TSTP Solution File: SEU362+1 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SEU362+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 : n028.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Apr 30 15:31:41 EDT 2024
% Result : Theorem 9.58s 1.70s
% Output : Refutation 9.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 1276
% Syntax : Number of formulae : 4322 ( 87 unt; 0 def)
% Number of atoms : 22312 ( 628 equ)
% Maximal formula atoms : 20 ( 5 avg)
% Number of connectives : 26877 (8887 ~;16555 |; 149 &)
% (1235 <=>; 51 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 6 avg)
% Maximal term depth : 12 ( 3 avg)
% Number of predicates : 1241 (1239 usr;1230 prp; 0-3 aty)
% Number of functors : 22 ( 22 usr; 11 con; 0-2 aty)
% Number of variables : 3912 (3841 !; 71 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f19927,plain,
$false,
inference(avatar_sat_refutation,[],[f161,f166,f171,f176,f181,f186,f191,f196,f201,f206,f211,f216,f221,f226,f230,f234,f238,f245,f249,f253,f257,f261,f265,f269,f274,f280,f284,f288,f292,f296,f300,f304,f308,f312,f316,f320,f333,f337,f341,f345,f349,f358,f372,f376,f385,f389,f402,f406,f410,f418,f422,f431,f450,f458,f464,f472,f478,f482,f486,f494,f498,f502,f506,f510,f514,f518,f526,f532,f536,f547,f551,f563,f567,f571,f575,f579,f583,f607,f611,f615,f619,f623,f644,f648,f655,f662,f669,f676,f680,f685,f690,f694,f702,f706,f707,f715,f720,f728,f735,f741,f745,f756,f760,f763,f767,f771,f777,f781,f785,f789,f793,f797,f801,f805,f831,f837,f841,f845,f849,f862,f866,f870,f882,f886,f890,f909,f918,f922,f932,f937,f938,f954,f962,f968,f979,f986,f1007,f1013,f1018,f1019,f1030,f1035,f1043,f1064,f1075,f1080,f1107,f1118,f1123,f1130,f1153,f1164,f1169,f1174,f1178,f1186,f1190,f1194,f1198,f1202,f1208,f1216,f1220,f1221,f1255,f1259,f1263,f1267,f1271,f1275,f1279,f1305,f1309,f1313,f1317,f1321,f1329,f1361,f1371,f1375,f1384,f1395,f1400,f1407,f1423,f1427,f1431,f1435,f1444,f1450,f1454,f1458,f1474,f1478,f1482,f1487,f1491,f1505,f1509,f1520,f1525,f1529,f1539,f1543,f1579,f1590,f1592,f1598,f1602,f1623,f1634,f1639,f1671,f1678,f1683,f1699,f1704,f1714,f1718,f1722,f1764,f1777,f1784,f1795,f1799,f1806,f1810,f1814,f1818,f1822,f1826,f1850,f1872,f1899,f1910,f1924,f1939,f1944,f1957,f1958,f1963,f1985,f1989,f1993,f1997,f2026,f2030,f2034,f2038,f2065,f2069,f2073,f2089,f2093,f2097,f2101,f2105,f2120,f2124,f2128,f2132,f2136,f2140,f2141,f2145,f2181,f2185,f2191,f2195,f2199,f2203,f2212,f2216,f2220,f2228,f2232,f2236,f2240,f2241,f2265,f2269,f2283,f2287,f2292,f2306,f2315,f2365,f2393,f2433,f2456,f2461,f2481,f2496,f2511,f2520,f2525,f2530,f2537,f2541,f2551,f2552,f2578,f2582,f2607,f2616,f2620,f2621,f2625,f2629,f2650,f2655,f2660,f2667,f2684,f2688,f2694,f2698,f2702,f2706,f2729,f2733,f2737,f2752,f2783,f2788,f2841,f2872,f2880,f2892,f2897,f2902,f2925,f2930,f2934,f2938,f2942,f2946,f2950,f2954,f2958,f2962,f2966,f2974,f3095,f3100,f3104,f3108,f3137,f3141,f3145,f3153,f3157,f3161,f3165,f3169,f3173,f3177,f3190,f3294,f3298,f3302,f3307,f3388,f3392,f3396,f3400,f3404,f3405,f3410,f3414,f3418,f3422,f3426,f3430,f3434,f3438,f3442,f3443,f3547,f3551,f3555,f3559,f3563,f3567,f3572,f3576,f3580,f3624,f3628,f3632,f3636,f3640,f3644,f3648,f3652,f3656,f3660,f3664,f3668,f3672,f3676,f3680,f3893,f3897,f3901,f3905,f3909,f3913,f3917,f3921,f3925,f3929,f3933,f3937,f3941,f3953,f3957,f4058,f4079,f4083,f4087,f4091,f4095,f4099,f4157,f4161,f4165,f4169,f4173,f4177,f4181,f4185,f4189,f4193,f4197,f4201,f4205,f4211,f4215,f4219,f4299,f4345,f4349,f4353,f4405,f4409,f4413,f4417,f4467,f4471,f4475,f4479,f4663,f4667,f4671,f4765,f4769,f4863,f4867,f4879,f4883,f4887,f4891,f4895,f4914,f4966,f4970,f4974,f4978,f4982,f4986,f4990,f5003,f5007,f5011,f5015,f5020,f5024,f5028,f5032,f5036,f5040,f5203,f5207,f5211,f5215,f5219,f5223,f5227,f5231,f5235,f5239,f5395,f5399,f5403,f5482,f5486,f5491,f5495,f5574,f5578,f5582,f5586,f5590,f5598,f5608,f5613,f5618,f5622,f5626,f5634,f5638,f5686,f5690,f5694,f5698,f5702,f5706,f5718,f5722,f5728,f5803,f5807,f5811,f5815,f5819,f5824,f5836,f5840,f5844,f5848,f5852,f5856,f5860,f5864,f5965,f5969,f5973,f5977,f5985,f5989,f5993,f5997,f6002,f6070,f6074,f6078,f6082,f6090,f6094,f6098,f6102,f6106,f6110,f6114,f6242,f6246,f6250,f6254,f6258,f6262,f6266,f6270,f6274,f6278,f6534,f6538,f6542,f6546,f6550,f6554,f6558,f6562,f6566,f6570,f6574,f6578,f6582,f6586,f6590,f6594,f6598,f6608,f6612,f6616,f6620,f6624,f6628,f6632,f6705,f7004,f7061,f7171,f7175,f7180,f7302,f7306,f7310,f7314,f7318,f7322,f7326,f7330,f7334,f7339,f7540,f7604,f7608,f7612,f7616,f7620,f7624,f7628,f7632,f7636,f7640,f7645,f7649,f7653,f7657,f7661,f7665,f7669,f7673,f7967,f8173,f8177,f8181,f8185,f8189,f8197,f8201,f8205,f8209,f8213,f8217,f8221,f8225,f8229,f8233,f8238,f8242,f8400,f8404,f8408,f8412,f8416,f8420,f8424,f8428,f8432,f8436,f8440,f8444,f8448,f8452,f8490,f8494,f8498,f8502,f8506,f8518,f8691,f8783,f8787,f8791,f8795,f8799,f8803,f8807,f8812,f8817,f8821,f8825,f8829,f8833,f8837,f8841,f8845,f9000,f9166,f9181,f9185,f9189,f9193,f9197,f9201,f9205,f9210,f9214,f9218,f9222,f9226,f9230,f9234,f9238,f9242,f9246,f9247,f9256,f9260,f9264,f9268,f9272,f9276,f9280,f9284,f9288,f9292,f9930,f9968,f9972,f9976,f9981,f9985,f9989,f9993,f9997,f10001,f10005,f10009,f10013,f10017,f10022,f10026,f10030,f10034,f10038,f10042,f10046,f10050,f10054,f10640,f10674,f10712,f10716,f10720,f10724,f10728,f10732,f10736,f10740,f10744,f10748,f10749,f10755,f10766,f10770,f10774,f10778,f10782,f10786,f10790,f10794,f10803,f10807,f10811,f10815,f10819,f10823,f10827,f10831,f11865,f11930,f11934,f11938,f11942,f11946,f11950,f11954,f11958,f11962,f11966,f11970,f11974,f11978,f11982,f12414,f12501,f12708,f12712,f12804,f12808,f12812,f12816,f12820,f12824,f12828,f12832,f12836,f12840,f12844,f12848,f12852,f12856,f12860,f12864,f12868,f13011,f13637,f13641,f13645,f13649,f13654,f13658,f13662,f13666,f13670,f13674,f13678,f14230,f14234,f14238,f14242,f14246,f14250,f14254,f14258,f14262,f14266,f14491,f14495,f14499,f14503,f14508,f14512,f14516,f14520,f14524,f14528,f14532,f14536,f14540,f14544,f14548,f14553,f14557,f14561,f14565,f14569,f14573,f14577,f14581,f14585,f14589,f14696,f14749,f15001,f15005,f15115,f15119,f15124,f15128,f15132,f15136,f15140,f15144,f15148,f15152,f15156,f15160,f15164,f15168,f15172,f15176,f15180,f15184,f15188,f15192,f15196,f15200,f15204,f15208,f15212,f15216,f15220,f15224,f15361,f15389,f15393,f15397,f15401,f15425,f15429,f15433,f15437,f15441,f15445,f15449,f15453,f15459,f15463,f15467,f15471,f15475,f15479,f15503,f15569,f15573,f15577,f15581,f15585,f15589,f15613,f15629,f15633,f15637,f15641,f15645,f15649,f15653,f15657,f15666,f15670,f15674,f15678,f15682,f15686,f15690,f15694,f15698,f15702,f15707,f15894,f15898,f15907,f15911,f15915,f15919,f15923,f15927,f15931,f15935,f15939,f15983,f15987,f15988,f15997,f16001,f16005,f16009,f16013,f16017,f16021,f16025,f16029,f16033,f16037,f16041,f16045,f16049,f16053,f16057,f16061,f16065,f16069,f16073,f16081,f16085,f16089,f16093,f16128,f16212,f16216,f16220,f16224,f16228,f16232,f16236,f16240,f16244,f16248,f16252,f16256,f16260,f16264,f16268,f16272,f16276,f16280,f16284,f16288,f16292,f16296,f16300,f16304,f16308,f16312,f16316,f16434,f16733,f16737,f16741,f16745,f16749,f16753,f16757,f16761,f16765,f16769,f16770,f16774,f16936,f16940,f16944,f16948,f16952,f16956,f16960,f16964,f17011,f17015,f17020,f17128,f17132,f17136,f17140,f17144,f17148,f17152,f17156,f17160,f17164,f17165,f17169,f17173,f17177,f17181,f17185,f17189,f17284,f17288,f17292,f17296,f17300,f17304,f17308,f17312,f17316,f17320,f17324,f17328,f17332,f17336,f17340,f17344,f17400,f17675,f17679,f17683,f17687,f17688,f17692,f17696,f17700,f17704,f17868,f17872,f17876,f17880,f17884,f17888,f17892,f17896,f18014,f18018,f18022,f18026,f18030,f18034,f18038,f18042,f18046,f18050,f18055,f18060,f18064,f18174,f18178,f18182,f18186,f18190,f18194,f18198,f18202,f18211,f18215,f18219,f18223,f18227,f18231,f18235,f18309,f18313,f18317,f18321,f18325,f18329,f18333,f18337,f18341,f18345,f18350,f18354,f18358,f18362,f18366,f18370,f18374,f18378,f18382,f18446,f18480,f18484,f18488,f18492,f18502,f18506,f18510,f18514,f18518,f18522,f18526,f18530,f18534,f18538,f18542,f18546,f18550,f18554,f18558,f18562,f18566,f18570,f18574,f18578,f18582,f18591,f18595,f18640,f18841,f18845,f18854,f18858,f18862,f18866,f18870,f18874,f18878,f18882,f18886,f18890,f18894,f18899,f18903,f18944,f18996,f19000,f19004,f19008,f19012,f19016,f19020,f19024,f19072,f19076,f19080,f19084,f19088,f19092,f19096,f19100,f19105,f19149,f19153,f19158,f19162,f19166,f19170,f19174,f19178,f19182,f19186,f19201,f19245,f19249,f19263,f19267,f19271,f19275,f19279,f19283,f19297,f19321,f19325,f19329,f19333,f19337,f19341,f19379,f19383,f19387,f19391,f19395,f19399,f19403,f19407,f19411,f19415,f19419,f19423,f19427,f19431,f19435,f19439,f19443,f19447,f19451,f19455,f19459,f19464,f19468,f19614,f19618,f19622,f19626,f19630,f19634,f19638,f19642,f19646,f19650,f19657,f19661,f19665,f19669,f19704,f19748,f19752,f19756,f19760,f19764,f19768,f19772,f19776,f19780,f19784,f19788,f19792,f19797,f19801,f19805,f19809,f19813,f19817,f19821,f19825,f19829,f19833,f19837,f19841,f19845,f19849,f19853,f19857,f19861,f19865,f19869,f19873,f19877,f19881,f19885,f19926]) ).
fof(f19926,plain,
( ~ spl16_8
| ~ spl16_1
| spl16_6
| ~ spl16_2
| spl16_186
| ~ spl16_7
| ~ spl16_468 ),
inference(avatar_split_clause,[],[f5601,f5596,f188,f1536,f163,f183,f158,f193]) ).
fof(f193,plain,
( spl16_8
<=> element(sK4,the_carrier(sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_8])]) ).
fof(f158,plain,
( spl16_1
<=> rel_str(sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1])]) ).
fof(f183,plain,
( spl16_6
<=> related(sK0,sK4,sK5) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_6])]) ).
fof(f163,plain,
( spl16_2
<=> subrelstr(sK1,sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_2])]) ).
fof(f1536,plain,
( spl16_186
<=> empty(the_InternalRel(sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_186])]) ).
fof(f188,plain,
( spl16_7
<=> element(sK5,the_carrier(sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_7])]) ).
fof(f5596,plain,
( spl16_468
<=> ! [X0] :
( ~ rel_str(X0)
| empty(the_InternalRel(X0))
| ~ subrelstr(sK1,X0)
| related(X0,sK4,sK5)
| ~ element(sK5,the_carrier(X0))
| ~ element(sK4,the_carrier(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_468])]) ).
fof(f5601,plain,
( empty(the_InternalRel(sK0))
| ~ subrelstr(sK1,sK0)
| related(sK0,sK4,sK5)
| ~ rel_str(sK0)
| ~ element(sK4,the_carrier(sK0))
| ~ spl16_7
| ~ spl16_468 ),
inference(resolution,[],[f5597,f190]) ).
fof(f190,plain,
( element(sK5,the_carrier(sK0))
| ~ spl16_7 ),
inference(avatar_component_clause,[],[f188]) ).
fof(f5597,plain,
( ! [X0] :
( ~ element(sK5,the_carrier(X0))
| empty(the_InternalRel(X0))
| ~ subrelstr(sK1,X0)
| related(X0,sK4,sK5)
| ~ rel_str(X0)
| ~ element(sK4,the_carrier(X0)) )
| ~ spl16_468 ),
inference(avatar_component_clause,[],[f5596]) ).
fof(f19885,plain,
( spl16_1229
| ~ spl16_306
| ~ spl16_451 ),
inference(avatar_split_clause,[],[f5375,f5221,f2964,f19883]) ).
fof(f19883,plain,
( spl16_1229
<=> ! [X0] :
( empty(sK7(sK9(sK9(powerset(powerset(powerset(X0)))))))
| empty(sK9(sK9(powerset(powerset(powerset(X0))))))
| element(sK9(sK7(sK7(sK9(sK7(sK9(sK9(powerset(powerset(powerset(X0)))))))))),X0)
| empty(sK9(powerset(powerset(powerset(X0)))))
| empty(sK7(sK7(sK9(sK7(sK9(sK9(powerset(powerset(powerset(X0))))))))))
| empty(sK9(sK7(sK9(sK9(powerset(powerset(powerset(X0))))))))
| empty(sK7(sK9(sK7(sK9(sK9(powerset(powerset(powerset(X0))))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1229])]) ).
fof(f2964,plain,
( spl16_306
<=> ! [X0] :
( empty(sK7(X0))
| empty(sK7(sK7(X0)))
| empty(X0)
| in(sK9(sK7(sK7(X0))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_306])]) ).
fof(f5221,plain,
( spl16_451
<=> ! [X0,X1] :
( empty(sK9(powerset(powerset(powerset(X0)))))
| empty(sK7(sK9(sK9(powerset(powerset(powerset(X0)))))))
| empty(sK9(sK9(powerset(powerset(powerset(X0))))))
| element(X1,X0)
| ~ in(X1,sK9(sK7(sK9(sK9(powerset(powerset(powerset(X0)))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_451])]) ).
fof(f5375,plain,
( ! [X0] :
( empty(sK7(sK9(sK9(powerset(powerset(powerset(X0)))))))
| empty(sK9(sK9(powerset(powerset(powerset(X0))))))
| element(sK9(sK7(sK7(sK9(sK7(sK9(sK9(powerset(powerset(powerset(X0)))))))))),X0)
| empty(sK9(powerset(powerset(powerset(X0)))))
| empty(sK7(sK7(sK9(sK7(sK9(sK9(powerset(powerset(powerset(X0))))))))))
| empty(sK9(sK7(sK9(sK9(powerset(powerset(powerset(X0))))))))
| empty(sK7(sK9(sK7(sK9(sK9(powerset(powerset(powerset(X0))))))))) )
| ~ spl16_306
| ~ spl16_451 ),
inference(resolution,[],[f5222,f2965]) ).
fof(f2965,plain,
( ! [X0] :
( in(sK9(sK7(sK7(X0))),X0)
| empty(sK7(sK7(X0)))
| empty(X0)
| empty(sK7(X0)) )
| ~ spl16_306 ),
inference(avatar_component_clause,[],[f2964]) ).
fof(f5222,plain,
( ! [X0,X1] :
( ~ in(X1,sK9(sK7(sK9(sK9(powerset(powerset(powerset(X0))))))))
| empty(sK7(sK9(sK9(powerset(powerset(powerset(X0)))))))
| empty(sK9(sK9(powerset(powerset(powerset(X0))))))
| element(X1,X0)
| empty(sK9(powerset(powerset(powerset(X0))))) )
| ~ spl16_451 ),
inference(avatar_component_clause,[],[f5221]) ).
fof(f19881,plain,
( spl16_1228
| ~ spl16_305
| ~ spl16_451 ),
inference(avatar_split_clause,[],[f5374,f5221,f2960,f19879]) ).
fof(f19879,plain,
( spl16_1228
<=> ! [X0] :
( empty(sK7(sK9(sK9(powerset(powerset(powerset(X0)))))))
| empty(sK9(sK9(powerset(powerset(powerset(X0))))))
| element(sK9(sK7(sK6(sK9(sK7(sK9(sK9(powerset(powerset(powerset(X0)))))))))),X0)
| empty(sK9(powerset(powerset(powerset(X0)))))
| empty(sK7(sK6(sK9(sK7(sK9(sK9(powerset(powerset(powerset(X0))))))))))
| empty(sK9(sK7(sK9(sK9(powerset(powerset(powerset(X0))))))))
| empty(sK6(sK9(sK7(sK9(sK9(powerset(powerset(powerset(X0))))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1228])]) ).
fof(f2960,plain,
( spl16_305
<=> ! [X0] :
( empty(sK6(X0))
| empty(sK7(sK6(X0)))
| empty(X0)
| in(sK9(sK7(sK6(X0))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_305])]) ).
fof(f5374,plain,
( ! [X0] :
( empty(sK7(sK9(sK9(powerset(powerset(powerset(X0)))))))
| empty(sK9(sK9(powerset(powerset(powerset(X0))))))
| element(sK9(sK7(sK6(sK9(sK7(sK9(sK9(powerset(powerset(powerset(X0)))))))))),X0)
| empty(sK9(powerset(powerset(powerset(X0)))))
| empty(sK7(sK6(sK9(sK7(sK9(sK9(powerset(powerset(powerset(X0))))))))))
| empty(sK9(sK7(sK9(sK9(powerset(powerset(powerset(X0))))))))
| empty(sK6(sK9(sK7(sK9(sK9(powerset(powerset(powerset(X0))))))))) )
| ~ spl16_305
| ~ spl16_451 ),
inference(resolution,[],[f5222,f2961]) ).
fof(f2961,plain,
( ! [X0] :
( in(sK9(sK7(sK6(X0))),X0)
| empty(sK7(sK6(X0)))
| empty(X0)
| empty(sK6(X0)) )
| ~ spl16_305 ),
inference(avatar_component_clause,[],[f2960]) ).
fof(f19877,plain,
( spl16_1227
| ~ spl16_304
| ~ spl16_451 ),
inference(avatar_split_clause,[],[f5368,f5221,f2956,f19875]) ).
fof(f19875,plain,
( spl16_1227
<=> ! [X0] :
( empty(sK7(sK9(sK9(powerset(powerset(powerset(X0)))))))
| empty(sK9(sK9(powerset(powerset(powerset(X0))))))
| element(sK9(sK6(sK7(sK9(sK7(sK9(sK9(powerset(powerset(powerset(X0)))))))))),X0)
| empty(sK9(powerset(powerset(powerset(X0)))))
| empty(sK6(sK7(sK9(sK7(sK9(sK9(powerset(powerset(powerset(X0))))))))))
| empty(sK9(sK7(sK9(sK9(powerset(powerset(powerset(X0))))))))
| empty(sK7(sK9(sK7(sK9(sK9(powerset(powerset(powerset(X0))))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1227])]) ).
fof(f2956,plain,
( spl16_304
<=> ! [X0] :
( empty(sK7(X0))
| empty(sK6(sK7(X0)))
| empty(X0)
| in(sK9(sK6(sK7(X0))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_304])]) ).
fof(f5368,plain,
( ! [X0] :
( empty(sK7(sK9(sK9(powerset(powerset(powerset(X0)))))))
| empty(sK9(sK9(powerset(powerset(powerset(X0))))))
| element(sK9(sK6(sK7(sK9(sK7(sK9(sK9(powerset(powerset(powerset(X0)))))))))),X0)
| empty(sK9(powerset(powerset(powerset(X0)))))
| empty(sK6(sK7(sK9(sK7(sK9(sK9(powerset(powerset(powerset(X0))))))))))
| empty(sK9(sK7(sK9(sK9(powerset(powerset(powerset(X0))))))))
| empty(sK7(sK9(sK7(sK9(sK9(powerset(powerset(powerset(X0))))))))) )
| ~ spl16_304
| ~ spl16_451 ),
inference(resolution,[],[f5222,f2957]) ).
fof(f2957,plain,
( ! [X0] :
( in(sK9(sK6(sK7(X0))),X0)
| empty(sK6(sK7(X0)))
| empty(X0)
| empty(sK7(X0)) )
| ~ spl16_304 ),
inference(avatar_component_clause,[],[f2956]) ).
fof(f19873,plain,
( spl16_1226
| ~ spl16_303
| ~ spl16_451 ),
inference(avatar_split_clause,[],[f5367,f5221,f2952,f19871]) ).
fof(f19871,plain,
( spl16_1226
<=> ! [X0] :
( empty(sK7(sK9(sK9(powerset(powerset(powerset(X0)))))))
| empty(sK9(sK9(powerset(powerset(powerset(X0))))))
| element(sK9(sK6(sK6(sK9(sK7(sK9(sK9(powerset(powerset(powerset(X0)))))))))),X0)
| empty(sK9(powerset(powerset(powerset(X0)))))
| empty(sK6(sK6(sK9(sK7(sK9(sK9(powerset(powerset(powerset(X0))))))))))
| empty(sK9(sK7(sK9(sK9(powerset(powerset(powerset(X0))))))))
| empty(sK6(sK9(sK7(sK9(sK9(powerset(powerset(powerset(X0))))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1226])]) ).
fof(f2952,plain,
( spl16_303
<=> ! [X0] :
( empty(sK6(X0))
| empty(sK6(sK6(X0)))
| empty(X0)
| in(sK9(sK6(sK6(X0))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_303])]) ).
fof(f5367,plain,
( ! [X0] :
( empty(sK7(sK9(sK9(powerset(powerset(powerset(X0)))))))
| empty(sK9(sK9(powerset(powerset(powerset(X0))))))
| element(sK9(sK6(sK6(sK9(sK7(sK9(sK9(powerset(powerset(powerset(X0)))))))))),X0)
| empty(sK9(powerset(powerset(powerset(X0)))))
| empty(sK6(sK6(sK9(sK7(sK9(sK9(powerset(powerset(powerset(X0))))))))))
| empty(sK9(sK7(sK9(sK9(powerset(powerset(powerset(X0))))))))
| empty(sK6(sK9(sK7(sK9(sK9(powerset(powerset(powerset(X0))))))))) )
| ~ spl16_303
| ~ spl16_451 ),
inference(resolution,[],[f5222,f2953]) ).
fof(f2953,plain,
( ! [X0] :
( in(sK9(sK6(sK6(X0))),X0)
| empty(sK6(sK6(X0)))
| empty(X0)
| empty(sK6(X0)) )
| ~ spl16_303 ),
inference(avatar_component_clause,[],[f2952]) ).
fof(f19869,plain,
( spl16_1225
| ~ spl16_306
| ~ spl16_450 ),
inference(avatar_split_clause,[],[f5350,f5217,f2964,f19867]) ).
fof(f19867,plain,
( spl16_1225
<=> ! [X0] :
( empty(sK6(sK9(sK9(powerset(powerset(powerset(X0)))))))
| empty(sK9(sK9(powerset(powerset(powerset(X0))))))
| element(sK9(sK7(sK7(sK9(sK6(sK9(sK9(powerset(powerset(powerset(X0)))))))))),X0)
| empty(sK9(powerset(powerset(powerset(X0)))))
| empty(sK7(sK7(sK9(sK6(sK9(sK9(powerset(powerset(powerset(X0))))))))))
| empty(sK9(sK6(sK9(sK9(powerset(powerset(powerset(X0))))))))
| empty(sK7(sK9(sK6(sK9(sK9(powerset(powerset(powerset(X0))))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1225])]) ).
fof(f5217,plain,
( spl16_450
<=> ! [X0,X1] :
( empty(sK9(powerset(powerset(powerset(X0)))))
| empty(sK6(sK9(sK9(powerset(powerset(powerset(X0)))))))
| empty(sK9(sK9(powerset(powerset(powerset(X0))))))
| element(X1,X0)
| ~ in(X1,sK9(sK6(sK9(sK9(powerset(powerset(powerset(X0)))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_450])]) ).
fof(f5350,plain,
( ! [X0] :
( empty(sK6(sK9(sK9(powerset(powerset(powerset(X0)))))))
| empty(sK9(sK9(powerset(powerset(powerset(X0))))))
| element(sK9(sK7(sK7(sK9(sK6(sK9(sK9(powerset(powerset(powerset(X0)))))))))),X0)
| empty(sK9(powerset(powerset(powerset(X0)))))
| empty(sK7(sK7(sK9(sK6(sK9(sK9(powerset(powerset(powerset(X0))))))))))
| empty(sK9(sK6(sK9(sK9(powerset(powerset(powerset(X0))))))))
| empty(sK7(sK9(sK6(sK9(sK9(powerset(powerset(powerset(X0))))))))) )
| ~ spl16_306
| ~ spl16_450 ),
inference(resolution,[],[f5218,f2965]) ).
fof(f5218,plain,
( ! [X0,X1] :
( ~ in(X1,sK9(sK6(sK9(sK9(powerset(powerset(powerset(X0))))))))
| empty(sK6(sK9(sK9(powerset(powerset(powerset(X0)))))))
| empty(sK9(sK9(powerset(powerset(powerset(X0))))))
| element(X1,X0)
| empty(sK9(powerset(powerset(powerset(X0))))) )
| ~ spl16_450 ),
inference(avatar_component_clause,[],[f5217]) ).
fof(f19865,plain,
( spl16_1224
| ~ spl16_305
| ~ spl16_450 ),
inference(avatar_split_clause,[],[f5349,f5217,f2960,f19863]) ).
fof(f19863,plain,
( spl16_1224
<=> ! [X0] :
( empty(sK6(sK9(sK9(powerset(powerset(powerset(X0)))))))
| empty(sK9(sK9(powerset(powerset(powerset(X0))))))
| element(sK9(sK7(sK6(sK9(sK6(sK9(sK9(powerset(powerset(powerset(X0)))))))))),X0)
| empty(sK9(powerset(powerset(powerset(X0)))))
| empty(sK7(sK6(sK9(sK6(sK9(sK9(powerset(powerset(powerset(X0))))))))))
| empty(sK9(sK6(sK9(sK9(powerset(powerset(powerset(X0))))))))
| empty(sK6(sK9(sK6(sK9(sK9(powerset(powerset(powerset(X0))))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1224])]) ).
fof(f5349,plain,
( ! [X0] :
( empty(sK6(sK9(sK9(powerset(powerset(powerset(X0)))))))
| empty(sK9(sK9(powerset(powerset(powerset(X0))))))
| element(sK9(sK7(sK6(sK9(sK6(sK9(sK9(powerset(powerset(powerset(X0)))))))))),X0)
| empty(sK9(powerset(powerset(powerset(X0)))))
| empty(sK7(sK6(sK9(sK6(sK9(sK9(powerset(powerset(powerset(X0))))))))))
| empty(sK9(sK6(sK9(sK9(powerset(powerset(powerset(X0))))))))
| empty(sK6(sK9(sK6(sK9(sK9(powerset(powerset(powerset(X0))))))))) )
| ~ spl16_305
| ~ spl16_450 ),
inference(resolution,[],[f5218,f2961]) ).
fof(f19861,plain,
( spl16_1223
| ~ spl16_304
| ~ spl16_450 ),
inference(avatar_split_clause,[],[f5343,f5217,f2956,f19859]) ).
fof(f19859,plain,
( spl16_1223
<=> ! [X0] :
( empty(sK6(sK9(sK9(powerset(powerset(powerset(X0)))))))
| empty(sK9(sK9(powerset(powerset(powerset(X0))))))
| element(sK9(sK6(sK7(sK9(sK6(sK9(sK9(powerset(powerset(powerset(X0)))))))))),X0)
| empty(sK9(powerset(powerset(powerset(X0)))))
| empty(sK6(sK7(sK9(sK6(sK9(sK9(powerset(powerset(powerset(X0))))))))))
| empty(sK9(sK6(sK9(sK9(powerset(powerset(powerset(X0))))))))
| empty(sK7(sK9(sK6(sK9(sK9(powerset(powerset(powerset(X0))))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1223])]) ).
fof(f5343,plain,
( ! [X0] :
( empty(sK6(sK9(sK9(powerset(powerset(powerset(X0)))))))
| empty(sK9(sK9(powerset(powerset(powerset(X0))))))
| element(sK9(sK6(sK7(sK9(sK6(sK9(sK9(powerset(powerset(powerset(X0)))))))))),X0)
| empty(sK9(powerset(powerset(powerset(X0)))))
| empty(sK6(sK7(sK9(sK6(sK9(sK9(powerset(powerset(powerset(X0))))))))))
| empty(sK9(sK6(sK9(sK9(powerset(powerset(powerset(X0))))))))
| empty(sK7(sK9(sK6(sK9(sK9(powerset(powerset(powerset(X0))))))))) )
| ~ spl16_304
| ~ spl16_450 ),
inference(resolution,[],[f5218,f2957]) ).
fof(f19857,plain,
( spl16_1222
| ~ spl16_303
| ~ spl16_450 ),
inference(avatar_split_clause,[],[f5342,f5217,f2952,f19855]) ).
fof(f19855,plain,
( spl16_1222
<=> ! [X0] :
( empty(sK6(sK9(sK9(powerset(powerset(powerset(X0)))))))
| empty(sK9(sK9(powerset(powerset(powerset(X0))))))
| element(sK9(sK6(sK6(sK9(sK6(sK9(sK9(powerset(powerset(powerset(X0)))))))))),X0)
| empty(sK9(powerset(powerset(powerset(X0)))))
| empty(sK6(sK6(sK9(sK6(sK9(sK9(powerset(powerset(powerset(X0))))))))))
| empty(sK9(sK6(sK9(sK9(powerset(powerset(powerset(X0))))))))
| empty(sK6(sK9(sK6(sK9(sK9(powerset(powerset(powerset(X0))))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1222])]) ).
fof(f5342,plain,
( ! [X0] :
( empty(sK6(sK9(sK9(powerset(powerset(powerset(X0)))))))
| empty(sK9(sK9(powerset(powerset(powerset(X0))))))
| element(sK9(sK6(sK6(sK9(sK6(sK9(sK9(powerset(powerset(powerset(X0)))))))))),X0)
| empty(sK9(powerset(powerset(powerset(X0)))))
| empty(sK6(sK6(sK9(sK6(sK9(sK9(powerset(powerset(powerset(X0))))))))))
| empty(sK9(sK6(sK9(sK9(powerset(powerset(powerset(X0))))))))
| empty(sK6(sK9(sK6(sK9(sK9(powerset(powerset(powerset(X0))))))))) )
| ~ spl16_303
| ~ spl16_450 ),
inference(resolution,[],[f5218,f2953]) ).
fof(f19853,plain,
( spl16_1221
| ~ spl16_326
| ~ spl16_449 ),
inference(avatar_split_clause,[],[f5326,f5213,f3305,f19851]) ).
fof(f19851,plain,
( spl16_1221
<=> ! [X0] :
( empty(powerset(powerset(X0)))
| empty(sK7(sK9(sK7(powerset(powerset(X0))))))
| empty(sK9(sK7(powerset(powerset(X0)))))
| element(sK9(sK7(sK9(powerset(sK9(sK7(sK9(sK7(powerset(powerset(X0)))))))))),X0)
| empty(sK7(powerset(powerset(X0))))
| empty(sK7(sK9(powerset(sK9(sK7(sK9(sK7(powerset(powerset(X0))))))))))
| empty(sK9(sK7(sK9(sK7(powerset(powerset(X0)))))))
| empty(sK9(powerset(sK9(sK7(sK9(sK7(powerset(powerset(X0))))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1221])]) ).
fof(f3305,plain,
( spl16_326
<=> ! [X0] :
( empty(sK9(powerset(X0)))
| empty(sK7(sK9(powerset(X0))))
| empty(X0)
| in(sK9(sK7(sK9(powerset(X0)))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_326])]) ).
fof(f5213,plain,
( spl16_449
<=> ! [X0,X1] :
( empty(sK7(powerset(powerset(X0))))
| empty(powerset(powerset(X0)))
| empty(sK7(sK9(sK7(powerset(powerset(X0))))))
| empty(sK9(sK7(powerset(powerset(X0)))))
| element(X1,X0)
| ~ in(X1,sK9(sK7(sK9(sK7(powerset(powerset(X0))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_449])]) ).
fof(f5326,plain,
( ! [X0] :
( empty(powerset(powerset(X0)))
| empty(sK7(sK9(sK7(powerset(powerset(X0))))))
| empty(sK9(sK7(powerset(powerset(X0)))))
| element(sK9(sK7(sK9(powerset(sK9(sK7(sK9(sK7(powerset(powerset(X0)))))))))),X0)
| empty(sK7(powerset(powerset(X0))))
| empty(sK7(sK9(powerset(sK9(sK7(sK9(sK7(powerset(powerset(X0))))))))))
| empty(sK9(sK7(sK9(sK7(powerset(powerset(X0)))))))
| empty(sK9(powerset(sK9(sK7(sK9(sK7(powerset(powerset(X0))))))))) )
| ~ spl16_326
| ~ spl16_449 ),
inference(resolution,[],[f5214,f3306]) ).
fof(f3306,plain,
( ! [X0] :
( in(sK9(sK7(sK9(powerset(X0)))),X0)
| empty(sK7(sK9(powerset(X0))))
| empty(X0)
| empty(sK9(powerset(X0))) )
| ~ spl16_326 ),
inference(avatar_component_clause,[],[f3305]) ).
fof(f5214,plain,
( ! [X0,X1] :
( ~ in(X1,sK9(sK7(sK9(sK7(powerset(powerset(X0)))))))
| empty(powerset(powerset(X0)))
| empty(sK7(sK9(sK7(powerset(powerset(X0))))))
| empty(sK9(sK7(powerset(powerset(X0)))))
| element(X1,X0)
| empty(sK7(powerset(powerset(X0)))) )
| ~ spl16_449 ),
inference(avatar_component_clause,[],[f5213]) ).
fof(f19849,plain,
( spl16_1220
| ~ spl16_325
| ~ spl16_449 ),
inference(avatar_split_clause,[],[f5319,f5213,f3300,f19847]) ).
fof(f19847,plain,
( spl16_1220
<=> ! [X0] :
( empty(powerset(powerset(X0)))
| empty(sK7(sK9(sK7(powerset(powerset(X0))))))
| empty(sK9(sK7(powerset(powerset(X0)))))
| element(sK9(sK6(sK9(powerset(sK9(sK7(sK9(sK7(powerset(powerset(X0)))))))))),X0)
| empty(sK7(powerset(powerset(X0))))
| empty(sK6(sK9(powerset(sK9(sK7(sK9(sK7(powerset(powerset(X0))))))))))
| empty(sK9(sK7(sK9(sK7(powerset(powerset(X0)))))))
| empty(sK9(powerset(sK9(sK7(sK9(sK7(powerset(powerset(X0))))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1220])]) ).
fof(f3300,plain,
( spl16_325
<=> ! [X0] :
( empty(sK9(powerset(X0)))
| empty(sK6(sK9(powerset(X0))))
| empty(X0)
| in(sK9(sK6(sK9(powerset(X0)))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_325])]) ).
fof(f5319,plain,
( ! [X0] :
( empty(powerset(powerset(X0)))
| empty(sK7(sK9(sK7(powerset(powerset(X0))))))
| empty(sK9(sK7(powerset(powerset(X0)))))
| element(sK9(sK6(sK9(powerset(sK9(sK7(sK9(sK7(powerset(powerset(X0)))))))))),X0)
| empty(sK7(powerset(powerset(X0))))
| empty(sK6(sK9(powerset(sK9(sK7(sK9(sK7(powerset(powerset(X0))))))))))
| empty(sK9(sK7(sK9(sK7(powerset(powerset(X0)))))))
| empty(sK9(powerset(sK9(sK7(sK9(sK7(powerset(powerset(X0))))))))) )
| ~ spl16_325
| ~ spl16_449 ),
inference(resolution,[],[f5214,f3301]) ).
fof(f3301,plain,
( ! [X0] :
( in(sK9(sK6(sK9(powerset(X0)))),X0)
| empty(sK6(sK9(powerset(X0))))
| empty(X0)
| empty(sK9(powerset(X0))) )
| ~ spl16_325 ),
inference(avatar_component_clause,[],[f3300]) ).
fof(f19845,plain,
( spl16_1219
| ~ spl16_326
| ~ spl16_448 ),
inference(avatar_split_clause,[],[f5301,f5209,f3305,f19843]) ).
fof(f19843,plain,
( spl16_1219
<=> ! [X0] :
( empty(powerset(powerset(X0)))
| empty(sK6(sK9(sK7(powerset(powerset(X0))))))
| empty(sK9(sK7(powerset(powerset(X0)))))
| element(sK9(sK7(sK9(powerset(sK9(sK6(sK9(sK7(powerset(powerset(X0)))))))))),X0)
| empty(sK7(powerset(powerset(X0))))
| empty(sK7(sK9(powerset(sK9(sK6(sK9(sK7(powerset(powerset(X0))))))))))
| empty(sK9(sK6(sK9(sK7(powerset(powerset(X0)))))))
| empty(sK9(powerset(sK9(sK6(sK9(sK7(powerset(powerset(X0))))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1219])]) ).
fof(f5209,plain,
( spl16_448
<=> ! [X0,X1] :
( empty(sK7(powerset(powerset(X0))))
| empty(powerset(powerset(X0)))
| empty(sK6(sK9(sK7(powerset(powerset(X0))))))
| empty(sK9(sK7(powerset(powerset(X0)))))
| element(X1,X0)
| ~ in(X1,sK9(sK6(sK9(sK7(powerset(powerset(X0))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_448])]) ).
fof(f5301,plain,
( ! [X0] :
( empty(powerset(powerset(X0)))
| empty(sK6(sK9(sK7(powerset(powerset(X0))))))
| empty(sK9(sK7(powerset(powerset(X0)))))
| element(sK9(sK7(sK9(powerset(sK9(sK6(sK9(sK7(powerset(powerset(X0)))))))))),X0)
| empty(sK7(powerset(powerset(X0))))
| empty(sK7(sK9(powerset(sK9(sK6(sK9(sK7(powerset(powerset(X0))))))))))
| empty(sK9(sK6(sK9(sK7(powerset(powerset(X0)))))))
| empty(sK9(powerset(sK9(sK6(sK9(sK7(powerset(powerset(X0))))))))) )
| ~ spl16_326
| ~ spl16_448 ),
inference(resolution,[],[f5210,f3306]) ).
fof(f5210,plain,
( ! [X0,X1] :
( ~ in(X1,sK9(sK6(sK9(sK7(powerset(powerset(X0)))))))
| empty(powerset(powerset(X0)))
| empty(sK6(sK9(sK7(powerset(powerset(X0))))))
| empty(sK9(sK7(powerset(powerset(X0)))))
| element(X1,X0)
| empty(sK7(powerset(powerset(X0)))) )
| ~ spl16_448 ),
inference(avatar_component_clause,[],[f5209]) ).
fof(f19841,plain,
( spl16_1218
| ~ spl16_325
| ~ spl16_448 ),
inference(avatar_split_clause,[],[f5294,f5209,f3300,f19839]) ).
fof(f19839,plain,
( spl16_1218
<=> ! [X0] :
( empty(powerset(powerset(X0)))
| empty(sK6(sK9(sK7(powerset(powerset(X0))))))
| empty(sK9(sK7(powerset(powerset(X0)))))
| element(sK9(sK6(sK9(powerset(sK9(sK6(sK9(sK7(powerset(powerset(X0)))))))))),X0)
| empty(sK7(powerset(powerset(X0))))
| empty(sK6(sK9(powerset(sK9(sK6(sK9(sK7(powerset(powerset(X0))))))))))
| empty(sK9(sK6(sK9(sK7(powerset(powerset(X0)))))))
| empty(sK9(powerset(sK9(sK6(sK9(sK7(powerset(powerset(X0))))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1218])]) ).
fof(f5294,plain,
( ! [X0] :
( empty(powerset(powerset(X0)))
| empty(sK6(sK9(sK7(powerset(powerset(X0))))))
| empty(sK9(sK7(powerset(powerset(X0)))))
| element(sK9(sK6(sK9(powerset(sK9(sK6(sK9(sK7(powerset(powerset(X0)))))))))),X0)
| empty(sK7(powerset(powerset(X0))))
| empty(sK6(sK9(powerset(sK9(sK6(sK9(sK7(powerset(powerset(X0))))))))))
| empty(sK9(sK6(sK9(sK7(powerset(powerset(X0)))))))
| empty(sK9(powerset(sK9(sK6(sK9(sK7(powerset(powerset(X0))))))))) )
| ~ spl16_325
| ~ spl16_448 ),
inference(resolution,[],[f5210,f3301]) ).
fof(f19837,plain,
( spl16_1217
| ~ spl16_326
| ~ spl16_447 ),
inference(avatar_split_clause,[],[f5276,f5205,f3305,f19835]) ).
fof(f19835,plain,
( spl16_1217
<=> ! [X0] :
( empty(powerset(powerset(X0)))
| empty(sK7(sK9(sK6(powerset(powerset(X0))))))
| empty(sK9(sK6(powerset(powerset(X0)))))
| element(sK9(sK7(sK9(powerset(sK9(sK7(sK9(sK6(powerset(powerset(X0)))))))))),X0)
| empty(sK6(powerset(powerset(X0))))
| empty(sK7(sK9(powerset(sK9(sK7(sK9(sK6(powerset(powerset(X0))))))))))
| empty(sK9(sK7(sK9(sK6(powerset(powerset(X0)))))))
| empty(sK9(powerset(sK9(sK7(sK9(sK6(powerset(powerset(X0))))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1217])]) ).
fof(f5205,plain,
( spl16_447
<=> ! [X0,X1] :
( empty(sK6(powerset(powerset(X0))))
| empty(powerset(powerset(X0)))
| empty(sK7(sK9(sK6(powerset(powerset(X0))))))
| empty(sK9(sK6(powerset(powerset(X0)))))
| element(X1,X0)
| ~ in(X1,sK9(sK7(sK9(sK6(powerset(powerset(X0))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_447])]) ).
fof(f5276,plain,
( ! [X0] :
( empty(powerset(powerset(X0)))
| empty(sK7(sK9(sK6(powerset(powerset(X0))))))
| empty(sK9(sK6(powerset(powerset(X0)))))
| element(sK9(sK7(sK9(powerset(sK9(sK7(sK9(sK6(powerset(powerset(X0)))))))))),X0)
| empty(sK6(powerset(powerset(X0))))
| empty(sK7(sK9(powerset(sK9(sK7(sK9(sK6(powerset(powerset(X0))))))))))
| empty(sK9(sK7(sK9(sK6(powerset(powerset(X0)))))))
| empty(sK9(powerset(sK9(sK7(sK9(sK6(powerset(powerset(X0))))))))) )
| ~ spl16_326
| ~ spl16_447 ),
inference(resolution,[],[f5206,f3306]) ).
fof(f5206,plain,
( ! [X0,X1] :
( ~ in(X1,sK9(sK7(sK9(sK6(powerset(powerset(X0)))))))
| empty(powerset(powerset(X0)))
| empty(sK7(sK9(sK6(powerset(powerset(X0))))))
| empty(sK9(sK6(powerset(powerset(X0)))))
| element(X1,X0)
| empty(sK6(powerset(powerset(X0)))) )
| ~ spl16_447 ),
inference(avatar_component_clause,[],[f5205]) ).
fof(f19833,plain,
( spl16_1216
| ~ spl16_325
| ~ spl16_447 ),
inference(avatar_split_clause,[],[f5269,f5205,f3300,f19831]) ).
fof(f19831,plain,
( spl16_1216
<=> ! [X0] :
( empty(powerset(powerset(X0)))
| empty(sK7(sK9(sK6(powerset(powerset(X0))))))
| empty(sK9(sK6(powerset(powerset(X0)))))
| element(sK9(sK6(sK9(powerset(sK9(sK7(sK9(sK6(powerset(powerset(X0)))))))))),X0)
| empty(sK6(powerset(powerset(X0))))
| empty(sK6(sK9(powerset(sK9(sK7(sK9(sK6(powerset(powerset(X0))))))))))
| empty(sK9(sK7(sK9(sK6(powerset(powerset(X0)))))))
| empty(sK9(powerset(sK9(sK7(sK9(sK6(powerset(powerset(X0))))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1216])]) ).
fof(f5269,plain,
( ! [X0] :
( empty(powerset(powerset(X0)))
| empty(sK7(sK9(sK6(powerset(powerset(X0))))))
| empty(sK9(sK6(powerset(powerset(X0)))))
| element(sK9(sK6(sK9(powerset(sK9(sK7(sK9(sK6(powerset(powerset(X0)))))))))),X0)
| empty(sK6(powerset(powerset(X0))))
| empty(sK6(sK9(powerset(sK9(sK7(sK9(sK6(powerset(powerset(X0))))))))))
| empty(sK9(sK7(sK9(sK6(powerset(powerset(X0)))))))
| empty(sK9(powerset(sK9(sK7(sK9(sK6(powerset(powerset(X0))))))))) )
| ~ spl16_325
| ~ spl16_447 ),
inference(resolution,[],[f5206,f3301]) ).
fof(f19829,plain,
( spl16_1215
| ~ spl16_326
| ~ spl16_446 ),
inference(avatar_split_clause,[],[f5251,f5201,f3305,f19827]) ).
fof(f19827,plain,
( spl16_1215
<=> ! [X0] :
( empty(powerset(powerset(X0)))
| empty(sK6(sK9(sK6(powerset(powerset(X0))))))
| empty(sK9(sK6(powerset(powerset(X0)))))
| element(sK9(sK7(sK9(powerset(sK9(sK6(sK9(sK6(powerset(powerset(X0)))))))))),X0)
| empty(sK6(powerset(powerset(X0))))
| empty(sK7(sK9(powerset(sK9(sK6(sK9(sK6(powerset(powerset(X0))))))))))
| empty(sK9(sK6(sK9(sK6(powerset(powerset(X0)))))))
| empty(sK9(powerset(sK9(sK6(sK9(sK6(powerset(powerset(X0))))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1215])]) ).
fof(f5201,plain,
( spl16_446
<=> ! [X0,X1] :
( empty(sK6(powerset(powerset(X0))))
| empty(powerset(powerset(X0)))
| empty(sK6(sK9(sK6(powerset(powerset(X0))))))
| empty(sK9(sK6(powerset(powerset(X0)))))
| element(X1,X0)
| ~ in(X1,sK9(sK6(sK9(sK6(powerset(powerset(X0))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_446])]) ).
fof(f5251,plain,
( ! [X0] :
( empty(powerset(powerset(X0)))
| empty(sK6(sK9(sK6(powerset(powerset(X0))))))
| empty(sK9(sK6(powerset(powerset(X0)))))
| element(sK9(sK7(sK9(powerset(sK9(sK6(sK9(sK6(powerset(powerset(X0)))))))))),X0)
| empty(sK6(powerset(powerset(X0))))
| empty(sK7(sK9(powerset(sK9(sK6(sK9(sK6(powerset(powerset(X0))))))))))
| empty(sK9(sK6(sK9(sK6(powerset(powerset(X0)))))))
| empty(sK9(powerset(sK9(sK6(sK9(sK6(powerset(powerset(X0))))))))) )
| ~ spl16_326
| ~ spl16_446 ),
inference(resolution,[],[f5202,f3306]) ).
fof(f5202,plain,
( ! [X0,X1] :
( ~ in(X1,sK9(sK6(sK9(sK6(powerset(powerset(X0)))))))
| empty(powerset(powerset(X0)))
| empty(sK6(sK9(sK6(powerset(powerset(X0))))))
| empty(sK9(sK6(powerset(powerset(X0)))))
| element(X1,X0)
| empty(sK6(powerset(powerset(X0)))) )
| ~ spl16_446 ),
inference(avatar_component_clause,[],[f5201]) ).
fof(f19825,plain,
( spl16_1214
| ~ spl16_325
| ~ spl16_446 ),
inference(avatar_split_clause,[],[f5244,f5201,f3300,f19823]) ).
fof(f19823,plain,
( spl16_1214
<=> ! [X0] :
( empty(powerset(powerset(X0)))
| empty(sK6(sK9(sK6(powerset(powerset(X0))))))
| empty(sK9(sK6(powerset(powerset(X0)))))
| element(sK9(sK6(sK9(powerset(sK9(sK6(sK9(sK6(powerset(powerset(X0)))))))))),X0)
| empty(sK6(powerset(powerset(X0))))
| empty(sK6(sK9(powerset(sK9(sK6(sK9(sK6(powerset(powerset(X0))))))))))
| empty(sK9(sK6(sK9(sK6(powerset(powerset(X0)))))))
| empty(sK9(powerset(sK9(sK6(sK9(sK6(powerset(powerset(X0))))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1214])]) ).
fof(f5244,plain,
( ! [X0] :
( empty(powerset(powerset(X0)))
| empty(sK6(sK9(sK6(powerset(powerset(X0))))))
| empty(sK9(sK6(powerset(powerset(X0)))))
| element(sK9(sK6(sK9(powerset(sK9(sK6(sK9(sK6(powerset(powerset(X0)))))))))),X0)
| empty(sK6(powerset(powerset(X0))))
| empty(sK6(sK9(powerset(sK9(sK6(sK9(sK6(powerset(powerset(X0))))))))))
| empty(sK9(sK6(sK9(sK6(powerset(powerset(X0)))))))
| empty(sK9(powerset(sK9(sK6(sK9(sK6(powerset(powerset(X0))))))))) )
| ~ spl16_325
| ~ spl16_446 ),
inference(resolution,[],[f5202,f3301]) ).
fof(f19821,plain,
( spl16_1213
| ~ spl16_369
| ~ spl16_415 ),
inference(avatar_split_clause,[],[f4638,f4477,f3907,f19819]) ).
fof(f19819,plain,
( spl16_1213
<=> ! [X0] :
( empty(powerset(sK9(sK7(sK7(powerset(X0))))))
| empty(sK7(sK9(sK7(powerset(sK9(sK7(sK7(powerset(X0)))))))))
| empty(sK9(sK7(powerset(sK9(sK7(sK7(powerset(X0))))))))
| empty(sK9(sK7(sK7(powerset(X0)))))
| empty(sK7(powerset(sK9(sK7(sK7(powerset(X0)))))))
| empty(sK7(sK7(powerset(X0))))
| empty(powerset(X0))
| element(sK9(sK7(sK9(sK7(powerset(sK9(sK7(sK7(powerset(X0))))))))),X0)
| empty(sK7(powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1213])]) ).
fof(f3907,plain,
( spl16_369
<=> ! [X0,X1] :
( empty(sK7(powerset(X0)))
| empty(sK7(sK7(powerset(X0))))
| empty(powerset(X0))
| element(X1,X0)
| ~ in(X1,sK9(sK7(sK7(powerset(X0))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_369])]) ).
fof(f4477,plain,
( spl16_415
<=> ! [X0] :
( empty(sK7(powerset(X0)))
| empty(powerset(X0))
| empty(sK7(sK9(sK7(powerset(X0)))))
| empty(sK9(sK7(powerset(X0))))
| empty(X0)
| in(sK9(sK7(sK9(sK7(powerset(X0))))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_415])]) ).
fof(f4638,plain,
( ! [X0] :
( empty(powerset(sK9(sK7(sK7(powerset(X0))))))
| empty(sK7(sK9(sK7(powerset(sK9(sK7(sK7(powerset(X0)))))))))
| empty(sK9(sK7(powerset(sK9(sK7(sK7(powerset(X0))))))))
| empty(sK9(sK7(sK7(powerset(X0)))))
| empty(sK7(powerset(sK9(sK7(sK7(powerset(X0)))))))
| empty(sK7(sK7(powerset(X0))))
| empty(powerset(X0))
| element(sK9(sK7(sK9(sK7(powerset(sK9(sK7(sK7(powerset(X0))))))))),X0)
| empty(sK7(powerset(X0))) )
| ~ spl16_369
| ~ spl16_415 ),
inference(resolution,[],[f4478,f3908]) ).
fof(f3908,plain,
( ! [X0,X1] :
( ~ in(X1,sK9(sK7(sK7(powerset(X0)))))
| empty(sK7(sK7(powerset(X0))))
| empty(powerset(X0))
| element(X1,X0)
| empty(sK7(powerset(X0))) )
| ~ spl16_369 ),
inference(avatar_component_clause,[],[f3907]) ).
fof(f4478,plain,
( ! [X0] :
( in(sK9(sK7(sK9(sK7(powerset(X0))))),X0)
| empty(powerset(X0))
| empty(sK7(sK9(sK7(powerset(X0)))))
| empty(sK9(sK7(powerset(X0))))
| empty(X0)
| empty(sK7(powerset(X0))) )
| ~ spl16_415 ),
inference(avatar_component_clause,[],[f4477]) ).
fof(f19817,plain,
( spl16_1212
| ~ spl16_368
| ~ spl16_415 ),
inference(avatar_split_clause,[],[f4636,f4477,f3903,f19815]) ).
fof(f19815,plain,
( spl16_1212
<=> ! [X0] :
( empty(powerset(sK9(sK7(sK6(powerset(X0))))))
| empty(sK7(sK9(sK7(powerset(sK9(sK7(sK6(powerset(X0)))))))))
| empty(sK9(sK7(powerset(sK9(sK7(sK6(powerset(X0))))))))
| empty(sK9(sK7(sK6(powerset(X0)))))
| empty(sK7(powerset(sK9(sK7(sK6(powerset(X0)))))))
| empty(sK7(sK6(powerset(X0))))
| empty(powerset(X0))
| element(sK9(sK7(sK9(sK7(powerset(sK9(sK7(sK6(powerset(X0))))))))),X0)
| empty(sK6(powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1212])]) ).
fof(f3903,plain,
( spl16_368
<=> ! [X0,X1] :
( empty(sK6(powerset(X0)))
| empty(sK7(sK6(powerset(X0))))
| empty(powerset(X0))
| element(X1,X0)
| ~ in(X1,sK9(sK7(sK6(powerset(X0))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_368])]) ).
fof(f4636,plain,
( ! [X0] :
( empty(powerset(sK9(sK7(sK6(powerset(X0))))))
| empty(sK7(sK9(sK7(powerset(sK9(sK7(sK6(powerset(X0)))))))))
| empty(sK9(sK7(powerset(sK9(sK7(sK6(powerset(X0))))))))
| empty(sK9(sK7(sK6(powerset(X0)))))
| empty(sK7(powerset(sK9(sK7(sK6(powerset(X0)))))))
| empty(sK7(sK6(powerset(X0))))
| empty(powerset(X0))
| element(sK9(sK7(sK9(sK7(powerset(sK9(sK7(sK6(powerset(X0))))))))),X0)
| empty(sK6(powerset(X0))) )
| ~ spl16_368
| ~ spl16_415 ),
inference(resolution,[],[f4478,f3904]) ).
fof(f3904,plain,
( ! [X0,X1] :
( ~ in(X1,sK9(sK7(sK6(powerset(X0)))))
| empty(sK7(sK6(powerset(X0))))
| empty(powerset(X0))
| element(X1,X0)
| empty(sK6(powerset(X0))) )
| ~ spl16_368 ),
inference(avatar_component_clause,[],[f3903]) ).
fof(f19813,plain,
( spl16_1211
| ~ spl16_366
| ~ spl16_415 ),
inference(avatar_split_clause,[],[f4630,f4477,f3895,f19811]) ).
fof(f19811,plain,
( spl16_1211
<=> ! [X0] :
( empty(powerset(sK9(sK6(sK7(powerset(X0))))))
| empty(sK7(sK9(sK7(powerset(sK9(sK6(sK7(powerset(X0)))))))))
| empty(sK9(sK7(powerset(sK9(sK6(sK7(powerset(X0))))))))
| empty(sK9(sK6(sK7(powerset(X0)))))
| empty(sK7(powerset(sK9(sK6(sK7(powerset(X0)))))))
| empty(sK6(sK7(powerset(X0))))
| empty(powerset(X0))
| element(sK9(sK7(sK9(sK7(powerset(sK9(sK6(sK7(powerset(X0))))))))),X0)
| empty(sK7(powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1211])]) ).
fof(f3895,plain,
( spl16_366
<=> ! [X0,X1] :
( empty(sK7(powerset(X0)))
| empty(sK6(sK7(powerset(X0))))
| empty(powerset(X0))
| element(X1,X0)
| ~ in(X1,sK9(sK6(sK7(powerset(X0))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_366])]) ).
fof(f4630,plain,
( ! [X0] :
( empty(powerset(sK9(sK6(sK7(powerset(X0))))))
| empty(sK7(sK9(sK7(powerset(sK9(sK6(sK7(powerset(X0)))))))))
| empty(sK9(sK7(powerset(sK9(sK6(sK7(powerset(X0))))))))
| empty(sK9(sK6(sK7(powerset(X0)))))
| empty(sK7(powerset(sK9(sK6(sK7(powerset(X0)))))))
| empty(sK6(sK7(powerset(X0))))
| empty(powerset(X0))
| element(sK9(sK7(sK9(sK7(powerset(sK9(sK6(sK7(powerset(X0))))))))),X0)
| empty(sK7(powerset(X0))) )
| ~ spl16_366
| ~ spl16_415 ),
inference(resolution,[],[f4478,f3896]) ).
fof(f3896,plain,
( ! [X0,X1] :
( ~ in(X1,sK9(sK6(sK7(powerset(X0)))))
| empty(sK6(sK7(powerset(X0))))
| empty(powerset(X0))
| element(X1,X0)
| empty(sK7(powerset(X0))) )
| ~ spl16_366 ),
inference(avatar_component_clause,[],[f3895]) ).
fof(f19809,plain,
( spl16_1210
| ~ spl16_365
| ~ spl16_415 ),
inference(avatar_split_clause,[],[f4628,f4477,f3891,f19807]) ).
fof(f19807,plain,
( spl16_1210
<=> ! [X0] :
( empty(powerset(sK9(sK6(sK6(powerset(X0))))))
| empty(sK7(sK9(sK7(powerset(sK9(sK6(sK6(powerset(X0)))))))))
| empty(sK9(sK7(powerset(sK9(sK6(sK6(powerset(X0))))))))
| empty(sK9(sK6(sK6(powerset(X0)))))
| empty(sK7(powerset(sK9(sK6(sK6(powerset(X0)))))))
| empty(sK6(sK6(powerset(X0))))
| empty(powerset(X0))
| element(sK9(sK7(sK9(sK7(powerset(sK9(sK6(sK6(powerset(X0))))))))),X0)
| empty(sK6(powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1210])]) ).
fof(f3891,plain,
( spl16_365
<=> ! [X0,X1] :
( empty(sK6(powerset(X0)))
| empty(sK6(sK6(powerset(X0))))
| empty(powerset(X0))
| element(X1,X0)
| ~ in(X1,sK9(sK6(sK6(powerset(X0))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_365])]) ).
fof(f4628,plain,
( ! [X0] :
( empty(powerset(sK9(sK6(sK6(powerset(X0))))))
| empty(sK7(sK9(sK7(powerset(sK9(sK6(sK6(powerset(X0)))))))))
| empty(sK9(sK7(powerset(sK9(sK6(sK6(powerset(X0))))))))
| empty(sK9(sK6(sK6(powerset(X0)))))
| empty(sK7(powerset(sK9(sK6(sK6(powerset(X0)))))))
| empty(sK6(sK6(powerset(X0))))
| empty(powerset(X0))
| element(sK9(sK7(sK9(sK7(powerset(sK9(sK6(sK6(powerset(X0))))))))),X0)
| empty(sK6(powerset(X0))) )
| ~ spl16_365
| ~ spl16_415 ),
inference(resolution,[],[f4478,f3892]) ).
fof(f3892,plain,
( ! [X0,X1] :
( ~ in(X1,sK9(sK6(sK6(powerset(X0)))))
| empty(sK6(sK6(powerset(X0))))
| empty(powerset(X0))
| element(X1,X0)
| empty(sK6(powerset(X0))) )
| ~ spl16_365 ),
inference(avatar_component_clause,[],[f3891]) ).
fof(f19805,plain,
( spl16_1209
| ~ spl16_369
| ~ spl16_414 ),
inference(avatar_split_clause,[],[f4593,f4473,f3907,f19803]) ).
fof(f19803,plain,
( spl16_1209
<=> ! [X0] :
( empty(powerset(sK9(sK7(sK7(powerset(X0))))))
| empty(sK6(sK9(sK7(powerset(sK9(sK7(sK7(powerset(X0)))))))))
| empty(sK9(sK7(powerset(sK9(sK7(sK7(powerset(X0))))))))
| empty(sK9(sK7(sK7(powerset(X0)))))
| empty(sK7(powerset(sK9(sK7(sK7(powerset(X0)))))))
| empty(sK7(sK7(powerset(X0))))
| empty(powerset(X0))
| element(sK9(sK6(sK9(sK7(powerset(sK9(sK7(sK7(powerset(X0))))))))),X0)
| empty(sK7(powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1209])]) ).
fof(f4473,plain,
( spl16_414
<=> ! [X0] :
( empty(sK7(powerset(X0)))
| empty(powerset(X0))
| empty(sK6(sK9(sK7(powerset(X0)))))
| empty(sK9(sK7(powerset(X0))))
| empty(X0)
| in(sK9(sK6(sK9(sK7(powerset(X0))))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_414])]) ).
fof(f4593,plain,
( ! [X0] :
( empty(powerset(sK9(sK7(sK7(powerset(X0))))))
| empty(sK6(sK9(sK7(powerset(sK9(sK7(sK7(powerset(X0)))))))))
| empty(sK9(sK7(powerset(sK9(sK7(sK7(powerset(X0))))))))
| empty(sK9(sK7(sK7(powerset(X0)))))
| empty(sK7(powerset(sK9(sK7(sK7(powerset(X0)))))))
| empty(sK7(sK7(powerset(X0))))
| empty(powerset(X0))
| element(sK9(sK6(sK9(sK7(powerset(sK9(sK7(sK7(powerset(X0))))))))),X0)
| empty(sK7(powerset(X0))) )
| ~ spl16_369
| ~ spl16_414 ),
inference(resolution,[],[f4474,f3908]) ).
fof(f4474,plain,
( ! [X0] :
( in(sK9(sK6(sK9(sK7(powerset(X0))))),X0)
| empty(powerset(X0))
| empty(sK6(sK9(sK7(powerset(X0)))))
| empty(sK9(sK7(powerset(X0))))
| empty(X0)
| empty(sK7(powerset(X0))) )
| ~ spl16_414 ),
inference(avatar_component_clause,[],[f4473]) ).
fof(f19801,plain,
( spl16_1208
| ~ spl16_368
| ~ spl16_414 ),
inference(avatar_split_clause,[],[f4591,f4473,f3903,f19799]) ).
fof(f19799,plain,
( spl16_1208
<=> ! [X0] :
( empty(powerset(sK9(sK7(sK6(powerset(X0))))))
| empty(sK6(sK9(sK7(powerset(sK9(sK7(sK6(powerset(X0)))))))))
| empty(sK9(sK7(powerset(sK9(sK7(sK6(powerset(X0))))))))
| empty(sK9(sK7(sK6(powerset(X0)))))
| empty(sK7(powerset(sK9(sK7(sK6(powerset(X0)))))))
| empty(sK7(sK6(powerset(X0))))
| empty(powerset(X0))
| element(sK9(sK6(sK9(sK7(powerset(sK9(sK7(sK6(powerset(X0))))))))),X0)
| empty(sK6(powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1208])]) ).
fof(f4591,plain,
( ! [X0] :
( empty(powerset(sK9(sK7(sK6(powerset(X0))))))
| empty(sK6(sK9(sK7(powerset(sK9(sK7(sK6(powerset(X0)))))))))
| empty(sK9(sK7(powerset(sK9(sK7(sK6(powerset(X0))))))))
| empty(sK9(sK7(sK6(powerset(X0)))))
| empty(sK7(powerset(sK9(sK7(sK6(powerset(X0)))))))
| empty(sK7(sK6(powerset(X0))))
| empty(powerset(X0))
| element(sK9(sK6(sK9(sK7(powerset(sK9(sK7(sK6(powerset(X0))))))))),X0)
| empty(sK6(powerset(X0))) )
| ~ spl16_368
| ~ spl16_414 ),
inference(resolution,[],[f4474,f3904]) ).
fof(f19797,plain,
( spl16_1207
| ~ spl16_884
| ~ spl16_12
| ~ spl16_473
| ~ spl16_971 ),
inference(avatar_split_clause,[],[f17942,f17017,f5624,f213,f15900,f19794]) ).
fof(f19794,plain,
( spl16_1207
<=> sK14 = the_InternalRel(sK8(sK8(sK8(sK8(sK1))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1207])]) ).
fof(f15900,plain,
( spl16_884
<=> rel_str(sK8(sK8(sK8(sK1)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_884])]) ).
fof(f213,plain,
( spl16_12
<=> empty(sK14) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_12])]) ).
fof(f5624,plain,
( spl16_473
<=> ! [X0] :
( sK14 = the_InternalRel(sK8(X0))
| ~ rel_str(X0)
| ~ empty(the_InternalRel(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_473])]) ).
fof(f17017,plain,
( spl16_971
<=> sK14 = the_InternalRel(sK8(sK8(sK8(sK1)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_971])]) ).
fof(f17942,plain,
( ~ empty(sK14)
| ~ rel_str(sK8(sK8(sK8(sK1))))
| sK14 = the_InternalRel(sK8(sK8(sK8(sK8(sK1)))))
| ~ spl16_473
| ~ spl16_971 ),
inference(superposition,[],[f5625,f17019]) ).
fof(f17019,plain,
( sK14 = the_InternalRel(sK8(sK8(sK8(sK1))))
| ~ spl16_971 ),
inference(avatar_component_clause,[],[f17017]) ).
fof(f5625,plain,
( ! [X0] :
( ~ empty(the_InternalRel(X0))
| ~ rel_str(X0)
| sK14 = the_InternalRel(sK8(X0)) )
| ~ spl16_473 ),
inference(avatar_component_clause,[],[f5624]) ).
fof(f19792,plain,
( spl16_1206
| ~ spl16_366
| ~ spl16_414 ),
inference(avatar_split_clause,[],[f4585,f4473,f3895,f19790]) ).
fof(f19790,plain,
( spl16_1206
<=> ! [X0] :
( empty(powerset(sK9(sK6(sK7(powerset(X0))))))
| empty(sK6(sK9(sK7(powerset(sK9(sK6(sK7(powerset(X0)))))))))
| empty(sK9(sK7(powerset(sK9(sK6(sK7(powerset(X0))))))))
| empty(sK9(sK6(sK7(powerset(X0)))))
| empty(sK7(powerset(sK9(sK6(sK7(powerset(X0)))))))
| empty(sK6(sK7(powerset(X0))))
| empty(powerset(X0))
| element(sK9(sK6(sK9(sK7(powerset(sK9(sK6(sK7(powerset(X0))))))))),X0)
| empty(sK7(powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1206])]) ).
fof(f4585,plain,
( ! [X0] :
( empty(powerset(sK9(sK6(sK7(powerset(X0))))))
| empty(sK6(sK9(sK7(powerset(sK9(sK6(sK7(powerset(X0)))))))))
| empty(sK9(sK7(powerset(sK9(sK6(sK7(powerset(X0))))))))
| empty(sK9(sK6(sK7(powerset(X0)))))
| empty(sK7(powerset(sK9(sK6(sK7(powerset(X0)))))))
| empty(sK6(sK7(powerset(X0))))
| empty(powerset(X0))
| element(sK9(sK6(sK9(sK7(powerset(sK9(sK6(sK7(powerset(X0))))))))),X0)
| empty(sK7(powerset(X0))) )
| ~ spl16_366
| ~ spl16_414 ),
inference(resolution,[],[f4474,f3896]) ).
fof(f19788,plain,
( spl16_1205
| ~ spl16_365
| ~ spl16_414 ),
inference(avatar_split_clause,[],[f4583,f4473,f3891,f19786]) ).
fof(f19786,plain,
( spl16_1205
<=> ! [X0] :
( empty(powerset(sK9(sK6(sK6(powerset(X0))))))
| empty(sK6(sK9(sK7(powerset(sK9(sK6(sK6(powerset(X0)))))))))
| empty(sK9(sK7(powerset(sK9(sK6(sK6(powerset(X0))))))))
| empty(sK9(sK6(sK6(powerset(X0)))))
| empty(sK7(powerset(sK9(sK6(sK6(powerset(X0)))))))
| empty(sK6(sK6(powerset(X0))))
| empty(powerset(X0))
| element(sK9(sK6(sK9(sK7(powerset(sK9(sK6(sK6(powerset(X0))))))))),X0)
| empty(sK6(powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1205])]) ).
fof(f4583,plain,
( ! [X0] :
( empty(powerset(sK9(sK6(sK6(powerset(X0))))))
| empty(sK6(sK9(sK7(powerset(sK9(sK6(sK6(powerset(X0)))))))))
| empty(sK9(sK7(powerset(sK9(sK6(sK6(powerset(X0))))))))
| empty(sK9(sK6(sK6(powerset(X0)))))
| empty(sK7(powerset(sK9(sK6(sK6(powerset(X0)))))))
| empty(sK6(sK6(powerset(X0))))
| empty(powerset(X0))
| element(sK9(sK6(sK9(sK7(powerset(sK9(sK6(sK6(powerset(X0))))))))),X0)
| empty(sK6(powerset(X0))) )
| ~ spl16_365
| ~ spl16_414 ),
inference(resolution,[],[f4474,f3892]) ).
fof(f19784,plain,
( spl16_1204
| ~ spl16_369
| ~ spl16_413 ),
inference(avatar_split_clause,[],[f4548,f4469,f3907,f19782]) ).
fof(f19782,plain,
( spl16_1204
<=> ! [X0] :
( empty(powerset(sK9(sK7(sK7(powerset(X0))))))
| empty(sK7(sK9(sK6(powerset(sK9(sK7(sK7(powerset(X0)))))))))
| empty(sK9(sK6(powerset(sK9(sK7(sK7(powerset(X0))))))))
| empty(sK9(sK7(sK7(powerset(X0)))))
| empty(sK6(powerset(sK9(sK7(sK7(powerset(X0)))))))
| empty(sK7(sK7(powerset(X0))))
| empty(powerset(X0))
| element(sK9(sK7(sK9(sK6(powerset(sK9(sK7(sK7(powerset(X0))))))))),X0)
| empty(sK7(powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1204])]) ).
fof(f4469,plain,
( spl16_413
<=> ! [X0] :
( empty(sK6(powerset(X0)))
| empty(powerset(X0))
| empty(sK7(sK9(sK6(powerset(X0)))))
| empty(sK9(sK6(powerset(X0))))
| empty(X0)
| in(sK9(sK7(sK9(sK6(powerset(X0))))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_413])]) ).
fof(f4548,plain,
( ! [X0] :
( empty(powerset(sK9(sK7(sK7(powerset(X0))))))
| empty(sK7(sK9(sK6(powerset(sK9(sK7(sK7(powerset(X0)))))))))
| empty(sK9(sK6(powerset(sK9(sK7(sK7(powerset(X0))))))))
| empty(sK9(sK7(sK7(powerset(X0)))))
| empty(sK6(powerset(sK9(sK7(sK7(powerset(X0)))))))
| empty(sK7(sK7(powerset(X0))))
| empty(powerset(X0))
| element(sK9(sK7(sK9(sK6(powerset(sK9(sK7(sK7(powerset(X0))))))))),X0)
| empty(sK7(powerset(X0))) )
| ~ spl16_369
| ~ spl16_413 ),
inference(resolution,[],[f4470,f3908]) ).
fof(f4470,plain,
( ! [X0] :
( in(sK9(sK7(sK9(sK6(powerset(X0))))),X0)
| empty(powerset(X0))
| empty(sK7(sK9(sK6(powerset(X0)))))
| empty(sK9(sK6(powerset(X0))))
| empty(X0)
| empty(sK6(powerset(X0))) )
| ~ spl16_413 ),
inference(avatar_component_clause,[],[f4469]) ).
fof(f19780,plain,
( spl16_1203
| ~ spl16_368
| ~ spl16_413 ),
inference(avatar_split_clause,[],[f4546,f4469,f3903,f19778]) ).
fof(f19778,plain,
( spl16_1203
<=> ! [X0] :
( empty(powerset(sK9(sK7(sK6(powerset(X0))))))
| empty(sK7(sK9(sK6(powerset(sK9(sK7(sK6(powerset(X0)))))))))
| empty(sK9(sK6(powerset(sK9(sK7(sK6(powerset(X0))))))))
| empty(sK9(sK7(sK6(powerset(X0)))))
| empty(sK6(powerset(sK9(sK7(sK6(powerset(X0)))))))
| empty(sK7(sK6(powerset(X0))))
| empty(powerset(X0))
| element(sK9(sK7(sK9(sK6(powerset(sK9(sK7(sK6(powerset(X0))))))))),X0)
| empty(sK6(powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1203])]) ).
fof(f4546,plain,
( ! [X0] :
( empty(powerset(sK9(sK7(sK6(powerset(X0))))))
| empty(sK7(sK9(sK6(powerset(sK9(sK7(sK6(powerset(X0)))))))))
| empty(sK9(sK6(powerset(sK9(sK7(sK6(powerset(X0))))))))
| empty(sK9(sK7(sK6(powerset(X0)))))
| empty(sK6(powerset(sK9(sK7(sK6(powerset(X0)))))))
| empty(sK7(sK6(powerset(X0))))
| empty(powerset(X0))
| element(sK9(sK7(sK9(sK6(powerset(sK9(sK7(sK6(powerset(X0))))))))),X0)
| empty(sK6(powerset(X0))) )
| ~ spl16_368
| ~ spl16_413 ),
inference(resolution,[],[f4470,f3904]) ).
fof(f19776,plain,
( spl16_1202
| ~ spl16_366
| ~ spl16_413 ),
inference(avatar_split_clause,[],[f4540,f4469,f3895,f19774]) ).
fof(f19774,plain,
( spl16_1202
<=> ! [X0] :
( empty(powerset(sK9(sK6(sK7(powerset(X0))))))
| empty(sK7(sK9(sK6(powerset(sK9(sK6(sK7(powerset(X0)))))))))
| empty(sK9(sK6(powerset(sK9(sK6(sK7(powerset(X0))))))))
| empty(sK9(sK6(sK7(powerset(X0)))))
| empty(sK6(powerset(sK9(sK6(sK7(powerset(X0)))))))
| empty(sK6(sK7(powerset(X0))))
| empty(powerset(X0))
| element(sK9(sK7(sK9(sK6(powerset(sK9(sK6(sK7(powerset(X0))))))))),X0)
| empty(sK7(powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1202])]) ).
fof(f4540,plain,
( ! [X0] :
( empty(powerset(sK9(sK6(sK7(powerset(X0))))))
| empty(sK7(sK9(sK6(powerset(sK9(sK6(sK7(powerset(X0)))))))))
| empty(sK9(sK6(powerset(sK9(sK6(sK7(powerset(X0))))))))
| empty(sK9(sK6(sK7(powerset(X0)))))
| empty(sK6(powerset(sK9(sK6(sK7(powerset(X0)))))))
| empty(sK6(sK7(powerset(X0))))
| empty(powerset(X0))
| element(sK9(sK7(sK9(sK6(powerset(sK9(sK6(sK7(powerset(X0))))))))),X0)
| empty(sK7(powerset(X0))) )
| ~ spl16_366
| ~ spl16_413 ),
inference(resolution,[],[f4470,f3896]) ).
fof(f19772,plain,
( spl16_1201
| ~ spl16_365
| ~ spl16_413 ),
inference(avatar_split_clause,[],[f4538,f4469,f3891,f19770]) ).
fof(f19770,plain,
( spl16_1201
<=> ! [X0] :
( empty(powerset(sK9(sK6(sK6(powerset(X0))))))
| empty(sK7(sK9(sK6(powerset(sK9(sK6(sK6(powerset(X0)))))))))
| empty(sK9(sK6(powerset(sK9(sK6(sK6(powerset(X0))))))))
| empty(sK9(sK6(sK6(powerset(X0)))))
| empty(sK6(powerset(sK9(sK6(sK6(powerset(X0)))))))
| empty(sK6(sK6(powerset(X0))))
| empty(powerset(X0))
| element(sK9(sK7(sK9(sK6(powerset(sK9(sK6(sK6(powerset(X0))))))))),X0)
| empty(sK6(powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1201])]) ).
fof(f4538,plain,
( ! [X0] :
( empty(powerset(sK9(sK6(sK6(powerset(X0))))))
| empty(sK7(sK9(sK6(powerset(sK9(sK6(sK6(powerset(X0)))))))))
| empty(sK9(sK6(powerset(sK9(sK6(sK6(powerset(X0))))))))
| empty(sK9(sK6(sK6(powerset(X0)))))
| empty(sK6(powerset(sK9(sK6(sK6(powerset(X0)))))))
| empty(sK6(sK6(powerset(X0))))
| empty(powerset(X0))
| element(sK9(sK7(sK9(sK6(powerset(sK9(sK6(sK6(powerset(X0))))))))),X0)
| empty(sK6(powerset(X0))) )
| ~ spl16_365
| ~ spl16_413 ),
inference(resolution,[],[f4470,f3892]) ).
fof(f19768,plain,
( spl16_1200
| ~ spl16_369
| ~ spl16_412 ),
inference(avatar_split_clause,[],[f4503,f4465,f3907,f19766]) ).
fof(f19766,plain,
( spl16_1200
<=> ! [X0] :
( empty(powerset(sK9(sK7(sK7(powerset(X0))))))
| empty(sK6(sK9(sK6(powerset(sK9(sK7(sK7(powerset(X0)))))))))
| empty(sK9(sK6(powerset(sK9(sK7(sK7(powerset(X0))))))))
| empty(sK9(sK7(sK7(powerset(X0)))))
| empty(sK6(powerset(sK9(sK7(sK7(powerset(X0)))))))
| empty(sK7(sK7(powerset(X0))))
| empty(powerset(X0))
| element(sK9(sK6(sK9(sK6(powerset(sK9(sK7(sK7(powerset(X0))))))))),X0)
| empty(sK7(powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1200])]) ).
fof(f4465,plain,
( spl16_412
<=> ! [X0] :
( empty(sK6(powerset(X0)))
| empty(powerset(X0))
| empty(sK6(sK9(sK6(powerset(X0)))))
| empty(sK9(sK6(powerset(X0))))
| empty(X0)
| in(sK9(sK6(sK9(sK6(powerset(X0))))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_412])]) ).
fof(f4503,plain,
( ! [X0] :
( empty(powerset(sK9(sK7(sK7(powerset(X0))))))
| empty(sK6(sK9(sK6(powerset(sK9(sK7(sK7(powerset(X0)))))))))
| empty(sK9(sK6(powerset(sK9(sK7(sK7(powerset(X0))))))))
| empty(sK9(sK7(sK7(powerset(X0)))))
| empty(sK6(powerset(sK9(sK7(sK7(powerset(X0)))))))
| empty(sK7(sK7(powerset(X0))))
| empty(powerset(X0))
| element(sK9(sK6(sK9(sK6(powerset(sK9(sK7(sK7(powerset(X0))))))))),X0)
| empty(sK7(powerset(X0))) )
| ~ spl16_369
| ~ spl16_412 ),
inference(resolution,[],[f4466,f3908]) ).
fof(f4466,plain,
( ! [X0] :
( in(sK9(sK6(sK9(sK6(powerset(X0))))),X0)
| empty(powerset(X0))
| empty(sK6(sK9(sK6(powerset(X0)))))
| empty(sK9(sK6(powerset(X0))))
| empty(X0)
| empty(sK6(powerset(X0))) )
| ~ spl16_412 ),
inference(avatar_component_clause,[],[f4465]) ).
fof(f19764,plain,
( spl16_1199
| ~ spl16_368
| ~ spl16_412 ),
inference(avatar_split_clause,[],[f4501,f4465,f3903,f19762]) ).
fof(f19762,plain,
( spl16_1199
<=> ! [X0] :
( empty(powerset(sK9(sK7(sK6(powerset(X0))))))
| empty(sK6(sK9(sK6(powerset(sK9(sK7(sK6(powerset(X0)))))))))
| empty(sK9(sK6(powerset(sK9(sK7(sK6(powerset(X0))))))))
| empty(sK9(sK7(sK6(powerset(X0)))))
| empty(sK6(powerset(sK9(sK7(sK6(powerset(X0)))))))
| empty(sK7(sK6(powerset(X0))))
| empty(powerset(X0))
| element(sK9(sK6(sK9(sK6(powerset(sK9(sK7(sK6(powerset(X0))))))))),X0)
| empty(sK6(powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1199])]) ).
fof(f4501,plain,
( ! [X0] :
( empty(powerset(sK9(sK7(sK6(powerset(X0))))))
| empty(sK6(sK9(sK6(powerset(sK9(sK7(sK6(powerset(X0)))))))))
| empty(sK9(sK6(powerset(sK9(sK7(sK6(powerset(X0))))))))
| empty(sK9(sK7(sK6(powerset(X0)))))
| empty(sK6(powerset(sK9(sK7(sK6(powerset(X0)))))))
| empty(sK7(sK6(powerset(X0))))
| empty(powerset(X0))
| element(sK9(sK6(sK9(sK6(powerset(sK9(sK7(sK6(powerset(X0))))))))),X0)
| empty(sK6(powerset(X0))) )
| ~ spl16_368
| ~ spl16_412 ),
inference(resolution,[],[f4466,f3904]) ).
fof(f19760,plain,
( spl16_1198
| ~ spl16_366
| ~ spl16_412 ),
inference(avatar_split_clause,[],[f4495,f4465,f3895,f19758]) ).
fof(f19758,plain,
( spl16_1198
<=> ! [X0] :
( empty(powerset(sK9(sK6(sK7(powerset(X0))))))
| empty(sK6(sK9(sK6(powerset(sK9(sK6(sK7(powerset(X0)))))))))
| empty(sK9(sK6(powerset(sK9(sK6(sK7(powerset(X0))))))))
| empty(sK9(sK6(sK7(powerset(X0)))))
| empty(sK6(powerset(sK9(sK6(sK7(powerset(X0)))))))
| empty(sK6(sK7(powerset(X0))))
| empty(powerset(X0))
| element(sK9(sK6(sK9(sK6(powerset(sK9(sK6(sK7(powerset(X0))))))))),X0)
| empty(sK7(powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1198])]) ).
fof(f4495,plain,
( ! [X0] :
( empty(powerset(sK9(sK6(sK7(powerset(X0))))))
| empty(sK6(sK9(sK6(powerset(sK9(sK6(sK7(powerset(X0)))))))))
| empty(sK9(sK6(powerset(sK9(sK6(sK7(powerset(X0))))))))
| empty(sK9(sK6(sK7(powerset(X0)))))
| empty(sK6(powerset(sK9(sK6(sK7(powerset(X0)))))))
| empty(sK6(sK7(powerset(X0))))
| empty(powerset(X0))
| element(sK9(sK6(sK9(sK6(powerset(sK9(sK6(sK7(powerset(X0))))))))),X0)
| empty(sK7(powerset(X0))) )
| ~ spl16_366
| ~ spl16_412 ),
inference(resolution,[],[f4466,f3896]) ).
fof(f19756,plain,
( spl16_1197
| ~ spl16_365
| ~ spl16_412 ),
inference(avatar_split_clause,[],[f4493,f4465,f3891,f19754]) ).
fof(f19754,plain,
( spl16_1197
<=> ! [X0] :
( empty(powerset(sK9(sK6(sK6(powerset(X0))))))
| empty(sK6(sK9(sK6(powerset(sK9(sK6(sK6(powerset(X0)))))))))
| empty(sK9(sK6(powerset(sK9(sK6(sK6(powerset(X0))))))))
| empty(sK9(sK6(sK6(powerset(X0)))))
| empty(sK6(powerset(sK9(sK6(sK6(powerset(X0)))))))
| empty(sK6(sK6(powerset(X0))))
| empty(powerset(X0))
| element(sK9(sK6(sK9(sK6(powerset(sK9(sK6(sK6(powerset(X0))))))))),X0)
| empty(sK6(powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1197])]) ).
fof(f4493,plain,
( ! [X0] :
( empty(powerset(sK9(sK6(sK6(powerset(X0))))))
| empty(sK6(sK9(sK6(powerset(sK9(sK6(sK6(powerset(X0)))))))))
| empty(sK9(sK6(powerset(sK9(sK6(sK6(powerset(X0))))))))
| empty(sK9(sK6(sK6(powerset(X0)))))
| empty(sK6(powerset(sK9(sK6(sK6(powerset(X0)))))))
| empty(sK6(sK6(powerset(X0))))
| empty(powerset(X0))
| element(sK9(sK6(sK9(sK6(powerset(sK9(sK6(sK6(powerset(X0))))))))),X0)
| empty(sK6(powerset(X0))) )
| ~ spl16_365
| ~ spl16_412 ),
inference(resolution,[],[f4466,f3892]) ).
fof(f19752,plain,
( spl16_1196
| ~ spl16_364
| ~ spl16_405 ),
inference(avatar_split_clause,[],[f4368,f4343,f3678,f19750]) ).
fof(f19750,plain,
( spl16_1196
<=> ! [X0] :
( empty(sK9(sK9(powerset(powerset(powerset(X0))))))
| element(sK9(sK9(sK7(powerset(sK9(sK9(sK9(powerset(powerset(powerset(X0)))))))))),X0)
| empty(sK9(powerset(powerset(powerset(X0)))))
| empty(powerset(sK9(sK9(sK9(powerset(powerset(powerset(X0))))))))
| empty(sK9(sK7(powerset(sK9(sK9(sK9(powerset(powerset(powerset(X0))))))))))
| empty(sK9(sK9(sK9(powerset(powerset(powerset(X0)))))))
| empty(sK7(powerset(sK9(sK9(sK9(powerset(powerset(powerset(X0))))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1196])]) ).
fof(f3678,plain,
( spl16_364
<=> ! [X0] :
( empty(sK7(powerset(X0)))
| empty(powerset(X0))
| empty(sK9(sK7(powerset(X0))))
| empty(X0)
| in(sK9(sK9(sK7(powerset(X0)))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_364])]) ).
fof(f4343,plain,
( spl16_405
<=> ! [X0,X1] :
( empty(sK9(powerset(powerset(powerset(X0)))))
| empty(sK9(sK9(powerset(powerset(powerset(X0))))))
| element(X1,X0)
| ~ in(X1,sK9(sK9(sK9(powerset(powerset(powerset(X0))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_405])]) ).
fof(f4368,plain,
( ! [X0] :
( empty(sK9(sK9(powerset(powerset(powerset(X0))))))
| element(sK9(sK9(sK7(powerset(sK9(sK9(sK9(powerset(powerset(powerset(X0)))))))))),X0)
| empty(sK9(powerset(powerset(powerset(X0)))))
| empty(powerset(sK9(sK9(sK9(powerset(powerset(powerset(X0))))))))
| empty(sK9(sK7(powerset(sK9(sK9(sK9(powerset(powerset(powerset(X0))))))))))
| empty(sK9(sK9(sK9(powerset(powerset(powerset(X0)))))))
| empty(sK7(powerset(sK9(sK9(sK9(powerset(powerset(powerset(X0))))))))) )
| ~ spl16_364
| ~ spl16_405 ),
inference(resolution,[],[f4344,f3679]) ).
fof(f3679,plain,
( ! [X0] :
( in(sK9(sK9(sK7(powerset(X0)))),X0)
| empty(powerset(X0))
| empty(sK9(sK7(powerset(X0))))
| empty(X0)
| empty(sK7(powerset(X0))) )
| ~ spl16_364 ),
inference(avatar_component_clause,[],[f3678]) ).
fof(f4344,plain,
( ! [X0,X1] :
( ~ in(X1,sK9(sK9(sK9(powerset(powerset(powerset(X0)))))))
| empty(sK9(sK9(powerset(powerset(powerset(X0))))))
| element(X1,X0)
| empty(sK9(powerset(powerset(powerset(X0))))) )
| ~ spl16_405 ),
inference(avatar_component_clause,[],[f4343]) ).
fof(f19748,plain,
( spl16_1195
| ~ spl16_363
| ~ spl16_405 ),
inference(avatar_split_clause,[],[f4367,f4343,f3674,f19746]) ).
fof(f19746,plain,
( spl16_1195
<=> ! [X0] :
( empty(sK9(sK9(powerset(powerset(powerset(X0))))))
| element(sK9(sK9(sK6(powerset(sK9(sK9(sK9(powerset(powerset(powerset(X0)))))))))),X0)
| empty(sK9(powerset(powerset(powerset(X0)))))
| empty(powerset(sK9(sK9(sK9(powerset(powerset(powerset(X0))))))))
| empty(sK9(sK6(powerset(sK9(sK9(sK9(powerset(powerset(powerset(X0))))))))))
| empty(sK9(sK9(sK9(powerset(powerset(powerset(X0)))))))
| empty(sK6(powerset(sK9(sK9(sK9(powerset(powerset(powerset(X0))))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1195])]) ).
fof(f3674,plain,
( spl16_363
<=> ! [X0] :
( empty(sK6(powerset(X0)))
| empty(powerset(X0))
| empty(sK9(sK6(powerset(X0))))
| empty(X0)
| in(sK9(sK9(sK6(powerset(X0)))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_363])]) ).
fof(f4367,plain,
( ! [X0] :
( empty(sK9(sK9(powerset(powerset(powerset(X0))))))
| element(sK9(sK9(sK6(powerset(sK9(sK9(sK9(powerset(powerset(powerset(X0)))))))))),X0)
| empty(sK9(powerset(powerset(powerset(X0)))))
| empty(powerset(sK9(sK9(sK9(powerset(powerset(powerset(X0))))))))
| empty(sK9(sK6(powerset(sK9(sK9(sK9(powerset(powerset(powerset(X0))))))))))
| empty(sK9(sK9(sK9(powerset(powerset(powerset(X0)))))))
| empty(sK6(powerset(sK9(sK9(sK9(powerset(powerset(powerset(X0))))))))) )
| ~ spl16_363
| ~ spl16_405 ),
inference(resolution,[],[f4344,f3675]) ).
fof(f3675,plain,
( ! [X0] :
( in(sK9(sK9(sK6(powerset(X0)))),X0)
| empty(powerset(X0))
| empty(sK9(sK6(powerset(X0))))
| empty(X0)
| empty(sK6(powerset(X0))) )
| ~ spl16_363 ),
inference(avatar_component_clause,[],[f3674]) ).
fof(f19704,plain,
( ~ spl16_1194
| ~ spl16_27
| ~ spl16_1004 ),
inference(avatar_split_clause,[],[f19652,f17397,f282,f19701]) ).
fof(f19701,plain,
( spl16_1194
<=> in(cartesian_product2(sK14,sK14),sK9(the_InternalRel(sK8(sK8(sK1))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1194])]) ).
fof(f282,plain,
( spl16_27
<=> ! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_27])]) ).
fof(f17397,plain,
( spl16_1004
<=> in(sK9(the_InternalRel(sK8(sK8(sK1)))),cartesian_product2(sK14,sK14)) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1004])]) ).
fof(f19652,plain,
( ~ in(cartesian_product2(sK14,sK14),sK9(the_InternalRel(sK8(sK8(sK1)))))
| ~ spl16_27
| ~ spl16_1004 ),
inference(resolution,[],[f17399,f283]) ).
fof(f283,plain,
( ! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) )
| ~ spl16_27 ),
inference(avatar_component_clause,[],[f282]) ).
fof(f17399,plain,
( in(sK9(the_InternalRel(sK8(sK8(sK1)))),cartesian_product2(sK14,sK14))
| ~ spl16_1004 ),
inference(avatar_component_clause,[],[f17397]) ).
fof(f19669,plain,
( spl16_1193
| ~ spl16_321
| ~ spl16_449 ),
inference(avatar_split_clause,[],[f5332,f5213,f3175,f19667]) ).
fof(f19667,plain,
( spl16_1193
<=> ! [X0] :
( empty(powerset(powerset(X0)))
| empty(sK7(sK9(sK7(powerset(powerset(X0))))))
| empty(sK9(sK7(powerset(powerset(X0)))))
| element(sK9(sK9(powerset(sK7(sK9(sK7(sK9(sK7(powerset(powerset(X0)))))))))),X0)
| empty(sK7(powerset(powerset(X0))))
| empty(sK7(sK9(sK7(sK9(sK7(powerset(powerset(X0))))))))
| empty(sK9(sK7(sK9(sK7(powerset(powerset(X0)))))))
| empty(sK9(powerset(sK7(sK9(sK7(sK9(sK7(powerset(powerset(X0)))))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1193])]) ).
fof(f3175,plain,
( spl16_321
<=> ! [X0] :
( empty(sK9(powerset(sK7(X0))))
| empty(sK7(X0))
| empty(X0)
| in(sK9(sK9(powerset(sK7(X0)))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_321])]) ).
fof(f5332,plain,
( ! [X0] :
( empty(powerset(powerset(X0)))
| empty(sK7(sK9(sK7(powerset(powerset(X0))))))
| empty(sK9(sK7(powerset(powerset(X0)))))
| element(sK9(sK9(powerset(sK7(sK9(sK7(sK9(sK7(powerset(powerset(X0)))))))))),X0)
| empty(sK7(powerset(powerset(X0))))
| empty(sK7(sK9(sK7(sK9(sK7(powerset(powerset(X0))))))))
| empty(sK9(sK7(sK9(sK7(powerset(powerset(X0)))))))
| empty(sK9(powerset(sK7(sK9(sK7(sK9(sK7(powerset(powerset(X0)))))))))) )
| ~ spl16_321
| ~ spl16_449 ),
inference(resolution,[],[f5214,f3176]) ).
fof(f3176,plain,
( ! [X0] :
( in(sK9(sK9(powerset(sK7(X0)))),X0)
| empty(sK7(X0))
| empty(X0)
| empty(sK9(powerset(sK7(X0)))) )
| ~ spl16_321 ),
inference(avatar_component_clause,[],[f3175]) ).
fof(f19665,plain,
( spl16_1192
| ~ spl16_320
| ~ spl16_449 ),
inference(avatar_split_clause,[],[f5331,f5213,f3171,f19663]) ).
fof(f19663,plain,
( spl16_1192
<=> ! [X0] :
( empty(powerset(powerset(X0)))
| empty(sK7(sK9(sK7(powerset(powerset(X0))))))
| empty(sK9(sK7(powerset(powerset(X0)))))
| element(sK9(sK9(powerset(sK6(sK9(sK7(sK9(sK7(powerset(powerset(X0)))))))))),X0)
| empty(sK7(powerset(powerset(X0))))
| empty(sK6(sK9(sK7(sK9(sK7(powerset(powerset(X0))))))))
| empty(sK9(sK7(sK9(sK7(powerset(powerset(X0)))))))
| empty(sK9(powerset(sK6(sK9(sK7(sK9(sK7(powerset(powerset(X0)))))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1192])]) ).
fof(f3171,plain,
( spl16_320
<=> ! [X0] :
( empty(sK9(powerset(sK6(X0))))
| empty(sK6(X0))
| empty(X0)
| in(sK9(sK9(powerset(sK6(X0)))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_320])]) ).
fof(f5331,plain,
( ! [X0] :
( empty(powerset(powerset(X0)))
| empty(sK7(sK9(sK7(powerset(powerset(X0))))))
| empty(sK9(sK7(powerset(powerset(X0)))))
| element(sK9(sK9(powerset(sK6(sK9(sK7(sK9(sK7(powerset(powerset(X0)))))))))),X0)
| empty(sK7(powerset(powerset(X0))))
| empty(sK6(sK9(sK7(sK9(sK7(powerset(powerset(X0))))))))
| empty(sK9(sK7(sK9(sK7(powerset(powerset(X0)))))))
| empty(sK9(powerset(sK6(sK9(sK7(sK9(sK7(powerset(powerset(X0)))))))))) )
| ~ spl16_320
| ~ spl16_449 ),
inference(resolution,[],[f5214,f3172]) ).
fof(f3172,plain,
( ! [X0] :
( in(sK9(sK9(powerset(sK6(X0)))),X0)
| empty(sK6(X0))
| empty(X0)
| empty(sK9(powerset(sK6(X0)))) )
| ~ spl16_320 ),
inference(avatar_component_clause,[],[f3171]) ).
fof(f19661,plain,
( spl16_1191
| ~ spl16_321
| ~ spl16_448 ),
inference(avatar_split_clause,[],[f5307,f5209,f3175,f19659]) ).
fof(f19659,plain,
( spl16_1191
<=> ! [X0] :
( empty(powerset(powerset(X0)))
| empty(sK6(sK9(sK7(powerset(powerset(X0))))))
| empty(sK9(sK7(powerset(powerset(X0)))))
| element(sK9(sK9(powerset(sK7(sK9(sK6(sK9(sK7(powerset(powerset(X0)))))))))),X0)
| empty(sK7(powerset(powerset(X0))))
| empty(sK7(sK9(sK6(sK9(sK7(powerset(powerset(X0))))))))
| empty(sK9(sK6(sK9(sK7(powerset(powerset(X0)))))))
| empty(sK9(powerset(sK7(sK9(sK6(sK9(sK7(powerset(powerset(X0)))))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1191])]) ).
fof(f5307,plain,
( ! [X0] :
( empty(powerset(powerset(X0)))
| empty(sK6(sK9(sK7(powerset(powerset(X0))))))
| empty(sK9(sK7(powerset(powerset(X0)))))
| element(sK9(sK9(powerset(sK7(sK9(sK6(sK9(sK7(powerset(powerset(X0)))))))))),X0)
| empty(sK7(powerset(powerset(X0))))
| empty(sK7(sK9(sK6(sK9(sK7(powerset(powerset(X0))))))))
| empty(sK9(sK6(sK9(sK7(powerset(powerset(X0)))))))
| empty(sK9(powerset(sK7(sK9(sK6(sK9(sK7(powerset(powerset(X0)))))))))) )
| ~ spl16_321
| ~ spl16_448 ),
inference(resolution,[],[f5210,f3176]) ).
fof(f19657,plain,
( spl16_1190
| ~ spl16_320
| ~ spl16_448 ),
inference(avatar_split_clause,[],[f5306,f5209,f3171,f19655]) ).
fof(f19655,plain,
( spl16_1190
<=> ! [X0] :
( empty(powerset(powerset(X0)))
| empty(sK6(sK9(sK7(powerset(powerset(X0))))))
| empty(sK9(sK7(powerset(powerset(X0)))))
| element(sK9(sK9(powerset(sK6(sK9(sK6(sK9(sK7(powerset(powerset(X0)))))))))),X0)
| empty(sK7(powerset(powerset(X0))))
| empty(sK6(sK9(sK6(sK9(sK7(powerset(powerset(X0))))))))
| empty(sK9(sK6(sK9(sK7(powerset(powerset(X0)))))))
| empty(sK9(powerset(sK6(sK9(sK6(sK9(sK7(powerset(powerset(X0)))))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1190])]) ).
fof(f5306,plain,
( ! [X0] :
( empty(powerset(powerset(X0)))
| empty(sK6(sK9(sK7(powerset(powerset(X0))))))
| empty(sK9(sK7(powerset(powerset(X0)))))
| element(sK9(sK9(powerset(sK6(sK9(sK6(sK9(sK7(powerset(powerset(X0)))))))))),X0)
| empty(sK7(powerset(powerset(X0))))
| empty(sK6(sK9(sK6(sK9(sK7(powerset(powerset(X0))))))))
| empty(sK9(sK6(sK9(sK7(powerset(powerset(X0)))))))
| empty(sK9(powerset(sK6(sK9(sK6(sK9(sK7(powerset(powerset(X0)))))))))) )
| ~ spl16_320
| ~ spl16_448 ),
inference(resolution,[],[f5210,f3172]) ).
fof(f19650,plain,
( spl16_1189
| ~ spl16_321
| ~ spl16_447 ),
inference(avatar_split_clause,[],[f5282,f5205,f3175,f19648]) ).
fof(f19648,plain,
( spl16_1189
<=> ! [X0] :
( empty(powerset(powerset(X0)))
| empty(sK7(sK9(sK6(powerset(powerset(X0))))))
| empty(sK9(sK6(powerset(powerset(X0)))))
| element(sK9(sK9(powerset(sK7(sK9(sK7(sK9(sK6(powerset(powerset(X0)))))))))),X0)
| empty(sK6(powerset(powerset(X0))))
| empty(sK7(sK9(sK7(sK9(sK6(powerset(powerset(X0))))))))
| empty(sK9(sK7(sK9(sK6(powerset(powerset(X0)))))))
| empty(sK9(powerset(sK7(sK9(sK7(sK9(sK6(powerset(powerset(X0)))))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1189])]) ).
fof(f5282,plain,
( ! [X0] :
( empty(powerset(powerset(X0)))
| empty(sK7(sK9(sK6(powerset(powerset(X0))))))
| empty(sK9(sK6(powerset(powerset(X0)))))
| element(sK9(sK9(powerset(sK7(sK9(sK7(sK9(sK6(powerset(powerset(X0)))))))))),X0)
| empty(sK6(powerset(powerset(X0))))
| empty(sK7(sK9(sK7(sK9(sK6(powerset(powerset(X0))))))))
| empty(sK9(sK7(sK9(sK6(powerset(powerset(X0)))))))
| empty(sK9(powerset(sK7(sK9(sK7(sK9(sK6(powerset(powerset(X0)))))))))) )
| ~ spl16_321
| ~ spl16_447 ),
inference(resolution,[],[f5206,f3176]) ).
fof(f19646,plain,
( spl16_1188
| ~ spl16_320
| ~ spl16_447 ),
inference(avatar_split_clause,[],[f5281,f5205,f3171,f19644]) ).
fof(f19644,plain,
( spl16_1188
<=> ! [X0] :
( empty(powerset(powerset(X0)))
| empty(sK7(sK9(sK6(powerset(powerset(X0))))))
| empty(sK9(sK6(powerset(powerset(X0)))))
| element(sK9(sK9(powerset(sK6(sK9(sK7(sK9(sK6(powerset(powerset(X0)))))))))),X0)
| empty(sK6(powerset(powerset(X0))))
| empty(sK6(sK9(sK7(sK9(sK6(powerset(powerset(X0))))))))
| empty(sK9(sK7(sK9(sK6(powerset(powerset(X0)))))))
| empty(sK9(powerset(sK6(sK9(sK7(sK9(sK6(powerset(powerset(X0)))))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1188])]) ).
fof(f5281,plain,
( ! [X0] :
( empty(powerset(powerset(X0)))
| empty(sK7(sK9(sK6(powerset(powerset(X0))))))
| empty(sK9(sK6(powerset(powerset(X0)))))
| element(sK9(sK9(powerset(sK6(sK9(sK7(sK9(sK6(powerset(powerset(X0)))))))))),X0)
| empty(sK6(powerset(powerset(X0))))
| empty(sK6(sK9(sK7(sK9(sK6(powerset(powerset(X0))))))))
| empty(sK9(sK7(sK9(sK6(powerset(powerset(X0)))))))
| empty(sK9(powerset(sK6(sK9(sK7(sK9(sK6(powerset(powerset(X0)))))))))) )
| ~ spl16_320
| ~ spl16_447 ),
inference(resolution,[],[f5206,f3172]) ).
fof(f19642,plain,
( spl16_1187
| ~ spl16_321
| ~ spl16_446 ),
inference(avatar_split_clause,[],[f5257,f5201,f3175,f19640]) ).
fof(f19640,plain,
( spl16_1187
<=> ! [X0] :
( empty(powerset(powerset(X0)))
| empty(sK6(sK9(sK6(powerset(powerset(X0))))))
| empty(sK9(sK6(powerset(powerset(X0)))))
| element(sK9(sK9(powerset(sK7(sK9(sK6(sK9(sK6(powerset(powerset(X0)))))))))),X0)
| empty(sK6(powerset(powerset(X0))))
| empty(sK7(sK9(sK6(sK9(sK6(powerset(powerset(X0))))))))
| empty(sK9(sK6(sK9(sK6(powerset(powerset(X0)))))))
| empty(sK9(powerset(sK7(sK9(sK6(sK9(sK6(powerset(powerset(X0)))))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1187])]) ).
fof(f5257,plain,
( ! [X0] :
( empty(powerset(powerset(X0)))
| empty(sK6(sK9(sK6(powerset(powerset(X0))))))
| empty(sK9(sK6(powerset(powerset(X0)))))
| element(sK9(sK9(powerset(sK7(sK9(sK6(sK9(sK6(powerset(powerset(X0)))))))))),X0)
| empty(sK6(powerset(powerset(X0))))
| empty(sK7(sK9(sK6(sK9(sK6(powerset(powerset(X0))))))))
| empty(sK9(sK6(sK9(sK6(powerset(powerset(X0)))))))
| empty(sK9(powerset(sK7(sK9(sK6(sK9(sK6(powerset(powerset(X0)))))))))) )
| ~ spl16_321
| ~ spl16_446 ),
inference(resolution,[],[f5202,f3176]) ).
fof(f19638,plain,
( spl16_1186
| ~ spl16_320
| ~ spl16_446 ),
inference(avatar_split_clause,[],[f5256,f5201,f3171,f19636]) ).
fof(f19636,plain,
( spl16_1186
<=> ! [X0] :
( empty(powerset(powerset(X0)))
| empty(sK6(sK9(sK6(powerset(powerset(X0))))))
| empty(sK9(sK6(powerset(powerset(X0)))))
| element(sK9(sK9(powerset(sK6(sK9(sK6(sK9(sK6(powerset(powerset(X0)))))))))),X0)
| empty(sK6(powerset(powerset(X0))))
| empty(sK6(sK9(sK6(sK9(sK6(powerset(powerset(X0))))))))
| empty(sK9(sK6(sK9(sK6(powerset(powerset(X0)))))))
| empty(sK9(powerset(sK6(sK9(sK6(sK9(sK6(powerset(powerset(X0)))))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1186])]) ).
fof(f5256,plain,
( ! [X0] :
( empty(powerset(powerset(X0)))
| empty(sK6(sK9(sK6(powerset(powerset(X0))))))
| empty(sK9(sK6(powerset(powerset(X0)))))
| element(sK9(sK9(powerset(sK6(sK9(sK6(sK9(sK6(powerset(powerset(X0)))))))))),X0)
| empty(sK6(powerset(powerset(X0))))
| empty(sK6(sK9(sK6(sK9(sK6(powerset(powerset(X0))))))))
| empty(sK9(sK6(sK9(sK6(powerset(powerset(X0)))))))
| empty(sK9(powerset(sK6(sK9(sK6(sK9(sK6(powerset(powerset(X0)))))))))) )
| ~ spl16_320
| ~ spl16_446 ),
inference(resolution,[],[f5202,f3172]) ).
fof(f19634,plain,
( spl16_1185
| ~ spl16_369
| ~ spl16_427 ),
inference(avatar_split_clause,[],[f4941,f4893,f3907,f19632]) ).
fof(f19632,plain,
( spl16_1185
<=> ! [X0] :
( empty(sK9(sK9(powerset(powerset(sK9(sK7(sK7(powerset(X0)))))))))
| empty(sK9(powerset(sK9(sK9(powerset(powerset(sK9(sK7(sK7(powerset(X0)))))))))))
| empty(sK9(sK7(sK7(powerset(X0)))))
| empty(sK9(powerset(powerset(sK9(sK7(sK7(powerset(X0))))))))
| empty(sK7(sK7(powerset(X0))))
| empty(powerset(X0))
| element(sK9(sK9(powerset(sK9(sK9(powerset(powerset(sK9(sK7(sK7(powerset(X0))))))))))),X0)
| empty(sK7(powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1185])]) ).
fof(f4893,plain,
( spl16_427
<=> ! [X0] :
( empty(sK9(powerset(powerset(X0))))
| empty(sK9(sK9(powerset(powerset(X0)))))
| empty(sK9(powerset(sK9(sK9(powerset(powerset(X0)))))))
| empty(X0)
| in(sK9(sK9(powerset(sK9(sK9(powerset(powerset(X0))))))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_427])]) ).
fof(f4941,plain,
( ! [X0] :
( empty(sK9(sK9(powerset(powerset(sK9(sK7(sK7(powerset(X0)))))))))
| empty(sK9(powerset(sK9(sK9(powerset(powerset(sK9(sK7(sK7(powerset(X0)))))))))))
| empty(sK9(sK7(sK7(powerset(X0)))))
| empty(sK9(powerset(powerset(sK9(sK7(sK7(powerset(X0))))))))
| empty(sK7(sK7(powerset(X0))))
| empty(powerset(X0))
| element(sK9(sK9(powerset(sK9(sK9(powerset(powerset(sK9(sK7(sK7(powerset(X0))))))))))),X0)
| empty(sK7(powerset(X0))) )
| ~ spl16_369
| ~ spl16_427 ),
inference(resolution,[],[f4894,f3908]) ).
fof(f4894,plain,
( ! [X0] :
( in(sK9(sK9(powerset(sK9(sK9(powerset(powerset(X0))))))),X0)
| empty(sK9(sK9(powerset(powerset(X0)))))
| empty(sK9(powerset(sK9(sK9(powerset(powerset(X0)))))))
| empty(X0)
| empty(sK9(powerset(powerset(X0)))) )
| ~ spl16_427 ),
inference(avatar_component_clause,[],[f4893]) ).
fof(f19630,plain,
( spl16_1184
| ~ spl16_368
| ~ spl16_427 ),
inference(avatar_split_clause,[],[f4939,f4893,f3903,f19628]) ).
fof(f19628,plain,
( spl16_1184
<=> ! [X0] :
( empty(sK9(sK9(powerset(powerset(sK9(sK7(sK6(powerset(X0)))))))))
| empty(sK9(powerset(sK9(sK9(powerset(powerset(sK9(sK7(sK6(powerset(X0)))))))))))
| empty(sK9(sK7(sK6(powerset(X0)))))
| empty(sK9(powerset(powerset(sK9(sK7(sK6(powerset(X0))))))))
| empty(sK7(sK6(powerset(X0))))
| empty(powerset(X0))
| element(sK9(sK9(powerset(sK9(sK9(powerset(powerset(sK9(sK7(sK6(powerset(X0))))))))))),X0)
| empty(sK6(powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1184])]) ).
fof(f4939,plain,
( ! [X0] :
( empty(sK9(sK9(powerset(powerset(sK9(sK7(sK6(powerset(X0)))))))))
| empty(sK9(powerset(sK9(sK9(powerset(powerset(sK9(sK7(sK6(powerset(X0)))))))))))
| empty(sK9(sK7(sK6(powerset(X0)))))
| empty(sK9(powerset(powerset(sK9(sK7(sK6(powerset(X0))))))))
| empty(sK7(sK6(powerset(X0))))
| empty(powerset(X0))
| element(sK9(sK9(powerset(sK9(sK9(powerset(powerset(sK9(sK7(sK6(powerset(X0))))))))))),X0)
| empty(sK6(powerset(X0))) )
| ~ spl16_368
| ~ spl16_427 ),
inference(resolution,[],[f4894,f3904]) ).
fof(f19626,plain,
( spl16_1183
| ~ spl16_366
| ~ spl16_427 ),
inference(avatar_split_clause,[],[f4933,f4893,f3895,f19624]) ).
fof(f19624,plain,
( spl16_1183
<=> ! [X0] :
( empty(sK9(sK9(powerset(powerset(sK9(sK6(sK7(powerset(X0)))))))))
| empty(sK9(powerset(sK9(sK9(powerset(powerset(sK9(sK6(sK7(powerset(X0)))))))))))
| empty(sK9(sK6(sK7(powerset(X0)))))
| empty(sK9(powerset(powerset(sK9(sK6(sK7(powerset(X0))))))))
| empty(sK6(sK7(powerset(X0))))
| empty(powerset(X0))
| element(sK9(sK9(powerset(sK9(sK9(powerset(powerset(sK9(sK6(sK7(powerset(X0))))))))))),X0)
| empty(sK7(powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1183])]) ).
fof(f4933,plain,
( ! [X0] :
( empty(sK9(sK9(powerset(powerset(sK9(sK6(sK7(powerset(X0)))))))))
| empty(sK9(powerset(sK9(sK9(powerset(powerset(sK9(sK6(sK7(powerset(X0)))))))))))
| empty(sK9(sK6(sK7(powerset(X0)))))
| empty(sK9(powerset(powerset(sK9(sK6(sK7(powerset(X0))))))))
| empty(sK6(sK7(powerset(X0))))
| empty(powerset(X0))
| element(sK9(sK9(powerset(sK9(sK9(powerset(powerset(sK9(sK6(sK7(powerset(X0))))))))))),X0)
| empty(sK7(powerset(X0))) )
| ~ spl16_366
| ~ spl16_427 ),
inference(resolution,[],[f4894,f3896]) ).
fof(f19622,plain,
( spl16_1182
| ~ spl16_365
| ~ spl16_427 ),
inference(avatar_split_clause,[],[f4931,f4893,f3891,f19620]) ).
fof(f19620,plain,
( spl16_1182
<=> ! [X0] :
( empty(sK9(sK9(powerset(powerset(sK9(sK6(sK6(powerset(X0)))))))))
| empty(sK9(powerset(sK9(sK9(powerset(powerset(sK9(sK6(sK6(powerset(X0)))))))))))
| empty(sK9(sK6(sK6(powerset(X0)))))
| empty(sK9(powerset(powerset(sK9(sK6(sK6(powerset(X0))))))))
| empty(sK6(sK6(powerset(X0))))
| empty(powerset(X0))
| element(sK9(sK9(powerset(sK9(sK9(powerset(powerset(sK9(sK6(sK6(powerset(X0))))))))))),X0)
| empty(sK6(powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1182])]) ).
fof(f4931,plain,
( ! [X0] :
( empty(sK9(sK9(powerset(powerset(sK9(sK6(sK6(powerset(X0)))))))))
| empty(sK9(powerset(sK9(sK9(powerset(powerset(sK9(sK6(sK6(powerset(X0)))))))))))
| empty(sK9(sK6(sK6(powerset(X0)))))
| empty(sK9(powerset(powerset(sK9(sK6(sK6(powerset(X0))))))))
| empty(sK6(sK6(powerset(X0))))
| empty(powerset(X0))
| element(sK9(sK9(powerset(sK9(sK9(powerset(powerset(sK9(sK6(sK6(powerset(X0))))))))))),X0)
| empty(sK6(powerset(X0))) )
| ~ spl16_365
| ~ spl16_427 ),
inference(resolution,[],[f4894,f3892]) ).
fof(f19618,plain,
( spl16_1181
| ~ spl16_364
| ~ spl16_390 ),
inference(avatar_split_clause,[],[f4266,f4167,f3678,f19616]) ).
fof(f19616,plain,
( spl16_1181
<=> ! [X0] :
( empty(sK9(powerset(powerset(X0))))
| element(sK9(sK9(sK7(powerset(sK9(sK9(powerset(sK9(powerset(powerset(X0)))))))))),X0)
| empty(sK9(powerset(sK9(powerset(powerset(X0))))))
| empty(powerset(sK9(sK9(powerset(sK9(powerset(powerset(X0))))))))
| empty(sK9(sK7(powerset(sK9(sK9(powerset(sK9(powerset(powerset(X0))))))))))
| empty(sK9(sK9(powerset(sK9(powerset(powerset(X0)))))))
| empty(sK7(powerset(sK9(sK9(powerset(sK9(powerset(powerset(X0))))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1181])]) ).
fof(f4167,plain,
( spl16_390
<=> ! [X0,X1] :
( empty(sK9(powerset(sK9(powerset(powerset(X0))))))
| empty(sK9(powerset(powerset(X0))))
| element(X1,X0)
| ~ in(X1,sK9(sK9(powerset(sK9(powerset(powerset(X0))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_390])]) ).
fof(f4266,plain,
( ! [X0] :
( empty(sK9(powerset(powerset(X0))))
| element(sK9(sK9(sK7(powerset(sK9(sK9(powerset(sK9(powerset(powerset(X0)))))))))),X0)
| empty(sK9(powerset(sK9(powerset(powerset(X0))))))
| empty(powerset(sK9(sK9(powerset(sK9(powerset(powerset(X0))))))))
| empty(sK9(sK7(powerset(sK9(sK9(powerset(sK9(powerset(powerset(X0))))))))))
| empty(sK9(sK9(powerset(sK9(powerset(powerset(X0)))))))
| empty(sK7(powerset(sK9(sK9(powerset(sK9(powerset(powerset(X0))))))))) )
| ~ spl16_364
| ~ spl16_390 ),
inference(resolution,[],[f4168,f3679]) ).
fof(f4168,plain,
( ! [X0,X1] :
( ~ in(X1,sK9(sK9(powerset(sK9(powerset(powerset(X0)))))))
| empty(sK9(powerset(powerset(X0))))
| element(X1,X0)
| empty(sK9(powerset(sK9(powerset(powerset(X0)))))) )
| ~ spl16_390 ),
inference(avatar_component_clause,[],[f4167]) ).
fof(f19614,plain,
( spl16_1180
| ~ spl16_363
| ~ spl16_390 ),
inference(avatar_split_clause,[],[f4265,f4167,f3674,f19612]) ).
fof(f19612,plain,
( spl16_1180
<=> ! [X0] :
( empty(sK9(powerset(powerset(X0))))
| element(sK9(sK9(sK6(powerset(sK9(sK9(powerset(sK9(powerset(powerset(X0)))))))))),X0)
| empty(sK9(powerset(sK9(powerset(powerset(X0))))))
| empty(powerset(sK9(sK9(powerset(sK9(powerset(powerset(X0))))))))
| empty(sK9(sK6(powerset(sK9(sK9(powerset(sK9(powerset(powerset(X0))))))))))
| empty(sK9(sK9(powerset(sK9(powerset(powerset(X0)))))))
| empty(sK6(powerset(sK9(sK9(powerset(sK9(powerset(powerset(X0))))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1180])]) ).
fof(f4265,plain,
( ! [X0] :
( empty(sK9(powerset(powerset(X0))))
| element(sK9(sK9(sK6(powerset(sK9(sK9(powerset(sK9(powerset(powerset(X0)))))))))),X0)
| empty(sK9(powerset(sK9(powerset(powerset(X0))))))
| empty(powerset(sK9(sK9(powerset(sK9(powerset(powerset(X0))))))))
| empty(sK9(sK6(powerset(sK9(sK9(powerset(sK9(powerset(powerset(X0))))))))))
| empty(sK9(sK9(powerset(sK9(powerset(powerset(X0)))))))
| empty(sK6(powerset(sK9(sK9(powerset(sK9(powerset(powerset(X0))))))))) )
| ~ spl16_363
| ~ spl16_390 ),
inference(resolution,[],[f4168,f3675]) ).
fof(f19468,plain,
( spl16_1179
| ~ spl16_306
| ~ spl16_449 ),
inference(avatar_split_clause,[],[f5325,f5213,f2964,f19466]) ).
fof(f19466,plain,
( spl16_1179
<=> ! [X0] :
( empty(powerset(powerset(X0)))
| empty(sK7(sK9(sK7(powerset(powerset(X0))))))
| empty(sK9(sK7(powerset(powerset(X0)))))
| element(sK9(sK7(sK7(sK9(sK7(sK9(sK7(powerset(powerset(X0))))))))),X0)
| empty(sK7(powerset(powerset(X0))))
| empty(sK7(sK7(sK9(sK7(sK9(sK7(powerset(powerset(X0)))))))))
| empty(sK9(sK7(sK9(sK7(powerset(powerset(X0)))))))
| empty(sK7(sK9(sK7(sK9(sK7(powerset(powerset(X0)))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1179])]) ).
fof(f5325,plain,
( ! [X0] :
( empty(powerset(powerset(X0)))
| empty(sK7(sK9(sK7(powerset(powerset(X0))))))
| empty(sK9(sK7(powerset(powerset(X0)))))
| element(sK9(sK7(sK7(sK9(sK7(sK9(sK7(powerset(powerset(X0))))))))),X0)
| empty(sK7(powerset(powerset(X0))))
| empty(sK7(sK7(sK9(sK7(sK9(sK7(powerset(powerset(X0)))))))))
| empty(sK9(sK7(sK9(sK7(powerset(powerset(X0)))))))
| empty(sK7(sK9(sK7(sK9(sK7(powerset(powerset(X0)))))))) )
| ~ spl16_306
| ~ spl16_449 ),
inference(resolution,[],[f5214,f2965]) ).
fof(f19464,plain,
( spl16_1178
| ~ spl16_305
| ~ spl16_449 ),
inference(avatar_split_clause,[],[f5324,f5213,f2960,f19462]) ).
fof(f19462,plain,
( spl16_1178
<=> ! [X0] :
( empty(powerset(powerset(X0)))
| empty(sK7(sK9(sK7(powerset(powerset(X0))))))
| empty(sK9(sK7(powerset(powerset(X0)))))
| element(sK9(sK7(sK6(sK9(sK7(sK9(sK7(powerset(powerset(X0))))))))),X0)
| empty(sK7(powerset(powerset(X0))))
| empty(sK7(sK6(sK9(sK7(sK9(sK7(powerset(powerset(X0)))))))))
| empty(sK9(sK7(sK9(sK7(powerset(powerset(X0)))))))
| empty(sK6(sK9(sK7(sK9(sK7(powerset(powerset(X0)))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1178])]) ).
fof(f5324,plain,
( ! [X0] :
( empty(powerset(powerset(X0)))
| empty(sK7(sK9(sK7(powerset(powerset(X0))))))
| empty(sK9(sK7(powerset(powerset(X0)))))
| element(sK9(sK7(sK6(sK9(sK7(sK9(sK7(powerset(powerset(X0))))))))),X0)
| empty(sK7(powerset(powerset(X0))))
| empty(sK7(sK6(sK9(sK7(sK9(sK7(powerset(powerset(X0)))))))))
| empty(sK9(sK7(sK9(sK7(powerset(powerset(X0)))))))
| empty(sK6(sK9(sK7(sK9(sK7(powerset(powerset(X0)))))))) )
| ~ spl16_305
| ~ spl16_449 ),
inference(resolution,[],[f5214,f2961]) ).
fof(f19459,plain,
( spl16_1177
| ~ spl16_304
| ~ spl16_449 ),
inference(avatar_split_clause,[],[f5318,f5213,f2956,f19457]) ).
fof(f19457,plain,
( spl16_1177
<=> ! [X0] :
( empty(powerset(powerset(X0)))
| empty(sK7(sK9(sK7(powerset(powerset(X0))))))
| empty(sK9(sK7(powerset(powerset(X0)))))
| element(sK9(sK6(sK7(sK9(sK7(sK9(sK7(powerset(powerset(X0))))))))),X0)
| empty(sK7(powerset(powerset(X0))))
| empty(sK6(sK7(sK9(sK7(sK9(sK7(powerset(powerset(X0)))))))))
| empty(sK9(sK7(sK9(sK7(powerset(powerset(X0)))))))
| empty(sK7(sK9(sK7(sK9(sK7(powerset(powerset(X0)))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1177])]) ).
fof(f5318,plain,
( ! [X0] :
( empty(powerset(powerset(X0)))
| empty(sK7(sK9(sK7(powerset(powerset(X0))))))
| empty(sK9(sK7(powerset(powerset(X0)))))
| element(sK9(sK6(sK7(sK9(sK7(sK9(sK7(powerset(powerset(X0))))))))),X0)
| empty(sK7(powerset(powerset(X0))))
| empty(sK6(sK7(sK9(sK7(sK9(sK7(powerset(powerset(X0)))))))))
| empty(sK9(sK7(sK9(sK7(powerset(powerset(X0)))))))
| empty(sK7(sK9(sK7(sK9(sK7(powerset(powerset(X0)))))))) )
| ~ spl16_304
| ~ spl16_449 ),
inference(resolution,[],[f5214,f2957]) ).
fof(f19455,plain,
( spl16_1176
| ~ spl16_303
| ~ spl16_449 ),
inference(avatar_split_clause,[],[f5317,f5213,f2952,f19453]) ).
fof(f19453,plain,
( spl16_1176
<=> ! [X0] :
( empty(powerset(powerset(X0)))
| empty(sK7(sK9(sK7(powerset(powerset(X0))))))
| empty(sK9(sK7(powerset(powerset(X0)))))
| element(sK9(sK6(sK6(sK9(sK7(sK9(sK7(powerset(powerset(X0))))))))),X0)
| empty(sK7(powerset(powerset(X0))))
| empty(sK6(sK6(sK9(sK7(sK9(sK7(powerset(powerset(X0)))))))))
| empty(sK9(sK7(sK9(sK7(powerset(powerset(X0)))))))
| empty(sK6(sK9(sK7(sK9(sK7(powerset(powerset(X0)))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1176])]) ).
fof(f5317,plain,
( ! [X0] :
( empty(powerset(powerset(X0)))
| empty(sK7(sK9(sK7(powerset(powerset(X0))))))
| empty(sK9(sK7(powerset(powerset(X0)))))
| element(sK9(sK6(sK6(sK9(sK7(sK9(sK7(powerset(powerset(X0))))))))),X0)
| empty(sK7(powerset(powerset(X0))))
| empty(sK6(sK6(sK9(sK7(sK9(sK7(powerset(powerset(X0)))))))))
| empty(sK9(sK7(sK9(sK7(powerset(powerset(X0)))))))
| empty(sK6(sK9(sK7(sK9(sK7(powerset(powerset(X0)))))))) )
| ~ spl16_303
| ~ spl16_449 ),
inference(resolution,[],[f5214,f2953]) ).
fof(f19451,plain,
( spl16_1175
| ~ spl16_306
| ~ spl16_448 ),
inference(avatar_split_clause,[],[f5300,f5209,f2964,f19449]) ).
fof(f19449,plain,
( spl16_1175
<=> ! [X0] :
( empty(powerset(powerset(X0)))
| empty(sK6(sK9(sK7(powerset(powerset(X0))))))
| empty(sK9(sK7(powerset(powerset(X0)))))
| element(sK9(sK7(sK7(sK9(sK6(sK9(sK7(powerset(powerset(X0))))))))),X0)
| empty(sK7(powerset(powerset(X0))))
| empty(sK7(sK7(sK9(sK6(sK9(sK7(powerset(powerset(X0)))))))))
| empty(sK9(sK6(sK9(sK7(powerset(powerset(X0)))))))
| empty(sK7(sK9(sK6(sK9(sK7(powerset(powerset(X0)))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1175])]) ).
fof(f5300,plain,
( ! [X0] :
( empty(powerset(powerset(X0)))
| empty(sK6(sK9(sK7(powerset(powerset(X0))))))
| empty(sK9(sK7(powerset(powerset(X0)))))
| element(sK9(sK7(sK7(sK9(sK6(sK9(sK7(powerset(powerset(X0))))))))),X0)
| empty(sK7(powerset(powerset(X0))))
| empty(sK7(sK7(sK9(sK6(sK9(sK7(powerset(powerset(X0)))))))))
| empty(sK9(sK6(sK9(sK7(powerset(powerset(X0)))))))
| empty(sK7(sK9(sK6(sK9(sK7(powerset(powerset(X0)))))))) )
| ~ spl16_306
| ~ spl16_448 ),
inference(resolution,[],[f5210,f2965]) ).
fof(f19447,plain,
( spl16_1174
| ~ spl16_305
| ~ spl16_448 ),
inference(avatar_split_clause,[],[f5299,f5209,f2960,f19445]) ).
fof(f19445,plain,
( spl16_1174
<=> ! [X0] :
( empty(powerset(powerset(X0)))
| empty(sK6(sK9(sK7(powerset(powerset(X0))))))
| empty(sK9(sK7(powerset(powerset(X0)))))
| element(sK9(sK7(sK6(sK9(sK6(sK9(sK7(powerset(powerset(X0))))))))),X0)
| empty(sK7(powerset(powerset(X0))))
| empty(sK7(sK6(sK9(sK6(sK9(sK7(powerset(powerset(X0)))))))))
| empty(sK9(sK6(sK9(sK7(powerset(powerset(X0)))))))
| empty(sK6(sK9(sK6(sK9(sK7(powerset(powerset(X0)))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1174])]) ).
fof(f5299,plain,
( ! [X0] :
( empty(powerset(powerset(X0)))
| empty(sK6(sK9(sK7(powerset(powerset(X0))))))
| empty(sK9(sK7(powerset(powerset(X0)))))
| element(sK9(sK7(sK6(sK9(sK6(sK9(sK7(powerset(powerset(X0))))))))),X0)
| empty(sK7(powerset(powerset(X0))))
| empty(sK7(sK6(sK9(sK6(sK9(sK7(powerset(powerset(X0)))))))))
| empty(sK9(sK6(sK9(sK7(powerset(powerset(X0)))))))
| empty(sK6(sK9(sK6(sK9(sK7(powerset(powerset(X0)))))))) )
| ~ spl16_305
| ~ spl16_448 ),
inference(resolution,[],[f5210,f2961]) ).
fof(f19443,plain,
( spl16_1173
| ~ spl16_304
| ~ spl16_448 ),
inference(avatar_split_clause,[],[f5293,f5209,f2956,f19441]) ).
fof(f19441,plain,
( spl16_1173
<=> ! [X0] :
( empty(powerset(powerset(X0)))
| empty(sK6(sK9(sK7(powerset(powerset(X0))))))
| empty(sK9(sK7(powerset(powerset(X0)))))
| element(sK9(sK6(sK7(sK9(sK6(sK9(sK7(powerset(powerset(X0))))))))),X0)
| empty(sK7(powerset(powerset(X0))))
| empty(sK6(sK7(sK9(sK6(sK9(sK7(powerset(powerset(X0)))))))))
| empty(sK9(sK6(sK9(sK7(powerset(powerset(X0)))))))
| empty(sK7(sK9(sK6(sK9(sK7(powerset(powerset(X0)))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1173])]) ).
fof(f5293,plain,
( ! [X0] :
( empty(powerset(powerset(X0)))
| empty(sK6(sK9(sK7(powerset(powerset(X0))))))
| empty(sK9(sK7(powerset(powerset(X0)))))
| element(sK9(sK6(sK7(sK9(sK6(sK9(sK7(powerset(powerset(X0))))))))),X0)
| empty(sK7(powerset(powerset(X0))))
| empty(sK6(sK7(sK9(sK6(sK9(sK7(powerset(powerset(X0)))))))))
| empty(sK9(sK6(sK9(sK7(powerset(powerset(X0)))))))
| empty(sK7(sK9(sK6(sK9(sK7(powerset(powerset(X0)))))))) )
| ~ spl16_304
| ~ spl16_448 ),
inference(resolution,[],[f5210,f2957]) ).
fof(f19439,plain,
( spl16_1172
| ~ spl16_303
| ~ spl16_448 ),
inference(avatar_split_clause,[],[f5292,f5209,f2952,f19437]) ).
fof(f19437,plain,
( spl16_1172
<=> ! [X0] :
( empty(powerset(powerset(X0)))
| empty(sK6(sK9(sK7(powerset(powerset(X0))))))
| empty(sK9(sK7(powerset(powerset(X0)))))
| element(sK9(sK6(sK6(sK9(sK6(sK9(sK7(powerset(powerset(X0))))))))),X0)
| empty(sK7(powerset(powerset(X0))))
| empty(sK6(sK6(sK9(sK6(sK9(sK7(powerset(powerset(X0)))))))))
| empty(sK9(sK6(sK9(sK7(powerset(powerset(X0)))))))
| empty(sK6(sK9(sK6(sK9(sK7(powerset(powerset(X0)))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1172])]) ).
fof(f5292,plain,
( ! [X0] :
( empty(powerset(powerset(X0)))
| empty(sK6(sK9(sK7(powerset(powerset(X0))))))
| empty(sK9(sK7(powerset(powerset(X0)))))
| element(sK9(sK6(sK6(sK9(sK6(sK9(sK7(powerset(powerset(X0))))))))),X0)
| empty(sK7(powerset(powerset(X0))))
| empty(sK6(sK6(sK9(sK6(sK9(sK7(powerset(powerset(X0)))))))))
| empty(sK9(sK6(sK9(sK7(powerset(powerset(X0)))))))
| empty(sK6(sK9(sK6(sK9(sK7(powerset(powerset(X0)))))))) )
| ~ spl16_303
| ~ spl16_448 ),
inference(resolution,[],[f5210,f2953]) ).
fof(f19435,plain,
( spl16_1171
| ~ spl16_306
| ~ spl16_447 ),
inference(avatar_split_clause,[],[f5275,f5205,f2964,f19433]) ).
fof(f19433,plain,
( spl16_1171
<=> ! [X0] :
( empty(powerset(powerset(X0)))
| empty(sK7(sK9(sK6(powerset(powerset(X0))))))
| empty(sK9(sK6(powerset(powerset(X0)))))
| element(sK9(sK7(sK7(sK9(sK7(sK9(sK6(powerset(powerset(X0))))))))),X0)
| empty(sK6(powerset(powerset(X0))))
| empty(sK7(sK7(sK9(sK7(sK9(sK6(powerset(powerset(X0)))))))))
| empty(sK9(sK7(sK9(sK6(powerset(powerset(X0)))))))
| empty(sK7(sK9(sK7(sK9(sK6(powerset(powerset(X0)))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1171])]) ).
fof(f5275,plain,
( ! [X0] :
( empty(powerset(powerset(X0)))
| empty(sK7(sK9(sK6(powerset(powerset(X0))))))
| empty(sK9(sK6(powerset(powerset(X0)))))
| element(sK9(sK7(sK7(sK9(sK7(sK9(sK6(powerset(powerset(X0))))))))),X0)
| empty(sK6(powerset(powerset(X0))))
| empty(sK7(sK7(sK9(sK7(sK9(sK6(powerset(powerset(X0)))))))))
| empty(sK9(sK7(sK9(sK6(powerset(powerset(X0)))))))
| empty(sK7(sK9(sK7(sK9(sK6(powerset(powerset(X0)))))))) )
| ~ spl16_306
| ~ spl16_447 ),
inference(resolution,[],[f5206,f2965]) ).
fof(f19431,plain,
( spl16_1170
| ~ spl16_305
| ~ spl16_447 ),
inference(avatar_split_clause,[],[f5274,f5205,f2960,f19429]) ).
fof(f19429,plain,
( spl16_1170
<=> ! [X0] :
( empty(powerset(powerset(X0)))
| empty(sK7(sK9(sK6(powerset(powerset(X0))))))
| empty(sK9(sK6(powerset(powerset(X0)))))
| element(sK9(sK7(sK6(sK9(sK7(sK9(sK6(powerset(powerset(X0))))))))),X0)
| empty(sK6(powerset(powerset(X0))))
| empty(sK7(sK6(sK9(sK7(sK9(sK6(powerset(powerset(X0)))))))))
| empty(sK9(sK7(sK9(sK6(powerset(powerset(X0)))))))
| empty(sK6(sK9(sK7(sK9(sK6(powerset(powerset(X0)))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1170])]) ).
fof(f5274,plain,
( ! [X0] :
( empty(powerset(powerset(X0)))
| empty(sK7(sK9(sK6(powerset(powerset(X0))))))
| empty(sK9(sK6(powerset(powerset(X0)))))
| element(sK9(sK7(sK6(sK9(sK7(sK9(sK6(powerset(powerset(X0))))))))),X0)
| empty(sK6(powerset(powerset(X0))))
| empty(sK7(sK6(sK9(sK7(sK9(sK6(powerset(powerset(X0)))))))))
| empty(sK9(sK7(sK9(sK6(powerset(powerset(X0)))))))
| empty(sK6(sK9(sK7(sK9(sK6(powerset(powerset(X0)))))))) )
| ~ spl16_305
| ~ spl16_447 ),
inference(resolution,[],[f5206,f2961]) ).
fof(f19427,plain,
( spl16_1169
| ~ spl16_304
| ~ spl16_447 ),
inference(avatar_split_clause,[],[f5268,f5205,f2956,f19425]) ).
fof(f19425,plain,
( spl16_1169
<=> ! [X0] :
( empty(powerset(powerset(X0)))
| empty(sK7(sK9(sK6(powerset(powerset(X0))))))
| empty(sK9(sK6(powerset(powerset(X0)))))
| element(sK9(sK6(sK7(sK9(sK7(sK9(sK6(powerset(powerset(X0))))))))),X0)
| empty(sK6(powerset(powerset(X0))))
| empty(sK6(sK7(sK9(sK7(sK9(sK6(powerset(powerset(X0)))))))))
| empty(sK9(sK7(sK9(sK6(powerset(powerset(X0)))))))
| empty(sK7(sK9(sK7(sK9(sK6(powerset(powerset(X0)))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1169])]) ).
fof(f5268,plain,
( ! [X0] :
( empty(powerset(powerset(X0)))
| empty(sK7(sK9(sK6(powerset(powerset(X0))))))
| empty(sK9(sK6(powerset(powerset(X0)))))
| element(sK9(sK6(sK7(sK9(sK7(sK9(sK6(powerset(powerset(X0))))))))),X0)
| empty(sK6(powerset(powerset(X0))))
| empty(sK6(sK7(sK9(sK7(sK9(sK6(powerset(powerset(X0)))))))))
| empty(sK9(sK7(sK9(sK6(powerset(powerset(X0)))))))
| empty(sK7(sK9(sK7(sK9(sK6(powerset(powerset(X0)))))))) )
| ~ spl16_304
| ~ spl16_447 ),
inference(resolution,[],[f5206,f2957]) ).
fof(f19423,plain,
( spl16_1168
| ~ spl16_303
| ~ spl16_447 ),
inference(avatar_split_clause,[],[f5267,f5205,f2952,f19421]) ).
fof(f19421,plain,
( spl16_1168
<=> ! [X0] :
( empty(powerset(powerset(X0)))
| empty(sK7(sK9(sK6(powerset(powerset(X0))))))
| empty(sK9(sK6(powerset(powerset(X0)))))
| element(sK9(sK6(sK6(sK9(sK7(sK9(sK6(powerset(powerset(X0))))))))),X0)
| empty(sK6(powerset(powerset(X0))))
| empty(sK6(sK6(sK9(sK7(sK9(sK6(powerset(powerset(X0)))))))))
| empty(sK9(sK7(sK9(sK6(powerset(powerset(X0)))))))
| empty(sK6(sK9(sK7(sK9(sK6(powerset(powerset(X0)))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1168])]) ).
fof(f5267,plain,
( ! [X0] :
( empty(powerset(powerset(X0)))
| empty(sK7(sK9(sK6(powerset(powerset(X0))))))
| empty(sK9(sK6(powerset(powerset(X0)))))
| element(sK9(sK6(sK6(sK9(sK7(sK9(sK6(powerset(powerset(X0))))))))),X0)
| empty(sK6(powerset(powerset(X0))))
| empty(sK6(sK6(sK9(sK7(sK9(sK6(powerset(powerset(X0)))))))))
| empty(sK9(sK7(sK9(sK6(powerset(powerset(X0)))))))
| empty(sK6(sK9(sK7(sK9(sK6(powerset(powerset(X0)))))))) )
| ~ spl16_303
| ~ spl16_447 ),
inference(resolution,[],[f5206,f2953]) ).
fof(f19419,plain,
( ~ spl16_641
| spl16_1167
| ~ spl16_48
| ~ spl16_805 ),
inference(avatar_split_clause,[],[f16823,f14693,f404,f19417,f9159]) ).
fof(f9159,plain,
( spl16_641
<=> rel_str(sK8(sK8(sK1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_641])]) ).
fof(f19417,plain,
( spl16_1167
<=> ! [X0] :
( subset(sK14,the_InternalRel(X0))
| ~ rel_str(X0)
| ~ subrelstr(sK8(sK8(sK1)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1167])]) ).
fof(f404,plain,
( spl16_48
<=> ! [X0,X1] :
( subset(the_InternalRel(X1),the_InternalRel(X0))
| ~ subrelstr(X1,X0)
| ~ rel_str(X1)
| ~ rel_str(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_48])]) ).
fof(f14693,plain,
( spl16_805
<=> sK14 = the_InternalRel(sK8(sK8(sK1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_805])]) ).
fof(f16823,plain,
( ! [X0] :
( subset(sK14,the_InternalRel(X0))
| ~ subrelstr(sK8(sK8(sK1)),X0)
| ~ rel_str(sK8(sK8(sK1)))
| ~ rel_str(X0) )
| ~ spl16_48
| ~ spl16_805 ),
inference(superposition,[],[f405,f14695]) ).
fof(f14695,plain,
( sK14 = the_InternalRel(sK8(sK8(sK1)))
| ~ spl16_805 ),
inference(avatar_component_clause,[],[f14693]) ).
fof(f405,plain,
( ! [X0,X1] :
( subset(the_InternalRel(X1),the_InternalRel(X0))
| ~ subrelstr(X1,X0)
| ~ rel_str(X1)
| ~ rel_str(X0) )
| ~ spl16_48 ),
inference(avatar_component_clause,[],[f404]) ).
fof(f19415,plain,
( spl16_1166
| ~ spl16_306
| ~ spl16_446 ),
inference(avatar_split_clause,[],[f5250,f5201,f2964,f19413]) ).
fof(f19413,plain,
( spl16_1166
<=> ! [X0] :
( empty(powerset(powerset(X0)))
| empty(sK6(sK9(sK6(powerset(powerset(X0))))))
| empty(sK9(sK6(powerset(powerset(X0)))))
| element(sK9(sK7(sK7(sK9(sK6(sK9(sK6(powerset(powerset(X0))))))))),X0)
| empty(sK6(powerset(powerset(X0))))
| empty(sK7(sK7(sK9(sK6(sK9(sK6(powerset(powerset(X0)))))))))
| empty(sK9(sK6(sK9(sK6(powerset(powerset(X0)))))))
| empty(sK7(sK9(sK6(sK9(sK6(powerset(powerset(X0)))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1166])]) ).
fof(f5250,plain,
( ! [X0] :
( empty(powerset(powerset(X0)))
| empty(sK6(sK9(sK6(powerset(powerset(X0))))))
| empty(sK9(sK6(powerset(powerset(X0)))))
| element(sK9(sK7(sK7(sK9(sK6(sK9(sK6(powerset(powerset(X0))))))))),X0)
| empty(sK6(powerset(powerset(X0))))
| empty(sK7(sK7(sK9(sK6(sK9(sK6(powerset(powerset(X0)))))))))
| empty(sK9(sK6(sK9(sK6(powerset(powerset(X0)))))))
| empty(sK7(sK9(sK6(sK9(sK6(powerset(powerset(X0)))))))) )
| ~ spl16_306
| ~ spl16_446 ),
inference(resolution,[],[f5202,f2965]) ).
fof(f19411,plain,
( spl16_1165
| ~ spl16_305
| ~ spl16_446 ),
inference(avatar_split_clause,[],[f5249,f5201,f2960,f19409]) ).
fof(f19409,plain,
( spl16_1165
<=> ! [X0] :
( empty(powerset(powerset(X0)))
| empty(sK6(sK9(sK6(powerset(powerset(X0))))))
| empty(sK9(sK6(powerset(powerset(X0)))))
| element(sK9(sK7(sK6(sK9(sK6(sK9(sK6(powerset(powerset(X0))))))))),X0)
| empty(sK6(powerset(powerset(X0))))
| empty(sK7(sK6(sK9(sK6(sK9(sK6(powerset(powerset(X0)))))))))
| empty(sK9(sK6(sK9(sK6(powerset(powerset(X0)))))))
| empty(sK6(sK9(sK6(sK9(sK6(powerset(powerset(X0)))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1165])]) ).
fof(f5249,plain,
( ! [X0] :
( empty(powerset(powerset(X0)))
| empty(sK6(sK9(sK6(powerset(powerset(X0))))))
| empty(sK9(sK6(powerset(powerset(X0)))))
| element(sK9(sK7(sK6(sK9(sK6(sK9(sK6(powerset(powerset(X0))))))))),X0)
| empty(sK6(powerset(powerset(X0))))
| empty(sK7(sK6(sK9(sK6(sK9(sK6(powerset(powerset(X0)))))))))
| empty(sK9(sK6(sK9(sK6(powerset(powerset(X0)))))))
| empty(sK6(sK9(sK6(sK9(sK6(powerset(powerset(X0)))))))) )
| ~ spl16_305
| ~ spl16_446 ),
inference(resolution,[],[f5202,f2961]) ).
fof(f19407,plain,
( spl16_1164
| ~ spl16_304
| ~ spl16_446 ),
inference(avatar_split_clause,[],[f5243,f5201,f2956,f19405]) ).
fof(f19405,plain,
( spl16_1164
<=> ! [X0] :
( empty(powerset(powerset(X0)))
| empty(sK6(sK9(sK6(powerset(powerset(X0))))))
| empty(sK9(sK6(powerset(powerset(X0)))))
| element(sK9(sK6(sK7(sK9(sK6(sK9(sK6(powerset(powerset(X0))))))))),X0)
| empty(sK6(powerset(powerset(X0))))
| empty(sK6(sK7(sK9(sK6(sK9(sK6(powerset(powerset(X0)))))))))
| empty(sK9(sK6(sK9(sK6(powerset(powerset(X0)))))))
| empty(sK7(sK9(sK6(sK9(sK6(powerset(powerset(X0)))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1164])]) ).
fof(f5243,plain,
( ! [X0] :
( empty(powerset(powerset(X0)))
| empty(sK6(sK9(sK6(powerset(powerset(X0))))))
| empty(sK9(sK6(powerset(powerset(X0)))))
| element(sK9(sK6(sK7(sK9(sK6(sK9(sK6(powerset(powerset(X0))))))))),X0)
| empty(sK6(powerset(powerset(X0))))
| empty(sK6(sK7(sK9(sK6(sK9(sK6(powerset(powerset(X0)))))))))
| empty(sK9(sK6(sK9(sK6(powerset(powerset(X0)))))))
| empty(sK7(sK9(sK6(sK9(sK6(powerset(powerset(X0)))))))) )
| ~ spl16_304
| ~ spl16_446 ),
inference(resolution,[],[f5202,f2957]) ).
fof(f19403,plain,
( spl16_1163
| ~ spl16_303
| ~ spl16_446 ),
inference(avatar_split_clause,[],[f5242,f5201,f2952,f19401]) ).
fof(f19401,plain,
( spl16_1163
<=> ! [X0] :
( empty(powerset(powerset(X0)))
| empty(sK6(sK9(sK6(powerset(powerset(X0))))))
| empty(sK9(sK6(powerset(powerset(X0)))))
| element(sK9(sK6(sK6(sK9(sK6(sK9(sK6(powerset(powerset(X0))))))))),X0)
| empty(sK6(powerset(powerset(X0))))
| empty(sK6(sK6(sK9(sK6(sK9(sK6(powerset(powerset(X0)))))))))
| empty(sK9(sK6(sK9(sK6(powerset(powerset(X0)))))))
| empty(sK6(sK9(sK6(sK9(sK6(powerset(powerset(X0)))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1163])]) ).
fof(f5242,plain,
( ! [X0] :
( empty(powerset(powerset(X0)))
| empty(sK6(sK9(sK6(powerset(powerset(X0))))))
| empty(sK9(sK6(powerset(powerset(X0)))))
| element(sK9(sK6(sK6(sK9(sK6(sK9(sK6(powerset(powerset(X0))))))))),X0)
| empty(sK6(powerset(powerset(X0))))
| empty(sK6(sK6(sK9(sK6(sK9(sK6(powerset(powerset(X0)))))))))
| empty(sK9(sK6(sK9(sK6(powerset(powerset(X0)))))))
| empty(sK6(sK9(sK6(sK9(sK6(powerset(powerset(X0)))))))) )
| ~ spl16_303
| ~ spl16_446 ),
inference(resolution,[],[f5202,f2953]) ).
fof(f19399,plain,
( spl16_1162
| ~ spl16_369
| ~ spl16_418 ),
inference(avatar_split_clause,[],[f4740,f4669,f3907,f19397]) ).
fof(f19397,plain,
( spl16_1162
<=> ! [X0] :
( empty(sK7(sK9(sK9(powerset(powerset(sK9(sK7(sK7(powerset(X0))))))))))
| empty(sK9(sK9(powerset(powerset(sK9(sK7(sK7(powerset(X0)))))))))
| empty(sK9(sK7(sK7(powerset(X0)))))
| empty(sK9(powerset(powerset(sK9(sK7(sK7(powerset(X0))))))))
| empty(sK7(sK7(powerset(X0))))
| empty(powerset(X0))
| element(sK9(sK7(sK9(sK9(powerset(powerset(sK9(sK7(sK7(powerset(X0)))))))))),X0)
| empty(sK7(powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1162])]) ).
fof(f4669,plain,
( spl16_418
<=> ! [X0] :
( empty(sK9(powerset(powerset(X0))))
| empty(sK7(sK9(sK9(powerset(powerset(X0))))))
| empty(sK9(sK9(powerset(powerset(X0)))))
| empty(X0)
| in(sK9(sK7(sK9(sK9(powerset(powerset(X0)))))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_418])]) ).
fof(f4740,plain,
( ! [X0] :
( empty(sK7(sK9(sK9(powerset(powerset(sK9(sK7(sK7(powerset(X0))))))))))
| empty(sK9(sK9(powerset(powerset(sK9(sK7(sK7(powerset(X0)))))))))
| empty(sK9(sK7(sK7(powerset(X0)))))
| empty(sK9(powerset(powerset(sK9(sK7(sK7(powerset(X0))))))))
| empty(sK7(sK7(powerset(X0))))
| empty(powerset(X0))
| element(sK9(sK7(sK9(sK9(powerset(powerset(sK9(sK7(sK7(powerset(X0)))))))))),X0)
| empty(sK7(powerset(X0))) )
| ~ spl16_369
| ~ spl16_418 ),
inference(resolution,[],[f4670,f3908]) ).
fof(f4670,plain,
( ! [X0] :
( in(sK9(sK7(sK9(sK9(powerset(powerset(X0)))))),X0)
| empty(sK7(sK9(sK9(powerset(powerset(X0))))))
| empty(sK9(sK9(powerset(powerset(X0)))))
| empty(X0)
| empty(sK9(powerset(powerset(X0)))) )
| ~ spl16_418 ),
inference(avatar_component_clause,[],[f4669]) ).
fof(f19395,plain,
( spl16_1161
| ~ spl16_368
| ~ spl16_418 ),
inference(avatar_split_clause,[],[f4738,f4669,f3903,f19393]) ).
fof(f19393,plain,
( spl16_1161
<=> ! [X0] :
( empty(sK7(sK9(sK9(powerset(powerset(sK9(sK7(sK6(powerset(X0))))))))))
| empty(sK9(sK9(powerset(powerset(sK9(sK7(sK6(powerset(X0)))))))))
| empty(sK9(sK7(sK6(powerset(X0)))))
| empty(sK9(powerset(powerset(sK9(sK7(sK6(powerset(X0))))))))
| empty(sK7(sK6(powerset(X0))))
| empty(powerset(X0))
| element(sK9(sK7(sK9(sK9(powerset(powerset(sK9(sK7(sK6(powerset(X0)))))))))),X0)
| empty(sK6(powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1161])]) ).
fof(f4738,plain,
( ! [X0] :
( empty(sK7(sK9(sK9(powerset(powerset(sK9(sK7(sK6(powerset(X0))))))))))
| empty(sK9(sK9(powerset(powerset(sK9(sK7(sK6(powerset(X0)))))))))
| empty(sK9(sK7(sK6(powerset(X0)))))
| empty(sK9(powerset(powerset(sK9(sK7(sK6(powerset(X0))))))))
| empty(sK7(sK6(powerset(X0))))
| empty(powerset(X0))
| element(sK9(sK7(sK9(sK9(powerset(powerset(sK9(sK7(sK6(powerset(X0)))))))))),X0)
| empty(sK6(powerset(X0))) )
| ~ spl16_368
| ~ spl16_418 ),
inference(resolution,[],[f4670,f3904]) ).
fof(f19391,plain,
( spl16_1160
| ~ spl16_366
| ~ spl16_418 ),
inference(avatar_split_clause,[],[f4732,f4669,f3895,f19389]) ).
fof(f19389,plain,
( spl16_1160
<=> ! [X0] :
( empty(sK7(sK9(sK9(powerset(powerset(sK9(sK6(sK7(powerset(X0))))))))))
| empty(sK9(sK9(powerset(powerset(sK9(sK6(sK7(powerset(X0)))))))))
| empty(sK9(sK6(sK7(powerset(X0)))))
| empty(sK9(powerset(powerset(sK9(sK6(sK7(powerset(X0))))))))
| empty(sK6(sK7(powerset(X0))))
| empty(powerset(X0))
| element(sK9(sK7(sK9(sK9(powerset(powerset(sK9(sK6(sK7(powerset(X0)))))))))),X0)
| empty(sK7(powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1160])]) ).
fof(f4732,plain,
( ! [X0] :
( empty(sK7(sK9(sK9(powerset(powerset(sK9(sK6(sK7(powerset(X0))))))))))
| empty(sK9(sK9(powerset(powerset(sK9(sK6(sK7(powerset(X0)))))))))
| empty(sK9(sK6(sK7(powerset(X0)))))
| empty(sK9(powerset(powerset(sK9(sK6(sK7(powerset(X0))))))))
| empty(sK6(sK7(powerset(X0))))
| empty(powerset(X0))
| element(sK9(sK7(sK9(sK9(powerset(powerset(sK9(sK6(sK7(powerset(X0)))))))))),X0)
| empty(sK7(powerset(X0))) )
| ~ spl16_366
| ~ spl16_418 ),
inference(resolution,[],[f4670,f3896]) ).
fof(f19387,plain,
( spl16_1159
| ~ spl16_365
| ~ spl16_418 ),
inference(avatar_split_clause,[],[f4730,f4669,f3891,f19385]) ).
fof(f19385,plain,
( spl16_1159
<=> ! [X0] :
( empty(sK7(sK9(sK9(powerset(powerset(sK9(sK6(sK6(powerset(X0))))))))))
| empty(sK9(sK9(powerset(powerset(sK9(sK6(sK6(powerset(X0)))))))))
| empty(sK9(sK6(sK6(powerset(X0)))))
| empty(sK9(powerset(powerset(sK9(sK6(sK6(powerset(X0))))))))
| empty(sK6(sK6(powerset(X0))))
| empty(powerset(X0))
| element(sK9(sK7(sK9(sK9(powerset(powerset(sK9(sK6(sK6(powerset(X0)))))))))),X0)
| empty(sK6(powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1159])]) ).
fof(f4730,plain,
( ! [X0] :
( empty(sK7(sK9(sK9(powerset(powerset(sK9(sK6(sK6(powerset(X0))))))))))
| empty(sK9(sK9(powerset(powerset(sK9(sK6(sK6(powerset(X0)))))))))
| empty(sK9(sK6(sK6(powerset(X0)))))
| empty(sK9(powerset(powerset(sK9(sK6(sK6(powerset(X0))))))))
| empty(sK6(sK6(powerset(X0))))
| empty(powerset(X0))
| element(sK9(sK7(sK9(sK9(powerset(powerset(sK9(sK6(sK6(powerset(X0)))))))))),X0)
| empty(sK6(powerset(X0))) )
| ~ spl16_365
| ~ spl16_418 ),
inference(resolution,[],[f4670,f3892]) ).
fof(f19383,plain,
( spl16_1158
| ~ spl16_369
| ~ spl16_417 ),
inference(avatar_split_clause,[],[f4695,f4665,f3907,f19381]) ).
fof(f19381,plain,
( spl16_1158
<=> ! [X0] :
( empty(sK6(sK9(sK9(powerset(powerset(sK9(sK7(sK7(powerset(X0))))))))))
| empty(sK9(sK9(powerset(powerset(sK9(sK7(sK7(powerset(X0)))))))))
| empty(sK9(sK7(sK7(powerset(X0)))))
| empty(sK9(powerset(powerset(sK9(sK7(sK7(powerset(X0))))))))
| empty(sK7(sK7(powerset(X0))))
| empty(powerset(X0))
| element(sK9(sK6(sK9(sK9(powerset(powerset(sK9(sK7(sK7(powerset(X0)))))))))),X0)
| empty(sK7(powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1158])]) ).
fof(f4665,plain,
( spl16_417
<=> ! [X0] :
( empty(sK9(powerset(powerset(X0))))
| empty(sK6(sK9(sK9(powerset(powerset(X0))))))
| empty(sK9(sK9(powerset(powerset(X0)))))
| empty(X0)
| in(sK9(sK6(sK9(sK9(powerset(powerset(X0)))))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_417])]) ).
fof(f4695,plain,
( ! [X0] :
( empty(sK6(sK9(sK9(powerset(powerset(sK9(sK7(sK7(powerset(X0))))))))))
| empty(sK9(sK9(powerset(powerset(sK9(sK7(sK7(powerset(X0)))))))))
| empty(sK9(sK7(sK7(powerset(X0)))))
| empty(sK9(powerset(powerset(sK9(sK7(sK7(powerset(X0))))))))
| empty(sK7(sK7(powerset(X0))))
| empty(powerset(X0))
| element(sK9(sK6(sK9(sK9(powerset(powerset(sK9(sK7(sK7(powerset(X0)))))))))),X0)
| empty(sK7(powerset(X0))) )
| ~ spl16_369
| ~ spl16_417 ),
inference(resolution,[],[f4666,f3908]) ).
fof(f4666,plain,
( ! [X0] :
( in(sK9(sK6(sK9(sK9(powerset(powerset(X0)))))),X0)
| empty(sK6(sK9(sK9(powerset(powerset(X0))))))
| empty(sK9(sK9(powerset(powerset(X0)))))
| empty(X0)
| empty(sK9(powerset(powerset(X0)))) )
| ~ spl16_417 ),
inference(avatar_component_clause,[],[f4665]) ).
fof(f19379,plain,
( spl16_1157
| ~ spl16_368
| ~ spl16_417 ),
inference(avatar_split_clause,[],[f4693,f4665,f3903,f19377]) ).
fof(f19377,plain,
( spl16_1157
<=> ! [X0] :
( empty(sK6(sK9(sK9(powerset(powerset(sK9(sK7(sK6(powerset(X0))))))))))
| empty(sK9(sK9(powerset(powerset(sK9(sK7(sK6(powerset(X0)))))))))
| empty(sK9(sK7(sK6(powerset(X0)))))
| empty(sK9(powerset(powerset(sK9(sK7(sK6(powerset(X0))))))))
| empty(sK7(sK6(powerset(X0))))
| empty(powerset(X0))
| element(sK9(sK6(sK9(sK9(powerset(powerset(sK9(sK7(sK6(powerset(X0)))))))))),X0)
| empty(sK6(powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1157])]) ).
fof(f4693,plain,
( ! [X0] :
( empty(sK6(sK9(sK9(powerset(powerset(sK9(sK7(sK6(powerset(X0))))))))))
| empty(sK9(sK9(powerset(powerset(sK9(sK7(sK6(powerset(X0)))))))))
| empty(sK9(sK7(sK6(powerset(X0)))))
| empty(sK9(powerset(powerset(sK9(sK7(sK6(powerset(X0))))))))
| empty(sK7(sK6(powerset(X0))))
| empty(powerset(X0))
| element(sK9(sK6(sK9(sK9(powerset(powerset(sK9(sK7(sK6(powerset(X0)))))))))),X0)
| empty(sK6(powerset(X0))) )
| ~ spl16_368
| ~ spl16_417 ),
inference(resolution,[],[f4666,f3904]) ).
fof(f19341,plain,
( spl16_1156
| ~ spl16_366
| ~ spl16_417 ),
inference(avatar_split_clause,[],[f4687,f4665,f3895,f19339]) ).
fof(f19339,plain,
( spl16_1156
<=> ! [X0] :
( empty(sK6(sK9(sK9(powerset(powerset(sK9(sK6(sK7(powerset(X0))))))))))
| empty(sK9(sK9(powerset(powerset(sK9(sK6(sK7(powerset(X0)))))))))
| empty(sK9(sK6(sK7(powerset(X0)))))
| empty(sK9(powerset(powerset(sK9(sK6(sK7(powerset(X0))))))))
| empty(sK6(sK7(powerset(X0))))
| empty(powerset(X0))
| element(sK9(sK6(sK9(sK9(powerset(powerset(sK9(sK6(sK7(powerset(X0)))))))))),X0)
| empty(sK7(powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1156])]) ).
fof(f4687,plain,
( ! [X0] :
( empty(sK6(sK9(sK9(powerset(powerset(sK9(sK6(sK7(powerset(X0))))))))))
| empty(sK9(sK9(powerset(powerset(sK9(sK6(sK7(powerset(X0)))))))))
| empty(sK9(sK6(sK7(powerset(X0)))))
| empty(sK9(powerset(powerset(sK9(sK6(sK7(powerset(X0))))))))
| empty(sK6(sK7(powerset(X0))))
| empty(powerset(X0))
| element(sK9(sK6(sK9(sK9(powerset(powerset(sK9(sK6(sK7(powerset(X0)))))))))),X0)
| empty(sK7(powerset(X0))) )
| ~ spl16_366
| ~ spl16_417 ),
inference(resolution,[],[f4666,f3896]) ).
fof(f19337,plain,
( spl16_1155
| ~ spl16_365
| ~ spl16_417 ),
inference(avatar_split_clause,[],[f4685,f4665,f3891,f19335]) ).
fof(f19335,plain,
( spl16_1155
<=> ! [X0] :
( empty(sK6(sK9(sK9(powerset(powerset(sK9(sK6(sK6(powerset(X0))))))))))
| empty(sK9(sK9(powerset(powerset(sK9(sK6(sK6(powerset(X0)))))))))
| empty(sK9(sK6(sK6(powerset(X0)))))
| empty(sK9(powerset(powerset(sK9(sK6(sK6(powerset(X0))))))))
| empty(sK6(sK6(powerset(X0))))
| empty(powerset(X0))
| element(sK9(sK6(sK9(sK9(powerset(powerset(sK9(sK6(sK6(powerset(X0)))))))))),X0)
| empty(sK6(powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1155])]) ).
fof(f4685,plain,
( ! [X0] :
( empty(sK6(sK9(sK9(powerset(powerset(sK9(sK6(sK6(powerset(X0))))))))))
| empty(sK9(sK9(powerset(powerset(sK9(sK6(sK6(powerset(X0)))))))))
| empty(sK9(sK6(sK6(powerset(X0)))))
| empty(sK9(powerset(powerset(sK9(sK6(sK6(powerset(X0))))))))
| empty(sK6(sK6(powerset(X0))))
| empty(powerset(X0))
| element(sK9(sK6(sK9(sK9(powerset(powerset(sK9(sK6(sK6(powerset(X0)))))))))),X0)
| empty(sK6(powerset(X0))) )
| ~ spl16_365
| ~ spl16_417 ),
inference(resolution,[],[f4666,f3892]) ).
fof(f19333,plain,
( spl16_1154
| ~ spl16_364
| ~ spl16_409 ),
inference(avatar_split_clause,[],[f4448,f4407,f3678,f19331]) ).
fof(f19331,plain,
( spl16_1154
<=> ! [X0] :
( empty(powerset(powerset(X0)))
| empty(sK9(sK7(powerset(powerset(X0)))))
| element(sK9(sK9(sK7(powerset(sK9(sK9(sK7(powerset(powerset(X0))))))))),X0)
| empty(sK7(powerset(powerset(X0))))
| empty(powerset(sK9(sK9(sK7(powerset(powerset(X0)))))))
| empty(sK9(sK7(powerset(sK9(sK9(sK7(powerset(powerset(X0)))))))))
| empty(sK9(sK9(sK7(powerset(powerset(X0))))))
| empty(sK7(powerset(sK9(sK9(sK7(powerset(powerset(X0)))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1154])]) ).
fof(f4407,plain,
( spl16_409
<=> ! [X0,X1] :
( empty(sK7(powerset(powerset(X0))))
| empty(powerset(powerset(X0)))
| empty(sK9(sK7(powerset(powerset(X0)))))
| element(X1,X0)
| ~ in(X1,sK9(sK9(sK7(powerset(powerset(X0)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_409])]) ).
fof(f4448,plain,
( ! [X0] :
( empty(powerset(powerset(X0)))
| empty(sK9(sK7(powerset(powerset(X0)))))
| element(sK9(sK9(sK7(powerset(sK9(sK9(sK7(powerset(powerset(X0))))))))),X0)
| empty(sK7(powerset(powerset(X0))))
| empty(powerset(sK9(sK9(sK7(powerset(powerset(X0)))))))
| empty(sK9(sK7(powerset(sK9(sK9(sK7(powerset(powerset(X0)))))))))
| empty(sK9(sK9(sK7(powerset(powerset(X0))))))
| empty(sK7(powerset(sK9(sK9(sK7(powerset(powerset(X0)))))))) )
| ~ spl16_364
| ~ spl16_409 ),
inference(resolution,[],[f4408,f3679]) ).
fof(f4408,plain,
( ! [X0,X1] :
( ~ in(X1,sK9(sK9(sK7(powerset(powerset(X0))))))
| empty(powerset(powerset(X0)))
| empty(sK9(sK7(powerset(powerset(X0)))))
| element(X1,X0)
| empty(sK7(powerset(powerset(X0)))) )
| ~ spl16_409 ),
inference(avatar_component_clause,[],[f4407]) ).
fof(f19329,plain,
( spl16_1153
| ~ spl16_363
| ~ spl16_409 ),
inference(avatar_split_clause,[],[f4447,f4407,f3674,f19327]) ).
fof(f19327,plain,
( spl16_1153
<=> ! [X0] :
( empty(powerset(powerset(X0)))
| empty(sK9(sK7(powerset(powerset(X0)))))
| element(sK9(sK9(sK6(powerset(sK9(sK9(sK7(powerset(powerset(X0))))))))),X0)
| empty(sK7(powerset(powerset(X0))))
| empty(powerset(sK9(sK9(sK7(powerset(powerset(X0)))))))
| empty(sK9(sK6(powerset(sK9(sK9(sK7(powerset(powerset(X0)))))))))
| empty(sK9(sK9(sK7(powerset(powerset(X0))))))
| empty(sK6(powerset(sK9(sK9(sK7(powerset(powerset(X0)))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1153])]) ).
fof(f4447,plain,
( ! [X0] :
( empty(powerset(powerset(X0)))
| empty(sK9(sK7(powerset(powerset(X0)))))
| element(sK9(sK9(sK6(powerset(sK9(sK9(sK7(powerset(powerset(X0))))))))),X0)
| empty(sK7(powerset(powerset(X0))))
| empty(powerset(sK9(sK9(sK7(powerset(powerset(X0)))))))
| empty(sK9(sK6(powerset(sK9(sK9(sK7(powerset(powerset(X0)))))))))
| empty(sK9(sK9(sK7(powerset(powerset(X0))))))
| empty(sK6(powerset(sK9(sK9(sK7(powerset(powerset(X0)))))))) )
| ~ spl16_363
| ~ spl16_409 ),
inference(resolution,[],[f4408,f3675]) ).
fof(f19325,plain,
( spl16_1152
| ~ spl16_364
| ~ spl16_408 ),
inference(avatar_split_clause,[],[f4432,f4403,f3678,f19323]) ).
fof(f19323,plain,
( spl16_1152
<=> ! [X0] :
( empty(powerset(powerset(X0)))
| empty(sK9(sK6(powerset(powerset(X0)))))
| element(sK9(sK9(sK7(powerset(sK9(sK9(sK6(powerset(powerset(X0))))))))),X0)
| empty(sK6(powerset(powerset(X0))))
| empty(powerset(sK9(sK9(sK6(powerset(powerset(X0)))))))
| empty(sK9(sK7(powerset(sK9(sK9(sK6(powerset(powerset(X0)))))))))
| empty(sK9(sK9(sK6(powerset(powerset(X0))))))
| empty(sK7(powerset(sK9(sK9(sK6(powerset(powerset(X0)))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1152])]) ).
fof(f4403,plain,
( spl16_408
<=> ! [X0,X1] :
( empty(sK6(powerset(powerset(X0))))
| empty(powerset(powerset(X0)))
| empty(sK9(sK6(powerset(powerset(X0)))))
| element(X1,X0)
| ~ in(X1,sK9(sK9(sK6(powerset(powerset(X0)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_408])]) ).
fof(f4432,plain,
( ! [X0] :
( empty(powerset(powerset(X0)))
| empty(sK9(sK6(powerset(powerset(X0)))))
| element(sK9(sK9(sK7(powerset(sK9(sK9(sK6(powerset(powerset(X0))))))))),X0)
| empty(sK6(powerset(powerset(X0))))
| empty(powerset(sK9(sK9(sK6(powerset(powerset(X0)))))))
| empty(sK9(sK7(powerset(sK9(sK9(sK6(powerset(powerset(X0)))))))))
| empty(sK9(sK9(sK6(powerset(powerset(X0))))))
| empty(sK7(powerset(sK9(sK9(sK6(powerset(powerset(X0)))))))) )
| ~ spl16_364
| ~ spl16_408 ),
inference(resolution,[],[f4404,f3679]) ).
fof(f4404,plain,
( ! [X0,X1] :
( ~ in(X1,sK9(sK9(sK6(powerset(powerset(X0))))))
| empty(powerset(powerset(X0)))
| empty(sK9(sK6(powerset(powerset(X0)))))
| element(X1,X0)
| empty(sK6(powerset(powerset(X0)))) )
| ~ spl16_408 ),
inference(avatar_component_clause,[],[f4403]) ).
fof(f19321,plain,
( spl16_1151
| ~ spl16_363
| ~ spl16_408 ),
inference(avatar_split_clause,[],[f4431,f4403,f3674,f19319]) ).
fof(f19319,plain,
( spl16_1151
<=> ! [X0] :
( empty(powerset(powerset(X0)))
| empty(sK9(sK6(powerset(powerset(X0)))))
| element(sK9(sK9(sK6(powerset(sK9(sK9(sK6(powerset(powerset(X0))))))))),X0)
| empty(sK6(powerset(powerset(X0))))
| empty(powerset(sK9(sK9(sK6(powerset(powerset(X0)))))))
| empty(sK9(sK6(powerset(sK9(sK9(sK6(powerset(powerset(X0)))))))))
| empty(sK9(sK9(sK6(powerset(powerset(X0))))))
| empty(sK6(powerset(sK9(sK9(sK6(powerset(powerset(X0)))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1151])]) ).
fof(f4431,plain,
( ! [X0] :
( empty(powerset(powerset(X0)))
| empty(sK9(sK6(powerset(powerset(X0)))))
| element(sK9(sK9(sK6(powerset(sK9(sK9(sK6(powerset(powerset(X0))))))))),X0)
| empty(sK6(powerset(powerset(X0))))
| empty(powerset(sK9(sK9(sK6(powerset(powerset(X0)))))))
| empty(sK9(sK6(powerset(sK9(sK9(sK6(powerset(powerset(X0)))))))))
| empty(sK9(sK9(sK6(powerset(powerset(X0))))))
| empty(sK6(powerset(sK9(sK9(sK6(powerset(powerset(X0)))))))) )
| ~ spl16_363
| ~ spl16_408 ),
inference(resolution,[],[f4404,f3675]) ).
fof(f19297,plain,
( spl16_1150
| ~ spl16_86
| ~ spl16_1101 ),
inference(avatar_split_clause,[],[f19055,f18851,f653,f19295]) ).
fof(f19295,plain,
( spl16_1150
<=> ! [X0] :
( ~ in(X0,the_InternalRel(sK8(sK8(sK8(sK8(sK1))))))
| element(X0,cartesian_product2(sK14,sK14)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1150])]) ).
fof(f653,plain,
( spl16_86
<=> ! [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,[spl16_86])]) ).
fof(f18851,plain,
( spl16_1101
<=> relation_of2_as_subset(the_InternalRel(sK8(sK8(sK8(sK8(sK1))))),sK14,sK14) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1101])]) ).
fof(f19055,plain,
( ! [X0] :
( ~ in(X0,the_InternalRel(sK8(sK8(sK8(sK8(sK1))))))
| element(X0,cartesian_product2(sK14,sK14)) )
| ~ spl16_86
| ~ spl16_1101 ),
inference(resolution,[],[f18853,f654]) ).
fof(f654,plain,
( ! [X2,X3,X0,X1] :
( ~ relation_of2_as_subset(X3,X1,X2)
| ~ in(X0,X3)
| element(X0,cartesian_product2(X1,X2)) )
| ~ spl16_86 ),
inference(avatar_component_clause,[],[f653]) ).
fof(f18853,plain,
( relation_of2_as_subset(the_InternalRel(sK8(sK8(sK8(sK8(sK1))))),sK14,sK14)
| ~ spl16_1101 ),
inference(avatar_component_clause,[],[f18851]) ).
fof(f19283,plain,
( spl16_1149
| ~ spl16_173
| ~ spl16_420 ),
inference(avatar_split_clause,[],[f4842,f4767,f1448,f19281]) ).
fof(f19281,plain,
( spl16_1149
<=> ! [X0] :
( empty(powerset(sK9(sK9(powerset(powerset(X0))))))
| empty(sK9(sK7(powerset(sK9(sK9(powerset(powerset(X0))))))))
| empty(sK9(powerset(sK9(sK7(powerset(sK9(sK9(powerset(powerset(X0))))))))))
| empty(sK9(sK9(powerset(powerset(X0)))))
| empty(sK7(powerset(sK9(sK9(powerset(powerset(X0)))))))
| element(sK9(sK9(powerset(sK9(sK7(powerset(sK9(sK9(powerset(powerset(X0)))))))))),X0)
| empty(sK9(powerset(powerset(X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1149])]) ).
fof(f1448,plain,
( spl16_173
<=> ! [X0,X1] :
( empty(sK9(powerset(powerset(X0))))
| element(X1,X0)
| ~ in(X1,sK9(sK9(powerset(powerset(X0))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_173])]) ).
fof(f4767,plain,
( spl16_420
<=> ! [X0] :
( empty(sK7(powerset(X0)))
| empty(powerset(X0))
| empty(sK9(sK7(powerset(X0))))
| empty(sK9(powerset(sK9(sK7(powerset(X0))))))
| empty(X0)
| in(sK9(sK9(powerset(sK9(sK7(powerset(X0)))))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_420])]) ).
fof(f4842,plain,
( ! [X0] :
( empty(powerset(sK9(sK9(powerset(powerset(X0))))))
| empty(sK9(sK7(powerset(sK9(sK9(powerset(powerset(X0))))))))
| empty(sK9(powerset(sK9(sK7(powerset(sK9(sK9(powerset(powerset(X0))))))))))
| empty(sK9(sK9(powerset(powerset(X0)))))
| empty(sK7(powerset(sK9(sK9(powerset(powerset(X0)))))))
| element(sK9(sK9(powerset(sK9(sK7(powerset(sK9(sK9(powerset(powerset(X0)))))))))),X0)
| empty(sK9(powerset(powerset(X0)))) )
| ~ spl16_173
| ~ spl16_420 ),
inference(resolution,[],[f4768,f1449]) ).
fof(f1449,plain,
( ! [X0,X1] :
( ~ in(X1,sK9(sK9(powerset(powerset(X0)))))
| element(X1,X0)
| empty(sK9(powerset(powerset(X0)))) )
| ~ spl16_173 ),
inference(avatar_component_clause,[],[f1448]) ).
fof(f4768,plain,
( ! [X0] :
( in(sK9(sK9(powerset(sK9(sK7(powerset(X0)))))),X0)
| empty(powerset(X0))
| empty(sK9(sK7(powerset(X0))))
| empty(sK9(powerset(sK9(sK7(powerset(X0))))))
| empty(X0)
| empty(sK7(powerset(X0))) )
| ~ spl16_420 ),
inference(avatar_component_clause,[],[f4767]) ).
fof(f19279,plain,
( spl16_1148
| ~ spl16_173
| ~ spl16_419 ),
inference(avatar_split_clause,[],[f4797,f4763,f1448,f19277]) ).
fof(f19277,plain,
( spl16_1148
<=> ! [X0] :
( empty(powerset(sK9(sK9(powerset(powerset(X0))))))
| empty(sK9(sK6(powerset(sK9(sK9(powerset(powerset(X0))))))))
| empty(sK9(powerset(sK9(sK6(powerset(sK9(sK9(powerset(powerset(X0))))))))))
| empty(sK9(sK9(powerset(powerset(X0)))))
| empty(sK6(powerset(sK9(sK9(powerset(powerset(X0)))))))
| element(sK9(sK9(powerset(sK9(sK6(powerset(sK9(sK9(powerset(powerset(X0)))))))))),X0)
| empty(sK9(powerset(powerset(X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1148])]) ).
fof(f4763,plain,
( spl16_419
<=> ! [X0] :
( empty(sK6(powerset(X0)))
| empty(powerset(X0))
| empty(sK9(sK6(powerset(X0))))
| empty(sK9(powerset(sK9(sK6(powerset(X0))))))
| empty(X0)
| in(sK9(sK9(powerset(sK9(sK6(powerset(X0)))))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_419])]) ).
fof(f4797,plain,
( ! [X0] :
( empty(powerset(sK9(sK9(powerset(powerset(X0))))))
| empty(sK9(sK6(powerset(sK9(sK9(powerset(powerset(X0))))))))
| empty(sK9(powerset(sK9(sK6(powerset(sK9(sK9(powerset(powerset(X0))))))))))
| empty(sK9(sK9(powerset(powerset(X0)))))
| empty(sK6(powerset(sK9(sK9(powerset(powerset(X0)))))))
| element(sK9(sK9(powerset(sK9(sK6(powerset(sK9(sK9(powerset(powerset(X0)))))))))),X0)
| empty(sK9(powerset(powerset(X0)))) )
| ~ spl16_173
| ~ spl16_419 ),
inference(resolution,[],[f4764,f1449]) ).
