
| in(X0,cartesian_product2(sK16,sK16)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_404])]) ).
fof(f5169,plain,
( ! [X0] :
( ~ in(powerset(X0),the_InternalRel(sK2))
| ~ subset(cartesian_product2(sK16,sK16),X0)
| empty(powerset(X0)) )
| ~ spl17_149
| ~ spl17_404 ),
inference(resolution,[],[f3829,f1156]) ).
fof(f1156,plain,
( ! [X0,X1] :
( ~ in(powerset(X0),X1)
| ~ subset(X1,X0)
| empty(powerset(X0)) )
| ~ spl17_149 ),
inference(avatar_component_clause,[],[f1155]) ).
fof(f3829,plain,
( ! [X0] :
( in(X0,cartesian_product2(sK16,sK16))
| ~ in(X0,the_InternalRel(sK2)) )
| ~ spl17_404 ),
inference(avatar_component_clause,[],[f3828]) ).
fof(f10130,plain,
( spl17_789
| ~ spl17_39
| ~ spl17_353 ),
inference(avatar_split_clause,[],[f3414,f3383,f355,f10128]) ).
fof(f10128,plain,
( spl17_789
<=> ! [X2,X0,X1] :
( sP0(powerset(X0),X1)
| sP0(X2,unordered_pair(singleton(sK8(powerset(X0),X1)),unordered_pair(sK9(powerset(X0),X1),sK8(powerset(X0),X1))))
| empty(X0)
| in(sK8(X2,unordered_pair(singleton(sK8(powerset(X0),X1)),unordered_pair(sK9(powerset(X0),X1),sK8(powerset(X0),X1)))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_789])]) ).
fof(f3414,plain,
( ! [X2,X0,X1] :
( sP0(powerset(X0),X1)
| sP0(X2,unordered_pair(singleton(sK8(powerset(X0),X1)),unordered_pair(sK9(powerset(X0),X1),sK8(powerset(X0),X1))))
| empty(X0)
| in(sK8(X2,unordered_pair(singleton(sK8(powerset(X0),X1)),unordered_pair(sK9(powerset(X0),X1),sK8(powerset(X0),X1)))),X0) )
| ~ spl17_39
| ~ spl17_353 ),
inference(resolution,[],[f3384,f356]) ).
fof(f10126,plain,
( spl17_788
| ~ spl17_39
| ~ spl17_352 ),
inference(avatar_split_clause,[],[f3410,f3379,f355,f10124]) ).
fof(f10124,plain,
( spl17_788
<=> ! [X2,X0,X1] :
( sP0(powerset(X0),X1)
| sP0(X2,unordered_pair(singleton(sK8(powerset(X0),X1)),unordered_pair(sK9(powerset(X0),X1),sK8(powerset(X0),X1))))
| empty(X0)
| in(sK7(X2,unordered_pair(singleton(sK8(powerset(X0),X1)),unordered_pair(sK9(powerset(X0),X1),sK8(powerset(X0),X1)))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_788])]) ).
fof(f3410,plain,
( ! [X2,X0,X1] :
( sP0(powerset(X0),X1)
| sP0(X2,unordered_pair(singleton(sK8(powerset(X0),X1)),unordered_pair(sK9(powerset(X0),X1),sK8(powerset(X0),X1))))
| empty(X0)
| in(sK7(X2,unordered_pair(singleton(sK8(powerset(X0),X1)),unordered_pair(sK9(powerset(X0),X1),sK8(powerset(X0),X1)))),X0) )
| ~ spl17_39
| ~ spl17_352 ),
inference(resolution,[],[f3380,f356]) ).
fof(f10122,plain,
( spl17_787
| ~ spl17_98
| ~ spl17_341 ),
inference(avatar_split_clause,[],[f3257,f3243,f788,f10120]) ).
fof(f10120,plain,
( spl17_787
<=> ! [X4,X0,X3,X2,X1] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),powerset(X2))
| in(unordered_pair(singleton(X3),unordered_pair(X3,X1)),powerset(X2))
| ~ in(X1,X4)
| ~ in(X0,X4)
| ~ in(X3,X4)
| ~ sP0(powerset(X2),X4)
| empty(powerset(X2))
| ~ subset(unordered_pair(singleton(X3),unordered_pair(X0,X3)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_787])]) ).
fof(f3257,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),powerset(X2))
| in(unordered_pair(singleton(X3),unordered_pair(X3,X1)),powerset(X2))
| ~ in(X1,X4)
| ~ in(X0,X4)
| ~ in(X3,X4)
| ~ sP0(powerset(X2),X4)
| empty(powerset(X2))
| ~ subset(unordered_pair(singleton(X3),unordered_pair(X0,X3)),X2) )
| ~ spl17_98
| ~ spl17_341 ),
inference(resolution,[],[f3244,f789]) ).
fof(f10118,plain,
( spl17_786
| ~ spl17_171
| ~ spl17_312 ),
inference(avatar_split_clause,[],[f2812,f2730,f1361,f10116]) ).
fof(f10116,plain,
( spl17_786
<=> ! [X2,X0,X1] :
( sP0(sK6(sK9(X0,powerset(X1))),X2)
| empty(sK9(X0,powerset(X1)))
| element(unordered_pair(singleton(sK7(sK6(sK9(X0,powerset(X1))),X2)),unordered_pair(sK8(sK6(sK9(X0,powerset(X1))),X2),sK7(sK6(sK9(X0,powerset(X1))),X2))),X1)
| sP0(X0,powerset(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_786])]) ).
fof(f2812,plain,
( ! [X2,X0,X1] :
( sP0(sK6(sK9(X0,powerset(X1))),X2)
| empty(sK9(X0,powerset(X1)))
| element(unordered_pair(singleton(sK7(sK6(sK9(X0,powerset(X1))),X2)),unordered_pair(sK8(sK6(sK9(X0,powerset(X1))),X2),sK7(sK6(sK9(X0,powerset(X1))),X2))),X1)
| sP0(X0,powerset(X1)) )
| ~ spl17_171
| ~ spl17_312 ),
inference(resolution,[],[f2731,f1362]) ).
fof(f10114,plain,
( spl17_785
| ~ spl17_169
| ~ spl17_312 ),
inference(avatar_split_clause,[],[f2806,f2730,f1353,f10112]) ).
fof(f10112,plain,
( spl17_785
<=> ! [X2,X0,X1] :
( sP0(sK6(sK8(X0,powerset(X1))),X2)
| empty(sK8(X0,powerset(X1)))
| element(unordered_pair(singleton(sK7(sK6(sK8(X0,powerset(X1))),X2)),unordered_pair(sK8(sK6(sK8(X0,powerset(X1))),X2),sK7(sK6(sK8(X0,powerset(X1))),X2))),X1)
| sP0(X0,powerset(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_785])]) ).
fof(f2806,plain,
( ! [X2,X0,X1] :
( sP0(sK6(sK8(X0,powerset(X1))),X2)
| empty(sK8(X0,powerset(X1)))
| element(unordered_pair(singleton(sK7(sK6(sK8(X0,powerset(X1))),X2)),unordered_pair(sK8(sK6(sK8(X0,powerset(X1))),X2),sK7(sK6(sK8(X0,powerset(X1))),X2))),X1)
| sP0(X0,powerset(X1)) )
| ~ spl17_169
| ~ spl17_312 ),
inference(resolution,[],[f2731,f1354]) ).
fof(f10110,plain,
( spl17_784
| ~ spl17_167
| ~ spl17_312 ),
inference(avatar_split_clause,[],[f2800,f2730,f1345,f10108]) ).
fof(f10108,plain,
( spl17_784
<=> ! [X2,X0,X1] :
( sP0(sK6(sK7(X0,powerset(X1))),X2)
| empty(sK7(X0,powerset(X1)))
| element(unordered_pair(singleton(sK7(sK6(sK7(X0,powerset(X1))),X2)),unordered_pair(sK8(sK6(sK7(X0,powerset(X1))),X2),sK7(sK6(sK7(X0,powerset(X1))),X2))),X1)
| sP0(X0,powerset(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_784])]) ).
fof(f2800,plain,
( ! [X2,X0,X1] :
( sP0(sK6(sK7(X0,powerset(X1))),X2)
| empty(sK7(X0,powerset(X1)))
| element(unordered_pair(singleton(sK7(sK6(sK7(X0,powerset(X1))),X2)),unordered_pair(sK8(sK6(sK7(X0,powerset(X1))),X2),sK7(sK6(sK7(X0,powerset(X1))),X2))),X1)
| sP0(X0,powerset(X1)) )
| ~ spl17_167
| ~ spl17_312 ),
inference(resolution,[],[f2731,f1346]) ).
fof(f10106,plain,
( spl17_783
| ~ spl17_171
| ~ spl17_311 ),
inference(avatar_split_clause,[],[f2763,f2726,f1361,f10104]) ).
fof(f10104,plain,
( spl17_783
<=> ! [X2,X0,X1] :
( sP0(sK6(sK9(X0,powerset(X1))),X2)
| empty(sK9(X0,powerset(X1)))
| element(unordered_pair(singleton(sK8(sK6(sK9(X0,powerset(X1))),X2)),unordered_pair(sK9(sK6(sK9(X0,powerset(X1))),X2),sK8(sK6(sK9(X0,powerset(X1))),X2))),X1)
| sP0(X0,powerset(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_783])]) ).
fof(f2763,plain,
( ! [X2,X0,X1] :
( sP0(sK6(sK9(X0,powerset(X1))),X2)
| empty(sK9(X0,powerset(X1)))
| element(unordered_pair(singleton(sK8(sK6(sK9(X0,powerset(X1))),X2)),unordered_pair(sK9(sK6(sK9(X0,powerset(X1))),X2),sK8(sK6(sK9(X0,powerset(X1))),X2))),X1)
| sP0(X0,powerset(X1)) )
| ~ spl17_171
| ~ spl17_311 ),
inference(resolution,[],[f2727,f1362]) ).
fof(f10102,plain,
( spl17_782
| ~ spl17_169
| ~ spl17_311 ),
inference(avatar_split_clause,[],[f2757,f2726,f1353,f10100]) ).
fof(f10100,plain,
( spl17_782
<=> ! [X2,X0,X1] :
( sP0(sK6(sK8(X0,powerset(X1))),X2)
| empty(sK8(X0,powerset(X1)))
| element(unordered_pair(singleton(sK8(sK6(sK8(X0,powerset(X1))),X2)),unordered_pair(sK9(sK6(sK8(X0,powerset(X1))),X2),sK8(sK6(sK8(X0,powerset(X1))),X2))),X1)
| sP0(X0,powerset(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_782])]) ).
fof(f2757,plain,
( ! [X2,X0,X1] :
( sP0(sK6(sK8(X0,powerset(X1))),X2)
| empty(sK8(X0,powerset(X1)))
| element(unordered_pair(singleton(sK8(sK6(sK8(X0,powerset(X1))),X2)),unordered_pair(sK9(sK6(sK8(X0,powerset(X1))),X2),sK8(sK6(sK8(X0,powerset(X1))),X2))),X1)
| sP0(X0,powerset(X1)) )
| ~ spl17_169
| ~ spl17_311 ),
inference(resolution,[],[f2727,f1354]) ).
fof(f10098,plain,
( spl17_781
| ~ spl17_167
| ~ spl17_311 ),
inference(avatar_split_clause,[],[f2751,f2726,f1345,f10096]) ).
fof(f10096,plain,
( spl17_781
<=> ! [X2,X0,X1] :
( sP0(sK6(sK7(X0,powerset(X1))),X2)
| empty(sK7(X0,powerset(X1)))
| element(unordered_pair(singleton(sK8(sK6(sK7(X0,powerset(X1))),X2)),unordered_pair(sK9(sK6(sK7(X0,powerset(X1))),X2),sK8(sK6(sK7(X0,powerset(X1))),X2))),X1)
| sP0(X0,powerset(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_781])]) ).
fof(f2751,plain,
( ! [X2,X0,X1] :
( sP0(sK6(sK7(X0,powerset(X1))),X2)
| empty(sK7(X0,powerset(X1)))
| element(unordered_pair(singleton(sK8(sK6(sK7(X0,powerset(X1))),X2)),unordered_pair(sK9(sK6(sK7(X0,powerset(X1))),X2),sK8(sK6(sK7(X0,powerset(X1))),X2))),X1)
| sP0(X0,powerset(X1)) )
| ~ spl17_167
| ~ spl17_311 ),
inference(resolution,[],[f2727,f1346]) ).
fof(f9797,plain,
( spl17_780
| ~ spl17_17
| ~ spl17_744 ),
inference(avatar_split_clause,[],[f9749,f9101,f255,f9794]) ).
fof(f9794,plain,
( spl17_780
<=> sP1(sK10(sK6(powerset(sK16)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_780])]) ).
fof(f9101,plain,
( spl17_744
<=> relation(sK10(sK6(powerset(sK16)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_744])]) ).
fof(f9749,plain,
( sP1(sK10(sK6(powerset(sK16))))
| ~ spl17_17
| ~ spl17_744 ),
inference(resolution,[],[f9103,f256]) ).
fof(f9103,plain,
( relation(sK10(sK6(powerset(sK16))))
| ~ spl17_744 ),
inference(avatar_component_clause,[],[f9101]) ).
fof(f9777,plain,
( spl17_779
| ~ spl17_98
| ~ spl17_363 ),
inference(avatar_split_clause,[],[f3485,f3459,f788,f9775]) ).
fof(f9775,plain,
( spl17_779
<=> ! [X4,X0,X3,X2,X1] :
( in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),powerset(X2))
| ~ in(X1,X3)
| ~ in(X4,X3)
| ~ in(X0,X3)
| ~ sP0(powerset(X2),X3)
| empty(powerset(X2))
| ~ subset(unordered_pair(singleton(X4),unordered_pair(X1,X4)),X2)
| ~ subset(unordered_pair(singleton(X0),unordered_pair(X4,X0)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_779])]) ).
fof(f3485,plain,
( ! [X2,X3,X0,X1,X4] :
( in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),powerset(X2))
| ~ in(X1,X3)
| ~ in(X4,X3)
| ~ in(X0,X3)
| ~ sP0(powerset(X2),X3)
| empty(powerset(X2))
| ~ subset(unordered_pair(singleton(X4),unordered_pair(X1,X4)),X2)
| ~ subset(unordered_pair(singleton(X0),unordered_pair(X4,X0)),X2) )
| ~ spl17_98
| ~ spl17_363 ),
inference(duplicate_literal_removal,[],[f3470]) ).
fof(f3470,plain,
( ! [X2,X3,X0,X1,X4] :
( in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),powerset(X2))
| ~ in(X1,X3)
| ~ in(X4,X3)
| ~ in(X0,X3)
| ~ sP0(powerset(X2),X3)
| empty(powerset(X2))
| ~ subset(unordered_pair(singleton(X4),unordered_pair(X1,X4)),X2)
| empty(powerset(X2))
| ~ subset(unordered_pair(singleton(X0),unordered_pair(X4,X0)),X2) )
| ~ spl17_98
| ~ spl17_363 ),
inference(resolution,[],[f3460,f789]) ).
fof(f9773,plain,
( spl17_778
| ~ spl17_30
| ~ spl17_360 ),
inference(avatar_split_clause,[],[f3453,f3441,f313,f9771]) ).
fof(f9771,plain,
( spl17_778
<=> ! [X4,X0,X3,X2,X1] :
( ~ subset(unordered_pair(singleton(X0),unordered_pair(X1,X0)),X2)
| empty(powerset(X2))
| in(unordered_pair(singleton(X0),unordered_pair(X0,X3)),powerset(X2))
| ~ in(X3,X4)
| ~ in(X1,X4)
| ~ in(X0,X4)
| ~ sP0(powerset(X2),X4)
| ~ subset(unordered_pair(singleton(X1),unordered_pair(X1,X3)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_778])]) ).
fof(f3453,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ subset(unordered_pair(singleton(X0),unordered_pair(X1,X0)),X2)
| empty(powerset(X2))
| in(unordered_pair(singleton(X0),unordered_pair(X0,X3)),powerset(X2))
| ~ in(X3,X4)
| ~ in(X1,X4)
| ~ in(X0,X4)
| ~ sP0(powerset(X2),X4)
| ~ subset(unordered_pair(singleton(X1),unordered_pair(X1,X3)),X2) )
| ~ spl17_30
| ~ spl17_360 ),
inference(superposition,[],[f3442,f314]) ).
fof(f9769,plain,
( spl17_777
| ~ spl17_51
| ~ spl17_338 ),
inference(avatar_split_clause,[],[f3233,f3192,f439,f9767]) ).
fof(f9767,plain,
( spl17_777
<=> ! [X0,X3,X2,X1] :
( sP0(X0,powerset(powerset(X1)))
| sP0(sK9(X0,powerset(powerset(X1))),X2)
| element(X3,X1)
| ~ in(X3,unordered_pair(singleton(sK7(sK9(X0,powerset(powerset(X1))),X2)),unordered_pair(sK8(sK9(X0,powerset(powerset(X1))),X2),sK7(sK9(X0,powerset(powerset(X1))),X2)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_777])]) ).
fof(f3233,plain,
( ! [X2,X3,X0,X1] :
( sP0(X0,powerset(powerset(X1)))
| sP0(sK9(X0,powerset(powerset(X1))),X2)
| element(X3,X1)
| ~ in(X3,unordered_pair(singleton(sK7(sK9(X0,powerset(powerset(X1))),X2)),unordered_pair(sK8(sK9(X0,powerset(powerset(X1))),X2),sK7(sK9(X0,powerset(powerset(X1))),X2)))) )
| ~ spl17_51
| ~ spl17_338 ),
inference(resolution,[],[f3193,f440]) ).
fof(f9765,plain,
( spl17_776
| ~ spl17_51
| ~ spl17_337 ),
inference(avatar_split_clause,[],[f3229,f3188,f439,f9763]) ).
fof(f9763,plain,
( spl17_776
<=> ! [X0,X3,X2,X1] :
( sP0(X0,powerset(powerset(X1)))
| sP0(sK9(X0,powerset(powerset(X1))),X2)
| element(X3,X1)
| ~ in(X3,unordered_pair(singleton(sK8(sK9(X0,powerset(powerset(X1))),X2)),unordered_pair(sK9(sK9(X0,powerset(powerset(X1))),X2),sK8(sK9(X0,powerset(powerset(X1))),X2)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_776])]) ).
fof(f3229,plain,
( ! [X2,X3,X0,X1] :
( sP0(X0,powerset(powerset(X1)))
| sP0(sK9(X0,powerset(powerset(X1))),X2)
| element(X3,X1)
| ~ in(X3,unordered_pair(singleton(sK8(sK9(X0,powerset(powerset(X1))),X2)),unordered_pair(sK9(sK9(X0,powerset(powerset(X1))),X2),sK8(sK9(X0,powerset(powerset(X1))),X2)))) )
| ~ spl17_51
| ~ spl17_337 ),
inference(resolution,[],[f3189,f440]) ).
fof(f9761,plain,
( spl17_775
| ~ spl17_51
| ~ spl17_336 ),
inference(avatar_split_clause,[],[f3225,f3184,f439,f9759]) ).
fof(f9759,plain,
( spl17_775
<=> ! [X0,X3,X2,X1] :
( sP0(X0,powerset(powerset(X1)))
| sP0(sK8(X0,powerset(powerset(X1))),X2)
| element(X3,X1)
| ~ in(X3,unordered_pair(singleton(sK7(sK8(X0,powerset(powerset(X1))),X2)),unordered_pair(sK8(sK8(X0,powerset(powerset(X1))),X2),sK7(sK8(X0,powerset(powerset(X1))),X2)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_775])]) ).
fof(f3225,plain,
( ! [X2,X3,X0,X1] :
( sP0(X0,powerset(powerset(X1)))
| sP0(sK8(X0,powerset(powerset(X1))),X2)
| element(X3,X1)
| ~ in(X3,unordered_pair(singleton(sK7(sK8(X0,powerset(powerset(X1))),X2)),unordered_pair(sK8(sK8(X0,powerset(powerset(X1))),X2),sK7(sK8(X0,powerset(powerset(X1))),X2)))) )
| ~ spl17_51
| ~ spl17_336 ),
inference(resolution,[],[f3185,f440]) ).
fof(f9757,plain,
( spl17_774
| ~ spl17_51
| ~ spl17_335 ),
inference(avatar_split_clause,[],[f3206,f3180,f439,f9755]) ).
fof(f9755,plain,
( spl17_774
<=> ! [X0,X3,X2,X1] :
( sP0(X0,powerset(powerset(X1)))
| sP0(sK8(X0,powerset(powerset(X1))),X2)
| element(X3,X1)
| ~ in(X3,unordered_pair(singleton(sK8(sK8(X0,powerset(powerset(X1))),X2)),unordered_pair(sK9(sK8(X0,powerset(powerset(X1))),X2),sK8(sK8(X0,powerset(powerset(X1))),X2)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_774])]) ).
fof(f3206,plain,
( ! [X2,X3,X0,X1] :
( sP0(X0,powerset(powerset(X1)))
| sP0(sK8(X0,powerset(powerset(X1))),X2)
| element(X3,X1)
| ~ in(X3,unordered_pair(singleton(sK8(sK8(X0,powerset(powerset(X1))),X2)),unordered_pair(sK9(sK8(X0,powerset(powerset(X1))),X2),sK8(sK8(X0,powerset(powerset(X1))),X2)))) )
| ~ spl17_51
| ~ spl17_335 ),
inference(resolution,[],[f3181,f440]) ).
fof(f9753,plain,
( spl17_773
| ~ spl17_51
| ~ spl17_334 ),
inference(avatar_split_clause,[],[f3202,f3176,f439,f9751]) ).
fof(f9751,plain,
( spl17_773
<=> ! [X0,X3,X2,X1] :
( sP0(X0,powerset(powerset(X1)))
| sP0(sK7(X0,powerset(powerset(X1))),X2)
| element(X3,X1)
| ~ in(X3,unordered_pair(singleton(sK7(sK7(X0,powerset(powerset(X1))),X2)),unordered_pair(sK8(sK7(X0,powerset(powerset(X1))),X2),sK7(sK7(X0,powerset(powerset(X1))),X2)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_773])]) ).
fof(f3202,plain,
( ! [X2,X3,X0,X1] :
( sP0(X0,powerset(powerset(X1)))
| sP0(sK7(X0,powerset(powerset(X1))),X2)
| element(X3,X1)
| ~ in(X3,unordered_pair(singleton(sK7(sK7(X0,powerset(powerset(X1))),X2)),unordered_pair(sK8(sK7(X0,powerset(powerset(X1))),X2),sK7(sK7(X0,powerset(powerset(X1))),X2)))) )
| ~ spl17_51
| ~ spl17_334 ),
inference(resolution,[],[f3177,f440]) ).
fof(f9748,plain,
( spl17_772
| ~ spl17_51
| ~ spl17_333 ),
inference(avatar_split_clause,[],[f3198,f3172,f439,f9746]) ).
fof(f9746,plain,
( spl17_772
<=> ! [X0,X3,X2,X1] :
( sP0(X0,powerset(powerset(X1)))
| sP0(sK7(X0,powerset(powerset(X1))),X2)
| element(X3,X1)
| ~ in(X3,unordered_pair(singleton(sK8(sK7(X0,powerset(powerset(X1))),X2)),unordered_pair(sK9(sK7(X0,powerset(powerset(X1))),X2),sK8(sK7(X0,powerset(powerset(X1))),X2)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_772])]) ).
fof(f3198,plain,
( ! [X2,X3,X0,X1] :
( sP0(X0,powerset(powerset(X1)))
| sP0(sK7(X0,powerset(powerset(X1))),X2)
| element(X3,X1)
| ~ in(X3,unordered_pair(singleton(sK8(sK7(X0,powerset(powerset(X1))),X2)),unordered_pair(sK9(sK7(X0,powerset(powerset(X1))),X2),sK8(sK7(X0,powerset(powerset(X1))),X2)))) )
| ~ spl17_51
| ~ spl17_333 ),
inference(resolution,[],[f3173,f440]) ).
fof(f9744,plain,
( spl17_771
| ~ spl17_60
| ~ spl17_292 ),
inference(avatar_split_clause,[],[f2599,f2530,f504,f9742]) ).
fof(f9742,plain,
( spl17_771
<=> ! [X2,X0,X1] :
( sP0(X0,sK6(powerset(X1)))
| element(unordered_pair(singleton(sK7(sK9(X0,sK6(powerset(X1))),X2)),unordered_pair(sK8(sK9(X0,sK6(powerset(X1))),X2),sK7(sK9(X0,sK6(powerset(X1))),X2))),X1)
| empty(powerset(X1))
| sP0(sK9(X0,sK6(powerset(X1))),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_771])]) ).
fof(f2599,plain,
( ! [X2,X0,X1] :
( sP0(X0,sK6(powerset(X1)))
| element(unordered_pair(singleton(sK7(sK9(X0,sK6(powerset(X1))),X2)),unordered_pair(sK8(sK9(X0,sK6(powerset(X1))),X2),sK7(sK9(X0,sK6(powerset(X1))),X2))),X1)
| empty(powerset(X1))
| sP0(sK9(X0,sK6(powerset(X1))),X2) )
| ~ spl17_60
| ~ spl17_292 ),
inference(resolution,[],[f2531,f505]) ).
fof(f9740,plain,
( spl17_770
| ~ spl17_59
| ~ spl17_292 ),
inference(avatar_split_clause,[],[f2598,f2530,f500,f9738]) ).
fof(f9738,plain,
( spl17_770
<=> ! [X2,X0,X1] :
( sP0(X0,sK6(powerset(X1)))
| element(unordered_pair(singleton(sK8(sK9(X0,sK6(powerset(X1))),X2)),unordered_pair(sK9(sK9(X0,sK6(powerset(X1))),X2),sK8(sK9(X0,sK6(powerset(X1))),X2))),X1)
| empty(powerset(X1))
| sP0(sK9(X0,sK6(powerset(X1))),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_770])]) ).
fof(f2598,plain,
( ! [X2,X0,X1] :
( sP0(X0,sK6(powerset(X1)))
| element(unordered_pair(singleton(sK8(sK9(X0,sK6(powerset(X1))),X2)),unordered_pair(sK9(sK9(X0,sK6(powerset(X1))),X2),sK8(sK9(X0,sK6(powerset(X1))),X2))),X1)
| empty(powerset(X1))
| sP0(sK9(X0,sK6(powerset(X1))),X2) )
| ~ spl17_59
| ~ spl17_292 ),
inference(resolution,[],[f2531,f501]) ).
fof(f9736,plain,
( spl17_769
| ~ spl17_60
| ~ spl17_291 ),
inference(avatar_split_clause,[],[f2585,f2526,f504,f9734]) ).
fof(f9734,plain,
( spl17_769
<=> ! [X2,X0,X1] :
( sP0(X0,sK6(powerset(X1)))
| element(unordered_pair(singleton(sK7(sK8(X0,sK6(powerset(X1))),X2)),unordered_pair(sK8(sK8(X0,sK6(powerset(X1))),X2),sK7(sK8(X0,sK6(powerset(X1))),X2))),X1)
| empty(powerset(X1))
| sP0(sK8(X0,sK6(powerset(X1))),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_769])]) ).
fof(f2585,plain,
( ! [X2,X0,X1] :
( sP0(X0,sK6(powerset(X1)))
| element(unordered_pair(singleton(sK7(sK8(X0,sK6(powerset(X1))),X2)),unordered_pair(sK8(sK8(X0,sK6(powerset(X1))),X2),sK7(sK8(X0,sK6(powerset(X1))),X2))),X1)
| empty(powerset(X1))
| sP0(sK8(X0,sK6(powerset(X1))),X2) )
| ~ spl17_60
| ~ spl17_291 ),
inference(resolution,[],[f2527,f505]) ).
fof(f9732,plain,
( spl17_768
| ~ spl17_59
| ~ spl17_291 ),
inference(avatar_split_clause,[],[f2584,f2526,f500,f9730]) ).
fof(f9730,plain,
( spl17_768
<=> ! [X2,X0,X1] :
( sP0(X0,sK6(powerset(X1)))
| element(unordered_pair(singleton(sK8(sK8(X0,sK6(powerset(X1))),X2)),unordered_pair(sK9(sK8(X0,sK6(powerset(X1))),X2),sK8(sK8(X0,sK6(powerset(X1))),X2))),X1)
| empty(powerset(X1))
| sP0(sK8(X0,sK6(powerset(X1))),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_768])]) ).
fof(f2584,plain,
( ! [X2,X0,X1] :
( sP0(X0,sK6(powerset(X1)))
| element(unordered_pair(singleton(sK8(sK8(X0,sK6(powerset(X1))),X2)),unordered_pair(sK9(sK8(X0,sK6(powerset(X1))),X2),sK8(sK8(X0,sK6(powerset(X1))),X2))),X1)
| empty(powerset(X1))
| sP0(sK8(X0,sK6(powerset(X1))),X2) )
| ~ spl17_59
| ~ spl17_291 ),
inference(resolution,[],[f2527,f501]) ).
fof(f9728,plain,
( spl17_767
| ~ spl17_60
| ~ spl17_290 ),
inference(avatar_split_clause,[],[f2571,f2522,f504,f9726]) ).
fof(f9726,plain,
( spl17_767
<=> ! [X2,X0,X1] :
( sP0(X0,sK6(powerset(X1)))
| element(unordered_pair(singleton(sK7(sK7(X0,sK6(powerset(X1))),X2)),unordered_pair(sK8(sK7(X0,sK6(powerset(X1))),X2),sK7(sK7(X0,sK6(powerset(X1))),X2))),X1)
| empty(powerset(X1))
| sP0(sK7(X0,sK6(powerset(X1))),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_767])]) ).
fof(f2571,plain,
( ! [X2,X0,X1] :
( sP0(X0,sK6(powerset(X1)))
| element(unordered_pair(singleton(sK7(sK7(X0,sK6(powerset(X1))),X2)),unordered_pair(sK8(sK7(X0,sK6(powerset(X1))),X2),sK7(sK7(X0,sK6(powerset(X1))),X2))),X1)
| empty(powerset(X1))
| sP0(sK7(X0,sK6(powerset(X1))),X2) )
| ~ spl17_60
| ~ spl17_290 ),
inference(resolution,[],[f2523,f505]) ).
fof(f9724,plain,
( spl17_766
| ~ spl17_59
| ~ spl17_290 ),
inference(avatar_split_clause,[],[f2570,f2522,f500,f9722]) ).
fof(f9722,plain,
( spl17_766
<=> ! [X2,X0,X1] :
( sP0(X0,sK6(powerset(X1)))
| element(unordered_pair(singleton(sK8(sK7(X0,sK6(powerset(X1))),X2)),unordered_pair(sK9(sK7(X0,sK6(powerset(X1))),X2),sK8(sK7(X0,sK6(powerset(X1))),X2))),X1)
| empty(powerset(X1))
| sP0(sK7(X0,sK6(powerset(X1))),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_766])]) ).
fof(f2570,plain,
( ! [X2,X0,X1] :
( sP0(X0,sK6(powerset(X1)))
| element(unordered_pair(singleton(sK8(sK7(X0,sK6(powerset(X1))),X2)),unordered_pair(sK9(sK7(X0,sK6(powerset(X1))),X2),sK8(sK7(X0,sK6(powerset(X1))),X2))),X1)
| empty(powerset(X1))
| sP0(sK7(X0,sK6(powerset(X1))),X2) )
| ~ spl17_59
| ~ spl17_290 ),
inference(resolution,[],[f2523,f501]) ).
fof(f9322,plain,
( spl17_765
| ~ spl17_39
| ~ spl17_347 ),
inference(avatar_split_clause,[],[f3317,f3306,f355,f9320]) ).
fof(f9320,plain,
( spl17_765
<=> ! [X0,X1] :
( sP0(powerset(X0),X1)
| empty(unordered_pair(singleton(sK7(powerset(X0),X1)),unordered_pair(sK8(powerset(X0),X1),sK7(powerset(X0),X1))))
| empty(X0)
| in(sK10(unordered_pair(singleton(sK7(powerset(X0),X1)),unordered_pair(sK8(powerset(X0),X1),sK7(powerset(X0),X1)))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_765])]) ).
fof(f3317,plain,
( ! [X0,X1] :
( sP0(powerset(X0),X1)
| empty(unordered_pair(singleton(sK7(powerset(X0),X1)),unordered_pair(sK8(powerset(X0),X1),sK7(powerset(X0),X1))))
| empty(X0)
| in(sK10(unordered_pair(singleton(sK7(powerset(X0),X1)),unordered_pair(sK8(powerset(X0),X1),sK7(powerset(X0),X1)))),X0) )
| ~ spl17_39
| ~ spl17_347 ),
inference(resolution,[],[f3307,f356]) ).
fof(f9318,plain,
( spl17_764
| ~ spl17_39
| ~ spl17_346 ),
inference(avatar_split_clause,[],[f3313,f3302,f355,f9316]) ).
fof(f9316,plain,
( spl17_764
<=> ! [X0,X1] :
( sP0(powerset(X0),X1)
| empty(unordered_pair(singleton(sK8(powerset(X0),X1)),unordered_pair(sK9(powerset(X0),X1),sK8(powerset(X0),X1))))
| empty(X0)
| in(sK10(unordered_pair(singleton(sK8(powerset(X0),X1)),unordered_pair(sK9(powerset(X0),X1),sK8(powerset(X0),X1)))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_764])]) ).
fof(f3313,plain,
( ! [X0,X1] :
( sP0(powerset(X0),X1)
| empty(unordered_pair(singleton(sK8(powerset(X0),X1)),unordered_pair(sK9(powerset(X0),X1),sK8(powerset(X0),X1))))
| empty(X0)
| in(sK10(unordered_pair(singleton(sK8(powerset(X0),X1)),unordered_pair(sK9(powerset(X0),X1),sK8(powerset(X0),X1)))),X0) )
| ~ spl17_39
| ~ spl17_346 ),
inference(resolution,[],[f3303,f356]) ).
fof(f9314,plain,
( spl17_763
| ~ spl17_49
| ~ spl17_338 ),
inference(avatar_split_clause,[],[f3232,f3192,f422,f9312]) ).
fof(f9312,plain,
( spl17_763
<=> ! [X2,X0,X1,X3] :
( sP0(X0,powerset(powerset(X1)))
| sP0(sK9(X0,powerset(powerset(X1))),X2)
| ~ empty(X1)
| ~ in(X3,unordered_pair(singleton(sK7(sK9(X0,powerset(powerset(X1))),X2)),unordered_pair(sK8(sK9(X0,powerset(powerset(X1))),X2),sK7(sK9(X0,powerset(powerset(X1))),X2)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_763])]) ).
fof(f3232,plain,
( ! [X2,X3,X0,X1] :
( sP0(X0,powerset(powerset(X1)))
| sP0(sK9(X0,powerset(powerset(X1))),X2)
| ~ empty(X1)
| ~ in(X3,unordered_pair(singleton(sK7(sK9(X0,powerset(powerset(X1))),X2)),unordered_pair(sK8(sK9(X0,powerset(powerset(X1))),X2),sK7(sK9(X0,powerset(powerset(X1))),X2)))) )
| ~ spl17_49
| ~ spl17_338 ),
inference(resolution,[],[f3193,f423]) ).
fof(f9310,plain,
( spl17_762
| ~ spl17_49
| ~ spl17_337 ),
inference(avatar_split_clause,[],[f3228,f3188,f422,f9308]) ).
fof(f9308,plain,
( spl17_762
<=> ! [X2,X0,X1,X3] :
( sP0(X0,powerset(powerset(X1)))
| sP0(sK9(X0,powerset(powerset(X1))),X2)
| ~ empty(X1)
| ~ in(X3,unordered_pair(singleton(sK8(sK9(X0,powerset(powerset(X1))),X2)),unordered_pair(sK9(sK9(X0,powerset(powerset(X1))),X2),sK8(sK9(X0,powerset(powerset(X1))),X2)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_762])]) ).
fof(f3228,plain,
( ! [X2,X3,X0,X1] :
( sP0(X0,powerset(powerset(X1)))
| sP0(sK9(X0,powerset(powerset(X1))),X2)
| ~ empty(X1)
| ~ in(X3,unordered_pair(singleton(sK8(sK9(X0,powerset(powerset(X1))),X2)),unordered_pair(sK9(sK9(X0,powerset(powerset(X1))),X2),sK8(sK9(X0,powerset(powerset(X1))),X2)))) )
| ~ spl17_49
| ~ spl17_337 ),
inference(resolution,[],[f3189,f423]) ).
fof(f9306,plain,
( spl17_761
| ~ spl17_49
| ~ spl17_336 ),
inference(avatar_split_clause,[],[f3224,f3184,f422,f9304]) ).
fof(f9304,plain,
( spl17_761
<=> ! [X2,X0,X1,X3] :
( sP0(X0,powerset(powerset(X1)))
| sP0(sK8(X0,powerset(powerset(X1))),X2)
| ~ empty(X1)
| ~ in(X3,unordered_pair(singleton(sK7(sK8(X0,powerset(powerset(X1))),X2)),unordered_pair(sK8(sK8(X0,powerset(powerset(X1))),X2),sK7(sK8(X0,powerset(powerset(X1))),X2)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_761])]) ).
fof(f3224,plain,
( ! [X2,X3,X0,X1] :
( sP0(X0,powerset(powerset(X1)))
| sP0(sK8(X0,powerset(powerset(X1))),X2)
| ~ empty(X1)
| ~ in(X3,unordered_pair(singleton(sK7(sK8(X0,powerset(powerset(X1))),X2)),unordered_pair(sK8(sK8(X0,powerset(powerset(X1))),X2),sK7(sK8(X0,powerset(powerset(X1))),X2)))) )
| ~ spl17_49
| ~ spl17_336 ),
inference(resolution,[],[f3185,f423]) ).
fof(f9302,plain,
( spl17_743
| ~ spl17_20
| ~ spl17_742 ),
inference(avatar_split_clause,[],[f9216,f9093,f267,f9097]) ).
fof(f9097,plain,
( spl17_743
<=> empty(powerset(sK16)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_743])]) ).
fof(f267,plain,
( spl17_20
<=> ! [X0] :
( ~ empty(sK6(X0))
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_20])]) ).
fof(f9093,plain,
( spl17_742
<=> empty(sK6(powerset(sK16))) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_742])]) ).
fof(f9216,plain,
( empty(powerset(sK16))
| ~ spl17_20
| ~ spl17_742 ),
inference(resolution,[],[f9095,f268]) ).
fof(f268,plain,
( ! [X0] :
( ~ empty(sK6(X0))
| empty(X0) )
| ~ spl17_20 ),
inference(avatar_component_clause,[],[f267]) ).
fof(f9095,plain,
( empty(sK6(powerset(sK16)))
| ~ spl17_742 ),
inference(avatar_component_clause,[],[f9093]) ).
fof(f9301,plain,
( spl17_760
| ~ spl17_49
| ~ spl17_335 ),
inference(avatar_split_clause,[],[f3205,f3180,f422,f9299]) ).
fof(f9299,plain,
( spl17_760
<=> ! [X2,X0,X1,X3] :
( sP0(X0,powerset(powerset(X1)))
| sP0(sK8(X0,powerset(powerset(X1))),X2)
| ~ empty(X1)
| ~ in(X3,unordered_pair(singleton(sK8(sK8(X0,powerset(powerset(X1))),X2)),unordered_pair(sK9(sK8(X0,powerset(powerset(X1))),X2),sK8(sK8(X0,powerset(powerset(X1))),X2)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_760])]) ).
fof(f3205,plain,
( ! [X2,X3,X0,X1] :
( sP0(X0,powerset(powerset(X1)))
| sP0(sK8(X0,powerset(powerset(X1))),X2)
| ~ empty(X1)
| ~ in(X3,unordered_pair(singleton(sK8(sK8(X0,powerset(powerset(X1))),X2)),unordered_pair(sK9(sK8(X0,powerset(powerset(X1))),X2),sK8(sK8(X0,powerset(powerset(X1))),X2)))) )
| ~ spl17_49
| ~ spl17_335 ),
inference(resolution,[],[f3181,f423]) ).
fof(f9297,plain,
( spl17_759
| ~ spl17_49
| ~ spl17_334 ),
inference(avatar_split_clause,[],[f3201,f3176,f422,f9295]) ).
fof(f9295,plain,
( spl17_759
<=> ! [X2,X0,X1,X3] :
( sP0(X0,powerset(powerset(X1)))
| sP0(sK7(X0,powerset(powerset(X1))),X2)
| ~ empty(X1)
| ~ in(X3,unordered_pair(singleton(sK7(sK7(X0,powerset(powerset(X1))),X2)),unordered_pair(sK8(sK7(X0,powerset(powerset(X1))),X2),sK7(sK7(X0,powerset(powerset(X1))),X2)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_759])]) ).
fof(f3201,plain,
( ! [X2,X3,X0,X1] :
( sP0(X0,powerset(powerset(X1)))
| sP0(sK7(X0,powerset(powerset(X1))),X2)
| ~ empty(X1)
| ~ in(X3,unordered_pair(singleton(sK7(sK7(X0,powerset(powerset(X1))),X2)),unordered_pair(sK8(sK7(X0,powerset(powerset(X1))),X2),sK7(sK7(X0,powerset(powerset(X1))),X2)))) )
| ~ spl17_49
| ~ spl17_334 ),
inference(resolution,[],[f3177,f423]) ).
fof(f9293,plain,
( spl17_758
| ~ spl17_49
| ~ spl17_333 ),
inference(avatar_split_clause,[],[f3197,f3172,f422,f9291]) ).
fof(f9291,plain,
( spl17_758
<=> ! [X2,X0,X1,X3] :
( sP0(X0,powerset(powerset(X1)))
| sP0(sK7(X0,powerset(powerset(X1))),X2)
| ~ empty(X1)
| ~ in(X3,unordered_pair(singleton(sK8(sK7(X0,powerset(powerset(X1))),X2)),unordered_pair(sK9(sK7(X0,powerset(powerset(X1))),X2),sK8(sK7(X0,powerset(powerset(X1))),X2)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_758])]) ).
fof(f3197,plain,
( ! [X2,X3,X0,X1] :
( sP0(X0,powerset(powerset(X1)))
| sP0(sK7(X0,powerset(powerset(X1))),X2)
| ~ empty(X1)
| ~ in(X3,unordered_pair(singleton(sK8(sK7(X0,powerset(powerset(X1))),X2)),unordered_pair(sK9(sK7(X0,powerset(powerset(X1))),X2),sK8(sK7(X0,powerset(powerset(X1))),X2)))) )
| ~ spl17_49
| ~ spl17_333 ),
inference(resolution,[],[f3173,f423]) ).
fof(f9251,plain,
( spl17_757
| ~ spl17_30
| ~ spl17_351 ),
inference(avatar_split_clause,[],[f3373,f3348,f313,f9249]) ).
fof(f9249,plain,
( spl17_757
<=> ! [X0,X3,X2,X1] :
( ~ in(unordered_pair(singleton(X2),unordered_pair(X2,sK7(X0,X1))),X0)
| in(unordered_pair(singleton(X2),unordered_pair(X2,sK8(X0,X1))),X0)
| ~ in(sK8(X0,X1),X3)
| ~ in(sK7(X0,X1),X3)
| ~ in(X2,X3)
| ~ sP0(X0,X3)
| sP0(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_757])]) ).
fof(f3373,plain,
( ! [X2,X3,X0,X1] :
( ~ in(unordered_pair(singleton(X2),unordered_pair(X2,sK7(X0,X1))),X0)
| in(unordered_pair(singleton(X2),unordered_pair(X2,sK8(X0,X1))),X0)
| ~ in(sK8(X0,X1),X3)
| ~ in(sK7(X0,X1),X3)
| ~ in(X2,X3)
| ~ sP0(X0,X3)
| sP0(X0,X1) )
| ~ spl17_30
| ~ spl17_351 ),
inference(superposition,[],[f3349,f314]) ).
fof(f9215,plain,
( spl17_756
| ~ spl17_30
| ~ spl17_350 ),
inference(avatar_split_clause,[],[f3359,f3344,f313,f9213]) ).
fof(f9213,plain,
( spl17_756
<=> ! [X0,X3,X2,X1] :
( ~ in(unordered_pair(singleton(X2),unordered_pair(X2,sK8(X0,X1))),X0)
| in(unordered_pair(singleton(X2),unordered_pair(X2,sK9(X0,X1))),X0)
| ~ in(sK9(X0,X1),X3)
| ~ in(sK8(X0,X1),X3)
| ~ in(X2,X3)
| ~ sP0(X0,X3)
| sP0(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_756])]) ).
fof(f3359,plain,
( ! [X2,X3,X0,X1] :
( ~ in(unordered_pair(singleton(X2),unordered_pair(X2,sK8(X0,X1))),X0)
| in(unordered_pair(singleton(X2),unordered_pair(X2,sK9(X0,X1))),X0)
| ~ in(sK9(X0,X1),X3)
| ~ in(sK8(X0,X1),X3)
| ~ in(X2,X3)
| ~ sP0(X0,X3)
| sP0(X0,X1) )
| ~ spl17_30
| ~ spl17_350 ),
inference(superposition,[],[f3345,f314]) ).
fof(f9211,plain,
( spl17_755
| ~ spl17_150
| ~ spl17_321 ),
inference(avatar_split_clause,[],[f2974,f2873,f1159,f9209]) ).
fof(f9209,plain,
( spl17_755
<=> ! [X2,X0,X1] :
( empty(sK13(X0,X1))
| sP0(sK10(powerset(sK13(X0,X1))),X2)
| element(unordered_pair(singleton(sK7(sK10(powerset(sK13(X0,X1))),X2)),unordered_pair(sK8(sK10(powerset(sK13(X0,X1))),X2),sK7(sK10(powerset(sK13(X0,X1))),X2))),cartesian_product2(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_755])]) ).
fof(f1159,plain,
( spl17_150
<=> ! [X2,X0,X1] :
( ~ in(X0,sK13(X1,X2))
| element(X0,cartesian_product2(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_150])]) ).
fof(f2974,plain,
( ! [X2,X0,X1] :
( empty(sK13(X0,X1))
| sP0(sK10(powerset(sK13(X0,X1))),X2)
| element(unordered_pair(singleton(sK7(sK10(powerset(sK13(X0,X1))),X2)),unordered_pair(sK8(sK10(powerset(sK13(X0,X1))),X2),sK7(sK10(powerset(sK13(X0,X1))),X2))),cartesian_product2(X0,X1)) )
| ~ spl17_150
| ~ spl17_321 ),
inference(resolution,[],[f2874,f1160]) ).
fof(f1160,plain,
( ! [X2,X0,X1] :
( ~ in(X0,sK13(X1,X2))
| element(X0,cartesian_product2(X1,X2)) )
| ~ spl17_150 ),
inference(avatar_component_clause,[],[f1159]) ).
fof(f9207,plain,
( spl17_754
| ~ spl17_151
| ~ spl17_321 ),
inference(avatar_split_clause,[],[f2973,f2873,f1163,f9205]) ).
fof(f9205,plain,
( spl17_754
<=> ! [X2,X0,X1] :
( empty(sK12(X0,X1))
| sP0(sK10(powerset(sK12(X0,X1))),X2)
| element(unordered_pair(singleton(sK7(sK10(powerset(sK12(X0,X1))),X2)),unordered_pair(sK8(sK10(powerset(sK12(X0,X1))),X2),sK7(sK10(powerset(sK12(X0,X1))),X2))),cartesian_product2(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_754])]) ).
fof(f1163,plain,
( spl17_151
<=> ! [X2,X0,X1] :
( ~ in(X0,sK12(X1,X2))
| element(X0,cartesian_product2(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_151])]) ).
fof(f2973,plain,
( ! [X2,X0,X1] :
( empty(sK12(X0,X1))
| sP0(sK10(powerset(sK12(X0,X1))),X2)
| element(unordered_pair(singleton(sK7(sK10(powerset(sK12(X0,X1))),X2)),unordered_pair(sK8(sK10(powerset(sK12(X0,X1))),X2),sK7(sK10(powerset(sK12(X0,X1))),X2))),cartesian_product2(X0,X1)) )
| ~ spl17_151
| ~ spl17_321 ),
inference(resolution,[],[f2874,f1164]) ).
fof(f1164,plain,
( ! [X2,X0,X1] :
( ~ in(X0,sK12(X1,X2))
| element(X0,cartesian_product2(X1,X2)) )
| ~ spl17_151 ),
inference(avatar_component_clause,[],[f1163]) ).
fof(f9203,plain,
( spl17_753
| ~ spl17_150
| ~ spl17_320 ),
inference(avatar_split_clause,[],[f2923,f2869,f1159,f9201]) ).
fof(f9201,plain,
( spl17_753
<=> ! [X2,X0,X1] :
( empty(sK13(X0,X1))
| sP0(sK10(powerset(sK13(X0,X1))),X2)
| element(unordered_pair(singleton(sK8(sK10(powerset(sK13(X0,X1))),X2)),unordered_pair(sK9(sK10(powerset(sK13(X0,X1))),X2),sK8(sK10(powerset(sK13(X0,X1))),X2))),cartesian_product2(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_753])]) ).
fof(f2923,plain,
( ! [X2,X0,X1] :
( empty(sK13(X0,X1))
| sP0(sK10(powerset(sK13(X0,X1))),X2)
| element(unordered_pair(singleton(sK8(sK10(powerset(sK13(X0,X1))),X2)),unordered_pair(sK9(sK10(powerset(sK13(X0,X1))),X2),sK8(sK10(powerset(sK13(X0,X1))),X2))),cartesian_product2(X0,X1)) )
| ~ spl17_150
| ~ spl17_320 ),
inference(resolution,[],[f2870,f1160]) ).
fof(f9199,plain,
( spl17_752
| ~ spl17_151
| ~ spl17_320 ),
inference(avatar_split_clause,[],[f2922,f2869,f1163,f9197]) ).
fof(f9197,plain,
( spl17_752
<=> ! [X2,X0,X1] :
( empty(sK12(X0,X1))
| sP0(sK10(powerset(sK12(X0,X1))),X2)
| element(unordered_pair(singleton(sK8(sK10(powerset(sK12(X0,X1))),X2)),unordered_pair(sK9(sK10(powerset(sK12(X0,X1))),X2),sK8(sK10(powerset(sK12(X0,X1))),X2))),cartesian_product2(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_752])]) ).
fof(f2922,plain,
( ! [X2,X0,X1] :
( empty(sK12(X0,X1))
| sP0(sK10(powerset(sK12(X0,X1))),X2)
| element(unordered_pair(singleton(sK8(sK10(powerset(sK12(X0,X1))),X2)),unordered_pair(sK9(sK10(powerset(sK12(X0,X1))),X2),sK8(sK10(powerset(sK12(X0,X1))),X2))),cartesian_product2(X0,X1)) )
| ~ spl17_151
| ~ spl17_320 ),
inference(resolution,[],[f2870,f1164]) ).
fof(f9177,plain,
( spl17_751
| ~ spl17_118
| ~ spl17_312 ),
inference(avatar_split_clause,[],[f2793,f2730,f956,f9175]) ).
fof(f9175,plain,
( spl17_751
<=> ! [X0,X1] :
( sP0(sK6(the_InternalRel(X0)),X1)
| empty(the_InternalRel(X0))
| related(X0,sK7(sK6(the_InternalRel(X0)),X1),sK8(sK6(the_InternalRel(X0)),X1))
| ~ element(sK8(sK6(the_InternalRel(X0)),X1),the_carrier(X0))
| ~ element(sK7(sK6(the_InternalRel(X0)),X1),the_carrier(X0))
| ~ rel_str(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_751])]) ).
fof(f2793,plain,
( ! [X0,X1] :
( sP0(sK6(the_InternalRel(X0)),X1)
| empty(the_InternalRel(X0))
| related(X0,sK7(sK6(the_InternalRel(X0)),X1),sK8(sK6(the_InternalRel(X0)),X1))
| ~ element(sK8(sK6(the_InternalRel(X0)),X1),the_carrier(X0))
| ~ element(sK7(sK6(the_InternalRel(X0)),X1),the_carrier(X0))
| ~ rel_str(X0) )
| ~ spl17_118
| ~ spl17_312 ),
inference(resolution,[],[f2731,f957]) ).
fof(f9155,plain,
( ~ spl17_14
| ~ spl17_743 ),
inference(avatar_contradiction_clause,[],[f9141]) ).
fof(f9141,plain,
( $false
| ~ spl17_14
| ~ spl17_743 ),
inference(resolution,[],[f9099,f244]) ).
fof(f244,plain,
( ! [X0] : ~ empty(powerset(X0))
| ~ spl17_14 ),
inference(avatar_component_clause,[],[f243]) ).
fof(f243,plain,
( spl17_14
<=> ! [X0] : ~ empty(powerset(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_14])]) ).
fof(f9099,plain,
( empty(powerset(sK16))
| ~ spl17_743 ),
inference(avatar_component_clause,[],[f9097]) ).
fof(f9140,plain,
( spl17_750
| ~ spl17_118
| ~ spl17_311 ),
inference(avatar_split_clause,[],[f2744,f2726,f956,f9138]) ).
fof(f9138,plain,
( spl17_750
<=> ! [X0,X1] :
( sP0(sK6(the_InternalRel(X0)),X1)
| empty(the_InternalRel(X0))
| related(X0,sK8(sK6(the_InternalRel(X0)),X1),sK9(sK6(the_InternalRel(X0)),X1))
| ~ element(sK9(sK6(the_InternalRel(X0)),X1),the_carrier(X0))
| ~ element(sK8(sK6(the_InternalRel(X0)),X1),the_carrier(X0))
| ~ rel_str(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_750])]) ).
fof(f2744,plain,
( ! [X0,X1] :
( sP0(sK6(the_InternalRel(X0)),X1)
| empty(the_InternalRel(X0))
| related(X0,sK8(sK6(the_InternalRel(X0)),X1),sK9(sK6(the_InternalRel(X0)),X1))
| ~ element(sK9(sK6(the_InternalRel(X0)),X1),the_carrier(X0))
| ~ element(sK8(sK6(the_InternalRel(X0)),X1),the_carrier(X0))
| ~ rel_str(X0) )
| ~ spl17_118
| ~ spl17_311 ),
inference(resolution,[],[f2727,f957]) ).
fof(f9136,plain,
( spl17_749
| ~ spl17_60
| ~ spl17_269 ),
inference(avatar_split_clause,[],[f2249,f2240,f504,f9134]) ).
fof(f9134,plain,
( spl17_749
<=> ! [X0,X1] :
( element(unordered_pair(singleton(sK7(sK10(sK10(powerset(powerset(X0)))),X1)),unordered_pair(sK8(sK10(sK10(powerset(powerset(X0)))),X1),sK7(sK10(sK10(powerset(powerset(X0)))),X1))),X0)
| empty(sK10(powerset(powerset(X0))))
| sP0(sK10(sK10(powerset(powerset(X0)))),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_749])]) ).
fof(f2249,plain,
( ! [X0,X1] :
( element(unordered_pair(singleton(sK7(sK10(sK10(powerset(powerset(X0)))),X1)),unordered_pair(sK8(sK10(sK10(powerset(powerset(X0)))),X1),sK7(sK10(sK10(powerset(powerset(X0)))),X1))),X0)
| empty(sK10(powerset(powerset(X0))))
| sP0(sK10(sK10(powerset(powerset(X0)))),X1) )
| ~ spl17_60
| ~ spl17_269 ),
inference(resolution,[],[f2241,f505]) ).
fof(f9132,plain,
( spl17_748
| ~ spl17_59
| ~ spl17_269 ),
inference(avatar_split_clause,[],[f2248,f2240,f500,f9130]) ).
fof(f9130,plain,
( spl17_748
<=> ! [X0,X1] :
( element(unordered_pair(singleton(sK8(sK10(sK10(powerset(powerset(X0)))),X1)),unordered_pair(sK9(sK10(sK10(powerset(powerset(X0)))),X1),sK8(sK10(sK10(powerset(powerset(X0)))),X1))),X0)
| empty(sK10(powerset(powerset(X0))))
| sP0(sK10(sK10(powerset(powerset(X0)))),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_748])]) ).
fof(f2248,plain,
( ! [X0,X1] :
( element(unordered_pair(singleton(sK8(sK10(sK10(powerset(powerset(X0)))),X1)),unordered_pair(sK9(sK10(sK10(powerset(powerset(X0)))),X1),sK8(sK10(sK10(powerset(powerset(X0)))),X1))),X0)
| empty(sK10(powerset(powerset(X0))))
| sP0(sK10(sK10(powerset(powerset(X0)))),X1) )
| ~ spl17_59
| ~ spl17_269 ),
inference(resolution,[],[f2241,f501]) ).
fof(f9116,plain,
( spl17_747
| ~ spl17_17
| ~ spl17_344 ),
inference(avatar_split_clause,[],[f3282,f3274,f255,f9114]) ).
fof(f9114,plain,
( spl17_747
<=> ! [X2,X0,X1] :
( sP0(sK6(powerset(cartesian_product2(X0,X1))),X2)
| empty(powerset(cartesian_product2(X0,X1)))
| sP1(unordered_pair(singleton(sK7(sK6(powerset(cartesian_product2(X0,X1))),X2)),unordered_pair(sK8(sK6(powerset(cartesian_product2(X0,X1))),X2),sK7(sK6(powerset(cartesian_product2(X0,X1))),X2)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_747])]) ).
fof(f3274,plain,
( spl17_344
<=> ! [X2,X0,X1] :
( empty(powerset(cartesian_product2(X0,X1)))
| sP0(sK6(powerset(cartesian_product2(X0,X1))),X2)
| relation(unordered_pair(singleton(sK7(sK6(powerset(cartesian_product2(X0,X1))),X2)),unordered_pair(sK8(sK6(powerset(cartesian_product2(X0,X1))),X2),sK7(sK6(powerset(cartesian_product2(X0,X1))),X2)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_344])]) ).
fof(f3282,plain,
( ! [X2,X0,X1] :
( sP0(sK6(powerset(cartesian_product2(X0,X1))),X2)
| empty(powerset(cartesian_product2(X0,X1)))
| sP1(unordered_pair(singleton(sK7(sK6(powerset(cartesian_product2(X0,X1))),X2)),unordered_pair(sK8(sK6(powerset(cartesian_product2(X0,X1))),X2),sK7(sK6(powerset(cartesian_product2(X0,X1))),X2)))) )
| ~ spl17_17
| ~ spl17_344 ),
inference(resolution,[],[f3275,f256]) ).
fof(f3275,plain,
( ! [X2,X0,X1] :
( relation(unordered_pair(singleton(sK7(sK6(powerset(cartesian_product2(X0,X1))),X2)),unordered_pair(sK8(sK6(powerset(cartesian_product2(X0,X1))),X2),sK7(sK6(powerset(cartesian_product2(X0,X1))),X2))))
| sP0(sK6(powerset(cartesian_product2(X0,X1))),X2)
| empty(powerset(cartesian_product2(X0,X1))) )
| ~ spl17_344 ),
inference(avatar_component_clause,[],[f3274]) ).
fof(f9112,plain,
( spl17_746
| ~ spl17_17
| ~ spl17_342 ),
inference(avatar_split_clause,[],[f3281,f3266,f255,f9110]) ).
fof(f9110,plain,
( spl17_746
<=> ! [X2,X0,X1] :
( sP0(sK6(powerset(cartesian_product2(X0,X1))),X2)
| empty(powerset(cartesian_product2(X0,X1)))
| sP1(unordered_pair(singleton(sK8(sK6(powerset(cartesian_product2(X0,X1))),X2)),unordered_pair(sK9(sK6(powerset(cartesian_product2(X0,X1))),X2),sK8(sK6(powerset(cartesian_product2(X0,X1))),X2)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_746])]) ).
fof(f3266,plain,
( spl17_342
<=> ! [X2,X0,X1] :
( empty(powerset(cartesian_product2(X0,X1)))
| sP0(sK6(powerset(cartesian_product2(X0,X1))),X2)
| relation(unordered_pair(singleton(sK8(sK6(powerset(cartesian_product2(X0,X1))),X2)),unordered_pair(sK9(sK6(powerset(cartesian_product2(X0,X1))),X2),sK8(sK6(powerset(cartesian_product2(X0,X1))),X2)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_342])]) ).
fof(f3281,plain,
( ! [X2,X0,X1] :
( sP0(sK6(powerset(cartesian_product2(X0,X1))),X2)
| empty(powerset(cartesian_product2(X0,X1)))
| sP1(unordered_pair(singleton(sK8(sK6(powerset(cartesian_product2(X0,X1))),X2)),unordered_pair(sK9(sK6(powerset(cartesian_product2(X0,X1))),X2),sK8(sK6(powerset(cartesian_product2(X0,X1))),X2)))) )
| ~ spl17_17
| ~ spl17_342 ),
inference(resolution,[],[f3267,f256]) ).
fof(f3267,plain,
( ! [X2,X0,X1] :
( relation(unordered_pair(singleton(sK8(sK6(powerset(cartesian_product2(X0,X1))),X2)),unordered_pair(sK9(sK6(powerset(cartesian_product2(X0,X1))),X2),sK8(sK6(powerset(cartesian_product2(X0,X1))),X2))))
| sP0(sK6(powerset(cartesian_product2(X0,X1))),X2)
| empty(powerset(cartesian_product2(X0,X1))) )
| ~ spl17_342 ),
inference(avatar_component_clause,[],[f3266]) ).
fof(f9108,plain,
( spl17_745
| ~ spl17_92
| ~ spl17_321 ),
inference(avatar_split_clause,[],[f2967,f2873,f733,f9106]) ).
fof(f9106,plain,
( spl17_745
<=> ! [X0,X1] :
( empty(sK10(powerset(X0)))
| sP0(sK10(powerset(sK10(powerset(X0)))),X1)
| element(unordered_pair(singleton(sK7(sK10(powerset(sK10(powerset(X0)))),X1)),unordered_pair(sK8(sK10(powerset(sK10(powerset(X0)))),X1),sK7(sK10(powerset(sK10(powerset(X0)))),X1))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_745])]) ).
fof(f733,plain,
( spl17_92
<=> ! [X0,X1] :
( element(X0,X1)
| ~ in(X0,sK10(powerset(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_92])]) ).
fof(f2967,plain,
( ! [X0,X1] :
( empty(sK10(powerset(X0)))
| sP0(sK10(powerset(sK10(powerset(X0)))),X1)
| element(unordered_pair(singleton(sK7(sK10(powerset(sK10(powerset(X0)))),X1)),unordered_pair(sK8(sK10(powerset(sK10(powerset(X0)))),X1),sK7(sK10(powerset(sK10(powerset(X0)))),X1))),X0) )
| ~ spl17_92
| ~ spl17_321 ),
inference(resolution,[],[f2874,f734]) ).
fof(f734,plain,
( ! [X0,X1] :
( ~ in(X0,sK10(powerset(X1)))
| element(X0,X1) )
| ~ spl17_92 ),
inference(avatar_component_clause,[],[f733]) ).
fof(f9104,plain,
( spl17_742
| spl17_743
| spl17_744
| ~ spl17_147
| ~ spl17_442 ),
inference(avatar_split_clause,[],[f4310,f4204,f1147,f9101,f9097,f9093]) ).
fof(f1147,plain,
( spl17_147
<=> ! [X0] :
( element(sK10(sK6(X0)),X0)
| empty(X0)
| empty(sK6(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_147])]) ).
fof(f4310,plain,
( relation(sK10(sK6(powerset(sK16))))
| empty(powerset(sK16))
| empty(sK6(powerset(sK16)))
| ~ spl17_147
| ~ spl17_442 ),
inference(resolution,[],[f4205,f1148]) ).
fof(f1148,plain,
( ! [X0] :
( element(sK10(sK6(X0)),X0)
| empty(X0)
| empty(sK6(X0)) )
| ~ spl17_147 ),
inference(avatar_component_clause,[],[f1147]) ).
fof(f9091,plain,
( spl17_741
| ~ spl17_92
| ~ spl17_320 ),
inference(avatar_split_clause,[],[f2916,f2869,f733,f9089]) ).
fof(f9089,plain,
( spl17_741
<=> ! [X0,X1] :
( empty(sK10(powerset(X0)))
| sP0(sK10(powerset(sK10(powerset(X0)))),X1)
| element(unordered_pair(singleton(sK8(sK10(powerset(sK10(powerset(X0)))),X1)),unordered_pair(sK9(sK10(powerset(sK10(powerset(X0)))),X1),sK8(sK10(powerset(sK10(powerset(X0)))),X1))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_741])]) ).
fof(f2916,plain,
( ! [X0,X1] :
( empty(sK10(powerset(X0)))
| sP0(sK10(powerset(sK10(powerset(X0)))),X1)
| element(unordered_pair(singleton(sK8(sK10(powerset(sK10(powerset(X0)))),X1)),unordered_pair(sK9(sK10(powerset(sK10(powerset(X0)))),X1),sK8(sK10(powerset(sK10(powerset(X0)))),X1))),X0) )
| ~ spl17_92
| ~ spl17_320 ),
inference(resolution,[],[f2870,f734]) ).
fof(f9077,plain,
( spl17_740
| ~ spl17_17
| ~ spl17_340 ),
inference(avatar_split_clause,[],[f3247,f3239,f255,f9075]) ).
fof(f9075,plain,
( spl17_740
<=> ! [X2,X0,X1] :
( sP0(sK10(powerset(powerset(cartesian_product2(X0,X1)))),X2)
| sP1(unordered_pair(singleton(sK7(sK10(powerset(powerset(cartesian_product2(X0,X1)))),X2)),unordered_pair(sK8(sK10(powerset(powerset(cartesian_product2(X0,X1)))),X2),sK7(sK10(powerset(powerset(cartesian_product2(X0,X1)))),X2)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_740])]) ).
fof(f3239,plain,
( spl17_340
<=> ! [X2,X0,X1] :
( sP0(sK10(powerset(powerset(cartesian_product2(X0,X1)))),X2)
| relation(unordered_pair(singleton(sK7(sK10(powerset(powerset(cartesian_product2(X0,X1)))),X2)),unordered_pair(sK8(sK10(powerset(powerset(cartesian_product2(X0,X1)))),X2),sK7(sK10(powerset(powerset(cartesian_product2(X0,X1)))),X2)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_340])]) ).
fof(f3247,plain,
( ! [X2,X0,X1] :
( sP0(sK10(powerset(powerset(cartesian_product2(X0,X1)))),X2)
| sP1(unordered_pair(singleton(sK7(sK10(powerset(powerset(cartesian_product2(X0,X1)))),X2)),unordered_pair(sK8(sK10(powerset(powerset(cartesian_product2(X0,X1)))),X2),sK7(sK10(powerset(powerset(cartesian_product2(X0,X1)))),X2)))) )
| ~ spl17_17
| ~ spl17_340 ),
inference(resolution,[],[f3240,f256]) ).
fof(f3240,plain,
( ! [X2,X0,X1] :
( relation(unordered_pair(singleton(sK7(sK10(powerset(powerset(cartesian_product2(X0,X1)))),X2)),unordered_pair(sK8(sK10(powerset(powerset(cartesian_product2(X0,X1)))),X2),sK7(sK10(powerset(powerset(cartesian_product2(X0,X1)))),X2))))
| sP0(sK10(powerset(powerset(cartesian_product2(X0,X1)))),X2) )
| ~ spl17_340 ),
inference(avatar_component_clause,[],[f3239]) ).
fof(f9073,plain,
( spl17_739
| ~ spl17_17
| ~ spl17_339 ),
inference(avatar_split_clause,[],[f3246,f3235,f255,f9071]) ).
fof(f9071,plain,
( spl17_739
<=> ! [X2,X0,X1] :
( sP0(sK10(powerset(powerset(cartesian_product2(X0,X1)))),X2)
| sP1(unordered_pair(singleton(sK8(sK10(powerset(powerset(cartesian_product2(X0,X1)))),X2)),unordered_pair(sK9(sK10(powerset(powerset(cartesian_product2(X0,X1)))),X2),sK8(sK10(powerset(powerset(cartesian_product2(X0,X1)))),X2)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_739])]) ).
fof(f3235,plain,
( spl17_339
<=> ! [X2,X0,X1] :
( sP0(sK10(powerset(powerset(cartesian_product2(X0,X1)))),X2)
| relation(unordered_pair(singleton(sK8(sK10(powerset(powerset(cartesian_product2(X0,X1)))),X2)),unordered_pair(sK9(sK10(powerset(powerset(cartesian_product2(X0,X1)))),X2),sK8(sK10(powerset(powerset(cartesian_product2(X0,X1)))),X2)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_339])]) ).
fof(f3246,plain,
( ! [X2,X0,X1] :
( sP0(sK10(powerset(powerset(cartesian_product2(X0,X1)))),X2)
| sP1(unordered_pair(singleton(sK8(sK10(powerset(powerset(cartesian_product2(X0,X1)))),X2)),unordered_pair(sK9(sK10(powerset(powerset(cartesian_product2(X0,X1)))),X2),sK8(sK10(powerset(powerset(cartesian_product2(X0,X1)))),X2)))) )
| ~ spl17_17
| ~ spl17_339 ),
inference(resolution,[],[f3236,f256]) ).
fof(f3236,plain,
( ! [X2,X0,X1] :
( relation(unordered_pair(singleton(sK8(sK10(powerset(powerset(cartesian_product2(X0,X1)))),X2)),unordered_pair(sK9(sK10(powerset(powerset(cartesian_product2(X0,X1)))),X2),sK8(sK10(powerset(powerset(cartesian_product2(X0,X1)))),X2))))
| sP0(sK10(powerset(powerset(cartesian_product2(X0,X1)))),X2) )
| ~ spl17_339 ),
inference(avatar_component_clause,[],[f3235]) ).
fof(f9069,plain,
( spl17_738
| ~ spl17_60
| ~ spl17_271 ),
inference(avatar_split_clause,[],[f2317,f2289,f504,f9067]) ).
fof(f9067,plain,
( spl17_738
<=> ! [X0,X1] :
( empty(sK6(powerset(X0)))
| element(unordered_pair(singleton(sK7(sK10(sK6(powerset(X0))),X1)),unordered_pair(sK8(sK10(sK6(powerset(X0))),X1),sK7(sK10(sK6(powerset(X0))),X1))),X0)
| empty(powerset(X0))
| sP0(sK10(sK6(powerset(X0))),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_738])]) ).
fof(f2317,plain,
( ! [X0,X1] :
( empty(sK6(powerset(X0)))
| element(unordered_pair(singleton(sK7(sK10(sK6(powerset(X0))),X1)),unordered_pair(sK8(sK10(sK6(powerset(X0))),X1),sK7(sK10(sK6(powerset(X0))),X1))),X0)
| empty(powerset(X0))
| sP0(sK10(sK6(powerset(X0))),X1) )
| ~ spl17_60
| ~ spl17_271 ),
inference(resolution,[],[f2290,f505]) ).
fof(f9065,plain,
( spl17_737
| ~ spl17_59
| ~ spl17_271 ),
inference(avatar_split_clause,[],[f2316,f2289,f500,f9063]) ).
fof(f9063,plain,
( spl17_737
<=> ! [X0,X1] :
( empty(sK6(powerset(X0)))
| element(unordered_pair(singleton(sK8(sK10(sK6(powerset(X0))),X1)),unordered_pair(sK9(sK10(sK6(powerset(X0))),X1),sK8(sK10(sK6(powerset(X0))),X1))),X0)
| empty(powerset(X0))
| sP0(sK10(sK6(powerset(X0))),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_737])]) ).
fof(f2316,plain,
( ! [X0,X1] :
( empty(sK6(powerset(X0)))
| element(unordered_pair(singleton(sK8(sK10(sK6(powerset(X0))),X1)),unordered_pair(sK9(sK10(sK6(powerset(X0))),X1),sK8(sK10(sK6(powerset(X0))),X1))),X0)
| empty(powerset(X0))
| sP0(sK10(sK6(powerset(X0))),X1) )
| ~ spl17_59
| ~ spl17_271 ),
inference(resolution,[],[f2290,f501]) ).
fof(f8469,plain,
( ~ spl17_2
| spl17_736
| ~ spl17_65
| ~ spl17_122
| ~ spl17_648 ),
inference(avatar_split_clause,[],[f7860,f7638,f973,f541,f8467,f184]) ).
fof(f8467,plain,
( spl17_736
<=> ! [X0] :
( ~ element(X0,sK16)
| ~ related(sK2,X0,X0)
| in(X0,sK16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_736])]) ).
fof(f973,plain,
( spl17_122
<=> ! [X2,X0,X1] :
( in(unordered_pair(singleton(X0),unordered_pair(X1,X0)),the_InternalRel(X2))
| ~ related(X2,X0,X1)
| ~ element(X1,the_carrier(X2))
| ~ element(X0,the_carrier(X2))
| ~ rel_str(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_122])]) ).
fof(f7860,plain,
( ! [X0] :
( ~ element(X0,sK16)
| in(X0,sK16)
| ~ related(sK2,X0,X0)
| ~ rel_str(sK2) )
| ~ spl17_65
| ~ spl17_122
| ~ spl17_648 ),
inference(forward_demodulation,[],[f7856,f543]) ).
fof(f7856,plain,
( ! [X0] :
( in(X0,sK16)
| ~ related(sK2,X0,X0)
| ~ element(X0,the_carrier(sK2))
| ~ rel_str(sK2) )
| ~ spl17_122
| ~ spl17_648 ),
inference(duplicate_literal_removal,[],[f7852]) ).
fof(f7852,plain,
( ! [X0] :
( in(X0,sK16)
| ~ related(sK2,X0,X0)
| ~ element(X0,the_carrier(sK2))
| ~ element(X0,the_carrier(sK2))
| ~ rel_str(sK2) )
| ~ spl17_122
| ~ spl17_648 ),
inference(resolution,[],[f7639,f974]) ).
fof(f974,plain,
( ! [X2,X0,X1] :
( in(unordered_pair(singleton(X0),unordered_pair(X1,X0)),the_InternalRel(X2))
| ~ related(X2,X0,X1)
| ~ element(X1,the_carrier(X2))
| ~ element(X0,the_carrier(X2))
| ~ rel_str(X2) )
| ~ spl17_122 ),
inference(avatar_component_clause,[],[f973]) ).
fof(f8420,plain,
( spl17_735
| ~ spl17_30
| ~ spl17_60
| ~ spl17_350 ),
inference(avatar_split_clause,[],[f3364,f3344,f504,f313,f8418]) ).
fof(f8418,plain,
( spl17_735
<=> ! [X2,X0,X1] :
( in(unordered_pair(singleton(sK7(X0,X1)),unordered_pair(sK9(X0,X1),sK7(X0,X1))),X0)
| ~ in(sK9(X0,X1),X2)
| ~ in(sK8(X0,X1),X2)
| ~ in(sK7(X0,X1),X2)
| ~ sP0(X0,X2)
| sP0(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_735])]) ).
fof(f3364,plain,
( ! [X2,X0,X1] :
( in(unordered_pair(singleton(sK7(X0,X1)),unordered_pair(sK9(X0,X1),sK7(X0,X1))),X0)
| ~ in(sK9(X0,X1),X2)
| ~ in(sK8(X0,X1),X2)
| ~ in(sK7(X0,X1),X2)
| ~ sP0(X0,X2)
| sP0(X0,X1) )
| ~ spl17_30
| ~ spl17_60
| ~ spl17_350 ),
inference(forward_demodulation,[],[f3363,f314]) ).
fof(f3363,plain,
( ! [X2,X0,X1] :
( in(unordered_pair(singleton(sK7(X0,X1)),unordered_pair(sK7(X0,X1),sK9(X0,X1))),X0)
| ~ in(sK9(X0,X1),X2)
| ~ in(sK8(X0,X1),X2)
| ~ in(sK7(X0,X1),X2)
| ~ sP0(X0,X2)
| sP0(X0,X1) )
| ~ spl17_60
| ~ spl17_350 ),
inference(duplicate_literal_removal,[],[f3351]) ).
fof(f3351,plain,
( ! [X2,X0,X1] :
( in(unordered_pair(singleton(sK7(X0,X1)),unordered_pair(sK7(X0,X1),sK9(X0,X1))),X0)
| ~ in(sK9(X0,X1),X2)
| ~ in(sK8(X0,X1),X2)
| ~ in(sK7(X0,X1),X2)
| ~ sP0(X0,X2)
| sP0(X0,X1)
| sP0(X0,X1) )
| ~ spl17_60
| ~ spl17_350 ),
inference(resolution,[],[f3345,f505]) ).
fof(f8399,plain,
( spl17_734
| ~ spl17_39
| ~ spl17_338 ),
inference(avatar_split_clause,[],[f3230,f3192,f355,f8397]) ).
fof(f8397,plain,
( spl17_734
<=> ! [X2,X0,X1] :
( sP0(X0,powerset(X1))
| sP0(sK9(X0,powerset(X1)),X2)
| empty(X1)
| in(unordered_pair(singleton(sK7(sK9(X0,powerset(X1)),X2)),unordered_pair(sK8(sK9(X0,powerset(X1)),X2),sK7(sK9(X0,powerset(X1)),X2))),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_734])]) ).
fof(f3230,plain,
( ! [X2,X0,X1] :
( sP0(X0,powerset(X1))
| sP0(sK9(X0,powerset(X1)),X2)
| empty(X1)
| in(unordered_pair(singleton(sK7(sK9(X0,powerset(X1)),X2)),unordered_pair(sK8(sK9(X0,powerset(X1)),X2),sK7(sK9(X0,powerset(X1)),X2))),X1) )
| ~ spl17_39
| ~ spl17_338 ),
inference(resolution,[],[f3193,f356]) ).
fof(f8395,plain,
( spl17_733
| ~ spl17_39
| ~ spl17_337 ),
inference(avatar_split_clause,[],[f3226,f3188,f355,f8393]) ).
fof(f8393,plain,
( spl17_733
<=> ! [X2,X0,X1] :
( sP0(X0,powerset(X1))
| sP0(sK9(X0,powerset(X1)),X2)
| empty(X1)
| in(unordered_pair(singleton(sK8(sK9(X0,powerset(X1)),X2)),unordered_pair(sK9(sK9(X0,powerset(X1)),X2),sK8(sK9(X0,powerset(X1)),X2))),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_733])]) ).
fof(f3226,plain,
( ! [X2,X0,X1] :
( sP0(X0,powerset(X1))
| sP0(sK9(X0,powerset(X1)),X2)
| empty(X1)
| in(unordered_pair(singleton(sK8(sK9(X0,powerset(X1)),X2)),unordered_pair(sK9(sK9(X0,powerset(X1)),X2),sK8(sK9(X0,powerset(X1)),X2))),X1) )
| ~ spl17_39
| ~ spl17_337 ),
inference(resolution,[],[f3189,f356]) ).
fof(f8391,plain,
( spl17_732
| ~ spl17_39
| ~ spl17_336 ),
inference(avatar_split_clause,[],[f3222,f3184,f355,f8389]) ).
fof(f8389,plain,
( spl17_732
<=> ! [X2,X0,X1] :
( sP0(X0,powerset(X1))
| sP0(sK8(X0,powerset(X1)),X2)
| empty(X1)
| in(unordered_pair(singleton(sK7(sK8(X0,powerset(X1)),X2)),unordered_pair(sK8(sK8(X0,powerset(X1)),X2),sK7(sK8(X0,powerset(X1)),X2))),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_732])]) ).
fof(f3222,plain,
( ! [X2,X0,X1] :
( sP0(X0,powerset(X1))
| sP0(sK8(X0,powerset(X1)),X2)
| empty(X1)
| in(unordered_pair(singleton(sK7(sK8(X0,powerset(X1)),X2)),unordered_pair(sK8(sK8(X0,powerset(X1)),X2),sK7(sK8(X0,powerset(X1)),X2))),X1) )
| ~ spl17_39
| ~ spl17_336 ),
inference(resolution,[],[f3185,f356]) ).
fof(f8387,plain,
( spl17_731
| ~ spl17_39
| ~ spl17_335 ),
inference(avatar_split_clause,[],[f3203,f3180,f355,f8385]) ).
fof(f8385,plain,
( spl17_731
<=> ! [X2,X0,X1] :
( sP0(X0,powerset(X1))
| sP0(sK8(X0,powerset(X1)),X2)
| empty(X1)
| in(unordered_pair(singleton(sK8(sK8(X0,powerset(X1)),X2)),unordered_pair(sK9(sK8(X0,powerset(X1)),X2),sK8(sK8(X0,powerset(X1)),X2))),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_731])]) ).
fof(f3203,plain,
( ! [X2,X0,X1] :
( sP0(X0,powerset(X1))
| sP0(sK8(X0,powerset(X1)),X2)
| empty(X1)
| in(unordered_pair(singleton(sK8(sK8(X0,powerset(X1)),X2)),unordered_pair(sK9(sK8(X0,powerset(X1)),X2),sK8(sK8(X0,powerset(X1)),X2))),X1) )
| ~ spl17_39
| ~ spl17_335 ),
inference(resolution,[],[f3181,f356]) ).
fof(f8383,plain,
( spl17_730
| ~ spl17_39
| ~ spl17_334 ),
inference(avatar_split_clause,[],[f3199,f3176,f355,f8381]) ).
fof(f8381,plain,
( spl17_730
<=> ! [X2,X0,X1] :
( sP0(X0,powerset(X1))
| sP0(sK7(X0,powerset(X1)),X2)
| empty(X1)
| in(unordered_pair(singleton(sK7(sK7(X0,powerset(X1)),X2)),unordered_pair(sK8(sK7(X0,powerset(X1)),X2),sK7(sK7(X0,powerset(X1)),X2))),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_730])]) ).
fof(f3199,plain,
( ! [X2,X0,X1] :
( sP0(X0,powerset(X1))
| sP0(sK7(X0,powerset(X1)),X2)
| empty(X1)
| in(unordered_pair(singleton(sK7(sK7(X0,powerset(X1)),X2)),unordered_pair(sK8(sK7(X0,powerset(X1)),X2),sK7(sK7(X0,powerset(X1)),X2))),X1) )
| ~ spl17_39
| ~ spl17_334 ),
inference(resolution,[],[f3177,f356]) ).
fof(f8379,plain,
( spl17_729
| ~ spl17_39
| ~ spl17_333 ),
inference(avatar_split_clause,[],[f3195,f3172,f355,f8377]) ).
fof(f8377,plain,
( spl17_729
<=> ! [X2,X0,X1] :
( sP0(X0,powerset(X1))
| sP0(sK7(X0,powerset(X1)),X2)
| empty(X1)
| in(unordered_pair(singleton(sK8(sK7(X0,powerset(X1)),X2)),unordered_pair(sK9(sK7(X0,powerset(X1)),X2),sK8(sK7(X0,powerset(X1)),X2))),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_729])]) ).
fof(f3195,plain,
( ! [X2,X0,X1] :
( sP0(X0,powerset(X1))
| sP0(sK7(X0,powerset(X1)),X2)
| empty(X1)
| in(unordered_pair(singleton(sK8(sK7(X0,powerset(X1)),X2)),unordered_pair(sK9(sK7(X0,powerset(X1)),X2),sK8(sK7(X0,powerset(X1)),X2))),X1) )
| ~ spl17_39
| ~ spl17_333 ),
inference(resolution,[],[f3173,f356]) ).
fof(f8375,plain,
( spl17_728
| ~ spl17_150
| ~ spl17_312 ),
inference(avatar_split_clause,[],[f2825,f2730,f1159,f8373]) ).
fof(f8373,plain,
( spl17_728
<=> ! [X2,X0,X1] :
( sP0(sK6(sK13(X0,X1)),X2)
| empty(sK13(X0,X1))
| element(unordered_pair(singleton(sK7(sK6(sK13(X0,X1)),X2)),unordered_pair(sK8(sK6(sK13(X0,X1)),X2),sK7(sK6(sK13(X0,X1)),X2))),cartesian_product2(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_728])]) ).
fof(f2825,plain,
( ! [X2,X0,X1] :
( sP0(sK6(sK13(X0,X1)),X2)
| empty(sK13(X0,X1))
| element(unordered_pair(singleton(sK7(sK6(sK13(X0,X1)),X2)),unordered_pair(sK8(sK6(sK13(X0,X1)),X2),sK7(sK6(sK13(X0,X1)),X2))),cartesian_product2(X0,X1)) )
| ~ spl17_150
| ~ spl17_312 ),
inference(resolution,[],[f2731,f1160]) ).
fof(f8371,plain,
( spl17_727
| ~ spl17_151
| ~ spl17_312 ),
inference(avatar_split_clause,[],[f2824,f2730,f1163,f8369]) ).
fof(f8369,plain,
( spl17_727
<=> ! [X2,X0,X1] :
( sP0(sK6(sK12(X0,X1)),X2)
| empty(sK12(X0,X1))
| element(unordered_pair(singleton(sK7(sK6(sK12(X0,X1)),X2)),unordered_pair(sK8(sK6(sK12(X0,X1)),X2),sK7(sK6(sK12(X0,X1)),X2))),cartesian_product2(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_727])]) ).
fof(f2824,plain,
( ! [X2,X0,X1] :
( sP0(sK6(sK12(X0,X1)),X2)
| empty(sK12(X0,X1))
| element(unordered_pair(singleton(sK7(sK6(sK12(X0,X1)),X2)),unordered_pair(sK8(sK6(sK12(X0,X1)),X2),sK7(sK6(sK12(X0,X1)),X2))),cartesian_product2(X0,X1)) )
| ~ spl17_151
| ~ spl17_312 ),
inference(resolution,[],[f2731,f1164]) ).
fof(f8367,plain,
( spl17_726
| ~ spl17_150
| ~ spl17_311 ),
inference(avatar_split_clause,[],[f2776,f2726,f1159,f8365]) ).
fof(f8365,plain,
( spl17_726
<=> ! [X2,X0,X1] :
( sP0(sK6(sK13(X0,X1)),X2)
| empty(sK13(X0,X1))
| element(unordered_pair(singleton(sK8(sK6(sK13(X0,X1)),X2)),unordered_pair(sK9(sK6(sK13(X0,X1)),X2),sK8(sK6(sK13(X0,X1)),X2))),cartesian_product2(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_726])]) ).
fof(f2776,plain,
( ! [X2,X0,X1] :
( sP0(sK6(sK13(X0,X1)),X2)
| empty(sK13(X0,X1))
| element(unordered_pair(singleton(sK8(sK6(sK13(X0,X1)),X2)),unordered_pair(sK9(sK6(sK13(X0,X1)),X2),sK8(sK6(sK13(X0,X1)),X2))),cartesian_product2(X0,X1)) )
| ~ spl17_150
| ~ spl17_311 ),
inference(resolution,[],[f2727,f1160]) ).
fof(f8363,plain,
( spl17_725
| ~ spl17_151
| ~ spl17_311 ),
inference(avatar_split_clause,[],[f2775,f2726,f1163,f8361]) ).
fof(f8361,plain,
( spl17_725
<=> ! [X2,X0,X1] :
( sP0(sK6(sK12(X0,X1)),X2)
| empty(sK12(X0,X1))
| element(unordered_pair(singleton(sK8(sK6(sK12(X0,X1)),X2)),unordered_pair(sK9(sK6(sK12(X0,X1)),X2),sK8(sK6(sK12(X0,X1)),X2))),cartesian_product2(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_725])]) ).
fof(f2775,plain,
( ! [X2,X0,X1] :
( sP0(sK6(sK12(X0,X1)),X2)
| empty(sK12(X0,X1))
| element(unordered_pair(singleton(sK8(sK6(sK12(X0,X1)),X2)),unordered_pair(sK9(sK6(sK12(X0,X1)),X2),sK8(sK6(sK12(X0,X1)),X2))),cartesian_product2(X0,X1)) )
| ~ spl17_151
| ~ spl17_311 ),
inference(resolution,[],[f2727,f1164]) ).
fof(f8357,plain,
( spl17_724
| ~ spl17_266
| ~ spl17_284 ),
inference(avatar_split_clause,[],[f2470,f2409,f2147,f8355]) ).
fof(f8355,plain,
( spl17_724
<=> ! [X2,X0,X1] :
( element(sK9(X0,sK10(powerset(sK9(X1,sK10(powerset(powerset(X2))))))),X2)
| sP0(X1,sK10(powerset(powerset(X2))))
| empty(sK9(X1,sK10(powerset(powerset(X2)))))
| sP0(X0,sK10(powerset(sK9(X1,sK10(powerset(powerset(X2))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_724])]) ).
fof(f2470,plain,
( ! [X2,X0,X1] :
( element(sK9(X0,sK10(powerset(sK9(X1,sK10(powerset(powerset(X2))))))),X2)
| sP0(X1,sK10(powerset(powerset(X2))))
| empty(sK9(X1,sK10(powerset(powerset(X2)))))
| sP0(X0,sK10(powerset(sK9(X1,sK10(powerset(powerset(X2))))))) )
| ~ spl17_266
| ~ spl17_284 ),
inference(resolution,[],[f2410,f2148]) ).
fof(f8353,plain,
( spl17_723
| ~ spl17_265
| ~ spl17_284 ),
inference(avatar_split_clause,[],[f2467,f2409,f2143,f8351]) ).
fof(f8351,plain,
( spl17_723
<=> ! [X2,X0,X1] :
( element(sK8(X0,sK10(powerset(sK9(X1,sK10(powerset(powerset(X2))))))),X2)
| sP0(X1,sK10(powerset(powerset(X2))))
| empty(sK9(X1,sK10(powerset(powerset(X2)))))
| sP0(X0,sK10(powerset(sK9(X1,sK10(powerset(powerset(X2))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_723])]) ).
fof(f2467,plain,
( ! [X2,X0,X1] :
( element(sK8(X0,sK10(powerset(sK9(X1,sK10(powerset(powerset(X2))))))),X2)
| sP0(X1,sK10(powerset(powerset(X2))))
| empty(sK9(X1,sK10(powerset(powerset(X2)))))
| sP0(X0,sK10(powerset(sK9(X1,sK10(powerset(powerset(X2))))))) )
| ~ spl17_265
| ~ spl17_284 ),
inference(resolution,[],[f2410,f2144]) ).
fof(f8349,plain,
( spl17_722
| ~ spl17_264
| ~ spl17_284 ),
inference(avatar_split_clause,[],[f2464,f2409,f2139,f8347]) ).
fof(f8347,plain,
( spl17_722
<=> ! [X2,X0,X1] :
( element(sK7(X0,sK10(powerset(sK9(X1,sK10(powerset(powerset(X2))))))),X2)
| sP0(X1,sK10(powerset(powerset(X2))))
| empty(sK9(X1,sK10(powerset(powerset(X2)))))
| sP0(X0,sK10(powerset(sK9(X1,sK10(powerset(powerset(X2))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_722])]) ).
fof(f2464,plain,
( ! [X2,X0,X1] :
( element(sK7(X0,sK10(powerset(sK9(X1,sK10(powerset(powerset(X2))))))),X2)
| sP0(X1,sK10(powerset(powerset(X2))))
| empty(sK9(X1,sK10(powerset(powerset(X2)))))
| sP0(X0,sK10(powerset(sK9(X1,sK10(powerset(powerset(X2))))))) )
| ~ spl17_264
| ~ spl17_284 ),
inference(resolution,[],[f2410,f2140]) ).
fof(f8345,plain,
( spl17_721
| ~ spl17_266
| ~ spl17_282 ),
inference(avatar_split_clause,[],[f2455,f2401,f2147,f8343]) ).
fof(f8343,plain,
( spl17_721
<=> ! [X2,X0,X1] :
( element(sK9(X0,sK10(powerset(sK8(X1,sK10(powerset(powerset(X2))))))),X2)
| sP0(X1,sK10(powerset(powerset(X2))))
| empty(sK8(X1,sK10(powerset(powerset(X2)))))
| sP0(X0,sK10(powerset(sK8(X1,sK10(powerset(powerset(X2))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_721])]) ).
fof(f2455,plain,
( ! [X2,X0,X1] :
( element(sK9(X0,sK10(powerset(sK8(X1,sK10(powerset(powerset(X2))))))),X2)
| sP0(X1,sK10(powerset(powerset(X2))))
| empty(sK8(X1,sK10(powerset(powerset(X2)))))
| sP0(X0,sK10(powerset(sK8(X1,sK10(powerset(powerset(X2))))))) )
| ~ spl17_266
| ~ spl17_282 ),
inference(resolution,[],[f2402,f2148]) ).
fof(f8341,plain,
( spl17_720
| ~ spl17_265
| ~ spl17_282 ),
inference(avatar_split_clause,[],[f2452,f2401,f2143,f8339]) ).
fof(f8339,plain,
( spl17_720
<=> ! [X2,X0,X1] :
( element(sK8(X0,sK10(powerset(sK8(X1,sK10(powerset(powerset(X2))))))),X2)
| sP0(X1,sK10(powerset(powerset(X2))))
| empty(sK8(X1,sK10(powerset(powerset(X2)))))
| sP0(X0,sK10(powerset(sK8(X1,sK10(powerset(powerset(X2))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_720])]) ).
