TSTP Solution File: SWV834-1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SWV834-1 : TPTP v8.1.2. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n026.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Apr 30 17:07:07 EDT 2024
% Result : Unsatisfiable 162.20s 23.58s
% Output : Refutation 162.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 2048
% Syntax : Number of formulae : 5660 ( 689 unt; 0 def)
% Number of atoms : 17643 (2320 equ)
% Maximal formula atoms : 9 ( 3 avg)
% Number of connectives : 22229 (10246 ~;10411 |; 0 &)
% (1572 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 6 avg)
% Maximal term depth : 14 ( 2 avg)
% Number of predicates : 1592 (1590 usr;1573 prp; 0-9 aty)
% Number of functors : 71 ( 71 usr; 14 con; 0-6 aty)
% Number of variables : 15864 (15864 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f161616,plain,
$false,
inference(avatar_sat_refutation,[],[f1020,f1025,f1030,f1035,f1040,f1045,f1050,f1055,f1060,f1065,f1070,f1075,f1080,f1084,f1088,f1092,f1096,f1100,f1104,f1108,f1112,f1116,f1120,f1125,f1129,f1133,f1137,f1141,f1145,f1149,f1153,f1157,f1161,f1165,f1169,f1173,f1177,f1181,f1185,f1189,f1196,f1200,f1204,f1208,f1212,f1216,f1220,f1225,f1230,f1234,f1239,f1243,f1248,f1252,f1256,f1260,f1264,f1268,f1272,f1276,f1281,f1285,f1289,f1293,f1297,f1302,f1310,f1318,f1322,f1326,f1330,f1334,f1338,f1342,f1346,f1350,f1355,f1359,f1363,f1368,f1372,f1376,f1387,f1394,f1401,f1405,f1409,f1413,f1417,f1421,f1425,f1429,f1433,f1437,f1442,f1446,f1450,f1454,f1474,f1486,f1490,f1494,f1498,f1502,f1506,f1510,f1514,f1518,f1522,f1527,f1531,f1535,f1539,f1543,f1547,f1551,f1555,f1578,f1589,f1593,f1597,f1601,f1605,f1609,f1613,f1617,f1621,f1625,f1629,f1633,f1637,f1641,f1645,f1649,f1654,f1672,f1682,f1686,f1690,f1694,f1698,f1702,f1706,f1710,f1714,f1718,f1722,f1726,f1730,f1734,f1781,f1796,f1800,f1804,f1808,f1812,f1816,f1820,f1824,f1828,f1832,f1836,f1840,f1844,f1848,f1852,f1856,f1860,f1867,f1871,f1875,f1879,f1884,f1889,f1893,f1906,f1943,f1978,f1982,f1986,f1991,f1995,f1999,f2003,f2007,f2011,f2015,f2019,f2023,f2027,f2031,f2035,f2039,f2043,f2047,f2051,f2056,f2060,f2064,f2068,f2078,f2082,f2155,f2189,f2215,f2219,f2223,f2227,f2231,f2235,f2239,f2249,f2253,f2257,f2261,f2265,f2269,f2273,f2277,f2281,f2285,f2289,f2293,f2297,f2301,f2368,f2582,f2627,f2631,f2635,f2639,f2643,f2647,f2651,f2656,f2660,f2664,f2668,f2672,f2676,f2680,f2684,f2688,f2692,f2696,f2701,f3035,f3053,f3057,f3061,f3075,f3079,f3083,f3087,f3091,f3095,f3099,f3103,f3107,f3111,f3115,f3119,f3123,f3127,f3131,f3135,f3139,f3625,f3629,f3633,f3637,f3641,f3646,f3650,f3654,f3658,f3662,f3667,f3671,f3858,f3865,f3869,f3881,f3885,f3889,f3893,f3897,f3901,f3905,f3909,f3913,f3917,f3929,f3933,f3937,f3941,f3945,f3949,f3953,f3957,f3961,f4361,f4558,f4563,f4567,f4571,f4575,f4579,f4583,f4587,f4591,f4596,f4600,f4604,f4608,f4612,f4616,f4620,f4836,f4870,f4874,f4878,f4882,f4886,f4890,f4894,f4898,f4902,f4906,f4910,f4914,f4918,f4922,f4927,f4931,f4935,f4939,f4943,f4947,f4951,f4955,f4959,f4963,f4968,f4972,f4976,f5572,f5586,f5590,f5594,f5598,f5602,f5606,f5610,f5614,f5618,f6024,f6029,f6033,f6037,f6041,f6045,f6049,f6053,f6057,f6061,f6065,f6069,f6073,f6077,f6081,f6085,f6089,f6093,f6097,f6101,f6105,f6361,f6495,f6518,f6522,f6526,f6530,f6534,f6680,f6746,f6750,f6754,f6758,f6762,f6766,f6770,f6774,f7118,f7122,f7126,f7130,f7134,f7138,f7142,f7146,f7150,f7154,f7158,f7162,f7244,f7681,f7685,f7689,f7693,f7697,f7701,f7706,f7845,f7850,f8334,f8338,f8342,f8346,f8381,f8385,f8389,f8393,f8397,f8401,f8405,f8409,f8413,f8418,f9208,f9293,f9297,f9301,f9305,f9309,f9313,f9317,f9322,f9349,f9353,f9764,f9768,f9774,f9780,f9784,f9788,f9792,f9796,f9800,f9804,f9808,f9812,f10478,f10482,f10487,f10491,f10734,f10767,f10776,f10780,f10785,f10789,f10793,f10797,f10802,f10951,f10955,f10959,f10963,f10967,f11015,f11019,f11023,f11027,f12562,f12566,f12597,f12601,f12605,f12609,f12837,f12860,f12864,f12868,f12873,f13116,f13219,f13223,f13227,f13236,f13240,f13346,f13350,f13376,f13398,f13402,f13406,f13482,f13486,f13490,f13532,f13537,f13564,f13568,f13681,f13709,f13713,f13834,f13839,f13957,f13961,f13966,f14091,f14097,f14472,f14478,f14488,f14493,f14497,f14773,f14778,f14806,f14812,f14858,f14864,f14868,f14880,f14886,f14892,f14898,f14919,f14925,f14943,f14950,f14957,f15040,f15045,f15193,f15198,f15378,f15385,f15492,f15499,f15577,f15584,f15648,f15655,f15660,f15667,f15672,f15679,f15744,f15751,f15755,f15822,f15827,f15831,f15835,f15839,f15843,f15847,f16036,f16040,f16044,f16048,f16052,f16056,f16060,f16064,f16068,f16072,f16076,f16554,f16558,f16562,f16566,f16570,f16574,f16581,f16585,f16589,f16593,f16597,f16851,f16855,f16859,f16863,f16867,f16871,f16875,f16879,f16883,f16887,f16891,f16895,f16899,f16903,f16907,f16914,f16918,f16941,f17367,f17371,f17375,f17379,f17383,f17387,f17391,f17395,f17399,f17403,f17407,f17411,f17415,f17426,f17430,f17434,f17438,f17442,f17446,f17450,f17454,f17458,f17462,f17469,f17473,f17477,f17481,f17485,f17489,f17493,f17497,f17501,f17505,f17509,f17636,f17640,f17644,f18131,f18469,f18683,f18687,f18691,f18695,f18699,f18703,f18707,f18711,f18715,f18719,f18723,f18727,f18731,f18741,f18745,f18749,f18753,f18757,f18761,f18765,f18769,f18773,f18777,f18803,f18807,f18811,f18815,f18819,f18823,f18827,f18831,f18835,f18839,f18843,f18847,f18851,f18855,f18859,f18863,f18890,f18894,f18898,f18902,f18922,f18948,f20076,f21020,f21187,f21191,f21195,f21199,f21203,f21207,f21211,f21215,f21222,f21226,f21230,f21234,f21238,f21242,f21246,f21250,f21254,f21258,f21268,f21272,f21276,f21280,f21284,f21288,f21292,f21296,f21300,f21452,f21456,f21460,f21464,f21468,f21472,f21681,f22208,f22212,f22216,f22220,f22224,f22228,f22232,f22236,f26018,f27512,f36606,f36610,f38621,f39818,f39822,f41034,f41088,f43090,f43273,f43472,f43720,f43981,f43985,f44005,f44015,f44398,f45378,f52438,f54021,f54349,f54604,f54708,f54732,f54736,f54782,f54867,f54871,f54981,f59318,f60367,f61294,f61456,f61700,f62499,f62506,f62598,f62602,f62606,f62610,f62614,f62618,f62622,f62626,f62630,f62710,f62714,f62718,f62722,f62726,f62730,f62734,f62738,f62742,f62746,f62779,f62783,f62787,f62791,f62795,f62799,f62803,f62807,f62811,f62815,f62849,f62853,f62857,f62861,f62865,f62869,f62873,f62877,f62881,f62885,f62923,f62927,f62931,f62965,f63566,f65762,f65877,f65881,f65885,f65889,f65893,f65897,f65901,f65908,f65912,f65916,f65920,f65924,f65928,f65932,f65936,f65940,f65944,f65948,f65952,f65956,f65960,f65964,f65968,f65972,f65976,f65980,f65984,f65988,f65993,f65997,f66001,f66005,f66009,f66013,f66017,f66021,f66025,f66029,f66033,f66037,f66235,f66419,f66423,f66427,f66431,f66435,f66439,f66443,f66447,f66451,f66455,f66459,f66463,f66467,f66471,f66475,f66479,f66483,f66487,f66491,f66495,f66683,f69772,f69776,f69807,f69811,f69815,f69819,f69823,f69827,f69831,f69835,f69839,f69843,f69847,f69851,f69855,f69859,f69863,f69867,f69871,f69875,f69879,f69883,f69887,f69942,f69946,f69950,f69954,f69958,f69962,f69966,f69970,f69974,f69978,f69982,f69986,f69990,f69994,f69998,f70002,f70006,f70010,f70014,f70018,f70022,f70077,f70081,f70085,f70089,f70093,f70097,f70101,f70105,f70109,f70113,f70117,f70121,f70125,f70129,f70133,f70137,f70141,f70145,f70149,f70153,f71226,f72518,f72937,f73675,f74830,f74834,f74838,f74842,f74846,f74850,f74854,f74858,f74862,f74866,f74870,f74874,f74878,f74882,f74945,f74949,f74953,f74957,f74961,f74965,f74969,f74973,f74977,f74981,f74985,f74989,f74993,f74997,f75001,f75005,f75009,f75013,f75017,f75021,f75025,f75153,f75157,f75161,f75165,f75169,f75173,f75177,f75181,f75204,f75208,f75212,f75216,f75220,f75224,f75228,f75232,f75236,f75240,f75244,f75248,f75302,f75306,f75310,f75314,f75318,f75322,f75326,f75330,f75334,f75338,f75342,f75346,f76727,f77631,f80985,f81170,f81174,f81178,f81182,f81186,f81190,f81194,f81257,f81261,f81265,f81269,f81273,f81277,f81281,f81285,f81289,f81293,f81297,f81301,f81305,f81309,f81313,f81317,f81321,f81325,f81329,f81333,f81337,f81341,f81345,f81349,f81353,f81357,f81361,f81365,f81369,f81373,f81377,f81381,f81516,f81520,f81524,f81528,f81532,f81536,f81540,f81544,f81548,f81552,f81605,f81609,f81613,f81617,f81621,f81625,f81629,f81633,f81637,f81641,f81695,f81699,f81703,f81707,f81711,f81715,f81719,f81723,f81727,f81731,f81736,f81740,f81744,f81748,f81752,f81756,f81760,f81764,f81768,f81772,f81812,f81816,f81820,f81824,f81828,f81832,f81836,f81840,f81844,f81848,f81852,f81856,f81860,f81864,f81868,f81872,f81876,f81880,f81884,f81888,f81892,f81926,f81930,f81934,f81938,f81942,f81946,f81950,f81954,f81958,f81962,f81966,f81970,f81974,f81978,f81982,f81986,f81990,f81994,f81998,f82002,f82006,f82184,f82188,f82192,f82196,f82200,f82204,f82208,f82212,f82216,f82220,f82225,f82229,f82233,f82237,f82241,f82245,f82253,f82260,f82264,f82268,f82272,f82276,f82280,f82284,f82288,f82292,f82296,f82300,f82415,f89182,f89987,f90979,f91691,f92697,f93690,f94583,f95246,f97325,f99800,f99804,f99808,f99812,f99816,f99820,f99824,f99828,f99832,f99838,f99842,f99846,f99850,f99854,f99858,f99862,f99866,f99870,f99874,f99880,f99884,f99888,f99892,f99896,f99900,f99904,f99908,f99912,f99916,f100005,f100009,f100013,f100017,f100021,f100025,f100029,f100033,f100037,f100041,f100276,f100280,f100284,f100288,f100292,f100296,f100300,f100304,f100308,f100312,f100317,f100321,f100325,f100329,f100333,f100337,f100341,f100345,f100349,f100353,f100357,f100431,f100435,f100439,f100443,f100447,f100451,f100455,f100459,f100463,f100467,f100702,f100706,f100710,f100714,f100718,f100722,f100726,f100730,f100734,f100738,f100743,f100747,f100751,f100755,f100759,f100763,f100767,f100771,f100775,f100779,f100783,f100859,f100863,f100867,f100871,f100875,f100879,f100883,f100887,f100891,f100898,f100932,f110294,f113188,f116165,f117094,f118826,f121487,f125500,f125504,f125508,f125512,f125516,f125520,f125527,f125531,f125535,f125539,f125543,f125547,f125551,f125555,f125559,f125563,f125645,f125649,f125653,f125657,f125661,f125665,f125669,f125673,f125677,f125681,f125765,f125769,f125773,f125777,f125781,f125785,f125789,f125793,f125797,f125801,f125805,f125809,f125813,f125817,f125821,f125825,f125829,f125833,f125837,f125841,f125845,f125849,f125853,f125857,f125861,f125865,f125869,f125873,f125877,f125881,f125885,f125889,f125893,f125897,f125901,f125905,f125909,f125913,f125917,f125921,f125925,f125929,f125933,f125937,f125941,f125945,f125949,f125953,f125957,f125961,f125965,f125969,f125973,f125977,f126061,f126065,f126069,f126073,f126077,f126081,f126085,f126089,f126093,f126097,f126143,f126147,f126151,f126155,f126159,f126163,f126167,f126171,f126175,f126179,f126220,f126224,f126228,f126232,f126236,f126240,f132724,f133639,f136659,f137437,f138126,f141684,f141688,f141712,f141716,f141720,f141724,f141728,f141732,f141736,f141740,f141744,f141748,f141752,f141756,f141760,f141764,f141768,f141772,f141776,f141780,f141784,f141788,f141792,f141796,f141800,f141804,f141808,f141812,f141816,f141820,f141824,f141828,f141832,f141836,f142026,f142030,f142034,f142038,f142042,f142046,f142050,f142054,f142058,f142062,f142301,f142305,f142309,f142313,f142317,f142321,f142325,f142329,f142333,f142337,f142341,f142345,f142349,f142353,f142357,f142361,f142365,f142369,f142373,f142377,f142381,f142385,f142389,f142393,f142397,f142401,f142405,f142409,f142413,f142417,f142421,f142425,f142431,f142435,f142439,f142974,f143551,f143555,f143559,f143563,f143569,f143573,f143577,f143581,f143585,f143589,f143593,f143597,f143601,f143605,f143609,f143613,f143617,f143621,f143625,f143629,f143633,f143637,f143641,f143645,f143649,f143653,f143657,f143661,f143665,f143669,f143673,f143677,f143681,f143685,f143689,f143693,f143697,f143701,f143705,f143709,f143713,f143717,f143721,f143725,f143729,f143733,f143738,f143742,f143746,f143750,f143754,f143758,f143762,f143766,f143770,f143774,f143778,f143782,f143786,f143790,f143794,f143798,f143802,f143806,f143810,f143814,f143818,f143822,f143826,f143830,f143834,f143838,f143842,f143846,f143850,f143854,f143858,f143862,f143866,f143870,f143874,f143878,f143882,f143886,f143890,f143894,f143898,f143902,f143906,f143910,f143914,f147788,f149435,f151668,f152718,f156896,f158279,f158793,f161615]) ).
fof(f161615,plain,
( spl0_41
| ~ spl0_51
| spl0_281
| ~ spl0_1512 ),
inference(avatar_split_clause,[],[f159055,f143699,f3862,f1237,f1193]) ).
fof(f1193,plain,
( spl0_41
<=> hBOOL(c_False) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_41])]) ).
fof(f1237,plain,
( spl0_51
<=> ! [X11,X57,X0,X8] : hAPP(c_COMBK(X11,X0,X8),X57) = X11 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_51])]) ).
fof(f3862,plain,
( spl0_281
<=> c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(c_COMBK(c_COMBK(c_False,tc_bool,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_bool),t_a),v_c,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_bool,tc_bool)),tc_fun(tc_fun(tc_Com_Ostate,tc_bool),tc_fun(tc_Com_Ostate,tc_bool)),t_a),c_COMBS(tc_Com_Ostate,tc_bool,tc_bool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_bool),tc_fun(tc_Com_Ostate,tc_fun(tc_bool,tc_bool)),t_a),hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),tc_Com_Ostate),c_and)),v_P)),t_a,tc_fun(tc_Com_Ostate,tc_bool),tc_fun(tc_Com_Ostate,tc_bool)),hAPP(hAPP(c_COMBB(tc_bool,tc_bool,tc_Com_Ostate),c_Not),v_b)),t_a)),t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_281])]) ).
fof(f143699,plain,
( spl0_1512
<=> ! [X3,X4,X0,X5,X2,X1] :
( hBOOL(hAPP(X0,v_sko__Hoare__Mirabelle__Xescape__2(X3,c_COMBK(X0,X1,X2),X4,X5)))
| c_Hoare__Mirabelle_Ohoare__derivs(X3,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(c_COMBK(X0,X1,X2),X5,X4,t_a)),t_a) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1512])]) ).
fof(f159055,plain,
( hBOOL(c_False)
| ~ spl0_51
| spl0_281
| ~ spl0_1512 ),
inference(forward_demodulation,[],[f159004,f1238]) ).
fof(f1238,plain,
( ! [X0,X11,X8,X57] : hAPP(c_COMBK(X11,X0,X8),X57) = X11
| ~ spl0_51 ),
inference(avatar_component_clause,[],[f1237]) ).
fof(f159004,plain,
( hBOOL(hAPP(c_COMBK(c_False,tc_bool,tc_Com_Ostate),v_sko__Hoare__Mirabelle__Xescape__2(v_G,c_COMBK(c_COMBK(c_False,tc_bool,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_bool),t_a),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_bool,tc_bool)),tc_fun(tc_fun(tc_Com_Ostate,tc_bool),tc_fun(tc_Com_Ostate,tc_bool)),t_a),c_COMBS(tc_Com_Ostate,tc_bool,tc_bool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_bool),tc_fun(tc_Com_Ostate,tc_fun(tc_bool,tc_bool)),t_a),hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),tc_Com_Ostate),c_and)),v_P)),t_a,tc_fun(tc_Com_Ostate,tc_bool),tc_fun(tc_Com_Ostate,tc_bool)),hAPP(hAPP(c_COMBB(tc_bool,tc_bool,tc_Com_Ostate),c_Not),v_b)),v_c)))
| spl0_281
| ~ spl0_1512 ),
inference(resolution,[],[f143700,f3864]) ).
fof(f3864,plain,
( ~ c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(c_COMBK(c_COMBK(c_False,tc_bool,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_bool),t_a),v_c,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_bool,tc_bool)),tc_fun(tc_fun(tc_Com_Ostate,tc_bool),tc_fun(tc_Com_Ostate,tc_bool)),t_a),c_COMBS(tc_Com_Ostate,tc_bool,tc_bool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_bool),tc_fun(tc_Com_Ostate,tc_fun(tc_bool,tc_bool)),t_a),hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),tc_Com_Ostate),c_and)),v_P)),t_a,tc_fun(tc_Com_Ostate,tc_bool),tc_fun(tc_Com_Ostate,tc_bool)),hAPP(hAPP(c_COMBB(tc_bool,tc_bool,tc_Com_Ostate),c_Not),v_b)),t_a)),t_a)
| spl0_281 ),
inference(avatar_component_clause,[],[f3862]) ).
fof(f143700,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( hBOOL(hAPP(X0,v_sko__Hoare__Mirabelle__Xescape__2(X3,c_COMBK(X0,X1,X2),X4,X5)))
| c_Hoare__Mirabelle_Ohoare__derivs(X3,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(c_COMBK(X0,X1,X2),X5,X4,t_a)),t_a) )
| ~ spl0_1512 ),
inference(avatar_component_clause,[],[f143699]) ).
fof(f158793,plain,
( spl0_1572
| ~ spl0_599
| ~ spl0_617 ),
inference(avatar_split_clause,[],[f18011,f17424,f16901,f158791]) ).
fof(f158791,plain,
( spl0_1572
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(X1,X3))
| hBOOL(c_in(X3,hAPP(hAPP(c_Set_Oinsert(X0),X2),X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1572])]) ).
fof(f16901,plain,
( spl0_599
<=> ! [X2,X0,X1] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X1),hAPP(hAPP(c_Set_Oinsert(X0),X2),X1)) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_599])]) ).
fof(f17424,plain,
( spl0_617
<=> ! [X0,X3,X2,X1] :
( hBOOL(c_in(X0,X1,X2))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X3),X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_617])]) ).
fof(f18011,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(X1,X3))
| hBOOL(c_in(X3,hAPP(hAPP(c_Set_Oinsert(X0),X2),X1),X0)) )
| ~ spl0_599
| ~ spl0_617 ),
inference(superposition,[],[f17425,f16902]) ).
fof(f16902,plain,
( ! [X2,X0,X1] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X1),hAPP(hAPP(c_Set_Oinsert(X0),X2),X1)) = X1
| ~ spl0_599 ),
inference(avatar_component_clause,[],[f16901]) ).
fof(f17425,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X3),X1),X0))
| hBOOL(c_in(X0,X1,X2)) )
| ~ spl0_617 ),
inference(avatar_component_clause,[],[f17424]) ).
fof(f158279,plain,
( spl0_1571
| ~ spl0_227
| ~ spl0_585 ),
inference(avatar_split_clause,[],[f16822,f16595,f2580,f158277]) ).
fof(f158277,plain,
( spl0_1571
<=> ! [X2,X0,X1] : hAPP(X1,X0) = c_Complete__Lattice_Ocomplete__lattice__class_OINFI(c_SetInterval_Oord__class_OatLeastAtMost(X0,X0,tc_bool),X1,tc_bool,tc_fun(X2,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1571])]) ).
fof(f2580,plain,
( spl0_227
<=> ! [X0] : hAPP(c_fequal(tc_bool),X0) = c_SetInterval_Oord__class_OatLeastAtMost(X0,X0,tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_227])]) ).
fof(f16595,plain,
( spl0_585
<=> ! [X0,X3,X2,X1] : hAPP(X2,X1) = c_Complete__Lattice_Ocomplete__lattice__class_OINFI(hAPP(c_fequal(X0),X1),X2,X0,tc_fun(X3,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_585])]) ).
fof(f16822,plain,
( ! [X2,X0,X1] : hAPP(X1,X0) = c_Complete__Lattice_Ocomplete__lattice__class_OINFI(c_SetInterval_Oord__class_OatLeastAtMost(X0,X0,tc_bool),X1,tc_bool,tc_fun(X2,tc_bool))
| ~ spl0_227
| ~ spl0_585 ),
inference(superposition,[],[f16596,f2581]) ).
fof(f2581,plain,
( ! [X0] : hAPP(c_fequal(tc_bool),X0) = c_SetInterval_Oord__class_OatLeastAtMost(X0,X0,tc_bool)
| ~ spl0_227 ),
inference(avatar_component_clause,[],[f2580]) ).
fof(f16596,plain,
( ! [X2,X3,X0,X1] : hAPP(X2,X1) = c_Complete__Lattice_Ocomplete__lattice__class_OINFI(hAPP(c_fequal(X0),X1),X2,X0,tc_fun(X3,tc_bool))
| ~ spl0_585 ),
inference(avatar_component_clause,[],[f16595]) ).
fof(f156896,plain,
( spl0_1570
| ~ spl0_227
| ~ spl0_584 ),
inference(avatar_split_clause,[],[f16646,f16591,f2580,f156894]) ).
fof(f156894,plain,
( spl0_1570
<=> ! [X2,X0,X1] : hAPP(X1,X0) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_SetInterval_Oord__class_OatLeastAtMost(X0,X0,tc_bool),X1,tc_bool,tc_fun(X2,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1570])]) ).
fof(f16591,plain,
( spl0_584
<=> ! [X0,X3,X2,X1] : hAPP(X2,X1) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_fequal(X0),X1),X2,X0,tc_fun(X3,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_584])]) ).
fof(f16646,plain,
( ! [X2,X0,X1] : hAPP(X1,X0) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_SetInterval_Oord__class_OatLeastAtMost(X0,X0,tc_bool),X1,tc_bool,tc_fun(X2,tc_bool))
| ~ spl0_227
| ~ spl0_584 ),
inference(superposition,[],[f16592,f2581]) ).
fof(f16592,plain,
( ! [X2,X3,X0,X1] : hAPP(X2,X1) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_fequal(X0),X1),X2,X0,tc_fun(X3,tc_bool))
| ~ spl0_584 ),
inference(avatar_component_clause,[],[f16591]) ).
fof(f152718,plain,
( spl0_1569
| ~ spl0_741
| ~ spl0_1567 ),
inference(avatar_split_clause,[],[f150346,f149433,f43088,f152716]) ).
fof(f152716,plain,
( spl0_1569
<=> ! [X0,X1] : hBOOL(hAPP(hAPP(c_lessequals(tc_bool),X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),X1),X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1569])]) ).
fof(f43088,plain,
( spl0_741
<=> ! [X0,X1] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),X1),X0)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_741])]) ).
fof(f149433,plain,
( spl0_1567
<=> ! [X0,X1] : hBOOL(hAPP(hAPP(c_lessequals(tc_bool),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),X1),X0)),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1567])]) ).
fof(f150346,plain,
( ! [X0,X1] : hBOOL(hAPP(hAPP(c_lessequals(tc_bool),X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),X1),X0)))
| ~ spl0_741
| ~ spl0_1567 ),
inference(superposition,[],[f149434,f43089]) ).
fof(f43089,plain,
( ! [X0,X1] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),X1),X0)) = X0
| ~ spl0_741 ),
inference(avatar_component_clause,[],[f43088]) ).
fof(f149434,plain,
( ! [X0,X1] : hBOOL(hAPP(hAPP(c_lessequals(tc_bool),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),X1),X0)),X0))
| ~ spl0_1567 ),
inference(avatar_component_clause,[],[f149433]) ).
fof(f151668,plain,
( spl0_1568
| ~ spl0_566
| ~ spl0_1567 ),
inference(avatar_split_clause,[],[f150344,f149433,f16046,f151666]) ).
fof(f151666,plain,
( spl0_1568
<=> ! [X0,X1] : hBOOL(hAPP(hAPP(c_lessequals(tc_bool),X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),X0),X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1568])]) ).
fof(f16046,plain,
( spl0_566
<=> ! [X0,X1] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),X0),X1)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_566])]) ).
fof(f150344,plain,
( ! [X0,X1] : hBOOL(hAPP(hAPP(c_lessequals(tc_bool),X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),X0),X1)))
| ~ spl0_566
| ~ spl0_1567 ),
inference(superposition,[],[f149434,f16047]) ).
fof(f16047,plain,
( ! [X0,X1] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),X0),X1)) = X0
| ~ spl0_566 ),
inference(avatar_component_clause,[],[f16046]) ).
fof(f149435,plain,
( spl0_1567
| ~ spl0_563
| ~ spl0_1566 ),
inference(avatar_split_clause,[],[f148724,f147786,f16034,f149433]) ).
fof(f16034,plain,
( spl0_563
<=> ! [X0,X1] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),X0),X1) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),X1),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_563])]) ).
fof(f147786,plain,
( spl0_1566
<=> ! [X0,X1] : hBOOL(hAPP(hAPP(c_lessequals(tc_bool),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),X0),X1)),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1566])]) ).
fof(f148724,plain,
( ! [X0,X1] : hBOOL(hAPP(hAPP(c_lessequals(tc_bool),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),X1),X0)),X0))
| ~ spl0_563
| ~ spl0_1566 ),
inference(superposition,[],[f147787,f16035]) ).
fof(f16035,plain,
( ! [X0,X1] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),X0),X1) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),X1),X0)
| ~ spl0_563 ),
inference(avatar_component_clause,[],[f16034]) ).
fof(f147787,plain,
( ! [X0,X1] : hBOOL(hAPP(hAPP(c_lessequals(tc_bool),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),X0),X1)),X0))
| ~ spl0_1566 ),
inference(avatar_component_clause,[],[f147786]) ).
fof(f147788,plain,
( ~ spl0_2
| spl0_1566
| ~ spl0_139
| ~ spl0_565 ),
inference(avatar_split_clause,[],[f16383,f16042,f1688,f147786,f1022]) ).
fof(f1022,plain,
( spl0_2
<=> class_Lattices_Oupper__semilattice(tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).
fof(f1688,plain,
( spl0_139
<=> ! [X2,X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_139])]) ).
fof(f16042,plain,
( spl0_565
<=> ! [X0,X1] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),X0),X1)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_565])]) ).
fof(f16383,plain,
( ! [X0,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_bool),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),X0),X1)),X0))
| ~ class_Lattices_Oupper__semilattice(tc_bool) )
| ~ spl0_139
| ~ spl0_565 ),
inference(superposition,[],[f1689,f16043]) ).
fof(f16043,plain,
( ! [X0,X1] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),X0),X1)) = X0
| ~ spl0_565 ),
inference(avatar_component_clause,[],[f16042]) ).
fof(f1689,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2)))
| ~ class_Lattices_Oupper__semilattice(X0) )
| ~ spl0_139 ),
inference(avatar_component_clause,[],[f1688]) ).
fof(f143914,plain,
( spl0_1565
| ~ spl0_233
| ~ spl0_733 ),
inference(avatar_split_clause,[],[f27518,f27510,f2645,f143912]) ).
fof(f143912,plain,
( spl0_1565
<=> ! [X5,X3,X4,X0,X6,X2,X1] : c_List_Ofilter(hAPP(X2,X1),c_List_Ofilter(X1,X6,X0),X0) = c_List_Ofilter(hAPP(hAPP(hAPP(c_COMBS(X3,X4,X5),c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool))),X2),X1),X6,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1565])]) ).
fof(f2645,plain,
( spl0_233
<=> ! [X11,X57,X0,X14,X67,X8] : hAPP(hAPP(hAPP(c_COMBS(X8,X14,X0),X11),X57),X67) = hAPP(hAPP(X11,X67),hAPP(X57,X67)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_233])]) ).
fof(f27510,plain,
( spl0_733
<=> ! [X11,X57,X0,X66] : c_List_Ofilter(X11,c_List_Ofilter(X57,X66,X0),X0) = c_List_Ofilter(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X57),X11),X66,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_733])]) ).
fof(f27518,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] : c_List_Ofilter(hAPP(X2,X1),c_List_Ofilter(X1,X6,X0),X0) = c_List_Ofilter(hAPP(hAPP(hAPP(c_COMBS(X3,X4,X5),c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool))),X2),X1),X6,X0)
| ~ spl0_233
| ~ spl0_733 ),
inference(superposition,[],[f27511,f2646]) ).
fof(f2646,plain,
( ! [X0,X11,X8,X57,X14,X67] : hAPP(hAPP(hAPP(c_COMBS(X8,X14,X0),X11),X57),X67) = hAPP(hAPP(X11,X67),hAPP(X57,X67))
| ~ spl0_233 ),
inference(avatar_component_clause,[],[f2645]) ).
fof(f27511,plain,
( ! [X0,X11,X57,X66] : c_List_Ofilter(X11,c_List_Ofilter(X57,X66,X0),X0) = c_List_Ofilter(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X57),X11),X66,X0)
| ~ spl0_733 ),
inference(avatar_component_clause,[],[f27510]) ).
fof(f143910,plain,
( spl0_1564
| ~ spl0_38
| ~ spl0_559 ),
inference(avatar_split_clause,[],[f15868,f15833,f1179,f143908]) ).
fof(f143908,plain,
( spl0_1564
<=> ! [X2,X0,X1] : c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)) = hAPP(hAPP(c_Set_Oinsert(X0),X1),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1564])]) ).
fof(f1179,plain,
( spl0_38
<=> ! [X0,X1] : hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_38])]) ).
fof(f15833,plain,
( spl0_559
<=> ! [X2,X0,X1] :
( hAPP(hAPP(c_Set_Oinsert(X0),X1),X2) = X2
| ~ hBOOL(hAPP(X2,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_559])]) ).
fof(f15868,plain,
( ! [X2,X0,X1] : c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)) = hAPP(hAPP(c_Set_Oinsert(X0),X1),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)))
| ~ spl0_38
| ~ spl0_559 ),
inference(resolution,[],[f15834,f1180]) ).
fof(f1180,plain,
( ! [X0,X1] : hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X1))
| ~ spl0_38 ),
inference(avatar_component_clause,[],[f1179]) ).
fof(f15834,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(X2,X1))
| hAPP(hAPP(c_Set_Oinsert(X0),X1),X2) = X2 )
| ~ spl0_559 ),
inference(avatar_component_clause,[],[f15833]) ).
fof(f143906,plain,
( spl0_1563
| ~ spl0_130
| ~ spl0_150
| ~ spl0_200
| ~ spl0_262
| ~ spl0_513 ),
inference(avatar_split_clause,[],[f14086,f13964,f3117,f2066,f1732,f1631,f143904]) ).
fof(f143904,plain,
( spl0_1563
<=> ! [X0,X3,X2,X1] :
( c_Fun_Oinj__on(X2,hAPP(c_fequal(X0),X1),X0,X3)
| hBOOL(c_in(hAPP(X2,X1),c_COMBK(c_False,tc_bool,X3),X3))
| ~ c_Fun_Oinj__on(X2,c_COMBK(c_False,tc_bool,X0),X0,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1563])]) ).
fof(f1631,plain,
( spl0_130
<=> ! [X5,X0] : hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X5),X5) = c_COMBK(c_False,tc_bool,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_130])]) ).
fof(f1732,plain,
( spl0_150
<=> ! [X0,X3] : hAPP(c_fequal(X0),X3) = hAPP(hAPP(c_Set_Oinsert(X0),X3),c_COMBK(c_False,tc_bool,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_150])]) ).
fof(f2066,plain,
( spl0_200
<=> ! [X5,X0] : c_COMBK(c_False,tc_bool,X0) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0)),X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_200])]) ).
fof(f3117,plain,
( spl0_262
<=> ! [X5,X0,X9,X8] : hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X5),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_COMBK(c_False,tc_bool,X8),X9,X8,tc_fun(X0,tc_bool))) = X5 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_262])]) ).
fof(f13964,plain,
( spl0_513
<=> ! [X5,X0,X3,X8,X7] :
( hBOOL(c_in(hAPP(X7,X3),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X5),hAPP(c_fequal(X0),X3)),hAPP(hAPP(c_COMBB(X8,tc_fun(X8,tc_bool),X0),hAPP(c_COMBC(c_Set_Oinsert(X8),X8,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8))),X7),X0,tc_fun(X8,tc_bool)),X8))
| ~ c_Fun_Oinj__on(X7,X5,X0,X8)
| c_Fun_Oinj__on(X7,hAPP(hAPP(c_Set_Oinsert(X0),X3),X5),X0,X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_513])]) ).
fof(f14086,plain,
( ! [X2,X3,X0,X1] :
( c_Fun_Oinj__on(X2,hAPP(c_fequal(X0),X1),X0,X3)
| hBOOL(c_in(hAPP(X2,X1),c_COMBK(c_False,tc_bool,X3),X3))
| ~ c_Fun_Oinj__on(X2,c_COMBK(c_False,tc_bool,X0),X0,X3) )
| ~ spl0_130
| ~ spl0_150
| ~ spl0_200
| ~ spl0_262
| ~ spl0_513 ),
inference(forward_demodulation,[],[f14085,f1733]) ).
fof(f1733,plain,
( ! [X3,X0] : hAPP(c_fequal(X0),X3) = hAPP(hAPP(c_Set_Oinsert(X0),X3),c_COMBK(c_False,tc_bool,X0))
| ~ spl0_150 ),
inference(avatar_component_clause,[],[f1732]) ).
fof(f14085,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(c_in(hAPP(X2,X1),c_COMBK(c_False,tc_bool,X3),X3))
| ~ c_Fun_Oinj__on(X2,c_COMBK(c_False,tc_bool,X0),X0,X3)
| c_Fun_Oinj__on(X2,hAPP(hAPP(c_Set_Oinsert(X0),X1),c_COMBK(c_False,tc_bool,X0)),X0,X3) )
| ~ spl0_130
| ~ spl0_200
| ~ spl0_262
| ~ spl0_513 ),
inference(forward_demodulation,[],[f14070,f3466]) ).
fof(f3466,plain,
( ! [X2,X0,X1] : c_COMBK(c_False,tc_bool,X0) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_COMBK(c_False,tc_bool,X1),X2,X1,tc_fun(X0,tc_bool))
| ~ spl0_130
| ~ spl0_262 ),
inference(superposition,[],[f3118,f1632]) ).
fof(f1632,plain,
( ! [X0,X5] : hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X5),X5) = c_COMBK(c_False,tc_bool,X0)
| ~ spl0_130 ),
inference(avatar_component_clause,[],[f1631]) ).
fof(f3118,plain,
( ! [X0,X8,X9,X5] : hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X5),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_COMBK(c_False,tc_bool,X8),X9,X8,tc_fun(X0,tc_bool))) = X5
| ~ spl0_262 ),
inference(avatar_component_clause,[],[f3117]) ).
fof(f14070,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(c_in(hAPP(X2,X1),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_COMBK(c_False,tc_bool,X0),hAPP(hAPP(c_COMBB(X3,tc_fun(X3,tc_bool),X0),hAPP(c_COMBC(c_Set_Oinsert(X3),X3,tc_fun(X3,tc_bool),tc_fun(X3,tc_bool)),c_COMBK(c_False,tc_bool,X3))),X2),X0,tc_fun(X3,tc_bool)),X3))
| ~ c_Fun_Oinj__on(X2,c_COMBK(c_False,tc_bool,X0),X0,X3)
| c_Fun_Oinj__on(X2,hAPP(hAPP(c_Set_Oinsert(X0),X1),c_COMBK(c_False,tc_bool,X0)),X0,X3) )
| ~ spl0_200
| ~ spl0_513 ),
inference(superposition,[],[f13965,f2067]) ).
fof(f2067,plain,
( ! [X0,X5] : c_COMBK(c_False,tc_bool,X0) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0)),X5)
| ~ spl0_200 ),
inference(avatar_component_clause,[],[f2066]) ).
fof(f13965,plain,
( ! [X3,X0,X8,X7,X5] :
( hBOOL(c_in(hAPP(X7,X3),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X5),hAPP(c_fequal(X0),X3)),hAPP(hAPP(c_COMBB(X8,tc_fun(X8,tc_bool),X0),hAPP(c_COMBC(c_Set_Oinsert(X8),X8,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8))),X7),X0,tc_fun(X8,tc_bool)),X8))
| ~ c_Fun_Oinj__on(X7,X5,X0,X8)
| c_Fun_Oinj__on(X7,hAPP(hAPP(c_Set_Oinsert(X0),X3),X5),X0,X8) )
| ~ spl0_513 ),
inference(avatar_component_clause,[],[f13964]) ).
fof(f143902,plain,
( spl0_1562
| ~ spl0_114
| ~ spl0_475 ),
inference(avatar_split_clause,[],[f12557,f11025,f1541,f143900]) ).
fof(f143900,plain,
( spl0_1562
<=> ! [X4,X0,X3,X2,X1] :
( c_Hoare__Mirabelle_Ohoare__derivs(X0,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(X1)),c_Hoare__Mirabelle_Otriple_Otriple(X2,c_Com_Ocom_OSemi(X3,c_Com_Ocom_OSKIP),X4,X1)),X1)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X0,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(X1)),c_Hoare__Mirabelle_Otriple_Otriple(X2,X3,X4,X1)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1562])]) ).
fof(f1541,plain,
( spl0_114
<=> ! [X0,X11,X39] : c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),c_Hoare__Mirabelle_Otriple_Otriple(X11,c_Com_Ocom_OSKIP,X11,X0)),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_114])]) ).
fof(f11025,plain,
( spl0_475
<=> ! [X35,X11,X40,X0,X57,X67,X39] :
( c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),c_Hoare__Mirabelle_Otriple_Otriple(X11,c_Com_Ocom_OSemi(X35,X40),X67,X0)),X0)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),c_Hoare__Mirabelle_Otriple_Otriple(X57,X40,X67,X0)),X0)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),c_Hoare__Mirabelle_Otriple_Otriple(X11,X35,X57,X0)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_475])]) ).
fof(f12557,plain,
( ! [X2,X3,X0,X1,X4] :
( c_Hoare__Mirabelle_Ohoare__derivs(X0,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(X1)),c_Hoare__Mirabelle_Otriple_Otriple(X2,c_Com_Ocom_OSemi(X3,c_Com_Ocom_OSKIP),X4,X1)),X1)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X0,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(X1)),c_Hoare__Mirabelle_Otriple_Otriple(X2,X3,X4,X1)),X1) )
| ~ spl0_114
| ~ spl0_475 ),
inference(resolution,[],[f11026,f1542]) ).
fof(f1542,plain,
( ! [X39,X0,X11] : c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),c_Hoare__Mirabelle_Otriple_Otriple(X11,c_Com_Ocom_OSKIP,X11,X0)),X0)
| ~ spl0_114 ),
inference(avatar_component_clause,[],[f1541]) ).
fof(f11026,plain,
( ! [X40,X39,X0,X11,X57,X35,X67] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),c_Hoare__Mirabelle_Otriple_Otriple(X57,X40,X67,X0)),X0)
| c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),c_Hoare__Mirabelle_Otriple_Otriple(X11,c_Com_Ocom_OSemi(X35,X40),X67,X0)),X0)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),c_Hoare__Mirabelle_Otriple_Otriple(X11,X35,X57,X0)),X0) )
| ~ spl0_475 ),
inference(avatar_component_clause,[],[f11025]) ).
fof(f143898,plain,
( spl0_1561
| ~ spl0_114
| ~ spl0_474 ),
inference(avatar_split_clause,[],[f12555,f11021,f1541,f143896]) ).
fof(f143896,plain,
( spl0_1561
<=> ! [X0,X3,X2,X1] :
( c_Hoare__Mirabelle_Ohoare__derivs(X0,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X1,c_Com_Ocom_OSKIP,X2,t_a)),t_a)
| hBOOL(hAPP(hAPP(X1,v_sko__Hoare__Mirabelle__Xconseq12__1(X1,X3,X2,X3)),v_sko__Hoare__Mirabelle__Xconseq12__2(X1,X3,X2,X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1561])]) ).
fof(f11021,plain,
( spl0_474
<=> ! [X35,X57,X11,X64,X39,X65] :
( c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X11,X35,X57,t_a)),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X65,X35,X64,t_a)),t_a)
| hBOOL(hAPP(hAPP(X11,v_sko__Hoare__Mirabelle__Xconseq12__1(X11,X65,X57,X64)),v_sko__Hoare__Mirabelle__Xconseq12__2(X11,X65,X57,X64))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_474])]) ).
fof(f12555,plain,
( ! [X2,X3,X0,X1] :
( c_Hoare__Mirabelle_Ohoare__derivs(X0,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X1,c_Com_Ocom_OSKIP,X2,t_a)),t_a)
| hBOOL(hAPP(hAPP(X1,v_sko__Hoare__Mirabelle__Xconseq12__1(X1,X3,X2,X3)),v_sko__Hoare__Mirabelle__Xconseq12__2(X1,X3,X2,X3))) )
| ~ spl0_114
| ~ spl0_474 ),
inference(resolution,[],[f11022,f1542]) ).
fof(f11022,plain,
( ! [X65,X39,X11,X57,X35,X64] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X65,X35,X64,t_a)),t_a)
| c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X11,X35,X57,t_a)),t_a)
| hBOOL(hAPP(hAPP(X11,v_sko__Hoare__Mirabelle__Xconseq12__1(X11,X65,X57,X64)),v_sko__Hoare__Mirabelle__Xconseq12__2(X11,X65,X57,X64))) )
| ~ spl0_474 ),
inference(avatar_component_clause,[],[f11021]) ).
fof(f143894,plain,
( spl0_1560
| ~ spl0_61
| ~ spl0_457 ),
inference(avatar_split_clause,[],[f10663,f10489,f1279,f143892]) ).
fof(f143892,plain,
( spl0_1560
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X1),X2))
| hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X2),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X2),X1)) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1560])]) ).
fof(f1279,plain,
( spl0_61
<=> ! [X0,X1] : hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X1),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_61])]) ).
fof(f10489,plain,
( spl0_457
<=> ! [X5,X0,X12,X9] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X5),X9))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X9),X12))
| hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X9),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X12),X5)) = X5 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_457])]) ).
fof(f10663,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X1),X2))
| hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X2),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X2),X1)) = X1 )
| ~ spl0_61
| ~ spl0_457 ),
inference(resolution,[],[f10490,f1280]) ).
fof(f1280,plain,
( ! [X0,X1] : hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X1),X1))
| ~ spl0_61 ),
inference(avatar_component_clause,[],[f1279]) ).
fof(f10490,plain,
( ! [X0,X9,X5,X12] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X9),X12))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X5),X9))
| hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X9),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X12),X5)) = X5 )
| ~ spl0_457 ),
inference(avatar_component_clause,[],[f10489]) ).
fof(f143890,plain,
( spl0_1559
| ~ spl0_284
| ~ spl0_447 ),
inference(avatar_split_clause,[],[f10140,f9786,f3883,f143888]) ).
fof(f143888,plain,
( spl0_1559
<=> ! [X0,X3,X2,X1] :
( ~ class_Lattices_Olattice(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X3))),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2)))
| ~ class_Lattices_Olower__semilattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1559])]) ).
fof(f3883,plain,
( spl0_284
<=> ! [X4,X0,X3,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),X4))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_284])]) ).
fof(f9786,plain,
( spl0_447
<=> ! [X0,X6,X2,X1] :
( ~ class_Lattices_Olattice(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X6))),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X6)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_447])]) ).
fof(f10140,plain,
( ! [X2,X3,X0,X1] :
( ~ class_Lattices_Olattice(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X3))),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2)))
| ~ class_Lattices_Olower__semilattice(X0) )
| ~ spl0_284
| ~ spl0_447 ),
inference(resolution,[],[f9787,f3884]) ).
fof(f3884,plain,
( ! [X3,X0,X1,X4] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),X4)))
| hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X3))
| ~ class_Lattices_Olower__semilattice(X0) )
| ~ spl0_284 ),
inference(avatar_component_clause,[],[f3883]) ).
fof(f9787,plain,
( ! [X2,X0,X1,X6] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X6))),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X6))))
| ~ class_Lattices_Olattice(X0) )
| ~ spl0_447 ),
inference(avatar_component_clause,[],[f9786]) ).
fof(f143886,plain,
( spl0_1558
| ~ spl0_285
| ~ spl0_447 ),
inference(avatar_split_clause,[],[f10139,f9786,f3887,f143884]) ).
fof(f143884,plain,
( spl0_1558
<=> ! [X0,X3,X2,X1] :
( ~ class_Lattices_Olattice(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X3))),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X3)))
| ~ class_Lattices_Olower__semilattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1558])]) ).
fof(f3887,plain,
( spl0_285
<=> ! [X4,X0,X3,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),X4))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_285])]) ).
fof(f10139,plain,
( ! [X2,X3,X0,X1] :
( ~ class_Lattices_Olattice(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X3))),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X3)))
| ~ class_Lattices_Olower__semilattice(X0) )
| ~ spl0_285
| ~ spl0_447 ),
inference(resolution,[],[f9787,f3888]) ).
fof(f3888,plain,
( ! [X3,X0,X1,X4] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),X4)))
| hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X4))
| ~ class_Lattices_Olower__semilattice(X0) )
| ~ spl0_285 ),
inference(avatar_component_clause,[],[f3887]) ).
fof(f143882,plain,
( spl0_1557
| ~ spl0_297
| ~ spl0_447 ),
inference(avatar_split_clause,[],[f10135,f9786,f3943,f143880]) ).
fof(f143880,plain,
( spl0_1557
<=> ! [X0,X3,X2,X1] :
( ~ class_Lattices_Olattice(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X3))))
| ~ class_Lattices_Oupper__semilattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1557])]) ).
fof(f3943,plain,
( spl0_297
<=> ! [X4,X0,X3,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),X3),X1))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X3),X4)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_297])]) ).
fof(f10135,plain,
( ! [X2,X3,X0,X1] :
( ~ class_Lattices_Olattice(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X3))))
| ~ class_Lattices_Oupper__semilattice(X0) )
| ~ spl0_297
| ~ spl0_447 ),
inference(resolution,[],[f9787,f3944]) ).
fof(f3944,plain,
( ! [X3,X0,X1,X4] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X3),X4)),X1))
| hBOOL(hAPP(hAPP(c_lessequals(X0),X3),X1))
| ~ class_Lattices_Oupper__semilattice(X0) )
| ~ spl0_297 ),
inference(avatar_component_clause,[],[f3943]) ).
fof(f143878,plain,
( spl0_1556
| ~ spl0_284
| ~ spl0_446 ),
inference(avatar_split_clause,[],[f9882,f9782,f3883,f143876]) ).
fof(f143876,plain,
( spl0_1556
<=> ! [X0,X3,X2,X1] :
( ~ class_Lattices_Olattice(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X3))),X1))
| ~ class_Lattices_Olower__semilattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1556])]) ).
fof(f9782,plain,
( spl0_446
<=> ! [X0,X6,X2,X1] :
( ~ class_Lattices_Olattice(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X6))),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X2),X6)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_446])]) ).
fof(f9882,plain,
( ! [X2,X3,X0,X1] :
( ~ class_Lattices_Olattice(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X3))),X1))
| ~ class_Lattices_Olower__semilattice(X0) )
| ~ spl0_284
| ~ spl0_446 ),
inference(resolution,[],[f9783,f3884]) ).
fof(f9783,plain,
( ! [X2,X0,X1,X6] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X6))),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X2),X6))))
| ~ class_Lattices_Olattice(X0) )
| ~ spl0_446 ),
inference(avatar_component_clause,[],[f9782]) ).
fof(f143874,plain,
( spl0_1555
| ~ spl0_296
| ~ spl0_446 ),
inference(avatar_split_clause,[],[f9878,f9782,f3939,f143872]) ).
fof(f143872,plain,
( spl0_1555
<=> ! [X0,X3,X2,X1] :
( ~ class_Lattices_Olattice(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X3),X2))))
| ~ class_Lattices_Oupper__semilattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1555])]) ).
fof(f3939,plain,
( spl0_296
<=> ! [X4,X0,X3,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),X4),X1))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X3),X4)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_296])]) ).
fof(f9878,plain,
( ! [X2,X3,X0,X1] :
( ~ class_Lattices_Olattice(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X3),X2))))
| ~ class_Lattices_Oupper__semilattice(X0) )
| ~ spl0_296
| ~ spl0_446 ),
inference(resolution,[],[f9783,f3940]) ).
fof(f3940,plain,
( ! [X3,X0,X1,X4] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X3),X4)),X1))
| hBOOL(hAPP(hAPP(c_lessequals(X0),X4),X1))
| ~ class_Lattices_Oupper__semilattice(X0) )
| ~ spl0_296 ),
inference(avatar_component_clause,[],[f3939]) ).
fof(f143870,plain,
( spl0_1554
| ~ spl0_297
| ~ spl0_446 ),
inference(avatar_split_clause,[],[f9877,f9782,f3943,f143868]) ).
fof(f143868,plain,
( spl0_1554
<=> ! [X0,X3,X2,X1] :
( ~ class_Lattices_Olattice(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X2),X3))))
| ~ class_Lattices_Oupper__semilattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1554])]) ).
fof(f9877,plain,
( ! [X2,X3,X0,X1] :
( ~ class_Lattices_Olattice(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X2),X3))))
| ~ class_Lattices_Oupper__semilattice(X0) )
| ~ spl0_297
| ~ spl0_446 ),
inference(resolution,[],[f9783,f3944]) ).
fof(f143866,plain,
( spl0_1553
| ~ spl0_42
| ~ spl0_559 ),
inference(avatar_split_clause,[],[f15857,f15833,f1198,f143864]) ).
fof(f143864,plain,
( spl0_1553
<=> ! [X2,X0,X1] : hAPP(c_fequal(X2),X1) = hAPP(hAPP(c_Set_Oinsert(X0),X1),hAPP(c_fequal(X2),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1553])]) ).
fof(f1198,plain,
( spl0_42
<=> ! [X0,X1] : hBOOL(hAPP(hAPP(c_fequal(X0),X1),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_42])]) ).
fof(f15857,plain,
( ! [X2,X0,X1] : hAPP(c_fequal(X2),X1) = hAPP(hAPP(c_Set_Oinsert(X0),X1),hAPP(c_fequal(X2),X1))
| ~ spl0_42
| ~ spl0_559 ),
inference(resolution,[],[f15834,f1199]) ).
fof(f1199,plain,
( ! [X0,X1] : hBOOL(hAPP(hAPP(c_fequal(X0),X1),X1))
| ~ spl0_42 ),
inference(avatar_component_clause,[],[f1198]) ).
fof(f143862,plain,
( spl0_1552
| ~ spl0_202
| ~ spl0_437 ),
inference(avatar_split_clause,[],[f9573,f9311,f2080,f143860]) ).
fof(f143860,plain,
( spl0_1552
<=> ! [X4,X0,X3,X2,X1] :
( ~ hBOOL(c_in(X4,hAPP(hAPP(c_Set_Oinsert(X0),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X2),X3)),X0))
| hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X0),X1),X3),X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1552])]) ).
fof(f2080,plain,
( spl0_202
<=> ! [X11,X0,X5,X1] :
( ~ hBOOL(c_in(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X5),X11),X0))
| hBOOL(hAPP(X11,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_202])]) ).