fof(f4764,plain,
( ! [X0] :
( in(sK9(sK9(powerset(sK9(sK6(powerset(X0)))))),X0)
| empty(powerset(X0))
| empty(sK9(sK6(powerset(X0))))
| empty(sK9(powerset(sK9(sK6(powerset(X0))))))
| empty(X0)
| empty(sK6(powerset(X0))) )
| ~ spl16_419 ),
inference(avatar_component_clause,[],[f4763]) ).
fof(f19275,plain,
( spl16_1147
| ~ spl16_364
| ~ spl16_388 ),
inference(avatar_split_clause,[],[f4250,f4159,f3678,f19273]) ).
fof(f19273,plain,
( spl16_1147
<=> ! [X0] :
( empty(sK7(powerset(X0)))
| empty(powerset(X0))
| element(sK9(sK9(sK7(powerset(sK9(sK9(powerset(sK7(powerset(X0))))))))),X0)
| empty(sK9(powerset(sK7(powerset(X0)))))
| empty(powerset(sK9(sK9(powerset(sK7(powerset(X0)))))))
| empty(sK9(sK7(powerset(sK9(sK9(powerset(sK7(powerset(X0)))))))))
| empty(sK9(sK9(powerset(sK7(powerset(X0))))))
| empty(sK7(powerset(sK9(sK9(powerset(sK7(powerset(X0)))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1147])]) ).
fof(f4159,plain,
( spl16_388
<=> ! [X0,X1] :
( empty(sK9(powerset(sK7(powerset(X0)))))
| empty(sK7(powerset(X0)))
| empty(powerset(X0))
| element(X1,X0)
| ~ in(X1,sK9(sK9(powerset(sK7(powerset(X0)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_388])]) ).
fof(f4250,plain,
( ! [X0] :
( empty(sK7(powerset(X0)))
| empty(powerset(X0))
| element(sK9(sK9(sK7(powerset(sK9(sK9(powerset(sK7(powerset(X0))))))))),X0)
| empty(sK9(powerset(sK7(powerset(X0)))))
| empty(powerset(sK9(sK9(powerset(sK7(powerset(X0)))))))
| empty(sK9(sK7(powerset(sK9(sK9(powerset(sK7(powerset(X0)))))))))
| empty(sK9(sK9(powerset(sK7(powerset(X0))))))
| empty(sK7(powerset(sK9(sK9(powerset(sK7(powerset(X0)))))))) )
| ~ spl16_364
| ~ spl16_388 ),
inference(resolution,[],[f4160,f3679]) ).
fof(f4160,plain,
( ! [X0,X1] :
( ~ in(X1,sK9(sK9(powerset(sK7(powerset(X0))))))
| empty(sK7(powerset(X0)))
| empty(powerset(X0))
| element(X1,X0)
| empty(sK9(powerset(sK7(powerset(X0))))) )
| ~ spl16_388 ),
inference(avatar_component_clause,[],[f4159]) ).
fof(f19271,plain,
( spl16_1146
| ~ spl16_363
| ~ spl16_388 ),
inference(avatar_split_clause,[],[f4249,f4159,f3674,f19269]) ).
fof(f19269,plain,
( spl16_1146
<=> ! [X0] :
( empty(sK7(powerset(X0)))
| empty(powerset(X0))
| element(sK9(sK9(sK6(powerset(sK9(sK9(powerset(sK7(powerset(X0))))))))),X0)
| empty(sK9(powerset(sK7(powerset(X0)))))
| empty(powerset(sK9(sK9(powerset(sK7(powerset(X0)))))))
| empty(sK9(sK6(powerset(sK9(sK9(powerset(sK7(powerset(X0)))))))))
| empty(sK9(sK9(powerset(sK7(powerset(X0))))))
| empty(sK6(powerset(sK9(sK9(powerset(sK7(powerset(X0)))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1146])]) ).
fof(f4249,plain,
( ! [X0] :
( empty(sK7(powerset(X0)))
| empty(powerset(X0))
| element(sK9(sK9(sK6(powerset(sK9(sK9(powerset(sK7(powerset(X0))))))))),X0)
| empty(sK9(powerset(sK7(powerset(X0)))))
| empty(powerset(sK9(sK9(powerset(sK7(powerset(X0)))))))
| empty(sK9(sK6(powerset(sK9(sK9(powerset(sK7(powerset(X0)))))))))
| empty(sK9(sK9(powerset(sK7(powerset(X0))))))
| empty(sK6(powerset(sK9(sK9(powerset(sK7(powerset(X0)))))))) )
| ~ spl16_363
| ~ spl16_388 ),
inference(resolution,[],[f4160,f3675]) ).
fof(f19267,plain,
( spl16_1145
| ~ spl16_364
| ~ spl16_387 ),
inference(avatar_split_clause,[],[f4234,f4155,f3678,f19265]) ).
fof(f19265,plain,
( spl16_1145
<=> ! [X0] :
( empty(sK6(powerset(X0)))
| empty(powerset(X0))
| element(sK9(sK9(sK7(powerset(sK9(sK9(powerset(sK6(powerset(X0))))))))),X0)
| empty(sK9(powerset(sK6(powerset(X0)))))
| empty(powerset(sK9(sK9(powerset(sK6(powerset(X0)))))))
| empty(sK9(sK7(powerset(sK9(sK9(powerset(sK6(powerset(X0)))))))))
| empty(sK9(sK9(powerset(sK6(powerset(X0))))))
| empty(sK7(powerset(sK9(sK9(powerset(sK6(powerset(X0)))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1145])]) ).
fof(f4155,plain,
( spl16_387
<=> ! [X0,X1] :
( empty(sK9(powerset(sK6(powerset(X0)))))
| empty(sK6(powerset(X0)))
| empty(powerset(X0))
| element(X1,X0)
| ~ in(X1,sK9(sK9(powerset(sK6(powerset(X0)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_387])]) ).
fof(f4234,plain,
( ! [X0] :
( empty(sK6(powerset(X0)))
| empty(powerset(X0))
| element(sK9(sK9(sK7(powerset(sK9(sK9(powerset(sK6(powerset(X0))))))))),X0)
| empty(sK9(powerset(sK6(powerset(X0)))))
| empty(powerset(sK9(sK9(powerset(sK6(powerset(X0)))))))
| empty(sK9(sK7(powerset(sK9(sK9(powerset(sK6(powerset(X0)))))))))
| empty(sK9(sK9(powerset(sK6(powerset(X0))))))
| empty(sK7(powerset(sK9(sK9(powerset(sK6(powerset(X0)))))))) )
| ~ spl16_364
| ~ spl16_387 ),
inference(resolution,[],[f4156,f3679]) ).
fof(f4156,plain,
( ! [X0,X1] :
( ~ in(X1,sK9(sK9(powerset(sK6(powerset(X0))))))
| empty(sK6(powerset(X0)))
| empty(powerset(X0))
| element(X1,X0)
| empty(sK9(powerset(sK6(powerset(X0))))) )
| ~ spl16_387 ),
inference(avatar_component_clause,[],[f4155]) ).
fof(f19263,plain,
( spl16_1144
| ~ spl16_363
| ~ spl16_387 ),
inference(avatar_split_clause,[],[f4233,f4155,f3674,f19261]) ).
fof(f19261,plain,
( spl16_1144
<=> ! [X0] :
( empty(sK6(powerset(X0)))
| empty(powerset(X0))
| element(sK9(sK9(sK6(powerset(sK9(sK9(powerset(sK6(powerset(X0))))))))),X0)
| empty(sK9(powerset(sK6(powerset(X0)))))
| empty(powerset(sK9(sK9(powerset(sK6(powerset(X0)))))))
| empty(sK9(sK6(powerset(sK9(sK9(powerset(sK6(powerset(X0)))))))))
| empty(sK9(sK9(powerset(sK6(powerset(X0))))))
| empty(sK6(powerset(sK9(sK9(powerset(sK6(powerset(X0)))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1144])]) ).
fof(f4233,plain,
( ! [X0] :
( empty(sK6(powerset(X0)))
| empty(powerset(X0))
| element(sK9(sK9(sK6(powerset(sK9(sK9(powerset(sK6(powerset(X0))))))))),X0)
| empty(sK9(powerset(sK6(powerset(X0)))))
| empty(powerset(sK9(sK9(powerset(sK6(powerset(X0)))))))
| empty(sK9(sK6(powerset(sK9(sK9(powerset(sK6(powerset(X0)))))))))
| empty(sK9(sK9(powerset(sK6(powerset(X0))))))
| empty(sK6(powerset(sK9(sK9(powerset(sK6(powerset(X0)))))))) )
| ~ spl16_363
| ~ spl16_387 ),
inference(resolution,[],[f4156,f3675]) ).
fof(f19249,plain,
( spl16_1143
| ~ spl16_152
| ~ spl16_462 ),
inference(avatar_split_clause,[],[f5561,f5493,f1257,f19247]) ).
fof(f19247,plain,
( spl16_1143
<=> ! [X0] :
( empty(sK9(sK9(powerset(powerset(powerset(X0))))))
| empty(sK9(powerset(sK9(sK9(powerset(powerset(powerset(X0))))))))
| element(sK9(sK9(powerset(sK9(sK9(powerset(sK9(sK9(powerset(powerset(powerset(X0))))))))))),X0)
| empty(sK9(powerset(powerset(powerset(X0)))))
| empty(sK9(sK9(powerset(sK9(sK9(powerset(powerset(powerset(X0)))))))))
| empty(sK9(powerset(sK9(sK9(powerset(sK9(sK9(powerset(powerset(powerset(X0))))))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1143])]) ).
fof(f1257,plain,
( spl16_152
<=> ! [X0] :
( empty(sK9(powerset(X0)))
| empty(X0)
| in(sK9(sK9(powerset(X0))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_152])]) ).
fof(f5493,plain,
( spl16_462
<=> ! [X0,X1] :
( empty(sK9(powerset(powerset(powerset(X0)))))
| empty(sK9(sK9(powerset(powerset(powerset(X0))))))
| empty(sK9(powerset(sK9(sK9(powerset(powerset(powerset(X0))))))))
| element(X1,X0)
| ~ in(X1,sK9(sK9(powerset(sK9(sK9(powerset(powerset(powerset(X0))))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_462])]) ).
fof(f5561,plain,
( ! [X0] :
( empty(sK9(sK9(powerset(powerset(powerset(X0))))))
| empty(sK9(powerset(sK9(sK9(powerset(powerset(powerset(X0))))))))
| element(sK9(sK9(powerset(sK9(sK9(powerset(sK9(sK9(powerset(powerset(powerset(X0))))))))))),X0)
| empty(sK9(powerset(powerset(powerset(X0)))))
| empty(sK9(sK9(powerset(sK9(sK9(powerset(powerset(powerset(X0)))))))))
| empty(sK9(powerset(sK9(sK9(powerset(sK9(sK9(powerset(powerset(powerset(X0))))))))))) )
| ~ spl16_152
| ~ spl16_462 ),
inference(resolution,[],[f5494,f1258]) ).
fof(f1258,plain,
( ! [X0] :
( in(sK9(sK9(powerset(X0))),X0)
| empty(X0)
| empty(sK9(powerset(X0))) )
| ~ spl16_152 ),
inference(avatar_component_clause,[],[f1257]) ).
fof(f5494,plain,
( ! [X0,X1] :
( ~ in(X1,sK9(sK9(powerset(sK9(sK9(powerset(powerset(powerset(X0)))))))))
| empty(sK9(sK9(powerset(powerset(powerset(X0))))))
| empty(sK9(powerset(sK9(sK9(powerset(powerset(powerset(X0))))))))
| element(X1,X0)
| empty(sK9(powerset(powerset(powerset(X0))))) )
| ~ spl16_462 ),
inference(avatar_component_clause,[],[f5493]) ).
fof(f19245,plain,
( spl16_1142
| ~ spl16_362
| ~ spl16_405 ),
inference(avatar_split_clause,[],[f4369,f4343,f3670,f19243]) ).
fof(f19243,plain,
( spl16_1142
<=> ! [X0] :
( empty(sK9(sK9(powerset(powerset(powerset(X0))))))
| element(sK9(sK9(sK9(powerset(powerset(sK9(sK9(sK9(powerset(powerset(powerset(X0))))))))))),X0)
| empty(sK9(powerset(powerset(powerset(X0)))))
| empty(sK9(sK9(powerset(powerset(sK9(sK9(sK9(powerset(powerset(powerset(X0)))))))))))
| empty(sK9(sK9(sK9(powerset(powerset(powerset(X0)))))))
| empty(sK9(powerset(powerset(sK9(sK9(sK9(powerset(powerset(powerset(X0)))))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1142])]) ).
fof(f3670,plain,
( spl16_362
<=> ! [X0] :
( empty(sK9(powerset(powerset(X0))))
| empty(sK9(sK9(powerset(powerset(X0)))))
| empty(X0)
| in(sK9(sK9(sK9(powerset(powerset(X0))))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_362])]) ).
fof(f4369,plain,
( ! [X0] :
( empty(sK9(sK9(powerset(powerset(powerset(X0))))))
| element(sK9(sK9(sK9(powerset(powerset(sK9(sK9(sK9(powerset(powerset(powerset(X0))))))))))),X0)
| empty(sK9(powerset(powerset(powerset(X0)))))
| empty(sK9(sK9(powerset(powerset(sK9(sK9(sK9(powerset(powerset(powerset(X0)))))))))))
| empty(sK9(sK9(sK9(powerset(powerset(powerset(X0)))))))
| empty(sK9(powerset(powerset(sK9(sK9(sK9(powerset(powerset(powerset(X0)))))))))) )
| ~ spl16_362
| ~ spl16_405 ),
inference(resolution,[],[f4344,f3671]) ).
fof(f3671,plain,
( ! [X0] :
( in(sK9(sK9(sK9(powerset(powerset(X0))))),X0)
| empty(sK9(sK9(powerset(powerset(X0)))))
| empty(X0)
| empty(sK9(powerset(powerset(X0)))) )
| ~ spl16_362 ),
inference(avatar_component_clause,[],[f3670]) ).
fof(f19201,plain,
( ~ spl16_163
| spl16_1141
| ~ spl16_82
| ~ spl16_1101 ),
inference(avatar_split_clause,[],[f19057,f18851,f617,f19198,f1358]) ).
fof(f1358,plain,
( spl16_163
<=> finite(cartesian_product2(sK14,sK14)) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_163])]) ).
fof(f19198,plain,
( spl16_1141
<=> finite(the_InternalRel(sK8(sK8(sK8(sK8(sK1)))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1141])]) ).
fof(f617,plain,
( spl16_82
<=> ! [X2,X0,X1] :
( ~ relation_of2_as_subset(X0,X1,X2)
| finite(X0)
| ~ finite(cartesian_product2(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_82])]) ).
fof(f19057,plain,
( finite(the_InternalRel(sK8(sK8(sK8(sK8(sK1))))))
| ~ finite(cartesian_product2(sK14,sK14))
| ~ spl16_82
| ~ spl16_1101 ),
inference(resolution,[],[f18853,f618]) ).
fof(f618,plain,
( ! [X2,X0,X1] :
( ~ relation_of2_as_subset(X0,X1,X2)
| finite(X0)
| ~ finite(cartesian_product2(X1,X2)) )
| ~ spl16_82 ),
inference(avatar_component_clause,[],[f617]) ).
fof(f19186,plain,
( spl16_1140
| ~ spl16_173
| ~ spl16_415 ),
inference(avatar_split_clause,[],[f4642,f4477,f1448,f19184]) ).
fof(f19184,plain,
( spl16_1140
<=> ! [X0] :
( empty(powerset(sK9(sK9(powerset(powerset(X0))))))
| empty(sK7(sK9(sK7(powerset(sK9(sK9(powerset(powerset(X0)))))))))
| empty(sK9(sK7(powerset(sK9(sK9(powerset(powerset(X0))))))))
| empty(sK9(sK9(powerset(powerset(X0)))))
| empty(sK7(powerset(sK9(sK9(powerset(powerset(X0)))))))
| element(sK9(sK7(sK9(sK7(powerset(sK9(sK9(powerset(powerset(X0))))))))),X0)
| empty(sK9(powerset(powerset(X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1140])]) ).
fof(f4642,plain,
( ! [X0] :
( empty(powerset(sK9(sK9(powerset(powerset(X0))))))
| empty(sK7(sK9(sK7(powerset(sK9(sK9(powerset(powerset(X0)))))))))
| empty(sK9(sK7(powerset(sK9(sK9(powerset(powerset(X0))))))))
| empty(sK9(sK9(powerset(powerset(X0)))))
| empty(sK7(powerset(sK9(sK9(powerset(powerset(X0)))))))
| element(sK9(sK7(sK9(sK7(powerset(sK9(sK9(powerset(powerset(X0))))))))),X0)
| empty(sK9(powerset(powerset(X0)))) )
| ~ spl16_173
| ~ spl16_415 ),
inference(resolution,[],[f4478,f1449]) ).
fof(f19182,plain,
( spl16_1139
| ~ spl16_173
| ~ spl16_414 ),
inference(avatar_split_clause,[],[f4597,f4473,f1448,f19180]) ).
fof(f19180,plain,
( spl16_1139
<=> ! [X0] :
( empty(powerset(sK9(sK9(powerset(powerset(X0))))))
| empty(sK6(sK9(sK7(powerset(sK9(sK9(powerset(powerset(X0)))))))))
| empty(sK9(sK7(powerset(sK9(sK9(powerset(powerset(X0))))))))
| empty(sK9(sK9(powerset(powerset(X0)))))
| empty(sK7(powerset(sK9(sK9(powerset(powerset(X0)))))))
| element(sK9(sK6(sK9(sK7(powerset(sK9(sK9(powerset(powerset(X0))))))))),X0)
| empty(sK9(powerset(powerset(X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1139])]) ).
fof(f4597,plain,
( ! [X0] :
( empty(powerset(sK9(sK9(powerset(powerset(X0))))))
| empty(sK6(sK9(sK7(powerset(sK9(sK9(powerset(powerset(X0)))))))))
| empty(sK9(sK7(powerset(sK9(sK9(powerset(powerset(X0))))))))
| empty(sK9(sK9(powerset(powerset(X0)))))
| empty(sK7(powerset(sK9(sK9(powerset(powerset(X0)))))))
| element(sK9(sK6(sK9(sK7(powerset(sK9(sK9(powerset(powerset(X0))))))))),X0)
| empty(sK9(powerset(powerset(X0)))) )
| ~ spl16_173
| ~ spl16_414 ),
inference(resolution,[],[f4474,f1449]) ).
fof(f19178,plain,
( spl16_1138
| ~ spl16_173
| ~ spl16_413 ),
inference(avatar_split_clause,[],[f4552,f4469,f1448,f19176]) ).
fof(f19176,plain,
( spl16_1138
<=> ! [X0] :
( empty(powerset(sK9(sK9(powerset(powerset(X0))))))
| empty(sK7(sK9(sK6(powerset(sK9(sK9(powerset(powerset(X0)))))))))
| empty(sK9(sK6(powerset(sK9(sK9(powerset(powerset(X0))))))))
| empty(sK9(sK9(powerset(powerset(X0)))))
| empty(sK6(powerset(sK9(sK9(powerset(powerset(X0)))))))
| element(sK9(sK7(sK9(sK6(powerset(sK9(sK9(powerset(powerset(X0))))))))),X0)
| empty(sK9(powerset(powerset(X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1138])]) ).
fof(f4552,plain,
( ! [X0] :
( empty(powerset(sK9(sK9(powerset(powerset(X0))))))
| empty(sK7(sK9(sK6(powerset(sK9(sK9(powerset(powerset(X0)))))))))
| empty(sK9(sK6(powerset(sK9(sK9(powerset(powerset(X0))))))))
| empty(sK9(sK9(powerset(powerset(X0)))))
| empty(sK6(powerset(sK9(sK9(powerset(powerset(X0)))))))
| element(sK9(sK7(sK9(sK6(powerset(sK9(sK9(powerset(powerset(X0))))))))),X0)
| empty(sK9(powerset(powerset(X0)))) )
| ~ spl16_173
| ~ spl16_413 ),
inference(resolution,[],[f4470,f1449]) ).
fof(f19174,plain,
( spl16_1137
| ~ spl16_173
| ~ spl16_412 ),
inference(avatar_split_clause,[],[f4507,f4465,f1448,f19172]) ).
fof(f19172,plain,
( spl16_1137
<=> ! [X0] :
( empty(powerset(sK9(sK9(powerset(powerset(X0))))))
| empty(sK6(sK9(sK6(powerset(sK9(sK9(powerset(powerset(X0)))))))))
| empty(sK9(sK6(powerset(sK9(sK9(powerset(powerset(X0))))))))
| empty(sK9(sK9(powerset(powerset(X0)))))
| empty(sK6(powerset(sK9(sK9(powerset(powerset(X0)))))))
| element(sK9(sK6(sK9(sK6(powerset(sK9(sK9(powerset(powerset(X0))))))))),X0)
| empty(sK9(powerset(powerset(X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1137])]) ).
fof(f4507,plain,
( ! [X0] :
( empty(powerset(sK9(sK9(powerset(powerset(X0))))))
| empty(sK6(sK9(sK6(powerset(sK9(sK9(powerset(powerset(X0)))))))))
| empty(sK9(sK6(powerset(sK9(sK9(powerset(powerset(X0))))))))
| empty(sK9(sK9(powerset(powerset(X0)))))
| empty(sK6(powerset(sK9(sK9(powerset(powerset(X0)))))))
| element(sK9(sK6(sK9(sK6(powerset(sK9(sK9(powerset(powerset(X0))))))))),X0)
| empty(sK9(powerset(powerset(X0)))) )
| ~ spl16_173
| ~ spl16_412 ),
inference(resolution,[],[f4466,f1449]) ).
fof(f19170,plain,
( spl16_1136
| ~ spl16_349
| ~ spl16_405 ),
inference(avatar_split_clause,[],[f4366,f4343,f3578,f19168]) ).
fof(f19168,plain,
( spl16_1136
<=> ! [X0] :
( empty(sK9(sK9(powerset(powerset(powerset(X0))))))
| element(sK9(sK9(powerset(sK9(powerset(sK9(sK9(sK9(powerset(powerset(powerset(X0))))))))))),X0)
| empty(sK9(powerset(powerset(powerset(X0)))))
| empty(sK9(powerset(sK9(sK9(sK9(powerset(powerset(powerset(X0)))))))))
| empty(sK9(sK9(sK9(powerset(powerset(powerset(X0)))))))
| empty(sK9(powerset(sK9(powerset(sK9(sK9(sK9(powerset(powerset(powerset(X0))))))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1136])]) ).
fof(f3578,plain,
( spl16_349
<=> ! [X0] :
( empty(sK9(powerset(sK9(powerset(X0)))))
| empty(sK9(powerset(X0)))
| empty(X0)
| in(sK9(sK9(powerset(sK9(powerset(X0))))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_349])]) ).
fof(f4366,plain,
( ! [X0] :
( empty(sK9(sK9(powerset(powerset(powerset(X0))))))
| element(sK9(sK9(powerset(sK9(powerset(sK9(sK9(sK9(powerset(powerset(powerset(X0))))))))))),X0)
| empty(sK9(powerset(powerset(powerset(X0)))))
| empty(sK9(powerset(sK9(sK9(sK9(powerset(powerset(powerset(X0)))))))))
| empty(sK9(sK9(sK9(powerset(powerset(powerset(X0)))))))
| empty(sK9(powerset(sK9(powerset(sK9(sK9(sK9(powerset(powerset(powerset(X0))))))))))) )
| ~ spl16_349
| ~ spl16_405 ),
inference(resolution,[],[f4344,f3579]) ).
fof(f3579,plain,
( ! [X0] :
( in(sK9(sK9(powerset(sK9(powerset(X0))))),X0)
| empty(sK9(powerset(X0)))
| empty(X0)
| empty(sK9(powerset(sK9(powerset(X0))))) )
| ~ spl16_349 ),
inference(avatar_component_clause,[],[f3578]) ).
fof(f19166,plain,
( spl16_1135
| ~ spl16_362
| ~ spl16_390 ),
inference(avatar_split_clause,[],[f4267,f4167,f3670,f19164]) ).
fof(f19164,plain,
( spl16_1135
<=> ! [X0] :
( empty(sK9(powerset(powerset(X0))))
| element(sK9(sK9(sK9(powerset(powerset(sK9(sK9(powerset(sK9(powerset(powerset(X0))))))))))),X0)
| empty(sK9(powerset(sK9(powerset(powerset(X0))))))
| empty(sK9(sK9(powerset(powerset(sK9(sK9(powerset(sK9(powerset(powerset(X0)))))))))))
| empty(sK9(sK9(powerset(sK9(powerset(powerset(X0)))))))
| empty(sK9(powerset(powerset(sK9(sK9(powerset(sK9(powerset(powerset(X0)))))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1135])]) ).
fof(f4267,plain,
( ! [X0] :
( empty(sK9(powerset(powerset(X0))))
| element(sK9(sK9(sK9(powerset(powerset(sK9(sK9(powerset(sK9(powerset(powerset(X0))))))))))),X0)
| empty(sK9(powerset(sK9(powerset(powerset(X0))))))
| empty(sK9(sK9(powerset(powerset(sK9(sK9(powerset(sK9(powerset(powerset(X0)))))))))))
| empty(sK9(sK9(powerset(sK9(powerset(powerset(X0)))))))
| empty(sK9(powerset(powerset(sK9(sK9(powerset(sK9(powerset(powerset(X0)))))))))) )
| ~ spl16_362
| ~ spl16_390 ),
inference(resolution,[],[f4168,f3671]) ).
fof(f19162,plain,
( spl16_1134
| ~ spl16_364
| ~ spl16_371 ),
inference(avatar_split_clause,[],[f4052,f3915,f3678,f19160]) ).
fof(f19160,plain,
( spl16_1134
<=> ! [X0] :
( empty(sK7(sK9(powerset(powerset(X0)))))
| element(sK9(sK9(sK7(powerset(sK9(sK7(sK9(powerset(powerset(X0))))))))),X0)
| empty(sK9(powerset(powerset(X0))))
| empty(powerset(sK9(sK7(sK9(powerset(powerset(X0)))))))
| empty(sK9(sK7(powerset(sK9(sK7(sK9(powerset(powerset(X0)))))))))
| empty(sK9(sK7(sK9(powerset(powerset(X0))))))
| empty(sK7(powerset(sK9(sK7(sK9(powerset(powerset(X0)))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1134])]) ).
fof(f3915,plain,
( spl16_371
<=> ! [X0,X1] :
( empty(sK9(powerset(powerset(X0))))
| empty(sK7(sK9(powerset(powerset(X0)))))
| element(X1,X0)
| ~ in(X1,sK9(sK7(sK9(powerset(powerset(X0)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_371])]) ).
fof(f4052,plain,
( ! [X0] :
( empty(sK7(sK9(powerset(powerset(X0)))))
| element(sK9(sK9(sK7(powerset(sK9(sK7(sK9(powerset(powerset(X0))))))))),X0)
| empty(sK9(powerset(powerset(X0))))
| empty(powerset(sK9(sK7(sK9(powerset(powerset(X0)))))))
| empty(sK9(sK7(powerset(sK9(sK7(sK9(powerset(powerset(X0)))))))))
| empty(sK9(sK7(sK9(powerset(powerset(X0))))))
| empty(sK7(powerset(sK9(sK7(sK9(powerset(powerset(X0)))))))) )
| ~ spl16_364
| ~ spl16_371 ),
inference(resolution,[],[f3916,f3679]) ).
fof(f3916,plain,
( ! [X0,X1] :
( ~ in(X1,sK9(sK7(sK9(powerset(powerset(X0))))))
| empty(sK7(sK9(powerset(powerset(X0)))))
| element(X1,X0)
| empty(sK9(powerset(powerset(X0)))) )
| ~ spl16_371 ),
inference(avatar_component_clause,[],[f3915]) ).
fof(f19158,plain,
( spl16_1133
| ~ spl16_363
| ~ spl16_371 ),
inference(avatar_split_clause,[],[f4051,f3915,f3674,f19156]) ).
fof(f19156,plain,
( spl16_1133
<=> ! [X0] :
( empty(sK7(sK9(powerset(powerset(X0)))))
| element(sK9(sK9(sK6(powerset(sK9(sK7(sK9(powerset(powerset(X0))))))))),X0)
| empty(sK9(powerset(powerset(X0))))
| empty(powerset(sK9(sK7(sK9(powerset(powerset(X0)))))))
| empty(sK9(sK6(powerset(sK9(sK7(sK9(powerset(powerset(X0)))))))))
| empty(sK9(sK7(sK9(powerset(powerset(X0))))))
| empty(sK6(powerset(sK9(sK7(sK9(powerset(powerset(X0)))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1133])]) ).
fof(f4051,plain,
( ! [X0] :
( empty(sK7(sK9(powerset(powerset(X0)))))
| element(sK9(sK9(sK6(powerset(sK9(sK7(sK9(powerset(powerset(X0))))))))),X0)
| empty(sK9(powerset(powerset(X0))))
| empty(powerset(sK9(sK7(sK9(powerset(powerset(X0)))))))
| empty(sK9(sK6(powerset(sK9(sK7(sK9(powerset(powerset(X0)))))))))
| empty(sK9(sK7(sK9(powerset(powerset(X0))))))
| empty(sK6(powerset(sK9(sK7(sK9(powerset(powerset(X0)))))))) )
| ~ spl16_363
| ~ spl16_371 ),
inference(resolution,[],[f3916,f3675]) ).
fof(f19153,plain,
( spl16_1132
| ~ spl16_364
| ~ spl16_370 ),
inference(avatar_split_clause,[],[f4036,f3911,f3678,f19151]) ).
fof(f19151,plain,
( spl16_1132
<=> ! [X0] :
( empty(sK6(sK9(powerset(powerset(X0)))))
| element(sK9(sK9(sK7(powerset(sK9(sK6(sK9(powerset(powerset(X0))))))))),X0)
| empty(sK9(powerset(powerset(X0))))
| empty(powerset(sK9(sK6(sK9(powerset(powerset(X0)))))))
| empty(sK9(sK7(powerset(sK9(sK6(sK9(powerset(powerset(X0)))))))))
| empty(sK9(sK6(sK9(powerset(powerset(X0))))))
| empty(sK7(powerset(sK9(sK6(sK9(powerset(powerset(X0)))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1132])]) ).
fof(f3911,plain,
( spl16_370
<=> ! [X0,X1] :
( empty(sK9(powerset(powerset(X0))))
| empty(sK6(sK9(powerset(powerset(X0)))))
| element(X1,X0)
| ~ in(X1,sK9(sK6(sK9(powerset(powerset(X0)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_370])]) ).
fof(f4036,plain,
( ! [X0] :
( empty(sK6(sK9(powerset(powerset(X0)))))
| element(sK9(sK9(sK7(powerset(sK9(sK6(sK9(powerset(powerset(X0))))))))),X0)
| empty(sK9(powerset(powerset(X0))))
| empty(powerset(sK9(sK6(sK9(powerset(powerset(X0)))))))
| empty(sK9(sK7(powerset(sK9(sK6(sK9(powerset(powerset(X0)))))))))
| empty(sK9(sK6(sK9(powerset(powerset(X0))))))
| empty(sK7(powerset(sK9(sK6(sK9(powerset(powerset(X0)))))))) )
| ~ spl16_364
| ~ spl16_370 ),
inference(resolution,[],[f3912,f3679]) ).
fof(f3912,plain,
( ! [X0,X1] :
( ~ in(X1,sK9(sK6(sK9(powerset(powerset(X0))))))
| empty(sK6(sK9(powerset(powerset(X0)))))
| element(X1,X0)
| empty(sK9(powerset(powerset(X0)))) )
| ~ spl16_370 ),
inference(avatar_component_clause,[],[f3911]) ).
fof(f19149,plain,
( spl16_1131
| ~ spl16_363
| ~ spl16_370 ),
inference(avatar_split_clause,[],[f4035,f3911,f3674,f19147]) ).
fof(f19147,plain,
( spl16_1131
<=> ! [X0] :
( empty(sK6(sK9(powerset(powerset(X0)))))
| element(sK9(sK9(sK6(powerset(sK9(sK6(sK9(powerset(powerset(X0))))))))),X0)
| empty(sK9(powerset(powerset(X0))))
| empty(powerset(sK9(sK6(sK9(powerset(powerset(X0)))))))
| empty(sK9(sK6(powerset(sK9(sK6(sK9(powerset(powerset(X0)))))))))
| empty(sK9(sK6(sK9(powerset(powerset(X0))))))
| empty(sK6(powerset(sK9(sK6(sK9(powerset(powerset(X0)))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1131])]) ).
fof(f4035,plain,
( ! [X0] :
( empty(sK6(sK9(powerset(powerset(X0)))))
| element(sK9(sK9(sK6(powerset(sK9(sK6(sK9(powerset(powerset(X0))))))))),X0)
| empty(sK9(powerset(powerset(X0))))
| empty(powerset(sK9(sK6(sK9(powerset(powerset(X0)))))))
| empty(sK9(sK6(powerset(sK9(sK6(sK9(powerset(powerset(X0)))))))))
| empty(sK9(sK6(sK9(powerset(powerset(X0))))))
| empty(sK6(powerset(sK9(sK6(sK9(powerset(powerset(X0)))))))) )
| ~ spl16_363
| ~ spl16_370 ),
inference(resolution,[],[f3912,f3675]) ).
fof(f19105,plain,
( spl16_1130
| ~ spl16_40
| ~ spl16_1101 ),
inference(avatar_split_clause,[],[f19058,f18851,f343,f19102]) ).
fof(f19102,plain,
( spl16_1130
<=> relation_of2(the_InternalRel(sK8(sK8(sK8(sK8(sK1))))),sK14,sK14) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1130])]) ).
fof(f343,plain,
( spl16_40
<=> ! [X2,X0,X1] :
( relation_of2(X2,X0,X1)
| ~ relation_of2_as_subset(X2,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_40])]) ).
fof(f19058,plain,
( relation_of2(the_InternalRel(sK8(sK8(sK8(sK8(sK1))))),sK14,sK14)
| ~ spl16_40
| ~ spl16_1101 ),
inference(resolution,[],[f18853,f344]) ).
fof(f344,plain,
( ! [X2,X0,X1] :
( ~ relation_of2_as_subset(X2,X0,X1)
| relation_of2(X2,X0,X1) )
| ~ spl16_40 ),
inference(avatar_component_clause,[],[f343]) ).
fof(f19100,plain,
( spl16_1129
| ~ spl16_150
| ~ spl16_462 ),
inference(avatar_split_clause,[],[f5554,f5493,f1218,f19098]) ).
fof(f19098,plain,
( spl16_1129
<=> ! [X0] :
( empty(sK9(sK9(powerset(powerset(powerset(X0))))))
| empty(sK9(powerset(sK9(sK9(powerset(powerset(powerset(X0))))))))
| element(sK9(sK7(sK9(sK9(powerset(sK9(sK9(powerset(powerset(powerset(X0)))))))))),X0)
| empty(sK9(powerset(powerset(powerset(X0)))))
| empty(sK7(sK9(sK9(powerset(sK9(sK9(powerset(powerset(powerset(X0))))))))))
| empty(sK9(sK9(powerset(sK9(sK9(powerset(powerset(powerset(X0))))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1129])]) ).
fof(f1218,plain,
( spl16_150
<=> ! [X0] :
( empty(X0)
| empty(sK7(X0))
| in(sK9(sK7(X0)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_150])]) ).
fof(f5554,plain,
( ! [X0] :
( empty(sK9(sK9(powerset(powerset(powerset(X0))))))
| empty(sK9(powerset(sK9(sK9(powerset(powerset(powerset(X0))))))))
| element(sK9(sK7(sK9(sK9(powerset(sK9(sK9(powerset(powerset(powerset(X0)))))))))),X0)
| empty(sK9(powerset(powerset(powerset(X0)))))
| empty(sK7(sK9(sK9(powerset(sK9(sK9(powerset(powerset(powerset(X0))))))))))
| empty(sK9(sK9(powerset(sK9(sK9(powerset(powerset(powerset(X0))))))))) )
| ~ spl16_150
| ~ spl16_462 ),
inference(resolution,[],[f5494,f1219]) ).
fof(f1219,plain,
( ! [X0] :
( in(sK9(sK7(X0)),X0)
| empty(sK7(X0))
| empty(X0) )
| ~ spl16_150 ),
inference(avatar_component_clause,[],[f1218]) ).
fof(f19096,plain,
( spl16_1128
| ~ spl16_149
| ~ spl16_462 ),
inference(avatar_split_clause,[],[f5547,f5493,f1214,f19094]) ).
fof(f19094,plain,
( spl16_1128
<=> ! [X0] :
( empty(sK9(sK9(powerset(powerset(powerset(X0))))))
| empty(sK9(powerset(sK9(sK9(powerset(powerset(powerset(X0))))))))
| element(sK9(sK6(sK9(sK9(powerset(sK9(sK9(powerset(powerset(powerset(X0)))))))))),X0)
| empty(sK9(powerset(powerset(powerset(X0)))))
| empty(sK6(sK9(sK9(powerset(sK9(sK9(powerset(powerset(powerset(X0))))))))))
| empty(sK9(sK9(powerset(sK9(sK9(powerset(powerset(powerset(X0))))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1128])]) ).
fof(f1214,plain,
( spl16_149
<=> ! [X0] :
( empty(X0)
| empty(sK6(X0))
| in(sK9(sK6(X0)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_149])]) ).
fof(f5547,plain,
( ! [X0] :
( empty(sK9(sK9(powerset(powerset(powerset(X0))))))
| empty(sK9(powerset(sK9(sK9(powerset(powerset(powerset(X0))))))))
| element(sK9(sK6(sK9(sK9(powerset(sK9(sK9(powerset(powerset(powerset(X0)))))))))),X0)
| empty(sK9(powerset(powerset(powerset(X0)))))
| empty(sK6(sK9(sK9(powerset(sK9(sK9(powerset(powerset(powerset(X0))))))))))
| empty(sK9(sK9(powerset(sK9(sK9(powerset(powerset(powerset(X0))))))))) )
| ~ spl16_149
| ~ spl16_462 ),
inference(resolution,[],[f5494,f1215]) ).
fof(f1215,plain,
( ! [X0] :
( in(sK9(sK6(X0)),X0)
| empty(sK6(X0))
| empty(X0) )
| ~ spl16_149 ),
inference(avatar_component_clause,[],[f1214]) ).
fof(f19092,plain,
( spl16_1127
| ~ spl16_152
| ~ spl16_460 ),
inference(avatar_split_clause,[],[f5536,f5484,f1257,f19090]) ).
fof(f19090,plain,
( spl16_1127
<=> ! [X0] :
( empty(powerset(powerset(X0)))
| empty(sK9(sK7(powerset(powerset(X0)))))
| empty(sK9(powerset(sK9(sK7(powerset(powerset(X0)))))))
| element(sK9(sK9(powerset(sK9(sK9(powerset(sK9(sK7(powerset(powerset(X0)))))))))),X0)
| empty(sK7(powerset(powerset(X0))))
| empty(sK9(sK9(powerset(sK9(sK7(powerset(powerset(X0))))))))
| empty(sK9(powerset(sK9(sK9(powerset(sK9(sK7(powerset(powerset(X0)))))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1127])]) ).
fof(f5484,plain,
( spl16_460
<=> ! [X0,X1] :
( empty(sK7(powerset(powerset(X0))))
| empty(powerset(powerset(X0)))
| empty(sK9(sK7(powerset(powerset(X0)))))
| empty(sK9(powerset(sK9(sK7(powerset(powerset(X0)))))))
| element(X1,X0)
| ~ in(X1,sK9(sK9(powerset(sK9(sK7(powerset(powerset(X0)))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_460])]) ).
fof(f5536,plain,
( ! [X0] :
( empty(powerset(powerset(X0)))
| empty(sK9(sK7(powerset(powerset(X0)))))
| empty(sK9(powerset(sK9(sK7(powerset(powerset(X0)))))))
| element(sK9(sK9(powerset(sK9(sK9(powerset(sK9(sK7(powerset(powerset(X0)))))))))),X0)
| empty(sK7(powerset(powerset(X0))))
| empty(sK9(sK9(powerset(sK9(sK7(powerset(powerset(X0))))))))
| empty(sK9(powerset(sK9(sK9(powerset(sK9(sK7(powerset(powerset(X0)))))))))) )
| ~ spl16_152
| ~ spl16_460 ),
inference(resolution,[],[f5485,f1258]) ).
fof(f5485,plain,
( ! [X0,X1] :
( ~ in(X1,sK9(sK9(powerset(sK9(sK7(powerset(powerset(X0))))))))
| empty(powerset(powerset(X0)))
| empty(sK9(sK7(powerset(powerset(X0)))))
| empty(sK9(powerset(sK9(sK7(powerset(powerset(X0)))))))
| element(X1,X0)
| empty(sK7(powerset(powerset(X0)))) )
| ~ spl16_460 ),
inference(avatar_component_clause,[],[f5484]) ).
fof(f19088,plain,
( spl16_1126
| ~ spl16_152
| ~ spl16_459 ),
inference(avatar_split_clause,[],[f5511,f5480,f1257,f19086]) ).
fof(f19086,plain,
( spl16_1126
<=> ! [X0] :
( empty(powerset(powerset(X0)))
| empty(sK9(sK6(powerset(powerset(X0)))))
| empty(sK9(powerset(sK9(sK6(powerset(powerset(X0)))))))
| element(sK9(sK9(powerset(sK9(sK9(powerset(sK9(sK6(powerset(powerset(X0)))))))))),X0)
| empty(sK6(powerset(powerset(X0))))
| empty(sK9(sK9(powerset(sK9(sK6(powerset(powerset(X0))))))))
| empty(sK9(powerset(sK9(sK9(powerset(sK9(sK6(powerset(powerset(X0)))))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1126])]) ).
fof(f5480,plain,
( spl16_459
<=> ! [X0,X1] :
( empty(sK6(powerset(powerset(X0))))
| empty(powerset(powerset(X0)))
| empty(sK9(sK6(powerset(powerset(X0)))))
| empty(sK9(powerset(sK9(sK6(powerset(powerset(X0)))))))
| element(X1,X0)
| ~ in(X1,sK9(sK9(powerset(sK9(sK6(powerset(powerset(X0)))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_459])]) ).
fof(f5511,plain,
( ! [X0] :
( empty(powerset(powerset(X0)))
| empty(sK9(sK6(powerset(powerset(X0)))))
| empty(sK9(powerset(sK9(sK6(powerset(powerset(X0)))))))
| element(sK9(sK9(powerset(sK9(sK9(powerset(sK9(sK6(powerset(powerset(X0)))))))))),X0)
| empty(sK6(powerset(powerset(X0))))
| empty(sK9(sK9(powerset(sK9(sK6(powerset(powerset(X0))))))))
| empty(sK9(powerset(sK9(sK9(powerset(sK9(sK6(powerset(powerset(X0)))))))))) )
| ~ spl16_152
| ~ spl16_459 ),
inference(resolution,[],[f5481,f1258]) ).
fof(f5481,plain,
( ! [X0,X1] :
( ~ in(X1,sK9(sK9(powerset(sK9(sK6(powerset(powerset(X0))))))))
| empty(powerset(powerset(X0)))
| empty(sK9(sK6(powerset(powerset(X0)))))
| empty(sK9(powerset(sK9(sK6(powerset(powerset(X0)))))))
| element(X1,X0)
| empty(sK6(powerset(powerset(X0)))) )
| ~ spl16_459 ),
inference(avatar_component_clause,[],[f5480]) ).
fof(f19084,plain,
( spl16_1125
| ~ spl16_173
| ~ spl16_427 ),
inference(avatar_split_clause,[],[f4945,f4893,f1448,f19082]) ).
fof(f19082,plain,
( spl16_1125
<=> ! [X0] :
( empty(sK9(sK9(powerset(powerset(sK9(sK9(powerset(powerset(X0)))))))))
| empty(sK9(powerset(sK9(sK9(powerset(powerset(sK9(sK9(powerset(powerset(X0)))))))))))
| empty(sK9(sK9(powerset(powerset(X0)))))
| empty(sK9(powerset(powerset(sK9(sK9(powerset(powerset(X0))))))))
| element(sK9(sK9(powerset(sK9(sK9(powerset(powerset(sK9(sK9(powerset(powerset(X0))))))))))),X0)
| empty(sK9(powerset(powerset(X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1125])]) ).
fof(f4945,plain,
( ! [X0] :
( empty(sK9(sK9(powerset(powerset(sK9(sK9(powerset(powerset(X0)))))))))
| empty(sK9(powerset(sK9(sK9(powerset(powerset(sK9(sK9(powerset(powerset(X0)))))))))))
| empty(sK9(sK9(powerset(powerset(X0)))))
| empty(sK9(powerset(powerset(sK9(sK9(powerset(powerset(X0))))))))
| element(sK9(sK9(powerset(sK9(sK9(powerset(powerset(sK9(sK9(powerset(powerset(X0))))))))))),X0)
| empty(sK9(powerset(powerset(X0)))) )
| ~ spl16_173
| ~ spl16_427 ),
inference(resolution,[],[f4894,f1449]) ).
fof(f19080,plain,
( spl16_1124
| ~ spl16_362
| ~ spl16_409 ),
inference(avatar_split_clause,[],[f4449,f4407,f3670,f19078]) ).
fof(f19078,plain,
( spl16_1124
<=> ! [X0] :
( empty(powerset(powerset(X0)))
| empty(sK9(sK7(powerset(powerset(X0)))))
| element(sK9(sK9(sK9(powerset(powerset(sK9(sK9(sK7(powerset(powerset(X0)))))))))),X0)
| empty(sK7(powerset(powerset(X0))))
| empty(sK9(sK9(powerset(powerset(sK9(sK9(sK7(powerset(powerset(X0))))))))))
| empty(sK9(sK9(sK7(powerset(powerset(X0))))))
| empty(sK9(powerset(powerset(sK9(sK9(sK7(powerset(powerset(X0))))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1124])]) ).
fof(f4449,plain,
( ! [X0] :
( empty(powerset(powerset(X0)))
| empty(sK9(sK7(powerset(powerset(X0)))))
| element(sK9(sK9(sK9(powerset(powerset(sK9(sK9(sK7(powerset(powerset(X0)))))))))),X0)
| empty(sK7(powerset(powerset(X0))))
| empty(sK9(sK9(powerset(powerset(sK9(sK9(sK7(powerset(powerset(X0))))))))))
| empty(sK9(sK9(sK7(powerset(powerset(X0))))))
| empty(sK9(powerset(powerset(sK9(sK9(sK7(powerset(powerset(X0))))))))) )
| ~ spl16_362
| ~ spl16_409 ),
inference(resolution,[],[f4408,f3671]) ).
fof(f19076,plain,
( spl16_1123
| ~ spl16_362
| ~ spl16_408 ),
inference(avatar_split_clause,[],[f4433,f4403,f3670,f19074]) ).
fof(f19074,plain,
( spl16_1123
<=> ! [X0] :
( empty(powerset(powerset(X0)))
| empty(sK9(sK6(powerset(powerset(X0)))))
| element(sK9(sK9(sK9(powerset(powerset(sK9(sK9(sK6(powerset(powerset(X0)))))))))),X0)
| empty(sK6(powerset(powerset(X0))))
| empty(sK9(sK9(powerset(powerset(sK9(sK9(sK6(powerset(powerset(X0))))))))))
| empty(sK9(sK9(sK6(powerset(powerset(X0))))))
| empty(sK9(powerset(powerset(sK9(sK9(sK6(powerset(powerset(X0))))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1123])]) ).
fof(f4433,plain,
( ! [X0] :
( empty(powerset(powerset(X0)))
| empty(sK9(sK6(powerset(powerset(X0)))))
| element(sK9(sK9(sK9(powerset(powerset(sK9(sK9(sK6(powerset(powerset(X0)))))))))),X0)
| empty(sK6(powerset(powerset(X0))))
| empty(sK9(sK9(powerset(powerset(sK9(sK9(sK6(powerset(powerset(X0))))))))))
| empty(sK9(sK9(sK6(powerset(powerset(X0))))))
| empty(sK9(powerset(powerset(sK9(sK9(sK6(powerset(powerset(X0))))))))) )
| ~ spl16_362
| ~ spl16_408 ),
inference(resolution,[],[f4404,f3671]) ).
fof(f19072,plain,
( spl16_1122
| ~ spl16_349
| ~ spl16_390 ),
inference(avatar_split_clause,[],[f4264,f4167,f3578,f19070]) ).
fof(f19070,plain,
( spl16_1122
<=> ! [X0] :
( empty(sK9(powerset(powerset(X0))))
| element(sK9(sK9(powerset(sK9(powerset(sK9(sK9(powerset(sK9(powerset(powerset(X0))))))))))),X0)
| empty(sK9(powerset(sK9(powerset(powerset(X0))))))
| empty(sK9(powerset(sK9(sK9(powerset(sK9(powerset(powerset(X0)))))))))
| empty(sK9(sK9(powerset(sK9(powerset(powerset(X0)))))))
| empty(sK9(powerset(sK9(powerset(sK9(sK9(powerset(sK9(powerset(powerset(X0))))))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1122])]) ).
fof(f4264,plain,
( ! [X0] :
( empty(sK9(powerset(powerset(X0))))
| element(sK9(sK9(powerset(sK9(powerset(sK9(sK9(powerset(sK9(powerset(powerset(X0))))))))))),X0)
| empty(sK9(powerset(sK9(powerset(powerset(X0))))))
| empty(sK9(powerset(sK9(sK9(powerset(sK9(powerset(powerset(X0)))))))))
| empty(sK9(sK9(powerset(sK9(powerset(powerset(X0)))))))
| empty(sK9(powerset(sK9(powerset(sK9(sK9(powerset(sK9(powerset(powerset(X0))))))))))) )
| ~ spl16_349
| ~ spl16_390 ),
inference(resolution,[],[f4168,f3579]) ).
fof(f19024,plain,
( spl16_1121
| ~ spl16_177
| ~ spl16_420 ),
inference(avatar_split_clause,[],[f4834,f4767,f1476,f19022]) ).
fof(f19022,plain,
( spl16_1121
<=> ! [X0] :
( empty(powerset(sK9(sK7(powerset(X0)))))
| empty(sK9(sK7(powerset(sK9(sK7(powerset(X0)))))))
| empty(sK9(powerset(sK9(sK7(powerset(sK9(sK7(powerset(X0)))))))))
| empty(sK9(sK7(powerset(X0))))
| empty(sK7(powerset(sK9(sK7(powerset(X0))))))
| empty(sK7(powerset(X0)))
| element(sK9(sK9(powerset(sK9(sK7(powerset(sK9(sK7(powerset(X0))))))))),X0)
| empty(powerset(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1121])]) ).
fof(f1476,plain,
( spl16_177
<=> ! [X0,X1] :
( empty(powerset(X0))
| empty(sK7(powerset(X0)))
| element(X1,X0)
| ~ in(X1,sK9(sK7(powerset(X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_177])]) ).
fof(f4834,plain,
( ! [X0] :
( empty(powerset(sK9(sK7(powerset(X0)))))
| empty(sK9(sK7(powerset(sK9(sK7(powerset(X0)))))))
| empty(sK9(powerset(sK9(sK7(powerset(sK9(sK7(powerset(X0)))))))))
| empty(sK9(sK7(powerset(X0))))
| empty(sK7(powerset(sK9(sK7(powerset(X0))))))
| empty(sK7(powerset(X0)))
| element(sK9(sK9(powerset(sK9(sK7(powerset(sK9(sK7(powerset(X0))))))))),X0)
| empty(powerset(X0)) )
| ~ spl16_177
| ~ spl16_420 ),
inference(resolution,[],[f4768,f1477]) ).
fof(f1477,plain,
( ! [X0,X1] :
( ~ in(X1,sK9(sK7(powerset(X0))))
| empty(sK7(powerset(X0)))
| element(X1,X0)
| empty(powerset(X0)) )
| ~ spl16_177 ),
inference(avatar_component_clause,[],[f1476]) ).
fof(f19020,plain,
( spl16_1120
| ~ spl16_176
| ~ spl16_420 ),
inference(avatar_split_clause,[],[f4826,f4767,f1472,f19018]) ).
fof(f19018,plain,
( spl16_1120
<=> ! [X0] :
( empty(powerset(sK9(sK6(powerset(X0)))))
| empty(sK9(sK7(powerset(sK9(sK6(powerset(X0)))))))
| empty(sK9(powerset(sK9(sK7(powerset(sK9(sK6(powerset(X0)))))))))
| empty(sK9(sK6(powerset(X0))))
| empty(sK7(powerset(sK9(sK6(powerset(X0))))))
| empty(sK6(powerset(X0)))
| element(sK9(sK9(powerset(sK9(sK7(powerset(sK9(sK6(powerset(X0))))))))),X0)
| empty(powerset(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1120])]) ).
fof(f1472,plain,
( spl16_176
<=> ! [X0,X1] :
( empty(powerset(X0))
| empty(sK6(powerset(X0)))
| element(X1,X0)
| ~ in(X1,sK9(sK6(powerset(X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_176])]) ).
fof(f4826,plain,
( ! [X0] :
( empty(powerset(sK9(sK6(powerset(X0)))))
| empty(sK9(sK7(powerset(sK9(sK6(powerset(X0)))))))
| empty(sK9(powerset(sK9(sK7(powerset(sK9(sK6(powerset(X0)))))))))
| empty(sK9(sK6(powerset(X0))))
| empty(sK7(powerset(sK9(sK6(powerset(X0))))))
| empty(sK6(powerset(X0)))
| element(sK9(sK9(powerset(sK9(sK7(powerset(sK9(sK6(powerset(X0))))))))),X0)
| empty(powerset(X0)) )
| ~ spl16_176
| ~ spl16_420 ),
inference(resolution,[],[f4768,f1473]) ).
fof(f1473,plain,
( ! [X0,X1] :
( ~ in(X1,sK9(sK6(powerset(X0))))
| empty(sK6(powerset(X0)))
| element(X1,X0)
| empty(powerset(X0)) )
| ~ spl16_176 ),
inference(avatar_component_clause,[],[f1472]) ).
fof(f19016,plain,
( spl16_1119
| ~ spl16_177
| ~ spl16_419 ),
inference(avatar_split_clause,[],[f4789,f4763,f1476,f19014]) ).
fof(f19014,plain,
( spl16_1119
<=> ! [X0] :
( empty(powerset(sK9(sK7(powerset(X0)))))
| empty(sK9(sK6(powerset(sK9(sK7(powerset(X0)))))))
| empty(sK9(powerset(sK9(sK6(powerset(sK9(sK7(powerset(X0)))))))))
| empty(sK9(sK7(powerset(X0))))
| empty(sK6(powerset(sK9(sK7(powerset(X0))))))
| empty(sK7(powerset(X0)))
| element(sK9(sK9(powerset(sK9(sK6(powerset(sK9(sK7(powerset(X0))))))))),X0)
| empty(powerset(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1119])]) ).
fof(f4789,plain,
( ! [X0] :
( empty(powerset(sK9(sK7(powerset(X0)))))
| empty(sK9(sK6(powerset(sK9(sK7(powerset(X0)))))))
| empty(sK9(powerset(sK9(sK6(powerset(sK9(sK7(powerset(X0)))))))))
| empty(sK9(sK7(powerset(X0))))
| empty(sK6(powerset(sK9(sK7(powerset(X0))))))
| empty(sK7(powerset(X0)))
| element(sK9(sK9(powerset(sK9(sK6(powerset(sK9(sK7(powerset(X0))))))))),X0)
| empty(powerset(X0)) )
| ~ spl16_177
| ~ spl16_419 ),
inference(resolution,[],[f4764,f1477]) ).
fof(f19012,plain,
( spl16_1118
| ~ spl16_176
| ~ spl16_419 ),
inference(avatar_split_clause,[],[f4781,f4763,f1472,f19010]) ).
fof(f19010,plain,
( spl16_1118
<=> ! [X0] :
( empty(powerset(sK9(sK6(powerset(X0)))))
| empty(sK9(sK6(powerset(sK9(sK6(powerset(X0)))))))
| empty(sK9(powerset(sK9(sK6(powerset(sK9(sK6(powerset(X0)))))))))
| empty(sK9(sK6(powerset(X0))))
| empty(sK6(powerset(sK9(sK6(powerset(X0))))))
| empty(sK6(powerset(X0)))
| element(sK9(sK9(powerset(sK9(sK6(powerset(sK9(sK6(powerset(X0))))))))),X0)
| empty(powerset(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1118])]) ).
fof(f4781,plain,
( ! [X0] :
( empty(powerset(sK9(sK6(powerset(X0)))))
| empty(sK9(sK6(powerset(sK9(sK6(powerset(X0)))))))
| empty(sK9(powerset(sK9(sK6(powerset(sK9(sK6(powerset(X0)))))))))
| empty(sK9(sK6(powerset(X0))))
| empty(sK6(powerset(sK9(sK6(powerset(X0))))))
| empty(sK6(powerset(X0)))
| element(sK9(sK9(powerset(sK9(sK6(powerset(sK9(sK6(powerset(X0))))))))),X0)
| empty(powerset(X0)) )
| ~ spl16_176
| ~ spl16_419 ),
inference(resolution,[],[f4764,f1473]) ).
fof(f19008,plain,
( spl16_1117
| ~ spl16_349
| ~ spl16_409 ),
inference(avatar_split_clause,[],[f4446,f4407,f3578,f19006]) ).
fof(f19006,plain,
( spl16_1117
<=> ! [X0] :
( empty(powerset(powerset(X0)))
| empty(sK9(sK7(powerset(powerset(X0)))))
| element(sK9(sK9(powerset(sK9(powerset(sK9(sK9(sK7(powerset(powerset(X0)))))))))),X0)
| empty(sK7(powerset(powerset(X0))))
| empty(sK9(powerset(sK9(sK9(sK7(powerset(powerset(X0))))))))
| empty(sK9(sK9(sK7(powerset(powerset(X0))))))
| empty(sK9(powerset(sK9(powerset(sK9(sK9(sK7(powerset(powerset(X0)))))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1117])]) ).
fof(f4446,plain,
( ! [X0] :
( empty(powerset(powerset(X0)))
| empty(sK9(sK7(powerset(powerset(X0)))))
| element(sK9(sK9(powerset(sK9(powerset(sK9(sK9(sK7(powerset(powerset(X0)))))))))),X0)
| empty(sK7(powerset(powerset(X0))))
| empty(sK9(powerset(sK9(sK9(sK7(powerset(powerset(X0))))))))
| empty(sK9(sK9(sK7(powerset(powerset(X0))))))
| empty(sK9(powerset(sK9(powerset(sK9(sK9(sK7(powerset(powerset(X0)))))))))) )
| ~ spl16_349
| ~ spl16_409 ),
inference(resolution,[],[f4408,f3579]) ).
fof(f19004,plain,
( spl16_1116
| ~ spl16_349
| ~ spl16_408 ),
inference(avatar_split_clause,[],[f4430,f4403,f3578,f19002]) ).
fof(f19002,plain,
( spl16_1116
<=> ! [X0] :
( empty(powerset(powerset(X0)))
| empty(sK9(sK6(powerset(powerset(X0)))))
| element(sK9(sK9(powerset(sK9(powerset(sK9(sK9(sK6(powerset(powerset(X0)))))))))),X0)
| empty(sK6(powerset(powerset(X0))))
| empty(sK9(powerset(sK9(sK9(sK6(powerset(powerset(X0))))))))
| empty(sK9(sK9(sK6(powerset(powerset(X0))))))
| empty(sK9(powerset(sK9(powerset(sK9(sK9(sK6(powerset(powerset(X0)))))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1116])]) ).
fof(f4430,plain,
( ! [X0] :
( empty(powerset(powerset(X0)))
| empty(sK9(sK6(powerset(powerset(X0)))))
| element(sK9(sK9(powerset(sK9(powerset(sK9(sK9(sK6(powerset(powerset(X0)))))))))),X0)
| empty(sK6(powerset(powerset(X0))))
| empty(sK9(powerset(sK9(sK9(sK6(powerset(powerset(X0))))))))
| empty(sK9(sK9(sK6(powerset(powerset(X0))))))
| empty(sK9(powerset(sK9(powerset(sK9(sK9(sK6(powerset(powerset(X0)))))))))) )
| ~ spl16_349
| ~ spl16_408 ),
inference(resolution,[],[f4404,f3579]) ).
fof(f19000,plain,
( spl16_1115
| ~ spl16_326
| ~ spl16_405 ),
inference(avatar_split_clause,[],[f4362,f4343,f3305,f18998]) ).
fof(f18998,plain,
( spl16_1115
<=> ! [X0] :
( empty(sK9(sK9(powerset(powerset(powerset(X0))))))
| element(sK9(sK7(sK9(powerset(sK9(sK9(sK9(powerset(powerset(powerset(X0)))))))))),X0)
| empty(sK9(powerset(powerset(powerset(X0)))))
| empty(sK7(sK9(powerset(sK9(sK9(sK9(powerset(powerset(powerset(X0))))))))))
| empty(sK9(sK9(sK9(powerset(powerset(powerset(X0)))))))
| empty(sK9(powerset(sK9(sK9(sK9(powerset(powerset(powerset(X0))))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1115])]) ).
fof(f4362,plain,
( ! [X0] :
( empty(sK9(sK9(powerset(powerset(powerset(X0))))))
| element(sK9(sK7(sK9(powerset(sK9(sK9(sK9(powerset(powerset(powerset(X0)))))))))),X0)
| empty(sK9(powerset(powerset(powerset(X0)))))
| empty(sK7(sK9(powerset(sK9(sK9(sK9(powerset(powerset(powerset(X0))))))))))
| empty(sK9(sK9(sK9(powerset(powerset(powerset(X0)))))))
| empty(sK9(powerset(sK9(sK9(sK9(powerset(powerset(powerset(X0))))))))) )
| ~ spl16_326
| ~ spl16_405 ),
inference(resolution,[],[f4344,f3306]) ).
fof(f18996,plain,
( spl16_1114
| ~ spl16_325
| ~ spl16_405 ),
inference(avatar_split_clause,[],[f4358,f4343,f3300,f18994]) ).
fof(f18994,plain,
( spl16_1114
<=> ! [X0] :
( empty(sK9(sK9(powerset(powerset(powerset(X0))))))
| element(sK9(sK6(sK9(powerset(sK9(sK9(sK9(powerset(powerset(powerset(X0)))))))))),X0)
| empty(sK9(powerset(powerset(powerset(X0)))))
| empty(sK6(sK9(powerset(sK9(sK9(sK9(powerset(powerset(powerset(X0))))))))))
| empty(sK9(sK9(sK9(powerset(powerset(powerset(X0)))))))
| empty(sK9(powerset(sK9(sK9(sK9(powerset(powerset(powerset(X0))))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1114])]) ).
fof(f4358,plain,
( ! [X0] :
( empty(sK9(sK9(powerset(powerset(powerset(X0))))))
| element(sK9(sK6(sK9(powerset(sK9(sK9(sK9(powerset(powerset(powerset(X0)))))))))),X0)
| empty(sK9(powerset(powerset(powerset(X0)))))
| empty(sK6(sK9(powerset(sK9(sK9(sK9(powerset(powerset(powerset(X0))))))))))
| empty(sK9(sK9(sK9(powerset(powerset(powerset(X0)))))))
| empty(sK9(powerset(sK9(sK9(sK9(powerset(powerset(powerset(X0))))))))) )
| ~ spl16_325
| ~ spl16_405 ),
inference(resolution,[],[f4344,f3301]) ).
fof(f18944,plain,
( ~ spl16_884
| ~ spl16_58
| spl16_1100 ),
inference(avatar_split_clause,[],[f18895,f18847,f476,f15900]) ).
fof(f476,plain,
( spl16_58
<=> ! [X0] :
( rel_str(sK8(X0))
| ~ rel_str(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_58])]) ).
fof(f18847,plain,
( spl16_1100
<=> rel_str(sK8(sK8(sK8(sK8(sK1))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1100])]) ).
fof(f18895,plain,
( ~ rel_str(sK8(sK8(sK8(sK1))))
| ~ spl16_58
| spl16_1100 ),
inference(resolution,[],[f18849,f477]) ).
fof(f477,plain,
( ! [X0] :
( rel_str(sK8(X0))
| ~ rel_str(X0) )
| ~ spl16_58 ),
inference(avatar_component_clause,[],[f476]) ).
fof(f18849,plain,
( ~ rel_str(sK8(sK8(sK8(sK8(sK1)))))
| spl16_1100 ),
inference(avatar_component_clause,[],[f18847]) ).
fof(f18903,plain,
( spl16_1113
| ~ spl16_150
| ~ spl16_460 ),
inference(avatar_split_clause,[],[f5529,f5484,f1218,f18901]) ).
fof(f18901,plain,
( spl16_1113
<=> ! [X0] :
( empty(powerset(powerset(X0)))
| empty(sK9(sK7(powerset(powerset(X0)))))
| empty(sK9(powerset(sK9(sK7(powerset(powerset(X0)))))))
| element(sK9(sK7(sK9(sK9(powerset(sK9(sK7(powerset(powerset(X0))))))))),X0)
| empty(sK7(powerset(powerset(X0))))
| empty(sK7(sK9(sK9(powerset(sK9(sK7(powerset(powerset(X0)))))))))
| empty(sK9(sK9(powerset(sK9(sK7(powerset(powerset(X0)))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1113])]) ).
fof(f5529,plain,
( ! [X0] :
( empty(powerset(powerset(X0)))
| empty(sK9(sK7(powerset(powerset(X0)))))
| empty(sK9(powerset(sK9(sK7(powerset(powerset(X0)))))))
| element(sK9(sK7(sK9(sK9(powerset(sK9(sK7(powerset(powerset(X0))))))))),X0)
| empty(sK7(powerset(powerset(X0))))
| empty(sK7(sK9(sK9(powerset(sK9(sK7(powerset(powerset(X0)))))))))
| empty(sK9(sK9(powerset(sK9(sK7(powerset(powerset(X0)))))))) )
| ~ spl16_150
| ~ spl16_460 ),
inference(resolution,[],[f5485,f1219]) ).
fof(f18899,plain,
( spl16_1112
| ~ spl16_149
| ~ spl16_460 ),
inference(avatar_split_clause,[],[f5522,f5484,f1214,f18897]) ).
fof(f18897,plain,
( spl16_1112
<=> ! [X0] :
( empty(powerset(powerset(X0)))
| empty(sK9(sK7(powerset(powerset(X0)))))
| empty(sK9(powerset(sK9(sK7(powerset(powerset(X0)))))))
| element(sK9(sK6(sK9(sK9(powerset(sK9(sK7(powerset(powerset(X0))))))))),X0)
| empty(sK7(powerset(powerset(X0))))
| empty(sK6(sK9(sK9(powerset(sK9(sK7(powerset(powerset(X0)))))))))
| empty(sK9(sK9(powerset(sK9(sK7(powerset(powerset(X0)))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1112])]) ).
fof(f5522,plain,
( ! [X0] :
( empty(powerset(powerset(X0)))
| empty(sK9(sK7(powerset(powerset(X0)))))
| empty(sK9(powerset(sK9(sK7(powerset(powerset(X0)))))))
| element(sK9(sK6(sK9(sK9(powerset(sK9(sK7(powerset(powerset(X0))))))))),X0)
| empty(sK7(powerset(powerset(X0))))
| empty(sK6(sK9(sK9(powerset(sK9(sK7(powerset(powerset(X0)))))))))
| empty(sK9(sK9(powerset(sK9(sK7(powerset(powerset(X0)))))))) )
| ~ spl16_149
| ~ spl16_460 ),
inference(resolution,[],[f5485,f1215]) ).
fof(f18894,plain,
( spl16_1111
| ~ spl16_150
| ~ spl16_459 ),
inference(avatar_split_clause,[],[f5504,f5480,f1218,f18892]) ).
fof(f18892,plain,
( spl16_1111
<=> ! [X0] :
( empty(powerset(powerset(X0)))
| empty(sK9(sK6(powerset(powerset(X0)))))
| empty(sK9(powerset(sK9(sK6(powerset(powerset(X0)))))))
| element(sK9(sK7(sK9(sK9(powerset(sK9(sK6(powerset(powerset(X0))))))))),X0)
| empty(sK6(powerset(powerset(X0))))
| empty(sK7(sK9(sK9(powerset(sK9(sK6(powerset(powerset(X0)))))))))
| empty(sK9(sK9(powerset(sK9(sK6(powerset(powerset(X0)))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1111])]) ).
fof(f5504,plain,
( ! [X0] :
( empty(powerset(powerset(X0)))
| empty(sK9(sK6(powerset(powerset(X0)))))
| empty(sK9(powerset(sK9(sK6(powerset(powerset(X0)))))))
| element(sK9(sK7(sK9(sK9(powerset(sK9(sK6(powerset(powerset(X0))))))))),X0)
| empty(sK6(powerset(powerset(X0))))
| empty(sK7(sK9(sK9(powerset(sK9(sK6(powerset(powerset(X0)))))))))
| empty(sK9(sK9(powerset(sK9(sK6(powerset(powerset(X0)))))))) )
| ~ spl16_150
| ~ spl16_459 ),
inference(resolution,[],[f5481,f1219]) ).
fof(f18890,plain,
( spl16_1110
| ~ spl16_149
| ~ spl16_459 ),
inference(avatar_split_clause,[],[f5497,f5480,f1214,f18888]) ).
fof(f18888,plain,
( spl16_1110
<=> ! [X0] :
( empty(powerset(powerset(X0)))
| empty(sK9(sK6(powerset(powerset(X0)))))
| empty(sK9(powerset(sK9(sK6(powerset(powerset(X0)))))))
| element(sK9(sK6(sK9(sK9(powerset(sK9(sK6(powerset(powerset(X0))))))))),X0)
| empty(sK6(powerset(powerset(X0))))
| empty(sK6(sK9(sK9(powerset(sK9(sK6(powerset(powerset(X0)))))))))
| empty(sK9(sK9(powerset(sK9(sK6(powerset(powerset(X0)))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1110])]) ).
fof(f5497,plain,
( ! [X0] :
( empty(powerset(powerset(X0)))
| empty(sK9(sK6(powerset(powerset(X0)))))
| empty(sK9(powerset(sK9(sK6(powerset(powerset(X0)))))))
| element(sK9(sK6(sK9(sK9(powerset(sK9(sK6(powerset(powerset(X0))))))))),X0)
| empty(sK6(powerset(powerset(X0))))
| empty(sK6(sK9(sK9(powerset(sK9(sK6(powerset(powerset(X0)))))))))
| empty(sK9(sK9(powerset(sK9(sK6(powerset(powerset(X0)))))))) )
| ~ spl16_149
| ~ spl16_459 ),
inference(resolution,[],[f5481,f1215]) ).
fof(f18886,plain,
( spl16_1109
| ~ spl16_152
| ~ spl16_451 ),
inference(avatar_split_clause,[],[f5380,f5221,f1257,f18884]) ).
fof(f18884,plain,
( spl16_1109
<=> ! [X0] :
( empty(sK7(sK9(sK9(powerset(powerset(powerset(X0)))))))
| empty(sK9(sK9(powerset(powerset(powerset(X0))))))
| element(sK9(sK9(powerset(sK9(sK7(sK9(sK9(powerset(powerset(powerset(X0)))))))))),X0)
| empty(sK9(powerset(powerset(powerset(X0)))))
| empty(sK9(sK7(sK9(sK9(powerset(powerset(powerset(X0))))))))
| empty(sK9(powerset(sK9(sK7(sK9(sK9(powerset(powerset(powerset(X0)))))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1109])]) ).
fof(f5380,plain,
( ! [X0] :
( empty(sK7(sK9(sK9(powerset(powerset(powerset(X0)))))))
| empty(sK9(sK9(powerset(powerset(powerset(X0))))))
| element(sK9(sK9(powerset(sK9(sK7(sK9(sK9(powerset(powerset(powerset(X0)))))))))),X0)
| empty(sK9(powerset(powerset(powerset(X0)))))
| empty(sK9(sK7(sK9(sK9(powerset(powerset(powerset(X0))))))))
| empty(sK9(powerset(sK9(sK7(sK9(sK9(powerset(powerset(powerset(X0)))))))))) )
| ~ spl16_152
| ~ spl16_451 ),
inference(resolution,[],[f5222,f1258]) ).
fof(f18882,plain,
( spl16_1108
| ~ spl16_152
| ~ spl16_450 ),
inference(avatar_split_clause,[],[f5355,f5217,f1257,f18880]) ).
fof(f18880,plain,
( spl16_1108
<=> ! [X0] :
( empty(sK6(sK9(sK9(powerset(powerset(powerset(X0)))))))
| empty(sK9(sK9(powerset(powerset(powerset(X0))))))
| element(sK9(sK9(powerset(sK9(sK6(sK9(sK9(powerset(powerset(powerset(X0)))))))))),X0)
| empty(sK9(powerset(powerset(powerset(X0)))))
| empty(sK9(sK6(sK9(sK9(powerset(powerset(powerset(X0))))))))
| empty(sK9(powerset(sK9(sK6(sK9(sK9(powerset(powerset(powerset(X0)))))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1108])]) ).
fof(f5355,plain,
( ! [X0] :
( empty(sK6(sK9(sK9(powerset(powerset(powerset(X0)))))))
| empty(sK9(sK9(powerset(powerset(powerset(X0))))))
| element(sK9(sK9(powerset(sK9(sK6(sK9(sK9(powerset(powerset(powerset(X0)))))))))),X0)
| empty(sK9(powerset(powerset(powerset(X0)))))
| empty(sK9(sK6(sK9(sK9(powerset(powerset(powerset(X0))))))))
| empty(sK9(powerset(sK9(sK6(sK9(sK9(powerset(powerset(powerset(X0)))))))))) )
| ~ spl16_152
| ~ spl16_450 ),
inference(resolution,[],[f5218,f1258]) ).
fof(f18878,plain,
( spl16_1107
| ~ spl16_173
| ~ spl16_418 ),
inference(avatar_split_clause,[],[f4744,f4669,f1448,f18876]) ).
fof(f18876,plain,
( spl16_1107
<=> ! [X0] :
( empty(sK7(sK9(sK9(powerset(powerset(sK9(sK9(powerset(powerset(X0))))))))))
| empty(sK9(sK9(powerset(powerset(sK9(sK9(powerset(powerset(X0)))))))))
| empty(sK9(sK9(powerset(powerset(X0)))))
| empty(sK9(powerset(powerset(sK9(sK9(powerset(powerset(X0))))))))
| element(sK9(sK7(sK9(sK9(powerset(powerset(sK9(sK9(powerset(powerset(X0)))))))))),X0)
| empty(sK9(powerset(powerset(X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1107])]) ).
fof(f4744,plain,
( ! [X0] :
( empty(sK7(sK9(sK9(powerset(powerset(sK9(sK9(powerset(powerset(X0))))))))))
| empty(sK9(sK9(powerset(powerset(sK9(sK9(powerset(powerset(X0)))))))))
| empty(sK9(sK9(powerset(powerset(X0)))))
| empty(sK9(powerset(powerset(sK9(sK9(powerset(powerset(X0))))))))
| element(sK9(sK7(sK9(sK9(powerset(powerset(sK9(sK9(powerset(powerset(X0)))))))))),X0)
| empty(sK9(powerset(powerset(X0)))) )
| ~ spl16_173
| ~ spl16_418 ),
inference(resolution,[],[f4670,f1449]) ).
fof(f18874,plain,
( spl16_1106
| ~ spl16_173
| ~ spl16_417 ),
inference(avatar_split_clause,[],[f4699,f4665,f1448,f18872]) ).
fof(f18872,plain,
( spl16_1106
<=> ! [X0] :
( empty(sK6(sK9(sK9(powerset(powerset(sK9(sK9(powerset(powerset(X0))))))))))
| empty(sK9(sK9(powerset(powerset(sK9(sK9(powerset(powerset(X0)))))))))
| empty(sK9(sK9(powerset(powerset(X0)))))
| empty(sK9(powerset(powerset(sK9(sK9(powerset(powerset(X0))))))))
| element(sK9(sK6(sK9(sK9(powerset(powerset(sK9(sK9(powerset(powerset(X0)))))))))),X0)
| empty(sK9(powerset(powerset(X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1106])]) ).
fof(f4699,plain,
( ! [X0] :
( empty(sK6(sK9(sK9(powerset(powerset(sK9(sK9(powerset(powerset(X0))))))))))
| empty(sK9(sK9(powerset(powerset(sK9(sK9(powerset(powerset(X0)))))))))
| empty(sK9(sK9(powerset(powerset(X0)))))
| empty(sK9(powerset(powerset(sK9(sK9(powerset(powerset(X0))))))))
| element(sK9(sK6(sK9(sK9(powerset(powerset(sK9(sK9(powerset(powerset(X0)))))))))),X0)
| empty(sK9(powerset(powerset(X0)))) )
| ~ spl16_173
| ~ spl16_417 ),
inference(resolution,[],[f4666,f1449]) ).
fof(f18870,plain,
( spl16_1105
| ~ spl16_321
| ~ spl16_405 ),
inference(avatar_split_clause,[],[f4365,f4343,f3175,f18868]) ).
fof(f18868,plain,
( spl16_1105
<=> ! [X0] :
( empty(sK9(sK9(powerset(powerset(powerset(X0))))))
| element(sK9(sK9(powerset(sK7(sK9(sK9(sK9(powerset(powerset(powerset(X0)))))))))),X0)
| empty(sK9(powerset(powerset(powerset(X0)))))
| empty(sK7(sK9(sK9(sK9(powerset(powerset(powerset(X0))))))))
| empty(sK9(sK9(sK9(powerset(powerset(powerset(X0)))))))
| empty(sK9(powerset(sK7(sK9(sK9(sK9(powerset(powerset(powerset(X0)))))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1105])]) ).
fof(f4365,plain,
( ! [X0] :
( empty(sK9(sK9(powerset(powerset(powerset(X0))))))
| element(sK9(sK9(powerset(sK7(sK9(sK9(sK9(powerset(powerset(powerset(X0)))))))))),X0)
| empty(sK9(powerset(powerset(powerset(X0)))))
| empty(sK7(sK9(sK9(sK9(powerset(powerset(powerset(X0))))))))
| empty(sK9(sK9(sK9(powerset(powerset(powerset(X0)))))))
| empty(sK9(powerset(sK7(sK9(sK9(sK9(powerset(powerset(powerset(X0)))))))))) )
| ~ spl16_321
| ~ spl16_405 ),
inference(resolution,[],[f4344,f3176]) ).
fof(f18866,plain,
( spl16_1104
| ~ spl16_320
| ~ spl16_405 ),
inference(avatar_split_clause,[],[f4364,f4343,f3171,f18864]) ).
fof(f18864,plain,
( spl16_1104
<=> ! [X0] :
( empty(sK9(sK9(powerset(powerset(powerset(X0))))))
| element(sK9(sK9(powerset(sK6(sK9(sK9(sK9(powerset(powerset(powerset(X0)))))))))),X0)
| empty(sK9(powerset(powerset(powerset(X0)))))
| empty(sK6(sK9(sK9(sK9(powerset(powerset(powerset(X0))))))))
| empty(sK9(sK9(sK9(powerset(powerset(powerset(X0)))))))
| empty(sK9(powerset(sK6(sK9(sK9(sK9(powerset(powerset(powerset(X0)))))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1104])]) ).
fof(f4364,plain,
( ! [X0] :
( empty(sK9(sK9(powerset(powerset(powerset(X0))))))
| element(sK9(sK9(powerset(sK6(sK9(sK9(sK9(powerset(powerset(powerset(X0)))))))))),X0)
| empty(sK9(powerset(powerset(powerset(X0)))))
| empty(sK6(sK9(sK9(sK9(powerset(powerset(powerset(X0))))))))
| empty(sK9(sK9(sK9(powerset(powerset(powerset(X0)))))))
| empty(sK9(powerset(sK6(sK9(sK9(sK9(powerset(powerset(powerset(X0)))))))))) )
| ~ spl16_320
| ~ spl16_405 ),
inference(resolution,[],[f4344,f3172]) ).
fof(f18862,plain,
( spl16_1103
| ~ spl16_326
| ~ spl16_390 ),
inference(avatar_split_clause,[],[f4260,f4167,f3305,f18860]) ).
fof(f18860,plain,
( spl16_1103
<=> ! [X0] :
( empty(sK9(powerset(powerset(X0))))
| element(sK9(sK7(sK9(powerset(sK9(sK9(powerset(sK9(powerset(powerset(X0)))))))))),X0)
| empty(sK9(powerset(sK9(powerset(powerset(X0))))))
| empty(sK7(sK9(powerset(sK9(sK9(powerset(sK9(powerset(powerset(X0))))))))))
| empty(sK9(sK9(powerset(sK9(powerset(powerset(X0)))))))
| empty(sK9(powerset(sK9(sK9(powerset(sK9(powerset(powerset(X0))))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1103])]) ).
fof(f4260,plain,
( ! [X0] :
( empty(sK9(powerset(powerset(X0))))
| element(sK9(sK7(sK9(powerset(sK9(sK9(powerset(sK9(powerset(powerset(X0)))))))))),X0)
| empty(sK9(powerset(sK9(powerset(powerset(X0))))))
| empty(sK7(sK9(powerset(sK9(sK9(powerset(sK9(powerset(powerset(X0))))))))))
| empty(sK9(sK9(powerset(sK9(powerset(powerset(X0)))))))
| empty(sK9(powerset(sK9(sK9(powerset(sK9(powerset(powerset(X0))))))))) )
| ~ spl16_326
| ~ spl16_390 ),
inference(resolution,[],[f4168,f3306]) ).
fof(f18858,plain,
( spl16_1102
| ~ spl16_325
| ~ spl16_390 ),
inference(avatar_split_clause,[],[f4256,f4167,f3300,f18856]) ).
fof(f18856,plain,
( spl16_1102
<=> ! [X0] :
( empty(sK9(powerset(powerset(X0))))
| element(sK9(sK6(sK9(powerset(sK9(sK9(powerset(sK9(powerset(powerset(X0)))))))))),X0)
| empty(sK9(powerset(sK9(powerset(powerset(X0))))))
| empty(sK6(sK9(powerset(sK9(sK9(powerset(sK9(powerset(powerset(X0))))))))))
| empty(sK9(sK9(powerset(sK9(powerset(powerset(X0)))))))
| empty(sK9(powerset(sK9(sK9(powerset(sK9(powerset(powerset(X0))))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1102])]) ).
fof(f4256,plain,
( ! [X0] :
( empty(sK9(powerset(powerset(X0))))
| element(sK9(sK6(sK9(powerset(sK9(sK9(powerset(sK9(powerset(powerset(X0)))))))))),X0)
| empty(sK9(powerset(sK9(powerset(powerset(X0))))))
| empty(sK6(sK9(powerset(sK9(sK9(powerset(sK9(powerset(powerset(X0))))))))))
| empty(sK9(sK9(powerset(sK9(powerset(powerset(X0)))))))
| empty(sK9(powerset(sK9(sK9(powerset(sK9(powerset(powerset(X0))))))))) )
| ~ spl16_325
| ~ spl16_390 ),
inference(resolution,[],[f4168,f3301]) ).
fof(f18854,plain,
( ~ spl16_1100
| spl16_1101
| ~ spl16_43
| ~ spl16_1097 ),
inference(avatar_split_clause,[],[f18694,f18637,f370,f18851,f18847]) ).
fof(f370,plain,
( spl16_43
<=> ! [X0] :
( relation_of2_as_subset(the_InternalRel(X0),the_carrier(X0),the_carrier(X0))
| ~ rel_str(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_43])]) ).
fof(f18637,plain,
( spl16_1097
<=> sK14 = the_carrier(sK8(sK8(sK8(sK8(sK1))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1097])]) ).
fof(f18694,plain,
( relation_of2_as_subset(the_InternalRel(sK8(sK8(sK8(sK8(sK1))))),sK14,sK14)
| ~ rel_str(sK8(sK8(sK8(sK8(sK1)))))
| ~ spl16_43
| ~ spl16_1097 ),
inference(superposition,[],[f371,f18639]) ).
fof(f18639,plain,
( sK14 = the_carrier(sK8(sK8(sK8(sK8(sK1)))))
| ~ spl16_1097 ),
inference(avatar_component_clause,[],[f18637]) ).
fof(f371,plain,
( ! [X0] :
( relation_of2_as_subset(the_InternalRel(X0),the_carrier(X0),the_carrier(X0))
| ~ rel_str(X0) )
| ~ spl16_43 ),
inference(avatar_component_clause,[],[f370]) ).
fof(f18845,plain,
( spl16_1099
| ~ spl16_362
| ~ spl16_388 ),
inference(avatar_split_clause,[],[f4251,f4159,f3670,f18843]) ).
fof(f18843,plain,
( spl16_1099
<=> ! [X0] :
( empty(sK7(powerset(X0)))
| empty(powerset(X0))
| element(sK9(sK9(sK9(powerset(powerset(sK9(sK9(powerset(sK7(powerset(X0)))))))))),X0)
| empty(sK9(powerset(sK7(powerset(X0)))))
| empty(sK9(sK9(powerset(powerset(sK9(sK9(powerset(sK7(powerset(X0))))))))))
| empty(sK9(sK9(powerset(sK7(powerset(X0))))))
| empty(sK9(powerset(powerset(sK9(sK9(powerset(sK7(powerset(X0))))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1099])]) ).
fof(f4251,plain,
( ! [X0] :
( empty(sK7(powerset(X0)))
| empty(powerset(X0))
| element(sK9(sK9(sK9(powerset(powerset(sK9(sK9(powerset(sK7(powerset(X0)))))))))),X0)
| empty(sK9(powerset(sK7(powerset(X0)))))
| empty(sK9(sK9(powerset(powerset(sK9(sK9(powerset(sK7(powerset(X0))))))))))
| empty(sK9(sK9(powerset(sK7(powerset(X0))))))
| empty(sK9(powerset(powerset(sK9(sK9(powerset(sK7(powerset(X0))))))))) )
| ~ spl16_362
| ~ spl16_388 ),
inference(resolution,[],[f4160,f3671]) ).
fof(f18841,plain,
( spl16_1098
| ~ spl16_362
| ~ spl16_387 ),
inference(avatar_split_clause,[],[f4235,f4155,f3670,f18839]) ).
fof(f18839,plain,
( spl16_1098
<=> ! [X0] :
( empty(sK6(powerset(X0)))
| empty(powerset(X0))
| element(sK9(sK9(sK9(powerset(powerset(sK9(sK9(powerset(sK6(powerset(X0)))))))))),X0)
| empty(sK9(powerset(sK6(powerset(X0)))))
| empty(sK9(sK9(powerset(powerset(sK9(sK9(powerset(sK6(powerset(X0))))))))))
| empty(sK9(sK9(powerset(sK6(powerset(X0))))))
| empty(sK9(powerset(powerset(sK9(sK9(powerset(sK6(powerset(X0))))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1098])]) ).
fof(f4235,plain,
( ! [X0] :
( empty(sK6(powerset(X0)))
| empty(powerset(X0))
| element(sK9(sK9(sK9(powerset(powerset(sK9(sK9(powerset(sK6(powerset(X0)))))))))),X0)
| empty(sK9(powerset(sK6(powerset(X0)))))
| empty(sK9(sK9(powerset(powerset(sK9(sK9(powerset(sK6(powerset(X0))))))))))
| empty(sK9(sK9(powerset(sK6(powerset(X0))))))
| empty(sK9(powerset(powerset(sK9(sK9(powerset(sK6(powerset(X0))))))))) )
| ~ spl16_362
| ~ spl16_387 ),
inference(resolution,[],[f4156,f3671]) ).
fof(f18640,plain,
( spl16_1097
| ~ spl16_884
| ~ spl16_12
| ~ spl16_472
| ~ spl16_881 ),
inference(avatar_split_clause,[],[f15808,f15704,f5620,f213,f15900,f18637]) ).
fof(f5620,plain,
( spl16_472
<=> ! [X0] :
( sK14 = the_carrier(sK8(X0))
| ~ rel_str(X0)
| ~ empty(the_carrier(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_472])]) ).
fof(f15704,plain,
( spl16_881
<=> sK14 = the_carrier(sK8(sK8(sK8(sK1)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_881])]) ).
fof(f15808,plain,
( ~ empty(sK14)
| ~ rel_str(sK8(sK8(sK8(sK1))))
| sK14 = the_carrier(sK8(sK8(sK8(sK8(sK1)))))
| ~ spl16_472
| ~ spl16_881 ),
inference(superposition,[],[f5621,f15706]) ).
fof(f15706,plain,
( sK14 = the_carrier(sK8(sK8(sK8(sK1))))
| ~ spl16_881 ),
inference(avatar_component_clause,[],[f15704]) ).
fof(f5621,plain,
( ! [X0] :
( ~ empty(the_carrier(X0))
| ~ rel_str(X0)
| sK14 = the_carrier(sK8(X0)) )
| ~ spl16_472 ),
inference(avatar_component_clause,[],[f5620]) ).
fof(f18595,plain,
( spl16_1096
| ~ spl16_177
| ~ spl16_427 ),
inference(avatar_split_clause,[],[f4937,f4893,f1476,f18593]) ).
fof(f18593,plain,
( spl16_1096
<=> ! [X0] :
( empty(sK9(sK9(powerset(powerset(sK9(sK7(powerset(X0))))))))
| empty(sK9(powerset(sK9(sK9(powerset(powerset(sK9(sK7(powerset(X0))))))))))
| empty(sK9(sK7(powerset(X0))))
| empty(sK9(powerset(powerset(sK9(sK7(powerset(X0)))))))
| empty(sK7(powerset(X0)))
| element(sK9(sK9(powerset(sK9(sK9(powerset(powerset(sK9(sK7(powerset(X0)))))))))),X0)
| empty(powerset(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1096])]) ).
fof(f4937,plain,
( ! [X0] :
( empty(sK9(sK9(powerset(powerset(sK9(sK7(powerset(X0))))))))
| empty(sK9(powerset(sK9(sK9(powerset(powerset(sK9(sK7(powerset(X0))))))))))
| empty(sK9(sK7(powerset(X0))))
| empty(sK9(powerset(powerset(sK9(sK7(powerset(X0)))))))
| empty(sK7(powerset(X0)))
| element(sK9(sK9(powerset(sK9(sK9(powerset(powerset(sK9(sK7(powerset(X0)))))))))),X0)
| empty(powerset(X0)) )
| ~ spl16_177
| ~ spl16_427 ),
inference(resolution,[],[f4894,f1477]) ).
fof(f18591,plain,
( spl16_1095
| ~ spl16_176
| ~ spl16_427 ),
inference(avatar_split_clause,[],[f4929,f4893,f1472,f18589]) ).
fof(f18589,plain,
( spl16_1095
<=> ! [X0] :
( empty(sK9(sK9(powerset(powerset(sK9(sK6(powerset(X0))))))))
| empty(sK9(powerset(sK9(sK9(powerset(powerset(sK9(sK6(powerset(X0))))))))))
| empty(sK9(sK6(powerset(X0))))
| empty(sK9(powerset(powerset(sK9(sK6(powerset(X0)))))))
| empty(sK6(powerset(X0)))
| element(sK9(sK9(powerset(sK9(sK9(powerset(powerset(sK9(sK6(powerset(X0)))))))))),X0)
| empty(powerset(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1095])]) ).
fof(f4929,plain,
( ! [X0] :
( empty(sK9(sK9(powerset(powerset(sK9(sK6(powerset(X0))))))))
| empty(sK9(powerset(sK9(sK9(powerset(powerset(sK9(sK6(powerset(X0))))))))))
| empty(sK9(sK6(powerset(X0))))
| empty(sK9(powerset(powerset(sK9(sK6(powerset(X0)))))))
| empty(sK6(powerset(X0)))
| element(sK9(sK9(powerset(sK9(sK9(powerset(powerset(sK9(sK6(powerset(X0)))))))))),X0)
| empty(powerset(X0)) )
| ~ spl16_176
| ~ spl16_427 ),
inference(resolution,[],[f4894,f1473]) ).
fof(f18582,plain,
( spl16_1094
| ~ spl16_177
| ~ spl16_415 ),
inference(avatar_split_clause,[],[f4634,f4477,f1476,f18580]) ).
fof(f18580,plain,
( spl16_1094
<=> ! [X0] :
( empty(powerset(sK9(sK7(powerset(X0)))))
| empty(sK7(sK9(sK7(powerset(sK9(sK7(powerset(X0))))))))
| empty(sK9(sK7(powerset(sK9(sK7(powerset(X0)))))))
| empty(sK9(sK7(powerset(X0))))
| empty(sK7(powerset(sK9(sK7(powerset(X0))))))
| empty(sK7(powerset(X0)))
| element(sK9(sK7(sK9(sK7(powerset(sK9(sK7(powerset(X0)))))))),X0)
| empty(powerset(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1094])]) ).
fof(f4634,plain,
( ! [X0] :
( empty(powerset(sK9(sK7(powerset(X0)))))
| empty(sK7(sK9(sK7(powerset(sK9(sK7(powerset(X0))))))))
| empty(sK9(sK7(powerset(sK9(sK7(powerset(X0)))))))
| empty(sK9(sK7(powerset(X0))))
| empty(sK7(powerset(sK9(sK7(powerset(X0))))))
| empty(sK7(powerset(X0)))
| element(sK9(sK7(sK9(sK7(powerset(sK9(sK7(powerset(X0)))))))),X0)
| empty(powerset(X0)) )
| ~ spl16_177
| ~ spl16_415 ),
inference(resolution,[],[f4478,f1477]) ).
fof(f18578,plain,
( spl16_1093
| ~ spl16_176
| ~ spl16_415 ),
inference(avatar_split_clause,[],[f4626,f4477,f1472,f18576]) ).
fof(f18576,plain,
( spl16_1093
<=> ! [X0] :
( empty(powerset(sK9(sK6(powerset(X0)))))
| empty(sK7(sK9(sK7(powerset(sK9(sK6(powerset(X0))))))))
| empty(sK9(sK7(powerset(sK9(sK6(powerset(X0)))))))
| empty(sK9(sK6(powerset(X0))))
| empty(sK7(powerset(sK9(sK6(powerset(X0))))))
| empty(sK6(powerset(X0)))
| element(sK9(sK7(sK9(sK7(powerset(sK9(sK6(powerset(X0)))))))),X0)
| empty(powerset(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1093])]) ).
fof(f4626,plain,
( ! [X0] :
( empty(powerset(sK9(sK6(powerset(X0)))))
| empty(sK7(sK9(sK7(powerset(sK9(sK6(powerset(X0))))))))
| empty(sK9(sK7(powerset(sK9(sK6(powerset(X0)))))))
| empty(sK9(sK6(powerset(X0))))
| empty(sK7(powerset(sK9(sK6(powerset(X0))))))
| empty(sK6(powerset(X0)))
| element(sK9(sK7(sK9(sK7(powerset(sK9(sK6(powerset(X0)))))))),X0)
| empty(powerset(X0)) )
| ~ spl16_176
| ~ spl16_415 ),
inference(resolution,[],[f4478,f1473]) ).
fof(f18574,plain,
( spl16_1092
| ~ spl16_177
| ~ spl16_414 ),
inference(avatar_split_clause,[],[f4589,f4473,f1476,f18572]) ).
fof(f18572,plain,
( spl16_1092
<=> ! [X0] :
( empty(powerset(sK9(sK7(powerset(X0)))))
| empty(sK6(sK9(sK7(powerset(sK9(sK7(powerset(X0))))))))
| empty(sK9(sK7(powerset(sK9(sK7(powerset(X0)))))))
| empty(sK9(sK7(powerset(X0))))
| empty(sK7(powerset(sK9(sK7(powerset(X0))))))
| empty(sK7(powerset(X0)))
| element(sK9(sK6(sK9(sK7(powerset(sK9(sK7(powerset(X0)))))))),X0)
| empty(powerset(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1092])]) ).
fof(f4589,plain,
( ! [X0] :
( empty(powerset(sK9(sK7(powerset(X0)))))
| empty(sK6(sK9(sK7(powerset(sK9(sK7(powerset(X0))))))))
| empty(sK9(sK7(powerset(sK9(sK7(powerset(X0)))))))
| empty(sK9(sK7(powerset(X0))))
| empty(sK7(powerset(sK9(sK7(powerset(X0))))))
| empty(sK7(powerset(X0)))
| element(sK9(sK6(sK9(sK7(powerset(sK9(sK7(powerset(X0)))))))),X0)
| empty(powerset(X0)) )
| ~ spl16_177
| ~ spl16_414 ),
inference(resolution,[],[f4474,f1477]) ).
fof(f18570,plain,
( spl16_1091
| ~ spl16_176
| ~ spl16_414 ),
inference(avatar_split_clause,[],[f4581,f4473,f1472,f18568]) ).
fof(f18568,plain,
( spl16_1091
<=> ! [X0] :
( empty(powerset(sK9(sK6(powerset(X0)))))
| empty(sK6(sK9(sK7(powerset(sK9(sK6(powerset(X0))))))))
| empty(sK9(sK7(powerset(sK9(sK6(powerset(X0)))))))
| empty(sK9(sK6(powerset(X0))))
| empty(sK7(powerset(sK9(sK6(powerset(X0))))))
| empty(sK6(powerset(X0)))
| element(sK9(sK6(sK9(sK7(powerset(sK9(sK6(powerset(X0)))))))),X0)
| empty(powerset(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1091])]) ).
fof(f4581,plain,
( ! [X0] :
( empty(powerset(sK9(sK6(powerset(X0)))))
| empty(sK6(sK9(sK7(powerset(sK9(sK6(powerset(X0))))))))
| empty(sK9(sK7(powerset(sK9(sK6(powerset(X0)))))))
| empty(sK9(sK6(powerset(X0))))
| empty(sK7(powerset(sK9(sK6(powerset(X0))))))
| empty(sK6(powerset(X0)))
| element(sK9(sK6(sK9(sK7(powerset(sK9(sK6(powerset(X0)))))))),X0)
| empty(powerset(X0)) )
| ~ spl16_176
| ~ spl16_414 ),
inference(resolution,[],[f4474,f1473]) ).
fof(f18566,plain,
( spl16_1090
| ~ spl16_177
| ~ spl16_413 ),
inference(avatar_split_clause,[],[f4544,f4469,f1476,f18564]) ).
fof(f18564,plain,
( spl16_1090
<=> ! [X0] :
( empty(powerset(sK9(sK7(powerset(X0)))))
| empty(sK7(sK9(sK6(powerset(sK9(sK7(powerset(X0))))))))
| empty(sK9(sK6(powerset(sK9(sK7(powerset(X0)))))))
| empty(sK9(sK7(powerset(X0))))
| empty(sK6(powerset(sK9(sK7(powerset(X0))))))
| empty(sK7(powerset(X0)))
| element(sK9(sK7(sK9(sK6(powerset(sK9(sK7(powerset(X0)))))))),X0)
| empty(powerset(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1090])]) ).
fof(f4544,plain,
( ! [X0] :
( empty(powerset(sK9(sK7(powerset(X0)))))
| empty(sK7(sK9(sK6(powerset(sK9(sK7(powerset(X0))))))))
| empty(sK9(sK6(powerset(sK9(sK7(powerset(X0)))))))
| empty(sK9(sK7(powerset(X0))))
| empty(sK6(powerset(sK9(sK7(powerset(X0))))))
| empty(sK7(powerset(X0)))
| element(sK9(sK7(sK9(sK6(powerset(sK9(sK7(powerset(X0)))))))),X0)
| empty(powerset(X0)) )
| ~ spl16_177
| ~ spl16_413 ),
inference(resolution,[],[f4470,f1477]) ).
fof(f18562,plain,
( spl16_1089
| ~ spl16_176
| ~ spl16_413 ),
inference(avatar_split_clause,[],[f4536,f4469,f1472,f18560]) ).
fof(f18560,plain,
( spl16_1089
<=> ! [X0] :
( empty(powerset(sK9(sK6(powerset(X0)))))
| empty(sK7(sK9(sK6(powerset(sK9(sK6(powerset(X0))))))))
| empty(sK9(sK6(powerset(sK9(sK6(powerset(X0)))))))
| empty(sK9(sK6(powerset(X0))))
| empty(sK6(powerset(sK9(sK6(powerset(X0))))))
| empty(sK6(powerset(X0)))
| element(sK9(sK7(sK9(sK6(powerset(sK9(sK6(powerset(X0)))))))),X0)
| empty(powerset(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1089])]) ).
fof(f4536,plain,
( ! [X0] :
( empty(powerset(sK9(sK6(powerset(X0)))))
| empty(sK7(sK9(sK6(powerset(sK9(sK6(powerset(X0))))))))
| empty(sK9(sK6(powerset(sK9(sK6(powerset(X0)))))))
| empty(sK9(sK6(powerset(X0))))
| empty(sK6(powerset(sK9(sK6(powerset(X0))))))
| empty(sK6(powerset(X0)))
| element(sK9(sK7(sK9(sK6(powerset(sK9(sK6(powerset(X0)))))))),X0)
| empty(powerset(X0)) )
| ~ spl16_176
| ~ spl16_413 ),
inference(resolution,[],[f4470,f1473]) ).
fof(f18558,plain,
( spl16_1088
| ~ spl16_177
| ~ spl16_412 ),
inference(avatar_split_clause,[],[f4499,f4465,f1476,f18556]) ).
fof(f18556,plain,
( spl16_1088
<=> ! [X0] :
( empty(powerset(sK9(sK7(powerset(X0)))))
| empty(sK6(sK9(sK6(powerset(sK9(sK7(powerset(X0))))))))
| empty(sK9(sK6(powerset(sK9(sK7(powerset(X0)))))))
| empty(sK9(sK7(powerset(X0))))
| empty(sK6(powerset(sK9(sK7(powerset(X0))))))
| empty(sK7(powerset(X0)))
| element(sK9(sK6(sK9(sK6(powerset(sK9(sK7(powerset(X0)))))))),X0)
| empty(powerset(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1088])]) ).
fof(f4499,plain,
( ! [X0] :
( empty(powerset(sK9(sK7(powerset(X0)))))
| empty(sK6(sK9(sK6(powerset(sK9(sK7(powerset(X0))))))))
| empty(sK9(sK6(powerset(sK9(sK7(powerset(X0)))))))
| empty(sK9(sK7(powerset(X0))))
| empty(sK6(powerset(sK9(sK7(powerset(X0))))))
| empty(sK7(powerset(X0)))
| element(sK9(sK6(sK9(sK6(powerset(sK9(sK7(powerset(X0)))))))),X0)
| empty(powerset(X0)) )
| ~ spl16_177
| ~ spl16_412 ),
inference(resolution,[],[f4466,f1477]) ).
fof(f18554,plain,
( spl16_1087
| ~ spl16_176
| ~ spl16_412 ),
inference(avatar_split_clause,[],[f4491,f4465,f1472,f18552]) ).
fof(f18552,plain,
( spl16_1087
<=> ! [X0] :
( empty(powerset(sK9(sK6(powerset(X0)))))
| empty(sK6(sK9(sK6(powerset(sK9(sK6(powerset(X0))))))))
| empty(sK9(sK6(powerset(sK9(sK6(powerset(X0)))))))
| empty(sK9(sK6(powerset(X0))))
| empty(sK6(powerset(sK9(sK6(powerset(X0))))))
| empty(sK6(powerset(X0)))
| element(sK9(sK6(sK9(sK6(powerset(sK9(sK6(powerset(X0)))))))),X0)
| empty(powerset(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1087])]) ).
fof(f4491,plain,
( ! [X0] :
( empty(powerset(sK9(sK6(powerset(X0)))))
| empty(sK6(sK9(sK6(powerset(sK9(sK6(powerset(X0))))))))
| empty(sK9(sK6(powerset(sK9(sK6(powerset(X0)))))))
| empty(sK9(sK6(powerset(X0))))
| empty(sK6(powerset(sK9(sK6(powerset(X0))))))
| empty(sK6(powerset(X0)))
| element(sK9(sK6(sK9(sK6(powerset(sK9(sK6(powerset(X0)))))))),X0)
| empty(powerset(X0)) )
| ~ spl16_176
| ~ spl16_412 ),
inference(resolution,[],[f4466,f1473]) ).
fof(f18550,plain,
( spl16_1086
| ~ spl16_326
| ~ spl16_409 ),
inference(avatar_split_clause,[],[f4442,f4407,f3305,f18548]) ).
fof(f18548,plain,
( spl16_1086
<=> ! [X0] :
( empty(powerset(powerset(X0)))
| empty(sK9(sK7(powerset(powerset(X0)))))
| element(sK9(sK7(sK9(powerset(sK9(sK9(sK7(powerset(powerset(X0))))))))),X0)
| empty(sK7(powerset(powerset(X0))))
| empty(sK7(sK9(powerset(sK9(sK9(sK7(powerset(powerset(X0)))))))))
| empty(sK9(sK9(sK7(powerset(powerset(X0))))))
| empty(sK9(powerset(sK9(sK9(sK7(powerset(powerset(X0)))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1086])]) ).
fof(f4442,plain,
( ! [X0] :
( empty(powerset(powerset(X0)))
| empty(sK9(sK7(powerset(powerset(X0)))))
| element(sK9(sK7(sK9(powerset(sK9(sK9(sK7(powerset(powerset(X0))))))))),X0)
| empty(sK7(powerset(powerset(X0))))
| empty(sK7(sK9(powerset(sK9(sK9(sK7(powerset(powerset(X0)))))))))
| empty(sK9(sK9(sK7(powerset(powerset(X0))))))
| empty(sK9(powerset(sK9(sK9(sK7(powerset(powerset(X0)))))))) )
| ~ spl16_326
| ~ spl16_409 ),
inference(resolution,[],[f4408,f3306]) ).
fof(f18546,plain,
( spl16_1085
| ~ spl16_325
| ~ spl16_409 ),
inference(avatar_split_clause,[],[f4438,f4407,f3300,f18544]) ).
fof(f18544,plain,
( spl16_1085
<=> ! [X0] :
( empty(powerset(powerset(X0)))
| empty(sK9(sK7(powerset(powerset(X0)))))
| element(sK9(sK6(sK9(powerset(sK9(sK9(sK7(powerset(powerset(X0))))))))),X0)
| empty(sK7(powerset(powerset(X0))))
| empty(sK6(sK9(powerset(sK9(sK9(sK7(powerset(powerset(X0)))))))))
| empty(sK9(sK9(sK7(powerset(powerset(X0))))))
| empty(sK9(powerset(sK9(sK9(sK7(powerset(powerset(X0)))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1085])]) ).
fof(f4438,plain,
( ! [X0] :
( empty(powerset(powerset(X0)))
| empty(sK9(sK7(powerset(powerset(X0)))))
| element(sK9(sK6(sK9(powerset(sK9(sK9(sK7(powerset(powerset(X0))))))))),X0)
| empty(sK7(powerset(powerset(X0))))
| empty(sK6(sK9(powerset(sK9(sK9(sK7(powerset(powerset(X0)))))))))
| empty(sK9(sK9(sK7(powerset(powerset(X0))))))
| empty(sK9(powerset(sK9(sK9(sK7(powerset(powerset(X0)))))))) )
| ~ spl16_325
| ~ spl16_409 ),
inference(resolution,[],[f4408,f3301]) ).
fof(f18542,plain,
( ~ spl16_641
| spl16_1084
| ~ spl16_47
| ~ spl16_577 ),
inference(avatar_split_clause,[],[f7791,f7642,f400,f18540,f9159]) ).
fof(f18540,plain,
( spl16_1084
<=> ! [X0] :
( subset(the_carrier(X0),sK14)
| ~ rel_str(X0)
| ~ subrelstr(X0,sK8(sK8(sK1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1084])]) ).
fof(f400,plain,
( spl16_47
<=> ! [X0,X1] :
( subset(the_carrier(X1),the_carrier(X0))
| ~ subrelstr(X1,X0)
| ~ rel_str(X1)
| ~ rel_str(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_47])]) ).
fof(f7642,plain,
( spl16_577
<=> sK14 = the_carrier(sK8(sK8(sK1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_577])]) ).
fof(f7791,plain,
( ! [X0] :
( subset(the_carrier(X0),sK14)
| ~ subrelstr(X0,sK8(sK8(sK1)))
| ~ rel_str(X0)
| ~ rel_str(sK8(sK8(sK1))) )
| ~ spl16_47
| ~ spl16_577 ),
inference(superposition,[],[f401,f7644]) ).
fof(f7644,plain,
( sK14 = the_carrier(sK8(sK8(sK1)))
| ~ spl16_577 ),
inference(avatar_component_clause,[],[f7642]) ).
fof(f401,plain,
( ! [X0,X1] :
( subset(the_carrier(X1),the_carrier(X0))
| ~ subrelstr(X1,X0)
| ~ rel_str(X1)
| ~ rel_str(X0) )
| ~ spl16_47 ),
inference(avatar_component_clause,[],[f400]) ).
fof(f18538,plain,
( spl16_1083
| ~ spl16_326
| ~ spl16_408 ),
inference(avatar_split_clause,[],[f4426,f4403,f3305,f18536]) ).
fof(f18536,plain,
( spl16_1083
<=> ! [X0] :
( empty(powerset(powerset(X0)))
| empty(sK9(sK6(powerset(powerset(X0)))))
| element(sK9(sK7(sK9(powerset(sK9(sK9(sK6(powerset(powerset(X0))))))))),X0)
| empty(sK6(powerset(powerset(X0))))
| empty(sK7(sK9(powerset(sK9(sK9(sK6(powerset(powerset(X0)))))))))
| empty(sK9(sK9(sK6(powerset(powerset(X0))))))
| empty(sK9(powerset(sK9(sK9(sK6(powerset(powerset(X0)))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1083])]) ).
fof(f4426,plain,
( ! [X0] :
( empty(powerset(powerset(X0)))
| empty(sK9(sK6(powerset(powerset(X0)))))
| element(sK9(sK7(sK9(powerset(sK9(sK9(sK6(powerset(powerset(X0))))))))),X0)
| empty(sK6(powerset(powerset(X0))))
| empty(sK7(sK9(powerset(sK9(sK9(sK6(powerset(powerset(X0)))))))))
| empty(sK9(sK9(sK6(powerset(powerset(X0))))))
| empty(sK9(powerset(sK9(sK9(sK6(powerset(powerset(X0)))))))) )
| ~ spl16_326
| ~ spl16_408 ),
inference(resolution,[],[f4404,f3306]) ).
fof(f18534,plain,
( spl16_1082
| ~ spl16_325
| ~ spl16_408 ),
inference(avatar_split_clause,[],[f4422,f4403,f3300,f18532]) ).
fof(f18532,plain,
( spl16_1082
<=> ! [X0] :
( empty(powerset(powerset(X0)))
| empty(sK9(sK6(powerset(powerset(X0)))))
| element(sK9(sK6(sK9(powerset(sK9(sK9(sK6(powerset(powerset(X0))))))))),X0)
| empty(sK6(powerset(powerset(X0))))
| empty(sK6(sK9(powerset(sK9(sK9(sK6(powerset(powerset(X0)))))))))
| empty(sK9(sK9(sK6(powerset(powerset(X0))))))
| empty(sK9(powerset(sK9(sK9(sK6(powerset(powerset(X0)))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1082])]) ).
fof(f4422,plain,
( ! [X0] :
( empty(powerset(powerset(X0)))
| empty(sK9(sK6(powerset(powerset(X0)))))
| element(sK9(sK6(sK9(powerset(sK9(sK9(sK6(powerset(powerset(X0))))))))),X0)
| empty(sK6(powerset(powerset(X0))))
| empty(sK6(sK9(powerset(sK9(sK9(sK6(powerset(powerset(X0)))))))))
| empty(sK9(sK9(sK6(powerset(powerset(X0))))))
| empty(sK9(powerset(sK9(sK9(sK6(powerset(powerset(X0)))))))) )
| ~ spl16_325
| ~ spl16_408 ),
inference(resolution,[],[f4404,f3301]) ).
fof(f18530,plain,
( spl16_1081
| ~ spl16_321
| ~ spl16_390 ),
inference(avatar_split_clause,[],[f4263,f4167,f3175,f18528]) ).
fof(f18528,plain,
( spl16_1081
<=> ! [X0] :
( empty(sK9(powerset(powerset(X0))))
| element(sK9(sK9(powerset(sK7(sK9(sK9(powerset(sK9(powerset(powerset(X0)))))))))),X0)
| empty(sK9(powerset(sK9(powerset(powerset(X0))))))
| empty(sK7(sK9(sK9(powerset(sK9(powerset(powerset(X0))))))))
| empty(sK9(sK9(powerset(sK9(powerset(powerset(X0)))))))
| empty(sK9(powerset(sK7(sK9(sK9(powerset(sK9(powerset(powerset(X0)))))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1081])]) ).
fof(f4263,plain,
( ! [X0] :
( empty(sK9(powerset(powerset(X0))))
| element(sK9(sK9(powerset(sK7(sK9(sK9(powerset(sK9(powerset(powerset(X0)))))))))),X0)
| empty(sK9(powerset(sK9(powerset(powerset(X0))))))
| empty(sK7(sK9(sK9(powerset(sK9(powerset(powerset(X0))))))))
| empty(sK9(sK9(powerset(sK9(powerset(powerset(X0)))))))
| empty(sK9(powerset(sK7(sK9(sK9(powerset(sK9(powerset(powerset(X0)))))))))) )
| ~ spl16_321
| ~ spl16_390 ),
inference(resolution,[],[f4168,f3176]) ).
fof(f18526,plain,
( spl16_1080
| ~ spl16_320
| ~ spl16_390 ),
inference(avatar_split_clause,[],[f4262,f4167,f3171,f18524]) ).
fof(f18524,plain,
( spl16_1080
<=> ! [X0] :
( empty(sK9(powerset(powerset(X0))))
| element(sK9(sK9(powerset(sK6(sK9(sK9(powerset(sK9(powerset(powerset(X0)))))))))),X0)
| empty(sK9(powerset(sK9(powerset(powerset(X0))))))
| empty(sK6(sK9(sK9(powerset(sK9(powerset(powerset(X0))))))))
| empty(sK9(sK9(powerset(sK9(powerset(powerset(X0)))))))
| empty(sK9(powerset(sK6(sK9(sK9(powerset(sK9(powerset(powerset(X0)))))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1080])]) ).
fof(f4262,plain,
( ! [X0] :
( empty(sK9(powerset(powerset(X0))))
| element(sK9(sK9(powerset(sK6(sK9(sK9(powerset(sK9(powerset(powerset(X0)))))))))),X0)
| empty(sK9(powerset(sK9(powerset(powerset(X0))))))
| empty(sK6(sK9(sK9(powerset(sK9(powerset(powerset(X0))))))))
| empty(sK9(sK9(powerset(sK9(powerset(powerset(X0)))))))
| empty(sK9(powerset(sK6(sK9(sK9(powerset(sK9(powerset(powerset(X0)))))))))) )
| ~ spl16_320
| ~ spl16_390 ),
inference(resolution,[],[f4168,f3172]) ).
fof(f18522,plain,
( spl16_1079
| ~ spl16_349
| ~ spl16_388 ),
inference(avatar_split_clause,[],[f4248,f4159,f3578,f18520]) ).
fof(f18520,plain,
( spl16_1079
<=> ! [X0] :
( empty(sK7(powerset(X0)))
| empty(powerset(X0))
| element(sK9(sK9(powerset(sK9(powerset(sK9(sK9(powerset(sK7(powerset(X0)))))))))),X0)
| empty(sK9(powerset(sK7(powerset(X0)))))
| empty(sK9(powerset(sK9(sK9(powerset(sK7(powerset(X0))))))))
| empty(sK9(sK9(powerset(sK7(powerset(X0))))))
| empty(sK9(powerset(sK9(powerset(sK9(sK9(powerset(sK7(powerset(X0)))))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1079])]) ).
fof(f4248,plain,
( ! [X0] :
( empty(sK7(powerset(X0)))
| empty(powerset(X0))
| element(sK9(sK9(powerset(sK9(powerset(sK9(sK9(powerset(sK7(powerset(X0)))))))))),X0)
| empty(sK9(powerset(sK7(powerset(X0)))))
| empty(sK9(powerset(sK9(sK9(powerset(sK7(powerset(X0))))))))
| empty(sK9(sK9(powerset(sK7(powerset(X0))))))
| empty(sK9(powerset(sK9(powerset(sK9(sK9(powerset(sK7(powerset(X0)))))))))) )
| ~ spl16_349
| ~ spl16_388 ),
inference(resolution,[],[f4160,f3579]) ).
fof(f18518,plain,
( spl16_1078
| ~ spl16_349
| ~ spl16_387 ),
inference(avatar_split_clause,[],[f4232,f4155,f3578,f18516]) ).
fof(f18516,plain,
( spl16_1078
<=> ! [X0] :
( empty(sK6(powerset(X0)))
| empty(powerset(X0))
| element(sK9(sK9(powerset(sK9(powerset(sK9(sK9(powerset(sK6(powerset(X0)))))))))),X0)
| empty(sK9(powerset(sK6(powerset(X0)))))
| empty(sK9(powerset(sK9(sK9(powerset(sK6(powerset(X0))))))))
| empty(sK9(sK9(powerset(sK6(powerset(X0))))))
| empty(sK9(powerset(sK9(powerset(sK9(sK9(powerset(sK6(powerset(X0)))))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1078])]) ).
fof(f4232,plain,
( ! [X0] :
( empty(sK6(powerset(X0)))
| empty(powerset(X0))
| element(sK9(sK9(powerset(sK9(powerset(sK9(sK9(powerset(sK6(powerset(X0)))))))))),X0)
| empty(sK9(powerset(sK6(powerset(X0)))))
| empty(sK9(powerset(sK9(sK9(powerset(sK6(powerset(X0))))))))
| empty(sK9(sK9(powerset(sK6(powerset(X0))))))
| empty(sK9(powerset(sK9(powerset(sK9(sK9(powerset(sK6(powerset(X0)))))))))) )
| ~ spl16_349
| ~ spl16_387 ),
inference(resolution,[],[f4156,f3579]) ).
fof(f18514,plain,
( spl16_1077
| ~ spl16_364
| ~ spl16_369 ),
inference(avatar_split_clause,[],[f4020,f3907,f3678,f18512]) ).
fof(f18512,plain,
( spl16_1077
<=> ! [X0] :
( empty(sK7(sK7(powerset(X0))))
| empty(powerset(X0))
| element(sK9(sK9(sK7(powerset(sK9(sK7(sK7(powerset(X0)))))))),X0)
| empty(sK7(powerset(X0)))
| empty(powerset(sK9(sK7(sK7(powerset(X0))))))
| empty(sK9(sK7(powerset(sK9(sK7(sK7(powerset(X0))))))))
| empty(sK9(sK7(sK7(powerset(X0)))))
| empty(sK7(powerset(sK9(sK7(sK7(powerset(X0))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1077])]) ).
fof(f4020,plain,
( ! [X0] :
( empty(sK7(sK7(powerset(X0))))
| empty(powerset(X0))
| element(sK9(sK9(sK7(powerset(sK9(sK7(sK7(powerset(X0)))))))),X0)
| empty(sK7(powerset(X0)))
| empty(powerset(sK9(sK7(sK7(powerset(X0))))))
| empty(sK9(sK7(powerset(sK9(sK7(sK7(powerset(X0))))))))
| empty(sK9(sK7(sK7(powerset(X0)))))
| empty(sK7(powerset(sK9(sK7(sK7(powerset(X0))))))) )
| ~ spl16_364
| ~ spl16_369 ),
inference(resolution,[],[f3908,f3679]) ).
fof(f18510,plain,
( spl16_1076
| ~ spl16_363
| ~ spl16_369 ),
inference(avatar_split_clause,[],[f4019,f3907,f3674,f18508]) ).
fof(f18508,plain,
( spl16_1076
<=> ! [X0] :
( empty(sK7(sK7(powerset(X0))))
| empty(powerset(X0))
| element(sK9(sK9(sK6(powerset(sK9(sK7(sK7(powerset(X0)))))))),X0)
| empty(sK7(powerset(X0)))
| empty(powerset(sK9(sK7(sK7(powerset(X0))))))
| empty(sK9(sK6(powerset(sK9(sK7(sK7(powerset(X0))))))))
| empty(sK9(sK7(sK7(powerset(X0)))))
| empty(sK6(powerset(sK9(sK7(sK7(powerset(X0))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1076])]) ).
fof(f4019,plain,
( ! [X0] :
( empty(sK7(sK7(powerset(X0))))
| empty(powerset(X0))
| element(sK9(sK9(sK6(powerset(sK9(sK7(sK7(powerset(X0)))))))),X0)
| empty(sK7(powerset(X0)))
| empty(powerset(sK9(sK7(sK7(powerset(X0))))))
| empty(sK9(sK6(powerset(sK9(sK7(sK7(powerset(X0))))))))
| empty(sK9(sK7(sK7(powerset(X0)))))
| empty(sK6(powerset(sK9(sK7(sK7(powerset(X0))))))) )
| ~ spl16_363
| ~ spl16_369 ),
inference(resolution,[],[f3908,f3675]) ).
fof(f18506,plain,
( spl16_1075
| ~ spl16_364
| ~ spl16_368 ),
inference(avatar_split_clause,[],[f4004,f3903,f3678,f18504]) ).
fof(f18504,plain,
( spl16_1075
<=> ! [X0] :
( empty(sK7(sK6(powerset(X0))))
| empty(powerset(X0))
| element(sK9(sK9(sK7(powerset(sK9(sK7(sK6(powerset(X0)))))))),X0)
| empty(sK6(powerset(X0)))
| empty(powerset(sK9(sK7(sK6(powerset(X0))))))
| empty(sK9(sK7(powerset(sK9(sK7(sK6(powerset(X0))))))))
| empty(sK9(sK7(sK6(powerset(X0)))))
| empty(sK7(powerset(sK9(sK7(sK6(powerset(X0))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1075])]) ).
fof(f4004,plain,
( ! [X0] :
( empty(sK7(sK6(powerset(X0))))
| empty(powerset(X0))
| element(sK9(sK9(sK7(powerset(sK9(sK7(sK6(powerset(X0)))))))),X0)
| empty(sK6(powerset(X0)))
| empty(powerset(sK9(sK7(sK6(powerset(X0))))))
| empty(sK9(sK7(powerset(sK9(sK7(sK6(powerset(X0))))))))
| empty(sK9(sK7(sK6(powerset(X0)))))
| empty(sK7(powerset(sK9(sK7(sK6(powerset(X0))))))) )
| ~ spl16_364
| ~ spl16_368 ),
inference(resolution,[],[f3904,f3679]) ).
fof(f18502,plain,
( spl16_1074
| ~ spl16_363
| ~ spl16_368 ),
inference(avatar_split_clause,[],[f4003,f3903,f3674,f18500]) ).
fof(f18500,plain,
( spl16_1074
<=> ! [X0] :
( empty(sK7(sK6(powerset(X0))))
| empty(powerset(X0))
| element(sK9(sK9(sK6(powerset(sK9(sK7(sK6(powerset(X0)))))))),X0)
| empty(sK6(powerset(X0)))
| empty(powerset(sK9(sK7(sK6(powerset(X0))))))
| empty(sK9(sK6(powerset(sK9(sK7(sK6(powerset(X0))))))))
| empty(sK9(sK7(sK6(powerset(X0)))))
| empty(sK6(powerset(sK9(sK7(sK6(powerset(X0))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1074])]) ).
fof(f4003,plain,
( ! [X0] :
( empty(sK7(sK6(powerset(X0))))
| empty(powerset(X0))
| element(sK9(sK9(sK6(powerset(sK9(sK7(sK6(powerset(X0)))))))),X0)
| empty(sK6(powerset(X0)))
| empty(powerset(sK9(sK7(sK6(powerset(X0))))))
| empty(sK9(sK6(powerset(sK9(sK7(sK6(powerset(X0))))))))
| empty(sK9(sK7(sK6(powerset(X0)))))
| empty(sK6(powerset(sK9(sK7(sK6(powerset(X0))))))) )
| ~ spl16_363
| ~ spl16_368 ),
inference(resolution,[],[f3904,f3675]) ).
fof(f18492,plain,
( spl16_1073
| ~ spl16_364
| ~ spl16_366 ),
inference(avatar_split_clause,[],[f3988,f3895,f3678,f18490]) ).
fof(f18490,plain,
( spl16_1073
<=> ! [X0] :
( empty(sK6(sK7(powerset(X0))))
| empty(powerset(X0))
| element(sK9(sK9(sK7(powerset(sK9(sK6(sK7(powerset(X0)))))))),X0)
| empty(sK7(powerset(X0)))
| empty(powerset(sK9(sK6(sK7(powerset(X0))))))
| empty(sK9(sK7(powerset(sK9(sK6(sK7(powerset(X0))))))))
| empty(sK9(sK6(sK7(powerset(X0)))))
| empty(sK7(powerset(sK9(sK6(sK7(powerset(X0))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1073])]) ).
fof(f3988,plain,
( ! [X0] :
( empty(sK6(sK7(powerset(X0))))
| empty(powerset(X0))
| element(sK9(sK9(sK7(powerset(sK9(sK6(sK7(powerset(X0)))))))),X0)
| empty(sK7(powerset(X0)))
| empty(powerset(sK9(sK6(sK7(powerset(X0))))))
| empty(sK9(sK7(powerset(sK9(sK6(sK7(powerset(X0))))))))
| empty(sK9(sK6(sK7(powerset(X0)))))
| empty(sK7(powerset(sK9(sK6(sK7(powerset(X0))))))) )
| ~ spl16_364
| ~ spl16_366 ),
inference(resolution,[],[f3896,f3679]) ).
fof(f18488,plain,
( spl16_1072
| ~ spl16_363
| ~ spl16_366 ),
inference(avatar_split_clause,[],[f3987,f3895,f3674,f18486]) ).
fof(f18486,plain,
( spl16_1072
<=> ! [X0] :
( empty(sK6(sK7(powerset(X0))))
| empty(powerset(X0))
| element(sK9(sK9(sK6(powerset(sK9(sK6(sK7(powerset(X0)))))))),X0)
| empty(sK7(powerset(X0)))
| empty(powerset(sK9(sK6(sK7(powerset(X0))))))
| empty(sK9(sK6(powerset(sK9(sK6(sK7(powerset(X0))))))))
| empty(sK9(sK6(sK7(powerset(X0)))))
| empty(sK6(powerset(sK9(sK6(sK7(powerset(X0))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1072])]) ).
fof(f3987,plain,
( ! [X0] :
( empty(sK6(sK7(powerset(X0))))
| empty(powerset(X0))
| element(sK9(sK9(sK6(powerset(sK9(sK6(sK7(powerset(X0)))))))),X0)
| empty(sK7(powerset(X0)))
| empty(powerset(sK9(sK6(sK7(powerset(X0))))))
| empty(sK9(sK6(powerset(sK9(sK6(sK7(powerset(X0))))))))
| empty(sK9(sK6(sK7(powerset(X0)))))
| empty(sK6(powerset(sK9(sK6(sK7(powerset(X0))))))) )
| ~ spl16_363
| ~ spl16_366 ),
inference(resolution,[],[f3896,f3675]) ).
fof(f18484,plain,
( spl16_1071
| ~ spl16_364
| ~ spl16_365 ),
inference(avatar_split_clause,[],[f3972,f3891,f3678,f18482]) ).
fof(f18482,plain,
( spl16_1071
<=> ! [X0] :
( empty(sK6(sK6(powerset(X0))))
| empty(powerset(X0))
| element(sK9(sK9(sK7(powerset(sK9(sK6(sK6(powerset(X0)))))))),X0)
| empty(sK6(powerset(X0)))
| empty(powerset(sK9(sK6(sK6(powerset(X0))))))
| empty(sK9(sK7(powerset(sK9(sK6(sK6(powerset(X0))))))))
| empty(sK9(sK6(sK6(powerset(X0)))))
| empty(sK7(powerset(sK9(sK6(sK6(powerset(X0))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1071])]) ).
fof(f3972,plain,
( ! [X0] :
( empty(sK6(sK6(powerset(X0))))
| empty(powerset(X0))
| element(sK9(sK9(sK7(powerset(sK9(sK6(sK6(powerset(X0)))))))),X0)
| empty(sK6(powerset(X0)))
| empty(powerset(sK9(sK6(sK6(powerset(X0))))))
| empty(sK9(sK7(powerset(sK9(sK6(sK6(powerset(X0))))))))
| empty(sK9(sK6(sK6(powerset(X0)))))
| empty(sK7(powerset(sK9(sK6(sK6(powerset(X0))))))) )
| ~ spl16_364
| ~ spl16_365 ),
inference(resolution,[],[f3892,f3679]) ).
fof(f18480,plain,
( spl16_1070
| ~ spl16_363
| ~ spl16_365 ),
inference(avatar_split_clause,[],[f3971,f3891,f3674,f18478]) ).
fof(f18478,plain,
( spl16_1070
<=> ! [X0] :
( empty(sK6(sK6(powerset(X0))))
| empty(powerset(X0))
| element(sK9(sK9(sK6(powerset(sK9(sK6(sK6(powerset(X0)))))))),X0)
| empty(sK6(powerset(X0)))
| empty(powerset(sK9(sK6(sK6(powerset(X0))))))
| empty(sK9(sK6(powerset(sK9(sK6(sK6(powerset(X0))))))))
| empty(sK9(sK6(sK6(powerset(X0)))))
| empty(sK6(powerset(sK9(sK6(sK6(powerset(X0))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1070])]) ).
fof(f3971,plain,
( ! [X0] :
( empty(sK6(sK6(powerset(X0))))
| empty(powerset(X0))
| element(sK9(sK9(sK6(powerset(sK9(sK6(sK6(powerset(X0)))))))),X0)
| empty(sK6(powerset(X0)))
| empty(powerset(sK9(sK6(sK6(powerset(X0))))))
| empty(sK9(sK6(powerset(sK9(sK6(sK6(powerset(X0))))))))
| empty(sK9(sK6(sK6(powerset(X0)))))
| empty(sK6(powerset(sK9(sK6(sK6(powerset(X0))))))) )
| ~ spl16_363
| ~ spl16_365 ),
inference(resolution,[],[f3892,f3675]) ).
fof(f18446,plain,
( ~ spl16_641
| spl16_1069
| ~ spl16_47
| ~ spl16_577 ),
inference(avatar_split_clause,[],[f7790,f7642,f400,f18444,f9159]) ).
fof(f18444,plain,
( spl16_1069
<=> ! [X0] :
( subset(sK14,the_carrier(X0))
| ~ rel_str(X0)
| ~ subrelstr(sK8(sK8(sK1)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1069])]) ).
fof(f7790,plain,
( ! [X0] :
( subset(sK14,the_carrier(X0))
| ~ subrelstr(sK8(sK8(sK1)),X0)
| ~ rel_str(sK8(sK8(sK1)))
| ~ rel_str(X0) )
| ~ spl16_47
| ~ spl16_577 ),
inference(superposition,[],[f401,f7644]) ).
fof(f18382,plain,
( spl16_1068
| ~ spl16_150
| ~ spl16_451 ),
inference(avatar_split_clause,[],[f5373,f5221,f1218,f18380]) ).
fof(f18380,plain,
( spl16_1068
<=> ! [X0] :
( empty(sK7(sK9(sK9(powerset(powerset(powerset(X0)))))))
| empty(sK9(sK9(powerset(powerset(powerset(X0))))))
| element(sK9(sK7(sK9(sK7(sK9(sK9(powerset(powerset(powerset(X0))))))))),X0)
| empty(sK9(powerset(powerset(powerset(X0)))))
| empty(sK7(sK9(sK7(sK9(sK9(powerset(powerset(powerset(X0)))))))))
| empty(sK9(sK7(sK9(sK9(powerset(powerset(powerset(X0)))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1068])]) ).
fof(f5373,plain,
( ! [X0] :
( empty(sK7(sK9(sK9(powerset(powerset(powerset(X0)))))))
| empty(sK9(sK9(powerset(powerset(powerset(X0))))))
| element(sK9(sK7(sK9(sK7(sK9(sK9(powerset(powerset(powerset(X0))))))))),X0)
| empty(sK9(powerset(powerset(powerset(X0)))))
| empty(sK7(sK9(sK7(sK9(sK9(powerset(powerset(powerset(X0)))))))))
| empty(sK9(sK7(sK9(sK9(powerset(powerset(powerset(X0)))))))) )
| ~ spl16_150
| ~ spl16_451 ),
inference(resolution,[],[f5222,f1219]) ).
fof(f18378,plain,
( spl16_1067
| ~ spl16_149
| ~ spl16_451 ),
inference(avatar_split_clause,[],[f5366,f5221,f1214,f18376]) ).
fof(f18376,plain,
( spl16_1067
<=> ! [X0] :
( empty(sK7(sK9(sK9(powerset(powerset(powerset(X0)))))))
| empty(sK9(sK9(powerset(powerset(powerset(X0))))))
| element(sK9(sK6(sK9(sK7(sK9(sK9(powerset(powerset(powerset(X0))))))))),X0)
| empty(sK9(powerset(powerset(powerset(X0)))))
| empty(sK6(sK9(sK7(sK9(sK9(powerset(powerset(powerset(X0)))))))))
| empty(sK9(sK7(sK9(sK9(powerset(powerset(powerset(X0)))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1067])]) ).
fof(f5366,plain,
( ! [X0] :
( empty(sK7(sK9(sK9(powerset(powerset(powerset(X0)))))))
| empty(sK9(sK9(powerset(powerset(powerset(X0))))))
| element(sK9(sK6(sK9(sK7(sK9(sK9(powerset(powerset(powerset(X0))))))))),X0)
| empty(sK9(powerset(powerset(powerset(X0)))))
| empty(sK6(sK9(sK7(sK9(sK9(powerset(powerset(powerset(X0)))))))))
| empty(sK9(sK7(sK9(sK9(powerset(powerset(powerset(X0)))))))) )
| ~ spl16_149
| ~ spl16_451 ),
inference(resolution,[],[f5222,f1215]) ).
fof(f18374,plain,
( spl16_1066
| ~ spl16_150
| ~ spl16_450 ),
inference(avatar_split_clause,[],[f5348,f5217,f1218,f18372]) ).
fof(f18372,plain,
( spl16_1066
<=> ! [X0] :
( empty(sK6(sK9(sK9(powerset(powerset(powerset(X0)))))))
| empty(sK9(sK9(powerset(powerset(powerset(X0))))))
| element(sK9(sK7(sK9(sK6(sK9(sK9(powerset(powerset(powerset(X0))))))))),X0)
| empty(sK9(powerset(powerset(powerset(X0)))))
| empty(sK7(sK9(sK6(sK9(sK9(powerset(powerset(powerset(X0)))))))))
| empty(sK9(sK6(sK9(sK9(powerset(powerset(powerset(X0)))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1066])]) ).
fof(f5348,plain,
( ! [X0] :
( empty(sK6(sK9(sK9(powerset(powerset(powerset(X0)))))))
| empty(sK9(sK9(powerset(powerset(powerset(X0))))))
| element(sK9(sK7(sK9(sK6(sK9(sK9(powerset(powerset(powerset(X0))))))))),X0)
| empty(sK9(powerset(powerset(powerset(X0)))))
| empty(sK7(sK9(sK6(sK9(sK9(powerset(powerset(powerset(X0)))))))))
| empty(sK9(sK6(sK9(sK9(powerset(powerset(powerset(X0)))))))) )
| ~ spl16_150
| ~ spl16_450 ),
inference(resolution,[],[f5218,f1219]) ).
fof(f18370,plain,
( spl16_1065
| ~ spl16_149
| ~ spl16_450 ),
inference(avatar_split_clause,[],[f5341,f5217,f1214,f18368]) ).
fof(f18368,plain,
( spl16_1065
<=> ! [X0] :
( empty(sK6(sK9(sK9(powerset(powerset(powerset(X0)))))))
| empty(sK9(sK9(powerset(powerset(powerset(X0))))))
| element(sK9(sK6(sK9(sK6(sK9(sK9(powerset(powerset(powerset(X0))))))))),X0)
| empty(sK9(powerset(powerset(powerset(X0)))))
| empty(sK6(sK9(sK6(sK9(sK9(powerset(powerset(powerset(X0)))))))))
| empty(sK9(sK6(sK9(sK9(powerset(powerset(powerset(X0)))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1065])]) ).
fof(f5341,plain,
( ! [X0] :
( empty(sK6(sK9(sK9(powerset(powerset(powerset(X0)))))))
| empty(sK9(sK9(powerset(powerset(powerset(X0))))))
| element(sK9(sK6(sK9(sK6(sK9(sK9(powerset(powerset(powerset(X0))))))))),X0)
| empty(sK9(powerset(powerset(powerset(X0)))))
| empty(sK6(sK9(sK6(sK9(sK9(powerset(powerset(powerset(X0)))))))))
| empty(sK9(sK6(sK9(sK9(powerset(powerset(powerset(X0)))))))) )
| ~ spl16_149
| ~ spl16_450 ),
inference(resolution,[],[f5218,f1215]) ).
fof(f18366,plain,
( spl16_1064
| ~ spl16_152
| ~ spl16_449 ),
inference(avatar_split_clause,[],[f5330,f5213,f1257,f18364]) ).
fof(f18364,plain,
( spl16_1064
<=> ! [X0] :
( empty(powerset(powerset(X0)))
| empty(sK7(sK9(sK7(powerset(powerset(X0))))))
| empty(sK9(sK7(powerset(powerset(X0)))))
| element(sK9(sK9(powerset(sK9(sK7(sK9(sK7(powerset(powerset(X0))))))))),X0)
| empty(sK7(powerset(powerset(X0))))
| empty(sK9(sK7(sK9(sK7(powerset(powerset(X0)))))))
| empty(sK9(powerset(sK9(sK7(sK9(sK7(powerset(powerset(X0))))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1064])]) ).
fof(f5330,plain,
( ! [X0] :
( empty(powerset(powerset(X0)))
| empty(sK7(sK9(sK7(powerset(powerset(X0))))))
| empty(sK9(sK7(powerset(powerset(X0)))))
| element(sK9(sK9(powerset(sK9(sK7(sK9(sK7(powerset(powerset(X0))))))))),X0)
| empty(sK7(powerset(powerset(X0))))
| empty(sK9(sK7(sK9(sK7(powerset(powerset(X0)))))))
| empty(sK9(powerset(sK9(sK7(sK9(sK7(powerset(powerset(X0))))))))) )
| ~ spl16_152
| ~ spl16_449 ),
inference(resolution,[],[f5214,f1258]) ).
fof(f18362,plain,
( spl16_1063
| ~ spl16_152
| ~ spl16_448 ),
inference(avatar_split_clause,[],[f5305,f5209,f1257,f18360]) ).
fof(f18360,plain,
( spl16_1063
<=> ! [X0] :
( empty(powerset(powerset(X0)))
| empty(sK6(sK9(sK7(powerset(powerset(X0))))))
| empty(sK9(sK7(powerset(powerset(X0)))))
| element(sK9(sK9(powerset(sK9(sK6(sK9(sK7(powerset(powerset(X0))))))))),X0)
| empty(sK7(powerset(powerset(X0))))
| empty(sK9(sK6(sK9(sK7(powerset(powerset(X0)))))))
| empty(sK9(powerset(sK9(sK6(sK9(sK7(powerset(powerset(X0))))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1063])]) ).
fof(f5305,plain,
( ! [X0] :
( empty(powerset(powerset(X0)))
| empty(sK6(sK9(sK7(powerset(powerset(X0))))))
| empty(sK9(sK7(powerset(powerset(X0)))))
| element(sK9(sK9(powerset(sK9(sK6(sK9(sK7(powerset(powerset(X0))))))))),X0)
| empty(sK7(powerset(powerset(X0))))
| empty(sK9(sK6(sK9(sK7(powerset(powerset(X0)))))))
| empty(sK9(powerset(sK9(sK6(sK9(sK7(powerset(powerset(X0))))))))) )
| ~ spl16_152
| ~ spl16_448 ),
inference(resolution,[],[f5210,f1258]) ).
fof(f18358,plain,
( spl16_1062
| ~ spl16_152
| ~ spl16_447 ),
inference(avatar_split_clause,[],[f5280,f5205,f1257,f18356]) ).
fof(f18356,plain,
( spl16_1062
<=> ! [X0] :
( empty(powerset(powerset(X0)))
| empty(sK7(sK9(sK6(powerset(powerset(X0))))))
| empty(sK9(sK6(powerset(powerset(X0)))))
| element(sK9(sK9(powerset(sK9(sK7(sK9(sK6(powerset(powerset(X0))))))))),X0)
| empty(sK6(powerset(powerset(X0))))
| empty(sK9(sK7(sK9(sK6(powerset(powerset(X0)))))))
| empty(sK9(powerset(sK9(sK7(sK9(sK6(powerset(powerset(X0))))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1062])]) ).
fof(f5280,plain,
( ! [X0] :
( empty(powerset(powerset(X0)))
| empty(sK7(sK9(sK6(powerset(powerset(X0))))))
| empty(sK9(sK6(powerset(powerset(X0)))))
| element(sK9(sK9(powerset(sK9(sK7(sK9(sK6(powerset(powerset(X0))))))))),X0)
| empty(sK6(powerset(powerset(X0))))
| empty(sK9(sK7(sK9(sK6(powerset(powerset(X0)))))))
| empty(sK9(powerset(sK9(sK7(sK9(sK6(powerset(powerset(X0))))))))) )
| ~ spl16_152
| ~ spl16_447 ),
inference(resolution,[],[f5206,f1258]) ).
fof(f18354,plain,
( spl16_1061
| ~ spl16_152
| ~ spl16_446 ),
inference(avatar_split_clause,[],[f5255,f5201,f1257,f18352]) ).
fof(f18352,plain,
( spl16_1061
<=> ! [X0] :
( empty(powerset(powerset(X0)))
| empty(sK6(sK9(sK6(powerset(powerset(X0))))))
| empty(sK9(sK6(powerset(powerset(X0)))))
| element(sK9(sK9(powerset(sK9(sK6(sK9(sK6(powerset(powerset(X0))))))))),X0)
| empty(sK6(powerset(powerset(X0))))
| empty(sK9(sK6(sK9(sK6(powerset(powerset(X0)))))))
| empty(sK9(powerset(sK9(sK6(sK9(sK6(powerset(powerset(X0))))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1061])]) ).
fof(f5255,plain,
( ! [X0] :
( empty(powerset(powerset(X0)))
| empty(sK6(sK9(sK6(powerset(powerset(X0))))))
| empty(sK9(sK6(powerset(powerset(X0)))))
| element(sK9(sK9(powerset(sK9(sK6(sK9(sK6(powerset(powerset(X0))))))))),X0)
| empty(sK6(powerset(powerset(X0))))
| empty(sK9(sK6(sK9(sK6(powerset(powerset(X0)))))))
| empty(sK9(powerset(sK9(sK6(sK9(sK6(powerset(powerset(X0))))))))) )
| ~ spl16_152
| ~ spl16_446 ),
inference(resolution,[],[f5202,f1258]) ).
fof(f18350,plain,
( ~ spl16_1060
| ~ spl16_641
| spl16_1043
| ~ spl16_499
| ~ spl16_805 ),
inference(avatar_split_clause,[],[f16863,f14693,f5963,f18208,f9159,f18347]) ).
fof(f18347,plain,
( spl16_1060
<=> subrelstr(sK0,sK8(sK8(sK1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1060])]) ).
fof(f18208,plain,
( spl16_1043
<=> element(ordered_pair(sK4,sK5),sK14) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1043])]) ).
fof(f5963,plain,
( spl16_499
<=> ! [X0] :
( element(ordered_pair(sK4,sK5),the_InternalRel(X0))
| ~ rel_str(X0)
| ~ subrelstr(sK0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_499])]) ).
fof(f16863,plain,
( element(ordered_pair(sK4,sK5),sK14)
| ~ rel_str(sK8(sK8(sK1)))
| ~ subrelstr(sK0,sK8(sK8(sK1)))
| ~ spl16_499
| ~ spl16_805 ),
inference(superposition,[],[f5964,f14695]) ).
fof(f5964,plain,
( ! [X0] :
( element(ordered_pair(sK4,sK5),the_InternalRel(X0))
| ~ rel_str(X0)
| ~ subrelstr(sK0,X0) )
| ~ spl16_499 ),
inference(avatar_component_clause,[],[f5963]) ).
fof(f18345,plain,
( spl16_1059
| ~ spl16_321
| ~ spl16_409 ),
inference(avatar_split_clause,[],[f4445,f4407,f3175,f18343]) ).
fof(f18343,plain,
( spl16_1059
<=> ! [X0] :
( empty(powerset(powerset(X0)))
| empty(sK9(sK7(powerset(powerset(X0)))))
| element(sK9(sK9(powerset(sK7(sK9(sK9(sK7(powerset(powerset(X0))))))))),X0)
| empty(sK7(powerset(powerset(X0))))
| empty(sK7(sK9(sK9(sK7(powerset(powerset(X0)))))))
| empty(sK9(sK9(sK7(powerset(powerset(X0))))))
| empty(sK9(powerset(sK7(sK9(sK9(sK7(powerset(powerset(X0))))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1059])]) ).
fof(f4445,plain,
( ! [X0] :
( empty(powerset(powerset(X0)))
| empty(sK9(sK7(powerset(powerset(X0)))))
| element(sK9(sK9(powerset(sK7(sK9(sK9(sK7(powerset(powerset(X0))))))))),X0)
| empty(sK7(powerset(powerset(X0))))
| empty(sK7(sK9(sK9(sK7(powerset(powerset(X0)))))))
| empty(sK9(sK9(sK7(powerset(powerset(X0))))))
| empty(sK9(powerset(sK7(sK9(sK9(sK7(powerset(powerset(X0))))))))) )
| ~ spl16_321
| ~ spl16_409 ),
inference(resolution,[],[f4408,f3176]) ).
fof(f18341,plain,
( spl16_1058
| ~ spl16_320
| ~ spl16_409 ),
inference(avatar_split_clause,[],[f4444,f4407,f3171,f18339]) ).
fof(f18339,plain,
( spl16_1058
<=> ! [X0] :
( empty(powerset(powerset(X0)))
| empty(sK9(sK7(powerset(powerset(X0)))))
| element(sK9(sK9(powerset(sK6(sK9(sK9(sK7(powerset(powerset(X0))))))))),X0)
| empty(sK7(powerset(powerset(X0))))
| empty(sK6(sK9(sK9(sK7(powerset(powerset(X0)))))))
| empty(sK9(sK9(sK7(powerset(powerset(X0))))))
| empty(sK9(powerset(sK6(sK9(sK9(sK7(powerset(powerset(X0))))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1058])]) ).
fof(f4444,plain,
( ! [X0] :
( empty(powerset(powerset(X0)))
| empty(sK9(sK7(powerset(powerset(X0)))))
| element(sK9(sK9(powerset(sK6(sK9(sK9(sK7(powerset(powerset(X0))))))))),X0)
| empty(sK7(powerset(powerset(X0))))
| empty(sK6(sK9(sK9(sK7(powerset(powerset(X0)))))))
| empty(sK9(sK9(sK7(powerset(powerset(X0))))))
| empty(sK9(powerset(sK6(sK9(sK9(sK7(powerset(powerset(X0))))))))) )
| ~ spl16_320
| ~ spl16_409 ),
inference(resolution,[],[f4408,f3172]) ).
fof(f18337,plain,
( spl16_1057
| ~ spl16_321
| ~ spl16_408 ),
inference(avatar_split_clause,[],[f4429,f4403,f3175,f18335]) ).
fof(f18335,plain,
( spl16_1057
<=> ! [X0] :
( empty(powerset(powerset(X0)))
| empty(sK9(sK6(powerset(powerset(X0)))))
| element(sK9(sK9(powerset(sK7(sK9(sK9(sK6(powerset(powerset(X0))))))))),X0)
| empty(sK6(powerset(powerset(X0))))
| empty(sK7(sK9(sK9(sK6(powerset(powerset(X0)))))))
| empty(sK9(sK9(sK6(powerset(powerset(X0))))))
| empty(sK9(powerset(sK7(sK9(sK9(sK6(powerset(powerset(X0))))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1057])]) ).
fof(f4429,plain,
( ! [X0] :
( empty(powerset(powerset(X0)))
| empty(sK9(sK6(powerset(powerset(X0)))))
| element(sK9(sK9(powerset(sK7(sK9(sK9(sK6(powerset(powerset(X0))))))))),X0)
| empty(sK6(powerset(powerset(X0))))
| empty(sK7(sK9(sK9(sK6(powerset(powerset(X0)))))))
| empty(sK9(sK9(sK6(powerset(powerset(X0))))))
| empty(sK9(powerset(sK7(sK9(sK9(sK6(powerset(powerset(X0))))))))) )
| ~ spl16_321
| ~ spl16_408 ),
inference(resolution,[],[f4404,f3176]) ).
fof(f18333,plain,
( spl16_1056
| ~ spl16_320
| ~ spl16_408 ),
inference(avatar_split_clause,[],[f4428,f4403,f3171,f18331]) ).
fof(f18331,plain,
( spl16_1056
<=> ! [X0] :
( empty(powerset(powerset(X0)))
| empty(sK9(sK6(powerset(powerset(X0)))))
| element(sK9(sK9(powerset(sK6(sK9(sK9(sK6(powerset(powerset(X0))))))))),X0)
| empty(sK6(powerset(powerset(X0))))
| empty(sK6(sK9(sK9(sK6(powerset(powerset(X0)))))))
| empty(sK9(sK9(sK6(powerset(powerset(X0))))))
| empty(sK9(powerset(sK6(sK9(sK9(sK6(powerset(powerset(X0))))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1056])]) ).
fof(f4428,plain,
( ! [X0] :
( empty(powerset(powerset(X0)))
| empty(sK9(sK6(powerset(powerset(X0)))))
| element(sK9(sK9(powerset(sK6(sK9(sK9(sK6(powerset(powerset(X0))))))))),X0)
| empty(sK6(powerset(powerset(X0))))
| empty(sK6(sK9(sK9(sK6(powerset(powerset(X0)))))))
| empty(sK9(sK9(sK6(powerset(powerset(X0))))))
| empty(sK9(powerset(sK6(sK9(sK9(sK6(powerset(powerset(X0))))))))) )
| ~ spl16_320
| ~ spl16_408 ),
inference(resolution,[],[f4404,f3172]) ).
fof(f18329,plain,
( spl16_1055
| ~ spl16_306
| ~ spl16_405 ),
inference(avatar_split_clause,[],[f4361,f4343,f2964,f18327]) ).
fof(f18327,plain,
( spl16_1055
<=> ! [X0] :
( empty(sK9(sK9(powerset(powerset(powerset(X0))))))
| element(sK9(sK7(sK7(sK9(sK9(sK9(powerset(powerset(powerset(X0))))))))),X0)
| empty(sK9(powerset(powerset(powerset(X0)))))
| empty(sK7(sK7(sK9(sK9(sK9(powerset(powerset(powerset(X0)))))))))
| empty(sK9(sK9(sK9(powerset(powerset(powerset(X0)))))))
| empty(sK7(sK9(sK9(sK9(powerset(powerset(powerset(X0)))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1055])]) ).
fof(f4361,plain,
( ! [X0] :
( empty(sK9(sK9(powerset(powerset(powerset(X0))))))
| element(sK9(sK7(sK7(sK9(sK9(sK9(powerset(powerset(powerset(X0))))))))),X0)
| empty(sK9(powerset(powerset(powerset(X0)))))
| empty(sK7(sK7(sK9(sK9(sK9(powerset(powerset(powerset(X0)))))))))
| empty(sK9(sK9(sK9(powerset(powerset(powerset(X0)))))))
| empty(sK7(sK9(sK9(sK9(powerset(powerset(powerset(X0)))))))) )
| ~ spl16_306
| ~ spl16_405 ),
inference(resolution,[],[f4344,f2965]) ).
fof(f18325,plain,
( spl16_1054
| ~ spl16_305
| ~ spl16_405 ),
inference(avatar_split_clause,[],[f4360,f4343,f2960,f18323]) ).
fof(f18323,plain,
( spl16_1054
<=> ! [X0] :
( empty(sK9(sK9(powerset(powerset(powerset(X0))))))
| element(sK9(sK7(sK6(sK9(sK9(sK9(powerset(powerset(powerset(X0))))))))),X0)
| empty(sK9(powerset(powerset(powerset(X0)))))
| empty(sK7(sK6(sK9(sK9(sK9(powerset(powerset(powerset(X0)))))))))
| empty(sK9(sK9(sK9(powerset(powerset(powerset(X0)))))))
| empty(sK6(sK9(sK9(sK9(powerset(powerset(powerset(X0)))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1054])]) ).
fof(f4360,plain,
( ! [X0] :
( empty(sK9(sK9(powerset(powerset(powerset(X0))))))
| element(sK9(sK7(sK6(sK9(sK9(sK9(powerset(powerset(powerset(X0))))))))),X0)
| empty(sK9(powerset(powerset(powerset(X0)))))
| empty(sK7(sK6(sK9(sK9(sK9(powerset(powerset(powerset(X0)))))))))
| empty(sK9(sK9(sK9(powerset(powerset(powerset(X0)))))))
| empty(sK6(sK9(sK9(sK9(powerset(powerset(powerset(X0)))))))) )
| ~ spl16_305
| ~ spl16_405 ),
inference(resolution,[],[f4344,f2961]) ).
fof(f18321,plain,
( spl16_1053
| ~ spl16_304
| ~ spl16_405 ),
inference(avatar_split_clause,[],[f4357,f4343,f2956,f18319]) ).
fof(f18319,plain,
( spl16_1053
<=> ! [X0] :
( empty(sK9(sK9(powerset(powerset(powerset(X0))))))
| element(sK9(sK6(sK7(sK9(sK9(sK9(powerset(powerset(powerset(X0))))))))),X0)
| empty(sK9(powerset(powerset(powerset(X0)))))
| empty(sK6(sK7(sK9(sK9(sK9(powerset(powerset(powerset(X0)))))))))
| empty(sK9(sK9(sK9(powerset(powerset(powerset(X0)))))))
| empty(sK7(sK9(sK9(sK9(powerset(powerset(powerset(X0)))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1053])]) ).
fof(f4357,plain,
( ! [X0] :
( empty(sK9(sK9(powerset(powerset(powerset(X0))))))
| element(sK9(sK6(sK7(sK9(sK9(sK9(powerset(powerset(powerset(X0))))))))),X0)
| empty(sK9(powerset(powerset(powerset(X0)))))
| empty(sK6(sK7(sK9(sK9(sK9(powerset(powerset(powerset(X0)))))))))
| empty(sK9(sK9(sK9(powerset(powerset(powerset(X0)))))))
| empty(sK7(sK9(sK9(sK9(powerset(powerset(powerset(X0)))))))) )
| ~ spl16_304
| ~ spl16_405 ),
inference(resolution,[],[f4344,f2957]) ).
fof(f18317,plain,
( spl16_1052
| ~ spl16_303
| ~ spl16_405 ),
inference(avatar_split_clause,[],[f4356,f4343,f2952,f18315]) ).
fof(f18315,plain,
( spl16_1052
<=> ! [X0] :
( empty(sK9(sK9(powerset(powerset(powerset(X0))))))
| element(sK9(sK6(sK6(sK9(sK9(sK9(powerset(powerset(powerset(X0))))))))),X0)
| empty(sK9(powerset(powerset(powerset(X0)))))
| empty(sK6(sK6(sK9(sK9(sK9(powerset(powerset(powerset(X0)))))))))
| empty(sK9(sK9(sK9(powerset(powerset(powerset(X0)))))))
| empty(sK6(sK9(sK9(sK9(powerset(powerset(powerset(X0)))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1052])]) ).
fof(f4356,plain,
( ! [X0] :
( empty(sK9(sK9(powerset(powerset(powerset(X0))))))
| element(sK9(sK6(sK6(sK9(sK9(sK9(powerset(powerset(powerset(X0))))))))),X0)
| empty(sK9(powerset(powerset(powerset(X0)))))
| empty(sK6(sK6(sK9(sK9(sK9(powerset(powerset(powerset(X0)))))))))
| empty(sK9(sK9(sK9(powerset(powerset(powerset(X0)))))))
| empty(sK6(sK9(sK9(sK9(powerset(powerset(powerset(X0)))))))) )
| ~ spl16_303
| ~ spl16_405 ),
inference(resolution,[],[f4344,f2953]) ).
fof(f18313,plain,
( spl16_1051
| ~ spl16_362
| ~ spl16_371 ),
inference(avatar_split_clause,[],[f4053,f3915,f3670,f18311]) ).
fof(f18311,plain,
( spl16_1051
<=> ! [X0] :
( empty(sK7(sK9(powerset(powerset(X0)))))
| element(sK9(sK9(sK9(powerset(powerset(sK9(sK7(sK9(powerset(powerset(X0)))))))))),X0)
| empty(sK9(powerset(powerset(X0))))
| empty(sK9(sK9(powerset(powerset(sK9(sK7(sK9(powerset(powerset(X0))))))))))
| empty(sK9(sK7(sK9(powerset(powerset(X0))))))
| empty(sK9(powerset(powerset(sK9(sK7(sK9(powerset(powerset(X0))))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1051])]) ).
fof(f4053,plain,
( ! [X0] :
( empty(sK7(sK9(powerset(powerset(X0)))))
| element(sK9(sK9(sK9(powerset(powerset(sK9(sK7(sK9(powerset(powerset(X0)))))))))),X0)
| empty(sK9(powerset(powerset(X0))))
| empty(sK9(sK9(powerset(powerset(sK9(sK7(sK9(powerset(powerset(X0))))))))))
| empty(sK9(sK7(sK9(powerset(powerset(X0))))))
| empty(sK9(powerset(powerset(sK9(sK7(sK9(powerset(powerset(X0))))))))) )
| ~ spl16_362
| ~ spl16_371 ),
inference(resolution,[],[f3916,f3671]) ).
fof(f18309,plain,
( spl16_1050
| ~ spl16_362
| ~ spl16_370 ),
inference(avatar_split_clause,[],[f4037,f3911,f3670,f18307]) ).
fof(f18307,plain,
( spl16_1050
<=> ! [X0] :
( empty(sK6(sK9(powerset(powerset(X0)))))
| element(sK9(sK9(sK9(powerset(powerset(sK9(sK6(sK9(powerset(powerset(X0)))))))))),X0)
| empty(sK9(powerset(powerset(X0))))
| empty(sK9(sK9(powerset(powerset(sK9(sK6(sK9(powerset(powerset(X0))))))))))
| empty(sK9(sK6(sK9(powerset(powerset(X0))))))
| empty(sK9(powerset(powerset(sK9(sK6(sK9(powerset(powerset(X0))))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1050])]) ).
fof(f4037,plain,
( ! [X0] :
( empty(sK6(sK9(powerset(powerset(X0)))))
| element(sK9(sK9(sK9(powerset(powerset(sK9(sK6(sK9(powerset(powerset(X0)))))))))),X0)
| empty(sK9(powerset(powerset(X0))))
| empty(sK9(sK9(powerset(powerset(sK9(sK6(sK9(powerset(powerset(X0))))))))))
| empty(sK9(sK6(sK9(powerset(powerset(X0))))))
| empty(sK9(powerset(powerset(sK9(sK6(sK9(powerset(powerset(X0))))))))) )
| ~ spl16_362
| ~ spl16_370 ),
inference(resolution,[],[f3912,f3671]) ).
fof(f18235,plain,
( spl16_1049
| ~ spl16_177
| ~ spl16_418 ),
inference(avatar_split_clause,[],[f4736,f4669,f1476,f18233]) ).
fof(f18233,plain,
( spl16_1049
<=> ! [X0] :
( empty(sK7(sK9(sK9(powerset(powerset(sK9(sK7(powerset(X0)))))))))
| empty(sK9(sK9(powerset(powerset(sK9(sK7(powerset(X0))))))))
| empty(sK9(sK7(powerset(X0))))
| empty(sK9(powerset(powerset(sK9(sK7(powerset(X0)))))))
| empty(sK7(powerset(X0)))
| element(sK9(sK7(sK9(sK9(powerset(powerset(sK9(sK7(powerset(X0))))))))),X0)
| empty(powerset(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1049])]) ).
fof(f4736,plain,
( ! [X0] :
( empty(sK7(sK9(sK9(powerset(powerset(sK9(sK7(powerset(X0)))))))))
| empty(sK9(sK9(powerset(powerset(sK9(sK7(powerset(X0))))))))
| empty(sK9(sK7(powerset(X0))))
| empty(sK9(powerset(powerset(sK9(sK7(powerset(X0)))))))
| empty(sK7(powerset(X0)))
| element(sK9(sK7(sK9(sK9(powerset(powerset(sK9(sK7(powerset(X0))))))))),X0)
| empty(powerset(X0)) )
| ~ spl16_177
| ~ spl16_418 ),
inference(resolution,[],[f4670,f1477]) ).
fof(f18231,plain,
( spl16_1048
| ~ spl16_176
| ~ spl16_418 ),
inference(avatar_split_clause,[],[f4728,f4669,f1472,f18229]) ).
fof(f18229,plain,
( spl16_1048
<=> ! [X0] :
( empty(sK7(sK9(sK9(powerset(powerset(sK9(sK6(powerset(X0)))))))))
| empty(sK9(sK9(powerset(powerset(sK9(sK6(powerset(X0))))))))
| empty(sK9(sK6(powerset(X0))))
| empty(sK9(powerset(powerset(sK9(sK6(powerset(X0)))))))
| empty(sK6(powerset(X0)))
| element(sK9(sK7(sK9(sK9(powerset(powerset(sK9(sK6(powerset(X0))))))))),X0)
| empty(powerset(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1048])]) ).
fof(f4728,plain,
( ! [X0] :
( empty(sK7(sK9(sK9(powerset(powerset(sK9(sK6(powerset(X0)))))))))
| empty(sK9(sK9(powerset(powerset(sK9(sK6(powerset(X0))))))))
| empty(sK9(sK6(powerset(X0))))
| empty(sK9(powerset(powerset(sK9(sK6(powerset(X0)))))))
| empty(sK6(powerset(X0)))
| element(sK9(sK7(sK9(sK9(powerset(powerset(sK9(sK6(powerset(X0))))))))),X0)
| empty(powerset(X0)) )
| ~ spl16_176
| ~ spl16_418 ),
inference(resolution,[],[f4670,f1473]) ).
fof(f18227,plain,
( spl16_1047
| ~ spl16_177
| ~ spl16_417 ),
inference(avatar_split_clause,[],[f4691,f4665,f1476,f18225]) ).
fof(f18225,plain,
( spl16_1047
<=> ! [X0] :
( empty(sK6(sK9(sK9(powerset(powerset(sK9(sK7(powerset(X0)))))))))
| empty(sK9(sK9(powerset(powerset(sK9(sK7(powerset(X0))))))))
| empty(sK9(sK7(powerset(X0))))
| empty(sK9(powerset(powerset(sK9(sK7(powerset(X0)))))))
| empty(sK7(powerset(X0)))
| element(sK9(sK6(sK9(sK9(powerset(powerset(sK9(sK7(powerset(X0))))))))),X0)
| empty(powerset(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1047])]) ).
fof(f4691,plain,
( ! [X0] :
( empty(sK6(sK9(sK9(powerset(powerset(sK9(sK7(powerset(X0)))))))))
| empty(sK9(sK9(powerset(powerset(sK9(sK7(powerset(X0))))))))
| empty(sK9(sK7(powerset(X0))))
| empty(sK9(powerset(powerset(sK9(sK7(powerset(X0)))))))
| empty(sK7(powerset(X0)))
| element(sK9(sK6(sK9(sK9(powerset(powerset(sK9(sK7(powerset(X0))))))))),X0)
| empty(powerset(X0)) )
| ~ spl16_177
| ~ spl16_417 ),
inference(resolution,[],[f4666,f1477]) ).
fof(f18223,plain,
( spl16_1046
| ~ spl16_176
| ~ spl16_417 ),
inference(avatar_split_clause,[],[f4683,f4665,f1472,f18221]) ).
fof(f18221,plain,
( spl16_1046
<=> ! [X0] :
( empty(sK6(sK9(sK9(powerset(powerset(sK9(sK6(powerset(X0)))))))))
| empty(sK9(sK9(powerset(powerset(sK9(sK6(powerset(X0))))))))
| empty(sK9(sK6(powerset(X0))))
| empty(sK9(powerset(powerset(sK9(sK6(powerset(X0)))))))
| empty(sK6(powerset(X0)))
| element(sK9(sK6(sK9(sK9(powerset(powerset(sK9(sK6(powerset(X0))))))))),X0)
| empty(powerset(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1046])]) ).
fof(f4683,plain,
( ! [X0] :
( empty(sK6(sK9(sK9(powerset(powerset(sK9(sK6(powerset(X0)))))))))
| empty(sK9(sK9(powerset(powerset(sK9(sK6(powerset(X0))))))))
| empty(sK9(sK6(powerset(X0))))
| empty(sK9(powerset(powerset(sK9(sK6(powerset(X0)))))))
| empty(sK6(powerset(X0)))
| element(sK9(sK6(sK9(sK9(powerset(powerset(sK9(sK6(powerset(X0))))))))),X0)
| empty(powerset(X0)) )
| ~ spl16_176
| ~ spl16_417 ),
inference(resolution,[],[f4666,f1473]) ).
fof(f18219,plain,
( spl16_1045
| ~ spl16_306
| ~ spl16_390 ),
inference(avatar_split_clause,[],[f4259,f4167,f2964,f18217]) ).
fof(f18217,plain,
( spl16_1045
<=> ! [X0] :
( empty(sK9(powerset(powerset(X0))))
| element(sK9(sK7(sK7(sK9(sK9(powerset(sK9(powerset(powerset(X0))))))))),X0)
| empty(sK9(powerset(sK9(powerset(powerset(X0))))))
| empty(sK7(sK7(sK9(sK9(powerset(sK9(powerset(powerset(X0)))))))))
| empty(sK9(sK9(powerset(sK9(powerset(powerset(X0)))))))
| empty(sK7(sK9(sK9(powerset(sK9(powerset(powerset(X0)))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1045])]) ).
fof(f4259,plain,
( ! [X0] :
( empty(sK9(powerset(powerset(X0))))
| element(sK9(sK7(sK7(sK9(sK9(powerset(sK9(powerset(powerset(X0))))))))),X0)
| empty(sK9(powerset(sK9(powerset(powerset(X0))))))
| empty(sK7(sK7(sK9(sK9(powerset(sK9(powerset(powerset(X0)))))))))
| empty(sK9(sK9(powerset(sK9(powerset(powerset(X0)))))))
| empty(sK7(sK9(sK9(powerset(sK9(powerset(powerset(X0)))))))) )
| ~ spl16_306
| ~ spl16_390 ),
inference(resolution,[],[f4168,f2965]) ).
fof(f18215,plain,
( spl16_1044
| ~ spl16_305
| ~ spl16_390 ),
inference(avatar_split_clause,[],[f4258,f4167,f2960,f18213]) ).
fof(f18213,plain,
( spl16_1044
<=> ! [X0] :
( empty(sK9(powerset(powerset(X0))))
| element(sK9(sK7(sK6(sK9(sK9(powerset(sK9(powerset(powerset(X0))))))))),X0)
| empty(sK9(powerset(sK9(powerset(powerset(X0))))))
| empty(sK7(sK6(sK9(sK9(powerset(sK9(powerset(powerset(X0)))))))))
| empty(sK9(sK9(powerset(sK9(powerset(powerset(X0)))))))
| empty(sK6(sK9(sK9(powerset(sK9(powerset(powerset(X0)))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1044])]) ).
fof(f4258,plain,
( ! [X0] :
( empty(sK9(powerset(powerset(X0))))
| element(sK9(sK7(sK6(sK9(sK9(powerset(sK9(powerset(powerset(X0))))))))),X0)
| empty(sK9(powerset(sK9(powerset(powerset(X0))))))
| empty(sK7(sK6(sK9(sK9(powerset(sK9(powerset(powerset(X0)))))))))
| empty(sK9(sK9(powerset(sK9(powerset(powerset(X0)))))))
| empty(sK6(sK9(sK9(powerset(sK9(powerset(powerset(X0)))))))) )
| ~ spl16_305
| ~ spl16_390 ),
inference(resolution,[],[f4168,f2961]) ).
fof(f18211,plain,
( ~ spl16_641
| ~ spl16_1042
| spl16_1043
| ~ spl16_196
| ~ spl16_805 ),
inference(avatar_split_clause,[],[f16836,f14693,f1697,f18208,f18204,f9159]) ).
fof(f18204,plain,
( spl16_1042
<=> subrelstr(sK1,sK8(sK8(sK1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1042])]) ).
fof(f1697,plain,
( spl16_196
<=> ! [X0] :
( ~ subrelstr(sK1,X0)
| element(ordered_pair(sK4,sK5),the_InternalRel(X0))
| ~ rel_str(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_196])]) ).
fof(f16836,plain,
( element(ordered_pair(sK4,sK5),sK14)
| ~ subrelstr(sK1,sK8(sK8(sK1)))
| ~ rel_str(sK8(sK8(sK1)))
| ~ spl16_196
| ~ spl16_805 ),
inference(superposition,[],[f1698,f14695]) ).
fof(f1698,plain,
( ! [X0] :
( element(ordered_pair(sK4,sK5),the_InternalRel(X0))
| ~ subrelstr(sK1,X0)
| ~ rel_str(X0) )
| ~ spl16_196 ),
inference(avatar_component_clause,[],[f1697]) ).
fof(f18202,plain,
( spl16_1041
| ~ spl16_304
| ~ spl16_390 ),
inference(avatar_split_clause,[],[f4255,f4167,f2956,f18200]) ).
fof(f18200,plain,
( spl16_1041
<=> ! [X0] :
( empty(sK9(powerset(powerset(X0))))
| element(sK9(sK6(sK7(sK9(sK9(powerset(sK9(powerset(powerset(X0))))))))),X0)
| empty(sK9(powerset(sK9(powerset(powerset(X0))))))
| empty(sK6(sK7(sK9(sK9(powerset(sK9(powerset(powerset(X0)))))))))
| empty(sK9(sK9(powerset(sK9(powerset(powerset(X0)))))))
| empty(sK7(sK9(sK9(powerset(sK9(powerset(powerset(X0)))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1041])]) ).
fof(f4255,plain,
( ! [X0] :
( empty(sK9(powerset(powerset(X0))))
| element(sK9(sK6(sK7(sK9(sK9(powerset(sK9(powerset(powerset(X0))))))))),X0)
| empty(sK9(powerset(sK9(powerset(powerset(X0))))))
| empty(sK6(sK7(sK9(sK9(powerset(sK9(powerset(powerset(X0)))))))))
| empty(sK9(sK9(powerset(sK9(powerset(powerset(X0)))))))
| empty(sK7(sK9(sK9(powerset(sK9(powerset(powerset(X0)))))))) )
| ~ spl16_304
| ~ spl16_390 ),
inference(resolution,[],[f4168,f2957]) ).
fof(f18198,plain,
( spl16_1040
| ~ spl16_303
| ~ spl16_390 ),
inference(avatar_split_clause,[],[f4254,f4167,f2952,f18196]) ).
fof(f18196,plain,
( spl16_1040
<=> ! [X0] :
( empty(sK9(powerset(powerset(X0))))
| element(sK9(sK6(sK6(sK9(sK9(powerset(sK9(powerset(powerset(X0))))))))),X0)
| empty(sK9(powerset(sK9(powerset(powerset(X0))))))
| empty(sK6(sK6(sK9(sK9(powerset(sK9(powerset(powerset(X0)))))))))
| empty(sK9(sK9(powerset(sK9(powerset(powerset(X0)))))))
| empty(sK6(sK9(sK9(powerset(sK9(powerset(powerset(X0)))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1040])]) ).
fof(f4254,plain,
( ! [X0] :
( empty(sK9(powerset(powerset(X0))))
| element(sK9(sK6(sK6(sK9(sK9(powerset(sK9(powerset(powerset(X0))))))))),X0)
| empty(sK9(powerset(sK9(powerset(powerset(X0))))))
| empty(sK6(sK6(sK9(sK9(powerset(sK9(powerset(powerset(X0)))))))))
| empty(sK9(sK9(powerset(sK9(powerset(powerset(X0)))))))
| empty(sK6(sK9(sK9(powerset(sK9(powerset(powerset(X0)))))))) )
| ~ spl16_303
| ~ spl16_390 ),
inference(resolution,[],[f4168,f2953]) ).
fof(f18194,plain,
( spl16_1039
| ~ spl16_326
| ~ spl16_388 ),
inference(avatar_split_clause,[],[f4244,f4159,f3305,f18192]) ).
fof(f18192,plain,
( spl16_1039
<=> ! [X0] :
( empty(sK7(powerset(X0)))
| empty(powerset(X0))
| element(sK9(sK7(sK9(powerset(sK9(sK9(powerset(sK7(powerset(X0))))))))),X0)
| empty(sK9(powerset(sK7(powerset(X0)))))
| empty(sK7(sK9(powerset(sK9(sK9(powerset(sK7(powerset(X0)))))))))
| empty(sK9(sK9(powerset(sK7(powerset(X0))))))
| empty(sK9(powerset(sK9(sK9(powerset(sK7(powerset(X0)))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1039])]) ).
fof(f4244,plain,
( ! [X0] :
( empty(sK7(powerset(X0)))
| empty(powerset(X0))
| element(sK9(sK7(sK9(powerset(sK9(sK9(powerset(sK7(powerset(X0))))))))),X0)
| empty(sK9(powerset(sK7(powerset(X0)))))
| empty(sK7(sK9(powerset(sK9(sK9(powerset(sK7(powerset(X0)))))))))
| empty(sK9(sK9(powerset(sK7(powerset(X0))))))
| empty(sK9(powerset(sK9(sK9(powerset(sK7(powerset(X0)))))))) )
| ~ spl16_326
| ~ spl16_388 ),
inference(resolution,[],[f4160,f3306]) ).
fof(f18190,plain,
( spl16_1038
| ~ spl16_325
| ~ spl16_388 ),
inference(avatar_split_clause,[],[f4240,f4159,f3300,f18188]) ).
fof(f18188,plain,
( spl16_1038
<=> ! [X0] :
( empty(sK7(powerset(X0)))
| empty(powerset(X0))
| element(sK9(sK6(sK9(powerset(sK9(sK9(powerset(sK7(powerset(X0))))))))),X0)
| empty(sK9(powerset(sK7(powerset(X0)))))
| empty(sK6(sK9(powerset(sK9(sK9(powerset(sK7(powerset(X0)))))))))
| empty(sK9(sK9(powerset(sK7(powerset(X0))))))
| empty(sK9(powerset(sK9(sK9(powerset(sK7(powerset(X0)))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1038])]) ).
fof(f4240,plain,
( ! [X0] :
( empty(sK7(powerset(X0)))
| empty(powerset(X0))
| element(sK9(sK6(sK9(powerset(sK9(sK9(powerset(sK7(powerset(X0))))))))),X0)
| empty(sK9(powerset(sK7(powerset(X0)))))
| empty(sK6(sK9(powerset(sK9(sK9(powerset(sK7(powerset(X0)))))))))
| empty(sK9(sK9(powerset(sK7(powerset(X0))))))
| empty(sK9(powerset(sK9(sK9(powerset(sK7(powerset(X0)))))))) )
| ~ spl16_325
| ~ spl16_388 ),
inference(resolution,[],[f4160,f3301]) ).
fof(f18186,plain,
( spl16_1037
| ~ spl16_326
| ~ spl16_387 ),
inference(avatar_split_clause,[],[f4228,f4155,f3305,f18184]) ).
fof(f18184,plain,
( spl16_1037
<=> ! [X0] :
( empty(sK6(powerset(X0)))
| empty(powerset(X0))
| element(sK9(sK7(sK9(powerset(sK9(sK9(powerset(sK6(powerset(X0))))))))),X0)
| empty(sK9(powerset(sK6(powerset(X0)))))
| empty(sK7(sK9(powerset(sK9(sK9(powerset(sK6(powerset(X0)))))))))
| empty(sK9(sK9(powerset(sK6(powerset(X0))))))
| empty(sK9(powerset(sK9(sK9(powerset(sK6(powerset(X0)))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1037])]) ).
fof(f4228,plain,
( ! [X0] :
( empty(sK6(powerset(X0)))
| empty(powerset(X0))
| element(sK9(sK7(sK9(powerset(sK9(sK9(powerset(sK6(powerset(X0))))))))),X0)
| empty(sK9(powerset(sK6(powerset(X0)))))
| empty(sK7(sK9(powerset(sK9(sK9(powerset(sK6(powerset(X0)))))))))
| empty(sK9(sK9(powerset(sK6(powerset(X0))))))
| empty(sK9(powerset(sK9(sK9(powerset(sK6(powerset(X0)))))))) )
| ~ spl16_326
| ~ spl16_387 ),
inference(resolution,[],[f4156,f3306]) ).
fof(f18182,plain,
( spl16_1036
| ~ spl16_325
| ~ spl16_387 ),
inference(avatar_split_clause,[],[f4224,f4155,f3300,f18180]) ).
fof(f18180,plain,
( spl16_1036
<=> ! [X0] :
( empty(sK6(powerset(X0)))
| empty(powerset(X0))
| element(sK9(sK6(sK9(powerset(sK9(sK9(powerset(sK6(powerset(X0))))))))),X0)
| empty(sK9(powerset(sK6(powerset(X0)))))
| empty(sK6(sK9(powerset(sK9(sK9(powerset(sK6(powerset(X0)))))))))
| empty(sK9(sK9(powerset(sK6(powerset(X0))))))
| empty(sK9(powerset(sK9(sK9(powerset(sK6(powerset(X0)))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1036])]) ).
fof(f4224,plain,
( ! [X0] :
( empty(sK6(powerset(X0)))
| empty(powerset(X0))
| element(sK9(sK6(sK9(powerset(sK9(sK9(powerset(sK6(powerset(X0))))))))),X0)
| empty(sK9(powerset(sK6(powerset(X0)))))
| empty(sK6(sK9(powerset(sK9(sK9(powerset(sK6(powerset(X0)))))))))
| empty(sK9(sK9(powerset(sK6(powerset(X0))))))
| empty(sK9(powerset(sK9(sK9(powerset(sK6(powerset(X0)))))))) )
| ~ spl16_325
| ~ spl16_387 ),
inference(resolution,[],[f4156,f3301]) ).
fof(f18178,plain,
( spl16_1035
| ~ spl16_349
| ~ spl16_371 ),
inference(avatar_split_clause,[],[f4050,f3915,f3578,f18176]) ).
fof(f18176,plain,
( spl16_1035
<=> ! [X0] :
( empty(sK7(sK9(powerset(powerset(X0)))))
| element(sK9(sK9(powerset(sK9(powerset(sK9(sK7(sK9(powerset(powerset(X0)))))))))),X0)
| empty(sK9(powerset(powerset(X0))))
| empty(sK9(powerset(sK9(sK7(sK9(powerset(powerset(X0))))))))
| empty(sK9(sK7(sK9(powerset(powerset(X0))))))
| empty(sK9(powerset(sK9(powerset(sK9(sK7(sK9(powerset(powerset(X0)))))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1035])]) ).