fof(f2452,plain,
( ! [X2,X0,X1] :
( element(sK8(X0,sK10(powerset(sK8(X1,sK10(powerset(powerset(X2))))))),X2)
| sP0(X1,sK10(powerset(powerset(X2))))
| empty(sK8(X1,sK10(powerset(powerset(X2)))))
| sP0(X0,sK10(powerset(sK8(X1,sK10(powerset(powerset(X2))))))) )
| ~ spl17_265
| ~ spl17_282 ),
inference(resolution,[],[f2402,f2144]) ).
fof(f8337,plain,
( spl17_719
| ~ spl17_264
| ~ spl17_282 ),
inference(avatar_split_clause,[],[f2449,f2401,f2139,f8335]) ).
fof(f8335,plain,
( spl17_719
<=> ! [X2,X0,X1] :
( element(sK7(X0,sK10(powerset(sK8(X1,sK10(powerset(powerset(X2))))))),X2)
| sP0(X1,sK10(powerset(powerset(X2))))
| empty(sK8(X1,sK10(powerset(powerset(X2)))))
| sP0(X0,sK10(powerset(sK8(X1,sK10(powerset(powerset(X2))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_719])]) ).
fof(f2449,plain,
( ! [X2,X0,X1] :
( element(sK7(X0,sK10(powerset(sK8(X1,sK10(powerset(powerset(X2))))))),X2)
| sP0(X1,sK10(powerset(powerset(X2))))
| empty(sK8(X1,sK10(powerset(powerset(X2)))))
| sP0(X0,sK10(powerset(sK8(X1,sK10(powerset(powerset(X2))))))) )
| ~ spl17_264
| ~ spl17_282 ),
inference(resolution,[],[f2402,f2140]) ).
fof(f8333,plain,
( spl17_718
| ~ spl17_266
| ~ spl17_280 ),
inference(avatar_split_clause,[],[f2440,f2393,f2147,f8331]) ).
fof(f8331,plain,
( spl17_718
<=> ! [X2,X0,X1] :
( element(sK9(X0,sK10(powerset(sK7(X1,sK10(powerset(powerset(X2))))))),X2)
| sP0(X1,sK10(powerset(powerset(X2))))
| empty(sK7(X1,sK10(powerset(powerset(X2)))))
| sP0(X0,sK10(powerset(sK7(X1,sK10(powerset(powerset(X2))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_718])]) ).
fof(f2440,plain,
( ! [X2,X0,X1] :
( element(sK9(X0,sK10(powerset(sK7(X1,sK10(powerset(powerset(X2))))))),X2)
| sP0(X1,sK10(powerset(powerset(X2))))
| empty(sK7(X1,sK10(powerset(powerset(X2)))))
| sP0(X0,sK10(powerset(sK7(X1,sK10(powerset(powerset(X2))))))) )
| ~ spl17_266
| ~ spl17_280 ),
inference(resolution,[],[f2394,f2148]) ).
fof(f8329,plain,
( spl17_717
| ~ spl17_265
| ~ spl17_280 ),
inference(avatar_split_clause,[],[f2437,f2393,f2143,f8327]) ).
fof(f8327,plain,
( spl17_717
<=> ! [X2,X0,X1] :
( element(sK8(X0,sK10(powerset(sK7(X1,sK10(powerset(powerset(X2))))))),X2)
| sP0(X1,sK10(powerset(powerset(X2))))
| empty(sK7(X1,sK10(powerset(powerset(X2)))))
| sP0(X0,sK10(powerset(sK7(X1,sK10(powerset(powerset(X2))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_717])]) ).
fof(f2437,plain,
( ! [X2,X0,X1] :
( element(sK8(X0,sK10(powerset(sK7(X1,sK10(powerset(powerset(X2))))))),X2)
| sP0(X1,sK10(powerset(powerset(X2))))
| empty(sK7(X1,sK10(powerset(powerset(X2)))))
| sP0(X0,sK10(powerset(sK7(X1,sK10(powerset(powerset(X2))))))) )
| ~ spl17_265
| ~ spl17_280 ),
inference(resolution,[],[f2394,f2144]) ).
fof(f8325,plain,
( spl17_716
| ~ spl17_264
| ~ spl17_280 ),
inference(avatar_split_clause,[],[f2434,f2393,f2139,f8323]) ).
fof(f8323,plain,
( spl17_716
<=> ! [X2,X0,X1] :
( element(sK7(X0,sK10(powerset(sK7(X1,sK10(powerset(powerset(X2))))))),X2)
| sP0(X1,sK10(powerset(powerset(X2))))
| empty(sK7(X1,sK10(powerset(powerset(X2)))))
| sP0(X0,sK10(powerset(sK7(X1,sK10(powerset(powerset(X2))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_716])]) ).
fof(f2434,plain,
( ! [X2,X0,X1] :
( element(sK7(X0,sK10(powerset(sK7(X1,sK10(powerset(powerset(X2))))))),X2)
| sP0(X1,sK10(powerset(powerset(X2))))
| empty(sK7(X1,sK10(powerset(powerset(X2)))))
| sP0(X0,sK10(powerset(sK7(X1,sK10(powerset(powerset(X2))))))) )
| ~ spl17_264
| ~ spl17_280 ),
inference(resolution,[],[f2394,f2140]) ).
fof(f8315,plain,
( ~ spl17_159
| spl17_715
| ~ spl17_34
| ~ spl17_704 ),
inference(avatar_split_clause,[],[f8256,f8211,f335,f8313,f1219]) ).
fof(f1219,plain,
( spl17_159
<=> sP1(the_InternalRel(sK2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_159])]) ).
fof(f8313,plain,
( spl17_715
<=> ! [X0] : is_transitive_in(the_InternalRel(sK2),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_715])]) ).
fof(f8211,plain,
( spl17_704
<=> ! [X0] : sP0(the_InternalRel(sK2),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_704])]) ).
fof(f8256,plain,
( ! [X0] :
( is_transitive_in(the_InternalRel(sK2),X0)
| ~ sP1(the_InternalRel(sK2)) )
| ~ spl17_34
| ~ spl17_704 ),
inference(resolution,[],[f8212,f336]) ).
fof(f8212,plain,
( ! [X0] : sP0(the_InternalRel(sK2),X0)
| ~ spl17_704 ),
inference(avatar_component_clause,[],[f8211]) ).
fof(f8253,plain,
( spl17_714
| ~ spl17_95
| ~ spl17_321 ),
inference(avatar_split_clause,[],[f2948,f2873,f765,f8251]) ).
fof(f8251,plain,
( spl17_714
<=> ! [X0,X1] :
( empty(sK6(X0))
| sP0(sK10(powerset(sK6(X0))),X1)
| element(unordered_pair(singleton(sK7(sK10(powerset(sK6(X0))),X1)),unordered_pair(sK8(sK10(powerset(sK6(X0))),X1),sK7(sK10(powerset(sK6(X0))),X1))),X0)
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_714])]) ).
fof(f765,plain,
( spl17_95
<=> ! [X0,X1] :
( element(X0,X1)
| ~ in(X0,sK6(X1))
| empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_95])]) ).
fof(f2948,plain,
( ! [X0,X1] :
( empty(sK6(X0))
| sP0(sK10(powerset(sK6(X0))),X1)
| element(unordered_pair(singleton(sK7(sK10(powerset(sK6(X0))),X1)),unordered_pair(sK8(sK10(powerset(sK6(X0))),X1),sK7(sK10(powerset(sK6(X0))),X1))),X0)
| empty(X0) )
| ~ spl17_95
| ~ spl17_321 ),
inference(resolution,[],[f2874,f766]) ).
fof(f766,plain,
( ! [X0,X1] :
( ~ in(X0,sK6(X1))
| element(X0,X1)
| empty(X1) )
| ~ spl17_95 ),
inference(avatar_component_clause,[],[f765]) ).
fof(f8249,plain,
( spl17_713
| ~ spl17_95
| ~ spl17_320 ),
inference(avatar_split_clause,[],[f2897,f2869,f765,f8247]) ).
fof(f8247,plain,
( spl17_713
<=> ! [X0,X1] :
( empty(sK6(X0))
| sP0(sK10(powerset(sK6(X0))),X1)
| element(unordered_pair(singleton(sK8(sK10(powerset(sK6(X0))),X1)),unordered_pair(sK9(sK10(powerset(sK6(X0))),X1),sK8(sK10(powerset(sK6(X0))),X1))),X0)
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_713])]) ).
fof(f2897,plain,
( ! [X0,X1] :
( empty(sK6(X0))
| sP0(sK10(powerset(sK6(X0))),X1)
| element(unordered_pair(singleton(sK8(sK10(powerset(sK6(X0))),X1)),unordered_pair(sK9(sK10(powerset(sK6(X0))),X1),sK8(sK10(powerset(sK6(X0))),X1))),X0)
| empty(X0) )
| ~ spl17_95
| ~ spl17_320 ),
inference(resolution,[],[f2870,f766]) ).
fof(f8245,plain,
( spl17_712
| ~ spl17_266
| ~ spl17_292 ),
inference(avatar_split_clause,[],[f2611,f2530,f2147,f8243]) ).
fof(f8243,plain,
( spl17_712
<=> ! [X2,X0,X1] :
( sP0(X0,sK6(powerset(X1)))
| element(sK9(X2,sK10(powerset(sK9(X0,sK6(powerset(X1)))))),X1)
| empty(powerset(X1))
| empty(sK9(X0,sK6(powerset(X1))))
| sP0(X2,sK10(powerset(sK9(X0,sK6(powerset(X1)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_712])]) ).
fof(f2611,plain,
( ! [X2,X0,X1] :
( sP0(X0,sK6(powerset(X1)))
| element(sK9(X2,sK10(powerset(sK9(X0,sK6(powerset(X1)))))),X1)
| empty(powerset(X1))
| empty(sK9(X0,sK6(powerset(X1))))
| sP0(X2,sK10(powerset(sK9(X0,sK6(powerset(X1)))))) )
| ~ spl17_266
| ~ spl17_292 ),
inference(resolution,[],[f2531,f2148]) ).
fof(f8241,plain,
( spl17_711
| ~ spl17_265
| ~ spl17_292 ),
inference(avatar_split_clause,[],[f2608,f2530,f2143,f8239]) ).
fof(f8239,plain,
( spl17_711
<=> ! [X2,X0,X1] :
( sP0(X0,sK6(powerset(X1)))
| element(sK8(X2,sK10(powerset(sK9(X0,sK6(powerset(X1)))))),X1)
| empty(powerset(X1))
| empty(sK9(X0,sK6(powerset(X1))))
| sP0(X2,sK10(powerset(sK9(X0,sK6(powerset(X1)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_711])]) ).
fof(f2608,plain,
( ! [X2,X0,X1] :
( sP0(X0,sK6(powerset(X1)))
| element(sK8(X2,sK10(powerset(sK9(X0,sK6(powerset(X1)))))),X1)
| empty(powerset(X1))
| empty(sK9(X0,sK6(powerset(X1))))
| sP0(X2,sK10(powerset(sK9(X0,sK6(powerset(X1)))))) )
| ~ spl17_265
| ~ spl17_292 ),
inference(resolution,[],[f2531,f2144]) ).
fof(f8237,plain,
( spl17_710
| ~ spl17_264
| ~ spl17_292 ),
inference(avatar_split_clause,[],[f2605,f2530,f2139,f8235]) ).
fof(f8235,plain,
( spl17_710
<=> ! [X2,X0,X1] :
( sP0(X0,sK6(powerset(X1)))
| element(sK7(X2,sK10(powerset(sK9(X0,sK6(powerset(X1)))))),X1)
| empty(powerset(X1))
| empty(sK9(X0,sK6(powerset(X1))))
| sP0(X2,sK10(powerset(sK9(X0,sK6(powerset(X1)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_710])]) ).
fof(f2605,plain,
( ! [X2,X0,X1] :
( sP0(X0,sK6(powerset(X1)))
| element(sK7(X2,sK10(powerset(sK9(X0,sK6(powerset(X1)))))),X1)
| empty(powerset(X1))
| empty(sK9(X0,sK6(powerset(X1))))
| sP0(X2,sK10(powerset(sK9(X0,sK6(powerset(X1)))))) )
| ~ spl17_264
| ~ spl17_292 ),
inference(resolution,[],[f2531,f2140]) ).
fof(f8233,plain,
( spl17_709
| ~ spl17_266
| ~ spl17_291 ),
inference(avatar_split_clause,[],[f2597,f2526,f2147,f8231]) ).
fof(f8231,plain,
( spl17_709
<=> ! [X2,X0,X1] :
( sP0(X0,sK6(powerset(X1)))
| element(sK9(X2,sK10(powerset(sK8(X0,sK6(powerset(X1)))))),X1)
| empty(powerset(X1))
| empty(sK8(X0,sK6(powerset(X1))))
| sP0(X2,sK10(powerset(sK8(X0,sK6(powerset(X1)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_709])]) ).
fof(f2597,plain,
( ! [X2,X0,X1] :
( sP0(X0,sK6(powerset(X1)))
| element(sK9(X2,sK10(powerset(sK8(X0,sK6(powerset(X1)))))),X1)
| empty(powerset(X1))
| empty(sK8(X0,sK6(powerset(X1))))
| sP0(X2,sK10(powerset(sK8(X0,sK6(powerset(X1)))))) )
| ~ spl17_266
| ~ spl17_291 ),
inference(resolution,[],[f2527,f2148]) ).
fof(f8229,plain,
( spl17_708
| ~ spl17_265
| ~ spl17_291 ),
inference(avatar_split_clause,[],[f2594,f2526,f2143,f8227]) ).
fof(f8227,plain,
( spl17_708
<=> ! [X2,X0,X1] :
( sP0(X0,sK6(powerset(X1)))
| element(sK8(X2,sK10(powerset(sK8(X0,sK6(powerset(X1)))))),X1)
| empty(powerset(X1))
| empty(sK8(X0,sK6(powerset(X1))))
| sP0(X2,sK10(powerset(sK8(X0,sK6(powerset(X1)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_708])]) ).
fof(f2594,plain,
( ! [X2,X0,X1] :
( sP0(X0,sK6(powerset(X1)))
| element(sK8(X2,sK10(powerset(sK8(X0,sK6(powerset(X1)))))),X1)
| empty(powerset(X1))
| empty(sK8(X0,sK6(powerset(X1))))
| sP0(X2,sK10(powerset(sK8(X0,sK6(powerset(X1)))))) )
| ~ spl17_265
| ~ spl17_291 ),
inference(resolution,[],[f2527,f2144]) ).
fof(f8225,plain,
( spl17_707
| ~ spl17_264
| ~ spl17_291 ),
inference(avatar_split_clause,[],[f2591,f2526,f2139,f8223]) ).
fof(f8223,plain,
( spl17_707
<=> ! [X2,X0,X1] :
( sP0(X0,sK6(powerset(X1)))
| element(sK7(X2,sK10(powerset(sK8(X0,sK6(powerset(X1)))))),X1)
| empty(powerset(X1))
| empty(sK8(X0,sK6(powerset(X1))))
| sP0(X2,sK10(powerset(sK8(X0,sK6(powerset(X1)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_707])]) ).
fof(f2591,plain,
( ! [X2,X0,X1] :
( sP0(X0,sK6(powerset(X1)))
| element(sK7(X2,sK10(powerset(sK8(X0,sK6(powerset(X1)))))),X1)
| empty(powerset(X1))
| empty(sK8(X0,sK6(powerset(X1))))
| sP0(X2,sK10(powerset(sK8(X0,sK6(powerset(X1)))))) )
| ~ spl17_264
| ~ spl17_291 ),
inference(resolution,[],[f2527,f2140]) ).
fof(f8221,plain,
( spl17_706
| ~ spl17_266
| ~ spl17_290 ),
inference(avatar_split_clause,[],[f2583,f2522,f2147,f8219]) ).
fof(f8219,plain,
( spl17_706
<=> ! [X2,X0,X1] :
( sP0(X0,sK6(powerset(X1)))
| element(sK9(X2,sK10(powerset(sK7(X0,sK6(powerset(X1)))))),X1)
| empty(powerset(X1))
| empty(sK7(X0,sK6(powerset(X1))))
| sP0(X2,sK10(powerset(sK7(X0,sK6(powerset(X1)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_706])]) ).
fof(f2583,plain,
( ! [X2,X0,X1] :
( sP0(X0,sK6(powerset(X1)))
| element(sK9(X2,sK10(powerset(sK7(X0,sK6(powerset(X1)))))),X1)
| empty(powerset(X1))
| empty(sK7(X0,sK6(powerset(X1))))
| sP0(X2,sK10(powerset(sK7(X0,sK6(powerset(X1)))))) )
| ~ spl17_266
| ~ spl17_290 ),
inference(resolution,[],[f2523,f2148]) ).
fof(f8217,plain,
( spl17_705
| ~ spl17_265
| ~ spl17_290 ),
inference(avatar_split_clause,[],[f2580,f2522,f2143,f8215]) ).
fof(f8215,plain,
( spl17_705
<=> ! [X2,X0,X1] :
( sP0(X0,sK6(powerset(X1)))
| element(sK8(X2,sK10(powerset(sK7(X0,sK6(powerset(X1)))))),X1)
| empty(powerset(X1))
| empty(sK7(X0,sK6(powerset(X1))))
| sP0(X2,sK10(powerset(sK7(X0,sK6(powerset(X1)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_705])]) ).
fof(f2580,plain,
( ! [X2,X0,X1] :
( sP0(X0,sK6(powerset(X1)))
| element(sK8(X2,sK10(powerset(sK7(X0,sK6(powerset(X1)))))),X1)
| empty(powerset(X1))
| empty(sK7(X0,sK6(powerset(X1))))
| sP0(X2,sK10(powerset(sK7(X0,sK6(powerset(X1)))))) )
| ~ spl17_265
| ~ spl17_290 ),
inference(resolution,[],[f2523,f2144]) ).
fof(f8213,plain,
( spl17_704
| ~ spl17_72
| ~ spl17_687 ),
inference(avatar_split_clause,[],[f8155,f8062,f578,f8211]) ).
fof(f8062,plain,
( spl17_687
<=> ! [X0] :
( in(sK8(the_InternalRel(sK2),X0),sK16)
| sP0(the_InternalRel(sK2),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_687])]) ).
fof(f8155,plain,
( ! [X0] : sP0(the_InternalRel(sK2),X0)
| ~ spl17_72
| ~ spl17_687 ),
inference(resolution,[],[f8063,f579]) ).
fof(f8063,plain,
( ! [X0] :
( in(sK8(the_InternalRel(sK2),X0),sK16)
| sP0(the_InternalRel(sK2),X0) )
| ~ spl17_687 ),
inference(avatar_component_clause,[],[f8062]) ).
fof(f8209,plain,
( spl17_703
| ~ spl17_264
| ~ spl17_290 ),
inference(avatar_split_clause,[],[f2577,f2522,f2139,f8207]) ).
fof(f8207,plain,
( spl17_703
<=> ! [X2,X0,X1] :
( sP0(X0,sK6(powerset(X1)))
| element(sK7(X2,sK10(powerset(sK7(X0,sK6(powerset(X1)))))),X1)
| empty(powerset(X1))
| empty(sK7(X0,sK6(powerset(X1))))
| sP0(X2,sK10(powerset(sK7(X0,sK6(powerset(X1)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_703])]) ).
fof(f2577,plain,
( ! [X2,X0,X1] :
( sP0(X0,sK6(powerset(X1)))
| element(sK7(X2,sK10(powerset(sK7(X0,sK6(powerset(X1)))))),X1)
| empty(powerset(X1))
| empty(sK7(X0,sK6(powerset(X1))))
| sP0(X2,sK10(powerset(sK7(X0,sK6(powerset(X1)))))) )
| ~ spl17_264
| ~ spl17_290 ),
inference(resolution,[],[f2523,f2140]) ).
fof(f8129,plain,
( spl17_702
| ~ spl17_92
| ~ spl17_312 ),
inference(avatar_split_clause,[],[f2818,f2730,f733,f8127]) ).
fof(f8127,plain,
( spl17_702
<=> ! [X0,X1] :
( sP0(sK6(sK10(powerset(X0))),X1)
| empty(sK10(powerset(X0)))
| element(unordered_pair(singleton(sK7(sK6(sK10(powerset(X0))),X1)),unordered_pair(sK8(sK6(sK10(powerset(X0))),X1),sK7(sK6(sK10(powerset(X0))),X1))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_702])]) ).
fof(f2818,plain,
( ! [X0,X1] :
( sP0(sK6(sK10(powerset(X0))),X1)
| empty(sK10(powerset(X0)))
| element(unordered_pair(singleton(sK7(sK6(sK10(powerset(X0))),X1)),unordered_pair(sK8(sK6(sK10(powerset(X0))),X1),sK7(sK6(sK10(powerset(X0))),X1))),X0) )
| ~ spl17_92
| ~ spl17_312 ),
inference(resolution,[],[f2731,f734]) ).
fof(f8125,plain,
( spl17_701
| ~ spl17_92
| ~ spl17_311 ),
inference(avatar_split_clause,[],[f2769,f2726,f733,f8123]) ).
fof(f8123,plain,
( spl17_701
<=> ! [X0,X1] :
( sP0(sK6(sK10(powerset(X0))),X1)
| empty(sK10(powerset(X0)))
| element(unordered_pair(singleton(sK8(sK6(sK10(powerset(X0))),X1)),unordered_pair(sK9(sK6(sK10(powerset(X0))),X1),sK8(sK6(sK10(powerset(X0))),X1))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_701])]) ).
fof(f2769,plain,
( ! [X0,X1] :
( sP0(sK6(sK10(powerset(X0))),X1)
| empty(sK10(powerset(X0)))
| element(unordered_pair(singleton(sK8(sK6(sK10(powerset(X0))),X1)),unordered_pair(sK9(sK6(sK10(powerset(X0))),X1),sK8(sK6(sK10(powerset(X0))),X1))),X0) )
| ~ spl17_92
| ~ spl17_311 ),
inference(resolution,[],[f2727,f734]) ).
fof(f8121,plain,
( spl17_700
| ~ spl17_241
| ~ spl17_284 ),
inference(avatar_split_clause,[],[f2469,f2409,f1933,f8119]) ).
fof(f8119,plain,
( spl17_700
<=> ! [X2,X0,X1] :
( element(sK9(X0,sK6(sK9(X1,sK10(powerset(powerset(X2)))))),X2)
| sP0(X1,sK10(powerset(powerset(X2))))
| sP0(X0,sK6(sK9(X1,sK10(powerset(powerset(X2))))))
| empty(sK9(X1,sK10(powerset(powerset(X2))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_700])]) ).
fof(f2469,plain,
( ! [X2,X0,X1] :
( element(sK9(X0,sK6(sK9(X1,sK10(powerset(powerset(X2)))))),X2)
| sP0(X1,sK10(powerset(powerset(X2))))
| sP0(X0,sK6(sK9(X1,sK10(powerset(powerset(X2))))))
| empty(sK9(X1,sK10(powerset(powerset(X2))))) )
| ~ spl17_241
| ~ spl17_284 ),
inference(resolution,[],[f2410,f1934]) ).
fof(f8117,plain,
( spl17_699
| ~ spl17_240
| ~ spl17_284 ),
inference(avatar_split_clause,[],[f2466,f2409,f1929,f8115]) ).
fof(f8115,plain,
( spl17_699
<=> ! [X2,X0,X1] :
( element(sK8(X0,sK6(sK9(X1,sK10(powerset(powerset(X2)))))),X2)
| sP0(X1,sK10(powerset(powerset(X2))))
| sP0(X0,sK6(sK9(X1,sK10(powerset(powerset(X2))))))
| empty(sK9(X1,sK10(powerset(powerset(X2))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_699])]) ).
fof(f2466,plain,
( ! [X2,X0,X1] :
( element(sK8(X0,sK6(sK9(X1,sK10(powerset(powerset(X2)))))),X2)
| sP0(X1,sK10(powerset(powerset(X2))))
| sP0(X0,sK6(sK9(X1,sK10(powerset(powerset(X2))))))
| empty(sK9(X1,sK10(powerset(powerset(X2))))) )
| ~ spl17_240
| ~ spl17_284 ),
inference(resolution,[],[f2410,f1930]) ).
fof(f8113,plain,
( spl17_698
| ~ spl17_239
| ~ spl17_284 ),
inference(avatar_split_clause,[],[f2463,f2409,f1925,f8111]) ).
fof(f8111,plain,
( spl17_698
<=> ! [X2,X0,X1] :
( element(sK7(X0,sK6(sK9(X1,sK10(powerset(powerset(X2)))))),X2)
| sP0(X1,sK10(powerset(powerset(X2))))
| sP0(X0,sK6(sK9(X1,sK10(powerset(powerset(X2))))))
| empty(sK9(X1,sK10(powerset(powerset(X2))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_698])]) ).
fof(f2463,plain,
( ! [X2,X0,X1] :
( element(sK7(X0,sK6(sK9(X1,sK10(powerset(powerset(X2)))))),X2)
| sP0(X1,sK10(powerset(powerset(X2))))
| sP0(X0,sK6(sK9(X1,sK10(powerset(powerset(X2))))))
| empty(sK9(X1,sK10(powerset(powerset(X2))))) )
| ~ spl17_239
| ~ spl17_284 ),
inference(resolution,[],[f2410,f1926]) ).
fof(f8109,plain,
( spl17_697
| ~ spl17_60
| ~ spl17_663 ),
inference(avatar_split_clause,[],[f8001,f7742,f504,f8107]) ).
fof(f8107,plain,
( spl17_697
<=> ! [X0] :
( in(sK7(the_InternalRel(sK2),X0),sK16)
| sP0(the_InternalRel(sK2),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_697])]) ).
fof(f8001,plain,
( ! [X0] :
( in(sK7(the_InternalRel(sK2),X0),sK16)
| sP0(the_InternalRel(sK2),X0) )
| ~ spl17_60
| ~ spl17_663 ),
inference(resolution,[],[f7743,f505]) ).
fof(f8105,plain,
( spl17_696
| ~ spl17_229
| ~ spl17_284 ),
inference(avatar_split_clause,[],[f2461,f2409,f1885,f8103]) ).
fof(f8103,plain,
( spl17_696
<=> ! [X0,X1] :
( element(sK10(sK10(powerset(sK9(X0,sK10(powerset(powerset(X1))))))),X1)
| sP0(X0,sK10(powerset(powerset(X1))))
| empty(sK9(X0,sK10(powerset(powerset(X1)))))
| empty(sK10(powerset(sK9(X0,sK10(powerset(powerset(X1))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_696])]) ).
fof(f2461,plain,
( ! [X0,X1] :
( element(sK10(sK10(powerset(sK9(X0,sK10(powerset(powerset(X1))))))),X1)
| sP0(X0,sK10(powerset(powerset(X1))))
| empty(sK9(X0,sK10(powerset(powerset(X1)))))
| empty(sK10(powerset(sK9(X0,sK10(powerset(powerset(X1))))))) )
| ~ spl17_229
| ~ spl17_284 ),
inference(resolution,[],[f2410,f1886]) ).
fof(f8101,plain,
( spl17_695
| ~ spl17_241
| ~ spl17_282 ),
inference(avatar_split_clause,[],[f2454,f2401,f1933,f8099]) ).
fof(f8099,plain,
( spl17_695
<=> ! [X2,X0,X1] :
( element(sK9(X0,sK6(sK8(X1,sK10(powerset(powerset(X2)))))),X2)
| sP0(X1,sK10(powerset(powerset(X2))))
| sP0(X0,sK6(sK8(X1,sK10(powerset(powerset(X2))))))
| empty(sK8(X1,sK10(powerset(powerset(X2))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_695])]) ).
fof(f2454,plain,
( ! [X2,X0,X1] :
( element(sK9(X0,sK6(sK8(X1,sK10(powerset(powerset(X2)))))),X2)
| sP0(X1,sK10(powerset(powerset(X2))))
| sP0(X0,sK6(sK8(X1,sK10(powerset(powerset(X2))))))
| empty(sK8(X1,sK10(powerset(powerset(X2))))) )
| ~ spl17_241
| ~ spl17_282 ),
inference(resolution,[],[f2402,f1934]) ).
fof(f8097,plain,
( spl17_694
| ~ spl17_240
| ~ spl17_282 ),
inference(avatar_split_clause,[],[f2451,f2401,f1929,f8095]) ).
fof(f8095,plain,
( spl17_694
<=> ! [X2,X0,X1] :
( element(sK8(X0,sK6(sK8(X1,sK10(powerset(powerset(X2)))))),X2)
| sP0(X1,sK10(powerset(powerset(X2))))
| sP0(X0,sK6(sK8(X1,sK10(powerset(powerset(X2))))))
| empty(sK8(X1,sK10(powerset(powerset(X2))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_694])]) ).
fof(f2451,plain,
( ! [X2,X0,X1] :
( element(sK8(X0,sK6(sK8(X1,sK10(powerset(powerset(X2)))))),X2)
| sP0(X1,sK10(powerset(powerset(X2))))
| sP0(X0,sK6(sK8(X1,sK10(powerset(powerset(X2))))))
| empty(sK8(X1,sK10(powerset(powerset(X2))))) )
| ~ spl17_240
| ~ spl17_282 ),
inference(resolution,[],[f2402,f1930]) ).
fof(f8093,plain,
( spl17_693
| ~ spl17_239
| ~ spl17_282 ),
inference(avatar_split_clause,[],[f2448,f2401,f1925,f8091]) ).
fof(f8091,plain,
( spl17_693
<=> ! [X2,X0,X1] :
( element(sK7(X0,sK6(sK8(X1,sK10(powerset(powerset(X2)))))),X2)
| sP0(X1,sK10(powerset(powerset(X2))))
| sP0(X0,sK6(sK8(X1,sK10(powerset(powerset(X2))))))
| empty(sK8(X1,sK10(powerset(powerset(X2))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_693])]) ).
fof(f2448,plain,
( ! [X2,X0,X1] :
( element(sK7(X0,sK6(sK8(X1,sK10(powerset(powerset(X2)))))),X2)
| sP0(X1,sK10(powerset(powerset(X2))))
| sP0(X0,sK6(sK8(X1,sK10(powerset(powerset(X2))))))
| empty(sK8(X1,sK10(powerset(powerset(X2))))) )
| ~ spl17_239
| ~ spl17_282 ),
inference(resolution,[],[f2402,f1926]) ).
fof(f8089,plain,
( spl17_692
| ~ spl17_229
| ~ spl17_282 ),
inference(avatar_split_clause,[],[f2446,f2401,f1885,f8087]) ).
fof(f8087,plain,
( spl17_692
<=> ! [X0,X1] :
( element(sK10(sK10(powerset(sK8(X0,sK10(powerset(powerset(X1))))))),X1)
| sP0(X0,sK10(powerset(powerset(X1))))
| empty(sK8(X0,sK10(powerset(powerset(X1)))))
| empty(sK10(powerset(sK8(X0,sK10(powerset(powerset(X1))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_692])]) ).
fof(f2446,plain,
( ! [X0,X1] :
( element(sK10(sK10(powerset(sK8(X0,sK10(powerset(powerset(X1))))))),X1)
| sP0(X0,sK10(powerset(powerset(X1))))
| empty(sK8(X0,sK10(powerset(powerset(X1)))))
| empty(sK10(powerset(sK8(X0,sK10(powerset(powerset(X1))))))) )
| ~ spl17_229
| ~ spl17_282 ),
inference(resolution,[],[f2402,f1886]) ).
fof(f8085,plain,
( spl17_691
| ~ spl17_241
| ~ spl17_280 ),
inference(avatar_split_clause,[],[f2439,f2393,f1933,f8083]) ).
fof(f8083,plain,
( spl17_691
<=> ! [X2,X0,X1] :
( element(sK9(X0,sK6(sK7(X1,sK10(powerset(powerset(X2)))))),X2)
| sP0(X1,sK10(powerset(powerset(X2))))
| sP0(X0,sK6(sK7(X1,sK10(powerset(powerset(X2))))))
| empty(sK7(X1,sK10(powerset(powerset(X2))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_691])]) ).
fof(f2439,plain,
( ! [X2,X0,X1] :
( element(sK9(X0,sK6(sK7(X1,sK10(powerset(powerset(X2)))))),X2)
| sP0(X1,sK10(powerset(powerset(X2))))
| sP0(X0,sK6(sK7(X1,sK10(powerset(powerset(X2))))))
| empty(sK7(X1,sK10(powerset(powerset(X2))))) )
| ~ spl17_241
| ~ spl17_280 ),
inference(resolution,[],[f2394,f1934]) ).
fof(f8081,plain,
( spl17_690
| ~ spl17_240
| ~ spl17_280 ),
inference(avatar_split_clause,[],[f2436,f2393,f1929,f8079]) ).
fof(f8079,plain,
( spl17_690
<=> ! [X2,X0,X1] :
( element(sK8(X0,sK6(sK7(X1,sK10(powerset(powerset(X2)))))),X2)
| sP0(X1,sK10(powerset(powerset(X2))))
| sP0(X0,sK6(sK7(X1,sK10(powerset(powerset(X2))))))
| empty(sK7(X1,sK10(powerset(powerset(X2))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_690])]) ).
fof(f2436,plain,
( ! [X2,X0,X1] :
( element(sK8(X0,sK6(sK7(X1,sK10(powerset(powerset(X2)))))),X2)
| sP0(X1,sK10(powerset(powerset(X2))))
| sP0(X0,sK6(sK7(X1,sK10(powerset(powerset(X2))))))
| empty(sK7(X1,sK10(powerset(powerset(X2))))) )
| ~ spl17_240
| ~ spl17_280 ),
inference(resolution,[],[f2394,f1930]) ).
fof(f8077,plain,
( spl17_689
| ~ spl17_239
| ~ spl17_280 ),
inference(avatar_split_clause,[],[f2433,f2393,f1925,f8075]) ).
fof(f8075,plain,
( spl17_689
<=> ! [X2,X0,X1] :
( element(sK7(X0,sK6(sK7(X1,sK10(powerset(powerset(X2)))))),X2)
| sP0(X1,sK10(powerset(powerset(X2))))
| sP0(X0,sK6(sK7(X1,sK10(powerset(powerset(X2))))))
| empty(sK7(X1,sK10(powerset(powerset(X2))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_689])]) ).
fof(f2433,plain,
( ! [X2,X0,X1] :
( element(sK7(X0,sK6(sK7(X1,sK10(powerset(powerset(X2)))))),X2)
| sP0(X1,sK10(powerset(powerset(X2))))
| sP0(X0,sK6(sK7(X1,sK10(powerset(powerset(X2))))))
| empty(sK7(X1,sK10(powerset(powerset(X2))))) )
| ~ spl17_239
| ~ spl17_280 ),
inference(resolution,[],[f2394,f1926]) ).
fof(f8073,plain,
( spl17_688
| ~ spl17_229
| ~ spl17_280 ),
inference(avatar_split_clause,[],[f2431,f2393,f1885,f8071]) ).
fof(f8071,plain,
( spl17_688
<=> ! [X0,X1] :
( element(sK10(sK10(powerset(sK7(X0,sK10(powerset(powerset(X1))))))),X1)
| sP0(X0,sK10(powerset(powerset(X1))))
| empty(sK7(X0,sK10(powerset(powerset(X1)))))
| empty(sK10(powerset(sK7(X0,sK10(powerset(powerset(X1))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_688])]) ).
fof(f2431,plain,
( ! [X0,X1] :
( element(sK10(sK10(powerset(sK7(X0,sK10(powerset(powerset(X1))))))),X1)
| sP0(X0,sK10(powerset(powerset(X1))))
| empty(sK7(X0,sK10(powerset(powerset(X1)))))
| empty(sK10(powerset(sK7(X0,sK10(powerset(powerset(X1))))))) )
| ~ spl17_229
| ~ spl17_280 ),
inference(resolution,[],[f2394,f1886]) ).
fof(f8064,plain,
( spl17_687
| ~ spl17_59
| ~ spl17_663 ),
inference(avatar_split_clause,[],[f7998,f7742,f500,f8062]) ).
fof(f7998,plain,
( ! [X0] :
( in(sK8(the_InternalRel(sK2),X0),sK16)
| sP0(the_InternalRel(sK2),X0) )
| ~ spl17_59
| ~ spl17_663 ),
inference(resolution,[],[f7743,f501]) ).
fof(f7988,plain,
( spl17_686
| ~ spl17_241
| ~ spl17_292 ),
inference(avatar_split_clause,[],[f2610,f2530,f1933,f7986]) ).
fof(f7986,plain,
( spl17_686
<=> ! [X2,X0,X1] :
( sP0(X0,sK6(powerset(X1)))
| element(sK9(X2,sK6(sK9(X0,sK6(powerset(X1))))),X1)
| empty(powerset(X1))
| sP0(X2,sK6(sK9(X0,sK6(powerset(X1)))))
| empty(sK9(X0,sK6(powerset(X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_686])]) ).
fof(f2610,plain,
( ! [X2,X0,X1] :
( sP0(X0,sK6(powerset(X1)))
| element(sK9(X2,sK6(sK9(X0,sK6(powerset(X1))))),X1)
| empty(powerset(X1))
| sP0(X2,sK6(sK9(X0,sK6(powerset(X1)))))
| empty(sK9(X0,sK6(powerset(X1)))) )
| ~ spl17_241
| ~ spl17_292 ),
inference(resolution,[],[f2531,f1934]) ).
fof(f7984,plain,
( spl17_685
| ~ spl17_240
| ~ spl17_292 ),
inference(avatar_split_clause,[],[f2607,f2530,f1929,f7982]) ).
fof(f7982,plain,
( spl17_685
<=> ! [X2,X0,X1] :
( sP0(X0,sK6(powerset(X1)))
| element(sK8(X2,sK6(sK9(X0,sK6(powerset(X1))))),X1)
| empty(powerset(X1))
| sP0(X2,sK6(sK9(X0,sK6(powerset(X1)))))
| empty(sK9(X0,sK6(powerset(X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_685])]) ).
fof(f2607,plain,
( ! [X2,X0,X1] :
( sP0(X0,sK6(powerset(X1)))
| element(sK8(X2,sK6(sK9(X0,sK6(powerset(X1))))),X1)
| empty(powerset(X1))
| sP0(X2,sK6(sK9(X0,sK6(powerset(X1)))))
| empty(sK9(X0,sK6(powerset(X1)))) )
| ~ spl17_240
| ~ spl17_292 ),
inference(resolution,[],[f2531,f1930]) ).
fof(f7980,plain,
( spl17_684
| ~ spl17_239
| ~ spl17_292 ),
inference(avatar_split_clause,[],[f2604,f2530,f1925,f7978]) ).
fof(f7978,plain,
( spl17_684
<=> ! [X2,X0,X1] :
( sP0(X0,sK6(powerset(X1)))
| element(sK7(X2,sK6(sK9(X0,sK6(powerset(X1))))),X1)
| empty(powerset(X1))
| sP0(X2,sK6(sK9(X0,sK6(powerset(X1)))))
| empty(sK9(X0,sK6(powerset(X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_684])]) ).
fof(f2604,plain,
( ! [X2,X0,X1] :
( sP0(X0,sK6(powerset(X1)))
| element(sK7(X2,sK6(sK9(X0,sK6(powerset(X1))))),X1)
| empty(powerset(X1))
| sP0(X2,sK6(sK9(X0,sK6(powerset(X1)))))
| empty(sK9(X0,sK6(powerset(X1)))) )
| ~ spl17_239
| ~ spl17_292 ),
inference(resolution,[],[f2531,f1926]) ).
fof(f7976,plain,
( spl17_683
| ~ spl17_229
| ~ spl17_292 ),
inference(avatar_split_clause,[],[f2602,f2530,f1885,f7974]) ).
fof(f7974,plain,
( spl17_683
<=> ! [X0,X1] :
( sP0(X0,sK6(powerset(X1)))
| element(sK10(sK10(powerset(sK9(X0,sK6(powerset(X1)))))),X1)
| empty(powerset(X1))
| empty(sK9(X0,sK6(powerset(X1))))
| empty(sK10(powerset(sK9(X0,sK6(powerset(X1)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_683])]) ).
fof(f2602,plain,
( ! [X0,X1] :
( sP0(X0,sK6(powerset(X1)))
| element(sK10(sK10(powerset(sK9(X0,sK6(powerset(X1)))))),X1)
| empty(powerset(X1))
| empty(sK9(X0,sK6(powerset(X1))))
| empty(sK10(powerset(sK9(X0,sK6(powerset(X1)))))) )
| ~ spl17_229
| ~ spl17_292 ),
inference(resolution,[],[f2531,f1886]) ).
fof(f7972,plain,
( spl17_682
| ~ spl17_241
| ~ spl17_291 ),
inference(avatar_split_clause,[],[f2596,f2526,f1933,f7970]) ).
fof(f7970,plain,
( spl17_682
<=> ! [X2,X0,X1] :
( sP0(X0,sK6(powerset(X1)))
| element(sK9(X2,sK6(sK8(X0,sK6(powerset(X1))))),X1)
| empty(powerset(X1))
| sP0(X2,sK6(sK8(X0,sK6(powerset(X1)))))
| empty(sK8(X0,sK6(powerset(X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_682])]) ).
fof(f2596,plain,
( ! [X2,X0,X1] :
( sP0(X0,sK6(powerset(X1)))
| element(sK9(X2,sK6(sK8(X0,sK6(powerset(X1))))),X1)
| empty(powerset(X1))
| sP0(X2,sK6(sK8(X0,sK6(powerset(X1)))))
| empty(sK8(X0,sK6(powerset(X1)))) )
| ~ spl17_241
| ~ spl17_291 ),
inference(resolution,[],[f2527,f1934]) ).
fof(f7968,plain,
( spl17_681
| ~ spl17_240
| ~ spl17_291 ),
inference(avatar_split_clause,[],[f2593,f2526,f1929,f7966]) ).
fof(f7966,plain,
( spl17_681
<=> ! [X2,X0,X1] :
( sP0(X0,sK6(powerset(X1)))
| element(sK8(X2,sK6(sK8(X0,sK6(powerset(X1))))),X1)
| empty(powerset(X1))
| sP0(X2,sK6(sK8(X0,sK6(powerset(X1)))))
| empty(sK8(X0,sK6(powerset(X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_681])]) ).
fof(f2593,plain,
( ! [X2,X0,X1] :
( sP0(X0,sK6(powerset(X1)))
| element(sK8(X2,sK6(sK8(X0,sK6(powerset(X1))))),X1)
| empty(powerset(X1))
| sP0(X2,sK6(sK8(X0,sK6(powerset(X1)))))
| empty(sK8(X0,sK6(powerset(X1)))) )
| ~ spl17_240
| ~ spl17_291 ),
inference(resolution,[],[f2527,f1930]) ).
fof(f7964,plain,
( spl17_680
| ~ spl17_239
| ~ spl17_291 ),
inference(avatar_split_clause,[],[f2590,f2526,f1925,f7962]) ).
fof(f7962,plain,
( spl17_680
<=> ! [X2,X0,X1] :
( sP0(X0,sK6(powerset(X1)))
| element(sK7(X2,sK6(sK8(X0,sK6(powerset(X1))))),X1)
| empty(powerset(X1))
| sP0(X2,sK6(sK8(X0,sK6(powerset(X1)))))
| empty(sK8(X0,sK6(powerset(X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_680])]) ).
fof(f2590,plain,
( ! [X2,X0,X1] :
( sP0(X0,sK6(powerset(X1)))
| element(sK7(X2,sK6(sK8(X0,sK6(powerset(X1))))),X1)
| empty(powerset(X1))
| sP0(X2,sK6(sK8(X0,sK6(powerset(X1)))))
| empty(sK8(X0,sK6(powerset(X1)))) )
| ~ spl17_239
| ~ spl17_291 ),
inference(resolution,[],[f2527,f1926]) ).
fof(f7960,plain,
( spl17_679
| ~ spl17_229
| ~ spl17_291 ),
inference(avatar_split_clause,[],[f2588,f2526,f1885,f7958]) ).
fof(f7958,plain,
( spl17_679
<=> ! [X0,X1] :
( sP0(X0,sK6(powerset(X1)))
| element(sK10(sK10(powerset(sK8(X0,sK6(powerset(X1)))))),X1)
| empty(powerset(X1))
| empty(sK8(X0,sK6(powerset(X1))))
| empty(sK10(powerset(sK8(X0,sK6(powerset(X1)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_679])]) ).
fof(f2588,plain,
( ! [X0,X1] :
( sP0(X0,sK6(powerset(X1)))
| element(sK10(sK10(powerset(sK8(X0,sK6(powerset(X1)))))),X1)
| empty(powerset(X1))
| empty(sK8(X0,sK6(powerset(X1))))
| empty(sK10(powerset(sK8(X0,sK6(powerset(X1)))))) )
| ~ spl17_229
| ~ spl17_291 ),
inference(resolution,[],[f2527,f1886]) ).
fof(f7956,plain,
( spl17_678
| ~ spl17_241
| ~ spl17_290 ),
inference(avatar_split_clause,[],[f2582,f2522,f1933,f7954]) ).
fof(f7954,plain,
( spl17_678
<=> ! [X2,X0,X1] :
( sP0(X0,sK6(powerset(X1)))
| element(sK9(X2,sK6(sK7(X0,sK6(powerset(X1))))),X1)
| empty(powerset(X1))
| sP0(X2,sK6(sK7(X0,sK6(powerset(X1)))))
| empty(sK7(X0,sK6(powerset(X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_678])]) ).
fof(f2582,plain,
( ! [X2,X0,X1] :
( sP0(X0,sK6(powerset(X1)))
| element(sK9(X2,sK6(sK7(X0,sK6(powerset(X1))))),X1)
| empty(powerset(X1))
| sP0(X2,sK6(sK7(X0,sK6(powerset(X1)))))
| empty(sK7(X0,sK6(powerset(X1)))) )
| ~ spl17_241
| ~ spl17_290 ),
inference(resolution,[],[f2523,f1934]) ).
fof(f7940,plain,
( spl17_677
| ~ spl17_240
| ~ spl17_290 ),
inference(avatar_split_clause,[],[f2579,f2522,f1929,f7938]) ).
fof(f7938,plain,
( spl17_677
<=> ! [X2,X0,X1] :
( sP0(X0,sK6(powerset(X1)))
| element(sK8(X2,sK6(sK7(X0,sK6(powerset(X1))))),X1)
| empty(powerset(X1))
| sP0(X2,sK6(sK7(X0,sK6(powerset(X1)))))
| empty(sK7(X0,sK6(powerset(X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_677])]) ).
fof(f2579,plain,
( ! [X2,X0,X1] :
( sP0(X0,sK6(powerset(X1)))
| element(sK8(X2,sK6(sK7(X0,sK6(powerset(X1))))),X1)
| empty(powerset(X1))
| sP0(X2,sK6(sK7(X0,sK6(powerset(X1)))))
| empty(sK7(X0,sK6(powerset(X1)))) )
| ~ spl17_240
| ~ spl17_290 ),
inference(resolution,[],[f2523,f1930]) ).
fof(f7936,plain,
( spl17_676
| ~ spl17_239
| ~ spl17_290 ),
inference(avatar_split_clause,[],[f2576,f2522,f1925,f7934]) ).
fof(f7934,plain,
( spl17_676
<=> ! [X2,X0,X1] :
( sP0(X0,sK6(powerset(X1)))
| element(sK7(X2,sK6(sK7(X0,sK6(powerset(X1))))),X1)
| empty(powerset(X1))
| sP0(X2,sK6(sK7(X0,sK6(powerset(X1)))))
| empty(sK7(X0,sK6(powerset(X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_676])]) ).
fof(f2576,plain,
( ! [X2,X0,X1] :
( sP0(X0,sK6(powerset(X1)))
| element(sK7(X2,sK6(sK7(X0,sK6(powerset(X1))))),X1)
| empty(powerset(X1))
| sP0(X2,sK6(sK7(X0,sK6(powerset(X1)))))
| empty(sK7(X0,sK6(powerset(X1)))) )
| ~ spl17_239
| ~ spl17_290 ),
inference(resolution,[],[f2523,f1926]) ).
fof(f7932,plain,
( spl17_675
| ~ spl17_229
| ~ spl17_290 ),
inference(avatar_split_clause,[],[f2574,f2522,f1885,f7930]) ).
fof(f7930,plain,
( spl17_675
<=> ! [X0,X1] :
( sP0(X0,sK6(powerset(X1)))
| element(sK10(sK10(powerset(sK7(X0,sK6(powerset(X1)))))),X1)
| empty(powerset(X1))
| empty(sK7(X0,sK6(powerset(X1))))
| empty(sK10(powerset(sK7(X0,sK6(powerset(X1)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_675])]) ).
fof(f2574,plain,
( ! [X0,X1] :
( sP0(X0,sK6(powerset(X1)))
| element(sK10(sK10(powerset(sK7(X0,sK6(powerset(X1)))))),X1)
| empty(powerset(X1))
| empty(sK7(X0,sK6(powerset(X1))))
| empty(sK10(powerset(sK7(X0,sK6(powerset(X1)))))) )
| ~ spl17_229
| ~ spl17_290 ),
inference(resolution,[],[f2523,f1886]) ).
fof(f7834,plain,
( spl17_674
| ~ spl17_39
| ~ spl17_319 ),
inference(avatar_split_clause,[],[f2879,f2865,f355,f7832]) ).
fof(f7832,plain,
( spl17_674
<=> ! [X2,X0,X1] :
( sP0(sK12(X0,X1),X2)
| empty(cartesian_product2(X0,X1))
| in(unordered_pair(singleton(sK7(sK12(X0,X1),X2)),unordered_pair(sK8(sK12(X0,X1),X2),sK7(sK12(X0,X1),X2))),cartesian_product2(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_674])]) ).
fof(f2865,plain,
( spl17_319
<=> ! [X2,X0,X1] :
( element(unordered_pair(singleton(sK7(sK12(X0,X1),X2)),unordered_pair(sK8(sK12(X0,X1),X2),sK7(sK12(X0,X1),X2))),cartesian_product2(X0,X1))
| sP0(sK12(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_319])]) ).
fof(f2879,plain,
( ! [X2,X0,X1] :
( sP0(sK12(X0,X1),X2)
| empty(cartesian_product2(X0,X1))
| in(unordered_pair(singleton(sK7(sK12(X0,X1),X2)),unordered_pair(sK8(sK12(X0,X1),X2),sK7(sK12(X0,X1),X2))),cartesian_product2(X0,X1)) )
| ~ spl17_39
| ~ spl17_319 ),
inference(resolution,[],[f2866,f356]) ).
fof(f2866,plain,
( ! [X2,X0,X1] :
( element(unordered_pair(singleton(sK7(sK12(X0,X1),X2)),unordered_pair(sK8(sK12(X0,X1),X2),sK7(sK12(X0,X1),X2))),cartesian_product2(X0,X1))
| sP0(sK12(X0,X1),X2) )
| ~ spl17_319 ),
inference(avatar_component_clause,[],[f2865]) ).
fof(f7830,plain,
( spl17_673
| ~ spl17_39
| ~ spl17_318 ),
inference(avatar_split_clause,[],[f2878,f2861,f355,f7828]) ).
fof(f7828,plain,
( spl17_673
<=> ! [X2,X0,X1] :
( sP0(sK12(X0,X1),X2)
| empty(cartesian_product2(X0,X1))
| in(unordered_pair(singleton(sK8(sK12(X0,X1),X2)),unordered_pair(sK9(sK12(X0,X1),X2),sK8(sK12(X0,X1),X2))),cartesian_product2(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_673])]) ).
fof(f2861,plain,
( spl17_318
<=> ! [X2,X0,X1] :
( element(unordered_pair(singleton(sK8(sK12(X0,X1),X2)),unordered_pair(sK9(sK12(X0,X1),X2),sK8(sK12(X0,X1),X2))),cartesian_product2(X0,X1))
| sP0(sK12(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_318])]) ).
fof(f2878,plain,
( ! [X2,X0,X1] :
( sP0(sK12(X0,X1),X2)
| empty(cartesian_product2(X0,X1))
| in(unordered_pair(singleton(sK8(sK12(X0,X1),X2)),unordered_pair(sK9(sK12(X0,X1),X2),sK8(sK12(X0,X1),X2))),cartesian_product2(X0,X1)) )
| ~ spl17_39
| ~ spl17_318 ),
inference(resolution,[],[f2862,f356]) ).
fof(f2862,plain,
( ! [X2,X0,X1] :
( element(unordered_pair(singleton(sK8(sK12(X0,X1),X2)),unordered_pair(sK9(sK12(X0,X1),X2),sK8(sK12(X0,X1),X2))),cartesian_product2(X0,X1))
| sP0(sK12(X0,X1),X2) )
| ~ spl17_318 ),
inference(avatar_component_clause,[],[f2861]) ).
fof(f7826,plain,
( spl17_672
| ~ spl17_39
| ~ spl17_317 ),
inference(avatar_split_clause,[],[f2877,f2857,f355,f7824]) ).
fof(f7824,plain,
( spl17_672
<=> ! [X2,X0,X1] :
( sP0(sK13(X0,X1),X2)
| empty(cartesian_product2(X0,X1))
| in(unordered_pair(singleton(sK7(sK13(X0,X1),X2)),unordered_pair(sK8(sK13(X0,X1),X2),sK7(sK13(X0,X1),X2))),cartesian_product2(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_672])]) ).
fof(f2857,plain,
( spl17_317
<=> ! [X2,X0,X1] :
( element(unordered_pair(singleton(sK7(sK13(X0,X1),X2)),unordered_pair(sK8(sK13(X0,X1),X2),sK7(sK13(X0,X1),X2))),cartesian_product2(X0,X1))
| sP0(sK13(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_317])]) ).
fof(f2877,plain,
( ! [X2,X0,X1] :
( sP0(sK13(X0,X1),X2)
| empty(cartesian_product2(X0,X1))
| in(unordered_pair(singleton(sK7(sK13(X0,X1),X2)),unordered_pair(sK8(sK13(X0,X1),X2),sK7(sK13(X0,X1),X2))),cartesian_product2(X0,X1)) )
| ~ spl17_39
| ~ spl17_317 ),
inference(resolution,[],[f2858,f356]) ).
fof(f2858,plain,
( ! [X2,X0,X1] :
( element(unordered_pair(singleton(sK7(sK13(X0,X1),X2)),unordered_pair(sK8(sK13(X0,X1),X2),sK7(sK13(X0,X1),X2))),cartesian_product2(X0,X1))
| sP0(sK13(X0,X1),X2) )
| ~ spl17_317 ),
inference(avatar_component_clause,[],[f2857]) ).
fof(f7822,plain,
( spl17_671
| ~ spl17_39
| ~ spl17_315 ),
inference(avatar_split_clause,[],[f2876,f2849,f355,f7820]) ).
fof(f7820,plain,
( spl17_671
<=> ! [X2,X0,X1] :
( sP0(sK13(X0,X1),X2)
| empty(cartesian_product2(X0,X1))
| in(unordered_pair(singleton(sK8(sK13(X0,X1),X2)),unordered_pair(sK9(sK13(X0,X1),X2),sK8(sK13(X0,X1),X2))),cartesian_product2(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_671])]) ).
fof(f2849,plain,
( spl17_315
<=> ! [X2,X0,X1] :
( element(unordered_pair(singleton(sK8(sK13(X0,X1),X2)),unordered_pair(sK9(sK13(X0,X1),X2),sK8(sK13(X0,X1),X2))),cartesian_product2(X0,X1))
| sP0(sK13(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_315])]) ).
fof(f2876,plain,
( ! [X2,X0,X1] :
( sP0(sK13(X0,X1),X2)
| empty(cartesian_product2(X0,X1))
| in(unordered_pair(singleton(sK8(sK13(X0,X1),X2)),unordered_pair(sK9(sK13(X0,X1),X2),sK8(sK13(X0,X1),X2))),cartesian_product2(X0,X1)) )
| ~ spl17_39
| ~ spl17_315 ),
inference(resolution,[],[f2850,f356]) ).
fof(f2850,plain,
( ! [X2,X0,X1] :
( element(unordered_pair(singleton(sK8(sK13(X0,X1),X2)),unordered_pair(sK9(sK13(X0,X1),X2),sK8(sK13(X0,X1),X2))),cartesian_product2(X0,X1))
| sP0(sK13(X0,X1),X2) )
| ~ spl17_315 ),
inference(avatar_component_clause,[],[f2849]) ).
fof(f7818,plain,
( spl17_670
| ~ spl17_224
| ~ spl17_284 ),
inference(avatar_split_clause,[],[f2460,f2409,f1808,f7816]) ).
fof(f7816,plain,
( spl17_670
<=> ! [X0,X1] :
( element(sK10(sK6(sK9(X0,sK10(powerset(powerset(X1)))))),X1)
| sP0(X0,sK10(powerset(powerset(X1))))
| empty(sK6(sK9(X0,sK10(powerset(powerset(X1))))))
| empty(sK9(X0,sK10(powerset(powerset(X1))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_670])]) ).
fof(f2460,plain,
( ! [X0,X1] :
( element(sK10(sK6(sK9(X0,sK10(powerset(powerset(X1)))))),X1)
| sP0(X0,sK10(powerset(powerset(X1))))
| empty(sK6(sK9(X0,sK10(powerset(powerset(X1))))))
| empty(sK9(X0,sK10(powerset(powerset(X1))))) )
| ~ spl17_224
| ~ spl17_284 ),
inference(resolution,[],[f2410,f1809]) ).
fof(f7814,plain,
( spl17_669
| ~ spl17_224
| ~ spl17_282 ),
inference(avatar_split_clause,[],[f2445,f2401,f1808,f7812]) ).
fof(f7812,plain,
( spl17_669
<=> ! [X0,X1] :
( element(sK10(sK6(sK8(X0,sK10(powerset(powerset(X1)))))),X1)
| sP0(X0,sK10(powerset(powerset(X1))))
| empty(sK6(sK8(X0,sK10(powerset(powerset(X1))))))
| empty(sK8(X0,sK10(powerset(powerset(X1))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_669])]) ).
fof(f2445,plain,
( ! [X0,X1] :
( element(sK10(sK6(sK8(X0,sK10(powerset(powerset(X1)))))),X1)
| sP0(X0,sK10(powerset(powerset(X1))))
| empty(sK6(sK8(X0,sK10(powerset(powerset(X1))))))
| empty(sK8(X0,sK10(powerset(powerset(X1))))) )
| ~ spl17_224
| ~ spl17_282 ),
inference(resolution,[],[f2402,f1809]) ).
fof(f7810,plain,
( spl17_668
| ~ spl17_224
| ~ spl17_280 ),
inference(avatar_split_clause,[],[f2430,f2393,f1808,f7808]) ).
fof(f7808,plain,
( spl17_668
<=> ! [X0,X1] :
( element(sK10(sK6(sK7(X0,sK10(powerset(powerset(X1)))))),X1)
| sP0(X0,sK10(powerset(powerset(X1))))
| empty(sK6(sK7(X0,sK10(powerset(powerset(X1))))))
| empty(sK7(X0,sK10(powerset(powerset(X1))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_668])]) ).
fof(f2430,plain,
( ! [X0,X1] :
( element(sK10(sK6(sK7(X0,sK10(powerset(powerset(X1)))))),X1)
| sP0(X0,sK10(powerset(powerset(X1))))
| empty(sK6(sK7(X0,sK10(powerset(powerset(X1))))))
| empty(sK7(X0,sK10(powerset(powerset(X1))))) )
| ~ spl17_224
| ~ spl17_280 ),
inference(resolution,[],[f2394,f1809]) ).
fof(f7806,plain,
( spl17_667
| ~ spl17_103
| ~ spl17_404 ),
inference(avatar_split_clause,[],[f5180,f3828,f823,f7804]) ).
fof(f823,plain,
( spl17_103
<=> ! [X0,X3,X2,X1] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X1,X0)),cartesian_product2(X2,X3))
| in(X1,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_103])]) ).
fof(f5180,plain,
( ! [X0,X1] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X1,X0)),the_InternalRel(sK2))
| in(X1,sK16) )
| ~ spl17_103
| ~ spl17_404 ),
inference(resolution,[],[f3829,f824]) ).
fof(f824,plain,
( ! [X2,X3,X0,X1] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X1,X0)),cartesian_product2(X2,X3))
| in(X1,X3) )
| ~ spl17_103 ),
inference(avatar_component_clause,[],[f823]) ).
fof(f7802,plain,
( spl17_666
| ~ spl17_266
| ~ spl17_269 ),
inference(avatar_split_clause,[],[f2261,f2240,f2147,f7800]) ).
fof(f7800,plain,
( spl17_666
<=> ! [X0,X1] :
( element(sK9(X0,sK10(powerset(sK10(sK10(powerset(powerset(X1))))))),X1)
| empty(sK10(powerset(powerset(X1))))
| empty(sK10(sK10(powerset(powerset(X1)))))
| sP0(X0,sK10(powerset(sK10(sK10(powerset(powerset(X1))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_666])]) ).
fof(f2261,plain,
( ! [X0,X1] :
( element(sK9(X0,sK10(powerset(sK10(sK10(powerset(powerset(X1))))))),X1)
| empty(sK10(powerset(powerset(X1))))
| empty(sK10(sK10(powerset(powerset(X1)))))
| sP0(X0,sK10(powerset(sK10(sK10(powerset(powerset(X1))))))) )
| ~ spl17_266
| ~ spl17_269 ),
inference(resolution,[],[f2241,f2148]) ).
fof(f7798,plain,
( spl17_665
| ~ spl17_265
| ~ spl17_269 ),
inference(avatar_split_clause,[],[f2258,f2240,f2143,f7796]) ).
fof(f7796,plain,
( spl17_665
<=> ! [X0,X1] :
( element(sK8(X0,sK10(powerset(sK10(sK10(powerset(powerset(X1))))))),X1)
| empty(sK10(powerset(powerset(X1))))
| empty(sK10(sK10(powerset(powerset(X1)))))
| sP0(X0,sK10(powerset(sK10(sK10(powerset(powerset(X1))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_665])]) ).
fof(f2258,plain,
( ! [X0,X1] :
( element(sK8(X0,sK10(powerset(sK10(sK10(powerset(powerset(X1))))))),X1)
| empty(sK10(powerset(powerset(X1))))
| empty(sK10(sK10(powerset(powerset(X1)))))
| sP0(X0,sK10(powerset(sK10(sK10(powerset(powerset(X1))))))) )
| ~ spl17_265
| ~ spl17_269 ),
inference(resolution,[],[f2241,f2144]) ).
fof(f7794,plain,
( spl17_664
| ~ spl17_264
| ~ spl17_269 ),
inference(avatar_split_clause,[],[f2255,f2240,f2139,f7792]) ).
fof(f7792,plain,
( spl17_664
<=> ! [X0,X1] :
( element(sK7(X0,sK10(powerset(sK10(sK10(powerset(powerset(X1))))))),X1)
| empty(sK10(powerset(powerset(X1))))
| empty(sK10(sK10(powerset(powerset(X1)))))
| sP0(X0,sK10(powerset(sK10(sK10(powerset(powerset(X1))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_664])]) ).
fof(f2255,plain,
( ! [X0,X1] :
( element(sK7(X0,sK10(powerset(sK10(sK10(powerset(powerset(X1))))))),X1)
| empty(sK10(powerset(powerset(X1))))
| empty(sK10(sK10(powerset(powerset(X1)))))
| sP0(X0,sK10(powerset(sK10(sK10(powerset(powerset(X1))))))) )
| ~ spl17_264
| ~ spl17_269 ),
inference(resolution,[],[f2241,f2140]) ).
fof(f7744,plain,
( spl17_663
| ~ spl17_104
| ~ spl17_404 ),
inference(avatar_split_clause,[],[f5179,f3828,f827,f7742]) ).
fof(f827,plain,
( spl17_104
<=> ! [X0,X3,X2,X1] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X1,X0)),cartesian_product2(X2,X3))
| in(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_104])]) ).
fof(f5179,plain,
( ! [X0,X1] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X1,X0)),the_InternalRel(sK2))
| in(X0,sK16) )
| ~ spl17_104
| ~ spl17_404 ),
inference(resolution,[],[f3829,f828]) ).
fof(f828,plain,
( ! [X2,X3,X0,X1] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X1,X0)),cartesian_product2(X2,X3))
| in(X0,X2) )
| ~ spl17_104 ),
inference(avatar_component_clause,[],[f827]) ).
fof(f7730,plain,
( spl17_662
| ~ spl17_75
| ~ spl17_330 ),
inference(avatar_split_clause,[],[f3113,f3050,f643,f7728]) ).
fof(f7728,plain,
( spl17_662
<=> ! [X0,X1] :
( ~ empty(X0)
| sP0(sK10(powerset(powerset(X0))),X1)
| empty(unordered_pair(singleton(sK7(sK10(powerset(powerset(X0))),X1)),unordered_pair(sK8(sK10(powerset(powerset(X0))),X1),sK7(sK10(powerset(powerset(X0))),X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_662])]) ).
fof(f3050,plain,
( spl17_330
<=> ! [X2,X0,X1] :
( sP0(sK10(powerset(powerset(X0))),X1)
| ~ empty(X0)
| ~ in(X2,unordered_pair(singleton(sK7(sK10(powerset(powerset(X0))),X1)),unordered_pair(sK8(sK10(powerset(powerset(X0))),X1),sK7(sK10(powerset(powerset(X0))),X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_330])]) ).
fof(f3113,plain,
( ! [X0,X1] :
( ~ empty(X0)
| sP0(sK10(powerset(powerset(X0))),X1)
| empty(unordered_pair(singleton(sK7(sK10(powerset(powerset(X0))),X1)),unordered_pair(sK8(sK10(powerset(powerset(X0))),X1),sK7(sK10(powerset(powerset(X0))),X1)))) )
| ~ spl17_75
| ~ spl17_330 ),
inference(resolution,[],[f3051,f644]) ).
fof(f3051,plain,
( ! [X2,X0,X1] :
( ~ in(X2,unordered_pair(singleton(sK7(sK10(powerset(powerset(X0))),X1)),unordered_pair(sK8(sK10(powerset(powerset(X0))),X1),sK7(sK10(powerset(powerset(X0))),X1))))
| ~ empty(X0)
| sP0(sK10(powerset(powerset(X0))),X1) )
| ~ spl17_330 ),
inference(avatar_component_clause,[],[f3050]) ).
fof(f7726,plain,
( spl17_661
| ~ spl17_75
| ~ spl17_329 ),
inference(avatar_split_clause,[],[f3095,f3046,f643,f7724]) ).
fof(f3046,plain,
( spl17_329
<=> ! [X2,X0,X1] :
( sP0(sK10(powerset(powerset(X0))),X1)
| ~ empty(X0)
| ~ in(X2,unordered_pair(singleton(sK8(sK10(powerset(powerset(X0))),X1)),unordered_pair(sK9(sK10(powerset(powerset(X0))),X1),sK8(sK10(powerset(powerset(X0))),X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_329])]) ).
fof(f3095,plain,
( ! [X0,X1] :
( ~ empty(X0)
| sP0(sK10(powerset(powerset(X0))),X1)
| empty(unordered_pair(singleton(sK8(sK10(powerset(powerset(X0))),X1)),unordered_pair(sK9(sK10(powerset(powerset(X0))),X1),sK8(sK10(powerset(powerset(X0))),X1)))) )
| ~ spl17_75
| ~ spl17_329 ),
inference(resolution,[],[f3047,f644]) ).
fof(f3047,plain,
( ! [X2,X0,X1] :
( ~ in(X2,unordered_pair(singleton(sK8(sK10(powerset(powerset(X0))),X1)),unordered_pair(sK9(sK10(powerset(powerset(X0))),X1),sK8(sK10(powerset(powerset(X0))),X1))))
| ~ empty(X0)
| sP0(sK10(powerset(powerset(X0))),X1) )
| ~ spl17_329 ),
inference(avatar_component_clause,[],[f3046]) ).
fof(f7722,plain,
( spl17_660
| ~ spl17_95
| ~ spl17_312 ),
inference(avatar_split_clause,[],[f2799,f2730,f765,f7720]) ).
fof(f7720,plain,
( spl17_660
<=> ! [X0,X1] :
( sP0(sK6(sK6(X0)),X1)
| empty(sK6(X0))
| element(unordered_pair(singleton(sK7(sK6(sK6(X0)),X1)),unordered_pair(sK8(sK6(sK6(X0)),X1),sK7(sK6(sK6(X0)),X1))),X0)
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_660])]) ).
fof(f2799,plain,
( ! [X0,X1] :
( sP0(sK6(sK6(X0)),X1)
| empty(sK6(X0))
| element(unordered_pair(singleton(sK7(sK6(sK6(X0)),X1)),unordered_pair(sK8(sK6(sK6(X0)),X1),sK7(sK6(sK6(X0)),X1))),X0)
| empty(X0) )
| ~ spl17_95
| ~ spl17_312 ),
inference(resolution,[],[f2731,f766]) ).
fof(f7718,plain,
( spl17_659
| ~ spl17_95
| ~ spl17_311 ),
inference(avatar_split_clause,[],[f2750,f2726,f765,f7716]) ).
fof(f7716,plain,
( spl17_659
<=> ! [X0,X1] :
( sP0(sK6(sK6(X0)),X1)
| empty(sK6(X0))
| element(unordered_pair(singleton(sK8(sK6(sK6(X0)),X1)),unordered_pair(sK9(sK6(sK6(X0)),X1),sK8(sK6(sK6(X0)),X1))),X0)
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_659])]) ).
fof(f2750,plain,
( ! [X0,X1] :
( sP0(sK6(sK6(X0)),X1)
| empty(sK6(X0))
| element(unordered_pair(singleton(sK8(sK6(sK6(X0)),X1)),unordered_pair(sK9(sK6(sK6(X0)),X1),sK8(sK6(sK6(X0)),X1))),X0)
| empty(X0) )
| ~ spl17_95
| ~ spl17_311 ),
inference(resolution,[],[f2727,f766]) ).
fof(f7714,plain,
( spl17_658
| ~ spl17_224
| ~ spl17_292 ),
inference(avatar_split_clause,[],[f2601,f2530,f1808,f7712]) ).
fof(f7712,plain,
( spl17_658
<=> ! [X0,X1] :
( sP0(X0,sK6(powerset(X1)))
| element(sK10(sK6(sK9(X0,sK6(powerset(X1))))),X1)
| empty(powerset(X1))
| empty(sK6(sK9(X0,sK6(powerset(X1)))))
| empty(sK9(X0,sK6(powerset(X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_658])]) ).
fof(f2601,plain,
( ! [X0,X1] :
( sP0(X0,sK6(powerset(X1)))
| element(sK10(sK6(sK9(X0,sK6(powerset(X1))))),X1)
| empty(powerset(X1))
| empty(sK6(sK9(X0,sK6(powerset(X1)))))
| empty(sK9(X0,sK6(powerset(X1)))) )
| ~ spl17_224
| ~ spl17_292 ),
inference(resolution,[],[f2531,f1809]) ).
fof(f7710,plain,
( spl17_657
| ~ spl17_224
| ~ spl17_291 ),
inference(avatar_split_clause,[],[f2587,f2526,f1808,f7708]) ).
fof(f7708,plain,
( spl17_657
<=> ! [X0,X1] :
( sP0(X0,sK6(powerset(X1)))
| element(sK10(sK6(sK8(X0,sK6(powerset(X1))))),X1)
| empty(powerset(X1))
| empty(sK6(sK8(X0,sK6(powerset(X1)))))
| empty(sK8(X0,sK6(powerset(X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_657])]) ).
fof(f2587,plain,
( ! [X0,X1] :
( sP0(X0,sK6(powerset(X1)))
| element(sK10(sK6(sK8(X0,sK6(powerset(X1))))),X1)
| empty(powerset(X1))
| empty(sK6(sK8(X0,sK6(powerset(X1)))))
| empty(sK8(X0,sK6(powerset(X1)))) )
| ~ spl17_224
| ~ spl17_291 ),
inference(resolution,[],[f2527,f1809]) ).
fof(f7706,plain,
( spl17_656
| ~ spl17_224
| ~ spl17_290 ),
inference(avatar_split_clause,[],[f2573,f2522,f1808,f7704]) ).
fof(f7704,plain,
( spl17_656
<=> ! [X0,X1] :
( sP0(X0,sK6(powerset(X1)))
| element(sK10(sK6(sK7(X0,sK6(powerset(X1))))),X1)
| empty(powerset(X1))
| empty(sK6(sK7(X0,sK6(powerset(X1)))))
| empty(sK7(X0,sK6(powerset(X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_656])]) ).
fof(f2573,plain,
( ! [X0,X1] :
( sP0(X0,sK6(powerset(X1)))
| element(sK10(sK6(sK7(X0,sK6(powerset(X1))))),X1)
| empty(powerset(X1))
| empty(sK6(sK7(X0,sK6(powerset(X1)))))
| empty(sK7(X0,sK6(powerset(X1)))) )
| ~ spl17_224
| ~ spl17_290 ),
inference(resolution,[],[f2523,f1809]) ).
fof(f7702,plain,
( spl17_655
| ~ spl17_266
| ~ spl17_271 ),
inference(avatar_split_clause,[],[f2329,f2289,f2147,f7700]) ).
fof(f7700,plain,
( spl17_655
<=> ! [X0,X1] :
( empty(sK6(powerset(X0)))
| element(sK9(X1,sK10(powerset(sK10(sK6(powerset(X0)))))),X0)
| empty(powerset(X0))
| empty(sK10(sK6(powerset(X0))))
| sP0(X1,sK10(powerset(sK10(sK6(powerset(X0)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_655])]) ).
fof(f2329,plain,
( ! [X0,X1] :
( empty(sK6(powerset(X0)))
| element(sK9(X1,sK10(powerset(sK10(sK6(powerset(X0)))))),X0)
| empty(powerset(X0))
| empty(sK10(sK6(powerset(X0))))
| sP0(X1,sK10(powerset(sK10(sK6(powerset(X0)))))) )
| ~ spl17_266
| ~ spl17_271 ),
inference(resolution,[],[f2290,f2148]) ).
fof(f7698,plain,
( spl17_654
| ~ spl17_52
| ~ spl17_404 ),
inference(avatar_split_clause,[],[f5174,f3828,f452,f7696]) ).
fof(f452,plain,
( spl17_52
<=> ! [X0,X3,X2,X1] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),cartesian_product2(X2,X3))
| in(X1,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_52])]) ).
fof(f5174,plain,
( ! [X0,X1] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),the_InternalRel(sK2))
| in(X1,sK16) )
| ~ spl17_52
| ~ spl17_404 ),
inference(resolution,[],[f3829,f453]) ).
fof(f453,plain,
( ! [X2,X3,X0,X1] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),cartesian_product2(X2,X3))
| in(X1,X3) )
| ~ spl17_52 ),
inference(avatar_component_clause,[],[f452]) ).
fof(f7694,plain,
( spl17_653
| ~ spl17_265
| ~ spl17_271 ),
inference(avatar_split_clause,[],[f2326,f2289,f2143,f7692]) ).
fof(f7692,plain,
( spl17_653
<=> ! [X0,X1] :
( empty(sK6(powerset(X0)))
| element(sK8(X1,sK10(powerset(sK10(sK6(powerset(X0)))))),X0)
| empty(powerset(X0))
| empty(sK10(sK6(powerset(X0))))
| sP0(X1,sK10(powerset(sK10(sK6(powerset(X0)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_653])]) ).
fof(f2326,plain,
( ! [X0,X1] :
( empty(sK6(powerset(X0)))
| element(sK8(X1,sK10(powerset(sK10(sK6(powerset(X0)))))),X0)
| empty(powerset(X0))
| empty(sK10(sK6(powerset(X0))))
| sP0(X1,sK10(powerset(sK10(sK6(powerset(X0)))))) )
| ~ spl17_265
| ~ spl17_271 ),
inference(resolution,[],[f2290,f2144]) ).
fof(f7690,plain,
( spl17_652
| ~ spl17_264
| ~ spl17_271 ),
inference(avatar_split_clause,[],[f2323,f2289,f2139,f7688]) ).
fof(f7688,plain,
( spl17_652
<=> ! [X0,X1] :
( empty(sK6(powerset(X0)))
| element(sK7(X1,sK10(powerset(sK10(sK6(powerset(X0)))))),X0)
| empty(powerset(X0))
| empty(sK10(sK6(powerset(X0))))
| sP0(X1,sK10(powerset(sK10(sK6(powerset(X0)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_652])]) ).
fof(f2323,plain,
( ! [X0,X1] :
( empty(sK6(powerset(X0)))
| element(sK7(X1,sK10(powerset(sK10(sK6(powerset(X0)))))),X0)
| empty(powerset(X0))
| empty(sK10(sK6(powerset(X0))))
| sP0(X1,sK10(powerset(sK10(sK6(powerset(X0)))))) )
| ~ spl17_264
| ~ spl17_271 ),
inference(resolution,[],[f2290,f2140]) ).
fof(f7652,plain,
( spl17_651
| ~ spl17_75
| ~ spl17_325 ),
inference(avatar_split_clause,[],[f3021,f2994,f643,f7650]) ).
fof(f7650,plain,
( spl17_651
<=> ! [X0,X1] :
( sP0(sK6(powerset(X0)),X1)
| ~ empty(X0)
| empty(powerset(X0))
| empty(unordered_pair(singleton(sK7(sK6(powerset(X0)),X1)),unordered_pair(sK8(sK6(powerset(X0)),X1),sK7(sK6(powerset(X0)),X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_651])]) ).
fof(f2994,plain,
( spl17_325
<=> ! [X2,X0,X1] :
( empty(powerset(X0))
| sP0(sK6(powerset(X0)),X1)
| ~ empty(X0)
| ~ in(X2,unordered_pair(singleton(sK7(sK6(powerset(X0)),X1)),unordered_pair(sK8(sK6(powerset(X0)),X1),sK7(sK6(powerset(X0)),X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_325])]) ).
fof(f3021,plain,
( ! [X0,X1] :
( sP0(sK6(powerset(X0)),X1)
| ~ empty(X0)
| empty(powerset(X0))
| empty(unordered_pair(singleton(sK7(sK6(powerset(X0)),X1)),unordered_pair(sK8(sK6(powerset(X0)),X1),sK7(sK6(powerset(X0)),X1)))) )
| ~ spl17_75
| ~ spl17_325 ),
inference(resolution,[],[f2995,f644]) ).
fof(f2995,plain,
( ! [X2,X0,X1] :
( ~ in(X2,unordered_pair(singleton(sK7(sK6(powerset(X0)),X1)),unordered_pair(sK8(sK6(powerset(X0)),X1),sK7(sK6(powerset(X0)),X1))))
| sP0(sK6(powerset(X0)),X1)
| ~ empty(X0)
| empty(powerset(X0)) )
| ~ spl17_325 ),
inference(avatar_component_clause,[],[f2994]) ).
fof(f7648,plain,
( spl17_650
| ~ spl17_75
| ~ spl17_324 ),
inference(avatar_split_clause,[],[f3003,f2990,f643,f7646]) ).
fof(f2990,plain,
( spl17_324
<=> ! [X2,X0,X1] :
( empty(powerset(X0))
| sP0(sK6(powerset(X0)),X1)
| ~ empty(X0)
| ~ in(X2,unordered_pair(singleton(sK8(sK6(powerset(X0)),X1)),unordered_pair(sK9(sK6(powerset(X0)),X1),sK8(sK6(powerset(X0)),X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_324])]) ).
fof(f3003,plain,
( ! [X0,X1] :
( sP0(sK6(powerset(X0)),X1)
| ~ empty(X0)
| empty(powerset(X0))
| empty(unordered_pair(singleton(sK8(sK6(powerset(X0)),X1)),unordered_pair(sK9(sK6(powerset(X0)),X1),sK8(sK6(powerset(X0)),X1)))) )
| ~ spl17_75
| ~ spl17_324 ),
inference(resolution,[],[f2991,f644]) ).
fof(f2991,plain,
( ! [X2,X0,X1] :
( ~ in(X2,unordered_pair(singleton(sK8(sK6(powerset(X0)),X1)),unordered_pair(sK9(sK6(powerset(X0)),X1),sK8(sK6(powerset(X0)),X1))))
| sP0(sK6(powerset(X0)),X1)
| ~ empty(X0)
| empty(powerset(X0)) )
| ~ spl17_324 ),
inference(avatar_component_clause,[],[f2990]) ).
fof(f7644,plain,
( spl17_649
| ~ spl17_241
| ~ spl17_269 ),
inference(avatar_split_clause,[],[f2260,f2240,f1933,f7642]) ).
fof(f7642,plain,
( spl17_649
<=> ! [X0,X1] :
( element(sK9(X0,sK6(sK10(sK10(powerset(powerset(X1)))))),X1)
| empty(sK10(powerset(powerset(X1))))
| sP0(X0,sK6(sK10(sK10(powerset(powerset(X1))))))
| empty(sK10(sK10(powerset(powerset(X1))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_649])]) ).
fof(f2260,plain,
( ! [X0,X1] :
( element(sK9(X0,sK6(sK10(sK10(powerset(powerset(X1)))))),X1)
| empty(sK10(powerset(powerset(X1))))
| sP0(X0,sK6(sK10(sK10(powerset(powerset(X1))))))
| empty(sK10(sK10(powerset(powerset(X1))))) )
| ~ spl17_241
| ~ spl17_269 ),
inference(resolution,[],[f2241,f1934]) ).
fof(f7640,plain,
( spl17_648
| ~ spl17_53
| ~ spl17_404 ),
inference(avatar_split_clause,[],[f5173,f3828,f459,f7638]) ).
fof(f459,plain,
( spl17_53
<=> ! [X0,X3,X2,X1] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),cartesian_product2(X2,X3))
| in(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_53])]) ).
fof(f5173,plain,
( ! [X0,X1] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),the_InternalRel(sK2))
| in(X0,sK16) )
| ~ spl17_53
| ~ spl17_404 ),
inference(resolution,[],[f3829,f460]) ).
fof(f460,plain,
( ! [X2,X3,X0,X1] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),cartesian_product2(X2,X3))
| in(X0,X2) )
| ~ spl17_53 ),
inference(avatar_component_clause,[],[f459]) ).
fof(f7636,plain,
( spl17_647
| ~ spl17_240
| ~ spl17_269 ),
inference(avatar_split_clause,[],[f2257,f2240,f1929,f7634]) ).
fof(f7634,plain,
( spl17_647
<=> ! [X0,X1] :
( element(sK8(X0,sK6(sK10(sK10(powerset(powerset(X1)))))),X1)
| empty(sK10(powerset(powerset(X1))))
| sP0(X0,sK6(sK10(sK10(powerset(powerset(X1))))))
| empty(sK10(sK10(powerset(powerset(X1))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_647])]) ).
fof(f2257,plain,
( ! [X0,X1] :
( element(sK8(X0,sK6(sK10(sK10(powerset(powerset(X1)))))),X1)
| empty(sK10(powerset(powerset(X1))))
| sP0(X0,sK6(sK10(sK10(powerset(powerset(X1))))))
| empty(sK10(sK10(powerset(powerset(X1))))) )
| ~ spl17_240
| ~ spl17_269 ),
inference(resolution,[],[f2241,f1930]) ).
fof(f7632,plain,
( spl17_646
| ~ spl17_239
| ~ spl17_269 ),
inference(avatar_split_clause,[],[f2254,f2240,f1925,f7630]) ).
fof(f7630,plain,
( spl17_646
<=> ! [X0,X1] :
( element(sK7(X0,sK6(sK10(sK10(powerset(powerset(X1)))))),X1)
| empty(sK10(powerset(powerset(X1))))
| sP0(X0,sK6(sK10(sK10(powerset(powerset(X1))))))
| empty(sK10(sK10(powerset(powerset(X1))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_646])]) ).
fof(f2254,plain,
( ! [X0,X1] :
( element(sK7(X0,sK6(sK10(sK10(powerset(powerset(X1)))))),X1)
| empty(sK10(powerset(powerset(X1))))
| sP0(X0,sK6(sK10(sK10(powerset(powerset(X1))))))
| empty(sK10(sK10(powerset(powerset(X1))))) )
| ~ spl17_239
| ~ spl17_269 ),
inference(resolution,[],[f2241,f1926]) ).
fof(f7628,plain,
( spl17_645
| ~ spl17_229
| ~ spl17_269 ),
inference(avatar_split_clause,[],[f2252,f2240,f1885,f7626]) ).
fof(f7626,plain,
( spl17_645
<=> ! [X0] :
( element(sK10(sK10(powerset(sK10(sK10(powerset(powerset(X0))))))),X0)
| empty(sK10(powerset(powerset(X0))))
| empty(sK10(sK10(powerset(powerset(X0)))))
| empty(sK10(powerset(sK10(sK10(powerset(powerset(X0))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_645])]) ).
fof(f2252,plain,
( ! [X0] :
( element(sK10(sK10(powerset(sK10(sK10(powerset(powerset(X0))))))),X0)
| empty(sK10(powerset(powerset(X0))))
| empty(sK10(sK10(powerset(powerset(X0)))))
| empty(sK10(powerset(sK10(sK10(powerset(powerset(X0))))))) )
| ~ spl17_229
| ~ spl17_269 ),
inference(resolution,[],[f2241,f1886]) ).
fof(f7562,plain,
( spl17_644
| ~ spl17_101
| ~ spl17_314 ),
inference(avatar_split_clause,[],[f2847,f2836,f809,f7560]) ).
fof(f7560,plain,
( spl17_644
<=> ! [X0,X1] :
( ~ in(X0,the_carrier(X1))
| in(unordered_pair(singleton(X0),unordered_pair(X0,X0)),the_InternalRel(X1))
| ~ related(X1,X0,X0)
| ~ element(X0,the_carrier(X1))
| ~ rel_str(X1)
| ~ transitive_relstr(X1)
| ~ sP1(the_InternalRel(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_644])]) ).
fof(f809,plain,
( spl17_101
<=> ! [X0] :
( ~ transitive_relstr(X0)
| ~ rel_str(X0)
| sP0(the_InternalRel(X0),the_carrier(X0))
| ~ sP1(the_InternalRel(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_101])]) ).
fof(f2836,plain,
( spl17_314
<=> ! [X2,X0,X1] :
( in(unordered_pair(singleton(X0),unordered_pair(X0,X0)),the_InternalRel(X1))
| ~ in(X0,X2)
| ~ sP0(the_InternalRel(X1),X2)
| ~ related(X1,X0,X0)
| ~ element(X0,the_carrier(X1))
| ~ rel_str(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_314])]) ).
fof(f2847,plain,
( ! [X0,X1] :
( ~ in(X0,the_carrier(X1))
| in(unordered_pair(singleton(X0),unordered_pair(X0,X0)),the_InternalRel(X1))
| ~ related(X1,X0,X0)
| ~ element(X0,the_carrier(X1))
| ~ rel_str(X1)
| ~ transitive_relstr(X1)
| ~ sP1(the_InternalRel(X1)) )
| ~ spl17_101
| ~ spl17_314 ),
inference(duplicate_literal_removal,[],[f2839]) ).
fof(f2839,plain,
( ! [X0,X1] :
( ~ in(X0,the_carrier(X1))
| in(unordered_pair(singleton(X0),unordered_pair(X0,X0)),the_InternalRel(X1))
| ~ related(X1,X0,X0)
| ~ element(X0,the_carrier(X1))
| ~ rel_str(X1)
| ~ rel_str(X1)
| ~ transitive_relstr(X1)
| ~ sP1(the_InternalRel(X1)) )
| ~ spl17_101
| ~ spl17_314 ),
inference(resolution,[],[f2837,f810]) ).
fof(f810,plain,
( ! [X0] :
( sP0(the_InternalRel(X0),the_carrier(X0))
| ~ rel_str(X0)
| ~ transitive_relstr(X0)
| ~ sP1(the_InternalRel(X0)) )
| ~ spl17_101 ),
inference(avatar_component_clause,[],[f809]) ).
fof(f2837,plain,
( ! [X2,X0,X1] :
( ~ sP0(the_InternalRel(X1),X2)
| ~ in(X0,X2)
| in(unordered_pair(singleton(X0),unordered_pair(X0,X0)),the_InternalRel(X1))
| ~ related(X1,X0,X0)
| ~ element(X0,the_carrier(X1))
| ~ rel_str(X1) )
| ~ spl17_314 ),
inference(avatar_component_clause,[],[f2836]) ).
fof(f7558,plain,
( spl17_643
| ~ spl17_174
| ~ spl17_304 ),
inference(avatar_split_clause,[],[f2677,f2657,f1407,f7556]) ).
fof(f7556,plain,
( spl17_643
<=> ! [X2,X0,X1] :
( ~ rel_str(X0)
| empty(cartesian_product2(the_carrier(X0),the_carrier(X0)))
| ~ in(powerset(cartesian_product2(X1,X2)),the_InternalRel(X0))
| ~ relation_of2_as_subset(cartesian_product2(the_carrier(X0),the_carrier(X0)),X1,X2)
| empty(powerset(cartesian_product2(X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_643])]) ).
fof(f1407,plain,
( spl17_174
<=> ! [X2,X0,X1] :
( empty(powerset(cartesian_product2(X0,X1)))
| ~ relation_of2_as_subset(X2,X0,X1)
| ~ in(powerset(cartesian_product2(X0,X1)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_174])]) ).
fof(f2677,plain,
( ! [X2,X0,X1] :
( ~ rel_str(X0)
| empty(cartesian_product2(the_carrier(X0),the_carrier(X0)))
| ~ in(powerset(cartesian_product2(X1,X2)),the_InternalRel(X0))
| ~ relation_of2_as_subset(cartesian_product2(the_carrier(X0),the_carrier(X0)),X1,X2)
| empty(powerset(cartesian_product2(X1,X2))) )
| ~ spl17_174
| ~ spl17_304 ),
inference(resolution,[],[f2658,f1408]) ).
fof(f1408,plain,
( ! [X2,X0,X1] :
( ~ in(powerset(cartesian_product2(X0,X1)),X2)
| ~ relation_of2_as_subset(X2,X0,X1)
| empty(powerset(cartesian_product2(X0,X1))) )
| ~ spl17_174 ),
inference(avatar_component_clause,[],[f1407]) ).
fof(f7554,plain,
( spl17_642
| ~ spl17_241
| ~ spl17_271 ),
inference(avatar_split_clause,[],[f2328,f2289,f1933,f7552]) ).
fof(f7552,plain,
( spl17_642
<=> ! [X0,X1] :
( empty(sK6(powerset(X0)))
| element(sK9(X1,sK6(sK10(sK6(powerset(X0))))),X0)
| empty(powerset(X0))
| sP0(X1,sK6(sK10(sK6(powerset(X0)))))
| empty(sK10(sK6(powerset(X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_642])]) ).
fof(f2328,plain,
( ! [X0,X1] :
( empty(sK6(powerset(X0)))
| element(sK9(X1,sK6(sK10(sK6(powerset(X0))))),X0)
| empty(powerset(X0))
| sP0(X1,sK6(sK10(sK6(powerset(X0)))))
| empty(sK10(sK6(powerset(X0)))) )
| ~ spl17_241
| ~ spl17_271 ),
inference(resolution,[],[f2290,f1934]) ).
fof(f7550,plain,
( spl17_641
| ~ spl17_240
| ~ spl17_271 ),
inference(avatar_split_clause,[],[f2325,f2289,f1929,f7548]) ).
fof(f7548,plain,
( spl17_641
<=> ! [X0,X1] :
( empty(sK6(powerset(X0)))
| element(sK8(X1,sK6(sK10(sK6(powerset(X0))))),X0)
| empty(powerset(X0))
| sP0(X1,sK6(sK10(sK6(powerset(X0)))))
| empty(sK10(sK6(powerset(X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_641])]) ).
fof(f2325,plain,
( ! [X0,X1] :
( empty(sK6(powerset(X0)))
| element(sK8(X1,sK6(sK10(sK6(powerset(X0))))),X0)
| empty(powerset(X0))
| sP0(X1,sK6(sK10(sK6(powerset(X0)))))
| empty(sK10(sK6(powerset(X0)))) )
| ~ spl17_240
| ~ spl17_271 ),
inference(resolution,[],[f2290,f1930]) ).
fof(f7546,plain,
( spl17_640
| ~ spl17_239
| ~ spl17_271 ),
inference(avatar_split_clause,[],[f2322,f2289,f1925,f7544]) ).
fof(f7544,plain,
( spl17_640
<=> ! [X0,X1] :
( empty(sK6(powerset(X0)))
| element(sK7(X1,sK6(sK10(sK6(powerset(X0))))),X0)
| empty(powerset(X0))
| sP0(X1,sK6(sK10(sK6(powerset(X0)))))
| empty(sK10(sK6(powerset(X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_640])]) ).
