TSTP Solution File: SEU098+1 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SEU098+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun May 5 09:26:59 EDT 2024
% Result : Theorem 1.61s 0.59s
% Output : Refutation 1.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 791
% Syntax : Number of formulae : 2578 ( 246 unt; 0 def)
% Number of atoms : 8600 ( 581 equ)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 10557 (4535 ~;4922 |; 339 &)
% ( 692 <=>; 67 =>; 0 <=; 2 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 711 ( 709 usr; 689 prp; 0-3 aty)
% Number of functors : 40 ( 40 usr; 24 con; 0-4 aty)
% Number of variables : 2482 (2404 !; 78 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f10322,plain,
$false,
inference(avatar_sat_refutation,[],[f391,f396,f405,f410,f415,f420,f425,f430,f435,f440,f445,f450,f455,f460,f465,f470,f475,f480,f485,f490,f495,f500,f505,f510,f515,f520,f525,f530,f535,f540,f545,f550,f555,f560,f565,f570,f575,f580,f585,f590,f595,f600,f605,f610,f615,f620,f625,f630,f635,f640,f645,f650,f655,f660,f665,f670,f675,f680,f685,f690,f695,f700,f705,f710,f715,f720,f724,f728,f732,f736,f740,f744,f748,f752,f756,f760,f765,f770,f774,f778,f782,f786,f790,f794,f798,f802,f806,f810,f814,f885,f889,f893,f897,f901,f905,f909,f913,f917,f922,f926,f930,f934,f938,f942,f947,f979,f983,f988,f993,f997,f1001,f1014,f1018,f1023,f1028,f1032,f1036,f1040,f1044,f1048,f1052,f1056,f1060,f1064,f1069,f1112,f1136,f1140,f1144,f1148,f1152,f1156,f1160,f1164,f1169,f1174,f1210,f1215,f1219,f1223,f1227,f1231,f1251,f1255,f1259,f1263,f1267,f1291,f1305,f1310,f1315,f1350,f1355,f1361,f1367,f1372,f1378,f1384,f1389,f1395,f1404,f1409,f1414,f1419,f1424,f1429,f1435,f1440,f1445,f1450,f1455,f1459,f1488,f1493,f1498,f1502,f1507,f1522,f1527,f1531,f1535,f1539,f1543,f1547,f1555,f1559,f1563,f1567,f1571,f1575,f1579,f1583,f1587,f1592,f1600,f1610,f1619,f1620,f1621,f1622,f1623,f1624,f1625,f1626,f1710,f1734,f1756,f1776,f1780,f1784,f1788,f1792,f1796,f1800,f1804,f1808,f1812,f1816,f1868,f1872,f1876,f1880,f1884,f1899,f1903,f1907,f1911,f1916,f1920,f1924,f1928,f1932,f1936,f1940,f1944,f1948,f1952,f1956,f1961,f1965,f1969,f1973,f1977,f2062,f2066,f2070,f2074,f2078,f2082,f2086,f2090,f2094,f2127,f2131,f2135,f2139,f2143,f2147,f2151,f2171,f2175,f2189,f2193,f2200,f2207,f2229,f2241,f2246,f2250,f2254,f2258,f2267,f2273,f2285,f2290,f2298,f2307,f2315,f2323,f2331,f2339,f2346,f2394,f2408,f2424,f2428,f2433,f2437,f2441,f2455,f2460,f2464,f2468,f2472,f2488,f2492,f2496,f2500,f2504,f2612,f2616,f2622,f2626,f2630,f2634,f2638,f2642,f2646,f2787,f2805,f2807,f2810,f2812,f2824,f2828,f2832,f2841,f2845,f2849,f2853,f2857,f2861,f2865,f2869,f2873,f2877,f2930,f2935,f2939,f2943,f2947,f2951,f2963,f2967,f2981,f2987,f3020,f3024,f3037,f3041,f3063,f3067,f3157,f3161,f3166,f3195,f3197,f3200,f3202,f3227,f3229,f3232,f3234,f3259,f3261,f3264,f3266,f3278,f3295,f3297,f3300,f3302,f3327,f3329,f3332,f3337,f3339,f3364,f3366,f3369,f3371,f3396,f3398,f3400,f3403,f3405,f3417,f3421,f3425,f3429,f3433,f3442,f3465,f3469,f3473,f3477,f3481,f3485,f3489,f3493,f3497,f3501,f3506,f3510,f3514,f3518,f3522,f3878,f3882,f3886,f3890,f3894,f3898,f4061,f4065,f4069,f4073,f4077,f4081,f4085,f4089,f4093,f4097,f4101,f4105,f4109,f4140,f4144,f4153,f4165,f4177,f4189,f4197,f4206,f4218,f4230,f4314,f4480,f4484,f4488,f4492,f4496,f4500,f4504,f4508,f4512,f4516,f4520,f4525,f4529,f4533,f4537,f4541,f4545,f4549,f4644,f4649,f4653,f4657,f4661,f4698,f4702,f4706,f4710,f4714,f4718,f4722,f4726,f4730,f4734,f4738,f4743,f4774,f4778,f4782,f4786,f4790,f4802,f4806,f4810,f4814,f4818,f4843,f4847,f4851,f4870,f4874,f4878,f4882,f4886,f4890,f4894,f4898,f4902,f4906,f4910,f4995,f4999,f5003,f5014,f5018,f5030,f5034,f5065,f5069,f5073,f5097,f5101,f5105,f5117,f5121,f5125,f5129,f5149,f5153,f5157,f5161,f5198,f5245,f5249,f5260,f5264,f5274,f5284,f5289,f5293,f5348,f5353,f5408,f5413,f5468,f5473,f5529,f5533,f5538,f5542,f5547,f5551,f5556,f5560,f5567,f5572,f5627,f5632,f5687,f5692,f5700,f5704,f5709,f5717,f5722,f5726,f5732,f5736,f5740,f5744,f5748,f5752,f5756,f5760,f5764,f5768,f5772,f5776,f5780,f5784,f5788,f5792,f5796,f5800,f6659,f6663,f6667,f6671,f6675,f6679,f6683,f6687,f6691,f6695,f6699,f6703,f6707,f6711,f6715,f6719,f6723,f6727,f6731,f6735,f6739,f6743,f6747,f6751,f6755,f6872,f7274,f7614,f7618,f7622,f7626,f7630,f7634,f7638,f7642,f7646,f7650,f7689,f7693,f7697,f7701,f7705,f7709,f7713,f7717,f7721,f7725,f7764,f7768,f7772,f7776,f7780,f8288,f8562,f8566,f8570,f8574,f8578,f8582,f8586,f8590,f8594,f8598,f8602,f8606,f8610,f8614,f8618,f8622,f8626,f8630,f8634,f8638,f8642,f8646,f8650,f8924,f9147,f9151,f9155,f9159,f9163,f9167,f9171,f9175,f9179,f9183,f9187,f9191,f9195,f9313,f9471,f9475,f9479,f9945,f9949,f9953,f9957,f9961,f9965,f9969,f9973,f9977,f9981,f9985,f10009,f10135,f10139,f10144,f10148,f10152,f10156,f10196,f10200,f10205,f10239,f10243,f10247,f10251,f10255,f10259,f10264,f10268,f10272,f10276,f10312,f10314,f10319,f10321]) ).
fof(f10321,plain,
( ~ spl30_3
| ~ spl30_1
| spl30_4
| ~ spl30_319
| ~ spl30_688 ),
inference(avatar_split_clause,[],[f10320,f10316,f2863,f402,f388,f398]) ).
fof(f398,plain,
( spl30_3
<=> finite(relation_dom(sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_3])]) ).
fof(f388,plain,
( spl30_1
<=> relation(sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_1])]) ).
fof(f402,plain,
( spl30_4
<=> finite(sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_4])]) ).
fof(f2863,plain,
( spl30_319
<=> ! [X0] :
( ~ relation(X0)
| finite(X0)
| ~ finite(relation_rng(X0))
| ~ finite(relation_dom(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_319])]) ).
fof(f10316,plain,
( spl30_688
<=> finite(relation_rng(sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_688])]) ).
fof(f10320,plain,
( finite(sK0)
| ~ relation(sK0)
| ~ finite(relation_dom(sK0))
| ~ spl30_319
| ~ spl30_688 ),
inference(resolution,[],[f10318,f2864]) ).
fof(f2864,plain,
( ! [X0] :
( ~ finite(relation_rng(X0))
| finite(X0)
| ~ relation(X0)
| ~ finite(relation_dom(X0)) )
| ~ spl30_319 ),
inference(avatar_component_clause,[],[f2863]) ).
fof(f10318,plain,
( finite(relation_rng(sK0))
| ~ spl30_688 ),
inference(avatar_component_clause,[],[f10316]) ).
fof(f10319,plain,
( ~ spl30_1
| ~ spl30_2
| spl30_688
| ~ spl30_3
| ~ spl30_145 ),
inference(avatar_split_clause,[],[f10313,f1253,f398,f10316,f393,f388]) ).
fof(f393,plain,
( spl30_2
<=> function(sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_2])]) ).
fof(f1253,plain,
( spl30_145
<=> ! [X0] :
( finite(relation_rng(X0))
| ~ finite(relation_dom(X0))
| ~ function(X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_145])]) ).
fof(f10313,plain,
( finite(relation_rng(sK0))
| ~ function(sK0)
| ~ relation(sK0)
| ~ spl30_3
| ~ spl30_145 ),
inference(resolution,[],[f400,f1254]) ).
fof(f1254,plain,
( ! [X0] :
( ~ finite(relation_dom(X0))
| finite(relation_rng(X0))
| ~ function(X0)
| ~ relation(X0) )
| ~ spl30_145 ),
inference(avatar_component_clause,[],[f1253]) ).
fof(f400,plain,
( finite(relation_dom(sK0))
| ~ spl30_3 ),
inference(avatar_component_clause,[],[f398]) ).
fof(f10314,plain,
( ~ spl30_3
| ~ spl30_4 ),
inference(avatar_split_clause,[],[f230,f402,f398]) ).
fof(f230,plain,
( ~ finite(sK0)
| ~ finite(relation_dom(sK0)) ),
inference(cnf_transformation,[],[f166]) ).
fof(f166,plain,
( ( ~ finite(sK0)
| ~ finite(relation_dom(sK0)) )
& ( finite(sK0)
| finite(relation_dom(sK0)) )
& function(sK0)
& relation(sK0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f164,f165]) ).
fof(f165,plain,
( ? [X0] :
( ( ~ finite(X0)
| ~ finite(relation_dom(X0)) )
& ( finite(X0)
| finite(relation_dom(X0)) )
& function(X0)
& relation(X0) )
=> ( ( ~ finite(sK0)
| ~ finite(relation_dom(sK0)) )
& ( finite(sK0)
| finite(relation_dom(sK0)) )
& function(sK0)
& relation(sK0) ) ),
introduced(choice_axiom,[]) ).
fof(f164,plain,
? [X0] :
( ( ~ finite(X0)
| ~ finite(relation_dom(X0)) )
& ( finite(X0)
| finite(relation_dom(X0)) )
& function(X0)
& relation(X0) ),
inference(flattening,[],[f163]) ).
fof(f163,plain,
? [X0] :
( ( ~ finite(X0)
| ~ finite(relation_dom(X0)) )
& ( finite(X0)
| finite(relation_dom(X0)) )
& function(X0)
& relation(X0) ),
inference(nnf_transformation,[],[f103]) ).
fof(f103,plain,
? [X0] :
( ( finite(relation_dom(X0))
<~> finite(X0) )
& function(X0)
& relation(X0) ),
inference(flattening,[],[f102]) ).
fof(f102,plain,
? [X0] :
( ( finite(relation_dom(X0))
<~> finite(X0) )
& function(X0)
& relation(X0) ),
inference(ennf_transformation,[],[f74]) ).
fof(f74,negated_conjecture,
~ ! [X0] :
( ( function(X0)
& relation(X0) )
=> ( finite(relation_dom(X0))
<=> finite(X0) ) ),
inference(negated_conjecture,[],[f73]) ).
fof(f73,conjecture,
! [X0] :
( ( function(X0)
& relation(X0) )
=> ( finite(relation_dom(X0))
<=> finite(X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t29_finset_1) ).
fof(f10312,plain,
( ~ spl30_90
| spl30_684 ),
inference(avatar_contradiction_clause,[],[f10311]) ).
fof(f10311,plain,
( $false
| ~ spl30_90
| spl30_684 ),
inference(resolution,[],[f10263,f813]) ).
fof(f813,plain,
( ! [X0,X1] : relation(first_projection_as_func_of(X0,X1))
| ~ spl30_90 ),
inference(avatar_component_clause,[],[f812]) ).
fof(f812,plain,
( spl30_90
<=> ! [X0,X1] : relation(first_projection_as_func_of(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_90])]) ).
fof(f10263,plain,
( ~ relation(first_projection_as_func_of(relation_dom(sK0),relation_rng(sK0)))
| spl30_684 ),
inference(avatar_component_clause,[],[f10261]) ).
fof(f10261,plain,
( spl30_684
<=> relation(first_projection_as_func_of(relation_dom(sK0),relation_rng(sK0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_684])]) ).
fof(f10276,plain,
( spl30_687
| ~ spl30_108
| ~ spl30_482 ),
inference(avatar_split_clause,[],[f4923,f4884,f981,f10274]) ).
fof(f10274,plain,
( spl30_687
<=> ! [X2,X0,X1] :
( empty(cartesian_product2(cartesian_product2(X0,X1),X0))
| ~ in(X2,first_projection_as_func_of(X0,X1))
| ~ in(cartesian_product2(cartesian_product2(X0,X1),X0),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_687])]) ).
fof(f981,plain,
( spl30_108
<=> ! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_108])]) ).
fof(f4884,plain,
( spl30_482
<=> ! [X2,X0,X1] :
( ~ in(X0,first_projection_as_func_of(X1,X2))
| empty(cartesian_product2(cartesian_product2(X1,X2),X1))
| in(X0,cartesian_product2(cartesian_product2(X1,X2),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_482])]) ).
fof(f4923,plain,
( ! [X2,X0,X1] :
( empty(cartesian_product2(cartesian_product2(X0,X1),X0))
| ~ in(X2,first_projection_as_func_of(X0,X1))
| ~ in(cartesian_product2(cartesian_product2(X0,X1),X0),X2) )
| ~ spl30_108
| ~ spl30_482 ),
inference(resolution,[],[f4885,f982]) ).
fof(f982,plain,
( ! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) )
| ~ spl30_108 ),
inference(avatar_component_clause,[],[f981]) ).
fof(f4885,plain,
( ! [X2,X0,X1] :
( in(X0,cartesian_product2(cartesian_product2(X1,X2),X1))
| empty(cartesian_product2(cartesian_product2(X1,X2),X1))
| ~ in(X0,first_projection_as_func_of(X1,X2)) )
| ~ spl30_482 ),
inference(avatar_component_clause,[],[f4884]) ).
fof(f10272,plain,
( spl30_686
| ~ spl30_108
| ~ spl30_481 ),
inference(avatar_split_clause,[],[f4916,f4880,f981,f10270]) ).
fof(f10270,plain,
( spl30_686
<=> ! [X0,X1] :
( ~ relation(X0)
| empty(cartesian_product2(relation_dom(X0),relation_rng(X0)))
| ~ in(X1,X0)
| ~ in(cartesian_product2(relation_dom(X0),relation_rng(X0)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_686])]) ).
fof(f4880,plain,
( spl30_481
<=> ! [X0,X1] :
( ~ in(X0,X1)
| ~ relation(X1)
| empty(cartesian_product2(relation_dom(X1),relation_rng(X1)))
| in(X0,cartesian_product2(relation_dom(X1),relation_rng(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_481])]) ).
fof(f4916,plain,
( ! [X0,X1] :
( ~ relation(X0)
| empty(cartesian_product2(relation_dom(X0),relation_rng(X0)))
| ~ in(X1,X0)
| ~ in(cartesian_product2(relation_dom(X0),relation_rng(X0)),X1) )
| ~ spl30_108
| ~ spl30_481 ),
inference(resolution,[],[f4881,f982]) ).
fof(f4881,plain,
( ! [X0,X1] :
( in(X0,cartesian_product2(relation_dom(X1),relation_rng(X1)))
| ~ relation(X1)
| empty(cartesian_product2(relation_dom(X1),relation_rng(X1)))
| ~ in(X0,X1) )
| ~ spl30_481 ),
inference(avatar_component_clause,[],[f4880]) ).
fof(f10268,plain,
( spl30_685
| ~ spl30_235
| ~ spl30_449 ),
inference(avatar_split_clause,[],[f4670,f4647,f1971,f10266]) ).
fof(f10266,plain,
( spl30_685
<=> ! [X0] :
( empty(sK4(powerset(X0)))
| empty(sK4(powerset(sK4(powerset(X0)))))
| element(sK4(sK4(powerset(sK4(powerset(X0))))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_685])]) ).
fof(f1971,plain,
( spl30_235
<=> ! [X0,X1] :
( element(X0,X1)
| ~ in(X0,sK4(powerset(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_235])]) ).
fof(f4647,plain,
( spl30_449
<=> ! [X0] :
( empty(sK4(powerset(X0)))
| empty(X0)
| in(sK4(sK4(powerset(X0))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_449])]) ).
fof(f4670,plain,
( ! [X0] :
( empty(sK4(powerset(X0)))
| empty(sK4(powerset(sK4(powerset(X0)))))
| element(sK4(sK4(powerset(sK4(powerset(X0))))),X0) )
| ~ spl30_235
| ~ spl30_449 ),
inference(resolution,[],[f4648,f1972]) ).
fof(f1972,plain,
( ! [X0,X1] :
( ~ in(X0,sK4(powerset(X1)))
| element(X0,X1) )
| ~ spl30_235 ),
inference(avatar_component_clause,[],[f1971]) ).
fof(f4648,plain,
( ! [X0] :
( in(sK4(sK4(powerset(X0))),X0)
| empty(X0)
| empty(sK4(powerset(X0))) )
| ~ spl30_449 ),
inference(avatar_component_clause,[],[f4647]) ).
fof(f10264,plain,
( ~ spl30_684
| ~ spl30_305
| ~ spl30_4
| spl30_3
| ~ spl30_146
| ~ spl30_671 ),
inference(avatar_split_clause,[],[f10201,f10141,f1257,f398,f402,f2790,f10261]) ).
fof(f2790,plain,
( spl30_305
<=> function(first_projection_as_func_of(relation_dom(sK0),relation_rng(sK0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_305])]) ).
fof(f1257,plain,
( spl30_146
<=> ! [X0,X1] :
( finite(relation_image(X0,X1))
| ~ finite(X1)
| ~ function(X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_146])]) ).
fof(f10141,plain,
( spl30_671
<=> relation_dom(sK0) = relation_image(first_projection_as_func_of(relation_dom(sK0),relation_rng(sK0)),sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_671])]) ).
fof(f10201,plain,
( finite(relation_dom(sK0))
| ~ finite(sK0)
| ~ function(first_projection_as_func_of(relation_dom(sK0),relation_rng(sK0)))
| ~ relation(first_projection_as_func_of(relation_dom(sK0),relation_rng(sK0)))
| ~ spl30_146
| ~ spl30_671 ),
inference(superposition,[],[f1258,f10143]) ).
fof(f10143,plain,
( relation_dom(sK0) = relation_image(first_projection_as_func_of(relation_dom(sK0),relation_rng(sK0)),sK0)
| ~ spl30_671 ),
inference(avatar_component_clause,[],[f10141]) ).
fof(f1258,plain,
( ! [X0,X1] :
( finite(relation_image(X0,X1))
| ~ finite(X1)
| ~ function(X0)
| ~ relation(X0) )
| ~ spl30_146 ),
inference(avatar_component_clause,[],[f1257]) ).
fof(f10259,plain,
( spl30_683
| ~ spl30_321
| ~ spl30_412 ),
inference(avatar_split_clause,[],[f4471,f4138,f2871,f10257]) ).
fof(f10257,plain,
( spl30_683
<=> ! [X0,X1] :
( empty(sK3(sK8(X0,X1)))
| empty(sK8(X0,X1))
| element(sK4(sK3(sK8(X0,X1))),cartesian_product2(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_683])]) ).
fof(f2871,plain,
( spl30_321
<=> ! [X2,X0,X1] :
( ~ in(X0,sK8(X1,X2))
| element(X0,cartesian_product2(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_321])]) ).
fof(f4138,plain,
( spl30_412
<=> ! [X0] :
( empty(X0)
| empty(sK3(X0))
| in(sK4(sK3(X0)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_412])]) ).
fof(f4471,plain,
( ! [X0,X1] :
( empty(sK3(sK8(X0,X1)))
| empty(sK8(X0,X1))
| element(sK4(sK3(sK8(X0,X1))),cartesian_product2(X0,X1)) )
| ~ spl30_321
| ~ spl30_412 ),
inference(resolution,[],[f4139,f2872]) ).
fof(f2872,plain,
( ! [X2,X0,X1] :
( ~ in(X0,sK8(X1,X2))
| element(X0,cartesian_product2(X1,X2)) )
| ~ spl30_321 ),
inference(avatar_component_clause,[],[f2871]) ).
fof(f4139,plain,
( ! [X0] :
( in(sK4(sK3(X0)),X0)
| empty(sK3(X0))
| empty(X0) )
| ~ spl30_412 ),
inference(avatar_component_clause,[],[f4138]) ).
fof(f10255,plain,
( spl30_682
| ~ spl30_322
| ~ spl30_412 ),
inference(avatar_split_clause,[],[f4469,f4138,f2875,f10253]) ).
fof(f10253,plain,
( spl30_682
<=> ! [X0,X1] :
( empty(sK3(sK7(X0,X1)))
| empty(sK7(X0,X1))
| element(sK4(sK3(sK7(X0,X1))),cartesian_product2(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_682])]) ).
fof(f2875,plain,
( spl30_322
<=> ! [X2,X0,X1] :
( ~ in(X0,sK7(X1,X2))
| element(X0,cartesian_product2(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_322])]) ).
fof(f4469,plain,
( ! [X0,X1] :
( empty(sK3(sK7(X0,X1)))
| empty(sK7(X0,X1))
| element(sK4(sK3(sK7(X0,X1))),cartesian_product2(X0,X1)) )
| ~ spl30_322
| ~ spl30_412 ),
inference(resolution,[],[f4139,f2876]) ).
fof(f2876,plain,
( ! [X2,X0,X1] :
( ~ in(X0,sK7(X1,X2))
| element(X0,cartesian_product2(X1,X2)) )
| ~ spl30_322 ),
inference(avatar_component_clause,[],[f2875]) ).
fof(f10251,plain,
( spl30_681
| ~ spl30_321
| ~ spl30_411 ),
inference(avatar_split_clause,[],[f4456,f4107,f2871,f10249]) ).
fof(f10249,plain,
( spl30_681
<=> ! [X0,X1] :
( empty(sK2(sK8(X0,X1)))
| empty(sK8(X0,X1))
| element(sK4(sK2(sK8(X0,X1))),cartesian_product2(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_681])]) ).
fof(f4107,plain,
( spl30_411
<=> ! [X0] :
( empty(X0)
| empty(sK2(X0))
| in(sK4(sK2(X0)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_411])]) ).
fof(f4456,plain,
( ! [X0,X1] :
( empty(sK2(sK8(X0,X1)))
| empty(sK8(X0,X1))
| element(sK4(sK2(sK8(X0,X1))),cartesian_product2(X0,X1)) )
| ~ spl30_321
| ~ spl30_411 ),
inference(resolution,[],[f4108,f2872]) ).
fof(f4108,plain,
( ! [X0] :
( in(sK4(sK2(X0)),X0)
| empty(sK2(X0))
| empty(X0) )
| ~ spl30_411 ),
inference(avatar_component_clause,[],[f4107]) ).
fof(f10247,plain,
( spl30_680
| ~ spl30_322
| ~ spl30_411 ),
inference(avatar_split_clause,[],[f4454,f4107,f2875,f10245]) ).
fof(f10245,plain,
( spl30_680
<=> ! [X0,X1] :
( empty(sK2(sK7(X0,X1)))
| empty(sK7(X0,X1))
| element(sK4(sK2(sK7(X0,X1))),cartesian_product2(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_680])]) ).
fof(f4454,plain,
( ! [X0,X1] :
( empty(sK2(sK7(X0,X1)))
| empty(sK7(X0,X1))
| element(sK4(sK2(sK7(X0,X1))),cartesian_product2(X0,X1)) )
| ~ spl30_322
| ~ spl30_411 ),
inference(resolution,[],[f4108,f2876]) ).
fof(f10243,plain,
( spl30_679
| ~ spl30_321
| ~ spl30_410 ),
inference(avatar_split_clause,[],[f4441,f4103,f2871,f10241]) ).
fof(f10241,plain,
( spl30_679
<=> ! [X0,X1] :
( empty(sK1(sK8(X0,X1)))
| empty(sK8(X0,X1))
| element(sK4(sK1(sK8(X0,X1))),cartesian_product2(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_679])]) ).
fof(f4103,plain,
( spl30_410
<=> ! [X0] :
( empty(X0)
| empty(sK1(X0))
| in(sK4(sK1(X0)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_410])]) ).
fof(f4441,plain,
( ! [X0,X1] :
( empty(sK1(sK8(X0,X1)))
| empty(sK8(X0,X1))
| element(sK4(sK1(sK8(X0,X1))),cartesian_product2(X0,X1)) )
| ~ spl30_321
| ~ spl30_410 ),
inference(resolution,[],[f4104,f2872]) ).
fof(f4104,plain,
( ! [X0] :
( in(sK4(sK1(X0)),X0)
| empty(sK1(X0))
| empty(X0) )
| ~ spl30_410 ),
inference(avatar_component_clause,[],[f4103]) ).
fof(f10239,plain,
( spl30_678
| ~ spl30_322
| ~ spl30_410 ),
inference(avatar_split_clause,[],[f4439,f4103,f2875,f10237]) ).
fof(f10237,plain,
( spl30_678
<=> ! [X0,X1] :
( empty(sK1(sK7(X0,X1)))
| empty(sK7(X0,X1))
| element(sK4(sK1(sK7(X0,X1))),cartesian_product2(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_678])]) ).
fof(f4439,plain,
( ! [X0,X1] :
( empty(sK1(sK7(X0,X1)))
| empty(sK7(X0,X1))
| element(sK4(sK1(sK7(X0,X1))),cartesian_product2(X0,X1)) )
| ~ spl30_322
| ~ spl30_410 ),
inference(resolution,[],[f4104,f2876]) ).
fof(f10205,plain,
( spl30_677
| ~ spl30_244
| ~ spl30_449 ),
inference(avatar_split_clause,[],[f4669,f4647,f2088,f10203]) ).
fof(f10203,plain,
( spl30_677
<=> ! [X0] :
( empty(sK3(X0))
| empty(sK4(powerset(sK3(X0))))
| element(sK4(sK4(powerset(sK3(X0)))),X0)
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_677])]) ).
fof(f2088,plain,
( spl30_244
<=> ! [X0,X1] :
( element(X0,X1)
| ~ in(X0,sK3(X1))
| empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_244])]) ).
fof(f4669,plain,
( ! [X0] :
( empty(sK3(X0))
| empty(sK4(powerset(sK3(X0))))
| element(sK4(sK4(powerset(sK3(X0)))),X0)
| empty(X0) )
| ~ spl30_244
| ~ spl30_449 ),
inference(resolution,[],[f4648,f2089]) ).
fof(f2089,plain,
( ! [X0,X1] :
( ~ in(X0,sK3(X1))
| element(X0,X1)
| empty(X1) )
| ~ spl30_244 ),
inference(avatar_component_clause,[],[f2088]) ).
fof(f10200,plain,
( spl30_676
| ~ spl30_243
| ~ spl30_449 ),
inference(avatar_split_clause,[],[f4668,f4647,f2084,f10198]) ).
fof(f10198,plain,
( spl30_676
<=> ! [X0] :
( empty(sK2(X0))
| empty(sK4(powerset(sK2(X0))))
| element(sK4(sK4(powerset(sK2(X0)))),X0)
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_676])]) ).
fof(f2084,plain,
( spl30_243
<=> ! [X0,X1] :
( element(X0,X1)
| ~ in(X0,sK2(X1))
| empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_243])]) ).
fof(f4668,plain,
( ! [X0] :
( empty(sK2(X0))
| empty(sK4(powerset(sK2(X0))))
| element(sK4(sK4(powerset(sK2(X0)))),X0)
| empty(X0) )
| ~ spl30_243
| ~ spl30_449 ),
inference(resolution,[],[f4648,f2085]) ).
fof(f2085,plain,
( ! [X0,X1] :
( ~ in(X0,sK2(X1))
| element(X0,X1)
| empty(X1) )
| ~ spl30_243 ),
inference(avatar_component_clause,[],[f2084]) ).
fof(f10196,plain,
( spl30_675
| ~ spl30_242
| ~ spl30_449 ),
inference(avatar_split_clause,[],[f4667,f4647,f2080,f10194]) ).
fof(f10194,plain,
( spl30_675
<=> ! [X0] :
( empty(sK1(X0))
| empty(sK4(powerset(sK1(X0))))
| element(sK4(sK4(powerset(sK1(X0)))),X0)
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_675])]) ).
fof(f2080,plain,
( spl30_242
<=> ! [X0,X1] :
( element(X0,X1)
| ~ in(X0,sK1(X1))
| empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_242])]) ).
fof(f4667,plain,
( ! [X0] :
( empty(sK1(X0))
| empty(sK4(powerset(sK1(X0))))
| element(sK4(sK4(powerset(sK1(X0)))),X0)
| empty(X0) )
| ~ spl30_242
| ~ spl30_449 ),
inference(resolution,[],[f4648,f2081]) ).
fof(f2081,plain,
( ! [X0,X1] :
( ~ in(X0,sK1(X1))
| element(X0,X1)
| empty(X1) )
| ~ spl30_242 ),
inference(avatar_component_clause,[],[f2080]) ).
fof(f10156,plain,
( spl30_674
| ~ spl30_131
| ~ spl30_452 ),
inference(avatar_split_clause,[],[f4690,f4659,f1146,f10154]) ).
fof(f10154,plain,
( spl30_674
<=> ! [X0,X1] :
( empty(sK7(X0,X1))
| empty(cartesian_product2(X0,X1))
| in(sK4(sK7(X0,X1)),cartesian_product2(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_674])]) ).
fof(f1146,plain,
( spl30_131
<=> ! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_131])]) ).
fof(f4659,plain,
( spl30_452
<=> ! [X0,X1] :
( element(sK4(sK7(X0,X1)),cartesian_product2(X0,X1))
| empty(sK7(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_452])]) ).
fof(f4690,plain,
( ! [X0,X1] :
( empty(sK7(X0,X1))
| empty(cartesian_product2(X0,X1))
| in(sK4(sK7(X0,X1)),cartesian_product2(X0,X1)) )
| ~ spl30_131
| ~ spl30_452 ),
inference(resolution,[],[f4660,f1147]) ).
fof(f1147,plain,
( ! [X0,X1] :
( ~ element(X0,X1)
| empty(X1)
| in(X0,X1) )
| ~ spl30_131 ),
inference(avatar_component_clause,[],[f1146]) ).
fof(f4660,plain,
( ! [X0,X1] :
( element(sK4(sK7(X0,X1)),cartesian_product2(X0,X1))
| empty(sK7(X0,X1)) )
| ~ spl30_452 ),
inference(avatar_component_clause,[],[f4659]) ).
fof(f10152,plain,
( spl30_673
| ~ spl30_131
| ~ spl30_451 ),
inference(avatar_split_clause,[],[f4686,f4655,f1146,f10150]) ).
fof(f10150,plain,
( spl30_673
<=> ! [X0,X1] :
( empty(sK8(X0,X1))
| empty(cartesian_product2(X0,X1))
| in(sK4(sK8(X0,X1)),cartesian_product2(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_673])]) ).
fof(f4655,plain,
( spl30_451
<=> ! [X0,X1] :
( element(sK4(sK8(X0,X1)),cartesian_product2(X0,X1))
| empty(sK8(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_451])]) ).
fof(f4686,plain,
( ! [X0,X1] :
( empty(sK8(X0,X1))
| empty(cartesian_product2(X0,X1))
| in(sK4(sK8(X0,X1)),cartesian_product2(X0,X1)) )
| ~ spl30_131
| ~ spl30_451 ),
inference(resolution,[],[f4656,f1147]) ).
fof(f4656,plain,
( ! [X0,X1] :
( element(sK4(sK8(X0,X1)),cartesian_product2(X0,X1))
| empty(sK8(X0,X1)) )
| ~ spl30_451 ),
inference(avatar_component_clause,[],[f4655]) ).
fof(f10148,plain,
( spl30_672
| ~ spl30_235
| ~ spl30_412 ),
inference(avatar_split_clause,[],[f4467,f4138,f1971,f10146]) ).
fof(f10146,plain,
( spl30_672
<=> ! [X0] :
( empty(sK3(sK4(powerset(X0))))
| empty(sK4(powerset(X0)))
| element(sK4(sK3(sK4(powerset(X0)))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_672])]) ).
fof(f4467,plain,
( ! [X0] :
( empty(sK3(sK4(powerset(X0))))
| empty(sK4(powerset(X0)))
| element(sK4(sK3(sK4(powerset(X0)))),X0) )
| ~ spl30_235
| ~ spl30_412 ),
inference(resolution,[],[f4139,f1972]) ).
fof(f10144,plain,
( spl30_671
| ~ spl30_179
| ~ spl30_667 ),
inference(avatar_split_clause,[],[f10081,f9983,f1519,f10141]) ).
fof(f1519,plain,
( spl30_179
<=> relation_dom(sK0) = function_image(cartesian_product2(relation_dom(sK0),relation_rng(sK0)),relation_dom(sK0),first_projection_as_func_of(relation_dom(sK0),relation_rng(sK0)),sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_179])]) ).
fof(f9983,plain,
( spl30_667
<=> ! [X2,X0,X1] : function_image(cartesian_product2(X0,X1),X0,first_projection_as_func_of(X0,X1),X2) = relation_image(first_projection_as_func_of(X0,X1),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_667])]) ).
fof(f10081,plain,
( relation_dom(sK0) = relation_image(first_projection_as_func_of(relation_dom(sK0),relation_rng(sK0)),sK0)
| ~ spl30_179
| ~ spl30_667 ),
inference(superposition,[],[f9984,f1521]) ).
fof(f1521,plain,
( relation_dom(sK0) = function_image(cartesian_product2(relation_dom(sK0),relation_rng(sK0)),relation_dom(sK0),first_projection_as_func_of(relation_dom(sK0),relation_rng(sK0)),sK0)
| ~ spl30_179 ),
inference(avatar_component_clause,[],[f1519]) ).
fof(f9984,plain,
( ! [X2,X0,X1] : function_image(cartesian_product2(X0,X1),X0,first_projection_as_func_of(X0,X1),X2) = relation_image(first_projection_as_func_of(X0,X1),X2)
| ~ spl30_667 ),
inference(avatar_component_clause,[],[f9983]) ).
fof(f10139,plain,
( spl30_670
| ~ spl30_235
| ~ spl30_411 ),
inference(avatar_split_clause,[],[f4452,f4107,f1971,f10137]) ).
fof(f10137,plain,
( spl30_670
<=> ! [X0] :
( empty(sK2(sK4(powerset(X0))))
| empty(sK4(powerset(X0)))
| element(sK4(sK2(sK4(powerset(X0)))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_670])]) ).
fof(f4452,plain,
( ! [X0] :
( empty(sK2(sK4(powerset(X0))))
| empty(sK4(powerset(X0)))
| element(sK4(sK2(sK4(powerset(X0)))),X0) )
| ~ spl30_235
| ~ spl30_411 ),
inference(resolution,[],[f4108,f1972]) ).
fof(f10135,plain,
( spl30_669
| ~ spl30_235
| ~ spl30_410 ),
inference(avatar_split_clause,[],[f4437,f4103,f1971,f10133]) ).
fof(f10133,plain,
( spl30_669
<=> ! [X0] :
( empty(sK1(sK4(powerset(X0))))
| empty(sK4(powerset(X0)))
| element(sK4(sK1(sK4(powerset(X0)))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_669])]) ).
fof(f4437,plain,
( ! [X0] :
( empty(sK1(sK4(powerset(X0))))
| empty(sK4(powerset(X0)))
| element(sK4(sK1(sK4(powerset(X0)))),X0) )
| ~ spl30_235
| ~ spl30_410 ),
inference(resolution,[],[f4104,f1972]) ).
fof(f10009,plain,
( spl30_668
| ~ spl30_98
| ~ spl30_545 ),
inference(avatar_split_clause,[],[f5901,f5730,f911,f10007]) ).
fof(f10007,plain,
( spl30_668
<=> ! [X0] :
( sK10 = relation_dom(sK4(powerset(relation_dom(relation_rng(X0)))))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_668])]) ).
fof(f911,plain,
( spl30_98
<=> ! [X0] :
( empty(relation_rng(X0))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_98])]) ).
fof(f5730,plain,
( spl30_545
<=> ! [X0] :
( sK10 = relation_dom(sK4(powerset(relation_dom(X0))))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_545])]) ).
fof(f5901,plain,
( ! [X0] :
( sK10 = relation_dom(sK4(powerset(relation_dom(relation_rng(X0)))))
| ~ empty(X0) )
| ~ spl30_98
| ~ spl30_545 ),
inference(resolution,[],[f5731,f912]) ).
fof(f912,plain,
( ! [X0] :
( empty(relation_rng(X0))
| ~ empty(X0) )
| ~ spl30_98 ),
inference(avatar_component_clause,[],[f911]) ).
fof(f5731,plain,
( ! [X0] :
( ~ empty(X0)
| sK10 = relation_dom(sK4(powerset(relation_dom(X0)))) )
| ~ spl30_545 ),
inference(avatar_component_clause,[],[f5730]) ).
fof(f9985,plain,
( spl30_667
| ~ spl30_89
| ~ spl30_491 ),
inference(avatar_split_clause,[],[f5010,f5001,f808,f9983]) ).
fof(f808,plain,
( spl30_89
<=> ! [X0,X1] : function(first_projection_as_func_of(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_89])]) ).
fof(f5001,plain,
( spl30_491
<=> ! [X2,X0,X1] :
( function_image(cartesian_product2(X0,X1),X0,first_projection_as_func_of(X0,X1),X2) = relation_image(first_projection_as_func_of(X0,X1),X2)
| ~ function(first_projection_as_func_of(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_491])]) ).
fof(f5010,plain,
( ! [X2,X0,X1] : function_image(cartesian_product2(X0,X1),X0,first_projection_as_func_of(X0,X1),X2) = relation_image(first_projection_as_func_of(X0,X1),X2)
| ~ spl30_89
| ~ spl30_491 ),
inference(resolution,[],[f5002,f809]) ).
fof(f809,plain,
( ! [X0,X1] : function(first_projection_as_func_of(X0,X1))
| ~ spl30_89 ),
inference(avatar_component_clause,[],[f808]) ).
fof(f5002,plain,
( ! [X2,X0,X1] :
( ~ function(first_projection_as_func_of(X0,X1))
| function_image(cartesian_product2(X0,X1),X0,first_projection_as_func_of(X0,X1),X2) = relation_image(first_projection_as_func_of(X0,X1),X2) )
| ~ spl30_491 ),
inference(avatar_component_clause,[],[f5001]) ).
fof(f9981,plain,
( spl30_666
| ~ spl30_244
| ~ spl30_412 ),
inference(avatar_split_clause,[],[f4466,f4138,f2088,f9979]) ).
fof(f9979,plain,
( spl30_666
<=> ! [X0] :
( empty(sK3(sK3(X0)))
| empty(sK3(X0))
| element(sK4(sK3(sK3(X0))),X0)
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_666])]) ).
fof(f4466,plain,
( ! [X0] :
( empty(sK3(sK3(X0)))
| empty(sK3(X0))
| element(sK4(sK3(sK3(X0))),X0)
| empty(X0) )
| ~ spl30_244
| ~ spl30_412 ),
inference(resolution,[],[f4139,f2089]) ).
fof(f9977,plain,
( spl30_665
| ~ spl30_243
| ~ spl30_412 ),
inference(avatar_split_clause,[],[f4465,f4138,f2084,f9975]) ).
fof(f9975,plain,
( spl30_665
<=> ! [X0] :
( empty(sK3(sK2(X0)))
| empty(sK2(X0))
| element(sK4(sK3(sK2(X0))),X0)
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_665])]) ).
fof(f4465,plain,
( ! [X0] :
( empty(sK3(sK2(X0)))
| empty(sK2(X0))
| element(sK4(sK3(sK2(X0))),X0)
| empty(X0) )
| ~ spl30_243
| ~ spl30_412 ),
inference(resolution,[],[f4139,f2085]) ).
fof(f9973,plain,
( spl30_664
| ~ spl30_242
| ~ spl30_412 ),
inference(avatar_split_clause,[],[f4464,f4138,f2080,f9971]) ).
fof(f9971,plain,
( spl30_664
<=> ! [X0] :
( empty(sK3(sK1(X0)))
| empty(sK1(X0))
| element(sK4(sK3(sK1(X0))),X0)
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_664])]) ).
fof(f4464,plain,
( ! [X0] :
( empty(sK3(sK1(X0)))
| empty(sK1(X0))
| element(sK4(sK3(sK1(X0))),X0)
| empty(X0) )
| ~ spl30_242
| ~ spl30_412 ),
inference(resolution,[],[f4139,f2081]) ).
fof(f9969,plain,
( spl30_663
| ~ spl30_244
| ~ spl30_411 ),
inference(avatar_split_clause,[],[f4451,f4107,f2088,f9967]) ).
fof(f9967,plain,
( spl30_663
<=> ! [X0] :
( empty(sK2(sK3(X0)))
| empty(sK3(X0))
| element(sK4(sK2(sK3(X0))),X0)
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_663])]) ).
fof(f4451,plain,
( ! [X0] :
( empty(sK2(sK3(X0)))
| empty(sK3(X0))
| element(sK4(sK2(sK3(X0))),X0)
| empty(X0) )
| ~ spl30_244
| ~ spl30_411 ),
inference(resolution,[],[f4108,f2089]) ).
fof(f9965,plain,
( spl30_662
| ~ spl30_243
| ~ spl30_411 ),
inference(avatar_split_clause,[],[f4450,f4107,f2084,f9963]) ).
fof(f9963,plain,
( spl30_662
<=> ! [X0] :
( empty(sK2(sK2(X0)))
| empty(sK2(X0))
| element(sK4(sK2(sK2(X0))),X0)
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_662])]) ).
fof(f4450,plain,
( ! [X0] :
( empty(sK2(sK2(X0)))
| empty(sK2(X0))
| element(sK4(sK2(sK2(X0))),X0)
| empty(X0) )
| ~ spl30_243
| ~ spl30_411 ),
inference(resolution,[],[f4108,f2085]) ).
fof(f9961,plain,
( spl30_661
| ~ spl30_242
| ~ spl30_411 ),
inference(avatar_split_clause,[],[f4449,f4107,f2080,f9959]) ).
fof(f9959,plain,
( spl30_661
<=> ! [X0] :
( empty(sK2(sK1(X0)))
| empty(sK1(X0))
| element(sK4(sK2(sK1(X0))),X0)
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_661])]) ).
fof(f4449,plain,
( ! [X0] :
( empty(sK2(sK1(X0)))
| empty(sK1(X0))
| element(sK4(sK2(sK1(X0))),X0)
| empty(X0) )
| ~ spl30_242
| ~ spl30_411 ),
inference(resolution,[],[f4108,f2081]) ).
fof(f9957,plain,
( spl30_660
| ~ spl30_244
| ~ spl30_410 ),
inference(avatar_split_clause,[],[f4436,f4103,f2088,f9955]) ).
fof(f9955,plain,
( spl30_660
<=> ! [X0] :
( empty(sK1(sK3(X0)))
| empty(sK3(X0))
| element(sK4(sK1(sK3(X0))),X0)
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_660])]) ).
fof(f4436,plain,
( ! [X0] :
( empty(sK1(sK3(X0)))
| empty(sK3(X0))
| element(sK4(sK1(sK3(X0))),X0)
| empty(X0) )
| ~ spl30_244
| ~ spl30_410 ),
inference(resolution,[],[f4104,f2089]) ).
fof(f9953,plain,
( spl30_659
| ~ spl30_101
| ~ spl30_545 ),
inference(avatar_split_clause,[],[f5900,f5730,f924,f9951]) ).
fof(f9951,plain,
( spl30_659
<=> ! [X0] :
( sK10 = relation_dom(sK4(powerset(relation_dom(relation_dom(X0)))))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_659])]) ).
fof(f924,plain,
( spl30_101
<=> ! [X0] :
( empty(relation_dom(X0))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_101])]) ).
fof(f5900,plain,
( ! [X0] :
( sK10 = relation_dom(sK4(powerset(relation_dom(relation_dom(X0)))))
| ~ empty(X0) )
| ~ spl30_101
| ~ spl30_545 ),
inference(resolution,[],[f5731,f925]) ).
fof(f925,plain,
( ! [X0] :
( empty(relation_dom(X0))
| ~ empty(X0) )
| ~ spl30_101 ),
inference(avatar_component_clause,[],[f924]) ).
fof(f9949,plain,
( spl30_658
| ~ spl30_243
| ~ spl30_410 ),
inference(avatar_split_clause,[],[f4435,f4103,f2084,f9947]) ).
fof(f9947,plain,
( spl30_658
<=> ! [X0] :
( empty(sK1(sK2(X0)))
| empty(sK2(X0))
| element(sK4(sK1(sK2(X0))),X0)
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_658])]) ).
fof(f4435,plain,
( ! [X0] :
( empty(sK1(sK2(X0)))
| empty(sK2(X0))
| element(sK4(sK1(sK2(X0))),X0)
| empty(X0) )
| ~ spl30_243
| ~ spl30_410 ),
inference(resolution,[],[f4104,f2085]) ).
fof(f9945,plain,
( spl30_657
| ~ spl30_242
| ~ spl30_410 ),
inference(avatar_split_clause,[],[f4434,f4103,f2080,f9943]) ).
fof(f9943,plain,
( spl30_657
<=> ! [X0] :
( empty(sK1(sK1(X0)))
| empty(sK1(X0))
| element(sK4(sK1(sK1(X0))),X0)
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_657])]) ).
fof(f4434,plain,
( ! [X0] :
( empty(sK1(sK1(X0)))
| empty(sK1(X0))
| element(sK4(sK1(sK1(X0))),X0)
| empty(X0) )
| ~ spl30_242
| ~ spl30_410 ),
inference(resolution,[],[f4104,f2081]) ).
fof(f9479,plain,
( spl30_656
| ~ spl30_207
| ~ spl30_474 ),
inference(avatar_split_clause,[],[f4835,f4816,f1798,f9477]) ).
fof(f9477,plain,
( spl30_656
<=> ! [X0] :
( empty(sK3(powerset(X0)))
| ~ empty(X0)
| empty(powerset(X0))
| empty(sK4(sK3(powerset(X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_656])]) ).
fof(f1798,plain,
( spl30_207
<=> ! [X0] :
( empty(X0)
| in(sK4(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_207])]) ).
fof(f4816,plain,
( spl30_474
<=> ! [X0,X1] :
( empty(powerset(X0))
| empty(sK3(powerset(X0)))
| ~ empty(X0)
| ~ in(X1,sK4(sK3(powerset(X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_474])]) ).
fof(f4835,plain,
( ! [X0] :
( empty(sK3(powerset(X0)))
| ~ empty(X0)
| empty(powerset(X0))
| empty(sK4(sK3(powerset(X0)))) )
| ~ spl30_207
| ~ spl30_474 ),
inference(resolution,[],[f4817,f1799]) ).
fof(f1799,plain,
( ! [X0] :
( in(sK4(X0),X0)
| empty(X0) )
| ~ spl30_207 ),
inference(avatar_component_clause,[],[f1798]) ).
fof(f4817,plain,
( ! [X0,X1] :
( ~ in(X1,sK4(sK3(powerset(X0))))
| empty(sK3(powerset(X0)))
| ~ empty(X0)
| empty(powerset(X0)) )
| ~ spl30_474 ),
inference(avatar_component_clause,[],[f4816]) ).
fof(f9475,plain,
( spl30_655
| ~ spl30_207
| ~ spl30_473 ),
inference(avatar_split_clause,[],[f4830,f4812,f1798,f9473]) ).
fof(f9473,plain,
( spl30_655
<=> ! [X0] :
( empty(sK2(powerset(X0)))
| ~ empty(X0)
| empty(powerset(X0))
| empty(sK4(sK2(powerset(X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_655])]) ).
fof(f4812,plain,
( spl30_473
<=> ! [X0,X1] :
( empty(powerset(X0))
| empty(sK2(powerset(X0)))
| ~ empty(X0)
| ~ in(X1,sK4(sK2(powerset(X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_473])]) ).
fof(f4830,plain,
( ! [X0] :
( empty(sK2(powerset(X0)))
| ~ empty(X0)
| empty(powerset(X0))
| empty(sK4(sK2(powerset(X0)))) )
| ~ spl30_207
| ~ spl30_473 ),
inference(resolution,[],[f4813,f1799]) ).
fof(f4813,plain,
( ! [X0,X1] :
( ~ in(X1,sK4(sK2(powerset(X0))))
| empty(sK2(powerset(X0)))
| ~ empty(X0)
| empty(powerset(X0)) )
| ~ spl30_473 ),
inference(avatar_component_clause,[],[f4812]) ).
fof(f9471,plain,
( spl30_654
| ~ spl30_207
| ~ spl30_472 ),
inference(avatar_split_clause,[],[f4825,f4808,f1798,f9469]) ).
fof(f9469,plain,
( spl30_654
<=> ! [X0] :
( empty(sK1(powerset(X0)))
| ~ empty(X0)
| empty(powerset(X0))
| empty(sK4(sK1(powerset(X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_654])]) ).
fof(f4808,plain,
( spl30_472
<=> ! [X0,X1] :
( empty(powerset(X0))
| empty(sK1(powerset(X0)))
| ~ empty(X0)
| ~ in(X1,sK4(sK1(powerset(X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_472])]) ).
fof(f4825,plain,
( ! [X0] :
( empty(sK1(powerset(X0)))
| ~ empty(X0)
| empty(powerset(X0))
| empty(sK4(sK1(powerset(X0)))) )
| ~ spl30_207
| ~ spl30_472 ),
inference(resolution,[],[f4809,f1799]) ).
fof(f4809,plain,
( ! [X0,X1] :
( ~ in(X1,sK4(sK1(powerset(X0))))
| empty(sK1(powerset(X0)))
| ~ empty(X0)
| empty(powerset(X0)) )
| ~ spl30_472 ),
inference(avatar_component_clause,[],[f4808]) ).
fof(f9313,plain,
( spl30_653
| ~ spl30_98
| ~ spl30_539 ),
inference(avatar_split_clause,[],[f5866,f5698,f911,f9311]) ).
fof(f9311,plain,
( spl30_653
<=> ! [X0] :
( sK10 = relation_rng(sK4(powerset(relation_rng(relation_rng(X0)))))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_653])]) ).
fof(f5698,plain,
( spl30_539
<=> ! [X0] :
( sK10 = relation_rng(sK4(powerset(relation_rng(X0))))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_539])]) ).
fof(f5866,plain,
( ! [X0] :
( sK10 = relation_rng(sK4(powerset(relation_rng(relation_rng(X0)))))
| ~ empty(X0) )
| ~ spl30_98
| ~ spl30_539 ),
inference(resolution,[],[f5699,f912]) ).
fof(f5699,plain,
( ! [X0] :
( ~ empty(X0)
| sK10 = relation_rng(sK4(powerset(relation_rng(X0)))) )
| ~ spl30_539 ),
inference(avatar_component_clause,[],[f5698]) ).
fof(f9195,plain,
( spl30_652
| ~ spl30_207
| ~ spl30_465 ),
inference(avatar_split_clause,[],[f4791,f4772,f1798,f9193]) ).
fof(f9193,plain,
( spl30_652
<=> ! [X0] :
( ~ empty(X0)
| empty(sK4(powerset(powerset(X0))))
| empty(sK4(sK4(powerset(powerset(X0))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_652])]) ).
fof(f4772,plain,
( spl30_465
<=> ! [X0,X1] :
( empty(sK4(powerset(powerset(X0))))
| ~ empty(X0)
| ~ in(X1,sK4(sK4(powerset(powerset(X0))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_465])]) ).
fof(f4791,plain,
( ! [X0] :
( ~ empty(X0)
| empty(sK4(powerset(powerset(X0))))
| empty(sK4(sK4(powerset(powerset(X0))))) )
| ~ spl30_207
| ~ spl30_465 ),
inference(resolution,[],[f4773,f1799]) ).
fof(f4773,plain,
( ! [X0,X1] :
( ~ in(X1,sK4(sK4(powerset(powerset(X0)))))
| ~ empty(X0)
| empty(sK4(powerset(powerset(X0)))) )
| ~ spl30_465 ),
inference(avatar_component_clause,[],[f4772]) ).
fof(f9191,plain,
( spl30_651
| ~ spl30_101
| ~ spl30_539 ),
inference(avatar_split_clause,[],[f5865,f5698,f924,f9189]) ).
fof(f9189,plain,
( spl30_651
<=> ! [X0] :
( sK10 = relation_rng(sK4(powerset(relation_rng(relation_dom(X0)))))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_651])]) ).
fof(f5865,plain,
( ! [X0] :
( sK10 = relation_rng(sK4(powerset(relation_rng(relation_dom(X0)))))
| ~ empty(X0) )
| ~ spl30_101
| ~ spl30_539 ),
inference(resolution,[],[f5699,f925]) ).
fof(f9187,plain,
( spl30_650
| ~ spl30_117
| ~ spl30_452 ),
inference(avatar_split_clause,[],[f4693,f4659,f1030,f9185]) ).
fof(f9185,plain,
( spl30_650
<=> ! [X0,X1] :
( empty(sK7(X0,X1))
| epsilon_transitive(sK4(sK7(X0,X1)))
| ~ ordinal(cartesian_product2(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_650])]) ).
fof(f1030,plain,
( spl30_117
<=> ! [X0,X1] :
( epsilon_transitive(X1)
| ~ element(X1,X0)
| ~ ordinal(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_117])]) ).
fof(f4693,plain,
( ! [X0,X1] :
( empty(sK7(X0,X1))
| epsilon_transitive(sK4(sK7(X0,X1)))
| ~ ordinal(cartesian_product2(X0,X1)) )
| ~ spl30_117
| ~ spl30_452 ),
inference(resolution,[],[f4660,f1031]) ).
fof(f1031,plain,
( ! [X0,X1] :
( ~ element(X1,X0)
| epsilon_transitive(X1)
| ~ ordinal(X0) )
| ~ spl30_117 ),
inference(avatar_component_clause,[],[f1030]) ).
fof(f9183,plain,
( spl30_649
| ~ spl30_118
| ~ spl30_452 ),
inference(avatar_split_clause,[],[f4692,f4659,f1034,f9181]) ).
fof(f9181,plain,
( spl30_649
<=> ! [X0,X1] :
( empty(sK7(X0,X1))
| epsilon_connected(sK4(sK7(X0,X1)))
| ~ ordinal(cartesian_product2(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_649])]) ).
fof(f1034,plain,
( spl30_118
<=> ! [X0,X1] :
( epsilon_connected(X1)
| ~ element(X1,X0)
| ~ ordinal(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_118])]) ).
fof(f4692,plain,
( ! [X0,X1] :
( empty(sK7(X0,X1))
| epsilon_connected(sK4(sK7(X0,X1)))
| ~ ordinal(cartesian_product2(X0,X1)) )
| ~ spl30_118
| ~ spl30_452 ),
inference(resolution,[],[f4660,f1035]) ).
fof(f1035,plain,
( ! [X0,X1] :
( ~ element(X1,X0)
| epsilon_connected(X1)
| ~ ordinal(X0) )
| ~ spl30_118 ),
inference(avatar_component_clause,[],[f1034]) ).
fof(f9179,plain,
( spl30_648
| ~ spl30_119
| ~ spl30_452 ),
inference(avatar_split_clause,[],[f4691,f4659,f1038,f9177]) ).
fof(f9177,plain,
( spl30_648
<=> ! [X0,X1] :
( empty(sK7(X0,X1))
| ordinal(sK4(sK7(X0,X1)))
| ~ ordinal(cartesian_product2(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_648])]) ).
fof(f1038,plain,
( spl30_119
<=> ! [X0,X1] :
( ordinal(X1)
| ~ element(X1,X0)
| ~ ordinal(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_119])]) ).
fof(f4691,plain,
( ! [X0,X1] :
( empty(sK7(X0,X1))
| ordinal(sK4(sK7(X0,X1)))
| ~ ordinal(cartesian_product2(X0,X1)) )
| ~ spl30_119
| ~ spl30_452 ),
inference(resolution,[],[f4660,f1039]) ).
fof(f1039,plain,
( ! [X0,X1] :
( ~ element(X1,X0)
| ordinal(X1)
| ~ ordinal(X0) )
| ~ spl30_119 ),
inference(avatar_component_clause,[],[f1038]) ).
fof(f9175,plain,
( spl30_647
| ~ spl30_117
| ~ spl30_451 ),
inference(avatar_split_clause,[],[f4689,f4655,f1030,f9173]) ).
fof(f9173,plain,
( spl30_647
<=> ! [X0,X1] :
( empty(sK8(X0,X1))
| epsilon_transitive(sK4(sK8(X0,X1)))
| ~ ordinal(cartesian_product2(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_647])]) ).
fof(f4689,plain,
( ! [X0,X1] :
( empty(sK8(X0,X1))
| epsilon_transitive(sK4(sK8(X0,X1)))
| ~ ordinal(cartesian_product2(X0,X1)) )
| ~ spl30_117
| ~ spl30_451 ),
inference(resolution,[],[f4656,f1031]) ).
fof(f9171,plain,
( spl30_646
| ~ spl30_118
| ~ spl30_451 ),
inference(avatar_split_clause,[],[f4688,f4655,f1034,f9169]) ).
fof(f9169,plain,
( spl30_646
<=> ! [X0,X1] :
( empty(sK8(X0,X1))
| epsilon_connected(sK4(sK8(X0,X1)))
| ~ ordinal(cartesian_product2(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_646])]) ).
fof(f4688,plain,
( ! [X0,X1] :
( empty(sK8(X0,X1))
| epsilon_connected(sK4(sK8(X0,X1)))
| ~ ordinal(cartesian_product2(X0,X1)) )
| ~ spl30_118
| ~ spl30_451 ),
inference(resolution,[],[f4656,f1035]) ).
fof(f9167,plain,
( spl30_645
| ~ spl30_119
| ~ spl30_451 ),
inference(avatar_split_clause,[],[f4687,f4655,f1038,f9165]) ).
fof(f9165,plain,
( spl30_645
<=> ! [X0,X1] :
( empty(sK8(X0,X1))
| ordinal(sK4(sK8(X0,X1)))
| ~ ordinal(cartesian_product2(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_645])]) ).
fof(f4687,plain,
( ! [X0,X1] :
( empty(sK8(X0,X1))
| ordinal(sK4(sK8(X0,X1)))
| ~ ordinal(cartesian_product2(X0,X1)) )
| ~ spl30_119
| ~ spl30_451 ),
inference(resolution,[],[f4656,f1039]) ).
fof(f9163,plain,
( spl30_644
| ~ spl30_289
| ~ spl30_434 ),
inference(avatar_split_clause,[],[f4611,f4494,f2470,f9161]) ).
fof(f9161,plain,
( spl30_644
<=> ! [X0,X1] :
( sK4(powerset(X1)) = relation_rng(relation_rng(sK4(powerset(X0))))
| ~ empty(X0)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_644])]) ).
fof(f2470,plain,
( spl30_289
<=> ! [X0] :
( ~ empty(X0)
| empty(sK4(powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_289])]) ).
fof(f4494,plain,
( spl30_434
<=> ! [X0,X1] :
( relation_rng(relation_rng(sK4(powerset(X0)))) = X1
| ~ empty(X1)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_434])]) ).
fof(f4611,plain,
( ! [X0,X1] :
( sK4(powerset(X1)) = relation_rng(relation_rng(sK4(powerset(X0))))
| ~ empty(X0)
| ~ empty(X1) )
| ~ spl30_289
| ~ spl30_434 ),
inference(resolution,[],[f4495,f2471]) ).
fof(f2471,plain,
( ! [X0] :
( empty(sK4(powerset(X0)))
| ~ empty(X0) )
| ~ spl30_289 ),
inference(avatar_component_clause,[],[f2470]) ).
fof(f4495,plain,
( ! [X0,X1] :
( ~ empty(X1)
| relation_rng(relation_rng(sK4(powerset(X0)))) = X1
| ~ empty(X0) )
| ~ spl30_434 ),
inference(avatar_component_clause,[],[f4494]) ).
fof(f9159,plain,
( spl30_643
| ~ spl30_289
| ~ spl30_433 ),
inference(avatar_split_clause,[],[f4592,f4490,f2470,f9157]) ).
fof(f9157,plain,
( spl30_643
<=> ! [X0,X1] :
( sK4(powerset(X1)) = relation_rng(relation_dom(sK4(powerset(X0))))
| ~ empty(X0)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_643])]) ).
fof(f4490,plain,
( spl30_433
<=> ! [X0,X1] :
( relation_rng(relation_dom(sK4(powerset(X0)))) = X1
| ~ empty(X1)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_433])]) ).
fof(f4592,plain,
( ! [X0,X1] :
( sK4(powerset(X1)) = relation_rng(relation_dom(sK4(powerset(X0))))
| ~ empty(X0)
| ~ empty(X1) )
| ~ spl30_289
| ~ spl30_433 ),
inference(resolution,[],[f4491,f2471]) ).
fof(f4491,plain,
( ! [X0,X1] :
( ~ empty(X1)
| relation_rng(relation_dom(sK4(powerset(X0)))) = X1
| ~ empty(X0) )
| ~ spl30_433 ),
inference(avatar_component_clause,[],[f4490]) ).
fof(f9155,plain,
( spl30_642
| ~ spl30_289
| ~ spl30_432 ),
inference(avatar_split_clause,[],[f4573,f4486,f2470,f9153]) ).
fof(f9153,plain,
( spl30_642
<=> ! [X0,X1] :
( sK4(powerset(X1)) = relation_dom(relation_rng(sK4(powerset(X0))))
| ~ empty(X0)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_642])]) ).
fof(f4486,plain,
( spl30_432
<=> ! [X0,X1] :
( relation_dom(relation_rng(sK4(powerset(X0)))) = X1
| ~ empty(X1)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_432])]) ).
fof(f4573,plain,
( ! [X0,X1] :
( sK4(powerset(X1)) = relation_dom(relation_rng(sK4(powerset(X0))))
| ~ empty(X0)
| ~ empty(X1) )
| ~ spl30_289
| ~ spl30_432 ),
inference(resolution,[],[f4487,f2471]) ).
fof(f4487,plain,
( ! [X0,X1] :
( ~ empty(X1)
| relation_dom(relation_rng(sK4(powerset(X0)))) = X1
| ~ empty(X0) )
| ~ spl30_432 ),
inference(avatar_component_clause,[],[f4486]) ).
fof(f9151,plain,
( spl30_641
| ~ spl30_289
| ~ spl30_431 ),
inference(avatar_split_clause,[],[f4554,f4482,f2470,f9149]) ).
fof(f9149,plain,
( spl30_641
<=> ! [X0,X1] :
( sK4(powerset(X1)) = relation_dom(relation_dom(sK4(powerset(X0))))
| ~ empty(X0)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_641])]) ).
fof(f4482,plain,
( spl30_431
<=> ! [X0,X1] :
( relation_dom(relation_dom(sK4(powerset(X0)))) = X1
| ~ empty(X1)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_431])]) ).
fof(f4554,plain,
( ! [X0,X1] :
( sK4(powerset(X1)) = relation_dom(relation_dom(sK4(powerset(X0))))
| ~ empty(X0)
| ~ empty(X1) )
| ~ spl30_289
| ~ spl30_431 ),
inference(resolution,[],[f4483,f2471]) ).
fof(f4483,plain,
( ! [X0,X1] :
( ~ empty(X1)
| relation_dom(relation_dom(sK4(powerset(X0)))) = X1
| ~ empty(X0) )
| ~ spl30_431 ),
inference(avatar_component_clause,[],[f4482]) ).
fof(f9147,plain,
( spl30_640
| ~ spl30_98
| ~ spl30_518 ),
inference(avatar_split_clause,[],[f5831,f5291,f911,f9145]) ).
fof(f9145,plain,
( spl30_640
<=> ! [X0] :
( sK10 = relation_rng(sK4(powerset(relation_dom(relation_rng(X0)))))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_640])]) ).
fof(f5291,plain,
( spl30_518
<=> ! [X0] :
( sK10 = relation_rng(sK4(powerset(relation_dom(X0))))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_518])]) ).
fof(f5831,plain,
( ! [X0] :
( sK10 = relation_rng(sK4(powerset(relation_dom(relation_rng(X0)))))
| ~ empty(X0) )
| ~ spl30_98
| ~ spl30_518 ),
inference(resolution,[],[f5292,f912]) ).
fof(f5292,plain,
( ! [X0] :
( ~ empty(X0)
| sK10 = relation_rng(sK4(powerset(relation_dom(X0)))) )
| ~ spl30_518 ),
inference(avatar_component_clause,[],[f5291]) ).
fof(f8924,plain,
( spl30_639
| ~ spl30_101
| ~ spl30_518 ),
inference(avatar_split_clause,[],[f5830,f5291,f924,f8922]) ).
fof(f8922,plain,
( spl30_639
<=> ! [X0] :
( sK10 = relation_rng(sK4(powerset(relation_dom(relation_dom(X0)))))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_639])]) ).
fof(f5830,plain,
( ! [X0] :
( sK10 = relation_rng(sK4(powerset(relation_dom(relation_dom(X0)))))
| ~ empty(X0) )
| ~ spl30_101
| ~ spl30_518 ),
inference(resolution,[],[f5292,f925]) ).
fof(f8650,plain,
( spl30_638
| ~ spl30_98
| ~ spl30_511 ),
inference(avatar_split_clause,[],[f5804,f5243,f911,f8648]) ).
fof(f8648,plain,
( spl30_638
<=> ! [X0] :
( sK10 = sK4(powerset(sK4(powerset(relation_rng(X0)))))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_638])]) ).
fof(f5243,plain,
( spl30_511
<=> ! [X0] :
( sK10 = sK4(powerset(sK4(powerset(X0))))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_511])]) ).
fof(f5804,plain,
( ! [X0] :
( sK10 = sK4(powerset(sK4(powerset(relation_rng(X0)))))
| ~ empty(X0) )
| ~ spl30_98
| ~ spl30_511 ),
inference(resolution,[],[f5244,f912]) ).
fof(f5244,plain,
( ! [X0] :
( ~ empty(X0)
| sK10 = sK4(powerset(sK4(powerset(X0)))) )
| ~ spl30_511 ),
inference(avatar_component_clause,[],[f5243]) ).
fof(f8646,plain,
( spl30_637
| ~ spl30_77
| ~ spl30_469 ),
inference(avatar_split_clause,[],[f4796,f4788,f758,f8644]) ).
fof(f8644,plain,
( spl30_637
<=> ! [X0] :
( empty(powerset(X0))
| empty(powerset(powerset(X0)))
| ~ subset(powerset(powerset(X0)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_637])]) ).
fof(f758,plain,
( spl30_77
<=> ! [X0] : subset(X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_77])]) ).
fof(f4788,plain,
( spl30_469
<=> ! [X0,X1] :
( ~ subset(powerset(X0),X1)
| empty(powerset(X1))
| empty(powerset(X0))
| ~ subset(powerset(X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_469])]) ).
fof(f4796,plain,
( ! [X0] :
( empty(powerset(X0))
| empty(powerset(powerset(X0)))
| ~ subset(powerset(powerset(X0)),X0) )
| ~ spl30_77
| ~ spl30_469 ),
inference(resolution,[],[f4789,f759]) ).
fof(f759,plain,
( ! [X0] : subset(X0,X0)
| ~ spl30_77 ),
inference(avatar_component_clause,[],[f758]) ).
fof(f4789,plain,
( ! [X0,X1] :
( ~ subset(powerset(X1),X0)
| empty(powerset(X1))
| empty(powerset(X0))
| ~ subset(powerset(X0),X1) )
| ~ spl30_469 ),
inference(avatar_component_clause,[],[f4788]) ).
fof(f8642,plain,
( spl30_636
| ~ spl30_108
| ~ spl30_449 ),
inference(avatar_split_clause,[],[f4664,f4647,f981,f8640]) ).
fof(f8640,plain,
( spl30_636
<=> ! [X0] :
( empty(X0)
| empty(sK4(powerset(X0)))
| ~ in(X0,sK4(sK4(powerset(X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_636])]) ).
fof(f4664,plain,
( ! [X0] :
( empty(X0)
| empty(sK4(powerset(X0)))
| ~ in(X0,sK4(sK4(powerset(X0)))) )
| ~ spl30_108
| ~ spl30_449 ),
inference(resolution,[],[f4648,f982]) ).
fof(f8638,plain,
( spl30_635
| ~ spl30_98
| ~ spl30_434 ),
inference(avatar_split_clause,[],[f4610,f4494,f911,f8636]) ).
fof(f8636,plain,
( spl30_635
<=> ! [X0,X1] :
( relation_rng(X1) = relation_rng(relation_rng(sK4(powerset(X0))))
| ~ empty(X0)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_635])]) ).
fof(f4610,plain,
( ! [X0,X1] :
( relation_rng(X1) = relation_rng(relation_rng(sK4(powerset(X0))))
| ~ empty(X0)
| ~ empty(X1) )
| ~ spl30_98
| ~ spl30_434 ),
inference(resolution,[],[f4495,f912]) ).
fof(f8634,plain,
( spl30_634
| ~ spl30_101
| ~ spl30_434 ),
inference(avatar_split_clause,[],[f4609,f4494,f924,f8632]) ).