fof(f9311,plain,
( spl0_437
<=> ! [X9,X0,X5,X3] : hAPP(hAPP(c_Set_Oinsert(X0),X3),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X5),X9)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Set_Oinsert(X0),X3),X5)),hAPP(hAPP(c_Set_Oinsert(X0),X3),X9)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_437])]) ).
fof(f9573,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ hBOOL(c_in(X4,hAPP(hAPP(c_Set_Oinsert(X0),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X2),X3)),X0))
| hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X0),X1),X3),X4)) )
| ~ spl0_202
| ~ spl0_437 ),
inference(superposition,[],[f2081,f9312]) ).
fof(f9312,plain,
( ! [X3,X0,X9,X5] : hAPP(hAPP(c_Set_Oinsert(X0),X3),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X5),X9)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Set_Oinsert(X0),X3),X5)),hAPP(hAPP(c_Set_Oinsert(X0),X3),X9))
| ~ spl0_437 ),
inference(avatar_component_clause,[],[f9311]) ).
fof(f2081,plain,
( ! [X0,X11,X1,X5] :
( ~ hBOOL(c_in(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X5),X11),X0))
| hBOOL(hAPP(X11,X1)) )
| ~ spl0_202 ),
inference(avatar_component_clause,[],[f2080]) ).
fof(f143858,plain,
( spl0_1551
| ~ spl0_190
| ~ spl0_437 ),
inference(avatar_split_clause,[],[f9572,f9311,f2025,f143856]) ).
fof(f143856,plain,
( spl0_1551
<=> ! [X0,X3,X2,X1] : hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Set_Oinsert(X0),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X2),X3))),hAPP(hAPP(c_Set_Oinsert(X0),X1),X3))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1551])]) ).
fof(f2025,plain,
( spl0_190
<=> ! [X9,X5,X0] : hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X5),X9)),X9)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_190])]) ).
fof(f9572,plain,
( ! [X2,X3,X0,X1] : hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Set_Oinsert(X0),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X2),X3))),hAPP(hAPP(c_Set_Oinsert(X0),X1),X3)))
| ~ spl0_190
| ~ spl0_437 ),
inference(superposition,[],[f2026,f9312]) ).
fof(f2026,plain,
( ! [X0,X9,X5] : hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X5),X9)),X9))
| ~ spl0_190 ),
inference(avatar_component_clause,[],[f2025]) ).
fof(f143854,plain,
( spl0_1550
| ~ spl0_189
| ~ spl0_437 ),
inference(avatar_split_clause,[],[f9571,f9311,f2021,f143852]) ).
fof(f143852,plain,
( spl0_1550
<=> ! [X0,X3,X2,X1] : hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Set_Oinsert(X0),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X2),X3))),hAPP(hAPP(c_Set_Oinsert(X0),X1),X2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1550])]) ).
fof(f2021,plain,
( spl0_189
<=> ! [X9,X5,X0] : hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X5),X9)),X5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_189])]) ).
fof(f9571,plain,
( ! [X2,X3,X0,X1] : hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Set_Oinsert(X0),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X2),X3))),hAPP(hAPP(c_Set_Oinsert(X0),X1),X2)))
| ~ spl0_189
| ~ spl0_437 ),
inference(superposition,[],[f2022,f9312]) ).
fof(f2022,plain,
( ! [X0,X9,X5] : hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X5),X9)),X5))
| ~ spl0_189 ),
inference(avatar_component_clause,[],[f2021]) ).
fof(f143850,plain,
( spl0_1549
| ~ spl0_265
| ~ spl0_429 ),
inference(avatar_split_clause,[],[f9130,f8411,f3129,f143848]) ).
fof(f143848,plain,
( spl0_1549
<=> ! [X0,X3,X2,X1] :
( c_COMBK(c_False,tc_bool,X0) != hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X2),X3))
| c_COMBK(c_False,tc_bool,X0) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1549])]) ).
fof(f3129,plain,
( spl0_265
<=> ! [X5,X9,X0] :
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X5),X9) != c_COMBK(c_False,tc_bool,X0)
| c_COMBK(c_False,tc_bool,X0) = X9 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_265])]) ).
fof(f8411,plain,
( spl0_429
<=> ! [X5,X0,X12,X9] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X5),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X9),X12)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X5),X9)),X12) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_429])]) ).
fof(f9130,plain,
( ! [X2,X3,X0,X1] :
( c_COMBK(c_False,tc_bool,X0) != hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X2),X3))
| c_COMBK(c_False,tc_bool,X0) = X3 )
| ~ spl0_265
| ~ spl0_429 ),
inference(superposition,[],[f3130,f8412]) ).
fof(f8412,plain,
( ! [X0,X9,X5,X12] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X5),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X9),X12)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X5),X9)),X12)
| ~ spl0_429 ),
inference(avatar_component_clause,[],[f8411]) ).
fof(f3130,plain,
( ! [X0,X9,X5] :
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X5),X9) != c_COMBK(c_False,tc_bool,X0)
| c_COMBK(c_False,tc_bool,X0) = X9 )
| ~ spl0_265 ),
inference(avatar_component_clause,[],[f3129]) ).
fof(f143846,plain,
( spl0_1548
| ~ spl0_266
| ~ spl0_428 ),
inference(avatar_split_clause,[],[f8926,f8407,f3133,f143844]) ).
fof(f143844,plain,
( spl0_1548
<=> ! [X0,X3,X2,X1] :
( c_COMBK(c_False,tc_bool,X0) != hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X3))
| c_COMBK(c_False,tc_bool,X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1548])]) ).
fof(f3133,plain,
( spl0_266
<=> ! [X5,X9,X0] :
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X5),X9) != c_COMBK(c_False,tc_bool,X0)
| c_COMBK(c_False,tc_bool,X0) = X5 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_266])]) ).
fof(f8407,plain,
( spl0_428
<=> ! [X5,X0,X12,X9] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X5),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X9),X12)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X9),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X5),X12)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_428])]) ).
fof(f8926,plain,
( ! [X2,X3,X0,X1] :
( c_COMBK(c_False,tc_bool,X0) != hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X3))
| c_COMBK(c_False,tc_bool,X0) = X1 )
| ~ spl0_266
| ~ spl0_428 ),
inference(superposition,[],[f3134,f8408]) ).
fof(f8408,plain,
( ! [X0,X9,X5,X12] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X5),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X9),X12)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X9),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X5),X12))
| ~ spl0_428 ),
inference(avatar_component_clause,[],[f8407]) ).
fof(f3134,plain,
( ! [X0,X9,X5] :
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X5),X9) != c_COMBK(c_False,tc_bool,X0)
| c_COMBK(c_False,tc_bool,X0) = X5 )
| ~ spl0_266 ),
inference(avatar_component_clause,[],[f3133]) ).
fof(f143842,plain,
( spl0_1547
| ~ spl0_150
| ~ spl0_170
| ~ spl0_342
| ~ spl0_422 ),
inference(avatar_split_clause,[],[f8470,f8383,f4957,f1869,f1732,f143840]) ).
fof(f143840,plain,
( spl0_1547
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),hAPP(c_fequal(X1),X3)),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X0),X2))
| ~ hBOOL(c_in(X3,X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1547])]) ).
fof(f1869,plain,
( spl0_170
<=> ! [X11,X57,X0,X14,X67,X8] : hAPP(hAPP(c_COMBC(X11,X8,X14,X0),X57),X67) = hAPP(hAPP(X11,X67),X57) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_170])]) ).
fof(f4957,plain,
( spl0_342
<=> ! [X5,X0] : c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,hAPP(c_COMBC(c_Set_Oinsert(X0),X0,tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0)),X0,tc_fun(X0,tc_bool)) = X5 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_342])]) ).
fof(f8383,plain,
( spl0_422
<=> ! [X5,X9,X0,X8,X36,X1] :
( ~ hBOOL(c_in(X1,X36,X8))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),hAPP(X5,X1)),X9))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X36,X5,X8,tc_fun(X0,tc_bool))),X9)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_422])]) ).
fof(f8470,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),hAPP(c_fequal(X1),X3)),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X0),X2))
| ~ hBOOL(c_in(X3,X0,X1)) )
| ~ spl0_150
| ~ spl0_170
| ~ spl0_342
| ~ spl0_422 ),
inference(forward_demodulation,[],[f8469,f1733]) ).
fof(f8469,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_COMBK(c_False,tc_bool,X1))),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X0),X2))
| ~ hBOOL(c_in(X3,X0,X1)) )
| ~ spl0_170
| ~ spl0_342
| ~ spl0_422 ),
inference(forward_demodulation,[],[f8464,f1870]) ).
fof(f1870,plain,
( ! [X0,X11,X8,X57,X14,X67] : hAPP(hAPP(c_COMBC(X11,X8,X14,X0),X57),X67) = hAPP(hAPP(X11,X67),X57)
| ~ spl0_170 ),
inference(avatar_component_clause,[],[f1869]) ).
fof(f8464,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X0),X2))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),hAPP(hAPP(c_COMBC(c_Set_Oinsert(X1),X1,tc_fun(X1,tc_bool),tc_fun(X1,tc_bool)),c_COMBK(c_False,tc_bool,X1)),X3)),X2))
| ~ hBOOL(c_in(X3,X0,X1)) )
| ~ spl0_342
| ~ spl0_422 ),
inference(superposition,[],[f8384,f4958]) ).
fof(f4958,plain,
( ! [X0,X5] : c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,hAPP(c_COMBC(c_Set_Oinsert(X0),X0,tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0)),X0,tc_fun(X0,tc_bool)) = X5
| ~ spl0_342 ),
inference(avatar_component_clause,[],[f4957]) ).
fof(f8384,plain,
( ! [X0,X36,X1,X8,X9,X5] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X36,X5,X8,tc_fun(X0,tc_bool))),X9))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),hAPP(X5,X1)),X9))
| ~ hBOOL(c_in(X1,X36,X8)) )
| ~ spl0_422 ),
inference(avatar_component_clause,[],[f8383]) ).
fof(f143838,plain,
( spl0_1546
| ~ spl0_202
| ~ spl0_412 ),
inference(avatar_split_clause,[],[f8292,f7695,f2080,f143836]) ).
fof(f143836,plain,
( spl0_1546
<=> ! [X2,X4,X0,X3,X5,X1] :
( ~ hBOOL(c_in(X5,c_Complete__Lattice_Ocomplete__lattice__class_OINFI(hAPP(hAPP(c_Set_Oinsert(X4),X2),X3),X1,X4,tc_fun(X0,tc_bool)),X0))
| hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X3,X1,X4,tc_fun(X0,tc_bool)),X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1546])]) ).
fof(f7695,plain,
( spl0_412
<=> ! [X3,X9,X0,X5,X8] : c_Complete__Lattice_Ocomplete__lattice__class_OINFI(hAPP(hAPP(c_Set_Oinsert(X8),X3),X5),X9,X8,tc_fun(X0,tc_bool)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),hAPP(X9,X3)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,X9,X8,tc_fun(X0,tc_bool))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_412])]) ).
fof(f8292,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ hBOOL(c_in(X5,c_Complete__Lattice_Ocomplete__lattice__class_OINFI(hAPP(hAPP(c_Set_Oinsert(X4),X2),X3),X1,X4,tc_fun(X0,tc_bool)),X0))
| hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X3,X1,X4,tc_fun(X0,tc_bool)),X5)) )
| ~ spl0_202
| ~ spl0_412 ),
inference(superposition,[],[f2081,f7696]) ).
fof(f7696,plain,
( ! [X3,X0,X8,X9,X5] : c_Complete__Lattice_Ocomplete__lattice__class_OINFI(hAPP(hAPP(c_Set_Oinsert(X8),X3),X5),X9,X8,tc_fun(X0,tc_bool)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),hAPP(X9,X3)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,X9,X8,tc_fun(X0,tc_bool)))
| ~ spl0_412 ),
inference(avatar_component_clause,[],[f7695]) ).
fof(f143834,plain,
( spl0_1545
| ~ spl0_190
| ~ spl0_412 ),
inference(avatar_split_clause,[],[f8291,f7695,f2025,f143832]) ).
fof(f143832,plain,
( spl0_1545
<=> ! [X2,X4,X0,X3,X1] : hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(hAPP(hAPP(c_Set_Oinsert(X4),X2),X3),X1,X4,tc_fun(X0,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X3,X1,X4,tc_fun(X0,tc_bool)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1545])]) ).
fof(f8291,plain,
( ! [X2,X3,X0,X1,X4] : hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(hAPP(hAPP(c_Set_Oinsert(X4),X2),X3),X1,X4,tc_fun(X0,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X3,X1,X4,tc_fun(X0,tc_bool))))
| ~ spl0_190
| ~ spl0_412 ),
inference(superposition,[],[f2026,f7696]) ).
fof(f143830,plain,
( spl0_1544
| ~ spl0_184
| ~ spl0_410 ),
inference(avatar_split_clause,[],[f8124,f7687,f2001,f143828]) ).
fof(f143828,plain,
( spl0_1544
<=> ! [X2,X4,X0,X3,X1] : hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,X1,X4,tc_fun(X0,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_Set_Oinsert(X4),X2),X3),X1,X4,tc_fun(X0,tc_bool)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1544])]) ).
fof(f2001,plain,
( spl0_184
<=> ! [X9,X5,X0] : hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X9),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X5),X9))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_184])]) ).
fof(f7687,plain,
( spl0_410
<=> ! [X3,X9,X0,X5,X8] : c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_Set_Oinsert(X8),X3),X5),X9,X8,tc_fun(X0,tc_bool)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),hAPP(X9,X3)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,X9,X8,tc_fun(X0,tc_bool))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_410])]) ).
fof(f8124,plain,
( ! [X2,X3,X0,X1,X4] : hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,X1,X4,tc_fun(X0,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_Set_Oinsert(X4),X2),X3),X1,X4,tc_fun(X0,tc_bool))))
| ~ spl0_184
| ~ spl0_410 ),
inference(superposition,[],[f2002,f7688]) ).
fof(f7688,plain,
( ! [X3,X0,X8,X9,X5] : c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_Set_Oinsert(X8),X3),X5),X9,X8,tc_fun(X0,tc_bool)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),hAPP(X9,X3)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,X9,X8,tc_fun(X0,tc_bool)))
| ~ spl0_410 ),
inference(avatar_component_clause,[],[f7687]) ).
fof(f2002,plain,
( ! [X0,X9,X5] : hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X9),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X5),X9)))
| ~ spl0_184 ),
inference(avatar_component_clause,[],[f2001]) ).
fof(f143826,plain,
( spl0_1543
| ~ spl0_130
| ~ spl0_262
| ~ spl0_263
| ~ spl0_416 ),
inference(avatar_split_clause,[],[f7975,f7848,f3121,f3117,f1631,f143824]) ).
fof(f143824,plain,
( spl0_1543
<=> ! [X4,X0,X1] :
( c_COMBK(c_False,tc_bool,X4) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X4,tc_bool)),hAPP(c_fequal(X4),c_COMBK(c_False,tc_bool,X0))),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1))
| hBOOL(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1543])]) ).
fof(f3121,plain,
( spl0_263
<=> ! [X5,X0,X9,X8] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X5),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_COMBK(c_False,tc_bool,X8),X9,X8,tc_fun(X0,tc_bool))) = X5 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_263])]) ).
fof(f7848,plain,
( spl0_416
<=> ! [X0,X11,X3] :
( c_COMBK(c_False,tc_bool,X0) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),hAPP(c_fequal(X0),X3)),X11)
| hBOOL(hAPP(X11,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_416])]) ).
fof(f7975,plain,
( ! [X0,X1,X4] :
( c_COMBK(c_False,tc_bool,X4) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X4,tc_bool)),hAPP(c_fequal(X4),c_COMBK(c_False,tc_bool,X0))),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1))
| hBOOL(X1) )
| ~ spl0_130
| ~ spl0_262
| ~ spl0_263
| ~ spl0_416 ),
inference(forward_demodulation,[],[f7946,f3466]) ).
fof(f7946,plain,
( ! [X2,X3,X0,X1,X4] :
( hBOOL(X1)
| c_COMBK(c_False,tc_bool,X4) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X4,tc_bool)),hAPP(c_fequal(X4),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_COMBK(c_False,tc_bool,X2),X3,X2,tc_fun(X0,tc_bool)))),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1)) )
| ~ spl0_263
| ~ spl0_416 ),
inference(superposition,[],[f7849,f3122]) ).
fof(f3122,plain,
( ! [X0,X8,X9,X5] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X5),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_COMBK(c_False,tc_bool,X8),X9,X8,tc_fun(X0,tc_bool))) = X5
| ~ spl0_263 ),
inference(avatar_component_clause,[],[f3121]) ).
fof(f7849,plain,
( ! [X3,X0,X11] :
( hBOOL(hAPP(X11,X3))
| c_COMBK(c_False,tc_bool,X0) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),hAPP(c_fequal(X0),X3)),X11) )
| ~ spl0_416 ),
inference(avatar_component_clause,[],[f7848]) ).
fof(f143822,plain,
( spl0_1542
| ~ spl0_30
| ~ spl0_558 ),
inference(avatar_split_clause,[],[f15852,f15829,f1147,f143820]) ).
fof(f143820,plain,
( spl0_1542
<=> ! [X0,X3,X2,X1] :
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_fun(X1,X2))),X3),X3) = X3
| ~ class_Lattices_Olattice(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1542])]) ).
fof(f1147,plain,
( spl0_30
<=> ! [X75,X74] :
( ~ class_Lattices_Olattice(X75)
| class_Lattices_Olattice(tc_fun(X74,X75)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_30])]) ).
fof(f15829,plain,
( spl0_558
<=> ! [X2,X0,X1] :
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,X1)),X2),X2) = X2
| ~ class_Lattices_Olattice(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_558])]) ).
fof(f15852,plain,
( ! [X2,X3,X0,X1] :
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_fun(X1,X2))),X3),X3) = X3
| ~ class_Lattices_Olattice(X2) )
| ~ spl0_30
| ~ spl0_558 ),
inference(resolution,[],[f15830,f1148]) ).
fof(f1148,plain,
( ! [X74,X75] :
( class_Lattices_Olattice(tc_fun(X74,X75))
| ~ class_Lattices_Olattice(X75) )
| ~ spl0_30 ),
inference(avatar_component_clause,[],[f1147]) ).
fof(f15830,plain,
( ! [X2,X0,X1] :
( ~ class_Lattices_Olattice(X1)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,X1)),X2),X2) = X2 )
| ~ spl0_558 ),
inference(avatar_component_clause,[],[f15829]) ).
fof(f143818,plain,
( spl0_1541
| ~ spl0_130
| ~ spl0_262
| ~ spl0_416 ),
inference(avatar_split_clause,[],[f7974,f7848,f3117,f1631,f143816]) ).
fof(f143816,plain,
( spl0_1541
<=> ! [X4,X0,X1] :
( c_COMBK(c_False,tc_bool,X4) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X4,tc_bool)),hAPP(c_fequal(X4),c_COMBK(c_False,tc_bool,X0))),hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X1))
| hBOOL(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1541])]) ).
fof(f7974,plain,
( ! [X0,X1,X4] :
( c_COMBK(c_False,tc_bool,X4) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X4,tc_bool)),hAPP(c_fequal(X4),c_COMBK(c_False,tc_bool,X0))),hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X1))
| hBOOL(X1) )
| ~ spl0_130
| ~ spl0_262
| ~ spl0_416 ),
inference(forward_demodulation,[],[f7945,f3466]) ).
fof(f7945,plain,
( ! [X2,X3,X0,X1,X4] :
( hBOOL(X1)
| c_COMBK(c_False,tc_bool,X4) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X4,tc_bool)),hAPP(c_fequal(X4),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_COMBK(c_False,tc_bool,X2),X3,X2,tc_fun(X0,tc_bool)))),hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X1)) )
| ~ spl0_262
| ~ spl0_416 ),
inference(superposition,[],[f7849,f3118]) ).
fof(f143814,plain,
( spl0_1540
| ~ spl0_120
| ~ spl0_416 ),
inference(avatar_split_clause,[],[f7957,f7848,f1591,f143812]) ).
fof(f143812,plain,
( spl0_1540
<=> ! [X4,X0,X3,X2,X1] :
( hBOOL(X0)
| c_COMBK(c_False,tc_bool,X4) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X4,tc_bool)),hAPP(c_fequal(X4),v_x)),c_Fun_Ocomp(c_COMBK(X0,X1,X2),X3,X2,X1,t_a)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1540])]) ).
fof(f1591,plain,
( spl0_120
<=> ! [X35,X7,X14,X8] : hAPP(c_Fun_Ocomp(c_COMBK(X35,X8,X14),X7,X14,X8,t_a),v_x) = X35 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_120])]) ).
fof(f7957,plain,
( ! [X2,X3,X0,X1,X4] :
( hBOOL(X0)
| c_COMBK(c_False,tc_bool,X4) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X4,tc_bool)),hAPP(c_fequal(X4),v_x)),c_Fun_Ocomp(c_COMBK(X0,X1,X2),X3,X2,X1,t_a)) )
| ~ spl0_120
| ~ spl0_416 ),
inference(superposition,[],[f7849,f1592]) ).
fof(f1592,plain,
( ! [X8,X7,X14,X35] : hAPP(c_Fun_Ocomp(c_COMBK(X35,X8,X14),X7,X14,X8,t_a),v_x) = X35
| ~ spl0_120 ),
inference(avatar_component_clause,[],[f1591]) ).
fof(f143810,plain,
( spl0_1539
| ~ spl0_125
| ~ spl0_416 ),
inference(avatar_split_clause,[],[f7947,f7848,f1611,f143808]) ).
fof(f143808,plain,
( spl0_1539
<=> ! [X2,X0,X1] :
( hBOOL(X1)
| c_COMBK(c_False,tc_bool,X2) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),hAPP(c_fequal(X2),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)))),hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1539])]) ).
fof(f1611,plain,
( spl0_125
<=> ! [X5,X0] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X5),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool))) = X5 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_125])]) ).
fof(f7947,plain,
( ! [X2,X0,X1] :
( hBOOL(X1)
| c_COMBK(c_False,tc_bool,X2) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),hAPP(c_fequal(X2),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)))),hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X1)) )
| ~ spl0_125
| ~ spl0_416 ),
inference(superposition,[],[f7849,f1612]) ).
fof(f1612,plain,
( ! [X0,X5] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X5),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool))) = X5
| ~ spl0_125 ),
inference(avatar_component_clause,[],[f1611]) ).
fof(f143806,plain,
( spl0_1538
| ~ spl0_133
| ~ spl0_416 ),
inference(avatar_split_clause,[],[f7918,f7848,f1643,f143804]) ).
fof(f143804,plain,
( spl0_1538
<=> ! [X2,X0,X1] :
( hBOOL(X1)
| c_COMBK(c_False,tc_bool,X2) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),hAPP(c_fequal(X2),X1)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1538])]) ).
fof(f1643,plain,
( spl0_133
<=> ! [X9,X0] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0)),X9) = X9 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_133])]) ).
fof(f7918,plain,
( ! [X2,X0,X1] :
( hBOOL(X1)
| c_COMBK(c_False,tc_bool,X2) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),hAPP(c_fequal(X2),X1)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0))) )
| ~ spl0_133
| ~ spl0_416 ),
inference(superposition,[],[f7849,f1644]) ).
fof(f1644,plain,
( ! [X0,X9] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0)),X9) = X9
| ~ spl0_133 ),
inference(avatar_component_clause,[],[f1643]) ).
fof(f143802,plain,
( spl0_1537
| ~ spl0_123
| ~ spl0_416 ),
inference(avatar_split_clause,[],[f7916,f7848,f1603,f143800]) ).
fof(f143800,plain,
( spl0_1537
<=> ! [X2,X0,X1] :
( hBOOL(X1)
| c_COMBK(c_False,tc_bool,X2) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),hAPP(c_fequal(X2),X1)),hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1537])]) ).
fof(f1603,plain,
( spl0_123
<=> ! [X9,X0] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool))),X9) = X9 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_123])]) ).
fof(f7916,plain,
( ! [X2,X0,X1] :
( hBOOL(X1)
| c_COMBK(c_False,tc_bool,X2) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),hAPP(c_fequal(X2),X1)),hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)))) )
| ~ spl0_123
| ~ spl0_416 ),
inference(superposition,[],[f7849,f1604]) ).
fof(f1604,plain,
( ! [X0,X9] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool))),X9) = X9
| ~ spl0_123 ),
inference(avatar_component_clause,[],[f1603]) ).
fof(f143798,plain,
( spl0_1536
| ~ spl0_130
| ~ spl0_416 ),
inference(avatar_split_clause,[],[f7915,f7848,f1631,f143796]) ).
fof(f143796,plain,
( spl0_1536
<=> ! [X2,X0,X1] :
( hBOOL(c_COMBK(c_False,tc_bool,X0))
| c_COMBK(c_False,tc_bool,X2) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),hAPP(c_fequal(X2),X1)),hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1536])]) ).
fof(f7915,plain,
( ! [X2,X0,X1] :
( hBOOL(c_COMBK(c_False,tc_bool,X0))
| c_COMBK(c_False,tc_bool,X2) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),hAPP(c_fequal(X2),X1)),hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X1)) )
| ~ spl0_130
| ~ spl0_416 ),
inference(superposition,[],[f7849,f1632]) ).
fof(f143794,plain,
( spl0_1535
| ~ spl0_120
| ~ spl0_414 ),
inference(avatar_split_clause,[],[f7814,f7704,f1591,f143792]) ).
fof(f143792,plain,
( spl0_1535
<=> ! [X4,X0,X3,X2,X1] :
( ~ hBOOL(X0)
| hAPP(c_fequal(X4),v_x) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X4,tc_bool)),hAPP(c_fequal(X4),v_x)),c_Fun_Ocomp(c_COMBK(X0,X1,X2),X3,X2,X1,t_a)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1535])]) ).
fof(f7704,plain,
( spl0_414
<=> ! [X0,X11,X3] :
( hAPP(c_fequal(X0),X3) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),hAPP(c_fequal(X0),X3)),X11)
| ~ hBOOL(hAPP(X11,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_414])]) ).
fof(f7814,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ hBOOL(X0)
| hAPP(c_fequal(X4),v_x) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X4,tc_bool)),hAPP(c_fequal(X4),v_x)),c_Fun_Ocomp(c_COMBK(X0,X1,X2),X3,X2,X1,t_a)) )
| ~ spl0_120
| ~ spl0_414 ),
inference(superposition,[],[f7705,f1592]) ).
fof(f7705,plain,
( ! [X3,X0,X11] :
( ~ hBOOL(hAPP(X11,X3))
| hAPP(c_fequal(X0),X3) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),hAPP(c_fequal(X0),X3)),X11) )
| ~ spl0_414 ),
inference(avatar_component_clause,[],[f7704]) ).
fof(f143790,plain,
( spl0_1534
| ~ spl0_133
| ~ spl0_414 ),
inference(avatar_split_clause,[],[f7775,f7704,f1643,f143788]) ).
fof(f143788,plain,
( spl0_1534
<=> ! [X2,X0,X1] :
( ~ hBOOL(X1)
| hAPP(c_fequal(X2),X1) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),hAPP(c_fequal(X2),X1)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1534])]) ).
fof(f7775,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(X1)
| hAPP(c_fequal(X2),X1) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),hAPP(c_fequal(X2),X1)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0))) )
| ~ spl0_133
| ~ spl0_414 ),
inference(superposition,[],[f7705,f1644]) ).
fof(f143786,plain,
( spl0_1533
| ~ spl0_123
| ~ spl0_414 ),
inference(avatar_split_clause,[],[f7773,f7704,f1603,f143784]) ).
fof(f143784,plain,
( spl0_1533
<=> ! [X2,X0,X1] :
( ~ hBOOL(X1)
| hAPP(c_fequal(X2),X1) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),hAPP(c_fequal(X2),X1)),hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1533])]) ).
fof(f7773,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(X1)
| hAPP(c_fequal(X2),X1) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),hAPP(c_fequal(X2),X1)),hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)))) )
| ~ spl0_123
| ~ spl0_414 ),
inference(superposition,[],[f7705,f1604]) ).
fof(f143782,plain,
( spl0_1532
| ~ spl0_130
| ~ spl0_414 ),
inference(avatar_split_clause,[],[f7772,f7704,f1631,f143780]) ).
fof(f143780,plain,
( spl0_1532
<=> ! [X2,X0,X1] :
( ~ hBOOL(c_COMBK(c_False,tc_bool,X0))
| hAPP(c_fequal(X2),X1) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),hAPP(c_fequal(X2),X1)),hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1532])]) ).
fof(f7772,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(c_COMBK(c_False,tc_bool,X0))
| hAPP(c_fequal(X2),X1) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),hAPP(c_fequal(X2),X1)),hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X1)) )
| ~ spl0_130
| ~ spl0_414 ),
inference(superposition,[],[f7705,f1632]) ).
fof(f143778,plain,
( spl0_1531
| ~ spl0_30
| ~ spl0_557 ),
inference(avatar_split_clause,[],[f15850,f15825,f1147,f143776]) ).
fof(f143776,plain,
( spl0_1531
<=> ! [X0,X3,X2,X1] :
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_fun(X1,X2))),X3),X3) = X3
| ~ class_Lattices_Olattice(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1531])]) ).
fof(f15825,plain,
( spl0_557
<=> ! [X2,X0,X1] :
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,X1)),X2),X2) = X2
| ~ class_Lattices_Olattice(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_557])]) ).
fof(f15850,plain,
( ! [X2,X3,X0,X1] :
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_fun(X1,X2))),X3),X3) = X3
| ~ class_Lattices_Olattice(X2) )
| ~ spl0_30
| ~ spl0_557 ),
inference(resolution,[],[f15826,f1148]) ).
fof(f15826,plain,
( ! [X2,X0,X1] :
( ~ class_Lattices_Olattice(X1)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,X1)),X2),X2) = X2 )
| ~ spl0_557 ),
inference(avatar_component_clause,[],[f15825]) ).
fof(f143774,plain,
( spl0_1530
| ~ spl0_143
| ~ spl0_414 ),
inference(avatar_split_clause,[],[f7723,f7704,f1704,f143772]) ).
fof(f143772,plain,
( spl0_1530
<=> ! [X0,X3,X2,X1] :
( hAPP(c_fequal(X0),X1) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),hAPP(c_fequal(X0),X1)),hAPP(c_lessequals(X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),X3),X1)))
| ~ class_Lattices_Olattice(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1530])]) ).
fof(f1704,plain,
( spl0_143
<=> ! [X2,X0,X1] :
( ~ class_Lattices_Olattice(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2)),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_143])]) ).
fof(f7723,plain,
( ! [X2,X3,X0,X1] :
( hAPP(c_fequal(X0),X1) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),hAPP(c_fequal(X0),X1)),hAPP(c_lessequals(X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),X3),X1)))
| ~ class_Lattices_Olattice(X2) )
| ~ spl0_143
| ~ spl0_414 ),
inference(resolution,[],[f7705,f1705]) ).
fof(f1705,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2)),X2))
| ~ class_Lattices_Olattice(X0) )
| ~ spl0_143 ),
inference(avatar_component_clause,[],[f1704]) ).
fof(f143770,plain,
( spl0_1529
| ~ spl0_144
| ~ spl0_414 ),
inference(avatar_split_clause,[],[f7722,f7704,f1708,f143768]) ).
fof(f143768,plain,
( spl0_1529
<=> ! [X0,X3,X2,X1] :
( hAPP(c_fequal(X0),X1) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),hAPP(c_fequal(X0),X1)),hAPP(c_lessequals(X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),X3),X1)))
| ~ class_Lattices_Olower__semilattice(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1529])]) ).
fof(f1708,plain,
( spl0_144
<=> ! [X2,X0,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2)),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_144])]) ).
fof(f7722,plain,
( ! [X2,X3,X0,X1] :
( hAPP(c_fequal(X0),X1) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),hAPP(c_fequal(X0),X1)),hAPP(c_lessequals(X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),X3),X1)))
| ~ class_Lattices_Olower__semilattice(X2) )
| ~ spl0_144
| ~ spl0_414 ),
inference(resolution,[],[f7705,f1709]) ).
fof(f1709,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2)),X2))
| ~ class_Lattices_Olower__semilattice(X0) )
| ~ spl0_144 ),
inference(avatar_component_clause,[],[f1708]) ).
fof(f143766,plain,
( spl0_1528
| ~ spl0_142
| ~ spl0_414 ),
inference(avatar_split_clause,[],[f7717,f7704,f1700,f143764]) ).
fof(f143764,plain,
( spl0_1528
<=> ! [X0,X3,X2,X1] :
( hAPP(c_fequal(X0),X1) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),hAPP(c_fequal(X0),X1)),hAPP(c_lessequals(X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),X1),X3)))
| ~ class_Lattices_Olattice(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1528])]) ).
fof(f1700,plain,
( spl0_142
<=> ! [X2,X0,X1] :
( ~ class_Lattices_Olattice(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_142])]) ).
fof(f7717,plain,
( ! [X2,X3,X0,X1] :
( hAPP(c_fequal(X0),X1) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),hAPP(c_fequal(X0),X1)),hAPP(c_lessequals(X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),X1),X3)))
| ~ class_Lattices_Olattice(X2) )
| ~ spl0_142
| ~ spl0_414 ),
inference(resolution,[],[f7705,f1701]) ).
fof(f1701,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2)),X1))
| ~ class_Lattices_Olattice(X0) )
| ~ spl0_142 ),
inference(avatar_component_clause,[],[f1700]) ).
fof(f143762,plain,
( spl0_1527
| ~ spl0_145
| ~ spl0_414 ),
inference(avatar_split_clause,[],[f7716,f7704,f1712,f143760]) ).
fof(f143760,plain,
( spl0_1527
<=> ! [X0,X3,X2,X1] :
( hAPP(c_fequal(X0),X1) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),hAPP(c_fequal(X0),X1)),hAPP(c_lessequals(X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),X1),X3)))
| ~ class_Lattices_Olower__semilattice(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1527])]) ).
fof(f1712,plain,
( spl0_145
<=> ! [X2,X0,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_145])]) ).
fof(f7716,plain,
( ! [X2,X3,X0,X1] :
( hAPP(c_fequal(X0),X1) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),hAPP(c_fequal(X0),X1)),hAPP(c_lessequals(X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),X1),X3)))
| ~ class_Lattices_Olower__semilattice(X2) )
| ~ spl0_145
| ~ spl0_414 ),
inference(resolution,[],[f7705,f1713]) ).
fof(f1713,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2)),X1))
| ~ class_Lattices_Olower__semilattice(X0) )
| ~ spl0_145 ),
inference(avatar_component_clause,[],[f1712]) ).
fof(f143758,plain,
( spl0_1526
| ~ spl0_16
| ~ spl0_406 ),
inference(avatar_split_clause,[],[f7676,f7160,f1090,f143756]) ).
fof(f143756,plain,
( spl0_1526
<=> ! [X2,X0,X1] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X1),X2) = hAPP(hAPP(c_COMBS(X0,tc_bool,tc_bool),hAPP(hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),X0),c_and),X1)),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1526])]) ).
fof(f1090,plain,
( spl0_16
<=> ! [X0,X11] : c_Collect(X11,X0) = X11 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_16])]) ).
fof(f7160,plain,
( spl0_406
<=> ! [X57,X0,X11] : c_Collect(hAPP(hAPP(c_COMBS(X0,tc_bool,tc_bool),hAPP(hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),X0),c_and),X11)),X57),X0) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X11),X57) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_406])]) ).
fof(f7676,plain,
( ! [X2,X0,X1] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X1),X2) = hAPP(hAPP(c_COMBS(X0,tc_bool,tc_bool),hAPP(hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),X0),c_and),X1)),X2)
| ~ spl0_16
| ~ spl0_406 ),
inference(superposition,[],[f7161,f1091]) ).
fof(f1091,plain,
( ! [X0,X11] : c_Collect(X11,X0) = X11
| ~ spl0_16 ),
inference(avatar_component_clause,[],[f1090]) ).
fof(f7161,plain,
( ! [X0,X11,X57] : c_Collect(hAPP(hAPP(c_COMBS(X0,tc_bool,tc_bool),hAPP(hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),X0),c_and),X11)),X57),X0) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X11),X57)
| ~ spl0_406 ),
inference(avatar_component_clause,[],[f7160]) ).
fof(f143754,plain,
( spl0_1525
| ~ spl0_16
| ~ spl0_405 ),
inference(avatar_split_clause,[],[f7673,f7156,f1090,f143752]) ).
fof(f143752,plain,
( spl0_1525
<=> ! [X2,X0,X1] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X2) = hAPP(hAPP(c_COMBS(X0,tc_bool,tc_bool),hAPP(hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),X0),c_or),X1)),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1525])]) ).
fof(f7156,plain,
( spl0_405
<=> ! [X57,X0,X11] : c_Collect(hAPP(hAPP(c_COMBS(X0,tc_bool,tc_bool),hAPP(hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),X0),c_or),X11)),X57),X0) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X11),X57) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_405])]) ).
fof(f7673,plain,
( ! [X2,X0,X1] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X2) = hAPP(hAPP(c_COMBS(X0,tc_bool,tc_bool),hAPP(hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),X0),c_or),X1)),X2)
| ~ spl0_16
| ~ spl0_405 ),
inference(superposition,[],[f7157,f1091]) ).
fof(f7157,plain,
( ! [X0,X11,X57] : c_Collect(hAPP(hAPP(c_COMBS(X0,tc_bool,tc_bool),hAPP(hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),X0),c_or),X11)),X57),X0) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X11),X57)
| ~ spl0_405 ),
inference(avatar_component_clause,[],[f7156]) ).
fof(f143750,plain,
( spl0_1524
| ~ spl0_185
| ~ spl0_391 ),
inference(avatar_split_clause,[],[f7011,f6760,f2005,f143748]) ).
fof(f143748,plain,
( spl0_1524
<=> ! [X0,X3,X2,X1] : hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Set_Oinsert(X0),X1),X2)),hAPP(hAPP(c_Set_Oinsert(X0),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X2),X3)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1524])]) ).
fof(f2005,plain,
( spl0_185
<=> ! [X9,X5,X0] : hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X5),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X5),X9))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_185])]) ).
fof(f6760,plain,
( spl0_391
<=> ! [X0,X12,X9,X3] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Set_Oinsert(X0),X3),X9)),X12) = hAPP(hAPP(c_Set_Oinsert(X0),X3),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X9),X12)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_391])]) ).
fof(f7011,plain,
( ! [X2,X3,X0,X1] : hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Set_Oinsert(X0),X1),X2)),hAPP(hAPP(c_Set_Oinsert(X0),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X2),X3))))
| ~ spl0_185
| ~ spl0_391 ),
inference(superposition,[],[f2006,f6761]) ).
fof(f6761,plain,
( ! [X3,X0,X9,X12] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Set_Oinsert(X0),X3),X9)),X12) = hAPP(hAPP(c_Set_Oinsert(X0),X3),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X9),X12))
| ~ spl0_391 ),
inference(avatar_component_clause,[],[f6760]) ).
fof(f2006,plain,
( ! [X0,X9,X5] : hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X5),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X5),X9)))
| ~ spl0_185 ),
inference(avatar_component_clause,[],[f2005]) ).
fof(f143746,plain,
( spl0_1523
| ~ spl0_182
| ~ spl0_391 ),
inference(avatar_split_clause,[],[f7009,f6760,f1993,f143744]) ).
fof(f143744,plain,
( spl0_1523
<=> ! [X0,X3,X2,X1] :
( c_Finite__Set_Ofinite(hAPP(hAPP(c_Set_Oinsert(X0),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X2),X3)),X0)
| ~ c_Finite__Set_Ofinite(X3,X0)
| ~ c_Finite__Set_Ofinite(hAPP(hAPP(c_Set_Oinsert(X0),X1),X2),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1523])]) ).
fof(f1993,plain,
( spl0_182
<=> ! [X38,X0,X39] :
( ~ c_Finite__Set_Ofinite(X38,X0)
| ~ c_Finite__Set_Ofinite(X39,X0)
| c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X38),X39),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_182])]) ).
fof(f7009,plain,
( ! [X2,X3,X0,X1] :
( c_Finite__Set_Ofinite(hAPP(hAPP(c_Set_Oinsert(X0),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X2),X3)),X0)
| ~ c_Finite__Set_Ofinite(X3,X0)
| ~ c_Finite__Set_Ofinite(hAPP(hAPP(c_Set_Oinsert(X0),X1),X2),X0) )
| ~ spl0_182
| ~ spl0_391 ),
inference(superposition,[],[f1994,f6761]) ).
fof(f1994,plain,
( ! [X38,X39,X0] :
( c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X38),X39),X0)
| ~ c_Finite__Set_Ofinite(X39,X0)
| ~ c_Finite__Set_Ofinite(X38,X0) )
| ~ spl0_182 ),
inference(avatar_component_clause,[],[f1993]) ).
fof(f143742,plain,
( spl0_1522
| ~ spl0_252
| ~ spl0_390 ),
inference(avatar_split_clause,[],[f6943,f6756,f3077,f143740]) ).
fof(f143740,plain,
( spl0_1522
<=> ! [X2,X4,X0,X3,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X2),hAPP(hAPP(c_Set_Oinsert(X0),X1),X3))),X4))
| hBOOL(c_in(X1,X4,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1522])]) ).
fof(f3077,plain,
( spl0_252
<=> ! [X9,X0,X5,X1] :
( hBOOL(c_in(X1,X9,X0))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Set_Oinsert(X0),X1),X5)),X9)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_252])]) ).
fof(f6756,plain,
( spl0_390
<=> ! [X5,X0,X9,X3] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X5),hAPP(hAPP(c_Set_Oinsert(X0),X3),X9)) = hAPP(hAPP(c_Set_Oinsert(X0),X3),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X5),X9)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_390])]) ).
fof(f6943,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X2),hAPP(hAPP(c_Set_Oinsert(X0),X1),X3))),X4))
| hBOOL(c_in(X1,X4,X0)) )
| ~ spl0_252
| ~ spl0_390 ),
inference(superposition,[],[f3078,f6757]) ).
fof(f6757,plain,
( ! [X3,X0,X9,X5] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X5),hAPP(hAPP(c_Set_Oinsert(X0),X3),X9)) = hAPP(hAPP(c_Set_Oinsert(X0),X3),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X5),X9))
| ~ spl0_390 ),
inference(avatar_component_clause,[],[f6756]) ).
fof(f3078,plain,
( ! [X0,X1,X9,X5] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Set_Oinsert(X0),X1),X5)),X9))
| hBOOL(c_in(X1,X9,X0)) )
| ~ spl0_252 ),
inference(avatar_component_clause,[],[f3077]) ).
fof(f143738,plain,
( spl0_1521
| ~ spl0_184
| ~ spl0_390 ),
inference(avatar_split_clause,[],[f6884,f6756,f2001,f143736]) ).
fof(f143736,plain,
( spl0_1521
<=> ! [X0,X3,X2,X1] : hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Set_Oinsert(X0),X2),X3)),hAPP(hAPP(c_Set_Oinsert(X0),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X3)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1521])]) ).
fof(f6884,plain,
( ! [X2,X3,X0,X1] : hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Set_Oinsert(X0),X2),X3)),hAPP(hAPP(c_Set_Oinsert(X0),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X3))))
| ~ spl0_184
| ~ spl0_390 ),
inference(superposition,[],[f2002,f6757]) ).
fof(f143733,plain,
( spl0_1520
| ~ spl0_182
| ~ spl0_390 ),
inference(avatar_split_clause,[],[f6883,f6756,f1993,f143731]) ).
fof(f143731,plain,
( spl0_1520
<=> ! [X0,X3,X2,X1] :
( c_Finite__Set_Ofinite(hAPP(hAPP(c_Set_Oinsert(X0),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X3)),X0)
| ~ c_Finite__Set_Ofinite(hAPP(hAPP(c_Set_Oinsert(X0),X2),X3),X0)
| ~ c_Finite__Set_Ofinite(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1520])]) ).
fof(f6883,plain,
( ! [X2,X3,X0,X1] :
( c_Finite__Set_Ofinite(hAPP(hAPP(c_Set_Oinsert(X0),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X3)),X0)
| ~ c_Finite__Set_Ofinite(hAPP(hAPP(c_Set_Oinsert(X0),X2),X3),X0)
| ~ c_Finite__Set_Ofinite(X1,X0) )
| ~ spl0_182
| ~ spl0_390 ),
inference(superposition,[],[f1994,f6757]) ).
fof(f143729,plain,
( spl0_1519
| ~ spl0_57
| ~ spl0_389 ),
inference(avatar_split_clause,[],[f6814,f6752,f1262,f143727]) ).
fof(f143727,plain,
( spl0_1519
<=> ! [X0,X3,X2,X1] :
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X1),X2) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Set_Oinsert(X0),X3),X1)),X2)
| hBOOL(hAPP(X2,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1519])]) ).
fof(f1262,plain,
( spl0_57
<=> ! [X0,X1,X10] :
( hBOOL(hAPP(X10,X1))
| ~ hBOOL(c_in(X1,X10,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_57])]) ).
fof(f6752,plain,
( spl0_389
<=> ! [X0,X12,X9,X3] :
( hBOOL(c_in(X3,X12,X0))
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X9),X12) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Set_Oinsert(X0),X3),X9)),X12) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_389])]) ).
fof(f6814,plain,
( ! [X2,X3,X0,X1] :
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X1),X2) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Set_Oinsert(X0),X3),X1)),X2)
| hBOOL(hAPP(X2,X3)) )
| ~ spl0_57
| ~ spl0_389 ),
inference(resolution,[],[f6753,f1263]) ).
fof(f1263,plain,
( ! [X10,X0,X1] :
( ~ hBOOL(c_in(X1,X10,X0))
| hBOOL(hAPP(X10,X1)) )
| ~ spl0_57 ),
inference(avatar_component_clause,[],[f1262]) ).
fof(f6753,plain,
( ! [X3,X0,X9,X12] :
( hBOOL(c_in(X3,X12,X0))
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X9),X12) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Set_Oinsert(X0),X3),X9)),X12) )
| ~ spl0_389 ),
inference(avatar_component_clause,[],[f6752]) ).
fof(f143725,plain,
( spl0_1518
| ~ spl0_57
| ~ spl0_388 ),
inference(avatar_split_clause,[],[f6791,f6748,f1262,f143723]) ).
fof(f143723,plain,
( spl0_1518
<=> ! [X0,X3,X2,X1] :
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X1),X2) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X1),hAPP(hAPP(c_Set_Oinsert(X0),X3),X2))
| hBOOL(hAPP(X1,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1518])]) ).
fof(f6748,plain,
( spl0_388
<=> ! [X9,X0,X5,X3] :
( hBOOL(c_in(X3,X5,X0))
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X5),X9) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X5),hAPP(hAPP(c_Set_Oinsert(X0),X3),X9)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_388])]) ).
fof(f6791,plain,
( ! [X2,X3,X0,X1] :
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X1),X2) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X1),hAPP(hAPP(c_Set_Oinsert(X0),X3),X2))
| hBOOL(hAPP(X1,X3)) )
| ~ spl0_57
| ~ spl0_388 ),
inference(resolution,[],[f6749,f1263]) ).
fof(f6749,plain,
( ! [X3,X0,X9,X5] :
( hBOOL(c_in(X3,X5,X0))
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X5),X9) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X5),hAPP(hAPP(c_Set_Oinsert(X0),X3),X9)) )
| ~ spl0_388 ),
inference(avatar_component_clause,[],[f6748]) ).
fof(f143721,plain,
( spl0_1517
| ~ spl0_56
| ~ spl0_387 ),
inference(avatar_split_clause,[],[f6776,f6744,f1258,f143719]) ).
fof(f143719,plain,
( spl0_1517
<=> ! [X0,X3,X2,X1] :
( hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X1),X2) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Set_Oinsert(X0),X3),X1)),X2)
| ~ hBOOL(hAPP(X2,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1517])]) ).
fof(f1258,plain,
( spl0_56
<=> ! [X0,X1,X10] :
( ~ hBOOL(hAPP(X10,X1))
| hBOOL(c_in(X1,X10,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_56])]) ).
fof(f6744,plain,
( spl0_387
<=> ! [X9,X0,X5,X1] :
( ~ hBOOL(c_in(X1,X9,X0))
| hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X5),X9) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Set_Oinsert(X0),X1),X5)),X9) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_387])]) ).
fof(f6776,plain,
( ! [X2,X3,X0,X1] :
( hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X1),X2) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Set_Oinsert(X0),X3),X1)),X2)
| ~ hBOOL(hAPP(X2,X3)) )
| ~ spl0_56
| ~ spl0_387 ),
inference(resolution,[],[f6745,f1259]) ).
fof(f1259,plain,
( ! [X10,X0,X1] :
( hBOOL(c_in(X1,X10,X0))
| ~ hBOOL(hAPP(X10,X1)) )
| ~ spl0_56 ),
inference(avatar_component_clause,[],[f1258]) ).
fof(f6745,plain,
( ! [X0,X1,X9,X5] :
( ~ hBOOL(c_in(X1,X9,X0))
| hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X5),X9) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Set_Oinsert(X0),X1),X5)),X9) )
| ~ spl0_387 ),
inference(avatar_component_clause,[],[f6744]) ).
fof(f143717,plain,
( spl0_1516
| ~ spl0_51
| ~ spl0_384 ),
inference(avatar_split_clause,[],[f6731,f6532,f1237,f143715]) ).
fof(f143715,plain,
( spl0_1516
<=> ! [X3,X4,X0,X5,X2,X1] :
( hBOOL(hAPP(X0,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(X3,c_COMBK(X0,X1,X2),X4,X5)))
| c_Hoare__Mirabelle_Ohoare__derivs(X3,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(c_COMBK(X0,X1,X2),X5,X4,t_a)),t_a) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1516])]) ).
fof(f6532,plain,
( spl0_384
<=> ! [X35,X57,X11,X39] :
( c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X11,X35,X57,t_a)),t_a)
| hBOOL(hAPP(hAPP(X11,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1(X39,X11,X57,X35)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(X39,X11,X57,X35))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_384])]) ).
fof(f6731,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( hBOOL(hAPP(X0,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(X3,c_COMBK(X0,X1,X2),X4,X5)))
| c_Hoare__Mirabelle_Ohoare__derivs(X3,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(c_COMBK(X0,X1,X2),X5,X4,t_a)),t_a) )
| ~ spl0_51
| ~ spl0_384 ),
inference(superposition,[],[f6533,f1238]) ).
fof(f6533,plain,
( ! [X39,X11,X57,X35] :
( hBOOL(hAPP(hAPP(X11,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1(X39,X11,X57,X35)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(X39,X11,X57,X35)))
| c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X11,X35,X57,t_a)),t_a) )
| ~ spl0_384 ),
inference(avatar_component_clause,[],[f6532]) ).
fof(f143713,plain,
( spl0_1515
| ~ spl0_81
| ~ spl0_384 ),
inference(avatar_split_clause,[],[f6712,f6532,f1370,f143711]) ).
fof(f143711,plain,
( spl0_1515
<=> ! [X0,X3,X2,X1] :
( c_Hoare__Mirabelle_Ohoare__derivs(X0,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(c_fequal(X1),X2,X3,t_a)),t_a)
| v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1(X0,c_fequal(X1),X3,X2) = v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(X0,c_fequal(X1),X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1515])]) ).
fof(f1370,plain,
( spl0_81
<=> ! [X0,X76,X56] :
( X56 = X76
| ~ hBOOL(hAPP(hAPP(c_fequal(X0),X56),X76)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_81])]) ).
fof(f6712,plain,
( ! [X2,X3,X0,X1] :
( c_Hoare__Mirabelle_Ohoare__derivs(X0,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(c_fequal(X1),X2,X3,t_a)),t_a)
| v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1(X0,c_fequal(X1),X3,X2) = v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(X0,c_fequal(X1),X3,X2) )
| ~ spl0_81
| ~ spl0_384 ),
inference(resolution,[],[f6533,f1371]) ).
fof(f1371,plain,
( ! [X0,X56,X76] :
( ~ hBOOL(hAPP(hAPP(c_fequal(X0),X56),X76))
| X56 = X76 )
| ~ spl0_81 ),
inference(avatar_component_clause,[],[f1370]) ).
fof(f143709,plain,
( spl0_1514
| ~ spl0_51
| ~ spl0_383 ),
inference(avatar_split_clause,[],[f6661,f6528,f1237,f143707]) ).
fof(f143707,plain,
( spl0_1514
<=> ! [X3,X4,X0,X5,X2,X1] :
( hBOOL(hAPP(X0,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2(X3,c_COMBK(X0,X1,X2),X4,X5)))
| c_Hoare__Mirabelle_Ohoare__derivs(X3,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(c_COMBK(X0,X1,X2),X5,X4,t_a)),t_a) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1514])]) ).
fof(f6528,plain,
( spl0_383
<=> ! [X35,X57,X11,X39] :
( c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X11,X35,X57,t_a)),t_a)
| hBOOL(hAPP(hAPP(X11,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1(X39,X11,X57,X35)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2(X39,X11,X57,X35))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_383])]) ).
fof(f6661,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( hBOOL(hAPP(X0,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2(X3,c_COMBK(X0,X1,X2),X4,X5)))
| c_Hoare__Mirabelle_Ohoare__derivs(X3,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(c_COMBK(X0,X1,X2),X5,X4,t_a)),t_a) )
| ~ spl0_51
| ~ spl0_383 ),
inference(superposition,[],[f6529,f1238]) ).
fof(f6529,plain,
( ! [X39,X11,X57,X35] :
( hBOOL(hAPP(hAPP(X11,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1(X39,X11,X57,X35)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2(X39,X11,X57,X35)))
| c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X11,X35,X57,t_a)),t_a) )
| ~ spl0_383 ),
inference(avatar_component_clause,[],[f6528]) ).
fof(f143705,plain,
( spl0_1513
| ~ spl0_81
| ~ spl0_383 ),
inference(avatar_split_clause,[],[f6642,f6528,f1370,f143703]) ).
fof(f143703,plain,
( spl0_1513
<=> ! [X0,X3,X2,X1] :
( c_Hoare__Mirabelle_Ohoare__derivs(X0,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(c_fequal(X1),X2,X3,t_a)),t_a)
| v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1(X0,c_fequal(X1),X3,X2) = v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2(X0,c_fequal(X1),X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1513])]) ).