fof(f2322,plain,
( ! [X0,X1] :
( empty(sK6(powerset(X0)))
| element(sK7(X1,sK6(sK10(sK6(powerset(X0))))),X0)
| empty(powerset(X0))
| sP0(X1,sK6(sK10(sK6(powerset(X0)))))
| empty(sK10(sK6(powerset(X0)))) )
| ~ spl17_239
| ~ spl17_271 ),
inference(resolution,[],[f2290,f1926]) ).
fof(f7542,plain,
( spl17_639
| ~ spl17_229
| ~ spl17_271 ),
inference(avatar_split_clause,[],[f2320,f2289,f1885,f7540]) ).
fof(f7540,plain,
( spl17_639
<=> ! [X0] :
( empty(sK6(powerset(X0)))
| element(sK10(sK10(powerset(sK10(sK6(powerset(X0)))))),X0)
| empty(powerset(X0))
| empty(sK10(sK6(powerset(X0))))
| empty(sK10(powerset(sK10(sK6(powerset(X0)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_639])]) ).
fof(f2320,plain,
( ! [X0] :
( empty(sK6(powerset(X0)))
| element(sK10(sK10(powerset(sK10(sK6(powerset(X0)))))),X0)
| empty(powerset(X0))
| empty(sK10(sK6(powerset(X0))))
| empty(sK10(powerset(sK10(sK6(powerset(X0)))))) )
| ~ spl17_229
| ~ spl17_271 ),
inference(resolution,[],[f2290,f1886]) ).
fof(f7521,plain,
( spl17_638
| ~ spl17_17
| ~ spl17_601 ),
inference(avatar_split_clause,[],[f7432,f7036,f255,f7518]) ).
fof(f7518,plain,
( spl17_638
<=> sP1(sK10(sK10(powerset(powerset(sK16))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_638])]) ).
fof(f7036,plain,
( spl17_601
<=> relation(sK10(sK10(powerset(powerset(sK16))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_601])]) ).
fof(f7432,plain,
( sP1(sK10(sK10(powerset(powerset(sK16)))))
| ~ spl17_17
| ~ spl17_601 ),
inference(resolution,[],[f7038,f256]) ).
fof(f7038,plain,
( relation(sK10(sK10(powerset(powerset(sK16)))))
| ~ spl17_601 ),
inference(avatar_component_clause,[],[f7036]) ).
fof(f7481,plain,
( spl17_637
| ~ spl17_25
| ~ spl17_321 ),
inference(avatar_split_clause,[],[f2945,f2873,f292,f7479]) ).
fof(f7479,plain,
( spl17_637
<=> ! [X0,X1] :
( empty(X0)
| sP0(sK10(powerset(X0)),X1)
| ~ in(X0,unordered_pair(singleton(sK7(sK10(powerset(X0)),X1)),unordered_pair(sK8(sK10(powerset(X0)),X1),sK7(sK10(powerset(X0)),X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_637])]) ).
fof(f2945,plain,
( ! [X0,X1] :
( empty(X0)
| sP0(sK10(powerset(X0)),X1)
| ~ in(X0,unordered_pair(singleton(sK7(sK10(powerset(X0)),X1)),unordered_pair(sK8(sK10(powerset(X0)),X1),sK7(sK10(powerset(X0)),X1)))) )
| ~ spl17_25
| ~ spl17_321 ),
inference(resolution,[],[f2874,f293]) ).
fof(f7477,plain,
( spl17_636
| ~ spl17_25
| ~ spl17_320 ),
inference(avatar_split_clause,[],[f2894,f2869,f292,f7475]) ).
fof(f7475,plain,
( spl17_636
<=> ! [X0,X1] :
( empty(X0)
| sP0(sK10(powerset(X0)),X1)
| ~ in(X0,unordered_pair(singleton(sK8(sK10(powerset(X0)),X1)),unordered_pair(sK9(sK10(powerset(X0)),X1),sK8(sK10(powerset(X0)),X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_636])]) ).
fof(f2894,plain,
( ! [X0,X1] :
( empty(X0)
| sP0(sK10(powerset(X0)),X1)
| ~ in(X0,unordered_pair(singleton(sK8(sK10(powerset(X0)),X1)),unordered_pair(sK9(sK10(powerset(X0)),X1),sK8(sK10(powerset(X0)),X1)))) )
| ~ spl17_25
| ~ spl17_320 ),
inference(resolution,[],[f2870,f293]) ).
fof(f7473,plain,
( spl17_635
| ~ spl17_224
| ~ spl17_269 ),
inference(avatar_split_clause,[],[f2251,f2240,f1808,f7471]) ).
fof(f7471,plain,
( spl17_635
<=> ! [X0] :
( element(sK10(sK6(sK10(sK10(powerset(powerset(X0)))))),X0)
| empty(sK10(powerset(powerset(X0))))
| empty(sK6(sK10(sK10(powerset(powerset(X0))))))
| empty(sK10(sK10(powerset(powerset(X0))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_635])]) ).
fof(f2251,plain,
( ! [X0] :
( element(sK10(sK6(sK10(sK10(powerset(powerset(X0)))))),X0)
| empty(sK10(powerset(powerset(X0))))
| empty(sK6(sK10(sK10(powerset(powerset(X0))))))
| empty(sK10(sK10(powerset(powerset(X0))))) )
| ~ spl17_224
| ~ spl17_269 ),
inference(resolution,[],[f2241,f1809]) ).
fof(f7469,plain,
( spl17_634
| ~ spl17_171
| ~ spl17_266 ),
inference(avatar_split_clause,[],[f2226,f2147,f1361,f7467]) ).
fof(f7467,plain,
( spl17_634
<=> ! [X2,X0,X1] :
( empty(sK9(X0,powerset(X1)))
| sP0(X2,sK10(powerset(sK9(X0,powerset(X1)))))
| element(sK9(X2,sK10(powerset(sK9(X0,powerset(X1))))),X1)
| sP0(X0,powerset(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_634])]) ).
fof(f2226,plain,
( ! [X2,X0,X1] :
( empty(sK9(X0,powerset(X1)))
| sP0(X2,sK10(powerset(sK9(X0,powerset(X1)))))
| element(sK9(X2,sK10(powerset(sK9(X0,powerset(X1))))),X1)
| sP0(X0,powerset(X1)) )
| ~ spl17_171
| ~ spl17_266 ),
inference(resolution,[],[f2148,f1362]) ).
fof(f7465,plain,
( spl17_633
| ~ spl17_169
| ~ spl17_266 ),
inference(avatar_split_clause,[],[f2224,f2147,f1353,f7463]) ).
fof(f7463,plain,
( spl17_633
<=> ! [X2,X0,X1] :
( empty(sK8(X0,powerset(X1)))
| sP0(X2,sK10(powerset(sK8(X0,powerset(X1)))))
| element(sK9(X2,sK10(powerset(sK8(X0,powerset(X1))))),X1)
| sP0(X0,powerset(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_633])]) ).
fof(f2224,plain,
( ! [X2,X0,X1] :
( empty(sK8(X0,powerset(X1)))
| sP0(X2,sK10(powerset(sK8(X0,powerset(X1)))))
| element(sK9(X2,sK10(powerset(sK8(X0,powerset(X1))))),X1)
| sP0(X0,powerset(X1)) )
| ~ spl17_169
| ~ spl17_266 ),
inference(resolution,[],[f2148,f1354]) ).
fof(f7461,plain,
( spl17_632
| ~ spl17_167
| ~ spl17_266 ),
inference(avatar_split_clause,[],[f2222,f2147,f1345,f7459]) ).
fof(f7459,plain,
( spl17_632
<=> ! [X2,X0,X1] :
( empty(sK7(X0,powerset(X1)))
| sP0(X2,sK10(powerset(sK7(X0,powerset(X1)))))
| element(sK9(X2,sK10(powerset(sK7(X0,powerset(X1))))),X1)
| sP0(X0,powerset(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_632])]) ).
fof(f2222,plain,
( ! [X2,X0,X1] :
( empty(sK7(X0,powerset(X1)))
| sP0(X2,sK10(powerset(sK7(X0,powerset(X1)))))
| element(sK9(X2,sK10(powerset(sK7(X0,powerset(X1))))),X1)
| sP0(X0,powerset(X1)) )
| ~ spl17_167
| ~ spl17_266 ),
inference(resolution,[],[f2148,f1346]) ).
fof(f7457,plain,
( spl17_631
| ~ spl17_171
| ~ spl17_265 ),
inference(avatar_split_clause,[],[f2205,f2143,f1361,f7455]) ).
fof(f7455,plain,
( spl17_631
<=> ! [X2,X0,X1] :
( empty(sK9(X0,powerset(X1)))
| sP0(X2,sK10(powerset(sK9(X0,powerset(X1)))))
| element(sK8(X2,sK10(powerset(sK9(X0,powerset(X1))))),X1)
| sP0(X0,powerset(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_631])]) ).
fof(f2205,plain,
( ! [X2,X0,X1] :
( empty(sK9(X0,powerset(X1)))
| sP0(X2,sK10(powerset(sK9(X0,powerset(X1)))))
| element(sK8(X2,sK10(powerset(sK9(X0,powerset(X1))))),X1)
| sP0(X0,powerset(X1)) )
| ~ spl17_171
| ~ spl17_265 ),
inference(resolution,[],[f2144,f1362]) ).
fof(f7453,plain,
( spl17_630
| ~ spl17_169
| ~ spl17_265 ),
inference(avatar_split_clause,[],[f2203,f2143,f1353,f7451]) ).
fof(f7451,plain,
( spl17_630
<=> ! [X2,X0,X1] :
( empty(sK8(X0,powerset(X1)))
| sP0(X2,sK10(powerset(sK8(X0,powerset(X1)))))
| element(sK8(X2,sK10(powerset(sK8(X0,powerset(X1))))),X1)
| sP0(X0,powerset(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_630])]) ).
fof(f2203,plain,
( ! [X2,X0,X1] :
( empty(sK8(X0,powerset(X1)))
| sP0(X2,sK10(powerset(sK8(X0,powerset(X1)))))
| element(sK8(X2,sK10(powerset(sK8(X0,powerset(X1))))),X1)
| sP0(X0,powerset(X1)) )
| ~ spl17_169
| ~ spl17_265 ),
inference(resolution,[],[f2144,f1354]) ).
fof(f7449,plain,
( spl17_629
| ~ spl17_167
| ~ spl17_265 ),
inference(avatar_split_clause,[],[f2201,f2143,f1345,f7447]) ).
fof(f7447,plain,
( spl17_629
<=> ! [X2,X0,X1] :
( empty(sK7(X0,powerset(X1)))
| sP0(X2,sK10(powerset(sK7(X0,powerset(X1)))))
| element(sK8(X2,sK10(powerset(sK7(X0,powerset(X1))))),X1)
| sP0(X0,powerset(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_629])]) ).
fof(f2201,plain,
( ! [X2,X0,X1] :
( empty(sK7(X0,powerset(X1)))
| sP0(X2,sK10(powerset(sK7(X0,powerset(X1)))))
| element(sK8(X2,sK10(powerset(sK7(X0,powerset(X1))))),X1)
| sP0(X0,powerset(X1)) )
| ~ spl17_167
| ~ spl17_265 ),
inference(resolution,[],[f2144,f1346]) ).
fof(f7445,plain,
( spl17_628
| ~ spl17_171
| ~ spl17_264 ),
inference(avatar_split_clause,[],[f2184,f2139,f1361,f7443]) ).
fof(f7443,plain,
( spl17_628
<=> ! [X2,X0,X1] :
( empty(sK9(X0,powerset(X1)))
| sP0(X2,sK10(powerset(sK9(X0,powerset(X1)))))
| element(sK7(X2,sK10(powerset(sK9(X0,powerset(X1))))),X1)
| sP0(X0,powerset(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_628])]) ).
fof(f2184,plain,
( ! [X2,X0,X1] :
( empty(sK9(X0,powerset(X1)))
| sP0(X2,sK10(powerset(sK9(X0,powerset(X1)))))
| element(sK7(X2,sK10(powerset(sK9(X0,powerset(X1))))),X1)
| sP0(X0,powerset(X1)) )
| ~ spl17_171
| ~ spl17_264 ),
inference(resolution,[],[f2140,f1362]) ).
fof(f7441,plain,
( spl17_627
| ~ spl17_169
| ~ spl17_264 ),
inference(avatar_split_clause,[],[f2182,f2139,f1353,f7439]) ).
fof(f7439,plain,
( spl17_627
<=> ! [X2,X0,X1] :
( empty(sK8(X0,powerset(X1)))
| sP0(X2,sK10(powerset(sK8(X0,powerset(X1)))))
| element(sK7(X2,sK10(powerset(sK8(X0,powerset(X1))))),X1)
| sP0(X0,powerset(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_627])]) ).
fof(f2182,plain,
( ! [X2,X0,X1] :
( empty(sK8(X0,powerset(X1)))
| sP0(X2,sK10(powerset(sK8(X0,powerset(X1)))))
| element(sK7(X2,sK10(powerset(sK8(X0,powerset(X1))))),X1)
| sP0(X0,powerset(X1)) )
| ~ spl17_169
| ~ spl17_264 ),
inference(resolution,[],[f2140,f1354]) ).
fof(f7437,plain,
( spl17_626
| ~ spl17_167
| ~ spl17_264 ),
inference(avatar_split_clause,[],[f2180,f2139,f1345,f7435]) ).
fof(f7435,plain,
( spl17_626
<=> ! [X2,X0,X1] :
( empty(sK7(X0,powerset(X1)))
| sP0(X2,sK10(powerset(sK7(X0,powerset(X1)))))
| element(sK7(X2,sK10(powerset(sK7(X0,powerset(X1))))),X1)
| sP0(X0,powerset(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_626])]) ).
fof(f2180,plain,
( ! [X2,X0,X1] :
( empty(sK7(X0,powerset(X1)))
| sP0(X2,sK10(powerset(sK7(X0,powerset(X1)))))
| element(sK7(X2,sK10(powerset(sK7(X0,powerset(X1))))),X1)
| sP0(X0,powerset(X1)) )
| ~ spl17_167
| ~ spl17_264 ),
inference(resolution,[],[f2140,f1346]) ).
fof(f7418,plain,
( spl17_625
| ~ spl17_41
| ~ spl17_301 ),
inference(avatar_split_clause,[],[f2649,f2566,f363,f7416]) ).
fof(f7416,plain,
( spl17_625
<=> ! [X0,X3,X2,X1] :
( sP0(X0,powerset(powerset(cartesian_product2(X1,X2))))
| sP0(X3,sK9(X0,powerset(powerset(cartesian_product2(X1,X2)))))
| relation(sK9(X3,sK9(X0,powerset(powerset(cartesian_product2(X1,X2)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_625])]) ).
fof(f2566,plain,
( spl17_301
<=> ! [X2,X0,X1] :
( element(sK9(X0,sK9(X1,powerset(X2))),X2)
| sP0(X1,powerset(X2))
| sP0(X0,sK9(X1,powerset(X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_301])]) ).
fof(f2649,plain,
( ! [X2,X3,X0,X1] :
( sP0(X0,powerset(powerset(cartesian_product2(X1,X2))))
| sP0(X3,sK9(X0,powerset(powerset(cartesian_product2(X1,X2)))))
| relation(sK9(X3,sK9(X0,powerset(powerset(cartesian_product2(X1,X2)))))) )
| ~ spl17_41
| ~ spl17_301 ),
inference(resolution,[],[f2567,f364]) ).
fof(f2567,plain,
( ! [X2,X0,X1] :
( element(sK9(X0,sK9(X1,powerset(X2))),X2)
| sP0(X1,powerset(X2))
| sP0(X0,sK9(X1,powerset(X2))) )
| ~ spl17_301 ),
inference(avatar_component_clause,[],[f2566]) ).
fof(f7413,plain,
( spl17_624
| ~ spl17_41
| ~ spl17_300 ),
inference(avatar_split_clause,[],[f2645,f2562,f363,f7411]) ).
fof(f7411,plain,
( spl17_624
<=> ! [X0,X3,X2,X1] :
( sP0(X0,powerset(powerset(cartesian_product2(X1,X2))))
| sP0(X3,sK9(X0,powerset(powerset(cartesian_product2(X1,X2)))))
| relation(sK8(X3,sK9(X0,powerset(powerset(cartesian_product2(X1,X2)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_624])]) ).
fof(f2562,plain,
( spl17_300
<=> ! [X2,X0,X1] :
( element(sK8(X0,sK9(X1,powerset(X2))),X2)
| sP0(X1,powerset(X2))
| sP0(X0,sK9(X1,powerset(X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_300])]) ).
fof(f2645,plain,
( ! [X2,X3,X0,X1] :
( sP0(X0,powerset(powerset(cartesian_product2(X1,X2))))
| sP0(X3,sK9(X0,powerset(powerset(cartesian_product2(X1,X2)))))
| relation(sK8(X3,sK9(X0,powerset(powerset(cartesian_product2(X1,X2)))))) )
| ~ spl17_41
| ~ spl17_300 ),
inference(resolution,[],[f2563,f364]) ).
fof(f2563,plain,
( ! [X2,X0,X1] :
( element(sK8(X0,sK9(X1,powerset(X2))),X2)
| sP0(X1,powerset(X2))
| sP0(X0,sK9(X1,powerset(X2))) )
| ~ spl17_300 ),
inference(avatar_component_clause,[],[f2562]) ).
fof(f7409,plain,
( spl17_623
| ~ spl17_41
| ~ spl17_299 ),
inference(avatar_split_clause,[],[f2641,f2558,f363,f7407]) ).
fof(f7407,plain,
( spl17_623
<=> ! [X0,X3,X2,X1] :
( sP0(X0,powerset(powerset(cartesian_product2(X1,X2))))
| sP0(X3,sK9(X0,powerset(powerset(cartesian_product2(X1,X2)))))
| relation(sK7(X3,sK9(X0,powerset(powerset(cartesian_product2(X1,X2)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_623])]) ).
fof(f2558,plain,
( spl17_299
<=> ! [X2,X0,X1] :
( element(sK7(X0,sK9(X1,powerset(X2))),X2)
| sP0(X1,powerset(X2))
| sP0(X0,sK9(X1,powerset(X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_299])]) ).
fof(f2641,plain,
( ! [X2,X3,X0,X1] :
( sP0(X0,powerset(powerset(cartesian_product2(X1,X2))))
| sP0(X3,sK9(X0,powerset(powerset(cartesian_product2(X1,X2)))))
| relation(sK7(X3,sK9(X0,powerset(powerset(cartesian_product2(X1,X2)))))) )
| ~ spl17_41
| ~ spl17_299 ),
inference(resolution,[],[f2559,f364]) ).
fof(f2559,plain,
( ! [X2,X0,X1] :
( element(sK7(X0,sK9(X1,powerset(X2))),X2)
| sP0(X1,powerset(X2))
| sP0(X0,sK9(X1,powerset(X2))) )
| ~ spl17_299 ),
inference(avatar_component_clause,[],[f2558]) ).
fof(f7405,plain,
( spl17_622
| ~ spl17_41
| ~ spl17_298 ),
inference(avatar_split_clause,[],[f2637,f2554,f363,f7403]) ).
fof(f7403,plain,
( spl17_622
<=> ! [X0,X3,X2,X1] :
( sP0(X0,powerset(powerset(cartesian_product2(X1,X2))))
| sP0(X3,sK8(X0,powerset(powerset(cartesian_product2(X1,X2)))))
| relation(sK9(X3,sK8(X0,powerset(powerset(cartesian_product2(X1,X2)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_622])]) ).
fof(f2554,plain,
( spl17_298
<=> ! [X2,X0,X1] :
( element(sK9(X0,sK8(X1,powerset(X2))),X2)
| sP0(X1,powerset(X2))
| sP0(X0,sK8(X1,powerset(X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_298])]) ).
fof(f2637,plain,
( ! [X2,X3,X0,X1] :
( sP0(X0,powerset(powerset(cartesian_product2(X1,X2))))
| sP0(X3,sK8(X0,powerset(powerset(cartesian_product2(X1,X2)))))
| relation(sK9(X3,sK8(X0,powerset(powerset(cartesian_product2(X1,X2)))))) )
| ~ spl17_41
| ~ spl17_298 ),
inference(resolution,[],[f2555,f364]) ).
fof(f2555,plain,
( ! [X2,X0,X1] :
( element(sK9(X0,sK8(X1,powerset(X2))),X2)
| sP0(X1,powerset(X2))
| sP0(X0,sK8(X1,powerset(X2))) )
| ~ spl17_298 ),
inference(avatar_component_clause,[],[f2554]) ).
fof(f7401,plain,
( spl17_621
| ~ spl17_41
| ~ spl17_297 ),
inference(avatar_split_clause,[],[f2633,f2550,f363,f7399]) ).
fof(f7399,plain,
( spl17_621
<=> ! [X0,X3,X2,X1] :
( sP0(X0,powerset(powerset(cartesian_product2(X1,X2))))
| sP0(X3,sK8(X0,powerset(powerset(cartesian_product2(X1,X2)))))
| relation(sK8(X3,sK8(X0,powerset(powerset(cartesian_product2(X1,X2)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_621])]) ).
fof(f2550,plain,
( spl17_297
<=> ! [X2,X0,X1] :
( element(sK8(X0,sK8(X1,powerset(X2))),X2)
| sP0(X1,powerset(X2))
| sP0(X0,sK8(X1,powerset(X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_297])]) ).
fof(f2633,plain,
( ! [X2,X3,X0,X1] :
( sP0(X0,powerset(powerset(cartesian_product2(X1,X2))))
| sP0(X3,sK8(X0,powerset(powerset(cartesian_product2(X1,X2)))))
| relation(sK8(X3,sK8(X0,powerset(powerset(cartesian_product2(X1,X2)))))) )
| ~ spl17_41
| ~ spl17_297 ),
inference(resolution,[],[f2551,f364]) ).
fof(f2551,plain,
( ! [X2,X0,X1] :
( element(sK8(X0,sK8(X1,powerset(X2))),X2)
| sP0(X1,powerset(X2))
| sP0(X0,sK8(X1,powerset(X2))) )
| ~ spl17_297 ),
inference(avatar_component_clause,[],[f2550]) ).
fof(f7397,plain,
( spl17_620
| ~ spl17_41
| ~ spl17_296 ),
inference(avatar_split_clause,[],[f2629,f2546,f363,f7395]) ).
fof(f7395,plain,
( spl17_620
<=> ! [X0,X3,X2,X1] :
( sP0(X0,powerset(powerset(cartesian_product2(X1,X2))))
| sP0(X3,sK8(X0,powerset(powerset(cartesian_product2(X1,X2)))))
| relation(sK7(X3,sK8(X0,powerset(powerset(cartesian_product2(X1,X2)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_620])]) ).
fof(f2546,plain,
( spl17_296
<=> ! [X2,X0,X1] :
( element(sK7(X0,sK8(X1,powerset(X2))),X2)
| sP0(X1,powerset(X2))
| sP0(X0,sK8(X1,powerset(X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_296])]) ).
fof(f2629,plain,
( ! [X2,X3,X0,X1] :
( sP0(X0,powerset(powerset(cartesian_product2(X1,X2))))
| sP0(X3,sK8(X0,powerset(powerset(cartesian_product2(X1,X2)))))
| relation(sK7(X3,sK8(X0,powerset(powerset(cartesian_product2(X1,X2)))))) )
| ~ spl17_41
| ~ spl17_296 ),
inference(resolution,[],[f2547,f364]) ).
fof(f2547,plain,
( ! [X2,X0,X1] :
( element(sK7(X0,sK8(X1,powerset(X2))),X2)
| sP0(X1,powerset(X2))
| sP0(X0,sK8(X1,powerset(X2))) )
| ~ spl17_296 ),
inference(avatar_component_clause,[],[f2546]) ).
fof(f7393,plain,
( spl17_619
| ~ spl17_41
| ~ spl17_295 ),
inference(avatar_split_clause,[],[f2625,f2542,f363,f7391]) ).
fof(f7391,plain,
( spl17_619
<=> ! [X0,X3,X2,X1] :
( sP0(X0,powerset(powerset(cartesian_product2(X1,X2))))
| sP0(X3,sK7(X0,powerset(powerset(cartesian_product2(X1,X2)))))
| relation(sK9(X3,sK7(X0,powerset(powerset(cartesian_product2(X1,X2)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_619])]) ).
fof(f2542,plain,
( spl17_295
<=> ! [X2,X0,X1] :
( element(sK9(X0,sK7(X1,powerset(X2))),X2)
| sP0(X1,powerset(X2))
| sP0(X0,sK7(X1,powerset(X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_295])]) ).
fof(f2625,plain,
( ! [X2,X3,X0,X1] :
( sP0(X0,powerset(powerset(cartesian_product2(X1,X2))))
| sP0(X3,sK7(X0,powerset(powerset(cartesian_product2(X1,X2)))))
| relation(sK9(X3,sK7(X0,powerset(powerset(cartesian_product2(X1,X2)))))) )
| ~ spl17_41
| ~ spl17_295 ),
inference(resolution,[],[f2543,f364]) ).
fof(f2543,plain,
( ! [X2,X0,X1] :
( element(sK9(X0,sK7(X1,powerset(X2))),X2)
| sP0(X1,powerset(X2))
| sP0(X0,sK7(X1,powerset(X2))) )
| ~ spl17_295 ),
inference(avatar_component_clause,[],[f2542]) ).
fof(f7389,plain,
( spl17_618
| ~ spl17_41
| ~ spl17_294 ),
inference(avatar_split_clause,[],[f2621,f2538,f363,f7387]) ).
fof(f7387,plain,
( spl17_618
<=> ! [X0,X3,X2,X1] :
( sP0(X0,powerset(powerset(cartesian_product2(X1,X2))))
| sP0(X3,sK7(X0,powerset(powerset(cartesian_product2(X1,X2)))))
| relation(sK8(X3,sK7(X0,powerset(powerset(cartesian_product2(X1,X2)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_618])]) ).
fof(f2538,plain,
( spl17_294
<=> ! [X2,X0,X1] :
( element(sK8(X0,sK7(X1,powerset(X2))),X2)
| sP0(X1,powerset(X2))
| sP0(X0,sK7(X1,powerset(X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_294])]) ).
fof(f2621,plain,
( ! [X2,X3,X0,X1] :
( sP0(X0,powerset(powerset(cartesian_product2(X1,X2))))
| sP0(X3,sK7(X0,powerset(powerset(cartesian_product2(X1,X2)))))
| relation(sK8(X3,sK7(X0,powerset(powerset(cartesian_product2(X1,X2)))))) )
| ~ spl17_41
| ~ spl17_294 ),
inference(resolution,[],[f2539,f364]) ).
fof(f2539,plain,
( ! [X2,X0,X1] :
( element(sK8(X0,sK7(X1,powerset(X2))),X2)
| sP0(X1,powerset(X2))
| sP0(X0,sK7(X1,powerset(X2))) )
| ~ spl17_294 ),
inference(avatar_component_clause,[],[f2538]) ).
fof(f7385,plain,
( spl17_617
| ~ spl17_41
| ~ spl17_293 ),
inference(avatar_split_clause,[],[f2613,f2534,f363,f7383]) ).
fof(f7383,plain,
( spl17_617
<=> ! [X0,X3,X2,X1] :
( sP0(X0,powerset(powerset(cartesian_product2(X1,X2))))
| sP0(X3,sK7(X0,powerset(powerset(cartesian_product2(X1,X2)))))
| relation(sK7(X3,sK7(X0,powerset(powerset(cartesian_product2(X1,X2)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_617])]) ).
fof(f2534,plain,
( spl17_293
<=> ! [X2,X0,X1] :
( element(sK7(X0,sK7(X1,powerset(X2))),X2)
| sP0(X1,powerset(X2))
| sP0(X0,sK7(X1,powerset(X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_293])]) ).
fof(f2613,plain,
( ! [X2,X3,X0,X1] :
( sP0(X0,powerset(powerset(cartesian_product2(X1,X2))))
| sP0(X3,sK7(X0,powerset(powerset(cartesian_product2(X1,X2)))))
| relation(sK7(X3,sK7(X0,powerset(powerset(cartesian_product2(X1,X2)))))) )
| ~ spl17_41
| ~ spl17_293 ),
inference(resolution,[],[f2535,f364]) ).
fof(f2535,plain,
( ! [X2,X0,X1] :
( element(sK7(X0,sK7(X1,powerset(X2))),X2)
| sP0(X1,powerset(X2))
| sP0(X0,sK7(X1,powerset(X2))) )
| ~ spl17_293 ),
inference(avatar_component_clause,[],[f2534]) ).
fof(f7381,plain,
( spl17_616
| ~ spl17_224
| ~ spl17_271 ),
inference(avatar_split_clause,[],[f2319,f2289,f1808,f7379]) ).
fof(f7379,plain,
( spl17_616
<=> ! [X0] :
( empty(sK6(powerset(X0)))
| element(sK10(sK6(sK10(sK6(powerset(X0))))),X0)
| empty(powerset(X0))
| empty(sK6(sK10(sK6(powerset(X0)))))
| empty(sK10(sK6(powerset(X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_616])]) ).
fof(f2319,plain,
( ! [X0] :
( empty(sK6(powerset(X0)))
| element(sK10(sK6(sK10(sK6(powerset(X0))))),X0)
| empty(powerset(X0))
| empty(sK6(sK10(sK6(powerset(X0)))))
| empty(sK10(sK6(powerset(X0)))) )
| ~ spl17_224
| ~ spl17_271 ),
inference(resolution,[],[f2290,f1809]) ).
fof(f7377,plain,
( spl17_615
| ~ spl17_69
| ~ spl17_600 ),
inference(avatar_split_clause,[],[f7251,f7032,f567,f7374]) ).
fof(f7374,plain,
( spl17_615
<=> sK16 = sK10(powerset(powerset(sK16))) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_615])]) ).
fof(f567,plain,
( spl17_69
<=> ! [X0] :
( sK16 = X0
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_69])]) ).
fof(f7032,plain,
( spl17_600
<=> empty(sK10(powerset(powerset(sK16)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_600])]) ).
fof(f7251,plain,
( sK16 = sK10(powerset(powerset(sK16)))
| ~ spl17_69
| ~ spl17_600 ),
inference(resolution,[],[f7034,f568]) ).
fof(f568,plain,
( ! [X0] :
( ~ empty(X0)
| sK16 = X0 )
| ~ spl17_69 ),
inference(avatar_component_clause,[],[f567]) ).
fof(f7034,plain,
( empty(sK10(powerset(powerset(sK16))))
| ~ spl17_600 ),
inference(avatar_component_clause,[],[f7032]) ).
fof(f7312,plain,
( spl17_614
| ~ spl17_74
| ~ spl17_314 ),
inference(avatar_split_clause,[],[f2840,f2836,f633,f7310]) ).
fof(f7310,plain,
( spl17_614
<=> ! [X2,X0,X1] :
( ~ in(X0,X1)
| in(unordered_pair(singleton(X0),unordered_pair(X0,X0)),the_InternalRel(X2))
| ~ related(X2,X0,X0)
| ~ element(X0,the_carrier(X2))
| ~ rel_str(X2)
| ~ empty(the_InternalRel(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_614])]) ).
fof(f633,plain,
( spl17_74
<=> ! [X0,X1] :
( sP0(X0,X1)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_74])]) ).
fof(f2840,plain,
( ! [X2,X0,X1] :
( ~ in(X0,X1)
| in(unordered_pair(singleton(X0),unordered_pair(X0,X0)),the_InternalRel(X2))
| ~ related(X2,X0,X0)
| ~ element(X0,the_carrier(X2))
| ~ rel_str(X2)
| ~ empty(the_InternalRel(X2)) )
| ~ spl17_74
| ~ spl17_314 ),
inference(resolution,[],[f2837,f634]) ).
fof(f634,plain,
( ! [X0,X1] :
( sP0(X0,X1)
| ~ empty(X0) )
| ~ spl17_74 ),
inference(avatar_component_clause,[],[f633]) ).
fof(f7308,plain,
( spl17_613
| ~ spl17_171
| ~ spl17_241 ),
inference(avatar_split_clause,[],[f2058,f1933,f1361,f7306]) ).
fof(f7306,plain,
( spl17_613
<=> ! [X2,X0,X1] :
( sP0(X0,sK6(sK9(X1,powerset(X2))))
| empty(sK9(X1,powerset(X2)))
| element(sK9(X0,sK6(sK9(X1,powerset(X2)))),X2)
| sP0(X1,powerset(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_613])]) ).
fof(f2058,plain,
( ! [X2,X0,X1] :
( sP0(X0,sK6(sK9(X1,powerset(X2))))
| empty(sK9(X1,powerset(X2)))
| element(sK9(X0,sK6(sK9(X1,powerset(X2)))),X2)
| sP0(X1,powerset(X2)) )
| ~ spl17_171
| ~ spl17_241 ),
inference(resolution,[],[f1934,f1362]) ).
fof(f7304,plain,
( spl17_612
| ~ spl17_169
| ~ spl17_241 ),
inference(avatar_split_clause,[],[f2056,f1933,f1353,f7302]) ).
fof(f7302,plain,
( spl17_612
<=> ! [X2,X0,X1] :
( sP0(X0,sK6(sK8(X1,powerset(X2))))
| empty(sK8(X1,powerset(X2)))
| element(sK9(X0,sK6(sK8(X1,powerset(X2)))),X2)
| sP0(X1,powerset(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_612])]) ).
fof(f2056,plain,
( ! [X2,X0,X1] :
( sP0(X0,sK6(sK8(X1,powerset(X2))))
| empty(sK8(X1,powerset(X2)))
| element(sK9(X0,sK6(sK8(X1,powerset(X2)))),X2)
| sP0(X1,powerset(X2)) )
| ~ spl17_169
| ~ spl17_241 ),
inference(resolution,[],[f1934,f1354]) ).
fof(f7300,plain,
( spl17_611
| ~ spl17_167
| ~ spl17_241 ),
inference(avatar_split_clause,[],[f2054,f1933,f1345,f7298]) ).
fof(f7298,plain,
( spl17_611
<=> ! [X2,X0,X1] :
( sP0(X0,sK6(sK7(X1,powerset(X2))))
| empty(sK7(X1,powerset(X2)))
| element(sK9(X0,sK6(sK7(X1,powerset(X2)))),X2)
| sP0(X1,powerset(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_611])]) ).
fof(f2054,plain,
( ! [X2,X0,X1] :
( sP0(X0,sK6(sK7(X1,powerset(X2))))
| empty(sK7(X1,powerset(X2)))
| element(sK9(X0,sK6(sK7(X1,powerset(X2)))),X2)
| sP0(X1,powerset(X2)) )
| ~ spl17_167
| ~ spl17_241 ),
inference(resolution,[],[f1934,f1346]) ).
fof(f7296,plain,
( spl17_610
| ~ spl17_171
| ~ spl17_240 ),
inference(avatar_split_clause,[],[f2039,f1929,f1361,f7294]) ).
fof(f7294,plain,
( spl17_610
<=> ! [X2,X0,X1] :
( sP0(X0,sK6(sK9(X1,powerset(X2))))
| empty(sK9(X1,powerset(X2)))
| element(sK8(X0,sK6(sK9(X1,powerset(X2)))),X2)
| sP0(X1,powerset(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_610])]) ).
fof(f2039,plain,
( ! [X2,X0,X1] :
( sP0(X0,sK6(sK9(X1,powerset(X2))))
| empty(sK9(X1,powerset(X2)))
| element(sK8(X0,sK6(sK9(X1,powerset(X2)))),X2)
| sP0(X1,powerset(X2)) )
| ~ spl17_171
| ~ spl17_240 ),
inference(resolution,[],[f1930,f1362]) ).
fof(f7292,plain,
( spl17_609
| ~ spl17_169
| ~ spl17_240 ),
inference(avatar_split_clause,[],[f2037,f1929,f1353,f7290]) ).
fof(f7290,plain,
( spl17_609
<=> ! [X2,X0,X1] :
( sP0(X0,sK6(sK8(X1,powerset(X2))))
| empty(sK8(X1,powerset(X2)))
| element(sK8(X0,sK6(sK8(X1,powerset(X2)))),X2)
| sP0(X1,powerset(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_609])]) ).
fof(f2037,plain,
( ! [X2,X0,X1] :
( sP0(X0,sK6(sK8(X1,powerset(X2))))
| empty(sK8(X1,powerset(X2)))
| element(sK8(X0,sK6(sK8(X1,powerset(X2)))),X2)
| sP0(X1,powerset(X2)) )
| ~ spl17_169
| ~ spl17_240 ),
inference(resolution,[],[f1930,f1354]) ).
fof(f7288,plain,
( spl17_608
| ~ spl17_167
| ~ spl17_240 ),
inference(avatar_split_clause,[],[f2035,f1929,f1345,f7286]) ).
fof(f7286,plain,
( spl17_608
<=> ! [X2,X0,X1] :
( sP0(X0,sK6(sK7(X1,powerset(X2))))
| empty(sK7(X1,powerset(X2)))
| element(sK8(X0,sK6(sK7(X1,powerset(X2)))),X2)
| sP0(X1,powerset(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_608])]) ).
fof(f2035,plain,
( ! [X2,X0,X1] :
( sP0(X0,sK6(sK7(X1,powerset(X2))))
| empty(sK7(X1,powerset(X2)))
| element(sK8(X0,sK6(sK7(X1,powerset(X2)))),X2)
| sP0(X1,powerset(X2)) )
| ~ spl17_167
| ~ spl17_240 ),
inference(resolution,[],[f1930,f1346]) ).
fof(f7284,plain,
( spl17_607
| ~ spl17_171
| ~ spl17_239 ),
inference(avatar_split_clause,[],[f2020,f1925,f1361,f7282]) ).
fof(f7282,plain,
( spl17_607
<=> ! [X2,X0,X1] :
( sP0(X0,sK6(sK9(X1,powerset(X2))))
| empty(sK9(X1,powerset(X2)))
| element(sK7(X0,sK6(sK9(X1,powerset(X2)))),X2)
| sP0(X1,powerset(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_607])]) ).
fof(f2020,plain,
( ! [X2,X0,X1] :
( sP0(X0,sK6(sK9(X1,powerset(X2))))
| empty(sK9(X1,powerset(X2)))
| element(sK7(X0,sK6(sK9(X1,powerset(X2)))),X2)
| sP0(X1,powerset(X2)) )
| ~ spl17_171
| ~ spl17_239 ),
inference(resolution,[],[f1926,f1362]) ).
fof(f7249,plain,
( spl17_606
| ~ spl17_169
| ~ spl17_239 ),
inference(avatar_split_clause,[],[f2018,f1925,f1353,f7247]) ).
fof(f7247,plain,
( spl17_606
<=> ! [X2,X0,X1] :
( sP0(X0,sK6(sK8(X1,powerset(X2))))
| empty(sK8(X1,powerset(X2)))
| element(sK7(X0,sK6(sK8(X1,powerset(X2)))),X2)
| sP0(X1,powerset(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_606])]) ).
fof(f2018,plain,
( ! [X2,X0,X1] :
( sP0(X0,sK6(sK8(X1,powerset(X2))))
| empty(sK8(X1,powerset(X2)))
| element(sK7(X0,sK6(sK8(X1,powerset(X2)))),X2)
| sP0(X1,powerset(X2)) )
| ~ spl17_169
| ~ spl17_239 ),
inference(resolution,[],[f1926,f1354]) ).
fof(f7245,plain,
( spl17_605
| ~ spl17_167
| ~ spl17_239 ),
inference(avatar_split_clause,[],[f2016,f1925,f1345,f7243]) ).
fof(f7243,plain,
( spl17_605
<=> ! [X2,X0,X1] :
( sP0(X0,sK6(sK7(X1,powerset(X2))))
| empty(sK7(X1,powerset(X2)))
| element(sK7(X0,sK6(sK7(X1,powerset(X2)))),X2)
| sP0(X1,powerset(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_605])]) ).
fof(f2016,plain,
( ! [X2,X0,X1] :
( sP0(X0,sK6(sK7(X1,powerset(X2))))
| empty(sK7(X1,powerset(X2)))
| element(sK7(X0,sK6(sK7(X1,powerset(X2)))),X2)
| sP0(X1,powerset(X2)) )
| ~ spl17_167
| ~ spl17_239 ),
inference(resolution,[],[f1926,f1346]) ).
fof(f7241,plain,
( spl17_604
| ~ spl17_171
| ~ spl17_229 ),
inference(avatar_split_clause,[],[f1988,f1885,f1361,f7239]) ).
fof(f7239,plain,
( spl17_604
<=> ! [X0,X1] :
( empty(sK9(X0,powerset(X1)))
| empty(sK10(powerset(sK9(X0,powerset(X1)))))
| element(sK10(sK10(powerset(sK9(X0,powerset(X1))))),X1)
| sP0(X0,powerset(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_604])]) ).
fof(f1988,plain,
( ! [X0,X1] :
( empty(sK9(X0,powerset(X1)))
| empty(sK10(powerset(sK9(X0,powerset(X1)))))
| element(sK10(sK10(powerset(sK9(X0,powerset(X1))))),X1)
| sP0(X0,powerset(X1)) )
| ~ spl17_171
| ~ spl17_229 ),
inference(resolution,[],[f1886,f1362]) ).
fof(f7237,plain,
( spl17_603
| ~ spl17_169
| ~ spl17_229 ),
inference(avatar_split_clause,[],[f1986,f1885,f1353,f7235]) ).
fof(f7235,plain,
( spl17_603
<=> ! [X0,X1] :
( empty(sK8(X0,powerset(X1)))
| empty(sK10(powerset(sK8(X0,powerset(X1)))))
| element(sK10(sK10(powerset(sK8(X0,powerset(X1))))),X1)
| sP0(X0,powerset(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_603])]) ).
fof(f1986,plain,
( ! [X0,X1] :
( empty(sK8(X0,powerset(X1)))
| empty(sK10(powerset(sK8(X0,powerset(X1)))))
| element(sK10(sK10(powerset(sK8(X0,powerset(X1))))),X1)
| sP0(X0,powerset(X1)) )
| ~ spl17_169
| ~ spl17_229 ),
inference(resolution,[],[f1886,f1354]) ).
fof(f7233,plain,
( spl17_602
| ~ spl17_167
| ~ spl17_229 ),
inference(avatar_split_clause,[],[f1984,f1885,f1345,f7231]) ).
fof(f7231,plain,
( spl17_602
<=> ! [X0,X1] :
( empty(sK7(X0,powerset(X1)))
| empty(sK10(powerset(sK7(X0,powerset(X1)))))
| element(sK10(sK10(powerset(sK7(X0,powerset(X1))))),X1)
| sP0(X0,powerset(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_602])]) ).
fof(f1984,plain,
( ! [X0,X1] :
( empty(sK7(X0,powerset(X1)))
| empty(sK10(powerset(sK7(X0,powerset(X1)))))
| element(sK10(sK10(powerset(sK7(X0,powerset(X1))))),X1)
| sP0(X0,powerset(X1)) )
| ~ spl17_167
| ~ spl17_229 ),
inference(resolution,[],[f1886,f1346]) ).
fof(f7039,plain,
( spl17_600
| spl17_601
| ~ spl17_146
| ~ spl17_442 ),
inference(avatar_split_clause,[],[f4313,f4204,f1143,f7036,f7032]) ).
fof(f1143,plain,
( spl17_146
<=> ! [X0] :
( element(sK10(sK10(powerset(X0))),X0)
| empty(sK10(powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_146])]) ).
fof(f4313,plain,
( relation(sK10(sK10(powerset(powerset(sK16)))))
| empty(sK10(powerset(powerset(sK16))))
| ~ spl17_146
| ~ spl17_442 ),
inference(resolution,[],[f4205,f1144]) ).
fof(f1144,plain,
( ! [X0] :
( element(sK10(sK10(powerset(X0))),X0)
| empty(sK10(powerset(X0))) )
| ~ spl17_146 ),
inference(avatar_component_clause,[],[f1143]) ).
fof(f6785,plain,
( spl17_599
| ~ spl17_51
| ~ spl17_301 ),
inference(avatar_split_clause,[],[f2651,f2566,f439,f6783]) ).
fof(f6783,plain,
( spl17_599
<=> ! [X0,X3,X2,X1] :
( sP0(X0,powerset(powerset(X1)))
| sP0(X2,sK9(X0,powerset(powerset(X1))))
| element(X3,X1)
| ~ in(X3,sK9(X2,sK9(X0,powerset(powerset(X1))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_599])]) ).
fof(f2651,plain,
( ! [X2,X3,X0,X1] :
( sP0(X0,powerset(powerset(X1)))
| sP0(X2,sK9(X0,powerset(powerset(X1))))
| element(X3,X1)
| ~ in(X3,sK9(X2,sK9(X0,powerset(powerset(X1))))) )
| ~ spl17_51
| ~ spl17_301 ),
inference(resolution,[],[f2567,f440]) ).
fof(f6781,plain,
( spl17_598
| ~ spl17_51
| ~ spl17_300 ),
inference(avatar_split_clause,[],[f2647,f2562,f439,f6779]) ).
fof(f6779,plain,
( spl17_598
<=> ! [X0,X3,X2,X1] :
( sP0(X0,powerset(powerset(X1)))
| sP0(X2,sK9(X0,powerset(powerset(X1))))
| element(X3,X1)
| ~ in(X3,sK8(X2,sK9(X0,powerset(powerset(X1))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_598])]) ).
fof(f2647,plain,
( ! [X2,X3,X0,X1] :
( sP0(X0,powerset(powerset(X1)))
| sP0(X2,sK9(X0,powerset(powerset(X1))))
| element(X3,X1)
| ~ in(X3,sK8(X2,sK9(X0,powerset(powerset(X1))))) )
| ~ spl17_51
| ~ spl17_300 ),
inference(resolution,[],[f2563,f440]) ).
fof(f6777,plain,
( spl17_597
| ~ spl17_51
| ~ spl17_299 ),
inference(avatar_split_clause,[],[f2643,f2558,f439,f6775]) ).
fof(f6775,plain,
( spl17_597
<=> ! [X0,X3,X2,X1] :
( sP0(X0,powerset(powerset(X1)))
| sP0(X2,sK9(X0,powerset(powerset(X1))))
| element(X3,X1)
| ~ in(X3,sK7(X2,sK9(X0,powerset(powerset(X1))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_597])]) ).
fof(f2643,plain,
( ! [X2,X3,X0,X1] :
( sP0(X0,powerset(powerset(X1)))
| sP0(X2,sK9(X0,powerset(powerset(X1))))
| element(X3,X1)
| ~ in(X3,sK7(X2,sK9(X0,powerset(powerset(X1))))) )
| ~ spl17_51
| ~ spl17_299 ),
inference(resolution,[],[f2559,f440]) ).
fof(f6773,plain,
( spl17_596
| ~ spl17_51
| ~ spl17_298 ),
inference(avatar_split_clause,[],[f2639,f2554,f439,f6771]) ).
fof(f6771,plain,
( spl17_596
<=> ! [X0,X3,X2,X1] :
( sP0(X0,powerset(powerset(X1)))
| sP0(X2,sK8(X0,powerset(powerset(X1))))
| element(X3,X1)
| ~ in(X3,sK9(X2,sK8(X0,powerset(powerset(X1))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_596])]) ).
fof(f2639,plain,
( ! [X2,X3,X0,X1] :
( sP0(X0,powerset(powerset(X1)))
| sP0(X2,sK8(X0,powerset(powerset(X1))))
| element(X3,X1)
| ~ in(X3,sK9(X2,sK8(X0,powerset(powerset(X1))))) )
| ~ spl17_51
| ~ spl17_298 ),
inference(resolution,[],[f2555,f440]) ).
fof(f6769,plain,
( spl17_595
| ~ spl17_51
| ~ spl17_297 ),
inference(avatar_split_clause,[],[f2635,f2550,f439,f6767]) ).
fof(f6767,plain,
( spl17_595
<=> ! [X0,X3,X2,X1] :
( sP0(X0,powerset(powerset(X1)))
| sP0(X2,sK8(X0,powerset(powerset(X1))))
| element(X3,X1)
| ~ in(X3,sK8(X2,sK8(X0,powerset(powerset(X1))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_595])]) ).
fof(f2635,plain,
( ! [X2,X3,X0,X1] :
( sP0(X0,powerset(powerset(X1)))
| sP0(X2,sK8(X0,powerset(powerset(X1))))
| element(X3,X1)
| ~ in(X3,sK8(X2,sK8(X0,powerset(powerset(X1))))) )
| ~ spl17_51
| ~ spl17_297 ),
inference(resolution,[],[f2551,f440]) ).
fof(f6765,plain,
( spl17_594
| ~ spl17_51
| ~ spl17_296 ),
inference(avatar_split_clause,[],[f2631,f2546,f439,f6763]) ).
fof(f6763,plain,
( spl17_594
<=> ! [X0,X3,X2,X1] :
( sP0(X0,powerset(powerset(X1)))
| sP0(X2,sK8(X0,powerset(powerset(X1))))
| element(X3,X1)
| ~ in(X3,sK7(X2,sK8(X0,powerset(powerset(X1))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_594])]) ).
fof(f2631,plain,
( ! [X2,X3,X0,X1] :
( sP0(X0,powerset(powerset(X1)))
| sP0(X2,sK8(X0,powerset(powerset(X1))))
| element(X3,X1)
| ~ in(X3,sK7(X2,sK8(X0,powerset(powerset(X1))))) )
| ~ spl17_51
| ~ spl17_296 ),
inference(resolution,[],[f2547,f440]) ).
fof(f6761,plain,
( spl17_593
| ~ spl17_51
| ~ spl17_295 ),
inference(avatar_split_clause,[],[f2627,f2542,f439,f6759]) ).
fof(f6759,plain,
( spl17_593
<=> ! [X0,X3,X2,X1] :
( sP0(X0,powerset(powerset(X1)))
| sP0(X2,sK7(X0,powerset(powerset(X1))))
| element(X3,X1)
| ~ in(X3,sK9(X2,sK7(X0,powerset(powerset(X1))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_593])]) ).
fof(f2627,plain,
( ! [X2,X3,X0,X1] :
( sP0(X0,powerset(powerset(X1)))
| sP0(X2,sK7(X0,powerset(powerset(X1))))
| element(X3,X1)
| ~ in(X3,sK9(X2,sK7(X0,powerset(powerset(X1))))) )
| ~ spl17_51
| ~ spl17_295 ),
inference(resolution,[],[f2543,f440]) ).
fof(f6757,plain,
( spl17_592
| ~ spl17_51
| ~ spl17_294 ),
inference(avatar_split_clause,[],[f2623,f2538,f439,f6755]) ).
fof(f6755,plain,
( spl17_592
<=> ! [X0,X3,X2,X1] :
( sP0(X0,powerset(powerset(X1)))
| sP0(X2,sK7(X0,powerset(powerset(X1))))
| element(X3,X1)
| ~ in(X3,sK8(X2,sK7(X0,powerset(powerset(X1))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_592])]) ).
fof(f2623,plain,
( ! [X2,X3,X0,X1] :
( sP0(X0,powerset(powerset(X1)))
| sP0(X2,sK7(X0,powerset(powerset(X1))))
| element(X3,X1)
| ~ in(X3,sK8(X2,sK7(X0,powerset(powerset(X1))))) )
| ~ spl17_51
| ~ spl17_294 ),
inference(resolution,[],[f2539,f440]) ).
fof(f6753,plain,
( spl17_591
| ~ spl17_51
| ~ spl17_293 ),
inference(avatar_split_clause,[],[f2615,f2534,f439,f6751]) ).
fof(f6751,plain,
( spl17_591
<=> ! [X0,X3,X2,X1] :
( sP0(X0,powerset(powerset(X1)))
| sP0(X2,sK7(X0,powerset(powerset(X1))))
| element(X3,X1)
| ~ in(X3,sK7(X2,sK7(X0,powerset(powerset(X1))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_591])]) ).
fof(f2615,plain,
( ! [X2,X3,X0,X1] :
( sP0(X0,powerset(powerset(X1)))
| sP0(X2,sK7(X0,powerset(powerset(X1))))
| element(X3,X1)
| ~ in(X3,sK7(X2,sK7(X0,powerset(powerset(X1))))) )
| ~ spl17_51
| ~ spl17_293 ),
inference(resolution,[],[f2535,f440]) ).
fof(f6749,plain,
( spl17_590
| ~ spl17_38
| ~ spl17_292 ),
inference(avatar_split_clause,[],[f2609,f2530,f351,f6747]) ).
fof(f6747,plain,
( spl17_590
<=> ! [X2,X0,X1] :
( sP0(X0,sK6(powerset(X1)))
| element(sK9(X2,sK9(X0,sK6(powerset(X1)))),X1)
| empty(powerset(X1))
| sP0(X2,sK9(X0,sK6(powerset(X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_590])]) ).
fof(f2609,plain,
( ! [X2,X0,X1] :
( sP0(X0,sK6(powerset(X1)))
| element(sK9(X2,sK9(X0,sK6(powerset(X1)))),X1)
| empty(powerset(X1))
| sP0(X2,sK9(X0,sK6(powerset(X1)))) )
| ~ spl17_38
| ~ spl17_292 ),
inference(resolution,[],[f2531,f352]) ).
fof(f6745,plain,
( spl17_589
| ~ spl17_37
| ~ spl17_292 ),
inference(avatar_split_clause,[],[f2606,f2530,f347,f6743]) ).
fof(f6743,plain,
( spl17_589
<=> ! [X2,X0,X1] :
( sP0(X0,sK6(powerset(X1)))
| element(sK8(X2,sK9(X0,sK6(powerset(X1)))),X1)
| empty(powerset(X1))
| sP0(X2,sK9(X0,sK6(powerset(X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_589])]) ).
fof(f2606,plain,
( ! [X2,X0,X1] :
( sP0(X0,sK6(powerset(X1)))
| element(sK8(X2,sK9(X0,sK6(powerset(X1)))),X1)
| empty(powerset(X1))
| sP0(X2,sK9(X0,sK6(powerset(X1)))) )
| ~ spl17_37
| ~ spl17_292 ),
inference(resolution,[],[f2531,f348]) ).
fof(f6741,plain,
( spl17_588
| ~ spl17_35
| ~ spl17_292 ),
inference(avatar_split_clause,[],[f2603,f2530,f339,f6739]) ).
fof(f6739,plain,
( spl17_588
<=> ! [X2,X0,X1] :
( sP0(X0,sK6(powerset(X1)))
| element(sK7(X2,sK9(X0,sK6(powerset(X1)))),X1)
| empty(powerset(X1))
| sP0(X2,sK9(X0,sK6(powerset(X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_588])]) ).
fof(f2603,plain,
( ! [X2,X0,X1] :
( sP0(X0,sK6(powerset(X1)))
| element(sK7(X2,sK9(X0,sK6(powerset(X1)))),X1)
| empty(powerset(X1))
| sP0(X2,sK9(X0,sK6(powerset(X1)))) )
| ~ spl17_35
| ~ spl17_292 ),
inference(resolution,[],[f2531,f340]) ).
fof(f6737,plain,
( spl17_587
| ~ spl17_38
| ~ spl17_291 ),
inference(avatar_split_clause,[],[f2595,f2526,f351,f6735]) ).
fof(f6735,plain,
( spl17_587
<=> ! [X2,X0,X1] :
( sP0(X0,sK6(powerset(X1)))
| element(sK9(X2,sK8(X0,sK6(powerset(X1)))),X1)
| empty(powerset(X1))
| sP0(X2,sK8(X0,sK6(powerset(X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_587])]) ).
fof(f2595,plain,
( ! [X2,X0,X1] :
( sP0(X0,sK6(powerset(X1)))
| element(sK9(X2,sK8(X0,sK6(powerset(X1)))),X1)
| empty(powerset(X1))
| sP0(X2,sK8(X0,sK6(powerset(X1)))) )
| ~ spl17_38
| ~ spl17_291 ),
inference(resolution,[],[f2527,f352]) ).
fof(f6733,plain,
( spl17_586
| ~ spl17_37
| ~ spl17_291 ),
inference(avatar_split_clause,[],[f2592,f2526,f347,f6731]) ).
fof(f6731,plain,
( spl17_586
<=> ! [X2,X0,X1] :
( sP0(X0,sK6(powerset(X1)))
| element(sK8(X2,sK8(X0,sK6(powerset(X1)))),X1)
| empty(powerset(X1))
| sP0(X2,sK8(X0,sK6(powerset(X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_586])]) ).
fof(f2592,plain,
( ! [X2,X0,X1] :
( sP0(X0,sK6(powerset(X1)))
| element(sK8(X2,sK8(X0,sK6(powerset(X1)))),X1)
| empty(powerset(X1))
| sP0(X2,sK8(X0,sK6(powerset(X1)))) )
| ~ spl17_37
| ~ spl17_291 ),
inference(resolution,[],[f2527,f348]) ).
fof(f6729,plain,
( spl17_585
| ~ spl17_35
| ~ spl17_291 ),
inference(avatar_split_clause,[],[f2589,f2526,f339,f6727]) ).
fof(f6727,plain,
( spl17_585
<=> ! [X2,X0,X1] :
( sP0(X0,sK6(powerset(X1)))
| element(sK7(X2,sK8(X0,sK6(powerset(X1)))),X1)
| empty(powerset(X1))
| sP0(X2,sK8(X0,sK6(powerset(X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_585])]) ).
fof(f2589,plain,
( ! [X2,X0,X1] :
( sP0(X0,sK6(powerset(X1)))
| element(sK7(X2,sK8(X0,sK6(powerset(X1)))),X1)
| empty(powerset(X1))
| sP0(X2,sK8(X0,sK6(powerset(X1)))) )
| ~ spl17_35
| ~ spl17_291 ),
inference(resolution,[],[f2527,f340]) ).
fof(f6725,plain,
( spl17_584
| ~ spl17_17
| ~ spl17_551 ),
inference(avatar_split_clause,[],[f6294,f6079,f255,f6723]) ).
fof(f6723,plain,
( spl17_584
<=> ! [X0] :
( sP0(X0,powerset(sK16))
| sP1(sK9(X0,powerset(sK16))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_584])]) ).
fof(f6079,plain,
( spl17_551
<=> ! [X0] :
( relation(sK9(X0,powerset(sK16)))
| sP0(X0,powerset(sK16)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_551])]) ).
fof(f6294,plain,
( ! [X0] :
( sP0(X0,powerset(sK16))
| sP1(sK9(X0,powerset(sK16))) )
| ~ spl17_17
| ~ spl17_551 ),
inference(resolution,[],[f6080,f256]) ).
fof(f6080,plain,
( ! [X0] :
( relation(sK9(X0,powerset(sK16)))
| sP0(X0,powerset(sK16)) )
| ~ spl17_551 ),
inference(avatar_component_clause,[],[f6079]) ).
fof(f6721,plain,
( spl17_583
| ~ spl17_38
| ~ spl17_290 ),
inference(avatar_split_clause,[],[f2581,f2522,f351,f6719]) ).
fof(f6719,plain,
( spl17_583
<=> ! [X2,X0,X1] :
( sP0(X0,sK6(powerset(X1)))
| element(sK9(X2,sK7(X0,sK6(powerset(X1)))),X1)
| empty(powerset(X1))
| sP0(X2,sK7(X0,sK6(powerset(X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_583])]) ).
fof(f2581,plain,
( ! [X2,X0,X1] :
( sP0(X0,sK6(powerset(X1)))
| element(sK9(X2,sK7(X0,sK6(powerset(X1)))),X1)
| empty(powerset(X1))
| sP0(X2,sK7(X0,sK6(powerset(X1)))) )
| ~ spl17_38
| ~ spl17_290 ),
inference(resolution,[],[f2523,f352]) ).
fof(f6717,plain,
( spl17_582
| ~ spl17_37
| ~ spl17_290 ),
inference(avatar_split_clause,[],[f2578,f2522,f347,f6715]) ).
fof(f6715,plain,
( spl17_582
<=> ! [X2,X0,X1] :
( sP0(X0,sK6(powerset(X1)))
| element(sK8(X2,sK7(X0,sK6(powerset(X1)))),X1)
| empty(powerset(X1))
| sP0(X2,sK7(X0,sK6(powerset(X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_582])]) ).
fof(f2578,plain,
( ! [X2,X0,X1] :
( sP0(X0,sK6(powerset(X1)))
| element(sK8(X2,sK7(X0,sK6(powerset(X1)))),X1)
| empty(powerset(X1))
| sP0(X2,sK7(X0,sK6(powerset(X1)))) )
| ~ spl17_37
| ~ spl17_290 ),
inference(resolution,[],[f2523,f348]) ).
fof(f6713,plain,
( spl17_581
| ~ spl17_35
| ~ spl17_290 ),
inference(avatar_split_clause,[],[f2575,f2522,f339,f6711]) ).
fof(f6711,plain,
( spl17_581
<=> ! [X2,X0,X1] :
( sP0(X0,sK6(powerset(X1)))
| element(sK7(X2,sK7(X0,sK6(powerset(X1)))),X1)
| empty(powerset(X1))
| sP0(X2,sK7(X0,sK6(powerset(X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_581])]) ).
fof(f2575,plain,
( ! [X2,X0,X1] :
( sP0(X0,sK6(powerset(X1)))
| element(sK7(X2,sK7(X0,sK6(powerset(X1)))),X1)
| empty(powerset(X1))
| sP0(X2,sK7(X0,sK6(powerset(X1)))) )
| ~ spl17_35
| ~ spl17_290 ),
inference(resolution,[],[f2523,f340]) ).
fof(f6709,plain,
( spl17_580
| ~ spl17_38
| ~ spl17_284 ),
inference(avatar_split_clause,[],[f2468,f2409,f351,f6707]) ).
fof(f6707,plain,
( spl17_580
<=> ! [X2,X0,X1] :
( element(sK9(X0,sK9(X1,sK10(powerset(powerset(X2))))),X2)
| sP0(X1,sK10(powerset(powerset(X2))))
| sP0(X0,sK9(X1,sK10(powerset(powerset(X2))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_580])]) ).
fof(f2468,plain,
( ! [X2,X0,X1] :
( element(sK9(X0,sK9(X1,sK10(powerset(powerset(X2))))),X2)
| sP0(X1,sK10(powerset(powerset(X2))))
| sP0(X0,sK9(X1,sK10(powerset(powerset(X2))))) )
| ~ spl17_38
| ~ spl17_284 ),
inference(resolution,[],[f2410,f352]) ).
fof(f6705,plain,
( spl17_579
| ~ spl17_37
| ~ spl17_284 ),
inference(avatar_split_clause,[],[f2465,f2409,f347,f6703]) ).
fof(f6703,plain,
( spl17_579
<=> ! [X2,X0,X1] :
( element(sK8(X0,sK9(X1,sK10(powerset(powerset(X2))))),X2)
| sP0(X1,sK10(powerset(powerset(X2))))
| sP0(X0,sK9(X1,sK10(powerset(powerset(X2))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_579])]) ).
fof(f2465,plain,
( ! [X2,X0,X1] :
( element(sK8(X0,sK9(X1,sK10(powerset(powerset(X2))))),X2)
| sP0(X1,sK10(powerset(powerset(X2))))
| sP0(X0,sK9(X1,sK10(powerset(powerset(X2))))) )
| ~ spl17_37
| ~ spl17_284 ),
inference(resolution,[],[f2410,f348]) ).
fof(f6701,plain,
( spl17_578
| ~ spl17_35
| ~ spl17_284 ),
inference(avatar_split_clause,[],[f2462,f2409,f339,f6699]) ).
fof(f6699,plain,
( spl17_578
<=> ! [X2,X0,X1] :
( element(sK7(X0,sK9(X1,sK10(powerset(powerset(X2))))),X2)
| sP0(X1,sK10(powerset(powerset(X2))))
| sP0(X0,sK9(X1,sK10(powerset(powerset(X2))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_578])]) ).
fof(f2462,plain,
( ! [X2,X0,X1] :
( element(sK7(X0,sK9(X1,sK10(powerset(powerset(X2))))),X2)
| sP0(X1,sK10(powerset(powerset(X2))))
| sP0(X0,sK9(X1,sK10(powerset(powerset(X2))))) )
| ~ spl17_35
| ~ spl17_284 ),
inference(resolution,[],[f2410,f340]) ).
fof(f6697,plain,
( spl17_577
| ~ spl17_38
| ~ spl17_282 ),
inference(avatar_split_clause,[],[f2453,f2401,f351,f6695]) ).
fof(f6695,plain,
( spl17_577
<=> ! [X2,X0,X1] :
( element(sK9(X0,sK8(X1,sK10(powerset(powerset(X2))))),X2)
| sP0(X1,sK10(powerset(powerset(X2))))
| sP0(X0,sK8(X1,sK10(powerset(powerset(X2))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_577])]) ).
fof(f2453,plain,
( ! [X2,X0,X1] :
( element(sK9(X0,sK8(X1,sK10(powerset(powerset(X2))))),X2)
| sP0(X1,sK10(powerset(powerset(X2))))
| sP0(X0,sK8(X1,sK10(powerset(powerset(X2))))) )
| ~ spl17_38
| ~ spl17_282 ),
inference(resolution,[],[f2402,f352]) ).
fof(f6693,plain,
( spl17_576
| ~ spl17_37
| ~ spl17_282 ),
inference(avatar_split_clause,[],[f2450,f2401,f347,f6691]) ).
fof(f6691,plain,
( spl17_576
<=> ! [X2,X0,X1] :
( element(sK8(X0,sK8(X1,sK10(powerset(powerset(X2))))),X2)
| sP0(X1,sK10(powerset(powerset(X2))))
| sP0(X0,sK8(X1,sK10(powerset(powerset(X2))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_576])]) ).
fof(f2450,plain,
( ! [X2,X0,X1] :
( element(sK8(X0,sK8(X1,sK10(powerset(powerset(X2))))),X2)
| sP0(X1,sK10(powerset(powerset(X2))))
| sP0(X0,sK8(X1,sK10(powerset(powerset(X2))))) )
| ~ spl17_37
| ~ spl17_282 ),
inference(resolution,[],[f2402,f348]) ).
fof(f6689,plain,
( spl17_575
| ~ spl17_35
| ~ spl17_282 ),
inference(avatar_split_clause,[],[f2447,f2401,f339,f6687]) ).
fof(f6687,plain,
( spl17_575
<=> ! [X2,X0,X1] :
( element(sK7(X0,sK8(X1,sK10(powerset(powerset(X2))))),X2)
| sP0(X1,sK10(powerset(powerset(X2))))
| sP0(X0,sK8(X1,sK10(powerset(powerset(X2))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_575])]) ).
fof(f2447,plain,
( ! [X2,X0,X1] :
( element(sK7(X0,sK8(X1,sK10(powerset(powerset(X2))))),X2)
| sP0(X1,sK10(powerset(powerset(X2))))
| sP0(X0,sK8(X1,sK10(powerset(powerset(X2))))) )
| ~ spl17_35
| ~ spl17_282 ),
inference(resolution,[],[f2402,f340]) ).
fof(f6685,plain,
( spl17_574
| ~ spl17_38
| ~ spl17_280 ),
inference(avatar_split_clause,[],[f2438,f2393,f351,f6683]) ).
fof(f6683,plain,
( spl17_574
<=> ! [X2,X0,X1] :
( element(sK9(X0,sK7(X1,sK10(powerset(powerset(X2))))),X2)
| sP0(X1,sK10(powerset(powerset(X2))))
| sP0(X0,sK7(X1,sK10(powerset(powerset(X2))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_574])]) ).
fof(f2438,plain,
( ! [X2,X0,X1] :
( element(sK9(X0,sK7(X1,sK10(powerset(powerset(X2))))),X2)
| sP0(X1,sK10(powerset(powerset(X2))))
| sP0(X0,sK7(X1,sK10(powerset(powerset(X2))))) )
| ~ spl17_38
| ~ spl17_280 ),
inference(resolution,[],[f2394,f352]) ).
fof(f6681,plain,
( spl17_573
| ~ spl17_17
| ~ spl17_540 ),
inference(avatar_split_clause,[],[f6253,f6035,f255,f6679]) ).
fof(f6679,plain,
( spl17_573
<=> ! [X0] :
( sP0(X0,powerset(sK16))
| sP1(sK8(X0,powerset(sK16))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_573])]) ).
fof(f6035,plain,
( spl17_540
<=> ! [X0] :
( relation(sK8(X0,powerset(sK16)))
| sP0(X0,powerset(sK16)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_540])]) ).
fof(f6253,plain,
( ! [X0] :
( sP0(X0,powerset(sK16))
| sP1(sK8(X0,powerset(sK16))) )
| ~ spl17_17
| ~ spl17_540 ),
inference(resolution,[],[f6036,f256]) ).
fof(f6036,plain,
( ! [X0] :
( relation(sK8(X0,powerset(sK16)))
| sP0(X0,powerset(sK16)) )
| ~ spl17_540 ),
inference(avatar_component_clause,[],[f6035]) ).
fof(f6677,plain,
( spl17_572
| ~ spl17_37
| ~ spl17_280 ),
inference(avatar_split_clause,[],[f2435,f2393,f347,f6675]) ).
fof(f6675,plain,
( spl17_572
<=> ! [X2,X0,X1] :
( element(sK8(X0,sK7(X1,sK10(powerset(powerset(X2))))),X2)
| sP0(X1,sK10(powerset(powerset(X2))))
| sP0(X0,sK7(X1,sK10(powerset(powerset(X2))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_572])]) ).
fof(f2435,plain,
( ! [X2,X0,X1] :
( element(sK8(X0,sK7(X1,sK10(powerset(powerset(X2))))),X2)
| sP0(X1,sK10(powerset(powerset(X2))))
| sP0(X0,sK7(X1,sK10(powerset(powerset(X2))))) )
| ~ spl17_37
| ~ spl17_280 ),
inference(resolution,[],[f2394,f348]) ).
fof(f6673,plain,
( spl17_571
| ~ spl17_35
| ~ spl17_280 ),
inference(avatar_split_clause,[],[f2432,f2393,f339,f6671]) ).
fof(f6671,plain,
( spl17_571
<=> ! [X2,X0,X1] :
( element(sK7(X0,sK7(X1,sK10(powerset(powerset(X2))))),X2)
| sP0(X1,sK10(powerset(powerset(X2))))
| sP0(X0,sK7(X1,sK10(powerset(powerset(X2))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_571])]) ).
fof(f2432,plain,
( ! [X2,X0,X1] :
( element(sK7(X0,sK7(X1,sK10(powerset(powerset(X2))))),X2)
| sP0(X1,sK10(powerset(powerset(X2))))
| sP0(X0,sK7(X1,sK10(powerset(powerset(X2))))) )
| ~ spl17_35
| ~ spl17_280 ),
inference(resolution,[],[f2394,f340]) ).
fof(f6669,plain,
( spl17_570
| ~ spl17_41
| ~ spl17_277 ),
inference(avatar_split_clause,[],[f2385,f2313,f363,f6667]) ).
fof(f6667,plain,
( spl17_570
<=> ! [X2,X0,X1] :
( sP0(X0,powerset(powerset(cartesian_product2(X1,X2))))
| empty(sK9(X0,powerset(powerset(cartesian_product2(X1,X2)))))
| relation(sK10(sK9(X0,powerset(powerset(cartesian_product2(X1,X2)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_570])]) ).
fof(f2313,plain,
( spl17_277
<=> ! [X0,X1] :
( element(sK10(sK9(X0,powerset(X1))),X1)
| sP0(X0,powerset(X1))
| empty(sK9(X0,powerset(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_277])]) ).
fof(f2385,plain,
( ! [X2,X0,X1] :
( sP0(X0,powerset(powerset(cartesian_product2(X1,X2))))
| empty(sK9(X0,powerset(powerset(cartesian_product2(X1,X2)))))
| relation(sK10(sK9(X0,powerset(powerset(cartesian_product2(X1,X2)))))) )
| ~ spl17_41
| ~ spl17_277 ),
inference(resolution,[],[f2314,f364]) ).
fof(f2314,plain,
( ! [X0,X1] :
( element(sK10(sK9(X0,powerset(X1))),X1)
| sP0(X0,powerset(X1))
| empty(sK9(X0,powerset(X1))) )
| ~ spl17_277 ),
inference(avatar_component_clause,[],[f2313]) ).
fof(f6665,plain,
( spl17_569
| ~ spl17_41
| ~ spl17_276 ),
inference(avatar_split_clause,[],[f2381,f2309,f363,f6663]) ).
fof(f6663,plain,
( spl17_569
<=> ! [X2,X0,X1] :
( sP0(X0,powerset(powerset(cartesian_product2(X1,X2))))
| empty(sK8(X0,powerset(powerset(cartesian_product2(X1,X2)))))
| relation(sK10(sK8(X0,powerset(powerset(cartesian_product2(X1,X2)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_569])]) ).
fof(f2309,plain,
( spl17_276
<=> ! [X0,X1] :
( element(sK10(sK8(X0,powerset(X1))),X1)
| sP0(X0,powerset(X1))
| empty(sK8(X0,powerset(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_276])]) ).
fof(f2381,plain,
( ! [X2,X0,X1] :
( sP0(X0,powerset(powerset(cartesian_product2(X1,X2))))
| empty(sK8(X0,powerset(powerset(cartesian_product2(X1,X2)))))
| relation(sK10(sK8(X0,powerset(powerset(cartesian_product2(X1,X2)))))) )
| ~ spl17_41
| ~ spl17_276 ),
inference(resolution,[],[f2310,f364]) ).
fof(f2310,plain,
( ! [X0,X1] :
( element(sK10(sK8(X0,powerset(X1))),X1)
| sP0(X0,powerset(X1))
| empty(sK8(X0,powerset(X1))) )
| ~ spl17_276 ),
inference(avatar_component_clause,[],[f2309]) ).
fof(f6661,plain,
( spl17_568
| ~ spl17_41
| ~ spl17_275 ),
inference(avatar_split_clause,[],[f2377,f2305,f363,f6659]) ).
fof(f6659,plain,
( spl17_568
<=> ! [X2,X0,X1] :
( sP0(X0,powerset(powerset(cartesian_product2(X1,X2))))
| empty(sK7(X0,powerset(powerset(cartesian_product2(X1,X2)))))
| relation(sK10(sK7(X0,powerset(powerset(cartesian_product2(X1,X2)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_568])]) ).
fof(f2305,plain,
( spl17_275
<=> ! [X0,X1] :
( element(sK10(sK7(X0,powerset(X1))),X1)
| sP0(X0,powerset(X1))
| empty(sK7(X0,powerset(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_275])]) ).
fof(f2377,plain,
( ! [X2,X0,X1] :
( sP0(X0,powerset(powerset(cartesian_product2(X1,X2))))
| empty(sK7(X0,powerset(powerset(cartesian_product2(X1,X2)))))
| relation(sK10(sK7(X0,powerset(powerset(cartesian_product2(X1,X2)))))) )
| ~ spl17_41
| ~ spl17_275 ),
inference(resolution,[],[f2306,f364]) ).
fof(f2306,plain,
( ! [X0,X1] :
( element(sK10(sK7(X0,powerset(X1))),X1)
| sP0(X0,powerset(X1))
| empty(sK7(X0,powerset(X1))) )
| ~ spl17_275 ),
inference(avatar_component_clause,[],[f2305]) ).
fof(f6579,plain,
( spl17_567
| ~ spl17_17
| ~ spl17_534 ),
inference(avatar_split_clause,[],[f6207,f5930,f255,f6577]) ).
fof(f6577,plain,
( spl17_567
<=> ! [X0] :
( sP0(X0,powerset(sK16))
| sP1(sK7(X0,powerset(sK16))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_567])]) ).
fof(f5930,plain,
( spl17_534
<=> ! [X0] :
( relation(sK7(X0,powerset(sK16)))
| sP0(X0,powerset(sK16)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_534])]) ).
fof(f6207,plain,
( ! [X0] :
( sP0(X0,powerset(sK16))
| sP1(sK7(X0,powerset(sK16))) )
| ~ spl17_17
| ~ spl17_534 ),
inference(resolution,[],[f5931,f256]) ).
fof(f5931,plain,
( ! [X0] :
( relation(sK7(X0,powerset(sK16)))
| sP0(X0,powerset(sK16)) )
| ~ spl17_534 ),
inference(avatar_component_clause,[],[f5930]) ).
fof(f6293,plain,
( spl17_566
| ~ spl17_25
| ~ spl17_312 ),
inference(avatar_split_clause,[],[f2796,f2730,f292,f6291]) ).
fof(f6291,plain,
( spl17_566
<=> ! [X0,X1] :
( sP0(sK6(X0),X1)
| empty(X0)
| ~ in(X0,unordered_pair(singleton(sK7(sK6(X0),X1)),unordered_pair(sK8(sK6(X0),X1),sK7(sK6(X0),X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_566])]) ).
fof(f2796,plain,
( ! [X0,X1] :
( sP0(sK6(X0),X1)
| empty(X0)
| ~ in(X0,unordered_pair(singleton(sK7(sK6(X0),X1)),unordered_pair(sK8(sK6(X0),X1),sK7(sK6(X0),X1)))) )
| ~ spl17_25
| ~ spl17_312 ),
inference(resolution,[],[f2731,f293]) ).
fof(f6289,plain,
( spl17_565
| ~ spl17_25
| ~ spl17_311 ),
inference(avatar_split_clause,[],[f2747,f2726,f292,f6287]) ).
fof(f6287,plain,
( spl17_565
<=> ! [X0,X1] :
( sP0(sK6(X0),X1)
| empty(X0)
| ~ in(X0,unordered_pair(singleton(sK8(sK6(X0),X1)),unordered_pair(sK9(sK6(X0),X1),sK8(sK6(X0),X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_565])]) ).
fof(f2747,plain,
( ! [X0,X1] :
( sP0(sK6(X0),X1)
| empty(X0)
| ~ in(X0,unordered_pair(singleton(sK8(sK6(X0),X1)),unordered_pair(sK9(sK6(X0),X1),sK8(sK6(X0),X1)))) )
| ~ spl17_25
| ~ spl17_311 ),
inference(resolution,[],[f2727,f293]) ).
fof(f6285,plain,
( spl17_564
| ~ spl17_149
| ~ spl17_304 ),
inference(avatar_split_clause,[],[f2676,f2657,f1155,f6283]) ).
fof(f6283,plain,
( spl17_564
<=> ! [X0,X1] :
( ~ rel_str(X0)
| empty(cartesian_product2(the_carrier(X0),the_carrier(X0)))
| ~ in(powerset(X1),the_InternalRel(X0))
| ~ subset(cartesian_product2(the_carrier(X0),the_carrier(X0)),X1)
| empty(powerset(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_564])]) ).
fof(f2676,plain,
( ! [X0,X1] :
( ~ rel_str(X0)
| empty(cartesian_product2(the_carrier(X0),the_carrier(X0)))
| ~ in(powerset(X1),the_InternalRel(X0))
| ~ subset(cartesian_product2(the_carrier(X0),the_carrier(X0)),X1)
| empty(powerset(X1)) )
| ~ spl17_149
| ~ spl17_304 ),
inference(resolution,[],[f2658,f1156]) ).
fof(f6281,plain,
( spl17_563
| ~ spl17_49
| ~ spl17_301 ),
inference(avatar_split_clause,[],[f2650,f2566,f422,f6279]) ).
fof(f6279,plain,
( spl17_563
<=> ! [X2,X0,X1,X3] :
( sP0(X0,powerset(powerset(X1)))
| sP0(X2,sK9(X0,powerset(powerset(X1))))
| ~ empty(X1)
| ~ in(X3,sK9(X2,sK9(X0,powerset(powerset(X1))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_563])]) ).
fof(f2650,plain,
( ! [X2,X3,X0,X1] :
( sP0(X0,powerset(powerset(X1)))
| sP0(X2,sK9(X0,powerset(powerset(X1))))
| ~ empty(X1)
| ~ in(X3,sK9(X2,sK9(X0,powerset(powerset(X1))))) )
| ~ spl17_49
| ~ spl17_301 ),
inference(resolution,[],[f2567,f423]) ).
fof(f6277,plain,
( spl17_562
| ~ spl17_49
| ~ spl17_300 ),
inference(avatar_split_clause,[],[f2646,f2562,f422,f6275]) ).
fof(f6275,plain,
( spl17_562
<=> ! [X2,X0,X1,X3] :
( sP0(X0,powerset(powerset(X1)))
| sP0(X2,sK9(X0,powerset(powerset(X1))))
| ~ empty(X1)
| ~ in(X3,sK8(X2,sK9(X0,powerset(powerset(X1))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_562])]) ).
fof(f2646,plain,
( ! [X2,X3,X0,X1] :
( sP0(X0,powerset(powerset(X1)))
| sP0(X2,sK9(X0,powerset(powerset(X1))))
| ~ empty(X1)
| ~ in(X3,sK8(X2,sK9(X0,powerset(powerset(X1))))) )
| ~ spl17_49
| ~ spl17_300 ),
inference(resolution,[],[f2563,f423]) ).
fof(f6273,plain,
( spl17_561
| ~ spl17_49
| ~ spl17_299 ),
inference(avatar_split_clause,[],[f2642,f2558,f422,f6271]) ).
fof(f6271,plain,
( spl17_561
<=> ! [X2,X0,X1,X3] :
( sP0(X0,powerset(powerset(X1)))
| sP0(X2,sK9(X0,powerset(powerset(X1))))
| ~ empty(X1)
| ~ in(X3,sK7(X2,sK9(X0,powerset(powerset(X1))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_561])]) ).
fof(f2642,plain,
( ! [X2,X3,X0,X1] :
( sP0(X0,powerset(powerset(X1)))
| sP0(X2,sK9(X0,powerset(powerset(X1))))
| ~ empty(X1)
| ~ in(X3,sK7(X2,sK9(X0,powerset(powerset(X1))))) )
| ~ spl17_49
| ~ spl17_299 ),
inference(resolution,[],[f2559,f423]) ).
fof(f6269,plain,
( spl17_560
| ~ spl17_49
| ~ spl17_298 ),
inference(avatar_split_clause,[],[f2638,f2554,f422,f6267]) ).
fof(f6267,plain,
( spl17_560
<=> ! [X2,X0,X1,X3] :
( sP0(X0,powerset(powerset(X1)))
| sP0(X2,sK8(X0,powerset(powerset(X1))))
| ~ empty(X1)
| ~ in(X3,sK9(X2,sK8(X0,powerset(powerset(X1))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_560])]) ).
fof(f2638,plain,
( ! [X2,X3,X0,X1] :
( sP0(X0,powerset(powerset(X1)))
| sP0(X2,sK8(X0,powerset(powerset(X1))))
| ~ empty(X1)
| ~ in(X3,sK9(X2,sK8(X0,powerset(powerset(X1))))) )
| ~ spl17_49
| ~ spl17_298 ),
inference(resolution,[],[f2555,f423]) ).
fof(f6265,plain,
( spl17_559
| ~ spl17_49
| ~ spl17_297 ),
inference(avatar_split_clause,[],[f2634,f2550,f422,f6263]) ).
fof(f6263,plain,
( spl17_559
<=> ! [X2,X0,X1,X3] :
( sP0(X0,powerset(powerset(X1)))
| sP0(X2,sK8(X0,powerset(powerset(X1))))
| ~ empty(X1)
| ~ in(X3,sK8(X2,sK8(X0,powerset(powerset(X1))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_559])]) ).
fof(f2634,plain,
( ! [X2,X3,X0,X1] :
( sP0(X0,powerset(powerset(X1)))
| sP0(X2,sK8(X0,powerset(powerset(X1))))
| ~ empty(X1)
| ~ in(X3,sK8(X2,sK8(X0,powerset(powerset(X1))))) )
| ~ spl17_49
| ~ spl17_297 ),
inference(resolution,[],[f2551,f423]) ).
fof(f6261,plain,
( spl17_558
| ~ spl17_49
| ~ spl17_296 ),
inference(avatar_split_clause,[],[f2630,f2546,f422,f6259]) ).
fof(f6259,plain,
( spl17_558
<=> ! [X2,X0,X1,X3] :
( sP0(X0,powerset(powerset(X1)))
| sP0(X2,sK8(X0,powerset(powerset(X1))))
| ~ empty(X1)
| ~ in(X3,sK7(X2,sK8(X0,powerset(powerset(X1))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_558])]) ).
fof(f2630,plain,
( ! [X2,X3,X0,X1] :
( sP0(X0,powerset(powerset(X1)))
| sP0(X2,sK8(X0,powerset(powerset(X1))))
| ~ empty(X1)
| ~ in(X3,sK7(X2,sK8(X0,powerset(powerset(X1))))) )
| ~ spl17_49
| ~ spl17_296 ),
inference(resolution,[],[f2547,f423]) ).
fof(f6257,plain,
( spl17_557
| ~ spl17_49
| ~ spl17_295 ),
inference(avatar_split_clause,[],[f2626,f2542,f422,f6255]) ).
fof(f6255,plain,
( spl17_557
<=> ! [X2,X0,X1,X3] :
( sP0(X0,powerset(powerset(X1)))
| sP0(X2,sK7(X0,powerset(powerset(X1))))
| ~ empty(X1)
| ~ in(X3,sK9(X2,sK7(X0,powerset(powerset(X1))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_557])]) ).
fof(f2626,plain,
( ! [X2,X3,X0,X1] :
( sP0(X0,powerset(powerset(X1)))
| sP0(X2,sK7(X0,powerset(powerset(X1))))
| ~ empty(X1)
| ~ in(X3,sK9(X2,sK7(X0,powerset(powerset(X1))))) )
| ~ spl17_49
| ~ spl17_295 ),
inference(resolution,[],[f2543,f423]) ).
fof(f6252,plain,
( spl17_556
| ~ spl17_49
| ~ spl17_294 ),
inference(avatar_split_clause,[],[f2622,f2538,f422,f6250]) ).
fof(f6250,plain,
( spl17_556
<=> ! [X2,X0,X1,X3] :
( sP0(X0,powerset(powerset(X1)))
| sP0(X2,sK7(X0,powerset(powerset(X1))))
| ~ empty(X1)
| ~ in(X3,sK8(X2,sK7(X0,powerset(powerset(X1))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_556])]) ).
fof(f2622,plain,
( ! [X2,X3,X0,X1] :
( sP0(X0,powerset(powerset(X1)))
| sP0(X2,sK7(X0,powerset(powerset(X1))))
| ~ empty(X1)
| ~ in(X3,sK8(X2,sK7(X0,powerset(powerset(X1))))) )
| ~ spl17_49
| ~ spl17_294 ),
inference(resolution,[],[f2539,f423]) ).
fof(f6248,plain,
( spl17_555
| ~ spl17_49
| ~ spl17_293 ),
inference(avatar_split_clause,[],[f2614,f2534,f422,f6246]) ).
fof(f6246,plain,
( spl17_555
<=> ! [X2,X0,X1,X3] :
( sP0(X0,powerset(powerset(X1)))
| sP0(X2,sK7(X0,powerset(powerset(X1))))
| ~ empty(X1)
| ~ in(X3,sK7(X2,sK7(X0,powerset(powerset(X1))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_555])]) ).
fof(f2614,plain,
( ! [X2,X3,X0,X1] :
( sP0(X0,powerset(powerset(X1)))
| sP0(X2,sK7(X0,powerset(powerset(X1))))
| ~ empty(X1)
| ~ in(X3,sK7(X2,sK7(X0,powerset(powerset(X1))))) )
| ~ spl17_49
| ~ spl17_293 ),
inference(resolution,[],[f2535,f423]) ).
fof(f6244,plain,
( spl17_554
| ~ spl17_171
| ~ spl17_224 ),
inference(avatar_split_clause,[],[f1829,f1808,f1361,f6242]) ).
fof(f6242,plain,
( spl17_554
<=> ! [X0,X1] :
( empty(sK6(sK9(X0,powerset(X1))))
| empty(sK9(X0,powerset(X1)))
| element(sK10(sK6(sK9(X0,powerset(X1)))),X1)
| sP0(X0,powerset(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_554])]) ).
fof(f1829,plain,
( ! [X0,X1] :
( empty(sK6(sK9(X0,powerset(X1))))
| empty(sK9(X0,powerset(X1)))
| element(sK10(sK6(sK9(X0,powerset(X1)))),X1)
| sP0(X0,powerset(X1)) )
| ~ spl17_171
| ~ spl17_224 ),
inference(resolution,[],[f1809,f1362]) ).
fof(f6240,plain,
( spl17_553
| ~ spl17_169
| ~ spl17_224 ),
inference(avatar_split_clause,[],[f1827,f1808,f1353,f6238]) ).
fof(f6238,plain,
( spl17_553
<=> ! [X0,X1] :
( empty(sK6(sK8(X0,powerset(X1))))
| empty(sK8(X0,powerset(X1)))
| element(sK10(sK6(sK8(X0,powerset(X1)))),X1)
| sP0(X0,powerset(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_553])]) ).
fof(f1827,plain,
( ! [X0,X1] :
( empty(sK6(sK8(X0,powerset(X1))))
| empty(sK8(X0,powerset(X1)))
| element(sK10(sK6(sK8(X0,powerset(X1)))),X1)
| sP0(X0,powerset(X1)) )
| ~ spl17_169
| ~ spl17_224 ),
inference(resolution,[],[f1809,f1354]) ).
fof(f6236,plain,
( spl17_552
| ~ spl17_167
| ~ spl17_224 ),
inference(avatar_split_clause,[],[f1825,f1808,f1345,f6234]) ).
fof(f6234,plain,
( spl17_552
<=> ! [X0,X1] :
( empty(sK6(sK7(X0,powerset(X1))))
| empty(sK7(X0,powerset(X1)))
| element(sK10(sK6(sK7(X0,powerset(X1)))),X1)
| sP0(X0,powerset(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_552])]) ).
fof(f1825,plain,
( ! [X0,X1] :
( empty(sK6(sK7(X0,powerset(X1))))
| empty(sK7(X0,powerset(X1)))
| element(sK10(sK6(sK7(X0,powerset(X1)))),X1)
| sP0(X0,powerset(X1)) )
| ~ spl17_167
| ~ spl17_224 ),
inference(resolution,[],[f1809,f1346]) ).
fof(f6081,plain,
( spl17_551
| ~ spl17_89
| ~ spl17_442 ),
inference(avatar_split_clause,[],[f4330,f4204,f721,f6079]) ).
fof(f721,plain,
( spl17_89
<=> ! [X0,X1] :
( sP0(X0,X1)
| element(sK9(X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_89])]) ).
fof(f4330,plain,
( ! [X0] :
( relation(sK9(X0,powerset(sK16)))
| sP0(X0,powerset(sK16)) )
| ~ spl17_89
| ~ spl17_442 ),
inference(resolution,[],[f4205,f722]) ).
fof(f722,plain,
( ! [X0,X1] :
( element(sK9(X0,X1),X1)
| sP0(X0,X1) )
| ~ spl17_89 ),
inference(avatar_component_clause,[],[f721]) ).
fof(f6077,plain,
( spl17_550
| ~ spl17_75
| ~ spl17_292 ),
inference(avatar_split_clause,[],[f2600,f2530,f643,f6075]) ).
fof(f6075,plain,
( spl17_550
<=> ! [X0,X1] :
( sP0(X0,sK6(powerset(X1)))
| element(sK10(sK9(X0,sK6(powerset(X1)))),X1)
| empty(powerset(X1))
| empty(sK9(X0,sK6(powerset(X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_550])]) ).
fof(f2600,plain,
( ! [X0,X1] :
( sP0(X0,sK6(powerset(X1)))
| element(sK10(sK9(X0,sK6(powerset(X1)))),X1)
| empty(powerset(X1))
| empty(sK9(X0,sK6(powerset(X1)))) )
| ~ spl17_75
| ~ spl17_292 ),
inference(resolution,[],[f2531,f644]) ).
fof(f6073,plain,
( spl17_549
| ~ spl17_75
| ~ spl17_291 ),
inference(avatar_split_clause,[],[f2586,f2526,f643,f6071]) ).
fof(f6071,plain,
( spl17_549
<=> ! [X0,X1] :
( sP0(X0,sK6(powerset(X1)))
| element(sK10(sK8(X0,sK6(powerset(X1)))),X1)
| empty(powerset(X1))
| empty(sK8(X0,sK6(powerset(X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_549])]) ).
fof(f2586,plain,
( ! [X0,X1] :
( sP0(X0,sK6(powerset(X1)))
| element(sK10(sK8(X0,sK6(powerset(X1)))),X1)
| empty(powerset(X1))
| empty(sK8(X0,sK6(powerset(X1)))) )
| ~ spl17_75
| ~ spl17_291 ),
inference(resolution,[],[f2527,f644]) ).