fof(f8632,plain,
( spl30_634
<=> ! [X0,X1] :
( relation_dom(X1) = relation_rng(relation_rng(sK4(powerset(X0))))
| ~ empty(X0)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_634])]) ).
fof(f4609,plain,
( ! [X0,X1] :
( relation_dom(X1) = relation_rng(relation_rng(sK4(powerset(X0))))
| ~ empty(X0)
| ~ empty(X1) )
| ~ spl30_101
| ~ spl30_434 ),
inference(resolution,[],[f4495,f925]) ).
fof(f8630,plain,
( spl30_633
| ~ spl30_98
| ~ spl30_433 ),
inference(avatar_split_clause,[],[f4591,f4490,f911,f8628]) ).
fof(f8628,plain,
( spl30_633
<=> ! [X0,X1] :
( relation_rng(X1) = relation_rng(relation_dom(sK4(powerset(X0))))
| ~ empty(X0)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_633])]) ).
fof(f4591,plain,
( ! [X0,X1] :
( relation_rng(X1) = relation_rng(relation_dom(sK4(powerset(X0))))
| ~ empty(X0)
| ~ empty(X1) )
| ~ spl30_98
| ~ spl30_433 ),
inference(resolution,[],[f4491,f912]) ).
fof(f8626,plain,
( spl30_632
| ~ spl30_101
| ~ spl30_433 ),
inference(avatar_split_clause,[],[f4590,f4490,f924,f8624]) ).
fof(f8624,plain,
( spl30_632
<=> ! [X0,X1] :
( relation_dom(X1) = relation_rng(relation_dom(sK4(powerset(X0))))
| ~ empty(X0)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_632])]) ).
fof(f4590,plain,
( ! [X0,X1] :
( relation_dom(X1) = relation_rng(relation_dom(sK4(powerset(X0))))
| ~ empty(X0)
| ~ empty(X1) )
| ~ spl30_101
| ~ spl30_433 ),
inference(resolution,[],[f4491,f925]) ).
fof(f8622,plain,
( spl30_631
| ~ spl30_98
| ~ spl30_432 ),
inference(avatar_split_clause,[],[f4572,f4486,f911,f8620]) ).
fof(f8620,plain,
( spl30_631
<=> ! [X0,X1] :
( relation_rng(X1) = relation_dom(relation_rng(sK4(powerset(X0))))
| ~ empty(X0)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_631])]) ).
fof(f4572,plain,
( ! [X0,X1] :
( relation_rng(X1) = relation_dom(relation_rng(sK4(powerset(X0))))
| ~ empty(X0)
| ~ empty(X1) )
| ~ spl30_98
| ~ spl30_432 ),
inference(resolution,[],[f4487,f912]) ).
fof(f8618,plain,
( spl30_630
| ~ spl30_101
| ~ spl30_432 ),
inference(avatar_split_clause,[],[f4571,f4486,f924,f8616]) ).
fof(f8616,plain,
( spl30_630
<=> ! [X0,X1] :
( relation_dom(X1) = relation_dom(relation_rng(sK4(powerset(X0))))
| ~ empty(X0)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_630])]) ).
fof(f4571,plain,
( ! [X0,X1] :
( relation_dom(X1) = relation_dom(relation_rng(sK4(powerset(X0))))
| ~ empty(X0)
| ~ empty(X1) )
| ~ spl30_101
| ~ spl30_432 ),
inference(resolution,[],[f4487,f925]) ).
fof(f8614,plain,
( spl30_629
| ~ spl30_98
| ~ spl30_431 ),
inference(avatar_split_clause,[],[f4553,f4482,f911,f8612]) ).
fof(f8612,plain,
( spl30_629
<=> ! [X0,X1] :
( relation_rng(X1) = relation_dom(relation_dom(sK4(powerset(X0))))
| ~ empty(X0)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_629])]) ).
fof(f4553,plain,
( ! [X0,X1] :
( relation_rng(X1) = relation_dom(relation_dom(sK4(powerset(X0))))
| ~ empty(X0)
| ~ empty(X1) )
| ~ spl30_98
| ~ spl30_431 ),
inference(resolution,[],[f4483,f912]) ).
fof(f8610,plain,
( spl30_628
| ~ spl30_101
| ~ spl30_431 ),
inference(avatar_split_clause,[],[f4552,f4482,f924,f8608]) ).
fof(f8608,plain,
( spl30_628
<=> ! [X0,X1] :
( relation_dom(X1) = relation_dom(relation_dom(sK4(powerset(X0))))
| ~ empty(X0)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_628])]) ).
fof(f4552,plain,
( ! [X0,X1] :
( relation_dom(X1) = relation_dom(relation_dom(sK4(powerset(X0))))
| ~ empty(X0)
| ~ empty(X1) )
| ~ spl30_101
| ~ spl30_431 ),
inference(resolution,[],[f4483,f925]) ).
fof(f8606,plain,
( spl30_627
| ~ spl30_101
| ~ spl30_511 ),
inference(avatar_split_clause,[],[f5803,f5243,f924,f8604]) ).
fof(f8604,plain,
( spl30_627
<=> ! [X0] :
( sK10 = sK4(powerset(sK4(powerset(relation_dom(X0)))))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_627])]) ).
fof(f5803,plain,
( ! [X0] :
( sK10 = sK4(powerset(sK4(powerset(relation_dom(X0)))))
| ~ empty(X0) )
| ~ spl30_101
| ~ spl30_511 ),
inference(resolution,[],[f5244,f925]) ).
fof(f8602,plain,
( spl30_626
| ~ spl30_289
| ~ spl30_409 ),
inference(avatar_split_clause,[],[f4414,f4099,f2470,f8600]) ).
fof(f8600,plain,
( spl30_626
<=> ! [X0,X1] :
( sK4(powerset(X1)) = relation_rng(relation_rng(relation_rng(X0)))
| ~ empty(X0)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_626])]) ).
fof(f4099,plain,
( spl30_409
<=> ! [X0,X1] :
( relation_rng(relation_rng(relation_rng(X0))) = X1
| ~ empty(X1)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_409])]) ).
fof(f4414,plain,
( ! [X0,X1] :
( sK4(powerset(X1)) = relation_rng(relation_rng(relation_rng(X0)))
| ~ empty(X0)
| ~ empty(X1) )
| ~ spl30_289
| ~ spl30_409 ),
inference(resolution,[],[f4100,f2471]) ).
fof(f4100,plain,
( ! [X0,X1] :
( ~ empty(X1)
| relation_rng(relation_rng(relation_rng(X0))) = X1
| ~ empty(X0) )
| ~ spl30_409 ),
inference(avatar_component_clause,[],[f4099]) ).
fof(f8598,plain,
( spl30_625
| ~ spl30_289
| ~ spl30_408 ),
inference(avatar_split_clause,[],[f4395,f4095,f2470,f8596]) ).
fof(f8596,plain,
( spl30_625
<=> ! [X0,X1] :
( sK4(powerset(X1)) = relation_rng(relation_rng(relation_dom(X0)))
| ~ empty(X0)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_625])]) ).
fof(f4095,plain,
( spl30_408
<=> ! [X0,X1] :
( relation_rng(relation_rng(relation_dom(X0))) = X1
| ~ empty(X1)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_408])]) ).
fof(f4395,plain,
( ! [X0,X1] :
( sK4(powerset(X1)) = relation_rng(relation_rng(relation_dom(X0)))
| ~ empty(X0)
| ~ empty(X1) )
| ~ spl30_289
| ~ spl30_408 ),
inference(resolution,[],[f4096,f2471]) ).
fof(f4096,plain,
( ! [X0,X1] :
( ~ empty(X1)
| relation_rng(relation_rng(relation_dom(X0))) = X1
| ~ empty(X0) )
| ~ spl30_408 ),
inference(avatar_component_clause,[],[f4095]) ).
fof(f8594,plain,
( spl30_624
| ~ spl30_289
| ~ spl30_407 ),
inference(avatar_split_clause,[],[f4376,f4091,f2470,f8592]) ).
fof(f8592,plain,
( spl30_624
<=> ! [X0,X1] :
( sK4(powerset(X1)) = relation_rng(relation_dom(relation_rng(X0)))
| ~ empty(X0)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_624])]) ).
fof(f4091,plain,
( spl30_407
<=> ! [X0,X1] :
( relation_rng(relation_dom(relation_rng(X0))) = X1
| ~ empty(X1)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_407])]) ).
fof(f4376,plain,
( ! [X0,X1] :
( sK4(powerset(X1)) = relation_rng(relation_dom(relation_rng(X0)))
| ~ empty(X0)
| ~ empty(X1) )
| ~ spl30_289
| ~ spl30_407 ),
inference(resolution,[],[f4092,f2471]) ).
fof(f4092,plain,
( ! [X0,X1] :
( ~ empty(X1)
| relation_rng(relation_dom(relation_rng(X0))) = X1
| ~ empty(X0) )
| ~ spl30_407 ),
inference(avatar_component_clause,[],[f4091]) ).
fof(f8590,plain,
( spl30_623
| ~ spl30_289
| ~ spl30_406 ),
inference(avatar_split_clause,[],[f4357,f4087,f2470,f8588]) ).
fof(f8588,plain,
( spl30_623
<=> ! [X0,X1] :
( sK4(powerset(X1)) = relation_rng(relation_dom(relation_dom(X0)))
| ~ empty(X0)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_623])]) ).
fof(f4087,plain,
( spl30_406
<=> ! [X0,X1] :
( relation_rng(relation_dom(relation_dom(X0))) = X1
| ~ empty(X1)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_406])]) ).
fof(f4357,plain,
( ! [X0,X1] :
( sK4(powerset(X1)) = relation_rng(relation_dom(relation_dom(X0)))
| ~ empty(X0)
| ~ empty(X1) )
| ~ spl30_289
| ~ spl30_406 ),
inference(resolution,[],[f4088,f2471]) ).
fof(f4088,plain,
( ! [X0,X1] :
( ~ empty(X1)
| relation_rng(relation_dom(relation_dom(X0))) = X1
| ~ empty(X0) )
| ~ spl30_406 ),
inference(avatar_component_clause,[],[f4087]) ).
fof(f8586,plain,
( spl30_622
| ~ spl30_289
| ~ spl30_405 ),
inference(avatar_split_clause,[],[f4338,f4083,f2470,f8584]) ).
fof(f8584,plain,
( spl30_622
<=> ! [X0,X1] :
( sK4(powerset(X1)) = relation_dom(relation_rng(relation_rng(X0)))
| ~ empty(X0)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_622])]) ).
fof(f4083,plain,
( spl30_405
<=> ! [X0,X1] :
( relation_dom(relation_rng(relation_rng(X0))) = X1
| ~ empty(X1)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_405])]) ).
fof(f4338,plain,
( ! [X0,X1] :
( sK4(powerset(X1)) = relation_dom(relation_rng(relation_rng(X0)))
| ~ empty(X0)
| ~ empty(X1) )
| ~ spl30_289
| ~ spl30_405 ),
inference(resolution,[],[f4084,f2471]) ).
fof(f4084,plain,
( ! [X0,X1] :
( ~ empty(X1)
| relation_dom(relation_rng(relation_rng(X0))) = X1
| ~ empty(X0) )
| ~ spl30_405 ),
inference(avatar_component_clause,[],[f4083]) ).
fof(f8582,plain,
( spl30_621
| ~ spl30_289
| ~ spl30_404 ),
inference(avatar_split_clause,[],[f4319,f4079,f2470,f8580]) ).
fof(f8580,plain,
( spl30_621
<=> ! [X0,X1] :
( sK4(powerset(X1)) = relation_dom(relation_rng(relation_dom(X0)))
| ~ empty(X0)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_621])]) ).
fof(f4079,plain,
( spl30_404
<=> ! [X0,X1] :
( relation_dom(relation_rng(relation_dom(X0))) = X1
| ~ empty(X1)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_404])]) ).
fof(f4319,plain,
( ! [X0,X1] :
( sK4(powerset(X1)) = relation_dom(relation_rng(relation_dom(X0)))
| ~ empty(X0)
| ~ empty(X1) )
| ~ spl30_289
| ~ spl30_404 ),
inference(resolution,[],[f4080,f2471]) ).
fof(f4080,plain,
( ! [X0,X1] :
( ~ empty(X1)
| relation_dom(relation_rng(relation_dom(X0))) = X1
| ~ empty(X0) )
| ~ spl30_404 ),
inference(avatar_component_clause,[],[f4079]) ).
fof(f8578,plain,
( spl30_620
| ~ spl30_289
| ~ spl30_403 ),
inference(avatar_split_clause,[],[f4295,f4075,f2470,f8576]) ).
fof(f8576,plain,
( spl30_620
<=> ! [X0,X1] :
( sK4(powerset(X1)) = relation_dom(relation_dom(relation_rng(X0)))
| ~ empty(X0)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_620])]) ).
fof(f4075,plain,
( spl30_403
<=> ! [X0,X1] :
( relation_dom(relation_dom(relation_rng(X0))) = X1
| ~ empty(X1)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_403])]) ).
fof(f4295,plain,
( ! [X0,X1] :
( sK4(powerset(X1)) = relation_dom(relation_dom(relation_rng(X0)))
| ~ empty(X0)
| ~ empty(X1) )
| ~ spl30_289
| ~ spl30_403 ),
inference(resolution,[],[f4076,f2471]) ).
fof(f4076,plain,
( ! [X0,X1] :
( ~ empty(X1)
| relation_dom(relation_dom(relation_rng(X0))) = X1
| ~ empty(X0) )
| ~ spl30_403 ),
inference(avatar_component_clause,[],[f4075]) ).
fof(f8574,plain,
( spl30_619
| ~ spl30_289
| ~ spl30_402 ),
inference(avatar_split_clause,[],[f4276,f4071,f2470,f8572]) ).
fof(f8572,plain,
( spl30_619
<=> ! [X0,X1] :
( sK4(powerset(X1)) = relation_dom(relation_dom(relation_dom(X0)))
| ~ empty(X0)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_619])]) ).
fof(f4071,plain,
( spl30_402
<=> ! [X0,X1] :
( relation_dom(relation_dom(relation_dom(X0))) = X1
| ~ empty(X1)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_402])]) ).
fof(f4276,plain,
( ! [X0,X1] :
( sK4(powerset(X1)) = relation_dom(relation_dom(relation_dom(X0)))
| ~ empty(X0)
| ~ empty(X1) )
| ~ spl30_289
| ~ spl30_402 ),
inference(resolution,[],[f4072,f2471]) ).
fof(f4072,plain,
( ! [X0,X1] :
( ~ empty(X1)
| relation_dom(relation_dom(relation_dom(X0))) = X1
| ~ empty(X0) )
| ~ spl30_402 ),
inference(avatar_component_clause,[],[f4071]) ).
fof(f8570,plain,
( spl30_618
| ~ spl30_289
| ~ spl30_400 ),
inference(avatar_split_clause,[],[f4257,f4063,f2470,f8568]) ).
fof(f8568,plain,
( spl30_618
<=> ! [X0,X1] :
( ~ empty(X0)
| sK4(powerset(X1)) = relation_rng(sK4(powerset(X0)))
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_618])]) ).
fof(f4063,plain,
( spl30_400
<=> ! [X0,X1] :
( ~ empty(X0)
| ~ empty(X1)
| relation_rng(sK4(powerset(X0))) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_400])]) ).
fof(f4257,plain,
( ! [X0,X1] :
( ~ empty(X0)
| sK4(powerset(X1)) = relation_rng(sK4(powerset(X0)))
| ~ empty(X1) )
| ~ spl30_289
| ~ spl30_400 ),
inference(resolution,[],[f4064,f2471]) ).
fof(f4064,plain,
( ! [X0,X1] :
( ~ empty(X1)
| ~ empty(X0)
| relation_rng(sK4(powerset(X0))) = X1 )
| ~ spl30_400 ),
inference(avatar_component_clause,[],[f4063]) ).
fof(f8566,plain,
( spl30_617
| ~ spl30_289
| ~ spl30_399 ),
inference(avatar_split_clause,[],[f4238,f4059,f2470,f8564]) ).
fof(f8564,plain,
( spl30_617
<=> ! [X0,X1] :
( ~ empty(X0)
| sK4(powerset(X1)) = relation_dom(sK4(powerset(X0)))
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_617])]) ).
fof(f4059,plain,
( spl30_399
<=> ! [X0,X1] :
( ~ empty(X0)
| ~ empty(X1)
| relation_dom(sK4(powerset(X0))) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_399])]) ).
fof(f4238,plain,
( ! [X0,X1] :
( ~ empty(X0)
| sK4(powerset(X1)) = relation_dom(sK4(powerset(X0)))
| ~ empty(X1) )
| ~ spl30_289
| ~ spl30_399 ),
inference(resolution,[],[f4060,f2471]) ).
fof(f4060,plain,
( ! [X0,X1] :
( ~ empty(X1)
| ~ empty(X0)
| relation_dom(sK4(powerset(X0))) = X1 )
| ~ spl30_399 ),
inference(avatar_component_clause,[],[f4059]) ).
fof(f8562,plain,
( spl30_616
| ~ spl30_289
| ~ spl30_401 ),
inference(avatar_split_clause,[],[f5039,f4067,f2470,f8560]) ).
fof(f8560,plain,
( spl30_616
<=> ! [X0] :
( sK10 = sK4(powerset(relation_rng(sK4(powerset(X0)))))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_616])]) ).
fof(f4067,plain,
( spl30_401
<=> ! [X0] :
( sK10 = sK4(powerset(relation_rng(X0)))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_401])]) ).
fof(f5039,plain,
( ! [X0] :
( sK10 = sK4(powerset(relation_rng(sK4(powerset(X0)))))
| ~ empty(X0) )
| ~ spl30_289
| ~ spl30_401 ),
inference(resolution,[],[f4068,f2471]) ).
fof(f4068,plain,
( ! [X0] :
( ~ empty(X0)
| sK10 = sK4(powerset(relation_rng(X0))) )
| ~ spl30_401 ),
inference(avatar_component_clause,[],[f4067]) ).
fof(f8288,plain,
( spl30_615
| ~ spl30_289
| ~ spl30_395 ),
inference(avatar_split_clause,[],[f4114,f3884,f2470,f8286]) ).
fof(f8286,plain,
( spl30_615
<=> ! [X0] :
( sK10 = sK4(powerset(relation_dom(sK4(powerset(X0)))))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_615])]) ).
fof(f3884,plain,
( spl30_395
<=> ! [X0] :
( sK10 = sK4(powerset(relation_dom(X0)))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_395])]) ).
fof(f4114,plain,
( ! [X0] :
( sK10 = sK4(powerset(relation_dom(sK4(powerset(X0)))))
| ~ empty(X0) )
| ~ spl30_289
| ~ spl30_395 ),
inference(resolution,[],[f3885,f2471]) ).
fof(f3885,plain,
( ! [X0] :
( ~ empty(X0)
| sK10 = sK4(powerset(relation_dom(X0))) )
| ~ spl30_395 ),
inference(avatar_component_clause,[],[f3884]) ).
fof(f7780,plain,
( spl30_614
| ~ spl30_98
| ~ spl30_409 ),
inference(avatar_split_clause,[],[f4413,f4099,f911,f7778]) ).
fof(f7778,plain,
( spl30_614
<=> ! [X0,X1] :
( relation_rng(X1) = relation_rng(relation_rng(relation_rng(X0)))
| ~ empty(X0)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_614])]) ).
fof(f4413,plain,
( ! [X0,X1] :
( relation_rng(X1) = relation_rng(relation_rng(relation_rng(X0)))
| ~ empty(X0)
| ~ empty(X1) )
| ~ spl30_98
| ~ spl30_409 ),
inference(resolution,[],[f4100,f912]) ).
fof(f7776,plain,
( spl30_613
| ~ spl30_101
| ~ spl30_409 ),
inference(avatar_split_clause,[],[f4412,f4099,f924,f7774]) ).
fof(f7774,plain,
( spl30_613
<=> ! [X0,X1] :
( relation_dom(X1) = relation_rng(relation_rng(relation_rng(X0)))
| ~ empty(X0)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_613])]) ).
fof(f4412,plain,
( ! [X0,X1] :
( relation_dom(X1) = relation_rng(relation_rng(relation_rng(X0)))
| ~ empty(X0)
| ~ empty(X1) )
| ~ spl30_101
| ~ spl30_409 ),
inference(resolution,[],[f4100,f925]) ).
fof(f7772,plain,
( spl30_612
| ~ spl30_98
| ~ spl30_408 ),
inference(avatar_split_clause,[],[f4394,f4095,f911,f7770]) ).
fof(f7770,plain,
( spl30_612
<=> ! [X0,X1] :
( relation_rng(X1) = relation_rng(relation_rng(relation_dom(X0)))
| ~ empty(X0)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_612])]) ).
fof(f4394,plain,
( ! [X0,X1] :
( relation_rng(X1) = relation_rng(relation_rng(relation_dom(X0)))
| ~ empty(X0)
| ~ empty(X1) )
| ~ spl30_98
| ~ spl30_408 ),
inference(resolution,[],[f4096,f912]) ).
fof(f7768,plain,
( spl30_611
| ~ spl30_101
| ~ spl30_408 ),
inference(avatar_split_clause,[],[f4393,f4095,f924,f7766]) ).
fof(f7766,plain,
( spl30_611
<=> ! [X0,X1] :
( relation_dom(X1) = relation_rng(relation_rng(relation_dom(X0)))
| ~ empty(X0)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_611])]) ).
fof(f4393,plain,
( ! [X0,X1] :
( relation_dom(X1) = relation_rng(relation_rng(relation_dom(X0)))
| ~ empty(X0)
| ~ empty(X1) )
| ~ spl30_101
| ~ spl30_408 ),
inference(resolution,[],[f4096,f925]) ).
fof(f7764,plain,
( spl30_610
| ~ spl30_98
| ~ spl30_407 ),
inference(avatar_split_clause,[],[f4375,f4091,f911,f7762]) ).
fof(f7762,plain,
( spl30_610
<=> ! [X0,X1] :
( relation_rng(X1) = relation_rng(relation_dom(relation_rng(X0)))
| ~ empty(X0)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_610])]) ).
fof(f4375,plain,
( ! [X0,X1] :
( relation_rng(X1) = relation_rng(relation_dom(relation_rng(X0)))
| ~ empty(X0)
| ~ empty(X1) )
| ~ spl30_98
| ~ spl30_407 ),
inference(resolution,[],[f4092,f912]) ).
fof(f7725,plain,
( spl30_609
| ~ spl30_101
| ~ spl30_407 ),
inference(avatar_split_clause,[],[f4374,f4091,f924,f7723]) ).
fof(f7723,plain,
( spl30_609
<=> ! [X0,X1] :
( relation_dom(X1) = relation_rng(relation_dom(relation_rng(X0)))
| ~ empty(X0)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_609])]) ).
fof(f4374,plain,
( ! [X0,X1] :
( relation_dom(X1) = relation_rng(relation_dom(relation_rng(X0)))
| ~ empty(X0)
| ~ empty(X1) )
| ~ spl30_101
| ~ spl30_407 ),
inference(resolution,[],[f4092,f925]) ).
fof(f7721,plain,
( spl30_608
| ~ spl30_98
| ~ spl30_406 ),
inference(avatar_split_clause,[],[f4356,f4087,f911,f7719]) ).
fof(f7719,plain,
( spl30_608
<=> ! [X0,X1] :
( relation_rng(X1) = relation_rng(relation_dom(relation_dom(X0)))
| ~ empty(X0)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_608])]) ).
fof(f4356,plain,
( ! [X0,X1] :
( relation_rng(X1) = relation_rng(relation_dom(relation_dom(X0)))
| ~ empty(X0)
| ~ empty(X1) )
| ~ spl30_98
| ~ spl30_406 ),
inference(resolution,[],[f4088,f912]) ).
fof(f7717,plain,
( spl30_607
| ~ spl30_101
| ~ spl30_406 ),
inference(avatar_split_clause,[],[f4355,f4087,f924,f7715]) ).
fof(f7715,plain,
( spl30_607
<=> ! [X0,X1] :
( relation_dom(X1) = relation_rng(relation_dom(relation_dom(X0)))
| ~ empty(X0)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_607])]) ).
fof(f4355,plain,
( ! [X0,X1] :
( relation_dom(X1) = relation_rng(relation_dom(relation_dom(X0)))
| ~ empty(X0)
| ~ empty(X1) )
| ~ spl30_101
| ~ spl30_406 ),
inference(resolution,[],[f4088,f925]) ).
fof(f7713,plain,
( spl30_606
| ~ spl30_98
| ~ spl30_405 ),
inference(avatar_split_clause,[],[f4337,f4083,f911,f7711]) ).
fof(f7711,plain,
( spl30_606
<=> ! [X0,X1] :
( relation_rng(X1) = relation_dom(relation_rng(relation_rng(X0)))
| ~ empty(X0)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_606])]) ).
fof(f4337,plain,
( ! [X0,X1] :
( relation_rng(X1) = relation_dom(relation_rng(relation_rng(X0)))
| ~ empty(X0)
| ~ empty(X1) )
| ~ spl30_98
| ~ spl30_405 ),
inference(resolution,[],[f4084,f912]) ).
fof(f7709,plain,
( spl30_605
| ~ spl30_101
| ~ spl30_405 ),
inference(avatar_split_clause,[],[f4336,f4083,f924,f7707]) ).
fof(f7707,plain,
( spl30_605
<=> ! [X0,X1] :
( relation_dom(X1) = relation_dom(relation_rng(relation_rng(X0)))
| ~ empty(X0)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_605])]) ).
fof(f4336,plain,
( ! [X0,X1] :
( relation_dom(X1) = relation_dom(relation_rng(relation_rng(X0)))
| ~ empty(X0)
| ~ empty(X1) )
| ~ spl30_101
| ~ spl30_405 ),
inference(resolution,[],[f4084,f925]) ).
fof(f7705,plain,
( spl30_604
| ~ spl30_98
| ~ spl30_404 ),
inference(avatar_split_clause,[],[f4318,f4079,f911,f7703]) ).
fof(f7703,plain,
( spl30_604
<=> ! [X0,X1] :
( relation_rng(X1) = relation_dom(relation_rng(relation_dom(X0)))
| ~ empty(X0)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_604])]) ).
fof(f4318,plain,
( ! [X0,X1] :
( relation_rng(X1) = relation_dom(relation_rng(relation_dom(X0)))
| ~ empty(X0)
| ~ empty(X1) )
| ~ spl30_98
| ~ spl30_404 ),
inference(resolution,[],[f4080,f912]) ).
fof(f7701,plain,
( spl30_603
| ~ spl30_101
| ~ spl30_404 ),
inference(avatar_split_clause,[],[f4317,f4079,f924,f7699]) ).
fof(f7699,plain,
( spl30_603
<=> ! [X0,X1] :
( relation_dom(X1) = relation_dom(relation_rng(relation_dom(X0)))
| ~ empty(X0)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_603])]) ).
fof(f4317,plain,
( ! [X0,X1] :
( relation_dom(X1) = relation_dom(relation_rng(relation_dom(X0)))
| ~ empty(X0)
| ~ empty(X1) )
| ~ spl30_101
| ~ spl30_404 ),
inference(resolution,[],[f4080,f925]) ).
fof(f7697,plain,
( spl30_602
| ~ spl30_98
| ~ spl30_403 ),
inference(avatar_split_clause,[],[f4294,f4075,f911,f7695]) ).
fof(f7695,plain,
( spl30_602
<=> ! [X0,X1] :
( relation_rng(X1) = relation_dom(relation_dom(relation_rng(X0)))
| ~ empty(X0)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_602])]) ).
fof(f4294,plain,
( ! [X0,X1] :
( relation_rng(X1) = relation_dom(relation_dom(relation_rng(X0)))
| ~ empty(X0)
| ~ empty(X1) )
| ~ spl30_98
| ~ spl30_403 ),
inference(resolution,[],[f4076,f912]) ).
fof(f7693,plain,
( spl30_601
| ~ spl30_101
| ~ spl30_403 ),
inference(avatar_split_clause,[],[f4293,f4075,f924,f7691]) ).
fof(f7691,plain,
( spl30_601
<=> ! [X0,X1] :
( relation_dom(X1) = relation_dom(relation_dom(relation_rng(X0)))
| ~ empty(X0)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_601])]) ).
fof(f4293,plain,
( ! [X0,X1] :
( relation_dom(X1) = relation_dom(relation_dom(relation_rng(X0)))
| ~ empty(X0)
| ~ empty(X1) )
| ~ spl30_101
| ~ spl30_403 ),
inference(resolution,[],[f4076,f925]) ).
fof(f7689,plain,
( spl30_600
| ~ spl30_98
| ~ spl30_402 ),
inference(avatar_split_clause,[],[f4275,f4071,f911,f7687]) ).
fof(f7687,plain,
( spl30_600
<=> ! [X0,X1] :
( relation_rng(X1) = relation_dom(relation_dom(relation_dom(X0)))
| ~ empty(X0)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_600])]) ).
fof(f4275,plain,
( ! [X0,X1] :
( relation_rng(X1) = relation_dom(relation_dom(relation_dom(X0)))
| ~ empty(X0)
| ~ empty(X1) )
| ~ spl30_98
| ~ spl30_402 ),
inference(resolution,[],[f4072,f912]) ).
fof(f7650,plain,
( spl30_599
| ~ spl30_101
| ~ spl30_402 ),
inference(avatar_split_clause,[],[f4274,f4071,f924,f7648]) ).
fof(f7648,plain,
( spl30_599
<=> ! [X0,X1] :
( relation_dom(X1) = relation_dom(relation_dom(relation_dom(X0)))
| ~ empty(X0)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_599])]) ).
fof(f4274,plain,
( ! [X0,X1] :
( relation_dom(X1) = relation_dom(relation_dom(relation_dom(X0)))
| ~ empty(X0)
| ~ empty(X1) )
| ~ spl30_101
| ~ spl30_402 ),
inference(resolution,[],[f4072,f925]) ).
fof(f7646,plain,
( spl30_598
| ~ spl30_98
| ~ spl30_400 ),
inference(avatar_split_clause,[],[f4256,f4063,f911,f7644]) ).
fof(f7644,plain,
( spl30_598
<=> ! [X0,X1] :
( ~ empty(X0)
| relation_rng(X1) = relation_rng(sK4(powerset(X0)))
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_598])]) ).
fof(f4256,plain,
( ! [X0,X1] :
( ~ empty(X0)
| relation_rng(X1) = relation_rng(sK4(powerset(X0)))
| ~ empty(X1) )
| ~ spl30_98
| ~ spl30_400 ),
inference(resolution,[],[f4064,f912]) ).
fof(f7642,plain,
( spl30_597
| ~ spl30_101
| ~ spl30_400 ),
inference(avatar_split_clause,[],[f4255,f4063,f924,f7640]) ).
fof(f7640,plain,
( spl30_597
<=> ! [X0,X1] :
( ~ empty(X0)
| relation_dom(X1) = relation_rng(sK4(powerset(X0)))
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_597])]) ).
fof(f4255,plain,
( ! [X0,X1] :
( ~ empty(X0)
| relation_dom(X1) = relation_rng(sK4(powerset(X0)))
| ~ empty(X1) )
| ~ spl30_101
| ~ spl30_400 ),
inference(resolution,[],[f4064,f925]) ).
fof(f7638,plain,
( spl30_596
| ~ spl30_98
| ~ spl30_399 ),
inference(avatar_split_clause,[],[f4237,f4059,f911,f7636]) ).
fof(f7636,plain,
( spl30_596
<=> ! [X0,X1] :
( ~ empty(X0)
| relation_rng(X1) = relation_dom(sK4(powerset(X0)))
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_596])]) ).
fof(f4237,plain,
( ! [X0,X1] :
( ~ empty(X0)
| relation_rng(X1) = relation_dom(sK4(powerset(X0)))
| ~ empty(X1) )
| ~ spl30_98
| ~ spl30_399 ),
inference(resolution,[],[f4060,f912]) ).
fof(f7634,plain,
( spl30_595
| ~ spl30_101
| ~ spl30_399 ),
inference(avatar_split_clause,[],[f4236,f4059,f924,f7632]) ).
fof(f7632,plain,
( spl30_595
<=> ! [X0,X1] :
( ~ empty(X0)
| relation_dom(X1) = relation_dom(sK4(powerset(X0)))
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_595])]) ).
fof(f4236,plain,
( ! [X0,X1] :
( ~ empty(X0)
| relation_dom(X1) = relation_dom(sK4(powerset(X0)))
| ~ empty(X1) )
| ~ spl30_101
| ~ spl30_399 ),
inference(resolution,[],[f4060,f925]) ).
fof(f7630,plain,
( spl30_594
| ~ spl30_289
| ~ spl30_398 ),
inference(avatar_split_clause,[],[f4027,f3896,f2470,f7628]) ).
fof(f7628,plain,
( spl30_594
<=> ! [X0] :
( sK10 = relation_dom(relation_rng(sK4(powerset(sK4(powerset(X0))))))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_594])]) ).
fof(f3896,plain,
( spl30_398
<=> ! [X0] :
( sK10 = relation_dom(relation_rng(sK4(powerset(X0))))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_398])]) ).
fof(f4027,plain,
( ! [X0] :
( sK10 = relation_dom(relation_rng(sK4(powerset(sK4(powerset(X0))))))
| ~ empty(X0) )
| ~ spl30_289
| ~ spl30_398 ),
inference(resolution,[],[f3897,f2471]) ).
fof(f3897,plain,
( ! [X0] :
( ~ empty(X0)
| sK10 = relation_dom(relation_rng(sK4(powerset(X0)))) )
| ~ spl30_398 ),
inference(avatar_component_clause,[],[f3896]) ).
fof(f7626,plain,
( spl30_593
| ~ spl30_289
| ~ spl30_397 ),
inference(avatar_split_clause,[],[f3992,f3892,f2470,f7624]) ).
fof(f7624,plain,
( spl30_593
<=> ! [X0] :
( sK10 = relation_dom(relation_dom(sK4(powerset(sK4(powerset(X0))))))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_593])]) ).
fof(f3892,plain,
( spl30_397
<=> ! [X0] :
( sK10 = relation_dom(relation_dom(sK4(powerset(X0))))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_397])]) ).
fof(f3992,plain,
( ! [X0] :
( sK10 = relation_dom(relation_dom(sK4(powerset(sK4(powerset(X0))))))
| ~ empty(X0) )
| ~ spl30_289
| ~ spl30_397 ),
inference(resolution,[],[f3893,f2471]) ).
fof(f3893,plain,
( ! [X0] :
( ~ empty(X0)
| sK10 = relation_dom(relation_dom(sK4(powerset(X0)))) )
| ~ spl30_397 ),
inference(avatar_component_clause,[],[f3892]) ).
fof(f7622,plain,
( spl30_592
| ~ spl30_289
| ~ spl30_396 ),
inference(avatar_split_clause,[],[f3957,f3888,f2470,f7620]) ).
fof(f7620,plain,
( spl30_592
<=> ! [X0] :
( sK10 = relation_rng(relation_rng(sK4(powerset(sK4(powerset(X0))))))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_592])]) ).
fof(f3888,plain,
( spl30_396
<=> ! [X0] :
( sK10 = relation_rng(relation_rng(sK4(powerset(X0))))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_396])]) ).
fof(f3957,plain,
( ! [X0] :
( sK10 = relation_rng(relation_rng(sK4(powerset(sK4(powerset(X0))))))
| ~ empty(X0) )
| ~ spl30_289
| ~ spl30_396 ),
inference(resolution,[],[f3889,f2471]) ).
fof(f3889,plain,
( ! [X0] :
( ~ empty(X0)
| sK10 = relation_rng(relation_rng(sK4(powerset(X0)))) )
| ~ spl30_396 ),
inference(avatar_component_clause,[],[f3888]) ).
fof(f7618,plain,
( spl30_591
| ~ spl30_289
| ~ spl30_394 ),
inference(avatar_split_clause,[],[f3922,f3880,f2470,f7616]) ).
fof(f7616,plain,
( spl30_591
<=> ! [X0] :
( sK10 = relation_rng(relation_dom(sK4(powerset(sK4(powerset(X0))))))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_591])]) ).
fof(f3880,plain,
( spl30_394
<=> ! [X0] :
( sK10 = relation_rng(relation_dom(sK4(powerset(X0))))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_394])]) ).
fof(f3922,plain,
( ! [X0] :
( sK10 = relation_rng(relation_dom(sK4(powerset(sK4(powerset(X0))))))
| ~ empty(X0) )
| ~ spl30_289
| ~ spl30_394 ),
inference(resolution,[],[f3881,f2471]) ).
fof(f3881,plain,
( ! [X0] :
( ~ empty(X0)
| sK10 = relation_rng(relation_dom(sK4(powerset(X0)))) )
| ~ spl30_394 ),
inference(avatar_component_clause,[],[f3880]) ).
fof(f7614,plain,
( spl30_590
| ~ spl30_289
| ~ spl30_393 ),
inference(avatar_split_clause,[],[f3903,f3876,f2470,f7612]) ).
fof(f7612,plain,
( spl30_590
<=> ! [X0,X1] :
( sK4(powerset(X0)) = sK4(powerset(X1))
| ~ empty(X0)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_590])]) ).
fof(f3876,plain,
( spl30_393
<=> ! [X0,X1] :
( ~ empty(X0)
| sK4(powerset(X0)) = X1
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_393])]) ).
fof(f3903,plain,
( ! [X0,X1] :
( sK4(powerset(X0)) = sK4(powerset(X1))
| ~ empty(X0)
| ~ empty(X1) )
| ~ spl30_289
| ~ spl30_393 ),
inference(resolution,[],[f3877,f2471]) ).
fof(f3877,plain,
( ! [X0,X1] :
( ~ empty(X1)
| sK4(powerset(X0)) = X1
| ~ empty(X0) )
| ~ spl30_393 ),
inference(avatar_component_clause,[],[f3876]) ).
fof(f7274,plain,
( spl30_589
| ~ spl30_98
| ~ spl30_401 ),
inference(avatar_split_clause,[],[f5038,f4067,f911,f7272]) ).
fof(f7272,plain,
( spl30_589
<=> ! [X0] :
( sK10 = sK4(powerset(relation_rng(relation_rng(X0))))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_589])]) ).
fof(f5038,plain,
( ! [X0] :
( sK10 = sK4(powerset(relation_rng(relation_rng(X0))))
| ~ empty(X0) )
| ~ spl30_98
| ~ spl30_401 ),
inference(resolution,[],[f4068,f912]) ).
fof(f6872,plain,
( spl30_588
| ~ spl30_101
| ~ spl30_401 ),
inference(avatar_split_clause,[],[f5037,f4067,f924,f6870]) ).
fof(f6870,plain,
( spl30_588
<=> ! [X0] :
( sK10 = sK4(powerset(relation_rng(relation_dom(X0))))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_588])]) ).
fof(f5037,plain,
( ! [X0] :
( sK10 = sK4(powerset(relation_rng(relation_dom(X0))))
| ~ empty(X0) )
| ~ spl30_101
| ~ spl30_401 ),
inference(resolution,[],[f4068,f925]) ).
fof(f6755,plain,
( spl30_587
| ~ spl30_108
| ~ spl30_412 ),
inference(avatar_split_clause,[],[f4461,f4138,f981,f6753]) ).
fof(f6753,plain,
( spl30_587
<=> ! [X0] :
( empty(sK3(X0))
| empty(X0)
| ~ in(X0,sK4(sK3(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_587])]) ).
fof(f4461,plain,
( ! [X0] :
( empty(sK3(X0))
| empty(X0)
| ~ in(X0,sK4(sK3(X0))) )
| ~ spl30_108
| ~ spl30_412 ),
inference(resolution,[],[f4139,f982]) ).
fof(f6751,plain,
( spl30_586
| ~ spl30_108
| ~ spl30_411 ),
inference(avatar_split_clause,[],[f4446,f4107,f981,f6749]) ).
fof(f6749,plain,
( spl30_586
<=> ! [X0] :
( empty(sK2(X0))
| empty(X0)
| ~ in(X0,sK4(sK2(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_586])]) ).
fof(f4446,plain,
( ! [X0] :
( empty(sK2(X0))
| empty(X0)
| ~ in(X0,sK4(sK2(X0))) )
| ~ spl30_108
| ~ spl30_411 ),
inference(resolution,[],[f4108,f982]) ).
fof(f6747,plain,
( spl30_585
| ~ spl30_108
| ~ spl30_410 ),
inference(avatar_split_clause,[],[f4431,f4103,f981,f6745]) ).
fof(f6745,plain,
( spl30_585
<=> ! [X0] :
( empty(sK1(X0))
| empty(X0)
| ~ in(X0,sK4(sK1(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_585])]) ).
fof(f4431,plain,
( ! [X0] :
( empty(sK1(X0))
| empty(X0)
| ~ in(X0,sK4(sK1(X0))) )
| ~ spl30_108
| ~ spl30_410 ),
inference(resolution,[],[f4104,f982]) ).
fof(f6743,plain,
( spl30_584
| ~ spl30_98
| ~ spl30_398 ),
inference(avatar_split_clause,[],[f4026,f3896,f911,f6741]) ).
fof(f6741,plain,
( spl30_584
<=> ! [X0] :
( sK10 = relation_dom(relation_rng(sK4(powerset(relation_rng(X0)))))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_584])]) ).
fof(f4026,plain,
( ! [X0] :
( sK10 = relation_dom(relation_rng(sK4(powerset(relation_rng(X0)))))
| ~ empty(X0) )
| ~ spl30_98
| ~ spl30_398 ),
inference(resolution,[],[f3897,f912]) ).
fof(f6739,plain,
( spl30_583
| ~ spl30_101
| ~ spl30_398 ),
inference(avatar_split_clause,[],[f4025,f3896,f924,f6737]) ).
fof(f6737,plain,
( spl30_583
<=> ! [X0] :
( sK10 = relation_dom(relation_rng(sK4(powerset(relation_dom(X0)))))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_583])]) ).
fof(f4025,plain,
( ! [X0] :
( sK10 = relation_dom(relation_rng(sK4(powerset(relation_dom(X0)))))
| ~ empty(X0) )
| ~ spl30_101
| ~ spl30_398 ),
inference(resolution,[],[f3897,f925]) ).
fof(f6735,plain,
( spl30_582
| ~ spl30_98
| ~ spl30_397 ),
inference(avatar_split_clause,[],[f3991,f3892,f911,f6733]) ).
fof(f6733,plain,
( spl30_582
<=> ! [X0] :
( sK10 = relation_dom(relation_dom(sK4(powerset(relation_rng(X0)))))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_582])]) ).
fof(f3991,plain,
( ! [X0] :
( sK10 = relation_dom(relation_dom(sK4(powerset(relation_rng(X0)))))
| ~ empty(X0) )
| ~ spl30_98
| ~ spl30_397 ),
inference(resolution,[],[f3893,f912]) ).
fof(f6731,plain,
( spl30_581
| ~ spl30_101
| ~ spl30_397 ),
inference(avatar_split_clause,[],[f3990,f3892,f924,f6729]) ).
fof(f6729,plain,
( spl30_581
<=> ! [X0] :
( sK10 = relation_dom(relation_dom(sK4(powerset(relation_dom(X0)))))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_581])]) ).
fof(f3990,plain,
( ! [X0] :
( sK10 = relation_dom(relation_dom(sK4(powerset(relation_dom(X0)))))
| ~ empty(X0) )
| ~ spl30_101
| ~ spl30_397 ),
inference(resolution,[],[f3893,f925]) ).
fof(f6727,plain,
( spl30_580
| ~ spl30_98
| ~ spl30_395 ),
inference(avatar_split_clause,[],[f4113,f3884,f911,f6725]) ).
fof(f6725,plain,
( spl30_580
<=> ! [X0] :
( sK10 = sK4(powerset(relation_dom(relation_rng(X0))))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_580])]) ).
fof(f4113,plain,
( ! [X0] :
( sK10 = sK4(powerset(relation_dom(relation_rng(X0))))
| ~ empty(X0) )
| ~ spl30_98
| ~ spl30_395 ),
inference(resolution,[],[f3885,f912]) ).
fof(f6723,plain,
( spl30_579
| ~ spl30_98
| ~ spl30_396 ),
inference(avatar_split_clause,[],[f3956,f3888,f911,f6721]) ).
fof(f6721,plain,
( spl30_579
<=> ! [X0] :
( sK10 = relation_rng(relation_rng(sK4(powerset(relation_rng(X0)))))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_579])]) ).
fof(f3956,plain,
( ! [X0] :
( sK10 = relation_rng(relation_rng(sK4(powerset(relation_rng(X0)))))
| ~ empty(X0) )
| ~ spl30_98
| ~ spl30_396 ),
inference(resolution,[],[f3889,f912]) ).
fof(f6719,plain,
( spl30_578
| ~ spl30_101
| ~ spl30_396 ),
inference(avatar_split_clause,[],[f3955,f3888,f924,f6717]) ).
fof(f6717,plain,
( spl30_578
<=> ! [X0] :
( sK10 = relation_rng(relation_rng(sK4(powerset(relation_dom(X0)))))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_578])]) ).
fof(f3955,plain,
( ! [X0] :
( sK10 = relation_rng(relation_rng(sK4(powerset(relation_dom(X0)))))
| ~ empty(X0) )
| ~ spl30_101
| ~ spl30_396 ),
inference(resolution,[],[f3889,f925]) ).
fof(f6715,plain,
( spl30_577
| ~ spl30_98
| ~ spl30_394 ),
inference(avatar_split_clause,[],[f3921,f3880,f911,f6713]) ).
fof(f6713,plain,
( spl30_577
<=> ! [X0] :
( sK10 = relation_rng(relation_dom(sK4(powerset(relation_rng(X0)))))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_577])]) ).
fof(f3921,plain,
( ! [X0] :
( sK10 = relation_rng(relation_dom(sK4(powerset(relation_rng(X0)))))
| ~ empty(X0) )
| ~ spl30_98
| ~ spl30_394 ),
inference(resolution,[],[f3881,f912]) ).
fof(f6711,plain,
( spl30_576
| ~ spl30_101
| ~ spl30_394 ),
inference(avatar_split_clause,[],[f3920,f3880,f924,f6709]) ).
fof(f6709,plain,
( spl30_576
<=> ! [X0] :
( sK10 = relation_rng(relation_dom(sK4(powerset(relation_dom(X0)))))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_576])]) ).
fof(f3920,plain,
( ! [X0] :
( sK10 = relation_rng(relation_dom(sK4(powerset(relation_dom(X0)))))
| ~ empty(X0) )
| ~ spl30_101
| ~ spl30_394 ),
inference(resolution,[],[f3881,f925]) ).
fof(f6707,plain,
( spl30_575
| ~ spl30_98
| ~ spl30_393 ),
inference(avatar_split_clause,[],[f3902,f3876,f911,f6705]) ).
fof(f6705,plain,
( spl30_575
<=> ! [X0,X1] :
( sK4(powerset(X0)) = relation_rng(X1)
| ~ empty(X0)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_575])]) ).
fof(f3902,plain,
( ! [X0,X1] :
( sK4(powerset(X0)) = relation_rng(X1)
| ~ empty(X0)
| ~ empty(X1) )
| ~ spl30_98
| ~ spl30_393 ),
inference(resolution,[],[f3877,f912]) ).
fof(f6703,plain,
( spl30_574
| ~ spl30_101
| ~ spl30_393 ),
inference(avatar_split_clause,[],[f3901,f3876,f924,f6701]) ).
fof(f6701,plain,
( spl30_574
<=> ! [X0,X1] :
( sK4(powerset(X0)) = relation_dom(X1)
| ~ empty(X0)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_574])]) ).
fof(f3901,plain,
( ! [X0,X1] :
( sK4(powerset(X0)) = relation_dom(X1)
| ~ empty(X0)
| ~ empty(X1) )
| ~ spl30_101
| ~ spl30_393 ),
inference(resolution,[],[f3877,f925]) ).
fof(f6699,plain,
( spl30_573
| ~ spl30_289
| ~ spl30_387 ),
inference(avatar_split_clause,[],[f3844,f3499,f2470,f6697]) ).
fof(f6697,plain,
( spl30_573
<=> ! [X0] :
( sK10 = relation_dom(relation_rng(relation_rng(sK4(powerset(X0)))))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_573])]) ).
fof(f3499,plain,
( spl30_387
<=> ! [X0] :
( sK10 = relation_dom(relation_rng(relation_rng(X0)))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_387])]) ).
fof(f3844,plain,
( ! [X0] :
( sK10 = relation_dom(relation_rng(relation_rng(sK4(powerset(X0)))))
| ~ empty(X0) )
| ~ spl30_289
| ~ spl30_387 ),
inference(resolution,[],[f3500,f2471]) ).
fof(f3500,plain,
( ! [X0] :
( ~ empty(X0)
| sK10 = relation_dom(relation_rng(relation_rng(X0))) )
| ~ spl30_387 ),
inference(avatar_component_clause,[],[f3499]) ).
fof(f6695,plain,
( spl30_572
| ~ spl30_289
| ~ spl30_386 ),
inference(avatar_split_clause,[],[f3809,f3495,f2470,f6693]) ).
fof(f6693,plain,
( spl30_572
<=> ! [X0] :
( sK10 = relation_dom(relation_rng(relation_dom(sK4(powerset(X0)))))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_572])]) ).
fof(f3495,plain,
( spl30_386
<=> ! [X0] :
( sK10 = relation_dom(relation_rng(relation_dom(X0)))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_386])]) ).
fof(f3809,plain,
( ! [X0] :
( sK10 = relation_dom(relation_rng(relation_dom(sK4(powerset(X0)))))
| ~ empty(X0) )
| ~ spl30_289
| ~ spl30_386 ),
inference(resolution,[],[f3496,f2471]) ).
fof(f3496,plain,
( ! [X0] :
( ~ empty(X0)
| sK10 = relation_dom(relation_rng(relation_dom(X0))) )
| ~ spl30_386 ),
inference(avatar_component_clause,[],[f3495]) ).
fof(f6691,plain,
( spl30_571
| ~ spl30_289
| ~ spl30_385 ),
inference(avatar_split_clause,[],[f3774,f3491,f2470,f6689]) ).
fof(f6689,plain,
( spl30_571
<=> ! [X0] :
( sK10 = relation_dom(relation_dom(relation_rng(sK4(powerset(X0)))))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_571])]) ).
fof(f3491,plain,
( spl30_385
<=> ! [X0] :
( sK10 = relation_dom(relation_dom(relation_rng(X0)))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_385])]) ).
fof(f3774,plain,
( ! [X0] :
( sK10 = relation_dom(relation_dom(relation_rng(sK4(powerset(X0)))))
| ~ empty(X0) )
| ~ spl30_289
| ~ spl30_385 ),
inference(resolution,[],[f3492,f2471]) ).
fof(f3492,plain,
( ! [X0] :
( ~ empty(X0)
| sK10 = relation_dom(relation_dom(relation_rng(X0))) )
| ~ spl30_385 ),
inference(avatar_component_clause,[],[f3491]) ).
fof(f6687,plain,
( spl30_570
| ~ spl30_289
| ~ spl30_384 ),
inference(avatar_split_clause,[],[f3739,f3487,f2470,f6685]) ).
fof(f6685,plain,
( spl30_570
<=> ! [X0] :
( sK10 = relation_dom(relation_dom(relation_dom(sK4(powerset(X0)))))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_570])]) ).
fof(f3487,plain,
( spl30_384
<=> ! [X0] :
( sK10 = relation_dom(relation_dom(relation_dom(X0)))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_384])]) ).
fof(f3739,plain,
( ! [X0] :
( sK10 = relation_dom(relation_dom(relation_dom(sK4(powerset(X0)))))
| ~ empty(X0) )
| ~ spl30_289
| ~ spl30_384 ),
inference(resolution,[],[f3488,f2471]) ).
fof(f3488,plain,
( ! [X0] :
( ~ empty(X0)
| sK10 = relation_dom(relation_dom(relation_dom(X0))) )
| ~ spl30_384 ),
inference(avatar_component_clause,[],[f3487]) ).
fof(f6683,plain,
( spl30_569
| ~ spl30_101
| ~ spl30_395 ),
inference(avatar_split_clause,[],[f4112,f3884,f924,f6681]) ).
fof(f6681,plain,
( spl30_569
<=> ! [X0] :
( sK10 = sK4(powerset(relation_dom(relation_dom(X0))))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_569])]) ).
fof(f4112,plain,
( ! [X0] :
( sK10 = sK4(powerset(relation_dom(relation_dom(X0))))
| ~ empty(X0) )
| ~ spl30_101
| ~ spl30_395 ),
inference(resolution,[],[f3885,f925]) ).
fof(f6679,plain,
( spl30_568
| ~ spl30_289
| ~ spl30_383 ),
inference(avatar_split_clause,[],[f3686,f3483,f2470,f6677]) ).
fof(f6677,plain,
( spl30_568
<=> ! [X0] :
( sK10 = relation_rng(relation_rng(relation_rng(sK4(powerset(X0)))))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_568])]) ).
fof(f3483,plain,
( spl30_383
<=> ! [X0] :
( sK10 = relation_rng(relation_rng(relation_rng(X0)))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_383])]) ).
fof(f3686,plain,
( ! [X0] :
( sK10 = relation_rng(relation_rng(relation_rng(sK4(powerset(X0)))))
| ~ empty(X0) )
| ~ spl30_289
| ~ spl30_383 ),
inference(resolution,[],[f3484,f2471]) ).
fof(f3484,plain,
( ! [X0] :
( ~ empty(X0)
| sK10 = relation_rng(relation_rng(relation_rng(X0))) )
| ~ spl30_383 ),
inference(avatar_component_clause,[],[f3483]) ).
fof(f6675,plain,
( spl30_567
| ~ spl30_289
| ~ spl30_382 ),
inference(avatar_split_clause,[],[f3651,f3479,f2470,f6673]) ).
fof(f6673,plain,
( spl30_567
<=> ! [X0] :
( sK10 = relation_rng(relation_rng(relation_dom(sK4(powerset(X0)))))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_567])]) ).
fof(f3479,plain,
( spl30_382
<=> ! [X0] :
( sK10 = relation_rng(relation_rng(relation_dom(X0)))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_382])]) ).
fof(f3651,plain,
( ! [X0] :
( sK10 = relation_rng(relation_rng(relation_dom(sK4(powerset(X0)))))
| ~ empty(X0) )
| ~ spl30_289
| ~ spl30_382 ),
inference(resolution,[],[f3480,f2471]) ).
fof(f3480,plain,
( ! [X0] :
( ~ empty(X0)
| sK10 = relation_rng(relation_rng(relation_dom(X0))) )
| ~ spl30_382 ),
inference(avatar_component_clause,[],[f3479]) ).
fof(f6671,plain,
( spl30_566
| ~ spl30_289
| ~ spl30_381 ),
inference(avatar_split_clause,[],[f3616,f3475,f2470,f6669]) ).
fof(f6669,plain,
( spl30_566
<=> ! [X0] :
( sK10 = relation_rng(relation_dom(relation_rng(sK4(powerset(X0)))))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_566])]) ).
fof(f3475,plain,
( spl30_381
<=> ! [X0] :
( sK10 = relation_rng(relation_dom(relation_rng(X0)))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_381])]) ).
fof(f3616,plain,
( ! [X0] :
( sK10 = relation_rng(relation_dom(relation_rng(sK4(powerset(X0)))))
| ~ empty(X0) )
| ~ spl30_289
| ~ spl30_381 ),
inference(resolution,[],[f3476,f2471]) ).
fof(f3476,plain,
( ! [X0] :
( ~ empty(X0)
| sK10 = relation_rng(relation_dom(relation_rng(X0))) )
| ~ spl30_381 ),
inference(avatar_component_clause,[],[f3475]) ).
fof(f6667,plain,
( spl30_565
| ~ spl30_289
| ~ spl30_380 ),
inference(avatar_split_clause,[],[f3581,f3471,f2470,f6665]) ).
fof(f6665,plain,
( spl30_565
<=> ! [X0] :
( sK10 = relation_rng(relation_dom(relation_dom(sK4(powerset(X0)))))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_565])]) ).
fof(f3471,plain,
( spl30_380
<=> ! [X0] :
( sK10 = relation_rng(relation_dom(relation_dom(X0)))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_380])]) ).
fof(f3581,plain,
( ! [X0] :
( sK10 = relation_rng(relation_dom(relation_dom(sK4(powerset(X0)))))
| ~ empty(X0) )
| ~ spl30_289
| ~ spl30_380 ),
inference(resolution,[],[f3472,f2471]) ).
fof(f3472,plain,
( ! [X0] :
( ~ empty(X0)
| sK10 = relation_rng(relation_dom(relation_dom(X0))) )
| ~ spl30_380 ),
inference(avatar_component_clause,[],[f3471]) ).
fof(f6663,plain,
( spl30_564
| ~ spl30_289
| ~ spl30_379 ),
inference(avatar_split_clause,[],[f3554,f3467,f2470,f6661]) ).
fof(f6661,plain,
( spl30_564
<=> ! [X0] :
( sK10 = relation_dom(sK4(powerset(sK4(powerset(X0)))))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_564])]) ).
fof(f3467,plain,
( spl30_379
<=> ! [X0] :
( ~ empty(X0)
| sK10 = relation_dom(sK4(powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_379])]) ).
fof(f3554,plain,
( ! [X0] :
( sK10 = relation_dom(sK4(powerset(sK4(powerset(X0)))))
| ~ empty(X0) )
| ~ spl30_289
| ~ spl30_379 ),
inference(resolution,[],[f3468,f2471]) ).
fof(f3468,plain,
( ! [X0] :
( ~ empty(X0)
| sK10 = relation_dom(sK4(powerset(X0))) )
| ~ spl30_379 ),
inference(avatar_component_clause,[],[f3467]) ).
fof(f6659,plain,
( spl30_563
| ~ spl30_289
| ~ spl30_378 ),
inference(avatar_split_clause,[],[f3527,f3463,f2470,f6657]) ).
fof(f6657,plain,
( spl30_563
<=> ! [X0] :
( sK10 = relation_rng(sK4(powerset(sK4(powerset(X0)))))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_563])]) ).
fof(f3463,plain,
( spl30_378
<=> ! [X0] :
( ~ empty(X0)
| sK10 = relation_rng(sK4(powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_378])]) ).
fof(f3527,plain,
( ! [X0] :
( sK10 = relation_rng(sK4(powerset(sK4(powerset(X0)))))
| ~ empty(X0) )
| ~ spl30_289
| ~ spl30_378 ),
inference(resolution,[],[f3464,f2471]) ).
fof(f3464,plain,
( ! [X0] :
( ~ empty(X0)
| sK10 = relation_rng(sK4(powerset(X0))) )
| ~ spl30_378 ),
inference(avatar_component_clause,[],[f3463]) ).
fof(f5800,plain,
( spl30_562
| ~ spl30_98
| ~ spl30_387 ),
inference(avatar_split_clause,[],[f3843,f3499,f911,f5798]) ).
fof(f5798,plain,
( spl30_562
<=> ! [X0] :
( sK10 = relation_dom(relation_rng(relation_rng(relation_rng(X0))))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_562])]) ).
fof(f3843,plain,
( ! [X0] :
( sK10 = relation_dom(relation_rng(relation_rng(relation_rng(X0))))
| ~ empty(X0) )
| ~ spl30_98
| ~ spl30_387 ),
inference(resolution,[],[f3500,f912]) ).
fof(f5796,plain,
( spl30_561
| ~ spl30_101
| ~ spl30_387 ),
inference(avatar_split_clause,[],[f3842,f3499,f924,f5794]) ).
fof(f5794,plain,
( spl30_561
<=> ! [X0] :
( sK10 = relation_dom(relation_rng(relation_rng(relation_dom(X0))))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_561])]) ).
fof(f3842,plain,
( ! [X0] :
( sK10 = relation_dom(relation_rng(relation_rng(relation_dom(X0))))
| ~ empty(X0) )
| ~ spl30_101
| ~ spl30_387 ),
inference(resolution,[],[f3500,f925]) ).
fof(f5792,plain,
( spl30_560
| ~ spl30_98
| ~ spl30_386 ),
inference(avatar_split_clause,[],[f3808,f3495,f911,f5790]) ).
fof(f5790,plain,
( spl30_560
<=> ! [X0] :
( sK10 = relation_dom(relation_rng(relation_dom(relation_rng(X0))))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_560])]) ).
fof(f3808,plain,
( ! [X0] :
( sK10 = relation_dom(relation_rng(relation_dom(relation_rng(X0))))
| ~ empty(X0) )
| ~ spl30_98
| ~ spl30_386 ),
inference(resolution,[],[f3496,f912]) ).
fof(f5788,plain,
( spl30_559
| ~ spl30_101
| ~ spl30_386 ),
inference(avatar_split_clause,[],[f3807,f3495,f924,f5786]) ).
fof(f5786,plain,
( spl30_559
<=> ! [X0] :
( sK10 = relation_dom(relation_rng(relation_dom(relation_dom(X0))))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_559])]) ).
fof(f3807,plain,
( ! [X0] :
( sK10 = relation_dom(relation_rng(relation_dom(relation_dom(X0))))
| ~ empty(X0) )
| ~ spl30_101
| ~ spl30_386 ),
inference(resolution,[],[f3496,f925]) ).
fof(f5784,plain,
( spl30_558
| ~ spl30_98
| ~ spl30_385 ),
inference(avatar_split_clause,[],[f3773,f3491,f911,f5782]) ).
fof(f5782,plain,
( spl30_558
<=> ! [X0] :
( sK10 = relation_dom(relation_dom(relation_rng(relation_rng(X0))))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_558])]) ).
fof(f3773,plain,
( ! [X0] :
( sK10 = relation_dom(relation_dom(relation_rng(relation_rng(X0))))
| ~ empty(X0) )
| ~ spl30_98
| ~ spl30_385 ),
inference(resolution,[],[f3492,f912]) ).
fof(f5780,plain,
( spl30_557
| ~ spl30_101
| ~ spl30_385 ),
inference(avatar_split_clause,[],[f3772,f3491,f924,f5778]) ).
fof(f5778,plain,
( spl30_557
<=> ! [X0] :
( sK10 = relation_dom(relation_dom(relation_rng(relation_dom(X0))))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_557])]) ).
fof(f3772,plain,
( ! [X0] :
( sK10 = relation_dom(relation_dom(relation_rng(relation_dom(X0))))
| ~ empty(X0) )
| ~ spl30_101
| ~ spl30_385 ),
inference(resolution,[],[f3492,f925]) ).
fof(f5776,plain,
( spl30_556
| ~ spl30_98
| ~ spl30_384 ),
inference(avatar_split_clause,[],[f3738,f3487,f911,f5774]) ).
fof(f5774,plain,
( spl30_556
<=> ! [X0] :
( sK10 = relation_dom(relation_dom(relation_dom(relation_rng(X0))))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_556])]) ).
fof(f3738,plain,
( ! [X0] :
( sK10 = relation_dom(relation_dom(relation_dom(relation_rng(X0))))
| ~ empty(X0) )
| ~ spl30_98
| ~ spl30_384 ),
inference(resolution,[],[f3488,f912]) ).
fof(f5772,plain,
( spl30_555
| ~ spl30_101
| ~ spl30_384 ),
inference(avatar_split_clause,[],[f3737,f3487,f924,f5770]) ).
fof(f5770,plain,
( spl30_555
<=> ! [X0] :
( sK10 = relation_dom(relation_dom(relation_dom(relation_dom(X0))))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_555])]) ).
fof(f3737,plain,
( ! [X0] :
( sK10 = relation_dom(relation_dom(relation_dom(relation_dom(X0))))
| ~ empty(X0) )
| ~ spl30_101
| ~ spl30_384 ),
inference(resolution,[],[f3488,f925]) ).
fof(f5768,plain,
( spl30_554
| ~ spl30_98
| ~ spl30_383 ),
inference(avatar_split_clause,[],[f3685,f3483,f911,f5766]) ).
fof(f5766,plain,
( spl30_554
<=> ! [X0] :
( sK10 = relation_rng(relation_rng(relation_rng(relation_rng(X0))))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_554])]) ).
fof(f3685,plain,
( ! [X0] :
( sK10 = relation_rng(relation_rng(relation_rng(relation_rng(X0))))
| ~ empty(X0) )
| ~ spl30_98
| ~ spl30_383 ),
inference(resolution,[],[f3484,f912]) ).
fof(f5764,plain,
( spl30_553
| ~ spl30_101
| ~ spl30_383 ),
inference(avatar_split_clause,[],[f3684,f3483,f924,f5762]) ).
fof(f5762,plain,
( spl30_553
<=> ! [X0] :
( sK10 = relation_rng(relation_rng(relation_rng(relation_dom(X0))))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_553])]) ).
fof(f3684,plain,
( ! [X0] :
( sK10 = relation_rng(relation_rng(relation_rng(relation_dom(X0))))
| ~ empty(X0) )
| ~ spl30_101
| ~ spl30_383 ),
inference(resolution,[],[f3484,f925]) ).
fof(f5760,plain,
( spl30_552
| ~ spl30_98
| ~ spl30_382 ),
inference(avatar_split_clause,[],[f3650,f3479,f911,f5758]) ).
fof(f5758,plain,
( spl30_552
<=> ! [X0] :
( sK10 = relation_rng(relation_rng(relation_dom(relation_rng(X0))))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_552])]) ).
fof(f3650,plain,
( ! [X0] :
( sK10 = relation_rng(relation_rng(relation_dom(relation_rng(X0))))
| ~ empty(X0) )
| ~ spl30_98
| ~ spl30_382 ),
inference(resolution,[],[f3480,f912]) ).
fof(f5756,plain,
( spl30_551
| ~ spl30_101
| ~ spl30_382 ),
inference(avatar_split_clause,[],[f3649,f3479,f924,f5754]) ).
fof(f5754,plain,
( spl30_551
<=> ! [X0] :
( sK10 = relation_rng(relation_rng(relation_dom(relation_dom(X0))))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_551])]) ).
fof(f3649,plain,
( ! [X0] :
( sK10 = relation_rng(relation_rng(relation_dom(relation_dom(X0))))
| ~ empty(X0) )
| ~ spl30_101
| ~ spl30_382 ),
inference(resolution,[],[f3480,f925]) ).
fof(f5752,plain,
( spl30_550
| ~ spl30_98
| ~ spl30_381 ),
inference(avatar_split_clause,[],[f3615,f3475,f911,f5750]) ).
fof(f5750,plain,
( spl30_550
<=> ! [X0] :
( sK10 = relation_rng(relation_dom(relation_rng(relation_rng(X0))))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_550])]) ).
fof(f3615,plain,
( ! [X0] :
( sK10 = relation_rng(relation_dom(relation_rng(relation_rng(X0))))
| ~ empty(X0) )
| ~ spl30_98
| ~ spl30_381 ),
inference(resolution,[],[f3476,f912]) ).
fof(f5748,plain,
( spl30_549
| ~ spl30_101
| ~ spl30_381 ),
inference(avatar_split_clause,[],[f3614,f3475,f924,f5746]) ).
fof(f5746,plain,
( spl30_549
<=> ! [X0] :
( sK10 = relation_rng(relation_dom(relation_rng(relation_dom(X0))))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_549])]) ).
fof(f3614,plain,
( ! [X0] :
( sK10 = relation_rng(relation_dom(relation_rng(relation_dom(X0))))
| ~ empty(X0) )
| ~ spl30_101
| ~ spl30_381 ),
inference(resolution,[],[f3476,f925]) ).
fof(f5744,plain,
( spl30_548
| ~ spl30_98
| ~ spl30_380 ),
inference(avatar_split_clause,[],[f3580,f3471,f911,f5742]) ).
fof(f5742,plain,
( spl30_548
<=> ! [X0] :
( sK10 = relation_rng(relation_dom(relation_dom(relation_rng(X0))))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_548])]) ).
fof(f3580,plain,
( ! [X0] :
( sK10 = relation_rng(relation_dom(relation_dom(relation_rng(X0))))
| ~ empty(X0) )
| ~ spl30_98
| ~ spl30_380 ),
inference(resolution,[],[f3472,f912]) ).
fof(f5740,plain,
( spl30_547
| ~ spl30_101
| ~ spl30_380 ),
inference(avatar_split_clause,[],[f3579,f3471,f924,f5738]) ).
fof(f5738,plain,
( spl30_547
<=> ! [X0] :
( sK10 = relation_rng(relation_dom(relation_dom(relation_dom(X0))))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_547])]) ).
fof(f3579,plain,
( ! [X0] :
( sK10 = relation_rng(relation_dom(relation_dom(relation_dom(X0))))
| ~ empty(X0) )
| ~ spl30_101
| ~ spl30_380 ),
inference(resolution,[],[f3472,f925]) ).
fof(f5736,plain,
( spl30_546
| ~ spl30_98
| ~ spl30_379 ),
inference(avatar_split_clause,[],[f3553,f3467,f911,f5734]) ).
fof(f5734,plain,
( spl30_546
<=> ! [X0] :
( sK10 = relation_dom(sK4(powerset(relation_rng(X0))))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_546])]) ).
fof(f3553,plain,
( ! [X0] :
( sK10 = relation_dom(sK4(powerset(relation_rng(X0))))
| ~ empty(X0) )
| ~ spl30_98
| ~ spl30_379 ),
inference(resolution,[],[f3468,f912]) ).
fof(f5732,plain,
( spl30_545
| ~ spl30_101
| ~ spl30_379 ),
inference(avatar_split_clause,[],[f3552,f3467,f924,f5730]) ).
fof(f3552,plain,
( ! [X0] :
( sK10 = relation_dom(sK4(powerset(relation_dom(X0))))
| ~ empty(X0) )
| ~ spl30_101
| ~ spl30_379 ),
inference(resolution,[],[f3468,f925]) ).
fof(f5726,plain,
( spl30_544
| ~ spl30_333
| ~ spl30_341 ),
inference(avatar_split_clause,[],[f3177,f3164,f3018,f5724]) ).