fof(f4050,plain,
( ! [X0] :
( empty(sK7(sK9(powerset(powerset(X0)))))
| element(sK9(sK9(powerset(sK9(powerset(sK9(sK7(sK9(powerset(powerset(X0)))))))))),X0)
| empty(sK9(powerset(powerset(X0))))
| empty(sK9(powerset(sK9(sK7(sK9(powerset(powerset(X0))))))))
| empty(sK9(sK7(sK9(powerset(powerset(X0))))))
| empty(sK9(powerset(sK9(powerset(sK9(sK7(sK9(powerset(powerset(X0)))))))))) )
| ~ spl16_349
| ~ spl16_371 ),
inference(resolution,[],[f3916,f3579]) ).
fof(f18174,plain,
( spl16_1034
| ~ spl16_349
| ~ spl16_370 ),
inference(avatar_split_clause,[],[f4034,f3911,f3578,f18172]) ).
fof(f18172,plain,
( spl16_1034
<=> ! [X0] :
( empty(sK6(sK9(powerset(powerset(X0)))))
| element(sK9(sK9(powerset(sK9(powerset(sK9(sK6(sK9(powerset(powerset(X0)))))))))),X0)
| empty(sK9(powerset(powerset(X0))))
| empty(sK9(powerset(sK9(sK6(sK9(powerset(powerset(X0))))))))
| empty(sK9(sK6(sK9(powerset(powerset(X0))))))
| empty(sK9(powerset(sK9(powerset(sK9(sK6(sK9(powerset(powerset(X0)))))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1034])]) ).
fof(f4034,plain,
( ! [X0] :
( empty(sK6(sK9(powerset(powerset(X0)))))
| element(sK9(sK9(powerset(sK9(powerset(sK9(sK6(sK9(powerset(powerset(X0)))))))))),X0)
| empty(sK9(powerset(powerset(X0))))
| empty(sK9(powerset(sK9(sK6(sK9(powerset(powerset(X0))))))))
| empty(sK9(sK6(sK9(powerset(powerset(X0))))))
| empty(sK9(powerset(sK9(powerset(sK9(sK6(sK9(powerset(powerset(X0)))))))))) )
| ~ spl16_349
| ~ spl16_370 ),
inference(resolution,[],[f3912,f3579]) ).
fof(f18064,plain,
( spl16_1033
| ~ spl16_150
| ~ spl16_449 ),
inference(avatar_split_clause,[],[f5323,f5213,f1218,f18062]) ).
fof(f18062,plain,
( spl16_1033
<=> ! [X0] :
( empty(powerset(powerset(X0)))
| empty(sK7(sK9(sK7(powerset(powerset(X0))))))
| empty(sK9(sK7(powerset(powerset(X0)))))
| element(sK9(sK7(sK9(sK7(sK9(sK7(powerset(powerset(X0)))))))),X0)
| empty(sK7(powerset(powerset(X0))))
| empty(sK7(sK9(sK7(sK9(sK7(powerset(powerset(X0))))))))
| empty(sK9(sK7(sK9(sK7(powerset(powerset(X0))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1033])]) ).
fof(f5323,plain,
( ! [X0] :
( empty(powerset(powerset(X0)))
| empty(sK7(sK9(sK7(powerset(powerset(X0))))))
| empty(sK9(sK7(powerset(powerset(X0)))))
| element(sK9(sK7(sK9(sK7(sK9(sK7(powerset(powerset(X0)))))))),X0)
| empty(sK7(powerset(powerset(X0))))
| empty(sK7(sK9(sK7(sK9(sK7(powerset(powerset(X0))))))))
| empty(sK9(sK7(sK9(sK7(powerset(powerset(X0))))))) )
| ~ spl16_150
| ~ spl16_449 ),
inference(resolution,[],[f5214,f1219]) ).
fof(f18060,plain,
( spl16_1032
| ~ spl16_149
| ~ spl16_449 ),
inference(avatar_split_clause,[],[f5316,f5213,f1214,f18058]) ).
fof(f18058,plain,
( spl16_1032
<=> ! [X0] :
( empty(powerset(powerset(X0)))
| empty(sK7(sK9(sK7(powerset(powerset(X0))))))
| empty(sK9(sK7(powerset(powerset(X0)))))
| element(sK9(sK6(sK9(sK7(sK9(sK7(powerset(powerset(X0)))))))),X0)
| empty(sK7(powerset(powerset(X0))))
| empty(sK6(sK9(sK7(sK9(sK7(powerset(powerset(X0))))))))
| empty(sK9(sK7(sK9(sK7(powerset(powerset(X0))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1032])]) ).
fof(f5316,plain,
( ! [X0] :
( empty(powerset(powerset(X0)))
| empty(sK7(sK9(sK7(powerset(powerset(X0))))))
| empty(sK9(sK7(powerset(powerset(X0)))))
| element(sK9(sK6(sK9(sK7(sK9(sK7(powerset(powerset(X0)))))))),X0)
| empty(sK7(powerset(powerset(X0))))
| empty(sK6(sK9(sK7(sK9(sK7(powerset(powerset(X0))))))))
| empty(sK9(sK7(sK9(sK7(powerset(powerset(X0))))))) )
| ~ spl16_149
| ~ spl16_449 ),
inference(resolution,[],[f5214,f1215]) ).
fof(f18055,plain,
( ~ spl16_1031
| ~ spl16_194
| spl16_949 ),
inference(avatar_split_clause,[],[f16965,f16431,f1676,f18052]) ).
fof(f18052,plain,
( spl16_1031
<=> in(sK9(the_InternalRel(sK8(sK8(sK1)))),the_InternalRel(sK1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1031])]) ).
fof(f1676,plain,
( spl16_194
<=> ! [X0] :
( ~ in(X0,the_InternalRel(sK1))
| element(X0,cartesian_product2(sK14,sK14)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_194])]) ).
fof(f16431,plain,
( spl16_949
<=> element(sK9(the_InternalRel(sK8(sK8(sK1)))),cartesian_product2(sK14,sK14)) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_949])]) ).
fof(f16965,plain,
( ~ in(sK9(the_InternalRel(sK8(sK8(sK1)))),the_InternalRel(sK1))
| ~ spl16_194
| spl16_949 ),
inference(resolution,[],[f16432,f1677]) ).
fof(f1677,plain,
( ! [X0] :
( element(X0,cartesian_product2(sK14,sK14))
| ~ in(X0,the_InternalRel(sK1)) )
| ~ spl16_194 ),
inference(avatar_component_clause,[],[f1676]) ).
fof(f16432,plain,
( ~ element(sK9(the_InternalRel(sK8(sK8(sK1)))),cartesian_product2(sK14,sK14))
| spl16_949 ),
inference(avatar_component_clause,[],[f16431]) ).
fof(f18050,plain,
( spl16_1030
| ~ spl16_150
| ~ spl16_448 ),
inference(avatar_split_clause,[],[f5298,f5209,f1218,f18048]) ).
fof(f18048,plain,
( spl16_1030
<=> ! [X0] :
( empty(powerset(powerset(X0)))
| empty(sK6(sK9(sK7(powerset(powerset(X0))))))
| empty(sK9(sK7(powerset(powerset(X0)))))
| element(sK9(sK7(sK9(sK6(sK9(sK7(powerset(powerset(X0)))))))),X0)
| empty(sK7(powerset(powerset(X0))))
| empty(sK7(sK9(sK6(sK9(sK7(powerset(powerset(X0))))))))
| empty(sK9(sK6(sK9(sK7(powerset(powerset(X0))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1030])]) ).
fof(f5298,plain,
( ! [X0] :
( empty(powerset(powerset(X0)))
| empty(sK6(sK9(sK7(powerset(powerset(X0))))))
| empty(sK9(sK7(powerset(powerset(X0)))))
| element(sK9(sK7(sK9(sK6(sK9(sK7(powerset(powerset(X0)))))))),X0)
| empty(sK7(powerset(powerset(X0))))
| empty(sK7(sK9(sK6(sK9(sK7(powerset(powerset(X0))))))))
| empty(sK9(sK6(sK9(sK7(powerset(powerset(X0))))))) )
| ~ spl16_150
| ~ spl16_448 ),
inference(resolution,[],[f5210,f1219]) ).
fof(f18046,plain,
( spl16_1029
| ~ spl16_149
| ~ spl16_448 ),
inference(avatar_split_clause,[],[f5291,f5209,f1214,f18044]) ).
fof(f18044,plain,
( spl16_1029
<=> ! [X0] :
( empty(powerset(powerset(X0)))
| empty(sK6(sK9(sK7(powerset(powerset(X0))))))
| empty(sK9(sK7(powerset(powerset(X0)))))
| element(sK9(sK6(sK9(sK6(sK9(sK7(powerset(powerset(X0)))))))),X0)
| empty(sK7(powerset(powerset(X0))))
| empty(sK6(sK9(sK6(sK9(sK7(powerset(powerset(X0))))))))
| empty(sK9(sK6(sK9(sK7(powerset(powerset(X0))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1029])]) ).
fof(f5291,plain,
( ! [X0] :
( empty(powerset(powerset(X0)))
| empty(sK6(sK9(sK7(powerset(powerset(X0))))))
| empty(sK9(sK7(powerset(powerset(X0)))))
| element(sK9(sK6(sK9(sK6(sK9(sK7(powerset(powerset(X0)))))))),X0)
| empty(sK7(powerset(powerset(X0))))
| empty(sK6(sK9(sK6(sK9(sK7(powerset(powerset(X0))))))))
| empty(sK9(sK6(sK9(sK7(powerset(powerset(X0))))))) )
| ~ spl16_149
| ~ spl16_448 ),
inference(resolution,[],[f5210,f1215]) ).
fof(f18042,plain,
( spl16_1028
| ~ spl16_150
| ~ spl16_447 ),
inference(avatar_split_clause,[],[f5273,f5205,f1218,f18040]) ).
fof(f18040,plain,
( spl16_1028
<=> ! [X0] :
( empty(powerset(powerset(X0)))
| empty(sK7(sK9(sK6(powerset(powerset(X0))))))
| empty(sK9(sK6(powerset(powerset(X0)))))
| element(sK9(sK7(sK9(sK7(sK9(sK6(powerset(powerset(X0)))))))),X0)
| empty(sK6(powerset(powerset(X0))))
| empty(sK7(sK9(sK7(sK9(sK6(powerset(powerset(X0))))))))
| empty(sK9(sK7(sK9(sK6(powerset(powerset(X0))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1028])]) ).
fof(f5273,plain,
( ! [X0] :
( empty(powerset(powerset(X0)))
| empty(sK7(sK9(sK6(powerset(powerset(X0))))))
| empty(sK9(sK6(powerset(powerset(X0)))))
| element(sK9(sK7(sK9(sK7(sK9(sK6(powerset(powerset(X0)))))))),X0)
| empty(sK6(powerset(powerset(X0))))
| empty(sK7(sK9(sK7(sK9(sK6(powerset(powerset(X0))))))))
| empty(sK9(sK7(sK9(sK6(powerset(powerset(X0))))))) )
| ~ spl16_150
| ~ spl16_447 ),
inference(resolution,[],[f5206,f1219]) ).
fof(f18038,plain,
( spl16_1027
| ~ spl16_149
| ~ spl16_447 ),
inference(avatar_split_clause,[],[f5266,f5205,f1214,f18036]) ).
fof(f18036,plain,
( spl16_1027
<=> ! [X0] :
( empty(powerset(powerset(X0)))
| empty(sK7(sK9(sK6(powerset(powerset(X0))))))
| empty(sK9(sK6(powerset(powerset(X0)))))
| element(sK9(sK6(sK9(sK7(sK9(sK6(powerset(powerset(X0)))))))),X0)
| empty(sK6(powerset(powerset(X0))))
| empty(sK6(sK9(sK7(sK9(sK6(powerset(powerset(X0))))))))
| empty(sK9(sK7(sK9(sK6(powerset(powerset(X0))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1027])]) ).
fof(f5266,plain,
( ! [X0] :
( empty(powerset(powerset(X0)))
| empty(sK7(sK9(sK6(powerset(powerset(X0))))))
| empty(sK9(sK6(powerset(powerset(X0)))))
| element(sK9(sK6(sK9(sK7(sK9(sK6(powerset(powerset(X0)))))))),X0)
| empty(sK6(powerset(powerset(X0))))
| empty(sK6(sK9(sK7(sK9(sK6(powerset(powerset(X0))))))))
| empty(sK9(sK7(sK9(sK6(powerset(powerset(X0))))))) )
| ~ spl16_149
| ~ spl16_447 ),
inference(resolution,[],[f5206,f1215]) ).
fof(f18034,plain,
( spl16_1026
| ~ spl16_150
| ~ spl16_446 ),
inference(avatar_split_clause,[],[f5248,f5201,f1218,f18032]) ).
fof(f18032,plain,
( spl16_1026
<=> ! [X0] :
( empty(powerset(powerset(X0)))
| empty(sK6(sK9(sK6(powerset(powerset(X0))))))
| empty(sK9(sK6(powerset(powerset(X0)))))
| element(sK9(sK7(sK9(sK6(sK9(sK6(powerset(powerset(X0)))))))),X0)
| empty(sK6(powerset(powerset(X0))))
| empty(sK7(sK9(sK6(sK9(sK6(powerset(powerset(X0))))))))
| empty(sK9(sK6(sK9(sK6(powerset(powerset(X0))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1026])]) ).
fof(f5248,plain,
( ! [X0] :
( empty(powerset(powerset(X0)))
| empty(sK6(sK9(sK6(powerset(powerset(X0))))))
| empty(sK9(sK6(powerset(powerset(X0)))))
| element(sK9(sK7(sK9(sK6(sK9(sK6(powerset(powerset(X0)))))))),X0)
| empty(sK6(powerset(powerset(X0))))
| empty(sK7(sK9(sK6(sK9(sK6(powerset(powerset(X0))))))))
| empty(sK9(sK6(sK9(sK6(powerset(powerset(X0))))))) )
| ~ spl16_150
| ~ spl16_446 ),
inference(resolution,[],[f5202,f1219]) ).
fof(f18030,plain,
( spl16_1025
| ~ spl16_149
| ~ spl16_446 ),
inference(avatar_split_clause,[],[f5241,f5201,f1214,f18028]) ).
fof(f18028,plain,
( spl16_1025
<=> ! [X0] :
( empty(powerset(powerset(X0)))
| empty(sK6(sK9(sK6(powerset(powerset(X0))))))
| empty(sK9(sK6(powerset(powerset(X0)))))
| element(sK9(sK6(sK9(sK6(sK9(sK6(powerset(powerset(X0)))))))),X0)
| empty(sK6(powerset(powerset(X0))))
| empty(sK6(sK9(sK6(sK9(sK6(powerset(powerset(X0))))))))
| empty(sK9(sK6(sK9(sK6(powerset(powerset(X0))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1025])]) ).
fof(f5241,plain,
( ! [X0] :
( empty(powerset(powerset(X0)))
| empty(sK6(sK9(sK6(powerset(powerset(X0))))))
| empty(sK9(sK6(powerset(powerset(X0)))))
| element(sK9(sK6(sK9(sK6(sK9(sK6(powerset(powerset(X0)))))))),X0)
| empty(sK6(powerset(powerset(X0))))
| empty(sK6(sK9(sK6(sK9(sK6(powerset(powerset(X0))))))))
| empty(sK9(sK6(sK9(sK6(powerset(powerset(X0))))))) )
| ~ spl16_149
| ~ spl16_446 ),
inference(resolution,[],[f5202,f1215]) ).
fof(f18026,plain,
( spl16_1024
| ~ spl16_306
| ~ spl16_409 ),
inference(avatar_split_clause,[],[f4441,f4407,f2964,f18024]) ).
fof(f18024,plain,
( spl16_1024
<=> ! [X0] :
( empty(powerset(powerset(X0)))
| empty(sK9(sK7(powerset(powerset(X0)))))
| element(sK9(sK7(sK7(sK9(sK9(sK7(powerset(powerset(X0)))))))),X0)
| empty(sK7(powerset(powerset(X0))))
| empty(sK7(sK7(sK9(sK9(sK7(powerset(powerset(X0))))))))
| empty(sK9(sK9(sK7(powerset(powerset(X0))))))
| empty(sK7(sK9(sK9(sK7(powerset(powerset(X0))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1024])]) ).
fof(f4441,plain,
( ! [X0] :
( empty(powerset(powerset(X0)))
| empty(sK9(sK7(powerset(powerset(X0)))))
| element(sK9(sK7(sK7(sK9(sK9(sK7(powerset(powerset(X0)))))))),X0)
| empty(sK7(powerset(powerset(X0))))
| empty(sK7(sK7(sK9(sK9(sK7(powerset(powerset(X0))))))))
| empty(sK9(sK9(sK7(powerset(powerset(X0))))))
| empty(sK7(sK9(sK9(sK7(powerset(powerset(X0))))))) )
| ~ spl16_306
| ~ spl16_409 ),
inference(resolution,[],[f4408,f2965]) ).
fof(f18022,plain,
( spl16_1023
| ~ spl16_305
| ~ spl16_409 ),
inference(avatar_split_clause,[],[f4440,f4407,f2960,f18020]) ).
fof(f18020,plain,
( spl16_1023
<=> ! [X0] :
( empty(powerset(powerset(X0)))
| empty(sK9(sK7(powerset(powerset(X0)))))
| element(sK9(sK7(sK6(sK9(sK9(sK7(powerset(powerset(X0)))))))),X0)
| empty(sK7(powerset(powerset(X0))))
| empty(sK7(sK6(sK9(sK9(sK7(powerset(powerset(X0))))))))
| empty(sK9(sK9(sK7(powerset(powerset(X0))))))
| empty(sK6(sK9(sK9(sK7(powerset(powerset(X0))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1023])]) ).
fof(f4440,plain,
( ! [X0] :
( empty(powerset(powerset(X0)))
| empty(sK9(sK7(powerset(powerset(X0)))))
| element(sK9(sK7(sK6(sK9(sK9(sK7(powerset(powerset(X0)))))))),X0)
| empty(sK7(powerset(powerset(X0))))
| empty(sK7(sK6(sK9(sK9(sK7(powerset(powerset(X0))))))))
| empty(sK9(sK9(sK7(powerset(powerset(X0))))))
| empty(sK6(sK9(sK9(sK7(powerset(powerset(X0))))))) )
| ~ spl16_305
| ~ spl16_409 ),
inference(resolution,[],[f4408,f2961]) ).
fof(f18018,plain,
( spl16_1022
| ~ spl16_304
| ~ spl16_409 ),
inference(avatar_split_clause,[],[f4437,f4407,f2956,f18016]) ).
fof(f18016,plain,
( spl16_1022
<=> ! [X0] :
( empty(powerset(powerset(X0)))
| empty(sK9(sK7(powerset(powerset(X0)))))
| element(sK9(sK6(sK7(sK9(sK9(sK7(powerset(powerset(X0)))))))),X0)
| empty(sK7(powerset(powerset(X0))))
| empty(sK6(sK7(sK9(sK9(sK7(powerset(powerset(X0))))))))
| empty(sK9(sK9(sK7(powerset(powerset(X0))))))
| empty(sK7(sK9(sK9(sK7(powerset(powerset(X0))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1022])]) ).
fof(f4437,plain,
( ! [X0] :
( empty(powerset(powerset(X0)))
| empty(sK9(sK7(powerset(powerset(X0)))))
| element(sK9(sK6(sK7(sK9(sK9(sK7(powerset(powerset(X0)))))))),X0)
| empty(sK7(powerset(powerset(X0))))
| empty(sK6(sK7(sK9(sK9(sK7(powerset(powerset(X0))))))))
| empty(sK9(sK9(sK7(powerset(powerset(X0))))))
| empty(sK7(sK9(sK9(sK7(powerset(powerset(X0))))))) )
| ~ spl16_304
| ~ spl16_409 ),
inference(resolution,[],[f4408,f2957]) ).
fof(f18014,plain,
( spl16_1021
| ~ spl16_303
| ~ spl16_409 ),
inference(avatar_split_clause,[],[f4436,f4407,f2952,f18012]) ).
fof(f18012,plain,
( spl16_1021
<=> ! [X0] :
( empty(powerset(powerset(X0)))
| empty(sK9(sK7(powerset(powerset(X0)))))
| element(sK9(sK6(sK6(sK9(sK9(sK7(powerset(powerset(X0)))))))),X0)
| empty(sK7(powerset(powerset(X0))))
| empty(sK6(sK6(sK9(sK9(sK7(powerset(powerset(X0))))))))
| empty(sK9(sK9(sK7(powerset(powerset(X0))))))
| empty(sK6(sK9(sK9(sK7(powerset(powerset(X0))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1021])]) ).
fof(f4436,plain,
( ! [X0] :
( empty(powerset(powerset(X0)))
| empty(sK9(sK7(powerset(powerset(X0)))))
| element(sK9(sK6(sK6(sK9(sK9(sK7(powerset(powerset(X0)))))))),X0)
| empty(sK7(powerset(powerset(X0))))
| empty(sK6(sK6(sK9(sK9(sK7(powerset(powerset(X0))))))))
| empty(sK9(sK9(sK7(powerset(powerset(X0))))))
| empty(sK6(sK9(sK9(sK7(powerset(powerset(X0))))))) )
| ~ spl16_303
| ~ spl16_409 ),
inference(resolution,[],[f4408,f2953]) ).
fof(f17896,plain,
( spl16_1020
| ~ spl16_306
| ~ spl16_408 ),
inference(avatar_split_clause,[],[f4425,f4403,f2964,f17894]) ).
fof(f17894,plain,
( spl16_1020
<=> ! [X0] :
( empty(powerset(powerset(X0)))
| empty(sK9(sK6(powerset(powerset(X0)))))
| element(sK9(sK7(sK7(sK9(sK9(sK6(powerset(powerset(X0)))))))),X0)
| empty(sK6(powerset(powerset(X0))))
| empty(sK7(sK7(sK9(sK9(sK6(powerset(powerset(X0))))))))
| empty(sK9(sK9(sK6(powerset(powerset(X0))))))
| empty(sK7(sK9(sK9(sK6(powerset(powerset(X0))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1020])]) ).
fof(f4425,plain,
( ! [X0] :
( empty(powerset(powerset(X0)))
| empty(sK9(sK6(powerset(powerset(X0)))))
| element(sK9(sK7(sK7(sK9(sK9(sK6(powerset(powerset(X0)))))))),X0)
| empty(sK6(powerset(powerset(X0))))
| empty(sK7(sK7(sK9(sK9(sK6(powerset(powerset(X0))))))))
| empty(sK9(sK9(sK6(powerset(powerset(X0))))))
| empty(sK7(sK9(sK9(sK6(powerset(powerset(X0))))))) )
| ~ spl16_306
| ~ spl16_408 ),
inference(resolution,[],[f4404,f2965]) ).
fof(f17892,plain,
( spl16_1019
| ~ spl16_305
| ~ spl16_408 ),
inference(avatar_split_clause,[],[f4424,f4403,f2960,f17890]) ).
fof(f17890,plain,
( spl16_1019
<=> ! [X0] :
( empty(powerset(powerset(X0)))
| empty(sK9(sK6(powerset(powerset(X0)))))
| element(sK9(sK7(sK6(sK9(sK9(sK6(powerset(powerset(X0)))))))),X0)
| empty(sK6(powerset(powerset(X0))))
| empty(sK7(sK6(sK9(sK9(sK6(powerset(powerset(X0))))))))
| empty(sK9(sK9(sK6(powerset(powerset(X0))))))
| empty(sK6(sK9(sK9(sK6(powerset(powerset(X0))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1019])]) ).
fof(f4424,plain,
( ! [X0] :
( empty(powerset(powerset(X0)))
| empty(sK9(sK6(powerset(powerset(X0)))))
| element(sK9(sK7(sK6(sK9(sK9(sK6(powerset(powerset(X0)))))))),X0)
| empty(sK6(powerset(powerset(X0))))
| empty(sK7(sK6(sK9(sK9(sK6(powerset(powerset(X0))))))))
| empty(sK9(sK9(sK6(powerset(powerset(X0))))))
| empty(sK6(sK9(sK9(sK6(powerset(powerset(X0))))))) )
| ~ spl16_305
| ~ spl16_408 ),
inference(resolution,[],[f4404,f2961]) ).
fof(f17888,plain,
( spl16_1018
| ~ spl16_304
| ~ spl16_408 ),
inference(avatar_split_clause,[],[f4421,f4403,f2956,f17886]) ).
fof(f17886,plain,
( spl16_1018
<=> ! [X0] :
( empty(powerset(powerset(X0)))
| empty(sK9(sK6(powerset(powerset(X0)))))
| element(sK9(sK6(sK7(sK9(sK9(sK6(powerset(powerset(X0)))))))),X0)
| empty(sK6(powerset(powerset(X0))))
| empty(sK6(sK7(sK9(sK9(sK6(powerset(powerset(X0))))))))
| empty(sK9(sK9(sK6(powerset(powerset(X0))))))
| empty(sK7(sK9(sK9(sK6(powerset(powerset(X0))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1018])]) ).
fof(f4421,plain,
( ! [X0] :
( empty(powerset(powerset(X0)))
| empty(sK9(sK6(powerset(powerset(X0)))))
| element(sK9(sK6(sK7(sK9(sK9(sK6(powerset(powerset(X0)))))))),X0)
| empty(sK6(powerset(powerset(X0))))
| empty(sK6(sK7(sK9(sK9(sK6(powerset(powerset(X0))))))))
| empty(sK9(sK9(sK6(powerset(powerset(X0))))))
| empty(sK7(sK9(sK9(sK6(powerset(powerset(X0))))))) )
| ~ spl16_304
| ~ spl16_408 ),
inference(resolution,[],[f4404,f2957]) ).
fof(f17884,plain,
( spl16_1017
| ~ spl16_303
| ~ spl16_408 ),
inference(avatar_split_clause,[],[f4420,f4403,f2952,f17882]) ).
fof(f17882,plain,
( spl16_1017
<=> ! [X0] :
( empty(powerset(powerset(X0)))
| empty(sK9(sK6(powerset(powerset(X0)))))
| element(sK9(sK6(sK6(sK9(sK9(sK6(powerset(powerset(X0)))))))),X0)
| empty(sK6(powerset(powerset(X0))))
| empty(sK6(sK6(sK9(sK9(sK6(powerset(powerset(X0))))))))
| empty(sK9(sK9(sK6(powerset(powerset(X0))))))
| empty(sK6(sK9(sK9(sK6(powerset(powerset(X0))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1017])]) ).
fof(f4420,plain,
( ! [X0] :
( empty(powerset(powerset(X0)))
| empty(sK9(sK6(powerset(powerset(X0)))))
| element(sK9(sK6(sK6(sK9(sK9(sK6(powerset(powerset(X0)))))))),X0)
| empty(sK6(powerset(powerset(X0))))
| empty(sK6(sK6(sK9(sK9(sK6(powerset(powerset(X0))))))))
| empty(sK9(sK9(sK6(powerset(powerset(X0))))))
| empty(sK6(sK9(sK9(sK6(powerset(powerset(X0))))))) )
| ~ spl16_303
| ~ spl16_408 ),
inference(resolution,[],[f4404,f2953]) ).
fof(f17880,plain,
( spl16_1016
| ~ spl16_321
| ~ spl16_388 ),
inference(avatar_split_clause,[],[f4247,f4159,f3175,f17878]) ).
fof(f17878,plain,
( spl16_1016
<=> ! [X0] :
( empty(sK7(powerset(X0)))
| empty(powerset(X0))
| element(sK9(sK9(powerset(sK7(sK9(sK9(powerset(sK7(powerset(X0))))))))),X0)
| empty(sK9(powerset(sK7(powerset(X0)))))
| empty(sK7(sK9(sK9(powerset(sK7(powerset(X0)))))))
| empty(sK9(sK9(powerset(sK7(powerset(X0))))))
| empty(sK9(powerset(sK7(sK9(sK9(powerset(sK7(powerset(X0))))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1016])]) ).
fof(f4247,plain,
( ! [X0] :
( empty(sK7(powerset(X0)))
| empty(powerset(X0))
| element(sK9(sK9(powerset(sK7(sK9(sK9(powerset(sK7(powerset(X0))))))))),X0)
| empty(sK9(powerset(sK7(powerset(X0)))))
| empty(sK7(sK9(sK9(powerset(sK7(powerset(X0)))))))
| empty(sK9(sK9(powerset(sK7(powerset(X0))))))
| empty(sK9(powerset(sK7(sK9(sK9(powerset(sK7(powerset(X0))))))))) )
| ~ spl16_321
| ~ spl16_388 ),
inference(resolution,[],[f4160,f3176]) ).
fof(f17876,plain,
( spl16_1015
| ~ spl16_320
| ~ spl16_388 ),
inference(avatar_split_clause,[],[f4246,f4159,f3171,f17874]) ).
fof(f17874,plain,
( spl16_1015
<=> ! [X0] :
( empty(sK7(powerset(X0)))
| empty(powerset(X0))
| element(sK9(sK9(powerset(sK6(sK9(sK9(powerset(sK7(powerset(X0))))))))),X0)
| empty(sK9(powerset(sK7(powerset(X0)))))
| empty(sK6(sK9(sK9(powerset(sK7(powerset(X0)))))))
| empty(sK9(sK9(powerset(sK7(powerset(X0))))))
| empty(sK9(powerset(sK6(sK9(sK9(powerset(sK7(powerset(X0))))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1015])]) ).
fof(f4246,plain,
( ! [X0] :
( empty(sK7(powerset(X0)))
| empty(powerset(X0))
| element(sK9(sK9(powerset(sK6(sK9(sK9(powerset(sK7(powerset(X0))))))))),X0)
| empty(sK9(powerset(sK7(powerset(X0)))))
| empty(sK6(sK9(sK9(powerset(sK7(powerset(X0)))))))
| empty(sK9(sK9(powerset(sK7(powerset(X0))))))
| empty(sK9(powerset(sK6(sK9(sK9(powerset(sK7(powerset(X0))))))))) )
| ~ spl16_320
| ~ spl16_388 ),
inference(resolution,[],[f4160,f3172]) ).
fof(f17872,plain,
( spl16_1014
| ~ spl16_321
| ~ spl16_387 ),
inference(avatar_split_clause,[],[f4231,f4155,f3175,f17870]) ).
fof(f17870,plain,
( spl16_1014
<=> ! [X0] :
( empty(sK6(powerset(X0)))
| empty(powerset(X0))
| element(sK9(sK9(powerset(sK7(sK9(sK9(powerset(sK6(powerset(X0))))))))),X0)
| empty(sK9(powerset(sK6(powerset(X0)))))
| empty(sK7(sK9(sK9(powerset(sK6(powerset(X0)))))))
| empty(sK9(sK9(powerset(sK6(powerset(X0))))))
| empty(sK9(powerset(sK7(sK9(sK9(powerset(sK6(powerset(X0))))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1014])]) ).
fof(f4231,plain,
( ! [X0] :
( empty(sK6(powerset(X0)))
| empty(powerset(X0))
| element(sK9(sK9(powerset(sK7(sK9(sK9(powerset(sK6(powerset(X0))))))))),X0)
| empty(sK9(powerset(sK6(powerset(X0)))))
| empty(sK7(sK9(sK9(powerset(sK6(powerset(X0)))))))
| empty(sK9(sK9(powerset(sK6(powerset(X0))))))
| empty(sK9(powerset(sK7(sK9(sK9(powerset(sK6(powerset(X0))))))))) )
| ~ spl16_321
| ~ spl16_387 ),
inference(resolution,[],[f4156,f3176]) ).
fof(f17868,plain,
( spl16_1013
| ~ spl16_320
| ~ spl16_387 ),
inference(avatar_split_clause,[],[f4230,f4155,f3171,f17866]) ).
fof(f17866,plain,
( spl16_1013
<=> ! [X0] :
( empty(sK6(powerset(X0)))
| empty(powerset(X0))
| element(sK9(sK9(powerset(sK6(sK9(sK9(powerset(sK6(powerset(X0))))))))),X0)
| empty(sK9(powerset(sK6(powerset(X0)))))
| empty(sK6(sK9(sK9(powerset(sK6(powerset(X0)))))))
| empty(sK9(sK9(powerset(sK6(powerset(X0))))))
| empty(sK9(powerset(sK6(sK9(sK9(powerset(sK6(powerset(X0))))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1013])]) ).
fof(f4230,plain,
( ! [X0] :
( empty(sK6(powerset(X0)))
| empty(powerset(X0))
| element(sK9(sK9(powerset(sK6(sK9(sK9(powerset(sK6(powerset(X0))))))))),X0)
| empty(sK9(powerset(sK6(powerset(X0)))))
| empty(sK6(sK9(sK9(powerset(sK6(powerset(X0)))))))
| empty(sK9(sK9(powerset(sK6(powerset(X0))))))
| empty(sK9(powerset(sK6(sK9(sK9(powerset(sK6(powerset(X0))))))))) )
| ~ spl16_320
| ~ spl16_387 ),
inference(resolution,[],[f4156,f3172]) ).
fof(f17704,plain,
( spl16_1012
| ~ spl16_326
| ~ spl16_371 ),
inference(avatar_split_clause,[],[f4046,f3915,f3305,f17702]) ).
fof(f17702,plain,
( spl16_1012
<=> ! [X0] :
( empty(sK7(sK9(powerset(powerset(X0)))))
| element(sK9(sK7(sK9(powerset(sK9(sK7(sK9(powerset(powerset(X0))))))))),X0)
| empty(sK9(powerset(powerset(X0))))
| empty(sK7(sK9(powerset(sK9(sK7(sK9(powerset(powerset(X0)))))))))
| empty(sK9(sK7(sK9(powerset(powerset(X0))))))
| empty(sK9(powerset(sK9(sK7(sK9(powerset(powerset(X0)))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1012])]) ).
fof(f4046,plain,
( ! [X0] :
( empty(sK7(sK9(powerset(powerset(X0)))))
| element(sK9(sK7(sK9(powerset(sK9(sK7(sK9(powerset(powerset(X0))))))))),X0)
| empty(sK9(powerset(powerset(X0))))
| empty(sK7(sK9(powerset(sK9(sK7(sK9(powerset(powerset(X0)))))))))
| empty(sK9(sK7(sK9(powerset(powerset(X0))))))
| empty(sK9(powerset(sK9(sK7(sK9(powerset(powerset(X0)))))))) )
| ~ spl16_326
| ~ spl16_371 ),
inference(resolution,[],[f3916,f3306]) ).
fof(f17700,plain,
( spl16_1011
| ~ spl16_325
| ~ spl16_371 ),
inference(avatar_split_clause,[],[f4042,f3915,f3300,f17698]) ).
fof(f17698,plain,
( spl16_1011
<=> ! [X0] :
( empty(sK7(sK9(powerset(powerset(X0)))))
| element(sK9(sK6(sK9(powerset(sK9(sK7(sK9(powerset(powerset(X0))))))))),X0)
| empty(sK9(powerset(powerset(X0))))
| empty(sK6(sK9(powerset(sK9(sK7(sK9(powerset(powerset(X0)))))))))
| empty(sK9(sK7(sK9(powerset(powerset(X0))))))
| empty(sK9(powerset(sK9(sK7(sK9(powerset(powerset(X0)))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1011])]) ).
fof(f4042,plain,
( ! [X0] :
( empty(sK7(sK9(powerset(powerset(X0)))))
| element(sK9(sK6(sK9(powerset(sK9(sK7(sK9(powerset(powerset(X0))))))))),X0)
| empty(sK9(powerset(powerset(X0))))
| empty(sK6(sK9(powerset(sK9(sK7(sK9(powerset(powerset(X0)))))))))
| empty(sK9(sK7(sK9(powerset(powerset(X0))))))
| empty(sK9(powerset(sK9(sK7(sK9(powerset(powerset(X0)))))))) )
| ~ spl16_325
| ~ spl16_371 ),
inference(resolution,[],[f3916,f3301]) ).
fof(f17696,plain,
( spl16_1010
| ~ spl16_326
| ~ spl16_370 ),
inference(avatar_split_clause,[],[f4030,f3911,f3305,f17694]) ).
fof(f17694,plain,
( spl16_1010
<=> ! [X0] :
( empty(sK6(sK9(powerset(powerset(X0)))))
| element(sK9(sK7(sK9(powerset(sK9(sK6(sK9(powerset(powerset(X0))))))))),X0)
| empty(sK9(powerset(powerset(X0))))
| empty(sK7(sK9(powerset(sK9(sK6(sK9(powerset(powerset(X0)))))))))
| empty(sK9(sK6(sK9(powerset(powerset(X0))))))
| empty(sK9(powerset(sK9(sK6(sK9(powerset(powerset(X0)))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1010])]) ).
fof(f4030,plain,
( ! [X0] :
( empty(sK6(sK9(powerset(powerset(X0)))))
| element(sK9(sK7(sK9(powerset(sK9(sK6(sK9(powerset(powerset(X0))))))))),X0)
| empty(sK9(powerset(powerset(X0))))
| empty(sK7(sK9(powerset(sK9(sK6(sK9(powerset(powerset(X0)))))))))
| empty(sK9(sK6(sK9(powerset(powerset(X0))))))
| empty(sK9(powerset(sK9(sK6(sK9(powerset(powerset(X0)))))))) )
| ~ spl16_326
| ~ spl16_370 ),
inference(resolution,[],[f3912,f3306]) ).
fof(f17692,plain,
( spl16_1009
| ~ spl16_325
| ~ spl16_370 ),
inference(avatar_split_clause,[],[f4026,f3911,f3300,f17690]) ).
fof(f17690,plain,
( spl16_1009
<=> ! [X0] :
( empty(sK6(sK9(powerset(powerset(X0)))))
| element(sK9(sK6(sK9(powerset(sK9(sK6(sK9(powerset(powerset(X0))))))))),X0)
| empty(sK9(powerset(powerset(X0))))
| empty(sK6(sK9(powerset(sK9(sK6(sK9(powerset(powerset(X0)))))))))
| empty(sK9(sK6(sK9(powerset(powerset(X0))))))
| empty(sK9(powerset(sK9(sK6(sK9(powerset(powerset(X0)))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1009])]) ).
fof(f4026,plain,
( ! [X0] :
( empty(sK6(sK9(powerset(powerset(X0)))))
| element(sK9(sK6(sK9(powerset(sK9(sK6(sK9(powerset(powerset(X0))))))))),X0)
| empty(sK9(powerset(powerset(X0))))
| empty(sK6(sK9(powerset(sK9(sK6(sK9(powerset(powerset(X0)))))))))
| empty(sK9(sK6(sK9(powerset(powerset(X0))))))
| empty(sK9(powerset(sK9(sK6(sK9(powerset(powerset(X0)))))))) )
| ~ spl16_325
| ~ spl16_370 ),
inference(resolution,[],[f3912,f3301]) ).
fof(f17688,plain,
( spl16_805
| ~ spl16_23
| ~ spl16_57
| ~ spl16_948 ),
inference(avatar_split_clause,[],[f16566,f16427,f469,f263,f14693]) ).
fof(f263,plain,
( spl16_23
<=> ! [X0] :
( empty_set = X0
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_23])]) ).
fof(f469,plain,
( spl16_57
<=> empty_set = sK14 ),
introduced(avatar_definition,[new_symbols(naming,[spl16_57])]) ).
fof(f16427,plain,
( spl16_948
<=> empty(the_InternalRel(sK8(sK8(sK1)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_948])]) ).
fof(f16566,plain,
( sK14 = the_InternalRel(sK8(sK8(sK1)))
| ~ spl16_23
| ~ spl16_57
| ~ spl16_948 ),
inference(forward_demodulation,[],[f16486,f471]) ).
fof(f471,plain,
( empty_set = sK14
| ~ spl16_57 ),
inference(avatar_component_clause,[],[f469]) ).
fof(f16486,plain,
( empty_set = the_InternalRel(sK8(sK8(sK1)))
| ~ spl16_23
| ~ spl16_948 ),
inference(resolution,[],[f16429,f264]) ).
fof(f264,plain,
( ! [X0] :
( ~ empty(X0)
| empty_set = X0 )
| ~ spl16_23 ),
inference(avatar_component_clause,[],[f263]) ).
fof(f16429,plain,
( empty(the_InternalRel(sK8(sK8(sK1))))
| ~ spl16_948 ),
inference(avatar_component_clause,[],[f16427]) ).
fof(f17687,plain,
( spl16_1008
| ~ spl16_362
| ~ spl16_369 ),
inference(avatar_split_clause,[],[f4021,f3907,f3670,f17685]) ).
fof(f17685,plain,
( spl16_1008
<=> ! [X0] :
( empty(sK7(sK7(powerset(X0))))
| empty(powerset(X0))
| element(sK9(sK9(sK9(powerset(powerset(sK9(sK7(sK7(powerset(X0))))))))),X0)
| empty(sK7(powerset(X0)))
| empty(sK9(sK9(powerset(powerset(sK9(sK7(sK7(powerset(X0)))))))))
| empty(sK9(sK7(sK7(powerset(X0)))))
| empty(sK9(powerset(powerset(sK9(sK7(sK7(powerset(X0)))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1008])]) ).
fof(f4021,plain,
( ! [X0] :
( empty(sK7(sK7(powerset(X0))))
| empty(powerset(X0))
| element(sK9(sK9(sK9(powerset(powerset(sK9(sK7(sK7(powerset(X0))))))))),X0)
| empty(sK7(powerset(X0)))
| empty(sK9(sK9(powerset(powerset(sK9(sK7(sK7(powerset(X0)))))))))
| empty(sK9(sK7(sK7(powerset(X0)))))
| empty(sK9(powerset(powerset(sK9(sK7(sK7(powerset(X0)))))))) )
| ~ spl16_362
| ~ spl16_369 ),
inference(resolution,[],[f3908,f3671]) ).
fof(f17683,plain,
( spl16_1007
| ~ spl16_362
| ~ spl16_368 ),
inference(avatar_split_clause,[],[f4005,f3903,f3670,f17681]) ).
fof(f17681,plain,
( spl16_1007
<=> ! [X0] :
( empty(sK7(sK6(powerset(X0))))
| empty(powerset(X0))
| element(sK9(sK9(sK9(powerset(powerset(sK9(sK7(sK6(powerset(X0))))))))),X0)
| empty(sK6(powerset(X0)))
| empty(sK9(sK9(powerset(powerset(sK9(sK7(sK6(powerset(X0)))))))))
| empty(sK9(sK7(sK6(powerset(X0)))))
| empty(sK9(powerset(powerset(sK9(sK7(sK6(powerset(X0)))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1007])]) ).
fof(f4005,plain,
( ! [X0] :
( empty(sK7(sK6(powerset(X0))))
| empty(powerset(X0))
| element(sK9(sK9(sK9(powerset(powerset(sK9(sK7(sK6(powerset(X0))))))))),X0)
| empty(sK6(powerset(X0)))
| empty(sK9(sK9(powerset(powerset(sK9(sK7(sK6(powerset(X0)))))))))
| empty(sK9(sK7(sK6(powerset(X0)))))
| empty(sK9(powerset(powerset(sK9(sK7(sK6(powerset(X0)))))))) )
| ~ spl16_362
| ~ spl16_368 ),
inference(resolution,[],[f3904,f3671]) ).
fof(f17679,plain,
( spl16_1006
| ~ spl16_362
| ~ spl16_366 ),
inference(avatar_split_clause,[],[f3989,f3895,f3670,f17677]) ).
fof(f17677,plain,
( spl16_1006
<=> ! [X0] :
( empty(sK6(sK7(powerset(X0))))
| empty(powerset(X0))
| element(sK9(sK9(sK9(powerset(powerset(sK9(sK6(sK7(powerset(X0))))))))),X0)
| empty(sK7(powerset(X0)))
| empty(sK9(sK9(powerset(powerset(sK9(sK6(sK7(powerset(X0)))))))))
| empty(sK9(sK6(sK7(powerset(X0)))))
| empty(sK9(powerset(powerset(sK9(sK6(sK7(powerset(X0)))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1006])]) ).
fof(f3989,plain,
( ! [X0] :
( empty(sK6(sK7(powerset(X0))))
| empty(powerset(X0))
| element(sK9(sK9(sK9(powerset(powerset(sK9(sK6(sK7(powerset(X0))))))))),X0)
| empty(sK7(powerset(X0)))
| empty(sK9(sK9(powerset(powerset(sK9(sK6(sK7(powerset(X0)))))))))
| empty(sK9(sK6(sK7(powerset(X0)))))
| empty(sK9(powerset(powerset(sK9(sK6(sK7(powerset(X0)))))))) )
| ~ spl16_362
| ~ spl16_366 ),
inference(resolution,[],[f3896,f3671]) ).
fof(f17675,plain,
( spl16_1005
| ~ spl16_362
| ~ spl16_365 ),
inference(avatar_split_clause,[],[f3973,f3891,f3670,f17673]) ).
fof(f17673,plain,
( spl16_1005
<=> ! [X0] :
( empty(sK6(sK6(powerset(X0))))
| empty(powerset(X0))
| element(sK9(sK9(sK9(powerset(powerset(sK9(sK6(sK6(powerset(X0))))))))),X0)
| empty(sK6(powerset(X0)))
| empty(sK9(sK9(powerset(powerset(sK9(sK6(sK6(powerset(X0)))))))))
| empty(sK9(sK6(sK6(powerset(X0)))))
| empty(sK9(powerset(powerset(sK9(sK6(sK6(powerset(X0)))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1005])]) ).
fof(f3973,plain,
( ! [X0] :
( empty(sK6(sK6(powerset(X0))))
| empty(powerset(X0))
| element(sK9(sK9(sK9(powerset(powerset(sK9(sK6(sK6(powerset(X0))))))))),X0)
| empty(sK6(powerset(X0)))
| empty(sK9(sK9(powerset(powerset(sK9(sK6(sK6(powerset(X0)))))))))
| empty(sK9(sK6(sK6(powerset(X0)))))
| empty(sK9(powerset(powerset(sK9(sK6(sK6(powerset(X0)))))))) )
| ~ spl16_362
| ~ spl16_365 ),
inference(resolution,[],[f3892,f3671]) ).
fof(f17400,plain,
( spl16_1004
| spl16_165
| ~ spl16_38
| ~ spl16_949 ),
inference(avatar_split_clause,[],[f17345,f16431,f335,f1368,f17397]) ).
fof(f1368,plain,
( spl16_165
<=> empty(cartesian_product2(sK14,sK14)) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_165])]) ).
fof(f335,plain,
( spl16_38
<=> ! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_38])]) ).
fof(f17345,plain,
( empty(cartesian_product2(sK14,sK14))
| in(sK9(the_InternalRel(sK8(sK8(sK1)))),cartesian_product2(sK14,sK14))
| ~ spl16_38
| ~ spl16_949 ),
inference(resolution,[],[f16433,f336]) ).
fof(f336,plain,
( ! [X0,X1] :
( ~ element(X0,X1)
| empty(X1)
| in(X0,X1) )
| ~ spl16_38 ),
inference(avatar_component_clause,[],[f335]) ).
fof(f16433,plain,
( element(sK9(the_InternalRel(sK8(sK8(sK1)))),cartesian_product2(sK14,sK14))
| ~ spl16_949 ),
inference(avatar_component_clause,[],[f16431]) ).
fof(f17344,plain,
( spl16_1003
| ~ spl16_306
| ~ spl16_388 ),
inference(avatar_split_clause,[],[f4243,f4159,f2964,f17342]) ).
fof(f17342,plain,
( spl16_1003
<=> ! [X0] :
( empty(sK7(powerset(X0)))
| empty(powerset(X0))
| element(sK9(sK7(sK7(sK9(sK9(powerset(sK7(powerset(X0)))))))),X0)
| empty(sK9(powerset(sK7(powerset(X0)))))
| empty(sK7(sK7(sK9(sK9(powerset(sK7(powerset(X0))))))))
| empty(sK9(sK9(powerset(sK7(powerset(X0))))))
| empty(sK7(sK9(sK9(powerset(sK7(powerset(X0))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1003])]) ).
fof(f4243,plain,
( ! [X0] :
( empty(sK7(powerset(X0)))
| empty(powerset(X0))
| element(sK9(sK7(sK7(sK9(sK9(powerset(sK7(powerset(X0)))))))),X0)
| empty(sK9(powerset(sK7(powerset(X0)))))
| empty(sK7(sK7(sK9(sK9(powerset(sK7(powerset(X0))))))))
| empty(sK9(sK9(powerset(sK7(powerset(X0))))))
| empty(sK7(sK9(sK9(powerset(sK7(powerset(X0))))))) )
| ~ spl16_306
| ~ spl16_388 ),
inference(resolution,[],[f4160,f2965]) ).
fof(f17340,plain,
( spl16_1002
| ~ spl16_305
| ~ spl16_388 ),
inference(avatar_split_clause,[],[f4242,f4159,f2960,f17338]) ).
fof(f17338,plain,
( spl16_1002
<=> ! [X0] :
( empty(sK7(powerset(X0)))
| empty(powerset(X0))
| element(sK9(sK7(sK6(sK9(sK9(powerset(sK7(powerset(X0)))))))),X0)
| empty(sK9(powerset(sK7(powerset(X0)))))
| empty(sK7(sK6(sK9(sK9(powerset(sK7(powerset(X0))))))))
| empty(sK9(sK9(powerset(sK7(powerset(X0))))))
| empty(sK6(sK9(sK9(powerset(sK7(powerset(X0))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1002])]) ).
fof(f4242,plain,
( ! [X0] :
( empty(sK7(powerset(X0)))
| empty(powerset(X0))
| element(sK9(sK7(sK6(sK9(sK9(powerset(sK7(powerset(X0)))))))),X0)
| empty(sK9(powerset(sK7(powerset(X0)))))
| empty(sK7(sK6(sK9(sK9(powerset(sK7(powerset(X0))))))))
| empty(sK9(sK9(powerset(sK7(powerset(X0))))))
| empty(sK6(sK9(sK9(powerset(sK7(powerset(X0))))))) )
| ~ spl16_305
| ~ spl16_388 ),
inference(resolution,[],[f4160,f2961]) ).
fof(f17336,plain,
( spl16_1001
| ~ spl16_304
| ~ spl16_388 ),
inference(avatar_split_clause,[],[f4239,f4159,f2956,f17334]) ).
fof(f17334,plain,
( spl16_1001
<=> ! [X0] :
( empty(sK7(powerset(X0)))
| empty(powerset(X0))
| element(sK9(sK6(sK7(sK9(sK9(powerset(sK7(powerset(X0)))))))),X0)
| empty(sK9(powerset(sK7(powerset(X0)))))
| empty(sK6(sK7(sK9(sK9(powerset(sK7(powerset(X0))))))))
| empty(sK9(sK9(powerset(sK7(powerset(X0))))))
| empty(sK7(sK9(sK9(powerset(sK7(powerset(X0))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1001])]) ).
fof(f4239,plain,
( ! [X0] :
( empty(sK7(powerset(X0)))
| empty(powerset(X0))
| element(sK9(sK6(sK7(sK9(sK9(powerset(sK7(powerset(X0)))))))),X0)
| empty(sK9(powerset(sK7(powerset(X0)))))
| empty(sK6(sK7(sK9(sK9(powerset(sK7(powerset(X0))))))))
| empty(sK9(sK9(powerset(sK7(powerset(X0))))))
| empty(sK7(sK9(sK9(powerset(sK7(powerset(X0))))))) )
| ~ spl16_304
| ~ spl16_388 ),
inference(resolution,[],[f4160,f2957]) ).
fof(f17332,plain,
( spl16_1000
| ~ spl16_303
| ~ spl16_388 ),
inference(avatar_split_clause,[],[f4238,f4159,f2952,f17330]) ).
fof(f17330,plain,
( spl16_1000
<=> ! [X0] :
( empty(sK7(powerset(X0)))
| empty(powerset(X0))
| element(sK9(sK6(sK6(sK9(sK9(powerset(sK7(powerset(X0)))))))),X0)
| empty(sK9(powerset(sK7(powerset(X0)))))
| empty(sK6(sK6(sK9(sK9(powerset(sK7(powerset(X0))))))))
| empty(sK9(sK9(powerset(sK7(powerset(X0))))))
| empty(sK6(sK9(sK9(powerset(sK7(powerset(X0))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1000])]) ).
fof(f4238,plain,
( ! [X0] :
( empty(sK7(powerset(X0)))
| empty(powerset(X0))
| element(sK9(sK6(sK6(sK9(sK9(powerset(sK7(powerset(X0)))))))),X0)
| empty(sK9(powerset(sK7(powerset(X0)))))
| empty(sK6(sK6(sK9(sK9(powerset(sK7(powerset(X0))))))))
| empty(sK9(sK9(powerset(sK7(powerset(X0))))))
| empty(sK6(sK9(sK9(powerset(sK7(powerset(X0))))))) )
| ~ spl16_303
| ~ spl16_388 ),
inference(resolution,[],[f4160,f2953]) ).
fof(f17328,plain,
( spl16_999
| ~ spl16_306
| ~ spl16_387 ),
inference(avatar_split_clause,[],[f4227,f4155,f2964,f17326]) ).
fof(f17326,plain,
( spl16_999
<=> ! [X0] :
( empty(sK6(powerset(X0)))
| empty(powerset(X0))
| element(sK9(sK7(sK7(sK9(sK9(powerset(sK6(powerset(X0)))))))),X0)
| empty(sK9(powerset(sK6(powerset(X0)))))
| empty(sK7(sK7(sK9(sK9(powerset(sK6(powerset(X0))))))))
| empty(sK9(sK9(powerset(sK6(powerset(X0))))))
| empty(sK7(sK9(sK9(powerset(sK6(powerset(X0))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_999])]) ).
fof(f4227,plain,
( ! [X0] :
( empty(sK6(powerset(X0)))
| empty(powerset(X0))
| element(sK9(sK7(sK7(sK9(sK9(powerset(sK6(powerset(X0)))))))),X0)
| empty(sK9(powerset(sK6(powerset(X0)))))
| empty(sK7(sK7(sK9(sK9(powerset(sK6(powerset(X0))))))))
| empty(sK9(sK9(powerset(sK6(powerset(X0))))))
| empty(sK7(sK9(sK9(powerset(sK6(powerset(X0))))))) )
| ~ spl16_306
| ~ spl16_387 ),
inference(resolution,[],[f4156,f2965]) ).
fof(f17324,plain,
( spl16_998
| ~ spl16_305
| ~ spl16_387 ),
inference(avatar_split_clause,[],[f4226,f4155,f2960,f17322]) ).
fof(f17322,plain,
( spl16_998
<=> ! [X0] :
( empty(sK6(powerset(X0)))
| empty(powerset(X0))
| element(sK9(sK7(sK6(sK9(sK9(powerset(sK6(powerset(X0)))))))),X0)
| empty(sK9(powerset(sK6(powerset(X0)))))
| empty(sK7(sK6(sK9(sK9(powerset(sK6(powerset(X0))))))))
| empty(sK9(sK9(powerset(sK6(powerset(X0))))))
| empty(sK6(sK9(sK9(powerset(sK6(powerset(X0))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_998])]) ).
fof(f4226,plain,
( ! [X0] :
( empty(sK6(powerset(X0)))
| empty(powerset(X0))
| element(sK9(sK7(sK6(sK9(sK9(powerset(sK6(powerset(X0)))))))),X0)
| empty(sK9(powerset(sK6(powerset(X0)))))
| empty(sK7(sK6(sK9(sK9(powerset(sK6(powerset(X0))))))))
| empty(sK9(sK9(powerset(sK6(powerset(X0))))))
| empty(sK6(sK9(sK9(powerset(sK6(powerset(X0))))))) )
| ~ spl16_305
| ~ spl16_387 ),
inference(resolution,[],[f4156,f2961]) ).
fof(f17320,plain,
( spl16_997
| ~ spl16_304
| ~ spl16_387 ),
inference(avatar_split_clause,[],[f4223,f4155,f2956,f17318]) ).
fof(f17318,plain,
( spl16_997
<=> ! [X0] :
( empty(sK6(powerset(X0)))
| empty(powerset(X0))
| element(sK9(sK6(sK7(sK9(sK9(powerset(sK6(powerset(X0)))))))),X0)
| empty(sK9(powerset(sK6(powerset(X0)))))
| empty(sK6(sK7(sK9(sK9(powerset(sK6(powerset(X0))))))))
| empty(sK9(sK9(powerset(sK6(powerset(X0))))))
| empty(sK7(sK9(sK9(powerset(sK6(powerset(X0))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_997])]) ).
fof(f4223,plain,
( ! [X0] :
( empty(sK6(powerset(X0)))
| empty(powerset(X0))
| element(sK9(sK6(sK7(sK9(sK9(powerset(sK6(powerset(X0)))))))),X0)
| empty(sK9(powerset(sK6(powerset(X0)))))
| empty(sK6(sK7(sK9(sK9(powerset(sK6(powerset(X0))))))))
| empty(sK9(sK9(powerset(sK6(powerset(X0))))))
| empty(sK7(sK9(sK9(powerset(sK6(powerset(X0))))))) )
| ~ spl16_304
| ~ spl16_387 ),
inference(resolution,[],[f4156,f2957]) ).
fof(f17316,plain,
( spl16_996
| ~ spl16_303
| ~ spl16_387 ),
inference(avatar_split_clause,[],[f4222,f4155,f2952,f17314]) ).
fof(f17314,plain,
( spl16_996
<=> ! [X0] :
( empty(sK6(powerset(X0)))
| empty(powerset(X0))
| element(sK9(sK6(sK6(sK9(sK9(powerset(sK6(powerset(X0)))))))),X0)
| empty(sK9(powerset(sK6(powerset(X0)))))
| empty(sK6(sK6(sK9(sK9(powerset(sK6(powerset(X0))))))))
| empty(sK9(sK9(powerset(sK6(powerset(X0))))))
| empty(sK6(sK9(sK9(powerset(sK6(powerset(X0))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_996])]) ).
fof(f4222,plain,
( ! [X0] :
( empty(sK6(powerset(X0)))
| empty(powerset(X0))
| element(sK9(sK6(sK6(sK9(sK9(powerset(sK6(powerset(X0)))))))),X0)
| empty(sK9(powerset(sK6(powerset(X0)))))
| empty(sK6(sK6(sK9(sK9(powerset(sK6(powerset(X0))))))))
| empty(sK9(sK9(powerset(sK6(powerset(X0))))))
| empty(sK6(sK9(sK9(powerset(sK6(powerset(X0))))))) )
| ~ spl16_303
| ~ spl16_387 ),
inference(resolution,[],[f4156,f2953]) ).
fof(f17312,plain,
( spl16_995
| ~ spl16_321
| ~ spl16_371 ),
inference(avatar_split_clause,[],[f4049,f3915,f3175,f17310]) ).
fof(f17310,plain,
( spl16_995
<=> ! [X0] :
( empty(sK7(sK9(powerset(powerset(X0)))))
| element(sK9(sK9(powerset(sK7(sK9(sK7(sK9(powerset(powerset(X0))))))))),X0)
| empty(sK9(powerset(powerset(X0))))
| empty(sK7(sK9(sK7(sK9(powerset(powerset(X0)))))))
| empty(sK9(sK7(sK9(powerset(powerset(X0))))))
| empty(sK9(powerset(sK7(sK9(sK7(sK9(powerset(powerset(X0))))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_995])]) ).
fof(f4049,plain,
( ! [X0] :
( empty(sK7(sK9(powerset(powerset(X0)))))
| element(sK9(sK9(powerset(sK7(sK9(sK7(sK9(powerset(powerset(X0))))))))),X0)
| empty(sK9(powerset(powerset(X0))))
| empty(sK7(sK9(sK7(sK9(powerset(powerset(X0)))))))
| empty(sK9(sK7(sK9(powerset(powerset(X0))))))
| empty(sK9(powerset(sK7(sK9(sK7(sK9(powerset(powerset(X0))))))))) )
| ~ spl16_321
| ~ spl16_371 ),
inference(resolution,[],[f3916,f3176]) ).
fof(f17308,plain,
( spl16_994
| ~ spl16_320
| ~ spl16_371 ),
inference(avatar_split_clause,[],[f4048,f3915,f3171,f17306]) ).
fof(f17306,plain,
( spl16_994
<=> ! [X0] :
( empty(sK7(sK9(powerset(powerset(X0)))))
| element(sK9(sK9(powerset(sK6(sK9(sK7(sK9(powerset(powerset(X0))))))))),X0)
| empty(sK9(powerset(powerset(X0))))
| empty(sK6(sK9(sK7(sK9(powerset(powerset(X0)))))))
| empty(sK9(sK7(sK9(powerset(powerset(X0))))))
| empty(sK9(powerset(sK6(sK9(sK7(sK9(powerset(powerset(X0))))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_994])]) ).
fof(f4048,plain,
( ! [X0] :
( empty(sK7(sK9(powerset(powerset(X0)))))
| element(sK9(sK9(powerset(sK6(sK9(sK7(sK9(powerset(powerset(X0))))))))),X0)
| empty(sK9(powerset(powerset(X0))))
| empty(sK6(sK9(sK7(sK9(powerset(powerset(X0)))))))
| empty(sK9(sK7(sK9(powerset(powerset(X0))))))
| empty(sK9(powerset(sK6(sK9(sK7(sK9(powerset(powerset(X0))))))))) )
| ~ spl16_320
| ~ spl16_371 ),
inference(resolution,[],[f3916,f3172]) ).
fof(f17304,plain,
( spl16_993
| ~ spl16_321
| ~ spl16_370 ),
inference(avatar_split_clause,[],[f4033,f3911,f3175,f17302]) ).
fof(f17302,plain,
( spl16_993
<=> ! [X0] :
( empty(sK6(sK9(powerset(powerset(X0)))))
| element(sK9(sK9(powerset(sK7(sK9(sK6(sK9(powerset(powerset(X0))))))))),X0)
| empty(sK9(powerset(powerset(X0))))
| empty(sK7(sK9(sK6(sK9(powerset(powerset(X0)))))))
| empty(sK9(sK6(sK9(powerset(powerset(X0))))))
| empty(sK9(powerset(sK7(sK9(sK6(sK9(powerset(powerset(X0))))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_993])]) ).
fof(f4033,plain,
( ! [X0] :
( empty(sK6(sK9(powerset(powerset(X0)))))
| element(sK9(sK9(powerset(sK7(sK9(sK6(sK9(powerset(powerset(X0))))))))),X0)
| empty(sK9(powerset(powerset(X0))))
| empty(sK7(sK9(sK6(sK9(powerset(powerset(X0)))))))
| empty(sK9(sK6(sK9(powerset(powerset(X0))))))
| empty(sK9(powerset(sK7(sK9(sK6(sK9(powerset(powerset(X0))))))))) )
| ~ spl16_321
| ~ spl16_370 ),
inference(resolution,[],[f3912,f3176]) ).
fof(f17300,plain,
( spl16_992
| ~ spl16_320
| ~ spl16_370 ),
inference(avatar_split_clause,[],[f4032,f3911,f3171,f17298]) ).
fof(f17298,plain,
( spl16_992
<=> ! [X0] :
( empty(sK6(sK9(powerset(powerset(X0)))))
| element(sK9(sK9(powerset(sK6(sK9(sK6(sK9(powerset(powerset(X0))))))))),X0)
| empty(sK9(powerset(powerset(X0))))
| empty(sK6(sK9(sK6(sK9(powerset(powerset(X0)))))))
| empty(sK9(sK6(sK9(powerset(powerset(X0))))))
| empty(sK9(powerset(sK6(sK9(sK6(sK9(powerset(powerset(X0))))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_992])]) ).
fof(f4032,plain,
( ! [X0] :
( empty(sK6(sK9(powerset(powerset(X0)))))
| element(sK9(sK9(powerset(sK6(sK9(sK6(sK9(powerset(powerset(X0))))))))),X0)
| empty(sK9(powerset(powerset(X0))))
| empty(sK6(sK9(sK6(sK9(powerset(powerset(X0)))))))
| empty(sK9(sK6(sK9(powerset(powerset(X0))))))
| empty(sK9(powerset(sK6(sK9(sK6(sK9(powerset(powerset(X0))))))))) )
| ~ spl16_320
| ~ spl16_370 ),
inference(resolution,[],[f3912,f3172]) ).
fof(f17296,plain,
( spl16_991
| ~ spl16_349
| ~ spl16_369 ),
inference(avatar_split_clause,[],[f4018,f3907,f3578,f17294]) ).
fof(f17294,plain,
( spl16_991
<=> ! [X0] :
( empty(sK7(sK7(powerset(X0))))
| empty(powerset(X0))
| element(sK9(sK9(powerset(sK9(powerset(sK9(sK7(sK7(powerset(X0))))))))),X0)
| empty(sK7(powerset(X0)))
| empty(sK9(powerset(sK9(sK7(sK7(powerset(X0)))))))
| empty(sK9(sK7(sK7(powerset(X0)))))
| empty(sK9(powerset(sK9(powerset(sK9(sK7(sK7(powerset(X0))))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_991])]) ).
fof(f4018,plain,
( ! [X0] :
( empty(sK7(sK7(powerset(X0))))
| empty(powerset(X0))
| element(sK9(sK9(powerset(sK9(powerset(sK9(sK7(sK7(powerset(X0))))))))),X0)
| empty(sK7(powerset(X0)))
| empty(sK9(powerset(sK9(sK7(sK7(powerset(X0)))))))
| empty(sK9(sK7(sK7(powerset(X0)))))
| empty(sK9(powerset(sK9(powerset(sK9(sK7(sK7(powerset(X0))))))))) )
| ~ spl16_349
| ~ spl16_369 ),
inference(resolution,[],[f3908,f3579]) ).
fof(f17292,plain,
( spl16_990
| ~ spl16_349
| ~ spl16_368 ),
inference(avatar_split_clause,[],[f4002,f3903,f3578,f17290]) ).
fof(f17290,plain,
( spl16_990
<=> ! [X0] :
( empty(sK7(sK6(powerset(X0))))
| empty(powerset(X0))
| element(sK9(sK9(powerset(sK9(powerset(sK9(sK7(sK6(powerset(X0))))))))),X0)
| empty(sK6(powerset(X0)))
| empty(sK9(powerset(sK9(sK7(sK6(powerset(X0)))))))
| empty(sK9(sK7(sK6(powerset(X0)))))
| empty(sK9(powerset(sK9(powerset(sK9(sK7(sK6(powerset(X0))))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_990])]) ).
fof(f4002,plain,
( ! [X0] :
( empty(sK7(sK6(powerset(X0))))
| empty(powerset(X0))
| element(sK9(sK9(powerset(sK9(powerset(sK9(sK7(sK6(powerset(X0))))))))),X0)
| empty(sK6(powerset(X0)))
| empty(sK9(powerset(sK9(sK7(sK6(powerset(X0)))))))
| empty(sK9(sK7(sK6(powerset(X0)))))
| empty(sK9(powerset(sK9(powerset(sK9(sK7(sK6(powerset(X0))))))))) )
| ~ spl16_349
| ~ spl16_368 ),
inference(resolution,[],[f3904,f3579]) ).
fof(f17288,plain,
( spl16_989
| ~ spl16_349
| ~ spl16_366 ),
inference(avatar_split_clause,[],[f3986,f3895,f3578,f17286]) ).
fof(f17286,plain,
( spl16_989
<=> ! [X0] :
( empty(sK6(sK7(powerset(X0))))
| empty(powerset(X0))
| element(sK9(sK9(powerset(sK9(powerset(sK9(sK6(sK7(powerset(X0))))))))),X0)
| empty(sK7(powerset(X0)))
| empty(sK9(powerset(sK9(sK6(sK7(powerset(X0)))))))
| empty(sK9(sK6(sK7(powerset(X0)))))
| empty(sK9(powerset(sK9(powerset(sK9(sK6(sK7(powerset(X0))))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_989])]) ).
fof(f3986,plain,
( ! [X0] :
( empty(sK6(sK7(powerset(X0))))
| empty(powerset(X0))
| element(sK9(sK9(powerset(sK9(powerset(sK9(sK6(sK7(powerset(X0))))))))),X0)
| empty(sK7(powerset(X0)))
| empty(sK9(powerset(sK9(sK6(sK7(powerset(X0)))))))
| empty(sK9(sK6(sK7(powerset(X0)))))
| empty(sK9(powerset(sK9(powerset(sK9(sK6(sK7(powerset(X0))))))))) )
| ~ spl16_349
| ~ spl16_366 ),
inference(resolution,[],[f3896,f3579]) ).
fof(f17284,plain,
( spl16_988
| ~ spl16_349
| ~ spl16_365 ),
inference(avatar_split_clause,[],[f3970,f3891,f3578,f17282]) ).
fof(f17282,plain,
( spl16_988
<=> ! [X0] :
( empty(sK6(sK6(powerset(X0))))
| empty(powerset(X0))
| element(sK9(sK9(powerset(sK9(powerset(sK9(sK6(sK6(powerset(X0))))))))),X0)
| empty(sK6(powerset(X0)))
| empty(sK9(powerset(sK9(sK6(sK6(powerset(X0)))))))
| empty(sK9(sK6(sK6(powerset(X0)))))
| empty(sK9(powerset(sK9(powerset(sK9(sK6(sK6(powerset(X0))))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_988])]) ).
fof(f3970,plain,
( ! [X0] :
( empty(sK6(sK6(powerset(X0))))
| empty(powerset(X0))
| element(sK9(sK9(powerset(sK9(powerset(sK9(sK6(sK6(powerset(X0))))))))),X0)
| empty(sK6(powerset(X0)))
| empty(sK9(powerset(sK9(sK6(sK6(powerset(X0)))))))
| empty(sK9(sK6(sK6(powerset(X0)))))
| empty(sK9(powerset(sK9(powerset(sK9(sK6(sK6(powerset(X0))))))))) )
| ~ spl16_349
| ~ spl16_365 ),
inference(resolution,[],[f3892,f3579]) ).
fof(f17189,plain,
( spl16_987
| ~ spl16_306
| ~ spl16_371 ),
inference(avatar_split_clause,[],[f4045,f3915,f2964,f17187]) ).
fof(f17187,plain,
( spl16_987
<=> ! [X0] :
( empty(sK7(sK9(powerset(powerset(X0)))))
| element(sK9(sK7(sK7(sK9(sK7(sK9(powerset(powerset(X0)))))))),X0)
| empty(sK9(powerset(powerset(X0))))
| empty(sK7(sK7(sK9(sK7(sK9(powerset(powerset(X0))))))))
| empty(sK9(sK7(sK9(powerset(powerset(X0))))))
| empty(sK7(sK9(sK7(sK9(powerset(powerset(X0))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_987])]) ).
fof(f4045,plain,
( ! [X0] :
( empty(sK7(sK9(powerset(powerset(X0)))))
| element(sK9(sK7(sK7(sK9(sK7(sK9(powerset(powerset(X0)))))))),X0)
| empty(sK9(powerset(powerset(X0))))
| empty(sK7(sK7(sK9(sK7(sK9(powerset(powerset(X0))))))))
| empty(sK9(sK7(sK9(powerset(powerset(X0))))))
| empty(sK7(sK9(sK7(sK9(powerset(powerset(X0))))))) )
| ~ spl16_306
| ~ spl16_371 ),
inference(resolution,[],[f3916,f2965]) ).
fof(f17185,plain,
( spl16_986
| ~ spl16_305
| ~ spl16_371 ),
inference(avatar_split_clause,[],[f4044,f3915,f2960,f17183]) ).
fof(f17183,plain,
( spl16_986
<=> ! [X0] :
( empty(sK7(sK9(powerset(powerset(X0)))))
| element(sK9(sK7(sK6(sK9(sK7(sK9(powerset(powerset(X0)))))))),X0)
| empty(sK9(powerset(powerset(X0))))
| empty(sK7(sK6(sK9(sK7(sK9(powerset(powerset(X0))))))))
| empty(sK9(sK7(sK9(powerset(powerset(X0))))))
| empty(sK6(sK9(sK7(sK9(powerset(powerset(X0))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_986])]) ).
fof(f4044,plain,
( ! [X0] :
( empty(sK7(sK9(powerset(powerset(X0)))))
| element(sK9(sK7(sK6(sK9(sK7(sK9(powerset(powerset(X0)))))))),X0)
| empty(sK9(powerset(powerset(X0))))
| empty(sK7(sK6(sK9(sK7(sK9(powerset(powerset(X0))))))))
| empty(sK9(sK7(sK9(powerset(powerset(X0))))))
| empty(sK6(sK9(sK7(sK9(powerset(powerset(X0))))))) )
| ~ spl16_305
| ~ spl16_371 ),
inference(resolution,[],[f3916,f2961]) ).
fof(f17181,plain,
( spl16_985
| ~ spl16_304
| ~ spl16_371 ),
inference(avatar_split_clause,[],[f4041,f3915,f2956,f17179]) ).
fof(f17179,plain,
( spl16_985
<=> ! [X0] :
( empty(sK7(sK9(powerset(powerset(X0)))))
| element(sK9(sK6(sK7(sK9(sK7(sK9(powerset(powerset(X0)))))))),X0)
| empty(sK9(powerset(powerset(X0))))
| empty(sK6(sK7(sK9(sK7(sK9(powerset(powerset(X0))))))))
| empty(sK9(sK7(sK9(powerset(powerset(X0))))))
| empty(sK7(sK9(sK7(sK9(powerset(powerset(X0))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_985])]) ).
fof(f4041,plain,
( ! [X0] :
( empty(sK7(sK9(powerset(powerset(X0)))))
| element(sK9(sK6(sK7(sK9(sK7(sK9(powerset(powerset(X0)))))))),X0)
| empty(sK9(powerset(powerset(X0))))
| empty(sK6(sK7(sK9(sK7(sK9(powerset(powerset(X0))))))))
| empty(sK9(sK7(sK9(powerset(powerset(X0))))))
| empty(sK7(sK9(sK7(sK9(powerset(powerset(X0))))))) )
| ~ spl16_304
| ~ spl16_371 ),
inference(resolution,[],[f3916,f2957]) ).
fof(f17177,plain,
( spl16_984
| ~ spl16_303
| ~ spl16_371 ),
inference(avatar_split_clause,[],[f4040,f3915,f2952,f17175]) ).
fof(f17175,plain,
( spl16_984
<=> ! [X0] :
( empty(sK7(sK9(powerset(powerset(X0)))))
| element(sK9(sK6(sK6(sK9(sK7(sK9(powerset(powerset(X0)))))))),X0)
| empty(sK9(powerset(powerset(X0))))
| empty(sK6(sK6(sK9(sK7(sK9(powerset(powerset(X0))))))))
| empty(sK9(sK7(sK9(powerset(powerset(X0))))))
| empty(sK6(sK9(sK7(sK9(powerset(powerset(X0))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_984])]) ).
fof(f4040,plain,
( ! [X0] :
( empty(sK7(sK9(powerset(powerset(X0)))))
| element(sK9(sK6(sK6(sK9(sK7(sK9(powerset(powerset(X0)))))))),X0)
| empty(sK9(powerset(powerset(X0))))
| empty(sK6(sK6(sK9(sK7(sK9(powerset(powerset(X0))))))))
| empty(sK9(sK7(sK9(powerset(powerset(X0))))))
| empty(sK6(sK9(sK7(sK9(powerset(powerset(X0))))))) )
| ~ spl16_303
| ~ spl16_371 ),
inference(resolution,[],[f3916,f2953]) ).
fof(f17173,plain,
( spl16_983
| ~ spl16_306
| ~ spl16_370 ),
inference(avatar_split_clause,[],[f4029,f3911,f2964,f17171]) ).
fof(f17171,plain,
( spl16_983
<=> ! [X0] :
( empty(sK6(sK9(powerset(powerset(X0)))))
| element(sK9(sK7(sK7(sK9(sK6(sK9(powerset(powerset(X0)))))))),X0)
| empty(sK9(powerset(powerset(X0))))
| empty(sK7(sK7(sK9(sK6(sK9(powerset(powerset(X0))))))))
| empty(sK9(sK6(sK9(powerset(powerset(X0))))))
| empty(sK7(sK9(sK6(sK9(powerset(powerset(X0))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_983])]) ).
fof(f4029,plain,
( ! [X0] :
( empty(sK6(sK9(powerset(powerset(X0)))))
| element(sK9(sK7(sK7(sK9(sK6(sK9(powerset(powerset(X0)))))))),X0)
| empty(sK9(powerset(powerset(X0))))
| empty(sK7(sK7(sK9(sK6(sK9(powerset(powerset(X0))))))))
| empty(sK9(sK6(sK9(powerset(powerset(X0))))))
| empty(sK7(sK9(sK6(sK9(powerset(powerset(X0))))))) )
| ~ spl16_306
| ~ spl16_370 ),
inference(resolution,[],[f3912,f2965]) ).
fof(f17169,plain,
( spl16_982
| ~ spl16_305
| ~ spl16_370 ),
inference(avatar_split_clause,[],[f4028,f3911,f2960,f17167]) ).
fof(f17167,plain,
( spl16_982
<=> ! [X0] :
( empty(sK6(sK9(powerset(powerset(X0)))))
| element(sK9(sK7(sK6(sK9(sK6(sK9(powerset(powerset(X0)))))))),X0)
| empty(sK9(powerset(powerset(X0))))
| empty(sK7(sK6(sK9(sK6(sK9(powerset(powerset(X0))))))))
| empty(sK9(sK6(sK9(powerset(powerset(X0))))))
| empty(sK6(sK9(sK6(sK9(powerset(powerset(X0))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_982])]) ).
fof(f4028,plain,
( ! [X0] :
( empty(sK6(sK9(powerset(powerset(X0)))))
| element(sK9(sK7(sK6(sK9(sK6(sK9(powerset(powerset(X0)))))))),X0)
| empty(sK9(powerset(powerset(X0))))
| empty(sK7(sK6(sK9(sK6(sK9(powerset(powerset(X0))))))))
| empty(sK9(sK6(sK9(powerset(powerset(X0))))))
| empty(sK6(sK9(sK6(sK9(powerset(powerset(X0))))))) )
| ~ spl16_305
| ~ spl16_370 ),
inference(resolution,[],[f3912,f2961]) ).
fof(f17165,plain,
( ~ spl16_12
| ~ spl16_805
| spl16_948 ),
inference(avatar_split_clause,[],[f17124,f16427,f14693,f213]) ).
fof(f17124,plain,
( ~ empty(sK14)
| ~ spl16_805
| spl16_948 ),
inference(forward_demodulation,[],[f16428,f14695]) ).
fof(f16428,plain,
( ~ empty(the_InternalRel(sK8(sK8(sK1))))
| spl16_948 ),
inference(avatar_component_clause,[],[f16427]) ).
fof(f17164,plain,
( spl16_981
| ~ spl16_304
| ~ spl16_370 ),
inference(avatar_split_clause,[],[f4025,f3911,f2956,f17162]) ).
fof(f17162,plain,
( spl16_981
<=> ! [X0] :
( empty(sK6(sK9(powerset(powerset(X0)))))
| element(sK9(sK6(sK7(sK9(sK6(sK9(powerset(powerset(X0)))))))),X0)
| empty(sK9(powerset(powerset(X0))))
| empty(sK6(sK7(sK9(sK6(sK9(powerset(powerset(X0))))))))
| empty(sK9(sK6(sK9(powerset(powerset(X0))))))
| empty(sK7(sK9(sK6(sK9(powerset(powerset(X0))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_981])]) ).
fof(f4025,plain,
( ! [X0] :
( empty(sK6(sK9(powerset(powerset(X0)))))
| element(sK9(sK6(sK7(sK9(sK6(sK9(powerset(powerset(X0)))))))),X0)
| empty(sK9(powerset(powerset(X0))))
| empty(sK6(sK7(sK9(sK6(sK9(powerset(powerset(X0))))))))
| empty(sK9(sK6(sK9(powerset(powerset(X0))))))
| empty(sK7(sK9(sK6(sK9(powerset(powerset(X0))))))) )
| ~ spl16_304
| ~ spl16_370 ),
inference(resolution,[],[f3912,f2957]) ).
fof(f17160,plain,
( spl16_980
| ~ spl16_303
| ~ spl16_370 ),
inference(avatar_split_clause,[],[f4024,f3911,f2952,f17158]) ).
fof(f17158,plain,
( spl16_980
<=> ! [X0] :
( empty(sK6(sK9(powerset(powerset(X0)))))
| element(sK9(sK6(sK6(sK9(sK6(sK9(powerset(powerset(X0)))))))),X0)
| empty(sK9(powerset(powerset(X0))))
| empty(sK6(sK6(sK9(sK6(sK9(powerset(powerset(X0))))))))
| empty(sK9(sK6(sK9(powerset(powerset(X0))))))
| empty(sK6(sK9(sK6(sK9(powerset(powerset(X0))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_980])]) ).
fof(f4024,plain,
( ! [X0] :
( empty(sK6(sK9(powerset(powerset(X0)))))
| element(sK9(sK6(sK6(sK9(sK6(sK9(powerset(powerset(X0)))))))),X0)
| empty(sK9(powerset(powerset(X0))))
| empty(sK6(sK6(sK9(sK6(sK9(powerset(powerset(X0))))))))
| empty(sK9(sK6(sK9(powerset(powerset(X0))))))
| empty(sK6(sK9(sK6(sK9(powerset(powerset(X0))))))) )
| ~ spl16_303
| ~ spl16_370 ),
inference(resolution,[],[f3912,f2953]) ).
fof(f17156,plain,
( spl16_979
| ~ spl16_326
| ~ spl16_369 ),
inference(avatar_split_clause,[],[f4014,f3907,f3305,f17154]) ).
fof(f17154,plain,
( spl16_979
<=> ! [X0] :
( empty(sK7(sK7(powerset(X0))))
| empty(powerset(X0))
| element(sK9(sK7(sK9(powerset(sK9(sK7(sK7(powerset(X0)))))))),X0)
| empty(sK7(powerset(X0)))
| empty(sK7(sK9(powerset(sK9(sK7(sK7(powerset(X0))))))))
| empty(sK9(sK7(sK7(powerset(X0)))))
| empty(sK9(powerset(sK9(sK7(sK7(powerset(X0))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_979])]) ).
fof(f4014,plain,
( ! [X0] :
( empty(sK7(sK7(powerset(X0))))
| empty(powerset(X0))
| element(sK9(sK7(sK9(powerset(sK9(sK7(sK7(powerset(X0)))))))),X0)
| empty(sK7(powerset(X0)))
| empty(sK7(sK9(powerset(sK9(sK7(sK7(powerset(X0))))))))
| empty(sK9(sK7(sK7(powerset(X0)))))
| empty(sK9(powerset(sK9(sK7(sK7(powerset(X0))))))) )
| ~ spl16_326
| ~ spl16_369 ),
inference(resolution,[],[f3908,f3306]) ).
fof(f17152,plain,
( spl16_978
| ~ spl16_325
| ~ spl16_369 ),
inference(avatar_split_clause,[],[f4010,f3907,f3300,f17150]) ).
fof(f17150,plain,
( spl16_978
<=> ! [X0] :
( empty(sK7(sK7(powerset(X0))))
| empty(powerset(X0))
| element(sK9(sK6(sK9(powerset(sK9(sK7(sK7(powerset(X0)))))))),X0)
| empty(sK7(powerset(X0)))
| empty(sK6(sK9(powerset(sK9(sK7(sK7(powerset(X0))))))))
| empty(sK9(sK7(sK7(powerset(X0)))))
| empty(sK9(powerset(sK9(sK7(sK7(powerset(X0))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_978])]) ).
fof(f4010,plain,
( ! [X0] :
( empty(sK7(sK7(powerset(X0))))
| empty(powerset(X0))
| element(sK9(sK6(sK9(powerset(sK9(sK7(sK7(powerset(X0)))))))),X0)
| empty(sK7(powerset(X0)))
| empty(sK6(sK9(powerset(sK9(sK7(sK7(powerset(X0))))))))
| empty(sK9(sK7(sK7(powerset(X0)))))
| empty(sK9(powerset(sK9(sK7(sK7(powerset(X0))))))) )
| ~ spl16_325
| ~ spl16_369 ),
inference(resolution,[],[f3908,f3301]) ).
fof(f17148,plain,
( spl16_977
| ~ spl16_326
| ~ spl16_368 ),
inference(avatar_split_clause,[],[f3998,f3903,f3305,f17146]) ).
fof(f17146,plain,
( spl16_977
<=> ! [X0] :
( empty(sK7(sK6(powerset(X0))))
| empty(powerset(X0))
| element(sK9(sK7(sK9(powerset(sK9(sK7(sK6(powerset(X0)))))))),X0)
| empty(sK6(powerset(X0)))
| empty(sK7(sK9(powerset(sK9(sK7(sK6(powerset(X0))))))))
| empty(sK9(sK7(sK6(powerset(X0)))))
| empty(sK9(powerset(sK9(sK7(sK6(powerset(X0))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_977])]) ).
fof(f3998,plain,
( ! [X0] :
( empty(sK7(sK6(powerset(X0))))
| empty(powerset(X0))
| element(sK9(sK7(sK9(powerset(sK9(sK7(sK6(powerset(X0)))))))),X0)
| empty(sK6(powerset(X0)))
| empty(sK7(sK9(powerset(sK9(sK7(sK6(powerset(X0))))))))
| empty(sK9(sK7(sK6(powerset(X0)))))
| empty(sK9(powerset(sK9(sK7(sK6(powerset(X0))))))) )
| ~ spl16_326
| ~ spl16_368 ),
inference(resolution,[],[f3904,f3306]) ).
fof(f17144,plain,
( spl16_976
| ~ spl16_325
| ~ spl16_368 ),
inference(avatar_split_clause,[],[f3994,f3903,f3300,f17142]) ).
fof(f17142,plain,
( spl16_976
<=> ! [X0] :
( empty(sK7(sK6(powerset(X0))))
| empty(powerset(X0))
| element(sK9(sK6(sK9(powerset(sK9(sK7(sK6(powerset(X0)))))))),X0)
| empty(sK6(powerset(X0)))
| empty(sK6(sK9(powerset(sK9(sK7(sK6(powerset(X0))))))))
| empty(sK9(sK7(sK6(powerset(X0)))))
| empty(sK9(powerset(sK9(sK7(sK6(powerset(X0))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_976])]) ).
fof(f3994,plain,
( ! [X0] :
( empty(sK7(sK6(powerset(X0))))
| empty(powerset(X0))
| element(sK9(sK6(sK9(powerset(sK9(sK7(sK6(powerset(X0)))))))),X0)
| empty(sK6(powerset(X0)))
| empty(sK6(sK9(powerset(sK9(sK7(sK6(powerset(X0))))))))
| empty(sK9(sK7(sK6(powerset(X0)))))
| empty(sK9(powerset(sK9(sK7(sK6(powerset(X0))))))) )
| ~ spl16_325
| ~ spl16_368 ),
inference(resolution,[],[f3904,f3301]) ).
fof(f17140,plain,
( spl16_975
| ~ spl16_326
| ~ spl16_366 ),
inference(avatar_split_clause,[],[f3982,f3895,f3305,f17138]) ).
fof(f17138,plain,
( spl16_975
<=> ! [X0] :
( empty(sK6(sK7(powerset(X0))))
| empty(powerset(X0))
| element(sK9(sK7(sK9(powerset(sK9(sK6(sK7(powerset(X0)))))))),X0)
| empty(sK7(powerset(X0)))
| empty(sK7(sK9(powerset(sK9(sK6(sK7(powerset(X0))))))))
| empty(sK9(sK6(sK7(powerset(X0)))))
| empty(sK9(powerset(sK9(sK6(sK7(powerset(X0))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_975])]) ).
fof(f3982,plain,
( ! [X0] :
( empty(sK6(sK7(powerset(X0))))
| empty(powerset(X0))
| element(sK9(sK7(sK9(powerset(sK9(sK6(sK7(powerset(X0)))))))),X0)
| empty(sK7(powerset(X0)))
| empty(sK7(sK9(powerset(sK9(sK6(sK7(powerset(X0))))))))
| empty(sK9(sK6(sK7(powerset(X0)))))
| empty(sK9(powerset(sK9(sK6(sK7(powerset(X0))))))) )
| ~ spl16_326
| ~ spl16_366 ),
inference(resolution,[],[f3896,f3306]) ).
fof(f17136,plain,
( spl16_974
| ~ spl16_325
| ~ spl16_366 ),
inference(avatar_split_clause,[],[f3978,f3895,f3300,f17134]) ).
fof(f17134,plain,
( spl16_974
<=> ! [X0] :
( empty(sK6(sK7(powerset(X0))))
| empty(powerset(X0))
| element(sK9(sK6(sK9(powerset(sK9(sK6(sK7(powerset(X0)))))))),X0)
| empty(sK7(powerset(X0)))
| empty(sK6(sK9(powerset(sK9(sK6(sK7(powerset(X0))))))))
| empty(sK9(sK6(sK7(powerset(X0)))))
| empty(sK9(powerset(sK9(sK6(sK7(powerset(X0))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_974])]) ).
fof(f3978,plain,
( ! [X0] :
( empty(sK6(sK7(powerset(X0))))
| empty(powerset(X0))
| element(sK9(sK6(sK9(powerset(sK9(sK6(sK7(powerset(X0)))))))),X0)
| empty(sK7(powerset(X0)))
| empty(sK6(sK9(powerset(sK9(sK6(sK7(powerset(X0))))))))
| empty(sK9(sK6(sK7(powerset(X0)))))
| empty(sK9(powerset(sK9(sK6(sK7(powerset(X0))))))) )
| ~ spl16_325
| ~ spl16_366 ),
inference(resolution,[],[f3896,f3301]) ).
fof(f17132,plain,
( spl16_973
| ~ spl16_326
| ~ spl16_365 ),
inference(avatar_split_clause,[],[f3966,f3891,f3305,f17130]) ).
fof(f17130,plain,
( spl16_973
<=> ! [X0] :
( empty(sK6(sK6(powerset(X0))))
| empty(powerset(X0))
| element(sK9(sK7(sK9(powerset(sK9(sK6(sK6(powerset(X0)))))))),X0)
| empty(sK6(powerset(X0)))
| empty(sK7(sK9(powerset(sK9(sK6(sK6(powerset(X0))))))))
| empty(sK9(sK6(sK6(powerset(X0)))))
| empty(sK9(powerset(sK9(sK6(sK6(powerset(X0))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_973])]) ).
fof(f3966,plain,
( ! [X0] :
( empty(sK6(sK6(powerset(X0))))
| empty(powerset(X0))
| element(sK9(sK7(sK9(powerset(sK9(sK6(sK6(powerset(X0)))))))),X0)
| empty(sK6(powerset(X0)))
| empty(sK7(sK9(powerset(sK9(sK6(sK6(powerset(X0))))))))
| empty(sK9(sK6(sK6(powerset(X0)))))
| empty(sK9(powerset(sK9(sK6(sK6(powerset(X0))))))) )
| ~ spl16_326
| ~ spl16_365 ),
inference(resolution,[],[f3892,f3306]) ).
fof(f17128,plain,
( spl16_972
| ~ spl16_325
| ~ spl16_365 ),
inference(avatar_split_clause,[],[f3962,f3891,f3300,f17126]) ).
fof(f17126,plain,
( spl16_972
<=> ! [X0] :
( empty(sK6(sK6(powerset(X0))))
| empty(powerset(X0))
| element(sK9(sK6(sK9(powerset(sK9(sK6(sK6(powerset(X0)))))))),X0)
| empty(sK6(powerset(X0)))
| empty(sK6(sK9(powerset(sK9(sK6(sK6(powerset(X0))))))))
| empty(sK9(sK6(sK6(powerset(X0)))))
| empty(sK9(powerset(sK9(sK6(sK6(powerset(X0))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_972])]) ).
fof(f3962,plain,
( ! [X0] :
( empty(sK6(sK6(powerset(X0))))
| empty(powerset(X0))
| element(sK9(sK6(sK9(powerset(sK9(sK6(sK6(powerset(X0)))))))),X0)
| empty(sK6(powerset(X0)))
| empty(sK6(sK9(powerset(sK9(sK6(sK6(powerset(X0))))))))
| empty(sK9(sK6(sK6(powerset(X0)))))
| empty(sK9(powerset(sK9(sK6(sK6(powerset(X0))))))) )
| ~ spl16_325
| ~ spl16_365 ),
inference(resolution,[],[f3892,f3301]) ).
fof(f17020,plain,
( spl16_971
| ~ spl16_641
| ~ spl16_473
| ~ spl16_948 ),
inference(avatar_split_clause,[],[f16484,f16427,f5624,f9159,f17017]) ).
fof(f16484,plain,
( ~ rel_str(sK8(sK8(sK1)))
| sK14 = the_InternalRel(sK8(sK8(sK8(sK1))))
| ~ spl16_473
| ~ spl16_948 ),
inference(resolution,[],[f16429,f5625]) ).
fof(f17015,plain,
( spl16_970
| ~ spl16_173
| ~ spl16_364 ),
inference(avatar_split_clause,[],[f3884,f3678,f1448,f17013]) ).
fof(f17013,plain,
( spl16_970
<=> ! [X0] :
( empty(powerset(sK9(sK9(powerset(powerset(X0))))))
| empty(sK9(sK7(powerset(sK9(sK9(powerset(powerset(X0))))))))
| empty(sK9(sK9(powerset(powerset(X0)))))
| empty(sK7(powerset(sK9(sK9(powerset(powerset(X0)))))))
| element(sK9(sK9(sK7(powerset(sK9(sK9(powerset(powerset(X0)))))))),X0)
| empty(sK9(powerset(powerset(X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_970])]) ).
fof(f3884,plain,
( ! [X0] :
( empty(powerset(sK9(sK9(powerset(powerset(X0))))))
| empty(sK9(sK7(powerset(sK9(sK9(powerset(powerset(X0))))))))
| empty(sK9(sK9(powerset(powerset(X0)))))
| empty(sK7(powerset(sK9(sK9(powerset(powerset(X0)))))))
| element(sK9(sK9(sK7(powerset(sK9(sK9(powerset(powerset(X0)))))))),X0)
| empty(sK9(powerset(powerset(X0)))) )
| ~ spl16_173
| ~ spl16_364 ),
inference(resolution,[],[f3679,f1449]) ).
fof(f17011,plain,
( spl16_969
| ~ spl16_173
| ~ spl16_363 ),
inference(avatar_split_clause,[],[f3857,f3674,f1448,f17009]) ).
fof(f17009,plain,
( spl16_969
<=> ! [X0] :
( empty(powerset(sK9(sK9(powerset(powerset(X0))))))
| empty(sK9(sK6(powerset(sK9(sK9(powerset(powerset(X0))))))))
| empty(sK9(sK9(powerset(powerset(X0)))))
| empty(sK6(powerset(sK9(sK9(powerset(powerset(X0)))))))
| element(sK9(sK9(sK6(powerset(sK9(sK9(powerset(powerset(X0)))))))),X0)
| empty(sK9(powerset(powerset(X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_969])]) ).
fof(f3857,plain,
( ! [X0] :
( empty(powerset(sK9(sK9(powerset(powerset(X0))))))
| empty(sK9(sK6(powerset(sK9(sK9(powerset(powerset(X0))))))))
| empty(sK9(sK9(powerset(powerset(X0)))))
| empty(sK6(powerset(sK9(sK9(powerset(powerset(X0)))))))
| element(sK9(sK9(sK6(powerset(sK9(sK9(powerset(powerset(X0)))))))),X0)
| empty(sK9(powerset(powerset(X0)))) )
| ~ spl16_173
| ~ spl16_363 ),
inference(resolution,[],[f3675,f1449]) ).
fof(f16964,plain,
( spl16_968
| ~ spl16_321
| ~ spl16_369 ),
inference(avatar_split_clause,[],[f4017,f3907,f3175,f16962]) ).
fof(f16962,plain,
( spl16_968
<=> ! [X0] :
( empty(sK7(sK7(powerset(X0))))
| empty(powerset(X0))
| element(sK9(sK9(powerset(sK7(sK9(sK7(sK7(powerset(X0)))))))),X0)
| empty(sK7(powerset(X0)))
| empty(sK7(sK9(sK7(sK7(powerset(X0))))))
| empty(sK9(sK7(sK7(powerset(X0)))))
| empty(sK9(powerset(sK7(sK9(sK7(sK7(powerset(X0)))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_968])]) ).
fof(f4017,plain,
( ! [X0] :
( empty(sK7(sK7(powerset(X0))))
| empty(powerset(X0))
| element(sK9(sK9(powerset(sK7(sK9(sK7(sK7(powerset(X0)))))))),X0)
| empty(sK7(powerset(X0)))
| empty(sK7(sK9(sK7(sK7(powerset(X0))))))
| empty(sK9(sK7(sK7(powerset(X0)))))
| empty(sK9(powerset(sK7(sK9(sK7(sK7(powerset(X0)))))))) )
| ~ spl16_321
| ~ spl16_369 ),
inference(resolution,[],[f3908,f3176]) ).
fof(f16960,plain,
( spl16_967
| ~ spl16_320
| ~ spl16_369 ),
inference(avatar_split_clause,[],[f4016,f3907,f3171,f16958]) ).
fof(f16958,plain,
( spl16_967
<=> ! [X0] :
( empty(sK7(sK7(powerset(X0))))
| empty(powerset(X0))
| element(sK9(sK9(powerset(sK6(sK9(sK7(sK7(powerset(X0)))))))),X0)
| empty(sK7(powerset(X0)))
| empty(sK6(sK9(sK7(sK7(powerset(X0))))))
| empty(sK9(sK7(sK7(powerset(X0)))))
| empty(sK9(powerset(sK6(sK9(sK7(sK7(powerset(X0)))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_967])]) ).
fof(f4016,plain,
( ! [X0] :
( empty(sK7(sK7(powerset(X0))))
| empty(powerset(X0))
| element(sK9(sK9(powerset(sK6(sK9(sK7(sK7(powerset(X0)))))))),X0)
| empty(sK7(powerset(X0)))
| empty(sK6(sK9(sK7(sK7(powerset(X0))))))
| empty(sK9(sK7(sK7(powerset(X0)))))
| empty(sK9(powerset(sK6(sK9(sK7(sK7(powerset(X0)))))))) )
| ~ spl16_320
| ~ spl16_369 ),
inference(resolution,[],[f3908,f3172]) ).
fof(f16956,plain,
( spl16_966
| ~ spl16_321
| ~ spl16_368 ),
inference(avatar_split_clause,[],[f4001,f3903,f3175,f16954]) ).
fof(f16954,plain,
( spl16_966
<=> ! [X0] :
( empty(sK7(sK6(powerset(X0))))
| empty(powerset(X0))
| element(sK9(sK9(powerset(sK7(sK9(sK7(sK6(powerset(X0)))))))),X0)
| empty(sK6(powerset(X0)))
| empty(sK7(sK9(sK7(sK6(powerset(X0))))))
| empty(sK9(sK7(sK6(powerset(X0)))))
| empty(sK9(powerset(sK7(sK9(sK7(sK6(powerset(X0)))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_966])]) ).
fof(f4001,plain,
( ! [X0] :
( empty(sK7(sK6(powerset(X0))))
| empty(powerset(X0))
| element(sK9(sK9(powerset(sK7(sK9(sK7(sK6(powerset(X0)))))))),X0)
| empty(sK6(powerset(X0)))
| empty(sK7(sK9(sK7(sK6(powerset(X0))))))
| empty(sK9(sK7(sK6(powerset(X0)))))
| empty(sK9(powerset(sK7(sK9(sK7(sK6(powerset(X0)))))))) )
| ~ spl16_321
| ~ spl16_368 ),
inference(resolution,[],[f3904,f3176]) ).
fof(f16952,plain,
( spl16_965
| ~ spl16_320
| ~ spl16_368 ),
inference(avatar_split_clause,[],[f4000,f3903,f3171,f16950]) ).
fof(f16950,plain,
( spl16_965
<=> ! [X0] :
( empty(sK7(sK6(powerset(X0))))
| empty(powerset(X0))
| element(sK9(sK9(powerset(sK6(sK9(sK7(sK6(powerset(X0)))))))),X0)
| empty(sK6(powerset(X0)))
| empty(sK6(sK9(sK7(sK6(powerset(X0))))))
| empty(sK9(sK7(sK6(powerset(X0)))))
| empty(sK9(powerset(sK6(sK9(sK7(sK6(powerset(X0)))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_965])]) ).
fof(f4000,plain,
( ! [X0] :
( empty(sK7(sK6(powerset(X0))))
| empty(powerset(X0))
| element(sK9(sK9(powerset(sK6(sK9(sK7(sK6(powerset(X0)))))))),X0)
| empty(sK6(powerset(X0)))
| empty(sK6(sK9(sK7(sK6(powerset(X0))))))
| empty(sK9(sK7(sK6(powerset(X0)))))
| empty(sK9(powerset(sK6(sK9(sK7(sK6(powerset(X0)))))))) )
| ~ spl16_320
| ~ spl16_368 ),
inference(resolution,[],[f3904,f3172]) ).
fof(f16948,plain,
( spl16_964
| ~ spl16_321
| ~ spl16_366 ),
inference(avatar_split_clause,[],[f3985,f3895,f3175,f16946]) ).
fof(f16946,plain,
( spl16_964
<=> ! [X0] :
( empty(sK6(sK7(powerset(X0))))
| empty(powerset(X0))
| element(sK9(sK9(powerset(sK7(sK9(sK6(sK7(powerset(X0)))))))),X0)
| empty(sK7(powerset(X0)))
| empty(sK7(sK9(sK6(sK7(powerset(X0))))))
| empty(sK9(sK6(sK7(powerset(X0)))))
| empty(sK9(powerset(sK7(sK9(sK6(sK7(powerset(X0)))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_964])]) ).
fof(f3985,plain,
( ! [X0] :
( empty(sK6(sK7(powerset(X0))))
| empty(powerset(X0))
| element(sK9(sK9(powerset(sK7(sK9(sK6(sK7(powerset(X0)))))))),X0)
| empty(sK7(powerset(X0)))
| empty(sK7(sK9(sK6(sK7(powerset(X0))))))
| empty(sK9(sK6(sK7(powerset(X0)))))
| empty(sK9(powerset(sK7(sK9(sK6(sK7(powerset(X0)))))))) )
| ~ spl16_321
| ~ spl16_366 ),
inference(resolution,[],[f3896,f3176]) ).
fof(f16944,plain,
( spl16_963
| ~ spl16_320
| ~ spl16_366 ),
inference(avatar_split_clause,[],[f3984,f3895,f3171,f16942]) ).
fof(f16942,plain,
( spl16_963
<=> ! [X0] :
( empty(sK6(sK7(powerset(X0))))
| empty(powerset(X0))
| element(sK9(sK9(powerset(sK6(sK9(sK6(sK7(powerset(X0)))))))),X0)
| empty(sK7(powerset(X0)))
| empty(sK6(sK9(sK6(sK7(powerset(X0))))))
| empty(sK9(sK6(sK7(powerset(X0)))))
| empty(sK9(powerset(sK6(sK9(sK6(sK7(powerset(X0)))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_963])]) ).
fof(f3984,plain,
( ! [X0] :
( empty(sK6(sK7(powerset(X0))))
| empty(powerset(X0))
| element(sK9(sK9(powerset(sK6(sK9(sK6(sK7(powerset(X0)))))))),X0)
| empty(sK7(powerset(X0)))
| empty(sK6(sK9(sK6(sK7(powerset(X0))))))
| empty(sK9(sK6(sK7(powerset(X0)))))
| empty(sK9(powerset(sK6(sK9(sK6(sK7(powerset(X0)))))))) )
| ~ spl16_320
| ~ spl16_366 ),
inference(resolution,[],[f3896,f3172]) ).
fof(f16940,plain,
( spl16_962
| ~ spl16_321
| ~ spl16_365 ),
inference(avatar_split_clause,[],[f3969,f3891,f3175,f16938]) ).
fof(f16938,plain,
( spl16_962
<=> ! [X0] :
( empty(sK6(sK6(powerset(X0))))
| empty(powerset(X0))
| element(sK9(sK9(powerset(sK7(sK9(sK6(sK6(powerset(X0)))))))),X0)
| empty(sK6(powerset(X0)))
| empty(sK7(sK9(sK6(sK6(powerset(X0))))))
| empty(sK9(sK6(sK6(powerset(X0)))))
| empty(sK9(powerset(sK7(sK9(sK6(sK6(powerset(X0)))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_962])]) ).
fof(f3969,plain,
( ! [X0] :
( empty(sK6(sK6(powerset(X0))))
| empty(powerset(X0))
| element(sK9(sK9(powerset(sK7(sK9(sK6(sK6(powerset(X0)))))))),X0)
| empty(sK6(powerset(X0)))
| empty(sK7(sK9(sK6(sK6(powerset(X0))))))
| empty(sK9(sK6(sK6(powerset(X0)))))
| empty(sK9(powerset(sK7(sK9(sK6(sK6(powerset(X0)))))))) )
| ~ spl16_321
| ~ spl16_365 ),
inference(resolution,[],[f3892,f3176]) ).
fof(f16936,plain,
( spl16_961
| ~ spl16_320
| ~ spl16_365 ),
inference(avatar_split_clause,[],[f3968,f3891,f3171,f16934]) ).
fof(f16934,plain,
( spl16_961
<=> ! [X0] :
( empty(sK6(sK6(powerset(X0))))
| empty(powerset(X0))
| element(sK9(sK9(powerset(sK6(sK9(sK6(sK6(powerset(X0)))))))),X0)
| empty(sK6(powerset(X0)))
| empty(sK6(sK9(sK6(sK6(powerset(X0))))))
| empty(sK9(sK6(sK6(powerset(X0)))))
| empty(sK9(powerset(sK6(sK9(sK6(sK6(powerset(X0)))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_961])]) ).
fof(f3968,plain,
( ! [X0] :
( empty(sK6(sK6(powerset(X0))))
| empty(powerset(X0))
| element(sK9(sK9(powerset(sK6(sK9(sK6(sK6(powerset(X0)))))))),X0)
| empty(sK6(powerset(X0)))
| empty(sK6(sK9(sK6(sK6(powerset(X0))))))
| empty(sK9(sK6(sK6(powerset(X0)))))
| empty(sK9(powerset(sK6(sK9(sK6(sK6(powerset(X0)))))))) )
| ~ spl16_320
| ~ spl16_365 ),
inference(resolution,[],[f3892,f3172]) ).
fof(f16774,plain,
( spl16_960
| ~ spl16_65
| ~ spl16_462 ),
inference(avatar_split_clause,[],[f5546,f5493,f508,f16772]) ).
fof(f16772,plain,
( spl16_960
<=> ! [X0] :
( empty(sK9(sK9(powerset(powerset(powerset(X0))))))
| empty(sK9(powerset(sK9(sK9(powerset(powerset(powerset(X0))))))))
| element(sK9(sK9(sK9(powerset(sK9(sK9(powerset(powerset(powerset(X0))))))))),X0)
| empty(sK9(powerset(powerset(powerset(X0)))))
| empty(sK9(sK9(powerset(sK9(sK9(powerset(powerset(powerset(X0))))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_960])]) ).
fof(f508,plain,
( spl16_65
<=> ! [X0] :
( empty(X0)
| in(sK9(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_65])]) ).
fof(f5546,plain,
( ! [X0] :
( empty(sK9(sK9(powerset(powerset(powerset(X0))))))
| empty(sK9(powerset(sK9(sK9(powerset(powerset(powerset(X0))))))))
| element(sK9(sK9(sK9(powerset(sK9(sK9(powerset(powerset(powerset(X0))))))))),X0)
| empty(sK9(powerset(powerset(powerset(X0)))))
| empty(sK9(sK9(powerset(sK9(sK9(powerset(powerset(powerset(X0))))))))) )
| ~ spl16_65
| ~ spl16_462 ),
inference(resolution,[],[f5494,f509]) ).
fof(f509,plain,
( ! [X0] :
( in(sK9(X0),X0)
| empty(X0) )
| ~ spl16_65 ),
inference(avatar_component_clause,[],[f508]) ).
fof(f16770,plain,
( spl16_805
| ~ spl16_23
| ~ spl16_57
| ~ spl16_948 ),
inference(avatar_split_clause,[],[f16566,f16427,f469,f263,f14693]) ).
fof(f16769,plain,
( spl16_959
| ~ spl16_120
| ~ spl16_427 ),
inference(avatar_split_clause,[],[f4923,f4893,f884,f16767]) ).
fof(f16767,plain,
( spl16_959
<=> ! [X0,X1] :
( empty(sK9(sK9(powerset(powerset(the_InternalRel(X0))))))
| empty(sK9(powerset(sK9(sK9(powerset(powerset(the_InternalRel(X0))))))))
| empty(the_InternalRel(X0))
| empty(sK9(powerset(powerset(the_InternalRel(X0)))))
| element(sK9(sK9(powerset(sK9(sK9(powerset(powerset(the_InternalRel(X0)))))))),the_InternalRel(X1))
| ~ subrelstr(X0,X1)
| ~ rel_str(X0)
| ~ rel_str(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_959])]) ).
fof(f884,plain,
( spl16_120
<=> ! [X2,X0,X1] :
( ~ in(X0,the_InternalRel(X1))
| element(X0,the_InternalRel(X2))
| ~ subrelstr(X1,X2)
| ~ rel_str(X1)
| ~ rel_str(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_120])]) ).
fof(f4923,plain,
( ! [X0,X1] :
( empty(sK9(sK9(powerset(powerset(the_InternalRel(X0))))))
| empty(sK9(powerset(sK9(sK9(powerset(powerset(the_InternalRel(X0))))))))
| empty(the_InternalRel(X0))
| empty(sK9(powerset(powerset(the_InternalRel(X0)))))
| element(sK9(sK9(powerset(sK9(sK9(powerset(powerset(the_InternalRel(X0)))))))),the_InternalRel(X1))
| ~ subrelstr(X0,X1)
| ~ rel_str(X0)
| ~ rel_str(X1) )
| ~ spl16_120
| ~ spl16_427 ),
inference(resolution,[],[f4894,f885]) ).
fof(f885,plain,
( ! [X2,X0,X1] :
( ~ in(X0,the_InternalRel(X1))
| element(X0,the_InternalRel(X2))
| ~ subrelstr(X1,X2)
| ~ rel_str(X1)
| ~ rel_str(X2) )
| ~ spl16_120 ),
inference(avatar_component_clause,[],[f884]) ).
fof(f16765,plain,
( spl16_958
| ~ spl16_119
| ~ spl16_427 ),
inference(avatar_split_clause,[],[f4921,f4893,f880,f16763]) ).
fof(f16763,plain,
( spl16_958
<=> ! [X0,X1] :
( empty(sK9(sK9(powerset(powerset(the_carrier(X0))))))
| empty(sK9(powerset(sK9(sK9(powerset(powerset(the_carrier(X0))))))))
| empty(the_carrier(X0))
| empty(sK9(powerset(powerset(the_carrier(X0)))))
| element(sK9(sK9(powerset(sK9(sK9(powerset(powerset(the_carrier(X0)))))))),the_carrier(X1))
| ~ subrelstr(X0,X1)
| ~ rel_str(X0)
| ~ rel_str(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_958])]) ).
fof(f880,plain,
( spl16_119
<=> ! [X2,X0,X1] :
( ~ in(X0,the_carrier(X1))
| element(X0,the_carrier(X2))
| ~ subrelstr(X1,X2)
| ~ rel_str(X1)
| ~ rel_str(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_119])]) ).
fof(f4921,plain,
( ! [X0,X1] :
( empty(sK9(sK9(powerset(powerset(the_carrier(X0))))))
| empty(sK9(powerset(sK9(sK9(powerset(powerset(the_carrier(X0))))))))
| empty(the_carrier(X0))
| empty(sK9(powerset(powerset(the_carrier(X0)))))
| element(sK9(sK9(powerset(sK9(sK9(powerset(powerset(the_carrier(X0)))))))),the_carrier(X1))
| ~ subrelstr(X0,X1)
| ~ rel_str(X0)
| ~ rel_str(X1) )
| ~ spl16_119
| ~ spl16_427 ),
inference(resolution,[],[f4894,f881]) ).
fof(f881,plain,
( ! [X2,X0,X1] :
( ~ in(X0,the_carrier(X1))
| element(X0,the_carrier(X2))
| ~ subrelstr(X1,X2)
| ~ rel_str(X1)
| ~ rel_str(X2) )
| ~ spl16_119 ),
inference(avatar_component_clause,[],[f880]) ).
fof(f16761,plain,
( spl16_957
| ~ spl16_110
| ~ spl16_420 ),
inference(avatar_split_clause,[],[f4858,f4767,f799,f16759]) ).
fof(f16759,plain,
( spl16_957
<=> ! [X0,X1] :
( empty(powerset(sK11(X0,X1)))
| empty(sK9(sK7(powerset(sK11(X0,X1)))))
| empty(sK9(powerset(sK9(sK7(powerset(sK11(X0,X1)))))))
| empty(sK11(X0,X1))
| empty(sK7(powerset(sK11(X0,X1))))
| element(sK9(sK9(powerset(sK9(sK7(powerset(sK11(X0,X1))))))),cartesian_product2(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_957])]) ).
fof(f799,plain,
( spl16_110
<=> ! [X2,X0,X1] :
( ~ in(X0,sK11(X1,X2))
| element(X0,cartesian_product2(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_110])]) ).
fof(f4858,plain,
( ! [X0,X1] :
( empty(powerset(sK11(X0,X1)))
| empty(sK9(sK7(powerset(sK11(X0,X1)))))
| empty(sK9(powerset(sK9(sK7(powerset(sK11(X0,X1)))))))
| empty(sK11(X0,X1))
| empty(sK7(powerset(sK11(X0,X1))))
| element(sK9(sK9(powerset(sK9(sK7(powerset(sK11(X0,X1))))))),cartesian_product2(X0,X1)) )
| ~ spl16_110
| ~ spl16_420 ),
inference(resolution,[],[f4768,f800]) ).
fof(f800,plain,
( ! [X2,X0,X1] :
( ~ in(X0,sK11(X1,X2))
| element(X0,cartesian_product2(X1,X2)) )
| ~ spl16_110 ),
inference(avatar_component_clause,[],[f799]) ).
fof(f16757,plain,
( spl16_956
| ~ spl16_111
| ~ spl16_420 ),
inference(avatar_split_clause,[],[f4856,f4767,f803,f16755]) ).
fof(f16755,plain,
( spl16_956
<=> ! [X0,X1] :
( empty(powerset(sK10(X0,X1)))
| empty(sK9(sK7(powerset(sK10(X0,X1)))))
| empty(sK9(powerset(sK9(sK7(powerset(sK10(X0,X1)))))))
| empty(sK10(X0,X1))
| empty(sK7(powerset(sK10(X0,X1))))
| element(sK9(sK9(powerset(sK9(sK7(powerset(sK10(X0,X1))))))),cartesian_product2(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_956])]) ).
fof(f803,plain,
( spl16_111
<=> ! [X2,X0,X1] :
( ~ in(X0,sK10(X1,X2))
| element(X0,cartesian_product2(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_111])]) ).
fof(f4856,plain,
( ! [X0,X1] :
( empty(powerset(sK10(X0,X1)))
| empty(sK9(sK7(powerset(sK10(X0,X1)))))
| empty(sK9(powerset(sK9(sK7(powerset(sK10(X0,X1)))))))
| empty(sK10(X0,X1))
| empty(sK7(powerset(sK10(X0,X1))))
| element(sK9(sK9(powerset(sK9(sK7(powerset(sK10(X0,X1))))))),cartesian_product2(X0,X1)) )
| ~ spl16_111
| ~ spl16_420 ),
inference(resolution,[],[f4768,f804]) ).
fof(f804,plain,
( ! [X2,X0,X1] :
( ~ in(X0,sK10(X1,X2))
| element(X0,cartesian_product2(X1,X2)) )
| ~ spl16_111 ),
inference(avatar_component_clause,[],[f803]) ).
fof(f16753,plain,
( spl16_955
| ~ spl16_120
| ~ spl16_420 ),
inference(avatar_split_clause,[],[f4820,f4767,f884,f16751]) ).
fof(f16751,plain,
( spl16_955
<=> ! [X0,X1] :
( empty(powerset(the_InternalRel(X0)))
| empty(sK9(sK7(powerset(the_InternalRel(X0)))))
| empty(sK9(powerset(sK9(sK7(powerset(the_InternalRel(X0)))))))
| empty(the_InternalRel(X0))
| empty(sK7(powerset(the_InternalRel(X0))))
| element(sK9(sK9(powerset(sK9(sK7(powerset(the_InternalRel(X0))))))),the_InternalRel(X1))
| ~ subrelstr(X0,X1)
| ~ rel_str(X0)
| ~ rel_str(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_955])]) ).
fof(f4820,plain,
( ! [X0,X1] :
( empty(powerset(the_InternalRel(X0)))
| empty(sK9(sK7(powerset(the_InternalRel(X0)))))
| empty(sK9(powerset(sK9(sK7(powerset(the_InternalRel(X0)))))))
| empty(the_InternalRel(X0))
| empty(sK7(powerset(the_InternalRel(X0))))
| element(sK9(sK9(powerset(sK9(sK7(powerset(the_InternalRel(X0))))))),the_InternalRel(X1))
| ~ subrelstr(X0,X1)
| ~ rel_str(X0)
| ~ rel_str(X1) )
| ~ spl16_120
| ~ spl16_420 ),
inference(resolution,[],[f4768,f885]) ).
fof(f16749,plain,
( spl16_954
| ~ spl16_119
| ~ spl16_420 ),
inference(avatar_split_clause,[],[f4818,f4767,f880,f16747]) ).
fof(f16747,plain,
( spl16_954
<=> ! [X0,X1] :
( empty(powerset(the_carrier(X0)))
| empty(sK9(sK7(powerset(the_carrier(X0)))))
| empty(sK9(powerset(sK9(sK7(powerset(the_carrier(X0)))))))
| empty(the_carrier(X0))
| empty(sK7(powerset(the_carrier(X0))))
| element(sK9(sK9(powerset(sK9(sK7(powerset(the_carrier(X0))))))),the_carrier(X1))
| ~ subrelstr(X0,X1)
| ~ rel_str(X0)
| ~ rel_str(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_954])]) ).
fof(f4818,plain,
( ! [X0,X1] :
( empty(powerset(the_carrier(X0)))
| empty(sK9(sK7(powerset(the_carrier(X0)))))
| empty(sK9(powerset(sK9(sK7(powerset(the_carrier(X0)))))))
| empty(the_carrier(X0))
| empty(sK7(powerset(the_carrier(X0))))
| element(sK9(sK9(powerset(sK9(sK7(powerset(the_carrier(X0))))))),the_carrier(X1))
| ~ subrelstr(X0,X1)
| ~ rel_str(X0)
| ~ rel_str(X1) )
| ~ spl16_119
| ~ spl16_420 ),
inference(resolution,[],[f4768,f881]) ).
fof(f16745,plain,
( spl16_953
| ~ spl16_110
| ~ spl16_419 ),
inference(avatar_split_clause,[],[f4813,f4763,f799,f16743]) ).
fof(f16743,plain,
( spl16_953
<=> ! [X0,X1] :
( empty(powerset(sK11(X0,X1)))
| empty(sK9(sK6(powerset(sK11(X0,X1)))))
| empty(sK9(powerset(sK9(sK6(powerset(sK11(X0,X1)))))))
| empty(sK11(X0,X1))
| empty(sK6(powerset(sK11(X0,X1))))
| element(sK9(sK9(powerset(sK9(sK6(powerset(sK11(X0,X1))))))),cartesian_product2(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_953])]) ).
fof(f4813,plain,
( ! [X0,X1] :
( empty(powerset(sK11(X0,X1)))
| empty(sK9(sK6(powerset(sK11(X0,X1)))))
| empty(sK9(powerset(sK9(sK6(powerset(sK11(X0,X1)))))))
| empty(sK11(X0,X1))
| empty(sK6(powerset(sK11(X0,X1))))
| element(sK9(sK9(powerset(sK9(sK6(powerset(sK11(X0,X1))))))),cartesian_product2(X0,X1)) )
| ~ spl16_110
| ~ spl16_419 ),
inference(resolution,[],[f4764,f800]) ).
fof(f16741,plain,
( spl16_952
| ~ spl16_111
| ~ spl16_419 ),
inference(avatar_split_clause,[],[f4811,f4763,f803,f16739]) ).
fof(f16739,plain,
( spl16_952
<=> ! [X0,X1] :
( empty(powerset(sK10(X0,X1)))
| empty(sK9(sK6(powerset(sK10(X0,X1)))))
| empty(sK9(powerset(sK9(sK6(powerset(sK10(X0,X1)))))))
| empty(sK10(X0,X1))
| empty(sK6(powerset(sK10(X0,X1))))
| element(sK9(sK9(powerset(sK9(sK6(powerset(sK10(X0,X1))))))),cartesian_product2(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_952])]) ).
fof(f4811,plain,
( ! [X0,X1] :
( empty(powerset(sK10(X0,X1)))
| empty(sK9(sK6(powerset(sK10(X0,X1)))))
| empty(sK9(powerset(sK9(sK6(powerset(sK10(X0,X1)))))))
| empty(sK10(X0,X1))
| empty(sK6(powerset(sK10(X0,X1))))
| element(sK9(sK9(powerset(sK9(sK6(powerset(sK10(X0,X1))))))),cartesian_product2(X0,X1)) )
| ~ spl16_111
| ~ spl16_419 ),
inference(resolution,[],[f4764,f804]) ).
fof(f16737,plain,
( spl16_951
| ~ spl16_120
| ~ spl16_419 ),
inference(avatar_split_clause,[],[f4775,f4763,f884,f16735]) ).
fof(f16735,plain,
( spl16_951
<=> ! [X0,X1] :
( empty(powerset(the_InternalRel(X0)))
| empty(sK9(sK6(powerset(the_InternalRel(X0)))))
| empty(sK9(powerset(sK9(sK6(powerset(the_InternalRel(X0)))))))
| empty(the_InternalRel(X0))
| empty(sK6(powerset(the_InternalRel(X0))))
| element(sK9(sK9(powerset(sK9(sK6(powerset(the_InternalRel(X0))))))),the_InternalRel(X1))
| ~ subrelstr(X0,X1)
| ~ rel_str(X0)
| ~ rel_str(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_951])]) ).
fof(f4775,plain,
( ! [X0,X1] :
( empty(powerset(the_InternalRel(X0)))
| empty(sK9(sK6(powerset(the_InternalRel(X0)))))
| empty(sK9(powerset(sK9(sK6(powerset(the_InternalRel(X0)))))))
| empty(the_InternalRel(X0))
| empty(sK6(powerset(the_InternalRel(X0))))
| element(sK9(sK9(powerset(sK9(sK6(powerset(the_InternalRel(X0))))))),the_InternalRel(X1))
| ~ subrelstr(X0,X1)
| ~ rel_str(X0)
| ~ rel_str(X1) )
| ~ spl16_120
| ~ spl16_419 ),
inference(resolution,[],[f4764,f885]) ).
fof(f16733,plain,
( spl16_950
| ~ spl16_119
| ~ spl16_419 ),
inference(avatar_split_clause,[],[f4773,f4763,f880,f16731]) ).
fof(f16731,plain,
( spl16_950
<=> ! [X0,X1] :
( empty(powerset(the_carrier(X0)))
| empty(sK9(sK6(powerset(the_carrier(X0)))))
| empty(sK9(powerset(sK9(sK6(powerset(the_carrier(X0)))))))
| empty(the_carrier(X0))
| empty(sK6(powerset(the_carrier(X0))))
| element(sK9(sK9(powerset(sK9(sK6(powerset(the_carrier(X0))))))),the_carrier(X1))
| ~ subrelstr(X0,X1)
| ~ rel_str(X0)
| ~ rel_str(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_950])]) ).
fof(f4773,plain,
( ! [X0,X1] :
( empty(powerset(the_carrier(X0)))
| empty(sK9(sK6(powerset(the_carrier(X0)))))
| empty(sK9(powerset(sK9(sK6(powerset(the_carrier(X0)))))))
| empty(the_carrier(X0))
| empty(sK6(powerset(the_carrier(X0))))
| element(sK9(sK9(powerset(sK9(sK6(powerset(the_carrier(X0))))))),the_carrier(X1))
| ~ subrelstr(X0,X1)
| ~ rel_str(X0)
| ~ rel_str(X1) )
| ~ spl16_119
| ~ spl16_419 ),
inference(resolution,[],[f4764,f881]) ).
fof(f16434,plain,
( spl16_948
| spl16_949
| ~ spl16_65
| ~ spl16_693 ),
inference(avatar_split_clause,[],[f10682,f10638,f508,f16431,f16427]) ).
fof(f10638,plain,
( spl16_693
<=> ! [X0] :
( ~ in(X0,the_InternalRel(sK8(sK8(sK1))))
| element(X0,cartesian_product2(sK14,sK14)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_693])]) ).
fof(f10682,plain,
( element(sK9(the_InternalRel(sK8(sK8(sK1)))),cartesian_product2(sK14,sK14))
| empty(the_InternalRel(sK8(sK8(sK1))))
| ~ spl16_65
| ~ spl16_693 ),
inference(resolution,[],[f10639,f509]) ).
fof(f10639,plain,
( ! [X0] :
( ~ in(X0,the_InternalRel(sK8(sK8(sK1))))
| element(X0,cartesian_product2(sK14,sK14)) )
| ~ spl16_693 ),
inference(avatar_component_clause,[],[f10638]) ).
fof(f16316,plain,
( spl16_947
| ~ spl16_65
| ~ spl16_460 ),
inference(avatar_split_clause,[],[f5521,f5484,f508,f16314]) ).
fof(f16314,plain,
( spl16_947
<=> ! [X0] :
( empty(powerset(powerset(X0)))
| empty(sK9(sK7(powerset(powerset(X0)))))
| empty(sK9(powerset(sK9(sK7(powerset(powerset(X0)))))))
| element(sK9(sK9(sK9(powerset(sK9(sK7(powerset(powerset(X0)))))))),X0)
| empty(sK7(powerset(powerset(X0))))
| empty(sK9(sK9(powerset(sK9(sK7(powerset(powerset(X0)))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_947])]) ).
fof(f5521,plain,
( ! [X0] :
( empty(powerset(powerset(X0)))
| empty(sK9(sK7(powerset(powerset(X0)))))
| empty(sK9(powerset(sK9(sK7(powerset(powerset(X0)))))))
| element(sK9(sK9(sK9(powerset(sK9(sK7(powerset(powerset(X0)))))))),X0)
| empty(sK7(powerset(powerset(X0))))
| empty(sK9(sK9(powerset(sK9(sK7(powerset(powerset(X0)))))))) )
| ~ spl16_65
| ~ spl16_460 ),
inference(resolution,[],[f5485,f509]) ).
fof(f16312,plain,
( spl16_946
| ~ spl16_65
| ~ spl16_459 ),
inference(avatar_split_clause,[],[f5496,f5480,f508,f16310]) ).
fof(f16310,plain,
( spl16_946
<=> ! [X0] :
( empty(powerset(powerset(X0)))
| empty(sK9(sK6(powerset(powerset(X0)))))
| empty(sK9(powerset(sK9(sK6(powerset(powerset(X0)))))))
| element(sK9(sK9(sK9(powerset(sK9(sK6(powerset(powerset(X0)))))))),X0)
| empty(sK6(powerset(powerset(X0))))
| empty(sK9(sK9(powerset(sK9(sK6(powerset(powerset(X0)))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_946])]) ).
fof(f5496,plain,
( ! [X0] :
( empty(powerset(powerset(X0)))
| empty(sK9(sK6(powerset(powerset(X0)))))
| empty(sK9(powerset(sK9(sK6(powerset(powerset(X0)))))))
| element(sK9(sK9(sK9(powerset(sK9(sK6(powerset(powerset(X0)))))))),X0)
| empty(sK6(powerset(powerset(X0))))
| empty(sK9(sK9(powerset(sK9(sK6(powerset(powerset(X0)))))))) )
| ~ spl16_65
| ~ spl16_459 ),
inference(resolution,[],[f5481,f509]) ).
fof(f16308,plain,
( spl16_945
| ~ spl16_110
| ~ spl16_427 ),
inference(avatar_split_clause,[],[f4961,f4893,f799,f16306]) ).
fof(f16306,plain,
( spl16_945
<=> ! [X0,X1] :
( empty(sK9(sK9(powerset(powerset(sK11(X0,X1))))))
| empty(sK9(powerset(sK9(sK9(powerset(powerset(sK11(X0,X1))))))))
| empty(sK11(X0,X1))
| empty(sK9(powerset(powerset(sK11(X0,X1)))))
| element(sK9(sK9(powerset(sK9(sK9(powerset(powerset(sK11(X0,X1)))))))),cartesian_product2(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_945])]) ).
fof(f4961,plain,
( ! [X0,X1] :
( empty(sK9(sK9(powerset(powerset(sK11(X0,X1))))))
| empty(sK9(powerset(sK9(sK9(powerset(powerset(sK11(X0,X1))))))))
| empty(sK11(X0,X1))
| empty(sK9(powerset(powerset(sK11(X0,X1)))))
| element(sK9(sK9(powerset(sK9(sK9(powerset(powerset(sK11(X0,X1)))))))),cartesian_product2(X0,X1)) )
| ~ spl16_110
| ~ spl16_427 ),
inference(resolution,[],[f4894,f800]) ).
fof(f16304,plain,
( spl16_944
| ~ spl16_111
| ~ spl16_427 ),
inference(avatar_split_clause,[],[f4959,f4893,f803,f16302]) ).
fof(f16302,plain,
( spl16_944
<=> ! [X0,X1] :
( empty(sK9(sK9(powerset(powerset(sK10(X0,X1))))))
| empty(sK9(powerset(sK9(sK9(powerset(powerset(sK10(X0,X1))))))))
| empty(sK10(X0,X1))
| empty(sK9(powerset(powerset(sK10(X0,X1)))))
| element(sK9(sK9(powerset(sK9(sK9(powerset(powerset(sK10(X0,X1)))))))),cartesian_product2(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_944])]) ).
fof(f4959,plain,
( ! [X0,X1] :
( empty(sK9(sK9(powerset(powerset(sK10(X0,X1))))))
| empty(sK9(powerset(sK9(sK9(powerset(powerset(sK10(X0,X1))))))))
| empty(sK10(X0,X1))
| empty(sK9(powerset(powerset(sK10(X0,X1)))))
| element(sK9(sK9(powerset(sK9(sK9(powerset(powerset(sK10(X0,X1)))))))),cartesian_product2(X0,X1)) )
| ~ spl16_111
| ~ spl16_427 ),
inference(resolution,[],[f4894,f804]) ).
fof(f16300,plain,
( spl16_943
| ~ spl16_152
| ~ spl16_405 ),
inference(avatar_split_clause,[],[f4363,f4343,f1257,f16298]) ).
fof(f16298,plain,
( spl16_943
<=> ! [X0] :
( empty(sK9(sK9(powerset(powerset(powerset(X0))))))
| element(sK9(sK9(powerset(sK9(sK9(sK9(powerset(powerset(powerset(X0))))))))),X0)
| empty(sK9(powerset(powerset(powerset(X0)))))
| empty(sK9(sK9(sK9(powerset(powerset(powerset(X0)))))))
| empty(sK9(powerset(sK9(sK9(sK9(powerset(powerset(powerset(X0))))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_943])]) ).
fof(f4363,plain,
( ! [X0] :
( empty(sK9(sK9(powerset(powerset(powerset(X0))))))
| element(sK9(sK9(powerset(sK9(sK9(sK9(powerset(powerset(powerset(X0))))))))),X0)
| empty(sK9(powerset(powerset(powerset(X0)))))
| empty(sK9(sK9(sK9(powerset(powerset(powerset(X0)))))))
| empty(sK9(powerset(sK9(sK9(sK9(powerset(powerset(powerset(X0))))))))) )
| ~ spl16_152
| ~ spl16_405 ),
inference(resolution,[],[f4344,f1258]) ).
fof(f16296,plain,
( spl16_942
| ~ spl16_86
| ~ spl16_885 ),
inference(avatar_split_clause,[],[f16074,f15904,f653,f16294]) ).
fof(f16294,plain,
( spl16_942
<=> ! [X0] :
( ~ in(X0,the_InternalRel(sK8(sK8(sK8(sK1)))))
| element(X0,cartesian_product2(sK14,sK14)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_942])]) ).
fof(f15904,plain,
( spl16_885
<=> relation_of2_as_subset(the_InternalRel(sK8(sK8(sK8(sK1)))),sK14,sK14) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_885])]) ).
fof(f16074,plain,
( ! [X0] :
( ~ in(X0,the_InternalRel(sK8(sK8(sK8(sK1)))))
| element(X0,cartesian_product2(sK14,sK14)) )
| ~ spl16_86
| ~ spl16_885 ),
inference(resolution,[],[f15906,f654]) ).
fof(f15906,plain,
( relation_of2_as_subset(the_InternalRel(sK8(sK8(sK8(sK1)))),sK14,sK14)
| ~ spl16_885 ),
inference(avatar_component_clause,[],[f15904]) ).
fof(f16292,plain,
( spl16_941
| ~ spl16_306
| ~ spl16_369 ),
inference(avatar_split_clause,[],[f4013,f3907,f2964,f16290]) ).
fof(f16290,plain,
( spl16_941
<=> ! [X0] :
( empty(sK7(sK7(powerset(X0))))
| empty(powerset(X0))
| element(sK9(sK7(sK7(sK9(sK7(sK7(powerset(X0))))))),X0)
| empty(sK7(powerset(X0)))
| empty(sK7(sK7(sK9(sK7(sK7(powerset(X0)))))))
| empty(sK9(sK7(sK7(powerset(X0)))))
| empty(sK7(sK9(sK7(sK7(powerset(X0)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_941])]) ).
fof(f4013,plain,
( ! [X0] :
( empty(sK7(sK7(powerset(X0))))
| empty(powerset(X0))
| element(sK9(sK7(sK7(sK9(sK7(sK7(powerset(X0))))))),X0)
| empty(sK7(powerset(X0)))
| empty(sK7(sK7(sK9(sK7(sK7(powerset(X0)))))))
| empty(sK9(sK7(sK7(powerset(X0)))))
| empty(sK7(sK9(sK7(sK7(powerset(X0)))))) )
| ~ spl16_306
| ~ spl16_369 ),
inference(resolution,[],[f3908,f2965]) ).
fof(f16288,plain,
( spl16_940
| ~ spl16_305
| ~ spl16_369 ),
inference(avatar_split_clause,[],[f4012,f3907,f2960,f16286]) ).
fof(f16286,plain,
( spl16_940
<=> ! [X0] :
( empty(sK7(sK7(powerset(X0))))
| empty(powerset(X0))
| element(sK9(sK7(sK6(sK9(sK7(sK7(powerset(X0))))))),X0)
| empty(sK7(powerset(X0)))
| empty(sK7(sK6(sK9(sK7(sK7(powerset(X0)))))))
| empty(sK9(sK7(sK7(powerset(X0)))))
| empty(sK6(sK9(sK7(sK7(powerset(X0)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_940])]) ).
fof(f4012,plain,
( ! [X0] :
( empty(sK7(sK7(powerset(X0))))
| empty(powerset(X0))
| element(sK9(sK7(sK6(sK9(sK7(sK7(powerset(X0))))))),X0)
| empty(sK7(powerset(X0)))
| empty(sK7(sK6(sK9(sK7(sK7(powerset(X0)))))))
| empty(sK9(sK7(sK7(powerset(X0)))))
| empty(sK6(sK9(sK7(sK7(powerset(X0)))))) )
| ~ spl16_305
| ~ spl16_369 ),
inference(resolution,[],[f3908,f2961]) ).
fof(f16284,plain,
( spl16_939
| ~ spl16_304
| ~ spl16_369 ),
inference(avatar_split_clause,[],[f4009,f3907,f2956,f16282]) ).
fof(f16282,plain,
( spl16_939
<=> ! [X0] :
( empty(sK7(sK7(powerset(X0))))
| empty(powerset(X0))
| element(sK9(sK6(sK7(sK9(sK7(sK7(powerset(X0))))))),X0)
| empty(sK7(powerset(X0)))
| empty(sK6(sK7(sK9(sK7(sK7(powerset(X0)))))))
| empty(sK9(sK7(sK7(powerset(X0)))))
| empty(sK7(sK9(sK7(sK7(powerset(X0)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_939])]) ).
fof(f4009,plain,
( ! [X0] :
( empty(sK7(sK7(powerset(X0))))
| empty(powerset(X0))
| element(sK9(sK6(sK7(sK9(sK7(sK7(powerset(X0))))))),X0)
| empty(sK7(powerset(X0)))
| empty(sK6(sK7(sK9(sK7(sK7(powerset(X0)))))))
| empty(sK9(sK7(sK7(powerset(X0)))))
| empty(sK7(sK9(sK7(sK7(powerset(X0)))))) )
| ~ spl16_304
| ~ spl16_369 ),
inference(resolution,[],[f3908,f2957]) ).
fof(f16280,plain,
( spl16_938
| ~ spl16_303
| ~ spl16_369 ),
inference(avatar_split_clause,[],[f4008,f3907,f2952,f16278]) ).
fof(f16278,plain,
( spl16_938
<=> ! [X0] :
( empty(sK7(sK7(powerset(X0))))
| empty(powerset(X0))
| element(sK9(sK6(sK6(sK9(sK7(sK7(powerset(X0))))))),X0)
| empty(sK7(powerset(X0)))
| empty(sK6(sK6(sK9(sK7(sK7(powerset(X0)))))))
| empty(sK9(sK7(sK7(powerset(X0)))))
| empty(sK6(sK9(sK7(sK7(powerset(X0)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_938])]) ).
fof(f4008,plain,
( ! [X0] :
( empty(sK7(sK7(powerset(X0))))
| empty(powerset(X0))
| element(sK9(sK6(sK6(sK9(sK7(sK7(powerset(X0))))))),X0)
| empty(sK7(powerset(X0)))
| empty(sK6(sK6(sK9(sK7(sK7(powerset(X0)))))))
| empty(sK9(sK7(sK7(powerset(X0)))))
| empty(sK6(sK9(sK7(sK7(powerset(X0)))))) )
| ~ spl16_303
| ~ spl16_369 ),
inference(resolution,[],[f3908,f2953]) ).
fof(f16276,plain,
( spl16_937
| ~ spl16_306
| ~ spl16_368 ),
inference(avatar_split_clause,[],[f3997,f3903,f2964,f16274]) ).
fof(f16274,plain,
( spl16_937
<=> ! [X0] :
( empty(sK7(sK6(powerset(X0))))
| empty(powerset(X0))
| element(sK9(sK7(sK7(sK9(sK7(sK6(powerset(X0))))))),X0)
| empty(sK6(powerset(X0)))
| empty(sK7(sK7(sK9(sK7(sK6(powerset(X0)))))))
| empty(sK9(sK7(sK6(powerset(X0)))))
| empty(sK7(sK9(sK7(sK6(powerset(X0)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_937])]) ).
fof(f3997,plain,
( ! [X0] :
( empty(sK7(sK6(powerset(X0))))
| empty(powerset(X0))
| element(sK9(sK7(sK7(sK9(sK7(sK6(powerset(X0))))))),X0)
| empty(sK6(powerset(X0)))
| empty(sK7(sK7(sK9(sK7(sK6(powerset(X0)))))))
| empty(sK9(sK7(sK6(powerset(X0)))))
| empty(sK7(sK9(sK7(sK6(powerset(X0)))))) )
| ~ spl16_306
| ~ spl16_368 ),
inference(resolution,[],[f3904,f2965]) ).
fof(f16272,plain,
( spl16_936
| ~ spl16_305
| ~ spl16_368 ),
inference(avatar_split_clause,[],[f3996,f3903,f2960,f16270]) ).
fof(f16270,plain,
( spl16_936
<=> ! [X0] :
( empty(sK7(sK6(powerset(X0))))
| empty(powerset(X0))
| element(sK9(sK7(sK6(sK9(sK7(sK6(powerset(X0))))))),X0)
| empty(sK6(powerset(X0)))
| empty(sK7(sK6(sK9(sK7(sK6(powerset(X0)))))))
| empty(sK9(sK7(sK6(powerset(X0)))))
| empty(sK6(sK9(sK7(sK6(powerset(X0)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_936])]) ).
fof(f3996,plain,
( ! [X0] :
( empty(sK7(sK6(powerset(X0))))
| empty(powerset(X0))
| element(sK9(sK7(sK6(sK9(sK7(sK6(powerset(X0))))))),X0)
| empty(sK6(powerset(X0)))
| empty(sK7(sK6(sK9(sK7(sK6(powerset(X0)))))))
| empty(sK9(sK7(sK6(powerset(X0)))))
| empty(sK6(sK9(sK7(sK6(powerset(X0)))))) )
| ~ spl16_305
| ~ spl16_368 ),
inference(resolution,[],[f3904,f2961]) ).
fof(f16268,plain,
( spl16_935
| ~ spl16_304
| ~ spl16_368 ),
inference(avatar_split_clause,[],[f3993,f3903,f2956,f16266]) ).
fof(f16266,plain,
( spl16_935
<=> ! [X0] :
( empty(sK7(sK6(powerset(X0))))
| empty(powerset(X0))
| element(sK9(sK6(sK7(sK9(sK7(sK6(powerset(X0))))))),X0)
| empty(sK6(powerset(X0)))
| empty(sK6(sK7(sK9(sK7(sK6(powerset(X0)))))))
| empty(sK9(sK7(sK6(powerset(X0)))))
| empty(sK7(sK9(sK7(sK6(powerset(X0)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_935])]) ).
fof(f3993,plain,
( ! [X0] :
( empty(sK7(sK6(powerset(X0))))
| empty(powerset(X0))
| element(sK9(sK6(sK7(sK9(sK7(sK6(powerset(X0))))))),X0)
| empty(sK6(powerset(X0)))
| empty(sK6(sK7(sK9(sK7(sK6(powerset(X0)))))))
| empty(sK9(sK7(sK6(powerset(X0)))))
| empty(sK7(sK9(sK7(sK6(powerset(X0)))))) )
| ~ spl16_304
| ~ spl16_368 ),
inference(resolution,[],[f3904,f2957]) ).
fof(f16264,plain,
( spl16_934
| ~ spl16_303
| ~ spl16_368 ),
inference(avatar_split_clause,[],[f3992,f3903,f2952,f16262]) ).
fof(f16262,plain,
( spl16_934
<=> ! [X0] :
( empty(sK7(sK6(powerset(X0))))
| empty(powerset(X0))
| element(sK9(sK6(sK6(sK9(sK7(sK6(powerset(X0))))))),X0)
| empty(sK6(powerset(X0)))
| empty(sK6(sK6(sK9(sK7(sK6(powerset(X0)))))))
| empty(sK9(sK7(sK6(powerset(X0)))))
| empty(sK6(sK9(sK7(sK6(powerset(X0)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_934])]) ).
fof(f3992,plain,
( ! [X0] :
( empty(sK7(sK6(powerset(X0))))
| empty(powerset(X0))
| element(sK9(sK6(sK6(sK9(sK7(sK6(powerset(X0))))))),X0)
| empty(sK6(powerset(X0)))
| empty(sK6(sK6(sK9(sK7(sK6(powerset(X0)))))))
| empty(sK9(sK7(sK6(powerset(X0)))))
| empty(sK6(sK9(sK7(sK6(powerset(X0)))))) )
| ~ spl16_303
| ~ spl16_368 ),
inference(resolution,[],[f3904,f2953]) ).
fof(f16260,plain,
( spl16_933
| ~ spl16_306
| ~ spl16_366 ),
inference(avatar_split_clause,[],[f3981,f3895,f2964,f16258]) ).
fof(f16258,plain,
( spl16_933
<=> ! [X0] :
( empty(sK6(sK7(powerset(X0))))
| empty(powerset(X0))
| element(sK9(sK7(sK7(sK9(sK6(sK7(powerset(X0))))))),X0)
| empty(sK7(powerset(X0)))
| empty(sK7(sK7(sK9(sK6(sK7(powerset(X0)))))))
| empty(sK9(sK6(sK7(powerset(X0)))))
| empty(sK7(sK9(sK6(sK7(powerset(X0)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_933])]) ).
fof(f3981,plain,
( ! [X0] :
( empty(sK6(sK7(powerset(X0))))
| empty(powerset(X0))
| element(sK9(sK7(sK7(sK9(sK6(sK7(powerset(X0))))))),X0)
| empty(sK7(powerset(X0)))
| empty(sK7(sK7(sK9(sK6(sK7(powerset(X0)))))))
| empty(sK9(sK6(sK7(powerset(X0)))))
| empty(sK7(sK9(sK6(sK7(powerset(X0)))))) )
| ~ spl16_306
| ~ spl16_366 ),
inference(resolution,[],[f3896,f2965]) ).
fof(f16256,plain,
( spl16_932
| ~ spl16_305
| ~ spl16_366 ),
inference(avatar_split_clause,[],[f3980,f3895,f2960,f16254]) ).
fof(f16254,plain,
( spl16_932
<=> ! [X0] :
( empty(sK6(sK7(powerset(X0))))
| empty(powerset(X0))
| element(sK9(sK7(sK6(sK9(sK6(sK7(powerset(X0))))))),X0)
| empty(sK7(powerset(X0)))
| empty(sK7(sK6(sK9(sK6(sK7(powerset(X0)))))))
| empty(sK9(sK6(sK7(powerset(X0)))))
| empty(sK6(sK9(sK6(sK7(powerset(X0)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_932])]) ).
fof(f3980,plain,
( ! [X0] :
( empty(sK6(sK7(powerset(X0))))
| empty(powerset(X0))
| element(sK9(sK7(sK6(sK9(sK6(sK7(powerset(X0))))))),X0)
| empty(sK7(powerset(X0)))
| empty(sK7(sK6(sK9(sK6(sK7(powerset(X0)))))))
| empty(sK9(sK6(sK7(powerset(X0)))))
| empty(sK6(sK9(sK6(sK7(powerset(X0)))))) )
| ~ spl16_305
| ~ spl16_366 ),
inference(resolution,[],[f3896,f2961]) ).
fof(f16252,plain,
( spl16_931
| ~ spl16_304
| ~ spl16_366 ),
inference(avatar_split_clause,[],[f3977,f3895,f2956,f16250]) ).
fof(f16250,plain,
( spl16_931
<=> ! [X0] :
( empty(sK6(sK7(powerset(X0))))
| empty(powerset(X0))
| element(sK9(sK6(sK7(sK9(sK6(sK7(powerset(X0))))))),X0)
| empty(sK7(powerset(X0)))
| empty(sK6(sK7(sK9(sK6(sK7(powerset(X0)))))))
| empty(sK9(sK6(sK7(powerset(X0)))))
| empty(sK7(sK9(sK6(sK7(powerset(X0)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_931])]) ).
fof(f3977,plain,
( ! [X0] :
( empty(sK6(sK7(powerset(X0))))
| empty(powerset(X0))
| element(sK9(sK6(sK7(sK9(sK6(sK7(powerset(X0))))))),X0)
| empty(sK7(powerset(X0)))
| empty(sK6(sK7(sK9(sK6(sK7(powerset(X0)))))))
| empty(sK9(sK6(sK7(powerset(X0)))))
| empty(sK7(sK9(sK6(sK7(powerset(X0)))))) )
| ~ spl16_304
| ~ spl16_366 ),
inference(resolution,[],[f3896,f2957]) ).
fof(f16248,plain,
( spl16_930
| ~ spl16_303
| ~ spl16_366 ),
inference(avatar_split_clause,[],[f3976,f3895,f2952,f16246]) ).
fof(f16246,plain,
( spl16_930
<=> ! [X0] :
( empty(sK6(sK7(powerset(X0))))
| empty(powerset(X0))
| element(sK9(sK6(sK6(sK9(sK6(sK7(powerset(X0))))))),X0)
| empty(sK7(powerset(X0)))
| empty(sK6(sK6(sK9(sK6(sK7(powerset(X0)))))))
| empty(sK9(sK6(sK7(powerset(X0)))))
| empty(sK6(sK9(sK6(sK7(powerset(X0)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_930])]) ).
fof(f3976,plain,
( ! [X0] :
( empty(sK6(sK7(powerset(X0))))
| empty(powerset(X0))
| element(sK9(sK6(sK6(sK9(sK6(sK7(powerset(X0))))))),X0)
| empty(sK7(powerset(X0)))
| empty(sK6(sK6(sK9(sK6(sK7(powerset(X0)))))))
| empty(sK9(sK6(sK7(powerset(X0)))))
| empty(sK6(sK9(sK6(sK7(powerset(X0)))))) )
| ~ spl16_303
| ~ spl16_366 ),
inference(resolution,[],[f3896,f2953]) ).
fof(f16244,plain,
( spl16_929
| ~ spl16_306
| ~ spl16_365 ),
inference(avatar_split_clause,[],[f3965,f3891,f2964,f16242]) ).
fof(f16242,plain,
( spl16_929
<=> ! [X0] :
( empty(sK6(sK6(powerset(X0))))
| empty(powerset(X0))
| element(sK9(sK7(sK7(sK9(sK6(sK6(powerset(X0))))))),X0)
| empty(sK6(powerset(X0)))
| empty(sK7(sK7(sK9(sK6(sK6(powerset(X0)))))))
| empty(sK9(sK6(sK6(powerset(X0)))))
| empty(sK7(sK9(sK6(sK6(powerset(X0)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_929])]) ).
fof(f3965,plain,
( ! [X0] :
( empty(sK6(sK6(powerset(X0))))
| empty(powerset(X0))
| element(sK9(sK7(sK7(sK9(sK6(sK6(powerset(X0))))))),X0)
| empty(sK6(powerset(X0)))
| empty(sK7(sK7(sK9(sK6(sK6(powerset(X0)))))))
| empty(sK9(sK6(sK6(powerset(X0)))))
| empty(sK7(sK9(sK6(sK6(powerset(X0)))))) )
| ~ spl16_306
| ~ spl16_365 ),
inference(resolution,[],[f3892,f2965]) ).
fof(f16240,plain,
( spl16_928
| ~ spl16_305
| ~ spl16_365 ),
inference(avatar_split_clause,[],[f3964,f3891,f2960,f16238]) ).
fof(f16238,plain,
( spl16_928
<=> ! [X0] :
( empty(sK6(sK6(powerset(X0))))
| empty(powerset(X0))
| element(sK9(sK7(sK6(sK9(sK6(sK6(powerset(X0))))))),X0)
| empty(sK6(powerset(X0)))
| empty(sK7(sK6(sK9(sK6(sK6(powerset(X0)))))))
| empty(sK9(sK6(sK6(powerset(X0)))))
| empty(sK6(sK9(sK6(sK6(powerset(X0)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_928])]) ).
fof(f3964,plain,
( ! [X0] :
( empty(sK6(sK6(powerset(X0))))
| empty(powerset(X0))
| element(sK9(sK7(sK6(sK9(sK6(sK6(powerset(X0))))))),X0)
| empty(sK6(powerset(X0)))
| empty(sK7(sK6(sK9(sK6(sK6(powerset(X0)))))))
| empty(sK9(sK6(sK6(powerset(X0)))))
| empty(sK6(sK9(sK6(sK6(powerset(X0)))))) )
| ~ spl16_305
| ~ spl16_365 ),
inference(resolution,[],[f3892,f2961]) ).
fof(f16236,plain,
( spl16_927
| ~ spl16_304
| ~ spl16_365 ),
inference(avatar_split_clause,[],[f3961,f3891,f2956,f16234]) ).
fof(f16234,plain,
( spl16_927
<=> ! [X0] :
( empty(sK6(sK6(powerset(X0))))
| empty(powerset(X0))
| element(sK9(sK6(sK7(sK9(sK6(sK6(powerset(X0))))))),X0)
| empty(sK6(powerset(X0)))
| empty(sK6(sK7(sK9(sK6(sK6(powerset(X0)))))))
| empty(sK9(sK6(sK6(powerset(X0)))))
| empty(sK7(sK9(sK6(sK6(powerset(X0)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_927])]) ).
fof(f3961,plain,
( ! [X0] :
( empty(sK6(sK6(powerset(X0))))
| empty(powerset(X0))
| element(sK9(sK6(sK7(sK9(sK6(sK6(powerset(X0))))))),X0)
| empty(sK6(powerset(X0)))
| empty(sK6(sK7(sK9(sK6(sK6(powerset(X0)))))))
| empty(sK9(sK6(sK6(powerset(X0)))))
| empty(sK7(sK9(sK6(sK6(powerset(X0)))))) )
| ~ spl16_304
| ~ spl16_365 ),
inference(resolution,[],[f3892,f2957]) ).
fof(f16232,plain,
( spl16_926
| ~ spl16_303
| ~ spl16_365 ),
inference(avatar_split_clause,[],[f3960,f3891,f2952,f16230]) ).
fof(f16230,plain,
( spl16_926
<=> ! [X0] :
( empty(sK6(sK6(powerset(X0))))
| empty(powerset(X0))
| element(sK9(sK6(sK6(sK9(sK6(sK6(powerset(X0))))))),X0)
| empty(sK6(powerset(X0)))
| empty(sK6(sK6(sK9(sK6(sK6(powerset(X0)))))))
| empty(sK9(sK6(sK6(powerset(X0)))))
| empty(sK6(sK9(sK6(sK6(powerset(X0)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_926])]) ).
fof(f3960,plain,
( ! [X0] :
( empty(sK6(sK6(powerset(X0))))
| empty(powerset(X0))
| element(sK9(sK6(sK6(sK9(sK6(sK6(powerset(X0))))))),X0)
| empty(sK6(powerset(X0)))
| empty(sK6(sK6(sK9(sK6(sK6(powerset(X0)))))))
| empty(sK9(sK6(sK6(powerset(X0)))))
| empty(sK6(sK9(sK6(sK6(powerset(X0)))))) )
| ~ spl16_303
| ~ spl16_365 ),
inference(resolution,[],[f3892,f2953]) ).
fof(f16228,plain,
( spl16_925
| ~ spl16_177
| ~ spl16_364 ),
inference(avatar_split_clause,[],[f3879,f3678,f1476,f16226]) ).
fof(f16226,plain,
( spl16_925
<=> ! [X0] :
( empty(powerset(sK9(sK7(powerset(X0)))))
| empty(sK9(sK7(powerset(sK9(sK7(powerset(X0)))))))
| empty(sK9(sK7(powerset(X0))))
| empty(sK7(powerset(sK9(sK7(powerset(X0))))))
| empty(sK7(powerset(X0)))
| element(sK9(sK9(sK7(powerset(sK9(sK7(powerset(X0))))))),X0)
| empty(powerset(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_925])]) ).
fof(f3879,plain,
( ! [X0] :
( empty(powerset(sK9(sK7(powerset(X0)))))
| empty(sK9(sK7(powerset(sK9(sK7(powerset(X0)))))))
| empty(sK9(sK7(powerset(X0))))
| empty(sK7(powerset(sK9(sK7(powerset(X0))))))
| empty(sK7(powerset(X0)))
| element(sK9(sK9(sK7(powerset(sK9(sK7(powerset(X0))))))),X0)
| empty(powerset(X0)) )
| ~ spl16_177
| ~ spl16_364 ),
inference(resolution,[],[f3679,f1477]) ).
fof(f16224,plain,
( spl16_924
| ~ spl16_176
| ~ spl16_364 ),
inference(avatar_split_clause,[],[f3874,f3678,f1472,f16222]) ).
fof(f16222,plain,
( spl16_924
<=> ! [X0] :
( empty(powerset(sK9(sK6(powerset(X0)))))
| empty(sK9(sK7(powerset(sK9(sK6(powerset(X0)))))))
| empty(sK9(sK6(powerset(X0))))
| empty(sK7(powerset(sK9(sK6(powerset(X0))))))
| empty(sK6(powerset(X0)))
| element(sK9(sK9(sK7(powerset(sK9(sK6(powerset(X0))))))),X0)
| empty(powerset(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_924])]) ).
fof(f3874,plain,
( ! [X0] :
( empty(powerset(sK9(sK6(powerset(X0)))))
| empty(sK9(sK7(powerset(sK9(sK6(powerset(X0)))))))
| empty(sK9(sK6(powerset(X0))))
| empty(sK7(powerset(sK9(sK6(powerset(X0))))))
| empty(sK6(powerset(X0)))
| element(sK9(sK9(sK7(powerset(sK9(sK6(powerset(X0))))))),X0)
| empty(powerset(X0)) )
| ~ spl16_176
| ~ spl16_364 ),
inference(resolution,[],[f3679,f1473]) ).
fof(f16220,plain,
( spl16_923
| ~ spl16_177
| ~ spl16_363 ),
inference(avatar_split_clause,[],[f3852,f3674,f1476,f16218]) ).
fof(f16218,plain,
( spl16_923
<=> ! [X0] :
( empty(powerset(sK9(sK7(powerset(X0)))))
| empty(sK9(sK6(powerset(sK9(sK7(powerset(X0)))))))
| empty(sK9(sK7(powerset(X0))))
| empty(sK6(powerset(sK9(sK7(powerset(X0))))))
| empty(sK7(powerset(X0)))
| element(sK9(sK9(sK6(powerset(sK9(sK7(powerset(X0))))))),X0)
| empty(powerset(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_923])]) ).
fof(f3852,plain,
( ! [X0] :
( empty(powerset(sK9(sK7(powerset(X0)))))
| empty(sK9(sK6(powerset(sK9(sK7(powerset(X0)))))))
| empty(sK9(sK7(powerset(X0))))
| empty(sK6(powerset(sK9(sK7(powerset(X0))))))
| empty(sK7(powerset(X0)))
| element(sK9(sK9(sK6(powerset(sK9(sK7(powerset(X0))))))),X0)
| empty(powerset(X0)) )
| ~ spl16_177
| ~ spl16_363 ),
inference(resolution,[],[f3675,f1477]) ).
fof(f16216,plain,
( spl16_922
| ~ spl16_176
| ~ spl16_363 ),
inference(avatar_split_clause,[],[f3847,f3674,f1472,f16214]) ).
fof(f16214,plain,
( spl16_922
<=> ! [X0] :
( empty(powerset(sK9(sK6(powerset(X0)))))
| empty(sK9(sK6(powerset(sK9(sK6(powerset(X0)))))))
| empty(sK9(sK6(powerset(X0))))
| empty(sK6(powerset(sK9(sK6(powerset(X0))))))
| empty(sK6(powerset(X0)))
| element(sK9(sK9(sK6(powerset(sK9(sK6(powerset(X0))))))),X0)
| empty(powerset(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_922])]) ).
fof(f3847,plain,
( ! [X0] :
( empty(powerset(sK9(sK6(powerset(X0)))))
| empty(sK9(sK6(powerset(sK9(sK6(powerset(X0)))))))
| empty(sK9(sK6(powerset(X0))))
| empty(sK6(powerset(sK9(sK6(powerset(X0))))))
| empty(sK6(powerset(X0)))
| element(sK9(sK9(sK6(powerset(sK9(sK6(powerset(X0))))))),X0)
| empty(powerset(X0)) )
| ~ spl16_176
| ~ spl16_363 ),
inference(resolution,[],[f3675,f1473]) ).
fof(f16212,plain,
( ~ spl16_163
| spl16_921
| ~ spl16_82
| ~ spl16_885 ),
inference(avatar_split_clause,[],[f16076,f15904,f617,f16209,f1358]) ).
fof(f16209,plain,
( spl16_921
<=> finite(the_InternalRel(sK8(sK8(sK8(sK1))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_921])]) ).
fof(f16076,plain,
( finite(the_InternalRel(sK8(sK8(sK8(sK1)))))
| ~ finite(cartesian_product2(sK14,sK14))
| ~ spl16_82
| ~ spl16_885 ),
inference(resolution,[],[f15906,f618]) ).
fof(f16128,plain,
( spl16_920
| ~ spl16_40
| ~ spl16_885 ),
inference(avatar_split_clause,[],[f16077,f15904,f343,f16125]) ).
fof(f16125,plain,
( spl16_920
<=> relation_of2(the_InternalRel(sK8(sK8(sK8(sK1)))),sK14,sK14) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_920])]) ).
fof(f16077,plain,
( relation_of2(the_InternalRel(sK8(sK8(sK8(sK1)))),sK14,sK14)
| ~ spl16_40
| ~ spl16_885 ),
inference(resolution,[],[f15906,f344]) ).
fof(f16093,plain,
( spl16_919
| ~ spl16_72
| ~ spl16_420 ),
inference(avatar_split_clause,[],[f4824,f4767,f549,f16091]) ).
fof(f16091,plain,
( spl16_919
<=> ! [X0] :
( empty(powerset(sK9(powerset(X0))))
| empty(sK9(sK7(powerset(sK9(powerset(X0))))))
| empty(sK9(powerset(sK9(sK7(powerset(sK9(powerset(X0))))))))
| empty(sK9(powerset(X0)))
| empty(sK7(powerset(sK9(powerset(X0)))))
| element(sK9(sK9(powerset(sK9(sK7(powerset(sK9(powerset(X0)))))))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_919])]) ).
fof(f549,plain,
( spl16_72
<=> ! [X0,X1] :
( element(X0,X1)
| ~ in(X0,sK9(powerset(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_72])]) ).
fof(f4824,plain,
( ! [X0] :
( empty(powerset(sK9(powerset(X0))))
| empty(sK9(sK7(powerset(sK9(powerset(X0))))))
| empty(sK9(powerset(sK9(sK7(powerset(sK9(powerset(X0))))))))
| empty(sK9(powerset(X0)))
| empty(sK7(powerset(sK9(powerset(X0)))))
| element(sK9(sK9(powerset(sK9(sK7(powerset(sK9(powerset(X0)))))))),X0) )
| ~ spl16_72
| ~ spl16_420 ),
inference(resolution,[],[f4768,f550]) ).
fof(f550,plain,
( ! [X0,X1] :
( ~ in(X0,sK9(powerset(X1)))
| element(X0,X1) )
| ~ spl16_72 ),
inference(avatar_component_clause,[],[f549]) ).
fof(f16089,plain,
( spl16_918
| ~ spl16_72
| ~ spl16_419 ),
inference(avatar_split_clause,[],[f4779,f4763,f549,f16087]) ).
fof(f16087,plain,
( spl16_918
<=> ! [X0] :
( empty(powerset(sK9(powerset(X0))))
| empty(sK9(sK6(powerset(sK9(powerset(X0))))))
| empty(sK9(powerset(sK9(sK6(powerset(sK9(powerset(X0))))))))
| empty(sK9(powerset(X0)))
| empty(sK6(powerset(sK9(powerset(X0)))))
| element(sK9(sK9(powerset(sK9(sK6(powerset(sK9(powerset(X0)))))))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_918])]) ).
fof(f4779,plain,
( ! [X0] :
( empty(powerset(sK9(powerset(X0))))
| empty(sK9(sK6(powerset(sK9(powerset(X0))))))
| empty(sK9(powerset(sK9(sK6(powerset(sK9(powerset(X0))))))))
| empty(sK9(powerset(X0)))
| empty(sK6(powerset(sK9(powerset(X0)))))
| element(sK9(sK9(powerset(sK9(sK6(powerset(sK9(powerset(X0)))))))),X0) )
| ~ spl16_72
| ~ spl16_419 ),
inference(resolution,[],[f4764,f550]) ).
fof(f16085,plain,
( spl16_917
| ~ spl16_120
| ~ spl16_418 ),
inference(avatar_split_clause,[],[f4722,f4669,f884,f16083]) ).
fof(f16083,plain,
( spl16_917
<=> ! [X0,X1] :
( empty(sK7(sK9(sK9(powerset(powerset(the_InternalRel(X0)))))))
| empty(sK9(sK9(powerset(powerset(the_InternalRel(X0))))))
| empty(the_InternalRel(X0))
| empty(sK9(powerset(powerset(the_InternalRel(X0)))))
| element(sK9(sK7(sK9(sK9(powerset(powerset(the_InternalRel(X0))))))),the_InternalRel(X1))
| ~ subrelstr(X0,X1)
| ~ rel_str(X0)
| ~ rel_str(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_917])]) ).
fof(f4722,plain,
( ! [X0,X1] :
( empty(sK7(sK9(sK9(powerset(powerset(the_InternalRel(X0)))))))
| empty(sK9(sK9(powerset(powerset(the_InternalRel(X0))))))
| empty(the_InternalRel(X0))
| empty(sK9(powerset(powerset(the_InternalRel(X0)))))
| element(sK9(sK7(sK9(sK9(powerset(powerset(the_InternalRel(X0))))))),the_InternalRel(X1))
| ~ subrelstr(X0,X1)
| ~ rel_str(X0)
| ~ rel_str(X1) )
| ~ spl16_120
| ~ spl16_418 ),
inference(resolution,[],[f4670,f885]) ).
fof(f16081,plain,
( spl16_916
| ~ spl16_119
| ~ spl16_418 ),
inference(avatar_split_clause,[],[f4720,f4669,f880,f16079]) ).
fof(f16079,plain,
( spl16_916
<=> ! [X0,X1] :
( empty(sK7(sK9(sK9(powerset(powerset(the_carrier(X0)))))))
| empty(sK9(sK9(powerset(powerset(the_carrier(X0))))))
| empty(the_carrier(X0))
| empty(sK9(powerset(powerset(the_carrier(X0)))))
| element(sK9(sK7(sK9(sK9(powerset(powerset(the_carrier(X0))))))),the_carrier(X1))
| ~ subrelstr(X0,X1)
| ~ rel_str(X0)
| ~ rel_str(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_916])]) ).
fof(f4720,plain,
( ! [X0,X1] :
( empty(sK7(sK9(sK9(powerset(powerset(the_carrier(X0)))))))
| empty(sK9(sK9(powerset(powerset(the_carrier(X0))))))
| empty(the_carrier(X0))
| empty(sK9(powerset(powerset(the_carrier(X0)))))
| element(sK9(sK7(sK9(sK9(powerset(powerset(the_carrier(X0))))))),the_carrier(X1))
| ~ subrelstr(X0,X1)
| ~ rel_str(X0)
| ~ rel_str(X1) )
| ~ spl16_119
| ~ spl16_418 ),
inference(resolution,[],[f4670,f881]) ).
fof(f16073,plain,
( spl16_915
| ~ spl16_120
| ~ spl16_417 ),
inference(avatar_split_clause,[],[f4677,f4665,f884,f16071]) ).
fof(f16071,plain,
( spl16_915
<=> ! [X0,X1] :
( empty(sK6(sK9(sK9(powerset(powerset(the_InternalRel(X0)))))))
| empty(sK9(sK9(powerset(powerset(the_InternalRel(X0))))))
| empty(the_InternalRel(X0))
| empty(sK9(powerset(powerset(the_InternalRel(X0)))))
| element(sK9(sK6(sK9(sK9(powerset(powerset(the_InternalRel(X0))))))),the_InternalRel(X1))
| ~ subrelstr(X0,X1)
| ~ rel_str(X0)
| ~ rel_str(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_915])]) ).
fof(f4677,plain,
( ! [X0,X1] :
( empty(sK6(sK9(sK9(powerset(powerset(the_InternalRel(X0)))))))
| empty(sK9(sK9(powerset(powerset(the_InternalRel(X0))))))
| empty(the_InternalRel(X0))
| empty(sK9(powerset(powerset(the_InternalRel(X0)))))
| element(sK9(sK6(sK9(sK9(powerset(powerset(the_InternalRel(X0))))))),the_InternalRel(X1))
| ~ subrelstr(X0,X1)
| ~ rel_str(X0)
| ~ rel_str(X1) )
| ~ spl16_120
| ~ spl16_417 ),
inference(resolution,[],[f4666,f885]) ).
fof(f16069,plain,
( spl16_914
| ~ spl16_119
| ~ spl16_417 ),
inference(avatar_split_clause,[],[f4675,f4665,f880,f16067]) ).
fof(f16067,plain,
( spl16_914
<=> ! [X0,X1] :
( empty(sK6(sK9(sK9(powerset(powerset(the_carrier(X0)))))))
| empty(sK9(sK9(powerset(powerset(the_carrier(X0))))))
| empty(the_carrier(X0))
| empty(sK9(powerset(powerset(the_carrier(X0)))))
| element(sK9(sK6(sK9(sK9(powerset(powerset(the_carrier(X0))))))),the_carrier(X1))
| ~ subrelstr(X0,X1)
| ~ rel_str(X0)
| ~ rel_str(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_914])]) ).
fof(f4675,plain,
( ! [X0,X1] :
( empty(sK6(sK9(sK9(powerset(powerset(the_carrier(X0)))))))
| empty(sK9(sK9(powerset(powerset(the_carrier(X0))))))
| empty(the_carrier(X0))
| empty(sK9(powerset(powerset(the_carrier(X0)))))
| element(sK9(sK6(sK9(sK9(powerset(powerset(the_carrier(X0))))))),the_carrier(X1))
| ~ subrelstr(X0,X1)
| ~ rel_str(X0)
| ~ rel_str(X1) )
| ~ spl16_119
| ~ spl16_417 ),
inference(resolution,[],[f4666,f881]) ).
fof(f16065,plain,
( spl16_913
| ~ spl16_110
| ~ spl16_415 ),
inference(avatar_split_clause,[],[f4658,f4477,f799,f16063]) ).
fof(f16063,plain,
( spl16_913
<=> ! [X0,X1] :
( empty(powerset(sK11(X0,X1)))
| empty(sK7(sK9(sK7(powerset(sK11(X0,X1))))))
| empty(sK9(sK7(powerset(sK11(X0,X1)))))
| empty(sK11(X0,X1))
| empty(sK7(powerset(sK11(X0,X1))))
| element(sK9(sK7(sK9(sK7(powerset(sK11(X0,X1)))))),cartesian_product2(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_913])]) ).
fof(f4658,plain,
( ! [X0,X1] :
( empty(powerset(sK11(X0,X1)))
| empty(sK7(sK9(sK7(powerset(sK11(X0,X1))))))
| empty(sK9(sK7(powerset(sK11(X0,X1)))))
| empty(sK11(X0,X1))
| empty(sK7(powerset(sK11(X0,X1))))
| element(sK9(sK7(sK9(sK7(powerset(sK11(X0,X1)))))),cartesian_product2(X0,X1)) )
| ~ spl16_110
| ~ spl16_415 ),
inference(resolution,[],[f4478,f800]) ).
fof(f16061,plain,
( spl16_912
| ~ spl16_111
| ~ spl16_415 ),
inference(avatar_split_clause,[],[f4656,f4477,f803,f16059]) ).
fof(f16059,plain,
( spl16_912
<=> ! [X0,X1] :
( empty(powerset(sK10(X0,X1)))
| empty(sK7(sK9(sK7(powerset(sK10(X0,X1))))))
| empty(sK9(sK7(powerset(sK10(X0,X1)))))
| empty(sK10(X0,X1))
| empty(sK7(powerset(sK10(X0,X1))))
| element(sK9(sK7(sK9(sK7(powerset(sK10(X0,X1)))))),cartesian_product2(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_912])]) ).
fof(f4656,plain,
( ! [X0,X1] :
( empty(powerset(sK10(X0,X1)))
| empty(sK7(sK9(sK7(powerset(sK10(X0,X1))))))
| empty(sK9(sK7(powerset(sK10(X0,X1)))))
| empty(sK10(X0,X1))
| empty(sK7(powerset(sK10(X0,X1))))
| element(sK9(sK7(sK9(sK7(powerset(sK10(X0,X1)))))),cartesian_product2(X0,X1)) )
| ~ spl16_111
| ~ spl16_415 ),
inference(resolution,[],[f4478,f804]) ).
fof(f16057,plain,
( spl16_911
| ~ spl16_120
| ~ spl16_415 ),
inference(avatar_split_clause,[],[f4620,f4477,f884,f16055]) ).
fof(f16055,plain,
( spl16_911
<=> ! [X0,X1] :
( empty(powerset(the_InternalRel(X0)))
| empty(sK7(sK9(sK7(powerset(the_InternalRel(X0))))))
| empty(sK9(sK7(powerset(the_InternalRel(X0)))))
| empty(the_InternalRel(X0))
| empty(sK7(powerset(the_InternalRel(X0))))
| element(sK9(sK7(sK9(sK7(powerset(the_InternalRel(X0)))))),the_InternalRel(X1))
| ~ subrelstr(X0,X1)
| ~ rel_str(X0)
| ~ rel_str(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_911])]) ).
fof(f4620,plain,
( ! [X0,X1] :
( empty(powerset(the_InternalRel(X0)))
| empty(sK7(sK9(sK7(powerset(the_InternalRel(X0))))))
| empty(sK9(sK7(powerset(the_InternalRel(X0)))))
| empty(the_InternalRel(X0))
| empty(sK7(powerset(the_InternalRel(X0))))
| element(sK9(sK7(sK9(sK7(powerset(the_InternalRel(X0)))))),the_InternalRel(X1))
| ~ subrelstr(X0,X1)
| ~ rel_str(X0)
| ~ rel_str(X1) )
| ~ spl16_120
| ~ spl16_415 ),
inference(resolution,[],[f4478,f885]) ).
fof(f16053,plain,
( spl16_910
| ~ spl16_119
| ~ spl16_415 ),
inference(avatar_split_clause,[],[f4618,f4477,f880,f16051]) ).
fof(f16051,plain,
( spl16_910
<=> ! [X0,X1] :
( empty(powerset(the_carrier(X0)))
| empty(sK7(sK9(sK7(powerset(the_carrier(X0))))))
| empty(sK9(sK7(powerset(the_carrier(X0)))))
| empty(the_carrier(X0))
| empty(sK7(powerset(the_carrier(X0))))
| element(sK9(sK7(sK9(sK7(powerset(the_carrier(X0)))))),the_carrier(X1))
| ~ subrelstr(X0,X1)
| ~ rel_str(X0)
| ~ rel_str(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_910])]) ).
fof(f4618,plain,
( ! [X0,X1] :
( empty(powerset(the_carrier(X0)))
| empty(sK7(sK9(sK7(powerset(the_carrier(X0))))))
| empty(sK9(sK7(powerset(the_carrier(X0)))))
| empty(the_carrier(X0))
| empty(sK7(powerset(the_carrier(X0))))
| element(sK9(sK7(sK9(sK7(powerset(the_carrier(X0)))))),the_carrier(X1))
| ~ subrelstr(X0,X1)
| ~ rel_str(X0)
| ~ rel_str(X1) )
| ~ spl16_119
| ~ spl16_415 ),
inference(resolution,[],[f4478,f881]) ).
fof(f16049,plain,
( spl16_909
| ~ spl16_110
| ~ spl16_414 ),
inference(avatar_split_clause,[],[f4613,f4473,f799,f16047]) ).
fof(f16047,plain,
( spl16_909
<=> ! [X0,X1] :
( empty(powerset(sK11(X0,X1)))
| empty(sK6(sK9(sK7(powerset(sK11(X0,X1))))))
| empty(sK9(sK7(powerset(sK11(X0,X1)))))
| empty(sK11(X0,X1))
| empty(sK7(powerset(sK11(X0,X1))))
| element(sK9(sK6(sK9(sK7(powerset(sK11(X0,X1)))))),cartesian_product2(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_909])]) ).
fof(f4613,plain,
( ! [X0,X1] :
( empty(powerset(sK11(X0,X1)))
| empty(sK6(sK9(sK7(powerset(sK11(X0,X1))))))
| empty(sK9(sK7(powerset(sK11(X0,X1)))))
| empty(sK11(X0,X1))
| empty(sK7(powerset(sK11(X0,X1))))
| element(sK9(sK6(sK9(sK7(powerset(sK11(X0,X1)))))),cartesian_product2(X0,X1)) )
| ~ spl16_110
| ~ spl16_414 ),
inference(resolution,[],[f4474,f800]) ).
fof(f16045,plain,
( spl16_908
| ~ spl16_111
| ~ spl16_414 ),
inference(avatar_split_clause,[],[f4611,f4473,f803,f16043]) ).
fof(f16043,plain,
( spl16_908
<=> ! [X0,X1] :
( empty(powerset(sK10(X0,X1)))
| empty(sK6(sK9(sK7(powerset(sK10(X0,X1))))))
| empty(sK9(sK7(powerset(sK10(X0,X1)))))
| empty(sK10(X0,X1))
| empty(sK7(powerset(sK10(X0,X1))))
| element(sK9(sK6(sK9(sK7(powerset(sK10(X0,X1)))))),cartesian_product2(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_908])]) ).
fof(f4611,plain,
( ! [X0,X1] :
( empty(powerset(sK10(X0,X1)))
| empty(sK6(sK9(sK7(powerset(sK10(X0,X1))))))
| empty(sK9(sK7(powerset(sK10(X0,X1)))))
| empty(sK10(X0,X1))
| empty(sK7(powerset(sK10(X0,X1))))
| element(sK9(sK6(sK9(sK7(powerset(sK10(X0,X1)))))),cartesian_product2(X0,X1)) )
| ~ spl16_111
| ~ spl16_414 ),
inference(resolution,[],[f4474,f804]) ).
fof(f16041,plain,
( spl16_907
| ~ spl16_120
| ~ spl16_414 ),
inference(avatar_split_clause,[],[f4575,f4473,f884,f16039]) ).
fof(f16039,plain,
( spl16_907
<=> ! [X0,X1] :
( empty(powerset(the_InternalRel(X0)))
| empty(sK6(sK9(sK7(powerset(the_InternalRel(X0))))))
| empty(sK9(sK7(powerset(the_InternalRel(X0)))))
| empty(the_InternalRel(X0))
| empty(sK7(powerset(the_InternalRel(X0))))
| element(sK9(sK6(sK9(sK7(powerset(the_InternalRel(X0)))))),the_InternalRel(X1))
| ~ subrelstr(X0,X1)
| ~ rel_str(X0)
| ~ rel_str(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_907])]) ).
fof(f4575,plain,
( ! [X0,X1] :
( empty(powerset(the_InternalRel(X0)))
| empty(sK6(sK9(sK7(powerset(the_InternalRel(X0))))))
| empty(sK9(sK7(powerset(the_InternalRel(X0)))))
| empty(the_InternalRel(X0))
| empty(sK7(powerset(the_InternalRel(X0))))
| element(sK9(sK6(sK9(sK7(powerset(the_InternalRel(X0)))))),the_InternalRel(X1))
| ~ subrelstr(X0,X1)
| ~ rel_str(X0)
| ~ rel_str(X1) )
| ~ spl16_120
| ~ spl16_414 ),
inference(resolution,[],[f4474,f885]) ).
fof(f16037,plain,
( spl16_906
| ~ spl16_119
| ~ spl16_414 ),
inference(avatar_split_clause,[],[f4573,f4473,f880,f16035]) ).
fof(f16035,plain,
( spl16_906
<=> ! [X0,X1] :
( empty(powerset(the_carrier(X0)))
| empty(sK6(sK9(sK7(powerset(the_carrier(X0))))))
| empty(sK9(sK7(powerset(the_carrier(X0)))))
| empty(the_carrier(X0))
| empty(sK7(powerset(the_carrier(X0))))
| element(sK9(sK6(sK9(sK7(powerset(the_carrier(X0)))))),the_carrier(X1))
| ~ subrelstr(X0,X1)
| ~ rel_str(X0)
| ~ rel_str(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_906])]) ).
fof(f4573,plain,
( ! [X0,X1] :
( empty(powerset(the_carrier(X0)))
| empty(sK6(sK9(sK7(powerset(the_carrier(X0))))))
| empty(sK9(sK7(powerset(the_carrier(X0)))))
| empty(the_carrier(X0))
| empty(sK7(powerset(the_carrier(X0))))
| element(sK9(sK6(sK9(sK7(powerset(the_carrier(X0)))))),the_carrier(X1))
| ~ subrelstr(X0,X1)
| ~ rel_str(X0)
| ~ rel_str(X1) )
| ~ spl16_119
| ~ spl16_414 ),
inference(resolution,[],[f4474,f881]) ).