fof(f6069,plain,
( spl17_548
| ~ spl17_75
| ~ spl17_290 ),
inference(avatar_split_clause,[],[f2572,f2522,f643,f6067]) ).
fof(f6067,plain,
( spl17_548
<=> ! [X0,X1] :
( sP0(X0,sK6(powerset(X1)))
| element(sK10(sK7(X0,sK6(powerset(X1)))),X1)
| empty(powerset(X1))
| empty(sK7(X0,sK6(powerset(X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_548])]) ).
fof(f2572,plain,
( ! [X0,X1] :
( sP0(X0,sK6(powerset(X1)))
| element(sK10(sK7(X0,sK6(powerset(X1)))),X1)
| empty(powerset(X1))
| empty(sK7(X0,sK6(powerset(X1)))) )
| ~ spl17_75
| ~ spl17_290 ),
inference(resolution,[],[f2523,f644]) ).
fof(f6065,plain,
( spl17_547
| ~ spl17_75
| ~ spl17_284 ),
inference(avatar_split_clause,[],[f2459,f2409,f643,f6063]) ).
fof(f6063,plain,
( spl17_547
<=> ! [X0,X1] :
( element(sK10(sK9(X0,sK10(powerset(powerset(X1))))),X1)
| sP0(X0,sK10(powerset(powerset(X1))))
| empty(sK9(X0,sK10(powerset(powerset(X1))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_547])]) ).
fof(f2459,plain,
( ! [X0,X1] :
( element(sK10(sK9(X0,sK10(powerset(powerset(X1))))),X1)
| sP0(X0,sK10(powerset(powerset(X1))))
| empty(sK9(X0,sK10(powerset(powerset(X1))))) )
| ~ spl17_75
| ~ spl17_284 ),
inference(resolution,[],[f2410,f644]) ).
fof(f6061,plain,
( spl17_546
| ~ spl17_75
| ~ spl17_282 ),
inference(avatar_split_clause,[],[f2444,f2401,f643,f6059]) ).
fof(f6059,plain,
( spl17_546
<=> ! [X0,X1] :
( element(sK10(sK8(X0,sK10(powerset(powerset(X1))))),X1)
| sP0(X0,sK10(powerset(powerset(X1))))
| empty(sK8(X0,sK10(powerset(powerset(X1))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_546])]) ).
fof(f2444,plain,
( ! [X0,X1] :
( element(sK10(sK8(X0,sK10(powerset(powerset(X1))))),X1)
| sP0(X0,sK10(powerset(powerset(X1))))
| empty(sK8(X0,sK10(powerset(powerset(X1))))) )
| ~ spl17_75
| ~ spl17_282 ),
inference(resolution,[],[f2402,f644]) ).
fof(f6057,plain,
( spl17_545
| ~ spl17_75
| ~ spl17_280 ),
inference(avatar_split_clause,[],[f2429,f2393,f643,f6055]) ).
fof(f6055,plain,
( spl17_545
<=> ! [X0,X1] :
( element(sK10(sK7(X0,sK10(powerset(powerset(X1))))),X1)
| sP0(X0,sK10(powerset(powerset(X1))))
| empty(sK7(X0,sK10(powerset(powerset(X1))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_545])]) ).
fof(f2429,plain,
( ! [X0,X1] :
( element(sK10(sK7(X0,sK10(powerset(powerset(X1))))),X1)
| sP0(X0,sK10(powerset(powerset(X1))))
| empty(sK7(X0,sK10(powerset(powerset(X1))))) )
| ~ spl17_75
| ~ spl17_280 ),
inference(resolution,[],[f2394,f644]) ).
fof(f6053,plain,
( spl17_544
| ~ spl17_51
| ~ spl17_277 ),
inference(avatar_split_clause,[],[f2387,f2313,f439,f6051]) ).
fof(f6051,plain,
( spl17_544
<=> ! [X2,X0,X1] :
( sP0(X0,powerset(powerset(X1)))
| empty(sK9(X0,powerset(powerset(X1))))
| element(X2,X1)
| ~ in(X2,sK10(sK9(X0,powerset(powerset(X1))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_544])]) ).
fof(f2387,plain,
( ! [X2,X0,X1] :
( sP0(X0,powerset(powerset(X1)))
| empty(sK9(X0,powerset(powerset(X1))))
| element(X2,X1)
| ~ in(X2,sK10(sK9(X0,powerset(powerset(X1))))) )
| ~ spl17_51
| ~ spl17_277 ),
inference(resolution,[],[f2314,f440]) ).
fof(f6049,plain,
( spl17_543
| ~ spl17_51
| ~ spl17_276 ),
inference(avatar_split_clause,[],[f2383,f2309,f439,f6047]) ).
fof(f6047,plain,
( spl17_543
<=> ! [X2,X0,X1] :
( sP0(X0,powerset(powerset(X1)))
| empty(sK8(X0,powerset(powerset(X1))))
| element(X2,X1)
| ~ in(X2,sK10(sK8(X0,powerset(powerset(X1))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_543])]) ).
fof(f2383,plain,
( ! [X2,X0,X1] :
( sP0(X0,powerset(powerset(X1)))
| empty(sK8(X0,powerset(powerset(X1))))
| element(X2,X1)
| ~ in(X2,sK10(sK8(X0,powerset(powerset(X1))))) )
| ~ spl17_51
| ~ spl17_276 ),
inference(resolution,[],[f2310,f440]) ).
fof(f6045,plain,
( spl17_542
| ~ spl17_51
| ~ spl17_275 ),
inference(avatar_split_clause,[],[f2379,f2305,f439,f6043]) ).
fof(f6043,plain,
( spl17_542
<=> ! [X2,X0,X1] :
( sP0(X0,powerset(powerset(X1)))
| empty(sK7(X0,powerset(powerset(X1))))
| element(X2,X1)
| ~ in(X2,sK10(sK7(X0,powerset(powerset(X1))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_542])]) ).
fof(f2379,plain,
( ! [X2,X0,X1] :
( sP0(X0,powerset(powerset(X1)))
| empty(sK7(X0,powerset(powerset(X1))))
| element(X2,X1)
| ~ in(X2,sK10(sK7(X0,powerset(powerset(X1))))) )
| ~ spl17_51
| ~ spl17_275 ),
inference(resolution,[],[f2306,f440]) ).
fof(f6041,plain,
( spl17_541
| ~ spl17_150
| ~ spl17_266 ),
inference(avatar_split_clause,[],[f2232,f2147,f1159,f6039]) ).
fof(f6039,plain,
( spl17_541
<=> ! [X2,X0,X1] :
( empty(sK13(X0,X1))
| sP0(X2,sK10(powerset(sK13(X0,X1))))
| element(sK9(X2,sK10(powerset(sK13(X0,X1)))),cartesian_product2(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_541])]) ).
fof(f2232,plain,
( ! [X2,X0,X1] :
( empty(sK13(X0,X1))
| sP0(X2,sK10(powerset(sK13(X0,X1))))
| element(sK9(X2,sK10(powerset(sK13(X0,X1)))),cartesian_product2(X0,X1)) )
| ~ spl17_150
| ~ spl17_266 ),
inference(resolution,[],[f2148,f1160]) ).
fof(f6037,plain,
( spl17_540
| ~ spl17_87
| ~ spl17_442 ),
inference(avatar_split_clause,[],[f4325,f4204,f713,f6035]) ).
fof(f713,plain,
( spl17_87
<=> ! [X0,X1] :
( sP0(X0,X1)
| element(sK8(X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_87])]) ).
fof(f4325,plain,
( ! [X0] :
( relation(sK8(X0,powerset(sK16)))
| sP0(X0,powerset(sK16)) )
| ~ spl17_87
| ~ spl17_442 ),
inference(resolution,[],[f4205,f714]) ).
fof(f714,plain,
( ! [X0,X1] :
( element(sK8(X0,X1),X1)
| sP0(X0,X1) )
| ~ spl17_87 ),
inference(avatar_component_clause,[],[f713]) ).
fof(f6033,plain,
( spl17_539
| ~ spl17_151
| ~ spl17_266 ),
inference(avatar_split_clause,[],[f2231,f2147,f1163,f6031]) ).
fof(f6031,plain,
( spl17_539
<=> ! [X2,X0,X1] :
( empty(sK12(X0,X1))
| sP0(X2,sK10(powerset(sK12(X0,X1))))
| element(sK9(X2,sK10(powerset(sK12(X0,X1)))),cartesian_product2(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_539])]) ).
fof(f2231,plain,
( ! [X2,X0,X1] :
( empty(sK12(X0,X1))
| sP0(X2,sK10(powerset(sK12(X0,X1))))
| element(sK9(X2,sK10(powerset(sK12(X0,X1)))),cartesian_product2(X0,X1)) )
| ~ spl17_151
| ~ spl17_266 ),
inference(resolution,[],[f2148,f1164]) ).
fof(f6029,plain,
( spl17_538
| ~ spl17_150
| ~ spl17_265 ),
inference(avatar_split_clause,[],[f2211,f2143,f1159,f6027]) ).
fof(f6027,plain,
( spl17_538
<=> ! [X2,X0,X1] :
( empty(sK13(X0,X1))
| sP0(X2,sK10(powerset(sK13(X0,X1))))
| element(sK8(X2,sK10(powerset(sK13(X0,X1)))),cartesian_product2(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_538])]) ).
fof(f2211,plain,
( ! [X2,X0,X1] :
( empty(sK13(X0,X1))
| sP0(X2,sK10(powerset(sK13(X0,X1))))
| element(sK8(X2,sK10(powerset(sK13(X0,X1)))),cartesian_product2(X0,X1)) )
| ~ spl17_150
| ~ spl17_265 ),
inference(resolution,[],[f2144,f1160]) ).
fof(f6025,plain,
( spl17_537
| ~ spl17_151
| ~ spl17_265 ),
inference(avatar_split_clause,[],[f2210,f2143,f1163,f6023]) ).
fof(f6023,plain,
( spl17_537
<=> ! [X2,X0,X1] :
( empty(sK12(X0,X1))
| sP0(X2,sK10(powerset(sK12(X0,X1))))
| element(sK8(X2,sK10(powerset(sK12(X0,X1)))),cartesian_product2(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_537])]) ).
fof(f2210,plain,
( ! [X2,X0,X1] :
( empty(sK12(X0,X1))
| sP0(X2,sK10(powerset(sK12(X0,X1))))
| element(sK8(X2,sK10(powerset(sK12(X0,X1)))),cartesian_product2(X0,X1)) )
| ~ spl17_151
| ~ spl17_265 ),
inference(resolution,[],[f2144,f1164]) ).
fof(f6021,plain,
( spl17_536
| ~ spl17_150
| ~ spl17_264 ),
inference(avatar_split_clause,[],[f2190,f2139,f1159,f6019]) ).
fof(f6019,plain,
( spl17_536
<=> ! [X2,X0,X1] :
( empty(sK13(X0,X1))
| sP0(X2,sK10(powerset(sK13(X0,X1))))
| element(sK7(X2,sK10(powerset(sK13(X0,X1)))),cartesian_product2(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_536])]) ).
fof(f2190,plain,
( ! [X2,X0,X1] :
( empty(sK13(X0,X1))
| sP0(X2,sK10(powerset(sK13(X0,X1))))
| element(sK7(X2,sK10(powerset(sK13(X0,X1)))),cartesian_product2(X0,X1)) )
| ~ spl17_150
| ~ spl17_264 ),
inference(resolution,[],[f2140,f1160]) ).
fof(f6017,plain,
( spl17_535
| ~ spl17_151
| ~ spl17_264 ),
inference(avatar_split_clause,[],[f2189,f2139,f1163,f6015]) ).
fof(f6015,plain,
( spl17_535
<=> ! [X2,X0,X1] :
( empty(sK12(X0,X1))
| sP0(X2,sK10(powerset(sK12(X0,X1))))
| element(sK7(X2,sK10(powerset(sK12(X0,X1)))),cartesian_product2(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_535])]) ).
fof(f2189,plain,
( ! [X2,X0,X1] :
( empty(sK12(X0,X1))
| sP0(X2,sK10(powerset(sK12(X0,X1))))
| element(sK7(X2,sK10(powerset(sK12(X0,X1)))),cartesian_product2(X0,X1)) )
| ~ spl17_151
| ~ spl17_264 ),
inference(resolution,[],[f2140,f1164]) ).
fof(f5932,plain,
( spl17_534
| ~ spl17_85
| ~ spl17_442 ),
inference(avatar_split_clause,[],[f4320,f4204,f705,f5930]) ).
fof(f705,plain,
( spl17_85
<=> ! [X0,X1] :
( sP0(X0,X1)
| element(sK7(X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_85])]) ).
fof(f4320,plain,
( ! [X0] :
( relation(sK7(X0,powerset(sK16)))
| sP0(X0,powerset(sK16)) )
| ~ spl17_85
| ~ spl17_442 ),
inference(resolution,[],[f4205,f706]) ).
fof(f706,plain,
( ! [X0,X1] :
( element(sK7(X0,X1),X1)
| sP0(X0,X1) )
| ~ spl17_85 ),
inference(avatar_component_clause,[],[f705]) ).
fof(f5822,plain,
( spl17_533
| ~ spl17_103
| ~ spl17_304 ),
inference(avatar_split_clause,[],[f2685,f2657,f823,f5820]) ).
fof(f5820,plain,
( spl17_533
<=> ! [X2,X0,X1] :
( ~ rel_str(X0)
| empty(cartesian_product2(the_carrier(X0),the_carrier(X0)))
| ~ in(unordered_pair(singleton(X1),unordered_pair(X2,X1)),the_InternalRel(X0))
| in(X2,the_carrier(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_533])]) ).
fof(f2685,plain,
( ! [X2,X0,X1] :
( ~ rel_str(X0)
| empty(cartesian_product2(the_carrier(X0),the_carrier(X0)))
| ~ in(unordered_pair(singleton(X1),unordered_pair(X2,X1)),the_InternalRel(X0))
| in(X2,the_carrier(X0)) )
| ~ spl17_103
| ~ spl17_304 ),
inference(resolution,[],[f2658,f824]) ).
fof(f5818,plain,
( spl17_532
| ~ spl17_104
| ~ spl17_304 ),
inference(avatar_split_clause,[],[f2684,f2657,f827,f5816]) ).
fof(f5816,plain,
( spl17_532
<=> ! [X2,X0,X1] :
( ~ rel_str(X0)
| empty(cartesian_product2(the_carrier(X0),the_carrier(X0)))
| ~ in(unordered_pair(singleton(X1),unordered_pair(X2,X1)),the_InternalRel(X0))
| in(X1,the_carrier(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_532])]) ).
fof(f2684,plain,
( ! [X2,X0,X1] :
( ~ rel_str(X0)
| empty(cartesian_product2(the_carrier(X0),the_carrier(X0)))
| ~ in(unordered_pair(singleton(X1),unordered_pair(X2,X1)),the_InternalRel(X0))
| in(X1,the_carrier(X0)) )
| ~ spl17_104
| ~ spl17_304 ),
inference(resolution,[],[f2658,f828]) ).
fof(f5814,plain,
( spl17_531
| ~ spl17_52
| ~ spl17_304 ),
inference(avatar_split_clause,[],[f2680,f2657,f452,f5812]) ).
fof(f5812,plain,
( spl17_531
<=> ! [X2,X0,X1] :
( ~ rel_str(X0)
| empty(cartesian_product2(the_carrier(X0),the_carrier(X0)))
| ~ in(unordered_pair(singleton(X1),unordered_pair(X1,X2)),the_InternalRel(X0))
| in(X2,the_carrier(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_531])]) ).
fof(f2680,plain,
( ! [X2,X0,X1] :
( ~ rel_str(X0)
| empty(cartesian_product2(the_carrier(X0),the_carrier(X0)))
| ~ in(unordered_pair(singleton(X1),unordered_pair(X1,X2)),the_InternalRel(X0))
| in(X2,the_carrier(X0)) )
| ~ spl17_52
| ~ spl17_304 ),
inference(resolution,[],[f2658,f453]) ).
fof(f5810,plain,
( spl17_530
| ~ spl17_53
| ~ spl17_304 ),
inference(avatar_split_clause,[],[f2679,f2657,f459,f5808]) ).
fof(f5808,plain,
( spl17_530
<=> ! [X2,X0,X1] :
( ~ rel_str(X0)
| empty(cartesian_product2(the_carrier(X0),the_carrier(X0)))
| ~ in(unordered_pair(singleton(X1),unordered_pair(X1,X2)),the_InternalRel(X0))
| in(X1,the_carrier(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_530])]) ).
fof(f2679,plain,
( ! [X2,X0,X1] :
( ~ rel_str(X0)
| empty(cartesian_product2(the_carrier(X0),the_carrier(X0)))
| ~ in(unordered_pair(singleton(X1),unordered_pair(X1,X2)),the_InternalRel(X0))
| in(X1,the_carrier(X0)) )
| ~ spl17_53
| ~ spl17_304 ),
inference(resolution,[],[f2658,f460]) ).
fof(f5806,plain,
( spl17_529
| ~ spl17_49
| ~ spl17_277 ),
inference(avatar_split_clause,[],[f2386,f2313,f422,f5804]) ).
fof(f5804,plain,
( spl17_529
<=> ! [X2,X0,X1] :
( sP0(X0,powerset(powerset(X1)))
| empty(sK9(X0,powerset(powerset(X1))))
| ~ empty(X1)
| ~ in(X2,sK10(sK9(X0,powerset(powerset(X1))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_529])]) ).
fof(f2386,plain,
( ! [X2,X0,X1] :
( sP0(X0,powerset(powerset(X1)))
| empty(sK9(X0,powerset(powerset(X1))))
| ~ empty(X1)
| ~ in(X2,sK10(sK9(X0,powerset(powerset(X1))))) )
| ~ spl17_49
| ~ spl17_277 ),
inference(resolution,[],[f2314,f423]) ).
fof(f5802,plain,
( spl17_528
| ~ spl17_49
| ~ spl17_276 ),
inference(avatar_split_clause,[],[f2382,f2309,f422,f5800]) ).
fof(f5800,plain,
( spl17_528
<=> ! [X2,X0,X1] :
( sP0(X0,powerset(powerset(X1)))
| empty(sK8(X0,powerset(powerset(X1))))
| ~ empty(X1)
| ~ in(X2,sK10(sK8(X0,powerset(powerset(X1))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_528])]) ).
fof(f2382,plain,
( ! [X2,X0,X1] :
( sP0(X0,powerset(powerset(X1)))
| empty(sK8(X0,powerset(powerset(X1))))
| ~ empty(X1)
| ~ in(X2,sK10(sK8(X0,powerset(powerset(X1))))) )
| ~ spl17_49
| ~ spl17_276 ),
inference(resolution,[],[f2310,f423]) ).
fof(f5798,plain,
( spl17_527
| ~ spl17_49
| ~ spl17_275 ),
inference(avatar_split_clause,[],[f2378,f2305,f422,f5796]) ).
fof(f5796,plain,
( spl17_527
<=> ! [X2,X0,X1] :
( sP0(X0,powerset(powerset(X1)))
| empty(sK7(X0,powerset(powerset(X1))))
| ~ empty(X1)
| ~ in(X2,sK10(sK7(X0,powerset(powerset(X1))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_527])]) ).
fof(f2378,plain,
( ! [X2,X0,X1] :
( sP0(X0,powerset(powerset(X1)))
| empty(sK7(X0,powerset(powerset(X1))))
| ~ empty(X1)
| ~ in(X2,sK10(sK7(X0,powerset(powerset(X1))))) )
| ~ spl17_49
| ~ spl17_275 ),
inference(resolution,[],[f2306,f423]) ).
fof(f5794,plain,
( spl17_526
| ~ spl17_38
| ~ spl17_271 ),
inference(avatar_split_clause,[],[f2327,f2289,f351,f5792]) ).
fof(f5792,plain,
( spl17_526
<=> ! [X0,X1] :
( empty(sK6(powerset(X0)))
| element(sK9(X1,sK10(sK6(powerset(X0)))),X0)
| empty(powerset(X0))
| sP0(X1,sK10(sK6(powerset(X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_526])]) ).
fof(f2327,plain,
( ! [X0,X1] :
( empty(sK6(powerset(X0)))
| element(sK9(X1,sK10(sK6(powerset(X0)))),X0)
| empty(powerset(X0))
| sP0(X1,sK10(sK6(powerset(X0)))) )
| ~ spl17_38
| ~ spl17_271 ),
inference(resolution,[],[f2290,f352]) ).
fof(f5790,plain,
( spl17_525
| ~ spl17_37
| ~ spl17_271 ),
inference(avatar_split_clause,[],[f2324,f2289,f347,f5788]) ).
fof(f5788,plain,
( spl17_525
<=> ! [X0,X1] :
( empty(sK6(powerset(X0)))
| element(sK8(X1,sK10(sK6(powerset(X0)))),X0)
| empty(powerset(X0))
| sP0(X1,sK10(sK6(powerset(X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_525])]) ).
fof(f2324,plain,
( ! [X0,X1] :
( empty(sK6(powerset(X0)))
| element(sK8(X1,sK10(sK6(powerset(X0)))),X0)
| empty(powerset(X0))
| sP0(X1,sK10(sK6(powerset(X0)))) )
| ~ spl17_37
| ~ spl17_271 ),
inference(resolution,[],[f2290,f348]) ).
fof(f5786,plain,
( spl17_524
| ~ spl17_35
| ~ spl17_271 ),
inference(avatar_split_clause,[],[f2321,f2289,f339,f5784]) ).
fof(f5784,plain,
( spl17_524
<=> ! [X0,X1] :
( empty(sK6(powerset(X0)))
| element(sK7(X1,sK10(sK6(powerset(X0)))),X0)
| empty(powerset(X0))
| sP0(X1,sK10(sK6(powerset(X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_524])]) ).
fof(f2321,plain,
( ! [X0,X1] :
( empty(sK6(powerset(X0)))
| element(sK7(X1,sK10(sK6(powerset(X0)))),X0)
| empty(powerset(X0))
| sP0(X1,sK10(sK6(powerset(X0)))) )
| ~ spl17_35
| ~ spl17_271 ),
inference(resolution,[],[f2290,f340]) ).
fof(f5782,plain,
( spl17_523
| ~ spl17_38
| ~ spl17_269 ),
inference(avatar_split_clause,[],[f2259,f2240,f351,f5780]) ).
fof(f5780,plain,
( spl17_523
<=> ! [X0,X1] :
( element(sK9(X0,sK10(sK10(powerset(powerset(X1))))),X1)
| empty(sK10(powerset(powerset(X1))))
| sP0(X0,sK10(sK10(powerset(powerset(X1))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_523])]) ).
fof(f2259,plain,
( ! [X0,X1] :
( element(sK9(X0,sK10(sK10(powerset(powerset(X1))))),X1)
| empty(sK10(powerset(powerset(X1))))
| sP0(X0,sK10(sK10(powerset(powerset(X1))))) )
| ~ spl17_38
| ~ spl17_269 ),
inference(resolution,[],[f2241,f352]) ).
fof(f5778,plain,
( spl17_522
| ~ spl17_37
| ~ spl17_269 ),
inference(avatar_split_clause,[],[f2256,f2240,f347,f5776]) ).
fof(f5776,plain,
( spl17_522
<=> ! [X0,X1] :
( element(sK8(X0,sK10(sK10(powerset(powerset(X1))))),X1)
| empty(sK10(powerset(powerset(X1))))
| sP0(X0,sK10(sK10(powerset(powerset(X1))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_522])]) ).
fof(f2256,plain,
( ! [X0,X1] :
( element(sK8(X0,sK10(sK10(powerset(powerset(X1))))),X1)
| empty(sK10(powerset(powerset(X1))))
| sP0(X0,sK10(sK10(powerset(powerset(X1))))) )
| ~ spl17_37
| ~ spl17_269 ),
inference(resolution,[],[f2241,f348]) ).
fof(f5774,plain,
( ~ spl17_521
| ~ spl17_404
| ~ spl17_519 ),
inference(avatar_split_clause,[],[f5519,f5207,f3828,f5771]) ).
fof(f5771,plain,
( spl17_521
<=> in(cartesian_product2(sK16,sK16),the_InternalRel(sK2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_521])]) ).
fof(f5519,plain,
( ~ in(cartesian_product2(sK16,sK16),the_InternalRel(sK2))
| ~ spl17_404
| ~ spl17_519 ),
inference(duplicate_literal_removal,[],[f5516]) ).
fof(f5516,plain,
( ~ in(cartesian_product2(sK16,sK16),the_InternalRel(sK2))
| ~ in(cartesian_product2(sK16,sK16),the_InternalRel(sK2))
| ~ spl17_404
| ~ spl17_519 ),
inference(resolution,[],[f5208,f3829]) ).
fof(f5769,plain,
( spl17_520
| ~ spl17_35
| ~ spl17_269 ),
inference(avatar_split_clause,[],[f2253,f2240,f339,f5767]) ).
fof(f5767,plain,
( spl17_520
<=> ! [X0,X1] :
( element(sK7(X0,sK10(sK10(powerset(powerset(X1))))),X1)
| empty(sK10(powerset(powerset(X1))))
| sP0(X0,sK10(sK10(powerset(powerset(X1))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_520])]) ).
fof(f2253,plain,
( ! [X0,X1] :
( element(sK7(X0,sK10(sK10(powerset(powerset(X1))))),X1)
| empty(sK10(powerset(powerset(X1))))
| sP0(X0,sK10(sK10(powerset(powerset(X1))))) )
| ~ spl17_35
| ~ spl17_269 ),
inference(resolution,[],[f2241,f340]) ).
fof(f5209,plain,
( spl17_519
| ~ spl17_25
| ~ spl17_404 ),
inference(avatar_split_clause,[],[f5167,f3828,f292,f5207]) ).
fof(f5167,plain,
( ! [X0] :
( ~ in(X0,the_InternalRel(sK2))
| ~ in(cartesian_product2(sK16,sK16),X0) )
| ~ spl17_25
| ~ spl17_404 ),
inference(resolution,[],[f3829,f293]) ).
fof(f5197,plain,
( spl17_518
| ~ spl17_103
| ~ spl17_321 ),
inference(avatar_split_clause,[],[f2936,f2873,f823,f5195]) ).
fof(f5195,plain,
( spl17_518
<=> ! [X2,X0,X1] :
( empty(cartesian_product2(X0,X1))
| sP0(sK10(powerset(cartesian_product2(X0,X1))),X2)
| in(sK8(sK10(powerset(cartesian_product2(X0,X1))),X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_518])]) ).
fof(f2936,plain,
( ! [X2,X0,X1] :
( empty(cartesian_product2(X0,X1))
| sP0(sK10(powerset(cartesian_product2(X0,X1))),X2)
| in(sK8(sK10(powerset(cartesian_product2(X0,X1))),X2),X1) )
| ~ spl17_103
| ~ spl17_321 ),
inference(resolution,[],[f2874,f824]) ).
fof(f5193,plain,
( spl17_517
| ~ spl17_104
| ~ spl17_321 ),
inference(avatar_split_clause,[],[f2935,f2873,f827,f5191]) ).
fof(f5191,plain,
( spl17_517
<=> ! [X2,X0,X1] :
( empty(cartesian_product2(X0,X1))
| sP0(sK10(powerset(cartesian_product2(X0,X1))),X2)
| in(sK7(sK10(powerset(cartesian_product2(X0,X1))),X2),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_517])]) ).
fof(f2935,plain,
( ! [X2,X0,X1] :
( empty(cartesian_product2(X0,X1))
| sP0(sK10(powerset(cartesian_product2(X0,X1))),X2)
| in(sK7(sK10(powerset(cartesian_product2(X0,X1))),X2),X0) )
| ~ spl17_104
| ~ spl17_321 ),
inference(resolution,[],[f2874,f828]) ).
fof(f5164,plain,
( spl17_516
| ~ spl17_103
| ~ spl17_320 ),
inference(avatar_split_clause,[],[f2885,f2869,f823,f5162]) ).
fof(f5162,plain,
( spl17_516
<=> ! [X2,X0,X1] :
( empty(cartesian_product2(X0,X1))
| sP0(sK10(powerset(cartesian_product2(X0,X1))),X2)
| in(sK9(sK10(powerset(cartesian_product2(X0,X1))),X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_516])]) ).
fof(f2885,plain,
( ! [X2,X0,X1] :
( empty(cartesian_product2(X0,X1))
| sP0(sK10(powerset(cartesian_product2(X0,X1))),X2)
| in(sK9(sK10(powerset(cartesian_product2(X0,X1))),X2),X1) )
| ~ spl17_103
| ~ spl17_320 ),
inference(resolution,[],[f2870,f824]) ).
fof(f5160,plain,
( spl17_515
| ~ spl17_104
| ~ spl17_320 ),
inference(avatar_split_clause,[],[f2884,f2869,f827,f5158]) ).
fof(f5158,plain,
( spl17_515
<=> ! [X2,X0,X1] :
( empty(cartesian_product2(X0,X1))
| sP0(sK10(powerset(cartesian_product2(X0,X1))),X2)
| in(sK8(sK10(powerset(cartesian_product2(X0,X1))),X2),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_515])]) ).
fof(f2884,plain,
( ! [X2,X0,X1] :
( empty(cartesian_product2(X0,X1))
| sP0(sK10(powerset(cartesian_product2(X0,X1))),X2)
| in(sK8(sK10(powerset(cartesian_product2(X0,X1))),X2),X0) )
| ~ spl17_104
| ~ spl17_320 ),
inference(resolution,[],[f2870,f828]) ).
fof(f5156,plain,
( spl17_514
| ~ spl17_17
| ~ spl17_307 ),
inference(avatar_split_clause,[],[f2705,f2700,f255,f5154]) ).
fof(f5154,plain,
( spl17_514
<=> ! [X2,X0,X1] :
( sP0(X0,sK6(powerset(cartesian_product2(X1,X2))))
| empty(powerset(cartesian_product2(X1,X2)))
| sP1(sK9(X0,sK6(powerset(cartesian_product2(X1,X2))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_514])]) ).
fof(f2700,plain,
( spl17_307
<=> ! [X2,X0,X1] :
( empty(powerset(cartesian_product2(X0,X1)))
| sP0(X2,sK6(powerset(cartesian_product2(X0,X1))))
| relation(sK9(X2,sK6(powerset(cartesian_product2(X0,X1))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_307])]) ).
fof(f2705,plain,
( ! [X2,X0,X1] :
( sP0(X0,sK6(powerset(cartesian_product2(X1,X2))))
| empty(powerset(cartesian_product2(X1,X2)))
| sP1(sK9(X0,sK6(powerset(cartesian_product2(X1,X2))))) )
| ~ spl17_17
| ~ spl17_307 ),
inference(resolution,[],[f2701,f256]) ).
fof(f2701,plain,
( ! [X2,X0,X1] :
( relation(sK9(X2,sK6(powerset(cartesian_product2(X0,X1)))))
| sP0(X2,sK6(powerset(cartesian_product2(X0,X1))))
| empty(powerset(cartesian_product2(X0,X1))) )
| ~ spl17_307 ),
inference(avatar_component_clause,[],[f2700]) ).
fof(f5152,plain,
( spl17_513
| ~ spl17_17
| ~ spl17_306 ),
inference(avatar_split_clause,[],[f2704,f2696,f255,f5150]) ).
fof(f5150,plain,
( spl17_513
<=> ! [X2,X0,X1] :
( sP0(X0,sK6(powerset(cartesian_product2(X1,X2))))
| empty(powerset(cartesian_product2(X1,X2)))
| sP1(sK8(X0,sK6(powerset(cartesian_product2(X1,X2))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_513])]) ).
fof(f2696,plain,
( spl17_306
<=> ! [X2,X0,X1] :
( empty(powerset(cartesian_product2(X0,X1)))
| sP0(X2,sK6(powerset(cartesian_product2(X0,X1))))
| relation(sK8(X2,sK6(powerset(cartesian_product2(X0,X1))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_306])]) ).
fof(f2704,plain,
( ! [X2,X0,X1] :
( sP0(X0,sK6(powerset(cartesian_product2(X1,X2))))
| empty(powerset(cartesian_product2(X1,X2)))
| sP1(sK8(X0,sK6(powerset(cartesian_product2(X1,X2))))) )
| ~ spl17_17
| ~ spl17_306 ),
inference(resolution,[],[f2697,f256]) ).
fof(f2697,plain,
( ! [X2,X0,X1] :
( relation(sK8(X2,sK6(powerset(cartesian_product2(X0,X1)))))
| sP0(X2,sK6(powerset(cartesian_product2(X0,X1))))
| empty(powerset(cartesian_product2(X0,X1))) )
| ~ spl17_306 ),
inference(avatar_component_clause,[],[f2696]) ).
fof(f5148,plain,
( spl17_512
| ~ spl17_17
| ~ spl17_305 ),
inference(avatar_split_clause,[],[f2703,f2692,f255,f5146]) ).
fof(f5146,plain,
( spl17_512
<=> ! [X2,X0,X1] :
( sP0(X0,sK6(powerset(cartesian_product2(X1,X2))))
| empty(powerset(cartesian_product2(X1,X2)))
| sP1(sK7(X0,sK6(powerset(cartesian_product2(X1,X2))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_512])]) ).
fof(f2692,plain,
( spl17_305
<=> ! [X2,X0,X1] :
( empty(powerset(cartesian_product2(X0,X1)))
| sP0(X2,sK6(powerset(cartesian_product2(X0,X1))))
| relation(sK7(X2,sK6(powerset(cartesian_product2(X0,X1))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_305])]) ).
fof(f2703,plain,
( ! [X2,X0,X1] :
( sP0(X0,sK6(powerset(cartesian_product2(X1,X2))))
| empty(powerset(cartesian_product2(X1,X2)))
| sP1(sK7(X0,sK6(powerset(cartesian_product2(X1,X2))))) )
| ~ spl17_17
| ~ spl17_305 ),
inference(resolution,[],[f2693,f256]) ).
fof(f2693,plain,
( ! [X2,X0,X1] :
( relation(sK7(X2,sK6(powerset(cartesian_product2(X0,X1)))))
| sP0(X2,sK6(powerset(cartesian_product2(X0,X1))))
| empty(powerset(cartesian_product2(X0,X1))) )
| ~ spl17_305 ),
inference(avatar_component_clause,[],[f2692]) ).
fof(f5144,plain,
( spl17_511
| ~ spl17_39
| ~ spl17_301 ),
inference(avatar_split_clause,[],[f2648,f2566,f355,f5142]) ).
fof(f5142,plain,
( spl17_511
<=> ! [X2,X0,X1] :
( sP0(X0,powerset(X1))
| sP0(X2,sK9(X0,powerset(X1)))
| empty(X1)
| in(sK9(X2,sK9(X0,powerset(X1))),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_511])]) ).
fof(f2648,plain,
( ! [X2,X0,X1] :
( sP0(X0,powerset(X1))
| sP0(X2,sK9(X0,powerset(X1)))
| empty(X1)
| in(sK9(X2,sK9(X0,powerset(X1))),X1) )
| ~ spl17_39
| ~ spl17_301 ),
inference(resolution,[],[f2567,f356]) ).
fof(f5140,plain,
( spl17_510
| ~ spl17_39
| ~ spl17_300 ),
inference(avatar_split_clause,[],[f2644,f2562,f355,f5138]) ).
fof(f5138,plain,
( spl17_510
<=> ! [X2,X0,X1] :
( sP0(X0,powerset(X1))
| sP0(X2,sK9(X0,powerset(X1)))
| empty(X1)
| in(sK8(X2,sK9(X0,powerset(X1))),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_510])]) ).
fof(f2644,plain,
( ! [X2,X0,X1] :
( sP0(X0,powerset(X1))
| sP0(X2,sK9(X0,powerset(X1)))
| empty(X1)
| in(sK8(X2,sK9(X0,powerset(X1))),X1) )
| ~ spl17_39
| ~ spl17_300 ),
inference(resolution,[],[f2563,f356]) ).
fof(f5136,plain,
( spl17_509
| ~ spl17_39
| ~ spl17_299 ),
inference(avatar_split_clause,[],[f2640,f2558,f355,f5134]) ).
fof(f5134,plain,
( spl17_509
<=> ! [X2,X0,X1] :
( sP0(X0,powerset(X1))
| sP0(X2,sK9(X0,powerset(X1)))
| empty(X1)
| in(sK7(X2,sK9(X0,powerset(X1))),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_509])]) ).
fof(f2640,plain,
( ! [X2,X0,X1] :
( sP0(X0,powerset(X1))
| sP0(X2,sK9(X0,powerset(X1)))
| empty(X1)
| in(sK7(X2,sK9(X0,powerset(X1))),X1) )
| ~ spl17_39
| ~ spl17_299 ),
inference(resolution,[],[f2559,f356]) ).
fof(f5132,plain,
( spl17_508
| ~ spl17_39
| ~ spl17_298 ),
inference(avatar_split_clause,[],[f2636,f2554,f355,f5130]) ).
fof(f5130,plain,
( spl17_508
<=> ! [X2,X0,X1] :
( sP0(X0,powerset(X1))
| sP0(X2,sK8(X0,powerset(X1)))
| empty(X1)
| in(sK9(X2,sK8(X0,powerset(X1))),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_508])]) ).
fof(f2636,plain,
( ! [X2,X0,X1] :
( sP0(X0,powerset(X1))
| sP0(X2,sK8(X0,powerset(X1)))
| empty(X1)
| in(sK9(X2,sK8(X0,powerset(X1))),X1) )
| ~ spl17_39
| ~ spl17_298 ),
inference(resolution,[],[f2555,f356]) ).
fof(f5128,plain,
( spl17_507
| ~ spl17_39
| ~ spl17_297 ),
inference(avatar_split_clause,[],[f2632,f2550,f355,f5126]) ).
fof(f5126,plain,
( spl17_507
<=> ! [X2,X0,X1] :
( sP0(X0,powerset(X1))
| sP0(X2,sK8(X0,powerset(X1)))
| empty(X1)
| in(sK8(X2,sK8(X0,powerset(X1))),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_507])]) ).
fof(f2632,plain,
( ! [X2,X0,X1] :
( sP0(X0,powerset(X1))
| sP0(X2,sK8(X0,powerset(X1)))
| empty(X1)
| in(sK8(X2,sK8(X0,powerset(X1))),X1) )
| ~ spl17_39
| ~ spl17_297 ),
inference(resolution,[],[f2551,f356]) ).
fof(f5124,plain,
( spl17_421
| ~ spl17_9
| ~ spl17_24
| ~ spl17_459 ),
inference(avatar_split_clause,[],[f5070,f4452,f287,f219,f3926]) ).
fof(f3926,plain,
( spl17_421
<=> sK16 = cartesian_product2(sK16,sK16) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_421])]) ).
fof(f219,plain,
( spl17_9
<=> empty(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_9])]) ).
fof(f287,plain,
( spl17_24
<=> empty_set = sK16 ),
introduced(avatar_definition,[new_symbols(naming,[spl17_24])]) ).
fof(f4452,plain,
( spl17_459
<=> ! [X0] :
( cartesian_product2(sK16,sK16) = X0
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_459])]) ).
fof(f5070,plain,
( sK16 = cartesian_product2(sK16,sK16)
| ~ spl17_9
| ~ spl17_24
| ~ spl17_459 ),
inference(forward_demodulation,[],[f5055,f289]) ).
fof(f289,plain,
( empty_set = sK16
| ~ spl17_24 ),
inference(avatar_component_clause,[],[f287]) ).
fof(f5055,plain,
( empty_set = cartesian_product2(sK16,sK16)
| ~ spl17_9
| ~ spl17_459 ),
inference(resolution,[],[f4453,f221]) ).
fof(f221,plain,
( empty(empty_set)
| ~ spl17_9 ),
inference(avatar_component_clause,[],[f219]) ).
fof(f4453,plain,
( ! [X0] :
( ~ empty(X0)
| cartesian_product2(sK16,sK16) = X0 )
| ~ spl17_459 ),
inference(avatar_component_clause,[],[f4452]) ).
fof(f5123,plain,
( spl17_506
| ~ spl17_39
| ~ spl17_296 ),
inference(avatar_split_clause,[],[f2628,f2546,f355,f5121]) ).
fof(f5121,plain,
( spl17_506
<=> ! [X2,X0,X1] :
( sP0(X0,powerset(X1))
| sP0(X2,sK8(X0,powerset(X1)))
| empty(X1)
| in(sK7(X2,sK8(X0,powerset(X1))),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_506])]) ).
fof(f2628,plain,
( ! [X2,X0,X1] :
( sP0(X0,powerset(X1))
| sP0(X2,sK8(X0,powerset(X1)))
| empty(X1)
| in(sK7(X2,sK8(X0,powerset(X1))),X1) )
| ~ spl17_39
| ~ spl17_296 ),
inference(resolution,[],[f2547,f356]) ).
fof(f5119,plain,
( spl17_505
| ~ spl17_39
| ~ spl17_295 ),
inference(avatar_split_clause,[],[f2624,f2542,f355,f5117]) ).
fof(f5117,plain,
( spl17_505
<=> ! [X2,X0,X1] :
( sP0(X0,powerset(X1))
| sP0(X2,sK7(X0,powerset(X1)))
| empty(X1)
| in(sK9(X2,sK7(X0,powerset(X1))),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_505])]) ).
fof(f2624,plain,
( ! [X2,X0,X1] :
( sP0(X0,powerset(X1))
| sP0(X2,sK7(X0,powerset(X1)))
| empty(X1)
| in(sK9(X2,sK7(X0,powerset(X1))),X1) )
| ~ spl17_39
| ~ spl17_295 ),
inference(resolution,[],[f2543,f356]) ).
fof(f5115,plain,
( spl17_504
| ~ spl17_39
| ~ spl17_294 ),
inference(avatar_split_clause,[],[f2620,f2538,f355,f5113]) ).
fof(f5113,plain,
( spl17_504
<=> ! [X2,X0,X1] :
( sP0(X0,powerset(X1))
| sP0(X2,sK7(X0,powerset(X1)))
| empty(X1)
| in(sK8(X2,sK7(X0,powerset(X1))),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_504])]) ).
fof(f2620,plain,
( ! [X2,X0,X1] :
( sP0(X0,powerset(X1))
| sP0(X2,sK7(X0,powerset(X1)))
| empty(X1)
| in(sK8(X2,sK7(X0,powerset(X1))),X1) )
| ~ spl17_39
| ~ spl17_294 ),
inference(resolution,[],[f2539,f356]) ).
fof(f5111,plain,
( spl17_503
| ~ spl17_39
| ~ spl17_293 ),
inference(avatar_split_clause,[],[f2612,f2534,f355,f5109]) ).
fof(f5109,plain,
( spl17_503
<=> ! [X2,X0,X1] :
( sP0(X0,powerset(X1))
| sP0(X2,sK7(X0,powerset(X1)))
| empty(X1)
| in(sK7(X2,sK7(X0,powerset(X1))),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_503])]) ).
fof(f2612,plain,
( ! [X2,X0,X1] :
( sP0(X0,powerset(X1))
| sP0(X2,sK7(X0,powerset(X1)))
| empty(X1)
| in(sK7(X2,sK7(X0,powerset(X1))),X1) )
| ~ spl17_39
| ~ spl17_293 ),
inference(resolution,[],[f2535,f356]) ).
fof(f5107,plain,
( spl17_502
| ~ spl17_92
| ~ spl17_266 ),
inference(avatar_split_clause,[],[f2228,f2147,f733,f5105]) ).
fof(f5105,plain,
( spl17_502
<=> ! [X0,X1] :
( empty(sK10(powerset(X0)))
| sP0(X1,sK10(powerset(sK10(powerset(X0)))))
| element(sK9(X1,sK10(powerset(sK10(powerset(X0))))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_502])]) ).
fof(f2228,plain,
( ! [X0,X1] :
( empty(sK10(powerset(X0)))
| sP0(X1,sK10(powerset(sK10(powerset(X0)))))
| element(sK9(X1,sK10(powerset(sK10(powerset(X0))))),X0) )
| ~ spl17_92
| ~ spl17_266 ),
inference(resolution,[],[f2148,f734]) ).
fof(f5103,plain,
( spl17_501
| ~ spl17_92
| ~ spl17_265 ),
inference(avatar_split_clause,[],[f2207,f2143,f733,f5101]) ).
fof(f5101,plain,
( spl17_501
<=> ! [X0,X1] :
( empty(sK10(powerset(X0)))
| sP0(X1,sK10(powerset(sK10(powerset(X0)))))
| element(sK8(X1,sK10(powerset(sK10(powerset(X0))))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_501])]) ).
fof(f2207,plain,
( ! [X0,X1] :
( empty(sK10(powerset(X0)))
| sP0(X1,sK10(powerset(sK10(powerset(X0)))))
| element(sK8(X1,sK10(powerset(sK10(powerset(X0))))),X0) )
| ~ spl17_92
| ~ spl17_265 ),
inference(resolution,[],[f2144,f734]) ).
fof(f5099,plain,
( spl17_500
| ~ spl17_92
| ~ spl17_264 ),
inference(avatar_split_clause,[],[f2186,f2139,f733,f5097]) ).
fof(f5097,plain,
( spl17_500
<=> ! [X0,X1] :
( empty(sK10(powerset(X0)))
| sP0(X1,sK10(powerset(sK10(powerset(X0)))))
| element(sK7(X1,sK10(powerset(sK10(powerset(X0))))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_500])]) ).
fof(f2186,plain,
( ! [X0,X1] :
( empty(sK10(powerset(X0)))
| sP0(X1,sK10(powerset(sK10(powerset(X0)))))
| element(sK7(X1,sK10(powerset(sK10(powerset(X0))))),X0) )
| ~ spl17_92
| ~ spl17_264 ),
inference(resolution,[],[f2140,f734]) ).
fof(f5095,plain,
( spl17_499
| ~ spl17_150
| ~ spl17_241 ),
inference(avatar_split_clause,[],[f2063,f1933,f1159,f5093]) ).
fof(f5093,plain,
( spl17_499
<=> ! [X2,X0,X1] :
( sP0(X0,sK6(sK13(X1,X2)))
| empty(sK13(X1,X2))
| element(sK9(X0,sK6(sK13(X1,X2))),cartesian_product2(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_499])]) ).
fof(f2063,plain,
( ! [X2,X0,X1] :
( sP0(X0,sK6(sK13(X1,X2)))
| empty(sK13(X1,X2))
| element(sK9(X0,sK6(sK13(X1,X2))),cartesian_product2(X1,X2)) )
| ~ spl17_150
| ~ spl17_241 ),
inference(resolution,[],[f1934,f1160]) ).
fof(f5091,plain,
( spl17_498
| ~ spl17_151
| ~ spl17_241 ),
inference(avatar_split_clause,[],[f2062,f1933,f1163,f5089]) ).
fof(f5089,plain,
( spl17_498
<=> ! [X2,X0,X1] :
( sP0(X0,sK6(sK12(X1,X2)))
| empty(sK12(X1,X2))
| element(sK9(X0,sK6(sK12(X1,X2))),cartesian_product2(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_498])]) ).
fof(f2062,plain,
( ! [X2,X0,X1] :
( sP0(X0,sK6(sK12(X1,X2)))
| empty(sK12(X1,X2))
| element(sK9(X0,sK6(sK12(X1,X2))),cartesian_product2(X1,X2)) )
| ~ spl17_151
| ~ spl17_241 ),
inference(resolution,[],[f1934,f1164]) ).
fof(f5087,plain,
( spl17_497
| ~ spl17_150
| ~ spl17_240 ),
inference(avatar_split_clause,[],[f2044,f1929,f1159,f5085]) ).
fof(f5085,plain,
( spl17_497
<=> ! [X2,X0,X1] :
( sP0(X0,sK6(sK13(X1,X2)))
| empty(sK13(X1,X2))
| element(sK8(X0,sK6(sK13(X1,X2))),cartesian_product2(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_497])]) ).
fof(f2044,plain,
( ! [X2,X0,X1] :
( sP0(X0,sK6(sK13(X1,X2)))
| empty(sK13(X1,X2))
| element(sK8(X0,sK6(sK13(X1,X2))),cartesian_product2(X1,X2)) )
| ~ spl17_150
| ~ spl17_240 ),
inference(resolution,[],[f1930,f1160]) ).
fof(f5054,plain,
( spl17_496
| ~ spl17_151
| ~ spl17_240 ),
inference(avatar_split_clause,[],[f2043,f1929,f1163,f5052]) ).
fof(f5052,plain,
( spl17_496
<=> ! [X2,X0,X1] :
( sP0(X0,sK6(sK12(X1,X2)))
| empty(sK12(X1,X2))
| element(sK8(X0,sK6(sK12(X1,X2))),cartesian_product2(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_496])]) ).
fof(f2043,plain,
( ! [X2,X0,X1] :
( sP0(X0,sK6(sK12(X1,X2)))
| empty(sK12(X1,X2))
| element(sK8(X0,sK6(sK12(X1,X2))),cartesian_product2(X1,X2)) )
| ~ spl17_151
| ~ spl17_240 ),
inference(resolution,[],[f1930,f1164]) ).
fof(f5050,plain,
( spl17_495
| ~ spl17_150
| ~ spl17_239 ),
inference(avatar_split_clause,[],[f2025,f1925,f1159,f5048]) ).
fof(f5048,plain,
( spl17_495
<=> ! [X2,X0,X1] :
( sP0(X0,sK6(sK13(X1,X2)))
| empty(sK13(X1,X2))
| element(sK7(X0,sK6(sK13(X1,X2))),cartesian_product2(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_495])]) ).
fof(f2025,plain,
( ! [X2,X0,X1] :
( sP0(X0,sK6(sK13(X1,X2)))
| empty(sK13(X1,X2))
| element(sK7(X0,sK6(sK13(X1,X2))),cartesian_product2(X1,X2)) )
| ~ spl17_150
| ~ spl17_239 ),
inference(resolution,[],[f1926,f1160]) ).
fof(f5046,plain,
( spl17_494
| ~ spl17_151
| ~ spl17_239 ),
inference(avatar_split_clause,[],[f2024,f1925,f1163,f5044]) ).
fof(f5044,plain,
( spl17_494
<=> ! [X2,X0,X1] :
( sP0(X0,sK6(sK12(X1,X2)))
| empty(sK12(X1,X2))
| element(sK7(X0,sK6(sK12(X1,X2))),cartesian_product2(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_494])]) ).
fof(f2024,plain,
( ! [X2,X0,X1] :
( sP0(X0,sK6(sK12(X1,X2)))
| empty(sK12(X1,X2))
| element(sK7(X0,sK6(sK12(X1,X2))),cartesian_product2(X1,X2)) )
| ~ spl17_151
| ~ spl17_239 ),
inference(resolution,[],[f1926,f1164]) ).
fof(f5042,plain,
( spl17_493
| ~ spl17_150
| ~ spl17_229 ),
inference(avatar_split_clause,[],[f1993,f1885,f1159,f5040]) ).
fof(f5040,plain,
( spl17_493
<=> ! [X0,X1] :
( empty(sK13(X0,X1))
| empty(sK10(powerset(sK13(X0,X1))))
| element(sK10(sK10(powerset(sK13(X0,X1)))),cartesian_product2(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_493])]) ).
fof(f1993,plain,
( ! [X0,X1] :
( empty(sK13(X0,X1))
| empty(sK10(powerset(sK13(X0,X1))))
| element(sK10(sK10(powerset(sK13(X0,X1)))),cartesian_product2(X0,X1)) )
| ~ spl17_150
| ~ spl17_229 ),
inference(resolution,[],[f1886,f1160]) ).
fof(f5038,plain,
( spl17_492
| ~ spl17_151
| ~ spl17_229 ),
inference(avatar_split_clause,[],[f1992,f1885,f1163,f5036]) ).
fof(f5036,plain,
( spl17_492
<=> ! [X0,X1] :
( empty(sK12(X0,X1))
| empty(sK10(powerset(sK12(X0,X1))))
| element(sK10(sK10(powerset(sK12(X0,X1)))),cartesian_product2(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_492])]) ).
fof(f1992,plain,
( ! [X0,X1] :
( empty(sK12(X0,X1))
| empty(sK10(powerset(sK12(X0,X1))))
| element(sK10(sK10(powerset(sK12(X0,X1)))),cartesian_product2(X0,X1)) )
| ~ spl17_151
| ~ spl17_229 ),
inference(resolution,[],[f1886,f1164]) ).
fof(f5002,plain,
( spl17_491
| ~ spl17_25
| ~ spl17_304 ),
inference(avatar_split_clause,[],[f2675,f2657,f292,f5000]) ).
fof(f5000,plain,
( spl17_491
<=> ! [X0,X1] :
( ~ rel_str(X0)
| empty(cartesian_product2(the_carrier(X0),the_carrier(X0)))
| ~ in(X1,the_InternalRel(X0))
| ~ in(cartesian_product2(the_carrier(X0),the_carrier(X0)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_491])]) ).
fof(f2675,plain,
( ! [X0,X1] :
( ~ rel_str(X0)
| empty(cartesian_product2(the_carrier(X0),the_carrier(X0)))
| ~ in(X1,the_InternalRel(X0))
| ~ in(cartesian_product2(the_carrier(X0),the_carrier(X0)),X1) )
| ~ spl17_25
| ~ spl17_304 ),
inference(resolution,[],[f2658,f293]) ).
fof(f4998,plain,
( spl17_490
| ~ spl17_16
| ~ spl17_303 ),
inference(avatar_split_clause,[],[f2672,f2653,f251,f4996]) ).
fof(f4996,plain,
( spl17_490
<=> ! [X0,X1] :
( empty(powerset(powerset(cartesian_product2(X0,X1))))
| empty(powerset(cartesian_product2(X0,X1)))
| ~ relation_of2_as_subset(powerset(powerset(cartesian_product2(X0,X1))),X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_490])]) ).
fof(f2653,plain,
( spl17_303
<=> ! [X2,X0,X1] :
( ~ subset(powerset(cartesian_product2(X0,X1)),X2)
| empty(powerset(X2))
| empty(powerset(cartesian_product2(X0,X1)))
| ~ relation_of2_as_subset(powerset(X2),X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_303])]) ).
fof(f2672,plain,
( ! [X0,X1] :
( empty(powerset(powerset(cartesian_product2(X0,X1))))
| empty(powerset(cartesian_product2(X0,X1)))
| ~ relation_of2_as_subset(powerset(powerset(cartesian_product2(X0,X1))),X0,X1) )
| ~ spl17_16
| ~ spl17_303 ),
inference(resolution,[],[f2654,f252]) ).
fof(f2654,plain,
( ! [X2,X0,X1] :
( ~ subset(powerset(cartesian_product2(X0,X1)),X2)
| empty(powerset(X2))
| empty(powerset(cartesian_product2(X0,X1)))
| ~ relation_of2_as_subset(powerset(X2),X0,X1) )
| ~ spl17_303 ),
inference(avatar_component_clause,[],[f2653]) ).
fof(f4994,plain,
( spl17_489
| ~ spl17_75
| ~ spl17_271 ),
inference(avatar_split_clause,[],[f2318,f2289,f643,f4992]) ).
fof(f4992,plain,
( spl17_489
<=> ! [X0] :
( empty(sK6(powerset(X0)))
| element(sK10(sK10(sK6(powerset(X0)))),X0)
| empty(powerset(X0))
| empty(sK10(sK6(powerset(X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_489])]) ).
fof(f2318,plain,
( ! [X0] :
( empty(sK6(powerset(X0)))
| element(sK10(sK10(sK6(powerset(X0)))),X0)
| empty(powerset(X0))
| empty(sK10(sK6(powerset(X0)))) )
| ~ spl17_75
| ~ spl17_271 ),
inference(resolution,[],[f2290,f644]) ).
fof(f4990,plain,
( spl17_488
| ~ spl17_75
| ~ spl17_269 ),
inference(avatar_split_clause,[],[f2250,f2240,f643,f4988]) ).
fof(f4988,plain,
( spl17_488
<=> ! [X0] :
( element(sK10(sK10(sK10(powerset(powerset(X0))))),X0)
| empty(sK10(powerset(powerset(X0))))
| empty(sK10(sK10(powerset(powerset(X0))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_488])]) ).
fof(f2250,plain,
( ! [X0] :
( element(sK10(sK10(sK10(powerset(powerset(X0))))),X0)
| empty(sK10(powerset(powerset(X0))))
| empty(sK10(sK10(powerset(powerset(X0))))) )
| ~ spl17_75
| ~ spl17_269 ),
inference(resolution,[],[f2241,f644]) ).
fof(f4986,plain,
( spl17_487
| ~ spl17_95
| ~ spl17_266 ),
inference(avatar_split_clause,[],[f2221,f2147,f765,f4984]) ).
fof(f4984,plain,
( spl17_487
<=> ! [X0,X1] :
( empty(sK6(X0))
| sP0(X1,sK10(powerset(sK6(X0))))
| element(sK9(X1,sK10(powerset(sK6(X0)))),X0)
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_487])]) ).
fof(f2221,plain,
( ! [X0,X1] :
( empty(sK6(X0))
| sP0(X1,sK10(powerset(sK6(X0))))
| element(sK9(X1,sK10(powerset(sK6(X0)))),X0)
| empty(X0) )
| ~ spl17_95
| ~ spl17_266 ),
inference(resolution,[],[f2148,f766]) ).
fof(f4982,plain,
( spl17_486
| ~ spl17_95
| ~ spl17_265 ),
inference(avatar_split_clause,[],[f2200,f2143,f765,f4980]) ).
fof(f4980,plain,
( spl17_486
<=> ! [X0,X1] :
( empty(sK6(X0))
| sP0(X1,sK10(powerset(sK6(X0))))
| element(sK8(X1,sK10(powerset(sK6(X0)))),X0)
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_486])]) ).
fof(f2200,plain,
( ! [X0,X1] :
( empty(sK6(X0))
| sP0(X1,sK10(powerset(sK6(X0))))
| element(sK8(X1,sK10(powerset(sK6(X0)))),X0)
| empty(X0) )
| ~ spl17_95
| ~ spl17_265 ),
inference(resolution,[],[f2144,f766]) ).
fof(f4978,plain,
( spl17_485
| ~ spl17_95
| ~ spl17_264 ),
inference(avatar_split_clause,[],[f2179,f2139,f765,f4976]) ).
fof(f4976,plain,
( spl17_485
<=> ! [X0,X1] :
( empty(sK6(X0))
| sP0(X1,sK10(powerset(sK6(X0))))
| element(sK7(X1,sK10(powerset(sK6(X0)))),X0)
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_485])]) ).
fof(f2179,plain,
( ! [X0,X1] :
( empty(sK6(X0))
| sP0(X1,sK10(powerset(sK6(X0))))
| element(sK7(X1,sK10(powerset(sK6(X0)))),X0)
| empty(X0) )
| ~ spl17_95
| ~ spl17_264 ),
inference(resolution,[],[f2140,f766]) ).
fof(f4680,plain,
( ~ spl17_12
| spl17_403
| ~ spl17_421 ),
inference(avatar_split_clause,[],[f4635,f3926,f3824,f234]) ).
fof(f234,plain,
( spl17_12
<=> empty(sK16) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_12])]) ).
fof(f3824,plain,
( spl17_403
<=> empty(cartesian_product2(sK16,sK16)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_403])]) ).
fof(f4635,plain,
( ~ empty(sK16)
| spl17_403
| ~ spl17_421 ),
inference(forward_demodulation,[],[f3825,f3928]) ).
fof(f3928,plain,
( sK16 = cartesian_product2(sK16,sK16)
| ~ spl17_421 ),
inference(avatar_component_clause,[],[f3926]) ).
fof(f3825,plain,
( ~ empty(cartesian_product2(sK16,sK16))
| spl17_403 ),
inference(avatar_component_clause,[],[f3824]) ).
fof(f4630,plain,
( spl17_131
| ~ spl17_75
| ~ spl17_464 ),
inference(avatar_split_clause,[],[f4573,f4521,f643,f1061]) ).
fof(f4521,plain,
( spl17_464
<=> ! [X0] : ~ in(X0,the_InternalRel(sK2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_464])]) ).
fof(f4573,plain,
( empty(the_InternalRel(sK2))
| ~ spl17_75
| ~ spl17_464 ),
inference(resolution,[],[f4522,f644]) ).
fof(f4522,plain,
( ! [X0] : ~ in(X0,the_InternalRel(sK2))
| ~ spl17_464 ),
inference(avatar_component_clause,[],[f4521]) ).
fof(f4629,plain,
( spl17_484
| ~ spl17_103
| ~ spl17_312 ),
inference(avatar_split_clause,[],[f2787,f2730,f823,f4627]) ).
fof(f4627,plain,
( spl17_484
<=> ! [X2,X0,X1] :
( sP0(sK6(cartesian_product2(X0,X1)),X2)
| empty(cartesian_product2(X0,X1))
| in(sK8(sK6(cartesian_product2(X0,X1)),X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_484])]) ).
fof(f2787,plain,
( ! [X2,X0,X1] :
( sP0(sK6(cartesian_product2(X0,X1)),X2)
| empty(cartesian_product2(X0,X1))
| in(sK8(sK6(cartesian_product2(X0,X1)),X2),X1) )
| ~ spl17_103
| ~ spl17_312 ),
inference(resolution,[],[f2731,f824]) ).
fof(f4625,plain,
( spl17_483
| ~ spl17_104
| ~ spl17_312 ),
inference(avatar_split_clause,[],[f2786,f2730,f827,f4623]) ).
fof(f4623,plain,
( spl17_483
<=> ! [X2,X0,X1] :
( sP0(sK6(cartesian_product2(X0,X1)),X2)
| empty(cartesian_product2(X0,X1))
| in(sK7(sK6(cartesian_product2(X0,X1)),X2),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_483])]) ).
fof(f2786,plain,
( ! [X2,X0,X1] :
( sP0(sK6(cartesian_product2(X0,X1)),X2)
| empty(cartesian_product2(X0,X1))
| in(sK7(sK6(cartesian_product2(X0,X1)),X2),X0) )
| ~ spl17_104
| ~ spl17_312 ),
inference(resolution,[],[f2731,f828]) ).
fof(f4621,plain,
( spl17_482
| ~ spl17_103
| ~ spl17_311 ),
inference(avatar_split_clause,[],[f2738,f2726,f823,f4619]) ).
fof(f2738,plain,
( ! [X2,X0,X1] :
( sP0(sK6(cartesian_product2(X0,X1)),X2)
| empty(cartesian_product2(X0,X1))
| in(sK9(sK6(cartesian_product2(X0,X1)),X2),X1) )
| ~ spl17_103
| ~ spl17_311 ),
inference(resolution,[],[f2727,f824]) ).
fof(f4617,plain,
( spl17_481
| ~ spl17_104
| ~ spl17_311 ),
inference(avatar_split_clause,[],[f2737,f2726,f827,f4615]) ).
fof(f2737,plain,
( ! [X2,X0,X1] :
( sP0(sK6(cartesian_product2(X0,X1)),X2)
| empty(cartesian_product2(X0,X1))
| in(sK8(sK6(cartesian_product2(X0,X1)),X2),X0) )
| ~ spl17_104
| ~ spl17_311 ),
inference(resolution,[],[f2727,f828]) ).
fof(f4613,plain,
( spl17_480
| ~ spl17_17
| ~ spl17_289 ),
inference(avatar_split_clause,[],[f2569,f2518,f255,f4611]) ).
fof(f4611,plain,
( spl17_480
<=> ! [X0,X1] :
( empty(sK6(powerset(cartesian_product2(X0,X1))))
| empty(powerset(cartesian_product2(X0,X1)))
| sP1(sK10(sK6(powerset(cartesian_product2(X0,X1))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_480])]) ).
fof(f2518,plain,
( spl17_289
<=> ! [X0,X1] :
( empty(powerset(cartesian_product2(X0,X1)))
| empty(sK6(powerset(cartesian_product2(X0,X1))))
| relation(sK10(sK6(powerset(cartesian_product2(X0,X1))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_289])]) ).
fof(f2569,plain,
( ! [X0,X1] :
( empty(sK6(powerset(cartesian_product2(X0,X1))))
| empty(powerset(cartesian_product2(X0,X1)))
| sP1(sK10(sK6(powerset(cartesian_product2(X0,X1))))) )
| ~ spl17_17
| ~ spl17_289 ),
inference(resolution,[],[f2519,f256]) ).
fof(f2519,plain,
( ! [X0,X1] :
( relation(sK10(sK6(powerset(cartesian_product2(X0,X1)))))
| empty(sK6(powerset(cartesian_product2(X0,X1))))
| empty(powerset(cartesian_product2(X0,X1))) )
| ~ spl17_289 ),
inference(avatar_component_clause,[],[f2518]) ).
fof(f4609,plain,
( spl17_479
| ~ spl17_39
| ~ spl17_277 ),
inference(avatar_split_clause,[],[f2384,f2313,f355,f4607]) ).
fof(f4607,plain,
( spl17_479
<=> ! [X0,X1] :
( sP0(X0,powerset(X1))
| empty(sK9(X0,powerset(X1)))
| empty(X1)
| in(sK10(sK9(X0,powerset(X1))),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_479])]) ).
fof(f2384,plain,
( ! [X0,X1] :
( sP0(X0,powerset(X1))
| empty(sK9(X0,powerset(X1)))
| empty(X1)
| in(sK10(sK9(X0,powerset(X1))),X1) )
| ~ spl17_39
| ~ spl17_277 ),
inference(resolution,[],[f2314,f356]) ).
fof(f4605,plain,
( spl17_478
| ~ spl17_39
| ~ spl17_276 ),
inference(avatar_split_clause,[],[f2380,f2309,f355,f4603]) ).
fof(f4603,plain,
( spl17_478
<=> ! [X0,X1] :
( sP0(X0,powerset(X1))
| empty(sK8(X0,powerset(X1)))
| empty(X1)
| in(sK10(sK8(X0,powerset(X1))),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_478])]) ).
fof(f2380,plain,
( ! [X0,X1] :
( sP0(X0,powerset(X1))
| empty(sK8(X0,powerset(X1)))
| empty(X1)
| in(sK10(sK8(X0,powerset(X1))),X1) )
| ~ spl17_39
| ~ spl17_276 ),
inference(resolution,[],[f2310,f356]) ).
fof(f4601,plain,
( spl17_477
| ~ spl17_39
| ~ spl17_275 ),
inference(avatar_split_clause,[],[f2376,f2305,f355,f4599]) ).
fof(f4599,plain,
( spl17_477
<=> ! [X0,X1] :
( sP0(X0,powerset(X1))
| empty(sK7(X0,powerset(X1)))
| empty(X1)
| in(sK10(sK7(X0,powerset(X1))),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_477])]) ).
fof(f2376,plain,
( ! [X0,X1] :
( sP0(X0,powerset(X1))
| empty(sK7(X0,powerset(X1)))
| empty(X1)
| in(sK10(sK7(X0,powerset(X1))),X1) )
| ~ spl17_39
| ~ spl17_275 ),
inference(resolution,[],[f2306,f356]) ).
fof(f4597,plain,
( spl17_476
| ~ spl17_39
| ~ spl17_263 ),
inference(avatar_split_clause,[],[f2171,f2134,f355,f4595]) ).
fof(f4595,plain,
( spl17_476
<=> ! [X2,X0,X1] :
( sP0(X0,sK12(X1,X2))
| empty(cartesian_product2(X1,X2))
| in(sK9(X0,sK12(X1,X2)),cartesian_product2(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_476])]) ).
fof(f2134,plain,
( spl17_263
<=> ! [X2,X0,X1] :
( element(sK9(X0,sK12(X1,X2)),cartesian_product2(X1,X2))
| sP0(X0,sK12(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_263])]) ).
fof(f2171,plain,
( ! [X2,X0,X1] :
( sP0(X0,sK12(X1,X2))
| empty(cartesian_product2(X1,X2))
| in(sK9(X0,sK12(X1,X2)),cartesian_product2(X1,X2)) )
| ~ spl17_39
| ~ spl17_263 ),
inference(resolution,[],[f2135,f356]) ).
fof(f2135,plain,
( ! [X2,X0,X1] :
( element(sK9(X0,sK12(X1,X2)),cartesian_product2(X1,X2))
| sP0(X0,sK12(X1,X2)) )
| ~ spl17_263 ),
inference(avatar_component_clause,[],[f2134]) ).
fof(f4593,plain,
( spl17_475
| ~ spl17_39
| ~ spl17_262 ),
inference(avatar_split_clause,[],[f2166,f2130,f355,f4591]) ).
fof(f4591,plain,
( spl17_475
<=> ! [X2,X0,X1] :
( sP0(X0,sK12(X1,X2))
| empty(cartesian_product2(X1,X2))
| in(sK8(X0,sK12(X1,X2)),cartesian_product2(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_475])]) ).
fof(f2130,plain,
( spl17_262
<=> ! [X2,X0,X1] :
( element(sK8(X0,sK12(X1,X2)),cartesian_product2(X1,X2))
| sP0(X0,sK12(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_262])]) ).
fof(f2166,plain,
( ! [X2,X0,X1] :
( sP0(X0,sK12(X1,X2))
| empty(cartesian_product2(X1,X2))
| in(sK8(X0,sK12(X1,X2)),cartesian_product2(X1,X2)) )
| ~ spl17_39
| ~ spl17_262 ),
inference(resolution,[],[f2131,f356]) ).
fof(f2131,plain,
( ! [X2,X0,X1] :
( element(sK8(X0,sK12(X1,X2)),cartesian_product2(X1,X2))
| sP0(X0,sK12(X1,X2)) )
| ~ spl17_262 ),
inference(avatar_component_clause,[],[f2130]) ).
fof(f4563,plain,
( spl17_474
| ~ spl17_39
| ~ spl17_261 ),
inference(avatar_split_clause,[],[f2165,f2126,f355,f4561]) ).
fof(f4561,plain,
( spl17_474
<=> ! [X2,X0,X1] :
( sP0(X0,sK12(X1,X2))
| empty(cartesian_product2(X1,X2))
| in(sK7(X0,sK12(X1,X2)),cartesian_product2(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_474])]) ).
fof(f2126,plain,
( spl17_261
<=> ! [X2,X0,X1] :
( element(sK7(X0,sK12(X1,X2)),cartesian_product2(X1,X2))
| sP0(X0,sK12(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_261])]) ).
fof(f2165,plain,
( ! [X2,X0,X1] :
( sP0(X0,sK12(X1,X2))
| empty(cartesian_product2(X1,X2))
| in(sK7(X0,sK12(X1,X2)),cartesian_product2(X1,X2)) )
| ~ spl17_39
| ~ spl17_261 ),
inference(resolution,[],[f2127,f356]) ).
fof(f2127,plain,
( ! [X2,X0,X1] :
( element(sK7(X0,sK12(X1,X2)),cartesian_product2(X1,X2))
| sP0(X0,sK12(X1,X2)) )
| ~ spl17_261 ),
inference(avatar_component_clause,[],[f2126]) ).
fof(f4559,plain,
( spl17_473
| ~ spl17_39
| ~ spl17_260 ),
inference(avatar_split_clause,[],[f2164,f2122,f355,f4557]) ).
fof(f4557,plain,
( spl17_473
<=> ! [X2,X0,X1] :
( sP0(X0,sK13(X1,X2))
| empty(cartesian_product2(X1,X2))
| in(sK9(X0,sK13(X1,X2)),cartesian_product2(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_473])]) ).
fof(f2122,plain,
( spl17_260
<=> ! [X2,X0,X1] :
( element(sK9(X0,sK13(X1,X2)),cartesian_product2(X1,X2))
| sP0(X0,sK13(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_260])]) ).
fof(f2164,plain,
( ! [X2,X0,X1] :
( sP0(X0,sK13(X1,X2))
| empty(cartesian_product2(X1,X2))
| in(sK9(X0,sK13(X1,X2)),cartesian_product2(X1,X2)) )
| ~ spl17_39
| ~ spl17_260 ),
inference(resolution,[],[f2123,f356]) ).
fof(f2123,plain,
( ! [X2,X0,X1] :
( element(sK9(X0,sK13(X1,X2)),cartesian_product2(X1,X2))
| sP0(X0,sK13(X1,X2)) )
| ~ spl17_260 ),
inference(avatar_component_clause,[],[f2122]) ).
fof(f4555,plain,
( spl17_472
| ~ spl17_39
| ~ spl17_259 ),
inference(avatar_split_clause,[],[f2163,f2118,f355,f4553]) ).
fof(f4553,plain,
( spl17_472
<=> ! [X2,X0,X1] :
( sP0(X0,sK13(X1,X2))
| empty(cartesian_product2(X1,X2))
| in(sK8(X0,sK13(X1,X2)),cartesian_product2(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_472])]) ).
fof(f2118,plain,
( spl17_259
<=> ! [X2,X0,X1] :
( element(sK8(X0,sK13(X1,X2)),cartesian_product2(X1,X2))
| sP0(X0,sK13(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_259])]) ).
fof(f2163,plain,
( ! [X2,X0,X1] :
( sP0(X0,sK13(X1,X2))
| empty(cartesian_product2(X1,X2))
| in(sK8(X0,sK13(X1,X2)),cartesian_product2(X1,X2)) )
| ~ spl17_39
| ~ spl17_259 ),
inference(resolution,[],[f2119,f356]) ).
fof(f2119,plain,
( ! [X2,X0,X1] :
( element(sK8(X0,sK13(X1,X2)),cartesian_product2(X1,X2))
| sP0(X0,sK13(X1,X2)) )
| ~ spl17_259 ),
inference(avatar_component_clause,[],[f2118]) ).
fof(f4551,plain,
( spl17_471
| ~ spl17_39
| ~ spl17_258 ),
inference(avatar_split_clause,[],[f2162,f2114,f355,f4549]) ).
fof(f4549,plain,
( spl17_471
<=> ! [X2,X0,X1] :
( sP0(X0,sK13(X1,X2))
| empty(cartesian_product2(X1,X2))
| in(sK7(X0,sK13(X1,X2)),cartesian_product2(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_471])]) ).
fof(f2114,plain,
( spl17_258
<=> ! [X2,X0,X1] :
( element(sK7(X0,sK13(X1,X2)),cartesian_product2(X1,X2))
| sP0(X0,sK13(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_258])]) ).
fof(f2162,plain,
( ! [X2,X0,X1] :
( sP0(X0,sK13(X1,X2))
| empty(cartesian_product2(X1,X2))
| in(sK7(X0,sK13(X1,X2)),cartesian_product2(X1,X2)) )
| ~ spl17_39
| ~ spl17_258 ),
inference(resolution,[],[f2115,f356]) ).
fof(f2115,plain,
( ! [X2,X0,X1] :
( element(sK7(X0,sK13(X1,X2)),cartesian_product2(X1,X2))
| sP0(X0,sK13(X1,X2)) )
| ~ spl17_258 ),
inference(avatar_component_clause,[],[f2114]) ).
fof(f4547,plain,
( spl17_470
| ~ spl17_92
| ~ spl17_241 ),
inference(avatar_split_clause,[],[f2060,f1933,f733,f4545]) ).
fof(f4545,plain,
( spl17_470
<=> ! [X0,X1] :
( sP0(X0,sK6(sK10(powerset(X1))))
| empty(sK10(powerset(X1)))
| element(sK9(X0,sK6(sK10(powerset(X1)))),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_470])]) ).
fof(f2060,plain,
( ! [X0,X1] :
( sP0(X0,sK6(sK10(powerset(X1))))
| empty(sK10(powerset(X1)))
| element(sK9(X0,sK6(sK10(powerset(X1)))),X1) )
| ~ spl17_92
| ~ spl17_241 ),
inference(resolution,[],[f1934,f734]) ).
fof(f4543,plain,
( spl17_469
| ~ spl17_92
| ~ spl17_240 ),
inference(avatar_split_clause,[],[f2041,f1929,f733,f4541]) ).
fof(f4541,plain,
( spl17_469
<=> ! [X0,X1] :
( sP0(X0,sK6(sK10(powerset(X1))))
| empty(sK10(powerset(X1)))
| element(sK8(X0,sK6(sK10(powerset(X1)))),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_469])]) ).
fof(f2041,plain,
( ! [X0,X1] :
( sP0(X0,sK6(sK10(powerset(X1))))
| empty(sK10(powerset(X1)))
| element(sK8(X0,sK6(sK10(powerset(X1)))),X1) )
| ~ spl17_92
| ~ spl17_240 ),
inference(resolution,[],[f1930,f734]) ).
fof(f4539,plain,
( spl17_468
| ~ spl17_92
| ~ spl17_239 ),
inference(avatar_split_clause,[],[f2022,f1925,f733,f4537]) ).
fof(f4537,plain,
( spl17_468
<=> ! [X0,X1] :
( sP0(X0,sK6(sK10(powerset(X1))))
| empty(sK10(powerset(X1)))
| element(sK7(X0,sK6(sK10(powerset(X1)))),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_468])]) ).
fof(f2022,plain,
( ! [X0,X1] :
( sP0(X0,sK6(sK10(powerset(X1))))
| empty(sK10(powerset(X1)))
| element(sK7(X0,sK6(sK10(powerset(X1)))),X1) )
| ~ spl17_92
| ~ spl17_239 ),
inference(resolution,[],[f1926,f734]) ).
fof(f4535,plain,
( spl17_467
| ~ spl17_92
| ~ spl17_229 ),
inference(avatar_split_clause,[],[f1990,f1885,f733,f4533]) ).
fof(f4533,plain,
( spl17_467
<=> ! [X0] :
( empty(sK10(powerset(X0)))
| empty(sK10(powerset(sK10(powerset(X0)))))
| element(sK10(sK10(powerset(sK10(powerset(X0))))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_467])]) ).
fof(f1990,plain,
( ! [X0] :
( empty(sK10(powerset(X0)))
| empty(sK10(powerset(sK10(powerset(X0)))))
| element(sK10(sK10(powerset(sK10(powerset(X0))))),X0) )
| ~ spl17_92
| ~ spl17_229 ),
inference(resolution,[],[f1886,f734]) ).
fof(f4531,plain,
( spl17_466
| ~ spl17_150
| ~ spl17_224 ),
inference(avatar_split_clause,[],[f1834,f1808,f1159,f4529]) ).
fof(f4529,plain,
( spl17_466
<=> ! [X0,X1] :
( empty(sK6(sK13(X0,X1)))
| empty(sK13(X0,X1))
| element(sK10(sK6(sK13(X0,X1))),cartesian_product2(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_466])]) ).
fof(f1834,plain,
( ! [X0,X1] :
( empty(sK6(sK13(X0,X1)))
| empty(sK13(X0,X1))
| element(sK10(sK6(sK13(X0,X1))),cartesian_product2(X0,X1)) )
| ~ spl17_150
| ~ spl17_224 ),
inference(resolution,[],[f1809,f1160]) ).
fof(f4527,plain,
( spl17_465
| ~ spl17_151
| ~ spl17_224 ),
inference(avatar_split_clause,[],[f1833,f1808,f1163,f4525]) ).
fof(f4525,plain,
( spl17_465
<=> ! [X0,X1] :
( empty(sK6(sK12(X0,X1)))
| empty(sK12(X0,X1))
| element(sK10(sK6(sK12(X0,X1))),cartesian_product2(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_465])]) ).
fof(f1833,plain,
( ! [X0,X1] :
( empty(sK6(sK12(X0,X1)))
| empty(sK12(X0,X1))
| element(sK10(sK6(sK12(X0,X1))),cartesian_product2(X0,X1)) )
| ~ spl17_151
| ~ spl17_224 ),
inference(resolution,[],[f1809,f1164]) ).
fof(f4523,plain,
( spl17_464
| ~ spl17_105
| ~ spl17_448 ),
inference(avatar_split_clause,[],[f4497,f4408,f841,f4521]) ).
fof(f4408,plain,
( spl17_448
<=> ! [X0,X1] :
( ~ relation_of2_as_subset(X0,sK16,sK16)
| ~ in(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_448])]) ).
fof(f4497,plain,
( ! [X0] : ~ in(X0,the_InternalRel(sK2))
| ~ spl17_105
| ~ spl17_448 ),
inference(resolution,[],[f4409,f843]) ).
fof(f843,plain,
( relation_of2_as_subset(the_InternalRel(sK2),sK16,sK16)
| ~ spl17_105 ),
inference(avatar_component_clause,[],[f841]) ).
fof(f4409,plain,
( ! [X0,X1] :
( ~ relation_of2_as_subset(X0,sK16,sK16)
| ~ in(X1,X0) )
| ~ spl17_448 ),
inference(avatar_component_clause,[],[f4408]) ).
fof(f4471,plain,
( spl17_463
| ~ spl17_35
| ~ spl17_287 ),
inference(avatar_split_clause,[],[f2508,f2423,f339,f4469]) ).
fof(f4469,plain,
( spl17_463
<=> ! [X2,X0,X1] :
( sP0(X0,sK6(powerset(X1)))
| ~ empty(X1)
| empty(powerset(X1))
| sP0(X2,sK9(X0,sK6(powerset(X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_463])]) ).
fof(f2423,plain,
( spl17_287
<=> ! [X2,X0,X1] :
( empty(powerset(X0))
| sP0(X1,sK6(powerset(X0)))
| ~ empty(X0)
| ~ in(X2,sK9(X1,sK6(powerset(X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_287])]) ).
fof(f2508,plain,
( ! [X2,X0,X1] :
( sP0(X0,sK6(powerset(X1)))
| ~ empty(X1)
| empty(powerset(X1))
| sP0(X2,sK9(X0,sK6(powerset(X1)))) )
| ~ spl17_35
| ~ spl17_287 ),
inference(resolution,[],[f2424,f340]) ).
fof(f2424,plain,
( ! [X2,X0,X1] :
( ~ in(X2,sK9(X1,sK6(powerset(X0))))
| sP0(X1,sK6(powerset(X0)))
| ~ empty(X0)
| empty(powerset(X0)) )
| ~ spl17_287 ),
inference(avatar_component_clause,[],[f2423]) ).
fof(f4467,plain,
( spl17_462
| ~ spl17_59
| ~ spl17_287 ),
inference(avatar_split_clause,[],[f2503,f2423,f500,f4465]) ).
fof(f4465,plain,
( spl17_462
<=> ! [X2,X0,X1] :
( sP0(X0,sK6(powerset(X1)))
| ~ empty(X1)
| empty(powerset(X1))
| sP0(sK9(X0,sK6(powerset(X1))),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_462])]) ).
fof(f2503,plain,
( ! [X2,X0,X1] :
( sP0(X0,sK6(powerset(X1)))
| ~ empty(X1)
| empty(powerset(X1))
| sP0(sK9(X0,sK6(powerset(X1))),X2) )
| ~ spl17_59
| ~ spl17_287 ),
inference(resolution,[],[f2424,f501]) ).
fof(f4463,plain,
( spl17_461
| ~ spl17_35
| ~ spl17_286 ),
inference(avatar_split_clause,[],[f2494,f2419,f339,f4461]) ).
fof(f4461,plain,
( spl17_461
<=> ! [X2,X0,X1] :
( sP0(X0,sK6(powerset(X1)))
| ~ empty(X1)
| empty(powerset(X1))
| sP0(X2,sK8(X0,sK6(powerset(X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_461])]) ).
fof(f2419,plain,
( spl17_286
<=> ! [X2,X0,X1] :
( empty(powerset(X0))
| sP0(X1,sK6(powerset(X0)))
| ~ empty(X0)
| ~ in(X2,sK8(X1,sK6(powerset(X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_286])]) ).
fof(f2494,plain,
( ! [X2,X0,X1] :
( sP0(X0,sK6(powerset(X1)))
| ~ empty(X1)
| empty(powerset(X1))
| sP0(X2,sK8(X0,sK6(powerset(X1)))) )
| ~ spl17_35
| ~ spl17_286 ),
inference(resolution,[],[f2420,f340]) ).
fof(f2420,plain,
( ! [X2,X0,X1] :
( ~ in(X2,sK8(X1,sK6(powerset(X0))))
| sP0(X1,sK6(powerset(X0)))
| ~ empty(X0)
| empty(powerset(X0)) )
| ~ spl17_286 ),
inference(avatar_component_clause,[],[f2419]) ).
fof(f4459,plain,
( spl17_460
| ~ spl17_59
| ~ spl17_286 ),
inference(avatar_split_clause,[],[f2489,f2419,f500,f4457]) ).
fof(f4457,plain,
( spl17_460
<=> ! [X2,X0,X1] :
( sP0(X0,sK6(powerset(X1)))
| ~ empty(X1)
| empty(powerset(X1))
| sP0(sK8(X0,sK6(powerset(X1))),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_460])]) ).
fof(f2489,plain,
( ! [X2,X0,X1] :
( sP0(X0,sK6(powerset(X1)))
| ~ empty(X1)
| empty(powerset(X1))
| sP0(sK8(X0,sK6(powerset(X1))),X2) )
| ~ spl17_59
| ~ spl17_286 ),
inference(resolution,[],[f2420,f501]) ).
fof(f4454,plain,
( spl17_459
| ~ spl17_32
| ~ spl17_403 ),
inference(avatar_split_clause,[],[f3869,f3824,f321,f4452]) ).
fof(f321,plain,
( spl17_32
<=> ! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_32])]) ).
fof(f3869,plain,
( ! [X0] :
( cartesian_product2(sK16,sK16) = X0
| ~ empty(X0) )
| ~ spl17_32
| ~ spl17_403 ),
inference(resolution,[],[f3826,f322]) ).
fof(f322,plain,
( ! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) )
| ~ spl17_32 ),
inference(avatar_component_clause,[],[f321]) ).
fof(f3826,plain,
( empty(cartesian_product2(sK16,sK16))
| ~ spl17_403 ),
inference(avatar_component_clause,[],[f3824]) ).
fof(f4450,plain,
( spl17_458
| ~ spl17_35
| ~ spl17_285 ),
inference(avatar_split_clause,[],[f2476,f2415,f339,f4448]) ).
fof(f4448,plain,
( spl17_458
<=> ! [X2,X0,X1] :
( sP0(X0,sK6(powerset(X1)))
| ~ empty(X1)
| empty(powerset(X1))
| sP0(X2,sK7(X0,sK6(powerset(X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_458])]) ).
fof(f2415,plain,
( spl17_285
<=> ! [X2,X0,X1] :
( empty(powerset(X0))
| sP0(X1,sK6(powerset(X0)))
| ~ empty(X0)
| ~ in(X2,sK7(X1,sK6(powerset(X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_285])]) ).
fof(f2476,plain,
( ! [X2,X0,X1] :
( sP0(X0,sK6(powerset(X1)))
| ~ empty(X1)
| empty(powerset(X1))
| sP0(X2,sK7(X0,sK6(powerset(X1)))) )
| ~ spl17_35
| ~ spl17_285 ),
inference(resolution,[],[f2416,f340]) ).
fof(f2416,plain,
( ! [X2,X0,X1] :
( ~ in(X2,sK7(X1,sK6(powerset(X0))))
| sP0(X1,sK6(powerset(X0)))
| ~ empty(X0)
| empty(powerset(X0)) )
| ~ spl17_285 ),
inference(avatar_component_clause,[],[f2415]) ).
fof(f4446,plain,
( spl17_457
| ~ spl17_59
| ~ spl17_285 ),
inference(avatar_split_clause,[],[f2471,f2415,f500,f4444]) ).
fof(f4444,plain,
( spl17_457
<=> ! [X2,X0,X1] :
( sP0(X0,sK6(powerset(X1)))
| ~ empty(X1)
| empty(powerset(X1))
| sP0(sK7(X0,sK6(powerset(X1))),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_457])]) ).
fof(f2471,plain,
( ! [X2,X0,X1] :
( sP0(X0,sK6(powerset(X1)))
| ~ empty(X1)
| empty(powerset(X1))
| sP0(sK7(X0,sK6(powerset(X1))),X2) )
| ~ spl17_59
| ~ spl17_285 ),
inference(resolution,[],[f2416,f501]) ).
fof(f4442,plain,
( spl17_456
| ~ spl17_17
| ~ spl17_283 ),
inference(avatar_split_clause,[],[f2456,f2405,f255,f4440]) ).
fof(f4440,plain,
( spl17_456
<=> ! [X2,X0,X1] :
( sP0(X0,sK10(powerset(powerset(cartesian_product2(X1,X2)))))
| sP1(sK9(X0,sK10(powerset(powerset(cartesian_product2(X1,X2)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_456])]) ).
fof(f2405,plain,
( spl17_283
<=> ! [X2,X0,X1] :
( sP0(X0,sK10(powerset(powerset(cartesian_product2(X1,X2)))))
| relation(sK9(X0,sK10(powerset(powerset(cartesian_product2(X1,X2)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_283])]) ).
fof(f2456,plain,
( ! [X2,X0,X1] :
( sP0(X0,sK10(powerset(powerset(cartesian_product2(X1,X2)))))
| sP1(sK9(X0,sK10(powerset(powerset(cartesian_product2(X1,X2)))))) )
| ~ spl17_17
| ~ spl17_283 ),
inference(resolution,[],[f2406,f256]) ).
fof(f2406,plain,
( ! [X2,X0,X1] :
( relation(sK9(X0,sK10(powerset(powerset(cartesian_product2(X1,X2))))))
| sP0(X0,sK10(powerset(powerset(cartesian_product2(X1,X2))))) )
| ~ spl17_283 ),
inference(avatar_component_clause,[],[f2405]) ).
fof(f4438,plain,
( spl17_455
| ~ spl17_17
| ~ spl17_281 ),
inference(avatar_split_clause,[],[f2441,f2397,f255,f4436]) ).
fof(f4436,plain,
( spl17_455
<=> ! [X2,X0,X1] :
( sP0(X0,sK10(powerset(powerset(cartesian_product2(X1,X2)))))
| sP1(sK8(X0,sK10(powerset(powerset(cartesian_product2(X1,X2)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_455])]) ).
fof(f2397,plain,
( spl17_281
<=> ! [X2,X0,X1] :
( sP0(X0,sK10(powerset(powerset(cartesian_product2(X1,X2)))))
| relation(sK8(X0,sK10(powerset(powerset(cartesian_product2(X1,X2)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_281])]) ).
fof(f2441,plain,
( ! [X2,X0,X1] :
( sP0(X0,sK10(powerset(powerset(cartesian_product2(X1,X2)))))
| sP1(sK8(X0,sK10(powerset(powerset(cartesian_product2(X1,X2)))))) )
| ~ spl17_17
| ~ spl17_281 ),
inference(resolution,[],[f2398,f256]) ).
fof(f2398,plain,
( ! [X2,X0,X1] :
( relation(sK8(X0,sK10(powerset(powerset(cartesian_product2(X1,X2))))))
| sP0(X0,sK10(powerset(powerset(cartesian_product2(X1,X2))))) )
| ~ spl17_281 ),
inference(avatar_component_clause,[],[f2397]) ).
fof(f4434,plain,
( spl17_454
| ~ spl17_17
| ~ spl17_279 ),
inference(avatar_split_clause,[],[f2426,f2389,f255,f4432]) ).
fof(f4432,plain,
( spl17_454
<=> ! [X2,X0,X1] :
( sP0(X0,sK10(powerset(powerset(cartesian_product2(X1,X2)))))
| sP1(sK7(X0,sK10(powerset(powerset(cartesian_product2(X1,X2)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_454])]) ).
fof(f2389,plain,
( spl17_279
<=> ! [X2,X0,X1] :
( sP0(X0,sK10(powerset(powerset(cartesian_product2(X1,X2)))))
| relation(sK7(X0,sK10(powerset(powerset(cartesian_product2(X1,X2)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_279])]) ).
fof(f2426,plain,
( ! [X2,X0,X1] :
( sP0(X0,sK10(powerset(powerset(cartesian_product2(X1,X2)))))
| sP1(sK7(X0,sK10(powerset(powerset(cartesian_product2(X1,X2)))))) )
| ~ spl17_17
| ~ spl17_279 ),
inference(resolution,[],[f2390,f256]) ).
fof(f2390,plain,
( ! [X2,X0,X1] :
( relation(sK7(X0,sK10(powerset(powerset(cartesian_product2(X1,X2))))))
| sP0(X0,sK10(powerset(powerset(cartesian_product2(X1,X2))))) )
| ~ spl17_279 ),
inference(avatar_component_clause,[],[f2389]) ).
fof(f4430,plain,
( spl17_453
| ~ spl17_95
| ~ spl17_241 ),
inference(avatar_split_clause,[],[f2053,f1933,f765,f4428]) ).
fof(f4428,plain,
( spl17_453
<=> ! [X0,X1] :
( sP0(X0,sK6(sK6(X1)))
| empty(sK6(X1))
| element(sK9(X0,sK6(sK6(X1))),X1)
| empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_453])]) ).
fof(f2053,plain,
( ! [X0,X1] :
( sP0(X0,sK6(sK6(X1)))
| empty(sK6(X1))
| element(sK9(X0,sK6(sK6(X1))),X1)
| empty(X1) )
| ~ spl17_95
| ~ spl17_241 ),
inference(resolution,[],[f1934,f766]) ).