fof(f5724,plain,
( spl30_544
<=> ! [X0,X1] :
( ~ in(powerset(relation_dom(first_projection_as_func_of(X0,X1))),relation_dom(first_projection_as_func_of(X0,X1)))
| ~ function(first_projection_as_func_of(relation_dom(first_projection_as_func_of(X0,X1)),relation_rng(first_projection_as_func_of(X0,X1))))
| empty(powerset(relation_dom(first_projection_as_func_of(X0,X1))))
| ~ relation_of2(first_projection_as_func_of(relation_dom(first_projection_as_func_of(X0,X1)),relation_rng(first_projection_as_func_of(X0,X1))),cartesian_product2(relation_dom(first_projection_as_func_of(X0,X1)),relation_rng(first_projection_as_func_of(X0,X1))),relation_dom(first_projection_as_func_of(X0,X1)))
| ~ quasi_total(first_projection_as_func_of(relation_dom(first_projection_as_func_of(X0,X1)),relation_rng(first_projection_as_func_of(X0,X1))),cartesian_product2(relation_dom(first_projection_as_func_of(X0,X1)),relation_rng(first_projection_as_func_of(X0,X1))),relation_dom(first_projection_as_func_of(X0,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_544])]) ).
fof(f3018,plain,
( spl30_333
<=> ! [X0,X3,X2,X1] :
( ~ quasi_total(X0,X1,X2)
| ~ function(X0)
| empty(powerset(X2))
| ~ relation_of2(X0,X1,X2)
| ~ in(powerset(X2),function_image(X1,X2,X0,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_333])]) ).
fof(f3164,plain,
( spl30_341
<=> ! [X0,X1] : relation_dom(first_projection_as_func_of(X0,X1)) = function_image(cartesian_product2(relation_dom(first_projection_as_func_of(X0,X1)),relation_rng(first_projection_as_func_of(X0,X1))),relation_dom(first_projection_as_func_of(X0,X1)),first_projection_as_func_of(relation_dom(first_projection_as_func_of(X0,X1)),relation_rng(first_projection_as_func_of(X0,X1))),first_projection_as_func_of(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_341])]) ).
fof(f3177,plain,
( ! [X0,X1] :
( ~ in(powerset(relation_dom(first_projection_as_func_of(X0,X1))),relation_dom(first_projection_as_func_of(X0,X1)))
| ~ function(first_projection_as_func_of(relation_dom(first_projection_as_func_of(X0,X1)),relation_rng(first_projection_as_func_of(X0,X1))))
| empty(powerset(relation_dom(first_projection_as_func_of(X0,X1))))
| ~ relation_of2(first_projection_as_func_of(relation_dom(first_projection_as_func_of(X0,X1)),relation_rng(first_projection_as_func_of(X0,X1))),cartesian_product2(relation_dom(first_projection_as_func_of(X0,X1)),relation_rng(first_projection_as_func_of(X0,X1))),relation_dom(first_projection_as_func_of(X0,X1)))
| ~ quasi_total(first_projection_as_func_of(relation_dom(first_projection_as_func_of(X0,X1)),relation_rng(first_projection_as_func_of(X0,X1))),cartesian_product2(relation_dom(first_projection_as_func_of(X0,X1)),relation_rng(first_projection_as_func_of(X0,X1))),relation_dom(first_projection_as_func_of(X0,X1))) )
| ~ spl30_333
| ~ spl30_341 ),
inference(superposition,[],[f3019,f3165]) ).
fof(f3165,plain,
( ! [X0,X1] : relation_dom(first_projection_as_func_of(X0,X1)) = function_image(cartesian_product2(relation_dom(first_projection_as_func_of(X0,X1)),relation_rng(first_projection_as_func_of(X0,X1))),relation_dom(first_projection_as_func_of(X0,X1)),first_projection_as_func_of(relation_dom(first_projection_as_func_of(X0,X1)),relation_rng(first_projection_as_func_of(X0,X1))),first_projection_as_func_of(X0,X1))
| ~ spl30_341 ),
inference(avatar_component_clause,[],[f3164]) ).
fof(f3019,plain,
( ! [X2,X3,X0,X1] :
( ~ in(powerset(X2),function_image(X1,X2,X0,X3))
| ~ function(X0)
| empty(powerset(X2))
| ~ relation_of2(X0,X1,X2)
| ~ quasi_total(X0,X1,X2) )
| ~ spl30_333 ),
inference(avatar_component_clause,[],[f3018]) ).
fof(f5722,plain,
( spl30_543
| ~ spl30_279
| ~ spl30_341 ),
inference(avatar_split_clause,[],[f3175,f3164,f2406,f5720]) ).
fof(f5720,plain,
( spl30_543
<=> ! [X0,X1] :
( in(relation_dom(first_projection_as_func_of(X0,X1)),powerset(relation_dom(first_projection_as_func_of(X0,X1))))
| ~ quasi_total(first_projection_as_func_of(relation_dom(first_projection_as_func_of(X0,X1)),relation_rng(first_projection_as_func_of(X0,X1))),cartesian_product2(relation_dom(first_projection_as_func_of(X0,X1)),relation_rng(first_projection_as_func_of(X0,X1))),relation_dom(first_projection_as_func_of(X0,X1)))
| ~ function(first_projection_as_func_of(relation_dom(first_projection_as_func_of(X0,X1)),relation_rng(first_projection_as_func_of(X0,X1))))
| empty(powerset(relation_dom(first_projection_as_func_of(X0,X1))))
| ~ relation_of2(first_projection_as_func_of(relation_dom(first_projection_as_func_of(X0,X1)),relation_rng(first_projection_as_func_of(X0,X1))),cartesian_product2(relation_dom(first_projection_as_func_of(X0,X1)),relation_rng(first_projection_as_func_of(X0,X1))),relation_dom(first_projection_as_func_of(X0,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_543])]) ).
fof(f2406,plain,
( spl30_279
<=> ! [X0,X3,X2,X1] :
( ~ relation_of2(X0,X1,X2)
| ~ quasi_total(X0,X1,X2)
| ~ function(X0)
| empty(powerset(X2))
| in(function_image(X1,X2,X0,X3),powerset(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_279])]) ).
fof(f3175,plain,
( ! [X0,X1] :
( in(relation_dom(first_projection_as_func_of(X0,X1)),powerset(relation_dom(first_projection_as_func_of(X0,X1))))
| ~ quasi_total(first_projection_as_func_of(relation_dom(first_projection_as_func_of(X0,X1)),relation_rng(first_projection_as_func_of(X0,X1))),cartesian_product2(relation_dom(first_projection_as_func_of(X0,X1)),relation_rng(first_projection_as_func_of(X0,X1))),relation_dom(first_projection_as_func_of(X0,X1)))
| ~ function(first_projection_as_func_of(relation_dom(first_projection_as_func_of(X0,X1)),relation_rng(first_projection_as_func_of(X0,X1))))
| empty(powerset(relation_dom(first_projection_as_func_of(X0,X1))))
| ~ relation_of2(first_projection_as_func_of(relation_dom(first_projection_as_func_of(X0,X1)),relation_rng(first_projection_as_func_of(X0,X1))),cartesian_product2(relation_dom(first_projection_as_func_of(X0,X1)),relation_rng(first_projection_as_func_of(X0,X1))),relation_dom(first_projection_as_func_of(X0,X1))) )
| ~ spl30_279
| ~ spl30_341 ),
inference(superposition,[],[f2407,f3165]) ).
fof(f2407,plain,
( ! [X2,X3,X0,X1] :
( in(function_image(X1,X2,X0,X3),powerset(X2))
| ~ quasi_total(X0,X1,X2)
| ~ function(X0)
| empty(powerset(X2))
| ~ relation_of2(X0,X1,X2) )
| ~ spl30_279 ),
inference(avatar_component_clause,[],[f2406]) ).
fof(f5717,plain,
( spl30_542
| ~ spl30_149
| ~ spl30_341 ),
inference(avatar_split_clause,[],[f3167,f3164,f1289,f5715]) ).
fof(f5715,plain,
( spl30_542
<=> ! [X0,X1] :
( element(relation_dom(first_projection_as_func_of(X0,X1)),powerset(relation_dom(first_projection_as_func_of(X0,X1))))
| ~ relation_of2(first_projection_as_func_of(relation_dom(first_projection_as_func_of(X0,X1)),relation_rng(first_projection_as_func_of(X0,X1))),cartesian_product2(relation_dom(first_projection_as_func_of(X0,X1)),relation_rng(first_projection_as_func_of(X0,X1))),relation_dom(first_projection_as_func_of(X0,X1)))
| ~ quasi_total(first_projection_as_func_of(relation_dom(first_projection_as_func_of(X0,X1)),relation_rng(first_projection_as_func_of(X0,X1))),cartesian_product2(relation_dom(first_projection_as_func_of(X0,X1)),relation_rng(first_projection_as_func_of(X0,X1))),relation_dom(first_projection_as_func_of(X0,X1)))
| ~ function(first_projection_as_func_of(relation_dom(first_projection_as_func_of(X0,X1)),relation_rng(first_projection_as_func_of(X0,X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_542])]) ).
fof(f1289,plain,
( spl30_149
<=> ! [X0,X3,X2,X1] :
( element(function_image(X0,X1,X2,X3),powerset(X1))
| ~ relation_of2(X2,X0,X1)
| ~ quasi_total(X2,X0,X1)
| ~ function(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_149])]) ).
fof(f3167,plain,
( ! [X0,X1] :
( element(relation_dom(first_projection_as_func_of(X0,X1)),powerset(relation_dom(first_projection_as_func_of(X0,X1))))
| ~ relation_of2(first_projection_as_func_of(relation_dom(first_projection_as_func_of(X0,X1)),relation_rng(first_projection_as_func_of(X0,X1))),cartesian_product2(relation_dom(first_projection_as_func_of(X0,X1)),relation_rng(first_projection_as_func_of(X0,X1))),relation_dom(first_projection_as_func_of(X0,X1)))
| ~ quasi_total(first_projection_as_func_of(relation_dom(first_projection_as_func_of(X0,X1)),relation_rng(first_projection_as_func_of(X0,X1))),cartesian_product2(relation_dom(first_projection_as_func_of(X0,X1)),relation_rng(first_projection_as_func_of(X0,X1))),relation_dom(first_projection_as_func_of(X0,X1)))
| ~ function(first_projection_as_func_of(relation_dom(first_projection_as_func_of(X0,X1)),relation_rng(first_projection_as_func_of(X0,X1)))) )
| ~ spl30_149
| ~ spl30_341 ),
inference(superposition,[],[f1290,f3165]) ).
fof(f1290,plain,
( ! [X2,X3,X0,X1] :
( element(function_image(X0,X1,X2,X3),powerset(X1))
| ~ relation_of2(X2,X0,X1)
| ~ quasi_total(X2,X0,X1)
| ~ function(X2) )
| ~ spl30_149 ),
inference(avatar_component_clause,[],[f1289]) ).
fof(f5709,plain,
( spl30_541
| ~ spl30_89
| ~ spl30_491
| ~ spl30_540 ),
inference(avatar_split_clause,[],[f5705,f5702,f5001,f808,f5707]) ).
fof(f5707,plain,
( spl30_541
<=> ! [X0,X3,X2,X1] :
( relation_dom(relation_rng(function_image(X0,X1,X2,X3))) = relation_image(first_projection_as_func_of(relation_dom(relation_rng(function_image(X0,X1,X2,X3))),relation_rng(relation_rng(function_image(X0,X1,X2,X3)))),relation_rng(function_image(X0,X1,X2,X3)))
| ~ function(X2)
| ~ empty(X1)
| ~ relation_of2(X2,X0,X1)
| ~ quasi_total(X2,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_541])]) ).
fof(f5702,plain,
( spl30_540
<=> ! [X0,X3,X2,X1] :
( relation_dom(relation_rng(function_image(X0,X1,X2,X3))) = function_image(cartesian_product2(relation_dom(relation_rng(function_image(X0,X1,X2,X3))),relation_rng(relation_rng(function_image(X0,X1,X2,X3)))),relation_dom(relation_rng(function_image(X0,X1,X2,X3))),first_projection_as_func_of(relation_dom(relation_rng(function_image(X0,X1,X2,X3))),relation_rng(relation_rng(function_image(X0,X1,X2,X3)))),relation_rng(function_image(X0,X1,X2,X3)))
| ~ function(X2)
| ~ empty(X1)
| ~ relation_of2(X2,X0,X1)
| ~ quasi_total(X2,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_540])]) ).
fof(f5705,plain,
( ! [X2,X3,X0,X1] :
( relation_dom(relation_rng(function_image(X0,X1,X2,X3))) = relation_image(first_projection_as_func_of(relation_dom(relation_rng(function_image(X0,X1,X2,X3))),relation_rng(relation_rng(function_image(X0,X1,X2,X3)))),relation_rng(function_image(X0,X1,X2,X3)))
| ~ function(X2)
| ~ empty(X1)
| ~ relation_of2(X2,X0,X1)
| ~ quasi_total(X2,X0,X1) )
| ~ spl30_89
| ~ spl30_491
| ~ spl30_540 ),
inference(forward_demodulation,[],[f5703,f5010]) ).
fof(f5703,plain,
( ! [X2,X3,X0,X1] :
( relation_dom(relation_rng(function_image(X0,X1,X2,X3))) = function_image(cartesian_product2(relation_dom(relation_rng(function_image(X0,X1,X2,X3))),relation_rng(relation_rng(function_image(X0,X1,X2,X3)))),relation_dom(relation_rng(function_image(X0,X1,X2,X3))),first_projection_as_func_of(relation_dom(relation_rng(function_image(X0,X1,X2,X3))),relation_rng(relation_rng(function_image(X0,X1,X2,X3)))),relation_rng(function_image(X0,X1,X2,X3)))
| ~ function(X2)
| ~ empty(X1)
| ~ relation_of2(X2,X0,X1)
| ~ quasi_total(X2,X0,X1) )
| ~ spl30_540 ),
inference(avatar_component_clause,[],[f5702]) ).
fof(f5704,plain,
( spl30_540
| ~ spl30_332
| ~ spl30_338 ),
inference(avatar_split_clause,[],[f3111,f3065,f2985,f5702]) ).
fof(f2985,plain,
( spl30_332
<=> ! [X0,X3,X2,X1] :
( ~ quasi_total(X0,X1,X2)
| ~ function(X0)
| ~ empty(X2)
| ~ relation_of2(X0,X1,X2)
| empty(function_image(X1,X2,X0,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_332])]) ).
fof(f3065,plain,
( spl30_338
<=> ! [X0] :
( relation_dom(relation_rng(X0)) = function_image(cartesian_product2(relation_dom(relation_rng(X0)),relation_rng(relation_rng(X0))),relation_dom(relation_rng(X0)),first_projection_as_func_of(relation_dom(relation_rng(X0)),relation_rng(relation_rng(X0))),relation_rng(X0))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_338])]) ).
fof(f3111,plain,
( ! [X2,X3,X0,X1] :
( relation_dom(relation_rng(function_image(X0,X1,X2,X3))) = function_image(cartesian_product2(relation_dom(relation_rng(function_image(X0,X1,X2,X3))),relation_rng(relation_rng(function_image(X0,X1,X2,X3)))),relation_dom(relation_rng(function_image(X0,X1,X2,X3))),first_projection_as_func_of(relation_dom(relation_rng(function_image(X0,X1,X2,X3))),relation_rng(relation_rng(function_image(X0,X1,X2,X3)))),relation_rng(function_image(X0,X1,X2,X3)))
| ~ function(X2)
| ~ empty(X1)
| ~ relation_of2(X2,X0,X1)
| ~ quasi_total(X2,X0,X1) )
| ~ spl30_332
| ~ spl30_338 ),
inference(resolution,[],[f3066,f2986]) ).
fof(f2986,plain,
( ! [X2,X3,X0,X1] :
( empty(function_image(X1,X2,X0,X3))
| ~ function(X0)
| ~ empty(X2)
| ~ relation_of2(X0,X1,X2)
| ~ quasi_total(X0,X1,X2) )
| ~ spl30_332 ),
inference(avatar_component_clause,[],[f2985]) ).
fof(f3066,plain,
( ! [X0] :
( ~ empty(X0)
| relation_dom(relation_rng(X0)) = function_image(cartesian_product2(relation_dom(relation_rng(X0)),relation_rng(relation_rng(X0))),relation_dom(relation_rng(X0)),first_projection_as_func_of(relation_dom(relation_rng(X0)),relation_rng(relation_rng(X0))),relation_rng(X0)) )
| ~ spl30_338 ),
inference(avatar_component_clause,[],[f3065]) ).
fof(f5700,plain,
( spl30_539
| ~ spl30_98
| ~ spl30_378 ),
inference(avatar_split_clause,[],[f3526,f3463,f911,f5698]) ).
fof(f3526,plain,
( ! [X0] :
( sK10 = relation_rng(sK4(powerset(relation_rng(X0))))
| ~ empty(X0) )
| ~ spl30_98
| ~ spl30_378 ),
inference(resolution,[],[f3464,f912]) ).
fof(f5692,plain,
( spl30_538
| ~ spl30_89
| ~ spl30_491
| ~ spl30_537 ),
inference(avatar_split_clause,[],[f5688,f5685,f5001,f808,f5690]) ).
fof(f5690,plain,
( spl30_538
<=> ! [X0,X3,X2,X1] :
( relation_dom(relation_dom(function_image(X0,X1,X2,X3))) = relation_image(first_projection_as_func_of(relation_dom(relation_dom(function_image(X0,X1,X2,X3))),relation_rng(relation_dom(function_image(X0,X1,X2,X3)))),relation_dom(function_image(X0,X1,X2,X3)))
| ~ function(X2)
| ~ empty(X1)
| ~ relation_of2(X2,X0,X1)
| ~ quasi_total(X2,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_538])]) ).
fof(f5685,plain,
( spl30_537
<=> ! [X0,X3,X2,X1] :
( relation_dom(relation_dom(function_image(X0,X1,X2,X3))) = function_image(cartesian_product2(relation_dom(relation_dom(function_image(X0,X1,X2,X3))),relation_rng(relation_dom(function_image(X0,X1,X2,X3)))),relation_dom(relation_dom(function_image(X0,X1,X2,X3))),first_projection_as_func_of(relation_dom(relation_dom(function_image(X0,X1,X2,X3))),relation_rng(relation_dom(function_image(X0,X1,X2,X3)))),relation_dom(function_image(X0,X1,X2,X3)))
| ~ function(X2)
| ~ empty(X1)
| ~ relation_of2(X2,X0,X1)
| ~ quasi_total(X2,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_537])]) ).
fof(f5688,plain,
( ! [X2,X3,X0,X1] :
( relation_dom(relation_dom(function_image(X0,X1,X2,X3))) = relation_image(first_projection_as_func_of(relation_dom(relation_dom(function_image(X0,X1,X2,X3))),relation_rng(relation_dom(function_image(X0,X1,X2,X3)))),relation_dom(function_image(X0,X1,X2,X3)))
| ~ function(X2)
| ~ empty(X1)
| ~ relation_of2(X2,X0,X1)
| ~ quasi_total(X2,X0,X1) )
| ~ spl30_89
| ~ spl30_491
| ~ spl30_537 ),
inference(forward_demodulation,[],[f5686,f5010]) ).
fof(f5686,plain,
( ! [X2,X3,X0,X1] :
( relation_dom(relation_dom(function_image(X0,X1,X2,X3))) = function_image(cartesian_product2(relation_dom(relation_dom(function_image(X0,X1,X2,X3))),relation_rng(relation_dom(function_image(X0,X1,X2,X3)))),relation_dom(relation_dom(function_image(X0,X1,X2,X3))),first_projection_as_func_of(relation_dom(relation_dom(function_image(X0,X1,X2,X3))),relation_rng(relation_dom(function_image(X0,X1,X2,X3)))),relation_dom(function_image(X0,X1,X2,X3)))
| ~ function(X2)
| ~ empty(X1)
| ~ relation_of2(X2,X0,X1)
| ~ quasi_total(X2,X0,X1) )
| ~ spl30_537 ),
inference(avatar_component_clause,[],[f5685]) ).
fof(f5687,plain,
( spl30_537
| ~ spl30_332
| ~ spl30_337 ),
inference(avatar_split_clause,[],[f3068,f3061,f2985,f5685]) ).
fof(f3061,plain,
( spl30_337
<=> ! [X0] :
( relation_dom(relation_dom(X0)) = function_image(cartesian_product2(relation_dom(relation_dom(X0)),relation_rng(relation_dom(X0))),relation_dom(relation_dom(X0)),first_projection_as_func_of(relation_dom(relation_dom(X0)),relation_rng(relation_dom(X0))),relation_dom(X0))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_337])]) ).
fof(f3068,plain,
( ! [X2,X3,X0,X1] :
( relation_dom(relation_dom(function_image(X0,X1,X2,X3))) = function_image(cartesian_product2(relation_dom(relation_dom(function_image(X0,X1,X2,X3))),relation_rng(relation_dom(function_image(X0,X1,X2,X3)))),relation_dom(relation_dom(function_image(X0,X1,X2,X3))),first_projection_as_func_of(relation_dom(relation_dom(function_image(X0,X1,X2,X3))),relation_rng(relation_dom(function_image(X0,X1,X2,X3)))),relation_dom(function_image(X0,X1,X2,X3)))
| ~ function(X2)
| ~ empty(X1)
| ~ relation_of2(X2,X0,X1)
| ~ quasi_total(X2,X0,X1) )
| ~ spl30_332
| ~ spl30_337 ),
inference(resolution,[],[f3062,f2986]) ).
fof(f3062,plain,
( ! [X0] :
( ~ empty(X0)
| relation_dom(relation_dom(X0)) = function_image(cartesian_product2(relation_dom(relation_dom(X0)),relation_rng(relation_dom(X0))),relation_dom(relation_dom(X0)),first_projection_as_func_of(relation_dom(relation_dom(X0)),relation_rng(relation_dom(X0))),relation_dom(X0)) )
| ~ spl30_337 ),
inference(avatar_component_clause,[],[f3061]) ).
fof(f5632,plain,
( spl30_536
| ~ spl30_89
| ~ spl30_491
| ~ spl30_535 ),
inference(avatar_split_clause,[],[f5628,f5625,f5001,f808,f5630]) ).
fof(f5630,plain,
( spl30_536
<=> ! [X0] :
( relation_dom(relation_rng(sK4(powerset(X0)))) = relation_image(first_projection_as_func_of(relation_dom(relation_rng(sK4(powerset(X0)))),relation_rng(relation_rng(sK4(powerset(X0))))),relation_rng(sK4(powerset(X0))))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_536])]) ).
fof(f5625,plain,
( spl30_535
<=> ! [X0] :
( relation_dom(relation_rng(sK4(powerset(X0)))) = function_image(cartesian_product2(relation_dom(relation_rng(sK4(powerset(X0)))),relation_rng(relation_rng(sK4(powerset(X0))))),relation_dom(relation_rng(sK4(powerset(X0)))),first_projection_as_func_of(relation_dom(relation_rng(sK4(powerset(X0)))),relation_rng(relation_rng(sK4(powerset(X0))))),relation_rng(sK4(powerset(X0))))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_535])]) ).
fof(f5628,plain,
( ! [X0] :
( relation_dom(relation_rng(sK4(powerset(X0)))) = relation_image(first_projection_as_func_of(relation_dom(relation_rng(sK4(powerset(X0)))),relation_rng(relation_rng(sK4(powerset(X0))))),relation_rng(sK4(powerset(X0))))
| ~ empty(X0) )
| ~ spl30_89
| ~ spl30_491
| ~ spl30_535 ),
inference(forward_demodulation,[],[f5626,f5010]) ).
fof(f5626,plain,
( ! [X0] :
( relation_dom(relation_rng(sK4(powerset(X0)))) = function_image(cartesian_product2(relation_dom(relation_rng(sK4(powerset(X0)))),relation_rng(relation_rng(sK4(powerset(X0))))),relation_dom(relation_rng(sK4(powerset(X0)))),first_projection_as_func_of(relation_dom(relation_rng(sK4(powerset(X0)))),relation_rng(relation_rng(sK4(powerset(X0))))),relation_rng(sK4(powerset(X0))))
| ~ empty(X0) )
| ~ spl30_535 ),
inference(avatar_component_clause,[],[f5625]) ).
fof(f5627,plain,
( spl30_535
| ~ spl30_289
| ~ spl30_338 ),
inference(avatar_split_clause,[],[f3115,f3065,f2470,f5625]) ).
fof(f3115,plain,
( ! [X0] :
( relation_dom(relation_rng(sK4(powerset(X0)))) = function_image(cartesian_product2(relation_dom(relation_rng(sK4(powerset(X0)))),relation_rng(relation_rng(sK4(powerset(X0))))),relation_dom(relation_rng(sK4(powerset(X0)))),first_projection_as_func_of(relation_dom(relation_rng(sK4(powerset(X0)))),relation_rng(relation_rng(sK4(powerset(X0))))),relation_rng(sK4(powerset(X0))))
| ~ empty(X0) )
| ~ spl30_289
| ~ spl30_338 ),
inference(resolution,[],[f3066,f2471]) ).
fof(f5572,plain,
( spl30_534
| ~ spl30_89
| ~ spl30_491
| ~ spl30_533 ),
inference(avatar_split_clause,[],[f5568,f5565,f5001,f808,f5570]) ).
fof(f5570,plain,
( spl30_534
<=> ! [X0] :
( relation_dom(relation_dom(sK4(powerset(X0)))) = relation_image(first_projection_as_func_of(relation_dom(relation_dom(sK4(powerset(X0)))),relation_rng(relation_dom(sK4(powerset(X0))))),relation_dom(sK4(powerset(X0))))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_534])]) ).
fof(f5565,plain,
( spl30_533
<=> ! [X0] :
( relation_dom(relation_dom(sK4(powerset(X0)))) = function_image(cartesian_product2(relation_dom(relation_dom(sK4(powerset(X0)))),relation_rng(relation_dom(sK4(powerset(X0))))),relation_dom(relation_dom(sK4(powerset(X0)))),first_projection_as_func_of(relation_dom(relation_dom(sK4(powerset(X0)))),relation_rng(relation_dom(sK4(powerset(X0))))),relation_dom(sK4(powerset(X0))))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_533])]) ).
fof(f5568,plain,
( ! [X0] :
( relation_dom(relation_dom(sK4(powerset(X0)))) = relation_image(first_projection_as_func_of(relation_dom(relation_dom(sK4(powerset(X0)))),relation_rng(relation_dom(sK4(powerset(X0))))),relation_dom(sK4(powerset(X0))))
| ~ empty(X0) )
| ~ spl30_89
| ~ spl30_491
| ~ spl30_533 ),
inference(forward_demodulation,[],[f5566,f5010]) ).
fof(f5566,plain,
( ! [X0] :
( relation_dom(relation_dom(sK4(powerset(X0)))) = function_image(cartesian_product2(relation_dom(relation_dom(sK4(powerset(X0)))),relation_rng(relation_dom(sK4(powerset(X0))))),relation_dom(relation_dom(sK4(powerset(X0)))),first_projection_as_func_of(relation_dom(relation_dom(sK4(powerset(X0)))),relation_rng(relation_dom(sK4(powerset(X0))))),relation_dom(sK4(powerset(X0))))
| ~ empty(X0) )
| ~ spl30_533 ),
inference(avatar_component_clause,[],[f5565]) ).
fof(f5567,plain,
( spl30_533
| ~ spl30_289
| ~ spl30_337 ),
inference(avatar_split_clause,[],[f3072,f3061,f2470,f5565]) ).
fof(f3072,plain,
( ! [X0] :
( relation_dom(relation_dom(sK4(powerset(X0)))) = function_image(cartesian_product2(relation_dom(relation_dom(sK4(powerset(X0)))),relation_rng(relation_dom(sK4(powerset(X0))))),relation_dom(relation_dom(sK4(powerset(X0)))),first_projection_as_func_of(relation_dom(relation_dom(sK4(powerset(X0)))),relation_rng(relation_dom(sK4(powerset(X0))))),relation_dom(sK4(powerset(X0))))
| ~ empty(X0) )
| ~ spl30_289
| ~ spl30_337 ),
inference(resolution,[],[f3062,f2471]) ).
fof(f5560,plain,
( spl30_532
| ~ spl30_134
| ~ spl30_336 ),
inference(avatar_split_clause,[],[f3050,f3039,f1158,f5558]) ).
fof(f5558,plain,
( spl30_532
<=> ! [X4,X0,X3,X2,X1] :
( ~ function(X0)
| ~ quasi_total(X0,X1,powerset(cartesian_product2(X2,X3)))
| ~ relation_of2(X0,X1,powerset(cartesian_product2(X2,X3)))
| empty(function_image(X1,powerset(cartesian_product2(X2,X3)),X0,X4))
| relation(sK4(function_image(X1,powerset(cartesian_product2(X2,X3)),X0,X4))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_532])]) ).
fof(f1158,plain,
( spl30_134
<=> ! [X2,X0,X1] :
( relation(X2)
| ~ element(X2,powerset(cartesian_product2(X0,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_134])]) ).
fof(f3039,plain,
( spl30_336
<=> ! [X0,X3,X2,X1] :
( ~ quasi_total(X0,X1,X2)
| ~ function(X0)
| element(sK4(function_image(X1,X2,X0,X3)),X2)
| ~ relation_of2(X0,X1,X2)
| empty(function_image(X1,X2,X0,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_336])]) ).
fof(f3050,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ function(X0)
| ~ quasi_total(X0,X1,powerset(cartesian_product2(X2,X3)))
| ~ relation_of2(X0,X1,powerset(cartesian_product2(X2,X3)))
| empty(function_image(X1,powerset(cartesian_product2(X2,X3)),X0,X4))
| relation(sK4(function_image(X1,powerset(cartesian_product2(X2,X3)),X0,X4))) )
| ~ spl30_134
| ~ spl30_336 ),
inference(resolution,[],[f3040,f1159]) ).
fof(f1159,plain,
( ! [X2,X0,X1] :
( ~ element(X2,powerset(cartesian_product2(X0,X1)))
| relation(X2) )
| ~ spl30_134 ),
inference(avatar_component_clause,[],[f1158]) ).
fof(f3040,plain,
( ! [X2,X3,X0,X1] :
( element(sK4(function_image(X1,X2,X0,X3)),X2)
| ~ function(X0)
| ~ quasi_total(X0,X1,X2)
| ~ relation_of2(X0,X1,X2)
| empty(function_image(X1,X2,X0,X3)) )
| ~ spl30_336 ),
inference(avatar_component_clause,[],[f3039]) ).
fof(f5556,plain,
( spl30_531
| ~ spl30_89
| ~ spl30_491
| ~ spl30_530 ),
inference(avatar_split_clause,[],[f5552,f5549,f5001,f808,f5554]) ).
fof(f5554,plain,
( spl30_531
<=> ! [X0,X1] :
( relation_dom(cartesian_product2(X0,X1)) = relation_image(first_projection_as_func_of(relation_dom(cartesian_product2(X0,X1)),relation_rng(cartesian_product2(X0,X1))),cartesian_product2(X0,X1))
| ~ function(cartesian_product2(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_531])]) ).
fof(f5549,plain,
( spl30_530
<=> ! [X0,X1] :
( ~ function(cartesian_product2(X0,X1))
| relation_dom(cartesian_product2(X0,X1)) = function_image(cartesian_product2(relation_dom(cartesian_product2(X0,X1)),relation_rng(cartesian_product2(X0,X1))),relation_dom(cartesian_product2(X0,X1)),first_projection_as_func_of(relation_dom(cartesian_product2(X0,X1)),relation_rng(cartesian_product2(X0,X1))),cartesian_product2(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_530])]) ).
fof(f5552,plain,
( ! [X0,X1] :
( relation_dom(cartesian_product2(X0,X1)) = relation_image(first_projection_as_func_of(relation_dom(cartesian_product2(X0,X1)),relation_rng(cartesian_product2(X0,X1))),cartesian_product2(X0,X1))
| ~ function(cartesian_product2(X0,X1)) )
| ~ spl30_89
| ~ spl30_491
| ~ spl30_530 ),
inference(forward_demodulation,[],[f5550,f5010]) ).
fof(f5550,plain,
( ! [X0,X1] :
( ~ function(cartesian_product2(X0,X1))
| relation_dom(cartesian_product2(X0,X1)) = function_image(cartesian_product2(relation_dom(cartesian_product2(X0,X1)),relation_rng(cartesian_product2(X0,X1))),relation_dom(cartesian_product2(X0,X1)),first_projection_as_func_of(relation_dom(cartesian_product2(X0,X1)),relation_rng(cartesian_product2(X0,X1))),cartesian_product2(X0,X1)) )
| ~ spl30_530 ),
inference(avatar_component_clause,[],[f5549]) ).
fof(f5551,plain,
( spl30_530
| ~ spl30_152
| ~ spl30_250 ),
inference(avatar_split_clause,[],[f2347,f2141,f1313,f5549]) ).
fof(f1313,plain,
( spl30_152
<=> ! [X0] :
( relation_dom(X0) = function_image(cartesian_product2(relation_dom(X0),relation_rng(X0)),relation_dom(X0),first_projection_as_func_of(relation_dom(X0),relation_rng(X0)),X0)
| ~ function(X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_152])]) ).
fof(f2141,plain,
( spl30_250
<=> ! [X0,X1] : relation(cartesian_product2(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_250])]) ).
fof(f2347,plain,
( ! [X0,X1] :
( ~ function(cartesian_product2(X0,X1))
| relation_dom(cartesian_product2(X0,X1)) = function_image(cartesian_product2(relation_dom(cartesian_product2(X0,X1)),relation_rng(cartesian_product2(X0,X1))),relation_dom(cartesian_product2(X0,X1)),first_projection_as_func_of(relation_dom(cartesian_product2(X0,X1)),relation_rng(cartesian_product2(X0,X1))),cartesian_product2(X0,X1)) )
| ~ spl30_152
| ~ spl30_250 ),
inference(resolution,[],[f2142,f1314]) ).
fof(f1314,plain,
( ! [X0] :
( ~ relation(X0)
| ~ function(X0)
| relation_dom(X0) = function_image(cartesian_product2(relation_dom(X0),relation_rng(X0)),relation_dom(X0),first_projection_as_func_of(relation_dom(X0),relation_rng(X0)),X0) )
| ~ spl30_152 ),
inference(avatar_component_clause,[],[f1313]) ).
fof(f2142,plain,
( ! [X0,X1] : relation(cartesian_product2(X0,X1))
| ~ spl30_250 ),
inference(avatar_component_clause,[],[f2141]) ).
fof(f5547,plain,
( spl30_529
| ~ spl30_89
| ~ spl30_491
| ~ spl30_528 ),
inference(avatar_split_clause,[],[f5543,f5540,f5001,f808,f5545]) ).
fof(f5545,plain,
( spl30_529
<=> ! [X0,X1] :
( relation_dom(sK7(X0,X1)) = relation_image(first_projection_as_func_of(relation_dom(sK7(X0,X1)),relation_rng(sK7(X0,X1))),sK7(X0,X1))
| ~ function(sK7(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_529])]) ).
fof(f5540,plain,
( spl30_528
<=> ! [X0,X1] :
( ~ function(sK7(X0,X1))
| relation_dom(sK7(X0,X1)) = function_image(cartesian_product2(relation_dom(sK7(X0,X1)),relation_rng(sK7(X0,X1))),relation_dom(sK7(X0,X1)),first_projection_as_func_of(relation_dom(sK7(X0,X1)),relation_rng(sK7(X0,X1))),sK7(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_528])]) ).
fof(f5543,plain,
( ! [X0,X1] :
( relation_dom(sK7(X0,X1)) = relation_image(first_projection_as_func_of(relation_dom(sK7(X0,X1)),relation_rng(sK7(X0,X1))),sK7(X0,X1))
| ~ function(sK7(X0,X1)) )
| ~ spl30_89
| ~ spl30_491
| ~ spl30_528 ),
inference(forward_demodulation,[],[f5541,f5010]) ).
fof(f5541,plain,
( ! [X0,X1] :
( ~ function(sK7(X0,X1))
| relation_dom(sK7(X0,X1)) = function_image(cartesian_product2(relation_dom(sK7(X0,X1)),relation_rng(sK7(X0,X1))),relation_dom(sK7(X0,X1)),first_projection_as_func_of(relation_dom(sK7(X0,X1)),relation_rng(sK7(X0,X1))),sK7(X0,X1)) )
| ~ spl30_528 ),
inference(avatar_component_clause,[],[f5540]) ).
fof(f5542,plain,
( spl30_528
| ~ spl30_152
| ~ spl30_237 ),
inference(avatar_split_clause,[],[f2302,f2060,f1313,f5540]) ).
fof(f2060,plain,
( spl30_237
<=> ! [X0,X1] : relation(sK7(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_237])]) ).
fof(f2302,plain,
( ! [X0,X1] :
( ~ function(sK7(X0,X1))
| relation_dom(sK7(X0,X1)) = function_image(cartesian_product2(relation_dom(sK7(X0,X1)),relation_rng(sK7(X0,X1))),relation_dom(sK7(X0,X1)),first_projection_as_func_of(relation_dom(sK7(X0,X1)),relation_rng(sK7(X0,X1))),sK7(X0,X1)) )
| ~ spl30_152
| ~ spl30_237 ),
inference(resolution,[],[f2061,f1314]) ).
fof(f2061,plain,
( ! [X0,X1] : relation(sK7(X0,X1))
| ~ spl30_237 ),
inference(avatar_component_clause,[],[f2060]) ).
fof(f5538,plain,
( spl30_527
| ~ spl30_89
| ~ spl30_491
| ~ spl30_526 ),
inference(avatar_split_clause,[],[f5534,f5531,f5001,f808,f5536]) ).
fof(f5536,plain,
( spl30_527
<=> ! [X0,X1] :
( relation_dom(sK8(X0,X1)) = relation_image(first_projection_as_func_of(relation_dom(sK8(X0,X1)),relation_rng(sK8(X0,X1))),sK8(X0,X1))
| ~ function(sK8(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_527])]) ).
fof(f5531,plain,
( spl30_526
<=> ! [X0,X1] :
( ~ function(sK8(X0,X1))
| relation_dom(sK8(X0,X1)) = function_image(cartesian_product2(relation_dom(sK8(X0,X1)),relation_rng(sK8(X0,X1))),relation_dom(sK8(X0,X1)),first_projection_as_func_of(relation_dom(sK8(X0,X1)),relation_rng(sK8(X0,X1))),sK8(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_526])]) ).
fof(f5534,plain,
( ! [X0,X1] :
( relation_dom(sK8(X0,X1)) = relation_image(first_projection_as_func_of(relation_dom(sK8(X0,X1)),relation_rng(sK8(X0,X1))),sK8(X0,X1))
| ~ function(sK8(X0,X1)) )
| ~ spl30_89
| ~ spl30_491
| ~ spl30_526 ),
inference(forward_demodulation,[],[f5532,f5010]) ).
fof(f5532,plain,
( ! [X0,X1] :
( ~ function(sK8(X0,X1))
| relation_dom(sK8(X0,X1)) = function_image(cartesian_product2(relation_dom(sK8(X0,X1)),relation_rng(sK8(X0,X1))),relation_dom(sK8(X0,X1)),first_projection_as_func_of(relation_dom(sK8(X0,X1)),relation_rng(sK8(X0,X1))),sK8(X0,X1)) )
| ~ spl30_526 ),
inference(avatar_component_clause,[],[f5531]) ).
fof(f5533,plain,
( spl30_526
| ~ spl30_152
| ~ spl30_236 ),
inference(avatar_split_clause,[],[f2268,f1975,f1313,f5531]) ).
fof(f1975,plain,
( spl30_236
<=> ! [X0,X1] : relation(sK8(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_236])]) ).
fof(f2268,plain,
( ! [X0,X1] :
( ~ function(sK8(X0,X1))
| relation_dom(sK8(X0,X1)) = function_image(cartesian_product2(relation_dom(sK8(X0,X1)),relation_rng(sK8(X0,X1))),relation_dom(sK8(X0,X1)),first_projection_as_func_of(relation_dom(sK8(X0,X1)),relation_rng(sK8(X0,X1))),sK8(X0,X1)) )
| ~ spl30_152
| ~ spl30_236 ),
inference(resolution,[],[f1976,f1314]) ).
fof(f1976,plain,
( ! [X0,X1] : relation(sK8(X0,X1))
| ~ spl30_236 ),
inference(avatar_component_clause,[],[f1975]) ).
fof(f5529,plain,
( spl30_525
| ~ spl30_6
| ~ spl30_168
| ~ spl30_221
| ~ spl30_232
| ~ spl30_517 ),
inference(avatar_split_clause,[],[f5310,f5287,f1958,f1913,f1432,f412,f5526]) ).
fof(f5526,plain,
( spl30_525
<=> sK10 = relation_image(first_projection_as_func_of(sK10,sK10),sK10) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_525])]) ).
fof(f412,plain,
( spl30_6
<=> empty(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_6])]) ).
fof(f1432,plain,
( spl30_168
<=> empty_set = sK10 ),
introduced(avatar_definition,[new_symbols(naming,[spl30_168])]) ).
fof(f1913,plain,
( spl30_221
<=> sK10 = relation_rng(sK10) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_221])]) ).
fof(f1958,plain,
( spl30_232
<=> sK10 = relation_dom(sK10) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_232])]) ).
fof(f5287,plain,
( spl30_517
<=> ! [X0] :
( relation_dom(relation_dom(relation_dom(X0))) = relation_image(first_projection_as_func_of(relation_dom(relation_dom(relation_dom(X0))),relation_rng(relation_dom(relation_dom(X0)))),relation_dom(relation_dom(X0)))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_517])]) ).
fof(f5310,plain,
( sK10 = relation_image(first_projection_as_func_of(sK10,sK10),sK10)
| ~ spl30_6
| ~ spl30_168
| ~ spl30_221
| ~ spl30_232
| ~ spl30_517 ),
inference(forward_demodulation,[],[f5309,f1960]) ).
fof(f1960,plain,
( sK10 = relation_dom(sK10)
| ~ spl30_232 ),
inference(avatar_component_clause,[],[f1958]) ).
fof(f5309,plain,
( relation_dom(sK10) = relation_image(first_projection_as_func_of(relation_dom(sK10),sK10),sK10)
| ~ spl30_6
| ~ spl30_168
| ~ spl30_221
| ~ spl30_232
| ~ spl30_517 ),
inference(forward_demodulation,[],[f5308,f1915]) ).
fof(f1915,plain,
( sK10 = relation_rng(sK10)
| ~ spl30_221 ),
inference(avatar_component_clause,[],[f1913]) ).
fof(f5308,plain,
( relation_dom(sK10) = relation_image(first_projection_as_func_of(relation_dom(sK10),relation_rng(sK10)),sK10)
| ~ spl30_6
| ~ spl30_168
| ~ spl30_232
| ~ spl30_517 ),
inference(forward_demodulation,[],[f5307,f1960]) ).
fof(f5307,plain,
( relation_dom(relation_dom(sK10)) = relation_image(first_projection_as_func_of(relation_dom(relation_dom(sK10)),relation_rng(relation_dom(sK10))),relation_dom(sK10))
| ~ spl30_6
| ~ spl30_168
| ~ spl30_232
| ~ spl30_517 ),
inference(forward_demodulation,[],[f5306,f1960]) ).
fof(f5306,plain,
( relation_dom(relation_dom(relation_dom(sK10))) = relation_image(first_projection_as_func_of(relation_dom(relation_dom(relation_dom(sK10))),relation_rng(relation_dom(relation_dom(sK10)))),relation_dom(relation_dom(sK10)))
| ~ spl30_6
| ~ spl30_168
| ~ spl30_517 ),
inference(forward_demodulation,[],[f5295,f1434]) ).
fof(f1434,plain,
( empty_set = sK10
| ~ spl30_168 ),
inference(avatar_component_clause,[],[f1432]) ).
fof(f5295,plain,
( relation_dom(relation_dom(relation_dom(empty_set))) = relation_image(first_projection_as_func_of(relation_dom(relation_dom(relation_dom(empty_set))),relation_rng(relation_dom(relation_dom(empty_set)))),relation_dom(relation_dom(empty_set)))
| ~ spl30_6
| ~ spl30_517 ),
inference(resolution,[],[f5288,f414]) ).
fof(f414,plain,
( empty(empty_set)
| ~ spl30_6 ),
inference(avatar_component_clause,[],[f412]) ).
fof(f5288,plain,
( ! [X0] :
( ~ empty(X0)
| relation_dom(relation_dom(relation_dom(X0))) = relation_image(first_projection_as_func_of(relation_dom(relation_dom(relation_dom(X0))),relation_rng(relation_dom(relation_dom(X0)))),relation_dom(relation_dom(X0))) )
| ~ spl30_517 ),
inference(avatar_component_clause,[],[f5287]) ).
fof(f5473,plain,
( spl30_524
| ~ spl30_89
| ~ spl30_491
| ~ spl30_523 ),
inference(avatar_split_clause,[],[f5469,f5466,f5001,f808,f5471]) ).
fof(f5471,plain,
( spl30_524
<=> ! [X0] :
( relation_dom(relation_rng(relation_rng(X0))) = relation_image(first_projection_as_func_of(relation_dom(relation_rng(relation_rng(X0))),relation_rng(relation_rng(relation_rng(X0)))),relation_rng(relation_rng(X0)))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_524])]) ).
fof(f5466,plain,
( spl30_523
<=> ! [X0] :
( relation_dom(relation_rng(relation_rng(X0))) = function_image(cartesian_product2(relation_dom(relation_rng(relation_rng(X0))),relation_rng(relation_rng(relation_rng(X0)))),relation_dom(relation_rng(relation_rng(X0))),first_projection_as_func_of(relation_dom(relation_rng(relation_rng(X0))),relation_rng(relation_rng(relation_rng(X0)))),relation_rng(relation_rng(X0)))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_523])]) ).
fof(f5469,plain,
( ! [X0] :
( relation_dom(relation_rng(relation_rng(X0))) = relation_image(first_projection_as_func_of(relation_dom(relation_rng(relation_rng(X0))),relation_rng(relation_rng(relation_rng(X0)))),relation_rng(relation_rng(X0)))
| ~ empty(X0) )
| ~ spl30_89
| ~ spl30_491
| ~ spl30_523 ),
inference(forward_demodulation,[],[f5467,f5010]) ).
fof(f5467,plain,
( ! [X0] :
( relation_dom(relation_rng(relation_rng(X0))) = function_image(cartesian_product2(relation_dom(relation_rng(relation_rng(X0))),relation_rng(relation_rng(relation_rng(X0)))),relation_dom(relation_rng(relation_rng(X0))),first_projection_as_func_of(relation_dom(relation_rng(relation_rng(X0))),relation_rng(relation_rng(relation_rng(X0)))),relation_rng(relation_rng(X0)))
| ~ empty(X0) )
| ~ spl30_523 ),
inference(avatar_component_clause,[],[f5466]) ).
fof(f5468,plain,
( spl30_523
| ~ spl30_98
| ~ spl30_338 ),
inference(avatar_split_clause,[],[f3114,f3065,f911,f5466]) ).
fof(f3114,plain,
( ! [X0] :
( relation_dom(relation_rng(relation_rng(X0))) = function_image(cartesian_product2(relation_dom(relation_rng(relation_rng(X0))),relation_rng(relation_rng(relation_rng(X0)))),relation_dom(relation_rng(relation_rng(X0))),first_projection_as_func_of(relation_dom(relation_rng(relation_rng(X0))),relation_rng(relation_rng(relation_rng(X0)))),relation_rng(relation_rng(X0)))
| ~ empty(X0) )
| ~ spl30_98
| ~ spl30_338 ),
inference(resolution,[],[f3066,f912]) ).
fof(f5413,plain,
( spl30_522
| ~ spl30_89
| ~ spl30_491
| ~ spl30_521 ),
inference(avatar_split_clause,[],[f5409,f5406,f5001,f808,f5411]) ).
fof(f5411,plain,
( spl30_522
<=> ! [X0] :
( relation_dom(relation_rng(relation_dom(X0))) = relation_image(first_projection_as_func_of(relation_dom(relation_rng(relation_dom(X0))),relation_rng(relation_rng(relation_dom(X0)))),relation_rng(relation_dom(X0)))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_522])]) ).
fof(f5406,plain,
( spl30_521
<=> ! [X0] :
( relation_dom(relation_rng(relation_dom(X0))) = function_image(cartesian_product2(relation_dom(relation_rng(relation_dom(X0))),relation_rng(relation_rng(relation_dom(X0)))),relation_dom(relation_rng(relation_dom(X0))),first_projection_as_func_of(relation_dom(relation_rng(relation_dom(X0))),relation_rng(relation_rng(relation_dom(X0)))),relation_rng(relation_dom(X0)))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_521])]) ).
fof(f5409,plain,
( ! [X0] :
( relation_dom(relation_rng(relation_dom(X0))) = relation_image(first_projection_as_func_of(relation_dom(relation_rng(relation_dom(X0))),relation_rng(relation_rng(relation_dom(X0)))),relation_rng(relation_dom(X0)))
| ~ empty(X0) )
| ~ spl30_89
| ~ spl30_491
| ~ spl30_521 ),
inference(forward_demodulation,[],[f5407,f5010]) ).
fof(f5407,plain,
( ! [X0] :
( relation_dom(relation_rng(relation_dom(X0))) = function_image(cartesian_product2(relation_dom(relation_rng(relation_dom(X0))),relation_rng(relation_rng(relation_dom(X0)))),relation_dom(relation_rng(relation_dom(X0))),first_projection_as_func_of(relation_dom(relation_rng(relation_dom(X0))),relation_rng(relation_rng(relation_dom(X0)))),relation_rng(relation_dom(X0)))
| ~ empty(X0) )
| ~ spl30_521 ),
inference(avatar_component_clause,[],[f5406]) ).
fof(f5408,plain,
( spl30_521
| ~ spl30_101
| ~ spl30_338 ),
inference(avatar_split_clause,[],[f3113,f3065,f924,f5406]) ).
fof(f3113,plain,
( ! [X0] :
( relation_dom(relation_rng(relation_dom(X0))) = function_image(cartesian_product2(relation_dom(relation_rng(relation_dom(X0))),relation_rng(relation_rng(relation_dom(X0)))),relation_dom(relation_rng(relation_dom(X0))),first_projection_as_func_of(relation_dom(relation_rng(relation_dom(X0))),relation_rng(relation_rng(relation_dom(X0)))),relation_rng(relation_dom(X0)))
| ~ empty(X0) )
| ~ spl30_101
| ~ spl30_338 ),
inference(resolution,[],[f3066,f925]) ).
fof(f5353,plain,
( spl30_520
| ~ spl30_89
| ~ spl30_491
| ~ spl30_519 ),
inference(avatar_split_clause,[],[f5349,f5346,f5001,f808,f5351]) ).
fof(f5351,plain,
( spl30_520
<=> ! [X0] :
( relation_dom(relation_dom(relation_rng(X0))) = relation_image(first_projection_as_func_of(relation_dom(relation_dom(relation_rng(X0))),relation_rng(relation_dom(relation_rng(X0)))),relation_dom(relation_rng(X0)))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_520])]) ).
fof(f5346,plain,
( spl30_519
<=> ! [X0] :
( relation_dom(relation_dom(relation_rng(X0))) = function_image(cartesian_product2(relation_dom(relation_dom(relation_rng(X0))),relation_rng(relation_dom(relation_rng(X0)))),relation_dom(relation_dom(relation_rng(X0))),first_projection_as_func_of(relation_dom(relation_dom(relation_rng(X0))),relation_rng(relation_dom(relation_rng(X0)))),relation_dom(relation_rng(X0)))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_519])]) ).
fof(f5349,plain,
( ! [X0] :
( relation_dom(relation_dom(relation_rng(X0))) = relation_image(first_projection_as_func_of(relation_dom(relation_dom(relation_rng(X0))),relation_rng(relation_dom(relation_rng(X0)))),relation_dom(relation_rng(X0)))
| ~ empty(X0) )
| ~ spl30_89
| ~ spl30_491
| ~ spl30_519 ),
inference(forward_demodulation,[],[f5347,f5010]) ).
fof(f5347,plain,
( ! [X0] :
( relation_dom(relation_dom(relation_rng(X0))) = function_image(cartesian_product2(relation_dom(relation_dom(relation_rng(X0))),relation_rng(relation_dom(relation_rng(X0)))),relation_dom(relation_dom(relation_rng(X0))),first_projection_as_func_of(relation_dom(relation_dom(relation_rng(X0))),relation_rng(relation_dom(relation_rng(X0)))),relation_dom(relation_rng(X0)))
| ~ empty(X0) )
| ~ spl30_519 ),
inference(avatar_component_clause,[],[f5346]) ).
fof(f5348,plain,
( spl30_519
| ~ spl30_98
| ~ spl30_337 ),
inference(avatar_split_clause,[],[f3071,f3061,f911,f5346]) ).
fof(f3071,plain,
( ! [X0] :
( relation_dom(relation_dom(relation_rng(X0))) = function_image(cartesian_product2(relation_dom(relation_dom(relation_rng(X0))),relation_rng(relation_dom(relation_rng(X0)))),relation_dom(relation_dom(relation_rng(X0))),first_projection_as_func_of(relation_dom(relation_dom(relation_rng(X0))),relation_rng(relation_dom(relation_rng(X0)))),relation_dom(relation_rng(X0)))
| ~ empty(X0) )
| ~ spl30_98
| ~ spl30_337 ),
inference(resolution,[],[f3062,f912]) ).
fof(f5293,plain,
( spl30_518
| ~ spl30_101
| ~ spl30_378 ),
inference(avatar_split_clause,[],[f3525,f3463,f924,f5291]) ).
fof(f3525,plain,
( ! [X0] :
( sK10 = relation_rng(sK4(powerset(relation_dom(X0))))
| ~ empty(X0) )
| ~ spl30_101
| ~ spl30_378 ),
inference(resolution,[],[f3464,f925]) ).
fof(f5289,plain,
( spl30_517
| ~ spl30_89
| ~ spl30_491
| ~ spl30_516 ),
inference(avatar_split_clause,[],[f5285,f5282,f5001,f808,f5287]) ).
fof(f5282,plain,
( spl30_516
<=> ! [X0] :
( relation_dom(relation_dom(relation_dom(X0))) = function_image(cartesian_product2(relation_dom(relation_dom(relation_dom(X0))),relation_rng(relation_dom(relation_dom(X0)))),relation_dom(relation_dom(relation_dom(X0))),first_projection_as_func_of(relation_dom(relation_dom(relation_dom(X0))),relation_rng(relation_dom(relation_dom(X0)))),relation_dom(relation_dom(X0)))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_516])]) ).
fof(f5285,plain,
( ! [X0] :
( relation_dom(relation_dom(relation_dom(X0))) = relation_image(first_projection_as_func_of(relation_dom(relation_dom(relation_dom(X0))),relation_rng(relation_dom(relation_dom(X0)))),relation_dom(relation_dom(X0)))
| ~ empty(X0) )
| ~ spl30_89
| ~ spl30_491
| ~ spl30_516 ),
inference(forward_demodulation,[],[f5283,f5010]) ).
fof(f5283,plain,
( ! [X0] :
( relation_dom(relation_dom(relation_dom(X0))) = function_image(cartesian_product2(relation_dom(relation_dom(relation_dom(X0))),relation_rng(relation_dom(relation_dom(X0)))),relation_dom(relation_dom(relation_dom(X0))),first_projection_as_func_of(relation_dom(relation_dom(relation_dom(X0))),relation_rng(relation_dom(relation_dom(X0)))),relation_dom(relation_dom(X0)))
| ~ empty(X0) )
| ~ spl30_516 ),
inference(avatar_component_clause,[],[f5282]) ).
fof(f5284,plain,
( spl30_516
| ~ spl30_101
| ~ spl30_337 ),
inference(avatar_split_clause,[],[f3070,f3061,f924,f5282]) ).
fof(f3070,plain,
( ! [X0] :
( relation_dom(relation_dom(relation_dom(X0))) = function_image(cartesian_product2(relation_dom(relation_dom(relation_dom(X0))),relation_rng(relation_dom(relation_dom(X0)))),relation_dom(relation_dom(relation_dom(X0))),first_projection_as_func_of(relation_dom(relation_dom(relation_dom(X0))),relation_rng(relation_dom(relation_dom(X0)))),relation_dom(relation_dom(X0)))
| ~ empty(X0) )
| ~ spl30_101
| ~ spl30_337 ),
inference(resolution,[],[f3062,f925]) ).
fof(f5274,plain,
( spl30_515
| ~ spl30_148
| ~ spl30_336 ),
inference(avatar_split_clause,[],[f3047,f3039,f1265,f5272]) ).
fof(f5272,plain,
( spl30_515
<=> ! [X4,X0,X3,X2,X1] :
( ~ function(X0)
| ~ quasi_total(X0,X1,powerset(X2))
| ~ relation_of2(X0,X1,powerset(X2))
| empty(function_image(X1,powerset(X2),X0,X3))
| element(X4,X2)
| ~ in(X4,sK4(function_image(X1,powerset(X2),X0,X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_515])]) ).
fof(f1265,plain,
( spl30_148
<=> ! [X2,X0,X1] :
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_148])]) ).
fof(f3047,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ function(X0)
| ~ quasi_total(X0,X1,powerset(X2))
| ~ relation_of2(X0,X1,powerset(X2))
| empty(function_image(X1,powerset(X2),X0,X3))
| element(X4,X2)
| ~ in(X4,sK4(function_image(X1,powerset(X2),X0,X3))) )
| ~ spl30_148
| ~ spl30_336 ),
inference(resolution,[],[f3040,f1266]) ).
fof(f1266,plain,
( ! [X2,X0,X1] :
( ~ element(X1,powerset(X2))
| element(X0,X2)
| ~ in(X0,X1) )
| ~ spl30_148 ),
inference(avatar_component_clause,[],[f1265]) ).
fof(f5264,plain,
( spl30_514
| ~ spl30_143
| ~ spl30_336 ),
inference(avatar_split_clause,[],[f3046,f3039,f1229,f5262]) ).
fof(f5262,plain,
( spl30_514
<=> ! [X4,X0,X3,X2,X1] :
( ~ function(X0)
| ~ quasi_total(X0,X1,powerset(X2))
| ~ relation_of2(X0,X1,powerset(X2))
| empty(function_image(X1,powerset(X2),X0,X3))
| ~ empty(X2)
| ~ in(X4,sK4(function_image(X1,powerset(X2),X0,X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_514])]) ).
fof(f1229,plain,
( spl30_143
<=> ! [X2,X0,X1] :
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_143])]) ).
fof(f3046,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ function(X0)
| ~ quasi_total(X0,X1,powerset(X2))
| ~ relation_of2(X0,X1,powerset(X2))
| empty(function_image(X1,powerset(X2),X0,X3))
| ~ empty(X2)
| ~ in(X4,sK4(function_image(X1,powerset(X2),X0,X3))) )
| ~ spl30_143
| ~ spl30_336 ),
inference(resolution,[],[f3040,f1230]) ).
fof(f1230,plain,
( ! [X2,X0,X1] :
( ~ element(X1,powerset(X2))
| ~ empty(X2)
| ~ in(X0,X1) )
| ~ spl30_143 ),
inference(avatar_component_clause,[],[f1229]) ).
fof(f5260,plain,
( spl30_513
| ~ spl30_128
| ~ spl30_336 ),
inference(avatar_split_clause,[],[f3048,f3039,f1134,f5258]) ).
fof(f5258,plain,
( spl30_513
<=> ! [X0,X3,X2,X1] :
( ~ function(X0)
| ~ quasi_total(X0,X1,powerset(X2))
| ~ relation_of2(X0,X1,powerset(X2))
| empty(function_image(X1,powerset(X2),X0,X3))
| finite(sK4(function_image(X1,powerset(X2),X0,X3)))
| ~ finite(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_513])]) ).
fof(f1134,plain,
( spl30_128
<=> ! [X0,X1] :
( finite(X1)
| ~ element(X1,powerset(X0))
| ~ finite(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_128])]) ).
fof(f3048,plain,
( ! [X2,X3,X0,X1] :
( ~ function(X0)
| ~ quasi_total(X0,X1,powerset(X2))
| ~ relation_of2(X0,X1,powerset(X2))
| empty(function_image(X1,powerset(X2),X0,X3))
| finite(sK4(function_image(X1,powerset(X2),X0,X3)))
| ~ finite(X2) )
| ~ spl30_128
| ~ spl30_336 ),
inference(resolution,[],[f3040,f1135]) ).
fof(f1135,plain,
( ! [X0,X1] :
( ~ element(X1,powerset(X0))
| finite(X1)
| ~ finite(X0) )
| ~ spl30_128 ),
inference(avatar_component_clause,[],[f1134]) ).
fof(f5249,plain,
( spl30_512
| ~ spl30_123
| ~ spl30_336 ),
inference(avatar_split_clause,[],[f3049,f3039,f1054,f5247]) ).
fof(f5247,plain,
( spl30_512
<=> ! [X0,X3,X2,X1] :
( ~ function(X0)
| ~ quasi_total(X0,X1,powerset(X2))
| ~ relation_of2(X0,X1,powerset(X2))
| empty(function_image(X1,powerset(X2),X0,X3))
| subset(sK4(function_image(X1,powerset(X2),X0,X3)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_512])]) ).
fof(f1054,plain,
( spl30_123
<=> ! [X0,X1] :
( subset(X0,X1)
| ~ element(X0,powerset(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_123])]) ).
fof(f3049,plain,
( ! [X2,X3,X0,X1] :
( ~ function(X0)
| ~ quasi_total(X0,X1,powerset(X2))
| ~ relation_of2(X0,X1,powerset(X2))
| empty(function_image(X1,powerset(X2),X0,X3))
| subset(sK4(function_image(X1,powerset(X2),X0,X3)),X2) )
| ~ spl30_123
| ~ spl30_336 ),
inference(resolution,[],[f3040,f1055]) ).
fof(f1055,plain,
( ! [X0,X1] :
( ~ element(X0,powerset(X1))
| subset(X0,X1) )
| ~ spl30_123 ),
inference(avatar_component_clause,[],[f1054]) ).
fof(f5245,plain,
( spl30_511
| ~ spl30_289
| ~ spl30_377 ),
inference(avatar_split_clause,[],[f3447,f3440,f2470,f5243]) ).
fof(f3440,plain,
( spl30_377
<=> ! [X0] :
( ~ empty(X0)
| sK10 = sK4(powerset(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_377])]) ).
fof(f3447,plain,
( ! [X0] :
( sK10 = sK4(powerset(sK4(powerset(X0))))
| ~ empty(X0) )
| ~ spl30_289
| ~ spl30_377 ),
inference(resolution,[],[f3441,f2471]) ).
fof(f3441,plain,
( ! [X0] :
( ~ empty(X0)
| sK10 = sK4(powerset(X0)) )
| ~ spl30_377 ),
inference(avatar_component_clause,[],[f3440]) ).
fof(f5198,plain,
( spl30_510
| ~ spl30_131
| ~ spl30_336 ),
inference(avatar_split_clause,[],[f3042,f3039,f1146,f5196]) ).
fof(f5196,plain,
( spl30_510
<=> ! [X0,X3,X2,X1] :
( ~ function(X0)
| ~ quasi_total(X0,X1,X2)
| ~ relation_of2(X0,X1,X2)
| empty(function_image(X1,X2,X0,X3))
| empty(X2)
| in(sK4(function_image(X1,X2,X0,X3)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_510])]) ).
fof(f3042,plain,
( ! [X2,X3,X0,X1] :
( ~ function(X0)
| ~ quasi_total(X0,X1,X2)
| ~ relation_of2(X0,X1,X2)
| empty(function_image(X1,X2,X0,X3))
| empty(X2)
| in(sK4(function_image(X1,X2,X0,X3)),X2) )
| ~ spl30_131
| ~ spl30_336 ),
inference(resolution,[],[f3040,f1147]) ).
fof(f5161,plain,
( spl30_509
| ~ spl30_117
| ~ spl30_336 ),
inference(avatar_split_clause,[],[f3045,f3039,f1030,f5159]) ).
fof(f5159,plain,
( spl30_509
<=> ! [X0,X3,X2,X1] :
( ~ function(X0)
| ~ quasi_total(X0,X1,X2)
| ~ relation_of2(X0,X1,X2)
| empty(function_image(X1,X2,X0,X3))
| epsilon_transitive(sK4(function_image(X1,X2,X0,X3)))
| ~ ordinal(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_509])]) ).
fof(f3045,plain,
( ! [X2,X3,X0,X1] :
( ~ function(X0)
| ~ quasi_total(X0,X1,X2)
| ~ relation_of2(X0,X1,X2)
| empty(function_image(X1,X2,X0,X3))
| epsilon_transitive(sK4(function_image(X1,X2,X0,X3)))
| ~ ordinal(X2) )
| ~ spl30_117
| ~ spl30_336 ),
inference(resolution,[],[f3040,f1031]) ).
fof(f5157,plain,
( spl30_508
| ~ spl30_118
| ~ spl30_336 ),
inference(avatar_split_clause,[],[f3044,f3039,f1034,f5155]) ).
fof(f5155,plain,
( spl30_508
<=> ! [X0,X3,X2,X1] :
( ~ function(X0)
| ~ quasi_total(X0,X1,X2)
| ~ relation_of2(X0,X1,X2)
| empty(function_image(X1,X2,X0,X3))
| epsilon_connected(sK4(function_image(X1,X2,X0,X3)))
| ~ ordinal(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_508])]) ).
fof(f3044,plain,
( ! [X2,X3,X0,X1] :
( ~ function(X0)
| ~ quasi_total(X0,X1,X2)
| ~ relation_of2(X0,X1,X2)
| empty(function_image(X1,X2,X0,X3))
| epsilon_connected(sK4(function_image(X1,X2,X0,X3)))
| ~ ordinal(X2) )
| ~ spl30_118
| ~ spl30_336 ),
inference(resolution,[],[f3040,f1035]) ).
fof(f5153,plain,
( spl30_507
| ~ spl30_119
| ~ spl30_336 ),
inference(avatar_split_clause,[],[f3043,f3039,f1038,f5151]) ).
fof(f5151,plain,
( spl30_507
<=> ! [X0,X3,X2,X1] :
( ~ function(X0)
| ~ quasi_total(X0,X1,X2)
| ~ relation_of2(X0,X1,X2)
| empty(function_image(X1,X2,X0,X3))
| ordinal(sK4(function_image(X1,X2,X0,X3)))
| ~ ordinal(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_507])]) ).
fof(f3043,plain,
( ! [X2,X3,X0,X1] :
( ~ function(X0)
| ~ quasi_total(X0,X1,X2)
| ~ relation_of2(X0,X1,X2)
| empty(function_image(X1,X2,X0,X3))
| ordinal(sK4(function_image(X1,X2,X0,X3)))
| ~ ordinal(X2) )
| ~ spl30_119
| ~ spl30_336 ),
inference(resolution,[],[f3040,f1039]) ).
fof(f5149,plain,
( spl30_506
| ~ spl30_258
| ~ spl30_331 ),
inference(avatar_split_clause,[],[f2983,f2979,f2205,f5147]) ).
fof(f5147,plain,
( spl30_506
<=> ! [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,[spl30_506])]) ).
fof(f2205,plain,
( spl30_258
<=> ! [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,[spl30_258])]) ).
fof(f2979,plain,
( spl30_331
<=> ! [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,[spl30_331])]) ).
fof(f2983,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) )
| ~ spl30_258
| ~ spl30_331 ),
inference(resolution,[],[f2980,f2206]) ).
fof(f2206,plain,
( ! [X2,X0,X1] :
( in(X0,powerset(cartesian_product2(X1,X2)))
| empty(powerset(cartesian_product2(X1,X2)))
| ~ relation_of2_as_subset(X0,X1,X2) )
| ~ spl30_258 ),
inference(avatar_component_clause,[],[f2205]) ).
fof(f2980,plain,
( ! [X2,X0,X1] :
( ~ in(powerset(cartesian_product2(X0,X1)),X2)
| ~ relation_of2_as_subset(X2,X0,X1)
| empty(powerset(cartesian_product2(X0,X1))) )
| ~ spl30_331 ),
inference(avatar_component_clause,[],[f2979]) ).
fof(f5129,plain,
( spl30_505
| ~ spl30_301
| ~ spl30_332 ),
inference(avatar_split_clause,[],[f3007,f2985,f2636,f5127]) ).
fof(f5127,plain,
( spl30_505
<=> ! [X4,X0,X3,X2,X1] :
( ~ function(X0)
| ~ empty(X1)
| ~ relation_of2(X0,X2,X1)
| ~ quasi_total(X0,X2,X1)
| relation_rng(relation_rng(function_image(X2,X1,X0,X3))) = X4
| ~ empty(X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_505])]) ).
fof(f2636,plain,
( spl30_301
<=> ! [X0,X1] :
( ~ empty(X0)
| relation_rng(relation_rng(X1)) = X0
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_301])]) ).
fof(f3007,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ function(X0)
| ~ empty(X1)
| ~ relation_of2(X0,X2,X1)
| ~ quasi_total(X0,X2,X1)
| relation_rng(relation_rng(function_image(X2,X1,X0,X3))) = X4
| ~ empty(X4) )
| ~ spl30_301
| ~ spl30_332 ),
inference(resolution,[],[f2986,f2637]) ).
fof(f2637,plain,
( ! [X0,X1] :
( ~ empty(X1)
| relation_rng(relation_rng(X1)) = X0
| ~ empty(X0) )
| ~ spl30_301 ),
inference(avatar_component_clause,[],[f2636]) ).
fof(f5125,plain,
( spl30_504
| ~ spl30_300
| ~ spl30_332 ),
inference(avatar_split_clause,[],[f3006,f2985,f2632,f5123]) ).
fof(f5123,plain,
( spl30_504
<=> ! [X4,X0,X3,X2,X1] :
( ~ function(X0)
| ~ empty(X1)
| ~ relation_of2(X0,X2,X1)
| ~ quasi_total(X0,X2,X1)
| relation_rng(relation_dom(function_image(X2,X1,X0,X3))) = X4
| ~ empty(X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_504])]) ).
fof(f2632,plain,
( spl30_300
<=> ! [X0,X1] :
( ~ empty(X0)
| relation_rng(relation_dom(X1)) = X0
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_300])]) ).