fof(f16033,plain,
( spl16_905
| ~ spl16_110
| ~ spl16_413 ),
inference(avatar_split_clause,[],[f4568,f4469,f799,f16031]) ).
fof(f16031,plain,
( spl16_905
<=> ! [X0,X1] :
( empty(powerset(sK11(X0,X1)))
| empty(sK7(sK9(sK6(powerset(sK11(X0,X1))))))
| empty(sK9(sK6(powerset(sK11(X0,X1)))))
| empty(sK11(X0,X1))
| empty(sK6(powerset(sK11(X0,X1))))
| element(sK9(sK7(sK9(sK6(powerset(sK11(X0,X1)))))),cartesian_product2(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_905])]) ).
fof(f4568,plain,
( ! [X0,X1] :
( empty(powerset(sK11(X0,X1)))
| empty(sK7(sK9(sK6(powerset(sK11(X0,X1))))))
| empty(sK9(sK6(powerset(sK11(X0,X1)))))
| empty(sK11(X0,X1))
| empty(sK6(powerset(sK11(X0,X1))))
| element(sK9(sK7(sK9(sK6(powerset(sK11(X0,X1)))))),cartesian_product2(X0,X1)) )
| ~ spl16_110
| ~ spl16_413 ),
inference(resolution,[],[f4470,f800]) ).
fof(f16029,plain,
( spl16_904
| ~ spl16_111
| ~ spl16_413 ),
inference(avatar_split_clause,[],[f4566,f4469,f803,f16027]) ).
fof(f16027,plain,
( spl16_904
<=> ! [X0,X1] :
( empty(powerset(sK10(X0,X1)))
| empty(sK7(sK9(sK6(powerset(sK10(X0,X1))))))
| empty(sK9(sK6(powerset(sK10(X0,X1)))))
| empty(sK10(X0,X1))
| empty(sK6(powerset(sK10(X0,X1))))
| element(sK9(sK7(sK9(sK6(powerset(sK10(X0,X1)))))),cartesian_product2(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_904])]) ).
fof(f4566,plain,
( ! [X0,X1] :
( empty(powerset(sK10(X0,X1)))
| empty(sK7(sK9(sK6(powerset(sK10(X0,X1))))))
| empty(sK9(sK6(powerset(sK10(X0,X1)))))
| empty(sK10(X0,X1))
| empty(sK6(powerset(sK10(X0,X1))))
| element(sK9(sK7(sK9(sK6(powerset(sK10(X0,X1)))))),cartesian_product2(X0,X1)) )
| ~ spl16_111
| ~ spl16_413 ),
inference(resolution,[],[f4470,f804]) ).
fof(f16025,plain,
( spl16_903
| ~ spl16_120
| ~ spl16_413 ),
inference(avatar_split_clause,[],[f4530,f4469,f884,f16023]) ).
fof(f16023,plain,
( spl16_903
<=> ! [X0,X1] :
( empty(powerset(the_InternalRel(X0)))
| empty(sK7(sK9(sK6(powerset(the_InternalRel(X0))))))
| empty(sK9(sK6(powerset(the_InternalRel(X0)))))
| empty(the_InternalRel(X0))
| empty(sK6(powerset(the_InternalRel(X0))))
| element(sK9(sK7(sK9(sK6(powerset(the_InternalRel(X0)))))),the_InternalRel(X1))
| ~ subrelstr(X0,X1)
| ~ rel_str(X0)
| ~ rel_str(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_903])]) ).
fof(f4530,plain,
( ! [X0,X1] :
( empty(powerset(the_InternalRel(X0)))
| empty(sK7(sK9(sK6(powerset(the_InternalRel(X0))))))
| empty(sK9(sK6(powerset(the_InternalRel(X0)))))
| empty(the_InternalRel(X0))
| empty(sK6(powerset(the_InternalRel(X0))))
| element(sK9(sK7(sK9(sK6(powerset(the_InternalRel(X0)))))),the_InternalRel(X1))
| ~ subrelstr(X0,X1)
| ~ rel_str(X0)
| ~ rel_str(X1) )
| ~ spl16_120
| ~ spl16_413 ),
inference(resolution,[],[f4470,f885]) ).
fof(f16021,plain,
( spl16_902
| ~ spl16_119
| ~ spl16_413 ),
inference(avatar_split_clause,[],[f4528,f4469,f880,f16019]) ).
fof(f16019,plain,
( spl16_902
<=> ! [X0,X1] :
( empty(powerset(the_carrier(X0)))
| empty(sK7(sK9(sK6(powerset(the_carrier(X0))))))
| empty(sK9(sK6(powerset(the_carrier(X0)))))
| empty(the_carrier(X0))
| empty(sK6(powerset(the_carrier(X0))))
| element(sK9(sK7(sK9(sK6(powerset(the_carrier(X0)))))),the_carrier(X1))
| ~ subrelstr(X0,X1)
| ~ rel_str(X0)
| ~ rel_str(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_902])]) ).
fof(f4528,plain,
( ! [X0,X1] :
( empty(powerset(the_carrier(X0)))
| empty(sK7(sK9(sK6(powerset(the_carrier(X0))))))
| empty(sK9(sK6(powerset(the_carrier(X0)))))
| empty(the_carrier(X0))
| empty(sK6(powerset(the_carrier(X0))))
| element(sK9(sK7(sK9(sK6(powerset(the_carrier(X0)))))),the_carrier(X1))
| ~ subrelstr(X0,X1)
| ~ rel_str(X0)
| ~ rel_str(X1) )
| ~ spl16_119
| ~ spl16_413 ),
inference(resolution,[],[f4470,f881]) ).
fof(f16017,plain,
( spl16_901
| ~ spl16_110
| ~ spl16_412 ),
inference(avatar_split_clause,[],[f4523,f4465,f799,f16015]) ).
fof(f16015,plain,
( spl16_901
<=> ! [X0,X1] :
( empty(powerset(sK11(X0,X1)))
| empty(sK6(sK9(sK6(powerset(sK11(X0,X1))))))
| empty(sK9(sK6(powerset(sK11(X0,X1)))))
| empty(sK11(X0,X1))
| empty(sK6(powerset(sK11(X0,X1))))
| element(sK9(sK6(sK9(sK6(powerset(sK11(X0,X1)))))),cartesian_product2(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_901])]) ).
fof(f4523,plain,
( ! [X0,X1] :
( empty(powerset(sK11(X0,X1)))
| empty(sK6(sK9(sK6(powerset(sK11(X0,X1))))))
| empty(sK9(sK6(powerset(sK11(X0,X1)))))
| empty(sK11(X0,X1))
| empty(sK6(powerset(sK11(X0,X1))))
| element(sK9(sK6(sK9(sK6(powerset(sK11(X0,X1)))))),cartesian_product2(X0,X1)) )
| ~ spl16_110
| ~ spl16_412 ),
inference(resolution,[],[f4466,f800]) ).
fof(f16013,plain,
( spl16_900
| ~ spl16_111
| ~ spl16_412 ),
inference(avatar_split_clause,[],[f4521,f4465,f803,f16011]) ).
fof(f16011,plain,
( spl16_900
<=> ! [X0,X1] :
( empty(powerset(sK10(X0,X1)))
| empty(sK6(sK9(sK6(powerset(sK10(X0,X1))))))
| empty(sK9(sK6(powerset(sK10(X0,X1)))))
| empty(sK10(X0,X1))
| empty(sK6(powerset(sK10(X0,X1))))
| element(sK9(sK6(sK9(sK6(powerset(sK10(X0,X1)))))),cartesian_product2(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_900])]) ).
fof(f4521,plain,
( ! [X0,X1] :
( empty(powerset(sK10(X0,X1)))
| empty(sK6(sK9(sK6(powerset(sK10(X0,X1))))))
| empty(sK9(sK6(powerset(sK10(X0,X1)))))
| empty(sK10(X0,X1))
| empty(sK6(powerset(sK10(X0,X1))))
| element(sK9(sK6(sK9(sK6(powerset(sK10(X0,X1)))))),cartesian_product2(X0,X1)) )
| ~ spl16_111
| ~ spl16_412 ),
inference(resolution,[],[f4466,f804]) ).
fof(f16009,plain,
( spl16_899
| ~ spl16_120
| ~ spl16_412 ),
inference(avatar_split_clause,[],[f4485,f4465,f884,f16007]) ).
fof(f16007,plain,
( spl16_899
<=> ! [X0,X1] :
( empty(powerset(the_InternalRel(X0)))
| empty(sK6(sK9(sK6(powerset(the_InternalRel(X0))))))
| empty(sK9(sK6(powerset(the_InternalRel(X0)))))
| empty(the_InternalRel(X0))
| empty(sK6(powerset(the_InternalRel(X0))))
| element(sK9(sK6(sK9(sK6(powerset(the_InternalRel(X0)))))),the_InternalRel(X1))
| ~ subrelstr(X0,X1)
| ~ rel_str(X0)
| ~ rel_str(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_899])]) ).
fof(f4485,plain,
( ! [X0,X1] :
( empty(powerset(the_InternalRel(X0)))
| empty(sK6(sK9(sK6(powerset(the_InternalRel(X0))))))
| empty(sK9(sK6(powerset(the_InternalRel(X0)))))
| empty(the_InternalRel(X0))
| empty(sK6(powerset(the_InternalRel(X0))))
| element(sK9(sK6(sK9(sK6(powerset(the_InternalRel(X0)))))),the_InternalRel(X1))
| ~ subrelstr(X0,X1)
| ~ rel_str(X0)
| ~ rel_str(X1) )
| ~ spl16_120
| ~ spl16_412 ),
inference(resolution,[],[f4466,f885]) ).
fof(f16005,plain,
( spl16_898
| ~ spl16_119
| ~ spl16_412 ),
inference(avatar_split_clause,[],[f4483,f4465,f880,f16003]) ).
fof(f16003,plain,
( spl16_898
<=> ! [X0,X1] :
( empty(powerset(the_carrier(X0)))
| empty(sK6(sK9(sK6(powerset(the_carrier(X0))))))
| empty(sK9(sK6(powerset(the_carrier(X0)))))
| empty(the_carrier(X0))
| empty(sK6(powerset(the_carrier(X0))))
| element(sK9(sK6(sK9(sK6(powerset(the_carrier(X0)))))),the_carrier(X1))
| ~ subrelstr(X0,X1)
| ~ rel_str(X0)
| ~ rel_str(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_898])]) ).
fof(f4483,plain,
( ! [X0,X1] :
( empty(powerset(the_carrier(X0)))
| empty(sK6(sK9(sK6(powerset(the_carrier(X0))))))
| empty(sK9(sK6(powerset(the_carrier(X0)))))
| empty(the_carrier(X0))
| empty(sK6(powerset(the_carrier(X0))))
| element(sK9(sK6(sK9(sK6(powerset(the_carrier(X0)))))),the_carrier(X1))
| ~ subrelstr(X0,X1)
| ~ rel_str(X0)
| ~ rel_str(X1) )
| ~ spl16_119
| ~ spl16_412 ),
inference(resolution,[],[f4466,f881]) ).
fof(f16001,plain,
( spl16_897
| ~ spl16_152
| ~ spl16_409 ),
inference(avatar_split_clause,[],[f4443,f4407,f1257,f15999]) ).
fof(f15999,plain,
( spl16_897
<=> ! [X0] :
( empty(powerset(powerset(X0)))
| empty(sK9(sK7(powerset(powerset(X0)))))
| element(sK9(sK9(powerset(sK9(sK9(sK7(powerset(powerset(X0)))))))),X0)
| empty(sK7(powerset(powerset(X0))))
| empty(sK9(sK9(sK7(powerset(powerset(X0))))))
| empty(sK9(powerset(sK9(sK9(sK7(powerset(powerset(X0)))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_897])]) ).
fof(f4443,plain,
( ! [X0] :
( empty(powerset(powerset(X0)))
| empty(sK9(sK7(powerset(powerset(X0)))))
| element(sK9(sK9(powerset(sK9(sK9(sK7(powerset(powerset(X0)))))))),X0)
| empty(sK7(powerset(powerset(X0))))
| empty(sK9(sK9(sK7(powerset(powerset(X0))))))
| empty(sK9(powerset(sK9(sK9(sK7(powerset(powerset(X0)))))))) )
| ~ spl16_152
| ~ spl16_409 ),
inference(resolution,[],[f4408,f1258]) ).
fof(f15997,plain,
( spl16_896
| ~ spl16_152
| ~ spl16_408 ),
inference(avatar_split_clause,[],[f4427,f4403,f1257,f15995]) ).
fof(f15995,plain,
( spl16_896
<=> ! [X0] :
( empty(powerset(powerset(X0)))
| empty(sK9(sK6(powerset(powerset(X0)))))
| element(sK9(sK9(powerset(sK9(sK9(sK6(powerset(powerset(X0)))))))),X0)
| empty(sK6(powerset(powerset(X0))))
| empty(sK9(sK9(sK6(powerset(powerset(X0))))))
| empty(sK9(powerset(sK9(sK9(sK6(powerset(powerset(X0)))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_896])]) ).
fof(f4427,plain,
( ! [X0] :
( empty(powerset(powerset(X0)))
| empty(sK9(sK6(powerset(powerset(X0)))))
| element(sK9(sK9(powerset(sK9(sK9(sK6(powerset(powerset(X0)))))))),X0)
| empty(sK6(powerset(powerset(X0))))
| empty(sK9(sK9(sK6(powerset(powerset(X0))))))
| empty(sK9(powerset(sK9(sK9(sK6(powerset(powerset(X0)))))))) )
| ~ spl16_152
| ~ spl16_408 ),
inference(resolution,[],[f4404,f1258]) ).
fof(f15988,plain,
( ~ spl16_641
| ~ spl16_58
| spl16_884 ),
inference(avatar_split_clause,[],[f15950,f15900,f476,f9159]) ).
fof(f15950,plain,
( ~ rel_str(sK8(sK8(sK1)))
| ~ spl16_58
| spl16_884 ),
inference(resolution,[],[f15902,f477]) ).
fof(f15902,plain,
( ~ rel_str(sK8(sK8(sK8(sK1))))
| spl16_884 ),
inference(avatar_component_clause,[],[f15900]) ).
fof(f15987,plain,
( spl16_895
| ~ spl16_152
| ~ spl16_390 ),
inference(avatar_split_clause,[],[f4261,f4167,f1257,f15985]) ).
fof(f15985,plain,
( spl16_895
<=> ! [X0] :
( empty(sK9(powerset(powerset(X0))))
| element(sK9(sK9(powerset(sK9(sK9(powerset(sK9(powerset(powerset(X0))))))))),X0)
| empty(sK9(powerset(sK9(powerset(powerset(X0))))))
| empty(sK9(sK9(powerset(sK9(powerset(powerset(X0)))))))
| empty(sK9(powerset(sK9(sK9(powerset(sK9(powerset(powerset(X0))))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_895])]) ).
fof(f4261,plain,
( ! [X0] :
( empty(sK9(powerset(powerset(X0))))
| element(sK9(sK9(powerset(sK9(sK9(powerset(sK9(powerset(powerset(X0))))))))),X0)
| empty(sK9(powerset(sK9(powerset(powerset(X0))))))
| empty(sK9(sK9(powerset(sK9(powerset(powerset(X0)))))))
| empty(sK9(powerset(sK9(sK9(powerset(sK9(powerset(powerset(X0))))))))) )
| ~ spl16_152
| ~ spl16_390 ),
inference(resolution,[],[f4168,f1258]) ).
fof(f15983,plain,
( spl16_894
| ~ spl16_173
| ~ spl16_362 ),
inference(avatar_split_clause,[],[f3830,f3670,f1448,f15981]) ).
fof(f15981,plain,
( spl16_894
<=> ! [X0] :
( empty(sK9(sK9(powerset(powerset(sK9(sK9(powerset(powerset(X0)))))))))
| empty(sK9(sK9(powerset(powerset(X0)))))
| empty(sK9(powerset(powerset(sK9(sK9(powerset(powerset(X0))))))))
| element(sK9(sK9(sK9(powerset(powerset(sK9(sK9(powerset(powerset(X0))))))))),X0)
| empty(sK9(powerset(powerset(X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_894])]) ).
fof(f3830,plain,
( ! [X0] :
( empty(sK9(sK9(powerset(powerset(sK9(sK9(powerset(powerset(X0)))))))))
| empty(sK9(sK9(powerset(powerset(X0)))))
| empty(sK9(powerset(powerset(sK9(sK9(powerset(powerset(X0))))))))
| element(sK9(sK9(sK9(powerset(powerset(sK9(sK9(powerset(powerset(X0))))))))),X0)
| empty(sK9(powerset(powerset(X0)))) )
| ~ spl16_173
| ~ spl16_362 ),
inference(resolution,[],[f3671,f1449]) ).
fof(f15939,plain,
( spl16_893
| ~ spl16_65
| ~ spl16_451 ),
inference(avatar_split_clause,[],[f5365,f5221,f508,f15937]) ).
fof(f15937,plain,
( spl16_893
<=> ! [X0] :
( empty(sK7(sK9(sK9(powerset(powerset(powerset(X0)))))))
| empty(sK9(sK9(powerset(powerset(powerset(X0))))))
| element(sK9(sK9(sK7(sK9(sK9(powerset(powerset(powerset(X0)))))))),X0)
| empty(sK9(powerset(powerset(powerset(X0)))))
| empty(sK9(sK7(sK9(sK9(powerset(powerset(powerset(X0)))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_893])]) ).
fof(f5365,plain,
( ! [X0] :
( empty(sK7(sK9(sK9(powerset(powerset(powerset(X0)))))))
| empty(sK9(sK9(powerset(powerset(powerset(X0))))))
| element(sK9(sK9(sK7(sK9(sK9(powerset(powerset(powerset(X0)))))))),X0)
| empty(sK9(powerset(powerset(powerset(X0)))))
| empty(sK9(sK7(sK9(sK9(powerset(powerset(powerset(X0)))))))) )
| ~ spl16_65
| ~ spl16_451 ),
inference(resolution,[],[f5222,f509]) ).
fof(f15935,plain,
( spl16_892
| ~ spl16_65
| ~ spl16_450 ),
inference(avatar_split_clause,[],[f5340,f5217,f508,f15933]) ).
fof(f15933,plain,
( spl16_892
<=> ! [X0] :
( empty(sK6(sK9(sK9(powerset(powerset(powerset(X0)))))))
| empty(sK9(sK9(powerset(powerset(powerset(X0))))))
| element(sK9(sK9(sK6(sK9(sK9(powerset(powerset(powerset(X0)))))))),X0)
| empty(sK9(powerset(powerset(powerset(X0)))))
| empty(sK9(sK6(sK9(sK9(powerset(powerset(powerset(X0)))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_892])]) ).
fof(f5340,plain,
( ! [X0] :
( empty(sK6(sK9(sK9(powerset(powerset(powerset(X0)))))))
| empty(sK9(sK9(powerset(powerset(powerset(X0))))))
| element(sK9(sK9(sK6(sK9(sK9(powerset(powerset(powerset(X0)))))))),X0)
| empty(sK9(powerset(powerset(powerset(X0)))))
| empty(sK9(sK6(sK9(sK9(powerset(powerset(powerset(X0)))))))) )
| ~ spl16_65
| ~ spl16_450 ),
inference(resolution,[],[f5218,f509]) ).
fof(f15931,plain,
( spl16_891
| ~ spl16_72
| ~ spl16_427 ),
inference(avatar_split_clause,[],[f4927,f4893,f549,f15929]) ).
fof(f15929,plain,
( spl16_891
<=> ! [X0] :
( empty(sK9(sK9(powerset(powerset(sK9(powerset(X0)))))))
| empty(sK9(powerset(sK9(sK9(powerset(powerset(sK9(powerset(X0)))))))))
| empty(sK9(powerset(X0)))
| empty(sK9(powerset(powerset(sK9(powerset(X0))))))
| element(sK9(sK9(powerset(sK9(sK9(powerset(powerset(sK9(powerset(X0))))))))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_891])]) ).
fof(f4927,plain,
( ! [X0] :
( empty(sK9(sK9(powerset(powerset(sK9(powerset(X0)))))))
| empty(sK9(powerset(sK9(sK9(powerset(powerset(sK9(powerset(X0)))))))))
| empty(sK9(powerset(X0)))
| empty(sK9(powerset(powerset(sK9(powerset(X0))))))
| element(sK9(sK9(powerset(sK9(sK9(powerset(powerset(sK9(powerset(X0))))))))),X0) )
| ~ spl16_72
| ~ spl16_427 ),
inference(resolution,[],[f4894,f550]) ).
fof(f15927,plain,
( spl16_890
| ~ spl16_110
| ~ spl16_418 ),
inference(avatar_split_clause,[],[f4760,f4669,f799,f15925]) ).
fof(f15925,plain,
( spl16_890
<=> ! [X0,X1] :
( empty(sK7(sK9(sK9(powerset(powerset(sK11(X0,X1)))))))
| empty(sK9(sK9(powerset(powerset(sK11(X0,X1))))))
| empty(sK11(X0,X1))
| empty(sK9(powerset(powerset(sK11(X0,X1)))))
| element(sK9(sK7(sK9(sK9(powerset(powerset(sK11(X0,X1))))))),cartesian_product2(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_890])]) ).
fof(f4760,plain,
( ! [X0,X1] :
( empty(sK7(sK9(sK9(powerset(powerset(sK11(X0,X1)))))))
| empty(sK9(sK9(powerset(powerset(sK11(X0,X1))))))
| empty(sK11(X0,X1))
| empty(sK9(powerset(powerset(sK11(X0,X1)))))
| element(sK9(sK7(sK9(sK9(powerset(powerset(sK11(X0,X1))))))),cartesian_product2(X0,X1)) )
| ~ spl16_110
| ~ spl16_418 ),
inference(resolution,[],[f4670,f800]) ).
fof(f15923,plain,
( spl16_889
| ~ spl16_111
| ~ spl16_418 ),
inference(avatar_split_clause,[],[f4758,f4669,f803,f15921]) ).
fof(f15921,plain,
( spl16_889
<=> ! [X0,X1] :
( empty(sK7(sK9(sK9(powerset(powerset(sK10(X0,X1)))))))
| empty(sK9(sK9(powerset(powerset(sK10(X0,X1))))))
| empty(sK10(X0,X1))
| empty(sK9(powerset(powerset(sK10(X0,X1)))))
| element(sK9(sK7(sK9(sK9(powerset(powerset(sK10(X0,X1))))))),cartesian_product2(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_889])]) ).
fof(f4758,plain,
( ! [X0,X1] :
( empty(sK7(sK9(sK9(powerset(powerset(sK10(X0,X1)))))))
| empty(sK9(sK9(powerset(powerset(sK10(X0,X1))))))
| empty(sK10(X0,X1))
| empty(sK9(powerset(powerset(sK10(X0,X1)))))
| element(sK9(sK7(sK9(sK9(powerset(powerset(sK10(X0,X1))))))),cartesian_product2(X0,X1)) )
| ~ spl16_111
| ~ spl16_418 ),
inference(resolution,[],[f4670,f804]) ).
fof(f15919,plain,
( spl16_888
| ~ spl16_110
| ~ spl16_417 ),
inference(avatar_split_clause,[],[f4715,f4665,f799,f15917]) ).
fof(f15917,plain,
( spl16_888
<=> ! [X0,X1] :
( empty(sK6(sK9(sK9(powerset(powerset(sK11(X0,X1)))))))
| empty(sK9(sK9(powerset(powerset(sK11(X0,X1))))))
| empty(sK11(X0,X1))
| empty(sK9(powerset(powerset(sK11(X0,X1)))))
| element(sK9(sK6(sK9(sK9(powerset(powerset(sK11(X0,X1))))))),cartesian_product2(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_888])]) ).
fof(f4715,plain,
( ! [X0,X1] :
( empty(sK6(sK9(sK9(powerset(powerset(sK11(X0,X1)))))))
| empty(sK9(sK9(powerset(powerset(sK11(X0,X1))))))
| empty(sK11(X0,X1))
| empty(sK9(powerset(powerset(sK11(X0,X1)))))
| element(sK9(sK6(sK9(sK9(powerset(powerset(sK11(X0,X1))))))),cartesian_product2(X0,X1)) )
| ~ spl16_110
| ~ spl16_417 ),
inference(resolution,[],[f4666,f800]) ).
fof(f15915,plain,
( spl16_887
| ~ spl16_111
| ~ spl16_417 ),
inference(avatar_split_clause,[],[f4713,f4665,f803,f15913]) ).
fof(f15913,plain,
( spl16_887
<=> ! [X0,X1] :
( empty(sK6(sK9(sK9(powerset(powerset(sK10(X0,X1)))))))
| empty(sK9(sK9(powerset(powerset(sK10(X0,X1))))))
| empty(sK10(X0,X1))
| empty(sK9(powerset(powerset(sK10(X0,X1)))))
| element(sK9(sK6(sK9(sK9(powerset(powerset(sK10(X0,X1))))))),cartesian_product2(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_887])]) ).
fof(f4713,plain,
( ! [X0,X1] :
( empty(sK6(sK9(sK9(powerset(powerset(sK10(X0,X1)))))))
| empty(sK9(sK9(powerset(powerset(sK10(X0,X1))))))
| empty(sK10(X0,X1))
| empty(sK9(powerset(powerset(sK10(X0,X1)))))
| element(sK9(sK6(sK9(sK9(powerset(powerset(sK10(X0,X1))))))),cartesian_product2(X0,X1)) )
| ~ spl16_111
| ~ spl16_417 ),
inference(resolution,[],[f4666,f804]) ).
fof(f15911,plain,
( spl16_886
| ~ spl16_150
| ~ spl16_405 ),
inference(avatar_split_clause,[],[f4359,f4343,f1218,f15909]) ).
fof(f15909,plain,
( spl16_886
<=> ! [X0] :
( empty(sK9(sK9(powerset(powerset(powerset(X0))))))
| element(sK9(sK7(sK9(sK9(sK9(powerset(powerset(powerset(X0)))))))),X0)
| empty(sK9(powerset(powerset(powerset(X0)))))
| empty(sK7(sK9(sK9(sK9(powerset(powerset(powerset(X0))))))))
| empty(sK9(sK9(sK9(powerset(powerset(powerset(X0))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_886])]) ).
fof(f4359,plain,
( ! [X0] :
( empty(sK9(sK9(powerset(powerset(powerset(X0))))))
| element(sK9(sK7(sK9(sK9(sK9(powerset(powerset(powerset(X0)))))))),X0)
| empty(sK9(powerset(powerset(powerset(X0)))))
| empty(sK7(sK9(sK9(sK9(powerset(powerset(powerset(X0))))))))
| empty(sK9(sK9(sK9(powerset(powerset(powerset(X0))))))) )
| ~ spl16_150
| ~ spl16_405 ),
inference(resolution,[],[f4344,f1219]) ).
fof(f15907,plain,
( ~ spl16_884
| spl16_885
| ~ spl16_43
| ~ spl16_881 ),
inference(avatar_split_clause,[],[f15761,f15704,f370,f15904,f15900]) ).
fof(f15761,plain,
( relation_of2_as_subset(the_InternalRel(sK8(sK8(sK8(sK1)))),sK14,sK14)
| ~ rel_str(sK8(sK8(sK8(sK1))))
| ~ spl16_43
| ~ spl16_881 ),
inference(superposition,[],[f371,f15706]) ).
fof(f15898,plain,
( spl16_883
| ~ spl16_149
| ~ spl16_405 ),
inference(avatar_split_clause,[],[f4355,f4343,f1214,f15896]) ).
fof(f15896,plain,
( spl16_883
<=> ! [X0] :
( empty(sK9(sK9(powerset(powerset(powerset(X0))))))
| element(sK9(sK6(sK9(sK9(sK9(powerset(powerset(powerset(X0)))))))),X0)
| empty(sK9(powerset(powerset(powerset(X0)))))
| empty(sK6(sK9(sK9(sK9(powerset(powerset(powerset(X0))))))))
| empty(sK9(sK9(sK9(powerset(powerset(powerset(X0))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_883])]) ).
fof(f4355,plain,
( ! [X0] :
( empty(sK9(sK9(powerset(powerset(powerset(X0))))))
| element(sK9(sK6(sK9(sK9(sK9(powerset(powerset(powerset(X0)))))))),X0)
| empty(sK9(powerset(powerset(powerset(X0)))))
| empty(sK6(sK9(sK9(sK9(powerset(powerset(powerset(X0))))))))
| empty(sK9(sK9(sK9(powerset(powerset(powerset(X0))))))) )
| ~ spl16_149
| ~ spl16_405 ),
inference(resolution,[],[f4344,f1215]) ).
fof(f15894,plain,
( spl16_882
| ~ spl16_173
| ~ spl16_349 ),
inference(avatar_split_clause,[],[f3613,f3578,f1448,f15892]) ).
fof(f15892,plain,
( spl16_882
<=> ! [X0] :
( empty(sK9(powerset(sK9(sK9(powerset(powerset(X0)))))))
| empty(sK9(sK9(powerset(powerset(X0)))))
| empty(sK9(powerset(sK9(powerset(sK9(sK9(powerset(powerset(X0)))))))))
| element(sK9(sK9(powerset(sK9(powerset(sK9(sK9(powerset(powerset(X0))))))))),X0)
| empty(sK9(powerset(powerset(X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_882])]) ).
fof(f3613,plain,
( ! [X0] :
( empty(sK9(powerset(sK9(sK9(powerset(powerset(X0)))))))
| empty(sK9(sK9(powerset(powerset(X0)))))
| empty(sK9(powerset(sK9(powerset(sK9(sK9(powerset(powerset(X0)))))))))
| element(sK9(sK9(powerset(sK9(powerset(sK9(sK9(powerset(powerset(X0))))))))),X0)
| empty(sK9(powerset(powerset(X0)))) )
| ~ spl16_173
| ~ spl16_349 ),
inference(resolution,[],[f3579,f1449]) ).
fof(f15707,plain,
( spl16_881
| ~ spl16_641
| ~ spl16_12
| ~ spl16_472
| ~ spl16_577 ),
inference(avatar_split_clause,[],[f7837,f7642,f5620,f213,f9159,f15704]) ).
fof(f7837,plain,
( ~ empty(sK14)
| ~ rel_str(sK8(sK8(sK1)))
| sK14 = the_carrier(sK8(sK8(sK8(sK1))))
| ~ spl16_472
| ~ spl16_577 ),
inference(superposition,[],[f5621,f7644]) ).
fof(f15702,plain,
( spl16_880
| ~ spl16_65
| ~ spl16_449 ),
inference(avatar_split_clause,[],[f5315,f5213,f508,f15700]) ).
fof(f15700,plain,
( spl16_880
<=> ! [X0] :
( empty(powerset(powerset(X0)))
| empty(sK7(sK9(sK7(powerset(powerset(X0))))))
| empty(sK9(sK7(powerset(powerset(X0)))))
| element(sK9(sK9(sK7(sK9(sK7(powerset(powerset(X0))))))),X0)
| empty(sK7(powerset(powerset(X0))))
| empty(sK9(sK7(sK9(sK7(powerset(powerset(X0))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_880])]) ).
fof(f5315,plain,
( ! [X0] :
( empty(powerset(powerset(X0)))
| empty(sK7(sK9(sK7(powerset(powerset(X0))))))
| empty(sK9(sK7(powerset(powerset(X0)))))
| element(sK9(sK9(sK7(sK9(sK7(powerset(powerset(X0))))))),X0)
| empty(sK7(powerset(powerset(X0))))
| empty(sK9(sK7(sK9(sK7(powerset(powerset(X0))))))) )
| ~ spl16_65
| ~ spl16_449 ),
inference(resolution,[],[f5214,f509]) ).
fof(f15698,plain,
( spl16_879
| ~ spl16_65
| ~ spl16_448 ),
inference(avatar_split_clause,[],[f5290,f5209,f508,f15696]) ).
fof(f15696,plain,
( spl16_879
<=> ! [X0] :
( empty(powerset(powerset(X0)))
| empty(sK6(sK9(sK7(powerset(powerset(X0))))))
| empty(sK9(sK7(powerset(powerset(X0)))))
| element(sK9(sK9(sK6(sK9(sK7(powerset(powerset(X0))))))),X0)
| empty(sK7(powerset(powerset(X0))))
| empty(sK9(sK6(sK9(sK7(powerset(powerset(X0))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_879])]) ).
fof(f5290,plain,
( ! [X0] :
( empty(powerset(powerset(X0)))
| empty(sK6(sK9(sK7(powerset(powerset(X0))))))
| empty(sK9(sK7(powerset(powerset(X0)))))
| element(sK9(sK9(sK6(sK9(sK7(powerset(powerset(X0))))))),X0)
| empty(sK7(powerset(powerset(X0))))
| empty(sK9(sK6(sK9(sK7(powerset(powerset(X0))))))) )
| ~ spl16_65
| ~ spl16_448 ),
inference(resolution,[],[f5210,f509]) ).
fof(f15694,plain,
( spl16_878
| ~ spl16_65
| ~ spl16_447 ),
inference(avatar_split_clause,[],[f5265,f5205,f508,f15692]) ).
fof(f15692,plain,
( spl16_878
<=> ! [X0] :
( empty(powerset(powerset(X0)))
| empty(sK7(sK9(sK6(powerset(powerset(X0))))))
| empty(sK9(sK6(powerset(powerset(X0)))))
| element(sK9(sK9(sK7(sK9(sK6(powerset(powerset(X0))))))),X0)
| empty(sK6(powerset(powerset(X0))))
| empty(sK9(sK7(sK9(sK6(powerset(powerset(X0))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_878])]) ).
fof(f5265,plain,
( ! [X0] :
( empty(powerset(powerset(X0)))
| empty(sK7(sK9(sK6(powerset(powerset(X0))))))
| empty(sK9(sK6(powerset(powerset(X0)))))
| element(sK9(sK9(sK7(sK9(sK6(powerset(powerset(X0))))))),X0)
| empty(sK6(powerset(powerset(X0))))
| empty(sK9(sK7(sK9(sK6(powerset(powerset(X0))))))) )
| ~ spl16_65
| ~ spl16_447 ),
inference(resolution,[],[f5206,f509]) ).
fof(f15690,plain,
( spl16_877
| ~ spl16_65
| ~ spl16_446 ),
inference(avatar_split_clause,[],[f5240,f5201,f508,f15688]) ).
fof(f15688,plain,
( spl16_877
<=> ! [X0] :
( empty(powerset(powerset(X0)))
| empty(sK6(sK9(sK6(powerset(powerset(X0))))))
| empty(sK9(sK6(powerset(powerset(X0)))))
| element(sK9(sK9(sK6(sK9(sK6(powerset(powerset(X0))))))),X0)
| empty(sK6(powerset(powerset(X0))))
| empty(sK9(sK6(sK9(sK6(powerset(powerset(X0))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_877])]) ).
fof(f5240,plain,
( ! [X0] :
( empty(powerset(powerset(X0)))
| empty(sK6(sK9(sK6(powerset(powerset(X0))))))
| empty(sK9(sK6(powerset(powerset(X0)))))
| element(sK9(sK9(sK6(sK9(sK6(powerset(powerset(X0))))))),X0)
| empty(sK6(powerset(powerset(X0))))
| empty(sK9(sK6(sK9(sK6(powerset(powerset(X0))))))) )
| ~ spl16_65
| ~ spl16_446 ),
inference(resolution,[],[f5202,f509]) ).
fof(f15686,plain,
( spl16_876
| ~ spl16_72
| ~ spl16_415 ),
inference(avatar_split_clause,[],[f4624,f4477,f549,f15684]) ).
fof(f15684,plain,
( spl16_876
<=> ! [X0] :
( empty(powerset(sK9(powerset(X0))))
| empty(sK7(sK9(sK7(powerset(sK9(powerset(X0)))))))
| empty(sK9(sK7(powerset(sK9(powerset(X0))))))
| empty(sK9(powerset(X0)))
| empty(sK7(powerset(sK9(powerset(X0)))))
| element(sK9(sK7(sK9(sK7(powerset(sK9(powerset(X0))))))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_876])]) ).
fof(f4624,plain,
( ! [X0] :
( empty(powerset(sK9(powerset(X0))))
| empty(sK7(sK9(sK7(powerset(sK9(powerset(X0)))))))
| empty(sK9(sK7(powerset(sK9(powerset(X0))))))
| empty(sK9(powerset(X0)))
| empty(sK7(powerset(sK9(powerset(X0)))))
| element(sK9(sK7(sK9(sK7(powerset(sK9(powerset(X0))))))),X0) )
| ~ spl16_72
| ~ spl16_415 ),
inference(resolution,[],[f4478,f550]) ).
fof(f15682,plain,
( spl16_875
| ~ spl16_72
| ~ spl16_414 ),
inference(avatar_split_clause,[],[f4579,f4473,f549,f15680]) ).
fof(f15680,plain,
( spl16_875
<=> ! [X0] :
( empty(powerset(sK9(powerset(X0))))
| empty(sK6(sK9(sK7(powerset(sK9(powerset(X0)))))))
| empty(sK9(sK7(powerset(sK9(powerset(X0))))))
| empty(sK9(powerset(X0)))
| empty(sK7(powerset(sK9(powerset(X0)))))
| element(sK9(sK6(sK9(sK7(powerset(sK9(powerset(X0))))))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_875])]) ).
fof(f4579,plain,
( ! [X0] :
( empty(powerset(sK9(powerset(X0))))
| empty(sK6(sK9(sK7(powerset(sK9(powerset(X0)))))))
| empty(sK9(sK7(powerset(sK9(powerset(X0))))))
| empty(sK9(powerset(X0)))
| empty(sK7(powerset(sK9(powerset(X0)))))
| element(sK9(sK6(sK9(sK7(powerset(sK9(powerset(X0))))))),X0) )
| ~ spl16_72
| ~ spl16_414 ),
inference(resolution,[],[f4474,f550]) ).
fof(f15678,plain,
( spl16_874
| ~ spl16_72
| ~ spl16_413 ),
inference(avatar_split_clause,[],[f4534,f4469,f549,f15676]) ).
fof(f15676,plain,
( spl16_874
<=> ! [X0] :
( empty(powerset(sK9(powerset(X0))))
| empty(sK7(sK9(sK6(powerset(sK9(powerset(X0)))))))
| empty(sK9(sK6(powerset(sK9(powerset(X0))))))
| empty(sK9(powerset(X0)))
| empty(sK6(powerset(sK9(powerset(X0)))))
| element(sK9(sK7(sK9(sK6(powerset(sK9(powerset(X0))))))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_874])]) ).
fof(f4534,plain,
( ! [X0] :
( empty(powerset(sK9(powerset(X0))))
| empty(sK7(sK9(sK6(powerset(sK9(powerset(X0)))))))
| empty(sK9(sK6(powerset(sK9(powerset(X0))))))
| empty(sK9(powerset(X0)))
| empty(sK6(powerset(sK9(powerset(X0)))))
| element(sK9(sK7(sK9(sK6(powerset(sK9(powerset(X0))))))),X0) )
| ~ spl16_72
| ~ spl16_413 ),
inference(resolution,[],[f4470,f550]) ).
fof(f15674,plain,
( spl16_873
| ~ spl16_72
| ~ spl16_412 ),
inference(avatar_split_clause,[],[f4489,f4465,f549,f15672]) ).
fof(f15672,plain,
( spl16_873
<=> ! [X0] :
( empty(powerset(sK9(powerset(X0))))
| empty(sK6(sK9(sK6(powerset(sK9(powerset(X0)))))))
| empty(sK9(sK6(powerset(sK9(powerset(X0))))))
| empty(sK9(powerset(X0)))
| empty(sK6(powerset(sK9(powerset(X0)))))
| element(sK9(sK6(sK9(sK6(powerset(sK9(powerset(X0))))))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_873])]) ).
fof(f4489,plain,
( ! [X0] :
( empty(powerset(sK9(powerset(X0))))
| empty(sK6(sK9(sK6(powerset(sK9(powerset(X0)))))))
| empty(sK9(sK6(powerset(sK9(powerset(X0))))))
| empty(sK9(powerset(X0)))
| empty(sK6(powerset(sK9(powerset(X0)))))
| element(sK9(sK6(sK9(sK6(powerset(sK9(powerset(X0))))))),X0) )
| ~ spl16_72
| ~ spl16_412 ),
inference(resolution,[],[f4466,f550]) ).
fof(f15670,plain,
( spl16_872
| ~ spl16_150
| ~ spl16_409 ),
inference(avatar_split_clause,[],[f4439,f4407,f1218,f15668]) ).
fof(f15668,plain,
( spl16_872
<=> ! [X0] :
( empty(powerset(powerset(X0)))
| empty(sK9(sK7(powerset(powerset(X0)))))
| element(sK9(sK7(sK9(sK9(sK7(powerset(powerset(X0))))))),X0)
| empty(sK7(powerset(powerset(X0))))
| empty(sK7(sK9(sK9(sK7(powerset(powerset(X0)))))))
| empty(sK9(sK9(sK7(powerset(powerset(X0)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_872])]) ).
fof(f4439,plain,
( ! [X0] :
( empty(powerset(powerset(X0)))
| empty(sK9(sK7(powerset(powerset(X0)))))
| element(sK9(sK7(sK9(sK9(sK7(powerset(powerset(X0))))))),X0)
| empty(sK7(powerset(powerset(X0))))
| empty(sK7(sK9(sK9(sK7(powerset(powerset(X0)))))))
| empty(sK9(sK9(sK7(powerset(powerset(X0)))))) )
| ~ spl16_150
| ~ spl16_409 ),
inference(resolution,[],[f4408,f1219]) ).
fof(f15666,plain,
( spl16_871
| ~ spl16_149
| ~ spl16_409 ),
inference(avatar_split_clause,[],[f4435,f4407,f1214,f15664]) ).
fof(f15664,plain,
( spl16_871
<=> ! [X0] :
( empty(powerset(powerset(X0)))
| empty(sK9(sK7(powerset(powerset(X0)))))
| element(sK9(sK6(sK9(sK9(sK7(powerset(powerset(X0))))))),X0)
| empty(sK7(powerset(powerset(X0))))
| empty(sK6(sK9(sK9(sK7(powerset(powerset(X0)))))))
| empty(sK9(sK9(sK7(powerset(powerset(X0)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_871])]) ).
fof(f4435,plain,
( ! [X0] :
( empty(powerset(powerset(X0)))
| empty(sK9(sK7(powerset(powerset(X0)))))
| element(sK9(sK6(sK9(sK9(sK7(powerset(powerset(X0))))))),X0)
| empty(sK7(powerset(powerset(X0))))
| empty(sK6(sK9(sK9(sK7(powerset(powerset(X0)))))))
| empty(sK9(sK9(sK7(powerset(powerset(X0)))))) )
| ~ spl16_149
| ~ spl16_409 ),
inference(resolution,[],[f4408,f1215]) ).
fof(f15657,plain,
( spl16_870
| ~ spl16_150
| ~ spl16_408 ),
inference(avatar_split_clause,[],[f4423,f4403,f1218,f15655]) ).
fof(f15655,plain,
( spl16_870
<=> ! [X0] :
( empty(powerset(powerset(X0)))
| empty(sK9(sK6(powerset(powerset(X0)))))
| element(sK9(sK7(sK9(sK9(sK6(powerset(powerset(X0))))))),X0)
| empty(sK6(powerset(powerset(X0))))
| empty(sK7(sK9(sK9(sK6(powerset(powerset(X0)))))))
| empty(sK9(sK9(sK6(powerset(powerset(X0)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_870])]) ).
fof(f4423,plain,
( ! [X0] :
( empty(powerset(powerset(X0)))
| empty(sK9(sK6(powerset(powerset(X0)))))
| element(sK9(sK7(sK9(sK9(sK6(powerset(powerset(X0))))))),X0)
| empty(sK6(powerset(powerset(X0))))
| empty(sK7(sK9(sK9(sK6(powerset(powerset(X0)))))))
| empty(sK9(sK9(sK6(powerset(powerset(X0)))))) )
| ~ spl16_150
| ~ spl16_408 ),
inference(resolution,[],[f4404,f1219]) ).
fof(f15653,plain,
( spl16_869
| ~ spl16_149
| ~ spl16_408 ),
inference(avatar_split_clause,[],[f4419,f4403,f1214,f15651]) ).
fof(f15651,plain,
( spl16_869
<=> ! [X0] :
( empty(powerset(powerset(X0)))
| empty(sK9(sK6(powerset(powerset(X0)))))
| element(sK9(sK6(sK9(sK9(sK6(powerset(powerset(X0))))))),X0)
| empty(sK6(powerset(powerset(X0))))
| empty(sK6(sK9(sK9(sK6(powerset(powerset(X0)))))))
| empty(sK9(sK9(sK6(powerset(powerset(X0)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_869])]) ).
fof(f4419,plain,
( ! [X0] :
( empty(powerset(powerset(X0)))
| empty(sK9(sK6(powerset(powerset(X0)))))
| element(sK9(sK6(sK9(sK9(sK6(powerset(powerset(X0))))))),X0)
| empty(sK6(powerset(powerset(X0))))
| empty(sK6(sK9(sK9(sK6(powerset(powerset(X0)))))))
| empty(sK9(sK9(sK6(powerset(powerset(X0)))))) )
| ~ spl16_149
| ~ spl16_408 ),
inference(resolution,[],[f4404,f1215]) ).
fof(f15649,plain,
( spl16_868
| ~ spl16_150
| ~ spl16_390 ),
inference(avatar_split_clause,[],[f4257,f4167,f1218,f15647]) ).
fof(f15647,plain,
( spl16_868
<=> ! [X0] :
( empty(sK9(powerset(powerset(X0))))
| element(sK9(sK7(sK9(sK9(powerset(sK9(powerset(powerset(X0)))))))),X0)
| empty(sK9(powerset(sK9(powerset(powerset(X0))))))
| empty(sK7(sK9(sK9(powerset(sK9(powerset(powerset(X0))))))))
| empty(sK9(sK9(powerset(sK9(powerset(powerset(X0))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_868])]) ).
fof(f4257,plain,
( ! [X0] :
( empty(sK9(powerset(powerset(X0))))
| element(sK9(sK7(sK9(sK9(powerset(sK9(powerset(powerset(X0)))))))),X0)
| empty(sK9(powerset(sK9(powerset(powerset(X0))))))
| empty(sK7(sK9(sK9(powerset(sK9(powerset(powerset(X0))))))))
| empty(sK9(sK9(powerset(sK9(powerset(powerset(X0))))))) )
| ~ spl16_150
| ~ spl16_390 ),
inference(resolution,[],[f4168,f1219]) ).
fof(f15645,plain,
( spl16_867
| ~ spl16_149
| ~ spl16_390 ),
inference(avatar_split_clause,[],[f4253,f4167,f1214,f15643]) ).
fof(f15643,plain,
( spl16_867
<=> ! [X0] :
( empty(sK9(powerset(powerset(X0))))
| element(sK9(sK6(sK9(sK9(powerset(sK9(powerset(powerset(X0)))))))),X0)
| empty(sK9(powerset(sK9(powerset(powerset(X0))))))
| empty(sK6(sK9(sK9(powerset(sK9(powerset(powerset(X0))))))))
| empty(sK9(sK9(powerset(sK9(powerset(powerset(X0))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_867])]) ).
fof(f4253,plain,
( ! [X0] :
( empty(sK9(powerset(powerset(X0))))
| element(sK9(sK6(sK9(sK9(powerset(sK9(powerset(powerset(X0)))))))),X0)
| empty(sK9(powerset(sK9(powerset(powerset(X0))))))
| empty(sK6(sK9(sK9(powerset(sK9(powerset(powerset(X0))))))))
| empty(sK9(sK9(powerset(sK9(powerset(powerset(X0))))))) )
| ~ spl16_149
| ~ spl16_390 ),
inference(resolution,[],[f4168,f1215]) ).
fof(f15641,plain,
( spl16_866
| ~ spl16_152
| ~ spl16_388 ),
inference(avatar_split_clause,[],[f4245,f4159,f1257,f15639]) ).
fof(f15639,plain,
( spl16_866
<=> ! [X0] :
( empty(sK7(powerset(X0)))
| empty(powerset(X0))
| element(sK9(sK9(powerset(sK9(sK9(powerset(sK7(powerset(X0)))))))),X0)
| empty(sK9(powerset(sK7(powerset(X0)))))
| empty(sK9(sK9(powerset(sK7(powerset(X0))))))
| empty(sK9(powerset(sK9(sK9(powerset(sK7(powerset(X0)))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_866])]) ).
fof(f4245,plain,
( ! [X0] :
( empty(sK7(powerset(X0)))
| empty(powerset(X0))
| element(sK9(sK9(powerset(sK9(sK9(powerset(sK7(powerset(X0)))))))),X0)
| empty(sK9(powerset(sK7(powerset(X0)))))
| empty(sK9(sK9(powerset(sK7(powerset(X0))))))
| empty(sK9(powerset(sK9(sK9(powerset(sK7(powerset(X0)))))))) )
| ~ spl16_152
| ~ spl16_388 ),
inference(resolution,[],[f4160,f1258]) ).
fof(f15637,plain,
( spl16_865
| ~ spl16_152
| ~ spl16_387 ),
inference(avatar_split_clause,[],[f4229,f4155,f1257,f15635]) ).
fof(f15635,plain,
( spl16_865
<=> ! [X0] :
( empty(sK6(powerset(X0)))
| empty(powerset(X0))
| element(sK9(sK9(powerset(sK9(sK9(powerset(sK6(powerset(X0)))))))),X0)
| empty(sK9(powerset(sK6(powerset(X0)))))
| empty(sK9(sK9(powerset(sK6(powerset(X0))))))
| empty(sK9(powerset(sK9(sK9(powerset(sK6(powerset(X0)))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_865])]) ).
fof(f4229,plain,
( ! [X0] :
( empty(sK6(powerset(X0)))
| empty(powerset(X0))
| element(sK9(sK9(powerset(sK9(sK9(powerset(sK6(powerset(X0)))))))),X0)
| empty(sK9(powerset(sK6(powerset(X0)))))
| empty(sK9(sK9(powerset(sK6(powerset(X0))))))
| empty(sK9(powerset(sK9(sK9(powerset(sK6(powerset(X0)))))))) )
| ~ spl16_152
| ~ spl16_387 ),
inference(resolution,[],[f4156,f1258]) ).
fof(f15633,plain,
( spl16_864
| ~ spl16_177
| ~ spl16_362 ),
inference(avatar_split_clause,[],[f3825,f3670,f1476,f15631]) ).
fof(f15631,plain,
( spl16_864
<=> ! [X0] :
( empty(sK9(sK9(powerset(powerset(sK9(sK7(powerset(X0))))))))
| empty(sK9(sK7(powerset(X0))))
| empty(sK9(powerset(powerset(sK9(sK7(powerset(X0)))))))
| empty(sK7(powerset(X0)))
| element(sK9(sK9(sK9(powerset(powerset(sK9(sK7(powerset(X0)))))))),X0)
| empty(powerset(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_864])]) ).
fof(f3825,plain,
( ! [X0] :
( empty(sK9(sK9(powerset(powerset(sK9(sK7(powerset(X0))))))))
| empty(sK9(sK7(powerset(X0))))
| empty(sK9(powerset(powerset(sK9(sK7(powerset(X0)))))))
| empty(sK7(powerset(X0)))
| element(sK9(sK9(sK9(powerset(powerset(sK9(sK7(powerset(X0)))))))),X0)
| empty(powerset(X0)) )
| ~ spl16_177
| ~ spl16_362 ),
inference(resolution,[],[f3671,f1477]) ).
fof(f15629,plain,
( spl16_863
| ~ spl16_176
| ~ spl16_362 ),
inference(avatar_split_clause,[],[f3820,f3670,f1472,f15627]) ).
fof(f15627,plain,
( spl16_863
<=> ! [X0] :
( empty(sK9(sK9(powerset(powerset(sK9(sK6(powerset(X0))))))))
| empty(sK9(sK6(powerset(X0))))
| empty(sK9(powerset(powerset(sK9(sK6(powerset(X0)))))))
| empty(sK6(powerset(X0)))
| element(sK9(sK9(sK9(powerset(powerset(sK9(sK6(powerset(X0)))))))),X0)
| empty(powerset(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_863])]) ).
fof(f3820,plain,
( ! [X0] :
( empty(sK9(sK9(powerset(powerset(sK9(sK6(powerset(X0))))))))
| empty(sK9(sK6(powerset(X0))))
| empty(sK9(powerset(powerset(sK9(sK6(powerset(X0)))))))
| empty(sK6(powerset(X0)))
| element(sK9(sK9(sK9(powerset(powerset(sK9(sK6(powerset(X0)))))))),X0)
| empty(powerset(X0)) )
| ~ spl16_176
| ~ spl16_362 ),
inference(resolution,[],[f3671,f1473]) ).
fof(f15613,plain,
( ~ spl16_224
| spl16_862
| ~ spl16_47
| ~ spl16_565 ),
inference(avatar_split_clause,[],[f7548,f7336,f400,f15611,f2058]) ).
fof(f2058,plain,
( spl16_224
<=> rel_str(sK8(sK1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_224])]) ).
fof(f15611,plain,
( spl16_862
<=> ! [X0] :
( subset(the_carrier(X0),sK14)
| ~ rel_str(X0)
| ~ subrelstr(X0,sK8(sK1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_862])]) ).
fof(f7336,plain,
( spl16_565
<=> sK14 = the_carrier(sK8(sK1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_565])]) ).
fof(f7548,plain,
( ! [X0] :
( subset(the_carrier(X0),sK14)
| ~ subrelstr(X0,sK8(sK1))
| ~ rel_str(X0)
| ~ rel_str(sK8(sK1)) )
| ~ spl16_47
| ~ spl16_565 ),
inference(superposition,[],[f401,f7338]) ).
fof(f7338,plain,
( sK14 = the_carrier(sK8(sK1))
| ~ spl16_565 ),
inference(avatar_component_clause,[],[f7336]) ).
fof(f15589,plain,
( spl16_861
| ~ spl16_72
| ~ spl16_418 ),
inference(avatar_split_clause,[],[f4726,f4669,f549,f15587]) ).
fof(f15587,plain,
( spl16_861
<=> ! [X0] :
( empty(sK7(sK9(sK9(powerset(powerset(sK9(powerset(X0))))))))
| empty(sK9(sK9(powerset(powerset(sK9(powerset(X0)))))))
| empty(sK9(powerset(X0)))
| empty(sK9(powerset(powerset(sK9(powerset(X0))))))
| element(sK9(sK7(sK9(sK9(powerset(powerset(sK9(powerset(X0)))))))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_861])]) ).
fof(f4726,plain,
( ! [X0] :
( empty(sK7(sK9(sK9(powerset(powerset(sK9(powerset(X0))))))))
| empty(sK9(sK9(powerset(powerset(sK9(powerset(X0)))))))
| empty(sK9(powerset(X0)))
| empty(sK9(powerset(powerset(sK9(powerset(X0))))))
| element(sK9(sK7(sK9(sK9(powerset(powerset(sK9(powerset(X0)))))))),X0) )
| ~ spl16_72
| ~ spl16_418 ),
inference(resolution,[],[f4670,f550]) ).
fof(f15585,plain,
( spl16_860
| ~ spl16_72
| ~ spl16_417 ),
inference(avatar_split_clause,[],[f4681,f4665,f549,f15583]) ).
fof(f15583,plain,
( spl16_860
<=> ! [X0] :
( empty(sK6(sK9(sK9(powerset(powerset(sK9(powerset(X0))))))))
| empty(sK9(sK9(powerset(powerset(sK9(powerset(X0)))))))
| empty(sK9(powerset(X0)))
| empty(sK9(powerset(powerset(sK9(powerset(X0))))))
| element(sK9(sK6(sK9(sK9(powerset(powerset(sK9(powerset(X0)))))))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_860])]) ).
fof(f4681,plain,
( ! [X0] :
( empty(sK6(sK9(sK9(powerset(powerset(sK9(powerset(X0))))))))
| empty(sK9(sK9(powerset(powerset(sK9(powerset(X0)))))))
| empty(sK9(powerset(X0)))
| empty(sK9(powerset(powerset(sK9(powerset(X0))))))
| element(sK9(sK6(sK9(sK9(powerset(powerset(sK9(powerset(X0)))))))),X0) )
| ~ spl16_72
| ~ spl16_417 ),
inference(resolution,[],[f4666,f550]) ).
fof(f15581,plain,
( spl16_859
| ~ spl16_177
| ~ spl16_349 ),
inference(avatar_split_clause,[],[f3611,f3578,f1476,f15579]) ).
fof(f15579,plain,
( spl16_859
<=> ! [X0] :
( empty(sK9(powerset(sK9(sK7(powerset(X0))))))
| empty(sK9(sK7(powerset(X0))))
| empty(sK9(powerset(sK9(powerset(sK9(sK7(powerset(X0))))))))
| empty(sK7(powerset(X0)))
| element(sK9(sK9(powerset(sK9(powerset(sK9(sK7(powerset(X0)))))))),X0)
| empty(powerset(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_859])]) ).
fof(f3611,plain,
( ! [X0] :
( empty(sK9(powerset(sK9(sK7(powerset(X0))))))
| empty(sK9(sK7(powerset(X0))))
| empty(sK9(powerset(sK9(powerset(sK9(sK7(powerset(X0))))))))
| empty(sK7(powerset(X0)))
| element(sK9(sK9(powerset(sK9(powerset(sK9(sK7(powerset(X0)))))))),X0)
| empty(powerset(X0)) )
| ~ spl16_177
| ~ spl16_349 ),
inference(resolution,[],[f3579,f1477]) ).
fof(f15577,plain,
( spl16_858
| ~ spl16_176
| ~ spl16_349 ),
inference(avatar_split_clause,[],[f3609,f3578,f1472,f15575]) ).
fof(f15575,plain,
( spl16_858
<=> ! [X0] :
( empty(sK9(powerset(sK9(sK6(powerset(X0))))))
| empty(sK9(sK6(powerset(X0))))
| empty(sK9(powerset(sK9(powerset(sK9(sK6(powerset(X0))))))))
| empty(sK6(powerset(X0)))
| element(sK9(sK9(powerset(sK9(powerset(sK9(sK6(powerset(X0)))))))),X0)
| empty(powerset(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_858])]) ).
fof(f3609,plain,
( ! [X0] :
( empty(sK9(powerset(sK9(sK6(powerset(X0))))))
| empty(sK9(sK6(powerset(X0))))
| empty(sK9(powerset(sK9(powerset(sK9(sK6(powerset(X0))))))))
| empty(sK6(powerset(X0)))
| element(sK9(sK9(powerset(sK9(powerset(sK9(sK6(powerset(X0)))))))),X0)
| empty(powerset(X0)) )
| ~ spl16_176
| ~ spl16_349 ),
inference(resolution,[],[f3579,f1473]) ).
fof(f15573,plain,
( spl16_857
| ~ spl16_173
| ~ spl16_326 ),
inference(avatar_split_clause,[],[f3377,f3305,f1448,f15571]) ).
fof(f15571,plain,
( spl16_857
<=> ! [X0] :
( empty(sK7(sK9(powerset(sK9(sK9(powerset(powerset(X0))))))))
| empty(sK9(sK9(powerset(powerset(X0)))))
| empty(sK9(powerset(sK9(sK9(powerset(powerset(X0)))))))
| element(sK9(sK7(sK9(powerset(sK9(sK9(powerset(powerset(X0)))))))),X0)
| empty(sK9(powerset(powerset(X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_857])]) ).
fof(f3377,plain,
( ! [X0] :
( empty(sK7(sK9(powerset(sK9(sK9(powerset(powerset(X0))))))))
| empty(sK9(sK9(powerset(powerset(X0)))))
| empty(sK9(powerset(sK9(sK9(powerset(powerset(X0)))))))
| element(sK9(sK7(sK9(powerset(sK9(sK9(powerset(powerset(X0)))))))),X0)
| empty(sK9(powerset(powerset(X0)))) )
| ~ spl16_173
| ~ spl16_326 ),
inference(resolution,[],[f3306,f1449]) ).
fof(f15569,plain,
( spl16_856
| ~ spl16_173
| ~ spl16_325 ),
inference(avatar_split_clause,[],[f3354,f3300,f1448,f15567]) ).
fof(f15567,plain,
( spl16_856
<=> ! [X0] :
( empty(sK6(sK9(powerset(sK9(sK9(powerset(powerset(X0))))))))
| empty(sK9(sK9(powerset(powerset(X0)))))
| empty(sK9(powerset(sK9(sK9(powerset(powerset(X0)))))))
| element(sK9(sK6(sK9(powerset(sK9(sK9(powerset(powerset(X0)))))))),X0)
| empty(sK9(powerset(powerset(X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_856])]) ).
fof(f3354,plain,
( ! [X0] :
( empty(sK6(sK9(powerset(sK9(sK9(powerset(powerset(X0))))))))
| empty(sK9(sK9(powerset(powerset(X0)))))
| empty(sK9(powerset(sK9(sK9(powerset(powerset(X0)))))))
| element(sK9(sK6(sK9(powerset(sK9(sK9(powerset(powerset(X0)))))))),X0)
| empty(sK9(powerset(powerset(X0)))) )
| ~ spl16_173
| ~ spl16_325 ),
inference(resolution,[],[f3301,f1449]) ).
fof(f15503,plain,
( ~ spl16_224
| spl16_855
| ~ spl16_47
| ~ spl16_565 ),
inference(avatar_split_clause,[],[f7547,f7336,f400,f15501,f2058]) ).
fof(f15501,plain,
( spl16_855
<=> ! [X0] :
( subset(sK14,the_carrier(X0))
| ~ rel_str(X0)
| ~ subrelstr(sK8(sK1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_855])]) ).
fof(f7547,plain,
( ! [X0] :
( subset(sK14,the_carrier(X0))
| ~ subrelstr(sK8(sK1),X0)
| ~ rel_str(sK8(sK1))
| ~ rel_str(X0) )
| ~ spl16_47
| ~ spl16_565 ),
inference(superposition,[],[f401,f7338]) ).
fof(f15479,plain,
( spl16_854
| ~ spl16_77
| ~ spl16_427 ),
inference(avatar_split_clause,[],[f4926,f4893,f577,f15477]) ).
fof(f15477,plain,
( spl16_854
<=> ! [X0] :
( empty(sK9(sK9(powerset(powerset(sK7(X0))))))
| empty(sK9(powerset(sK9(sK9(powerset(powerset(sK7(X0))))))))
| empty(sK7(X0))
| empty(sK9(powerset(powerset(sK7(X0)))))
| element(sK9(sK9(powerset(sK9(sK9(powerset(powerset(sK7(X0)))))))),X0)
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_854])]) ).
fof(f577,plain,
( spl16_77
<=> ! [X0,X1] :
( element(X0,X1)
| ~ in(X0,sK7(X1))
| empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_77])]) ).
fof(f4926,plain,
( ! [X0] :
( empty(sK9(sK9(powerset(powerset(sK7(X0))))))
| empty(sK9(powerset(sK9(sK9(powerset(powerset(sK7(X0))))))))
| empty(sK7(X0))
| empty(sK9(powerset(powerset(sK7(X0)))))
| element(sK9(sK9(powerset(sK9(sK9(powerset(powerset(sK7(X0)))))))),X0)
| empty(X0) )
| ~ spl16_77
| ~ spl16_427 ),
inference(resolution,[],[f4894,f578]) ).
fof(f578,plain,
( ! [X0,X1] :
( ~ in(X0,sK7(X1))
| element(X0,X1)
| empty(X1) )
| ~ spl16_77 ),
inference(avatar_component_clause,[],[f577]) ).
fof(f15475,plain,
( spl16_853
| ~ spl16_76
| ~ spl16_427 ),
inference(avatar_split_clause,[],[f4925,f4893,f573,f15473]) ).
fof(f15473,plain,
( spl16_853
<=> ! [X0] :
( empty(sK9(sK9(powerset(powerset(sK6(X0))))))
| empty(sK9(powerset(sK9(sK9(powerset(powerset(sK6(X0))))))))
| empty(sK6(X0))
| empty(sK9(powerset(powerset(sK6(X0)))))
| element(sK9(sK9(powerset(sK9(sK9(powerset(powerset(sK6(X0)))))))),X0)
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_853])]) ).
fof(f573,plain,
( spl16_76
<=> ! [X0,X1] :
( element(X0,X1)
| ~ in(X0,sK6(X1))
| empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_76])]) ).
fof(f4925,plain,
( ! [X0] :
( empty(sK9(sK9(powerset(powerset(sK6(X0))))))
| empty(sK9(powerset(sK9(sK9(powerset(powerset(sK6(X0))))))))
| empty(sK6(X0))
| empty(sK9(powerset(powerset(sK6(X0)))))
| element(sK9(sK9(powerset(sK9(sK9(powerset(powerset(sK6(X0)))))))),X0)
| empty(X0) )
| ~ spl16_76
| ~ spl16_427 ),
inference(resolution,[],[f4894,f574]) ).
fof(f574,plain,
( ! [X0,X1] :
( ~ in(X0,sK6(X1))
| element(X0,X1)
| empty(X1) )
| ~ spl16_76 ),
inference(avatar_component_clause,[],[f573]) ).
fof(f15471,plain,
( spl16_852
| ~ spl16_77
| ~ spl16_420 ),
inference(avatar_split_clause,[],[f4823,f4767,f577,f15469]) ).
fof(f15469,plain,
( spl16_852
<=> ! [X0] :
( empty(powerset(sK7(X0)))
| empty(sK9(sK7(powerset(sK7(X0)))))
| empty(sK9(powerset(sK9(sK7(powerset(sK7(X0)))))))
| empty(sK7(X0))
| empty(sK7(powerset(sK7(X0))))
| element(sK9(sK9(powerset(sK9(sK7(powerset(sK7(X0))))))),X0)
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_852])]) ).
fof(f4823,plain,
( ! [X0] :
( empty(powerset(sK7(X0)))
| empty(sK9(sK7(powerset(sK7(X0)))))
| empty(sK9(powerset(sK9(sK7(powerset(sK7(X0)))))))
| empty(sK7(X0))
| empty(sK7(powerset(sK7(X0))))
| element(sK9(sK9(powerset(sK9(sK7(powerset(sK7(X0))))))),X0)
| empty(X0) )
| ~ spl16_77
| ~ spl16_420 ),
inference(resolution,[],[f4768,f578]) ).
fof(f15467,plain,
( spl16_851
| ~ spl16_76
| ~ spl16_420 ),
inference(avatar_split_clause,[],[f4822,f4767,f573,f15465]) ).
fof(f15465,plain,
( spl16_851
<=> ! [X0] :
( empty(powerset(sK6(X0)))
| empty(sK9(sK7(powerset(sK6(X0)))))
| empty(sK9(powerset(sK9(sK7(powerset(sK6(X0)))))))
| empty(sK6(X0))
| empty(sK7(powerset(sK6(X0))))
| element(sK9(sK9(powerset(sK9(sK7(powerset(sK6(X0))))))),X0)
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_851])]) ).
fof(f4822,plain,
( ! [X0] :
( empty(powerset(sK6(X0)))
| empty(sK9(sK7(powerset(sK6(X0)))))
| empty(sK9(powerset(sK9(sK7(powerset(sK6(X0)))))))
| empty(sK6(X0))
| empty(sK7(powerset(sK6(X0))))
| element(sK9(sK9(powerset(sK9(sK7(powerset(sK6(X0))))))),X0)
| empty(X0) )
| ~ spl16_76
| ~ spl16_420 ),
inference(resolution,[],[f4768,f574]) ).
fof(f15463,plain,
( spl16_850
| ~ spl16_77
| ~ spl16_419 ),
inference(avatar_split_clause,[],[f4778,f4763,f577,f15461]) ).
fof(f15461,plain,
( spl16_850
<=> ! [X0] :
( empty(powerset(sK7(X0)))
| empty(sK9(sK6(powerset(sK7(X0)))))
| empty(sK9(powerset(sK9(sK6(powerset(sK7(X0)))))))
| empty(sK7(X0))
| empty(sK6(powerset(sK7(X0))))
| element(sK9(sK9(powerset(sK9(sK6(powerset(sK7(X0))))))),X0)
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_850])]) ).
fof(f4778,plain,
( ! [X0] :
( empty(powerset(sK7(X0)))
| empty(sK9(sK6(powerset(sK7(X0)))))
| empty(sK9(powerset(sK9(sK6(powerset(sK7(X0)))))))
| empty(sK7(X0))
| empty(sK6(powerset(sK7(X0))))
| element(sK9(sK9(powerset(sK9(sK6(powerset(sK7(X0))))))),X0)
| empty(X0) )
| ~ spl16_77
| ~ spl16_419 ),
inference(resolution,[],[f4764,f578]) ).
fof(f15459,plain,
( spl16_849
| ~ spl16_76
| ~ spl16_419 ),
inference(avatar_split_clause,[],[f4777,f4763,f573,f15457]) ).
fof(f15457,plain,
( spl16_849
<=> ! [X0] :
( empty(powerset(sK6(X0)))
| empty(sK9(sK6(powerset(sK6(X0)))))
| empty(sK9(powerset(sK9(sK6(powerset(sK6(X0)))))))
| empty(sK6(X0))
| empty(sK6(powerset(sK6(X0))))
| element(sK9(sK9(powerset(sK9(sK6(powerset(sK6(X0))))))),X0)
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_849])]) ).
fof(f4777,plain,
( ! [X0] :
( empty(powerset(sK6(X0)))
| empty(sK9(sK6(powerset(sK6(X0)))))
| empty(sK9(powerset(sK9(sK6(powerset(sK6(X0)))))))
| empty(sK6(X0))
| empty(sK6(powerset(sK6(X0))))
| element(sK9(sK9(powerset(sK9(sK6(powerset(sK6(X0))))))),X0)
| empty(X0) )
| ~ spl16_76
| ~ spl16_419 ),
inference(resolution,[],[f4764,f574]) ).
fof(f15453,plain,
( spl16_848
| ~ spl16_150
| ~ spl16_388 ),
inference(avatar_split_clause,[],[f4241,f4159,f1218,f15451]) ).
fof(f15451,plain,
( spl16_848
<=> ! [X0] :
( empty(sK7(powerset(X0)))
| empty(powerset(X0))
| element(sK9(sK7(sK9(sK9(powerset(sK7(powerset(X0))))))),X0)
| empty(sK9(powerset(sK7(powerset(X0)))))
| empty(sK7(sK9(sK9(powerset(sK7(powerset(X0)))))))
| empty(sK9(sK9(powerset(sK7(powerset(X0)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_848])]) ).
fof(f4241,plain,
( ! [X0] :
( empty(sK7(powerset(X0)))
| empty(powerset(X0))
| element(sK9(sK7(sK9(sK9(powerset(sK7(powerset(X0))))))),X0)
| empty(sK9(powerset(sK7(powerset(X0)))))
| empty(sK7(sK9(sK9(powerset(sK7(powerset(X0)))))))
| empty(sK9(sK9(powerset(sK7(powerset(X0)))))) )
| ~ spl16_150
| ~ spl16_388 ),
inference(resolution,[],[f4160,f1219]) ).
fof(f15449,plain,
( spl16_847
| ~ spl16_149
| ~ spl16_388 ),
inference(avatar_split_clause,[],[f4237,f4159,f1214,f15447]) ).
fof(f15447,plain,
( spl16_847
<=> ! [X0] :
( empty(sK7(powerset(X0)))
| empty(powerset(X0))
| element(sK9(sK6(sK9(sK9(powerset(sK7(powerset(X0))))))),X0)
| empty(sK9(powerset(sK7(powerset(X0)))))
| empty(sK6(sK9(sK9(powerset(sK7(powerset(X0)))))))
| empty(sK9(sK9(powerset(sK7(powerset(X0)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_847])]) ).
fof(f4237,plain,
( ! [X0] :
( empty(sK7(powerset(X0)))
| empty(powerset(X0))
| element(sK9(sK6(sK9(sK9(powerset(sK7(powerset(X0))))))),X0)
| empty(sK9(powerset(sK7(powerset(X0)))))
| empty(sK6(sK9(sK9(powerset(sK7(powerset(X0)))))))
| empty(sK9(sK9(powerset(sK7(powerset(X0)))))) )
| ~ spl16_149
| ~ spl16_388 ),
inference(resolution,[],[f4160,f1215]) ).
fof(f15445,plain,
( spl16_846
| ~ spl16_150
| ~ spl16_387 ),
inference(avatar_split_clause,[],[f4225,f4155,f1218,f15443]) ).
fof(f15443,plain,
( spl16_846
<=> ! [X0] :
( empty(sK6(powerset(X0)))
| empty(powerset(X0))
| element(sK9(sK7(sK9(sK9(powerset(sK6(powerset(X0))))))),X0)
| empty(sK9(powerset(sK6(powerset(X0)))))
| empty(sK7(sK9(sK9(powerset(sK6(powerset(X0)))))))
| empty(sK9(sK9(powerset(sK6(powerset(X0)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_846])]) ).
fof(f4225,plain,
( ! [X0] :
( empty(sK6(powerset(X0)))
| empty(powerset(X0))
| element(sK9(sK7(sK9(sK9(powerset(sK6(powerset(X0))))))),X0)
| empty(sK9(powerset(sK6(powerset(X0)))))
| empty(sK7(sK9(sK9(powerset(sK6(powerset(X0)))))))
| empty(sK9(sK9(powerset(sK6(powerset(X0)))))) )
| ~ spl16_150
| ~ spl16_387 ),
inference(resolution,[],[f4156,f1219]) ).
fof(f15441,plain,
( spl16_845
| ~ spl16_149
| ~ spl16_387 ),
inference(avatar_split_clause,[],[f4221,f4155,f1214,f15439]) ).
fof(f15439,plain,
( spl16_845
<=> ! [X0] :
( empty(sK6(powerset(X0)))
| empty(powerset(X0))
| element(sK9(sK6(sK9(sK9(powerset(sK6(powerset(X0))))))),X0)
| empty(sK9(powerset(sK6(powerset(X0)))))
| empty(sK6(sK9(sK9(powerset(sK6(powerset(X0)))))))
| empty(sK9(sK9(powerset(sK6(powerset(X0)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_845])]) ).
fof(f4221,plain,
( ! [X0] :
( empty(sK6(powerset(X0)))
| empty(powerset(X0))
| element(sK9(sK6(sK9(sK9(powerset(sK6(powerset(X0))))))),X0)
| empty(sK9(powerset(sK6(powerset(X0)))))
| empty(sK6(sK9(sK9(powerset(sK6(powerset(X0)))))))
| empty(sK9(sK9(powerset(sK6(powerset(X0)))))) )
| ~ spl16_149
| ~ spl16_387 ),
inference(resolution,[],[f4156,f1215]) ).
fof(f15437,plain,
( spl16_844
| ~ spl16_152
| ~ spl16_371 ),
inference(avatar_split_clause,[],[f4047,f3915,f1257,f15435]) ).
fof(f15435,plain,
( spl16_844
<=> ! [X0] :
( empty(sK7(sK9(powerset(powerset(X0)))))
| element(sK9(sK9(powerset(sK9(sK7(sK9(powerset(powerset(X0)))))))),X0)
| empty(sK9(powerset(powerset(X0))))
| empty(sK9(sK7(sK9(powerset(powerset(X0))))))
| empty(sK9(powerset(sK9(sK7(sK9(powerset(powerset(X0)))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_844])]) ).
fof(f4047,plain,
( ! [X0] :
( empty(sK7(sK9(powerset(powerset(X0)))))
| element(sK9(sK9(powerset(sK9(sK7(sK9(powerset(powerset(X0)))))))),X0)
| empty(sK9(powerset(powerset(X0))))
| empty(sK9(sK7(sK9(powerset(powerset(X0))))))
| empty(sK9(powerset(sK9(sK7(sK9(powerset(powerset(X0)))))))) )
| ~ spl16_152
| ~ spl16_371 ),
inference(resolution,[],[f3916,f1258]) ).
fof(f15433,plain,
( spl16_843
| ~ spl16_152
| ~ spl16_370 ),
inference(avatar_split_clause,[],[f4031,f3911,f1257,f15431]) ).
fof(f15431,plain,
( spl16_843
<=> ! [X0] :
( empty(sK6(sK9(powerset(powerset(X0)))))
| element(sK9(sK9(powerset(sK9(sK6(sK9(powerset(powerset(X0)))))))),X0)
| empty(sK9(powerset(powerset(X0))))
| empty(sK9(sK6(sK9(powerset(powerset(X0))))))
| empty(sK9(powerset(sK9(sK6(sK9(powerset(powerset(X0)))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_843])]) ).
fof(f4031,plain,
( ! [X0] :
( empty(sK6(sK9(powerset(powerset(X0)))))
| element(sK9(sK9(powerset(sK9(sK6(sK9(powerset(powerset(X0)))))))),X0)
| empty(sK9(powerset(powerset(X0))))
| empty(sK9(sK6(sK9(powerset(powerset(X0))))))
| empty(sK9(powerset(sK9(sK6(sK9(powerset(powerset(X0)))))))) )
| ~ spl16_152
| ~ spl16_370 ),
inference(resolution,[],[f3912,f1258]) ).
fof(f15429,plain,
( spl16_842
| ~ spl16_173
| ~ spl16_321 ),
inference(avatar_split_clause,[],[f3285,f3175,f1448,f15427]) ).
fof(f15427,plain,
( spl16_842
<=> ! [X0] :
( empty(sK7(sK9(sK9(powerset(powerset(X0))))))
| empty(sK9(sK9(powerset(powerset(X0)))))
| empty(sK9(powerset(sK7(sK9(sK9(powerset(powerset(X0))))))))
| element(sK9(sK9(powerset(sK7(sK9(sK9(powerset(powerset(X0)))))))),X0)
| empty(sK9(powerset(powerset(X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_842])]) ).
fof(f3285,plain,
( ! [X0] :
( empty(sK7(sK9(sK9(powerset(powerset(X0))))))
| empty(sK9(sK9(powerset(powerset(X0)))))
| empty(sK9(powerset(sK7(sK9(sK9(powerset(powerset(X0))))))))
| element(sK9(sK9(powerset(sK7(sK9(sK9(powerset(powerset(X0)))))))),X0)
| empty(sK9(powerset(powerset(X0)))) )
| ~ spl16_173
| ~ spl16_321 ),
inference(resolution,[],[f3176,f1449]) ).
fof(f15425,plain,
( spl16_841
| ~ spl16_173
| ~ spl16_320 ),
inference(avatar_split_clause,[],[f3264,f3171,f1448,f15423]) ).
fof(f15423,plain,
( spl16_841
<=> ! [X0] :
( empty(sK6(sK9(sK9(powerset(powerset(X0))))))
| empty(sK9(sK9(powerset(powerset(X0)))))
| empty(sK9(powerset(sK6(sK9(sK9(powerset(powerset(X0))))))))
| element(sK9(sK9(powerset(sK6(sK9(sK9(powerset(powerset(X0)))))))),X0)
| empty(sK9(powerset(powerset(X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_841])]) ).
fof(f3264,plain,
( ! [X0] :
( empty(sK6(sK9(sK9(powerset(powerset(X0))))))
| empty(sK9(sK9(powerset(powerset(X0)))))
| empty(sK9(powerset(sK6(sK9(sK9(powerset(powerset(X0))))))))
| element(sK9(sK9(powerset(sK6(sK9(sK9(powerset(powerset(X0)))))))),X0)
| empty(sK9(powerset(powerset(X0)))) )
| ~ spl16_173
| ~ spl16_320 ),
inference(resolution,[],[f3172,f1449]) ).
fof(f15401,plain,
( spl16_840
| ~ spl16_177
| ~ spl16_326 ),
inference(avatar_split_clause,[],[f3375,f3305,f1476,f15399]) ).
fof(f15399,plain,
( spl16_840
<=> ! [X0] :
( empty(sK7(sK9(powerset(sK9(sK7(powerset(X0)))))))
| empty(sK9(sK7(powerset(X0))))
| empty(sK9(powerset(sK9(sK7(powerset(X0))))))
| empty(sK7(powerset(X0)))
| element(sK9(sK7(sK9(powerset(sK9(sK7(powerset(X0))))))),X0)
| empty(powerset(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_840])]) ).
fof(f3375,plain,
( ! [X0] :
( empty(sK7(sK9(powerset(sK9(sK7(powerset(X0)))))))
| empty(sK9(sK7(powerset(X0))))
| empty(sK9(powerset(sK9(sK7(powerset(X0))))))
| empty(sK7(powerset(X0)))
| element(sK9(sK7(sK9(powerset(sK9(sK7(powerset(X0))))))),X0)
| empty(powerset(X0)) )
| ~ spl16_177
| ~ spl16_326 ),
inference(resolution,[],[f3306,f1477]) ).
fof(f15397,plain,
( spl16_839
| ~ spl16_176
| ~ spl16_326 ),
inference(avatar_split_clause,[],[f3373,f3305,f1472,f15395]) ).
fof(f15395,plain,
( spl16_839
<=> ! [X0] :
( empty(sK7(sK9(powerset(sK9(sK6(powerset(X0)))))))
| empty(sK9(sK6(powerset(X0))))
| empty(sK9(powerset(sK9(sK6(powerset(X0))))))
| empty(sK6(powerset(X0)))
| element(sK9(sK7(sK9(powerset(sK9(sK6(powerset(X0))))))),X0)
| empty(powerset(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_839])]) ).
fof(f3373,plain,
( ! [X0] :
( empty(sK7(sK9(powerset(sK9(sK6(powerset(X0)))))))
| empty(sK9(sK6(powerset(X0))))
| empty(sK9(powerset(sK9(sK6(powerset(X0))))))
| empty(sK6(powerset(X0)))
| element(sK9(sK7(sK9(powerset(sK9(sK6(powerset(X0))))))),X0)
| empty(powerset(X0)) )
| ~ spl16_176
| ~ spl16_326 ),
inference(resolution,[],[f3306,f1473]) ).
fof(f15393,plain,
( spl16_838
| ~ spl16_177
| ~ spl16_325 ),
inference(avatar_split_clause,[],[f3352,f3300,f1476,f15391]) ).
fof(f15391,plain,
( spl16_838
<=> ! [X0] :
( empty(sK6(sK9(powerset(sK9(sK7(powerset(X0)))))))
| empty(sK9(sK7(powerset(X0))))
| empty(sK9(powerset(sK9(sK7(powerset(X0))))))
| empty(sK7(powerset(X0)))
| element(sK9(sK6(sK9(powerset(sK9(sK7(powerset(X0))))))),X0)
| empty(powerset(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_838])]) ).
fof(f3352,plain,
( ! [X0] :
( empty(sK6(sK9(powerset(sK9(sK7(powerset(X0)))))))
| empty(sK9(sK7(powerset(X0))))
| empty(sK9(powerset(sK9(sK7(powerset(X0))))))
| empty(sK7(powerset(X0)))
| element(sK9(sK6(sK9(powerset(sK9(sK7(powerset(X0))))))),X0)
| empty(powerset(X0)) )
| ~ spl16_177
| ~ spl16_325 ),
inference(resolution,[],[f3301,f1477]) ).
fof(f15389,plain,
( spl16_837
| ~ spl16_176
| ~ spl16_325 ),
inference(avatar_split_clause,[],[f3350,f3300,f1472,f15387]) ).
fof(f15387,plain,
( spl16_837
<=> ! [X0] :
( empty(sK6(sK9(powerset(sK9(sK6(powerset(X0)))))))
| empty(sK9(sK6(powerset(X0))))
| empty(sK9(powerset(sK9(sK6(powerset(X0))))))
| empty(sK6(powerset(X0)))
| element(sK9(sK6(sK9(powerset(sK9(sK6(powerset(X0))))))),X0)
| empty(powerset(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_837])]) ).
fof(f3350,plain,
( ! [X0] :
( empty(sK6(sK9(powerset(sK9(sK6(powerset(X0)))))))
| empty(sK9(sK6(powerset(X0))))
| empty(sK9(powerset(sK9(sK6(powerset(X0))))))
| empty(sK6(powerset(X0)))
| element(sK9(sK6(sK9(powerset(sK9(sK6(powerset(X0))))))),X0)
| empty(powerset(X0)) )
| ~ spl16_176
| ~ spl16_325 ),
inference(resolution,[],[f3301,f1473]) ).
fof(f15361,plain,
( ~ spl16_836
| ~ spl16_27
| ~ spl16_738 ),
inference(avatar_split_clause,[],[f15297,f12411,f282,f15358]) ).
fof(f15358,plain,
( spl16_836
<=> in(cartesian_product2(sK14,sK14),sK9(the_InternalRel(sK8(sK1)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_836])]) ).
fof(f12411,plain,
( spl16_738
<=> in(sK9(the_InternalRel(sK8(sK1))),cartesian_product2(sK14,sK14)) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_738])]) ).
fof(f15297,plain,
( ~ in(cartesian_product2(sK14,sK14),sK9(the_InternalRel(sK8(sK1))))
| ~ spl16_27
| ~ spl16_738 ),
inference(resolution,[],[f12413,f283]) ).
fof(f12413,plain,
( in(sK9(the_InternalRel(sK8(sK1))),cartesian_product2(sK14,sK14))
| ~ spl16_738 ),
inference(avatar_component_clause,[],[f12411]) ).
fof(f15224,plain,
( spl16_835
| ~ spl16_77
| ~ spl16_418 ),
inference(avatar_split_clause,[],[f4725,f4669,f577,f15222]) ).
fof(f15222,plain,
( spl16_835
<=> ! [X0] :
( empty(sK7(sK9(sK9(powerset(powerset(sK7(X0)))))))
| empty(sK9(sK9(powerset(powerset(sK7(X0))))))
| empty(sK7(X0))
| empty(sK9(powerset(powerset(sK7(X0)))))
| element(sK9(sK7(sK9(sK9(powerset(powerset(sK7(X0))))))),X0)
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_835])]) ).
fof(f4725,plain,
( ! [X0] :
( empty(sK7(sK9(sK9(powerset(powerset(sK7(X0)))))))
| empty(sK9(sK9(powerset(powerset(sK7(X0))))))
| empty(sK7(X0))
| empty(sK9(powerset(powerset(sK7(X0)))))
| element(sK9(sK7(sK9(sK9(powerset(powerset(sK7(X0))))))),X0)
| empty(X0) )
| ~ spl16_77
| ~ spl16_418 ),
inference(resolution,[],[f4670,f578]) ).
fof(f15220,plain,
( spl16_834
| ~ spl16_76
| ~ spl16_418 ),
inference(avatar_split_clause,[],[f4724,f4669,f573,f15218]) ).
fof(f15218,plain,
( spl16_834
<=> ! [X0] :
( empty(sK7(sK9(sK9(powerset(powerset(sK6(X0)))))))
| empty(sK9(sK9(powerset(powerset(sK6(X0))))))
| empty(sK6(X0))
| empty(sK9(powerset(powerset(sK6(X0)))))
| element(sK9(sK7(sK9(sK9(powerset(powerset(sK6(X0))))))),X0)
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_834])]) ).
fof(f4724,plain,
( ! [X0] :
( empty(sK7(sK9(sK9(powerset(powerset(sK6(X0)))))))
| empty(sK9(sK9(powerset(powerset(sK6(X0))))))
| empty(sK6(X0))
| empty(sK9(powerset(powerset(sK6(X0)))))
| element(sK9(sK7(sK9(sK9(powerset(powerset(sK6(X0))))))),X0)
| empty(X0) )
| ~ spl16_76
| ~ spl16_418 ),
inference(resolution,[],[f4670,f574]) ).
fof(f15216,plain,
( spl16_833
| ~ spl16_77
| ~ spl16_417 ),
inference(avatar_split_clause,[],[f4680,f4665,f577,f15214]) ).
fof(f15214,plain,
( spl16_833
<=> ! [X0] :
( empty(sK6(sK9(sK9(powerset(powerset(sK7(X0)))))))
| empty(sK9(sK9(powerset(powerset(sK7(X0))))))
| empty(sK7(X0))
| empty(sK9(powerset(powerset(sK7(X0)))))
| element(sK9(sK6(sK9(sK9(powerset(powerset(sK7(X0))))))),X0)
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_833])]) ).
fof(f4680,plain,
( ! [X0] :
( empty(sK6(sK9(sK9(powerset(powerset(sK7(X0)))))))
| empty(sK9(sK9(powerset(powerset(sK7(X0))))))
| empty(sK7(X0))
| empty(sK9(powerset(powerset(sK7(X0)))))
| element(sK9(sK6(sK9(sK9(powerset(powerset(sK7(X0))))))),X0)
| empty(X0) )
| ~ spl16_77
| ~ spl16_417 ),
inference(resolution,[],[f4666,f578]) ).
fof(f15212,plain,
( spl16_832
| ~ spl16_76
| ~ spl16_417 ),
inference(avatar_split_clause,[],[f4679,f4665,f573,f15210]) ).
fof(f15210,plain,
( spl16_832
<=> ! [X0] :
( empty(sK6(sK9(sK9(powerset(powerset(sK6(X0)))))))
| empty(sK9(sK9(powerset(powerset(sK6(X0))))))
| empty(sK6(X0))
| empty(sK9(powerset(powerset(sK6(X0)))))
| element(sK9(sK6(sK9(sK9(powerset(powerset(sK6(X0))))))),X0)
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_832])]) ).
fof(f4679,plain,
( ! [X0] :
( empty(sK6(sK9(sK9(powerset(powerset(sK6(X0)))))))
| empty(sK9(sK9(powerset(powerset(sK6(X0))))))
| empty(sK6(X0))
| empty(sK9(powerset(powerset(sK6(X0)))))
| element(sK9(sK6(sK9(sK9(powerset(powerset(sK6(X0))))))),X0)
| empty(X0) )
| ~ spl16_76
| ~ spl16_417 ),
inference(resolution,[],[f4666,f574]) ).
fof(f15208,plain,
( spl16_831
| ~ spl16_77
| ~ spl16_415 ),
inference(avatar_split_clause,[],[f4623,f4477,f577,f15206]) ).
fof(f15206,plain,
( spl16_831
<=> ! [X0] :
( empty(powerset(sK7(X0)))
| empty(sK7(sK9(sK7(powerset(sK7(X0))))))
| empty(sK9(sK7(powerset(sK7(X0)))))
| empty(sK7(X0))
| empty(sK7(powerset(sK7(X0))))
| element(sK9(sK7(sK9(sK7(powerset(sK7(X0)))))),X0)
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_831])]) ).
fof(f4623,plain,
( ! [X0] :
( empty(powerset(sK7(X0)))
| empty(sK7(sK9(sK7(powerset(sK7(X0))))))
| empty(sK9(sK7(powerset(sK7(X0)))))
| empty(sK7(X0))
| empty(sK7(powerset(sK7(X0))))
| element(sK9(sK7(sK9(sK7(powerset(sK7(X0)))))),X0)
| empty(X0) )
| ~ spl16_77
| ~ spl16_415 ),
inference(resolution,[],[f4478,f578]) ).
fof(f15204,plain,
( spl16_830
| ~ spl16_76
| ~ spl16_415 ),
inference(avatar_split_clause,[],[f4622,f4477,f573,f15202]) ).
fof(f15202,plain,
( spl16_830
<=> ! [X0] :
( empty(powerset(sK6(X0)))
| empty(sK7(sK9(sK7(powerset(sK6(X0))))))
| empty(sK9(sK7(powerset(sK6(X0)))))
| empty(sK6(X0))
| empty(sK7(powerset(sK6(X0))))
| element(sK9(sK7(sK9(sK7(powerset(sK6(X0)))))),X0)
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_830])]) ).
fof(f4622,plain,
( ! [X0] :
( empty(powerset(sK6(X0)))
| empty(sK7(sK9(sK7(powerset(sK6(X0))))))
| empty(sK9(sK7(powerset(sK6(X0)))))
| empty(sK6(X0))
| empty(sK7(powerset(sK6(X0))))
| element(sK9(sK7(sK9(sK7(powerset(sK6(X0)))))),X0)
| empty(X0) )
| ~ spl16_76
| ~ spl16_415 ),
inference(resolution,[],[f4478,f574]) ).
fof(f15200,plain,
( spl16_829
| ~ spl16_77
| ~ spl16_414 ),
inference(avatar_split_clause,[],[f4578,f4473,f577,f15198]) ).
fof(f15198,plain,
( spl16_829
<=> ! [X0] :
( empty(powerset(sK7(X0)))
| empty(sK6(sK9(sK7(powerset(sK7(X0))))))
| empty(sK9(sK7(powerset(sK7(X0)))))
| empty(sK7(X0))
| empty(sK7(powerset(sK7(X0))))
| element(sK9(sK6(sK9(sK7(powerset(sK7(X0)))))),X0)
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_829])]) ).
fof(f4578,plain,
( ! [X0] :
( empty(powerset(sK7(X0)))
| empty(sK6(sK9(sK7(powerset(sK7(X0))))))
| empty(sK9(sK7(powerset(sK7(X0)))))
| empty(sK7(X0))
| empty(sK7(powerset(sK7(X0))))
| element(sK9(sK6(sK9(sK7(powerset(sK7(X0)))))),X0)
| empty(X0) )
| ~ spl16_77
| ~ spl16_414 ),
inference(resolution,[],[f4474,f578]) ).
fof(f15196,plain,
( spl16_828
| ~ spl16_76
| ~ spl16_414 ),
inference(avatar_split_clause,[],[f4577,f4473,f573,f15194]) ).
fof(f15194,plain,
( spl16_828
<=> ! [X0] :
( empty(powerset(sK6(X0)))
| empty(sK6(sK9(sK7(powerset(sK6(X0))))))
| empty(sK9(sK7(powerset(sK6(X0)))))
| empty(sK6(X0))
| empty(sK7(powerset(sK6(X0))))
| element(sK9(sK6(sK9(sK7(powerset(sK6(X0)))))),X0)
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_828])]) ).
fof(f4577,plain,
( ! [X0] :
( empty(powerset(sK6(X0)))
| empty(sK6(sK9(sK7(powerset(sK6(X0))))))
| empty(sK9(sK7(powerset(sK6(X0)))))
| empty(sK6(X0))
| empty(sK7(powerset(sK6(X0))))
| element(sK9(sK6(sK9(sK7(powerset(sK6(X0)))))),X0)
| empty(X0) )
| ~ spl16_76
| ~ spl16_414 ),
inference(resolution,[],[f4474,f574]) ).
fof(f15192,plain,
( spl16_827
| ~ spl16_77
| ~ spl16_413 ),
inference(avatar_split_clause,[],[f4533,f4469,f577,f15190]) ).
fof(f15190,plain,
( spl16_827
<=> ! [X0] :
( empty(powerset(sK7(X0)))
| empty(sK7(sK9(sK6(powerset(sK7(X0))))))
| empty(sK9(sK6(powerset(sK7(X0)))))
| empty(sK7(X0))
| empty(sK6(powerset(sK7(X0))))
| element(sK9(sK7(sK9(sK6(powerset(sK7(X0)))))),X0)
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_827])]) ).
fof(f4533,plain,
( ! [X0] :
( empty(powerset(sK7(X0)))
| empty(sK7(sK9(sK6(powerset(sK7(X0))))))
| empty(sK9(sK6(powerset(sK7(X0)))))
| empty(sK7(X0))
| empty(sK6(powerset(sK7(X0))))
| element(sK9(sK7(sK9(sK6(powerset(sK7(X0)))))),X0)
| empty(X0) )
| ~ spl16_77
| ~ spl16_413 ),
inference(resolution,[],[f4470,f578]) ).
fof(f15188,plain,
( spl16_826
| ~ spl16_76
| ~ spl16_413 ),
inference(avatar_split_clause,[],[f4532,f4469,f573,f15186]) ).
fof(f15186,plain,
( spl16_826
<=> ! [X0] :
( empty(powerset(sK6(X0)))
| empty(sK7(sK9(sK6(powerset(sK6(X0))))))
| empty(sK9(sK6(powerset(sK6(X0)))))
| empty(sK6(X0))
| empty(sK6(powerset(sK6(X0))))
| element(sK9(sK7(sK9(sK6(powerset(sK6(X0)))))),X0)
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_826])]) ).
fof(f4532,plain,
( ! [X0] :
( empty(powerset(sK6(X0)))
| empty(sK7(sK9(sK6(powerset(sK6(X0))))))
| empty(sK9(sK6(powerset(sK6(X0)))))
| empty(sK6(X0))
| empty(sK6(powerset(sK6(X0))))
| element(sK9(sK7(sK9(sK6(powerset(sK6(X0)))))),X0)
| empty(X0) )
| ~ spl16_76
| ~ spl16_413 ),
inference(resolution,[],[f4470,f574]) ).
fof(f15184,plain,
( spl16_825
| ~ spl16_77
| ~ spl16_412 ),
inference(avatar_split_clause,[],[f4488,f4465,f577,f15182]) ).
fof(f15182,plain,
( spl16_825
<=> ! [X0] :
( empty(powerset(sK7(X0)))
| empty(sK6(sK9(sK6(powerset(sK7(X0))))))
| empty(sK9(sK6(powerset(sK7(X0)))))
| empty(sK7(X0))
| empty(sK6(powerset(sK7(X0))))
| element(sK9(sK6(sK9(sK6(powerset(sK7(X0)))))),X0)
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_825])]) ).
fof(f4488,plain,
( ! [X0] :
( empty(powerset(sK7(X0)))
| empty(sK6(sK9(sK6(powerset(sK7(X0))))))
| empty(sK9(sK6(powerset(sK7(X0)))))
| empty(sK7(X0))
| empty(sK6(powerset(sK7(X0))))
| element(sK9(sK6(sK9(sK6(powerset(sK7(X0)))))),X0)
| empty(X0) )
| ~ spl16_77
| ~ spl16_412 ),
inference(resolution,[],[f4466,f578]) ).
fof(f15180,plain,
( spl16_824
| ~ spl16_76
| ~ spl16_412 ),
inference(avatar_split_clause,[],[f4487,f4465,f573,f15178]) ).
fof(f15178,plain,
( spl16_824
<=> ! [X0] :
( empty(powerset(sK6(X0)))
| empty(sK6(sK9(sK6(powerset(sK6(X0))))))
| empty(sK9(sK6(powerset(sK6(X0)))))
| empty(sK6(X0))
| empty(sK6(powerset(sK6(X0))))
| element(sK9(sK6(sK9(sK6(powerset(sK6(X0)))))),X0)
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_824])]) ).
fof(f4487,plain,
( ! [X0] :
( empty(powerset(sK6(X0)))
| empty(sK6(sK9(sK6(powerset(sK6(X0))))))
| empty(sK9(sK6(powerset(sK6(X0)))))
| empty(sK6(X0))
| empty(sK6(powerset(sK6(X0))))
| element(sK9(sK6(sK9(sK6(powerset(sK6(X0)))))),X0)
| empty(X0) )
| ~ spl16_76
| ~ spl16_412 ),
inference(resolution,[],[f4466,f574]) ).
fof(f15176,plain,
( spl16_823
| ~ spl16_150
| ~ spl16_371 ),
inference(avatar_split_clause,[],[f4043,f3915,f1218,f15174]) ).
fof(f15174,plain,
( spl16_823
<=> ! [X0] :
( empty(sK7(sK9(powerset(powerset(X0)))))
| element(sK9(sK7(sK9(sK7(sK9(powerset(powerset(X0))))))),X0)
| empty(sK9(powerset(powerset(X0))))
| empty(sK7(sK9(sK7(sK9(powerset(powerset(X0)))))))
| empty(sK9(sK7(sK9(powerset(powerset(X0)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_823])]) ).
fof(f4043,plain,
( ! [X0] :
( empty(sK7(sK9(powerset(powerset(X0)))))
| element(sK9(sK7(sK9(sK7(sK9(powerset(powerset(X0))))))),X0)
| empty(sK9(powerset(powerset(X0))))
| empty(sK7(sK9(sK7(sK9(powerset(powerset(X0)))))))
| empty(sK9(sK7(sK9(powerset(powerset(X0)))))) )
| ~ spl16_150
| ~ spl16_371 ),
inference(resolution,[],[f3916,f1219]) ).
fof(f15172,plain,
( spl16_822
| ~ spl16_149
| ~ spl16_371 ),
inference(avatar_split_clause,[],[f4039,f3915,f1214,f15170]) ).
fof(f15170,plain,
( spl16_822
<=> ! [X0] :
( empty(sK7(sK9(powerset(powerset(X0)))))
| element(sK9(sK6(sK9(sK7(sK9(powerset(powerset(X0))))))),X0)
| empty(sK9(powerset(powerset(X0))))
| empty(sK6(sK9(sK7(sK9(powerset(powerset(X0)))))))
| empty(sK9(sK7(sK9(powerset(powerset(X0)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_822])]) ).
fof(f4039,plain,
( ! [X0] :
( empty(sK7(sK9(powerset(powerset(X0)))))
| element(sK9(sK6(sK9(sK7(sK9(powerset(powerset(X0))))))),X0)
| empty(sK9(powerset(powerset(X0))))
| empty(sK6(sK9(sK7(sK9(powerset(powerset(X0)))))))
| empty(sK9(sK7(sK9(powerset(powerset(X0)))))) )
| ~ spl16_149
| ~ spl16_371 ),
inference(resolution,[],[f3916,f1215]) ).
fof(f15168,plain,
( spl16_821
| ~ spl16_150
| ~ spl16_370 ),
inference(avatar_split_clause,[],[f4027,f3911,f1218,f15166]) ).
fof(f15166,plain,
( spl16_821
<=> ! [X0] :
( empty(sK6(sK9(powerset(powerset(X0)))))
| element(sK9(sK7(sK9(sK6(sK9(powerset(powerset(X0))))))),X0)
| empty(sK9(powerset(powerset(X0))))
| empty(sK7(sK9(sK6(sK9(powerset(powerset(X0)))))))
| empty(sK9(sK6(sK9(powerset(powerset(X0)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_821])]) ).
fof(f4027,plain,
( ! [X0] :
( empty(sK6(sK9(powerset(powerset(X0)))))
| element(sK9(sK7(sK9(sK6(sK9(powerset(powerset(X0))))))),X0)
| empty(sK9(powerset(powerset(X0))))
| empty(sK7(sK9(sK6(sK9(powerset(powerset(X0)))))))
| empty(sK9(sK6(sK9(powerset(powerset(X0)))))) )
| ~ spl16_150
| ~ spl16_370 ),
inference(resolution,[],[f3912,f1219]) ).
fof(f15164,plain,
( spl16_820
| ~ spl16_149
| ~ spl16_370 ),
inference(avatar_split_clause,[],[f4023,f3911,f1214,f15162]) ).
fof(f15162,plain,
( spl16_820
<=> ! [X0] :
( empty(sK6(sK9(powerset(powerset(X0)))))
| element(sK9(sK6(sK9(sK6(sK9(powerset(powerset(X0))))))),X0)
| empty(sK9(powerset(powerset(X0))))
| empty(sK6(sK9(sK6(sK9(powerset(powerset(X0)))))))
| empty(sK9(sK6(sK9(powerset(powerset(X0)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_820])]) ).
fof(f4023,plain,
( ! [X0] :
( empty(sK6(sK9(powerset(powerset(X0)))))
| element(sK9(sK6(sK9(sK6(sK9(powerset(powerset(X0))))))),X0)
| empty(sK9(powerset(powerset(X0))))
| empty(sK6(sK9(sK6(sK9(powerset(powerset(X0)))))))
| empty(sK9(sK6(sK9(powerset(powerset(X0)))))) )
| ~ spl16_149
| ~ spl16_370 ),
inference(resolution,[],[f3912,f1215]) ).
fof(f15160,plain,
( spl16_819
| ~ spl16_152
| ~ spl16_369 ),
inference(avatar_split_clause,[],[f4015,f3907,f1257,f15158]) ).
fof(f15158,plain,
( spl16_819
<=> ! [X0] :
( empty(sK7(sK7(powerset(X0))))
| empty(powerset(X0))
| element(sK9(sK9(powerset(sK9(sK7(sK7(powerset(X0))))))),X0)
| empty(sK7(powerset(X0)))
| empty(sK9(sK7(sK7(powerset(X0)))))
| empty(sK9(powerset(sK9(sK7(sK7(powerset(X0))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_819])]) ).
fof(f4015,plain,
( ! [X0] :
( empty(sK7(sK7(powerset(X0))))
| empty(powerset(X0))
| element(sK9(sK9(powerset(sK9(sK7(sK7(powerset(X0))))))),X0)
| empty(sK7(powerset(X0)))
| empty(sK9(sK7(sK7(powerset(X0)))))
| empty(sK9(powerset(sK9(sK7(sK7(powerset(X0))))))) )
| ~ spl16_152
| ~ spl16_369 ),
inference(resolution,[],[f3908,f1258]) ).
fof(f15156,plain,
( spl16_818
| ~ spl16_152
| ~ spl16_368 ),
inference(avatar_split_clause,[],[f3999,f3903,f1257,f15154]) ).
fof(f15154,plain,
( spl16_818
<=> ! [X0] :
( empty(sK7(sK6(powerset(X0))))
| empty(powerset(X0))
| element(sK9(sK9(powerset(sK9(sK7(sK6(powerset(X0))))))),X0)
| empty(sK6(powerset(X0)))
| empty(sK9(sK7(sK6(powerset(X0)))))
| empty(sK9(powerset(sK9(sK7(sK6(powerset(X0))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_818])]) ).
fof(f3999,plain,
( ! [X0] :
( empty(sK7(sK6(powerset(X0))))
| empty(powerset(X0))
| element(sK9(sK9(powerset(sK9(sK7(sK6(powerset(X0))))))),X0)
| empty(sK6(powerset(X0)))
| empty(sK9(sK7(sK6(powerset(X0)))))
| empty(sK9(powerset(sK9(sK7(sK6(powerset(X0))))))) )
| ~ spl16_152
| ~ spl16_368 ),
inference(resolution,[],[f3904,f1258]) ).
fof(f15152,plain,
( spl16_817
| ~ spl16_152
| ~ spl16_366 ),
inference(avatar_split_clause,[],[f3983,f3895,f1257,f15150]) ).
fof(f15150,plain,
( spl16_817
<=> ! [X0] :
( empty(sK6(sK7(powerset(X0))))
| empty(powerset(X0))
| element(sK9(sK9(powerset(sK9(sK6(sK7(powerset(X0))))))),X0)
| empty(sK7(powerset(X0)))
| empty(sK9(sK6(sK7(powerset(X0)))))
| empty(sK9(powerset(sK9(sK6(sK7(powerset(X0))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_817])]) ).
fof(f3983,plain,
( ! [X0] :
( empty(sK6(sK7(powerset(X0))))
| empty(powerset(X0))
| element(sK9(sK9(powerset(sK9(sK6(sK7(powerset(X0))))))),X0)
| empty(sK7(powerset(X0)))
| empty(sK9(sK6(sK7(powerset(X0)))))
| empty(sK9(powerset(sK9(sK6(sK7(powerset(X0))))))) )
| ~ spl16_152
| ~ spl16_366 ),
inference(resolution,[],[f3896,f1258]) ).
fof(f15148,plain,
( spl16_816
| ~ spl16_152
| ~ spl16_365 ),
inference(avatar_split_clause,[],[f3967,f3891,f1257,f15146]) ).
fof(f15146,plain,
( spl16_816
<=> ! [X0] :
( empty(sK6(sK6(powerset(X0))))
| empty(powerset(X0))
| element(sK9(sK9(powerset(sK9(sK6(sK6(powerset(X0))))))),X0)
| empty(sK6(powerset(X0)))
| empty(sK9(sK6(sK6(powerset(X0)))))
| empty(sK9(powerset(sK9(sK6(sK6(powerset(X0))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_816])]) ).
fof(f3967,plain,
( ! [X0] :
( empty(sK6(sK6(powerset(X0))))
| empty(powerset(X0))
| element(sK9(sK9(powerset(sK9(sK6(sK6(powerset(X0))))))),X0)
| empty(sK6(powerset(X0)))
| empty(sK9(sK6(sK6(powerset(X0)))))
| empty(sK9(powerset(sK9(sK6(sK6(powerset(X0))))))) )
| ~ spl16_152
| ~ spl16_365 ),
inference(resolution,[],[f3892,f1258]) ).
fof(f15144,plain,
( spl16_815
| ~ spl16_177
| ~ spl16_321 ),
inference(avatar_split_clause,[],[f3283,f3175,f1476,f15142]) ).
fof(f15142,plain,
( spl16_815
<=> ! [X0] :
( empty(sK7(sK9(sK7(powerset(X0)))))
| empty(sK9(sK7(powerset(X0))))
| empty(sK9(powerset(sK7(sK9(sK7(powerset(X0)))))))
| empty(sK7(powerset(X0)))
| element(sK9(sK9(powerset(sK7(sK9(sK7(powerset(X0))))))),X0)
| empty(powerset(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_815])]) ).
fof(f3283,plain,
( ! [X0] :
( empty(sK7(sK9(sK7(powerset(X0)))))
| empty(sK9(sK7(powerset(X0))))
| empty(sK9(powerset(sK7(sK9(sK7(powerset(X0)))))))
| empty(sK7(powerset(X0)))
| element(sK9(sK9(powerset(sK7(sK9(sK7(powerset(X0))))))),X0)
| empty(powerset(X0)) )
| ~ spl16_177
| ~ spl16_321 ),
inference(resolution,[],[f3176,f1477]) ).
fof(f15140,plain,
( spl16_814
| ~ spl16_176
| ~ spl16_321 ),
inference(avatar_split_clause,[],[f3281,f3175,f1472,f15138]) ).
fof(f15138,plain,
( spl16_814
<=> ! [X0] :
( empty(sK7(sK9(sK6(powerset(X0)))))
| empty(sK9(sK6(powerset(X0))))
| empty(sK9(powerset(sK7(sK9(sK6(powerset(X0)))))))
| empty(sK6(powerset(X0)))
| element(sK9(sK9(powerset(sK7(sK9(sK6(powerset(X0))))))),X0)
| empty(powerset(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_814])]) ).
fof(f3281,plain,
( ! [X0] :
( empty(sK7(sK9(sK6(powerset(X0)))))
| empty(sK9(sK6(powerset(X0))))
| empty(sK9(powerset(sK7(sK9(sK6(powerset(X0)))))))
| empty(sK6(powerset(X0)))
| element(sK9(sK9(powerset(sK7(sK9(sK6(powerset(X0))))))),X0)
| empty(powerset(X0)) )
| ~ spl16_176
| ~ spl16_321 ),
inference(resolution,[],[f3176,f1473]) ).
fof(f15136,plain,
( spl16_813
| ~ spl16_177
| ~ spl16_320 ),
inference(avatar_split_clause,[],[f3262,f3171,f1476,f15134]) ).
fof(f15134,plain,
( spl16_813
<=> ! [X0] :
( empty(sK6(sK9(sK7(powerset(X0)))))
| empty(sK9(sK7(powerset(X0))))
| empty(sK9(powerset(sK6(sK9(sK7(powerset(X0)))))))
| empty(sK7(powerset(X0)))
| element(sK9(sK9(powerset(sK6(sK9(sK7(powerset(X0))))))),X0)
| empty(powerset(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_813])]) ).
fof(f3262,plain,
( ! [X0] :
( empty(sK6(sK9(sK7(powerset(X0)))))
| empty(sK9(sK7(powerset(X0))))
| empty(sK9(powerset(sK6(sK9(sK7(powerset(X0)))))))
| empty(sK7(powerset(X0)))
| element(sK9(sK9(powerset(sK6(sK9(sK7(powerset(X0))))))),X0)
| empty(powerset(X0)) )
| ~ spl16_177
| ~ spl16_320 ),
inference(resolution,[],[f3172,f1477]) ).
fof(f15132,plain,
( spl16_812
| ~ spl16_176
| ~ spl16_320 ),
inference(avatar_split_clause,[],[f3260,f3171,f1472,f15130]) ).
fof(f15130,plain,
( spl16_812
<=> ! [X0] :
( empty(sK6(sK9(sK6(powerset(X0)))))
| empty(sK9(sK6(powerset(X0))))
| empty(sK9(powerset(sK6(sK9(sK6(powerset(X0)))))))
| empty(sK6(powerset(X0)))
| element(sK9(sK9(powerset(sK6(sK9(sK6(powerset(X0))))))),X0)
| empty(powerset(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_812])]) ).
fof(f3260,plain,
( ! [X0] :
( empty(sK6(sK9(sK6(powerset(X0)))))
| empty(sK9(sK6(powerset(X0))))
| empty(sK9(powerset(sK6(sK9(sK6(powerset(X0)))))))
| empty(sK6(powerset(X0)))
| element(sK9(sK9(powerset(sK6(sK9(sK6(powerset(X0))))))),X0)
| empty(powerset(X0)) )
| ~ spl16_176
| ~ spl16_320 ),
inference(resolution,[],[f3172,f1473]) ).
fof(f15128,plain,
( spl16_811
| ~ spl16_173
| ~ spl16_306 ),
inference(avatar_split_clause,[],[f3086,f2964,f1448,f15126]) ).
fof(f15126,plain,
( spl16_811
<=> ! [X0] :
( empty(sK7(sK7(sK9(sK9(powerset(powerset(X0)))))))
| empty(sK9(sK9(powerset(powerset(X0)))))
| empty(sK7(sK9(sK9(powerset(powerset(X0))))))
| element(sK9(sK7(sK7(sK9(sK9(powerset(powerset(X0))))))),X0)
| empty(sK9(powerset(powerset(X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_811])]) ).
fof(f3086,plain,
( ! [X0] :
( empty(sK7(sK7(sK9(sK9(powerset(powerset(X0)))))))
| empty(sK9(sK9(powerset(powerset(X0)))))
| empty(sK7(sK9(sK9(powerset(powerset(X0))))))
| element(sK9(sK7(sK7(sK9(sK9(powerset(powerset(X0))))))),X0)
| empty(sK9(powerset(powerset(X0)))) )
| ~ spl16_173
| ~ spl16_306 ),
inference(resolution,[],[f2965,f1449]) ).
fof(f15124,plain,
( spl16_810
| ~ spl16_173
| ~ spl16_305 ),
inference(avatar_split_clause,[],[f3065,f2960,f1448,f15122]) ).
fof(f15122,plain,
( spl16_810
<=> ! [X0] :
( empty(sK7(sK6(sK9(sK9(powerset(powerset(X0)))))))
| empty(sK9(sK9(powerset(powerset(X0)))))
| empty(sK6(sK9(sK9(powerset(powerset(X0))))))
| element(sK9(sK7(sK6(sK9(sK9(powerset(powerset(X0))))))),X0)
| empty(sK9(powerset(powerset(X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_810])]) ).
fof(f3065,plain,
( ! [X0] :
( empty(sK7(sK6(sK9(sK9(powerset(powerset(X0)))))))
| empty(sK9(sK9(powerset(powerset(X0)))))
| empty(sK6(sK9(sK9(powerset(powerset(X0))))))
| element(sK9(sK7(sK6(sK9(sK9(powerset(powerset(X0))))))),X0)
| empty(sK9(powerset(powerset(X0)))) )
| ~ spl16_173
| ~ spl16_305 ),
inference(resolution,[],[f2961,f1449]) ).
fof(f15119,plain,
( spl16_809
| ~ spl16_173
| ~ spl16_304 ),
inference(avatar_split_clause,[],[f3044,f2956,f1448,f15117]) ).
fof(f15117,plain,
( spl16_809
<=> ! [X0] :
( empty(sK6(sK7(sK9(sK9(powerset(powerset(X0)))))))
| empty(sK9(sK9(powerset(powerset(X0)))))
| empty(sK7(sK9(sK9(powerset(powerset(X0))))))
| element(sK9(sK6(sK7(sK9(sK9(powerset(powerset(X0))))))),X0)
| empty(sK9(powerset(powerset(X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_809])]) ).
fof(f3044,plain,
( ! [X0] :
( empty(sK6(sK7(sK9(sK9(powerset(powerset(X0)))))))
| empty(sK9(sK9(powerset(powerset(X0)))))
| empty(sK7(sK9(sK9(powerset(powerset(X0))))))
| element(sK9(sK6(sK7(sK9(sK9(powerset(powerset(X0))))))),X0)
| empty(sK9(powerset(powerset(X0)))) )
| ~ spl16_173
| ~ spl16_304 ),
inference(resolution,[],[f2957,f1449]) ).
fof(f15115,plain,
( spl16_808
| ~ spl16_173
| ~ spl16_303 ),
inference(avatar_split_clause,[],[f3023,f2952,f1448,f15113]) ).
fof(f15113,plain,
( spl16_808
<=> ! [X0] :
( empty(sK6(sK6(sK9(sK9(powerset(powerset(X0)))))))
| empty(sK9(sK9(powerset(powerset(X0)))))
| empty(sK6(sK9(sK9(powerset(powerset(X0))))))
| element(sK9(sK6(sK6(sK9(sK9(powerset(powerset(X0))))))),X0)
| empty(sK9(powerset(powerset(X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_808])]) ).
fof(f3023,plain,
( ! [X0] :
( empty(sK6(sK6(sK9(sK9(powerset(powerset(X0)))))))
| empty(sK9(sK9(powerset(powerset(X0)))))
| empty(sK6(sK9(sK9(powerset(powerset(X0))))))
| element(sK9(sK6(sK6(sK9(sK9(powerset(powerset(X0))))))),X0)
| empty(sK9(powerset(powerset(X0)))) )
| ~ spl16_173
| ~ spl16_303 ),
inference(resolution,[],[f2953,f1449]) ).
fof(f15005,plain,
( spl16_807
| ~ spl16_324
| ~ spl16_351 ),
inference(avatar_split_clause,[],[f3702,f3626,f3296,f15003]) ).
fof(f15003,plain,
( spl16_807
<=> ! [X0,X1] :
( empty(powerset(X0))
| empty(sK7(powerset(X0)))
| ~ empty(X0)
| sK9(powerset(sK9(sK7(powerset(X0))))) = sK9(powerset(sK9(powerset(powerset(X1)))))
| ~ empty(X1)
| sK14 = sK9(powerset(sK9(powerset(sK9(sK9(powerset(powerset(X1)))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_807])]) ).
fof(f3296,plain,
( spl16_324
<=> ! [X0] :
( empty(sK9(powerset(powerset(X0))))
| ~ empty(X0)
| sK14 = sK9(powerset(sK9(powerset(sK9(sK9(powerset(powerset(X0)))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_324])]) ).
fof(f3626,plain,
( spl16_351
<=> ! [X0,X1] :
( ~ empty(X0)
| empty(powerset(X0))
| empty(sK7(powerset(X0)))
| ~ empty(X1)
| sK9(powerset(X1)) = sK9(powerset(sK9(sK7(powerset(X0))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_351])]) ).
fof(f3702,plain,
( ! [X0,X1] :
( empty(powerset(X0))
| empty(sK7(powerset(X0)))
| ~ empty(X0)
| sK9(powerset(sK9(sK7(powerset(X0))))) = sK9(powerset(sK9(powerset(powerset(X1)))))
| ~ empty(X1)
| sK14 = sK9(powerset(sK9(powerset(sK9(sK9(powerset(powerset(X1)))))))) )
| ~ spl16_324
| ~ spl16_351 ),
inference(resolution,[],[f3627,f3297]) ).
fof(f3297,plain,
( ! [X0] :
( empty(sK9(powerset(powerset(X0))))
| ~ empty(X0)
| sK14 = sK9(powerset(sK9(powerset(sK9(sK9(powerset(powerset(X0)))))))) )
| ~ spl16_324 ),
inference(avatar_component_clause,[],[f3296]) ).
fof(f3627,plain,
( ! [X0,X1] :
( ~ empty(X1)
| empty(powerset(X0))
| empty(sK7(powerset(X0)))
| ~ empty(X0)
| sK9(powerset(X1)) = sK9(powerset(sK9(sK7(powerset(X0))))) )
| ~ spl16_351 ),
inference(avatar_component_clause,[],[f3626]) ).
fof(f15001,plain,
( spl16_806
| ~ spl16_324
| ~ spl16_350 ),
inference(avatar_split_clause,[],[f3685,f3622,f3296,f14999]) ).
fof(f14999,plain,
( spl16_806
<=> ! [X0,X1] :
( empty(powerset(X0))
| empty(sK6(powerset(X0)))
| ~ empty(X0)
| sK9(powerset(sK9(sK6(powerset(X0))))) = sK9(powerset(sK9(powerset(powerset(X1)))))
| ~ empty(X1)
| sK14 = sK9(powerset(sK9(powerset(sK9(sK9(powerset(powerset(X1)))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_806])]) ).
fof(f3622,plain,
( spl16_350
<=> ! [X0,X1] :
( ~ empty(X0)
| empty(powerset(X0))
| empty(sK6(powerset(X0)))
| ~ empty(X1)
| sK9(powerset(X1)) = sK9(powerset(sK9(sK6(powerset(X0))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_350])]) ).
fof(f3685,plain,
( ! [X0,X1] :
( empty(powerset(X0))
| empty(sK6(powerset(X0)))
| ~ empty(X0)
| sK9(powerset(sK9(sK6(powerset(X0))))) = sK9(powerset(sK9(powerset(powerset(X1)))))
| ~ empty(X1)
| sK14 = sK9(powerset(sK9(powerset(sK9(sK9(powerset(powerset(X1)))))))) )
| ~ spl16_324
| ~ spl16_350 ),
inference(resolution,[],[f3623,f3297]) ).
fof(f3623,plain,
( ! [X0,X1] :
( ~ empty(X1)
| empty(powerset(X0))
| empty(sK6(powerset(X0)))
| ~ empty(X0)
| sK9(powerset(X1)) = sK9(powerset(sK9(sK6(powerset(X0))))) )
| ~ spl16_350 ),
inference(avatar_component_clause,[],[f3622]) ).
fof(f14749,plain,
( ~ spl16_12
| spl16_714
| ~ spl16_723 ),
inference(avatar_split_clause,[],[f14700,f11862,f10796,f213]) ).
fof(f10796,plain,
( spl16_714
<=> empty(the_InternalRel(sK8(sK1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_714])]) ).
fof(f11862,plain,
( spl16_723
<=> sK14 = the_InternalRel(sK8(sK1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_723])]) ).
fof(f14700,plain,
( ~ empty(sK14)
| spl16_714
| ~ spl16_723 ),
inference(forward_demodulation,[],[f10797,f11864]) ).
fof(f11864,plain,
( sK14 = the_InternalRel(sK8(sK1))
| ~ spl16_723 ),
inference(avatar_component_clause,[],[f11862]) ).
fof(f10797,plain,
( ~ empty(the_InternalRel(sK8(sK1)))
| spl16_714 ),
inference(avatar_component_clause,[],[f10796]) ).
fof(f14696,plain,
( spl16_805
| ~ spl16_224
| ~ spl16_473
| ~ spl16_714 ),
inference(avatar_split_clause,[],[f10928,f10796,f5624,f2058,f14693]) ).
fof(f10928,plain,
( ~ rel_str(sK8(sK1))
| sK14 = the_InternalRel(sK8(sK8(sK1)))
| ~ spl16_473
| ~ spl16_714 ),
inference(resolution,[],[f10798,f5625]) ).
fof(f10798,plain,
( empty(the_InternalRel(sK8(sK1)))
| ~ spl16_714 ),
inference(avatar_component_clause,[],[f10796]) ).
fof(f14589,plain,
( spl16_804
| ~ spl16_65
| ~ spl16_458 ),
inference(avatar_split_clause,[],[f5454,f5401,f508,f14587]) ).
fof(f14587,plain,
( spl16_804
<=> ! [X0] :
( empty(sK9(sK9(powerset(powerset(powerset(X0))))))
| empty(sK9(powerset(sK9(sK9(powerset(powerset(powerset(X0))))))))
| ~ empty(X0)
| empty(sK9(powerset(powerset(powerset(X0)))))
| empty(sK9(sK9(powerset(sK9(sK9(powerset(powerset(powerset(X0))))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_804])]) ).
fof(f5401,plain,
( spl16_458
<=> ! [X0,X1] :
( empty(sK9(powerset(powerset(powerset(X0)))))
| empty(sK9(sK9(powerset(powerset(powerset(X0))))))
| empty(sK9(powerset(sK9(sK9(powerset(powerset(powerset(X0))))))))
| ~ empty(X0)
| ~ in(X1,sK9(sK9(powerset(sK9(sK9(powerset(powerset(powerset(X0))))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_458])]) ).
fof(f5454,plain,
( ! [X0] :
( empty(sK9(sK9(powerset(powerset(powerset(X0))))))
| empty(sK9(powerset(sK9(sK9(powerset(powerset(powerset(X0))))))))
| ~ empty(X0)
| empty(sK9(powerset(powerset(powerset(X0)))))
| empty(sK9(sK9(powerset(sK9(sK9(powerset(powerset(powerset(X0))))))))) )
| ~ spl16_65
| ~ spl16_458 ),
inference(resolution,[],[f5402,f509]) ).
fof(f5402,plain,
( ! [X0,X1] :
( ~ in(X1,sK9(sK9(powerset(sK9(sK9(powerset(powerset(powerset(X0)))))))))
| empty(sK9(sK9(powerset(powerset(powerset(X0))))))
| empty(sK9(powerset(sK9(sK9(powerset(powerset(powerset(X0))))))))
| ~ empty(X0)
| empty(sK9(powerset(powerset(powerset(X0))))) )
| ~ spl16_458 ),
inference(avatar_component_clause,[],[f5401]) ).
fof(f14585,plain,
( spl16_803
| ~ spl16_65
| ~ spl16_457 ),
inference(avatar_split_clause,[],[f5429,f5397,f508,f14583]) ).
fof(f14583,plain,
( spl16_803
<=> ! [X0] :
( empty(powerset(powerset(X0)))
| empty(sK9(sK7(powerset(powerset(X0)))))
| empty(sK9(powerset(sK9(sK7(powerset(powerset(X0)))))))
| ~ empty(X0)
| empty(sK7(powerset(powerset(X0))))
| empty(sK9(sK9(powerset(sK9(sK7(powerset(powerset(X0)))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_803])]) ).
fof(f5397,plain,
( spl16_457
<=> ! [X0,X1] :
( empty(sK7(powerset(powerset(X0))))
| empty(powerset(powerset(X0)))
| empty(sK9(sK7(powerset(powerset(X0)))))
| empty(sK9(powerset(sK9(sK7(powerset(powerset(X0)))))))
| ~ empty(X0)
| ~ in(X1,sK9(sK9(powerset(sK9(sK7(powerset(powerset(X0)))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_457])]) ).
fof(f5429,plain,
( ! [X0] :
( empty(powerset(powerset(X0)))
| empty(sK9(sK7(powerset(powerset(X0)))))
| empty(sK9(powerset(sK9(sK7(powerset(powerset(X0)))))))
| ~ empty(X0)
| empty(sK7(powerset(powerset(X0))))
| empty(sK9(sK9(powerset(sK9(sK7(powerset(powerset(X0)))))))) )
| ~ spl16_65
| ~ spl16_457 ),
inference(resolution,[],[f5398,f509]) ).
fof(f5398,plain,
( ! [X0,X1] :
( ~ in(X1,sK9(sK9(powerset(sK9(sK7(powerset(powerset(X0))))))))
| empty(powerset(powerset(X0)))
| empty(sK9(sK7(powerset(powerset(X0)))))
| empty(sK9(powerset(sK9(sK7(powerset(powerset(X0)))))))
| ~ empty(X0)
| empty(sK7(powerset(powerset(X0)))) )
| ~ spl16_457 ),
inference(avatar_component_clause,[],[f5397]) ).
fof(f14581,plain,
( spl16_802
| ~ spl16_65
| ~ spl16_456 ),
inference(avatar_split_clause,[],[f5404,f5393,f508,f14579]) ).
fof(f14579,plain,
( spl16_802
<=> ! [X0] :
( empty(powerset(powerset(X0)))
| empty(sK9(sK6(powerset(powerset(X0)))))
| empty(sK9(powerset(sK9(sK6(powerset(powerset(X0)))))))
| ~ empty(X0)
| empty(sK6(powerset(powerset(X0))))
| empty(sK9(sK9(powerset(sK9(sK6(powerset(powerset(X0)))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_802])]) ).
fof(f5393,plain,
( spl16_456
<=> ! [X0,X1] :
( empty(sK6(powerset(powerset(X0))))
| empty(powerset(powerset(X0)))
| empty(sK9(sK6(powerset(powerset(X0)))))
| empty(sK9(powerset(sK9(sK6(powerset(powerset(X0)))))))
| ~ empty(X0)
| ~ in(X1,sK9(sK9(powerset(sK9(sK6(powerset(powerset(X0)))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_456])]) ).
fof(f5404,plain,
( ! [X0] :
( empty(powerset(powerset(X0)))
| empty(sK9(sK6(powerset(powerset(X0)))))
| empty(sK9(powerset(sK9(sK6(powerset(powerset(X0)))))))
| ~ empty(X0)
| empty(sK6(powerset(powerset(X0))))
| empty(sK9(sK9(powerset(sK9(sK6(powerset(powerset(X0)))))))) )
| ~ spl16_65
| ~ spl16_456 ),
inference(resolution,[],[f5394,f509]) ).
fof(f5394,plain,
( ! [X0,X1] :
( ~ in(X1,sK9(sK9(powerset(sK9(sK6(powerset(powerset(X0))))))))
| empty(powerset(powerset(X0)))
| empty(sK9(sK6(powerset(powerset(X0)))))
| empty(sK9(powerset(sK9(sK6(powerset(powerset(X0)))))))
| ~ empty(X0)
| empty(sK6(powerset(powerset(X0)))) )
| ~ spl16_456 ),
inference(avatar_component_clause,[],[f5393]) ).
fof(f14577,plain,
( spl16_801
| ~ spl16_150
| ~ spl16_369 ),
inference(avatar_split_clause,[],[f4011,f3907,f1218,f14575]) ).
fof(f14575,plain,
( spl16_801
<=> ! [X0] :
( empty(sK7(sK7(powerset(X0))))
| empty(powerset(X0))
| element(sK9(sK7(sK9(sK7(sK7(powerset(X0)))))),X0)
| empty(sK7(powerset(X0)))
| empty(sK7(sK9(sK7(sK7(powerset(X0))))))
| empty(sK9(sK7(sK7(powerset(X0))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_801])]) ).
fof(f4011,plain,
( ! [X0] :
( empty(sK7(sK7(powerset(X0))))
| empty(powerset(X0))
| element(sK9(sK7(sK9(sK7(sK7(powerset(X0)))))),X0)
| empty(sK7(powerset(X0)))
| empty(sK7(sK9(sK7(sK7(powerset(X0))))))
| empty(sK9(sK7(sK7(powerset(X0))))) )
| ~ spl16_150
| ~ spl16_369 ),
inference(resolution,[],[f3908,f1219]) ).
fof(f14573,plain,
( spl16_800
| ~ spl16_149
| ~ spl16_369 ),
inference(avatar_split_clause,[],[f4007,f3907,f1214,f14571]) ).
fof(f14571,plain,
( spl16_800
<=> ! [X0] :
( empty(sK7(sK7(powerset(X0))))
| empty(powerset(X0))
| element(sK9(sK6(sK9(sK7(sK7(powerset(X0)))))),X0)
| empty(sK7(powerset(X0)))
| empty(sK6(sK9(sK7(sK7(powerset(X0))))))
| empty(sK9(sK7(sK7(powerset(X0))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_800])]) ).
fof(f4007,plain,
( ! [X0] :
( empty(sK7(sK7(powerset(X0))))
| empty(powerset(X0))
| element(sK9(sK6(sK9(sK7(sK7(powerset(X0)))))),X0)
| empty(sK7(powerset(X0)))
| empty(sK6(sK9(sK7(sK7(powerset(X0))))))
| empty(sK9(sK7(sK7(powerset(X0))))) )
| ~ spl16_149
| ~ spl16_369 ),
inference(resolution,[],[f3908,f1215]) ).
fof(f14569,plain,
( spl16_799
| ~ spl16_150
| ~ spl16_368 ),
inference(avatar_split_clause,[],[f3995,f3903,f1218,f14567]) ).
fof(f14567,plain,
( spl16_799
<=> ! [X0] :
( empty(sK7(sK6(powerset(X0))))
| empty(powerset(X0))
| element(sK9(sK7(sK9(sK7(sK6(powerset(X0)))))),X0)
| empty(sK6(powerset(X0)))
| empty(sK7(sK9(sK7(sK6(powerset(X0))))))
| empty(sK9(sK7(sK6(powerset(X0))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_799])]) ).
fof(f3995,plain,
( ! [X0] :
( empty(sK7(sK6(powerset(X0))))
| empty(powerset(X0))
| element(sK9(sK7(sK9(sK7(sK6(powerset(X0)))))),X0)
| empty(sK6(powerset(X0)))
| empty(sK7(sK9(sK7(sK6(powerset(X0))))))
| empty(sK9(sK7(sK6(powerset(X0))))) )
| ~ spl16_150
| ~ spl16_368 ),
inference(resolution,[],[f3904,f1219]) ).
fof(f14565,plain,
( spl16_798
| ~ spl16_149
| ~ spl16_368 ),
inference(avatar_split_clause,[],[f3991,f3903,f1214,f14563]) ).
fof(f14563,plain,
( spl16_798
<=> ! [X0] :
( empty(sK7(sK6(powerset(X0))))
| empty(powerset(X0))
| element(sK9(sK6(sK9(sK7(sK6(powerset(X0)))))),X0)
| empty(sK6(powerset(X0)))
| empty(sK6(sK9(sK7(sK6(powerset(X0))))))
| empty(sK9(sK7(sK6(powerset(X0))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_798])]) ).
fof(f3991,plain,
( ! [X0] :
( empty(sK7(sK6(powerset(X0))))
| empty(powerset(X0))
| element(sK9(sK6(sK9(sK7(sK6(powerset(X0)))))),X0)
| empty(sK6(powerset(X0)))
| empty(sK6(sK9(sK7(sK6(powerset(X0))))))
| empty(sK9(sK7(sK6(powerset(X0))))) )
| ~ spl16_149
| ~ spl16_368 ),
inference(resolution,[],[f3904,f1215]) ).
fof(f14561,plain,
( spl16_797
| ~ spl16_150
| ~ spl16_366 ),
inference(avatar_split_clause,[],[f3979,f3895,f1218,f14559]) ).
fof(f14559,plain,
( spl16_797
<=> ! [X0] :
( empty(sK6(sK7(powerset(X0))))
| empty(powerset(X0))
| element(sK9(sK7(sK9(sK6(sK7(powerset(X0)))))),X0)
| empty(sK7(powerset(X0)))
| empty(sK7(sK9(sK6(sK7(powerset(X0))))))
| empty(sK9(sK6(sK7(powerset(X0))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_797])]) ).
fof(f3979,plain,
( ! [X0] :
( empty(sK6(sK7(powerset(X0))))
| empty(powerset(X0))
| element(sK9(sK7(sK9(sK6(sK7(powerset(X0)))))),X0)
| empty(sK7(powerset(X0)))
| empty(sK7(sK9(sK6(sK7(powerset(X0))))))
| empty(sK9(sK6(sK7(powerset(X0))))) )
| ~ spl16_150
| ~ spl16_366 ),
inference(resolution,[],[f3896,f1219]) ).
fof(f14557,plain,
( spl16_796
| ~ spl16_149
| ~ spl16_366 ),
inference(avatar_split_clause,[],[f3975,f3895,f1214,f14555]) ).
fof(f14555,plain,
( spl16_796
<=> ! [X0] :
( empty(sK6(sK7(powerset(X0))))
| empty(powerset(X0))
| element(sK9(sK6(sK9(sK6(sK7(powerset(X0)))))),X0)
| empty(sK7(powerset(X0)))
| empty(sK6(sK9(sK6(sK7(powerset(X0))))))
| empty(sK9(sK6(sK7(powerset(X0))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_796])]) ).
fof(f3975,plain,
( ! [X0] :
( empty(sK6(sK7(powerset(X0))))
| empty(powerset(X0))
| element(sK9(sK6(sK9(sK6(sK7(powerset(X0)))))),X0)
| empty(sK7(powerset(X0)))
| empty(sK6(sK9(sK6(sK7(powerset(X0))))))
| empty(sK9(sK6(sK7(powerset(X0))))) )
| ~ spl16_149
| ~ spl16_366 ),
inference(resolution,[],[f3896,f1215]) ).
fof(f14553,plain,
( spl16_795
| ~ spl16_150
| ~ spl16_365 ),
inference(avatar_split_clause,[],[f3963,f3891,f1218,f14551]) ).
fof(f14551,plain,
( spl16_795
<=> ! [X0] :
( empty(sK6(sK6(powerset(X0))))
| empty(powerset(X0))
| element(sK9(sK7(sK9(sK6(sK6(powerset(X0)))))),X0)
| empty(sK6(powerset(X0)))
| empty(sK7(sK9(sK6(sK6(powerset(X0))))))
| empty(sK9(sK6(sK6(powerset(X0))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_795])]) ).
fof(f3963,plain,
( ! [X0] :
( empty(sK6(sK6(powerset(X0))))
| empty(powerset(X0))
| element(sK9(sK7(sK9(sK6(sK6(powerset(X0)))))),X0)
| empty(sK6(powerset(X0)))
| empty(sK7(sK9(sK6(sK6(powerset(X0))))))
| empty(sK9(sK6(sK6(powerset(X0))))) )
| ~ spl16_150
| ~ spl16_365 ),
inference(resolution,[],[f3892,f1219]) ).
fof(f14548,plain,
( spl16_794
| ~ spl16_149
| ~ spl16_365 ),
inference(avatar_split_clause,[],[f3959,f3891,f1214,f14546]) ).
fof(f14546,plain,
( spl16_794
<=> ! [X0] :
( empty(sK6(sK6(powerset(X0))))
| empty(powerset(X0))
| element(sK9(sK6(sK9(sK6(sK6(powerset(X0)))))),X0)
| empty(sK6(powerset(X0)))
| empty(sK6(sK9(sK6(sK6(powerset(X0))))))
| empty(sK9(sK6(sK6(powerset(X0))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_794])]) ).
fof(f3959,plain,
( ! [X0] :
( empty(sK6(sK6(powerset(X0))))
| empty(powerset(X0))
| element(sK9(sK6(sK9(sK6(sK6(powerset(X0)))))),X0)
| empty(sK6(powerset(X0)))
| empty(sK6(sK9(sK6(sK6(powerset(X0))))))
| empty(sK9(sK6(sK6(powerset(X0))))) )
| ~ spl16_149
| ~ spl16_365 ),
inference(resolution,[],[f3892,f1215]) ).
fof(f14544,plain,
( spl16_793
| ~ spl16_120
| ~ spl16_364 ),
inference(avatar_split_clause,[],[f3868,f3678,f884,f14542]) ).
fof(f14542,plain,
( spl16_793
<=> ! [X0,X1] :
( empty(powerset(the_InternalRel(X0)))
| empty(sK9(sK7(powerset(the_InternalRel(X0)))))
| empty(the_InternalRel(X0))
| empty(sK7(powerset(the_InternalRel(X0))))
| element(sK9(sK9(sK7(powerset(the_InternalRel(X0))))),the_InternalRel(X1))
| ~ subrelstr(X0,X1)
| ~ rel_str(X0)
| ~ rel_str(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_793])]) ).
fof(f3868,plain,
( ! [X0,X1] :
( empty(powerset(the_InternalRel(X0)))
| empty(sK9(sK7(powerset(the_InternalRel(X0)))))
| empty(the_InternalRel(X0))
| empty(sK7(powerset(the_InternalRel(X0))))
| element(sK9(sK9(sK7(powerset(the_InternalRel(X0))))),the_InternalRel(X1))
| ~ subrelstr(X0,X1)
| ~ rel_str(X0)
| ~ rel_str(X1) )
| ~ spl16_120
| ~ spl16_364 ),
inference(resolution,[],[f3679,f885]) ).
fof(f14540,plain,
( spl16_792
| ~ spl16_119
| ~ spl16_364 ),
inference(avatar_split_clause,[],[f3866,f3678,f880,f14538]) ).
fof(f14538,plain,
( spl16_792
<=> ! [X0,X1] :
( empty(powerset(the_carrier(X0)))
| empty(sK9(sK7(powerset(the_carrier(X0)))))
| empty(the_carrier(X0))
| empty(sK7(powerset(the_carrier(X0))))
| element(sK9(sK9(sK7(powerset(the_carrier(X0))))),the_carrier(X1))
| ~ subrelstr(X0,X1)
| ~ rel_str(X0)
| ~ rel_str(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_792])]) ).
fof(f3866,plain,
( ! [X0,X1] :
( empty(powerset(the_carrier(X0)))
| empty(sK9(sK7(powerset(the_carrier(X0)))))
| empty(the_carrier(X0))
| empty(sK7(powerset(the_carrier(X0))))
| element(sK9(sK9(sK7(powerset(the_carrier(X0))))),the_carrier(X1))
| ~ subrelstr(X0,X1)
| ~ rel_str(X0)
| ~ rel_str(X1) )
| ~ spl16_119
| ~ spl16_364 ),
inference(resolution,[],[f3679,f881]) ).
fof(f14536,plain,
( spl16_791
| ~ spl16_120
| ~ spl16_363 ),
inference(avatar_split_clause,[],[f3841,f3674,f884,f14534]) ).
fof(f14534,plain,
( spl16_791
<=> ! [X0,X1] :
( empty(powerset(the_InternalRel(X0)))
| empty(sK9(sK6(powerset(the_InternalRel(X0)))))
| empty(the_InternalRel(X0))
| empty(sK6(powerset(the_InternalRel(X0))))
| element(sK9(sK9(sK6(powerset(the_InternalRel(X0))))),the_InternalRel(X1))
| ~ subrelstr(X0,X1)
| ~ rel_str(X0)
| ~ rel_str(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_791])]) ).
fof(f3841,plain,
( ! [X0,X1] :
( empty(powerset(the_InternalRel(X0)))
| empty(sK9(sK6(powerset(the_InternalRel(X0)))))
| empty(the_InternalRel(X0))
| empty(sK6(powerset(the_InternalRel(X0))))
| element(sK9(sK9(sK6(powerset(the_InternalRel(X0))))),the_InternalRel(X1))
| ~ subrelstr(X0,X1)
| ~ rel_str(X0)
| ~ rel_str(X1) )
| ~ spl16_120
| ~ spl16_363 ),
inference(resolution,[],[f3675,f885]) ).
fof(f14532,plain,
( spl16_790
| ~ spl16_119
| ~ spl16_363 ),
inference(avatar_split_clause,[],[f3839,f3674,f880,f14530]) ).
fof(f14530,plain,
( spl16_790
<=> ! [X0,X1] :
( empty(powerset(the_carrier(X0)))
| empty(sK9(sK6(powerset(the_carrier(X0)))))
| empty(the_carrier(X0))
| empty(sK6(powerset(the_carrier(X0))))
| element(sK9(sK9(sK6(powerset(the_carrier(X0))))),the_carrier(X1))
| ~ subrelstr(X0,X1)
| ~ rel_str(X0)
| ~ rel_str(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_790])]) ).
fof(f3839,plain,
( ! [X0,X1] :
( empty(powerset(the_carrier(X0)))
| empty(sK9(sK6(powerset(the_carrier(X0)))))
| empty(the_carrier(X0))
| empty(sK6(powerset(the_carrier(X0))))
| element(sK9(sK9(sK6(powerset(the_carrier(X0))))),the_carrier(X1))
| ~ subrelstr(X0,X1)
| ~ rel_str(X0)
| ~ rel_str(X1) )
| ~ spl16_119
| ~ spl16_363 ),
inference(resolution,[],[f3675,f881]) ).
fof(f14528,plain,
( spl16_789
| ~ spl16_324
| ~ spl16_341 ),
inference(avatar_split_clause,[],[f3585,f3545,f3296,f14526]) ).
fof(f14526,plain,
( spl16_789
<=> ! [X0,X1] :
( ~ empty(X0)
| empty(sK9(powerset(powerset(X0))))
| sK9(powerset(sK9(sK9(powerset(powerset(X0)))))) = sK9(powerset(sK9(powerset(powerset(X1)))))
| ~ empty(X1)
| sK14 = sK9(powerset(sK9(powerset(sK9(sK9(powerset(powerset(X1)))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_789])]) ).
fof(f3545,plain,
( spl16_341
<=> ! [X0,X1] :
( empty(sK9(powerset(powerset(X0))))
| ~ empty(X0)
| ~ empty(X1)
| sK9(powerset(X1)) = sK9(powerset(sK9(sK9(powerset(powerset(X0)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_341])]) ).
fof(f3585,plain,
( ! [X0,X1] :
( ~ empty(X0)
| empty(sK9(powerset(powerset(X0))))
| sK9(powerset(sK9(sK9(powerset(powerset(X0)))))) = sK9(powerset(sK9(powerset(powerset(X1)))))
| ~ empty(X1)
| sK14 = sK9(powerset(sK9(powerset(sK9(sK9(powerset(powerset(X1)))))))) )
| ~ spl16_324
| ~ spl16_341 ),
inference(resolution,[],[f3546,f3297]) ).
fof(f3546,plain,
( ! [X0,X1] :
( ~ empty(X1)
| ~ empty(X0)
| empty(sK9(powerset(powerset(X0))))
| sK9(powerset(X1)) = sK9(powerset(sK9(sK9(powerset(powerset(X0)))))) )
| ~ spl16_341 ),
inference(avatar_component_clause,[],[f3545]) ).
fof(f14524,plain,
( spl16_788
| ~ spl16_177
| ~ spl16_306 ),
inference(avatar_split_clause,[],[f3084,f2964,f1476,f14522]) ).
fof(f14522,plain,
( spl16_788
<=> ! [X0] :
( empty(sK7(sK7(sK9(sK7(powerset(X0))))))
| empty(sK9(sK7(powerset(X0))))
| empty(sK7(sK9(sK7(powerset(X0)))))
| empty(sK7(powerset(X0)))
| element(sK9(sK7(sK7(sK9(sK7(powerset(X0)))))),X0)
| empty(powerset(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_788])]) ).
fof(f3084,plain,
( ! [X0] :
( empty(sK7(sK7(sK9(sK7(powerset(X0))))))
| empty(sK9(sK7(powerset(X0))))
| empty(sK7(sK9(sK7(powerset(X0)))))
| empty(sK7(powerset(X0)))
| element(sK9(sK7(sK7(sK9(sK7(powerset(X0)))))),X0)
| empty(powerset(X0)) )
| ~ spl16_177
| ~ spl16_306 ),
inference(resolution,[],[f2965,f1477]) ).
fof(f14520,plain,
( spl16_787
| ~ spl16_176
| ~ spl16_306 ),
inference(avatar_split_clause,[],[f3082,f2964,f1472,f14518]) ).
fof(f14518,plain,
( spl16_787
<=> ! [X0] :
( empty(sK7(sK7(sK9(sK6(powerset(X0))))))
| empty(sK9(sK6(powerset(X0))))
| empty(sK7(sK9(sK6(powerset(X0)))))
| empty(sK6(powerset(X0)))
| element(sK9(sK7(sK7(sK9(sK6(powerset(X0)))))),X0)
| empty(powerset(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_787])]) ).
fof(f3082,plain,
( ! [X0] :
( empty(sK7(sK7(sK9(sK6(powerset(X0))))))
| empty(sK9(sK6(powerset(X0))))
| empty(sK7(sK9(sK6(powerset(X0)))))
| empty(sK6(powerset(X0)))
| element(sK9(sK7(sK7(sK9(sK6(powerset(X0)))))),X0)
| empty(powerset(X0)) )
| ~ spl16_176
| ~ spl16_306 ),
inference(resolution,[],[f2965,f1473]) ).
fof(f14516,plain,
( spl16_786
| ~ spl16_177
| ~ spl16_305 ),
inference(avatar_split_clause,[],[f3063,f2960,f1476,f14514]) ).
fof(f14514,plain,
( spl16_786
<=> ! [X0] :
( empty(sK7(sK6(sK9(sK7(powerset(X0))))))
| empty(sK9(sK7(powerset(X0))))
| empty(sK6(sK9(sK7(powerset(X0)))))
| empty(sK7(powerset(X0)))
| element(sK9(sK7(sK6(sK9(sK7(powerset(X0)))))),X0)
| empty(powerset(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_786])]) ).
fof(f3063,plain,
( ! [X0] :
( empty(sK7(sK6(sK9(sK7(powerset(X0))))))
| empty(sK9(sK7(powerset(X0))))
| empty(sK6(sK9(sK7(powerset(X0)))))
| empty(sK7(powerset(X0)))
| element(sK9(sK7(sK6(sK9(sK7(powerset(X0)))))),X0)
| empty(powerset(X0)) )
| ~ spl16_177
| ~ spl16_305 ),
inference(resolution,[],[f2961,f1477]) ).
fof(f14512,plain,
( spl16_785
| ~ spl16_176
| ~ spl16_305 ),
inference(avatar_split_clause,[],[f3061,f2960,f1472,f14510]) ).
fof(f14510,plain,
( spl16_785
<=> ! [X0] :
( empty(sK7(sK6(sK9(sK6(powerset(X0))))))
| empty(sK9(sK6(powerset(X0))))
| empty(sK6(sK9(sK6(powerset(X0)))))
| empty(sK6(powerset(X0)))
| element(sK9(sK7(sK6(sK9(sK6(powerset(X0)))))),X0)
| empty(powerset(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_785])]) ).
fof(f3061,plain,
( ! [X0] :
( empty(sK7(sK6(sK9(sK6(powerset(X0))))))
| empty(sK9(sK6(powerset(X0))))
| empty(sK6(sK9(sK6(powerset(X0)))))
| empty(sK6(powerset(X0)))
| element(sK9(sK7(sK6(sK9(sK6(powerset(X0)))))),X0)
| empty(powerset(X0)) )
| ~ spl16_176
| ~ spl16_305 ),
inference(resolution,[],[f2961,f1473]) ).
fof(f14508,plain,
( ~ spl16_784
| ~ spl16_723
| spl16_738 ),
inference(avatar_split_clause,[],[f14468,f12411,f11862,f14505]) ).
fof(f14505,plain,
( spl16_784
<=> in(sK9(sK14),cartesian_product2(sK14,sK14)) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_784])]) ).
fof(f14468,plain,
( ~ in(sK9(sK14),cartesian_product2(sK14,sK14))
| ~ spl16_723
| spl16_738 ),
inference(superposition,[],[f12412,f11864]) ).
fof(f12412,plain,
( ~ in(sK9(the_InternalRel(sK8(sK1))),cartesian_product2(sK14,sK14))
| spl16_738 ),
inference(avatar_component_clause,[],[f12411]) ).
fof(f14503,plain,
( spl16_783
| ~ spl16_177
| ~ spl16_304 ),
inference(avatar_split_clause,[],[f3042,f2956,f1476,f14501]) ).
fof(f14501,plain,
( spl16_783
<=> ! [X0] :
( empty(sK6(sK7(sK9(sK7(powerset(X0))))))
| empty(sK9(sK7(powerset(X0))))
| empty(sK7(sK9(sK7(powerset(X0)))))
| empty(sK7(powerset(X0)))
| element(sK9(sK6(sK7(sK9(sK7(powerset(X0)))))),X0)
| empty(powerset(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_783])]) ).
fof(f3042,plain,
( ! [X0] :
( empty(sK6(sK7(sK9(sK7(powerset(X0))))))
| empty(sK9(sK7(powerset(X0))))
| empty(sK7(sK9(sK7(powerset(X0)))))
| empty(sK7(powerset(X0)))
| element(sK9(sK6(sK7(sK9(sK7(powerset(X0)))))),X0)
| empty(powerset(X0)) )
| ~ spl16_177
| ~ spl16_304 ),
inference(resolution,[],[f2957,f1477]) ).
fof(f14499,plain,
( spl16_782
| ~ spl16_176
| ~ spl16_304 ),
inference(avatar_split_clause,[],[f3040,f2956,f1472,f14497]) ).
fof(f14497,plain,
( spl16_782
<=> ! [X0] :
( empty(sK6(sK7(sK9(sK6(powerset(X0))))))
| empty(sK9(sK6(powerset(X0))))
| empty(sK7(sK9(sK6(powerset(X0)))))
| empty(sK6(powerset(X0)))
| element(sK9(sK6(sK7(sK9(sK6(powerset(X0)))))),X0)
| empty(powerset(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_782])]) ).
fof(f3040,plain,
( ! [X0] :
( empty(sK6(sK7(sK9(sK6(powerset(X0))))))
| empty(sK9(sK6(powerset(X0))))
| empty(sK7(sK9(sK6(powerset(X0)))))
| empty(sK6(powerset(X0)))
| element(sK9(sK6(sK7(sK9(sK6(powerset(X0)))))),X0)
| empty(powerset(X0)) )
| ~ spl16_176
| ~ spl16_304 ),
inference(resolution,[],[f2957,f1473]) ).
fof(f14495,plain,
( spl16_781
| ~ spl16_177
| ~ spl16_303 ),
inference(avatar_split_clause,[],[f3021,f2952,f1476,f14493]) ).
fof(f14493,plain,
( spl16_781
<=> ! [X0] :
( empty(sK6(sK6(sK9(sK7(powerset(X0))))))
| empty(sK9(sK7(powerset(X0))))
| empty(sK6(sK9(sK7(powerset(X0)))))
| empty(sK7(powerset(X0)))
| element(sK9(sK6(sK6(sK9(sK7(powerset(X0)))))),X0)
| empty(powerset(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_781])]) ).
fof(f3021,plain,
( ! [X0] :
( empty(sK6(sK6(sK9(sK7(powerset(X0))))))
| empty(sK9(sK7(powerset(X0))))
| empty(sK6(sK9(sK7(powerset(X0)))))
| empty(sK7(powerset(X0)))
| element(sK9(sK6(sK6(sK9(sK7(powerset(X0)))))),X0)
| empty(powerset(X0)) )
| ~ spl16_177
| ~ spl16_303 ),
inference(resolution,[],[f2953,f1477]) ).
fof(f14491,plain,
( spl16_780
| ~ spl16_176
| ~ spl16_303 ),
inference(avatar_split_clause,[],[f3019,f2952,f1472,f14489]) ).
fof(f14489,plain,
( spl16_780
<=> ! [X0] :
( empty(sK6(sK6(sK9(sK6(powerset(X0))))))
| empty(sK9(sK6(powerset(X0))))
| empty(sK6(sK9(sK6(powerset(X0)))))
| empty(sK6(powerset(X0)))
| element(sK9(sK6(sK6(sK9(sK6(powerset(X0)))))),X0)
| empty(powerset(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_780])]) ).
fof(f3019,plain,
( ! [X0] :
( empty(sK6(sK6(sK9(sK6(powerset(X0))))))
| empty(sK9(sK6(powerset(X0))))
| empty(sK6(sK9(sK6(powerset(X0)))))
| empty(sK6(powerset(X0)))
| element(sK9(sK6(sK6(sK9(sK6(powerset(X0)))))),X0)
| empty(powerset(X0)) )
| ~ spl16_176
| ~ spl16_303 ),
inference(resolution,[],[f2953,f1473]) ).
fof(f14266,plain,
( spl16_779
| ~ spl16_110
| ~ spl16_364 ),
inference(avatar_split_clause,[],[f3888,f3678,f799,f14264]) ).
fof(f14264,plain,
( spl16_779
<=> ! [X0,X1] :
( empty(powerset(sK11(X0,X1)))
| empty(sK9(sK7(powerset(sK11(X0,X1)))))
| empty(sK11(X0,X1))
| empty(sK7(powerset(sK11(X0,X1))))
| element(sK9(sK9(sK7(powerset(sK11(X0,X1))))),cartesian_product2(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_779])]) ).
fof(f3888,plain,
( ! [X0,X1] :
( empty(powerset(sK11(X0,X1)))
| empty(sK9(sK7(powerset(sK11(X0,X1)))))
| empty(sK11(X0,X1))
| empty(sK7(powerset(sK11(X0,X1))))
| element(sK9(sK9(sK7(powerset(sK11(X0,X1))))),cartesian_product2(X0,X1)) )
| ~ spl16_110
| ~ spl16_364 ),
inference(resolution,[],[f3679,f800]) ).
fof(f14262,plain,
( spl16_778
| ~ spl16_111
| ~ spl16_364 ),
inference(avatar_split_clause,[],[f3886,f3678,f803,f14260]) ).
fof(f14260,plain,
( spl16_778
<=> ! [X0,X1] :
( empty(powerset(sK10(X0,X1)))
| empty(sK9(sK7(powerset(sK10(X0,X1)))))
| empty(sK10(X0,X1))
| empty(sK7(powerset(sK10(X0,X1))))
| element(sK9(sK9(sK7(powerset(sK10(X0,X1))))),cartesian_product2(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_778])]) ).
fof(f3886,plain,
( ! [X0,X1] :
( empty(powerset(sK10(X0,X1)))
| empty(sK9(sK7(powerset(sK10(X0,X1)))))
| empty(sK10(X0,X1))
| empty(sK7(powerset(sK10(X0,X1))))
| element(sK9(sK9(sK7(powerset(sK10(X0,X1))))),cartesian_product2(X0,X1)) )
| ~ spl16_111
| ~ spl16_364 ),
inference(resolution,[],[f3679,f804]) ).
fof(f14258,plain,
( spl16_777
| ~ spl16_110
| ~ spl16_363 ),
inference(avatar_split_clause,[],[f3861,f3674,f799,f14256]) ).
fof(f14256,plain,
( spl16_777
<=> ! [X0,X1] :
( empty(powerset(sK11(X0,X1)))
| empty(sK9(sK6(powerset(sK11(X0,X1)))))
| empty(sK11(X0,X1))
| empty(sK6(powerset(sK11(X0,X1))))
| element(sK9(sK9(sK6(powerset(sK11(X0,X1))))),cartesian_product2(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_777])]) ).
fof(f3861,plain,
( ! [X0,X1] :
( empty(powerset(sK11(X0,X1)))
| empty(sK9(sK6(powerset(sK11(X0,X1)))))
| empty(sK11(X0,X1))
| empty(sK6(powerset(sK11(X0,X1))))
| element(sK9(sK9(sK6(powerset(sK11(X0,X1))))),cartesian_product2(X0,X1)) )
| ~ spl16_110
| ~ spl16_363 ),
inference(resolution,[],[f3675,f800]) ).
fof(f14254,plain,
( spl16_776
| ~ spl16_111
| ~ spl16_363 ),
inference(avatar_split_clause,[],[f3859,f3674,f803,f14252]) ).
fof(f14252,plain,
( spl16_776
<=> ! [X0,X1] :
( empty(powerset(sK10(X0,X1)))
| empty(sK9(sK6(powerset(sK10(X0,X1)))))
| empty(sK10(X0,X1))
| empty(sK6(powerset(sK10(X0,X1))))
| element(sK9(sK9(sK6(powerset(sK10(X0,X1))))),cartesian_product2(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_776])]) ).
fof(f3859,plain,
( ! [X0,X1] :
( empty(powerset(sK10(X0,X1)))
| empty(sK9(sK6(powerset(sK10(X0,X1)))))
| empty(sK10(X0,X1))
| empty(sK6(powerset(sK10(X0,X1))))
| element(sK9(sK9(sK6(powerset(sK10(X0,X1))))),cartesian_product2(X0,X1)) )
| ~ spl16_111
| ~ spl16_363 ),
inference(resolution,[],[f3675,f804]) ).
fof(f14250,plain,
( spl16_775
| ~ spl16_120
| ~ spl16_362 ),
inference(avatar_split_clause,[],[f3814,f3670,f884,f14248]) ).
fof(f14248,plain,
( spl16_775
<=> ! [X0,X1] :
( empty(sK9(sK9(powerset(powerset(the_InternalRel(X0))))))
| empty(the_InternalRel(X0))
| empty(sK9(powerset(powerset(the_InternalRel(X0)))))
| element(sK9(sK9(sK9(powerset(powerset(the_InternalRel(X0)))))),the_InternalRel(X1))
| ~ subrelstr(X0,X1)
| ~ rel_str(X0)
| ~ rel_str(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_775])]) ).
fof(f3814,plain,
( ! [X0,X1] :
( empty(sK9(sK9(powerset(powerset(the_InternalRel(X0))))))
| empty(the_InternalRel(X0))
| empty(sK9(powerset(powerset(the_InternalRel(X0)))))
| element(sK9(sK9(sK9(powerset(powerset(the_InternalRel(X0)))))),the_InternalRel(X1))
| ~ subrelstr(X0,X1)
| ~ rel_str(X0)
| ~ rel_str(X1) )
| ~ spl16_120
| ~ spl16_362 ),
inference(resolution,[],[f3671,f885]) ).
fof(f14246,plain,
( spl16_774
| ~ spl16_119
| ~ spl16_362 ),
inference(avatar_split_clause,[],[f3812,f3670,f880,f14244]) ).
fof(f14244,plain,
( spl16_774
<=> ! [X0,X1] :
( empty(sK9(sK9(powerset(powerset(the_carrier(X0))))))
| empty(the_carrier(X0))
| empty(sK9(powerset(powerset(the_carrier(X0)))))
| element(sK9(sK9(sK9(powerset(powerset(the_carrier(X0)))))),the_carrier(X1))
| ~ subrelstr(X0,X1)
| ~ rel_str(X0)
| ~ rel_str(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_774])]) ).
fof(f3812,plain,
( ! [X0,X1] :
( empty(sK9(sK9(powerset(powerset(the_carrier(X0))))))
| empty(the_carrier(X0))
| empty(sK9(powerset(powerset(the_carrier(X0)))))
| element(sK9(sK9(sK9(powerset(powerset(the_carrier(X0)))))),the_carrier(X1))
| ~ subrelstr(X0,X1)
| ~ rel_str(X0)
| ~ rel_str(X1) )
| ~ spl16_119
| ~ spl16_362 ),
inference(resolution,[],[f3671,f881]) ).
fof(f14242,plain,
( spl16_773
| ~ spl16_309
| ~ spl16_351 ),
inference(avatar_split_clause,[],[f3703,f3626,f3098,f14240]) ).
fof(f14240,plain,
( spl16_773
<=> ! [X0,X1] :
( empty(powerset(X0))
| empty(sK7(powerset(X0)))
| ~ empty(X0)
| sK9(powerset(sK9(sK7(powerset(X0))))) = sK9(powerset(sK9(powerset(powerset(X1)))))
| ~ empty(X1)
| sK14 = sK9(powerset(sK9(sK9(powerset(powerset(X1)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_773])]) ).
fof(f3098,plain,
( spl16_309
<=> ! [X0] :
( empty(sK9(powerset(powerset(X0))))
| ~ empty(X0)
| sK14 = sK9(powerset(sK9(sK9(powerset(powerset(X0)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_309])]) ).
fof(f3703,plain,
( ! [X0,X1] :
( empty(powerset(X0))
| empty(sK7(powerset(X0)))
| ~ empty(X0)
| sK9(powerset(sK9(sK7(powerset(X0))))) = sK9(powerset(sK9(powerset(powerset(X1)))))
| ~ empty(X1)
| sK14 = sK9(powerset(sK9(sK9(powerset(powerset(X1)))))) )
| ~ spl16_309
| ~ spl16_351 ),
inference(resolution,[],[f3627,f3099]) ).
fof(f3099,plain,
( ! [X0] :
( empty(sK9(powerset(powerset(X0))))
| ~ empty(X0)
| sK14 = sK9(powerset(sK9(sK9(powerset(powerset(X0)))))) )
| ~ spl16_309 ),
inference(avatar_component_clause,[],[f3098]) ).
fof(f14238,plain,
( spl16_772
| ~ spl16_309
| ~ spl16_350 ),
inference(avatar_split_clause,[],[f3686,f3622,f3098,f14236]) ).
fof(f14236,plain,
( spl16_772
<=> ! [X0,X1] :
( empty(powerset(X0))
| empty(sK6(powerset(X0)))
| ~ empty(X0)
| sK9(powerset(sK9(sK6(powerset(X0))))) = sK9(powerset(sK9(powerset(powerset(X1)))))
| ~ empty(X1)
| sK14 = sK9(powerset(sK9(sK9(powerset(powerset(X1)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_772])]) ).
fof(f3686,plain,
( ! [X0,X1] :
( empty(powerset(X0))
| empty(sK6(powerset(X0)))
| ~ empty(X0)
| sK9(powerset(sK9(sK6(powerset(X0))))) = sK9(powerset(sK9(powerset(powerset(X1)))))
| ~ empty(X1)
| sK14 = sK9(powerset(sK9(sK9(powerset(powerset(X1)))))) )
| ~ spl16_309
| ~ spl16_350 ),
inference(resolution,[],[f3623,f3099]) ).
fof(f14234,plain,
( spl16_771
| ~ spl16_324
| ~ spl16_331 ),
inference(avatar_split_clause,[],[f3488,f3402,f3296,f14232]) ).
fof(f14232,plain,
( spl16_771
<=> ! [X0,X1] :
( empty(powerset(X0))
| empty(sK7(powerset(X0)))
| sK9(sK7(powerset(X0))) = sK9(powerset(sK9(powerset(powerset(X1)))))
| ~ empty(X0)
| ~ empty(X1)
| sK14 = sK9(powerset(sK9(powerset(sK9(sK9(powerset(powerset(X1)))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_771])]) ).
fof(f3402,plain,
( spl16_331
<=> ! [X0,X1] :
( ~ empty(X0)
| empty(powerset(X0))
| empty(sK7(powerset(X0)))
| sK9(powerset(X1)) = sK9(sK7(powerset(X0)))
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_331])]) ).
fof(f3488,plain,
( ! [X0,X1] :
( empty(powerset(X0))
| empty(sK7(powerset(X0)))
| sK9(sK7(powerset(X0))) = sK9(powerset(sK9(powerset(powerset(X1)))))
| ~ empty(X0)
| ~ empty(X1)
| sK14 = sK9(powerset(sK9(powerset(sK9(sK9(powerset(powerset(X1)))))))) )
| ~ spl16_324
| ~ spl16_331 ),
inference(resolution,[],[f3403,f3297]) ).
fof(f3403,plain,
( ! [X0,X1] :
( ~ empty(X1)
| empty(powerset(X0))
| empty(sK7(powerset(X0)))
| sK9(powerset(X1)) = sK9(sK7(powerset(X0)))
| ~ empty(X0) )
| ~ spl16_331 ),
inference(avatar_component_clause,[],[f3402]) ).
fof(f14230,plain,
( spl16_770
| ~ spl16_324
| ~ spl16_329 ),
inference(avatar_split_clause,[],[f3454,f3394,f3296,f14228]) ).
fof(f14228,plain,
( spl16_770
<=> ! [X0,X1] :
( empty(powerset(X0))
| empty(sK6(powerset(X0)))
| sK9(sK6(powerset(X0))) = sK9(powerset(sK9(powerset(powerset(X1)))))
| ~ empty(X0)
| ~ empty(X1)
| sK14 = sK9(powerset(sK9(powerset(sK9(sK9(powerset(powerset(X1)))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_770])]) ).
fof(f3394,plain,
( spl16_329
<=> ! [X0,X1] :
( ~ empty(X0)
| empty(powerset(X0))
| empty(sK6(powerset(X0)))
| sK9(powerset(X1)) = sK9(sK6(powerset(X0)))
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_329])]) ).
fof(f3454,plain,
( ! [X0,X1] :
( empty(powerset(X0))
| empty(sK6(powerset(X0)))
| sK9(sK6(powerset(X0))) = sK9(powerset(sK9(powerset(powerset(X1)))))
| ~ empty(X0)
| ~ empty(X1)
| sK14 = sK9(powerset(sK9(powerset(sK9(sK9(powerset(powerset(X1)))))))) )
| ~ spl16_324
| ~ spl16_329 ),
inference(resolution,[],[f3395,f3297]) ).
fof(f3395,plain,
( ! [X0,X1] :
( ~ empty(X1)
| empty(powerset(X0))
| empty(sK6(powerset(X0)))
| sK9(powerset(X1)) = sK9(sK6(powerset(X0)))
| ~ empty(X0) )
| ~ spl16_329 ),
inference(avatar_component_clause,[],[f3394]) ).
fof(f13678,plain,
( spl16_769
| ~ spl16_65
| ~ spl16_442 ),
inference(avatar_split_clause,[],[f5166,f5026,f508,f13676]) ).
fof(f13676,plain,
( spl16_769
<=> ! [X0] :
( empty(sK7(sK9(sK9(powerset(powerset(powerset(X0)))))))
| empty(sK9(sK9(powerset(powerset(powerset(X0))))))
| ~ empty(X0)
| empty(sK9(powerset(powerset(powerset(X0)))))
| empty(sK9(sK7(sK9(sK9(powerset(powerset(powerset(X0)))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_769])]) ).
fof(f5026,plain,
( spl16_442
<=> ! [X0,X1] :
( empty(sK9(powerset(powerset(powerset(X0)))))
| empty(sK7(sK9(sK9(powerset(powerset(powerset(X0)))))))
| empty(sK9(sK9(powerset(powerset(powerset(X0))))))
| ~ empty(X0)
| ~ in(X1,sK9(sK7(sK9(sK9(powerset(powerset(powerset(X0)))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_442])]) ).
fof(f5166,plain,
( ! [X0] :
( empty(sK7(sK9(sK9(powerset(powerset(powerset(X0)))))))
| empty(sK9(sK9(powerset(powerset(powerset(X0))))))
| ~ empty(X0)
| empty(sK9(powerset(powerset(powerset(X0)))))
| empty(sK9(sK7(sK9(sK9(powerset(powerset(powerset(X0)))))))) )
| ~ spl16_65
| ~ spl16_442 ),
inference(resolution,[],[f5027,f509]) ).
fof(f5027,plain,
( ! [X0,X1] :
( ~ in(X1,sK9(sK7(sK9(sK9(powerset(powerset(powerset(X0))))))))
| empty(sK7(sK9(sK9(powerset(powerset(powerset(X0)))))))
| empty(sK9(sK9(powerset(powerset(powerset(X0))))))
| ~ empty(X0)
| empty(sK9(powerset(powerset(powerset(X0))))) )
| ~ spl16_442 ),
inference(avatar_component_clause,[],[f5026]) ).
fof(f13674,plain,
( spl16_768
| ~ spl16_65
| ~ spl16_441 ),
inference(avatar_split_clause,[],[f5141,f5022,f508,f13672]) ).
fof(f13672,plain,
( spl16_768
<=> ! [X0] :
( empty(sK6(sK9(sK9(powerset(powerset(powerset(X0)))))))
| empty(sK9(sK9(powerset(powerset(powerset(X0))))))
| ~ empty(X0)
| empty(sK9(powerset(powerset(powerset(X0)))))
| empty(sK9(sK6(sK9(sK9(powerset(powerset(powerset(X0)))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_768])]) ).
fof(f5022,plain,
( spl16_441
<=> ! [X0,X1] :
( empty(sK9(powerset(powerset(powerset(X0)))))
| empty(sK6(sK9(sK9(powerset(powerset(powerset(X0)))))))
| empty(sK9(sK9(powerset(powerset(powerset(X0))))))
| ~ empty(X0)
| ~ in(X1,sK9(sK6(sK9(sK9(powerset(powerset(powerset(X0)))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_441])]) ).
fof(f5141,plain,
( ! [X0] :
( empty(sK6(sK9(sK9(powerset(powerset(powerset(X0)))))))
| empty(sK9(sK9(powerset(powerset(powerset(X0))))))
| ~ empty(X0)
| empty(sK9(powerset(powerset(powerset(X0)))))
| empty(sK9(sK6(sK9(sK9(powerset(powerset(powerset(X0)))))))) )
| ~ spl16_65
| ~ spl16_441 ),
inference(resolution,[],[f5023,f509]) ).
fof(f5023,plain,
( ! [X0,X1] :
( ~ in(X1,sK9(sK6(sK9(sK9(powerset(powerset(powerset(X0))))))))
| empty(sK6(sK9(sK9(powerset(powerset(powerset(X0)))))))
| empty(sK9(sK9(powerset(powerset(powerset(X0))))))
| ~ empty(X0)
| empty(sK9(powerset(powerset(powerset(X0))))) )
| ~ spl16_441 ),
inference(avatar_component_clause,[],[f5022]) ).
fof(f13670,plain,
( spl16_767
| ~ spl16_65
| ~ spl16_439 ),
inference(avatar_split_clause,[],[f5116,f5013,f508,f13668]) ).
fof(f13668,plain,
( spl16_767
<=> ! [X0] :
( empty(powerset(powerset(X0)))
| empty(sK7(sK9(sK7(powerset(powerset(X0))))))
| empty(sK9(sK7(powerset(powerset(X0)))))
| ~ empty(X0)
| empty(sK7(powerset(powerset(X0))))
| empty(sK9(sK7(sK9(sK7(powerset(powerset(X0))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_767])]) ).
fof(f5013,plain,
( spl16_439
<=> ! [X0,X1] :
( empty(sK7(powerset(powerset(X0))))
| empty(powerset(powerset(X0)))
| empty(sK7(sK9(sK7(powerset(powerset(X0))))))
| empty(sK9(sK7(powerset(powerset(X0)))))
| ~ empty(X0)
| ~ in(X1,sK9(sK7(sK9(sK7(powerset(powerset(X0))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_439])]) ).
fof(f5116,plain,
( ! [X0] :
( empty(powerset(powerset(X0)))
| empty(sK7(sK9(sK7(powerset(powerset(X0))))))
| empty(sK9(sK7(powerset(powerset(X0)))))
| ~ empty(X0)
| empty(sK7(powerset(powerset(X0))))
| empty(sK9(sK7(sK9(sK7(powerset(powerset(X0))))))) )
| ~ spl16_65
| ~ spl16_439 ),
inference(resolution,[],[f5014,f509]) ).
fof(f5014,plain,
( ! [X0,X1] :
( ~ in(X1,sK9(sK7(sK9(sK7(powerset(powerset(X0)))))))
| empty(powerset(powerset(X0)))
| empty(sK7(sK9(sK7(powerset(powerset(X0))))))
| empty(sK9(sK7(powerset(powerset(X0)))))
| ~ empty(X0)
| empty(sK7(powerset(powerset(X0)))) )
| ~ spl16_439 ),
inference(avatar_component_clause,[],[f5013]) ).
fof(f13666,plain,
( spl16_766
| ~ spl16_65
| ~ spl16_438 ),
inference(avatar_split_clause,[],[f5091,f5009,f508,f13664]) ).
fof(f13664,plain,
( spl16_766
<=> ! [X0] :
( empty(powerset(powerset(X0)))
| empty(sK6(sK9(sK7(powerset(powerset(X0))))))
| empty(sK9(sK7(powerset(powerset(X0)))))
| ~ empty(X0)
| empty(sK7(powerset(powerset(X0))))
| empty(sK9(sK6(sK9(sK7(powerset(powerset(X0))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_766])]) ).
fof(f5009,plain,
( spl16_438
<=> ! [X0,X1] :
( empty(sK7(powerset(powerset(X0))))
| empty(powerset(powerset(X0)))
| empty(sK6(sK9(sK7(powerset(powerset(X0))))))
| empty(sK9(sK7(powerset(powerset(X0)))))
| ~ empty(X0)
| ~ in(X1,sK9(sK6(sK9(sK7(powerset(powerset(X0))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_438])]) ).
fof(f5091,plain,
( ! [X0] :
( empty(powerset(powerset(X0)))
| empty(sK6(sK9(sK7(powerset(powerset(X0))))))
| empty(sK9(sK7(powerset(powerset(X0)))))
| ~ empty(X0)
| empty(sK7(powerset(powerset(X0))))
| empty(sK9(sK6(sK9(sK7(powerset(powerset(X0))))))) )
| ~ spl16_65
| ~ spl16_438 ),
inference(resolution,[],[f5010,f509]) ).
fof(f5010,plain,
( ! [X0,X1] :
( ~ in(X1,sK9(sK6(sK9(sK7(powerset(powerset(X0)))))))
| empty(powerset(powerset(X0)))
| empty(sK6(sK9(sK7(powerset(powerset(X0))))))
| empty(sK9(sK7(powerset(powerset(X0)))))
| ~ empty(X0)
| empty(sK7(powerset(powerset(X0)))) )
| ~ spl16_438 ),
inference(avatar_component_clause,[],[f5009]) ).
fof(f13662,plain,
( spl16_765
| ~ spl16_65
| ~ spl16_437 ),
inference(avatar_split_clause,[],[f5066,f5005,f508,f13660]) ).
fof(f13660,plain,
( spl16_765
<=> ! [X0] :
( empty(powerset(powerset(X0)))
| empty(sK7(sK9(sK6(powerset(powerset(X0))))))
| empty(sK9(sK6(powerset(powerset(X0)))))
| ~ empty(X0)
| empty(sK6(powerset(powerset(X0))))
| empty(sK9(sK7(sK9(sK6(powerset(powerset(X0))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_765])]) ).
fof(f5005,plain,
( spl16_437
<=> ! [X0,X1] :
( empty(sK6(powerset(powerset(X0))))
| empty(powerset(powerset(X0)))
| empty(sK7(sK9(sK6(powerset(powerset(X0))))))
| empty(sK9(sK6(powerset(powerset(X0)))))
| ~ empty(X0)
| ~ in(X1,sK9(sK7(sK9(sK6(powerset(powerset(X0))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_437])]) ).
fof(f5066,plain,
( ! [X0] :
( empty(powerset(powerset(X0)))
| empty(sK7(sK9(sK6(powerset(powerset(X0))))))
| empty(sK9(sK6(powerset(powerset(X0)))))
| ~ empty(X0)
| empty(sK6(powerset(powerset(X0))))
| empty(sK9(sK7(sK9(sK6(powerset(powerset(X0))))))) )
| ~ spl16_65
| ~ spl16_437 ),
inference(resolution,[],[f5006,f509]) ).
fof(f5006,plain,
( ! [X0,X1] :
( ~ in(X1,sK9(sK7(sK9(sK6(powerset(powerset(X0)))))))
| empty(powerset(powerset(X0)))
| empty(sK7(sK9(sK6(powerset(powerset(X0))))))
| empty(sK9(sK6(powerset(powerset(X0)))))
| ~ empty(X0)
| empty(sK6(powerset(powerset(X0)))) )
| ~ spl16_437 ),
inference(avatar_component_clause,[],[f5005]) ).
fof(f13658,plain,
( spl16_764
| ~ spl16_65
| ~ spl16_436 ),
inference(avatar_split_clause,[],[f5041,f5001,f508,f13656]) ).
fof(f13656,plain,
( spl16_764
<=> ! [X0] :
( empty(powerset(powerset(X0)))
| empty(sK6(sK9(sK6(powerset(powerset(X0))))))
| empty(sK9(sK6(powerset(powerset(X0)))))
| ~ empty(X0)
| empty(sK6(powerset(powerset(X0))))
| empty(sK9(sK6(sK9(sK6(powerset(powerset(X0))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_764])]) ).
fof(f5001,plain,
( spl16_436
<=> ! [X0,X1] :
( empty(sK6(powerset(powerset(X0))))
| empty(powerset(powerset(X0)))
| empty(sK6(sK9(sK6(powerset(powerset(X0))))))
| empty(sK9(sK6(powerset(powerset(X0)))))
| ~ empty(X0)
| ~ in(X1,sK9(sK6(sK9(sK6(powerset(powerset(X0))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_436])]) ).
fof(f5041,plain,
( ! [X0] :
( empty(powerset(powerset(X0)))
| empty(sK6(sK9(sK6(powerset(powerset(X0))))))
| empty(sK9(sK6(powerset(powerset(X0)))))
| ~ empty(X0)
| empty(sK6(powerset(powerset(X0))))
| empty(sK9(sK6(sK9(sK6(powerset(powerset(X0))))))) )
| ~ spl16_65
| ~ spl16_436 ),
inference(resolution,[],[f5002,f509]) ).