fof(f6642,plain,
( ! [X2,X3,X0,X1] :
( c_Hoare__Mirabelle_Ohoare__derivs(X0,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(c_fequal(X1),X2,X3,t_a)),t_a)
| v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1(X0,c_fequal(X1),X3,X2) = v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2(X0,c_fequal(X1),X3,X2) )
| ~ spl0_81
| ~ spl0_383 ),
inference(resolution,[],[f6529,f1371]) ).
fof(f143701,plain,
( spl0_1512
| ~ spl0_51
| ~ spl0_382 ),
inference(avatar_split_clause,[],[f6599,f6524,f1237,f143699]) ).
fof(f6524,plain,
( spl0_382
<=> ! [X35,X57,X11,X39] :
( c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X11,X35,X57,t_a)),t_a)
| hBOOL(hAPP(hAPP(X11,v_sko__Hoare__Mirabelle__Xescape__1(X39,X11,X57,X35)),v_sko__Hoare__Mirabelle__Xescape__2(X39,X11,X57,X35))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_382])]) ).
fof(f6599,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( hBOOL(hAPP(X0,v_sko__Hoare__Mirabelle__Xescape__2(X3,c_COMBK(X0,X1,X2),X4,X5)))
| c_Hoare__Mirabelle_Ohoare__derivs(X3,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(c_COMBK(X0,X1,X2),X5,X4,t_a)),t_a) )
| ~ spl0_51
| ~ spl0_382 ),
inference(superposition,[],[f6525,f1238]) ).
fof(f6525,plain,
( ! [X39,X11,X57,X35] :
( hBOOL(hAPP(hAPP(X11,v_sko__Hoare__Mirabelle__Xescape__1(X39,X11,X57,X35)),v_sko__Hoare__Mirabelle__Xescape__2(X39,X11,X57,X35)))
| c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X11,X35,X57,t_a)),t_a) )
| ~ spl0_382 ),
inference(avatar_component_clause,[],[f6524]) ).
fof(f143697,plain,
( spl0_1511
| ~ spl0_81
| ~ spl0_382 ),
inference(avatar_split_clause,[],[f6580,f6524,f1370,f143695]) ).
fof(f143695,plain,
( spl0_1511
<=> ! [X0,X3,X2,X1] :
( c_Hoare__Mirabelle_Ohoare__derivs(X0,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(c_fequal(X1),X2,X3,t_a)),t_a)
| v_sko__Hoare__Mirabelle__Xescape__1(X0,c_fequal(X1),X3,X2) = v_sko__Hoare__Mirabelle__Xescape__2(X0,c_fequal(X1),X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1511])]) ).
fof(f6580,plain,
( ! [X2,X3,X0,X1] :
( c_Hoare__Mirabelle_Ohoare__derivs(X0,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(c_fequal(X1),X2,X3,t_a)),t_a)
| v_sko__Hoare__Mirabelle__Xescape__1(X0,c_fequal(X1),X3,X2) = v_sko__Hoare__Mirabelle__Xescape__2(X0,c_fequal(X1),X3,X2) )
| ~ spl0_81
| ~ spl0_382 ),
inference(resolution,[],[f6525,f1371]) ).
fof(f143693,plain,
( ~ spl0_3
| spl0_1510
| ~ spl0_176
| ~ spl0_211 ),
inference(avatar_split_clause,[],[f3259,f2237,f1904,f143691,f1027]) ).
fof(f1027,plain,
( spl0_3
<=> class_Lattices_Olower__semilattice(tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).
fof(f143691,plain,
( spl0_1510
<=> ! [X0] :
( c_Orderings_Otop__class_Otop(tc_bool) != X0
| hBOOL(hAPP(hAPP(c_lessequals(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1510])]) ).
fof(f1904,plain,
( spl0_176
<=> ! [X0] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_176])]) ).
fof(f2237,plain,
( spl0_211
<=> ! [X2,X0,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2))
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2) != X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_211])]) ).
fof(f3259,plain,
( ! [X0] :
( c_Orderings_Otop__class_Otop(tc_bool) != X0
| hBOOL(hAPP(hAPP(c_lessequals(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),X0))
| ~ class_Lattices_Olower__semilattice(tc_bool) )
| ~ spl0_176
| ~ spl0_211 ),
inference(superposition,[],[f2238,f1905]) ).
fof(f1905,plain,
( ! [X0] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),X0) = X0
| ~ spl0_176 ),
inference(avatar_component_clause,[],[f1904]) ).
fof(f2238,plain,
( ! [X2,X0,X1] :
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2) != X1
| hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2))
| ~ class_Lattices_Olower__semilattice(X0) )
| ~ spl0_211 ),
inference(avatar_component_clause,[],[f2237]) ).
fof(f143689,plain,
( spl0_1509
| ~ spl0_234
| ~ spl0_372 ),
inference(avatar_split_clause,[],[f6419,f6083,f2649,f143687]) ).
fof(f143687,plain,
( spl0_1509
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Set_Oinsert(X0),X1),X2)),X3))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),hAPP(c_fequal(X0),X1)),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1509])]) ).
fof(f2649,plain,
( spl0_234
<=> ! [X5,X0,X3] : hAPP(hAPP(c_Set_Oinsert(X0),X3),X5) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),hAPP(c_fequal(X0),X3)),X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_234])]) ).
fof(f6083,plain,
( spl0_372
<=> ! [X5,X0,X12,X9] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X5),X12))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X5),X9)),X12)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_372])]) ).
fof(f6419,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Set_Oinsert(X0),X1),X2)),X3))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),hAPP(c_fequal(X0),X1)),X3)) )
| ~ spl0_234
| ~ spl0_372 ),
inference(superposition,[],[f6084,f2650]) ).
fof(f2650,plain,
( ! [X3,X0,X5] : hAPP(hAPP(c_Set_Oinsert(X0),X3),X5) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),hAPP(c_fequal(X0),X3)),X5)
| ~ spl0_234 ),
inference(avatar_component_clause,[],[f2649]) ).
fof(f6084,plain,
( ! [X0,X9,X5,X12] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X5),X9)),X12))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X5),X12)) )
| ~ spl0_372 ),
inference(avatar_component_clause,[],[f6083]) ).
fof(f143685,plain,
( spl0_1508
| ~ spl0_51
| ~ spl0_120
| ~ spl0_137
| ~ spl0_365 ),
inference(avatar_split_clause,[],[f6275,f6055,f1680,f1591,f1237,f143683]) ).
fof(f143683,plain,
( spl0_1508
<=> ! [X5,X3,X4,X2,X7,X0,X6,X1] :
( ~ hBOOL(c_in(X4,X5,X6))
| ~ hBOOL(c_in(v_x,X5,X6))
| ~ c_Fun_Oinj__on(c_Fun_Ocomp(c_COMBK(X0,X1,X2),X3,X2,X1,t_a),X5,X6,X7)
| v_x = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1508])]) ).
fof(f1680,plain,
( spl0_137
<=> ! [X41,X4,X0,X14,X3,X8] : hAPP(X3,hAPP(X4,X41)) = hAPP(c_Fun_Ocomp(X3,X4,X14,X8,X0),X41) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_137])]) ).
fof(f6055,plain,
( spl0_365
<=> ! [X7,X0,X8,X5,X1,X30] :
( X1 = X30
| ~ hBOOL(c_in(X30,X5,X0))
| ~ hBOOL(c_in(X1,X5,X0))
| ~ c_Fun_Oinj__on(X7,X5,X0,X8)
| hAPP(X7,X1) != hAPP(X7,X30) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_365])]) ).
fof(f6275,plain,
( ! [X2,X3,X0,X1,X6,X7,X4,X5] :
( ~ hBOOL(c_in(X4,X5,X6))
| ~ hBOOL(c_in(v_x,X5,X6))
| ~ c_Fun_Oinj__on(c_Fun_Ocomp(c_COMBK(X0,X1,X2),X3,X2,X1,t_a),X5,X6,X7)
| v_x = X4 )
| ~ spl0_51
| ~ spl0_120
| ~ spl0_137
| ~ spl0_365 ),
inference(trivial_inequality_removal,[],[f6274]) ).
fof(f6274,plain,
( ! [X2,X3,X0,X1,X6,X7,X4,X5] :
( X0 != X0
| ~ hBOOL(c_in(X4,X5,X6))
| ~ hBOOL(c_in(v_x,X5,X6))
| ~ c_Fun_Oinj__on(c_Fun_Ocomp(c_COMBK(X0,X1,X2),X3,X2,X1,t_a),X5,X6,X7)
| v_x = X4 )
| ~ spl0_51
| ~ spl0_120
| ~ spl0_137
| ~ spl0_365 ),
inference(forward_demodulation,[],[f6273,f1238]) ).
fof(f6273,plain,
( ! [X2,X3,X0,X1,X6,X7,X4,X5] :
( hAPP(c_COMBK(X0,X1,X2),hAPP(X3,X4)) != X0
| ~ hBOOL(c_in(X4,X5,X6))
| ~ hBOOL(c_in(v_x,X5,X6))
| ~ c_Fun_Oinj__on(c_Fun_Ocomp(c_COMBK(X0,X1,X2),X3,X2,X1,t_a),X5,X6,X7)
| v_x = X4 )
| ~ spl0_120
| ~ spl0_137
| ~ spl0_365 ),
inference(forward_demodulation,[],[f6185,f1681]) ).
fof(f1681,plain,
( ! [X3,X41,X0,X8,X14,X4] : hAPP(X3,hAPP(X4,X41)) = hAPP(c_Fun_Ocomp(X3,X4,X14,X8,X0),X41)
| ~ spl0_137 ),
inference(avatar_component_clause,[],[f1680]) ).
fof(f6185,plain,
( ! [X2,X3,X0,X1,X6,X7,X4,X5] :
( hAPP(c_Fun_Ocomp(c_COMBK(X0,X1,X2),X3,X2,X1,t_a),X4) != X0
| ~ hBOOL(c_in(X4,X5,X6))
| ~ hBOOL(c_in(v_x,X5,X6))
| ~ c_Fun_Oinj__on(c_Fun_Ocomp(c_COMBK(X0,X1,X2),X3,X2,X1,t_a),X5,X6,X7)
| v_x = X4 )
| ~ spl0_120
| ~ spl0_365 ),
inference(superposition,[],[f6056,f1592]) ).
fof(f6056,plain,
( ! [X0,X1,X8,X7,X5,X30] :
( hAPP(X7,X1) != hAPP(X7,X30)
| ~ hBOOL(c_in(X30,X5,X0))
| ~ hBOOL(c_in(X1,X5,X0))
| ~ c_Fun_Oinj__on(X7,X5,X0,X8)
| X1 = X30 )
| ~ spl0_365 ),
inference(avatar_component_clause,[],[f6055]) ).
fof(f143681,plain,
( spl0_1507
| ~ spl0_201
| ~ spl0_365 ),
inference(avatar_split_clause,[],[f6264,f6055,f2076,f143679]) ).
fof(f143679,plain,
( spl0_1507
<=> ! [X5,X4,X0,X3,X2,X1] :
( ~ hBOOL(c_in(X2,X3,X4))
| ~ hBOOL(c_in(X1,X3,X4))
| ~ c_Fun_Oinj__on(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0)),X3,X4,X5)
| X1 = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1507])]) ).
fof(f2076,plain,
( spl0_201
<=> ! [X9,X0] : c_COMBK(c_False,tc_bool,X0) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0)),X9) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_201])]) ).
fof(f6264,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ hBOOL(c_in(X2,X3,X4))
| ~ hBOOL(c_in(X1,X3,X4))
| ~ c_Fun_Oinj__on(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0)),X3,X4,X5)
| X1 = X2 )
| ~ spl0_201
| ~ spl0_365 ),
inference(trivial_inequality_removal,[],[f6263]) ).
fof(f6263,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( c_COMBK(c_False,tc_bool,X0) != c_COMBK(c_False,tc_bool,X0)
| ~ hBOOL(c_in(X2,X3,X4))
| ~ hBOOL(c_in(X1,X3,X4))
| ~ c_Fun_Oinj__on(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0)),X3,X4,X5)
| X1 = X2 )
| ~ spl0_201
| ~ spl0_365 ),
inference(forward_demodulation,[],[f6151,f2077]) ).
fof(f2077,plain,
( ! [X0,X9] : c_COMBK(c_False,tc_bool,X0) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0)),X9)
| ~ spl0_201 ),
inference(avatar_component_clause,[],[f2076]) ).
fof(f6151,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( c_COMBK(c_False,tc_bool,X0) != hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0)),X2)
| ~ hBOOL(c_in(X2,X3,X4))
| ~ hBOOL(c_in(X1,X3,X4))
| ~ c_Fun_Oinj__on(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0)),X3,X4,X5)
| X1 = X2 )
| ~ spl0_201
| ~ spl0_365 ),
inference(superposition,[],[f6056,f2077]) ).
fof(f143677,plain,
( spl0_1506
| ~ spl0_200
| ~ spl0_365 ),
inference(avatar_split_clause,[],[f6262,f6055,f2066,f143675]) ).
fof(f143675,plain,
( spl0_1506
<=> ! [X5,X4,X0,X3,X2,X1] :
( ~ hBOOL(c_in(X2,X3,X4))
| ~ hBOOL(c_in(X1,X3,X4))
| ~ c_Fun_Oinj__on(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0)),X3,X4,X5)
| X1 = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1506])]) ).
fof(f6262,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ hBOOL(c_in(X2,X3,X4))
| ~ hBOOL(c_in(X1,X3,X4))
| ~ c_Fun_Oinj__on(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0)),X3,X4,X5)
| X1 = X2 )
| ~ spl0_200
| ~ spl0_365 ),
inference(trivial_inequality_removal,[],[f6261]) ).
fof(f6261,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( c_COMBK(c_False,tc_bool,X0) != c_COMBK(c_False,tc_bool,X0)
| ~ hBOOL(c_in(X2,X3,X4))
| ~ hBOOL(c_in(X1,X3,X4))
| ~ c_Fun_Oinj__on(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0)),X3,X4,X5)
| X1 = X2 )
| ~ spl0_200
| ~ spl0_365 ),
inference(forward_demodulation,[],[f6150,f2067]) ).
fof(f6150,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( c_COMBK(c_False,tc_bool,X0) != hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0)),X2)
| ~ hBOOL(c_in(X2,X3,X4))
| ~ hBOOL(c_in(X1,X3,X4))
| ~ c_Fun_Oinj__on(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0)),X3,X4,X5)
| X1 = X2 )
| ~ spl0_200
| ~ spl0_365 ),
inference(superposition,[],[f6056,f2067]) ).
fof(f143673,plain,
( spl0_1505
| ~ spl0_178
| ~ spl0_365 ),
inference(avatar_split_clause,[],[f6259,f6055,f1976,f143671]) ).
fof(f143671,plain,
( spl0_1505
<=> ! [X5,X4,X0,X3,X2,X1] :
( ~ hBOOL(c_in(X2,X3,X4))
| ~ hBOOL(c_in(X1,X3,X4))
| ~ c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool))),X3,X4,X5)
| X1 = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1505])]) ).
fof(f1976,plain,
( spl0_178
<=> ! [X9,X0] : c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool))),X9) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_178])]) ).
fof(f6259,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ hBOOL(c_in(X2,X3,X4))
| ~ hBOOL(c_in(X1,X3,X4))
| ~ c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool))),X3,X4,X5)
| X1 = X2 )
| ~ spl0_178
| ~ spl0_365 ),
inference(trivial_inequality_removal,[],[f6258]) ).
fof(f6258,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)) != c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool))
| ~ hBOOL(c_in(X2,X3,X4))
| ~ hBOOL(c_in(X1,X3,X4))
| ~ c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool))),X3,X4,X5)
| X1 = X2 )
| ~ spl0_178
| ~ spl0_365 ),
inference(forward_demodulation,[],[f6148,f1977]) ).
fof(f1977,plain,
( ! [X0,X9] : c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool))),X9)
| ~ spl0_178 ),
inference(avatar_component_clause,[],[f1976]) ).
fof(f6148,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)) != hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool))),X2)
| ~ hBOOL(c_in(X2,X3,X4))
| ~ hBOOL(c_in(X1,X3,X4))
| ~ c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool))),X3,X4,X5)
| X1 = X2 )
| ~ spl0_178
| ~ spl0_365 ),
inference(superposition,[],[f6056,f1977]) ).
fof(f143669,plain,
( spl0_1504
| ~ spl0_249
| ~ spl0_352 ),
inference(avatar_split_clause,[],[f5906,f5600,f3055,f143667]) ).
fof(f143667,plain,
( spl0_1504
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(X1,X3))
| hBOOL(hAPP(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X1),X2),X3))
| hBOOL(hAPP(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X1),X2),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1504])]) ).
fof(f3055,plain,
( spl0_249
<=> ! [X9,X5,X1,X0] :
( hBOOL(hAPP(X9,X1))
| hBOOL(hAPP(X5,X1))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X5),X9),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_249])]) ).
fof(f5600,plain,
( spl0_352
<=> ! [X9,X5,X0] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X5),X9)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X5),X9)) = X5 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_352])]) ).
fof(f5906,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(X1,X3))
| hBOOL(hAPP(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X1),X2),X3))
| hBOOL(hAPP(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X1),X2),X3)) )
| ~ spl0_249
| ~ spl0_352 ),
inference(superposition,[],[f3056,f5601]) ).
fof(f5601,plain,
( ! [X0,X9,X5] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X5),X9)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X5),X9)) = X5
| ~ spl0_352 ),
inference(avatar_component_clause,[],[f5600]) ).
fof(f3056,plain,
( ! [X0,X1,X9,X5] :
( ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X5),X9),X1))
| hBOOL(hAPP(X5,X1))
| hBOOL(hAPP(X9,X1)) )
| ~ spl0_249 ),
inference(avatar_component_clause,[],[f3055]) ).
fof(f143665,plain,
( spl0_1503
| ~ spl0_265
| ~ spl0_350 ),
inference(avatar_split_clause,[],[f5773,f5592,f3129,f143663]) ).
fof(f143663,plain,
( spl0_1503
<=> ! [X2,X0,X1] :
( c_COMBK(c_False,tc_bool,X0) != hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X2)
| c_COMBK(c_False,tc_bool,X0) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1503])]) ).
fof(f5592,plain,
( spl0_350
<=> ! [X9,X5,X0] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X5),X9) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X5),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X9),X5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_350])]) ).
fof(f5773,plain,
( ! [X2,X0,X1] :
( c_COMBK(c_False,tc_bool,X0) != hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X2)
| c_COMBK(c_False,tc_bool,X0) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X2),X1) )
| ~ spl0_265
| ~ spl0_350 ),
inference(superposition,[],[f3130,f5593]) ).
fof(f5593,plain,
( ! [X0,X9,X5] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X5),X9) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X5),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X9),X5))
| ~ spl0_350 ),
inference(avatar_component_clause,[],[f5592]) ).
fof(f143661,plain,
( spl0_1502
| ~ spl0_249
| ~ spl0_350 ),
inference(avatar_split_clause,[],[f5771,f5592,f3055,f143659]) ).
fof(f143659,plain,
( spl0_1502
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X2),X3))
| hBOOL(hAPP(X1,X3))
| hBOOL(hAPP(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X2),X1),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1502])]) ).
fof(f5771,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X2),X3))
| hBOOL(hAPP(X1,X3))
| hBOOL(hAPP(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X2),X1),X3)) )
| ~ spl0_249
| ~ spl0_350 ),
inference(superposition,[],[f3056,f5593]) ).
fof(f143657,plain,
( spl0_1501
| ~ spl0_266
| ~ spl0_349 ),
inference(avatar_split_clause,[],[f5711,f5588,f3133,f143655]) ).
fof(f143655,plain,
( spl0_1501
<=> ! [X2,X0,X1] :
( c_COMBK(c_False,tc_bool,X0) != hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X2)
| c_COMBK(c_False,tc_bool,X0) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1501])]) ).
fof(f5588,plain,
( spl0_349
<=> ! [X9,X5,X0] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X9),X5)),X5) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X9),X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_349])]) ).
fof(f5711,plain,
( ! [X2,X0,X1] :
( c_COMBK(c_False,tc_bool,X0) != hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X2)
| c_COMBK(c_False,tc_bool,X0) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X1),X2) )
| ~ spl0_266
| ~ spl0_349 ),
inference(superposition,[],[f3134,f5589]) ).
fof(f5589,plain,
( ! [X0,X9,X5] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X9),X5)),X5) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X9),X5)
| ~ spl0_349 ),
inference(avatar_component_clause,[],[f5588]) ).
fof(f143653,plain,
( spl0_1500
| ~ spl0_256
| ~ spl0_349 ),
inference(avatar_split_clause,[],[f5709,f5588,f3093,f143651]) ).
fof(f143651,plain,
( spl0_1500
<=> ! [X2,X0,X1] :
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X2) != X2
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X1),X2)),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1500])]) ).
fof(f3093,plain,
( spl0_256
<=> ! [X9,X5,X0] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X5),X9))
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X5),X9) != X9 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_256])]) ).
fof(f5709,plain,
( ! [X2,X0,X1] :
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X2) != X2
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X1),X2)),X2)) )
| ~ spl0_256
| ~ spl0_349 ),
inference(superposition,[],[f3094,f5589]) ).
fof(f3094,plain,
( ! [X0,X9,X5] :
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X5),X9) != X9
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X5),X9)) )
| ~ spl0_256 ),
inference(avatar_component_clause,[],[f3093]) ).
fof(f143649,plain,
( spl0_1499
| ~ spl0_249
| ~ spl0_349 ),
inference(avatar_split_clause,[],[f5708,f5588,f3055,f143647]) ).
fof(f143647,plain,
( spl0_1499
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X2),X3))
| hBOOL(hAPP(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X1),X2),X3))
| hBOOL(hAPP(X2,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1499])]) ).
fof(f5708,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X2),X3))
| hBOOL(hAPP(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X1),X2),X3))
| hBOOL(hAPP(X2,X3)) )
| ~ spl0_249
| ~ spl0_349 ),
inference(superposition,[],[f3056,f5589]) ).
fof(f143645,plain,
( spl0_1498
| ~ spl0_128
| ~ spl0_344 ),
inference(avatar_split_clause,[],[f5528,f4966,f1623,f143643]) ).
fof(f143643,plain,
( spl0_1498
<=> ! [X2,X0,X1] :
( hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Set_Oinsert(X0),X1),X2)),hAPP(c_fequal(X0),X1)) = X2
| hAPP(hAPP(c_Set_Oinsert(X0),X1),X2) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1498])]) ).
fof(f1623,plain,
( spl0_128
<=> ! [X5,X0,X3] :
( ~ hBOOL(c_in(X3,X5,X0))
| hAPP(hAPP(c_Set_Oinsert(X0),X3),X5) = X5 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_128])]) ).
fof(f4966,plain,
( spl0_344
<=> ! [X5,X1,X0] :
( hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Set_Oinsert(X0),X1),X5)),hAPP(c_fequal(X0),X1)) = X5
| hBOOL(c_in(X1,X5,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_344])]) ).
fof(f5528,plain,
( ! [X2,X0,X1] :
( hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Set_Oinsert(X0),X1),X2)),hAPP(c_fequal(X0),X1)) = X2
| hAPP(hAPP(c_Set_Oinsert(X0),X1),X2) = X2 )
| ~ spl0_128
| ~ spl0_344 ),
inference(resolution,[],[f4967,f1624]) ).
fof(f1624,plain,
( ! [X3,X0,X5] :
( ~ hBOOL(c_in(X3,X5,X0))
| hAPP(hAPP(c_Set_Oinsert(X0),X3),X5) = X5 )
| ~ spl0_128 ),
inference(avatar_component_clause,[],[f1623]) ).
fof(f4967,plain,
( ! [X0,X1,X5] :
( hBOOL(c_in(X1,X5,X0))
| hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Set_Oinsert(X0),X1),X5)),hAPP(c_fequal(X0),X1)) = X5 )
| ~ spl0_344 ),
inference(avatar_component_clause,[],[f4966]) ).
fof(f143641,plain,
( spl0_1497
| ~ spl0_194
| ~ spl0_343 ),
inference(avatar_split_clause,[],[f5517,f4961,f2041,f143639]) ).
fof(f143639,plain,
( spl0_1497
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X0),X1),X2),X3))
| hBOOL(hAPP(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X2),hAPP(c_fequal(X0),X1)),X3))
| X1 = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1497])]) ).
fof(f2041,plain,
( spl0_194
<=> ! [X2,X5,X1,X0] :
( X1 = X2
| hBOOL(hAPP(X5,X1))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X0),X2),X5),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_194])]) ).
fof(f4961,plain,
( spl0_343
<=> ! [X5,X0,X3] : hAPP(hAPP(c_Set_Oinsert(X0),X3),X5) = hAPP(hAPP(c_Set_Oinsert(X0),X3),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X5),hAPP(c_fequal(X0),X3))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_343])]) ).
fof(f5517,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X0),X1),X2),X3))
| hBOOL(hAPP(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X2),hAPP(c_fequal(X0),X1)),X3))
| X1 = X3 )
| ~ spl0_194
| ~ spl0_343 ),
inference(superposition,[],[f2042,f4962]) ).
fof(f4962,plain,
( ! [X3,X0,X5] : hAPP(hAPP(c_Set_Oinsert(X0),X3),X5) = hAPP(hAPP(c_Set_Oinsert(X0),X3),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X5),hAPP(c_fequal(X0),X3)))
| ~ spl0_343 ),
inference(avatar_component_clause,[],[f4961]) ).
fof(f2042,plain,
( ! [X2,X0,X1,X5] :
( ~ hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X0),X2),X5),X1))
| hBOOL(hAPP(X5,X1))
| X1 = X2 )
| ~ spl0_194 ),
inference(avatar_component_clause,[],[f2041]) ).
fof(f143637,plain,
( spl0_1496
| ~ spl0_233
| ~ spl0_343 ),
inference(avatar_split_clause,[],[f5495,f4961,f2645,f143635]) ).
fof(f143635,plain,
( spl0_1496
<=> ! [X2,X4,X0,X3,X1] : hAPP(hAPP(c_Set_Oinsert(X0),X1),X1) = hAPP(hAPP(c_Set_Oinsert(X0),X1),hAPP(hAPP(hAPP(c_COMBS(X2,X3,X4),c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool))),c_fequal(X0)),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1496])]) ).
fof(f5495,plain,
( ! [X2,X3,X0,X1,X4] : hAPP(hAPP(c_Set_Oinsert(X0),X1),X1) = hAPP(hAPP(c_Set_Oinsert(X0),X1),hAPP(hAPP(hAPP(c_COMBS(X2,X3,X4),c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool))),c_fequal(X0)),X1))
| ~ spl0_233
| ~ spl0_343 ),
inference(superposition,[],[f4962,f2646]) ).
fof(f143633,plain,
( spl0_1495
| ~ spl0_217
| ~ spl0_341 ),
inference(avatar_split_clause,[],[f5464,f4953,f2267,f143631]) ).
fof(f143631,plain,
( spl0_1495
<=> ! [X2,X0,X1] :
( ~ c_Finite__Set_Ofinite(X0,X1)
| ~ hBOOL(c_in(X2,X0,X1))
| ~ class_Lattices_Olower__semilattice(X1)
| ~ class_Lattices_Oupper__semilattice(X1)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),c_The(c_Finite__Set_Ofold1Set(c_Lattices_Olower__semilattice__class_Oinf(X1),X0,X1),X1)),X2) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1495])]) ).
fof(f2267,plain,
( spl0_217
<=> ! [X2,X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2))
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_217])]) ).
fof(f4953,plain,
( spl0_341
<=> ! [X5,X0,X3] :
( ~ class_Lattices_Olower__semilattice(X0)
| ~ c_Finite__Set_Ofinite(X5,X0)
| ~ hBOOL(c_in(X3,X5,X0))
| hBOOL(hAPP(hAPP(c_lessequals(X0),c_The(c_Finite__Set_Ofold1Set(c_Lattices_Olower__semilattice__class_Oinf(X0),X5,X0),X0)),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_341])]) ).
fof(f5464,plain,
( ! [X2,X0,X1] :
( ~ c_Finite__Set_Ofinite(X0,X1)
| ~ hBOOL(c_in(X2,X0,X1))
| ~ class_Lattices_Olower__semilattice(X1)
| ~ class_Lattices_Oupper__semilattice(X1)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),c_The(c_Finite__Set_Ofold1Set(c_Lattices_Olower__semilattice__class_Oinf(X1),X0,X1),X1)),X2) = X2 )
| ~ spl0_217
| ~ spl0_341 ),
inference(resolution,[],[f4954,f2268]) ).
fof(f2268,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2))
| ~ class_Lattices_Oupper__semilattice(X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2) = X2 )
| ~ spl0_217 ),
inference(avatar_component_clause,[],[f2267]) ).
fof(f4954,plain,
( ! [X3,X0,X5] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),c_The(c_Finite__Set_Ofold1Set(c_Lattices_Olower__semilattice__class_Oinf(X0),X5,X0),X0)),X3))
| ~ c_Finite__Set_Ofinite(X5,X0)
| ~ hBOOL(c_in(X3,X5,X0))
| ~ class_Lattices_Olower__semilattice(X0) )
| ~ spl0_341 ),
inference(avatar_component_clause,[],[f4953]) ).
fof(f143629,plain,
( spl0_1494
| ~ spl0_215
| ~ spl0_341 ),
inference(avatar_split_clause,[],[f5463,f4953,f2259,f143627]) ).
fof(f143627,plain,
( spl0_1494
<=> ! [X2,X0,X1] :
( ~ c_Finite__Set_Ofinite(X0,X1)
| ~ hBOOL(c_in(X2,X0,X1))
| ~ class_Lattices_Olower__semilattice(X1)
| ~ class_Lattices_Oupper__semilattice(X1)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),c_The(c_Finite__Set_Ofold1Set(c_Lattices_Olower__semilattice__class_Oinf(X1),X0,X1),X1)) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1494])]) ).
fof(f2259,plain,
( spl0_215
<=> ! [X2,X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X2),X1))
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_215])]) ).
fof(f5463,plain,
( ! [X2,X0,X1] :
( ~ c_Finite__Set_Ofinite(X0,X1)
| ~ hBOOL(c_in(X2,X0,X1))
| ~ class_Lattices_Olower__semilattice(X1)
| ~ class_Lattices_Oupper__semilattice(X1)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),c_The(c_Finite__Set_Ofold1Set(c_Lattices_Olower__semilattice__class_Oinf(X1),X0,X1),X1)) = X2 )
| ~ spl0_215
| ~ spl0_341 ),
inference(resolution,[],[f4954,f2260]) ).
fof(f2260,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X2),X1))
| ~ class_Lattices_Oupper__semilattice(X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2) = X1 )
| ~ spl0_215 ),
inference(avatar_component_clause,[],[f2259]) ).
fof(f143625,plain,
( spl0_1493
| ~ spl0_194
| ~ spl0_340 ),
inference(avatar_split_clause,[],[f5412,f4949,f2041,f143623]) ).
fof(f143623,plain,
( spl0_1493
<=> ! [X2,X4,X0,X3,X1] :
( ~ hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X0),X2),hAPP(hAPP(c_Set_Oinsert(X0),X1),X3)),X4))
| hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X0),X2),X3),X4))
| X1 = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1493])]) ).
fof(f4949,plain,
( spl0_340
<=> ! [X0,X5,X2,X1] : hAPP(hAPP(c_Set_Oinsert(X0),X1),hAPP(hAPP(c_Set_Oinsert(X0),X2),X5)) = hAPP(hAPP(c_Set_Oinsert(X0),X2),hAPP(hAPP(c_Set_Oinsert(X0),X1),X5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_340])]) ).
fof(f5412,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X0),X2),hAPP(hAPP(c_Set_Oinsert(X0),X1),X3)),X4))
| hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X0),X2),X3),X4))
| X1 = X4 )
| ~ spl0_194
| ~ spl0_340 ),
inference(superposition,[],[f2042,f4950]) ).
fof(f4950,plain,
( ! [X2,X0,X1,X5] : hAPP(hAPP(c_Set_Oinsert(X0),X1),hAPP(hAPP(c_Set_Oinsert(X0),X2),X5)) = hAPP(hAPP(c_Set_Oinsert(X0),X2),hAPP(hAPP(c_Set_Oinsert(X0),X1),X5))
| ~ spl0_340 ),
inference(avatar_component_clause,[],[f4949]) ).
fof(f143621,plain,
( spl0_1492
| ~ spl0_233
| ~ spl0_340 ),
inference(avatar_split_clause,[],[f5384,f4949,f2645,f143619]) ).
fof(f143619,plain,
( spl0_1492
<=> ! [X3,X4,X0,X5,X2,X1] : hAPP(hAPP(hAPP(c_COMBS(X3,X4,X5),c_Set_Oinsert(X0)),hAPP(c_Set_Oinsert(X0),X2)),X1) = hAPP(hAPP(c_Set_Oinsert(X0),X2),hAPP(hAPP(c_Set_Oinsert(X0),X1),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1492])]) ).
fof(f5384,plain,
( ! [X2,X3,X0,X1,X4,X5] : hAPP(hAPP(hAPP(c_COMBS(X3,X4,X5),c_Set_Oinsert(X0)),hAPP(c_Set_Oinsert(X0),X2)),X1) = hAPP(hAPP(c_Set_Oinsert(X0),X2),hAPP(hAPP(c_Set_Oinsert(X0),X1),X1))
| ~ spl0_233
| ~ spl0_340 ),
inference(superposition,[],[f4950,f2646]) ).
fof(f143617,plain,
( spl0_1491
| ~ spl0_225
| ~ spl0_339 ),
inference(avatar_split_clause,[],[f5370,f4945,f2299,f143615]) ).
fof(f143615,plain,
( spl0_1491
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ class_Orderings_Opreorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),hAPP(c_Complete__Lattice_OSup__class_OSup(X0),X3)))
| ~ hBOOL(c_in(X2,X3,X0))
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1491])]) ).
fof(f2299,plain,
( spl0_225
<=> ! [X5,X0,X1] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
| ~ hBOOL(c_in(X1,X5,X0))
| hBOOL(hAPP(hAPP(c_lessequals(X0),X1),hAPP(c_Complete__Lattice_OSup__class_OSup(X0),X5))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_225])]) ).
fof(f4945,plain,
( spl0_339
<=> ! [X0,X6,X2,X1] :
( ~ class_Orderings_Opreorder(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X2),X6))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X6)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_339])]) ).
fof(f5370,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ class_Orderings_Opreorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),hAPP(c_Complete__Lattice_OSup__class_OSup(X0),X3)))
| ~ hBOOL(c_in(X2,X3,X0))
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) )
| ~ spl0_225
| ~ spl0_339 ),
inference(resolution,[],[f4946,f2300]) ).
fof(f2300,plain,
( ! [X0,X1,X5] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),X1),hAPP(c_Complete__Lattice_OSup__class_OSup(X0),X5)))
| ~ hBOOL(c_in(X1,X5,X0))
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) )
| ~ spl0_225 ),
inference(avatar_component_clause,[],[f2299]) ).
fof(f4946,plain,
( ! [X2,X0,X1,X6] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X2),X6))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ class_Orderings_Opreorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X6)) )
| ~ spl0_339 ),
inference(avatar_component_clause,[],[f4945]) ).
fof(f143613,plain,
( spl0_1490
| ~ spl0_218
| ~ spl0_339 ),
inference(avatar_split_clause,[],[f5356,f4945,f2271,f143611]) ).
fof(f143611,plain,
( spl0_1490
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),hAPP(c_Complete__Lattice_OInf__class_OInf(X0),X2)))
| ~ class_Orderings_Opreorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X3))
| ~ hBOOL(c_in(X3,X2,X0))
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1490])]) ).
fof(f2271,plain,
( spl0_218
<=> ! [X5,X0,X1] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
| ~ hBOOL(c_in(X1,X5,X0))
| hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(c_Complete__Lattice_OInf__class_OInf(X0),X5)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_218])]) ).
fof(f5356,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),hAPP(c_Complete__Lattice_OInf__class_OInf(X0),X2)))
| ~ class_Orderings_Opreorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X3))
| ~ hBOOL(c_in(X3,X2,X0))
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) )
| ~ spl0_218
| ~ spl0_339 ),
inference(resolution,[],[f4946,f2272]) ).
fof(f2272,plain,
( ! [X0,X1,X5] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(c_Complete__Lattice_OInf__class_OInf(X0),X5)),X1))
| ~ hBOOL(c_in(X1,X5,X0))
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) )
| ~ spl0_218 ),
inference(avatar_component_clause,[],[f2271]) ).
fof(f143609,plain,
( spl0_1489
| spl0_581
| ~ spl0_118
| ~ spl0_230 ),
inference(avatar_split_clause,[],[f2766,f2633,f1576,f16579,f143607]) ).
fof(f143607,plain,
( spl0_1489
<=> ! [X2,X3] : ~ c_Fun_Oinj__on(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),c_False),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2,X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1489])]) ).
fof(f16579,plain,
( spl0_581
<=> ! [X4,X3] : X3 = X4 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_581])]) ).
fof(f1576,plain,
( spl0_118
<=> ! [X0] : c_False = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),c_False),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_118])]) ).
fof(f2633,plain,
( spl0_230
<=> ! [X7,X8,X0,X2,X1] :
( X1 = X2
| hAPP(X7,X1) != hAPP(X7,X2)
| ~ c_Fun_Oinj__on(X7,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0,X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_230])]) ).
fof(f2766,plain,
( ! [X2,X3,X0,X1] :
( X0 = X1
| ~ c_Fun_Oinj__on(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),c_False),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2,X3) )
| ~ spl0_118
| ~ spl0_230 ),
inference(trivial_inequality_removal,[],[f2765]) ).
fof(f2765,plain,
( ! [X2,X3,X0,X1] :
( c_False != c_False
| X0 = X1
| ~ c_Fun_Oinj__on(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),c_False),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2,X3) )
| ~ spl0_118
| ~ spl0_230 ),
inference(forward_demodulation,[],[f2704,f1577]) ).
fof(f1577,plain,
( ! [X0] : c_False = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),c_False),X0)
| ~ spl0_118 ),
inference(avatar_component_clause,[],[f1576]) ).
fof(f2704,plain,
( ! [X2,X3,X0,X1] :
( c_False != hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),c_False),X1)
| X0 = X1
| ~ c_Fun_Oinj__on(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),c_False),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2,X3) )
| ~ spl0_118
| ~ spl0_230 ),
inference(superposition,[],[f2634,f1577]) ).
fof(f2634,plain,
( ! [X2,X0,X1,X8,X7] :
( hAPP(X7,X1) != hAPP(X7,X2)
| X1 = X2
| ~ c_Fun_Oinj__on(X7,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0,X8) )
| ~ spl0_230 ),
inference(avatar_component_clause,[],[f2633]) ).
fof(f143605,plain,
( spl0_1488
| ~ spl0_225
| ~ spl0_338 ),
inference(avatar_split_clause,[],[f5335,f4941,f2299,f143603]) ).
fof(f143603,plain,
( spl0_1488
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(c_Complete__Lattice_OSup__class_OSup(X0),X1)),X2))
| ~ class_Orderings_Opreorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X3),X2))
| ~ hBOOL(c_in(X3,X1,X0))
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1488])]) ).
fof(f4941,plain,
( spl0_338
<=> ! [X0,X6,X2,X1] :
( ~ class_Orderings_Opreorder(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X2),X6))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X6)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_338])]) ).
fof(f5335,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(c_Complete__Lattice_OSup__class_OSup(X0),X1)),X2))
| ~ class_Orderings_Opreorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X3),X2))
| ~ hBOOL(c_in(X3,X1,X0))
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) )
| ~ spl0_225
| ~ spl0_338 ),
inference(resolution,[],[f4942,f2300]) ).
fof(f4942,plain,
( ! [X2,X0,X1,X6] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X2),X6))
| ~ class_Orderings_Opreorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X6)) )
| ~ spl0_338 ),
inference(avatar_component_clause,[],[f4941]) ).
fof(f143601,plain,
( spl0_1487
| ~ spl0_218
| ~ spl0_338 ),
inference(avatar_split_clause,[],[f5321,f4941,f2271,f143599]) ).
fof(f143599,plain,
( spl0_1487
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ class_Orderings_Opreorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(c_Complete__Lattice_OInf__class_OInf(X0),X3)),X2))
| ~ hBOOL(c_in(X1,X3,X0))
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1487])]) ).
fof(f5321,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ class_Orderings_Opreorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(c_Complete__Lattice_OInf__class_OInf(X0),X3)),X2))
| ~ hBOOL(c_in(X1,X3,X0))
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) )
| ~ spl0_218
| ~ spl0_338 ),
inference(resolution,[],[f4942,f2272]) ).
fof(f143597,plain,
( spl0_1486
| ~ spl0_225
| ~ spl0_337 ),
inference(avatar_split_clause,[],[f5290,f4937,f2299,f143595]) ).
fof(f143595,plain,
( spl0_1486
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2))
| ~ class_Orderings_Opreorder(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),X1),hAPP(c_Complete__Lattice_OSup__class_OSup(X0),X3)))
| ~ hBOOL(c_in(X2,X3,X0))
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1486])]) ).
fof(f4937,plain,
( spl0_337
<=> ! [X0,X6,X2,X1] :
( ~ class_Orderings_Opreorder(X0)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X2),X6))
| hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X6)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_337])]) ).
fof(f5290,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2))
| ~ class_Orderings_Opreorder(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),X1),hAPP(c_Complete__Lattice_OSup__class_OSup(X0),X3)))
| ~ hBOOL(c_in(X2,X3,X0))
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) )
| ~ spl0_225
| ~ spl0_337 ),
inference(resolution,[],[f4938,f2300]) ).
fof(f4938,plain,
( ! [X2,X0,X1,X6] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X2),X6))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2))
| ~ class_Orderings_Opreorder(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X6)) )
| ~ spl0_337 ),
inference(avatar_component_clause,[],[f4937]) ).
fof(f143593,plain,
( spl0_1485
| ~ spl0_218
| ~ spl0_337 ),
inference(avatar_split_clause,[],[f5276,f4937,f2271,f143591]) ).
fof(f143591,plain,
( spl0_1485
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X1),hAPP(c_Complete__Lattice_OInf__class_OInf(X0),X2)))
| ~ class_Orderings_Opreorder(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X3))
| ~ hBOOL(c_in(X3,X2,X0))
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1485])]) ).
fof(f5276,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X1),hAPP(c_Complete__Lattice_OInf__class_OInf(X0),X2)))
| ~ class_Orderings_Opreorder(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X3))
| ~ hBOOL(c_in(X3,X2,X0))
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) )
| ~ spl0_218
| ~ spl0_337 ),
inference(resolution,[],[f4938,f2272]) ).
fof(f143589,plain,
( spl0_1484
| ~ spl0_225
| ~ spl0_336 ),
inference(avatar_split_clause,[],[f5254,f4933,f2299,f143587]) ).
fof(f143587,plain,
( spl0_1484
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),hAPP(c_Complete__Lattice_OSup__class_OSup(X0),X3)))
| ~ hBOOL(c_in(X2,X3,X0))
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1484])]) ).
fof(f4933,plain,
( spl0_336
<=> ! [X0,X6,X2,X1] :
( ~ class_Orderings_Oorder(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X6),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X2),X1))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X6),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_336])]) ).
fof(f5254,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),hAPP(c_Complete__Lattice_OSup__class_OSup(X0),X3)))
| ~ hBOOL(c_in(X2,X3,X0))
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) )
| ~ spl0_225
| ~ spl0_336 ),
inference(resolution,[],[f4934,f2300]) ).
fof(f4934,plain,
( ! [X2,X0,X1,X6] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X2),X1))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X6),X2))
| ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X6),X1)) )
| ~ spl0_336 ),
inference(avatar_component_clause,[],[f4933]) ).
fof(f143585,plain,
( spl0_1483
| ~ spl0_218
| ~ spl0_336 ),
inference(avatar_split_clause,[],[f5240,f4933,f2271,f143583]) ).
fof(f143583,plain,
( spl0_1483
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),hAPP(c_Complete__Lattice_OInf__class_OInf(X0),X2)))
| ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X3))
| ~ hBOOL(c_in(X3,X2,X0))
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1483])]) ).
fof(f5240,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),hAPP(c_Complete__Lattice_OInf__class_OInf(X0),X2)))
| ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X3))
| ~ hBOOL(c_in(X3,X2,X0))
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) )
| ~ spl0_218
| ~ spl0_336 ),
inference(resolution,[],[f4934,f2272]) ).
fof(f143581,plain,
( spl0_1482
| ~ spl0_225
| ~ spl0_335 ),
inference(avatar_split_clause,[],[f5218,f4929,f2299,f143579]) ).
fof(f143579,plain,
( spl0_1482
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(c_Complete__Lattice_OSup__class_OSup(X0),X1)),X2))
| ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X3),X2))
| ~ hBOOL(c_in(X3,X1,X0))
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1482])]) ).
fof(f4929,plain,
( spl0_335
<=> ! [X0,X6,X2,X1] :
( ~ class_Orderings_Oorder(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X2),X1))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X6),X2))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X6),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_335])]) ).
fof(f5218,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(c_Complete__Lattice_OSup__class_OSup(X0),X1)),X2))
| ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X3),X2))
| ~ hBOOL(c_in(X3,X1,X0))
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) )
| ~ spl0_225
| ~ spl0_335 ),
inference(resolution,[],[f4930,f2300]) ).
fof(f4930,plain,
( ! [X2,X0,X1,X6] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X6),X2))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X2),X1))
| ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X6),X1)) )
| ~ spl0_335 ),
inference(avatar_component_clause,[],[f4929]) ).
fof(f143577,plain,
( spl0_1481
| ~ spl0_218
| ~ spl0_335 ),
inference(avatar_split_clause,[],[f5204,f4929,f2271,f143575]) ).
fof(f143575,plain,
( spl0_1481
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(c_Complete__Lattice_OInf__class_OInf(X0),X3)),X2))
| ~ hBOOL(c_in(X1,X3,X0))
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1481])]) ).
fof(f5204,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(c_Complete__Lattice_OInf__class_OInf(X0),X3)),X2))
| ~ hBOOL(c_in(X1,X3,X0))
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) )
| ~ spl0_218
| ~ spl0_335 ),
inference(resolution,[],[f4930,f2272]) ).
fof(f143573,plain,
( spl0_1480
| ~ spl0_225
| ~ spl0_334 ),
inference(avatar_split_clause,[],[f5182,f4925,f2299,f143571]) ).
fof(f143571,plain,
( spl0_1480
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(c_Complete__Lattice_OSup__class_OSup(X0),X1)),X2))
| ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),X3),X2))
| ~ hBOOL(c_in(X3,X1,X0))
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1480])]) ).
fof(f4925,plain,
( spl0_334
<=> ! [X0,X6,X2,X1] :
( ~ class_Orderings_Oorder(X0)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X2),X1))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X6),X2))
| hBOOL(hAPP(hAPP(c_lessequals(X0),X6),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_334])]) ).
fof(f5182,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(c_Complete__Lattice_OSup__class_OSup(X0),X1)),X2))
| ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),X3),X2))
| ~ hBOOL(c_in(X3,X1,X0))
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) )
| ~ spl0_225
| ~ spl0_334 ),
inference(resolution,[],[f4926,f2300]) ).
fof(f4926,plain,
( ! [X2,X0,X1,X6] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X6),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X2),X1))
| ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),X6),X1)) )
| ~ spl0_334 ),
inference(avatar_component_clause,[],[f4925]) ).
fof(f143569,plain,
( spl0_1479
| ~ spl0_218
| ~ spl0_334 ),
inference(avatar_split_clause,[],[f5168,f4925,f2271,f143567]) ).
fof(f143567,plain,
( spl0_1479
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2))
| ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(c_Complete__Lattice_OInf__class_OInf(X0),X3)),X2))
| ~ hBOOL(c_in(X1,X3,X0))
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1479])]) ).
fof(f5168,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2))
| ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(c_Complete__Lattice_OInf__class_OInf(X0),X3)),X2))
| ~ hBOOL(c_in(X1,X3,X0))
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) )
| ~ spl0_218
| ~ spl0_334 ),
inference(resolution,[],[f4926,f2272]) ).
fof(f143563,plain,
( spl0_1478
| ~ spl0_80
| ~ spl0_325 ),
inference(avatar_split_clause,[],[f5046,f4888,f1365,f143561]) ).
fof(f143561,plain,
( spl0_1478
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(c_in(X0,hAPP(c_HOL_Oord__class_Oless(tc_bool),v_P),X1))
| ~ hBOOL(c_in(hAPP(c_Not,v_P),X2,X3))
| hBOOL(c_in(X0,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,c_and,X3,tc_fun(X1,tc_bool)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1478])]) ).
fof(f1365,plain,
( spl0_80
<=> hAPP(c_HOL_Oord__class_Oless(tc_bool),v_P) = hAPP(c_and,hAPP(c_Not,v_P)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_80])]) ).
fof(f4888,plain,
( spl0_325
<=> ! [X3,X4,X9,X0,X5,X8] :
( ~ hBOOL(c_in(X3,X5,X0))
| ~ hBOOL(c_in(X4,hAPP(X9,X3),X8))
| hBOOL(c_in(X4,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,X9,X0,tc_fun(X8,tc_bool)),X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_325])]) ).
fof(f5046,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(c_in(X0,hAPP(c_HOL_Oord__class_Oless(tc_bool),v_P),X1))
| ~ hBOOL(c_in(hAPP(c_Not,v_P),X2,X3))
| hBOOL(c_in(X0,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,c_and,X3,tc_fun(X1,tc_bool)),X1)) )
| ~ spl0_80
| ~ spl0_325 ),
inference(superposition,[],[f4889,f1367]) ).
fof(f1367,plain,
( hAPP(c_HOL_Oord__class_Oless(tc_bool),v_P) = hAPP(c_and,hAPP(c_Not,v_P))
| ~ spl0_80 ),
inference(avatar_component_clause,[],[f1365]) ).
fof(f4889,plain,
( ! [X3,X0,X8,X9,X4,X5] :
( ~ hBOOL(c_in(X4,hAPP(X9,X3),X8))
| ~ hBOOL(c_in(X3,X5,X0))
| hBOOL(c_in(X4,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,X9,X0,tc_fun(X8,tc_bool)),X8)) )
| ~ spl0_325 ),
inference(avatar_component_clause,[],[f4888]) ).
fof(f143559,plain,
( spl0_1477
| ~ spl0_79
| ~ spl0_325 ),
inference(avatar_split_clause,[],[f5008,f4888,f1361,f143557]) ).
fof(f143557,plain,
( spl0_1477
<=> ! [X3,X4,X0,X5,X2,X1] :
( ~ hBOOL(c_in(X2,X1,X3))
| ~ hBOOL(c_in(X1,X4,X5))
| hBOOL(c_in(X2,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X1),X5,tc_fun(X3,tc_bool)),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1477])]) ).
fof(f1361,plain,
( spl0_79
<=> ! [X5,X0] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X5),X5) = X5 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_79])]) ).
fof(f5008,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ hBOOL(c_in(X2,X1,X3))
| ~ hBOOL(c_in(X1,X4,X5))
| hBOOL(c_in(X2,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X1),X5,tc_fun(X3,tc_bool)),X3)) )
| ~ spl0_79
| ~ spl0_325 ),
inference(superposition,[],[f4889,f1362]) ).
fof(f1362,plain,
( ! [X0,X5] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X5),X5) = X5
| ~ spl0_79 ),
inference(avatar_component_clause,[],[f1361]) ).
fof(f143555,plain,
( spl0_1476
| ~ spl0_68
| ~ spl0_325 ),
inference(avatar_split_clause,[],[f5007,f4888,f1316,f143553]) ).
fof(f143553,plain,
( spl0_1476
<=> ! [X3,X4,X0,X5,X2,X1] :
( ~ hBOOL(c_in(X2,X1,X3))
| ~ hBOOL(c_in(X1,X4,X5))
| hBOOL(c_in(X2,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X5,tc_fun(X3,tc_bool)),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1476])]) ).
fof(f1316,plain,
( spl0_68
<=> ! [X5,X0] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X5),X5) = X5 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_68])]) ).
fof(f5007,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ hBOOL(c_in(X2,X1,X3))
| ~ hBOOL(c_in(X1,X4,X5))
| hBOOL(c_in(X2,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X5,tc_fun(X3,tc_bool)),X3)) )
| ~ spl0_68
| ~ spl0_325 ),
inference(superposition,[],[f4889,f1317]) ).
fof(f1317,plain,
( ! [X0,X5] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X5),X5) = X5
| ~ spl0_68 ),
inference(avatar_component_clause,[],[f1316]) ).
fof(f143551,plain,
( spl0_1475
| ~ spl0_112
| ~ spl0_318 ),
inference(avatar_split_clause,[],[f4863,f4618,f1533,f143549]) ).
fof(f143549,plain,
( spl0_1475
<=> ! [X4,X0,X3,X2,X1] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X0,X1,X2)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X0,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(X2)),X3),X2)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X4,X0,X2)
| c_Hoare__Mirabelle_Ohoare__derivs(X4,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X2)),X3),X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1475])]) ).
fof(f1533,plain,
( spl0_112
<=> ! [X0,X69,X39,X68] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X69,X68,X0)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X39,X69,X0)
| c_Hoare__Mirabelle_Ohoare__derivs(X39,X68,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_112])]) ).
fof(f4618,plain,
( spl0_318
<=> ! [X58,X0,X39,X68] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),X58),X0)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X39,X68,X0)
| c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X0)),X58),X68),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_318])]) ).
fof(f4863,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X0,X1,X2)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X0,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(X2)),X3),X2)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X4,X0,X2)
| c_Hoare__Mirabelle_Ohoare__derivs(X4,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X2)),X3),X1),X2) )
| ~ spl0_112
| ~ spl0_318 ),
inference(resolution,[],[f4619,f1534]) ).
fof(f1534,plain,
( ! [X39,X0,X68,X69] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X69,X68,X0)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X39,X69,X0)
| c_Hoare__Mirabelle_Ohoare__derivs(X39,X68,X0) )
| ~ spl0_112 ),
inference(avatar_component_clause,[],[f1533]) ).
fof(f4619,plain,
( ! [X58,X39,X0,X68] :
( c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X0)),X58),X68),X0)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X39,X68,X0)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),X58),X0) )
| ~ spl0_318 ),
inference(avatar_component_clause,[],[f4618]) ).