fof(f4426,plain,
( spl17_452
| ~ spl17_95
| ~ spl17_240 ),
inference(avatar_split_clause,[],[f2034,f1929,f765,f4424]) ).
fof(f4424,plain,
( spl17_452
<=> ! [X0,X1] :
( sP0(X0,sK6(sK6(X1)))
| empty(sK6(X1))
| element(sK8(X0,sK6(sK6(X1))),X1)
| empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_452])]) ).
fof(f2034,plain,
( ! [X0,X1] :
( sP0(X0,sK6(sK6(X1)))
| empty(sK6(X1))
| element(sK8(X0,sK6(sK6(X1))),X1)
| empty(X1) )
| ~ spl17_95
| ~ spl17_240 ),
inference(resolution,[],[f1930,f766]) ).
fof(f4422,plain,
( spl17_451
| ~ spl17_95
| ~ spl17_239 ),
inference(avatar_split_clause,[],[f2015,f1925,f765,f4420]) ).
fof(f4420,plain,
( spl17_451
<=> ! [X0,X1] :
( sP0(X0,sK6(sK6(X1)))
| empty(sK6(X1))
| element(sK7(X0,sK6(sK6(X1))),X1)
| empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_451])]) ).
fof(f2015,plain,
( ! [X0,X1] :
( sP0(X0,sK6(sK6(X1)))
| empty(sK6(X1))
| element(sK7(X0,sK6(sK6(X1))),X1)
| empty(X1) )
| ~ spl17_95
| ~ spl17_239 ),
inference(resolution,[],[f1926,f766]) ).
fof(f4418,plain,
( spl17_450
| ~ spl17_34
| ~ spl17_237 ),
inference(avatar_split_clause,[],[f2005,f1917,f335,f4416]) ).
fof(f4416,plain,
( spl17_450
<=> ! [X2,X0,X1] :
( sP0(X0,powerset(X1))
| ~ empty(X1)
| is_transitive_in(sK9(X0,powerset(X1)),X2)
| ~ sP1(sK9(X0,powerset(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_450])]) ).
fof(f1917,plain,
( spl17_237
<=> ! [X2,X0,X1] :
( ~ empty(X0)
| sP0(X1,powerset(X0))
| sP0(sK9(X1,powerset(X0)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_237])]) ).
fof(f2005,plain,
( ! [X2,X0,X1] :
( sP0(X0,powerset(X1))
| ~ empty(X1)
| is_transitive_in(sK9(X0,powerset(X1)),X2)
| ~ sP1(sK9(X0,powerset(X1))) )
| ~ spl17_34
| ~ spl17_237 ),
inference(resolution,[],[f1918,f336]) ).
fof(f1918,plain,
( ! [X2,X0,X1] :
( sP0(sK9(X1,powerset(X0)),X2)
| sP0(X1,powerset(X0))
| ~ empty(X0) )
| ~ spl17_237 ),
inference(avatar_component_clause,[],[f1917]) ).
fof(f4414,plain,
( spl17_449
| ~ spl17_34
| ~ spl17_234 ),
inference(avatar_split_clause,[],[f2002,f1905,f335,f4412]) ).
fof(f4412,plain,
( spl17_449
<=> ! [X2,X0,X1] :
( sP0(X0,powerset(X1))
| ~ empty(X1)
| is_transitive_in(sK8(X0,powerset(X1)),X2)
| ~ sP1(sK8(X0,powerset(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_449])]) ).
fof(f1905,plain,
( spl17_234
<=> ! [X2,X0,X1] :
( ~ empty(X0)
| sP0(X1,powerset(X0))
| sP0(sK8(X1,powerset(X0)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_234])]) ).
fof(f2002,plain,
( ! [X2,X0,X1] :
( sP0(X0,powerset(X1))
| ~ empty(X1)
| is_transitive_in(sK8(X0,powerset(X1)),X2)
| ~ sP1(sK8(X0,powerset(X1))) )
| ~ spl17_34
| ~ spl17_234 ),
inference(resolution,[],[f1906,f336]) ).
fof(f1906,plain,
( ! [X2,X0,X1] :
( sP0(sK8(X1,powerset(X0)),X2)
| sP0(X1,powerset(X0))
| ~ empty(X0) )
| ~ spl17_234 ),
inference(avatar_component_clause,[],[f1905]) ).
fof(f4410,plain,
( spl17_448
| ~ spl17_100
| ~ spl17_403 ),
inference(avatar_split_clause,[],[f3866,f3824,f805,f4408]) ).
fof(f805,plain,
( spl17_100
<=> ! [X2,X0,X1,X3] :
( ~ relation_of2_as_subset(X0,X1,X2)
| ~ empty(cartesian_product2(X1,X2))
| ~ in(X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_100])]) ).
fof(f3866,plain,
( ! [X0,X1] :
( ~ relation_of2_as_subset(X0,sK16,sK16)
| ~ in(X1,X0) )
| ~ spl17_100
| ~ spl17_403 ),
inference(resolution,[],[f3826,f806]) ).
fof(f806,plain,
( ! [X2,X3,X0,X1] :
( ~ empty(cartesian_product2(X1,X2))
| ~ relation_of2_as_subset(X0,X1,X2)
| ~ in(X3,X0) )
| ~ spl17_100 ),
inference(avatar_component_clause,[],[f805]) ).
fof(f4406,plain,
( spl17_447
| ~ spl17_34
| ~ spl17_232 ),
inference(avatar_split_clause,[],[f1999,f1897,f335,f4404]) ).
fof(f4404,plain,
( spl17_447
<=> ! [X2,X0,X1] :
( sP0(X0,powerset(X1))
| ~ empty(X1)
| is_transitive_in(sK7(X0,powerset(X1)),X2)
| ~ sP1(sK7(X0,powerset(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_447])]) ).
fof(f1897,plain,
( spl17_232
<=> ! [X2,X0,X1] :
( ~ empty(X0)
| sP0(X1,powerset(X0))
| sP0(sK7(X1,powerset(X0)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_232])]) ).
fof(f1999,plain,
( ! [X2,X0,X1] :
( sP0(X0,powerset(X1))
| ~ empty(X1)
| is_transitive_in(sK7(X0,powerset(X1)),X2)
| ~ sP1(sK7(X0,powerset(X1))) )
| ~ spl17_34
| ~ spl17_232 ),
inference(resolution,[],[f1898,f336]) ).
fof(f1898,plain,
( ! [X2,X0,X1] :
( sP0(sK7(X1,powerset(X0)),X2)
| sP0(X1,powerset(X0))
| ~ empty(X0) )
| ~ spl17_232 ),
inference(avatar_component_clause,[],[f1897]) ).
fof(f4402,plain,
( spl17_446
| ~ spl17_95
| ~ spl17_229 ),
inference(avatar_split_clause,[],[f1983,f1885,f765,f4400]) ).
fof(f4400,plain,
( spl17_446
<=> ! [X0] :
( empty(sK6(X0))
| empty(sK10(powerset(sK6(X0))))
| element(sK10(sK10(powerset(sK6(X0)))),X0)
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_446])]) ).
fof(f1983,plain,
( ! [X0] :
( empty(sK6(X0))
| empty(sK10(powerset(sK6(X0))))
| element(sK10(sK10(powerset(sK6(X0)))),X0)
| empty(X0) )
| ~ spl17_95
| ~ spl17_229 ),
inference(resolution,[],[f1886,f766]) ).
fof(f4218,plain,
( spl17_445
| ~ spl17_75
| ~ spl17_287 ),
inference(avatar_split_clause,[],[f2505,f2423,f643,f4216]) ).
fof(f4216,plain,
( spl17_445
<=> ! [X0,X1] :
( sP0(X0,sK6(powerset(X1)))
| ~ empty(X1)
| empty(powerset(X1))
| empty(sK9(X0,sK6(powerset(X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_445])]) ).
fof(f2505,plain,
( ! [X0,X1] :
( sP0(X0,sK6(powerset(X1)))
| ~ empty(X1)
| empty(powerset(X1))
| empty(sK9(X0,sK6(powerset(X1)))) )
| ~ spl17_75
| ~ spl17_287 ),
inference(resolution,[],[f2424,f644]) ).
fof(f4214,plain,
( spl17_444
| ~ spl17_75
| ~ spl17_286 ),
inference(avatar_split_clause,[],[f2491,f2419,f643,f4212]) ).
fof(f4212,plain,
( spl17_444
<=> ! [X0,X1] :
( sP0(X0,sK6(powerset(X1)))
| ~ empty(X1)
| empty(powerset(X1))
| empty(sK8(X0,sK6(powerset(X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_444])]) ).
fof(f2491,plain,
( ! [X0,X1] :
( sP0(X0,sK6(powerset(X1)))
| ~ empty(X1)
| empty(powerset(X1))
| empty(sK8(X0,sK6(powerset(X1)))) )
| ~ spl17_75
| ~ spl17_286 ),
inference(resolution,[],[f2420,f644]) ).
fof(f4210,plain,
( spl17_443
| ~ spl17_75
| ~ spl17_285 ),
inference(avatar_split_clause,[],[f2473,f2415,f643,f4208]) ).
fof(f4208,plain,
( spl17_443
<=> ! [X0,X1] :
( sP0(X0,sK6(powerset(X1)))
| ~ empty(X1)
| empty(powerset(X1))
| empty(sK7(X0,sK6(powerset(X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_443])]) ).
fof(f2473,plain,
( ! [X0,X1] :
( sP0(X0,sK6(powerset(X1)))
| ~ empty(X1)
| empty(powerset(X1))
| empty(sK7(X0,sK6(powerset(X1)))) )
| ~ spl17_75
| ~ spl17_285 ),
inference(resolution,[],[f2416,f644]) ).
fof(f4206,plain,
( spl17_442
| ~ spl17_41
| ~ spl17_421 ),
inference(avatar_split_clause,[],[f3985,f3926,f363,f4204]) ).
fof(f3985,plain,
( ! [X0] :
( ~ element(X0,powerset(sK16))
| relation(X0) )
| ~ spl17_41
| ~ spl17_421 ),
inference(superposition,[],[f364,f3928]) ).
fof(f4202,plain,
( spl17_441
| ~ spl17_35
| ~ spl17_274 ),
inference(avatar_split_clause,[],[f2367,f2301,f339,f4200]) ).
fof(f4200,plain,
( spl17_441
<=> ! [X2,X0,X1] :
( ~ empty(X0)
| sP0(X1,sK10(powerset(powerset(X0))))
| sP0(X2,sK9(X1,sK10(powerset(powerset(X0))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_441])]) ).
fof(f2301,plain,
( spl17_274
<=> ! [X2,X0,X1] :
( sP0(X0,sK10(powerset(powerset(X1))))
| ~ empty(X1)
| ~ in(X2,sK9(X0,sK10(powerset(powerset(X1))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_274])]) ).
fof(f2367,plain,
( ! [X2,X0,X1] :
( ~ empty(X0)
| sP0(X1,sK10(powerset(powerset(X0))))
| sP0(X2,sK9(X1,sK10(powerset(powerset(X0))))) )
| ~ spl17_35
| ~ spl17_274 ),
inference(resolution,[],[f2302,f340]) ).
fof(f2302,plain,
( ! [X2,X0,X1] :
( ~ in(X2,sK9(X0,sK10(powerset(powerset(X1)))))
| ~ empty(X1)
| sP0(X0,sK10(powerset(powerset(X1)))) )
| ~ spl17_274 ),
inference(avatar_component_clause,[],[f2301]) ).
fof(f4198,plain,
( spl17_440
| ~ spl17_59
| ~ spl17_274 ),
inference(avatar_split_clause,[],[f2362,f2301,f500,f4196]) ).
fof(f4196,plain,
( spl17_440
<=> ! [X2,X0,X1] :
( ~ empty(X0)
| sP0(X1,sK10(powerset(powerset(X0))))
| sP0(sK9(X1,sK10(powerset(powerset(X0)))),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_440])]) ).
fof(f2362,plain,
( ! [X2,X0,X1] :
( ~ empty(X0)
| sP0(X1,sK10(powerset(powerset(X0))))
| sP0(sK9(X1,sK10(powerset(powerset(X0)))),X2) )
| ~ spl17_59
| ~ spl17_274 ),
inference(resolution,[],[f2302,f501]) ).
fof(f4194,plain,
( spl17_439
| ~ spl17_35
| ~ spl17_273 ),
inference(avatar_split_clause,[],[f2349,f2297,f339,f4192]) ).
fof(f4192,plain,
( spl17_439
<=> ! [X2,X0,X1] :
( ~ empty(X0)
| sP0(X1,sK10(powerset(powerset(X0))))
| sP0(X2,sK8(X1,sK10(powerset(powerset(X0))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_439])]) ).
fof(f2297,plain,
( spl17_273
<=> ! [X2,X0,X1] :
( sP0(X0,sK10(powerset(powerset(X1))))
| ~ empty(X1)
| ~ in(X2,sK8(X0,sK10(powerset(powerset(X1))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_273])]) ).
fof(f2349,plain,
( ! [X2,X0,X1] :
( ~ empty(X0)
| sP0(X1,sK10(powerset(powerset(X0))))
| sP0(X2,sK8(X1,sK10(powerset(powerset(X0))))) )
| ~ spl17_35
| ~ spl17_273 ),
inference(resolution,[],[f2298,f340]) ).
fof(f2298,plain,
( ! [X2,X0,X1] :
( ~ in(X2,sK8(X0,sK10(powerset(powerset(X1)))))
| ~ empty(X1)
| sP0(X0,sK10(powerset(powerset(X1)))) )
| ~ spl17_273 ),
inference(avatar_component_clause,[],[f2297]) ).
fof(f4190,plain,
( spl17_438
| ~ spl17_59
| ~ spl17_273 ),
inference(avatar_split_clause,[],[f2344,f2297,f500,f4188]) ).
fof(f4188,plain,
( spl17_438
<=> ! [X2,X0,X1] :
( ~ empty(X0)
| sP0(X1,sK10(powerset(powerset(X0))))
| sP0(sK8(X1,sK10(powerset(powerset(X0)))),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_438])]) ).
fof(f2344,plain,
( ! [X2,X0,X1] :
( ~ empty(X0)
| sP0(X1,sK10(powerset(powerset(X0))))
| sP0(sK8(X1,sK10(powerset(powerset(X0)))),X2) )
| ~ spl17_59
| ~ spl17_273 ),
inference(resolution,[],[f2298,f501]) ).
fof(f4186,plain,
( spl17_437
| ~ spl17_35
| ~ spl17_272 ),
inference(avatar_split_clause,[],[f2335,f2293,f339,f4184]) ).
fof(f4184,plain,
( spl17_437
<=> ! [X2,X0,X1] :
( ~ empty(X0)
| sP0(X1,sK10(powerset(powerset(X0))))
| sP0(X2,sK7(X1,sK10(powerset(powerset(X0))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_437])]) ).
fof(f2293,plain,
( spl17_272
<=> ! [X2,X0,X1] :
( sP0(X0,sK10(powerset(powerset(X1))))
| ~ empty(X1)
| ~ in(X2,sK7(X0,sK10(powerset(powerset(X1))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_272])]) ).
fof(f2335,plain,
( ! [X2,X0,X1] :
( ~ empty(X0)
| sP0(X1,sK10(powerset(powerset(X0))))
| sP0(X2,sK7(X1,sK10(powerset(powerset(X0))))) )
| ~ spl17_35
| ~ spl17_272 ),
inference(resolution,[],[f2294,f340]) ).
fof(f2294,plain,
( ! [X2,X0,X1] :
( ~ in(X2,sK7(X0,sK10(powerset(powerset(X1)))))
| ~ empty(X1)
| sP0(X0,sK10(powerset(powerset(X1)))) )
| ~ spl17_272 ),
inference(avatar_component_clause,[],[f2293]) ).
fof(f4182,plain,
( spl17_436
| ~ spl17_59
| ~ spl17_272 ),
inference(avatar_split_clause,[],[f2330,f2293,f500,f4180]) ).
fof(f4180,plain,
( spl17_436
<=> ! [X2,X0,X1] :
( ~ empty(X0)
| sP0(X1,sK10(powerset(powerset(X0))))
| sP0(sK7(X1,sK10(powerset(powerset(X0)))),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_436])]) ).
fof(f2330,plain,
( ! [X2,X0,X1] :
( ~ empty(X0)
| sP0(X1,sK10(powerset(powerset(X0))))
| sP0(sK7(X1,sK10(powerset(powerset(X0)))),X2) )
| ~ spl17_59
| ~ spl17_272 ),
inference(resolution,[],[f2294,f501]) ).
fof(f4178,plain,
( spl17_435
| ~ spl17_39
| ~ spl17_231 ),
inference(avatar_split_clause,[],[f1998,f1893,f355,f4176]) ).
fof(f4176,plain,
( spl17_435
<=> ! [X0,X1] :
( empty(sK12(X0,X1))
| empty(cartesian_product2(X0,X1))
| in(sK10(sK12(X0,X1)),cartesian_product2(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_435])]) ).
fof(f1893,plain,
( spl17_231
<=> ! [X0,X1] :
( element(sK10(sK12(X0,X1)),cartesian_product2(X0,X1))
| empty(sK12(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_231])]) ).
fof(f1998,plain,
( ! [X0,X1] :
( empty(sK12(X0,X1))
| empty(cartesian_product2(X0,X1))
| in(sK10(sK12(X0,X1)),cartesian_product2(X0,X1)) )
| ~ spl17_39
| ~ spl17_231 ),
inference(resolution,[],[f1894,f356]) ).
fof(f1894,plain,
( ! [X0,X1] :
( element(sK10(sK12(X0,X1)),cartesian_product2(X0,X1))
| empty(sK12(X0,X1)) )
| ~ spl17_231 ),
inference(avatar_component_clause,[],[f1893]) ).
fof(f4174,plain,
( spl17_434
| ~ spl17_39
| ~ spl17_230 ),
inference(avatar_split_clause,[],[f1997,f1889,f355,f4172]) ).
fof(f4172,plain,
( spl17_434
<=> ! [X0,X1] :
( empty(sK13(X0,X1))
| empty(cartesian_product2(X0,X1))
| in(sK10(sK13(X0,X1)),cartesian_product2(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_434])]) ).
fof(f1889,plain,
( spl17_230
<=> ! [X0,X1] :
( element(sK10(sK13(X0,X1)),cartesian_product2(X0,X1))
| empty(sK13(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_230])]) ).
fof(f1997,plain,
( ! [X0,X1] :
( empty(sK13(X0,X1))
| empty(cartesian_product2(X0,X1))
| in(sK10(sK13(X0,X1)),cartesian_product2(X0,X1)) )
| ~ spl17_39
| ~ spl17_230 ),
inference(resolution,[],[f1890,f356]) ).
fof(f1890,plain,
( ! [X0,X1] :
( element(sK10(sK13(X0,X1)),cartesian_product2(X0,X1))
| empty(sK13(X0,X1)) )
| ~ spl17_230 ),
inference(avatar_component_clause,[],[f1889]) ).
fof(f4170,plain,
( spl17_433
| ~ spl17_217
| ~ spl17_228 ),
inference(avatar_split_clause,[],[f1880,f1849,f1769,f4168]) ).
fof(f4168,plain,
( spl17_433
<=> ! [X2,X0,X1] :
( sP0(X0,powerset(X1))
| ~ empty(X1)
| sK9(X0,powerset(X1)) = sK10(powerset(X2))
| ~ empty(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_433])]) ).
fof(f1769,plain,
( spl17_217
<=> ! [X0,X1] :
( ~ empty(X0)
| sK10(powerset(X0)) = X1
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_217])]) ).
fof(f1849,plain,
( spl17_228
<=> ! [X0,X1] :
( ~ empty(X0)
| sP0(X1,powerset(X0))
| empty(sK9(X1,powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_228])]) ).
fof(f1880,plain,
( ! [X2,X0,X1] :
( sP0(X0,powerset(X1))
| ~ empty(X1)
| sK9(X0,powerset(X1)) = sK10(powerset(X2))
| ~ empty(X2) )
| ~ spl17_217
| ~ spl17_228 ),
inference(resolution,[],[f1850,f1770]) ).
fof(f1770,plain,
( ! [X0,X1] :
( ~ empty(X1)
| sK10(powerset(X0)) = X1
| ~ empty(X0) )
| ~ spl17_217 ),
inference(avatar_component_clause,[],[f1769]) ).
fof(f1850,plain,
( ! [X0,X1] :
( empty(sK9(X1,powerset(X0)))
| sP0(X1,powerset(X0))
| ~ empty(X0) )
| ~ spl17_228 ),
inference(avatar_component_clause,[],[f1849]) ).
fof(f4166,plain,
( spl17_432
| ~ spl17_217
| ~ spl17_227 ),
inference(avatar_split_clause,[],[f1876,f1845,f1769,f4164]) ).
fof(f4164,plain,
( spl17_432
<=> ! [X2,X0,X1] :
( sP0(X0,powerset(X1))
| ~ empty(X1)
| sK8(X0,powerset(X1)) = sK10(powerset(X2))
| ~ empty(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_432])]) ).
fof(f1845,plain,
( spl17_227
<=> ! [X0,X1] :
( ~ empty(X0)
| sP0(X1,powerset(X0))
| empty(sK8(X1,powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_227])]) ).
fof(f1876,plain,
( ! [X2,X0,X1] :
( sP0(X0,powerset(X1))
| ~ empty(X1)
| sK8(X0,powerset(X1)) = sK10(powerset(X2))
| ~ empty(X2) )
| ~ spl17_217
| ~ spl17_227 ),
inference(resolution,[],[f1846,f1770]) ).
fof(f1846,plain,
( ! [X0,X1] :
( empty(sK8(X1,powerset(X0)))
| sP0(X1,powerset(X0))
| ~ empty(X0) )
| ~ spl17_227 ),
inference(avatar_component_clause,[],[f1845]) ).
fof(f4161,plain,
( spl17_431
| ~ spl17_217
| ~ spl17_226 ),
inference(avatar_split_clause,[],[f1872,f1841,f1769,f4159]) ).
fof(f4159,plain,
( spl17_431
<=> ! [X2,X0,X1] :
( sP0(X0,powerset(X1))
| ~ empty(X1)
| sK7(X0,powerset(X1)) = sK10(powerset(X2))
| ~ empty(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_431])]) ).
fof(f1841,plain,
( spl17_226
<=> ! [X0,X1] :
( ~ empty(X0)
| sP0(X1,powerset(X0))
| empty(sK7(X1,powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_226])]) ).
fof(f1872,plain,
( ! [X2,X0,X1] :
( sP0(X0,powerset(X1))
| ~ empty(X1)
| sK7(X0,powerset(X1)) = sK10(powerset(X2))
| ~ empty(X2) )
| ~ spl17_217
| ~ spl17_226 ),
inference(resolution,[],[f1842,f1770]) ).
fof(f1842,plain,
( ! [X0,X1] :
( empty(sK7(X1,powerset(X0)))
| sP0(X1,powerset(X0))
| ~ empty(X0) )
| ~ spl17_226 ),
inference(avatar_component_clause,[],[f1841]) ).
fof(f4157,plain,
( spl17_430
| ~ spl17_92
| ~ spl17_224 ),
inference(avatar_split_clause,[],[f1831,f1808,f733,f4155]) ).
fof(f4155,plain,
( spl17_430
<=> ! [X0] :
( empty(sK6(sK10(powerset(X0))))
| empty(sK10(powerset(X0)))
| element(sK10(sK6(sK10(powerset(X0)))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_430])]) ).
fof(f1831,plain,
( ! [X0] :
( empty(sK6(sK10(powerset(X0))))
| empty(sK10(powerset(X0)))
| element(sK10(sK6(sK10(powerset(X0)))),X0) )
| ~ spl17_92
| ~ spl17_224 ),
inference(resolution,[],[f1809,f734]) ).
fof(f4113,plain,
( spl17_429
| ~ spl17_75
| ~ spl17_274 ),
inference(avatar_split_clause,[],[f2364,f2301,f643,f4111]) ).
fof(f4111,plain,
( spl17_429
<=> ! [X0,X1] :
( ~ empty(X0)
| sP0(X1,sK10(powerset(powerset(X0))))
| empty(sK9(X1,sK10(powerset(powerset(X0))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_429])]) ).
fof(f2364,plain,
( ! [X0,X1] :
( ~ empty(X0)
| sP0(X1,sK10(powerset(powerset(X0))))
| empty(sK9(X1,sK10(powerset(powerset(X0))))) )
| ~ spl17_75
| ~ spl17_274 ),
inference(resolution,[],[f2302,f644]) ).
fof(f4109,plain,
( spl17_428
| ~ spl17_82
| ~ spl17_421 ),
inference(avatar_split_clause,[],[f3991,f3926,f682,f4107]) ).
fof(f4107,plain,
( spl17_428
<=> ! [X0] :
( ~ subset(X0,sK16)
| relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_428])]) ).
fof(f682,plain,
( spl17_82
<=> ! [X2,X0,X1] :
( relation(X0)
| ~ subset(X0,cartesian_product2(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_82])]) ).
fof(f3991,plain,
( ! [X0] :
( ~ subset(X0,sK16)
| relation(X0) )
| ~ spl17_82
| ~ spl17_421 ),
inference(superposition,[],[f683,f3928]) ).
fof(f683,plain,
( ! [X2,X0,X1] :
( ~ subset(X0,cartesian_product2(X1,X2))
| relation(X0) )
| ~ spl17_82 ),
inference(avatar_component_clause,[],[f682]) ).
fof(f4105,plain,
( spl17_427
| ~ spl17_75
| ~ spl17_273 ),
inference(avatar_split_clause,[],[f2346,f2297,f643,f4103]) ).
fof(f4103,plain,
( spl17_427
<=> ! [X0,X1] :
( ~ empty(X0)
| sP0(X1,sK10(powerset(powerset(X0))))
| empty(sK8(X1,sK10(powerset(powerset(X0))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_427])]) ).
fof(f2346,plain,
( ! [X0,X1] :
( ~ empty(X0)
| sP0(X1,sK10(powerset(powerset(X0))))
| empty(sK8(X1,sK10(powerset(powerset(X0))))) )
| ~ spl17_75
| ~ spl17_273 ),
inference(resolution,[],[f2298,f644]) ).
fof(f4101,plain,
( spl17_426
| ~ spl17_75
| ~ spl17_272 ),
inference(avatar_split_clause,[],[f2332,f2293,f643,f4099]) ).
fof(f4099,plain,
( spl17_426
<=> ! [X0,X1] :
( ~ empty(X0)
| sP0(X1,sK10(powerset(powerset(X0))))
| empty(sK7(X1,sK10(powerset(powerset(X0))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_426])]) ).
fof(f2332,plain,
( ! [X0,X1] :
( ~ empty(X0)
| sP0(X1,sK10(powerset(powerset(X0))))
| empty(sK7(X1,sK10(powerset(powerset(X0))))) )
| ~ spl17_75
| ~ spl17_272 ),
inference(resolution,[],[f2294,f644]) ).
fof(f4097,plain,
( spl17_425
| ~ spl17_35
| ~ spl17_270 ),
inference(avatar_split_clause,[],[f2267,f2244,f339,f4095]) ).
fof(f4095,plain,
( spl17_425
<=> ! [X0,X1] :
( empty(sK6(powerset(X0)))
| ~ empty(X0)
| empty(powerset(X0))
| sP0(X1,sK10(sK6(powerset(X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_425])]) ).
fof(f2244,plain,
( spl17_270
<=> ! [X0,X1] :
( empty(powerset(X0))
| empty(sK6(powerset(X0)))
| ~ empty(X0)
| ~ in(X1,sK10(sK6(powerset(X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_270])]) ).
fof(f2267,plain,
( ! [X0,X1] :
( empty(sK6(powerset(X0)))
| ~ empty(X0)
| empty(powerset(X0))
| sP0(X1,sK10(sK6(powerset(X0)))) )
| ~ spl17_35
| ~ spl17_270 ),
inference(resolution,[],[f2245,f340]) ).
fof(f2245,plain,
( ! [X0,X1] :
( ~ in(X1,sK10(sK6(powerset(X0))))
| empty(sK6(powerset(X0)))
| ~ empty(X0)
| empty(powerset(X0)) )
| ~ spl17_270 ),
inference(avatar_component_clause,[],[f2244]) ).
fof(f4093,plain,
( spl17_424
| ~ spl17_59
| ~ spl17_270 ),
inference(avatar_split_clause,[],[f2262,f2244,f500,f4091]) ).
fof(f4091,plain,
( spl17_424
<=> ! [X0,X1] :
( empty(sK6(powerset(X0)))
| ~ empty(X0)
| empty(powerset(X0))
| sP0(sK10(sK6(powerset(X0))),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_424])]) ).
fof(f2262,plain,
( ! [X0,X1] :
( empty(sK6(powerset(X0)))
| ~ empty(X0)
| empty(powerset(X0))
| sP0(sK10(sK6(powerset(X0))),X1) )
| ~ spl17_59
| ~ spl17_270 ),
inference(resolution,[],[f2245,f501]) ).
fof(f4089,plain,
( spl17_423
| ~ spl17_17
| ~ spl17_268 ),
inference(avatar_split_clause,[],[f2247,f2236,f255,f4087]) ).
fof(f4087,plain,
( spl17_423
<=> ! [X0,X1] :
( empty(sK10(powerset(powerset(cartesian_product2(X0,X1)))))
| sP1(sK10(sK10(powerset(powerset(cartesian_product2(X0,X1)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_423])]) ).
fof(f2236,plain,
( spl17_268
<=> ! [X0,X1] :
( empty(sK10(powerset(powerset(cartesian_product2(X0,X1)))))
| relation(sK10(sK10(powerset(powerset(cartesian_product2(X0,X1)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_268])]) ).
fof(f2247,plain,
( ! [X0,X1] :
( empty(sK10(powerset(powerset(cartesian_product2(X0,X1)))))
| sP1(sK10(sK10(powerset(powerset(cartesian_product2(X0,X1)))))) )
| ~ spl17_17
| ~ spl17_268 ),
inference(resolution,[],[f2237,f256]) ).
fof(f2237,plain,
( ! [X0,X1] :
( relation(sK10(sK10(powerset(powerset(cartesian_product2(X0,X1))))))
| empty(sK10(powerset(powerset(cartesian_product2(X0,X1))))) )
| ~ spl17_268 ),
inference(avatar_component_clause,[],[f2236]) ).
fof(f4085,plain,
( spl17_422
| ~ spl17_95
| ~ spl17_224 ),
inference(avatar_split_clause,[],[f1824,f1808,f765,f4083]) ).
fof(f4083,plain,
( spl17_422
<=> ! [X0] :
( empty(sK6(sK6(X0)))
| empty(sK6(X0))
| element(sK10(sK6(sK6(X0))),X0)
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_422])]) ).
fof(f1824,plain,
( ! [X0] :
( empty(sK6(sK6(X0)))
| empty(sK6(X0))
| element(sK10(sK6(sK6(X0))),X0)
| empty(X0) )
| ~ spl17_95
| ~ spl17_224 ),
inference(resolution,[],[f1809,f766]) ).
fof(f3929,plain,
( spl17_421
| ~ spl17_69
| ~ spl17_403 ),
inference(avatar_split_clause,[],[f3870,f3824,f567,f3926]) ).
fof(f3870,plain,
( sK16 = cartesian_product2(sK16,sK16)
| ~ spl17_69
| ~ spl17_403 ),
inference(resolution,[],[f3826,f568]) ).
fof(f3921,plain,
( spl17_420
| ~ spl17_75
| ~ spl17_270 ),
inference(avatar_split_clause,[],[f2264,f2244,f643,f3919]) ).
fof(f3919,plain,
( spl17_420
<=> ! [X0] :
( empty(sK6(powerset(X0)))
| ~ empty(X0)
| empty(powerset(X0))
| empty(sK10(sK6(powerset(X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_420])]) ).
fof(f2264,plain,
( ! [X0] :
( empty(sK6(powerset(X0)))
| ~ empty(X0)
| empty(powerset(X0))
| empty(sK10(sK6(powerset(X0)))) )
| ~ spl17_75
| ~ spl17_270 ),
inference(resolution,[],[f2245,f644]) ).
fof(f3917,plain,
( spl17_419
| ~ spl17_25
| ~ spl17_266 ),
inference(avatar_split_clause,[],[f2216,f2147,f292,f3915]) ).
fof(f3915,plain,
( spl17_419
<=> ! [X0,X1] :
( empty(X0)
| sP0(X1,sK10(powerset(X0)))
| ~ in(X0,sK9(X1,sK10(powerset(X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_419])]) ).
fof(f2216,plain,
( ! [X0,X1] :
( empty(X0)
| sP0(X1,sK10(powerset(X0)))
| ~ in(X0,sK9(X1,sK10(powerset(X0)))) )
| ~ spl17_25
| ~ spl17_266 ),
inference(resolution,[],[f2148,f293]) ).
fof(f3913,plain,
( spl17_418
| ~ spl17_25
| ~ spl17_265 ),
inference(avatar_split_clause,[],[f2195,f2143,f292,f3911]) ).
fof(f3911,plain,
( spl17_418
<=> ! [X0,X1] :
( empty(X0)
| sP0(X1,sK10(powerset(X0)))
| ~ in(X0,sK8(X1,sK10(powerset(X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_418])]) ).
fof(f2195,plain,
( ! [X0,X1] :
( empty(X0)
| sP0(X1,sK10(powerset(X0)))
| ~ in(X0,sK8(X1,sK10(powerset(X0)))) )
| ~ spl17_25
| ~ spl17_265 ),
inference(resolution,[],[f2144,f293]) ).
fof(f3909,plain,
( spl17_417
| ~ spl17_25
| ~ spl17_264 ),
inference(avatar_split_clause,[],[f2174,f2139,f292,f3907]) ).
fof(f3907,plain,
( spl17_417
<=> ! [X0,X1] :
( empty(X0)
| sP0(X1,sK10(powerset(X0)))
| ~ in(X0,sK7(X1,sK10(powerset(X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_417])]) ).
fof(f2174,plain,
( ! [X0,X1] :
( empty(X0)
| sP0(X1,sK10(powerset(X0)))
| ~ in(X0,sK7(X1,sK10(powerset(X0)))) )
| ~ spl17_25
| ~ spl17_264 ),
inference(resolution,[],[f2140,f293]) ).
fof(f3905,plain,
( spl17_416
| ~ spl17_35
| ~ spl17_256 ),
inference(avatar_split_clause,[],[f2155,f2106,f339,f3903]) ).
fof(f3903,plain,
( spl17_416
<=> ! [X0,X1] :
( ~ empty(X0)
| empty(sK10(powerset(powerset(X0))))
| sP0(X1,sK10(sK10(powerset(powerset(X0))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_416])]) ).
fof(f2106,plain,
( spl17_256
<=> ! [X0,X1] :
( empty(sK10(powerset(powerset(X0))))
| ~ empty(X0)
| ~ in(X1,sK10(sK10(powerset(powerset(X0))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_256])]) ).
fof(f2155,plain,
( ! [X0,X1] :
( ~ empty(X0)
| empty(sK10(powerset(powerset(X0))))
| sP0(X1,sK10(sK10(powerset(powerset(X0))))) )
| ~ spl17_35
| ~ spl17_256 ),
inference(resolution,[],[f2107,f340]) ).
fof(f2107,plain,
( ! [X0,X1] :
( ~ in(X1,sK10(sK10(powerset(powerset(X0)))))
| ~ empty(X0)
| empty(sK10(powerset(powerset(X0)))) )
| ~ spl17_256 ),
inference(avatar_component_clause,[],[f2106]) ).
fof(f3901,plain,
( spl17_415
| ~ spl17_59
| ~ spl17_256 ),
inference(avatar_split_clause,[],[f2150,f2106,f500,f3899]) ).
fof(f3899,plain,
( spl17_415
<=> ! [X0,X1] :
( ~ empty(X0)
| empty(sK10(powerset(powerset(X0))))
| sP0(sK10(sK10(powerset(powerset(X0)))),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_415])]) ).
fof(f2150,plain,
( ! [X0,X1] :
( ~ empty(X0)
| empty(sK10(powerset(powerset(X0))))
| sP0(sK10(sK10(powerset(powerset(X0)))),X1) )
| ~ spl17_59
| ~ spl17_256 ),
inference(resolution,[],[f2107,f501]) ).
fof(f3897,plain,
( spl17_414
| ~ spl17_34
| ~ spl17_238 ),
inference(avatar_split_clause,[],[f2006,f1921,f335,f3895]) ).
fof(f3895,plain,
( spl17_414
<=> ! [X2,X0,X1] :
( sP0(X0,powerset(X1))
| ~ empty(X1)
| is_transitive_in(X2,sK9(X0,powerset(X1)))
| ~ sP1(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_414])]) ).
fof(f1921,plain,
( spl17_238
<=> ! [X2,X0,X1] :
( ~ empty(X0)
| sP0(X1,powerset(X0))
| sP0(X2,sK9(X1,powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_238])]) ).
fof(f2006,plain,
( ! [X2,X0,X1] :
( sP0(X0,powerset(X1))
| ~ empty(X1)
| is_transitive_in(X2,sK9(X0,powerset(X1)))
| ~ sP1(X2) )
| ~ spl17_34
| ~ spl17_238 ),
inference(resolution,[],[f1922,f336]) ).
fof(f1922,plain,
( ! [X2,X0,X1] :
( sP0(X2,sK9(X1,powerset(X0)))
| sP0(X1,powerset(X0))
| ~ empty(X0) )
| ~ spl17_238 ),
inference(avatar_component_clause,[],[f1921]) ).
fof(f3893,plain,
( spl17_413
| ~ spl17_34
| ~ spl17_236 ),
inference(avatar_split_clause,[],[f2003,f1913,f335,f3891]) ).
fof(f3891,plain,
( spl17_413
<=> ! [X2,X0,X1] :
( sP0(X0,powerset(X1))
| ~ empty(X1)
| is_transitive_in(X2,sK8(X0,powerset(X1)))
| ~ sP1(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_413])]) ).
fof(f1913,plain,
( spl17_236
<=> ! [X2,X0,X1] :
( ~ empty(X0)
| sP0(X1,powerset(X0))
| sP0(X2,sK8(X1,powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_236])]) ).
fof(f2003,plain,
( ! [X2,X0,X1] :
( sP0(X0,powerset(X1))
| ~ empty(X1)
| is_transitive_in(X2,sK8(X0,powerset(X1)))
| ~ sP1(X2) )
| ~ spl17_34
| ~ spl17_236 ),
inference(resolution,[],[f1914,f336]) ).
fof(f1914,plain,
( ! [X2,X0,X1] :
( sP0(X2,sK8(X1,powerset(X0)))
| sP0(X1,powerset(X0))
| ~ empty(X0) )
| ~ spl17_236 ),
inference(avatar_component_clause,[],[f1913]) ).
fof(f3889,plain,
( spl17_412
| ~ spl17_34
| ~ spl17_233 ),
inference(avatar_split_clause,[],[f2000,f1901,f335,f3887]) ).
fof(f3887,plain,
( spl17_412
<=> ! [X2,X0,X1] :
( sP0(X0,powerset(X1))
| ~ empty(X1)
| is_transitive_in(X2,sK7(X0,powerset(X1)))
| ~ sP1(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_412])]) ).
fof(f1901,plain,
( spl17_233
<=> ! [X2,X0,X1] :
( ~ empty(X0)
| sP0(X1,powerset(X0))
| sP0(X2,sK7(X1,powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_233])]) ).
fof(f2000,plain,
( ! [X2,X0,X1] :
( sP0(X0,powerset(X1))
| ~ empty(X1)
| is_transitive_in(X2,sK7(X0,powerset(X1)))
| ~ sP1(X2) )
| ~ spl17_34
| ~ spl17_233 ),
inference(resolution,[],[f1902,f336]) ).
fof(f1902,plain,
( ! [X2,X0,X1] :
( sP0(X2,sK7(X1,powerset(X0)))
| sP0(X1,powerset(X0))
| ~ empty(X0) )
| ~ spl17_233 ),
inference(avatar_component_clause,[],[f1901]) ).
fof(f3865,plain,
( spl17_411
| ~ spl17_32
| ~ spl17_228 ),
inference(avatar_split_clause,[],[f1883,f1849,f321,f3863]) ).
fof(f3863,plain,
( spl17_411
<=> ! [X2,X0,X1] :
( sP0(X0,powerset(X1))
| ~ empty(X1)
| sK9(X0,powerset(X1)) = X2
| ~ empty(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_411])]) ).
fof(f1883,plain,
( ! [X2,X0,X1] :
( sP0(X0,powerset(X1))
| ~ empty(X1)
| sK9(X0,powerset(X1)) = X2
| ~ empty(X2) )
| ~ spl17_32
| ~ spl17_228 ),
inference(resolution,[],[f1850,f322]) ).
fof(f3861,plain,
( spl17_410
| ~ spl17_214
| ~ spl17_228 ),
inference(avatar_split_clause,[],[f1881,f1849,f1749,f3859]) ).
fof(f3859,plain,
( spl17_410
<=> ! [X0,X1] :
( sP0(X0,powerset(X1))
| ~ empty(X1)
| sK16 = sK10(powerset(sK9(X0,powerset(X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_410])]) ).
fof(f1749,plain,
( spl17_214
<=> ! [X0] :
( ~ empty(X0)
| sK16 = sK10(powerset(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_214])]) ).
fof(f1881,plain,
( ! [X0,X1] :
( sP0(X0,powerset(X1))
| ~ empty(X1)
| sK16 = sK10(powerset(sK9(X0,powerset(X1)))) )
| ~ spl17_214
| ~ spl17_228 ),
inference(resolution,[],[f1850,f1750]) ).
fof(f1750,plain,
( ! [X0] :
( ~ empty(X0)
| sK16 = sK10(powerset(X0)) )
| ~ spl17_214 ),
inference(avatar_component_clause,[],[f1749]) ).
fof(f3857,plain,
( spl17_409
| ~ spl17_32
| ~ spl17_227 ),
inference(avatar_split_clause,[],[f1879,f1845,f321,f3855]) ).
fof(f3855,plain,
( spl17_409
<=> ! [X2,X0,X1] :
( sP0(X0,powerset(X1))
| ~ empty(X1)
| sK8(X0,powerset(X1)) = X2
| ~ empty(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_409])]) ).
fof(f1879,plain,
( ! [X2,X0,X1] :
( sP0(X0,powerset(X1))
| ~ empty(X1)
| sK8(X0,powerset(X1)) = X2
| ~ empty(X2) )
| ~ spl17_32
| ~ spl17_227 ),
inference(resolution,[],[f1846,f322]) ).
fof(f3853,plain,
( spl17_408
| ~ spl17_214
| ~ spl17_227 ),
inference(avatar_split_clause,[],[f1877,f1845,f1749,f3851]) ).
fof(f3851,plain,
( spl17_408
<=> ! [X0,X1] :
( sP0(X0,powerset(X1))
| ~ empty(X1)
| sK16 = sK10(powerset(sK8(X0,powerset(X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_408])]) ).
fof(f1877,plain,
( ! [X0,X1] :
( sP0(X0,powerset(X1))
| ~ empty(X1)
| sK16 = sK10(powerset(sK8(X0,powerset(X1)))) )
| ~ spl17_214
| ~ spl17_227 ),
inference(resolution,[],[f1846,f1750]) ).
fof(f3849,plain,
( spl17_407
| ~ spl17_32
| ~ spl17_226 ),
inference(avatar_split_clause,[],[f1875,f1841,f321,f3847]) ).
fof(f3847,plain,
( spl17_407
<=> ! [X2,X0,X1] :
( sP0(X0,powerset(X1))
| ~ empty(X1)
| sK7(X0,powerset(X1)) = X2
| ~ empty(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_407])]) ).
fof(f1875,plain,
( ! [X2,X0,X1] :
( sP0(X0,powerset(X1))
| ~ empty(X1)
| sK7(X0,powerset(X1)) = X2
| ~ empty(X2) )
| ~ spl17_32
| ~ spl17_226 ),
inference(resolution,[],[f1842,f322]) ).
fof(f3845,plain,
( spl17_406
| ~ spl17_214
| ~ spl17_226 ),
inference(avatar_split_clause,[],[f1873,f1841,f1749,f3843]) ).
fof(f3843,plain,
( spl17_406
<=> ! [X0,X1] :
( sP0(X0,powerset(X1))
| ~ empty(X1)
| sK16 = sK10(powerset(sK7(X0,powerset(X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_406])]) ).
fof(f1873,plain,
( ! [X0,X1] :
( sP0(X0,powerset(X1))
| ~ empty(X1)
| sK16 = sK10(powerset(sK7(X0,powerset(X1)))) )
| ~ spl17_214
| ~ spl17_226 ),
inference(resolution,[],[f1842,f1750]) ).
fof(f3834,plain,
( spl17_405
| ~ spl17_75
| ~ spl17_256 ),
inference(avatar_split_clause,[],[f2152,f2106,f643,f3832]) ).
fof(f3832,plain,
( spl17_405
<=> ! [X0] :
( ~ empty(X0)
| empty(sK10(powerset(powerset(X0))))
| empty(sK10(sK10(powerset(powerset(X0))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_405])]) ).
fof(f2152,plain,
( ! [X0] :
( ~ empty(X0)
| empty(sK10(powerset(powerset(X0))))
| empty(sK10(sK10(powerset(powerset(X0))))) )
| ~ spl17_75
| ~ spl17_256 ),
inference(resolution,[],[f2107,f644]) ).
fof(f3830,plain,
( spl17_403
| spl17_404
| ~ spl17_39
| ~ spl17_399 ),
inference(avatar_split_clause,[],[f3799,f3796,f355,f3828,f3824]) ).
fof(f3796,plain,
( spl17_399
<=> ! [X0] :
( ~ in(X0,the_InternalRel(sK2))
| element(X0,cartesian_product2(sK16,sK16)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_399])]) ).
fof(f3799,plain,
( ! [X0] :
( ~ in(X0,the_InternalRel(sK2))
| empty(cartesian_product2(sK16,sK16))
| in(X0,cartesian_product2(sK16,sK16)) )
| ~ spl17_39
| ~ spl17_399 ),
inference(resolution,[],[f3797,f356]) ).
fof(f3797,plain,
( ! [X0] :
( element(X0,cartesian_product2(sK16,sK16))
| ~ in(X0,the_InternalRel(sK2)) )
| ~ spl17_399 ),
inference(avatar_component_clause,[],[f3796]) ).
fof(f3811,plain,
( spl17_402
| ~ spl17_16
| ~ spl17_257 ),
inference(avatar_split_clause,[],[f2161,f2110,f251,f3809]) ).
fof(f3809,plain,
( spl17_402
<=> ! [X0] :
( empty(powerset(X0))
| empty(powerset(powerset(X0)))
| ~ subset(powerset(powerset(X0)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_402])]) ).
fof(f2110,plain,
( spl17_257
<=> ! [X0,X1] :
( ~ subset(powerset(X0),X1)
| empty(powerset(X1))
| empty(powerset(X0))
| ~ subset(powerset(X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_257])]) ).
fof(f2161,plain,
( ! [X0] :
( empty(powerset(X0))
| empty(powerset(powerset(X0)))
| ~ subset(powerset(powerset(X0)),X0) )
| ~ spl17_16
| ~ spl17_257 ),
inference(resolution,[],[f2111,f252]) ).
fof(f2111,plain,
( ! [X0,X1] :
( ~ subset(powerset(X1),X0)
| empty(powerset(X1))
| empty(powerset(X0))
| ~ subset(powerset(X0),X1) )
| ~ spl17_257 ),
inference(avatar_component_clause,[],[f2110]) ).
fof(f3807,plain,
( spl17_401
| ~ spl17_25
| ~ spl17_241 ),
inference(avatar_split_clause,[],[f2048,f1933,f292,f3805]) ).
fof(f3805,plain,
( spl17_401
<=> ! [X0,X1] :
( sP0(X0,sK6(X1))
| empty(X1)
| ~ in(X1,sK9(X0,sK6(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_401])]) ).
fof(f2048,plain,
( ! [X0,X1] :
( sP0(X0,sK6(X1))
| empty(X1)
| ~ in(X1,sK9(X0,sK6(X1))) )
| ~ spl17_25
| ~ spl17_241 ),
inference(resolution,[],[f1934,f293]) ).
fof(f3803,plain,
( spl17_400
| ~ spl17_25
| ~ spl17_240 ),
inference(avatar_split_clause,[],[f2029,f1929,f292,f3801]) ).
fof(f3801,plain,
( spl17_400
<=> ! [X0,X1] :
( sP0(X0,sK6(X1))
| empty(X1)
| ~ in(X1,sK8(X0,sK6(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_400])]) ).
fof(f2029,plain,
( ! [X0,X1] :
( sP0(X0,sK6(X1))
| empty(X1)
| ~ in(X1,sK8(X0,sK6(X1))) )
| ~ spl17_25
| ~ spl17_240 ),
inference(resolution,[],[f1930,f293]) ).
fof(f3798,plain,
( spl17_399
| ~ spl17_102
| ~ spl17_105 ),
inference(avatar_split_clause,[],[f1051,f841,f813,f3796]) ).
fof(f813,plain,
( spl17_102
<=> ! [X0,X3,X2,X1] :
( element(X0,cartesian_product2(X1,X2))
| ~ in(X0,X3)
| ~ relation_of2_as_subset(X3,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_102])]) ).
fof(f1051,plain,
( ! [X0] :
( ~ in(X0,the_InternalRel(sK2))
| element(X0,cartesian_product2(sK16,sK16)) )
| ~ spl17_102
| ~ spl17_105 ),
inference(resolution,[],[f843,f814]) ).
fof(f814,plain,
( ! [X2,X3,X0,X1] :
( ~ relation_of2_as_subset(X3,X1,X2)
| ~ in(X0,X3)
| element(X0,cartesian_product2(X1,X2)) )
| ~ spl17_102 ),
inference(avatar_component_clause,[],[f813]) ).
fof(f3793,plain,
( spl17_398
| ~ spl17_42
| ~ spl17_105 ),
inference(avatar_split_clause,[],[f1053,f841,f367,f3790]) ).
fof(f367,plain,
( spl17_42
<=> ! [X2,X0,X1] :
( relation_of2(X2,X0,X1)
| ~ relation_of2_as_subset(X2,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_42])]) ).
fof(f1053,plain,
( relation_of2(the_InternalRel(sK2),sK16,sK16)
| ~ spl17_42
| ~ spl17_105 ),
inference(resolution,[],[f843,f368]) ).
fof(f368,plain,
( ! [X2,X0,X1] :
( ~ relation_of2_as_subset(X2,X0,X1)
| relation_of2(X2,X0,X1) )
| ~ spl17_42 ),
inference(avatar_component_clause,[],[f367]) ).
fof(f3787,plain,
( ~ spl17_2
| ~ spl17_1
| spl17_397
| ~ spl17_45
| ~ spl17_65 ),
inference(avatar_split_clause,[],[f597,f541,f405,f3784,f179,f184]) ).
fof(f179,plain,
( spl17_1
<=> transitive_relstr(sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1])]) ).
fof(f3784,plain,
( spl17_397
<=> is_transitive_in(the_InternalRel(sK2),sK16) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_397])]) ).
fof(f405,plain,
( spl17_45
<=> ! [X0] :
( is_transitive_in(the_InternalRel(X0),the_carrier(X0))
| ~ transitive_relstr(X0)
| ~ rel_str(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_45])]) ).
fof(f597,plain,
( is_transitive_in(the_InternalRel(sK2),sK16)
| ~ transitive_relstr(sK2)
| ~ rel_str(sK2)
| ~ spl17_45
| ~ spl17_65 ),
inference(superposition,[],[f406,f543]) ).
fof(f406,plain,
( ! [X0] :
( is_transitive_in(the_InternalRel(X0),the_carrier(X0))
| ~ transitive_relstr(X0)
| ~ rel_str(X0) )
| ~ spl17_45 ),
inference(avatar_component_clause,[],[f405]) ).
fof(f3779,plain,
( ~ spl17_396
| ~ spl17_65
| spl17_127 ),
inference(avatar_split_clause,[],[f3756,f1038,f541,f3776]) ).
fof(f3776,plain,
( spl17_396
<=> in(sK16,sK5) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_396])]) ).
fof(f1038,plain,
( spl17_127
<=> in(the_carrier(sK2),sK5) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_127])]) ).
fof(f3756,plain,
( ~ in(sK16,sK5)
| ~ spl17_65
| spl17_127 ),
inference(superposition,[],[f1040,f543]) ).
fof(f1040,plain,
( ~ in(the_carrier(sK2),sK5)
| spl17_127 ),
inference(avatar_component_clause,[],[f1038]) ).
fof(f3774,plain,
( ~ spl17_395
| ~ spl17_65
| spl17_125 ),
inference(avatar_split_clause,[],[f3755,f1018,f541,f3771]) ).
fof(f3771,plain,
( spl17_395
<=> in(sK16,sK4) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_395])]) ).
fof(f1018,plain,
( spl17_125
<=> in(the_carrier(sK2),sK4) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_125])]) ).
fof(f3755,plain,
( ~ in(sK16,sK4)
| ~ spl17_65
| spl17_125 ),
inference(superposition,[],[f1020,f543]) ).
fof(f1020,plain,
( ~ in(the_carrier(sK2),sK4)
| spl17_125 ),
inference(avatar_component_clause,[],[f1018]) ).
fof(f3769,plain,
( ~ spl17_394
| ~ spl17_65
| spl17_119 ),
inference(avatar_split_clause,[],[f3754,f960,f541,f3766]) ).
fof(f3766,plain,
( spl17_394
<=> in(sK16,sK3) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_394])]) ).
fof(f960,plain,
( spl17_119
<=> in(the_carrier(sK2),sK3) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_119])]) ).
fof(f3754,plain,
( ~ in(sK16,sK3)
| ~ spl17_65
| spl17_119 ),
inference(superposition,[],[f962,f543]) ).
fof(f962,plain,
( ~ in(the_carrier(sK2),sK3)
| spl17_119 ),
inference(avatar_component_clause,[],[f960]) ).
fof(f3748,plain,
( ~ spl17_72
| ~ spl17_112 ),
inference(avatar_contradiction_clause,[],[f3744]) ).
fof(f3744,plain,
( $false
| ~ spl17_72
| ~ spl17_112 ),
inference(resolution,[],[f897,f579]) ).
fof(f897,plain,
( in(sK5,sK16)
| ~ spl17_112 ),
inference(avatar_component_clause,[],[f895]) ).
fof(f3738,plain,
( ~ spl17_159
| ~ spl17_1
| ~ spl17_4
| ~ spl17_2
| ~ spl17_5
| spl17_393
| ~ spl17_106
| ~ spl17_107
| ~ spl17_7
| ~ spl17_368 ),
inference(avatar_split_clause,[],[f3527,f3523,f209,f858,f849,f3736,f199,f184,f194,f179,f1219]) ).
fof(f3527,plain,
( ! [X0] :
( ~ in(sK5,the_carrier(sK2))
| ~ in(sK4,the_carrier(sK2))
| in(unordered_pair(singleton(sK4),unordered_pair(sK4,X0)),the_InternalRel(sK2))
| ~ related(sK2,sK5,X0)
| ~ element(X0,the_carrier(sK2))
| ~ element(sK5,the_carrier(sK2))
| ~ rel_str(sK2)
| ~ in(X0,the_carrier(sK2))
| ~ element(sK4,the_carrier(sK2))
| ~ transitive_relstr(sK2)
| ~ sP1(the_InternalRel(sK2)) )
| ~ spl17_7
| ~ spl17_368 ),
inference(resolution,[],[f3524,f211]) ).
fof(f3718,plain,
( spl17_392
| ~ spl17_60
| ~ spl17_188 ),
inference(avatar_split_clause,[],[f1525,f1511,f504,f3716]) ).
fof(f1525,plain,
( ! [X2,X0,X1] :
( element(unordered_pair(singleton(sK7(unordered_pair(singleton(sK7(powerset(X0),X1)),unordered_pair(sK8(powerset(X0),X1),sK7(powerset(X0),X1))),X2)),unordered_pair(sK8(unordered_pair(singleton(sK7(powerset(X0),X1)),unordered_pair(sK8(powerset(X0),X1),sK7(powerset(X0),X1))),X2),sK7(unordered_pair(singleton(sK7(powerset(X0),X1)),unordered_pair(sK8(powerset(X0),X1),sK7(powerset(X0),X1))),X2))),X0)
| sP0(powerset(X0),X1)
| sP0(unordered_pair(singleton(sK7(powerset(X0),X1)),unordered_pair(sK8(powerset(X0),X1),sK7(powerset(X0),X1))),X2) )
| ~ spl17_60
| ~ spl17_188 ),
inference(resolution,[],[f1512,f505]) ).
fof(f3714,plain,
( spl17_391
| ~ spl17_59
| ~ spl17_188 ),
inference(avatar_split_clause,[],[f1524,f1511,f500,f3712]) ).
fof(f1524,plain,
( ! [X2,X0,X1] :
( element(unordered_pair(singleton(sK8(unordered_pair(singleton(sK7(powerset(X0),X1)),unordered_pair(sK8(powerset(X0),X1),sK7(powerset(X0),X1))),X2)),unordered_pair(sK9(unordered_pair(singleton(sK7(powerset(X0),X1)),unordered_pair(sK8(powerset(X0),X1),sK7(powerset(X0),X1))),X2),sK8(unordered_pair(singleton(sK7(powerset(X0),X1)),unordered_pair(sK8(powerset(X0),X1),sK7(powerset(X0),X1))),X2))),X0)
| sP0(powerset(X0),X1)
| sP0(unordered_pair(singleton(sK7(powerset(X0),X1)),unordered_pair(sK8(powerset(X0),X1),sK7(powerset(X0),X1))),X2) )
| ~ spl17_59
| ~ spl17_188 ),
inference(resolution,[],[f1512,f501]) ).
fof(f3710,plain,
( spl17_390
| ~ spl17_60
| ~ spl17_187 ),
inference(avatar_split_clause,[],[f1515,f1507,f504,f3708]) ).
fof(f1515,plain,
( ! [X2,X0,X1] :
( element(unordered_pair(singleton(sK7(unordered_pair(singleton(sK8(powerset(X0),X1)),unordered_pair(sK9(powerset(X0),X1),sK8(powerset(X0),X1))),X2)),unordered_pair(sK8(unordered_pair(singleton(sK8(powerset(X0),X1)),unordered_pair(sK9(powerset(X0),X1),sK8(powerset(X0),X1))),X2),sK7(unordered_pair(singleton(sK8(powerset(X0),X1)),unordered_pair(sK9(powerset(X0),X1),sK8(powerset(X0),X1))),X2))),X0)
| sP0(powerset(X0),X1)
| sP0(unordered_pair(singleton(sK8(powerset(X0),X1)),unordered_pair(sK9(powerset(X0),X1),sK8(powerset(X0),X1))),X2) )
| ~ spl17_60
| ~ spl17_187 ),
inference(resolution,[],[f1508,f505]) ).
fof(f3706,plain,
( spl17_389
| ~ spl17_59
| ~ spl17_187 ),
inference(avatar_split_clause,[],[f1514,f1507,f500,f3704]) ).
fof(f1514,plain,
( ! [X2,X0,X1] :
( element(unordered_pair(singleton(sK8(unordered_pair(singleton(sK8(powerset(X0),X1)),unordered_pair(sK9(powerset(X0),X1),sK8(powerset(X0),X1))),X2)),unordered_pair(sK9(unordered_pair(singleton(sK8(powerset(X0),X1)),unordered_pair(sK9(powerset(X0),X1),sK8(powerset(X0),X1))),X2),sK8(unordered_pair(singleton(sK8(powerset(X0),X1)),unordered_pair(sK9(powerset(X0),X1),sK8(powerset(X0),X1))),X2))),X0)
| sP0(powerset(X0),X1)
| sP0(unordered_pair(singleton(sK8(powerset(X0),X1)),unordered_pair(sK9(powerset(X0),X1),sK8(powerset(X0),X1))),X2) )
| ~ spl17_59
| ~ spl17_187 ),
inference(resolution,[],[f1508,f501]) ).
fof(f3698,plain,
( spl17_388
| ~ spl17_60
| ~ spl17_209 ),
inference(avatar_split_clause,[],[f1722,f1710,f504,f3696]) ).
fof(f3696,plain,
( spl17_388
<=> ! [X4,X0,X3,X2,X1] :
( in(unordered_pair(singleton(X0),unordered_pair(X0,sK8(powerset(cartesian_product2(X1,X2)),X3))),powerset(cartesian_product2(X1,X2)))
| ~ in(sK8(powerset(cartesian_product2(X1,X2)),X3),X4)
| ~ in(sK7(powerset(cartesian_product2(X1,X2)),X3),X4)
| ~ in(X0,X4)
| ~ sP0(powerset(cartesian_product2(X1,X2)),X4)
| empty(powerset(cartesian_product2(X1,X2)))
| ~ relation_of2_as_subset(unordered_pair(singleton(X0),unordered_pair(X0,sK7(powerset(cartesian_product2(X1,X2)),X3))),X1,X2)
| sP0(powerset(cartesian_product2(X1,X2)),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_388])]) ).
fof(f1722,plain,
( ! [X2,X3,X0,X1,X4] :
( in(unordered_pair(singleton(X0),unordered_pair(X0,sK8(powerset(cartesian_product2(X1,X2)),X3))),powerset(cartesian_product2(X1,X2)))
| ~ in(sK8(powerset(cartesian_product2(X1,X2)),X3),X4)
| ~ in(sK7(powerset(cartesian_product2(X1,X2)),X3),X4)
| ~ in(X0,X4)
| ~ sP0(powerset(cartesian_product2(X1,X2)),X4)
| empty(powerset(cartesian_product2(X1,X2)))
| ~ relation_of2_as_subset(unordered_pair(singleton(X0),unordered_pair(X0,sK7(powerset(cartesian_product2(X1,X2)),X3))),X1,X2)
| sP0(powerset(cartesian_product2(X1,X2)),X3) )
| ~ spl17_60
| ~ spl17_209 ),
inference(resolution,[],[f1711,f505]) ).
fof(f3694,plain,
( spl17_387
| ~ spl17_59
| ~ spl17_209 ),
inference(avatar_split_clause,[],[f1721,f1710,f500,f3692]) ).
fof(f3692,plain,
( spl17_387
<=> ! [X4,X0,X3,X2,X1] :
( in(unordered_pair(singleton(X0),unordered_pair(X0,sK9(powerset(cartesian_product2(X1,X2)),X3))),powerset(cartesian_product2(X1,X2)))
| ~ in(sK9(powerset(cartesian_product2(X1,X2)),X3),X4)
| ~ in(sK8(powerset(cartesian_product2(X1,X2)),X3),X4)
| ~ in(X0,X4)
| ~ sP0(powerset(cartesian_product2(X1,X2)),X4)
| empty(powerset(cartesian_product2(X1,X2)))
| ~ relation_of2_as_subset(unordered_pair(singleton(X0),unordered_pair(X0,sK8(powerset(cartesian_product2(X1,X2)),X3))),X1,X2)
| sP0(powerset(cartesian_product2(X1,X2)),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_387])]) ).
fof(f1721,plain,
( ! [X2,X3,X0,X1,X4] :
( in(unordered_pair(singleton(X0),unordered_pair(X0,sK9(powerset(cartesian_product2(X1,X2)),X3))),powerset(cartesian_product2(X1,X2)))
| ~ in(sK9(powerset(cartesian_product2(X1,X2)),X3),X4)
| ~ in(sK8(powerset(cartesian_product2(X1,X2)),X3),X4)
| ~ in(X0,X4)
| ~ sP0(powerset(cartesian_product2(X1,X2)),X4)
| empty(powerset(cartesian_product2(X1,X2)))
| ~ relation_of2_as_subset(unordered_pair(singleton(X0),unordered_pair(X0,sK8(powerset(cartesian_product2(X1,X2)),X3))),X1,X2)
| sP0(powerset(cartesian_product2(X1,X2)),X3) )
| ~ spl17_59
| ~ spl17_209 ),
inference(resolution,[],[f1711,f501]) ).
fof(f3687,plain,
( spl17_386
| ~ spl17_60
| ~ spl17_207 ),
inference(avatar_split_clause,[],[f1700,f1686,f504,f3685]) ).
fof(f3685,plain,
( spl17_386
<=> ! [X0,X3,X2,X1] :
( in(unordered_pair(singleton(sK7(the_InternalRel(X0),X1)),unordered_pair(sK7(the_InternalRel(X0),X1),X2)),the_InternalRel(X0))
| ~ in(X2,X3)
| ~ in(sK8(the_InternalRel(X0),X1),X3)
| ~ in(sK7(the_InternalRel(X0),X1),X3)
| ~ sP0(the_InternalRel(X0),X3)
| ~ related(X0,sK8(the_InternalRel(X0),X1),X2)
| ~ element(X2,the_carrier(X0))
| ~ element(sK8(the_InternalRel(X0),X1),the_carrier(X0))
| ~ rel_str(X0)
| sP0(the_InternalRel(X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_386])]) ).
fof(f1700,plain,
( ! [X2,X3,X0,X1] :
( in(unordered_pair(singleton(sK7(the_InternalRel(X0),X1)),unordered_pair(sK7(the_InternalRel(X0),X1),X2)),the_InternalRel(X0))
| ~ in(X2,X3)
| ~ in(sK8(the_InternalRel(X0),X1),X3)
| ~ in(sK7(the_InternalRel(X0),X1),X3)
| ~ sP0(the_InternalRel(X0),X3)
| ~ related(X0,sK8(the_InternalRel(X0),X1),X2)
| ~ element(X2,the_carrier(X0))
| ~ element(sK8(the_InternalRel(X0),X1),the_carrier(X0))
| ~ rel_str(X0)
| sP0(the_InternalRel(X0),X1) )
| ~ spl17_60
| ~ spl17_207 ),
inference(resolution,[],[f1687,f505]) ).
fof(f3683,plain,
( ~ spl17_2
| spl17_384
| ~ spl17_385
| ~ spl17_3
| ~ spl17_47
| ~ spl17_118
| ~ spl17_373 ),
inference(avatar_split_clause,[],[f3607,f3555,f956,f413,f189,f3680,f3676,f184]) ).
fof(f3676,plain,
( spl17_384
<=> related(sK2,sK3,sK3) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_384])]) ).
fof(f3680,plain,
( spl17_385
<=> related(sK2,sK4,sK3) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_385])]) ).
fof(f413,plain,
( spl17_47
<=> in(sK3,the_carrier(sK2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_47])]) ).
fof(f3607,plain,
( ~ in(sK3,the_carrier(sK2))
| ~ element(sK3,the_carrier(sK2))
| ~ related(sK2,sK4,sK3)
| related(sK2,sK3,sK3)
| ~ rel_str(sK2)
| ~ spl17_118
| ~ spl17_373 ),
inference(duplicate_literal_removal,[],[f3595]) ).
fof(f3595,plain,
( ~ in(sK3,the_carrier(sK2))
| ~ element(sK3,the_carrier(sK2))
| ~ related(sK2,sK4,sK3)
| related(sK2,sK3,sK3)
| ~ element(sK3,the_carrier(sK2))
| ~ element(sK3,the_carrier(sK2))
| ~ rel_str(sK2)
| ~ spl17_118
| ~ spl17_373 ),
inference(resolution,[],[f3556,f957]) ).
fof(f3674,plain,
( spl17_383
| ~ spl17_59
| ~ spl17_207 ),
inference(avatar_split_clause,[],[f1699,f1686,f500,f3672]) ).
fof(f3672,plain,
( spl17_383
<=> ! [X0,X3,X2,X1] :
( in(unordered_pair(singleton(sK8(the_InternalRel(X0),X1)),unordered_pair(sK8(the_InternalRel(X0),X1),X2)),the_InternalRel(X0))
| ~ in(X2,X3)
| ~ in(sK9(the_InternalRel(X0),X1),X3)
| ~ in(sK8(the_InternalRel(X0),X1),X3)
| ~ sP0(the_InternalRel(X0),X3)
| ~ related(X0,sK9(the_InternalRel(X0),X1),X2)
| ~ element(X2,the_carrier(X0))
| ~ element(sK9(the_InternalRel(X0),X1),the_carrier(X0))
| ~ rel_str(X0)
| sP0(the_InternalRel(X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_383])]) ).
fof(f1699,plain,
( ! [X2,X3,X0,X1] :
( in(unordered_pair(singleton(sK8(the_InternalRel(X0),X1)),unordered_pair(sK8(the_InternalRel(X0),X1),X2)),the_InternalRel(X0))
| ~ in(X2,X3)
| ~ in(sK9(the_InternalRel(X0),X1),X3)
| ~ in(sK8(the_InternalRel(X0),X1),X3)
| ~ sP0(the_InternalRel(X0),X3)
| ~ related(X0,sK9(the_InternalRel(X0),X1),X2)
| ~ element(X2,the_carrier(X0))
| ~ element(sK9(the_InternalRel(X0),X1),the_carrier(X0))
| ~ rel_str(X0)
| sP0(the_InternalRel(X0),X1) )
| ~ spl17_59
| ~ spl17_207 ),
inference(resolution,[],[f1687,f501]) ).
fof(f3667,plain,
( spl17_382
| ~ spl17_60
| ~ spl17_206 ),
inference(avatar_split_clause,[],[f1692,f1682,f504,f3665]) ).
fof(f3665,plain,
( spl17_382
<=> ! [X0,X3,X2,X1] :
( in(unordered_pair(singleton(X0),unordered_pair(X0,sK8(the_InternalRel(X1),X2))),the_InternalRel(X1))
| ~ in(sK8(the_InternalRel(X1),X2),X3)
| ~ in(sK7(the_InternalRel(X1),X2),X3)
| ~ in(X0,X3)
| ~ sP0(the_InternalRel(X1),X3)
| ~ related(X1,X0,sK7(the_InternalRel(X1),X2))
| ~ element(sK7(the_InternalRel(X1),X2),the_carrier(X1))
| ~ element(X0,the_carrier(X1))
| ~ rel_str(X1)
| sP0(the_InternalRel(X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_382])]) ).
fof(f1692,plain,
( ! [X2,X3,X0,X1] :
( in(unordered_pair(singleton(X0),unordered_pair(X0,sK8(the_InternalRel(X1),X2))),the_InternalRel(X1))
| ~ in(sK8(the_InternalRel(X1),X2),X3)
| ~ in(sK7(the_InternalRel(X1),X2),X3)
| ~ in(X0,X3)
| ~ sP0(the_InternalRel(X1),X3)
| ~ related(X1,X0,sK7(the_InternalRel(X1),X2))
| ~ element(sK7(the_InternalRel(X1),X2),the_carrier(X1))
| ~ element(X0,the_carrier(X1))
| ~ rel_str(X1)
| sP0(the_InternalRel(X1),X2) )
| ~ spl17_60
| ~ spl17_206 ),
inference(resolution,[],[f1683,f505]) ).
fof(f3663,plain,
( spl17_381
| ~ spl17_59
| ~ spl17_206 ),
inference(avatar_split_clause,[],[f1691,f1682,f500,f3661]) ).
fof(f3661,plain,
( spl17_381
<=> ! [X0,X3,X2,X1] :
( in(unordered_pair(singleton(X0),unordered_pair(X0,sK9(the_InternalRel(X1),X2))),the_InternalRel(X1))
| ~ in(sK9(the_InternalRel(X1),X2),X3)
| ~ in(sK8(the_InternalRel(X1),X2),X3)
| ~ in(X0,X3)
| ~ sP0(the_InternalRel(X1),X3)
| ~ related(X1,X0,sK8(the_InternalRel(X1),X2))
| ~ element(sK8(the_InternalRel(X1),X2),the_carrier(X1))
| ~ element(X0,the_carrier(X1))
| ~ rel_str(X1)
| sP0(the_InternalRel(X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_381])]) ).
fof(f1691,plain,
( ! [X2,X3,X0,X1] :
( in(unordered_pair(singleton(X0),unordered_pair(X0,sK9(the_InternalRel(X1),X2))),the_InternalRel(X1))
| ~ in(sK9(the_InternalRel(X1),X2),X3)
| ~ in(sK8(the_InternalRel(X1),X2),X3)
| ~ in(X0,X3)
| ~ sP0(the_InternalRel(X1),X3)
| ~ related(X1,X0,sK8(the_InternalRel(X1),X2))
| ~ element(sK8(the_InternalRel(X1),X2),the_carrier(X1))
| ~ element(X0,the_carrier(X1))
| ~ rel_str(X1)
| sP0(the_InternalRel(X1),X2) )
| ~ spl17_59
| ~ spl17_206 ),
inference(resolution,[],[f1683,f501]) ).
fof(f3621,plain,
( spl17_380
| ~ spl17_30
| ~ spl17_209 ),
inference(avatar_split_clause,[],[f1723,f1710,f313,f3619]) ).
fof(f3619,plain,
( spl17_380
<=> ! [X5,X4,X0,X3,X2,X1] :
( ~ in(unordered_pair(singleton(X1),unordered_pair(X1,X0)),powerset(cartesian_product2(X2,X3)))
| in(unordered_pair(singleton(X4),unordered_pair(X4,X0)),powerset(cartesian_product2(X2,X3)))
| ~ in(X0,X5)
| ~ in(X1,X5)
| ~ in(X4,X5)
| ~ sP0(powerset(cartesian_product2(X2,X3)),X5)
| empty(powerset(cartesian_product2(X2,X3)))
| ~ relation_of2_as_subset(unordered_pair(singleton(X4),unordered_pair(X4,X1)),X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_380])]) ).
fof(f1723,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ in(unordered_pair(singleton(X1),unordered_pair(X1,X0)),powerset(cartesian_product2(X2,X3)))
| in(unordered_pair(singleton(X4),unordered_pair(X4,X0)),powerset(cartesian_product2(X2,X3)))
| ~ in(X0,X5)
| ~ in(X1,X5)
| ~ in(X4,X5)
| ~ sP0(powerset(cartesian_product2(X2,X3)),X5)
| empty(powerset(cartesian_product2(X2,X3)))
| ~ relation_of2_as_subset(unordered_pair(singleton(X4),unordered_pair(X4,X1)),X2,X3) )
| ~ spl17_30
| ~ spl17_209 ),
inference(superposition,[],[f1711,f314]) ).
fof(f3617,plain,
( spl17_379
| ~ spl17_30
| ~ spl17_208 ),
inference(avatar_split_clause,[],[f1715,f1706,f313,f3615]) ).
fof(f1706,plain,
( spl17_208
<=> ! [X5,X4,X0,X3,X2,X1] :
( empty(powerset(cartesian_product2(X0,X1)))
| ~ relation_of2_as_subset(unordered_pair(singleton(X2),unordered_pair(X2,X3)),X0,X1)
| ~ in(unordered_pair(singleton(X4),unordered_pair(X4,X2)),powerset(cartesian_product2(X0,X1)))
| in(unordered_pair(singleton(X4),unordered_pair(X4,X3)),powerset(cartesian_product2(X0,X1)))
| ~ in(X3,X5)
| ~ in(X2,X5)
| ~ in(X4,X5)
| ~ sP0(powerset(cartesian_product2(X0,X1)),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_208])]) ).
fof(f1715,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X1,X0)),powerset(cartesian_product2(X2,X3)))
| ~ relation_of2_as_subset(unordered_pair(singleton(X1),unordered_pair(X1,X4)),X2,X3)
| empty(powerset(cartesian_product2(X2,X3)))
| in(unordered_pair(singleton(X0),unordered_pair(X0,X4)),powerset(cartesian_product2(X2,X3)))
| ~ in(X4,X5)
| ~ in(X1,X5)
| ~ in(X0,X5)
| ~ sP0(powerset(cartesian_product2(X2,X3)),X5) )
| ~ spl17_30
| ~ spl17_208 ),
inference(superposition,[],[f1707,f314]) ).
fof(f1707,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ in(unordered_pair(singleton(X4),unordered_pair(X4,X2)),powerset(cartesian_product2(X0,X1)))
| ~ relation_of2_as_subset(unordered_pair(singleton(X2),unordered_pair(X2,X3)),X0,X1)
| empty(powerset(cartesian_product2(X0,X1)))
| in(unordered_pair(singleton(X4),unordered_pair(X4,X3)),powerset(cartesian_product2(X0,X1)))
| ~ in(X3,X5)
| ~ in(X2,X5)
| ~ in(X4,X5)
| ~ sP0(powerset(cartesian_product2(X0,X1)),X5) )
| ~ spl17_208 ),
inference(avatar_component_clause,[],[f1706]) ).
fof(f3587,plain,
( spl17_378
| ~ spl17_108
| ~ spl17_197 ),
inference(avatar_split_clause,[],[f1589,f1581,f864,f3585]) ).
fof(f1589,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X1,X0)),powerset(cartesian_product2(X2,X3)))
| in(unordered_pair(singleton(X0),unordered_pair(X0,X4)),powerset(cartesian_product2(X2,X3)))
| ~ in(X4,X5)
| ~ in(X1,X5)
| ~ in(X0,X5)
| ~ sP0(powerset(cartesian_product2(X2,X3)),X5)
| empty(powerset(cartesian_product2(X2,X3)))
| ~ relation_of2_as_subset(unordered_pair(singleton(X1),unordered_pair(X4,X1)),X2,X3) )
| ~ spl17_108
| ~ spl17_197 ),
inference(resolution,[],[f1582,f865]) ).
fof(f3575,plain,
( spl17_377
| ~ spl17_98
| ~ spl17_209 ),
inference(avatar_split_clause,[],[f1725,f1710,f788,f3573]) ).
fof(f3573,plain,
( spl17_377
<=> ! [X5,X4,X0,X3,X2,X1] :
( in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),powerset(cartesian_product2(X2,X3)))
| ~ in(X1,X4)
| ~ in(X5,X4)
| ~ in(X0,X4)
| ~ sP0(powerset(cartesian_product2(X2,X3)),X4)
| empty(powerset(cartesian_product2(X2,X3)))
| ~ relation_of2_as_subset(unordered_pair(singleton(X0),unordered_pair(X0,X5)),X2,X3)
| ~ subset(unordered_pair(singleton(X5),unordered_pair(X1,X5)),cartesian_product2(X2,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_377])]) ).
fof(f1725,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),powerset(cartesian_product2(X2,X3)))
| ~ in(X1,X4)
| ~ in(X5,X4)
| ~ in(X0,X4)
| ~ sP0(powerset(cartesian_product2(X2,X3)),X4)
| empty(powerset(cartesian_product2(X2,X3)))
| ~ relation_of2_as_subset(unordered_pair(singleton(X0),unordered_pair(X0,X5)),X2,X3)
| ~ subset(unordered_pair(singleton(X5),unordered_pair(X1,X5)),cartesian_product2(X2,X3)) )
| ~ spl17_98
| ~ spl17_209 ),
inference(duplicate_literal_removal,[],[f1720]) ).
fof(f1720,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),powerset(cartesian_product2(X2,X3)))
| ~ in(X1,X4)
| ~ in(X5,X4)
| ~ in(X0,X4)
| ~ sP0(powerset(cartesian_product2(X2,X3)),X4)
| empty(powerset(cartesian_product2(X2,X3)))
| ~ relation_of2_as_subset(unordered_pair(singleton(X0),unordered_pair(X0,X5)),X2,X3)
| empty(powerset(cartesian_product2(X2,X3)))
| ~ subset(unordered_pair(singleton(X5),unordered_pair(X1,X5)),cartesian_product2(X2,X3)) )
| ~ spl17_98
| ~ spl17_209 ),
inference(resolution,[],[f1711,f789]) ).
fof(f3571,plain,
( spl17_376
| ~ spl17_98
| ~ spl17_208 ),
inference(avatar_split_clause,[],[f1717,f1706,f788,f3569]) ).
fof(f1717,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ relation_of2_as_subset(unordered_pair(singleton(X0),unordered_pair(X0,X1)),X2,X3)
| empty(powerset(cartesian_product2(X2,X3)))
| in(unordered_pair(singleton(X4),unordered_pair(X4,X1)),powerset(cartesian_product2(X2,X3)))
| ~ in(X1,X5)
| ~ in(X0,X5)
| ~ in(X4,X5)
| ~ sP0(powerset(cartesian_product2(X2,X3)),X5)
| ~ subset(unordered_pair(singleton(X4),unordered_pair(X4,X0)),cartesian_product2(X2,X3)) )
| ~ spl17_98
| ~ spl17_208 ),
inference(duplicate_literal_removal,[],[f1714]) ).
fof(f1714,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ relation_of2_as_subset(unordered_pair(singleton(X0),unordered_pair(X0,X1)),X2,X3)
| empty(powerset(cartesian_product2(X2,X3)))
| in(unordered_pair(singleton(X4),unordered_pair(X4,X1)),powerset(cartesian_product2(X2,X3)))
| ~ in(X1,X5)
| ~ in(X0,X5)
| ~ in(X4,X5)
| ~ sP0(powerset(cartesian_product2(X2,X3)),X5)
| empty(powerset(cartesian_product2(X2,X3)))
| ~ subset(unordered_pair(singleton(X4),unordered_pair(X4,X0)),cartesian_product2(X2,X3)) )
| ~ spl17_98
| ~ spl17_208 ),
inference(resolution,[],[f1707,f789]) ).
fof(f3567,plain,
( spl17_375
| ~ spl17_108
| ~ spl17_203 ),
inference(avatar_split_clause,[],[f1665,f1650,f864,f3565]) ).
fof(f1665,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),powerset(cartesian_product2(X2,X3)))
| ~ in(X1,X4)
| ~ in(X5,X4)
| ~ in(X0,X4)
| ~ sP0(powerset(cartesian_product2(X2,X3)),X4)
| empty(powerset(cartesian_product2(X2,X3)))
| ~ subset(unordered_pair(singleton(X0),unordered_pair(X0,X5)),cartesian_product2(X2,X3))
| ~ relation_of2_as_subset(unordered_pair(singleton(X5),unordered_pair(X1,X5)),X2,X3) )
| ~ spl17_108
| ~ spl17_203 ),
inference(duplicate_literal_removal,[],[f1660]) ).
fof(f1660,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),powerset(cartesian_product2(X2,X3)))
| ~ in(X1,X4)
| ~ in(X5,X4)
| ~ in(X0,X4)
| ~ sP0(powerset(cartesian_product2(X2,X3)),X4)
| empty(powerset(cartesian_product2(X2,X3)))
| ~ subset(unordered_pair(singleton(X0),unordered_pair(X0,X5)),cartesian_product2(X2,X3))
| empty(powerset(cartesian_product2(X2,X3)))
| ~ relation_of2_as_subset(unordered_pair(singleton(X5),unordered_pair(X1,X5)),X2,X3) )
| ~ spl17_108
| ~ spl17_203 ),
inference(resolution,[],[f1651,f865]) ).
fof(f3563,plain,
( spl17_374
| ~ spl17_108
| ~ spl17_202 ),
inference(avatar_split_clause,[],[f1657,f1646,f864,f3561]) ).
fof(f3561,plain,
( spl17_374
<=> ! [X5,X4,X0,X3,X2,X1] :
( ~ subset(unordered_pair(singleton(X0),unordered_pair(X0,X1)),cartesian_product2(X2,X3))
| empty(powerset(cartesian_product2(X2,X3)))
| in(unordered_pair(singleton(X4),unordered_pair(X4,X1)),powerset(cartesian_product2(X2,X3)))
| ~ in(X1,X5)
| ~ in(X0,X5)
| ~ in(X4,X5)
| ~ sP0(powerset(cartesian_product2(X2,X3)),X5)
| ~ relation_of2_as_subset(unordered_pair(singleton(X4),unordered_pair(X4,X0)),X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_374])]) ).
fof(f1646,plain,
( spl17_202
<=> ! [X4,X0,X3,X2,X1] :
( empty(powerset(X0))
| ~ subset(unordered_pair(singleton(X1),unordered_pair(X1,X2)),X0)
| ~ in(unordered_pair(singleton(X3),unordered_pair(X3,X1)),powerset(X0))
| in(unordered_pair(singleton(X3),unordered_pair(X3,X2)),powerset(X0))
| ~ in(X2,X4)
| ~ in(X1,X4)
| ~ in(X3,X4)
| ~ sP0(powerset(X0),X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_202])]) ).
fof(f1657,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ subset(unordered_pair(singleton(X0),unordered_pair(X0,X1)),cartesian_product2(X2,X3))
| empty(powerset(cartesian_product2(X2,X3)))
| in(unordered_pair(singleton(X4),unordered_pair(X4,X1)),powerset(cartesian_product2(X2,X3)))
| ~ in(X1,X5)
| ~ in(X0,X5)
| ~ in(X4,X5)
| ~ sP0(powerset(cartesian_product2(X2,X3)),X5)
| ~ relation_of2_as_subset(unordered_pair(singleton(X4),unordered_pair(X4,X0)),X2,X3) )
| ~ spl17_108
| ~ spl17_202 ),
inference(duplicate_literal_removal,[],[f1654]) ).
fof(f1654,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ subset(unordered_pair(singleton(X0),unordered_pair(X0,X1)),cartesian_product2(X2,X3))
| empty(powerset(cartesian_product2(X2,X3)))
| in(unordered_pair(singleton(X4),unordered_pair(X4,X1)),powerset(cartesian_product2(X2,X3)))
| ~ in(X1,X5)
| ~ in(X0,X5)
| ~ in(X4,X5)
| ~ sP0(powerset(cartesian_product2(X2,X3)),X5)
| empty(powerset(cartesian_product2(X2,X3)))
| ~ relation_of2_as_subset(unordered_pair(singleton(X4),unordered_pair(X4,X0)),X2,X3) )
| ~ spl17_108
| ~ spl17_202 ),
inference(resolution,[],[f1647,f865]) ).
fof(f1647,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ in(unordered_pair(singleton(X3),unordered_pair(X3,X1)),powerset(X0))
| ~ subset(unordered_pair(singleton(X1),unordered_pair(X1,X2)),X0)
| empty(powerset(X0))
| in(unordered_pair(singleton(X3),unordered_pair(X3,X2)),powerset(X0))
| ~ in(X2,X4)
| ~ in(X1,X4)
| ~ in(X3,X4)
| ~ sP0(powerset(X0),X4) )
| ~ spl17_202 ),
inference(avatar_component_clause,[],[f1646]) ).
fof(f3557,plain,
( ~ spl17_159
| ~ spl17_1
| ~ spl17_3
| ~ spl17_2
| ~ spl17_4
| spl17_373
| ~ spl17_47
| ~ spl17_106
| ~ spl17_6
| ~ spl17_368 ),
inference(avatar_split_clause,[],[f3526,f3523,f204,f849,f413,f3555,f194,f184,f189,f179,f1219]) ).
fof(f3526,plain,
( ! [X0] :
( ~ in(sK4,the_carrier(sK2))
| ~ in(sK3,the_carrier(sK2))
| in(unordered_pair(singleton(sK3),unordered_pair(sK3,X0)),the_InternalRel(sK2))
| ~ related(sK2,sK4,X0)
| ~ element(X0,the_carrier(sK2))
| ~ element(sK4,the_carrier(sK2))
| ~ rel_str(sK2)
| ~ in(X0,the_carrier(sK2))
| ~ element(sK3,the_carrier(sK2))
| ~ transitive_relstr(sK2)
| ~ sP1(the_InternalRel(sK2)) )
| ~ spl17_6
| ~ spl17_368 ),
inference(resolution,[],[f3524,f206]) ).
fof(f3547,plain,
( spl17_372
| ~ spl17_108
| ~ spl17_209 ),
inference(avatar_split_clause,[],[f1726,f1710,f864,f3545]) ).
fof(f3545,plain,
( spl17_372
<=> ! [X5,X4,X0,X3,X2,X1] :
( in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),powerset(cartesian_product2(X2,X3)))
| ~ in(X1,X4)
| ~ in(X5,X4)
| ~ in(X0,X4)
| ~ sP0(powerset(cartesian_product2(X2,X3)),X4)
| empty(powerset(cartesian_product2(X2,X3)))
| ~ relation_of2_as_subset(unordered_pair(singleton(X0),unordered_pair(X0,X5)),X2,X3)
| ~ relation_of2_as_subset(unordered_pair(singleton(X5),unordered_pair(X1,X5)),X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_372])]) ).
fof(f1726,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),powerset(cartesian_product2(X2,X3)))
| ~ in(X1,X4)
| ~ in(X5,X4)
| ~ in(X0,X4)
| ~ sP0(powerset(cartesian_product2(X2,X3)),X4)
| empty(powerset(cartesian_product2(X2,X3)))
| ~ relation_of2_as_subset(unordered_pair(singleton(X0),unordered_pair(X0,X5)),X2,X3)
| ~ relation_of2_as_subset(unordered_pair(singleton(X5),unordered_pair(X1,X5)),X2,X3) )
| ~ spl17_108
| ~ spl17_209 ),
inference(duplicate_literal_removal,[],[f1719]) ).
fof(f1719,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),powerset(cartesian_product2(X2,X3)))
| ~ in(X1,X4)
| ~ in(X5,X4)
| ~ in(X0,X4)
| ~ sP0(powerset(cartesian_product2(X2,X3)),X4)
| empty(powerset(cartesian_product2(X2,X3)))
| ~ relation_of2_as_subset(unordered_pair(singleton(X0),unordered_pair(X0,X5)),X2,X3)
| empty(powerset(cartesian_product2(X2,X3)))
| ~ relation_of2_as_subset(unordered_pair(singleton(X5),unordered_pair(X1,X5)),X2,X3) )
| ~ spl17_108
| ~ spl17_209 ),
inference(resolution,[],[f1711,f865]) ).
fof(f3543,plain,
( spl17_371
| ~ spl17_108
| ~ spl17_208 ),
inference(avatar_split_clause,[],[f1718,f1706,f864,f3541]) ).
fof(f1718,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ relation_of2_as_subset(unordered_pair(singleton(X0),unordered_pair(X0,X1)),X2,X3)
| empty(powerset(cartesian_product2(X2,X3)))
| in(unordered_pair(singleton(X4),unordered_pair(X4,X1)),powerset(cartesian_product2(X2,X3)))
| ~ in(X1,X5)
| ~ in(X0,X5)
| ~ in(X4,X5)
| ~ sP0(powerset(cartesian_product2(X2,X3)),X5)
| ~ relation_of2_as_subset(unordered_pair(singleton(X4),unordered_pair(X4,X0)),X2,X3) )
| ~ spl17_108
| ~ spl17_208 ),
inference(duplicate_literal_removal,[],[f1713]) ).
fof(f1713,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ relation_of2_as_subset(unordered_pair(singleton(X0),unordered_pair(X0,X1)),X2,X3)
| empty(powerset(cartesian_product2(X2,X3)))
| in(unordered_pair(singleton(X4),unordered_pair(X4,X1)),powerset(cartesian_product2(X2,X3)))
| ~ in(X1,X5)
| ~ in(X0,X5)
| ~ in(X4,X5)
| ~ sP0(powerset(cartesian_product2(X2,X3)),X5)
| empty(powerset(cartesian_product2(X2,X3)))
| ~ relation_of2_as_subset(unordered_pair(singleton(X4),unordered_pair(X4,X0)),X2,X3) )
| ~ spl17_108
| ~ spl17_208 ),
inference(resolution,[],[f1707,f865]) ).
fof(f3539,plain,
( spl17_370
| ~ spl17_60
| ~ spl17_203 ),
inference(avatar_split_clause,[],[f1662,f1650,f504,f3537]) ).
fof(f3537,plain,
( spl17_370
<=> ! [X0,X3,X2,X1] :
( in(unordered_pair(singleton(X0),unordered_pair(X0,sK8(powerset(X1),X2))),powerset(X1))
| ~ in(sK8(powerset(X1),X2),X3)
| ~ in(sK7(powerset(X1),X2),X3)
| ~ in(X0,X3)
| ~ sP0(powerset(X1),X3)
| empty(powerset(X1))
| ~ subset(unordered_pair(singleton(X0),unordered_pair(X0,sK7(powerset(X1),X2))),X1)
| sP0(powerset(X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_370])]) ).
fof(f1662,plain,
( ! [X2,X3,X0,X1] :
( in(unordered_pair(singleton(X0),unordered_pair(X0,sK8(powerset(X1),X2))),powerset(X1))
| ~ in(sK8(powerset(X1),X2),X3)
| ~ in(sK7(powerset(X1),X2),X3)
| ~ in(X0,X3)
| ~ sP0(powerset(X1),X3)
| empty(powerset(X1))
| ~ subset(unordered_pair(singleton(X0),unordered_pair(X0,sK7(powerset(X1),X2))),X1)
| sP0(powerset(X1),X2) )
| ~ spl17_60
| ~ spl17_203 ),
inference(resolution,[],[f1651,f505]) ).