fof(f3006,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ function(X0)
| ~ empty(X1)
| ~ relation_of2(X0,X2,X1)
| ~ quasi_total(X0,X2,X1)
| relation_rng(relation_dom(function_image(X2,X1,X0,X3))) = X4
| ~ empty(X4) )
| ~ spl30_300
| ~ spl30_332 ),
inference(resolution,[],[f2986,f2633]) ).
fof(f2633,plain,
( ! [X0,X1] :
( ~ empty(X1)
| relation_rng(relation_dom(X1)) = X0
| ~ empty(X0) )
| ~ spl30_300 ),
inference(avatar_component_clause,[],[f2632]) ).
fof(f5121,plain,
( spl30_503
| ~ spl30_299
| ~ spl30_332 ),
inference(avatar_split_clause,[],[f3005,f2985,f2628,f5119]) ).
fof(f5119,plain,
( spl30_503
<=> ! [X4,X0,X3,X2,X1] :
( ~ function(X0)
| ~ empty(X1)
| ~ relation_of2(X0,X2,X1)
| ~ quasi_total(X0,X2,X1)
| relation_dom(relation_rng(function_image(X2,X1,X0,X3))) = X4
| ~ empty(X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_503])]) ).
fof(f2628,plain,
( spl30_299
<=> ! [X0,X1] :
( ~ empty(X0)
| relation_dom(relation_rng(X1)) = X0
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_299])]) ).
fof(f3005,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ function(X0)
| ~ empty(X1)
| ~ relation_of2(X0,X2,X1)
| ~ quasi_total(X0,X2,X1)
| relation_dom(relation_rng(function_image(X2,X1,X0,X3))) = X4
| ~ empty(X4) )
| ~ spl30_299
| ~ spl30_332 ),
inference(resolution,[],[f2986,f2629]) ).
fof(f2629,plain,
( ! [X0,X1] :
( ~ empty(X1)
| relation_dom(relation_rng(X1)) = X0
| ~ empty(X0) )
| ~ spl30_299 ),
inference(avatar_component_clause,[],[f2628]) ).
fof(f5117,plain,
( spl30_502
| ~ spl30_297
| ~ spl30_332 ),
inference(avatar_split_clause,[],[f3004,f2985,f2620,f5115]) ).
fof(f5115,plain,
( spl30_502
<=> ! [X4,X0,X3,X2,X1] :
( ~ function(X0)
| ~ empty(X1)
| ~ relation_of2(X0,X2,X1)
| ~ quasi_total(X0,X2,X1)
| relation_dom(relation_dom(function_image(X2,X1,X0,X3))) = X4
| ~ empty(X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_502])]) ).
fof(f2620,plain,
( spl30_297
<=> ! [X0,X1] :
( ~ empty(X0)
| relation_dom(relation_dom(X1)) = X0
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_297])]) ).
fof(f3004,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ function(X0)
| ~ empty(X1)
| ~ relation_of2(X0,X2,X1)
| ~ quasi_total(X0,X2,X1)
| relation_dom(relation_dom(function_image(X2,X1,X0,X3))) = X4
| ~ empty(X4) )
| ~ spl30_297
| ~ spl30_332 ),
inference(resolution,[],[f2986,f2621]) ).
fof(f2621,plain,
( ! [X0,X1] :
( ~ empty(X1)
| relation_dom(relation_dom(X1)) = X0
| ~ empty(X0) )
| ~ spl30_297 ),
inference(avatar_component_clause,[],[f2620]) ).
fof(f5105,plain,
( spl30_501
| ~ spl30_133
| ~ spl30_413 ),
inference(avatar_split_clause,[],[f4475,f4142,f1154,f5103]) ).
fof(f5103,plain,
( spl30_501
<=> ! [X0,X1] :
( ~ finite(X0)
| finite(first_projection_as_func_of(X0,X1))
| ~ finite(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_501])]) ).
fof(f1154,plain,
( spl30_133
<=> ! [X0,X1] :
( finite(cartesian_product2(X0,X1))
| ~ finite(X1)
| ~ finite(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_133])]) ).
fof(f4142,plain,
( spl30_413
<=> ! [X0,X1] :
( finite(first_projection_as_func_of(X0,X1))
| ~ finite(X0)
| ~ finite(cartesian_product2(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_413])]) ).
fof(f4475,plain,
( ! [X0,X1] :
( ~ finite(X0)
| finite(first_projection_as_func_of(X0,X1))
| ~ finite(X1) )
| ~ spl30_133
| ~ spl30_413 ),
inference(duplicate_literal_removal,[],[f4474]) ).
fof(f4474,plain,
( ! [X0,X1] :
( ~ finite(X0)
| finite(first_projection_as_func_of(X0,X1))
| ~ finite(X1)
| ~ finite(X0) )
| ~ spl30_133
| ~ spl30_413 ),
inference(resolution,[],[f4143,f1155]) ).
fof(f1155,plain,
( ! [X0,X1] :
( finite(cartesian_product2(X0,X1))
| ~ finite(X1)
| ~ finite(X0) )
| ~ spl30_133 ),
inference(avatar_component_clause,[],[f1154]) ).
fof(f4143,plain,
( ! [X0,X1] :
( ~ finite(cartesian_product2(X0,X1))
| ~ finite(X0)
| finite(first_projection_as_func_of(X0,X1)) )
| ~ spl30_413 ),
inference(avatar_component_clause,[],[f4142]) ).
fof(f5101,plain,
( spl30_500
| ~ spl30_231
| ~ spl30_332 ),
inference(avatar_split_clause,[],[f2999,f2985,f1954,f5099]) ).
fof(f5099,plain,
( spl30_500
<=> ! [X4,X0,X3,X2,X1] :
( ~ function(X0)
| ~ empty(X1)
| ~ relation_of2(X0,X2,X1)
| ~ quasi_total(X0,X2,X1)
| ~ empty(X3)
| relation_rng(function_image(X2,X1,X0,X4)) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_500])]) ).
fof(f1954,plain,
( spl30_231
<=> ! [X0,X1] :
( relation_rng(X1) = X0
| ~ empty(X0)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_231])]) ).
fof(f2999,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ function(X0)
| ~ empty(X1)
| ~ relation_of2(X0,X2,X1)
| ~ quasi_total(X0,X2,X1)
| ~ empty(X3)
| relation_rng(function_image(X2,X1,X0,X4)) = X3 )
| ~ spl30_231
| ~ spl30_332 ),
inference(resolution,[],[f2986,f1955]) ).
fof(f1955,plain,
( ! [X0,X1] :
( ~ empty(X1)
| ~ empty(X0)
| relation_rng(X1) = X0 )
| ~ spl30_231 ),
inference(avatar_component_clause,[],[f1954]) ).
fof(f5097,plain,
( spl30_499
| ~ spl30_230
| ~ spl30_332 ),
inference(avatar_split_clause,[],[f2998,f2985,f1950,f5095]) ).
fof(f5095,plain,
( spl30_499
<=> ! [X4,X0,X3,X2,X1] :
( ~ function(X0)
| ~ empty(X1)
| ~ relation_of2(X0,X2,X1)
| ~ quasi_total(X0,X2,X1)
| ~ empty(X3)
| relation_dom(function_image(X2,X1,X0,X4)) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_499])]) ).
fof(f1950,plain,
( spl30_230
<=> ! [X0,X1] :
( relation_dom(X1) = X0
| ~ empty(X0)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_230])]) ).
fof(f2998,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ function(X0)
| ~ empty(X1)
| ~ relation_of2(X0,X2,X1)
| ~ quasi_total(X0,X2,X1)
| ~ empty(X3)
| relation_dom(function_image(X2,X1,X0,X4)) = X3 )
| ~ spl30_230
| ~ spl30_332 ),
inference(resolution,[],[f2986,f1951]) ).
fof(f1951,plain,
( ! [X0,X1] :
( ~ empty(X1)
| ~ empty(X0)
| relation_dom(X1) = X0 )
| ~ spl30_230 ),
inference(avatar_component_clause,[],[f1950]) ).
fof(f5073,plain,
( spl30_498
| ~ spl30_294
| ~ spl30_332 ),
inference(avatar_split_clause,[],[f3003,f2985,f2502,f5071]) ).
fof(f5071,plain,
( spl30_498
<=> ! [X0,X3,X2,X1] :
( ~ function(X0)
| ~ empty(X1)
| ~ relation_of2(X0,X2,X1)
| ~ quasi_total(X0,X2,X1)
| sK10 = relation_dom(relation_rng(function_image(X2,X1,X0,X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_498])]) ).
fof(f2502,plain,
( spl30_294
<=> ! [X0] :
( sK10 = relation_dom(relation_rng(X0))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_294])]) ).
fof(f3003,plain,
( ! [X2,X3,X0,X1] :
( ~ function(X0)
| ~ empty(X1)
| ~ relation_of2(X0,X2,X1)
| ~ quasi_total(X0,X2,X1)
| sK10 = relation_dom(relation_rng(function_image(X2,X1,X0,X3))) )
| ~ spl30_294
| ~ spl30_332 ),
inference(resolution,[],[f2986,f2503]) ).
fof(f2503,plain,
( ! [X0] :
( ~ empty(X0)
| sK10 = relation_dom(relation_rng(X0)) )
| ~ spl30_294 ),
inference(avatar_component_clause,[],[f2502]) ).
fof(f5069,plain,
( spl30_497
| ~ spl30_292
| ~ spl30_332 ),
inference(avatar_split_clause,[],[f3002,f2985,f2494,f5067]) ).
fof(f5067,plain,
( spl30_497
<=> ! [X0,X3,X2,X1] :
( ~ function(X0)
| ~ empty(X1)
| ~ relation_of2(X0,X2,X1)
| ~ quasi_total(X0,X2,X1)
| sK10 = relation_dom(relation_dom(function_image(X2,X1,X0,X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_497])]) ).
fof(f2494,plain,
( spl30_292
<=> ! [X0] :
( sK10 = relation_dom(relation_dom(X0))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_292])]) ).
fof(f3002,plain,
( ! [X2,X3,X0,X1] :
( ~ function(X0)
| ~ empty(X1)
| ~ relation_of2(X0,X2,X1)
| ~ quasi_total(X0,X2,X1)
| sK10 = relation_dom(relation_dom(function_image(X2,X1,X0,X3))) )
| ~ spl30_292
| ~ spl30_332 ),
inference(resolution,[],[f2986,f2495]) ).
fof(f2495,plain,
( ! [X0] :
( ~ empty(X0)
| sK10 = relation_dom(relation_dom(X0)) )
| ~ spl30_292 ),
inference(avatar_component_clause,[],[f2494]) ).
fof(f5065,plain,
( spl30_496
| ~ spl30_291
| ~ spl30_332 ),
inference(avatar_split_clause,[],[f3001,f2985,f2490,f5063]) ).
fof(f5063,plain,
( spl30_496
<=> ! [X0,X3,X2,X1] :
( ~ function(X0)
| ~ empty(X1)
| ~ relation_of2(X0,X2,X1)
| ~ quasi_total(X0,X2,X1)
| sK10 = relation_rng(relation_rng(function_image(X2,X1,X0,X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_496])]) ).
fof(f2490,plain,
( spl30_291
<=> ! [X0] :
( sK10 = relation_rng(relation_rng(X0))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_291])]) ).
fof(f3001,plain,
( ! [X2,X3,X0,X1] :
( ~ function(X0)
| ~ empty(X1)
| ~ relation_of2(X0,X2,X1)
| ~ quasi_total(X0,X2,X1)
| sK10 = relation_rng(relation_rng(function_image(X2,X1,X0,X3))) )
| ~ spl30_291
| ~ spl30_332 ),
inference(resolution,[],[f2986,f2491]) ).
fof(f2491,plain,
( ! [X0] :
( ~ empty(X0)
| sK10 = relation_rng(relation_rng(X0)) )
| ~ spl30_291 ),
inference(avatar_component_clause,[],[f2490]) ).
fof(f5034,plain,
( spl30_495
| ~ spl30_290
| ~ spl30_332 ),
inference(avatar_split_clause,[],[f3000,f2985,f2486,f5032]) ).
fof(f5032,plain,
( spl30_495
<=> ! [X0,X3,X2,X1] :
( ~ function(X0)
| ~ empty(X1)
| ~ relation_of2(X0,X2,X1)
| ~ quasi_total(X0,X2,X1)
| sK10 = relation_rng(relation_dom(function_image(X2,X1,X0,X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_495])]) ).
fof(f2486,plain,
( spl30_290
<=> ! [X0] :
( sK10 = relation_rng(relation_dom(X0))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_290])]) ).
fof(f3000,plain,
( ! [X2,X3,X0,X1] :
( ~ function(X0)
| ~ empty(X1)
| ~ relation_of2(X0,X2,X1)
| ~ quasi_total(X0,X2,X1)
| sK10 = relation_rng(relation_dom(function_image(X2,X1,X0,X3))) )
| ~ spl30_290
| ~ spl30_332 ),
inference(resolution,[],[f2986,f2487]) ).
fof(f2487,plain,
( ! [X0] :
( ~ empty(X0)
| sK10 = relation_rng(relation_dom(X0)) )
| ~ spl30_290 ),
inference(avatar_component_clause,[],[f2486]) ).
fof(f5030,plain,
( spl30_494
| ~ spl30_125
| ~ spl30_332 ),
inference(avatar_split_clause,[],[f2994,f2985,f1062,f5028]) ).
fof(f5028,plain,
( spl30_494
<=> ! [X4,X0,X3,X2,X1] :
( ~ function(X0)
| ~ empty(X1)
| ~ relation_of2(X0,X2,X1)
| ~ quasi_total(X0,X2,X1)
| function_image(X2,X1,X0,X4) = X3
| ~ empty(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_494])]) ).
fof(f1062,plain,
( spl30_125
<=> ! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_125])]) ).
fof(f2994,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ function(X0)
| ~ empty(X1)
| ~ relation_of2(X0,X2,X1)
| ~ quasi_total(X0,X2,X1)
| function_image(X2,X1,X0,X4) = X3
| ~ empty(X3) )
| ~ spl30_125
| ~ spl30_332 ),
inference(resolution,[],[f2986,f1063]) ).
fof(f1063,plain,
( ! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) )
| ~ spl30_125 ),
inference(avatar_component_clause,[],[f1062]) ).
fof(f5018,plain,
( spl30_493
| ~ spl30_202
| ~ spl30_332 ),
inference(avatar_split_clause,[],[f2997,f2985,f1778,f5016]) ).
fof(f5016,plain,
( spl30_493
<=> ! [X0,X3,X2,X1] :
( ~ function(X0)
| ~ empty(X1)
| ~ relation_of2(X0,X2,X1)
| ~ quasi_total(X0,X2,X1)
| sK10 = relation_dom(function_image(X2,X1,X0,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_493])]) ).
fof(f1778,plain,
( spl30_202
<=> ! [X0] :
( relation_dom(X0) = sK10
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_202])]) ).
fof(f2997,plain,
( ! [X2,X3,X0,X1] :
( ~ function(X0)
| ~ empty(X1)
| ~ relation_of2(X0,X2,X1)
| ~ quasi_total(X0,X2,X1)
| sK10 = relation_dom(function_image(X2,X1,X0,X3)) )
| ~ spl30_202
| ~ spl30_332 ),
inference(resolution,[],[f2986,f1779]) ).
fof(f1779,plain,
( ! [X0] :
( ~ empty(X0)
| relation_dom(X0) = sK10 )
| ~ spl30_202 ),
inference(avatar_component_clause,[],[f1778]) ).
fof(f5014,plain,
( spl30_492
| ~ spl30_201
| ~ spl30_332 ),
inference(avatar_split_clause,[],[f2996,f2985,f1774,f5012]) ).
fof(f5012,plain,
( spl30_492
<=> ! [X0,X3,X2,X1] :
( ~ function(X0)
| ~ empty(X1)
| ~ relation_of2(X0,X2,X1)
| ~ quasi_total(X0,X2,X1)
| sK10 = relation_rng(function_image(X2,X1,X0,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_492])]) ).
fof(f1774,plain,
( spl30_201
<=> ! [X0] :
( relation_rng(X0) = sK10
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_201])]) ).
fof(f2996,plain,
( ! [X2,X3,X0,X1] :
( ~ function(X0)
| ~ empty(X1)
| ~ relation_of2(X0,X2,X1)
| ~ quasi_total(X0,X2,X1)
| sK10 = relation_rng(function_image(X2,X1,X0,X3)) )
| ~ spl30_201
| ~ spl30_332 ),
inference(resolution,[],[f2986,f1775]) ).
fof(f1775,plain,
( ! [X0] :
( ~ empty(X0)
| relation_rng(X0) = sK10 )
| ~ spl30_201 ),
inference(avatar_component_clause,[],[f1774]) ).
fof(f5003,plain,
( spl30_491
| ~ spl30_129
| ~ spl30_339 ),
inference(avatar_split_clause,[],[f3162,f3155,f1138,f5001]) ).
fof(f1138,plain,
( spl30_129
<=> ! [X0,X1] : quasi_total(first_projection_as_func_of(X0,X1),cartesian_product2(X0,X1),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_129])]) ).
fof(f3155,plain,
( spl30_339
<=> ! [X2,X0,X1] :
( function_image(cartesian_product2(X0,X1),X0,first_projection_as_func_of(X0,X1),X2) = relation_image(first_projection_as_func_of(X0,X1),X2)
| ~ quasi_total(first_projection_as_func_of(X0,X1),cartesian_product2(X0,X1),X0)
| ~ function(first_projection_as_func_of(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_339])]) ).
fof(f3162,plain,
( ! [X2,X0,X1] :
( function_image(cartesian_product2(X0,X1),X0,first_projection_as_func_of(X0,X1),X2) = relation_image(first_projection_as_func_of(X0,X1),X2)
| ~ function(first_projection_as_func_of(X0,X1)) )
| ~ spl30_129
| ~ spl30_339 ),
inference(resolution,[],[f3156,f1139]) ).
fof(f1139,plain,
( ! [X0,X1] : quasi_total(first_projection_as_func_of(X0,X1),cartesian_product2(X0,X1),X0)
| ~ spl30_129 ),
inference(avatar_component_clause,[],[f1138]) ).
fof(f3156,plain,
( ! [X2,X0,X1] :
( ~ quasi_total(first_projection_as_func_of(X0,X1),cartesian_product2(X0,X1),X0)
| function_image(cartesian_product2(X0,X1),X0,first_projection_as_func_of(X0,X1),X2) = relation_image(first_projection_as_func_of(X0,X1),X2)
| ~ function(first_projection_as_func_of(X0,X1)) )
| ~ spl30_339 ),
inference(avatar_component_clause,[],[f3155]) ).
fof(f4999,plain,
( spl30_490
| ~ spl30_194
| ~ spl30_332 ),
inference(avatar_split_clause,[],[f2995,f2985,f1585,f4997]) ).
fof(f4997,plain,
( spl30_490
<=> ! [X0,X3,X2,X1] :
( ~ function(X0)
| ~ empty(X1)
| ~ relation_of2(X0,X2,X1)
| ~ quasi_total(X0,X2,X1)
| sK10 = function_image(X2,X1,X0,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_490])]) ).
fof(f1585,plain,
( spl30_194
<=> ! [X0] :
( sK10 = X0
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_194])]) ).
fof(f2995,plain,
( ! [X2,X3,X0,X1] :
( ~ function(X0)
| ~ empty(X1)
| ~ relation_of2(X0,X2,X1)
| ~ quasi_total(X0,X2,X1)
| sK10 = function_image(X2,X1,X0,X3) )
| ~ spl30_194
| ~ spl30_332 ),
inference(resolution,[],[f2986,f1586]) ).
fof(f1586,plain,
( ! [X0] :
( ~ empty(X0)
| sK10 = X0 )
| ~ spl30_194 ),
inference(avatar_component_clause,[],[f1585]) ).
fof(f4995,plain,
( spl30_489
| ~ spl30_258
| ~ spl30_318 ),
inference(avatar_split_clause,[],[f2921,f2859,f2205,f4993]) ).
fof(f4993,plain,
( spl30_489
<=> ! [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,[spl30_489])]) ).
fof(f2859,plain,
( spl30_318
<=> ! [X0,X1] :
( empty(powerset(X0))
| ~ subset(X1,X0)
| ~ in(powerset(X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_318])]) ).
fof(f2921,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) )
| ~ spl30_258
| ~ spl30_318 ),
inference(resolution,[],[f2860,f2206]) ).
fof(f2860,plain,
( ! [X0,X1] :
( ~ in(powerset(X0),X1)
| ~ subset(X1,X0)
| empty(powerset(X0)) )
| ~ spl30_318 ),
inference(avatar_component_clause,[],[f2859]) ).
fof(f4910,plain,
( spl30_488
| ~ spl30_87
| ~ spl30_332 ),
inference(avatar_split_clause,[],[f2993,f2985,f800,f4908]) ).
fof(f4908,plain,
( spl30_488
<=> ! [X0,X3,X2,X1] :
( ~ function(X0)
| ~ empty(X1)
| ~ relation_of2(X0,X2,X1)
| ~ quasi_total(X0,X2,X1)
| ordinal(function_image(X2,X1,X0,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_488])]) ).
fof(f800,plain,
( spl30_87
<=> ! [X0] :
( ordinal(X0)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_87])]) ).
fof(f2993,plain,
( ! [X2,X3,X0,X1] :
( ~ function(X0)
| ~ empty(X1)
| ~ relation_of2(X0,X2,X1)
| ~ quasi_total(X0,X2,X1)
| ordinal(function_image(X2,X1,X0,X3)) )
| ~ spl30_87
| ~ spl30_332 ),
inference(resolution,[],[f2986,f801]) ).
fof(f801,plain,
( ! [X0] :
( ~ empty(X0)
| ordinal(X0) )
| ~ spl30_87 ),
inference(avatar_component_clause,[],[f800]) ).
fof(f4906,plain,
( spl30_487
| ~ spl30_86
| ~ spl30_332 ),
inference(avatar_split_clause,[],[f2992,f2985,f796,f4904]) ).
fof(f4904,plain,
( spl30_487
<=> ! [X0,X3,X2,X1] :
( ~ function(X0)
| ~ empty(X1)
| ~ relation_of2(X0,X2,X1)
| ~ quasi_total(X0,X2,X1)
| epsilon_connected(function_image(X2,X1,X0,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_487])]) ).
fof(f796,plain,
( spl30_86
<=> ! [X0] :
( epsilon_connected(X0)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_86])]) ).
fof(f2992,plain,
( ! [X2,X3,X0,X1] :
( ~ function(X0)
| ~ empty(X1)
| ~ relation_of2(X0,X2,X1)
| ~ quasi_total(X0,X2,X1)
| epsilon_connected(function_image(X2,X1,X0,X3)) )
| ~ spl30_86
| ~ spl30_332 ),
inference(resolution,[],[f2986,f797]) ).
fof(f797,plain,
( ! [X0] :
( ~ empty(X0)
| epsilon_connected(X0) )
| ~ spl30_86 ),
inference(avatar_component_clause,[],[f796]) ).
fof(f4902,plain,
( spl30_486
| ~ spl30_85
| ~ spl30_332 ),
inference(avatar_split_clause,[],[f2991,f2985,f792,f4900]) ).
fof(f4900,plain,
( spl30_486
<=> ! [X0,X3,X2,X1] :
( ~ function(X0)
| ~ empty(X1)
| ~ relation_of2(X0,X2,X1)
| ~ quasi_total(X0,X2,X1)
| epsilon_transitive(function_image(X2,X1,X0,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_486])]) ).
fof(f792,plain,
( spl30_85
<=> ! [X0] :
( epsilon_transitive(X0)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_85])]) ).
fof(f2991,plain,
( ! [X2,X3,X0,X1] :
( ~ function(X0)
| ~ empty(X1)
| ~ relation_of2(X0,X2,X1)
| ~ quasi_total(X0,X2,X1)
| epsilon_transitive(function_image(X2,X1,X0,X3)) )
| ~ spl30_85
| ~ spl30_332 ),
inference(resolution,[],[f2986,f793]) ).
fof(f793,plain,
( ! [X0] :
( ~ empty(X0)
| epsilon_transitive(X0) )
| ~ spl30_85 ),
inference(avatar_component_clause,[],[f792]) ).
fof(f4898,plain,
( spl30_485
| ~ spl30_84
| ~ spl30_332 ),
inference(avatar_split_clause,[],[f2990,f2985,f788,f4896]) ).
fof(f4896,plain,
( spl30_485
<=> ! [X0,X3,X2,X1] :
( ~ function(X0)
| ~ empty(X1)
| ~ relation_of2(X0,X2,X1)
| ~ quasi_total(X0,X2,X1)
| relation(function_image(X2,X1,X0,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_485])]) ).
fof(f788,plain,
( spl30_84
<=> ! [X0] :
( relation(X0)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_84])]) ).
fof(f2990,plain,
( ! [X2,X3,X0,X1] :
( ~ function(X0)
| ~ empty(X1)
| ~ relation_of2(X0,X2,X1)
| ~ quasi_total(X0,X2,X1)
| relation(function_image(X2,X1,X0,X3)) )
| ~ spl30_84
| ~ spl30_332 ),
inference(resolution,[],[f2986,f789]) ).
fof(f789,plain,
( ! [X0] :
( ~ empty(X0)
| relation(X0) )
| ~ spl30_84 ),
inference(avatar_component_clause,[],[f788]) ).
fof(f4894,plain,
( spl30_484
| ~ spl30_83
| ~ spl30_332 ),
inference(avatar_split_clause,[],[f2989,f2985,f784,f4892]) ).
fof(f4892,plain,
( spl30_484
<=> ! [X0,X3,X2,X1] :
( ~ function(X0)
| ~ empty(X1)
| ~ relation_of2(X0,X2,X1)
| ~ quasi_total(X0,X2,X1)
| function(function_image(X2,X1,X0,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_484])]) ).
fof(f784,plain,
( spl30_83
<=> ! [X0] :
( function(X0)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_83])]) ).
fof(f2989,plain,
( ! [X2,X3,X0,X1] :
( ~ function(X0)
| ~ empty(X1)
| ~ relation_of2(X0,X2,X1)
| ~ quasi_total(X0,X2,X1)
| function(function_image(X2,X1,X0,X3)) )
| ~ spl30_83
| ~ spl30_332 ),
inference(resolution,[],[f2986,f785]) ).
fof(f785,plain,
( ! [X0] :
( ~ empty(X0)
| function(X0) )
| ~ spl30_83 ),
inference(avatar_component_clause,[],[f784]) ).
fof(f4890,plain,
( spl30_483
| ~ spl30_82
| ~ spl30_332 ),
inference(avatar_split_clause,[],[f2988,f2985,f780,f4888]) ).
fof(f4888,plain,
( spl30_483
<=> ! [X0,X3,X2,X1] :
( ~ function(X0)
| ~ empty(X1)
| ~ relation_of2(X0,X2,X1)
| ~ quasi_total(X0,X2,X1)
| finite(function_image(X2,X1,X0,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_483])]) ).
fof(f780,plain,
( spl30_82
<=> ! [X0] :
( finite(X0)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_82])]) ).
fof(f2988,plain,
( ! [X2,X3,X0,X1] :
( ~ function(X0)
| ~ empty(X1)
| ~ relation_of2(X0,X2,X1)
| ~ quasi_total(X0,X2,X1)
| finite(function_image(X2,X1,X0,X3)) )
| ~ spl30_82
| ~ spl30_332 ),
inference(resolution,[],[f2986,f781]) ).
fof(f781,plain,
( ! [X0] :
( ~ empty(X0)
| finite(X0) )
| ~ spl30_82 ),
inference(avatar_component_clause,[],[f780]) ).
fof(f4886,plain,
( spl30_482
| ~ spl30_131
| ~ spl30_330 ),
inference(avatar_split_clause,[],[f2974,f2965,f1146,f4884]) ).
fof(f2965,plain,
( spl30_330
<=> ! [X2,X0,X1] :
( ~ in(X0,first_projection_as_func_of(X1,X2))
| element(X0,cartesian_product2(cartesian_product2(X1,X2),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_330])]) ).
fof(f2974,plain,
( ! [X2,X0,X1] :
( ~ in(X0,first_projection_as_func_of(X1,X2))
| empty(cartesian_product2(cartesian_product2(X1,X2),X1))
| in(X0,cartesian_product2(cartesian_product2(X1,X2),X1)) )
| ~ spl30_131
| ~ spl30_330 ),
inference(resolution,[],[f2966,f1147]) ).
fof(f2966,plain,
( ! [X2,X0,X1] :
( element(X0,cartesian_product2(cartesian_product2(X1,X2),X1))
| ~ in(X0,first_projection_as_func_of(X1,X2)) )
| ~ spl30_330 ),
inference(avatar_component_clause,[],[f2965]) ).
fof(f4882,plain,
( spl30_481
| ~ spl30_131
| ~ spl30_329 ),
inference(avatar_split_clause,[],[f2968,f2961,f1146,f4880]) ).
fof(f2961,plain,
( spl30_329
<=> ! [X0,X1] :
( ~ in(X0,X1)
| element(X0,cartesian_product2(relation_dom(X1),relation_rng(X1)))
| ~ relation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_329])]) ).
fof(f2968,plain,
( ! [X0,X1] :
( ~ in(X0,X1)
| ~ relation(X1)
| empty(cartesian_product2(relation_dom(X1),relation_rng(X1)))
| in(X0,cartesian_product2(relation_dom(X1),relation_rng(X1))) )
| ~ spl30_131
| ~ spl30_329 ),
inference(resolution,[],[f2962,f1147]) ).
fof(f2962,plain,
( ! [X0,X1] :
( element(X0,cartesian_product2(relation_dom(X1),relation_rng(X1)))
| ~ in(X0,X1)
| ~ relation(X1) )
| ~ spl30_329 ),
inference(avatar_component_clause,[],[f2961]) ).
fof(f4878,plain,
( spl30_480
| ~ spl30_134
| ~ spl30_314 ),
inference(avatar_split_clause,[],[f2918,f2843,f1158,f4876]) ).
fof(f4876,plain,
( spl30_480
<=> ! [X0,X1] :
( empty(powerset(cartesian_product2(X0,X1)))
| empty(sK3(powerset(cartesian_product2(X0,X1))))
| relation(sK4(sK3(powerset(cartesian_product2(X0,X1))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_480])]) ).
fof(f2843,plain,
( spl30_314
<=> ! [X0] :
( element(sK4(sK3(X0)),X0)
| empty(X0)
| empty(sK3(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_314])]) ).
fof(f2918,plain,
( ! [X0,X1] :
( empty(powerset(cartesian_product2(X0,X1)))
| empty(sK3(powerset(cartesian_product2(X0,X1))))
| relation(sK4(sK3(powerset(cartesian_product2(X0,X1))))) )
| ~ spl30_134
| ~ spl30_314 ),
inference(resolution,[],[f2844,f1159]) ).
fof(f2844,plain,
( ! [X0] :
( element(sK4(sK3(X0)),X0)
| empty(X0)
| empty(sK3(X0)) )
| ~ spl30_314 ),
inference(avatar_component_clause,[],[f2843]) ).
fof(f4874,plain,
( spl30_479
| ~ spl30_134
| ~ spl30_311 ),
inference(avatar_split_clause,[],[f2908,f2830,f1158,f4872]) ).
fof(f4872,plain,
( spl30_479
<=> ! [X0,X1] :
( empty(powerset(cartesian_product2(X0,X1)))
| empty(sK2(powerset(cartesian_product2(X0,X1))))
| relation(sK4(sK2(powerset(cartesian_product2(X0,X1))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_479])]) ).
fof(f2830,plain,
( spl30_311
<=> ! [X0] :
( element(sK4(sK2(X0)),X0)
| empty(X0)
| empty(sK2(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_311])]) ).
fof(f2908,plain,
( ! [X0,X1] :
( empty(powerset(cartesian_product2(X0,X1)))
| empty(sK2(powerset(cartesian_product2(X0,X1))))
| relation(sK4(sK2(powerset(cartesian_product2(X0,X1))))) )
| ~ spl30_134
| ~ spl30_311 ),
inference(resolution,[],[f2831,f1159]) ).
fof(f2831,plain,
( ! [X0] :
( element(sK4(sK2(X0)),X0)
| empty(X0)
| empty(sK2(X0)) )
| ~ spl30_311 ),
inference(avatar_component_clause,[],[f2830]) ).
fof(f4870,plain,
( spl30_478
| ~ spl30_134
| ~ spl30_310 ),
inference(avatar_split_clause,[],[f2898,f2826,f1158,f4868]) ).
fof(f4868,plain,
( spl30_478
<=> ! [X0,X1] :
( empty(powerset(cartesian_product2(X0,X1)))
| empty(sK1(powerset(cartesian_product2(X0,X1))))
| relation(sK4(sK1(powerset(cartesian_product2(X0,X1))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_478])]) ).
fof(f2826,plain,
( spl30_310
<=> ! [X0] :
( element(sK4(sK1(X0)),X0)
| empty(X0)
| empty(sK1(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_310])]) ).
fof(f2898,plain,
( ! [X0,X1] :
( empty(powerset(cartesian_product2(X0,X1)))
| empty(sK1(powerset(cartesian_product2(X0,X1))))
| relation(sK4(sK1(powerset(cartesian_product2(X0,X1))))) )
| ~ spl30_134
| ~ spl30_310 ),
inference(resolution,[],[f2827,f1159]) ).
fof(f2827,plain,
( ! [X0] :
( element(sK4(sK1(X0)),X0)
| empty(X0)
| empty(sK1(X0)) )
| ~ spl30_310 ),
inference(avatar_component_clause,[],[f2826]) ).
fof(f4851,plain,
( spl30_477
| ~ spl30_148
| ~ spl30_314 ),
inference(avatar_split_clause,[],[f2915,f2843,f1265,f4849]) ).
fof(f4849,plain,
( spl30_477
<=> ! [X0,X1] :
( empty(powerset(X0))
| empty(sK3(powerset(X0)))
| element(X1,X0)
| ~ in(X1,sK4(sK3(powerset(X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_477])]) ).
fof(f2915,plain,
( ! [X0,X1] :
( empty(powerset(X0))
| empty(sK3(powerset(X0)))
| element(X1,X0)
| ~ in(X1,sK4(sK3(powerset(X0)))) )
| ~ spl30_148
| ~ spl30_314 ),
inference(resolution,[],[f2844,f1266]) ).
fof(f4847,plain,
( spl30_476
| ~ spl30_148
| ~ spl30_311 ),
inference(avatar_split_clause,[],[f2905,f2830,f1265,f4845]) ).
fof(f4845,plain,
( spl30_476
<=> ! [X0,X1] :
( empty(powerset(X0))
| empty(sK2(powerset(X0)))
| element(X1,X0)
| ~ in(X1,sK4(sK2(powerset(X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_476])]) ).
fof(f2905,plain,
( ! [X0,X1] :
( empty(powerset(X0))
| empty(sK2(powerset(X0)))
| element(X1,X0)
| ~ in(X1,sK4(sK2(powerset(X0)))) )
| ~ spl30_148
| ~ spl30_311 ),
inference(resolution,[],[f2831,f1266]) ).
fof(f4843,plain,
( spl30_475
| ~ spl30_148
| ~ spl30_310 ),
inference(avatar_split_clause,[],[f2895,f2826,f1265,f4841]) ).
fof(f4841,plain,
( spl30_475
<=> ! [X0,X1] :
( empty(powerset(X0))
| empty(sK1(powerset(X0)))
| element(X1,X0)
| ~ in(X1,sK4(sK1(powerset(X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_475])]) ).
fof(f2895,plain,
( ! [X0,X1] :
( empty(powerset(X0))
| empty(sK1(powerset(X0)))
| element(X1,X0)
| ~ in(X1,sK4(sK1(powerset(X0)))) )
| ~ spl30_148
| ~ spl30_310 ),
inference(resolution,[],[f2827,f1266]) ).
fof(f4818,plain,
( spl30_474
| ~ spl30_143
| ~ spl30_314 ),
inference(avatar_split_clause,[],[f2914,f2843,f1229,f4816]) ).
fof(f2914,plain,
( ! [X0,X1] :
( empty(powerset(X0))
| empty(sK3(powerset(X0)))
| ~ empty(X0)
| ~ in(X1,sK4(sK3(powerset(X0)))) )
| ~ spl30_143
| ~ spl30_314 ),
inference(resolution,[],[f2844,f1230]) ).
fof(f4814,plain,
( spl30_473
| ~ spl30_143
| ~ spl30_311 ),
inference(avatar_split_clause,[],[f2904,f2830,f1229,f4812]) ).
fof(f2904,plain,
( ! [X0,X1] :
( empty(powerset(X0))
| empty(sK2(powerset(X0)))
| ~ empty(X0)
| ~ in(X1,sK4(sK2(powerset(X0)))) )
| ~ spl30_143
| ~ spl30_311 ),
inference(resolution,[],[f2831,f1230]) ).
fof(f4810,plain,
( spl30_472
| ~ spl30_143
| ~ spl30_310 ),
inference(avatar_split_clause,[],[f2894,f2826,f1229,f4808]) ).
fof(f2894,plain,
( ! [X0,X1] :
( empty(powerset(X0))
| empty(sK1(powerset(X0)))
| ~ empty(X0)
| ~ in(X1,sK4(sK1(powerset(X0)))) )
| ~ spl30_143
| ~ spl30_310 ),
inference(resolution,[],[f2827,f1230]) ).
fof(f4806,plain,
( spl30_471
| ~ spl30_134
| ~ spl30_309 ),
inference(avatar_split_clause,[],[f2886,f2822,f1158,f4804]) ).
fof(f4804,plain,
( spl30_471
<=> ! [X0,X1] :
( empty(sK4(powerset(powerset(cartesian_product2(X0,X1)))))
| relation(sK4(sK4(powerset(powerset(cartesian_product2(X0,X1)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_471])]) ).
fof(f2822,plain,
( spl30_309
<=> ! [X0] :
( element(sK4(sK4(powerset(X0))),X0)
| empty(sK4(powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_309])]) ).
fof(f2886,plain,
( ! [X0,X1] :
( empty(sK4(powerset(powerset(cartesian_product2(X0,X1)))))
| relation(sK4(sK4(powerset(powerset(cartesian_product2(X0,X1)))))) )
| ~ spl30_134
| ~ spl30_309 ),
inference(resolution,[],[f2823,f1159]) ).
fof(f2823,plain,
( ! [X0] :
( element(sK4(sK4(powerset(X0))),X0)
| empty(sK4(powerset(X0))) )
| ~ spl30_309 ),
inference(avatar_component_clause,[],[f2822]) ).
fof(f4802,plain,
( spl30_470
| ~ spl30_148
| ~ spl30_309 ),
inference(avatar_split_clause,[],[f2883,f2822,f1265,f4800]) ).
fof(f4800,plain,
( spl30_470
<=> ! [X0,X1] :
( empty(sK4(powerset(powerset(X0))))
| element(X1,X0)
| ~ in(X1,sK4(sK4(powerset(powerset(X0))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_470])]) ).
fof(f2883,plain,
( ! [X0,X1] :
( empty(sK4(powerset(powerset(X0))))
| element(X1,X0)
| ~ in(X1,sK4(sK4(powerset(powerset(X0))))) )
| ~ spl30_148
| ~ spl30_309 ),
inference(resolution,[],[f2823,f1266]) ).
fof(f4790,plain,
( spl30_469
| ~ spl30_249
| ~ spl30_318 ),
inference(avatar_split_clause,[],[f2920,f2859,f2137,f4788]) ).
fof(f2137,plain,
( spl30_249
<=> ! [X0,X1] :
( empty(powerset(X0))
| in(X1,powerset(X0))
| ~ subset(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_249])]) ).
fof(f2920,plain,
( ! [X0,X1] :
( ~ subset(powerset(X0),X1)
| empty(powerset(X1))
| empty(powerset(X0))
| ~ subset(powerset(X1),X0) )
| ~ spl30_249
| ~ spl30_318 ),
inference(resolution,[],[f2860,f2138]) ).
fof(f2138,plain,
( ! [X0,X1] :
( in(X1,powerset(X0))
| empty(powerset(X0))
| ~ subset(X1,X0) )
| ~ spl30_249 ),
inference(avatar_component_clause,[],[f2137]) ).
fof(f4786,plain,
( spl30_468
| ~ spl30_128
| ~ spl30_314 ),
inference(avatar_split_clause,[],[f2916,f2843,f1134,f4784]) ).
fof(f4784,plain,
( spl30_468
<=> ! [X0] :
( empty(powerset(X0))
| empty(sK3(powerset(X0)))
| finite(sK4(sK3(powerset(X0))))
| ~ finite(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_468])]) ).
fof(f2916,plain,
( ! [X0] :
( empty(powerset(X0))
| empty(sK3(powerset(X0)))
| finite(sK4(sK3(powerset(X0))))
| ~ finite(X0) )
| ~ spl30_128
| ~ spl30_314 ),
inference(resolution,[],[f2844,f1135]) ).
fof(f4782,plain,
( spl30_467
| ~ spl30_128
| ~ spl30_311 ),
inference(avatar_split_clause,[],[f2906,f2830,f1134,f4780]) ).
fof(f4780,plain,
( spl30_467
<=> ! [X0] :
( empty(powerset(X0))
| empty(sK2(powerset(X0)))
| finite(sK4(sK2(powerset(X0))))
| ~ finite(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_467])]) ).
fof(f2906,plain,
( ! [X0] :
( empty(powerset(X0))
| empty(sK2(powerset(X0)))
| finite(sK4(sK2(powerset(X0))))
| ~ finite(X0) )
| ~ spl30_128
| ~ spl30_311 ),
inference(resolution,[],[f2831,f1135]) ).
fof(f4778,plain,
( spl30_466
| ~ spl30_128
| ~ spl30_310 ),
inference(avatar_split_clause,[],[f2896,f2826,f1134,f4776]) ).
fof(f4776,plain,
( spl30_466
<=> ! [X0] :
( empty(powerset(X0))
| empty(sK1(powerset(X0)))
| finite(sK4(sK1(powerset(X0))))
| ~ finite(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_466])]) ).
fof(f2896,plain,
( ! [X0] :
( empty(powerset(X0))
| empty(sK1(powerset(X0)))
| finite(sK4(sK1(powerset(X0))))
| ~ finite(X0) )
| ~ spl30_128
| ~ spl30_310 ),
inference(resolution,[],[f2827,f1135]) ).
fof(f4774,plain,
( spl30_465
| ~ spl30_143
| ~ spl30_309 ),
inference(avatar_split_clause,[],[f2882,f2822,f1229,f4772]) ).
fof(f2882,plain,
( ! [X0,X1] :
( empty(sK4(powerset(powerset(X0))))
| ~ empty(X0)
| ~ in(X1,sK4(sK4(powerset(powerset(X0))))) )
| ~ spl30_143
| ~ spl30_309 ),
inference(resolution,[],[f2823,f1230]) ).
fof(f4743,plain,
( ~ spl30_464
| ~ spl30_108
| ~ spl30_427 ),
inference(avatar_split_clause,[],[f4233,f4223,f981,f4740]) ).
fof(f4740,plain,
( spl30_464
<=> in(powerset(relation_dom(sK25)),relation_dom(sK25)) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_464])]) ).
fof(f4223,plain,
( spl30_427
<=> in(relation_dom(sK25),powerset(relation_dom(sK25))) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_427])]) ).
fof(f4233,plain,
( ~ in(powerset(relation_dom(sK25)),relation_dom(sK25))
| ~ spl30_108
| ~ spl30_427 ),
inference(resolution,[],[f4225,f982]) ).
fof(f4225,plain,
( in(relation_dom(sK25),powerset(relation_dom(sK25)))
| ~ spl30_427 ),
inference(avatar_component_clause,[],[f4223]) ).
fof(f4738,plain,
( spl30_463
| ~ spl30_117
| ~ spl30_330 ),
inference(avatar_split_clause,[],[f2977,f2965,f1030,f4736]) ).
fof(f4736,plain,
( spl30_463
<=> ! [X2,X0,X1] :
( ~ in(X0,first_projection_as_func_of(X1,X2))
| epsilon_transitive(X0)
| ~ ordinal(cartesian_product2(cartesian_product2(X1,X2),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_463])]) ).
fof(f2977,plain,
( ! [X2,X0,X1] :
( ~ in(X0,first_projection_as_func_of(X1,X2))
| epsilon_transitive(X0)
| ~ ordinal(cartesian_product2(cartesian_product2(X1,X2),X1)) )
| ~ spl30_117
| ~ spl30_330 ),
inference(resolution,[],[f2966,f1031]) ).
fof(f4734,plain,
( spl30_462
| ~ spl30_118
| ~ spl30_330 ),
inference(avatar_split_clause,[],[f2976,f2965,f1034,f4732]) ).
fof(f4732,plain,
( spl30_462
<=> ! [X2,X0,X1] :
( ~ in(X0,first_projection_as_func_of(X1,X2))
| epsilon_connected(X0)
| ~ ordinal(cartesian_product2(cartesian_product2(X1,X2),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_462])]) ).
fof(f2976,plain,
( ! [X2,X0,X1] :
( ~ in(X0,first_projection_as_func_of(X1,X2))
| epsilon_connected(X0)
| ~ ordinal(cartesian_product2(cartesian_product2(X1,X2),X1)) )
| ~ spl30_118
| ~ spl30_330 ),
inference(resolution,[],[f2966,f1035]) ).
fof(f4730,plain,
( spl30_461
| ~ spl30_119
| ~ spl30_330 ),
inference(avatar_split_clause,[],[f2975,f2965,f1038,f4728]) ).
fof(f4728,plain,
( spl30_461
<=> ! [X2,X0,X1] :
( ~ in(X0,first_projection_as_func_of(X1,X2))
| ordinal(X0)
| ~ ordinal(cartesian_product2(cartesian_product2(X1,X2),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_461])]) ).
fof(f2975,plain,
( ! [X2,X0,X1] :
( ~ in(X0,first_projection_as_func_of(X1,X2))
| ordinal(X0)
| ~ ordinal(cartesian_product2(cartesian_product2(X1,X2),X1)) )
| ~ spl30_119
| ~ spl30_330 ),
inference(resolution,[],[f2966,f1039]) ).
fof(f4726,plain,
( spl30_460
| ~ spl30_117
| ~ spl30_329 ),
inference(avatar_split_clause,[],[f2971,f2961,f1030,f4724]) ).
fof(f4724,plain,
( spl30_460
<=> ! [X0,X1] :
( ~ in(X0,X1)
| ~ relation(X1)
| epsilon_transitive(X0)
| ~ ordinal(cartesian_product2(relation_dom(X1),relation_rng(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_460])]) ).
fof(f2971,plain,
( ! [X0,X1] :
( ~ in(X0,X1)
| ~ relation(X1)
| epsilon_transitive(X0)
| ~ ordinal(cartesian_product2(relation_dom(X1),relation_rng(X1))) )
| ~ spl30_117
| ~ spl30_329 ),
inference(resolution,[],[f2962,f1031]) ).
fof(f4722,plain,
( spl30_459
| ~ spl30_118
| ~ spl30_329 ),
inference(avatar_split_clause,[],[f2970,f2961,f1034,f4720]) ).
fof(f4720,plain,
( spl30_459
<=> ! [X0,X1] :
( ~ in(X0,X1)
| ~ relation(X1)
| epsilon_connected(X0)
| ~ ordinal(cartesian_product2(relation_dom(X1),relation_rng(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_459])]) ).
fof(f2970,plain,
( ! [X0,X1] :
( ~ in(X0,X1)
| ~ relation(X1)
| epsilon_connected(X0)
| ~ ordinal(cartesian_product2(relation_dom(X1),relation_rng(X1))) )
| ~ spl30_118
| ~ spl30_329 ),
inference(resolution,[],[f2962,f1035]) ).
fof(f4718,plain,
( spl30_458
| ~ spl30_119
| ~ spl30_329 ),
inference(avatar_split_clause,[],[f2969,f2961,f1038,f4716]) ).
fof(f4716,plain,
( spl30_458
<=> ! [X0,X1] :
( ~ in(X0,X1)
| ~ relation(X1)
| ordinal(X0)
| ~ ordinal(cartesian_product2(relation_dom(X1),relation_rng(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_458])]) ).
fof(f2969,plain,
( ! [X0,X1] :
( ~ in(X0,X1)
| ~ relation(X1)
| ordinal(X0)
| ~ ordinal(cartesian_product2(relation_dom(X1),relation_rng(X1))) )
| ~ spl30_119
| ~ spl30_329 ),
inference(resolution,[],[f2962,f1039]) ).
fof(f4714,plain,
( spl30_457
| ~ spl30_123
| ~ spl30_314 ),
inference(avatar_split_clause,[],[f2917,f2843,f1054,f4712]) ).
fof(f4712,plain,
( spl30_457
<=> ! [X0] :
( empty(powerset(X0))
| empty(sK3(powerset(X0)))
| subset(sK4(sK3(powerset(X0))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_457])]) ).
fof(f2917,plain,
( ! [X0] :
( empty(powerset(X0))
| empty(sK3(powerset(X0)))
| subset(sK4(sK3(powerset(X0))),X0) )
| ~ spl30_123
| ~ spl30_314 ),
inference(resolution,[],[f2844,f1055]) ).
fof(f4710,plain,
( spl30_456
| ~ spl30_123
| ~ spl30_311 ),
inference(avatar_split_clause,[],[f2907,f2830,f1054,f4708]) ).
fof(f4708,plain,
( spl30_456
<=> ! [X0] :
( empty(powerset(X0))
| empty(sK2(powerset(X0)))
| subset(sK4(sK2(powerset(X0))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_456])]) ).
fof(f2907,plain,
( ! [X0] :
( empty(powerset(X0))
| empty(sK2(powerset(X0)))
| subset(sK4(sK2(powerset(X0))),X0) )
| ~ spl30_123
| ~ spl30_311 ),
inference(resolution,[],[f2831,f1055]) ).
fof(f4706,plain,
( spl30_455
| ~ spl30_123
| ~ spl30_310 ),
inference(avatar_split_clause,[],[f2897,f2826,f1054,f4704]) ).
fof(f4704,plain,
( spl30_455
<=> ! [X0] :
( empty(powerset(X0))
| empty(sK1(powerset(X0)))
| subset(sK4(sK1(powerset(X0))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_455])]) ).
fof(f2897,plain,
( ! [X0] :
( empty(powerset(X0))
| empty(sK1(powerset(X0)))
| subset(sK4(sK1(powerset(X0))),X0) )
| ~ spl30_123
| ~ spl30_310 ),
inference(resolution,[],[f2827,f1055]) ).
fof(f4702,plain,
( spl30_454
| ~ spl30_128
| ~ spl30_309 ),
inference(avatar_split_clause,[],[f2884,f2822,f1134,f4700]) ).
fof(f4700,plain,
( spl30_454
<=> ! [X0] :
( empty(sK4(powerset(powerset(X0))))
| finite(sK4(sK4(powerset(powerset(X0)))))
| ~ finite(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_454])]) ).
fof(f2884,plain,
( ! [X0] :
( empty(sK4(powerset(powerset(X0))))
| finite(sK4(sK4(powerset(powerset(X0)))))
| ~ finite(X0) )
| ~ spl30_128
| ~ spl30_309 ),
inference(resolution,[],[f2823,f1135]) ).
fof(f4698,plain,
( ~ spl30_453
| ~ spl30_108
| ~ spl30_425 ),
inference(avatar_split_clause,[],[f4221,f4211,f981,f4695]) ).
fof(f4695,plain,
( spl30_453
<=> in(powerset(relation_dom(sK24)),relation_dom(sK24)) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_453])]) ).
fof(f4211,plain,
( spl30_425
<=> in(relation_dom(sK24),powerset(relation_dom(sK24))) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_425])]) ).
fof(f4221,plain,
( ~ in(powerset(relation_dom(sK24)),relation_dom(sK24))
| ~ spl30_108
| ~ spl30_425 ),
inference(resolution,[],[f4213,f982]) ).
fof(f4213,plain,
( in(relation_dom(sK24),powerset(relation_dom(sK24)))
| ~ spl30_425 ),
inference(avatar_component_clause,[],[f4211]) ).
fof(f4661,plain,
( spl30_452
| ~ spl30_207
| ~ spl30_322 ),
inference(avatar_split_clause,[],[f2931,f2875,f1798,f4659]) ).
fof(f2931,plain,
( ! [X0,X1] :
( element(sK4(sK7(X0,X1)),cartesian_product2(X0,X1))
| empty(sK7(X0,X1)) )
| ~ spl30_207
| ~ spl30_322 ),
inference(resolution,[],[f2876,f1799]) ).
fof(f4657,plain,
( spl30_451
| ~ spl30_207
| ~ spl30_321 ),
inference(avatar_split_clause,[],[f2925,f2871,f1798,f4655]) ).
fof(f2925,plain,
( ! [X0,X1] :
( element(sK4(sK8(X0,X1)),cartesian_product2(X0,X1))
| empty(sK8(X0,X1)) )
| ~ spl30_207
| ~ spl30_321 ),
inference(resolution,[],[f2872,f1799]) ).
fof(f4653,plain,
( spl30_450
| ~ spl30_123
| ~ spl30_309 ),
inference(avatar_split_clause,[],[f2885,f2822,f1054,f4651]) ).
fof(f4651,plain,
( spl30_450
<=> ! [X0] :
( empty(sK4(powerset(powerset(X0))))
| subset(sK4(sK4(powerset(powerset(X0)))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_450])]) ).
fof(f2885,plain,
( ! [X0] :
( empty(sK4(powerset(powerset(X0))))
| subset(sK4(sK4(powerset(powerset(X0)))),X0) )
| ~ spl30_123
| ~ spl30_309 ),
inference(resolution,[],[f2823,f1055]) ).
fof(f4649,plain,
( spl30_449
| ~ spl30_131
| ~ spl30_309 ),
inference(avatar_split_clause,[],[f2878,f2822,f1146,f4647]) ).
fof(f2878,plain,
( ! [X0] :
( empty(sK4(powerset(X0)))
| empty(X0)
| in(sK4(sK4(powerset(X0))),X0) )
| ~ spl30_131
| ~ spl30_309 ),
inference(resolution,[],[f2823,f1147]) ).
fof(f4644,plain,
( ~ spl30_448
| ~ spl30_108
| ~ spl30_423 ),
inference(avatar_split_clause,[],[f4209,f4199,f981,f4641]) ).
fof(f4641,plain,
( spl30_448
<=> in(powerset(relation_dom(sK23)),relation_dom(sK23)) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_448])]) ).
fof(f4199,plain,
( spl30_423
<=> in(relation_dom(sK23),powerset(relation_dom(sK23))) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_423])]) ).
fof(f4209,plain,
( ~ in(powerset(relation_dom(sK23)),relation_dom(sK23))
| ~ spl30_108
| ~ spl30_423 ),
inference(resolution,[],[f4201,f982]) ).
fof(f4201,plain,
( in(relation_dom(sK23),powerset(relation_dom(sK23)))
| ~ spl30_423 ),
inference(avatar_component_clause,[],[f4199]) ).
fof(f4549,plain,
( spl30_447
| ~ spl30_117
| ~ spl30_314 ),
inference(avatar_split_clause,[],[f2913,f2843,f1030,f4547]) ).
fof(f4547,plain,
( spl30_447
<=> ! [X0] :
( empty(X0)
| empty(sK3(X0))
| epsilon_transitive(sK4(sK3(X0)))
| ~ ordinal(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_447])]) ).
fof(f2913,plain,
( ! [X0] :
( empty(X0)
| empty(sK3(X0))
| epsilon_transitive(sK4(sK3(X0)))
| ~ ordinal(X0) )
| ~ spl30_117
| ~ spl30_314 ),
inference(resolution,[],[f2844,f1031]) ).
fof(f4545,plain,
( spl30_446
| ~ spl30_118
| ~ spl30_314 ),
inference(avatar_split_clause,[],[f2912,f2843,f1034,f4543]) ).
fof(f4543,plain,
( spl30_446
<=> ! [X0] :
( empty(X0)
| empty(sK3(X0))
| epsilon_connected(sK4(sK3(X0)))
| ~ ordinal(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_446])]) ).
fof(f2912,plain,
( ! [X0] :
( empty(X0)
| empty(sK3(X0))
| epsilon_connected(sK4(sK3(X0)))
| ~ ordinal(X0) )
| ~ spl30_118
| ~ spl30_314 ),
inference(resolution,[],[f2844,f1035]) ).
fof(f4541,plain,
( spl30_445
| ~ spl30_119
| ~ spl30_314 ),
inference(avatar_split_clause,[],[f2911,f2843,f1038,f4539]) ).
fof(f4539,plain,
( spl30_445
<=> ! [X0] :
( empty(X0)
| empty(sK3(X0))
| ordinal(sK4(sK3(X0)))
| ~ ordinal(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_445])]) ).
fof(f2911,plain,
( ! [X0] :
( empty(X0)
| empty(sK3(X0))
| ordinal(sK4(sK3(X0)))
| ~ ordinal(X0) )
| ~ spl30_119
| ~ spl30_314 ),
inference(resolution,[],[f2844,f1039]) ).
fof(f4537,plain,
( spl30_444
| ~ spl30_117
| ~ spl30_311 ),
inference(avatar_split_clause,[],[f2903,f2830,f1030,f4535]) ).
fof(f4535,plain,
( spl30_444
<=> ! [X0] :
( empty(X0)
| empty(sK2(X0))
| epsilon_transitive(sK4(sK2(X0)))
| ~ ordinal(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_444])]) ).
fof(f2903,plain,
( ! [X0] :
( empty(X0)
| empty(sK2(X0))
| epsilon_transitive(sK4(sK2(X0)))
| ~ ordinal(X0) )
| ~ spl30_117
| ~ spl30_311 ),
inference(resolution,[],[f2831,f1031]) ).
fof(f4533,plain,
( spl30_443
| ~ spl30_118
| ~ spl30_311 ),
inference(avatar_split_clause,[],[f2902,f2830,f1034,f4531]) ).
fof(f4531,plain,
( spl30_443
<=> ! [X0] :
( empty(X0)
| empty(sK2(X0))
| epsilon_connected(sK4(sK2(X0)))
| ~ ordinal(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_443])]) ).
fof(f2902,plain,
( ! [X0] :
( empty(X0)
| empty(sK2(X0))
| epsilon_connected(sK4(sK2(X0)))
| ~ ordinal(X0) )
| ~ spl30_118
| ~ spl30_311 ),
inference(resolution,[],[f2831,f1035]) ).
fof(f4529,plain,
( spl30_442
| ~ spl30_119
| ~ spl30_311 ),
inference(avatar_split_clause,[],[f2901,f2830,f1038,f4527]) ).
fof(f4527,plain,
( spl30_442
<=> ! [X0] :
( empty(X0)
| empty(sK2(X0))
| ordinal(sK4(sK2(X0)))
| ~ ordinal(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_442])]) ).
fof(f2901,plain,
( ! [X0] :
( empty(X0)
| empty(sK2(X0))
| ordinal(sK4(sK2(X0)))
| ~ ordinal(X0) )
| ~ spl30_119
| ~ spl30_311 ),
inference(resolution,[],[f2831,f1039]) ).
fof(f4525,plain,
( ~ spl30_441
| ~ spl30_108
| ~ spl30_420 ),
inference(avatar_split_clause,[],[f4192,f4182,f981,f4522]) ).
fof(f4522,plain,
( spl30_441
<=> in(powerset(relation_dom(sK22)),relation_dom(sK22)) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_441])]) ).
fof(f4182,plain,
( spl30_420
<=> in(relation_dom(sK22),powerset(relation_dom(sK22))) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_420])]) ).
fof(f4192,plain,
( ~ in(powerset(relation_dom(sK22)),relation_dom(sK22))
| ~ spl30_108
| ~ spl30_420 ),
inference(resolution,[],[f4184,f982]) ).
fof(f4184,plain,
( in(relation_dom(sK22),powerset(relation_dom(sK22)))
| ~ spl30_420 ),
inference(avatar_component_clause,[],[f4182]) ).
fof(f4520,plain,
( spl30_440
| ~ spl30_117
| ~ spl30_310 ),
inference(avatar_split_clause,[],[f2893,f2826,f1030,f4518]) ).
fof(f4518,plain,
( spl30_440
<=> ! [X0] :
( empty(X0)
| empty(sK1(X0))
| epsilon_transitive(sK4(sK1(X0)))
| ~ ordinal(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_440])]) ).
fof(f2893,plain,
( ! [X0] :
( empty(X0)
| empty(sK1(X0))
| epsilon_transitive(sK4(sK1(X0)))
| ~ ordinal(X0) )
| ~ spl30_117
| ~ spl30_310 ),
inference(resolution,[],[f2827,f1031]) ).
fof(f4516,plain,
( spl30_439
| ~ spl30_118
| ~ spl30_310 ),
inference(avatar_split_clause,[],[f2892,f2826,f1034,f4514]) ).
fof(f4514,plain,
( spl30_439
<=> ! [X0] :
( empty(X0)
| empty(sK1(X0))
| epsilon_connected(sK4(sK1(X0)))
| ~ ordinal(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_439])]) ).
fof(f2892,plain,
( ! [X0] :
( empty(X0)
| empty(sK1(X0))
| epsilon_connected(sK4(sK1(X0)))
| ~ ordinal(X0) )
| ~ spl30_118
| ~ spl30_310 ),
inference(resolution,[],[f2827,f1035]) ).
fof(f4512,plain,
( spl30_438
| ~ spl30_119
| ~ spl30_310 ),
inference(avatar_split_clause,[],[f2891,f2826,f1038,f4510]) ).
fof(f4510,plain,
( spl30_438
<=> ! [X0] :
( empty(X0)
| empty(sK1(X0))
| ordinal(sK4(sK1(X0)))
| ~ ordinal(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_438])]) ).
fof(f2891,plain,
( ! [X0] :
( empty(X0)
| empty(sK1(X0))
| ordinal(sK4(sK1(X0)))
| ~ ordinal(X0) )
| ~ spl30_119
| ~ spl30_310 ),
inference(resolution,[],[f2827,f1039]) ).
fof(f4508,plain,
( spl30_437
| ~ spl30_117
| ~ spl30_309 ),
inference(avatar_split_clause,[],[f2881,f2822,f1030,f4506]) ).
fof(f4506,plain,
( spl30_437
<=> ! [X0] :
( empty(sK4(powerset(X0)))
| epsilon_transitive(sK4(sK4(powerset(X0))))
| ~ ordinal(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_437])]) ).
fof(f2881,plain,
( ! [X0] :
( empty(sK4(powerset(X0)))
| epsilon_transitive(sK4(sK4(powerset(X0))))
| ~ ordinal(X0) )
| ~ spl30_117
| ~ spl30_309 ),
inference(resolution,[],[f2823,f1031]) ).
fof(f4504,plain,
( spl30_436
| ~ spl30_118
| ~ spl30_309 ),
inference(avatar_split_clause,[],[f2880,f2822,f1034,f4502]) ).
fof(f4502,plain,
( spl30_436
<=> ! [X0] :
( empty(sK4(powerset(X0)))
| epsilon_connected(sK4(sK4(powerset(X0))))
| ~ ordinal(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_436])]) ).
fof(f2880,plain,
( ! [X0] :
( empty(sK4(powerset(X0)))
| epsilon_connected(sK4(sK4(powerset(X0))))
| ~ ordinal(X0) )
| ~ spl30_118
| ~ spl30_309 ),
inference(resolution,[],[f2823,f1035]) ).
fof(f4500,plain,
( spl30_435
| ~ spl30_119
| ~ spl30_309 ),
inference(avatar_split_clause,[],[f2879,f2822,f1038,f4498]) ).
fof(f4498,plain,
( spl30_435
<=> ! [X0] :
( empty(sK4(powerset(X0)))
| ordinal(sK4(sK4(powerset(X0))))
| ~ ordinal(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_435])]) ).
fof(f2879,plain,
( ! [X0] :
( empty(sK4(powerset(X0)))
| ordinal(sK4(sK4(powerset(X0))))
| ~ ordinal(X0) )
| ~ spl30_119
| ~ spl30_309 ),
inference(resolution,[],[f2823,f1039]) ).
fof(f4496,plain,
( spl30_434
| ~ spl30_289
| ~ spl30_301 ),
inference(avatar_split_clause,[],[f2752,f2636,f2470,f4494]) ).
fof(f2752,plain,
( ! [X0,X1] :
( relation_rng(relation_rng(sK4(powerset(X0)))) = X1
| ~ empty(X1)
| ~ empty(X0) )
| ~ spl30_289
| ~ spl30_301 ),
inference(resolution,[],[f2637,f2471]) ).
fof(f4492,plain,
( spl30_433
| ~ spl30_289
| ~ spl30_300 ),
inference(avatar_split_clause,[],[f2718,f2632,f2470,f4490]) ).
fof(f2718,plain,
( ! [X0,X1] :
( relation_rng(relation_dom(sK4(powerset(X0)))) = X1
| ~ empty(X1)
| ~ empty(X0) )
| ~ spl30_289
| ~ spl30_300 ),
inference(resolution,[],[f2633,f2471]) ).
fof(f4488,plain,
( spl30_432
| ~ spl30_289
| ~ spl30_299 ),
inference(avatar_split_clause,[],[f2684,f2628,f2470,f4486]) ).
fof(f2684,plain,
( ! [X0,X1] :
( relation_dom(relation_rng(sK4(powerset(X0)))) = X1
| ~ empty(X1)
| ~ empty(X0) )
| ~ spl30_289
| ~ spl30_299 ),
inference(resolution,[],[f2629,f2471]) ).
fof(f4484,plain,
( spl30_431
| ~ spl30_289
| ~ spl30_297 ),
inference(avatar_split_clause,[],[f2650,f2620,f2470,f4482]) ).
fof(f2650,plain,
( ! [X0,X1] :
( relation_dom(relation_dom(sK4(powerset(X0)))) = X1
| ~ empty(X1)
| ~ empty(X0) )
| ~ spl30_289
| ~ spl30_297 ),
inference(resolution,[],[f2621,f2471]) ).
fof(f4480,plain,
( ~ spl30_430
| ~ spl30_108
| ~ spl30_418 ),
inference(avatar_split_clause,[],[f4180,f4170,f981,f4477]) ).
fof(f4477,plain,
( spl30_430
<=> in(powerset(relation_dom(sK21)),relation_dom(sK21)) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_430])]) ).
fof(f4170,plain,
( spl30_418
<=> in(relation_dom(sK21),powerset(relation_dom(sK21))) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_418])]) ).
fof(f4180,plain,
( ~ in(powerset(relation_dom(sK21)),relation_dom(sK21))
| ~ spl30_108
| ~ spl30_418 ),
inference(resolution,[],[f4172,f982]) ).
fof(f4172,plain,
( in(relation_dom(sK21),powerset(relation_dom(sK21)))
| ~ spl30_418 ),
inference(avatar_component_clause,[],[f4170]) ).
fof(f4314,plain,
( ~ spl30_429
| ~ spl30_108
| ~ spl30_416 ),
inference(avatar_split_clause,[],[f4168,f4158,f981,f4311]) ).
fof(f4311,plain,
( spl30_429
<=> in(powerset(relation_dom(sK20)),relation_dom(sK20)) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_429])]) ).
fof(f4158,plain,
( spl30_416
<=> in(relation_dom(sK20),powerset(relation_dom(sK20))) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_416])]) ).
fof(f4168,plain,
( ~ in(powerset(relation_dom(sK20)),relation_dom(sK20))
| ~ spl30_108
| ~ spl30_416 ),
inference(resolution,[],[f4160,f982]) ).
fof(f4160,plain,
( in(relation_dom(sK20),powerset(relation_dom(sK20)))
| ~ spl30_416 ),
inference(avatar_component_clause,[],[f4158]) ).
fof(f4230,plain,
( spl30_427
| spl30_428
| ~ spl30_131
| ~ spl30_371 ),
inference(avatar_split_clause,[],[f3410,f3393,f1146,f4227,f4223]) ).
fof(f4227,plain,
( spl30_428
<=> empty(powerset(relation_dom(sK25))) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_428])]) ).
fof(f3393,plain,
( spl30_371
<=> element(relation_dom(sK25),powerset(relation_dom(sK25))) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_371])]) ).
fof(f3410,plain,
( empty(powerset(relation_dom(sK25)))
| in(relation_dom(sK25),powerset(relation_dom(sK25)))
| ~ spl30_131
| ~ spl30_371 ),
inference(resolution,[],[f3395,f1147]) ).
fof(f3395,plain,
( element(relation_dom(sK25),powerset(relation_dom(sK25)))
| ~ spl30_371 ),
inference(avatar_component_clause,[],[f3393]) ).
fof(f4218,plain,
( spl30_425
| spl30_426
| ~ spl30_131
| ~ spl30_367 ),
inference(avatar_split_clause,[],[f3376,f3361,f1146,f4215,f4211]) ).
fof(f4215,plain,
( spl30_426
<=> empty(powerset(relation_dom(sK24))) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_426])]) ).
fof(f3361,plain,
( spl30_367
<=> element(relation_dom(sK24),powerset(relation_dom(sK24))) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_367])]) ).
fof(f3376,plain,
( empty(powerset(relation_dom(sK24)))
| in(relation_dom(sK24),powerset(relation_dom(sK24)))
| ~ spl30_131
| ~ spl30_367 ),
inference(resolution,[],[f3363,f1147]) ).
fof(f3363,plain,
( element(relation_dom(sK24),powerset(relation_dom(sK24)))
| ~ spl30_367 ),
inference(avatar_component_clause,[],[f3361]) ).
fof(f4206,plain,
( spl30_423
| spl30_424
| ~ spl30_131
| ~ spl30_362 ),
inference(avatar_split_clause,[],[f3344,f3324,f1146,f4203,f4199]) ).
fof(f4203,plain,
( spl30_424
<=> empty(powerset(relation_dom(sK23))) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_424])]) ).
fof(f3324,plain,
( spl30_362
<=> element(relation_dom(sK23),powerset(relation_dom(sK23))) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_362])]) ).
fof(f3344,plain,
( empty(powerset(relation_dom(sK23)))
| in(relation_dom(sK23),powerset(relation_dom(sK23)))
| ~ spl30_131
| ~ spl30_362 ),
inference(resolution,[],[f3326,f1147]) ).