fof(f142974,plain,
( spl0_1474
| ~ spl0_13
| ~ spl0_303
| ~ spl0_309 ),
inference(avatar_split_clause,[],[f4828,f4581,f4556,f1077,f142972]) ).
fof(f142972,plain,
( spl0_1474
<=> ! [X3,X4,X0,X5,X2,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_bool),hAPP(hAPP(X0,X1),X2)),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,X0,X4,tc_fun(X5,tc_bool)),X2)))
| ~ hBOOL(c_in(X1,X3,X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1474])]) ).
fof(f1077,plain,
( spl0_13
<=> class_HOL_Oord(tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).
fof(f4556,plain,
( spl0_303
<=> ! [X3,X9,X0,X5,X8] :
( ~ hBOOL(c_in(X3,X5,X0))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X8,tc_bool)),hAPP(X9,X3)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,X9,X0,tc_fun(X8,tc_bool)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_303])]) ).
fof(f4581,plain,
( spl0_309
<=> ! [X1,X13,X0,X8,X7] :
( ~ class_HOL_Oord(X8)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,X8)),X7),X13))
| hBOOL(hAPP(hAPP(c_lessequals(X8),hAPP(X7,X1)),hAPP(X13,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_309])]) ).
fof(f4828,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ class_HOL_Oord(tc_bool)
| hBOOL(hAPP(hAPP(c_lessequals(tc_bool),hAPP(hAPP(X0,X1),X2)),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,X0,X4,tc_fun(X5,tc_bool)),X2)))
| ~ hBOOL(c_in(X1,X3,X4)) )
| ~ spl0_303
| ~ spl0_309 ),
inference(resolution,[],[f4582,f4557]) ).
fof(f4557,plain,
( ! [X3,X0,X8,X9,X5] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X8,tc_bool)),hAPP(X9,X3)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,X9,X0,tc_fun(X8,tc_bool))))
| ~ hBOOL(c_in(X3,X5,X0)) )
| ~ spl0_303 ),
inference(avatar_component_clause,[],[f4556]) ).
fof(f4582,plain,
( ! [X0,X1,X8,X7,X13] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,X8)),X7),X13))
| ~ class_HOL_Oord(X8)
| hBOOL(hAPP(hAPP(c_lessequals(X8),hAPP(X7,X1)),hAPP(X13,X1))) )
| ~ spl0_309 ),
inference(avatar_component_clause,[],[f4581]) ).
fof(f142439,plain,
( spl0_1473
| ~ spl0_13
| ~ spl0_307
| ~ spl0_309 ),
inference(avatar_split_clause,[],[f4825,f4581,f4573,f1077,f142437]) ).
fof(f142437,plain,
( spl0_1473
<=> ! [X2,X3,X4,X0,X5,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_bool),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X0,X1,X2,tc_fun(X3,tc_bool)),X4)),hAPP(hAPP(X1,X5),X4)))
| ~ hBOOL(c_in(X5,X0,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1473])]) ).
fof(f4573,plain,
( spl0_307
<=> ! [X9,X0,X8,X5,X3] :
( ~ hBOOL(c_in(X3,X5,X0))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X8,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,X9,X0,tc_fun(X8,tc_bool))),hAPP(X9,X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_307])]) ).
fof(f4825,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ class_HOL_Oord(tc_bool)
| hBOOL(hAPP(hAPP(c_lessequals(tc_bool),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X0,X1,X2,tc_fun(X3,tc_bool)),X4)),hAPP(hAPP(X1,X5),X4)))
| ~ hBOOL(c_in(X5,X0,X2)) )
| ~ spl0_307
| ~ spl0_309 ),
inference(resolution,[],[f4582,f4574]) ).
fof(f4574,plain,
( ! [X3,X0,X8,X9,X5] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X8,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,X9,X0,tc_fun(X8,tc_bool))),hAPP(X9,X3)))
| ~ hBOOL(c_in(X3,X5,X0)) )
| ~ spl0_307 ),
inference(avatar_component_clause,[],[f4573]) ).
fof(f142435,plain,
( spl0_1472
| ~ spl0_183
| ~ spl0_307 ),
inference(avatar_split_clause,[],[f4729,f4573,f1997,f142433]) ).
fof(f142433,plain,
( spl0_1472
<=> ! [X4,X0,X3,X2,X1] :
( ~ hBOOL(c_in(X0,X1,X2))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X3,tc_bool)),hAPP(X4,X0)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,X4,X2,tc_fun(X3,tc_bool))))
| ~ class_Orderings_Opreorder(tc_fun(X3,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1472])]) ).
fof(f1997,plain,
( spl0_183
<=> ! [X2,X0,X1] :
( ~ class_Orderings_Opreorder(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X2),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_183])]) ).
fof(f4729,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ hBOOL(c_in(X0,X1,X2))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X3,tc_bool)),hAPP(X4,X0)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,X4,X2,tc_fun(X3,tc_bool))))
| ~ class_Orderings_Opreorder(tc_fun(X3,tc_bool)) )
| ~ spl0_183
| ~ spl0_307 ),
inference(resolution,[],[f4574,f1998]) ).
fof(f1998,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X2),X1))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ class_Orderings_Opreorder(X0) )
| ~ spl0_183 ),
inference(avatar_component_clause,[],[f1997]) ).
fof(f142431,plain,
( spl0_1471
| ~ spl0_183
| ~ spl0_303 ),
inference(avatar_split_clause,[],[f4633,f4556,f1997,f142429]) ).
fof(f142429,plain,
( spl0_1471
<=> ! [X4,X0,X3,X2,X1] :
( ~ hBOOL(c_in(X0,X1,X2))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X3,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,X4,X2,tc_fun(X3,tc_bool))),hAPP(X4,X0)))
| ~ class_Orderings_Opreorder(tc_fun(X3,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1471])]) ).
fof(f4633,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ hBOOL(c_in(X0,X1,X2))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X3,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,X4,X2,tc_fun(X3,tc_bool))),hAPP(X4,X0)))
| ~ class_Orderings_Opreorder(tc_fun(X3,tc_bool)) )
| ~ spl0_183
| ~ spl0_303 ),
inference(resolution,[],[f4557,f1998]) ).
fof(f142425,plain,
( spl0_1470
| ~ spl0_295
| ~ spl0_297 ),
inference(avatar_split_clause,[],[f4530,f3943,f3935,f142423]) ).
fof(f142423,plain,
( spl0_1470
<=> ! [X4,X0,X3,X2,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X2),X3)))
| ~ class_Lattices_Oupper__semilattice(X0)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X4)),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1470])]) ).
fof(f3935,plain,
( spl0_295
<=> ! [X4,X0,X3,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X0),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X3),X4))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_295])]) ).
fof(f4530,plain,
( ! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X2),X3)))
| ~ class_Lattices_Oupper__semilattice(X0)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X4)),X2)) )
| ~ spl0_295
| ~ spl0_297 ),
inference(duplicate_literal_removal,[],[f4505]) ).
fof(f4505,plain,
( ! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X2),X3)))
| ~ class_Lattices_Oupper__semilattice(X0)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X4)),X2))
| ~ class_Lattices_Oupper__semilattice(X0) )
| ~ spl0_295
| ~ spl0_297 ),
inference(resolution,[],[f3944,f3936]) ).
fof(f3936,plain,
( ! [X3,X0,X1,X4] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X3),X4)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X3))
| ~ class_Lattices_Oupper__semilattice(X0) )
| ~ spl0_295 ),
inference(avatar_component_clause,[],[f3935]) ).
fof(f142421,plain,
( spl0_1469
| ~ spl0_294
| ~ spl0_297 ),
inference(avatar_split_clause,[],[f4529,f3943,f3931,f142419]) ).
fof(f142419,plain,
( spl0_1469
<=> ! [X4,X0,X3,X2,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X2),X3)))
| ~ class_Lattices_Oupper__semilattice(X0)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X4)),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1469])]) ).
fof(f3931,plain,
( spl0_294
<=> ! [X4,X0,X3,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X4))
| hBOOL(hAPP(hAPP(c_lessequals(X0),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X3),X4))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_294])]) ).
fof(f4529,plain,
( ! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X2),X3)))
| ~ class_Lattices_Oupper__semilattice(X0)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X4)),X3)) )
| ~ spl0_294
| ~ spl0_297 ),
inference(duplicate_literal_removal,[],[f4506]) ).
fof(f4506,plain,
( ! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X2),X3)))
| ~ class_Lattices_Oupper__semilattice(X0)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X4)),X3))
| ~ class_Lattices_Oupper__semilattice(X0) )
| ~ spl0_294
| ~ spl0_297 ),
inference(resolution,[],[f3944,f3932]) ).
fof(f3932,plain,
( ! [X3,X0,X1,X4] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X3),X4)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X4))
| ~ class_Lattices_Oupper__semilattice(X0) )
| ~ spl0_294 ),
inference(avatar_component_clause,[],[f3931]) ).
fof(f142417,plain,
( spl0_1468
| ~ spl0_233
| ~ spl0_297 ),
inference(avatar_split_clause,[],[f4523,f3943,f2645,f142415]) ).
fof(f142415,plain,
( spl0_1468
<=> ! [X5,X3,X4,X0,X6,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(hAPP(c_COMBS(X3,X4,X5),c_Lattices_Oupper__semilattice__class_Osup(X0)),X2),X1)),X6))
| hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X6))
| ~ class_Lattices_Oupper__semilattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1468])]) ).
fof(f4523,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(hAPP(c_COMBS(X3,X4,X5),c_Lattices_Oupper__semilattice__class_Osup(X0)),X2),X1)),X6))
| hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X6))
| ~ class_Lattices_Oupper__semilattice(X0) )
| ~ spl0_233
| ~ spl0_297 ),
inference(superposition,[],[f3944,f2646]) ).
fof(f142413,plain,
( spl0_1467
| ~ spl0_295
| ~ spl0_296 ),
inference(avatar_split_clause,[],[f4493,f3939,f3935,f142411]) ).
fof(f142411,plain,
( spl0_1467
<=> ! [X4,X0,X3,X2,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X2),X3)))
| ~ class_Lattices_Oupper__semilattice(X0)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X4),X1)),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1467])]) ).
fof(f4493,plain,
( ! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X2),X3)))
| ~ class_Lattices_Oupper__semilattice(X0)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X4),X1)),X2)) )
| ~ spl0_295
| ~ spl0_296 ),
inference(duplicate_literal_removal,[],[f4468]) ).
fof(f4468,plain,
( ! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X2),X3)))
| ~ class_Lattices_Oupper__semilattice(X0)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X4),X1)),X2))
| ~ class_Lattices_Oupper__semilattice(X0) )
| ~ spl0_295
| ~ spl0_296 ),
inference(resolution,[],[f3940,f3936]) ).
fof(f142409,plain,
( spl0_1466
| ~ spl0_294
| ~ spl0_296 ),
inference(avatar_split_clause,[],[f4492,f3939,f3931,f142407]) ).
fof(f142407,plain,
( spl0_1466
<=> ! [X4,X0,X3,X2,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X2),X3)))
| ~ class_Lattices_Oupper__semilattice(X0)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X4),X1)),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1466])]) ).
fof(f4492,plain,
( ! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X2),X3)))
| ~ class_Lattices_Oupper__semilattice(X0)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X4),X1)),X3)) )
| ~ spl0_294
| ~ spl0_296 ),
inference(duplicate_literal_removal,[],[f4469]) ).
fof(f4469,plain,
( ! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X2),X3)))
| ~ class_Lattices_Oupper__semilattice(X0)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X4),X1)),X3))
| ~ class_Lattices_Oupper__semilattice(X0) )
| ~ spl0_294
| ~ spl0_296 ),
inference(resolution,[],[f3940,f3932]) ).
fof(f142405,plain,
( spl0_1465
| ~ spl0_233
| ~ spl0_295 ),
inference(avatar_split_clause,[],[f4450,f3935,f2645,f142403]) ).
fof(f142403,plain,
( spl0_1465
<=> ! [X3,X4,X0,X6,X5,X2,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),X6),hAPP(hAPP(hAPP(c_COMBS(X3,X4,X5),c_Lattices_Oupper__semilattice__class_Osup(X0)),X2),X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X6),X1))
| ~ class_Lattices_Oupper__semilattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1465])]) ).
fof(f4450,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),X6),hAPP(hAPP(hAPP(c_COMBS(X3,X4,X5),c_Lattices_Oupper__semilattice__class_Osup(X0)),X2),X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X6),X1))
| ~ class_Lattices_Oupper__semilattice(X0) )
| ~ spl0_233
| ~ spl0_295 ),
inference(superposition,[],[f3936,f2646]) ).
fof(f142401,plain,
( spl0_1464
| ~ spl0_233
| ~ spl0_292 ),
inference(avatar_split_clause,[],[f4351,f3915,f2645,f142399]) ).
fof(f142399,plain,
( spl0_1464
<=> ! [X3,X4,X0,X6,X5,X2,X1] :
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X6),hAPP(hAPP(hAPP(c_COMBS(X3,X4,X5),c_Lattices_Oupper__semilattice__class_Osup(X0)),X2),X1)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X6),X1))
| ~ class_Lattices_Oupper__semilattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1464])]) ).
fof(f3915,plain,
( spl0_292
<=> ! [X4,X0,X3,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X3),X4))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_292])]) ).
fof(f4351,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] :
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X6),hAPP(hAPP(hAPP(c_COMBS(X3,X4,X5),c_Lattices_Oupper__semilattice__class_Osup(X0)),X2),X1)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X6),X1))
| ~ class_Lattices_Oupper__semilattice(X0) )
| ~ spl0_233
| ~ spl0_292 ),
inference(superposition,[],[f3916,f2646]) ).
fof(f3916,plain,
( ! [X3,X0,X1,X4] :
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X3),X4)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X3))
| ~ class_Lattices_Oupper__semilattice(X0) )
| ~ spl0_292 ),
inference(avatar_component_clause,[],[f3915]) ).
fof(f142397,plain,
( spl0_1463
| ~ spl0_233
| ~ spl0_291 ),
inference(avatar_split_clause,[],[f4328,f3911,f2645,f142395]) ).
fof(f142395,plain,
( spl0_1463
<=> ! [X5,X3,X4,X0,X6,X2,X1] :
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(hAPP(c_COMBS(X3,X4,X5),c_Lattices_Olower__semilattice__class_Oinf(X0)),X2),X1)),X6))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X6))
| ~ class_Lattices_Olower__semilattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1463])]) ).
fof(f3911,plain,
( spl0_291
<=> ! [X4,X0,X3,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X3),X1))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),X4)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_291])]) ).
fof(f4328,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] :
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(hAPP(c_COMBS(X3,X4,X5),c_Lattices_Olower__semilattice__class_Oinf(X0)),X2),X1)),X6))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X6))
| ~ class_Lattices_Olower__semilattice(X0) )
| ~ spl0_233
| ~ spl0_291 ),
inference(superposition,[],[f3912,f2646]) ).
fof(f3912,plain,
( ! [X3,X0,X1,X4] :
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),X4)),X1))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X3),X1))
| ~ class_Lattices_Olower__semilattice(X0) )
| ~ spl0_291 ),
inference(avatar_component_clause,[],[f3911]) ).
fof(f142393,plain,
( spl0_1462
| ~ spl0_185
| ~ spl0_289 ),
inference(avatar_split_clause,[],[f4274,f3903,f2005,f142391]) ).
fof(f142391,plain,
( spl0_1462
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X2)),X1))
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X2) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1462])]) ).
fof(f3903,plain,
( spl0_289
<=> ! [X9,X5,X0] :
( X5 = X9
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X5),X9))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X9),X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_289])]) ).
fof(f4274,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X2)),X1))
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X2) = X1 )
| ~ spl0_185
| ~ spl0_289 ),
inference(resolution,[],[f3904,f2006]) ).
fof(f3904,plain,
( ! [X0,X9,X5] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X9),X5))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X5),X9))
| X5 = X9 )
| ~ spl0_289 ),
inference(avatar_component_clause,[],[f3903]) ).
fof(f142389,plain,
( spl0_1461
| ~ spl0_184
| ~ spl0_289 ),
inference(avatar_split_clause,[],[f4273,f3903,f2001,f142387]) ).
fof(f142387,plain,
( spl0_1461
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X2)),X2))
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X2) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1461])]) ).
fof(f4273,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X2)),X2))
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X2) = X2 )
| ~ spl0_184
| ~ spl0_289 ),
inference(resolution,[],[f3904,f2002]) ).
fof(f142385,plain,
( spl0_1460
| ~ spl0_31
| ~ spl0_1170 ),
inference(avatar_split_clause,[],[f99876,f92695,f1151,f142383]) ).
fof(f142383,plain,
( spl0_1460
<=> ! [X0,X1] :
( c_False = hAPP(c_Complete__Lattice_OInf__class_OInf(tc_bool),hAPP(c_lessequals(tc_fun(X0,X1)),c_False))
| ~ class_Orderings_Oorder(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1460])]) ).
fof(f1151,plain,
( spl0_31
<=> ! [X75,X74] :
( ~ class_Orderings_Oorder(X75)
| class_Orderings_Oorder(tc_fun(X74,X75)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_31])]) ).
fof(f92695,plain,
( spl0_1170
<=> ! [X0] :
( c_False = hAPP(c_Complete__Lattice_OInf__class_OInf(tc_bool),hAPP(c_lessequals(X0),c_False))
| ~ class_Orderings_Oorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1170])]) ).
fof(f99876,plain,
( ! [X0,X1] :
( c_False = hAPP(c_Complete__Lattice_OInf__class_OInf(tc_bool),hAPP(c_lessequals(tc_fun(X0,X1)),c_False))
| ~ class_Orderings_Oorder(X1) )
| ~ spl0_31
| ~ spl0_1170 ),
inference(resolution,[],[f92696,f1152]) ).
fof(f1152,plain,
( ! [X74,X75] :
( class_Orderings_Oorder(tc_fun(X74,X75))
| ~ class_Orderings_Oorder(X75) )
| ~ spl0_31 ),
inference(avatar_component_clause,[],[f1151]) ).
fof(f92696,plain,
( ! [X0] :
( ~ class_Orderings_Oorder(X0)
| c_False = hAPP(c_Complete__Lattice_OInf__class_OInf(tc_bool),hAPP(c_lessequals(X0),c_False)) )
| ~ spl0_1170 ),
inference(avatar_component_clause,[],[f92695]) ).
fof(f142381,plain,
( spl0_1459
| ~ spl0_190
| ~ spl0_289 ),
inference(avatar_split_clause,[],[f4266,f3903,f2025,f142379]) ).
fof(f142379,plain,
( spl0_1459
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X2),X1)))
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X2),X1) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1459])]) ).
fof(f4266,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X2),X1)))
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X2),X1) = X1 )
| ~ spl0_190
| ~ spl0_289 ),
inference(resolution,[],[f3904,f2026]) ).
fof(f142377,plain,
( spl0_1458
| ~ spl0_186
| ~ spl0_289 ),
inference(avatar_split_clause,[],[f4263,f3903,f2009,f142375]) ).
fof(f142375,plain,
( spl0_1458
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X1),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X1),X2)))
| hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X1),X2) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1458])]) ).
fof(f2009,plain,
( spl0_186
<=> ! [X9,X5,X0] : hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X5),X9)),X5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_186])]) ).
fof(f4263,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X1),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X1),X2)))
| hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X1),X2) = X1 )
| ~ spl0_186
| ~ spl0_289 ),
inference(resolution,[],[f3904,f2010]) ).
fof(f2010,plain,
( ! [X0,X9,X5] : hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X5),X9)),X5))
| ~ spl0_186 ),
inference(avatar_component_clause,[],[f2009]) ).
fof(f142373,plain,
( spl0_1457
| ~ spl0_189
| ~ spl0_289 ),
inference(avatar_split_clause,[],[f4260,f3903,f2021,f142371]) ).
fof(f142371,plain,
( spl0_1457
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X1),X2)))
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X1),X2) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1457])]) ).
fof(f4260,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X1),X2)))
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X1),X2) = X1 )
| ~ spl0_189
| ~ spl0_289 ),
inference(resolution,[],[f3904,f2022]) ).
fof(f142369,plain,
( spl0_1456
| ~ spl0_199
| ~ spl0_288 ),
inference(avatar_split_clause,[],[f4243,f3899,f2062,f142367]) ).
fof(f142367,plain,
( spl0_1456
<=> ! [X4,X0,X3,X2,X1] :
( ~ hBOOL(c_COMBK(c_False,tc_bool,X0))
| ~ hBOOL(c_in(X1,X2,X3))
| hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X3,tc_fun(X4,tc_bool)),c_COMBK(c_False,tc_bool,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1456])]) ).
fof(f2062,plain,
( spl0_199
<=> ! [X5,X0] : c_COMBK(c_False,tc_bool,X0) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X5),c_COMBK(c_False,tc_bool,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_199])]) ).
fof(f3899,plain,
( spl0_288
<=> ! [X4,X9,X0,X8,X5,X3] :
( ~ hBOOL(c_in(X3,X5,X0))
| ~ hBOOL(hAPP(hAPP(X9,X3),X4))
| hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,X9,X0,tc_fun(X8,tc_bool)),X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_288])]) ).
fof(f4243,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ hBOOL(c_COMBK(c_False,tc_bool,X0))
| ~ hBOOL(c_in(X1,X2,X3))
| hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X3,tc_fun(X4,tc_bool)),c_COMBK(c_False,tc_bool,X0))) )
| ~ spl0_199
| ~ spl0_288 ),
inference(superposition,[],[f3900,f2063]) ).
fof(f2063,plain,
( ! [X0,X5] : c_COMBK(c_False,tc_bool,X0) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X5),c_COMBK(c_False,tc_bool,X0))
| ~ spl0_199 ),
inference(avatar_component_clause,[],[f2062]) ).
fof(f3900,plain,
( ! [X3,X0,X8,X9,X4,X5] :
( ~ hBOOL(hAPP(hAPP(X9,X3),X4))
| ~ hBOOL(c_in(X3,X5,X0))
| hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,X9,X0,tc_fun(X8,tc_bool)),X4)) )
| ~ spl0_288 ),
inference(avatar_component_clause,[],[f3899]) ).
fof(f142365,plain,
( spl0_1455
| ~ spl0_198
| ~ spl0_288 ),
inference(avatar_split_clause,[],[f4238,f3899,f2058,f142363]) ).
fof(f142363,plain,
( spl0_1455
<=> ! [X4,X0,X3,X2,X1] :
( ~ hBOOL(c_COMBK(c_False,tc_bool,X0))
| ~ hBOOL(c_in(X1,X2,X3))
| hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X3,tc_fun(X4,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1455])]) ).
fof(f2058,plain,
( spl0_198
<=> ! [X5,X0] : hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X5),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool))) = c_COMBK(c_False,tc_bool,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_198])]) ).
fof(f4238,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ hBOOL(c_COMBK(c_False,tc_bool,X0))
| ~ hBOOL(c_in(X1,X2,X3))
| hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X3,tc_fun(X4,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)))) )
| ~ spl0_198
| ~ spl0_288 ),
inference(superposition,[],[f3900,f2059]) ).
fof(f2059,plain,
( ! [X0,X5] : hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X5),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool))) = c_COMBK(c_False,tc_bool,X0)
| ~ spl0_198 ),
inference(avatar_component_clause,[],[f2058]) ).
fof(f142361,plain,
( spl0_1454
| ~ spl0_179
| ~ spl0_288 ),
inference(avatar_split_clause,[],[f4237,f3899,f1980,f142359]) ).
fof(f142359,plain,
( spl0_1454
<=> ! [X4,X0,X3,X2,X1] :
( ~ hBOOL(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)))
| ~ hBOOL(c_in(X1,X2,X3))
| hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X3,tc_fun(X4,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1454])]) ).
fof(f1980,plain,
( spl0_179
<=> ! [X5,X0] : c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X5),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_179])]) ).
fof(f4237,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ hBOOL(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)))
| ~ hBOOL(c_in(X1,X2,X3))
| hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X3,tc_fun(X4,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)))) )
| ~ spl0_179
| ~ spl0_288 ),
inference(superposition,[],[f3900,f1981]) ).
fof(f1981,plain,
( ! [X0,X5] : c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X5),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)))
| ~ spl0_179 ),
inference(avatar_component_clause,[],[f1980]) ).
fof(f142357,plain,
( spl0_1453
| ~ spl0_195
| ~ spl0_288 ),
inference(avatar_split_clause,[],[f4229,f3899,f2045,f142355]) ).
fof(f142355,plain,
( spl0_1453
<=> ! [X2,X3,X0,X1,X8,X6,X7,X4,X5] :
( ~ hBOOL(hAPP(X3,hAPP(X4,X5)))
| ~ hBOOL(c_in(X4,X6,X7))
| hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X6,hAPP(c_COMBB(X0,X1,X2),X3),X7,tc_fun(X8,tc_bool)),X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1453])]) ).
fof(f2045,plain,
( spl0_195
<=> ! [X57,X11,X14,X0,X67,X8] : hAPP(hAPP(hAPP(c_COMBB(X8,X0,X14),X11),X57),X67) = hAPP(X11,hAPP(X57,X67)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_195])]) ).
fof(f4229,plain,
( ! [X2,X3,X0,X1,X8,X6,X7,X4,X5] :
( ~ hBOOL(hAPP(X3,hAPP(X4,X5)))
| ~ hBOOL(c_in(X4,X6,X7))
| hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X6,hAPP(c_COMBB(X0,X1,X2),X3),X7,tc_fun(X8,tc_bool)),X5)) )
| ~ spl0_195
| ~ spl0_288 ),
inference(superposition,[],[f3900,f2046]) ).
fof(f2046,plain,
( ! [X0,X11,X8,X57,X14,X67] : hAPP(hAPP(hAPP(c_COMBB(X8,X0,X14),X11),X57),X67) = hAPP(X11,hAPP(X57,X67))
| ~ spl0_195 ),
inference(avatar_component_clause,[],[f2045]) ).
fof(f142353,plain,
( spl0_1452
| ~ spl0_201
| ~ spl0_288 ),
inference(avatar_split_clause,[],[f4221,f3899,f2076,f142351]) ).
fof(f142351,plain,
( spl0_1452
<=> ! [X4,X0,X3,X2,X1] :
( ~ hBOOL(c_COMBK(c_False,tc_bool,X0))
| ~ hBOOL(c_in(c_COMBK(c_False,tc_bool,X0),X2,X3))
| hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X3,tc_fun(X4,tc_bool)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1452])]) ).
fof(f4221,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ hBOOL(c_COMBK(c_False,tc_bool,X0))
| ~ hBOOL(c_in(c_COMBK(c_False,tc_bool,X0),X2,X3))
| hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X3,tc_fun(X4,tc_bool)),X1)) )
| ~ spl0_201
| ~ spl0_288 ),
inference(superposition,[],[f3900,f2077]) ).
fof(f142349,plain,
( spl0_1451
| ~ spl0_200
| ~ spl0_288 ),
inference(avatar_split_clause,[],[f4220,f3899,f2066,f142347]) ).
fof(f142347,plain,
( spl0_1451
<=> ! [X4,X0,X3,X2,X1] :
( ~ hBOOL(c_COMBK(c_False,tc_bool,X0))
| ~ hBOOL(c_in(c_COMBK(c_False,tc_bool,X0),X2,X3))
| hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X3,tc_fun(X4,tc_bool)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1451])]) ).
fof(f4220,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ hBOOL(c_COMBK(c_False,tc_bool,X0))
| ~ hBOOL(c_in(c_COMBK(c_False,tc_bool,X0),X2,X3))
| hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X3,tc_fun(X4,tc_bool)),X1)) )
| ~ spl0_200
| ~ spl0_288 ),
inference(superposition,[],[f3900,f2067]) ).
fof(f142345,plain,
( spl0_1450
| ~ spl0_178
| ~ spl0_288 ),
inference(avatar_split_clause,[],[f4218,f3899,f1976,f142343]) ).
fof(f142343,plain,
( spl0_1450
<=> ! [X4,X0,X3,X2,X1] :
( ~ hBOOL(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)))
| ~ hBOOL(c_in(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X2,X3))
| hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X3,tc_fun(X4,tc_bool)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1450])]) ).
fof(f4218,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ hBOOL(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)))
| ~ hBOOL(c_in(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X2,X3))
| hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X3,tc_fun(X4,tc_bool)),X1)) )
| ~ spl0_178
| ~ spl0_288 ),
inference(superposition,[],[f3900,f1977]) ).
fof(f142341,plain,
( spl0_1449
| ~ spl0_29
| ~ spl0_1169 ),
inference(avatar_split_clause,[],[f99834,f91689,f1143,f142339]) ).
fof(f142339,plain,
( spl0_1449
<=> ! [X0,X1] :
( c_False = hAPP(c_Complete__Lattice_OInf__class_OInf(tc_bool),hAPP(c_lessequals(tc_fun(X0,X1)),c_False))
| ~ class_Orderings_Opreorder(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1449])]) ).
fof(f1143,plain,
( spl0_29
<=> ! [X75,X74] :
( ~ class_Orderings_Opreorder(X75)
| class_Orderings_Opreorder(tc_fun(X74,X75)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_29])]) ).
fof(f91689,plain,
( spl0_1169
<=> ! [X0] :
( c_False = hAPP(c_Complete__Lattice_OInf__class_OInf(tc_bool),hAPP(c_lessequals(X0),c_False))
| ~ class_Orderings_Opreorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1169])]) ).
fof(f99834,plain,
( ! [X0,X1] :
( c_False = hAPP(c_Complete__Lattice_OInf__class_OInf(tc_bool),hAPP(c_lessequals(tc_fun(X0,X1)),c_False))
| ~ class_Orderings_Opreorder(X1) )
| ~ spl0_29
| ~ spl0_1169 ),
inference(resolution,[],[f91690,f1144]) ).
fof(f1144,plain,
( ! [X74,X75] :
( class_Orderings_Opreorder(tc_fun(X74,X75))
| ~ class_Orderings_Opreorder(X75) )
| ~ spl0_29 ),
inference(avatar_component_clause,[],[f1143]) ).
fof(f91690,plain,
( ! [X0] :
( ~ class_Orderings_Opreorder(X0)
| c_False = hAPP(c_Complete__Lattice_OInf__class_OInf(tc_bool),hAPP(c_lessequals(X0),c_False)) )
| ~ spl0_1169 ),
inference(avatar_component_clause,[],[f91689]) ).
fof(f142337,plain,
( spl0_1448
| ~ spl0_225
| ~ spl0_288 ),
inference(avatar_split_clause,[],[f4158,f3899,f2299,f142335]) ).
fof(f142335,plain,
( spl0_1448
<=> ! [X3,X4,X0,X5,X2,X1] :
( ~ hBOOL(c_in(X0,X1,X2))
| hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,c_lessequals(X3),X2,tc_fun(X4,tc_bool)),hAPP(c_Complete__Lattice_OSup__class_OSup(X3),X5)))
| ~ hBOOL(c_in(X0,X5,X3))
| ~ class_Complete__Lattice_Ocomplete__lattice(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1448])]) ).
fof(f4158,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ hBOOL(c_in(X0,X1,X2))
| hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,c_lessequals(X3),X2,tc_fun(X4,tc_bool)),hAPP(c_Complete__Lattice_OSup__class_OSup(X3),X5)))
| ~ hBOOL(c_in(X0,X5,X3))
| ~ class_Complete__Lattice_Ocomplete__lattice(X3) )
| ~ spl0_225
| ~ spl0_288 ),
inference(resolution,[],[f3900,f2300]) ).
fof(f142333,plain,
( spl0_1447
| ~ spl0_218
| ~ spl0_288 ),
inference(avatar_split_clause,[],[f4143,f3899,f2271,f142331]) ).
fof(f142331,plain,
( spl0_1447
<=> ! [X5,X4,X0,X3,X2,X1] :
( ~ hBOOL(c_in(hAPP(c_Complete__Lattice_OInf__class_OInf(X0),X1),X2,X3))
| hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,c_lessequals(X0),X3,tc_fun(X4,tc_bool)),X5))
| ~ hBOOL(c_in(X5,X1,X0))
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1447])]) ).
fof(f4143,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ hBOOL(c_in(hAPP(c_Complete__Lattice_OInf__class_OInf(X0),X1),X2,X3))
| hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,c_lessequals(X0),X3,tc_fun(X4,tc_bool)),X5))
| ~ hBOOL(c_in(X5,X1,X0))
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) )
| ~ spl0_218
| ~ spl0_288 ),
inference(resolution,[],[f3900,f2272]) ).
fof(f142329,plain,
( spl0_1446
| ~ spl0_285
| ~ spl0_287 ),
inference(avatar_split_clause,[],[f4125,f3895,f3887,f142327]) ).
fof(f142327,plain,
( spl0_1446
<=> ! [X4,X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X3)))
| ~ class_Lattices_Olower__semilattice(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X4),X1)),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1446])]) ).
fof(f3895,plain,
( spl0_287
<=> ! [X4,X0,X3,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X4),X1))
| hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),X4)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_287])]) ).
fof(f4125,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X3)))
| ~ class_Lattices_Olower__semilattice(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X4),X1)),X3)) )
| ~ spl0_285
| ~ spl0_287 ),
inference(duplicate_literal_removal,[],[f4107]) ).
fof(f4107,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X3)))
| ~ class_Lattices_Olower__semilattice(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X4),X1)),X3))
| ~ class_Lattices_Olower__semilattice(X0) )
| ~ spl0_285
| ~ spl0_287 ),
inference(resolution,[],[f3896,f3888]) ).
fof(f3896,plain,
( ! [X3,X0,X1,X4] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),X4)),X1))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X4),X1))
| ~ class_Lattices_Olower__semilattice(X0) )
| ~ spl0_287 ),
inference(avatar_component_clause,[],[f3895]) ).
fof(f142325,plain,
( spl0_1445
| ~ spl0_284
| ~ spl0_287 ),
inference(avatar_split_clause,[],[f4124,f3895,f3883,f142323]) ).
fof(f142323,plain,
( spl0_1445
<=> ! [X4,X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X3)))
| ~ class_Lattices_Olower__semilattice(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X4),X1)),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1445])]) ).
fof(f4124,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X3)))
| ~ class_Lattices_Olower__semilattice(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X4),X1)),X2)) )
| ~ spl0_284
| ~ spl0_287 ),
inference(duplicate_literal_removal,[],[f4108]) ).
fof(f4108,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X3)))
| ~ class_Lattices_Olower__semilattice(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X4),X1)),X2))
| ~ class_Lattices_Olower__semilattice(X0) )
| ~ spl0_284
| ~ spl0_287 ),
inference(resolution,[],[f3896,f3884]) ).
fof(f142321,plain,
( spl0_1444
| ~ spl0_169
| ~ spl0_287 ),
inference(avatar_split_clause,[],[f4091,f3895,f1865,f142319]) ).
fof(f142319,plain,
( spl0_1444
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X1),X2))
| ~ class_Lattices_Olower__semilattice(tc_fun(X0,tc_bool))
| c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X3),X1),X0)
| ~ c_Finite__Set_Ofinite(X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1444])]) ).
fof(f1865,plain,
( spl0_169
<=> ! [X5,X9,X0] :
( ~ c_Finite__Set_Ofinite(X9,X0)
| c_Finite__Set_Ofinite(X5,X0)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X5),X9)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_169])]) ).
fof(f4091,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X1),X2))
| ~ class_Lattices_Olower__semilattice(tc_fun(X0,tc_bool))
| c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X3),X1),X0)
| ~ c_Finite__Set_Ofinite(X2,X0) )
| ~ spl0_169
| ~ spl0_287 ),
inference(resolution,[],[f3896,f1866]) ).
fof(f1866,plain,
( ! [X0,X9,X5] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X5),X9))
| c_Finite__Set_Ofinite(X5,X0)
| ~ c_Finite__Set_Ofinite(X9,X0) )
| ~ spl0_169 ),
inference(avatar_component_clause,[],[f1865]) ).
fof(f142317,plain,
( spl0_1443
| ~ spl0_285
| ~ spl0_286 ),
inference(avatar_split_clause,[],[f4087,f3891,f3887,f142315]) ).
fof(f142315,plain,
( spl0_1443
<=> ! [X4,X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X3)))
| ~ class_Lattices_Olower__semilattice(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X4)),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1443])]) ).
fof(f3891,plain,
( spl0_286
<=> ! [X4,X0,X3,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X3),X1))
| hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),X4)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_286])]) ).
fof(f4087,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X3)))
| ~ class_Lattices_Olower__semilattice(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X4)),X3)) )
| ~ spl0_285
| ~ spl0_286 ),
inference(duplicate_literal_removal,[],[f4069]) ).
fof(f4069,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X3)))
| ~ class_Lattices_Olower__semilattice(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X4)),X3))
| ~ class_Lattices_Olower__semilattice(X0) )
| ~ spl0_285
| ~ spl0_286 ),
inference(resolution,[],[f3892,f3888]) ).
fof(f3892,plain,
( ! [X3,X0,X1,X4] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),X4)),X1))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X3),X1))
| ~ class_Lattices_Olower__semilattice(X0) )
| ~ spl0_286 ),
inference(avatar_component_clause,[],[f3891]) ).
fof(f142313,plain,
( spl0_1442
| ~ spl0_284
| ~ spl0_286 ),
inference(avatar_split_clause,[],[f4086,f3891,f3883,f142311]) ).
fof(f142311,plain,
( spl0_1442
<=> ! [X4,X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X3)))
| ~ class_Lattices_Olower__semilattice(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X4)),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1442])]) ).
fof(f4086,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X3)))
| ~ class_Lattices_Olower__semilattice(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X4)),X2)) )
| ~ spl0_284
| ~ spl0_286 ),
inference(duplicate_literal_removal,[],[f4070]) ).
fof(f4070,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X3)))
| ~ class_Lattices_Olower__semilattice(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X4)),X2))
| ~ class_Lattices_Olower__semilattice(X0) )
| ~ spl0_284
| ~ spl0_286 ),
inference(resolution,[],[f3892,f3884]) ).
fof(f142309,plain,
( spl0_1441
| ~ spl0_233
| ~ spl0_286 ),
inference(avatar_split_clause,[],[f4080,f3891,f2645,f142307]) ).
fof(f142307,plain,
( spl0_1441
<=> ! [X5,X3,X4,X0,X6,X2,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(hAPP(c_COMBS(X3,X4,X5),c_Lattices_Olower__semilattice__class_Oinf(X0)),X2),X1)),X6))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X6))
| ~ class_Lattices_Olower__semilattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1441])]) ).
fof(f4080,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(hAPP(c_COMBS(X3,X4,X5),c_Lattices_Olower__semilattice__class_Oinf(X0)),X2),X1)),X6))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X6))
| ~ class_Lattices_Olower__semilattice(X0) )
| ~ spl0_233
| ~ spl0_286 ),
inference(superposition,[],[f3892,f2646]) ).
fof(f142305,plain,
( spl0_1440
| ~ spl0_233
| ~ spl0_284 ),
inference(avatar_split_clause,[],[f4011,f3883,f2645,f142303]) ).
fof(f142303,plain,
( spl0_1440
<=> ! [X3,X4,X0,X6,X5,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X6),hAPP(hAPP(hAPP(c_COMBS(X3,X4,X5),c_Lattices_Olower__semilattice__class_Oinf(X0)),X2),X1)))
| hBOOL(hAPP(hAPP(c_lessequals(X0),X6),X1))
| ~ class_Lattices_Olower__semilattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1440])]) ).
fof(f4011,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X6),hAPP(hAPP(hAPP(c_COMBS(X3,X4,X5),c_Lattices_Olower__semilattice__class_Oinf(X0)),X2),X1)))
| hBOOL(hAPP(hAPP(c_lessequals(X0),X6),X1))
| ~ class_Lattices_Olower__semilattice(X0) )
| ~ spl0_233
| ~ spl0_284 ),
inference(superposition,[],[f3884,f2646]) ).
fof(f142301,plain,
( spl0_1439
| ~ spl0_211
| ~ spl0_275 ),
inference(avatar_split_clause,[],[f3834,f3652,f2237,f142299]) ).
fof(f142299,plain,
( spl0_1439
<=> ! [X2,X0,X1] :
( c_COMBK(c_False,tc_bool,X0) != X1
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X1),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X2),X1)))
| ~ class_Lattices_Olower__semilattice(tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1439])]) ).
fof(f3652,plain,
( spl0_275
<=> ! [X5,X9,X0] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X5),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X9),X5)) = c_COMBK(c_False,tc_bool,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_275])]) ).
fof(f3834,plain,
( ! [X2,X0,X1] :
( c_COMBK(c_False,tc_bool,X0) != X1
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X1),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X2),X1)))
| ~ class_Lattices_Olower__semilattice(tc_fun(X0,tc_bool)) )
| ~ spl0_211
| ~ spl0_275 ),
inference(superposition,[],[f2238,f3653]) ).
fof(f3653,plain,
( ! [X0,X9,X5] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X5),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X9),X5)) = c_COMBK(c_False,tc_bool,X0)
| ~ spl0_275 ),
inference(avatar_component_clause,[],[f3652]) ).
fof(f142062,plain,
( spl0_1438
| ~ spl0_30
| ~ spl0_272 ),
inference(avatar_split_clause,[],[f3798,f3639,f1147,f142060]) ).
fof(f142060,plain,
( spl0_1438
<=> ! [X0,X3,X2,X1] :
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,X1)),X2),X3) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,X1)),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,X1)),X2),X3))
| ~ class_Lattices_Olattice(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1438])]) ).
fof(f3639,plain,
( spl0_272
<=> ! [X2,X0,X1] :
( ~ class_Lattices_Olattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_272])]) ).
fof(f3798,plain,
( ! [X2,X3,X0,X1] :
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,X1)),X2),X3) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,X1)),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,X1)),X2),X3))
| ~ class_Lattices_Olattice(X1) )
| ~ spl0_30
| ~ spl0_272 ),
inference(resolution,[],[f3640,f1148]) ).
fof(f3640,plain,
( ! [X2,X0,X1] :
( ~ class_Lattices_Olattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2)) )
| ~ spl0_272 ),
inference(avatar_component_clause,[],[f3639]) ).
fof(f142058,plain,
( spl0_1437
| ~ spl0_130
| ~ spl0_262
| ~ spl0_263
| ~ spl0_271 ),
inference(avatar_split_clause,[],[f3796,f3635,f3121,f3117,f1631,f142056]) ).
fof(f142056,plain,
( spl0_1437
<=> ! [X5,X4,X0,X6,X1] :
( ~ hBOOL(c_in(c_COMBK(c_False,tc_bool,X0),X5,X6))
| hBOOL(hAPP(hAPP(c_lessequals(X4),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X6,X4)),X1))
| ~ class_Complete__Lattice_Ocomplete__lattice(X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1437])]) ).
fof(f3635,plain,
( spl0_271
<=> ! [X18,X19,X0,X5,X8] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X8)
| ~ hBOOL(c_in(X19,X5,X0))
| hBOOL(hAPP(hAPP(c_lessequals(X8),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,X18,X0,X8)),hAPP(X18,X19))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_271])]) ).
fof(f3796,plain,
( ! [X0,X1,X6,X4,X5] :
( ~ hBOOL(c_in(c_COMBK(c_False,tc_bool,X0),X5,X6))
| hBOOL(hAPP(hAPP(c_lessequals(X4),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X6,X4)),X1))
| ~ class_Complete__Lattice_Ocomplete__lattice(X4) )
| ~ spl0_130
| ~ spl0_262
| ~ spl0_263
| ~ spl0_271 ),
inference(forward_demodulation,[],[f3777,f3466]) ).
fof(f3777,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] :
( hBOOL(hAPP(hAPP(c_lessequals(X4),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X6,X4)),X1))
| ~ hBOOL(c_in(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_COMBK(c_False,tc_bool,X2),X3,X2,tc_fun(X0,tc_bool)),X5,X6))
| ~ class_Complete__Lattice_Ocomplete__lattice(X4) )
| ~ spl0_263
| ~ spl0_271 ),
inference(superposition,[],[f3636,f3122]) ).
fof(f3636,plain,
( ! [X0,X18,X8,X19,X5] :
( hBOOL(hAPP(hAPP(c_lessequals(X8),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,X18,X0,X8)),hAPP(X18,X19)))
| ~ hBOOL(c_in(X19,X5,X0))
| ~ class_Complete__Lattice_Ocomplete__lattice(X8) )
| ~ spl0_271 ),
inference(avatar_component_clause,[],[f3635]) ).
fof(f142054,plain,
( spl0_1436
| ~ spl0_130
| ~ spl0_262
| ~ spl0_271 ),
inference(avatar_split_clause,[],[f3795,f3635,f3117,f1631,f142052]) ).
fof(f142052,plain,
( spl0_1436
<=> ! [X5,X4,X0,X6,X1] :
( ~ hBOOL(c_in(c_COMBK(c_False,tc_bool,X0),X5,X6))
| hBOOL(hAPP(hAPP(c_lessequals(X4),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X1),X6,X4)),X1))
| ~ class_Complete__Lattice_Ocomplete__lattice(X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1436])]) ).
fof(f3795,plain,
( ! [X0,X1,X6,X4,X5] :
( ~ hBOOL(c_in(c_COMBK(c_False,tc_bool,X0),X5,X6))
| hBOOL(hAPP(hAPP(c_lessequals(X4),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X1),X6,X4)),X1))
| ~ class_Complete__Lattice_Ocomplete__lattice(X4) )
| ~ spl0_130
| ~ spl0_262
| ~ spl0_271 ),
inference(forward_demodulation,[],[f3776,f3466]) ).
fof(f3776,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] :
( hBOOL(hAPP(hAPP(c_lessequals(X4),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X1),X6,X4)),X1))
| ~ hBOOL(c_in(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_COMBK(c_False,tc_bool,X2),X3,X2,tc_fun(X0,tc_bool)),X5,X6))
| ~ class_Complete__Lattice_Ocomplete__lattice(X4) )
| ~ spl0_262
| ~ spl0_271 ),
inference(superposition,[],[f3636,f3118]) ).
fof(f142050,plain,
( spl0_1435
| ~ spl0_120
| ~ spl0_271 ),
inference(avatar_split_clause,[],[f3788,f3635,f1591,f142048]) ).
fof(f142048,plain,
( spl0_1435
<=> ! [X2,X3,X4,X0,X6,X5,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(X4),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,c_Fun_Ocomp(c_COMBK(X0,X1,X2),X3,X2,X1,t_a),X6,X4)),X0))
| ~ hBOOL(c_in(v_x,X5,X6))
| ~ class_Complete__Lattice_Ocomplete__lattice(X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1435])]) ).
fof(f3788,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] :
( hBOOL(hAPP(hAPP(c_lessequals(X4),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,c_Fun_Ocomp(c_COMBK(X0,X1,X2),X3,X2,X1,t_a),X6,X4)),X0))
| ~ hBOOL(c_in(v_x,X5,X6))
| ~ class_Complete__Lattice_Ocomplete__lattice(X4) )
| ~ spl0_120
| ~ spl0_271 ),
inference(superposition,[],[f3636,f1592]) ).
fof(f142046,plain,
( spl0_1434
| ~ spl0_125
| ~ spl0_271 ),
inference(avatar_split_clause,[],[f3778,f3635,f1611,f142044]) ).
fof(f142044,plain,
( spl0_1434
<=> ! [X4,X0,X3,X2,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(X2),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X3,hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X1),X4,X2)),X1))
| ~ hBOOL(c_in(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X3,X4))
| ~ class_Complete__Lattice_Ocomplete__lattice(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1434])]) ).
fof(f3778,plain,
( ! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(hAPP(c_lessequals(X2),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X3,hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X1),X4,X2)),X1))
| ~ hBOOL(c_in(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X3,X4))
| ~ class_Complete__Lattice_Ocomplete__lattice(X2) )
| ~ spl0_125
| ~ spl0_271 ),
inference(superposition,[],[f3636,f1612]) ).
fof(f142042,plain,
( spl0_1433
| ~ spl0_133
| ~ spl0_271 ),
inference(avatar_split_clause,[],[f3762,f3635,f1643,f142040]) ).
fof(f142040,plain,
( spl0_1433
<=> ! [X4,X0,X3,X2,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(X2),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X3,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0)),X4,X2)),X1))
| ~ hBOOL(c_in(X1,X3,X4))
| ~ class_Complete__Lattice_Ocomplete__lattice(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1433])]) ).
fof(f3762,plain,
( ! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(hAPP(c_lessequals(X2),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X3,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0)),X4,X2)),X1))
| ~ hBOOL(c_in(X1,X3,X4))
| ~ class_Complete__Lattice_Ocomplete__lattice(X2) )
| ~ spl0_133
| ~ spl0_271 ),
inference(superposition,[],[f3636,f1644]) ).
fof(f142038,plain,
( spl0_1432
| ~ spl0_123
| ~ spl0_271 ),
inference(avatar_split_clause,[],[f3760,f3635,f1603,f142036]) ).
fof(f142036,plain,
( spl0_1432
<=> ! [X4,X0,X3,X2,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(X2),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X3,hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool))),X4,X2)),X1))
| ~ hBOOL(c_in(X1,X3,X4))
| ~ class_Complete__Lattice_Ocomplete__lattice(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1432])]) ).
fof(f3760,plain,
( ! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(hAPP(c_lessequals(X2),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X3,hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool))),X4,X2)),X1))
| ~ hBOOL(c_in(X1,X3,X4))
| ~ class_Complete__Lattice_Ocomplete__lattice(X2) )
| ~ spl0_123
| ~ spl0_271 ),
inference(superposition,[],[f3636,f1604]) ).
fof(f142034,plain,
( spl0_1431
| ~ spl0_130
| ~ spl0_271 ),
inference(avatar_split_clause,[],[f3759,f3635,f1631,f142032]) ).
fof(f142032,plain,
( spl0_1431
<=> ! [X4,X0,X3,X2,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(X2),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X3,hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X1),X4,X2)),c_COMBK(c_False,tc_bool,X0)))
| ~ hBOOL(c_in(X1,X3,X4))
| ~ class_Complete__Lattice_Ocomplete__lattice(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1431])]) ).
fof(f3759,plain,
( ! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(hAPP(c_lessequals(X2),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X3,hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X1),X4,X2)),c_COMBK(c_False,tc_bool,X0)))
| ~ hBOOL(c_in(X1,X3,X4))
| ~ class_Complete__Lattice_Ocomplete__lattice(X2) )
| ~ spl0_130
| ~ spl0_271 ),
inference(superposition,[],[f3636,f1632]) ).
fof(f142030,plain,
( spl0_1430
| ~ spl0_25
| ~ spl0_269 ),
inference(avatar_split_clause,[],[f3733,f3627,f1127,f142028]) ).
fof(f142028,plain,
( spl0_1430
<=> ! [X0,X3,X2,X1] :
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,X1)),X2),X3) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,X1)),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,X1)),X2),X3))
| ~ class_Lattices_Olattice(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1430])]) ).
fof(f1127,plain,
( spl0_25
<=> ! [X75,X74] :
( ~ class_Lattices_Olattice(X75)
| class_Lattices_Oupper__semilattice(tc_fun(X74,X75)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_25])]) ).
fof(f3627,plain,
( spl0_269
<=> ! [X2,X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_269])]) ).
fof(f3733,plain,
( ! [X2,X3,X0,X1] :
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,X1)),X2),X3) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,X1)),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,X1)),X2),X3))
| ~ class_Lattices_Olattice(X1) )
| ~ spl0_25
| ~ spl0_269 ),
inference(resolution,[],[f3628,f1128]) ).
fof(f1128,plain,
( ! [X74,X75] :
( class_Lattices_Oupper__semilattice(tc_fun(X74,X75))
| ~ class_Lattices_Olattice(X75) )
| ~ spl0_25 ),
inference(avatar_component_clause,[],[f1127]) ).
fof(f3628,plain,
( ! [X2,X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2)) )
| ~ spl0_269 ),
inference(avatar_component_clause,[],[f3627]) ).
fof(f142026,plain,
( spl0_1429
| ~ spl0_130
| ~ spl0_262
| ~ spl0_263
| ~ spl0_268 ),
inference(avatar_split_clause,[],[f3731,f3623,f3121,f3117,f1631,f142024]) ).
fof(f142024,plain,
( spl0_1429
<=> ! [X5,X4,X0,X6,X1] :
( ~ hBOOL(c_in(c_COMBK(c_False,tc_bool,X0),X5,X6))
| hBOOL(hAPP(hAPP(c_lessequals(X4),X1),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X6,X4)))
| ~ class_Complete__Lattice_Ocomplete__lattice(X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1429])]) ).
fof(f3623,plain,
( spl0_268
<=> ! [X18,X19,X0,X5,X8] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X8)
| ~ hBOOL(c_in(X19,X5,X0))
| hBOOL(hAPP(hAPP(c_lessequals(X8),hAPP(X18,X19)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,X18,X0,X8))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_268])]) ).
fof(f3731,plain,
( ! [X0,X1,X6,X4,X5] :
( ~ hBOOL(c_in(c_COMBK(c_False,tc_bool,X0),X5,X6))
| hBOOL(hAPP(hAPP(c_lessequals(X4),X1),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X6,X4)))
| ~ class_Complete__Lattice_Ocomplete__lattice(X4) )
| ~ spl0_130
| ~ spl0_262
| ~ spl0_263
| ~ spl0_268 ),
inference(forward_demodulation,[],[f3713,f3466]) ).
fof(f3713,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] :
( hBOOL(hAPP(hAPP(c_lessequals(X4),X1),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X6,X4)))
| ~ hBOOL(c_in(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_COMBK(c_False,tc_bool,X2),X3,X2,tc_fun(X0,tc_bool)),X5,X6))
| ~ class_Complete__Lattice_Ocomplete__lattice(X4) )
| ~ spl0_263
| ~ spl0_268 ),
inference(superposition,[],[f3624,f3122]) ).
fof(f3624,plain,
( ! [X0,X18,X8,X19,X5] :
( hBOOL(hAPP(hAPP(c_lessequals(X8),hAPP(X18,X19)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,X18,X0,X8)))
| ~ hBOOL(c_in(X19,X5,X0))
| ~ class_Complete__Lattice_Ocomplete__lattice(X8) )
| ~ spl0_268 ),
inference(avatar_component_clause,[],[f3623]) ).
fof(f141836,plain,
( spl0_1428
| ~ spl0_130
| ~ spl0_262
| ~ spl0_268 ),
inference(avatar_split_clause,[],[f3730,f3623,f3117,f1631,f141834]) ).