fof(f3535,plain,
( spl17_369
| ~ spl17_59
| ~ spl17_203 ),
inference(avatar_split_clause,[],[f1661,f1650,f500,f3533]) ).
fof(f3533,plain,
( spl17_369
<=> ! [X0,X3,X2,X1] :
( in(unordered_pair(singleton(X0),unordered_pair(X0,sK9(powerset(X1),X2))),powerset(X1))
| ~ in(sK9(powerset(X1),X2),X3)
| ~ in(sK8(powerset(X1),X2),X3)
| ~ in(X0,X3)
| ~ sP0(powerset(X1),X3)
| empty(powerset(X1))
| ~ subset(unordered_pair(singleton(X0),unordered_pair(X0,sK8(powerset(X1),X2))),X1)
| sP0(powerset(X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_369])]) ).
fof(f1661,plain,
( ! [X2,X3,X0,X1] :
( in(unordered_pair(singleton(X0),unordered_pair(X0,sK9(powerset(X1),X2))),powerset(X1))
| ~ in(sK9(powerset(X1),X2),X3)
| ~ in(sK8(powerset(X1),X2),X3)
| ~ in(X0,X3)
| ~ sP0(powerset(X1),X3)
| empty(powerset(X1))
| ~ subset(unordered_pair(singleton(X0),unordered_pair(X0,sK8(powerset(X1),X2))),X1)
| sP0(powerset(X1),X2) )
| ~ spl17_59
| ~ spl17_203 ),
inference(resolution,[],[f1651,f501]) ).
fof(f3525,plain,
( spl17_368
| ~ spl17_101
| ~ spl17_204 ),
inference(avatar_split_clause,[],[f1680,f1668,f809,f3523]) ).
fof(f1668,plain,
( spl17_204
<=> ! [X4,X0,X3,X2,X1] :
( in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),the_InternalRel(X2))
| ~ in(X1,X3)
| ~ in(X4,X3)
| ~ in(X0,X3)
| ~ sP0(the_InternalRel(X2),X3)
| ~ related(X2,X4,X1)
| ~ element(X1,the_carrier(X2))
| ~ element(X4,the_carrier(X2))
| ~ rel_str(X2)
| ~ related(X2,X0,X4)
| ~ element(X0,the_carrier(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_204])]) ).
fof(f1680,plain,
( ! [X2,X3,X0,X1] :
( ~ in(X0,the_carrier(X1))
| ~ in(X2,the_carrier(X1))
| ~ in(X3,the_carrier(X1))
| in(unordered_pair(singleton(X3),unordered_pair(X3,X0)),the_InternalRel(X1))
| ~ related(X1,X2,X0)
| ~ element(X0,the_carrier(X1))
| ~ element(X2,the_carrier(X1))
| ~ rel_str(X1)
| ~ related(X1,X3,X2)
| ~ element(X3,the_carrier(X1))
| ~ transitive_relstr(X1)
| ~ sP1(the_InternalRel(X1)) )
| ~ spl17_101
| ~ spl17_204 ),
inference(duplicate_literal_removal,[],[f1675]) ).
fof(f1675,plain,
( ! [X2,X3,X0,X1] :
( ~ in(X0,the_carrier(X1))
| ~ in(X2,the_carrier(X1))
| ~ in(X3,the_carrier(X1))
| in(unordered_pair(singleton(X3),unordered_pair(X3,X0)),the_InternalRel(X1))
| ~ related(X1,X2,X0)
| ~ element(X0,the_carrier(X1))
| ~ element(X2,the_carrier(X1))
| ~ rel_str(X1)
| ~ related(X1,X3,X2)
| ~ element(X3,the_carrier(X1))
| ~ rel_str(X1)
| ~ transitive_relstr(X1)
| ~ sP1(the_InternalRel(X1)) )
| ~ spl17_101
| ~ spl17_204 ),
inference(resolution,[],[f1669,f810]) ).
fof(f1669,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ sP0(the_InternalRel(X2),X3)
| ~ in(X1,X3)
| ~ in(X4,X3)
| ~ in(X0,X3)
| in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),the_InternalRel(X2))
| ~ related(X2,X4,X1)
| ~ element(X1,the_carrier(X2))
| ~ element(X4,the_carrier(X2))
| ~ rel_str(X2)
| ~ related(X2,X0,X4)
| ~ element(X0,the_carrier(X2)) )
| ~ spl17_204 ),
inference(avatar_component_clause,[],[f1668]) ).
fof(f3515,plain,
( spl17_367
| ~ spl17_25
| ~ spl17_239 ),
inference(avatar_split_clause,[],[f2010,f1925,f292,f3513]) ).
fof(f3513,plain,
( spl17_367
<=> ! [X0,X1] :
( sP0(X0,sK6(X1))
| empty(X1)
| ~ in(X1,sK7(X0,sK6(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_367])]) ).
fof(f2010,plain,
( ! [X0,X1] :
( sP0(X0,sK6(X1))
| empty(X1)
| ~ in(X1,sK7(X0,sK6(X1))) )
| ~ spl17_25
| ~ spl17_239 ),
inference(resolution,[],[f1926,f293]) ).
fof(f3511,plain,
( spl17_366
| ~ spl17_30
| ~ spl17_206 ),
inference(avatar_split_clause,[],[f1693,f1682,f313,f3509]) ).
fof(f3509,plain,
( spl17_366
<=> ! [X4,X0,X3,X2,X1] :
( ~ in(unordered_pair(singleton(X1),unordered_pair(X1,X0)),the_InternalRel(X2))
| in(unordered_pair(singleton(X3),unordered_pair(X3,X0)),the_InternalRel(X2))
| ~ in(X0,X4)
| ~ in(X1,X4)
| ~ in(X3,X4)
| ~ sP0(the_InternalRel(X2),X4)
| ~ related(X2,X3,X1)
| ~ element(X1,the_carrier(X2))
| ~ element(X3,the_carrier(X2))
| ~ rel_str(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_366])]) ).
fof(f1693,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ in(unordered_pair(singleton(X1),unordered_pair(X1,X0)),the_InternalRel(X2))
| in(unordered_pair(singleton(X3),unordered_pair(X3,X0)),the_InternalRel(X2))
| ~ in(X0,X4)
| ~ in(X1,X4)
| ~ in(X3,X4)
| ~ sP0(the_InternalRel(X2),X4)
| ~ related(X2,X3,X1)
| ~ element(X1,the_carrier(X2))
| ~ element(X3,the_carrier(X2))
| ~ rel_str(X2) )
| ~ spl17_30
| ~ spl17_206 ),
inference(superposition,[],[f1683,f314]) ).
fof(f3469,plain,
( spl17_365
| ~ spl17_30
| ~ spl17_203 ),
inference(avatar_split_clause,[],[f1663,f1650,f313,f3467]) ).
fof(f3467,plain,
( spl17_365
<=> ! [X4,X0,X3,X2,X1] :
( ~ in(unordered_pair(singleton(X1),unordered_pair(X1,X0)),powerset(X2))
| in(unordered_pair(singleton(X3),unordered_pair(X3,X0)),powerset(X2))
| ~ in(X0,X4)
| ~ in(X1,X4)
| ~ in(X3,X4)
| ~ sP0(powerset(X2),X4)
| empty(powerset(X2))
| ~ subset(unordered_pair(singleton(X3),unordered_pair(X3,X1)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_365])]) ).
fof(f1663,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ in(unordered_pair(singleton(X1),unordered_pair(X1,X0)),powerset(X2))
| in(unordered_pair(singleton(X3),unordered_pair(X3,X0)),powerset(X2))
| ~ in(X0,X4)
| ~ in(X1,X4)
| ~ in(X3,X4)
| ~ sP0(powerset(X2),X4)
| empty(powerset(X2))
| ~ subset(unordered_pair(singleton(X3),unordered_pair(X3,X1)),X2) )
| ~ spl17_30
| ~ spl17_203 ),
inference(superposition,[],[f1651,f314]) ).
fof(f3465,plain,
( spl17_364
| ~ spl17_30
| ~ spl17_202 ),
inference(avatar_split_clause,[],[f1655,f1646,f313,f3463]) ).
fof(f1655,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X1,X0)),powerset(X2))
| ~ subset(unordered_pair(singleton(X1),unordered_pair(X1,X3)),X2)
| empty(powerset(X2))
| in(unordered_pair(singleton(X0),unordered_pair(X0,X3)),powerset(X2))
| ~ in(X3,X4)
| ~ in(X1,X4)
| ~ in(X0,X4)
| ~ sP0(powerset(X2),X4) )
| ~ spl17_30
| ~ spl17_202 ),
inference(superposition,[],[f1647,f314]) ).
fof(f3461,plain,
( spl17_363
| ~ spl17_98
| ~ spl17_197 ),
inference(avatar_split_clause,[],[f1588,f1581,f788,f3459]) ).
fof(f1588,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X1,X0)),powerset(X2))
| in(unordered_pair(singleton(X0),unordered_pair(X0,X3)),powerset(X2))
| ~ in(X3,X4)
| ~ in(X1,X4)
| ~ in(X0,X4)
| ~ sP0(powerset(X2),X4)
| empty(powerset(X2))
| ~ subset(unordered_pair(singleton(X1),unordered_pair(X3,X1)),X2) )
| ~ spl17_98
| ~ spl17_197 ),
inference(resolution,[],[f1582,f789]) ).
fof(f3451,plain,
( spl17_362
| ~ spl17_98
| ~ spl17_203 ),
inference(avatar_split_clause,[],[f1666,f1650,f788,f3449]) ).
fof(f1666,plain,
( ! [X2,X3,X0,X1,X4] :
( in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),powerset(X2))
| ~ in(X1,X3)
| ~ in(X4,X3)
| ~ in(X0,X3)
| ~ sP0(powerset(X2),X3)
| empty(powerset(X2))
| ~ subset(unordered_pair(singleton(X0),unordered_pair(X0,X4)),X2)
| ~ subset(unordered_pair(singleton(X4),unordered_pair(X1,X4)),X2) )
| ~ spl17_98
| ~ spl17_203 ),
inference(duplicate_literal_removal,[],[f1659]) ).
fof(f1659,plain,
( ! [X2,X3,X0,X1,X4] :
( in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),powerset(X2))
| ~ in(X1,X3)
| ~ in(X4,X3)
| ~ in(X0,X3)
| ~ sP0(powerset(X2),X3)
| empty(powerset(X2))
| ~ subset(unordered_pair(singleton(X0),unordered_pair(X0,X4)),X2)
| empty(powerset(X2))
| ~ subset(unordered_pair(singleton(X4),unordered_pair(X1,X4)),X2) )
| ~ spl17_98
| ~ spl17_203 ),
inference(resolution,[],[f1651,f789]) ).
fof(f3447,plain,
( spl17_361
| ~ spl17_25
| ~ spl17_229 ),
inference(avatar_split_clause,[],[f1978,f1885,f292,f3445]) ).
fof(f3445,plain,
( spl17_361
<=> ! [X0] :
( empty(X0)
| empty(sK10(powerset(X0)))
| ~ in(X0,sK10(sK10(powerset(X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_361])]) ).
fof(f1978,plain,
( ! [X0] :
( empty(X0)
| empty(sK10(powerset(X0)))
| ~ in(X0,sK10(sK10(powerset(X0)))) )
| ~ spl17_25
| ~ spl17_229 ),
inference(resolution,[],[f1886,f293]) ).
fof(f3443,plain,
( spl17_360
| ~ spl17_98
| ~ spl17_202 ),
inference(avatar_split_clause,[],[f1658,f1646,f788,f3441]) ).
fof(f1658,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ subset(unordered_pair(singleton(X0),unordered_pair(X0,X1)),X2)
| empty(powerset(X2))
| in(unordered_pair(singleton(X3),unordered_pair(X3,X1)),powerset(X2))
| ~ in(X1,X4)
| ~ in(X0,X4)
| ~ in(X3,X4)
| ~ sP0(powerset(X2),X4)
| ~ subset(unordered_pair(singleton(X3),unordered_pair(X3,X0)),X2) )
| ~ spl17_98
| ~ spl17_202 ),
inference(duplicate_literal_removal,[],[f1653]) ).
fof(f1653,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ subset(unordered_pair(singleton(X0),unordered_pair(X0,X1)),X2)
| empty(powerset(X2))
| in(unordered_pair(singleton(X3),unordered_pair(X3,X1)),powerset(X2))
| ~ in(X1,X4)
| ~ in(X0,X4)
| ~ in(X3,X4)
| ~ sP0(powerset(X2),X4)
| empty(powerset(X2))
| ~ subset(unordered_pair(singleton(X3),unordered_pair(X3,X0)),X2) )
| ~ spl17_98
| ~ spl17_202 ),
inference(resolution,[],[f1647,f789]) ).
fof(f3409,plain,
( spl17_359
| ~ spl17_30
| ~ spl17_200 ),
inference(avatar_split_clause,[],[f1635,f1624,f313,f3407]) ).
fof(f1635,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ in(unordered_pair(singleton(X1),unordered_pair(X1,X0)),cartesian_product2(X2,X3))
| in(unordered_pair(singleton(X4),unordered_pair(X4,X0)),cartesian_product2(X2,X3))
| ~ in(X0,X5)
| ~ in(X1,X5)
| ~ in(X4,X5)
| ~ sP0(cartesian_product2(X2,X3),X5)
| ~ in(X1,X3)
| ~ in(X4,X2) )
| ~ spl17_30
| ~ spl17_200 ),
inference(superposition,[],[f1625,f314]) ).
fof(f3405,plain,
( spl17_358
| ~ spl17_38
| ~ spl17_188 ),
inference(avatar_split_clause,[],[f1532,f1511,f351,f3403]) ).
fof(f1532,plain,
( ! [X2,X0,X1] :
( element(sK9(X0,unordered_pair(singleton(sK7(powerset(X1),X2)),unordered_pair(sK8(powerset(X1),X2),sK7(powerset(X1),X2)))),X1)
| sP0(powerset(X1),X2)
| sP0(X0,unordered_pair(singleton(sK7(powerset(X1),X2)),unordered_pair(sK8(powerset(X1),X2),sK7(powerset(X1),X2)))) )
| ~ spl17_38
| ~ spl17_188 ),
inference(resolution,[],[f1512,f352]) ).
fof(f3401,plain,
( spl17_357
| ~ spl17_69
| ~ spl17_228 ),
inference(avatar_split_clause,[],[f1882,f1849,f567,f3399]) ).
fof(f3399,plain,
( spl17_357
<=> ! [X0,X1] :
( sP0(X0,powerset(X1))
| ~ empty(X1)
| sK16 = sK9(X0,powerset(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_357])]) ).
fof(f1882,plain,
( ! [X0,X1] :
( sP0(X0,powerset(X1))
| ~ empty(X1)
| sK16 = sK9(X0,powerset(X1)) )
| ~ spl17_69
| ~ spl17_228 ),
inference(resolution,[],[f1850,f568]) ).
fof(f3397,plain,
( spl17_356
| ~ spl17_37
| ~ spl17_188 ),
inference(avatar_split_clause,[],[f1530,f1511,f347,f3395]) ).
fof(f1530,plain,
( ! [X2,X0,X1] :
( element(sK8(X0,unordered_pair(singleton(sK7(powerset(X1),X2)),unordered_pair(sK8(powerset(X1),X2),sK7(powerset(X1),X2)))),X1)
| sP0(powerset(X1),X2)
| sP0(X0,unordered_pair(singleton(sK7(powerset(X1),X2)),unordered_pair(sK8(powerset(X1),X2),sK7(powerset(X1),X2)))) )
| ~ spl17_37
| ~ spl17_188 ),
inference(resolution,[],[f1512,f348]) ).
fof(f3393,plain,
( spl17_355
| ~ spl17_35
| ~ spl17_188 ),
inference(avatar_split_clause,[],[f1529,f1511,f339,f3391]) ).
fof(f1529,plain,
( ! [X2,X0,X1] :
( element(sK7(X0,unordered_pair(singleton(sK7(powerset(X1),X2)),unordered_pair(sK8(powerset(X1),X2),sK7(powerset(X1),X2)))),X1)
| sP0(powerset(X1),X2)
| sP0(X0,unordered_pair(singleton(sK7(powerset(X1),X2)),unordered_pair(sK8(powerset(X1),X2),sK7(powerset(X1),X2)))) )
| ~ spl17_35
| ~ spl17_188 ),
inference(resolution,[],[f1512,f340]) ).
fof(f3389,plain,
( spl17_354
| ~ spl17_38
| ~ spl17_187 ),
inference(avatar_split_clause,[],[f1522,f1507,f351,f3387]) ).
fof(f1522,plain,
( ! [X2,X0,X1] :
( element(sK9(X0,unordered_pair(singleton(sK8(powerset(X1),X2)),unordered_pair(sK9(powerset(X1),X2),sK8(powerset(X1),X2)))),X1)
| sP0(powerset(X1),X2)
| sP0(X0,unordered_pair(singleton(sK8(powerset(X1),X2)),unordered_pair(sK9(powerset(X1),X2),sK8(powerset(X1),X2)))) )
| ~ spl17_38
| ~ spl17_187 ),
inference(resolution,[],[f1508,f352]) ).
fof(f3385,plain,
( spl17_353
| ~ spl17_37
| ~ spl17_187 ),
inference(avatar_split_clause,[],[f1520,f1507,f347,f3383]) ).
fof(f1520,plain,
( ! [X2,X0,X1] :
( element(sK8(X0,unordered_pair(singleton(sK8(powerset(X1),X2)),unordered_pair(sK9(powerset(X1),X2),sK8(powerset(X1),X2)))),X1)
| sP0(powerset(X1),X2)
| sP0(X0,unordered_pair(singleton(sK8(powerset(X1),X2)),unordered_pair(sK9(powerset(X1),X2),sK8(powerset(X1),X2)))) )
| ~ spl17_37
| ~ spl17_187 ),
inference(resolution,[],[f1508,f348]) ).
fof(f3381,plain,
( spl17_352
| ~ spl17_35
| ~ spl17_187 ),
inference(avatar_split_clause,[],[f1519,f1507,f339,f3379]) ).
fof(f1519,plain,
( ! [X2,X0,X1] :
( element(sK7(X0,unordered_pair(singleton(sK8(powerset(X1),X2)),unordered_pair(sK9(powerset(X1),X2),sK8(powerset(X1),X2)))),X1)
| sP0(powerset(X1),X2)
| sP0(X0,unordered_pair(singleton(sK8(powerset(X1),X2)),unordered_pair(sK9(powerset(X1),X2),sK8(powerset(X1),X2)))) )
| ~ spl17_35
| ~ spl17_187 ),
inference(resolution,[],[f1508,f340]) ).
fof(f3350,plain,
( spl17_351
| ~ spl17_60
| ~ spl17_197 ),
inference(avatar_split_clause,[],[f1585,f1581,f504,f3348]) ).
fof(f1585,plain,
( ! [X2,X3,X0,X1] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(sK7(X1,X2),X0)),X1)
| in(unordered_pair(singleton(X0),unordered_pair(X0,sK8(X1,X2))),X1)
| ~ in(sK8(X1,X2),X3)
| ~ in(sK7(X1,X2),X3)
| ~ in(X0,X3)
| ~ sP0(X1,X3)
| sP0(X1,X2) )
| ~ spl17_60
| ~ spl17_197 ),
inference(resolution,[],[f1582,f505]) ).
fof(f3346,plain,
( spl17_350
| ~ spl17_59
| ~ spl17_197 ),
inference(avatar_split_clause,[],[f1584,f1581,f500,f3344]) ).
fof(f1584,plain,
( ! [X2,X3,X0,X1] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(sK8(X1,X2),X0)),X1)
| in(unordered_pair(singleton(X0),unordered_pair(X0,sK9(X1,X2))),X1)
| ~ in(sK9(X1,X2),X3)
| ~ in(sK8(X1,X2),X3)
| ~ in(X0,X3)
| ~ sP0(X1,X3)
| sP0(X1,X2) )
| ~ spl17_59
| ~ spl17_197 ),
inference(resolution,[],[f1582,f501]) ).
fof(f3324,plain,
( spl17_349
| ~ spl17_69
| ~ spl17_227 ),
inference(avatar_split_clause,[],[f1878,f1845,f567,f3322]) ).
fof(f3322,plain,
( spl17_349
<=> ! [X0,X1] :
( sP0(X0,powerset(X1))
| ~ empty(X1)
| sK16 = sK8(X0,powerset(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_349])]) ).
fof(f1878,plain,
( ! [X0,X1] :
( sP0(X0,powerset(X1))
| ~ empty(X1)
| sK16 = sK8(X0,powerset(X1)) )
| ~ spl17_69
| ~ spl17_227 ),
inference(resolution,[],[f1846,f568]) ).
fof(f3312,plain,
( spl17_348
| ~ spl17_64
| ~ spl17_197 ),
inference(avatar_split_clause,[],[f1594,f1581,f528,f3310]) ).
fof(f3310,plain,
( spl17_348
<=> ! [X0,X3,X2,X1] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X1,X0)),the_InternalRel(X2))
| in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),the_InternalRel(X2))
| ~ in(X1,X3)
| ~ in(X0,X3)
| ~ sP0(the_InternalRel(X2),X3)
| ~ related(X2,X1,X1)
| ~ element(X1,the_carrier(X2))
| ~ rel_str(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_348])]) ).
fof(f1594,plain,
( ! [X2,X3,X0,X1] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X1,X0)),the_InternalRel(X2))
| in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),the_InternalRel(X2))
| ~ in(X1,X3)
| ~ in(X0,X3)
| ~ sP0(the_InternalRel(X2),X3)
| ~ related(X2,X1,X1)
| ~ element(X1,the_carrier(X2))
| ~ rel_str(X2) )
| ~ spl17_64
| ~ spl17_197 ),
inference(duplicate_literal_removal,[],[f1590]) ).
fof(f1590,plain,
( ! [X2,X3,X0,X1] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X1,X0)),the_InternalRel(X2))
| in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),the_InternalRel(X2))
| ~ in(X1,X3)
| ~ in(X1,X3)
| ~ in(X0,X3)
| ~ sP0(the_InternalRel(X2),X3)
| ~ related(X2,X1,X1)
| ~ element(X1,the_carrier(X2))
| ~ element(X1,the_carrier(X2))
| ~ rel_str(X2) )
| ~ spl17_64
| ~ spl17_197 ),
inference(resolution,[],[f1582,f529]) ).
fof(f3308,plain,
( spl17_347
| ~ spl17_75
| ~ spl17_188 ),
inference(avatar_split_clause,[],[f1528,f1511,f643,f3306]) ).
fof(f1528,plain,
( ! [X0,X1] :
( element(sK10(unordered_pair(singleton(sK7(powerset(X0),X1)),unordered_pair(sK8(powerset(X0),X1),sK7(powerset(X0),X1)))),X0)
| sP0(powerset(X0),X1)
| empty(unordered_pair(singleton(sK7(powerset(X0),X1)),unordered_pair(sK8(powerset(X0),X1),sK7(powerset(X0),X1)))) )
| ~ spl17_75
| ~ spl17_188 ),
inference(resolution,[],[f1512,f644]) ).
fof(f3304,plain,
( spl17_346
| ~ spl17_75
| ~ spl17_187 ),
inference(avatar_split_clause,[],[f1518,f1507,f643,f3302]) ).
fof(f1518,plain,
( ! [X0,X1] :
( element(sK10(unordered_pair(singleton(sK8(powerset(X0),X1)),unordered_pair(sK9(powerset(X0),X1),sK8(powerset(X0),X1)))),X0)
| sP0(powerset(X0),X1)
| empty(unordered_pair(singleton(sK8(powerset(X0),X1)),unordered_pair(sK9(powerset(X0),X1),sK8(powerset(X0),X1)))) )
| ~ spl17_75
| ~ spl17_187 ),
inference(resolution,[],[f1508,f644]) ).
fof(f3280,plain,
( spl17_345
| ~ spl17_54
| ~ spl17_197 ),
inference(avatar_split_clause,[],[f1595,f1581,f467,f3278]) ).
fof(f467,plain,
( spl17_54
<=> ! [X0,X3,X2,X1] :
( in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),cartesian_product2(X2,X3))
| ~ in(X1,X3)
| ~ in(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_54])]) ).
fof(f1595,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X1,X0)),cartesian_product2(X2,X3))
| in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),cartesian_product2(X2,X3))
| ~ in(X1,X4)
| ~ in(X0,X4)
| ~ sP0(cartesian_product2(X2,X3),X4)
| ~ in(X1,X3)
| ~ in(X1,X2) )
| ~ spl17_54
| ~ spl17_197 ),
inference(duplicate_literal_removal,[],[f1586]) ).
fof(f1586,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X1,X0)),cartesian_product2(X2,X3))
| in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),cartesian_product2(X2,X3))
| ~ in(X1,X4)
| ~ in(X1,X4)
| ~ in(X0,X4)
| ~ sP0(cartesian_product2(X2,X3),X4)
| ~ in(X1,X3)
| ~ in(X1,X2) )
| ~ spl17_54
| ~ spl17_197 ),
inference(resolution,[],[f1582,f468]) ).
fof(f468,plain,
( ! [X2,X3,X0,X1] :
( in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),cartesian_product2(X2,X3))
| ~ in(X1,X3)
| ~ in(X0,X2) )
| ~ spl17_54 ),
inference(avatar_component_clause,[],[f467]) ).
fof(f3276,plain,
( spl17_344
| ~ spl17_41
| ~ spl17_180 ),
inference(avatar_split_clause,[],[f1469,f1444,f363,f3274]) ).
fof(f1444,plain,
( spl17_180
<=> ! [X0,X1] :
( element(unordered_pair(singleton(sK7(sK6(X0),X1)),unordered_pair(sK8(sK6(X0),X1),sK7(sK6(X0),X1))),X0)
| empty(X0)
| sP0(sK6(X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_180])]) ).
fof(f1469,plain,
( ! [X2,X0,X1] :
( empty(powerset(cartesian_product2(X0,X1)))
| sP0(sK6(powerset(cartesian_product2(X0,X1))),X2)
| relation(unordered_pair(singleton(sK7(sK6(powerset(cartesian_product2(X0,X1))),X2)),unordered_pair(sK8(sK6(powerset(cartesian_product2(X0,X1))),X2),sK7(sK6(powerset(cartesian_product2(X0,X1))),X2)))) )
| ~ spl17_41
| ~ spl17_180 ),
inference(resolution,[],[f1445,f364]) ).
fof(f1445,plain,
( ! [X0,X1] :
( element(unordered_pair(singleton(sK7(sK6(X0),X1)),unordered_pair(sK8(sK6(X0),X1),sK7(sK6(X0),X1))),X0)
| empty(X0)
| sP0(sK6(X0),X1) )
| ~ spl17_180 ),
inference(avatar_component_clause,[],[f1444]) ).
fof(f3272,plain,
( spl17_343
| ~ spl17_69
| ~ spl17_226 ),
inference(avatar_split_clause,[],[f1874,f1841,f567,f3270]) ).
fof(f3270,plain,
( spl17_343
<=> ! [X0,X1] :
( sP0(X0,powerset(X1))
| ~ empty(X1)
| sK16 = sK7(X0,powerset(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_343])]) ).
fof(f1874,plain,
( ! [X0,X1] :
( sP0(X0,powerset(X1))
| ~ empty(X1)
| sK16 = sK7(X0,powerset(X1)) )
| ~ spl17_69
| ~ spl17_226 ),
inference(resolution,[],[f1842,f568]) ).
fof(f3268,plain,
( spl17_342
| ~ spl17_41
| ~ spl17_179 ),
inference(avatar_split_clause,[],[f1464,f1440,f363,f3266]) ).
fof(f1440,plain,
( spl17_179
<=> ! [X0,X1] :
( element(unordered_pair(singleton(sK8(sK6(X0),X1)),unordered_pair(sK9(sK6(X0),X1),sK8(sK6(X0),X1))),X0)
| empty(X0)
| sP0(sK6(X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_179])]) ).
fof(f1464,plain,
( ! [X2,X0,X1] :
( empty(powerset(cartesian_product2(X0,X1)))
| sP0(sK6(powerset(cartesian_product2(X0,X1))),X2)
| relation(unordered_pair(singleton(sK8(sK6(powerset(cartesian_product2(X0,X1))),X2)),unordered_pair(sK9(sK6(powerset(cartesian_product2(X0,X1))),X2),sK8(sK6(powerset(cartesian_product2(X0,X1))),X2)))) )
| ~ spl17_41
| ~ spl17_179 ),
inference(resolution,[],[f1441,f364]) ).
fof(f1441,plain,
( ! [X0,X1] :
( element(unordered_pair(singleton(sK8(sK6(X0),X1)),unordered_pair(sK9(sK6(X0),X1),sK8(sK6(X0),X1))),X0)
| empty(X0)
| sP0(sK6(X0),X1) )
| ~ spl17_179 ),
inference(avatar_component_clause,[],[f1440]) ).
fof(f3245,plain,
( spl17_341
| ~ spl17_30
| ~ spl17_197 ),
inference(avatar_split_clause,[],[f1592,f1581,f313,f3243]) ).
fof(f1592,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ in(unordered_pair(singleton(X1),unordered_pair(X1,X0)),X2)
| ~ in(unordered_pair(singleton(X3),unordered_pair(X1,X3)),X2)
| in(unordered_pair(singleton(X3),unordered_pair(X3,X0)),X2)
| ~ in(X0,X4)
| ~ in(X1,X4)
| ~ in(X3,X4)
| ~ sP0(X2,X4) )
| ~ spl17_30
| ~ spl17_197 ),
inference(superposition,[],[f1582,f314]) ).
fof(f3241,plain,
( spl17_340
| ~ spl17_41
| ~ spl17_190 ),
inference(avatar_split_clause,[],[f1547,f1539,f363,f3239]) ).
fof(f1539,plain,
( spl17_190
<=> ! [X0,X1] :
( element(unordered_pair(singleton(sK7(sK10(powerset(X0)),X1)),unordered_pair(sK8(sK10(powerset(X0)),X1),sK7(sK10(powerset(X0)),X1))),X0)
| sP0(sK10(powerset(X0)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_190])]) ).
fof(f1547,plain,
( ! [X2,X0,X1] :
( sP0(sK10(powerset(powerset(cartesian_product2(X0,X1)))),X2)
| relation(unordered_pair(singleton(sK7(sK10(powerset(powerset(cartesian_product2(X0,X1)))),X2)),unordered_pair(sK8(sK10(powerset(powerset(cartesian_product2(X0,X1)))),X2),sK7(sK10(powerset(powerset(cartesian_product2(X0,X1)))),X2)))) )
| ~ spl17_41
| ~ spl17_190 ),
inference(resolution,[],[f1540,f364]) ).
fof(f1540,plain,
( ! [X0,X1] :
( element(unordered_pair(singleton(sK7(sK10(powerset(X0)),X1)),unordered_pair(sK8(sK10(powerset(X0)),X1),sK7(sK10(powerset(X0)),X1))),X0)
| sP0(sK10(powerset(X0)),X1) )
| ~ spl17_190 ),
inference(avatar_component_clause,[],[f1539]) ).
fof(f3237,plain,
( spl17_339
| ~ spl17_41
| ~ spl17_189 ),
inference(avatar_split_clause,[],[f1543,f1535,f363,f3235]) ).
fof(f1535,plain,
( spl17_189
<=> ! [X0,X1] :
( element(unordered_pair(singleton(sK8(sK10(powerset(X0)),X1)),unordered_pair(sK9(sK10(powerset(X0)),X1),sK8(sK10(powerset(X0)),X1))),X0)
| sP0(sK10(powerset(X0)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_189])]) ).
fof(f1543,plain,
( ! [X2,X0,X1] :
( sP0(sK10(powerset(powerset(cartesian_product2(X0,X1)))),X2)
| relation(unordered_pair(singleton(sK8(sK10(powerset(powerset(cartesian_product2(X0,X1)))),X2)),unordered_pair(sK9(sK10(powerset(powerset(cartesian_product2(X0,X1)))),X2),sK8(sK10(powerset(powerset(cartesian_product2(X0,X1)))),X2)))) )
| ~ spl17_41
| ~ spl17_189 ),
inference(resolution,[],[f1536,f364]) ).
fof(f1536,plain,
( ! [X0,X1] :
( element(unordered_pair(singleton(sK8(sK10(powerset(X0)),X1)),unordered_pair(sK9(sK10(powerset(X0)),X1),sK8(sK10(powerset(X0)),X1))),X0)
| sP0(sK10(powerset(X0)),X1) )
| ~ spl17_189 ),
inference(avatar_component_clause,[],[f1535]) ).
fof(f3194,plain,
( spl17_338
| ~ spl17_60
| ~ spl17_171 ),
inference(avatar_split_clause,[],[f1396,f1361,f504,f3192]) ).
fof(f1396,plain,
( ! [X2,X0,X1] :
( element(unordered_pair(singleton(sK7(sK9(X0,powerset(X1)),X2)),unordered_pair(sK8(sK9(X0,powerset(X1)),X2),sK7(sK9(X0,powerset(X1)),X2))),X1)
| sP0(X0,powerset(X1))
| sP0(sK9(X0,powerset(X1)),X2) )
| ~ spl17_60
| ~ spl17_171 ),
inference(resolution,[],[f1362,f505]) ).
fof(f3190,plain,
( spl17_337
| ~ spl17_59
| ~ spl17_171 ),
inference(avatar_split_clause,[],[f1395,f1361,f500,f3188]) ).
fof(f1395,plain,
( ! [X2,X0,X1] :
( element(unordered_pair(singleton(sK8(sK9(X0,powerset(X1)),X2)),unordered_pair(sK9(sK9(X0,powerset(X1)),X2),sK8(sK9(X0,powerset(X1)),X2))),X1)
| sP0(X0,powerset(X1))
| sP0(sK9(X0,powerset(X1)),X2) )
| ~ spl17_59
| ~ spl17_171 ),
inference(resolution,[],[f1362,f501]) ).
fof(f3186,plain,
( spl17_336
| ~ spl17_60
| ~ spl17_169 ),
inference(avatar_split_clause,[],[f1381,f1353,f504,f3184]) ).
fof(f1381,plain,
( ! [X2,X0,X1] :
( element(unordered_pair(singleton(sK7(sK8(X0,powerset(X1)),X2)),unordered_pair(sK8(sK8(X0,powerset(X1)),X2),sK7(sK8(X0,powerset(X1)),X2))),X1)
| sP0(X0,powerset(X1))
| sP0(sK8(X0,powerset(X1)),X2) )
| ~ spl17_60
| ~ spl17_169 ),
inference(resolution,[],[f1354,f505]) ).
fof(f3182,plain,
( spl17_335
| ~ spl17_59
| ~ spl17_169 ),
inference(avatar_split_clause,[],[f1380,f1353,f500,f3180]) ).
fof(f1380,plain,
( ! [X2,X0,X1] :
( element(unordered_pair(singleton(sK8(sK8(X0,powerset(X1)),X2)),unordered_pair(sK9(sK8(X0,powerset(X1)),X2),sK8(sK8(X0,powerset(X1)),X2))),X1)
| sP0(X0,powerset(X1))
| sP0(sK8(X0,powerset(X1)),X2) )
| ~ spl17_59
| ~ spl17_169 ),
inference(resolution,[],[f1354,f501]) ).
fof(f3178,plain,
( spl17_334
| ~ spl17_60
| ~ spl17_167 ),
inference(avatar_split_clause,[],[f1370,f1345,f504,f3176]) ).
fof(f1370,plain,
( ! [X2,X0,X1] :
( element(unordered_pair(singleton(sK7(sK7(X0,powerset(X1)),X2)),unordered_pair(sK8(sK7(X0,powerset(X1)),X2),sK7(sK7(X0,powerset(X1)),X2))),X1)
| sP0(X0,powerset(X1))
| sP0(sK7(X0,powerset(X1)),X2) )
| ~ spl17_60
| ~ spl17_167 ),
inference(resolution,[],[f1346,f505]) ).
fof(f3174,plain,
( spl17_333
| ~ spl17_59
| ~ spl17_167 ),
inference(avatar_split_clause,[],[f1369,f1345,f500,f3172]) ).
fof(f1369,plain,
( ! [X2,X0,X1] :
( element(unordered_pair(singleton(sK8(sK7(X0,powerset(X1)),X2)),unordered_pair(sK9(sK7(X0,powerset(X1)),X2),sK8(sK7(X0,powerset(X1)),X2))),X1)
| sP0(X0,powerset(X1))
| sP0(sK7(X0,powerset(X1)),X2) )
| ~ spl17_59
| ~ spl17_167 ),
inference(resolution,[],[f1346,f501]) ).
fof(f3132,plain,
( spl17_332
| ~ spl17_51
| ~ spl17_190 ),
inference(avatar_split_clause,[],[f1549,f1539,f439,f3130]) ).
fof(f1549,plain,
( ! [X2,X0,X1] :
( sP0(sK10(powerset(powerset(X0))),X1)
| element(X2,X0)
| ~ in(X2,unordered_pair(singleton(sK7(sK10(powerset(powerset(X0))),X1)),unordered_pair(sK8(sK10(powerset(powerset(X0))),X1),sK7(sK10(powerset(powerset(X0))),X1)))) )
| ~ spl17_51
| ~ spl17_190 ),
inference(resolution,[],[f1540,f440]) ).
fof(f3128,plain,
( spl17_331
| ~ spl17_51
| ~ spl17_189 ),
inference(avatar_split_clause,[],[f1545,f1535,f439,f3126]) ).
fof(f1545,plain,
( ! [X2,X0,X1] :
( sP0(sK10(powerset(powerset(X0))),X1)
| element(X2,X0)
| ~ in(X2,unordered_pair(singleton(sK8(sK10(powerset(powerset(X0))),X1)),unordered_pair(sK9(sK10(powerset(powerset(X0))),X1),sK8(sK10(powerset(powerset(X0))),X1)))) )
| ~ spl17_51
| ~ spl17_189 ),
inference(resolution,[],[f1536,f440]) ).
fof(f3052,plain,
( spl17_330
| ~ spl17_49
| ~ spl17_190 ),
inference(avatar_split_clause,[],[f1548,f1539,f422,f3050]) ).
fof(f1548,plain,
( ! [X2,X0,X1] :
( sP0(sK10(powerset(powerset(X0))),X1)
| ~ empty(X0)
| ~ in(X2,unordered_pair(singleton(sK7(sK10(powerset(powerset(X0))),X1)),unordered_pair(sK8(sK10(powerset(powerset(X0))),X1),sK7(sK10(powerset(powerset(X0))),X1)))) )
| ~ spl17_49
| ~ spl17_190 ),
inference(resolution,[],[f1540,f423]) ).
fof(f3048,plain,
( spl17_329
| ~ spl17_49
| ~ spl17_189 ),
inference(avatar_split_clause,[],[f1544,f1535,f422,f3046]) ).
fof(f1544,plain,
( ! [X2,X0,X1] :
( sP0(sK10(powerset(powerset(X0))),X1)
| ~ empty(X0)
| ~ in(X2,unordered_pair(singleton(sK8(sK10(powerset(powerset(X0))),X1)),unordered_pair(sK9(sK10(powerset(powerset(X0))),X1),sK8(sK10(powerset(powerset(X0))),X1)))) )
| ~ spl17_49
| ~ spl17_189 ),
inference(resolution,[],[f1536,f423]) ).
fof(f3044,plain,
( spl17_328
| ~ spl17_51
| ~ spl17_180 ),
inference(avatar_split_clause,[],[f1471,f1444,f439,f3042]) ).
fof(f1471,plain,
( ! [X2,X0,X1] :
( empty(powerset(X0))
| sP0(sK6(powerset(X0)),X1)
| element(X2,X0)
| ~ in(X2,unordered_pair(singleton(sK7(sK6(powerset(X0)),X1)),unordered_pair(sK8(sK6(powerset(X0)),X1),sK7(sK6(powerset(X0)),X1)))) )
| ~ spl17_51
| ~ spl17_180 ),
inference(resolution,[],[f1445,f440]) ).
fof(f3040,plain,
( spl17_327
| ~ spl17_34
| ~ spl17_316 ),
inference(avatar_split_clause,[],[f2930,f2853,f335,f3038]) ).
fof(f3038,plain,
( spl17_327
<=> ! [X0,X1] :
( ~ empty(X0)
| is_transitive_in(powerset(X0),X1)
| ~ sP1(powerset(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_327])]) ).
fof(f2853,plain,
( spl17_316
<=> ! [X0,X1] :
( sP0(powerset(X0),X1)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_316])]) ).
fof(f2930,plain,
( ! [X0,X1] :
( ~ empty(X0)
| is_transitive_in(powerset(X0),X1)
| ~ sP1(powerset(X0)) )
| ~ spl17_34
| ~ spl17_316 ),
inference(resolution,[],[f2854,f336]) ).
fof(f2854,plain,
( ! [X0,X1] :
( sP0(powerset(X0),X1)
| ~ empty(X0) )
| ~ spl17_316 ),
inference(avatar_component_clause,[],[f2853]) ).
fof(f3036,plain,
( spl17_326
| ~ spl17_51
| ~ spl17_179 ),
inference(avatar_split_clause,[],[f1466,f1440,f439,f3034]) ).
fof(f1466,plain,
( ! [X2,X0,X1] :
( empty(powerset(X0))
| sP0(sK6(powerset(X0)),X1)
| element(X2,X0)
| ~ in(X2,unordered_pair(singleton(sK8(sK6(powerset(X0)),X1)),unordered_pair(sK9(sK6(powerset(X0)),X1),sK8(sK6(powerset(X0)),X1)))) )
| ~ spl17_51
| ~ spl17_179 ),
inference(resolution,[],[f1441,f440]) ).
fof(f2996,plain,
( spl17_325
| ~ spl17_49
| ~ spl17_180 ),
inference(avatar_split_clause,[],[f1470,f1444,f422,f2994]) ).
fof(f1470,plain,
( ! [X2,X0,X1] :
( empty(powerset(X0))
| sP0(sK6(powerset(X0)),X1)
| ~ empty(X0)
| ~ in(X2,unordered_pair(singleton(sK7(sK6(powerset(X0)),X1)),unordered_pair(sK8(sK6(powerset(X0)),X1),sK7(sK6(powerset(X0)),X1)))) )
| ~ spl17_49
| ~ spl17_180 ),
inference(resolution,[],[f1445,f423]) ).
fof(f2992,plain,
( spl17_324
| ~ spl17_49
| ~ spl17_179 ),
inference(avatar_split_clause,[],[f1465,f1440,f422,f2990]) ).
fof(f1465,plain,
( ! [X2,X0,X1] :
( empty(powerset(X0))
| sP0(sK6(powerset(X0)),X1)
| ~ empty(X0)
| ~ in(X2,unordered_pair(singleton(sK8(sK6(powerset(X0)),X1)),unordered_pair(sK9(sK6(powerset(X0)),X1),sK8(sK6(powerset(X0)),X1)))) )
| ~ spl17_49
| ~ spl17_179 ),
inference(resolution,[],[f1441,f423]) ).
fof(f2988,plain,
( spl17_323
| ~ spl17_17
| ~ spl17_192 ),
inference(avatar_split_clause,[],[f1559,f1555,f255,f2986]) ).
fof(f2986,plain,
( spl17_323
<=> ! [X2,X0,X1] :
( sP0(powerset(cartesian_product2(X0,X1)),X2)
| sP1(unordered_pair(singleton(sK7(powerset(cartesian_product2(X0,X1)),X2)),unordered_pair(sK8(powerset(cartesian_product2(X0,X1)),X2),sK7(powerset(cartesian_product2(X0,X1)),X2)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_323])]) ).
fof(f1555,plain,
( spl17_192
<=> ! [X2,X0,X1] :
( sP0(powerset(cartesian_product2(X0,X1)),X2)
| relation(unordered_pair(singleton(sK7(powerset(cartesian_product2(X0,X1)),X2)),unordered_pair(sK8(powerset(cartesian_product2(X0,X1)),X2),sK7(powerset(cartesian_product2(X0,X1)),X2)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_192])]) ).
fof(f1559,plain,
( ! [X2,X0,X1] :
( sP0(powerset(cartesian_product2(X0,X1)),X2)
| sP1(unordered_pair(singleton(sK7(powerset(cartesian_product2(X0,X1)),X2)),unordered_pair(sK8(powerset(cartesian_product2(X0,X1)),X2),sK7(powerset(cartesian_product2(X0,X1)),X2)))) )
| ~ spl17_17
| ~ spl17_192 ),
inference(resolution,[],[f1556,f256]) ).
fof(f1556,plain,
( ! [X2,X0,X1] :
( relation(unordered_pair(singleton(sK7(powerset(cartesian_product2(X0,X1)),X2)),unordered_pair(sK8(powerset(cartesian_product2(X0,X1)),X2),sK7(powerset(cartesian_product2(X0,X1)),X2))))
| sP0(powerset(cartesian_product2(X0,X1)),X2) )
| ~ spl17_192 ),
inference(avatar_component_clause,[],[f1555]) ).
fof(f2984,plain,
( spl17_322
| ~ spl17_17
| ~ spl17_191 ),
inference(avatar_split_clause,[],[f1558,f1551,f255,f2982]) ).
fof(f2982,plain,
( spl17_322
<=> ! [X2,X0,X1] :
( sP0(powerset(cartesian_product2(X0,X1)),X2)
| sP1(unordered_pair(singleton(sK8(powerset(cartesian_product2(X0,X1)),X2)),unordered_pair(sK9(powerset(cartesian_product2(X0,X1)),X2),sK8(powerset(cartesian_product2(X0,X1)),X2)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_322])]) ).
fof(f1551,plain,
( spl17_191
<=> ! [X2,X0,X1] :
( sP0(powerset(cartesian_product2(X0,X1)),X2)
| relation(unordered_pair(singleton(sK8(powerset(cartesian_product2(X0,X1)),X2)),unordered_pair(sK9(powerset(cartesian_product2(X0,X1)),X2),sK8(powerset(cartesian_product2(X0,X1)),X2)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_191])]) ).
fof(f1558,plain,
( ! [X2,X0,X1] :
( sP0(powerset(cartesian_product2(X0,X1)),X2)
| sP1(unordered_pair(singleton(sK8(powerset(cartesian_product2(X0,X1)),X2)),unordered_pair(sK9(powerset(cartesian_product2(X0,X1)),X2),sK8(powerset(cartesian_product2(X0,X1)),X2)))) )
| ~ spl17_17
| ~ spl17_191 ),
inference(resolution,[],[f1552,f256]) ).
fof(f1552,plain,
( ! [X2,X0,X1] :
( relation(unordered_pair(singleton(sK8(powerset(cartesian_product2(X0,X1)),X2)),unordered_pair(sK9(powerset(cartesian_product2(X0,X1)),X2),sK8(powerset(cartesian_product2(X0,X1)),X2))))
| sP0(powerset(cartesian_product2(X0,X1)),X2) )
| ~ spl17_191 ),
inference(avatar_component_clause,[],[f1551]) ).
fof(f2875,plain,
( spl17_321
| ~ spl17_39
| ~ spl17_190 ),
inference(avatar_split_clause,[],[f1546,f1539,f355,f2873]) ).
fof(f1546,plain,
( ! [X0,X1] :
( sP0(sK10(powerset(X0)),X1)
| empty(X0)
| in(unordered_pair(singleton(sK7(sK10(powerset(X0)),X1)),unordered_pair(sK8(sK10(powerset(X0)),X1),sK7(sK10(powerset(X0)),X1))),X0) )
| ~ spl17_39
| ~ spl17_190 ),
inference(resolution,[],[f1540,f356]) ).
fof(f2871,plain,
( spl17_320
| ~ spl17_39
| ~ spl17_189 ),
inference(avatar_split_clause,[],[f1542,f1535,f355,f2869]) ).
fof(f1542,plain,
( ! [X0,X1] :
( sP0(sK10(powerset(X0)),X1)
| empty(X0)
| in(unordered_pair(singleton(sK8(sK10(powerset(X0)),X1)),unordered_pair(sK9(sK10(powerset(X0)),X1),sK8(sK10(powerset(X0)),X1))),X0) )
| ~ spl17_39
| ~ spl17_189 ),
inference(resolution,[],[f1536,f356]) ).
fof(f2867,plain,
( spl17_319
| ~ spl17_60
| ~ spl17_151 ),
inference(avatar_split_clause,[],[f1185,f1163,f504,f2865]) ).
fof(f1185,plain,
( ! [X2,X0,X1] :
( element(unordered_pair(singleton(sK7(sK12(X0,X1),X2)),unordered_pair(sK8(sK12(X0,X1),X2),sK7(sK12(X0,X1),X2))),cartesian_product2(X0,X1))
| sP0(sK12(X0,X1),X2) )
| ~ spl17_60
| ~ spl17_151 ),
inference(resolution,[],[f1164,f505]) ).
fof(f2863,plain,
( spl17_318
| ~ spl17_59
| ~ spl17_151 ),
inference(avatar_split_clause,[],[f1184,f1163,f500,f2861]) ).
fof(f1184,plain,
( ! [X2,X0,X1] :
( element(unordered_pair(singleton(sK8(sK12(X0,X1),X2)),unordered_pair(sK9(sK12(X0,X1),X2),sK8(sK12(X0,X1),X2))),cartesian_product2(X0,X1))
| sP0(sK12(X0,X1),X2) )
| ~ spl17_59
| ~ spl17_151 ),
inference(resolution,[],[f1164,f501]) ).
fof(f2859,plain,
( spl17_317
| ~ spl17_60
| ~ spl17_150 ),
inference(avatar_split_clause,[],[f1179,f1159,f504,f2857]) ).
fof(f1179,plain,
( ! [X2,X0,X1] :
( element(unordered_pair(singleton(sK7(sK13(X0,X1),X2)),unordered_pair(sK8(sK13(X0,X1),X2),sK7(sK13(X0,X1),X2))),cartesian_product2(X0,X1))
| sP0(sK13(X0,X1),X2) )
| ~ spl17_60
| ~ spl17_150 ),
inference(resolution,[],[f1160,f505]) ).
fof(f2855,plain,
( spl17_316
| ~ spl17_19
| ~ spl17_308 ),
inference(avatar_split_clause,[],[f2718,f2707,f263,f2853]) ).
fof(f2707,plain,
( spl17_308
<=> ! [X0,X1] :
( ~ empty(X0)
| sP0(powerset(X0),X1)
| empty(unordered_pair(singleton(sK8(powerset(X0),X1)),unordered_pair(sK9(powerset(X0),X1),sK8(powerset(X0),X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_308])]) ).
fof(f2718,plain,
( ! [X0,X1] :
( sP0(powerset(X0),X1)
| ~ empty(X0) )
| ~ spl17_19
| ~ spl17_308 ),
inference(resolution,[],[f2708,f264]) ).
fof(f2708,plain,
( ! [X0,X1] :
( empty(unordered_pair(singleton(sK8(powerset(X0),X1)),unordered_pair(sK9(powerset(X0),X1),sK8(powerset(X0),X1))))
| sP0(powerset(X0),X1)
| ~ empty(X0) )
| ~ spl17_308 ),
inference(avatar_component_clause,[],[f2707]) ).
fof(f2851,plain,
( spl17_315
| ~ spl17_59
| ~ spl17_150 ),
inference(avatar_split_clause,[],[f1178,f1159,f500,f2849]) ).
fof(f1178,plain,
( ! [X2,X0,X1] :
( element(unordered_pair(singleton(sK8(sK13(X0,X1),X2)),unordered_pair(sK9(sK13(X0,X1),X2),sK8(sK13(X0,X1),X2))),cartesian_product2(X0,X1))
| sP0(sK13(X0,X1),X2) )
| ~ spl17_59
| ~ spl17_150 ),
inference(resolution,[],[f1160,f501]) ).
fof(f2838,plain,
( spl17_314
| ~ spl17_64
| ~ spl17_199 ),
inference(avatar_split_clause,[],[f1620,f1610,f528,f2836]) ).
fof(f1610,plain,
( spl17_199
<=> ! [X0,X3,X2,X1] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X1,X0)),the_InternalRel(X2))
| in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),the_InternalRel(X2))
| ~ in(X1,X3)
| ~ in(X0,X3)
| ~ sP0(the_InternalRel(X2),X3)
| ~ related(X2,X0,X0)
| ~ element(X0,the_carrier(X2))
| ~ rel_str(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_199])]) ).
fof(f1620,plain,
( ! [X2,X0,X1] :
( in(unordered_pair(singleton(X0),unordered_pair(X0,X0)),the_InternalRel(X1))
| ~ in(X0,X2)
| ~ sP0(the_InternalRel(X1),X2)
| ~ related(X1,X0,X0)
| ~ element(X0,the_carrier(X1))
| ~ rel_str(X1) )
| ~ spl17_64
| ~ spl17_199 ),
inference(duplicate_literal_removal,[],[f1613]) ).
fof(f1613,plain,
( ! [X2,X0,X1] :
( in(unordered_pair(singleton(X0),unordered_pair(X0,X0)),the_InternalRel(X1))
| ~ in(X0,X2)
| ~ in(X0,X2)
| ~ sP0(the_InternalRel(X1),X2)
| ~ related(X1,X0,X0)
| ~ element(X0,the_carrier(X1))
| ~ rel_str(X1)
| ~ related(X1,X0,X0)
| ~ element(X0,the_carrier(X1))
| ~ element(X0,the_carrier(X1))
| ~ rel_str(X1) )
| ~ spl17_64
| ~ spl17_199 ),
inference(resolution,[],[f1611,f529]) ).
fof(f1611,plain,
( ! [X2,X3,X0,X1] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X1,X0)),the_InternalRel(X2))
| in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),the_InternalRel(X2))
| ~ in(X1,X3)
| ~ in(X0,X3)
| ~ sP0(the_InternalRel(X2),X3)
| ~ related(X2,X0,X0)
| ~ element(X0,the_carrier(X2))
| ~ rel_str(X2) )
| ~ spl17_199 ),
inference(avatar_component_clause,[],[f1610]) ).
fof(f2834,plain,
( spl17_313
| ~ spl17_108
| ~ spl17_174 ),
inference(avatar_split_clause,[],[f1411,f1407,f864,f2832]) ).
fof(f2832,plain,
( spl17_313
<=> ! [X0,X3,X2,X1] :
( ~ relation_of2_as_subset(powerset(cartesian_product2(X0,X1)),X2,X3)
| empty(powerset(cartesian_product2(X2,X3)))
| empty(powerset(cartesian_product2(X0,X1)))
| ~ relation_of2_as_subset(powerset(cartesian_product2(X2,X3)),X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_313])]) ).
fof(f1411,plain,
( ! [X2,X3,X0,X1] :
( ~ relation_of2_as_subset(powerset(cartesian_product2(X0,X1)),X2,X3)
| empty(powerset(cartesian_product2(X2,X3)))
| empty(powerset(cartesian_product2(X0,X1)))
| ~ relation_of2_as_subset(powerset(cartesian_product2(X2,X3)),X0,X1) )
| ~ spl17_108
| ~ spl17_174 ),
inference(resolution,[],[f1408,f865]) ).
fof(f2732,plain,
( spl17_312
| ~ spl17_39
| ~ spl17_180 ),
inference(avatar_split_clause,[],[f1472,f1444,f355,f2730]) ).
fof(f1472,plain,
( ! [X0,X1] :
( empty(X0)
| sP0(sK6(X0),X1)
| in(unordered_pair(singleton(sK7(sK6(X0),X1)),unordered_pair(sK8(sK6(X0),X1),sK7(sK6(X0),X1))),X0) )
| ~ spl17_39
| ~ spl17_180 ),
inference(duplicate_literal_removal,[],[f1468]) ).
fof(f1468,plain,
( ! [X0,X1] :
( empty(X0)
| sP0(sK6(X0),X1)
| empty(X0)
| in(unordered_pair(singleton(sK7(sK6(X0),X1)),unordered_pair(sK8(sK6(X0),X1),sK7(sK6(X0),X1))),X0) )
| ~ spl17_39
| ~ spl17_180 ),
inference(resolution,[],[f1445,f356]) ).
fof(f2728,plain,
( spl17_311
| ~ spl17_39
| ~ spl17_179 ),
inference(avatar_split_clause,[],[f1467,f1440,f355,f2726]) ).
fof(f1467,plain,
( ! [X0,X1] :
( empty(X0)
| sP0(sK6(X0),X1)
| in(unordered_pair(singleton(sK8(sK6(X0),X1)),unordered_pair(sK9(sK6(X0),X1),sK8(sK6(X0),X1))),X0) )
| ~ spl17_39
| ~ spl17_179 ),
inference(duplicate_literal_removal,[],[f1463]) ).
fof(f1463,plain,
( ! [X0,X1] :
( empty(X0)
| sP0(sK6(X0),X1)
| empty(X0)
| in(unordered_pair(singleton(sK8(sK6(X0),X1)),unordered_pair(sK9(sK6(X0),X1),sK8(sK6(X0),X1))),X0) )
| ~ spl17_39
| ~ spl17_179 ),
inference(resolution,[],[f1441,f356]) ).
fof(f2717,plain,
( spl17_310
| ~ spl17_140
| ~ spl17_267 ),
inference(avatar_split_clause,[],[f2280,f2168,f1107,f2715]) ).
fof(f2715,plain,
( spl17_310
<=> ! [X0] :
( sK16 = sK10(powerset(sK10(powerset(sK10(powerset(X0))))))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_310])]) ).
fof(f1107,plain,
( spl17_140
<=> ! [X0] :
( ~ empty(X0)
| empty(sK10(powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_140])]) ).
fof(f2168,plain,
( spl17_267
<=> ! [X0] :
( sK16 = sK10(powerset(sK10(powerset(X0))))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_267])]) ).
fof(f2280,plain,
( ! [X0] :
( sK16 = sK10(powerset(sK10(powerset(sK10(powerset(X0))))))
| ~ empty(X0) )
| ~ spl17_140
| ~ spl17_267 ),
inference(resolution,[],[f2169,f1108]) ).
fof(f1108,plain,
( ! [X0] :
( empty(sK10(powerset(X0)))
| ~ empty(X0) )
| ~ spl17_140 ),
inference(avatar_component_clause,[],[f1107]) ).
fof(f2169,plain,
( ! [X0] :
( ~ empty(X0)
| sK16 = sK10(powerset(sK10(powerset(X0)))) )
| ~ spl17_267 ),
inference(avatar_component_clause,[],[f2168]) ).
fof(f2713,plain,
( spl17_309
| ~ spl17_75
| ~ spl17_182 ),
inference(avatar_split_clause,[],[f1491,f1452,f643,f2711]) ).
fof(f2711,plain,
( spl17_309
<=> ! [X0,X1] :
( ~ empty(X0)
| sP0(powerset(X0),X1)
| empty(unordered_pair(singleton(sK7(powerset(X0),X1)),unordered_pair(sK8(powerset(X0),X1),sK7(powerset(X0),X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_309])]) ).
fof(f1452,plain,
( spl17_182
<=> ! [X2,X0,X1] :
( sP0(powerset(X0),X1)
| ~ empty(X0)
| ~ in(X2,unordered_pair(singleton(sK7(powerset(X0),X1)),unordered_pair(sK8(powerset(X0),X1),sK7(powerset(X0),X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_182])]) ).
fof(f1491,plain,
( ! [X0,X1] :
( ~ empty(X0)
| sP0(powerset(X0),X1)
| empty(unordered_pair(singleton(sK7(powerset(X0),X1)),unordered_pair(sK8(powerset(X0),X1),sK7(powerset(X0),X1)))) )
| ~ spl17_75
| ~ spl17_182 ),
inference(resolution,[],[f1453,f644]) ).
fof(f1453,plain,
( ! [X2,X0,X1] :
( ~ in(X2,unordered_pair(singleton(sK7(powerset(X0),X1)),unordered_pair(sK8(powerset(X0),X1),sK7(powerset(X0),X1))))
| ~ empty(X0)
| sP0(powerset(X0),X1) )
| ~ spl17_182 ),
inference(avatar_component_clause,[],[f1452]) ).
fof(f2709,plain,
( spl17_308
| ~ spl17_75
| ~ spl17_181 ),
inference(avatar_split_clause,[],[f1477,f1448,f643,f2707]) ).
fof(f1448,plain,
( spl17_181
<=> ! [X2,X0,X1] :
( sP0(powerset(X0),X1)
| ~ empty(X0)
| ~ in(X2,unordered_pair(singleton(sK8(powerset(X0),X1)),unordered_pair(sK9(powerset(X0),X1),sK8(powerset(X0),X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_181])]) ).
fof(f1477,plain,
( ! [X0,X1] :
( ~ empty(X0)
| sP0(powerset(X0),X1)
| empty(unordered_pair(singleton(sK8(powerset(X0),X1)),unordered_pair(sK9(powerset(X0),X1),sK8(powerset(X0),X1)))) )
| ~ spl17_75
| ~ spl17_181 ),
inference(resolution,[],[f1449,f644]) ).
fof(f1449,plain,
( ! [X2,X0,X1] :
( ~ in(X2,unordered_pair(singleton(sK8(powerset(X0),X1)),unordered_pair(sK9(powerset(X0),X1),sK8(powerset(X0),X1))))
| ~ empty(X0)
| sP0(powerset(X0),X1) )
| ~ spl17_181 ),
inference(avatar_component_clause,[],[f1448]) ).
fof(f2702,plain,
( spl17_307
| ~ spl17_41
| ~ spl17_161 ),
inference(avatar_split_clause,[],[f1288,f1228,f363,f2700]) ).
fof(f1228,plain,
( spl17_161
<=> ! [X0,X1] :
( element(sK9(X0,sK6(X1)),X1)
| empty(X1)
| sP0(X0,sK6(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_161])]) ).
fof(f1288,plain,
( ! [X2,X0,X1] :
( empty(powerset(cartesian_product2(X0,X1)))
| sP0(X2,sK6(powerset(cartesian_product2(X0,X1))))
| relation(sK9(X2,sK6(powerset(cartesian_product2(X0,X1))))) )
| ~ spl17_41
| ~ spl17_161 ),
inference(resolution,[],[f1229,f364]) ).
fof(f1229,plain,
( ! [X0,X1] :
( element(sK9(X0,sK6(X1)),X1)
| empty(X1)
| sP0(X0,sK6(X1)) )
| ~ spl17_161 ),
inference(avatar_component_clause,[],[f1228]) ).
fof(f2698,plain,
( spl17_306
| ~ spl17_41
| ~ spl17_160 ),
inference(avatar_split_clause,[],[f1283,f1224,f363,f2696]) ).
fof(f1224,plain,
( spl17_160
<=> ! [X0,X1] :
( element(sK8(X0,sK6(X1)),X1)
| empty(X1)
| sP0(X0,sK6(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_160])]) ).
fof(f1283,plain,
( ! [X2,X0,X1] :
( empty(powerset(cartesian_product2(X0,X1)))
| sP0(X2,sK6(powerset(cartesian_product2(X0,X1))))
| relation(sK8(X2,sK6(powerset(cartesian_product2(X0,X1))))) )
| ~ spl17_41
| ~ spl17_160 ),
inference(resolution,[],[f1225,f364]) ).
fof(f1225,plain,
( ! [X0,X1] :
( element(sK8(X0,sK6(X1)),X1)
| empty(X1)
| sP0(X0,sK6(X1)) )
| ~ spl17_160 ),
inference(avatar_component_clause,[],[f1224]) ).
fof(f2694,plain,
( spl17_305
| ~ spl17_41
| ~ spl17_158 ),
inference(avatar_split_clause,[],[f1278,f1215,f363,f2692]) ).
fof(f1215,plain,
( spl17_158
<=> ! [X0,X1] :
( element(sK7(X0,sK6(X1)),X1)
| empty(X1)
| sP0(X0,sK6(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_158])]) ).
fof(f1278,plain,
( ! [X2,X0,X1] :
( empty(powerset(cartesian_product2(X0,X1)))
| sP0(X2,sK6(powerset(cartesian_product2(X0,X1))))
| relation(sK7(X2,sK6(powerset(cartesian_product2(X0,X1))))) )
| ~ spl17_41
| ~ spl17_158 ),
inference(resolution,[],[f1216,f364]) ).
fof(f1216,plain,
( ! [X0,X1] :
( element(sK7(X0,sK6(X1)),X1)
| empty(X1)
| sP0(X0,sK6(X1)) )
| ~ spl17_158 ),
inference(avatar_component_clause,[],[f1215]) ).
fof(f2659,plain,
( spl17_304
| ~ spl17_39
| ~ spl17_172 ),
inference(avatar_split_clause,[],[f1405,f1365,f355,f2657]) ).
fof(f1365,plain,
( spl17_172
<=> ! [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,[spl17_172])]) ).
fof(f1405,plain,
( ! [X0,X1] :
( ~ in(X0,the_InternalRel(X1))
| ~ rel_str(X1)
| empty(cartesian_product2(the_carrier(X1),the_carrier(X1)))
| in(X0,cartesian_product2(the_carrier(X1),the_carrier(X1))) )
| ~ spl17_39
| ~ spl17_172 ),
inference(resolution,[],[f1366,f356]) ).
fof(f1366,plain,
( ! [X0,X1] :
( element(X0,cartesian_product2(the_carrier(X1),the_carrier(X1)))
| ~ in(X0,the_InternalRel(X1))
| ~ rel_str(X1) )
| ~ spl17_172 ),
inference(avatar_component_clause,[],[f1365]) ).
fof(f2655,plain,
( spl17_303
| ~ spl17_108
| ~ spl17_149 ),
inference(avatar_split_clause,[],[f1177,f1155,f864,f2653]) ).
fof(f1177,plain,
( ! [X2,X0,X1] :
( ~ subset(powerset(cartesian_product2(X0,X1)),X2)
| empty(powerset(X2))
| empty(powerset(cartesian_product2(X0,X1)))
| ~ relation_of2_as_subset(powerset(X2),X0,X1) )
| ~ spl17_108
| ~ spl17_149 ),
inference(resolution,[],[f1156,f865]) ).
fof(f2619,plain,
( spl17_302
| ~ spl17_140
| ~ spl17_217 ),
inference(avatar_split_clause,[],[f1785,f1769,f1107,f2617]) ).
fof(f2617,plain,
( spl17_302
<=> ! [X0,X1] :
( sK10(powerset(X0)) = sK10(powerset(X1))
| ~ empty(X0)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_302])]) ).
fof(f1785,plain,
( ! [X0,X1] :
( sK10(powerset(X0)) = sK10(powerset(X1))
| ~ empty(X0)
| ~ empty(X1) )
| ~ spl17_140
| ~ spl17_217 ),
inference(resolution,[],[f1770,f1108]) ).
fof(f2568,plain,
( spl17_301
| ~ spl17_38
| ~ spl17_171 ),
inference(avatar_split_clause,[],[f1403,f1361,f351,f2566]) ).
fof(f1403,plain,
( ! [X2,X0,X1] :
( element(sK9(X0,sK9(X1,powerset(X2))),X2)
| sP0(X1,powerset(X2))
| sP0(X0,sK9(X1,powerset(X2))) )
| ~ spl17_38
| ~ spl17_171 ),
inference(resolution,[],[f1362,f352]) ).
fof(f2564,plain,
( spl17_300
| ~ spl17_37
| ~ spl17_171 ),
inference(avatar_split_clause,[],[f1401,f1361,f347,f2562]) ).
fof(f1401,plain,
( ! [X2,X0,X1] :
( element(sK8(X0,sK9(X1,powerset(X2))),X2)
| sP0(X1,powerset(X2))
| sP0(X0,sK9(X1,powerset(X2))) )
| ~ spl17_37
| ~ spl17_171 ),
inference(resolution,[],[f1362,f348]) ).
fof(f2560,plain,
( spl17_299
| ~ spl17_35
| ~ spl17_171 ),
inference(avatar_split_clause,[],[f1400,f1361,f339,f2558]) ).
fof(f1400,plain,
( ! [X2,X0,X1] :
( element(sK7(X0,sK9(X1,powerset(X2))),X2)
| sP0(X1,powerset(X2))
| sP0(X0,sK9(X1,powerset(X2))) )
| ~ spl17_35
| ~ spl17_171 ),
inference(resolution,[],[f1362,f340]) ).
fof(f2556,plain,
( spl17_298
| ~ spl17_38
| ~ spl17_169 ),
inference(avatar_split_clause,[],[f1388,f1353,f351,f2554]) ).
fof(f1388,plain,
( ! [X2,X0,X1] :
( element(sK9(X0,sK8(X1,powerset(X2))),X2)
| sP0(X1,powerset(X2))
| sP0(X0,sK8(X1,powerset(X2))) )
| ~ spl17_38
| ~ spl17_169 ),
inference(resolution,[],[f1354,f352]) ).
fof(f2552,plain,
( spl17_297
| ~ spl17_37
| ~ spl17_169 ),
inference(avatar_split_clause,[],[f1386,f1353,f347,f2550]) ).
fof(f1386,plain,
( ! [X2,X0,X1] :
( element(sK8(X0,sK8(X1,powerset(X2))),X2)
| sP0(X1,powerset(X2))
| sP0(X0,sK8(X1,powerset(X2))) )
| ~ spl17_37
| ~ spl17_169 ),
inference(resolution,[],[f1354,f348]) ).
fof(f2548,plain,
( spl17_296
| ~ spl17_35
| ~ spl17_169 ),
inference(avatar_split_clause,[],[f1385,f1353,f339,f2546]) ).
fof(f1385,plain,
( ! [X2,X0,X1] :
( element(sK7(X0,sK8(X1,powerset(X2))),X2)
| sP0(X1,powerset(X2))
| sP0(X0,sK8(X1,powerset(X2))) )
| ~ spl17_35
| ~ spl17_169 ),
inference(resolution,[],[f1354,f340]) ).
fof(f2544,plain,
( spl17_295
| ~ spl17_38
| ~ spl17_167 ),
inference(avatar_split_clause,[],[f1377,f1345,f351,f2542]) ).
fof(f1377,plain,
( ! [X2,X0,X1] :
( element(sK9(X0,sK7(X1,powerset(X2))),X2)
| sP0(X1,powerset(X2))
| sP0(X0,sK7(X1,powerset(X2))) )
| ~ spl17_38
| ~ spl17_167 ),
inference(resolution,[],[f1346,f352]) ).
fof(f2540,plain,
( spl17_294
| ~ spl17_37
| ~ spl17_167 ),
inference(avatar_split_clause,[],[f1375,f1345,f347,f2538]) ).
fof(f1375,plain,
( ! [X2,X0,X1] :
( element(sK8(X0,sK7(X1,powerset(X2))),X2)
| sP0(X1,powerset(X2))
| sP0(X0,sK7(X1,powerset(X2))) )
| ~ spl17_37
| ~ spl17_167 ),
inference(resolution,[],[f1346,f348]) ).
fof(f2536,plain,
( spl17_293
| ~ spl17_35
| ~ spl17_167 ),
inference(avatar_split_clause,[],[f1374,f1345,f339,f2534]) ).
fof(f1374,plain,
( ! [X2,X0,X1] :
( element(sK7(X0,sK7(X1,powerset(X2))),X2)
| sP0(X1,powerset(X2))
| sP0(X0,sK7(X1,powerset(X2))) )
| ~ spl17_35
| ~ spl17_167 ),
inference(resolution,[],[f1346,f340]) ).
fof(f2532,plain,
( spl17_292
| ~ spl17_51
| ~ spl17_161 ),
inference(avatar_split_clause,[],[f1290,f1228,f439,f2530]) ).
fof(f1290,plain,
( ! [X2,X0,X1] :
( empty(powerset(X0))
| sP0(X1,sK6(powerset(X0)))
| element(X2,X0)
| ~ in(X2,sK9(X1,sK6(powerset(X0)))) )
| ~ spl17_51
| ~ spl17_161 ),
inference(resolution,[],[f1229,f440]) ).
fof(f2528,plain,
( spl17_291
| ~ spl17_51
| ~ spl17_160 ),
inference(avatar_split_clause,[],[f1285,f1224,f439,f2526]) ).
fof(f1285,plain,
( ! [X2,X0,X1] :
( empty(powerset(X0))
| sP0(X1,sK6(powerset(X0)))
| element(X2,X0)
| ~ in(X2,sK8(X1,sK6(powerset(X0)))) )
| ~ spl17_51
| ~ spl17_160 ),
inference(resolution,[],[f1225,f440]) ).
fof(f2524,plain,
( spl17_290
| ~ spl17_51
| ~ spl17_158 ),
inference(avatar_split_clause,[],[f1280,f1215,f439,f2522]) ).
fof(f1280,plain,
( ! [X2,X0,X1] :
( empty(powerset(X0))
| sP0(X1,sK6(powerset(X0)))
| element(X2,X0)
| ~ in(X2,sK7(X1,sK6(powerset(X0)))) )
| ~ spl17_51
| ~ spl17_158 ),
inference(resolution,[],[f1216,f440]) ).
fof(f2520,plain,
( spl17_289
| ~ spl17_41
| ~ spl17_147 ),
inference(avatar_split_clause,[],[f1171,f1147,f363,f2518]) ).
fof(f1171,plain,
( ! [X0,X1] :
( empty(powerset(cartesian_product2(X0,X1)))
| empty(sK6(powerset(cartesian_product2(X0,X1))))
| relation(sK10(sK6(powerset(cartesian_product2(X0,X1))))) )
| ~ spl17_41
| ~ spl17_147 ),
inference(resolution,[],[f1148,f364]) ).
fof(f2488,plain,
( spl17_288
| ~ spl17_25
| ~ spl17_224 ),
inference(avatar_split_clause,[],[f1819,f1808,f292,f2486]) ).
fof(f2486,plain,
( spl17_288
<=> ! [X0] :
( empty(sK6(X0))
| empty(X0)
| ~ in(X0,sK10(sK6(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_288])]) ).
fof(f1819,plain,
( ! [X0] :
( empty(sK6(X0))
| empty(X0)
| ~ in(X0,sK10(sK6(X0))) )
| ~ spl17_25
| ~ spl17_224 ),
inference(resolution,[],[f1809,f293]) ).
fof(f2425,plain,
( spl17_287
| ~ spl17_49
| ~ spl17_161 ),
inference(avatar_split_clause,[],[f1289,f1228,f422,f2423]) ).
fof(f1289,plain,
( ! [X2,X0,X1] :
( empty(powerset(X0))
| sP0(X1,sK6(powerset(X0)))
| ~ empty(X0)
| ~ in(X2,sK9(X1,sK6(powerset(X0)))) )
| ~ spl17_49
| ~ spl17_161 ),
inference(resolution,[],[f1229,f423]) ).
fof(f2421,plain,
( spl17_286
| ~ spl17_49
| ~ spl17_160 ),
inference(avatar_split_clause,[],[f1284,f1224,f422,f2419]) ).
fof(f1284,plain,
( ! [X2,X0,X1] :
( empty(powerset(X0))
| sP0(X1,sK6(powerset(X0)))
| ~ empty(X0)
| ~ in(X2,sK8(X1,sK6(powerset(X0)))) )
| ~ spl17_49
| ~ spl17_160 ),
inference(resolution,[],[f1225,f423]) ).
fof(f2417,plain,
( spl17_285
| ~ spl17_49
| ~ spl17_158 ),
inference(avatar_split_clause,[],[f1279,f1215,f422,f2415]) ).
fof(f1279,plain,
( ! [X2,X0,X1] :
( empty(powerset(X0))
| sP0(X1,sK6(powerset(X0)))
| ~ empty(X0)
| ~ in(X2,sK7(X1,sK6(powerset(X0)))) )
| ~ spl17_49
| ~ spl17_158 ),
inference(resolution,[],[f1216,f423]) ).
fof(f2411,plain,
( spl17_284
| ~ spl17_51
| ~ spl17_157 ),
inference(avatar_split_clause,[],[f1276,f1211,f439,f2409]) ).
fof(f1276,plain,
( ! [X2,X0,X1] :
( sP0(X0,sK10(powerset(powerset(X1))))
| element(X2,X1)
| ~ in(X2,sK9(X0,sK10(powerset(powerset(X1))))) )
| ~ spl17_51
| ~ spl17_157 ),
inference(resolution,[],[f1212,f440]) ).
fof(f2407,plain,
( spl17_283
| ~ spl17_41
| ~ spl17_157 ),
inference(avatar_split_clause,[],[f1274,f1211,f363,f2405]) ).
fof(f1274,plain,
( ! [X2,X0,X1] :
( sP0(X0,sK10(powerset(powerset(cartesian_product2(X1,X2)))))
| relation(sK9(X0,sK10(powerset(powerset(cartesian_product2(X1,X2)))))) )
| ~ spl17_41
| ~ spl17_157 ),
inference(resolution,[],[f1212,f364]) ).
fof(f2403,plain,
( spl17_282
| ~ spl17_51
| ~ spl17_156 ),
inference(avatar_split_clause,[],[f1272,f1207,f439,f2401]) ).
fof(f1272,plain,
( ! [X2,X0,X1] :
( sP0(X0,sK10(powerset(powerset(X1))))
| element(X2,X1)
| ~ in(X2,sK8(X0,sK10(powerset(powerset(X1))))) )
| ~ spl17_51
| ~ spl17_156 ),
inference(resolution,[],[f1208,f440]) ).
fof(f2399,plain,
( spl17_281
| ~ spl17_41
| ~ spl17_156 ),
inference(avatar_split_clause,[],[f1270,f1207,f363,f2397]) ).
fof(f1270,plain,
( ! [X2,X0,X1] :
( sP0(X0,sK10(powerset(powerset(cartesian_product2(X1,X2)))))
| relation(sK8(X0,sK10(powerset(powerset(cartesian_product2(X1,X2)))))) )
| ~ spl17_41
| ~ spl17_156 ),
inference(resolution,[],[f1208,f364]) ).
fof(f2395,plain,
( spl17_280
| ~ spl17_51
| ~ spl17_155 ),
inference(avatar_split_clause,[],[f1268,f1203,f439,f2393]) ).
fof(f1268,plain,
( ! [X2,X0,X1] :
( sP0(X0,sK10(powerset(powerset(X1))))
| element(X2,X1)
| ~ in(X2,sK7(X0,sK10(powerset(powerset(X1))))) )
| ~ spl17_51
| ~ spl17_155 ),
inference(resolution,[],[f1204,f440]) ).
fof(f2391,plain,
( spl17_279
| ~ spl17_41
| ~ spl17_155 ),
inference(avatar_split_clause,[],[f1266,f1203,f363,f2389]) ).
fof(f1266,plain,
( ! [X2,X0,X1] :
( sP0(X0,sK10(powerset(powerset(cartesian_product2(X1,X2)))))
| relation(sK7(X0,sK10(powerset(powerset(cartesian_product2(X1,X2)))))) )
| ~ spl17_41
| ~ spl17_155 ),
inference(resolution,[],[f1204,f364]) ).
fof(f2361,plain,
( spl17_278
| ~ spl17_34
| ~ spl17_255 ),
inference(avatar_split_clause,[],[f2137,f2102,f335,f2359]) ).
fof(f2359,plain,
( spl17_278
<=> ! [X2,X0,X1] :
( is_transitive_in(cartesian_product2(X0,X1),X2)
| ~ sP1(cartesian_product2(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_278])]) ).
fof(f2102,plain,
( spl17_255
<=> ! [X2,X0,X1] : sP0(cartesian_product2(X0,X1),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_255])]) ).
fof(f2137,plain,
( ! [X2,X0,X1] :
( is_transitive_in(cartesian_product2(X0,X1),X2)
| ~ sP1(cartesian_product2(X0,X1)) )
| ~ spl17_34
| ~ spl17_255 ),
inference(resolution,[],[f2103,f336]) ).
fof(f2103,plain,
( ! [X2,X0,X1] : sP0(cartesian_product2(X0,X1),X2)
| ~ spl17_255 ),
inference(avatar_component_clause,[],[f2102]) ).
fof(f2315,plain,
( spl17_277
| ~ spl17_75
| ~ spl17_171 ),
inference(avatar_split_clause,[],[f1399,f1361,f643,f2313]) ).
fof(f1399,plain,
( ! [X0,X1] :
( element(sK10(sK9(X0,powerset(X1))),X1)
| sP0(X0,powerset(X1))
| empty(sK9(X0,powerset(X1))) )
| ~ spl17_75
| ~ spl17_171 ),
inference(resolution,[],[f1362,f644]) ).
fof(f2311,plain,
( spl17_276
| ~ spl17_75
| ~ spl17_169 ),
inference(avatar_split_clause,[],[f1384,f1353,f643,f2309]) ).
fof(f1384,plain,
( ! [X0,X1] :
( element(sK10(sK8(X0,powerset(X1))),X1)
| sP0(X0,powerset(X1))
| empty(sK8(X0,powerset(X1))) )
| ~ spl17_75
| ~ spl17_169 ),
inference(resolution,[],[f1354,f644]) ).
fof(f2307,plain,
( spl17_275
| ~ spl17_75
| ~ spl17_167 ),
inference(avatar_split_clause,[],[f1373,f1345,f643,f2305]) ).
fof(f1373,plain,
( ! [X0,X1] :
( element(sK10(sK7(X0,powerset(X1))),X1)
| sP0(X0,powerset(X1))
| empty(sK7(X0,powerset(X1))) )
| ~ spl17_75
| ~ spl17_167 ),
inference(resolution,[],[f1346,f644]) ).
fof(f2303,plain,
( spl17_274
| ~ spl17_49
| ~ spl17_157 ),
inference(avatar_split_clause,[],[f1275,f1211,f422,f2301]) ).
fof(f1275,plain,
( ! [X2,X0,X1] :
( sP0(X0,sK10(powerset(powerset(X1))))
| ~ empty(X1)
| ~ in(X2,sK9(X0,sK10(powerset(powerset(X1))))) )
| ~ spl17_49
| ~ spl17_157 ),
inference(resolution,[],[f1212,f423]) ).
fof(f2299,plain,
( spl17_273
| ~ spl17_49
| ~ spl17_156 ),
inference(avatar_split_clause,[],[f1271,f1207,f422,f2297]) ).
fof(f1271,plain,
( ! [X2,X0,X1] :
( sP0(X0,sK10(powerset(powerset(X1))))
| ~ empty(X1)
| ~ in(X2,sK8(X0,sK10(powerset(powerset(X1))))) )
| ~ spl17_49
| ~ spl17_156 ),
inference(resolution,[],[f1208,f423]) ).
fof(f2295,plain,
( spl17_272
| ~ spl17_49
| ~ spl17_155 ),
inference(avatar_split_clause,[],[f1267,f1203,f422,f2293]) ).
fof(f1267,plain,
( ! [X2,X0,X1] :
( sP0(X0,sK10(powerset(powerset(X1))))
| ~ empty(X1)
| ~ in(X2,sK7(X0,sK10(powerset(powerset(X1))))) )
| ~ spl17_49
| ~ spl17_155 ),
inference(resolution,[],[f1204,f423]) ).
fof(f2291,plain,
( spl17_271
| ~ spl17_51
| ~ spl17_147 ),
inference(avatar_split_clause,[],[f1173,f1147,f439,f2289]) ).
fof(f1173,plain,
( ! [X0,X1] :
( empty(powerset(X0))
| empty(sK6(powerset(X0)))
| element(X1,X0)
| ~ in(X1,sK10(sK6(powerset(X0)))) )
| ~ spl17_51
| ~ spl17_147 ),
inference(resolution,[],[f1148,f440]) ).
fof(f2246,plain,
( spl17_270
| ~ spl17_49
| ~ spl17_147 ),
inference(avatar_split_clause,[],[f1172,f1147,f422,f2244]) ).
fof(f1172,plain,
( ! [X0,X1] :
( empty(powerset(X0))
| empty(sK6(powerset(X0)))
| ~ empty(X0)
| ~ in(X1,sK10(sK6(powerset(X0)))) )
| ~ spl17_49
| ~ spl17_147 ),
inference(resolution,[],[f1148,f423]) ).
fof(f2242,plain,
( spl17_269
| ~ spl17_51
| ~ spl17_146 ),
inference(avatar_split_clause,[],[f1169,f1143,f439,f2240]) ).
fof(f1169,plain,
( ! [X0,X1] :
( empty(sK10(powerset(powerset(X0))))
| element(X1,X0)
| ~ in(X1,sK10(sK10(powerset(powerset(X0))))) )
| ~ spl17_51
| ~ spl17_146 ),
inference(resolution,[],[f1144,f440]) ).
fof(f2238,plain,
( spl17_268
| ~ spl17_41
| ~ spl17_146 ),
inference(avatar_split_clause,[],[f1167,f1143,f363,f2236]) ).
fof(f1167,plain,
( ! [X0,X1] :
( empty(sK10(powerset(powerset(cartesian_product2(X0,X1)))))
| relation(sK10(sK10(powerset(powerset(cartesian_product2(X0,X1)))))) )
| ~ spl17_41
| ~ spl17_146 ),
inference(resolution,[],[f1144,f364]) ).
fof(f2170,plain,
( spl17_267
| ~ spl17_140
| ~ spl17_214 ),
inference(avatar_split_clause,[],[f1761,f1749,f1107,f2168]) ).
fof(f1761,plain,
( ! [X0] :
( sK16 = sK10(powerset(sK10(powerset(X0))))
| ~ empty(X0) )
| ~ spl17_140
| ~ spl17_214 ),
inference(resolution,[],[f1750,f1108]) ).
fof(f2149,plain,
( spl17_266
| ~ spl17_39
| ~ spl17_157 ),
inference(avatar_split_clause,[],[f1273,f1211,f355,f2147]) ).
fof(f1273,plain,
( ! [X0,X1] :
( sP0(X0,sK10(powerset(X1)))
| empty(X1)
| in(sK9(X0,sK10(powerset(X1))),X1) )
| ~ spl17_39
| ~ spl17_157 ),
inference(resolution,[],[f1212,f356]) ).
fof(f2145,plain,
( spl17_265
| ~ spl17_39
| ~ spl17_156 ),
inference(avatar_split_clause,[],[f1269,f1207,f355,f2143]) ).
fof(f1269,plain,
( ! [X0,X1] :
( sP0(X0,sK10(powerset(X1)))
| empty(X1)
| in(sK8(X0,sK10(powerset(X1))),X1) )
| ~ spl17_39
| ~ spl17_156 ),
inference(resolution,[],[f1208,f356]) ).
fof(f2141,plain,
( spl17_264
| ~ spl17_39
| ~ spl17_155 ),
inference(avatar_split_clause,[],[f1265,f1203,f355,f2139]) ).
fof(f1265,plain,
( ! [X0,X1] :
( sP0(X0,sK10(powerset(X1)))
| empty(X1)
| in(sK7(X0,sK10(powerset(X1))),X1) )
| ~ spl17_39
| ~ spl17_155 ),
inference(resolution,[],[f1204,f356]) ).
fof(f2136,plain,
( spl17_263
| ~ spl17_38
| ~ spl17_151 ),
inference(avatar_split_clause,[],[f1189,f1163,f351,f2134]) ).
fof(f1189,plain,
( ! [X2,X0,X1] :
( element(sK9(X0,sK12(X1,X2)),cartesian_product2(X1,X2))
| sP0(X0,sK12(X1,X2)) )
| ~ spl17_38
| ~ spl17_151 ),
inference(resolution,[],[f1164,f352]) ).
fof(f2132,plain,
( spl17_262
| ~ spl17_37
| ~ spl17_151 ),
inference(avatar_split_clause,[],[f1188,f1163,f347,f2130]) ).
fof(f1188,plain,
( ! [X2,X0,X1] :
( element(sK8(X0,sK12(X1,X2)),cartesian_product2(X1,X2))
| sP0(X0,sK12(X1,X2)) )
| ~ spl17_37
| ~ spl17_151 ),
inference(resolution,[],[f1164,f348]) ).
fof(f2128,plain,
( spl17_261
| ~ spl17_35
| ~ spl17_151 ),
inference(avatar_split_clause,[],[f1187,f1163,f339,f2126]) ).
fof(f1187,plain,
( ! [X2,X0,X1] :
( element(sK7(X0,sK12(X1,X2)),cartesian_product2(X1,X2))
| sP0(X0,sK12(X1,X2)) )
| ~ spl17_35
| ~ spl17_151 ),
inference(resolution,[],[f1164,f340]) ).
fof(f2124,plain,
( spl17_260
| ~ spl17_38
| ~ spl17_150 ),
inference(avatar_split_clause,[],[f1183,f1159,f351,f2122]) ).
fof(f1183,plain,
( ! [X2,X0,X1] :
( element(sK9(X0,sK13(X1,X2)),cartesian_product2(X1,X2))
| sP0(X0,sK13(X1,X2)) )
| ~ spl17_38
| ~ spl17_150 ),
inference(resolution,[],[f1160,f352]) ).
fof(f2120,plain,
( spl17_259
| ~ spl17_37
| ~ spl17_150 ),
inference(avatar_split_clause,[],[f1182,f1159,f347,f2118]) ).
fof(f1182,plain,
( ! [X2,X0,X1] :
( element(sK8(X0,sK13(X1,X2)),cartesian_product2(X1,X2))
| sP0(X0,sK13(X1,X2)) )
| ~ spl17_37
| ~ spl17_150 ),
inference(resolution,[],[f1160,f348]) ).
fof(f2116,plain,
( spl17_258
| ~ spl17_35
| ~ spl17_150 ),
inference(avatar_split_clause,[],[f1181,f1159,f339,f2114]) ).
fof(f1181,plain,
( ! [X2,X0,X1] :
( element(sK7(X0,sK13(X1,X2)),cartesian_product2(X1,X2))
| sP0(X0,sK13(X1,X2)) )
| ~ spl17_35
| ~ spl17_150 ),
inference(resolution,[],[f1160,f340]) ).
fof(f2112,plain,
( spl17_257
| ~ spl17_98
| ~ spl17_149 ),
inference(avatar_split_clause,[],[f1176,f1155,f788,f2110]) ).
fof(f1176,plain,
( ! [X0,X1] :
( ~ subset(powerset(X0),X1)
| empty(powerset(X1))
| empty(powerset(X0))
| ~ subset(powerset(X1),X0) )
| ~ spl17_98
| ~ spl17_149 ),
inference(resolution,[],[f1156,f789]) ).
fof(f2108,plain,
( spl17_256
| ~ spl17_49
| ~ spl17_146 ),
inference(avatar_split_clause,[],[f1168,f1143,f422,f2106]) ).
fof(f1168,plain,
( ! [X0,X1] :
( empty(sK10(powerset(powerset(X0))))
| ~ empty(X0)
| ~ in(X1,sK10(sK10(powerset(powerset(X0))))) )
| ~ spl17_49
| ~ spl17_146 ),
inference(resolution,[],[f1144,f423]) ).
fof(f2104,plain,
( spl17_255
| ~ spl17_165
| ~ spl17_251 ),
inference(avatar_split_clause,[],[f2088,f1973,f1244,f2102]) ).
fof(f1244,plain,
( spl17_165
<=> ! [X2,X0,X1] :
( in(sK7(cartesian_product2(X0,X1),X2),X0)
| sP0(cartesian_product2(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_165])]) ).
fof(f1973,plain,
( spl17_251
<=> ! [X2,X0,X1] :
( ~ in(sK7(cartesian_product2(X0,X1),X2),X0)
| sP0(cartesian_product2(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_251])]) ).
fof(f2088,plain,
( ! [X2,X0,X1] : sP0(cartesian_product2(X0,X1),X2)
| ~ spl17_165
| ~ spl17_251 ),
inference(duplicate_literal_removal,[],[f2081]) ).
fof(f2081,plain,
( ! [X2,X0,X1] :
( sP0(cartesian_product2(X0,X1),X2)
| sP0(cartesian_product2(X0,X1),X2) )
| ~ spl17_165
| ~ spl17_251 ),
inference(resolution,[],[f1974,f1245]) ).
fof(f1245,plain,
( ! [X2,X0,X1] :
( in(sK7(cartesian_product2(X0,X1),X2),X0)
| sP0(cartesian_product2(X0,X1),X2) )
| ~ spl17_165 ),
inference(avatar_component_clause,[],[f1244]) ).
fof(f1974,plain,
( ! [X2,X0,X1] :
( ~ in(sK7(cartesian_product2(X0,X1),X2),X0)
| sP0(cartesian_product2(X0,X1),X2) )
| ~ spl17_251 ),
inference(avatar_component_clause,[],[f1973]) ).
fof(f2100,plain,
( spl17_254
| ~ spl17_17
| ~ spl17_170 ),
inference(avatar_split_clause,[],[f1394,f1357,f255,f2098]) ).
fof(f2098,plain,
( spl17_254
<=> ! [X2,X0,X1] :
( sP0(X0,powerset(cartesian_product2(X1,X2)))
| sP1(sK9(X0,powerset(cartesian_product2(X1,X2)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_254])]) ).