fof(f3326,plain,
( element(relation_dom(sK23),powerset(relation_dom(sK23)))
| ~ spl30_362 ),
inference(avatar_component_clause,[],[f3324]) ).
fof(f4197,plain,
( ~ spl30_422
| ~ spl30_108
| ~ spl30_414 ),
inference(avatar_split_clause,[],[f4156,f4146,f981,f4194]) ).
fof(f4194,plain,
( spl30_422
<=> in(powerset(relation_dom(sK18)),relation_dom(sK18)) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_422])]) ).
fof(f4146,plain,
( spl30_414
<=> in(relation_dom(sK18),powerset(relation_dom(sK18))) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_414])]) ).
fof(f4156,plain,
( ~ in(powerset(relation_dom(sK18)),relation_dom(sK18))
| ~ spl30_108
| ~ spl30_414 ),
inference(resolution,[],[f4148,f982]) ).
fof(f4148,plain,
( in(relation_dom(sK18),powerset(relation_dom(sK18)))
| ~ spl30_414 ),
inference(avatar_component_clause,[],[f4146]) ).
fof(f4189,plain,
( spl30_420
| spl30_421
| ~ spl30_131
| ~ spl30_358 ),
inference(avatar_split_clause,[],[f3307,f3292,f1146,f4186,f4182]) ).
fof(f4186,plain,
( spl30_421
<=> empty(powerset(relation_dom(sK22))) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_421])]) ).
fof(f3292,plain,
( spl30_358
<=> element(relation_dom(sK22),powerset(relation_dom(sK22))) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_358])]) ).
fof(f3307,plain,
( empty(powerset(relation_dom(sK22)))
| in(relation_dom(sK22),powerset(relation_dom(sK22)))
| ~ spl30_131
| ~ spl30_358 ),
inference(resolution,[],[f3294,f1147]) ).
fof(f3294,plain,
( element(relation_dom(sK22),powerset(relation_dom(sK22)))
| ~ spl30_358 ),
inference(avatar_component_clause,[],[f3292]) ).
fof(f4177,plain,
( spl30_418
| spl30_419
| ~ spl30_131
| ~ spl30_353 ),
inference(avatar_split_clause,[],[f3271,f3256,f1146,f4174,f4170]) ).
fof(f4174,plain,
( spl30_419
<=> empty(powerset(relation_dom(sK21))) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_419])]) ).
fof(f3256,plain,
( spl30_353
<=> element(relation_dom(sK21),powerset(relation_dom(sK21))) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_353])]) ).
fof(f3271,plain,
( empty(powerset(relation_dom(sK21)))
| in(relation_dom(sK21),powerset(relation_dom(sK21)))
| ~ spl30_131
| ~ spl30_353 ),
inference(resolution,[],[f3258,f1147]) ).
fof(f3258,plain,
( element(relation_dom(sK21),powerset(relation_dom(sK21)))
| ~ spl30_353 ),
inference(avatar_component_clause,[],[f3256]) ).
fof(f4165,plain,
( spl30_416
| spl30_417
| ~ spl30_131
| ~ spl30_349 ),
inference(avatar_split_clause,[],[f3239,f3224,f1146,f4162,f4158]) ).
fof(f4162,plain,
( spl30_417
<=> empty(powerset(relation_dom(sK20))) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_417])]) ).
fof(f3224,plain,
( spl30_349
<=> element(relation_dom(sK20),powerset(relation_dom(sK20))) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_349])]) ).
fof(f3239,plain,
( empty(powerset(relation_dom(sK20)))
| in(relation_dom(sK20),powerset(relation_dom(sK20)))
| ~ spl30_131
| ~ spl30_349 ),
inference(resolution,[],[f3226,f1147]) ).
fof(f3226,plain,
( element(relation_dom(sK20),powerset(relation_dom(sK20)))
| ~ spl30_349 ),
inference(avatar_component_clause,[],[f3224]) ).
fof(f4153,plain,
( spl30_414
| spl30_415
| ~ spl30_131
| ~ spl30_345 ),
inference(avatar_split_clause,[],[f3207,f3192,f1146,f4150,f4146]) ).
fof(f4150,plain,
( spl30_415
<=> empty(powerset(relation_dom(sK18))) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_415])]) ).
fof(f3192,plain,
( spl30_345
<=> element(relation_dom(sK18),powerset(relation_dom(sK18))) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_345])]) ).
fof(f3207,plain,
( empty(powerset(relation_dom(sK18)))
| in(relation_dom(sK18),powerset(relation_dom(sK18)))
| ~ spl30_131
| ~ spl30_345 ),
inference(resolution,[],[f3194,f1147]) ).
fof(f3194,plain,
( element(relation_dom(sK18),powerset(relation_dom(sK18)))
| ~ spl30_345 ),
inference(avatar_component_clause,[],[f3192]) ).
fof(f4144,plain,
( spl30_413
| ~ spl30_133
| ~ spl30_320 ),
inference(avatar_split_clause,[],[f2924,f2867,f1154,f4142]) ).
fof(f2867,plain,
( spl30_320
<=> ! [X0,X1] :
( finite(first_projection_as_func_of(X0,X1))
| ~ finite(cartesian_product2(cartesian_product2(X0,X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_320])]) ).
fof(f2924,plain,
( ! [X0,X1] :
( finite(first_projection_as_func_of(X0,X1))
| ~ finite(X0)
| ~ finite(cartesian_product2(X0,X1)) )
| ~ spl30_133
| ~ spl30_320 ),
inference(resolution,[],[f2868,f1155]) ).
fof(f2868,plain,
( ! [X0,X1] :
( ~ finite(cartesian_product2(cartesian_product2(X0,X1),X0))
| finite(first_projection_as_func_of(X0,X1)) )
| ~ spl30_320 ),
inference(avatar_component_clause,[],[f2867]) ).
fof(f4140,plain,
( spl30_412
| ~ spl30_131
| ~ spl30_314 ),
inference(avatar_split_clause,[],[f2919,f2843,f1146,f4138]) ).
fof(f2919,plain,
( ! [X0] :
( empty(X0)
| empty(sK3(X0))
| in(sK4(sK3(X0)),X0) )
| ~ spl30_131
| ~ spl30_314 ),
inference(duplicate_literal_removal,[],[f2910]) ).
fof(f2910,plain,
( ! [X0] :
( empty(X0)
| empty(sK3(X0))
| empty(X0)
| in(sK4(sK3(X0)),X0) )
| ~ spl30_131
| ~ spl30_314 ),
inference(resolution,[],[f2844,f1147]) ).
fof(f4109,plain,
( spl30_411
| ~ spl30_131
| ~ spl30_311 ),
inference(avatar_split_clause,[],[f2909,f2830,f1146,f4107]) ).
fof(f2909,plain,
( ! [X0] :
( empty(X0)
| empty(sK2(X0))
| in(sK4(sK2(X0)),X0) )
| ~ spl30_131
| ~ spl30_311 ),
inference(duplicate_literal_removal,[],[f2900]) ).
fof(f2900,plain,
( ! [X0] :
( empty(X0)
| empty(sK2(X0))
| empty(X0)
| in(sK4(sK2(X0)),X0) )
| ~ spl30_131
| ~ spl30_311 ),
inference(resolution,[],[f2831,f1147]) ).
fof(f4105,plain,
( spl30_410
| ~ spl30_131
| ~ spl30_310 ),
inference(avatar_split_clause,[],[f2899,f2826,f1146,f4103]) ).
fof(f2899,plain,
( ! [X0] :
( empty(X0)
| empty(sK1(X0))
| in(sK4(sK1(X0)),X0) )
| ~ spl30_131
| ~ spl30_310 ),
inference(duplicate_literal_removal,[],[f2890]) ).
fof(f2890,plain,
( ! [X0] :
( empty(X0)
| empty(sK1(X0))
| empty(X0)
| in(sK4(sK1(X0)),X0) )
| ~ spl30_131
| ~ spl30_310 ),
inference(resolution,[],[f2827,f1147]) ).
fof(f4101,plain,
( spl30_409
| ~ spl30_98
| ~ spl30_301 ),
inference(avatar_split_clause,[],[f2751,f2636,f911,f4099]) ).
fof(f2751,plain,
( ! [X0,X1] :
( relation_rng(relation_rng(relation_rng(X0))) = X1
| ~ empty(X1)
| ~ empty(X0) )
| ~ spl30_98
| ~ spl30_301 ),
inference(resolution,[],[f2637,f912]) ).
fof(f4097,plain,
( spl30_408
| ~ spl30_101
| ~ spl30_301 ),
inference(avatar_split_clause,[],[f2750,f2636,f924,f4095]) ).
fof(f2750,plain,
( ! [X0,X1] :
( relation_rng(relation_rng(relation_dom(X0))) = X1
| ~ empty(X1)
| ~ empty(X0) )
| ~ spl30_101
| ~ spl30_301 ),
inference(resolution,[],[f2637,f925]) ).
fof(f4093,plain,
( spl30_407
| ~ spl30_98
| ~ spl30_300 ),
inference(avatar_split_clause,[],[f2717,f2632,f911,f4091]) ).
fof(f2717,plain,
( ! [X0,X1] :
( relation_rng(relation_dom(relation_rng(X0))) = X1
| ~ empty(X1)
| ~ empty(X0) )
| ~ spl30_98
| ~ spl30_300 ),
inference(resolution,[],[f2633,f912]) ).
fof(f4089,plain,
( spl30_406
| ~ spl30_101
| ~ spl30_300 ),
inference(avatar_split_clause,[],[f2716,f2632,f924,f4087]) ).
fof(f2716,plain,
( ! [X0,X1] :
( relation_rng(relation_dom(relation_dom(X0))) = X1
| ~ empty(X1)
| ~ empty(X0) )
| ~ spl30_101
| ~ spl30_300 ),
inference(resolution,[],[f2633,f925]) ).
fof(f4085,plain,
( spl30_405
| ~ spl30_98
| ~ spl30_299 ),
inference(avatar_split_clause,[],[f2683,f2628,f911,f4083]) ).
fof(f2683,plain,
( ! [X0,X1] :
( relation_dom(relation_rng(relation_rng(X0))) = X1
| ~ empty(X1)
| ~ empty(X0) )
| ~ spl30_98
| ~ spl30_299 ),
inference(resolution,[],[f2629,f912]) ).
fof(f4081,plain,
( spl30_404
| ~ spl30_101
| ~ spl30_299 ),
inference(avatar_split_clause,[],[f2682,f2628,f924,f4079]) ).
fof(f2682,plain,
( ! [X0,X1] :
( relation_dom(relation_rng(relation_dom(X0))) = X1
| ~ empty(X1)
| ~ empty(X0) )
| ~ spl30_101
| ~ spl30_299 ),
inference(resolution,[],[f2629,f925]) ).
fof(f4077,plain,
( spl30_403
| ~ spl30_98
| ~ spl30_297 ),
inference(avatar_split_clause,[],[f2649,f2620,f911,f4075]) ).
fof(f2649,plain,
( ! [X0,X1] :
( relation_dom(relation_dom(relation_rng(X0))) = X1
| ~ empty(X1)
| ~ empty(X0) )
| ~ spl30_98
| ~ spl30_297 ),
inference(resolution,[],[f2621,f912]) ).
fof(f4073,plain,
( spl30_402
| ~ spl30_101
| ~ spl30_297 ),
inference(avatar_split_clause,[],[f2648,f2620,f924,f4071]) ).
fof(f2648,plain,
( ! [X0,X1] :
( relation_dom(relation_dom(relation_dom(X0))) = X1
| ~ empty(X1)
| ~ empty(X0) )
| ~ spl30_101
| ~ spl30_297 ),
inference(resolution,[],[f2621,f925]) ).
fof(f4069,plain,
( spl30_401
| ~ spl30_98
| ~ spl30_377 ),
inference(avatar_split_clause,[],[f3446,f3440,f911,f4067]) ).
fof(f3446,plain,
( ! [X0] :
( sK10 = sK4(powerset(relation_rng(X0)))
| ~ empty(X0) )
| ~ spl30_98
| ~ spl30_377 ),
inference(resolution,[],[f3441,f912]) ).
fof(f4065,plain,
( spl30_400
| ~ spl30_231
| ~ spl30_289 ),
inference(avatar_split_clause,[],[f2484,f2470,f1954,f4063]) ).
fof(f2484,plain,
( ! [X0,X1] :
( ~ empty(X0)
| ~ empty(X1)
| relation_rng(sK4(powerset(X0))) = X1 )
| ~ spl30_231
| ~ spl30_289 ),
inference(resolution,[],[f2471,f1955]) ).
fof(f4061,plain,
( spl30_399
| ~ spl30_230
| ~ spl30_289 ),
inference(avatar_split_clause,[],[f2483,f2470,f1950,f4059]) ).
fof(f2483,plain,
( ! [X0,X1] :
( ~ empty(X0)
| ~ empty(X1)
| relation_dom(sK4(powerset(X0))) = X1 )
| ~ spl30_230
| ~ spl30_289 ),
inference(resolution,[],[f2471,f1951]) ).
fof(f3898,plain,
( spl30_398
| ~ spl30_289
| ~ spl30_294 ),
inference(avatar_split_clause,[],[f2586,f2502,f2470,f3896]) ).
fof(f2586,plain,
( ! [X0] :
( sK10 = relation_dom(relation_rng(sK4(powerset(X0))))
| ~ empty(X0) )
| ~ spl30_289
| ~ spl30_294 ),
inference(resolution,[],[f2503,f2471]) ).
fof(f3894,plain,
( spl30_397
| ~ spl30_289
| ~ spl30_292 ),
inference(avatar_split_clause,[],[f2560,f2494,f2470,f3892]) ).
fof(f2560,plain,
( ! [X0] :
( sK10 = relation_dom(relation_dom(sK4(powerset(X0))))
| ~ empty(X0) )
| ~ spl30_289
| ~ spl30_292 ),
inference(resolution,[],[f2495,f2471]) ).
fof(f3890,plain,
( spl30_396
| ~ spl30_289
| ~ spl30_291 ),
inference(avatar_split_clause,[],[f2534,f2490,f2470,f3888]) ).
fof(f2534,plain,
( ! [X0] :
( sK10 = relation_rng(relation_rng(sK4(powerset(X0))))
| ~ empty(X0) )
| ~ spl30_289
| ~ spl30_291 ),
inference(resolution,[],[f2491,f2471]) ).
fof(f3886,plain,
( spl30_395
| ~ spl30_101
| ~ spl30_377 ),
inference(avatar_split_clause,[],[f3445,f3440,f924,f3884]) ).
fof(f3445,plain,
( ! [X0] :
( sK10 = sK4(powerset(relation_dom(X0)))
| ~ empty(X0) )
| ~ spl30_101
| ~ spl30_377 ),
inference(resolution,[],[f3441,f925]) ).
fof(f3882,plain,
( spl30_394
| ~ spl30_289
| ~ spl30_290 ),
inference(avatar_split_clause,[],[f2508,f2486,f2470,f3880]) ).
fof(f2508,plain,
( ! [X0] :
( sK10 = relation_rng(relation_dom(sK4(powerset(X0))))
| ~ empty(X0) )
| ~ spl30_289
| ~ spl30_290 ),
inference(resolution,[],[f2487,f2471]) ).
fof(f3878,plain,
( spl30_393
| ~ spl30_125
| ~ spl30_289 ),
inference(avatar_split_clause,[],[f2479,f2470,f1062,f3876]) ).
fof(f2479,plain,
( ! [X0,X1] :
( ~ empty(X0)
| sK4(powerset(X0)) = X1
| ~ empty(X1) )
| ~ spl30_125
| ~ spl30_289 ),
inference(resolution,[],[f2471,f1063]) ).
fof(f3522,plain,
( spl30_392
| ~ spl30_207
| ~ spl30_303 ),
inference(avatar_split_clause,[],[f2788,f2644,f1798,f3520]) ).
fof(f3520,plain,
( spl30_392
<=> ! [X0,X1] :
( ~ empty(cartesian_product2(X0,X1))
| empty(sK7(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_392])]) ).
fof(f2644,plain,
( spl30_303
<=> ! [X2,X0,X1] :
( ~ empty(cartesian_product2(X0,X1))
| ~ in(X2,sK7(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_303])]) ).
fof(f2788,plain,
( ! [X0,X1] :
( ~ empty(cartesian_product2(X0,X1))
| empty(sK7(X0,X1)) )
| ~ spl30_207
| ~ spl30_303 ),
inference(resolution,[],[f2645,f1799]) ).
fof(f2645,plain,
( ! [X2,X0,X1] :
( ~ in(X2,sK7(X0,X1))
| ~ empty(cartesian_product2(X0,X1)) )
| ~ spl30_303 ),
inference(avatar_component_clause,[],[f2644]) ).
fof(f3518,plain,
( spl30_391
| ~ spl30_207
| ~ spl30_302 ),
inference(avatar_split_clause,[],[f2783,f2640,f1798,f3516]) ).
fof(f3516,plain,
( spl30_391
<=> ! [X0,X1] :
( ~ empty(cartesian_product2(X0,X1))
| empty(sK8(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_391])]) ).
fof(f2640,plain,
( spl30_302
<=> ! [X2,X0,X1] :
( ~ empty(cartesian_product2(X0,X1))
| ~ in(X2,sK8(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_302])]) ).
fof(f2783,plain,
( ! [X0,X1] :
( ~ empty(cartesian_product2(X0,X1))
| empty(sK8(X0,X1)) )
| ~ spl30_207
| ~ spl30_302 ),
inference(resolution,[],[f2641,f1799]) ).
fof(f2641,plain,
( ! [X2,X0,X1] :
( ~ in(X2,sK8(X0,X1))
| ~ empty(cartesian_product2(X0,X1)) )
| ~ spl30_302 ),
inference(avatar_component_clause,[],[f2640]) ).
fof(f3514,plain,
( spl30_390
| ~ spl30_133
| ~ spl30_296 ),
inference(avatar_split_clause,[],[f2618,f2614,f1154,f3512]) ).
fof(f3512,plain,
( spl30_390
<=> ! [X0,X1] :
( finite(sK7(X0,X1))
| ~ finite(X1)
| ~ finite(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_390])]) ).
fof(f2614,plain,
( spl30_296
<=> ! [X0,X1] :
( finite(sK7(X0,X1))
| ~ finite(cartesian_product2(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_296])]) ).
fof(f2618,plain,
( ! [X0,X1] :
( finite(sK7(X0,X1))
| ~ finite(X1)
| ~ finite(X0) )
| ~ spl30_133
| ~ spl30_296 ),
inference(resolution,[],[f2615,f1155]) ).
fof(f2615,plain,
( ! [X0,X1] :
( ~ finite(cartesian_product2(X0,X1))
| finite(sK7(X0,X1)) )
| ~ spl30_296 ),
inference(avatar_component_clause,[],[f2614]) ).
fof(f3510,plain,
( spl30_389
| ~ spl30_133
| ~ spl30_295 ),
inference(avatar_split_clause,[],[f2617,f2610,f1154,f3508]) ).
fof(f3508,plain,
( spl30_389
<=> ! [X0,X1] :
( finite(sK8(X0,X1))
| ~ finite(X1)
| ~ finite(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_389])]) ).
fof(f2610,plain,
( spl30_295
<=> ! [X0,X1] :
( finite(sK8(X0,X1))
| ~ finite(cartesian_product2(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_295])]) ).
fof(f2617,plain,
( ! [X0,X1] :
( finite(sK8(X0,X1))
| ~ finite(X1)
| ~ finite(X0) )
| ~ spl30_133
| ~ spl30_295 ),
inference(resolution,[],[f2611,f1155]) ).
fof(f2611,plain,
( ! [X0,X1] :
( ~ finite(cartesian_product2(X0,X1))
| finite(sK8(X0,X1)) )
| ~ spl30_295 ),
inference(avatar_component_clause,[],[f2610]) ).
fof(f3506,plain,
( spl30_388
| ~ spl30_6
| ~ spl30_168
| ~ spl30_377 ),
inference(avatar_split_clause,[],[f3455,f3440,f1432,f412,f3503]) ).
fof(f3503,plain,
( spl30_388
<=> sK10 = sK4(powerset(sK10)) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_388])]) ).
fof(f3455,plain,
( sK10 = sK4(powerset(sK10))
| ~ spl30_6
| ~ spl30_168
| ~ spl30_377 ),
inference(forward_demodulation,[],[f3444,f1434]) ).
fof(f3444,plain,
( sK10 = sK4(powerset(empty_set))
| ~ spl30_6
| ~ spl30_377 ),
inference(resolution,[],[f3441,f414]) ).
fof(f3501,plain,
( spl30_387
| ~ spl30_98
| ~ spl30_294 ),
inference(avatar_split_clause,[],[f2585,f2502,f911,f3499]) ).
fof(f2585,plain,
( ! [X0] :
( sK10 = relation_dom(relation_rng(relation_rng(X0)))
| ~ empty(X0) )
| ~ spl30_98
| ~ spl30_294 ),
inference(resolution,[],[f2503,f912]) ).
fof(f3497,plain,
( spl30_386
| ~ spl30_101
| ~ spl30_294 ),
inference(avatar_split_clause,[],[f2584,f2502,f924,f3495]) ).
fof(f2584,plain,
( ! [X0] :
( sK10 = relation_dom(relation_rng(relation_dom(X0)))
| ~ empty(X0) )
| ~ spl30_101
| ~ spl30_294 ),
inference(resolution,[],[f2503,f925]) ).
fof(f3493,plain,
( spl30_385
| ~ spl30_98
| ~ spl30_292 ),
inference(avatar_split_clause,[],[f2559,f2494,f911,f3491]) ).
fof(f2559,plain,
( ! [X0] :
( sK10 = relation_dom(relation_dom(relation_rng(X0)))
| ~ empty(X0) )
| ~ spl30_98
| ~ spl30_292 ),
inference(resolution,[],[f2495,f912]) ).
fof(f3489,plain,
( spl30_384
| ~ spl30_101
| ~ spl30_292 ),
inference(avatar_split_clause,[],[f2558,f2494,f924,f3487]) ).
fof(f2558,plain,
( ! [X0] :
( sK10 = relation_dom(relation_dom(relation_dom(X0)))
| ~ empty(X0) )
| ~ spl30_101
| ~ spl30_292 ),
inference(resolution,[],[f2495,f925]) ).
fof(f3485,plain,
( spl30_383
| ~ spl30_98
| ~ spl30_291 ),
inference(avatar_split_clause,[],[f2533,f2490,f911,f3483]) ).
fof(f2533,plain,
( ! [X0] :
( sK10 = relation_rng(relation_rng(relation_rng(X0)))
| ~ empty(X0) )
| ~ spl30_98
| ~ spl30_291 ),
inference(resolution,[],[f2491,f912]) ).
fof(f3481,plain,
( spl30_382
| ~ spl30_101
| ~ spl30_291 ),
inference(avatar_split_clause,[],[f2532,f2490,f924,f3479]) ).
fof(f2532,plain,
( ! [X0] :
( sK10 = relation_rng(relation_rng(relation_dom(X0)))
| ~ empty(X0) )
| ~ spl30_101
| ~ spl30_291 ),
inference(resolution,[],[f2491,f925]) ).
fof(f3477,plain,
( spl30_381
| ~ spl30_98
| ~ spl30_290 ),
inference(avatar_split_clause,[],[f2507,f2486,f911,f3475]) ).
fof(f2507,plain,
( ! [X0] :
( sK10 = relation_rng(relation_dom(relation_rng(X0)))
| ~ empty(X0) )
| ~ spl30_98
| ~ spl30_290 ),
inference(resolution,[],[f2487,f912]) ).
fof(f3473,plain,
( spl30_380
| ~ spl30_101
| ~ spl30_290 ),
inference(avatar_split_clause,[],[f2506,f2486,f924,f3471]) ).
fof(f2506,plain,
( ! [X0] :
( sK10 = relation_rng(relation_dom(relation_dom(X0)))
| ~ empty(X0) )
| ~ spl30_101
| ~ spl30_290 ),
inference(resolution,[],[f2487,f925]) ).
fof(f3469,plain,
( spl30_379
| ~ spl30_202
| ~ spl30_289 ),
inference(avatar_split_clause,[],[f2482,f2470,f1778,f3467]) ).
fof(f2482,plain,
( ! [X0] :
( ~ empty(X0)
| sK10 = relation_dom(sK4(powerset(X0))) )
| ~ spl30_202
| ~ spl30_289 ),
inference(resolution,[],[f2471,f1779]) ).
fof(f3465,plain,
( spl30_378
| ~ spl30_201
| ~ spl30_289 ),
inference(avatar_split_clause,[],[f2481,f2470,f1774,f3463]) ).
fof(f2481,plain,
( ! [X0] :
( ~ empty(X0)
| sK10 = relation_rng(sK4(powerset(X0))) )
| ~ spl30_201
| ~ spl30_289 ),
inference(resolution,[],[f2471,f1775]) ).
fof(f3442,plain,
( spl30_377
| ~ spl30_194
| ~ spl30_289 ),
inference(avatar_split_clause,[],[f2480,f2470,f1585,f3440]) ).
fof(f2480,plain,
( ! [X0] :
( ~ empty(X0)
| sK10 = sK4(powerset(X0)) )
| ~ spl30_194
| ~ spl30_289 ),
inference(resolution,[],[f2471,f1586]) ).
fof(f3433,plain,
( spl30_376
| ~ spl30_152
| ~ spl30_280 ),
inference(avatar_split_clause,[],[f2429,f2422,f1313,f3431]) ).
fof(f3431,plain,
( spl30_376
<=> ! [X4,X0,X3,X2,X1] :
( ~ quasi_total(X0,X1,cartesian_product2(X2,X3))
| ~ function(X0)
| ~ relation_of2(X0,X1,cartesian_product2(X2,X3))
| ~ function(function_image(X1,cartesian_product2(X2,X3),X0,X4))
| relation_dom(function_image(X1,cartesian_product2(X2,X3),X0,X4)) = function_image(cartesian_product2(relation_dom(function_image(X1,cartesian_product2(X2,X3),X0,X4)),relation_rng(function_image(X1,cartesian_product2(X2,X3),X0,X4))),relation_dom(function_image(X1,cartesian_product2(X2,X3),X0,X4)),first_projection_as_func_of(relation_dom(function_image(X1,cartesian_product2(X2,X3),X0,X4)),relation_rng(function_image(X1,cartesian_product2(X2,X3),X0,X4))),function_image(X1,cartesian_product2(X2,X3),X0,X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_376])]) ).
fof(f2422,plain,
( spl30_280
<=> ! [X4,X0,X3,X2,X1] :
( ~ relation_of2(X0,X1,cartesian_product2(X2,X3))
| ~ quasi_total(X0,X1,cartesian_product2(X2,X3))
| ~ function(X0)
| relation(function_image(X1,cartesian_product2(X2,X3),X0,X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_280])]) ).
fof(f2429,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ quasi_total(X0,X1,cartesian_product2(X2,X3))
| ~ function(X0)
| ~ relation_of2(X0,X1,cartesian_product2(X2,X3))
| ~ function(function_image(X1,cartesian_product2(X2,X3),X0,X4))
| relation_dom(function_image(X1,cartesian_product2(X2,X3),X0,X4)) = function_image(cartesian_product2(relation_dom(function_image(X1,cartesian_product2(X2,X3),X0,X4)),relation_rng(function_image(X1,cartesian_product2(X2,X3),X0,X4))),relation_dom(function_image(X1,cartesian_product2(X2,X3),X0,X4)),first_projection_as_func_of(relation_dom(function_image(X1,cartesian_product2(X2,X3),X0,X4)),relation_rng(function_image(X1,cartesian_product2(X2,X3),X0,X4))),function_image(X1,cartesian_product2(X2,X3),X0,X4)) )
| ~ spl30_152
| ~ spl30_280 ),
inference(resolution,[],[f2423,f1314]) ).
fof(f2423,plain,
( ! [X2,X3,X0,X1,X4] :
( relation(function_image(X1,cartesian_product2(X2,X3),X0,X4))
| ~ quasi_total(X0,X1,cartesian_product2(X2,X3))
| ~ function(X0)
| ~ relation_of2(X0,X1,cartesian_product2(X2,X3)) )
| ~ spl30_280 ),
inference(avatar_component_clause,[],[f2422]) ).
fof(f3429,plain,
( spl30_375
| ~ spl30_152
| ~ spl30_208 ),
inference(avatar_split_clause,[],[f1858,f1802,f1313,f3427]) ).
fof(f3427,plain,
( spl30_375
<=> ! [X0,X1] :
( ~ function(sK4(powerset(cartesian_product2(X0,X1))))
| relation_dom(sK4(powerset(cartesian_product2(X0,X1)))) = function_image(cartesian_product2(relation_dom(sK4(powerset(cartesian_product2(X0,X1)))),relation_rng(sK4(powerset(cartesian_product2(X0,X1))))),relation_dom(sK4(powerset(cartesian_product2(X0,X1)))),first_projection_as_func_of(relation_dom(sK4(powerset(cartesian_product2(X0,X1)))),relation_rng(sK4(powerset(cartesian_product2(X0,X1))))),sK4(powerset(cartesian_product2(X0,X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_375])]) ).
fof(f1802,plain,
( spl30_208
<=> ! [X0,X1] : relation(sK4(powerset(cartesian_product2(X0,X1)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_208])]) ).
fof(f1858,plain,
( ! [X0,X1] :
( ~ function(sK4(powerset(cartesian_product2(X0,X1))))
| relation_dom(sK4(powerset(cartesian_product2(X0,X1)))) = function_image(cartesian_product2(relation_dom(sK4(powerset(cartesian_product2(X0,X1)))),relation_rng(sK4(powerset(cartesian_product2(X0,X1))))),relation_dom(sK4(powerset(cartesian_product2(X0,X1)))),first_projection_as_func_of(relation_dom(sK4(powerset(cartesian_product2(X0,X1)))),relation_rng(sK4(powerset(cartesian_product2(X0,X1))))),sK4(powerset(cartesian_product2(X0,X1)))) )
| ~ spl30_152
| ~ spl30_208 ),
inference(resolution,[],[f1803,f1314]) ).
fof(f1803,plain,
( ! [X0,X1] : relation(sK4(powerset(cartesian_product2(X0,X1))))
| ~ spl30_208 ),
inference(avatar_component_clause,[],[f1802]) ).
fof(f3425,plain,
( spl30_374
| ~ spl30_152
| ~ spl30_240 ),
inference(avatar_split_clause,[],[f2106,f2072,f1313,f3423]) ).
fof(f3423,plain,
( spl30_374
<=> ! [X0,X1] :
( empty(cartesian_product2(X0,X1))
| ~ function(sK3(cartesian_product2(X0,X1)))
| relation_dom(sK3(cartesian_product2(X0,X1))) = function_image(cartesian_product2(relation_dom(sK3(cartesian_product2(X0,X1))),relation_rng(sK3(cartesian_product2(X0,X1)))),relation_dom(sK3(cartesian_product2(X0,X1))),first_projection_as_func_of(relation_dom(sK3(cartesian_product2(X0,X1))),relation_rng(sK3(cartesian_product2(X0,X1)))),sK3(cartesian_product2(X0,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_374])]) ).
fof(f2072,plain,
( spl30_240
<=> ! [X0,X1] :
( relation(sK3(cartesian_product2(X0,X1)))
| empty(cartesian_product2(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_240])]) ).
fof(f2106,plain,
( ! [X0,X1] :
( empty(cartesian_product2(X0,X1))
| ~ function(sK3(cartesian_product2(X0,X1)))
| relation_dom(sK3(cartesian_product2(X0,X1))) = function_image(cartesian_product2(relation_dom(sK3(cartesian_product2(X0,X1))),relation_rng(sK3(cartesian_product2(X0,X1)))),relation_dom(sK3(cartesian_product2(X0,X1))),first_projection_as_func_of(relation_dom(sK3(cartesian_product2(X0,X1))),relation_rng(sK3(cartesian_product2(X0,X1)))),sK3(cartesian_product2(X0,X1))) )
| ~ spl30_152
| ~ spl30_240 ),
inference(resolution,[],[f2073,f1314]) ).
fof(f2073,plain,
( ! [X0,X1] :
( relation(sK3(cartesian_product2(X0,X1)))
| empty(cartesian_product2(X0,X1)) )
| ~ spl30_240 ),
inference(avatar_component_clause,[],[f2072]) ).
fof(f3421,plain,
( spl30_373
| ~ spl30_152
| ~ spl30_239 ),
inference(avatar_split_clause,[],[f2096,f2068,f1313,f3419]) ).
fof(f3419,plain,
( spl30_373
<=> ! [X0,X1] :
( empty(cartesian_product2(X0,X1))
| ~ function(sK2(cartesian_product2(X0,X1)))
| relation_dom(sK2(cartesian_product2(X0,X1))) = function_image(cartesian_product2(relation_dom(sK2(cartesian_product2(X0,X1))),relation_rng(sK2(cartesian_product2(X0,X1)))),relation_dom(sK2(cartesian_product2(X0,X1))),first_projection_as_func_of(relation_dom(sK2(cartesian_product2(X0,X1))),relation_rng(sK2(cartesian_product2(X0,X1)))),sK2(cartesian_product2(X0,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_373])]) ).
fof(f2068,plain,
( spl30_239
<=> ! [X0,X1] :
( relation(sK2(cartesian_product2(X0,X1)))
| empty(cartesian_product2(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_239])]) ).
fof(f2096,plain,
( ! [X0,X1] :
( empty(cartesian_product2(X0,X1))
| ~ function(sK2(cartesian_product2(X0,X1)))
| relation_dom(sK2(cartesian_product2(X0,X1))) = function_image(cartesian_product2(relation_dom(sK2(cartesian_product2(X0,X1))),relation_rng(sK2(cartesian_product2(X0,X1)))),relation_dom(sK2(cartesian_product2(X0,X1))),first_projection_as_func_of(relation_dom(sK2(cartesian_product2(X0,X1))),relation_rng(sK2(cartesian_product2(X0,X1)))),sK2(cartesian_product2(X0,X1))) )
| ~ spl30_152
| ~ spl30_239 ),
inference(resolution,[],[f2069,f1314]) ).
fof(f2069,plain,
( ! [X0,X1] :
( relation(sK2(cartesian_product2(X0,X1)))
| empty(cartesian_product2(X0,X1)) )
| ~ spl30_239 ),
inference(avatar_component_clause,[],[f2068]) ).
fof(f3417,plain,
( spl30_372
| ~ spl30_152
| ~ spl30_238 ),
inference(avatar_split_clause,[],[f2095,f2064,f1313,f3415]) ).
fof(f3415,plain,
( spl30_372
<=> ! [X0,X1] :
( empty(cartesian_product2(X0,X1))
| ~ function(sK1(cartesian_product2(X0,X1)))
| relation_dom(sK1(cartesian_product2(X0,X1))) = function_image(cartesian_product2(relation_dom(sK1(cartesian_product2(X0,X1))),relation_rng(sK1(cartesian_product2(X0,X1)))),relation_dom(sK1(cartesian_product2(X0,X1))),first_projection_as_func_of(relation_dom(sK1(cartesian_product2(X0,X1))),relation_rng(sK1(cartesian_product2(X0,X1)))),sK1(cartesian_product2(X0,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_372])]) ).
fof(f2064,plain,
( spl30_238
<=> ! [X0,X1] :
( relation(sK1(cartesian_product2(X0,X1)))
| empty(cartesian_product2(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_238])]) ).
fof(f2095,plain,
( ! [X0,X1] :
( empty(cartesian_product2(X0,X1))
| ~ function(sK1(cartesian_product2(X0,X1)))
| relation_dom(sK1(cartesian_product2(X0,X1))) = function_image(cartesian_product2(relation_dom(sK1(cartesian_product2(X0,X1))),relation_rng(sK1(cartesian_product2(X0,X1)))),relation_dom(sK1(cartesian_product2(X0,X1))),first_projection_as_func_of(relation_dom(sK1(cartesian_product2(X0,X1))),relation_rng(sK1(cartesian_product2(X0,X1)))),sK1(cartesian_product2(X0,X1))) )
| ~ spl30_152
| ~ spl30_238 ),
inference(resolution,[],[f2065,f1314]) ).
fof(f2065,plain,
( ! [X0,X1] :
( relation(sK1(cartesian_product2(X0,X1)))
| empty(cartesian_product2(X0,X1)) )
| ~ spl30_238 ),
inference(avatar_component_clause,[],[f2064]) ).
fof(f3405,plain,
( ~ spl30_233
| spl30_370 ),
inference(avatar_contradiction_clause,[],[f3404]) ).
fof(f3404,plain,
( $false
| ~ spl30_233
| spl30_370 ),
inference(resolution,[],[f3391,f1964]) ).
fof(f1964,plain,
( ! [X0,X1] : relation_of2(first_projection_as_func_of(X0,X1),cartesian_product2(X0,X1),X0)
| ~ spl30_233 ),
inference(avatar_component_clause,[],[f1963]) ).
fof(f1963,plain,
( spl30_233
<=> ! [X0,X1] : relation_of2(first_projection_as_func_of(X0,X1),cartesian_product2(X0,X1),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_233])]) ).
fof(f3391,plain,
( ~ relation_of2(first_projection_as_func_of(relation_dom(sK25),relation_rng(sK25)),cartesian_product2(relation_dom(sK25),relation_rng(sK25)),relation_dom(sK25))
| spl30_370 ),
inference(avatar_component_clause,[],[f3389]) ).
fof(f3389,plain,
( spl30_370
<=> relation_of2(first_projection_as_func_of(relation_dom(sK25),relation_rng(sK25)),cartesian_product2(relation_dom(sK25),relation_rng(sK25)),relation_dom(sK25)) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_370])]) ).
fof(f3403,plain,
( ~ spl30_129
| spl30_369 ),
inference(avatar_contradiction_clause,[],[f3402]) ).
fof(f3402,plain,
( $false
| ~ spl30_129
| spl30_369 ),
inference(resolution,[],[f3387,f1139]) ).
fof(f3387,plain,
( ~ quasi_total(first_projection_as_func_of(relation_dom(sK25),relation_rng(sK25)),cartesian_product2(relation_dom(sK25),relation_rng(sK25)),relation_dom(sK25))
| spl30_369 ),
inference(avatar_component_clause,[],[f3385]) ).
fof(f3385,plain,
( spl30_369
<=> quasi_total(first_projection_as_func_of(relation_dom(sK25),relation_rng(sK25)),cartesian_product2(relation_dom(sK25),relation_rng(sK25)),relation_dom(sK25)) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_369])]) ).
fof(f3400,plain,
( ~ spl30_77
| spl30_363 ),
inference(avatar_contradiction_clause,[],[f3399]) ).
fof(f3399,plain,
( $false
| ~ spl30_77
| spl30_363 ),
inference(resolution,[],[f3336,f759]) ).
fof(f3336,plain,
( ~ subset(relation_dom(sK23),relation_dom(sK23))
| spl30_363 ),
inference(avatar_component_clause,[],[f3334]) ).
fof(f3334,plain,
( spl30_363
<=> subset(relation_dom(sK23),relation_dom(sK23)) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_363])]) ).
fof(f3398,plain,
( ~ spl30_89
| spl30_368 ),
inference(avatar_contradiction_clause,[],[f3397]) ).
fof(f3397,plain,
( $false
| ~ spl30_89
| spl30_368 ),
inference(resolution,[],[f3383,f809]) ).
fof(f3383,plain,
( ~ function(first_projection_as_func_of(relation_dom(sK25),relation_rng(sK25)))
| spl30_368 ),
inference(avatar_component_clause,[],[f3381]) ).
fof(f3381,plain,
( spl30_368
<=> function(first_projection_as_func_of(relation_dom(sK25),relation_rng(sK25))) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_368])]) ).
fof(f3396,plain,
( ~ spl30_368
| ~ spl30_369
| ~ spl30_370
| spl30_371
| ~ spl30_149
| ~ spl30_275 ),
inference(avatar_split_clause,[],[f2334,f2328,f1289,f3393,f3389,f3385,f3381]) ).
fof(f2328,plain,
( spl30_275
<=> relation_dom(sK25) = function_image(cartesian_product2(relation_dom(sK25),relation_rng(sK25)),relation_dom(sK25),first_projection_as_func_of(relation_dom(sK25),relation_rng(sK25)),sK25) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_275])]) ).
fof(f2334,plain,
( element(relation_dom(sK25),powerset(relation_dom(sK25)))
| ~ relation_of2(first_projection_as_func_of(relation_dom(sK25),relation_rng(sK25)),cartesian_product2(relation_dom(sK25),relation_rng(sK25)),relation_dom(sK25))
| ~ quasi_total(first_projection_as_func_of(relation_dom(sK25),relation_rng(sK25)),cartesian_product2(relation_dom(sK25),relation_rng(sK25)),relation_dom(sK25))
| ~ function(first_projection_as_func_of(relation_dom(sK25),relation_rng(sK25)))
| ~ spl30_149
| ~ spl30_275 ),
inference(superposition,[],[f1290,f2330]) ).
fof(f2330,plain,
( relation_dom(sK25) = function_image(cartesian_product2(relation_dom(sK25),relation_rng(sK25)),relation_dom(sK25),first_projection_as_func_of(relation_dom(sK25),relation_rng(sK25)),sK25)
| ~ spl30_275 ),
inference(avatar_component_clause,[],[f2328]) ).
fof(f3371,plain,
( ~ spl30_233
| spl30_366 ),
inference(avatar_contradiction_clause,[],[f3370]) ).
fof(f3370,plain,
( $false
| ~ spl30_233
| spl30_366 ),
inference(resolution,[],[f3359,f1964]) ).
fof(f3359,plain,
( ~ relation_of2(first_projection_as_func_of(relation_dom(sK24),relation_rng(sK24)),cartesian_product2(relation_dom(sK24),relation_rng(sK24)),relation_dom(sK24))
| spl30_366 ),
inference(avatar_component_clause,[],[f3357]) ).
fof(f3357,plain,
( spl30_366
<=> relation_of2(first_projection_as_func_of(relation_dom(sK24),relation_rng(sK24)),cartesian_product2(relation_dom(sK24),relation_rng(sK24)),relation_dom(sK24)) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_366])]) ).
fof(f3369,plain,
( ~ spl30_129
| spl30_365 ),
inference(avatar_contradiction_clause,[],[f3368]) ).
fof(f3368,plain,
( $false
| ~ spl30_129
| spl30_365 ),
inference(resolution,[],[f3355,f1139]) ).
fof(f3355,plain,
( ~ quasi_total(first_projection_as_func_of(relation_dom(sK24),relation_rng(sK24)),cartesian_product2(relation_dom(sK24),relation_rng(sK24)),relation_dom(sK24))
| spl30_365 ),
inference(avatar_component_clause,[],[f3353]) ).
fof(f3353,plain,
( spl30_365
<=> quasi_total(first_projection_as_func_of(relation_dom(sK24),relation_rng(sK24)),cartesian_product2(relation_dom(sK24),relation_rng(sK24)),relation_dom(sK24)) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_365])]) ).
fof(f3366,plain,
( ~ spl30_89
| spl30_364 ),
inference(avatar_contradiction_clause,[],[f3365]) ).
fof(f3365,plain,
( $false
| ~ spl30_89
| spl30_364 ),
inference(resolution,[],[f3351,f809]) ).
fof(f3351,plain,
( ~ function(first_projection_as_func_of(relation_dom(sK24),relation_rng(sK24)))
| spl30_364 ),
inference(avatar_component_clause,[],[f3349]) ).
fof(f3349,plain,
( spl30_364
<=> function(first_projection_as_func_of(relation_dom(sK24),relation_rng(sK24))) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_364])]) ).
fof(f3364,plain,
( ~ spl30_364
| ~ spl30_365
| ~ spl30_366
| spl30_367
| ~ spl30_149
| ~ spl30_274 ),
inference(avatar_split_clause,[],[f2326,f2320,f1289,f3361,f3357,f3353,f3349]) ).
fof(f2320,plain,
( spl30_274
<=> relation_dom(sK24) = function_image(cartesian_product2(relation_dom(sK24),relation_rng(sK24)),relation_dom(sK24),first_projection_as_func_of(relation_dom(sK24),relation_rng(sK24)),sK24) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_274])]) ).
fof(f2326,plain,
( element(relation_dom(sK24),powerset(relation_dom(sK24)))
| ~ relation_of2(first_projection_as_func_of(relation_dom(sK24),relation_rng(sK24)),cartesian_product2(relation_dom(sK24),relation_rng(sK24)),relation_dom(sK24))
| ~ quasi_total(first_projection_as_func_of(relation_dom(sK24),relation_rng(sK24)),cartesian_product2(relation_dom(sK24),relation_rng(sK24)),relation_dom(sK24))
| ~ function(first_projection_as_func_of(relation_dom(sK24),relation_rng(sK24)))
| ~ spl30_149
| ~ spl30_274 ),
inference(superposition,[],[f1290,f2322]) ).
fof(f2322,plain,
( relation_dom(sK24) = function_image(cartesian_product2(relation_dom(sK24),relation_rng(sK24)),relation_dom(sK24),first_projection_as_func_of(relation_dom(sK24),relation_rng(sK24)),sK24)
| ~ spl30_274 ),
inference(avatar_component_clause,[],[f2320]) ).
fof(f3339,plain,
( ~ spl30_233
| spl30_361 ),
inference(avatar_contradiction_clause,[],[f3338]) ).
fof(f3338,plain,
( $false
| ~ spl30_233
| spl30_361 ),
inference(resolution,[],[f3322,f1964]) ).
fof(f3322,plain,
( ~ relation_of2(first_projection_as_func_of(relation_dom(sK23),relation_rng(sK23)),cartesian_product2(relation_dom(sK23),relation_rng(sK23)),relation_dom(sK23))
| spl30_361 ),
inference(avatar_component_clause,[],[f3320]) ).
fof(f3320,plain,
( spl30_361
<=> relation_of2(first_projection_as_func_of(relation_dom(sK23),relation_rng(sK23)),cartesian_product2(relation_dom(sK23),relation_rng(sK23)),relation_dom(sK23)) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_361])]) ).
fof(f3337,plain,
( ~ spl30_363
| ~ spl30_124
| spl30_362 ),
inference(avatar_split_clause,[],[f3330,f3324,f1058,f3334]) ).
fof(f1058,plain,
( spl30_124
<=> ! [X0,X1] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_124])]) ).
fof(f3330,plain,
( ~ subset(relation_dom(sK23),relation_dom(sK23))
| ~ spl30_124
| spl30_362 ),
inference(resolution,[],[f3325,f1059]) ).
fof(f1059,plain,
( ! [X0,X1] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) )
| ~ spl30_124 ),
inference(avatar_component_clause,[],[f1058]) ).
fof(f3325,plain,
( ~ element(relation_dom(sK23),powerset(relation_dom(sK23)))
| spl30_362 ),
inference(avatar_component_clause,[],[f3324]) ).
fof(f3332,plain,
( ~ spl30_129
| spl30_360 ),
inference(avatar_contradiction_clause,[],[f3331]) ).
fof(f3331,plain,
( $false
| ~ spl30_129
| spl30_360 ),
inference(resolution,[],[f3318,f1139]) ).
fof(f3318,plain,
( ~ quasi_total(first_projection_as_func_of(relation_dom(sK23),relation_rng(sK23)),cartesian_product2(relation_dom(sK23),relation_rng(sK23)),relation_dom(sK23))
| spl30_360 ),
inference(avatar_component_clause,[],[f3316]) ).
fof(f3316,plain,
( spl30_360
<=> quasi_total(first_projection_as_func_of(relation_dom(sK23),relation_rng(sK23)),cartesian_product2(relation_dom(sK23),relation_rng(sK23)),relation_dom(sK23)) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_360])]) ).
fof(f3329,plain,
( ~ spl30_89
| spl30_359 ),
inference(avatar_contradiction_clause,[],[f3328]) ).
fof(f3328,plain,
( $false
| ~ spl30_89
| spl30_359 ),
inference(resolution,[],[f3314,f809]) ).
fof(f3314,plain,
( ~ function(first_projection_as_func_of(relation_dom(sK23),relation_rng(sK23)))
| spl30_359 ),
inference(avatar_component_clause,[],[f3312]) ).
fof(f3312,plain,
( spl30_359
<=> function(first_projection_as_func_of(relation_dom(sK23),relation_rng(sK23))) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_359])]) ).
fof(f3327,plain,
( ~ spl30_359
| ~ spl30_360
| ~ spl30_361
| spl30_362
| ~ spl30_149
| ~ spl30_273 ),
inference(avatar_split_clause,[],[f2318,f2312,f1289,f3324,f3320,f3316,f3312]) ).
fof(f2312,plain,
( spl30_273
<=> relation_dom(sK23) = function_image(cartesian_product2(relation_dom(sK23),relation_rng(sK23)),relation_dom(sK23),first_projection_as_func_of(relation_dom(sK23),relation_rng(sK23)),sK23) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_273])]) ).
fof(f2318,plain,
( element(relation_dom(sK23),powerset(relation_dom(sK23)))
| ~ relation_of2(first_projection_as_func_of(relation_dom(sK23),relation_rng(sK23)),cartesian_product2(relation_dom(sK23),relation_rng(sK23)),relation_dom(sK23))
| ~ quasi_total(first_projection_as_func_of(relation_dom(sK23),relation_rng(sK23)),cartesian_product2(relation_dom(sK23),relation_rng(sK23)),relation_dom(sK23))
| ~ function(first_projection_as_func_of(relation_dom(sK23),relation_rng(sK23)))
| ~ spl30_149
| ~ spl30_273 ),
inference(superposition,[],[f1290,f2314]) ).
fof(f2314,plain,
( relation_dom(sK23) = function_image(cartesian_product2(relation_dom(sK23),relation_rng(sK23)),relation_dom(sK23),first_projection_as_func_of(relation_dom(sK23),relation_rng(sK23)),sK23)
| ~ spl30_273 ),
inference(avatar_component_clause,[],[f2312]) ).
fof(f3302,plain,
( ~ spl30_233
| spl30_357 ),
inference(avatar_contradiction_clause,[],[f3301]) ).
fof(f3301,plain,
( $false
| ~ spl30_233
| spl30_357 ),
inference(resolution,[],[f3290,f1964]) ).
fof(f3290,plain,
( ~ relation_of2(first_projection_as_func_of(relation_dom(sK22),relation_rng(sK22)),cartesian_product2(relation_dom(sK22),relation_rng(sK22)),relation_dom(sK22))
| spl30_357 ),
inference(avatar_component_clause,[],[f3288]) ).
fof(f3288,plain,
( spl30_357
<=> relation_of2(first_projection_as_func_of(relation_dom(sK22),relation_rng(sK22)),cartesian_product2(relation_dom(sK22),relation_rng(sK22)),relation_dom(sK22)) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_357])]) ).
fof(f3300,plain,
( ~ spl30_129
| spl30_356 ),
inference(avatar_contradiction_clause,[],[f3299]) ).
fof(f3299,plain,
( $false
| ~ spl30_129
| spl30_356 ),
inference(resolution,[],[f3286,f1139]) ).
fof(f3286,plain,
( ~ quasi_total(first_projection_as_func_of(relation_dom(sK22),relation_rng(sK22)),cartesian_product2(relation_dom(sK22),relation_rng(sK22)),relation_dom(sK22))
| spl30_356 ),
inference(avatar_component_clause,[],[f3284]) ).
fof(f3284,plain,
( spl30_356
<=> quasi_total(first_projection_as_func_of(relation_dom(sK22),relation_rng(sK22)),cartesian_product2(relation_dom(sK22),relation_rng(sK22)),relation_dom(sK22)) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_356])]) ).
fof(f3297,plain,
( ~ spl30_89
| spl30_355 ),
inference(avatar_contradiction_clause,[],[f3296]) ).
fof(f3296,plain,
( $false
| ~ spl30_89
| spl30_355 ),
inference(resolution,[],[f3282,f809]) ).
fof(f3282,plain,
( ~ function(first_projection_as_func_of(relation_dom(sK22),relation_rng(sK22)))
| spl30_355 ),
inference(avatar_component_clause,[],[f3280]) ).
fof(f3280,plain,
( spl30_355
<=> function(first_projection_as_func_of(relation_dom(sK22),relation_rng(sK22))) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_355])]) ).
fof(f3295,plain,
( ~ spl30_355
| ~ spl30_356
| ~ spl30_357
| spl30_358
| ~ spl30_149
| ~ spl30_272 ),
inference(avatar_split_clause,[],[f2310,f2304,f1289,f3292,f3288,f3284,f3280]) ).
fof(f2304,plain,
( spl30_272
<=> relation_dom(sK22) = function_image(cartesian_product2(relation_dom(sK22),relation_rng(sK22)),relation_dom(sK22),first_projection_as_func_of(relation_dom(sK22),relation_rng(sK22)),sK22) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_272])]) ).
fof(f2310,plain,
( element(relation_dom(sK22),powerset(relation_dom(sK22)))
| ~ relation_of2(first_projection_as_func_of(relation_dom(sK22),relation_rng(sK22)),cartesian_product2(relation_dom(sK22),relation_rng(sK22)),relation_dom(sK22))
| ~ quasi_total(first_projection_as_func_of(relation_dom(sK22),relation_rng(sK22)),cartesian_product2(relation_dom(sK22),relation_rng(sK22)),relation_dom(sK22))
| ~ function(first_projection_as_func_of(relation_dom(sK22),relation_rng(sK22)))
| ~ spl30_149
| ~ spl30_272 ),
inference(superposition,[],[f1290,f2306]) ).
fof(f2306,plain,
( relation_dom(sK22) = function_image(cartesian_product2(relation_dom(sK22),relation_rng(sK22)),relation_dom(sK22),first_projection_as_func_of(relation_dom(sK22),relation_rng(sK22)),sK22)
| ~ spl30_272 ),
inference(avatar_component_clause,[],[f2304]) ).
fof(f3278,plain,
( spl30_354
| ~ spl30_87
| ~ spl30_289 ),
inference(avatar_split_clause,[],[f2478,f2470,f800,f3276]) ).
fof(f3276,plain,
( spl30_354
<=> ! [X0] :
( ~ empty(X0)
| ordinal(sK4(powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_354])]) ).
fof(f2478,plain,
( ! [X0] :
( ~ empty(X0)
| ordinal(sK4(powerset(X0))) )
| ~ spl30_87
| ~ spl30_289 ),
inference(resolution,[],[f2471,f801]) ).
fof(f3266,plain,
( ~ spl30_233
| spl30_352 ),
inference(avatar_contradiction_clause,[],[f3265]) ).
fof(f3265,plain,
( $false
| ~ spl30_233
| spl30_352 ),
inference(resolution,[],[f3254,f1964]) ).
fof(f3254,plain,
( ~ relation_of2(first_projection_as_func_of(relation_dom(sK21),relation_rng(sK21)),cartesian_product2(relation_dom(sK21),relation_rng(sK21)),relation_dom(sK21))
| spl30_352 ),
inference(avatar_component_clause,[],[f3252]) ).
fof(f3252,plain,
( spl30_352
<=> relation_of2(first_projection_as_func_of(relation_dom(sK21),relation_rng(sK21)),cartesian_product2(relation_dom(sK21),relation_rng(sK21)),relation_dom(sK21)) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_352])]) ).
fof(f3264,plain,
( ~ spl30_129
| spl30_351 ),
inference(avatar_contradiction_clause,[],[f3263]) ).
fof(f3263,plain,
( $false
| ~ spl30_129
| spl30_351 ),
inference(resolution,[],[f3250,f1139]) ).
fof(f3250,plain,
( ~ quasi_total(first_projection_as_func_of(relation_dom(sK21),relation_rng(sK21)),cartesian_product2(relation_dom(sK21),relation_rng(sK21)),relation_dom(sK21))
| spl30_351 ),
inference(avatar_component_clause,[],[f3248]) ).
fof(f3248,plain,
( spl30_351
<=> quasi_total(first_projection_as_func_of(relation_dom(sK21),relation_rng(sK21)),cartesian_product2(relation_dom(sK21),relation_rng(sK21)),relation_dom(sK21)) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_351])]) ).
fof(f3261,plain,
( ~ spl30_89
| spl30_350 ),
inference(avatar_contradiction_clause,[],[f3260]) ).
fof(f3260,plain,
( $false
| ~ spl30_89
| spl30_350 ),
inference(resolution,[],[f3246,f809]) ).
fof(f3246,plain,
( ~ function(first_projection_as_func_of(relation_dom(sK21),relation_rng(sK21)))
| spl30_350 ),
inference(avatar_component_clause,[],[f3244]) ).
fof(f3244,plain,
( spl30_350
<=> function(first_projection_as_func_of(relation_dom(sK21),relation_rng(sK21))) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_350])]) ).
fof(f3259,plain,
( ~ spl30_350
| ~ spl30_351
| ~ spl30_352
| spl30_353
| ~ spl30_149
| ~ spl30_271 ),
inference(avatar_split_clause,[],[f2301,f2295,f1289,f3256,f3252,f3248,f3244]) ).
fof(f2295,plain,
( spl30_271
<=> relation_dom(sK21) = function_image(cartesian_product2(relation_dom(sK21),relation_rng(sK21)),relation_dom(sK21),first_projection_as_func_of(relation_dom(sK21),relation_rng(sK21)),sK21) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_271])]) ).
fof(f2301,plain,
( element(relation_dom(sK21),powerset(relation_dom(sK21)))
| ~ relation_of2(first_projection_as_func_of(relation_dom(sK21),relation_rng(sK21)),cartesian_product2(relation_dom(sK21),relation_rng(sK21)),relation_dom(sK21))
| ~ quasi_total(first_projection_as_func_of(relation_dom(sK21),relation_rng(sK21)),cartesian_product2(relation_dom(sK21),relation_rng(sK21)),relation_dom(sK21))
| ~ function(first_projection_as_func_of(relation_dom(sK21),relation_rng(sK21)))
| ~ spl30_149
| ~ spl30_271 ),
inference(superposition,[],[f1290,f2297]) ).
fof(f2297,plain,
( relation_dom(sK21) = function_image(cartesian_product2(relation_dom(sK21),relation_rng(sK21)),relation_dom(sK21),first_projection_as_func_of(relation_dom(sK21),relation_rng(sK21)),sK21)
| ~ spl30_271 ),
inference(avatar_component_clause,[],[f2295]) ).
fof(f3234,plain,
( ~ spl30_233
| spl30_348 ),
inference(avatar_contradiction_clause,[],[f3233]) ).
fof(f3233,plain,
( $false
| ~ spl30_233
| spl30_348 ),
inference(resolution,[],[f3222,f1964]) ).
fof(f3222,plain,
( ~ relation_of2(first_projection_as_func_of(relation_dom(sK20),relation_rng(sK20)),cartesian_product2(relation_dom(sK20),relation_rng(sK20)),relation_dom(sK20))
| spl30_348 ),
inference(avatar_component_clause,[],[f3220]) ).
fof(f3220,plain,
( spl30_348
<=> relation_of2(first_projection_as_func_of(relation_dom(sK20),relation_rng(sK20)),cartesian_product2(relation_dom(sK20),relation_rng(sK20)),relation_dom(sK20)) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_348])]) ).
fof(f3232,plain,
( ~ spl30_129
| spl30_347 ),
inference(avatar_contradiction_clause,[],[f3231]) ).
fof(f3231,plain,
( $false
| ~ spl30_129
| spl30_347 ),
inference(resolution,[],[f3218,f1139]) ).
fof(f3218,plain,
( ~ quasi_total(first_projection_as_func_of(relation_dom(sK20),relation_rng(sK20)),cartesian_product2(relation_dom(sK20),relation_rng(sK20)),relation_dom(sK20))
| spl30_347 ),
inference(avatar_component_clause,[],[f3216]) ).
fof(f3216,plain,
( spl30_347
<=> quasi_total(first_projection_as_func_of(relation_dom(sK20),relation_rng(sK20)),cartesian_product2(relation_dom(sK20),relation_rng(sK20)),relation_dom(sK20)) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_347])]) ).
fof(f3229,plain,
( ~ spl30_89
| spl30_346 ),
inference(avatar_contradiction_clause,[],[f3228]) ).
fof(f3228,plain,
( $false
| ~ spl30_89
| spl30_346 ),
inference(resolution,[],[f3214,f809]) ).
fof(f3214,plain,
( ~ function(first_projection_as_func_of(relation_dom(sK20),relation_rng(sK20)))
| spl30_346 ),
inference(avatar_component_clause,[],[f3212]) ).
fof(f3212,plain,
( spl30_346
<=> function(first_projection_as_func_of(relation_dom(sK20),relation_rng(sK20))) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_346])]) ).
fof(f3227,plain,
( ~ spl30_346
| ~ spl30_347
| ~ spl30_348
| spl30_349
| ~ spl30_149
| ~ spl30_270 ),
inference(avatar_split_clause,[],[f2293,f2287,f1289,f3224,f3220,f3216,f3212]) ).
fof(f2287,plain,
( spl30_270
<=> relation_dom(sK20) = function_image(cartesian_product2(relation_dom(sK20),relation_rng(sK20)),relation_dom(sK20),first_projection_as_func_of(relation_dom(sK20),relation_rng(sK20)),sK20) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_270])]) ).
fof(f2293,plain,
( element(relation_dom(sK20),powerset(relation_dom(sK20)))
| ~ relation_of2(first_projection_as_func_of(relation_dom(sK20),relation_rng(sK20)),cartesian_product2(relation_dom(sK20),relation_rng(sK20)),relation_dom(sK20))
| ~ quasi_total(first_projection_as_func_of(relation_dom(sK20),relation_rng(sK20)),cartesian_product2(relation_dom(sK20),relation_rng(sK20)),relation_dom(sK20))
| ~ function(first_projection_as_func_of(relation_dom(sK20),relation_rng(sK20)))
| ~ spl30_149
| ~ spl30_270 ),
inference(superposition,[],[f1290,f2289]) ).
fof(f2289,plain,
( relation_dom(sK20) = function_image(cartesian_product2(relation_dom(sK20),relation_rng(sK20)),relation_dom(sK20),first_projection_as_func_of(relation_dom(sK20),relation_rng(sK20)),sK20)
| ~ spl30_270 ),
inference(avatar_component_clause,[],[f2287]) ).
fof(f3202,plain,
( ~ spl30_233
| spl30_344 ),
inference(avatar_contradiction_clause,[],[f3201]) ).
fof(f3201,plain,
( $false
| ~ spl30_233
| spl30_344 ),
inference(resolution,[],[f3190,f1964]) ).
fof(f3190,plain,
( ~ relation_of2(first_projection_as_func_of(relation_dom(sK18),relation_rng(sK18)),cartesian_product2(relation_dom(sK18),relation_rng(sK18)),relation_dom(sK18))
| spl30_344 ),
inference(avatar_component_clause,[],[f3188]) ).
fof(f3188,plain,
( spl30_344
<=> relation_of2(first_projection_as_func_of(relation_dom(sK18),relation_rng(sK18)),cartesian_product2(relation_dom(sK18),relation_rng(sK18)),relation_dom(sK18)) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_344])]) ).
fof(f3200,plain,
( ~ spl30_129
| spl30_343 ),
inference(avatar_contradiction_clause,[],[f3199]) ).
fof(f3199,plain,
( $false
| ~ spl30_129
| spl30_343 ),
inference(resolution,[],[f3186,f1139]) ).
fof(f3186,plain,
( ~ quasi_total(first_projection_as_func_of(relation_dom(sK18),relation_rng(sK18)),cartesian_product2(relation_dom(sK18),relation_rng(sK18)),relation_dom(sK18))
| spl30_343 ),
inference(avatar_component_clause,[],[f3184]) ).
fof(f3184,plain,
( spl30_343
<=> quasi_total(first_projection_as_func_of(relation_dom(sK18),relation_rng(sK18)),cartesian_product2(relation_dom(sK18),relation_rng(sK18)),relation_dom(sK18)) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_343])]) ).
fof(f3197,plain,
( ~ spl30_89
| spl30_342 ),
inference(avatar_contradiction_clause,[],[f3196]) ).
fof(f3196,plain,
( $false
| ~ spl30_89
| spl30_342 ),
inference(resolution,[],[f3182,f809]) ).
fof(f3182,plain,
( ~ function(first_projection_as_func_of(relation_dom(sK18),relation_rng(sK18)))
| spl30_342 ),
inference(avatar_component_clause,[],[f3180]) ).
fof(f3180,plain,
( spl30_342
<=> function(first_projection_as_func_of(relation_dom(sK18),relation_rng(sK18))) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_342])]) ).
fof(f3195,plain,
( ~ spl30_342
| ~ spl30_343
| ~ spl30_344
| spl30_345
| ~ spl30_149
| ~ spl30_267 ),
inference(avatar_split_clause,[],[f2276,f2270,f1289,f3192,f3188,f3184,f3180]) ).
fof(f2270,plain,
( spl30_267
<=> relation_dom(sK18) = function_image(cartesian_product2(relation_dom(sK18),relation_rng(sK18)),relation_dom(sK18),first_projection_as_func_of(relation_dom(sK18),relation_rng(sK18)),sK18) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_267])]) ).
fof(f2276,plain,
( element(relation_dom(sK18),powerset(relation_dom(sK18)))
| ~ relation_of2(first_projection_as_func_of(relation_dom(sK18),relation_rng(sK18)),cartesian_product2(relation_dom(sK18),relation_rng(sK18)),relation_dom(sK18))
| ~ quasi_total(first_projection_as_func_of(relation_dom(sK18),relation_rng(sK18)),cartesian_product2(relation_dom(sK18),relation_rng(sK18)),relation_dom(sK18))
| ~ function(first_projection_as_func_of(relation_dom(sK18),relation_rng(sK18)))
| ~ spl30_149
| ~ spl30_267 ),
inference(superposition,[],[f1290,f2272]) ).
fof(f2272,plain,
( relation_dom(sK18) = function_image(cartesian_product2(relation_dom(sK18),relation_rng(sK18)),relation_dom(sK18),first_projection_as_func_of(relation_dom(sK18),relation_rng(sK18)),sK18)
| ~ spl30_267 ),
inference(avatar_component_clause,[],[f2270]) ).
fof(f3166,plain,
( spl30_341
| ~ spl30_89
| ~ spl30_285 ),
inference(avatar_split_clause,[],[f2456,f2453,f808,f3164]) ).
fof(f2453,plain,
( spl30_285
<=> ! [X0,X1] :
( ~ function(first_projection_as_func_of(X0,X1))
| relation_dom(first_projection_as_func_of(X0,X1)) = function_image(cartesian_product2(relation_dom(first_projection_as_func_of(X0,X1)),relation_rng(first_projection_as_func_of(X0,X1))),relation_dom(first_projection_as_func_of(X0,X1)),first_projection_as_func_of(relation_dom(first_projection_as_func_of(X0,X1)),relation_rng(first_projection_as_func_of(X0,X1))),first_projection_as_func_of(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_285])]) ).
fof(f2456,plain,
( ! [X0,X1] : relation_dom(first_projection_as_func_of(X0,X1)) = function_image(cartesian_product2(relation_dom(first_projection_as_func_of(X0,X1)),relation_rng(first_projection_as_func_of(X0,X1))),relation_dom(first_projection_as_func_of(X0,X1)),first_projection_as_func_of(relation_dom(first_projection_as_func_of(X0,X1)),relation_rng(first_projection_as_func_of(X0,X1))),first_projection_as_func_of(X0,X1))
| ~ spl30_89
| ~ spl30_285 ),
inference(resolution,[],[f2454,f809]) ).
fof(f2454,plain,
( ! [X0,X1] :
( ~ function(first_projection_as_func_of(X0,X1))
| relation_dom(first_projection_as_func_of(X0,X1)) = function_image(cartesian_product2(relation_dom(first_projection_as_func_of(X0,X1)),relation_rng(first_projection_as_func_of(X0,X1))),relation_dom(first_projection_as_func_of(X0,X1)),first_projection_as_func_of(relation_dom(first_projection_as_func_of(X0,X1)),relation_rng(first_projection_as_func_of(X0,X1))),first_projection_as_func_of(X0,X1)) )
| ~ spl30_285 ),
inference(avatar_component_clause,[],[f2453]) ).
fof(f3161,plain,
( spl30_340
| ~ spl30_86
| ~ spl30_289 ),
inference(avatar_split_clause,[],[f2477,f2470,f796,f3159]) ).
fof(f3159,plain,
( spl30_340
<=> ! [X0] :
( ~ empty(X0)
| epsilon_connected(sK4(powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_340])]) ).
fof(f2477,plain,
( ! [X0] :
( ~ empty(X0)
| epsilon_connected(sK4(powerset(X0))) )
| ~ spl30_86
| ~ spl30_289 ),
inference(resolution,[],[f2471,f797]) ).
fof(f3157,plain,
( spl30_339
| ~ spl30_151
| ~ spl30_233 ),
inference(avatar_split_clause,[],[f2049,f1963,f1308,f3155]) ).
fof(f1308,plain,
( spl30_151
<=> ! [X0,X3,X2,X1] :
( function_image(X0,X1,X2,X3) = relation_image(X2,X3)
| ~ relation_of2(X2,X0,X1)
| ~ quasi_total(X2,X0,X1)
| ~ function(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_151])]) ).
fof(f2049,plain,
( ! [X2,X0,X1] :
( function_image(cartesian_product2(X0,X1),X0,first_projection_as_func_of(X0,X1),X2) = relation_image(first_projection_as_func_of(X0,X1),X2)
| ~ quasi_total(first_projection_as_func_of(X0,X1),cartesian_product2(X0,X1),X0)
| ~ function(first_projection_as_func_of(X0,X1)) )
| ~ spl30_151
| ~ spl30_233 ),
inference(resolution,[],[f1964,f1309]) ).
fof(f1309,plain,
( ! [X2,X3,X0,X1] :
( ~ relation_of2(X2,X0,X1)
| function_image(X0,X1,X2,X3) = relation_image(X2,X3)
| ~ quasi_total(X2,X0,X1)
| ~ function(X2) )
| ~ spl30_151 ),
inference(avatar_component_clause,[],[f1308]) ).
fof(f3067,plain,
( spl30_338
| ~ spl30_181
| ~ spl30_284 ),
inference(avatar_split_clause,[],[f2449,f2439,f1529,f3065]) ).