fof(f141834,plain,
( spl0_1428
<=> ! [X5,X4,X0,X6,X1] :
( ~ hBOOL(c_in(c_COMBK(c_False,tc_bool,X0),X5,X6))
| hBOOL(hAPP(hAPP(c_lessequals(X4),X1),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X1),X6,X4)))
| ~ class_Complete__Lattice_Ocomplete__lattice(X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1428])]) ).
fof(f3730,plain,
( ! [X0,X1,X6,X4,X5] :
( ~ hBOOL(c_in(c_COMBK(c_False,tc_bool,X0),X5,X6))
| hBOOL(hAPP(hAPP(c_lessequals(X4),X1),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X1),X6,X4)))
| ~ class_Complete__Lattice_Ocomplete__lattice(X4) )
| ~ spl0_130
| ~ spl0_262
| ~ spl0_268 ),
inference(forward_demodulation,[],[f3712,f3466]) ).
fof(f3712,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] :
( hBOOL(hAPP(hAPP(c_lessequals(X4),X1),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X1),X6,X4)))
| ~ hBOOL(c_in(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_COMBK(c_False,tc_bool,X2),X3,X2,tc_fun(X0,tc_bool)),X5,X6))
| ~ class_Complete__Lattice_Ocomplete__lattice(X4) )
| ~ spl0_262
| ~ spl0_268 ),
inference(superposition,[],[f3624,f3118]) ).
fof(f141832,plain,
( spl0_1427
| ~ spl0_120
| ~ spl0_268 ),
inference(avatar_split_clause,[],[f3724,f3623,f1591,f141830]) ).
fof(f141830,plain,
( spl0_1427
<=> ! [X2,X3,X4,X0,X6,X5,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(X4),X0),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,c_Fun_Ocomp(c_COMBK(X0,X1,X2),X3,X2,X1,t_a),X6,X4)))
| ~ hBOOL(c_in(v_x,X5,X6))
| ~ class_Complete__Lattice_Ocomplete__lattice(X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1427])]) ).
fof(f3724,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] :
( hBOOL(hAPP(hAPP(c_lessequals(X4),X0),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,c_Fun_Ocomp(c_COMBK(X0,X1,X2),X3,X2,X1,t_a),X6,X4)))
| ~ hBOOL(c_in(v_x,X5,X6))
| ~ class_Complete__Lattice_Ocomplete__lattice(X4) )
| ~ spl0_120
| ~ spl0_268 ),
inference(superposition,[],[f3624,f1592]) ).
fof(f141828,plain,
( spl0_1426
| ~ spl0_125
| ~ spl0_268 ),
inference(avatar_split_clause,[],[f3714,f3623,f1611,f141826]) ).
fof(f141826,plain,
( spl0_1426
<=> ! [X4,X0,X3,X2,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(X2),X1),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X1),X4,X2)))
| ~ hBOOL(c_in(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X3,X4))
| ~ class_Complete__Lattice_Ocomplete__lattice(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1426])]) ).
fof(f3714,plain,
( ! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(hAPP(c_lessequals(X2),X1),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X1),X4,X2)))
| ~ hBOOL(c_in(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X3,X4))
| ~ class_Complete__Lattice_Ocomplete__lattice(X2) )
| ~ spl0_125
| ~ spl0_268 ),
inference(superposition,[],[f3624,f1612]) ).
fof(f141824,plain,
( spl0_1425
| ~ spl0_133
| ~ spl0_268 ),
inference(avatar_split_clause,[],[f3698,f3623,f1643,f141822]) ).
fof(f141822,plain,
( spl0_1425
<=> ! [X4,X0,X3,X2,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(X2),X1),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0)),X4,X2)))
| ~ hBOOL(c_in(X1,X3,X4))
| ~ class_Complete__Lattice_Ocomplete__lattice(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1425])]) ).
fof(f3698,plain,
( ! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(hAPP(c_lessequals(X2),X1),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0)),X4,X2)))
| ~ hBOOL(c_in(X1,X3,X4))
| ~ class_Complete__Lattice_Ocomplete__lattice(X2) )
| ~ spl0_133
| ~ spl0_268 ),
inference(superposition,[],[f3624,f1644]) ).
fof(f141820,plain,
( spl0_1424
| ~ spl0_123
| ~ spl0_268 ),
inference(avatar_split_clause,[],[f3696,f3623,f1603,f141818]) ).
fof(f141818,plain,
( spl0_1424
<=> ! [X4,X0,X3,X2,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(X2),X1),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool))),X4,X2)))
| ~ hBOOL(c_in(X1,X3,X4))
| ~ class_Complete__Lattice_Ocomplete__lattice(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1424])]) ).
fof(f3696,plain,
( ! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(hAPP(c_lessequals(X2),X1),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool))),X4,X2)))
| ~ hBOOL(c_in(X1,X3,X4))
| ~ class_Complete__Lattice_Ocomplete__lattice(X2) )
| ~ spl0_123
| ~ spl0_268 ),
inference(superposition,[],[f3624,f1604]) ).
fof(f141816,plain,
( spl0_1423
| ~ spl0_130
| ~ spl0_268 ),
inference(avatar_split_clause,[],[f3695,f3623,f1631,f141814]) ).
fof(f141814,plain,
( spl0_1423
<=> ! [X4,X0,X3,X2,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(X2),c_COMBK(c_False,tc_bool,X0)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X1),X4,X2)))
| ~ hBOOL(c_in(X1,X3,X4))
| ~ class_Complete__Lattice_Ocomplete__lattice(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1423])]) ).
fof(f3695,plain,
( ! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(hAPP(c_lessequals(X2),c_COMBK(c_False,tc_bool,X0)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X1),X4,X2)))
| ~ hBOOL(c_in(X1,X3,X4))
| ~ class_Complete__Lattice_Ocomplete__lattice(X2) )
| ~ spl0_130
| ~ spl0_268 ),
inference(superposition,[],[f3624,f1632]) ).
fof(f141812,plain,
( spl0_1422
| ~ spl0_233
| ~ spl0_265 ),
inference(avatar_split_clause,[],[f3606,f3129,f2645,f141810]) ).
fof(f141810,plain,
( spl0_1422
<=> ! [X3,X4,X0,X5,X2,X1] :
( c_COMBK(c_False,tc_bool,X0) != hAPP(hAPP(hAPP(c_COMBS(X3,X4,X5),c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool))),X2),X1)
| c_COMBK(c_False,tc_bool,X0) = hAPP(X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1422])]) ).
fof(f3606,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( c_COMBK(c_False,tc_bool,X0) != hAPP(hAPP(hAPP(c_COMBS(X3,X4,X5),c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool))),X2),X1)
| c_COMBK(c_False,tc_bool,X0) = hAPP(X2,X1) )
| ~ spl0_233
| ~ spl0_265 ),
inference(superposition,[],[f3130,f2646]) ).
fof(f141808,plain,
( spl0_1421
| ~ spl0_146
| ~ spl0_260 ),
inference(avatar_split_clause,[],[f3459,f3109,f1716,f141806]) ).
fof(f141806,plain,
( spl0_1421
<=> ! [X2,X0,X1] :
( hAPP(hAPP(c_Set_Oinsert(X0),X1),X2) = X2
| ~ class_Orderings_Oorder(tc_fun(X0,tc_bool))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),X2),hAPP(hAPP(c_Set_Oinsert(X0),X1),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1421])]) ).
fof(f1716,plain,
( spl0_146
<=> ! [X9,X0,X3] : hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X9),hAPP(hAPP(c_Set_Oinsert(X0),X3),X9))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_146])]) ).
fof(f3109,plain,
( spl0_260
<=> ! [X4,X0,X3] :
( ~ class_Orderings_Oorder(X0)
| X3 = X4
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X4),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X4),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_260])]) ).
fof(f3459,plain,
( ! [X2,X0,X1] :
( hAPP(hAPP(c_Set_Oinsert(X0),X1),X2) = X2
| ~ class_Orderings_Oorder(tc_fun(X0,tc_bool))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),X2),hAPP(hAPP(c_Set_Oinsert(X0),X1),X2))) )
| ~ spl0_146
| ~ spl0_260 ),
inference(resolution,[],[f3110,f1717]) ).
fof(f1717,plain,
( ! [X3,X0,X9] : hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X9),hAPP(hAPP(c_Set_Oinsert(X0),X3),X9)))
| ~ spl0_146 ),
inference(avatar_component_clause,[],[f1716]) ).
fof(f3110,plain,
( ! [X3,X0,X4] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X4),X3))
| X3 = X4
| ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X4),X3)) )
| ~ spl0_260 ),
inference(avatar_component_clause,[],[f3109]) ).
fof(f141804,plain,
( spl0_1420
| ~ spl0_233
| ~ spl0_259 ),
inference(avatar_split_clause,[],[f3434,f3105,f2645,f141802]) ).
fof(f141802,plain,
( spl0_1420
<=> ! [X5,X3,X4,X0,X6,X2,X1] :
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_COMBS(X3,X4,X5),c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool))),X2),X1),X6))
| ~ hBOOL(hAPP(hAPP(X2,X1),X6))
| ~ hBOOL(hAPP(X1,X6)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1420])]) ).
fof(f3105,plain,
( spl0_259
<=> ! [X9,X5,X1,X0] :
( ~ hBOOL(hAPP(X5,X1))
| ~ hBOOL(hAPP(X9,X1))
| hBOOL(hAPP(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X5),X9),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_259])]) ).
fof(f3434,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] :
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_COMBS(X3,X4,X5),c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool))),X2),X1),X6))
| ~ hBOOL(hAPP(hAPP(X2,X1),X6))
| ~ hBOOL(hAPP(X1,X6)) )
| ~ spl0_233
| ~ spl0_259 ),
inference(superposition,[],[f3106,f2646]) ).
fof(f3106,plain,
( ! [X0,X1,X9,X5] :
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X5),X9),X1))
| ~ hBOOL(hAPP(X9,X1))
| ~ hBOOL(hAPP(X5,X1)) )
| ~ spl0_259 ),
inference(avatar_component_clause,[],[f3105]) ).
fof(f141800,plain,
( spl0_1419
| ~ spl0_233
| ~ spl0_258 ),
inference(avatar_split_clause,[],[f3425,f3101,f2645,f141798]) ).
fof(f141798,plain,
( spl0_1419
<=> ! [X3,X4,X0,X7,X6,X5,X2,X1] :
( ~ hBOOL(hAPP(hAPP(hAPP(c_COMBS(X3,X4,X5),c_lessequals(tc_fun(X0,tc_bool))),X2),X1))
| c_Fun_Oinj__on(X6,X1,X0,X7)
| ~ c_Fun_Oinj__on(X6,hAPP(X2,X1),X0,X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1419])]) ).
fof(f3101,plain,
( spl0_258
<=> ! [X5,X0,X9,X8,X7] :
( ~ c_Fun_Oinj__on(X7,X9,X0,X8)
| c_Fun_Oinj__on(X7,X5,X0,X8)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X5),X9)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_258])]) ).
fof(f3425,plain,
( ! [X2,X3,X0,X1,X6,X7,X4,X5] :
( ~ hBOOL(hAPP(hAPP(hAPP(c_COMBS(X3,X4,X5),c_lessequals(tc_fun(X0,tc_bool))),X2),X1))
| c_Fun_Oinj__on(X6,X1,X0,X7)
| ~ c_Fun_Oinj__on(X6,hAPP(X2,X1),X0,X7) )
| ~ spl0_233
| ~ spl0_258 ),
inference(superposition,[],[f3102,f2646]) ).
fof(f3102,plain,
( ! [X0,X8,X9,X7,X5] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X5),X9))
| c_Fun_Oinj__on(X7,X5,X0,X8)
| ~ c_Fun_Oinj__on(X7,X9,X0,X8) )
| ~ spl0_258 ),
inference(avatar_component_clause,[],[f3101]) ).
fof(f141796,plain,
( spl0_1418
| ~ spl0_742
| ~ spl0_941 ),
inference(avatar_split_clause,[],[f81384,f71224,f43271,f141794]) ).
fof(f141794,plain,
( spl0_1418
<=> ! [X0,X1] : hAPP(hAPP(c_fequal(tc_bool),X1),X0) = hAPP(c_SetInterval_Oord__class_OatLeastAtMost(X1,X1,tc_bool),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1418])]) ).
fof(f43271,plain,
( spl0_742
<=> ! [X2,X0,X1] : hAPP(hAPP(c_fequal(X0),X1),X2) = hAPP(hAPP(c_fequal(X0),X2),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_742])]) ).
fof(f71224,plain,
( spl0_941
<=> ! [X0,X1] : hAPP(c_SetInterval_Oord__class_OatLeastAtMost(X0,X0,tc_bool),X1) = hAPP(hAPP(c_fequal(tc_bool),X1),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_941])]) ).
fof(f81384,plain,
( ! [X0,X1] : hAPP(hAPP(c_fequal(tc_bool),X1),X0) = hAPP(c_SetInterval_Oord__class_OatLeastAtMost(X1,X1,tc_bool),X0)
| ~ spl0_742
| ~ spl0_941 ),
inference(superposition,[],[f71225,f43272]) ).
fof(f43272,plain,
( ! [X2,X0,X1] : hAPP(hAPP(c_fequal(X0),X1),X2) = hAPP(hAPP(c_fequal(X0),X2),X1)
| ~ spl0_742 ),
inference(avatar_component_clause,[],[f43271]) ).
fof(f71225,plain,
( ! [X0,X1] : hAPP(c_SetInterval_Oord__class_OatLeastAtMost(X0,X0,tc_bool),X1) = hAPP(hAPP(c_fequal(tc_bool),X1),X0)
| ~ spl0_941 ),
inference(avatar_component_clause,[],[f71224]) ).
fof(f141792,plain,
( spl0_1417
| ~ spl0_225
| ~ spl0_258 ),
inference(avatar_split_clause,[],[f3422,f3101,f2299,f141790]) ).
fof(f141790,plain,
( spl0_1417
<=> ! [X4,X0,X3,X2,X1] :
( c_Fun_Oinj__on(X0,X1,X2,X3)
| ~ c_Fun_Oinj__on(X0,hAPP(c_Complete__Lattice_OSup__class_OSup(tc_fun(X2,tc_bool)),X4),X2,X3)
| ~ hBOOL(c_in(X1,X4,tc_fun(X2,tc_bool)))
| ~ class_Complete__Lattice_Ocomplete__lattice(tc_fun(X2,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1417])]) ).
fof(f3422,plain,
( ! [X2,X3,X0,X1,X4] :
( c_Fun_Oinj__on(X0,X1,X2,X3)
| ~ c_Fun_Oinj__on(X0,hAPP(c_Complete__Lattice_OSup__class_OSup(tc_fun(X2,tc_bool)),X4),X2,X3)
| ~ hBOOL(c_in(X1,X4,tc_fun(X2,tc_bool)))
| ~ class_Complete__Lattice_Ocomplete__lattice(tc_fun(X2,tc_bool)) )
| ~ spl0_225
| ~ spl0_258 ),
inference(resolution,[],[f3102,f2300]) ).
fof(f141788,plain,
( spl0_1416
| ~ spl0_218
| ~ spl0_258 ),
inference(avatar_split_clause,[],[f3413,f3101,f2271,f141786]) ).
fof(f141786,plain,
( spl0_1416
<=> ! [X4,X0,X3,X2,X1] :
( c_Fun_Oinj__on(X0,hAPP(c_Complete__Lattice_OInf__class_OInf(tc_fun(X1,tc_bool)),X2),X1,X3)
| ~ c_Fun_Oinj__on(X0,X4,X1,X3)
| ~ hBOOL(c_in(X4,X2,tc_fun(X1,tc_bool)))
| ~ class_Complete__Lattice_Ocomplete__lattice(tc_fun(X1,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1416])]) ).
fof(f3413,plain,
( ! [X2,X3,X0,X1,X4] :
( c_Fun_Oinj__on(X0,hAPP(c_Complete__Lattice_OInf__class_OInf(tc_fun(X1,tc_bool)),X2),X1,X3)
| ~ c_Fun_Oinj__on(X0,X4,X1,X3)
| ~ hBOOL(c_in(X4,X2,tc_fun(X1,tc_bool)))
| ~ class_Complete__Lattice_Ocomplete__lattice(tc_fun(X1,tc_bool)) )
| ~ spl0_218
| ~ spl0_258 ),
inference(resolution,[],[f3102,f2272]) ).
fof(f141784,plain,
( spl0_1415
| ~ spl0_233
| ~ spl0_257 ),
inference(avatar_split_clause,[],[f3399,f3097,f2645,f141782]) ).
fof(f141782,plain,
( spl0_1415
<=> ! [X3,X4,X0,X6,X5,X2,X1] :
( ~ hBOOL(hAPP(hAPP(hAPP(c_COMBS(X3,X4,X5),c_lessequals(tc_fun(X0,tc_bool))),X2),X1))
| hBOOL(c_in(X6,hAPP(X2,X1),X0))
| ~ hBOOL(c_in(X6,X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1415])]) ).
fof(f3097,plain,
( spl0_257
<=> ! [X35,X9,X0,X5] :
( ~ hBOOL(c_in(X35,X5,X0))
| hBOOL(c_in(X35,X9,X0))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X5),X9)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_257])]) ).
fof(f3399,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] :
( ~ hBOOL(hAPP(hAPP(hAPP(c_COMBS(X3,X4,X5),c_lessequals(tc_fun(X0,tc_bool))),X2),X1))
| hBOOL(c_in(X6,hAPP(X2,X1),X0))
| ~ hBOOL(c_in(X6,X1,X0)) )
| ~ spl0_233
| ~ spl0_257 ),
inference(superposition,[],[f3098,f2646]) ).
fof(f3098,plain,
( ! [X0,X9,X5,X35] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X5),X9))
| hBOOL(c_in(X35,X9,X0))
| ~ hBOOL(c_in(X35,X5,X0)) )
| ~ spl0_257 ),
inference(avatar_component_clause,[],[f3097]) ).
fof(f141780,plain,
( spl0_1414
| ~ spl0_225
| ~ spl0_257 ),
inference(avatar_split_clause,[],[f3396,f3097,f2299,f141778]) ).
fof(f141778,plain,
( spl0_1414
<=> ! [X0,X3,X2,X1] :
( hBOOL(c_in(X0,hAPP(c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_bool)),X2),X1))
| ~ hBOOL(c_in(X0,X3,X1))
| ~ hBOOL(c_in(X3,X2,tc_fun(X1,tc_bool)))
| ~ class_Complete__Lattice_Ocomplete__lattice(tc_fun(X1,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1414])]) ).
fof(f3396,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(c_in(X0,hAPP(c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_bool)),X2),X1))
| ~ hBOOL(c_in(X0,X3,X1))
| ~ hBOOL(c_in(X3,X2,tc_fun(X1,tc_bool)))
| ~ class_Complete__Lattice_Ocomplete__lattice(tc_fun(X1,tc_bool)) )
| ~ spl0_225
| ~ spl0_257 ),
inference(resolution,[],[f3098,f2300]) ).
fof(f141776,plain,
( spl0_1413
| ~ spl0_218
| ~ spl0_257 ),
inference(avatar_split_clause,[],[f3387,f3097,f2271,f141774]) ).
fof(f141774,plain,
( spl0_1413
<=> ! [X0,X3,X2,X1] :
( hBOOL(c_in(X0,X1,X2))
| ~ hBOOL(c_in(X0,hAPP(c_Complete__Lattice_OInf__class_OInf(tc_fun(X2,tc_bool)),X3),X2))
| ~ hBOOL(c_in(X1,X3,tc_fun(X2,tc_bool)))
| ~ class_Complete__Lattice_Ocomplete__lattice(tc_fun(X2,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1413])]) ).
fof(f3387,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(c_in(X0,X1,X2))
| ~ hBOOL(c_in(X0,hAPP(c_Complete__Lattice_OInf__class_OInf(tc_fun(X2,tc_bool)),X3),X2))
| ~ hBOOL(c_in(X1,X3,tc_fun(X2,tc_bool)))
| ~ class_Complete__Lattice_Ocomplete__lattice(tc_fun(X2,tc_bool)) )
| ~ spl0_218
| ~ spl0_257 ),
inference(resolution,[],[f3098,f2272]) ).
fof(f141772,plain,
( spl0_1412
| ~ spl0_218
| ~ spl0_255 ),
inference(avatar_split_clause,[],[f3348,f3089,f2271,f141770]) ).
fof(f141770,plain,
( spl0_1412
<=> ! [X2,X0,X1] :
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),hAPP(c_Complete__Lattice_OInf__class_OInf(tc_fun(X0,tc_bool)),X2)) = X1
| ~ hBOOL(c_in(X1,X2,tc_fun(X0,tc_bool)))
| ~ class_Complete__Lattice_Ocomplete__lattice(tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1412])]) ).
fof(f3089,plain,
( spl0_255
<=> ! [X9,X5,X0] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X9),X5))
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X5),X9) = X5 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_255])]) ).
fof(f3348,plain,
( ! [X2,X0,X1] :
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),hAPP(c_Complete__Lattice_OInf__class_OInf(tc_fun(X0,tc_bool)),X2)) = X1
| ~ hBOOL(c_in(X1,X2,tc_fun(X0,tc_bool)))
| ~ class_Complete__Lattice_Ocomplete__lattice(tc_fun(X0,tc_bool)) )
| ~ spl0_218
| ~ spl0_255 ),
inference(resolution,[],[f3090,f2272]) ).
fof(f3090,plain,
( ! [X0,X9,X5] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X9),X5))
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X5),X9) = X5 )
| ~ spl0_255 ),
inference(avatar_component_clause,[],[f3089]) ).
fof(f141768,plain,
( spl0_1411
| ~ spl0_218
| ~ spl0_254 ),
inference(avatar_split_clause,[],[f3322,f3085,f2271,f141766]) ).
fof(f141766,plain,
( spl0_1411
<=> ! [X2,X0,X1] :
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),hAPP(c_Complete__Lattice_OInf__class_OInf(tc_fun(X0,tc_bool)),X1)),X2) = X2
| ~ hBOOL(c_in(X2,X1,tc_fun(X0,tc_bool)))
| ~ class_Complete__Lattice_Ocomplete__lattice(tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1411])]) ).
fof(f3085,plain,
( spl0_254
<=> ! [X9,X5,X0] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X5),X9))
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X5),X9) = X9 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_254])]) ).
fof(f3322,plain,
( ! [X2,X0,X1] :
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),hAPP(c_Complete__Lattice_OInf__class_OInf(tc_fun(X0,tc_bool)),X1)),X2) = X2
| ~ hBOOL(c_in(X2,X1,tc_fun(X0,tc_bool)))
| ~ class_Complete__Lattice_Ocomplete__lattice(tc_fun(X0,tc_bool)) )
| ~ spl0_218
| ~ spl0_254 ),
inference(resolution,[],[f3086,f2272]) ).
fof(f3086,plain,
( ! [X0,X9,X5] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X5),X9))
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X5),X9) = X9 )
| ~ spl0_254 ),
inference(avatar_component_clause,[],[f3085]) ).
fof(f141764,plain,
( spl0_1410
| ~ spl0_225
| ~ spl0_252 ),
inference(avatar_split_clause,[],[f3273,f3077,f2299,f141762]) ).
fof(f141762,plain,
( spl0_1410
<=> ! [X0,X3,X2,X1] :
( hBOOL(c_in(X0,hAPP(c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_bool)),X2),X1))
| ~ hBOOL(c_in(hAPP(hAPP(c_Set_Oinsert(X1),X0),X3),X2,tc_fun(X1,tc_bool)))
| ~ class_Complete__Lattice_Ocomplete__lattice(tc_fun(X1,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1410])]) ).
fof(f3273,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(c_in(X0,hAPP(c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_bool)),X2),X1))
| ~ hBOOL(c_in(hAPP(hAPP(c_Set_Oinsert(X1),X0),X3),X2,tc_fun(X1,tc_bool)))
| ~ class_Complete__Lattice_Ocomplete__lattice(tc_fun(X1,tc_bool)) )
| ~ spl0_225
| ~ spl0_252 ),
inference(resolution,[],[f3078,f2300]) ).
fof(f141760,plain,
( spl0_1409
| ~ spl0_225
| ~ spl0_251 ),
inference(avatar_split_clause,[],[f3242,f3073,f2299,f141758]) ).
fof(f141758,plain,
( spl0_1409
<=> ! [X2,X0,X1] :
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),hAPP(c_Complete__Lattice_OSup__class_OSup(tc_fun(X0,tc_bool)),X1)),X2) = X2
| ~ hBOOL(c_in(X2,X1,tc_fun(X0,tc_bool)))
| ~ class_Complete__Lattice_Ocomplete__lattice(tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1409])]) ).
fof(f3073,plain,
( spl0_251
<=> ! [X9,X5,X0] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X9),X5))
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X5),X9) = X9 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_251])]) ).
fof(f3242,plain,
( ! [X2,X0,X1] :
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),hAPP(c_Complete__Lattice_OSup__class_OSup(tc_fun(X0,tc_bool)),X1)),X2) = X2
| ~ hBOOL(c_in(X2,X1,tc_fun(X0,tc_bool)))
| ~ class_Complete__Lattice_Ocomplete__lattice(tc_fun(X0,tc_bool)) )
| ~ spl0_225
| ~ spl0_251 ),
inference(resolution,[],[f3074,f2300]) ).
fof(f3074,plain,
( ! [X0,X9,X5] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X9),X5))
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X5),X9) = X9 )
| ~ spl0_251 ),
inference(avatar_component_clause,[],[f3073]) ).
fof(f141756,plain,
( spl0_1408
| ~ spl0_233
| ~ spl0_250 ),
inference(avatar_split_clause,[],[f3219,f3059,f2645,f141754]) ).
fof(f141754,plain,
( spl0_1408
<=> ! [X3,X4,X0,X5,X2,X1] :
( ~ hBOOL(hAPP(hAPP(hAPP(c_COMBS(X3,X4,X5),c_lessequals(tc_fun(X0,tc_bool))),X2),X1))
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X1),hAPP(X2,X1)) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1408])]) ).
fof(f3059,plain,
( spl0_250
<=> ! [X9,X5,X0] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X5),X9))
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X5),X9) = X5 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_250])]) ).
fof(f3219,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ hBOOL(hAPP(hAPP(hAPP(c_COMBS(X3,X4,X5),c_lessequals(tc_fun(X0,tc_bool))),X2),X1))
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X1),hAPP(X2,X1)) = X1 )
| ~ spl0_233
| ~ spl0_250 ),
inference(superposition,[],[f3060,f2646]) ).
fof(f3060,plain,
( ! [X0,X9,X5] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X5),X9))
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X5),X9) = X5 )
| ~ spl0_250 ),
inference(avatar_component_clause,[],[f3059]) ).
fof(f141752,plain,
( spl0_1407
| ~ spl0_227
| ~ spl0_941 ),
inference(avatar_split_clause,[],[f81383,f71224,f2580,f141750]) ).
fof(f141750,plain,
( spl0_1407
<=> ! [X0,X1] : hAPP(c_SetInterval_Oord__class_OatLeastAtMost(X0,X0,tc_bool),X1) = hAPP(c_SetInterval_Oord__class_OatLeastAtMost(X1,X1,tc_bool),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1407])]) ).
fof(f81383,plain,
( ! [X0,X1] : hAPP(c_SetInterval_Oord__class_OatLeastAtMost(X0,X0,tc_bool),X1) = hAPP(c_SetInterval_Oord__class_OatLeastAtMost(X1,X1,tc_bool),X0)
| ~ spl0_227
| ~ spl0_941 ),
inference(superposition,[],[f71225,f2581]) ).
fof(f141748,plain,
( spl0_1406
| ~ spl0_225
| ~ spl0_250 ),
inference(avatar_split_clause,[],[f3216,f3059,f2299,f141746]) ).
fof(f141746,plain,
( spl0_1406
<=> ! [X2,X0,X1] :
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X1),hAPP(c_Complete__Lattice_OSup__class_OSup(tc_fun(X0,tc_bool)),X2)) = X1
| ~ hBOOL(c_in(X1,X2,tc_fun(X0,tc_bool)))
| ~ class_Complete__Lattice_Ocomplete__lattice(tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1406])]) ).
fof(f3216,plain,
( ! [X2,X0,X1] :
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X1),hAPP(c_Complete__Lattice_OSup__class_OSup(tc_fun(X0,tc_bool)),X2)) = X1
| ~ hBOOL(c_in(X1,X2,tc_fun(X0,tc_bool)))
| ~ class_Complete__Lattice_Ocomplete__lattice(tc_fun(X0,tc_bool)) )
| ~ spl0_225
| ~ spl0_250 ),
inference(resolution,[],[f3060,f2300]) ).
fof(f141744,plain,
( spl0_1405
| ~ spl0_233
| ~ spl0_249 ),
inference(avatar_split_clause,[],[f3190,f3055,f2645,f141742]) ).
fof(f141742,plain,
( spl0_1405
<=> ! [X5,X3,X4,X0,X6,X2,X1] :
( ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_COMBS(X3,X4,X5),c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool))),X2),X1),X6))
| hBOOL(hAPP(X1,X6))
| hBOOL(hAPP(hAPP(X2,X1),X6)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1405])]) ).
fof(f3190,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] :
( ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_COMBS(X3,X4,X5),c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool))),X2),X1),X6))
| hBOOL(hAPP(X1,X6))
| hBOOL(hAPP(hAPP(X2,X1),X6)) )
| ~ spl0_233
| ~ spl0_249 ),
inference(superposition,[],[f3056,f2646]) ).
fof(f141740,plain,
( spl0_1404
| ~ spl0_137
| ~ spl0_248 ),
inference(avatar_split_clause,[],[f3179,f3051,f1680,f141738]) ).
fof(f141738,plain,
( spl0_1404
<=> ! [X2,X3,X0,X1,X8,X6,X7,X4,X5] :
( ~ c_Finite__Set_Ofinite(hAPP(X0,hAPP(X1,X5)),X6)
| ~ hBOOL(c_in(X5,X7,X8))
| c_Finite__Set_Ofinite(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X7,c_Fun_Ocomp(X0,X1,X2,X3,X4),X8,tc_fun(X6,tc_bool)),X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1404])]) ).
fof(f3051,plain,
( spl0_248
<=> ! [X5,X0,X8,X36,X1] :
( ~ hBOOL(c_in(X1,X36,X0))
| ~ c_Finite__Set_Ofinite(hAPP(X5,X1),X8)
| c_Finite__Set_Ofinite(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X36,X5,X0,tc_fun(X8,tc_bool)),X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_248])]) ).
fof(f3179,plain,
( ! [X2,X3,X0,X1,X8,X6,X7,X4,X5] :
( ~ c_Finite__Set_Ofinite(hAPP(X0,hAPP(X1,X5)),X6)
| ~ hBOOL(c_in(X5,X7,X8))
| c_Finite__Set_Ofinite(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X7,c_Fun_Ocomp(X0,X1,X2,X3,X4),X8,tc_fun(X6,tc_bool)),X6) )
| ~ spl0_137
| ~ spl0_248 ),
inference(superposition,[],[f3052,f1681]) ).
fof(f3052,plain,
( ! [X0,X36,X1,X8,X5] :
( ~ c_Finite__Set_Ofinite(hAPP(X5,X1),X8)
| ~ hBOOL(c_in(X1,X36,X0))
| c_Finite__Set_Ofinite(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X36,X5,X0,tc_fun(X8,tc_bool)),X8) )
| ~ spl0_248 ),
inference(avatar_component_clause,[],[f3051]) ).
fof(f141736,plain,
( spl0_1403
| ~ spl0_150
| ~ spl0_248 ),
inference(avatar_split_clause,[],[f3173,f3051,f1732,f141734]) ).
fof(f141734,plain,
( spl0_1403
<=> ! [X4,X0,X3,X2,X1] :
( ~ c_Finite__Set_Ofinite(hAPP(c_fequal(X0),X1),X2)
| ~ hBOOL(c_in(c_COMBK(c_False,tc_bool,X0),X3,X4))
| c_Finite__Set_Ofinite(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X3,hAPP(c_Set_Oinsert(X0),X1),X4,tc_fun(X2,tc_bool)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1403])]) ).
fof(f3173,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ c_Finite__Set_Ofinite(hAPP(c_fequal(X0),X1),X2)
| ~ hBOOL(c_in(c_COMBK(c_False,tc_bool,X0),X3,X4))
| c_Finite__Set_Ofinite(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X3,hAPP(c_Set_Oinsert(X0),X1),X4,tc_fun(X2,tc_bool)),X2) )
| ~ spl0_150
| ~ spl0_248 ),
inference(superposition,[],[f3052,f1733]) ).
fof(f141732,plain,
( spl0_1402
| ~ spl0_236
| ~ spl0_245 ),
inference(avatar_split_clause,[],[f3048,f2694,f2658,f141730]) ).
fof(f141730,plain,
( spl0_1402
<=> ! [X0,X1] :
( ~ class_Orderings_Oorder(tc_fun(X0,tc_bool))
| c_COMBK(c_False,tc_bool,tc_fun(X0,tc_bool)) = c_SetInterval_Oord__class_OatLeastAtMost(X1,c_COMBK(c_False,tc_bool,X0),tc_fun(X0,tc_bool))
| c_COMBK(c_False,tc_bool,X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1402])]) ).
fof(f2658,plain,
( spl0_236
<=> ! [X5,X0] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X5),c_COMBK(c_False,tc_bool,X0)))
| c_COMBK(c_False,tc_bool,X0) = X5 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_236])]) ).
fof(f2694,plain,
( spl0_245
<=> ! [X4,X0,X3] :
( c_SetInterval_Oord__class_OatLeastAtMost(X3,X4,X0) = c_COMBK(c_False,tc_bool,X0)
| ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),X3),X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_245])]) ).
fof(f3048,plain,
( ! [X0,X1] :
( ~ class_Orderings_Oorder(tc_fun(X0,tc_bool))
| c_COMBK(c_False,tc_bool,tc_fun(X0,tc_bool)) = c_SetInterval_Oord__class_OatLeastAtMost(X1,c_COMBK(c_False,tc_bool,X0),tc_fun(X0,tc_bool))
| c_COMBK(c_False,tc_bool,X0) = X1 )
| ~ spl0_236
| ~ spl0_245 ),
inference(resolution,[],[f2695,f2659]) ).
fof(f2659,plain,
( ! [X0,X5] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X5),c_COMBK(c_False,tc_bool,X0)))
| c_COMBK(c_False,tc_bool,X0) = X5 )
| ~ spl0_236 ),
inference(avatar_component_clause,[],[f2658]) ).
fof(f2695,plain,
( ! [X3,X0,X4] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),X3),X4))
| ~ class_Orderings_Oorder(X0)
| c_SetInterval_Oord__class_OatLeastAtMost(X3,X4,X0) = c_COMBK(c_False,tc_bool,X0) )
| ~ spl0_245 ),
inference(avatar_component_clause,[],[f2694]) ).
fof(f141728,plain,
( spl0_1401
| ~ spl0_215
| ~ spl0_233 ),
inference(avatar_split_clause,[],[f2961,f2645,f2259,f141726]) ).
fof(f141726,plain,
( spl0_1401
<=> ! [X3,X4,X0,X5,X2,X1] :
( ~ hBOOL(hAPP(hAPP(hAPP(c_COMBS(X3,X4,X5),c_lessequals(X0)),X2),X1))
| ~ class_Lattices_Oupper__semilattice(X0)
| hAPP(X2,X1) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),hAPP(X2,X1)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1401])]) ).
fof(f2961,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ hBOOL(hAPP(hAPP(hAPP(c_COMBS(X3,X4,X5),c_lessequals(X0)),X2),X1))
| ~ class_Lattices_Oupper__semilattice(X0)
| hAPP(X2,X1) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),hAPP(X2,X1)),X1) )
| ~ spl0_215
| ~ spl0_233 ),
inference(superposition,[],[f2260,f2646]) ).
fof(f141724,plain,
( spl0_1400
| ~ spl0_217
| ~ spl0_233 ),
inference(avatar_split_clause,[],[f2960,f2645,f2267,f141722]) ).
fof(f141722,plain,
( spl0_1400
<=> ! [X3,X4,X0,X5,X2,X1] :
( ~ hBOOL(hAPP(hAPP(hAPP(c_COMBS(X3,X4,X5),c_lessequals(X0)),X2),X1))
| ~ class_Lattices_Oupper__semilattice(X0)
| hAPP(X2,X1) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),hAPP(X2,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1400])]) ).
fof(f2960,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ hBOOL(hAPP(hAPP(hAPP(c_COMBS(X3,X4,X5),c_lessequals(X0)),X2),X1))
| ~ class_Lattices_Oupper__semilattice(X0)
| hAPP(X2,X1) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),hAPP(X2,X1)) )
| ~ spl0_217
| ~ spl0_233 ),
inference(superposition,[],[f2268,f2646]) ).
fof(f141720,plain,
( spl0_1399
| ~ spl0_216
| ~ spl0_233 ),
inference(avatar_split_clause,[],[f2919,f2645,f2263,f141718]) ).
fof(f141718,plain,
( spl0_1399
<=> ! [X3,X4,X0,X5,X2,X1] :
( hAPP(X2,X1) != hAPP(hAPP(hAPP(c_COMBS(X3,X4,X5),c_Lattices_Oupper__semilattice__class_Osup(X0)),X2),X1)
| hBOOL(hAPP(hAPP(c_lessequals(X0),X1),hAPP(X2,X1)))
| ~ class_Lattices_Oupper__semilattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1399])]) ).
fof(f2263,plain,
( spl0_216
<=> ! [X2,X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2))
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2) != X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_216])]) ).
fof(f2919,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( hAPP(X2,X1) != hAPP(hAPP(hAPP(c_COMBS(X3,X4,X5),c_Lattices_Oupper__semilattice__class_Osup(X0)),X2),X1)
| hBOOL(hAPP(hAPP(c_lessequals(X0),X1),hAPP(X2,X1)))
| ~ class_Lattices_Oupper__semilattice(X0) )
| ~ spl0_216
| ~ spl0_233 ),
inference(superposition,[],[f2264,f2646]) ).
fof(f2264,plain,
( ! [X2,X0,X1] :
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2) != X2
| hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2))
| ~ class_Lattices_Oupper__semilattice(X0) )
| ~ spl0_216 ),
inference(avatar_component_clause,[],[f2263]) ).
fof(f141716,plain,
( spl0_1398
| ~ spl0_170
| ~ spl0_233 ),
inference(avatar_split_clause,[],[f2857,f2645,f1869,f141714]) ).
fof(f141714,plain,
( spl0_1398
<=> ! [X2,X3,X0,X1,X8,X6,X9,X7,X4,X5] : hAPP(hAPP(hAPP(c_COMBS(X6,X7,X8),X9),hAPP(c_COMBC(X0,X1,X2,X3),X4)),X5) = hAPP(hAPP(X9,X5),hAPP(hAPP(X0,X5),X4)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1398])]) ).
fof(f2857,plain,
( ! [X2,X3,X0,X1,X8,X6,X9,X7,X4,X5] : hAPP(hAPP(hAPP(c_COMBS(X6,X7,X8),X9),hAPP(c_COMBC(X0,X1,X2,X3),X4)),X5) = hAPP(hAPP(X9,X5),hAPP(hAPP(X0,X5),X4))
| ~ spl0_170
| ~ spl0_233 ),
inference(superposition,[],[f2646,f1870]) ).
fof(f141712,plain,
( spl0_1397
| ~ spl0_170
| ~ spl0_233 ),
inference(avatar_split_clause,[],[f2827,f2645,f1869,f141710]) ).
fof(f141710,plain,
( spl0_1397
<=> ! [X2,X3,X0,X1,X8,X6,X9,X7,X4,X5] : hAPP(hAPP(hAPP(c_COMBS(X6,X7,X8),hAPP(c_COMBC(X0,X1,X2,X3),X4)),X9),X5) = hAPP(hAPP(hAPP(X0,X5),X4),hAPP(X9,X5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1397])]) ).
fof(f2827,plain,
( ! [X2,X3,X0,X1,X8,X6,X9,X7,X4,X5] : hAPP(hAPP(hAPP(c_COMBS(X6,X7,X8),hAPP(c_COMBC(X0,X1,X2,X3),X4)),X9),X5) = hAPP(hAPP(hAPP(X0,X5),X4),hAPP(X9,X5))
| ~ spl0_170
| ~ spl0_233 ),
inference(superposition,[],[f2646,f1870]) ).
fof(f141688,plain,
( spl0_1396
| ~ spl0_79
| ~ spl0_230 ),
inference(avatar_split_clause,[],[f2707,f2633,f1361,f141686]) ).
fof(f141686,plain,
( spl0_1396
<=> ! [X4,X0,X3,X2,X1] :
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X1),X2) != X1
| X1 = X2
| ~ c_Fun_Oinj__on(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X1),c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1396])]) ).
fof(f2707,plain,
( ! [X2,X3,X0,X1,X4] :
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X1),X2) != X1
| X1 = X2
| ~ c_Fun_Oinj__on(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X1),c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3,X4) )
| ~ spl0_79
| ~ spl0_230 ),
inference(superposition,[],[f2634,f1362]) ).
fof(f141684,plain,
( spl0_1395
| ~ spl0_68
| ~ spl0_230 ),
inference(avatar_split_clause,[],[f2706,f2633,f1316,f141682]) ).
fof(f141682,plain,
( spl0_1395
<=> ! [X4,X0,X3,X2,X1] :
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X2) != X1
| X1 = X2
| ~ c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1395])]) ).
fof(f2706,plain,
( ! [X2,X3,X0,X1,X4] :
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X2) != X1
| X1 = X2
| ~ c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3,X4) )
| ~ spl0_68
| ~ spl0_230 ),
inference(superposition,[],[f2634,f1317]) ).
fof(f138126,plain,
( spl0_1394
| ~ spl0_227
| ~ spl0_1353 ),
inference(avatar_split_clause,[],[f135954,f125935,f2580,f138124]) ).
fof(f138124,plain,
( spl0_1394
<=> ! [X0,X1] : c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(tc_bool,tc_bool)),X1),c_SetInterval_Oord__class_OatLeastAtMost(X0,X0,tc_bool)),tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1394])]) ).
fof(f125935,plain,
( spl0_1353
<=> ! [X2,X0,X1] : c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X1),hAPP(c_fequal(X0),X2)),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1353])]) ).
fof(f135954,plain,
( ! [X0,X1] : c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(tc_bool,tc_bool)),X1),c_SetInterval_Oord__class_OatLeastAtMost(X0,X0,tc_bool)),tc_bool)
| ~ spl0_227
| ~ spl0_1353 ),
inference(superposition,[],[f125936,f2581]) ).
fof(f125936,plain,
( ! [X2,X0,X1] : c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X1),hAPP(c_fequal(X0),X2)),X0)
| ~ spl0_1353 ),
inference(avatar_component_clause,[],[f125935]) ).
fof(f137437,plain,
( spl0_1393
| ~ spl0_227
| ~ spl0_1342 ),
inference(avatar_split_clause,[],[f126188,f125891,f2580,f137435]) ).
fof(f137435,plain,
( spl0_1393
<=> ! [X0,X1] : c_Finite__Set_Ofinite(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(tc_bool,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X0,X0,tc_bool)),X1),tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1393])]) ).
fof(f125891,plain,
( spl0_1342
<=> ! [X2,X0,X1] : c_Finite__Set_Ofinite(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),hAPP(c_fequal(X0),X1)),X2),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1342])]) ).
fof(f126188,plain,
( ! [X0,X1] : c_Finite__Set_Ofinite(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(tc_bool,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X0,X0,tc_bool)),X1),tc_bool)
| ~ spl0_227
| ~ spl0_1342 ),
inference(superposition,[],[f125892,f2581]) ).
fof(f125892,plain,
( ! [X2,X0,X1] : c_Finite__Set_Ofinite(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),hAPP(c_fequal(X0),X1)),X2),X0)
| ~ spl0_1342 ),
inference(avatar_component_clause,[],[f125891]) ).
fof(f136659,plain,
( spl0_1392
| ~ spl0_227
| ~ spl0_1331 ),
inference(avatar_split_clause,[],[f126100,f125847,f2580,f136657]) ).
fof(f136657,plain,
( spl0_1392
<=> ! [X0,X1] : c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(tc_bool,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X0,X0,tc_bool)),X1),tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1392])]) ).
fof(f125847,plain,
( spl0_1331
<=> ! [X2,X0,X1] : c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),hAPP(c_fequal(X0),X1)),X2),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1331])]) ).
fof(f126100,plain,
( ! [X0,X1] : c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(tc_bool,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X0,X0,tc_bool)),X1),tc_bool)
| ~ spl0_227
| ~ spl0_1331 ),
inference(superposition,[],[f125848,f2581]) ).
fof(f125848,plain,
( ! [X2,X0,X1] : c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),hAPP(c_fequal(X0),X1)),X2),X0)
| ~ spl0_1331 ),
inference(avatar_component_clause,[],[f125847]) ).
fof(f133639,plain,
( spl0_1391
| ~ spl0_227
| ~ spl0_1390 ),
inference(avatar_split_clause,[],[f133071,f132722,f2580,f133637]) ).
fof(f133637,plain,
( spl0_1391
<=> ! [X0,X1] : c_Finite__Set_Ofinite(hAPP(hAPP(c_Set_Oinsert(tc_bool),X1),c_SetInterval_Oord__class_OatLeastAtMost(X0,X0,tc_bool)),tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1391])]) ).
fof(f132722,plain,
( spl0_1390
<=> ! [X2,X0,X1] : c_Finite__Set_Ofinite(hAPP(hAPP(c_Set_Oinsert(X0),X1),hAPP(c_fequal(X0),X2)),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1390])]) ).
fof(f133071,plain,
( ! [X0,X1] : c_Finite__Set_Ofinite(hAPP(hAPP(c_Set_Oinsert(tc_bool),X1),c_SetInterval_Oord__class_OatLeastAtMost(X0,X0,tc_bool)),tc_bool)
| ~ spl0_227
| ~ spl0_1390 ),
inference(superposition,[],[f132723,f2581]) ).
fof(f132723,plain,
( ! [X2,X0,X1] : c_Finite__Set_Ofinite(hAPP(hAPP(c_Set_Oinsert(X0),X1),hAPP(c_fequal(X0),X2)),X0)
| ~ spl0_1390 ),
inference(avatar_component_clause,[],[f132722]) ).
fof(f132724,plain,
( spl0_1390
| ~ spl0_920
| ~ spl0_1342 ),
inference(avatar_split_clause,[],[f126185,f125891,f70020,f132722]) ).
fof(f70020,plain,
( spl0_920
<=> ! [X2,X0,X1] :
( c_Finite__Set_Ofinite(hAPP(hAPP(c_Set_Oinsert(X0),X1),X2),X0)
| ~ c_Finite__Set_Ofinite(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X2),hAPP(c_fequal(X0),X1)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_920])]) ).
fof(f126185,plain,
( ! [X2,X0,X1] : c_Finite__Set_Ofinite(hAPP(hAPP(c_Set_Oinsert(X0),X1),hAPP(c_fequal(X0),X2)),X0)
| ~ spl0_920
| ~ spl0_1342 ),
inference(resolution,[],[f125892,f70021]) ).
fof(f70021,plain,
( ! [X2,X0,X1] :
( ~ c_Finite__Set_Ofinite(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X2),hAPP(c_fequal(X0),X1)),X0)
| c_Finite__Set_Ofinite(hAPP(hAPP(c_Set_Oinsert(X0),X1),X2),X0) )
| ~ spl0_920 ),
inference(avatar_component_clause,[],[f70020]) ).
fof(f126240,plain,
( spl0_1389
| ~ spl0_510
| ~ spl0_753 ),
inference(avatar_split_clause,[],[f55085,f54602,f13837,f126238]) ).
fof(f126238,plain,
( spl0_1389
<=> ! [X4,X0,X3,X2,X1] :
( ~ c_Fun_Oinj__on(X0,hAPP(hAPP(c_Set_Oinsert(X1),X2),X3),X1,X4)
| ~ hBOOL(c_in(X2,hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X1,tc_bool)),X3),hAPP(c_fequal(X1),X2)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1389])]) ).
fof(f13837,plain,
( spl0_510
<=> ! [X5,X0,X3,X8,X7] :
( ~ hBOOL(c_in(hAPP(X7,X3),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X5),hAPP(c_fequal(X0),X3)),hAPP(hAPP(c_COMBB(X8,tc_fun(X8,tc_bool),X0),hAPP(c_COMBC(c_Set_Oinsert(X8),X8,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8))),X7),X0,tc_fun(X8,tc_bool)),X8))
| ~ c_Fun_Oinj__on(X7,hAPP(hAPP(c_Set_Oinsert(X0),X3),X5),X0,X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_510])]) ).
fof(f54602,plain,
( spl0_753
<=> ! [X1,X0,X5,X8,X7] :
( hBOOL(c_in(hAPP(X7,X1),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,hAPP(hAPP(c_COMBB(X0,tc_fun(X0,tc_bool),X8),hAPP(c_COMBC(c_Set_Oinsert(X0),X0,tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0))),X7),X8,tc_fun(X0,tc_bool)),X0))
| ~ hBOOL(c_in(X1,X5,X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_753])]) ).
fof(f55085,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ c_Fun_Oinj__on(X0,hAPP(hAPP(c_Set_Oinsert(X1),X2),X3),X1,X4)
| ~ hBOOL(c_in(X2,hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X1,tc_bool)),X3),hAPP(c_fequal(X1),X2)),X1)) )
| ~ spl0_510
| ~ spl0_753 ),
inference(resolution,[],[f13838,f54603]) ).
fof(f54603,plain,
( ! [X0,X1,X8,X7,X5] :
( hBOOL(c_in(hAPP(X7,X1),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,hAPP(hAPP(c_COMBB(X0,tc_fun(X0,tc_bool),X8),hAPP(c_COMBC(c_Set_Oinsert(X0),X0,tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0))),X7),X8,tc_fun(X0,tc_bool)),X0))
| ~ hBOOL(c_in(X1,X5,X8)) )
| ~ spl0_753 ),
inference(avatar_component_clause,[],[f54602]) ).
fof(f13838,plain,
( ! [X3,X0,X8,X7,X5] :
( ~ hBOOL(c_in(hAPP(X7,X3),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X5),hAPP(c_fequal(X0),X3)),hAPP(hAPP(c_COMBB(X8,tc_fun(X8,tc_bool),X0),hAPP(c_COMBC(c_Set_Oinsert(X8),X8,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8))),X7),X0,tc_fun(X8,tc_bool)),X8))
| ~ c_Fun_Oinj__on(X7,hAPP(hAPP(c_Set_Oinsert(X0),X3),X5),X0,X8) )
| ~ spl0_510 ),
inference(avatar_component_clause,[],[f13837]) ).
fof(f126236,plain,
( spl0_1388
| ~ spl0_426
| ~ spl0_427
| ~ spl0_733 ),
inference(avatar_split_clause,[],[f50374,f27510,f8403,f8399,f126234]) ).
fof(f126234,plain,
( spl0_1388
<=> ! [X4,X0,X3,X2,X1] : c_List_Ofilter(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X2),X3),c_List_Ofilter(X1,X4,X0),X0) = c_List_Ofilter(X3,c_List_Ofilter(X1,c_List_Ofilter(X2,X4,X0),X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1388])]) ).
fof(f8399,plain,
( spl0_426
<=> ! [X9,X0,X12,X5] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X5),X9)),X12) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X5),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X9),X12)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_426])]) ).
fof(f8403,plain,
( spl0_427
<=> ! [X5,X0,X12,X9] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X5),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X9),X12)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X9),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X5),X12)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_427])]) ).
fof(f50374,plain,
( ! [X2,X3,X0,X1,X4] : c_List_Ofilter(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X2),X3),c_List_Ofilter(X1,X4,X0),X0) = c_List_Ofilter(X3,c_List_Ofilter(X1,c_List_Ofilter(X2,X4,X0),X0),X0)
| ~ spl0_426
| ~ spl0_427
| ~ spl0_733 ),
inference(forward_demodulation,[],[f50269,f31846]) ).
fof(f31846,plain,
( ! [X2,X3,X0,X1,X4] : c_List_Ofilter(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X2),X3)),X4,X0) = c_List_Ofilter(X3,c_List_Ofilter(X2,c_List_Ofilter(X1,X4,X0),X0),X0)
| ~ spl0_426
| ~ spl0_733 ),
inference(forward_demodulation,[],[f31804,f27511]) ).
fof(f31804,plain,
( ! [X2,X3,X0,X1,X4] : c_List_Ofilter(X3,c_List_Ofilter(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X1),X2),X4,X0),X0) = c_List_Ofilter(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X2),X3)),X4,X0)
| ~ spl0_426
| ~ spl0_733 ),
inference(superposition,[],[f27511,f8400]) ).
fof(f8400,plain,
( ! [X0,X9,X5,X12] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X5),X9)),X12) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X5),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X9),X12))
| ~ spl0_426 ),
inference(avatar_component_clause,[],[f8399]) ).
fof(f50269,plain,
( ! [X2,X3,X0,X1,X4] : c_List_Ofilter(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X2),X3),c_List_Ofilter(X1,X4,X0),X0) = c_List_Ofilter(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X1),X3)),X4,X0)
| ~ spl0_427
| ~ spl0_733 ),
inference(superposition,[],[f27511,f8404]) ).
fof(f8404,plain,
( ! [X0,X9,X5,X12] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X5),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X9),X12)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X9),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X5),X12))
| ~ spl0_427 ),
inference(avatar_component_clause,[],[f8403]) ).
fof(f126232,plain,
( spl0_1387
| ~ spl0_122
| ~ spl0_455 ),
inference(avatar_split_clause,[],[f10605,f10480,f1599,f126230]) ).
fof(f126230,plain,
( spl0_1387
<=> ! [X4,X0,X3,X2,X1] :
( ~ c_Finite__Set_Ofinite(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X1),X4),X2,X3,tc_fun(X0,tc_bool)),X0)
| c_Finite__Set_Ofinite(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,X2,X3,tc_fun(X0,tc_bool)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1387])]) ).
fof(f1599,plain,
( spl0_122
<=> ! [X38,X0,X39] :
( c_Finite__Set_Ofinite(X39,X0)
| ~ c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X38),X39),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_122])]) ).