fof(f1357,plain,
( spl17_170
<=> ! [X2,X0,X1] :
( sP0(X0,powerset(cartesian_product2(X1,X2)))
| relation(sK9(X0,powerset(cartesian_product2(X1,X2)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_170])]) ).
fof(f1394,plain,
( ! [X2,X0,X1] :
( sP0(X0,powerset(cartesian_product2(X1,X2)))
| sP1(sK9(X0,powerset(cartesian_product2(X1,X2)))) )
| ~ spl17_17
| ~ spl17_170 ),
inference(resolution,[],[f1358,f256]) ).
fof(f1358,plain,
( ! [X2,X0,X1] :
( relation(sK9(X0,powerset(cartesian_product2(X1,X2))))
| sP0(X0,powerset(cartesian_product2(X1,X2))) )
| ~ spl17_170 ),
inference(avatar_component_clause,[],[f1357]) ).
fof(f2096,plain,
( spl17_253
| ~ spl17_17
| ~ spl17_168 ),
inference(avatar_split_clause,[],[f1379,f1349,f255,f2094]) ).
fof(f2094,plain,
( spl17_253
<=> ! [X2,X0,X1] :
( sP0(X0,powerset(cartesian_product2(X1,X2)))
| sP1(sK8(X0,powerset(cartesian_product2(X1,X2)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_253])]) ).
fof(f1349,plain,
( spl17_168
<=> ! [X2,X0,X1] :
( sP0(X0,powerset(cartesian_product2(X1,X2)))
| relation(sK8(X0,powerset(cartesian_product2(X1,X2)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_168])]) ).
fof(f1379,plain,
( ! [X2,X0,X1] :
( sP0(X0,powerset(cartesian_product2(X1,X2)))
| sP1(sK8(X0,powerset(cartesian_product2(X1,X2)))) )
| ~ spl17_17
| ~ spl17_168 ),
inference(resolution,[],[f1350,f256]) ).
fof(f1350,plain,
( ! [X2,X0,X1] :
( relation(sK8(X0,powerset(cartesian_product2(X1,X2))))
| sP0(X0,powerset(cartesian_product2(X1,X2))) )
| ~ spl17_168 ),
inference(avatar_component_clause,[],[f1349]) ).
fof(f2092,plain,
( spl17_252
| ~ spl17_17
| ~ spl17_166 ),
inference(avatar_split_clause,[],[f1368,f1341,f255,f2090]) ).
fof(f2090,plain,
( spl17_252
<=> ! [X2,X0,X1] :
( sP0(X0,powerset(cartesian_product2(X1,X2)))
| sP1(sK7(X0,powerset(cartesian_product2(X1,X2)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_252])]) ).
fof(f1341,plain,
( spl17_166
<=> ! [X2,X0,X1] :
( sP0(X0,powerset(cartesian_product2(X1,X2)))
| relation(sK7(X0,powerset(cartesian_product2(X1,X2)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_166])]) ).
fof(f1368,plain,
( ! [X2,X0,X1] :
( sP0(X0,powerset(cartesian_product2(X1,X2)))
| sP1(sK7(X0,powerset(cartesian_product2(X1,X2)))) )
| ~ spl17_17
| ~ spl17_166 ),
inference(resolution,[],[f1342,f256]) ).
fof(f1342,plain,
( ! [X2,X0,X1] :
( relation(sK7(X0,powerset(cartesian_product2(X1,X2))))
| sP0(X0,powerset(cartesian_product2(X1,X2))) )
| ~ spl17_166 ),
inference(avatar_component_clause,[],[f1341]) ).
fof(f1975,plain,
( spl17_251
| ~ spl17_162
| ~ spl17_177 ),
inference(avatar_split_clause,[],[f1438,f1426,f1232,f1973]) ).
fof(f1232,plain,
( spl17_162
<=> ! [X2,X0,X1] :
( in(sK9(cartesian_product2(X0,X1),X2),X1)
| sP0(cartesian_product2(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_162])]) ).
fof(f1426,plain,
( spl17_177
<=> ! [X2,X0,X1] :
( ~ in(sK9(cartesian_product2(X0,X1),X2),X1)
| ~ in(sK7(cartesian_product2(X0,X1),X2),X0)
| sP0(cartesian_product2(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_177])]) ).
fof(f1438,plain,
( ! [X2,X0,X1] :
( ~ in(sK7(cartesian_product2(X0,X1),X2),X0)
| sP0(cartesian_product2(X0,X1),X2) )
| ~ spl17_162
| ~ spl17_177 ),
inference(duplicate_literal_removal,[],[f1433]) ).
fof(f1433,plain,
( ! [X2,X0,X1] :
( ~ in(sK7(cartesian_product2(X0,X1),X2),X0)
| sP0(cartesian_product2(X0,X1),X2)
| sP0(cartesian_product2(X0,X1),X2) )
| ~ spl17_162
| ~ spl17_177 ),
inference(resolution,[],[f1427,f1233]) ).
fof(f1233,plain,
( ! [X2,X0,X1] :
( in(sK9(cartesian_product2(X0,X1),X2),X1)
| sP0(cartesian_product2(X0,X1),X2) )
| ~ spl17_162 ),
inference(avatar_component_clause,[],[f1232]) ).
fof(f1427,plain,
( ! [X2,X0,X1] :
( ~ in(sK9(cartesian_product2(X0,X1),X2),X1)
| ~ in(sK7(cartesian_product2(X0,X1),X2),X0)
| sP0(cartesian_product2(X0,X1),X2) )
| ~ spl17_177 ),
inference(avatar_component_clause,[],[f1426]) ).
fof(f1971,plain,
( spl17_250
| ~ spl17_25
| ~ spl17_165 ),
inference(avatar_split_clause,[],[f1330,f1244,f292,f1969]) ).
fof(f1969,plain,
( spl17_250
<=> ! [X2,X0,X1] :
( sP0(cartesian_product2(X0,X1),X2)
| ~ in(X0,sK7(cartesian_product2(X0,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_250])]) ).
fof(f1330,plain,
( ! [X2,X0,X1] :
( sP0(cartesian_product2(X0,X1),X2)
| ~ in(X0,sK7(cartesian_product2(X0,X1),X2)) )
| ~ spl17_25
| ~ spl17_165 ),
inference(resolution,[],[f1245,f293]) ).
fof(f1967,plain,
( spl17_249
| ~ spl17_26
| ~ spl17_165 ),
inference(avatar_split_clause,[],[f1329,f1244,f296,f1965]) ).
fof(f1965,plain,
( spl17_249
<=> ! [X2,X0,X1] :
( sP0(cartesian_product2(X0,X1),X2)
| element(sK7(cartesian_product2(X0,X1),X2),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_249])]) ).
fof(f1329,plain,
( ! [X2,X0,X1] :
( sP0(cartesian_product2(X0,X1),X2)
| element(sK7(cartesian_product2(X0,X1),X2),X0) )
| ~ spl17_26
| ~ spl17_165 ),
inference(resolution,[],[f1245,f297]) ).
fof(f1963,plain,
( spl17_248
| ~ spl17_25
| ~ spl17_164 ),
inference(avatar_split_clause,[],[f1318,f1240,f292,f1961]) ).
fof(f1961,plain,
( spl17_248
<=> ! [X2,X0,X1] :
( sP0(cartesian_product2(X0,X1),X2)
| ~ in(X0,sK8(cartesian_product2(X0,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_248])]) ).
fof(f1240,plain,
( spl17_164
<=> ! [X2,X0,X1] :
( in(sK8(cartesian_product2(X0,X1),X2),X0)
| sP0(cartesian_product2(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_164])]) ).
fof(f1318,plain,
( ! [X2,X0,X1] :
( sP0(cartesian_product2(X0,X1),X2)
| ~ in(X0,sK8(cartesian_product2(X0,X1),X2)) )
| ~ spl17_25
| ~ spl17_164 ),
inference(resolution,[],[f1241,f293]) ).
fof(f1241,plain,
( ! [X2,X0,X1] :
( in(sK8(cartesian_product2(X0,X1),X2),X0)
| sP0(cartesian_product2(X0,X1),X2) )
| ~ spl17_164 ),
inference(avatar_component_clause,[],[f1240]) ).
fof(f1959,plain,
( spl17_247
| ~ spl17_26
| ~ spl17_164 ),
inference(avatar_split_clause,[],[f1317,f1240,f296,f1957]) ).
fof(f1957,plain,
( spl17_247
<=> ! [X2,X0,X1] :
( sP0(cartesian_product2(X0,X1),X2)
| element(sK8(cartesian_product2(X0,X1),X2),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_247])]) ).
fof(f1317,plain,
( ! [X2,X0,X1] :
( sP0(cartesian_product2(X0,X1),X2)
| element(sK8(cartesian_product2(X0,X1),X2),X0) )
| ~ spl17_26
| ~ spl17_164 ),
inference(resolution,[],[f1241,f297]) ).
fof(f1955,plain,
( spl17_246
| ~ spl17_211
| ~ spl17_223 ),
inference(avatar_split_clause,[],[f1816,f1804,f1733,f1953]) ).
fof(f1953,plain,
( spl17_246
<=> ! [X0] :
( ~ empty(the_InternalRel(X0))
| transitive_relstr(X0)
| ~ rel_str(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_246])]) ).
fof(f1733,plain,
( spl17_211
<=> ! [X0] :
( ~ rel_str(X0)
| sP1(the_InternalRel(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_211])]) ).
fof(f1804,plain,
( spl17_223
<=> ! [X0] :
( ~ empty(the_InternalRel(X0))
| ~ sP1(the_InternalRel(X0))
| transitive_relstr(X0)
| ~ rel_str(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_223])]) ).
fof(f1816,plain,
( ! [X0] :
( ~ empty(the_InternalRel(X0))
| transitive_relstr(X0)
| ~ rel_str(X0) )
| ~ spl17_211
| ~ spl17_223 ),
inference(duplicate_literal_removal,[],[f1815]) ).
fof(f1815,plain,
( ! [X0] :
( ~ empty(the_InternalRel(X0))
| transitive_relstr(X0)
| ~ rel_str(X0)
| ~ rel_str(X0) )
| ~ spl17_211
| ~ spl17_223 ),
inference(resolution,[],[f1805,f1734]) ).
fof(f1734,plain,
( ! [X0] :
( sP1(the_InternalRel(X0))
| ~ rel_str(X0) )
| ~ spl17_211 ),
inference(avatar_component_clause,[],[f1733]) ).
fof(f1805,plain,
( ! [X0] :
( ~ sP1(the_InternalRel(X0))
| ~ empty(the_InternalRel(X0))
| transitive_relstr(X0)
| ~ rel_str(X0) )
| ~ spl17_223 ),
inference(avatar_component_clause,[],[f1804]) ).
fof(f1951,plain,
( spl17_245
| ~ spl17_25
| ~ spl17_163 ),
inference(avatar_split_clause,[],[f1306,f1236,f292,f1949]) ).
fof(f1949,plain,
( spl17_245
<=> ! [X2,X0,X1] :
( sP0(cartesian_product2(X0,X1),X2)
| ~ in(X1,sK8(cartesian_product2(X0,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_245])]) ).
fof(f1236,plain,
( spl17_163
<=> ! [X2,X0,X1] :
( in(sK8(cartesian_product2(X0,X1),X2),X1)
| sP0(cartesian_product2(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_163])]) ).
fof(f1306,plain,
( ! [X2,X0,X1] :
( sP0(cartesian_product2(X0,X1),X2)
| ~ in(X1,sK8(cartesian_product2(X0,X1),X2)) )
| ~ spl17_25
| ~ spl17_163 ),
inference(resolution,[],[f1237,f293]) ).
fof(f1237,plain,
( ! [X2,X0,X1] :
( in(sK8(cartesian_product2(X0,X1),X2),X1)
| sP0(cartesian_product2(X0,X1),X2) )
| ~ spl17_163 ),
inference(avatar_component_clause,[],[f1236]) ).
fof(f1947,plain,
( spl17_244
| ~ spl17_26
| ~ spl17_163 ),
inference(avatar_split_clause,[],[f1305,f1236,f296,f1945]) ).
fof(f1945,plain,
( spl17_244
<=> ! [X2,X0,X1] :
( sP0(cartesian_product2(X0,X1),X2)
| element(sK8(cartesian_product2(X0,X1),X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_244])]) ).
fof(f1305,plain,
( ! [X2,X0,X1] :
( sP0(cartesian_product2(X0,X1),X2)
| element(sK8(cartesian_product2(X0,X1),X2),X1) )
| ~ spl17_26
| ~ spl17_163 ),
inference(resolution,[],[f1237,f297]) ).
fof(f1943,plain,
( spl17_243
| ~ spl17_25
| ~ spl17_162 ),
inference(avatar_split_clause,[],[f1294,f1232,f292,f1941]) ).
fof(f1941,plain,
( spl17_243
<=> ! [X2,X0,X1] :
( sP0(cartesian_product2(X0,X1),X2)
| ~ in(X1,sK9(cartesian_product2(X0,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_243])]) ).
fof(f1294,plain,
( ! [X2,X0,X1] :
( sP0(cartesian_product2(X0,X1),X2)
| ~ in(X1,sK9(cartesian_product2(X0,X1),X2)) )
| ~ spl17_25
| ~ spl17_162 ),
inference(resolution,[],[f1233,f293]) ).
fof(f1939,plain,
( spl17_242
| ~ spl17_26
| ~ spl17_162 ),
inference(avatar_split_clause,[],[f1293,f1232,f296,f1937]) ).
fof(f1937,plain,
( spl17_242
<=> ! [X2,X0,X1] :
( sP0(cartesian_product2(X0,X1),X2)
| element(sK9(cartesian_product2(X0,X1),X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_242])]) ).
fof(f1293,plain,
( ! [X2,X0,X1] :
( sP0(cartesian_product2(X0,X1),X2)
| element(sK9(cartesian_product2(X0,X1),X2),X1) )
| ~ spl17_26
| ~ spl17_162 ),
inference(resolution,[],[f1233,f297]) ).
fof(f1935,plain,
( spl17_241
| ~ spl17_39
| ~ spl17_161 ),
inference(avatar_split_clause,[],[f1291,f1228,f355,f1933]) ).
fof(f1291,plain,
( ! [X0,X1] :
( empty(X0)
| sP0(X1,sK6(X0))
| in(sK9(X1,sK6(X0)),X0) )
| ~ spl17_39
| ~ spl17_161 ),
inference(duplicate_literal_removal,[],[f1287]) ).
fof(f1287,plain,
( ! [X0,X1] :
( empty(X0)
| sP0(X1,sK6(X0))
| empty(X0)
| in(sK9(X1,sK6(X0)),X0) )
| ~ spl17_39
| ~ spl17_161 ),
inference(resolution,[],[f1229,f356]) ).
fof(f1931,plain,
( spl17_240
| ~ spl17_39
| ~ spl17_160 ),
inference(avatar_split_clause,[],[f1286,f1224,f355,f1929]) ).
fof(f1286,plain,
( ! [X0,X1] :
( empty(X0)
| sP0(X1,sK6(X0))
| in(sK8(X1,sK6(X0)),X0) )
| ~ spl17_39
| ~ spl17_160 ),
inference(duplicate_literal_removal,[],[f1282]) ).
fof(f1282,plain,
( ! [X0,X1] :
( empty(X0)
| sP0(X1,sK6(X0))
| empty(X0)
| in(sK8(X1,sK6(X0)),X0) )
| ~ spl17_39
| ~ spl17_160 ),
inference(resolution,[],[f1225,f356]) ).
fof(f1927,plain,
( spl17_239
| ~ spl17_39
| ~ spl17_158 ),
inference(avatar_split_clause,[],[f1281,f1215,f355,f1925]) ).
fof(f1281,plain,
( ! [X0,X1] :
( empty(X0)
| sP0(X1,sK6(X0))
| in(sK7(X1,sK6(X0)),X0) )
| ~ spl17_39
| ~ spl17_158 ),
inference(duplicate_literal_removal,[],[f1277]) ).
fof(f1277,plain,
( ! [X0,X1] :
( empty(X0)
| sP0(X1,sK6(X0))
| empty(X0)
| in(sK7(X1,sK6(X0)),X0) )
| ~ spl17_39
| ~ spl17_158 ),
inference(resolution,[],[f1216,f356]) ).
fof(f1923,plain,
( spl17_238
| ~ spl17_35
| ~ spl17_154 ),
inference(avatar_split_clause,[],[f1262,f1199,f339,f1921]) ).
fof(f1199,plain,
( spl17_154
<=> ! [X2,X0,X1] :
( sP0(X0,powerset(X1))
| ~ empty(X1)
| ~ in(X2,sK9(X0,powerset(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_154])]) ).
fof(f1262,plain,
( ! [X2,X0,X1] :
( ~ empty(X0)
| sP0(X1,powerset(X0))
| sP0(X2,sK9(X1,powerset(X0))) )
| ~ spl17_35
| ~ spl17_154 ),
inference(resolution,[],[f1200,f340]) ).
fof(f1200,plain,
( ! [X2,X0,X1] :
( ~ in(X2,sK9(X0,powerset(X1)))
| ~ empty(X1)
| sP0(X0,powerset(X1)) )
| ~ spl17_154 ),
inference(avatar_component_clause,[],[f1199]) ).
fof(f1919,plain,
( spl17_237
| ~ spl17_59
| ~ spl17_154 ),
inference(avatar_split_clause,[],[f1259,f1199,f500,f1917]) ).
fof(f1259,plain,
( ! [X2,X0,X1] :
( ~ empty(X0)
| sP0(X1,powerset(X0))
| sP0(sK9(X1,powerset(X0)),X2) )
| ~ spl17_59
| ~ spl17_154 ),
inference(resolution,[],[f1200,f501]) ).
fof(f1915,plain,
( spl17_236
| ~ spl17_35
| ~ spl17_153 ),
inference(avatar_split_clause,[],[f1256,f1195,f339,f1913]) ).
fof(f1195,plain,
( spl17_153
<=> ! [X2,X0,X1] :
( sP0(X0,powerset(X1))
| ~ empty(X1)
| ~ in(X2,sK8(X0,powerset(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_153])]) ).
fof(f1256,plain,
( ! [X2,X0,X1] :
( ~ empty(X0)
| sP0(X1,powerset(X0))
| sP0(X2,sK8(X1,powerset(X0))) )
| ~ spl17_35
| ~ spl17_153 ),
inference(resolution,[],[f1196,f340]) ).
fof(f1196,plain,
( ! [X2,X0,X1] :
( ~ in(X2,sK8(X0,powerset(X1)))
| ~ empty(X1)
| sP0(X0,powerset(X1)) )
| ~ spl17_153 ),
inference(avatar_component_clause,[],[f1195]) ).
fof(f1911,plain,
( spl17_235
| ~ spl17_211
| ~ spl17_222 ),
inference(avatar_split_clause,[],[f1813,f1800,f1733,f1909]) ).
fof(f1909,plain,
( spl17_235
<=> ! [X0] :
( ~ empty(the_carrier(X0))
| transitive_relstr(X0)
| ~ rel_str(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_235])]) ).
fof(f1800,plain,
( spl17_222
<=> ! [X0] :
( ~ empty(the_carrier(X0))
| ~ sP1(the_InternalRel(X0))
| transitive_relstr(X0)
| ~ rel_str(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_222])]) ).
fof(f1813,plain,
( ! [X0] :
( ~ empty(the_carrier(X0))
| transitive_relstr(X0)
| ~ rel_str(X0) )
| ~ spl17_211
| ~ spl17_222 ),
inference(duplicate_literal_removal,[],[f1812]) ).
fof(f1812,plain,
( ! [X0] :
( ~ empty(the_carrier(X0))
| transitive_relstr(X0)
| ~ rel_str(X0)
| ~ rel_str(X0) )
| ~ spl17_211
| ~ spl17_222 ),
inference(resolution,[],[f1801,f1734]) ).
fof(f1801,plain,
( ! [X0] :
( ~ sP1(the_InternalRel(X0))
| ~ empty(the_carrier(X0))
| transitive_relstr(X0)
| ~ rel_str(X0) )
| ~ spl17_222 ),
inference(avatar_component_clause,[],[f1800]) ).
fof(f1907,plain,
( spl17_234
| ~ spl17_59
| ~ spl17_153 ),
inference(avatar_split_clause,[],[f1253,f1195,f500,f1905]) ).
fof(f1253,plain,
( ! [X2,X0,X1] :
( ~ empty(X0)
| sP0(X1,powerset(X0))
| sP0(sK8(X1,powerset(X0)),X2) )
| ~ spl17_59
| ~ spl17_153 ),
inference(resolution,[],[f1196,f501]) ).
fof(f1903,plain,
( spl17_233
| ~ spl17_35
| ~ spl17_152 ),
inference(avatar_split_clause,[],[f1250,f1191,f339,f1901]) ).
fof(f1191,plain,
( spl17_152
<=> ! [X2,X0,X1] :
( sP0(X0,powerset(X1))
| ~ empty(X1)
| ~ in(X2,sK7(X0,powerset(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_152])]) ).
fof(f1250,plain,
( ! [X2,X0,X1] :
( ~ empty(X0)
| sP0(X1,powerset(X0))
| sP0(X2,sK7(X1,powerset(X0))) )
| ~ spl17_35
| ~ spl17_152 ),
inference(resolution,[],[f1192,f340]) ).
fof(f1192,plain,
( ! [X2,X0,X1] :
( ~ in(X2,sK7(X0,powerset(X1)))
| ~ empty(X1)
| sP0(X0,powerset(X1)) )
| ~ spl17_152 ),
inference(avatar_component_clause,[],[f1191]) ).
fof(f1899,plain,
( spl17_232
| ~ spl17_59
| ~ spl17_152 ),
inference(avatar_split_clause,[],[f1247,f1191,f500,f1897]) ).
fof(f1247,plain,
( ! [X2,X0,X1] :
( ~ empty(X0)
| sP0(X1,powerset(X0))
| sP0(sK7(X1,powerset(X0)),X2) )
| ~ spl17_59
| ~ spl17_152 ),
inference(resolution,[],[f1192,f501]) ).
fof(f1895,plain,
( spl17_231
| ~ spl17_75
| ~ spl17_151 ),
inference(avatar_split_clause,[],[f1186,f1163,f643,f1893]) ).
fof(f1186,plain,
( ! [X0,X1] :
( element(sK10(sK12(X0,X1)),cartesian_product2(X0,X1))
| empty(sK12(X0,X1)) )
| ~ spl17_75
| ~ spl17_151 ),
inference(resolution,[],[f1164,f644]) ).
fof(f1891,plain,
( spl17_230
| ~ spl17_75
| ~ spl17_150 ),
inference(avatar_split_clause,[],[f1180,f1159,f643,f1889]) ).
fof(f1180,plain,
( ! [X0,X1] :
( element(sK10(sK13(X0,X1)),cartesian_product2(X0,X1))
| empty(sK13(X0,X1)) )
| ~ spl17_75
| ~ spl17_150 ),
inference(resolution,[],[f1160,f644]) ).
fof(f1887,plain,
( spl17_229
| ~ spl17_39
| ~ spl17_146 ),
inference(avatar_split_clause,[],[f1166,f1143,f355,f1885]) ).
fof(f1166,plain,
( ! [X0] :
( empty(sK10(powerset(X0)))
| empty(X0)
| in(sK10(sK10(powerset(X0))),X0) )
| ~ spl17_39
| ~ spl17_146 ),
inference(resolution,[],[f1144,f356]) ).
fof(f1851,plain,
( spl17_228
| ~ spl17_75
| ~ spl17_154 ),
inference(avatar_split_clause,[],[f1261,f1199,f643,f1849]) ).
fof(f1261,plain,
( ! [X0,X1] :
( ~ empty(X0)
| sP0(X1,powerset(X0))
| empty(sK9(X1,powerset(X0))) )
| ~ spl17_75
| ~ spl17_154 ),
inference(resolution,[],[f1200,f644]) ).
fof(f1847,plain,
( spl17_227
| ~ spl17_75
| ~ spl17_153 ),
inference(avatar_split_clause,[],[f1255,f1195,f643,f1845]) ).
fof(f1255,plain,
( ! [X0,X1] :
( ~ empty(X0)
| sP0(X1,powerset(X0))
| empty(sK8(X1,powerset(X0))) )
| ~ spl17_75
| ~ spl17_153 ),
inference(resolution,[],[f1196,f644]) ).
fof(f1843,plain,
( spl17_226
| ~ spl17_75
| ~ spl17_152 ),
inference(avatar_split_clause,[],[f1249,f1191,f643,f1841]) ).
fof(f1249,plain,
( ! [X0,X1] :
( ~ empty(X0)
| sP0(X1,powerset(X0))
| empty(sK7(X1,powerset(X0))) )
| ~ spl17_75
| ~ spl17_152 ),
inference(resolution,[],[f1192,f644]) ).
fof(f1839,plain,
( spl17_225
| ~ spl17_34
| ~ spl17_143 ),
inference(avatar_split_clause,[],[f1135,f1122,f335,f1837]) ).
fof(f1837,plain,
( spl17_225
<=> ! [X0,X1] :
( ~ empty(X0)
| is_transitive_in(sK10(powerset(X0)),X1)
| ~ sP1(sK10(powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_225])]) ).
fof(f1122,plain,
( spl17_143
<=> ! [X0,X1] :
( ~ empty(X0)
| sP0(sK10(powerset(X0)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_143])]) ).
fof(f1135,plain,
( ! [X0,X1] :
( ~ empty(X0)
| is_transitive_in(sK10(powerset(X0)),X1)
| ~ sP1(sK10(powerset(X0))) )
| ~ spl17_34
| ~ spl17_143 ),
inference(resolution,[],[f1123,f336]) ).
fof(f1123,plain,
( ! [X0,X1] :
( sP0(sK10(powerset(X0)),X1)
| ~ empty(X0) )
| ~ spl17_143 ),
inference(avatar_component_clause,[],[f1122]) ).
fof(f1810,plain,
( spl17_224
| ~ spl17_39
| ~ spl17_147 ),
inference(avatar_split_clause,[],[f1174,f1147,f355,f1808]) ).
fof(f1174,plain,
( ! [X0] :
( empty(X0)
| empty(sK6(X0))
| in(sK10(sK6(X0)),X0) )
| ~ spl17_39
| ~ spl17_147 ),
inference(duplicate_literal_removal,[],[f1170]) ).
fof(f1170,plain,
( ! [X0] :
( empty(X0)
| empty(sK6(X0))
| empty(X0)
| in(sK10(sK6(X0)),X0) )
| ~ spl17_39
| ~ spl17_147 ),
inference(resolution,[],[f1148,f356]) ).
fof(f1806,plain,
( spl17_223
| ~ spl17_46
| ~ spl17_142 ),
inference(avatar_split_clause,[],[f1133,f1118,f409,f1804]) ).
fof(f409,plain,
( spl17_46
<=> ! [X0] :
( transitive_relstr(X0)
| ~ is_transitive_in(the_InternalRel(X0),the_carrier(X0))
| ~ rel_str(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_46])]) ).
fof(f1118,plain,
( spl17_142
<=> ! [X0,X1] :
( ~ empty(X0)
| is_transitive_in(X0,X1)
| ~ sP1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_142])]) ).
fof(f1133,plain,
( ! [X0] :
( ~ empty(the_InternalRel(X0))
| ~ sP1(the_InternalRel(X0))
| transitive_relstr(X0)
| ~ rel_str(X0) )
| ~ spl17_46
| ~ spl17_142 ),
inference(resolution,[],[f1119,f410]) ).
fof(f410,plain,
( ! [X0] :
( ~ is_transitive_in(the_InternalRel(X0),the_carrier(X0))
| transitive_relstr(X0)
| ~ rel_str(X0) )
| ~ spl17_46 ),
inference(avatar_component_clause,[],[f409]) ).
fof(f1119,plain,
( ! [X0,X1] :
( is_transitive_in(X0,X1)
| ~ empty(X0)
| ~ sP1(X0) )
| ~ spl17_142 ),
inference(avatar_component_clause,[],[f1118]) ).
fof(f1802,plain,
( spl17_222
| ~ spl17_46
| ~ spl17_141 ),
inference(avatar_split_clause,[],[f1130,f1114,f409,f1800]) ).
fof(f1114,plain,
( spl17_141
<=> ! [X0,X1] :
( ~ empty(X0)
| is_transitive_in(X1,X0)
| ~ sP1(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_141])]) ).
fof(f1130,plain,
( ! [X0] :
( ~ empty(the_carrier(X0))
| ~ sP1(the_InternalRel(X0))
| transitive_relstr(X0)
| ~ rel_str(X0) )
| ~ spl17_46
| ~ spl17_141 ),
inference(resolution,[],[f1115,f410]) ).
fof(f1115,plain,
( ! [X0,X1] :
( is_transitive_in(X1,X0)
| ~ empty(X0)
| ~ sP1(X1) )
| ~ spl17_141 ),
inference(avatar_component_clause,[],[f1114]) ).
fof(f1798,plain,
( spl17_221
| ~ spl17_9
| ~ spl17_24
| ~ spl17_214 ),
inference(avatar_split_clause,[],[f1764,f1749,f287,f219,f1795]) ).
fof(f1795,plain,
( spl17_221
<=> sK16 = sK10(powerset(sK16)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_221])]) ).
fof(f1764,plain,
( sK16 = sK10(powerset(sK16))
| ~ spl17_9
| ~ spl17_24
| ~ spl17_214 ),
inference(forward_demodulation,[],[f1760,f289]) ).
fof(f1760,plain,
( sK16 = sK10(powerset(empty_set))
| ~ spl17_9
| ~ spl17_214 ),
inference(resolution,[],[f1750,f221]) ).
fof(f1783,plain,
( spl17_220
| ~ spl17_83
| ~ spl17_164 ),
inference(avatar_split_clause,[],[f1324,f1240,f686,f1781]) ).
fof(f1781,plain,
( spl17_220
<=> ! [X2,X0,X1] :
( sP0(cartesian_product2(sK10(powerset(X0)),X1),X2)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_220])]) ).
fof(f686,plain,
( spl17_83
<=> ! [X0,X1] :
( ~ empty(X0)
| ~ in(X1,sK10(powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_83])]) ).
fof(f1324,plain,
( ! [X2,X0,X1] :
( sP0(cartesian_product2(sK10(powerset(X0)),X1),X2)
| ~ empty(X0) )
| ~ spl17_83
| ~ spl17_164 ),
inference(resolution,[],[f1241,f687]) ).
fof(f687,plain,
( ! [X0,X1] :
( ~ in(X1,sK10(powerset(X0)))
| ~ empty(X0) )
| ~ spl17_83 ),
inference(avatar_component_clause,[],[f686]) ).
fof(f1779,plain,
( spl17_219
| ~ spl17_83
| ~ spl17_162 ),
inference(avatar_split_clause,[],[f1300,f1232,f686,f1777]) ).
fof(f1777,plain,
( spl17_219
<=> ! [X2,X0,X1] :
( sP0(cartesian_product2(X0,sK10(powerset(X1))),X2)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_219])]) ).
fof(f1300,plain,
( ! [X2,X0,X1] :
( sP0(cartesian_product2(X0,sK10(powerset(X1))),X2)
| ~ empty(X1) )
| ~ spl17_83
| ~ spl17_162 ),
inference(resolution,[],[f1233,f687]) ).
fof(f1775,plain,
( spl17_218
| ~ spl17_34
| ~ spl17_144 ),
inference(avatar_split_clause,[],[f1136,f1126,f335,f1773]) ).
fof(f1773,plain,
( spl17_218
<=> ! [X0,X1] :
( ~ empty(X0)
| is_transitive_in(X1,sK10(powerset(X0)))
| ~ sP1(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_218])]) ).
fof(f1126,plain,
( spl17_144
<=> ! [X0,X1] :
( ~ empty(X0)
| sP0(X1,sK10(powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_144])]) ).
fof(f1136,plain,
( ! [X0,X1] :
( ~ empty(X0)
| is_transitive_in(X1,sK10(powerset(X0)))
| ~ sP1(X1) )
| ~ spl17_34
| ~ spl17_144 ),
inference(resolution,[],[f1127,f336]) ).
fof(f1127,plain,
( ! [X0,X1] :
( sP0(X1,sK10(powerset(X0)))
| ~ empty(X0) )
| ~ spl17_144 ),
inference(avatar_component_clause,[],[f1126]) ).
fof(f1771,plain,
( spl17_217
| ~ spl17_32
| ~ spl17_140 ),
inference(avatar_split_clause,[],[f1112,f1107,f321,f1769]) ).
fof(f1112,plain,
( ! [X0,X1] :
( ~ empty(X0)
| sK10(powerset(X0)) = X1
| ~ empty(X1) )
| ~ spl17_32
| ~ spl17_140 ),
inference(resolution,[],[f1108,f322]) ).
fof(f1759,plain,
( spl17_216
| ~ spl17_23
| ~ spl17_164 ),
inference(avatar_split_clause,[],[f1316,f1240,f279,f1757]) ).
fof(f1757,plain,
( spl17_216
<=> ! [X2,X0,X1] :
( sP0(cartesian_product2(X0,X1),X2)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_216])]) ).
fof(f1316,plain,
( ! [X2,X0,X1] :
( sP0(cartesian_product2(X0,X1),X2)
| ~ empty(X0) )
| ~ spl17_23
| ~ spl17_164 ),
inference(resolution,[],[f1241,f280]) ).
fof(f1755,plain,
( spl17_215
| ~ spl17_23
| ~ spl17_162 ),
inference(avatar_split_clause,[],[f1292,f1232,f279,f1753]) ).
fof(f1753,plain,
( spl17_215
<=> ! [X2,X0,X1] :
( sP0(cartesian_product2(X0,X1),X2)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_215])]) ).
fof(f1292,plain,
( ! [X2,X0,X1] :
( sP0(cartesian_product2(X0,X1),X2)
| ~ empty(X1) )
| ~ spl17_23
| ~ spl17_162 ),
inference(resolution,[],[f1233,f280]) ).
fof(f1751,plain,
( spl17_214
| ~ spl17_69
| ~ spl17_140 ),
inference(avatar_split_clause,[],[f1111,f1107,f567,f1749]) ).
fof(f1111,plain,
( ! [X0] :
( ~ empty(X0)
| sK16 = sK10(powerset(X0)) )
| ~ spl17_69
| ~ spl17_140 ),
inference(resolution,[],[f1108,f568]) ).
fof(f1743,plain,
( spl17_213
| ~ spl17_72
| ~ spl17_164 ),
inference(avatar_split_clause,[],[f1327,f1240,f578,f1741]) ).
fof(f1741,plain,
( spl17_213
<=> ! [X0,X1] : sP0(cartesian_product2(sK16,X0),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_213])]) ).
fof(f1327,plain,
( ! [X0,X1] : sP0(cartesian_product2(sK16,X0),X1)
| ~ spl17_72
| ~ spl17_164 ),
inference(resolution,[],[f1241,f579]) ).
fof(f1739,plain,
( spl17_212
| ~ spl17_72
| ~ spl17_162 ),
inference(avatar_split_clause,[],[f1303,f1232,f578,f1737]) ).
fof(f1737,plain,
( spl17_212
<=> ! [X0,X1] : sP0(cartesian_product2(X0,sK16),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_212])]) ).
fof(f1303,plain,
( ! [X0,X1] : sP0(cartesian_product2(X0,sK16),X1)
| ~ spl17_72
| ~ spl17_162 ),
inference(resolution,[],[f1233,f579]) ).
fof(f1735,plain,
( spl17_211
| ~ spl17_17
| ~ spl17_137 ),
inference(avatar_split_clause,[],[f1097,f1094,f255,f1733]) ).
fof(f1094,plain,
( spl17_137
<=> ! [X0] :
( relation(the_InternalRel(X0))
| ~ rel_str(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_137])]) ).
fof(f1097,plain,
( ! [X0] :
( ~ rel_str(X0)
| sP1(the_InternalRel(X0)) )
| ~ spl17_17
| ~ spl17_137 ),
inference(resolution,[],[f1095,f256]) ).
fof(f1095,plain,
( ! [X0] :
( relation(the_InternalRel(X0))
| ~ rel_str(X0) )
| ~ spl17_137 ),
inference(avatar_component_clause,[],[f1094]) ).
fof(f1731,plain,
( spl17_210
| ~ spl17_34
| ~ spl17_130 ),
inference(avatar_split_clause,[],[f1059,f1055,f335,f1729]) ).
fof(f1729,plain,
( spl17_210
<=> ! [X0] :
( is_transitive_in(X0,sK16)
| ~ sP1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_210])]) ).
fof(f1055,plain,
( spl17_130
<=> ! [X0] : sP0(X0,sK16) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_130])]) ).
fof(f1059,plain,
( ! [X0] :
( is_transitive_in(X0,sK16)
| ~ sP1(X0) )
| ~ spl17_34
| ~ spl17_130 ),
inference(resolution,[],[f1056,f336]) ).
fof(f1056,plain,
( ! [X0] : sP0(X0,sK16)
| ~ spl17_130 ),
inference(avatar_component_clause,[],[f1055]) ).
fof(f1712,plain,
( spl17_209
| ~ spl17_108
| ~ spl17_123 ),
inference(avatar_split_clause,[],[f1006,f1000,f864,f1710]) ).
fof(f1006,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X1,X0)),powerset(cartesian_product2(X2,X3)))
| in(unordered_pair(singleton(X4),unordered_pair(X4,X1)),powerset(cartesian_product2(X2,X3)))
| ~ in(X1,X5)
| ~ in(X0,X5)
| ~ in(X4,X5)
| ~ sP0(powerset(cartesian_product2(X2,X3)),X5)
| empty(powerset(cartesian_product2(X2,X3)))
| ~ relation_of2_as_subset(unordered_pair(singleton(X4),unordered_pair(X4,X0)),X2,X3) )
| ~ spl17_108
| ~ spl17_123 ),
inference(resolution,[],[f1001,f865]) ).
fof(f1708,plain,
( spl17_208
| ~ spl17_67
| ~ spl17_108 ),
inference(avatar_split_clause,[],[f871,f864,f553,f1706]) ).
fof(f871,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( empty(powerset(cartesian_product2(X0,X1)))
| ~ relation_of2_as_subset(unordered_pair(singleton(X2),unordered_pair(X2,X3)),X0,X1)
| ~ in(unordered_pair(singleton(X4),unordered_pair(X4,X2)),powerset(cartesian_product2(X0,X1)))
| in(unordered_pair(singleton(X4),unordered_pair(X4,X3)),powerset(cartesian_product2(X0,X1)))
| ~ in(X3,X5)
| ~ in(X2,X5)
| ~ in(X4,X5)
| ~ sP0(powerset(cartesian_product2(X0,X1)),X5) )
| ~ spl17_67
| ~ spl17_108 ),
inference(resolution,[],[f865,f554]) ).
fof(f1688,plain,
( spl17_207
| ~ spl17_30
| ~ spl17_126 ),
inference(avatar_split_clause,[],[f1033,f1028,f313,f1686]) ).
fof(f1028,plain,
( spl17_126
<=> ! [X4,X0,X3,X2,X1] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),the_InternalRel(X2))
| in(unordered_pair(singleton(X0),unordered_pair(X0,X3)),the_InternalRel(X2))
| ~ in(X3,X4)
| ~ in(X1,X4)
| ~ in(X0,X4)
| ~ sP0(the_InternalRel(X2),X4)
| ~ related(X2,X1,X3)
| ~ element(X3,the_carrier(X2))
| ~ element(X1,the_carrier(X2))
| ~ rel_str(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_126])]) ).
fof(f1033,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X1,X0)),the_InternalRel(X2))
| in(unordered_pair(singleton(X0),unordered_pair(X0,X3)),the_InternalRel(X2))
| ~ in(X3,X4)
| ~ in(X1,X4)
| ~ in(X0,X4)
| ~ sP0(the_InternalRel(X2),X4)
| ~ related(X2,X1,X3)
| ~ element(X3,the_carrier(X2))
| ~ element(X1,the_carrier(X2))
| ~ rel_str(X2) )
| ~ spl17_30
| ~ spl17_126 ),
inference(superposition,[],[f1029,f314]) ).
fof(f1029,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),the_InternalRel(X2))
| in(unordered_pair(singleton(X0),unordered_pair(X0,X3)),the_InternalRel(X2))
| ~ in(X3,X4)
| ~ in(X1,X4)
| ~ in(X0,X4)
| ~ sP0(the_InternalRel(X2),X4)
| ~ related(X2,X1,X3)
| ~ element(X3,the_carrier(X2))
| ~ element(X1,the_carrier(X2))
| ~ rel_str(X2) )
| ~ spl17_126 ),
inference(avatar_component_clause,[],[f1028]) ).
fof(f1684,plain,
( spl17_206
| ~ spl17_64
| ~ spl17_123 ),
inference(avatar_split_clause,[],[f1007,f1000,f528,f1682]) ).
fof(f1007,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X1,X0)),the_InternalRel(X2))
| in(unordered_pair(singleton(X3),unordered_pair(X3,X1)),the_InternalRel(X2))
| ~ in(X1,X4)
| ~ in(X0,X4)
| ~ in(X3,X4)
| ~ sP0(the_InternalRel(X2),X4)
| ~ related(X2,X3,X0)
| ~ element(X0,the_carrier(X2))
| ~ element(X3,the_carrier(X2))
| ~ rel_str(X2) )
| ~ spl17_64
| ~ spl17_123 ),
inference(resolution,[],[f1001,f529]) ).
fof(f1674,plain,
( ~ spl17_128
| spl17_205
| ~ spl17_34
| ~ spl17_129 ),
inference(avatar_split_clause,[],[f1058,f1048,f335,f1672,f1043]) ).
fof(f1043,plain,
( spl17_128
<=> sP1(sK16) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_128])]) ).
fof(f1672,plain,
( spl17_205
<=> ! [X0] : is_transitive_in(sK16,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_205])]) ).
fof(f1048,plain,
( spl17_129
<=> ! [X0] : sP0(sK16,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_129])]) ).
fof(f1058,plain,
( ! [X0] :
( is_transitive_in(sK16,X0)
| ~ sP1(sK16) )
| ~ spl17_34
| ~ spl17_129 ),
inference(resolution,[],[f1049,f336]) ).
fof(f1049,plain,
( ! [X0] : sP0(sK16,X0)
| ~ spl17_129 ),
inference(avatar_component_clause,[],[f1048]) ).
fof(f1670,plain,
( spl17_204
| ~ spl17_64
| ~ spl17_126 ),
inference(avatar_split_clause,[],[f1036,f1028,f528,f1668]) ).
fof(f1036,plain,
( ! [X2,X3,X0,X1,X4] :
( in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),the_InternalRel(X2))
| ~ in(X1,X3)
| ~ in(X4,X3)
| ~ in(X0,X3)
| ~ sP0(the_InternalRel(X2),X3)
| ~ related(X2,X4,X1)
| ~ element(X1,the_carrier(X2))
| ~ element(X4,the_carrier(X2))
| ~ rel_str(X2)
| ~ related(X2,X0,X4)
| ~ element(X0,the_carrier(X2)) )
| ~ spl17_64
| ~ spl17_126 ),
inference(duplicate_literal_removal,[],[f1031]) ).
fof(f1031,plain,
( ! [X2,X3,X0,X1,X4] :
( in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),the_InternalRel(X2))
| ~ in(X1,X3)
| ~ in(X4,X3)
| ~ in(X0,X3)
| ~ sP0(the_InternalRel(X2),X3)
| ~ related(X2,X4,X1)
| ~ element(X1,the_carrier(X2))
| ~ element(X4,the_carrier(X2))
| ~ rel_str(X2)
| ~ related(X2,X0,X4)
| ~ element(X4,the_carrier(X2))
| ~ element(X0,the_carrier(X2))
| ~ rel_str(X2) )
| ~ spl17_64
| ~ spl17_126 ),
inference(resolution,[],[f1029,f529]) ).
fof(f1652,plain,
( spl17_203
| ~ spl17_98
| ~ spl17_123 ),
inference(avatar_split_clause,[],[f1005,f1000,f788,f1650]) ).
fof(f1005,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X1,X0)),powerset(X2))
| in(unordered_pair(singleton(X3),unordered_pair(X3,X1)),powerset(X2))
| ~ in(X1,X4)
| ~ in(X0,X4)
| ~ in(X3,X4)
| ~ sP0(powerset(X2),X4)
| empty(powerset(X2))
| ~ subset(unordered_pair(singleton(X3),unordered_pair(X3,X0)),X2) )
| ~ spl17_98
| ~ spl17_123 ),
inference(resolution,[],[f1001,f789]) ).
fof(f1648,plain,
( spl17_202
| ~ spl17_67
| ~ spl17_98 ),
inference(avatar_split_clause,[],[f802,f788,f553,f1646]) ).
fof(f802,plain,
( ! [X2,X3,X0,X1,X4] :
( empty(powerset(X0))
| ~ subset(unordered_pair(singleton(X1),unordered_pair(X1,X2)),X0)
| ~ in(unordered_pair(singleton(X3),unordered_pair(X3,X1)),powerset(X0))
| in(unordered_pair(singleton(X3),unordered_pair(X3,X2)),powerset(X0))
| ~ in(X2,X4)
| ~ in(X1,X4)
| ~ in(X3,X4)
| ~ sP0(powerset(X0),X4) )
| ~ spl17_67
| ~ spl17_98 ),
inference(resolution,[],[f789,f554]) ).
fof(f1630,plain,
( spl17_201
| ~ spl17_30
| ~ spl17_124 ),
inference(avatar_split_clause,[],[f1024,f1014,f313,f1628]) ).
fof(f1024,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X1,X0)),cartesian_product2(X2,X3))
| in(unordered_pair(singleton(X0),unordered_pair(X0,X4)),cartesian_product2(X2,X3))
| ~ in(X4,X5)
| ~ in(X1,X5)
| ~ in(X0,X5)
| ~ sP0(cartesian_product2(X2,X3),X5)
| ~ in(X4,X3)
| ~ in(X1,X2) )
| ~ spl17_30
| ~ spl17_124 ),
inference(superposition,[],[f1015,f314]) ).
fof(f1626,plain,
( spl17_200
| ~ spl17_54
| ~ spl17_123 ),
inference(avatar_split_clause,[],[f1003,f1000,f467,f1624]) ).
fof(f1003,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X1,X0)),cartesian_product2(X2,X3))
| in(unordered_pair(singleton(X4),unordered_pair(X4,X1)),cartesian_product2(X2,X3))
| ~ in(X1,X5)
| ~ in(X0,X5)
| ~ in(X4,X5)
| ~ sP0(cartesian_product2(X2,X3),X5)
| ~ in(X0,X3)
| ~ in(X4,X2) )
| ~ spl17_54
| ~ spl17_123 ),
inference(resolution,[],[f1001,f468]) ).
fof(f1612,plain,
( spl17_199
| ~ spl17_122
| ~ spl17_123 ),
inference(avatar_split_clause,[],[f1011,f1000,f973,f1610]) ).
fof(f1011,plain,
( ! [X2,X3,X0,X1] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X1,X0)),the_InternalRel(X2))
| in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),the_InternalRel(X2))
| ~ in(X1,X3)
| ~ in(X0,X3)
| ~ sP0(the_InternalRel(X2),X3)
| ~ related(X2,X0,X0)
| ~ element(X0,the_carrier(X2))
| ~ rel_str(X2) )
| ~ spl17_122
| ~ spl17_123 ),
inference(duplicate_literal_removal,[],[f1008]) ).
fof(f1008,plain,
( ! [X2,X3,X0,X1] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X1,X0)),the_InternalRel(X2))
| in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),the_InternalRel(X2))
| ~ in(X1,X3)
| ~ in(X0,X3)
| ~ in(X0,X3)
| ~ sP0(the_InternalRel(X2),X3)
| ~ related(X2,X0,X0)
| ~ element(X0,the_carrier(X2))
| ~ element(X0,the_carrier(X2))
| ~ rel_str(X2) )
| ~ spl17_122
| ~ spl17_123 ),
inference(resolution,[],[f1001,f974]) ).
fof(f1599,plain,
( spl17_198
| ~ spl17_111
| ~ spl17_123 ),
inference(avatar_split_clause,[],[f1012,f1000,f881,f1597]) ).
fof(f881,plain,
( spl17_111
<=> ! [X0,X3,X2,X1] :
( in(unordered_pair(singleton(X0),unordered_pair(X1,X0)),cartesian_product2(X2,X3))
| ~ in(X1,X3)
| ~ in(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_111])]) ).
fof(f1012,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X1,X0)),cartesian_product2(X2,X3))
| in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),cartesian_product2(X2,X3))
| ~ in(X1,X4)
| ~ in(X0,X4)
| ~ sP0(cartesian_product2(X2,X3),X4)
| ~ in(X0,X3)
| ~ in(X0,X2) )
| ~ spl17_111
| ~ spl17_123 ),
inference(duplicate_literal_removal,[],[f1004]) ).
fof(f1004,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X1,X0)),cartesian_product2(X2,X3))
| in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),cartesian_product2(X2,X3))
| ~ in(X1,X4)
| ~ in(X0,X4)
| ~ in(X0,X4)
| ~ sP0(cartesian_product2(X2,X3),X4)
| ~ in(X0,X3)
| ~ in(X0,X2) )
| ~ spl17_111
| ~ spl17_123 ),
inference(resolution,[],[f1001,f882]) ).
fof(f882,plain,
( ! [X2,X3,X0,X1] :
( in(unordered_pair(singleton(X0),unordered_pair(X1,X0)),cartesian_product2(X2,X3))
| ~ in(X1,X3)
| ~ in(X0,X2) )
| ~ spl17_111 ),
inference(avatar_component_clause,[],[f881]) ).
fof(f1583,plain,
( spl17_197
| ~ spl17_30
| ~ spl17_123 ),
inference(avatar_split_clause,[],[f1009,f1000,f313,f1581]) ).
fof(f1009,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X1,X0)),X2)
| ~ in(unordered_pair(singleton(X1),unordered_pair(X3,X1)),X2)
| in(unordered_pair(singleton(X0),unordered_pair(X0,X3)),X2)
| ~ in(X3,X4)
| ~ in(X1,X4)
| ~ in(X0,X4)
| ~ sP0(X2,X4) )
| ~ spl17_30
| ~ spl17_123 ),
inference(superposition,[],[f1001,f314]) ).
fof(f1579,plain,
( spl17_196
| ~ spl17_58
| ~ spl17_108 ),
inference(avatar_split_clause,[],[f870,f864,f496,f1577]) ).
fof(f1577,plain,
( spl17_196
<=> ! [X2,X0,X1] :
( empty(powerset(cartesian_product2(X0,X1)))
| ~ relation_of2_as_subset(unordered_pair(singleton(sK7(powerset(cartesian_product2(X0,X1)),X2)),unordered_pair(sK9(powerset(cartesian_product2(X0,X1)),X2),sK7(powerset(cartesian_product2(X0,X1)),X2))),X0,X1)
| sP0(powerset(cartesian_product2(X0,X1)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_196])]) ).
fof(f496,plain,
( spl17_58
<=> ! [X0,X1] :
( ~ in(unordered_pair(singleton(sK7(X0,X1)),unordered_pair(sK9(X0,X1),sK7(X0,X1))),X0)
| sP0(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_58])]) ).
fof(f870,plain,
( ! [X2,X0,X1] :
( empty(powerset(cartesian_product2(X0,X1)))
| ~ relation_of2_as_subset(unordered_pair(singleton(sK7(powerset(cartesian_product2(X0,X1)),X2)),unordered_pair(sK9(powerset(cartesian_product2(X0,X1)),X2),sK7(powerset(cartesian_product2(X0,X1)),X2))),X0,X1)
| sP0(powerset(cartesian_product2(X0,X1)),X2) )
| ~ spl17_58
| ~ spl17_108 ),
inference(resolution,[],[f865,f497]) ).
fof(f497,plain,
( ! [X0,X1] :
( ~ in(unordered_pair(singleton(sK7(X0,X1)),unordered_pair(sK9(X0,X1),sK7(X0,X1))),X0)
| sP0(X0,X1) )
| ~ spl17_58 ),
inference(avatar_component_clause,[],[f496]) ).
fof(f1571,plain,
( spl17_195
| ~ spl17_58
| ~ spl17_122 ),
inference(avatar_split_clause,[],[f989,f973,f496,f1569]) ).
fof(f1569,plain,
( spl17_195
<=> ! [X0,X1] :
( ~ related(X0,sK7(the_InternalRel(X0),X1),sK9(the_InternalRel(X0),X1))
| ~ element(sK9(the_InternalRel(X0),X1),the_carrier(X0))
| ~ element(sK7(the_InternalRel(X0),X1),the_carrier(X0))
| ~ rel_str(X0)
| sP0(the_InternalRel(X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_195])]) ).
fof(f989,plain,
( ! [X0,X1] :
( ~ related(X0,sK7(the_InternalRel(X0),X1),sK9(the_InternalRel(X0),X1))
| ~ element(sK9(the_InternalRel(X0),X1),the_carrier(X0))
| ~ element(sK7(the_InternalRel(X0),X1),the_carrier(X0))
| ~ rel_str(X0)
| sP0(the_InternalRel(X0),X1) )
| ~ spl17_58
| ~ spl17_122 ),
inference(resolution,[],[f974,f497]) ).
fof(f1567,plain,
( spl17_194
| ~ spl17_60
| ~ spl17_118 ),
inference(avatar_split_clause,[],[f978,f956,f504,f1565]) ).
fof(f978,plain,
( ! [X0,X1] :
( related(X0,sK7(the_InternalRel(X0),X1),sK8(the_InternalRel(X0),X1))
| ~ element(sK8(the_InternalRel(X0),X1),the_carrier(X0))
| ~ element(sK7(the_InternalRel(X0),X1),the_carrier(X0))
| ~ rel_str(X0)
| sP0(the_InternalRel(X0),X1) )
| ~ spl17_60
| ~ spl17_118 ),
inference(resolution,[],[f957,f505]) ).
fof(f1563,plain,
( spl17_193
| ~ spl17_59
| ~ spl17_118 ),
inference(avatar_split_clause,[],[f977,f956,f500,f1561]) ).
fof(f977,plain,
( ! [X0,X1] :
( related(X0,sK8(the_InternalRel(X0),X1),sK9(the_InternalRel(X0),X1))
| ~ element(sK9(the_InternalRel(X0),X1),the_carrier(X0))
| ~ element(sK8(the_InternalRel(X0),X1),the_carrier(X0))
| ~ rel_str(X0)
| sP0(the_InternalRel(X0),X1) )
| ~ spl17_59
| ~ spl17_118 ),
inference(resolution,[],[f957,f501]) ).
fof(f1557,plain,
( spl17_192
| ~ spl17_41
| ~ spl17_115 ),
inference(avatar_split_clause,[],[f950,f934,f363,f1555]) ).
fof(f934,plain,
( spl17_115
<=> ! [X0,X1] :
( sP0(X0,X1)
| element(unordered_pair(singleton(sK7(X0,X1)),unordered_pair(sK8(X0,X1),sK7(X0,X1))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_115])]) ).
fof(f950,plain,
( ! [X2,X0,X1] :
( sP0(powerset(cartesian_product2(X0,X1)),X2)
| relation(unordered_pair(singleton(sK7(powerset(cartesian_product2(X0,X1)),X2)),unordered_pair(sK8(powerset(cartesian_product2(X0,X1)),X2),sK7(powerset(cartesian_product2(X0,X1)),X2)))) )
| ~ spl17_41
| ~ spl17_115 ),
inference(resolution,[],[f935,f364]) ).
fof(f935,plain,
( ! [X0,X1] :
( element(unordered_pair(singleton(sK7(X0,X1)),unordered_pair(sK8(X0,X1),sK7(X0,X1))),X0)
| sP0(X0,X1) )
| ~ spl17_115 ),
inference(avatar_component_clause,[],[f934]) ).
fof(f1553,plain,
( spl17_191
| ~ spl17_41
| ~ spl17_113 ),
inference(avatar_split_clause,[],[f946,f926,f363,f1551]) ).
fof(f926,plain,
( spl17_113
<=> ! [X0,X1] :
( sP0(X0,X1)
| element(unordered_pair(singleton(sK8(X0,X1)),unordered_pair(sK9(X0,X1),sK8(X0,X1))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_113])]) ).
fof(f946,plain,
( ! [X2,X0,X1] :
( sP0(powerset(cartesian_product2(X0,X1)),X2)
| relation(unordered_pair(singleton(sK8(powerset(cartesian_product2(X0,X1)),X2)),unordered_pair(sK9(powerset(cartesian_product2(X0,X1)),X2),sK8(powerset(cartesian_product2(X0,X1)),X2)))) )
| ~ spl17_41
| ~ spl17_113 ),
inference(resolution,[],[f927,f364]) ).
fof(f927,plain,
( ! [X0,X1] :
( element(unordered_pair(singleton(sK8(X0,X1)),unordered_pair(sK9(X0,X1),sK8(X0,X1))),X0)
| sP0(X0,X1) )
| ~ spl17_113 ),
inference(avatar_component_clause,[],[f926]) ).
fof(f1541,plain,
( spl17_190
| ~ spl17_60
| ~ spl17_92 ),
inference(avatar_split_clause,[],[f751,f733,f504,f1539]) ).
fof(f751,plain,
( ! [X0,X1] :
( element(unordered_pair(singleton(sK7(sK10(powerset(X0)),X1)),unordered_pair(sK8(sK10(powerset(X0)),X1),sK7(sK10(powerset(X0)),X1))),X0)
| sP0(sK10(powerset(X0)),X1) )
| ~ spl17_60
| ~ spl17_92 ),
inference(resolution,[],[f734,f505]) ).
fof(f1537,plain,
( spl17_189
| ~ spl17_59
| ~ spl17_92 ),
inference(avatar_split_clause,[],[f750,f733,f500,f1535]) ).
fof(f750,plain,
( ! [X0,X1] :
( element(unordered_pair(singleton(sK8(sK10(powerset(X0)),X1)),unordered_pair(sK9(sK10(powerset(X0)),X1),sK8(sK10(powerset(X0)),X1))),X0)
| sP0(sK10(powerset(X0)),X1) )
| ~ spl17_59
| ~ spl17_92 ),
inference(resolution,[],[f734,f501]) ).
fof(f1513,plain,
( spl17_188
| ~ spl17_51
| ~ spl17_115 ),
inference(avatar_split_clause,[],[f952,f934,f439,f1511]) ).
fof(f952,plain,
( ! [X2,X0,X1] :
( sP0(powerset(X0),X1)
| element(X2,X0)
| ~ in(X2,unordered_pair(singleton(sK7(powerset(X0),X1)),unordered_pair(sK8(powerset(X0),X1),sK7(powerset(X0),X1)))) )
| ~ spl17_51
| ~ spl17_115 ),
inference(resolution,[],[f935,f440]) ).
fof(f1509,plain,
( spl17_187
| ~ spl17_51
| ~ spl17_113 ),
inference(avatar_split_clause,[],[f948,f926,f439,f1507]) ).
fof(f948,plain,
( ! [X2,X0,X1] :
( sP0(powerset(X0),X1)
| element(X2,X0)
| ~ in(X2,unordered_pair(singleton(sK8(powerset(X0),X1)),unordered_pair(sK9(powerset(X0),X1),sK8(powerset(X0),X1)))) )
| ~ spl17_51
| ~ spl17_113 ),
inference(resolution,[],[f927,f440]) ).
fof(f1505,plain,
( spl17_186
| ~ spl17_58
| ~ spl17_98 ),
inference(avatar_split_clause,[],[f801,f788,f496,f1503]) ).
fof(f1503,plain,
( spl17_186
<=> ! [X0,X1] :
( empty(powerset(X0))
| ~ subset(unordered_pair(singleton(sK7(powerset(X0),X1)),unordered_pair(sK9(powerset(X0),X1),sK7(powerset(X0),X1))),X0)
| sP0(powerset(X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_186])]) ).
fof(f801,plain,
( ! [X0,X1] :
( empty(powerset(X0))
| ~ subset(unordered_pair(singleton(sK7(powerset(X0),X1)),unordered_pair(sK9(powerset(X0),X1),sK7(powerset(X0),X1))),X0)
| sP0(powerset(X0),X1) )
| ~ spl17_58
| ~ spl17_98 ),
inference(resolution,[],[f789,f497]) ).
fof(f1486,plain,
( spl17_185
| ~ spl17_17
| ~ spl17_135 ),
inference(avatar_split_clause,[],[f1092,f1078,f255,f1484]) ).
fof(f1484,plain,
( spl17_185
<=> ! [X0,X1] : sP1(cartesian_product2(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_185])]) ).
fof(f1078,plain,
( spl17_135
<=> ! [X0,X1] : relation(cartesian_product2(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_135])]) ).
fof(f1092,plain,
( ! [X0,X1] : sP1(cartesian_product2(X0,X1))
| ~ spl17_17
| ~ spl17_135 ),
inference(resolution,[],[f1079,f256]) ).
fof(f1079,plain,
( ! [X0,X1] : relation(cartesian_product2(X0,X1))
| ~ spl17_135 ),
inference(avatar_component_clause,[],[f1078]) ).
fof(f1462,plain,
( spl17_184
| ~ spl17_30
| ~ spl17_121 ),
inference(avatar_split_clause,[],[f985,f969,f313,f1460]) ).
fof(f1460,plain,
( spl17_184
<=> ! [X2,X0,X1] :
( ~ in(the_InternalRel(X2),unordered_pair(singleton(X0),unordered_pair(X1,X0)))
| ~ element(X1,the_carrier(X2))
| ~ element(X0,the_carrier(X2))
| ~ rel_str(X2)
| ~ related(X2,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_184])]) ).
fof(f969,plain,
( spl17_121
<=> ! [X2,X0,X1] :
( ~ related(X0,X1,X2)
| ~ element(X2,the_carrier(X0))
| ~ element(X1,the_carrier(X0))
| ~ rel_str(X0)
| ~ in(the_InternalRel(X0),unordered_pair(singleton(X1),unordered_pair(X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_121])]) ).
fof(f985,plain,
( ! [X2,X0,X1] :
( ~ in(the_InternalRel(X2),unordered_pair(singleton(X0),unordered_pair(X1,X0)))
| ~ element(X1,the_carrier(X2))
| ~ element(X0,the_carrier(X2))
| ~ rel_str(X2)
| ~ related(X2,X0,X1) )
| ~ spl17_30
| ~ spl17_121 ),
inference(superposition,[],[f970,f314]) ).
fof(f970,plain,
( ! [X2,X0,X1] :
( ~ in(the_InternalRel(X0),unordered_pair(singleton(X1),unordered_pair(X1,X2)))
| ~ element(X2,the_carrier(X0))
| ~ element(X1,the_carrier(X0))
| ~ rel_str(X0)
| ~ related(X0,X1,X2) )
| ~ spl17_121 ),
inference(avatar_component_clause,[],[f969]) ).
fof(f1458,plain,
( spl17_183
| ~ spl17_30
| ~ spl17_120 ),
inference(avatar_split_clause,[],[f983,f965,f313,f1456]) ).
fof(f1456,plain,
( spl17_183
<=> ! [X2,X0,X1] :
( element(unordered_pair(singleton(X0),unordered_pair(X1,X0)),the_InternalRel(X2))
| ~ element(X1,the_carrier(X2))
| ~ element(X0,the_carrier(X2))
| ~ rel_str(X2)
| ~ related(X2,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_183])]) ).
fof(f965,plain,
( spl17_120
<=> ! [X2,X0,X1] :
( ~ related(X0,X1,X2)
| ~ element(X2,the_carrier(X0))
| ~ element(X1,the_carrier(X0))
| ~ rel_str(X0)
| element(unordered_pair(singleton(X1),unordered_pair(X1,X2)),the_InternalRel(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_120])]) ).
fof(f983,plain,
( ! [X2,X0,X1] :
( element(unordered_pair(singleton(X0),unordered_pair(X1,X0)),the_InternalRel(X2))
| ~ element(X1,the_carrier(X2))
| ~ element(X0,the_carrier(X2))
| ~ rel_str(X2)
| ~ related(X2,X0,X1) )
| ~ spl17_30
| ~ spl17_120 ),
inference(superposition,[],[f966,f314]) ).
fof(f966,plain,
( ! [X2,X0,X1] :
( element(unordered_pair(singleton(X1),unordered_pair(X1,X2)),the_InternalRel(X0))
| ~ element(X2,the_carrier(X0))
| ~ element(X1,the_carrier(X0))
| ~ rel_str(X0)
| ~ related(X0,X1,X2) )
| ~ spl17_120 ),
inference(avatar_component_clause,[],[f965]) ).
fof(f1454,plain,
( spl17_182
| ~ spl17_49
| ~ spl17_115 ),
inference(avatar_split_clause,[],[f951,f934,f422,f1452]) ).
fof(f951,plain,
( ! [X2,X0,X1] :
( sP0(powerset(X0),X1)
| ~ empty(X0)
| ~ in(X2,unordered_pair(singleton(sK7(powerset(X0),X1)),unordered_pair(sK8(powerset(X0),X1),sK7(powerset(X0),X1)))) )
| ~ spl17_49
| ~ spl17_115 ),
inference(resolution,[],[f935,f423]) ).
fof(f1450,plain,
( spl17_181
| ~ spl17_49
| ~ spl17_113 ),
inference(avatar_split_clause,[],[f947,f926,f422,f1448]) ).
fof(f947,plain,
( ! [X2,X0,X1] :
( sP0(powerset(X0),X1)
| ~ empty(X0)
| ~ in(X2,unordered_pair(singleton(sK8(powerset(X0),X1)),unordered_pair(sK9(powerset(X0),X1),sK8(powerset(X0),X1)))) )
| ~ spl17_49
| ~ spl17_113 ),
inference(resolution,[],[f927,f423]) ).
fof(f1446,plain,
( spl17_180
| ~ spl17_60
| ~ spl17_95 ),
inference(avatar_split_clause,[],[f777,f765,f504,f1444]) ).
fof(f777,plain,
( ! [X0,X1] :
( element(unordered_pair(singleton(sK7(sK6(X0),X1)),unordered_pair(sK8(sK6(X0),X1),sK7(sK6(X0),X1))),X0)
| empty(X0)
| sP0(sK6(X0),X1) )
| ~ spl17_60
| ~ spl17_95 ),
inference(resolution,[],[f766,f505]) ).
fof(f1442,plain,
( spl17_179
| ~ spl17_59
| ~ spl17_95 ),
inference(avatar_split_clause,[],[f776,f765,f500,f1440]) ).
fof(f776,plain,
( ! [X0,X1] :
( element(unordered_pair(singleton(sK8(sK6(X0),X1)),unordered_pair(sK9(sK6(X0),X1),sK8(sK6(X0),X1))),X0)
| empty(X0)
| sP0(sK6(X0),X1) )
| ~ spl17_59
| ~ spl17_95 ),
inference(resolution,[],[f766,f501]) ).
fof(f1432,plain,
( spl17_178
| ~ spl17_17
| ~ spl17_134 ),
inference(avatar_split_clause,[],[f1091,f1074,f255,f1430]) ).
fof(f1430,plain,
( spl17_178
<=> ! [X0,X1] : sP1(sK12(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_178])]) ).
fof(f1074,plain,
( spl17_134
<=> ! [X0,X1] : relation(sK12(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_134])]) ).
fof(f1091,plain,
( ! [X0,X1] : sP1(sK12(X0,X1))
| ~ spl17_17
| ~ spl17_134 ),
inference(resolution,[],[f1075,f256]) ).
fof(f1075,plain,
( ! [X0,X1] : relation(sK12(X0,X1))
| ~ spl17_134 ),
inference(avatar_component_clause,[],[f1074]) ).
fof(f1428,plain,
( spl17_177
| ~ spl17_58
| ~ spl17_111 ),
inference(avatar_split_clause,[],[f917,f881,f496,f1426]) ).
fof(f917,plain,
( ! [X2,X0,X1] :
( ~ in(sK9(cartesian_product2(X0,X1),X2),X1)
| ~ in(sK7(cartesian_product2(X0,X1),X2),X0)
| sP0(cartesian_product2(X0,X1),X2) )
| ~ spl17_58
| ~ spl17_111 ),
inference(resolution,[],[f882,f497]) ).
fof(f1419,plain,
( spl17_176
| ~ spl17_30
| ~ spl17_110 ),
inference(avatar_split_clause,[],[f911,f877,f313,f1417]) ).
fof(f1417,plain,
( spl17_176
<=> ! [X0,X3,X2,X1] :
( ~ in(cartesian_product2(X2,X3),unordered_pair(singleton(X0),unordered_pair(X1,X0)))
| ~ in(X0,X2)
| ~ in(X1,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_176])]) ).
fof(f877,plain,
( spl17_110
<=> ! [X0,X3,X2,X1] :
( ~ in(X0,X1)
| ~ in(X2,X3)
| ~ in(cartesian_product2(X3,X1),unordered_pair(singleton(X2),unordered_pair(X2,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_110])]) ).
fof(f911,plain,
( ! [X2,X3,X0,X1] :
( ~ in(cartesian_product2(X2,X3),unordered_pair(singleton(X0),unordered_pair(X1,X0)))
| ~ in(X0,X2)
| ~ in(X1,X3) )
| ~ spl17_30
| ~ spl17_110 ),
inference(superposition,[],[f878,f314]) ).
fof(f878,plain,
( ! [X2,X3,X0,X1] :
( ~ in(cartesian_product2(X3,X1),unordered_pair(singleton(X2),unordered_pair(X2,X0)))
| ~ in(X2,X3)
| ~ in(X0,X1) )
| ~ spl17_110 ),
inference(avatar_component_clause,[],[f877]) ).
fof(f1415,plain,
( spl17_175
| ~ spl17_30
| ~ spl17_109 ),
inference(avatar_split_clause,[],[f909,f873,f313,f1413]) ).
fof(f1413,plain,
( spl17_175
<=> ! [X0,X3,X2,X1] :
( element(unordered_pair(singleton(X0),unordered_pair(X1,X0)),cartesian_product2(X2,X3))
| ~ in(X0,X2)
| ~ in(X1,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_175])]) ).
fof(f873,plain,
( spl17_109
<=> ! [X0,X3,X2,X1] :
( ~ in(X0,X1)
| ~ in(X2,X3)
| element(unordered_pair(singleton(X2),unordered_pair(X2,X0)),cartesian_product2(X3,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_109])]) ).
fof(f909,plain,
( ! [X2,X3,X0,X1] :
( element(unordered_pair(singleton(X0),unordered_pair(X1,X0)),cartesian_product2(X2,X3))
| ~ in(X0,X2)
| ~ in(X1,X3) )
| ~ spl17_30
| ~ spl17_109 ),
inference(superposition,[],[f874,f314]) ).
fof(f874,plain,
( ! [X2,X3,X0,X1] :
( element(unordered_pair(singleton(X2),unordered_pair(X2,X0)),cartesian_product2(X3,X1))
| ~ in(X2,X3)
| ~ in(X0,X1) )
| ~ spl17_109 ),
inference(avatar_component_clause,[],[f873]) ).
fof(f1409,plain,
( spl17_174
| ~ spl17_25
| ~ spl17_108 ),
inference(avatar_split_clause,[],[f869,f864,f292,f1407]) ).
fof(f869,plain,
( ! [X2,X0,X1] :
( empty(powerset(cartesian_product2(X0,X1)))
| ~ relation_of2_as_subset(X2,X0,X1)
| ~ in(powerset(cartesian_product2(X0,X1)),X2) )
| ~ spl17_25
| ~ spl17_108 ),
inference(resolution,[],[f865,f293]) ).
fof(f1393,plain,
( spl17_173
| ~ spl17_17
| ~ spl17_133 ),
inference(avatar_split_clause,[],[f1090,f1070,f255,f1391]) ).
fof(f1391,plain,
( spl17_173
<=> ! [X0,X1] : sP1(sK13(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_173])]) ).
fof(f1070,plain,
( spl17_133
<=> ! [X0,X1] : relation(sK13(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_133])]) ).
fof(f1090,plain,
( ! [X0,X1] : sP1(sK13(X0,X1))
| ~ spl17_17
| ~ spl17_133 ),
inference(resolution,[],[f1071,f256]) ).
fof(f1071,plain,
( ! [X0,X1] : relation(sK13(X0,X1))
| ~ spl17_133 ),
inference(avatar_component_clause,[],[f1070]) ).
fof(f1367,plain,
( spl17_172
| ~ spl17_44
| ~ spl17_102 ),
inference(avatar_split_clause,[],[f820,f813,f401,f1365]) ).
fof(f401,plain,
( spl17_44
<=> ! [X0] :
( relation_of2_as_subset(the_InternalRel(X0),the_carrier(X0),the_carrier(X0))
| ~ rel_str(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_44])]) ).
fof(f820,plain,
( ! [X0,X1] :
( ~ in(X0,the_InternalRel(X1))
| element(X0,cartesian_product2(the_carrier(X1),the_carrier(X1)))
| ~ rel_str(X1) )
| ~ spl17_44
| ~ spl17_102 ),
inference(resolution,[],[f814,f402]) ).
fof(f402,plain,
( ! [X0] :
( relation_of2_as_subset(the_InternalRel(X0),the_carrier(X0),the_carrier(X0))
| ~ rel_str(X0) )
| ~ spl17_44 ),
inference(avatar_component_clause,[],[f401]) ).
fof(f1363,plain,
( spl17_171
| ~ spl17_51
| ~ spl17_89 ),
inference(avatar_split_clause,[],[f748,f721,f439,f1361]) ).
fof(f748,plain,
( ! [X2,X0,X1] :
( sP0(X0,powerset(X1))
| element(X2,X1)
| ~ in(X2,sK9(X0,powerset(X1))) )
| ~ spl17_51
| ~ spl17_89 ),
inference(resolution,[],[f722,f440]) ).
fof(f1359,plain,
( spl17_170
| ~ spl17_41
| ~ spl17_89 ),
inference(avatar_split_clause,[],[f746,f721,f363,f1357]) ).
fof(f746,plain,
( ! [X2,X0,X1] :
( sP0(X0,powerset(cartesian_product2(X1,X2)))
| relation(sK9(X0,powerset(cartesian_product2(X1,X2)))) )
| ~ spl17_41
| ~ spl17_89 ),
inference(resolution,[],[f722,f364]) ).
fof(f1355,plain,
( spl17_169
| ~ spl17_51
| ~ spl17_87 ),
inference(avatar_split_clause,[],[f744,f713,f439,f1353]) ).
fof(f744,plain,
( ! [X2,X0,X1] :
( sP0(X0,powerset(X1))
| element(X2,X1)
| ~ in(X2,sK8(X0,powerset(X1))) )
| ~ spl17_51
| ~ spl17_87 ),
inference(resolution,[],[f714,f440]) ).
fof(f1351,plain,
( spl17_168
| ~ spl17_41
| ~ spl17_87 ),
inference(avatar_split_clause,[],[f742,f713,f363,f1349]) ).
fof(f742,plain,
( ! [X2,X0,X1] :
( sP0(X0,powerset(cartesian_product2(X1,X2)))
| relation(sK8(X0,powerset(cartesian_product2(X1,X2)))) )
| ~ spl17_41
| ~ spl17_87 ),
inference(resolution,[],[f714,f364]) ).
fof(f1347,plain,
( spl17_167
| ~ spl17_51
| ~ spl17_85 ),
inference(avatar_split_clause,[],[f739,f705,f439,f1345]) ).
fof(f739,plain,
( ! [X2,X0,X1] :
( sP0(X0,powerset(X1))
| element(X2,X1)
| ~ in(X2,sK7(X0,powerset(X1))) )
| ~ spl17_51
| ~ spl17_85 ),
inference(resolution,[],[f706,f440]) ).
fof(f1343,plain,
( spl17_166
| ~ spl17_41
| ~ spl17_85 ),
inference(avatar_split_clause,[],[f737,f705,f363,f1341]) ).
fof(f737,plain,
( ! [X2,X0,X1] :
( sP0(X0,powerset(cartesian_product2(X1,X2)))
| relation(sK7(X0,powerset(cartesian_product2(X1,X2)))) )
| ~ spl17_41
| ~ spl17_85 ),
inference(resolution,[],[f706,f364]) ).
fof(f1246,plain,
( spl17_165
| ~ spl17_60
| ~ spl17_104 ),
inference(avatar_split_clause,[],[f837,f827,f504,f1244]) ).
fof(f837,plain,
( ! [X2,X0,X1] :
( in(sK7(cartesian_product2(X0,X1),X2),X0)
| sP0(cartesian_product2(X0,X1),X2) )
| ~ spl17_60
| ~ spl17_104 ),
inference(resolution,[],[f828,f505]) ).
fof(f1242,plain,
( spl17_164
| ~ spl17_59
| ~ spl17_104 ),
inference(avatar_split_clause,[],[f836,f827,f500,f1240]) ).
fof(f836,plain,
( ! [X2,X0,X1] :
( in(sK8(cartesian_product2(X0,X1),X2),X0)
| sP0(cartesian_product2(X0,X1),X2) )
| ~ spl17_59
| ~ spl17_104 ),
inference(resolution,[],[f828,f501]) ).
fof(f1238,plain,
( spl17_163
| ~ spl17_60
| ~ spl17_103 ),
inference(avatar_split_clause,[],[f832,f823,f504,f1236]) ).
fof(f832,plain,
( ! [X2,X0,X1] :
( in(sK8(cartesian_product2(X0,X1),X2),X1)
| sP0(cartesian_product2(X0,X1),X2) )
| ~ spl17_60
| ~ spl17_103 ),
inference(resolution,[],[f824,f505]) ).
fof(f1234,plain,
( spl17_162
| ~ spl17_59
| ~ spl17_103 ),
inference(avatar_split_clause,[],[f831,f823,f500,f1232]) ).
fof(f831,plain,
( ! [X2,X0,X1] :
( in(sK9(cartesian_product2(X0,X1),X2),X1)
| sP0(cartesian_product2(X0,X1),X2) )
| ~ spl17_59
| ~ spl17_103 ),
inference(resolution,[],[f824,f501]) ).
fof(f1230,plain,
( spl17_161
| ~ spl17_38
| ~ spl17_95 ),
inference(avatar_split_clause,[],[f781,f765,f351,f1228]) ).
fof(f781,plain,
( ! [X0,X1] :
( element(sK9(X0,sK6(X1)),X1)
| empty(X1)
| sP0(X0,sK6(X1)) )
| ~ spl17_38
| ~ spl17_95 ),
inference(resolution,[],[f766,f352]) ).
fof(f1226,plain,
( spl17_160
| ~ spl17_37
| ~ spl17_95 ),
inference(avatar_split_clause,[],[f780,f765,f347,f1224]) ).
fof(f780,plain,
( ! [X0,X1] :
( element(sK8(X0,sK6(X1)),X1)
| empty(X1)
| sP0(X0,sK6(X1)) )
| ~ spl17_37
| ~ spl17_95 ),
inference(resolution,[],[f766,f348]) ).
fof(f1222,plain,
( spl17_159
| ~ spl17_17
| ~ spl17_136 ),
inference(avatar_split_clause,[],[f1175,f1086,f255,f1219]) ).
fof(f1086,plain,
( spl17_136
<=> relation(the_InternalRel(sK2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_136])]) ).
fof(f1175,plain,
( sP1(the_InternalRel(sK2))
| ~ spl17_17
| ~ spl17_136 ),
inference(resolution,[],[f1088,f256]) ).
fof(f1088,plain,
( relation(the_InternalRel(sK2))
| ~ spl17_136 ),
inference(avatar_component_clause,[],[f1086]) ).
fof(f1217,plain,
( spl17_158
| ~ spl17_35
| ~ spl17_95 ),
inference(avatar_split_clause,[],[f779,f765,f339,f1215]) ).
fof(f779,plain,
( ! [X0,X1] :
( element(sK7(X0,sK6(X1)),X1)
| empty(X1)
| sP0(X0,sK6(X1)) )
| ~ spl17_35
| ~ spl17_95 ),
inference(resolution,[],[f766,f340]) ).
fof(f1213,plain,
( spl17_157
| ~ spl17_38
| ~ spl17_92 ),
inference(avatar_split_clause,[],[f755,f733,f351,f1211]) ).
fof(f755,plain,
( ! [X0,X1] :
( element(sK9(X0,sK10(powerset(X1))),X1)
| sP0(X0,sK10(powerset(X1))) )
| ~ spl17_38
| ~ spl17_92 ),
inference(resolution,[],[f734,f352]) ).
fof(f1209,plain,
( spl17_156
| ~ spl17_37
| ~ spl17_92 ),
inference(avatar_split_clause,[],[f754,f733,f347,f1207]) ).
fof(f754,plain,
( ! [X0,X1] :
( element(sK8(X0,sK10(powerset(X1))),X1)
| sP0(X0,sK10(powerset(X1))) )
| ~ spl17_37
| ~ spl17_92 ),
inference(resolution,[],[f734,f348]) ).
fof(f1205,plain,
( spl17_155
| ~ spl17_35
| ~ spl17_92 ),
inference(avatar_split_clause,[],[f753,f733,f339,f1203]) ).
fof(f753,plain,
( ! [X0,X1] :
( element(sK7(X0,sK10(powerset(X1))),X1)
| sP0(X0,sK10(powerset(X1))) )
| ~ spl17_35
| ~ spl17_92 ),
inference(resolution,[],[f734,f340]) ).
fof(f1201,plain,
( spl17_154
| ~ spl17_49
| ~ spl17_89 ),
inference(avatar_split_clause,[],[f747,f721,f422,f1199]) ).
fof(f747,plain,
( ! [X2,X0,X1] :
( sP0(X0,powerset(X1))
| ~ empty(X1)
| ~ in(X2,sK9(X0,powerset(X1))) )
| ~ spl17_49
| ~ spl17_89 ),
inference(resolution,[],[f722,f423]) ).
fof(f1197,plain,
( spl17_153
| ~ spl17_49
| ~ spl17_87 ),
inference(avatar_split_clause,[],[f743,f713,f422,f1195]) ).
fof(f743,plain,
( ! [X2,X0,X1] :
( sP0(X0,powerset(X1))
| ~ empty(X1)
| ~ in(X2,sK8(X0,powerset(X1))) )
| ~ spl17_49
| ~ spl17_87 ),
inference(resolution,[],[f714,f423]) ).
fof(f1193,plain,
( spl17_152
| ~ spl17_49
| ~ spl17_85 ),
inference(avatar_split_clause,[],[f738,f705,f422,f1191]) ).
fof(f738,plain,
( ! [X2,X0,X1] :
( sP0(X0,powerset(X1))
| ~ empty(X1)
| ~ in(X2,sK7(X0,powerset(X1))) )
| ~ spl17_49
| ~ spl17_85 ),
inference(resolution,[],[f706,f423]) ).
fof(f1165,plain,
( spl17_151
| ~ spl17_78
| ~ spl17_102 ),
inference(avatar_split_clause,[],[f821,f813,f655,f1163]) ).
fof(f655,plain,
( spl17_78
<=> ! [X0,X1] : relation_of2_as_subset(sK12(X0,X1),X0,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_78])]) ).
fof(f821,plain,
( ! [X2,X0,X1] :
( ~ in(X0,sK12(X1,X2))
| element(X0,cartesian_product2(X1,X2)) )
| ~ spl17_78
| ~ spl17_102 ),
inference(resolution,[],[f814,f656]) ).
fof(f656,plain,
( ! [X0,X1] : relation_of2_as_subset(sK12(X0,X1),X0,X1)
| ~ spl17_78 ),
inference(avatar_component_clause,[],[f655]) ).
fof(f1161,plain,
( spl17_150
| ~ spl17_28
| ~ spl17_102 ),
inference(avatar_split_clause,[],[f819,f813,f304,f1159]) ).
fof(f304,plain,
( spl17_28
<=> ! [X0,X1] : relation_of2_as_subset(sK13(X0,X1),X0,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_28])]) ).
fof(f819,plain,
( ! [X2,X0,X1] :
( ~ in(X0,sK13(X1,X2))
| element(X0,cartesian_product2(X1,X2)) )
| ~ spl17_28
| ~ spl17_102 ),
inference(resolution,[],[f814,f305]) ).
fof(f305,plain,
( ! [X0,X1] : relation_of2_as_subset(sK13(X0,X1),X0,X1)
| ~ spl17_28 ),
inference(avatar_component_clause,[],[f304]) ).
fof(f1157,plain,
( spl17_149
| ~ spl17_25
| ~ spl17_98 ),
inference(avatar_split_clause,[],[f800,f788,f292,f1155]) ).
fof(f800,plain,
( ! [X0,X1] :
( empty(powerset(X0))
| ~ subset(X1,X0)
| ~ in(powerset(X0),X1) )
| ~ spl17_25
| ~ spl17_98 ),
inference(resolution,[],[f789,f293]) ).
fof(f1153,plain,
( spl17_148
| ~ spl17_25
| ~ spl17_97 ),
inference(avatar_split_clause,[],[f797,f784,f292,f1151]) ).
fof(f1151,plain,
( spl17_148
<=> ! [X0] :
( empty(powerset(X0))
| empty(X0)
| ~ in(powerset(X0),sK6(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_148])]) ).
fof(f784,plain,
( spl17_97
<=> ! [X0] :
( empty(powerset(X0))
| in(sK6(X0),powerset(X0))
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_97])]) ).
fof(f797,plain,
( ! [X0] :
( empty(powerset(X0))
| empty(X0)
| ~ in(powerset(X0),sK6(X0)) )
| ~ spl17_25
| ~ spl17_97 ),
inference(resolution,[],[f785,f293]) ).
fof(f785,plain,
( ! [X0] :
( in(sK6(X0),powerset(X0))
| empty(powerset(X0))
| empty(X0) )
| ~ spl17_97 ),
inference(avatar_component_clause,[],[f784]) ).
fof(f1149,plain,
( spl17_147
| ~ spl17_75
| ~ spl17_95 ),
inference(avatar_split_clause,[],[f778,f765,f643,f1147]) ).
fof(f778,plain,
( ! [X0] :
( element(sK10(sK6(X0)),X0)
| empty(X0)
| empty(sK6(X0)) )
| ~ spl17_75
| ~ spl17_95 ),
inference(resolution,[],[f766,f644]) ).
fof(f1145,plain,
( spl17_146
| ~ spl17_75
| ~ spl17_92 ),
inference(avatar_split_clause,[],[f752,f733,f643,f1143]) ).
fof(f752,plain,
( ! [X0] :
( element(sK10(sK10(powerset(X0))),X0)
| empty(sK10(powerset(X0))) )
| ~ spl17_75
| ~ spl17_92 ),
inference(resolution,[],[f734,f644]) ).
fof(f1141,plain,
( ~ spl17_2
| spl17_136
| ~ spl17_137 ),
inference(avatar_split_clause,[],[f1110,f1094,f1086,f184]) ).
fof(f1110,plain,
( ~ rel_str(sK2)
| spl17_136
| ~ spl17_137 ),
inference(resolution,[],[f1087,f1095]) ).
fof(f1087,plain,
( ~ relation(the_InternalRel(sK2))
| spl17_136 ),
inference(avatar_component_clause,[],[f1086]) ).
fof(f1140,plain,
( spl17_145
| ~ spl17_17
| ~ spl17_93 ),
inference(avatar_split_clause,[],[f773,f757,f255,f1138]) ).
fof(f1138,plain,
( spl17_145
<=> ! [X0,X1] :
( empty(cartesian_product2(X0,X1))
| sP1(sK6(cartesian_product2(X0,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_145])]) ).
fof(f757,plain,
( spl17_93
<=> ! [X0,X1] :
( relation(sK6(cartesian_product2(X0,X1)))
| empty(cartesian_product2(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_93])]) ).
fof(f773,plain,
( ! [X0,X1] :
( empty(cartesian_product2(X0,X1))
| sP1(sK6(cartesian_product2(X0,X1))) )
| ~ spl17_17
| ~ spl17_93 ),
inference(resolution,[],[f758,f256]) ).
fof(f758,plain,
( ! [X0,X1] :
( relation(sK6(cartesian_product2(X0,X1)))
| empty(cartesian_product2(X0,X1)) )
| ~ spl17_93 ),
inference(avatar_component_clause,[],[f757]) ).
fof(f1128,plain,
( spl17_144
| ~ spl17_35
| ~ spl17_83 ),
inference(avatar_split_clause,[],[f696,f686,f339,f1126]) ).
fof(f696,plain,
( ! [X0,X1] :
( ~ empty(X0)
| sP0(X1,sK10(powerset(X0))) )
| ~ spl17_35
| ~ spl17_83 ),
inference(resolution,[],[f687,f340]) ).
fof(f1124,plain,
( spl17_143
| ~ spl17_59
| ~ spl17_83 ),
inference(avatar_split_clause,[],[f693,f686,f500,f1122]) ).
fof(f693,plain,
( ! [X0,X1] :
( ~ empty(X0)
| sP0(sK10(powerset(X0)),X1) )
| ~ spl17_59
| ~ spl17_83 ),
inference(resolution,[],[f687,f501]) ).
fof(f1120,plain,
( spl17_142
| ~ spl17_34
| ~ spl17_74 ),
inference(avatar_split_clause,[],[f641,f633,f335,f1118]) ).
fof(f641,plain,
( ! [X0,X1] :
( ~ empty(X0)
| is_transitive_in(X0,X1)
| ~ sP1(X0) )
| ~ spl17_34
| ~ spl17_74 ),
inference(resolution,[],[f634,f336]) ).
fof(f1116,plain,
( spl17_141
| ~ spl17_34
| ~ spl17_70 ),
inference(avatar_split_clause,[],[f640,f571,f335,f1114]) ).
fof(f571,plain,
( spl17_70
<=> ! [X0,X1] :
( sP0(X0,X1)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_70])]) ).
fof(f640,plain,
( ! [X0,X1] :
( ~ empty(X0)
| is_transitive_in(X1,X0)
| ~ sP1(X1) )
| ~ spl17_34
| ~ spl17_70 ),
inference(resolution,[],[f572,f336]) ).
fof(f572,plain,
( ! [X0,X1] :
( sP0(X0,X1)
| ~ empty(X1) )
| ~ spl17_70 ),
inference(avatar_component_clause,[],[f571]) ).
fof(f1109,plain,
( spl17_140
| ~ spl17_75
| ~ spl17_83 ),
inference(avatar_split_clause,[],[f695,f686,f643,f1107]) ).
fof(f695,plain,
( ! [X0] :
( ~ empty(X0)
| empty(sK10(powerset(X0))) )
| ~ spl17_75
| ~ spl17_83 ),
inference(resolution,[],[f687,f644]) ).
fof(f1105,plain,
( spl17_139
| ~ spl17_17
| ~ spl17_76 ),
inference(avatar_split_clause,[],[f671,f647,f255,f1103]) ).
fof(f1103,plain,
( spl17_139
<=> ! [X0,X1] : sP1(sK10(powerset(cartesian_product2(X0,X1)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_139])]) ).
fof(f647,plain,
( spl17_76
<=> ! [X0,X1] : relation(sK10(powerset(cartesian_product2(X0,X1)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_76])]) ).
fof(f671,plain,
( ! [X0,X1] : sP1(sK10(powerset(cartesian_product2(X0,X1))))
| ~ spl17_17
| ~ spl17_76 ),
inference(resolution,[],[f648,f256]) ).
fof(f648,plain,
( ! [X0,X1] : relation(sK10(powerset(cartesian_product2(X0,X1))))
| ~ spl17_76 ),
inference(avatar_component_clause,[],[f647]) ).
fof(f1101,plain,
( spl17_138
| ~ spl17_25
| ~ spl17_75 ),
inference(avatar_split_clause,[],[f664,f643,f292,f1099]) ).
fof(f1099,plain,
( spl17_138
<=> ! [X0] :
( empty(X0)
| ~ in(X0,sK10(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_138])]) ).
fof(f664,plain,
( ! [X0] :
( empty(X0)
| ~ in(X0,sK10(X0)) )
| ~ spl17_25
| ~ spl17_75 ),
inference(resolution,[],[f644,f293]) ).
fof(f1096,plain,
( spl17_137
| ~ spl17_44
| ~ spl17_79 ),
inference(avatar_split_clause,[],[f675,f659,f401,f1094]) ).
fof(f659,plain,
( spl17_79
<=> ! [X2,X0,X1] :
( ~ relation_of2_as_subset(X0,X1,X2)
| relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_79])]) ).
fof(f675,plain,
( ! [X0] :
( relation(the_InternalRel(X0))
| ~ rel_str(X0) )
| ~ spl17_44
| ~ spl17_79 ),
inference(resolution,[],[f660,f402]) ).
fof(f660,plain,
( ! [X2,X0,X1] :
( ~ relation_of2_as_subset(X0,X1,X2)
| relation(X0) )
| ~ spl17_79 ),
inference(avatar_component_clause,[],[f659]) ).