fof(f1529,plain,
( spl30_181
<=> ! [X0] :
( ~ empty(X0)
| function(relation_rng(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_181])]) ).
fof(f2439,plain,
( spl30_284
<=> ! [X0] :
( ~ function(relation_rng(X0))
| relation_dom(relation_rng(X0)) = function_image(cartesian_product2(relation_dom(relation_rng(X0)),relation_rng(relation_rng(X0))),relation_dom(relation_rng(X0)),first_projection_as_func_of(relation_dom(relation_rng(X0)),relation_rng(relation_rng(X0))),relation_rng(X0))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_284])]) ).
fof(f2449,plain,
( ! [X0] :
( relation_dom(relation_rng(X0)) = function_image(cartesian_product2(relation_dom(relation_rng(X0)),relation_rng(relation_rng(X0))),relation_dom(relation_rng(X0)),first_projection_as_func_of(relation_dom(relation_rng(X0)),relation_rng(relation_rng(X0))),relation_rng(X0))
| ~ empty(X0) )
| ~ spl30_181
| ~ spl30_284 ),
inference(duplicate_literal_removal,[],[f2447]) ).
fof(f2447,plain,
( ! [X0] :
( relation_dom(relation_rng(X0)) = function_image(cartesian_product2(relation_dom(relation_rng(X0)),relation_rng(relation_rng(X0))),relation_dom(relation_rng(X0)),first_projection_as_func_of(relation_dom(relation_rng(X0)),relation_rng(relation_rng(X0))),relation_rng(X0))
| ~ empty(X0)
| ~ empty(X0) )
| ~ spl30_181
| ~ spl30_284 ),
inference(resolution,[],[f2440,f1530]) ).
fof(f1530,plain,
( ! [X0] :
( function(relation_rng(X0))
| ~ empty(X0) )
| ~ spl30_181 ),
inference(avatar_component_clause,[],[f1529]) ).
fof(f2440,plain,
( ! [X0] :
( ~ function(relation_rng(X0))
| relation_dom(relation_rng(X0)) = function_image(cartesian_product2(relation_dom(relation_rng(X0)),relation_rng(relation_rng(X0))),relation_dom(relation_rng(X0)),first_projection_as_func_of(relation_dom(relation_rng(X0)),relation_rng(relation_rng(X0))),relation_rng(X0))
| ~ empty(X0) )
| ~ spl30_284 ),
inference(avatar_component_clause,[],[f2439]) ).
fof(f3063,plain,
( spl30_337
| ~ spl30_186
| ~ spl30_283 ),
inference(avatar_split_clause,[],[f2444,f2435,f1553,f3061]) ).
fof(f1553,plain,
( spl30_186
<=> ! [X0] :
( ~ empty(X0)
| function(relation_dom(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_186])]) ).
fof(f2435,plain,
( spl30_283
<=> ! [X0] :
( ~ function(relation_dom(X0))
| relation_dom(relation_dom(X0)) = function_image(cartesian_product2(relation_dom(relation_dom(X0)),relation_rng(relation_dom(X0))),relation_dom(relation_dom(X0)),first_projection_as_func_of(relation_dom(relation_dom(X0)),relation_rng(relation_dom(X0))),relation_dom(X0))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_283])]) ).
fof(f2444,plain,
( ! [X0] :
( relation_dom(relation_dom(X0)) = function_image(cartesian_product2(relation_dom(relation_dom(X0)),relation_rng(relation_dom(X0))),relation_dom(relation_dom(X0)),first_projection_as_func_of(relation_dom(relation_dom(X0)),relation_rng(relation_dom(X0))),relation_dom(X0))
| ~ empty(X0) )
| ~ spl30_186
| ~ spl30_283 ),
inference(duplicate_literal_removal,[],[f2442]) ).
fof(f2442,plain,
( ! [X0] :
( relation_dom(relation_dom(X0)) = function_image(cartesian_product2(relation_dom(relation_dom(X0)),relation_rng(relation_dom(X0))),relation_dom(relation_dom(X0)),first_projection_as_func_of(relation_dom(relation_dom(X0)),relation_rng(relation_dom(X0))),relation_dom(X0))
| ~ empty(X0)
| ~ empty(X0) )
| ~ spl30_186
| ~ spl30_283 ),
inference(resolution,[],[f2436,f1554]) ).
fof(f1554,plain,
( ! [X0] :
( function(relation_dom(X0))
| ~ empty(X0) )
| ~ spl30_186 ),
inference(avatar_component_clause,[],[f1553]) ).
fof(f2436,plain,
( ! [X0] :
( ~ function(relation_dom(X0))
| relation_dom(relation_dom(X0)) = function_image(cartesian_product2(relation_dom(relation_dom(X0)),relation_rng(relation_dom(X0))),relation_dom(relation_dom(X0)),first_projection_as_func_of(relation_dom(relation_dom(X0)),relation_rng(relation_dom(X0))),relation_dom(X0))
| ~ empty(X0) )
| ~ spl30_283 ),
inference(avatar_component_clause,[],[f2435]) ).
fof(f3041,plain,
( spl30_336
| ~ spl30_207
| ~ spl30_278 ),
inference(avatar_split_clause,[],[f2395,f2392,f1798,f3039]) ).
fof(f2392,plain,
( spl30_278
<=> ! [X4,X0,X3,X2,X1] :
( ~ relation_of2(X0,X1,X2)
| ~ quasi_total(X0,X1,X2)
| ~ function(X0)
| element(X3,X2)
| ~ in(X3,function_image(X1,X2,X0,X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_278])]) ).
fof(f2395,plain,
( ! [X2,X3,X0,X1] :
( ~ quasi_total(X0,X1,X2)
| ~ function(X0)
| element(sK4(function_image(X1,X2,X0,X3)),X2)
| ~ relation_of2(X0,X1,X2)
| empty(function_image(X1,X2,X0,X3)) )
| ~ spl30_207
| ~ spl30_278 ),
inference(resolution,[],[f2393,f1799]) ).
fof(f2393,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ in(X3,function_image(X1,X2,X0,X4))
| ~ quasi_total(X0,X1,X2)
| ~ function(X0)
| element(X3,X2)
| ~ relation_of2(X0,X1,X2) )
| ~ spl30_278 ),
inference(avatar_component_clause,[],[f2392]) ).
fof(f3037,plain,
( spl30_335
| ~ spl30_151
| ~ spl30_209 ),
inference(avatar_split_clause,[],[f1859,f1806,f1308,f3035]) ).
fof(f3035,plain,
( spl30_335
<=> ! [X2,X0,X1] :
( function_image(X0,X1,sK8(X0,X1),X2) = relation_image(sK8(X0,X1),X2)
| ~ quasi_total(sK8(X0,X1),X0,X1)
| ~ function(sK8(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_335])]) ).
fof(f1806,plain,
( spl30_209
<=> ! [X0,X1] : relation_of2(sK8(X0,X1),X0,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_209])]) ).
fof(f1859,plain,
( ! [X2,X0,X1] :
( function_image(X0,X1,sK8(X0,X1),X2) = relation_image(sK8(X0,X1),X2)
| ~ quasi_total(sK8(X0,X1),X0,X1)
| ~ function(sK8(X0,X1)) )
| ~ spl30_151
| ~ spl30_209 ),
inference(resolution,[],[f1807,f1309]) ).
fof(f1807,plain,
( ! [X0,X1] : relation_of2(sK8(X0,X1),X0,X1)
| ~ spl30_209 ),
inference(avatar_component_clause,[],[f1806]) ).
fof(f3024,plain,
( spl30_334
| ~ spl30_85
| ~ spl30_289 ),
inference(avatar_split_clause,[],[f2476,f2470,f792,f3022]) ).
fof(f3022,plain,
( spl30_334
<=> ! [X0] :
( ~ empty(X0)
| epsilon_transitive(sK4(powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_334])]) ).
fof(f2476,plain,
( ! [X0] :
( ~ empty(X0)
| epsilon_transitive(sK4(powerset(X0))) )
| ~ spl30_85
| ~ spl30_289 ),
inference(resolution,[],[f2471,f793]) ).
fof(f3020,plain,
( spl30_333
| ~ spl30_108
| ~ spl30_279 ),
inference(avatar_split_clause,[],[f2411,f2406,f981,f3018]) ).
fof(f2411,plain,
( ! [X2,X3,X0,X1] :
( ~ quasi_total(X0,X1,X2)
| ~ function(X0)
| empty(powerset(X2))
| ~ relation_of2(X0,X1,X2)
| ~ in(powerset(X2),function_image(X1,X2,X0,X3)) )
| ~ spl30_108
| ~ spl30_279 ),
inference(resolution,[],[f2407,f982]) ).
fof(f2987,plain,
( spl30_332
| ~ spl30_207
| ~ spl30_261 ),
inference(avatar_split_clause,[],[f2351,f2244,f1798,f2985]) ).
fof(f2244,plain,
( spl30_261
<=> ! [X4,X0,X3,X2,X1] :
( ~ relation_of2(X0,X1,X2)
| ~ quasi_total(X0,X1,X2)
| ~ function(X0)
| ~ empty(X2)
| ~ in(X3,function_image(X1,X2,X0,X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_261])]) ).
fof(f2351,plain,
( ! [X2,X3,X0,X1] :
( ~ quasi_total(X0,X1,X2)
| ~ function(X0)
| ~ empty(X2)
| ~ relation_of2(X0,X1,X2)
| empty(function_image(X1,X2,X0,X3)) )
| ~ spl30_207
| ~ spl30_261 ),
inference(resolution,[],[f2245,f1799]) ).
fof(f2245,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ in(X3,function_image(X1,X2,X0,X4))
| ~ quasi_total(X0,X1,X2)
| ~ function(X0)
| ~ empty(X2)
| ~ relation_of2(X0,X1,X2) )
| ~ spl30_261 ),
inference(avatar_component_clause,[],[f2244]) ).
fof(f2981,plain,
( spl30_331
| ~ spl30_108
| ~ spl30_258 ),
inference(avatar_split_clause,[],[f2210,f2205,f981,f2979]) ).
fof(f2210,plain,
( ! [X2,X0,X1] :
( empty(powerset(cartesian_product2(X0,X1)))
| ~ relation_of2_as_subset(X2,X0,X1)
| ~ in(powerset(cartesian_product2(X0,X1)),X2) )
| ~ spl30_108
| ~ spl30_258 ),
inference(resolution,[],[f2206,f982]) ).
fof(f2967,plain,
( spl30_330
| ~ spl30_130
| ~ spl30_257 ),
inference(avatar_split_clause,[],[f2202,f2198,f1142,f2965]) ).
fof(f1142,plain,
( spl30_130
<=> ! [X0,X1] : relation_of2_as_subset(first_projection_as_func_of(X0,X1),cartesian_product2(X0,X1),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_130])]) ).
fof(f2198,plain,
( spl30_257
<=> ! [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,[spl30_257])]) ).
fof(f2202,plain,
( ! [X2,X0,X1] :
( ~ in(X0,first_projection_as_func_of(X1,X2))
| element(X0,cartesian_product2(cartesian_product2(X1,X2),X1)) )
| ~ spl30_130
| ~ spl30_257 ),
inference(resolution,[],[f2199,f1143]) ).
fof(f1143,plain,
( ! [X0,X1] : relation_of2_as_subset(first_projection_as_func_of(X0,X1),cartesian_product2(X0,X1),X0)
| ~ spl30_130 ),
inference(avatar_component_clause,[],[f1142]) ).
fof(f2199,plain,
( ! [X2,X3,X0,X1] :
( ~ relation_of2_as_subset(X3,X1,X2)
| ~ in(X0,X3)
| element(X0,cartesian_product2(X1,X2)) )
| ~ spl30_257 ),
inference(avatar_component_clause,[],[f2198]) ).
fof(f2963,plain,
( spl30_329
| ~ spl30_139
| ~ spl30_245 ),
inference(avatar_split_clause,[],[f2117,f2092,f1213,f2961]) ).
fof(f1213,plain,
( spl30_139
<=> ! [X0] :
( subset(X0,cartesian_product2(relation_dom(X0),relation_rng(X0)))
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_139])]) ).
fof(f2092,plain,
( spl30_245
<=> ! [X2,X0,X1] :
( element(X0,X1)
| ~ in(X0,X2)
| ~ subset(X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_245])]) ).
fof(f2117,plain,
( ! [X0,X1] :
( ~ in(X0,X1)
| element(X0,cartesian_product2(relation_dom(X1),relation_rng(X1)))
| ~ relation(X1) )
| ~ spl30_139
| ~ spl30_245 ),
inference(resolution,[],[f2093,f1214]) ).
fof(f1214,plain,
( ! [X0] :
( subset(X0,cartesian_product2(relation_dom(X0),relation_rng(X0)))
| ~ relation(X0) )
| ~ spl30_139 ),
inference(avatar_component_clause,[],[f1213]) ).
fof(f2093,plain,
( ! [X2,X0,X1] :
( ~ subset(X2,X1)
| ~ in(X0,X2)
| element(X0,X1) )
| ~ spl30_245 ),
inference(avatar_component_clause,[],[f2092]) ).
fof(f2951,plain,
( spl30_328
| ~ spl30_130
| ~ spl30_253 ),
inference(avatar_split_clause,[],[f2195,f2169,f1142,f2949]) ).
fof(f2949,plain,
( spl30_328
<=> ! [X2,X0,X1] :
( ~ empty(cartesian_product2(cartesian_product2(X0,X1),X0))
| ~ in(X2,first_projection_as_func_of(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_328])]) ).
fof(f2169,plain,
( spl30_253
<=> ! [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,[spl30_253])]) ).
fof(f2195,plain,
( ! [X2,X0,X1] :
( ~ empty(cartesian_product2(cartesian_product2(X0,X1),X0))
| ~ in(X2,first_projection_as_func_of(X0,X1)) )
| ~ spl30_130
| ~ spl30_253 ),
inference(resolution,[],[f2170,f1143]) ).
fof(f2170,plain,
( ! [X2,X3,X0,X1] :
( ~ relation_of2_as_subset(X0,X1,X2)
| ~ empty(cartesian_product2(X1,X2))
| ~ in(X3,X0) )
| ~ spl30_253 ),
inference(avatar_component_clause,[],[f2169]) ).
fof(f2947,plain,
( spl30_327
| ~ spl30_139
| ~ spl30_234 ),
inference(avatar_split_clause,[],[f2052,f1967,f1213,f2945]) ).
fof(f2945,plain,
( spl30_327
<=> ! [X0,X1] :
( ~ in(X0,X1)
| ~ empty(cartesian_product2(relation_dom(X1),relation_rng(X1)))
| ~ relation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_327])]) ).
fof(f1967,plain,
( spl30_234
<=> ! [X2,X0,X1] :
( ~ empty(X0)
| ~ in(X1,X2)
| ~ subset(X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_234])]) ).
fof(f2052,plain,
( ! [X0,X1] :
( ~ in(X0,X1)
| ~ empty(cartesian_product2(relation_dom(X1),relation_rng(X1)))
| ~ relation(X1) )
| ~ spl30_139
| ~ spl30_234 ),
inference(resolution,[],[f1968,f1214]) ).
fof(f1968,plain,
( ! [X2,X0,X1] :
( ~ subset(X2,X0)
| ~ in(X1,X2)
| ~ empty(X0) )
| ~ spl30_234 ),
inference(avatar_component_clause,[],[f1967]) ).
fof(f2943,plain,
( spl30_326
| ~ spl30_139
| ~ spl30_229 ),
inference(avatar_split_clause,[],[f1993,f1946,f1213,f2941]) ).
fof(f2941,plain,
( spl30_326
<=> ! [X0] :
( epsilon_transitive(X0)
| ~ ordinal(powerset(cartesian_product2(relation_dom(X0),relation_rng(X0))))
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_326])]) ).
fof(f1946,plain,
( spl30_229
<=> ! [X0,X1] :
( ~ subset(X0,X1)
| epsilon_transitive(X0)
| ~ ordinal(powerset(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_229])]) ).
fof(f1993,plain,
( ! [X0] :
( epsilon_transitive(X0)
| ~ ordinal(powerset(cartesian_product2(relation_dom(X0),relation_rng(X0))))
| ~ relation(X0) )
| ~ spl30_139
| ~ spl30_229 ),
inference(resolution,[],[f1947,f1214]) ).
fof(f1947,plain,
( ! [X0,X1] :
( ~ subset(X0,X1)
| epsilon_transitive(X0)
| ~ ordinal(powerset(X1)) )
| ~ spl30_229 ),
inference(avatar_component_clause,[],[f1946]) ).
fof(f2939,plain,
( spl30_325
| ~ spl30_139
| ~ spl30_228 ),
inference(avatar_split_clause,[],[f1986,f1942,f1213,f2937]) ).
fof(f2937,plain,
( spl30_325
<=> ! [X0] :
( epsilon_connected(X0)
| ~ ordinal(powerset(cartesian_product2(relation_dom(X0),relation_rng(X0))))
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_325])]) ).
fof(f1942,plain,
( spl30_228
<=> ! [X0,X1] :
( ~ subset(X0,X1)
| epsilon_connected(X0)
| ~ ordinal(powerset(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_228])]) ).
fof(f1986,plain,
( ! [X0] :
( epsilon_connected(X0)
| ~ ordinal(powerset(cartesian_product2(relation_dom(X0),relation_rng(X0))))
| ~ relation(X0) )
| ~ spl30_139
| ~ spl30_228 ),
inference(resolution,[],[f1943,f1214]) ).
fof(f1943,plain,
( ! [X0,X1] :
( ~ subset(X0,X1)
| epsilon_connected(X0)
| ~ ordinal(powerset(X1)) )
| ~ spl30_228 ),
inference(avatar_component_clause,[],[f1942]) ).
fof(f2935,plain,
( spl30_324
| ~ spl30_139
| ~ spl30_227 ),
inference(avatar_split_clause,[],[f1979,f1938,f1213,f2933]) ).
fof(f2933,plain,
( spl30_324
<=> ! [X0] :
( ordinal(X0)
| ~ ordinal(powerset(cartesian_product2(relation_dom(X0),relation_rng(X0))))
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_324])]) ).
fof(f1938,plain,
( spl30_227
<=> ! [X0,X1] :
( ~ subset(X0,X1)
| ordinal(X0)
| ~ ordinal(powerset(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_227])]) ).
fof(f1979,plain,
( ! [X0] :
( ordinal(X0)
| ~ ordinal(powerset(cartesian_product2(relation_dom(X0),relation_rng(X0))))
| ~ relation(X0) )
| ~ spl30_139
| ~ spl30_227 ),
inference(resolution,[],[f1939,f1214]) ).
fof(f1939,plain,
( ! [X0,X1] :
( ~ subset(X0,X1)
| ordinal(X0)
| ~ ordinal(powerset(X1)) )
| ~ spl30_227 ),
inference(avatar_component_clause,[],[f1938]) ).
fof(f2930,plain,
( ~ spl30_323
| ~ spl30_108
| ~ spl30_312 ),
inference(avatar_split_clause,[],[f2889,f2834,f981,f2927]) ).
fof(f2927,plain,
( spl30_323
<=> in(powerset(relation_dom(sK0)),relation_dom(sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_323])]) ).
fof(f2834,plain,
( spl30_312
<=> in(relation_dom(sK0),powerset(relation_dom(sK0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_312])]) ).
fof(f2889,plain,
( ~ in(powerset(relation_dom(sK0)),relation_dom(sK0))
| ~ spl30_108
| ~ spl30_312 ),
inference(resolution,[],[f2836,f982]) ).
fof(f2836,plain,
( in(relation_dom(sK0),powerset(relation_dom(sK0)))
| ~ spl30_312 ),
inference(avatar_component_clause,[],[f2834]) ).
fof(f2877,plain,
( spl30_322
| ~ spl30_210
| ~ spl30_257 ),
inference(avatar_split_clause,[],[f2203,f2198,f1810,f2875]) ).
fof(f1810,plain,
( spl30_210
<=> ! [X0,X1] : relation_of2_as_subset(sK7(X0,X1),X0,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_210])]) ).
fof(f2203,plain,
( ! [X2,X0,X1] :
( ~ in(X0,sK7(X1,X2))
| element(X0,cartesian_product2(X1,X2)) )
| ~ spl30_210
| ~ spl30_257 ),
inference(resolution,[],[f2199,f1811]) ).
fof(f1811,plain,
( ! [X0,X1] : relation_of2_as_subset(sK7(X0,X1),X0,X1)
| ~ spl30_210 ),
inference(avatar_component_clause,[],[f1810]) ).
fof(f2873,plain,
( spl30_321
| ~ spl30_112
| ~ spl30_257 ),
inference(avatar_split_clause,[],[f2201,f2198,f999,f2871]) ).
fof(f999,plain,
( spl30_112
<=> ! [X0,X1] : relation_of2_as_subset(sK8(X0,X1),X0,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_112])]) ).
fof(f2201,plain,
( ! [X2,X0,X1] :
( ~ in(X0,sK8(X1,X2))
| element(X0,cartesian_product2(X1,X2)) )
| ~ spl30_112
| ~ spl30_257 ),
inference(resolution,[],[f2199,f1000]) ).
fof(f1000,plain,
( ! [X0,X1] : relation_of2_as_subset(sK8(X0,X1),X0,X1)
| ~ spl30_112 ),
inference(avatar_component_clause,[],[f999]) ).
fof(f2869,plain,
( spl30_320
| ~ spl30_130
| ~ spl30_252 ),
inference(avatar_split_clause,[],[f2166,f2149,f1142,f2867]) ).
fof(f2149,plain,
( spl30_252
<=> ! [X2,X0,X1] :
( ~ relation_of2_as_subset(X0,X1,X2)
| finite(X0)
| ~ finite(cartesian_product2(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_252])]) ).
fof(f2166,plain,
( ! [X0,X1] :
( finite(first_projection_as_func_of(X0,X1))
| ~ finite(cartesian_product2(cartesian_product2(X0,X1),X0)) )
| ~ spl30_130
| ~ spl30_252 ),
inference(resolution,[],[f2150,f1143]) ).
fof(f2150,plain,
( ! [X2,X0,X1] :
( ~ relation_of2_as_subset(X0,X1,X2)
| finite(X0)
| ~ finite(cartesian_product2(X1,X2)) )
| ~ spl30_252 ),
inference(avatar_component_clause,[],[f2149]) ).
fof(f2865,plain,
( spl30_319
| ~ spl30_133
| ~ spl30_251 ),
inference(avatar_split_clause,[],[f2164,f2145,f1154,f2863]) ).
fof(f2145,plain,
( spl30_251
<=> ! [X0] :
( ~ relation(X0)
| ~ finite(cartesian_product2(relation_dom(X0),relation_rng(X0)))
| finite(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_251])]) ).
fof(f2164,plain,
( ! [X0] :
( ~ relation(X0)
| finite(X0)
| ~ finite(relation_rng(X0))
| ~ finite(relation_dom(X0)) )
| ~ spl30_133
| ~ spl30_251 ),
inference(resolution,[],[f2146,f1155]) ).
fof(f2146,plain,
( ! [X0] :
( ~ finite(cartesian_product2(relation_dom(X0),relation_rng(X0)))
| ~ relation(X0)
| finite(X0) )
| ~ spl30_251 ),
inference(avatar_component_clause,[],[f2145]) ).
fof(f2861,plain,
( spl30_318
| ~ spl30_108
| ~ spl30_249 ),
inference(avatar_split_clause,[],[f2163,f2137,f981,f2859]) ).
fof(f2163,plain,
( ! [X0,X1] :
( empty(powerset(X0))
| ~ subset(X1,X0)
| ~ in(powerset(X0),X1) )
| ~ spl30_108
| ~ spl30_249 ),
inference(resolution,[],[f2138,f982]) ).
fof(f2857,plain,
( spl30_317
| ~ spl30_108
| ~ spl30_248 ),
inference(avatar_split_clause,[],[f2160,f2133,f981,f2855]) ).
fof(f2855,plain,
( spl30_317
<=> ! [X0] :
( empty(powerset(X0))
| empty(X0)
| ~ in(powerset(X0),sK3(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_317])]) ).
fof(f2133,plain,
( spl30_248
<=> ! [X0] :
( empty(powerset(X0))
| in(sK3(X0),powerset(X0))
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_248])]) ).
fof(f2160,plain,
( ! [X0] :
( empty(powerset(X0))
| empty(X0)
| ~ in(powerset(X0),sK3(X0)) )
| ~ spl30_108
| ~ spl30_248 ),
inference(resolution,[],[f2134,f982]) ).
fof(f2134,plain,
( ! [X0] :
( in(sK3(X0),powerset(X0))
| empty(powerset(X0))
| empty(X0) )
| ~ spl30_248 ),
inference(avatar_component_clause,[],[f2133]) ).
fof(f2853,plain,
( spl30_316
| ~ spl30_108
| ~ spl30_247 ),
inference(avatar_split_clause,[],[f2157,f2129,f981,f2851]) ).
fof(f2851,plain,
( spl30_316
<=> ! [X0] :
( empty(powerset(X0))
| empty(X0)
| ~ in(powerset(X0),sK2(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_316])]) ).
fof(f2129,plain,
( spl30_247
<=> ! [X0] :
( empty(powerset(X0))
| in(sK2(X0),powerset(X0))
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_247])]) ).
fof(f2157,plain,
( ! [X0] :
( empty(powerset(X0))
| empty(X0)
| ~ in(powerset(X0),sK2(X0)) )
| ~ spl30_108
| ~ spl30_247 ),
inference(resolution,[],[f2130,f982]) ).
fof(f2130,plain,
( ! [X0] :
( in(sK2(X0),powerset(X0))
| empty(powerset(X0))
| empty(X0) )
| ~ spl30_247 ),
inference(avatar_component_clause,[],[f2129]) ).
fof(f2849,plain,
( spl30_315
| ~ spl30_108
| ~ spl30_246 ),
inference(avatar_split_clause,[],[f2154,f2125,f981,f2847]) ).
fof(f2847,plain,
( spl30_315
<=> ! [X0] :
( empty(powerset(X0))
| empty(X0)
| ~ in(powerset(X0),sK1(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_315])]) ).
fof(f2125,plain,
( spl30_246
<=> ! [X0] :
( empty(powerset(X0))
| in(sK1(X0),powerset(X0))
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_246])]) ).
fof(f2154,plain,
( ! [X0] :
( empty(powerset(X0))
| empty(X0)
| ~ in(powerset(X0),sK1(X0)) )
| ~ spl30_108
| ~ spl30_246 ),
inference(resolution,[],[f2126,f982]) ).
fof(f2126,plain,
( ! [X0] :
( in(sK1(X0),powerset(X0))
| empty(powerset(X0))
| empty(X0) )
| ~ spl30_246 ),
inference(avatar_component_clause,[],[f2125]) ).
fof(f2845,plain,
( spl30_314
| ~ spl30_207
| ~ spl30_244 ),
inference(avatar_split_clause,[],[f2115,f2088,f1798,f2843]) ).
fof(f2115,plain,
( ! [X0] :
( element(sK4(sK3(X0)),X0)
| empty(X0)
| empty(sK3(X0)) )
| ~ spl30_207
| ~ spl30_244 ),
inference(resolution,[],[f2089,f1799]) ).
fof(f2841,plain,
( spl30_312
| spl30_313
| ~ spl30_131
| ~ spl30_308 ),
inference(avatar_split_clause,[],[f2817,f2802,f1146,f2838,f2834]) ).
fof(f2838,plain,
( spl30_313
<=> empty(powerset(relation_dom(sK0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_313])]) ).
fof(f2802,plain,
( spl30_308
<=> element(relation_dom(sK0),powerset(relation_dom(sK0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_308])]) ).
fof(f2817,plain,
( empty(powerset(relation_dom(sK0)))
| in(relation_dom(sK0),powerset(relation_dom(sK0)))
| ~ spl30_131
| ~ spl30_308 ),
inference(resolution,[],[f2804,f1147]) ).
fof(f2804,plain,
( element(relation_dom(sK0),powerset(relation_dom(sK0)))
| ~ spl30_308 ),
inference(avatar_component_clause,[],[f2802]) ).
fof(f2832,plain,
( spl30_311
| ~ spl30_207
| ~ spl30_243 ),
inference(avatar_split_clause,[],[f2114,f2084,f1798,f2830]) ).
fof(f2114,plain,
( ! [X0] :
( element(sK4(sK2(X0)),X0)
| empty(X0)
| empty(sK2(X0)) )
| ~ spl30_207
| ~ spl30_243 ),
inference(resolution,[],[f2085,f1799]) ).
fof(f2828,plain,
( spl30_310
| ~ spl30_207
| ~ spl30_242 ),
inference(avatar_split_clause,[],[f2113,f2080,f1798,f2826]) ).
fof(f2113,plain,
( ! [X0] :
( element(sK4(sK1(X0)),X0)
| empty(X0)
| empty(sK1(X0)) )
| ~ spl30_207
| ~ spl30_242 ),
inference(resolution,[],[f2081,f1799]) ).
fof(f2824,plain,
( spl30_309
| ~ spl30_207
| ~ spl30_235 ),
inference(avatar_split_clause,[],[f2058,f1971,f1798,f2822]) ).
fof(f2058,plain,
( ! [X0] :
( element(sK4(sK4(powerset(X0))),X0)
| empty(sK4(powerset(X0))) )
| ~ spl30_207
| ~ spl30_235 ),
inference(resolution,[],[f1972,f1799]) ).
fof(f2812,plain,
( ~ spl30_233
| spl30_307 ),
inference(avatar_contradiction_clause,[],[f2811]) ).
fof(f2811,plain,
( $false
| ~ spl30_233
| spl30_307 ),
inference(resolution,[],[f2800,f1964]) ).
fof(f2800,plain,
( ~ relation_of2(first_projection_as_func_of(relation_dom(sK0),relation_rng(sK0)),cartesian_product2(relation_dom(sK0),relation_rng(sK0)),relation_dom(sK0))
| spl30_307 ),
inference(avatar_component_clause,[],[f2798]) ).
fof(f2798,plain,
( spl30_307
<=> relation_of2(first_projection_as_func_of(relation_dom(sK0),relation_rng(sK0)),cartesian_product2(relation_dom(sK0),relation_rng(sK0)),relation_dom(sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_307])]) ).
fof(f2810,plain,
( ~ spl30_129
| spl30_306 ),
inference(avatar_contradiction_clause,[],[f2809]) ).
fof(f2809,plain,
( $false
| ~ spl30_129
| spl30_306 ),
inference(resolution,[],[f2796,f1139]) ).
fof(f2796,plain,
( ~ quasi_total(first_projection_as_func_of(relation_dom(sK0),relation_rng(sK0)),cartesian_product2(relation_dom(sK0),relation_rng(sK0)),relation_dom(sK0))
| spl30_306 ),
inference(avatar_component_clause,[],[f2794]) ).
fof(f2794,plain,
( spl30_306
<=> quasi_total(first_projection_as_func_of(relation_dom(sK0),relation_rng(sK0)),cartesian_product2(relation_dom(sK0),relation_rng(sK0)),relation_dom(sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_306])]) ).
fof(f2807,plain,
( ~ spl30_89
| spl30_305 ),
inference(avatar_contradiction_clause,[],[f2806]) ).
fof(f2806,plain,
( $false
| ~ spl30_89
| spl30_305 ),
inference(resolution,[],[f2792,f809]) ).
fof(f2792,plain,
( ~ function(first_projection_as_func_of(relation_dom(sK0),relation_rng(sK0)))
| spl30_305 ),
inference(avatar_component_clause,[],[f2790]) ).
fof(f2805,plain,
( ~ spl30_305
| ~ spl30_306
| ~ spl30_307
| spl30_308
| ~ spl30_149
| ~ spl30_179 ),
inference(avatar_split_clause,[],[f1523,f1519,f1289,f2802,f2798,f2794,f2790]) ).
fof(f1523,plain,
( element(relation_dom(sK0),powerset(relation_dom(sK0)))
| ~ relation_of2(first_projection_as_func_of(relation_dom(sK0),relation_rng(sK0)),cartesian_product2(relation_dom(sK0),relation_rng(sK0)),relation_dom(sK0))
| ~ quasi_total(first_projection_as_func_of(relation_dom(sK0),relation_rng(sK0)),cartesian_product2(relation_dom(sK0),relation_rng(sK0)),relation_dom(sK0))
| ~ function(first_projection_as_func_of(relation_dom(sK0),relation_rng(sK0)))
| ~ spl30_149
| ~ spl30_179 ),
inference(superposition,[],[f1290,f1521]) ).
fof(f2787,plain,
( spl30_304
| ~ spl30_84
| ~ spl30_289 ),
inference(avatar_split_clause,[],[f2475,f2470,f788,f2785]) ).
fof(f2785,plain,
( spl30_304
<=> ! [X0] :
( ~ empty(X0)
| relation(sK4(powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_304])]) ).
fof(f2475,plain,
( ! [X0] :
( ~ empty(X0)
| relation(sK4(powerset(X0))) )
| ~ spl30_84
| ~ spl30_289 ),
inference(resolution,[],[f2471,f789]) ).
fof(f2646,plain,
( spl30_303
| ~ spl30_210
| ~ spl30_253 ),
inference(avatar_split_clause,[],[f2196,f2169,f1810,f2644]) ).
fof(f2196,plain,
( ! [X2,X0,X1] :
( ~ empty(cartesian_product2(X0,X1))
| ~ in(X2,sK7(X0,X1)) )
| ~ spl30_210
| ~ spl30_253 ),
inference(resolution,[],[f2170,f1811]) ).
fof(f2642,plain,
( spl30_302
| ~ spl30_112
| ~ spl30_253 ),
inference(avatar_split_clause,[],[f2194,f2169,f999,f2640]) ).
fof(f2194,plain,
( ! [X2,X0,X1] :
( ~ empty(cartesian_product2(X0,X1))
| ~ in(X2,sK8(X0,X1)) )
| ~ spl30_112
| ~ spl30_253 ),
inference(resolution,[],[f2170,f1000]) ).
fof(f2638,plain,
( spl30_301
| ~ spl30_98
| ~ spl30_231 ),
inference(avatar_split_clause,[],[f2026,f1954,f911,f2636]) ).
fof(f2026,plain,
( ! [X0,X1] :
( ~ empty(X0)
| relation_rng(relation_rng(X1)) = X0
| ~ empty(X1) )
| ~ spl30_98
| ~ spl30_231 ),
inference(resolution,[],[f1955,f912]) ).
fof(f2634,plain,
( spl30_300
| ~ spl30_101
| ~ spl30_231 ),
inference(avatar_split_clause,[],[f2025,f1954,f924,f2632]) ).
fof(f2025,plain,
( ! [X0,X1] :
( ~ empty(X0)
| relation_rng(relation_dom(X1)) = X0
| ~ empty(X1) )
| ~ spl30_101
| ~ spl30_231 ),
inference(resolution,[],[f1955,f925]) ).
fof(f2630,plain,
( spl30_299
| ~ spl30_98
| ~ spl30_230 ),
inference(avatar_split_clause,[],[f2001,f1950,f911,f2628]) ).
fof(f2001,plain,
( ! [X0,X1] :
( ~ empty(X0)
| relation_dom(relation_rng(X1)) = X0
| ~ empty(X1) )
| ~ spl30_98
| ~ spl30_230 ),
inference(resolution,[],[f1951,f912]) ).
fof(f2626,plain,
( spl30_298
| ~ spl30_83
| ~ spl30_289 ),
inference(avatar_split_clause,[],[f2474,f2470,f784,f2624]) ).
fof(f2624,plain,
( spl30_298
<=> ! [X0] :
( ~ empty(X0)
| function(sK4(powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_298])]) ).
fof(f2474,plain,
( ! [X0] :
( ~ empty(X0)
| function(sK4(powerset(X0))) )
| ~ spl30_83
| ~ spl30_289 ),
inference(resolution,[],[f2471,f785]) ).
fof(f2622,plain,
( spl30_297
| ~ spl30_101
| ~ spl30_230 ),
inference(avatar_split_clause,[],[f2000,f1950,f924,f2620]) ).
fof(f2000,plain,
( ! [X0,X1] :
( ~ empty(X0)
| relation_dom(relation_dom(X1)) = X0
| ~ empty(X1) )
| ~ spl30_101
| ~ spl30_230 ),
inference(resolution,[],[f1951,f925]) ).
fof(f2616,plain,
( spl30_296
| ~ spl30_210
| ~ spl30_252 ),
inference(avatar_split_clause,[],[f2167,f2149,f1810,f2614]) ).
fof(f2167,plain,
( ! [X0,X1] :
( finite(sK7(X0,X1))
| ~ finite(cartesian_product2(X0,X1)) )
| ~ spl30_210
| ~ spl30_252 ),
inference(resolution,[],[f2150,f1811]) ).
fof(f2612,plain,
( spl30_295
| ~ spl30_112
| ~ spl30_252 ),
inference(avatar_split_clause,[],[f2165,f2149,f999,f2610]) ).
fof(f2165,plain,
( ! [X0,X1] :
( finite(sK8(X0,X1))
| ~ finite(cartesian_product2(X0,X1)) )
| ~ spl30_112
| ~ spl30_252 ),
inference(resolution,[],[f2150,f1000]) ).
fof(f2504,plain,
( spl30_294
| ~ spl30_98
| ~ spl30_202 ),
inference(avatar_split_clause,[],[f1836,f1778,f911,f2502]) ).
fof(f1836,plain,
( ! [X0] :
( sK10 = relation_dom(relation_rng(X0))
| ~ empty(X0) )
| ~ spl30_98
| ~ spl30_202 ),
inference(resolution,[],[f1779,f912]) ).
fof(f2500,plain,
( spl30_293
| ~ spl30_82
| ~ spl30_289 ),
inference(avatar_split_clause,[],[f2473,f2470,f780,f2498]) ).
fof(f2498,plain,
( spl30_293
<=> ! [X0] :
( ~ empty(X0)
| finite(sK4(powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_293])]) ).
fof(f2473,plain,
( ! [X0] :
( ~ empty(X0)
| finite(sK4(powerset(X0))) )
| ~ spl30_82
| ~ spl30_289 ),
inference(resolution,[],[f2471,f781]) ).
fof(f2496,plain,
( spl30_292
| ~ spl30_101
| ~ spl30_202 ),
inference(avatar_split_clause,[],[f1835,f1778,f924,f2494]) ).
fof(f1835,plain,
( ! [X0] :
( sK10 = relation_dom(relation_dom(X0))
| ~ empty(X0) )
| ~ spl30_101
| ~ spl30_202 ),
inference(resolution,[],[f1779,f925]) ).
fof(f2492,plain,
( spl30_291
| ~ spl30_98
| ~ spl30_201 ),
inference(avatar_split_clause,[],[f1819,f1774,f911,f2490]) ).
fof(f1819,plain,
( ! [X0] :
( sK10 = relation_rng(relation_rng(X0))
| ~ empty(X0) )
| ~ spl30_98
| ~ spl30_201 ),
inference(resolution,[],[f1775,f912]) ).
fof(f2488,plain,
( spl30_290
| ~ spl30_101
| ~ spl30_201 ),
inference(avatar_split_clause,[],[f1818,f1774,f924,f2486]) ).
fof(f1818,plain,
( ! [X0] :
( sK10 = relation_rng(relation_dom(X0))
| ~ empty(X0) )
| ~ spl30_101
| ~ spl30_201 ),
inference(resolution,[],[f1775,f925]) ).
fof(f2472,plain,
( spl30_289
| ~ spl30_207
| ~ spl30_216 ),
inference(avatar_split_clause,[],[f1895,f1882,f1798,f2470]) ).
fof(f1882,plain,
( spl30_216
<=> ! [X0,X1] :
( ~ empty(X0)
| ~ in(X1,sK4(powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_216])]) ).
fof(f1895,plain,
( ! [X0] :
( ~ empty(X0)
| empty(sK4(powerset(X0))) )
| ~ spl30_207
| ~ spl30_216 ),
inference(resolution,[],[f1883,f1799]) ).
fof(f1883,plain,
( ! [X0,X1] :
( ~ in(X1,sK4(powerset(X0)))
| ~ empty(X0) )
| ~ spl30_216 ),
inference(avatar_component_clause,[],[f1882]) ).
fof(f2468,plain,
( spl30_288
| ~ spl30_108
| ~ spl30_207 ),
inference(avatar_split_clause,[],[f1856,f1798,f981,f2466]) ).
fof(f2466,plain,
( spl30_288
<=> ! [X0] :
( empty(X0)
| ~ in(X0,sK4(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_288])]) ).
fof(f1856,plain,
( ! [X0] :
( empty(X0)
| ~ in(X0,sK4(X0)) )
| ~ spl30_108
| ~ spl30_207 ),
inference(resolution,[],[f1799,f982]) ).
fof(f2464,plain,
( spl30_287
| ~ spl30_77
| ~ spl30_229 ),
inference(avatar_split_clause,[],[f1992,f1946,f758,f2462]) ).
fof(f2462,plain,
( spl30_287
<=> ! [X0] :
( epsilon_transitive(X0)
| ~ ordinal(powerset(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_287])]) ).
fof(f1992,plain,
( ! [X0] :
( epsilon_transitive(X0)
| ~ ordinal(powerset(X0)) )
| ~ spl30_77
| ~ spl30_229 ),
inference(resolution,[],[f1947,f759]) ).
fof(f2460,plain,
( spl30_286
| ~ spl30_77
| ~ spl30_228 ),
inference(avatar_split_clause,[],[f1985,f1942,f758,f2458]) ).
fof(f2458,plain,
( spl30_286
<=> ! [X0] :
( epsilon_connected(X0)
| ~ ordinal(powerset(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_286])]) ).
fof(f1985,plain,
( ! [X0] :
( epsilon_connected(X0)
| ~ ordinal(powerset(X0)) )
| ~ spl30_77
| ~ spl30_228 ),
inference(resolution,[],[f1943,f759]) ).
fof(f2455,plain,
( spl30_285
| ~ spl30_90
| ~ spl30_152 ),
inference(avatar_split_clause,[],[f1316,f1313,f812,f2453]) ).
fof(f1316,plain,
( ! [X0,X1] :
( ~ function(first_projection_as_func_of(X0,X1))
| relation_dom(first_projection_as_func_of(X0,X1)) = function_image(cartesian_product2(relation_dom(first_projection_as_func_of(X0,X1)),relation_rng(first_projection_as_func_of(X0,X1))),relation_dom(first_projection_as_func_of(X0,X1)),first_projection_as_func_of(relation_dom(first_projection_as_func_of(X0,X1)),relation_rng(first_projection_as_func_of(X0,X1))),first_projection_as_func_of(X0,X1)) )
| ~ spl30_90
| ~ spl30_152 ),
inference(resolution,[],[f1314,f813]) ).
fof(f2441,plain,
( spl30_284
| ~ spl30_99
| ~ spl30_152 ),
inference(avatar_split_clause,[],[f1319,f1313,f915,f2439]) ).
fof(f915,plain,
( spl30_99
<=> ! [X0] :
( relation(relation_rng(X0))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_99])]) ).
fof(f1319,plain,
( ! [X0] :
( ~ function(relation_rng(X0))
| relation_dom(relation_rng(X0)) = function_image(cartesian_product2(relation_dom(relation_rng(X0)),relation_rng(relation_rng(X0))),relation_dom(relation_rng(X0)),first_projection_as_func_of(relation_dom(relation_rng(X0)),relation_rng(relation_rng(X0))),relation_rng(X0))
| ~ empty(X0) )
| ~ spl30_99
| ~ spl30_152 ),
inference(resolution,[],[f1314,f916]) ).
fof(f916,plain,
( ! [X0] :
( relation(relation_rng(X0))
| ~ empty(X0) )
| ~ spl30_99 ),
inference(avatar_component_clause,[],[f915]) ).
fof(f2437,plain,
( spl30_283
| ~ spl30_102
| ~ spl30_152 ),
inference(avatar_split_clause,[],[f1318,f1313,f928,f2435]) ).
fof(f928,plain,
( spl30_102
<=> ! [X0] :
( relation(relation_dom(X0))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_102])]) ).
fof(f1318,plain,
( ! [X0] :
( ~ function(relation_dom(X0))
| relation_dom(relation_dom(X0)) = function_image(cartesian_product2(relation_dom(relation_dom(X0)),relation_rng(relation_dom(X0))),relation_dom(relation_dom(X0)),first_projection_as_func_of(relation_dom(relation_dom(X0)),relation_rng(relation_dom(X0))),relation_dom(X0))
| ~ empty(X0) )
| ~ spl30_102
| ~ spl30_152 ),
inference(resolution,[],[f1314,f929]) ).
fof(f929,plain,
( ! [X0] :
( relation(relation_dom(X0))
| ~ empty(X0) )
| ~ spl30_102 ),
inference(avatar_component_clause,[],[f928]) ).
fof(f2433,plain,
( spl30_282
| ~ spl30_111
| ~ spl30_151 ),
inference(avatar_split_clause,[],[f1311,f1308,f995,f2431]) ).
fof(f2431,plain,
( spl30_282
<=> ! [X2,X0,X1] :
( function_image(X0,X1,sK7(X0,X1),X2) = relation_image(sK7(X0,X1),X2)
| ~ quasi_total(sK7(X0,X1),X0,X1)
| ~ function(sK7(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_282])]) ).
fof(f995,plain,
( spl30_111
<=> ! [X0,X1] : relation_of2(sK7(X0,X1),X0,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_111])]) ).
fof(f1311,plain,
( ! [X2,X0,X1] :
( function_image(X0,X1,sK7(X0,X1),X2) = relation_image(sK7(X0,X1),X2)
| ~ quasi_total(sK7(X0,X1),X0,X1)
| ~ function(sK7(X0,X1)) )
| ~ spl30_111
| ~ spl30_151 ),
inference(resolution,[],[f1309,f996]) ).
fof(f996,plain,
( ! [X0,X1] : relation_of2(sK7(X0,X1),X0,X1)
| ~ spl30_111 ),
inference(avatar_component_clause,[],[f995]) ).
fof(f2428,plain,
( spl30_281
| ~ spl30_77
| ~ spl30_227 ),
inference(avatar_split_clause,[],[f1978,f1938,f758,f2426]) ).
fof(f2426,plain,
( spl30_281
<=> ! [X0] :
( ordinal(X0)
| ~ ordinal(powerset(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_281])]) ).
fof(f1978,plain,
( ! [X0] :
( ordinal(X0)
| ~ ordinal(powerset(X0)) )
| ~ spl30_77
| ~ spl30_227 ),
inference(resolution,[],[f1939,f759]) ).
fof(f2424,plain,
( spl30_280
| ~ spl30_134
| ~ spl30_149 ),
inference(avatar_split_clause,[],[f1296,f1289,f1158,f2422]) ).
fof(f1296,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ relation_of2(X0,X1,cartesian_product2(X2,X3))
| ~ quasi_total(X0,X1,cartesian_product2(X2,X3))
| ~ function(X0)
| relation(function_image(X1,cartesian_product2(X2,X3),X0,X4)) )
| ~ spl30_134
| ~ spl30_149 ),
inference(resolution,[],[f1290,f1159]) ).
fof(f2408,plain,
( spl30_279
| ~ spl30_131
| ~ spl30_149 ),
inference(avatar_split_clause,[],[f1297,f1289,f1146,f2406]) ).
fof(f1297,plain,
( ! [X2,X3,X0,X1] :
( ~ relation_of2(X0,X1,X2)
| ~ quasi_total(X0,X1,X2)
| ~ function(X0)
| empty(powerset(X2))
| in(function_image(X1,X2,X0,X3),powerset(X2)) )
| ~ spl30_131
| ~ spl30_149 ),
inference(resolution,[],[f1290,f1147]) ).
fof(f2394,plain,
( spl30_278
| ~ spl30_148
| ~ spl30_149 ),
inference(avatar_split_clause,[],[f1292,f1289,f1265,f2392]) ).
fof(f1292,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ relation_of2(X0,X1,X2)
| ~ quasi_total(X0,X1,X2)
| ~ function(X0)
| element(X3,X2)
| ~ in(X3,function_image(X1,X2,X0,X4)) )
| ~ spl30_148
| ~ spl30_149 ),
inference(resolution,[],[f1290,f1266]) ).
fof(f2346,plain,
( spl30_277
| ~ spl30_221
| ~ spl30_232
| ~ spl30_276 ),
inference(avatar_split_clause,[],[f2341,f2336,f1958,f1913,f2343]) ).
fof(f2343,plain,
( spl30_277
<=> sK10 = function_image(cartesian_product2(sK10,sK10),sK10,first_projection_as_func_of(sK10,sK10),sK10) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_277])]) ).
fof(f2336,plain,
( spl30_276
<=> relation_dom(sK10) = function_image(cartesian_product2(relation_dom(sK10),relation_rng(sK10)),relation_dom(sK10),first_projection_as_func_of(relation_dom(sK10),relation_rng(sK10)),sK10) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_276])]) ).
fof(f2341,plain,
( sK10 = function_image(cartesian_product2(sK10,sK10),sK10,first_projection_as_func_of(sK10,sK10),sK10)
| ~ spl30_221
| ~ spl30_232
| ~ spl30_276 ),
inference(forward_demodulation,[],[f2340,f1960]) ).
fof(f2340,plain,
( relation_dom(sK10) = function_image(cartesian_product2(relation_dom(sK10),sK10),relation_dom(sK10),first_projection_as_func_of(relation_dom(sK10),sK10),sK10)
| ~ spl30_221
| ~ spl30_276 ),
inference(forward_demodulation,[],[f2338,f1915]) ).
fof(f2338,plain,
( relation_dom(sK10) = function_image(cartesian_product2(relation_dom(sK10),relation_rng(sK10)),relation_dom(sK10),first_projection_as_func_of(relation_dom(sK10),relation_rng(sK10)),sK10)
| ~ spl30_276 ),
inference(avatar_component_clause,[],[f2336]) ).
fof(f2339,plain,
( ~ spl30_127
| spl30_276
| ~ spl30_7
| ~ spl30_13
| ~ spl30_97
| ~ spl30_152 ),
inference(avatar_split_clause,[],[f1335,f1313,f907,f447,f417,f2336,f1109]) ).
fof(f1109,plain,
( spl30_127
<=> function(sK10) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_127])]) ).
fof(f417,plain,
( spl30_7
<=> relation(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_7])]) ).
fof(f447,plain,
( spl30_13
<=> empty(sK10) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_13])]) ).
fof(f907,plain,
( spl30_97
<=> ! [X0] :
( empty_set = X0
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_97])]) ).
fof(f1335,plain,
( relation_dom(sK10) = function_image(cartesian_product2(relation_dom(sK10),relation_rng(sK10)),relation_dom(sK10),first_projection_as_func_of(relation_dom(sK10),relation_rng(sK10)),sK10)
| ~ function(sK10)
| ~ spl30_7
| ~ spl30_13
| ~ spl30_97
| ~ spl30_152 ),
inference(forward_demodulation,[],[f1334,f951]) ).
fof(f951,plain,
( empty_set = sK10
| ~ spl30_13
| ~ spl30_97 ),
inference(resolution,[],[f908,f449]) ).
fof(f449,plain,
( empty(sK10)
| ~ spl30_13 ),
inference(avatar_component_clause,[],[f447]) ).
fof(f908,plain,
( ! [X0] :
( ~ empty(X0)
| empty_set = X0 )
| ~ spl30_97 ),
inference(avatar_component_clause,[],[f907]) ).
fof(f1334,plain,
( ~ function(sK10)
| relation_dom(empty_set) = function_image(cartesian_product2(relation_dom(empty_set),relation_rng(empty_set)),relation_dom(empty_set),first_projection_as_func_of(relation_dom(empty_set),relation_rng(empty_set)),empty_set)
| ~ spl30_7
| ~ spl30_13
| ~ spl30_97
| ~ spl30_152 ),
inference(forward_demodulation,[],[f1317,f951]) ).
fof(f1317,plain,
( ~ function(empty_set)
| relation_dom(empty_set) = function_image(cartesian_product2(relation_dom(empty_set),relation_rng(empty_set)),relation_dom(empty_set),first_projection_as_func_of(relation_dom(empty_set),relation_rng(empty_set)),empty_set)
| ~ spl30_7
| ~ spl30_152 ),
inference(resolution,[],[f1314,f419]) ).
fof(f419,plain,
( relation(empty_set)
| ~ spl30_7 ),
inference(avatar_component_clause,[],[f417]) ).
fof(f2331,plain,
( spl30_275
| ~ spl30_50
| ~ spl30_49
| ~ spl30_152 ),
inference(avatar_split_clause,[],[f1331,f1313,f627,f632,f2328]) ).
fof(f632,plain,
( spl30_50
<=> function(sK25) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_50])]) ).
fof(f627,plain,
( spl30_49
<=> relation(sK25) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_49])]) ).
fof(f1331,plain,
( ~ function(sK25)
| relation_dom(sK25) = function_image(cartesian_product2(relation_dom(sK25),relation_rng(sK25)),relation_dom(sK25),first_projection_as_func_of(relation_dom(sK25),relation_rng(sK25)),sK25)
| ~ spl30_49
| ~ spl30_152 ),
inference(resolution,[],[f1314,f629]) ).
fof(f629,plain,
( relation(sK25)
| ~ spl30_49 ),
inference(avatar_component_clause,[],[f627]) ).
fof(f2323,plain,
( spl30_274
| ~ spl30_47
| ~ spl30_46
| ~ spl30_152 ),
inference(avatar_split_clause,[],[f1330,f1313,f612,f617,f2320]) ).
fof(f617,plain,
( spl30_47
<=> function(sK24) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_47])]) ).
fof(f612,plain,
( spl30_46
<=> relation(sK24) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_46])]) ).
fof(f1330,plain,
( ~ function(sK24)
| relation_dom(sK24) = function_image(cartesian_product2(relation_dom(sK24),relation_rng(sK24)),relation_dom(sK24),first_projection_as_func_of(relation_dom(sK24),relation_rng(sK24)),sK24)
| ~ spl30_46
| ~ spl30_152 ),
inference(resolution,[],[f1314,f614]) ).
fof(f614,plain,
( relation(sK24)
| ~ spl30_46 ),
inference(avatar_component_clause,[],[f612]) ).
fof(f2315,plain,
( spl30_273
| ~ spl30_44
| ~ spl30_43
| ~ spl30_152 ),
inference(avatar_split_clause,[],[f1329,f1313,f597,f602,f2312]) ).
fof(f602,plain,
( spl30_44
<=> function(sK23) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_44])]) ).
fof(f597,plain,
( spl30_43
<=> relation(sK23) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_43])]) ).
fof(f1329,plain,
( ~ function(sK23)
| relation_dom(sK23) = function_image(cartesian_product2(relation_dom(sK23),relation_rng(sK23)),relation_dom(sK23),first_projection_as_func_of(relation_dom(sK23),relation_rng(sK23)),sK23)
| ~ spl30_43
| ~ spl30_152 ),
inference(resolution,[],[f1314,f599]) ).
fof(f599,plain,
( relation(sK23)
| ~ spl30_43 ),
inference(avatar_component_clause,[],[f597]) ).
fof(f2307,plain,
( spl30_272
| ~ spl30_42
| ~ spl30_41
| ~ spl30_152 ),
inference(avatar_split_clause,[],[f1328,f1313,f587,f592,f2304]) ).
fof(f592,plain,
( spl30_42
<=> function(sK22) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_42])]) ).
fof(f587,plain,
( spl30_41
<=> relation(sK22) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_41])]) ).
fof(f1328,plain,
( ~ function(sK22)
| relation_dom(sK22) = function_image(cartesian_product2(relation_dom(sK22),relation_rng(sK22)),relation_dom(sK22),first_projection_as_func_of(relation_dom(sK22),relation_rng(sK22)),sK22)
| ~ spl30_41
| ~ spl30_152 ),
inference(resolution,[],[f1314,f589]) ).
fof(f589,plain,
( relation(sK22)
| ~ spl30_41 ),
inference(avatar_component_clause,[],[f587]) ).
fof(f2298,plain,
( spl30_271
| ~ spl30_40
| ~ spl30_39
| ~ spl30_152 ),
inference(avatar_split_clause,[],[f1327,f1313,f577,f582,f2295]) ).
fof(f582,plain,
( spl30_40
<=> function(sK21) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_40])]) ).
fof(f577,plain,
( spl30_39
<=> relation(sK21) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_39])]) ).
fof(f1327,plain,
( ~ function(sK21)
| relation_dom(sK21) = function_image(cartesian_product2(relation_dom(sK21),relation_rng(sK21)),relation_dom(sK21),first_projection_as_func_of(relation_dom(sK21),relation_rng(sK21)),sK21)
| ~ spl30_39
| ~ spl30_152 ),
inference(resolution,[],[f1314,f579]) ).
fof(f579,plain,
( relation(sK21)
| ~ spl30_39 ),
inference(avatar_component_clause,[],[f577]) ).
fof(f2290,plain,
( spl30_270
| ~ spl30_38
| ~ spl30_37
| ~ spl30_152 ),
inference(avatar_split_clause,[],[f1326,f1313,f567,f572,f2287]) ).
fof(f572,plain,
( spl30_38
<=> function(sK20) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_38])]) ).
fof(f567,plain,
( spl30_37
<=> relation(sK20) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_37])]) ).
fof(f1326,plain,
( ~ function(sK20)
| relation_dom(sK20) = function_image(cartesian_product2(relation_dom(sK20),relation_rng(sK20)),relation_dom(sK20),first_projection_as_func_of(relation_dom(sK20),relation_rng(sK20)),sK20)
| ~ spl30_37
| ~ spl30_152 ),
inference(resolution,[],[f1314,f569]) ).
fof(f569,plain,
( relation(sK20)
| ~ spl30_37 ),
inference(avatar_component_clause,[],[f567]) ).
fof(f2285,plain,
( spl30_268
| ~ spl30_269
| ~ spl30_36
| ~ spl30_152 ),
inference(avatar_split_clause,[],[f1325,f1313,f562,f2282,f2278]) ).
fof(f2278,plain,
( spl30_268
<=> relation_dom(sK19) = function_image(cartesian_product2(relation_dom(sK19),relation_rng(sK19)),relation_dom(sK19),first_projection_as_func_of(relation_dom(sK19),relation_rng(sK19)),sK19) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_268])]) ).
fof(f2282,plain,
( spl30_269
<=> function(sK19) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_269])]) ).
fof(f562,plain,
( spl30_36
<=> relation(sK19) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_36])]) ).
fof(f1325,plain,
( ~ function(sK19)
| relation_dom(sK19) = function_image(cartesian_product2(relation_dom(sK19),relation_rng(sK19)),relation_dom(sK19),first_projection_as_func_of(relation_dom(sK19),relation_rng(sK19)),sK19)
| ~ spl30_36
| ~ spl30_152 ),
inference(resolution,[],[f1314,f564]) ).
fof(f564,plain,
( relation(sK19)
| ~ spl30_36 ),
inference(avatar_component_clause,[],[f562]) ).
fof(f2273,plain,
( spl30_267
| ~ spl30_35
| ~ spl30_34
| ~ spl30_152 ),
inference(avatar_split_clause,[],[f1324,f1313,f552,f557,f2270]) ).
fof(f557,plain,
( spl30_35
<=> function(sK18) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_35])]) ).
fof(f552,plain,
( spl30_34
<=> relation(sK18) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_34])]) ).
fof(f1324,plain,
( ~ function(sK18)
| relation_dom(sK18) = function_image(cartesian_product2(relation_dom(sK18),relation_rng(sK18)),relation_dom(sK18),first_projection_as_func_of(relation_dom(sK18),relation_rng(sK18)),sK18)
| ~ spl30_34
| ~ spl30_152 ),
inference(resolution,[],[f1314,f554]) ).
fof(f554,plain,
( relation(sK18)
| ~ spl30_34 ),
inference(avatar_component_clause,[],[f552]) ).
fof(f2267,plain,
( spl30_265
| ~ spl30_266
| ~ spl30_25
| ~ spl30_152 ),
inference(avatar_split_clause,[],[f1322,f1313,f507,f2264,f2260]) ).
fof(f2260,plain,
( spl30_265
<=> relation_dom(sK14) = function_image(cartesian_product2(relation_dom(sK14),relation_rng(sK14)),relation_dom(sK14),first_projection_as_func_of(relation_dom(sK14),relation_rng(sK14)),sK14) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_265])]) ).
fof(f2264,plain,
( spl30_266
<=> function(sK14) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_266])]) ).
fof(f507,plain,
( spl30_25
<=> relation(sK14) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_25])]) ).
fof(f1322,plain,
( ~ function(sK14)
| relation_dom(sK14) = function_image(cartesian_product2(relation_dom(sK14),relation_rng(sK14)),relation_dom(sK14),first_projection_as_func_of(relation_dom(sK14),relation_rng(sK14)),sK14)
| ~ spl30_25
| ~ spl30_152 ),
inference(resolution,[],[f1314,f509]) ).
fof(f509,plain,
( relation(sK14)
| ~ spl30_25 ),
inference(avatar_component_clause,[],[f507]) ).
fof(f2258,plain,
( spl30_264
| ~ spl30_117
| ~ spl30_149 ),
inference(avatar_split_clause,[],[f1300,f1289,f1030,f2256]) ).
fof(f2256,plain,
( spl30_264
<=> ! [X0,X3,X2,X1] :
( ~ relation_of2(X0,X1,X2)
| ~ quasi_total(X0,X1,X2)
| ~ function(X0)
| epsilon_transitive(function_image(X1,X2,X0,X3))
| ~ ordinal(powerset(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_264])]) ).
fof(f1300,plain,
( ! [X2,X3,X0,X1] :
( ~ relation_of2(X0,X1,X2)
| ~ quasi_total(X0,X1,X2)
| ~ function(X0)
| epsilon_transitive(function_image(X1,X2,X0,X3))
| ~ ordinal(powerset(X2)) )
| ~ spl30_117
| ~ spl30_149 ),
inference(resolution,[],[f1290,f1031]) ).
fof(f2254,plain,
( spl30_263
| ~ spl30_118
| ~ spl30_149 ),
inference(avatar_split_clause,[],[f1299,f1289,f1034,f2252]) ).
fof(f2252,plain,
( spl30_263
<=> ! [X0,X3,X2,X1] :
( ~ relation_of2(X0,X1,X2)
| ~ quasi_total(X0,X1,X2)
| ~ function(X0)
| epsilon_connected(function_image(X1,X2,X0,X3))
| ~ ordinal(powerset(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_263])]) ).
fof(f1299,plain,
( ! [X2,X3,X0,X1] :
( ~ relation_of2(X0,X1,X2)
| ~ quasi_total(X0,X1,X2)
| ~ function(X0)
| epsilon_connected(function_image(X1,X2,X0,X3))
| ~ ordinal(powerset(X2)) )
| ~ spl30_118
| ~ spl30_149 ),
inference(resolution,[],[f1290,f1035]) ).
fof(f2250,plain,
( spl30_262
| ~ spl30_119
| ~ spl30_149 ),
inference(avatar_split_clause,[],[f1298,f1289,f1038,f2248]) ).
fof(f2248,plain,
( spl30_262
<=> ! [X0,X3,X2,X1] :
( ~ relation_of2(X0,X1,X2)
| ~ quasi_total(X0,X1,X2)
| ~ function(X0)
| ordinal(function_image(X1,X2,X0,X3))
| ~ ordinal(powerset(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_262])]) ).
fof(f1298,plain,
( ! [X2,X3,X0,X1] :
( ~ relation_of2(X0,X1,X2)
| ~ quasi_total(X0,X1,X2)
| ~ function(X0)
| ordinal(function_image(X1,X2,X0,X3))
| ~ ordinal(powerset(X2)) )
| ~ spl30_119
| ~ spl30_149 ),
inference(resolution,[],[f1290,f1039]) ).
fof(f2246,plain,
( spl30_261
| ~ spl30_143
| ~ spl30_149 ),
inference(avatar_split_clause,[],[f1293,f1289,f1229,f2244]) ).
fof(f1293,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ relation_of2(X0,X1,X2)
| ~ quasi_total(X0,X1,X2)
| ~ function(X0)
| ~ empty(X2)
| ~ in(X3,function_image(X1,X2,X0,X4)) )
| ~ spl30_143
| ~ spl30_149 ),
inference(resolution,[],[f1290,f1230]) ).
fof(f2241,plain,
( spl30_260
| ~ spl30_128
| ~ spl30_149 ),
inference(avatar_split_clause,[],[f1294,f1289,f1134,f2239]) ).
fof(f2239,plain,
( spl30_260
<=> ! [X0,X3,X2,X1] :
( ~ relation_of2(X0,X1,X2)
| ~ quasi_total(X0,X1,X2)
| ~ function(X0)
| finite(function_image(X1,X2,X0,X3))
| ~ finite(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_260])]) ).
fof(f1294,plain,
( ! [X2,X3,X0,X1] :
( ~ relation_of2(X0,X1,X2)
| ~ quasi_total(X0,X1,X2)
| ~ function(X0)
| finite(function_image(X1,X2,X0,X3))
| ~ finite(X2) )
| ~ spl30_128
| ~ spl30_149 ),
inference(resolution,[],[f1290,f1135]) ).
fof(f2229,plain,
( spl30_259
| ~ spl30_123
| ~ spl30_149 ),
inference(avatar_split_clause,[],[f1295,f1289,f1054,f2227]) ).
fof(f2227,plain,
( spl30_259
<=> ! [X0,X3,X2,X1] :
( ~ relation_of2(X0,X1,X2)
| ~ quasi_total(X0,X1,X2)
| ~ function(X0)
| subset(function_image(X1,X2,X0,X3),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_259])]) ).
fof(f1295,plain,
( ! [X2,X3,X0,X1] :
( ~ relation_of2(X0,X1,X2)
| ~ quasi_total(X0,X1,X2)
| ~ function(X0)
| subset(function_image(X1,X2,X0,X3),X2) )
| ~ spl30_123
| ~ spl30_149 ),
inference(resolution,[],[f1290,f1055]) ).
fof(f2207,plain,
( spl30_258
| ~ spl30_131
| ~ spl30_147 ),
inference(avatar_split_clause,[],[f1272,f1261,f1146,f2205]) ).
fof(f1261,plain,
( spl30_147
<=> ! [X2,X0,X1] :
( element(X2,powerset(cartesian_product2(X0,X1)))
| ~ relation_of2_as_subset(X2,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_147])]) ).
fof(f1272,plain,
( ! [X2,X0,X1] :
( ~ relation_of2_as_subset(X0,X1,X2)
| empty(powerset(cartesian_product2(X1,X2)))
| in(X0,powerset(cartesian_product2(X1,X2))) )
| ~ spl30_131
| ~ spl30_147 ),
inference(resolution,[],[f1262,f1147]) ).
fof(f1262,plain,
( ! [X2,X0,X1] :
( element(X2,powerset(cartesian_product2(X0,X1)))
| ~ relation_of2_as_subset(X2,X0,X1) )
| ~ spl30_147 ),
inference(avatar_component_clause,[],[f1261]) ).
fof(f2200,plain,
( spl30_257
| ~ spl30_147
| ~ spl30_148 ),
inference(avatar_split_clause,[],[f1282,f1265,f1261,f2198]) ).
fof(f1282,plain,
( ! [X2,X3,X0,X1] :
( element(X0,cartesian_product2(X1,X2))
| ~ in(X0,X3)
| ~ relation_of2_as_subset(X3,X1,X2) )
| ~ spl30_147
| ~ spl30_148 ),
inference(resolution,[],[f1266,f1262]) ).
fof(f2193,plain,
( spl30_256
| ~ spl30_117
| ~ spl30_147 ),
inference(avatar_split_clause,[],[f1275,f1261,f1030,f2191]) ).
fof(f2191,plain,
( spl30_256
<=> ! [X2,X0,X1] :
( ~ relation_of2_as_subset(X0,X1,X2)
| epsilon_transitive(X0)
| ~ ordinal(powerset(cartesian_product2(X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_256])]) ).
fof(f1275,plain,
( ! [X2,X0,X1] :
( ~ relation_of2_as_subset(X0,X1,X2)
| epsilon_transitive(X0)
| ~ ordinal(powerset(cartesian_product2(X1,X2))) )
| ~ spl30_117
| ~ spl30_147 ),
inference(resolution,[],[f1262,f1031]) ).
fof(f2189,plain,
( spl30_255
| ~ spl30_118
| ~ spl30_147 ),
inference(avatar_split_clause,[],[f1274,f1261,f1034,f2187]) ).
fof(f2187,plain,
( spl30_255
<=> ! [X2,X0,X1] :
( ~ relation_of2_as_subset(X0,X1,X2)
| epsilon_connected(X0)
| ~ ordinal(powerset(cartesian_product2(X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_255])]) ).
fof(f1274,plain,
( ! [X2,X0,X1] :
( ~ relation_of2_as_subset(X0,X1,X2)
| epsilon_connected(X0)
| ~ ordinal(powerset(cartesian_product2(X1,X2))) )
| ~ spl30_118
| ~ spl30_147 ),
inference(resolution,[],[f1262,f1035]) ).
fof(f2175,plain,
( spl30_254
| ~ spl30_119
| ~ spl30_147 ),
inference(avatar_split_clause,[],[f1273,f1261,f1038,f2173]) ).
fof(f2173,plain,
( spl30_254
<=> ! [X2,X0,X1] :
( ~ relation_of2_as_subset(X0,X1,X2)
| ordinal(X0)
| ~ ordinal(powerset(cartesian_product2(X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_254])]) ).
fof(f1273,plain,
( ! [X2,X0,X1] :
( ~ relation_of2_as_subset(X0,X1,X2)
| ordinal(X0)
| ~ ordinal(powerset(cartesian_product2(X1,X2))) )
| ~ spl30_119
| ~ spl30_147 ),
inference(resolution,[],[f1262,f1039]) ).
fof(f2171,plain,
( spl30_253
| ~ spl30_143
| ~ spl30_147 ),
inference(avatar_split_clause,[],[f1269,f1261,f1229,f2169]) ).
fof(f1269,plain,
( ! [X2,X3,X0,X1] :
( ~ relation_of2_as_subset(X0,X1,X2)
| ~ empty(cartesian_product2(X1,X2))
| ~ in(X3,X0) )
| ~ spl30_143
| ~ spl30_147 ),
inference(resolution,[],[f1262,f1230]) ).