fof(f10480,plain,
( spl0_455
<=> ! [X5,X18,X0,X9,X8] : c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X8,tc_bool)),X5),X9),X18,X8,tc_fun(X0,tc_bool)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,X18,X8,tc_fun(X0,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X9,X18,X8,tc_fun(X0,tc_bool))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_455])]) ).
fof(f10605,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ c_Finite__Set_Ofinite(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X1),X4),X2,X3,tc_fun(X0,tc_bool)),X0)
| c_Finite__Set_Ofinite(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,X2,X3,tc_fun(X0,tc_bool)),X0) )
| ~ spl0_122
| ~ spl0_455 ),
inference(superposition,[],[f1600,f10481]) ).
fof(f10481,plain,
( ! [X0,X18,X8,X9,X5] : c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X8,tc_bool)),X5),X9),X18,X8,tc_fun(X0,tc_bool)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,X18,X8,tc_fun(X0,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X9,X18,X8,tc_fun(X0,tc_bool)))
| ~ spl0_455 ),
inference(avatar_component_clause,[],[f10480]) ).
fof(f1600,plain,
( ! [X38,X39,X0] :
( ~ c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X38),X39),X0)
| c_Finite__Set_Ofinite(X39,X0) )
| ~ spl0_122 ),
inference(avatar_component_clause,[],[f1599]) ).
fof(f126228,plain,
( spl0_1386
| ~ spl0_121
| ~ spl0_455 ),
inference(avatar_split_clause,[],[f10604,f10480,f1595,f126226]) ).
fof(f126226,plain,
( spl0_1386
<=> ! [X4,X0,X3,X2,X1] :
( ~ c_Finite__Set_Ofinite(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X1),X4),X2,X3,tc_fun(X0,tc_bool)),X0)
| c_Finite__Set_Ofinite(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,X2,X3,tc_fun(X0,tc_bool)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1386])]) ).
fof(f1595,plain,
( spl0_121
<=> ! [X38,X0,X39] :
( c_Finite__Set_Ofinite(X38,X0)
| ~ c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X38),X39),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_121])]) ).
fof(f10604,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ c_Finite__Set_Ofinite(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X1),X4),X2,X3,tc_fun(X0,tc_bool)),X0)
| c_Finite__Set_Ofinite(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,X2,X3,tc_fun(X0,tc_bool)),X0) )
| ~ spl0_121
| ~ spl0_455 ),
inference(superposition,[],[f1596,f10481]) ).
fof(f1596,plain,
( ! [X38,X39,X0] :
( ~ c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X38),X39),X0)
| c_Finite__Set_Ofinite(X38,X0) )
| ~ spl0_121 ),
inference(avatar_component_clause,[],[f1595]) ).
fof(f126224,plain,
( spl0_1385
| ~ spl0_127
| ~ spl0_454 ),
inference(avatar_split_clause,[],[f10522,f10476,f1619,f126222]) ).
fof(f126222,plain,
( spl0_1385
<=> ! [X4,X0,X3,X2,X1] :
( c_Finite__Set_Ofinite(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X1),X4),X2,X3,tc_fun(X0,tc_bool)),X0)
| ~ c_Finite__Set_Ofinite(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,X2,X3,tc_fun(X0,tc_bool)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1385])]) ).
fof(f1619,plain,
( spl0_127
<=> ! [X38,X0,X39] :
( ~ c_Finite__Set_Ofinite(X38,X0)
| c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X38),X39),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_127])]) ).
fof(f10476,plain,
( spl0_454
<=> ! [X5,X18,X0,X9,X8] : c_Complete__Lattice_Ocomplete__lattice__class_OINFI(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X8,tc_bool)),X5),X9),X18,X8,tc_fun(X0,tc_bool)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,X18,X8,tc_fun(X0,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X9,X18,X8,tc_fun(X0,tc_bool))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_454])]) ).
fof(f10522,plain,
( ! [X2,X3,X0,X1,X4] :
( c_Finite__Set_Ofinite(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X1),X4),X2,X3,tc_fun(X0,tc_bool)),X0)
| ~ c_Finite__Set_Ofinite(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,X2,X3,tc_fun(X0,tc_bool)),X0) )
| ~ spl0_127
| ~ spl0_454 ),
inference(superposition,[],[f1620,f10477]) ).
fof(f10477,plain,
( ! [X0,X18,X8,X9,X5] : c_Complete__Lattice_Ocomplete__lattice__class_OINFI(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X8,tc_bool)),X5),X9),X18,X8,tc_fun(X0,tc_bool)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,X18,X8,tc_fun(X0,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X9,X18,X8,tc_fun(X0,tc_bool)))
| ~ spl0_454 ),
inference(avatar_component_clause,[],[f10476]) ).
fof(f1620,plain,
( ! [X38,X39,X0] :
( c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X38),X39),X0)
| ~ c_Finite__Set_Ofinite(X38,X0) )
| ~ spl0_127 ),
inference(avatar_component_clause,[],[f1619]) ).
fof(f126220,plain,
( spl0_1384
| ~ spl0_126
| ~ spl0_454 ),
inference(avatar_split_clause,[],[f10521,f10476,f1615,f126218]) ).
fof(f126218,plain,
( spl0_1384
<=> ! [X4,X0,X3,X2,X1] :
( c_Finite__Set_Ofinite(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X1),X4),X2,X3,tc_fun(X0,tc_bool)),X0)
| ~ c_Finite__Set_Ofinite(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X4,X2,X3,tc_fun(X0,tc_bool)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1384])]) ).
fof(f1615,plain,
( spl0_126
<=> ! [X38,X0,X39] :
( ~ c_Finite__Set_Ofinite(X39,X0)
| c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X38),X39),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_126])]) ).
fof(f10521,plain,
( ! [X2,X3,X0,X1,X4] :
( c_Finite__Set_Ofinite(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X1),X4),X2,X3,tc_fun(X0,tc_bool)),X0)
| ~ c_Finite__Set_Ofinite(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X4,X2,X3,tc_fun(X0,tc_bool)),X0) )
| ~ spl0_126
| ~ spl0_454 ),
inference(superposition,[],[f1616,f10477]) ).
fof(f1616,plain,
( ! [X38,X39,X0] :
( c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X38),X39),X0)
| ~ c_Finite__Set_Ofinite(X39,X0) )
| ~ spl0_126 ),
inference(avatar_component_clause,[],[f1615]) ).
fof(f126179,plain,
( spl0_1383
| ~ spl0_275
| ~ spl0_441 ),
inference(avatar_split_clause,[],[f9721,f9351,f3652,f126177]) ).
fof(f126177,plain,
( spl0_1383
<=> ! [X0,X3,X2,X1] : c_COMBK(c_False,tc_bool,X0) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X3),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X1),hAPP(hAPP(c_Set_Oinsert(X0),X2),X3))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1383])]) ).
fof(f9351,plain,
( spl0_441
<=> ! [X9,X0,X5,X3] : hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X5),hAPP(hAPP(c_Set_Oinsert(X0),X3),X9)) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X5),hAPP(c_fequal(X0),X3))),X9) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_441])]) ).
fof(f9721,plain,
( ! [X2,X3,X0,X1] : c_COMBK(c_False,tc_bool,X0) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X3),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X1),hAPP(hAPP(c_Set_Oinsert(X0),X2),X3)))
| ~ spl0_275
| ~ spl0_441 ),
inference(superposition,[],[f3653,f9352]) ).
fof(f9352,plain,
( ! [X3,X0,X9,X5] : hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X5),hAPP(hAPP(c_Set_Oinsert(X0),X3),X9)) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X5),hAPP(c_fequal(X0),X3))),X9)
| ~ spl0_441 ),
inference(avatar_component_clause,[],[f9351]) ).
fof(f126175,plain,
( spl0_1382
| ~ spl0_207
| ~ spl0_440 ),
inference(avatar_split_clause,[],[f9659,f9347,f2221,f126173]) ).
fof(f126173,plain,
( spl0_1382
<=> ! [X4,X0,X3,X2,X1] :
( ~ hBOOL(c_in(X4,hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X1),hAPP(hAPP(c_Set_Oinsert(X0),X3),X2)),X0))
| ~ hBOOL(c_in(X4,hAPP(c_fequal(X0),X3),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1382])]) ).
fof(f2221,plain,
( spl0_207
<=> ! [X35,X9,X0,X5] :
( ~ hBOOL(c_in(X35,X9,X0))
| ~ hBOOL(c_in(X35,hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X5),X9),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_207])]) ).
fof(f9347,plain,
( spl0_440
<=> ! [X9,X0,X5,X3] : hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X5),hAPP(hAPP(c_Set_Oinsert(X0),X3),X9)) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X5),X9)),hAPP(c_fequal(X0),X3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_440])]) ).
fof(f9659,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ hBOOL(c_in(X4,hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X1),hAPP(hAPP(c_Set_Oinsert(X0),X3),X2)),X0))
| ~ hBOOL(c_in(X4,hAPP(c_fequal(X0),X3),X0)) )
| ~ spl0_207
| ~ spl0_440 ),
inference(superposition,[],[f2222,f9348]) ).
fof(f9348,plain,
( ! [X3,X0,X9,X5] : hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X5),hAPP(hAPP(c_Set_Oinsert(X0),X3),X9)) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X5),X9)),hAPP(c_fequal(X0),X3))
| ~ spl0_440 ),
inference(avatar_component_clause,[],[f9347]) ).
fof(f2222,plain,
( ! [X0,X9,X35,X5] :
( ~ hBOOL(c_in(X35,hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X5),X9),X0))
| ~ hBOOL(c_in(X35,X9,X0)) )
| ~ spl0_207 ),
inference(avatar_component_clause,[],[f2221]) ).
fof(f126171,plain,
( spl0_1381
| ~ spl0_164
| ~ spl0_437 ),
inference(avatar_split_clause,[],[f9570,f9311,f1842,f126169]) ).
fof(f126169,plain,
( spl0_1381
<=> ! [X4,X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X0),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X2),X3)),X4))
| hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X0),X1),X2),X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1381])]) ).
fof(f1842,plain,
( spl0_164
<=> ! [X9,X5,X1,X0] :
( hBOOL(hAPP(X5,X1))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X5),X9),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_164])]) ).
fof(f9570,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X0),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X2),X3)),X4))
| hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X0),X1),X2),X4)) )
| ~ spl0_164
| ~ spl0_437 ),
inference(superposition,[],[f1843,f9312]) ).
fof(f1843,plain,
( ! [X0,X1,X9,X5] :
( ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X5),X9),X1))
| hBOOL(hAPP(X5,X1)) )
| ~ spl0_164 ),
inference(avatar_component_clause,[],[f1842]) ).
fof(f126167,plain,
( spl0_1380
| ~ spl0_163
| ~ spl0_437 ),
inference(avatar_split_clause,[],[f9569,f9311,f1838,f126165]) ).
fof(f126165,plain,
( spl0_1380
<=> ! [X4,X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X0),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X2),X3)),X4))
| hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X0),X1),X3),X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1380])]) ).
fof(f1838,plain,
( spl0_163
<=> ! [X9,X5,X1,X0] :
( hBOOL(hAPP(X9,X1))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X5),X9),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_163])]) ).
fof(f9569,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X0),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X2),X3)),X4))
| hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X0),X1),X3),X4)) )
| ~ spl0_163
| ~ spl0_437 ),
inference(superposition,[],[f1839,f9312]) ).
fof(f1839,plain,
( ! [X0,X1,X9,X5] :
( ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X5),X9),X1))
| hBOOL(hAPP(X9,X1)) )
| ~ spl0_163 ),
inference(avatar_component_clause,[],[f1838]) ).
fof(f126163,plain,
( spl0_1379
| ~ spl0_51
| ~ spl0_79
| ~ spl0_278
| ~ spl0_412 ),
inference(avatar_split_clause,[],[f8330,f7695,f3665,f1361,f1237,f126161]) ).
fof(f126161,plain,
( spl0_1379
<=> ! [X4,X0,X3,X2,X1] :
( c_Complete__Lattice_Ocomplete__lattice__class_OINFI(hAPP(hAPP(c_Set_Oinsert(X3),X4),X0),c_COMBK(X1,tc_fun(X2,tc_bool),X3),X3,tc_fun(X2,tc_bool)) = X1
| c_COMBK(c_False,tc_bool,X3) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1379])]) ).
fof(f3665,plain,
( spl0_278
<=> ! [X35,X0,X5,X8] :
( c_COMBK(c_False,tc_bool,X8) = X5
| c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,c_COMBK(X35,tc_fun(X0,tc_bool),X8),X8,tc_fun(X0,tc_bool)) = X35 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_278])]) ).
fof(f8330,plain,
( ! [X2,X3,X0,X1,X4] :
( c_Complete__Lattice_Ocomplete__lattice__class_OINFI(hAPP(hAPP(c_Set_Oinsert(X3),X4),X0),c_COMBK(X1,tc_fun(X2,tc_bool),X3),X3,tc_fun(X2,tc_bool)) = X1
| c_COMBK(c_False,tc_bool,X3) = X0 )
| ~ spl0_51
| ~ spl0_79
| ~ spl0_278
| ~ spl0_412 ),
inference(forward_demodulation,[],[f8329,f1362]) ).
fof(f8329,plain,
( ! [X2,X3,X0,X1,X4] :
( c_Complete__Lattice_Ocomplete__lattice__class_OINFI(hAPP(hAPP(c_Set_Oinsert(X3),X4),X0),c_COMBK(X1,tc_fun(X2,tc_bool),X3),X3,tc_fun(X2,tc_bool)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X1),X1)
| c_COMBK(c_False,tc_bool,X3) = X0 )
| ~ spl0_51
| ~ spl0_278
| ~ spl0_412 ),
inference(forward_demodulation,[],[f8259,f1238]) ).
fof(f8259,plain,
( ! [X2,X3,X0,X1,X4] :
( c_Complete__Lattice_Ocomplete__lattice__class_OINFI(hAPP(hAPP(c_Set_Oinsert(X3),X4),X0),c_COMBK(X1,tc_fun(X2,tc_bool),X3),X3,tc_fun(X2,tc_bool)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),hAPP(c_COMBK(X1,tc_fun(X2,tc_bool),X3),X4)),X1)
| c_COMBK(c_False,tc_bool,X3) = X0 )
| ~ spl0_278
| ~ spl0_412 ),
inference(superposition,[],[f7696,f3666]) ).
fof(f3666,plain,
( ! [X0,X8,X5,X35] :
( c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,c_COMBK(X35,tc_fun(X0,tc_bool),X8),X8,tc_fun(X0,tc_bool)) = X35
| c_COMBK(c_False,tc_bool,X8) = X5 )
| ~ spl0_278 ),
inference(avatar_component_clause,[],[f3665]) ).
fof(f126159,plain,
( spl0_1378
| ~ spl0_163
| ~ spl0_412 ),
inference(avatar_split_clause,[],[f8288,f7695,f1838,f126157]) ).
fof(f126157,plain,
( spl0_1378
<=> ! [X2,X3,X4,X0,X5,X1] :
( ~ hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(hAPP(hAPP(c_Set_Oinsert(X4),X2),X3),X1,X4,tc_fun(X0,tc_bool)),X5))
| hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X3,X1,X4,tc_fun(X0,tc_bool)),X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1378])]) ).
fof(f8288,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(hAPP(hAPP(c_Set_Oinsert(X4),X2),X3),X1,X4,tc_fun(X0,tc_bool)),X5))
| hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X3,X1,X4,tc_fun(X0,tc_bool)),X5)) )
| ~ spl0_163
| ~ spl0_412 ),
inference(superposition,[],[f1839,f7696]) ).
fof(f126155,plain,
( spl0_1377
| ~ spl0_51
| ~ spl0_68
| ~ spl0_279
| ~ spl0_410 ),
inference(avatar_split_clause,[],[f8164,f7687,f3669,f1316,f1237,f126153]) ).
fof(f126153,plain,
( spl0_1377
<=> ! [X4,X0,X3,X2,X1] :
( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_Set_Oinsert(X3),X4),X0),c_COMBK(X1,tc_fun(X2,tc_bool),X3),X3,tc_fun(X2,tc_bool)) = X1
| c_COMBK(c_False,tc_bool,X3) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1377])]) ).
fof(f3669,plain,
( spl0_279
<=> ! [X35,X0,X5,X8] :
( c_COMBK(c_False,tc_bool,X8) = X5
| c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,c_COMBK(X35,tc_fun(X0,tc_bool),X8),X8,tc_fun(X0,tc_bool)) = X35 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_279])]) ).
fof(f8164,plain,
( ! [X2,X3,X0,X1,X4] :
( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_Set_Oinsert(X3),X4),X0),c_COMBK(X1,tc_fun(X2,tc_bool),X3),X3,tc_fun(X2,tc_bool)) = X1
| c_COMBK(c_False,tc_bool,X3) = X0 )
| ~ spl0_51
| ~ spl0_68
| ~ spl0_279
| ~ spl0_410 ),
inference(forward_demodulation,[],[f8163,f1317]) ).
fof(f8163,plain,
( ! [X2,X3,X0,X1,X4] :
( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_Set_Oinsert(X3),X4),X0),c_COMBK(X1,tc_fun(X2,tc_bool),X3),X3,tc_fun(X2,tc_bool)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X1),X1)
| c_COMBK(c_False,tc_bool,X3) = X0 )
| ~ spl0_51
| ~ spl0_279
| ~ spl0_410 ),
inference(forward_demodulation,[],[f8087,f1238]) ).
fof(f8087,plain,
( ! [X2,X3,X0,X1,X4] :
( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_Set_Oinsert(X3),X4),X0),c_COMBK(X1,tc_fun(X2,tc_bool),X3),X3,tc_fun(X2,tc_bool)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),hAPP(c_COMBK(X1,tc_fun(X2,tc_bool),X3),X4)),X1)
| c_COMBK(c_False,tc_bool,X3) = X0 )
| ~ spl0_279
| ~ spl0_410 ),
inference(superposition,[],[f7688,f3670]) ).
fof(f3670,plain,
( ! [X0,X8,X5,X35] :
( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,c_COMBK(X35,tc_fun(X0,tc_bool),X8),X8,tc_fun(X0,tc_bool)) = X35
| c_COMBK(c_False,tc_bool,X8) = X5 )
| ~ spl0_279 ),
inference(avatar_component_clause,[],[f3669]) ).
fof(f126151,plain,
( spl0_1376
| ~ spl0_266
| ~ spl0_410 ),
inference(avatar_split_clause,[],[f8135,f7687,f3133,f126149]) ).
fof(f126149,plain,
( spl0_1376
<=> ! [X2,X4,X0,X3,X1] :
( c_COMBK(c_False,tc_bool,X0) != c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_Set_Oinsert(X4),X2),X3),X1,X4,tc_fun(X0,tc_bool))
| c_COMBK(c_False,tc_bool,X0) = hAPP(X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1376])]) ).
fof(f8135,plain,
( ! [X2,X3,X0,X1,X4] :
( c_COMBK(c_False,tc_bool,X0) != c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_Set_Oinsert(X4),X2),X3),X1,X4,tc_fun(X0,tc_bool))
| c_COMBK(c_False,tc_bool,X0) = hAPP(X1,X2) )
| ~ spl0_266
| ~ spl0_410 ),
inference(superposition,[],[f3134,f7688]) ).
fof(f126147,plain,
( spl0_1375
| ~ spl0_152
| ~ spl0_410 ),
inference(avatar_split_clause,[],[f8121,f7687,f1794,f126145]) ).
fof(f126145,plain,
( spl0_1375
<=> ! [X2,X3,X4,X0,X5,X1] :
( hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_Set_Oinsert(X4),X2),X3),X1,X4,tc_fun(X0,tc_bool)),X5))
| ~ hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,X1,X4,tc_fun(X0,tc_bool)),X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1375])]) ).
fof(f1794,plain,
( spl0_152
<=> ! [X9,X5,X1,X0] :
( ~ hBOOL(hAPP(X9,X1))
| hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X5),X9),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_152])]) ).
fof(f8121,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_Set_Oinsert(X4),X2),X3),X1,X4,tc_fun(X0,tc_bool)),X5))
| ~ hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,X1,X4,tc_fun(X0,tc_bool)),X5)) )
| ~ spl0_152
| ~ spl0_410 ),
inference(superposition,[],[f1795,f7688]) ).
fof(f1795,plain,
( ! [X0,X1,X9,X5] :
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X5),X9),X1))
| ~ hBOOL(hAPP(X9,X1)) )
| ~ spl0_152 ),
inference(avatar_component_clause,[],[f1794]) ).
fof(f126143,plain,
( spl0_1374
| ~ spl0_135
| ~ spl0_416 ),
inference(avatar_split_clause,[],[f7906,f7848,f1652,f126141]) ).
fof(f126141,plain,
( spl0_1374
<=> ! [X4,X0,X3,X2,X1] :
( c_COMBK(c_False,tc_bool,X0) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),hAPP(c_fequal(X0),X1)),c_Finite__Set_Ofold1Set(X2,hAPP(c_fequal(X3),X4),X3))
| X1 = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1374])]) ).
fof(f1652,plain,
( spl0_135
<=> ! [X4,X0,X3,X7] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(X7,hAPP(c_fequal(X0),X3),X0),X4))
| X3 = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_135])]) ).
fof(f7906,plain,
( ! [X2,X3,X0,X1,X4] :
( c_COMBK(c_False,tc_bool,X0) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),hAPP(c_fequal(X0),X1)),c_Finite__Set_Ofold1Set(X2,hAPP(c_fequal(X3),X4),X3))
| X1 = X4 )
| ~ spl0_135
| ~ spl0_416 ),
inference(resolution,[],[f7849,f1653]) ).
fof(f1653,plain,
( ! [X3,X0,X7,X4] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(X7,hAPP(c_fequal(X0),X3),X0),X4))
| X3 = X4 )
| ~ spl0_135 ),
inference(avatar_component_clause,[],[f1652]) ).
fof(f126097,plain,
( spl0_1373
| ~ spl0_129
| ~ spl0_414 ),
inference(avatar_split_clause,[],[f7729,f7704,f1627,f126095]) ).
fof(f126095,plain,
( spl0_1373
<=> ! [X4,X0,X3,X2,X1] :
( hAPP(c_fequal(X0),X1) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),hAPP(c_fequal(X0),X1)),hAPP(hAPP(c_Set_Oinsert(X2),X3),X4))
| ~ hBOOL(hAPP(X4,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1373])]) ).
fof(f1627,plain,
( spl0_129
<=> ! [X2,X5,X1,X0] :
( ~ hBOOL(hAPP(X5,X1))
| hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X0),X2),X5),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_129])]) ).
fof(f7729,plain,
( ! [X2,X3,X0,X1,X4] :
( hAPP(c_fequal(X0),X1) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),hAPP(c_fequal(X0),X1)),hAPP(hAPP(c_Set_Oinsert(X2),X3),X4))
| ~ hBOOL(hAPP(X4,X1)) )
| ~ spl0_129
| ~ spl0_414 ),
inference(resolution,[],[f7705,f1628]) ).
fof(f1628,plain,
( ! [X2,X0,X1,X5] :
( hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X0),X2),X5),X1))
| ~ hBOOL(hAPP(X5,X1)) )
| ~ spl0_129 ),
inference(avatar_component_clause,[],[f1627]) ).
fof(f126093,plain,
( spl0_1372
| ~ spl0_169
| ~ spl0_401 ),
inference(avatar_split_clause,[],[f7382,f7140,f1865,f126091]) ).
fof(f126091,plain,
( spl0_1372
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X1),X2))
| c_Finite__Set_Ofinite(hAPP(hAPP(c_Set_Oinsert(X0),X3),X1),X0)
| ~ c_Finite__Set_Ofinite(hAPP(hAPP(c_Set_Oinsert(X0),X3),X2),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1372])]) ).
fof(f7140,plain,
( spl0_401
<=> ! [X51,X0,X12,X3] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X12),X51))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Set_Oinsert(X0),X3),X12)),hAPP(hAPP(c_Set_Oinsert(X0),X3),X51))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_401])]) ).
fof(f7382,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X1),X2))
| c_Finite__Set_Ofinite(hAPP(hAPP(c_Set_Oinsert(X0),X3),X1),X0)
| ~ c_Finite__Set_Ofinite(hAPP(hAPP(c_Set_Oinsert(X0),X3),X2),X0) )
| ~ spl0_169
| ~ spl0_401 ),
inference(resolution,[],[f7141,f1866]) ).
fof(f7141,plain,
( ! [X51,X3,X0,X12] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Set_Oinsert(X0),X3),X12)),hAPP(hAPP(c_Set_Oinsert(X0),X3),X51)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X12),X51)) )
| ~ spl0_401 ),
inference(avatar_component_clause,[],[f7140]) ).
fof(f126089,plain,
( spl0_1371
| ~ spl0_169
| ~ spl0_400 ),
inference(avatar_split_clause,[],[f7336,f7136,f1865,f126087]) ).
fof(f126087,plain,
( spl0_1371
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X1),X2))
| ~ hBOOL(c_in(X3,X2,X0))
| c_Finite__Set_Ofinite(hAPP(hAPP(c_Set_Oinsert(X0),X3),X1),X0)
| ~ c_Finite__Set_Ofinite(X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1371])]) ).
fof(f7136,plain,
( spl0_400
<=> ! [X9,X0,X5,X1] :
( ~ hBOOL(c_in(X1,X9,X0))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X5),X9))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Set_Oinsert(X0),X1),X5)),X9)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_400])]) ).
fof(f7336,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X1),X2))
| ~ hBOOL(c_in(X3,X2,X0))
| c_Finite__Set_Ofinite(hAPP(hAPP(c_Set_Oinsert(X0),X3),X1),X0)
| ~ c_Finite__Set_Ofinite(X2,X0) )
| ~ spl0_169
| ~ spl0_400 ),
inference(resolution,[],[f7137,f1866]) ).
fof(f7137,plain,
( ! [X0,X1,X9,X5] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Set_Oinsert(X0),X1),X5)),X9))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X5),X9))
| ~ hBOOL(c_in(X1,X9,X0)) )
| ~ spl0_400 ),
inference(avatar_component_clause,[],[f7136]) ).
fof(f126085,plain,
( spl0_1370
| ~ spl0_185
| ~ spl0_392 ),
inference(avatar_split_clause,[],[f7093,f6764,f2005,f126083]) ).
fof(f126083,plain,
( spl0_1370
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X1),X2))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X2),X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1370])]) ).
fof(f6764,plain,
( spl0_392
<=> ! [X5,X0,X12,X9] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X5),X9))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X9),X12))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X5),X12)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_392])]) ).
fof(f7093,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X1),X2))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X2),X3))) )
| ~ spl0_185
| ~ spl0_392 ),
inference(resolution,[],[f6765,f2006]) ).
fof(f6765,plain,
( ! [X0,X9,X5,X12] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X9),X12))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X5),X9))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X5),X12)) )
| ~ spl0_392 ),
inference(avatar_component_clause,[],[f6764]) ).
fof(f126081,plain,
( spl0_1369
| ~ spl0_184
| ~ spl0_392 ),
inference(avatar_split_clause,[],[f7092,f6764,f2001,f126079]) ).
fof(f126079,plain,
( spl0_1369
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X1),X2))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X3),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1369])]) ).
fof(f7092,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X1),X2))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X3),X2))) )
| ~ spl0_184
| ~ spl0_392 ),
inference(resolution,[],[f6765,f2002]) ).
fof(f126077,plain,
( spl0_1368
| ~ spl0_186
| ~ spl0_392 ),
inference(avatar_split_clause,[],[f7081,f6764,f2009,f126075]) ).
fof(f126075,plain,
( spl0_1368
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X1),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X2),X3)))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1368])]) ).
fof(f7081,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X1),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X2),X3)))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X1),X2)) )
| ~ spl0_186
| ~ spl0_392 ),
inference(resolution,[],[f6765,f2010]) ).
fof(f126073,plain,
( spl0_1367
| ~ spl0_153
| ~ spl0_391 ),
inference(avatar_split_clause,[],[f7008,f6760,f1798,f126071]) ).
fof(f126071,plain,
( spl0_1367
<=> ! [X4,X0,X3,X2,X1] :
( hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X0),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X2),X3)),X4))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X0),X1),X2),X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1367])]) ).
fof(f1798,plain,
( spl0_153
<=> ! [X9,X5,X1,X0] :
( ~ hBOOL(hAPP(X5,X1))
| hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X5),X9),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_153])]) ).
fof(f7008,plain,
( ! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X0),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X2),X3)),X4))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X0),X1),X2),X4)) )
| ~ spl0_153
| ~ spl0_391 ),
inference(superposition,[],[f1799,f6761]) ).
fof(f1799,plain,
( ! [X0,X1,X9,X5] :
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X5),X9),X1))
| ~ hBOOL(hAPP(X5,X1)) )
| ~ spl0_153 ),
inference(avatar_component_clause,[],[f1798]) ).
fof(f126069,plain,
( spl0_1366
| ~ spl0_92
| ~ spl0_390 ),
inference(avatar_split_clause,[],[f6934,f6756,f1427,f126067]) ).
fof(f126067,plain,
( spl0_1366
<=> ! [X0,X3,X2,X1] :
( ~ c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X2),hAPP(hAPP(c_Set_Oinsert(X0),X1),X3)),X0)
| c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X2),X3),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1366])]) ).
fof(f1427,plain,
( spl0_92
<=> ! [X5,X0,X3] :
( c_Finite__Set_Ofinite(X5,X0)
| ~ c_Finite__Set_Ofinite(hAPP(hAPP(c_Set_Oinsert(X0),X3),X5),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_92])]) ).
fof(f6934,plain,
( ! [X2,X3,X0,X1] :
( ~ c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X2),hAPP(hAPP(c_Set_Oinsert(X0),X1),X3)),X0)
| c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X2),X3),X0) )
| ~ spl0_92
| ~ spl0_390 ),
inference(superposition,[],[f1428,f6757]) ).
fof(f1428,plain,
( ! [X3,X0,X5] :
( ~ c_Finite__Set_Ofinite(hAPP(hAPP(c_Set_Oinsert(X0),X3),X5),X0)
| c_Finite__Set_Ofinite(X5,X0) )
| ~ spl0_92 ),
inference(avatar_component_clause,[],[f1427]) ).
fof(f126065,plain,
( spl0_1365
| ~ spl0_90
| ~ spl0_390 ),
inference(avatar_split_clause,[],[f6933,f6756,f1419,f126063]) ).
fof(f126063,plain,
( spl0_1365
<=> ! [X0,X3,X2,X1] :
( c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X2),hAPP(hAPP(c_Set_Oinsert(X0),X1),X3)),X0)
| ~ c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X2),X3),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1365])]) ).
fof(f1419,plain,
( spl0_90
<=> ! [X5,X0,X3] :
( ~ c_Finite__Set_Ofinite(X5,X0)
| c_Finite__Set_Ofinite(hAPP(hAPP(c_Set_Oinsert(X0),X3),X5),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_90])]) ).
fof(f6933,plain,
( ! [X2,X3,X0,X1] :
( c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X2),hAPP(hAPP(c_Set_Oinsert(X0),X1),X3)),X0)
| ~ c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X2),X3),X0) )
| ~ spl0_90
| ~ spl0_390 ),
inference(superposition,[],[f1420,f6757]) ).
fof(f1420,plain,
( ! [X3,X0,X5] :
( c_Finite__Set_Ofinite(hAPP(hAPP(c_Set_Oinsert(X0),X3),X5),X0)
| ~ c_Finite__Set_Ofinite(X5,X0) )
| ~ spl0_90 ),
inference(avatar_component_clause,[],[f1419]) ).
fof(f126061,plain,
( spl0_1364
| ~ spl0_152
| ~ spl0_390 ),
inference(avatar_split_clause,[],[f6881,f6756,f1794,f126059]) ).
fof(f126059,plain,
( spl0_1364
<=> ! [X2,X4,X0,X3,X1] :
( hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X0),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X3)),X4))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X0),X2),X3),X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1364])]) ).
fof(f6881,plain,
( ! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X0),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X3)),X4))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X0),X2),X3),X4)) )
| ~ spl0_152
| ~ spl0_390 ),
inference(superposition,[],[f1795,f6757]) ).
fof(f125977,plain,
( spl0_1363
| ~ spl0_233
| ~ spl0_375 ),
inference(avatar_split_clause,[],[f6482,f6095,f2645,f125975]) ).
fof(f125975,plain,
( spl0_1363
<=> ! [X5,X3,X4,X2,X0,X6,X1] :
( hAPP(hAPP(hAPP(c_COMBS(X2,X3,X4),c_Set_Oinsert(X0)),c_fequal(X0)),X1) != hAPP(hAPP(c_Set_Oinsert(X0),X5),hAPP(c_fequal(X0),X6))
| X1 = X6 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1363])]) ).
fof(f6095,plain,
( spl0_375
<=> ! [X35,X4,X40,X0,X3] :
( hAPP(hAPP(c_Set_Oinsert(X0),X3),hAPP(c_fequal(X0),X4)) != hAPP(hAPP(c_Set_Oinsert(X0),X35),hAPP(c_fequal(X0),X40))
| X4 = X40
| X3 = X40 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_375])]) ).
fof(f6482,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] :
( hAPP(hAPP(hAPP(c_COMBS(X2,X3,X4),c_Set_Oinsert(X0)),c_fequal(X0)),X1) != hAPP(hAPP(c_Set_Oinsert(X0),X5),hAPP(c_fequal(X0),X6))
| X1 = X6 )
| ~ spl0_233
| ~ spl0_375 ),
inference(duplicate_literal_removal,[],[f6478]) ).
fof(f6478,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] :
( hAPP(hAPP(hAPP(c_COMBS(X2,X3,X4),c_Set_Oinsert(X0)),c_fequal(X0)),X1) != hAPP(hAPP(c_Set_Oinsert(X0),X5),hAPP(c_fequal(X0),X6))
| X1 = X6
| X1 = X6 )
| ~ spl0_233
| ~ spl0_375 ),
inference(superposition,[],[f6096,f2646]) ).
fof(f6096,plain,
( ! [X40,X3,X0,X4,X35] :
( hAPP(hAPP(c_Set_Oinsert(X0),X3),hAPP(c_fequal(X0),X4)) != hAPP(hAPP(c_Set_Oinsert(X0),X35),hAPP(c_fequal(X0),X40))
| X4 = X40
| X3 = X40 )
| ~ spl0_375 ),
inference(avatar_component_clause,[],[f6095]) ).
fof(f125973,plain,
( spl0_1362
| ~ spl0_233
| ~ spl0_374 ),
inference(avatar_split_clause,[],[f6476,f6091,f2645,f125971]) ).
fof(f125971,plain,
( spl0_1362
<=> ! [X5,X3,X4,X2,X0,X6,X1] :
( hAPP(hAPP(hAPP(c_COMBS(X2,X3,X4),c_Set_Oinsert(X0)),c_fequal(X0)),X1) != hAPP(hAPP(c_Set_Oinsert(X0),X5),hAPP(c_fequal(X0),X6))
| X1 = X5 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1362])]) ).
fof(f6091,plain,
( spl0_374
<=> ! [X35,X4,X40,X0,X3] :
( hAPP(hAPP(c_Set_Oinsert(X0),X3),hAPP(c_fequal(X0),X4)) != hAPP(hAPP(c_Set_Oinsert(X0),X35),hAPP(c_fequal(X0),X40))
| X3 = X35
| X3 = X40 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_374])]) ).
fof(f6476,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] :
( hAPP(hAPP(hAPP(c_COMBS(X2,X3,X4),c_Set_Oinsert(X0)),c_fequal(X0)),X1) != hAPP(hAPP(c_Set_Oinsert(X0),X5),hAPP(c_fequal(X0),X6))
| X1 = X5 )
| ~ spl0_233
| ~ spl0_374 ),
inference(duplicate_literal_removal,[],[f6474]) ).
fof(f6474,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] :
( hAPP(hAPP(hAPP(c_COMBS(X2,X3,X4),c_Set_Oinsert(X0)),c_fequal(X0)),X1) != hAPP(hAPP(c_Set_Oinsert(X0),X5),hAPP(c_fequal(X0),X6))
| X1 = X5
| X1 = X5 )
| ~ spl0_233
| ~ spl0_374 ),
inference(superposition,[],[f6092,f2646]) ).
fof(f6092,plain,
( ! [X40,X3,X0,X4,X35] :
( hAPP(hAPP(c_Set_Oinsert(X0),X3),hAPP(c_fequal(X0),X4)) != hAPP(hAPP(c_Set_Oinsert(X0),X35),hAPP(c_fequal(X0),X40))
| X3 = X35
| X3 = X40 )
| ~ spl0_374 ),
inference(avatar_component_clause,[],[f6091]) ).
fof(f125969,plain,
( spl0_1361
| ~ spl0_352
| ~ spl0_373 ),
inference(avatar_split_clause,[],[f6463,f6087,f5600,f125967]) ).
fof(f125967,plain,
( spl0_1361
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X1),X3))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X1),X2)),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1361])]) ).
fof(f6087,plain,
( spl0_373
<=> ! [X9,X0,X12,X5] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X9),X12))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X5),X9)),X12)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_373])]) ).
fof(f6463,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X1),X3))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X1),X2)),X3)) )
| ~ spl0_352
| ~ spl0_373 ),
inference(superposition,[],[f6088,f5601]) ).
fof(f6088,plain,
( ! [X0,X9,X5,X12] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X5),X9)),X12))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X9),X12)) )
| ~ spl0_373 ),
inference(avatar_component_clause,[],[f6087]) ).
fof(f125965,plain,
( spl0_1360
| ~ spl0_303
| ~ spl0_373 ),
inference(avatar_split_clause,[],[f6449,f6087,f4556,f125963]) ).
fof(f125963,plain,
( spl0_1360
<=> ! [X4,X0,X3,X2,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X1),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X3),X4,tc_fun(X0,tc_bool))))
| ~ hBOOL(c_in(X1,X2,X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1360])]) ).
fof(f6449,plain,
( ! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X1),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X3),X4,tc_fun(X0,tc_bool))))
| ~ hBOOL(c_in(X1,X2,X4)) )
| ~ spl0_303
| ~ spl0_373 ),
inference(resolution,[],[f6088,f4557]) ).
fof(f125961,plain,
( spl0_1359
| ~ spl0_352
| ~ spl0_372 ),
inference(avatar_split_clause,[],[f6425,f6083,f5600,f125959]) ).
fof(f125959,plain,
( spl0_1359
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X1),X3))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X1),X2)),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1359])]) ).
fof(f6425,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X1),X3))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X1),X2)),X3)) )
| ~ spl0_352
| ~ spl0_372 ),
inference(superposition,[],[f6084,f5601]) ).
fof(f125957,plain,
( spl0_1358
| ~ spl0_303
| ~ spl0_372 ),
inference(avatar_split_clause,[],[f6411,f6083,f4556,f125955]) ).
fof(f125955,plain,
( spl0_1358
<=> ! [X4,X0,X3,X2,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X1),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X3,tc_fun(X0,tc_bool))))
| ~ hBOOL(c_in(X4,X2,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1358])]) ).
fof(f6411,plain,
( ! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X1),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X3,tc_fun(X0,tc_bool))))
| ~ hBOOL(c_in(X4,X2,X3)) )
| ~ spl0_303
| ~ spl0_372 ),
inference(resolution,[],[f6084,f4557]) ).
fof(f125953,plain,
( spl0_1357
| ~ spl0_307
| ~ spl0_367 ),
inference(avatar_split_clause,[],[f6325,f6063,f4573,f125951]) ).
fof(f125951,plain,
( spl0_1357
<=> ! [X4,X0,X3,X2,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X2),X3,tc_fun(X0,tc_bool))),X2))
| ~ hBOOL(c_in(X4,X1,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1357])]) ).
fof(f6063,plain,
( spl0_367
<=> ! [X5,X0,X12,X9] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X12),X5))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X12),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X5),X9))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_367])]) ).
fof(f6325,plain,
( ! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X2),X3,tc_fun(X0,tc_bool))),X2))
| ~ hBOOL(c_in(X4,X1,X3)) )
| ~ spl0_307
| ~ spl0_367 ),
inference(resolution,[],[f6064,f4574]) ).
fof(f6064,plain,
( ! [X0,X9,X5,X12] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X12),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X5),X9)))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X12),X5)) )
| ~ spl0_367 ),
inference(avatar_component_clause,[],[f6063]) ).
fof(f125949,plain,
( spl0_1356
| ~ spl0_307
| ~ spl0_366 ),
inference(avatar_split_clause,[],[f6292,f6059,f4573,f125947]) ).
fof(f125947,plain,
( spl0_1356
<=> ! [X4,X0,X3,X2,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X2),X3,tc_fun(X0,tc_bool))),X4))
| ~ hBOOL(c_in(X4,X1,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1356])]) ).
fof(f6059,plain,
( spl0_366
<=> ! [X9,X0,X12,X5] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X12),X9))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X12),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X5),X9))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_366])]) ).
fof(f6292,plain,
( ! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X2),X3,tc_fun(X0,tc_bool))),X4))
| ~ hBOOL(c_in(X4,X1,X3)) )
| ~ spl0_307
| ~ spl0_366 ),
inference(resolution,[],[f6060,f4574]) ).
fof(f6060,plain,
( ! [X0,X9,X5,X12] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X12),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X5),X9)))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X12),X9)) )
| ~ spl0_366 ),
inference(avatar_component_clause,[],[f6059]) ).
fof(f125945,plain,
( spl0_1355
| ~ spl0_258
| ~ spl0_347 ),
inference(avatar_split_clause,[],[f5626,f5570,f3101,f125943]) ).
fof(f125943,plain,
( spl0_1355
<=> ! [X5,X6,X4,X0,X3,X2,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2))
| ~ class_Orderings_Oorder(X0)
| c_Fun_Oinj__on(X3,c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X0),X0,X4)
| ~ c_Fun_Oinj__on(X3,c_SetInterval_Oord__class_OatLeastAtMost(X5,X6,X0),X0,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1355])]) ).
fof(f5570,plain,
( spl0_347
<=> ! [X35,X4,X40,X0,X3] :
( ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),X3),X4))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X3,X4,X0)),c_SetInterval_Oord__class_OatLeastAtMost(X35,X40,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_347])]) ).
fof(f5626,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2))
| ~ class_Orderings_Oorder(X0)
| c_Fun_Oinj__on(X3,c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X0),X0,X4)
| ~ c_Fun_Oinj__on(X3,c_SetInterval_Oord__class_OatLeastAtMost(X5,X6,X0),X0,X4) )
| ~ spl0_258
| ~ spl0_347 ),
inference(resolution,[],[f5571,f3102]) ).
fof(f5571,plain,
( ! [X40,X3,X0,X4,X35] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X3,X4,X0)),c_SetInterval_Oord__class_OatLeastAtMost(X35,X40,X0)))
| hBOOL(hAPP(hAPP(c_lessequals(X0),X3),X4))
| ~ class_Orderings_Oorder(X0) )
| ~ spl0_347 ),
inference(avatar_component_clause,[],[f5570]) ).
fof(f125941,plain,
( spl0_1354
| ~ spl0_257
| ~ spl0_347 ),
inference(avatar_split_clause,[],[f5625,f5570,f3097,f125939]) ).
fof(f125939,plain,
( spl0_1354
<=> ! [X3,X4,X0,X5,X2,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2))
| ~ class_Orderings_Oorder(X0)
| hBOOL(c_in(X3,c_SetInterval_Oord__class_OatLeastAtMost(X4,X5,X0),X0))
| ~ hBOOL(c_in(X3,c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X0),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1354])]) ).
fof(f5625,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2))
| ~ class_Orderings_Oorder(X0)
| hBOOL(c_in(X3,c_SetInterval_Oord__class_OatLeastAtMost(X4,X5,X0),X0))
| ~ hBOOL(c_in(X3,c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X0),X0)) )
| ~ spl0_257
| ~ spl0_347 ),
inference(resolution,[],[f5571,f3098]) ).
fof(f125937,plain,
( spl0_1353
| ~ spl0_190
| ~ spl0_1276 ),
inference(avatar_split_clause,[],[f110416,f100896,f2025,f125935]) ).
fof(f100896,plain,
( spl0_1276
<=> ! [X4,X1,X3] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X4),hAPP(c_fequal(X1),X3)))
| c_Finite__Set_Ofinite(X4,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1276])]) ).
fof(f110416,plain,
( ! [X2,X0,X1] : c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X1),hAPP(c_fequal(X0),X2)),X0)
| ~ spl0_190
| ~ spl0_1276 ),
inference(resolution,[],[f100897,f2026]) ).
fof(f100897,plain,
( ! [X3,X1,X4] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X4),hAPP(c_fequal(X1),X3)))
| c_Finite__Set_Ofinite(X4,X1) )
| ~ spl0_1276 ),
inference(avatar_component_clause,[],[f100896]) ).
fof(f125933,plain,
( spl0_1352
| ~ spl0_183
| ~ spl0_341 ),
inference(avatar_split_clause,[],[f5460,f4953,f1997,f125931]) ).
fof(f125931,plain,
( spl0_1352
<=> ! [X2,X0,X1] :
( ~ c_Finite__Set_Ofinite(X0,X1)
| ~ hBOOL(c_in(X2,X0,X1))
| ~ class_Lattices_Olower__semilattice(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),c_The(c_Finite__Set_Ofold1Set(c_Lattices_Olower__semilattice__class_Oinf(X1),X0,X1),X1)))
| ~ class_Orderings_Opreorder(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1352])]) ).
fof(f5460,plain,
( ! [X2,X0,X1] :
( ~ c_Finite__Set_Ofinite(X0,X1)
| ~ hBOOL(c_in(X2,X0,X1))
| ~ class_Lattices_Olower__semilattice(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),c_The(c_Finite__Set_Ofold1Set(c_Lattices_Olower__semilattice__class_Oinf(X1),X0,X1),X1)))
| ~ class_Orderings_Opreorder(X1) )
| ~ spl0_183
| ~ spl0_341 ),
inference(resolution,[],[f4954,f1998]) ).
fof(f125929,plain,
( spl0_1351
| ~ spl0_168
| ~ spl0_340 ),
inference(avatar_split_clause,[],[f5411,f4949,f1858,f125927]) ).
fof(f125927,plain,
( spl0_1351
<=> ! [X2,X3,X4,X0,X5,X1] :
( ~ c_Fun_Oinj__on(X4,hAPP(hAPP(c_Set_Oinsert(X0),X2),hAPP(hAPP(c_Set_Oinsert(X0),X1),X3)),X0,X5)
| c_Fun_Oinj__on(X4,hAPP(hAPP(c_Set_Oinsert(X0),X2),X3),X0,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1351])]) ).
fof(f1858,plain,
( spl0_168
<=> ! [X3,X0,X5,X8,X7] :
( c_Fun_Oinj__on(X7,X5,X0,X8)
| ~ c_Fun_Oinj__on(X7,hAPP(hAPP(c_Set_Oinsert(X0),X3),X5),X0,X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_168])]) ).
fof(f5411,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ c_Fun_Oinj__on(X4,hAPP(hAPP(c_Set_Oinsert(X0),X2),hAPP(hAPP(c_Set_Oinsert(X0),X1),X3)),X0,X5)
| c_Fun_Oinj__on(X4,hAPP(hAPP(c_Set_Oinsert(X0),X2),X3),X0,X5) )
| ~ spl0_168
| ~ spl0_340 ),
inference(superposition,[],[f1859,f4950]) ).
fof(f1859,plain,
( ! [X3,X0,X8,X7,X5] :
( ~ c_Fun_Oinj__on(X7,hAPP(hAPP(c_Set_Oinsert(X0),X3),X5),X0,X8)
| c_Fun_Oinj__on(X7,X5,X0,X8) )
| ~ spl0_168 ),
inference(avatar_component_clause,[],[f1858]) ).
fof(f125925,plain,
( spl0_1350
| ~ spl0_167
| ~ spl0_340 ),
inference(avatar_split_clause,[],[f5410,f4949,f1854,f125923]) ).
fof(f125923,plain,
( spl0_1350
<=> ! [X4,X0,X3,X2,X1] :
( hBOOL(c_in(X4,hAPP(hAPP(c_Set_Oinsert(X0),X2),hAPP(hAPP(c_Set_Oinsert(X0),X1),X3)),X0))
| ~ hBOOL(c_in(X4,hAPP(hAPP(c_Set_Oinsert(X0),X2),X3),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1350])]) ).
fof(f1854,plain,
( spl0_167
<=> ! [X4,X0,X5,X3] :
( ~ hBOOL(c_in(X3,X5,X0))
| hBOOL(c_in(X3,hAPP(hAPP(c_Set_Oinsert(X0),X4),X5),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_167])]) ).
fof(f5410,plain,
( ! [X2,X3,X0,X1,X4] :
( hBOOL(c_in(X4,hAPP(hAPP(c_Set_Oinsert(X0),X2),hAPP(hAPP(c_Set_Oinsert(X0),X1),X3)),X0))
| ~ hBOOL(c_in(X4,hAPP(hAPP(c_Set_Oinsert(X0),X2),X3),X0)) )
| ~ spl0_167
| ~ spl0_340 ),
inference(superposition,[],[f1855,f4950]) ).
fof(f1855,plain,
( ! [X3,X0,X4,X5] :
( hBOOL(c_in(X3,hAPP(hAPP(c_Set_Oinsert(X0),X4),X5),X0))
| ~ hBOOL(c_in(X3,X5,X0)) )
| ~ spl0_167 ),
inference(avatar_component_clause,[],[f1854]) ).
fof(f125921,plain,
( spl0_1349
| ~ spl0_108
| ~ spl0_339 ),
inference(avatar_split_clause,[],[f5376,f4945,f1516,f125919]) ).
fof(f125919,plain,
( spl0_1349
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),X1),X2))
| ~ class_Orderings_Opreorder(tc_fun(X0,tc_bool))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),X1),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1349])]) ).
fof(f1516,plain,
( spl0_108
<=> ! [X5,X0] : hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X5),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_108])]) ).
fof(f5376,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),X1),X2))
| ~ class_Orderings_Opreorder(tc_fun(X0,tc_bool))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),X1),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)))) )
| ~ spl0_108
| ~ spl0_339 ),
inference(resolution,[],[f4946,f1517]) ).
fof(f1517,plain,
( ! [X0,X5] : hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X5),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool))))
| ~ spl0_108 ),
inference(avatar_component_clause,[],[f1516]) ).
fof(f125917,plain,
( spl0_1348
| ~ spl0_113
| ~ spl0_338 ),
inference(avatar_split_clause,[],[f5317,f4941,f1537,f125915]) ).
fof(f125915,plain,
( spl0_1348
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),X1),X2))
| ~ class_Orderings_Opreorder(tc_fun(X0,tc_bool))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0)),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1348])]) ).
fof(f1537,plain,
( spl0_113
<=> ! [X5,X0] : hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0)),X5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_113])]) ).
fof(f5317,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),X1),X2))
| ~ class_Orderings_Opreorder(tc_fun(X0,tc_bool))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0)),X2)) )
| ~ spl0_113
| ~ spl0_338 ),
inference(resolution,[],[f4942,f1538]) ).
fof(f1538,plain,
( ! [X0,X5] : hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0)),X5))
| ~ spl0_113 ),
inference(avatar_component_clause,[],[f1537]) ).
fof(f125913,plain,
( spl0_1347
| ~ spl0_245
| ~ spl0_336 ),
inference(avatar_split_clause,[],[f5262,f4933,f2694,f125911]) ).
fof(f125911,plain,
( spl0_1347
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X3))
| c_COMBK(c_False,tc_bool,X0) = c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1347])]) ).
fof(f5262,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X3))
| c_COMBK(c_False,tc_bool,X0) = c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X0) )
| ~ spl0_245
| ~ spl0_336 ),
inference(duplicate_literal_removal,[],[f5241]) ).
fof(f5241,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X3))
| ~ class_Orderings_Oorder(X0)
| c_COMBK(c_False,tc_bool,X0) = c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X0) )
| ~ spl0_245
| ~ spl0_336 ),
inference(resolution,[],[f4934,f2695]) ).
fof(f125909,plain,
( spl0_1346
| ~ spl0_108
| ~ spl0_336 ),
inference(avatar_split_clause,[],[f5260,f4933,f1516,f125907]) ).
fof(f125907,plain,
( spl0_1346
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),X1),X2))
| ~ class_Orderings_Oorder(tc_fun(X0,tc_bool))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),X1),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1346])]) ).
fof(f5260,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),X1),X2))
| ~ class_Orderings_Oorder(tc_fun(X0,tc_bool))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),X1),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)))) )
| ~ spl0_108
| ~ spl0_336 ),
inference(resolution,[],[f4934,f1517]) ).
fof(f125905,plain,
( spl0_1345
| ~ spl0_113
| ~ spl0_336 ),
inference(avatar_split_clause,[],[f5236,f4933,f1537,f125903]) ).
fof(f125903,plain,
( spl0_1345
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),X1),c_COMBK(c_False,tc_bool,X0)))
| ~ class_Orderings_Oorder(tc_fun(X0,tc_bool))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1345])]) ).
fof(f5236,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),X1),c_COMBK(c_False,tc_bool,X0)))
| ~ class_Orderings_Oorder(tc_fun(X0,tc_bool))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),X1),X2)) )
| ~ spl0_113
| ~ spl0_336 ),
inference(resolution,[],[f4934,f1538]) ).
fof(f125901,plain,
( spl0_1344
| ~ spl0_245
| ~ spl0_335 ),
inference(avatar_split_clause,[],[f5226,f4929,f2694,f125899]) ).
fof(f125899,plain,
( spl0_1344
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X3),X2))
| c_COMBK(c_False,tc_bool,X0) = c_SetInterval_Oord__class_OatLeastAtMost(X3,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1344])]) ).
fof(f5226,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X3),X2))
| c_COMBK(c_False,tc_bool,X0) = c_SetInterval_Oord__class_OatLeastAtMost(X3,X1,X0) )
| ~ spl0_245
| ~ spl0_335 ),
inference(duplicate_literal_removal,[],[f5205]) ).
fof(f5205,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X3),X2))
| ~ class_Orderings_Oorder(X0)
| c_COMBK(c_False,tc_bool,X0) = c_SetInterval_Oord__class_OatLeastAtMost(X3,X1,X0) )
| ~ spl0_245
| ~ spl0_335 ),
inference(resolution,[],[f4930,f2695]) ).
fof(f125897,plain,
( spl0_1343
| ~ spl0_108
| ~ spl0_335 ),
inference(avatar_split_clause,[],[f5224,f4929,f1516,f125895]) ).