fof(f5002,plain,
( ! [X0,X1] :
( ~ in(X1,sK9(sK6(sK9(sK6(powerset(powerset(X0)))))))
| empty(powerset(powerset(X0)))
| empty(sK6(sK9(sK6(powerset(powerset(X0))))))
| empty(sK9(sK6(powerset(powerset(X0)))))
| ~ empty(X0)
| empty(sK6(powerset(powerset(X0)))) )
| ~ spl16_436 ),
inference(avatar_component_clause,[],[f5001]) ).
fof(f13654,plain,
( ~ spl16_763
| ~ spl16_194
| spl16_758 ),
inference(avatar_split_clause,[],[f13604,f13008,f1676,f13651]) ).
fof(f13651,plain,
( spl16_763
<=> in(sK9(sK14),the_InternalRel(sK1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_763])]) ).
fof(f13008,plain,
( spl16_758
<=> element(sK9(sK14),cartesian_product2(sK14,sK14)) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_758])]) ).
fof(f13604,plain,
( ~ in(sK9(sK14),the_InternalRel(sK1))
| ~ spl16_194
| spl16_758 ),
inference(resolution,[],[f13010,f1677]) ).
fof(f13010,plain,
( ~ element(sK9(sK14),cartesian_product2(sK14,sK14))
| spl16_758 ),
inference(avatar_component_clause,[],[f13008]) ).
fof(f13649,plain,
( spl16_762
| ~ spl16_120
| ~ spl16_349 ),
inference(avatar_split_clause,[],[f3603,f3578,f884,f13647]) ).
fof(f13647,plain,
( spl16_762
<=> ! [X0,X1] :
( empty(sK9(powerset(the_InternalRel(X0))))
| empty(the_InternalRel(X0))
| empty(sK9(powerset(sK9(powerset(the_InternalRel(X0))))))
| element(sK9(sK9(powerset(sK9(powerset(the_InternalRel(X0)))))),the_InternalRel(X1))
| ~ subrelstr(X0,X1)
| ~ rel_str(X0)
| ~ rel_str(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_762])]) ).
fof(f3603,plain,
( ! [X0,X1] :
( empty(sK9(powerset(the_InternalRel(X0))))
| empty(the_InternalRel(X0))
| empty(sK9(powerset(sK9(powerset(the_InternalRel(X0))))))
| element(sK9(sK9(powerset(sK9(powerset(the_InternalRel(X0)))))),the_InternalRel(X1))
| ~ subrelstr(X0,X1)
| ~ rel_str(X0)
| ~ rel_str(X1) )
| ~ spl16_120
| ~ spl16_349 ),
inference(resolution,[],[f3579,f885]) ).
fof(f13645,plain,
( spl16_761
| ~ spl16_119
| ~ spl16_349 ),
inference(avatar_split_clause,[],[f3601,f3578,f880,f13643]) ).
fof(f13643,plain,
( spl16_761
<=> ! [X0,X1] :
( empty(sK9(powerset(the_carrier(X0))))
| empty(the_carrier(X0))
| empty(sK9(powerset(sK9(powerset(the_carrier(X0))))))
| element(sK9(sK9(powerset(sK9(powerset(the_carrier(X0)))))),the_carrier(X1))
| ~ subrelstr(X0,X1)
| ~ rel_str(X0)
| ~ rel_str(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_761])]) ).
fof(f3601,plain,
( ! [X0,X1] :
( empty(sK9(powerset(the_carrier(X0))))
| empty(the_carrier(X0))
| empty(sK9(powerset(sK9(powerset(the_carrier(X0))))))
| element(sK9(sK9(powerset(sK9(powerset(the_carrier(X0)))))),the_carrier(X1))
| ~ subrelstr(X0,X1)
| ~ rel_str(X0)
| ~ rel_str(X1) )
| ~ spl16_119
| ~ spl16_349 ),
inference(resolution,[],[f3579,f881]) ).
fof(f13641,plain,
( spl16_760
| ~ spl16_309
| ~ spl16_341 ),
inference(avatar_split_clause,[],[f3586,f3545,f3098,f13639]) ).
fof(f13639,plain,
( spl16_760
<=> ! [X0,X1] :
( ~ empty(X0)
| empty(sK9(powerset(powerset(X0))))
| sK9(powerset(sK9(sK9(powerset(powerset(X0)))))) = sK9(powerset(sK9(powerset(powerset(X1)))))
| ~ empty(X1)
| sK14 = sK9(powerset(sK9(sK9(powerset(powerset(X1)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_760])]) ).
fof(f3586,plain,
( ! [X0,X1] :
( ~ empty(X0)
| empty(sK9(powerset(powerset(X0))))
| sK9(powerset(sK9(sK9(powerset(powerset(X0)))))) = sK9(powerset(sK9(powerset(powerset(X1)))))
| ~ empty(X1)
| sK14 = sK9(powerset(sK9(sK9(powerset(powerset(X1)))))) )
| ~ spl16_309
| ~ spl16_341 ),
inference(resolution,[],[f3546,f3099]) ).
fof(f13637,plain,
( spl16_759
| ~ spl16_323
| ~ spl16_324 ),
inference(avatar_split_clause,[],[f3337,f3296,f3292,f13635]) ).
fof(f13635,plain,
( spl16_759
<=> ! [X0,X1] :
( ~ empty(X0)
| sK14 = sK9(powerset(sK9(powerset(sK9(sK9(powerset(powerset(X0))))))))
| ~ empty(X1)
| sK9(sK9(powerset(powerset(X1)))) = sK9(powerset(sK9(powerset(powerset(X0)))))
| empty(sK9(powerset(powerset(X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_759])]) ).
fof(f3292,plain,
( spl16_323
<=> ! [X0,X1] :
( empty(sK9(powerset(powerset(X0))))
| ~ empty(X0)
| sK9(powerset(X1)) = sK9(sK9(powerset(powerset(X0))))
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_323])]) ).
fof(f3337,plain,
( ! [X0,X1] :
( ~ empty(X0)
| sK14 = sK9(powerset(sK9(powerset(sK9(sK9(powerset(powerset(X0))))))))
| ~ empty(X1)
| sK9(sK9(powerset(powerset(X1)))) = sK9(powerset(sK9(powerset(powerset(X0)))))
| empty(sK9(powerset(powerset(X1)))) )
| ~ spl16_323
| ~ spl16_324 ),
inference(resolution,[],[f3297,f3293]) ).
fof(f3293,plain,
( ! [X0,X1] :
( ~ empty(X1)
| ~ empty(X0)
| sK9(powerset(X1)) = sK9(sK9(powerset(powerset(X0))))
| empty(sK9(powerset(powerset(X0)))) )
| ~ spl16_323 ),
inference(avatar_component_clause,[],[f3292]) ).
fof(f13011,plain,
( ~ spl16_758
| spl16_715
| ~ spl16_723 ),
inference(avatar_split_clause,[],[f12502,f11862,f10800,f13008]) ).
fof(f10800,plain,
( spl16_715
<=> element(sK9(the_InternalRel(sK8(sK1))),cartesian_product2(sK14,sK14)) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_715])]) ).
fof(f12502,plain,
( ~ element(sK9(sK14),cartesian_product2(sK14,sK14))
| spl16_715
| ~ spl16_723 ),
inference(forward_demodulation,[],[f10801,f11864]) ).
fof(f10801,plain,
( ~ element(sK9(the_InternalRel(sK8(sK1))),cartesian_product2(sK14,sK14))
| spl16_715 ),
inference(avatar_component_clause,[],[f10800]) ).
fof(f12868,plain,
( spl16_757
| ~ spl16_27
| ~ spl16_427 ),
inference(avatar_split_clause,[],[f4919,f4893,f282,f12866]) ).
fof(f12866,plain,
( spl16_757
<=> ! [X0] :
( empty(sK9(sK9(powerset(powerset(X0)))))
| empty(sK9(powerset(sK9(sK9(powerset(powerset(X0)))))))
| empty(X0)
| empty(sK9(powerset(powerset(X0))))
| ~ in(X0,sK9(sK9(powerset(sK9(sK9(powerset(powerset(X0)))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_757])]) ).
fof(f4919,plain,
( ! [X0] :
( empty(sK9(sK9(powerset(powerset(X0)))))
| empty(sK9(powerset(sK9(sK9(powerset(powerset(X0)))))))
| empty(X0)
| empty(sK9(powerset(powerset(X0))))
| ~ in(X0,sK9(sK9(powerset(sK9(sK9(powerset(powerset(X0)))))))) )
| ~ spl16_27
| ~ spl16_427 ),
inference(resolution,[],[f4894,f283]) ).
fof(f12864,plain,
( spl16_756
| ~ spl16_120
| ~ spl16_411 ),
inference(avatar_split_clause,[],[f4463,f4415,f884,f12862]) ).
fof(f12862,plain,
( spl16_756
<=> ! [X2,X0,X1] :
( empty(the_InternalRel(X0))
| ~ subrelstr(X0,X1)
| ~ rel_str(X0)
| ~ rel_str(X1)
| empty(the_InternalRel(X1))
| empty(sK9(powerset(the_InternalRel(X0))))
| element(sK9(sK9(powerset(the_InternalRel(X0)))),the_InternalRel(X2))
| ~ subrelstr(X1,X2)
| ~ rel_str(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_756])]) ).
fof(f4415,plain,
( spl16_411
<=> ! [X0,X1] :
( empty(sK9(powerset(the_InternalRel(X0))))
| empty(the_InternalRel(X0))
| ~ subrelstr(X0,X1)
| ~ rel_str(X0)
| ~ rel_str(X1)
| empty(the_InternalRel(X1))
| in(sK9(sK9(powerset(the_InternalRel(X0)))),the_InternalRel(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_411])]) ).
fof(f4463,plain,
( ! [X2,X0,X1] :
( empty(the_InternalRel(X0))
| ~ subrelstr(X0,X1)
| ~ rel_str(X0)
| ~ rel_str(X1)
| empty(the_InternalRel(X1))
| empty(sK9(powerset(the_InternalRel(X0))))
| element(sK9(sK9(powerset(the_InternalRel(X0)))),the_InternalRel(X2))
| ~ subrelstr(X1,X2)
| ~ rel_str(X2) )
| ~ spl16_120
| ~ spl16_411 ),
inference(duplicate_literal_removal,[],[f4457]) ).
fof(f4457,plain,
( ! [X2,X0,X1] :
( empty(the_InternalRel(X0))
| ~ subrelstr(X0,X1)
| ~ rel_str(X0)
| ~ rel_str(X1)
| empty(the_InternalRel(X1))
| empty(sK9(powerset(the_InternalRel(X0))))
| element(sK9(sK9(powerset(the_InternalRel(X0)))),the_InternalRel(X2))
| ~ subrelstr(X1,X2)
| ~ rel_str(X1)
| ~ rel_str(X2) )
| ~ spl16_120
| ~ spl16_411 ),
inference(resolution,[],[f4416,f885]) ).
fof(f4416,plain,
( ! [X0,X1] :
( in(sK9(sK9(powerset(the_InternalRel(X0)))),the_InternalRel(X1))
| empty(the_InternalRel(X0))
| ~ subrelstr(X0,X1)
| ~ rel_str(X0)
| ~ rel_str(X1)
| empty(the_InternalRel(X1))
| empty(sK9(powerset(the_InternalRel(X0)))) )
| ~ spl16_411 ),
inference(avatar_component_clause,[],[f4415]) ).
fof(f12860,plain,
( spl16_755
| ~ spl16_119
| ~ spl16_410 ),
inference(avatar_split_clause,[],[f4456,f4411,f880,f12858]) ).
fof(f12858,plain,
( spl16_755
<=> ! [X2,X0,X1] :
( empty(the_carrier(X0))
| ~ subrelstr(X0,X1)
| ~ rel_str(X0)
| ~ rel_str(X1)
| empty(the_carrier(X1))
| empty(sK9(powerset(the_carrier(X0))))
| element(sK9(sK9(powerset(the_carrier(X0)))),the_carrier(X2))
| ~ subrelstr(X1,X2)
| ~ rel_str(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_755])]) ).
fof(f4411,plain,
( spl16_410
<=> ! [X0,X1] :
( empty(sK9(powerset(the_carrier(X0))))
| empty(the_carrier(X0))
| ~ subrelstr(X0,X1)
| ~ rel_str(X0)
| ~ rel_str(X1)
| empty(the_carrier(X1))
| in(sK9(sK9(powerset(the_carrier(X0)))),the_carrier(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_410])]) ).
fof(f4456,plain,
( ! [X2,X0,X1] :
( empty(the_carrier(X0))
| ~ subrelstr(X0,X1)
| ~ rel_str(X0)
| ~ rel_str(X1)
| empty(the_carrier(X1))
| empty(sK9(powerset(the_carrier(X0))))
| element(sK9(sK9(powerset(the_carrier(X0)))),the_carrier(X2))
| ~ subrelstr(X1,X2)
| ~ rel_str(X2) )
| ~ spl16_119
| ~ spl16_410 ),
inference(duplicate_literal_removal,[],[f4450]) ).
fof(f4450,plain,
( ! [X2,X0,X1] :
( empty(the_carrier(X0))
| ~ subrelstr(X0,X1)
| ~ rel_str(X0)
| ~ rel_str(X1)
| empty(the_carrier(X1))
| empty(sK9(powerset(the_carrier(X0))))
| element(sK9(sK9(powerset(the_carrier(X0)))),the_carrier(X2))
| ~ subrelstr(X1,X2)
| ~ rel_str(X1)
| ~ rel_str(X2) )
| ~ spl16_119
| ~ spl16_410 ),
inference(resolution,[],[f4412,f881]) ).
fof(f4412,plain,
( ! [X0,X1] :
( in(sK9(sK9(powerset(the_carrier(X0)))),the_carrier(X1))
| empty(the_carrier(X0))
| ~ subrelstr(X0,X1)
| ~ rel_str(X0)
| ~ rel_str(X1)
| empty(the_carrier(X1))
| empty(sK9(powerset(the_carrier(X0)))) )
| ~ spl16_410 ),
inference(avatar_component_clause,[],[f4411]) ).
fof(f12856,plain,
( spl16_754
| ~ spl16_65
| ~ spl16_409 ),
inference(avatar_split_clause,[],[f4434,f4407,f508,f12854]) ).
fof(f12854,plain,
( spl16_754
<=> ! [X0] :
( empty(powerset(powerset(X0)))
| empty(sK9(sK7(powerset(powerset(X0)))))
| element(sK9(sK9(sK9(sK7(powerset(powerset(X0)))))),X0)
| empty(sK7(powerset(powerset(X0))))
| empty(sK9(sK9(sK7(powerset(powerset(X0)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_754])]) ).
fof(f4434,plain,
( ! [X0] :
( empty(powerset(powerset(X0)))
| empty(sK9(sK7(powerset(powerset(X0)))))
| element(sK9(sK9(sK9(sK7(powerset(powerset(X0)))))),X0)
| empty(sK7(powerset(powerset(X0))))
| empty(sK9(sK9(sK7(powerset(powerset(X0)))))) )
| ~ spl16_65
| ~ spl16_409 ),
inference(resolution,[],[f4408,f509]) ).
fof(f12852,plain,
( spl16_753
| ~ spl16_65
| ~ spl16_408 ),
inference(avatar_split_clause,[],[f4418,f4403,f508,f12850]) ).
fof(f12850,plain,
( spl16_753
<=> ! [X0] :
( empty(powerset(powerset(X0)))
| empty(sK9(sK6(powerset(powerset(X0)))))
| element(sK9(sK9(sK9(sK6(powerset(powerset(X0)))))),X0)
| empty(sK6(powerset(powerset(X0))))
| empty(sK9(sK9(sK6(powerset(powerset(X0)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_753])]) ).
fof(f4418,plain,
( ! [X0] :
( empty(powerset(powerset(X0)))
| empty(sK9(sK6(powerset(powerset(X0)))))
| element(sK9(sK9(sK9(sK6(powerset(powerset(X0)))))),X0)
| empty(sK6(powerset(powerset(X0))))
| empty(sK9(sK9(sK6(powerset(powerset(X0)))))) )
| ~ spl16_65
| ~ spl16_408 ),
inference(resolution,[],[f4404,f509]) ).
fof(f12848,plain,
( spl16_752
| ~ spl16_65
| ~ spl16_405 ),
inference(avatar_split_clause,[],[f4354,f4343,f508,f12846]) ).
fof(f12846,plain,
( spl16_752
<=> ! [X0] :
( empty(sK9(sK9(powerset(powerset(powerset(X0))))))
| element(sK9(sK9(sK9(sK9(powerset(powerset(powerset(X0))))))),X0)
| empty(sK9(powerset(powerset(powerset(X0)))))
| empty(sK9(sK9(sK9(powerset(powerset(powerset(X0))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_752])]) ).
fof(f4354,plain,
( ! [X0] :
( empty(sK9(sK9(powerset(powerset(powerset(X0))))))
| element(sK9(sK9(sK9(sK9(powerset(powerset(powerset(X0))))))),X0)
| empty(sK9(powerset(powerset(powerset(X0)))))
| empty(sK9(sK9(sK9(powerset(powerset(powerset(X0))))))) )
| ~ spl16_65
| ~ spl16_405 ),
inference(resolution,[],[f4344,f509]) ).
fof(f12844,plain,
( spl16_751
| ~ spl16_72
| ~ spl16_364 ),
inference(avatar_split_clause,[],[f3872,f3678,f549,f12842]) ).
fof(f12842,plain,
( spl16_751
<=> ! [X0] :
( empty(powerset(sK9(powerset(X0))))
| empty(sK9(sK7(powerset(sK9(powerset(X0))))))
| empty(sK9(powerset(X0)))
| empty(sK7(powerset(sK9(powerset(X0)))))
| element(sK9(sK9(sK7(powerset(sK9(powerset(X0)))))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_751])]) ).
fof(f3872,plain,
( ! [X0] :
( empty(powerset(sK9(powerset(X0))))
| empty(sK9(sK7(powerset(sK9(powerset(X0))))))
| empty(sK9(powerset(X0)))
| empty(sK7(powerset(sK9(powerset(X0)))))
| element(sK9(sK9(sK7(powerset(sK9(powerset(X0)))))),X0) )
| ~ spl16_72
| ~ spl16_364 ),
inference(resolution,[],[f3679,f550]) ).
fof(f12840,plain,
( spl16_750
| ~ spl16_72
| ~ spl16_363 ),
inference(avatar_split_clause,[],[f3845,f3674,f549,f12838]) ).
fof(f12838,plain,
( spl16_750
<=> ! [X0] :
( empty(powerset(sK9(powerset(X0))))
| empty(sK9(sK6(powerset(sK9(powerset(X0))))))
| empty(sK9(powerset(X0)))
| empty(sK6(powerset(sK9(powerset(X0)))))
| element(sK9(sK9(sK6(powerset(sK9(powerset(X0)))))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_750])]) ).
fof(f3845,plain,
( ! [X0] :
( empty(powerset(sK9(powerset(X0))))
| empty(sK9(sK6(powerset(sK9(powerset(X0))))))
| empty(sK9(powerset(X0)))
| empty(sK6(powerset(sK9(powerset(X0)))))
| element(sK9(sK9(sK6(powerset(sK9(powerset(X0)))))),X0) )
| ~ spl16_72
| ~ spl16_363 ),
inference(resolution,[],[f3675,f550]) ).
fof(f12836,plain,
( spl16_749
| ~ spl16_110
| ~ spl16_362 ),
inference(avatar_split_clause,[],[f3834,f3670,f799,f12834]) ).
fof(f12834,plain,
( spl16_749
<=> ! [X0,X1] :
( empty(sK9(sK9(powerset(powerset(sK11(X0,X1))))))
| empty(sK11(X0,X1))
| empty(sK9(powerset(powerset(sK11(X0,X1)))))
| element(sK9(sK9(sK9(powerset(powerset(sK11(X0,X1)))))),cartesian_product2(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_749])]) ).
fof(f3834,plain,
( ! [X0,X1] :
( empty(sK9(sK9(powerset(powerset(sK11(X0,X1))))))
| empty(sK11(X0,X1))
| empty(sK9(powerset(powerset(sK11(X0,X1)))))
| element(sK9(sK9(sK9(powerset(powerset(sK11(X0,X1)))))),cartesian_product2(X0,X1)) )
| ~ spl16_110
| ~ spl16_362 ),
inference(resolution,[],[f3671,f800]) ).
fof(f12832,plain,
( spl16_748
| ~ spl16_111
| ~ spl16_362 ),
inference(avatar_split_clause,[],[f3832,f3670,f803,f12830]) ).
fof(f12830,plain,
( spl16_748
<=> ! [X0,X1] :
( empty(sK9(sK9(powerset(powerset(sK10(X0,X1))))))
| empty(sK10(X0,X1))
| empty(sK9(powerset(powerset(sK10(X0,X1)))))
| element(sK9(sK9(sK9(powerset(powerset(sK10(X0,X1)))))),cartesian_product2(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_748])]) ).
fof(f3832,plain,
( ! [X0,X1] :
( empty(sK9(sK9(powerset(powerset(sK10(X0,X1))))))
| empty(sK10(X0,X1))
| empty(sK9(powerset(powerset(sK10(X0,X1)))))
| element(sK9(sK9(sK9(powerset(powerset(sK10(X0,X1)))))),cartesian_product2(X0,X1)) )
| ~ spl16_111
| ~ spl16_362 ),
inference(resolution,[],[f3671,f804]) ).
fof(f12828,plain,
( spl16_747
| ~ spl16_215
| ~ spl16_351 ),
inference(avatar_split_clause,[],[f3706,f3626,f1961,f12826]) ).
fof(f12826,plain,
( spl16_747
<=> ! [X0,X1] :
( empty(powerset(X0))
| empty(sK7(powerset(X0)))
| ~ empty(X0)
| sK9(powerset(sK9(sK7(powerset(X0))))) = sK9(powerset(sK9(sK7(powerset(X1)))))
| ~ empty(X1)
| empty(powerset(X1))
| empty(sK7(powerset(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_747])]) ).
fof(f1961,plain,
( spl16_215
<=> ! [X0] :
( empty(sK7(powerset(X0)))
| ~ empty(X0)
| empty(powerset(X0))
| empty(sK9(sK7(powerset(X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_215])]) ).
fof(f3706,plain,
( ! [X0,X1] :
( empty(powerset(X0))
| empty(sK7(powerset(X0)))
| ~ empty(X0)
| sK9(powerset(sK9(sK7(powerset(X0))))) = sK9(powerset(sK9(sK7(powerset(X1)))))
| ~ empty(X1)
| empty(powerset(X1))
| empty(sK7(powerset(X1))) )
| ~ spl16_215
| ~ spl16_351 ),
inference(resolution,[],[f3627,f1962]) ).
fof(f1962,plain,
( ! [X0] :
( empty(sK9(sK7(powerset(X0))))
| ~ empty(X0)
| empty(powerset(X0))
| empty(sK7(powerset(X0))) )
| ~ spl16_215 ),
inference(avatar_component_clause,[],[f1961]) ).
fof(f12824,plain,
( spl16_746
| ~ spl16_286
| ~ spl16_351 ),
inference(avatar_split_clause,[],[f3704,f3626,f2727,f12822]) ).
fof(f12822,plain,
( spl16_746
<=> ! [X0,X1] :
( empty(powerset(X0))
| empty(sK7(powerset(X0)))
| ~ empty(X0)
| sK9(powerset(sK9(sK7(powerset(X0))))) = sK9(powerset(sK9(powerset(powerset(X1)))))
| sK14 = sK9(sK9(powerset(powerset(X1))))
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_746])]) ).
fof(f2727,plain,
( spl16_286
<=> ! [X0] :
( sK14 = sK9(sK9(powerset(powerset(X0))))
| empty(sK9(powerset(powerset(X0))))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_286])]) ).
fof(f3704,plain,
( ! [X0,X1] :
( empty(powerset(X0))
| empty(sK7(powerset(X0)))
| ~ empty(X0)
| sK9(powerset(sK9(sK7(powerset(X0))))) = sK9(powerset(sK9(powerset(powerset(X1)))))
| sK14 = sK9(sK9(powerset(powerset(X1))))
| ~ empty(X1) )
| ~ spl16_286
| ~ spl16_351 ),
inference(resolution,[],[f3627,f2728]) ).
fof(f2728,plain,
( ! [X0] :
( empty(sK9(powerset(powerset(X0))))
| sK14 = sK9(sK9(powerset(powerset(X0))))
| ~ empty(X0) )
| ~ spl16_286 ),
inference(avatar_component_clause,[],[f2727]) ).
fof(f12820,plain,
( spl16_745
| ~ spl16_215
| ~ spl16_350 ),
inference(avatar_split_clause,[],[f3689,f3622,f1961,f12818]) ).
fof(f12818,plain,
( spl16_745
<=> ! [X0,X1] :
( empty(powerset(X0))
| empty(sK6(powerset(X0)))
| ~ empty(X0)
| sK9(powerset(sK9(sK6(powerset(X0))))) = sK9(powerset(sK9(sK7(powerset(X1)))))
| ~ empty(X1)
| empty(powerset(X1))
| empty(sK7(powerset(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_745])]) ).
fof(f3689,plain,
( ! [X0,X1] :
( empty(powerset(X0))
| empty(sK6(powerset(X0)))
| ~ empty(X0)
| sK9(powerset(sK9(sK6(powerset(X0))))) = sK9(powerset(sK9(sK7(powerset(X1)))))
| ~ empty(X1)
| empty(powerset(X1))
| empty(sK7(powerset(X1))) )
| ~ spl16_215
| ~ spl16_350 ),
inference(resolution,[],[f3623,f1962]) ).
fof(f12816,plain,
( spl16_744
| ~ spl16_214
| ~ spl16_350 ),
inference(avatar_split_clause,[],[f3688,f3622,f1955,f12814]) ).
fof(f12814,plain,
( spl16_744
<=> ! [X0,X1] :
( empty(powerset(X0))
| empty(sK6(powerset(X0)))
| ~ empty(X0)
| sK9(powerset(sK9(sK6(powerset(X0))))) = sK9(powerset(sK9(sK6(powerset(X1)))))
| ~ empty(X1)
| empty(powerset(X1))
| empty(sK6(powerset(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_744])]) ).
fof(f1955,plain,
( spl16_214
<=> ! [X0] :
( empty(sK6(powerset(X0)))
| ~ empty(X0)
| empty(powerset(X0))
| empty(sK9(sK6(powerset(X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_214])]) ).
fof(f3688,plain,
( ! [X0,X1] :
( empty(powerset(X0))
| empty(sK6(powerset(X0)))
| ~ empty(X0)
| sK9(powerset(sK9(sK6(powerset(X0))))) = sK9(powerset(sK9(sK6(powerset(X1)))))
| ~ empty(X1)
| empty(powerset(X1))
| empty(sK6(powerset(X1))) )
| ~ spl16_214
| ~ spl16_350 ),
inference(resolution,[],[f3623,f1956]) ).
fof(f1956,plain,
( ! [X0] :
( empty(sK9(sK6(powerset(X0))))
| ~ empty(X0)
| empty(powerset(X0))
| empty(sK6(powerset(X0))) )
| ~ spl16_214 ),
inference(avatar_component_clause,[],[f1955]) ).
fof(f12812,plain,
( spl16_743
| ~ spl16_286
| ~ spl16_350 ),
inference(avatar_split_clause,[],[f3687,f3622,f2727,f12810]) ).
fof(f12810,plain,
( spl16_743
<=> ! [X0,X1] :
( empty(powerset(X0))
| empty(sK6(powerset(X0)))
| ~ empty(X0)
| sK9(powerset(sK9(sK6(powerset(X0))))) = sK9(powerset(sK9(powerset(powerset(X1)))))
| sK14 = sK9(sK9(powerset(powerset(X1))))
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_743])]) ).
fof(f3687,plain,
( ! [X0,X1] :
( empty(powerset(X0))
| empty(sK6(powerset(X0)))
| ~ empty(X0)
| sK9(powerset(sK9(sK6(powerset(X0))))) = sK9(powerset(sK9(powerset(powerset(X1)))))
| sK14 = sK9(sK9(powerset(powerset(X1))))
| ~ empty(X1) )
| ~ spl16_286
| ~ spl16_350 ),
inference(resolution,[],[f3623,f2728]) ).
fof(f12808,plain,
( spl16_742
| ~ spl16_309
| ~ spl16_331 ),
inference(avatar_split_clause,[],[f3489,f3402,f3098,f12806]) ).
fof(f12806,plain,
( spl16_742
<=> ! [X0,X1] :
( empty(powerset(X0))
| empty(sK7(powerset(X0)))
| sK9(sK7(powerset(X0))) = sK9(powerset(sK9(powerset(powerset(X1)))))
| ~ empty(X0)
| ~ empty(X1)
| sK14 = sK9(powerset(sK9(sK9(powerset(powerset(X1)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_742])]) ).
fof(f3489,plain,
( ! [X0,X1] :
( empty(powerset(X0))
| empty(sK7(powerset(X0)))
| sK9(sK7(powerset(X0))) = sK9(powerset(sK9(powerset(powerset(X1)))))
| ~ empty(X0)
| ~ empty(X1)
| sK14 = sK9(powerset(sK9(sK9(powerset(powerset(X1)))))) )
| ~ spl16_309
| ~ spl16_331 ),
inference(resolution,[],[f3403,f3099]) ).
fof(f12804,plain,
( spl16_741
| ~ spl16_309
| ~ spl16_329 ),
inference(avatar_split_clause,[],[f3455,f3394,f3098,f12802]) ).
fof(f12802,plain,
( spl16_741
<=> ! [X0,X1] :
( empty(powerset(X0))
| empty(sK6(powerset(X0)))
| sK9(sK6(powerset(X0))) = sK9(powerset(sK9(powerset(powerset(X1)))))
| ~ empty(X0)
| ~ empty(X1)
| sK14 = sK9(powerset(sK9(sK9(powerset(powerset(X1)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_741])]) ).
fof(f3455,plain,
( ! [X0,X1] :
( empty(powerset(X0))
| empty(sK6(powerset(X0)))
| sK9(sK6(powerset(X0))) = sK9(powerset(sK9(powerset(powerset(X1)))))
| ~ empty(X0)
| ~ empty(X1)
| sK14 = sK9(powerset(sK9(sK9(powerset(powerset(X1)))))) )
| ~ spl16_309
| ~ spl16_329 ),
inference(resolution,[],[f3395,f3099]) ).
fof(f12712,plain,
( spl16_740
| ~ spl16_318
| ~ spl16_324 ),
inference(avatar_split_clause,[],[f3336,f3296,f3163,f12710]) ).
fof(f12710,plain,
( spl16_740
<=> ! [X0,X1] :
( ~ empty(X0)
| sK14 = sK9(powerset(sK9(powerset(sK9(sK9(powerset(powerset(X0))))))))
| empty(powerset(X1))
| empty(sK7(powerset(X1)))
| sK9(powerset(powerset(X0))) = sK9(sK7(powerset(X1)))
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_740])]) ).
fof(f3163,plain,
( spl16_318
<=> ! [X0,X1] :
( ~ empty(X0)
| empty(powerset(X0))
| empty(sK7(powerset(X0)))
| sK9(sK7(powerset(X0))) = X1
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_318])]) ).
fof(f3336,plain,
( ! [X0,X1] :
( ~ empty(X0)
| sK14 = sK9(powerset(sK9(powerset(sK9(sK9(powerset(powerset(X0))))))))
| empty(powerset(X1))
| empty(sK7(powerset(X1)))
| sK9(powerset(powerset(X0))) = sK9(sK7(powerset(X1)))
| ~ empty(X1) )
| ~ spl16_318
| ~ spl16_324 ),
inference(resolution,[],[f3297,f3164]) ).
fof(f3164,plain,
( ! [X0,X1] :
( ~ empty(X1)
| empty(powerset(X0))
| empty(sK7(powerset(X0)))
| sK9(sK7(powerset(X0))) = X1
| ~ empty(X0) )
| ~ spl16_318 ),
inference(avatar_component_clause,[],[f3163]) ).
fof(f12708,plain,
( spl16_739
| ~ spl16_316
| ~ spl16_324 ),
inference(avatar_split_clause,[],[f3335,f3296,f3155,f12706]) ).
fof(f12706,plain,
( spl16_739
<=> ! [X0,X1] :
( ~ empty(X0)
| sK14 = sK9(powerset(sK9(powerset(sK9(sK9(powerset(powerset(X0))))))))
| empty(powerset(X1))
| empty(sK6(powerset(X1)))
| sK9(powerset(powerset(X0))) = sK9(sK6(powerset(X1)))
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_739])]) ).
fof(f3155,plain,
( spl16_316
<=> ! [X0,X1] :
( ~ empty(X0)
| empty(powerset(X0))
| empty(sK6(powerset(X0)))
| sK9(sK6(powerset(X0))) = X1
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_316])]) ).
fof(f3335,plain,
( ! [X0,X1] :
( ~ empty(X0)
| sK14 = sK9(powerset(sK9(powerset(sK9(sK9(powerset(powerset(X0))))))))
| empty(powerset(X1))
| empty(sK6(powerset(X1)))
| sK9(powerset(powerset(X0))) = sK9(sK6(powerset(X1)))
| ~ empty(X1) )
| ~ spl16_316
| ~ spl16_324 ),
inference(resolution,[],[f3297,f3156]) ).
fof(f3156,plain,
( ! [X0,X1] :
( ~ empty(X1)
| empty(powerset(X0))
| empty(sK6(powerset(X0)))
| sK9(sK6(powerset(X0))) = X1
| ~ empty(X0) )
| ~ spl16_316 ),
inference(avatar_component_clause,[],[f3155]) ).
fof(f12501,plain,
( spl16_96
| ~ spl16_65
| ~ spl16_164 ),
inference(avatar_split_clause,[],[f12474,f1365,f508,f725]) ).
fof(f725,plain,
( spl16_96
<=> empty(the_InternalRel(sK1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_96])]) ).
fof(f1365,plain,
( spl16_164
<=> ! [X0] : ~ in(X0,the_InternalRel(sK1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_164])]) ).
fof(f12474,plain,
( empty(the_InternalRel(sK1))
| ~ spl16_65
| ~ spl16_164 ),
inference(resolution,[],[f1366,f509]) ).
fof(f1366,plain,
( ! [X0] : ~ in(X0,the_InternalRel(sK1))
| ~ spl16_164 ),
inference(avatar_component_clause,[],[f1365]) ).
fof(f12414,plain,
( spl16_738
| spl16_165
| ~ spl16_38
| ~ spl16_715 ),
inference(avatar_split_clause,[],[f12078,f10800,f335,f1368,f12411]) ).
fof(f12078,plain,
( empty(cartesian_product2(sK14,sK14))
| in(sK9(the_InternalRel(sK8(sK1))),cartesian_product2(sK14,sK14))
| ~ spl16_38
| ~ spl16_715 ),
inference(resolution,[],[f10802,f336]) ).
fof(f10802,plain,
( element(sK9(the_InternalRel(sK8(sK1))),cartesian_product2(sK14,sK14))
| ~ spl16_715 ),
inference(avatar_component_clause,[],[f10800]) ).
fof(f11982,plain,
( spl16_737
| ~ spl16_27
| ~ spl16_420 ),
inference(avatar_split_clause,[],[f4816,f4767,f282,f11980]) ).
fof(f11980,plain,
( spl16_737
<=> ! [X0] :
( empty(powerset(X0))
| empty(sK9(sK7(powerset(X0))))
| empty(sK9(powerset(sK9(sK7(powerset(X0))))))
| empty(X0)
| empty(sK7(powerset(X0)))
| ~ in(X0,sK9(sK9(powerset(sK9(sK7(powerset(X0))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_737])]) ).
fof(f4816,plain,
( ! [X0] :
( empty(powerset(X0))
| empty(sK9(sK7(powerset(X0))))
| empty(sK9(powerset(sK9(sK7(powerset(X0))))))
| empty(X0)
| empty(sK7(powerset(X0)))
| ~ in(X0,sK9(sK9(powerset(sK9(sK7(powerset(X0))))))) )
| ~ spl16_27
| ~ spl16_420 ),
inference(resolution,[],[f4768,f283]) ).
fof(f11978,plain,
( spl16_736
| ~ spl16_27
| ~ spl16_419 ),
inference(avatar_split_clause,[],[f4771,f4763,f282,f11976]) ).
fof(f11976,plain,
( spl16_736
<=> ! [X0] :
( empty(powerset(X0))
| empty(sK9(sK6(powerset(X0))))
| empty(sK9(powerset(sK9(sK6(powerset(X0))))))
| empty(X0)
| empty(sK6(powerset(X0)))
| ~ in(X0,sK9(sK9(powerset(sK9(sK6(powerset(X0))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_736])]) ).
fof(f4771,plain,
( ! [X0] :
( empty(powerset(X0))
| empty(sK9(sK6(powerset(X0))))
| empty(sK9(powerset(sK9(sK6(powerset(X0))))))
| empty(X0)
| empty(sK6(powerset(X0)))
| ~ in(X0,sK9(sK9(powerset(sK9(sK6(powerset(X0))))))) )
| ~ spl16_27
| ~ spl16_419 ),
inference(resolution,[],[f4764,f283]) ).
fof(f11974,plain,
( spl16_735
| ~ spl16_65
| ~ spl16_390 ),
inference(avatar_split_clause,[],[f4252,f4167,f508,f11972]) ).
fof(f11972,plain,
( spl16_735
<=> ! [X0] :
( empty(sK9(powerset(powerset(X0))))
| element(sK9(sK9(sK9(powerset(sK9(powerset(powerset(X0))))))),X0)
| empty(sK9(powerset(sK9(powerset(powerset(X0))))))
| empty(sK9(sK9(powerset(sK9(powerset(powerset(X0))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_735])]) ).
fof(f4252,plain,
( ! [X0] :
( empty(sK9(powerset(powerset(X0))))
| element(sK9(sK9(sK9(powerset(sK9(powerset(powerset(X0))))))),X0)
| empty(sK9(powerset(sK9(powerset(powerset(X0))))))
| empty(sK9(sK9(powerset(sK9(powerset(powerset(X0))))))) )
| ~ spl16_65
| ~ spl16_390 ),
inference(resolution,[],[f4168,f509]) ).
fof(f11970,plain,
( spl16_734
| ~ spl16_110
| ~ spl16_349 ),
inference(avatar_split_clause,[],[f3617,f3578,f799,f11968]) ).
fof(f11968,plain,
( spl16_734
<=> ! [X0,X1] :
( empty(sK9(powerset(sK11(X0,X1))))
| empty(sK11(X0,X1))
| empty(sK9(powerset(sK9(powerset(sK11(X0,X1))))))
| element(sK9(sK9(powerset(sK9(powerset(sK11(X0,X1)))))),cartesian_product2(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_734])]) ).
fof(f3617,plain,
( ! [X0,X1] :
( empty(sK9(powerset(sK11(X0,X1))))
| empty(sK11(X0,X1))
| empty(sK9(powerset(sK9(powerset(sK11(X0,X1))))))
| element(sK9(sK9(powerset(sK9(powerset(sK11(X0,X1)))))),cartesian_product2(X0,X1)) )
| ~ spl16_110
| ~ spl16_349 ),
inference(resolution,[],[f3579,f800]) ).
fof(f11966,plain,
( spl16_733
| ~ spl16_111
| ~ spl16_349 ),
inference(avatar_split_clause,[],[f3615,f3578,f803,f11964]) ).
fof(f11964,plain,
( spl16_733
<=> ! [X0,X1] :
( empty(sK9(powerset(sK10(X0,X1))))
| empty(sK10(X0,X1))
| empty(sK9(powerset(sK9(powerset(sK10(X0,X1))))))
| element(sK9(sK9(powerset(sK9(powerset(sK10(X0,X1)))))),cartesian_product2(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_733])]) ).
fof(f3615,plain,
( ! [X0,X1] :
( empty(sK9(powerset(sK10(X0,X1))))
| empty(sK10(X0,X1))
| empty(sK9(powerset(sK9(powerset(sK10(X0,X1))))))
| element(sK9(sK9(powerset(sK9(powerset(sK10(X0,X1)))))),cartesian_product2(X0,X1)) )
| ~ spl16_111
| ~ spl16_349 ),
inference(resolution,[],[f3579,f804]) ).
fof(f11962,plain,
( spl16_732
| ~ spl16_215
| ~ spl16_341 ),
inference(avatar_split_clause,[],[f3589,f3545,f1961,f11960]) ).
fof(f11960,plain,
( spl16_732
<=> ! [X0,X1] :
( ~ empty(X0)
| empty(sK9(powerset(powerset(X0))))
| sK9(powerset(sK9(sK9(powerset(powerset(X0)))))) = sK9(powerset(sK9(sK7(powerset(X1)))))
| ~ empty(X1)
| empty(powerset(X1))
| empty(sK7(powerset(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_732])]) ).
fof(f3589,plain,
( ! [X0,X1] :
( ~ empty(X0)
| empty(sK9(powerset(powerset(X0))))
| sK9(powerset(sK9(sK9(powerset(powerset(X0)))))) = sK9(powerset(sK9(sK7(powerset(X1)))))
| ~ empty(X1)
| empty(powerset(X1))
| empty(sK7(powerset(X1))) )
| ~ spl16_215
| ~ spl16_341 ),
inference(resolution,[],[f3546,f1962]) ).
fof(f11958,plain,
( spl16_731
| ~ spl16_214
| ~ spl16_341 ),
inference(avatar_split_clause,[],[f3588,f3545,f1955,f11956]) ).
fof(f11956,plain,
( spl16_731
<=> ! [X0,X1] :
( ~ empty(X0)
| empty(sK9(powerset(powerset(X0))))
| sK9(powerset(sK9(sK9(powerset(powerset(X0)))))) = sK9(powerset(sK9(sK6(powerset(X1)))))
| ~ empty(X1)
| empty(powerset(X1))
| empty(sK6(powerset(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_731])]) ).
fof(f3588,plain,
( ! [X0,X1] :
( ~ empty(X0)
| empty(sK9(powerset(powerset(X0))))
| sK9(powerset(sK9(sK9(powerset(powerset(X0)))))) = sK9(powerset(sK9(sK6(powerset(X1)))))
| ~ empty(X1)
| empty(powerset(X1))
| empty(sK6(powerset(X1))) )
| ~ spl16_214
| ~ spl16_341 ),
inference(resolution,[],[f3546,f1956]) ).
fof(f11954,plain,
( spl16_730
| ~ spl16_286
| ~ spl16_341 ),
inference(avatar_split_clause,[],[f3587,f3545,f2727,f11952]) ).
fof(f11952,plain,
( spl16_730
<=> ! [X0,X1] :
( ~ empty(X0)
| empty(sK9(powerset(powerset(X0))))
| sK9(powerset(sK9(sK9(powerset(powerset(X0)))))) = sK9(powerset(sK9(powerset(powerset(X1)))))
| sK14 = sK9(sK9(powerset(powerset(X1))))
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_730])]) ).
fof(f3587,plain,
( ! [X0,X1] :
( ~ empty(X0)
| empty(sK9(powerset(powerset(X0))))
| sK9(powerset(sK9(sK9(powerset(powerset(X0)))))) = sK9(powerset(sK9(powerset(powerset(X1)))))
| sK14 = sK9(sK9(powerset(powerset(X1))))
| ~ empty(X1) )
| ~ spl16_286
| ~ spl16_341 ),
inference(resolution,[],[f3546,f2728]) ).
fof(f11950,plain,
( spl16_729
| ~ spl16_120
| ~ spl16_326 ),
inference(avatar_split_clause,[],[f3367,f3305,f884,f11948]) ).
fof(f11948,plain,
( spl16_729
<=> ! [X0,X1] :
( empty(sK7(sK9(powerset(the_InternalRel(X0)))))
| empty(the_InternalRel(X0))
| empty(sK9(powerset(the_InternalRel(X0))))
| element(sK9(sK7(sK9(powerset(the_InternalRel(X0))))),the_InternalRel(X1))
| ~ subrelstr(X0,X1)
| ~ rel_str(X0)
| ~ rel_str(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_729])]) ).
fof(f3367,plain,
( ! [X0,X1] :
( empty(sK7(sK9(powerset(the_InternalRel(X0)))))
| empty(the_InternalRel(X0))
| empty(sK9(powerset(the_InternalRel(X0))))
| element(sK9(sK7(sK9(powerset(the_InternalRel(X0))))),the_InternalRel(X1))
| ~ subrelstr(X0,X1)
| ~ rel_str(X0)
| ~ rel_str(X1) )
| ~ spl16_120
| ~ spl16_326 ),
inference(resolution,[],[f3306,f885]) ).
fof(f11946,plain,
( spl16_728
| ~ spl16_119
| ~ spl16_326 ),
inference(avatar_split_clause,[],[f3365,f3305,f880,f11944]) ).
fof(f11944,plain,
( spl16_728
<=> ! [X0,X1] :
( empty(sK7(sK9(powerset(the_carrier(X0)))))
| empty(the_carrier(X0))
| empty(sK9(powerset(the_carrier(X0))))
| element(sK9(sK7(sK9(powerset(the_carrier(X0))))),the_carrier(X1))
| ~ subrelstr(X0,X1)
| ~ rel_str(X0)
| ~ rel_str(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_728])]) ).
fof(f3365,plain,
( ! [X0,X1] :
( empty(sK7(sK9(powerset(the_carrier(X0)))))
| empty(the_carrier(X0))
| empty(sK9(powerset(the_carrier(X0))))
| element(sK9(sK7(sK9(powerset(the_carrier(X0))))),the_carrier(X1))
| ~ subrelstr(X0,X1)
| ~ rel_str(X0)
| ~ rel_str(X1) )
| ~ spl16_119
| ~ spl16_326 ),
inference(resolution,[],[f3306,f881]) ).
fof(f11942,plain,
( spl16_727
| ~ spl16_120
| ~ spl16_325 ),
inference(avatar_split_clause,[],[f3344,f3300,f884,f11940]) ).
fof(f11940,plain,
( spl16_727
<=> ! [X0,X1] :
( empty(sK6(sK9(powerset(the_InternalRel(X0)))))
| empty(the_InternalRel(X0))
| empty(sK9(powerset(the_InternalRel(X0))))
| element(sK9(sK6(sK9(powerset(the_InternalRel(X0))))),the_InternalRel(X1))
| ~ subrelstr(X0,X1)
| ~ rel_str(X0)
| ~ rel_str(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_727])]) ).
fof(f3344,plain,
( ! [X0,X1] :
( empty(sK6(sK9(powerset(the_InternalRel(X0)))))
| empty(the_InternalRel(X0))
| empty(sK9(powerset(the_InternalRel(X0))))
| element(sK9(sK6(sK9(powerset(the_InternalRel(X0))))),the_InternalRel(X1))
| ~ subrelstr(X0,X1)
| ~ rel_str(X0)
| ~ rel_str(X1) )
| ~ spl16_120
| ~ spl16_325 ),
inference(resolution,[],[f3301,f885]) ).
fof(f11938,plain,
( spl16_726
| ~ spl16_119
| ~ spl16_325 ),
inference(avatar_split_clause,[],[f3342,f3300,f880,f11936]) ).
fof(f11936,plain,
( spl16_726
<=> ! [X0,X1] :
( empty(sK6(sK9(powerset(the_carrier(X0)))))
| empty(the_carrier(X0))
| empty(sK9(powerset(the_carrier(X0))))
| element(sK9(sK6(sK9(powerset(the_carrier(X0))))),the_carrier(X1))
| ~ subrelstr(X0,X1)
| ~ rel_str(X0)
| ~ rel_str(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_726])]) ).
fof(f3342,plain,
( ! [X0,X1] :
( empty(sK6(sK9(powerset(the_carrier(X0)))))
| empty(the_carrier(X0))
| empty(sK9(powerset(the_carrier(X0))))
| element(sK9(sK6(sK9(powerset(the_carrier(X0))))),the_carrier(X1))
| ~ subrelstr(X0,X1)
| ~ rel_str(X0)
| ~ rel_str(X1) )
| ~ spl16_119
| ~ spl16_325 ),
inference(resolution,[],[f3301,f881]) ).
fof(f11934,plain,
( spl16_725
| ~ spl16_308
| ~ spl16_324 ),
inference(avatar_split_clause,[],[f3334,f3296,f3093,f11932]) ).
fof(f11932,plain,
( spl16_725
<=> ! [X0,X1] :
( ~ empty(X0)
| sK14 = sK9(powerset(sK9(powerset(sK9(sK9(powerset(powerset(X0))))))))
| ~ empty(X1)
| sK9(powerset(powerset(X0))) = sK9(sK9(powerset(powerset(X1))))
| empty(sK9(powerset(powerset(X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_725])]) ).
fof(f3093,plain,
( spl16_308
<=> ! [X0,X1] :
( empty(sK9(powerset(powerset(X0))))
| ~ empty(X0)
| sK9(sK9(powerset(powerset(X0)))) = X1
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_308])]) ).
fof(f3334,plain,
( ! [X0,X1] :
( ~ empty(X0)
| sK14 = sK9(powerset(sK9(powerset(sK9(sK9(powerset(powerset(X0))))))))
| ~ empty(X1)
| sK9(powerset(powerset(X0))) = sK9(sK9(powerset(powerset(X1))))
| empty(sK9(powerset(powerset(X1)))) )
| ~ spl16_308
| ~ spl16_324 ),
inference(resolution,[],[f3297,f3094]) ).
fof(f3094,plain,
( ! [X0,X1] :
( ~ empty(X1)
| ~ empty(X0)
| sK9(sK9(powerset(powerset(X0)))) = X1
| empty(sK9(powerset(powerset(X0)))) )
| ~ spl16_308 ),
inference(avatar_component_clause,[],[f3093]) ).
fof(f11930,plain,
( spl16_724
| ~ spl16_309
| ~ spl16_323 ),
inference(avatar_split_clause,[],[f3312,f3292,f3098,f11928]) ).
fof(f11928,plain,
( spl16_724
<=> ! [X0,X1] :
( ~ empty(X0)
| sK9(sK9(powerset(powerset(X0)))) = sK9(powerset(sK9(powerset(powerset(X1)))))
| empty(sK9(powerset(powerset(X0))))
| ~ empty(X1)
| sK14 = sK9(powerset(sK9(sK9(powerset(powerset(X1)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_724])]) ).
fof(f3312,plain,
( ! [X0,X1] :
( ~ empty(X0)
| sK9(sK9(powerset(powerset(X0)))) = sK9(powerset(sK9(powerset(powerset(X1)))))
| empty(sK9(powerset(powerset(X0))))
| ~ empty(X1)
| sK14 = sK9(powerset(sK9(sK9(powerset(powerset(X1)))))) )
| ~ spl16_309
| ~ spl16_323 ),
inference(resolution,[],[f3293,f3099]) ).
fof(f11865,plain,
( spl16_723
| ~ spl16_23
| ~ spl16_57
| ~ spl16_714 ),
inference(avatar_split_clause,[],[f10990,f10796,f469,f263,f11862]) ).
fof(f10990,plain,
( sK14 = the_InternalRel(sK8(sK1))
| ~ spl16_23
| ~ spl16_57
| ~ spl16_714 ),
inference(forward_demodulation,[],[f10930,f471]) ).
fof(f10930,plain,
( empty_set = the_InternalRel(sK8(sK1))
| ~ spl16_23
| ~ spl16_714 ),
inference(resolution,[],[f10798,f264]) ).
fof(f10831,plain,
( spl16_722
| ~ spl16_27
| ~ spl16_418 ),
inference(avatar_split_clause,[],[f4718,f4669,f282,f10829]) ).
fof(f10829,plain,
( spl16_722
<=> ! [X0] :
( empty(sK7(sK9(sK9(powerset(powerset(X0))))))
| empty(sK9(sK9(powerset(powerset(X0)))))
| empty(X0)
| empty(sK9(powerset(powerset(X0))))
| ~ in(X0,sK9(sK7(sK9(sK9(powerset(powerset(X0))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_722])]) ).
fof(f4718,plain,
( ! [X0] :
( empty(sK7(sK9(sK9(powerset(powerset(X0))))))
| empty(sK9(sK9(powerset(powerset(X0)))))
| empty(X0)
| empty(sK9(powerset(powerset(X0))))
| ~ in(X0,sK9(sK7(sK9(sK9(powerset(powerset(X0))))))) )
| ~ spl16_27
| ~ spl16_418 ),
inference(resolution,[],[f4670,f283]) ).
fof(f10827,plain,
( spl16_721
| ~ spl16_27
| ~ spl16_417 ),
inference(avatar_split_clause,[],[f4673,f4665,f282,f10825]) ).
fof(f10825,plain,
( spl16_721
<=> ! [X0] :
( empty(sK6(sK9(sK9(powerset(powerset(X0))))))
| empty(sK9(sK9(powerset(powerset(X0)))))
| empty(X0)
| empty(sK9(powerset(powerset(X0))))
| ~ in(X0,sK9(sK6(sK9(sK9(powerset(powerset(X0))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_721])]) ).
fof(f4673,plain,
( ! [X0] :
( empty(sK6(sK9(sK9(powerset(powerset(X0))))))
| empty(sK9(sK9(powerset(powerset(X0)))))
| empty(X0)
| empty(sK9(powerset(powerset(X0))))
| ~ in(X0,sK9(sK6(sK9(sK9(powerset(powerset(X0))))))) )
| ~ spl16_27
| ~ spl16_417 ),
inference(resolution,[],[f4666,f283]) ).
fof(f10823,plain,
( spl16_720
| ~ spl16_120
| ~ spl16_401 ),
inference(avatar_split_clause,[],[f4341,f4213,f884,f10821]) ).
fof(f10821,plain,
( spl16_720
<=> ! [X2,X0,X1] :
( empty(sK7(the_InternalRel(X0)))
| ~ subrelstr(X0,X1)
| ~ rel_str(X0)
| ~ rel_str(X1)
| empty(the_InternalRel(X1))
| empty(the_InternalRel(X0))
| element(sK9(sK7(the_InternalRel(X0))),the_InternalRel(X2))
| ~ subrelstr(X1,X2)
| ~ rel_str(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_720])]) ).
fof(f4213,plain,
( spl16_401
<=> ! [X0,X1] :
( empty(the_InternalRel(X0))
| empty(sK7(the_InternalRel(X0)))
| ~ subrelstr(X0,X1)
| ~ rel_str(X0)
| ~ rel_str(X1)
| empty(the_InternalRel(X1))
| in(sK9(sK7(the_InternalRel(X0))),the_InternalRel(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_401])]) ).
fof(f4341,plain,
( ! [X2,X0,X1] :
( empty(sK7(the_InternalRel(X0)))
| ~ subrelstr(X0,X1)
| ~ rel_str(X0)
| ~ rel_str(X1)
| empty(the_InternalRel(X1))
| empty(the_InternalRel(X0))
| element(sK9(sK7(the_InternalRel(X0))),the_InternalRel(X2))
| ~ subrelstr(X1,X2)
| ~ rel_str(X2) )
| ~ spl16_120
| ~ spl16_401 ),
inference(duplicate_literal_removal,[],[f4335]) ).
fof(f4335,plain,
( ! [X2,X0,X1] :
( empty(sK7(the_InternalRel(X0)))
| ~ subrelstr(X0,X1)
| ~ rel_str(X0)
| ~ rel_str(X1)
| empty(the_InternalRel(X1))
| empty(the_InternalRel(X0))
| element(sK9(sK7(the_InternalRel(X0))),the_InternalRel(X2))
| ~ subrelstr(X1,X2)
| ~ rel_str(X1)
| ~ rel_str(X2) )
| ~ spl16_120
| ~ spl16_401 ),
inference(resolution,[],[f4214,f885]) ).
fof(f4214,plain,
( ! [X0,X1] :
( in(sK9(sK7(the_InternalRel(X0))),the_InternalRel(X1))
| empty(sK7(the_InternalRel(X0)))
| ~ subrelstr(X0,X1)
| ~ rel_str(X0)
| ~ rel_str(X1)
| empty(the_InternalRel(X1))
| empty(the_InternalRel(X0)) )
| ~ spl16_401 ),
inference(avatar_component_clause,[],[f4213]) ).
fof(f10819,plain,
( spl16_719
| ~ spl16_119
| ~ spl16_400 ),
inference(avatar_split_clause,[],[f4334,f4209,f880,f10817]) ).
fof(f10817,plain,
( spl16_719
<=> ! [X2,X0,X1] :
( empty(sK7(the_carrier(X0)))
| ~ subrelstr(X0,X1)
| ~ rel_str(X0)
| ~ rel_str(X1)
| empty(the_carrier(X1))
| empty(the_carrier(X0))
| element(sK9(sK7(the_carrier(X0))),the_carrier(X2))
| ~ subrelstr(X1,X2)
| ~ rel_str(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_719])]) ).
fof(f4209,plain,
( spl16_400
<=> ! [X0,X1] :
( empty(the_carrier(X0))
| empty(sK7(the_carrier(X0)))
| ~ subrelstr(X0,X1)
| ~ rel_str(X0)
| ~ rel_str(X1)
| empty(the_carrier(X1))
| in(sK9(sK7(the_carrier(X0))),the_carrier(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_400])]) ).
fof(f4334,plain,
( ! [X2,X0,X1] :
( empty(sK7(the_carrier(X0)))
| ~ subrelstr(X0,X1)
| ~ rel_str(X0)
| ~ rel_str(X1)
| empty(the_carrier(X1))
| empty(the_carrier(X0))
| element(sK9(sK7(the_carrier(X0))),the_carrier(X2))
| ~ subrelstr(X1,X2)
| ~ rel_str(X2) )
| ~ spl16_119
| ~ spl16_400 ),
inference(duplicate_literal_removal,[],[f4328]) ).
fof(f4328,plain,
( ! [X2,X0,X1] :
( empty(sK7(the_carrier(X0)))
| ~ subrelstr(X0,X1)
| ~ rel_str(X0)
| ~ rel_str(X1)
| empty(the_carrier(X1))
| empty(the_carrier(X0))
| element(sK9(sK7(the_carrier(X0))),the_carrier(X2))
| ~ subrelstr(X1,X2)
| ~ rel_str(X1)
| ~ rel_str(X2) )
| ~ spl16_119
| ~ spl16_400 ),
inference(resolution,[],[f4210,f881]) ).
fof(f4210,plain,
( ! [X0,X1] :
( in(sK9(sK7(the_carrier(X0))),the_carrier(X1))
| empty(sK7(the_carrier(X0)))
| ~ subrelstr(X0,X1)
| ~ rel_str(X0)
| ~ rel_str(X1)
| empty(the_carrier(X1))
| empty(the_carrier(X0)) )
| ~ spl16_400 ),
inference(avatar_component_clause,[],[f4209]) ).
fof(f10815,plain,
( spl16_718
| ~ spl16_120
| ~ spl16_399 ),
inference(avatar_split_clause,[],[f4327,f4203,f884,f10813]) ).
fof(f10813,plain,
( spl16_718
<=> ! [X2,X0,X1] :
( empty(sK6(the_InternalRel(X0)))
| ~ subrelstr(X0,X1)
| ~ rel_str(X0)
| ~ rel_str(X1)
| empty(the_InternalRel(X1))
| empty(the_InternalRel(X0))
| element(sK9(sK6(the_InternalRel(X0))),the_InternalRel(X2))
| ~ subrelstr(X1,X2)
| ~ rel_str(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_718])]) ).
fof(f4203,plain,
( spl16_399
<=> ! [X0,X1] :
( empty(the_InternalRel(X0))
| empty(sK6(the_InternalRel(X0)))
| ~ subrelstr(X0,X1)
| ~ rel_str(X0)
| ~ rel_str(X1)
| empty(the_InternalRel(X1))
| in(sK9(sK6(the_InternalRel(X0))),the_InternalRel(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_399])]) ).
fof(f4327,plain,
( ! [X2,X0,X1] :
( empty(sK6(the_InternalRel(X0)))
| ~ subrelstr(X0,X1)
| ~ rel_str(X0)
| ~ rel_str(X1)
| empty(the_InternalRel(X1))
| empty(the_InternalRel(X0))
| element(sK9(sK6(the_InternalRel(X0))),the_InternalRel(X2))
| ~ subrelstr(X1,X2)
| ~ rel_str(X2) )
| ~ spl16_120
| ~ spl16_399 ),
inference(duplicate_literal_removal,[],[f4321]) ).
fof(f4321,plain,
( ! [X2,X0,X1] :
( empty(sK6(the_InternalRel(X0)))
| ~ subrelstr(X0,X1)
| ~ rel_str(X0)
| ~ rel_str(X1)
| empty(the_InternalRel(X1))
| empty(the_InternalRel(X0))
| element(sK9(sK6(the_InternalRel(X0))),the_InternalRel(X2))
| ~ subrelstr(X1,X2)
| ~ rel_str(X1)
| ~ rel_str(X2) )
| ~ spl16_120
| ~ spl16_399 ),
inference(resolution,[],[f4204,f885]) ).
fof(f4204,plain,
( ! [X0,X1] :
( in(sK9(sK6(the_InternalRel(X0))),the_InternalRel(X1))
| empty(sK6(the_InternalRel(X0)))
| ~ subrelstr(X0,X1)
| ~ rel_str(X0)
| ~ rel_str(X1)
| empty(the_InternalRel(X1))
| empty(the_InternalRel(X0)) )
| ~ spl16_399 ),
inference(avatar_component_clause,[],[f4203]) ).
fof(f10811,plain,
( spl16_717
| ~ spl16_119
| ~ spl16_398 ),
inference(avatar_split_clause,[],[f4320,f4199,f880,f10809]) ).
fof(f10809,plain,
( spl16_717
<=> ! [X2,X0,X1] :
( empty(sK6(the_carrier(X0)))
| ~ subrelstr(X0,X1)
| ~ rel_str(X0)
| ~ rel_str(X1)
| empty(the_carrier(X1))
| empty(the_carrier(X0))
| element(sK9(sK6(the_carrier(X0))),the_carrier(X2))
| ~ subrelstr(X1,X2)
| ~ rel_str(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_717])]) ).
fof(f4199,plain,
( spl16_398
<=> ! [X0,X1] :
( empty(the_carrier(X0))
| empty(sK6(the_carrier(X0)))
| ~ subrelstr(X0,X1)
| ~ rel_str(X0)
| ~ rel_str(X1)
| empty(the_carrier(X1))
| in(sK9(sK6(the_carrier(X0))),the_carrier(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_398])]) ).
fof(f4320,plain,
( ! [X2,X0,X1] :
( empty(sK6(the_carrier(X0)))
| ~ subrelstr(X0,X1)
| ~ rel_str(X0)
| ~ rel_str(X1)
| empty(the_carrier(X1))
| empty(the_carrier(X0))
| element(sK9(sK6(the_carrier(X0))),the_carrier(X2))
| ~ subrelstr(X1,X2)
| ~ rel_str(X2) )
| ~ spl16_119
| ~ spl16_398 ),
inference(duplicate_literal_removal,[],[f4314]) ).
fof(f4314,plain,
( ! [X2,X0,X1] :
( empty(sK6(the_carrier(X0)))
| ~ subrelstr(X0,X1)
| ~ rel_str(X0)
| ~ rel_str(X1)
| empty(the_carrier(X1))
| empty(the_carrier(X0))
| element(sK9(sK6(the_carrier(X0))),the_carrier(X2))
| ~ subrelstr(X1,X2)
| ~ rel_str(X1)
| ~ rel_str(X2) )
| ~ spl16_119
| ~ spl16_398 ),
inference(resolution,[],[f4200,f881]) ).
fof(f4200,plain,
( ! [X0,X1] :
( in(sK9(sK6(the_carrier(X0))),the_carrier(X1))
| empty(sK6(the_carrier(X0)))
| ~ subrelstr(X0,X1)
| ~ rel_str(X0)
| ~ rel_str(X1)
| empty(the_carrier(X1))
| empty(the_carrier(X0)) )
| ~ spl16_398 ),
inference(avatar_component_clause,[],[f4199]) ).
fof(f10807,plain,
( spl16_716
| ~ spl16_65
| ~ spl16_388 ),
inference(avatar_split_clause,[],[f4236,f4159,f508,f10805]) ).
fof(f10805,plain,
( spl16_716
<=> ! [X0] :
( empty(sK7(powerset(X0)))
| empty(powerset(X0))
| element(sK9(sK9(sK9(powerset(sK7(powerset(X0)))))),X0)
| empty(sK9(powerset(sK7(powerset(X0)))))
| empty(sK9(sK9(powerset(sK7(powerset(X0)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_716])]) ).
fof(f4236,plain,
( ! [X0] :
( empty(sK7(powerset(X0)))
| empty(powerset(X0))
| element(sK9(sK9(sK9(powerset(sK7(powerset(X0)))))),X0)
| empty(sK9(powerset(sK7(powerset(X0)))))
| empty(sK9(sK9(powerset(sK7(powerset(X0)))))) )
| ~ spl16_65
| ~ spl16_388 ),
inference(resolution,[],[f4160,f509]) ).
fof(f10803,plain,
( spl16_714
| spl16_715
| ~ spl16_65
| ~ spl16_606 ),
inference(avatar_split_clause,[],[f8460,f8410,f508,f10800,f10796]) ).
fof(f8410,plain,
( spl16_606
<=> ! [X0] :
( ~ in(X0,the_InternalRel(sK8(sK1)))
| element(X0,cartesian_product2(sK14,sK14)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_606])]) ).
fof(f8460,plain,
( element(sK9(the_InternalRel(sK8(sK1))),cartesian_product2(sK14,sK14))
| empty(the_InternalRel(sK8(sK1)))
| ~ spl16_65
| ~ spl16_606 ),
inference(resolution,[],[f8411,f509]) ).
fof(f8411,plain,
( ! [X0] :
( ~ in(X0,the_InternalRel(sK8(sK1)))
| element(X0,cartesian_product2(sK14,sK14)) )
| ~ spl16_606 ),
inference(avatar_component_clause,[],[f8410]) ).
fof(f10794,plain,
( spl16_713
| ~ spl16_65
| ~ spl16_387 ),
inference(avatar_split_clause,[],[f4220,f4155,f508,f10792]) ).
fof(f10792,plain,
( spl16_713
<=> ! [X0] :
( empty(sK6(powerset(X0)))
| empty(powerset(X0))
| element(sK9(sK9(sK9(powerset(sK6(powerset(X0)))))),X0)
| empty(sK9(powerset(sK6(powerset(X0)))))
| empty(sK9(sK9(powerset(sK6(powerset(X0)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_713])]) ).
fof(f4220,plain,
( ! [X0] :
( empty(sK6(powerset(X0)))
| empty(powerset(X0))
| element(sK9(sK9(sK9(powerset(sK6(powerset(X0)))))),X0)
| empty(sK9(powerset(sK6(powerset(X0)))))
| empty(sK9(sK9(powerset(sK6(powerset(X0)))))) )
| ~ spl16_65
| ~ spl16_387 ),
inference(resolution,[],[f4156,f509]) ).
fof(f10790,plain,
( spl16_712
| ~ spl16_72
| ~ spl16_362 ),
inference(avatar_split_clause,[],[f3818,f3670,f549,f10788]) ).
fof(f10788,plain,
( spl16_712
<=> ! [X0] :
( empty(sK9(sK9(powerset(powerset(sK9(powerset(X0)))))))
| empty(sK9(powerset(X0)))
| empty(sK9(powerset(powerset(sK9(powerset(X0))))))
| element(sK9(sK9(sK9(powerset(powerset(sK9(powerset(X0))))))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_712])]) ).
fof(f3818,plain,
( ! [X0] :
( empty(sK9(sK9(powerset(powerset(sK9(powerset(X0)))))))
| empty(sK9(powerset(X0)))
| empty(sK9(powerset(powerset(sK9(powerset(X0))))))
| element(sK9(sK9(sK9(powerset(powerset(sK9(powerset(X0))))))),X0) )
| ~ spl16_72
| ~ spl16_362 ),
inference(resolution,[],[f3671,f550]) ).
fof(f10786,plain,
( spl16_711
| ~ spl16_208
| ~ spl16_351 ),
inference(avatar_split_clause,[],[f3699,f3626,f1820,f10784]) ).
fof(f10784,plain,
( spl16_711
<=> ! [X0,X1] :
( empty(powerset(X0))
| empty(sK7(powerset(X0)))
| ~ empty(X0)
| sK9(powerset(sK9(sK7(powerset(X0))))) = sK9(powerset(the_InternalRel(sK8(X1))))
| ~ rel_str(sK8(X1))
| ~ rel_str(X1)
| ~ empty(the_InternalRel(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_711])]) ).
fof(f1820,plain,
( spl16_208
<=> ! [X0] :
( ~ empty(the_InternalRel(X0))
| ~ rel_str(sK8(X0))
| ~ rel_str(X0)
| empty(the_InternalRel(sK8(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_208])]) ).
fof(f3699,plain,
( ! [X0,X1] :
( empty(powerset(X0))
| empty(sK7(powerset(X0)))
| ~ empty(X0)
| sK9(powerset(sK9(sK7(powerset(X0))))) = sK9(powerset(the_InternalRel(sK8(X1))))
| ~ rel_str(sK8(X1))
| ~ rel_str(X1)
| ~ empty(the_InternalRel(X1)) )
| ~ spl16_208
| ~ spl16_351 ),
inference(resolution,[],[f3627,f1821]) ).
fof(f1821,plain,
( ! [X0] :
( empty(the_InternalRel(sK8(X0)))
| ~ rel_str(sK8(X0))
| ~ rel_str(X0)
| ~ empty(the_InternalRel(X0)) )
| ~ spl16_208 ),
inference(avatar_component_clause,[],[f1820]) ).
fof(f10782,plain,
( spl16_710
| ~ spl16_207
| ~ spl16_351 ),
inference(avatar_split_clause,[],[f3698,f3626,f1816,f10780]) ).
fof(f10780,plain,
( spl16_710
<=> ! [X0,X1] :
( empty(powerset(X0))
| empty(sK7(powerset(X0)))
| ~ empty(X0)
| sK9(powerset(sK9(sK7(powerset(X0))))) = sK9(powerset(the_carrier(sK8(X1))))
| ~ rel_str(sK8(X1))
| ~ rel_str(X1)
| ~ empty(the_carrier(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_710])]) ).
fof(f1816,plain,
( spl16_207
<=> ! [X0] :
( ~ empty(the_carrier(X0))
| ~ rel_str(sK8(X0))
| ~ rel_str(X0)
| empty(the_carrier(sK8(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_207])]) ).
fof(f3698,plain,
( ! [X0,X1] :
( empty(powerset(X0))
| empty(sK7(powerset(X0)))
| ~ empty(X0)
| sK9(powerset(sK9(sK7(powerset(X0))))) = sK9(powerset(the_carrier(sK8(X1))))
| ~ rel_str(sK8(X1))
| ~ rel_str(X1)
| ~ empty(the_carrier(X1)) )
| ~ spl16_207
| ~ spl16_351 ),
inference(resolution,[],[f3627,f1817]) ).
fof(f1817,plain,
( ! [X0] :
( empty(the_carrier(sK8(X0)))
| ~ rel_str(sK8(X0))
| ~ rel_str(X0)
| ~ empty(the_carrier(X0)) )
| ~ spl16_207 ),
inference(avatar_component_clause,[],[f1816]) ).
fof(f10778,plain,
( spl16_709
| ~ spl16_208
| ~ spl16_350 ),
inference(avatar_split_clause,[],[f3682,f3622,f1820,f10776]) ).
fof(f10776,plain,
( spl16_709
<=> ! [X0,X1] :
( empty(powerset(X0))
| empty(sK6(powerset(X0)))
| ~ empty(X0)
| sK9(powerset(sK9(sK6(powerset(X0))))) = sK9(powerset(the_InternalRel(sK8(X1))))
| ~ rel_str(sK8(X1))
| ~ rel_str(X1)
| ~ empty(the_InternalRel(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_709])]) ).
fof(f3682,plain,
( ! [X0,X1] :
( empty(powerset(X0))
| empty(sK6(powerset(X0)))
| ~ empty(X0)
| sK9(powerset(sK9(sK6(powerset(X0))))) = sK9(powerset(the_InternalRel(sK8(X1))))
| ~ rel_str(sK8(X1))
| ~ rel_str(X1)
| ~ empty(the_InternalRel(X1)) )
| ~ spl16_208
| ~ spl16_350 ),
inference(resolution,[],[f3623,f1821]) ).
fof(f10774,plain,
( spl16_708
| ~ spl16_207
| ~ spl16_350 ),
inference(avatar_split_clause,[],[f3681,f3622,f1816,f10772]) ).
fof(f10772,plain,
( spl16_708
<=> ! [X0,X1] :
( empty(powerset(X0))
| empty(sK6(powerset(X0)))
| ~ empty(X0)
| sK9(powerset(sK9(sK6(powerset(X0))))) = sK9(powerset(the_carrier(sK8(X1))))
| ~ rel_str(sK8(X1))
| ~ rel_str(X1)
| ~ empty(the_carrier(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_708])]) ).
fof(f3681,plain,
( ! [X0,X1] :
( empty(powerset(X0))
| empty(sK6(powerset(X0)))
| ~ empty(X0)
| sK9(powerset(sK9(sK6(powerset(X0))))) = sK9(powerset(the_carrier(sK8(X1))))
| ~ rel_str(sK8(X1))
| ~ rel_str(X1)
| ~ empty(the_carrier(X1)) )
| ~ spl16_207
| ~ spl16_350 ),
inference(resolution,[],[f3623,f1817]) ).
fof(f10770,plain,
( spl16_707
| ~ spl16_213
| ~ spl16_341 ),
inference(avatar_split_clause,[],[f3590,f3545,f1942,f10768]) ).
fof(f10768,plain,
( spl16_707
<=> ! [X0,X1] :
( ~ empty(X0)
| empty(sK9(powerset(powerset(X0))))
| sK9(powerset(sK9(sK9(powerset(powerset(X0)))))) = sK9(powerset(sK9(sK9(powerset(powerset(X1))))))
| empty(sK9(powerset(powerset(X1))))
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_707])]) ).
fof(f1942,plain,
( spl16_213
<=> ! [X0] :
( ~ empty(X0)
| empty(sK9(powerset(powerset(X0))))
| empty(sK9(sK9(powerset(powerset(X0))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_213])]) ).
fof(f3590,plain,
( ! [X0,X1] :
( ~ empty(X0)
| empty(sK9(powerset(powerset(X0))))
| sK9(powerset(sK9(sK9(powerset(powerset(X0)))))) = sK9(powerset(sK9(sK9(powerset(powerset(X1))))))
| empty(sK9(powerset(powerset(X1))))
| ~ empty(X1) )
| ~ spl16_213
| ~ spl16_341 ),
inference(resolution,[],[f3546,f1943]) ).
fof(f1943,plain,
( ! [X0] :
( empty(sK9(sK9(powerset(powerset(X0)))))
| empty(sK9(powerset(powerset(X0))))
| ~ empty(X0) )
| ~ spl16_213 ),
inference(avatar_component_clause,[],[f1942]) ).
fof(f10766,plain,
( spl16_706
| ~ spl16_215
| ~ spl16_331 ),
inference(avatar_split_clause,[],[f3492,f3402,f1961,f10764]) ).
fof(f10764,plain,
( spl16_706
<=> ! [X0,X1] :
( empty(powerset(X0))
| empty(sK7(powerset(X0)))
| sK9(sK7(powerset(X0))) = sK9(powerset(sK9(sK7(powerset(X1)))))
| ~ empty(X0)
| ~ empty(X1)
| empty(powerset(X1))
| empty(sK7(powerset(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_706])]) ).
fof(f3492,plain,
( ! [X0,X1] :
( empty(powerset(X0))
| empty(sK7(powerset(X0)))
| sK9(sK7(powerset(X0))) = sK9(powerset(sK9(sK7(powerset(X1)))))
| ~ empty(X0)
| ~ empty(X1)
| empty(powerset(X1))
| empty(sK7(powerset(X1))) )
| ~ spl16_215
| ~ spl16_331 ),
inference(resolution,[],[f3403,f1962]) ).
fof(f10755,plain,
( spl16_705
| ~ spl16_28
| ~ spl16_190 ),
inference(avatar_split_clause,[],[f1663,f1600,f286,f10753]) ).
fof(f10753,plain,
( spl16_705
<=> ! [X0] :
( ~ subrelstr(sK1,X0)
| empty(the_carrier(X0))
| ~ rel_str(X0)
| element(sK5,the_carrier(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_705])]) ).
fof(f286,plain,
( spl16_28
<=> ! [X0,X1] :
( element(X0,X1)
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_28])]) ).
fof(f1600,plain,
( spl16_190
<=> ! [X0] :
( ~ rel_str(X0)
| ~ subrelstr(sK1,X0)
| empty(the_carrier(X0))
| in(sK5,the_carrier(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_190])]) ).
fof(f1663,plain,
( ! [X0] :
( ~ subrelstr(sK1,X0)
| empty(the_carrier(X0))
| ~ rel_str(X0)
| element(sK5,the_carrier(X0)) )
| ~ spl16_28
| ~ spl16_190 ),
inference(resolution,[],[f1601,f287]) ).
fof(f287,plain,
( ! [X0,X1] :
( ~ in(X0,X1)
| element(X0,X1) )
| ~ spl16_28 ),
inference(avatar_component_clause,[],[f286]) ).
fof(f1601,plain,
( ! [X0] :
( in(sK5,the_carrier(X0))
| ~ subrelstr(sK1,X0)
| empty(the_carrier(X0))
| ~ rel_str(X0) )
| ~ spl16_190 ),
inference(avatar_component_clause,[],[f1600]) ).
fof(f10749,plain,
( spl16_186
| ~ spl16_1
| spl16_6
| ~ spl16_2
| ~ spl16_8
| ~ spl16_535 ),
inference(avatar_split_clause,[],[f6601,f6556,f193,f163,f183,f158,f1536]) ).
fof(f6556,plain,
( spl16_535
<=> ! [X0] :
( empty(the_InternalRel(X0))
| ~ subrelstr(sK1,X0)
| related(X0,sK4,sK5)
| ~ rel_str(X0)
| ~ element(sK4,the_carrier(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_535])]) ).
fof(f6601,plain,
( ~ subrelstr(sK1,sK0)
| related(sK0,sK4,sK5)
| ~ rel_str(sK0)
| empty(the_InternalRel(sK0))
| ~ spl16_8
| ~ spl16_535 ),
inference(resolution,[],[f6557,f195]) ).
fof(f195,plain,
( element(sK4,the_carrier(sK0))
| ~ spl16_8 ),
inference(avatar_component_clause,[],[f193]) ).
fof(f6557,plain,
( ! [X0] :
( ~ element(sK4,the_carrier(X0))
| ~ subrelstr(sK1,X0)
| related(X0,sK4,sK5)
| ~ rel_str(X0)
| empty(the_InternalRel(X0)) )
| ~ spl16_535 ),
inference(avatar_component_clause,[],[f6556]) ).
fof(f10748,plain,
( spl16_704
| ~ spl16_214
| ~ spl16_331 ),
inference(avatar_split_clause,[],[f3491,f3402,f1955,f10746]) ).
fof(f10746,plain,
( spl16_704
<=> ! [X0,X1] :
( empty(powerset(X0))
| empty(sK7(powerset(X0)))
| sK9(sK7(powerset(X0))) = sK9(powerset(sK9(sK6(powerset(X1)))))
| ~ empty(X0)
| ~ empty(X1)
| empty(powerset(X1))
| empty(sK6(powerset(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_704])]) ).
fof(f3491,plain,
( ! [X0,X1] :
( empty(powerset(X0))
| empty(sK7(powerset(X0)))
| sK9(sK7(powerset(X0))) = sK9(powerset(sK9(sK6(powerset(X1)))))
| ~ empty(X0)
| ~ empty(X1)
| empty(powerset(X1))
| empty(sK6(powerset(X1))) )
| ~ spl16_214
| ~ spl16_331 ),
inference(resolution,[],[f3403,f1956]) ).
fof(f10744,plain,
( spl16_703
| ~ spl16_286
| ~ spl16_331 ),
inference(avatar_split_clause,[],[f3490,f3402,f2727,f10742]) ).
fof(f10742,plain,
( spl16_703
<=> ! [X0,X1] :
( empty(powerset(X0))
| empty(sK7(powerset(X0)))
| sK9(sK7(powerset(X0))) = sK9(powerset(sK9(powerset(powerset(X1)))))
| ~ empty(X0)
| sK14 = sK9(sK9(powerset(powerset(X1))))
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_703])]) ).
fof(f3490,plain,
( ! [X0,X1] :
( empty(powerset(X0))
| empty(sK7(powerset(X0)))
| sK9(sK7(powerset(X0))) = sK9(powerset(sK9(powerset(powerset(X1)))))
| ~ empty(X0)
| sK14 = sK9(sK9(powerset(powerset(X1))))
| ~ empty(X1) )
| ~ spl16_286
| ~ spl16_331 ),
inference(resolution,[],[f3403,f2728]) ).
fof(f10740,plain,
( spl16_702
| ~ spl16_215
| ~ spl16_329 ),
inference(avatar_split_clause,[],[f3458,f3394,f1961,f10738]) ).
fof(f10738,plain,
( spl16_702
<=> ! [X0,X1] :
( empty(powerset(X0))
| empty(sK6(powerset(X0)))
| sK9(sK6(powerset(X0))) = sK9(powerset(sK9(sK7(powerset(X1)))))
| ~ empty(X0)
| ~ empty(X1)
| empty(powerset(X1))
| empty(sK7(powerset(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_702])]) ).
fof(f3458,plain,
( ! [X0,X1] :
( empty(powerset(X0))
| empty(sK6(powerset(X0)))
| sK9(sK6(powerset(X0))) = sK9(powerset(sK9(sK7(powerset(X1)))))
| ~ empty(X0)
| ~ empty(X1)
| empty(powerset(X1))
| empty(sK7(powerset(X1))) )
| ~ spl16_215
| ~ spl16_329 ),
inference(resolution,[],[f3395,f1962]) ).
fof(f10736,plain,
( spl16_701
| ~ spl16_214
| ~ spl16_329 ),
inference(avatar_split_clause,[],[f3457,f3394,f1955,f10734]) ).
fof(f10734,plain,
( spl16_701
<=> ! [X0,X1] :
( empty(powerset(X0))
| empty(sK6(powerset(X0)))
| sK9(sK6(powerset(X0))) = sK9(powerset(sK9(sK6(powerset(X1)))))
| ~ empty(X0)
| ~ empty(X1)
| empty(powerset(X1))
| empty(sK6(powerset(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_701])]) ).
fof(f3457,plain,
( ! [X0,X1] :
( empty(powerset(X0))
| empty(sK6(powerset(X0)))
| sK9(sK6(powerset(X0))) = sK9(powerset(sK9(sK6(powerset(X1)))))
| ~ empty(X0)
| ~ empty(X1)
| empty(powerset(X1))
| empty(sK6(powerset(X1))) )
| ~ spl16_214
| ~ spl16_329 ),
inference(resolution,[],[f3395,f1956]) ).
fof(f10732,plain,
( spl16_700
| ~ spl16_286
| ~ spl16_329 ),
inference(avatar_split_clause,[],[f3456,f3394,f2727,f10730]) ).
fof(f10730,plain,
( spl16_700
<=> ! [X0,X1] :
( empty(powerset(X0))
| empty(sK6(powerset(X0)))
| sK9(sK6(powerset(X0))) = sK9(powerset(sK9(powerset(powerset(X1)))))
| ~ empty(X0)
| sK14 = sK9(sK9(powerset(powerset(X1))))
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_700])]) ).
fof(f3456,plain,
( ! [X0,X1] :
( empty(powerset(X0))
| empty(sK6(powerset(X0)))
| sK9(sK6(powerset(X0))) = sK9(powerset(sK9(powerset(powerset(X1)))))
| ~ empty(X0)
| sK14 = sK9(sK9(powerset(powerset(X1))))
| ~ empty(X1) )
| ~ spl16_286
| ~ spl16_329 ),
inference(resolution,[],[f3395,f2728]) ).
fof(f10728,plain,
( spl16_699
| ~ spl16_120
| ~ spl16_321 ),
inference(avatar_split_clause,[],[f3275,f3175,f884,f10726]) ).
fof(f10726,plain,
( spl16_699
<=> ! [X0,X1] :
( empty(sK7(the_InternalRel(X0)))
| empty(the_InternalRel(X0))
| empty(sK9(powerset(sK7(the_InternalRel(X0)))))
| element(sK9(sK9(powerset(sK7(the_InternalRel(X0))))),the_InternalRel(X1))
| ~ subrelstr(X0,X1)
| ~ rel_str(X0)
| ~ rel_str(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_699])]) ).
fof(f3275,plain,
( ! [X0,X1] :
( empty(sK7(the_InternalRel(X0)))
| empty(the_InternalRel(X0))
| empty(sK9(powerset(sK7(the_InternalRel(X0)))))
| element(sK9(sK9(powerset(sK7(the_InternalRel(X0))))),the_InternalRel(X1))
| ~ subrelstr(X0,X1)
| ~ rel_str(X0)
| ~ rel_str(X1) )
| ~ spl16_120
| ~ spl16_321 ),
inference(resolution,[],[f3176,f885]) ).
fof(f10724,plain,
( spl16_698
| ~ spl16_119
| ~ spl16_321 ),
inference(avatar_split_clause,[],[f3273,f3175,f880,f10722]) ).
fof(f10722,plain,
( spl16_698
<=> ! [X0,X1] :
( empty(sK7(the_carrier(X0)))
| empty(the_carrier(X0))
| empty(sK9(powerset(sK7(the_carrier(X0)))))
| element(sK9(sK9(powerset(sK7(the_carrier(X0))))),the_carrier(X1))
| ~ subrelstr(X0,X1)
| ~ rel_str(X0)
| ~ rel_str(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_698])]) ).
fof(f3273,plain,
( ! [X0,X1] :
( empty(sK7(the_carrier(X0)))
| empty(the_carrier(X0))
| empty(sK9(powerset(sK7(the_carrier(X0)))))
| element(sK9(sK9(powerset(sK7(the_carrier(X0))))),the_carrier(X1))
| ~ subrelstr(X0,X1)
| ~ rel_str(X0)
| ~ rel_str(X1) )
| ~ spl16_119
| ~ spl16_321 ),
inference(resolution,[],[f3176,f881]) ).
fof(f10720,plain,
( spl16_697
| ~ spl16_120
| ~ spl16_320 ),
inference(avatar_split_clause,[],[f3254,f3171,f884,f10718]) ).
fof(f10718,plain,
( spl16_697
<=> ! [X0,X1] :
( empty(sK6(the_InternalRel(X0)))
| empty(the_InternalRel(X0))
| empty(sK9(powerset(sK6(the_InternalRel(X0)))))
| element(sK9(sK9(powerset(sK6(the_InternalRel(X0))))),the_InternalRel(X1))
| ~ subrelstr(X0,X1)
| ~ rel_str(X0)
| ~ rel_str(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_697])]) ).
fof(f3254,plain,
( ! [X0,X1] :
( empty(sK6(the_InternalRel(X0)))
| empty(the_InternalRel(X0))
| empty(sK9(powerset(sK6(the_InternalRel(X0)))))
| element(sK9(sK9(powerset(sK6(the_InternalRel(X0))))),the_InternalRel(X1))
| ~ subrelstr(X0,X1)
| ~ rel_str(X0)
| ~ rel_str(X1) )
| ~ spl16_120
| ~ spl16_320 ),
inference(resolution,[],[f3172,f885]) ).
fof(f10716,plain,
( spl16_696
| ~ spl16_119
| ~ spl16_320 ),
inference(avatar_split_clause,[],[f3252,f3171,f880,f10714]) ).
fof(f10714,plain,
( spl16_696
<=> ! [X0,X1] :
( empty(sK6(the_carrier(X0)))
| empty(the_carrier(X0))
| empty(sK9(powerset(sK6(the_carrier(X0)))))
| element(sK9(sK9(powerset(sK6(the_carrier(X0))))),the_carrier(X1))
| ~ subrelstr(X0,X1)
| ~ rel_str(X0)
| ~ rel_str(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_696])]) ).
fof(f3252,plain,
( ! [X0,X1] :
( empty(sK6(the_carrier(X0)))
| empty(the_carrier(X0))
| empty(sK9(powerset(sK6(the_carrier(X0)))))
| element(sK9(sK9(powerset(sK6(the_carrier(X0))))),the_carrier(X1))
| ~ subrelstr(X0,X1)
| ~ rel_str(X0)
| ~ rel_str(X1) )
| ~ spl16_119
| ~ spl16_320 ),
inference(resolution,[],[f3172,f881]) ).
fof(f10712,plain,
( spl16_695
| ~ spl16_309
| ~ spl16_318 ),
inference(avatar_split_clause,[],[f3225,f3163,f3098,f10710]) ).
fof(f10710,plain,
( spl16_695
<=> ! [X0,X1] :
( empty(powerset(X0))
| empty(sK7(powerset(X0)))
| sK9(powerset(powerset(X1))) = sK9(sK7(powerset(X0)))
| ~ empty(X0)
| ~ empty(X1)
| sK14 = sK9(powerset(sK9(sK9(powerset(powerset(X1)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_695])]) ).
fof(f3225,plain,
( ! [X0,X1] :
( empty(powerset(X0))
| empty(sK7(powerset(X0)))
| sK9(powerset(powerset(X1))) = sK9(sK7(powerset(X0)))
| ~ empty(X0)
| ~ empty(X1)
| sK14 = sK9(powerset(sK9(sK9(powerset(powerset(X1)))))) )
| ~ spl16_309
| ~ spl16_318 ),
inference(resolution,[],[f3164,f3099]) ).
fof(f10674,plain,
( spl16_694
| ~ spl16_309
| ~ spl16_316 ),
inference(avatar_split_clause,[],[f3198,f3155,f3098,f10672]) ).
fof(f10672,plain,
( spl16_694
<=> ! [X0,X1] :
( empty(powerset(X0))
| empty(sK6(powerset(X0)))
| sK9(powerset(powerset(X1))) = sK9(sK6(powerset(X0)))
| ~ empty(X0)
| ~ empty(X1)
| sK14 = sK9(powerset(sK9(sK9(powerset(powerset(X1)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_694])]) ).
fof(f3198,plain,
( ! [X0,X1] :
( empty(powerset(X0))
| empty(sK6(powerset(X0)))
| sK9(powerset(powerset(X1))) = sK9(sK6(powerset(X0)))
| ~ empty(X0)
| ~ empty(X1)
| sK14 = sK9(powerset(sK9(sK9(powerset(powerset(X1)))))) )
| ~ spl16_309
| ~ spl16_316 ),
inference(resolution,[],[f3156,f3099]) ).
fof(f10640,plain,
( spl16_693
| ~ spl16_86
| ~ spl16_642 ),
inference(avatar_split_clause,[],[f9481,f9163,f653,f10638]) ).
fof(f9163,plain,
( spl16_642
<=> relation_of2_as_subset(the_InternalRel(sK8(sK8(sK1))),sK14,sK14) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_642])]) ).
fof(f9481,plain,
( ! [X0] :
( ~ in(X0,the_InternalRel(sK8(sK8(sK1))))
| element(X0,cartesian_product2(sK14,sK14)) )
| ~ spl16_86
| ~ spl16_642 ),
inference(resolution,[],[f9165,f654]) ).
fof(f9165,plain,
( relation_of2_as_subset(the_InternalRel(sK8(sK8(sK1))),sK14,sK14)
| ~ spl16_642 ),
inference(avatar_component_clause,[],[f9163]) ).
fof(f10054,plain,
( spl16_692
| ~ spl16_27
| ~ spl16_415 ),
inference(avatar_split_clause,[],[f4616,f4477,f282,f10052]) ).
fof(f10052,plain,
( spl16_692
<=> ! [X0] :
( empty(powerset(X0))
| empty(sK7(sK9(sK7(powerset(X0)))))
| empty(sK9(sK7(powerset(X0))))
| empty(X0)
| empty(sK7(powerset(X0)))
| ~ in(X0,sK9(sK7(sK9(sK7(powerset(X0)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_692])]) ).
fof(f4616,plain,
( ! [X0] :
( empty(powerset(X0))
| empty(sK7(sK9(sK7(powerset(X0)))))
| empty(sK9(sK7(powerset(X0))))
| empty(X0)
| empty(sK7(powerset(X0)))
| ~ in(X0,sK9(sK7(sK9(sK7(powerset(X0)))))) )
| ~ spl16_27
| ~ spl16_415 ),
inference(resolution,[],[f4478,f283]) ).
fof(f10050,plain,
( spl16_691
| ~ spl16_27
| ~ spl16_414 ),
inference(avatar_split_clause,[],[f4571,f4473,f282,f10048]) ).
fof(f10048,plain,
( spl16_691
<=> ! [X0] :
( empty(powerset(X0))
| empty(sK6(sK9(sK7(powerset(X0)))))
| empty(sK9(sK7(powerset(X0))))
| empty(X0)
| empty(sK7(powerset(X0)))
| ~ in(X0,sK9(sK6(sK9(sK7(powerset(X0)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_691])]) ).
fof(f4571,plain,
( ! [X0] :
( empty(powerset(X0))
| empty(sK6(sK9(sK7(powerset(X0)))))
| empty(sK9(sK7(powerset(X0))))
| empty(X0)
| empty(sK7(powerset(X0)))
| ~ in(X0,sK9(sK6(sK9(sK7(powerset(X0)))))) )
| ~ spl16_27
| ~ spl16_414 ),
inference(resolution,[],[f4474,f283]) ).
fof(f10046,plain,
( spl16_690
| ~ spl16_27
| ~ spl16_413 ),
inference(avatar_split_clause,[],[f4526,f4469,f282,f10044]) ).
fof(f10044,plain,
( spl16_690
<=> ! [X0] :
( empty(powerset(X0))
| empty(sK7(sK9(sK6(powerset(X0)))))
| empty(sK9(sK6(powerset(X0))))
| empty(X0)
| empty(sK6(powerset(X0)))
| ~ in(X0,sK9(sK7(sK9(sK6(powerset(X0)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_690])]) ).
fof(f4526,plain,
( ! [X0] :
( empty(powerset(X0))
| empty(sK7(sK9(sK6(powerset(X0)))))
| empty(sK9(sK6(powerset(X0))))
| empty(X0)
| empty(sK6(powerset(X0)))
| ~ in(X0,sK9(sK7(sK9(sK6(powerset(X0)))))) )
| ~ spl16_27
| ~ spl16_413 ),
inference(resolution,[],[f4470,f283]) ).
fof(f10042,plain,
( spl16_689
| ~ spl16_27
| ~ spl16_412 ),
inference(avatar_split_clause,[],[f4481,f4465,f282,f10040]) ).
fof(f10040,plain,
( spl16_689
<=> ! [X0] :
( empty(powerset(X0))
| empty(sK6(sK9(sK6(powerset(X0)))))
| empty(sK9(sK6(powerset(X0))))
| empty(X0)
| empty(sK6(powerset(X0)))
| ~ in(X0,sK9(sK6(sK9(sK6(powerset(X0)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_689])]) ).
fof(f4481,plain,
( ! [X0] :
( empty(powerset(X0))
| empty(sK6(sK9(sK6(powerset(X0)))))
| empty(sK9(sK6(powerset(X0))))
| empty(X0)
| empty(sK6(powerset(X0)))
| ~ in(X0,sK9(sK6(sK9(sK6(powerset(X0)))))) )
| ~ spl16_27
| ~ spl16_412 ),
inference(resolution,[],[f4466,f283]) ).
fof(f10038,plain,
( spl16_688
| ~ spl16_77
| ~ spl16_364 ),
inference(avatar_split_clause,[],[f3871,f3678,f577,f10036]) ).
fof(f10036,plain,
( spl16_688
<=> ! [X0] :
( empty(powerset(sK7(X0)))
| empty(sK9(sK7(powerset(sK7(X0)))))
| empty(sK7(X0))
| empty(sK7(powerset(sK7(X0))))
| element(sK9(sK9(sK7(powerset(sK7(X0))))),X0)
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_688])]) ).
fof(f3871,plain,
( ! [X0] :
( empty(powerset(sK7(X0)))
| empty(sK9(sK7(powerset(sK7(X0)))))
| empty(sK7(X0))
| empty(sK7(powerset(sK7(X0))))
| element(sK9(sK9(sK7(powerset(sK7(X0))))),X0)
| empty(X0) )
| ~ spl16_77
| ~ spl16_364 ),
inference(resolution,[],[f3679,f578]) ).
fof(f10034,plain,
( spl16_687
| ~ spl16_76
| ~ spl16_364 ),
inference(avatar_split_clause,[],[f3870,f3678,f573,f10032]) ).
fof(f10032,plain,
( spl16_687
<=> ! [X0] :
( empty(powerset(sK6(X0)))
| empty(sK9(sK7(powerset(sK6(X0)))))
| empty(sK6(X0))
| empty(sK7(powerset(sK6(X0))))
| element(sK9(sK9(sK7(powerset(sK6(X0))))),X0)
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_687])]) ).
fof(f3870,plain,
( ! [X0] :
( empty(powerset(sK6(X0)))
| empty(sK9(sK7(powerset(sK6(X0)))))
| empty(sK6(X0))
| empty(sK7(powerset(sK6(X0))))
| element(sK9(sK9(sK7(powerset(sK6(X0))))),X0)
| empty(X0) )
| ~ spl16_76
| ~ spl16_364 ),
inference(resolution,[],[f3679,f574]) ).
fof(f10030,plain,
( spl16_686
| ~ spl16_77
| ~ spl16_363 ),
inference(avatar_split_clause,[],[f3844,f3674,f577,f10028]) ).
fof(f10028,plain,
( spl16_686
<=> ! [X0] :
( empty(powerset(sK7(X0)))
| empty(sK9(sK6(powerset(sK7(X0)))))
| empty(sK7(X0))
| empty(sK6(powerset(sK7(X0))))
| element(sK9(sK9(sK6(powerset(sK7(X0))))),X0)
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_686])]) ).
fof(f3844,plain,
( ! [X0] :
( empty(powerset(sK7(X0)))
| empty(sK9(sK6(powerset(sK7(X0)))))
| empty(sK7(X0))
| empty(sK6(powerset(sK7(X0))))
| element(sK9(sK9(sK6(powerset(sK7(X0))))),X0)
| empty(X0) )
| ~ spl16_77
| ~ spl16_363 ),
inference(resolution,[],[f3675,f578]) ).
fof(f10026,plain,
( spl16_685
| ~ spl16_76
| ~ spl16_363 ),
inference(avatar_split_clause,[],[f3843,f3674,f573,f10024]) ).
fof(f10024,plain,
( spl16_685
<=> ! [X0] :
( empty(powerset(sK6(X0)))
| empty(sK9(sK6(powerset(sK6(X0)))))
| empty(sK6(X0))
| empty(sK6(powerset(sK6(X0))))
| element(sK9(sK9(sK6(powerset(sK6(X0))))),X0)
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_685])]) ).
fof(f3843,plain,
( ! [X0] :
( empty(powerset(sK6(X0)))
| empty(sK9(sK6(powerset(sK6(X0)))))
| empty(sK6(X0))
| empty(sK6(powerset(sK6(X0))))
| element(sK9(sK9(sK6(powerset(sK6(X0))))),X0)
| empty(X0) )
| ~ spl16_76
| ~ spl16_363 ),
inference(resolution,[],[f3675,f574]) ).
fof(f10022,plain,
( ~ spl16_163
| spl16_684
| ~ spl16_82
| ~ spl16_642 ),
inference(avatar_split_clause,[],[f9483,f9163,f617,f10019,f1358]) ).
fof(f10019,plain,
( spl16_684
<=> finite(the_InternalRel(sK8(sK8(sK1)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_684])]) ).
fof(f9483,plain,
( finite(the_InternalRel(sK8(sK8(sK1))))
| ~ finite(cartesian_product2(sK14,sK14))
| ~ spl16_82
| ~ spl16_642 ),
inference(resolution,[],[f9165,f618]) ).
fof(f10017,plain,
( spl16_683
| ~ spl16_72
| ~ spl16_349 ),
inference(avatar_split_clause,[],[f3607,f3578,f549,f10015]) ).
fof(f10015,plain,
( spl16_683
<=> ! [X0] :
( empty(sK9(powerset(sK9(powerset(X0)))))
| empty(sK9(powerset(X0)))
| empty(sK9(powerset(sK9(powerset(sK9(powerset(X0)))))))
| element(sK9(sK9(powerset(sK9(powerset(sK9(powerset(X0))))))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_683])]) ).
fof(f3607,plain,
( ! [X0] :
( empty(sK9(powerset(sK9(powerset(X0)))))
| empty(sK9(powerset(X0)))
| empty(sK9(powerset(sK9(powerset(sK9(powerset(X0)))))))
| element(sK9(sK9(powerset(sK9(powerset(sK9(powerset(X0))))))),X0) )
| ~ spl16_72
| ~ spl16_349 ),
inference(resolution,[],[f3579,f550]) ).
fof(f10013,plain,
( spl16_682
| ~ spl16_208
| ~ spl16_341 ),
inference(avatar_split_clause,[],[f3582,f3545,f1820,f10011]) ).
fof(f10011,plain,
( spl16_682
<=> ! [X0,X1] :
( ~ empty(X0)
| empty(sK9(powerset(powerset(X0))))
| sK9(powerset(sK9(sK9(powerset(powerset(X0)))))) = sK9(powerset(the_InternalRel(sK8(X1))))
| ~ rel_str(sK8(X1))
| ~ rel_str(X1)
| ~ empty(the_InternalRel(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_682])]) ).
fof(f3582,plain,
( ! [X0,X1] :
( ~ empty(X0)
| empty(sK9(powerset(powerset(X0))))
| sK9(powerset(sK9(sK9(powerset(powerset(X0)))))) = sK9(powerset(the_InternalRel(sK8(X1))))
| ~ rel_str(sK8(X1))
| ~ rel_str(X1)
| ~ empty(the_InternalRel(X1)) )
| ~ spl16_208
| ~ spl16_341 ),
inference(resolution,[],[f3546,f1821]) ).
fof(f10009,plain,
( spl16_681
| ~ spl16_207
| ~ spl16_341 ),
inference(avatar_split_clause,[],[f3581,f3545,f1816,f10007]) ).
fof(f10007,plain,
( spl16_681
<=> ! [X0,X1] :
( ~ empty(X0)
| empty(sK9(powerset(powerset(X0))))
| sK9(powerset(sK9(sK9(powerset(powerset(X0)))))) = sK9(powerset(the_carrier(sK8(X1))))
| ~ rel_str(sK8(X1))
| ~ rel_str(X1)
| ~ empty(the_carrier(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_681])]) ).
fof(f3581,plain,
( ! [X0,X1] :
( ~ empty(X0)
| empty(sK9(powerset(powerset(X0))))
| sK9(powerset(sK9(sK9(powerset(powerset(X0)))))) = sK9(powerset(the_carrier(sK8(X1))))
| ~ rel_str(sK8(X1))
| ~ rel_str(X1)
| ~ empty(the_carrier(X1)) )
| ~ spl16_207
| ~ spl16_341 ),
inference(resolution,[],[f3546,f1817]) ).
fof(f10005,plain,
( spl16_680
| ~ spl16_213
| ~ spl16_331 ),
inference(avatar_split_clause,[],[f3493,f3402,f1942,f10003]) ).
fof(f10003,plain,
( spl16_680
<=> ! [X0,X1] :
( empty(powerset(X0))
| empty(sK7(powerset(X0)))
| sK9(sK7(powerset(X0))) = sK9(powerset(sK9(sK9(powerset(powerset(X1))))))
| ~ empty(X0)
| empty(sK9(powerset(powerset(X1))))
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_680])]) ).
fof(f3493,plain,
( ! [X0,X1] :
( empty(powerset(X0))
| empty(sK7(powerset(X0)))
| sK9(sK7(powerset(X0))) = sK9(powerset(sK9(sK9(powerset(powerset(X1))))))
| ~ empty(X0)
| empty(sK9(powerset(powerset(X1))))
| ~ empty(X1) )
| ~ spl16_213
| ~ spl16_331 ),
inference(resolution,[],[f3403,f1943]) ).
fof(f10001,plain,
( spl16_679
| ~ spl16_213
| ~ spl16_329 ),
inference(avatar_split_clause,[],[f3459,f3394,f1942,f9999]) ).
fof(f9999,plain,
( spl16_679
<=> ! [X0,X1] :
( empty(powerset(X0))
| empty(sK6(powerset(X0)))
| sK9(sK6(powerset(X0))) = sK9(powerset(sK9(sK9(powerset(powerset(X1))))))
| ~ empty(X0)
| empty(sK9(powerset(powerset(X1))))
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_679])]) ).
fof(f3459,plain,
( ! [X0,X1] :
( empty(powerset(X0))
| empty(sK6(powerset(X0)))
| sK9(sK6(powerset(X0))) = sK9(powerset(sK9(sK9(powerset(powerset(X1))))))
| ~ empty(X0)
| empty(sK9(powerset(powerset(X1))))
| ~ empty(X1) )
| ~ spl16_213
| ~ spl16_329 ),
inference(resolution,[],[f3395,f1943]) ).
fof(f9997,plain,
( spl16_678
| ~ spl16_110
| ~ spl16_326 ),
inference(avatar_split_clause,[],[f3381,f3305,f799,f9995]) ).
fof(f9995,plain,
( spl16_678
<=> ! [X0,X1] :
( empty(sK7(sK9(powerset(sK11(X0,X1)))))
| empty(sK11(X0,X1))
| empty(sK9(powerset(sK11(X0,X1))))
| element(sK9(sK7(sK9(powerset(sK11(X0,X1))))),cartesian_product2(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_678])]) ).
fof(f3381,plain,
( ! [X0,X1] :
( empty(sK7(sK9(powerset(sK11(X0,X1)))))
| empty(sK11(X0,X1))
| empty(sK9(powerset(sK11(X0,X1))))
| element(sK9(sK7(sK9(powerset(sK11(X0,X1))))),cartesian_product2(X0,X1)) )
| ~ spl16_110
| ~ spl16_326 ),
inference(resolution,[],[f3306,f800]) ).
fof(f9993,plain,
( spl16_677
| ~ spl16_111
| ~ spl16_326 ),
inference(avatar_split_clause,[],[f3379,f3305,f803,f9991]) ).
fof(f9991,plain,
( spl16_677
<=> ! [X0,X1] :
( empty(sK7(sK9(powerset(sK10(X0,X1)))))
| empty(sK10(X0,X1))
| empty(sK9(powerset(sK10(X0,X1))))
| element(sK9(sK7(sK9(powerset(sK10(X0,X1))))),cartesian_product2(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_677])]) ).
fof(f3379,plain,
( ! [X0,X1] :
( empty(sK7(sK9(powerset(sK10(X0,X1)))))
| empty(sK10(X0,X1))
| empty(sK9(powerset(sK10(X0,X1))))
| element(sK9(sK7(sK9(powerset(sK10(X0,X1))))),cartesian_product2(X0,X1)) )
| ~ spl16_111
| ~ spl16_326 ),
inference(resolution,[],[f3306,f804]) ).
fof(f9989,plain,
( spl16_676
| ~ spl16_110
| ~ spl16_325 ),
inference(avatar_split_clause,[],[f3358,f3300,f799,f9987]) ).
fof(f9987,plain,
( spl16_676
<=> ! [X0,X1] :
( empty(sK6(sK9(powerset(sK11(X0,X1)))))
| empty(sK11(X0,X1))
| empty(sK9(powerset(sK11(X0,X1))))
| element(sK9(sK6(sK9(powerset(sK11(X0,X1))))),cartesian_product2(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_676])]) ).
fof(f3358,plain,
( ! [X0,X1] :
( empty(sK6(sK9(powerset(sK11(X0,X1)))))
| empty(sK11(X0,X1))
| empty(sK9(powerset(sK11(X0,X1))))
| element(sK9(sK6(sK9(powerset(sK11(X0,X1))))),cartesian_product2(X0,X1)) )
| ~ spl16_110
| ~ spl16_325 ),
inference(resolution,[],[f3301,f800]) ).
fof(f9985,plain,
( spl16_675
| ~ spl16_111
| ~ spl16_325 ),
inference(avatar_split_clause,[],[f3356,f3300,f803,f9983]) ).
fof(f9983,plain,
( spl16_675
<=> ! [X0,X1] :
( empty(sK6(sK9(powerset(sK10(X0,X1)))))
| empty(sK10(X0,X1))
| empty(sK9(powerset(sK10(X0,X1))))
| element(sK9(sK6(sK9(powerset(sK10(X0,X1))))),cartesian_product2(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_675])]) ).
fof(f3356,plain,
( ! [X0,X1] :
( empty(sK6(sK9(powerset(sK10(X0,X1)))))
| empty(sK10(X0,X1))
| empty(sK9(powerset(sK10(X0,X1))))
| element(sK9(sK6(sK9(powerset(sK10(X0,X1))))),cartesian_product2(X0,X1)) )
| ~ spl16_111
| ~ spl16_325 ),
inference(resolution,[],[f3301,f804]) ).
fof(f9981,plain,
( spl16_674
| ~ spl16_215
| ~ spl16_323 ),
inference(avatar_split_clause,[],[f3315,f3292,f1961,f9979]) ).
fof(f9979,plain,
( spl16_674
<=> ! [X0,X1] :
( ~ empty(X0)
| sK9(sK9(powerset(powerset(X0)))) = sK9(powerset(sK9(sK7(powerset(X1)))))
| empty(sK9(powerset(powerset(X0))))
| ~ empty(X1)
| empty(powerset(X1))
| empty(sK7(powerset(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_674])]) ).
fof(f3315,plain,
( ! [X0,X1] :
( ~ empty(X0)
| sK9(sK9(powerset(powerset(X0)))) = sK9(powerset(sK9(sK7(powerset(X1)))))
| empty(sK9(powerset(powerset(X0))))
| ~ empty(X1)
| empty(powerset(X1))
| empty(sK7(powerset(X1))) )
| ~ spl16_215
| ~ spl16_323 ),
inference(resolution,[],[f3293,f1962]) ).
fof(f9976,plain,
( spl16_673
| ~ spl16_214
| ~ spl16_323 ),
inference(avatar_split_clause,[],[f3314,f3292,f1955,f9974]) ).
fof(f9974,plain,
( spl16_673
<=> ! [X0,X1] :
( ~ empty(X0)
| sK9(sK9(powerset(powerset(X0)))) = sK9(powerset(sK9(sK6(powerset(X1)))))
| empty(sK9(powerset(powerset(X0))))
| ~ empty(X1)
| empty(powerset(X1))
| empty(sK6(powerset(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_673])]) ).
fof(f3314,plain,
( ! [X0,X1] :
( ~ empty(X0)
| sK9(sK9(powerset(powerset(X0)))) = sK9(powerset(sK9(sK6(powerset(X1)))))
| empty(sK9(powerset(powerset(X0))))
| ~ empty(X1)
| empty(powerset(X1))
| empty(sK6(powerset(X1))) )
| ~ spl16_214
| ~ spl16_323 ),
inference(resolution,[],[f3293,f1956]) ).
fof(f9972,plain,
( spl16_672
| ~ spl16_286
| ~ spl16_323 ),
inference(avatar_split_clause,[],[f3313,f3292,f2727,f9970]) ).
fof(f9970,plain,
( spl16_672
<=> ! [X0,X1] :
( ~ empty(X0)
| sK9(sK9(powerset(powerset(X0)))) = sK9(powerset(sK9(powerset(powerset(X1)))))
| empty(sK9(powerset(powerset(X0))))
| sK14 = sK9(sK9(powerset(powerset(X1))))
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_672])]) ).
fof(f3313,plain,
( ! [X0,X1] :
( ~ empty(X0)
| sK9(sK9(powerset(powerset(X0)))) = sK9(powerset(sK9(powerset(powerset(X1)))))
| empty(sK9(powerset(powerset(X0))))
| sK14 = sK9(sK9(powerset(powerset(X1))))
| ~ empty(X1) )
| ~ spl16_286
| ~ spl16_323 ),
inference(resolution,[],[f3293,f2728]) ).
fof(f9968,plain,
( spl16_671
| ~ spl16_308
| ~ spl16_309 ),
inference(avatar_split_clause,[],[f3131,f3098,f3093,f9966]) ).
fof(f9966,plain,
( spl16_671
<=> ! [X0,X1] :
( ~ empty(X0)
| sK14 = sK9(powerset(sK9(sK9(powerset(powerset(X0))))))
| ~ empty(X1)
| sK9(powerset(powerset(X0))) = sK9(sK9(powerset(powerset(X1))))
| empty(sK9(powerset(powerset(X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_671])]) ).
fof(f3131,plain,
( ! [X0,X1] :
( ~ empty(X0)
| sK14 = sK9(powerset(sK9(sK9(powerset(powerset(X0))))))
| ~ empty(X1)
| sK9(powerset(powerset(X0))) = sK9(sK9(powerset(powerset(X1))))
| empty(sK9(powerset(powerset(X1)))) )
| ~ spl16_308
| ~ spl16_309 ),
inference(resolution,[],[f3099,f3094]) ).
fof(f9930,plain,
( spl16_670
| ~ spl16_40
| ~ spl16_642 ),
inference(avatar_split_clause,[],[f9484,f9163,f343,f9927]) ).
fof(f9927,plain,
( spl16_670
<=> relation_of2(the_InternalRel(sK8(sK8(sK1))),sK14,sK14) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_670])]) ).
fof(f9484,plain,
( relation_of2(the_InternalRel(sK8(sK8(sK1))),sK14,sK14)
| ~ spl16_40
| ~ spl16_642 ),
inference(resolution,[],[f9165,f344]) ).
fof(f9292,plain,
( spl16_669
| ~ spl16_65
| ~ spl16_371 ),
inference(avatar_split_clause,[],[f4038,f3915,f508,f9290]) ).
fof(f9290,plain,
( spl16_669
<=> ! [X0] :
( empty(sK7(sK9(powerset(powerset(X0)))))
| element(sK9(sK9(sK7(sK9(powerset(powerset(X0)))))),X0)
| empty(sK9(powerset(powerset(X0))))
| empty(sK9(sK7(sK9(powerset(powerset(X0)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_669])]) ).
fof(f4038,plain,
( ! [X0] :
( empty(sK7(sK9(powerset(powerset(X0)))))
| element(sK9(sK9(sK7(sK9(powerset(powerset(X0)))))),X0)
| empty(sK9(powerset(powerset(X0))))
| empty(sK9(sK7(sK9(powerset(powerset(X0)))))) )
| ~ spl16_65
| ~ spl16_371 ),
inference(resolution,[],[f3916,f509]) ).
fof(f9288,plain,
( spl16_668
| ~ spl16_65
| ~ spl16_370 ),
inference(avatar_split_clause,[],[f4022,f3911,f508,f9286]) ).
fof(f9286,plain,
( spl16_668
<=> ! [X0] :
( empty(sK6(sK9(powerset(powerset(X0)))))
| element(sK9(sK9(sK6(sK9(powerset(powerset(X0)))))),X0)
| empty(sK9(powerset(powerset(X0))))
| empty(sK9(sK6(sK9(powerset(powerset(X0)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_668])]) ).
fof(f4022,plain,
( ! [X0] :
( empty(sK6(sK9(powerset(powerset(X0)))))
| element(sK9(sK9(sK6(sK9(powerset(powerset(X0)))))),X0)
| empty(sK9(powerset(powerset(X0))))
| empty(sK9(sK6(sK9(powerset(powerset(X0)))))) )
| ~ spl16_65
| ~ spl16_370 ),
inference(resolution,[],[f3912,f509]) ).
fof(f9284,plain,
( spl16_667
| ~ spl16_77
| ~ spl16_362 ),
inference(avatar_split_clause,[],[f3817,f3670,f577,f9282]) ).
fof(f9282,plain,
( spl16_667
<=> ! [X0] :
( empty(sK9(sK9(powerset(powerset(sK7(X0))))))
| empty(sK7(X0))
| empty(sK9(powerset(powerset(sK7(X0)))))
| element(sK9(sK9(sK9(powerset(powerset(sK7(X0)))))),X0)
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_667])]) ).
fof(f3817,plain,
( ! [X0] :
( empty(sK9(sK9(powerset(powerset(sK7(X0))))))
| empty(sK7(X0))
| empty(sK9(powerset(powerset(sK7(X0)))))
| element(sK9(sK9(sK9(powerset(powerset(sK7(X0)))))),X0)
| empty(X0) )
| ~ spl16_77
| ~ spl16_362 ),
inference(resolution,[],[f3671,f578]) ).
fof(f9280,plain,
( spl16_666
| ~ spl16_76
| ~ spl16_362 ),
inference(avatar_split_clause,[],[f3816,f3670,f573,f9278]) ).
fof(f9278,plain,
( spl16_666
<=> ! [X0] :
( empty(sK9(sK9(powerset(powerset(sK6(X0))))))
| empty(sK6(X0))
| empty(sK9(powerset(powerset(sK6(X0)))))
| element(sK9(sK9(sK9(powerset(powerset(sK6(X0)))))),X0)
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_666])]) ).
fof(f3816,plain,
( ! [X0] :
( empty(sK9(sK9(powerset(powerset(sK6(X0))))))
| empty(sK6(X0))
| empty(sK9(powerset(powerset(sK6(X0)))))
| element(sK9(sK9(sK9(powerset(powerset(sK6(X0)))))),X0)
| empty(X0) )
| ~ spl16_76
| ~ spl16_362 ),
inference(resolution,[],[f3671,f574]) ).
fof(f9276,plain,
( spl16_665
| ~ spl16_208
| ~ spl16_331 ),
inference(avatar_split_clause,[],[f3485,f3402,f1820,f9274]) ).
fof(f9274,plain,
( spl16_665
<=> ! [X0,X1] :
( empty(powerset(X0))
| empty(sK7(powerset(X0)))
| sK9(sK7(powerset(X0))) = sK9(powerset(the_InternalRel(sK8(X1))))
| ~ empty(X0)
| ~ rel_str(sK8(X1))
| ~ rel_str(X1)
| ~ empty(the_InternalRel(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_665])]) ).
fof(f3485,plain,
( ! [X0,X1] :
( empty(powerset(X0))
| empty(sK7(powerset(X0)))
| sK9(sK7(powerset(X0))) = sK9(powerset(the_InternalRel(sK8(X1))))
| ~ empty(X0)
| ~ rel_str(sK8(X1))
| ~ rel_str(X1)
| ~ empty(the_InternalRel(X1)) )
| ~ spl16_208
| ~ spl16_331 ),
inference(resolution,[],[f3403,f1821]) ).
fof(f9272,plain,
( spl16_664
| ~ spl16_207
| ~ spl16_331 ),
inference(avatar_split_clause,[],[f3484,f3402,f1816,f9270]) ).
fof(f9270,plain,
( spl16_664
<=> ! [X0,X1] :
( empty(powerset(X0))
| empty(sK7(powerset(X0)))
| sK9(sK7(powerset(X0))) = sK9(powerset(the_carrier(sK8(X1))))
| ~ empty(X0)
| ~ rel_str(sK8(X1))
| ~ rel_str(X1)
| ~ empty(the_carrier(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_664])]) ).
fof(f3484,plain,
( ! [X0,X1] :
( empty(powerset(X0))
| empty(sK7(powerset(X0)))
| sK9(sK7(powerset(X0))) = sK9(powerset(the_carrier(sK8(X1))))
| ~ empty(X0)
| ~ rel_str(sK8(X1))
| ~ rel_str(X1)
| ~ empty(the_carrier(X1)) )
| ~ spl16_207
| ~ spl16_331 ),
inference(resolution,[],[f3403,f1817]) ).
fof(f9268,plain,
( spl16_663
| ~ spl16_208
| ~ spl16_329 ),
inference(avatar_split_clause,[],[f3451,f3394,f1820,f9266]) ).
fof(f9266,plain,
( spl16_663
<=> ! [X0,X1] :
( empty(powerset(X0))
| empty(sK6(powerset(X0)))
| sK9(sK6(powerset(X0))) = sK9(powerset(the_InternalRel(sK8(X1))))
| ~ empty(X0)
| ~ rel_str(sK8(X1))
| ~ rel_str(X1)
| ~ empty(the_InternalRel(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_663])]) ).
fof(f3451,plain,
( ! [X0,X1] :
( empty(powerset(X0))
| empty(sK6(powerset(X0)))
| sK9(sK6(powerset(X0))) = sK9(powerset(the_InternalRel(sK8(X1))))
| ~ empty(X0)
| ~ rel_str(sK8(X1))
| ~ rel_str(X1)
| ~ empty(the_InternalRel(X1)) )
| ~ spl16_208
| ~ spl16_329 ),
inference(resolution,[],[f3395,f1821]) ).
fof(f9264,plain,
( spl16_662
| ~ spl16_207
| ~ spl16_329 ),
inference(avatar_split_clause,[],[f3450,f3394,f1816,f9262]) ).
fof(f9262,plain,
( spl16_662
<=> ! [X0,X1] :
( empty(powerset(X0))
| empty(sK6(powerset(X0)))
| sK9(sK6(powerset(X0))) = sK9(powerset(the_carrier(sK8(X1))))
| ~ empty(X0)
| ~ rel_str(sK8(X1))
| ~ rel_str(X1)
| ~ empty(the_carrier(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_662])]) ).
fof(f3450,plain,
( ! [X0,X1] :
( empty(powerset(X0))
| empty(sK6(powerset(X0)))
| sK9(sK6(powerset(X0))) = sK9(powerset(the_carrier(sK8(X1))))
| ~ empty(X0)
| ~ rel_str(sK8(X1))
| ~ rel_str(X1)
| ~ empty(the_carrier(X1)) )
| ~ spl16_207
| ~ spl16_329 ),
inference(resolution,[],[f3395,f1817]) ).
fof(f9260,plain,
( spl16_661
| ~ spl16_282
| ~ spl16_324 ),
inference(avatar_split_clause,[],[f3333,f3296,f2692,f9258]) ).
fof(f9258,plain,
( spl16_661
<=> ! [X0,X1] :
( ~ empty(X0)
| sK14 = sK9(powerset(sK9(powerset(sK9(sK9(powerset(powerset(X0))))))))
| sK9(powerset(X1)) = sK9(powerset(sK9(powerset(sK9(powerset(powerset(X0)))))))
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_661])]) ).
fof(f2692,plain,
( spl16_282
<=> ! [X0,X1] :
( ~ empty(X0)
| sK9(powerset(X0)) = sK9(powerset(sK9(powerset(X1))))
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_282])]) ).
fof(f3333,plain,
( ! [X0,X1] :
( ~ empty(X0)
| sK14 = sK9(powerset(sK9(powerset(sK9(sK9(powerset(powerset(X0))))))))
| sK9(powerset(X1)) = sK9(powerset(sK9(powerset(sK9(powerset(powerset(X0)))))))
| ~ empty(X1) )
| ~ spl16_282
| ~ spl16_324 ),
inference(resolution,[],[f3297,f2693]) ).
fof(f2693,plain,
( ! [X0,X1] :
( ~ empty(X1)
| sK9(powerset(X0)) = sK9(powerset(sK9(powerset(X1))))
| ~ empty(X0) )
| ~ spl16_282 ),
inference(avatar_component_clause,[],[f2692]) ).
fof(f9256,plain,
( spl16_660
| ~ spl16_213
| ~ spl16_323 ),
inference(avatar_split_clause,[],[f3316,f3292,f1942,f9254]) ).
fof(f9254,plain,
( spl16_660
<=> ! [X0,X1] :
( ~ empty(X0)
| sK9(sK9(powerset(powerset(X0)))) = sK9(powerset(sK9(sK9(powerset(powerset(X1))))))
| empty(sK9(powerset(powerset(X0))))
| empty(sK9(powerset(powerset(X1))))
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_660])]) ).
fof(f3316,plain,
( ! [X0,X1] :
( ~ empty(X0)
| sK9(sK9(powerset(powerset(X0)))) = sK9(powerset(sK9(sK9(powerset(powerset(X1))))))
| empty(sK9(powerset(powerset(X0))))
| empty(sK9(powerset(powerset(X1))))
| ~ empty(X1) )
| ~ spl16_213
| ~ spl16_323 ),
inference(resolution,[],[f3293,f1943]) ).
fof(f9247,plain,
( ~ spl16_224
| ~ spl16_58
| spl16_641 ),
inference(avatar_split_clause,[],[f9206,f9159,f476,f2058]) ).
fof(f9206,plain,
( ~ rel_str(sK8(sK1))
| ~ spl16_58
| spl16_641 ),
inference(resolution,[],[f9161,f477]) ).
fof(f9161,plain,
( ~ rel_str(sK8(sK8(sK1)))
| spl16_641 ),
inference(avatar_component_clause,[],[f9159]) ).
fof(f9246,plain,
( spl16_659
| ~ spl16_110
| ~ spl16_321 ),
inference(avatar_split_clause,[],[f3289,f3175,f799,f9244]) ).
fof(f9244,plain,
( spl16_659
<=> ! [X0,X1] :
( empty(sK7(sK11(X0,X1)))
| empty(sK11(X0,X1))
| empty(sK9(powerset(sK7(sK11(X0,X1)))))
| element(sK9(sK9(powerset(sK7(sK11(X0,X1))))),cartesian_product2(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_659])]) ).
fof(f3289,plain,
( ! [X0,X1] :
( empty(sK7(sK11(X0,X1)))
| empty(sK11(X0,X1))
| empty(sK9(powerset(sK7(sK11(X0,X1)))))
| element(sK9(sK9(powerset(sK7(sK11(X0,X1))))),cartesian_product2(X0,X1)) )
| ~ spl16_110
| ~ spl16_321 ),
inference(resolution,[],[f3176,f800]) ).
fof(f9242,plain,
( spl16_658
| ~ spl16_111
| ~ spl16_321 ),
inference(avatar_split_clause,[],[f3287,f3175,f803,f9240]) ).
fof(f9240,plain,
( spl16_658
<=> ! [X0,X1] :
( empty(sK7(sK10(X0,X1)))
| empty(sK10(X0,X1))
| empty(sK9(powerset(sK7(sK10(X0,X1)))))
| element(sK9(sK9(powerset(sK7(sK10(X0,X1))))),cartesian_product2(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_658])]) ).
fof(f3287,plain,
( ! [X0,X1] :
( empty(sK7(sK10(X0,X1)))
| empty(sK10(X0,X1))
| empty(sK9(powerset(sK7(sK10(X0,X1)))))
| element(sK9(sK9(powerset(sK7(sK10(X0,X1))))),cartesian_product2(X0,X1)) )
| ~ spl16_111
| ~ spl16_321 ),
inference(resolution,[],[f3176,f804]) ).
fof(f9238,plain,
( spl16_657
| ~ spl16_110
| ~ spl16_320 ),
inference(avatar_split_clause,[],[f3268,f3171,f799,f9236]) ).
fof(f9236,plain,
( spl16_657
<=> ! [X0,X1] :
( empty(sK6(sK11(X0,X1)))
| empty(sK11(X0,X1))
| empty(sK9(powerset(sK6(sK11(X0,X1)))))
| element(sK9(sK9(powerset(sK6(sK11(X0,X1))))),cartesian_product2(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_657])]) ).
fof(f3268,plain,
( ! [X0,X1] :
( empty(sK6(sK11(X0,X1)))
| empty(sK11(X0,X1))
| empty(sK9(powerset(sK6(sK11(X0,X1)))))
| element(sK9(sK9(powerset(sK6(sK11(X0,X1))))),cartesian_product2(X0,X1)) )
| ~ spl16_110
| ~ spl16_320 ),
inference(resolution,[],[f3172,f800]) ).
fof(f9234,plain,
( spl16_656
| ~ spl16_111
| ~ spl16_320 ),
inference(avatar_split_clause,[],[f3266,f3171,f803,f9232]) ).
fof(f9232,plain,
( spl16_656
<=> ! [X0,X1] :
( empty(sK6(sK10(X0,X1)))
| empty(sK10(X0,X1))
| empty(sK9(powerset(sK6(sK10(X0,X1)))))
| element(sK9(sK9(powerset(sK6(sK10(X0,X1))))),cartesian_product2(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_656])]) ).
fof(f3266,plain,
( ! [X0,X1] :
( empty(sK6(sK10(X0,X1)))
| empty(sK10(X0,X1))
| empty(sK9(powerset(sK6(sK10(X0,X1)))))
| element(sK9(sK9(powerset(sK6(sK10(X0,X1))))),cartesian_product2(X0,X1)) )
| ~ spl16_111
| ~ spl16_320 ),
inference(resolution,[],[f3172,f804]) ).
fof(f9230,plain,
( spl16_655
| ~ spl16_215
| ~ spl16_318 ),
inference(avatar_split_clause,[],[f3228,f3163,f1961,f9228]) ).
fof(f9228,plain,
( spl16_655
<=> ! [X0,X1] :
( empty(powerset(X0))
| empty(sK7(powerset(X0)))
| sK9(sK7(powerset(X0))) = sK9(sK7(powerset(X1)))
| ~ empty(X0)
| ~ empty(X1)
| empty(powerset(X1))
| empty(sK7(powerset(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_655])]) ).
fof(f3228,plain,
( ! [X0,X1] :
( empty(powerset(X0))
| empty(sK7(powerset(X0)))
| sK9(sK7(powerset(X0))) = sK9(sK7(powerset(X1)))
| ~ empty(X0)
| ~ empty(X1)
| empty(powerset(X1))
| empty(sK7(powerset(X1))) )
| ~ spl16_215
| ~ spl16_318 ),
inference(resolution,[],[f3164,f1962]) ).
fof(f9226,plain,
( spl16_654
| ~ spl16_286
| ~ spl16_318 ),
inference(avatar_split_clause,[],[f3226,f3163,f2727,f9224]) ).
fof(f9224,plain,
( spl16_654
<=> ! [X0,X1] :
( empty(powerset(X0))
| empty(sK7(powerset(X0)))
| sK9(powerset(powerset(X1))) = sK9(sK7(powerset(X0)))
| ~ empty(X0)
| sK14 = sK9(sK9(powerset(powerset(X1))))
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_654])]) ).
fof(f3226,plain,
( ! [X0,X1] :
( empty(powerset(X0))
| empty(sK7(powerset(X0)))
| sK9(powerset(powerset(X1))) = sK9(sK7(powerset(X0)))
| ~ empty(X0)
| sK14 = sK9(sK9(powerset(powerset(X1))))
| ~ empty(X1) )
| ~ spl16_286
| ~ spl16_318 ),
inference(resolution,[],[f3164,f2728]) ).
fof(f9222,plain,
( spl16_653
| ~ spl16_215
| ~ spl16_316 ),
inference(avatar_split_clause,[],[f3201,f3155,f1961,f9220]) ).
fof(f9220,plain,
( spl16_653
<=> ! [X0,X1] :
( empty(powerset(X0))
| empty(sK6(powerset(X0)))
| sK9(sK6(powerset(X0))) = sK9(sK7(powerset(X1)))
| ~ empty(X0)
| ~ empty(X1)
| empty(powerset(X1))
| empty(sK7(powerset(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_653])]) ).
fof(f3201,plain,
( ! [X0,X1] :
( empty(powerset(X0))
| empty(sK6(powerset(X0)))
| sK9(sK6(powerset(X0))) = sK9(sK7(powerset(X1)))
| ~ empty(X0)
| ~ empty(X1)
| empty(powerset(X1))
| empty(sK7(powerset(X1))) )
| ~ spl16_215
| ~ spl16_316 ),
inference(resolution,[],[f3156,f1962]) ).
fof(f9218,plain,
( spl16_652
| ~ spl16_214
| ~ spl16_316 ),
inference(avatar_split_clause,[],[f3200,f3155,f1955,f9216]) ).
fof(f9216,plain,
( spl16_652
<=> ! [X0,X1] :
( empty(powerset(X0))
| empty(sK6(powerset(X0)))
| sK9(sK6(powerset(X0))) = sK9(sK6(powerset(X1)))
| ~ empty(X0)
| ~ empty(X1)
| empty(powerset(X1))
| empty(sK6(powerset(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_652])]) ).
fof(f3200,plain,
( ! [X0,X1] :
( empty(powerset(X0))
| empty(sK6(powerset(X0)))
| sK9(sK6(powerset(X0))) = sK9(sK6(powerset(X1)))
| ~ empty(X0)
| ~ empty(X1)
| empty(powerset(X1))
| empty(sK6(powerset(X1))) )
| ~ spl16_214
| ~ spl16_316 ),
inference(resolution,[],[f3156,f1956]) ).
fof(f9214,plain,
( spl16_651
| ~ spl16_286
| ~ spl16_316 ),
inference(avatar_split_clause,[],[f3199,f3155,f2727,f9212]) ).
fof(f9212,plain,
( spl16_651
<=> ! [X0,X1] :
( empty(powerset(X0))
| empty(sK6(powerset(X0)))
| sK9(powerset(powerset(X1))) = sK9(sK6(powerset(X0)))
| ~ empty(X0)
| sK14 = sK9(sK9(powerset(powerset(X1))))
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_651])]) ).
fof(f3199,plain,
( ! [X0,X1] :
( empty(powerset(X0))
| empty(sK6(powerset(X0)))
| sK9(powerset(powerset(X1))) = sK9(sK6(powerset(X0)))
| ~ empty(X0)
| sK14 = sK9(sK9(powerset(powerset(X1))))
| ~ empty(X1) )
| ~ spl16_286
| ~ spl16_316 ),
inference(resolution,[],[f3156,f2728]) ).
fof(f9210,plain,
( spl16_650
| ~ spl16_120
| ~ spl16_306 ),
inference(avatar_split_clause,[],[f3076,f2964,f884,f9208]) ).
fof(f9208,plain,
( spl16_650
<=> ! [X0,X1] :
( empty(sK7(sK7(the_InternalRel(X0))))
| empty(the_InternalRel(X0))
| empty(sK7(the_InternalRel(X0)))
| element(sK9(sK7(sK7(the_InternalRel(X0)))),the_InternalRel(X1))
| ~ subrelstr(X0,X1)
| ~ rel_str(X0)
| ~ rel_str(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_650])]) ).
fof(f3076,plain,
( ! [X0,X1] :
( empty(sK7(sK7(the_InternalRel(X0))))
| empty(the_InternalRel(X0))
| empty(sK7(the_InternalRel(X0)))
| element(sK9(sK7(sK7(the_InternalRel(X0)))),the_InternalRel(X1))
| ~ subrelstr(X0,X1)
| ~ rel_str(X0)
| ~ rel_str(X1) )
| ~ spl16_120
| ~ spl16_306 ),
inference(resolution,[],[f2965,f885]) ).
fof(f9205,plain,
( spl16_649
| ~ spl16_119
| ~ spl16_306 ),
inference(avatar_split_clause,[],[f3074,f2964,f880,f9203]) ).
fof(f9203,plain,
( spl16_649
<=> ! [X0,X1] :
( empty(sK7(sK7(the_carrier(X0))))
| empty(the_carrier(X0))
| empty(sK7(the_carrier(X0)))
| element(sK9(sK7(sK7(the_carrier(X0)))),the_carrier(X1))
| ~ subrelstr(X0,X1)
| ~ rel_str(X0)
| ~ rel_str(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_649])]) ).
fof(f3074,plain,
( ! [X0,X1] :
( empty(sK7(sK7(the_carrier(X0))))
| empty(the_carrier(X0))
| empty(sK7(the_carrier(X0)))
| element(sK9(sK7(sK7(the_carrier(X0)))),the_carrier(X1))
| ~ subrelstr(X0,X1)
| ~ rel_str(X0)
| ~ rel_str(X1) )
| ~ spl16_119
| ~ spl16_306 ),
inference(resolution,[],[f2965,f881]) ).
fof(f9201,plain,
( spl16_648
| ~ spl16_120
| ~ spl16_305 ),
inference(avatar_split_clause,[],[f3055,f2960,f884,f9199]) ).
fof(f9199,plain,
( spl16_648
<=> ! [X0,X1] :
( empty(sK7(sK6(the_InternalRel(X0))))
| empty(the_InternalRel(X0))
| empty(sK6(the_InternalRel(X0)))
| element(sK9(sK7(sK6(the_InternalRel(X0)))),the_InternalRel(X1))
| ~ subrelstr(X0,X1)
| ~ rel_str(X0)
| ~ rel_str(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_648])]) ).
fof(f3055,plain,
( ! [X0,X1] :
( empty(sK7(sK6(the_InternalRel(X0))))
| empty(the_InternalRel(X0))
| empty(sK6(the_InternalRel(X0)))
| element(sK9(sK7(sK6(the_InternalRel(X0)))),the_InternalRel(X1))
| ~ subrelstr(X0,X1)
| ~ rel_str(X0)
| ~ rel_str(X1) )
| ~ spl16_120
| ~ spl16_305 ),
inference(resolution,[],[f2961,f885]) ).
fof(f9197,plain,
( spl16_647
| ~ spl16_119
| ~ spl16_305 ),
inference(avatar_split_clause,[],[f3053,f2960,f880,f9195]) ).
fof(f9195,plain,
( spl16_647
<=> ! [X0,X1] :
( empty(sK7(sK6(the_carrier(X0))))
| empty(the_carrier(X0))
| empty(sK6(the_carrier(X0)))
| element(sK9(sK7(sK6(the_carrier(X0)))),the_carrier(X1))
| ~ subrelstr(X0,X1)
| ~ rel_str(X0)
| ~ rel_str(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_647])]) ).
fof(f3053,plain,
( ! [X0,X1] :
( empty(sK7(sK6(the_carrier(X0))))
| empty(the_carrier(X0))
| empty(sK6(the_carrier(X0)))
| element(sK9(sK7(sK6(the_carrier(X0)))),the_carrier(X1))
| ~ subrelstr(X0,X1)
| ~ rel_str(X0)
| ~ rel_str(X1) )
| ~ spl16_119
| ~ spl16_305 ),
inference(resolution,[],[f2961,f881]) ).
fof(f9193,plain,
( spl16_646
| ~ spl16_120
| ~ spl16_304 ),
inference(avatar_split_clause,[],[f3034,f2956,f884,f9191]) ).
fof(f9191,plain,
( spl16_646
<=> ! [X0,X1] :
( empty(sK6(sK7(the_InternalRel(X0))))
| empty(the_InternalRel(X0))
| empty(sK7(the_InternalRel(X0)))
| element(sK9(sK6(sK7(the_InternalRel(X0)))),the_InternalRel(X1))
| ~ subrelstr(X0,X1)
| ~ rel_str(X0)
| ~ rel_str(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_646])]) ).
fof(f3034,plain,
( ! [X0,X1] :
( empty(sK6(sK7(the_InternalRel(X0))))
| empty(the_InternalRel(X0))
| empty(sK7(the_InternalRel(X0)))
| element(sK9(sK6(sK7(the_InternalRel(X0)))),the_InternalRel(X1))
| ~ subrelstr(X0,X1)
| ~ rel_str(X0)
| ~ rel_str(X1) )
| ~ spl16_120
| ~ spl16_304 ),
inference(resolution,[],[f2957,f885]) ).
fof(f9189,plain,
( spl16_645
| ~ spl16_119
| ~ spl16_304 ),
inference(avatar_split_clause,[],[f3032,f2956,f880,f9187]) ).
fof(f9187,plain,
( spl16_645
<=> ! [X0,X1] :
( empty(sK6(sK7(the_carrier(X0))))
| empty(the_carrier(X0))
| empty(sK7(the_carrier(X0)))
| element(sK9(sK6(sK7(the_carrier(X0)))),the_carrier(X1))
| ~ subrelstr(X0,X1)
| ~ rel_str(X0)
| ~ rel_str(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_645])]) ).
fof(f3032,plain,
( ! [X0,X1] :
( empty(sK6(sK7(the_carrier(X0))))
| empty(the_carrier(X0))
| empty(sK7(the_carrier(X0)))
| element(sK9(sK6(sK7(the_carrier(X0)))),the_carrier(X1))
| ~ subrelstr(X0,X1)
| ~ rel_str(X0)
| ~ rel_str(X1) )
| ~ spl16_119
| ~ spl16_304 ),
inference(resolution,[],[f2957,f881]) ).
fof(f9185,plain,
( spl16_644
| ~ spl16_120
| ~ spl16_303 ),
inference(avatar_split_clause,[],[f3013,f2952,f884,f9183]) ).
fof(f9183,plain,
( spl16_644
<=> ! [X0,X1] :
( empty(sK6(sK6(the_InternalRel(X0))))
| empty(the_InternalRel(X0))
| empty(sK6(the_InternalRel(X0)))
| element(sK9(sK6(sK6(the_InternalRel(X0)))),the_InternalRel(X1))
| ~ subrelstr(X0,X1)
| ~ rel_str(X0)
| ~ rel_str(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_644])]) ).
fof(f3013,plain,
( ! [X0,X1] :
( empty(sK6(sK6(the_InternalRel(X0))))
| empty(the_InternalRel(X0))
| empty(sK6(the_InternalRel(X0)))
| element(sK9(sK6(sK6(the_InternalRel(X0)))),the_InternalRel(X1))
| ~ subrelstr(X0,X1)
| ~ rel_str(X0)
| ~ rel_str(X1) )
| ~ spl16_120
| ~ spl16_303 ),
inference(resolution,[],[f2953,f885]) ).
fof(f9181,plain,
( spl16_643
| ~ spl16_119
| ~ spl16_303 ),
inference(avatar_split_clause,[],[f3011,f2952,f880,f9179]) ).
fof(f9179,plain,
( spl16_643
<=> ! [X0,X1] :
( empty(sK6(sK6(the_carrier(X0))))
| empty(the_carrier(X0))
| empty(sK6(the_carrier(X0)))
| element(sK9(sK6(sK6(the_carrier(X0)))),the_carrier(X1))
| ~ subrelstr(X0,X1)
| ~ rel_str(X0)
| ~ rel_str(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_643])]) ).
fof(f3011,plain,
( ! [X0,X1] :
( empty(sK6(sK6(the_carrier(X0))))
| empty(the_carrier(X0))
| empty(sK6(the_carrier(X0)))
| element(sK9(sK6(sK6(the_carrier(X0)))),the_carrier(X1))
| ~ subrelstr(X0,X1)
| ~ rel_str(X0)
| ~ rel_str(X1) )
| ~ spl16_119
| ~ spl16_303 ),
inference(resolution,[],[f2953,f881]) ).
fof(f9166,plain,
( ~ spl16_641
| spl16_642
| ~ spl16_43
| ~ spl16_577 ),
inference(avatar_split_clause,[],[f7789,f7642,f370,f9163,f9159]) ).
fof(f7789,plain,
( relation_of2_as_subset(the_InternalRel(sK8(sK8(sK1))),sK14,sK14)
| ~ rel_str(sK8(sK8(sK1)))
| ~ spl16_43
| ~ spl16_577 ),
inference(superposition,[],[f371,f7644]) ).
fof(f9000,plain,
( spl16_640
| ~ spl16_224
| ~ spl16_477
| ~ spl16_555 ),
inference(avatar_split_clause,[],[f7185,f7177,f5688,f2058,f8998]) ).
fof(f8998,plain,
( spl16_640
<=> ! [X0] :
( the_carrier(sK8(sK8(sK1))) = X0
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_640])]) ).
fof(f5688,plain,
( spl16_477
<=> ! [X0,X1] :
( ~ rel_str(X0)
| ~ empty(the_carrier(X0))
| the_carrier(sK8(X0)) = X1
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_477])]) ).
fof(f7177,plain,
( spl16_555
<=> empty(the_carrier(sK8(sK1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_555])]) ).
fof(f7185,plain,
( ! [X0] :
( ~ rel_str(sK8(sK1))
| the_carrier(sK8(sK8(sK1))) = X0
| ~ empty(X0) )
| ~ spl16_477
| ~ spl16_555 ),
inference(resolution,[],[f7179,f5689]) ).
fof(f5689,plain,
( ! [X0,X1] :
( ~ empty(the_carrier(X0))
| ~ rel_str(X0)
| the_carrier(sK8(X0)) = X1
| ~ empty(X1) )
| ~ spl16_477 ),
inference(avatar_component_clause,[],[f5688]) ).
fof(f7179,plain,
( empty(the_carrier(sK8(sK1)))
| ~ spl16_555 ),
inference(avatar_component_clause,[],[f7177]) ).
fof(f8845,plain,
( spl16_639
| ~ spl16_27
| ~ spl16_411 ),
inference(avatar_split_clause,[],[f4460,f4415,f282,f8843]) ).
fof(f8843,plain,
( spl16_639
<=> ! [X0,X1] :
( empty(the_InternalRel(X0))
| ~ subrelstr(X0,X1)
| ~ rel_str(X0)
| ~ rel_str(X1)
| empty(the_InternalRel(X1))
| empty(sK9(powerset(the_InternalRel(X0))))
| ~ in(the_InternalRel(X1),sK9(sK9(powerset(the_InternalRel(X0))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_639])]) ).
fof(f4460,plain,
( ! [X0,X1] :
( empty(the_InternalRel(X0))
| ~ subrelstr(X0,X1)
| ~ rel_str(X0)
| ~ rel_str(X1)
| empty(the_InternalRel(X1))
| empty(sK9(powerset(the_InternalRel(X0))))
| ~ in(the_InternalRel(X1),sK9(sK9(powerset(the_InternalRel(X0))))) )
| ~ spl16_27
| ~ spl16_411 ),
inference(resolution,[],[f4416,f283]) ).
fof(f8841,plain,
( spl16_638
| ~ spl16_27
| ~ spl16_410 ),
inference(avatar_split_clause,[],[f4453,f4411,f282,f8839]) ).
fof(f8839,plain,
( spl16_638
<=> ! [X0,X1] :
( empty(the_carrier(X0))
| ~ subrelstr(X0,X1)
| ~ rel_str(X0)
| ~ rel_str(X1)
| empty(the_carrier(X1))
| empty(sK9(powerset(the_carrier(X0))))
| ~ in(the_carrier(X1),sK9(sK9(powerset(the_carrier(X0))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_638])]) ).
fof(f4453,plain,
( ! [X0,X1] :
( empty(the_carrier(X0))
| ~ subrelstr(X0,X1)
| ~ rel_str(X0)
| ~ rel_str(X1)
| empty(the_carrier(X1))
| empty(sK9(powerset(the_carrier(X0))))
| ~ in(the_carrier(X1),sK9(sK9(powerset(the_carrier(X0))))) )
| ~ spl16_27
| ~ spl16_410 ),
inference(resolution,[],[f4412,f283]) ).
fof(f8837,plain,
( spl16_637
| ~ spl16_65
| ~ spl16_369 ),
inference(avatar_split_clause,[],[f4006,f3907,f508,f8835]) ).
fof(f8835,plain,
( spl16_637
<=> ! [X0] :
( empty(sK7(sK7(powerset(X0))))
| empty(powerset(X0))
| element(sK9(sK9(sK7(sK7(powerset(X0))))),X0)
| empty(sK7(powerset(X0)))
| empty(sK9(sK7(sK7(powerset(X0))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_637])]) ).
fof(f4006,plain,
( ! [X0] :
( empty(sK7(sK7(powerset(X0))))
| empty(powerset(X0))
| element(sK9(sK9(sK7(sK7(powerset(X0))))),X0)
| empty(sK7(powerset(X0)))
| empty(sK9(sK7(sK7(powerset(X0))))) )
| ~ spl16_65
| ~ spl16_369 ),
inference(resolution,[],[f3908,f509]) ).
fof(f8833,plain,
( spl16_636
| ~ spl16_65
| ~ spl16_368 ),
inference(avatar_split_clause,[],[f3990,f3903,f508,f8831]) ).
fof(f8831,plain,
( spl16_636
<=> ! [X0] :
( empty(sK7(sK6(powerset(X0))))
| empty(powerset(X0))
| element(sK9(sK9(sK7(sK6(powerset(X0))))),X0)
| empty(sK6(powerset(X0)))
| empty(sK9(sK7(sK6(powerset(X0))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_636])]) ).
fof(f3990,plain,
( ! [X0] :
( empty(sK7(sK6(powerset(X0))))
| empty(powerset(X0))
| element(sK9(sK9(sK7(sK6(powerset(X0))))),X0)
| empty(sK6(powerset(X0)))
| empty(sK9(sK7(sK6(powerset(X0))))) )
| ~ spl16_65
| ~ spl16_368 ),
inference(resolution,[],[f3904,f509]) ).
fof(f8829,plain,
( spl16_635
| ~ spl16_65
| ~ spl16_366 ),
inference(avatar_split_clause,[],[f3974,f3895,f508,f8827]) ).
fof(f8827,plain,
( spl16_635
<=> ! [X0] :
( empty(sK6(sK7(powerset(X0))))
| empty(powerset(X0))
| element(sK9(sK9(sK6(sK7(powerset(X0))))),X0)
| empty(sK7(powerset(X0)))
| empty(sK9(sK6(sK7(powerset(X0))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_635])]) ).
fof(f3974,plain,
( ! [X0] :
( empty(sK6(sK7(powerset(X0))))
| empty(powerset(X0))
| element(sK9(sK9(sK6(sK7(powerset(X0))))),X0)
| empty(sK7(powerset(X0)))
| empty(sK9(sK6(sK7(powerset(X0))))) )
| ~ spl16_65
| ~ spl16_366 ),
inference(resolution,[],[f3896,f509]) ).
fof(f8825,plain,
( spl16_634
| ~ spl16_65
| ~ spl16_365 ),
inference(avatar_split_clause,[],[f3958,f3891,f508,f8823]) ).
fof(f8823,plain,
( spl16_634
<=> ! [X0] :
( empty(sK6(sK6(powerset(X0))))
| empty(powerset(X0))
| element(sK9(sK9(sK6(sK6(powerset(X0))))),X0)
| empty(sK6(powerset(X0)))
| empty(sK9(sK6(sK6(powerset(X0))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_634])]) ).
fof(f3958,plain,
( ! [X0] :
( empty(sK6(sK6(powerset(X0))))
| empty(powerset(X0))
| element(sK9(sK9(sK6(sK6(powerset(X0))))),X0)
| empty(sK6(powerset(X0)))
| empty(sK9(sK6(sK6(powerset(X0))))) )
| ~ spl16_65
| ~ spl16_365 ),
inference(resolution,[],[f3892,f509]) ).
fof(f8821,plain,
( spl16_633
| ~ spl16_77
| ~ spl16_349 ),
inference(avatar_split_clause,[],[f3606,f3578,f577,f8819]) ).
fof(f8819,plain,
( spl16_633
<=> ! [X0] :
( empty(sK9(powerset(sK7(X0))))
| empty(sK7(X0))
| empty(sK9(powerset(sK9(powerset(sK7(X0))))))
| element(sK9(sK9(powerset(sK9(powerset(sK7(X0)))))),X0)
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_633])]) ).
fof(f3606,plain,
( ! [X0] :
( empty(sK9(powerset(sK7(X0))))
| empty(sK7(X0))
| empty(sK9(powerset(sK9(powerset(sK7(X0))))))
| element(sK9(sK9(powerset(sK9(powerset(sK7(X0)))))),X0)
| empty(X0) )
| ~ spl16_77
| ~ spl16_349 ),
inference(resolution,[],[f3579,f578]) ).
fof(f8817,plain,
( spl16_632
| ~ spl16_76
| ~ spl16_349 ),
inference(avatar_split_clause,[],[f3605,f3578,f573,f8815]) ).
fof(f8815,plain,
( spl16_632
<=> ! [X0] :
( empty(sK9(powerset(sK6(X0))))
| empty(sK6(X0))
| empty(sK9(powerset(sK9(powerset(sK6(X0))))))
| element(sK9(sK9(powerset(sK9(powerset(sK6(X0)))))),X0)
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_632])]) ).
fof(f3605,plain,
( ! [X0] :
( empty(sK9(powerset(sK6(X0))))
| empty(sK6(X0))
| empty(sK9(powerset(sK9(powerset(sK6(X0))))))
| element(sK9(sK9(powerset(sK9(powerset(sK6(X0)))))),X0)
| empty(X0) )
| ~ spl16_76
| ~ spl16_349 ),
inference(resolution,[],[f3579,f574]) ).
fof(f8812,plain,
( spl16_631
| ~ spl16_224
| ~ spl16_479
| ~ spl16_555 ),
inference(avatar_split_clause,[],[f7184,f7177,f5696,f2058,f8809]) ).
fof(f8809,plain,
( spl16_631
<=> sK14 = sK9(powerset(the_carrier(sK8(sK8(sK1))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_631])]) ).
fof(f5696,plain,
( spl16_479
<=> ! [X0] :
( ~ rel_str(X0)
| ~ empty(the_carrier(X0))
| sK14 = sK9(powerset(the_carrier(sK8(X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_479])]) ).
fof(f7184,plain,
( ~ rel_str(sK8(sK1))
| sK14 = sK9(powerset(the_carrier(sK8(sK8(sK1)))))
| ~ spl16_479
| ~ spl16_555 ),
inference(resolution,[],[f7179,f5697]) ).
fof(f5697,plain,
( ! [X0] :
( ~ empty(the_carrier(X0))
| ~ rel_str(X0)
| sK14 = sK9(powerset(the_carrier(sK8(X0)))) )
| ~ spl16_479 ),
inference(avatar_component_clause,[],[f5696]) ).
fof(f8807,plain,
( spl16_630
| ~ spl16_72
| ~ spl16_326 ),
inference(avatar_split_clause,[],[f3371,f3305,f549,f8805]) ).
fof(f8805,plain,
( spl16_630
<=> ! [X0] :
( empty(sK7(sK9(powerset(sK9(powerset(X0))))))
| empty(sK9(powerset(X0)))
| empty(sK9(powerset(sK9(powerset(X0)))))
| element(sK9(sK7(sK9(powerset(sK9(powerset(X0)))))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_630])]) ).
fof(f3371,plain,
( ! [X0] :
( empty(sK7(sK9(powerset(sK9(powerset(X0))))))
| empty(sK9(powerset(X0)))
| empty(sK9(powerset(sK9(powerset(X0)))))
| element(sK9(sK7(sK9(powerset(sK9(powerset(X0)))))),X0) )
| ~ spl16_72
| ~ spl16_326 ),
inference(resolution,[],[f3306,f550]) ).
fof(f8803,plain,
( spl16_629
| ~ spl16_72
| ~ spl16_325 ),
inference(avatar_split_clause,[],[f3348,f3300,f549,f8801]) ).
fof(f8801,plain,
( spl16_629
<=> ! [X0] :
( empty(sK6(sK9(powerset(sK9(powerset(X0))))))
| empty(sK9(powerset(X0)))
| empty(sK9(powerset(sK9(powerset(X0)))))
| element(sK9(sK6(sK9(powerset(sK9(powerset(X0)))))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_629])]) ).
fof(f3348,plain,
( ! [X0] :
( empty(sK6(sK9(powerset(sK9(powerset(X0))))))
| empty(sK9(powerset(X0)))
| empty(sK9(powerset(sK9(powerset(X0)))))
| element(sK9(sK6(sK9(powerset(sK9(powerset(X0)))))),X0) )
| ~ spl16_72
| ~ spl16_325 ),
inference(resolution,[],[f3301,f550]) ).
fof(f8799,plain,
( spl16_628
| ~ spl16_208
| ~ spl16_323 ),
inference(avatar_split_clause,[],[f3309,f3292,f1820,f8797]) ).
fof(f8797,plain,
( spl16_628
<=> ! [X0,X1] :
( ~ empty(X0)
| sK9(sK9(powerset(powerset(X0)))) = sK9(powerset(the_InternalRel(sK8(X1))))
| empty(sK9(powerset(powerset(X0))))
| ~ rel_str(sK8(X1))
| ~ rel_str(X1)
| ~ empty(the_InternalRel(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_628])]) ).
fof(f3309,plain,
( ! [X0,X1] :
( ~ empty(X0)
| sK9(sK9(powerset(powerset(X0)))) = sK9(powerset(the_InternalRel(sK8(X1))))
| empty(sK9(powerset(powerset(X0))))
| ~ rel_str(sK8(X1))
| ~ rel_str(X1)
| ~ empty(the_InternalRel(X1)) )
| ~ spl16_208
| ~ spl16_323 ),
inference(resolution,[],[f3293,f1821]) ).
fof(f8795,plain,
( spl16_627
| ~ spl16_207
| ~ spl16_323 ),
inference(avatar_split_clause,[],[f3308,f3292,f1816,f8793]) ).
fof(f8793,plain,
( spl16_627
<=> ! [X0,X1] :
( ~ empty(X0)
| sK9(sK9(powerset(powerset(X0)))) = sK9(powerset(the_carrier(sK8(X1))))
| empty(sK9(powerset(powerset(X0))))
| ~ rel_str(sK8(X1))
| ~ rel_str(X1)
| ~ empty(the_carrier(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_627])]) ).
fof(f3308,plain,
( ! [X0,X1] :
( ~ empty(X0)
| sK9(sK9(powerset(powerset(X0)))) = sK9(powerset(the_carrier(sK8(X1))))
| empty(sK9(powerset(powerset(X0))))
| ~ rel_str(sK8(X1))
| ~ rel_str(X1)
| ~ empty(the_carrier(X1)) )
| ~ spl16_207
| ~ spl16_323 ),
inference(resolution,[],[f3293,f1817]) ).
fof(f8791,plain,
( spl16_626
| ~ spl16_215
| ~ spl16_308 ),
inference(avatar_split_clause,[],[f3115,f3093,f1961,f8789]) ).
fof(f8789,plain,
( spl16_626
<=> ! [X0,X1] :
( ~ empty(X0)
| sK9(sK9(powerset(powerset(X0)))) = sK9(sK7(powerset(X1)))
| empty(sK9(powerset(powerset(X0))))
| ~ empty(X1)
| empty(powerset(X1))
| empty(sK7(powerset(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_626])]) ).
fof(f3115,plain,
( ! [X0,X1] :
( ~ empty(X0)
| sK9(sK9(powerset(powerset(X0)))) = sK9(sK7(powerset(X1)))
| empty(sK9(powerset(powerset(X0))))
| ~ empty(X1)
| empty(powerset(X1))
| empty(sK7(powerset(X1))) )
| ~ spl16_215
| ~ spl16_308 ),
inference(resolution,[],[f3094,f1962]) ).
fof(f8787,plain,
( spl16_625
| ~ spl16_214
| ~ spl16_308 ),
inference(avatar_split_clause,[],[f3114,f3093,f1955,f8785]) ).
fof(f8785,plain,
( spl16_625
<=> ! [X0,X1] :
( ~ empty(X0)
| sK9(sK9(powerset(powerset(X0)))) = sK9(sK6(powerset(X1)))
| empty(sK9(powerset(powerset(X0))))
| ~ empty(X1)
| empty(powerset(X1))
| empty(sK6(powerset(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_625])]) ).
fof(f3114,plain,
( ! [X0,X1] :
( ~ empty(X0)
| sK9(sK9(powerset(powerset(X0)))) = sK9(sK6(powerset(X1)))
| empty(sK9(powerset(powerset(X0))))
| ~ empty(X1)
| empty(powerset(X1))
| empty(sK6(powerset(X1))) )
| ~ spl16_214
| ~ spl16_308 ),
inference(resolution,[],[f3094,f1956]) ).
fof(f8783,plain,
( spl16_624
| ~ spl16_286
| ~ spl16_308 ),
inference(avatar_split_clause,[],[f3113,f3093,f2727,f8781]) ).
fof(f8781,plain,
( spl16_624
<=> ! [X0,X1] :
( ~ empty(X0)
| sK9(sK9(powerset(powerset(X0)))) = sK9(powerset(powerset(X1)))
| empty(sK9(powerset(powerset(X0))))
| sK14 = sK9(sK9(powerset(powerset(X1))))
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_624])]) ).
fof(f3113,plain,
( ! [X0,X1] :
( ~ empty(X0)
| sK9(sK9(powerset(powerset(X0)))) = sK9(powerset(powerset(X1)))
| empty(sK9(powerset(powerset(X0))))
| sK14 = sK9(sK9(powerset(powerset(X1))))
| ~ empty(X1) )
| ~ spl16_286
| ~ spl16_308 ),
inference(resolution,[],[f3094,f2728]) ).
fof(f8691,plain,
( spl16_623
| ~ spl16_42
| ~ spl16_12
| ~ spl16_61
| ~ spl16_479 ),
inference(avatar_split_clause,[],[f7116,f5696,f491,f213,f355,f8688]) ).
fof(f8688,plain,
( spl16_623
<=> sK14 = sK9(powerset(the_carrier(sK8(sK1)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_623])]) ).
fof(f355,plain,
( spl16_42
<=> rel_str(sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_42])]) ).
fof(f491,plain,
( spl16_61
<=> the_carrier(sK1) = sK14 ),
introduced(avatar_definition,[new_symbols(naming,[spl16_61])]) ).
fof(f7116,plain,
( ~ empty(sK14)
| ~ rel_str(sK1)
| sK14 = sK9(powerset(the_carrier(sK8(sK1))))
| ~ spl16_61
| ~ spl16_479 ),
inference(superposition,[],[f5697,f493]) ).
fof(f493,plain,
( the_carrier(sK1) = sK14
| ~ spl16_61 ),
inference(avatar_component_clause,[],[f491]) ).
fof(f8518,plain,
( spl16_622
| ~ spl16_42
| ~ spl16_12
| ~ spl16_61
| ~ spl16_477 ),
inference(avatar_split_clause,[],[f7115,f5688,f491,f213,f355,f8516]) ).
fof(f8516,plain,
( spl16_622
<=> ! [X0] :
( the_carrier(sK8(sK1)) = X0
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_622])]) ).
fof(f7115,plain,
( ! [X0] :
( ~ empty(sK14)
| ~ rel_str(sK1)
| the_carrier(sK8(sK1)) = X0
| ~ empty(X0) )
| ~ spl16_61
| ~ spl16_477 ),
inference(superposition,[],[f5689,f493]) ).
fof(f8506,plain,
( spl16_621
| ~ spl16_279
| ~ spl16_324 ),
inference(avatar_split_clause,[],[f3332,f3296,f2665,f8504]) ).
fof(f8504,plain,
( spl16_621
<=> ! [X0] :
( ~ empty(X0)
| sK14 = sK9(powerset(sK9(powerset(sK9(sK9(powerset(powerset(X0))))))))
| sK14 = sK9(powerset(sK9(powerset(sK9(powerset(sK9(powerset(powerset(X0))))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_621])]) ).
fof(f2665,plain,
( spl16_279
<=> ! [X0] :
( sK14 = sK9(powerset(sK9(powerset(sK9(powerset(X0))))))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_279])]) ).
fof(f3332,plain,
( ! [X0] :
( ~ empty(X0)
| sK14 = sK9(powerset(sK9(powerset(sK9(sK9(powerset(powerset(X0))))))))
| sK14 = sK9(powerset(sK9(powerset(sK9(powerset(sK9(powerset(powerset(X0))))))))) )
| ~ spl16_279
| ~ spl16_324 ),
inference(resolution,[],[f3297,f2666]) ).
fof(f2666,plain,
( ! [X0] :
( ~ empty(X0)
| sK14 = sK9(powerset(sK9(powerset(sK9(powerset(X0)))))) )
| ~ spl16_279 ),
inference(avatar_component_clause,[],[f2665]) ).
fof(f8502,plain,
( spl16_620
| ~ spl16_204
| ~ spl16_324 ),
inference(avatar_split_clause,[],[f3331,f3296,f1797,f8500]) ).
fof(f8500,plain,
( spl16_620
<=> ! [X0,X1] :
( ~ empty(X0)
| sK14 = sK9(powerset(sK9(powerset(sK9(sK9(powerset(powerset(X0))))))))
| ~ empty(X1)
| sK9(powerset(X1)) = sK9(powerset(sK9(powerset(powerset(X0))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_620])]) ).
fof(f1797,plain,
( spl16_204
<=> ! [X0,X1] :
( sK9(powerset(X0)) = sK9(powerset(X1))
| ~ empty(X0)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_204])]) ).
fof(f3331,plain,
( ! [X0,X1] :
( ~ empty(X0)
| sK14 = sK9(powerset(sK9(powerset(sK9(sK9(powerset(powerset(X0))))))))
| ~ empty(X1)
| sK9(powerset(X1)) = sK9(powerset(sK9(powerset(powerset(X0))))) )
| ~ spl16_204
| ~ spl16_324 ),
inference(resolution,[],[f3297,f1798]) ).
fof(f1798,plain,
( ! [X0,X1] :
( ~ empty(X1)
| ~ empty(X0)
| sK9(powerset(X0)) = sK9(powerset(X1)) )
| ~ spl16_204 ),
inference(avatar_component_clause,[],[f1797]) ).
fof(f8498,plain,
( spl16_619
| ~ spl16_72
| ~ spl16_321 ),
inference(avatar_split_clause,[],[f3279,f3175,f549,f8496]) ).
fof(f8496,plain,
( spl16_619
<=> ! [X0] :
( empty(sK7(sK9(powerset(X0))))
| empty(sK9(powerset(X0)))
| empty(sK9(powerset(sK7(sK9(powerset(X0))))))
| element(sK9(sK9(powerset(sK7(sK9(powerset(X0)))))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_619])]) ).
fof(f3279,plain,
( ! [X0] :
( empty(sK7(sK9(powerset(X0))))
| empty(sK9(powerset(X0)))
| empty(sK9(powerset(sK7(sK9(powerset(X0))))))
| element(sK9(sK9(powerset(sK7(sK9(powerset(X0)))))),X0) )
| ~ spl16_72
| ~ spl16_321 ),
inference(resolution,[],[f3176,f550]) ).
fof(f8494,plain,
( spl16_618
| ~ spl16_72
| ~ spl16_320 ),
inference(avatar_split_clause,[],[f3258,f3171,f549,f8492]) ).
fof(f8492,plain,
( spl16_618
<=> ! [X0] :
( empty(sK6(sK9(powerset(X0))))
| empty(sK9(powerset(X0)))
| empty(sK9(powerset(sK6(sK9(powerset(X0))))))
| element(sK9(sK9(powerset(sK6(sK9(powerset(X0)))))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_618])]) ).
fof(f3258,plain,
( ! [X0] :
( empty(sK6(sK9(powerset(X0))))
| empty(sK9(powerset(X0)))
| empty(sK9(powerset(sK6(sK9(powerset(X0))))))
| element(sK9(sK9(powerset(sK6(sK9(powerset(X0)))))),X0) )
| ~ spl16_72
| ~ spl16_320 ),
inference(resolution,[],[f3172,f550]) ).
fof(f8490,plain,
( spl16_617
| ~ spl16_208
| ~ spl16_318 ),
inference(avatar_split_clause,[],[f3222,f3163,f1820,f8488]) ).
fof(f8488,plain,
( spl16_617
<=> ! [X0,X1] :
( empty(powerset(X0))
| empty(sK7(powerset(X0)))
| sK9(sK7(powerset(X0))) = the_InternalRel(sK8(X1))
| ~ empty(X0)
| ~ rel_str(sK8(X1))
| ~ rel_str(X1)
| ~ empty(the_InternalRel(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_617])]) ).
fof(f3222,plain,
( ! [X0,X1] :
( empty(powerset(X0))
| empty(sK7(powerset(X0)))
| sK9(sK7(powerset(X0))) = the_InternalRel(sK8(X1))
| ~ empty(X0)
| ~ rel_str(sK8(X1))
| ~ rel_str(X1)
| ~ empty(the_InternalRel(X1)) )
| ~ spl16_208
| ~ spl16_318 ),
inference(resolution,[],[f3164,f1821]) ).
fof(f8452,plain,
( spl16_616
| ~ spl16_207
| ~ spl16_318 ),
inference(avatar_split_clause,[],[f3221,f3163,f1816,f8450]) ).
fof(f8450,plain,
( spl16_616
<=> ! [X0,X1] :
( empty(powerset(X0))
| empty(sK7(powerset(X0)))
| sK9(sK7(powerset(X0))) = the_carrier(sK8(X1))
| ~ empty(X0)
| ~ rel_str(sK8(X1))
| ~ rel_str(X1)
| ~ empty(the_carrier(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_616])]) ).
fof(f3221,plain,
( ! [X0,X1] :
( empty(powerset(X0))
| empty(sK7(powerset(X0)))
| sK9(sK7(powerset(X0))) = the_carrier(sK8(X1))
| ~ empty(X0)
| ~ rel_str(sK8(X1))
| ~ rel_str(X1)
| ~ empty(the_carrier(X1)) )
| ~ spl16_207
| ~ spl16_318 ),
inference(resolution,[],[f3164,f1817]) ).
fof(f8448,plain,
( spl16_615
| ~ spl16_208
| ~ spl16_316 ),
inference(avatar_split_clause,[],[f3195,f3155,f1820,f8446]) ).
fof(f8446,plain,
( spl16_615
<=> ! [X0,X1] :
( empty(powerset(X0))
| empty(sK6(powerset(X0)))
| sK9(sK6(powerset(X0))) = the_InternalRel(sK8(X1))
| ~ empty(X0)
| ~ rel_str(sK8(X1))
| ~ rel_str(X1)
| ~ empty(the_InternalRel(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_615])]) ).
fof(f3195,plain,
( ! [X0,X1] :
( empty(powerset(X0))
| empty(sK6(powerset(X0)))
| sK9(sK6(powerset(X0))) = the_InternalRel(sK8(X1))
| ~ empty(X0)
| ~ rel_str(sK8(X1))
| ~ rel_str(X1)
| ~ empty(the_InternalRel(X1)) )
| ~ spl16_208
| ~ spl16_316 ),
inference(resolution,[],[f3156,f1821]) ).
fof(f8444,plain,
( spl16_614
| ~ spl16_207
| ~ spl16_316 ),
inference(avatar_split_clause,[],[f3194,f3155,f1816,f8442]) ).
fof(f8442,plain,
( spl16_614
<=> ! [X0,X1] :
( empty(powerset(X0))
| empty(sK6(powerset(X0)))
| sK9(sK6(powerset(X0))) = the_carrier(sK8(X1))
| ~ empty(X0)
| ~ rel_str(sK8(X1))
| ~ rel_str(X1)
| ~ empty(the_carrier(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_614])]) ).
fof(f3194,plain,
( ! [X0,X1] :
( empty(powerset(X0))
| empty(sK6(powerset(X0)))
| sK9(sK6(powerset(X0))) = the_carrier(sK8(X1))
| ~ empty(X0)
| ~ rel_str(sK8(X1))
| ~ rel_str(X1)
| ~ empty(the_carrier(X1)) )
| ~ spl16_207
| ~ spl16_316 ),
inference(resolution,[],[f3156,f1817]) ).
fof(f8440,plain,
( spl16_613
| ~ spl16_282
| ~ spl16_309 ),
inference(avatar_split_clause,[],[f3130,f3098,f2692,f8438]) ).
fof(f8438,plain,
( spl16_613
<=> ! [X0,X1] :
( ~ empty(X0)
| sK14 = sK9(powerset(sK9(sK9(powerset(powerset(X0))))))
| sK9(powerset(X1)) = sK9(powerset(sK9(powerset(sK9(powerset(powerset(X0)))))))
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_613])]) ).
fof(f3130,plain,
( ! [X0,X1] :
( ~ empty(X0)
| sK14 = sK9(powerset(sK9(sK9(powerset(powerset(X0))))))
| sK9(powerset(X1)) = sK9(powerset(sK9(powerset(sK9(powerset(powerset(X0)))))))
| ~ empty(X1) )
| ~ spl16_282
| ~ spl16_309 ),
inference(resolution,[],[f3099,f2693]) ).
fof(f8436,plain,
( spl16_612
| ~ spl16_213
| ~ spl16_308 ),
inference(avatar_split_clause,[],[f3116,f3093,f1942,f8434]) ).
fof(f8434,plain,
( spl16_612
<=> ! [X0,X1] :
( ~ empty(X0)
| sK9(sK9(powerset(powerset(X0)))) = sK9(sK9(powerset(powerset(X1))))
| empty(sK9(powerset(powerset(X0))))
| empty(sK9(powerset(powerset(X1))))
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_612])]) ).
fof(f3116,plain,
( ! [X0,X1] :
( ~ empty(X0)
| sK9(sK9(powerset(powerset(X0)))) = sK9(sK9(powerset(powerset(X1))))
| empty(sK9(powerset(powerset(X0))))
| empty(sK9(powerset(powerset(X1))))
| ~ empty(X1) )
| ~ spl16_213
| ~ spl16_308 ),
inference(resolution,[],[f3094,f1943]) ).
fof(f8432,plain,
( spl16_611
| ~ spl16_110
| ~ spl16_306 ),
inference(avatar_split_clause,[],[f3090,f2964,f799,f8430]) ).
fof(f8430,plain,
( spl16_611
<=> ! [X0,X1] :
( empty(sK7(sK7(sK11(X0,X1))))
| empty(sK11(X0,X1))
| empty(sK7(sK11(X0,X1)))
| element(sK9(sK7(sK7(sK11(X0,X1)))),cartesian_product2(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_611])]) ).
fof(f3090,plain,
( ! [X0,X1] :
( empty(sK7(sK7(sK11(X0,X1))))
| empty(sK11(X0,X1))
| empty(sK7(sK11(X0,X1)))
| element(sK9(sK7(sK7(sK11(X0,X1)))),cartesian_product2(X0,X1)) )
| ~ spl16_110
| ~ spl16_306 ),
inference(resolution,[],[f2965,f800]) ).
fof(f8428,plain,
( spl16_610
| ~ spl16_111
| ~ spl16_306 ),
inference(avatar_split_clause,[],[f3088,f2964,f803,f8426]) ).
fof(f8426,plain,
( spl16_610
<=> ! [X0,X1] :
( empty(sK7(sK7(sK10(X0,X1))))
| empty(sK10(X0,X1))
| empty(sK7(sK10(X0,X1)))
| element(sK9(sK7(sK7(sK10(X0,X1)))),cartesian_product2(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_610])]) ).
fof(f3088,plain,
( ! [X0,X1] :
( empty(sK7(sK7(sK10(X0,X1))))
| empty(sK10(X0,X1))
| empty(sK7(sK10(X0,X1)))
| element(sK9(sK7(sK7(sK10(X0,X1)))),cartesian_product2(X0,X1)) )
| ~ spl16_111
| ~ spl16_306 ),
inference(resolution,[],[f2965,f804]) ).
fof(f8424,plain,
( spl16_609
| ~ spl16_110
| ~ spl16_305 ),
inference(avatar_split_clause,[],[f3069,f2960,f799,f8422]) ).
fof(f8422,plain,
( spl16_609
<=> ! [X0,X1] :
( empty(sK7(sK6(sK11(X0,X1))))
| empty(sK11(X0,X1))
| empty(sK6(sK11(X0,X1)))
| element(sK9(sK7(sK6(sK11(X0,X1)))),cartesian_product2(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_609])]) ).
fof(f3069,plain,
( ! [X0,X1] :
( empty(sK7(sK6(sK11(X0,X1))))
| empty(sK11(X0,X1))
| empty(sK6(sK11(X0,X1)))
| element(sK9(sK7(sK6(sK11(X0,X1)))),cartesian_product2(X0,X1)) )
| ~ spl16_110
| ~ spl16_305 ),
inference(resolution,[],[f2961,f800]) ).
fof(f8420,plain,
( spl16_608
| ~ spl16_111
| ~ spl16_305 ),
inference(avatar_split_clause,[],[f3067,f2960,f803,f8418]) ).
fof(f8418,plain,
( spl16_608
<=> ! [X0,X1] :
( empty(sK7(sK6(sK10(X0,X1))))
| empty(sK10(X0,X1))
| empty(sK6(sK10(X0,X1)))
| element(sK9(sK7(sK6(sK10(X0,X1)))),cartesian_product2(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_608])]) ).
fof(f3067,plain,
( ! [X0,X1] :
( empty(sK7(sK6(sK10(X0,X1))))
| empty(sK10(X0,X1))
| empty(sK6(sK10(X0,X1)))
| element(sK9(sK7(sK6(sK10(X0,X1)))),cartesian_product2(X0,X1)) )
| ~ spl16_111
| ~ spl16_305 ),
inference(resolution,[],[f2961,f804]) ).
fof(f8416,plain,
( spl16_607
| ~ spl16_110
| ~ spl16_304 ),
inference(avatar_split_clause,[],[f3048,f2956,f799,f8414]) ).
fof(f8414,plain,
( spl16_607
<=> ! [X0,X1] :
( empty(sK6(sK7(sK11(X0,X1))))
| empty(sK11(X0,X1))
| empty(sK7(sK11(X0,X1)))
| element(sK9(sK6(sK7(sK11(X0,X1)))),cartesian_product2(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_607])]) ).
fof(f3048,plain,
( ! [X0,X1] :
( empty(sK6(sK7(sK11(X0,X1))))
| empty(sK11(X0,X1))
| empty(sK7(sK11(X0,X1)))
| element(sK9(sK6(sK7(sK11(X0,X1)))),cartesian_product2(X0,X1)) )
| ~ spl16_110
| ~ spl16_304 ),
inference(resolution,[],[f2957,f800]) ).
fof(f8412,plain,
( spl16_606
| ~ spl16_86
| ~ spl16_585 ),
inference(avatar_split_clause,[],[f8190,f7964,f653,f8410]) ).
fof(f7964,plain,
( spl16_585
<=> relation_of2_as_subset(the_InternalRel(sK8(sK1)),sK14,sK14) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_585])]) ).
fof(f8190,plain,
( ! [X0] :
( ~ in(X0,the_InternalRel(sK8(sK1)))
| element(X0,cartesian_product2(sK14,sK14)) )
| ~ spl16_86
| ~ spl16_585 ),
inference(resolution,[],[f7966,f654]) ).
fof(f7966,plain,
( relation_of2_as_subset(the_InternalRel(sK8(sK1)),sK14,sK14)
| ~ spl16_585 ),
inference(avatar_component_clause,[],[f7964]) ).
fof(f8408,plain,
( spl16_605
| ~ spl16_111
| ~ spl16_304 ),
inference(avatar_split_clause,[],[f3046,f2956,f803,f8406]) ).
fof(f8406,plain,
( spl16_605
<=> ! [X0,X1] :
( empty(sK6(sK7(sK10(X0,X1))))
| empty(sK10(X0,X1))
| empty(sK7(sK10(X0,X1)))
| element(sK9(sK6(sK7(sK10(X0,X1)))),cartesian_product2(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_605])]) ).
fof(f3046,plain,
( ! [X0,X1] :
( empty(sK6(sK7(sK10(X0,X1))))
| empty(sK10(X0,X1))
| empty(sK7(sK10(X0,X1)))
| element(sK9(sK6(sK7(sK10(X0,X1)))),cartesian_product2(X0,X1)) )
| ~ spl16_111
| ~ spl16_304 ),
inference(resolution,[],[f2957,f804]) ).
fof(f8404,plain,
( spl16_604
| ~ spl16_110
| ~ spl16_303 ),
inference(avatar_split_clause,[],[f3027,f2952,f799,f8402]) ).
fof(f8402,plain,
( spl16_604
<=> ! [X0,X1] :
( empty(sK6(sK6(sK11(X0,X1))))
| empty(sK11(X0,X1))
| empty(sK6(sK11(X0,X1)))
| element(sK9(sK6(sK6(sK11(X0,X1)))),cartesian_product2(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_604])]) ).
fof(f3027,plain,
( ! [X0,X1] :
( empty(sK6(sK6(sK11(X0,X1))))
| empty(sK11(X0,X1))
| empty(sK6(sK11(X0,X1)))
| element(sK9(sK6(sK6(sK11(X0,X1)))),cartesian_product2(X0,X1)) )
| ~ spl16_110
| ~ spl16_303 ),
inference(resolution,[],[f2953,f800]) ).