fof(f2151,plain,
( spl30_252
| ~ spl30_128
| ~ spl30_147 ),
inference(avatar_split_clause,[],[f1270,f1261,f1134,f2149]) ).
fof(f1270,plain,
( ! [X2,X0,X1] :
( ~ relation_of2_as_subset(X0,X1,X2)
| finite(X0)
| ~ finite(cartesian_product2(X1,X2)) )
| ~ spl30_128
| ~ spl30_147 ),
inference(resolution,[],[f1262,f1135]) ).
fof(f2147,plain,
( spl30_251
| ~ spl30_122
| ~ spl30_139 ),
inference(avatar_split_clause,[],[f1232,f1213,f1050,f2145]) ).
fof(f1050,plain,
( spl30_122
<=> ! [X0,X1] :
( finite(X0)
| ~ finite(X1)
| ~ subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_122])]) ).
fof(f1232,plain,
( ! [X0] :
( ~ relation(X0)
| ~ finite(cartesian_product2(relation_dom(X0),relation_rng(X0)))
| finite(X0) )
| ~ spl30_122
| ~ spl30_139 ),
inference(resolution,[],[f1214,f1051]) ).
fof(f1051,plain,
( ! [X0,X1] :
( ~ subset(X0,X1)
| ~ finite(X1)
| finite(X0) )
| ~ spl30_122 ),
inference(avatar_component_clause,[],[f1050]) ).
fof(f2143,plain,
( spl30_250
| ~ spl30_77
| ~ spl30_215 ),
inference(avatar_split_clause,[],[f1889,f1878,f758,f2141]) ).
fof(f1878,plain,
( spl30_215
<=> ! [X2,X0,X1] :
( relation(X0)
| ~ subset(X0,cartesian_product2(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_215])]) ).
fof(f1889,plain,
( ! [X0,X1] : relation(cartesian_product2(X0,X1))
| ~ spl30_77
| ~ spl30_215 ),
inference(resolution,[],[f1879,f759]) ).
fof(f1879,plain,
( ! [X2,X0,X1] :
( ~ subset(X0,cartesian_product2(X1,X2))
| relation(X0) )
| ~ spl30_215 ),
inference(avatar_component_clause,[],[f1878]) ).
fof(f2139,plain,
( spl30_249
| ~ spl30_124
| ~ spl30_131 ),
inference(avatar_split_clause,[],[f1190,f1146,f1058,f2137]) ).
fof(f1190,plain,
( ! [X0,X1] :
( empty(powerset(X0))
| in(X1,powerset(X0))
| ~ subset(X1,X0) )
| ~ spl30_124
| ~ spl30_131 ),
inference(resolution,[],[f1147,f1059]) ).
fof(f2135,plain,
( spl30_248
| ~ spl30_116
| ~ spl30_131 ),
inference(avatar_split_clause,[],[f1187,f1146,f1026,f2133]) ).
fof(f1026,plain,
( spl30_116
<=> ! [X0] :
( element(sK3(X0),powerset(X0))
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_116])]) ).
fof(f1187,plain,
( ! [X0] :
( empty(powerset(X0))
| in(sK3(X0),powerset(X0))
| empty(X0) )
| ~ spl30_116
| ~ spl30_131 ),
inference(resolution,[],[f1147,f1027]) ).
fof(f1027,plain,
( ! [X0] :
( element(sK3(X0),powerset(X0))
| empty(X0) )
| ~ spl30_116 ),
inference(avatar_component_clause,[],[f1026]) ).
fof(f2131,plain,
( spl30_247
| ~ spl30_114
| ~ spl30_131 ),
inference(avatar_split_clause,[],[f1186,f1146,f1016,f2129]) ).
fof(f1016,plain,
( spl30_114
<=> ! [X0] :
( element(sK2(X0),powerset(X0))
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_114])]) ).
fof(f1186,plain,
( ! [X0] :
( empty(powerset(X0))
| in(sK2(X0),powerset(X0))
| empty(X0) )
| ~ spl30_114
| ~ spl30_131 ),
inference(resolution,[],[f1147,f1017]) ).
fof(f1017,plain,
( ! [X0] :
( element(sK2(X0),powerset(X0))
| empty(X0) )
| ~ spl30_114 ),
inference(avatar_component_clause,[],[f1016]) ).
fof(f2127,plain,
( spl30_246
| ~ spl30_113
| ~ spl30_131 ),
inference(avatar_split_clause,[],[f1185,f1146,f1012,f2125]) ).
fof(f1012,plain,
( spl30_113
<=> ! [X0] :
( element(sK1(X0),powerset(X0))
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_113])]) ).
fof(f1185,plain,
( ! [X0] :
( empty(powerset(X0))
| in(sK1(X0),powerset(X0))
| empty(X0) )
| ~ spl30_113
| ~ spl30_131 ),
inference(resolution,[],[f1147,f1013]) ).
fof(f1013,plain,
( ! [X0] :
( element(sK1(X0),powerset(X0))
| empty(X0) )
| ~ spl30_113 ),
inference(avatar_component_clause,[],[f1012]) ).
fof(f2094,plain,
( spl30_245
| ~ spl30_124
| ~ spl30_148 ),
inference(avatar_split_clause,[],[f1281,f1265,f1058,f2092]) ).
fof(f1281,plain,
( ! [X2,X0,X1] :
( element(X0,X1)
| ~ in(X0,X2)
| ~ subset(X2,X1) )
| ~ spl30_124
| ~ spl30_148 ),
inference(resolution,[],[f1266,f1059]) ).
fof(f2090,plain,
( spl30_244
| ~ spl30_116
| ~ spl30_148 ),
inference(avatar_split_clause,[],[f1278,f1265,f1026,f2088]) ).
fof(f1278,plain,
( ! [X0,X1] :
( element(X0,X1)
| ~ in(X0,sK3(X1))
| empty(X1) )
| ~ spl30_116
| ~ spl30_148 ),
inference(resolution,[],[f1266,f1027]) ).
fof(f2086,plain,
( spl30_243
| ~ spl30_114
| ~ spl30_148 ),
inference(avatar_split_clause,[],[f1277,f1265,f1016,f2084]) ).
fof(f1277,plain,
( ! [X0,X1] :
( element(X0,X1)
| ~ in(X0,sK2(X1))
| empty(X1) )
| ~ spl30_114
| ~ spl30_148 ),
inference(resolution,[],[f1266,f1017]) ).
fof(f2082,plain,
( spl30_242
| ~ spl30_113
| ~ spl30_148 ),
inference(avatar_split_clause,[],[f1276,f1265,f1012,f2080]) ).
fof(f1276,plain,
( ! [X0,X1] :
( element(X0,X1)
| ~ in(X0,sK1(X1))
| empty(X1) )
| ~ spl30_113
| ~ spl30_148 ),
inference(resolution,[],[f1266,f1013]) ).
fof(f2078,plain,
( spl30_241
| ~ spl30_123
| ~ spl30_147 ),
inference(avatar_split_clause,[],[f1271,f1261,f1054,f2076]) ).
fof(f2076,plain,
( spl30_241
<=> ! [X2,X0,X1] :
( ~ relation_of2_as_subset(X0,X1,X2)
| subset(X0,cartesian_product2(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_241])]) ).
fof(f1271,plain,
( ! [X2,X0,X1] :
( ~ relation_of2_as_subset(X0,X1,X2)
| subset(X0,cartesian_product2(X1,X2)) )
| ~ spl30_123
| ~ spl30_147 ),
inference(resolution,[],[f1262,f1055]) ).
fof(f2074,plain,
( spl30_240
| ~ spl30_116
| ~ spl30_134 ),
inference(avatar_split_clause,[],[f1198,f1158,f1026,f2072]) ).
fof(f1198,plain,
( ! [X0,X1] :
( relation(sK3(cartesian_product2(X0,X1)))
| empty(cartesian_product2(X0,X1)) )
| ~ spl30_116
| ~ spl30_134 ),
inference(resolution,[],[f1159,f1027]) ).
fof(f2070,plain,
( spl30_239
| ~ spl30_114
| ~ spl30_134 ),
inference(avatar_split_clause,[],[f1197,f1158,f1016,f2068]) ).
fof(f1197,plain,
( ! [X0,X1] :
( relation(sK2(cartesian_product2(X0,X1)))
| empty(cartesian_product2(X0,X1)) )
| ~ spl30_114
| ~ spl30_134 ),
inference(resolution,[],[f1159,f1017]) ).
fof(f2066,plain,
( spl30_238
| ~ spl30_113
| ~ spl30_134 ),
inference(avatar_split_clause,[],[f1196,f1158,f1012,f2064]) ).
fof(f1196,plain,
( ! [X0,X1] :
( relation(sK1(cartesian_product2(X0,X1)))
| empty(cartesian_product2(X0,X1)) )
| ~ spl30_113
| ~ spl30_134 ),
inference(resolution,[],[f1159,f1013]) ).
fof(f2062,plain,
( spl30_237
| ~ spl30_210
| ~ spl30_211 ),
inference(avatar_split_clause,[],[f1864,f1814,f1810,f2060]) ).
fof(f1814,plain,
( spl30_211
<=> ! [X2,X0,X1] :
( ~ relation_of2_as_subset(X0,X1,X2)
| relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_211])]) ).
fof(f1864,plain,
( ! [X0,X1] : relation(sK7(X0,X1))
| ~ spl30_210
| ~ spl30_211 ),
inference(resolution,[],[f1815,f1811]) ).
fof(f1815,plain,
( ! [X2,X0,X1] :
( ~ relation_of2_as_subset(X0,X1,X2)
| relation(X0) )
| ~ spl30_211 ),
inference(avatar_component_clause,[],[f1814]) ).
fof(f1977,plain,
( spl30_236
| ~ spl30_112
| ~ spl30_211 ),
inference(avatar_split_clause,[],[f1862,f1814,f999,f1975]) ).
fof(f1862,plain,
( ! [X0,X1] : relation(sK8(X0,X1))
| ~ spl30_112
| ~ spl30_211 ),
inference(resolution,[],[f1815,f1000]) ).
fof(f1973,plain,
( spl30_235
| ~ spl30_88
| ~ spl30_148 ),
inference(avatar_split_clause,[],[f1283,f1265,f804,f1971]) ).
fof(f804,plain,
( spl30_88
<=> ! [X0] : element(sK4(X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_88])]) ).
fof(f1283,plain,
( ! [X0,X1] :
( element(X0,X1)
| ~ in(X0,sK4(powerset(X1))) )
| ~ spl30_88
| ~ spl30_148 ),
inference(resolution,[],[f1266,f805]) ).
fof(f805,plain,
( ! [X0] : element(sK4(X0),X0)
| ~ spl30_88 ),
inference(avatar_component_clause,[],[f804]) ).
fof(f1969,plain,
( spl30_234
| ~ spl30_124
| ~ spl30_143 ),
inference(avatar_split_clause,[],[f1241,f1229,f1058,f1967]) ).
fof(f1241,plain,
( ! [X2,X0,X1] :
( ~ empty(X0)
| ~ in(X1,X2)
| ~ subset(X2,X0) )
| ~ spl30_124
| ~ spl30_143 ),
inference(resolution,[],[f1230,f1059]) ).
fof(f1965,plain,
( spl30_233
| ~ spl30_130
| ~ spl30_135 ),
inference(avatar_split_clause,[],[f1204,f1162,f1142,f1963]) ).
fof(f1162,plain,
( spl30_135
<=> ! [X2,X0,X1] :
( relation_of2(X2,X0,X1)
| ~ relation_of2_as_subset(X2,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_135])]) ).
fof(f1204,plain,
( ! [X0,X1] : relation_of2(first_projection_as_func_of(X0,X1),cartesian_product2(X0,X1),X0)
| ~ spl30_130
| ~ spl30_135 ),
inference(resolution,[],[f1163,f1143]) ).
fof(f1163,plain,
( ! [X2,X0,X1] :
( ~ relation_of2_as_subset(X2,X0,X1)
| relation_of2(X2,X0,X1) )
| ~ spl30_135 ),
inference(avatar_component_clause,[],[f1162]) ).
fof(f1961,plain,
( spl30_232
| ~ spl30_6
| ~ spl30_168
| ~ spl30_202 ),
inference(avatar_split_clause,[],[f1844,f1778,f1432,f412,f1958]) ).
fof(f1844,plain,
( sK10 = relation_dom(sK10)
| ~ spl30_6
| ~ spl30_168
| ~ spl30_202 ),
inference(forward_demodulation,[],[f1834,f1434]) ).
fof(f1834,plain,
( sK10 = relation_dom(empty_set)
| ~ spl30_6
| ~ spl30_202 ),
inference(resolution,[],[f1779,f414]) ).
fof(f1956,plain,
( spl30_231
| ~ spl30_98
| ~ spl30_125 ),
inference(avatar_split_clause,[],[f1119,f1062,f911,f1954]) ).
fof(f1119,plain,
( ! [X0,X1] :
( relation_rng(X1) = X0
| ~ empty(X0)
| ~ empty(X1) )
| ~ spl30_98
| ~ spl30_125 ),
inference(resolution,[],[f1063,f912]) ).
fof(f1952,plain,
( spl30_230
| ~ spl30_101
| ~ spl30_125 ),
inference(avatar_split_clause,[],[f1118,f1062,f924,f1950]) ).
fof(f1118,plain,
( ! [X0,X1] :
( relation_dom(X1) = X0
| ~ empty(X0)
| ~ empty(X1) )
| ~ spl30_101
| ~ spl30_125 ),
inference(resolution,[],[f1063,f925]) ).
fof(f1948,plain,
( spl30_229
| ~ spl30_117
| ~ spl30_124 ),
inference(avatar_split_clause,[],[f1116,f1058,f1030,f1946]) ).
fof(f1116,plain,
( ! [X0,X1] :
( ~ subset(X0,X1)
| epsilon_transitive(X0)
| ~ ordinal(powerset(X1)) )
| ~ spl30_117
| ~ spl30_124 ),
inference(resolution,[],[f1059,f1031]) ).
fof(f1944,plain,
( spl30_228
| ~ spl30_118
| ~ spl30_124 ),
inference(avatar_split_clause,[],[f1115,f1058,f1034,f1942]) ).
fof(f1115,plain,
( ! [X0,X1] :
( ~ subset(X0,X1)
| epsilon_connected(X0)
| ~ ordinal(powerset(X1)) )
| ~ spl30_118
| ~ spl30_124 ),
inference(resolution,[],[f1059,f1035]) ).
fof(f1940,plain,
( spl30_227
| ~ spl30_119
| ~ spl30_124 ),
inference(avatar_split_clause,[],[f1114,f1058,f1038,f1938]) ).
fof(f1114,plain,
( ! [X0,X1] :
( ~ subset(X0,X1)
| ordinal(X0)
| ~ ordinal(powerset(X1)) )
| ~ spl30_119
| ~ spl30_124 ),
inference(resolution,[],[f1059,f1039]) ).
fof(f1936,plain,
( spl30_226
| ~ spl30_116
| ~ spl30_119 ),
inference(avatar_split_clause,[],[f1092,f1038,f1026,f1934]) ).
fof(f1934,plain,
( spl30_226
<=> ! [X0] :
( ordinal(sK3(X0))
| ~ ordinal(powerset(X0))
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_226])]) ).
fof(f1092,plain,
( ! [X0] :
( ordinal(sK3(X0))
| ~ ordinal(powerset(X0))
| empty(X0) )
| ~ spl30_116
| ~ spl30_119 ),
inference(resolution,[],[f1039,f1027]) ).
fof(f1932,plain,
( spl30_225
| ~ spl30_114
| ~ spl30_119 ),
inference(avatar_split_clause,[],[f1091,f1038,f1016,f1930]) ).
fof(f1930,plain,
( spl30_225
<=> ! [X0] :
( ordinal(sK2(X0))
| ~ ordinal(powerset(X0))
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_225])]) ).
fof(f1091,plain,
( ! [X0] :
( ordinal(sK2(X0))
| ~ ordinal(powerset(X0))
| empty(X0) )
| ~ spl30_114
| ~ spl30_119 ),
inference(resolution,[],[f1039,f1017]) ).
fof(f1928,plain,
( spl30_224
| ~ spl30_113
| ~ spl30_119 ),
inference(avatar_split_clause,[],[f1090,f1038,f1012,f1926]) ).
fof(f1926,plain,
( spl30_224
<=> ! [X0] :
( ordinal(sK1(X0))
| ~ ordinal(powerset(X0))
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_224])]) ).
fof(f1090,plain,
( ! [X0] :
( ordinal(sK1(X0))
| ~ ordinal(powerset(X0))
| empty(X0) )
| ~ spl30_113
| ~ spl30_119 ),
inference(resolution,[],[f1039,f1013]) ).
fof(f1924,plain,
( spl30_223
| ~ spl30_116
| ~ spl30_118 ),
inference(avatar_split_clause,[],[f1084,f1034,f1026,f1922]) ).
fof(f1922,plain,
( spl30_223
<=> ! [X0] :
( epsilon_connected(sK3(X0))
| ~ ordinal(powerset(X0))
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_223])]) ).
fof(f1084,plain,
( ! [X0] :
( epsilon_connected(sK3(X0))
| ~ ordinal(powerset(X0))
| empty(X0) )
| ~ spl30_116
| ~ spl30_118 ),
inference(resolution,[],[f1035,f1027]) ).
fof(f1920,plain,
( spl30_222
| ~ spl30_114
| ~ spl30_118 ),
inference(avatar_split_clause,[],[f1083,f1034,f1016,f1918]) ).
fof(f1918,plain,
( spl30_222
<=> ! [X0] :
( epsilon_connected(sK2(X0))
| ~ ordinal(powerset(X0))
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_222])]) ).
fof(f1083,plain,
( ! [X0] :
( epsilon_connected(sK2(X0))
| ~ ordinal(powerset(X0))
| empty(X0) )
| ~ spl30_114
| ~ spl30_118 ),
inference(resolution,[],[f1035,f1017]) ).
fof(f1916,plain,
( spl30_221
| ~ spl30_6
| ~ spl30_168
| ~ spl30_201 ),
inference(avatar_split_clause,[],[f1827,f1774,f1432,f412,f1913]) ).
fof(f1827,plain,
( sK10 = relation_rng(sK10)
| ~ spl30_6
| ~ spl30_168
| ~ spl30_201 ),
inference(forward_demodulation,[],[f1817,f1434]) ).
fof(f1817,plain,
( sK10 = relation_rng(empty_set)
| ~ spl30_6
| ~ spl30_201 ),
inference(resolution,[],[f1775,f414]) ).
fof(f1911,plain,
( spl30_220
| ~ spl30_113
| ~ spl30_118 ),
inference(avatar_split_clause,[],[f1082,f1034,f1012,f1909]) ).
fof(f1909,plain,
( spl30_220
<=> ! [X0] :
( epsilon_connected(sK1(X0))
| ~ ordinal(powerset(X0))
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_220])]) ).
fof(f1082,plain,
( ! [X0] :
( epsilon_connected(sK1(X0))
| ~ ordinal(powerset(X0))
| empty(X0) )
| ~ spl30_113
| ~ spl30_118 ),
inference(resolution,[],[f1035,f1013]) ).
fof(f1907,plain,
( spl30_219
| ~ spl30_116
| ~ spl30_117 ),
inference(avatar_split_clause,[],[f1076,f1030,f1026,f1905]) ).
fof(f1905,plain,
( spl30_219
<=> ! [X0] :
( epsilon_transitive(sK3(X0))
| ~ ordinal(powerset(X0))
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_219])]) ).
fof(f1076,plain,
( ! [X0] :
( epsilon_transitive(sK3(X0))
| ~ ordinal(powerset(X0))
| empty(X0) )
| ~ spl30_116
| ~ spl30_117 ),
inference(resolution,[],[f1031,f1027]) ).
fof(f1903,plain,
( spl30_218
| ~ spl30_114
| ~ spl30_117 ),
inference(avatar_split_clause,[],[f1075,f1030,f1016,f1901]) ).
fof(f1901,plain,
( spl30_218
<=> ! [X0] :
( epsilon_transitive(sK2(X0))
| ~ ordinal(powerset(X0))
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_218])]) ).
fof(f1075,plain,
( ! [X0] :
( epsilon_transitive(sK2(X0))
| ~ ordinal(powerset(X0))
| empty(X0) )
| ~ spl30_114
| ~ spl30_117 ),
inference(resolution,[],[f1031,f1017]) ).
fof(f1899,plain,
( spl30_217
| ~ spl30_113
| ~ spl30_117 ),
inference(avatar_split_clause,[],[f1074,f1030,f1012,f1897]) ).
fof(f1897,plain,
( spl30_217
<=> ! [X0] :
( epsilon_transitive(sK1(X0))
| ~ ordinal(powerset(X0))
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_217])]) ).
fof(f1074,plain,
( ! [X0] :
( epsilon_transitive(sK1(X0))
| ~ ordinal(powerset(X0))
| empty(X0) )
| ~ spl30_113
| ~ spl30_117 ),
inference(resolution,[],[f1031,f1013]) ).
fof(f1884,plain,
( spl30_216
| ~ spl30_88
| ~ spl30_143 ),
inference(avatar_split_clause,[],[f1242,f1229,f804,f1882]) ).
fof(f1242,plain,
( ! [X0,X1] :
( ~ empty(X0)
| ~ in(X1,sK4(powerset(X0))) )
| ~ spl30_88
| ~ spl30_143 ),
inference(resolution,[],[f1230,f805]) ).
fof(f1880,plain,
( spl30_215
| ~ spl30_124
| ~ spl30_134 ),
inference(avatar_split_clause,[],[f1201,f1158,f1058,f1878]) ).
fof(f1201,plain,
( ! [X2,X0,X1] :
( relation(X0)
| ~ subset(X0,cartesian_product2(X1,X2)) )
| ~ spl30_124
| ~ spl30_134 ),
inference(resolution,[],[f1159,f1059]) ).
fof(f1876,plain,
( spl30_214
| ~ spl30_103
| ~ spl30_176 ),
inference(avatar_split_clause,[],[f1508,f1496,f932,f1874]) ).
fof(f1874,plain,
( spl30_214
<=> ! [X0] : element(sK10,powerset(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_214])]) ).
fof(f932,plain,
( spl30_103
<=> ! [X0] : element(sK5(X0),powerset(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_103])]) ).
fof(f1496,plain,
( spl30_176
<=> ! [X0] : sK5(X0) = sK10 ),
introduced(avatar_definition,[new_symbols(naming,[spl30_176])]) ).
fof(f1508,plain,
( ! [X0] : element(sK10,powerset(X0))
| ~ spl30_103
| ~ spl30_176 ),
inference(superposition,[],[f933,f1497]) ).
fof(f1497,plain,
( ! [X0] : sK5(X0) = sK10
| ~ spl30_176 ),
inference(avatar_component_clause,[],[f1496]) ).
fof(f933,plain,
( ! [X0] : element(sK5(X0),powerset(X0))
| ~ spl30_103 ),
inference(avatar_component_clause,[],[f932]) ).
fof(f1872,plain,
( spl30_213
| ~ spl30_13
| ~ spl30_69
| ~ spl30_97
| ~ spl30_103
| ~ spl30_131 ),
inference(avatar_split_clause,[],[f1193,f1146,f932,f907,f726,f447,f1870]) ).
fof(f1870,plain,
( spl30_213
<=> ! [X0] :
( in(sK10,powerset(X0))
| empty(powerset(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_213])]) ).
fof(f726,plain,
( spl30_69
<=> ! [X0] : empty(sK5(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_69])]) ).
fof(f1193,plain,
( ! [X0] :
( in(sK10,powerset(X0))
| empty(powerset(X0)) )
| ~ spl30_13
| ~ spl30_69
| ~ spl30_97
| ~ spl30_103
| ~ spl30_131 ),
inference(forward_demodulation,[],[f1192,f951]) ).
fof(f1192,plain,
( ! [X0] :
( in(empty_set,powerset(X0))
| empty(powerset(X0)) )
| ~ spl30_69
| ~ spl30_97
| ~ spl30_103
| ~ spl30_131 ),
inference(forward_demodulation,[],[f1188,f949]) ).
fof(f949,plain,
( ! [X0] : empty_set = sK5(X0)
| ~ spl30_69
| ~ spl30_97 ),
inference(resolution,[],[f908,f727]) ).
fof(f727,plain,
( ! [X0] : empty(sK5(X0))
| ~ spl30_69 ),
inference(avatar_component_clause,[],[f726]) ).
fof(f1188,plain,
( ! [X0] :
( empty(powerset(X0))
| in(sK5(X0),powerset(X0)) )
| ~ spl30_103
| ~ spl30_131 ),
inference(resolution,[],[f1147,f933]) ).
fof(f1868,plain,
( spl30_212
| ~ spl30_113
| ~ spl30_128 ),
inference(avatar_split_clause,[],[f1175,f1134,f1012,f1866]) ).
fof(f1866,plain,
( spl30_212
<=> ! [X0] :
( finite(sK1(X0))
| ~ finite(X0)
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_212])]) ).
fof(f1175,plain,
( ! [X0] :
( finite(sK1(X0))
| ~ finite(X0)
| empty(X0) )
| ~ spl30_113
| ~ spl30_128 ),
inference(resolution,[],[f1135,f1013]) ).
fof(f1816,plain,
( spl30_211
| ~ spl30_134
| ~ spl30_147 ),
inference(avatar_split_clause,[],[f1268,f1261,f1158,f1814]) ).
fof(f1268,plain,
( ! [X2,X0,X1] :
( ~ relation_of2_as_subset(X0,X1,X2)
| relation(X0) )
| ~ spl30_134
| ~ spl30_147 ),
inference(resolution,[],[f1262,f1159]) ).
fof(f1812,plain,
( spl30_210
| ~ spl30_111
| ~ spl30_137 ),
inference(avatar_split_clause,[],[f1205,f1172,f995,f1810]) ).
fof(f1172,plain,
( spl30_137
<=> ! [X2,X0,X1] :
( relation_of2_as_subset(X2,X0,X1)
| ~ relation_of2(X2,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_137])]) ).
fof(f1205,plain,
( ! [X0,X1] : relation_of2_as_subset(sK7(X0,X1),X0,X1)
| ~ spl30_111
| ~ spl30_137 ),
inference(resolution,[],[f1173,f996]) ).
fof(f1173,plain,
( ! [X2,X0,X1] :
( ~ relation_of2(X2,X0,X1)
| relation_of2_as_subset(X2,X0,X1) )
| ~ spl30_137 ),
inference(avatar_component_clause,[],[f1172]) ).
fof(f1808,plain,
( spl30_209
| ~ spl30_112
| ~ spl30_135 ),
inference(avatar_split_clause,[],[f1203,f1162,f999,f1806]) ).
fof(f1203,plain,
( ! [X0,X1] : relation_of2(sK8(X0,X1),X0,X1)
| ~ spl30_112
| ~ spl30_135 ),
inference(resolution,[],[f1163,f1000]) ).
fof(f1804,plain,
( spl30_208
| ~ spl30_88
| ~ spl30_134 ),
inference(avatar_split_clause,[],[f1202,f1158,f804,f1802]) ).
fof(f1202,plain,
( ! [X0,X1] : relation(sK4(powerset(cartesian_product2(X0,X1))))
| ~ spl30_88
| ~ spl30_134 ),
inference(resolution,[],[f1159,f805]) ).
fof(f1800,plain,
( spl30_207
| ~ spl30_88
| ~ spl30_131 ),
inference(avatar_split_clause,[],[f1184,f1146,f804,f1798]) ).
fof(f1184,plain,
( ! [X0] :
( empty(X0)
| in(sK4(X0),X0) )
| ~ spl30_88
| ~ spl30_131 ),
inference(resolution,[],[f1147,f805]) ).
fof(f1796,plain,
( spl30_206
| ~ spl30_88
| ~ spl30_128 ),
inference(avatar_split_clause,[],[f1181,f1134,f804,f1794]) ).
fof(f1794,plain,
( spl30_206
<=> ! [X0] :
( finite(sK4(powerset(X0)))
| ~ finite(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_206])]) ).
fof(f1181,plain,
( ! [X0] :
( finite(sK4(powerset(X0)))
| ~ finite(X0) )
| ~ spl30_88
| ~ spl30_128 ),
inference(resolution,[],[f1135,f805]) ).
fof(f1792,plain,
( spl30_205
| ~ spl30_116
| ~ spl30_123 ),
inference(avatar_split_clause,[],[f1100,f1054,f1026,f1790]) ).
fof(f1790,plain,
( spl30_205
<=> ! [X0] :
( subset(sK3(X0),X0)
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_205])]) ).
fof(f1100,plain,
( ! [X0] :
( subset(sK3(X0),X0)
| empty(X0) )
| ~ spl30_116
| ~ spl30_123 ),
inference(resolution,[],[f1055,f1027]) ).
fof(f1788,plain,
( spl30_204
| ~ spl30_114
| ~ spl30_123 ),
inference(avatar_split_clause,[],[f1099,f1054,f1016,f1786]) ).
fof(f1786,plain,
( spl30_204
<=> ! [X0] :
( subset(sK2(X0),X0)
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_204])]) ).
fof(f1099,plain,
( ! [X0] :
( subset(sK2(X0),X0)
| empty(X0) )
| ~ spl30_114
| ~ spl30_123 ),
inference(resolution,[],[f1055,f1017]) ).
fof(f1784,plain,
( spl30_203
| ~ spl30_113
| ~ spl30_123 ),
inference(avatar_split_clause,[],[f1098,f1054,f1012,f1782]) ).
fof(f1782,plain,
( spl30_203
<=> ! [X0] :
( subset(sK1(X0),X0)
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_203])]) ).
fof(f1098,plain,
( ! [X0] :
( subset(sK1(X0),X0)
| empty(X0) )
| ~ spl30_113
| ~ spl30_123 ),
inference(resolution,[],[f1055,f1013]) ).
fof(f1780,plain,
( spl30_202
| ~ spl30_13
| ~ spl30_97
| ~ spl30_101 ),
inference(avatar_split_clause,[],[f975,f924,f907,f447,f1778]) ).
fof(f975,plain,
( ! [X0] :
( relation_dom(X0) = sK10
| ~ empty(X0) )
| ~ spl30_13
| ~ spl30_97
| ~ spl30_101 ),
inference(forward_demodulation,[],[f974,f951]) ).
fof(f974,plain,
( ! [X0] :
( ~ empty(X0)
| empty_set = relation_dom(X0) )
| ~ spl30_97
| ~ spl30_101 ),
inference(resolution,[],[f925,f908]) ).
fof(f1776,plain,
( spl30_201
| ~ spl30_13
| ~ spl30_97
| ~ spl30_98 ),
inference(avatar_split_clause,[],[f967,f911,f907,f447,f1774]) ).
fof(f967,plain,
( ! [X0] :
( relation_rng(X0) = sK10
| ~ empty(X0) )
| ~ spl30_13
| ~ spl30_97
| ~ spl30_98 ),
inference(forward_demodulation,[],[f966,f951]) ).
fof(f966,plain,
( ! [X0] :
( ~ empty(X0)
| empty_set = relation_rng(X0) )
| ~ spl30_97
| ~ spl30_98 ),
inference(resolution,[],[f912,f908]) ).
fof(f1756,plain,
( ~ spl30_200
| spl30_3
| ~ spl30_185 ),
inference(avatar_split_clause,[],[f1749,f1545,f398,f1753]) ).
fof(f1753,plain,
( spl30_200
<=> empty(sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_200])]) ).
fof(f1545,plain,
( spl30_185
<=> ! [X0] :
( ~ empty(X0)
| finite(relation_dom(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_185])]) ).
fof(f1749,plain,
( ~ empty(sK0)
| spl30_3
| ~ spl30_185 ),
inference(resolution,[],[f1546,f399]) ).
fof(f399,plain,
( ~ finite(relation_dom(sK0))
| spl30_3 ),
inference(avatar_component_clause,[],[f398]) ).
fof(f1546,plain,
( ! [X0] :
( finite(relation_dom(X0))
| ~ empty(X0) )
| ~ spl30_185 ),
inference(avatar_component_clause,[],[f1545]) ).
fof(f1734,plain,
( ~ spl30_199
| ~ spl30_108
| ~ spl30_195 ),
inference(avatar_split_clause,[],[f1594,f1589,f981,f1731]) ).
fof(f1731,plain,
( spl30_199
<=> in(positive_rationals,sK28) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_199])]) ).
fof(f1589,plain,
( spl30_195
<=> in(sK28,positive_rationals) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_195])]) ).
fof(f1594,plain,
( ~ in(positive_rationals,sK28)
| ~ spl30_108
| ~ spl30_195 ),
inference(resolution,[],[f1591,f982]) ).
fof(f1591,plain,
( in(sK28,positive_rationals)
| ~ spl30_195 ),
inference(avatar_component_clause,[],[f1589]) ).
fof(f1710,plain,
( spl30_194
| ~ spl30_97
| ~ spl30_168 ),
inference(avatar_split_clause,[],[f1627,f1432,f907,f1585]) ).
fof(f1627,plain,
( ! [X0] :
( sK10 = X0
| ~ empty(X0) )
| ~ spl30_97
| ~ spl30_168 ),
inference(forward_demodulation,[],[f908,f1434]) ).
fof(f1626,plain,
( ~ spl30_6
| ~ spl30_197 ),
inference(avatar_contradiction_clause,[],[f1611]) ).
fof(f1611,plain,
( $false
| ~ spl30_6
| ~ spl30_197 ),
inference(resolution,[],[f1606,f414]) ).
fof(f1606,plain,
( ! [X0] : ~ empty(X0)
| ~ spl30_197 ),
inference(avatar_component_clause,[],[f1605]) ).
fof(f1605,plain,
( spl30_197
<=> ! [X0] : ~ empty(X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_197])]) ).
fof(f1625,plain,
( ~ spl30_69
| ~ spl30_197 ),
inference(avatar_contradiction_clause,[],[f1612]) ).
fof(f1612,plain,
( $false
| ~ spl30_69
| ~ spl30_197 ),
inference(resolution,[],[f1606,f727]) ).
fof(f1624,plain,
( ~ spl30_70
| ~ spl30_197 ),
inference(avatar_contradiction_clause,[],[f1613]) ).
fof(f1613,plain,
( $false
| ~ spl30_70
| ~ spl30_197 ),
inference(resolution,[],[f1606,f731]) ).
fof(f731,plain,
( ! [X0] : empty(sK6(X0))
| ~ spl30_70 ),
inference(avatar_component_clause,[],[f730]) ).
fof(f730,plain,
( spl30_70
<=> ! [X0] : empty(sK6(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_70])]) ).
fof(f1623,plain,
( ~ spl30_13
| ~ spl30_197 ),
inference(avatar_contradiction_clause,[],[f1614]) ).
fof(f1614,plain,
( $false
| ~ spl30_13
| ~ spl30_197 ),
inference(resolution,[],[f1606,f449]) ).
fof(f1622,plain,
( ~ spl30_32
| ~ spl30_197 ),
inference(avatar_contradiction_clause,[],[f1615]) ).
fof(f1615,plain,
( $false
| ~ spl30_32
| ~ spl30_197 ),
inference(resolution,[],[f1606,f544]) ).
fof(f544,plain,
( empty(sK17)
| ~ spl30_32 ),
inference(avatar_component_clause,[],[f542]) ).
fof(f542,plain,
( spl30_32
<=> empty(sK17) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_32])]) ).
fof(f1621,plain,
( ~ spl30_53
| ~ spl30_197 ),
inference(avatar_contradiction_clause,[],[f1616]) ).
fof(f1616,plain,
( $false
| ~ spl30_53
| ~ spl30_197 ),
inference(resolution,[],[f1606,f649]) ).
fof(f649,plain,
( empty(sK26)
| ~ spl30_53 ),
inference(avatar_component_clause,[],[f647]) ).
fof(f647,plain,
( spl30_53
<=> empty(sK26) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_53])]) ).
fof(f1620,plain,
( ~ spl30_58
| ~ spl30_197 ),
inference(avatar_contradiction_clause,[],[f1617]) ).
fof(f1617,plain,
( $false
| ~ spl30_58
| ~ spl30_197 ),
inference(resolution,[],[f1606,f674]) ).
fof(f674,plain,
( empty(sK27)
| ~ spl30_58 ),
inference(avatar_component_clause,[],[f672]) ).
fof(f672,plain,
( spl30_58
<=> empty(sK27) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_58])]) ).
fof(f1619,plain,
( ~ spl30_64
| ~ spl30_197 ),
inference(avatar_contradiction_clause,[],[f1618]) ).
fof(f1618,plain,
( $false
| ~ spl30_64
| ~ spl30_197 ),
inference(resolution,[],[f1606,f704]) ).
fof(f704,plain,
( empty(sK29)
| ~ spl30_64 ),
inference(avatar_component_clause,[],[f702]) ).
fof(f702,plain,
( spl30_64
<=> empty(sK29) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_64])]) ).
fof(f1610,plain,
( spl30_197
| spl30_198
| ~ spl30_13
| ~ spl30_69
| ~ spl30_97
| ~ spl30_103
| ~ spl30_143 ),
inference(avatar_split_clause,[],[f1244,f1229,f932,f907,f726,f447,f1608,f1605]) ).
fof(f1608,plain,
( spl30_198
<=> ! [X1] : ~ in(X1,sK10) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_198])]) ).
fof(f1244,plain,
( ! [X0,X1] :
( ~ in(X1,sK10)
| ~ empty(X0) )
| ~ spl30_13
| ~ spl30_69
| ~ spl30_97
| ~ spl30_103
| ~ spl30_143 ),
inference(forward_demodulation,[],[f1243,f951]) ).
fof(f1243,plain,
( ! [X0,X1] :
( ~ in(X1,empty_set)
| ~ empty(X0) )
| ~ spl30_69
| ~ spl30_97
| ~ spl30_103
| ~ spl30_143 ),
inference(forward_demodulation,[],[f1239,f949]) ).
fof(f1239,plain,
( ! [X0,X1] :
( ~ empty(X0)
| ~ in(X1,sK5(X0)) )
| ~ spl30_103
| ~ spl30_143 ),
inference(resolution,[],[f1230,f933]) ).
fof(f1600,plain,
( spl30_5
| spl30_196
| ~ spl30_13
| ~ spl30_64
| ~ spl30_79
| ~ spl30_97
| ~ spl30_131 ),
inference(avatar_split_clause,[],[f1191,f1146,f907,f767,f702,f447,f1597,f407]) ).
fof(f407,plain,
( spl30_5
<=> empty(positive_rationals) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_5])]) ).
fof(f1597,plain,
( spl30_196
<=> in(sK10,positive_rationals) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_196])]) ).
fof(f767,plain,
( spl30_79
<=> element(sK29,positive_rationals) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_79])]) ).
fof(f1191,plain,
( in(sK10,positive_rationals)
| empty(positive_rationals)
| ~ spl30_13
| ~ spl30_64
| ~ spl30_79
| ~ spl30_97
| ~ spl30_131 ),
inference(forward_demodulation,[],[f1183,f959]) ).
fof(f959,plain,
( sK10 = sK29
| ~ spl30_13
| ~ spl30_64
| ~ spl30_97 ),
inference(forward_demodulation,[],[f955,f951]) ).
fof(f955,plain,
( empty_set = sK29
| ~ spl30_64
| ~ spl30_97 ),
inference(resolution,[],[f908,f704]) ).
fof(f1183,plain,
( empty(positive_rationals)
| in(sK29,positive_rationals)
| ~ spl30_79
| ~ spl30_131 ),
inference(resolution,[],[f1147,f769]) ).
fof(f769,plain,
( element(sK29,positive_rationals)
| ~ spl30_79 ),
inference(avatar_component_clause,[],[f767]) ).
fof(f1592,plain,
( spl30_195
| spl30_5
| ~ spl30_78
| ~ spl30_131 ),
inference(avatar_split_clause,[],[f1182,f1146,f762,f407,f1589]) ).
fof(f762,plain,
( spl30_78
<=> element(sK28,positive_rationals) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_78])]) ).
fof(f1182,plain,
( empty(positive_rationals)
| in(sK28,positive_rationals)
| ~ spl30_78
| ~ spl30_131 ),
inference(resolution,[],[f1147,f764]) ).
fof(f764,plain,
( element(sK28,positive_rationals)
| ~ spl30_78 ),
inference(avatar_component_clause,[],[f762]) ).
fof(f1587,plain,
( spl30_194
| ~ spl30_13
| ~ spl30_125 ),
inference(avatar_split_clause,[],[f1122,f1062,f447,f1585]) ).
fof(f1122,plain,
( ! [X0] :
( sK10 = X0
| ~ empty(X0) )
| ~ spl30_13
| ~ spl30_125 ),
inference(resolution,[],[f1063,f449]) ).
fof(f1583,plain,
( spl30_193
| ~ spl30_88
| ~ spl30_123 ),
inference(avatar_split_clause,[],[f1103,f1054,f804,f1581]) ).
fof(f1581,plain,
( spl30_193
<=> ! [X0] : subset(sK4(powerset(X0)),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_193])]) ).
fof(f1103,plain,
( ! [X0] : subset(sK4(powerset(X0)),X0)
| ~ spl30_88
| ~ spl30_123 ),
inference(resolution,[],[f1055,f805]) ).
fof(f1579,plain,
( spl30_192
| ~ spl30_88
| ~ spl30_119 ),
inference(avatar_split_clause,[],[f1089,f1038,f804,f1577]) ).
fof(f1577,plain,
( spl30_192
<=> ! [X0] :
( ordinal(sK4(X0))
| ~ ordinal(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_192])]) ).
fof(f1089,plain,
( ! [X0] :
( ordinal(sK4(X0))
| ~ ordinal(X0) )
| ~ spl30_88
| ~ spl30_119 ),
inference(resolution,[],[f1039,f805]) ).
fof(f1575,plain,
( spl30_191
| ~ spl30_88
| ~ spl30_118 ),
inference(avatar_split_clause,[],[f1081,f1034,f804,f1573]) ).
fof(f1573,plain,
( spl30_191
<=> ! [X0] :
( epsilon_connected(sK4(X0))
| ~ ordinal(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_191])]) ).
fof(f1081,plain,
( ! [X0] :
( epsilon_connected(sK4(X0))
| ~ ordinal(X0) )
| ~ spl30_88
| ~ spl30_118 ),
inference(resolution,[],[f1035,f805]) ).
fof(f1571,plain,
( spl30_190
| ~ spl30_88
| ~ spl30_117 ),
inference(avatar_split_clause,[],[f1073,f1030,f804,f1569]) ).
fof(f1569,plain,
( spl30_190
<=> ! [X0] :
( epsilon_transitive(sK4(X0))
| ~ ordinal(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_190])]) ).
fof(f1073,plain,
( ! [X0] :
( epsilon_transitive(sK4(X0))
| ~ ordinal(X0) )
| ~ spl30_88
| ~ spl30_117 ),
inference(resolution,[],[f1031,f805]) ).
fof(f1567,plain,
( spl30_189
| ~ spl30_87
| ~ spl30_101 ),
inference(avatar_split_clause,[],[f973,f924,f800,f1565]) ).
fof(f1565,plain,
( spl30_189
<=> ! [X0] :
( ~ empty(X0)
| ordinal(relation_dom(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_189])]) ).
fof(f973,plain,
( ! [X0] :
( ~ empty(X0)
| ordinal(relation_dom(X0)) )
| ~ spl30_87
| ~ spl30_101 ),
inference(resolution,[],[f925,f801]) ).
fof(f1563,plain,
( spl30_188
| ~ spl30_86
| ~ spl30_101 ),
inference(avatar_split_clause,[],[f972,f924,f796,f1561]) ).
fof(f1561,plain,
( spl30_188
<=> ! [X0] :
( ~ empty(X0)
| epsilon_connected(relation_dom(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_188])]) ).
fof(f972,plain,
( ! [X0] :
( ~ empty(X0)
| epsilon_connected(relation_dom(X0)) )
| ~ spl30_86
| ~ spl30_101 ),
inference(resolution,[],[f925,f797]) ).
fof(f1559,plain,
( spl30_187
| ~ spl30_85
| ~ spl30_101 ),
inference(avatar_split_clause,[],[f971,f924,f792,f1557]) ).
fof(f1557,plain,
( spl30_187
<=> ! [X0] :
( ~ empty(X0)
| epsilon_transitive(relation_dom(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_187])]) ).
fof(f971,plain,
( ! [X0] :
( ~ empty(X0)
| epsilon_transitive(relation_dom(X0)) )
| ~ spl30_85
| ~ spl30_101 ),
inference(resolution,[],[f925,f793]) ).
fof(f1555,plain,
( spl30_186
| ~ spl30_83
| ~ spl30_101 ),
inference(avatar_split_clause,[],[f969,f924,f784,f1553]) ).
fof(f969,plain,
( ! [X0] :
( ~ empty(X0)
| function(relation_dom(X0)) )
| ~ spl30_83
| ~ spl30_101 ),
inference(resolution,[],[f925,f785]) ).
fof(f1547,plain,
( spl30_185
| ~ spl30_82
| ~ spl30_101 ),
inference(avatar_split_clause,[],[f968,f924,f780,f1545]) ).
fof(f968,plain,
( ! [X0] :
( ~ empty(X0)
| finite(relation_dom(X0)) )
| ~ spl30_82
| ~ spl30_101 ),
inference(resolution,[],[f925,f781]) ).
fof(f1543,plain,
( spl30_184
| ~ spl30_87
| ~ spl30_98 ),
inference(avatar_split_clause,[],[f965,f911,f800,f1541]) ).
fof(f1541,plain,
( spl30_184
<=> ! [X0] :
( ~ empty(X0)
| ordinal(relation_rng(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_184])]) ).
fof(f965,plain,
( ! [X0] :
( ~ empty(X0)
| ordinal(relation_rng(X0)) )
| ~ spl30_87
| ~ spl30_98 ),
inference(resolution,[],[f912,f801]) ).
fof(f1539,plain,
( spl30_183
| ~ spl30_86
| ~ spl30_98 ),
inference(avatar_split_clause,[],[f964,f911,f796,f1537]) ).
fof(f1537,plain,
( spl30_183
<=> ! [X0] :
( ~ empty(X0)
| epsilon_connected(relation_rng(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_183])]) ).
fof(f964,plain,
( ! [X0] :
( ~ empty(X0)
| epsilon_connected(relation_rng(X0)) )
| ~ spl30_86
| ~ spl30_98 ),
inference(resolution,[],[f912,f797]) ).
fof(f1535,plain,
( spl30_182
| ~ spl30_85
| ~ spl30_98 ),
inference(avatar_split_clause,[],[f963,f911,f792,f1533]) ).
fof(f1533,plain,
( spl30_182
<=> ! [X0] :
( ~ empty(X0)
| epsilon_transitive(relation_rng(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_182])]) ).
fof(f963,plain,
( ! [X0] :
( ~ empty(X0)
| epsilon_transitive(relation_rng(X0)) )
| ~ spl30_85
| ~ spl30_98 ),
inference(resolution,[],[f912,f793]) ).
fof(f1531,plain,
( spl30_181
| ~ spl30_83
| ~ spl30_98 ),
inference(avatar_split_clause,[],[f961,f911,f784,f1529]) ).
fof(f961,plain,
( ! [X0] :
( ~ empty(X0)
| function(relation_rng(X0)) )
| ~ spl30_83
| ~ spl30_98 ),
inference(resolution,[],[f912,f785]) ).
fof(f1527,plain,
( spl30_180
| ~ spl30_82
| ~ spl30_98 ),
inference(avatar_split_clause,[],[f960,f911,f780,f1525]) ).
fof(f1525,plain,
( spl30_180
<=> ! [X0] :
( ~ empty(X0)
| finite(relation_rng(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_180])]) ).
fof(f960,plain,
( ! [X0] :
( ~ empty(X0)
| finite(relation_rng(X0)) )
| ~ spl30_82
| ~ spl30_98 ),
inference(resolution,[],[f912,f781]) ).
fof(f1522,plain,
( spl30_179
| ~ spl30_2
| ~ spl30_1
| ~ spl30_152 ),
inference(avatar_split_clause,[],[f1320,f1313,f388,f393,f1519]) ).
fof(f1320,plain,
( ~ function(sK0)
| relation_dom(sK0) = function_image(cartesian_product2(relation_dom(sK0),relation_rng(sK0)),relation_dom(sK0),first_projection_as_func_of(relation_dom(sK0),relation_rng(sK0)),sK0)
| ~ spl30_1
| ~ spl30_152 ),
inference(resolution,[],[f1314,f390]) ).
fof(f390,plain,
( relation(sK0)
| ~ spl30_1 ),
inference(avatar_component_clause,[],[f388]) ).
fof(f1507,plain,
( spl30_178
| ~ spl30_79
| ~ spl30_172 ),
inference(avatar_split_clause,[],[f1479,f1452,f767,f1504]) ).
fof(f1504,plain,
( spl30_178
<=> element(sK10,positive_rationals) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_178])]) ).
fof(f1452,plain,
( spl30_172
<=> sK10 = sK29 ),
introduced(avatar_definition,[new_symbols(naming,[spl30_172])]) ).
fof(f1479,plain,
( element(sK10,positive_rationals)
| ~ spl30_79
| ~ spl30_172 ),
inference(superposition,[],[f769,f1454]) ).
fof(f1454,plain,
( sK10 = sK29
| ~ spl30_172 ),
inference(avatar_component_clause,[],[f1452]) ).
fof(f1502,plain,
( spl30_177
| ~ spl30_168
| ~ spl30_175 ),
inference(avatar_split_clause,[],[f1494,f1491,f1432,f1500]) ).
fof(f1500,plain,
( spl30_177
<=> ! [X0] : sK6(X0) = sK10 ),
introduced(avatar_definition,[new_symbols(naming,[spl30_177])]) ).
fof(f1491,plain,
( spl30_175
<=> ! [X0] : empty_set = sK6(X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_175])]) ).
fof(f1494,plain,
( ! [X0] : sK6(X0) = sK10
| ~ spl30_168
| ~ spl30_175 ),
inference(forward_demodulation,[],[f1492,f1434]) ).
fof(f1492,plain,
( ! [X0] : empty_set = sK6(X0)
| ~ spl30_175 ),
inference(avatar_component_clause,[],[f1491]) ).
fof(f1498,plain,
( spl30_176
| ~ spl30_168
| ~ spl30_174 ),
inference(avatar_split_clause,[],[f1489,f1486,f1432,f1496]) ).
fof(f1486,plain,
( spl30_174
<=> ! [X0] : empty_set = sK5(X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_174])]) ).
fof(f1489,plain,
( ! [X0] : sK5(X0) = sK10
| ~ spl30_168
| ~ spl30_174 ),
inference(forward_demodulation,[],[f1487,f1434]) ).
fof(f1487,plain,
( ! [X0] : empty_set = sK5(X0)
| ~ spl30_174 ),
inference(avatar_component_clause,[],[f1486]) ).
fof(f1493,plain,
( spl30_175
| ~ spl30_70
| ~ spl30_97 ),
inference(avatar_split_clause,[],[f950,f907,f730,f1491]) ).
fof(f950,plain,
( ! [X0] : empty_set = sK6(X0)
| ~ spl30_70
| ~ spl30_97 ),
inference(resolution,[],[f908,f731]) ).
fof(f1488,plain,
( spl30_174
| ~ spl30_69
| ~ spl30_97 ),
inference(avatar_split_clause,[],[f949,f907,f726,f1486]) ).
fof(f1459,plain,
( spl30_173
| ~ spl30_13
| ~ spl30_69
| ~ spl30_97
| ~ spl30_103
| ~ spl30_123 ),
inference(avatar_split_clause,[],[f1105,f1054,f932,f907,f726,f447,f1457]) ).
fof(f1457,plain,
( spl30_173
<=> ! [X0] : subset(sK10,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_173])]) ).
fof(f1105,plain,
( ! [X0] : subset(sK10,X0)
| ~ spl30_13
| ~ spl30_69
| ~ spl30_97
| ~ spl30_103
| ~ spl30_123 ),
inference(forward_demodulation,[],[f1104,f951]) ).
fof(f1104,plain,
( ! [X0] : subset(empty_set,X0)
| ~ spl30_69
| ~ spl30_97
| ~ spl30_103
| ~ spl30_123 ),
inference(forward_demodulation,[],[f1101,f949]) ).
fof(f1101,plain,
( ! [X0] : subset(sK5(X0),X0)
| ~ spl30_103
| ~ spl30_123 ),
inference(resolution,[],[f1055,f933]) ).
fof(f1455,plain,
( spl30_172
| ~ spl30_13
| ~ spl30_64
| ~ spl30_97 ),
inference(avatar_split_clause,[],[f959,f907,f702,f447,f1452]) ).
fof(f1450,plain,
( spl30_171
| ~ spl30_13
| ~ spl30_58
| ~ spl30_97 ),
inference(avatar_split_clause,[],[f958,f907,f672,f447,f1447]) ).
fof(f1447,plain,
( spl30_171
<=> sK10 = sK27 ),
introduced(avatar_definition,[new_symbols(naming,[spl30_171])]) ).
fof(f958,plain,
( sK10 = sK27
| ~ spl30_13
| ~ spl30_58
| ~ spl30_97 ),
inference(forward_demodulation,[],[f954,f951]) ).
fof(f954,plain,
( empty_set = sK27
| ~ spl30_58
| ~ spl30_97 ),
inference(resolution,[],[f908,f674]) ).
fof(f1445,plain,
( spl30_170
| ~ spl30_13
| ~ spl30_53
| ~ spl30_97 ),
inference(avatar_split_clause,[],[f957,f907,f647,f447,f1442]) ).
fof(f1442,plain,
( spl30_170
<=> sK10 = sK26 ),
introduced(avatar_definition,[new_symbols(naming,[spl30_170])]) ).
fof(f957,plain,
( sK10 = sK26
| ~ spl30_13
| ~ spl30_53
| ~ spl30_97 ),
inference(forward_demodulation,[],[f953,f951]) ).
fof(f953,plain,
( empty_set = sK26
| ~ spl30_53
| ~ spl30_97 ),
inference(resolution,[],[f908,f649]) ).
fof(f1440,plain,
( spl30_169
| ~ spl30_13
| ~ spl30_32
| ~ spl30_97 ),
inference(avatar_split_clause,[],[f956,f907,f542,f447,f1437]) ).
fof(f1437,plain,
( spl30_169
<=> sK10 = sK17 ),
introduced(avatar_definition,[new_symbols(naming,[spl30_169])]) ).
fof(f956,plain,
( sK10 = sK17
| ~ spl30_13
| ~ spl30_32
| ~ spl30_97 ),
inference(forward_demodulation,[],[f952,f951]) ).
fof(f952,plain,
( empty_set = sK17
| ~ spl30_32
| ~ spl30_97 ),
inference(resolution,[],[f908,f544]) ).
fof(f1435,plain,
( spl30_168
| ~ spl30_13
| ~ spl30_97 ),
inference(avatar_split_clause,[],[f951,f907,f447,f1432]) ).
fof(f1429,plain,
( spl30_167
| ~ spl30_69
| ~ spl30_87 ),
inference(avatar_split_clause,[],[f874,f800,f726,f1427]) ).
fof(f1427,plain,
( spl30_167
<=> ! [X0] : ordinal(sK5(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_167])]) ).
fof(f874,plain,
( ! [X0] : ordinal(sK5(X0))
| ~ spl30_69
| ~ spl30_87 ),
inference(resolution,[],[f801,f727]) ).
fof(f1424,plain,
( spl30_166
| ~ spl30_69
| ~ spl30_86 ),
inference(avatar_split_clause,[],[f866,f796,f726,f1422]) ).
fof(f1422,plain,
( spl30_166
<=> ! [X0] : epsilon_connected(sK5(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_166])]) ).
fof(f866,plain,
( ! [X0] : epsilon_connected(sK5(X0))
| ~ spl30_69
| ~ spl30_86 ),
inference(resolution,[],[f797,f727]) ).
fof(f1419,plain,
( spl30_165
| ~ spl30_69
| ~ spl30_85 ),
inference(avatar_split_clause,[],[f858,f792,f726,f1417]) ).
fof(f1417,plain,
( spl30_165
<=> ! [X0] : epsilon_transitive(sK5(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_165])]) ).
fof(f858,plain,
( ! [X0] : epsilon_transitive(sK5(X0))
| ~ spl30_69
| ~ spl30_85 ),
inference(resolution,[],[f793,f727]) ).
fof(f1414,plain,
( spl30_164
| ~ spl30_69
| ~ spl30_84 ),
inference(avatar_split_clause,[],[f850,f788,f726,f1412]) ).
fof(f1412,plain,
( spl30_164
<=> ! [X0] : relation(sK5(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_164])]) ).
fof(f850,plain,
( ! [X0] : relation(sK5(X0))
| ~ spl30_69
| ~ spl30_84 ),
inference(resolution,[],[f789,f727]) ).
fof(f1409,plain,
( spl30_163
| ~ spl30_69
| ~ spl30_83 ),
inference(avatar_split_clause,[],[f842,f784,f726,f1407]) ).
fof(f1407,plain,
( spl30_163
<=> ! [X0] : function(sK5(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_163])]) ).
fof(f842,plain,
( ! [X0] : function(sK5(X0))
| ~ spl30_69
| ~ spl30_83 ),
inference(resolution,[],[f785,f727]) ).
fof(f1404,plain,
( spl30_162
| ~ spl30_69
| ~ spl30_82 ),
inference(avatar_split_clause,[],[f834,f780,f726,f1402]) ).
fof(f1402,plain,
( spl30_162
<=> ! [X0] : finite(sK5(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_162])]) ).
fof(f834,plain,
( ! [X0] : finite(sK5(X0))
| ~ spl30_69
| ~ spl30_82 ),
inference(resolution,[],[f781,f727]) ).
fof(f1395,plain,
( spl30_161
| ~ spl30_58
| ~ spl30_87 ),
inference(avatar_split_clause,[],[f879,f800,f672,f1392]) ).
fof(f1392,plain,
( spl30_161
<=> ordinal(sK27) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_161])]) ).
fof(f879,plain,
( ordinal(sK27)
| ~ spl30_58
| ~ spl30_87 ),
inference(resolution,[],[f801,f674]) ).
fof(f1389,plain,
( spl30_160
| ~ spl30_32
| ~ spl30_87 ),
inference(avatar_split_clause,[],[f877,f800,f542,f1386]) ).
fof(f1386,plain,
( spl30_160
<=> ordinal(sK17) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_160])]) ).
fof(f877,plain,
( ordinal(sK17)
| ~ spl30_32
| ~ spl30_87 ),
inference(resolution,[],[f801,f544]) ).
fof(f1384,plain,
( spl30_159
| ~ spl30_13
| ~ spl30_87 ),
inference(avatar_split_clause,[],[f876,f800,f447,f1381]) ).
fof(f1381,plain,
( spl30_159
<=> ordinal(sK10) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_159])]) ).
fof(f876,plain,
( ordinal(sK10)
| ~ spl30_13
| ~ spl30_87 ),
inference(resolution,[],[f801,f449]) ).
fof(f1378,plain,
( spl30_158
| ~ spl30_58
| ~ spl30_86 ),
inference(avatar_split_clause,[],[f871,f796,f672,f1375]) ).
fof(f1375,plain,
( spl30_158
<=> epsilon_connected(sK27) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_158])]) ).
fof(f871,plain,
( epsilon_connected(sK27)
| ~ spl30_58
| ~ spl30_86 ),
inference(resolution,[],[f797,f674]) ).
fof(f1372,plain,
( spl30_157
| ~ spl30_32
| ~ spl30_86 ),
inference(avatar_split_clause,[],[f869,f796,f542,f1369]) ).
fof(f1369,plain,
( spl30_157
<=> epsilon_connected(sK17) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_157])]) ).
fof(f869,plain,
( epsilon_connected(sK17)
| ~ spl30_32
| ~ spl30_86 ),
inference(resolution,[],[f797,f544]) ).
fof(f1367,plain,
( spl30_156
| ~ spl30_13
| ~ spl30_86 ),
inference(avatar_split_clause,[],[f868,f796,f447,f1364]) ).
fof(f1364,plain,
( spl30_156
<=> epsilon_connected(sK10) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_156])]) ).
fof(f868,plain,
( epsilon_connected(sK10)
| ~ spl30_13
| ~ spl30_86 ),
inference(resolution,[],[f797,f449]) ).
fof(f1361,plain,
( spl30_155
| ~ spl30_58
| ~ spl30_85 ),
inference(avatar_split_clause,[],[f863,f792,f672,f1358]) ).
fof(f1358,plain,
( spl30_155
<=> epsilon_transitive(sK27) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_155])]) ).
fof(f863,plain,
( epsilon_transitive(sK27)
| ~ spl30_58
| ~ spl30_85 ),
inference(resolution,[],[f793,f674]) ).
fof(f1355,plain,
( spl30_154
| ~ spl30_32
| ~ spl30_85 ),
inference(avatar_split_clause,[],[f861,f792,f542,f1352]) ).
fof(f1352,plain,
( spl30_154
<=> epsilon_transitive(sK17) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_154])]) ).
fof(f861,plain,
( epsilon_transitive(sK17)
| ~ spl30_32
| ~ spl30_85 ),
inference(resolution,[],[f793,f544]) ).
fof(f1350,plain,
( spl30_153
| ~ spl30_13
| ~ spl30_85 ),
inference(avatar_split_clause,[],[f860,f792,f447,f1347]) ).
fof(f1347,plain,
( spl30_153
<=> epsilon_transitive(sK10) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_153])]) ).
fof(f860,plain,
( epsilon_transitive(sK10)
| ~ spl30_13
| ~ spl30_85 ),
inference(resolution,[],[f793,f449]) ).
fof(f1315,plain,
spl30_152,
inference(avatar_split_clause,[],[f282,f1313]) ).
fof(f282,plain,
! [X0] :
( relation_dom(X0) = function_image(cartesian_product2(relation_dom(X0),relation_rng(X0)),relation_dom(X0),first_projection_as_func_of(relation_dom(X0),relation_rng(X0)),X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f131]) ).
fof(f131,plain,
! [X0] :
( relation_dom(X0) = function_image(cartesian_product2(relation_dom(X0),relation_rng(X0)),relation_dom(X0),first_projection_as_func_of(relation_dom(X0),relation_rng(X0)),X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(flattening,[],[f130]) ).
fof(f130,plain,
! [X0] :
( relation_dom(X0) = function_image(cartesian_product2(relation_dom(X0),relation_rng(X0)),relation_dom(X0),first_projection_as_func_of(relation_dom(X0),relation_rng(X0)),X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(ennf_transformation,[],[f66]) ).
fof(f66,axiom,
! [X0] :
( ( function(X0)
& relation(X0) )
=> relation_dom(X0) = function_image(cartesian_product2(relation_dom(X0),relation_rng(X0)),relation_dom(X0),first_projection_as_func_of(relation_dom(X0),relation_rng(X0)),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t100_funct_3) ).
fof(f1310,plain,
spl30_151,
inference(avatar_split_clause,[],[f326,f1308]) ).
fof(f326,plain,
! [X2,X3,X0,X1] :
( function_image(X0,X1,X2,X3) = relation_image(X2,X3)
| ~ relation_of2(X2,X0,X1)
| ~ quasi_total(X2,X0,X1)
| ~ function(X2) ),
inference(cnf_transformation,[],[f162]) ).
fof(f162,plain,
! [X0,X1,X2,X3] :
( function_image(X0,X1,X2,X3) = relation_image(X2,X3)
| ~ relation_of2(X2,X0,X1)
| ~ quasi_total(X2,X0,X1)
| ~ function(X2) ),
inference(flattening,[],[f161]) ).
fof(f161,plain,
! [X0,X1,X2,X3] :
( function_image(X0,X1,X2,X3) = relation_image(X2,X3)
| ~ relation_of2(X2,X0,X1)
| ~ quasi_total(X2,X0,X1)
| ~ function(X2) ),
inference(ennf_transformation,[],[f62]) ).
fof(f62,axiom,
! [X0,X1,X2,X3] :
( ( relation_of2(X2,X0,X1)
& quasi_total(X2,X0,X1)
& function(X2) )
=> function_image(X0,X1,X2,X3) = relation_image(X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k2_funct_2) ).
fof(f1305,plain,
( spl30_150
| ~ spl30_64
| ~ spl30_84 ),
inference(avatar_split_clause,[],[f856,f788,f702,f1302]) ).
fof(f1302,plain,
( spl30_150
<=> relation(sK29) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_150])]) ).
fof(f856,plain,
( relation(sK29)
| ~ spl30_64
| ~ spl30_84 ),
inference(resolution,[],[f789,f704]) ).
fof(f1291,plain,
spl30_149,
inference(avatar_split_clause,[],[f325,f1289]) ).
fof(f325,plain,
! [X2,X3,X0,X1] :
( element(function_image(X0,X1,X2,X3),powerset(X1))
| ~ relation_of2(X2,X0,X1)
| ~ quasi_total(X2,X0,X1)
| ~ function(X2) ),
inference(cnf_transformation,[],[f160]) ).
fof(f160,plain,
! [X0,X1,X2,X3] :
( element(function_image(X0,X1,X2,X3),powerset(X1))
| ~ relation_of2(X2,X0,X1)
| ~ quasi_total(X2,X0,X1)
| ~ function(X2) ),
inference(flattening,[],[f159]) ).
fof(f159,plain,
! [X0,X1,X2,X3] :
( element(function_image(X0,X1,X2,X3),powerset(X1))
| ~ relation_of2(X2,X0,X1)
| ~ quasi_total(X2,X0,X1)
| ~ function(X2) ),
inference(ennf_transformation,[],[f14]) ).
fof(f14,axiom,
! [X0,X1,X2,X3] :
( ( relation_of2(X2,X0,X1)
& quasi_total(X2,X0,X1)
& function(X2) )
=> element(function_image(X0,X1,X2,X3),powerset(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_funct_2) ).
fof(f1267,plain,
spl30_148,
inference(avatar_split_clause,[],[f321,f1265]) ).
fof(f321,plain,
! [X2,X0,X1] :
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f157]) ).
fof(f157,plain,
! [X0,X1,X2] :
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(flattening,[],[f156]) ).
fof(f156,plain,
! [X0,X1,X2] :
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f77]) ).
fof(f77,axiom,
! [X0,X1,X2] :
( ( element(X1,powerset(X2))
& in(X0,X1) )
=> element(X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_subset) ).
fof(f1263,plain,
spl30_147,
inference(avatar_split_clause,[],[f319,f1261]) ).
fof(f319,plain,
! [X2,X0,X1] :
( element(X2,powerset(cartesian_product2(X0,X1)))
| ~ relation_of2_as_subset(X2,X0,X1) ),
inference(cnf_transformation,[],[f154]) ).
fof(f154,plain,
! [X0,X1,X2] :
( element(X2,powerset(cartesian_product2(X0,X1)))
| ~ relation_of2_as_subset(X2,X0,X1) ),
inference(ennf_transformation,[],[f17]) ).
fof(f17,axiom,
! [X0,X1,X2] :
( relation_of2_as_subset(X2,X0,X1)
=> element(X2,powerset(cartesian_product2(X0,X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m2_relset_1) ).
fof(f1259,plain,
spl30_146,
inference(avatar_split_clause,[],[f310,f1257]) ).
fof(f310,plain,
! [X0,X1] :
( finite(relation_image(X0,X1))
| ~ finite(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f147]) ).
fof(f147,plain,
! [X0,X1] :
( finite(relation_image(X0,X1))
| ~ finite(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(flattening,[],[f146]) ).
fof(f146,plain,
! [X0,X1] :
( finite(relation_image(X0,X1))
| ~ finite(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(ennf_transformation,[],[f22]) ).
fof(f22,axiom,
! [X0,X1] :
( ( finite(X1)
& function(X0)
& relation(X0) )
=> finite(relation_image(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc13_finset_1) ).
fof(f1255,plain,
spl30_145,
inference(avatar_split_clause,[],[f283,f1253]) ).
fof(f283,plain,
! [X0] :
( finite(relation_rng(X0))
| ~ finite(relation_dom(X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f133]) ).
fof(f133,plain,
! [X0] :
( finite(relation_rng(X0))
| ~ finite(relation_dom(X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(flattening,[],[f132]) ).
fof(f132,plain,
! [X0] :
( finite(relation_rng(X0))
| ~ finite(relation_dom(X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(ennf_transformation,[],[f72]) ).
fof(f72,axiom,
! [X0] :
( ( function(X0)
& relation(X0) )
=> ( finite(relation_dom(X0))
=> finite(relation_rng(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t26_finset_1) ).
fof(f1251,plain,
( spl30_144
| ~ spl30_13
| ~ spl30_84 ),
inference(avatar_split_clause,[],[f852,f788,f447,f1248]) ).
fof(f1248,plain,
( spl30_144
<=> relation(sK10) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_144])]) ).
fof(f852,plain,
( relation(sK10)
| ~ spl30_13
| ~ spl30_84 ),
inference(resolution,[],[f789,f449]) ).
fof(f1231,plain,
spl30_143,
inference(avatar_split_clause,[],[f324,f1229]) ).
fof(f324,plain,
! [X2,X0,X1] :
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f158]) ).
fof(f158,plain,
! [X0,X1,X2] :
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f78]) ).
fof(f78,axiom,
! [X0,X1,X2] :
~ ( empty(X2)
& element(X1,powerset(X2))
& in(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_subset) ).
fof(f1227,plain,
spl30_142,
inference(avatar_split_clause,[],[f281,f1225]) ).
fof(f1225,plain,
( spl30_142
<=> ! [X0] :
( ordinal(relation_dom(X0))
| ~ transfinite_sequence(X0)
| ~ function(X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_142])]) ).
fof(f281,plain,
! [X0] :
( ordinal(relation_dom(X0))
| ~ transfinite_sequence(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f129]) ).
fof(f129,plain,
! [X0] :
( ( ordinal(relation_dom(X0))
& epsilon_connected(relation_dom(X0))
& epsilon_transitive(relation_dom(X0)) )
| ~ transfinite_sequence(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(flattening,[],[f128]) ).