fof(f125895,plain,
( spl0_1343
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool))),X1))
| ~ class_Orderings_Oorder(tc_fun(X0,tc_bool))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),X2),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1343])]) ).
fof(f5224,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool))),X1))
| ~ class_Orderings_Oorder(tc_fun(X0,tc_bool))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),X2),X1)) )
| ~ spl0_108
| ~ spl0_335 ),
inference(resolution,[],[f4930,f1517]) ).
fof(f125893,plain,
( spl0_1342
| ~ spl0_186
| ~ spl0_1276 ),
inference(avatar_split_clause,[],[f110409,f100896,f2009,f125891]) ).
fof(f110409,plain,
( ! [X2,X0,X1] : c_Finite__Set_Ofinite(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),hAPP(c_fequal(X0),X1)),X2),X0)
| ~ spl0_186
| ~ spl0_1276 ),
inference(resolution,[],[f100897,f2010]) ).
fof(f125889,plain,
( spl0_1341
| ~ spl0_113
| ~ spl0_335 ),
inference(avatar_split_clause,[],[f5200,f4929,f1537,f125887]) ).
fof(f125887,plain,
( spl0_1341
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),X1),X2))
| ~ class_Orderings_Oorder(tc_fun(X0,tc_bool))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0)),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1341])]) ).
fof(f5200,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),X1),X2))
| ~ class_Orderings_Oorder(tc_fun(X0,tc_bool))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0)),X2)) )
| ~ spl0_113
| ~ spl0_335 ),
inference(resolution,[],[f4930,f1538]) ).
fof(f125885,plain,
( spl0_1340
| ~ spl0_245
| ~ spl0_334 ),
inference(avatar_split_clause,[],[f5190,f4925,f2694,f125883]) ).
fof(f125883,plain,
( spl0_1340
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2))
| ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),X3),X2))
| c_COMBK(c_False,tc_bool,X0) = c_SetInterval_Oord__class_OatLeastAtMost(X3,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1340])]) ).
fof(f5190,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2))
| ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),X3),X2))
| c_COMBK(c_False,tc_bool,X0) = c_SetInterval_Oord__class_OatLeastAtMost(X3,X1,X0) )
| ~ spl0_245
| ~ spl0_334 ),
inference(duplicate_literal_removal,[],[f5169]) ).
fof(f5169,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2))
| ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),X3),X2))
| ~ class_Orderings_Oorder(X0)
| c_COMBK(c_False,tc_bool,X0) = c_SetInterval_Oord__class_OatLeastAtMost(X3,X1,X0) )
| ~ spl0_245
| ~ spl0_334 ),
inference(resolution,[],[f4926,f2695]) ).
fof(f125881,plain,
( spl0_1339
| ~ spl0_275
| ~ spl0_308 ),
inference(avatar_split_clause,[],[f4794,f4577,f3652,f125879]) ).
fof(f125879,plain,
( spl0_1339
<=> ! [X0,X3,X2,X1] :
( hBOOL(c_List_Olistsp(c_COMBK(c_False,tc_bool,X0),X3,X0))
| ~ hBOOL(c_List_Olistsp(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X2),X1),X3,X0))
| ~ hBOOL(c_List_Olistsp(X1,X3,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1339])]) ).
fof(f4577,plain,
( spl0_308
<=> ! [X9,X0,X5,X52] :
( ~ hBOOL(c_List_Olistsp(X5,X52,X0))
| ~ hBOOL(c_List_Olistsp(X9,X52,X0))
| hBOOL(c_List_Olistsp(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X5),X9),X52,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_308])]) ).
fof(f4794,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(c_List_Olistsp(c_COMBK(c_False,tc_bool,X0),X3,X0))
| ~ hBOOL(c_List_Olistsp(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X2),X1),X3,X0))
| ~ hBOOL(c_List_Olistsp(X1,X3,X0)) )
| ~ spl0_275
| ~ spl0_308 ),
inference(superposition,[],[f4578,f3653]) ).
fof(f4578,plain,
( ! [X0,X9,X52,X5] :
( hBOOL(c_List_Olistsp(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X5),X9),X52,X0))
| ~ hBOOL(c_List_Olistsp(X9,X52,X0))
| ~ hBOOL(c_List_Olistsp(X5,X52,X0)) )
| ~ spl0_308 ),
inference(avatar_component_clause,[],[f4577]) ).
fof(f125877,plain,
( spl0_1338
| ~ spl0_80
| ~ spl0_307 ),
inference(avatar_split_clause,[],[f4783,f4573,f1365,f125875]) ).
fof(f125875,plain,
( spl0_1338
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,c_and,X2,tc_fun(X0,tc_bool))),hAPP(c_HOL_Oord__class_Oless(tc_bool),v_P)))
| ~ hBOOL(c_in(hAPP(c_Not,v_P),X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1338])]) ).
fof(f4783,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,c_and,X2,tc_fun(X0,tc_bool))),hAPP(c_HOL_Oord__class_Oless(tc_bool),v_P)))
| ~ hBOOL(c_in(hAPP(c_Not,v_P),X1,X2)) )
| ~ spl0_80
| ~ spl0_307 ),
inference(superposition,[],[f4574,f1367]) ).
fof(f125873,plain,
( spl0_1337
| ~ spl0_79
| ~ spl0_307 ),
inference(avatar_split_clause,[],[f4745,f4573,f1361,f125871]) ).
fof(f125871,plain,
( spl0_1337
<=> ! [X4,X0,X3,X2,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X2,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X3,hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X1),X4,tc_fun(X2,tc_bool))),X1))
| ~ hBOOL(c_in(X1,X3,X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1337])]) ).
fof(f4745,plain,
( ! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X2,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X3,hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X1),X4,tc_fun(X2,tc_bool))),X1))
| ~ hBOOL(c_in(X1,X3,X4)) )
| ~ spl0_79
| ~ spl0_307 ),
inference(superposition,[],[f4574,f1362]) ).
fof(f125869,plain,
( spl0_1336
| ~ spl0_68
| ~ spl0_307 ),
inference(avatar_split_clause,[],[f4744,f4573,f1316,f125867]) ).
fof(f125867,plain,
( spl0_1336
<=> ! [X4,X0,X3,X2,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X2,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X3,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X4,tc_fun(X2,tc_bool))),X1))
| ~ hBOOL(c_in(X1,X3,X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1336])]) ).
fof(f4744,plain,
( ! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X2,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X3,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X4,tc_fun(X2,tc_bool))),X1))
| ~ hBOOL(c_in(X1,X3,X4)) )
| ~ spl0_68
| ~ spl0_307 ),
inference(superposition,[],[f4574,f1317]) ).
fof(f125865,plain,
( spl0_1335
| ~ spl0_255
| ~ spl0_307 ),
inference(avatar_split_clause,[],[f4725,f4573,f3089,f125863]) ).
fof(f125863,plain,
( spl0_1335
<=> ! [X4,X0,X3,X2,X1] :
( ~ hBOOL(c_in(X0,X1,X2))
| hAPP(X4,X0) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),hAPP(X4,X0)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,X4,X2,tc_fun(X3,tc_bool))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1335])]) ).
fof(f4725,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ hBOOL(c_in(X0,X1,X2))
| hAPP(X4,X0) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),hAPP(X4,X0)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,X4,X2,tc_fun(X3,tc_bool))) )
| ~ spl0_255
| ~ spl0_307 ),
inference(resolution,[],[f4574,f3090]) ).
fof(f125861,plain,
( spl0_1334
| ~ spl0_254
| ~ spl0_307 ),
inference(avatar_split_clause,[],[f4724,f4573,f3085,f125859]) ).
fof(f125859,plain,
( spl0_1334
<=> ! [X4,X0,X3,X2,X1] :
( ~ hBOOL(c_in(X0,X1,X2))
| hAPP(X4,X0) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,X4,X2,tc_fun(X3,tc_bool))),hAPP(X4,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1334])]) ).
fof(f4724,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ hBOOL(c_in(X0,X1,X2))
| hAPP(X4,X0) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,X4,X2,tc_fun(X3,tc_bool))),hAPP(X4,X0)) )
| ~ spl0_254
| ~ spl0_307 ),
inference(resolution,[],[f4574,f3086]) ).
fof(f125857,plain,
( spl0_1333
| ~ spl0_80
| ~ spl0_303 ),
inference(avatar_split_clause,[],[f4685,f4556,f1365,f125855]) ).
fof(f125855,plain,
( spl0_1333
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),hAPP(c_HOL_Oord__class_Oless(tc_bool),v_P)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,c_and,X2,tc_fun(X0,tc_bool))))
| ~ hBOOL(c_in(hAPP(c_Not,v_P),X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1333])]) ).
fof(f4685,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),hAPP(c_HOL_Oord__class_Oless(tc_bool),v_P)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,c_and,X2,tc_fun(X0,tc_bool))))
| ~ hBOOL(c_in(hAPP(c_Not,v_P),X1,X2)) )
| ~ spl0_80
| ~ spl0_303 ),
inference(superposition,[],[f4557,f1367]) ).
fof(f125853,plain,
( spl0_1332
| ~ spl0_79
| ~ spl0_303 ),
inference(avatar_split_clause,[],[f4647,f4556,f1361,f125851]) ).
fof(f125851,plain,
( spl0_1332
<=> ! [X4,X0,X3,X2,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X2,tc_bool)),X1),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X1),X4,tc_fun(X2,tc_bool))))
| ~ hBOOL(c_in(X1,X3,X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1332])]) ).
fof(f4647,plain,
( ! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X2,tc_bool)),X1),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X1),X4,tc_fun(X2,tc_bool))))
| ~ hBOOL(c_in(X1,X3,X4)) )
| ~ spl0_79
| ~ spl0_303 ),
inference(superposition,[],[f4557,f1362]) ).
fof(f125849,plain,
( spl0_1331
| ~ spl0_189
| ~ spl0_1276 ),
inference(avatar_split_clause,[],[f110406,f100896,f2021,f125847]) ).
fof(f110406,plain,
( ! [X2,X0,X1] : c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),hAPP(c_fequal(X0),X1)),X2),X0)
| ~ spl0_189
| ~ spl0_1276 ),
inference(resolution,[],[f100897,f2022]) ).
fof(f125845,plain,
( spl0_1330
| ~ spl0_68
| ~ spl0_303 ),
inference(avatar_split_clause,[],[f4646,f4556,f1316,f125843]) ).
fof(f125843,plain,
( spl0_1330
<=> ! [X4,X0,X3,X2,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X2,tc_bool)),X1),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X4,tc_fun(X2,tc_bool))))
| ~ hBOOL(c_in(X1,X3,X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1330])]) ).
fof(f4646,plain,
( ! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X2,tc_bool)),X1),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X4,tc_fun(X2,tc_bool))))
| ~ hBOOL(c_in(X1,X3,X4)) )
| ~ spl0_68
| ~ spl0_303 ),
inference(superposition,[],[f4557,f1317]) ).
fof(f125841,plain,
( spl0_1329
| ~ spl0_251
| ~ spl0_303 ),
inference(avatar_split_clause,[],[f4627,f4556,f3073,f125839]) ).
fof(f125839,plain,
( spl0_1329
<=> ! [X4,X0,X3,X2,X1] :
( ~ hBOOL(c_in(X0,X1,X2))
| hAPP(X4,X0) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,X4,X2,tc_fun(X3,tc_bool))),hAPP(X4,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1329])]) ).
fof(f4627,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ hBOOL(c_in(X0,X1,X2))
| hAPP(X4,X0) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,X4,X2,tc_fun(X3,tc_bool))),hAPP(X4,X0)) )
| ~ spl0_251
| ~ spl0_303 ),
inference(resolution,[],[f4557,f3074]) ).
fof(f125837,plain,
( spl0_1328
| ~ spl0_250
| ~ spl0_303 ),
inference(avatar_split_clause,[],[f4626,f4556,f3059,f125835]) ).
fof(f125835,plain,
( spl0_1328
<=> ! [X4,X0,X3,X2,X1] :
( ~ hBOOL(c_in(X0,X1,X2))
| hAPP(X4,X0) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),hAPP(X4,X0)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,X4,X2,tc_fun(X3,tc_bool))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1328])]) ).
fof(f4626,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ hBOOL(c_in(X0,X1,X2))
| hAPP(X4,X0) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),hAPP(X4,X0)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,X4,X2,tc_fun(X3,tc_bool))) )
| ~ spl0_250
| ~ spl0_303 ),
inference(resolution,[],[f4557,f3060]) ).
fof(f125833,plain,
( spl0_1327
| ~ spl0_245
| ~ spl0_297 ),
inference(avatar_split_clause,[],[f4500,f3943,f2694,f125831]) ).
fof(f125831,plain,
( spl0_1327
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2))
| ~ class_Lattices_Oupper__semilattice(X0)
| ~ class_Orderings_Oorder(X0)
| c_COMBK(c_False,tc_bool,X0) = c_SetInterval_Oord__class_OatLeastAtMost(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X3),X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1327])]) ).
fof(f4500,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2))
| ~ class_Lattices_Oupper__semilattice(X0)
| ~ class_Orderings_Oorder(X0)
| c_COMBK(c_False,tc_bool,X0) = c_SetInterval_Oord__class_OatLeastAtMost(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X3),X2,X0) )
| ~ spl0_245
| ~ spl0_297 ),
inference(resolution,[],[f3944,f2695]) ).
fof(f125829,plain,
( spl0_1326
| ~ spl0_245
| ~ spl0_296 ),
inference(avatar_split_clause,[],[f4463,f3939,f2694,f125827]) ).
fof(f125827,plain,
( spl0_1326
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2))
| ~ class_Lattices_Oupper__semilattice(X0)
| ~ class_Orderings_Oorder(X0)
| c_COMBK(c_False,tc_bool,X0) = c_SetInterval_Oord__class_OatLeastAtMost(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X3),X1),X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1326])]) ).
fof(f4463,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2))
| ~ class_Lattices_Oupper__semilattice(X0)
| ~ class_Orderings_Oorder(X0)
| c_COMBK(c_False,tc_bool,X0) = c_SetInterval_Oord__class_OatLeastAtMost(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X3),X1),X2,X0) )
| ~ spl0_245
| ~ spl0_296 ),
inference(resolution,[],[f3940,f2695]) ).
fof(f125825,plain,
( spl0_1325
| ~ spl0_243
| ~ spl0_293 ),
inference(avatar_split_clause,[],[f4364,f3927,f2686,f125823]) ).
fof(f125823,plain,
( spl0_1325
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ class_Lattices_Oupper__semilattice(X0)
| ~ class_Orderings_Oorder(X0)
| c_COMBK(c_False,tc_bool,X0) = c_SetInterval_Oord__class_OatLeastAtMost(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X3),X2),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1325])]) ).
fof(f2686,plain,
( spl0_243
<=> ! [X4,X0,X3] :
( c_SetInterval_Oord__class_OatLeastAtMost(X3,X4,X0) = c_COMBK(c_False,tc_bool,X0)
| ~ class_Orderings_Oorder(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X4),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_243])]) ).
fof(f3927,plain,
( spl0_293
<=> ! [X4,X0,X3,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X4))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X3),X4))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_293])]) ).
fof(f4364,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ class_Lattices_Oupper__semilattice(X0)
| ~ class_Orderings_Oorder(X0)
| c_COMBK(c_False,tc_bool,X0) = c_SetInterval_Oord__class_OatLeastAtMost(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X3),X2),X1,X0) )
| ~ spl0_243
| ~ spl0_293 ),
inference(resolution,[],[f3928,f2687]) ).
fof(f2687,plain,
( ! [X3,X0,X4] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X4),X3))
| ~ class_Orderings_Oorder(X0)
| c_SetInterval_Oord__class_OatLeastAtMost(X3,X4,X0) = c_COMBK(c_False,tc_bool,X0) )
| ~ spl0_243 ),
inference(avatar_component_clause,[],[f2686]) ).
fof(f3928,plain,
( ! [X3,X0,X1,X4] :
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X3),X4)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X4))
| ~ class_Lattices_Oupper__semilattice(X0) )
| ~ spl0_293 ),
inference(avatar_component_clause,[],[f3927]) ).
fof(f125821,plain,
( spl0_1324
| ~ spl0_179
| ~ spl0_292 ),
inference(avatar_split_clause,[],[f4353,f3915,f1980,f125819]) ).
fof(f125819,plain,
( spl0_1324
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),X2),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool))))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),X2),X1))
| ~ class_Lattices_Oupper__semilattice(tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1324])]) ).
fof(f4353,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),X2),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool))))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),X2),X1))
| ~ class_Lattices_Oupper__semilattice(tc_fun(X0,tc_bool)) )
| ~ spl0_179
| ~ spl0_292 ),
inference(superposition,[],[f3916,f1981]) ).
fof(f125817,plain,
( spl0_1323
| ~ spl0_133
| ~ spl0_292 ),
inference(avatar_split_clause,[],[f4346,f3915,f1643,f125815]) ).
fof(f125815,plain,
( spl0_1323
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),X2),X1))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),X2),c_COMBK(c_False,tc_bool,X0)))
| ~ class_Lattices_Oupper__semilattice(tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1323])]) ).
fof(f4346,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),X2),X1))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),X2),c_COMBK(c_False,tc_bool,X0)))
| ~ class_Lattices_Oupper__semilattice(tc_fun(X0,tc_bool)) )
| ~ spl0_133
| ~ spl0_292 ),
inference(superposition,[],[f3916,f1644]) ).
fof(f125813,plain,
( spl0_1322
| ~ spl0_243
| ~ spl0_292 ),
inference(avatar_split_clause,[],[f4336,f3915,f2686,f125811]) ).
fof(f125811,plain,
( spl0_1322
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ class_Lattices_Oupper__semilattice(X0)
| ~ class_Orderings_Oorder(X0)
| c_COMBK(c_False,tc_bool,X0) = c_SetInterval_Oord__class_OatLeastAtMost(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X2),X3),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1322])]) ).
fof(f4336,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ class_Lattices_Oupper__semilattice(X0)
| ~ class_Orderings_Oorder(X0)
| c_COMBK(c_False,tc_bool,X0) = c_SetInterval_Oord__class_OatLeastAtMost(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X2),X3),X1,X0) )
| ~ spl0_243
| ~ spl0_292 ),
inference(resolution,[],[f3916,f2687]) ).
fof(f125809,plain,
( spl0_1321
| ~ spl0_243
| ~ spl0_291 ),
inference(avatar_split_clause,[],[f4313,f3911,f2686,f125807]) ).
fof(f125807,plain,
( spl0_1321
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ class_Lattices_Olower__semilattice(X0)
| ~ class_Orderings_Oorder(X0)
| c_COMBK(c_False,tc_bool,X0) = c_SetInterval_Oord__class_OatLeastAtMost(X2,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X3),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1321])]) ).
fof(f4313,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ class_Lattices_Olower__semilattice(X0)
| ~ class_Orderings_Oorder(X0)
| c_COMBK(c_False,tc_bool,X0) = c_SetInterval_Oord__class_OatLeastAtMost(X2,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X3),X0) )
| ~ spl0_243
| ~ spl0_291 ),
inference(resolution,[],[f3912,f2687]) ).
fof(f125805,plain,
( spl0_1320
| ~ spl0_80
| ~ spl0_1145 ),
inference(avatar_split_clause,[],[f98169,f82218,f1365,f125803]) ).
fof(f125803,plain,
( spl0_1320
<=> ! [X2,X0,X1] : hAPP(c_HOL_Oord__class_Oless(tc_bool),v_P) = hAPP(c_Fun_Ocomp(c_and,c_Not,X0,X1,X2),v_P) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1320])]) ).
fof(f82218,plain,
( spl0_1145
<=> ! [X4,X7,X0,X6,X2,X1] :
( hAPP(c_HOL_Oord__class_Oless(tc_bool),v_P) = hAPP(c_Fun_Ocomp(X0,X1,X6,X4,X7),X2)
| hAPP(c_HOL_Oord__class_Oless(tc_bool),v_P) != hAPP(X0,hAPP(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1145])]) ).
fof(f98169,plain,
( ! [X2,X0,X1] : hAPP(c_HOL_Oord__class_Oless(tc_bool),v_P) = hAPP(c_Fun_Ocomp(c_and,c_Not,X0,X1,X2),v_P)
| ~ spl0_80
| ~ spl0_1145 ),
inference(trivial_inequality_removal,[],[f98168]) ).
fof(f98168,plain,
( ! [X2,X0,X1] :
( hAPP(c_HOL_Oord__class_Oless(tc_bool),v_P) != hAPP(c_HOL_Oord__class_Oless(tc_bool),v_P)
| hAPP(c_HOL_Oord__class_Oless(tc_bool),v_P) = hAPP(c_Fun_Ocomp(c_and,c_Not,X0,X1,X2),v_P) )
| ~ spl0_80
| ~ spl0_1145 ),
inference(superposition,[],[f82219,f1367]) ).
fof(f82219,plain,
( ! [X2,X0,X1,X6,X7,X4] :
( hAPP(c_HOL_Oord__class_Oless(tc_bool),v_P) != hAPP(X0,hAPP(X1,X2))
| hAPP(c_HOL_Oord__class_Oless(tc_bool),v_P) = hAPP(c_Fun_Ocomp(X0,X1,X6,X4,X7),X2) )
| ~ spl0_1145 ),
inference(avatar_component_clause,[],[f82218]) ).
fof(f125801,plain,
( spl0_1319
| ~ spl0_125
| ~ spl0_290 ),
inference(avatar_split_clause,[],[f4306,f3907,f1611,f125799]) ).
fof(f125799,plain,
( spl0_1319
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool))),X2))
| ~ class_Lattices_Olower__semilattice(tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1319])]) ).
fof(f3907,plain,
( spl0_290
<=> ! [X4,X0,X3,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X4),X1))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),X4)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_290])]) ).
fof(f4306,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool))),X2))
| ~ class_Lattices_Olower__semilattice(tc_fun(X0,tc_bool)) )
| ~ spl0_125
| ~ spl0_290 ),
inference(superposition,[],[f3908,f1612]) ).
fof(f3908,plain,
( ! [X3,X0,X1,X4] :
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),X4)),X1))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X4),X1))
| ~ class_Lattices_Olower__semilattice(X0) )
| ~ spl0_290 ),
inference(avatar_component_clause,[],[f3907]) ).
fof(f125797,plain,
( spl0_1318
| ~ spl0_201
| ~ spl0_290 ),
inference(avatar_split_clause,[],[f4301,f3907,f2076,f125795]) ).
fof(f125795,plain,
( spl0_1318
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0)),X2))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),X1),X2))
| ~ class_Lattices_Olower__semilattice(tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1318])]) ).
fof(f4301,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0)),X2))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),X1),X2))
| ~ class_Lattices_Olower__semilattice(tc_fun(X0,tc_bool)) )
| ~ spl0_201
| ~ spl0_290 ),
inference(superposition,[],[f3908,f2077]) ).
fof(f125793,plain,
( spl0_1317
| ~ spl0_243
| ~ spl0_290 ),
inference(avatar_split_clause,[],[f4290,f3907,f2686,f125791]) ).
fof(f125791,plain,
( spl0_1317
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ class_Lattices_Olower__semilattice(X0)
| ~ class_Orderings_Oorder(X0)
| c_COMBK(c_False,tc_bool,X0) = c_SetInterval_Oord__class_OatLeastAtMost(X2,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1317])]) ).
fof(f4290,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ class_Lattices_Olower__semilattice(X0)
| ~ class_Orderings_Oorder(X0)
| c_COMBK(c_False,tc_bool,X0) = c_SetInterval_Oord__class_OatLeastAtMost(X2,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),X1),X0) )
| ~ spl0_243
| ~ spl0_290 ),
inference(resolution,[],[f3908,f2687]) ).
fof(f125789,plain,
( spl0_1316
| ~ spl0_170
| ~ spl0_288 ),
inference(avatar_split_clause,[],[f4228,f3899,f1869,f125787]) ).
fof(f125787,plain,
( spl0_1316
<=> ! [X2,X3,X0,X1,X8,X6,X7,X4,X5] :
( ~ hBOOL(hAPP(hAPP(X0,X5),X4))
| ~ hBOOL(c_in(X4,X6,X7))
| hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X6,c_COMBC(X0,X1,X2,X3),X7,tc_fun(X8,tc_bool)),X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1316])]) ).
fof(f4228,plain,
( ! [X2,X3,X0,X1,X8,X6,X7,X4,X5] :
( ~ hBOOL(hAPP(hAPP(X0,X5),X4))
| ~ hBOOL(c_in(X4,X6,X7))
| hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X6,c_COMBC(X0,X1,X2,X3),X7,tc_fun(X8,tc_bool)),X5)) )
| ~ spl0_170
| ~ spl0_288 ),
inference(superposition,[],[f3900,f1870]) ).
fof(f125785,plain,
( spl0_1315
| ~ spl0_185
| ~ spl0_288 ),
inference(avatar_split_clause,[],[f4156,f3899,f2005,f125783]) ).
fof(f125783,plain,
( spl0_1315
<=> ! [X3,X4,X0,X5,X2,X1] :
( ~ hBOOL(c_in(X0,X1,X2))
| hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,c_lessequals(tc_fun(X3,tc_bool)),X2,tc_fun(X4,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X0),X5))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1315])]) ).
fof(f4156,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ hBOOL(c_in(X0,X1,X2))
| hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,c_lessequals(tc_fun(X3,tc_bool)),X2,tc_fun(X4,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X0),X5))) )
| ~ spl0_185
| ~ spl0_288 ),
inference(resolution,[],[f3900,f2006]) ).
fof(f125781,plain,
( spl0_1314
| ~ spl0_184
| ~ spl0_288 ),
inference(avatar_split_clause,[],[f4155,f3899,f2001,f125779]) ).
fof(f125779,plain,
( spl0_1314
<=> ! [X3,X4,X0,X5,X2,X1] :
( ~ hBOOL(c_in(X0,X1,X2))
| hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,c_lessequals(tc_fun(X3,tc_bool)),X2,tc_fun(X4,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X5),X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1314])]) ).
fof(f4155,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ hBOOL(c_in(X0,X1,X2))
| hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,c_lessequals(tc_fun(X3,tc_bool)),X2,tc_fun(X4,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X5),X0))) )
| ~ spl0_184
| ~ spl0_288 ),
inference(resolution,[],[f3900,f2002]) ).
fof(f125777,plain,
( spl0_1313
| ~ spl0_190
| ~ spl0_288 ),
inference(avatar_split_clause,[],[f4142,f3899,f2025,f125775]) ).
fof(f125775,plain,
( spl0_1313
<=> ! [X5,X4,X0,X3,X2,X1] :
( ~ hBOOL(c_in(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X1),X2),X3,X4))
| hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,c_lessequals(tc_fun(X0,tc_bool)),X4,tc_fun(X5,tc_bool)),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1313])]) ).
fof(f4142,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ hBOOL(c_in(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X1),X2),X3,X4))
| hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,c_lessequals(tc_fun(X0,tc_bool)),X4,tc_fun(X5,tc_bool)),X2)) )
| ~ spl0_190
| ~ spl0_288 ),
inference(resolution,[],[f3900,f2026]) ).
fof(f125773,plain,
( spl0_1312
| ~ spl0_186
| ~ spl0_288 ),
inference(avatar_split_clause,[],[f4137,f3899,f2009,f125771]) ).
fof(f125771,plain,
( spl0_1312
<=> ! [X5,X4,X0,X3,X2,X1] :
( ~ hBOOL(c_in(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X1),X2),X3,X4))
| hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,c_lessequals(tc_fun(X0,tc_bool)),X4,tc_fun(X5,tc_bool)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1312])]) ).
fof(f4137,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ hBOOL(c_in(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X1),X2),X3,X4))
| hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,c_lessequals(tc_fun(X0,tc_bool)),X4,tc_fun(X5,tc_bool)),X1)) )
| ~ spl0_186
| ~ spl0_288 ),
inference(resolution,[],[f3900,f2010]) ).
fof(f125769,plain,
( spl0_1311
| ~ spl0_189
| ~ spl0_288 ),
inference(avatar_split_clause,[],[f4136,f3899,f2021,f125767]) ).
fof(f125767,plain,
( spl0_1311
<=> ! [X5,X4,X0,X3,X2,X1] :
( ~ hBOOL(c_in(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X1),X2),X3,X4))
| hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,c_lessequals(tc_fun(X0,tc_bool)),X4,tc_fun(X5,tc_bool)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1311])]) ).
fof(f4136,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ hBOOL(c_in(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X1),X2),X3,X4))
| hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,c_lessequals(tc_fun(X0,tc_bool)),X4,tc_fun(X5,tc_bool)),X1)) )
| ~ spl0_189
| ~ spl0_288 ),
inference(resolution,[],[f3900,f2022]) ).
fof(f125765,plain,
( spl0_1310
| ~ spl0_245
| ~ spl0_285 ),
inference(avatar_split_clause,[],[f4034,f3887,f2694,f125763]) ).
fof(f125763,plain,
( spl0_1310
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2))
| ~ class_Lattices_Olower__semilattice(X0)
| ~ class_Orderings_Oorder(X0)
| c_COMBK(c_False,tc_bool,X0) = c_SetInterval_Oord__class_OatLeastAtMost(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),X2),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1310])]) ).
fof(f4034,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2))
| ~ class_Lattices_Olower__semilattice(X0)
| ~ class_Orderings_Oorder(X0)
| c_COMBK(c_False,tc_bool,X0) = c_SetInterval_Oord__class_OatLeastAtMost(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),X2),X0) )
| ~ spl0_245
| ~ spl0_285 ),
inference(resolution,[],[f3888,f2695]) ).
fof(f125681,plain,
( spl0_1309
| ~ spl0_245
| ~ spl0_284 ),
inference(avatar_split_clause,[],[f4001,f3883,f2694,f125679]) ).
fof(f125679,plain,
( spl0_1309
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2))
| ~ class_Lattices_Olower__semilattice(X0)
| ~ class_Orderings_Oorder(X0)
| c_COMBK(c_False,tc_bool,X0) = c_SetInterval_Oord__class_OatLeastAtMost(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X3),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1309])]) ).
fof(f4001,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2))
| ~ class_Lattices_Olower__semilattice(X0)
| ~ class_Orderings_Oorder(X0)
| c_COMBK(c_False,tc_bool,X0) = c_SetInterval_Oord__class_OatLeastAtMost(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X3),X0) )
| ~ spl0_245
| ~ spl0_284 ),
inference(resolution,[],[f3884,f2695]) ).
fof(f125677,plain,
( spl0_1308
| ~ spl0_217
| ~ spl0_271 ),
inference(avatar_split_clause,[],[f3748,f3635,f2267,f125675]) ).
fof(f125675,plain,
( spl0_1308
<=> ! [X4,X0,X3,X2,X1] :
( ~ hBOOL(c_in(X0,X1,X2))
| ~ class_Complete__Lattice_Ocomplete__lattice(X3)
| ~ class_Lattices_Oupper__semilattice(X3)
| hAPP(X4,X0) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,X4,X2,X3)),hAPP(X4,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1308])]) ).
fof(f3748,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ hBOOL(c_in(X0,X1,X2))
| ~ class_Complete__Lattice_Ocomplete__lattice(X3)
| ~ class_Lattices_Oupper__semilattice(X3)
| hAPP(X4,X0) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,X4,X2,X3)),hAPP(X4,X0)) )
| ~ spl0_217
| ~ spl0_271 ),
inference(resolution,[],[f3636,f2268]) ).
fof(f125673,plain,
( spl0_1307
| ~ spl0_215
| ~ spl0_271 ),
inference(avatar_split_clause,[],[f3747,f3635,f2259,f125671]) ).
fof(f125671,plain,
( spl0_1307
<=> ! [X4,X0,X3,X2,X1] :
( ~ hBOOL(c_in(X0,X1,X2))
| ~ class_Complete__Lattice_Ocomplete__lattice(X3)
| ~ class_Lattices_Oupper__semilattice(X3)
| hAPP(X4,X0) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),hAPP(X4,X0)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,X4,X2,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1307])]) ).
fof(f3747,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ hBOOL(c_in(X0,X1,X2))
| ~ class_Complete__Lattice_Ocomplete__lattice(X3)
| ~ class_Lattices_Oupper__semilattice(X3)
| hAPP(X4,X0) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),hAPP(X4,X0)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,X4,X2,X3)) )
| ~ spl0_215
| ~ spl0_271 ),
inference(resolution,[],[f3636,f2260]) ).
fof(f125669,plain,
( spl0_1306
| ~ spl0_212
| ~ spl0_268 ),
inference(avatar_split_clause,[],[f3683,f3623,f2247,f125667]) ).
fof(f125667,plain,
( spl0_1306
<=> ! [X4,X0,X3,X2,X1] :
( ~ hBOOL(c_in(X0,X1,X2))
| ~ class_Complete__Lattice_Ocomplete__lattice(X3)
| ~ class_Lattices_Olower__semilattice(X3)
| hAPP(X4,X0) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,X4,X2,X3)),hAPP(X4,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1306])]) ).
fof(f2247,plain,
( spl0_212
<=> ! [X2,X0,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X2),X1))
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_212])]) ).
fof(f3683,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ hBOOL(c_in(X0,X1,X2))
| ~ class_Complete__Lattice_Ocomplete__lattice(X3)
| ~ class_Lattices_Olower__semilattice(X3)
| hAPP(X4,X0) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,X4,X2,X3)),hAPP(X4,X0)) )
| ~ spl0_212
| ~ spl0_268 ),
inference(resolution,[],[f3624,f2248]) ).
fof(f2248,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X2),X1))
| ~ class_Lattices_Olower__semilattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2) = X2 )
| ~ spl0_212 ),
inference(avatar_component_clause,[],[f2247]) ).
fof(f125665,plain,
( spl0_1305
| ~ spl0_210
| ~ spl0_268 ),
inference(avatar_split_clause,[],[f3682,f3623,f2233,f125663]) ).
fof(f125663,plain,
( spl0_1305
<=> ! [X4,X0,X3,X2,X1] :
( ~ hBOOL(c_in(X0,X1,X2))
| ~ class_Complete__Lattice_Ocomplete__lattice(X3)
| ~ class_Lattices_Olower__semilattice(X3)
| hAPP(X4,X0) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),hAPP(X4,X0)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,X4,X2,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1305])]) ).
fof(f2233,plain,
( spl0_210
<=> ! [X2,X0,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2))
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_210])]) ).
fof(f3682,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ hBOOL(c_in(X0,X1,X2))
| ~ class_Complete__Lattice_Ocomplete__lattice(X3)
| ~ class_Lattices_Olower__semilattice(X3)
| hAPP(X4,X0) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),hAPP(X4,X0)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,X4,X2,X3)) )
| ~ spl0_210
| ~ spl0_268 ),
inference(resolution,[],[f3624,f2234]) ).
fof(f2234,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2))
| ~ class_Lattices_Olower__semilattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2) = X1 )
| ~ spl0_210 ),
inference(avatar_component_clause,[],[f2233]) ).
fof(f125661,plain,
( spl0_1304
| ~ spl0_225
| ~ spl0_260 ),
inference(avatar_split_clause,[],[f3460,f3109,f2299,f125659]) ).
fof(f125659,plain,
( spl0_1304
<=> ! [X2,X0,X1] :
( hAPP(c_Complete__Lattice_OSup__class_OSup(X0),X1) = X2
| ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X2),hAPP(c_Complete__Lattice_OSup__class_OSup(X0),X1)))
| ~ hBOOL(c_in(X2,X1,X0))
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1304])]) ).
fof(f3460,plain,
( ! [X2,X0,X1] :
( hAPP(c_Complete__Lattice_OSup__class_OSup(X0),X1) = X2
| ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X2),hAPP(c_Complete__Lattice_OSup__class_OSup(X0),X1)))
| ~ hBOOL(c_in(X2,X1,X0))
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) )
| ~ spl0_225
| ~ spl0_260 ),
inference(resolution,[],[f3110,f2300]) ).
fof(f125657,plain,
( spl0_1303
| ~ spl0_218
| ~ spl0_260 ),
inference(avatar_split_clause,[],[f3451,f3109,f2271,f125655]) ).
fof(f125655,plain,
( spl0_1303
<=> ! [X2,X0,X1] :
( hAPP(c_Complete__Lattice_OInf__class_OInf(X1),X2) = X0
| ~ class_Orderings_Oorder(X1)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(c_Complete__Lattice_OInf__class_OInf(X1),X2)),X0))
| ~ hBOOL(c_in(X0,X2,X1))
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1303])]) ).
fof(f3451,plain,
( ! [X2,X0,X1] :
( hAPP(c_Complete__Lattice_OInf__class_OInf(X1),X2) = X0
| ~ class_Orderings_Oorder(X1)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(c_Complete__Lattice_OInf__class_OInf(X1),X2)),X0))
| ~ hBOOL(c_in(X0,X2,X1))
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) )
| ~ spl0_218
| ~ spl0_260 ),
inference(resolution,[],[f3110,f2272]) ).
fof(f125653,plain,
( spl0_1302
| ~ spl0_225
| ~ spl0_253 ),
inference(avatar_split_clause,[],[f3304,f3081,f2299,f125651]) ).
fof(f125651,plain,
( spl0_1302
<=> ! [X2,X0,X1] :
( hAPP(c_Complete__Lattice_OSup__class_OSup(X0),X1) = X2
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(c_Complete__Lattice_OSup__class_OSup(X0),X1)),X2))
| ~ class_Orderings_Oorder(X0)
| ~ hBOOL(c_in(X2,X1,X0))
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1302])]) ).
fof(f3081,plain,
( spl0_253
<=> ! [X2,X0,X1] :
( ~ class_Orderings_Oorder(X0)
| X1 = X2
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X2),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_253])]) ).
fof(f3304,plain,
( ! [X2,X0,X1] :
( hAPP(c_Complete__Lattice_OSup__class_OSup(X0),X1) = X2
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(c_Complete__Lattice_OSup__class_OSup(X0),X1)),X2))
| ~ class_Orderings_Oorder(X0)
| ~ hBOOL(c_in(X2,X1,X0))
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) )
| ~ spl0_225
| ~ spl0_253 ),
inference(resolution,[],[f3082,f2300]) ).
fof(f3082,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X2),X1))
| X1 = X2
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2))
| ~ class_Orderings_Oorder(X0) )
| ~ spl0_253 ),
inference(avatar_component_clause,[],[f3081]) ).
fof(f125649,plain,
( spl0_1301
| ~ spl0_218
| ~ spl0_253 ),
inference(avatar_split_clause,[],[f3295,f3081,f2271,f125647]) ).
fof(f125647,plain,
( spl0_1301
<=> ! [X2,X0,X1] :
( hAPP(c_Complete__Lattice_OInf__class_OInf(X1),X2) = X0
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X0),hAPP(c_Complete__Lattice_OInf__class_OInf(X1),X2)))
| ~ class_Orderings_Oorder(X1)
| ~ hBOOL(c_in(X0,X2,X1))
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1301])]) ).
fof(f3295,plain,
( ! [X2,X0,X1] :
( hAPP(c_Complete__Lattice_OInf__class_OInf(X1),X2) = X0
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X0),hAPP(c_Complete__Lattice_OInf__class_OInf(X1),X2)))
| ~ class_Orderings_Oorder(X1)
| ~ hBOOL(c_in(X0,X2,X1))
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) )
| ~ spl0_218
| ~ spl0_253 ),
inference(resolution,[],[f3082,f2272]) ).
fof(f125645,plain,
( spl0_1300
| ~ spl0_120
| ~ spl0_248 ),
inference(avatar_split_clause,[],[f3178,f3051,f1591,f125643]) ).
fof(f125643,plain,
( spl0_1300
<=> ! [X5,X3,X4,X2,X0,X6,X1] :
( ~ c_Finite__Set_Ofinite(X0,X4)
| ~ hBOOL(c_in(v_x,X5,X6))
| c_Finite__Set_Ofinite(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,c_Fun_Ocomp(c_COMBK(X0,X1,X2),X3,X2,X1,t_a),X6,tc_fun(X4,tc_bool)),X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1300])]) ).
fof(f3178,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] :
( ~ c_Finite__Set_Ofinite(X0,X4)
| ~ hBOOL(c_in(v_x,X5,X6))
| c_Finite__Set_Ofinite(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,c_Fun_Ocomp(c_COMBK(X0,X1,X2),X3,X2,X1,t_a),X6,tc_fun(X4,tc_bool)),X4) )
| ~ spl0_120
| ~ spl0_248 ),
inference(superposition,[],[f3052,f1592]) ).
fof(f125563,plain,
( spl0_1299
| ~ spl0_131
| ~ spl0_248 ),
inference(avatar_split_clause,[],[f3174,f3051,f1635,f125561]) ).
fof(f125561,plain,
( spl0_1299
<=> ! [X4,X0,X3,X2,X1] :
( ~ c_Finite__Set_Ofinite(X1,X2)
| ~ hBOOL(c_in(c_COMBK(c_False,tc_bool,X0),X3,X4))
| c_Finite__Set_Ofinite(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X3,hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X1),X4,tc_fun(X2,tc_bool)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1299])]) ).
fof(f1635,plain,
( spl0_131
<=> ! [X5,X0] : hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X5),c_COMBK(c_False,tc_bool,X0)) = X5 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_131])]) ).
fof(f3174,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ c_Finite__Set_Ofinite(X1,X2)
| ~ hBOOL(c_in(c_COMBK(c_False,tc_bool,X0),X3,X4))
| c_Finite__Set_Ofinite(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X3,hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X1),X4,tc_fun(X2,tc_bool)),X2) )
| ~ spl0_131
| ~ spl0_248 ),
inference(superposition,[],[f3052,f1636]) ).
fof(f1636,plain,
( ! [X0,X5] : hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X5),c_COMBK(c_False,tc_bool,X0)) = X5
| ~ spl0_131 ),
inference(avatar_component_clause,[],[f1635]) ).
fof(f125559,plain,
( spl0_1298
| ~ spl0_132
| ~ spl0_248 ),
inference(avatar_split_clause,[],[f3172,f3051,f1639,f125557]) ).
fof(f125557,plain,
( spl0_1298
<=> ! [X4,X0,X3,X2,X1] :
( ~ c_Finite__Set_Ofinite(X1,X2)
| ~ hBOOL(c_in(c_COMBK(c_False,tc_bool,X0),X3,X4))
| c_Finite__Set_Ofinite(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X3,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X4,tc_fun(X2,tc_bool)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1298])]) ).
fof(f1639,plain,
( spl0_132
<=> ! [X5,X0] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X5),c_COMBK(c_False,tc_bool,X0)) = X5 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_132])]) ).
fof(f3172,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ c_Finite__Set_Ofinite(X1,X2)
| ~ hBOOL(c_in(c_COMBK(c_False,tc_bool,X0),X3,X4))
| c_Finite__Set_Ofinite(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X3,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X4,tc_fun(X2,tc_bool)),X2) )
| ~ spl0_132
| ~ spl0_248 ),
inference(superposition,[],[f3052,f1640]) ).
fof(f1640,plain,
( ! [X0,X5] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X5),c_COMBK(c_False,tc_bool,X0)) = X5
| ~ spl0_132 ),
inference(avatar_component_clause,[],[f1639]) ).
fof(f125555,plain,
( spl0_1297
| ~ spl0_125
| ~ spl0_248 ),
inference(avatar_split_clause,[],[f3168,f3051,f1611,f125553]) ).
fof(f125553,plain,
( spl0_1297
<=> ! [X4,X0,X3,X2,X1] :
( ~ c_Finite__Set_Ofinite(X1,X2)
| ~ hBOOL(c_in(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X3,X4))
| c_Finite__Set_Ofinite(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X3,hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X1),X4,tc_fun(X2,tc_bool)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1297])]) ).
fof(f3168,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ c_Finite__Set_Ofinite(X1,X2)
| ~ hBOOL(c_in(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X3,X4))
| c_Finite__Set_Ofinite(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X3,hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X1),X4,tc_fun(X2,tc_bool)),X2) )
| ~ spl0_125
| ~ spl0_248 ),
inference(superposition,[],[f3052,f1612]) ).
fof(f125551,plain,
( spl0_1296
| ~ spl0_133
| ~ spl0_248 ),
inference(avatar_split_clause,[],[f3155,f3051,f1643,f125549]) ).
fof(f125549,plain,
( spl0_1296
<=> ! [X4,X0,X3,X2,X1] :
( ~ c_Finite__Set_Ofinite(X1,X2)
| ~ hBOOL(c_in(X1,X3,X4))
| c_Finite__Set_Ofinite(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X3,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0)),X4,tc_fun(X2,tc_bool)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1296])]) ).
fof(f3155,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ c_Finite__Set_Ofinite(X1,X2)
| ~ hBOOL(c_in(X1,X3,X4))
| c_Finite__Set_Ofinite(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X3,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0)),X4,tc_fun(X2,tc_bool)),X2) )
| ~ spl0_133
| ~ spl0_248 ),
inference(superposition,[],[f3052,f1644]) ).
fof(f125547,plain,
( spl0_1295
| ~ spl0_123
| ~ spl0_248 ),
inference(avatar_split_clause,[],[f3153,f3051,f1603,f125545]) ).
fof(f125545,plain,
( spl0_1295
<=> ! [X4,X0,X3,X2,X1] :
( ~ c_Finite__Set_Ofinite(X1,X2)
| ~ hBOOL(c_in(X1,X3,X4))
| c_Finite__Set_Ofinite(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X3,hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool))),X4,tc_fun(X2,tc_bool)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1295])]) ).
fof(f3153,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ c_Finite__Set_Ofinite(X1,X2)
| ~ hBOOL(c_in(X1,X3,X4))
| c_Finite__Set_Ofinite(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X3,hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool))),X4,tc_fun(X2,tc_bool)),X2) )
| ~ spl0_123
| ~ spl0_248 ),
inference(superposition,[],[f3052,f1604]) ).
fof(f125543,plain,
( spl0_1294
| ~ spl0_130
| ~ spl0_248 ),
inference(avatar_split_clause,[],[f3152,f3051,f1631,f125541]) ).
fof(f125541,plain,
( spl0_1294
<=> ! [X4,X0,X3,X2,X1] :
( ~ c_Finite__Set_Ofinite(c_COMBK(c_False,tc_bool,X0),X2)
| ~ hBOOL(c_in(X1,X3,X4))
| c_Finite__Set_Ofinite(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X3,hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X1),X4,tc_fun(X2,tc_bool)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1294])]) ).
fof(f3152,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ c_Finite__Set_Ofinite(c_COMBK(c_False,tc_bool,X0),X2)
| ~ hBOOL(c_in(X1,X3,X4))
| c_Finite__Set_Ofinite(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X3,hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X1),X4,tc_fun(X2,tc_bool)),X2) )
| ~ spl0_130
| ~ spl0_248 ),
inference(superposition,[],[f3052,f1632]) ).
fof(f125539,plain,
( spl0_1293
| ~ spl0_182
| ~ spl0_248 ),
inference(avatar_split_clause,[],[f3140,f3051,f1993,f125537]) ).
fof(f125537,plain,
( spl0_1293
<=> ! [X4,X0,X3,X2,X1] :
( ~ hBOOL(c_in(X0,X1,X2))
| c_Finite__Set_Ofinite(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X4),X2,tc_fun(X3,tc_bool)),X3)
| ~ c_Finite__Set_Ofinite(X0,X3)
| ~ c_Finite__Set_Ofinite(X4,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1293])]) ).
fof(f3140,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ hBOOL(c_in(X0,X1,X2))
| c_Finite__Set_Ofinite(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X4),X2,tc_fun(X3,tc_bool)),X3)
| ~ c_Finite__Set_Ofinite(X0,X3)
| ~ c_Finite__Set_Ofinite(X4,X3) )
| ~ spl0_182
| ~ spl0_248 ),
inference(resolution,[],[f3052,f1994]) ).
fof(f125535,plain,
( spl0_1292
| ~ spl0_233
| ~ spl0_245 ),
inference(avatar_split_clause,[],[f3049,f2694,f2645,f125533]) ).
fof(f125533,plain,
( spl0_1292
<=> ! [X3,X4,X0,X5,X2,X1] :
( hBOOL(hAPP(hAPP(hAPP(c_COMBS(X3,X4,X5),c_lessequals(X0)),X2),X1))
| ~ class_Orderings_Oorder(X0)
| c_COMBK(c_False,tc_bool,X0) = c_SetInterval_Oord__class_OatLeastAtMost(X1,hAPP(X2,X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1292])]) ).
fof(f3049,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( hBOOL(hAPP(hAPP(hAPP(c_COMBS(X3,X4,X5),c_lessequals(X0)),X2),X1))
| ~ class_Orderings_Oorder(X0)
| c_COMBK(c_False,tc_bool,X0) = c_SetInterval_Oord__class_OatLeastAtMost(X1,hAPP(X2,X1),X0) )
| ~ spl0_233
| ~ spl0_245 ),
inference(superposition,[],[f2695,f2646]) ).
fof(f125531,plain,
( spl0_1291
| ~ spl0_224
| ~ spl0_245 ),
inference(avatar_split_clause,[],[f3041,f2694,f2295,f125529]) ).
fof(f125529,plain,
( spl0_1291
<=> ! [X0,X3,X2,X1] :
( ~ class_Orderings_Oorder(tc_fun(X0,tc_bool))
| c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,tc_fun(X0,tc_bool)) = c_COMBK(c_False,tc_bool,tc_fun(X0,tc_bool))
| hBOOL(hAPP(X2,X3))
| ~ hBOOL(hAPP(X1,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1291])]) ).
fof(f2295,plain,
( spl0_224
<=> ! [X11,X57,X0,X1] :
( ~ hBOOL(hAPP(X11,X1))
| hBOOL(hAPP(X57,X1))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X11),X57)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_224])]) ).
fof(f3041,plain,
( ! [X2,X3,X0,X1] :
( ~ class_Orderings_Oorder(tc_fun(X0,tc_bool))
| c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,tc_fun(X0,tc_bool)) = c_COMBK(c_False,tc_bool,tc_fun(X0,tc_bool))
| hBOOL(hAPP(X2,X3))
| ~ hBOOL(hAPP(X1,X3)) )
| ~ spl0_224
| ~ spl0_245 ),
inference(resolution,[],[f2695,f2296]) ).
fof(f2296,plain,
( ! [X0,X11,X1,X57] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X11),X57))
| hBOOL(hAPP(X57,X1))
| ~ hBOOL(hAPP(X11,X1)) )
| ~ spl0_224 ),
inference(avatar_component_clause,[],[f2295]) ).
fof(f125527,plain,
( spl0_1290
| ~ spl0_233
| ~ spl0_243 ),
inference(avatar_split_clause,[],[f3040,f2686,f2645,f125525]) ).
fof(f125525,plain,
( spl0_1290
<=> ! [X3,X4,X0,X5,X2,X1] :
( ~ hBOOL(hAPP(hAPP(hAPP(c_COMBS(X3,X4,X5),c_HOL_Oord__class_Oless(X0)),X2),X1))
| ~ class_Orderings_Oorder(X0)
| c_COMBK(c_False,tc_bool,X0) = c_SetInterval_Oord__class_OatLeastAtMost(hAPP(X2,X1),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1290])]) ).
fof(f3040,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ hBOOL(hAPP(hAPP(hAPP(c_COMBS(X3,X4,X5),c_HOL_Oord__class_Oless(X0)),X2),X1))
| ~ class_Orderings_Oorder(X0)
| c_COMBK(c_False,tc_bool,X0) = c_SetInterval_Oord__class_OatLeastAtMost(hAPP(X2,X1),X1,X0) )
| ~ spl0_233
| ~ spl0_243 ),
inference(superposition,[],[f2687,f2646]) ).
fof(f125520,plain,
( spl0_1289
| ~ spl0_218
| ~ spl0_236 ),
inference(avatar_split_clause,[],[f3031,f2658,f2271,f125518]) ).
fof(f125518,plain,
( spl0_1289
<=> ! [X0,X1] :
( c_COMBK(c_False,tc_bool,X0) = hAPP(c_Complete__Lattice_OInf__class_OInf(tc_fun(X0,tc_bool)),X1)
| ~ hBOOL(c_in(c_COMBK(c_False,tc_bool,X0),X1,tc_fun(X0,tc_bool)))
| ~ class_Complete__Lattice_Ocomplete__lattice(tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1289])]) ).
fof(f3031,plain,
( ! [X0,X1] :
( c_COMBK(c_False,tc_bool,X0) = hAPP(c_Complete__Lattice_OInf__class_OInf(tc_fun(X0,tc_bool)),X1)
| ~ hBOOL(c_in(c_COMBK(c_False,tc_bool,X0),X1,tc_fun(X0,tc_bool)))
| ~ class_Complete__Lattice_Ocomplete__lattice(tc_fun(X0,tc_bool)) )
| ~ spl0_218
| ~ spl0_236 ),
inference(resolution,[],[f2659,f2272]) ).
fof(f125516,plain,
( spl0_1288
| ~ spl0_194
| ~ spl0_233 ),
inference(avatar_split_clause,[],[f2967,f2645,f2041,f125514]) ).
fof(f125514,plain,
( spl0_1288
<=> ! [X5,X6,X4,X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(hAPP(c_COMBS(X4,X5,X6),hAPP(c_Set_Oinsert(X0),X1)),X3),X2))
| hBOOL(hAPP(X2,hAPP(X3,X2)))
| hAPP(X3,X2) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1288])]) ).
fof(f2967,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] :
( ~ hBOOL(hAPP(hAPP(hAPP(c_COMBS(X4,X5,X6),hAPP(c_Set_Oinsert(X0),X1)),X3),X2))
| hBOOL(hAPP(X2,hAPP(X3,X2)))
| hAPP(X3,X2) = X1 )
| ~ spl0_194
| ~ spl0_233 ),
inference(superposition,[],[f2042,f2646]) ).
fof(f125512,plain,
( spl0_1287
| ~ spl0_231
| ~ spl0_233 ),
inference(avatar_split_clause,[],[f2934,f2645,f2637,f125510]) ).
fof(f125510,plain,
( spl0_1287
<=> ! [X3,X4,X0,X6,X5,X2,X1] :
( ~ hBOOL(c_in(X6,hAPP(hAPP(hAPP(c_COMBS(X3,X4,X5),c_Set_Oinsert(X0)),X2),X1),X0))
| hBOOL(c_in(X6,hAPP(X2,X1),X0))
| X1 = X6 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1287])]) ).