fof(f8400,plain,
( spl16_603
| ~ spl16_111
| ~ spl16_303 ),
inference(avatar_split_clause,[],[f3025,f2952,f803,f8398]) ).
fof(f8398,plain,
( spl16_603
<=> ! [X0,X1] :
( empty(sK6(sK6(sK10(X0,X1))))
| empty(sK10(X0,X1))
| empty(sK6(sK10(X0,X1)))
| element(sK9(sK6(sK6(sK10(X0,X1)))),cartesian_product2(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_603])]) ).
fof(f3025,plain,
( ! [X0,X1] :
( empty(sK6(sK6(sK10(X0,X1))))
| empty(sK10(X0,X1))
| empty(sK6(sK10(X0,X1)))
| element(sK9(sK6(sK6(sK10(X0,X1)))),cartesian_product2(X0,X1)) )
| ~ spl16_111
| ~ spl16_303 ),
inference(resolution,[],[f2953,f804]) ).
fof(f8242,plain,
( spl16_602
| ~ spl16_65
| ~ spl16_407 ),
inference(avatar_split_clause,[],[f4386,f4351,f508,f8240]) ).
fof(f8240,plain,
( spl16_602
<=> ! [X0] :
( empty(powerset(powerset(X0)))
| empty(sK9(sK7(powerset(powerset(X0)))))
| ~ empty(X0)
| empty(sK7(powerset(powerset(X0))))
| empty(sK9(sK9(sK7(powerset(powerset(X0)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_602])]) ).
fof(f4351,plain,
( spl16_407
<=> ! [X0,X1] :
( empty(sK7(powerset(powerset(X0))))
| empty(powerset(powerset(X0)))
| empty(sK9(sK7(powerset(powerset(X0)))))
| ~ empty(X0)
| ~ in(X1,sK9(sK9(sK7(powerset(powerset(X0)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_407])]) ).
fof(f4386,plain,
( ! [X0] :
( empty(powerset(powerset(X0)))
| empty(sK9(sK7(powerset(powerset(X0)))))
| ~ empty(X0)
| empty(sK7(powerset(powerset(X0))))
| empty(sK9(sK9(sK7(powerset(powerset(X0)))))) )
| ~ spl16_65
| ~ spl16_407 ),
inference(resolution,[],[f4352,f509]) ).
fof(f4352,plain,
( ! [X0,X1] :
( ~ in(X1,sK9(sK9(sK7(powerset(powerset(X0))))))
| empty(powerset(powerset(X0)))
| empty(sK9(sK7(powerset(powerset(X0)))))
| ~ empty(X0)
| empty(sK7(powerset(powerset(X0)))) )
| ~ spl16_407 ),
inference(avatar_component_clause,[],[f4351]) ).
fof(f8238,plain,
( spl16_601
| ~ spl16_40
| ~ spl16_585 ),
inference(avatar_split_clause,[],[f8193,f7964,f343,f8235]) ).
fof(f8235,plain,
( spl16_601
<=> relation_of2(the_InternalRel(sK8(sK1)),sK14,sK14) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_601])]) ).
fof(f8193,plain,
( relation_of2(the_InternalRel(sK8(sK1)),sK14,sK14)
| ~ spl16_40
| ~ spl16_585 ),
inference(resolution,[],[f7966,f344]) ).
fof(f8233,plain,
( spl16_600
| ~ spl16_65
| ~ spl16_406 ),
inference(avatar_split_clause,[],[f4370,f4347,f508,f8231]) ).
fof(f8231,plain,
( spl16_600
<=> ! [X0] :
( empty(powerset(powerset(X0)))
| empty(sK9(sK6(powerset(powerset(X0)))))
| ~ empty(X0)
| empty(sK6(powerset(powerset(X0))))
| empty(sK9(sK9(sK6(powerset(powerset(X0)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_600])]) ).
fof(f4347,plain,
( spl16_406
<=> ! [X0,X1] :
( empty(sK6(powerset(powerset(X0))))
| empty(powerset(powerset(X0)))
| empty(sK9(sK6(powerset(powerset(X0)))))
| ~ empty(X0)
| ~ in(X1,sK9(sK9(sK6(powerset(powerset(X0)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_406])]) ).
fof(f4370,plain,
( ! [X0] :
( empty(powerset(powerset(X0)))
| empty(sK9(sK6(powerset(powerset(X0)))))
| ~ empty(X0)
| empty(sK6(powerset(powerset(X0))))
| empty(sK9(sK9(sK6(powerset(powerset(X0)))))) )
| ~ spl16_65
| ~ spl16_406 ),
inference(resolution,[],[f4348,f509]) ).
fof(f4348,plain,
( ! [X0,X1] :
( ~ in(X1,sK9(sK9(sK6(powerset(powerset(X0))))))
| empty(powerset(powerset(X0)))
| empty(sK9(sK6(powerset(powerset(X0)))))
| ~ empty(X0)
| empty(sK6(powerset(powerset(X0)))) )
| ~ spl16_406 ),
inference(avatar_component_clause,[],[f4347]) ).
fof(f8229,plain,
( spl16_599
| ~ spl16_27
| ~ spl16_401 ),
inference(avatar_split_clause,[],[f4338,f4213,f282,f8227]) ).
fof(f8227,plain,
( spl16_599
<=> ! [X0,X1] :
( empty(sK7(the_InternalRel(X0)))
| ~ subrelstr(X0,X1)
| ~ rel_str(X0)
| ~ rel_str(X1)
| empty(the_InternalRel(X1))
| empty(the_InternalRel(X0))
| ~ in(the_InternalRel(X1),sK9(sK7(the_InternalRel(X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_599])]) ).
fof(f4338,plain,
( ! [X0,X1] :
( empty(sK7(the_InternalRel(X0)))
| ~ subrelstr(X0,X1)
| ~ rel_str(X0)
| ~ rel_str(X1)
| empty(the_InternalRel(X1))
| empty(the_InternalRel(X0))
| ~ in(the_InternalRel(X1),sK9(sK7(the_InternalRel(X0)))) )
| ~ spl16_27
| ~ spl16_401 ),
inference(resolution,[],[f4214,f283]) ).
fof(f8225,plain,
( spl16_598
| ~ spl16_27
| ~ spl16_400 ),
inference(avatar_split_clause,[],[f4331,f4209,f282,f8223]) ).
fof(f8223,plain,
( spl16_598
<=> ! [X0,X1] :
( empty(sK7(the_carrier(X0)))
| ~ subrelstr(X0,X1)
| ~ rel_str(X0)
| ~ rel_str(X1)
| empty(the_carrier(X1))
| empty(the_carrier(X0))
| ~ in(the_carrier(X1),sK9(sK7(the_carrier(X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_598])]) ).
fof(f4331,plain,
( ! [X0,X1] :
( empty(sK7(the_carrier(X0)))
| ~ subrelstr(X0,X1)
| ~ rel_str(X0)
| ~ rel_str(X1)
| empty(the_carrier(X1))
| empty(the_carrier(X0))
| ~ in(the_carrier(X1),sK9(sK7(the_carrier(X0)))) )
| ~ spl16_27
| ~ spl16_400 ),
inference(resolution,[],[f4210,f283]) ).
fof(f8221,plain,
( spl16_597
| ~ spl16_27
| ~ spl16_399 ),
inference(avatar_split_clause,[],[f4324,f4203,f282,f8219]) ).
fof(f8219,plain,
( spl16_597
<=> ! [X0,X1] :
( empty(sK6(the_InternalRel(X0)))
| ~ subrelstr(X0,X1)
| ~ rel_str(X0)
| ~ rel_str(X1)
| empty(the_InternalRel(X1))
| empty(the_InternalRel(X0))
| ~ in(the_InternalRel(X1),sK9(sK6(the_InternalRel(X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_597])]) ).
fof(f4324,plain,
( ! [X0,X1] :
( empty(sK6(the_InternalRel(X0)))
| ~ subrelstr(X0,X1)
| ~ rel_str(X0)
| ~ rel_str(X1)
| empty(the_InternalRel(X1))
| empty(the_InternalRel(X0))
| ~ in(the_InternalRel(X1),sK9(sK6(the_InternalRel(X0)))) )
| ~ spl16_27
| ~ spl16_399 ),
inference(resolution,[],[f4204,f283]) ).
fof(f8217,plain,
( spl16_596
| ~ spl16_27
| ~ spl16_398 ),
inference(avatar_split_clause,[],[f4317,f4199,f282,f8215]) ).
fof(f8215,plain,
( spl16_596
<=> ! [X0,X1] :
( empty(sK6(the_carrier(X0)))
| ~ subrelstr(X0,X1)
| ~ rel_str(X0)
| ~ rel_str(X1)
| empty(the_carrier(X1))
| empty(the_carrier(X0))
| ~ in(the_carrier(X1),sK9(sK6(the_carrier(X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_596])]) ).
fof(f4317,plain,
( ! [X0,X1] :
( empty(sK6(the_carrier(X0)))
| ~ subrelstr(X0,X1)
| ~ rel_str(X0)
| ~ rel_str(X1)
| empty(the_carrier(X1))
| empty(the_carrier(X0))
| ~ in(the_carrier(X1),sK9(sK6(the_carrier(X0)))) )
| ~ spl16_27
| ~ spl16_398 ),
inference(resolution,[],[f4200,f283]) ).
fof(f8213,plain,
( spl16_595
| ~ spl16_27
| ~ spl16_397 ),
inference(avatar_split_clause,[],[f4312,f4195,f282,f8211]) ).
fof(f8211,plain,
( spl16_595
<=> ! [X0,X1] :
( empty(sK11(X0,X1))
| empty(cartesian_product2(X0,X1))
| empty(sK9(powerset(sK11(X0,X1))))
| ~ in(cartesian_product2(X0,X1),sK9(sK9(powerset(sK11(X0,X1))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_595])]) ).
fof(f4195,plain,
( spl16_397
<=> ! [X0,X1] :
( empty(sK9(powerset(sK11(X0,X1))))
| empty(sK11(X0,X1))
| empty(cartesian_product2(X0,X1))
| in(sK9(sK9(powerset(sK11(X0,X1)))),cartesian_product2(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_397])]) ).
fof(f4312,plain,
( ! [X0,X1] :
( empty(sK11(X0,X1))
| empty(cartesian_product2(X0,X1))
| empty(sK9(powerset(sK11(X0,X1))))
| ~ in(cartesian_product2(X0,X1),sK9(sK9(powerset(sK11(X0,X1))))) )
| ~ spl16_27
| ~ spl16_397 ),
inference(resolution,[],[f4196,f283]) ).
fof(f4196,plain,
( ! [X0,X1] :
( in(sK9(sK9(powerset(sK11(X0,X1)))),cartesian_product2(X0,X1))
| empty(sK11(X0,X1))
| empty(cartesian_product2(X0,X1))
| empty(sK9(powerset(sK11(X0,X1)))) )
| ~ spl16_397 ),
inference(avatar_component_clause,[],[f4195]) ).
fof(f8209,plain,
( spl16_594
| ~ spl16_27
| ~ spl16_396 ),
inference(avatar_split_clause,[],[f4308,f4191,f282,f8207]) ).
fof(f8207,plain,
( spl16_594
<=> ! [X0,X1] :
( empty(sK10(X0,X1))
| empty(cartesian_product2(X0,X1))
| empty(sK9(powerset(sK10(X0,X1))))
| ~ in(cartesian_product2(X0,X1),sK9(sK9(powerset(sK10(X0,X1))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_594])]) ).
fof(f4191,plain,
( spl16_396
<=> ! [X0,X1] :
( empty(sK9(powerset(sK10(X0,X1))))
| empty(sK10(X0,X1))
| empty(cartesian_product2(X0,X1))
| in(sK9(sK9(powerset(sK10(X0,X1)))),cartesian_product2(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_396])]) ).
fof(f4308,plain,
( ! [X0,X1] :
( empty(sK10(X0,X1))
| empty(cartesian_product2(X0,X1))
| empty(sK9(powerset(sK10(X0,X1))))
| ~ in(cartesian_product2(X0,X1),sK9(sK9(powerset(sK10(X0,X1))))) )
| ~ spl16_27
| ~ spl16_396 ),
inference(resolution,[],[f4192,f283]) ).
fof(f4192,plain,
( ! [X0,X1] :
( in(sK9(sK9(powerset(sK10(X0,X1)))),cartesian_product2(X0,X1))
| empty(sK10(X0,X1))
| empty(cartesian_product2(X0,X1))
| empty(sK9(powerset(sK10(X0,X1)))) )
| ~ spl16_396 ),
inference(avatar_component_clause,[],[f4191]) ).
fof(f8205,plain,
( spl16_593
| ~ spl16_26
| ~ spl16_395 ),
inference(avatar_split_clause,[],[f4305,f4187,f278,f8203]) ).
fof(f8203,plain,
( spl16_593
<=> ! [X0,X1] :
( ~ rel_str(sK8(X0))
| empty(the_InternalRel(X1))
| empty(the_InternalRel(sK8(X0)))
| ~ subrelstr(X1,sK8(X0))
| element(sK9(the_InternalRel(X1)),the_InternalRel(X0))
| ~ rel_str(X1)
| ~ rel_str(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_593])]) ).
fof(f278,plain,
( spl16_26
<=> ! [X0] :
( subrelstr(sK8(X0),X0)
| ~ rel_str(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_26])]) ).
fof(f4187,plain,
( spl16_395
<=> ! [X2,X0,X1] :
( ~ rel_str(X0)
| ~ rel_str(X1)
| empty(the_InternalRel(X0))
| empty(the_InternalRel(X1))
| ~ subrelstr(X0,X1)
| element(sK9(the_InternalRel(X0)),the_InternalRel(X2))
| ~ subrelstr(X1,X2)
| ~ rel_str(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_395])]) ).
fof(f4305,plain,
( ! [X0,X1] :
( ~ rel_str(sK8(X0))
| empty(the_InternalRel(X1))
| empty(the_InternalRel(sK8(X0)))
| ~ subrelstr(X1,sK8(X0))
| element(sK9(the_InternalRel(X1)),the_InternalRel(X0))
| ~ rel_str(X1)
| ~ rel_str(X0) )
| ~ spl16_26
| ~ spl16_395 ),
inference(duplicate_literal_removal,[],[f4302]) ).
fof(f4302,plain,
( ! [X0,X1] :
( ~ rel_str(sK8(X0))
| empty(the_InternalRel(X1))
| empty(the_InternalRel(sK8(X0)))
| ~ subrelstr(X1,sK8(X0))
| element(sK9(the_InternalRel(X1)),the_InternalRel(X0))
| ~ rel_str(X1)
| ~ rel_str(X0)
| ~ rel_str(X0) )
| ~ spl16_26
| ~ spl16_395 ),
inference(resolution,[],[f4188,f279]) ).
fof(f279,plain,
( ! [X0] :
( subrelstr(sK8(X0),X0)
| ~ rel_str(X0) )
| ~ spl16_26 ),
inference(avatar_component_clause,[],[f278]) ).
fof(f4188,plain,
( ! [X2,X0,X1] :
( ~ subrelstr(X1,X2)
| ~ rel_str(X1)
| empty(the_InternalRel(X0))
| empty(the_InternalRel(X1))
| ~ subrelstr(X0,X1)
| element(sK9(the_InternalRel(X0)),the_InternalRel(X2))
| ~ rel_str(X0)
| ~ rel_str(X2) )
| ~ spl16_395 ),
inference(avatar_component_clause,[],[f4187]) ).
fof(f8201,plain,
( spl16_592
| ~ spl16_26
| ~ spl16_394 ),
inference(avatar_split_clause,[],[f4289,f4183,f278,f8199]) ).
fof(f8199,plain,
( spl16_592
<=> ! [X0,X1] :
( ~ rel_str(sK8(X0))
| empty(the_carrier(X1))
| empty(the_carrier(sK8(X0)))
| ~ subrelstr(X1,sK8(X0))
| element(sK9(the_carrier(X1)),the_carrier(X0))
| ~ rel_str(X1)
| ~ rel_str(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_592])]) ).
fof(f4183,plain,
( spl16_394
<=> ! [X2,X0,X1] :
( ~ rel_str(X0)
| ~ rel_str(X1)
| empty(the_carrier(X0))
| empty(the_carrier(X1))
| ~ subrelstr(X0,X1)
| element(sK9(the_carrier(X0)),the_carrier(X2))
| ~ subrelstr(X1,X2)
| ~ rel_str(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_394])]) ).
fof(f4289,plain,
( ! [X0,X1] :
( ~ rel_str(sK8(X0))
| empty(the_carrier(X1))
| empty(the_carrier(sK8(X0)))
| ~ subrelstr(X1,sK8(X0))
| element(sK9(the_carrier(X1)),the_carrier(X0))
| ~ rel_str(X1)
| ~ rel_str(X0) )
| ~ spl16_26
| ~ spl16_394 ),
inference(duplicate_literal_removal,[],[f4286]) ).
fof(f4286,plain,
( ! [X0,X1] :
( ~ rel_str(sK8(X0))
| empty(the_carrier(X1))
| empty(the_carrier(sK8(X0)))
| ~ subrelstr(X1,sK8(X0))
| element(sK9(the_carrier(X1)),the_carrier(X0))
| ~ rel_str(X1)
| ~ rel_str(X0)
| ~ rel_str(X0) )
| ~ spl16_26
| ~ spl16_394 ),
inference(resolution,[],[f4184,f279]) ).
fof(f4184,plain,
( ! [X2,X0,X1] :
( ~ subrelstr(X1,X2)
| ~ rel_str(X1)
| empty(the_carrier(X0))
| empty(the_carrier(X1))
| ~ subrelstr(X0,X1)
| element(sK9(the_carrier(X0)),the_carrier(X2))
| ~ rel_str(X0)
| ~ rel_str(X2) )
| ~ spl16_394 ),
inference(avatar_component_clause,[],[f4183]) ).
fof(f8197,plain,
( spl16_591
| ~ spl16_77
| ~ spl16_326 ),
inference(avatar_split_clause,[],[f3370,f3305,f577,f8195]) ).
fof(f8195,plain,
( spl16_591
<=> ! [X0] :
( empty(sK7(sK9(powerset(sK7(X0)))))
| empty(sK7(X0))
| empty(sK9(powerset(sK7(X0))))
| element(sK9(sK7(sK9(powerset(sK7(X0))))),X0)
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_591])]) ).
fof(f3370,plain,
( ! [X0] :
( empty(sK7(sK9(powerset(sK7(X0)))))
| empty(sK7(X0))
| empty(sK9(powerset(sK7(X0))))
| element(sK9(sK7(sK9(powerset(sK7(X0))))),X0)
| empty(X0) )
| ~ spl16_77
| ~ spl16_326 ),
inference(resolution,[],[f3306,f578]) ).
fof(f8189,plain,
( spl16_590
| ~ spl16_76
| ~ spl16_326 ),
inference(avatar_split_clause,[],[f3369,f3305,f573,f8187]) ).
fof(f8187,plain,
( spl16_590
<=> ! [X0] :
( empty(sK7(sK9(powerset(sK6(X0)))))
| empty(sK6(X0))
| empty(sK9(powerset(sK6(X0))))
| element(sK9(sK7(sK9(powerset(sK6(X0))))),X0)
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_590])]) ).
fof(f3369,plain,
( ! [X0] :
( empty(sK7(sK9(powerset(sK6(X0)))))
| empty(sK6(X0))
| empty(sK9(powerset(sK6(X0))))
| element(sK9(sK7(sK9(powerset(sK6(X0))))),X0)
| empty(X0) )
| ~ spl16_76
| ~ spl16_326 ),
inference(resolution,[],[f3306,f574]) ).
fof(f8185,plain,
( spl16_589
| ~ spl16_77
| ~ spl16_325 ),
inference(avatar_split_clause,[],[f3347,f3300,f577,f8183]) ).
fof(f8183,plain,
( spl16_589
<=> ! [X0] :
( empty(sK6(sK9(powerset(sK7(X0)))))
| empty(sK7(X0))
| empty(sK9(powerset(sK7(X0))))
| element(sK9(sK6(sK9(powerset(sK7(X0))))),X0)
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_589])]) ).
fof(f3347,plain,
( ! [X0] :
( empty(sK6(sK9(powerset(sK7(X0)))))
| empty(sK7(X0))
| empty(sK9(powerset(sK7(X0))))
| element(sK9(sK6(sK9(powerset(sK7(X0))))),X0)
| empty(X0) )
| ~ spl16_77
| ~ spl16_325 ),
inference(resolution,[],[f3301,f578]) ).
fof(f8181,plain,
( spl16_588
| ~ spl16_76
| ~ spl16_325 ),
inference(avatar_split_clause,[],[f3346,f3300,f573,f8179]) ).
fof(f8179,plain,
( spl16_588
<=> ! [X0] :
( empty(sK6(sK9(powerset(sK6(X0)))))
| empty(sK6(X0))
| empty(sK9(powerset(sK6(X0))))
| element(sK9(sK6(sK9(powerset(sK6(X0))))),X0)
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_588])]) ).
fof(f3346,plain,
( ! [X0] :
( empty(sK6(sK9(powerset(sK6(X0)))))
| empty(sK6(X0))
| empty(sK9(powerset(sK6(X0))))
| element(sK9(sK6(sK9(powerset(sK6(X0))))),X0)
| empty(X0) )
| ~ spl16_76
| ~ spl16_325 ),
inference(resolution,[],[f3301,f574]) ).
fof(f8177,plain,
( spl16_587
| ~ spl16_208
| ~ spl16_308 ),
inference(avatar_split_clause,[],[f3110,f3093,f1820,f8175]) ).
fof(f8175,plain,
( spl16_587
<=> ! [X0,X1] :
( ~ empty(X0)
| sK9(sK9(powerset(powerset(X0)))) = the_InternalRel(sK8(X1))
| empty(sK9(powerset(powerset(X0))))
| ~ rel_str(sK8(X1))
| ~ rel_str(X1)
| ~ empty(the_InternalRel(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_587])]) ).
fof(f3110,plain,
( ! [X0,X1] :
( ~ empty(X0)
| sK9(sK9(powerset(powerset(X0)))) = the_InternalRel(sK8(X1))
| empty(sK9(powerset(powerset(X0))))
| ~ rel_str(sK8(X1))
| ~ rel_str(X1)
| ~ empty(the_InternalRel(X1)) )
| ~ spl16_208
| ~ spl16_308 ),
inference(resolution,[],[f3094,f1821]) ).
fof(f8173,plain,
( spl16_586
| ~ spl16_207
| ~ spl16_308 ),
inference(avatar_split_clause,[],[f3109,f3093,f1816,f8171]) ).
fof(f8171,plain,
( spl16_586
<=> ! [X0,X1] :
( ~ empty(X0)
| sK9(sK9(powerset(powerset(X0)))) = the_carrier(sK8(X1))
| empty(sK9(powerset(powerset(X0))))
| ~ rel_str(sK8(X1))
| ~ rel_str(X1)
| ~ empty(the_carrier(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_586])]) ).
fof(f3109,plain,
( ! [X0,X1] :
( ~ empty(X0)
| sK9(sK9(powerset(powerset(X0)))) = the_carrier(sK8(X1))
| empty(sK9(powerset(powerset(X0))))
| ~ rel_str(sK8(X1))
| ~ rel_str(X1)
| ~ empty(the_carrier(X1)) )
| ~ spl16_207
| ~ spl16_308 ),
inference(resolution,[],[f3094,f1817]) ).
fof(f7967,plain,
( ~ spl16_224
| spl16_585
| ~ spl16_43
| ~ spl16_565 ),
inference(avatar_split_clause,[],[f7546,f7336,f370,f7964,f2058]) ).
fof(f7546,plain,
( relation_of2_as_subset(the_InternalRel(sK8(sK1)),sK14,sK14)
| ~ rel_str(sK8(sK1))
| ~ spl16_43
| ~ spl16_565 ),
inference(superposition,[],[f371,f7338]) ).
fof(f7673,plain,
( spl16_584
| ~ spl16_65
| ~ spl16_391 ),
inference(avatar_split_clause,[],[f4268,f4171,f508,f7671]) ).
fof(f7671,plain,
( spl16_584
<=> ! [X0] :
( empty(sK9(sK9(powerset(powerset(powerset(X0))))))
| ~ empty(X0)
| empty(sK9(powerset(powerset(powerset(X0)))))
| empty(sK9(sK9(sK9(powerset(powerset(powerset(X0))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_584])]) ).
fof(f4171,plain,
( spl16_391
<=> ! [X0,X1] :
( empty(sK9(powerset(powerset(powerset(X0)))))
| empty(sK9(sK9(powerset(powerset(powerset(X0))))))
| ~ empty(X0)
| ~ in(X1,sK9(sK9(sK9(powerset(powerset(powerset(X0))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_391])]) ).
fof(f4268,plain,
( ! [X0] :
( empty(sK9(sK9(powerset(powerset(powerset(X0))))))
| ~ empty(X0)
| empty(sK9(powerset(powerset(powerset(X0)))))
| empty(sK9(sK9(sK9(powerset(powerset(powerset(X0))))))) )
| ~ spl16_65
| ~ spl16_391 ),
inference(resolution,[],[f4172,f509]) ).
fof(f4172,plain,
( ! [X0,X1] :
( ~ in(X1,sK9(sK9(sK9(powerset(powerset(powerset(X0)))))))
| empty(sK9(sK9(powerset(powerset(powerset(X0))))))
| ~ empty(X0)
| empty(sK9(powerset(powerset(powerset(X0))))) )
| ~ spl16_391 ),
inference(avatar_component_clause,[],[f4171]) ).
fof(f7669,plain,
( spl16_583
| ~ spl16_99
| ~ spl16_351 ),
inference(avatar_split_clause,[],[f3701,f3626,f743,f7667]) ).
fof(f7667,plain,
( spl16_583
<=> ! [X0,X1] :
( empty(powerset(X0))
| empty(sK7(powerset(X0)))
| ~ empty(X0)
| sK9(powerset(sK9(sK7(powerset(X0))))) = sK9(powerset(sK9(powerset(X1))))
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_583])]) ).
fof(f743,plain,
( spl16_99
<=> ! [X0] :
( ~ empty(X0)
| empty(sK9(powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_99])]) ).
fof(f3701,plain,
( ! [X0,X1] :
( empty(powerset(X0))
| empty(sK7(powerset(X0)))
| ~ empty(X0)
| sK9(powerset(sK9(sK7(powerset(X0))))) = sK9(powerset(sK9(powerset(X1))))
| ~ empty(X1) )
| ~ spl16_99
| ~ spl16_351 ),
inference(resolution,[],[f3627,f744]) ).
fof(f744,plain,
( ! [X0] :
( empty(sK9(powerset(X0)))
| ~ empty(X0) )
| ~ spl16_99 ),
inference(avatar_component_clause,[],[f743]) ).
fof(f7665,plain,
( spl16_582
| ~ spl16_99
| ~ spl16_350 ),
inference(avatar_split_clause,[],[f3684,f3622,f743,f7663]) ).
fof(f7663,plain,
( spl16_582
<=> ! [X0,X1] :
( empty(powerset(X0))
| empty(sK6(powerset(X0)))
| ~ empty(X0)
| sK9(powerset(sK9(sK6(powerset(X0))))) = sK9(powerset(sK9(powerset(X1))))
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_582])]) ).
fof(f3684,plain,
( ! [X0,X1] :
( empty(powerset(X0))
| empty(sK6(powerset(X0)))
| ~ empty(X0)
| sK9(powerset(sK9(sK6(powerset(X0))))) = sK9(powerset(sK9(powerset(X1))))
| ~ empty(X1) )
| ~ spl16_99
| ~ spl16_350 ),
inference(resolution,[],[f3623,f744]) ).
fof(f7661,plain,
( spl16_581
| ~ spl16_197
| ~ spl16_324 ),
inference(avatar_split_clause,[],[f3330,f3296,f1702,f7659]) ).
fof(f7659,plain,
( spl16_581
<=> ! [X0] :
( ~ empty(X0)
| sK14 = sK9(powerset(sK9(powerset(sK9(sK9(powerset(powerset(X0))))))))
| sK14 = sK9(powerset(sK9(powerset(sK9(powerset(powerset(X0))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_581])]) ).
fof(f1702,plain,
( spl16_197
<=> ! [X0] :
( sK14 = sK9(powerset(sK9(powerset(X0))))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_197])]) ).
fof(f3330,plain,
( ! [X0] :
( ~ empty(X0)
| sK14 = sK9(powerset(sK9(powerset(sK9(sK9(powerset(powerset(X0))))))))
| sK14 = sK9(powerset(sK9(powerset(sK9(powerset(powerset(X0))))))) )
| ~ spl16_197
| ~ spl16_324 ),
inference(resolution,[],[f3297,f1703]) ).
fof(f1703,plain,
( ! [X0] :
( ~ empty(X0)
| sK14 = sK9(powerset(sK9(powerset(X0)))) )
| ~ spl16_197 ),
inference(avatar_component_clause,[],[f1702]) ).
fof(f7657,plain,
( spl16_580
| ~ spl16_148
| ~ spl16_324 ),
inference(avatar_split_clause,[],[f3329,f3296,f1206,f7655]) ).
fof(f7655,plain,
( spl16_580
<=> ! [X0,X1] :
( ~ empty(X0)
| sK14 = sK9(powerset(sK9(powerset(sK9(sK9(powerset(powerset(X0))))))))
| sK9(powerset(X1)) = sK9(powerset(powerset(X0)))
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_580])]) ).
fof(f1206,plain,
( spl16_148
<=> ! [X0,X1] :
( ~ empty(X0)
| sK9(powerset(X0)) = X1
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_148])]) ).
fof(f3329,plain,
( ! [X0,X1] :
( ~ empty(X0)
| sK14 = sK9(powerset(sK9(powerset(sK9(sK9(powerset(powerset(X0))))))))
| sK9(powerset(X1)) = sK9(powerset(powerset(X0)))
| ~ empty(X1) )
| ~ spl16_148
| ~ spl16_324 ),
inference(resolution,[],[f3297,f1207]) ).
fof(f1207,plain,
( ! [X0,X1] :
( ~ empty(X1)
| sK9(powerset(X0)) = X1
| ~ empty(X0) )
| ~ spl16_148 ),
inference(avatar_component_clause,[],[f1206]) ).
fof(f7653,plain,
( spl16_579
| ~ spl16_77
| ~ spl16_321 ),
inference(avatar_split_clause,[],[f3278,f3175,f577,f7651]) ).
fof(f7651,plain,
( spl16_579
<=> ! [X0] :
( empty(sK7(sK7(X0)))
| empty(sK7(X0))
| empty(sK9(powerset(sK7(sK7(X0)))))
| element(sK9(sK9(powerset(sK7(sK7(X0))))),X0)
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_579])]) ).
fof(f3278,plain,
( ! [X0] :
( empty(sK7(sK7(X0)))
| empty(sK7(X0))
| empty(sK9(powerset(sK7(sK7(X0)))))
| element(sK9(sK9(powerset(sK7(sK7(X0))))),X0)
| empty(X0) )
| ~ spl16_77
| ~ spl16_321 ),
inference(resolution,[],[f3176,f578]) ).
fof(f7649,plain,
( spl16_578
| ~ spl16_76
| ~ spl16_321 ),
inference(avatar_split_clause,[],[f3277,f3175,f573,f7647]) ).
fof(f7647,plain,
( spl16_578
<=> ! [X0] :
( empty(sK7(sK6(X0)))
| empty(sK6(X0))
| empty(sK9(powerset(sK7(sK6(X0)))))
| element(sK9(sK9(powerset(sK7(sK6(X0))))),X0)
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_578])]) ).
fof(f3277,plain,
( ! [X0] :
( empty(sK7(sK6(X0)))
| empty(sK6(X0))
| empty(sK9(powerset(sK7(sK6(X0)))))
| element(sK9(sK9(powerset(sK7(sK6(X0))))),X0)
| empty(X0) )
| ~ spl16_76
| ~ spl16_321 ),
inference(resolution,[],[f3176,f574]) ).
fof(f7645,plain,
( spl16_577
| ~ spl16_224
| ~ spl16_472
| ~ spl16_555 ),
inference(avatar_split_clause,[],[f7186,f7177,f5620,f2058,f7642]) ).
fof(f7186,plain,
( ~ rel_str(sK8(sK1))
| sK14 = the_carrier(sK8(sK8(sK1)))
| ~ spl16_472
| ~ spl16_555 ),
inference(resolution,[],[f7179,f5621]) ).
fof(f7640,plain,
( spl16_576
| ~ spl16_77
| ~ spl16_320 ),
inference(avatar_split_clause,[],[f3257,f3171,f577,f7638]) ).
fof(f7638,plain,
( spl16_576
<=> ! [X0] :
( empty(sK6(sK7(X0)))
| empty(sK7(X0))
| empty(sK9(powerset(sK6(sK7(X0)))))
| element(sK9(sK9(powerset(sK6(sK7(X0))))),X0)
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_576])]) ).
fof(f3257,plain,
( ! [X0] :
( empty(sK6(sK7(X0)))
| empty(sK7(X0))
| empty(sK9(powerset(sK6(sK7(X0)))))
| element(sK9(sK9(powerset(sK6(sK7(X0))))),X0)
| empty(X0) )
| ~ spl16_77
| ~ spl16_320 ),
inference(resolution,[],[f3172,f578]) ).
fof(f7636,plain,
( spl16_575
| ~ spl16_76
| ~ spl16_320 ),
inference(avatar_split_clause,[],[f3256,f3171,f573,f7634]) ).
fof(f7634,plain,
( spl16_575
<=> ! [X0] :
( empty(sK6(sK6(X0)))
| empty(sK6(X0))
| empty(sK9(powerset(sK6(sK6(X0)))))
| element(sK9(sK9(powerset(sK6(sK6(X0))))),X0)
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_575])]) ).
fof(f3256,plain,
( ! [X0] :
( empty(sK6(sK6(X0)))
| empty(sK6(X0))
| empty(sK9(powerset(sK6(sK6(X0)))))
| element(sK9(sK9(powerset(sK6(sK6(X0))))),X0)
| empty(X0) )
| ~ spl16_76
| ~ spl16_320 ),
inference(resolution,[],[f3172,f574]) ).
fof(f7632,plain,
( spl16_574
| ~ spl16_279
| ~ spl16_309 ),
inference(avatar_split_clause,[],[f3129,f3098,f2665,f7630]) ).
fof(f7630,plain,
( spl16_574
<=> ! [X0] :
( ~ empty(X0)
| sK14 = sK9(powerset(sK9(sK9(powerset(powerset(X0))))))
| sK14 = sK9(powerset(sK9(powerset(sK9(powerset(sK9(powerset(powerset(X0))))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_574])]) ).
fof(f3129,plain,
( ! [X0] :
( ~ empty(X0)
| sK14 = sK9(powerset(sK9(sK9(powerset(powerset(X0))))))
| sK14 = sK9(powerset(sK9(powerset(sK9(powerset(sK9(powerset(powerset(X0))))))))) )
| ~ spl16_279
| ~ spl16_309 ),
inference(resolution,[],[f3099,f2666]) ).
fof(f7628,plain,
( spl16_573
| ~ spl16_204
| ~ spl16_309 ),
inference(avatar_split_clause,[],[f3128,f3098,f1797,f7626]) ).
fof(f7626,plain,
( spl16_573
<=> ! [X0,X1] :
( ~ empty(X0)
| sK14 = sK9(powerset(sK9(sK9(powerset(powerset(X0))))))
| ~ empty(X1)
| sK9(powerset(X1)) = sK9(powerset(sK9(powerset(powerset(X0))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_573])]) ).
fof(f3128,plain,
( ! [X0,X1] :
( ~ empty(X0)
| sK14 = sK9(powerset(sK9(sK9(powerset(powerset(X0))))))
| ~ empty(X1)
| sK9(powerset(X1)) = sK9(powerset(sK9(powerset(powerset(X0))))) )
| ~ spl16_204
| ~ spl16_309 ),
inference(resolution,[],[f3099,f1798]) ).
fof(f7624,plain,
( spl16_572
| ~ spl16_72
| ~ spl16_306 ),
inference(avatar_split_clause,[],[f3080,f2964,f549,f7622]) ).
fof(f7622,plain,
( spl16_572
<=> ! [X0] :
( empty(sK7(sK7(sK9(powerset(X0)))))
| empty(sK9(powerset(X0)))
| empty(sK7(sK9(powerset(X0))))
| element(sK9(sK7(sK7(sK9(powerset(X0))))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_572])]) ).
fof(f3080,plain,
( ! [X0] :
( empty(sK7(sK7(sK9(powerset(X0)))))
| empty(sK9(powerset(X0)))
| empty(sK7(sK9(powerset(X0))))
| element(sK9(sK7(sK7(sK9(powerset(X0))))),X0) )
| ~ spl16_72
| ~ spl16_306 ),
inference(resolution,[],[f2965,f550]) ).
fof(f7620,plain,
( spl16_571
| ~ spl16_72
| ~ spl16_305 ),
inference(avatar_split_clause,[],[f3059,f2960,f549,f7618]) ).
fof(f7618,plain,
( spl16_571
<=> ! [X0] :
( empty(sK7(sK6(sK9(powerset(X0)))))
| empty(sK9(powerset(X0)))
| empty(sK6(sK9(powerset(X0))))
| element(sK9(sK7(sK6(sK9(powerset(X0))))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_571])]) ).
fof(f3059,plain,
( ! [X0] :
( empty(sK7(sK6(sK9(powerset(X0)))))
| empty(sK9(powerset(X0)))
| empty(sK6(sK9(powerset(X0))))
| element(sK9(sK7(sK6(sK9(powerset(X0))))),X0) )
| ~ spl16_72
| ~ spl16_305 ),
inference(resolution,[],[f2961,f550]) ).
fof(f7616,plain,
( spl16_570
| ~ spl16_72
| ~ spl16_304 ),
inference(avatar_split_clause,[],[f3038,f2956,f549,f7614]) ).
fof(f7614,plain,
( spl16_570
<=> ! [X0] :
( empty(sK6(sK7(sK9(powerset(X0)))))
| empty(sK9(powerset(X0)))
| empty(sK7(sK9(powerset(X0))))
| element(sK9(sK6(sK7(sK9(powerset(X0))))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_570])]) ).
fof(f3038,plain,
( ! [X0] :
( empty(sK6(sK7(sK9(powerset(X0)))))
| empty(sK9(powerset(X0)))
| empty(sK7(sK9(powerset(X0))))
| element(sK9(sK6(sK7(sK9(powerset(X0))))),X0) )
| ~ spl16_72
| ~ spl16_304 ),
inference(resolution,[],[f2957,f550]) ).
fof(f7612,plain,
( spl16_569
| ~ spl16_72
| ~ spl16_303 ),
inference(avatar_split_clause,[],[f3017,f2952,f549,f7610]) ).
fof(f7610,plain,
( spl16_569
<=> ! [X0] :
( empty(sK6(sK6(sK9(powerset(X0)))))
| empty(sK9(powerset(X0)))
| empty(sK6(sK9(powerset(X0))))
| element(sK9(sK6(sK6(sK9(powerset(X0))))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_569])]) ).
fof(f3017,plain,
( ! [X0] :
( empty(sK6(sK6(sK9(powerset(X0)))))
| empty(sK9(powerset(X0)))
| empty(sK6(sK9(powerset(X0))))
| element(sK9(sK6(sK6(sK9(powerset(X0))))),X0) )
| ~ spl16_72
| ~ spl16_303 ),
inference(resolution,[],[f2953,f550]) ).
fof(f7608,plain,
( spl16_568
| ~ spl16_282
| ~ spl16_286 ),
inference(avatar_split_clause,[],[f2747,f2727,f2692,f7606]) ).
fof(f7606,plain,
( spl16_568
<=> ! [X0,X1] :
( sK14 = sK9(sK9(powerset(powerset(X0))))
| ~ empty(X0)
| sK9(powerset(X1)) = sK9(powerset(sK9(powerset(sK9(powerset(powerset(X0)))))))
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_568])]) ).
fof(f2747,plain,
( ! [X0,X1] :
( sK14 = sK9(sK9(powerset(powerset(X0))))
| ~ empty(X0)
| sK9(powerset(X1)) = sK9(powerset(sK9(powerset(sK9(powerset(powerset(X0)))))))
| ~ empty(X1) )
| ~ spl16_282
| ~ spl16_286 ),
inference(resolution,[],[f2728,f2693]) ).
fof(f7604,plain,
( spl16_567
| ~ spl16_215
| ~ spl16_282 ),
inference(avatar_split_clause,[],[f2712,f2692,f1961,f7602]) ).
fof(f7602,plain,
( spl16_567
<=> ! [X0,X1] :
( sK9(powerset(X0)) = sK9(powerset(sK9(powerset(sK9(sK7(powerset(X1)))))))
| ~ empty(X0)
| ~ empty(X1)
| empty(powerset(X1))
| empty(sK7(powerset(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_567])]) ).
fof(f2712,plain,
( ! [X0,X1] :
( sK9(powerset(X0)) = sK9(powerset(sK9(powerset(sK9(sK7(powerset(X1)))))))
| ~ empty(X0)
| ~ empty(X1)
| empty(powerset(X1))
| empty(sK7(powerset(X1))) )
| ~ spl16_215
| ~ spl16_282 ),
inference(resolution,[],[f2693,f1962]) ).
fof(f7540,plain,
( spl16_566
| ~ spl16_214
| ~ spl16_282 ),
inference(avatar_split_clause,[],[f2711,f2692,f1955,f7538]) ).
fof(f7538,plain,
( spl16_566
<=> ! [X0,X1] :
( sK9(powerset(X0)) = sK9(powerset(sK9(powerset(sK9(sK6(powerset(X1)))))))
| ~ empty(X0)
| ~ empty(X1)
| empty(powerset(X1))
| empty(sK6(powerset(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_566])]) ).
fof(f2711,plain,
( ! [X0,X1] :
( sK9(powerset(X0)) = sK9(powerset(sK9(powerset(sK9(sK6(powerset(X1)))))))
| ~ empty(X0)
| ~ empty(X1)
| empty(powerset(X1))
| empty(sK6(powerset(X1))) )
| ~ spl16_214
| ~ spl16_282 ),
inference(resolution,[],[f2693,f1956]) ).
fof(f7339,plain,
( spl16_565
| ~ spl16_23
| ~ spl16_57
| ~ spl16_555 ),
inference(avatar_split_clause,[],[f7226,f7177,f469,f263,f7336]) ).
fof(f7226,plain,
( sK14 = the_carrier(sK8(sK1))
| ~ spl16_23
| ~ spl16_57
| ~ spl16_555 ),
inference(forward_demodulation,[],[f7188,f471]) ).
fof(f7188,plain,
( empty_set = the_carrier(sK8(sK1))
| ~ spl16_23
| ~ spl16_555 ),
inference(resolution,[],[f7179,f264]) ).
fof(f7334,plain,
( spl16_564
| ~ spl16_65
| ~ spl16_383 ),
inference(avatar_split_clause,[],[f4132,f4085,f508,f7332]) ).
fof(f7332,plain,
( spl16_564
<=> ! [X0] :
( empty(sK9(powerset(powerset(X0))))
| ~ empty(X0)
| empty(sK9(powerset(sK9(powerset(powerset(X0))))))
| empty(sK9(sK9(powerset(sK9(powerset(powerset(X0))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_564])]) ).
fof(f4085,plain,
( spl16_383
<=> ! [X0,X1] :
( empty(sK9(powerset(sK9(powerset(powerset(X0))))))
| empty(sK9(powerset(powerset(X0))))
| ~ empty(X0)
| ~ in(X1,sK9(sK9(powerset(sK9(powerset(powerset(X0))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_383])]) ).
fof(f4132,plain,
( ! [X0] :
( empty(sK9(powerset(powerset(X0))))
| ~ empty(X0)
| empty(sK9(powerset(sK9(powerset(powerset(X0))))))
| empty(sK9(sK9(powerset(sK9(powerset(powerset(X0))))))) )
| ~ spl16_65
| ~ spl16_383 ),
inference(resolution,[],[f4086,f509]) ).
fof(f4086,plain,
( ! [X0,X1] :
( ~ in(X1,sK9(sK9(powerset(sK9(powerset(powerset(X0)))))))
| empty(sK9(powerset(powerset(X0))))
| ~ empty(X0)
| empty(sK9(powerset(sK9(powerset(powerset(X0)))))) )
| ~ spl16_383 ),
inference(avatar_component_clause,[],[f4085]) ).
fof(f7330,plain,
( spl16_563
| ~ spl16_65
| ~ spl16_382 ),
inference(avatar_split_clause,[],[f4116,f4081,f508,f7328]) ).
fof(f7328,plain,
( spl16_563
<=> ! [X0] :
( empty(sK7(powerset(X0)))
| empty(powerset(X0))
| ~ empty(X0)
| empty(sK9(powerset(sK7(powerset(X0)))))
| empty(sK9(sK9(powerset(sK7(powerset(X0)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_563])]) ).
fof(f4081,plain,
( spl16_382
<=> ! [X0,X1] :
( empty(sK9(powerset(sK7(powerset(X0)))))
| empty(sK7(powerset(X0)))
| empty(powerset(X0))
| ~ empty(X0)
| ~ in(X1,sK9(sK9(powerset(sK7(powerset(X0)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_382])]) ).
fof(f4116,plain,
( ! [X0] :
( empty(sK7(powerset(X0)))
| empty(powerset(X0))
| ~ empty(X0)
| empty(sK9(powerset(sK7(powerset(X0)))))
| empty(sK9(sK9(powerset(sK7(powerset(X0)))))) )
| ~ spl16_65
| ~ spl16_382 ),
inference(resolution,[],[f4082,f509]) ).
fof(f4082,plain,
( ! [X0,X1] :
( ~ in(X1,sK9(sK9(powerset(sK7(powerset(X0))))))
| empty(sK7(powerset(X0)))
| empty(powerset(X0))
| ~ empty(X0)
| empty(sK9(powerset(sK7(powerset(X0))))) )
| ~ spl16_382 ),
inference(avatar_component_clause,[],[f4081]) ).
fof(f7326,plain,
( spl16_562
| ~ spl16_65
| ~ spl16_381 ),
inference(avatar_split_clause,[],[f4100,f4077,f508,f7324]) ).
fof(f7324,plain,
( spl16_562
<=> ! [X0] :
( empty(sK6(powerset(X0)))
| empty(powerset(X0))
| ~ empty(X0)
| empty(sK9(powerset(sK6(powerset(X0)))))
| empty(sK9(sK9(powerset(sK6(powerset(X0)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_562])]) ).
fof(f4077,plain,
( spl16_381
<=> ! [X0,X1] :
( empty(sK9(powerset(sK6(powerset(X0)))))
| empty(sK6(powerset(X0)))
| empty(powerset(X0))
| ~ empty(X0)
| ~ in(X1,sK9(sK9(powerset(sK6(powerset(X0)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_381])]) ).
fof(f4100,plain,
( ! [X0] :
( empty(sK6(powerset(X0)))
| empty(powerset(X0))
| ~ empty(X0)
| empty(sK9(powerset(sK6(powerset(X0)))))
| empty(sK9(sK9(powerset(sK6(powerset(X0)))))) )
| ~ spl16_65
| ~ spl16_381 ),
inference(resolution,[],[f4078,f509]) ).
fof(f4078,plain,
( ! [X0,X1] :
( ~ in(X1,sK9(sK9(powerset(sK6(powerset(X0))))))
| empty(sK6(powerset(X0)))
| empty(powerset(X0))
| ~ empty(X0)
| empty(sK9(powerset(sK6(powerset(X0))))) )
| ~ spl16_381 ),
inference(avatar_component_clause,[],[f4077]) ).
fof(f7322,plain,
( spl16_561
| ~ spl16_27
| ~ spl16_377 ),
inference(avatar_split_clause,[],[f4071,f3939,f282,f7320]) ).
fof(f7320,plain,
( spl16_561
<=> ! [X0,X1] :
( empty(sK7(sK11(X0,X1)))
| empty(cartesian_product2(X0,X1))
| empty(sK11(X0,X1))
| ~ in(cartesian_product2(X0,X1),sK9(sK7(sK11(X0,X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_561])]) ).
fof(f3939,plain,
( spl16_377
<=> ! [X0,X1] :
( empty(sK11(X0,X1))
| empty(sK7(sK11(X0,X1)))
| empty(cartesian_product2(X0,X1))
| in(sK9(sK7(sK11(X0,X1))),cartesian_product2(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_377])]) ).
fof(f4071,plain,
( ! [X0,X1] :
( empty(sK7(sK11(X0,X1)))
| empty(cartesian_product2(X0,X1))
| empty(sK11(X0,X1))
| ~ in(cartesian_product2(X0,X1),sK9(sK7(sK11(X0,X1)))) )
| ~ spl16_27
| ~ spl16_377 ),
inference(resolution,[],[f3940,f283]) ).
fof(f3940,plain,
( ! [X0,X1] :
( in(sK9(sK7(sK11(X0,X1))),cartesian_product2(X0,X1))
| empty(sK7(sK11(X0,X1)))
| empty(cartesian_product2(X0,X1))
| empty(sK11(X0,X1)) )
| ~ spl16_377 ),
inference(avatar_component_clause,[],[f3939]) ).
fof(f7318,plain,
( spl16_560
| ~ spl16_27
| ~ spl16_376 ),
inference(avatar_split_clause,[],[f4067,f3935,f282,f7316]) ).
fof(f7316,plain,
( spl16_560
<=> ! [X0,X1] :
( empty(sK7(sK10(X0,X1)))
| empty(cartesian_product2(X0,X1))
| empty(sK10(X0,X1))
| ~ in(cartesian_product2(X0,X1),sK9(sK7(sK10(X0,X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_560])]) ).
fof(f3935,plain,
( spl16_376
<=> ! [X0,X1] :
( empty(sK10(X0,X1))
| empty(sK7(sK10(X0,X1)))
| empty(cartesian_product2(X0,X1))
| in(sK9(sK7(sK10(X0,X1))),cartesian_product2(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_376])]) ).
fof(f4067,plain,
( ! [X0,X1] :
( empty(sK7(sK10(X0,X1)))
| empty(cartesian_product2(X0,X1))
| empty(sK10(X0,X1))
| ~ in(cartesian_product2(X0,X1),sK9(sK7(sK10(X0,X1)))) )
| ~ spl16_27
| ~ spl16_376 ),
inference(resolution,[],[f3936,f283]) ).
fof(f3936,plain,
( ! [X0,X1] :
( in(sK9(sK7(sK10(X0,X1))),cartesian_product2(X0,X1))
| empty(sK7(sK10(X0,X1)))
| empty(cartesian_product2(X0,X1))
| empty(sK10(X0,X1)) )
| ~ spl16_376 ),
inference(avatar_component_clause,[],[f3935]) ).
fof(f7314,plain,
( spl16_559
| ~ spl16_27
| ~ spl16_375 ),
inference(avatar_split_clause,[],[f4064,f3931,f282,f7312]) ).
fof(f7312,plain,
( spl16_559
<=> ! [X0,X1] :
( empty(sK6(sK11(X0,X1)))
| empty(cartesian_product2(X0,X1))
| empty(sK11(X0,X1))
| ~ in(cartesian_product2(X0,X1),sK9(sK6(sK11(X0,X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_559])]) ).
fof(f3931,plain,
( spl16_375
<=> ! [X0,X1] :
( empty(sK11(X0,X1))
| empty(sK6(sK11(X0,X1)))
| empty(cartesian_product2(X0,X1))
| in(sK9(sK6(sK11(X0,X1))),cartesian_product2(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_375])]) ).
fof(f4064,plain,
( ! [X0,X1] :
( empty(sK6(sK11(X0,X1)))
| empty(cartesian_product2(X0,X1))
| empty(sK11(X0,X1))
| ~ in(cartesian_product2(X0,X1),sK9(sK6(sK11(X0,X1)))) )
| ~ spl16_27
| ~ spl16_375 ),
inference(resolution,[],[f3932,f283]) ).
fof(f3932,plain,
( ! [X0,X1] :
( in(sK9(sK6(sK11(X0,X1))),cartesian_product2(X0,X1))
| empty(sK6(sK11(X0,X1)))
| empty(cartesian_product2(X0,X1))
| empty(sK11(X0,X1)) )
| ~ spl16_375 ),
inference(avatar_component_clause,[],[f3931]) ).
fof(f7310,plain,
( spl16_558
| ~ spl16_27
| ~ spl16_374 ),
inference(avatar_split_clause,[],[f4060,f3927,f282,f7308]) ).
fof(f7308,plain,
( spl16_558
<=> ! [X0,X1] :
( empty(sK6(sK10(X0,X1)))
| empty(cartesian_product2(X0,X1))
| empty(sK10(X0,X1))
| ~ in(cartesian_product2(X0,X1),sK9(sK6(sK10(X0,X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_558])]) ).
fof(f3927,plain,
( spl16_374
<=> ! [X0,X1] :
( empty(sK10(X0,X1))
| empty(sK6(sK10(X0,X1)))
| empty(cartesian_product2(X0,X1))
| in(sK9(sK6(sK10(X0,X1))),cartesian_product2(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_374])]) ).
fof(f4060,plain,
( ! [X0,X1] :
( empty(sK6(sK10(X0,X1)))
| empty(cartesian_product2(X0,X1))
| empty(sK10(X0,X1))
| ~ in(cartesian_product2(X0,X1),sK9(sK6(sK10(X0,X1)))) )
| ~ spl16_27
| ~ spl16_374 ),
inference(resolution,[],[f3928,f283]) ).
fof(f3928,plain,
( ! [X0,X1] :
( in(sK9(sK6(sK10(X0,X1))),cartesian_product2(X0,X1))
| empty(sK6(sK10(X0,X1)))
| empty(cartesian_product2(X0,X1))
| empty(sK10(X0,X1)) )
| ~ spl16_374 ),
inference(avatar_component_clause,[],[f3927]) ).
fof(f7306,plain,
( spl16_557
| ~ spl16_99
| ~ spl16_341 ),
inference(avatar_split_clause,[],[f3584,f3545,f743,f7304]) ).
fof(f7304,plain,
( spl16_557
<=> ! [X0,X1] :
( ~ empty(X0)
| empty(sK9(powerset(powerset(X0))))
| sK9(powerset(sK9(sK9(powerset(powerset(X0)))))) = sK9(powerset(sK9(powerset(X1))))
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_557])]) ).
fof(f3584,plain,
( ! [X0,X1] :
( ~ empty(X0)
| empty(sK9(powerset(powerset(X0))))
| sK9(powerset(sK9(sK9(powerset(powerset(X0)))))) = sK9(powerset(sK9(powerset(X1))))
| ~ empty(X1) )
| ~ spl16_99
| ~ spl16_341 ),
inference(resolution,[],[f3546,f744]) ).
fof(f7302,plain,
( spl16_556
| ~ spl16_213
| ~ spl16_282 ),
inference(avatar_split_clause,[],[f2713,f2692,f1942,f7300]) ).
fof(f7300,plain,
( spl16_556
<=> ! [X0,X1] :
( sK9(powerset(X0)) = sK9(powerset(sK9(powerset(sK9(sK9(powerset(powerset(X1))))))))
| ~ empty(X0)
| empty(sK9(powerset(powerset(X1))))
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_556])]) ).
fof(f2713,plain,
( ! [X0,X1] :
( sK9(powerset(X0)) = sK9(powerset(sK9(powerset(sK9(sK9(powerset(powerset(X1))))))))
| ~ empty(X0)
| empty(sK9(powerset(powerset(X1))))
| ~ empty(X1) )
| ~ spl16_213
| ~ spl16_282 ),
inference(resolution,[],[f2693,f1943]) ).
fof(f7180,plain,
( ~ spl16_42
| spl16_555
| ~ spl16_224
| ~ spl16_26
| ~ spl16_264 ),
inference(avatar_split_clause,[],[f2531,f2528,f278,f2058,f7177,f355]) ).
fof(f2528,plain,
( spl16_264
<=> ! [X0] :
( ~ rel_str(X0)
| ~ subrelstr(X0,sK1)
| empty(the_carrier(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_264])]) ).
fof(f2531,plain,
( ~ rel_str(sK8(sK1))
| empty(the_carrier(sK8(sK1)))
| ~ rel_str(sK1)
| ~ spl16_26
| ~ spl16_264 ),
inference(resolution,[],[f2529,f279]) ).
fof(f2529,plain,
( ! [X0] :
( ~ subrelstr(X0,sK1)
| ~ rel_str(X0)
| empty(the_carrier(X0)) )
| ~ spl16_264 ),
inference(avatar_component_clause,[],[f2528]) ).
fof(f7175,plain,
( spl16_53
| ~ spl16_42
| ~ spl16_263
| ~ spl16_264 ),
inference(avatar_split_clause,[],[f2555,f2528,f2522,f355,f428]) ).
fof(f428,plain,
( spl16_53
<=> empty(the_carrier(sK1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_53])]) ).
fof(f2522,plain,
( spl16_263
<=> subrelstr(sK1,sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_263])]) ).
fof(f2555,plain,
( ~ rel_str(sK1)
| empty(the_carrier(sK1))
| ~ spl16_263
| ~ spl16_264 ),
inference(resolution,[],[f2523,f2529]) ).
fof(f2523,plain,
( subrelstr(sK1,sK1)
| ~ spl16_263 ),
inference(avatar_component_clause,[],[f2522]) ).
fof(f7171,plain,
( spl16_554
| ~ spl16_28
| ~ spl16_162 ),
inference(avatar_split_clause,[],[f1931,f1319,f286,f7169]) ).
fof(f7169,plain,
( spl16_554
<=> ! [X0] :
( ~ subrelstr(sK1,X0)
| empty(the_carrier(X0))
| ~ rel_str(X0)
| element(sK4,the_carrier(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_554])]) ).
fof(f1319,plain,
( spl16_162
<=> ! [X0] :
( ~ rel_str(X0)
| ~ subrelstr(sK1,X0)
| empty(the_carrier(X0))
| in(sK4,the_carrier(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_162])]) ).
fof(f1931,plain,
( ! [X0] :
( ~ subrelstr(sK1,X0)
| empty(the_carrier(X0))
| ~ rel_str(X0)
| element(sK4,the_carrier(X0)) )
| ~ spl16_28
| ~ spl16_162 ),
inference(resolution,[],[f1320,f287]) ).
fof(f1320,plain,
( ! [X0] :
( in(sK4,the_carrier(X0))
| ~ subrelstr(sK1,X0)
| empty(the_carrier(X0))
| ~ rel_str(X0) )
| ~ spl16_162 ),
inference(avatar_component_clause,[],[f1319]) ).
fof(f7061,plain,
( spl16_61
| ~ spl16_9
| ~ spl16_57
| ~ spl16_139
| ~ spl16_195 ),
inference(avatar_split_clause,[],[f7013,f1680,f1151,f469,f198,f491]) ).
fof(f198,plain,
( spl16_9
<=> empty(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_9])]) ).
fof(f1151,plain,
( spl16_139
<=> ! [X0] :
( ~ empty(X0)
| the_carrier(sK1) = sK9(powerset(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_139])]) ).
fof(f1680,plain,
( spl16_195
<=> sK14 = sK9(powerset(sK14)) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_195])]) ).
fof(f7013,plain,
( the_carrier(sK1) = sK14
| ~ spl16_9
| ~ spl16_57
| ~ spl16_139
| ~ spl16_195 ),
inference(forward_demodulation,[],[f2374,f1682]) ).
fof(f1682,plain,
( sK14 = sK9(powerset(sK14))
| ~ spl16_195 ),
inference(avatar_component_clause,[],[f1680]) ).
fof(f2374,plain,
( the_carrier(sK1) = sK9(powerset(sK14))
| ~ spl16_9
| ~ spl16_57
| ~ spl16_139 ),
inference(forward_demodulation,[],[f1350,f471]) ).
fof(f1350,plain,
( the_carrier(sK1) = sK9(powerset(empty_set))
| ~ spl16_9
| ~ spl16_139 ),
inference(resolution,[],[f1152,f200]) ).
fof(f200,plain,
( empty(empty_set)
| ~ spl16_9 ),
inference(avatar_component_clause,[],[f198]) ).
fof(f1152,plain,
( ! [X0] :
( ~ empty(X0)
| the_carrier(sK1) = sK9(powerset(X0)) )
| ~ spl16_139 ),
inference(avatar_component_clause,[],[f1151]) ).
fof(f7004,plain,
( spl16_186
| ~ spl16_1
| ~ spl16_2
| spl16_6
| ~ spl16_553 ),
inference(avatar_split_clause,[],[f6810,f6703,f183,f163,f158,f1536]) ).
fof(f6703,plain,
( spl16_553
<=> ! [X0] :
( ~ subrelstr(sK1,X0)
| related(X0,sK4,sK5)
| ~ rel_str(X0)
| empty(the_InternalRel(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_553])]) ).
fof(f6810,plain,
( ~ subrelstr(sK1,sK0)
| ~ rel_str(sK0)
| empty(the_InternalRel(sK0))
| spl16_6
| ~ spl16_553 ),
inference(resolution,[],[f6704,f185]) ).
fof(f185,plain,
( ~ related(sK0,sK4,sK5)
| spl16_6 ),
inference(avatar_component_clause,[],[f183]) ).
fof(f6704,plain,
( ! [X0] :
( related(X0,sK4,sK5)
| ~ subrelstr(sK1,X0)
| ~ rel_str(X0)
| empty(the_InternalRel(X0)) )
| ~ spl16_553 ),
inference(avatar_component_clause,[],[f6703]) ).
fof(f6705,plain,
( spl16_553
| ~ spl16_134
| ~ spl16_535 ),
inference(avatar_split_clause,[],[f6604,f6556,f1033,f6703]) ).
fof(f1033,plain,
( spl16_134
<=> ! [X0] :
( element(sK4,the_carrier(X0))
| ~ rel_str(X0)
| ~ subrelstr(sK1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_134])]) ).
fof(f6604,plain,
( ! [X0] :
( ~ subrelstr(sK1,X0)
| related(X0,sK4,sK5)
| ~ rel_str(X0)
| empty(the_InternalRel(X0)) )
| ~ spl16_134
| ~ spl16_535 ),
inference(duplicate_literal_removal,[],[f6599]) ).
fof(f6599,plain,
( ! [X0] :
( ~ subrelstr(sK1,X0)
| related(X0,sK4,sK5)
| ~ rel_str(X0)
| empty(the_InternalRel(X0))
| ~ rel_str(X0)
| ~ subrelstr(sK1,X0) )
| ~ spl16_134
| ~ spl16_535 ),
inference(resolution,[],[f6557,f1034]) ).
fof(f1034,plain,
( ! [X0] :
( element(sK4,the_carrier(X0))
| ~ rel_str(X0)
| ~ subrelstr(sK1,X0) )
| ~ spl16_134 ),
inference(avatar_component_clause,[],[f1033]) ).
fof(f6632,plain,
( spl16_552
| ~ spl16_27
| ~ spl16_364 ),
inference(avatar_split_clause,[],[f3864,f3678,f282,f6630]) ).
fof(f6630,plain,
( spl16_552
<=> ! [X0] :
( empty(powerset(X0))
| empty(sK9(sK7(powerset(X0))))
| empty(X0)
| empty(sK7(powerset(X0)))
| ~ in(X0,sK9(sK9(sK7(powerset(X0))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_552])]) ).
fof(f3864,plain,
( ! [X0] :
( empty(powerset(X0))
| empty(sK9(sK7(powerset(X0))))
| empty(X0)
| empty(sK7(powerset(X0)))
| ~ in(X0,sK9(sK9(sK7(powerset(X0))))) )
| ~ spl16_27
| ~ spl16_364 ),
inference(resolution,[],[f3679,f283]) ).
fof(f6628,plain,
( spl16_551
| ~ spl16_27
| ~ spl16_363 ),
inference(avatar_split_clause,[],[f3837,f3674,f282,f6626]) ).
fof(f6626,plain,
( spl16_551
<=> ! [X0] :
( empty(powerset(X0))
| empty(sK9(sK6(powerset(X0))))
| empty(X0)
| empty(sK6(powerset(X0)))
| ~ in(X0,sK9(sK9(sK6(powerset(X0))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_551])]) ).
fof(f3837,plain,
( ! [X0] :
( empty(powerset(X0))
| empty(sK9(sK6(powerset(X0))))
| empty(X0)
| empty(sK6(powerset(X0)))
| ~ in(X0,sK9(sK9(sK6(powerset(X0))))) )
| ~ spl16_27
| ~ spl16_363 ),
inference(resolution,[],[f3675,f283]) ).
fof(f6624,plain,
( spl16_550
| ~ spl16_27
| ~ spl16_362 ),
inference(avatar_split_clause,[],[f3810,f3670,f282,f6622]) ).
fof(f6622,plain,
( spl16_550
<=> ! [X0] :
( empty(sK9(sK9(powerset(powerset(X0)))))
| empty(X0)
| empty(sK9(powerset(powerset(X0))))
| ~ in(X0,sK9(sK9(sK9(powerset(powerset(X0)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_550])]) ).
fof(f3810,plain,
( ! [X0] :
( empty(sK9(sK9(powerset(powerset(X0)))))
| empty(X0)
| empty(sK9(powerset(powerset(X0))))
| ~ in(X0,sK9(sK9(sK9(powerset(powerset(X0)))))) )
| ~ spl16_27
| ~ spl16_362 ),
inference(resolution,[],[f3671,f283]) ).
fof(f6620,plain,
( spl16_549
| ~ spl16_99
| ~ spl16_331 ),
inference(avatar_split_clause,[],[f3487,f3402,f743,f6618]) ).
fof(f6618,plain,
( spl16_549
<=> ! [X0,X1] :
( empty(powerset(X0))
| empty(sK7(powerset(X0)))
| sK9(sK7(powerset(X0))) = sK9(powerset(sK9(powerset(X1))))
| ~ empty(X0)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_549])]) ).
fof(f3487,plain,
( ! [X0,X1] :
( empty(powerset(X0))
| empty(sK7(powerset(X0)))
| sK9(sK7(powerset(X0))) = sK9(powerset(sK9(powerset(X1))))
| ~ empty(X0)
| ~ empty(X1) )
| ~ spl16_99
| ~ spl16_331 ),
inference(resolution,[],[f3403,f744]) ).
fof(f6616,plain,
( spl16_548
| ~ spl16_99
| ~ spl16_329 ),
inference(avatar_split_clause,[],[f3453,f3394,f743,f6614]) ).
fof(f6614,plain,
( spl16_548
<=> ! [X0,X1] :
( empty(powerset(X0))
| empty(sK6(powerset(X0)))
| sK9(sK6(powerset(X0))) = sK9(powerset(sK9(powerset(X1))))
| ~ empty(X0)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_548])]) ).
fof(f3453,plain,
( ! [X0,X1] :
( empty(powerset(X0))
| empty(sK6(powerset(X0)))
| sK9(sK6(powerset(X0))) = sK9(powerset(sK9(powerset(X1))))
| ~ empty(X0)
| ~ empty(X1) )
| ~ spl16_99
| ~ spl16_329 ),
inference(resolution,[],[f3395,f744]) ).
fof(f6612,plain,
( spl16_547
| ~ spl16_142
| ~ spl16_324 ),
inference(avatar_split_clause,[],[f3328,f3296,f1176,f6610]) ).
fof(f6610,plain,
( spl16_547
<=> ! [X0] :
( ~ empty(X0)
| sK14 = sK9(powerset(sK9(powerset(sK9(sK9(powerset(powerset(X0))))))))
| sK14 = sK9(powerset(sK9(powerset(powerset(X0))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_547])]) ).
fof(f1176,plain,
( spl16_142
<=> ! [X0] :
( sK14 = sK9(powerset(X0))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_142])]) ).
fof(f3328,plain,
( ! [X0] :
( ~ empty(X0)
| sK14 = sK9(powerset(sK9(powerset(sK9(sK9(powerset(powerset(X0))))))))
| sK14 = sK9(powerset(sK9(powerset(powerset(X0))))) )
| ~ spl16_142
| ~ spl16_324 ),
inference(resolution,[],[f3297,f1177]) ).
fof(f1177,plain,
( ! [X0] :
( ~ empty(X0)
| sK14 = sK9(powerset(X0)) )
| ~ spl16_142 ),
inference(avatar_component_clause,[],[f1176]) ).
fof(f6608,plain,
( spl16_546
| ~ spl16_36
| ~ spl16_324 ),
inference(avatar_split_clause,[],[f3326,f3296,f318,f6606]) ).
fof(f6606,plain,
( spl16_546
<=> ! [X0,X1] :
( ~ empty(X0)
| sK14 = sK9(powerset(sK9(powerset(sK9(sK9(powerset(powerset(X0))))))))
| sK9(powerset(powerset(X0))) = X1
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_546])]) ).
fof(f318,plain,
( spl16_36
<=> ! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_36])]) ).
fof(f3326,plain,
( ! [X0,X1] :
( ~ empty(X0)
| sK14 = sK9(powerset(sK9(powerset(sK9(sK9(powerset(powerset(X0))))))))
| sK9(powerset(powerset(X0))) = X1
| ~ empty(X1) )
| ~ spl16_36
| ~ spl16_324 ),
inference(resolution,[],[f3297,f319]) ).
fof(f319,plain,
( ! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) )
| ~ spl16_36 ),
inference(avatar_component_clause,[],[f318]) ).
fof(f6598,plain,
( spl16_545
| ~ spl16_197
| ~ spl16_309 ),
inference(avatar_split_clause,[],[f3127,f3098,f1702,f6596]) ).
fof(f6596,plain,
( spl16_545
<=> ! [X0] :
( ~ empty(X0)
| sK14 = sK9(powerset(sK9(sK9(powerset(powerset(X0))))))
| sK14 = sK9(powerset(sK9(powerset(sK9(powerset(powerset(X0))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_545])]) ).
fof(f3127,plain,
( ! [X0] :
( ~ empty(X0)
| sK14 = sK9(powerset(sK9(sK9(powerset(powerset(X0))))))
| sK14 = sK9(powerset(sK9(powerset(sK9(powerset(powerset(X0))))))) )
| ~ spl16_197
| ~ spl16_309 ),
inference(resolution,[],[f3099,f1703]) ).
fof(f6594,plain,
( spl16_544
| ~ spl16_148
| ~ spl16_309 ),
inference(avatar_split_clause,[],[f3126,f3098,f1206,f6592]) ).
fof(f6592,plain,
( spl16_544
<=> ! [X0,X1] :
( ~ empty(X0)
| sK14 = sK9(powerset(sK9(sK9(powerset(powerset(X0))))))
| sK9(powerset(X1)) = sK9(powerset(powerset(X0)))
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_544])]) ).
fof(f3126,plain,
( ! [X0,X1] :
( ~ empty(X0)
| sK14 = sK9(powerset(sK9(sK9(powerset(powerset(X0))))))
| sK9(powerset(X1)) = sK9(powerset(powerset(X0)))
| ~ empty(X1) )
| ~ spl16_148
| ~ spl16_309 ),
inference(resolution,[],[f3099,f1207]) ).
fof(f6590,plain,
( spl16_543
| ~ spl16_77
| ~ spl16_306 ),
inference(avatar_split_clause,[],[f3079,f2964,f577,f6588]) ).
fof(f6588,plain,
( spl16_543
<=> ! [X0] :
( empty(sK7(sK7(sK7(X0))))
| empty(sK7(X0))
| empty(sK7(sK7(X0)))
| element(sK9(sK7(sK7(sK7(X0)))),X0)
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_543])]) ).
fof(f3079,plain,
( ! [X0] :
( empty(sK7(sK7(sK7(X0))))
| empty(sK7(X0))
| empty(sK7(sK7(X0)))
| element(sK9(sK7(sK7(sK7(X0)))),X0)
| empty(X0) )
| ~ spl16_77
| ~ spl16_306 ),
inference(resolution,[],[f2965,f578]) ).
fof(f6586,plain,
( spl16_542
| ~ spl16_76
| ~ spl16_306 ),
inference(avatar_split_clause,[],[f3078,f2964,f573,f6584]) ).
fof(f6584,plain,
( spl16_542
<=> ! [X0] :
( empty(sK7(sK7(sK6(X0))))
| empty(sK6(X0))
| empty(sK7(sK6(X0)))
| element(sK9(sK7(sK7(sK6(X0)))),X0)
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_542])]) ).
fof(f3078,plain,
( ! [X0] :
( empty(sK7(sK7(sK6(X0))))
| empty(sK6(X0))
| empty(sK7(sK6(X0)))
| element(sK9(sK7(sK7(sK6(X0)))),X0)
| empty(X0) )
| ~ spl16_76
| ~ spl16_306 ),
inference(resolution,[],[f2965,f574]) ).
fof(f6582,plain,
( spl16_541
| ~ spl16_77
| ~ spl16_305 ),
inference(avatar_split_clause,[],[f3058,f2960,f577,f6580]) ).
fof(f6580,plain,
( spl16_541
<=> ! [X0] :
( empty(sK7(sK6(sK7(X0))))
| empty(sK7(X0))
| empty(sK6(sK7(X0)))
| element(sK9(sK7(sK6(sK7(X0)))),X0)
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_541])]) ).
fof(f3058,plain,
( ! [X0] :
( empty(sK7(sK6(sK7(X0))))
| empty(sK7(X0))
| empty(sK6(sK7(X0)))
| element(sK9(sK7(sK6(sK7(X0)))),X0)
| empty(X0) )
| ~ spl16_77
| ~ spl16_305 ),
inference(resolution,[],[f2961,f578]) ).
fof(f6578,plain,
( spl16_540
| ~ spl16_76
| ~ spl16_305 ),
inference(avatar_split_clause,[],[f3057,f2960,f573,f6576]) ).
fof(f6576,plain,
( spl16_540
<=> ! [X0] :
( empty(sK7(sK6(sK6(X0))))
| empty(sK6(X0))
| empty(sK6(sK6(X0)))
| element(sK9(sK7(sK6(sK6(X0)))),X0)
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_540])]) ).
fof(f3057,plain,
( ! [X0] :
( empty(sK7(sK6(sK6(X0))))
| empty(sK6(X0))
| empty(sK6(sK6(X0)))
| element(sK9(sK7(sK6(sK6(X0)))),X0)
| empty(X0) )
| ~ spl16_76
| ~ spl16_305 ),
inference(resolution,[],[f2961,f574]) ).
fof(f6574,plain,
( spl16_539
| ~ spl16_77
| ~ spl16_304 ),
inference(avatar_split_clause,[],[f3037,f2956,f577,f6572]) ).
fof(f6572,plain,
( spl16_539
<=> ! [X0] :
( empty(sK6(sK7(sK7(X0))))
| empty(sK7(X0))
| empty(sK7(sK7(X0)))
| element(sK9(sK6(sK7(sK7(X0)))),X0)
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_539])]) ).
fof(f3037,plain,
( ! [X0] :
( empty(sK6(sK7(sK7(X0))))
| empty(sK7(X0))
| empty(sK7(sK7(X0)))
| element(sK9(sK6(sK7(sK7(X0)))),X0)
| empty(X0) )
| ~ spl16_77
| ~ spl16_304 ),
inference(resolution,[],[f2957,f578]) ).
fof(f6570,plain,
( spl16_538
| ~ spl16_76
| ~ spl16_304 ),
inference(avatar_split_clause,[],[f3036,f2956,f573,f6568]) ).
fof(f6568,plain,
( spl16_538
<=> ! [X0] :
( empty(sK6(sK7(sK6(X0))))
| empty(sK6(X0))
| empty(sK7(sK6(X0)))
| element(sK9(sK6(sK7(sK6(X0)))),X0)
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_538])]) ).
fof(f3036,plain,
( ! [X0] :
( empty(sK6(sK7(sK6(X0))))
| empty(sK6(X0))
| empty(sK7(sK6(X0)))
| element(sK9(sK6(sK7(sK6(X0)))),X0)
| empty(X0) )
| ~ spl16_76
| ~ spl16_304 ),
inference(resolution,[],[f2957,f574]) ).
fof(f6566,plain,
( spl16_537
| ~ spl16_77
| ~ spl16_303 ),
inference(avatar_split_clause,[],[f3016,f2952,f577,f6564]) ).
fof(f6564,plain,
( spl16_537
<=> ! [X0] :
( empty(sK6(sK6(sK7(X0))))
| empty(sK7(X0))
| empty(sK6(sK7(X0)))
| element(sK9(sK6(sK6(sK7(X0)))),X0)
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_537])]) ).
fof(f3016,plain,
( ! [X0] :
( empty(sK6(sK6(sK7(X0))))
| empty(sK7(X0))
| empty(sK6(sK7(X0)))
| element(sK9(sK6(sK6(sK7(X0)))),X0)
| empty(X0) )
| ~ spl16_77
| ~ spl16_303 ),
inference(resolution,[],[f2953,f578]) ).
fof(f6562,plain,
( spl16_536
| ~ spl16_76
| ~ spl16_303 ),
inference(avatar_split_clause,[],[f3015,f2952,f573,f6560]) ).
fof(f6560,plain,
( spl16_536
<=> ! [X0] :
( empty(sK6(sK6(sK6(X0))))
| empty(sK6(X0))
| empty(sK6(sK6(X0)))
| element(sK9(sK6(sK6(sK6(X0)))),X0)
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_536])]) ).
fof(f3015,plain,
( ! [X0] :
( empty(sK6(sK6(sK6(X0))))
| empty(sK6(X0))
| empty(sK6(sK6(X0)))
| element(sK9(sK6(sK6(sK6(X0)))),X0)
| empty(X0) )
| ~ spl16_76
| ~ spl16_303 ),
inference(resolution,[],[f2953,f574]) ).
fof(f6558,plain,
( spl16_535
| ~ spl16_138
| ~ spl16_468 ),
inference(avatar_split_clause,[],[f5603,f5596,f1121,f6556]) ).
fof(f1121,plain,
( spl16_138
<=> ! [X0] :
( element(sK5,the_carrier(X0))
| ~ rel_str(X0)
| ~ subrelstr(sK1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_138])]) ).
fof(f5603,plain,
( ! [X0] :
( empty(the_InternalRel(X0))
| ~ subrelstr(sK1,X0)
| related(X0,sK4,sK5)
| ~ rel_str(X0)
| ~ element(sK4,the_carrier(X0)) )
| ~ spl16_138
| ~ spl16_468 ),
inference(duplicate_literal_removal,[],[f5600]) ).
fof(f5600,plain,
( ! [X0] :
( empty(the_InternalRel(X0))
| ~ subrelstr(sK1,X0)
| related(X0,sK4,sK5)
| ~ rel_str(X0)
| ~ element(sK4,the_carrier(X0))
| ~ rel_str(X0)
| ~ subrelstr(sK1,X0) )
| ~ spl16_138
| ~ spl16_468 ),
inference(resolution,[],[f5597,f1122]) ).
fof(f1122,plain,
( ! [X0] :
( element(sK5,the_carrier(X0))
| ~ rel_str(X0)
| ~ subrelstr(sK1,X0) )
| ~ spl16_138 ),
inference(avatar_component_clause,[],[f1121]) ).
fof(f6554,plain,
( spl16_534
| ~ spl16_279
| ~ spl16_286 ),
inference(avatar_split_clause,[],[f2746,f2727,f2665,f6552]) ).
fof(f6552,plain,
( spl16_534
<=> ! [X0] :
( sK14 = sK9(sK9(powerset(powerset(X0))))
| ~ empty(X0)
| sK14 = sK9(powerset(sK9(powerset(sK9(powerset(sK9(powerset(powerset(X0))))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_534])]) ).
fof(f2746,plain,
( ! [X0] :
( sK14 = sK9(sK9(powerset(powerset(X0))))
| ~ empty(X0)
| sK14 = sK9(powerset(sK9(powerset(sK9(powerset(sK9(powerset(powerset(X0))))))))) )
| ~ spl16_279
| ~ spl16_286 ),
inference(resolution,[],[f2728,f2666]) ).
fof(f6550,plain,
( spl16_533
| ~ spl16_204
| ~ spl16_286 ),
inference(avatar_split_clause,[],[f2745,f2727,f1797,f6548]) ).
fof(f6548,plain,
( spl16_533
<=> ! [X0,X1] :
( sK14 = sK9(sK9(powerset(powerset(X0))))
| ~ empty(X0)
| ~ empty(X1)
| sK9(powerset(X1)) = sK9(powerset(sK9(powerset(powerset(X0))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_533])]) ).
fof(f2745,plain,
( ! [X0,X1] :
( sK14 = sK9(sK9(powerset(powerset(X0))))
| ~ empty(X0)
| ~ empty(X1)
| sK9(powerset(X1)) = sK9(powerset(sK9(powerset(powerset(X0))))) )
| ~ spl16_204
| ~ spl16_286 ),
inference(resolution,[],[f2728,f1798]) ).
fof(f6546,plain,
( spl16_532
| ~ spl16_208
| ~ spl16_282 ),
inference(avatar_split_clause,[],[f2708,f2692,f1820,f6544]) ).
fof(f6544,plain,
( spl16_532
<=> ! [X0,X1] :
( sK9(powerset(X0)) = sK9(powerset(sK9(powerset(the_InternalRel(sK8(X1))))))
| ~ empty(X0)
| ~ rel_str(sK8(X1))
| ~ rel_str(X1)
| ~ empty(the_InternalRel(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_532])]) ).
fof(f2708,plain,
( ! [X0,X1] :
( sK9(powerset(X0)) = sK9(powerset(sK9(powerset(the_InternalRel(sK8(X1))))))
| ~ empty(X0)
| ~ rel_str(sK8(X1))
| ~ rel_str(X1)
| ~ empty(the_InternalRel(X1)) )
| ~ spl16_208
| ~ spl16_282 ),
inference(resolution,[],[f2693,f1821]) ).
fof(f6542,plain,
( spl16_531
| ~ spl16_207
| ~ spl16_282 ),
inference(avatar_split_clause,[],[f2707,f2692,f1816,f6540]) ).
fof(f6540,plain,
( spl16_531
<=> ! [X0,X1] :
( sK9(powerset(X0)) = sK9(powerset(sK9(powerset(the_carrier(sK8(X1))))))
| ~ empty(X0)
| ~ rel_str(sK8(X1))
| ~ rel_str(X1)
| ~ empty(the_carrier(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_531])]) ).
fof(f2707,plain,
( ! [X0,X1] :
( sK9(powerset(X0)) = sK9(powerset(sK9(powerset(the_carrier(sK8(X1))))))
| ~ empty(X0)
| ~ rel_str(sK8(X1))
| ~ rel_str(X1)
| ~ empty(the_carrier(X1)) )
| ~ spl16_207
| ~ spl16_282 ),
inference(resolution,[],[f2693,f1817]) ).
fof(f6538,plain,
( spl16_530
| ~ spl16_215
| ~ spl16_279 ),
inference(avatar_split_clause,[],[f2673,f2665,f1961,f6536]) ).
fof(f6536,plain,
( spl16_530
<=> ! [X0] :
( sK14 = sK9(powerset(sK9(powerset(sK9(powerset(sK9(sK7(powerset(X0)))))))))
| ~ empty(X0)
| empty(powerset(X0))
| empty(sK7(powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_530])]) ).
fof(f2673,plain,
( ! [X0] :
( sK14 = sK9(powerset(sK9(powerset(sK9(powerset(sK9(sK7(powerset(X0)))))))))
| ~ empty(X0)
| empty(powerset(X0))
| empty(sK7(powerset(X0))) )
| ~ spl16_215
| ~ spl16_279 ),
inference(resolution,[],[f2666,f1962]) ).
fof(f6534,plain,
( spl16_529
| ~ spl16_214
| ~ spl16_279 ),
inference(avatar_split_clause,[],[f2672,f2665,f1955,f6532]) ).
fof(f6532,plain,
( spl16_529
<=> ! [X0] :
( sK14 = sK9(powerset(sK9(powerset(sK9(powerset(sK9(sK6(powerset(X0)))))))))
| ~ empty(X0)
| empty(powerset(X0))
| empty(sK6(powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_529])]) ).
fof(f2672,plain,
( ! [X0] :
( sK14 = sK9(powerset(sK9(powerset(sK9(powerset(sK9(sK6(powerset(X0)))))))))
| ~ empty(X0)
| empty(powerset(X0))
| empty(sK6(powerset(X0))) )
| ~ spl16_214
| ~ spl16_279 ),
inference(resolution,[],[f2666,f1956]) ).
fof(f6278,plain,
( spl16_528
| ~ spl16_65
| ~ spl16_357 ),
inference(avatar_split_clause,[],[f3787,f3650,f508,f6276]) ).
fof(f6276,plain,
( spl16_528
<=> ! [X0] :
( empty(sK7(sK9(powerset(powerset(X0)))))
| ~ empty(X0)
| empty(sK9(powerset(powerset(X0))))
| empty(sK9(sK7(sK9(powerset(powerset(X0)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_528])]) ).
fof(f3650,plain,
( spl16_357
<=> ! [X0,X1] :
( empty(sK9(powerset(powerset(X0))))
| empty(sK7(sK9(powerset(powerset(X0)))))
| ~ empty(X0)
| ~ in(X1,sK9(sK7(sK9(powerset(powerset(X0)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_357])]) ).
fof(f3787,plain,
( ! [X0] :
( empty(sK7(sK9(powerset(powerset(X0)))))
| ~ empty(X0)
| empty(sK9(powerset(powerset(X0))))
| empty(sK9(sK7(sK9(powerset(powerset(X0)))))) )
| ~ spl16_65
| ~ spl16_357 ),
inference(resolution,[],[f3651,f509]) ).
fof(f3651,plain,
( ! [X0,X1] :
( ~ in(X1,sK9(sK7(sK9(powerset(powerset(X0))))))
| empty(sK7(sK9(powerset(powerset(X0)))))
| ~ empty(X0)
| empty(sK9(powerset(powerset(X0)))) )
| ~ spl16_357 ),
inference(avatar_component_clause,[],[f3650]) ).
fof(f6274,plain,
( spl16_527
| ~ spl16_65
| ~ spl16_356 ),
inference(avatar_split_clause,[],[f3774,f3646,f508,f6272]) ).
fof(f6272,plain,
( spl16_527
<=> ! [X0] :
( empty(sK6(sK9(powerset(powerset(X0)))))
| ~ empty(X0)
| empty(sK9(powerset(powerset(X0))))
| empty(sK9(sK6(sK9(powerset(powerset(X0)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_527])]) ).
fof(f3646,plain,
( spl16_356
<=> ! [X0,X1] :
( empty(sK9(powerset(powerset(X0))))
| empty(sK6(sK9(powerset(powerset(X0)))))
| ~ empty(X0)
| ~ in(X1,sK9(sK6(sK9(powerset(powerset(X0)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_356])]) ).
fof(f3774,plain,
( ! [X0] :
( empty(sK6(sK9(powerset(powerset(X0)))))
| ~ empty(X0)
| empty(sK9(powerset(powerset(X0))))
| empty(sK9(sK6(sK9(powerset(powerset(X0)))))) )
| ~ spl16_65
| ~ spl16_356 ),
inference(resolution,[],[f3647,f509]) ).
fof(f3647,plain,
( ! [X0,X1] :
( ~ in(X1,sK9(sK6(sK9(powerset(powerset(X0))))))
| empty(sK6(sK9(powerset(powerset(X0)))))
| ~ empty(X0)
| empty(sK9(powerset(powerset(X0)))) )
| ~ spl16_356 ),
inference(avatar_component_clause,[],[f3646]) ).
fof(f6270,plain,
( spl16_526
| ~ spl16_65
| ~ spl16_355 ),
inference(avatar_split_clause,[],[f3754,f3642,f508,f6268]) ).
fof(f6268,plain,
( spl16_526
<=> ! [X0] :
( empty(sK7(sK7(powerset(X0))))
| empty(powerset(X0))
| ~ empty(X0)
| empty(sK7(powerset(X0)))
| empty(sK9(sK7(sK7(powerset(X0))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_526])]) ).
fof(f3642,plain,
( spl16_355
<=> ! [X0,X1] :
( empty(sK7(powerset(X0)))
| empty(sK7(sK7(powerset(X0))))
| empty(powerset(X0))
| ~ empty(X0)
| ~ in(X1,sK9(sK7(sK7(powerset(X0))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_355])]) ).
fof(f3754,plain,
( ! [X0] :
( empty(sK7(sK7(powerset(X0))))
| empty(powerset(X0))
| ~ empty(X0)
| empty(sK7(powerset(X0)))
| empty(sK9(sK7(sK7(powerset(X0))))) )
| ~ spl16_65
| ~ spl16_355 ),
inference(resolution,[],[f3643,f509]) ).
fof(f3643,plain,
( ! [X0,X1] :
( ~ in(X1,sK9(sK7(sK7(powerset(X0)))))
| empty(sK7(sK7(powerset(X0))))
| empty(powerset(X0))
| ~ empty(X0)
| empty(sK7(powerset(X0))) )
| ~ spl16_355 ),
inference(avatar_component_clause,[],[f3642]) ).
fof(f6266,plain,
( spl16_525
| ~ spl16_65
| ~ spl16_354 ),
inference(avatar_split_clause,[],[f3741,f3638,f508,f6264]) ).
fof(f6264,plain,
( spl16_525
<=> ! [X0] :
( empty(sK7(sK6(powerset(X0))))
| empty(powerset(X0))
| ~ empty(X0)
| empty(sK6(powerset(X0)))
| empty(sK9(sK7(sK6(powerset(X0))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_525])]) ).
fof(f3638,plain,
( spl16_354
<=> ! [X0,X1] :
( empty(sK6(powerset(X0)))
| empty(sK7(sK6(powerset(X0))))
| empty(powerset(X0))
| ~ empty(X0)
| ~ in(X1,sK9(sK7(sK6(powerset(X0))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_354])]) ).
fof(f3741,plain,
( ! [X0] :
( empty(sK7(sK6(powerset(X0))))
| empty(powerset(X0))
| ~ empty(X0)
| empty(sK6(powerset(X0)))
| empty(sK9(sK7(sK6(powerset(X0))))) )
| ~ spl16_65
| ~ spl16_354 ),
inference(resolution,[],[f3639,f509]) ).
fof(f3639,plain,
( ! [X0,X1] :
( ~ in(X1,sK9(sK7(sK6(powerset(X0)))))
| empty(sK7(sK6(powerset(X0))))
| empty(powerset(X0))
| ~ empty(X0)
| empty(sK6(powerset(X0))) )
| ~ spl16_354 ),
inference(avatar_component_clause,[],[f3638]) ).
fof(f6262,plain,
( spl16_524
| ~ spl16_65
| ~ spl16_353 ),
inference(avatar_split_clause,[],[f3728,f3634,f508,f6260]) ).
fof(f6260,plain,
( spl16_524
<=> ! [X0] :
( empty(sK6(sK7(powerset(X0))))
| empty(powerset(X0))
| ~ empty(X0)
| empty(sK7(powerset(X0)))
| empty(sK9(sK6(sK7(powerset(X0))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_524])]) ).
fof(f3634,plain,
( spl16_353
<=> ! [X0,X1] :
( empty(sK7(powerset(X0)))
| empty(sK6(sK7(powerset(X0))))
| empty(powerset(X0))
| ~ empty(X0)
| ~ in(X1,sK9(sK6(sK7(powerset(X0))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_353])]) ).
fof(f3728,plain,
( ! [X0] :
( empty(sK6(sK7(powerset(X0))))
| empty(powerset(X0))
| ~ empty(X0)
| empty(sK7(powerset(X0)))
| empty(sK9(sK6(sK7(powerset(X0))))) )
| ~ spl16_65
| ~ spl16_353 ),
inference(resolution,[],[f3635,f509]) ).
fof(f3635,plain,
( ! [X0,X1] :
( ~ in(X1,sK9(sK6(sK7(powerset(X0)))))
| empty(sK6(sK7(powerset(X0))))
| empty(powerset(X0))
| ~ empty(X0)
| empty(sK7(powerset(X0))) )
| ~ spl16_353 ),
inference(avatar_component_clause,[],[f3634]) ).
fof(f6258,plain,
( spl16_523
| ~ spl16_27
| ~ spl16_511 ),
inference(avatar_split_clause,[],[f6122,f6080,f282,f6256]) ).
fof(f6256,plain,
( spl16_523
<=> ! [X0] :
( ~ subrelstr(sK0,X0)
| empty(the_InternalRel(X0))
| ~ rel_str(X0)
| ~ in(the_InternalRel(X0),ordered_pair(sK4,sK5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_523])]) ).
fof(f6080,plain,
( spl16_511
<=> ! [X0] :
( ~ rel_str(X0)
| ~ subrelstr(sK0,X0)
| empty(the_InternalRel(X0))
| in(ordered_pair(sK4,sK5),the_InternalRel(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_511])]) ).
fof(f6122,plain,
( ! [X0] :
( ~ subrelstr(sK0,X0)
| empty(the_InternalRel(X0))
| ~ rel_str(X0)
| ~ in(the_InternalRel(X0),ordered_pair(sK4,sK5)) )
| ~ spl16_27
| ~ spl16_511 ),
inference(resolution,[],[f6081,f283]) ).
fof(f6081,plain,
( ! [X0] :
( in(ordered_pair(sK4,sK5),the_InternalRel(X0))
| ~ subrelstr(sK0,X0)
| empty(the_InternalRel(X0))
| ~ rel_str(X0) )
| ~ spl16_511 ),
inference(avatar_component_clause,[],[f6080]) ).
fof(f6254,plain,
( spl16_522
| ~ spl16_65
| ~ spl16_352 ),
inference(avatar_split_clause,[],[f3715,f3630,f508,f6252]) ).
fof(f6252,plain,
( spl16_522
<=> ! [X0] :
( empty(sK6(sK6(powerset(X0))))
| empty(powerset(X0))
| ~ empty(X0)
| empty(sK6(powerset(X0)))
| empty(sK9(sK6(sK6(powerset(X0))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_522])]) ).
fof(f3630,plain,
( spl16_352
<=> ! [X0,X1] :
( empty(sK6(powerset(X0)))
| empty(sK6(sK6(powerset(X0))))
| empty(powerset(X0))
| ~ empty(X0)
| ~ in(X1,sK9(sK6(sK6(powerset(X0))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_352])]) ).
fof(f3715,plain,
( ! [X0] :
( empty(sK6(sK6(powerset(X0))))
| empty(powerset(X0))
| ~ empty(X0)
| empty(sK6(powerset(X0)))
| empty(sK9(sK6(sK6(powerset(X0))))) )
| ~ spl16_65
| ~ spl16_352 ),
inference(resolution,[],[f3631,f509]) ).
fof(f3631,plain,
( ! [X0,X1] :
( ~ in(X1,sK9(sK6(sK6(powerset(X0)))))
| empty(sK6(sK6(powerset(X0))))
| empty(powerset(X0))
| ~ empty(X0)
| empty(sK6(powerset(X0))) )
| ~ spl16_352 ),
inference(avatar_component_clause,[],[f3630]) ).
fof(f6250,plain,
( spl16_521
| ~ spl16_27
| ~ spl16_349 ),
inference(avatar_split_clause,[],[f3599,f3578,f282,f6248]) ).
fof(f6248,plain,
( spl16_521
<=> ! [X0] :
( empty(sK9(powerset(X0)))
| empty(X0)
| empty(sK9(powerset(sK9(powerset(X0)))))
| ~ in(X0,sK9(sK9(powerset(sK9(powerset(X0)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_521])]) ).
fof(f3599,plain,
( ! [X0] :
( empty(sK9(powerset(X0)))
| empty(X0)
| empty(sK9(powerset(sK9(powerset(X0)))))
| ~ in(X0,sK9(sK9(powerset(sK9(powerset(X0)))))) )
| ~ spl16_27
| ~ spl16_349 ),
inference(resolution,[],[f3579,f283]) ).
fof(f6246,plain,
( spl16_520
| ~ spl16_99
| ~ spl16_323 ),
inference(avatar_split_clause,[],[f3311,f3292,f743,f6244]) ).
fof(f6244,plain,
( spl16_520
<=> ! [X0,X1] :
( ~ empty(X0)
| sK9(sK9(powerset(powerset(X0)))) = sK9(powerset(sK9(powerset(X1))))
| empty(sK9(powerset(powerset(X0))))
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_520])]) ).
fof(f3311,plain,
( ! [X0,X1] :
( ~ empty(X0)
| sK9(sK9(powerset(powerset(X0)))) = sK9(powerset(sK9(powerset(X1))))
| empty(sK9(powerset(powerset(X0))))
| ~ empty(X1) )
| ~ spl16_99
| ~ spl16_323 ),
inference(resolution,[],[f3293,f744]) ).
fof(f6242,plain,
( spl16_519
| ~ spl16_213
| ~ spl16_279 ),
inference(avatar_split_clause,[],[f2674,f2665,f1942,f6240]) ).
fof(f6240,plain,
( spl16_519
<=> ! [X0] :
( sK14 = sK9(powerset(sK9(powerset(sK9(powerset(sK9(sK9(powerset(powerset(X0))))))))))
| empty(sK9(powerset(powerset(X0))))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_519])]) ).
fof(f2674,plain,
( ! [X0] :
( sK14 = sK9(powerset(sK9(powerset(sK9(powerset(sK9(sK9(powerset(powerset(X0))))))))))
| empty(sK9(powerset(powerset(X0))))
| ~ empty(X0) )
| ~ spl16_213
| ~ spl16_279 ),
inference(resolution,[],[f2666,f1943]) ).
fof(f6114,plain,
( spl16_518
| ~ spl16_23
| ~ spl16_57
| ~ spl16_324 ),
inference(avatar_split_clause,[],[f3338,f3296,f469,f263,f6112]) ).
fof(f6112,plain,
( spl16_518
<=> ! [X0] :
( sK14 = sK9(powerset(powerset(X0)))
| ~ empty(X0)
| sK14 = sK9(powerset(sK9(powerset(sK9(sK9(powerset(powerset(X0)))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_518])]) ).
fof(f3338,plain,
( ! [X0] :
( sK14 = sK9(powerset(powerset(X0)))
| ~ empty(X0)
| sK14 = sK9(powerset(sK9(powerset(sK9(sK9(powerset(powerset(X0)))))))) )
| ~ spl16_23
| ~ spl16_57
| ~ spl16_324 ),
inference(forward_demodulation,[],[f3325,f471]) ).
fof(f3325,plain,
( ! [X0] :
( ~ empty(X0)
| sK14 = sK9(powerset(sK9(powerset(sK9(sK9(powerset(powerset(X0))))))))
| empty_set = sK9(powerset(powerset(X0))) )
| ~ spl16_23
| ~ spl16_324 ),
inference(resolution,[],[f3297,f264]) ).
fof(f6110,plain,
( spl16_517
| ~ spl16_142
| ~ spl16_309 ),
inference(avatar_split_clause,[],[f3125,f3098,f1176,f6108]) ).
fof(f6108,plain,
( spl16_517
<=> ! [X0] :
( ~ empty(X0)
| sK14 = sK9(powerset(sK9(sK9(powerset(powerset(X0))))))
| sK14 = sK9(powerset(sK9(powerset(powerset(X0))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_517])]) ).
fof(f3125,plain,
( ! [X0] :
( ~ empty(X0)
| sK14 = sK9(powerset(sK9(sK9(powerset(powerset(X0))))))
| sK14 = sK9(powerset(sK9(powerset(powerset(X0))))) )
| ~ spl16_142
| ~ spl16_309 ),
inference(resolution,[],[f3099,f1177]) ).
fof(f6106,plain,
( spl16_516
| ~ spl16_36
| ~ spl16_309 ),
inference(avatar_split_clause,[],[f3123,f3098,f318,f6104]) ).
fof(f6104,plain,
( spl16_516
<=> ! [X0,X1] :
( ~ empty(X0)
| sK14 = sK9(powerset(sK9(sK9(powerset(powerset(X0))))))
| sK9(powerset(powerset(X0))) = X1
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_516])]) ).
fof(f3123,plain,
( ! [X0,X1] :
( ~ empty(X0)
| sK14 = sK9(powerset(sK9(sK9(powerset(powerset(X0))))))
| sK9(powerset(powerset(X0))) = X1
| ~ empty(X1) )
| ~ spl16_36
| ~ spl16_309 ),
inference(resolution,[],[f3099,f319]) ).
fof(f6102,plain,
( spl16_515
| ~ spl16_197
| ~ spl16_286 ),
inference(avatar_split_clause,[],[f2744,f2727,f1702,f6100]) ).
fof(f6100,plain,
( spl16_515
<=> ! [X0] :
( sK14 = sK9(sK9(powerset(powerset(X0))))
| ~ empty(X0)
| sK14 = sK9(powerset(sK9(powerset(sK9(powerset(powerset(X0))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_515])]) ).
fof(f2744,plain,
( ! [X0] :
( sK14 = sK9(sK9(powerset(powerset(X0))))
| ~ empty(X0)
| sK14 = sK9(powerset(sK9(powerset(sK9(powerset(powerset(X0))))))) )
| ~ spl16_197
| ~ spl16_286 ),
inference(resolution,[],[f2728,f1703]) ).
fof(f6098,plain,
( spl16_514
| ~ spl16_148
| ~ spl16_286 ),
inference(avatar_split_clause,[],[f2743,f2727,f1206,f6096]) ).
fof(f6096,plain,
( spl16_514
<=> ! [X0,X1] :
( sK14 = sK9(sK9(powerset(powerset(X0))))
| ~ empty(X0)
| sK9(powerset(X1)) = sK9(powerset(powerset(X0)))
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_514])]) ).
fof(f2743,plain,
( ! [X0,X1] :
( sK14 = sK9(sK9(powerset(powerset(X0))))
| ~ empty(X0)
| sK9(powerset(X1)) = sK9(powerset(powerset(X0)))
| ~ empty(X1) )
| ~ spl16_148
| ~ spl16_286 ),
inference(resolution,[],[f2728,f1207]) ).
fof(f6094,plain,
( spl16_513
| ~ spl16_208
| ~ spl16_279 ),
inference(avatar_split_clause,[],[f2669,f2665,f1820,f6092]) ).
fof(f6092,plain,
( spl16_513
<=> ! [X0] :
( sK14 = sK9(powerset(sK9(powerset(sK9(powerset(the_InternalRel(sK8(X0))))))))
| ~ rel_str(sK8(X0))
| ~ rel_str(X0)
| ~ empty(the_InternalRel(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_513])]) ).
fof(f2669,plain,
( ! [X0] :
( sK14 = sK9(powerset(sK9(powerset(sK9(powerset(the_InternalRel(sK8(X0))))))))
| ~ rel_str(sK8(X0))
| ~ rel_str(X0)
| ~ empty(the_InternalRel(X0)) )
| ~ spl16_208
| ~ spl16_279 ),
inference(resolution,[],[f2666,f1821]) ).
fof(f6090,plain,
( spl16_512
| ~ spl16_207
| ~ spl16_279 ),
inference(avatar_split_clause,[],[f2668,f2665,f1816,f6088]) ).
fof(f6088,plain,
( spl16_512
<=> ! [X0] :
( sK14 = sK9(powerset(sK9(powerset(sK9(powerset(the_carrier(sK8(X0))))))))
| ~ rel_str(sK8(X0))
| ~ rel_str(X0)
| ~ empty(the_carrier(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_512])]) ).
fof(f2668,plain,
( ! [X0] :
( sK14 = sK9(powerset(sK9(powerset(sK9(powerset(the_carrier(sK8(X0))))))))
| ~ rel_str(sK8(X0))
| ~ rel_str(X0)
| ~ empty(the_carrier(X0)) )
| ~ spl16_207
| ~ spl16_279 ),
inference(resolution,[],[f2666,f1817]) ).
fof(f6082,plain,
( spl16_511
| ~ spl16_38
| ~ spl16_499 ),
inference(avatar_split_clause,[],[f5998,f5963,f335,f6080]) ).
fof(f5998,plain,
( ! [X0] :
( ~ rel_str(X0)
| ~ subrelstr(sK0,X0)
| empty(the_InternalRel(X0))
| in(ordered_pair(sK4,sK5),the_InternalRel(X0)) )
| ~ spl16_38
| ~ spl16_499 ),
inference(resolution,[],[f5964,f336]) ).
fof(f6078,plain,
( spl16_510
| ~ spl16_27
| ~ spl16_326 ),
inference(avatar_split_clause,[],[f3363,f3305,f282,f6076]) ).
fof(f6076,plain,
( spl16_510
<=> ! [X0] :
( empty(sK7(sK9(powerset(X0))))
| empty(X0)
| empty(sK9(powerset(X0)))
| ~ in(X0,sK9(sK7(sK9(powerset(X0))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_510])]) ).
fof(f3363,plain,
( ! [X0] :
( empty(sK7(sK9(powerset(X0))))
| empty(X0)
| empty(sK9(powerset(X0)))
| ~ in(X0,sK9(sK7(sK9(powerset(X0))))) )
| ~ spl16_27
| ~ spl16_326 ),
inference(resolution,[],[f3306,f283]) ).
fof(f6074,plain,
( spl16_509
| ~ spl16_27
| ~ spl16_325 ),
inference(avatar_split_clause,[],[f3340,f3300,f282,f6072]) ).
fof(f6072,plain,
( spl16_509
<=> ! [X0] :
( empty(sK6(sK9(powerset(X0))))
| empty(X0)
| empty(sK9(powerset(X0)))
| ~ in(X0,sK9(sK6(sK9(powerset(X0))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_509])]) ).
fof(f3340,plain,
( ! [X0] :
( empty(sK6(sK9(powerset(X0))))
| empty(X0)
| empty(sK9(powerset(X0)))
| ~ in(X0,sK9(sK6(sK9(powerset(X0))))) )
| ~ spl16_27
| ~ spl16_325 ),
inference(resolution,[],[f3301,f283]) ).
fof(f6070,plain,
( spl16_508
| ~ spl16_16
| ~ spl16_324 ),
inference(avatar_split_clause,[],[f3324,f3296,f232,f6068]) ).
fof(f6068,plain,
( spl16_508
<=> ! [X0] :
( ~ empty(X0)
| sK14 = sK9(powerset(sK9(powerset(sK9(sK9(powerset(powerset(X0))))))))
| finite(sK9(powerset(powerset(X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_508])]) ).
fof(f232,plain,
( spl16_16
<=> ! [X0] :
( finite(X0)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_16])]) ).
fof(f3324,plain,
( ! [X0] :
( ~ empty(X0)
| sK14 = sK9(powerset(sK9(powerset(sK9(sK9(powerset(powerset(X0))))))))
| finite(sK9(powerset(powerset(X0)))) )
| ~ spl16_16
| ~ spl16_324 ),
inference(resolution,[],[f3297,f233]) ).
fof(f233,plain,
( ! [X0] :
( ~ empty(X0)
| finite(X0) )
| ~ spl16_16 ),
inference(avatar_component_clause,[],[f232]) ).
fof(f6002,plain,
( spl16_507
| ~ spl16_27
| ~ spl16_321 ),
inference(avatar_split_clause,[],[f3271,f3175,f282,f6000]) ).
fof(f6000,plain,
( spl16_507
<=> ! [X0] :
( empty(sK7(X0))
| empty(X0)
| empty(sK9(powerset(sK7(X0))))
| ~ in(X0,sK9(sK9(powerset(sK7(X0))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_507])]) ).
fof(f3271,plain,
( ! [X0] :
( empty(sK7(X0))
| empty(X0)
| empty(sK9(powerset(sK7(X0))))
| ~ in(X0,sK9(sK9(powerset(sK7(X0))))) )
| ~ spl16_27
| ~ spl16_321 ),
inference(resolution,[],[f3176,f283]) ).
fof(f5997,plain,
( spl16_506
| ~ spl16_27
| ~ spl16_320 ),
inference(avatar_split_clause,[],[f3250,f3171,f282,f5995]) ).
fof(f5995,plain,
( spl16_506
<=> ! [X0] :
( empty(sK6(X0))
| empty(X0)
| empty(sK9(powerset(sK6(X0))))
| ~ in(X0,sK9(sK9(powerset(sK6(X0))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_506])]) ).
fof(f3250,plain,
( ! [X0] :
( empty(sK6(X0))
| empty(X0)
| empty(sK9(powerset(sK6(X0))))
| ~ in(X0,sK9(sK9(powerset(sK6(X0))))) )
| ~ spl16_27
| ~ spl16_320 ),
inference(resolution,[],[f3172,f283]) ).
fof(f5993,plain,
( spl16_505
| ~ spl16_23
| ~ spl16_57
| ~ spl16_309 ),
inference(avatar_split_clause,[],[f3132,f3098,f469,f263,f5991]) ).
fof(f5991,plain,
( spl16_505
<=> ! [X0] :
( sK14 = sK9(powerset(powerset(X0)))
| ~ empty(X0)
| sK14 = sK9(powerset(sK9(sK9(powerset(powerset(X0)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_505])]) ).
fof(f3132,plain,
( ! [X0] :
( sK14 = sK9(powerset(powerset(X0)))
| ~ empty(X0)
| sK14 = sK9(powerset(sK9(sK9(powerset(powerset(X0)))))) )
| ~ spl16_23
| ~ spl16_57
| ~ spl16_309 ),
inference(forward_demodulation,[],[f3122,f471]) ).
fof(f3122,plain,
( ! [X0] :
( ~ empty(X0)
| sK14 = sK9(powerset(sK9(sK9(powerset(powerset(X0))))))
| empty_set = sK9(powerset(powerset(X0))) )
| ~ spl16_23
| ~ spl16_309 ),
inference(resolution,[],[f3099,f264]) ).
fof(f5989,plain,
( spl16_504
| ~ spl16_142
| ~ spl16_286 ),
inference(avatar_split_clause,[],[f2742,f2727,f1176,f5987]) ).
fof(f5987,plain,
( spl16_504
<=> ! [X0] :
( sK14 = sK9(sK9(powerset(powerset(X0))))
| ~ empty(X0)
| sK14 = sK9(powerset(sK9(powerset(powerset(X0))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_504])]) ).
fof(f2742,plain,
( ! [X0] :
( sK14 = sK9(sK9(powerset(powerset(X0))))
| ~ empty(X0)
| sK14 = sK9(powerset(sK9(powerset(powerset(X0))))) )
| ~ spl16_142
| ~ spl16_286 ),
inference(resolution,[],[f2728,f1177]) ).
fof(f5985,plain,
( spl16_503
| ~ spl16_36
| ~ spl16_286 ),
inference(avatar_split_clause,[],[f2740,f2727,f318,f5983]) ).
fof(f5983,plain,
( spl16_503
<=> ! [X0,X1] :
( sK14 = sK9(sK9(powerset(powerset(X0))))
| ~ empty(X0)
| sK9(powerset(powerset(X0))) = X1
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_503])]) ).
fof(f2740,plain,
( ! [X0,X1] :
( sK14 = sK9(sK9(powerset(powerset(X0))))
| ~ empty(X0)
| sK9(powerset(powerset(X0))) = X1
| ~ empty(X1) )
| ~ spl16_36
| ~ spl16_286 ),
inference(resolution,[],[f2728,f319]) ).
fof(f5977,plain,
( spl16_502
| ~ spl16_58
| ~ spl16_328 ),
inference(avatar_split_clause,[],[f3449,f3390,f476,f5975]) ).
fof(f5975,plain,
( spl16_502
<=> ! [X0,X1] :
( ~ rel_str(X0)
| ~ empty(the_InternalRel(X0))
| ~ empty(X1)
| sK9(powerset(X1)) = sK9(powerset(the_InternalRel(sK8(X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_502])]) ).
fof(f3390,plain,
( spl16_328
<=> ! [X0,X1] :
( ~ rel_str(sK8(X0))
| ~ rel_str(X0)
| ~ empty(the_InternalRel(X0))
| ~ empty(X1)
| sK9(powerset(X1)) = sK9(powerset(the_InternalRel(sK8(X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_328])]) ).
fof(f3449,plain,
( ! [X0,X1] :
( ~ rel_str(X0)
| ~ empty(the_InternalRel(X0))
| ~ empty(X1)
| sK9(powerset(X1)) = sK9(powerset(the_InternalRel(sK8(X0)))) )
| ~ spl16_58
| ~ spl16_328 ),
inference(duplicate_literal_removal,[],[f3447]) ).
fof(f3447,plain,
( ! [X0,X1] :
( ~ rel_str(X0)
| ~ empty(the_InternalRel(X0))
| ~ empty(X1)
| sK9(powerset(X1)) = sK9(powerset(the_InternalRel(sK8(X0))))
| ~ rel_str(X0) )
| ~ spl16_58
| ~ spl16_328 ),
inference(resolution,[],[f3391,f477]) ).
fof(f3391,plain,
( ! [X0,X1] :
( ~ rel_str(sK8(X0))
| ~ rel_str(X0)
| ~ empty(the_InternalRel(X0))
| ~ empty(X1)
| sK9(powerset(X1)) = sK9(powerset(the_InternalRel(sK8(X0)))) )
| ~ spl16_328 ),
inference(avatar_component_clause,[],[f3390]) ).
fof(f5973,plain,
( spl16_501
| ~ spl16_58
| ~ spl16_327 ),
inference(avatar_split_clause,[],[f3446,f3386,f476,f5971]) ).
fof(f5971,plain,
( spl16_501
<=> ! [X0,X1] :
( ~ rel_str(X0)
| ~ empty(the_carrier(X0))
| ~ empty(X1)
| sK9(powerset(X1)) = sK9(powerset(the_carrier(sK8(X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_501])]) ).
fof(f3386,plain,
( spl16_327
<=> ! [X0,X1] :
( ~ rel_str(sK8(X0))
| ~ rel_str(X0)
| ~ empty(the_carrier(X0))
| ~ empty(X1)
| sK9(powerset(X1)) = sK9(powerset(the_carrier(sK8(X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_327])]) ).
fof(f3446,plain,
( ! [X0,X1] :
( ~ rel_str(X0)
| ~ empty(the_carrier(X0))
| ~ empty(X1)
| sK9(powerset(X1)) = sK9(powerset(the_carrier(sK8(X0)))) )
| ~ spl16_58
| ~ spl16_327 ),
inference(duplicate_literal_removal,[],[f3444]) ).
fof(f3444,plain,
( ! [X0,X1] :
( ~ rel_str(X0)
| ~ empty(the_carrier(X0))
| ~ empty(X1)
| sK9(powerset(X1)) = sK9(powerset(the_carrier(sK8(X0))))
| ~ rel_str(X0) )
| ~ spl16_58
| ~ spl16_327 ),
inference(resolution,[],[f3387,f477]) ).
fof(f3387,plain,
( ! [X0,X1] :
( ~ rel_str(sK8(X0))
| ~ rel_str(X0)
| ~ empty(the_carrier(X0))
| ~ empty(X1)
| sK9(powerset(X1)) = sK9(powerset(the_carrier(sK8(X0)))) )
| ~ spl16_327 ),
inference(avatar_component_clause,[],[f3386]) ).
fof(f5969,plain,
( spl16_500
| ~ spl16_16
| ~ spl16_309 ),
inference(avatar_split_clause,[],[f3121,f3098,f232,f5967]) ).
fof(f5967,plain,
( spl16_500
<=> ! [X0] :
( ~ empty(X0)
| sK14 = sK9(powerset(sK9(sK9(powerset(powerset(X0))))))
| finite(sK9(powerset(powerset(X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_500])]) ).
fof(f3121,plain,
( ! [X0] :
( ~ empty(X0)
| sK14 = sK9(powerset(sK9(sK9(powerset(powerset(X0))))))
| finite(sK9(powerset(powerset(X0)))) )
| ~ spl16_16
| ~ spl16_309 ),
inference(resolution,[],[f3099,f233]) ).
fof(f5965,plain,
( spl16_499
| ~ spl16_1
| spl16_186
| ~ spl16_2
| ~ spl16_467 ),
inference(avatar_split_clause,[],[f5591,f5588,f163,f1536,f158,f5963]) ).
fof(f5588,plain,
( spl16_467
<=> ! [X0,X1] :
( ~ rel_str(X0)
| empty(the_InternalRel(X0))
| ~ subrelstr(sK1,X0)
| element(ordered_pair(sK4,sK5),the_InternalRel(X1))
| ~ subrelstr(X0,X1)
| ~ rel_str(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_467])]) ).
fof(f5591,plain,
( ! [X0] :
( empty(the_InternalRel(sK0))
| ~ rel_str(sK0)
| element(ordered_pair(sK4,sK5),the_InternalRel(X0))
| ~ subrelstr(sK0,X0)
| ~ rel_str(X0) )
| ~ spl16_2
| ~ spl16_467 ),
inference(resolution,[],[f5589,f165]) ).
fof(f165,plain,
( subrelstr(sK1,sK0)
| ~ spl16_2 ),
inference(avatar_component_clause,[],[f163]) ).
fof(f5589,plain,
( ! [X0,X1] :
( ~ subrelstr(sK1,X0)
| empty(the_InternalRel(X0))
| ~ rel_str(X0)
| element(ordered_pair(sK4,sK5),the_InternalRel(X1))
| ~ subrelstr(X0,X1)
| ~ rel_str(X1) )
| ~ spl16_467 ),
inference(avatar_component_clause,[],[f5588]) ).
fof(f5864,plain,
( spl16_498
| ~ spl16_21
| ~ spl16_332 ),
inference(avatar_split_clause,[],[f3518,f3408,f255,f5862]) ).
fof(f5862,plain,
( spl16_498
<=> ! [X0] :
( empty(powerset(X0))
| ~ empty(X0)
| sK14 = sK9(powerset(sK9(powerset(sK9(sK7(powerset(X0))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_498])]) ).
fof(f255,plain,
( spl16_21
<=> ! [X0] :
( ~ empty(sK7(X0))
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_21])]) ).
fof(f3408,plain,
( spl16_332
<=> ! [X0] :
( ~ empty(X0)
| empty(powerset(X0))
| empty(sK7(powerset(X0)))
| sK14 = sK9(powerset(sK9(powerset(sK9(sK7(powerset(X0))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_332])]) ).
fof(f3518,plain,
( ! [X0] :
( empty(powerset(X0))
| ~ empty(X0)
| sK14 = sK9(powerset(sK9(powerset(sK9(sK7(powerset(X0))))))) )
| ~ spl16_21
| ~ spl16_332 ),
inference(duplicate_literal_removal,[],[f3501]) ).
fof(f3501,plain,
( ! [X0] :
( empty(powerset(X0))
| ~ empty(X0)
| sK14 = sK9(powerset(sK9(powerset(sK9(sK7(powerset(X0)))))))
| empty(powerset(X0)) )
| ~ spl16_21
| ~ spl16_332 ),
inference(resolution,[],[f3409,f256]) ).
fof(f256,plain,
( ! [X0] :
( ~ empty(sK7(X0))
| empty(X0) )
| ~ spl16_21 ),
inference(avatar_component_clause,[],[f255]) ).
fof(f3409,plain,
( ! [X0] :
( empty(sK7(powerset(X0)))
| empty(powerset(X0))
| ~ empty(X0)
| sK14 = sK9(powerset(sK9(powerset(sK9(sK7(powerset(X0))))))) )
| ~ spl16_332 ),
inference(avatar_component_clause,[],[f3408]) ).
fof(f5860,plain,
( spl16_497
| ~ spl16_19
| ~ spl16_330 ),
inference(avatar_split_clause,[],[f3483,f3398,f247,f5858]) ).
fof(f5858,plain,
( spl16_497
<=> ! [X0] :
( empty(powerset(X0))
| ~ empty(X0)
| sK14 = sK9(powerset(sK9(powerset(sK9(sK6(powerset(X0))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_497])]) ).
fof(f247,plain,
( spl16_19
<=> ! [X0] :
( ~ empty(sK6(X0))
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_19])]) ).
fof(f3398,plain,
( spl16_330
<=> ! [X0] :
( ~ empty(X0)
| empty(powerset(X0))
| empty(sK6(powerset(X0)))
| sK14 = sK9(powerset(sK9(powerset(sK9(sK6(powerset(X0))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_330])]) ).
fof(f3483,plain,
( ! [X0] :
( empty(powerset(X0))
| ~ empty(X0)
| sK14 = sK9(powerset(sK9(powerset(sK9(sK6(powerset(X0))))))) )
| ~ spl16_19
| ~ spl16_330 ),
inference(duplicate_literal_removal,[],[f3467]) ).
fof(f3467,plain,
( ! [X0] :
( empty(powerset(X0))
| ~ empty(X0)
| sK14 = sK9(powerset(sK9(powerset(sK9(sK6(powerset(X0)))))))
| empty(powerset(X0)) )
| ~ spl16_19
| ~ spl16_330 ),
inference(resolution,[],[f3399,f248]) ).
fof(f248,plain,
( ! [X0] :
( ~ empty(sK6(X0))
| empty(X0) )
| ~ spl16_19 ),
inference(avatar_component_clause,[],[f247]) ).
fof(f3399,plain,
( ! [X0] :
( empty(sK6(powerset(X0)))
| empty(powerset(X0))
| ~ empty(X0)
| sK14 = sK9(powerset(sK9(powerset(sK9(sK6(powerset(X0))))))) )
| ~ spl16_330 ),
inference(avatar_component_clause,[],[f3398]) ).
fof(f5856,plain,
( spl16_496
| ~ spl16_27
| ~ spl16_306 ),
inference(avatar_split_clause,[],[f3072,f2964,f282,f5854]) ).
fof(f5854,plain,
( spl16_496
<=> ! [X0] :
( empty(sK7(sK7(X0)))
| empty(X0)
| empty(sK7(X0))
| ~ in(X0,sK9(sK7(sK7(X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_496])]) ).
fof(f3072,plain,
( ! [X0] :
( empty(sK7(sK7(X0)))
| empty(X0)
| empty(sK7(X0))
| ~ in(X0,sK9(sK7(sK7(X0)))) )
| ~ spl16_27
| ~ spl16_306 ),
inference(resolution,[],[f2965,f283]) ).
fof(f5852,plain,
( spl16_495
| ~ spl16_27
| ~ spl16_305 ),
inference(avatar_split_clause,[],[f3051,f2960,f282,f5850]) ).
fof(f5850,plain,
( spl16_495
<=> ! [X0] :
( empty(sK7(sK6(X0)))
| empty(X0)
| empty(sK6(X0))
| ~ in(X0,sK9(sK7(sK6(X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_495])]) ).
fof(f3051,plain,
( ! [X0] :
( empty(sK7(sK6(X0)))
| empty(X0)
| empty(sK6(X0))
| ~ in(X0,sK9(sK7(sK6(X0)))) )
| ~ spl16_27
| ~ spl16_305 ),
inference(resolution,[],[f2961,f283]) ).
fof(f5848,plain,
( spl16_494
| ~ spl16_27
| ~ spl16_304 ),
inference(avatar_split_clause,[],[f3030,f2956,f282,f5846]) ).
fof(f5846,plain,
( spl16_494
<=> ! [X0] :
( empty(sK6(sK7(X0)))
| empty(X0)
| empty(sK7(X0))
| ~ in(X0,sK9(sK6(sK7(X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_494])]) ).
fof(f3030,plain,
( ! [X0] :
( empty(sK6(sK7(X0)))
| empty(X0)
| empty(sK7(X0))
| ~ in(X0,sK9(sK6(sK7(X0)))) )
| ~ spl16_27
| ~ spl16_304 ),
inference(resolution,[],[f2957,f283]) ).
fof(f5844,plain,
( spl16_493
| ~ spl16_27
| ~ spl16_303 ),
inference(avatar_split_clause,[],[f3009,f2952,f282,f5842]) ).
fof(f5842,plain,
( spl16_493
<=> ! [X0] :
( empty(sK6(sK6(X0)))
| empty(X0)
| empty(sK6(X0))
| ~ in(X0,sK9(sK6(sK6(X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_493])]) ).
fof(f3009,plain,
( ! [X0] :
( empty(sK6(sK6(X0)))
| empty(X0)
| empty(sK6(X0))
| ~ in(X0,sK9(sK6(sK6(X0)))) )
| ~ spl16_27
| ~ spl16_303 ),
inference(resolution,[],[f2953,f283]) ).
fof(f5840,plain,
( spl16_492
| ~ spl16_23
| ~ spl16_57
| ~ spl16_286 ),
inference(avatar_split_clause,[],[f2748,f2727,f469,f263,f5838]) ).
fof(f5838,plain,
( spl16_492
<=> ! [X0] :
( sK14 = sK9(powerset(powerset(X0)))
| sK14 = sK9(sK9(powerset(powerset(X0))))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_492])]) ).
fof(f2748,plain,
( ! [X0] :
( sK14 = sK9(powerset(powerset(X0)))
| sK14 = sK9(sK9(powerset(powerset(X0))))
| ~ empty(X0) )
| ~ spl16_23
| ~ spl16_57
| ~ spl16_286 ),
inference(forward_demodulation,[],[f2739,f471]) ).
fof(f2739,plain,
( ! [X0] :
( sK14 = sK9(sK9(powerset(powerset(X0))))
| ~ empty(X0)
| empty_set = sK9(powerset(powerset(X0))) )
| ~ spl16_23
| ~ spl16_286 ),
inference(resolution,[],[f2728,f264]) ).
fof(f5836,plain,
( spl16_491
| ~ spl16_99
| ~ spl16_282 ),
inference(avatar_split_clause,[],[f2710,f2692,f743,f5834]) ).
fof(f5834,plain,
( spl16_491
<=> ! [X0,X1] :
( sK9(powerset(X0)) = sK9(powerset(sK9(powerset(sK9(powerset(X1))))))
| ~ empty(X0)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_491])]) ).
fof(f2710,plain,
( ! [X0,X1] :
( sK9(powerset(X0)) = sK9(powerset(sK9(powerset(sK9(powerset(X1))))))
| ~ empty(X0)
| ~ empty(X1) )
| ~ spl16_99
| ~ spl16_282 ),
inference(resolution,[],[f2693,f744]) ).
fof(f5824,plain,
( spl16_403
| ~ spl16_490
| ~ spl16_15
| ~ spl16_478 ),
inference(avatar_split_clause,[],[f5723,f5692,f228,f5821,f4292]) ).
fof(f4292,plain,
( spl16_403
<=> empty(powerset(cartesian_product2(sK14,sK14))) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_403])]) ).
fof(f5821,plain,
( spl16_490
<=> in(powerset(cartesian_product2(sK14,sK14)),the_InternalRel(sK1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_490])]) ).
fof(f228,plain,
( spl16_15
<=> ! [X0] : subset(X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_15])]) ).
fof(f5692,plain,
( spl16_478
<=> ! [X0] :
( ~ in(powerset(X0),the_InternalRel(sK1))
| ~ subset(cartesian_product2(sK14,sK14),X0)
| empty(powerset(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_478])]) ).
fof(f5723,plain,
( ~ in(powerset(cartesian_product2(sK14,sK14)),the_InternalRel(sK1))
| empty(powerset(cartesian_product2(sK14,sK14)))
| ~ spl16_15
| ~ spl16_478 ),
inference(resolution,[],[f5693,f229]) ).
fof(f229,plain,
( ! [X0] : subset(X0,X0)
| ~ spl16_15 ),
inference(avatar_component_clause,[],[f228]) ).
fof(f5693,plain,
( ! [X0] :
( ~ subset(cartesian_product2(sK14,sK14),X0)
| ~ in(powerset(X0),the_InternalRel(sK1))
| empty(powerset(X0)) )
| ~ spl16_478 ),
inference(avatar_component_clause,[],[f5692]) ).
fof(f5819,plain,
( spl16_489
| ~ spl16_58
| ~ spl16_315 ),
inference(avatar_split_clause,[],[f3193,f3151,f476,f5817]) ).
fof(f5817,plain,
( spl16_489
<=> ! [X0] :
( ~ rel_str(X0)
| ~ empty(the_InternalRel(X0))
| sK14 = sK9(powerset(sK9(powerset(the_InternalRel(sK8(X0)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_489])]) ).
fof(f3151,plain,
( spl16_315
<=> ! [X0] :
( ~ rel_str(sK8(X0))
| ~ rel_str(X0)
| ~ empty(the_InternalRel(X0))
| sK14 = sK9(powerset(sK9(powerset(the_InternalRel(sK8(X0)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_315])]) ).
fof(f3193,plain,
( ! [X0] :
( ~ rel_str(X0)
| ~ empty(the_InternalRel(X0))
| sK14 = sK9(powerset(sK9(powerset(the_InternalRel(sK8(X0)))))) )
| ~ spl16_58
| ~ spl16_315 ),
inference(duplicate_literal_removal,[],[f3191]) ).
fof(f3191,plain,
( ! [X0] :
( ~ rel_str(X0)
| ~ empty(the_InternalRel(X0))
| sK14 = sK9(powerset(sK9(powerset(the_InternalRel(sK8(X0))))))
| ~ rel_str(X0) )
| ~ spl16_58
| ~ spl16_315 ),
inference(resolution,[],[f3152,f477]) ).
fof(f3152,plain,
( ! [X0] :
( ~ rel_str(sK8(X0))
| ~ rel_str(X0)
| ~ empty(the_InternalRel(X0))
| sK14 = sK9(powerset(sK9(powerset(the_InternalRel(sK8(X0)))))) )
| ~ spl16_315 ),
inference(avatar_component_clause,[],[f3151]) ).
fof(f5815,plain,
( spl16_488
| ~ spl16_58
| ~ spl16_314 ),
inference(avatar_split_clause,[],[f3186,f3143,f476,f5813]) ).
fof(f5813,plain,
( spl16_488
<=> ! [X0,X1] :
( ~ rel_str(X0)
| ~ empty(the_InternalRel(X0))
| sK9(powerset(X1)) = the_InternalRel(sK8(X0))
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_488])]) ).
fof(f3143,plain,
( spl16_314
<=> ! [X0,X1] :
( ~ rel_str(sK8(X0))
| ~ rel_str(X0)
| ~ empty(the_InternalRel(X0))
| sK9(powerset(X1)) = the_InternalRel(sK8(X0))
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_314])]) ).
fof(f3186,plain,
( ! [X0,X1] :
( ~ rel_str(X0)
| ~ empty(the_InternalRel(X0))
| sK9(powerset(X1)) = the_InternalRel(sK8(X0))
| ~ empty(X1) )
| ~ spl16_58
| ~ spl16_314 ),
inference(duplicate_literal_removal,[],[f3184]) ).
fof(f3184,plain,
( ! [X0,X1] :
( ~ rel_str(X0)
| ~ empty(the_InternalRel(X0))
| sK9(powerset(X1)) = the_InternalRel(sK8(X0))
| ~ empty(X1)
| ~ rel_str(X0) )
| ~ spl16_58
| ~ spl16_314 ),
inference(resolution,[],[f3144,f477]) ).
fof(f3144,plain,
( ! [X0,X1] :
( ~ rel_str(sK8(X0))
| ~ rel_str(X0)
| ~ empty(the_InternalRel(X0))
| sK9(powerset(X1)) = the_InternalRel(sK8(X0))
| ~ empty(X1) )
| ~ spl16_314 ),
inference(avatar_component_clause,[],[f3143]) ).
fof(f5811,plain,
( spl16_487
| ~ spl16_58
| ~ spl16_313 ),
inference(avatar_split_clause,[],[f3183,f3139,f476,f5809]) ).
fof(f5809,plain,
( spl16_487
<=> ! [X0] :
( ~ rel_str(X0)
| ~ empty(the_carrier(X0))
| sK14 = sK9(powerset(sK9(powerset(the_carrier(sK8(X0)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_487])]) ).
fof(f3139,plain,
( spl16_313
<=> ! [X0] :
( ~ rel_str(sK8(X0))
| ~ rel_str(X0)
| ~ empty(the_carrier(X0))
| sK14 = sK9(powerset(sK9(powerset(the_carrier(sK8(X0)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_313])]) ).
fof(f3183,plain,
( ! [X0] :
( ~ rel_str(X0)
| ~ empty(the_carrier(X0))
| sK14 = sK9(powerset(sK9(powerset(the_carrier(sK8(X0)))))) )
| ~ spl16_58
| ~ spl16_313 ),
inference(duplicate_literal_removal,[],[f3181]) ).
fof(f3181,plain,
( ! [X0] :
( ~ rel_str(X0)
| ~ empty(the_carrier(X0))
| sK14 = sK9(powerset(sK9(powerset(the_carrier(sK8(X0))))))
| ~ rel_str(X0) )
| ~ spl16_58
| ~ spl16_313 ),
inference(resolution,[],[f3140,f477]) ).
fof(f3140,plain,
( ! [X0] :
( ~ rel_str(sK8(X0))
| ~ rel_str(X0)
| ~ empty(the_carrier(X0))
| sK14 = sK9(powerset(sK9(powerset(the_carrier(sK8(X0)))))) )
| ~ spl16_313 ),
inference(avatar_component_clause,[],[f3139]) ).
fof(f5807,plain,
( spl16_486
| ~ spl16_58
| ~ spl16_312 ),
inference(avatar_split_clause,[],[f3180,f3135,f476,f5805]) ).
fof(f5805,plain,
( spl16_486
<=> ! [X0,X1] :
( ~ rel_str(X0)
| ~ empty(the_carrier(X0))
| sK9(powerset(X1)) = the_carrier(sK8(X0))
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_486])]) ).
fof(f3135,plain,
( spl16_312
<=> ! [X0,X1] :
( ~ rel_str(sK8(X0))
| ~ rel_str(X0)
| ~ empty(the_carrier(X0))
| sK9(powerset(X1)) = the_carrier(sK8(X0))
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_312])]) ).
fof(f3180,plain,
( ! [X0,X1] :
( ~ rel_str(X0)
| ~ empty(the_carrier(X0))
| sK9(powerset(X1)) = the_carrier(sK8(X0))
| ~ empty(X1) )
| ~ spl16_58
| ~ spl16_312 ),
inference(duplicate_literal_removal,[],[f3178]) ).
fof(f3178,plain,
( ! [X0,X1] :
( ~ rel_str(X0)
| ~ empty(the_carrier(X0))
| sK9(powerset(X1)) = the_carrier(sK8(X0))
| ~ empty(X1)
| ~ rel_str(X0) )
| ~ spl16_58
| ~ spl16_312 ),
inference(resolution,[],[f3136,f477]) ).
fof(f3136,plain,
( ! [X0,X1] :
( ~ rel_str(sK8(X0))
| ~ rel_str(X0)
| ~ empty(the_carrier(X0))
| sK9(powerset(X1)) = the_carrier(sK8(X0))
| ~ empty(X1) )
| ~ spl16_312 ),
inference(avatar_component_clause,[],[f3135]) ).
fof(f5803,plain,
( spl16_485
| ~ spl16_16
| ~ spl16_286 ),
inference(avatar_split_clause,[],[f2738,f2727,f232,f5801]) ).
fof(f5801,plain,
( spl16_485
<=> ! [X0] :
( sK14 = sK9(sK9(powerset(powerset(X0))))
| ~ empty(X0)
| finite(sK9(powerset(powerset(X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_485])]) ).
fof(f2738,plain,
( ! [X0] :
( sK14 = sK9(sK9(powerset(powerset(X0))))
| ~ empty(X0)
| finite(sK9(powerset(powerset(X0)))) )
| ~ spl16_16
| ~ spl16_286 ),
inference(resolution,[],[f2728,f233]) ).
fof(f5728,plain,
( spl16_484
| ~ spl16_21
| ~ spl16_319 ),
inference(avatar_split_clause,[],[f3248,f3167,f255,f5726]) ).
fof(f5726,plain,
( spl16_484
<=> ! [X0] :
( empty(powerset(X0))
| ~ empty(X0)
| sK14 = sK9(powerset(sK9(sK7(powerset(X0))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_484])]) ).
fof(f3167,plain,
( spl16_319
<=> ! [X0] :
( ~ empty(X0)
| empty(powerset(X0))
| empty(sK7(powerset(X0)))
| sK14 = sK9(powerset(sK9(sK7(powerset(X0))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_319])]) ).
fof(f3248,plain,
( ! [X0] :
( empty(powerset(X0))
| ~ empty(X0)
| sK14 = sK9(powerset(sK9(sK7(powerset(X0))))) )
| ~ spl16_21
| ~ spl16_319 ),
inference(duplicate_literal_removal,[],[f3234]) ).
fof(f3234,plain,
( ! [X0] :
( empty(powerset(X0))
| ~ empty(X0)
| sK14 = sK9(powerset(sK9(sK7(powerset(X0)))))
| empty(powerset(X0)) )
| ~ spl16_21
| ~ spl16_319 ),
inference(resolution,[],[f3168,f256]) ).
fof(f3168,plain,
( ! [X0] :
( empty(sK7(powerset(X0)))
| empty(powerset(X0))
| ~ empty(X0)
| sK14 = sK9(powerset(sK9(sK7(powerset(X0))))) )
| ~ spl16_319 ),
inference(avatar_component_clause,[],[f3167]) ).
fof(f5722,plain,
( spl16_483
| ~ spl16_19
| ~ spl16_317 ),
inference(avatar_split_clause,[],[f3220,f3159,f247,f5720]) ).
fof(f5720,plain,
( spl16_483
<=> ! [X0] :
( empty(powerset(X0))
| ~ empty(X0)
| sK14 = sK9(powerset(sK9(sK6(powerset(X0))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_483])]) ).
fof(f3159,plain,
( spl16_317
<=> ! [X0] :
( ~ empty(X0)
| empty(powerset(X0))
| empty(sK6(powerset(X0)))
| sK14 = sK9(powerset(sK9(sK6(powerset(X0))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_317])]) ).
fof(f3220,plain,
( ! [X0] :
( empty(powerset(X0))
| ~ empty(X0)
| sK14 = sK9(powerset(sK9(sK6(powerset(X0))))) )
| ~ spl16_19
| ~ spl16_317 ),
inference(duplicate_literal_removal,[],[f3207]) ).
fof(f3207,plain,
( ! [X0] :
( empty(powerset(X0))
| ~ empty(X0)
| sK14 = sK9(powerset(sK9(sK6(powerset(X0)))))
| empty(powerset(X0)) )
| ~ spl16_19
| ~ spl16_317 ),
inference(resolution,[],[f3160,f248]) ).
fof(f3160,plain,
( ! [X0] :
( empty(sK6(powerset(X0)))
| empty(powerset(X0))
| ~ empty(X0)
| sK14 = sK9(powerset(sK9(sK6(powerset(X0))))) )
| ~ spl16_317 ),
inference(avatar_component_clause,[],[f3159]) ).
fof(f5718,plain,
( spl16_482
| ~ spl16_99
| ~ spl16_279 ),
inference(avatar_split_clause,[],[f2671,f2665,f743,f5716]) ).
fof(f5716,plain,
( spl16_482
<=> ! [X0] :
( sK14 = sK9(powerset(sK9(powerset(sK9(powerset(sK9(powerset(X0))))))))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_482])]) ).
fof(f2671,plain,
( ! [X0] :
( sK14 = sK9(powerset(sK9(powerset(sK9(powerset(sK9(powerset(X0))))))))
| ~ empty(X0) )
| ~ spl16_99
| ~ spl16_279 ),
inference(resolution,[],[f2666,f744]) ).
fof(f5706,plain,
( spl16_481
| ~ spl16_58
| ~ spl16_300 ),
inference(avatar_split_clause,[],[f2983,f2940,f476,f5704]) ).
fof(f5704,plain,
( spl16_481
<=> ! [X0] :
( ~ rel_str(X0)
| ~ empty(the_InternalRel(X0))
| sK14 = sK9(powerset(the_InternalRel(sK8(X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_481])]) ).
fof(f2940,plain,
( spl16_300
<=> ! [X0] :
( ~ rel_str(sK8(X0))
| ~ rel_str(X0)
| ~ empty(the_InternalRel(X0))
| sK14 = sK9(powerset(the_InternalRel(sK8(X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_300])]) ).
fof(f2983,plain,
( ! [X0] :
( ~ rel_str(X0)
| ~ empty(the_InternalRel(X0))
| sK14 = sK9(powerset(the_InternalRel(sK8(X0)))) )
| ~ spl16_58
| ~ spl16_300 ),
inference(duplicate_literal_removal,[],[f2981]) ).
fof(f2981,plain,
( ! [X0] :
( ~ rel_str(X0)
| ~ empty(the_InternalRel(X0))
| sK14 = sK9(powerset(the_InternalRel(sK8(X0))))
| ~ rel_str(X0) )
| ~ spl16_58
| ~ spl16_300 ),
inference(resolution,[],[f2941,f477]) ).
fof(f2941,plain,
( ! [X0] :
( ~ rel_str(sK8(X0))
| ~ rel_str(X0)
| ~ empty(the_InternalRel(X0))
| sK14 = sK9(powerset(the_InternalRel(sK8(X0)))) )
| ~ spl16_300 ),
inference(avatar_component_clause,[],[f2940]) ).
fof(f5702,plain,
( spl16_480
| ~ spl16_58
| ~ spl16_299 ),
inference(avatar_split_clause,[],[f2980,f2936,f476,f5700]) ).
fof(f5700,plain,
( spl16_480
<=> ! [X0,X1] :
( ~ rel_str(X0)
| ~ empty(the_InternalRel(X0))
| the_InternalRel(sK8(X0)) = X1
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_480])]) ).
fof(f2936,plain,
( spl16_299
<=> ! [X0,X1] :
( ~ rel_str(sK8(X0))
| ~ rel_str(X0)
| ~ empty(the_InternalRel(X0))
| the_InternalRel(sK8(X0)) = X1
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_299])]) ).
fof(f2980,plain,
( ! [X0,X1] :
( ~ rel_str(X0)
| ~ empty(the_InternalRel(X0))
| the_InternalRel(sK8(X0)) = X1
| ~ empty(X1) )
| ~ spl16_58
| ~ spl16_299 ),
inference(duplicate_literal_removal,[],[f2978]) ).
fof(f2978,plain,
( ! [X0,X1] :
( ~ rel_str(X0)
| ~ empty(the_InternalRel(X0))
| the_InternalRel(sK8(X0)) = X1
| ~ empty(X1)
| ~ rel_str(X0) )
| ~ spl16_58
| ~ spl16_299 ),
inference(resolution,[],[f2937,f477]) ).
fof(f2937,plain,
( ! [X0,X1] :
( ~ rel_str(sK8(X0))
| ~ rel_str(X0)
| ~ empty(the_InternalRel(X0))
| the_InternalRel(sK8(X0)) = X1
| ~ empty(X1) )
| ~ spl16_299 ),
inference(avatar_component_clause,[],[f2936]) ).
fof(f5698,plain,
( spl16_479
| ~ spl16_58
| ~ spl16_298 ),
inference(avatar_split_clause,[],[f2977,f2932,f476,f5696]) ).
fof(f2932,plain,
( spl16_298
<=> ! [X0] :
( ~ rel_str(sK8(X0))
| ~ rel_str(X0)
| ~ empty(the_carrier(X0))
| sK14 = sK9(powerset(the_carrier(sK8(X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_298])]) ).
fof(f2977,plain,
( ! [X0] :
( ~ rel_str(X0)
| ~ empty(the_carrier(X0))
| sK14 = sK9(powerset(the_carrier(sK8(X0)))) )
| ~ spl16_58
| ~ spl16_298 ),
inference(duplicate_literal_removal,[],[f2975]) ).
fof(f2975,plain,
( ! [X0] :
( ~ rel_str(X0)
| ~ empty(the_carrier(X0))
| sK14 = sK9(powerset(the_carrier(sK8(X0))))
| ~ rel_str(X0) )
| ~ spl16_58
| ~ spl16_298 ),
inference(resolution,[],[f2933,f477]) ).
fof(f2933,plain,
( ! [X0] :
( ~ rel_str(sK8(X0))
| ~ rel_str(X0)
| ~ empty(the_carrier(X0))
| sK14 = sK9(powerset(the_carrier(sK8(X0)))) )
| ~ spl16_298 ),
inference(avatar_component_clause,[],[f2932]) ).
fof(f5694,plain,
( spl16_478
| ~ spl16_109
| ~ spl16_416 ),
inference(avatar_split_clause,[],[f4874,f4661,f795,f5692]) ).
fof(f795,plain,
( spl16_109
<=> ! [X0,X1] :
( empty(powerset(X0))
| ~ subset(X1,X0)
| ~ in(powerset(X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_109])]) ).
fof(f4661,plain,
( spl16_416
<=> ! [X0] :
( ~ in(X0,the_InternalRel(sK1))
| in(X0,cartesian_product2(sK14,sK14)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_416])]) ).
fof(f4874,plain,
( ! [X0] :
( ~ in(powerset(X0),the_InternalRel(sK1))
| ~ subset(cartesian_product2(sK14,sK14),X0)
| empty(powerset(X0)) )
| ~ spl16_109
| ~ spl16_416 ),
inference(resolution,[],[f4662,f796]) ).
fof(f796,plain,
( ! [X0,X1] :
( ~ in(powerset(X0),X1)
| ~ subset(X1,X0)
| empty(powerset(X0)) )
| ~ spl16_109 ),
inference(avatar_component_clause,[],[f795]) ).
fof(f4662,plain,
( ! [X0] :
( in(X0,cartesian_product2(sK14,sK14))
| ~ in(X0,the_InternalRel(sK1)) )
| ~ spl16_416 ),
inference(avatar_component_clause,[],[f4661]) ).
fof(f5690,plain,
( spl16_477
| ~ spl16_58
| ~ spl16_296 ),
inference(avatar_split_clause,[],[f2969,f2923,f476,f5688]) ).
fof(f2923,plain,
( spl16_296
<=> ! [X0,X1] :
( ~ rel_str(sK8(X0))
| ~ rel_str(X0)
| ~ empty(the_carrier(X0))
| the_carrier(sK8(X0)) = X1
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_296])]) ).
fof(f2969,plain,
( ! [X0,X1] :
( ~ rel_str(X0)
| ~ empty(the_carrier(X0))
| the_carrier(sK8(X0)) = X1
| ~ empty(X1) )
| ~ spl16_58
| ~ spl16_296 ),
inference(duplicate_literal_removal,[],[f2967]) ).
fof(f2967,plain,
( ! [X0,X1] :
( ~ rel_str(X0)
| ~ empty(the_carrier(X0))
| the_carrier(sK8(X0)) = X1
| ~ empty(X1)
| ~ rel_str(X0) )
| ~ spl16_58
| ~ spl16_296 ),
inference(resolution,[],[f2924,f477]) ).
fof(f2924,plain,
( ! [X0,X1] :
( ~ rel_str(sK8(X0))
| ~ rel_str(X0)
| ~ empty(the_carrier(X0))
| the_carrier(sK8(X0)) = X1
| ~ empty(X1) )
| ~ spl16_296 ),
inference(avatar_component_clause,[],[f2923]) ).
fof(f5686,plain,
( spl16_476
| ~ spl16_147
| ~ spl16_280 ),
inference(avatar_split_clause,[],[f2690,f2682,f1200,f5684]) ).
fof(f5684,plain,
( spl16_476
<=> ! [X0] :
( ~ rel_str(X0)
| ~ empty(the_carrier(X0))
| ~ rel_str(sK8(X0))
| finite(the_InternalRel(sK8(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_476])]) ).
fof(f1200,plain,
( spl16_147
<=> ! [X0] :
( finite(the_InternalRel(X0))
| ~ rel_str(X0)
| ~ finite(the_carrier(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_147])]) ).
fof(f2682,plain,
( spl16_280
<=> ! [X0] :
( ~ rel_str(sK8(X0))
| ~ rel_str(X0)
| ~ empty(the_carrier(X0))
| finite(the_carrier(sK8(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_280])]) ).
fof(f2690,plain,
( ! [X0] :
( ~ rel_str(X0)
| ~ empty(the_carrier(X0))
| ~ rel_str(sK8(X0))
| finite(the_InternalRel(sK8(X0))) )
| ~ spl16_147
| ~ spl16_280 ),
inference(duplicate_literal_removal,[],[f2689]) ).
fof(f2689,plain,
( ! [X0] :
( ~ rel_str(X0)
| ~ empty(the_carrier(X0))
| ~ rel_str(sK8(X0))
| ~ rel_str(sK8(X0))
| finite(the_InternalRel(sK8(X0))) )
| ~ spl16_147
| ~ spl16_280 ),
inference(resolution,[],[f2683,f1201]) ).
fof(f1201,plain,
( ! [X0] :
( ~ finite(the_carrier(X0))
| ~ rel_str(X0)
| finite(the_InternalRel(X0)) )
| ~ spl16_147 ),
inference(avatar_component_clause,[],[f1200]) ).
fof(f2683,plain,
( ! [X0] :
( finite(the_carrier(sK8(X0)))
| ~ rel_str(X0)
| ~ empty(the_carrier(X0))
| ~ rel_str(sK8(X0)) )
| ~ spl16_280 ),
inference(avatar_component_clause,[],[f2682]) ).
fof(f5638,plain,
( spl16_475
| ~ spl16_21
| ~ spl16_302 ),
inference(avatar_split_clause,[],[f3007,f2948,f255,f5636]) ).
fof(f5636,plain,
( spl16_475
<=> ! [X0] :
( ~ empty(X0)
| empty(powerset(X0))
| sK14 = sK9(sK7(powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_475])]) ).
fof(f2948,plain,
( spl16_302
<=> ! [X0] :
( sK14 = sK9(sK7(powerset(X0)))
| ~ empty(X0)
| empty(powerset(X0))
| empty(sK7(powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_302])]) ).
fof(f3007,plain,
( ! [X0] :
( ~ empty(X0)
| empty(powerset(X0))
| sK14 = sK9(sK7(powerset(X0))) )
| ~ spl16_21
| ~ spl16_302 ),
inference(duplicate_literal_removal,[],[f2996]) ).
fof(f2996,plain,
( ! [X0] :
( ~ empty(X0)
| empty(powerset(X0))
| sK14 = sK9(sK7(powerset(X0)))
| empty(powerset(X0)) )
| ~ spl16_21
| ~ spl16_302 ),
inference(resolution,[],[f2949,f256]) ).
fof(f2949,plain,
( ! [X0] :
( empty(sK7(powerset(X0)))
| ~ empty(X0)
| empty(powerset(X0))
| sK14 = sK9(sK7(powerset(X0))) )
| ~ spl16_302 ),
inference(avatar_component_clause,[],[f2948]) ).
fof(f5634,plain,
( spl16_474
| ~ spl16_19
| ~ spl16_301 ),
inference(avatar_split_clause,[],[f2995,f2944,f247,f5632]) ).
fof(f5632,plain,
( spl16_474
<=> ! [X0] :
( ~ empty(X0)
| empty(powerset(X0))
| sK14 = sK9(sK6(powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_474])]) ).
fof(f2944,plain,
( spl16_301
<=> ! [X0] :
( sK14 = sK9(sK6(powerset(X0)))
| ~ empty(X0)
| empty(powerset(X0))
| empty(sK6(powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_301])]) ).
fof(f2995,plain,
( ! [X0] :
( ~ empty(X0)
| empty(powerset(X0))
| sK14 = sK9(sK6(powerset(X0))) )
| ~ spl16_19
| ~ spl16_301 ),
inference(duplicate_literal_removal,[],[f2984]) ).
fof(f2984,plain,
( ! [X0] :
( ~ empty(X0)
| empty(powerset(X0))
| sK14 = sK9(sK6(powerset(X0)))
| empty(powerset(X0)) )
| ~ spl16_19
| ~ spl16_301 ),
inference(resolution,[],[f2945,f248]) ).
fof(f2945,plain,
( ! [X0] :
( empty(sK6(powerset(X0)))
| ~ empty(X0)
| empty(powerset(X0))
| sK14 = sK9(sK6(powerset(X0))) )
| ~ spl16_301 ),
inference(avatar_component_clause,[],[f2944]) ).
fof(f5626,plain,
( spl16_473
| ~ spl16_58
| ~ spl16_284 ),
inference(avatar_split_clause,[],[f2725,f2700,f476,f5624]) ).
fof(f2700,plain,
( spl16_284
<=> ! [X0] :
( sK14 = the_InternalRel(sK8(X0))
| ~ rel_str(sK8(X0))
| ~ rel_str(X0)
| ~ empty(the_InternalRel(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_284])]) ).
fof(f2725,plain,
( ! [X0] :
( sK14 = the_InternalRel(sK8(X0))
| ~ rel_str(X0)
| ~ empty(the_InternalRel(X0)) )
| ~ spl16_58
| ~ spl16_284 ),
inference(duplicate_literal_removal,[],[f2723]) ).
fof(f2723,plain,
( ! [X0] :
( sK14 = the_InternalRel(sK8(X0))
| ~ rel_str(X0)
| ~ empty(the_InternalRel(X0))
| ~ rel_str(X0) )
| ~ spl16_58
| ~ spl16_284 ),
inference(resolution,[],[f2701,f477]) ).
fof(f2701,plain,
( ! [X0] :
( ~ rel_str(sK8(X0))
| sK14 = the_InternalRel(sK8(X0))
| ~ rel_str(X0)
| ~ empty(the_InternalRel(X0)) )
| ~ spl16_284 ),
inference(avatar_component_clause,[],[f2700]) ).
fof(f5622,plain,
( spl16_472
| ~ spl16_58
| ~ spl16_283 ),
inference(avatar_split_clause,[],[f2722,f2696,f476,f5620]) ).
fof(f2696,plain,
( spl16_283
<=> ! [X0] :
( sK14 = the_carrier(sK8(X0))
| ~ rel_str(sK8(X0))
| ~ rel_str(X0)
| ~ empty(the_carrier(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_283])]) ).
fof(f2722,plain,
( ! [X0] :
( sK14 = the_carrier(sK8(X0))
| ~ rel_str(X0)
| ~ empty(the_carrier(X0)) )
| ~ spl16_58
| ~ spl16_283 ),
inference(duplicate_literal_removal,[],[f2720]) ).
fof(f2720,plain,
( ! [X0] :
( sK14 = the_carrier(sK8(X0))
| ~ rel_str(X0)
| ~ empty(the_carrier(X0))
| ~ rel_str(X0) )
| ~ spl16_58
| ~ spl16_283 ),
inference(resolution,[],[f2697,f477]) ).
fof(f2697,plain,
( ! [X0] :
( ~ rel_str(sK8(X0))
| sK14 = the_carrier(sK8(X0))
| ~ rel_str(X0)
| ~ empty(the_carrier(X0)) )
| ~ spl16_283 ),
inference(avatar_component_clause,[],[f2696]) ).
fof(f5618,plain,
( spl16_471
| ~ spl16_239
| ~ spl16_266 ),
inference(avatar_split_clause,[],[f2545,f2539,f2143,f5616]) ).
fof(f5616,plain,
( spl16_471
<=> ! [X0] :
( ~ in(cartesian_product2(the_carrier(X0),the_carrier(X0)),the_InternalRel(sK0))
| empty(cartesian_product2(the_carrier(X0),the_carrier(X0)))
| ~ in(cartesian_product2(sK14,sK14),the_InternalRel(X0))
| ~ rel_str(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_471])]) ).
fof(f2143,plain,
( spl16_239
<=> ! [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,[spl16_239])]) ).
fof(f2539,plain,
( spl16_266
<=> ! [X0] :
( ~ in(X0,the_InternalRel(sK0))
| in(X0,cartesian_product2(sK14,sK14)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_266])]) ).
fof(f2545,plain,
( ! [X0] :
( ~ in(cartesian_product2(the_carrier(X0),the_carrier(X0)),the_InternalRel(sK0))
| empty(cartesian_product2(the_carrier(X0),the_carrier(X0)))
| ~ in(cartesian_product2(sK14,sK14),the_InternalRel(X0))
| ~ rel_str(X0) )
| ~ spl16_239
| ~ spl16_266 ),
inference(resolution,[],[f2540,f2144]) ).
fof(f2144,plain,
( ! [X0,X1] :
( ~ in(cartesian_product2(the_carrier(X0),the_carrier(X0)),X1)
| empty(cartesian_product2(the_carrier(X0),the_carrier(X0)))
| ~ in(X1,the_InternalRel(X0))
| ~ rel_str(X0) )
| ~ spl16_239 ),
inference(avatar_component_clause,[],[f2143]) ).
fof(f2540,plain,
( ! [X0] :
( in(X0,cartesian_product2(sK14,sK14))
| ~ in(X0,the_InternalRel(sK0)) )
| ~ spl16_266 ),
inference(avatar_component_clause,[],[f2539]) ).
fof(f5613,plain,
( ~ spl16_1
| spl16_96
| spl16_470
| ~ spl16_42
| ~ spl16_2
| ~ spl16_395 ),
inference(avatar_split_clause,[],[f4300,f4187,f163,f355,f5611,f725,f158]) ).
fof(f5611,plain,
( spl16_470
<=> ! [X0] :
( empty(the_InternalRel(X0))
| ~ rel_str(X0)
| element(sK9(the_InternalRel(X0)),the_InternalRel(sK0))
| ~ subrelstr(X0,sK1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_470])]) ).
fof(f4300,plain,
( ! [X0] :
( ~ rel_str(sK1)
| empty(the_InternalRel(X0))
| empty(the_InternalRel(sK1))
| ~ subrelstr(X0,sK1)
| element(sK9(the_InternalRel(X0)),the_InternalRel(sK0))
| ~ rel_str(X0)
| ~ rel_str(sK0) )
| ~ spl16_2
| ~ spl16_395 ),
inference(resolution,[],[f4188,f165]) ).
fof(f5608,plain,
( ~ spl16_1
| spl16_53
| spl16_469
| ~ spl16_42
| ~ spl16_2
| ~ spl16_394 ),
inference(avatar_split_clause,[],[f4284,f4183,f163,f355,f5606,f428,f158]) ).
fof(f5606,plain,
( spl16_469
<=> ! [X0] :
( empty(the_carrier(X0))
| ~ rel_str(X0)
| element(sK9(the_carrier(X0)),the_carrier(sK0))
| ~ subrelstr(X0,sK1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_469])]) ).
fof(f4284,plain,
( ! [X0] :
( ~ rel_str(sK1)
| empty(the_carrier(X0))
| empty(the_carrier(sK1))
| ~ subrelstr(X0,sK1)
| element(sK9(the_carrier(X0)),the_carrier(sK0))
| ~ rel_str(X0)
| ~ rel_str(sK0) )
| ~ spl16_2
| ~ spl16_394 ),
inference(resolution,[],[f4184,f165]) ).
fof(f5598,plain,
( spl16_468
| ~ spl16_51
| ~ spl16_267 ),
inference(avatar_split_clause,[],[f2574,f2549,f420,f5596]) ).
fof(f420,plain,
( spl16_51
<=> ! [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) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_51])]) ).
fof(f2549,plain,
( spl16_267
<=> ! [X0] :
( ~ subrelstr(sK1,X0)
| ~ rel_str(X0)
| empty(the_InternalRel(X0))
| in(ordered_pair(sK4,sK5),the_InternalRel(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_267])]) ).
fof(f2574,plain,
( ! [X0] :
( ~ rel_str(X0)
| empty(the_InternalRel(X0))
| ~ subrelstr(sK1,X0)
| related(X0,sK4,sK5)
| ~ element(sK5,the_carrier(X0))
| ~ element(sK4,the_carrier(X0)) )
| ~ spl16_51
| ~ spl16_267 ),
inference(duplicate_literal_removal,[],[f2566]) ).
fof(f2566,plain,
( ! [X0] :
( ~ rel_str(X0)
| empty(the_InternalRel(X0))
| ~ subrelstr(sK1,X0)
| related(X0,sK4,sK5)
| ~ element(sK5,the_carrier(X0))
| ~ element(sK4,the_carrier(X0))
| ~ rel_str(X0) )
| ~ spl16_51
| ~ spl16_267 ),
inference(resolution,[],[f2550,f421]) ).
fof(f421,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) )
| ~ spl16_51 ),
inference(avatar_component_clause,[],[f420]) ).
fof(f2550,plain,
( ! [X0] :
( in(ordered_pair(sK4,sK5),the_InternalRel(X0))
| ~ rel_str(X0)
| empty(the_InternalRel(X0))
| ~ subrelstr(sK1,X0) )
| ~ spl16_267 ),
inference(avatar_component_clause,[],[f2549]) ).
fof(f5590,plain,
( spl16_467
| ~ spl16_120
| ~ spl16_267 ),
inference(avatar_split_clause,[],[f2573,f2549,f884,f5588]) ).
fof(f2573,plain,
( ! [X0,X1] :
( ~ rel_str(X0)
| empty(the_InternalRel(X0))
| ~ subrelstr(sK1,X0)
| element(ordered_pair(sK4,sK5),the_InternalRel(X1))
| ~ subrelstr(X0,X1)
| ~ rel_str(X1) )
| ~ spl16_120
| ~ spl16_267 ),
inference(duplicate_literal_removal,[],[f2567]) ).
fof(f2567,plain,
( ! [X0,X1] :
( ~ rel_str(X0)
| empty(the_InternalRel(X0))
| ~ subrelstr(sK1,X0)
| element(ordered_pair(sK4,sK5),the_InternalRel(X1))
| ~ subrelstr(X0,X1)
| ~ rel_str(X0)
| ~ rel_str(X1) )
| ~ spl16_120
| ~ spl16_267 ),
inference(resolution,[],[f2550,f885]) ).
fof(f5586,plain,
( spl16_466
| ~ spl16_121
| ~ spl16_266 ),
inference(avatar_split_clause,[],[f2547,f2539,f888,f5584]) ).
fof(f5584,plain,
( spl16_466
<=> ! [X0,X1] :
( ~ in(powerset(cartesian_product2(X0,X1)),the_InternalRel(sK0))
| ~ relation_of2_as_subset(cartesian_product2(sK14,sK14),X0,X1)
| empty(powerset(cartesian_product2(X0,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_466])]) ).
fof(f888,plain,
( spl16_121
<=> ! [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,[spl16_121])]) ).
fof(f2547,plain,
( ! [X0,X1] :
( ~ in(powerset(cartesian_product2(X0,X1)),the_InternalRel(sK0))
| ~ relation_of2_as_subset(cartesian_product2(sK14,sK14),X0,X1)
| empty(powerset(cartesian_product2(X0,X1))) )
| ~ spl16_121
| ~ spl16_266 ),
inference(resolution,[],[f2540,f889]) ).
fof(f889,plain,
( ! [X2,X0,X1] :
( ~ in(powerset(cartesian_product2(X0,X1)),X2)
| ~ relation_of2_as_subset(X2,X0,X1)
| empty(powerset(cartesian_product2(X0,X1))) )
| ~ spl16_121 ),
inference(avatar_component_clause,[],[f888]) ).
fof(f5582,plain,
( spl16_465
| ~ spl16_27
| ~ spl16_269 ),
inference(avatar_split_clause,[],[f2596,f2580,f282,f5580]) ).
fof(f5580,plain,
( spl16_465
<=> ! [X0,X1] :
( ~ in(X0,sK14)
| ~ rel_str(X1)
| empty(the_carrier(X1))
| ~ subrelstr(sK1,X1)
| ~ in(the_carrier(X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_465])]) ).
fof(f2580,plain,
( spl16_269
<=> ! [X0,X1] :
( ~ subrelstr(sK1,X0)
| ~ in(X1,sK14)
| ~ rel_str(X0)
| empty(the_carrier(X0))
| in(X1,the_carrier(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_269])]) ).
fof(f2596,plain,
( ! [X0,X1] :
( ~ in(X0,sK14)
| ~ rel_str(X1)
| empty(the_carrier(X1))
| ~ subrelstr(sK1,X1)
| ~ in(the_carrier(X1),X0) )
| ~ spl16_27
| ~ spl16_269 ),
inference(resolution,[],[f2581,f283]) ).
fof(f2581,plain,
( ! [X0,X1] :
( in(X1,the_carrier(X0))
| ~ in(X1,sK14)
| ~ rel_str(X0)
| empty(the_carrier(X0))
| ~ subrelstr(sK1,X0) )
| ~ spl16_269 ),
inference(avatar_component_clause,[],[f2580]) ).
fof(f5578,plain,
( spl16_464
| ~ spl16_27
| ~ spl16_268 ),
inference(avatar_split_clause,[],[f2586,f2576,f282,f5576]) ).
fof(f5576,plain,
( spl16_464
<=> ! [X0,X1] :
( ~ in(X0,sK14)
| ~ rel_str(X1)
| empty(the_carrier(X1))
| ~ subrelstr(sK0,X1)
| ~ in(the_carrier(X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_464])]) ).
fof(f2576,plain,
( spl16_268
<=> ! [X0,X1] :
( ~ subrelstr(sK0,X0)
| ~ in(X1,sK14)
| ~ rel_str(X0)
| empty(the_carrier(X0))
| in(X1,the_carrier(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_268])]) ).
fof(f2586,plain,
( ! [X0,X1] :
( ~ in(X0,sK14)
| ~ rel_str(X1)
| empty(the_carrier(X1))
| ~ subrelstr(sK0,X1)
| ~ in(the_carrier(X1),X0) )
| ~ spl16_27
| ~ spl16_268 ),
inference(resolution,[],[f2577,f283]) ).
fof(f2577,plain,
( ! [X0,X1] :
( in(X1,the_carrier(X0))
| ~ in(X1,sK14)
| ~ rel_str(X0)
| empty(the_carrier(X0))
| ~ subrelstr(sK0,X0) )
| ~ spl16_268 ),
inference(avatar_component_clause,[],[f2576]) ).
fof(f5574,plain,
( spl16_463
| ~ spl16_27
| ~ spl16_267 ),
inference(avatar_split_clause,[],[f2570,f2549,f282,f5572]) ).
fof(f5572,plain,
( spl16_463
<=> ! [X0] :
( ~ rel_str(X0)
| empty(the_InternalRel(X0))
| ~ subrelstr(sK1,X0)
| ~ in(the_InternalRel(X0),ordered_pair(sK4,sK5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_463])]) ).
fof(f2570,plain,
( ! [X0] :
( ~ rel_str(X0)
| empty(the_InternalRel(X0))
| ~ subrelstr(sK1,X0)
| ~ in(the_InternalRel(X0),ordered_pair(sK4,sK5)) )
| ~ spl16_27
| ~ spl16_267 ),
inference(resolution,[],[f2550,f283]) ).
fof(f5495,plain,
( spl16_462
| ~ spl16_46
| ~ spl16_258 ),
inference(avatar_split_clause,[],[f2307,f2304,f387,f5493]) ).
fof(f387,plain,
( spl16_46
<=> ! [X2,X0,X1] :
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_46])]) ).
fof(f2304,plain,
( spl16_258
<=> ! [X0] :
( element(sK9(sK9(powerset(sK9(sK9(powerset(powerset(X0))))))),X0)
| empty(sK9(powerset(powerset(X0))))
| empty(sK9(sK9(powerset(powerset(X0)))))
| empty(sK9(powerset(sK9(sK9(powerset(powerset(X0))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_258])]) ).
fof(f2307,plain,
( ! [X0,X1] :
( empty(sK9(powerset(powerset(powerset(X0)))))
| empty(sK9(sK9(powerset(powerset(powerset(X0))))))
| empty(sK9(powerset(sK9(sK9(powerset(powerset(powerset(X0))))))))
| element(X1,X0)
| ~ in(X1,sK9(sK9(powerset(sK9(sK9(powerset(powerset(powerset(X0))))))))) )
| ~ spl16_46
| ~ spl16_258 ),
inference(resolution,[],[f2305,f388]) ).
fof(f388,plain,
( ! [X2,X0,X1] :
( ~ element(X1,powerset(X2))
| element(X0,X2)
| ~ in(X0,X1) )
| ~ spl16_46 ),
inference(avatar_component_clause,[],[f387]) ).
fof(f2305,plain,
( ! [X0] :
( element(sK9(sK9(powerset(sK9(sK9(powerset(powerset(X0))))))),X0)
| empty(sK9(powerset(powerset(X0))))
| empty(sK9(sK9(powerset(powerset(X0)))))
| empty(sK9(powerset(sK9(sK9(powerset(powerset(X0))))))) )
| ~ spl16_258 ),
inference(avatar_component_clause,[],[f2304]) ).
fof(f5491,plain,
( spl16_403
| ~ spl16_461
| ~ spl16_15
| ~ spl16_452 ),
inference(avatar_split_clause,[],[f5390,f5225,f228,f5488,f4292]) ).
fof(f5488,plain,
( spl16_461
<=> in(powerset(cartesian_product2(sK14,sK14)),the_InternalRel(sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_461])]) ).
fof(f5225,plain,
( spl16_452
<=> ! [X0] :
( ~ in(powerset(X0),the_InternalRel(sK0))
| ~ subset(cartesian_product2(sK14,sK14),X0)
| empty(powerset(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_452])]) ).
fof(f5390,plain,
( ~ in(powerset(cartesian_product2(sK14,sK14)),the_InternalRel(sK0))
| empty(powerset(cartesian_product2(sK14,sK14)))
| ~ spl16_15
| ~ spl16_452 ),
inference(resolution,[],[f5226,f229]) ).
fof(f5226,plain,
( ! [X0] :
( ~ subset(cartesian_product2(sK14,sK14),X0)
| ~ in(powerset(X0),the_InternalRel(sK0))
| empty(powerset(X0)) )
| ~ spl16_452 ),
inference(avatar_component_clause,[],[f5225]) ).
fof(f5486,plain,
( spl16_460
| ~ spl16_46
| ~ spl16_256 ),
inference(avatar_split_clause,[],[f2298,f2285,f387,f5484]) ).
fof(f2285,plain,
( spl16_256
<=> ! [X0] :
( empty(sK7(powerset(X0)))
| element(sK9(sK9(powerset(sK9(sK7(powerset(X0)))))),X0)
| empty(powerset(X0))
| empty(sK9(sK7(powerset(X0))))
| empty(sK9(powerset(sK9(sK7(powerset(X0)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_256])]) ).
fof(f2298,plain,
( ! [X0,X1] :
( empty(sK7(powerset(powerset(X0))))
| empty(powerset(powerset(X0)))
| empty(sK9(sK7(powerset(powerset(X0)))))
| empty(sK9(powerset(sK9(sK7(powerset(powerset(X0)))))))
| element(X1,X0)
| ~ in(X1,sK9(sK9(powerset(sK9(sK7(powerset(powerset(X0)))))))) )
| ~ spl16_46
| ~ spl16_256 ),
inference(resolution,[],[f2286,f388]) ).
fof(f2286,plain,
( ! [X0] :
( element(sK9(sK9(powerset(sK9(sK7(powerset(X0)))))),X0)
| empty(sK7(powerset(X0)))
| empty(powerset(X0))
| empty(sK9(sK7(powerset(X0))))
| empty(sK9(powerset(sK9(sK7(powerset(X0)))))) )
| ~ spl16_256 ),
inference(avatar_component_clause,[],[f2285]) ).
fof(f5482,plain,
( spl16_459
| ~ spl16_46
| ~ spl16_255 ),
inference(avatar_split_clause,[],[f2293,f2281,f387,f5480]) ).
fof(f2281,plain,
( spl16_255
<=> ! [X0] :
( empty(sK6(powerset(X0)))
| element(sK9(sK9(powerset(sK9(sK6(powerset(X0)))))),X0)
| empty(powerset(X0))
| empty(sK9(sK6(powerset(X0))))
| empty(sK9(powerset(sK9(sK6(powerset(X0)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_255])]) ).
fof(f2293,plain,
( ! [X0,X1] :
( empty(sK6(powerset(powerset(X0))))
| empty(powerset(powerset(X0)))
| empty(sK9(sK6(powerset(powerset(X0)))))
| empty(sK9(powerset(sK9(sK6(powerset(powerset(X0)))))))
| element(X1,X0)
| ~ in(X1,sK9(sK9(powerset(sK9(sK6(powerset(powerset(X0)))))))) )
| ~ spl16_46
| ~ spl16_255 ),
inference(resolution,[],[f2282,f388]) ).
fof(f2282,plain,
( ! [X0] :
( element(sK9(sK9(powerset(sK9(sK6(powerset(X0)))))),X0)
| empty(sK6(powerset(X0)))
| empty(powerset(X0))
| empty(sK9(sK6(powerset(X0))))
| empty(sK9(powerset(sK9(sK6(powerset(X0)))))) )
| ~ spl16_255 ),
inference(avatar_component_clause,[],[f2281]) ).
fof(f5403,plain,
( spl16_458
| ~ spl16_44
| ~ spl16_258 ),
inference(avatar_split_clause,[],[f2308,f2304,f374,f5401]) ).
fof(f374,plain,
( spl16_44
<=> ! [X2,X0,X1] :
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_44])]) ).
fof(f2308,plain,
( ! [X0,X1] :
( empty(sK9(powerset(powerset(powerset(X0)))))
| empty(sK9(sK9(powerset(powerset(powerset(X0))))))
| empty(sK9(powerset(sK9(sK9(powerset(powerset(powerset(X0))))))))
| ~ empty(X0)
| ~ in(X1,sK9(sK9(powerset(sK9(sK9(powerset(powerset(powerset(X0))))))))) )
| ~ spl16_44
| ~ spl16_258 ),
inference(resolution,[],[f2305,f375]) ).
fof(f375,plain,
( ! [X2,X0,X1] :
( ~ element(X1,powerset(X2))
| ~ empty(X2)
| ~ in(X0,X1) )
| ~ spl16_44 ),
inference(avatar_component_clause,[],[f374]) ).
fof(f5399,plain,
( spl16_457
| ~ spl16_44
| ~ spl16_256 ),
inference(avatar_split_clause,[],[f2299,f2285,f374,f5397]) ).
fof(f2299,plain,
( ! [X0,X1] :
( empty(sK7(powerset(powerset(X0))))
| empty(powerset(powerset(X0)))
| empty(sK9(sK7(powerset(powerset(X0)))))
| empty(sK9(powerset(sK9(sK7(powerset(powerset(X0)))))))
| ~ empty(X0)
| ~ in(X1,sK9(sK9(powerset(sK9(sK7(powerset(powerset(X0)))))))) )
| ~ spl16_44
| ~ spl16_256 ),
inference(resolution,[],[f2286,f375]) ).
fof(f5395,plain,
( spl16_456
| ~ spl16_44
| ~ spl16_255 ),
inference(avatar_split_clause,[],[f2294,f2281,f374,f5393]) ).
fof(f2294,plain,
( ! [X0,X1] :
( empty(sK6(powerset(powerset(X0))))
| empty(powerset(powerset(X0)))
| empty(sK9(sK6(powerset(powerset(X0)))))
| empty(sK9(powerset(sK9(sK6(powerset(powerset(X0)))))))
| ~ empty(X0)
| ~ in(X1,sK9(sK9(powerset(sK9(sK6(powerset(powerset(X0)))))))) )
| ~ spl16_44
| ~ spl16_255 ),
inference(resolution,[],[f2282,f375]) ).
fof(f5239,plain,
( spl16_455
| ~ spl16_37
| ~ spl16_258 ),
inference(avatar_split_clause,[],[f2309,f2304,f331,f5237]) ).
fof(f5237,plain,
( spl16_455
<=> ! [X0] :
( empty(sK9(powerset(powerset(powerset(X0)))))
| empty(sK9(sK9(powerset(powerset(powerset(X0))))))
| empty(sK9(powerset(sK9(sK9(powerset(powerset(powerset(X0))))))))
| finite(sK9(sK9(powerset(sK9(sK9(powerset(powerset(powerset(X0)))))))))
| ~ finite(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_455])]) ).
fof(f331,plain,
( spl16_37
<=> ! [X0,X1] :
( finite(X1)
| ~ element(X1,powerset(X0))
| ~ finite(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_37])]) ).
fof(f2309,plain,
( ! [X0] :
( empty(sK9(powerset(powerset(powerset(X0)))))
| empty(sK9(sK9(powerset(powerset(powerset(X0))))))
| empty(sK9(powerset(sK9(sK9(powerset(powerset(powerset(X0))))))))
| finite(sK9(sK9(powerset(sK9(sK9(powerset(powerset(powerset(X0)))))))))
| ~ finite(X0) )
| ~ spl16_37
| ~ spl16_258 ),
inference(resolution,[],[f2305,f332]) ).
fof(f332,plain,
( ! [X0,X1] :
( ~ element(X1,powerset(X0))
| finite(X1)
| ~ finite(X0) )
| ~ spl16_37 ),
inference(avatar_component_clause,[],[f331]) ).
fof(f5235,plain,
( spl16_454
| ~ spl16_37
| ~ spl16_256 ),
inference(avatar_split_clause,[],[f2300,f2285,f331,f5233]) ).
fof(f5233,plain,
( spl16_454
<=> ! [X0] :
( empty(sK7(powerset(powerset(X0))))
| empty(powerset(powerset(X0)))
| empty(sK9(sK7(powerset(powerset(X0)))))
| empty(sK9(powerset(sK9(sK7(powerset(powerset(X0)))))))
| finite(sK9(sK9(powerset(sK9(sK7(powerset(powerset(X0))))))))
| ~ finite(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_454])]) ).
fof(f2300,plain,
( ! [X0] :
( empty(sK7(powerset(powerset(X0))))
| empty(powerset(powerset(X0)))
| empty(sK9(sK7(powerset(powerset(X0)))))
| empty(sK9(powerset(sK9(sK7(powerset(powerset(X0)))))))
| finite(sK9(sK9(powerset(sK9(sK7(powerset(powerset(X0))))))))
| ~ finite(X0) )
| ~ spl16_37
| ~ spl16_256 ),
inference(resolution,[],[f2286,f332]) ).
fof(f5231,plain,
( spl16_453
| ~ spl16_37
| ~ spl16_255 ),
inference(avatar_split_clause,[],[f2295,f2281,f331,f5229]) ).
fof(f5229,plain,
( spl16_453
<=> ! [X0] :
( empty(sK6(powerset(powerset(X0))))
| empty(powerset(powerset(X0)))
| empty(sK9(sK6(powerset(powerset(X0)))))
| empty(sK9(powerset(sK9(sK6(powerset(powerset(X0)))))))
| finite(sK9(sK9(powerset(sK9(sK6(powerset(powerset(X0))))))))
| ~ finite(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_453])]) ).
fof(f2295,plain,
( ! [X0] :
( empty(sK6(powerset(powerset(X0))))
| empty(powerset(powerset(X0)))
| empty(sK9(sK6(powerset(powerset(X0)))))
| empty(sK9(powerset(sK9(sK6(powerset(powerset(X0)))))))
| finite(sK9(sK9(powerset(sK9(sK6(powerset(powerset(X0))))))))
| ~ finite(X0) )
| ~ spl16_37
| ~ spl16_255 ),
inference(resolution,[],[f2282,f332]) ).
fof(f5227,plain,
( spl16_452
| ~ spl16_109
| ~ spl16_266 ),
inference(avatar_split_clause,[],[f2546,f2539,f795,f5225]) ).
fof(f2546,plain,
( ! [X0] :
( ~ in(powerset(X0),the_InternalRel(sK0))
| ~ subset(cartesian_product2(sK14,sK14),X0)
| empty(powerset(X0)) )
| ~ spl16_109
| ~ spl16_266 ),
inference(resolution,[],[f2540,f796]) ).
fof(f5223,plain,
( spl16_451
| ~ spl16_46
| ~ spl16_254 ),
inference(avatar_split_clause,[],[f2275,f2267,f387,f5221]) ).
fof(f2267,plain,
( spl16_254
<=> ! [X0] :
( element(sK9(sK7(sK9(sK9(powerset(powerset(X0)))))),X0)
| empty(sK9(powerset(powerset(X0))))
| empty(sK7(sK9(sK9(powerset(powerset(X0))))))
| empty(sK9(sK9(powerset(powerset(X0))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_254])]) ).