fof(f128,plain,
! [X0] :
( ( ordinal(relation_dom(X0))
& epsilon_connected(relation_dom(X0))
& epsilon_transitive(relation_dom(X0)) )
| ~ transfinite_sequence(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(ennf_transformation,[],[f29]) ).
fof(f29,axiom,
! [X0] :
( ( transfinite_sequence(X0)
& function(X0)
& relation(X0) )
=> ( ordinal(relation_dom(X0))
& epsilon_connected(relation_dom(X0))
& epsilon_transitive(relation_dom(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc5_ordinal1) ).
fof(f1223,plain,
spl30_141,
inference(avatar_split_clause,[],[f280,f1221]) ).
fof(f1221,plain,
( spl30_141
<=> ! [X0] :
( epsilon_connected(relation_dom(X0))
| ~ transfinite_sequence(X0)
| ~ function(X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_141])]) ).
fof(f280,plain,
! [X0] :
( epsilon_connected(relation_dom(X0))
| ~ transfinite_sequence(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f129]) ).
fof(f1219,plain,
spl30_140,
inference(avatar_split_clause,[],[f279,f1217]) ).
fof(f1217,plain,
( spl30_140
<=> ! [X0] :
( epsilon_transitive(relation_dom(X0))
| ~ transfinite_sequence(X0)
| ~ function(X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_140])]) ).
fof(f279,plain,
! [X0] :
( epsilon_transitive(relation_dom(X0))
| ~ transfinite_sequence(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f129]) ).
fof(f1215,plain,
spl30_139,
inference(avatar_split_clause,[],[f269,f1213]) ).
fof(f269,plain,
! [X0] :
( subset(X0,cartesian_product2(relation_dom(X0),relation_rng(X0)))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f117]) ).
fof(f117,plain,
! [X0] :
( subset(X0,cartesian_product2(relation_dom(X0),relation_rng(X0)))
| ~ relation(X0) ),
inference(ennf_transformation,[],[f71]) ).
fof(f71,axiom,
! [X0] :
( relation(X0)
=> subset(X0,cartesian_product2(relation_dom(X0),relation_rng(X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t21_relat_1) ).
fof(f1210,plain,
( spl30_138
| ~ spl30_64
| ~ spl30_83 ),
inference(avatar_split_clause,[],[f848,f784,f702,f1207]) ).
fof(f1207,plain,
( spl30_138
<=> function(sK29) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_138])]) ).
fof(f848,plain,
( function(sK29)
| ~ spl30_64
| ~ spl30_83 ),
inference(resolution,[],[f785,f704]) ).
fof(f1174,plain,
spl30_137,
inference(avatar_split_clause,[],[f323,f1172]) ).
fof(f323,plain,
! [X2,X0,X1] :
( relation_of2_as_subset(X2,X0,X1)
| ~ relation_of2(X2,X0,X1) ),
inference(cnf_transformation,[],[f184]) ).
fof(f184,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,[],[f64]) ).
fof(f64,axiom,
! [X0,X1,X2] :
( relation_of2_as_subset(X2,X0,X1)
<=> relation_of2(X2,X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_m2_relset_1) ).
fof(f1169,plain,
( spl30_136
| ~ spl30_32
| ~ spl30_83 ),
inference(avatar_split_clause,[],[f845,f784,f542,f1166]) ).
fof(f1166,plain,
( spl30_136
<=> function(sK17) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_136])]) ).
fof(f845,plain,
( function(sK17)
| ~ spl30_32
| ~ spl30_83 ),
inference(resolution,[],[f785,f544]) ).
fof(f1164,plain,
spl30_135,
inference(avatar_split_clause,[],[f322,f1162]) ).
fof(f322,plain,
! [X2,X0,X1] :
( relation_of2(X2,X0,X1)
| ~ relation_of2_as_subset(X2,X0,X1) ),
inference(cnf_transformation,[],[f184]) ).
fof(f1160,plain,
spl30_134,
inference(avatar_split_clause,[],[f320,f1158]) ).
fof(f320,plain,
! [X2,X0,X1] :
( relation(X2)
| ~ element(X2,powerset(cartesian_product2(X0,X1))) ),
inference(cnf_transformation,[],[f155]) ).
fof(f155,plain,
! [X0,X1,X2] :
( relation(X2)
| ~ element(X2,powerset(cartesian_product2(X0,X1))) ),
inference(ennf_transformation,[],[f7]) ).
fof(f7,axiom,
! [X0,X1,X2] :
( element(X2,powerset(cartesian_product2(X0,X1)))
=> relation(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_relset_1) ).
fof(f1156,plain,
spl30_133,
inference(avatar_split_clause,[],[f308,f1154]) ).
fof(f308,plain,
! [X0,X1] :
( finite(cartesian_product2(X0,X1))
| ~ finite(X1)
| ~ finite(X0) ),
inference(cnf_transformation,[],[f143]) ).
fof(f143,plain,
! [X0,X1] :
( finite(cartesian_product2(X0,X1))
| ~ finite(X1)
| ~ finite(X0) ),
inference(flattening,[],[f142]) ).
fof(f142,plain,
! [X0,X1] :
( finite(cartesian_product2(X0,X1))
| ~ finite(X1)
| ~ finite(X0) ),
inference(ennf_transformation,[],[f69]) ).
fof(f69,axiom,
! [X0,X1] :
( ( finite(X1)
& finite(X0) )
=> finite(cartesian_product2(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t19_finset_1) ).
fof(f1152,plain,
spl30_132,
inference(avatar_split_clause,[],[f307,f1150]) ).
fof(f1150,plain,
( spl30_132
<=> ! [X0,X1] :
( ~ empty(cartesian_product2(X0,X1))
| empty(X1)
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_132])]) ).
fof(f307,plain,
! [X0,X1] :
( ~ empty(cartesian_product2(X0,X1))
| empty(X1)
| empty(X0) ),
inference(cnf_transformation,[],[f141]) ).
fof(f141,plain,
! [X0,X1] :
( ~ empty(cartesian_product2(X0,X1))
| empty(X1)
| empty(X0) ),
inference(flattening,[],[f140]) ).
fof(f140,plain,
! [X0,X1] :
( ~ empty(cartesian_product2(X0,X1))
| empty(X1)
| empty(X0) ),
inference(ennf_transformation,[],[f28]) ).
fof(f28,axiom,
! [X0,X1] :
( ( ~ empty(X1)
& ~ empty(X0) )
=> ~ empty(cartesian_product2(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_subset_1) ).
fof(f1148,plain,
spl30_131,
inference(avatar_split_clause,[],[f306,f1146]) ).
fof(f306,plain,
! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(cnf_transformation,[],[f139]) ).
fof(f139,plain,
! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(flattening,[],[f138]) ).
fof(f138,plain,
! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(ennf_transformation,[],[f75]) ).
fof(f75,axiom,
! [X0,X1] :
( element(X0,X1)
=> ( in(X0,X1)
| empty(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_subset) ).
fof(f1144,plain,
spl30_130,
inference(avatar_split_clause,[],[f301,f1142]) ).
fof(f301,plain,
! [X0,X1] : relation_of2_as_subset(first_projection_as_func_of(X0,X1),cartesian_product2(X0,X1),X0),
inference(cnf_transformation,[],[f16]) ).
fof(f16,axiom,
! [X0,X1] :
( relation_of2_as_subset(first_projection_as_func_of(X0,X1),cartesian_product2(X0,X1),X0)
& quasi_total(first_projection_as_func_of(X0,X1),cartesian_product2(X0,X1),X0)
& function(first_projection_as_func_of(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k9_funct_3) ).
fof(f1140,plain,
spl30_129,
inference(avatar_split_clause,[],[f300,f1138]) ).
fof(f300,plain,
! [X0,X1] : quasi_total(first_projection_as_func_of(X0,X1),cartesian_product2(X0,X1),X0),
inference(cnf_transformation,[],[f16]) ).
fof(f1136,plain,
spl30_128,
inference(avatar_split_clause,[],[f252,f1134]) ).
fof(f252,plain,
! [X0,X1] :
( finite(X1)
| ~ element(X1,powerset(X0))
| ~ finite(X0) ),
inference(cnf_transformation,[],[f107]) ).
fof(f107,plain,
! [X0] :
( ! [X1] :
( finite(X1)
| ~ element(X1,powerset(X0)) )
| ~ finite(X0) ),
inference(ennf_transformation,[],[f9]) ).
fof(f9,axiom,
! [X0] :
( finite(X0)
=> ! [X1] :
( element(X1,powerset(X0))
=> finite(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc2_finset_1) ).
fof(f1112,plain,
( spl30_127
| ~ spl30_13
| ~ spl30_83 ),
inference(avatar_split_clause,[],[f844,f784,f447,f1109]) ).
fof(f844,plain,
( function(sK10)
| ~ spl30_13
| ~ spl30_83 ),
inference(resolution,[],[f785,f449]) ).
fof(f1069,plain,
( spl30_126
| ~ spl30_64
| ~ spl30_82 ),
inference(avatar_split_clause,[],[f840,f780,f702,f1066]) ).
fof(f1066,plain,
( spl30_126
<=> finite(sK29) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_126])]) ).
fof(f840,plain,
( finite(sK29)
| ~ spl30_64
| ~ spl30_82 ),
inference(resolution,[],[f781,f704]) ).
fof(f1064,plain,
spl30_125,
inference(avatar_split_clause,[],[f315,f1062]) ).
fof(f315,plain,
! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) ),
inference(cnf_transformation,[],[f152]) ).
fof(f152,plain,
! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) ),
inference(ennf_transformation,[],[f81]) ).
fof(f81,axiom,
! [X0,X1] :
~ ( empty(X1)
& X0 != X1
& empty(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_boole) ).
fof(f1060,plain,
spl30_124,
inference(avatar_split_clause,[],[f314,f1058]) ).
fof(f314,plain,
! [X0,X1] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f179]) ).
fof(f179,plain,
! [X0,X1] :
( ( element(X0,powerset(X1))
| ~ subset(X0,X1) )
& ( subset(X0,X1)
| ~ element(X0,powerset(X1)) ) ),
inference(nnf_transformation,[],[f76]) ).
fof(f76,axiom,
! [X0,X1] :
( element(X0,powerset(X1))
<=> subset(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_subset) ).
fof(f1056,plain,
spl30_123,
inference(avatar_split_clause,[],[f313,f1054]) ).
fof(f313,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f179]) ).
fof(f1052,plain,
spl30_122,
inference(avatar_split_clause,[],[f312,f1050]) ).
fof(f312,plain,
! [X0,X1] :
( finite(X0)
| ~ finite(X1)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f151]) ).
fof(f151,plain,
! [X0,X1] :
( finite(X0)
| ~ finite(X1)
| ~ subset(X0,X1) ),
inference(flattening,[],[f150]) ).
fof(f150,plain,
! [X0,X1] :
( finite(X0)
| ~ finite(X1)
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f67]) ).
fof(f67,axiom,
! [X0,X1] :
( ( finite(X1)
& subset(X0,X1) )
=> finite(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t13_finset_1) ).
fof(f1048,plain,
spl30_121,
inference(avatar_split_clause,[],[f274,f1046]) ).
fof(f1046,plain,
( spl30_121
<=> ! [X0] :
( ~ empty(relation_dom(X0))
| ~ relation(X0)
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_121])]) ).
fof(f274,plain,
! [X0] :
( ~ empty(relation_dom(X0))
| ~ relation(X0)
| empty(X0) ),
inference(cnf_transformation,[],[f123]) ).
fof(f123,plain,
! [X0] :
( ~ empty(relation_dom(X0))
| ~ relation(X0)
| empty(X0) ),
inference(flattening,[],[f122]) ).
fof(f122,plain,
! [X0] :
( ~ empty(relation_dom(X0))
| ~ relation(X0)
| empty(X0) ),
inference(ennf_transformation,[],[f30]) ).
fof(f30,axiom,
! [X0] :
( ( relation(X0)
& ~ empty(X0) )
=> ~ empty(relation_dom(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc5_relat_1) ).
fof(f1044,plain,
spl30_120,
inference(avatar_split_clause,[],[f273,f1042]) ).
fof(f1042,plain,
( spl30_120
<=> ! [X0] :
( ~ empty(relation_rng(X0))
| ~ relation(X0)
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_120])]) ).
fof(f273,plain,
! [X0] :
( ~ empty(relation_rng(X0))
| ~ relation(X0)
| empty(X0) ),
inference(cnf_transformation,[],[f121]) ).
fof(f121,plain,
! [X0] :
( ~ empty(relation_rng(X0))
| ~ relation(X0)
| empty(X0) ),
inference(flattening,[],[f120]) ).
fof(f120,plain,
! [X0] :
( ~ empty(relation_rng(X0))
| ~ relation(X0)
| empty(X0) ),
inference(ennf_transformation,[],[f32]) ).
fof(f32,axiom,
! [X0] :
( ( relation(X0)
& ~ empty(X0) )
=> ~ empty(relation_rng(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc6_relat_1) ).
fof(f1040,plain,
spl30_119,
inference(avatar_split_clause,[],[f257,f1038]) ).
fof(f257,plain,
! [X0,X1] :
( ordinal(X1)
| ~ element(X1,X0)
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f109]) ).
fof(f109,plain,
! [X0] :
( ! [X1] :
( ( ordinal(X1)
& epsilon_connected(X1)
& epsilon_transitive(X1) )
| ~ element(X1,X0) )
| ~ ordinal(X0) ),
inference(ennf_transformation,[],[f2]) ).
fof(f2,axiom,
! [X0] :
( ordinal(X0)
=> ! [X1] :
( element(X1,X0)
=> ( ordinal(X1)
& epsilon_connected(X1)
& epsilon_transitive(X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_arytm_3) ).
fof(f1036,plain,
spl30_118,
inference(avatar_split_clause,[],[f256,f1034]) ).
fof(f256,plain,
! [X0,X1] :
( epsilon_connected(X1)
| ~ element(X1,X0)
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f109]) ).
fof(f1032,plain,
spl30_117,
inference(avatar_split_clause,[],[f255,f1030]) ).
fof(f255,plain,
! [X0,X1] :
( epsilon_transitive(X1)
| ~ element(X1,X0)
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f109]) ).
fof(f1028,plain,
spl30_116,
inference(avatar_split_clause,[],[f249,f1026]) ).
fof(f249,plain,
! [X0] :
( element(sK3(X0),powerset(X0))
| empty(X0) ),
inference(cnf_transformation,[],[f172]) ).
fof(f172,plain,
! [X0] :
( ( finite(sK3(X0))
& ~ empty(sK3(X0))
& element(sK3(X0),powerset(X0)) )
| empty(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f106,f171]) ).
fof(f171,plain,
! [X0] :
( ? [X1] :
( finite(X1)
& ~ empty(X1)
& element(X1,powerset(X0)) )
=> ( finite(sK3(X0))
& ~ empty(sK3(X0))
& element(sK3(X0),powerset(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f106,plain,
! [X0] :
( ? [X1] :
( finite(X1)
& ~ empty(X1)
& element(X1,powerset(X0)) )
| empty(X0) ),
inference(ennf_transformation,[],[f58]) ).
fof(f58,axiom,
! [X0] :
( ~ empty(X0)
=> ? [X1] :
( finite(X1)
& ~ empty(X1)
& element(X1,powerset(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc4_finset_1) ).
fof(f1023,plain,
( spl30_115
| ~ spl30_58
| ~ spl30_82 ),
inference(avatar_split_clause,[],[f839,f780,f672,f1020]) ).
fof(f1020,plain,
( spl30_115
<=> finite(sK27) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_115])]) ).
fof(f839,plain,
( finite(sK27)
| ~ spl30_58
| ~ spl30_82 ),
inference(resolution,[],[f781,f674]) ).
fof(f1018,plain,
spl30_114,
inference(avatar_split_clause,[],[f246,f1016]) ).
fof(f246,plain,
! [X0] :
( element(sK2(X0),powerset(X0))
| empty(X0) ),
inference(cnf_transformation,[],[f170]) ).
fof(f170,plain,
! [X0] :
( ( finite(sK2(X0))
& ~ empty(sK2(X0))
& element(sK2(X0),powerset(X0)) )
| empty(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f105,f169]) ).
fof(f169,plain,
! [X0] :
( ? [X1] :
( finite(X1)
& ~ empty(X1)
& element(X1,powerset(X0)) )
=> ( finite(sK2(X0))
& ~ empty(sK2(X0))
& element(sK2(X0),powerset(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f105,plain,
! [X0] :
( ? [X1] :
( finite(X1)
& ~ empty(X1)
& element(X1,powerset(X0)) )
| empty(X0) ),
inference(ennf_transformation,[],[f54]) ).
fof(f54,axiom,
! [X0] :
( ~ empty(X0)
=> ? [X1] :
( finite(X1)
& ~ empty(X1)
& element(X1,powerset(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_finset_1) ).
fof(f1014,plain,
spl30_113,
inference(avatar_split_clause,[],[f244,f1012]) ).
fof(f244,plain,
! [X0] :
( element(sK1(X0),powerset(X0))
| empty(X0) ),
inference(cnf_transformation,[],[f168]) ).
fof(f168,plain,
! [X0] :
( ( ~ empty(sK1(X0))
& element(sK1(X0),powerset(X0)) )
| empty(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f104,f167]) ).
fof(f167,plain,
! [X0] :
( ? [X1] :
( ~ empty(X1)
& element(X1,powerset(X0)) )
=> ( ~ empty(sK1(X0))
& element(sK1(X0),powerset(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f104,plain,
! [X0] :
( ? [X1] :
( ~ empty(X1)
& element(X1,powerset(X0)) )
| empty(X0) ),
inference(ennf_transformation,[],[f43]) ).
fof(f43,axiom,
! [X0] :
( ~ empty(X0)
=> ? [X1] :
( ~ empty(X1)
& element(X1,powerset(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_subset_1) ).
fof(f1001,plain,
spl30_112,
inference(avatar_split_clause,[],[f318,f999]) ).
fof(f318,plain,
! [X0,X1] : relation_of2_as_subset(sK8(X0,X1),X0,X1),
inference(cnf_transformation,[],[f183]) ).
fof(f183,plain,
! [X0,X1] : relation_of2_as_subset(sK8(X0,X1),X0,X1),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK8])],[f20,f182]) ).
fof(f182,plain,
! [X0,X1] :
( ? [X2] : relation_of2_as_subset(X2,X0,X1)
=> relation_of2_as_subset(sK8(X0,X1),X0,X1) ),
introduced(choice_axiom,[]) ).
fof(f20,axiom,
! [X0,X1] :
? [X2] : relation_of2_as_subset(X2,X0,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m2_relset_1) ).
fof(f997,plain,
spl30_111,
inference(avatar_split_clause,[],[f317,f995]) ).
fof(f317,plain,
! [X0,X1] : relation_of2(sK7(X0,X1),X0,X1),
inference(cnf_transformation,[],[f181]) ).
fof(f181,plain,
! [X0,X1] : relation_of2(sK7(X0,X1),X0,X1),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK7])],[f18,f180]) ).
fof(f180,plain,
! [X0,X1] :
( ? [X2] : relation_of2(X2,X0,X1)
=> relation_of2(sK7(X0,X1),X0,X1) ),
introduced(choice_axiom,[]) ).
fof(f18,axiom,
! [X0,X1] :
? [X2] : relation_of2(X2,X0,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_relset_1) ).
fof(f993,plain,
spl30_110,
inference(avatar_split_clause,[],[f305,f991]) ).
fof(f991,plain,
( spl30_110
<=> ! [X0,X1] :
( element(X0,X1)
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_110])]) ).
fof(f305,plain,
! [X0,X1] :
( element(X0,X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f137]) ).
fof(f137,plain,
! [X0,X1] :
( element(X0,X1)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f70]) ).
fof(f70,axiom,
! [X0,X1] :
( in(X0,X1)
=> element(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_subset) ).
fof(f988,plain,
( spl30_109
| ~ spl30_53
| ~ spl30_82 ),
inference(avatar_split_clause,[],[f838,f780,f647,f985]) ).
fof(f985,plain,
( spl30_109
<=> finite(sK26) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_109])]) ).
fof(f838,plain,
( finite(sK26)
| ~ spl30_53
| ~ spl30_82 ),
inference(resolution,[],[f781,f649]) ).
fof(f983,plain,
spl30_108,
inference(avatar_split_clause,[],[f304,f981]) ).
fof(f304,plain,
! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f136]) ).
fof(f136,plain,
! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f1]) ).
fof(f1,axiom,
! [X0,X1] :
( in(X0,X1)
=> ~ in(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
fof(f979,plain,
spl30_107,
inference(avatar_split_clause,[],[f275,f977]) ).
fof(f977,plain,
( spl30_107
<=> ! [X0] :
( ordinal(X0)
| ~ epsilon_connected(X0)
| ~ epsilon_transitive(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_107])]) ).
fof(f275,plain,
! [X0] :
( ordinal(X0)
| ~ epsilon_connected(X0)
| ~ epsilon_transitive(X0) ),
inference(cnf_transformation,[],[f125]) ).
fof(f125,plain,
! [X0] :
( ordinal(X0)
| ~ epsilon_connected(X0)
| ~ epsilon_transitive(X0) ),
inference(flattening,[],[f124]) ).
fof(f124,plain,
! [X0] :
( ordinal(X0)
| ~ epsilon_connected(X0)
| ~ epsilon_transitive(X0) ),
inference(ennf_transformation,[],[f11]) ).
fof(f11,axiom,
! [X0] :
( ( epsilon_connected(X0)
& epsilon_transitive(X0) )
=> ordinal(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc2_ordinal1) ).
fof(f947,plain,
( spl30_106
| ~ spl30_32
| ~ spl30_82 ),
inference(avatar_split_clause,[],[f837,f780,f542,f944]) ).
fof(f944,plain,
( spl30_106
<=> finite(sK17) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_106])]) ).
fof(f837,plain,
( finite(sK17)
| ~ spl30_32
| ~ spl30_82 ),
inference(resolution,[],[f781,f544]) ).
fof(f942,plain,
spl30_105,
inference(avatar_split_clause,[],[f316,f940]) ).
fof(f940,plain,
( spl30_105
<=> ! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_105])]) ).
fof(f316,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f153]) ).
fof(f153,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f80]) ).
fof(f80,axiom,
! [X0,X1] :
~ ( empty(X1)
& in(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).
fof(f938,plain,
spl30_104,
inference(avatar_split_clause,[],[f289,f936]) ).
fof(f936,plain,
( spl30_104
<=> ! [X0] : element(sK6(X0),powerset(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_104])]) ).
fof(f289,plain,
! [X0] : element(sK6(X0),powerset(X0)),
inference(cnf_transformation,[],[f178]) ).
fof(f178,plain,
! [X0] :
( finite(sK6(X0))
& ordinal(sK6(X0))
& epsilon_connected(sK6(X0))
& epsilon_transitive(sK6(X0))
& function(sK6(X0))
& relation(sK6(X0))
& empty(sK6(X0))
& element(sK6(X0),powerset(X0)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6])],[f101,f177]) ).
fof(f177,plain,
! [X0] :
( ? [X1] :
( finite(X1)
& ordinal(X1)
& epsilon_connected(X1)
& epsilon_transitive(X1)
& function(X1)
& relation(X1)
& empty(X1)
& element(X1,powerset(X0)) )
=> ( finite(sK6(X0))
& ordinal(sK6(X0))
& epsilon_connected(sK6(X0))
& epsilon_transitive(sK6(X0))
& function(sK6(X0))
& relation(sK6(X0))
& empty(sK6(X0))
& element(sK6(X0),powerset(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f101,plain,
! [X0] :
? [X1] :
( finite(X1)
& ordinal(X1)
& epsilon_connected(X1)
& epsilon_transitive(X1)
& function(X1)
& relation(X1)
& empty(X1)
& element(X1,powerset(X0)) ),
inference(pure_predicate_removal,[],[f93]) ).
fof(f93,plain,
! [X0] :
? [X1] :
( finite(X1)
& natural(X1)
& ordinal(X1)
& epsilon_connected(X1)
& epsilon_transitive(X1)
& function(X1)
& relation(X1)
& empty(X1)
& element(X1,powerset(X0)) ),
inference(pure_predicate_removal,[],[f46]) ).
fof(f46,axiom,
! [X0] :
? [X1] :
( finite(X1)
& natural(X1)
& ordinal(X1)
& epsilon_connected(X1)
& epsilon_transitive(X1)
& one_to_one(X1)
& function(X1)
& relation(X1)
& empty(X1)
& element(X1,powerset(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_finset_1) ).
fof(f934,plain,
spl30_103,
inference(avatar_split_clause,[],[f287,f932]) ).
fof(f287,plain,
! [X0] : element(sK5(X0),powerset(X0)),
inference(cnf_transformation,[],[f176]) ).
fof(f176,plain,
! [X0] :
( empty(sK5(X0))
& element(sK5(X0),powerset(X0)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5])],[f51,f175]) ).
fof(f175,plain,
! [X0] :
( ? [X1] :
( empty(X1)
& element(X1,powerset(X0)) )
=> ( empty(sK5(X0))
& element(sK5(X0),powerset(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f51,axiom,
! [X0] :
? [X1] :
( empty(X1)
& element(X1,powerset(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_subset_1) ).
fof(f930,plain,
spl30_102,
inference(avatar_split_clause,[],[f268,f928]) ).
fof(f268,plain,
! [X0] :
( relation(relation_dom(X0))
| ~ empty(X0) ),
inference(cnf_transformation,[],[f116]) ).
fof(f116,plain,
! [X0] :
( ( relation(relation_dom(X0))
& empty(relation_dom(X0)) )
| ~ empty(X0) ),
inference(ennf_transformation,[],[f33]) ).
fof(f33,axiom,
! [X0] :
( empty(X0)
=> ( relation(relation_dom(X0))
& empty(relation_dom(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc7_relat_1) ).
fof(f926,plain,
spl30_101,
inference(avatar_split_clause,[],[f267,f924]) ).
fof(f267,plain,
! [X0] :
( empty(relation_dom(X0))
| ~ empty(X0) ),
inference(cnf_transformation,[],[f116]) ).
fof(f922,plain,
( spl30_100
| ~ spl30_13
| ~ spl30_82 ),
inference(avatar_split_clause,[],[f836,f780,f447,f919]) ).
fof(f919,plain,
( spl30_100
<=> finite(sK10) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_100])]) ).
fof(f836,plain,
( finite(sK10)
| ~ spl30_13
| ~ spl30_82 ),
inference(resolution,[],[f781,f449]) ).
fof(f917,plain,
spl30_99,
inference(avatar_split_clause,[],[f266,f915]) ).
fof(f266,plain,
! [X0] :
( relation(relation_rng(X0))
| ~ empty(X0) ),
inference(cnf_transformation,[],[f115]) ).
fof(f115,plain,
! [X0] :
( ( relation(relation_rng(X0))
& empty(relation_rng(X0)) )
| ~ empty(X0) ),
inference(ennf_transformation,[],[f35]) ).
fof(f35,axiom,
! [X0] :
( empty(X0)
=> ( relation(relation_rng(X0))
& empty(relation_rng(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc8_relat_1) ).
fof(f913,plain,
spl30_98,
inference(avatar_split_clause,[],[f265,f911]) ).
fof(f265,plain,
! [X0] :
( empty(relation_rng(X0))
| ~ empty(X0) ),
inference(cnf_transformation,[],[f115]) ).
fof(f909,plain,
spl30_97,
inference(avatar_split_clause,[],[f261,f907]) ).
fof(f261,plain,
! [X0] :
( empty_set = X0
| ~ empty(X0) ),
inference(cnf_transformation,[],[f113]) ).
fof(f113,plain,
! [X0] :
( empty_set = X0
| ~ empty(X0) ),
inference(ennf_transformation,[],[f79]) ).
fof(f79,axiom,
! [X0] :
( empty(X0)
=> empty_set = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).
fof(f905,plain,
spl30_96,
inference(avatar_split_clause,[],[f251,f903]) ).
fof(f903,plain,
( spl30_96
<=> ! [X0] :
( finite(sK3(X0))
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_96])]) ).
fof(f251,plain,
! [X0] :
( finite(sK3(X0))
| empty(X0) ),
inference(cnf_transformation,[],[f172]) ).
fof(f901,plain,
spl30_95,
inference(avatar_split_clause,[],[f250,f899]) ).
fof(f899,plain,
( spl30_95
<=> ! [X0] :
( ~ empty(sK3(X0))
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_95])]) ).
fof(f250,plain,
! [X0] :
( ~ empty(sK3(X0))
| empty(X0) ),
inference(cnf_transformation,[],[f172]) ).
fof(f897,plain,
spl30_94,
inference(avatar_split_clause,[],[f248,f895]) ).
fof(f895,plain,
( spl30_94
<=> ! [X0] :
( finite(sK2(X0))
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_94])]) ).
fof(f248,plain,
! [X0] :
( finite(sK2(X0))
| empty(X0) ),
inference(cnf_transformation,[],[f170]) ).
fof(f893,plain,
spl30_93,
inference(avatar_split_clause,[],[f247,f891]) ).
fof(f891,plain,
( spl30_93
<=> ! [X0] :
( ~ empty(sK2(X0))
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_93])]) ).
fof(f247,plain,
! [X0] :
( ~ empty(sK2(X0))
| empty(X0) ),
inference(cnf_transformation,[],[f170]) ).
fof(f889,plain,
spl30_92,
inference(avatar_split_clause,[],[f245,f887]) ).
fof(f887,plain,
( spl30_92
<=> ! [X0] :
( ~ empty(sK1(X0))
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_92])]) ).
fof(f245,plain,
! [X0] :
( ~ empty(sK1(X0))
| empty(X0) ),
inference(cnf_transformation,[],[f168]) ).
fof(f885,plain,
( spl30_91
| ~ spl30_6
| ~ spl30_82 ),
inference(avatar_split_clause,[],[f833,f780,f412,f882]) ).
fof(f882,plain,
( spl30_91
<=> finite(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_91])]) ).
fof(f833,plain,
( finite(empty_set)
| ~ spl30_6
| ~ spl30_82 ),
inference(resolution,[],[f781,f414]) ).
fof(f814,plain,
spl30_90,
inference(avatar_split_clause,[],[f386,f812]) ).
fof(f386,plain,
! [X0,X1] : relation(first_projection_as_func_of(X0,X1)),
inference(definition_unfolding,[],[f302,f298]) ).
fof(f298,plain,
! [X0,X1] : first_projection(X0,X1) = first_projection_as_func_of(X0,X1),
inference(cnf_transformation,[],[f63]) ).
fof(f63,axiom,
! [X0,X1] : first_projection(X0,X1) = first_projection_as_func_of(X0,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k9_funct_3) ).
fof(f302,plain,
! [X0,X1] : relation(first_projection(X0,X1)),
inference(cnf_transformation,[],[f15]) ).
fof(f15,axiom,
! [X0,X1] :
( function(first_projection(X0,X1))
& relation(first_projection(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k7_funct_3) ).
fof(f810,plain,
spl30_89,
inference(avatar_split_clause,[],[f299,f808]) ).
fof(f299,plain,
! [X0,X1] : function(first_projection_as_func_of(X0,X1)),
inference(cnf_transformation,[],[f16]) ).
fof(f806,plain,
spl30_88,
inference(avatar_split_clause,[],[f286,f804]) ).
fof(f286,plain,
! [X0] : element(sK4(X0),X0),
inference(cnf_transformation,[],[f174]) ).
fof(f174,plain,
! [X0] : element(sK4(X0),X0),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f19,f173]) ).
fof(f173,plain,
! [X0] :
( ? [X1] : element(X1,X0)
=> element(sK4(X0),X0) ),
introduced(choice_axiom,[]) ).
fof(f19,axiom,
! [X0] :
? [X1] : element(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_subset_1) ).
fof(f802,plain,
spl30_87,
inference(avatar_split_clause,[],[f264,f800]) ).
fof(f264,plain,
! [X0] :
( ordinal(X0)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f114]) ).
fof(f114,plain,
! [X0] :
( ( ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0) )
| ~ empty(X0) ),
inference(ennf_transformation,[],[f12]) ).
fof(f12,axiom,
! [X0] :
( empty(X0)
=> ( ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc3_ordinal1) ).
fof(f798,plain,
spl30_86,
inference(avatar_split_clause,[],[f263,f796]) ).
fof(f263,plain,
! [X0] :
( epsilon_connected(X0)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f114]) ).
fof(f794,plain,
spl30_85,
inference(avatar_split_clause,[],[f262,f792]) ).
fof(f262,plain,
! [X0] :
( epsilon_transitive(X0)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f114]) ).
fof(f790,plain,
spl30_84,
inference(avatar_split_clause,[],[f260,f788]) ).
fof(f260,plain,
! [X0] :
( relation(X0)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f112]) ).
fof(f112,plain,
! [X0] :
( relation(X0)
| ~ empty(X0) ),
inference(ennf_transformation,[],[f6]) ).
fof(f6,axiom,
! [X0] :
( empty(X0)
=> relation(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_relat_1) ).
fof(f786,plain,
spl30_83,
inference(avatar_split_clause,[],[f259,f784]) ).
fof(f259,plain,
! [X0] :
( function(X0)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f111]) ).
fof(f111,plain,
! [X0] :
( function(X0)
| ~ empty(X0) ),
inference(ennf_transformation,[],[f4]) ).
fof(f4,axiom,
! [X0] :
( empty(X0)
=> function(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_funct_1) ).
fof(f782,plain,
spl30_82,
inference(avatar_split_clause,[],[f258,f780]) ).
fof(f258,plain,
! [X0] :
( finite(X0)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f110]) ).
fof(f110,plain,
! [X0] :
( finite(X0)
| ~ empty(X0) ),
inference(ennf_transformation,[],[f3]) ).
fof(f3,axiom,
! [X0] :
( empty(X0)
=> finite(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_finset_1) ).
fof(f778,plain,
spl30_81,
inference(avatar_split_clause,[],[f254,f776]) ).
fof(f776,plain,
( spl30_81
<=> ! [X0] :
( epsilon_connected(X0)
| ~ ordinal(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_81])]) ).
fof(f254,plain,
! [X0] :
( epsilon_connected(X0)
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f108]) ).
fof(f108,plain,
! [X0] :
( ( epsilon_connected(X0)
& epsilon_transitive(X0) )
| ~ ordinal(X0) ),
inference(ennf_transformation,[],[f5]) ).
fof(f5,axiom,
! [X0] :
( ordinal(X0)
=> ( epsilon_connected(X0)
& epsilon_transitive(X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_ordinal1) ).
fof(f774,plain,
spl30_80,
inference(avatar_split_clause,[],[f253,f772]) ).
fof(f772,plain,
( spl30_80
<=> ! [X0] :
( epsilon_transitive(X0)
| ~ ordinal(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_80])]) ).
fof(f253,plain,
! [X0] :
( epsilon_transitive(X0)
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f108]) ).
fof(f770,plain,
spl30_79,
inference(avatar_split_clause,[],[f380,f767]) ).
fof(f380,plain,
element(sK29,positive_rationals),
inference(cnf_transformation,[],[f226]) ).
fof(f226,plain,
( ordinal(sK29)
& epsilon_connected(sK29)
& epsilon_transitive(sK29)
& empty(sK29)
& element(sK29,positive_rationals) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK29])],[f99,f225]) ).
fof(f225,plain,
( ? [X0] :
( ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0)
& empty(X0)
& element(X0,positive_rationals) )
=> ( ordinal(sK29)
& epsilon_connected(sK29)
& epsilon_transitive(sK29)
& empty(sK29)
& element(sK29,positive_rationals) ) ),
introduced(choice_axiom,[]) ).
fof(f99,plain,
? [X0] :
( ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0)
& empty(X0)
& element(X0,positive_rationals) ),
inference(pure_predicate_removal,[],[f53]) ).
fof(f53,axiom,
? [X0] :
( natural(X0)
& ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0)
& empty(X0)
& element(X0,positive_rationals) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_arytm_3) ).
fof(f765,plain,
spl30_78,
inference(avatar_split_clause,[],[f375,f762]) ).
fof(f375,plain,
element(sK28,positive_rationals),
inference(cnf_transformation,[],[f224]) ).
fof(f224,plain,
( ordinal(sK28)
& epsilon_connected(sK28)
& epsilon_transitive(sK28)
& ~ empty(sK28)
& element(sK28,positive_rationals) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK28])],[f45,f223]) ).
fof(f223,plain,
( ? [X0] :
( ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0)
& ~ empty(X0)
& element(X0,positive_rationals) )
=> ( ordinal(sK28)
& epsilon_connected(sK28)
& epsilon_transitive(sK28)
& ~ empty(sK28)
& element(sK28,positive_rationals) ) ),
introduced(choice_axiom,[]) ).
fof(f45,axiom,
? [X0] :
( ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0)
& ~ empty(X0)
& element(X0,positive_rationals) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_arytm_3) ).
fof(f760,plain,
spl30_77,
inference(avatar_split_clause,[],[f297,f758]) ).
fof(f297,plain,
! [X0] : subset(X0,X0),
inference(cnf_transformation,[],[f82]) ).
fof(f82,plain,
! [X0] : subset(X0,X0),
inference(rectify,[],[f65]) ).
fof(f65,axiom,
! [X0,X1] : subset(X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(f756,plain,
spl30_76,
inference(avatar_split_clause,[],[f296,f754]) ).
fof(f754,plain,
( spl30_76
<=> ! [X0] : finite(sK6(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_76])]) ).
fof(f296,plain,
! [X0] : finite(sK6(X0)),
inference(cnf_transformation,[],[f178]) ).
fof(f752,plain,
spl30_75,
inference(avatar_split_clause,[],[f295,f750]) ).
fof(f750,plain,
( spl30_75
<=> ! [X0] : ordinal(sK6(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_75])]) ).
fof(f295,plain,
! [X0] : ordinal(sK6(X0)),
inference(cnf_transformation,[],[f178]) ).
fof(f748,plain,
spl30_74,
inference(avatar_split_clause,[],[f294,f746]) ).
fof(f746,plain,
( spl30_74
<=> ! [X0] : epsilon_connected(sK6(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_74])]) ).
fof(f294,plain,
! [X0] : epsilon_connected(sK6(X0)),
inference(cnf_transformation,[],[f178]) ).
fof(f744,plain,
spl30_73,
inference(avatar_split_clause,[],[f293,f742]) ).
fof(f742,plain,
( spl30_73
<=> ! [X0] : epsilon_transitive(sK6(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_73])]) ).
fof(f293,plain,
! [X0] : epsilon_transitive(sK6(X0)),
inference(cnf_transformation,[],[f178]) ).
fof(f740,plain,
spl30_72,
inference(avatar_split_clause,[],[f292,f738]) ).
fof(f738,plain,
( spl30_72
<=> ! [X0] : function(sK6(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_72])]) ).
fof(f292,plain,
! [X0] : function(sK6(X0)),
inference(cnf_transformation,[],[f178]) ).
fof(f736,plain,
spl30_71,
inference(avatar_split_clause,[],[f291,f734]) ).
fof(f734,plain,
( spl30_71
<=> ! [X0] : relation(sK6(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_71])]) ).
fof(f291,plain,
! [X0] : relation(sK6(X0)),
inference(cnf_transformation,[],[f178]) ).
fof(f732,plain,
spl30_70,
inference(avatar_split_clause,[],[f290,f730]) ).
fof(f290,plain,
! [X0] : empty(sK6(X0)),
inference(cnf_transformation,[],[f178]) ).
fof(f728,plain,
spl30_69,
inference(avatar_split_clause,[],[f288,f726]) ).
fof(f288,plain,
! [X0] : empty(sK5(X0)),
inference(cnf_transformation,[],[f176]) ).
fof(f724,plain,
spl30_68,
inference(avatar_split_clause,[],[f243,f722]) ).
fof(f722,plain,
( spl30_68
<=> ! [X0] : ~ empty(powerset(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_68])]) ).
fof(f243,plain,
! [X0] : ~ empty(powerset(X0)),
inference(cnf_transformation,[],[f24]) ).
fof(f24,axiom,
! [X0] : ~ empty(powerset(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_subset_1) ).
fof(f720,plain,
spl30_67,
inference(avatar_split_clause,[],[f384,f717]) ).
fof(f717,plain,
( spl30_67
<=> ordinal(sK29) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_67])]) ).
fof(f384,plain,
ordinal(sK29),
inference(cnf_transformation,[],[f226]) ).
fof(f715,plain,
spl30_66,
inference(avatar_split_clause,[],[f383,f712]) ).
fof(f712,plain,
( spl30_66
<=> epsilon_connected(sK29) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_66])]) ).
fof(f383,plain,
epsilon_connected(sK29),
inference(cnf_transformation,[],[f226]) ).
fof(f710,plain,
spl30_65,
inference(avatar_split_clause,[],[f382,f707]) ).
fof(f707,plain,
( spl30_65
<=> epsilon_transitive(sK29) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_65])]) ).
fof(f382,plain,
epsilon_transitive(sK29),
inference(cnf_transformation,[],[f226]) ).
fof(f705,plain,
spl30_64,
inference(avatar_split_clause,[],[f381,f702]) ).
fof(f381,plain,
empty(sK29),
inference(cnf_transformation,[],[f226]) ).
fof(f700,plain,
spl30_63,
inference(avatar_split_clause,[],[f379,f697]) ).
fof(f697,plain,
( spl30_63
<=> ordinal(sK28) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_63])]) ).
fof(f379,plain,
ordinal(sK28),
inference(cnf_transformation,[],[f224]) ).
fof(f695,plain,
spl30_62,
inference(avatar_split_clause,[],[f378,f692]) ).
fof(f692,plain,
( spl30_62
<=> epsilon_connected(sK28) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_62])]) ).
fof(f378,plain,
epsilon_connected(sK28),
inference(cnf_transformation,[],[f224]) ).
fof(f690,plain,
spl30_61,
inference(avatar_split_clause,[],[f377,f687]) ).
fof(f687,plain,
( spl30_61
<=> epsilon_transitive(sK28) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_61])]) ).
fof(f377,plain,
epsilon_transitive(sK28),
inference(cnf_transformation,[],[f224]) ).
fof(f685,plain,
~ spl30_60,
inference(avatar_split_clause,[],[f376,f682]) ).
fof(f682,plain,
( spl30_60
<=> empty(sK28) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_60])]) ).
fof(f376,plain,
~ empty(sK28),
inference(cnf_transformation,[],[f224]) ).
fof(f680,plain,
spl30_59,
inference(avatar_split_clause,[],[f374,f677]) ).
fof(f677,plain,
( spl30_59
<=> function(sK27) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_59])]) ).
fof(f374,plain,
function(sK27),
inference(cnf_transformation,[],[f222]) ).
fof(f222,plain,
( function(sK27)
& empty(sK27)
& relation(sK27) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK27])],[f47,f221]) ).
fof(f221,plain,
( ? [X0] :
( function(X0)
& empty(X0)
& relation(X0) )
=> ( function(sK27)
& empty(sK27)
& relation(sK27) ) ),
introduced(choice_axiom,[]) ).
fof(f47,axiom,
? [X0] :
( function(X0)
& empty(X0)
& relation(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_funct_1) ).
fof(f675,plain,
spl30_58,
inference(avatar_split_clause,[],[f373,f672]) ).
fof(f373,plain,
empty(sK27),
inference(cnf_transformation,[],[f222]) ).
fof(f670,plain,
spl30_57,
inference(avatar_split_clause,[],[f372,f667]) ).
fof(f667,plain,
( spl30_57
<=> relation(sK27) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_57])]) ).
fof(f372,plain,
relation(sK27),
inference(cnf_transformation,[],[f222]) ).
fof(f665,plain,
spl30_56,
inference(avatar_split_clause,[],[f371,f662]) ).
fof(f662,plain,
( spl30_56
<=> ordinal(sK26) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_56])]) ).
fof(f371,plain,
ordinal(sK26),
inference(cnf_transformation,[],[f220]) ).
fof(f220,plain,
( ordinal(sK26)
& epsilon_connected(sK26)
& epsilon_transitive(sK26)
& empty(sK26)
& function(sK26)
& relation(sK26) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK26])],[f94,f219]) ).
fof(f219,plain,
( ? [X0] :
( ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0)
& empty(X0)
& function(X0)
& relation(X0) )
=> ( ordinal(sK26)
& epsilon_connected(sK26)
& epsilon_transitive(sK26)
& empty(sK26)
& function(sK26)
& relation(sK26) ) ),
introduced(choice_axiom,[]) ).
fof(f94,plain,
? [X0] :
( ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0)
& empty(X0)
& function(X0)
& relation(X0) ),
inference(pure_predicate_removal,[],[f48]) ).
fof(f48,axiom,
? [X0] :
( ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0)
& empty(X0)
& one_to_one(X0)
& function(X0)
& relation(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_ordinal1) ).
fof(f660,plain,
spl30_55,
inference(avatar_split_clause,[],[f370,f657]) ).
fof(f657,plain,
( spl30_55
<=> epsilon_connected(sK26) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_55])]) ).
fof(f370,plain,
epsilon_connected(sK26),
inference(cnf_transformation,[],[f220]) ).
fof(f655,plain,
spl30_54,
inference(avatar_split_clause,[],[f369,f652]) ).
fof(f652,plain,
( spl30_54
<=> epsilon_transitive(sK26) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_54])]) ).
fof(f369,plain,
epsilon_transitive(sK26),
inference(cnf_transformation,[],[f220]) ).
fof(f650,plain,
spl30_53,
inference(avatar_split_clause,[],[f368,f647]) ).
fof(f368,plain,
empty(sK26),
inference(cnf_transformation,[],[f220]) ).
fof(f645,plain,
spl30_52,
inference(avatar_split_clause,[],[f367,f642]) ).
fof(f642,plain,
( spl30_52
<=> function(sK26) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_52])]) ).
fof(f367,plain,
function(sK26),
inference(cnf_transformation,[],[f220]) ).
fof(f640,plain,
spl30_51,
inference(avatar_split_clause,[],[f366,f637]) ).
fof(f637,plain,
( spl30_51
<=> relation(sK26) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_51])]) ).
fof(f366,plain,
relation(sK26),
inference(cnf_transformation,[],[f220]) ).
fof(f635,plain,
spl30_50,
inference(avatar_split_clause,[],[f365,f632]) ).
fof(f365,plain,
function(sK25),
inference(cnf_transformation,[],[f218]) ).
fof(f218,plain,
( function(sK25)
& relation(sK25) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK25])],[f96,f217]) ).
fof(f217,plain,
( ? [X0] :
( function(X0)
& relation(X0) )
=> ( function(sK25)
& relation(sK25) ) ),
introduced(choice_axiom,[]) ).
fof(f96,plain,
? [X0] :
( function(X0)
& relation(X0) ),
inference(pure_predicate_removal,[],[f55]) ).
fof(f55,axiom,
? [X0] :
( one_to_one(X0)
& function(X0)
& relation(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_funct_1) ).
fof(f630,plain,
spl30_49,
inference(avatar_split_clause,[],[f364,f627]) ).
fof(f364,plain,
relation(sK25),
inference(cnf_transformation,[],[f218]) ).
fof(f625,plain,
spl30_48,
inference(avatar_split_clause,[],[f363,f622]) ).
fof(f622,plain,
( spl30_48
<=> transfinite_sequence(sK24) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_48])]) ).
fof(f363,plain,
transfinite_sequence(sK24),
inference(cnf_transformation,[],[f216]) ).
fof(f216,plain,
( transfinite_sequence(sK24)
& function(sK24)
& relation(sK24) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK24])],[f83,f215]) ).
fof(f215,plain,
( ? [X0] :
( transfinite_sequence(X0)
& function(X0)
& relation(X0) )
=> ( transfinite_sequence(sK24)
& function(sK24)
& relation(sK24) ) ),
introduced(choice_axiom,[]) ).
fof(f83,plain,
? [X0] :
( transfinite_sequence(X0)
& function(X0)
& relation(X0) ),
inference(pure_predicate_removal,[],[f49]) ).
fof(f49,axiom,
? [X0] :
( ordinal_yielding(X0)
& transfinite_sequence(X0)
& function(X0)
& relation(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_ordinal2) ).
fof(f620,plain,
spl30_47,
inference(avatar_split_clause,[],[f362,f617]) ).
fof(f362,plain,
function(sK24),
inference(cnf_transformation,[],[f216]) ).
fof(f615,plain,
spl30_46,
inference(avatar_split_clause,[],[f361,f612]) ).
fof(f361,plain,
relation(sK24),
inference(cnf_transformation,[],[f216]) ).
fof(f610,plain,
spl30_45,
inference(avatar_split_clause,[],[f360,f607]) ).
fof(f607,plain,
( spl30_45
<=> transfinite_sequence(sK23) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_45])]) ).
fof(f360,plain,
transfinite_sequence(sK23),
inference(cnf_transformation,[],[f214]) ).
fof(f214,plain,
( transfinite_sequence(sK23)
& function(sK23)
& relation(sK23) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK23])],[f60,f213]) ).
fof(f213,plain,
( ? [X0] :
( transfinite_sequence(X0)
& function(X0)
& relation(X0) )
=> ( transfinite_sequence(sK23)
& function(sK23)
& relation(sK23) ) ),
introduced(choice_axiom,[]) ).
fof(f60,axiom,
? [X0] :
( transfinite_sequence(X0)
& function(X0)
& relation(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc4_ordinal1) ).
fof(f605,plain,
spl30_44,
inference(avatar_split_clause,[],[f359,f602]) ).
fof(f359,plain,
function(sK23),
inference(cnf_transformation,[],[f214]) ).
fof(f600,plain,
spl30_43,
inference(avatar_split_clause,[],[f358,f597]) ).
fof(f358,plain,
relation(sK23),
inference(cnf_transformation,[],[f214]) ).
fof(f595,plain,
spl30_42,
inference(avatar_split_clause,[],[f357,f592]) ).
fof(f357,plain,
function(sK22),
inference(cnf_transformation,[],[f212]) ).
fof(f212,plain,
( function(sK22)
& relation(sK22) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK22])],[f85,f211]) ).
fof(f211,plain,
( ? [X0] :
( function(X0)
& relation(X0) )
=> ( function(sK22)
& relation(sK22) ) ),
introduced(choice_axiom,[]) ).
fof(f85,plain,
? [X0] :
( function(X0)
& relation(X0) ),
inference(pure_predicate_removal,[],[f38]) ).
fof(f38,axiom,
? [X0] :
( function_yielding(X0)
& function(X0)
& relation(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_funcop_1) ).
fof(f590,plain,
spl30_41,
inference(avatar_split_clause,[],[f356,f587]) ).
fof(f356,plain,
relation(sK22),
inference(cnf_transformation,[],[f212]) ).
fof(f585,plain,
spl30_40,
inference(avatar_split_clause,[],[f355,f582]) ).
fof(f355,plain,
function(sK21),
inference(cnf_transformation,[],[f210]) ).
fof(f210,plain,
( function(sK21)
& relation(sK21) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK21])],[f39,f209]) ).
fof(f209,plain,
( ? [X0] :
( function(X0)
& relation(X0) )
=> ( function(sK21)
& relation(sK21) ) ),
introduced(choice_axiom,[]) ).
fof(f39,axiom,
? [X0] :
( function(X0)
& relation(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_funct_1) ).
fof(f580,plain,
spl30_39,
inference(avatar_split_clause,[],[f354,f577]) ).
fof(f354,plain,
relation(sK21),
inference(cnf_transformation,[],[f210]) ).
fof(f575,plain,
spl30_38,
inference(avatar_split_clause,[],[f353,f572]) ).
fof(f353,plain,
function(sK20),
inference(cnf_transformation,[],[f208]) ).
fof(f208,plain,
( function(sK20)
& relation(sK20) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK20])],[f89,f207]) ).
fof(f207,plain,
( ? [X0] :
( function(X0)
& relation(X0) )
=> ( function(sK20)
& relation(sK20) ) ),
introduced(choice_axiom,[]) ).
fof(f89,plain,
? [X0] :
( function(X0)
& relation(X0) ),
inference(pure_predicate_removal,[],[f59]) ).
fof(f59,axiom,
? [X0] :
( function(X0)
& relation_empty_yielding(X0)
& relation(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc4_funct_1) ).
fof(f570,plain,
spl30_37,
inference(avatar_split_clause,[],[f352,f567]) ).
fof(f352,plain,
relation(sK20),
inference(cnf_transformation,[],[f208]) ).
fof(f565,plain,
spl30_36,
inference(avatar_split_clause,[],[f351,f562]) ).
fof(f351,plain,
relation(sK19),
inference(cnf_transformation,[],[f206]) ).
fof(f206,plain,
relation(sK19),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK19])],[f90,f205]) ).
fof(f205,plain,
( ? [X0] : relation(X0)
=> relation(sK19) ),
introduced(choice_axiom,[]) ).
fof(f90,plain,
? [X0] : relation(X0),
inference(pure_predicate_removal,[],[f57]) ).
fof(f57,axiom,
? [X0] :
( relation_empty_yielding(X0)
& relation(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_relat_1) ).
fof(f560,plain,
spl30_35,
inference(avatar_split_clause,[],[f350,f557]) ).
fof(f350,plain,
function(sK18),
inference(cnf_transformation,[],[f204]) ).
fof(f204,plain,
( function(sK18)
& relation(sK18) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK18])],[f87,f203]) ).
fof(f203,plain,
( ? [X0] :
( function(X0)
& relation(X0) )
=> ( function(sK18)
& relation(sK18) ) ),
introduced(choice_axiom,[]) ).
fof(f87,plain,
? [X0] :
( function(X0)
& relation(X0) ),
inference(pure_predicate_removal,[],[f61]) ).
fof(f61,axiom,
? [X0] :
( function(X0)
& relation_non_empty(X0)
& relation(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc5_funct_1) ).
fof(f555,plain,
spl30_34,
inference(avatar_split_clause,[],[f349,f552]) ).
fof(f349,plain,
relation(sK18),
inference(cnf_transformation,[],[f204]) ).
fof(f550,plain,
spl30_33,
inference(avatar_split_clause,[],[f348,f547]) ).
fof(f547,plain,
( spl30_33
<=> relation(sK17) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_33])]) ).
fof(f348,plain,
relation(sK17),
inference(cnf_transformation,[],[f202]) ).
fof(f202,plain,
( relation(sK17)
& empty(sK17) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK17])],[f42,f201]) ).
fof(f201,plain,
( ? [X0] :
( relation(X0)
& empty(X0) )
=> ( relation(sK17)
& empty(sK17) ) ),
introduced(choice_axiom,[]) ).
fof(f42,axiom,
? [X0] :
( relation(X0)
& empty(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_relat_1) ).
fof(f545,plain,
spl30_32,
inference(avatar_split_clause,[],[f347,f542]) ).
fof(f347,plain,
empty(sK17),
inference(cnf_transformation,[],[f202]) ).
fof(f540,plain,
spl30_31,
inference(avatar_split_clause,[],[f346,f537]) ).
fof(f537,plain,
( spl30_31
<=> ordinal(sK16) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_31])]) ).
fof(f346,plain,
ordinal(sK16),
inference(cnf_transformation,[],[f200]) ).
fof(f200,plain,
( ordinal(sK16)
& epsilon_connected(sK16)
& epsilon_transitive(sK16) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK16])],[f84,f199]) ).
fof(f199,plain,
( ? [X0] :
( ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0) )
=> ( ordinal(sK16)
& epsilon_connected(sK16)
& epsilon_transitive(sK16) ) ),
introduced(choice_axiom,[]) ).
fof(f84,plain,
? [X0] :
( ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0) ),
inference(pure_predicate_removal,[],[f41]) ).
fof(f41,axiom,
? [X0] :
( being_limit_ordinal(X0)
& ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_ordinal2) ).
fof(f535,plain,
spl30_30,
inference(avatar_split_clause,[],[f345,f532]) ).
fof(f532,plain,
( spl30_30
<=> epsilon_connected(sK16) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_30])]) ).
fof(f345,plain,
epsilon_connected(sK16),
inference(cnf_transformation,[],[f200]) ).
fof(f530,plain,
spl30_29,
inference(avatar_split_clause,[],[f344,f527]) ).
fof(f527,plain,
( spl30_29
<=> epsilon_transitive(sK16) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_29])]) ).
fof(f344,plain,
epsilon_transitive(sK16),
inference(cnf_transformation,[],[f200]) ).
fof(f525,plain,
spl30_28,
inference(avatar_split_clause,[],[f343,f522]) ).
fof(f522,plain,
( spl30_28
<=> ordinal(sK15) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_28])]) ).
fof(f343,plain,
ordinal(sK15),
inference(cnf_transformation,[],[f198]) ).
fof(f198,plain,
( ordinal(sK15)
& epsilon_connected(sK15)
& epsilon_transitive(sK15) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK15])],[f40,f197]) ).
fof(f197,plain,
( ? [X0] :
( ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0) )
=> ( ordinal(sK15)
& epsilon_connected(sK15)
& epsilon_transitive(sK15) ) ),
introduced(choice_axiom,[]) ).
fof(f40,axiom,
? [X0] :
( ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_ordinal1) ).
fof(f520,plain,
spl30_27,
inference(avatar_split_clause,[],[f342,f517]) ).
fof(f517,plain,
( spl30_27
<=> epsilon_connected(sK15) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_27])]) ).
fof(f342,plain,
epsilon_connected(sK15),
inference(cnf_transformation,[],[f198]) ).
fof(f515,plain,
spl30_26,
inference(avatar_split_clause,[],[f341,f512]) ).
fof(f512,plain,
( spl30_26
<=> epsilon_transitive(sK15) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_26])]) ).
fof(f341,plain,
epsilon_transitive(sK15),
inference(cnf_transformation,[],[f198]) ).
fof(f510,plain,
spl30_25,
inference(avatar_split_clause,[],[f340,f507]) ).
fof(f340,plain,
relation(sK14),
inference(cnf_transformation,[],[f196]) ).
fof(f196,plain,
( relation(sK14)
& ~ empty(sK14) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK14])],[f50,f195]) ).
fof(f195,plain,
( ? [X0] :
( relation(X0)
& ~ empty(X0) )
=> ( relation(sK14)
& ~ empty(sK14) ) ),
introduced(choice_axiom,[]) ).
fof(f50,axiom,
? [X0] :
( relation(X0)
& ~ empty(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_relat_1) ).
fof(f505,plain,
~ spl30_24,
inference(avatar_split_clause,[],[f339,f502]) ).
fof(f502,plain,
( spl30_24
<=> empty(sK14) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_24])]) ).
fof(f339,plain,
~ empty(sK14),
inference(cnf_transformation,[],[f196]) ).
fof(f500,plain,
spl30_23,
inference(avatar_split_clause,[],[f338,f497]) ).
fof(f497,plain,
( spl30_23
<=> ordinal(sK13) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_23])]) ).
fof(f338,plain,
ordinal(sK13),
inference(cnf_transformation,[],[f194]) ).
fof(f194,plain,
( ordinal(sK13)
& epsilon_connected(sK13)
& epsilon_transitive(sK13)
& ~ empty(sK13) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK13])],[f97,f193]) ).
fof(f193,plain,
( ? [X0] :
( ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0)
& ~ empty(X0) )
=> ( ordinal(sK13)
& epsilon_connected(sK13)
& epsilon_transitive(sK13)
& ~ empty(sK13) ) ),
introduced(choice_axiom,[]) ).
fof(f97,plain,
? [X0] :
( ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0)
& ~ empty(X0) ),
inference(pure_predicate_removal,[],[f36]) ).
fof(f36,axiom,
? [X0] :
( natural(X0)
& ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0)
& ~ empty(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_arytm_3) ).
fof(f495,plain,
spl30_22,
inference(avatar_split_clause,[],[f337,f492]) ).
fof(f492,plain,
( spl30_22
<=> epsilon_connected(sK13) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_22])]) ).
fof(f337,plain,
epsilon_connected(sK13),
inference(cnf_transformation,[],[f194]) ).
fof(f490,plain,
spl30_21,
inference(avatar_split_clause,[],[f336,f487]) ).
fof(f487,plain,
( spl30_21
<=> epsilon_transitive(sK13) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_21])]) ).
fof(f336,plain,
epsilon_transitive(sK13),
inference(cnf_transformation,[],[f194]) ).
fof(f485,plain,
~ spl30_20,
inference(avatar_split_clause,[],[f335,f482]) ).
fof(f482,plain,
( spl30_20
<=> empty(sK13) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_20])]) ).
fof(f335,plain,
~ empty(sK13),
inference(cnf_transformation,[],[f194]) ).
fof(f480,plain,
spl30_19,
inference(avatar_split_clause,[],[f334,f477]) ).
fof(f477,plain,
( spl30_19
<=> ordinal(sK12) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_19])]) ).
fof(f334,plain,
ordinal(sK12),
inference(cnf_transformation,[],[f192]) ).
fof(f192,plain,
( ordinal(sK12)
& epsilon_connected(sK12)
& epsilon_transitive(sK12)
& ~ empty(sK12) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK12])],[f56,f191]) ).
fof(f191,plain,
( ? [X0] :
( ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0)
& ~ empty(X0) )
=> ( ordinal(sK12)
& epsilon_connected(sK12)
& epsilon_transitive(sK12)
& ~ empty(sK12) ) ),
introduced(choice_axiom,[]) ).
fof(f56,axiom,
? [X0] :
( ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0)
& ~ empty(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_ordinal1) ).
fof(f475,plain,
spl30_18,
inference(avatar_split_clause,[],[f333,f472]) ).
fof(f472,plain,
( spl30_18
<=> epsilon_connected(sK12) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_18])]) ).
fof(f333,plain,
epsilon_connected(sK12),
inference(cnf_transformation,[],[f192]) ).
fof(f470,plain,
spl30_17,
inference(avatar_split_clause,[],[f332,f467]) ).
fof(f467,plain,
( spl30_17
<=> epsilon_transitive(sK12) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_17])]) ).
fof(f332,plain,
epsilon_transitive(sK12),
inference(cnf_transformation,[],[f192]) ).
fof(f465,plain,
~ spl30_16,
inference(avatar_split_clause,[],[f331,f462]) ).
fof(f462,plain,
( spl30_16
<=> empty(sK12) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_16])]) ).
fof(f331,plain,
~ empty(sK12),
inference(cnf_transformation,[],[f192]) ).
fof(f460,plain,
spl30_15,
inference(avatar_split_clause,[],[f330,f457]) ).
fof(f457,plain,
( spl30_15
<=> finite(sK11) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_15])]) ).
fof(f330,plain,
finite(sK11),
inference(cnf_transformation,[],[f190]) ).
fof(f190,plain,
( finite(sK11)
& ~ empty(sK11) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK11])],[f37,f189]) ).
fof(f189,plain,
( ? [X0] :
( finite(X0)
& ~ empty(X0) )
=> ( finite(sK11)
& ~ empty(sK11) ) ),
introduced(choice_axiom,[]) ).
fof(f37,axiom,
? [X0] :
( finite(X0)
& ~ empty(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_finset_1) ).
fof(f455,plain,
~ spl30_14,
inference(avatar_split_clause,[],[f329,f452]) ).
fof(f452,plain,
( spl30_14
<=> empty(sK11) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_14])]) ).
fof(f329,plain,
~ empty(sK11),
inference(cnf_transformation,[],[f190]) ).
fof(f450,plain,
spl30_13,
inference(avatar_split_clause,[],[f328,f447]) ).
fof(f328,plain,
empty(sK10),
inference(cnf_transformation,[],[f188]) ).
fof(f188,plain,
empty(sK10),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK10])],[f44,f187]) ).
fof(f187,plain,
( ? [X0] : empty(X0)
=> empty(sK10) ),
introduced(choice_axiom,[]) ).
fof(f44,axiom,
? [X0] : empty(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_xboole_0) ).
fof(f445,plain,
~ spl30_12,
inference(avatar_split_clause,[],[f327,f442]) ).
fof(f442,plain,
( spl30_12
<=> empty(sK9) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_12])]) ).
fof(f327,plain,
~ empty(sK9),
inference(cnf_transformation,[],[f186]) ).
fof(f186,plain,
~ empty(sK9),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK9])],[f52,f185]) ).
fof(f185,plain,
( ? [X0] : ~ empty(X0)
=> ~ empty(sK9) ),
introduced(choice_axiom,[]) ).
fof(f52,axiom,
? [X0] : ~ empty(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_xboole_0) ).
fof(f440,plain,
spl30_11,
inference(avatar_split_clause,[],[f242,f437]) ).
fof(f437,plain,
( spl30_11
<=> ordinal(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_11])]) ).
fof(f242,plain,
ordinal(empty_set),
inference(cnf_transformation,[],[f95]) ).
fof(f95,plain,
( ordinal(empty_set)
& epsilon_connected(empty_set)
& epsilon_transitive(empty_set)
& empty(empty_set)
& function(empty_set)
& relation(empty_set) ),
inference(pure_predicate_removal,[],[f91]) ).
fof(f91,plain,
( ordinal(empty_set)
& epsilon_connected(empty_set)
& epsilon_transitive(empty_set)
& empty(empty_set)
& one_to_one(empty_set)
& function(empty_set)
& relation(empty_set) ),
inference(pure_predicate_removal,[],[f26]) ).
fof(f26,axiom,
( ordinal(empty_set)
& epsilon_connected(empty_set)
& epsilon_transitive(empty_set)
& empty(empty_set)
& one_to_one(empty_set)
& function(empty_set)
& relation_empty_yielding(empty_set)
& relation(empty_set) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_ordinal1) ).
fof(f435,plain,
spl30_10,
inference(avatar_split_clause,[],[f241,f432]) ).
fof(f432,plain,
( spl30_10
<=> epsilon_connected(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_10])]) ).
fof(f241,plain,
epsilon_connected(empty_set),
inference(cnf_transformation,[],[f95]) ).
fof(f430,plain,
spl30_9,
inference(avatar_split_clause,[],[f240,f427]) ).
fof(f427,plain,
( spl30_9
<=> epsilon_transitive(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_9])]) ).
fof(f240,plain,
epsilon_transitive(empty_set),
inference(cnf_transformation,[],[f95]) ).
fof(f425,plain,
spl30_8,
inference(avatar_split_clause,[],[f238,f422]) ).
fof(f422,plain,
( spl30_8
<=> function(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_8])]) ).
fof(f238,plain,
function(empty_set),
inference(cnf_transformation,[],[f95]) ).
fof(f420,plain,
spl30_7,
inference(avatar_split_clause,[],[f234,f417]) ).
fof(f234,plain,
relation(empty_set),
inference(cnf_transformation,[],[f27]) ).
fof(f27,axiom,
( relation(empty_set)
& empty(empty_set) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_relat_1) ).
fof(f415,plain,
spl30_6,
inference(avatar_split_clause,[],[f232,f412]) ).
fof(f232,plain,
empty(empty_set),
inference(cnf_transformation,[],[f25]) ).
fof(f25,axiom,
empty(empty_set),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_xboole_0) ).
fof(f410,plain,
~ spl30_5,
inference(avatar_split_clause,[],[f231,f407]) ).
fof(f231,plain,
~ empty(positive_rationals),
inference(cnf_transformation,[],[f34]) ).
fof(f34,axiom,
~ empty(positive_rationals),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc8_arytm_3) ).
fof(f405,plain,
( spl30_3
| spl30_4 ),
inference(avatar_split_clause,[],[f229,f402,f398]) ).
fof(f229,plain,
( finite(sK0)
| finite(relation_dom(sK0)) ),
inference(cnf_transformation,[],[f166]) ).
fof(f396,plain,
spl30_2,
inference(avatar_split_clause,[],[f228,f393]) ).
fof(f228,plain,
function(sK0),
inference(cnf_transformation,[],[f166]) ).
fof(f391,plain,
spl30_1,
inference(avatar_split_clause,[],[f227,f388]) ).
fof(f227,plain,
relation(sK0),
inference(cnf_transformation,[],[f166]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.13 % Problem : SEU098+1 : TPTP v8.1.2. Released v3.2.0.
% 0.13/0.15 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.36 % Computer : n008.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Fri May 3 10:59:57 EDT 2024
% 0.15/0.36 % CPUTime :
% 0.15/0.36 % (3592)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.38 % (3599)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)
% 0.15/0.38 % (3595)WARNING: value z3 for option sas not known
% 0.15/0.38 % (3594)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.15/0.38 % (3593)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.15/0.38 % (3596)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.15/0.38 % (3595)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)
% 0.15/0.38 % (3597)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)
% 0.15/0.38 % (3598)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)
% 0.15/0.39 TRYING [1]
% 0.15/0.39 TRYING [2]
% 0.15/0.39 TRYING [3]
% 0.15/0.40 TRYING [1]
% 0.15/0.40 TRYING [2]
% 0.15/0.40 TRYING [4]
% 0.15/0.42 TRYING [1]
% 0.15/0.42 TRYING [2]
% 0.15/0.42 TRYING [3]
% 0.15/0.42 TRYING [3]
% 0.22/0.43 TRYING [4]
% 0.22/0.45 TRYING [5]
% 0.22/0.47 TRYING [4]
% 0.22/0.48 TRYING [5]
% 0.22/0.54 TRYING [6]
% 1.42/0.57 % (3597)First to succeed.
% 1.42/0.58 % (3595)Also succeeded, but the first one will report.
% 1.61/0.59 TRYING [6]
% 1.61/0.59 TRYING [5]
% 1.61/0.59 % (3640)fmb+10_1_fmbas=expand:fmbsr=1.1:gsp=on:nm=4_411 on theBenchmark for (411ds/0Mi)
% 1.61/0.59 TRYING [1]
% 1.61/0.59 TRYING [2]
% 1.61/0.59 % (3597)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3592"
% 1.61/0.59 TRYING [3]
% 1.61/0.59 % (3597)Refutation found. Thanks to Tanya!
% 1.61/0.59 % SZS status Theorem for theBenchmark
% 1.61/0.59 % SZS output start Proof for theBenchmark
% See solution above
% 1.61/0.61 % (3597)------------------------------
% 1.61/0.61 % (3597)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 1.61/0.61 % (3597)Termination reason: Refutation
% 1.61/0.61
% 1.61/0.61 % (3597)Memory used [KB]: 5194
% 1.61/0.61 % (3597)Time elapsed: 0.211 s
% 1.61/0.61 % (3597)Instructions burned: 504 (million)
% 1.61/0.61 % (3592)Success in time 0.233 s
%------------------------------------------------------------------------------