fof(f1089,plain,
( spl17_136
| ~ spl17_79
| ~ spl17_105 ),
inference(avatar_split_clause,[],[f1052,f841,f659,f1086]) ).
fof(f1052,plain,
( relation(the_InternalRel(sK2))
| ~ spl17_79
| ~ spl17_105 ),
inference(resolution,[],[f843,f660]) ).
fof(f1080,plain,
( spl17_135
| ~ spl17_16
| ~ spl17_82 ),
inference(avatar_split_clause,[],[f692,f682,f251,f1078]) ).
fof(f692,plain,
( ! [X0,X1] : relation(cartesian_product2(X0,X1))
| ~ spl17_16
| ~ spl17_82 ),
inference(resolution,[],[f683,f252]) ).
fof(f1076,plain,
( spl17_134
| ~ spl17_78
| ~ spl17_79 ),
inference(avatar_split_clause,[],[f676,f659,f655,f1074]) ).
fof(f676,plain,
( ! [X0,X1] : relation(sK12(X0,X1))
| ~ spl17_78
| ~ spl17_79 ),
inference(resolution,[],[f660,f656]) ).
fof(f1072,plain,
( spl17_133
| ~ spl17_28
| ~ spl17_79 ),
inference(avatar_split_clause,[],[f674,f659,f304,f1070]) ).
fof(f674,plain,
( ! [X0,X1] : relation(sK13(X0,X1))
| ~ spl17_28
| ~ spl17_79 ),
inference(resolution,[],[f660,f305]) ).
fof(f1068,plain,
( spl17_132
| ~ spl17_22
| ~ spl17_36 ),
inference(avatar_split_clause,[],[f377,f343,f275,f1066]) ).
fof(f1066,plain,
( spl17_132
<=> ! [X0] : element(sK16,powerset(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_132])]) ).
fof(f275,plain,
( spl17_22
<=> ! [X0] : element(sK11(X0),powerset(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_22])]) ).
fof(f343,plain,
( spl17_36
<=> ! [X0] : sK11(X0) = sK16 ),
introduced(avatar_definition,[new_symbols(naming,[spl17_36])]) ).
fof(f377,plain,
( ! [X0] : element(sK16,powerset(X0))
| ~ spl17_22
| ~ spl17_36 ),
inference(superposition,[],[f276,f344]) ).
fof(f344,plain,
( ! [X0] : sK11(X0) = sK16
| ~ spl17_36 ),
inference(avatar_component_clause,[],[f343]) ).
fof(f276,plain,
( ! [X0] : element(sK11(X0),powerset(X0))
| ~ spl17_22 ),
inference(avatar_component_clause,[],[f275]) ).
fof(f1064,plain,
( ~ spl17_131
| ~ spl17_2
| ~ spl17_3
| ~ spl17_4
| ~ spl17_6
| ~ spl17_117 ),
inference(avatar_split_clause,[],[f953,f942,f204,f194,f189,f184,f1061]) ).
fof(f942,plain,
( spl17_117
<=> ! [X2,X0,X1] :
( ~ related(X0,X1,X2)
| ~ element(X2,the_carrier(X0))
| ~ element(X1,the_carrier(X0))
| ~ rel_str(X0)
| ~ empty(the_InternalRel(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_117])]) ).
fof(f953,plain,
( ~ element(sK4,the_carrier(sK2))
| ~ element(sK3,the_carrier(sK2))
| ~ rel_str(sK2)
| ~ empty(the_InternalRel(sK2))
| ~ spl17_6
| ~ spl17_117 ),
inference(resolution,[],[f943,f206]) ).
fof(f943,plain,
( ! [X2,X0,X1] :
( ~ related(X0,X1,X2)
| ~ element(X2,the_carrier(X0))
| ~ element(X1,the_carrier(X0))
| ~ rel_str(X0)
| ~ empty(the_InternalRel(X0)) )
| ~ spl17_117 ),
inference(avatar_component_clause,[],[f942]) ).
fof(f1057,plain,
( spl17_130
| ~ spl17_35
| ~ spl17_72 ),
inference(avatar_split_clause,[],[f624,f578,f339,f1055]) ).
fof(f624,plain,
( ! [X0] : sP0(X0,sK16)
| ~ spl17_35
| ~ spl17_72 ),
inference(resolution,[],[f579,f340]) ).
fof(f1050,plain,
( spl17_129
| ~ spl17_59
| ~ spl17_72 ),
inference(avatar_split_clause,[],[f622,f578,f500,f1048]) ).
fof(f622,plain,
( ! [X0] : sP0(sK16,X0)
| ~ spl17_59
| ~ spl17_72 ),
inference(resolution,[],[f579,f501]) ).
fof(f1046,plain,
( spl17_128
| ~ spl17_17
| ~ spl17_68 ),
inference(avatar_split_clause,[],[f565,f561,f255,f1043]) ).
fof(f561,plain,
( spl17_68
<=> relation(sK16) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_68])]) ).
fof(f565,plain,
( sP1(sK16)
| ~ spl17_17
| ~ spl17_68 ),
inference(resolution,[],[f563,f256]) ).
fof(f563,plain,
( relation(sK16)
| ~ spl17_68 ),
inference(avatar_component_clause,[],[f561]) ).
fof(f1041,plain,
( ~ spl17_127
| ~ spl17_25
| ~ spl17_107 ),
inference(avatar_split_clause,[],[f907,f858,f292,f1038]) ).
fof(f907,plain,
( ~ in(the_carrier(sK2),sK5)
| ~ spl17_25
| ~ spl17_107 ),
inference(resolution,[],[f860,f293]) ).
fof(f1030,plain,
( spl17_126
| ~ spl17_64
| ~ spl17_67 ),
inference(avatar_split_clause,[],[f557,f553,f528,f1028]) ).
fof(f557,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),the_InternalRel(X2))
| in(unordered_pair(singleton(X0),unordered_pair(X0,X3)),the_InternalRel(X2))
| ~ in(X3,X4)
| ~ in(X1,X4)
| ~ in(X0,X4)
| ~ sP0(the_InternalRel(X2),X4)
| ~ related(X2,X1,X3)
| ~ element(X3,the_carrier(X2))
| ~ element(X1,the_carrier(X2))
| ~ rel_str(X2) )
| ~ spl17_64
| ~ spl17_67 ),
inference(resolution,[],[f554,f529]) ).
fof(f1021,plain,
( ~ spl17_125
| ~ spl17_25
| ~ spl17_106 ),
inference(avatar_split_clause,[],[f904,f849,f292,f1018]) ).
fof(f904,plain,
( ~ in(the_carrier(sK2),sK4)
| ~ spl17_25
| ~ spl17_106 ),
inference(resolution,[],[f851,f293]) ).
fof(f851,plain,
( in(sK4,the_carrier(sK2))
| ~ spl17_106 ),
inference(avatar_component_clause,[],[f849]) ).
fof(f1016,plain,
( spl17_124
| ~ spl17_54
| ~ spl17_67 ),
inference(avatar_split_clause,[],[f556,f553,f467,f1014]) ).
fof(f556,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),cartesian_product2(X2,X3))
| in(unordered_pair(singleton(X0),unordered_pair(X0,X4)),cartesian_product2(X2,X3))
| ~ in(X4,X5)
| ~ in(X1,X5)
| ~ in(X0,X5)
| ~ sP0(cartesian_product2(X2,X3),X5)
| ~ in(X4,X3)
| ~ in(X1,X2) )
| ~ spl17_54
| ~ spl17_67 ),
inference(resolution,[],[f554,f468]) ).
fof(f1002,plain,
( spl17_123
| ~ spl17_30
| ~ spl17_67 ),
inference(avatar_split_clause,[],[f558,f553,f313,f1000]) ).
fof(f558,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X1,X0)),X2)
| ~ in(unordered_pair(singleton(X3),unordered_pair(X3,X0)),X2)
| in(unordered_pair(singleton(X3),unordered_pair(X3,X1)),X2)
| ~ in(X1,X4)
| ~ in(X0,X4)
| ~ in(X3,X4)
| ~ sP0(X2,X4) )
| ~ spl17_30
| ~ spl17_67 ),
inference(superposition,[],[f554,f314]) ).
fof(f975,plain,
( spl17_122
| ~ spl17_30
| ~ spl17_64 ),
inference(avatar_split_clause,[],[f537,f528,f313,f973]) ).
fof(f537,plain,
( ! [X2,X0,X1] :
( in(unordered_pair(singleton(X0),unordered_pair(X1,X0)),the_InternalRel(X2))
| ~ related(X2,X0,X1)
| ~ element(X1,the_carrier(X2))
| ~ element(X0,the_carrier(X2))
| ~ rel_str(X2) )
| ~ spl17_30
| ~ spl17_64 ),
inference(superposition,[],[f529,f314]) ).
fof(f971,plain,
( spl17_121
| ~ spl17_25
| ~ spl17_64 ),
inference(avatar_split_clause,[],[f535,f528,f292,f969]) ).
fof(f535,plain,
( ! [X2,X0,X1] :
( ~ related(X0,X1,X2)
| ~ element(X2,the_carrier(X0))
| ~ element(X1,the_carrier(X0))
| ~ rel_str(X0)
| ~ in(the_InternalRel(X0),unordered_pair(singleton(X1),unordered_pair(X1,X2))) )
| ~ spl17_25
| ~ spl17_64 ),
inference(resolution,[],[f529,f293]) ).
fof(f967,plain,
( spl17_120
| ~ spl17_26
| ~ spl17_64 ),
inference(avatar_split_clause,[],[f534,f528,f296,f965]) ).
fof(f534,plain,
( ! [X2,X0,X1] :
( ~ related(X0,X1,X2)
| ~ element(X2,the_carrier(X0))
| ~ element(X1,the_carrier(X0))
| ~ rel_str(X0)
| element(unordered_pair(singleton(X1),unordered_pair(X1,X2)),the_InternalRel(X0)) )
| ~ spl17_26
| ~ spl17_64 ),
inference(resolution,[],[f529,f297]) ).
fof(f963,plain,
( ~ spl17_119
| ~ spl17_25
| ~ spl17_47 ),
inference(avatar_split_clause,[],[f847,f413,f292,f960]) ).
fof(f847,plain,
( ~ in(the_carrier(sK2),sK3)
| ~ spl17_25
| ~ spl17_47 ),
inference(resolution,[],[f415,f293]) ).
fof(f415,plain,
( in(sK3,the_carrier(sK2))
| ~ spl17_47 ),
inference(avatar_component_clause,[],[f413]) ).
fof(f958,plain,
( spl17_118
| ~ spl17_30
| ~ spl17_63 ),
inference(avatar_split_clause,[],[f531,f524,f313,f956]) ).
fof(f531,plain,
( ! [X2,X0,X1] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X1,X0)),the_InternalRel(X2))
| related(X2,X0,X1)
| ~ element(X1,the_carrier(X2))
| ~ element(X0,the_carrier(X2))
| ~ rel_str(X2) )
| ~ spl17_30
| ~ spl17_63 ),
inference(superposition,[],[f525,f314]) ).
fof(f944,plain,
( spl17_117
| ~ spl17_23
| ~ spl17_64 ),
inference(avatar_split_clause,[],[f536,f528,f279,f942]) ).
fof(f536,plain,
( ! [X2,X0,X1] :
( ~ related(X0,X1,X2)
| ~ element(X2,the_carrier(X0))
| ~ element(X1,the_carrier(X0))
| ~ rel_str(X0)
| ~ empty(the_InternalRel(X0)) )
| ~ spl17_23
| ~ spl17_64 ),
inference(resolution,[],[f529,f280]) ).
fof(f940,plain,
( spl17_116
| ~ spl17_25
| ~ spl17_60 ),
inference(avatar_split_clause,[],[f511,f504,f292,f938]) ).
fof(f938,plain,
( spl17_116
<=> ! [X0,X1] :
( sP0(X0,X1)
| ~ in(X0,unordered_pair(singleton(sK7(X0,X1)),unordered_pair(sK8(X0,X1),sK7(X0,X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_116])]) ).
fof(f511,plain,
( ! [X0,X1] :
( sP0(X0,X1)
| ~ in(X0,unordered_pair(singleton(sK7(X0,X1)),unordered_pair(sK8(X0,X1),sK7(X0,X1)))) )
| ~ spl17_25
| ~ spl17_60 ),
inference(resolution,[],[f505,f293]) ).
fof(f936,plain,
( spl17_115
| ~ spl17_26
| ~ spl17_60 ),
inference(avatar_split_clause,[],[f510,f504,f296,f934]) ).
fof(f510,plain,
( ! [X0,X1] :
( sP0(X0,X1)
| element(unordered_pair(singleton(sK7(X0,X1)),unordered_pair(sK8(X0,X1),sK7(X0,X1))),X0) )
| ~ spl17_26
| ~ spl17_60 ),
inference(resolution,[],[f505,f297]) ).
fof(f932,plain,
( spl17_114
| ~ spl17_25
| ~ spl17_59 ),
inference(avatar_split_clause,[],[f508,f500,f292,f930]) ).
fof(f930,plain,
( spl17_114
<=> ! [X0,X1] :
( sP0(X0,X1)
| ~ in(X0,unordered_pair(singleton(sK8(X0,X1)),unordered_pair(sK9(X0,X1),sK8(X0,X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_114])]) ).
fof(f508,plain,
( ! [X0,X1] :
( sP0(X0,X1)
| ~ in(X0,unordered_pair(singleton(sK8(X0,X1)),unordered_pair(sK9(X0,X1),sK8(X0,X1)))) )
| ~ spl17_25
| ~ spl17_59 ),
inference(resolution,[],[f501,f293]) ).
fof(f928,plain,
( spl17_113
| ~ spl17_26
| ~ spl17_59 ),
inference(avatar_split_clause,[],[f507,f500,f296,f926]) ).
fof(f507,plain,
( ! [X0,X1] :
( sP0(X0,X1)
| element(unordered_pair(singleton(sK8(X0,X1)),unordered_pair(sK9(X0,X1),sK8(X0,X1))),X0) )
| ~ spl17_26
| ~ spl17_59 ),
inference(resolution,[],[f501,f297]) ).
fof(f898,plain,
( spl17_112
| ~ spl17_65
| ~ spl17_107 ),
inference(avatar_split_clause,[],[f885,f858,f541,f895]) ).
fof(f885,plain,
( in(sK5,sK16)
| ~ spl17_65
| ~ spl17_107 ),
inference(forward_demodulation,[],[f860,f543]) ).
fof(f888,plain,
( ~ spl17_12
| spl17_48
| ~ spl17_65 ),
inference(avatar_split_clause,[],[f887,f541,f417,f234]) ).
fof(f887,plain,
( ~ empty(sK16)
| spl17_48
| ~ spl17_65 ),
inference(forward_demodulation,[],[f418,f543]) ).
fof(f418,plain,
( ~ empty(the_carrier(sK2))
| spl17_48 ),
inference(avatar_component_clause,[],[f417]) ).
fof(f884,plain,
( ~ spl17_48
| ~ spl17_23
| ~ spl17_47 ),
inference(avatar_split_clause,[],[f845,f413,f279,f417]) ).
fof(f845,plain,
( ~ empty(the_carrier(sK2))
| ~ spl17_23
| ~ spl17_47 ),
inference(resolution,[],[f415,f280]) ).
fof(f883,plain,
( spl17_111
| ~ spl17_30
| ~ spl17_54 ),
inference(avatar_split_clause,[],[f475,f467,f313,f881]) ).
fof(f475,plain,
( ! [X2,X3,X0,X1] :
( in(unordered_pair(singleton(X0),unordered_pair(X1,X0)),cartesian_product2(X2,X3))
| ~ in(X1,X3)
| ~ in(X0,X2) )
| ~ spl17_30
| ~ spl17_54 ),
inference(superposition,[],[f468,f314]) ).
fof(f879,plain,
( spl17_110
| ~ spl17_25
| ~ spl17_54 ),
inference(avatar_split_clause,[],[f473,f467,f292,f877]) ).
fof(f473,plain,
( ! [X2,X3,X0,X1] :
( ~ in(X0,X1)
| ~ in(X2,X3)
| ~ in(cartesian_product2(X3,X1),unordered_pair(singleton(X2),unordered_pair(X2,X0))) )
| ~ spl17_25
| ~ spl17_54 ),
inference(resolution,[],[f468,f293]) ).
fof(f875,plain,
( spl17_109
| ~ spl17_26
| ~ spl17_54 ),
inference(avatar_split_clause,[],[f472,f467,f296,f873]) ).
fof(f472,plain,
( ! [X2,X3,X0,X1] :
( ~ in(X0,X1)
| ~ in(X2,X3)
| element(unordered_pair(singleton(X2),unordered_pair(X2,X0)),cartesian_product2(X3,X1)) )
| ~ spl17_26
| ~ spl17_54 ),
inference(resolution,[],[f468,f297]) ).
fof(f866,plain,
( spl17_108
| ~ spl17_39
| ~ spl17_50 ),
inference(avatar_split_clause,[],[f444,f435,f355,f864]) ).
fof(f435,plain,
( spl17_50
<=> ! [X2,X0,X1] :
( element(X2,powerset(cartesian_product2(X0,X1)))
| ~ relation_of2_as_subset(X2,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_50])]) ).
fof(f444,plain,
( ! [X2,X0,X1] :
( ~ relation_of2_as_subset(X0,X1,X2)
| empty(powerset(cartesian_product2(X1,X2)))
| in(X0,powerset(cartesian_product2(X1,X2))) )
| ~ spl17_39
| ~ spl17_50 ),
inference(resolution,[],[f436,f356]) ).
fof(f436,plain,
( ! [X2,X0,X1] :
( element(X2,powerset(cartesian_product2(X0,X1)))
| ~ relation_of2_as_subset(X2,X0,X1) )
| ~ spl17_50 ),
inference(avatar_component_clause,[],[f435]) ).
fof(f861,plain,
( spl17_107
| spl17_48
| ~ spl17_5
| ~ spl17_39 ),
inference(avatar_split_clause,[],[f387,f355,f199,f417,f858]) ).
fof(f387,plain,
( empty(the_carrier(sK2))
| in(sK5,the_carrier(sK2))
| ~ spl17_5
| ~ spl17_39 ),
inference(resolution,[],[f356,f201]) ).
fof(f201,plain,
( element(sK5,the_carrier(sK2))
| ~ spl17_5 ),
inference(avatar_component_clause,[],[f199]) ).
fof(f852,plain,
( spl17_106
| spl17_48
| ~ spl17_4
| ~ spl17_39 ),
inference(avatar_split_clause,[],[f386,f355,f194,f417,f849]) ).
fof(f386,plain,
( empty(the_carrier(sK2))
| in(sK4,the_carrier(sK2))
| ~ spl17_4
| ~ spl17_39 ),
inference(resolution,[],[f356,f196]) ).
fof(f196,plain,
( element(sK4,the_carrier(sK2))
| ~ spl17_4 ),
inference(avatar_component_clause,[],[f194]) ).
fof(f844,plain,
( ~ spl17_2
| spl17_105
| ~ spl17_44
| ~ spl17_65 ),
inference(avatar_split_clause,[],[f598,f541,f401,f841,f184]) ).
fof(f598,plain,
( relation_of2_as_subset(the_InternalRel(sK2),sK16,sK16)
| ~ rel_str(sK2)
| ~ spl17_44
| ~ spl17_65 ),
inference(superposition,[],[f402,f543]) ).
fof(f829,plain,
( spl17_104
| ~ spl17_30
| ~ spl17_53 ),
inference(avatar_split_clause,[],[f464,f459,f313,f827]) ).
fof(f464,plain,
( ! [X2,X3,X0,X1] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X1,X0)),cartesian_product2(X2,X3))
| in(X0,X2) )
| ~ spl17_30
| ~ spl17_53 ),
inference(superposition,[],[f460,f314]) ).
fof(f825,plain,
( spl17_103
| ~ spl17_30
| ~ spl17_52 ),
inference(avatar_split_clause,[],[f462,f452,f313,f823]) ).
fof(f462,plain,
( ! [X2,X3,X0,X1] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X1,X0)),cartesian_product2(X2,X3))
| in(X1,X3) )
| ~ spl17_30
| ~ spl17_52 ),
inference(superposition,[],[f453,f314]) ).
fof(f815,plain,
( spl17_102
| ~ spl17_50
| ~ spl17_51 ),
inference(avatar_split_clause,[],[f448,f439,f435,f813]) ).
fof(f448,plain,
( ! [X2,X3,X0,X1] :
( element(X0,cartesian_product2(X1,X2))
| ~ in(X0,X3)
| ~ relation_of2_as_subset(X3,X1,X2) )
| ~ spl17_50
| ~ spl17_51 ),
inference(resolution,[],[f440,f436]) ).
fof(f811,plain,
( spl17_101
| ~ spl17_33
| ~ spl17_45 ),
inference(avatar_split_clause,[],[f426,f405,f331,f809]) ).
fof(f331,plain,
( spl17_33
<=> ! [X0,X1] :
( sP0(X0,X1)
| ~ is_transitive_in(X0,X1)
| ~ sP1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_33])]) ).
fof(f426,plain,
( ! [X0] :
( ~ transitive_relstr(X0)
| ~ rel_str(X0)
| sP0(the_InternalRel(X0),the_carrier(X0))
| ~ sP1(the_InternalRel(X0)) )
| ~ spl17_33
| ~ spl17_45 ),
inference(resolution,[],[f406,f332]) ).
fof(f332,plain,
( ! [X0,X1] :
( ~ is_transitive_in(X0,X1)
| sP0(X0,X1)
| ~ sP1(X0) )
| ~ spl17_33 ),
inference(avatar_component_clause,[],[f331]) ).
fof(f807,plain,
( spl17_100
| ~ spl17_49
| ~ spl17_50 ),
inference(avatar_split_clause,[],[f443,f435,f422,f805]) ).
fof(f443,plain,
( ! [X2,X3,X0,X1] :
( ~ relation_of2_as_subset(X0,X1,X2)
| ~ empty(cartesian_product2(X1,X2))
| ~ in(X3,X0) )
| ~ spl17_49
| ~ spl17_50 ),
inference(resolution,[],[f436,f423]) ).
fof(f794,plain,
( spl17_99
| ~ spl17_23
| ~ spl17_54 ),
inference(avatar_split_clause,[],[f474,f467,f279,f792]) ).
fof(f792,plain,
( spl17_99
<=> ! [X0,X3,X2,X1] :
( ~ in(X0,X1)
| ~ in(X2,X3)
| ~ empty(cartesian_product2(X3,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_99])]) ).
fof(f474,plain,
( ! [X2,X3,X0,X1] :
( ~ in(X0,X1)
| ~ in(X2,X3)
| ~ empty(cartesian_product2(X3,X1)) )
| ~ spl17_23
| ~ spl17_54 ),
inference(resolution,[],[f468,f280]) ).
fof(f790,plain,
( spl17_98
| ~ spl17_31
| ~ spl17_39 ),
inference(avatar_split_clause,[],[f391,f355,f317,f788]) ).
fof(f317,plain,
( spl17_31
<=> ! [X0,X1] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_31])]) ).
fof(f391,plain,
( ! [X0,X1] :
( empty(powerset(X0))
| in(X1,powerset(X0))
| ~ subset(X1,X0) )
| ~ spl17_31
| ~ spl17_39 ),
inference(resolution,[],[f356,f318]) ).
fof(f318,plain,
( ! [X0,X1] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) )
| ~ spl17_31 ),
inference(avatar_component_clause,[],[f317]) ).
fof(f786,plain,
( spl17_97
| ~ spl17_29
| ~ spl17_39 ),
inference(avatar_split_clause,[],[f390,f355,f308,f784]) ).
fof(f308,plain,
( spl17_29
<=> ! [X0] :
( element(sK6(X0),powerset(X0))
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_29])]) ).
fof(f390,plain,
( ! [X0] :
( empty(powerset(X0))
| in(sK6(X0),powerset(X0))
| empty(X0) )
| ~ spl17_29
| ~ spl17_39 ),
inference(resolution,[],[f356,f309]) ).
fof(f309,plain,
( ! [X0] :
( element(sK6(X0),powerset(X0))
| empty(X0) )
| ~ spl17_29 ),
inference(avatar_component_clause,[],[f308]) ).
fof(f771,plain,
( spl17_96
| ~ spl17_31
| ~ spl17_51 ),
inference(avatar_split_clause,[],[f447,f439,f317,f769]) ).
fof(f769,plain,
( spl17_96
<=> ! [X2,X0,X1] :
( element(X0,X1)
| ~ in(X0,X2)
| ~ subset(X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_96])]) ).
fof(f447,plain,
( ! [X2,X0,X1] :
( element(X0,X1)
| ~ in(X0,X2)
| ~ subset(X2,X1) )
| ~ spl17_31
| ~ spl17_51 ),
inference(resolution,[],[f440,f318]) ).
fof(f767,plain,
( spl17_95
| ~ spl17_29
| ~ spl17_51 ),
inference(avatar_split_clause,[],[f446,f439,f308,f765]) ).
fof(f446,plain,
( ! [X0,X1] :
( element(X0,X1)
| ~ in(X0,sK6(X1))
| empty(X1) )
| ~ spl17_29
| ~ spl17_51 ),
inference(resolution,[],[f440,f309]) ).
fof(f763,plain,
( spl17_94
| ~ spl17_42
| ~ spl17_44 ),
inference(avatar_split_clause,[],[f425,f401,f367,f761]) ).
fof(f761,plain,
( spl17_94
<=> ! [X0] :
( ~ rel_str(X0)
| relation_of2(the_InternalRel(X0),the_carrier(X0),the_carrier(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_94])]) ).
fof(f425,plain,
( ! [X0] :
( ~ rel_str(X0)
| relation_of2(the_InternalRel(X0),the_carrier(X0),the_carrier(X0)) )
| ~ spl17_42
| ~ spl17_44 ),
inference(resolution,[],[f402,f368]) ).
fof(f759,plain,
( spl17_93
| ~ spl17_29
| ~ spl17_41 ),
inference(avatar_split_clause,[],[f394,f363,f308,f757]) ).
fof(f394,plain,
( ! [X0,X1] :
( relation(sK6(cartesian_product2(X0,X1)))
| empty(cartesian_product2(X0,X1)) )
| ~ spl17_29
| ~ spl17_41 ),
inference(resolution,[],[f364,f309]) ).
fof(f735,plain,
( spl17_92
| ~ spl17_18
| ~ spl17_51 ),
inference(avatar_split_clause,[],[f449,f439,f259,f733]) ).
fof(f259,plain,
( spl17_18
<=> ! [X0] : element(sK10(X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_18])]) ).
fof(f449,plain,
( ! [X0,X1] :
( element(X0,X1)
| ~ in(X0,sK10(powerset(X1))) )
| ~ spl17_18
| ~ spl17_51 ),
inference(resolution,[],[f440,f260]) ).
fof(f260,plain,
( ! [X0] : element(sK10(X0),X0)
| ~ spl17_18 ),
inference(avatar_component_clause,[],[f259]) ).
fof(f731,plain,
( spl17_91
| ~ spl17_31
| ~ spl17_49 ),
inference(avatar_split_clause,[],[f431,f422,f317,f729]) ).
fof(f729,plain,
( spl17_91
<=> ! [X2,X0,X1] :
( ~ empty(X0)
| ~ in(X1,X2)
| ~ subset(X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_91])]) ).
fof(f431,plain,
( ! [X2,X0,X1] :
( ~ empty(X0)
| ~ in(X1,X2)
| ~ subset(X2,X0) )
| ~ spl17_31
| ~ spl17_49 ),
inference(resolution,[],[f423,f318]) ).
fof(f727,plain,
( spl17_90
| ~ spl17_25
| ~ spl17_38 ),
inference(avatar_split_clause,[],[f383,f351,f292,f725]) ).
fof(f725,plain,
( spl17_90
<=> ! [X0,X1] :
( sP0(X0,X1)
| ~ in(X1,sK9(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_90])]) ).
fof(f383,plain,
( ! [X0,X1] :
( sP0(X0,X1)
| ~ in(X1,sK9(X0,X1)) )
| ~ spl17_25
| ~ spl17_38 ),
inference(resolution,[],[f352,f293]) ).
fof(f723,plain,
( spl17_89
| ~ spl17_26
| ~ spl17_38 ),
inference(avatar_split_clause,[],[f382,f351,f296,f721]) ).
fof(f382,plain,
( ! [X0,X1] :
( sP0(X0,X1)
| element(sK9(X0,X1),X1) )
| ~ spl17_26
| ~ spl17_38 ),
inference(resolution,[],[f352,f297]) ).
fof(f719,plain,
( spl17_88
| ~ spl17_25
| ~ spl17_37 ),
inference(avatar_split_clause,[],[f380,f347,f292,f717]) ).
fof(f717,plain,
( spl17_88
<=> ! [X0,X1] :
( sP0(X0,X1)
| ~ in(X1,sK8(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_88])]) ).
fof(f380,plain,
( ! [X0,X1] :
( sP0(X0,X1)
| ~ in(X1,sK8(X0,X1)) )
| ~ spl17_25
| ~ spl17_37 ),
inference(resolution,[],[f348,f293]) ).
fof(f715,plain,
( spl17_87
| ~ spl17_26
| ~ spl17_37 ),
inference(avatar_split_clause,[],[f379,f347,f296,f713]) ).
fof(f379,plain,
( ! [X0,X1] :
( sP0(X0,X1)
| element(sK8(X0,X1),X1) )
| ~ spl17_26
| ~ spl17_37 ),
inference(resolution,[],[f348,f297]) ).
fof(f711,plain,
( spl17_86
| ~ spl17_25
| ~ spl17_35 ),
inference(avatar_split_clause,[],[f375,f339,f292,f709]) ).
fof(f709,plain,
( spl17_86
<=> ! [X0,X1] :
( sP0(X0,X1)
| ~ in(X1,sK7(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_86])]) ).
fof(f375,plain,
( ! [X0,X1] :
( sP0(X0,X1)
| ~ in(X1,sK7(X0,X1)) )
| ~ spl17_25
| ~ spl17_35 ),
inference(resolution,[],[f340,f293]) ).
fof(f707,plain,
( spl17_85
| ~ spl17_26
| ~ spl17_35 ),
inference(avatar_split_clause,[],[f374,f339,f296,f705]) ).
fof(f374,plain,
( ! [X0,X1] :
( sP0(X0,X1)
| element(sK7(X0,X1),X1) )
| ~ spl17_26
| ~ spl17_35 ),
inference(resolution,[],[f340,f297]) ).
fof(f703,plain,
( spl17_84
| ~ spl17_3
| ~ spl17_65 ),
inference(avatar_split_clause,[],[f595,f541,f189,f700]) ).
fof(f595,plain,
( element(sK3,sK16)
| ~ spl17_3
| ~ spl17_65 ),
inference(superposition,[],[f191,f543]) ).
fof(f191,plain,
( element(sK3,the_carrier(sK2))
| ~ spl17_3 ),
inference(avatar_component_clause,[],[f189]) ).
fof(f688,plain,
( spl17_83
| ~ spl17_18
| ~ spl17_49 ),
inference(avatar_split_clause,[],[f432,f422,f259,f686]) ).
fof(f432,plain,
( ! [X0,X1] :
( ~ empty(X0)
| ~ in(X1,sK10(powerset(X0))) )
| ~ spl17_18
| ~ spl17_49 ),
inference(resolution,[],[f423,f260]) ).
fof(f684,plain,
( spl17_82
| ~ spl17_31
| ~ spl17_41 ),
inference(avatar_split_clause,[],[f395,f363,f317,f682]) ).
fof(f395,plain,
( ! [X2,X0,X1] :
( relation(X0)
| ~ subset(X0,cartesian_product2(X1,X2)) )
| ~ spl17_31
| ~ spl17_41 ),
inference(resolution,[],[f364,f318]) ).
fof(f680,plain,
( spl17_81
| ~ spl17_22
| ~ spl17_36
| ~ spl17_39 ),
inference(avatar_split_clause,[],[f392,f355,f343,f275,f678]) ).
fof(f678,plain,
( spl17_81
<=> ! [X0] :
( in(sK16,powerset(X0))
| empty(powerset(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_81])]) ).
fof(f392,plain,
( ! [X0] :
( in(sK16,powerset(X0))
| empty(powerset(X0)) )
| ~ spl17_22
| ~ spl17_36
| ~ spl17_39 ),
inference(forward_demodulation,[],[f389,f344]) ).
fof(f389,plain,
( ! [X0] :
( empty(powerset(X0))
| in(sK11(X0),powerset(X0)) )
| ~ spl17_22
| ~ spl17_39 ),
inference(resolution,[],[f356,f276]) ).
fof(f670,plain,
( spl17_80
| ~ spl17_4
| ~ spl17_65 ),
inference(avatar_split_clause,[],[f594,f541,f194,f667]) ).
fof(f594,plain,
( element(sK4,sK16)
| ~ spl17_4
| ~ spl17_65 ),
inference(superposition,[],[f196,f543]) ).
fof(f661,plain,
( spl17_79
| ~ spl17_41
| ~ spl17_50 ),
inference(avatar_split_clause,[],[f442,f435,f363,f659]) ).
fof(f442,plain,
( ! [X2,X0,X1] :
( ~ relation_of2_as_subset(X0,X1,X2)
| relation(X0) )
| ~ spl17_41
| ~ spl17_50 ),
inference(resolution,[],[f436,f364]) ).
fof(f657,plain,
( spl17_78
| ~ spl17_27
| ~ spl17_43 ),
inference(avatar_split_clause,[],[f399,f371,f300,f655]) ).
fof(f300,plain,
( spl17_27
<=> ! [X0,X1] : relation_of2(sK12(X0,X1),X0,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_27])]) ).
fof(f399,plain,
( ! [X0,X1] : relation_of2_as_subset(sK12(X0,X1),X0,X1)
| ~ spl17_27
| ~ spl17_43 ),
inference(resolution,[],[f372,f301]) ).
fof(f301,plain,
( ! [X0,X1] : relation_of2(sK12(X0,X1),X0,X1)
| ~ spl17_27 ),
inference(avatar_component_clause,[],[f300]) ).
fof(f653,plain,
( spl17_77
| ~ spl17_28
| ~ spl17_42 ),
inference(avatar_split_clause,[],[f398,f367,f304,f651]) ).
fof(f651,plain,
( spl17_77
<=> ! [X0,X1] : relation_of2(sK13(X0,X1),X0,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_77])]) ).
fof(f398,plain,
( ! [X0,X1] : relation_of2(sK13(X0,X1),X0,X1)
| ~ spl17_28
| ~ spl17_42 ),
inference(resolution,[],[f368,f305]) ).
fof(f649,plain,
( spl17_76
| ~ spl17_18
| ~ spl17_41 ),
inference(avatar_split_clause,[],[f396,f363,f259,f647]) ).
fof(f396,plain,
( ! [X0,X1] : relation(sK10(powerset(cartesian_product2(X0,X1))))
| ~ spl17_18
| ~ spl17_41 ),
inference(resolution,[],[f364,f260]) ).
fof(f645,plain,
( spl17_75
| ~ spl17_18
| ~ spl17_39 ),
inference(avatar_split_clause,[],[f388,f355,f259,f643]) ).
fof(f388,plain,
( ! [X0] :
( empty(X0)
| in(sK10(X0),X0) )
| ~ spl17_18
| ~ spl17_39 ),
inference(resolution,[],[f356,f260]) ).
fof(f635,plain,
( spl17_74
| ~ spl17_23
| ~ spl17_59 ),
inference(avatar_split_clause,[],[f509,f500,f279,f633]) ).
fof(f509,plain,
( ! [X0,X1] :
( sP0(X0,X1)
| ~ empty(X0) )
| ~ spl17_23
| ~ spl17_59 ),
inference(resolution,[],[f501,f280]) ).
fof(f631,plain,
( spl17_73
| ~ spl17_5
| ~ spl17_65 ),
inference(avatar_split_clause,[],[f593,f541,f199,f628]) ).
fof(f628,plain,
( spl17_73
<=> element(sK5,sK16) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_73])]) ).
fof(f593,plain,
( element(sK5,sK16)
| ~ spl17_5
| ~ spl17_65 ),
inference(superposition,[],[f201,f543]) ).
fof(f608,plain,
( spl17_69
| ~ spl17_21
| ~ spl17_24 ),
inference(avatar_split_clause,[],[f589,f287,f271,f567]) ).
fof(f271,plain,
( spl17_21
<=> ! [X0] :
( empty_set = X0
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_21])]) ).
fof(f589,plain,
( ! [X0] :
( sK16 = X0
| ~ empty(X0) )
| ~ spl17_21
| ~ spl17_24 ),
inference(forward_demodulation,[],[f272,f289]) ).
fof(f272,plain,
( ! [X0] :
( ~ empty(X0)
| empty_set = X0 )
| ~ spl17_21 ),
inference(avatar_component_clause,[],[f271]) ).
fof(f588,plain,
( ~ spl17_48
| ~ spl17_71 ),
inference(avatar_contradiction_clause,[],[f581]) ).
fof(f581,plain,
( $false
| ~ spl17_48
| ~ spl17_71 ),
inference(resolution,[],[f576,f419]) ).
fof(f419,plain,
( empty(the_carrier(sK2))
| ~ spl17_48 ),
inference(avatar_component_clause,[],[f417]) ).
fof(f576,plain,
( ! [X0] : ~ empty(X0)
| ~ spl17_71 ),
inference(avatar_component_clause,[],[f575]) ).
fof(f575,plain,
( spl17_71
<=> ! [X0] : ~ empty(X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_71])]) ).
fof(f587,plain,
( ~ spl17_9
| ~ spl17_71 ),
inference(avatar_contradiction_clause,[],[f582]) ).
fof(f582,plain,
( $false
| ~ spl17_9
| ~ spl17_71 ),
inference(resolution,[],[f576,f221]) ).
fof(f586,plain,
( ~ spl17_15
| ~ spl17_71 ),
inference(avatar_contradiction_clause,[],[f583]) ).
fof(f583,plain,
( $false
| ~ spl17_15
| ~ spl17_71 ),
inference(resolution,[],[f576,f248]) ).
fof(f248,plain,
( ! [X0] : empty(sK11(X0))
| ~ spl17_15 ),
inference(avatar_component_clause,[],[f247]) ).
fof(f247,plain,
( spl17_15
<=> ! [X0] : empty(sK11(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_15])]) ).
fof(f585,plain,
( ~ spl17_12
| ~ spl17_71 ),
inference(avatar_contradiction_clause,[],[f584]) ).
fof(f584,plain,
( $false
| ~ spl17_12
| ~ spl17_71 ),
inference(resolution,[],[f576,f236]) ).
fof(f236,plain,
( empty(sK16)
| ~ spl17_12 ),
inference(avatar_component_clause,[],[f234]) ).
fof(f580,plain,
( spl17_71
| spl17_72
| ~ spl17_22
| ~ spl17_36
| ~ spl17_49 ),
inference(avatar_split_clause,[],[f433,f422,f343,f275,f578,f575]) ).
fof(f433,plain,
( ! [X0,X1] :
( ~ in(X1,sK16)
| ~ empty(X0) )
| ~ spl17_22
| ~ spl17_36
| ~ spl17_49 ),
inference(forward_demodulation,[],[f429,f344]) ).
fof(f429,plain,
( ! [X0,X1] :
( ~ empty(X0)
| ~ in(X1,sK11(X0)) )
| ~ spl17_22
| ~ spl17_49 ),
inference(resolution,[],[f423,f276]) ).
fof(f573,plain,
( spl17_70
| ~ spl17_23
| ~ spl17_35 ),
inference(avatar_split_clause,[],[f376,f339,f279,f571]) ).
fof(f376,plain,
( ! [X0,X1] :
( sP0(X0,X1)
| ~ empty(X1) )
| ~ spl17_23
| ~ spl17_35 ),
inference(resolution,[],[f340,f280]) ).
fof(f569,plain,
( spl17_69
| ~ spl17_12
| ~ spl17_32 ),
inference(avatar_split_clause,[],[f327,f321,f234,f567]) ).
fof(f327,plain,
( ! [X0] :
( sK16 = X0
| ~ empty(X0) )
| ~ spl17_12
| ~ spl17_32 ),
inference(resolution,[],[f322,f236]) ).
fof(f564,plain,
( spl17_68
| ~ spl17_22
| ~ spl17_36
| ~ spl17_41 ),
inference(avatar_split_clause,[],[f397,f363,f343,f275,f561]) ).
fof(f397,plain,
( relation(sK16)
| ~ spl17_22
| ~ spl17_36
| ~ spl17_41 ),
inference(forward_demodulation,[],[f393,f344]) ).
fof(f393,plain,
( ! [X0,X1] : relation(sK11(cartesian_product2(X0,X1)))
| ~ spl17_22
| ~ spl17_41 ),
inference(resolution,[],[f364,f276]) ).
fof(f555,plain,
( spl17_67
| ~ spl17_30
| ~ spl17_66 ),
inference(avatar_split_clause,[],[f551,f546,f313,f553]) ).
fof(f546,plain,
( spl17_66
<=> ! [X6,X0,X5,X1,X7] :
( in(unordered_pair(unordered_pair(X5,X7),singleton(X5)),X0)
| ~ in(unordered_pair(unordered_pair(X6,X7),singleton(X6)),X0)
| ~ in(unordered_pair(unordered_pair(X5,X6),singleton(X5)),X0)
| ~ in(X7,X1)
| ~ in(X6,X1)
| ~ in(X5,X1)
| ~ sP0(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_66])]) ).
fof(f551,plain,
( ! [X0,X1,X6,X7,X5] :
( ~ in(unordered_pair(singleton(X5),unordered_pair(X5,X6)),X0)
| ~ in(unordered_pair(singleton(X6),unordered_pair(X6,X7)),X0)
| in(unordered_pair(singleton(X5),unordered_pair(X5,X7)),X0)
| ~ in(X7,X1)
| ~ in(X6,X1)
| ~ in(X5,X1)
| ~ sP0(X0,X1) )
| ~ spl17_30
| ~ spl17_66 ),
inference(forward_demodulation,[],[f550,f314]) ).
fof(f550,plain,
( ! [X0,X1,X6,X7,X5] :
( ~ in(unordered_pair(singleton(X6),unordered_pair(X6,X7)),X0)
| in(unordered_pair(singleton(X5),unordered_pair(X5,X7)),X0)
| ~ in(unordered_pair(unordered_pair(X5,X6),singleton(X5)),X0)
| ~ in(X7,X1)
| ~ in(X6,X1)
| ~ in(X5,X1)
| ~ sP0(X0,X1) )
| ~ spl17_30
| ~ spl17_66 ),
inference(forward_demodulation,[],[f549,f314]) ).
fof(f549,plain,
( ! [X0,X1,X6,X7,X5] :
( in(unordered_pair(singleton(X5),unordered_pair(X5,X7)),X0)
| ~ in(unordered_pair(unordered_pair(X6,X7),singleton(X6)),X0)
| ~ in(unordered_pair(unordered_pair(X5,X6),singleton(X5)),X0)
| ~ in(X7,X1)
| ~ in(X6,X1)
| ~ in(X5,X1)
| ~ sP0(X0,X1) )
| ~ spl17_30
| ~ spl17_66 ),
inference(forward_demodulation,[],[f547,f314]) ).
fof(f547,plain,
( ! [X0,X1,X6,X7,X5] :
( in(unordered_pair(unordered_pair(X5,X7),singleton(X5)),X0)
| ~ in(unordered_pair(unordered_pair(X6,X7),singleton(X6)),X0)
| ~ in(unordered_pair(unordered_pair(X5,X6),singleton(X5)),X0)
| ~ in(X7,X1)
| ~ in(X6,X1)
| ~ in(X5,X1)
| ~ sP0(X0,X1) )
| ~ spl17_66 ),
inference(avatar_component_clause,[],[f546]) ).
fof(f548,plain,
spl17_66,
inference(avatar_split_clause,[],[f169,f546]) ).
fof(f169,plain,
! [X0,X1,X6,X7,X5] :
( in(unordered_pair(unordered_pair(X5,X7),singleton(X5)),X0)
| ~ in(unordered_pair(unordered_pair(X6,X7),singleton(X6)),X0)
| ~ in(unordered_pair(unordered_pair(X5,X6),singleton(X5)),X0)
| ~ in(X7,X1)
| ~ in(X6,X1)
| ~ in(X5,X1)
| ~ sP0(X0,X1) ),
inference(definition_unfolding,[],[f124,f144,f144,f144]) ).
fof(f144,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[],[f5]) ).
fof(f5,axiom,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_tarski) ).
fof(f124,plain,
! [X0,X1,X6,X7,X5] :
( in(ordered_pair(X5,X7),X0)
| ~ in(ordered_pair(X6,X7),X0)
| ~ in(ordered_pair(X5,X6),X0)
| ~ in(X7,X1)
| ~ in(X6,X1)
| ~ in(X5,X1)
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f89]) ).
fof(f89,plain,
! [X0,X1] :
( ( sP0(X0,X1)
| ( ~ in(ordered_pair(sK7(X0,X1),sK9(X0,X1)),X0)
& in(ordered_pair(sK8(X0,X1),sK9(X0,X1)),X0)
& in(ordered_pair(sK7(X0,X1),sK8(X0,X1)),X0)
& in(sK9(X0,X1),X1)
& in(sK8(X0,X1),X1)
& in(sK7(X0,X1),X1) ) )
& ( ! [X5,X6,X7] :
( in(ordered_pair(X5,X7),X0)
| ~ in(ordered_pair(X6,X7),X0)
| ~ in(ordered_pair(X5,X6),X0)
| ~ in(X7,X1)
| ~ in(X6,X1)
| ~ in(X5,X1) )
| ~ sP0(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK7,sK8,sK9])],[f87,f88]) ).
fof(f88,plain,
! [X0,X1] :
( ? [X2,X3,X4] :
( ~ in(ordered_pair(X2,X4),X0)
& in(ordered_pair(X3,X4),X0)
& in(ordered_pair(X2,X3),X0)
& in(X4,X1)
& in(X3,X1)
& in(X2,X1) )
=> ( ~ in(ordered_pair(sK7(X0,X1),sK9(X0,X1)),X0)
& in(ordered_pair(sK8(X0,X1),sK9(X0,X1)),X0)
& in(ordered_pair(sK7(X0,X1),sK8(X0,X1)),X0)
& in(sK9(X0,X1),X1)
& in(sK8(X0,X1),X1)
& in(sK7(X0,X1),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f87,plain,
! [X0,X1] :
( ( sP0(X0,X1)
| ? [X2,X3,X4] :
( ~ in(ordered_pair(X2,X4),X0)
& in(ordered_pair(X3,X4),X0)
& in(ordered_pair(X2,X3),X0)
& in(X4,X1)
& in(X3,X1)
& in(X2,X1) ) )
& ( ! [X5,X6,X7] :
( in(ordered_pair(X5,X7),X0)
| ~ in(ordered_pair(X6,X7),X0)
| ~ in(ordered_pair(X5,X6),X0)
| ~ in(X7,X1)
| ~ in(X6,X1)
| ~ in(X5,X1) )
| ~ sP0(X0,X1) ) ),
inference(rectify,[],[f86]) ).
fof(f86,plain,
! [X0,X1] :
( ( sP0(X0,X1)
| ? [X2,X3,X4] :
( ~ in(ordered_pair(X2,X4),X0)
& in(ordered_pair(X3,X4),X0)
& in(ordered_pair(X2,X3),X0)
& in(X4,X1)
& in(X3,X1)
& in(X2,X1) ) )
& ( ! [X2,X3,X4] :
( in(ordered_pair(X2,X4),X0)
| ~ in(ordered_pair(X3,X4),X0)
| ~ in(ordered_pair(X2,X3),X0)
| ~ in(X4,X1)
| ~ in(X3,X1)
| ~ in(X2,X1) )
| ~ sP0(X0,X1) ) ),
inference(nnf_transformation,[],[f75]) ).
fof(f75,plain,
! [X0,X1] :
( sP0(X0,X1)
<=> ! [X2,X3,X4] :
( in(ordered_pair(X2,X4),X0)
| ~ in(ordered_pair(X3,X4),X0)
| ~ in(ordered_pair(X2,X3),X0)
| ~ in(X4,X1)
| ~ in(X3,X1)
| ~ in(X2,X1) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f544,plain,
( spl17_65
| ~ spl17_21
| ~ spl17_24
| ~ spl17_48 ),
inference(avatar_split_clause,[],[f457,f417,f287,f271,f541]) ).
fof(f457,plain,
( the_carrier(sK2) = sK16
| ~ spl17_21
| ~ spl17_24
| ~ spl17_48 ),
inference(forward_demodulation,[],[f456,f289]) ).
fof(f456,plain,
( empty_set = the_carrier(sK2)
| ~ spl17_21
| ~ spl17_48 ),
inference(resolution,[],[f419,f272]) ).
fof(f530,plain,
( spl17_64
| ~ spl17_30
| ~ spl17_62 ),
inference(avatar_split_clause,[],[f522,f519,f313,f528]) ).
fof(f519,plain,
( spl17_62
<=> ! [X2,X0,X1] :
( in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),the_InternalRel(X0))
| ~ related(X0,X1,X2)
| ~ element(X2,the_carrier(X0))
| ~ element(X1,the_carrier(X0))
| ~ rel_str(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_62])]) ).
fof(f522,plain,
( ! [X2,X0,X1] :
( in(unordered_pair(singleton(X1),unordered_pair(X1,X2)),the_InternalRel(X0))
| ~ related(X0,X1,X2)
| ~ element(X2,the_carrier(X0))
| ~ element(X1,the_carrier(X0))
| ~ rel_str(X0) )
| ~ spl17_30
| ~ spl17_62 ),
inference(forward_demodulation,[],[f520,f314]) ).
fof(f520,plain,
( ! [X2,X0,X1] :
( in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),the_InternalRel(X0))
| ~ related(X0,X1,X2)
| ~ element(X2,the_carrier(X0))
| ~ element(X1,the_carrier(X0))
| ~ rel_str(X0) )
| ~ spl17_62 ),
inference(avatar_component_clause,[],[f519]) ).
fof(f526,plain,
( spl17_63
| ~ spl17_30
| ~ spl17_61 ),
inference(avatar_split_clause,[],[f517,f514,f313,f524]) ).
fof(f514,plain,
( spl17_61
<=> ! [X2,X0,X1] :
( related(X0,X1,X2)
| ~ in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),the_InternalRel(X0))
| ~ element(X2,the_carrier(X0))
| ~ element(X1,the_carrier(X0))
| ~ rel_str(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_61])]) ).
fof(f517,plain,
( ! [X2,X0,X1] :
( ~ in(unordered_pair(singleton(X1),unordered_pair(X1,X2)),the_InternalRel(X0))
| related(X0,X1,X2)
| ~ element(X2,the_carrier(X0))
| ~ element(X1,the_carrier(X0))
| ~ rel_str(X0) )
| ~ spl17_30
| ~ spl17_61 ),
inference(forward_demodulation,[],[f515,f314]) ).
fof(f515,plain,
( ! [X2,X0,X1] :
( related(X0,X1,X2)
| ~ in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),the_InternalRel(X0))
| ~ element(X2,the_carrier(X0))
| ~ element(X1,the_carrier(X0))
| ~ rel_str(X0) )
| ~ spl17_61 ),
inference(avatar_component_clause,[],[f514]) ).
fof(f521,plain,
spl17_62,
inference(avatar_split_clause,[],[f171,f519]) ).
fof(f171,plain,
! [X2,X0,X1] :
( in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),the_InternalRel(X0))
| ~ related(X0,X1,X2)
| ~ element(X2,the_carrier(X0))
| ~ element(X1,the_carrier(X0))
| ~ rel_str(X0) ),
inference(definition_unfolding,[],[f135,f144]) ).
fof(f135,plain,
! [X2,X0,X1] :
( in(ordered_pair(X1,X2),the_InternalRel(X0))
| ~ related(X0,X1,X2)
| ~ element(X2,the_carrier(X0))
| ~ element(X1,the_carrier(X0))
| ~ rel_str(X0) ),
inference(cnf_transformation,[],[f91]) ).
fof(f91,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( related(X0,X1,X2)
| ~ in(ordered_pair(X1,X2),the_InternalRel(X0)) )
& ( in(ordered_pair(X1,X2),the_InternalRel(X0))
| ~ related(X0,X1,X2) ) )
| ~ element(X2,the_carrier(X0)) )
| ~ element(X1,the_carrier(X0)) )
| ~ rel_str(X0) ),
inference(nnf_transformation,[],[f59]) ).
fof(f59,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( related(X0,X1,X2)
<=> in(ordered_pair(X1,X2),the_InternalRel(X0)) )
| ~ element(X2,the_carrier(X0)) )
| ~ element(X1,the_carrier(X0)) )
| ~ rel_str(X0) ),
inference(ennf_transformation,[],[f7]) ).
fof(f7,axiom,
! [X0] :
( rel_str(X0)
=> ! [X1] :
( element(X1,the_carrier(X0))
=> ! [X2] :
( element(X2,the_carrier(X0))
=> ( related(X0,X1,X2)
<=> in(ordered_pair(X1,X2),the_InternalRel(X0)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d9_orders_2) ).
fof(f516,plain,
spl17_61,
inference(avatar_split_clause,[],[f170,f514]) ).
fof(f170,plain,
! [X2,X0,X1] :
( related(X0,X1,X2)
| ~ in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),the_InternalRel(X0))
| ~ element(X2,the_carrier(X0))
| ~ element(X1,the_carrier(X0))
| ~ rel_str(X0) ),
inference(definition_unfolding,[],[f136,f144]) ).
fof(f136,plain,
! [X2,X0,X1] :
( related(X0,X1,X2)
| ~ in(ordered_pair(X1,X2),the_InternalRel(X0))
| ~ element(X2,the_carrier(X0))
| ~ element(X1,the_carrier(X0))
| ~ rel_str(X0) ),
inference(cnf_transformation,[],[f91]) ).
fof(f506,plain,
( spl17_60
| ~ spl17_30
| ~ spl17_57 ),
inference(avatar_split_clause,[],[f494,f490,f313,f504]) ).
fof(f490,plain,
( spl17_57
<=> ! [X0,X1] :
( sP0(X0,X1)
| in(unordered_pair(unordered_pair(sK7(X0,X1),sK8(X0,X1)),singleton(sK7(X0,X1))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_57])]) ).
fof(f494,plain,
( ! [X0,X1] :
( in(unordered_pair(singleton(sK7(X0,X1)),unordered_pair(sK8(X0,X1),sK7(X0,X1))),X0)
| sP0(X0,X1) )
| ~ spl17_30
| ~ spl17_57 ),
inference(forward_demodulation,[],[f493,f314]) ).
fof(f493,plain,
( ! [X0,X1] :
( in(unordered_pair(singleton(sK7(X0,X1)),unordered_pair(sK7(X0,X1),sK8(X0,X1))),X0)
| sP0(X0,X1) )
| ~ spl17_30
| ~ spl17_57 ),
inference(forward_demodulation,[],[f491,f314]) ).
fof(f491,plain,
( ! [X0,X1] :
( sP0(X0,X1)
| in(unordered_pair(unordered_pair(sK7(X0,X1),sK8(X0,X1)),singleton(sK7(X0,X1))),X0) )
| ~ spl17_57 ),
inference(avatar_component_clause,[],[f490]) ).
fof(f502,plain,
( spl17_59
| ~ spl17_30
| ~ spl17_56 ),
inference(avatar_split_clause,[],[f488,f484,f313,f500]) ).
fof(f484,plain,
( spl17_56
<=> ! [X0,X1] :
( sP0(X0,X1)
| in(unordered_pair(unordered_pair(sK8(X0,X1),sK9(X0,X1)),singleton(sK8(X0,X1))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_56])]) ).
fof(f488,plain,
( ! [X0,X1] :
( in(unordered_pair(singleton(sK8(X0,X1)),unordered_pair(sK9(X0,X1),sK8(X0,X1))),X0)
| sP0(X0,X1) )
| ~ spl17_30
| ~ spl17_56 ),
inference(forward_demodulation,[],[f487,f314]) ).
fof(f487,plain,
( ! [X0,X1] :
( in(unordered_pair(singleton(sK8(X0,X1)),unordered_pair(sK8(X0,X1),sK9(X0,X1))),X0)
| sP0(X0,X1) )
| ~ spl17_30
| ~ spl17_56 ),
inference(forward_demodulation,[],[f485,f314]) ).
fof(f485,plain,
( ! [X0,X1] :
( sP0(X0,X1)
| in(unordered_pair(unordered_pair(sK8(X0,X1),sK9(X0,X1)),singleton(sK8(X0,X1))),X0) )
| ~ spl17_56 ),
inference(avatar_component_clause,[],[f484]) ).
fof(f498,plain,
( spl17_58
| ~ spl17_30
| ~ spl17_55 ),
inference(avatar_split_clause,[],[f482,f478,f313,f496]) ).
fof(f478,plain,
( spl17_55
<=> ! [X0,X1] :
( sP0(X0,X1)
| ~ in(unordered_pair(unordered_pair(sK7(X0,X1),sK9(X0,X1)),singleton(sK7(X0,X1))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_55])]) ).
fof(f482,plain,
( ! [X0,X1] :
( ~ in(unordered_pair(singleton(sK7(X0,X1)),unordered_pair(sK9(X0,X1),sK7(X0,X1))),X0)
| sP0(X0,X1) )
| ~ spl17_30
| ~ spl17_55 ),
inference(forward_demodulation,[],[f481,f314]) ).
fof(f481,plain,
( ! [X0,X1] :
( ~ in(unordered_pair(singleton(sK7(X0,X1)),unordered_pair(sK7(X0,X1),sK9(X0,X1))),X0)
| sP0(X0,X1) )
| ~ spl17_30
| ~ spl17_55 ),
inference(forward_demodulation,[],[f479,f314]) ).
fof(f479,plain,
( ! [X0,X1] :
( sP0(X0,X1)
| ~ in(unordered_pair(unordered_pair(sK7(X0,X1),sK9(X0,X1)),singleton(sK7(X0,X1))),X0) )
| ~ spl17_55 ),
inference(avatar_component_clause,[],[f478]) ).
fof(f492,plain,
spl17_57,
inference(avatar_split_clause,[],[f168,f490]) ).
fof(f168,plain,
! [X0,X1] :
( sP0(X0,X1)
| in(unordered_pair(unordered_pair(sK7(X0,X1),sK8(X0,X1)),singleton(sK7(X0,X1))),X0) ),
inference(definition_unfolding,[],[f128,f144]) ).
fof(f128,plain,
! [X0,X1] :
( sP0(X0,X1)
| in(ordered_pair(sK7(X0,X1),sK8(X0,X1)),X0) ),
inference(cnf_transformation,[],[f89]) ).
fof(f486,plain,
spl17_56,
inference(avatar_split_clause,[],[f167,f484]) ).
fof(f167,plain,
! [X0,X1] :
( sP0(X0,X1)
| in(unordered_pair(unordered_pair(sK8(X0,X1),sK9(X0,X1)),singleton(sK8(X0,X1))),X0) ),
inference(definition_unfolding,[],[f129,f144]) ).
fof(f129,plain,
! [X0,X1] :
( sP0(X0,X1)
| in(ordered_pair(sK8(X0,X1),sK9(X0,X1)),X0) ),
inference(cnf_transformation,[],[f89]) ).
fof(f480,plain,
spl17_55,
inference(avatar_split_clause,[],[f166,f478]) ).
fof(f166,plain,
! [X0,X1] :
( sP0(X0,X1)
| ~ in(unordered_pair(unordered_pair(sK7(X0,X1),sK9(X0,X1)),singleton(sK7(X0,X1))),X0) ),
inference(definition_unfolding,[],[f130,f144]) ).
fof(f130,plain,
! [X0,X1] :
( sP0(X0,X1)
| ~ in(ordered_pair(sK7(X0,X1),sK9(X0,X1)),X0) ),
inference(cnf_transformation,[],[f89]) ).
fof(f469,plain,
spl17_54,
inference(avatar_split_clause,[],[f175,f467]) ).
fof(f175,plain,
! [X2,X3,X0,X1] :
( in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),cartesian_product2(X2,X3))
| ~ in(X1,X3)
| ~ in(X0,X2) ),
inference(forward_demodulation,[],[f172,f143]) ).
fof(f143,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f3]) ).
fof(f3,axiom,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
fof(f172,plain,
! [X2,X3,X0,X1] :
( in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),cartesian_product2(X2,X3))
| ~ in(X1,X3)
| ~ in(X0,X2) ),
inference(definition_unfolding,[],[f162,f144]) ).
fof(f162,plain,
! [X2,X3,X0,X1] :
( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| ~ in(X1,X3)
| ~ in(X0,X2) ),
inference(cnf_transformation,[],[f102]) ).
fof(f102,plain,
! [X0,X1,X2,X3] :
( ( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| ~ in(X1,X3)
| ~ in(X0,X2) )
& ( ( in(X1,X3)
& in(X0,X2) )
| ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ) ),
inference(flattening,[],[f101]) ).
fof(f101,plain,
! [X0,X1,X2,X3] :
( ( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| ~ in(X1,X3)
| ~ in(X0,X2) )
& ( ( in(X1,X3)
& in(X0,X2) )
| ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ) ),
inference(nnf_transformation,[],[f37]) ).
fof(f37,axiom,
! [X0,X1,X2,X3] :
( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
<=> ( in(X1,X3)
& in(X0,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t106_zfmisc_1) ).
fof(f461,plain,
spl17_53,
inference(avatar_split_clause,[],[f177,f459]) ).
fof(f177,plain,
! [X2,X3,X0,X1] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),cartesian_product2(X2,X3))
| in(X0,X2) ),
inference(forward_demodulation,[],[f174,f143]) ).
fof(f174,plain,
! [X2,X3,X0,X1] :
( in(X0,X2)
| ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),cartesian_product2(X2,X3)) ),
inference(definition_unfolding,[],[f160,f144]) ).
fof(f160,plain,
! [X2,X3,X0,X1] :
( in(X0,X2)
| ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ),
inference(cnf_transformation,[],[f102]) ).
fof(f454,plain,
spl17_52,
inference(avatar_split_clause,[],[f176,f452]) ).
fof(f176,plain,
! [X2,X3,X0,X1] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),cartesian_product2(X2,X3))
| in(X1,X3) ),
inference(forward_demodulation,[],[f173,f143]) ).
fof(f173,plain,
! [X2,X3,X0,X1] :
( in(X1,X3)
| ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),cartesian_product2(X2,X3)) ),
inference(definition_unfolding,[],[f161,f144]) ).
fof(f161,plain,
! [X2,X3,X0,X1] :
( in(X1,X3)
| ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ),
inference(cnf_transformation,[],[f102]) ).
fof(f441,plain,
spl17_51,
inference(avatar_split_clause,[],[f156,f439]) ).
fof(f156,plain,
! [X2,X0,X1] :
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f73]) ).
fof(f73,plain,
! [X0,X1,X2] :
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(flattening,[],[f72]) ).
fof(f72,plain,
! [X0,X1,X2] :
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f43]) ).
fof(f43,axiom,
! [X0,X1,X2] :
( ( element(X1,powerset(X2))
& in(X0,X1) )
=> element(X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_subset) ).
fof(f437,plain,
spl17_50,
inference(avatar_split_clause,[],[f154,f435]) ).
fof(f154,plain,
! [X2,X0,X1] :
( element(X2,powerset(cartesian_product2(X0,X1)))
| ~ relation_of2_as_subset(X2,X0,X1) ),
inference(cnf_transformation,[],[f70]) ).
fof(f70,plain,
! [X0,X1,X2] :
( element(X2,powerset(cartesian_product2(X0,X1)))
| ~ relation_of2_as_subset(X2,X0,X1) ),
inference(ennf_transformation,[],[f18]) ).
fof(f18,axiom,
! [X0,X1,X2] :
( relation_of2_as_subset(X2,X0,X1)
=> element(X2,powerset(cartesian_product2(X0,X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m2_relset_1) ).
fof(f424,plain,
spl17_49,
inference(avatar_split_clause,[],[f159,f422]) ).
fof(f159,plain,
! [X2,X0,X1] :
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f74]) ).
fof(f74,plain,
! [X0,X1,X2] :
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f44]) ).
fof(f44,axiom,
! [X0,X1,X2] :
~ ( empty(X2)
& element(X1,powerset(X2))
& in(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_subset) ).
fof(f420,plain,
( spl17_47
| spl17_48
| ~ spl17_3
| ~ spl17_39 ),
inference(avatar_split_clause,[],[f385,f355,f189,f417,f413]) ).
fof(f385,plain,
( empty(the_carrier(sK2))
| in(sK3,the_carrier(sK2))
| ~ spl17_3
| ~ spl17_39 ),
inference(resolution,[],[f356,f191]) ).
fof(f411,plain,
spl17_46,
inference(avatar_split_clause,[],[f134,f409]) ).
fof(f134,plain,
! [X0] :
( transitive_relstr(X0)
| ~ is_transitive_in(the_InternalRel(X0),the_carrier(X0))
| ~ rel_str(X0) ),
inference(cnf_transformation,[],[f90]) ).
fof(f90,plain,
! [X0] :
( ( ( transitive_relstr(X0)
| ~ is_transitive_in(the_InternalRel(X0),the_carrier(X0)) )
& ( is_transitive_in(the_InternalRel(X0),the_carrier(X0))
| ~ transitive_relstr(X0) ) )
| ~ rel_str(X0) ),
inference(nnf_transformation,[],[f58]) ).
fof(f58,plain,
! [X0] :
( ( transitive_relstr(X0)
<=> is_transitive_in(the_InternalRel(X0),the_carrier(X0)) )
| ~ rel_str(X0) ),
inference(ennf_transformation,[],[f4]) ).
fof(f4,axiom,
! [X0] :
( rel_str(X0)
=> ( transitive_relstr(X0)
<=> is_transitive_in(the_InternalRel(X0),the_carrier(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_orders_2) ).
fof(f407,plain,
spl17_45,
inference(avatar_split_clause,[],[f133,f405]) ).
fof(f133,plain,
! [X0] :
( is_transitive_in(the_InternalRel(X0),the_carrier(X0))
| ~ transitive_relstr(X0)
| ~ rel_str(X0) ),
inference(cnf_transformation,[],[f90]) ).
fof(f403,plain,
spl17_44,
inference(avatar_split_clause,[],[f132,f401]) ).
fof(f132,plain,
! [X0] :
( relation_of2_as_subset(the_InternalRel(X0),the_carrier(X0),the_carrier(X0))
| ~ rel_str(X0) ),
inference(cnf_transformation,[],[f57]) ).
fof(f57,plain,
! [X0] :
( relation_of2_as_subset(the_InternalRel(X0),the_carrier(X0),the_carrier(X0))
| ~ rel_str(X0) ),
inference(ennf_transformation,[],[f19]) ).
fof(f19,axiom,
! [X0] :
( rel_str(X0)
=> relation_of2_as_subset(the_InternalRel(X0),the_carrier(X0),the_carrier(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_u1_orders_2) ).
fof(f373,plain,
spl17_43,
inference(avatar_split_clause,[],[f158,f371]) ).
fof(f158,plain,
! [X2,X0,X1] :
( relation_of2_as_subset(X2,X0,X1)
| ~ relation_of2(X2,X0,X1) ),
inference(cnf_transformation,[],[f100]) ).
fof(f100,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,[],[f35]) ).
fof(f35,axiom,
! [X0,X1,X2] :
( relation_of2_as_subset(X2,X0,X1)
<=> relation_of2(X2,X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_m2_relset_1) ).
fof(f369,plain,
spl17_42,
inference(avatar_split_clause,[],[f157,f367]) ).
fof(f157,plain,
! [X2,X0,X1] :
( relation_of2(X2,X0,X1)
| ~ relation_of2_as_subset(X2,X0,X1) ),
inference(cnf_transformation,[],[f100]) ).
fof(f365,plain,
spl17_41,
inference(avatar_split_clause,[],[f155,f363]) ).
fof(f155,plain,
! [X2,X0,X1] :
( relation(X2)
| ~ element(X2,powerset(cartesian_product2(X0,X1))) ),
inference(cnf_transformation,[],[f71]) ).
fof(f71,plain,
! [X0,X1,X2] :
( relation(X2)
| ~ element(X2,powerset(cartesian_product2(X0,X1))) ),
inference(ennf_transformation,[],[f2]) ).
fof(f2,axiom,
! [X0,X1,X2] :
( element(X2,powerset(cartesian_product2(X0,X1)))
=> relation(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_relset_1) ).
fof(f361,plain,
spl17_40,
inference(avatar_split_clause,[],[f148,f359]) ).
fof(f359,plain,
( spl17_40
<=> ! [X0,X1] :
( ~ empty(cartesian_product2(X0,X1))
| empty(X1)
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_40])]) ).
fof(f148,plain,
! [X0,X1] :
( ~ empty(cartesian_product2(X0,X1))
| empty(X1)
| empty(X0) ),
inference(cnf_transformation,[],[f66]) ).
fof(f66,plain,
! [X0,X1] :
( ~ empty(cartesian_product2(X0,X1))
| empty(X1)
| empty(X0) ),
inference(flattening,[],[f65]) ).
fof(f65,plain,
! [X0,X1] :
( ~ empty(cartesian_product2(X0,X1))
| empty(X1)
| empty(X0) ),
inference(ennf_transformation,[],[f30]) ).
fof(f30,axiom,
! [X0,X1] :
( ( ~ empty(X1)
& ~ empty(X0) )
=> ~ empty(cartesian_product2(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_subset_1) ).
fof(f357,plain,
spl17_39,
inference(avatar_split_clause,[],[f147,f355]) ).
fof(f147,plain,
! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(cnf_transformation,[],[f64]) ).
fof(f64,plain,
! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(flattening,[],[f63]) ).
fof(f63,plain,
! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(ennf_transformation,[],[f41]) ).
fof(f41,axiom,
! [X0,X1] :
( element(X0,X1)
=> ( in(X0,X1)
| empty(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_subset) ).
fof(f353,plain,
spl17_38,
inference(avatar_split_clause,[],[f127,f351]) ).
fof(f127,plain,
! [X0,X1] :
( sP0(X0,X1)
| in(sK9(X0,X1),X1) ),
inference(cnf_transformation,[],[f89]) ).
fof(f349,plain,
spl17_37,
inference(avatar_split_clause,[],[f126,f347]) ).
fof(f126,plain,
! [X0,X1] :
( sP0(X0,X1)
| in(sK8(X0,X1),X1) ),
inference(cnf_transformation,[],[f89]) ).
fof(f345,plain,
( spl17_36
| ~ spl17_12
| ~ spl17_15
| ~ spl17_21 ),
inference(avatar_split_clause,[],[f285,f271,f247,f234,f343]) ).
fof(f285,plain,
( ! [X0] : sK11(X0) = sK16
| ~ spl17_12
| ~ spl17_15
| ~ spl17_21 ),
inference(forward_demodulation,[],[f284,f283]) ).
fof(f283,plain,
( empty_set = sK16
| ~ spl17_12
| ~ spl17_21 ),
inference(resolution,[],[f272,f236]) ).
fof(f284,plain,
( ! [X0] : empty_set = sK11(X0)
| ~ spl17_15
| ~ spl17_21 ),
inference(resolution,[],[f272,f248]) ).
fof(f341,plain,
spl17_35,
inference(avatar_split_clause,[],[f125,f339]) ).
fof(f125,plain,
! [X0,X1] :
( sP0(X0,X1)
| in(sK7(X0,X1),X1) ),
inference(cnf_transformation,[],[f89]) ).
fof(f337,plain,
spl17_34,
inference(avatar_split_clause,[],[f123,f335]) ).
fof(f123,plain,
! [X0,X1] :
( is_transitive_in(X0,X1)
| ~ sP0(X0,X1)
| ~ sP1(X0) ),
inference(cnf_transformation,[],[f85]) ).
fof(f85,plain,
! [X0] :
( ! [X1] :
( ( is_transitive_in(X0,X1)
| ~ sP0(X0,X1) )
& ( sP0(X0,X1)
| ~ is_transitive_in(X0,X1) ) )
| ~ sP1(X0) ),
inference(nnf_transformation,[],[f76]) ).
fof(f76,plain,
! [X0] :
( ! [X1] :
( is_transitive_in(X0,X1)
<=> sP0(X0,X1) )
| ~ sP1(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).
fof(f333,plain,
spl17_33,
inference(avatar_split_clause,[],[f122,f331]) ).
fof(f122,plain,
! [X0,X1] :
( sP0(X0,X1)
| ~ is_transitive_in(X0,X1)
| ~ sP1(X0) ),
inference(cnf_transformation,[],[f85]) ).
fof(f323,plain,
spl17_32,
inference(avatar_split_clause,[],[f150,f321]) ).
fof(f150,plain,
! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) ),
inference(cnf_transformation,[],[f68]) ).
fof(f68,plain,
! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) ),
inference(ennf_transformation,[],[f47]) ).
fof(f47,axiom,
! [X0,X1] :
~ ( empty(X1)
& X0 != X1
& empty(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_boole) ).
fof(f319,plain,
spl17_31,
inference(avatar_split_clause,[],[f149,f317]) ).
fof(f149,plain,
! [X0,X1] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f67]) ).
fof(f67,plain,
! [X0,X1] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f49]) ).
fof(f49,plain,
! [X0,X1] :
( subset(X0,X1)
=> element(X0,powerset(X1)) ),
inference(unused_predicate_definition_removal,[],[f42]) ).
fof(f42,axiom,
! [X0,X1] :
( element(X0,powerset(X1))
<=> subset(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_subset) ).
fof(f315,plain,
spl17_30,
inference(avatar_split_clause,[],[f143,f313]) ).
fof(f310,plain,
spl17_29,
inference(avatar_split_clause,[],[f120,f308]) ).
fof(f120,plain,
! [X0] :
( element(sK6(X0),powerset(X0))
| empty(X0) ),
inference(cnf_transformation,[],[f84]) ).
fof(f84,plain,
! [X0] :
( ( ~ empty(sK6(X0))
& element(sK6(X0),powerset(X0)) )
| empty(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6])],[f54,f83]) ).
fof(f83,plain,
! [X0] :
( ? [X1] :
( ~ empty(X1)
& element(X1,powerset(X0)) )
=> ( ~ empty(sK6(X0))
& element(sK6(X0),powerset(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f54,plain,
! [X0] :
( ? [X1] :
( ~ empty(X1)
& element(X1,powerset(X0)) )
| empty(X0) ),
inference(ennf_transformation,[],[f31]) ).
fof(f31,axiom,
! [X0] :
( ~ empty(X0)
=> ? [X1] :
( ~ empty(X1)
& element(X1,powerset(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_subset_1) ).
fof(f306,plain,
spl17_28,
inference(avatar_split_clause,[],[f153,f304]) ).
fof(f153,plain,
! [X0,X1] : relation_of2_as_subset(sK13(X0,X1),X0,X1),
inference(cnf_transformation,[],[f99]) ).
fof(f99,plain,
! [X0,X1] : relation_of2_as_subset(sK13(X0,X1),X0,X1),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK13])],[f25,f98]) ).
fof(f98,plain,
! [X0,X1] :
( ? [X2] : relation_of2_as_subset(X2,X0,X1)
=> relation_of2_as_subset(sK13(X0,X1),X0,X1) ),
introduced(choice_axiom,[]) ).
fof(f25,axiom,
! [X0,X1] :
? [X2] : relation_of2_as_subset(X2,X0,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m2_relset_1) ).
fof(f302,plain,
spl17_27,
inference(avatar_split_clause,[],[f152,f300]) ).
fof(f152,plain,
! [X0,X1] : relation_of2(sK12(X0,X1),X0,X1),
inference(cnf_transformation,[],[f97]) ).
fof(f97,plain,
! [X0,X1] : relation_of2(sK12(X0,X1),X0,X1),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK12])],[f23,f96]) ).
fof(f96,plain,
! [X0,X1] :
( ? [X2] : relation_of2(X2,X0,X1)
=> relation_of2(sK12(X0,X1),X0,X1) ),
introduced(choice_axiom,[]) ).
fof(f23,axiom,
! [X0,X1] :
? [X2] : relation_of2(X2,X0,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_relset_1) ).
fof(f298,plain,
spl17_26,
inference(avatar_split_clause,[],[f146,f296]) ).
fof(f146,plain,
! [X0,X1] :
( element(X0,X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f62]) ).
fof(f62,plain,
! [X0,X1] :
( element(X0,X1)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f38]) ).
fof(f38,axiom,
! [X0,X1] :
( in(X0,X1)
=> element(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_subset) ).
fof(f294,plain,
spl17_25,
inference(avatar_split_clause,[],[f145,f292]) ).
fof(f145,plain,
! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f61]) ).
fof(f61,plain,
! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f1]) ).
fof(f1,axiom,
! [X0,X1] :
( in(X0,X1)
=> ~ in(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
fof(f290,plain,
( spl17_24
| ~ spl17_12
| ~ spl17_21 ),
inference(avatar_split_clause,[],[f283,f271,f234,f287]) ).
fof(f281,plain,
spl17_23,
inference(avatar_split_clause,[],[f151,f279]) ).
fof(f151,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f69]) ).
fof(f69,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f46]) ).
fof(f46,axiom,
! [X0,X1] :
~ ( empty(X1)
& in(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).
fof(f277,plain,
spl17_22,
inference(avatar_split_clause,[],[f139,f275]) ).
fof(f139,plain,
! [X0] : element(sK11(X0),powerset(X0)),
inference(cnf_transformation,[],[f95]) ).
fof(f95,plain,
! [X0] :
( empty(sK11(X0))
& element(sK11(X0),powerset(X0)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK11])],[f33,f94]) ).
fof(f94,plain,
! [X0] :
( ? [X1] :
( empty(X1)
& element(X1,powerset(X0)) )
=> ( empty(sK11(X0))
& element(sK11(X0),powerset(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f33,axiom,
! [X0] :
? [X1] :
( empty(X1)
& element(X1,powerset(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_subset_1) ).
fof(f273,plain,
spl17_21,
inference(avatar_split_clause,[],[f137,f271]) ).
fof(f137,plain,
! [X0] :
( empty_set = X0
| ~ empty(X0) ),
inference(cnf_transformation,[],[f60]) ).
fof(f60,plain,
! [X0] :
( empty_set = X0
| ~ empty(X0) ),
inference(ennf_transformation,[],[f45]) ).
fof(f45,axiom,
! [X0] :
( empty(X0)
=> empty_set = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).
fof(f269,plain,
spl17_20,
inference(avatar_split_clause,[],[f121,f267]) ).
fof(f121,plain,
! [X0] :
( ~ empty(sK6(X0))
| empty(X0) ),
inference(cnf_transformation,[],[f84]) ).
fof(f265,plain,
spl17_19,
inference(avatar_split_clause,[],[f142,f263]) ).
fof(f142,plain,
! [X0,X1] : ~ empty(unordered_pair(X0,X1)),
inference(cnf_transformation,[],[f29]) ).
fof(f29,axiom,
! [X0,X1] : ~ empty(unordered_pair(X0,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_subset_1) ).
fof(f261,plain,
spl17_18,
inference(avatar_split_clause,[],[f138,f259]) ).
fof(f138,plain,
! [X0] : element(sK10(X0),X0),
inference(cnf_transformation,[],[f93]) ).
fof(f93,plain,
! [X0] : element(sK10(X0),X0),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK10])],[f24,f92]) ).
fof(f92,plain,
! [X0] :
( ? [X1] : element(X1,X0)
=> element(sK10(X0),X0) ),
introduced(choice_axiom,[]) ).
fof(f24,axiom,
! [X0] :
? [X1] : element(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_subset_1) ).
fof(f257,plain,
spl17_17,
inference(avatar_split_clause,[],[f131,f255]) ).
fof(f131,plain,
! [X0] :
( sP1(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f77]) ).
fof(f77,plain,
! [X0] :
( sP1(X0)
| ~ relation(X0) ),
inference(definition_folding,[],[f56,f76,f75]) ).
fof(f56,plain,
! [X0] :
( ! [X1] :
( is_transitive_in(X0,X1)
<=> ! [X2,X3,X4] :
( in(ordered_pair(X2,X4),X0)
| ~ in(ordered_pair(X3,X4),X0)
| ~ in(ordered_pair(X2,X3),X0)
| ~ in(X4,X1)
| ~ in(X3,X1)
| ~ in(X2,X1) ) )
| ~ relation(X0) ),
inference(flattening,[],[f55]) ).
fof(f55,plain,
! [X0] :
( ! [X1] :
( is_transitive_in(X0,X1)
<=> ! [X2,X3,X4] :
( in(ordered_pair(X2,X4),X0)
| ~ in(ordered_pair(X3,X4),X0)
| ~ in(ordered_pair(X2,X3),X0)
| ~ in(X4,X1)
| ~ in(X3,X1)
| ~ in(X2,X1) ) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f6]) ).
fof(f6,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( is_transitive_in(X0,X1)
<=> ! [X2,X3,X4] :
( ( in(ordered_pair(X3,X4),X0)
& in(ordered_pair(X2,X3),X0)
& in(X4,X1)
& in(X3,X1)
& in(X2,X1) )
=> in(ordered_pair(X2,X4),X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_relat_2) ).
fof(f253,plain,
spl17_16,
inference(avatar_split_clause,[],[f141,f251]) ).
fof(f141,plain,
! [X0] : subset(X0,X0),
inference(cnf_transformation,[],[f48]) ).
fof(f48,plain,
! [X0] : subset(X0,X0),
inference(rectify,[],[f36]) ).
fof(f36,axiom,
! [X0,X1] : subset(X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(f249,plain,
spl17_15,
inference(avatar_split_clause,[],[f140,f247]) ).
fof(f140,plain,
! [X0] : empty(sK11(X0)),
inference(cnf_transformation,[],[f95]) ).
fof(f245,plain,
spl17_14,
inference(avatar_split_clause,[],[f119,f243]) ).
fof(f119,plain,
! [X0] : ~ empty(powerset(X0)),
inference(cnf_transformation,[],[f26]) ).
fof(f26,axiom,
! [X0] : ~ empty(powerset(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_subset_1) ).
fof(f241,plain,
spl17_13,
inference(avatar_split_clause,[],[f118,f239]) ).
fof(f239,plain,
( spl17_13
<=> ! [X0] : ~ empty(singleton(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_13])]) ).
fof(f118,plain,
! [X0] : ~ empty(singleton(X0)),
inference(cnf_transformation,[],[f28]) ).
fof(f28,axiom,
! [X0] : ~ empty(singleton(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_subset_1) ).
fof(f237,plain,
spl17_12,
inference(avatar_split_clause,[],[f165,f234]) ).
fof(f165,plain,
empty(sK16),
inference(cnf_transformation,[],[f108]) ).
fof(f108,plain,
empty(sK16),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK16])],[f32,f107]) ).
fof(f107,plain,
( ? [X0] : empty(X0)
=> empty(sK16) ),
introduced(choice_axiom,[]) ).
fof(f32,axiom,
? [X0] : empty(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_xboole_0) ).
fof(f232,plain,
spl17_11,
inference(avatar_split_clause,[],[f164,f229]) ).
fof(f229,plain,
( spl17_11
<=> rel_str(sK15) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_11])]) ).
fof(f164,plain,
rel_str(sK15),
inference(cnf_transformation,[],[f106]) ).
fof(f106,plain,
rel_str(sK15),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK15])],[f21,f105]) ).
fof(f105,plain,
( ? [X0] : rel_str(X0)
=> rel_str(sK15) ),
introduced(choice_axiom,[]) ).
fof(f21,axiom,
? [X0] : rel_str(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_l1_orders_2) ).
fof(f227,plain,
~ spl17_10,
inference(avatar_split_clause,[],[f163,f224]) ).
fof(f224,plain,
( spl17_10
<=> empty(sK14) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_10])]) ).
fof(f163,plain,
~ empty(sK14),
inference(cnf_transformation,[],[f104]) ).
fof(f104,plain,
~ empty(sK14),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK14])],[f34,f103]) ).
fof(f103,plain,
( ? [X0] : ~ empty(X0)
=> ~ empty(sK14) ),
introduced(choice_axiom,[]) ).
fof(f34,axiom,
? [X0] : ~ empty(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_xboole_0) ).
fof(f222,plain,
spl17_9,
inference(avatar_split_clause,[],[f117,f219]) ).
fof(f117,plain,
empty(empty_set),
inference(cnf_transformation,[],[f27]) ).
fof(f27,axiom,
empty(empty_set),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_xboole_0) ).
fof(f217,plain,
~ spl17_8,
inference(avatar_split_clause,[],[f116,f214]) ).
fof(f116,plain,
~ related(sK2,sK3,sK5),
inference(cnf_transformation,[],[f82]) ).
fof(f82,plain,
( ~ related(sK2,sK3,sK5)
& related(sK2,sK4,sK5)
& related(sK2,sK3,sK4)
& element(sK5,the_carrier(sK2))
& element(sK4,the_carrier(sK2))
& element(sK3,the_carrier(sK2))
& rel_str(sK2)
& transitive_relstr(sK2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3,sK4,sK5])],[f53,f81,f80,f79,f78]) ).
fof(f78,plain,
( ? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ~ related(X0,X1,X3)
& related(X0,X2,X3)
& related(X0,X1,X2)
& element(X3,the_carrier(X0)) )
& element(X2,the_carrier(X0)) )
& element(X1,the_carrier(X0)) )
& rel_str(X0)
& transitive_relstr(X0) )
=> ( ? [X1] :
( ? [X2] :
( ? [X3] :
( ~ related(sK2,X1,X3)
& related(sK2,X2,X3)
& related(sK2,X1,X2)
& element(X3,the_carrier(sK2)) )
& element(X2,the_carrier(sK2)) )
& element(X1,the_carrier(sK2)) )
& rel_str(sK2)
& transitive_relstr(sK2) ) ),
introduced(choice_axiom,[]) ).
fof(f79,plain,
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ~ related(sK2,X1,X3)
& related(sK2,X2,X3)
& related(sK2,X1,X2)
& element(X3,the_carrier(sK2)) )
& element(X2,the_carrier(sK2)) )
& element(X1,the_carrier(sK2)) )
=> ( ? [X2] :
( ? [X3] :
( ~ related(sK2,sK3,X3)
& related(sK2,X2,X3)
& related(sK2,sK3,X2)
& element(X3,the_carrier(sK2)) )
& element(X2,the_carrier(sK2)) )
& element(sK3,the_carrier(sK2)) ) ),
introduced(choice_axiom,[]) ).
fof(f80,plain,
( ? [X2] :
( ? [X3] :
( ~ related(sK2,sK3,X3)
& related(sK2,X2,X3)
& related(sK2,sK3,X2)
& element(X3,the_carrier(sK2)) )
& element(X2,the_carrier(sK2)) )
=> ( ? [X3] :
( ~ related(sK2,sK3,X3)
& related(sK2,sK4,X3)
& related(sK2,sK3,sK4)
& element(X3,the_carrier(sK2)) )
& element(sK4,the_carrier(sK2)) ) ),
introduced(choice_axiom,[]) ).
fof(f81,plain,
( ? [X3] :
( ~ related(sK2,sK3,X3)
& related(sK2,sK4,X3)
& related(sK2,sK3,sK4)
& element(X3,the_carrier(sK2)) )
=> ( ~ related(sK2,sK3,sK5)
& related(sK2,sK4,sK5)
& related(sK2,sK3,sK4)
& element(sK5,the_carrier(sK2)) ) ),
introduced(choice_axiom,[]) ).
fof(f53,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ~ related(X0,X1,X3)
& related(X0,X2,X3)
& related(X0,X1,X2)
& element(X3,the_carrier(X0)) )
& element(X2,the_carrier(X0)) )
& element(X1,the_carrier(X0)) )
& rel_str(X0)
& transitive_relstr(X0) ),
inference(flattening,[],[f52]) ).
fof(f52,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ~ related(X0,X1,X3)
& related(X0,X2,X3)
& related(X0,X1,X2)
& element(X3,the_carrier(X0)) )
& element(X2,the_carrier(X0)) )
& element(X1,the_carrier(X0)) )
& rel_str(X0)
& transitive_relstr(X0) ),
inference(ennf_transformation,[],[f40]) ).
fof(f40,negated_conjecture,
~ ! [X0] :
( ( rel_str(X0)
& transitive_relstr(X0) )
=> ! [X1] :
( element(X1,the_carrier(X0))
=> ! [X2] :
( element(X2,the_carrier(X0))
=> ! [X3] :
( element(X3,the_carrier(X0))
=> ( ( related(X0,X2,X3)
& related(X0,X1,X2) )
=> related(X0,X1,X3) ) ) ) ) ),
inference(negated_conjecture,[],[f39]) ).
fof(f39,conjecture,
! [X0] :
( ( rel_str(X0)
& transitive_relstr(X0) )
=> ! [X1] :
( element(X1,the_carrier(X0))
=> ! [X2] :
( element(X2,the_carrier(X0))
=> ! [X3] :
( element(X3,the_carrier(X0))
=> ( ( related(X0,X2,X3)
& related(X0,X1,X2) )
=> related(X0,X1,X3) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t26_orders_2) ).
fof(f212,plain,
spl17_7,
inference(avatar_split_clause,[],[f115,f209]) ).
fof(f115,plain,
related(sK2,sK4,sK5),
inference(cnf_transformation,[],[f82]) ).
fof(f207,plain,
spl17_6,
inference(avatar_split_clause,[],[f114,f204]) ).
fof(f114,plain,
related(sK2,sK3,sK4),
inference(cnf_transformation,[],[f82]) ).
fof(f202,plain,
spl17_5,
inference(avatar_split_clause,[],[f113,f199]) ).
fof(f113,plain,
element(sK5,the_carrier(sK2)),
inference(cnf_transformation,[],[f82]) ).
fof(f197,plain,
spl17_4,
inference(avatar_split_clause,[],[f112,f194]) ).
fof(f112,plain,
element(sK4,the_carrier(sK2)),
inference(cnf_transformation,[],[f82]) ).
fof(f192,plain,
spl17_3,
inference(avatar_split_clause,[],[f111,f189]) ).
fof(f111,plain,
element(sK3,the_carrier(sK2)),
inference(cnf_transformation,[],[f82]) ).
fof(f187,plain,
spl17_2,
inference(avatar_split_clause,[],[f110,f184]) ).
fof(f110,plain,
rel_str(sK2),
inference(cnf_transformation,[],[f82]) ).
fof(f182,plain,
spl17_1,
inference(avatar_split_clause,[],[f109,f179]) ).
fof(f109,plain,
transitive_relstr(sK2),
inference(cnf_transformation,[],[f82]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SEU340+1 : TPTP v8.1.2. Released v3.3.0.
% 0.07/0.15 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.16/0.36 % Computer : n024.cluster.edu
% 0.16/0.36 % Model : x86_64 x86_64
% 0.16/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36 % Memory : 8042.1875MB
% 0.16/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36 % CPULimit : 300
% 0.16/0.36 % WCLimit : 300
% 0.16/0.36 % DateTime : Fri May 3 11:31:05 EDT 2024
% 0.16/0.36 % CPUTime :
% 0.16/0.37 % (4070)Running in auto input_syntax mode. Trying TPTP
% 0.16/0.38 % (4073)WARNING: value z3 for option sas not known
% 0.16/0.38 % (4072)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.16/0.38 % (4071)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.16/0.38 % (4074)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.16/0.38 % (4073)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.16/0.38 % (4075)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.16/0.38 % (4076)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.16/0.38 % (4077)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.16/0.39 TRYING [1]
% 0.16/0.39 TRYING [2]
% 0.16/0.39 TRYING [3]
% 0.16/0.40 TRYING [1]
% 0.16/0.40 TRYING [2]
% 0.22/0.41 TRYING [4]
% 0.22/0.42 TRYING [3]
% 0.22/0.45 TRYING [5]
% 0.22/0.47 TRYING [4]
% 0.22/0.52 TRYING [6]
% 0.22/0.55 TRYING [5]
% 2.05/0.68 TRYING [7]
% 3.54/0.87 TRYING [6]
% 6.34/1.32 % (4075)First to succeed.
% 6.94/1.36 TRYING [8]
% 7.22/1.41 % (4075)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-4070"
% 7.22/1.42 % (4075)Refutation found. Thanks to Tanya!
% 7.22/1.42 % SZS status Theorem for theBenchmark
% 7.22/1.42 % SZS output start Proof for theBenchmark
% See solution above
% 7.52/1.45 % (4075)------------------------------
% 7.52/1.45 % (4075)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 7.52/1.45 % (4075)Termination reason: Refutation
% 7.52/1.45
% 7.52/1.45 % (4075)Memory used [KB]: 14945
% 7.52/1.45 % (4075)Time elapsed: 1.030 s
% 7.52/1.45 % (4075)Instructions burned: 2198 (million)
% 7.52/1.45 % (4070)Success in time 1.044 s
%------------------------------------------------------------------------------