fof(f2275,plain,
( ! [X0,X1] :
( empty(sK9(powerset(powerset(powerset(X0)))))
| empty(sK7(sK9(sK9(powerset(powerset(powerset(X0)))))))
| empty(sK9(sK9(powerset(powerset(powerset(X0))))))
| element(X1,X0)
| ~ in(X1,sK9(sK7(sK9(sK9(powerset(powerset(powerset(X0)))))))) )
| ~ spl16_46
| ~ spl16_254 ),
inference(resolution,[],[f2268,f388]) ).
fof(f2268,plain,
( ! [X0] :
( element(sK9(sK7(sK9(sK9(powerset(powerset(X0)))))),X0)
| empty(sK9(powerset(powerset(X0))))
| empty(sK7(sK9(sK9(powerset(powerset(X0))))))
| empty(sK9(sK9(powerset(powerset(X0))))) )
| ~ spl16_254 ),
inference(avatar_component_clause,[],[f2267]) ).
fof(f5219,plain,
( spl16_450
| ~ spl16_46
| ~ spl16_253 ),
inference(avatar_split_clause,[],[f2270,f2263,f387,f5217]) ).
fof(f2263,plain,
( spl16_253
<=> ! [X0] :
( element(sK9(sK6(sK9(sK9(powerset(powerset(X0)))))),X0)
| empty(sK9(powerset(powerset(X0))))
| empty(sK6(sK9(sK9(powerset(powerset(X0))))))
| empty(sK9(sK9(powerset(powerset(X0))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_253])]) ).
fof(f2270,plain,
( ! [X0,X1] :
( empty(sK9(powerset(powerset(powerset(X0)))))
| empty(sK6(sK9(sK9(powerset(powerset(powerset(X0)))))))
| empty(sK9(sK9(powerset(powerset(powerset(X0))))))
| element(X1,X0)
| ~ in(X1,sK9(sK6(sK9(sK9(powerset(powerset(powerset(X0)))))))) )
| ~ spl16_46
| ~ spl16_253 ),
inference(resolution,[],[f2264,f388]) ).
fof(f2264,plain,
( ! [X0] :
( element(sK9(sK6(sK9(sK9(powerset(powerset(X0)))))),X0)
| empty(sK9(powerset(powerset(X0))))
| empty(sK6(sK9(sK9(powerset(powerset(X0))))))
| empty(sK9(sK9(powerset(powerset(X0))))) )
| ~ spl16_253 ),
inference(avatar_component_clause,[],[f2263]) ).
fof(f5215,plain,
( spl16_449
| ~ spl16_46
| ~ spl16_252 ),
inference(avatar_split_clause,[],[f2257,f2238,f387,f5213]) ).
fof(f2238,plain,
( spl16_252
<=> ! [X0] :
( empty(sK7(powerset(X0)))
| element(sK9(sK7(sK9(sK7(powerset(X0))))),X0)
| empty(powerset(X0))
| empty(sK7(sK9(sK7(powerset(X0)))))
| empty(sK9(sK7(powerset(X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_252])]) ).
fof(f2257,plain,
( ! [X0,X1] :
( empty(sK7(powerset(powerset(X0))))
| empty(powerset(powerset(X0)))
| empty(sK7(sK9(sK7(powerset(powerset(X0))))))
| empty(sK9(sK7(powerset(powerset(X0)))))
| element(X1,X0)
| ~ in(X1,sK9(sK7(sK9(sK7(powerset(powerset(X0))))))) )
| ~ spl16_46
| ~ spl16_252 ),
inference(resolution,[],[f2239,f388]) ).
fof(f2239,plain,
( ! [X0] :
( element(sK9(sK7(sK9(sK7(powerset(X0))))),X0)
| empty(sK7(powerset(X0)))
| empty(powerset(X0))
| empty(sK7(sK9(sK7(powerset(X0)))))
| empty(sK9(sK7(powerset(X0)))) )
| ~ spl16_252 ),
inference(avatar_component_clause,[],[f2238]) ).
fof(f5211,plain,
( spl16_448
| ~ spl16_46
| ~ spl16_251 ),
inference(avatar_split_clause,[],[f2252,f2234,f387,f5209]) ).
fof(f2234,plain,
( spl16_251
<=> ! [X0] :
( empty(sK7(powerset(X0)))
| element(sK9(sK6(sK9(sK7(powerset(X0))))),X0)
| empty(powerset(X0))
| empty(sK6(sK9(sK7(powerset(X0)))))
| empty(sK9(sK7(powerset(X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_251])]) ).
fof(f2252,plain,
( ! [X0,X1] :
( empty(sK7(powerset(powerset(X0))))
| empty(powerset(powerset(X0)))
| empty(sK6(sK9(sK7(powerset(powerset(X0))))))
| empty(sK9(sK7(powerset(powerset(X0)))))
| element(X1,X0)
| ~ in(X1,sK9(sK6(sK9(sK7(powerset(powerset(X0))))))) )
| ~ spl16_46
| ~ spl16_251 ),
inference(resolution,[],[f2235,f388]) ).
fof(f2235,plain,
( ! [X0] :
( element(sK9(sK6(sK9(sK7(powerset(X0))))),X0)
| empty(sK7(powerset(X0)))
| empty(powerset(X0))
| empty(sK6(sK9(sK7(powerset(X0)))))
| empty(sK9(sK7(powerset(X0)))) )
| ~ spl16_251 ),
inference(avatar_component_clause,[],[f2234]) ).
fof(f5207,plain,
( spl16_447
| ~ spl16_46
| ~ spl16_250 ),
inference(avatar_split_clause,[],[f2247,f2230,f387,f5205]) ).
fof(f2230,plain,
( spl16_250
<=> ! [X0] :
( empty(sK6(powerset(X0)))
| element(sK9(sK7(sK9(sK6(powerset(X0))))),X0)
| empty(powerset(X0))
| empty(sK7(sK9(sK6(powerset(X0)))))
| empty(sK9(sK6(powerset(X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_250])]) ).
fof(f2247,plain,
( ! [X0,X1] :
( empty(sK6(powerset(powerset(X0))))
| empty(powerset(powerset(X0)))
| empty(sK7(sK9(sK6(powerset(powerset(X0))))))
| empty(sK9(sK6(powerset(powerset(X0)))))
| element(X1,X0)
| ~ in(X1,sK9(sK7(sK9(sK6(powerset(powerset(X0))))))) )
| ~ spl16_46
| ~ spl16_250 ),
inference(resolution,[],[f2231,f388]) ).
fof(f2231,plain,
( ! [X0] :
( element(sK9(sK7(sK9(sK6(powerset(X0))))),X0)
| empty(sK6(powerset(X0)))
| empty(powerset(X0))
| empty(sK7(sK9(sK6(powerset(X0)))))
| empty(sK9(sK6(powerset(X0)))) )
| ~ spl16_250 ),
inference(avatar_component_clause,[],[f2230]) ).
fof(f5203,plain,
( spl16_446
| ~ spl16_46
| ~ spl16_249 ),
inference(avatar_split_clause,[],[f2242,f2226,f387,f5201]) ).
fof(f2226,plain,
( spl16_249
<=> ! [X0] :
( empty(sK6(powerset(X0)))
| element(sK9(sK6(sK9(sK6(powerset(X0))))),X0)
| empty(powerset(X0))
| empty(sK6(sK9(sK6(powerset(X0)))))
| empty(sK9(sK6(powerset(X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_249])]) ).
fof(f2242,plain,
( ! [X0,X1] :
( empty(sK6(powerset(powerset(X0))))
| empty(powerset(powerset(X0)))
| empty(sK6(sK9(sK6(powerset(powerset(X0))))))
| empty(sK9(sK6(powerset(powerset(X0)))))
| element(X1,X0)
| ~ in(X1,sK9(sK6(sK9(sK6(powerset(powerset(X0))))))) )
| ~ spl16_46
| ~ spl16_249 ),
inference(resolution,[],[f2227,f388]) ).
fof(f2227,plain,
( ! [X0] :
( element(sK9(sK6(sK9(sK6(powerset(X0))))),X0)
| empty(sK6(powerset(X0)))
| empty(powerset(X0))
| empty(sK6(sK9(sK6(powerset(X0)))))
| empty(sK9(sK6(powerset(X0)))) )
| ~ spl16_249 ),
inference(avatar_component_clause,[],[f2226]) ).
fof(f5040,plain,
( spl16_445
| ~ spl16_34
| ~ spl16_258 ),
inference(avatar_split_clause,[],[f2310,f2304,f310,f5038]) ).
fof(f5038,plain,
( spl16_445
<=> ! [X0] :
( empty(sK9(powerset(powerset(powerset(X0)))))
| empty(sK9(sK9(powerset(powerset(powerset(X0))))))
| empty(sK9(powerset(sK9(sK9(powerset(powerset(powerset(X0))))))))
| subset(sK9(sK9(powerset(sK9(sK9(powerset(powerset(powerset(X0)))))))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_445])]) ).
fof(f310,plain,
( spl16_34
<=> ! [X0,X1] :
( subset(X0,X1)
| ~ element(X0,powerset(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_34])]) ).
fof(f2310,plain,
( ! [X0] :
( empty(sK9(powerset(powerset(powerset(X0)))))
| empty(sK9(sK9(powerset(powerset(powerset(X0))))))
| empty(sK9(powerset(sK9(sK9(powerset(powerset(powerset(X0))))))))
| subset(sK9(sK9(powerset(sK9(sK9(powerset(powerset(powerset(X0)))))))),X0) )
| ~ spl16_34
| ~ spl16_258 ),
inference(resolution,[],[f2305,f311]) ).
fof(f311,plain,
( ! [X0,X1] :
( ~ element(X0,powerset(X1))
| subset(X0,X1) )
| ~ spl16_34 ),
inference(avatar_component_clause,[],[f310]) ).
fof(f5036,plain,
( spl16_444
| ~ spl16_34
| ~ spl16_256 ),
inference(avatar_split_clause,[],[f2301,f2285,f310,f5034]) ).
fof(f5034,plain,
( spl16_444
<=> ! [X0] :
( empty(sK7(powerset(powerset(X0))))
| empty(powerset(powerset(X0)))
| empty(sK9(sK7(powerset(powerset(X0)))))
| empty(sK9(powerset(sK9(sK7(powerset(powerset(X0)))))))
| subset(sK9(sK9(powerset(sK9(sK7(powerset(powerset(X0))))))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_444])]) ).
fof(f2301,plain,
( ! [X0] :
( empty(sK7(powerset(powerset(X0))))
| empty(powerset(powerset(X0)))
| empty(sK9(sK7(powerset(powerset(X0)))))
| empty(sK9(powerset(sK9(sK7(powerset(powerset(X0)))))))
| subset(sK9(sK9(powerset(sK9(sK7(powerset(powerset(X0))))))),X0) )
| ~ spl16_34
| ~ spl16_256 ),
inference(resolution,[],[f2286,f311]) ).
fof(f5032,plain,
( spl16_443
| ~ spl16_34
| ~ spl16_255 ),
inference(avatar_split_clause,[],[f2296,f2281,f310,f5030]) ).
fof(f5030,plain,
( spl16_443
<=> ! [X0] :
( empty(sK6(powerset(powerset(X0))))
| empty(powerset(powerset(X0)))
| empty(sK9(sK6(powerset(powerset(X0)))))
| empty(sK9(powerset(sK9(sK6(powerset(powerset(X0)))))))
| subset(sK9(sK9(powerset(sK9(sK6(powerset(powerset(X0))))))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_443])]) ).
fof(f2296,plain,
( ! [X0] :
( empty(sK6(powerset(powerset(X0))))
| empty(powerset(powerset(X0)))
| empty(sK9(sK6(powerset(powerset(X0)))))
| empty(sK9(powerset(sK9(sK6(powerset(powerset(X0)))))))
| subset(sK9(sK9(powerset(sK9(sK6(powerset(powerset(X0))))))),X0) )
| ~ spl16_34
| ~ spl16_255 ),
inference(resolution,[],[f2282,f311]) ).
fof(f5028,plain,
( spl16_442
| ~ spl16_44
| ~ spl16_254 ),
inference(avatar_split_clause,[],[f2276,f2267,f374,f5026]) ).
fof(f2276,plain,
( ! [X0,X1] :
( empty(sK9(powerset(powerset(powerset(X0)))))
| empty(sK7(sK9(sK9(powerset(powerset(powerset(X0)))))))
| empty(sK9(sK9(powerset(powerset(powerset(X0))))))
| ~ empty(X0)
| ~ in(X1,sK9(sK7(sK9(sK9(powerset(powerset(powerset(X0)))))))) )
| ~ spl16_44
| ~ spl16_254 ),
inference(resolution,[],[f2268,f375]) ).
fof(f5024,plain,
( spl16_441
| ~ spl16_44
| ~ spl16_253 ),
inference(avatar_split_clause,[],[f2271,f2263,f374,f5022]) ).
fof(f2271,plain,
( ! [X0,X1] :
( empty(sK9(powerset(powerset(powerset(X0)))))
| empty(sK6(sK9(sK9(powerset(powerset(powerset(X0)))))))
| empty(sK9(sK9(powerset(powerset(powerset(X0))))))
| ~ empty(X0)
| ~ in(X1,sK9(sK6(sK9(sK9(powerset(powerset(powerset(X0)))))))) )
| ~ spl16_44
| ~ spl16_253 ),
inference(resolution,[],[f2264,f375]) ).
fof(f5020,plain,
( ~ spl16_440
| ~ spl16_416
| ~ spl16_428 ),
inference(avatar_split_clause,[],[f4999,f4912,f4661,f5017]) ).
fof(f5017,plain,
( spl16_440
<=> in(cartesian_product2(sK14,sK14),the_InternalRel(sK1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_440])]) ).
fof(f4912,plain,
( spl16_428
<=> ! [X0] :
( ~ in(X0,the_InternalRel(sK1))
| ~ in(cartesian_product2(sK14,sK14),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_428])]) ).
fof(f4999,plain,
( ~ in(cartesian_product2(sK14,sK14),the_InternalRel(sK1))
| ~ spl16_416
| ~ spl16_428 ),
inference(duplicate_literal_removal,[],[f4994]) ).
fof(f4994,plain,
( ~ in(cartesian_product2(sK14,sK14),the_InternalRel(sK1))
| ~ in(cartesian_product2(sK14,sK14),the_InternalRel(sK1))
| ~ spl16_416
| ~ spl16_428 ),
inference(resolution,[],[f4913,f4662]) ).
fof(f4913,plain,
( ! [X0] :
( ~ in(cartesian_product2(sK14,sK14),X0)
| ~ in(X0,the_InternalRel(sK1)) )
| ~ spl16_428 ),
inference(avatar_component_clause,[],[f4912]) ).
fof(f5015,plain,
( spl16_439
| ~ spl16_44
| ~ spl16_252 ),
inference(avatar_split_clause,[],[f2258,f2238,f374,f5013]) ).
fof(f2258,plain,
( ! [X0,X1] :
( empty(sK7(powerset(powerset(X0))))
| empty(powerset(powerset(X0)))
| empty(sK7(sK9(sK7(powerset(powerset(X0))))))
| empty(sK9(sK7(powerset(powerset(X0)))))
| ~ empty(X0)
| ~ in(X1,sK9(sK7(sK9(sK7(powerset(powerset(X0))))))) )
| ~ spl16_44
| ~ spl16_252 ),
inference(resolution,[],[f2239,f375]) ).
fof(f5011,plain,
( spl16_438
| ~ spl16_44
| ~ spl16_251 ),
inference(avatar_split_clause,[],[f2253,f2234,f374,f5009]) ).
fof(f2253,plain,
( ! [X0,X1] :
( empty(sK7(powerset(powerset(X0))))
| empty(powerset(powerset(X0)))
| empty(sK6(sK9(sK7(powerset(powerset(X0))))))
| empty(sK9(sK7(powerset(powerset(X0)))))
| ~ empty(X0)
| ~ in(X1,sK9(sK6(sK9(sK7(powerset(powerset(X0))))))) )
| ~ spl16_44
| ~ spl16_251 ),
inference(resolution,[],[f2235,f375]) ).
fof(f5007,plain,
( spl16_437
| ~ spl16_44
| ~ spl16_250 ),
inference(avatar_split_clause,[],[f2248,f2230,f374,f5005]) ).
fof(f2248,plain,
( ! [X0,X1] :
( empty(sK6(powerset(powerset(X0))))
| empty(powerset(powerset(X0)))
| empty(sK7(sK9(sK6(powerset(powerset(X0))))))
| empty(sK9(sK6(powerset(powerset(X0)))))
| ~ empty(X0)
| ~ in(X1,sK9(sK7(sK9(sK6(powerset(powerset(X0))))))) )
| ~ spl16_44
| ~ spl16_250 ),
inference(resolution,[],[f2231,f375]) ).
fof(f5003,plain,
( spl16_436
| ~ spl16_44
| ~ spl16_249 ),
inference(avatar_split_clause,[],[f2243,f2226,f374,f5001]) ).
fof(f2243,plain,
( ! [X0,X1] :
( empty(sK6(powerset(powerset(X0))))
| empty(powerset(powerset(X0)))
| empty(sK6(sK9(sK6(powerset(powerset(X0))))))
| empty(sK9(sK6(powerset(powerset(X0)))))
| ~ empty(X0)
| ~ in(X1,sK9(sK6(sK9(sK6(powerset(powerset(X0))))))) )
| ~ spl16_44
| ~ spl16_249 ),
inference(resolution,[],[f2227,f375]) ).
fof(f4990,plain,
( spl16_435
| ~ spl16_37
| ~ spl16_254 ),
inference(avatar_split_clause,[],[f2277,f2267,f331,f4988]) ).
fof(f4988,plain,
( spl16_435
<=> ! [X0] :
( empty(sK9(powerset(powerset(powerset(X0)))))
| empty(sK7(sK9(sK9(powerset(powerset(powerset(X0)))))))
| empty(sK9(sK9(powerset(powerset(powerset(X0))))))
| finite(sK9(sK7(sK9(sK9(powerset(powerset(powerset(X0))))))))
| ~ finite(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_435])]) ).
fof(f2277,plain,
( ! [X0] :
( empty(sK9(powerset(powerset(powerset(X0)))))
| empty(sK7(sK9(sK9(powerset(powerset(powerset(X0)))))))
| empty(sK9(sK9(powerset(powerset(powerset(X0))))))
| finite(sK9(sK7(sK9(sK9(powerset(powerset(powerset(X0))))))))
| ~ finite(X0) )
| ~ spl16_37
| ~ spl16_254 ),
inference(resolution,[],[f2268,f332]) ).
fof(f4986,plain,
( spl16_434
| ~ spl16_37
| ~ spl16_253 ),
inference(avatar_split_clause,[],[f2272,f2263,f331,f4984]) ).
fof(f4984,plain,
( spl16_434
<=> ! [X0] :
( empty(sK9(powerset(powerset(powerset(X0)))))
| empty(sK6(sK9(sK9(powerset(powerset(powerset(X0)))))))
| empty(sK9(sK9(powerset(powerset(powerset(X0))))))
| finite(sK9(sK6(sK9(sK9(powerset(powerset(powerset(X0))))))))
| ~ finite(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_434])]) ).
fof(f2272,plain,
( ! [X0] :
( empty(sK9(powerset(powerset(powerset(X0)))))
| empty(sK6(sK9(sK9(powerset(powerset(powerset(X0)))))))
| empty(sK9(sK9(powerset(powerset(powerset(X0))))))
| finite(sK9(sK6(sK9(sK9(powerset(powerset(powerset(X0))))))))
| ~ finite(X0) )
| ~ spl16_37
| ~ spl16_253 ),
inference(resolution,[],[f2264,f332]) ).
fof(f4982,plain,
( spl16_433
| ~ spl16_37
| ~ spl16_252 ),
inference(avatar_split_clause,[],[f2259,f2238,f331,f4980]) ).
fof(f4980,plain,
( spl16_433
<=> ! [X0] :
( empty(sK7(powerset(powerset(X0))))
| empty(powerset(powerset(X0)))
| empty(sK7(sK9(sK7(powerset(powerset(X0))))))
| empty(sK9(sK7(powerset(powerset(X0)))))
| finite(sK9(sK7(sK9(sK7(powerset(powerset(X0)))))))
| ~ finite(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_433])]) ).
fof(f2259,plain,
( ! [X0] :
( empty(sK7(powerset(powerset(X0))))
| empty(powerset(powerset(X0)))
| empty(sK7(sK9(sK7(powerset(powerset(X0))))))
| empty(sK9(sK7(powerset(powerset(X0)))))
| finite(sK9(sK7(sK9(sK7(powerset(powerset(X0)))))))
| ~ finite(X0) )
| ~ spl16_37
| ~ spl16_252 ),
inference(resolution,[],[f2239,f332]) ).
fof(f4978,plain,
( spl16_432
| ~ spl16_37
| ~ spl16_251 ),
inference(avatar_split_clause,[],[f2254,f2234,f331,f4976]) ).
fof(f4976,plain,
( spl16_432
<=> ! [X0] :
( empty(sK7(powerset(powerset(X0))))
| empty(powerset(powerset(X0)))
| empty(sK6(sK9(sK7(powerset(powerset(X0))))))
| empty(sK9(sK7(powerset(powerset(X0)))))
| finite(sK9(sK6(sK9(sK7(powerset(powerset(X0)))))))
| ~ finite(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_432])]) ).
fof(f2254,plain,
( ! [X0] :
( empty(sK7(powerset(powerset(X0))))
| empty(powerset(powerset(X0)))
| empty(sK6(sK9(sK7(powerset(powerset(X0))))))
| empty(sK9(sK7(powerset(powerset(X0)))))
| finite(sK9(sK6(sK9(sK7(powerset(powerset(X0)))))))
| ~ finite(X0) )
| ~ spl16_37
| ~ spl16_251 ),
inference(resolution,[],[f2235,f332]) ).
fof(f4974,plain,
( spl16_431
| ~ spl16_37
| ~ spl16_250 ),
inference(avatar_split_clause,[],[f2249,f2230,f331,f4972]) ).
fof(f4972,plain,
( spl16_431
<=> ! [X0] :
( empty(sK6(powerset(powerset(X0))))
| empty(powerset(powerset(X0)))
| empty(sK7(sK9(sK6(powerset(powerset(X0))))))
| empty(sK9(sK6(powerset(powerset(X0)))))
| finite(sK9(sK7(sK9(sK6(powerset(powerset(X0)))))))
| ~ finite(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_431])]) ).
fof(f2249,plain,
( ! [X0] :
( empty(sK6(powerset(powerset(X0))))
| empty(powerset(powerset(X0)))
| empty(sK7(sK9(sK6(powerset(powerset(X0))))))
| empty(sK9(sK6(powerset(powerset(X0)))))
| finite(sK9(sK7(sK9(sK6(powerset(powerset(X0)))))))
| ~ finite(X0) )
| ~ spl16_37
| ~ spl16_250 ),
inference(resolution,[],[f2231,f332]) ).
fof(f4970,plain,
( spl16_430
| ~ spl16_37
| ~ spl16_249 ),
inference(avatar_split_clause,[],[f2244,f2226,f331,f4968]) ).
fof(f4968,plain,
( spl16_430
<=> ! [X0] :
( empty(sK6(powerset(powerset(X0))))
| empty(powerset(powerset(X0)))
| empty(sK6(sK9(sK6(powerset(powerset(X0))))))
| empty(sK9(sK6(powerset(powerset(X0)))))
| finite(sK9(sK6(sK9(sK6(powerset(powerset(X0)))))))
| ~ finite(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_430])]) ).
fof(f2244,plain,
( ! [X0] :
( empty(sK6(powerset(powerset(X0))))
| empty(powerset(powerset(X0)))
| empty(sK6(sK9(sK6(powerset(powerset(X0))))))
| empty(sK9(sK6(powerset(powerset(X0)))))
| finite(sK9(sK6(sK9(sK6(powerset(powerset(X0)))))))
| ~ finite(X0) )
| ~ spl16_37
| ~ spl16_249 ),
inference(resolution,[],[f2227,f332]) ).
fof(f4966,plain,
( spl16_429
| ~ spl16_182
| ~ spl16_239 ),
inference(avatar_split_clause,[],[f2177,f2143,f1507,f4964]) ).
fof(f4964,plain,
( spl16_429
<=> ! [X0,X1] :
( empty(cartesian_product2(the_carrier(X0),the_carrier(X0)))
| ~ in(cartesian_product2(the_carrier(X1),the_carrier(X1)),the_InternalRel(X0))
| ~ rel_str(X0)
| ~ rel_str(X1)
| empty(cartesian_product2(the_carrier(X1),the_carrier(X1)))
| ~ in(cartesian_product2(the_carrier(X0),the_carrier(X0)),the_InternalRel(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_429])]) ).
fof(f1507,plain,
( spl16_182
<=> ! [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,[spl16_182])]) ).
fof(f2177,plain,
( ! [X0,X1] :
( empty(cartesian_product2(the_carrier(X0),the_carrier(X0)))
| ~ in(cartesian_product2(the_carrier(X1),the_carrier(X1)),the_InternalRel(X0))
| ~ rel_str(X0)
| ~ rel_str(X1)
| empty(cartesian_product2(the_carrier(X1),the_carrier(X1)))
| ~ in(cartesian_product2(the_carrier(X0),the_carrier(X0)),the_InternalRel(X1)) )
| ~ spl16_182
| ~ spl16_239 ),
inference(resolution,[],[f2144,f1508]) ).
fof(f1508,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)) )
| ~ spl16_182 ),
inference(avatar_component_clause,[],[f1507]) ).
fof(f4914,plain,
( spl16_428
| ~ spl16_27
| ~ spl16_416 ),
inference(avatar_split_clause,[],[f4869,f4661,f282,f4912]) ).
fof(f4869,plain,
( ! [X0] :
( ~ in(X0,the_InternalRel(sK1))
| ~ in(cartesian_product2(sK14,sK14),X0) )
| ~ spl16_27
| ~ spl16_416 ),
inference(resolution,[],[f4662,f283]) ).
fof(f4895,plain,
( spl16_427
| ~ spl16_38
| ~ spl16_258 ),
inference(avatar_split_clause,[],[f2311,f2304,f335,f4893]) ).
fof(f2311,plain,
( ! [X0] :
( empty(sK9(powerset(powerset(X0))))
| empty(sK9(sK9(powerset(powerset(X0)))))
| empty(sK9(powerset(sK9(sK9(powerset(powerset(X0)))))))
| empty(X0)
| in(sK9(sK9(powerset(sK9(sK9(powerset(powerset(X0))))))),X0) )
| ~ spl16_38
| ~ spl16_258 ),
inference(resolution,[],[f2305,f336]) ).
fof(f4891,plain,
( spl16_426
| ~ spl16_34
| ~ spl16_254 ),
inference(avatar_split_clause,[],[f2278,f2267,f310,f4889]) ).
fof(f4889,plain,
( spl16_426
<=> ! [X0] :
( empty(sK9(powerset(powerset(powerset(X0)))))
| empty(sK7(sK9(sK9(powerset(powerset(powerset(X0)))))))
| empty(sK9(sK9(powerset(powerset(powerset(X0))))))
| subset(sK9(sK7(sK9(sK9(powerset(powerset(powerset(X0))))))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_426])]) ).
fof(f2278,plain,
( ! [X0] :
( empty(sK9(powerset(powerset(powerset(X0)))))
| empty(sK7(sK9(sK9(powerset(powerset(powerset(X0)))))))
| empty(sK9(sK9(powerset(powerset(powerset(X0))))))
| subset(sK9(sK7(sK9(sK9(powerset(powerset(powerset(X0))))))),X0) )
| ~ spl16_34
| ~ spl16_254 ),
inference(resolution,[],[f2268,f311]) ).
fof(f4887,plain,
( spl16_425
| ~ spl16_34
| ~ spl16_253 ),
inference(avatar_split_clause,[],[f2273,f2263,f310,f4885]) ).
fof(f4885,plain,
( spl16_425
<=> ! [X0] :
( empty(sK9(powerset(powerset(powerset(X0)))))
| empty(sK6(sK9(sK9(powerset(powerset(powerset(X0)))))))
| empty(sK9(sK9(powerset(powerset(powerset(X0))))))
| subset(sK9(sK6(sK9(sK9(powerset(powerset(powerset(X0))))))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_425])]) ).
fof(f2273,plain,
( ! [X0] :
( empty(sK9(powerset(powerset(powerset(X0)))))
| empty(sK6(sK9(sK9(powerset(powerset(powerset(X0)))))))
| empty(sK9(sK9(powerset(powerset(powerset(X0))))))
| subset(sK9(sK6(sK9(sK9(powerset(powerset(powerset(X0))))))),X0) )
| ~ spl16_34
| ~ spl16_253 ),
inference(resolution,[],[f2264,f311]) ).
fof(f4883,plain,
( spl16_424
| ~ spl16_34
| ~ spl16_252 ),
inference(avatar_split_clause,[],[f2260,f2238,f310,f4881]) ).
fof(f4881,plain,
( spl16_424
<=> ! [X0] :
( empty(sK7(powerset(powerset(X0))))
| empty(powerset(powerset(X0)))
| empty(sK7(sK9(sK7(powerset(powerset(X0))))))
| empty(sK9(sK7(powerset(powerset(X0)))))
| subset(sK9(sK7(sK9(sK7(powerset(powerset(X0)))))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_424])]) ).
fof(f2260,plain,
( ! [X0] :
( empty(sK7(powerset(powerset(X0))))
| empty(powerset(powerset(X0)))
| empty(sK7(sK9(sK7(powerset(powerset(X0))))))
| empty(sK9(sK7(powerset(powerset(X0)))))
| subset(sK9(sK7(sK9(sK7(powerset(powerset(X0)))))),X0) )
| ~ spl16_34
| ~ spl16_252 ),
inference(resolution,[],[f2239,f311]) ).
fof(f4879,plain,
( spl16_423
| ~ spl16_34
| ~ spl16_251 ),
inference(avatar_split_clause,[],[f2255,f2234,f310,f4877]) ).
fof(f4877,plain,
( spl16_423
<=> ! [X0] :
( empty(sK7(powerset(powerset(X0))))
| empty(powerset(powerset(X0)))
| empty(sK6(sK9(sK7(powerset(powerset(X0))))))
| empty(sK9(sK7(powerset(powerset(X0)))))
| subset(sK9(sK6(sK9(sK7(powerset(powerset(X0)))))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_423])]) ).
fof(f2255,plain,
( ! [X0] :
( empty(sK7(powerset(powerset(X0))))
| empty(powerset(powerset(X0)))
| empty(sK6(sK9(sK7(powerset(powerset(X0))))))
| empty(sK9(sK7(powerset(powerset(X0)))))
| subset(sK9(sK6(sK9(sK7(powerset(powerset(X0)))))),X0) )
| ~ spl16_34
| ~ spl16_251 ),
inference(resolution,[],[f2235,f311]) ).
fof(f4867,plain,
( spl16_422
| ~ spl16_34
| ~ spl16_250 ),
inference(avatar_split_clause,[],[f2250,f2230,f310,f4865]) ).
fof(f4865,plain,
( spl16_422
<=> ! [X0] :
( empty(sK6(powerset(powerset(X0))))
| empty(powerset(powerset(X0)))
| empty(sK7(sK9(sK6(powerset(powerset(X0))))))
| empty(sK9(sK6(powerset(powerset(X0)))))
| subset(sK9(sK7(sK9(sK6(powerset(powerset(X0)))))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_422])]) ).
fof(f2250,plain,
( ! [X0] :
( empty(sK6(powerset(powerset(X0))))
| empty(powerset(powerset(X0)))
| empty(sK7(sK9(sK6(powerset(powerset(X0))))))
| empty(sK9(sK6(powerset(powerset(X0)))))
| subset(sK9(sK7(sK9(sK6(powerset(powerset(X0)))))),X0) )
| ~ spl16_34
| ~ spl16_250 ),
inference(resolution,[],[f2231,f311]) ).
fof(f4863,plain,
( spl16_421
| ~ spl16_34
| ~ spl16_249 ),
inference(avatar_split_clause,[],[f2245,f2226,f310,f4861]) ).
fof(f4861,plain,
( spl16_421
<=> ! [X0] :
( empty(sK6(powerset(powerset(X0))))
| empty(powerset(powerset(X0)))
| empty(sK6(sK9(sK6(powerset(powerset(X0))))))
| empty(sK9(sK6(powerset(powerset(X0)))))
| subset(sK9(sK6(sK9(sK6(powerset(powerset(X0)))))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_421])]) ).
fof(f2245,plain,
( ! [X0] :
( empty(sK6(powerset(powerset(X0))))
| empty(powerset(powerset(X0)))
| empty(sK6(sK9(sK6(powerset(powerset(X0))))))
| empty(sK9(sK6(powerset(powerset(X0)))))
| subset(sK9(sK6(sK9(sK6(powerset(powerset(X0)))))),X0) )
| ~ spl16_34
| ~ spl16_249 ),
inference(resolution,[],[f2227,f311]) ).
fof(f4769,plain,
( spl16_420
| ~ spl16_38
| ~ spl16_256 ),
inference(avatar_split_clause,[],[f2302,f2285,f335,f4767]) ).
fof(f2302,plain,
( ! [X0] :
( empty(sK7(powerset(X0)))
| empty(powerset(X0))
| empty(sK9(sK7(powerset(X0))))
| empty(sK9(powerset(sK9(sK7(powerset(X0))))))
| empty(X0)
| in(sK9(sK9(powerset(sK9(sK7(powerset(X0)))))),X0) )
| ~ spl16_38
| ~ spl16_256 ),
inference(resolution,[],[f2286,f336]) ).
fof(f4765,plain,
( spl16_419
| ~ spl16_38
| ~ spl16_255 ),
inference(avatar_split_clause,[],[f2297,f2281,f335,f4763]) ).
fof(f2297,plain,
( ! [X0] :
( empty(sK6(powerset(X0)))
| empty(powerset(X0))
| empty(sK9(sK6(powerset(X0))))
| empty(sK9(powerset(sK9(sK6(powerset(X0))))))
| empty(X0)
| in(sK9(sK9(powerset(sK9(sK6(powerset(X0)))))),X0) )
| ~ spl16_38
| ~ spl16_255 ),
inference(resolution,[],[f2282,f336]) ).
fof(f4671,plain,
( spl16_418
| ~ spl16_38
| ~ spl16_254 ),
inference(avatar_split_clause,[],[f2279,f2267,f335,f4669]) ).
fof(f2279,plain,
( ! [X0] :
( empty(sK9(powerset(powerset(X0))))
| empty(sK7(sK9(sK9(powerset(powerset(X0))))))
| empty(sK9(sK9(powerset(powerset(X0)))))
| empty(X0)
| in(sK9(sK7(sK9(sK9(powerset(powerset(X0)))))),X0) )
| ~ spl16_38
| ~ spl16_254 ),
inference(resolution,[],[f2268,f336]) ).
fof(f4667,plain,
( spl16_417
| ~ spl16_38
| ~ spl16_253 ),
inference(avatar_split_clause,[],[f2274,f2263,f335,f4665]) ).
fof(f2274,plain,
( ! [X0] :
( empty(sK9(powerset(powerset(X0))))
| empty(sK6(sK9(sK9(powerset(powerset(X0))))))
| empty(sK9(sK9(powerset(powerset(X0)))))
| empty(X0)
| in(sK9(sK6(sK9(sK9(powerset(powerset(X0)))))),X0) )
| ~ spl16_38
| ~ spl16_253 ),
inference(resolution,[],[f2264,f336]) ).
fof(f4663,plain,
( spl16_165
| spl16_416
| ~ spl16_38
| ~ spl16_194 ),
inference(avatar_split_clause,[],[f2010,f1676,f335,f4661,f1368]) ).
fof(f2010,plain,
( ! [X0] :
( ~ in(X0,the_InternalRel(sK1))
| empty(cartesian_product2(sK14,sK14))
| in(X0,cartesian_product2(sK14,sK14)) )
| ~ spl16_38
| ~ spl16_194 ),
inference(resolution,[],[f1677,f336]) ).
fof(f4479,plain,
( spl16_415
| ~ spl16_38
| ~ spl16_252 ),
inference(avatar_split_clause,[],[f2261,f2238,f335,f4477]) ).
fof(f2261,plain,
( ! [X0] :
( empty(sK7(powerset(X0)))
| empty(powerset(X0))
| empty(sK7(sK9(sK7(powerset(X0)))))
| empty(sK9(sK7(powerset(X0))))
| empty(X0)
| in(sK9(sK7(sK9(sK7(powerset(X0))))),X0) )
| ~ spl16_38
| ~ spl16_252 ),
inference(resolution,[],[f2239,f336]) ).
fof(f4475,plain,
( spl16_414
| ~ spl16_38
| ~ spl16_251 ),
inference(avatar_split_clause,[],[f2256,f2234,f335,f4473]) ).
fof(f2256,plain,
( ! [X0] :
( empty(sK7(powerset(X0)))
| empty(powerset(X0))
| empty(sK6(sK9(sK7(powerset(X0)))))
| empty(sK9(sK7(powerset(X0))))
| empty(X0)
| in(sK9(sK6(sK9(sK7(powerset(X0))))),X0) )
| ~ spl16_38
| ~ spl16_251 ),
inference(resolution,[],[f2235,f336]) ).
fof(f4471,plain,
( spl16_413
| ~ spl16_38
| ~ spl16_250 ),
inference(avatar_split_clause,[],[f2251,f2230,f335,f4469]) ).
fof(f2251,plain,
( ! [X0] :
( empty(sK6(powerset(X0)))
| empty(powerset(X0))
| empty(sK7(sK9(sK6(powerset(X0)))))
| empty(sK9(sK6(powerset(X0))))
| empty(X0)
| in(sK9(sK7(sK9(sK6(powerset(X0))))),X0) )
| ~ spl16_38
| ~ spl16_250 ),
inference(resolution,[],[f2231,f336]) ).
fof(f4467,plain,
( spl16_412
| ~ spl16_38
| ~ spl16_249 ),
inference(avatar_split_clause,[],[f2246,f2226,f335,f4465]) ).
fof(f2246,plain,
( ! [X0] :
( empty(sK6(powerset(X0)))
| empty(powerset(X0))
| empty(sK6(sK9(sK6(powerset(X0)))))
| empty(sK9(sK6(powerset(X0))))
| empty(X0)
| in(sK9(sK6(sK9(sK6(powerset(X0))))),X0) )
| ~ spl16_38
| ~ spl16_249 ),
inference(resolution,[],[f2227,f336]) ).
fof(f4417,plain,
( spl16_411
| ~ spl16_38
| ~ spl16_247 ),
inference(avatar_split_clause,[],[f2222,f2214,f335,f4415]) ).
fof(f2214,plain,
( spl16_247
<=> ! [X0,X1] :
( empty(the_InternalRel(X0))
| empty(sK9(powerset(the_InternalRel(X0))))
| element(sK9(sK9(powerset(the_InternalRel(X0)))),the_InternalRel(X1))
| ~ subrelstr(X0,X1)
| ~ rel_str(X0)
| ~ rel_str(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_247])]) ).
fof(f2222,plain,
( ! [X0,X1] :
( empty(sK9(powerset(the_InternalRel(X0))))
| empty(the_InternalRel(X0))
| ~ subrelstr(X0,X1)
| ~ rel_str(X0)
| ~ rel_str(X1)
| empty(the_InternalRel(X1))
| in(sK9(sK9(powerset(the_InternalRel(X0)))),the_InternalRel(X1)) )
| ~ spl16_38
| ~ spl16_247 ),
inference(resolution,[],[f2215,f336]) ).
fof(f2215,plain,
( ! [X0,X1] :
( element(sK9(sK9(powerset(the_InternalRel(X0)))),the_InternalRel(X1))
| empty(sK9(powerset(the_InternalRel(X0))))
| empty(the_InternalRel(X0))
| ~ subrelstr(X0,X1)
| ~ rel_str(X0)
| ~ rel_str(X1) )
| ~ spl16_247 ),
inference(avatar_component_clause,[],[f2214]) ).
fof(f4413,plain,
( spl16_410
| ~ spl16_38
| ~ spl16_246 ),
inference(avatar_split_clause,[],[f2221,f2210,f335,f4411]) ).
fof(f2210,plain,
( spl16_246
<=> ! [X0,X1] :
( empty(the_carrier(X0))
| empty(sK9(powerset(the_carrier(X0))))
| element(sK9(sK9(powerset(the_carrier(X0)))),the_carrier(X1))
| ~ subrelstr(X0,X1)
| ~ rel_str(X0)
| ~ rel_str(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_246])]) ).
fof(f2221,plain,
( ! [X0,X1] :
( empty(sK9(powerset(the_carrier(X0))))
| empty(the_carrier(X0))
| ~ subrelstr(X0,X1)
| ~ rel_str(X0)
| ~ rel_str(X1)
| empty(the_carrier(X1))
| in(sK9(sK9(powerset(the_carrier(X0)))),the_carrier(X1)) )
| ~ spl16_38
| ~ spl16_246 ),
inference(resolution,[],[f2211,f336]) ).
fof(f2211,plain,
( ! [X0,X1] :
( element(sK9(sK9(powerset(the_carrier(X0)))),the_carrier(X1))
| empty(sK9(powerset(the_carrier(X0))))
| empty(the_carrier(X0))
| ~ subrelstr(X0,X1)
| ~ rel_str(X0)
| ~ rel_str(X1) )
| ~ spl16_246 ),
inference(avatar_component_clause,[],[f2210]) ).
fof(f4409,plain,
( spl16_409
| ~ spl16_46
| ~ spl16_235 ),
inference(avatar_split_clause,[],[f2156,f2126,f387,f4407]) ).
fof(f2126,plain,
( spl16_235
<=> ! [X0] :
( empty(sK7(powerset(X0)))
| element(sK9(sK9(sK7(powerset(X0)))),X0)
| empty(powerset(X0))
| empty(sK9(sK7(powerset(X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_235])]) ).
fof(f2156,plain,
( ! [X0,X1] :
( empty(sK7(powerset(powerset(X0))))
| empty(powerset(powerset(X0)))
| empty(sK9(sK7(powerset(powerset(X0)))))
| element(X1,X0)
| ~ in(X1,sK9(sK9(sK7(powerset(powerset(X0)))))) )
| ~ spl16_46
| ~ spl16_235 ),
inference(resolution,[],[f2127,f388]) ).
fof(f2127,plain,
( ! [X0] :
( element(sK9(sK9(sK7(powerset(X0)))),X0)
| empty(sK7(powerset(X0)))
| empty(powerset(X0))
| empty(sK9(sK7(powerset(X0)))) )
| ~ spl16_235 ),
inference(avatar_component_clause,[],[f2126]) ).
fof(f4405,plain,
( spl16_408
| ~ spl16_46
| ~ spl16_234 ),
inference(avatar_split_clause,[],[f2151,f2122,f387,f4403]) ).
fof(f2122,plain,
( spl16_234
<=> ! [X0] :
( empty(sK6(powerset(X0)))
| element(sK9(sK9(sK6(powerset(X0)))),X0)
| empty(powerset(X0))
| empty(sK9(sK6(powerset(X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_234])]) ).
fof(f2151,plain,
( ! [X0,X1] :
( empty(sK6(powerset(powerset(X0))))
| empty(powerset(powerset(X0)))
| empty(sK9(sK6(powerset(powerset(X0)))))
| element(X1,X0)
| ~ in(X1,sK9(sK9(sK6(powerset(powerset(X0)))))) )
| ~ spl16_46
| ~ spl16_234 ),
inference(resolution,[],[f2123,f388]) ).
fof(f2123,plain,
( ! [X0] :
( element(sK9(sK9(sK6(powerset(X0)))),X0)
| empty(sK6(powerset(X0)))
| empty(powerset(X0))
| empty(sK9(sK6(powerset(X0)))) )
| ~ spl16_234 ),
inference(avatar_component_clause,[],[f2122]) ).
fof(f4353,plain,
( spl16_407
| ~ spl16_44
| ~ spl16_235 ),
inference(avatar_split_clause,[],[f2157,f2126,f374,f4351]) ).
fof(f2157,plain,
( ! [X0,X1] :
( empty(sK7(powerset(powerset(X0))))
| empty(powerset(powerset(X0)))
| empty(sK9(sK7(powerset(powerset(X0)))))
| ~ empty(X0)
| ~ in(X1,sK9(sK9(sK7(powerset(powerset(X0)))))) )
| ~ spl16_44
| ~ spl16_235 ),
inference(resolution,[],[f2127,f375]) ).
fof(f4349,plain,
( spl16_406
| ~ spl16_44
| ~ spl16_234 ),
inference(avatar_split_clause,[],[f2152,f2122,f374,f4347]) ).
fof(f2152,plain,
( ! [X0,X1] :
( empty(sK6(powerset(powerset(X0))))
| empty(powerset(powerset(X0)))
| empty(sK9(sK6(powerset(powerset(X0)))))
| ~ empty(X0)
| ~ in(X1,sK9(sK9(sK6(powerset(powerset(X0)))))) )
| ~ spl16_44
| ~ spl16_234 ),
inference(resolution,[],[f2123,f375]) ).
fof(f4345,plain,
( spl16_405
| ~ spl16_46
| ~ spl16_233 ),
inference(avatar_split_clause,[],[f2146,f2118,f387,f4343]) ).
fof(f2118,plain,
( spl16_233
<=> ! [X0] :
( element(sK9(sK9(sK9(powerset(powerset(X0))))),X0)
| empty(sK9(powerset(powerset(X0))))
| empty(sK9(sK9(powerset(powerset(X0))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_233])]) ).
fof(f2146,plain,
( ! [X0,X1] :
( empty(sK9(powerset(powerset(powerset(X0)))))
| empty(sK9(sK9(powerset(powerset(powerset(X0))))))
| element(X1,X0)
| ~ in(X1,sK9(sK9(sK9(powerset(powerset(powerset(X0))))))) )
| ~ spl16_46
| ~ spl16_233 ),
inference(resolution,[],[f2119,f388]) ).
fof(f2119,plain,
( ! [X0] :
( element(sK9(sK9(sK9(powerset(powerset(X0))))),X0)
| empty(sK9(powerset(powerset(X0))))
| empty(sK9(sK9(powerset(powerset(X0))))) )
| ~ spl16_233 ),
inference(avatar_component_clause,[],[f2118]) ).
fof(f4299,plain,
( spl16_403
| ~ spl16_404
| ~ spl16_15
| ~ spl16_389 ),
inference(avatar_split_clause,[],[f4206,f4163,f228,f4296,f4292]) ).
fof(f4296,plain,
( spl16_404
<=> in(powerset(cartesian_product2(sK14,sK14)),sK14) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_404])]) ).
fof(f4163,plain,
( spl16_389
<=> ! [X0] :
( ~ in(powerset(X0),sK14)
| ~ subset(cartesian_product2(sK14,sK14),X0)
| empty(powerset(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_389])]) ).
fof(f4206,plain,
( ~ in(powerset(cartesian_product2(sK14,sK14)),sK14)
| empty(powerset(cartesian_product2(sK14,sK14)))
| ~ spl16_15
| ~ spl16_389 ),
inference(resolution,[],[f4164,f229]) ).
fof(f4164,plain,
( ! [X0] :
( ~ subset(cartesian_product2(sK14,sK14),X0)
| ~ in(powerset(X0),sK14)
| empty(powerset(X0)) )
| ~ spl16_389 ),
inference(avatar_component_clause,[],[f4163]) ).
fof(f4219,plain,
( spl16_402
| ~ spl16_15
| ~ spl16_248 ),
inference(avatar_split_clause,[],[f2223,f2218,f228,f4217]) ).
fof(f4217,plain,
( spl16_402
<=> ! [X0] :
( empty(cartesian_product2(the_carrier(X0),the_carrier(X0)))
| ~ in(powerset(cartesian_product2(the_carrier(X0),the_carrier(X0))),the_InternalRel(X0))
| ~ rel_str(X0)
| empty(powerset(cartesian_product2(the_carrier(X0),the_carrier(X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_402])]) ).
fof(f2218,plain,
( spl16_248
<=> ! [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,[spl16_248])]) ).
fof(f2223,plain,
( ! [X0] :
( empty(cartesian_product2(the_carrier(X0),the_carrier(X0)))
| ~ in(powerset(cartesian_product2(the_carrier(X0),the_carrier(X0))),the_InternalRel(X0))
| ~ rel_str(X0)
| empty(powerset(cartesian_product2(the_carrier(X0),the_carrier(X0)))) )
| ~ spl16_15
| ~ spl16_248 ),
inference(resolution,[],[f2219,f229]) ).
fof(f2219,plain,
( ! [X0,X1] :
( ~ subset(cartesian_product2(the_carrier(X0),the_carrier(X0)),X1)
| empty(cartesian_product2(the_carrier(X0),the_carrier(X0)))
| ~ in(powerset(X1),the_InternalRel(X0))
| ~ rel_str(X0)
| empty(powerset(X1)) )
| ~ spl16_248 ),
inference(avatar_component_clause,[],[f2218]) ).
fof(f4215,plain,
( spl16_401
| ~ spl16_38
| ~ spl16_245 ),
inference(avatar_split_clause,[],[f2207,f2201,f335,f4213]) ).
fof(f2201,plain,
( spl16_245
<=> ! [X0,X1] :
( empty(sK7(the_InternalRel(X0)))
| empty(the_InternalRel(X0))
| element(sK9(sK7(the_InternalRel(X0))),the_InternalRel(X1))
| ~ subrelstr(X0,X1)
| ~ rel_str(X0)
| ~ rel_str(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_245])]) ).
fof(f2207,plain,
( ! [X0,X1] :
( empty(the_InternalRel(X0))
| empty(sK7(the_InternalRel(X0)))
| ~ subrelstr(X0,X1)
| ~ rel_str(X0)
| ~ rel_str(X1)
| empty(the_InternalRel(X1))
| in(sK9(sK7(the_InternalRel(X0))),the_InternalRel(X1)) )
| ~ spl16_38
| ~ spl16_245 ),
inference(resolution,[],[f2202,f336]) ).
fof(f2202,plain,
( ! [X0,X1] :
( element(sK9(sK7(the_InternalRel(X0))),the_InternalRel(X1))
| empty(the_InternalRel(X0))
| empty(sK7(the_InternalRel(X0)))
| ~ subrelstr(X0,X1)
| ~ rel_str(X0)
| ~ rel_str(X1) )
| ~ spl16_245 ),
inference(avatar_component_clause,[],[f2201]) ).
fof(f4211,plain,
( spl16_400
| ~ spl16_38
| ~ spl16_244 ),
inference(avatar_split_clause,[],[f2206,f2197,f335,f4209]) ).
fof(f2197,plain,
( spl16_244
<=> ! [X0,X1] :
( empty(sK7(the_carrier(X0)))
| empty(the_carrier(X0))
| element(sK9(sK7(the_carrier(X0))),the_carrier(X1))
| ~ subrelstr(X0,X1)
| ~ rel_str(X0)
| ~ rel_str(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_244])]) ).
fof(f2206,plain,
( ! [X0,X1] :
( empty(the_carrier(X0))
| empty(sK7(the_carrier(X0)))
| ~ subrelstr(X0,X1)
| ~ rel_str(X0)
| ~ rel_str(X1)
| empty(the_carrier(X1))
| in(sK9(sK7(the_carrier(X0))),the_carrier(X1)) )
| ~ spl16_38
| ~ spl16_244 ),
inference(resolution,[],[f2198,f336]) ).
fof(f2198,plain,
( ! [X0,X1] :
( element(sK9(sK7(the_carrier(X0))),the_carrier(X1))
| empty(the_carrier(X0))
| empty(sK7(the_carrier(X0)))
| ~ subrelstr(X0,X1)
| ~ rel_str(X0)
| ~ rel_str(X1) )
| ~ spl16_244 ),
inference(avatar_component_clause,[],[f2197]) ).
fof(f4205,plain,
( spl16_399
| ~ spl16_38
| ~ spl16_243 ),
inference(avatar_split_clause,[],[f2205,f2193,f335,f4203]) ).
fof(f2193,plain,
( spl16_243
<=> ! [X0,X1] :
( empty(sK6(the_InternalRel(X0)))
| empty(the_InternalRel(X0))
| element(sK9(sK6(the_InternalRel(X0))),the_InternalRel(X1))
| ~ subrelstr(X0,X1)
| ~ rel_str(X0)
| ~ rel_str(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_243])]) ).
fof(f2205,plain,
( ! [X0,X1] :
( empty(the_InternalRel(X0))
| empty(sK6(the_InternalRel(X0)))
| ~ subrelstr(X0,X1)
| ~ rel_str(X0)
| ~ rel_str(X1)
| empty(the_InternalRel(X1))
| in(sK9(sK6(the_InternalRel(X0))),the_InternalRel(X1)) )
| ~ spl16_38
| ~ spl16_243 ),
inference(resolution,[],[f2194,f336]) ).
fof(f2194,plain,
( ! [X0,X1] :
( element(sK9(sK6(the_InternalRel(X0))),the_InternalRel(X1))
| empty(the_InternalRel(X0))
| empty(sK6(the_InternalRel(X0)))
| ~ subrelstr(X0,X1)
| ~ rel_str(X0)
| ~ rel_str(X1) )
| ~ spl16_243 ),
inference(avatar_component_clause,[],[f2193]) ).
fof(f4201,plain,
( spl16_398
| ~ spl16_38
| ~ spl16_242 ),
inference(avatar_split_clause,[],[f2204,f2189,f335,f4199]) ).
fof(f2189,plain,
( spl16_242
<=> ! [X0,X1] :
( empty(sK6(the_carrier(X0)))
| empty(the_carrier(X0))
| element(sK9(sK6(the_carrier(X0))),the_carrier(X1))
| ~ subrelstr(X0,X1)
| ~ rel_str(X0)
| ~ rel_str(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_242])]) ).
fof(f2204,plain,
( ! [X0,X1] :
( empty(the_carrier(X0))
| empty(sK6(the_carrier(X0)))
| ~ subrelstr(X0,X1)
| ~ rel_str(X0)
| ~ rel_str(X1)
| empty(the_carrier(X1))
| in(sK9(sK6(the_carrier(X0))),the_carrier(X1)) )
| ~ spl16_38
| ~ spl16_242 ),
inference(resolution,[],[f2190,f336]) ).
fof(f2190,plain,
( ! [X0,X1] :
( element(sK9(sK6(the_carrier(X0))),the_carrier(X1))
| empty(the_carrier(X0))
| empty(sK6(the_carrier(X0)))
| ~ subrelstr(X0,X1)
| ~ rel_str(X0)
| ~ rel_str(X1) )
| ~ spl16_242 ),
inference(avatar_component_clause,[],[f2189]) ).
fof(f4197,plain,
( spl16_397
| ~ spl16_38
| ~ spl16_241 ),
inference(avatar_split_clause,[],[f2187,f2183,f335,f4195]) ).
fof(f2183,plain,
( spl16_241
<=> ! [X0,X1] :
( empty(sK11(X0,X1))
| empty(sK9(powerset(sK11(X0,X1))))
| element(sK9(sK9(powerset(sK11(X0,X1)))),cartesian_product2(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_241])]) ).
fof(f2187,plain,
( ! [X0,X1] :
( empty(sK9(powerset(sK11(X0,X1))))
| empty(sK11(X0,X1))
| empty(cartesian_product2(X0,X1))
| in(sK9(sK9(powerset(sK11(X0,X1)))),cartesian_product2(X0,X1)) )
| ~ spl16_38
| ~ spl16_241 ),
inference(resolution,[],[f2184,f336]) ).
fof(f2184,plain,
( ! [X0,X1] :
( element(sK9(sK9(powerset(sK11(X0,X1)))),cartesian_product2(X0,X1))
| empty(sK9(powerset(sK11(X0,X1))))
| empty(sK11(X0,X1)) )
| ~ spl16_241 ),
inference(avatar_component_clause,[],[f2183]) ).
fof(f4193,plain,
( spl16_396
| ~ spl16_38
| ~ spl16_240 ),
inference(avatar_split_clause,[],[f2186,f2179,f335,f4191]) ).
fof(f2179,plain,
( spl16_240
<=> ! [X0,X1] :
( empty(sK10(X0,X1))
| empty(sK9(powerset(sK10(X0,X1))))
| element(sK9(sK9(powerset(sK10(X0,X1)))),cartesian_product2(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_240])]) ).
fof(f2186,plain,
( ! [X0,X1] :
( empty(sK9(powerset(sK10(X0,X1))))
| empty(sK10(X0,X1))
| empty(cartesian_product2(X0,X1))
| in(sK9(sK9(powerset(sK10(X0,X1)))),cartesian_product2(X0,X1)) )
| ~ spl16_38
| ~ spl16_240 ),
inference(resolution,[],[f2180,f336]) ).
fof(f2180,plain,
( ! [X0,X1] :
( element(sK9(sK9(powerset(sK10(X0,X1)))),cartesian_product2(X0,X1))
| empty(sK9(powerset(sK10(X0,X1))))
| empty(sK10(X0,X1)) )
| ~ spl16_240 ),
inference(avatar_component_clause,[],[f2179]) ).
fof(f4189,plain,
( spl16_395
| ~ spl16_120
| ~ spl16_237 ),
inference(avatar_split_clause,[],[f2174,f2134,f884,f4187]) ).
fof(f2134,plain,
( spl16_237
<=> ! [X0,X1] :
( ~ subrelstr(X0,X1)
| ~ rel_str(X0)
| ~ rel_str(X1)
| empty(the_InternalRel(X0))
| empty(the_InternalRel(X1))
| in(sK9(the_InternalRel(X0)),the_InternalRel(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_237])]) ).
fof(f2174,plain,
( ! [X2,X0,X1] :
( ~ rel_str(X0)
| ~ rel_str(X1)
| empty(the_InternalRel(X0))
| empty(the_InternalRel(X1))
| ~ subrelstr(X0,X1)
| element(sK9(the_InternalRel(X0)),the_InternalRel(X2))
| ~ subrelstr(X1,X2)
| ~ rel_str(X2) )
| ~ spl16_120
| ~ spl16_237 ),
inference(duplicate_literal_removal,[],[f2168]) ).
fof(f2168,plain,
( ! [X2,X0,X1] :
( ~ rel_str(X0)
| ~ rel_str(X1)
| empty(the_InternalRel(X0))
| empty(the_InternalRel(X1))
| ~ subrelstr(X0,X1)
| element(sK9(the_InternalRel(X0)),the_InternalRel(X2))
| ~ subrelstr(X1,X2)
| ~ rel_str(X1)
| ~ rel_str(X2) )
| ~ spl16_120
| ~ spl16_237 ),
inference(resolution,[],[f2135,f885]) ).
fof(f2135,plain,
( ! [X0,X1] :
( in(sK9(the_InternalRel(X0)),the_InternalRel(X1))
| ~ rel_str(X0)
| ~ rel_str(X1)
| empty(the_InternalRel(X0))
| empty(the_InternalRel(X1))
| ~ subrelstr(X0,X1) )
| ~ spl16_237 ),
inference(avatar_component_clause,[],[f2134]) ).
fof(f4185,plain,
( spl16_394
| ~ spl16_119
| ~ spl16_236 ),
inference(avatar_split_clause,[],[f2167,f2130,f880,f4183]) ).
fof(f2130,plain,
( spl16_236
<=> ! [X0,X1] :
( ~ subrelstr(X0,X1)
| ~ rel_str(X0)
| ~ rel_str(X1)
| empty(the_carrier(X0))
| empty(the_carrier(X1))
| in(sK9(the_carrier(X0)),the_carrier(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_236])]) ).
fof(f2167,plain,
( ! [X2,X0,X1] :
( ~ rel_str(X0)
| ~ rel_str(X1)
| empty(the_carrier(X0))
| empty(the_carrier(X1))
| ~ subrelstr(X0,X1)
| element(sK9(the_carrier(X0)),the_carrier(X2))
| ~ subrelstr(X1,X2)
| ~ rel_str(X2) )
| ~ spl16_119
| ~ spl16_236 ),
inference(duplicate_literal_removal,[],[f2161]) ).
fof(f2161,plain,
( ! [X2,X0,X1] :
( ~ rel_str(X0)
| ~ rel_str(X1)
| empty(the_carrier(X0))
| empty(the_carrier(X1))
| ~ subrelstr(X0,X1)
| element(sK9(the_carrier(X0)),the_carrier(X2))
| ~ subrelstr(X1,X2)
| ~ rel_str(X1)
| ~ rel_str(X2) )
| ~ spl16_119
| ~ spl16_236 ),
inference(resolution,[],[f2131,f881]) ).
fof(f2131,plain,
( ! [X0,X1] :
( in(sK9(the_carrier(X0)),the_carrier(X1))
| ~ rel_str(X0)
| ~ rel_str(X1)
| empty(the_carrier(X0))
| empty(the_carrier(X1))
| ~ subrelstr(X0,X1) )
| ~ spl16_236 ),
inference(avatar_component_clause,[],[f2130]) ).
fof(f4181,plain,
( spl16_393
| ~ spl16_37
| ~ spl16_235 ),
inference(avatar_split_clause,[],[f2158,f2126,f331,f4179]) ).
fof(f4179,plain,
( spl16_393
<=> ! [X0] :
( empty(sK7(powerset(powerset(X0))))
| empty(powerset(powerset(X0)))
| empty(sK9(sK7(powerset(powerset(X0)))))
| finite(sK9(sK9(sK7(powerset(powerset(X0))))))
| ~ finite(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_393])]) ).
fof(f2158,plain,
( ! [X0] :
( empty(sK7(powerset(powerset(X0))))
| empty(powerset(powerset(X0)))
| empty(sK9(sK7(powerset(powerset(X0)))))
| finite(sK9(sK9(sK7(powerset(powerset(X0))))))
| ~ finite(X0) )
| ~ spl16_37
| ~ spl16_235 ),
inference(resolution,[],[f2127,f332]) ).
fof(f4177,plain,
( spl16_392
| ~ spl16_37
| ~ spl16_234 ),
inference(avatar_split_clause,[],[f2153,f2122,f331,f4175]) ).
fof(f4175,plain,
( spl16_392
<=> ! [X0] :
( empty(sK6(powerset(powerset(X0))))
| empty(powerset(powerset(X0)))
| empty(sK9(sK6(powerset(powerset(X0)))))
| finite(sK9(sK9(sK6(powerset(powerset(X0))))))
| ~ finite(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_392])]) ).
fof(f2153,plain,
( ! [X0] :
( empty(sK6(powerset(powerset(X0))))
| empty(powerset(powerset(X0)))
| empty(sK9(sK6(powerset(powerset(X0)))))
| finite(sK9(sK9(sK6(powerset(powerset(X0))))))
| ~ finite(X0) )
| ~ spl16_37
| ~ spl16_234 ),
inference(resolution,[],[f2123,f332]) ).
fof(f4173,plain,
( spl16_391
| ~ spl16_44
| ~ spl16_233 ),
inference(avatar_split_clause,[],[f2147,f2118,f374,f4171]) ).
fof(f2147,plain,
( ! [X0,X1] :
( empty(sK9(powerset(powerset(powerset(X0)))))
| empty(sK9(sK9(powerset(powerset(powerset(X0))))))
| ~ empty(X0)
| ~ in(X1,sK9(sK9(sK9(powerset(powerset(powerset(X0))))))) )
| ~ spl16_44
| ~ spl16_233 ),
inference(resolution,[],[f2119,f375]) ).
fof(f4169,plain,
( spl16_390
| ~ spl16_46
| ~ spl16_232 ),
inference(avatar_split_clause,[],[f2111,f2103,f387,f4167]) ).
fof(f2103,plain,
( spl16_232
<=> ! [X0] :
( empty(sK9(powerset(X0)))
| empty(sK9(powerset(sK9(powerset(X0)))))
| element(sK9(sK9(powerset(sK9(powerset(X0))))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_232])]) ).
fof(f2111,plain,
( ! [X0,X1] :
( empty(sK9(powerset(sK9(powerset(powerset(X0))))))
| empty(sK9(powerset(powerset(X0))))
| element(X1,X0)
| ~ in(X1,sK9(sK9(powerset(sK9(powerset(powerset(X0))))))) )
| ~ spl16_46
| ~ spl16_232 ),
inference(resolution,[],[f2104,f388]) ).
fof(f2104,plain,
( ! [X0] :
( element(sK9(sK9(powerset(sK9(powerset(X0))))),X0)
| empty(sK9(powerset(sK9(powerset(X0)))))
| empty(sK9(powerset(X0))) )
| ~ spl16_232 ),
inference(avatar_component_clause,[],[f2103]) ).
fof(f4165,plain,
( spl16_389
| ~ spl16_109
| ~ spl16_360 ),
inference(avatar_split_clause,[],[f3772,f3662,f795,f4163]) ).
fof(f3662,plain,
( spl16_360
<=> ! [X0] :
( ~ in(X0,sK14)
| in(X0,cartesian_product2(sK14,sK14)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_360])]) ).
fof(f3772,plain,
( ! [X0] :
( ~ in(powerset(X0),sK14)
| ~ subset(cartesian_product2(sK14,sK14),X0)
| empty(powerset(X0)) )
| ~ spl16_109
| ~ spl16_360 ),
inference(resolution,[],[f3663,f796]) ).
fof(f3663,plain,
( ! [X0] :
( in(X0,cartesian_product2(sK14,sK14))
| ~ in(X0,sK14) )
| ~ spl16_360 ),
inference(avatar_component_clause,[],[f3662]) ).
fof(f4161,plain,
( spl16_388
| ~ spl16_46
| ~ spl16_227 ),
inference(avatar_split_clause,[],[f2080,f2071,f387,f4159]) ).
fof(f2071,plain,
( spl16_227
<=> ! [X0] :
( empty(sK7(X0))
| empty(sK9(powerset(sK7(X0))))
| element(sK9(sK9(powerset(sK7(X0)))),X0)
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_227])]) ).
fof(f2080,plain,
( ! [X0,X1] :
( empty(sK9(powerset(sK7(powerset(X0)))))
| empty(sK7(powerset(X0)))
| empty(powerset(X0))
| element(X1,X0)
| ~ in(X1,sK9(sK9(powerset(sK7(powerset(X0)))))) )
| ~ spl16_46
| ~ spl16_227 ),
inference(resolution,[],[f2072,f388]) ).
fof(f2072,plain,
( ! [X0] :
( element(sK9(sK9(powerset(sK7(X0)))),X0)
| empty(sK9(powerset(sK7(X0))))
| empty(sK7(X0))
| empty(X0) )
| ~ spl16_227 ),
inference(avatar_component_clause,[],[f2071]) ).
fof(f4157,plain,
( spl16_387
| ~ spl16_46
| ~ spl16_226 ),
inference(avatar_split_clause,[],[f2074,f2067,f387,f4155]) ).
fof(f2067,plain,
( spl16_226
<=> ! [X0] :
( empty(sK6(X0))
| empty(sK9(powerset(sK6(X0))))
| element(sK9(sK9(powerset(sK6(X0)))),X0)
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_226])]) ).
fof(f2074,plain,
( ! [X0,X1] :
( empty(sK9(powerset(sK6(powerset(X0)))))
| empty(sK6(powerset(X0)))
| empty(powerset(X0))
| element(X1,X0)
| ~ in(X1,sK9(sK9(powerset(sK6(powerset(X0)))))) )
| ~ spl16_46
| ~ spl16_226 ),
inference(resolution,[],[f2068,f388]) ).
fof(f2068,plain,
( ! [X0] :
( element(sK9(sK9(powerset(sK6(X0)))),X0)
| empty(sK9(powerset(sK6(X0))))
| empty(sK6(X0))
| empty(X0) )
| ~ spl16_226 ),
inference(avatar_component_clause,[],[f2067]) ).
fof(f4099,plain,
( spl16_386
| ~ spl16_34
| ~ spl16_235 ),
inference(avatar_split_clause,[],[f2159,f2126,f310,f4097]) ).
fof(f4097,plain,
( spl16_386
<=> ! [X0] :
( empty(sK7(powerset(powerset(X0))))
| empty(powerset(powerset(X0)))
| empty(sK9(sK7(powerset(powerset(X0)))))
| subset(sK9(sK9(sK7(powerset(powerset(X0))))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_386])]) ).
fof(f2159,plain,
( ! [X0] :
( empty(sK7(powerset(powerset(X0))))
| empty(powerset(powerset(X0)))
| empty(sK9(sK7(powerset(powerset(X0)))))
| subset(sK9(sK9(sK7(powerset(powerset(X0))))),X0) )
| ~ spl16_34
| ~ spl16_235 ),
inference(resolution,[],[f2127,f311]) ).
fof(f4095,plain,
( spl16_385
| ~ spl16_34
| ~ spl16_234 ),
inference(avatar_split_clause,[],[f2154,f2122,f310,f4093]) ).
fof(f4093,plain,
( spl16_385
<=> ! [X0] :
( empty(sK6(powerset(powerset(X0))))
| empty(powerset(powerset(X0)))
| empty(sK9(sK6(powerset(powerset(X0)))))
| subset(sK9(sK9(sK6(powerset(powerset(X0))))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_385])]) ).
fof(f2154,plain,
( ! [X0] :
( empty(sK6(powerset(powerset(X0))))
| empty(powerset(powerset(X0)))
| empty(sK9(sK6(powerset(powerset(X0)))))
| subset(sK9(sK9(sK6(powerset(powerset(X0))))),X0) )
| ~ spl16_34
| ~ spl16_234 ),
inference(resolution,[],[f2123,f311]) ).
fof(f4091,plain,
( spl16_384
| ~ spl16_37
| ~ spl16_233 ),
inference(avatar_split_clause,[],[f2148,f2118,f331,f4089]) ).
fof(f4089,plain,
( spl16_384
<=> ! [X0] :
( empty(sK9(powerset(powerset(powerset(X0)))))
| empty(sK9(sK9(powerset(powerset(powerset(X0))))))
| finite(sK9(sK9(sK9(powerset(powerset(powerset(X0)))))))
| ~ finite(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_384])]) ).
fof(f2148,plain,
( ! [X0] :
( empty(sK9(powerset(powerset(powerset(X0)))))
| empty(sK9(sK9(powerset(powerset(powerset(X0))))))
| finite(sK9(sK9(sK9(powerset(powerset(powerset(X0)))))))
| ~ finite(X0) )
| ~ spl16_37
| ~ spl16_233 ),
inference(resolution,[],[f2119,f332]) ).
fof(f4087,plain,
( spl16_383
| ~ spl16_44
| ~ spl16_232 ),
inference(avatar_split_clause,[],[f2112,f2103,f374,f4085]) ).
fof(f2112,plain,
( ! [X0,X1] :
( empty(sK9(powerset(sK9(powerset(powerset(X0))))))
| empty(sK9(powerset(powerset(X0))))
| ~ empty(X0)
| ~ in(X1,sK9(sK9(powerset(sK9(powerset(powerset(X0))))))) )
| ~ spl16_44
| ~ spl16_232 ),
inference(resolution,[],[f2104,f375]) ).
fof(f4083,plain,
( spl16_382
| ~ spl16_44
| ~ spl16_227 ),
inference(avatar_split_clause,[],[f2081,f2071,f374,f4081]) ).
fof(f2081,plain,
( ! [X0,X1] :
( empty(sK9(powerset(sK7(powerset(X0)))))
| empty(sK7(powerset(X0)))
| empty(powerset(X0))
| ~ empty(X0)
| ~ in(X1,sK9(sK9(powerset(sK7(powerset(X0)))))) )
| ~ spl16_44
| ~ spl16_227 ),
inference(resolution,[],[f2072,f375]) ).
fof(f4079,plain,
( spl16_381
| ~ spl16_44
| ~ spl16_226 ),
inference(avatar_split_clause,[],[f2075,f2067,f374,f4077]) ).
fof(f2075,plain,
( ! [X0,X1] :
( empty(sK9(powerset(sK6(powerset(X0)))))
| empty(sK6(powerset(X0)))
| empty(powerset(X0))
| ~ empty(X0)
| ~ in(X1,sK9(sK9(powerset(sK6(powerset(X0)))))) )
| ~ spl16_44
| ~ spl16_226 ),
inference(resolution,[],[f2068,f375]) ).
fof(f4058,plain,
( ~ spl16_380
| ~ spl16_360
| ~ spl16_367 ),
inference(avatar_split_clause,[],[f3949,f3899,f3662,f4055]) ).
fof(f4055,plain,
( spl16_380
<=> in(cartesian_product2(sK14,sK14),sK14) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_380])]) ).
fof(f3899,plain,
( spl16_367
<=> ! [X0] :
( ~ in(X0,sK14)
| ~ in(cartesian_product2(sK14,sK14),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_367])]) ).
fof(f3949,plain,
( ~ in(cartesian_product2(sK14,sK14),sK14)
| ~ spl16_360
| ~ spl16_367 ),
inference(duplicate_literal_removal,[],[f3945]) ).
fof(f3945,plain,
( ~ in(cartesian_product2(sK14,sK14),sK14)
| ~ in(cartesian_product2(sK14,sK14),sK14)
| ~ spl16_360
| ~ spl16_367 ),
inference(resolution,[],[f3900,f3663]) ).
fof(f3900,plain,
( ! [X0] :
( ~ in(cartesian_product2(sK14,sK14),X0)
| ~ in(X0,sK14) )
| ~ spl16_367 ),
inference(avatar_component_clause,[],[f3899]) ).
fof(f3957,plain,
( spl16_379
| ~ spl16_34
| ~ spl16_233 ),
inference(avatar_split_clause,[],[f2149,f2118,f310,f3955]) ).
fof(f3955,plain,
( spl16_379
<=> ! [X0] :
( empty(sK9(powerset(powerset(powerset(X0)))))
| empty(sK9(sK9(powerset(powerset(powerset(X0))))))
| subset(sK9(sK9(sK9(powerset(powerset(powerset(X0)))))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_379])]) ).
fof(f2149,plain,
( ! [X0] :
( empty(sK9(powerset(powerset(powerset(X0)))))
| empty(sK9(sK9(powerset(powerset(powerset(X0))))))
| subset(sK9(sK9(sK9(powerset(powerset(powerset(X0)))))),X0) )
| ~ spl16_34
| ~ spl16_233 ),
inference(resolution,[],[f2119,f311]) ).
fof(f3953,plain,
( spl16_378
| ~ spl16_37
| ~ spl16_232 ),
inference(avatar_split_clause,[],[f2113,f2103,f331,f3951]) ).
fof(f3951,plain,
( spl16_378
<=> ! [X0] :
( empty(sK9(powerset(sK9(powerset(powerset(X0))))))
| empty(sK9(powerset(powerset(X0))))
| finite(sK9(sK9(powerset(sK9(powerset(powerset(X0)))))))
| ~ finite(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_378])]) ).
fof(f2113,plain,
( ! [X0] :
( empty(sK9(powerset(sK9(powerset(powerset(X0))))))
| empty(sK9(powerset(powerset(X0))))
| finite(sK9(sK9(powerset(sK9(powerset(powerset(X0)))))))
| ~ finite(X0) )
| ~ spl16_37
| ~ spl16_232 ),
inference(resolution,[],[f2104,f332]) ).
fof(f3941,plain,
( spl16_377
| ~ spl16_38
| ~ spl16_231 ),
inference(avatar_split_clause,[],[f2110,f2099,f335,f3939]) ).
fof(f2099,plain,
( spl16_231
<=> ! [X0,X1] :
( empty(sK7(sK11(X0,X1)))
| empty(sK11(X0,X1))
| element(sK9(sK7(sK11(X0,X1))),cartesian_product2(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_231])]) ).
fof(f2110,plain,
( ! [X0,X1] :
( empty(sK11(X0,X1))
| empty(sK7(sK11(X0,X1)))
| empty(cartesian_product2(X0,X1))
| in(sK9(sK7(sK11(X0,X1))),cartesian_product2(X0,X1)) )
| ~ spl16_38
| ~ spl16_231 ),
inference(resolution,[],[f2100,f336]) ).
fof(f2100,plain,
( ! [X0,X1] :
( element(sK9(sK7(sK11(X0,X1))),cartesian_product2(X0,X1))
| empty(sK11(X0,X1))
| empty(sK7(sK11(X0,X1))) )
| ~ spl16_231 ),
inference(avatar_component_clause,[],[f2099]) ).
fof(f3937,plain,
( spl16_376
| ~ spl16_38
| ~ spl16_230 ),
inference(avatar_split_clause,[],[f2109,f2095,f335,f3935]) ).
fof(f2095,plain,
( spl16_230
<=> ! [X0,X1] :
( empty(sK7(sK10(X0,X1)))
| empty(sK10(X0,X1))
| element(sK9(sK7(sK10(X0,X1))),cartesian_product2(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_230])]) ).
fof(f2109,plain,
( ! [X0,X1] :
( empty(sK10(X0,X1))
| empty(sK7(sK10(X0,X1)))
| empty(cartesian_product2(X0,X1))
| in(sK9(sK7(sK10(X0,X1))),cartesian_product2(X0,X1)) )
| ~ spl16_38
| ~ spl16_230 ),
inference(resolution,[],[f2096,f336]) ).
fof(f2096,plain,
( ! [X0,X1] :
( element(sK9(sK7(sK10(X0,X1))),cartesian_product2(X0,X1))
| empty(sK10(X0,X1))
| empty(sK7(sK10(X0,X1))) )
| ~ spl16_230 ),
inference(avatar_component_clause,[],[f2095]) ).
fof(f3933,plain,
( spl16_375
| ~ spl16_38
| ~ spl16_229 ),
inference(avatar_split_clause,[],[f2108,f2091,f335,f3931]) ).
fof(f2091,plain,
( spl16_229
<=> ! [X0,X1] :
( empty(sK6(sK11(X0,X1)))
| empty(sK11(X0,X1))
| element(sK9(sK6(sK11(X0,X1))),cartesian_product2(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_229])]) ).
fof(f2108,plain,
( ! [X0,X1] :
( empty(sK11(X0,X1))
| empty(sK6(sK11(X0,X1)))
| empty(cartesian_product2(X0,X1))
| in(sK9(sK6(sK11(X0,X1))),cartesian_product2(X0,X1)) )
| ~ spl16_38
| ~ spl16_229 ),
inference(resolution,[],[f2092,f336]) ).
fof(f2092,plain,
( ! [X0,X1] :
( element(sK9(sK6(sK11(X0,X1))),cartesian_product2(X0,X1))
| empty(sK11(X0,X1))
| empty(sK6(sK11(X0,X1))) )
| ~ spl16_229 ),
inference(avatar_component_clause,[],[f2091]) ).
fof(f3929,plain,
( spl16_374
| ~ spl16_38
| ~ spl16_228 ),
inference(avatar_split_clause,[],[f2106,f2087,f335,f3927]) ).
fof(f2087,plain,
( spl16_228
<=> ! [X0,X1] :
( empty(sK6(sK10(X0,X1)))
| empty(sK10(X0,X1))
| element(sK9(sK6(sK10(X0,X1))),cartesian_product2(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_228])]) ).
fof(f2106,plain,
( ! [X0,X1] :
( empty(sK10(X0,X1))
| empty(sK6(sK10(X0,X1)))
| empty(cartesian_product2(X0,X1))
| in(sK9(sK6(sK10(X0,X1))),cartesian_product2(X0,X1)) )
| ~ spl16_38
| ~ spl16_228 ),
inference(resolution,[],[f2088,f336]) ).
fof(f2088,plain,
( ! [X0,X1] :
( element(sK9(sK6(sK10(X0,X1))),cartesian_product2(X0,X1))
| empty(sK10(X0,X1))
| empty(sK6(sK10(X0,X1))) )
| ~ spl16_228 ),
inference(avatar_component_clause,[],[f2087]) ).
fof(f3925,plain,
( spl16_373
| ~ spl16_37
| ~ spl16_227 ),
inference(avatar_split_clause,[],[f2082,f2071,f331,f3923]) ).
fof(f3923,plain,
( spl16_373
<=> ! [X0] :
( empty(sK9(powerset(sK7(powerset(X0)))))
| empty(sK7(powerset(X0)))
| empty(powerset(X0))
| finite(sK9(sK9(powerset(sK7(powerset(X0))))))
| ~ finite(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_373])]) ).
fof(f2082,plain,
( ! [X0] :
( empty(sK9(powerset(sK7(powerset(X0)))))
| empty(sK7(powerset(X0)))
| empty(powerset(X0))
| finite(sK9(sK9(powerset(sK7(powerset(X0))))))
| ~ finite(X0) )
| ~ spl16_37
| ~ spl16_227 ),
inference(resolution,[],[f2072,f332]) ).
fof(f3921,plain,
( spl16_372
| ~ spl16_37
| ~ spl16_226 ),
inference(avatar_split_clause,[],[f2076,f2067,f331,f3919]) ).
fof(f3919,plain,
( spl16_372
<=> ! [X0] :
( empty(sK9(powerset(sK6(powerset(X0)))))
| empty(sK6(powerset(X0)))
| empty(powerset(X0))
| finite(sK9(sK9(powerset(sK6(powerset(X0))))))
| ~ finite(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_372])]) ).
fof(f2076,plain,
( ! [X0] :
( empty(sK9(powerset(sK6(powerset(X0)))))
| empty(sK6(powerset(X0)))
| empty(powerset(X0))
| finite(sK9(sK9(powerset(sK6(powerset(X0))))))
| ~ finite(X0) )
| ~ spl16_37
| ~ spl16_226 ),
inference(resolution,[],[f2068,f332]) ).
fof(f3917,plain,
( spl16_371
| ~ spl16_46
| ~ spl16_221 ),
inference(avatar_split_clause,[],[f2045,f2028,f387,f3915]) ).
fof(f2028,plain,
( spl16_221
<=> ! [X0] :
( empty(sK7(sK9(powerset(X0))))
| empty(sK9(powerset(X0)))
| element(sK9(sK7(sK9(powerset(X0)))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_221])]) ).
fof(f2045,plain,
( ! [X0,X1] :
( empty(sK9(powerset(powerset(X0))))
| empty(sK7(sK9(powerset(powerset(X0)))))
| element(X1,X0)
| ~ in(X1,sK9(sK7(sK9(powerset(powerset(X0)))))) )
| ~ spl16_46
| ~ spl16_221 ),
inference(resolution,[],[f2029,f388]) ).
fof(f2029,plain,
( ! [X0] :
( element(sK9(sK7(sK9(powerset(X0)))),X0)
| empty(sK9(powerset(X0)))
| empty(sK7(sK9(powerset(X0)))) )
| ~ spl16_221 ),
inference(avatar_component_clause,[],[f2028]) ).
fof(f3913,plain,
( spl16_370
| ~ spl16_46
| ~ spl16_220 ),
inference(avatar_split_clause,[],[f2039,f2024,f387,f3911]) ).
fof(f2024,plain,
( spl16_220
<=> ! [X0] :
( empty(sK6(sK9(powerset(X0))))
| empty(sK9(powerset(X0)))
| element(sK9(sK6(sK9(powerset(X0)))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_220])]) ).
fof(f2039,plain,
( ! [X0,X1] :
( empty(sK9(powerset(powerset(X0))))
| empty(sK6(sK9(powerset(powerset(X0)))))
| element(X1,X0)
| ~ in(X1,sK9(sK6(sK9(powerset(powerset(X0)))))) )
| ~ spl16_46
| ~ spl16_220 ),
inference(resolution,[],[f2025,f388]) ).
fof(f2025,plain,
( ! [X0] :
( element(sK9(sK6(sK9(powerset(X0)))),X0)
| empty(sK9(powerset(X0)))
| empty(sK6(sK9(powerset(X0)))) )
| ~ spl16_220 ),
inference(avatar_component_clause,[],[f2024]) ).
fof(f3909,plain,
( spl16_369
| ~ spl16_46
| ~ spl16_219 ),
inference(avatar_split_clause,[],[f2017,f1995,f387,f3907]) ).
fof(f1995,plain,
( spl16_219
<=> ! [X0] :
( empty(sK7(sK7(X0)))
| empty(sK7(X0))
| element(sK9(sK7(sK7(X0))),X0)
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_219])]) ).
fof(f2017,plain,
( ! [X0,X1] :
( empty(sK7(powerset(X0)))
| empty(sK7(sK7(powerset(X0))))
| empty(powerset(X0))
| element(X1,X0)
| ~ in(X1,sK9(sK7(sK7(powerset(X0))))) )
| ~ spl16_46
| ~ spl16_219 ),
inference(resolution,[],[f1996,f388]) ).
fof(f1996,plain,
( ! [X0] :
( element(sK9(sK7(sK7(X0))),X0)
| empty(sK7(X0))
| empty(sK7(sK7(X0)))
| empty(X0) )
| ~ spl16_219 ),
inference(avatar_component_clause,[],[f1995]) ).
fof(f3905,plain,
( spl16_368
| ~ spl16_46
| ~ spl16_218 ),
inference(avatar_split_clause,[],[f2011,f1991,f387,f3903]) ).
fof(f1991,plain,
( spl16_218
<=> ! [X0] :
( empty(sK7(sK6(X0)))
| empty(sK6(X0))
| element(sK9(sK7(sK6(X0))),X0)
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_218])]) ).
fof(f2011,plain,
( ! [X0,X1] :
( empty(sK6(powerset(X0)))
| empty(sK7(sK6(powerset(X0))))
| empty(powerset(X0))
| element(X1,X0)
| ~ in(X1,sK9(sK7(sK6(powerset(X0))))) )
| ~ spl16_46
| ~ spl16_218 ),
inference(resolution,[],[f1992,f388]) ).
fof(f1992,plain,
( ! [X0] :
( element(sK9(sK7(sK6(X0))),X0)
| empty(sK6(X0))
| empty(sK7(sK6(X0)))
| empty(X0) )
| ~ spl16_218 ),
inference(avatar_component_clause,[],[f1991]) ).
fof(f3901,plain,
( spl16_367
| ~ spl16_27
| ~ spl16_360 ),
inference(avatar_split_clause,[],[f3768,f3662,f282,f3899]) ).
fof(f3768,plain,
( ! [X0] :
( ~ in(X0,sK14)
| ~ in(cartesian_product2(sK14,sK14),X0) )
| ~ spl16_27
| ~ spl16_360 ),
inference(resolution,[],[f3663,f283]) ).
fof(f3897,plain,
( spl16_366
| ~ spl16_46
| ~ spl16_217 ),
inference(avatar_split_clause,[],[f2004,f1987,f387,f3895]) ).
fof(f1987,plain,
( spl16_217
<=> ! [X0] :
( empty(sK6(sK7(X0)))
| empty(sK7(X0))
| element(sK9(sK6(sK7(X0))),X0)
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_217])]) ).
fof(f2004,plain,
( ! [X0,X1] :
( empty(sK7(powerset(X0)))
| empty(sK6(sK7(powerset(X0))))
| empty(powerset(X0))
| element(X1,X0)
| ~ in(X1,sK9(sK6(sK7(powerset(X0))))) )
| ~ spl16_46
| ~ spl16_217 ),
inference(resolution,[],[f1988,f388]) ).
fof(f1988,plain,
( ! [X0] :
( element(sK9(sK6(sK7(X0))),X0)
| empty(sK7(X0))
| empty(sK6(sK7(X0)))
| empty(X0) )
| ~ spl16_217 ),
inference(avatar_component_clause,[],[f1987]) ).
fof(f3893,plain,
( spl16_365
| ~ spl16_46
| ~ spl16_216 ),
inference(avatar_split_clause,[],[f1998,f1983,f387,f3891]) ).
fof(f1983,plain,
( spl16_216
<=> ! [X0] :
( empty(sK6(sK6(X0)))
| empty(sK6(X0))
| element(sK9(sK6(sK6(X0))),X0)
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_216])]) ).
fof(f1998,plain,
( ! [X0,X1] :
( empty(sK6(powerset(X0)))
| empty(sK6(sK6(powerset(X0))))
| empty(powerset(X0))
| element(X1,X0)
| ~ in(X1,sK9(sK6(sK6(powerset(X0))))) )
| ~ spl16_46
| ~ spl16_216 ),
inference(resolution,[],[f1984,f388]) ).
fof(f1984,plain,
( ! [X0] :
( element(sK9(sK6(sK6(X0))),X0)
| empty(sK6(X0))
| empty(sK6(sK6(X0)))
| empty(X0) )
| ~ spl16_216 ),
inference(avatar_component_clause,[],[f1983]) ).
fof(f3680,plain,
( spl16_364
| ~ spl16_38
| ~ spl16_235 ),
inference(avatar_split_clause,[],[f2160,f2126,f335,f3678]) ).
fof(f2160,plain,
( ! [X0] :
( empty(sK7(powerset(X0)))
| empty(powerset(X0))
| empty(sK9(sK7(powerset(X0))))
| empty(X0)
| in(sK9(sK9(sK7(powerset(X0)))),X0) )
| ~ spl16_38
| ~ spl16_235 ),
inference(resolution,[],[f2127,f336]) ).
fof(f3676,plain,
( spl16_363
| ~ spl16_38
| ~ spl16_234 ),
inference(avatar_split_clause,[],[f2155,f2122,f335,f3674]) ).
fof(f2155,plain,
( ! [X0] :
( empty(sK6(powerset(X0)))
| empty(powerset(X0))
| empty(sK9(sK6(powerset(X0))))
| empty(X0)
| in(sK9(sK9(sK6(powerset(X0)))),X0) )
| ~ spl16_38
| ~ spl16_234 ),
inference(resolution,[],[f2123,f336]) ).
fof(f3672,plain,
( spl16_362
| ~ spl16_38
| ~ spl16_233 ),
inference(avatar_split_clause,[],[f2150,f2118,f335,f3670]) ).
fof(f2150,plain,
( ! [X0] :
( empty(sK9(powerset(powerset(X0))))
| empty(sK9(sK9(powerset(powerset(X0)))))
| empty(X0)
| in(sK9(sK9(sK9(powerset(powerset(X0))))),X0) )
| ~ spl16_38
| ~ spl16_233 ),
inference(resolution,[],[f2119,f336]) ).
fof(f3668,plain,
( spl16_361
| ~ spl16_34
| ~ spl16_232 ),
inference(avatar_split_clause,[],[f2114,f2103,f310,f3666]) ).
fof(f3666,plain,
( spl16_361
<=> ! [X0] :
( empty(sK9(powerset(sK9(powerset(powerset(X0))))))
| empty(sK9(powerset(powerset(X0))))
| subset(sK9(sK9(powerset(sK9(powerset(powerset(X0)))))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_361])]) ).
fof(f2114,plain,
( ! [X0] :
( empty(sK9(powerset(sK9(powerset(powerset(X0))))))
| empty(sK9(powerset(powerset(X0))))
| subset(sK9(sK9(powerset(sK9(powerset(powerset(X0)))))),X0) )
| ~ spl16_34
| ~ spl16_232 ),
inference(resolution,[],[f2104,f311]) ).
fof(f3664,plain,
( spl16_165
| spl16_360
| ~ spl16_38
| ~ spl16_322 ),
inference(avatar_split_clause,[],[f3303,f3188,f335,f3662,f1368]) ).
fof(f3188,plain,
( spl16_322
<=> ! [X0] :
( ~ in(X0,sK14)
| element(X0,cartesian_product2(sK14,sK14)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_322])]) ).
fof(f3303,plain,
( ! [X0] :
( ~ in(X0,sK14)
| empty(cartesian_product2(sK14,sK14))
| in(X0,cartesian_product2(sK14,sK14)) )
| ~ spl16_38
| ~ spl16_322 ),
inference(resolution,[],[f3189,f336]) ).
fof(f3189,plain,
( ! [X0] :
( element(X0,cartesian_product2(sK14,sK14))
| ~ in(X0,sK14) )
| ~ spl16_322 ),
inference(avatar_component_clause,[],[f3188]) ).
fof(f3660,plain,
( spl16_359
| ~ spl16_34
| ~ spl16_227 ),
inference(avatar_split_clause,[],[f2083,f2071,f310,f3658]) ).
fof(f3658,plain,
( spl16_359
<=> ! [X0] :
( empty(sK9(powerset(sK7(powerset(X0)))))
| empty(sK7(powerset(X0)))
| empty(powerset(X0))
| subset(sK9(sK9(powerset(sK7(powerset(X0))))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_359])]) ).
fof(f2083,plain,
( ! [X0] :
( empty(sK9(powerset(sK7(powerset(X0)))))
| empty(sK7(powerset(X0)))
| empty(powerset(X0))
| subset(sK9(sK9(powerset(sK7(powerset(X0))))),X0) )
| ~ spl16_34
| ~ spl16_227 ),
inference(resolution,[],[f2072,f311]) ).
fof(f3656,plain,
( spl16_358
| ~ spl16_34
| ~ spl16_226 ),
inference(avatar_split_clause,[],[f2077,f2067,f310,f3654]) ).
fof(f3654,plain,
( spl16_358
<=> ! [X0] :
( empty(sK9(powerset(sK6(powerset(X0)))))
| empty(sK6(powerset(X0)))
| empty(powerset(X0))
| subset(sK9(sK9(powerset(sK6(powerset(X0))))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_358])]) ).
fof(f2077,plain,
( ! [X0] :
( empty(sK9(powerset(sK6(powerset(X0)))))
| empty(sK6(powerset(X0)))
| empty(powerset(X0))
| subset(sK9(sK9(powerset(sK6(powerset(X0))))),X0) )
| ~ spl16_34
| ~ spl16_226 ),
inference(resolution,[],[f2068,f311]) ).
fof(f3652,plain,
( spl16_357
| ~ spl16_44
| ~ spl16_221 ),
inference(avatar_split_clause,[],[f2046,f2028,f374,f3650]) ).
fof(f2046,plain,
( ! [X0,X1] :
( empty(sK9(powerset(powerset(X0))))
| empty(sK7(sK9(powerset(powerset(X0)))))
| ~ empty(X0)
| ~ in(X1,sK9(sK7(sK9(powerset(powerset(X0)))))) )
| ~ spl16_44
| ~ spl16_221 ),
inference(resolution,[],[f2029,f375]) ).
fof(f3648,plain,
( spl16_356
| ~ spl16_44
| ~ spl16_220 ),
inference(avatar_split_clause,[],[f2040,f2024,f374,f3646]) ).
fof(f2040,plain,
( ! [X0,X1] :
( empty(sK9(powerset(powerset(X0))))
| empty(sK6(sK9(powerset(powerset(X0)))))
| ~ empty(X0)
| ~ in(X1,sK9(sK6(sK9(powerset(powerset(X0)))))) )
| ~ spl16_44
| ~ spl16_220 ),
inference(resolution,[],[f2025,f375]) ).
fof(f3644,plain,
( spl16_355
| ~ spl16_44
| ~ spl16_219 ),
inference(avatar_split_clause,[],[f2018,f1995,f374,f3642]) ).
fof(f2018,plain,
( ! [X0,X1] :
( empty(sK7(powerset(X0)))
| empty(sK7(sK7(powerset(X0))))
| empty(powerset(X0))
| ~ empty(X0)
| ~ in(X1,sK9(sK7(sK7(powerset(X0))))) )
| ~ spl16_44
| ~ spl16_219 ),
inference(resolution,[],[f1996,f375]) ).
fof(f3640,plain,
( spl16_354
| ~ spl16_44
| ~ spl16_218 ),
inference(avatar_split_clause,[],[f2012,f1991,f374,f3638]) ).
fof(f2012,plain,
( ! [X0,X1] :
( empty(sK6(powerset(X0)))
| empty(sK7(sK6(powerset(X0))))
| empty(powerset(X0))
| ~ empty(X0)
| ~ in(X1,sK9(sK7(sK6(powerset(X0))))) )
| ~ spl16_44
| ~ spl16_218 ),
inference(resolution,[],[f1992,f375]) ).
fof(f3636,plain,
( spl16_353
| ~ spl16_44
| ~ spl16_217 ),
inference(avatar_split_clause,[],[f2005,f1987,f374,f3634]) ).
fof(f2005,plain,
( ! [X0,X1] :
( empty(sK7(powerset(X0)))
| empty(sK6(sK7(powerset(X0))))
| empty(powerset(X0))
| ~ empty(X0)
| ~ in(X1,sK9(sK6(sK7(powerset(X0))))) )
| ~ spl16_44
| ~ spl16_217 ),
inference(resolution,[],[f1988,f375]) ).
fof(f3632,plain,
( spl16_352
| ~ spl16_44
| ~ spl16_216 ),
inference(avatar_split_clause,[],[f1999,f1983,f374,f3630]) ).
fof(f1999,plain,
( ! [X0,X1] :
( empty(sK6(powerset(X0)))
| empty(sK6(sK6(powerset(X0))))
| empty(powerset(X0))
| ~ empty(X0)
| ~ in(X1,sK9(sK6(sK6(powerset(X0))))) )
| ~ spl16_44
| ~ spl16_216 ),
inference(resolution,[],[f1984,f375]) ).
fof(f3628,plain,
( spl16_351
| ~ spl16_204
| ~ spl16_215 ),
inference(avatar_split_clause,[],[f1980,f1961,f1797,f3626]) ).
fof(f1980,plain,
( ! [X0,X1] :
( ~ empty(X0)
| empty(powerset(X0))
| empty(sK7(powerset(X0)))
| ~ empty(X1)
| sK9(powerset(X1)) = sK9(powerset(sK9(sK7(powerset(X0))))) )
| ~ spl16_204
| ~ spl16_215 ),
inference(resolution,[],[f1962,f1798]) ).
fof(f3624,plain,
( spl16_350
| ~ spl16_204
| ~ spl16_214 ),
inference(avatar_split_clause,[],[f1971,f1955,f1797,f3622]) ).
fof(f1971,plain,
( ! [X0,X1] :
( ~ empty(X0)
| empty(powerset(X0))
| empty(sK6(powerset(X0)))
| ~ empty(X1)
| sK9(powerset(X1)) = sK9(powerset(sK9(sK6(powerset(X0))))) )
| ~ spl16_204
| ~ spl16_214 ),
inference(resolution,[],[f1956,f1798]) ).
fof(f3580,plain,
( spl16_349
| ~ spl16_38
| ~ spl16_232 ),
inference(avatar_split_clause,[],[f2115,f2103,f335,f3578]) ).
fof(f2115,plain,
( ! [X0] :
( empty(sK9(powerset(sK9(powerset(X0)))))
| empty(sK9(powerset(X0)))
| empty(X0)
| in(sK9(sK9(powerset(sK9(powerset(X0))))),X0) )
| ~ spl16_38
| ~ spl16_232 ),
inference(resolution,[],[f2104,f336]) ).
fof(f3576,plain,
( spl16_348
| ~ spl16_37
| ~ spl16_221 ),
inference(avatar_split_clause,[],[f2047,f2028,f331,f3574]) ).
fof(f3574,plain,
( spl16_348
<=> ! [X0] :
( empty(sK9(powerset(powerset(X0))))
| empty(sK7(sK9(powerset(powerset(X0)))))
| finite(sK9(sK7(sK9(powerset(powerset(X0))))))
| ~ finite(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_348])]) ).
fof(f2047,plain,
( ! [X0] :
( empty(sK9(powerset(powerset(X0))))
| empty(sK7(sK9(powerset(powerset(X0)))))
| finite(sK9(sK7(sK9(powerset(powerset(X0))))))
| ~ finite(X0) )
| ~ spl16_37
| ~ spl16_221 ),
inference(resolution,[],[f2029,f332]) ).
fof(f3572,plain,
( ~ spl16_347
| ~ spl16_266
| ~ spl16_289 ),
inference(avatar_split_clause,[],[f3537,f2750,f2539,f3569]) ).
fof(f3569,plain,
( spl16_347
<=> in(cartesian_product2(sK14,sK14),the_InternalRel(sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_347])]) ).
fof(f2750,plain,
( spl16_289
<=> ! [X0] :
( ~ in(X0,the_InternalRel(sK0))
| ~ in(cartesian_product2(sK14,sK14),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_289])]) ).
fof(f3537,plain,
( ~ in(cartesian_product2(sK14,sK14),the_InternalRel(sK0))
| ~ spl16_266
| ~ spl16_289 ),
inference(duplicate_literal_removal,[],[f3534]) ).
fof(f3534,plain,
( ~ in(cartesian_product2(sK14,sK14),the_InternalRel(sK0))
| ~ in(cartesian_product2(sK14,sK14),the_InternalRel(sK0))
| ~ spl16_266
| ~ spl16_289 ),
inference(resolution,[],[f2751,f2540]) ).
fof(f2751,plain,
( ! [X0] :
( ~ in(cartesian_product2(sK14,sK14),X0)
| ~ in(X0,the_InternalRel(sK0)) )
| ~ spl16_289 ),
inference(avatar_component_clause,[],[f2750]) ).
fof(f3567,plain,
( spl16_346
| ~ spl16_37
| ~ spl16_220 ),
inference(avatar_split_clause,[],[f2041,f2024,f331,f3565]) ).
fof(f3565,plain,
( spl16_346
<=> ! [X0] :
( empty(sK9(powerset(powerset(X0))))
| empty(sK6(sK9(powerset(powerset(X0)))))
| finite(sK9(sK6(sK9(powerset(powerset(X0))))))
| ~ finite(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_346])]) ).
fof(f2041,plain,
( ! [X0] :
( empty(sK9(powerset(powerset(X0))))
| empty(sK6(sK9(powerset(powerset(X0)))))
| finite(sK9(sK6(sK9(powerset(powerset(X0))))))
| ~ finite(X0) )
| ~ spl16_37
| ~ spl16_220 ),
inference(resolution,[],[f2025,f332]) ).
fof(f3563,plain,
( spl16_345
| ~ spl16_37
| ~ spl16_219 ),
inference(avatar_split_clause,[],[f2019,f1995,f331,f3561]) ).
fof(f3561,plain,
( spl16_345
<=> ! [X0] :
( empty(sK7(powerset(X0)))
| empty(sK7(sK7(powerset(X0))))
| empty(powerset(X0))
| finite(sK9(sK7(sK7(powerset(X0)))))
| ~ finite(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_345])]) ).
fof(f2019,plain,
( ! [X0] :
( empty(sK7(powerset(X0)))
| empty(sK7(sK7(powerset(X0))))
| empty(powerset(X0))
| finite(sK9(sK7(sK7(powerset(X0)))))
| ~ finite(X0) )
| ~ spl16_37
| ~ spl16_219 ),
inference(resolution,[],[f1996,f332]) ).
fof(f3559,plain,
( spl16_344
| ~ spl16_37
| ~ spl16_218 ),
inference(avatar_split_clause,[],[f2013,f1991,f331,f3557]) ).
fof(f3557,plain,
( spl16_344
<=> ! [X0] :
( empty(sK6(powerset(X0)))
| empty(sK7(sK6(powerset(X0))))
| empty(powerset(X0))
| finite(sK9(sK7(sK6(powerset(X0)))))
| ~ finite(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_344])]) ).
fof(f2013,plain,
( ! [X0] :
( empty(sK6(powerset(X0)))
| empty(sK7(sK6(powerset(X0))))
| empty(powerset(X0))
| finite(sK9(sK7(sK6(powerset(X0)))))
| ~ finite(X0) )
| ~ spl16_37
| ~ spl16_218 ),
inference(resolution,[],[f1992,f332]) ).
fof(f3555,plain,
( spl16_343
| ~ spl16_37
| ~ spl16_217 ),
inference(avatar_split_clause,[],[f2006,f1987,f331,f3553]) ).
fof(f3553,plain,
( spl16_343
<=> ! [X0] :
( empty(sK7(powerset(X0)))
| empty(sK6(sK7(powerset(X0))))
| empty(powerset(X0))
| finite(sK9(sK6(sK7(powerset(X0)))))
| ~ finite(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_343])]) ).
fof(f2006,plain,
( ! [X0] :
( empty(sK7(powerset(X0)))
| empty(sK6(sK7(powerset(X0))))
| empty(powerset(X0))
| finite(sK9(sK6(sK7(powerset(X0)))))
| ~ finite(X0) )
| ~ spl16_37
| ~ spl16_217 ),
inference(resolution,[],[f1988,f332]) ).
fof(f3551,plain,
( spl16_342
| ~ spl16_37
| ~ spl16_216 ),
inference(avatar_split_clause,[],[f2000,f1983,f331,f3549]) ).
fof(f3549,plain,
( spl16_342
<=> ! [X0] :
( empty(sK6(powerset(X0)))
| empty(sK6(sK6(powerset(X0))))
| empty(powerset(X0))
| finite(sK9(sK6(sK6(powerset(X0)))))
| ~ finite(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_342])]) ).
fof(f2000,plain,
( ! [X0] :
( empty(sK6(powerset(X0)))
| empty(sK6(sK6(powerset(X0))))
| empty(powerset(X0))
| finite(sK9(sK6(sK6(powerset(X0)))))
| ~ finite(X0) )
| ~ spl16_37
| ~ spl16_216 ),
inference(resolution,[],[f1984,f332]) ).
fof(f3547,plain,
( spl16_341
| ~ spl16_204
| ~ spl16_213 ),
inference(avatar_split_clause,[],[f1952,f1942,f1797,f3545]) ).
fof(f1952,plain,
( ! [X0,X1] :
( empty(sK9(powerset(powerset(X0))))
| ~ empty(X0)
| ~ empty(X1)
| sK9(powerset(X1)) = sK9(powerset(sK9(sK9(powerset(powerset(X0)))))) )
| ~ spl16_204
| ~ spl16_213 ),
inference(resolution,[],[f1943,f1798]) ).
fof(f3443,plain,
( spl16_289
| ~ spl16_27
| ~ spl16_266 ),
inference(avatar_split_clause,[],[f2543,f2539,f282,f2750]) ).
fof(f2543,plain,
( ! [X0] :
( ~ in(X0,the_InternalRel(sK0))
| ~ in(cartesian_product2(sK14,sK14),X0) )
| ~ spl16_27
| ~ spl16_266 ),
inference(resolution,[],[f2540,f283]) ).
fof(f3442,plain,
( spl16_340
| ~ spl16_27
| ~ spl16_237 ),
inference(avatar_split_clause,[],[f2171,f2134,f282,f3440]) ).
fof(f3440,plain,
( spl16_340
<=> ! [X0,X1] :
( ~ rel_str(X0)
| ~ rel_str(X1)
| empty(the_InternalRel(X0))
| empty(the_InternalRel(X1))
| ~ subrelstr(X0,X1)
| ~ in(the_InternalRel(X1),sK9(the_InternalRel(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_340])]) ).
fof(f2171,plain,
( ! [X0,X1] :
( ~ rel_str(X0)
| ~ rel_str(X1)
| empty(the_InternalRel(X0))
| empty(the_InternalRel(X1))
| ~ subrelstr(X0,X1)
| ~ in(the_InternalRel(X1),sK9(the_InternalRel(X0))) )
| ~ spl16_27
| ~ spl16_237 ),
inference(resolution,[],[f2135,f283]) ).
fof(f3438,plain,
( spl16_339
| ~ spl16_27
| ~ spl16_236 ),
inference(avatar_split_clause,[],[f2164,f2130,f282,f3436]) ).
fof(f3436,plain,
( spl16_339
<=> ! [X0,X1] :
( ~ rel_str(X0)
| ~ rel_str(X1)
| empty(the_carrier(X0))
| empty(the_carrier(X1))
| ~ subrelstr(X0,X1)
| ~ in(the_carrier(X1),sK9(the_carrier(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_339])]) ).
fof(f2164,plain,
( ! [X0,X1] :
( ~ rel_str(X0)
| ~ rel_str(X1)
| empty(the_carrier(X0))
| empty(the_carrier(X1))
| ~ subrelstr(X0,X1)
| ~ in(the_carrier(X1),sK9(the_carrier(X0))) )
| ~ spl16_27
| ~ spl16_236 ),
inference(resolution,[],[f2131,f283]) ).
fof(f3434,plain,
( spl16_338
| ~ spl16_34
| ~ spl16_221 ),
inference(avatar_split_clause,[],[f2048,f2028,f310,f3432]) ).
fof(f3432,plain,
( spl16_338
<=> ! [X0] :
( empty(sK9(powerset(powerset(X0))))
| empty(sK7(sK9(powerset(powerset(X0)))))
| subset(sK9(sK7(sK9(powerset(powerset(X0))))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_338])]) ).
fof(f2048,plain,
( ! [X0] :
( empty(sK9(powerset(powerset(X0))))
| empty(sK7(sK9(powerset(powerset(X0)))))
| subset(sK9(sK7(sK9(powerset(powerset(X0))))),X0) )
| ~ spl16_34
| ~ spl16_221 ),
inference(resolution,[],[f2029,f311]) ).
fof(f3430,plain,
( spl16_337
| ~ spl16_34
| ~ spl16_220 ),
inference(avatar_split_clause,[],[f2042,f2024,f310,f3428]) ).
fof(f3428,plain,
( spl16_337
<=> ! [X0] :
( empty(sK9(powerset(powerset(X0))))
| empty(sK6(sK9(powerset(powerset(X0)))))
| subset(sK9(sK6(sK9(powerset(powerset(X0))))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_337])]) ).
fof(f2042,plain,
( ! [X0] :
( empty(sK9(powerset(powerset(X0))))
| empty(sK6(sK9(powerset(powerset(X0)))))
| subset(sK9(sK6(sK9(powerset(powerset(X0))))),X0) )
| ~ spl16_34
| ~ spl16_220 ),
inference(resolution,[],[f2025,f311]) ).
fof(f3426,plain,
( spl16_336
| ~ spl16_34
| ~ spl16_219 ),
inference(avatar_split_clause,[],[f2020,f1995,f310,f3424]) ).
fof(f3424,plain,
( spl16_336
<=> ! [X0] :
( empty(sK7(powerset(X0)))
| empty(sK7(sK7(powerset(X0))))
| empty(powerset(X0))
| subset(sK9(sK7(sK7(powerset(X0)))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_336])]) ).
fof(f2020,plain,
( ! [X0] :
( empty(sK7(powerset(X0)))
| empty(sK7(sK7(powerset(X0))))
| empty(powerset(X0))
| subset(sK9(sK7(sK7(powerset(X0)))),X0) )
| ~ spl16_34
| ~ spl16_219 ),
inference(resolution,[],[f1996,f311]) ).
fof(f3422,plain,
( spl16_335
| ~ spl16_34
| ~ spl16_218 ),
inference(avatar_split_clause,[],[f2014,f1991,f310,f3420]) ).
fof(f3420,plain,
( spl16_335
<=> ! [X0] :
( empty(sK6(powerset(X0)))
| empty(sK7(sK6(powerset(X0))))
| empty(powerset(X0))
| subset(sK9(sK7(sK6(powerset(X0)))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_335])]) ).
fof(f2014,plain,
( ! [X0] :
( empty(sK6(powerset(X0)))
| empty(sK7(sK6(powerset(X0))))
| empty(powerset(X0))
| subset(sK9(sK7(sK6(powerset(X0)))),X0) )
| ~ spl16_34
| ~ spl16_218 ),
inference(resolution,[],[f1992,f311]) ).
fof(f3418,plain,
( spl16_334
| ~ spl16_34
| ~ spl16_217 ),
inference(avatar_split_clause,[],[f2007,f1987,f310,f3416]) ).
fof(f3416,plain,
( spl16_334
<=> ! [X0] :
( empty(sK7(powerset(X0)))
| empty(sK6(sK7(powerset(X0))))
| empty(powerset(X0))
| subset(sK9(sK6(sK7(powerset(X0)))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_334])]) ).
fof(f2007,plain,
( ! [X0] :
( empty(sK7(powerset(X0)))
| empty(sK6(sK7(powerset(X0))))
| empty(powerset(X0))
| subset(sK9(sK6(sK7(powerset(X0)))),X0) )
| ~ spl16_34
| ~ spl16_217 ),
inference(resolution,[],[f1988,f311]) ).
fof(f3414,plain,
( spl16_333
| ~ spl16_34
| ~ spl16_216 ),
inference(avatar_split_clause,[],[f2001,f1983,f310,f3412]) ).
fof(f3412,plain,
( spl16_333
<=> ! [X0] :
( empty(sK6(powerset(X0)))
| empty(sK6(sK6(powerset(X0))))
| empty(powerset(X0))
| subset(sK9(sK6(sK6(powerset(X0)))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_333])]) ).
fof(f2001,plain,
( ! [X0] :
( empty(sK6(powerset(X0)))
| empty(sK6(sK6(powerset(X0))))
| empty(powerset(X0))
| subset(sK9(sK6(sK6(powerset(X0)))),X0) )
| ~ spl16_34
| ~ spl16_216 ),
inference(resolution,[],[f1984,f311]) ).
fof(f3410,plain,
( spl16_332
| ~ spl16_197
| ~ spl16_215 ),
inference(avatar_split_clause,[],[f1979,f1961,f1702,f3408]) ).
fof(f1979,plain,
( ! [X0] :
( ~ empty(X0)
| empty(powerset(X0))
| empty(sK7(powerset(X0)))
| sK14 = sK9(powerset(sK9(powerset(sK9(sK7(powerset(X0))))))) )
| ~ spl16_197
| ~ spl16_215 ),
inference(resolution,[],[f1962,f1703]) ).
fof(f3405,plain,
( spl16_202
| ~ spl16_28
| ~ spl16_266 ),
inference(avatar_split_clause,[],[f2542,f2539,f286,f1782]) ).
fof(f1782,plain,
( spl16_202
<=> ! [X0] :
( ~ in(X0,the_InternalRel(sK0))
| element(X0,cartesian_product2(sK14,sK14)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_202])]) ).
fof(f2542,plain,
( ! [X0] :
( ~ in(X0,the_InternalRel(sK0))
| element(X0,cartesian_product2(sK14,sK14)) )
| ~ spl16_28
| ~ spl16_266 ),
inference(resolution,[],[f2540,f287]) ).
fof(f3404,plain,
( spl16_331
| ~ spl16_148
| ~ spl16_215 ),
inference(avatar_split_clause,[],[f1978,f1961,f1206,f3402]) ).
fof(f1978,plain,
( ! [X0,X1] :
( ~ empty(X0)
| empty(powerset(X0))
| empty(sK7(powerset(X0)))
| sK9(powerset(X1)) = sK9(sK7(powerset(X0)))
| ~ empty(X1) )
| ~ spl16_148
| ~ spl16_215 ),
inference(resolution,[],[f1962,f1207]) ).
fof(f3400,plain,
( spl16_330
| ~ spl16_197
| ~ spl16_214 ),
inference(avatar_split_clause,[],[f1970,f1955,f1702,f3398]) ).
fof(f1970,plain,
( ! [X0] :
( ~ empty(X0)
| empty(powerset(X0))
| empty(sK6(powerset(X0)))
| sK14 = sK9(powerset(sK9(powerset(sK9(sK6(powerset(X0))))))) )
| ~ spl16_197
| ~ spl16_214 ),
inference(resolution,[],[f1956,f1703]) ).
fof(f3396,plain,
( spl16_329
| ~ spl16_148
| ~ spl16_214 ),
inference(avatar_split_clause,[],[f1969,f1955,f1206,f3394]) ).
fof(f1969,plain,
( ! [X0,X1] :
( ~ empty(X0)
| empty(powerset(X0))
| empty(sK6(powerset(X0)))
| sK9(powerset(X1)) = sK9(sK6(powerset(X0)))
| ~ empty(X1) )
| ~ spl16_148
| ~ spl16_214 ),
inference(resolution,[],[f1956,f1207]) ).
fof(f3392,plain,
( spl16_328
| ~ spl16_204
| ~ spl16_208 ),
inference(avatar_split_clause,[],[f1845,f1820,f1797,f3390]) ).
fof(f1845,plain,
( ! [X0,X1] :
( ~ rel_str(sK8(X0))
| ~ rel_str(X0)
| ~ empty(the_InternalRel(X0))
| ~ empty(X1)
| sK9(powerset(X1)) = sK9(powerset(the_InternalRel(sK8(X0)))) )
| ~ spl16_204
| ~ spl16_208 ),
inference(resolution,[],[f1821,f1798]) ).
fof(f3388,plain,
( spl16_327
| ~ spl16_204
| ~ spl16_207 ),
inference(avatar_split_clause,[],[f1836,f1816,f1797,f3386]) ).
fof(f1836,plain,
( ! [X0,X1] :
( ~ rel_str(sK8(X0))
| ~ rel_str(X0)
| ~ empty(the_carrier(X0))
| ~ empty(X1)
| sK9(powerset(X1)) = sK9(powerset(the_carrier(sK8(X0)))) )
| ~ spl16_204
| ~ spl16_207 ),
inference(resolution,[],[f1817,f1798]) ).
fof(f3307,plain,
( spl16_326
| ~ spl16_38
| ~ spl16_221 ),
inference(avatar_split_clause,[],[f2049,f2028,f335,f3305]) ).
fof(f2049,plain,
( ! [X0] :
( empty(sK9(powerset(X0)))
| empty(sK7(sK9(powerset(X0))))
| empty(X0)
| in(sK9(sK7(sK9(powerset(X0)))),X0) )
| ~ spl16_38
| ~ spl16_221 ),
inference(resolution,[],[f2029,f336]) ).
fof(f3302,plain,
( spl16_325
| ~ spl16_38
| ~ spl16_220 ),
inference(avatar_split_clause,[],[f2043,f2024,f335,f3300]) ).
fof(f2043,plain,
( ! [X0] :
( empty(sK9(powerset(X0)))
| empty(sK6(sK9(powerset(X0))))
| empty(X0)
| in(sK9(sK6(sK9(powerset(X0)))),X0) )
| ~ spl16_38
| ~ spl16_220 ),
inference(resolution,[],[f2025,f336]) ).
fof(f3298,plain,
( spl16_324
| ~ spl16_197
| ~ spl16_213 ),
inference(avatar_split_clause,[],[f1951,f1942,f1702,f3296]) ).
fof(f1951,plain,
( ! [X0] :
( empty(sK9(powerset(powerset(X0))))
| ~ empty(X0)
| sK14 = sK9(powerset(sK9(powerset(sK9(sK9(powerset(powerset(X0)))))))) )
| ~ spl16_197
| ~ spl16_213 ),
inference(resolution,[],[f1943,f1703]) ).
fof(f3294,plain,
( spl16_323
| ~ spl16_148
| ~ spl16_213 ),
inference(avatar_split_clause,[],[f1950,f1942,f1206,f3292]) ).
fof(f1950,plain,
( ! [X0,X1] :
( empty(sK9(powerset(powerset(X0))))
| ~ empty(X0)
| sK9(powerset(X1)) = sK9(sK9(powerset(powerset(X0))))
| ~ empty(X1) )
| ~ spl16_148
| ~ spl16_213 ),
inference(resolution,[],[f1943,f1207]) ).
fof(f3190,plain,
( spl16_322
| ~ spl16_111
| ~ spl16_294 ),
inference(avatar_split_clause,[],[f2908,f2894,f803,f3188]) ).
fof(f2894,plain,
( spl16_294
<=> sK14 = sK10(sK14,sK14) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_294])]) ).
fof(f2908,plain,
( ! [X0] :
( ~ in(X0,sK14)
| element(X0,cartesian_product2(sK14,sK14)) )
| ~ spl16_111
| ~ spl16_294 ),
inference(superposition,[],[f804,f2896]) ).
fof(f2896,plain,
( sK14 = sK10(sK14,sK14)
| ~ spl16_294 ),
inference(avatar_component_clause,[],[f2894]) ).
fof(f3177,plain,
( spl16_321
| ~ spl16_38
| ~ spl16_227 ),
inference(avatar_split_clause,[],[f2085,f2071,f335,f3175]) ).
fof(f2085,plain,
( ! [X0] :
( empty(sK9(powerset(sK7(X0))))
| empty(sK7(X0))
| empty(X0)
| in(sK9(sK9(powerset(sK7(X0)))),X0) )
| ~ spl16_38
| ~ spl16_227 ),
inference(duplicate_literal_removal,[],[f2084]) ).
fof(f2084,plain,
( ! [X0] :
( empty(sK9(powerset(sK7(X0))))
| empty(sK7(X0))
| empty(X0)
| empty(X0)
| in(sK9(sK9(powerset(sK7(X0)))),X0) )
| ~ spl16_38
| ~ spl16_227 ),
inference(resolution,[],[f2072,f336]) ).
fof(f3173,plain,
( spl16_320
| ~ spl16_38
| ~ spl16_226 ),
inference(avatar_split_clause,[],[f2079,f2067,f335,f3171]) ).
fof(f2079,plain,
( ! [X0] :
( empty(sK9(powerset(sK6(X0))))
| empty(sK6(X0))
| empty(X0)
| in(sK9(sK9(powerset(sK6(X0)))),X0) )
| ~ spl16_38
| ~ spl16_226 ),
inference(duplicate_literal_removal,[],[f2078]) ).
fof(f2078,plain,
( ! [X0] :
( empty(sK9(powerset(sK6(X0))))
| empty(sK6(X0))
| empty(X0)
| empty(X0)
| in(sK9(sK9(powerset(sK6(X0)))),X0) )
| ~ spl16_38
| ~ spl16_226 ),
inference(resolution,[],[f2068,f336]) ).
fof(f3169,plain,
( spl16_319
| ~ spl16_142
| ~ spl16_215 ),
inference(avatar_split_clause,[],[f1977,f1961,f1176,f3167]) ).
fof(f1977,plain,
( ! [X0] :
( ~ empty(X0)
| empty(powerset(X0))
| empty(sK7(powerset(X0)))
| sK14 = sK9(powerset(sK9(sK7(powerset(X0))))) )
| ~ spl16_142
| ~ spl16_215 ),
inference(resolution,[],[f1962,f1177]) ).
fof(f3165,plain,
( spl16_318
| ~ spl16_36
| ~ spl16_215 ),
inference(avatar_split_clause,[],[f1975,f1961,f318,f3163]) ).
fof(f1975,plain,
( ! [X0,X1] :
( ~ empty(X0)
| empty(powerset(X0))
| empty(sK7(powerset(X0)))
| sK9(sK7(powerset(X0))) = X1
| ~ empty(X1) )
| ~ spl16_36
| ~ spl16_215 ),
inference(resolution,[],[f1962,f319]) ).
fof(f3161,plain,
( spl16_317
| ~ spl16_142
| ~ spl16_214 ),
inference(avatar_split_clause,[],[f1968,f1955,f1176,f3159]) ).
fof(f1968,plain,
( ! [X0] :
( ~ empty(X0)
| empty(powerset(X0))
| empty(sK6(powerset(X0)))
| sK14 = sK9(powerset(sK9(sK6(powerset(X0))))) )
| ~ spl16_142
| ~ spl16_214 ),
inference(resolution,[],[f1956,f1177]) ).
fof(f3157,plain,
( spl16_316
| ~ spl16_36
| ~ spl16_214 ),
inference(avatar_split_clause,[],[f1966,f1955,f318,f3155]) ).
fof(f1966,plain,
( ! [X0,X1] :
( ~ empty(X0)
| empty(powerset(X0))
| empty(sK6(powerset(X0)))
| sK9(sK6(powerset(X0))) = X1
| ~ empty(X1) )
| ~ spl16_36
| ~ spl16_214 ),
inference(resolution,[],[f1956,f319]) ).
fof(f3153,plain,
( spl16_315
| ~ spl16_197
| ~ spl16_208 ),
inference(avatar_split_clause,[],[f1844,f1820,f1702,f3151]) ).
fof(f1844,plain,
( ! [X0] :
( ~ rel_str(sK8(X0))
| ~ rel_str(X0)
| ~ empty(the_InternalRel(X0))
| sK14 = sK9(powerset(sK9(powerset(the_InternalRel(sK8(X0)))))) )
| ~ spl16_197
| ~ spl16_208 ),
inference(resolution,[],[f1821,f1703]) ).
fof(f3145,plain,
( spl16_314
| ~ spl16_148
| ~ spl16_208 ),
inference(avatar_split_clause,[],[f1843,f1820,f1206,f3143]) ).
fof(f1843,plain,
( ! [X0,X1] :
( ~ rel_str(sK8(X0))
| ~ rel_str(X0)
| ~ empty(the_InternalRel(X0))
| sK9(powerset(X1)) = the_InternalRel(sK8(X0))
| ~ empty(X1) )
| ~ spl16_148
| ~ spl16_208 ),
inference(resolution,[],[f1821,f1207]) ).
fof(f3141,plain,
( spl16_313
| ~ spl16_197
| ~ spl16_207 ),
inference(avatar_split_clause,[],[f1835,f1816,f1702,f3139]) ).
fof(f1835,plain,
( ! [X0] :
( ~ rel_str(sK8(X0))
| ~ rel_str(X0)
| ~ empty(the_carrier(X0))
| sK14 = sK9(powerset(sK9(powerset(the_carrier(sK8(X0)))))) )
| ~ spl16_197
| ~ spl16_207 ),
inference(resolution,[],[f1817,f1703]) ).
fof(f3137,plain,
( spl16_312
| ~ spl16_148
| ~ spl16_207 ),
inference(avatar_split_clause,[],[f1834,f1816,f1206,f3135]) ).
fof(f1834,plain,
( ! [X0,X1] :
( ~ rel_str(sK8(X0))
| ~ rel_str(X0)
| ~ empty(the_carrier(X0))
| sK9(powerset(X1)) = the_carrier(sK8(X0))
| ~ empty(X1) )
| ~ spl16_148
| ~ spl16_207 ),
inference(resolution,[],[f1817,f1207]) ).
fof(f3108,plain,
( spl16_311
| ~ spl16_27
| ~ spl16_223 ),
inference(avatar_split_clause,[],[f2055,f2036,f282,f3106]) ).
fof(f3106,plain,
( spl16_311
<=> ! [X0,X1] :
( empty(cartesian_product2(X0,X1))
| empty(sK10(X0,X1))
| ~ in(cartesian_product2(X0,X1),sK9(sK10(X0,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_311])]) ).
fof(f2036,plain,
( spl16_223
<=> ! [X0,X1] :
( empty(sK10(X0,X1))
| empty(cartesian_product2(X0,X1))
| in(sK9(sK10(X0,X1)),cartesian_product2(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_223])]) ).
fof(f2055,plain,
( ! [X0,X1] :
( empty(cartesian_product2(X0,X1))
| empty(sK10(X0,X1))
| ~ in(cartesian_product2(X0,X1),sK9(sK10(X0,X1))) )
| ~ spl16_27
| ~ spl16_223 ),
inference(resolution,[],[f2037,f283]) ).
fof(f2037,plain,
( ! [X0,X1] :
( in(sK9(sK10(X0,X1)),cartesian_product2(X0,X1))
| empty(cartesian_product2(X0,X1))
| empty(sK10(X0,X1)) )
| ~ spl16_223 ),
inference(avatar_component_clause,[],[f2036]) ).
fof(f3104,plain,
( spl16_310
| ~ spl16_27
| ~ spl16_222 ),
inference(avatar_split_clause,[],[f2052,f2032,f282,f3102]) ).
fof(f3102,plain,
( spl16_310
<=> ! [X0,X1] :
( empty(cartesian_product2(X0,X1))
| empty(sK11(X0,X1))
| ~ in(cartesian_product2(X0,X1),sK9(sK11(X0,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_310])]) ).
fof(f2032,plain,
( spl16_222
<=> ! [X0,X1] :
( empty(sK11(X0,X1))
| empty(cartesian_product2(X0,X1))
| in(sK9(sK11(X0,X1)),cartesian_product2(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_222])]) ).
fof(f2052,plain,
( ! [X0,X1] :
( empty(cartesian_product2(X0,X1))
| empty(sK11(X0,X1))
| ~ in(cartesian_product2(X0,X1),sK9(sK11(X0,X1))) )
| ~ spl16_27
| ~ spl16_222 ),
inference(resolution,[],[f2033,f283]) ).
fof(f2033,plain,
( ! [X0,X1] :
( in(sK9(sK11(X0,X1)),cartesian_product2(X0,X1))
| empty(cartesian_product2(X0,X1))
| empty(sK11(X0,X1)) )
| ~ spl16_222 ),
inference(avatar_component_clause,[],[f2032]) ).
fof(f3100,plain,
( spl16_309
| ~ spl16_142
| ~ spl16_213 ),
inference(avatar_split_clause,[],[f1949,f1942,f1176,f3098]) ).
fof(f1949,plain,
( ! [X0] :
( empty(sK9(powerset(powerset(X0))))
| ~ empty(X0)
| sK14 = sK9(powerset(sK9(sK9(powerset(powerset(X0)))))) )
| ~ spl16_142
| ~ spl16_213 ),
inference(resolution,[],[f1943,f1177]) ).
fof(f3095,plain,
( spl16_308
| ~ spl16_36
| ~ spl16_213 ),
inference(avatar_split_clause,[],[f1947,f1942,f318,f3093]) ).
fof(f1947,plain,
( ! [X0,X1] :
( empty(sK9(powerset(powerset(X0))))
| ~ empty(X0)
| sK9(sK9(powerset(powerset(X0)))) = X1
| ~ empty(X1) )
| ~ spl16_36
| ~ spl16_213 ),
inference(resolution,[],[f1943,f319]) ).
fof(f2974,plain,
( spl16_307
| ~ spl16_67
| ~ spl16_294 ),
inference(avatar_split_clause,[],[f2906,f2894,f516,f2971]) ).
fof(f2971,plain,
( spl16_307
<=> relation_of2_as_subset(sK14,sK14,sK14) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_307])]) ).
fof(f516,plain,
( spl16_67
<=> ! [X0,X1] : relation_of2_as_subset(sK10(X0,X1),X0,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_67])]) ).
fof(f2906,plain,
( relation_of2_as_subset(sK14,sK14,sK14)
| ~ spl16_67
| ~ spl16_294 ),
inference(superposition,[],[f517,f2896]) ).
fof(f517,plain,
( ! [X0,X1] : relation_of2_as_subset(sK10(X0,X1),X0,X1)
| ~ spl16_67 ),
inference(avatar_component_clause,[],[f516]) ).
fof(f2966,plain,
( spl16_306
| ~ spl16_38
| ~ spl16_219 ),
inference(avatar_split_clause,[],[f2022,f1995,f335,f2964]) ).
fof(f2022,plain,
( ! [X0] :
( empty(sK7(X0))
| empty(sK7(sK7(X0)))
| empty(X0)
| in(sK9(sK7(sK7(X0))),X0) )
| ~ spl16_38
| ~ spl16_219 ),
inference(duplicate_literal_removal,[],[f2021]) ).
fof(f2021,plain,
( ! [X0] :
( empty(sK7(X0))
| empty(sK7(sK7(X0)))
| empty(X0)
| empty(X0)
| in(sK9(sK7(sK7(X0))),X0) )
| ~ spl16_38
| ~ spl16_219 ),
inference(resolution,[],[f1996,f336]) ).
fof(f2962,plain,
( spl16_305
| ~ spl16_38
| ~ spl16_218 ),
inference(avatar_split_clause,[],[f2016,f1991,f335,f2960]) ).
fof(f2016,plain,
( ! [X0] :
( empty(sK6(X0))
| empty(sK7(sK6(X0)))
| empty(X0)
| in(sK9(sK7(sK6(X0))),X0) )
| ~ spl16_38
| ~ spl16_218 ),
inference(duplicate_literal_removal,[],[f2015]) ).
fof(f2015,plain,
( ! [X0] :
( empty(sK6(X0))
| empty(sK7(sK6(X0)))
| empty(X0)
| empty(X0)
| in(sK9(sK7(sK6(X0))),X0) )
| ~ spl16_38
| ~ spl16_218 ),
inference(resolution,[],[f1992,f336]) ).
fof(f2958,plain,
( spl16_304
| ~ spl16_38
| ~ spl16_217 ),
inference(avatar_split_clause,[],[f2009,f1987,f335,f2956]) ).
fof(f2009,plain,
( ! [X0] :
( empty(sK7(X0))
| empty(sK6(sK7(X0)))
| empty(X0)
| in(sK9(sK6(sK7(X0))),X0) )
| ~ spl16_38
| ~ spl16_217 ),
inference(duplicate_literal_removal,[],[f2008]) ).
fof(f2008,plain,
( ! [X0] :
( empty(sK7(X0))
| empty(sK6(sK7(X0)))
| empty(X0)
| empty(X0)
| in(sK9(sK6(sK7(X0))),X0) )
| ~ spl16_38
| ~ spl16_217 ),
inference(resolution,[],[f1988,f336]) ).
fof(f2954,plain,
( spl16_303
| ~ spl16_38
| ~ spl16_216 ),
inference(avatar_split_clause,[],[f2003,f1983,f335,f2952]) ).
fof(f2003,plain,
( ! [X0] :
( empty(sK6(X0))
| empty(sK6(sK6(X0)))
| empty(X0)
| in(sK9(sK6(sK6(X0))),X0) )
| ~ spl16_38
| ~ spl16_216 ),
inference(duplicate_literal_removal,[],[f2002]) ).
fof(f2002,plain,
( ! [X0] :
( empty(sK6(X0))
| empty(sK6(sK6(X0)))
| empty(X0)
| empty(X0)
| in(sK9(sK6(sK6(X0))),X0) )
| ~ spl16_38
| ~ spl16_216 ),
inference(resolution,[],[f1984,f336]) ).
fof(f2950,plain,
( spl16_302
| ~ spl16_23
| ~ spl16_57
| ~ spl16_215 ),
inference(avatar_split_clause,[],[f1981,f1961,f469,f263,f2948]) ).
fof(f1981,plain,
( ! [X0] :
( sK14 = sK9(sK7(powerset(X0)))
| ~ empty(X0)
| empty(powerset(X0))
| empty(sK7(powerset(X0))) )
| ~ spl16_23
| ~ spl16_57
| ~ spl16_215 ),
inference(forward_demodulation,[],[f1974,f471]) ).
fof(f1974,plain,
( ! [X0] :
( ~ empty(X0)
| empty(powerset(X0))
| empty(sK7(powerset(X0)))
| empty_set = sK9(sK7(powerset(X0))) )
| ~ spl16_23
| ~ spl16_215 ),
inference(resolution,[],[f1962,f264]) ).
fof(f2946,plain,
( spl16_301
| ~ spl16_23
| ~ spl16_57
| ~ spl16_214 ),
inference(avatar_split_clause,[],[f1972,f1955,f469,f263,f2944]) ).
fof(f1972,plain,
( ! [X0] :
( sK14 = sK9(sK6(powerset(X0)))
| ~ empty(X0)
| empty(powerset(X0))
| empty(sK6(powerset(X0))) )
| ~ spl16_23
| ~ spl16_57
| ~ spl16_214 ),
inference(forward_demodulation,[],[f1965,f471]) ).
fof(f1965,plain,
( ! [X0] :
( ~ empty(X0)
| empty(powerset(X0))
| empty(sK6(powerset(X0)))
| empty_set = sK9(sK6(powerset(X0))) )
| ~ spl16_23
| ~ spl16_214 ),
inference(resolution,[],[f1956,f264]) ).
fof(f2942,plain,
( spl16_300
| ~ spl16_142
| ~ spl16_208 ),
inference(avatar_split_clause,[],[f1842,f1820,f1176,f2940]) ).
fof(f1842,plain,
( ! [X0] :
( ~ rel_str(sK8(X0))
| ~ rel_str(X0)
| ~ empty(the_InternalRel(X0))
| sK14 = sK9(powerset(the_InternalRel(sK8(X0)))) )
| ~ spl16_142
| ~ spl16_208 ),
inference(resolution,[],[f1821,f1177]) ).
fof(f2938,plain,
( spl16_299
| ~ spl16_36
| ~ spl16_208 ),
inference(avatar_split_clause,[],[f1840,f1820,f318,f2936]) ).
fof(f1840,plain,
( ! [X0,X1] :
( ~ rel_str(sK8(X0))
| ~ rel_str(X0)
| ~ empty(the_InternalRel(X0))
| the_InternalRel(sK8(X0)) = X1
| ~ empty(X1) )
| ~ spl16_36
| ~ spl16_208 ),
inference(resolution,[],[f1821,f319]) ).
fof(f2934,plain,
( spl16_298
| ~ spl16_142
| ~ spl16_207 ),
inference(avatar_split_clause,[],[f1833,f1816,f1176,f2932]) ).
fof(f1833,plain,
( ! [X0] :
( ~ rel_str(sK8(X0))
| ~ rel_str(X0)
| ~ empty(the_carrier(X0))
| sK14 = sK9(powerset(the_carrier(sK8(X0)))) )
| ~ spl16_142
| ~ spl16_207 ),
inference(resolution,[],[f1817,f1177]) ).
fof(f2930,plain,
( spl16_297
| ~ spl16_29
| ~ spl16_294 ),
inference(avatar_split_clause,[],[f2905,f2894,f290,f2927]) ).
fof(f2927,plain,
( spl16_297
<=> relation_of2(sK14,sK14,sK14) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_297])]) ).
fof(f290,plain,
( spl16_29
<=> ! [X0,X1] : relation_of2(sK10(X0,X1),X0,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_29])]) ).
fof(f2905,plain,
( relation_of2(sK14,sK14,sK14)
| ~ spl16_29
| ~ spl16_294 ),
inference(superposition,[],[f291,f2896]) ).
fof(f291,plain,
( ! [X0,X1] : relation_of2(sK10(X0,X1),X0,X1)
| ~ spl16_29 ),
inference(avatar_component_clause,[],[f290]) ).
fof(f2925,plain,
( spl16_296
| ~ spl16_36
| ~ spl16_207 ),
inference(avatar_split_clause,[],[f1831,f1816,f318,f2923]) ).
fof(f1831,plain,
( ! [X0,X1] :
( ~ rel_str(sK8(X0))
| ~ rel_str(X0)
| ~ empty(the_carrier(X0))
| the_carrier(sK8(X0)) = X1
| ~ empty(X1) )
| ~ spl16_36
| ~ spl16_207 ),
inference(resolution,[],[f1817,f319]) ).
fof(f2902,plain,
( spl16_295
| ~ spl16_23
| ~ spl16_57
| ~ spl16_291 ),
inference(avatar_split_clause,[],[f2823,f2785,f469,f263,f2899]) ).
fof(f2899,plain,
( spl16_295
<=> sK14 = sK11(sK14,sK14) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_295])]) ).
fof(f2785,plain,
( spl16_291
<=> empty(sK11(sK14,sK14)) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_291])]) ).
fof(f2823,plain,
( sK14 = sK11(sK14,sK14)
| ~ spl16_23
| ~ spl16_57
| ~ spl16_291 ),
inference(forward_demodulation,[],[f2814,f471]) ).
fof(f2814,plain,
( empty_set = sK11(sK14,sK14)
| ~ spl16_23
| ~ spl16_291 ),
inference(resolution,[],[f2787,f264]) ).
fof(f2787,plain,
( empty(sK11(sK14,sK14))
| ~ spl16_291 ),
inference(avatar_component_clause,[],[f2785]) ).
fof(f2897,plain,
( spl16_294
| ~ spl16_23
| ~ spl16_57
| ~ spl16_290 ),
inference(avatar_split_clause,[],[f2799,f2780,f469,f263,f2894]) ).
fof(f2780,plain,
( spl16_290
<=> empty(sK10(sK14,sK14)) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_290])]) ).
fof(f2799,plain,
( sK14 = sK10(sK14,sK14)
| ~ spl16_23
| ~ spl16_57
| ~ spl16_290 ),
inference(forward_demodulation,[],[f2790,f471]) ).
fof(f2790,plain,
( empty_set = sK10(sK14,sK14)
| ~ spl16_23
| ~ spl16_290 ),
inference(resolution,[],[f2782,f264]) ).
fof(f2782,plain,
( empty(sK10(sK14,sK14))
| ~ spl16_290 ),
inference(avatar_component_clause,[],[f2780]) ).
fof(f2892,plain,
( ~ spl16_12
| spl16_165
| ~ spl16_292 ),
inference(avatar_split_clause,[],[f2891,f2838,f1368,f213]) ).
fof(f2838,plain,
( spl16_292
<=> sK14 = cartesian_product2(sK14,sK14) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_292])]) ).
fof(f2891,plain,
( ~ empty(sK14)
| spl16_165
| ~ spl16_292 ),
inference(forward_demodulation,[],[f1370,f2840]) ).
fof(f2840,plain,
( sK14 = cartesian_product2(sK14,sK14)
| ~ spl16_292 ),
inference(avatar_component_clause,[],[f2838]) ).
fof(f1370,plain,
( ~ empty(cartesian_product2(sK14,sK14))
| spl16_165 ),
inference(avatar_component_clause,[],[f1368]) ).
fof(f2880,plain,
( spl16_186
| ~ spl16_65
| ~ spl16_293 ),
inference(avatar_split_clause,[],[f2876,f2870,f508,f1536]) ).
fof(f2870,plain,
( spl16_293
<=> ! [X0] : ~ in(X0,the_InternalRel(sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_293])]) ).
fof(f2876,plain,
( empty(the_InternalRel(sK0))
| ~ spl16_65
| ~ spl16_293 ),
inference(resolution,[],[f2871,f509]) ).
fof(f2871,plain,
( ! [X0] : ~ in(X0,the_InternalRel(sK0))
| ~ spl16_293 ),
inference(avatar_component_clause,[],[f2870]) ).
fof(f2872,plain,
( spl16_293
| ~ spl16_165
| ~ spl16_85
| ~ spl16_137 ),
inference(avatar_split_clause,[],[f2513,f1104,f646,f1368,f2870]) ).
fof(f646,plain,
( spl16_85
<=> ! [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,[spl16_85])]) ).
fof(f1104,plain,
( spl16_137
<=> relation_of2_as_subset(the_InternalRel(sK0),sK14,sK14) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_137])]) ).
fof(f2513,plain,
( ! [X0] :
( ~ empty(cartesian_product2(sK14,sK14))
| ~ in(X0,the_InternalRel(sK0)) )
| ~ spl16_85
| ~ spl16_137 ),
inference(resolution,[],[f1106,f647]) ).
fof(f647,plain,
( ! [X2,X3,X0,X1] :
( ~ relation_of2_as_subset(X0,X1,X2)
| ~ empty(cartesian_product2(X1,X2))
| ~ in(X3,X0) )
| ~ spl16_85 ),
inference(avatar_component_clause,[],[f646]) ).
fof(f1106,plain,
( relation_of2_as_subset(the_InternalRel(sK0),sK14,sK14)
| ~ spl16_137 ),
inference(avatar_component_clause,[],[f1104]) ).
fof(f2841,plain,
( spl16_292
| ~ spl16_23
| ~ spl16_57
| ~ spl16_165 ),
inference(avatar_split_clause,[],[f2765,f1368,f469,f263,f2838]) ).
fof(f2765,plain,
( sK14 = cartesian_product2(sK14,sK14)
| ~ spl16_23
| ~ spl16_57
| ~ spl16_165 ),
inference(forward_demodulation,[],[f2756,f471]) ).
fof(f2756,plain,
( empty_set = cartesian_product2(sK14,sK14)
| ~ spl16_23
| ~ spl16_165 ),
inference(resolution,[],[f1369,f264]) ).
fof(f1369,plain,
( empty(cartesian_product2(sK14,sK14))
| ~ spl16_165 ),
inference(avatar_component_clause,[],[f1368]) ).
fof(f2788,plain,
( spl16_291
| ~ spl16_145
| ~ spl16_165 ),
inference(avatar_split_clause,[],[f2754,f1368,f1192,f2785]) ).
fof(f1192,plain,
( spl16_145
<=> ! [X0,X1] :
( ~ empty(cartesian_product2(X0,X1))
| empty(sK11(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_145])]) ).
fof(f2754,plain,
( empty(sK11(sK14,sK14))
| ~ spl16_145
| ~ spl16_165 ),
inference(resolution,[],[f1369,f1193]) ).
fof(f1193,plain,
( ! [X0,X1] :
( ~ empty(cartesian_product2(X0,X1))
| empty(sK11(X0,X1)) )
| ~ spl16_145 ),
inference(avatar_component_clause,[],[f1192]) ).
fof(f2783,plain,
( spl16_290
| ~ spl16_146
| ~ spl16_165 ),
inference(avatar_split_clause,[],[f2753,f1368,f1196,f2780]) ).
fof(f1196,plain,
( spl16_146
<=> ! [X0,X1] :
( ~ empty(cartesian_product2(X0,X1))
| empty(sK10(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_146])]) ).
fof(f2753,plain,
( empty(sK10(sK14,sK14))
| ~ spl16_146
| ~ spl16_165 ),
inference(resolution,[],[f1369,f1197]) ).
fof(f1197,plain,
( ! [X0,X1] :
( ~ empty(cartesian_product2(X0,X1))
| empty(sK10(X0,X1)) )
| ~ spl16_146 ),
inference(avatar_component_clause,[],[f1196]) ).
fof(f2752,plain,
( spl16_289
| ~ spl16_27
| ~ spl16_266 ),
inference(avatar_split_clause,[],[f2543,f2539,f282,f2750]) ).
fof(f2737,plain,
( spl16_288
| ~ spl16_16
| ~ spl16_215 ),
inference(avatar_split_clause,[],[f1973,f1961,f232,f2735]) ).
fof(f2735,plain,
( spl16_288
<=> ! [X0] :
( ~ empty(X0)
| empty(powerset(X0))
| empty(sK7(powerset(X0)))
| finite(sK9(sK7(powerset(X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_288])]) ).
fof(f1973,plain,
( ! [X0] :
( ~ empty(X0)
| empty(powerset(X0))
| empty(sK7(powerset(X0)))
| finite(sK9(sK7(powerset(X0)))) )
| ~ spl16_16
| ~ spl16_215 ),
inference(resolution,[],[f1962,f233]) ).
fof(f2733,plain,
( spl16_287
| ~ spl16_16
| ~ spl16_214 ),
inference(avatar_split_clause,[],[f1964,f1955,f232,f2731]) ).
fof(f2731,plain,
( spl16_287
<=> ! [X0] :
( ~ empty(X0)
| empty(powerset(X0))
| empty(sK6(powerset(X0)))
| finite(sK9(sK6(powerset(X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_287])]) ).
fof(f1964,plain,
( ! [X0] :
( ~ empty(X0)
| empty(powerset(X0))
| empty(sK6(powerset(X0)))
| finite(sK9(sK6(powerset(X0)))) )
| ~ spl16_16
| ~ spl16_214 ),
inference(resolution,[],[f1956,f233]) ).
fof(f2729,plain,
( spl16_286
| ~ spl16_23
| ~ spl16_57
| ~ spl16_213 ),
inference(avatar_split_clause,[],[f1953,f1942,f469,f263,f2727]) ).
fof(f1953,plain,
( ! [X0] :
( sK14 = sK9(sK9(powerset(powerset(X0))))
| empty(sK9(powerset(powerset(X0))))
| ~ empty(X0) )
| ~ spl16_23
| ~ spl16_57
| ~ spl16_213 ),
inference(forward_demodulation,[],[f1946,f471]) ).
fof(f1946,plain,
( ! [X0] :
( empty(sK9(powerset(powerset(X0))))
| ~ empty(X0)
| empty_set = sK9(sK9(powerset(powerset(X0)))) )
| ~ spl16_23
| ~ spl16_213 ),
inference(resolution,[],[f1943,f264]) ).
fof(f2706,plain,
( spl16_285
| ~ spl16_16
| ~ spl16_213 ),
inference(avatar_split_clause,[],[f1945,f1942,f232,f2704]) ).
fof(f2704,plain,
( spl16_285
<=> ! [X0] :
( empty(sK9(powerset(powerset(X0))))
| ~ empty(X0)
| finite(sK9(sK9(powerset(powerset(X0))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_285])]) ).
fof(f1945,plain,
( ! [X0] :
( empty(sK9(powerset(powerset(X0))))
| ~ empty(X0)
| finite(sK9(sK9(powerset(powerset(X0))))) )
| ~ spl16_16
| ~ spl16_213 ),
inference(resolution,[],[f1943,f233]) ).
fof(f2702,plain,
( spl16_284
| ~ spl16_23
| ~ spl16_57
| ~ spl16_208 ),
inference(avatar_split_clause,[],[f1846,f1820,f469,f263,f2700]) ).
fof(f1846,plain,
( ! [X0] :
( sK14 = the_InternalRel(sK8(X0))
| ~ rel_str(sK8(X0))
| ~ rel_str(X0)
| ~ empty(the_InternalRel(X0)) )
| ~ spl16_23
| ~ spl16_57
| ~ spl16_208 ),
inference(forward_demodulation,[],[f1839,f471]) ).
fof(f1839,plain,
( ! [X0] :
( ~ rel_str(sK8(X0))
| ~ rel_str(X0)
| ~ empty(the_InternalRel(X0))
| empty_set = the_InternalRel(sK8(X0)) )
| ~ spl16_23
| ~ spl16_208 ),
inference(resolution,[],[f1821,f264]) ).
fof(f2698,plain,
( spl16_283
| ~ spl16_23
| ~ spl16_57
| ~ spl16_207 ),
inference(avatar_split_clause,[],[f1837,f1816,f469,f263,f2696]) ).
fof(f1837,plain,
( ! [X0] :
( sK14 = the_carrier(sK8(X0))
| ~ rel_str(sK8(X0))
| ~ rel_str(X0)
| ~ empty(the_carrier(X0)) )
| ~ spl16_23
| ~ spl16_57
| ~ spl16_207 ),
inference(forward_demodulation,[],[f1830,f471]) ).
fof(f1830,plain,
( ! [X0] :
( ~ rel_str(sK8(X0))
| ~ rel_str(X0)
| ~ empty(the_carrier(X0))
| empty_set = the_carrier(sK8(X0)) )
| ~ spl16_23
| ~ spl16_207 ),
inference(resolution,[],[f1817,f264]) ).
fof(f2694,plain,
( spl16_282
| ~ spl16_99
| ~ spl16_204 ),
inference(avatar_split_clause,[],[f1802,f1797,f743,f2692]) ).
fof(f1802,plain,
( ! [X0,X1] :
( ~ empty(X0)
| sK9(powerset(X0)) = sK9(powerset(sK9(powerset(X1))))
| ~ empty(X1) )
| ~ spl16_99
| ~ spl16_204 ),
inference(resolution,[],[f1798,f744]) ).
fof(f2688,plain,
( spl16_281
| ~ spl16_16
| ~ spl16_208 ),
inference(avatar_split_clause,[],[f1838,f1820,f232,f2686]) ).
fof(f2686,plain,
( spl16_281
<=> ! [X0] :
( ~ rel_str(sK8(X0))
| ~ rel_str(X0)
| ~ empty(the_InternalRel(X0))
| finite(the_InternalRel(sK8(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_281])]) ).
fof(f1838,plain,
( ! [X0] :
( ~ rel_str(sK8(X0))
| ~ rel_str(X0)
| ~ empty(the_InternalRel(X0))
| finite(the_InternalRel(sK8(X0))) )
| ~ spl16_16
| ~ spl16_208 ),
inference(resolution,[],[f1821,f233]) ).
fof(f2684,plain,
( spl16_280
| ~ spl16_16
| ~ spl16_207 ),
inference(avatar_split_clause,[],[f1829,f1816,f232,f2682]) ).
fof(f1829,plain,
( ! [X0] :
( ~ rel_str(sK8(X0))
| ~ rel_str(X0)
| ~ empty(the_carrier(X0))
| finite(the_carrier(sK8(X0))) )
| ~ spl16_16
| ~ spl16_207 ),
inference(resolution,[],[f1817,f233]) ).
fof(f2667,plain,
( spl16_279
| ~ spl16_99
| ~ spl16_197 ),
inference(avatar_split_clause,[],[f1707,f1702,f743,f2665]) ).
fof(f1707,plain,
( ! [X0] :
( sK14 = sK9(powerset(sK9(powerset(sK9(powerset(X0))))))
| ~ empty(X0) )
| ~ spl16_99
| ~ spl16_197 ),
inference(resolution,[],[f1703,f744]) ).
fof(f2660,plain,
( spl16_278
| ~ spl16_224
| ~ spl16_147
| ~ spl16_225 ),
inference(avatar_split_clause,[],[f2288,f2062,f1200,f2058,f2657]) ).
fof(f2657,plain,
( spl16_278
<=> finite(the_InternalRel(sK8(sK1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_278])]) ).
fof(f2062,plain,
( spl16_225
<=> finite(the_carrier(sK8(sK1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_225])]) ).
fof(f2288,plain,
( ~ rel_str(sK8(sK1))
| finite(the_InternalRel(sK8(sK1)))
| ~ spl16_147
| ~ spl16_225 ),
inference(resolution,[],[f2064,f1201]) ).
fof(f2064,plain,
( finite(the_carrier(sK8(sK1)))
| ~ spl16_225 ),
inference(avatar_component_clause,[],[f2062]) ).
fof(f2655,plain,
( spl16_275
| spl16_277
| ~ spl16_65
| ~ spl16_195 ),
inference(avatar_split_clause,[],[f1693,f1680,f508,f2652,f2643]) ).
fof(f2643,plain,
( spl16_275
<=> empty(powerset(sK14)) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_275])]) ).
fof(f2652,plain,
( spl16_277
<=> in(sK14,powerset(sK14)) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_277])]) ).
fof(f1693,plain,
( in(sK14,powerset(sK14))
| empty(powerset(sK14))
| ~ spl16_65
| ~ spl16_195 ),
inference(superposition,[],[f509,f1682]) ).
fof(f2650,plain,
( spl16_275
| ~ spl16_276
| ~ spl16_98
| ~ spl16_195 ),
inference(avatar_split_clause,[],[f1692,f1680,f739,f2647,f2643]) ).
fof(f2647,plain,
( spl16_276
<=> in(powerset(sK14),sK14) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_276])]) ).
fof(f739,plain,
( spl16_98
<=> ! [X0] :
( empty(X0)
| ~ in(X0,sK9(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_98])]) ).
fof(f1692,plain,
( ~ in(powerset(sK14),sK14)
| empty(powerset(sK14))
| ~ spl16_98
| ~ spl16_195 ),
inference(superposition,[],[f740,f1682]) ).
fof(f740,plain,
( ! [X0] :
( ~ in(X0,sK9(X0))
| empty(X0) )
| ~ spl16_98 ),
inference(avatar_component_clause,[],[f739]) ).
fof(f2629,plain,
( spl16_274
| ~ spl16_119
| ~ spl16_190 ),
inference(avatar_split_clause,[],[f1667,f1600,f880,f2627]) ).
fof(f2627,plain,
( spl16_274
<=> ! [X0,X1] :
( ~ subrelstr(sK1,X0)
| empty(the_carrier(X0))
| ~ rel_str(X0)
| element(sK5,the_carrier(X1))
| ~ subrelstr(X0,X1)
| ~ rel_str(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_274])]) ).
fof(f1667,plain,
( ! [X0,X1] :
( ~ subrelstr(sK1,X0)
| empty(the_carrier(X0))
| ~ rel_str(X0)
| element(sK5,the_carrier(X1))
| ~ subrelstr(X0,X1)
| ~ rel_str(X1) )
| ~ spl16_119
| ~ spl16_190 ),
inference(duplicate_literal_removal,[],[f1661]) ).
fof(f1661,plain,
( ! [X0,X1] :
( ~ subrelstr(sK1,X0)
| empty(the_carrier(X0))
| ~ rel_str(X0)
| element(sK5,the_carrier(X1))
| ~ subrelstr(X0,X1)
| ~ rel_str(X0)
| ~ rel_str(X1) )
| ~ spl16_119
| ~ spl16_190 ),
inference(resolution,[],[f1601,f881]) ).
fof(f2625,plain,
( spl16_273
| ~ spl16_119
| ~ spl16_187 ),
inference(avatar_split_clause,[],[f1660,f1541,f880,f2623]) ).
fof(f2623,plain,
( spl16_273
<=> ! [X0,X1] :
( ~ subrelstr(sK0,X0)
| empty(the_carrier(X0))
| ~ rel_str(X0)
| element(sK5,the_carrier(X1))
| ~ subrelstr(X0,X1)
| ~ rel_str(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_273])]) ).
fof(f1541,plain,
( spl16_187
<=> ! [X0] :
( ~ rel_str(X0)
| ~ subrelstr(sK0,X0)
| empty(the_carrier(X0))
| in(sK5,the_carrier(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_187])]) ).
fof(f1660,plain,
( ! [X0,X1] :
( ~ subrelstr(sK0,X0)
| empty(the_carrier(X0))
| ~ rel_str(X0)
| element(sK5,the_carrier(X1))
| ~ subrelstr(X0,X1)
| ~ rel_str(X1) )
| ~ spl16_119
| ~ spl16_187 ),
inference(duplicate_literal_removal,[],[f1654]) ).
fof(f1654,plain,
( ! [X0,X1] :
( ~ subrelstr(sK0,X0)
| empty(the_carrier(X0))
| ~ rel_str(X0)
| element(sK5,the_carrier(X1))
| ~ subrelstr(X0,X1)
| ~ rel_str(X0)
| ~ rel_str(X1) )
| ~ spl16_119
| ~ spl16_187 ),
inference(resolution,[],[f1542,f881]) ).
fof(f1542,plain,
( ! [X0] :
( in(sK5,the_carrier(X0))
| ~ subrelstr(sK0,X0)
| empty(the_carrier(X0))
| ~ rel_str(X0) )
| ~ spl16_187 ),
inference(avatar_component_clause,[],[f1541]) ).
fof(f2621,plain,
( spl16_53
| ~ spl16_42
| ~ spl16_97
| ~ spl16_264 ),
inference(avatar_split_clause,[],[f2533,f2528,f733,f355,f428]) ).
fof(f733,plain,
( spl16_97
<=> ! [X0] :
( subrelstr(X0,X0)
| ~ rel_str(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_97])]) ).
fof(f2533,plain,
( ~ rel_str(sK1)
| empty(the_carrier(sK1))
| ~ spl16_97
| ~ spl16_264 ),
inference(duplicate_literal_removal,[],[f2532]) ).
fof(f2532,plain,
( ~ rel_str(sK1)
| empty(the_carrier(sK1))
| ~ rel_str(sK1)
| ~ spl16_97
| ~ spl16_264 ),
inference(resolution,[],[f2529,f734]) ).
fof(f734,plain,
( ! [X0] :
( subrelstr(X0,X0)
| ~ rel_str(X0) )
| ~ spl16_97 ),
inference(avatar_component_clause,[],[f733]) ).
fof(f2620,plain,
( spl16_272
| ~ spl16_119
| ~ spl16_162 ),
inference(avatar_split_clause,[],[f1653,f1319,f880,f2618]) ).
fof(f2618,plain,
( spl16_272
<=> ! [X0,X1] :
( ~ subrelstr(sK1,X0)
| empty(the_carrier(X0))
| ~ rel_str(X0)
| element(sK4,the_carrier(X1))
| ~ subrelstr(X0,X1)
| ~ rel_str(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_272])]) ).
fof(f1653,plain,
( ! [X0,X1] :
( ~ subrelstr(sK1,X0)
| empty(the_carrier(X0))
| ~ rel_str(X0)
| element(sK4,the_carrier(X1))
| ~ subrelstr(X0,X1)
| ~ rel_str(X1) )
| ~ spl16_119
| ~ spl16_162 ),
inference(duplicate_literal_removal,[],[f1647]) ).
fof(f1647,plain,
( ! [X0,X1] :
( ~ subrelstr(sK1,X0)
| empty(the_carrier(X0))
| ~ rel_str(X0)
| element(sK4,the_carrier(X1))
| ~ subrelstr(X0,X1)
| ~ rel_str(X0)
| ~ rel_str(X1) )
| ~ spl16_119
| ~ spl16_162 ),
inference(resolution,[],[f1320,f881]) ).
fof(f2616,plain,
( spl16_271
| ~ spl16_119
| ~ spl16_157 ),
inference(avatar_split_clause,[],[f1646,f1277,f880,f2614]) ).
fof(f2614,plain,
( spl16_271
<=> ! [X0,X1] :
( ~ subrelstr(sK0,X0)
| empty(the_carrier(X0))
| ~ rel_str(X0)
| element(sK4,the_carrier(X1))
| ~ subrelstr(X0,X1)
| ~ rel_str(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_271])]) ).
fof(f1277,plain,
( spl16_157
<=> ! [X0] :
( ~ rel_str(X0)
| ~ subrelstr(sK0,X0)
| empty(the_carrier(X0))
| in(sK4,the_carrier(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_157])]) ).
fof(f1646,plain,
( ! [X0,X1] :
( ~ subrelstr(sK0,X0)
| empty(the_carrier(X0))
| ~ rel_str(X0)
| element(sK4,the_carrier(X1))
| ~ subrelstr(X0,X1)
| ~ rel_str(X1) )
| ~ spl16_119
| ~ spl16_157 ),
inference(duplicate_literal_removal,[],[f1640]) ).
fof(f1640,plain,
( ! [X0,X1] :
( ~ subrelstr(sK0,X0)
| empty(the_carrier(X0))
| ~ rel_str(X0)
| element(sK4,the_carrier(X1))
| ~ subrelstr(X0,X1)
| ~ rel_str(X0)
| ~ rel_str(X1) )
| ~ spl16_119
| ~ spl16_157 ),
inference(resolution,[],[f1278,f881]) ).
fof(f1278,plain,
( ! [X0] :
( in(sK4,the_carrier(X0))
| ~ subrelstr(sK0,X0)
| empty(the_carrier(X0))
| ~ rel_str(X0) )
| ~ spl16_157 ),
inference(avatar_component_clause,[],[f1277]) ).
fof(f2607,plain,
( spl16_270
| ~ spl16_17
| ~ spl16_195 ),
inference(avatar_split_clause,[],[f1694,f1680,f236,f2604]) ).
fof(f2604,plain,
( spl16_270
<=> element(sK14,powerset(sK14)) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_270])]) ).
fof(f236,plain,
( spl16_17
<=> ! [X0] : element(sK9(X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_17])]) ).
fof(f1694,plain,
( element(sK14,powerset(sK14))
| ~ spl16_17
| ~ spl16_195 ),
inference(superposition,[],[f237,f1682]) ).
fof(f237,plain,
( ! [X0] : element(sK9(X0),X0)
| ~ spl16_17 ),
inference(avatar_component_clause,[],[f236]) ).
fof(f2582,plain,
( spl16_269
| ~ spl16_38
| ~ spl16_212 ),
inference(avatar_split_clause,[],[f2510,f1937,f335,f2580]) ).
fof(f1937,plain,
( spl16_212
<=> ! [X0,X1] :
( ~ rel_str(X0)
| ~ subrelstr(sK1,X0)
| ~ in(X1,sK14)
| element(X1,the_carrier(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_212])]) ).
fof(f2510,plain,
( ! [X0,X1] :
( ~ subrelstr(sK1,X0)
| ~ in(X1,sK14)
| ~ rel_str(X0)
| empty(the_carrier(X0))
| in(X1,the_carrier(X0)) )
| ~ spl16_38
| ~ spl16_212 ),
inference(resolution,[],[f1938,f336]) ).
fof(f1938,plain,
( ! [X0,X1] :
( element(X1,the_carrier(X0))
| ~ subrelstr(sK1,X0)
| ~ in(X1,sK14)
| ~ rel_str(X0) )
| ~ spl16_212 ),
inference(avatar_component_clause,[],[f1937]) ).
fof(f2578,plain,
( spl16_268
| ~ spl16_38
| ~ spl16_203 ),
inference(avatar_split_clause,[],[f2509,f1793,f335,f2576]) ).
fof(f1793,plain,
( spl16_203
<=> ! [X0,X1] :
( ~ rel_str(X0)
| ~ subrelstr(sK0,X0)
| ~ in(X1,sK14)
| element(X1,the_carrier(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_203])]) ).
fof(f2509,plain,
( ! [X0,X1] :
( ~ subrelstr(sK0,X0)
| ~ in(X1,sK14)
| ~ rel_str(X0)
| empty(the_carrier(X0))
| in(X1,the_carrier(X0)) )
| ~ spl16_38
| ~ spl16_203 ),
inference(resolution,[],[f1794,f336]) ).
fof(f1794,plain,
( ! [X0,X1] :
( element(X1,the_carrier(X0))
| ~ subrelstr(sK0,X0)
| ~ in(X1,sK14)
| ~ rel_str(X0) )
| ~ spl16_203 ),
inference(avatar_component_clause,[],[f1793]) ).
fof(f2552,plain,
( ~ spl16_42
| ~ spl16_97
| spl16_263 ),
inference(avatar_split_clause,[],[f2526,f2522,f733,f355]) ).
fof(f2526,plain,
( ~ rel_str(sK1)
| ~ spl16_97
| spl16_263 ),
inference(resolution,[],[f2524,f734]) ).
fof(f2524,plain,
( ~ subrelstr(sK1,sK1)
| spl16_263 ),
inference(avatar_component_clause,[],[f2522]) ).
fof(f2551,plain,
( spl16_267
| ~ spl16_38
| ~ spl16_196 ),
inference(avatar_split_clause,[],[f1700,f1697,f335,f2549]) ).
fof(f1700,plain,
( ! [X0] :
( ~ subrelstr(sK1,X0)
| ~ rel_str(X0)
| empty(the_InternalRel(X0))
| in(ordered_pair(sK4,sK5),the_InternalRel(X0)) )
| ~ spl16_38
| ~ spl16_196 ),
inference(resolution,[],[f1698,f336]) ).
fof(f2541,plain,
( spl16_165
| spl16_266
| ~ spl16_38
| ~ spl16_202 ),
inference(avatar_split_clause,[],[f2438,f1782,f335,f2539,f1368]) ).
fof(f2438,plain,
( ! [X0] :
( ~ in(X0,the_InternalRel(sK0))
| empty(cartesian_product2(sK14,sK14))
| in(X0,cartesian_product2(sK14,sK14)) )
| ~ spl16_38
| ~ spl16_202 ),
inference(resolution,[],[f1783,f336]) ).
fof(f1783,plain,
( ! [X0] :
( element(X0,cartesian_product2(sK14,sK14))
| ~ in(X0,the_InternalRel(sK0)) )
| ~ spl16_202 ),
inference(avatar_component_clause,[],[f1782]) ).
fof(f2537,plain,
( spl16_265
| ~ spl16_27
| ~ spl16_190 ),
inference(avatar_split_clause,[],[f1664,f1600,f282,f2535]) ).
fof(f2535,plain,
( spl16_265
<=> ! [X0] :
( ~ subrelstr(sK1,X0)
| empty(the_carrier(X0))
| ~ rel_str(X0)
| ~ in(the_carrier(X0),sK5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_265])]) ).
fof(f1664,plain,
( ! [X0] :
( ~ subrelstr(sK1,X0)
| empty(the_carrier(X0))
| ~ rel_str(X0)
| ~ in(the_carrier(X0),sK5) )
| ~ spl16_27
| ~ spl16_190 ),
inference(resolution,[],[f1601,f283]) ).
fof(f2530,plain,
( spl16_264
| ~ spl16_65
| ~ spl16_211 ),
inference(avatar_split_clause,[],[f2443,f1908,f508,f2528]) ).
fof(f1908,plain,
( spl16_211
<=> ! [X0,X1] :
( ~ rel_str(X0)
| ~ in(X1,the_carrier(X0))
| ~ subrelstr(X0,sK1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_211])]) ).
fof(f2443,plain,
( ! [X0] :
( ~ rel_str(X0)
| ~ subrelstr(X0,sK1)
| empty(the_carrier(X0)) )
| ~ spl16_65
| ~ spl16_211 ),
inference(resolution,[],[f1909,f509]) ).
fof(f1909,plain,
( ! [X0,X1] :
( ~ in(X1,the_carrier(X0))
| ~ rel_str(X0)
| ~ subrelstr(X0,sK1) )
| ~ spl16_211 ),
inference(avatar_component_clause,[],[f1908]) ).
fof(f2525,plain,
( ~ spl16_263
| ~ spl16_42
| ~ spl16_52
| ~ spl16_211 ),
inference(avatar_split_clause,[],[f2484,f1908,f424,f355,f2522]) ).
fof(f424,plain,
( spl16_52
<=> in(sK4,the_carrier(sK1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_52])]) ).
fof(f2484,plain,
( ~ rel_str(sK1)
| ~ subrelstr(sK1,sK1)
| ~ spl16_52
| ~ spl16_211 ),
inference(resolution,[],[f426,f1909]) ).
fof(f426,plain,
( in(sK4,the_carrier(sK1))
| ~ spl16_52 ),
inference(avatar_component_clause,[],[f424]) ).
fof(f2520,plain,
( ~ spl16_262
| ~ spl16_1
| ~ spl16_54
| ~ spl16_211 ),
inference(avatar_split_clause,[],[f2462,f1908,f443,f158,f2517]) ).
fof(f2517,plain,
( spl16_262
<=> subrelstr(sK0,sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_262])]) ).
fof(f443,plain,
( spl16_54
<=> in(sK5,the_carrier(sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_54])]) ).
fof(f2462,plain,
( ~ rel_str(sK0)
| ~ subrelstr(sK0,sK1)
| ~ spl16_54
| ~ spl16_211 ),
inference(resolution,[],[f445,f1909]) ).
fof(f445,plain,
( in(sK5,the_carrier(sK0))
| ~ spl16_54 ),
inference(avatar_component_clause,[],[f443]) ).
fof(f2511,plain,
( spl16_137
| ~ spl16_41
| ~ spl16_189 ),
inference(avatar_split_clause,[],[f1780,f1595,f347,f1104]) ).
fof(f347,plain,
( spl16_41
<=> ! [X2,X0,X1] :
( relation_of2_as_subset(X2,X0,X1)
| ~ relation_of2(X2,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_41])]) ).
fof(f1595,plain,
( spl16_189
<=> relation_of2(the_InternalRel(sK0),sK14,sK14) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_189])]) ).
fof(f1780,plain,
( relation_of2_as_subset(the_InternalRel(sK0),sK14,sK14)
| ~ spl16_41
| ~ spl16_189 ),
inference(resolution,[],[f1597,f348]) ).
fof(f348,plain,
( ! [X2,X0,X1] :
( ~ relation_of2(X2,X0,X1)
| relation_of2_as_subset(X2,X0,X1) )
| ~ spl16_41 ),
inference(avatar_component_clause,[],[f347]) ).
fof(f1597,plain,
( relation_of2(the_InternalRel(sK0),sK14,sK14)
| ~ spl16_189 ),
inference(avatar_component_clause,[],[f1595]) ).
fof(f2496,plain,
( ~ spl16_53
| ~ spl16_24
| ~ spl16_93 ),
inference(avatar_split_clause,[],[f1394,f699,f267,f428]) ).
fof(f267,plain,
( spl16_24
<=> ! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_24])]) ).
fof(f699,plain,
( spl16_93
<=> in(sK5,the_carrier(sK1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_93])]) ).
fof(f1394,plain,
( ~ empty(the_carrier(sK1))
| ~ spl16_24
| ~ spl16_93 ),
inference(resolution,[],[f701,f268]) ).
fof(f268,plain,
( ! [X0,X1] :
( ~ in(X0,X1)
| ~ empty(X1) )
| ~ spl16_24 ),
inference(avatar_component_clause,[],[f267]) ).
fof(f701,plain,
( in(sK5,the_carrier(sK1))
| ~ spl16_93 ),
inference(avatar_component_clause,[],[f699]) ).
fof(f2481,plain,
( spl16_261
| spl16_129
| ~ spl16_71
| ~ spl16_191 ),
inference(avatar_split_clause,[],[f1870,f1621,f545,f952,f2479]) ).
fof(f2479,plain,
( spl16_261
<=> ! [X1] : ~ in(X1,sK14) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_261])]) ).
fof(f952,plain,
( spl16_129
<=> ! [X0] :
( ~ empty(the_carrier(X0))
| ~ rel_str(X0)
| ~ subrelstr(sK1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_129])]) ).
fof(f545,plain,
( spl16_71
<=> ! [X2,X0,X1] :
( ~ empty(X0)
| ~ in(X1,X2)
| ~ subset(X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_71])]) ).
fof(f1621,plain,
( spl16_191
<=> ! [X0] :
( subset(sK14,the_carrier(X0))
| ~ rel_str(X0)
| ~ subrelstr(sK1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_191])]) ).
fof(f1870,plain,
( ! [X0,X1] :
( ~ rel_str(X0)
| ~ subrelstr(sK1,X0)
| ~ in(X1,sK14)
| ~ empty(the_carrier(X0)) )
| ~ spl16_71
| ~ spl16_191 ),
inference(resolution,[],[f1622,f546]) ).
fof(f546,plain,
( ! [X2,X0,X1] :
( ~ subset(X2,X0)
| ~ in(X1,X2)
| ~ empty(X0) )
| ~ spl16_71 ),
inference(avatar_component_clause,[],[f545]) ).
fof(f1622,plain,
( ! [X0] :
( subset(sK14,the_carrier(X0))
| ~ rel_str(X0)
| ~ subrelstr(sK1,X0) )
| ~ spl16_191 ),
inference(avatar_component_clause,[],[f1621]) ).
fof(f2461,plain,
( ~ spl16_55
| ~ spl16_24
| ~ spl16_56 ),
inference(avatar_split_clause,[],[f948,f455,f267,f447]) ).
fof(f447,plain,
( spl16_55
<=> empty(the_carrier(sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_55])]) ).
fof(f455,plain,
( spl16_56
<=> in(sK4,the_carrier(sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_56])]) ).
fof(f948,plain,
( ~ empty(the_carrier(sK0))
| ~ spl16_24
| ~ spl16_56 ),
inference(resolution,[],[f457,f268]) ).
fof(f457,plain,
( in(sK4,the_carrier(sK0))
| ~ spl16_56 ),
inference(avatar_component_clause,[],[f455]) ).
fof(f2456,plain,
( ~ spl16_25
| spl16_260
| ~ spl16_69
| ~ spl16_201 ),
inference(avatar_split_clause,[],[f2362,f1762,f530,f2454,f271]) ).
fof(f271,plain,
( spl16_25
<=> finite(sK14) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_25])]) ).
fof(f2454,plain,
( spl16_260
<=> ! [X0] :
( ~ rel_str(X0)
| finite(the_carrier(X0))
| ~ subrelstr(X0,sK0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_260])]) ).
fof(f530,plain,
( spl16_69
<=> ! [X0,X1] :
( finite(X0)
| ~ finite(X1)
| ~ subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_69])]) ).
fof(f1762,plain,
( spl16_201
<=> ! [X0] :
( subset(the_carrier(X0),sK14)
| ~ rel_str(X0)
| ~ subrelstr(X0,sK0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_201])]) ).
fof(f2362,plain,
( ! [X0] :
( ~ rel_str(X0)
| ~ subrelstr(X0,sK0)
| ~ finite(sK14)
| finite(the_carrier(X0)) )
| ~ spl16_69
| ~ spl16_201 ),
inference(resolution,[],[f1763,f531]) ).
fof(f531,plain,
( ! [X0,X1] :
( ~ subset(X0,X1)
| ~ finite(X1)
| finite(X0) )
| ~ spl16_69 ),
inference(avatar_component_clause,[],[f530]) ).
fof(f1763,plain,
( ! [X0] :
( subset(the_carrier(X0),sK14)
| ~ rel_str(X0)
| ~ subrelstr(X0,sK0) )
| ~ spl16_201 ),
inference(avatar_component_clause,[],[f1762]) ).
fof(f2433,plain,
( ~ spl16_1
| ~ spl16_12
| ~ spl16_97
| ~ spl16_126
| ~ spl16_128 ),
inference(avatar_split_clause,[],[f2368,f934,f920,f733,f213,f158]) ).
fof(f920,plain,
( spl16_126
<=> ! [X0] :
( ~ empty(the_carrier(X0))
| ~ rel_str(X0)
| ~ subrelstr(sK0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_126])]) ).
fof(f934,plain,
( spl16_128
<=> the_carrier(sK0) = sK14 ),
introduced(avatar_definition,[new_symbols(naming,[spl16_128])]) ).
fof(f2368,plain,
( ~ empty(sK14)
| ~ rel_str(sK0)
| ~ spl16_97
| ~ spl16_126
| ~ spl16_128 ),
inference(forward_demodulation,[],[f950,f936]) ).
fof(f936,plain,
( the_carrier(sK0) = sK14
| ~ spl16_128 ),
inference(avatar_component_clause,[],[f934]) ).
fof(f950,plain,
( ~ rel_str(sK0)
| ~ empty(the_carrier(sK0))
| ~ spl16_97
| ~ spl16_126 ),
inference(duplicate_literal_removal,[],[f949]) ).
fof(f949,plain,
( ~ rel_str(sK0)
| ~ empty(the_carrier(sK0))
| ~ rel_str(sK0)
| ~ spl16_97
| ~ spl16_126 ),
inference(resolution,[],[f921,f734]) ).
fof(f921,plain,
( ! [X0] :
( ~ subrelstr(sK0,X0)
| ~ rel_str(X0)
| ~ empty(the_carrier(X0)) )
| ~ spl16_126 ),
inference(avatar_component_clause,[],[f920]) ).
fof(f2393,plain,
( spl16_61
| ~ spl16_9
| ~ spl16_57
| ~ spl16_139
| ~ spl16_195 ),
inference(avatar_split_clause,[],[f1856,f1680,f1151,f469,f198,f491]) ).
fof(f1856,plain,
( the_carrier(sK1) = sK14
| ~ spl16_9
| ~ spl16_57
| ~ spl16_139
| ~ spl16_195 ),
inference(forward_demodulation,[],[f1855,f1682]) ).
fof(f1855,plain,
( the_carrier(sK1) = sK9(powerset(sK14))
| ~ spl16_9
| ~ spl16_57
| ~ spl16_139 ),
inference(forward_demodulation,[],[f1350,f471]) ).
fof(f2365,plain,
( ~ spl16_55
| ~ spl16_1
| ~ spl16_2
| ~ spl16_129 ),
inference(avatar_split_clause,[],[f1925,f952,f163,f158,f447]) ).
fof(f1925,plain,
( ~ rel_str(sK0)
| ~ empty(the_carrier(sK0))
| ~ spl16_2
| ~ spl16_129 ),
inference(resolution,[],[f953,f165]) ).
fof(f953,plain,
( ! [X0] :
( ~ subrelstr(sK1,X0)
| ~ rel_str(X0)
| ~ empty(the_carrier(X0)) )
| ~ spl16_129 ),
inference(avatar_component_clause,[],[f952]) ).
fof(f2315,plain,
( spl16_259
| ~ spl16_27
| ~ spl16_187 ),
inference(avatar_split_clause,[],[f1657,f1541,f282,f2313]) ).
fof(f2313,plain,
( spl16_259
<=> ! [X0] :
( ~ subrelstr(sK0,X0)
| empty(the_carrier(X0))
| ~ rel_str(X0)
| ~ in(the_carrier(X0),sK5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_259])]) ).
fof(f1657,plain,
( ! [X0] :
( ~ subrelstr(sK0,X0)
| empty(the_carrier(X0))
| ~ rel_str(X0)
| ~ in(the_carrier(X0),sK5) )
| ~ spl16_27
| ~ spl16_187 ),
inference(resolution,[],[f1542,f283]) ).
fof(f2306,plain,
( spl16_258
| ~ spl16_152
| ~ spl16_173 ),
inference(avatar_split_clause,[],[f1462,f1448,f1257,f2304]) ).
fof(f1462,plain,
( ! [X0] :
( element(sK9(sK9(powerset(sK9(sK9(powerset(powerset(X0))))))),X0)
| empty(sK9(powerset(powerset(X0))))
| empty(sK9(sK9(powerset(powerset(X0)))))
| empty(sK9(powerset(sK9(sK9(powerset(powerset(X0))))))) )
| ~ spl16_152
| ~ spl16_173 ),
inference(resolution,[],[f1449,f1258]) ).
fof(f2292,plain,
( spl16_257
| ~ spl16_121
| ~ spl16_182 ),
inference(avatar_split_clause,[],[f1516,f1507,f888,f2290]) ).
fof(f2290,plain,
( spl16_257
<=> ! [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,[spl16_257])]) ).
fof(f1516,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))) )
| ~ spl16_121
| ~ spl16_182 ),
inference(resolution,[],[f1508,f889]) ).
fof(f2287,plain,
( spl16_256
| ~ spl16_152
| ~ spl16_177 ),
inference(avatar_split_clause,[],[f1499,f1476,f1257,f2285]) ).
fof(f1499,plain,
( ! [X0] :
( empty(sK7(powerset(X0)))
| element(sK9(sK9(powerset(sK9(sK7(powerset(X0)))))),X0)
| empty(powerset(X0))
| empty(sK9(sK7(powerset(X0))))
| empty(sK9(powerset(sK9(sK7(powerset(X0)))))) )
| ~ spl16_152
| ~ spl16_177 ),
inference(resolution,[],[f1477,f1258]) ).
fof(f2283,plain,
( spl16_255
| ~ spl16_152
| ~ spl16_176 ),
inference(avatar_split_clause,[],[f1495,f1472,f1257,f2281]) ).
fof(f1495,plain,
( ! [X0] :
( empty(sK6(powerset(X0)))
| element(sK9(sK9(powerset(sK9(sK6(powerset(X0)))))),X0)
| empty(powerset(X0))
| empty(sK9(sK6(powerset(X0))))
| empty(sK9(powerset(sK9(sK6(powerset(X0)))))) )
| ~ spl16_152
| ~ spl16_176 ),
inference(resolution,[],[f1473,f1258]) ).
fof(f2269,plain,
( spl16_254
| ~ spl16_150
| ~ spl16_173 ),
inference(avatar_split_clause,[],[f1461,f1448,f1218,f2267]) ).
fof(f1461,plain,
( ! [X0] :
( element(sK9(sK7(sK9(sK9(powerset(powerset(X0)))))),X0)
| empty(sK9(powerset(powerset(X0))))
| empty(sK7(sK9(sK9(powerset(powerset(X0))))))
| empty(sK9(sK9(powerset(powerset(X0))))) )
| ~ spl16_150
| ~ spl16_173 ),
inference(resolution,[],[f1449,f1219]) ).
fof(f2265,plain,
( spl16_253
| ~ spl16_149
| ~ spl16_173 ),
inference(avatar_split_clause,[],[f1460,f1448,f1214,f2263]) ).
fof(f1460,plain,
( ! [X0] :
( element(sK9(sK6(sK9(sK9(powerset(powerset(X0)))))),X0)
| empty(sK9(powerset(powerset(X0))))
| empty(sK6(sK9(sK9(powerset(powerset(X0))))))
| empty(sK9(sK9(powerset(powerset(X0))))) )
| ~ spl16_149
| ~ spl16_173 ),
inference(resolution,[],[f1449,f1215]) ).
fof(f2241,plain,
( ~ spl16_42
| ~ spl16_224
| ~ spl16_123
| ~ spl16_155
| spl16_225 ),
inference(avatar_split_clause,[],[f2208,f2062,f1269,f906,f2058,f355]) ).
fof(f906,plain,
( spl16_123
<=> finite(the_carrier(sK1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_123])]) ).
fof(f1269,plain,
( spl16_155
<=> ! [X0] :
( finite(the_carrier(sK8(X0)))
| ~ finite(the_carrier(X0))
| ~ rel_str(sK8(X0))
| ~ rel_str(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_155])]) ).
fof(f2208,plain,
( ~ finite(the_carrier(sK1))
| ~ rel_str(sK8(sK1))
| ~ rel_str(sK1)
| ~ spl16_155
| spl16_225 ),
inference(resolution,[],[f2063,f1270]) ).
fof(f1270,plain,
( ! [X0] :
( finite(the_carrier(sK8(X0)))
| ~ finite(the_carrier(X0))
| ~ rel_str(sK8(X0))
| ~ rel_str(X0) )
| ~ spl16_155 ),
inference(avatar_component_clause,[],[f1269]) ).
fof(f2063,plain,
( ~ finite(the_carrier(sK8(sK1)))
| spl16_225 ),
inference(avatar_component_clause,[],[f2062]) ).
fof(f2240,plain,
( spl16_252
| ~ spl16_150
| ~ spl16_177 ),
inference(avatar_split_clause,[],[f1498,f1476,f1218,f2238]) ).
fof(f1498,plain,
( ! [X0] :
( empty(sK7(powerset(X0)))
| element(sK9(sK7(sK9(sK7(powerset(X0))))),X0)
| empty(powerset(X0))
| empty(sK7(sK9(sK7(powerset(X0)))))
| empty(sK9(sK7(powerset(X0)))) )
| ~ spl16_150
| ~ spl16_177 ),
inference(resolution,[],[f1477,f1219]) ).
fof(f2236,plain,
( spl16_251
| ~ spl16_149
| ~ spl16_177 ),
inference(avatar_split_clause,[],[f1497,f1476,f1214,f2234]) ).
fof(f1497,plain,
( ! [X0] :
( empty(sK7(powerset(X0)))
| element(sK9(sK6(sK9(sK7(powerset(X0))))),X0)
| empty(powerset(X0))
| empty(sK6(sK9(sK7(powerset(X0)))))
| empty(sK9(sK7(powerset(X0)))) )
| ~ spl16_149
| ~ spl16_177 ),
inference(resolution,[],[f1477,f1215]) ).
fof(f2232,plain,
( spl16_250
| ~ spl16_150
| ~ spl16_176 ),
inference(avatar_split_clause,[],[f1494,f1472,f1218,f2230]) ).
fof(f1494,plain,
( ! [X0] :
( empty(sK6(powerset(X0)))
| element(sK9(sK7(sK9(sK6(powerset(X0))))),X0)
| empty(powerset(X0))
| empty(sK7(sK9(sK6(powerset(X0)))))
| empty(sK9(sK6(powerset(X0)))) )
| ~ spl16_150
| ~ spl16_176 ),
inference(resolution,[],[f1473,f1219]) ).
fof(f2228,plain,
( spl16_249
| ~ spl16_149
| ~ spl16_176 ),
inference(avatar_split_clause,[],[f1493,f1472,f1214,f2226]) ).
fof(f1493,plain,
( ! [X0] :
( empty(sK6(powerset(X0)))
| element(sK9(sK6(sK9(sK6(powerset(X0))))),X0)
| empty(powerset(X0))
| empty(sK6(sK9(sK6(powerset(X0)))))
| empty(sK9(sK6(powerset(X0)))) )
| ~ spl16_149
| ~ spl16_176 ),
inference(resolution,[],[f1473,f1215]) ).
fof(f2220,plain,
( spl16_248
| ~ spl16_109
| ~ spl16_182 ),
inference(avatar_split_clause,[],[f1515,f1507,f795,f2218]) ).
fof(f1515,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)) )
| ~ spl16_109
| ~ spl16_182 ),
inference(resolution,[],[f1508,f796]) ).
fof(f2216,plain,
( spl16_247
| ~ spl16_120
| ~ spl16_152 ),
inference(avatar_split_clause,[],[f1288,f1257,f884,f2214]) ).
fof(f1288,plain,
( ! [X0,X1] :
( empty(the_InternalRel(X0))
| empty(sK9(powerset(the_InternalRel(X0))))
| element(sK9(sK9(powerset(the_InternalRel(X0)))),the_InternalRel(X1))
| ~ subrelstr(X0,X1)
| ~ rel_str(X0)
| ~ rel_str(X1) )
| ~ spl16_120
| ~ spl16_152 ),
inference(resolution,[],[f1258,f885]) ).
fof(f2212,plain,
( spl16_246
| ~ spl16_119
| ~ spl16_152 ),
inference(avatar_split_clause,[],[f1286,f1257,f880,f2210]) ).
fof(f1286,plain,
( ! [X0,X1] :
( empty(the_carrier(X0))
| empty(sK9(powerset(the_carrier(X0))))
| element(sK9(sK9(powerset(the_carrier(X0)))),the_carrier(X1))
| ~ subrelstr(X0,X1)
| ~ rel_str(X0)
| ~ rel_str(X1) )
| ~ spl16_119
| ~ spl16_152 ),
inference(resolution,[],[f1258,f881]) ).
fof(f2203,plain,
( spl16_245
| ~ spl16_120
| ~ spl16_150 ),
inference(avatar_split_clause,[],[f1242,f1218,f884,f2201]) ).
fof(f1242,plain,
( ! [X0,X1] :
( empty(sK7(the_InternalRel(X0)))
| empty(the_InternalRel(X0))
| element(sK9(sK7(the_InternalRel(X0))),the_InternalRel(X1))
| ~ subrelstr(X0,X1)
| ~ rel_str(X0)
| ~ rel_str(X1) )
| ~ spl16_120
| ~ spl16_150 ),
inference(resolution,[],[f1219,f885]) ).
fof(f2199,plain,
( spl16_244
| ~ spl16_119
| ~ spl16_150 ),
inference(avatar_split_clause,[],[f1240,f1218,f880,f2197]) ).
fof(f1240,plain,
( ! [X0,X1] :
( empty(sK7(the_carrier(X0)))
| empty(the_carrier(X0))
| element(sK9(sK7(the_carrier(X0))),the_carrier(X1))
| ~ subrelstr(X0,X1)
| ~ rel_str(X0)
| ~ rel_str(X1) )
| ~ spl16_119
| ~ spl16_150 ),
inference(resolution,[],[f1219,f881]) ).
fof(f2195,plain,
( spl16_243
| ~ spl16_120
| ~ spl16_149 ),
inference(avatar_split_clause,[],[f1227,f1214,f884,f2193]) ).
fof(f1227,plain,
( ! [X0,X1] :
( empty(sK6(the_InternalRel(X0)))
| empty(the_InternalRel(X0))
| element(sK9(sK6(the_InternalRel(X0))),the_InternalRel(X1))
| ~ subrelstr(X0,X1)
| ~ rel_str(X0)
| ~ rel_str(X1) )
| ~ spl16_120
| ~ spl16_149 ),
inference(resolution,[],[f1215,f885]) ).
fof(f2191,plain,
( spl16_242
| ~ spl16_119
| ~ spl16_149 ),
inference(avatar_split_clause,[],[f1225,f1214,f880,f2189]) ).
fof(f1225,plain,
( ! [X0,X1] :
( empty(sK6(the_carrier(X0)))
| empty(the_carrier(X0))
| element(sK9(sK6(the_carrier(X0))),the_carrier(X1))
| ~ subrelstr(X0,X1)
| ~ rel_str(X0)
| ~ rel_str(X1) )
| ~ spl16_119
| ~ spl16_149 ),
inference(resolution,[],[f1215,f881]) ).
fof(f2185,plain,
( spl16_241
| ~ spl16_110
| ~ spl16_152 ),
inference(avatar_split_clause,[],[f1296,f1257,f799,f2183]) ).
fof(f1296,plain,
( ! [X0,X1] :
( empty(sK11(X0,X1))
| empty(sK9(powerset(sK11(X0,X1))))
| element(sK9(sK9(powerset(sK11(X0,X1)))),cartesian_product2(X0,X1)) )
| ~ spl16_110
| ~ spl16_152 ),
inference(resolution,[],[f1258,f800]) ).
fof(f2181,plain,
( spl16_240
| ~ spl16_111
| ~ spl16_152 ),
inference(avatar_split_clause,[],[f1294,f1257,f803,f2179]) ).
fof(f1294,plain,
( ! [X0,X1] :
( empty(sK10(X0,X1))
| empty(sK9(powerset(sK10(X0,X1))))
| element(sK9(sK9(powerset(sK10(X0,X1)))),cartesian_product2(X0,X1)) )
| ~ spl16_111
| ~ spl16_152 ),
inference(resolution,[],[f1258,f804]) ).
fof(f2145,plain,
( spl16_239
| ~ spl16_27
| ~ spl16_182 ),
inference(avatar_split_clause,[],[f1513,f1507,f282,f2143]) ).
fof(f1513,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) )
| ~ spl16_27
| ~ spl16_182 ),
inference(resolution,[],[f1508,f283]) ).
fof(f2141,plain,
( ~ spl16_42
| ~ spl16_58
| spl16_224 ),
inference(avatar_split_clause,[],[f2107,f2058,f476,f355]) ).
fof(f2107,plain,
( ~ rel_str(sK1)
| ~ spl16_58
| spl16_224 ),
inference(resolution,[],[f2060,f477]) ).
fof(f2060,plain,
( ~ rel_str(sK8(sK1))
| spl16_224 ),
inference(avatar_component_clause,[],[f2058]) ).
fof(f2140,plain,
( spl16_238
| ~ spl16_15
| ~ spl16_181 ),
inference(avatar_split_clause,[],[f1510,f1503,f228,f2138]) ).
fof(f2138,plain,
( spl16_238
<=> ! [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,[spl16_238])]) ).
fof(f1503,plain,
( spl16_181
<=> ! [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,[spl16_181])]) ).
fof(f1510,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) )
| ~ spl16_15
| ~ spl16_181 ),
inference(resolution,[],[f1504,f229]) ).
fof(f1504,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) )
| ~ spl16_181 ),
inference(avatar_component_clause,[],[f1503]) ).
fof(f2136,plain,
( spl16_237
| ~ spl16_38
| ~ spl16_180 ),
inference(avatar_split_clause,[],[f1501,f1489,f335,f2134]) ).
fof(f1489,plain,
( spl16_180
<=> ! [X0,X1] :
( element(sK9(the_InternalRel(X0)),the_InternalRel(X1))
| ~ subrelstr(X0,X1)
| ~ rel_str(X0)
| ~ rel_str(X1)
| empty(the_InternalRel(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_180])]) ).
fof(f1501,plain,
( ! [X0,X1] :
( ~ subrelstr(X0,X1)
| ~ rel_str(X0)
| ~ rel_str(X1)
| empty(the_InternalRel(X0))
| empty(the_InternalRel(X1))
| in(sK9(the_InternalRel(X0)),the_InternalRel(X1)) )
| ~ spl16_38
| ~ spl16_180 ),
inference(resolution,[],[f1490,f336]) ).
fof(f1490,plain,
( ! [X0,X1] :
( element(sK9(the_InternalRel(X0)),the_InternalRel(X1))
| ~ subrelstr(X0,X1)
| ~ rel_str(X0)
| ~ rel_str(X1)
| empty(the_InternalRel(X0)) )
| ~ spl16_180 ),
inference(avatar_component_clause,[],[f1489]) ).
fof(f2132,plain,
( spl16_236
| ~ spl16_38
| ~ spl16_178 ),
inference(avatar_split_clause,[],[f1500,f1480,f335,f2130]) ).
fof(f1480,plain,
( spl16_178
<=> ! [X0,X1] :
( element(sK9(the_carrier(X0)),the_carrier(X1))
| ~ subrelstr(X0,X1)
| ~ rel_str(X0)
| ~ rel_str(X1)
| empty(the_carrier(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_178])]) ).
fof(f1500,plain,
( ! [X0,X1] :
( ~ subrelstr(X0,X1)
| ~ rel_str(X0)
| ~ rel_str(X1)
| empty(the_carrier(X0))
| empty(the_carrier(X1))
| in(sK9(the_carrier(X0)),the_carrier(X1)) )
| ~ spl16_38
| ~ spl16_178 ),
inference(resolution,[],[f1481,f336]) ).
fof(f1481,plain,
( ! [X0,X1] :
( element(sK9(the_carrier(X0)),the_carrier(X1))
| ~ subrelstr(X0,X1)
| ~ rel_str(X0)
| ~ rel_str(X1)
| empty(the_carrier(X0)) )
| ~ spl16_178 ),
inference(avatar_component_clause,[],[f1480]) ).
fof(f2128,plain,
( spl16_235
| ~ spl16_65
| ~ spl16_177 ),
inference(avatar_split_clause,[],[f1496,f1476,f508,f2126]) ).
fof(f1496,plain,
( ! [X0] :
( empty(sK7(powerset(X0)))
| element(sK9(sK9(sK7(powerset(X0)))),X0)
| empty(powerset(X0))
| empty(sK9(sK7(powerset(X0)))) )
| ~ spl16_65
| ~ spl16_177 ),
inference(resolution,[],[f1477,f509]) ).
fof(f2124,plain,
( spl16_234
| ~ spl16_65
| ~ spl16_176 ),
inference(avatar_split_clause,[],[f1492,f1472,f508,f2122]) ).
fof(f1492,plain,
( ! [X0] :
( empty(sK6(powerset(X0)))
| element(sK9(sK9(sK6(powerset(X0)))),X0)
| empty(powerset(X0))
| empty(sK9(sK6(powerset(X0)))) )
| ~ spl16_65
| ~ spl16_176 ),
inference(resolution,[],[f1473,f509]) ).
fof(f2120,plain,
( spl16_233
| ~ spl16_65
| ~ spl16_173 ),
inference(avatar_split_clause,[],[f1459,f1448,f508,f2118]) ).
fof(f1459,plain,
( ! [X0] :
( element(sK9(sK9(sK9(powerset(powerset(X0))))),X0)
| empty(sK9(powerset(powerset(X0))))
| empty(sK9(sK9(powerset(powerset(X0))))) )
| ~ spl16_65
| ~ spl16_173 ),
inference(resolution,[],[f1449,f509]) ).
fof(f2105,plain,
( spl16_232
| ~ spl16_72
| ~ spl16_152 ),
inference(avatar_split_clause,[],[f1292,f1257,f549,f2103]) ).
fof(f1292,plain,
( ! [X0] :
( empty(sK9(powerset(X0)))
| empty(sK9(powerset(sK9(powerset(X0)))))
| element(sK9(sK9(powerset(sK9(powerset(X0))))),X0) )
| ~ spl16_72
| ~ spl16_152 ),
inference(resolution,[],[f1258,f550]) ).
fof(f2101,plain,
( spl16_231
| ~ spl16_110
| ~ spl16_150 ),
inference(avatar_split_clause,[],[f1250,f1218,f799,f2099]) ).
fof(f1250,plain,
( ! [X0,X1] :
( empty(sK7(sK11(X0,X1)))
| empty(sK11(X0,X1))
| element(sK9(sK7(sK11(X0,X1))),cartesian_product2(X0,X1)) )
| ~ spl16_110
| ~ spl16_150 ),
inference(resolution,[],[f1219,f800]) ).
fof(f2097,plain,
( spl16_230
| ~ spl16_111
| ~ spl16_150 ),
inference(avatar_split_clause,[],[f1248,f1218,f803,f2095]) ).
fof(f1248,plain,
( ! [X0,X1] :
( empty(sK7(sK10(X0,X1)))
| empty(sK10(X0,X1))
| element(sK9(sK7(sK10(X0,X1))),cartesian_product2(X0,X1)) )
| ~ spl16_111
| ~ spl16_150 ),
inference(resolution,[],[f1219,f804]) ).
fof(f2093,plain,
( spl16_229
| ~ spl16_110
| ~ spl16_149 ),
inference(avatar_split_clause,[],[f1235,f1214,f799,f2091]) ).
fof(f1235,plain,
( ! [X0,X1] :
( empty(sK6(sK11(X0,X1)))
| empty(sK11(X0,X1))
| element(sK9(sK6(sK11(X0,X1))),cartesian_product2(X0,X1)) )
| ~ spl16_110
| ~ spl16_149 ),
inference(resolution,[],[f1215,f800]) ).
fof(f2089,plain,
( spl16_228
| ~ spl16_111
| ~ spl16_149 ),
inference(avatar_split_clause,[],[f1233,f1214,f803,f2087]) ).
fof(f1233,plain,
( ! [X0,X1] :
( empty(sK6(sK10(X0,X1)))
| empty(sK10(X0,X1))
| element(sK9(sK6(sK10(X0,X1))),cartesian_product2(X0,X1)) )
| ~ spl16_111
| ~ spl16_149 ),
inference(resolution,[],[f1215,f804]) ).
fof(f2073,plain,
( spl16_227
| ~ spl16_77
| ~ spl16_152 ),
inference(avatar_split_clause,[],[f1291,f1257,f577,f2071]) ).
fof(f1291,plain,
( ! [X0] :
( empty(sK7(X0))
| empty(sK9(powerset(sK7(X0))))
| element(sK9(sK9(powerset(sK7(X0)))),X0)
| empty(X0) )
| ~ spl16_77
| ~ spl16_152 ),
inference(resolution,[],[f1258,f578]) ).
fof(f2069,plain,
( spl16_226
| ~ spl16_76
| ~ spl16_152 ),
inference(avatar_split_clause,[],[f1290,f1257,f573,f2067]) ).
fof(f1290,plain,
( ! [X0] :
( empty(sK6(X0))
| empty(sK9(powerset(sK6(X0))))
| element(sK9(sK9(powerset(sK6(X0)))),X0)
| empty(X0) )
| ~ spl16_76
| ~ spl16_152 ),
inference(resolution,[],[f1258,f574]) ).
fof(f2065,plain,
( ~ spl16_42
| ~ spl16_224
| spl16_225
| ~ spl16_26
| ~ spl16_192 ),
inference(avatar_split_clause,[],[f1904,f1637,f278,f2062,f2058,f355]) ).
fof(f1637,plain,
( spl16_192
<=> ! [X0] :
( ~ rel_str(X0)
| finite(the_carrier(X0))
| ~ subrelstr(X0,sK1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_192])]) ).
fof(f1904,plain,
( finite(the_carrier(sK8(sK1)))
| ~ rel_str(sK8(sK1))
| ~ rel_str(sK1)
| ~ spl16_26
| ~ spl16_192 ),
inference(resolution,[],[f1638,f279]) ).
fof(f1638,plain,
( ! [X0] :
( ~ subrelstr(X0,sK1)
| finite(the_carrier(X0))
| ~ rel_str(X0) )
| ~ spl16_192 ),
inference(avatar_component_clause,[],[f1637]) ).
fof(f2038,plain,
( spl16_223
| ~ spl16_38
| ~ spl16_154 ),
inference(avatar_split_clause,[],[f1299,f1265,f335,f2036]) ).
fof(f1265,plain,
( spl16_154
<=> ! [X0,X1] :
( element(sK9(sK10(X0,X1)),cartesian_product2(X0,X1))
| empty(sK10(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_154])]) ).
fof(f1299,plain,
( ! [X0,X1] :
( empty(sK10(X0,X1))
| empty(cartesian_product2(X0,X1))
| in(sK9(sK10(X0,X1)),cartesian_product2(X0,X1)) )
| ~ spl16_38
| ~ spl16_154 ),
inference(resolution,[],[f1266,f336]) ).
fof(f1266,plain,
( ! [X0,X1] :
( element(sK9(sK10(X0,X1)),cartesian_product2(X0,X1))
| empty(sK10(X0,X1)) )
| ~ spl16_154 ),
inference(avatar_component_clause,[],[f1265]) ).
fof(f2034,plain,
( spl16_222
| ~ spl16_38
| ~ spl16_153 ),
inference(avatar_split_clause,[],[f1298,f1261,f335,f2032]) ).
fof(f1261,plain,
( spl16_153
<=> ! [X0,X1] :
( element(sK9(sK11(X0,X1)),cartesian_product2(X0,X1))
| empty(sK11(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_153])]) ).
fof(f1298,plain,
( ! [X0,X1] :
( empty(sK11(X0,X1))
| empty(cartesian_product2(X0,X1))
| in(sK9(sK11(X0,X1)),cartesian_product2(X0,X1)) )
| ~ spl16_38
| ~ spl16_153 ),
inference(resolution,[],[f1262,f336]) ).
fof(f1262,plain,
( ! [X0,X1] :
( element(sK9(sK11(X0,X1)),cartesian_product2(X0,X1))
| empty(sK11(X0,X1)) )
| ~ spl16_153 ),
inference(avatar_component_clause,[],[f1261]) ).
fof(f2030,plain,
( spl16_221
| ~ spl16_72
| ~ spl16_150 ),
inference(avatar_split_clause,[],[f1246,f1218,f549,f2028]) ).
fof(f1246,plain,
( ! [X0] :
( empty(sK7(sK9(powerset(X0))))
| empty(sK9(powerset(X0)))
| element(sK9(sK7(sK9(powerset(X0)))),X0) )
| ~ spl16_72
| ~ spl16_150 ),
inference(resolution,[],[f1219,f550]) ).
fof(f2026,plain,
( spl16_220
| ~ spl16_72
| ~ spl16_149 ),
inference(avatar_split_clause,[],[f1231,f1214,f549,f2024]) ).
fof(f1231,plain,
( ! [X0] :
( empty(sK6(sK9(powerset(X0))))
| empty(sK9(powerset(X0)))
| element(sK9(sK6(sK9(powerset(X0)))),X0) )
| ~ spl16_72
| ~ spl16_149 ),
inference(resolution,[],[f1215,f550]) ).
fof(f1997,plain,
( spl16_219
| ~ spl16_77
| ~ spl16_150 ),
inference(avatar_split_clause,[],[f1245,f1218,f577,f1995]) ).
fof(f1245,plain,
( ! [X0] :
( empty(sK7(sK7(X0)))
| empty(sK7(X0))
| element(sK9(sK7(sK7(X0))),X0)
| empty(X0) )
| ~ spl16_77
| ~ spl16_150 ),
inference(resolution,[],[f1219,f578]) ).
fof(f1993,plain,
( spl16_218
| ~ spl16_76
| ~ spl16_150 ),
inference(avatar_split_clause,[],[f1244,f1218,f573,f1991]) ).
fof(f1244,plain,
( ! [X0] :
( empty(sK7(sK6(X0)))
| empty(sK6(X0))
| element(sK9(sK7(sK6(X0))),X0)
| empty(X0) )
| ~ spl16_76
| ~ spl16_150 ),
inference(resolution,[],[f1219,f574]) ).
fof(f1989,plain,
( spl16_217
| ~ spl16_77
| ~ spl16_149 ),
inference(avatar_split_clause,[],[f1230,f1214,f577,f1987]) ).
fof(f1230,plain,
( ! [X0] :
( empty(sK6(sK7(X0)))
| empty(sK7(X0))
| element(sK9(sK6(sK7(X0))),X0)
| empty(X0) )
| ~ spl16_77
| ~ spl16_149 ),
inference(resolution,[],[f1215,f578]) ).
fof(f1985,plain,
( spl16_216
| ~ spl16_76
| ~ spl16_149 ),
inference(avatar_split_clause,[],[f1229,f1214,f573,f1983]) ).
fof(f1229,plain,
( ! [X0] :
( empty(sK6(sK6(X0)))
| empty(sK6(X0))
| element(sK9(sK6(sK6(X0))),X0)
| empty(X0) )
| ~ spl16_76
| ~ spl16_149 ),
inference(resolution,[],[f1215,f574]) ).
fof(f1963,plain,
( spl16_215
| ~ spl16_65
| ~ spl16_175 ),
inference(avatar_split_clause,[],[f1467,f1456,f508,f1961]) ).
fof(f1456,plain,
( spl16_175
<=> ! [X0,X1] :
( empty(powerset(X0))
| empty(sK7(powerset(X0)))
| ~ empty(X0)
| ~ in(X1,sK9(sK7(powerset(X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_175])]) ).
fof(f1467,plain,
( ! [X0] :
( empty(sK7(powerset(X0)))
| ~ empty(X0)
| empty(powerset(X0))
| empty(sK9(sK7(powerset(X0)))) )
| ~ spl16_65
| ~ spl16_175 ),
inference(resolution,[],[f1457,f509]) ).
fof(f1457,plain,
( ! [X0,X1] :
( ~ in(X1,sK9(sK7(powerset(X0))))
| empty(sK7(powerset(X0)))
| ~ empty(X0)
| empty(powerset(X0)) )
| ~ spl16_175 ),
inference(avatar_component_clause,[],[f1456]) ).
fof(f1958,plain,
( spl16_135
| ~ spl16_40
| ~ spl16_140 ),
inference(avatar_split_clause,[],[f1534,f1166,f343,f1061]) ).
fof(f1061,plain,
( spl16_135
<=> relation_of2(the_InternalRel(sK1),sK14,sK14) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_135])]) ).
fof(f1166,plain,
( spl16_140
<=> relation_of2_as_subset(the_InternalRel(sK1),sK14,sK14) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_140])]) ).
fof(f1534,plain,
( relation_of2(the_InternalRel(sK1),sK14,sK14)
| ~ spl16_40
| ~ spl16_140 ),
inference(resolution,[],[f1168,f344]) ).
fof(f1168,plain,
( relation_of2_as_subset(the_InternalRel(sK1),sK14,sK14)
| ~ spl16_140 ),
inference(avatar_component_clause,[],[f1166]) ).
fof(f1957,plain,
( spl16_214
| ~ spl16_65
| ~ spl16_174 ),
inference(avatar_split_clause,[],[f1463,f1452,f508,f1955]) ).
fof(f1452,plain,
( spl16_174
<=> ! [X0,X1] :
( empty(powerset(X0))
| empty(sK6(powerset(X0)))
| ~ empty(X0)
| ~ in(X1,sK9(sK6(powerset(X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_174])]) ).
fof(f1463,plain,
( ! [X0] :
( empty(sK6(powerset(X0)))
| ~ empty(X0)
| empty(powerset(X0))
| empty(sK9(sK6(powerset(X0)))) )
| ~ spl16_65
| ~ spl16_174 ),
inference(resolution,[],[f1453,f509]) ).
fof(f1453,plain,
( ! [X0,X1] :
( ~ in(X1,sK9(sK6(powerset(X0))))
| empty(sK6(powerset(X0)))
| ~ empty(X0)
| empty(powerset(X0)) )
| ~ spl16_174 ),
inference(avatar_component_clause,[],[f1452]) ).
fof(f1944,plain,
( spl16_213
| ~ spl16_65
| ~ spl16_168 ),
inference(avatar_split_clause,[],[f1436,f1421,f508,f1942]) ).
fof(f1421,plain,
( spl16_168
<=> ! [X0,X1] :
( empty(sK9(powerset(powerset(X0))))
| ~ empty(X0)
| ~ in(X1,sK9(sK9(powerset(powerset(X0))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_168])]) ).
fof(f1436,plain,
( ! [X0] :
( ~ empty(X0)
| empty(sK9(powerset(powerset(X0))))
| empty(sK9(sK9(powerset(powerset(X0))))) )
| ~ spl16_65
| ~ spl16_168 ),
inference(resolution,[],[f1422,f509]) ).
fof(f1422,plain,
( ! [X0,X1] :
( ~ in(X1,sK9(sK9(powerset(powerset(X0)))))
| ~ empty(X0)
| empty(sK9(powerset(powerset(X0)))) )
| ~ spl16_168 ),
inference(avatar_component_clause,[],[f1421]) ).
fof(f1939,plain,
( spl16_212
| ~ spl16_78
| ~ spl16_191 ),
inference(avatar_split_clause,[],[f1869,f1621,f581,f1937]) ).
fof(f581,plain,
( spl16_78
<=> ! [X2,X0,X1] :
( element(X0,X1)
| ~ in(X0,X2)
| ~ subset(X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_78])]) ).
fof(f1869,plain,
( ! [X0,X1] :
( ~ rel_str(X0)
| ~ subrelstr(sK1,X0)
| ~ in(X1,sK14)
| element(X1,the_carrier(X0)) )
| ~ spl16_78
| ~ spl16_191 ),
inference(resolution,[],[f1622,f582]) ).
fof(f582,plain,
( ! [X2,X0,X1] :
( ~ subset(X2,X1)
| ~ in(X0,X2)
| element(X0,X1) )
| ~ spl16_78 ),
inference(avatar_component_clause,[],[f581]) ).
fof(f1924,plain,
( ~ spl16_53
| ~ spl16_24
| ~ spl16_93 ),
inference(avatar_split_clause,[],[f1394,f699,f267,f428]) ).
fof(f1910,plain,
( ~ spl16_12
| spl16_211
| ~ spl16_71
| ~ spl16_166 ),
inference(avatar_split_clause,[],[f1618,f1373,f545,f1908,f213]) ).
fof(f1373,plain,
( spl16_166
<=> ! [X0] :
( subset(the_carrier(X0),sK14)
| ~ rel_str(X0)
| ~ subrelstr(X0,sK1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_166])]) ).
fof(f1618,plain,
( ! [X0,X1] :
( ~ rel_str(X0)
| ~ subrelstr(X0,sK1)
| ~ in(X1,the_carrier(X0))
| ~ empty(sK14) )
| ~ spl16_71
| ~ spl16_166 ),
inference(resolution,[],[f1374,f546]) ).
fof(f1374,plain,
( ! [X0] :
( subset(the_carrier(X0),sK14)
| ~ rel_str(X0)
| ~ subrelstr(X0,sK1) )
| ~ spl16_166 ),
inference(avatar_component_clause,[],[f1373]) ).
fof(f1899,plain,
( ~ spl16_53
| ~ spl16_42
| ~ spl16_97
| ~ spl16_129 ),
inference(avatar_split_clause,[],[f982,f952,f733,f355,f428]) ).
fof(f982,plain,
( ~ rel_str(sK1)
| ~ empty(the_carrier(sK1))
| ~ spl16_97
| ~ spl16_129 ),
inference(duplicate_literal_removal,[],[f981]) ).
fof(f981,plain,
( ~ rel_str(sK1)
| ~ empty(the_carrier(sK1))
| ~ rel_str(sK1)
| ~ spl16_97
| ~ spl16_129 ),
inference(resolution,[],[f953,f734]) ).
fof(f1872,plain,
( spl16_61
| ~ spl16_9
| ~ spl16_57
| ~ spl16_139
| ~ spl16_142 ),
inference(avatar_split_clause,[],[f1607,f1176,f1151,f469,f198,f491]) ).
fof(f1607,plain,
( the_carrier(sK1) = sK14
| ~ spl16_9
| ~ spl16_57
| ~ spl16_139
| ~ spl16_142 ),
inference(forward_demodulation,[],[f1606,f1182]) ).
fof(f1182,plain,
( sK14 = sK9(powerset(sK14))
| ~ spl16_9
| ~ spl16_57
| ~ spl16_142 ),
inference(forward_demodulation,[],[f1179,f471]) ).
fof(f1179,plain,
( sK14 = sK9(powerset(empty_set))
| ~ spl16_9
| ~ spl16_142 ),
inference(resolution,[],[f1177,f200]) ).
fof(f1606,plain,
( the_carrier(sK1) = sK9(powerset(sK14))
| ~ spl16_9
| ~ spl16_57
| ~ spl16_139 ),
inference(forward_demodulation,[],[f1350,f471]) ).
fof(f1850,plain,
( spl16_210
| ~ spl16_27
| ~ spl16_162 ),
inference(avatar_split_clause,[],[f1650,f1319,f282,f1848]) ).
fof(f1848,plain,
( spl16_210
<=> ! [X0] :
( ~ subrelstr(sK1,X0)
| empty(the_carrier(X0))
| ~ rel_str(X0)
| ~ in(the_carrier(X0),sK4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_210])]) ).
fof(f1650,plain,
( ! [X0] :
( ~ subrelstr(sK1,X0)
| empty(the_carrier(X0))
| ~ rel_str(X0)
| ~ in(the_carrier(X0),sK4) )
| ~ spl16_27
| ~ spl16_162 ),
inference(resolution,[],[f1320,f283]) ).
fof(f1826,plain,
( spl16_209
| ~ spl16_15
| ~ spl16_171 ),
inference(avatar_split_clause,[],[f1445,f1433,f228,f1824]) ).
fof(f1824,plain,
( spl16_209
<=> ! [X0] :
( empty(powerset(X0))
| empty(powerset(powerset(X0)))
| ~ subset(powerset(powerset(X0)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_209])]) ).
fof(f1433,plain,
( spl16_171
<=> ! [X0,X1] :
( ~ subset(powerset(X0),X1)
| empty(powerset(X1))
| empty(powerset(X0))
| ~ subset(powerset(X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_171])]) ).
fof(f1445,plain,
( ! [X0] :
( empty(powerset(X0))
| empty(powerset(powerset(X0)))
| ~ subset(powerset(powerset(X0)),X0) )
| ~ spl16_15
| ~ spl16_171 ),
inference(resolution,[],[f1434,f229]) ).
fof(f1434,plain,
( ! [X0,X1] :
( ~ subset(powerset(X1),X0)
| empty(powerset(X1))
| empty(powerset(X0))
| ~ subset(powerset(X0),X1) )
| ~ spl16_171 ),
inference(avatar_component_clause,[],[f1433]) ).
fof(f1822,plain,
( spl16_208
| ~ spl16_26
| ~ spl16_167 ),
inference(avatar_split_clause,[],[f1419,f1398,f278,f1820]) ).
fof(f1398,plain,
( spl16_167
<=> ! [X0,X1] :
( ~ empty(the_InternalRel(X0))
| ~ subrelstr(X1,X0)
| ~ rel_str(X1)
| ~ rel_str(X0)
| empty(the_InternalRel(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_167])]) ).
fof(f1419,plain,
( ! [X0] :
( ~ empty(the_InternalRel(X0))
| ~ rel_str(sK8(X0))
| ~ rel_str(X0)
| empty(the_InternalRel(sK8(X0))) )
| ~ spl16_26
| ~ spl16_167 ),
inference(duplicate_literal_removal,[],[f1416]) ).
fof(f1416,plain,
( ! [X0] :
( ~ empty(the_InternalRel(X0))
| ~ rel_str(sK8(X0))
| ~ rel_str(X0)
| empty(the_InternalRel(sK8(X0)))
| ~ rel_str(X0) )
| ~ spl16_26
| ~ spl16_167 ),
inference(resolution,[],[f1399,f279]) ).
fof(f1399,plain,
( ! [X0,X1] :
( ~ subrelstr(X1,X0)
| ~ empty(the_InternalRel(X0))
| ~ rel_str(X1)
| ~ rel_str(X0)
| empty(the_InternalRel(X1)) )
| ~ spl16_167 ),
inference(avatar_component_clause,[],[f1398]) ).
fof(f1818,plain,
( spl16_207
| ~ spl16_26
| ~ spl16_161 ),
inference(avatar_split_clause,[],[f1414,f1315,f278,f1816]) ).
fof(f1315,plain,
( spl16_161
<=> ! [X0,X1] :
( ~ empty(the_carrier(X0))
| ~ subrelstr(X1,X0)
| ~ rel_str(X1)
| ~ rel_str(X0)
| empty(the_carrier(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_161])]) ).
fof(f1414,plain,
( ! [X0] :
( ~ empty(the_carrier(X0))
| ~ rel_str(sK8(X0))
| ~ rel_str(X0)
| empty(the_carrier(sK8(X0))) )
| ~ spl16_26
| ~ spl16_161 ),
inference(duplicate_literal_removal,[],[f1411]) ).
fof(f1411,plain,
( ! [X0] :
( ~ empty(the_carrier(X0))
| ~ rel_str(sK8(X0))
| ~ rel_str(X0)
| empty(the_carrier(sK8(X0)))
| ~ rel_str(X0) )
| ~ spl16_26
| ~ spl16_161 ),
inference(resolution,[],[f1316,f279]) ).
fof(f1316,plain,
( ! [X0,X1] :
( ~ subrelstr(X1,X0)
| ~ empty(the_carrier(X0))
| ~ rel_str(X1)
| ~ rel_str(X0)
| empty(the_carrier(X1)) )
| ~ spl16_161 ),
inference(avatar_component_clause,[],[f1315]) ).
fof(f1814,plain,
( spl16_206
| ~ spl16_147
| ~ spl16_155 ),
inference(avatar_split_clause,[],[f1301,f1269,f1200,f1812]) ).
fof(f1812,plain,
( spl16_206
<=> ! [X0] :
( ~ finite(the_carrier(X0))
| ~ rel_str(sK8(X0))
| ~ rel_str(X0)
| finite(the_InternalRel(sK8(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_206])]) ).
fof(f1301,plain,
( ! [X0] :
( ~ finite(the_carrier(X0))
| ~ rel_str(sK8(X0))
| ~ rel_str(X0)
| finite(the_InternalRel(sK8(X0))) )
| ~ spl16_147
| ~ spl16_155 ),
inference(duplicate_literal_removal,[],[f1300]) ).
fof(f1300,plain,
( ! [X0] :
( ~ finite(the_carrier(X0))
| ~ rel_str(sK8(X0))
| ~ rel_str(X0)
| ~ rel_str(sK8(X0))
| finite(the_InternalRel(sK8(X0))) )
| ~ spl16_147
| ~ spl16_155 ),
inference(resolution,[],[f1270,f1201]) ).
fof(f1810,plain,
( spl16_205
| ~ spl16_27
| ~ spl16_152 ),
inference(avatar_split_clause,[],[f1284,f1257,f282,f1808]) ).
fof(f1808,plain,
( spl16_205
<=> ! [X0] :
( empty(X0)
| empty(sK9(powerset(X0)))
| ~ in(X0,sK9(sK9(powerset(X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_205])]) ).
fof(f1284,plain,
( ! [X0] :
( empty(X0)
| empty(sK9(powerset(X0)))
| ~ in(X0,sK9(sK9(powerset(X0)))) )
| ~ spl16_27
| ~ spl16_152 ),
inference(resolution,[],[f1258,f283]) ).
fof(f1806,plain,
( spl16_137
| ~ spl16_41
| ~ spl16_189 ),
inference(avatar_split_clause,[],[f1780,f1595,f347,f1104]) ).
fof(f1799,plain,
( spl16_204
| ~ spl16_99
| ~ spl16_148 ),
inference(avatar_split_clause,[],[f1211,f1206,f743,f1797]) ).
fof(f1211,plain,
( ! [X0,X1] :
( sK9(powerset(X0)) = sK9(powerset(X1))
| ~ empty(X0)
| ~ empty(X1) )
| ~ spl16_99
| ~ spl16_148 ),
inference(resolution,[],[f1207,f744]) ).
fof(f1795,plain,
( spl16_203
| ~ spl16_78
| ~ spl16_188 ),
inference(avatar_split_clause,[],[f1757,f1577,f581,f1793]) ).
fof(f1577,plain,
( spl16_188
<=> ! [X0] :
( subset(sK14,the_carrier(X0))
| ~ rel_str(X0)
| ~ subrelstr(sK0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_188])]) ).
fof(f1757,plain,
( ! [X0,X1] :
( ~ rel_str(X0)
| ~ subrelstr(sK0,X0)
| ~ in(X1,sK14)
| element(X1,the_carrier(X0)) )
| ~ spl16_78
| ~ spl16_188 ),
inference(resolution,[],[f1578,f582]) ).
fof(f1578,plain,
( ! [X0] :
( subset(sK14,the_carrier(X0))
| ~ rel_str(X0)
| ~ subrelstr(sK0,X0) )
| ~ spl16_188 ),
inference(avatar_component_clause,[],[f1577]) ).
fof(f1784,plain,
( spl16_202
| ~ spl16_86
| ~ spl16_137 ),
inference(avatar_split_clause,[],[f1572,f1104,f653,f1782]) ).
fof(f1572,plain,
( ! [X0] :
( ~ in(X0,the_InternalRel(sK0))
| element(X0,cartesian_product2(sK14,sK14)) )
| ~ spl16_86
| ~ spl16_137 ),
inference(resolution,[],[f1106,f654]) ).
fof(f1777,plain,
( ~ spl16_55
| ~ spl16_24
| ~ spl16_56 ),
inference(avatar_split_clause,[],[f948,f455,f267,f447]) ).
fof(f1764,plain,
( ~ spl16_1
| spl16_201
| ~ spl16_47
| ~ spl16_128 ),
inference(avatar_split_clause,[],[f1000,f934,f400,f1762,f158]) ).
fof(f1000,plain,
( ! [X0] :
( subset(the_carrier(X0),sK14)
| ~ subrelstr(X0,sK0)
| ~ rel_str(X0)
| ~ rel_str(sK0) )
| ~ spl16_47
| ~ spl16_128 ),
inference(superposition,[],[f401,f936]) ).
fof(f1722,plain,
( spl16_200
| ~ spl16_27
| ~ spl16_157 ),
inference(avatar_split_clause,[],[f1643,f1277,f282,f1720]) ).
fof(f1720,plain,
( spl16_200
<=> ! [X0] :
( ~ subrelstr(sK0,X0)
| empty(the_carrier(X0))
| ~ rel_str(X0)
| ~ in(the_carrier(X0),sK4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_200])]) ).
fof(f1643,plain,
( ! [X0] :
( ~ subrelstr(sK0,X0)
| empty(the_carrier(X0))
| ~ rel_str(X0)
| ~ in(the_carrier(X0),sK4) )
| ~ spl16_27
| ~ spl16_157 ),
inference(resolution,[],[f1278,f283]) ).
fof(f1718,plain,
( spl16_199
| ~ spl16_27
| ~ spl16_150 ),
inference(avatar_split_clause,[],[f1238,f1218,f282,f1716]) ).
fof(f1716,plain,
( spl16_199
<=> ! [X0] :
( empty(sK7(X0))
| empty(X0)
| ~ in(X0,sK9(sK7(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_199])]) ).
fof(f1238,plain,
( ! [X0] :
( empty(sK7(X0))
| empty(X0)
| ~ in(X0,sK9(sK7(X0))) )
| ~ spl16_27
| ~ spl16_150 ),
inference(resolution,[],[f1219,f283]) ).
fof(f1714,plain,
( spl16_198
| ~ spl16_27
| ~ spl16_149 ),
inference(avatar_split_clause,[],[f1223,f1214,f282,f1712]) ).
fof(f1712,plain,
( spl16_198
<=> ! [X0] :
( empty(sK6(X0))
| empty(X0)
| ~ in(X0,sK9(sK6(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_198])]) ).
fof(f1223,plain,
( ! [X0] :
( empty(sK6(X0))
| empty(X0)
| ~ in(X0,sK9(sK6(X0))) )
| ~ spl16_27
| ~ spl16_149 ),
inference(resolution,[],[f1215,f283]) ).
fof(f1704,plain,
( spl16_197
| ~ spl16_99
| ~ spl16_142 ),
inference(avatar_split_clause,[],[f1181,f1176,f743,f1702]) ).
fof(f1181,plain,
( ! [X0] :
( sK14 = sK9(powerset(sK9(powerset(X0))))
| ~ empty(X0) )
| ~ spl16_99
| ~ spl16_142 ),
inference(resolution,[],[f1177,f744]) ).
fof(f1699,plain,
( ~ spl16_3
| ~ spl16_4
| ~ spl16_42
| spl16_196
| ~ spl16_5
| ~ spl16_185 ),
inference(avatar_split_clause,[],[f1530,f1527,f178,f1697,f355,f173,f168]) ).
fof(f168,plain,
( spl16_3
<=> element(sK4,the_carrier(sK1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_3])]) ).
fof(f173,plain,
( spl16_4
<=> element(sK5,the_carrier(sK1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_4])]) ).
fof(f178,plain,
( spl16_5
<=> related(sK1,sK4,sK5) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_5])]) ).
fof(f1527,plain,
( spl16_185
<=> ! [X0,X3,X2,X1] :
( element(ordered_pair(X0,X1),the_InternalRel(X2))
| ~ subrelstr(X3,X2)
| ~ rel_str(X3)
| ~ rel_str(X2)
| ~ related(X3,X0,X1)
| ~ element(X1,the_carrier(X3))
| ~ element(X0,the_carrier(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_185])]) ).
fof(f1530,plain,
( ! [X0] :
( ~ subrelstr(sK1,X0)
| ~ rel_str(sK1)
| ~ rel_str(X0)
| element(ordered_pair(sK4,sK5),the_InternalRel(X0))
| ~ element(sK5,the_carrier(sK1))
| ~ element(sK4,the_carrier(sK1)) )
| ~ spl16_5
| ~ spl16_185 ),
inference(resolution,[],[f1528,f180]) ).
fof(f180,plain,
( related(sK1,sK4,sK5)
| ~ spl16_5 ),
inference(avatar_component_clause,[],[f178]) ).
fof(f1528,plain,
( ! [X2,X3,X0,X1] :
( ~ related(X3,X0,X1)
| ~ subrelstr(X3,X2)
| ~ rel_str(X3)
| ~ rel_str(X2)
| element(ordered_pair(X0,X1),the_InternalRel(X2))
| ~ element(X1,the_carrier(X3))
| ~ element(X0,the_carrier(X3)) )
| ~ spl16_185 ),
inference(avatar_component_clause,[],[f1527]) ).
fof(f1683,plain,
( spl16_195
| ~ spl16_9
| ~ spl16_57
| ~ spl16_142 ),
inference(avatar_split_clause,[],[f1182,f1176,f469,f198,f1680]) ).
fof(f1678,plain,
( spl16_194
| ~ spl16_86
| ~ spl16_140 ),
inference(avatar_split_clause,[],[f1531,f1166,f653,f1676]) ).
fof(f1531,plain,
( ! [X0] :
( ~ in(X0,the_InternalRel(sK1))
| element(X0,cartesian_product2(sK14,sK14)) )
| ~ spl16_86
| ~ spl16_140 ),
inference(resolution,[],[f1168,f654]) ).
fof(f1671,plain,
( ~ spl16_3
| ~ spl16_4
| ~ spl16_42
| spl16_193
| ~ spl16_5
| ~ spl16_183 ),
inference(avatar_split_clause,[],[f1521,f1518,f178,f1669,f355,f173,f168]) ).
fof(f1669,plain,
( spl16_193
<=> ! [X0] :
( ~ subrelstr(sK1,X0)
| ~ empty(the_InternalRel(X0))
| ~ rel_str(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_193])]) ).
fof(f1518,plain,
( spl16_183
<=> ! [X0,X3,X2,X1] :
( ~ empty(the_InternalRel(X0))
| ~ subrelstr(X1,X0)
| ~ rel_str(X1)
| ~ rel_str(X0)
| ~ related(X1,X2,X3)
| ~ element(X3,the_carrier(X1))
| ~ element(X2,the_carrier(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_183])]) ).
fof(f1521,plain,
( ! [X0] :
( ~ subrelstr(sK1,X0)
| ~ rel_str(sK1)
| ~ rel_str(X0)
| ~ empty(the_InternalRel(X0))
| ~ element(sK5,the_carrier(sK1))
| ~ element(sK4,the_carrier(sK1)) )
| ~ spl16_5
| ~ spl16_183 ),
inference(resolution,[],[f1519,f180]) ).
fof(f1519,plain,
( ! [X2,X3,X0,X1] :
( ~ related(X1,X2,X3)
| ~ subrelstr(X1,X0)
| ~ rel_str(X1)
| ~ rel_str(X0)
| ~ empty(the_InternalRel(X0))
| ~ element(X3,the_carrier(X1))
| ~ element(X2,the_carrier(X1)) )
| ~ spl16_183 ),
inference(avatar_component_clause,[],[f1518]) ).
fof(f1639,plain,
( ~ spl16_25
| spl16_192
| ~ spl16_69
| ~ spl16_166 ),
inference(avatar_split_clause,[],[f1619,f1373,f530,f1637,f271]) ).
fof(f1619,plain,
( ! [X0] :
( ~ rel_str(X0)
| ~ subrelstr(X0,sK1)
| ~ finite(sK14)
| finite(the_carrier(X0)) )
| ~ spl16_69
| ~ spl16_166 ),
inference(resolution,[],[f1374,f531]) ).
fof(f1634,plain,
( ~ spl16_53
| ~ spl16_24
| ~ spl16_93 ),
inference(avatar_split_clause,[],[f1394,f699,f267,f428]) ).
fof(f1623,plain,
( ~ spl16_42
| spl16_191
| ~ spl16_47
| ~ spl16_61 ),
inference(avatar_split_clause,[],[f602,f491,f400,f1621,f355]) ).
fof(f602,plain,
( ! [X0] :
( subset(sK14,the_carrier(X0))
| ~ subrelstr(sK1,X0)
| ~ rel_str(sK1)
| ~ rel_str(X0) )
| ~ spl16_47
| ~ spl16_61 ),
inference(superposition,[],[f401,f493]) ).
fof(f1602,plain,
( spl16_190
| ~ spl16_38
| ~ spl16_138 ),
inference(avatar_split_clause,[],[f1170,f1121,f335,f1600]) ).
fof(f1170,plain,
( ! [X0] :
( ~ rel_str(X0)
| ~ subrelstr(sK1,X0)
| empty(the_carrier(X0))
| in(sK5,the_carrier(X0)) )
| ~ spl16_38
| ~ spl16_138 ),
inference(resolution,[],[f1122,f336]) ).
fof(f1598,plain,
( spl16_189
| ~ spl16_40
| ~ spl16_137 ),
inference(avatar_split_clause,[],[f1575,f1104,f343,f1595]) ).
fof(f1575,plain,
( relation_of2(the_InternalRel(sK0),sK14,sK14)
| ~ spl16_40
| ~ spl16_137 ),
inference(resolution,[],[f1106,f344]) ).
fof(f1592,plain,
( spl16_124
| ~ spl16_1
| ~ spl16_122
| ~ spl16_147 ),
inference(avatar_split_clause,[],[f1204,f1200,f902,f158,f911]) ).
fof(f911,plain,
( spl16_124
<=> finite(the_InternalRel(sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_124])]) ).
fof(f902,plain,
( spl16_122
<=> finite(the_carrier(sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_122])]) ).
fof(f1204,plain,
( ~ rel_str(sK0)
| finite(the_InternalRel(sK0))
| ~ spl16_122
| ~ spl16_147 ),
inference(resolution,[],[f1201,f903]) ).
fof(f903,plain,
( finite(the_carrier(sK0))
| ~ spl16_122 ),
inference(avatar_component_clause,[],[f902]) ).
fof(f1590,plain,
( ~ spl16_55
| ~ spl16_24
| ~ spl16_56 ),
inference(avatar_split_clause,[],[f948,f455,f267,f447]) ).
fof(f1579,plain,
( ~ spl16_1
| spl16_188
| ~ spl16_47
| ~ spl16_128 ),
inference(avatar_split_clause,[],[f999,f934,f400,f1577,f158]) ).
fof(f999,plain,
( ! [X0] :
( subset(sK14,the_carrier(X0))
| ~ subrelstr(sK0,X0)
| ~ rel_str(sK0)
| ~ rel_str(X0) )
| ~ spl16_47
| ~ spl16_128 ),
inference(superposition,[],[f401,f936]) ).
fof(f1543,plain,
( spl16_187
| ~ spl16_38
| ~ spl16_136 ),
inference(avatar_split_clause,[],[f1119,f1078,f335,f1541]) ).
fof(f1078,plain,
( spl16_136
<=> ! [X0] :
( element(sK5,the_carrier(X0))
| ~ rel_str(X0)
| ~ subrelstr(sK0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_136])]) ).
fof(f1119,plain,
( ! [X0] :
( ~ rel_str(X0)
| ~ subrelstr(sK0,X0)
| empty(the_carrier(X0))
| in(sK5,the_carrier(X0)) )
| ~ spl16_38
| ~ spl16_136 ),
inference(resolution,[],[f1079,f336]) ).
fof(f1079,plain,
( ! [X0] :
( element(sK5,the_carrier(X0))
| ~ rel_str(X0)
| ~ subrelstr(sK0,X0) )
| ~ spl16_136 ),
inference(avatar_component_clause,[],[f1078]) ).
fof(f1539,plain,
( spl16_96
| ~ spl16_1
| ~ spl16_42
| ~ spl16_186
| ~ spl16_2
| ~ spl16_167 ),
inference(avatar_split_clause,[],[f1415,f1398,f163,f1536,f355,f158,f725]) ).
fof(f1415,plain,
( ~ empty(the_InternalRel(sK0))
| ~ rel_str(sK1)
| ~ rel_str(sK0)
| empty(the_InternalRel(sK1))
| ~ spl16_2
| ~ spl16_167 ),
inference(resolution,[],[f1399,f165]) ).
fof(f1529,plain,
( spl16_185
| ~ spl16_50
| ~ spl16_120 ),
inference(avatar_split_clause,[],[f898,f884,f416,f1527]) ).
fof(f416,plain,
( spl16_50
<=> ! [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) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_50])]) ).
fof(f898,plain,
( ! [X2,X3,X0,X1] :
( element(ordered_pair(X0,X1),the_InternalRel(X2))
| ~ subrelstr(X3,X2)
| ~ rel_str(X3)
| ~ rel_str(X2)
| ~ related(X3,X0,X1)
| ~ element(X1,the_carrier(X3))
| ~ element(X0,the_carrier(X3)) )
| ~ spl16_50
| ~ spl16_120 ),
inference(duplicate_literal_removal,[],[f896]) ).
fof(f896,plain,
( ! [X2,X3,X0,X1] :
( element(ordered_pair(X0,X1),the_InternalRel(X2))
| ~ subrelstr(X3,X2)
| ~ rel_str(X3)
| ~ rel_str(X2)
| ~ related(X3,X0,X1)
| ~ element(X1,the_carrier(X3))
| ~ element(X0,the_carrier(X3))
| ~ rel_str(X3) )
| ~ spl16_50
| ~ spl16_120 ),
inference(resolution,[],[f885,f417]) ).
fof(f417,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) )
| ~ spl16_50 ),
inference(avatar_component_clause,[],[f416]) ).
fof(f1525,plain,
( spl16_184
| ~ spl16_87
| ~ spl16_121 ),
inference(avatar_split_clause,[],[f900,f888,f660,f1523]) ).
fof(f1523,plain,
( spl16_184
<=> ! [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,[spl16_184])]) ).
fof(f660,plain,
( spl16_87
<=> ! [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,[spl16_87])]) ).
fof(f900,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) )
| ~ spl16_87
| ~ spl16_121 ),
inference(resolution,[],[f889,f661]) ).
fof(f661,plain,
( ! [X2,X0,X1] :
( in(X0,powerset(cartesian_product2(X1,X2)))
| empty(powerset(cartesian_product2(X1,X2)))
| ~ relation_of2_as_subset(X0,X1,X2) )
| ~ spl16_87 ),
inference(avatar_component_clause,[],[f660]) ).
fof(f1520,plain,
( spl16_183
| ~ spl16_50
| ~ spl16_118 ),
inference(avatar_split_clause,[],[f878,f868,f416,f1518]) ).
fof(f868,plain,
( spl16_118
<=> ! [X2,X0,X1] :
( ~ in(X0,the_InternalRel(X1))
| ~ empty(the_InternalRel(X2))
| ~ subrelstr(X1,X2)
| ~ rel_str(X1)
| ~ rel_str(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_118])]) ).
fof(f878,plain,
( ! [X2,X3,X0,X1] :
( ~ empty(the_InternalRel(X0))
| ~ subrelstr(X1,X0)
| ~ rel_str(X1)
| ~ rel_str(X0)
| ~ related(X1,X2,X3)
| ~ element(X3,the_carrier(X1))
| ~ element(X2,the_carrier(X1)) )
| ~ spl16_50
| ~ spl16_118 ),
inference(duplicate_literal_removal,[],[f876]) ).
fof(f876,plain,
( ! [X2,X3,X0,X1] :
( ~ empty(the_InternalRel(X0))
| ~ subrelstr(X1,X0)
| ~ rel_str(X1)
| ~ rel_str(X0)
| ~ related(X1,X2,X3)
| ~ element(X3,the_carrier(X1))
| ~ element(X2,the_carrier(X1))
| ~ rel_str(X1) )
| ~ spl16_50
| ~ spl16_118 ),
inference(resolution,[],[f869,f417]) ).
fof(f869,plain,
( ! [X2,X0,X1] :
( ~ in(X0,the_InternalRel(X1))
| ~ empty(the_InternalRel(X2))
| ~ subrelstr(X1,X2)
| ~ rel_str(X1)
| ~ rel_str(X2) )
| ~ spl16_118 ),
inference(avatar_component_clause,[],[f868]) ).
fof(f1509,plain,
( spl16_182
| ~ spl16_38
| ~ spl16_116 ),
inference(avatar_split_clause,[],[f861,f847,f335,f1507]) ).
fof(f847,plain,
( spl16_116
<=> ! [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,[spl16_116])]) ).
fof(f861,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))) )
| ~ spl16_38
| ~ spl16_116 ),
inference(resolution,[],[f848,f336]) ).
fof(f848,plain,
( ! [X0,X1] :
( element(X0,cartesian_product2(the_carrier(X1),the_carrier(X1)))
| ~ in(X0,the_InternalRel(X1))
| ~ rel_str(X1) )
| ~ spl16_116 ),
inference(avatar_component_clause,[],[f847]) ).
fof(f1505,plain,
( spl16_181
| ~ spl16_87
| ~ spl16_109 ),
inference(avatar_split_clause,[],[f824,f795,f660,f1503]) ).
fof(f824,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) )
| ~ spl16_87
| ~ spl16_109 ),
inference(resolution,[],[f796,f661]) ).
fof(f1491,plain,
( spl16_180
| ~ spl16_65
| ~ spl16_120 ),
inference(avatar_split_clause,[],[f897,f884,f508,f1489]) ).
fof(f897,plain,
( ! [X0,X1] :
( element(sK9(the_InternalRel(X0)),the_InternalRel(X1))
| ~ subrelstr(X0,X1)
| ~ rel_str(X0)
| ~ rel_str(X1)
| empty(the_InternalRel(X0)) )
| ~ spl16_65
| ~ spl16_120 ),
inference(resolution,[],[f885,f509]) ).
fof(f1487,plain,
( spl16_179
| ~ spl16_100
| ~ spl16_163 ),
inference(avatar_split_clause,[],[f1409,f1358,f754,f1484]) ).
fof(f1484,plain,
( spl16_179
<=> finite(sK11(sK14,sK14)) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_179])]) ).
fof(f754,plain,
( spl16_100
<=> ! [X0,X1] :
( finite(sK11(X0,X1))
| ~ finite(cartesian_product2(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_100])]) ).
fof(f1409,plain,
( finite(sK11(sK14,sK14))
| ~ spl16_100
| ~ spl16_163 ),
inference(resolution,[],[f1359,f755]) ).
fof(f755,plain,
( ! [X0,X1] :
( ~ finite(cartesian_product2(X0,X1))
| finite(sK11(X0,X1)) )
| ~ spl16_100 ),
inference(avatar_component_clause,[],[f754]) ).
fof(f1359,plain,
( finite(cartesian_product2(sK14,sK14))
| ~ spl16_163 ),
inference(avatar_component_clause,[],[f1358]) ).
fof(f1482,plain,
( spl16_178
| ~ spl16_65
| ~ spl16_119 ),
inference(avatar_split_clause,[],[f895,f880,f508,f1480]) ).
fof(f895,plain,
( ! [X0,X1] :
( element(sK9(the_carrier(X0)),the_carrier(X1))
| ~ subrelstr(X0,X1)
| ~ rel_str(X0)
| ~ rel_str(X1)
| empty(the_carrier(X0)) )
| ~ spl16_65
| ~ spl16_119 ),
inference(resolution,[],[f881,f509]) ).
fof(f1478,plain,
( spl16_177
| ~ spl16_46
| ~ spl16_106 ),
inference(avatar_split_clause,[],[f817,f783,f387,f1476]) ).
fof(f783,plain,
( spl16_106
<=> ! [X0] :
( element(sK9(sK7(X0)),X0)
| empty(X0)
| empty(sK7(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_106])]) ).
fof(f817,plain,
( ! [X0,X1] :
( empty(powerset(X0))
| empty(sK7(powerset(X0)))
| element(X1,X0)
| ~ in(X1,sK9(sK7(powerset(X0)))) )
| ~ spl16_46
| ~ spl16_106 ),
inference(resolution,[],[f784,f388]) ).
fof(f784,plain,
( ! [X0] :
( element(sK9(sK7(X0)),X0)
| empty(X0)
| empty(sK7(X0)) )
| ~ spl16_106 ),
inference(avatar_component_clause,[],[f783]) ).
fof(f1474,plain,
( spl16_176
| ~ spl16_46
| ~ spl16_105 ),
inference(avatar_split_clause,[],[f811,f779,f387,f1472]) ).
fof(f779,plain,
( spl16_105
<=> ! [X0] :
( element(sK9(sK6(X0)),X0)
| empty(X0)
| empty(sK6(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_105])]) ).
fof(f811,plain,
( ! [X0,X1] :
( empty(powerset(X0))
| empty(sK6(powerset(X0)))
| element(X1,X0)
| ~ in(X1,sK9(sK6(powerset(X0)))) )
| ~ spl16_46
| ~ spl16_105 ),
inference(resolution,[],[f780,f388]) ).
fof(f780,plain,
( ! [X0] :
( element(sK9(sK6(X0)),X0)
| empty(X0)
| empty(sK6(X0)) )
| ~ spl16_105 ),
inference(avatar_component_clause,[],[f779]) ).
fof(f1458,plain,
( spl16_175
| ~ spl16_44
| ~ spl16_106 ),
inference(avatar_split_clause,[],[f818,f783,f374,f1456]) ).
fof(f818,plain,
( ! [X0,X1] :
( empty(powerset(X0))
| empty(sK7(powerset(X0)))
| ~ empty(X0)
| ~ in(X1,sK9(sK7(powerset(X0)))) )
| ~ spl16_44
| ~ spl16_106 ),
inference(resolution,[],[f784,f375]) ).
fof(f1454,plain,
( spl16_174
| ~ spl16_44
| ~ spl16_105 ),
inference(avatar_split_clause,[],[f812,f779,f374,f1452]) ).
fof(f812,plain,
( ! [X0,X1] :
( empty(powerset(X0))
| empty(sK6(powerset(X0)))
| ~ empty(X0)
| ~ in(X1,sK9(sK6(powerset(X0)))) )
| ~ spl16_44
| ~ spl16_105 ),
inference(resolution,[],[f780,f375]) ).
fof(f1450,plain,
( spl16_173
| ~ spl16_46
| ~ spl16_104 ),
inference(avatar_split_clause,[],[f806,f775,f387,f1448]) ).
fof(f775,plain,
( spl16_104
<=> ! [X0] :
( element(sK9(sK9(powerset(X0))),X0)
| empty(sK9(powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_104])]) ).
fof(f806,plain,
( ! [X0,X1] :
( empty(sK9(powerset(powerset(X0))))
| element(X1,X0)
| ~ in(X1,sK9(sK9(powerset(powerset(X0))))) )
| ~ spl16_46
| ~ spl16_104 ),
inference(resolution,[],[f776,f388]) ).
fof(f776,plain,
( ! [X0] :
( element(sK9(sK9(powerset(X0))),X0)
| empty(sK9(powerset(X0))) )
| ~ spl16_104 ),
inference(avatar_component_clause,[],[f775]) ).
fof(f1444,plain,
( spl16_172
| ~ spl16_101
| ~ spl16_163 ),
inference(avatar_split_clause,[],[f1408,f1358,f758,f1441]) ).
fof(f1441,plain,
( spl16_172
<=> finite(sK10(sK14,sK14)) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_172])]) ).
fof(f758,plain,
( spl16_101
<=> ! [X0,X1] :
( finite(sK10(X0,X1))
| ~ finite(cartesian_product2(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_101])]) ).
fof(f1408,plain,
( finite(sK10(sK14,sK14))
| ~ spl16_101
| ~ spl16_163 ),
inference(resolution,[],[f1359,f759]) ).
fof(f759,plain,
( ! [X0,X1] :
( ~ finite(cartesian_product2(X0,X1))
| finite(sK10(X0,X1)) )
| ~ spl16_101 ),
inference(avatar_component_clause,[],[f758]) ).
fof(f1435,plain,
( spl16_171
| ~ spl16_81
| ~ spl16_109 ),
inference(avatar_split_clause,[],[f823,f795,f613,f1433]) ).
fof(f613,plain,
( spl16_81
<=> ! [X0,X1] :
( empty(powerset(X0))
| in(X1,powerset(X0))
| ~ subset(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_81])]) ).
fof(f823,plain,
( ! [X0,X1] :
( ~ subset(powerset(X0),X1)
| empty(powerset(X1))
| empty(powerset(X0))
| ~ subset(powerset(X1),X0) )
| ~ spl16_81
| ~ spl16_109 ),
inference(resolution,[],[f796,f614]) ).
fof(f614,plain,
( ! [X0,X1] :
( in(X1,powerset(X0))
| empty(powerset(X0))
| ~ subset(X1,X0) )
| ~ spl16_81 ),
inference(avatar_component_clause,[],[f613]) ).
fof(f1431,plain,
( spl16_170
| ~ spl16_37
| ~ spl16_106 ),
inference(avatar_split_clause,[],[f819,f783,f331,f1429]) ).
fof(f1429,plain,
( spl16_170
<=> ! [X0] :
( empty(powerset(X0))
| empty(sK7(powerset(X0)))
| finite(sK9(sK7(powerset(X0))))
| ~ finite(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_170])]) ).
fof(f819,plain,
( ! [X0] :
( empty(powerset(X0))
| empty(sK7(powerset(X0)))
| finite(sK9(sK7(powerset(X0))))
| ~ finite(X0) )
| ~ spl16_37
| ~ spl16_106 ),
inference(resolution,[],[f784,f332]) ).
fof(f1427,plain,
( spl16_169
| ~ spl16_37
| ~ spl16_105 ),
inference(avatar_split_clause,[],[f813,f779,f331,f1425]) ).
fof(f1425,plain,
( spl16_169
<=> ! [X0] :
( empty(powerset(X0))
| empty(sK6(powerset(X0)))
| finite(sK9(sK6(powerset(X0))))
| ~ finite(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_169])]) ).
fof(f813,plain,
( ! [X0] :
( empty(powerset(X0))
| empty(sK6(powerset(X0)))
| finite(sK9(sK6(powerset(X0))))
| ~ finite(X0) )
| ~ spl16_37
| ~ spl16_105 ),
inference(resolution,[],[f780,f332]) ).
fof(f1423,plain,
( spl16_168
| ~ spl16_44
| ~ spl16_104 ),
inference(avatar_split_clause,[],[f807,f775,f374,f1421]) ).
fof(f807,plain,
( ! [X0,X1] :
( empty(sK9(powerset(powerset(X0))))
| ~ empty(X0)
| ~ in(X1,sK9(sK9(powerset(powerset(X0))))) )
| ~ spl16_44
| ~ spl16_104 ),
inference(resolution,[],[f776,f375]) ).
fof(f1407,plain,
( ~ spl16_25
| ~ spl16_39
| spl16_163 ),
inference(avatar_split_clause,[],[f1363,f1358,f339,f271]) ).
fof(f339,plain,
( spl16_39
<=> ! [X0,X1] :
( finite(cartesian_product2(X0,X1))
| ~ finite(X1)
| ~ finite(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_39])]) ).
fof(f1363,plain,
( ~ finite(sK14)
| ~ spl16_39
| spl16_163 ),
inference(duplicate_literal_removal,[],[f1362]) ).
fof(f1362,plain,
( ~ finite(sK14)
| ~ finite(sK14)
| ~ spl16_39
| spl16_163 ),
inference(resolution,[],[f1360,f340]) ).
fof(f340,plain,
( ! [X0,X1] :
( finite(cartesian_product2(X0,X1))
| ~ finite(X1)
| ~ finite(X0) )
| ~ spl16_39 ),
inference(avatar_component_clause,[],[f339]) ).
fof(f1360,plain,
( ~ finite(cartesian_product2(sK14,sK14))
| spl16_163 ),
inference(avatar_component_clause,[],[f1358]) ).
fof(f1400,plain,
( spl16_167
| ~ spl16_65
| ~ spl16_118 ),
inference(avatar_split_clause,[],[f877,f868,f508,f1398]) ).
fof(f877,plain,
( ! [X0,X1] :
( ~ empty(the_InternalRel(X0))
| ~ subrelstr(X1,X0)
| ~ rel_str(X1)
| ~ rel_str(X0)
| empty(the_InternalRel(X1)) )
| ~ spl16_65
| ~ spl16_118 ),
inference(resolution,[],[f869,f509]) ).
fof(f1395,plain,
( ~ spl16_53
| ~ spl16_24
| ~ spl16_52 ),
inference(avatar_split_clause,[],[f697,f424,f267,f428]) ).
fof(f697,plain,
( ~ empty(the_carrier(sK1))
| ~ spl16_24
| ~ spl16_52 ),
inference(resolution,[],[f426,f268]) ).
fof(f1384,plain,
( ~ spl16_12
| ~ spl16_9
| ~ spl16_12
| ~ spl16_24
| ~ spl16_57
| ~ spl16_93
| ~ spl16_139
| ~ spl16_142 ),
inference(avatar_split_clause,[],[f1376,f1176,f1151,f699,f469,f267,f213,f198,f213]) ).
fof(f1376,plain,
( ~ empty(sK14)
| ~ spl16_9
| ~ spl16_12
| ~ spl16_24
| ~ spl16_57
| ~ spl16_93
| ~ spl16_139
| ~ spl16_142 ),
inference(forward_demodulation,[],[f710,f1355]) ).
fof(f1355,plain,
( the_carrier(sK1) = sK14
| ~ spl16_9
| ~ spl16_12
| ~ spl16_57
| ~ spl16_139
| ~ spl16_142 ),
inference(forward_demodulation,[],[f1351,f1182]) ).
fof(f1351,plain,
( the_carrier(sK1) = sK9(powerset(sK14))
| ~ spl16_12
| ~ spl16_139 ),
inference(resolution,[],[f1152,f215]) ).
fof(f215,plain,
( empty(sK14)
| ~ spl16_12 ),
inference(avatar_component_clause,[],[f213]) ).
fof(f710,plain,
( ~ empty(the_carrier(sK1))
| ~ spl16_24
| ~ spl16_93 ),
inference(resolution,[],[f701,f268]) ).
fof(f1375,plain,
( ~ spl16_42
| spl16_166
| ~ spl16_47
| ~ spl16_61 ),
inference(avatar_split_clause,[],[f601,f491,f400,f1373,f355]) ).
fof(f601,plain,
( ! [X0] :
( subset(the_carrier(X0),sK14)
| ~ subrelstr(X0,sK1)
| ~ rel_str(X0)
| ~ rel_str(sK1) )
| ~ spl16_47
| ~ spl16_61 ),
inference(superposition,[],[f401,f493]) ).
fof(f1371,plain,
( ~ spl16_42
| spl16_164
| ~ spl16_165
| ~ spl16_61
| ~ spl16_113 ),
inference(avatar_split_clause,[],[f1055,f835,f491,f1368,f1365,f355]) ).
fof(f835,plain,
( spl16_113
<=> ! [X0,X1] :
( ~ empty(cartesian_product2(the_carrier(X0),the_carrier(X0)))
| ~ in(X1,the_InternalRel(X0))
| ~ rel_str(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_113])]) ).
fof(f1055,plain,
( ! [X0] :
( ~ empty(cartesian_product2(sK14,sK14))
| ~ in(X0,the_InternalRel(sK1))
| ~ rel_str(sK1) )
| ~ spl16_61
| ~ spl16_113 ),
inference(superposition,[],[f836,f493]) ).
fof(f836,plain,
( ! [X0,X1] :
( ~ empty(cartesian_product2(the_carrier(X0),the_carrier(X0)))
| ~ in(X1,the_InternalRel(X0))
| ~ rel_str(X0) )
| ~ spl16_113 ),
inference(avatar_component_clause,[],[f835]) ).
fof(f1361,plain,
( ~ spl16_42
| spl16_125
| ~ spl16_163
| ~ spl16_61
| ~ spl16_112 ),
inference(avatar_split_clause,[],[f1054,f829,f491,f1358,f915,f355]) ).
fof(f915,plain,
( spl16_125
<=> finite(the_InternalRel(sK1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_125])]) ).
fof(f829,plain,
( spl16_112
<=> ! [X0] :
( finite(the_InternalRel(X0))
| ~ finite(cartesian_product2(the_carrier(X0),the_carrier(X0)))
| ~ rel_str(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_112])]) ).
fof(f1054,plain,
( ~ finite(cartesian_product2(sK14,sK14))
| finite(the_InternalRel(sK1))
| ~ rel_str(sK1)
| ~ spl16_61
| ~ spl16_112 ),
inference(superposition,[],[f830,f493]) ).
fof(f830,plain,
( ! [X0] :
( ~ finite(cartesian_product2(the_carrier(X0),the_carrier(X0)))
| finite(the_InternalRel(X0))
| ~ rel_str(X0) )
| ~ spl16_112 ),
inference(avatar_component_clause,[],[f829]) ).
fof(f1329,plain,
( spl16_61
| ~ spl16_9
| ~ spl16_57
| ~ spl16_92 ),
inference(avatar_split_clause,[],[f723,f688,f469,f198,f491]) ).
fof(f688,plain,
( spl16_92
<=> ! [X0] :
( the_carrier(sK1) = X0
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_92])]) ).
fof(f723,plain,
( the_carrier(sK1) = sK14
| ~ spl16_9
| ~ spl16_57
| ~ spl16_92 ),
inference(forward_demodulation,[],[f721,f471]) ).
fof(f721,plain,
( empty_set = the_carrier(sK1)
| ~ spl16_9
| ~ spl16_92 ),
inference(resolution,[],[f689,f200]) ).
fof(f689,plain,
( ! [X0] :
( ~ empty(X0)
| the_carrier(sK1) = X0 )
| ~ spl16_92 ),
inference(avatar_component_clause,[],[f688]) ).
fof(f1321,plain,
( spl16_162
| ~ spl16_38
| ~ spl16_134 ),
inference(avatar_split_clause,[],[f1076,f1033,f335,f1319]) ).
fof(f1076,plain,
( ! [X0] :
( ~ rel_str(X0)
| ~ subrelstr(sK1,X0)
| empty(the_carrier(X0))
| in(sK4,the_carrier(X0)) )
| ~ spl16_38
| ~ spl16_134 ),
inference(resolution,[],[f1034,f336]) ).
fof(f1317,plain,
( spl16_161
| ~ spl16_65
| ~ spl16_117 ),
inference(avatar_split_clause,[],[f875,f864,f508,f1315]) ).
fof(f864,plain,
( spl16_117
<=> ! [X2,X0,X1] :
( ~ in(X0,the_carrier(X1))
| ~ empty(the_carrier(X2))
| ~ subrelstr(X1,X2)
| ~ rel_str(X1)
| ~ rel_str(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_117])]) ).
fof(f875,plain,
( ! [X0,X1] :
( ~ empty(the_carrier(X0))
| ~ subrelstr(X1,X0)
| ~ rel_str(X1)
| ~ rel_str(X0)
| empty(the_carrier(X1)) )
| ~ spl16_65
| ~ spl16_117 ),
inference(resolution,[],[f865,f509]) ).
fof(f865,plain,
( ! [X2,X0,X1] :
( ~ in(X0,the_carrier(X1))
| ~ empty(the_carrier(X2))
| ~ subrelstr(X1,X2)
| ~ rel_str(X1)
| ~ rel_str(X2) )
| ~ spl16_117 ),
inference(avatar_component_clause,[],[f864]) ).
fof(f1313,plain,
( spl16_160
| ~ spl16_34
| ~ spl16_106 ),
inference(avatar_split_clause,[],[f820,f783,f310,f1311]) ).
fof(f1311,plain,
( spl16_160
<=> ! [X0] :
( empty(powerset(X0))
| empty(sK7(powerset(X0)))
| subset(sK9(sK7(powerset(X0))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_160])]) ).
fof(f820,plain,
( ! [X0] :
( empty(powerset(X0))
| empty(sK7(powerset(X0)))
| subset(sK9(sK7(powerset(X0))),X0) )
| ~ spl16_34
| ~ spl16_106 ),
inference(resolution,[],[f784,f311]) ).
fof(f1309,plain,
( spl16_159
| ~ spl16_34
| ~ spl16_105 ),
inference(avatar_split_clause,[],[f814,f779,f310,f1307]) ).
fof(f1307,plain,
( spl16_159
<=> ! [X0] :
( empty(powerset(X0))
| empty(sK6(powerset(X0)))
| subset(sK9(sK6(powerset(X0))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_159])]) ).
fof(f814,plain,
( ! [X0] :
( empty(powerset(X0))
| empty(sK6(powerset(X0)))
| subset(sK9(sK6(powerset(X0))),X0) )
| ~ spl16_34
| ~ spl16_105 ),
inference(resolution,[],[f780,f311]) ).
fof(f1305,plain,
( spl16_158
| ~ spl16_37
| ~ spl16_104 ),
inference(avatar_split_clause,[],[f808,f775,f331,f1303]) ).
fof(f1303,plain,
( spl16_158
<=> ! [X0] :
( empty(sK9(powerset(powerset(X0))))
| finite(sK9(sK9(powerset(powerset(X0)))))
| ~ finite(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_158])]) ).
fof(f808,plain,
( ! [X0] :
( empty(sK9(powerset(powerset(X0))))
| finite(sK9(sK9(powerset(powerset(X0)))))
| ~ finite(X0) )
| ~ spl16_37
| ~ spl16_104 ),
inference(resolution,[],[f776,f332]) ).
fof(f1279,plain,
( spl16_157
| ~ spl16_38
| ~ spl16_131 ),
inference(avatar_split_clause,[],[f1031,f984,f335,f1277]) ).
fof(f984,plain,
( spl16_131
<=> ! [X0] :
( element(sK4,the_carrier(X0))
| ~ rel_str(X0)
| ~ subrelstr(sK0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_131])]) ).
fof(f1031,plain,
( ! [X0] :
( ~ rel_str(X0)
| ~ subrelstr(sK0,X0)
| empty(the_carrier(X0))
| in(sK4,the_carrier(X0)) )
| ~ spl16_38
| ~ spl16_131 ),
inference(resolution,[],[f985,f336]) ).
fof(f985,plain,
( ! [X0] :
( element(sK4,the_carrier(X0))
| ~ rel_str(X0)
| ~ subrelstr(sK0,X0) )
| ~ spl16_131 ),
inference(avatar_component_clause,[],[f984]) ).
fof(f1275,plain,
( spl16_156
| ~ spl16_26
| ~ spl16_115 ),
inference(avatar_split_clause,[],[f860,f843,f278,f1273]) ).
fof(f1273,plain,
( spl16_156
<=> ! [X0] :
( finite(the_InternalRel(sK8(X0)))
| ~ finite(the_InternalRel(X0))
| ~ rel_str(sK8(X0))
| ~ rel_str(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_156])]) ).
fof(f843,plain,
( spl16_115
<=> ! [X0,X1] :
( ~ finite(the_InternalRel(X0))
| finite(the_InternalRel(X1))
| ~ subrelstr(X1,X0)
| ~ rel_str(X1)
| ~ rel_str(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_115])]) ).
fof(f860,plain,
( ! [X0] :
( finite(the_InternalRel(sK8(X0)))
| ~ finite(the_InternalRel(X0))
| ~ rel_str(sK8(X0))
| ~ rel_str(X0) )
| ~ spl16_26
| ~ spl16_115 ),
inference(duplicate_literal_removal,[],[f857]) ).
fof(f857,plain,
( ! [X0] :
( finite(the_InternalRel(sK8(X0)))
| ~ finite(the_InternalRel(X0))
| ~ rel_str(sK8(X0))
| ~ rel_str(X0)
| ~ rel_str(X0) )
| ~ spl16_26
| ~ spl16_115 ),
inference(resolution,[],[f844,f279]) ).
fof(f844,plain,
( ! [X0,X1] :
( ~ subrelstr(X1,X0)
| finite(the_InternalRel(X1))
| ~ finite(the_InternalRel(X0))
| ~ rel_str(X1)
| ~ rel_str(X0) )
| ~ spl16_115 ),
inference(avatar_component_clause,[],[f843]) ).
fof(f1271,plain,
( spl16_155
| ~ spl16_26
| ~ spl16_114 ),
inference(avatar_split_clause,[],[f854,f839,f278,f1269]) ).
fof(f839,plain,
( spl16_114
<=> ! [X0,X1] :
( ~ finite(the_carrier(X0))
| finite(the_carrier(X1))
| ~ subrelstr(X1,X0)
| ~ rel_str(X1)
| ~ rel_str(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_114])]) ).
fof(f854,plain,
( ! [X0] :
( finite(the_carrier(sK8(X0)))
| ~ finite(the_carrier(X0))
| ~ rel_str(sK8(X0))
| ~ rel_str(X0) )
| ~ spl16_26
| ~ spl16_114 ),
inference(duplicate_literal_removal,[],[f851]) ).
fof(f851,plain,
( ! [X0] :
( finite(the_carrier(sK8(X0)))
| ~ finite(the_carrier(X0))
| ~ rel_str(sK8(X0))
| ~ rel_str(X0)
| ~ rel_str(X0) )
| ~ spl16_26
| ~ spl16_114 ),
inference(resolution,[],[f840,f279]) ).
fof(f840,plain,
( ! [X0,X1] :
( ~ subrelstr(X1,X0)
| finite(the_carrier(X1))
| ~ finite(the_carrier(X0))
| ~ rel_str(X1)
| ~ rel_str(X0) )
| ~ spl16_114 ),
inference(avatar_component_clause,[],[f839]) ).
fof(f1267,plain,
( spl16_154
| ~ spl16_65
| ~ spl16_111 ),
inference(avatar_split_clause,[],[f826,f803,f508,f1265]) ).
fof(f826,plain,
( ! [X0,X1] :
( element(sK9(sK10(X0,X1)),cartesian_product2(X0,X1))
| empty(sK10(X0,X1)) )
| ~ spl16_65
| ~ spl16_111 ),
inference(resolution,[],[f804,f509]) ).
fof(f1263,plain,
( spl16_153
| ~ spl16_65
| ~ spl16_110 ),
inference(avatar_split_clause,[],[f825,f799,f508,f1261]) ).
fof(f825,plain,
( ! [X0,X1] :
( element(sK9(sK11(X0,X1)),cartesian_product2(X0,X1))
| empty(sK11(X0,X1)) )
| ~ spl16_65
| ~ spl16_110 ),
inference(resolution,[],[f800,f509]) ).
fof(f1259,plain,
( spl16_152
| ~ spl16_38
| ~ spl16_104 ),
inference(avatar_split_clause,[],[f810,f775,f335,f1257]) ).
fof(f810,plain,
( ! [X0] :
( empty(sK9(powerset(X0)))
| empty(X0)
| in(sK9(sK9(powerset(X0))),X0) )
| ~ spl16_38
| ~ spl16_104 ),
inference(resolution,[],[f776,f336]) ).
fof(f1255,plain,
( spl16_151
| ~ spl16_34
| ~ spl16_104 ),
inference(avatar_split_clause,[],[f809,f775,f310,f1253]) ).
fof(f1253,plain,
( spl16_151
<=> ! [X0] :
( empty(sK9(powerset(powerset(X0))))
| subset(sK9(sK9(powerset(powerset(X0)))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_151])]) ).
fof(f809,plain,
( ! [X0] :
( empty(sK9(powerset(powerset(X0))))
| subset(sK9(sK9(powerset(powerset(X0)))),X0) )
| ~ spl16_34
| ~ spl16_104 ),
inference(resolution,[],[f776,f311]) ).
fof(f1221,plain,
( spl16_125
| ~ spl16_42
| ~ spl16_123
| ~ spl16_147 ),
inference(avatar_split_clause,[],[f1203,f1200,f906,f355,f915]) ).
fof(f1203,plain,
( ~ rel_str(sK1)
| finite(the_InternalRel(sK1))
| ~ spl16_123
| ~ spl16_147 ),
inference(resolution,[],[f1201,f908]) ).
fof(f908,plain,
( finite(the_carrier(sK1))
| ~ spl16_123 ),
inference(avatar_component_clause,[],[f906]) ).
fof(f1220,plain,
( spl16_150
| ~ spl16_38
| ~ spl16_106 ),
inference(avatar_split_clause,[],[f822,f783,f335,f1218]) ).
fof(f822,plain,
( ! [X0] :
( empty(X0)
| empty(sK7(X0))
| in(sK9(sK7(X0)),X0) )
| ~ spl16_38
| ~ spl16_106 ),
inference(duplicate_literal_removal,[],[f821]) ).
fof(f821,plain,
( ! [X0] :
( empty(X0)
| empty(sK7(X0))
| empty(X0)
| in(sK9(sK7(X0)),X0) )
| ~ spl16_38
| ~ spl16_106 ),
inference(resolution,[],[f784,f336]) ).
fof(f1216,plain,
( spl16_149
| ~ spl16_38
| ~ spl16_105 ),
inference(avatar_split_clause,[],[f816,f779,f335,f1214]) ).
fof(f816,plain,
( ! [X0] :
( empty(X0)
| empty(sK6(X0))
| in(sK9(sK6(X0)),X0) )
| ~ spl16_38
| ~ spl16_105 ),
inference(duplicate_literal_removal,[],[f815]) ).
fof(f815,plain,
( ! [X0] :
( empty(X0)
| empty(sK6(X0))
| empty(X0)
| in(sK9(sK6(X0)),X0) )
| ~ spl16_38
| ~ spl16_105 ),
inference(resolution,[],[f780,f336]) ).
fof(f1208,plain,
( spl16_148
| ~ spl16_36
| ~ spl16_99 ),
inference(avatar_split_clause,[],[f748,f743,f318,f1206]) ).
fof(f748,plain,
( ! [X0,X1] :
( ~ empty(X0)
| sK9(powerset(X0)) = X1
| ~ empty(X1) )
| ~ spl16_36
| ~ spl16_99 ),
inference(resolution,[],[f744,f319]) ).
fof(f1202,plain,
( spl16_147
| ~ spl16_39
| ~ spl16_112 ),
inference(avatar_split_clause,[],[f833,f829,f339,f1200]) ).
fof(f833,plain,
( ! [X0] :
( finite(the_InternalRel(X0))
| ~ rel_str(X0)
| ~ finite(the_carrier(X0)) )
| ~ spl16_39
| ~ spl16_112 ),
inference(duplicate_literal_removal,[],[f832]) ).
fof(f832,plain,
( ! [X0] :
( finite(the_InternalRel(X0))
| ~ rel_str(X0)
| ~ finite(the_carrier(X0))
| ~ finite(the_carrier(X0)) )
| ~ spl16_39
| ~ spl16_112 ),
inference(resolution,[],[f830,f340]) ).
fof(f1198,plain,
( spl16_146
| ~ spl16_65
| ~ spl16_103 ),
inference(avatar_split_clause,[],[f773,f769,f508,f1196]) ).
fof(f769,plain,
( spl16_103
<=> ! [X2,X0,X1] :
( ~ empty(cartesian_product2(X0,X1))
| ~ in(X2,sK10(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_103])]) ).
fof(f773,plain,
( ! [X0,X1] :
( ~ empty(cartesian_product2(X0,X1))
| empty(sK10(X0,X1)) )
| ~ spl16_65
| ~ spl16_103 ),
inference(resolution,[],[f770,f509]) ).
fof(f770,plain,
( ! [X2,X0,X1] :
( ~ in(X2,sK10(X0,X1))
| ~ empty(cartesian_product2(X0,X1)) )
| ~ spl16_103 ),
inference(avatar_component_clause,[],[f769]) ).
fof(f1194,plain,
( spl16_145
| ~ spl16_65
| ~ spl16_102 ),
inference(avatar_split_clause,[],[f772,f765,f508,f1192]) ).
fof(f765,plain,
( spl16_102
<=> ! [X2,X0,X1] :
( ~ empty(cartesian_product2(X0,X1))
| ~ in(X2,sK11(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_102])]) ).
fof(f772,plain,
( ! [X0,X1] :
( ~ empty(cartesian_product2(X0,X1))
| empty(sK11(X0,X1)) )
| ~ spl16_65
| ~ spl16_102 ),
inference(resolution,[],[f766,f509]) ).
fof(f766,plain,
( ! [X2,X0,X1] :
( ~ in(X2,sK11(X0,X1))
| ~ empty(cartesian_product2(X0,X1)) )
| ~ spl16_102 ),
inference(avatar_component_clause,[],[f765]) ).
fof(f1190,plain,
( spl16_144
| ~ spl16_39
| ~ spl16_101 ),
inference(avatar_split_clause,[],[f762,f758,f339,f1188]) ).
fof(f1188,plain,
( spl16_144
<=> ! [X0,X1] :
( finite(sK10(X0,X1))
| ~ finite(X1)
| ~ finite(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_144])]) ).
fof(f762,plain,
( ! [X0,X1] :
( finite(sK10(X0,X1))
| ~ finite(X1)
| ~ finite(X0) )
| ~ spl16_39
| ~ spl16_101 ),
inference(resolution,[],[f759,f340]) ).
fof(f1186,plain,
( spl16_143
| ~ spl16_39
| ~ spl16_100 ),
inference(avatar_split_clause,[],[f761,f754,f339,f1184]) ).
fof(f1184,plain,
( spl16_143
<=> ! [X0,X1] :
( finite(sK11(X0,X1))
| ~ finite(X1)
| ~ finite(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_143])]) ).
fof(f761,plain,
( ! [X0,X1] :
( finite(sK11(X0,X1))
| ~ finite(X1)
| ~ finite(X0) )
| ~ spl16_39
| ~ spl16_100 ),
inference(resolution,[],[f755,f340]) ).
fof(f1178,plain,
( spl16_142
| ~ spl16_23
| ~ spl16_57
| ~ spl16_99 ),
inference(avatar_split_clause,[],[f752,f743,f469,f263,f1176]) ).
fof(f752,plain,
( ! [X0] :
( sK14 = sK9(powerset(X0))
| ~ empty(X0) )
| ~ spl16_23
| ~ spl16_57
| ~ spl16_99 ),
inference(forward_demodulation,[],[f749,f471]) ).
fof(f749,plain,
( ! [X0] :
( ~ empty(X0)
| empty_set = sK9(powerset(X0)) )
| ~ spl16_23
| ~ spl16_99 ),
inference(resolution,[],[f744,f264]) ).
fof(f1174,plain,
( spl16_141
| ~ spl16_16
| ~ spl16_99 ),
inference(avatar_split_clause,[],[f750,f743,f232,f1172]) ).
fof(f1172,plain,
( spl16_141
<=> ! [X0] :
( ~ empty(X0)
| finite(sK9(powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_141])]) ).
fof(f750,plain,
( ! [X0] :
( ~ empty(X0)
| finite(sK9(powerset(X0))) )
| ~ spl16_16
| ~ spl16_99 ),
inference(resolution,[],[f744,f233]) ).
fof(f1169,plain,
( spl16_140
| ~ spl16_41
| ~ spl16_135 ),
inference(avatar_split_clause,[],[f1149,f1061,f347,f1166]) ).
fof(f1149,plain,
( relation_of2_as_subset(the_InternalRel(sK1),sK14,sK14)
| ~ spl16_41
| ~ spl16_135 ),
inference(resolution,[],[f1063,f348]) ).
fof(f1063,plain,
( relation_of2(the_InternalRel(sK1),sK14,sK14)
| ~ spl16_135 ),
inference(avatar_component_clause,[],[f1061]) ).
fof(f1164,plain,
( ~ spl16_53
| ~ spl16_24
| ~ spl16_93 ),
inference(avatar_split_clause,[],[f710,f699,f267,f428]) ).
fof(f1153,plain,
( spl16_139
| ~ spl16_92
| ~ spl16_99 ),
inference(avatar_split_clause,[],[f746,f743,f688,f1151]) ).
fof(f746,plain,
( ! [X0] :
( ~ empty(X0)
| the_carrier(sK1) = sK9(powerset(X0)) )
| ~ spl16_92
| ~ spl16_99 ),
inference(resolution,[],[f744,f689]) ).
fof(f1130,plain,
( spl16_61
| ~ spl16_9
| ~ spl16_57
| ~ spl16_92 ),
inference(avatar_split_clause,[],[f723,f688,f469,f198,f491]) ).
fof(f1123,plain,
( ~ spl16_42
| spl16_138
| ~ spl16_93
| ~ spl16_119 ),
inference(avatar_split_clause,[],[f894,f880,f699,f1121,f355]) ).
fof(f894,plain,
( ! [X0] :
( element(sK5,the_carrier(X0))
| ~ subrelstr(sK1,X0)
| ~ rel_str(sK1)
| ~ rel_str(X0) )
| ~ spl16_93
| ~ spl16_119 ),
inference(resolution,[],[f881,f701]) ).
fof(f1118,plain,
( ~ spl16_55
| ~ spl16_24
| ~ spl16_56 ),
inference(avatar_split_clause,[],[f948,f455,f267,f447]) ).
fof(f1107,plain,
( ~ spl16_1
| spl16_137
| ~ spl16_43
| ~ spl16_128 ),
inference(avatar_split_clause,[],[f998,f934,f370,f1104,f158]) ).
fof(f998,plain,
( relation_of2_as_subset(the_InternalRel(sK0),sK14,sK14)
| ~ rel_str(sK0)
| ~ spl16_43
| ~ spl16_128 ),
inference(superposition,[],[f371,f936]) ).
fof(f1080,plain,
( ~ spl16_1
| spl16_136
| ~ spl16_54
| ~ spl16_119 ),
inference(avatar_split_clause,[],[f893,f880,f443,f1078,f158]) ).
fof(f893,plain,
( ! [X0] :
( element(sK5,the_carrier(X0))
| ~ subrelstr(sK0,X0)
| ~ rel_str(sK0)
| ~ rel_str(X0) )
| ~ spl16_54
| ~ spl16_119 ),
inference(resolution,[],[f881,f445]) ).
fof(f1075,plain,
( ~ spl16_53
| ~ spl16_24
| ~ spl16_93 ),
inference(avatar_split_clause,[],[f710,f699,f267,f428]) ).
fof(f1064,plain,
( ~ spl16_42
| spl16_135
| ~ spl16_61
| ~ spl16_74 ),
inference(avatar_split_clause,[],[f600,f565,f491,f1061,f355]) ).
fof(f565,plain,
( spl16_74
<=> ! [X0] :
( ~ rel_str(X0)
| relation_of2(the_InternalRel(X0),the_carrier(X0),the_carrier(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_74])]) ).
fof(f600,plain,
( relation_of2(the_InternalRel(sK1),sK14,sK14)
| ~ rel_str(sK1)
| ~ spl16_61
| ~ spl16_74 ),
inference(superposition,[],[f566,f493]) ).
fof(f566,plain,
( ! [X0] :
( relation_of2(the_InternalRel(X0),the_carrier(X0),the_carrier(X0))
| ~ rel_str(X0) )
| ~ spl16_74 ),
inference(avatar_component_clause,[],[f565]) ).
fof(f1043,plain,
( spl16_61
| ~ spl16_9
| ~ spl16_57
| ~ spl16_92 ),
inference(avatar_split_clause,[],[f723,f688,f469,f198,f491]) ).
fof(f1035,plain,
( ~ spl16_42
| spl16_134
| ~ spl16_52
| ~ spl16_119 ),
inference(avatar_split_clause,[],[f892,f880,f424,f1033,f355]) ).
fof(f892,plain,
( ! [X0] :
( element(sK4,the_carrier(X0))
| ~ subrelstr(sK1,X0)
| ~ rel_str(sK1)
| ~ rel_str(X0) )
| ~ spl16_52
| ~ spl16_119 ),
inference(resolution,[],[f881,f426]) ).
fof(f1030,plain,
( ~ spl16_55
| ~ spl16_24
| ~ spl16_56 ),
inference(avatar_split_clause,[],[f948,f455,f267,f447]) ).
fof(f1019,plain,
( ~ spl16_25
| spl16_122
| ~ spl16_128 ),
inference(avatar_split_clause,[],[f997,f934,f902,f271]) ).
fof(f997,plain,
( ~ finite(sK14)
| spl16_122
| ~ spl16_128 ),
inference(superposition,[],[f904,f936]) ).
fof(f904,plain,
( ~ finite(the_carrier(sK0))
| spl16_122 ),
inference(avatar_component_clause,[],[f902]) ).
fof(f1018,plain,
( ~ spl16_133
| spl16_73
| ~ spl16_128 ),
inference(avatar_split_clause,[],[f996,f934,f560,f1015]) ).
fof(f1015,plain,
( spl16_133
<=> in(sK14,sK4) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_133])]) ).
fof(f560,plain,
( spl16_73
<=> in(the_carrier(sK0),sK4) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_73])]) ).
fof(f996,plain,
( ~ in(sK14,sK4)
| spl16_73
| ~ spl16_128 ),
inference(superposition,[],[f562,f936]) ).
fof(f562,plain,
( ~ in(the_carrier(sK0),sK4)
| spl16_73 ),
inference(avatar_component_clause,[],[f560]) ).
fof(f1013,plain,
( ~ spl16_132
| spl16_68
| ~ spl16_128 ),
inference(avatar_split_clause,[],[f995,f934,f523,f1010]) ).
fof(f1010,plain,
( spl16_132
<=> in(sK14,sK5) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_132])]) ).
fof(f523,plain,
( spl16_68
<=> in(the_carrier(sK0),sK5) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_68])]) ).
fof(f995,plain,
( ~ in(sK14,sK5)
| spl16_68
| ~ spl16_128 ),
inference(superposition,[],[f525,f936]) ).
fof(f525,plain,
( ~ in(the_carrier(sK0),sK5)
| spl16_68 ),
inference(avatar_component_clause,[],[f523]) ).
fof(f1007,plain,
( spl16_130
| ~ spl16_8
| ~ spl16_128 ),
inference(avatar_split_clause,[],[f994,f934,f193,f965]) ).
fof(f965,plain,
( spl16_130
<=> element(sK4,sK14) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_130])]) ).
fof(f994,plain,
( element(sK4,sK14)
| ~ spl16_8
| ~ spl16_128 ),
inference(superposition,[],[f195,f936]) ).
fof(f986,plain,
( ~ spl16_1
| spl16_131
| ~ spl16_56
| ~ spl16_119 ),
inference(avatar_split_clause,[],[f891,f880,f455,f984,f158]) ).
fof(f891,plain,
( ! [X0] :
( element(sK4,the_carrier(X0))
| ~ subrelstr(sK0,X0)
| ~ rel_str(sK0)
| ~ rel_str(X0) )
| ~ spl16_56
| ~ spl16_119 ),
inference(resolution,[],[f881,f457]) ).
fof(f979,plain,
( ~ spl16_53
| ~ spl16_24
| ~ spl16_93 ),
inference(avatar_split_clause,[],[f710,f699,f267,f428]) ).
fof(f968,plain,
( spl16_130
| ~ spl16_3
| ~ spl16_61 ),
inference(avatar_split_clause,[],[f599,f491,f168,f965]) ).
fof(f599,plain,
( element(sK4,sK14)
| ~ spl16_3
| ~ spl16_61 ),
inference(superposition,[],[f170,f493]) ).
fof(f170,plain,
( element(sK4,the_carrier(sK1))
| ~ spl16_3 ),
inference(avatar_component_clause,[],[f168]) ).
fof(f962,plain,
( ~ spl16_53
| ~ spl16_24
| ~ spl16_93 ),
inference(avatar_split_clause,[],[f710,f699,f267,f428]) ).
fof(f954,plain,
( ~ spl16_42
| spl16_129
| ~ spl16_52
| ~ spl16_117 ),
inference(avatar_split_clause,[],[f872,f864,f424,f952,f355]) ).
fof(f872,plain,
( ! [X0] :
( ~ empty(the_carrier(X0))
| ~ subrelstr(sK1,X0)
| ~ rel_str(sK1)
| ~ rel_str(X0) )
| ~ spl16_52
| ~ spl16_117 ),
inference(resolution,[],[f865,f426]) ).
fof(f938,plain,
( ~ spl16_55
| ~ spl16_24
| ~ spl16_56 ),
inference(avatar_split_clause,[],[f467,f455,f267,f447]) ).
fof(f467,plain,
( ~ empty(the_carrier(sK0))
| ~ spl16_24
| ~ spl16_56 ),
inference(resolution,[],[f457,f268]) ).
fof(f937,plain,
( spl16_128
| ~ spl16_12
| ~ spl16_23
| ~ spl16_55 ),
inference(avatar_split_clause,[],[f462,f447,f263,f213,f934]) ).
fof(f462,plain,
( the_carrier(sK0) = sK14
| ~ spl16_12
| ~ spl16_23
| ~ spl16_55 ),
inference(forward_demodulation,[],[f460,f276]) ).
fof(f276,plain,
( empty_set = sK14
| ~ spl16_12
| ~ spl16_23 ),
inference(resolution,[],[f264,f215]) ).
fof(f460,plain,
( empty_set = the_carrier(sK0)
| ~ spl16_23
| ~ spl16_55 ),
inference(resolution,[],[f449,f264]) ).
fof(f449,plain,
( empty(the_carrier(sK0))
| ~ spl16_55 ),
inference(avatar_component_clause,[],[f447]) ).
fof(f932,plain,
( ~ spl16_127
| ~ spl16_12
| ~ spl16_23
| spl16_54
| ~ spl16_55 ),
inference(avatar_split_clause,[],[f927,f447,f443,f263,f213,f929]) ).
fof(f929,plain,
( spl16_127
<=> in(sK5,sK14) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_127])]) ).
fof(f927,plain,
( ~ in(sK5,sK14)
| ~ spl16_12
| ~ spl16_23
| spl16_54
| ~ spl16_55 ),
inference(forward_demodulation,[],[f444,f462]) ).
fof(f444,plain,
( ~ in(sK5,the_carrier(sK0))
| spl16_54 ),
inference(avatar_component_clause,[],[f443]) ).
fof(f922,plain,
( ~ spl16_1
| spl16_126
| ~ spl16_56
| ~ spl16_117 ),
inference(avatar_split_clause,[],[f871,f864,f455,f920,f158]) ).
fof(f871,plain,
( ! [X0] :
( ~ empty(the_carrier(X0))
| ~ subrelstr(sK0,X0)
| ~ rel_str(sK0)
| ~ rel_str(X0) )
| ~ spl16_56
| ~ spl16_117 ),
inference(resolution,[],[f865,f457]) ).
fof(f918,plain,
( ~ spl16_1
| ~ spl16_42
| ~ spl16_124
| spl16_125
| ~ spl16_2
| ~ spl16_115 ),
inference(avatar_split_clause,[],[f856,f843,f163,f915,f911,f355,f158]) ).
fof(f856,plain,
( finite(the_InternalRel(sK1))
| ~ finite(the_InternalRel(sK0))
| ~ rel_str(sK1)
| ~ rel_str(sK0)
| ~ spl16_2
| ~ spl16_115 ),
inference(resolution,[],[f844,f165]) ).
fof(f909,plain,
( ~ spl16_1
| ~ spl16_42
| ~ spl16_122
| spl16_123
| ~ spl16_2
| ~ spl16_114 ),
inference(avatar_split_clause,[],[f850,f839,f163,f906,f902,f355,f158]) ).
fof(f850,plain,
( finite(the_carrier(sK1))
| ~ finite(the_carrier(sK0))
| ~ rel_str(sK1)
| ~ rel_str(sK0)
| ~ spl16_2
| ~ spl16_114 ),
inference(resolution,[],[f840,f165]) ).
fof(f890,plain,
( spl16_121
| ~ spl16_27
| ~ spl16_87 ),
inference(avatar_split_clause,[],[f664,f660,f282,f888]) ).
fof(f664,plain,
( ! [X2,X0,X1] :
( empty(powerset(cartesian_product2(X0,X1)))
| ~ relation_of2_as_subset(X2,X0,X1)
| ~ in(powerset(cartesian_product2(X0,X1)),X2) )
| ~ spl16_27
| ~ spl16_87 ),
inference(resolution,[],[f661,f283]) ).
fof(f886,plain,
( spl16_120
| ~ spl16_48
| ~ spl16_78 ),
inference(avatar_split_clause,[],[f592,f581,f404,f884]) ).
fof(f592,plain,
( ! [X2,X0,X1] :
( ~ in(X0,the_InternalRel(X1))
| element(X0,the_InternalRel(X2))
| ~ subrelstr(X1,X2)
| ~ rel_str(X1)
| ~ rel_str(X2) )
| ~ spl16_48
| ~ spl16_78 ),
inference(resolution,[],[f582,f405]) ).
fof(f882,plain,
( spl16_119
| ~ spl16_47
| ~ spl16_78 ),
inference(avatar_split_clause,[],[f591,f581,f400,f880]) ).
fof(f591,plain,
( ! [X2,X0,X1] :
( ~ in(X0,the_carrier(X1))
| element(X0,the_carrier(X2))
| ~ subrelstr(X1,X2)
| ~ rel_str(X1)
| ~ rel_str(X2) )
| ~ spl16_47
| ~ spl16_78 ),
inference(resolution,[],[f582,f401]) ).
fof(f870,plain,
( spl16_118
| ~ spl16_48
| ~ spl16_71 ),
inference(avatar_split_clause,[],[f554,f545,f404,f868]) ).
fof(f554,plain,
( ! [X2,X0,X1] :
( ~ in(X0,the_InternalRel(X1))
| ~ empty(the_InternalRel(X2))
| ~ subrelstr(X1,X2)
| ~ rel_str(X1)
| ~ rel_str(X2) )
| ~ spl16_48
| ~ spl16_71 ),
inference(resolution,[],[f546,f405]) ).
fof(f866,plain,
( spl16_117
| ~ spl16_47
| ~ spl16_71 ),
inference(avatar_split_clause,[],[f553,f545,f400,f864]) ).
fof(f553,plain,
( ! [X2,X0,X1] :
( ~ in(X0,the_carrier(X1))
| ~ empty(the_carrier(X2))
| ~ subrelstr(X1,X2)
| ~ rel_str(X1)
| ~ rel_str(X2) )
| ~ spl16_47
| ~ spl16_71 ),
inference(resolution,[],[f546,f401]) ).
fof(f862,plain,
( spl16_61
| ~ spl16_9
| ~ spl16_57
| ~ spl16_92 ),
inference(avatar_split_clause,[],[f723,f688,f469,f198,f491]) ).
fof(f849,plain,
( spl16_116
| ~ spl16_43
| ~ spl16_86 ),
inference(avatar_split_clause,[],[f657,f653,f370,f847]) ).
fof(f657,plain,
( ! [X0,X1] :
( ~ in(X0,the_InternalRel(X1))
| element(X0,cartesian_product2(the_carrier(X1),the_carrier(X1)))
| ~ rel_str(X1) )
| ~ spl16_43
| ~ spl16_86 ),
inference(resolution,[],[f654,f371]) ).
fof(f845,plain,
( spl16_115
| ~ spl16_48
| ~ spl16_69 ),
inference(avatar_split_clause,[],[f539,f530,f404,f843]) ).
fof(f539,plain,
( ! [X0,X1] :
( ~ finite(the_InternalRel(X0))
| finite(the_InternalRel(X1))
| ~ subrelstr(X1,X0)
| ~ rel_str(X1)
| ~ rel_str(X0) )
| ~ spl16_48
| ~ spl16_69 ),
inference(resolution,[],[f531,f405]) ).
fof(f841,plain,
( spl16_114
| ~ spl16_47
| ~ spl16_69 ),
inference(avatar_split_clause,[],[f538,f530,f400,f839]) ).
fof(f538,plain,
( ! [X0,X1] :
( ~ finite(the_carrier(X0))
| finite(the_carrier(X1))
| ~ subrelstr(X1,X0)
| ~ rel_str(X1)
| ~ rel_str(X0) )
| ~ spl16_47
| ~ spl16_69 ),
inference(resolution,[],[f531,f401]) ).
fof(f837,plain,
( spl16_113
| ~ spl16_43
| ~ spl16_85 ),
inference(avatar_split_clause,[],[f650,f646,f370,f835]) ).
fof(f650,plain,
( ! [X0,X1] :
( ~ empty(cartesian_product2(the_carrier(X0),the_carrier(X0)))
| ~ in(X1,the_InternalRel(X0))
| ~ rel_str(X0) )
| ~ spl16_43
| ~ spl16_85 ),
inference(resolution,[],[f647,f371]) ).
fof(f831,plain,
( spl16_112
| ~ spl16_43
| ~ spl16_82 ),
inference(avatar_split_clause,[],[f634,f617,f370,f829]) ).
fof(f634,plain,
( ! [X0] :
( finite(the_InternalRel(X0))
| ~ finite(cartesian_product2(the_carrier(X0),the_carrier(X0)))
| ~ rel_str(X0) )
| ~ spl16_43
| ~ spl16_82 ),
inference(resolution,[],[f618,f371]) ).
fof(f805,plain,
( spl16_111
| ~ spl16_67
| ~ spl16_86 ),
inference(avatar_split_clause,[],[f658,f653,f516,f803]) ).
fof(f658,plain,
( ! [X2,X0,X1] :
( ~ in(X0,sK10(X1,X2))
| element(X0,cartesian_product2(X1,X2)) )
| ~ spl16_67
| ~ spl16_86 ),
inference(resolution,[],[f654,f517]) ).
fof(f801,plain,
( spl16_110
| ~ spl16_30
| ~ spl16_86 ),
inference(avatar_split_clause,[],[f656,f653,f294,f799]) ).
fof(f294,plain,
( spl16_30
<=> ! [X0,X1] : relation_of2_as_subset(sK11(X0,X1),X0,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_30])]) ).
fof(f656,plain,
( ! [X2,X0,X1] :
( ~ in(X0,sK11(X1,X2))
| element(X0,cartesian_product2(X1,X2)) )
| ~ spl16_30
| ~ spl16_86 ),
inference(resolution,[],[f654,f295]) ).
fof(f295,plain,
( ! [X0,X1] : relation_of2_as_subset(sK11(X0,X1),X0,X1)
| ~ spl16_30 ),
inference(avatar_component_clause,[],[f294]) ).
fof(f797,plain,
( spl16_109
| ~ spl16_27
| ~ spl16_81 ),
inference(avatar_split_clause,[],[f631,f613,f282,f795]) ).
fof(f631,plain,
( ! [X0,X1] :
( empty(powerset(X0))
| ~ subset(X1,X0)
| ~ in(powerset(X0),X1) )
| ~ spl16_27
| ~ spl16_81 ),
inference(resolution,[],[f614,f283]) ).
fof(f793,plain,
( spl16_108
| ~ spl16_27
| ~ spl16_80 ),
inference(avatar_split_clause,[],[f628,f609,f282,f791]) ).
fof(f791,plain,
( spl16_108
<=> ! [X0] :
( empty(powerset(X0))
| empty(X0)
| ~ in(powerset(X0),sK7(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_108])]) ).
fof(f609,plain,
( spl16_80
<=> ! [X0] :
( empty(powerset(X0))
| in(sK7(X0),powerset(X0))
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_80])]) ).
fof(f628,plain,
( ! [X0] :
( empty(powerset(X0))
| empty(X0)
| ~ in(powerset(X0),sK7(X0)) )
| ~ spl16_27
| ~ spl16_80 ),
inference(resolution,[],[f610,f283]) ).
fof(f610,plain,
( ! [X0] :
( in(sK7(X0),powerset(X0))
| empty(powerset(X0))
| empty(X0) )
| ~ spl16_80 ),
inference(avatar_component_clause,[],[f609]) ).
fof(f789,plain,
( spl16_107
| ~ spl16_27
| ~ spl16_79 ),
inference(avatar_split_clause,[],[f625,f605,f282,f787]) ).
fof(f787,plain,
( spl16_107
<=> ! [X0] :
( empty(powerset(X0))
| empty(X0)
| ~ in(powerset(X0),sK6(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_107])]) ).
fof(f605,plain,
( spl16_79
<=> ! [X0] :
( empty(powerset(X0))
| in(sK6(X0),powerset(X0))
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_79])]) ).
fof(f625,plain,
( ! [X0] :
( empty(powerset(X0))
| empty(X0)
| ~ in(powerset(X0),sK6(X0)) )
| ~ spl16_27
| ~ spl16_79 ),
inference(resolution,[],[f606,f283]) ).
fof(f606,plain,
( ! [X0] :
( in(sK6(X0),powerset(X0))
| empty(powerset(X0))
| empty(X0) )
| ~ spl16_79 ),
inference(avatar_component_clause,[],[f605]) ).
fof(f785,plain,
( spl16_106
| ~ spl16_65
| ~ spl16_77 ),
inference(avatar_split_clause,[],[f588,f577,f508,f783]) ).
fof(f588,plain,
( ! [X0] :
( element(sK9(sK7(X0)),X0)
| empty(X0)
| empty(sK7(X0)) )
| ~ spl16_65
| ~ spl16_77 ),
inference(resolution,[],[f578,f509]) ).
fof(f781,plain,
( spl16_105
| ~ spl16_65
| ~ spl16_76 ),
inference(avatar_split_clause,[],[f587,f573,f508,f779]) ).
fof(f587,plain,
( ! [X0] :
( element(sK9(sK6(X0)),X0)
| empty(X0)
| empty(sK6(X0)) )
| ~ spl16_65
| ~ spl16_76 ),
inference(resolution,[],[f574,f509]) ).
fof(f777,plain,
( spl16_104
| ~ spl16_65
| ~ spl16_72 ),
inference(avatar_split_clause,[],[f558,f549,f508,f775]) ).
fof(f558,plain,
( ! [X0] :
( element(sK9(sK9(powerset(X0))),X0)
| empty(sK9(powerset(X0))) )
| ~ spl16_65
| ~ spl16_72 ),
inference(resolution,[],[f550,f509]) ).
fof(f771,plain,
( spl16_103
| ~ spl16_67
| ~ spl16_85 ),
inference(avatar_split_clause,[],[f651,f646,f516,f769]) ).
fof(f651,plain,
( ! [X2,X0,X1] :
( ~ empty(cartesian_product2(X0,X1))
| ~ in(X2,sK10(X0,X1)) )
| ~ spl16_67
| ~ spl16_85 ),
inference(resolution,[],[f647,f517]) ).
fof(f767,plain,
( spl16_102
| ~ spl16_30
| ~ spl16_85 ),
inference(avatar_split_clause,[],[f649,f646,f294,f765]) ).
fof(f649,plain,
( ! [X2,X0,X1] :
( ~ empty(cartesian_product2(X0,X1))
| ~ in(X2,sK11(X0,X1)) )
| ~ spl16_30
| ~ spl16_85 ),
inference(resolution,[],[f647,f295]) ).
fof(f763,plain,
( ~ spl16_12
| ~ spl16_24
| ~ spl16_84 ),
inference(avatar_split_clause,[],[f731,f641,f267,f213]) ).
fof(f641,plain,
( spl16_84
<=> in(sK4,sK14) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_84])]) ).
fof(f731,plain,
( ~ empty(sK14)
| ~ spl16_24
| ~ spl16_84 ),
inference(resolution,[],[f642,f268]) ).
fof(f642,plain,
( in(sK4,sK14)
| ~ spl16_84 ),
inference(avatar_component_clause,[],[f641]) ).
fof(f760,plain,
( spl16_101
| ~ spl16_67
| ~ spl16_82 ),
inference(avatar_split_clause,[],[f635,f617,f516,f758]) ).
fof(f635,plain,
( ! [X0,X1] :
( finite(sK10(X0,X1))
| ~ finite(cartesian_product2(X0,X1)) )
| ~ spl16_67
| ~ spl16_82 ),
inference(resolution,[],[f618,f517]) ).
fof(f756,plain,
( spl16_100
| ~ spl16_30
| ~ spl16_82 ),
inference(avatar_split_clause,[],[f633,f617,f294,f754]) ).
fof(f633,plain,
( ! [X0,X1] :
( finite(sK11(X0,X1))
| ~ finite(cartesian_product2(X0,X1)) )
| ~ spl16_30
| ~ spl16_82 ),
inference(resolution,[],[f618,f295]) ).
fof(f745,plain,
( spl16_99
| ~ spl16_65
| ~ spl16_70 ),
inference(avatar_split_clause,[],[f543,f534,f508,f743]) ).
fof(f534,plain,
( spl16_70
<=> ! [X0,X1] :
( ~ empty(X0)
| ~ in(X1,sK9(powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_70])]) ).
fof(f543,plain,
( ! [X0] :
( ~ empty(X0)
| empty(sK9(powerset(X0))) )
| ~ spl16_65
| ~ spl16_70 ),
inference(resolution,[],[f535,f509]) ).
fof(f535,plain,
( ! [X0,X1] :
( ~ in(X1,sK9(powerset(X0)))
| ~ empty(X0) )
| ~ spl16_70 ),
inference(avatar_component_clause,[],[f534]) ).
fof(f741,plain,
( spl16_98
| ~ spl16_27
| ~ spl16_65 ),
inference(avatar_split_clause,[],[f520,f508,f282,f739]) ).
fof(f520,plain,
( ! [X0] :
( empty(X0)
| ~ in(X0,sK9(X0)) )
| ~ spl16_27
| ~ spl16_65 ),
inference(resolution,[],[f509,f283]) ).
fof(f735,plain,
( spl16_97
| ~ spl16_15
| ~ spl16_83 ),
inference(avatar_split_clause,[],[f637,f621,f228,f733]) ).
fof(f621,plain,
( spl16_83
<=> ! [X0] :
( subrelstr(X0,X0)
| ~ subset(the_carrier(X0),the_carrier(X0))
| ~ rel_str(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_83])]) ).
fof(f637,plain,
( ! [X0] :
( subrelstr(X0,X0)
| ~ rel_str(X0) )
| ~ spl16_15
| ~ spl16_83 ),
inference(resolution,[],[f622,f229]) ).
fof(f622,plain,
( ! [X0] :
( ~ subset(the_carrier(X0),the_carrier(X0))
| subrelstr(X0,X0)
| ~ rel_str(X0) )
| ~ spl16_83 ),
inference(avatar_component_clause,[],[f621]) ).
fof(f728,plain,
( ~ spl16_96
| ~ spl16_42
| ~ spl16_3
| ~ spl16_4
| ~ spl16_5
| ~ spl16_88 ),
inference(avatar_split_clause,[],[f670,f667,f178,f173,f168,f355,f725]) ).
fof(f667,plain,
( spl16_88
<=> ! [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,[spl16_88])]) ).
fof(f670,plain,
( ~ element(sK5,the_carrier(sK1))
| ~ element(sK4,the_carrier(sK1))
| ~ rel_str(sK1)
| ~ empty(the_InternalRel(sK1))
| ~ spl16_5
| ~ spl16_88 ),
inference(resolution,[],[f668,f180]) ).
fof(f668,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)) )
| ~ spl16_88 ),
inference(avatar_component_clause,[],[f667]) ).
fof(f720,plain,
( ~ spl16_95
| ~ spl16_27
| ~ spl16_93 ),
inference(avatar_split_clause,[],[f709,f699,f282,f717]) ).
fof(f717,plain,
( spl16_95
<=> in(the_carrier(sK1),sK5) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_95])]) ).
fof(f709,plain,
( ~ in(the_carrier(sK1),sK5)
| ~ spl16_27
| ~ spl16_93 ),
inference(resolution,[],[f701,f283]) ).
fof(f715,plain,
( ~ spl16_94
| ~ spl16_27
| ~ spl16_52 ),
inference(avatar_split_clause,[],[f696,f424,f282,f712]) ).
fof(f712,plain,
( spl16_94
<=> in(the_carrier(sK1),sK4) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_94])]) ).
fof(f696,plain,
( ~ in(the_carrier(sK1),sK4)
| ~ spl16_27
| ~ spl16_52 ),
inference(resolution,[],[f426,f283]) ).
fof(f707,plain,
( ~ spl16_53
| ~ spl16_24
| ~ spl16_52 ),
inference(avatar_split_clause,[],[f697,f424,f267,f428]) ).
fof(f706,plain,
( spl16_84
| ~ spl16_52
| ~ spl16_61 ),
inference(avatar_split_clause,[],[f693,f491,f424,f641]) ).
fof(f693,plain,
( in(sK4,sK14)
| ~ spl16_52
| ~ spl16_61 ),
inference(forward_demodulation,[],[f426,f493]) ).
fof(f702,plain,
( spl16_93
| spl16_53
| ~ spl16_4
| ~ spl16_38 ),
inference(avatar_split_clause,[],[f360,f335,f173,f428,f699]) ).
fof(f360,plain,
( empty(the_carrier(sK1))
| in(sK5,the_carrier(sK1))
| ~ spl16_4
| ~ spl16_38 ),
inference(resolution,[],[f336,f175]) ).
fof(f175,plain,
( element(sK5,the_carrier(sK1))
| ~ spl16_4 ),
inference(avatar_component_clause,[],[f173]) ).
fof(f694,plain,
( ~ spl16_12
| spl16_53
| ~ spl16_61 ),
inference(avatar_split_clause,[],[f692,f491,f428,f213]) ).
fof(f692,plain,
( ~ empty(sK14)
| spl16_53
| ~ spl16_61 ),
inference(forward_demodulation,[],[f429,f493]) ).
fof(f429,plain,
( ~ empty(the_carrier(sK1))
| spl16_53 ),
inference(avatar_component_clause,[],[f428]) ).
fof(f690,plain,
( spl16_92
| ~ spl16_36
| ~ spl16_53 ),
inference(avatar_split_clause,[],[f437,f428,f318,f688]) ).
fof(f437,plain,
( ! [X0] :
( the_carrier(sK1) = X0
| ~ empty(X0) )
| ~ spl16_36
| ~ spl16_53 ),
inference(resolution,[],[f430,f319]) ).
fof(f430,plain,
( empty(the_carrier(sK1))
| ~ spl16_53 ),
inference(avatar_component_clause,[],[f428]) ).
fof(f685,plain,
( spl16_91
| ~ spl16_4
| ~ spl16_61 ),
inference(avatar_split_clause,[],[f598,f491,f173,f682]) ).
fof(f682,plain,
( spl16_91
<=> element(sK5,sK14) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_91])]) ).
fof(f598,plain,
( element(sK5,sK14)
| ~ spl16_4
| ~ spl16_61 ),
inference(superposition,[],[f175,f493]) ).
fof(f680,plain,
( spl16_90
| ~ spl16_27
| ~ spl16_50 ),
inference(avatar_split_clause,[],[f433,f416,f282,f678]) ).
fof(f678,plain,
( spl16_90
<=> ! [X2,X0,X1] :
( ~ related(X0,X1,X2)
| ~ element(X2,the_carrier(X0))
| ~ element(X1,the_carrier(X0))
| ~ rel_str(X0)
| ~ in(the_InternalRel(X0),ordered_pair(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_90])]) ).
fof(f433,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),ordered_pair(X1,X2)) )
| ~ spl16_27
| ~ spl16_50 ),
inference(resolution,[],[f417,f283]) ).
fof(f676,plain,
( spl16_89
| ~ spl16_28
| ~ spl16_50 ),
inference(avatar_split_clause,[],[f432,f416,f286,f674]) ).
fof(f674,plain,
( spl16_89
<=> ! [X2,X0,X1] :
( ~ related(X0,X1,X2)
| ~ element(X2,the_carrier(X0))
| ~ element(X1,the_carrier(X0))
| ~ rel_str(X0)
| element(ordered_pair(X1,X2),the_InternalRel(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_89])]) ).
fof(f432,plain,
( ! [X2,X0,X1] :
( ~ related(X0,X1,X2)
| ~ element(X2,the_carrier(X0))
| ~ element(X1,the_carrier(X0))
| ~ rel_str(X0)
| element(ordered_pair(X1,X2),the_InternalRel(X0)) )
| ~ spl16_28
| ~ spl16_50 ),
inference(resolution,[],[f417,f287]) ).
fof(f669,plain,
( spl16_88
| ~ spl16_24
| ~ spl16_50 ),
inference(avatar_split_clause,[],[f434,f416,f267,f667]) ).
fof(f434,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)) )
| ~ spl16_24
| ~ spl16_50 ),
inference(resolution,[],[f417,f268]) ).
fof(f662,plain,
( spl16_87
| ~ spl16_38
| ~ spl16_45 ),
inference(avatar_split_clause,[],[f393,f383,f335,f660]) ).
fof(f383,plain,
( spl16_45
<=> ! [X2,X0,X1] :
( element(X2,powerset(cartesian_product2(X0,X1)))
| ~ relation_of2_as_subset(X2,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_45])]) ).
fof(f393,plain,
( ! [X2,X0,X1] :
( ~ relation_of2_as_subset(X0,X1,X2)
| empty(powerset(cartesian_product2(X1,X2)))
| in(X0,powerset(cartesian_product2(X1,X2))) )
| ~ spl16_38
| ~ spl16_45 ),
inference(resolution,[],[f384,f336]) ).
fof(f384,plain,
( ! [X2,X0,X1] :
( element(X2,powerset(cartesian_product2(X0,X1)))
| ~ relation_of2_as_subset(X2,X0,X1) )
| ~ spl16_45 ),
inference(avatar_component_clause,[],[f383]) ).
fof(f655,plain,
( spl16_86
| ~ spl16_45
| ~ spl16_46 ),
inference(avatar_split_clause,[],[f397,f387,f383,f653]) ).
fof(f397,plain,
( ! [X2,X3,X0,X1] :
( element(X0,cartesian_product2(X1,X2))
| ~ in(X0,X3)
| ~ relation_of2_as_subset(X3,X1,X2) )
| ~ spl16_45
| ~ spl16_46 ),
inference(resolution,[],[f388,f384]) ).
fof(f648,plain,
( spl16_85
| ~ spl16_44
| ~ spl16_45 ),
inference(avatar_split_clause,[],[f390,f383,f374,f646]) ).
fof(f390,plain,
( ! [X2,X3,X0,X1] :
( ~ relation_of2_as_subset(X0,X1,X2)
| ~ empty(cartesian_product2(X1,X2))
| ~ in(X3,X0) )
| ~ spl16_44
| ~ spl16_45 ),
inference(resolution,[],[f384,f375]) ).
fof(f644,plain,
( ~ spl16_84
| spl16_52
| ~ spl16_61 ),
inference(avatar_split_clause,[],[f596,f491,f424,f641]) ).
fof(f596,plain,
( ~ in(sK4,sK14)
| spl16_52
| ~ spl16_61 ),
inference(superposition,[],[f425,f493]) ).
fof(f425,plain,
( ~ in(sK4,the_carrier(sK1))
| spl16_52 ),
inference(avatar_component_clause,[],[f424]) ).
fof(f623,plain,
( spl16_83
| ~ spl16_15
| ~ spl16_49 ),
inference(avatar_split_clause,[],[f413,f408,f228,f621]) ).
fof(f408,plain,
( spl16_49
<=> ! [X0,X1] :
( subrelstr(X1,X0)
| ~ subset(the_InternalRel(X1),the_InternalRel(X0))
| ~ subset(the_carrier(X1),the_carrier(X0))
| ~ rel_str(X1)
| ~ rel_str(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_49])]) ).
fof(f413,plain,
( ! [X0] :
( subrelstr(X0,X0)
| ~ subset(the_carrier(X0),the_carrier(X0))
| ~ rel_str(X0) )
| ~ spl16_15
| ~ spl16_49 ),
inference(duplicate_literal_removal,[],[f412]) ).
fof(f412,plain,
( ! [X0] :
( subrelstr(X0,X0)
| ~ subset(the_carrier(X0),the_carrier(X0))
| ~ rel_str(X0)
| ~ rel_str(X0) )
| ~ spl16_15
| ~ spl16_49 ),
inference(resolution,[],[f409,f229]) ).
fof(f409,plain,
( ! [X0,X1] :
( ~ subset(the_InternalRel(X1),the_InternalRel(X0))
| subrelstr(X1,X0)
| ~ subset(the_carrier(X1),the_carrier(X0))
| ~ rel_str(X1)
| ~ rel_str(X0) )
| ~ spl16_49 ),
inference(avatar_component_clause,[],[f408]) ).
fof(f619,plain,
( spl16_82
| ~ spl16_37
| ~ spl16_45 ),
inference(avatar_split_clause,[],[f391,f383,f331,f617]) ).
fof(f391,plain,
( ! [X2,X0,X1] :
( ~ relation_of2_as_subset(X0,X1,X2)
| finite(X0)
| ~ finite(cartesian_product2(X1,X2)) )
| ~ spl16_37
| ~ spl16_45 ),
inference(resolution,[],[f384,f332]) ).
fof(f615,plain,
( spl16_81
| ~ spl16_35
| ~ spl16_38 ),
inference(avatar_split_clause,[],[f366,f335,f314,f613]) ).
fof(f314,plain,
( spl16_35
<=> ! [X0,X1] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_35])]) ).
fof(f366,plain,
( ! [X0,X1] :
( empty(powerset(X0))
| in(X1,powerset(X0))
| ~ subset(X1,X0) )
| ~ spl16_35
| ~ spl16_38 ),
inference(resolution,[],[f336,f315]) ).
fof(f315,plain,
( ! [X0,X1] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) )
| ~ spl16_35 ),
inference(avatar_component_clause,[],[f314]) ).
fof(f611,plain,
( spl16_80
| ~ spl16_32
| ~ spl16_38 ),
inference(avatar_split_clause,[],[f365,f335,f302,f609]) ).
fof(f302,plain,
( spl16_32
<=> ! [X0] :
( element(sK7(X0),powerset(X0))
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_32])]) ).
fof(f365,plain,
( ! [X0] :
( empty(powerset(X0))
| in(sK7(X0),powerset(X0))
| empty(X0) )
| ~ spl16_32
| ~ spl16_38 ),
inference(resolution,[],[f336,f303]) ).
fof(f303,plain,
( ! [X0] :
( element(sK7(X0),powerset(X0))
| empty(X0) )
| ~ spl16_32 ),
inference(avatar_component_clause,[],[f302]) ).
fof(f607,plain,
( spl16_79
| ~ spl16_31
| ~ spl16_38 ),
inference(avatar_split_clause,[],[f364,f335,f298,f605]) ).
fof(f298,plain,
( spl16_31
<=> ! [X0] :
( element(sK6(X0),powerset(X0))
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_31])]) ).
fof(f364,plain,
( ! [X0] :
( empty(powerset(X0))
| in(sK6(X0),powerset(X0))
| empty(X0) )
| ~ spl16_31
| ~ spl16_38 ),
inference(resolution,[],[f336,f299]) ).
fof(f299,plain,
( ! [X0] :
( element(sK6(X0),powerset(X0))
| empty(X0) )
| ~ spl16_31 ),
inference(avatar_component_clause,[],[f298]) ).
fof(f583,plain,
( spl16_78
| ~ spl16_35
| ~ spl16_46 ),
inference(avatar_split_clause,[],[f396,f387,f314,f581]) ).
fof(f396,plain,
( ! [X2,X0,X1] :
( element(X0,X1)
| ~ in(X0,X2)
| ~ subset(X2,X1) )
| ~ spl16_35
| ~ spl16_46 ),
inference(resolution,[],[f388,f315]) ).
fof(f579,plain,
( spl16_77
| ~ spl16_32
| ~ spl16_46 ),
inference(avatar_split_clause,[],[f395,f387,f302,f577]) ).
fof(f395,plain,
( ! [X0,X1] :
( element(X0,X1)
| ~ in(X0,sK7(X1))
| empty(X1) )
| ~ spl16_32
| ~ spl16_46 ),
inference(resolution,[],[f388,f303]) ).
fof(f575,plain,
( spl16_76
| ~ spl16_31
| ~ spl16_46 ),
inference(avatar_split_clause,[],[f394,f387,f298,f573]) ).
fof(f394,plain,
( ! [X0,X1] :
( element(X0,X1)
| ~ in(X0,sK6(X1))
| empty(X1) )
| ~ spl16_31
| ~ spl16_46 ),
inference(resolution,[],[f388,f299]) ).
fof(f571,plain,
( spl16_75
| ~ spl16_34
| ~ spl16_45 ),
inference(avatar_split_clause,[],[f392,f383,f310,f569]) ).
fof(f569,plain,
( spl16_75
<=> ! [X2,X0,X1] :
( ~ relation_of2_as_subset(X0,X1,X2)
| subset(X0,cartesian_product2(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_75])]) ).
fof(f392,plain,
( ! [X2,X0,X1] :
( ~ relation_of2_as_subset(X0,X1,X2)
| subset(X0,cartesian_product2(X1,X2)) )
| ~ spl16_34
| ~ spl16_45 ),
inference(resolution,[],[f384,f311]) ).
fof(f567,plain,
( spl16_74
| ~ spl16_40
| ~ spl16_43 ),
inference(avatar_split_clause,[],[f377,f370,f343,f565]) ).
fof(f377,plain,
( ! [X0] :
( ~ rel_str(X0)
| relation_of2(the_InternalRel(X0),the_carrier(X0),the_carrier(X0)) )
| ~ spl16_40
| ~ spl16_43 ),
inference(resolution,[],[f371,f344]) ).
fof(f563,plain,
( ~ spl16_73
| ~ spl16_27
| ~ spl16_56 ),
inference(avatar_split_clause,[],[f466,f455,f282,f560]) ).
fof(f466,plain,
( ~ in(the_carrier(sK0),sK4)
| ~ spl16_27
| ~ spl16_56 ),
inference(resolution,[],[f457,f283]) ).
fof(f551,plain,
( spl16_72
| ~ spl16_17
| ~ spl16_46 ),
inference(avatar_split_clause,[],[f398,f387,f236,f549]) ).
fof(f398,plain,
( ! [X0,X1] :
( element(X0,X1)
| ~ in(X0,sK9(powerset(X1))) )
| ~ spl16_17
| ~ spl16_46 ),
inference(resolution,[],[f388,f237]) ).
fof(f547,plain,
( spl16_71
| ~ spl16_35
| ~ spl16_44 ),
inference(avatar_split_clause,[],[f380,f374,f314,f545]) ).
fof(f380,plain,
( ! [X2,X0,X1] :
( ~ empty(X0)
| ~ in(X1,X2)
| ~ subset(X2,X0) )
| ~ spl16_35
| ~ spl16_44 ),
inference(resolution,[],[f375,f315]) ).
fof(f536,plain,
( spl16_70
| ~ spl16_17
| ~ spl16_44 ),
inference(avatar_split_clause,[],[f381,f374,f236,f534]) ).
fof(f381,plain,
( ! [X0,X1] :
( ~ empty(X0)
| ~ in(X1,sK9(powerset(X0))) )
| ~ spl16_17
| ~ spl16_44 ),
inference(resolution,[],[f375,f237]) ).
fof(f532,plain,
( spl16_69
| ~ spl16_35
| ~ spl16_37 ),
inference(avatar_split_clause,[],[f352,f331,f314,f530]) ).
fof(f352,plain,
( ! [X0,X1] :
( finite(X0)
| ~ finite(X1)
| ~ subset(X0,X1) )
| ~ spl16_35
| ~ spl16_37 ),
inference(resolution,[],[f332,f315]) ).
fof(f526,plain,
( ~ spl16_68
| ~ spl16_27
| ~ spl16_54 ),
inference(avatar_split_clause,[],[f452,f443,f282,f523]) ).
fof(f452,plain,
( ~ in(the_carrier(sK0),sK5)
| ~ spl16_27
| ~ spl16_54 ),
inference(resolution,[],[f445,f283]) ).
fof(f518,plain,
( spl16_67
| ~ spl16_29
| ~ spl16_41 ),
inference(avatar_split_clause,[],[f368,f347,f290,f516]) ).
fof(f368,plain,
( ! [X0,X1] : relation_of2_as_subset(sK10(X0,X1),X0,X1)
| ~ spl16_29
| ~ spl16_41 ),
inference(resolution,[],[f348,f291]) ).
fof(f514,plain,
( spl16_66
| ~ spl16_30
| ~ spl16_40 ),
inference(avatar_split_clause,[],[f367,f343,f294,f512]) ).
fof(f512,plain,
( spl16_66
<=> ! [X0,X1] : relation_of2(sK11(X0,X1),X0,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_66])]) ).
fof(f367,plain,
( ! [X0,X1] : relation_of2(sK11(X0,X1),X0,X1)
| ~ spl16_30
| ~ spl16_40 ),
inference(resolution,[],[f344,f295]) ).
fof(f510,plain,
( spl16_65
| ~ spl16_17
| ~ spl16_38 ),
inference(avatar_split_clause,[],[f363,f335,f236,f508]) ).
fof(f363,plain,
( ! [X0] :
( empty(X0)
| in(sK9(X0),X0) )
| ~ spl16_17
| ~ spl16_38 ),
inference(resolution,[],[f336,f237]) ).
fof(f506,plain,
( spl16_64
| ~ spl16_17
| ~ spl16_37 ),
inference(avatar_split_clause,[],[f353,f331,f236,f504]) ).
fof(f504,plain,
( spl16_64
<=> ! [X0] :
( finite(sK9(powerset(X0)))
| ~ finite(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_64])]) ).
fof(f353,plain,
( ! [X0] :
( finite(sK9(powerset(X0)))
| ~ finite(X0) )
| ~ spl16_17
| ~ spl16_37 ),
inference(resolution,[],[f332,f237]) ).
fof(f502,plain,
( spl16_63
| ~ spl16_32
| ~ spl16_34 ),
inference(avatar_split_clause,[],[f325,f310,f302,f500]) ).
fof(f500,plain,
( spl16_63
<=> ! [X0] :
( subset(sK7(X0),X0)
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_63])]) ).
fof(f325,plain,
( ! [X0] :
( subset(sK7(X0),X0)
| empty(X0) )
| ~ spl16_32
| ~ spl16_34 ),
inference(resolution,[],[f311,f303]) ).
fof(f498,plain,
( spl16_62
| ~ spl16_31
| ~ spl16_34 ),
inference(avatar_split_clause,[],[f324,f310,f298,f496]) ).
fof(f496,plain,
( spl16_62
<=> ! [X0] :
( subset(sK6(X0),X0)
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_62])]) ).
fof(f324,plain,
( ! [X0] :
( subset(sK6(X0),X0)
| empty(X0) )
| ~ spl16_31
| ~ spl16_34 ),
inference(resolution,[],[f311,f299]) ).
fof(f494,plain,
( spl16_61
| ~ spl16_12
| ~ spl16_23
| ~ spl16_53 ),
inference(avatar_split_clause,[],[f440,f428,f263,f213,f491]) ).
fof(f440,plain,
( the_carrier(sK1) = sK14
| ~ spl16_12
| ~ spl16_23
| ~ spl16_53 ),
inference(forward_demodulation,[],[f438,f276]) ).
fof(f438,plain,
( empty_set = the_carrier(sK1)
| ~ spl16_23
| ~ spl16_53 ),
inference(resolution,[],[f430,f264]) ).
fof(f486,plain,
( spl16_60
| ~ spl16_12
| ~ spl16_36 ),
inference(avatar_split_clause,[],[f329,f318,f213,f484]) ).
fof(f484,plain,
( spl16_60
<=> ! [X0] :
( sK14 = X0
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_60])]) ).
fof(f329,plain,
( ! [X0] :
( sK14 = X0
| ~ empty(X0) )
| ~ spl16_12
| ~ spl16_36 ),
inference(resolution,[],[f319,f215]) ).
fof(f482,plain,
( spl16_59
| ~ spl16_17
| ~ spl16_34 ),
inference(avatar_split_clause,[],[f326,f310,f236,f480]) ).
fof(f480,plain,
( spl16_59
<=> ! [X0] : subset(sK9(powerset(X0)),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_59])]) ).
fof(f326,plain,
( ! [X0] : subset(sK9(powerset(X0)),X0)
| ~ spl16_17
| ~ spl16_34 ),
inference(resolution,[],[f311,f237]) ).
fof(f478,plain,
( spl16_58
| ~ spl16_26
| ~ spl16_33 ),
inference(avatar_split_clause,[],[f323,f306,f278,f476]) ).
fof(f306,plain,
( spl16_33
<=> ! [X0,X1] :
( rel_str(X1)
| ~ subrelstr(X1,X0)
| ~ rel_str(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_33])]) ).
fof(f323,plain,
( ! [X0] :
( rel_str(sK8(X0))
| ~ rel_str(X0) )
| ~ spl16_26
| ~ spl16_33 ),
inference(duplicate_literal_removal,[],[f322]) ).
fof(f322,plain,
( ! [X0] :
( rel_str(sK8(X0))
| ~ rel_str(X0)
| ~ rel_str(X0) )
| ~ spl16_26
| ~ spl16_33 ),
inference(resolution,[],[f307,f279]) ).
fof(f307,plain,
( ! [X0,X1] :
( ~ subrelstr(X1,X0)
| rel_str(X1)
| ~ rel_str(X0) )
| ~ spl16_33 ),
inference(avatar_component_clause,[],[f306]) ).
fof(f472,plain,
( spl16_57
| ~ spl16_12
| ~ spl16_23 ),
inference(avatar_split_clause,[],[f276,f263,f213,f469]) ).
fof(f464,plain,
( ~ spl16_55
| ~ spl16_24
| ~ spl16_54 ),
inference(avatar_split_clause,[],[f453,f443,f267,f447]) ).
fof(f453,plain,
( ~ empty(the_carrier(sK0))
| ~ spl16_24
| ~ spl16_54 ),
inference(resolution,[],[f445,f268]) ).
fof(f458,plain,
( spl16_56
| spl16_55
| ~ spl16_8
| ~ spl16_38 ),
inference(avatar_split_clause,[],[f362,f335,f193,f447,f455]) ).
fof(f362,plain,
( empty(the_carrier(sK0))
| in(sK4,the_carrier(sK0))
| ~ spl16_8
| ~ spl16_38 ),
inference(resolution,[],[f336,f195]) ).
fof(f450,plain,
( spl16_54
| spl16_55
| ~ spl16_7
| ~ spl16_38 ),
inference(avatar_split_clause,[],[f361,f335,f188,f447,f443]) ).
fof(f361,plain,
( empty(the_carrier(sK0))
| in(sK5,the_carrier(sK0))
| ~ spl16_7
| ~ spl16_38 ),
inference(resolution,[],[f336,f190]) ).
fof(f431,plain,
( spl16_52
| spl16_53
| ~ spl16_3
| ~ spl16_38 ),
inference(avatar_split_clause,[],[f359,f335,f168,f428,f424]) ).
fof(f359,plain,
( empty(the_carrier(sK1))
| in(sK4,the_carrier(sK1))
| ~ spl16_3
| ~ spl16_38 ),
inference(resolution,[],[f336,f170]) ).
fof(f422,plain,
spl16_51,
inference(avatar_split_clause,[],[f127,f420]) ).
fof(f127,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,[],[f85]) ).
fof(f85,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,[],[f55]) ).
fof(f55,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,[],[f6]) ).
fof(f6,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/sandbox2/benchmark/theBenchmark.p',d9_orders_2) ).
fof(f418,plain,
spl16_50,
inference(avatar_split_clause,[],[f126,f416]) ).
fof(f126,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,[],[f85]) ).
fof(f410,plain,
spl16_49,
inference(avatar_split_clause,[],[f124,f408]) ).
fof(f124,plain,
! [X0,X1] :
( subrelstr(X1,X0)
| ~ subset(the_InternalRel(X1),the_InternalRel(X0))
| ~ subset(the_carrier(X1),the_carrier(X0))
| ~ rel_str(X1)
| ~ rel_str(X0) ),
inference(cnf_transformation,[],[f84]) ).
fof(f84,plain,
! [X0] :
( ! [X1] :
( ( ( subrelstr(X1,X0)
| ~ subset(the_InternalRel(X1),the_InternalRel(X0))
| ~ subset(the_carrier(X1),the_carrier(X0)) )
& ( ( subset(the_InternalRel(X1),the_InternalRel(X0))
& subset(the_carrier(X1),the_carrier(X0)) )
| ~ subrelstr(X1,X0) ) )
| ~ rel_str(X1) )
| ~ rel_str(X0) ),
inference(flattening,[],[f83]) ).
fof(f83,plain,
! [X0] :
( ! [X1] :
( ( ( subrelstr(X1,X0)
| ~ subset(the_InternalRel(X1),the_InternalRel(X0))
| ~ subset(the_carrier(X1),the_carrier(X0)) )
& ( ( subset(the_InternalRel(X1),the_InternalRel(X0))
& subset(the_carrier(X1),the_carrier(X0)) )
| ~ subrelstr(X1,X0) ) )
| ~ rel_str(X1) )
| ~ rel_str(X0) ),
inference(nnf_transformation,[],[f53]) ).
fof(f53,plain,
! [X0] :
( ! [X1] :
( ( subrelstr(X1,X0)
<=> ( subset(the_InternalRel(X1),the_InternalRel(X0))
& subset(the_carrier(X1),the_carrier(X0)) ) )
| ~ rel_str(X1) )
| ~ rel_str(X0) ),
inference(ennf_transformation,[],[f5]) ).
fof(f5,axiom,
! [X0] :
( rel_str(X0)
=> ! [X1] :
( rel_str(X1)
=> ( subrelstr(X1,X0)
<=> ( subset(the_InternalRel(X1),the_InternalRel(X0))
& subset(the_carrier(X1),the_carrier(X0)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d13_yellow_0) ).
fof(f406,plain,
spl16_48,
inference(avatar_split_clause,[],[f123,f404]) ).
fof(f123,plain,
! [X0,X1] :
( subset(the_InternalRel(X1),the_InternalRel(X0))
| ~ subrelstr(X1,X0)
| ~ rel_str(X1)
| ~ rel_str(X0) ),
inference(cnf_transformation,[],[f84]) ).
fof(f402,plain,
spl16_47,
inference(avatar_split_clause,[],[f122,f400]) ).
fof(f122,plain,
! [X0,X1] :
( subset(the_carrier(X1),the_carrier(X0))
| ~ subrelstr(X1,X0)
| ~ rel_str(X1)
| ~ rel_str(X0) ),
inference(cnf_transformation,[],[f84]) ).
fof(f389,plain,
spl16_46,
inference(avatar_split_clause,[],[f145,f387]) ).
fof(f145,plain,
! [X2,X0,X1] :
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f70]) ).
fof(f70,plain,
! [X0,X1,X2] :
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(flattening,[],[f69]) ).
fof(f69,plain,
! [X0,X1,X2] :
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f37]) ).
fof(f37,axiom,
! [X0,X1,X2] :
( ( element(X1,powerset(X2))
& in(X0,X1) )
=> element(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_subset) ).
fof(f385,plain,
spl16_45,
inference(avatar_split_clause,[],[f144,f383]) ).
fof(f144,plain,
! [X2,X0,X1] :
( element(X2,powerset(cartesian_product2(X0,X1)))
| ~ relation_of2_as_subset(X2,X0,X1) ),
inference(cnf_transformation,[],[f68]) ).
fof(f68,plain,
! [X0,X1,X2] :
( element(X2,powerset(cartesian_product2(X0,X1)))
| ~ relation_of2_as_subset(X2,X0,X1) ),
inference(ennf_transformation,[],[f16]) ).
fof(f16,axiom,
! [X0,X1,X2] :
( relation_of2_as_subset(X2,X0,X1)
=> element(X2,powerset(cartesian_product2(X0,X1))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m2_relset_1) ).
fof(f376,plain,
spl16_44,
inference(avatar_split_clause,[],[f148,f374]) ).
fof(f148,plain,
! [X2,X0,X1] :
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f71]) ).
fof(f71,plain,
! [X0,X1,X2] :
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f38]) ).
fof(f38,axiom,
! [X0,X1,X2] :
~ ( empty(X2)
& element(X1,powerset(X2))
& in(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_subset) ).
fof(f372,plain,
spl16_43,
inference(avatar_split_clause,[],[f121,f370]) ).
fof(f121,plain,
! [X0] :
( relation_of2_as_subset(the_InternalRel(X0),the_carrier(X0),the_carrier(X0))
| ~ rel_str(X0) ),
inference(cnf_transformation,[],[f52]) ).
fof(f52,plain,
! [X0] :
( relation_of2_as_subset(the_InternalRel(X0),the_carrier(X0),the_carrier(X0))
| ~ rel_str(X0) ),
inference(ennf_transformation,[],[f17]) ).
fof(f17,axiom,
! [X0] :
( rel_str(X0)
=> relation_of2_as_subset(the_InternalRel(X0),the_carrier(X0),the_carrier(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_u1_orders_2) ).
fof(f358,plain,
( ~ spl16_1
| spl16_42
| ~ spl16_2
| ~ spl16_33 ),
inference(avatar_split_clause,[],[f321,f306,f163,f355,f158]) ).
fof(f321,plain,
( rel_str(sK1)
| ~ rel_str(sK0)
| ~ spl16_2
| ~ spl16_33 ),
inference(resolution,[],[f307,f165]) ).
fof(f349,plain,
spl16_41,
inference(avatar_split_clause,[],[f147,f347]) ).
fof(f147,plain,
! [X2,X0,X1] :
( relation_of2_as_subset(X2,X0,X1)
| ~ relation_of2(X2,X0,X1) ),
inference(cnf_transformation,[],[f95]) ).
fof(f95,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,[],[f32]) ).
fof(f32,axiom,
! [X0,X1,X2] :
( relation_of2_as_subset(X2,X0,X1)
<=> relation_of2(X2,X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_m2_relset_1) ).
fof(f345,plain,
spl16_40,
inference(avatar_split_clause,[],[f146,f343]) ).
fof(f146,plain,
! [X2,X0,X1] :
( relation_of2(X2,X0,X1)
| ~ relation_of2_as_subset(X2,X0,X1) ),
inference(cnf_transformation,[],[f95]) ).
fof(f341,plain,
spl16_39,
inference(avatar_split_clause,[],[f137,f339]) ).
fof(f137,plain,
! [X0,X1] :
( finite(cartesian_product2(X0,X1))
| ~ finite(X1)
| ~ finite(X0) ),
inference(cnf_transformation,[],[f65]) ).
fof(f65,plain,
! [X0,X1] :
( finite(cartesian_product2(X0,X1))
| ~ finite(X1)
| ~ finite(X0) ),
inference(flattening,[],[f64]) ).
fof(f64,plain,
! [X0,X1] :
( finite(cartesian_product2(X0,X1))
| ~ finite(X1)
| ~ finite(X0) ),
inference(ennf_transformation,[],[f25]) ).
fof(f25,axiom,
! [X0,X1] :
( ( finite(X1)
& finite(X0) )
=> finite(cartesian_product2(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc14_finset_1) ).
fof(f337,plain,
spl16_38,
inference(avatar_split_clause,[],[f136,f335]) ).
fof(f136,plain,
! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(cnf_transformation,[],[f63]) ).
fof(f63,plain,
! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(flattening,[],[f62]) ).
fof(f62,plain,
! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(ennf_transformation,[],[f35]) ).
fof(f35,axiom,
! [X0,X1] :
( element(X0,X1)
=> ( in(X0,X1)
| empty(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
fof(f333,plain,
spl16_37,
inference(avatar_split_clause,[],[f131,f331]) ).
fof(f131,plain,
! [X0,X1] :
( finite(X1)
| ~ element(X1,powerset(X0))
| ~ finite(X0) ),
inference(cnf_transformation,[],[f59]) ).
fof(f59,plain,
! [X0] :
( ! [X1] :
( finite(X1)
| ~ element(X1,powerset(X0)) )
| ~ finite(X0) ),
inference(ennf_transformation,[],[f4]) ).
fof(f4,axiom,
! [X0] :
( finite(X0)
=> ! [X1] :
( element(X1,powerset(X0))
=> finite(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_finset_1) ).
fof(f320,plain,
spl16_36,
inference(avatar_split_clause,[],[f140,f318]) ).
fof(f140,plain,
! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) ),
inference(cnf_transformation,[],[f66]) ).
fof(f66,plain,
! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) ),
inference(ennf_transformation,[],[f43]) ).
fof(f43,axiom,
! [X0,X1] :
~ ( empty(X1)
& X0 != X1
& empty(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_boole) ).
fof(f316,plain,
spl16_35,
inference(avatar_split_clause,[],[f139,f314]) ).
fof(f139,plain,
! [X0,X1] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f90]) ).
fof(f90,plain,
! [X0,X1] :
( ( element(X0,powerset(X1))
| ~ subset(X0,X1) )
& ( subset(X0,X1)
| ~ element(X0,powerset(X1)) ) ),
inference(nnf_transformation,[],[f36]) ).
fof(f36,axiom,
! [X0,X1] :
( element(X0,powerset(X1))
<=> subset(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_subset) ).
fof(f312,plain,
spl16_34,
inference(avatar_split_clause,[],[f138,f310]) ).
fof(f138,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f90]) ).
fof(f308,plain,
spl16_33,
inference(avatar_split_clause,[],[f125,f306]) ).
fof(f125,plain,
! [X0,X1] :
( rel_str(X1)
| ~ subrelstr(X1,X0)
| ~ rel_str(X0) ),
inference(cnf_transformation,[],[f54]) ).
fof(f54,plain,
! [X0] :
( ! [X1] :
( rel_str(X1)
| ~ subrelstr(X1,X0) )
| ~ rel_str(X0) ),
inference(ennf_transformation,[],[f15]) ).
fof(f15,axiom,
! [X0] :
( rel_str(X0)
=> ! [X1] :
( subrelstr(X1,X0)
=> rel_str(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m1_yellow_0) ).
fof(f304,plain,
spl16_32,
inference(avatar_split_clause,[],[f118,f302]) ).
fof(f118,plain,
! [X0] :
( element(sK7(X0),powerset(X0))
| empty(X0) ),
inference(cnf_transformation,[],[f82]) ).
fof(f82,plain,
! [X0] :
( ( finite(sK7(X0))
& ~ empty(sK7(X0))
& element(sK7(X0),powerset(X0)) )
| empty(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK7])],[f51,f81]) ).
fof(f81,plain,
! [X0] :
( ? [X1] :
( finite(X1)
& ~ empty(X1)
& element(X1,powerset(X0)) )
=> ( finite(sK7(X0))
& ~ empty(sK7(X0))
& element(sK7(X0),powerset(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f51,plain,
! [X0] :
( ? [X1] :
( finite(X1)
& ~ empty(X1)
& element(X1,powerset(X0)) )
| empty(X0) ),
inference(ennf_transformation,[],[f31]) ).
fof(f31,axiom,
! [X0] :
( ~ empty(X0)
=> ? [X1] :
( finite(X1)
& ~ empty(X1)
& element(X1,powerset(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc4_finset_1) ).
fof(f300,plain,
spl16_31,
inference(avatar_split_clause,[],[f115,f298]) ).
fof(f115,plain,
! [X0] :
( element(sK6(X0),powerset(X0))
| empty(X0) ),
inference(cnf_transformation,[],[f80]) ).
fof(f80,plain,
! [X0] :
( ( finite(sK6(X0))
& ~ empty(sK6(X0))
& element(sK6(X0),powerset(X0)) )
| empty(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6])],[f50,f79]) ).
fof(f79,plain,
! [X0] :
( ? [X1] :
( finite(X1)
& ~ empty(X1)
& element(X1,powerset(X0)) )
=> ( finite(sK6(X0))
& ~ empty(sK6(X0))
& element(sK6(X0),powerset(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f50,plain,
! [X0] :
( ? [X1] :
( finite(X1)
& ~ empty(X1)
& element(X1,powerset(X0)) )
| empty(X0) ),
inference(ennf_transformation,[],[f30]) ).
fof(f30,axiom,
! [X0] :
( ~ empty(X0)
=> ? [X1] :
( finite(X1)
& ~ empty(X1)
& element(X1,powerset(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_finset_1) ).
fof(f296,plain,
spl16_30,
inference(avatar_split_clause,[],[f143,f294]) ).
fof(f143,plain,
! [X0,X1] : relation_of2_as_subset(sK11(X0,X1),X0,X1),
inference(cnf_transformation,[],[f94]) ).
fof(f94,plain,
! [X0,X1] : relation_of2_as_subset(sK11(X0,X1),X0,X1),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK11])],[f24,f93]) ).
fof(f93,plain,
! [X0,X1] :
( ? [X2] : relation_of2_as_subset(X2,X0,X1)
=> relation_of2_as_subset(sK11(X0,X1),X0,X1) ),
introduced(choice_axiom,[]) ).
fof(f24,axiom,
! [X0,X1] :
? [X2] : relation_of2_as_subset(X2,X0,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m2_relset_1) ).
fof(f292,plain,
spl16_29,
inference(avatar_split_clause,[],[f142,f290]) ).
fof(f142,plain,
! [X0,X1] : relation_of2(sK10(X0,X1),X0,X1),
inference(cnf_transformation,[],[f92]) ).
fof(f92,plain,
! [X0,X1] : relation_of2(sK10(X0,X1),X0,X1),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK10])],[f21,f91]) ).
fof(f91,plain,
! [X0,X1] :
( ? [X2] : relation_of2(X2,X0,X1)
=> relation_of2(sK10(X0,X1),X0,X1) ),
introduced(choice_axiom,[]) ).
fof(f21,axiom,
! [X0,X1] :
? [X2] : relation_of2(X2,X0,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_relset_1) ).
fof(f288,plain,
spl16_28,
inference(avatar_split_clause,[],[f135,f286]) ).
fof(f135,plain,
! [X0,X1] :
( element(X0,X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f61]) ).
fof(f61,plain,
! [X0,X1] :
( element(X0,X1)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f34]) ).
fof(f34,axiom,
! [X0,X1] :
( in(X0,X1)
=> element(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).
fof(f284,plain,
spl16_27,
inference(avatar_split_clause,[],[f134,f282]) ).
fof(f134,plain,
! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f60]) ).
fof(f60,plain,
! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f1]) ).
fof(f1,axiom,
! [X0,X1] :
( in(X0,X1)
=> ~ in(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
fof(f280,plain,
spl16_26,
inference(avatar_split_clause,[],[f128,f278]) ).
fof(f128,plain,
! [X0] :
( subrelstr(sK8(X0),X0)
| ~ rel_str(X0) ),
inference(cnf_transformation,[],[f87]) ).
fof(f87,plain,
! [X0] :
( subrelstr(sK8(X0),X0)
| ~ rel_str(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK8])],[f56,f86]) ).
fof(f86,plain,
! [X0] :
( ? [X1] : subrelstr(X1,X0)
=> subrelstr(sK8(X0),X0) ),
introduced(choice_axiom,[]) ).
fof(f56,plain,
! [X0] :
( ? [X1] : subrelstr(X1,X0)
| ~ rel_str(X0) ),
inference(ennf_transformation,[],[f23]) ).
fof(f23,axiom,
! [X0] :
( rel_str(X0)
=> ? [X1] : subrelstr(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_yellow_0) ).
fof(f274,plain,
( spl16_25
| ~ spl16_12
| ~ spl16_16 ),
inference(avatar_split_clause,[],[f240,f232,f213,f271]) ).
fof(f240,plain,
( finite(sK14)
| ~ spl16_12
| ~ spl16_16 ),
inference(resolution,[],[f233,f215]) ).
fof(f269,plain,
spl16_24,
inference(avatar_split_clause,[],[f141,f267]) ).
fof(f141,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f67]) ).
fof(f67,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f42]) ).
fof(f42,axiom,
! [X0,X1] :
~ ( empty(X1)
& in(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
fof(f265,plain,
spl16_23,
inference(avatar_split_clause,[],[f130,f263]) ).
fof(f130,plain,
! [X0] :
( empty_set = X0
| ~ empty(X0) ),
inference(cnf_transformation,[],[f58]) ).
fof(f58,plain,
! [X0] :
( empty_set = X0
| ~ empty(X0) ),
inference(ennf_transformation,[],[f41]) ).
fof(f41,axiom,
! [X0] :
( empty(X0)
=> empty_set = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
fof(f261,plain,
spl16_22,
inference(avatar_split_clause,[],[f120,f259]) ).
fof(f259,plain,
( spl16_22
<=> ! [X0] :
( finite(sK7(X0))
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_22])]) ).
fof(f120,plain,
! [X0] :
( finite(sK7(X0))
| empty(X0) ),
inference(cnf_transformation,[],[f82]) ).
fof(f257,plain,
spl16_21,
inference(avatar_split_clause,[],[f119,f255]) ).
fof(f119,plain,
! [X0] :
( ~ empty(sK7(X0))
| empty(X0) ),
inference(cnf_transformation,[],[f82]) ).
fof(f253,plain,
spl16_20,
inference(avatar_split_clause,[],[f117,f251]) ).
fof(f251,plain,
( spl16_20
<=> ! [X0] :
( finite(sK6(X0))
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_20])]) ).
fof(f117,plain,
! [X0] :
( finite(sK6(X0))
| empty(X0) ),
inference(cnf_transformation,[],[f80]) ).
fof(f249,plain,
spl16_19,
inference(avatar_split_clause,[],[f116,f247]) ).
fof(f116,plain,
! [X0] :
( ~ empty(sK6(X0))
| empty(X0) ),
inference(cnf_transformation,[],[f80]) ).
fof(f245,plain,
( spl16_18
| ~ spl16_9
| ~ spl16_16 ),
inference(avatar_split_clause,[],[f239,f232,f198,f242]) ).
fof(f242,plain,
( spl16_18
<=> finite(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_18])]) ).
fof(f239,plain,
( finite(empty_set)
| ~ spl16_9
| ~ spl16_16 ),
inference(resolution,[],[f233,f200]) ).
fof(f238,plain,
spl16_17,
inference(avatar_split_clause,[],[f132,f236]) ).
fof(f132,plain,
! [X0] : element(sK9(X0),X0),
inference(cnf_transformation,[],[f89]) ).
fof(f89,plain,
! [X0] : element(sK9(X0),X0),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK9])],[f22,f88]) ).
fof(f88,plain,
! [X0] :
( ? [X1] : element(X1,X0)
=> element(sK9(X0),X0) ),
introduced(choice_axiom,[]) ).
fof(f22,axiom,
! [X0] :
? [X1] : element(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).
fof(f234,plain,
spl16_16,
inference(avatar_split_clause,[],[f129,f232]) ).
fof(f129,plain,
! [X0] :
( finite(X0)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f57]) ).
fof(f57,plain,
! [X0] :
( finite(X0)
| ~ empty(X0) ),
inference(ennf_transformation,[],[f2]) ).
fof(f2,axiom,
! [X0] :
( empty(X0)
=> finite(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_finset_1) ).
fof(f230,plain,
spl16_15,
inference(avatar_split_clause,[],[f133,f228]) ).
fof(f133,plain,
! [X0] : subset(X0,X0),
inference(cnf_transformation,[],[f44]) ).
fof(f44,plain,
! [X0] : subset(X0,X0),
inference(rectify,[],[f33]) ).
fof(f33,axiom,
! [X0,X1] : subset(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(f226,plain,
spl16_14,
inference(avatar_split_clause,[],[f153,f223]) ).
fof(f223,plain,
( spl16_14
<=> finite(sK15) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_14])]) ).
fof(f153,plain,
finite(sK15),
inference(cnf_transformation,[],[f103]) ).
fof(f103,plain,
( finite(sK15)
& ~ empty(sK15) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK15])],[f27,f102]) ).
fof(f102,plain,
( ? [X0] :
( finite(X0)
& ~ empty(X0) )
=> ( finite(sK15)
& ~ empty(sK15) ) ),
introduced(choice_axiom,[]) ).
fof(f27,axiom,
? [X0] :
( finite(X0)
& ~ empty(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_finset_1) ).
fof(f221,plain,
~ spl16_13,
inference(avatar_split_clause,[],[f152,f218]) ).
fof(f218,plain,
( spl16_13
<=> empty(sK15) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_13])]) ).
fof(f152,plain,
~ empty(sK15),
inference(cnf_transformation,[],[f103]) ).
fof(f216,plain,
spl16_12,
inference(avatar_split_clause,[],[f151,f213]) ).
fof(f151,plain,
empty(sK14),
inference(cnf_transformation,[],[f101]) ).
fof(f101,plain,
empty(sK14),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK14])],[f28,f100]) ).
fof(f100,plain,
( ? [X0] : empty(X0)
=> empty(sK14) ),
introduced(choice_axiom,[]) ).
fof(f28,axiom,
? [X0] : empty(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).
fof(f211,plain,
spl16_11,
inference(avatar_split_clause,[],[f150,f208]) ).
fof(f208,plain,
( spl16_11
<=> rel_str(sK13) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_11])]) ).
fof(f150,plain,
rel_str(sK13),
inference(cnf_transformation,[],[f99]) ).
fof(f99,plain,
rel_str(sK13),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK13])],[f19,f98]) ).
fof(f98,plain,
( ? [X0] : rel_str(X0)
=> rel_str(sK13) ),
introduced(choice_axiom,[]) ).
fof(f19,axiom,
? [X0] : rel_str(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l1_orders_2) ).
fof(f206,plain,
~ spl16_10,
inference(avatar_split_clause,[],[f149,f203]) ).
fof(f203,plain,
( spl16_10
<=> empty(sK12) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_10])]) ).
fof(f149,plain,
~ empty(sK12),
inference(cnf_transformation,[],[f97]) ).
fof(f97,plain,
~ empty(sK12),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK12])],[f29,f96]) ).
fof(f96,plain,
( ? [X0] : ~ empty(X0)
=> ~ empty(sK12) ),
introduced(choice_axiom,[]) ).
fof(f29,axiom,
? [X0] : ~ empty(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_xboole_0) ).
fof(f201,plain,
spl16_9,
inference(avatar_split_clause,[],[f114,f198]) ).
fof(f114,plain,
empty(empty_set),
inference(cnf_transformation,[],[f26]) ).
fof(f26,axiom,
empty(empty_set),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_xboole_0) ).
fof(f196,plain,
spl16_8,
inference(avatar_split_clause,[],[f156,f193]) ).
fof(f156,plain,
element(sK4,the_carrier(sK0)),
inference(definition_unfolding,[],[f106,f110]) ).
fof(f110,plain,
sK2 = sK4,
inference(cnf_transformation,[],[f78]) ).
fof(f78,plain,
( ~ related(sK0,sK2,sK3)
& related(sK1,sK4,sK5)
& sK3 = sK5
& sK2 = sK4
& element(sK5,the_carrier(sK1))
& element(sK4,the_carrier(sK1))
& element(sK3,the_carrier(sK0))
& element(sK2,the_carrier(sK0))
& subrelstr(sK1,sK0)
& rel_str(sK0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5])],[f49,f77,f76,f75,f74,f73,f72]) ).
fof(f72,plain,
( ? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ related(X0,X2,X3)
& related(X1,X4,X5)
& X3 = X5
& X2 = X4
& element(X5,the_carrier(X1)) )
& element(X4,the_carrier(X1)) )
& element(X3,the_carrier(X0)) )
& element(X2,the_carrier(X0)) )
& subrelstr(X1,X0) )
& rel_str(X0) )
=> ( ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ related(sK0,X2,X3)
& related(X1,X4,X5)
& X3 = X5
& X2 = X4
& element(X5,the_carrier(X1)) )
& element(X4,the_carrier(X1)) )
& element(X3,the_carrier(sK0)) )
& element(X2,the_carrier(sK0)) )
& subrelstr(X1,sK0) )
& rel_str(sK0) ) ),
introduced(choice_axiom,[]) ).
fof(f73,plain,
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ related(sK0,X2,X3)
& related(X1,X4,X5)
& X3 = X5
& X2 = X4
& element(X5,the_carrier(X1)) )
& element(X4,the_carrier(X1)) )
& element(X3,the_carrier(sK0)) )
& element(X2,the_carrier(sK0)) )
& subrelstr(X1,sK0) )
=> ( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ related(sK0,X2,X3)
& related(sK1,X4,X5)
& X3 = X5
& X2 = X4
& element(X5,the_carrier(sK1)) )
& element(X4,the_carrier(sK1)) )
& element(X3,the_carrier(sK0)) )
& element(X2,the_carrier(sK0)) )
& subrelstr(sK1,sK0) ) ),
introduced(choice_axiom,[]) ).
fof(f74,plain,
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ related(sK0,X2,X3)
& related(sK1,X4,X5)
& X3 = X5
& X2 = X4
& element(X5,the_carrier(sK1)) )
& element(X4,the_carrier(sK1)) )
& element(X3,the_carrier(sK0)) )
& element(X2,the_carrier(sK0)) )
=> ( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ related(sK0,sK2,X3)
& related(sK1,X4,X5)
& X3 = X5
& sK2 = X4
& element(X5,the_carrier(sK1)) )
& element(X4,the_carrier(sK1)) )
& element(X3,the_carrier(sK0)) )
& element(sK2,the_carrier(sK0)) ) ),
introduced(choice_axiom,[]) ).
fof(f75,plain,
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ related(sK0,sK2,X3)
& related(sK1,X4,X5)
& X3 = X5
& sK2 = X4
& element(X5,the_carrier(sK1)) )
& element(X4,the_carrier(sK1)) )
& element(X3,the_carrier(sK0)) )
=> ( ? [X4] :
( ? [X5] :
( ~ related(sK0,sK2,sK3)
& related(sK1,X4,X5)
& sK3 = X5
& sK2 = X4
& element(X5,the_carrier(sK1)) )
& element(X4,the_carrier(sK1)) )
& element(sK3,the_carrier(sK0)) ) ),
introduced(choice_axiom,[]) ).
fof(f76,plain,
( ? [X4] :
( ? [X5] :
( ~ related(sK0,sK2,sK3)
& related(sK1,X4,X5)
& sK3 = X5
& sK2 = X4
& element(X5,the_carrier(sK1)) )
& element(X4,the_carrier(sK1)) )
=> ( ? [X5] :
( ~ related(sK0,sK2,sK3)
& related(sK1,sK4,X5)
& sK3 = X5
& sK2 = sK4
& element(X5,the_carrier(sK1)) )
& element(sK4,the_carrier(sK1)) ) ),
introduced(choice_axiom,[]) ).
fof(f77,plain,
( ? [X5] :
( ~ related(sK0,sK2,sK3)
& related(sK1,sK4,X5)
& sK3 = X5
& sK2 = sK4
& element(X5,the_carrier(sK1)) )
=> ( ~ related(sK0,sK2,sK3)
& related(sK1,sK4,sK5)
& sK3 = sK5
& sK2 = sK4
& element(sK5,the_carrier(sK1)) ) ),
introduced(choice_axiom,[]) ).
fof(f49,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ related(X0,X2,X3)
& related(X1,X4,X5)
& X3 = X5
& X2 = X4
& element(X5,the_carrier(X1)) )
& element(X4,the_carrier(X1)) )
& element(X3,the_carrier(X0)) )
& element(X2,the_carrier(X0)) )
& subrelstr(X1,X0) )
& rel_str(X0) ),
inference(flattening,[],[f48]) ).
fof(f48,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ related(X0,X2,X3)
& related(X1,X4,X5)
& X3 = X5
& X2 = X4
& element(X5,the_carrier(X1)) )
& element(X4,the_carrier(X1)) )
& element(X3,the_carrier(X0)) )
& element(X2,the_carrier(X0)) )
& subrelstr(X1,X0) )
& rel_str(X0) ),
inference(ennf_transformation,[],[f40]) ).
fof(f40,negated_conjecture,
~ ! [X0] :
( rel_str(X0)
=> ! [X1] :
( subrelstr(X1,X0)
=> ! [X2] :
( element(X2,the_carrier(X0))
=> ! [X3] :
( element(X3,the_carrier(X0))
=> ! [X4] :
( element(X4,the_carrier(X1))
=> ! [X5] :
( element(X5,the_carrier(X1))
=> ( ( related(X1,X4,X5)
& X3 = X5
& X2 = X4 )
=> related(X0,X2,X3) ) ) ) ) ) ) ),
inference(negated_conjecture,[],[f39]) ).
fof(f39,conjecture,
! [X0] :
( rel_str(X0)
=> ! [X1] :
( subrelstr(X1,X0)
=> ! [X2] :
( element(X2,the_carrier(X0))
=> ! [X3] :
( element(X3,the_carrier(X0))
=> ! [X4] :
( element(X4,the_carrier(X1))
=> ! [X5] :
( element(X5,the_carrier(X1))
=> ( ( related(X1,X4,X5)
& X3 = X5
& X2 = X4 )
=> related(X0,X2,X3) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t60_yellow_0) ).
fof(f106,plain,
element(sK2,the_carrier(sK0)),
inference(cnf_transformation,[],[f78]) ).
fof(f191,plain,
spl16_7,
inference(avatar_split_clause,[],[f155,f188]) ).
fof(f155,plain,
element(sK5,the_carrier(sK0)),
inference(definition_unfolding,[],[f107,f111]) ).
fof(f111,plain,
sK3 = sK5,
inference(cnf_transformation,[],[f78]) ).
fof(f107,plain,
element(sK3,the_carrier(sK0)),
inference(cnf_transformation,[],[f78]) ).
fof(f186,plain,
~ spl16_6,
inference(avatar_split_clause,[],[f154,f183]) ).
fof(f154,plain,
~ related(sK0,sK4,sK5),
inference(definition_unfolding,[],[f113,f110,f111]) ).
fof(f113,plain,
~ related(sK0,sK2,sK3),
inference(cnf_transformation,[],[f78]) ).
fof(f181,plain,
spl16_5,
inference(avatar_split_clause,[],[f112,f178]) ).
fof(f112,plain,
related(sK1,sK4,sK5),
inference(cnf_transformation,[],[f78]) ).
fof(f176,plain,
spl16_4,
inference(avatar_split_clause,[],[f109,f173]) ).
fof(f109,plain,
element(sK5,the_carrier(sK1)),
inference(cnf_transformation,[],[f78]) ).
fof(f171,plain,
spl16_3,
inference(avatar_split_clause,[],[f108,f168]) ).
fof(f108,plain,
element(sK4,the_carrier(sK1)),
inference(cnf_transformation,[],[f78]) ).
fof(f166,plain,
spl16_2,
inference(avatar_split_clause,[],[f105,f163]) ).
fof(f105,plain,
subrelstr(sK1,sK0),
inference(cnf_transformation,[],[f78]) ).
fof(f161,plain,
spl16_1,
inference(avatar_split_clause,[],[f104,f158]) ).
fof(f104,plain,
rel_str(sK0),
inference(cnf_transformation,[],[f78]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : SEU362+1 : TPTP v8.1.2. Released v3.3.0.
% 0.10/0.12 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.10/0.32 % Computer : n028.cluster.edu
% 0.10/0.32 % Model : x86_64 x86_64
% 0.10/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.32 % Memory : 8042.1875MB
% 0.10/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.32 % CPULimit : 300
% 0.10/0.32 % WCLimit : 300
% 0.10/0.32 % DateTime : Mon Apr 29 20:38:44 EDT 2024
% 0.10/0.32 % CPUTime :
% 0.10/0.32 % (29660)Running in auto input_syntax mode. Trying TPTP
% 0.10/0.34 % (29663)WARNING: value z3 for option sas not known
% 0.10/0.34 % (29665)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)
% 0.10/0.34 % (29662)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.10/0.34 % (29661)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.10/0.34 % (29663)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)
% 0.10/0.34 % (29667)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)
% 0.10/0.34 % (29666)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)
% 0.10/0.34 % (29664)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.10/0.34 TRYING [1]
% 0.10/0.34 TRYING [2]
% 0.10/0.35 TRYING [3]
% 0.10/0.35 TRYING [1]
% 0.10/0.35 TRYING [2]
% 0.10/0.35 TRYING [4]
% 0.10/0.36 TRYING [3]
% 0.10/0.37 TRYING [5]
% 0.10/0.40 TRYING [6]
% 0.10/0.41 TRYING [4]
% 0.16/0.47 TRYING [7]
% 2.23/0.68 TRYING [8]
% 5.29/1.13 TRYING [1]
% 5.29/1.13 TRYING [2]
% 5.29/1.13 TRYING [3]
% 5.29/1.14 TRYING [4]
% 5.29/1.16 TRYING [5]
% 6.16/1.21 TRYING [6]
% 6.16/1.24 TRYING [9]
% 7.12/1.34 TRYING [7]
% 8.53/1.62 % (29665)First to succeed.
% 8.53/1.63 TRYING [8]
% 9.58/1.70 % (29665)Refutation found. Thanks to Tanya!
% 9.58/1.70 % SZS status Theorem for theBenchmark
% 9.58/1.70 % SZS output start Proof for theBenchmark
% See solution above
% 9.58/1.74 % (29665)------------------------------
% 9.58/1.74 % (29665)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 9.58/1.74 % (29665)Termination reason: Refutation
% 9.58/1.74
% 9.58/1.74 % (29665)Memory used [KB]: 15658
% 9.58/1.74 % (29665)Time elapsed: 1.360 s
% 9.58/1.74 % (29665)Instructions burned: 3025 (million)
% 9.58/1.74 % (29665)------------------------------
% 9.58/1.74 % (29665)------------------------------
% 9.58/1.74 % (29660)Success in time 1.416 s
%------------------------------------------------------------------------------