fof(f2637,plain,
( spl0_231
<=> ! [X4,X0,X5,X3] :
( X3 = X4
| hBOOL(c_in(X3,X5,X0))
| ~ hBOOL(c_in(X3,hAPP(hAPP(c_Set_Oinsert(X0),X4),X5),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_231])]) ).
fof(f2934,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] :
( ~ hBOOL(c_in(X6,hAPP(hAPP(hAPP(c_COMBS(X3,X4,X5),c_Set_Oinsert(X0)),X2),X1),X0))
| hBOOL(c_in(X6,hAPP(X2,X1),X0))
| X1 = X6 )
| ~ spl0_231
| ~ spl0_233 ),
inference(superposition,[],[f2638,f2646]) ).
fof(f2638,plain,
( ! [X3,X0,X4,X5] :
( ~ hBOOL(c_in(X3,hAPP(hAPP(c_Set_Oinsert(X0),X4),X5),X0))
| hBOOL(c_in(X3,X5,X0))
| X3 = X4 )
| ~ spl0_231 ),
inference(avatar_component_clause,[],[f2637]) ).
fof(f125508,plain,
( spl0_1286
| ~ spl0_137
| ~ spl0_233 ),
inference(avatar_split_clause,[],[f2869,f2645,f1680,f125506]) ).
fof(f125506,plain,
( spl0_1286
<=> ! [X2,X3,X0,X1,X8,X6,X9,X7,X4,X5] : hAPP(hAPP(hAPP(c_COMBS(X6,X7,X8),X9),c_Fun_Ocomp(X0,X1,X2,X3,X4)),X5) = hAPP(hAPP(X9,X5),hAPP(X0,hAPP(X1,X5))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1286])]) ).
fof(f2869,plain,
( ! [X2,X3,X0,X1,X8,X6,X9,X7,X4,X5] : hAPP(hAPP(hAPP(c_COMBS(X6,X7,X8),X9),c_Fun_Ocomp(X0,X1,X2,X3,X4)),X5) = hAPP(hAPP(X9,X5),hAPP(X0,hAPP(X1,X5)))
| ~ spl0_137
| ~ spl0_233 ),
inference(superposition,[],[f2646,f1681]) ).
fof(f125504,plain,
( spl0_1285
| ~ spl0_137
| ~ spl0_233 ),
inference(avatar_split_clause,[],[f2839,f2645,f1680,f125502]) ).
fof(f125502,plain,
( spl0_1285
<=> ! [X2,X3,X0,X1,X8,X6,X9,X7,X4,X5] : hAPP(hAPP(hAPP(c_COMBS(X6,X7,X8),c_Fun_Ocomp(X0,X1,X2,X3,X4)),X9),X5) = hAPP(hAPP(X0,hAPP(X1,X5)),hAPP(X9,X5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1285])]) ).
fof(f2839,plain,
( ! [X2,X3,X0,X1,X8,X6,X9,X7,X4,X5] : hAPP(hAPP(hAPP(c_COMBS(X6,X7,X8),c_Fun_Ocomp(X0,X1,X2,X3,X4)),X9),X5) = hAPP(hAPP(X0,hAPP(X1,X5)),hAPP(X9,X5))
| ~ spl0_137
| ~ spl0_233 ),
inference(superposition,[],[f2646,f1681]) ).
fof(f125500,plain,
( spl0_1284
| ~ spl0_233 ),
inference(avatar_split_clause,[],[f2809,f2645,f125498]) ).
fof(f125498,plain,
( spl0_1284
<=> ! [X2,X3,X0,X1,X8,X6,X7,X4,X5] : hAPP(hAPP(X3,X8),hAPP(hAPP(X4,X3),X8)) = hAPP(hAPP(hAPP(hAPP(c_COMBS(X5,X6,X7),c_COMBS(X0,X1,X2)),X4),X3),X8) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1284])]) ).
fof(f2809,plain,
( ! [X2,X3,X0,X1,X8,X6,X7,X4,X5] : hAPP(hAPP(X3,X8),hAPP(hAPP(X4,X3),X8)) = hAPP(hAPP(hAPP(hAPP(c_COMBS(X5,X6,X7),c_COMBS(X0,X1,X2)),X4),X3),X8)
| ~ spl0_233 ),
inference(superposition,[],[f2646,f2646]) ).
fof(f121487,plain,
( spl0_1282
| ~ spl0_1283
| ~ spl0_227
| ~ spl0_1125 ),
inference(avatar_split_clause,[],[f82162,f81964,f2580,f121484,f121480]) ).
fof(f121480,plain,
( spl0_1282
<=> c_False = hAPP(c_Complete__Lattice_OInf__class_OInf(tc_bool),c_fequal(tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1282])]) ).
fof(f121484,plain,
( spl0_1283
<=> hBOOL(c_SetInterval_Oord__class_OatLeastAtMost(c_False,c_False,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1283])]) ).
fof(f81964,plain,
( spl0_1125
<=> ! [X0] :
( c_False = hAPP(c_Complete__Lattice_OInf__class_OInf(tc_bool),X0)
| ~ hBOOL(hAPP(X0,c_False)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1125])]) ).
fof(f82162,plain,
( ~ hBOOL(c_SetInterval_Oord__class_OatLeastAtMost(c_False,c_False,tc_bool))
| c_False = hAPP(c_Complete__Lattice_OInf__class_OInf(tc_bool),c_fequal(tc_bool))
| ~ spl0_227
| ~ spl0_1125 ),
inference(superposition,[],[f81965,f2581]) ).
fof(f81965,plain,
( ! [X0] :
( ~ hBOOL(hAPP(X0,c_False))
| c_False = hAPP(c_Complete__Lattice_OInf__class_OInf(tc_bool),X0) )
| ~ spl0_1125 ),
inference(avatar_component_clause,[],[f81964]) ).
fof(f118826,plain,
( spl0_1281
| ~ spl0_173
| ~ spl0_1125 ),
inference(avatar_split_clause,[],[f82032,f81964,f1882,f118824]) ).
fof(f118824,plain,
( spl0_1281
<=> ! [X0,X1] : c_False = hAPP(c_Complete__Lattice_OInf__class_OInf(tc_bool),c_Finite__Set_Ofold1Set(X0,hAPP(c_fequal(X1),c_False),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1281])]) ).
fof(f1882,plain,
( spl0_173
<=> ! [X0,X1,X7] : hBOOL(hAPP(c_Finite__Set_Ofold1Set(X7,hAPP(c_fequal(X0),X1),X0),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_173])]) ).
fof(f82032,plain,
( ! [X0,X1] : c_False = hAPP(c_Complete__Lattice_OInf__class_OInf(tc_bool),c_Finite__Set_Ofold1Set(X0,hAPP(c_fequal(X1),c_False),X1))
| ~ spl0_173
| ~ spl0_1125 ),
inference(resolution,[],[f81965,f1883]) ).
fof(f1883,plain,
( ! [X0,X1,X7] : hBOOL(hAPP(c_Finite__Set_Ofold1Set(X7,hAPP(c_fequal(X0),X1),X0),X1))
| ~ spl0_173 ),
inference(avatar_component_clause,[],[f1882]) ).
fof(f117094,plain,
( spl0_1280
| ~ spl0_519
| ~ spl0_1125 ),
inference(avatar_split_clause,[],[f82031,f81964,f14491,f117092]) ).
fof(f117092,plain,
( spl0_1280
<=> ! [X0] : c_False = hAPP(c_Complete__Lattice_OInf__class_OInf(tc_bool),c_Finite__Set_Ofold1Set(X0,c_SetInterval_Oord__class_OatLeastAtMost(c_False,c_False,tc_bool),tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1280])]) ).
fof(f14491,plain,
( spl0_519
<=> ! [X0,X1] : hBOOL(hAPP(c_Finite__Set_Ofold1Set(X1,c_SetInterval_Oord__class_OatLeastAtMost(X0,X0,tc_bool),tc_bool),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_519])]) ).
fof(f82031,plain,
( ! [X0] : c_False = hAPP(c_Complete__Lattice_OInf__class_OInf(tc_bool),c_Finite__Set_Ofold1Set(X0,c_SetInterval_Oord__class_OatLeastAtMost(c_False,c_False,tc_bool),tc_bool))
| ~ spl0_519
| ~ spl0_1125 ),
inference(resolution,[],[f81965,f14492]) ).
fof(f14492,plain,
( ! [X0,X1] : hBOOL(hAPP(c_Finite__Set_Ofold1Set(X1,c_SetInterval_Oord__class_OatLeastAtMost(X0,X0,tc_bool),tc_bool),X0))
| ~ spl0_519 ),
inference(avatar_component_clause,[],[f14491]) ).
fof(f116165,plain,
( spl0_1279
| ~ spl0_75
| ~ spl0_1125 ),
inference(avatar_split_clause,[],[f82024,f81964,f1344,f116163]) ).
fof(f116163,plain,
( spl0_1279
<=> ! [X0] :
( c_False = hAPP(c_Complete__Lattice_OInf__class_OInf(tc_bool),hAPP(c_lessequals(X0),c_Orderings_Obot__class_Obot(X0)))
| ~ class_Orderings_Obot(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1279])]) ).
fof(f1344,plain,
( spl0_75
<=> ! [X0,X1] :
( ~ class_Orderings_Obot(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),c_Orderings_Obot__class_Obot(X0)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_75])]) ).
fof(f82024,plain,
( ! [X0] :
( c_False = hAPP(c_Complete__Lattice_OInf__class_OInf(tc_bool),hAPP(c_lessequals(X0),c_Orderings_Obot__class_Obot(X0)))
| ~ class_Orderings_Obot(X0) )
| ~ spl0_75
| ~ spl0_1125 ),
inference(resolution,[],[f81965,f1345]) ).
fof(f1345,plain,
( ! [X0,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),c_Orderings_Obot__class_Obot(X0)),X1))
| ~ class_Orderings_Obot(X0) )
| ~ spl0_75 ),
inference(avatar_component_clause,[],[f1344]) ).
fof(f113188,plain,
( spl0_1278
| ~ spl0_38
| ~ spl0_910
| ~ spl0_1174 ),
inference(avatar_split_clause,[],[f111017,f97323,f69980,f1179,f113186]) ).
fof(f113186,plain,
( spl0_1278
<=> ! [X2,X3] : c_False = hAPP(c_Complete__Lattice_OInf__class_OInf(tc_bool),c_COMBK(c_Orderings_Otop__class_Otop(tc_bool),X2,X3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1278])]) ).
fof(f69980,plain,
( spl0_910
<=> ! [X0,X1] : hAPP(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X1) = c_Orderings_Otop__class_Otop(tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_910])]) ).
fof(f97323,plain,
( spl0_1174
<=> ! [X2,X0,X1] :
( ~ hBOOL(X0)
| c_False = hAPP(c_Complete__Lattice_OInf__class_OInf(tc_bool),c_COMBK(X0,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1174])]) ).
fof(f111017,plain,
( ! [X2,X3] : c_False = hAPP(c_Complete__Lattice_OInf__class_OInf(tc_bool),c_COMBK(c_Orderings_Otop__class_Otop(tc_bool),X2,X3))
| ~ spl0_38
| ~ spl0_910
| ~ spl0_1174 ),
inference(forward_demodulation,[],[f110813,f69981]) ).
fof(f69981,plain,
( ! [X0,X1] : hAPP(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X1) = c_Orderings_Otop__class_Otop(tc_bool)
| ~ spl0_910 ),
inference(avatar_component_clause,[],[f69980]) ).
fof(f110813,plain,
( ! [X2,X3,X0,X1] : c_False = hAPP(c_Complete__Lattice_OInf__class_OInf(tc_bool),c_COMBK(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X1),X2,X3))
| ~ spl0_38
| ~ spl0_1174 ),
inference(resolution,[],[f97324,f1180]) ).
fof(f97324,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(X0)
| c_False = hAPP(c_Complete__Lattice_OInf__class_OInf(tc_bool),c_COMBK(X0,X1,X2)) )
| ~ spl0_1174 ),
inference(avatar_component_clause,[],[f97323]) ).
fof(f110294,plain,
( spl0_41
| ~ spl0_51
| ~ spl0_150
| ~ spl0_567
| ~ spl0_642
| ~ spl0_1177
| ~ spl0_1275 ),
inference(avatar_split_clause,[],[f103305,f100893,f99806,f18467,f16050,f1732,f1237,f1193]) ).
fof(f16050,plain,
( spl0_567
<=> ! [X0,X1] : c_Finite__Set_Ofinite(hAPP(c_fequal(X0),X1),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_567])]) ).
fof(f18467,plain,
( spl0_642
<=> ! [X2,X0,X1] : hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X0),X2),hAPP(c_fequal(X0),X1)),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_642])]) ).
fof(f99806,plain,
( spl0_1177
<=> ! [X2,X3,X4,X0,X5,X1] : hAPP(X1,hAPP(X5,X1)) = hAPP(hAPP(hAPP(c_COMBS(X2,X3,X4),hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)))),X5),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1177])]) ).
fof(f100893,plain,
( spl0_1275
<=> ! [X2,X0] :
( ~ c_Finite__Set_Ofinite(X0,X2)
| c_COMBK(c_False,tc_bool,X2) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1275])]) ).
fof(f103305,plain,
( hBOOL(c_False)
| ~ spl0_51
| ~ spl0_150
| ~ spl0_567
| ~ spl0_642
| ~ spl0_1177
| ~ spl0_1275 ),
inference(forward_demodulation,[],[f103304,f1238]) ).
fof(f103304,plain,
( ! [X0,X6] : hBOOL(hAPP(c_COMBK(c_False,tc_bool,X0),X6))
| ~ spl0_150
| ~ spl0_567
| ~ spl0_642
| ~ spl0_1177
| ~ spl0_1275 ),
inference(forward_demodulation,[],[f103303,f103289]) ).
fof(f103289,plain,
( ! [X2,X3,X0,X1,X4,X5] : c_COMBK(c_False,tc_bool,X0) = hAPP(hAPP(hAPP(hAPP(c_COMBS(X2,X3,X4),hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X5,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_bool)))),X1),c_Set_Oinsert(X0)),c_COMBK(c_False,tc_bool,X0))
| ~ spl0_150
| ~ spl0_567
| ~ spl0_1177
| ~ spl0_1275 ),
inference(forward_demodulation,[],[f101896,f100900]) ).
fof(f100900,plain,
( ! [X0,X1] : hAPP(c_fequal(X0),X1) = c_COMBK(c_False,tc_bool,X0)
| ~ spl0_567
| ~ spl0_1275 ),
inference(resolution,[],[f100894,f16051]) ).
fof(f16051,plain,
( ! [X0,X1] : c_Finite__Set_Ofinite(hAPP(c_fequal(X0),X1),X0)
| ~ spl0_567 ),
inference(avatar_component_clause,[],[f16050]) ).
fof(f100894,plain,
( ! [X2,X0] :
( ~ c_Finite__Set_Ofinite(X0,X2)
| c_COMBK(c_False,tc_bool,X2) = X0 )
| ~ spl0_1275 ),
inference(avatar_component_clause,[],[f100893]) ).
fof(f101896,plain,
( ! [X2,X3,X0,X1,X4,X5] : hAPP(c_fequal(X0),hAPP(X1,c_Set_Oinsert(X0))) = hAPP(hAPP(hAPP(hAPP(c_COMBS(X2,X3,X4),hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X5,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_bool)))),X1),c_Set_Oinsert(X0)),c_COMBK(c_False,tc_bool,X0))
| ~ spl0_150
| ~ spl0_1177 ),
inference(superposition,[],[f1733,f99807]) ).
fof(f99807,plain,
( ! [X2,X3,X0,X1,X4,X5] : hAPP(X1,hAPP(X5,X1)) = hAPP(hAPP(hAPP(c_COMBS(X2,X3,X4),hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)))),X5),X1)
| ~ spl0_1177 ),
inference(avatar_component_clause,[],[f99806]) ).
fof(f103303,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] : hBOOL(hAPP(hAPP(hAPP(hAPP(hAPP(c_COMBS(X2,X3,X4),hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X5,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_bool)))),X1),c_Set_Oinsert(X0)),c_COMBK(c_False,tc_bool,X0)),X6))
| ~ spl0_567
| ~ spl0_642
| ~ spl0_1177
| ~ spl0_1275 ),
inference(forward_demodulation,[],[f101933,f100900]) ).
fof(f101933,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] : hBOOL(hAPP(hAPP(hAPP(hAPP(hAPP(c_COMBS(X2,X3,X4),hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X5,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_bool)))),X1),c_Set_Oinsert(X0)),hAPP(c_fequal(X0),X6)),X6))
| ~ spl0_642
| ~ spl0_1177 ),
inference(superposition,[],[f18468,f99807]) ).
fof(f18468,plain,
( ! [X2,X0,X1] : hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X0),X2),hAPP(c_fequal(X0),X1)),X1))
| ~ spl0_642 ),
inference(avatar_component_clause,[],[f18467]) ).
fof(f100932,plain,
( spl0_1277
| ~ spl0_213
| ~ spl0_349
| ~ spl0_352
| ~ spl0_515
| ~ spl0_666
| ~ spl0_667 ),
inference(avatar_split_clause,[],[f37128,f18805,f18801,f14095,f5600,f5588,f2251,f100930]) ).
fof(f100930,plain,
( spl0_1277
<=> ! [X2,X0,X1] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X2),X1)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X1),X2)) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1277])]) ).
fof(f2251,plain,
( spl0_213
<=> ! [X9,X5,X0] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X5),X9) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X9),X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_213])]) ).
fof(f14095,plain,
( spl0_515
<=> ! [X5,X0,X12,X9] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X12),X5)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X9),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X5),X12))) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X12),X5)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X9),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X5),X12))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_515])]) ).
fof(f18801,plain,
( spl0_666
<=> ! [X2,X0,X1] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X2),X1)) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_666])]) ).
fof(f18805,plain,
( spl0_667
<=> ! [X2,X0,X1] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X2)) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_667])]) ).
fof(f37128,plain,
( ! [X2,X0,X1] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X2),X1)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X1),X2)) = X1
| ~ spl0_213
| ~ spl0_349
| ~ spl0_352
| ~ spl0_515
| ~ spl0_666
| ~ spl0_667 ),
inference(forward_demodulation,[],[f37127,f18802]) ).
fof(f18802,plain,
( ! [X2,X0,X1] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X2),X1)) = X1
| ~ spl0_666 ),
inference(avatar_component_clause,[],[f18801]) ).
fof(f37127,plain,
( ! [X2,X0,X1] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X2),X1)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X2),X1)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X1),X2))
| ~ spl0_213
| ~ spl0_349
| ~ spl0_352
| ~ spl0_515
| ~ spl0_667 ),
inference(forward_demodulation,[],[f37126,f2252]) ).
fof(f2252,plain,
( ! [X0,X9,X5] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X5),X9) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X9),X5)
| ~ spl0_213 ),
inference(avatar_component_clause,[],[f2251]) ).
fof(f37126,plain,
( ! [X2,X0,X1] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X2),X1)),X1) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X2),X1)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X1),X2))
| ~ spl0_349
| ~ spl0_352
| ~ spl0_515
| ~ spl0_667 ),
inference(forward_demodulation,[],[f36878,f19301]) ).
fof(f19301,plain,
( ! [X2,X0,X1] : hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X1),X2) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X1),X2)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X2))
| ~ spl0_349
| ~ spl0_667 ),
inference(superposition,[],[f18806,f5589]) ).
fof(f18806,plain,
( ! [X2,X0,X1] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X2)) = X1
| ~ spl0_667 ),
inference(avatar_component_clause,[],[f18805]) ).
fof(f36878,plain,
( ! [X2,X0,X1] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X2),X1)),X1) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X2),X1)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X1),X2)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X2)))
| ~ spl0_352
| ~ spl0_515 ),
inference(superposition,[],[f14096,f5601]) ).
fof(f14096,plain,
( ! [X0,X9,X5,X12] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X12),X5)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X9),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X5),X12))) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X12),X5)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X9),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X5),X12)))
| ~ spl0_515 ),
inference(avatar_component_clause,[],[f14095]) ).
fof(f100898,plain,
( spl0_1275
| spl0_1276
| ~ spl0_496
| ~ spl0_498 ),
inference(avatar_split_clause,[],[f13471,f13404,f13396,f100896,f100893]) ).
fof(f13396,plain,
( spl0_496
<=> ! [X35,X0,X5,X8] :
( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X0,tc_fun(tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),X8),c_Set_Oinsert(X0)),c_COMBK(X35,X0,X8)),X8,tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0)),X8,tc_fun(X0,tc_bool)) = hAPP(c_fequal(X0),X35)
| c_COMBK(c_False,tc_bool,X8) = X5 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_496])]) ).
fof(f13404,plain,
( spl0_498
<=> ! [X9,X0,X5,X8,X7] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X8,tc_bool)),X9),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X8,tc_fun(tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),X0),c_Set_Oinsert(X8)),X7),X0,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8)),X0,tc_fun(X8,tc_bool))))
| ~ c_Finite__Set_Ofinite(X5,X0)
| c_Finite__Set_Ofinite(X9,X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_498])]) ).
fof(f13471,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X4),hAPP(c_fequal(X1),X3)))
| ~ c_Finite__Set_Ofinite(X0,X2)
| c_Finite__Set_Ofinite(X4,X1)
| c_COMBK(c_False,tc_bool,X2) = X0 )
| ~ spl0_496
| ~ spl0_498 ),
inference(superposition,[],[f13405,f13397]) ).
fof(f13397,plain,
( ! [X0,X8,X5,X35] :
( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X0,tc_fun(tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),X8),c_Set_Oinsert(X0)),c_COMBK(X35,X0,X8)),X8,tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0)),X8,tc_fun(X0,tc_bool)) = hAPP(c_fequal(X0),X35)
| c_COMBK(c_False,tc_bool,X8) = X5 )
| ~ spl0_496 ),
inference(avatar_component_clause,[],[f13396]) ).
fof(f13405,plain,
( ! [X0,X8,X9,X7,X5] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X8,tc_bool)),X9),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X8,tc_fun(tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),X0),c_Set_Oinsert(X8)),X7),X0,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8)),X0,tc_fun(X8,tc_bool))))
| ~ c_Finite__Set_Ofinite(X5,X0)
| c_Finite__Set_Ofinite(X9,X8) )
| ~ spl0_498 ),
inference(avatar_component_clause,[],[f13404]) ).
fof(f100891,plain,
( spl0_1274
| ~ spl0_130
| ~ spl0_132
| ~ spl0_470 ),
inference(avatar_split_clause,[],[f12285,f10961,f1639,f1631,f100889]) ).
fof(f100889,plain,
( spl0_1274
<=> ! [X2,X0,X1] : hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X1),X2) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X2),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1274])]) ).
fof(f10961,plain,
( spl0_470
<=> ! [X5,X0,X12,X9] : hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X5),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X9),X12)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X5),X9)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X5),X12)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_470])]) ).
fof(f12285,plain,
( ! [X2,X0,X1] : hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X1),X2) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X2),X1))
| ~ spl0_130
| ~ spl0_132
| ~ spl0_470 ),
inference(forward_demodulation,[],[f12175,f1640]) ).
fof(f12175,plain,
( ! [X2,X0,X1] : hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X2),X1)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X1),X2)),c_COMBK(c_False,tc_bool,X0))
| ~ spl0_130
| ~ spl0_470 ),
inference(superposition,[],[f10962,f1632]) ).
fof(f10962,plain,
( ! [X0,X9,X5,X12] : hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X5),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X9),X12)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X5),X9)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X5),X12))
| ~ spl0_470 ),
inference(avatar_component_clause,[],[f10961]) ).
fof(f100887,plain,
( spl0_1273
| ~ spl0_79
| ~ spl0_186
| ~ spl0_251
| ~ spl0_464 ),
inference(avatar_split_clause,[],[f11519,f10791,f3073,f2009,f1361,f100885]) ).
fof(f100885,plain,
( spl0_1273
<=> ! [X2,X0,X1] : hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X1),X2) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X1),X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1273])]) ).
fof(f10791,plain,
( spl0_464
<=> ! [X9,X0,X12,X5] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X12),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X5),X9)) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X12),X5)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X12),X9)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_464])]) ).
fof(f11519,plain,
( ! [X2,X0,X1] : hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X1),X2) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X1),X2))
| ~ spl0_79
| ~ spl0_186
| ~ spl0_251
| ~ spl0_464 ),
inference(forward_demodulation,[],[f11440,f3227]) ).
fof(f3227,plain,
( ! [X2,X0,X1] : hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X1),X2) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X1),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X1),X2))
| ~ spl0_186
| ~ spl0_251 ),
inference(resolution,[],[f3074,f2010]) ).
fof(f11440,plain,
( ! [X2,X0,X1] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X1),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X1),X2)) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X1),X2))
| ~ spl0_79
| ~ spl0_464 ),
inference(superposition,[],[f10792,f1362]) ).
fof(f10792,plain,
( ! [X0,X9,X5,X12] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X12),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X5),X9)) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X12),X5)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X12),X9))
| ~ spl0_464 ),
inference(avatar_component_clause,[],[f10791]) ).
fof(f100883,plain,
( spl0_1272
| ~ spl0_130
| ~ spl0_132
| ~ spl0_463 ),
inference(avatar_split_clause,[],[f11422,f10787,f1639,f1631,f100881]) ).
fof(f100881,plain,
( spl0_1272
<=> ! [X2,X0,X1] : hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X2),X1) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X2),X1)),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1272])]) ).
fof(f10787,plain,
( spl0_463
<=> ! [X9,X0,X12,X5] : hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X5),X9)),X12) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X5),X12)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X9),X12)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_463])]) ).
fof(f11422,plain,
( ! [X2,X0,X1] : hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X2),X1) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X2),X1)),X1)
| ~ spl0_130
| ~ spl0_132
| ~ spl0_463 ),
inference(forward_demodulation,[],[f11335,f1640]) ).
fof(f11335,plain,
( ! [X2,X0,X1] : hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X2),X1)),X1) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X2),X1)),c_COMBK(c_False,tc_bool,X0))
| ~ spl0_130
| ~ spl0_463 ),
inference(superposition,[],[f10788,f1632]) ).
fof(f10788,plain,
( ! [X0,X9,X5,X12] : hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X5),X9)),X12) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X5),X12)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X9),X12))
| ~ spl0_463 ),
inference(avatar_component_clause,[],[f10787]) ).
fof(f100879,plain,
( spl0_1271
| ~ spl0_130
| ~ spl0_133
| ~ spl0_463 ),
inference(avatar_split_clause,[],[f11415,f10787,f1643,f1631,f100877]) ).
fof(f100877,plain,
( spl0_1271
<=> ! [X2,X0,X1] : hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X2),X1) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X2)),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1271])]) ).
fof(f11415,plain,
( ! [X2,X0,X1] : hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X2),X1) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X2)),X1)
| ~ spl0_130
| ~ spl0_133
| ~ spl0_463 ),
inference(forward_demodulation,[],[f11325,f1644]) ).
fof(f11325,plain,
( ! [X2,X0,X1] : hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X2)),X1) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X2),X1))
| ~ spl0_130
| ~ spl0_463 ),
inference(superposition,[],[f10788,f1632]) ).
fof(f100875,plain,
( spl0_1270
| ~ spl0_208
| ~ spl0_466 ),
inference(avatar_split_clause,[],[f10851,f10800,f2225,f100873]) ).
fof(f100873,plain,
( spl0_1270
<=> ! [X4,X0,X3,X2,X1] :
( ~ hBOOL(c_in(X4,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X1),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X3),X2)),X0))
| hBOOL(c_in(X4,X3,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1270])]) ).
fof(f2225,plain,
( spl0_208
<=> ! [X35,X9,X0,X5] :
( hBOOL(c_in(X35,X9,X0))
| ~ hBOOL(c_in(X35,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X5),X9),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_208])]) ).
fof(f10800,plain,
( spl0_466
<=> ! [X9,X0,X12,X5] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X5),X9)),X12) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X5),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X12),X9)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_466])]) ).
fof(f10851,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ hBOOL(c_in(X4,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X1),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X3),X2)),X0))
| hBOOL(c_in(X4,X3,X0)) )
| ~ spl0_208
| ~ spl0_466 ),
inference(superposition,[],[f2226,f10801]) ).
fof(f10801,plain,
( ! [X0,X9,X5,X12] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X5),X9)),X12) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X5),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X12),X9))
| ~ spl0_466 ),
inference(avatar_component_clause,[],[f10800]) ).
fof(f2226,plain,
( ! [X0,X9,X35,X5] :
( ~ hBOOL(c_in(X35,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X5),X9),X0))
| hBOOL(c_in(X35,X9,X0)) )
| ~ spl0_208 ),
inference(avatar_component_clause,[],[f2225]) ).
fof(f100871,plain,
( spl0_1269
| ~ spl0_207
| ~ spl0_430 ),
inference(avatar_split_clause,[],[f9253,f8416,f2221,f100869]) ).
fof(f100869,plain,
( spl0_1269
<=> ! [X4,X0,X3,X2,X1] :
( ~ hBOOL(c_in(X4,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X1),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X2),X3)),X0))
| ~ hBOOL(c_in(X4,X3,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1269])]) ).
fof(f8416,plain,
( spl0_430
<=> ! [X9,X0,X12,X5] : hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X5),X9)),X12) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X5),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X9),X12)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_430])]) ).
fof(f9253,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ hBOOL(c_in(X4,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X1),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X2),X3)),X0))
| ~ hBOOL(c_in(X4,X3,X0)) )
| ~ spl0_207
| ~ spl0_430 ),
inference(superposition,[],[f2222,f8417]) ).
fof(f8417,plain,
( ! [X0,X9,X5,X12] : hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X5),X9)),X12) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X5),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X9),X12))
| ~ spl0_430 ),
inference(avatar_component_clause,[],[f8416]) ).
fof(f100867,plain,
( spl0_1268
| ~ spl0_221
| ~ spl0_429 ),
inference(avatar_split_clause,[],[f9126,f8411,f2283,f100865]) ).
fof(f100865,plain,
( spl0_1268
<=> ! [X4,X0,X3,X2,X1] :
( hBOOL(c_in(X4,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X2),X3)),X0))
| ~ hBOOL(c_in(X4,X3,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1268])]) ).
fof(f2283,plain,
( spl0_221
<=> ! [X35,X9,X0,X5] :
( ~ hBOOL(c_in(X35,X9,X0))
| hBOOL(c_in(X35,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X5),X9),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_221])]) ).
fof(f9126,plain,
( ! [X2,X3,X0,X1,X4] :
( hBOOL(c_in(X4,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X2),X3)),X0))
| ~ hBOOL(c_in(X4,X3,X0)) )
| ~ spl0_221
| ~ spl0_429 ),
inference(superposition,[],[f2284,f8412]) ).
fof(f2284,plain,
( ! [X0,X9,X35,X5] :
( hBOOL(c_in(X35,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X5),X9),X0))
| ~ hBOOL(c_in(X35,X9,X0)) )
| ~ spl0_221 ),
inference(avatar_component_clause,[],[f2283]) ).
fof(f100863,plain,
( spl0_1267
| ~ spl0_219
| ~ spl0_429 ),
inference(avatar_split_clause,[],[f9124,f8411,f2275,f100861]) ).
fof(f100861,plain,
( spl0_1267
<=> ! [X3,X4,X0,X5,X2,X1] :
( ~ c_Fun_Oinj__on(X4,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X2),X3)),X0,X5)
| c_Fun_Oinj__on(X4,X3,X0,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1267])]) ).
fof(f2275,plain,
( spl0_219
<=> ! [X5,X0,X9,X8,X7] :
( c_Fun_Oinj__on(X7,X9,X0,X8)
| ~ c_Fun_Oinj__on(X7,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X5),X9),X0,X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_219])]) ).
fof(f9124,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ c_Fun_Oinj__on(X4,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X2),X3)),X0,X5)
| c_Fun_Oinj__on(X4,X3,X0,X5) )
| ~ spl0_219
| ~ spl0_429 ),
inference(superposition,[],[f2276,f8412]) ).
fof(f2276,plain,
( ! [X0,X8,X9,X7,X5] :
( ~ c_Fun_Oinj__on(X7,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X5),X9),X0,X8)
| c_Fun_Oinj__on(X7,X9,X0,X8) )
| ~ spl0_219 ),
inference(avatar_component_clause,[],[f2275]) ).
fof(f100859,plain,
( spl0_1266
| ~ spl0_223
| ~ spl0_428 ),
inference(avatar_split_clause,[],[f8922,f8407,f2291,f100857]) ).
fof(f100857,plain,
( spl0_1266
<=> ! [X4,X0,X3,X2,X1] :
( hBOOL(c_in(X4,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X3)),X0))
| ~ hBOOL(c_in(X4,X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1266])]) ).
fof(f2291,plain,
( spl0_223
<=> ! [X35,X9,X0,X5] :
( ~ hBOOL(c_in(X35,X5,X0))
| hBOOL(c_in(X35,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X5),X9),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_223])]) ).
fof(f8922,plain,
( ! [X2,X3,X0,X1,X4] :
( hBOOL(c_in(X4,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X3)),X0))
| ~ hBOOL(c_in(X4,X1,X0)) )
| ~ spl0_223
| ~ spl0_428 ),
inference(superposition,[],[f2292,f8408]) ).
fof(f2292,plain,
( ! [X0,X9,X35,X5] :
( hBOOL(c_in(X35,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X5),X9),X0))
| ~ hBOOL(c_in(X35,X5,X0)) )
| ~ spl0_223 ),
inference(avatar_component_clause,[],[f2291]) ).
fof(f100783,plain,
( spl0_1265
| ~ spl0_220
| ~ spl0_428 ),
inference(avatar_split_clause,[],[f8920,f8407,f2279,f100781]) ).
fof(f100781,plain,
( spl0_1265
<=> ! [X2,X3,X4,X0,X5,X1] :
( ~ c_Fun_Oinj__on(X4,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X3)),X0,X5)
| c_Fun_Oinj__on(X4,X1,X0,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1265])]) ).
fof(f2279,plain,
( spl0_220
<=> ! [X9,X0,X5,X8,X7] :
( c_Fun_Oinj__on(X7,X5,X0,X8)
| ~ c_Fun_Oinj__on(X7,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X5),X9),X0,X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_220])]) ).
fof(f8920,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ c_Fun_Oinj__on(X4,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X3)),X0,X5)
| c_Fun_Oinj__on(X4,X1,X0,X5) )
| ~ spl0_220
| ~ spl0_428 ),
inference(superposition,[],[f2280,f8408]) ).
fof(f2280,plain,
( ! [X0,X8,X9,X7,X5] :
( ~ c_Fun_Oinj__on(X7,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X5),X9),X0,X8)
| c_Fun_Oinj__on(X7,X5,X0,X8) )
| ~ spl0_220 ),
inference(avatar_component_clause,[],[f2279]) ).
fof(f100779,plain,
( spl0_1264
| ~ spl0_209
| ~ spl0_427 ),
inference(avatar_split_clause,[],[f8702,f8403,f2229,f100777]) ).
fof(f100777,plain,
( spl0_1264
<=> ! [X4,X0,X3,X2,X1] :
( ~ hBOOL(c_in(X4,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X1),X3)),X0))
| hBOOL(c_in(X4,X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1264])]) ).
fof(f2229,plain,
( spl0_209
<=> ! [X35,X9,X0,X5] :
( hBOOL(c_in(X35,X5,X0))
| ~ hBOOL(c_in(X35,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X5),X9),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_209])]) ).
fof(f8702,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ hBOOL(c_in(X4,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X1),X3)),X0))
| hBOOL(c_in(X4,X1,X0)) )
| ~ spl0_209
| ~ spl0_427 ),
inference(superposition,[],[f2230,f8404]) ).
fof(f2230,plain,
( ! [X0,X9,X35,X5] :
( ~ hBOOL(c_in(X35,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X5),X9),X0))
| hBOOL(c_in(X35,X5,X0)) )
| ~ spl0_209 ),
inference(avatar_component_clause,[],[f2229]) ).
fof(f100775,plain,
( spl0_1263
| ~ spl0_208
| ~ spl0_426 ),
inference(avatar_split_clause,[],[f8570,f8399,f2225,f100773]) ).
fof(f100773,plain,
( spl0_1263
<=> ! [X4,X0,X3,X2,X1] :
( ~ hBOOL(c_in(X4,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X2),X3)),X0))
| hBOOL(c_in(X4,X3,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1263])]) ).
fof(f8570,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ hBOOL(c_in(X4,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X2),X3)),X0))
| hBOOL(c_in(X4,X3,X0)) )
| ~ spl0_208
| ~ spl0_426 ),
inference(superposition,[],[f2226,f8400]) ).
fof(f100771,plain,
( spl0_1262
| ~ spl0_113
| ~ spl0_414 ),
inference(avatar_split_clause,[],[f7721,f7704,f1537,f100769]) ).
fof(f100769,plain,
( spl0_1262
<=> ! [X2,X0,X1] : hAPP(c_fequal(X0),X1) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),hAPP(c_fequal(X0),X1)),hAPP(c_lessequals(tc_fun(X2,tc_bool)),c_COMBK(c_False,tc_bool,X2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1262])]) ).
fof(f7721,plain,
( ! [X2,X0,X1] : hAPP(c_fequal(X0),X1) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),hAPP(c_fequal(X0),X1)),hAPP(c_lessequals(tc_fun(X2,tc_bool)),c_COMBK(c_False,tc_bool,X2)))
| ~ spl0_113
| ~ spl0_414 ),
inference(resolution,[],[f7705,f1538]) ).
fof(f100767,plain,
( spl0_1261
| ~ spl0_213
| ~ spl0_352 ),
inference(avatar_split_clause,[],[f5878,f5600,f2251,f100765]) ).
fof(f100765,plain,
( spl0_1261
<=> ! [X2,X0,X1] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X1),X2)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X2),X1)) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1261])]) ).
fof(f5878,plain,
( ! [X2,X0,X1] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X1),X2)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X2),X1)) = X1
| ~ spl0_213
| ~ spl0_352 ),
inference(superposition,[],[f5601,f2252]) ).
fof(f100763,plain,
( spl0_1260
| ~ spl0_221
| ~ spl0_350 ),
inference(avatar_split_clause,[],[f5769,f5592,f2283,f100761]) ).
fof(f100761,plain,
( spl0_1260
<=> ! [X0,X3,X2,X1] :
( hBOOL(c_in(X3,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X2),X0))
| ~ hBOOL(c_in(X3,hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X2),X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1260])]) ).
fof(f5769,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(c_in(X3,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X2),X0))
| ~ hBOOL(c_in(X3,hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X2),X1),X0)) )
| ~ spl0_221
| ~ spl0_350 ),
inference(superposition,[],[f2284,f5593]) ).
fof(f100759,plain,
( spl0_1259
| ~ spl0_219
| ~ spl0_350 ),
inference(avatar_split_clause,[],[f5767,f5592,f2275,f100757]) ).
fof(f100757,plain,
( spl0_1259
<=> ! [X4,X0,X3,X2,X1] :
( ~ c_Fun_Oinj__on(X3,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X2),X0,X4)
| c_Fun_Oinj__on(X3,hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X2),X1),X0,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1259])]) ).
fof(f5767,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ c_Fun_Oinj__on(X3,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X2),X0,X4)
| c_Fun_Oinj__on(X3,hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X2),X1),X0,X4) )
| ~ spl0_219
| ~ spl0_350 ),
inference(superposition,[],[f2276,f5593]) ).
fof(f100755,plain,
( spl0_1258
| ~ spl0_223
| ~ spl0_349 ),
inference(avatar_split_clause,[],[f5707,f5588,f2291,f100753]) ).
fof(f100753,plain,
( spl0_1258
<=> ! [X0,X3,X2,X1] :
( hBOOL(c_in(X3,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X2),X0))
| ~ hBOOL(c_in(X3,hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X1),X2),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1258])]) ).
fof(f5707,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(c_in(X3,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X2),X0))
| ~ hBOOL(c_in(X3,hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X1),X2),X0)) )
| ~ spl0_223
| ~ spl0_349 ),
inference(superposition,[],[f2292,f5589]) ).
fof(f100751,plain,
( spl0_1257
| ~ spl0_220
| ~ spl0_349 ),
inference(avatar_split_clause,[],[f5705,f5588,f2279,f100749]) ).
fof(f100749,plain,
( spl0_1257
<=> ! [X4,X0,X3,X2,X1] :
( ~ c_Fun_Oinj__on(X3,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X2),X0,X4)
| c_Fun_Oinj__on(X3,hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X1),X2),X0,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1257])]) ).
fof(f5705,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ c_Fun_Oinj__on(X3,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X2),X0,X4)
| c_Fun_Oinj__on(X3,hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X1),X2),X0,X4) )
| ~ spl0_220
| ~ spl0_349 ),
inference(superposition,[],[f2280,f5589]) ).
fof(f100747,plain,
( spl0_1256
| ~ spl0_214
| ~ spl0_349 ),
inference(avatar_split_clause,[],[f5679,f5588,f2255,f100745]) ).
fof(f100745,plain,
( spl0_1256
<=> ! [X2,X0,X1] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X2) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X2),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X1),X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1256])]) ).
fof(f2255,plain,
( spl0_214
<=> ! [X9,X5,X0] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X5),X9) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X9),X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_214])]) ).
fof(f5679,plain,
( ! [X2,X0,X1] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X2) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X2),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X1),X2))
| ~ spl0_214
| ~ spl0_349 ),
inference(superposition,[],[f5589,f2256]) ).
fof(f2256,plain,
( ! [X0,X9,X5] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X5),X9) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X9),X5)
| ~ spl0_214 ),
inference(avatar_component_clause,[],[f2255]) ).
fof(f100743,plain,
( spl0_1255
| ~ spl0_38
| ~ spl0_910
| ~ spl0_1173 ),
inference(avatar_split_clause,[],[f100697,f95244,f69980,f1179,f100740]) ).
fof(f100740,plain,
( spl0_1255
<=> c_False = hAPP(c_Complete__Lattice_OInf__class_OInf(tc_bool),hAPP(c_HOL_Ominus__class_Ominus(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1255])]) ).
fof(f95244,plain,
( spl0_1173
<=> ! [X0] :
( ~ hBOOL(X0)
| c_False = hAPP(c_Complete__Lattice_OInf__class_OInf(tc_bool),hAPP(c_HOL_Ominus__class_Ominus(tc_bool),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1173])]) ).
fof(f100697,plain,
( c_False = hAPP(c_Complete__Lattice_OInf__class_OInf(tc_bool),hAPP(c_HOL_Ominus__class_Ominus(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)))
| ~ spl0_38
| ~ spl0_910
| ~ spl0_1173 ),
inference(forward_demodulation,[],[f100494,f69981]) ).
fof(f100494,plain,
( ! [X0,X1] : c_False = hAPP(c_Complete__Lattice_OInf__class_OInf(tc_bool),hAPP(c_HOL_Ominus__class_Ominus(tc_bool),hAPP(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X1)))
| ~ spl0_38
| ~ spl0_1173 ),
inference(resolution,[],[f95245,f1180]) ).
fof(f95245,plain,
( ! [X0] :
( ~ hBOOL(X0)
| c_False = hAPP(c_Complete__Lattice_OInf__class_OInf(tc_bool),hAPP(c_HOL_Ominus__class_Ominus(tc_bool),X0)) )
| ~ spl0_1173 ),
inference(avatar_component_clause,[],[f95244]) ).
fof(f100738,plain,
( spl0_1254
| ~ spl0_252
| ~ spl0_340 ),
inference(avatar_split_clause,[],[f5415,f4949,f3077,f100736]) ).
fof(f100736,plain,
( spl0_1254
<=> ! [X2,X4,X0,X3,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Set_Oinsert(X0),X2),hAPP(hAPP(c_Set_Oinsert(X0),X1),X3))),X4))
| hBOOL(c_in(X1,X4,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1254])]) ).
fof(f5415,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Set_Oinsert(X0),X2),hAPP(hAPP(c_Set_Oinsert(X0),X1),X3))),X4))
| hBOOL(c_in(X1,X4,X0)) )
| ~ spl0_252
| ~ spl0_340 ),
inference(superposition,[],[f3078,f4950]) ).
fof(f100734,plain,
( spl0_1253
| ~ spl0_146
| ~ spl0_340 ),
inference(avatar_split_clause,[],[f5409,f4949,f1716,f100732]) ).
fof(f100732,plain,
( spl0_1253
<=> ! [X0,X3,X2,X1] : hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Set_Oinsert(X0),X2),X3)),hAPP(hAPP(c_Set_Oinsert(X0),X2),hAPP(hAPP(c_Set_Oinsert(X0),X1),X3)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1253])]) ).
fof(f5409,plain,
( ! [X2,X3,X0,X1] : hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Set_Oinsert(X0),X2),X3)),hAPP(hAPP(c_Set_Oinsert(X0),X2),hAPP(hAPP(c_Set_Oinsert(X0),X1),X3))))
| ~ spl0_146
| ~ spl0_340 ),
inference(superposition,[],[f1717,f4950]) ).
fof(f100730,plain,
( spl0_1252
| ~ spl0_252
| ~ spl0_331 ),
inference(avatar_split_clause,[],[f5119,f4912,f3077,f100728]) ).
fof(f100728,plain,
( spl0_1252
<=> ! [X4,X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Set_Oinsert(X0),X1),X2)),X3))
| hBOOL(c_in(X1,hAPP(hAPP(c_Set_Oinsert(X0),X4),X3),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1252])]) ).
fof(f4912,plain,
( spl0_331
<=> ! [X5,X4,X0,X9] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X5),X9))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X5),hAPP(hAPP(c_Set_Oinsert(X0),X4),X9))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_331])]) ).
fof(f5119,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Set_Oinsert(X0),X1),X2)),X3))
| hBOOL(c_in(X1,hAPP(hAPP(c_Set_Oinsert(X0),X4),X3),X0)) )
| ~ spl0_252
| ~ spl0_331 ),
inference(resolution,[],[f4913,f3078]) ).
fof(f4913,plain,
( ! [X0,X9,X4,X5] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X5),hAPP(hAPP(c_Set_Oinsert(X0),X4),X9)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X5),X9)) )
| ~ spl0_331 ),
inference(avatar_component_clause,[],[f4912]) ).
fof(f100726,plain,
( spl0_1251
| ~ spl0_258
| ~ spl0_331 ),
inference(avatar_split_clause,[],[f5107,f4912,f3101,f100724]) ).
fof(f100724,plain,
( spl0_1251
<=> ! [X5,X4,X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X1),X2))
| c_Fun_Oinj__on(X3,X1,X0,X4)
| ~ c_Fun_Oinj__on(X3,hAPP(hAPP(c_Set_Oinsert(X0),X5),X2),X0,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1251])]) ).
fof(f5107,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X1),X2))
| c_Fun_Oinj__on(X3,X1,X0,X4)
| ~ c_Fun_Oinj__on(X3,hAPP(hAPP(c_Set_Oinsert(X0),X5),X2),X0,X4) )
| ~ spl0_258
| ~ spl0_331 ),
inference(resolution,[],[f4913,f3102]) ).
fof(f100722,plain,
( spl0_1250
| ~ spl0_257
| ~ spl0_331 ),
inference(avatar_split_clause,[],[f5106,f4912,f3097,f100720]) ).
fof(f100720,plain,
( spl0_1250
<=> ! [X4,X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X1),X2))
| hBOOL(c_in(X3,hAPP(hAPP(c_Set_Oinsert(X0),X4),X2),X0))
| ~ hBOOL(c_in(X3,X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1250])]) ).
fof(f5106,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X1),X2))
| hBOOL(c_in(X3,hAPP(hAPP(c_Set_Oinsert(X0),X4),X2),X0))
| ~ hBOOL(c_in(X3,X1,X0)) )
| ~ spl0_257
| ~ spl0_331 ),
inference(resolution,[],[f4913,f3098]) ).
fof(f100718,plain,
( spl0_1249
| ~ spl0_251
| ~ spl0_331 ),
inference(avatar_split_clause,[],[f5103,f4912,f3073,f100716]) ).
fof(f100716,plain,
( spl0_1249
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X1),X2))
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Set_Oinsert(X0),X3),X2)),X1) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1249])]) ).
fof(f5103,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X1),X2))
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Set_Oinsert(X0),X3),X2)),X1) = X1 )
| ~ spl0_251
| ~ spl0_331 ),
inference(resolution,[],[f4913,f3074]) ).
fof(f100714,plain,
( spl0_1248
| ~ spl0_250
| ~ spl0_331 ),
inference(avatar_split_clause,[],[f5102,f4912,f3059,f100712]) ).
fof(f100712,plain,
( spl0_1248
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X1),X2))
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X1),hAPP(hAPP(c_Set_Oinsert(X0),X3),X2)) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1248])]) ).
fof(f5102,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X1),X2))
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X1),hAPP(hAPP(c_Set_Oinsert(X0),X3),X2)) = X1 )
| ~ spl0_250
| ~ spl0_331 ),
inference(resolution,[],[f4913,f3060]) ).
fof(f100710,plain,
( spl0_1247
| ~ spl0_51
| ~ spl0_325 ),
inference(avatar_split_clause,[],[f5044,f4888,f1237,f100708]) ).
fof(f100708,plain,
( spl0_1247
<=> ! [X2,X6,X4,X1,X0,X5,X3,X7] :
( ~ hBOOL(c_in(X4,X0,X5))
| ~ hBOOL(c_in(X3,X6,X7))
| hBOOL(c_in(X4,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X6,c_COMBK(X0,X1,X2),X7,tc_fun(X5,tc_bool)),X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1247])]) ).
fof(f5044,plain,
( ! [X2,X3,X0,X1,X6,X7,X4,X5] :
( ~ hBOOL(c_in(X4,X0,X5))
| ~ hBOOL(c_in(X3,X6,X7))
| hBOOL(c_in(X4,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X6,c_COMBK(X0,X1,X2),X7,tc_fun(X5,tc_bool)),X5)) )
| ~ spl0_51
| ~ spl0_325 ),
inference(superposition,[],[f4889,f1238]) ).
fof(f100706,plain,
( spl0_1246
| ~ spl0_139
| ~ spl0_309 ),
inference(avatar_split_clause,[],[f4820,f4581,f1688,f100704]) ).
fof(f100704,plain,
( spl0_1246
<=> ! [X4,X0,X3,X2,X1] :
( ~ class_HOL_Oord(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(X1,X2)),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,X0)),X4),X1),X2)))
| ~ class_Lattices_Oupper__semilattice(tc_fun(X3,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1246])]) ).
fof(f4820,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ class_HOL_Oord(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(X1,X2)),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,X0)),X4),X1),X2)))
| ~ class_Lattices_Oupper__semilattice(tc_fun(X3,X0)) )
| ~ spl0_139
| ~ spl0_309 ),
inference(resolution,[],[f4582,f1689]) ).
fof(f100702,plain,
( spl0_1245
| ~ spl0_140
| ~ spl0_309 ),
inference(avatar_split_clause,[],[f4819,f4581,f1692,f100700]) ).
fof(f100700,plain,
( spl0_1245
<=> ! [X4,X0,X3,X2,X1] :
( ~ class_HOL_Oord(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(X1,X2)),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,X0)),X4),X1),X2)))
| ~ class_Lattices_Olattice(tc_fun(X3,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1245])]) ).
fof(f1692,plain,
( spl0_140
<=> ! [X2,X0,X1] :
( ~ class_Lattices_Olattice(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_140])]) ).
fof(f4819,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ class_HOL_Oord(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(X1,X2)),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,X0)),X4),X1),X2)))
| ~ class_Lattices_Olattice(tc_fun(X3,X0)) )
| ~ spl0_140
| ~ spl0_309 ),
inference(resolution,[],[f4582,f1693]) ).
fof(f1693,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2)))
| ~ class_Lattices_Olattice(X0) )
| ~ spl0_140 ),
inference(avatar_component_clause,[],[f1692]) ).
fof(f100467,plain,
( spl0_1244
| ~ spl0_138
| ~ spl0_309 ),
inference(avatar_split_clause,[],[f4818,f4581,f1684,f100465]) ).
fof(f100465,plain,
( spl0_1244
<=> ! [X4,X0,X3,X2,X1] :
( ~ class_HOL_Oord(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(X1,X2)),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,X0)),X1),X4),X2)))
| ~ class_Lattices_Oupper__semilattice(tc_fun(X3,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1244])]) ).
fof(f1684,plain,
( spl0_138
<=> ! [X2,X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_138])]) ).
fof(f4818,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ class_HOL_Oord(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(X1,X2)),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,X0)),X1),X4),X2)))
| ~ class_Lattices_Oupper__semilattice(tc_fun(X3,X0)) )
| ~ spl0_138
| ~ spl0_309 ),
inference(resolution,[],[f4582,f1685]) ).
fof(f1685,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2)))
| ~ class_Lattices_Oupper__semilattice(X0) )
| ~ spl0_138 ),
inference(avatar_component_clause,[],[f1684]) ).
fof(f100463,plain,
( spl0_1243
| ~ spl0_141
| ~ spl0_309 ),
inference(avatar_split_clause,[],[f4817,f4581,f1696,f100461]) ).
fof(f100461,plain,
( spl0_1243
<=> ! [X4,X0,X3,X2,X1] :
( ~ class_HOL_Oord(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(X1,X2)),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,X0)),X1),X4),X2)))
| ~ class_Lattices_Olattice(tc_fun(X3,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1243])]) ).
fof(f1696,plain,
( spl0_141
<=> ! [X2,X0,X1] :
( ~ class_Lattices_Olattice(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_141])]) ).
fof(f4817,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ class_HOL_Oord(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(X1,X2)),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,X0)),X1),X4),X2)))
| ~ class_Lattices_Olattice(tc_fun(X3,X0)) )
| ~ spl0_141
| ~ spl0_309 ),
inference(resolution,[],[f4582,f1697]) ).
fof(f1697,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2)))
| ~ class_Lattices_Olattice(X0) )
| ~ spl0_141 ),
inference(avatar_component_clause,[],[f1696]) ).
fof(f100459,plain,
( spl0_1242
| ~ spl0_143
| ~ spl0_309 ),
inference(avatar_split_clause,[],[f4810,f4581,f1704,f100457]) ).
fof(f100457,plain,
( spl0_1242
<=> ! [X4,X0,X3,X2,X1] :
( ~ class_HOL_Oord(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,X0)),X2),X3),X4)),hAPP(X3,X4)))
| ~ class_Lattices_Olattice(tc_fun(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1242])]) ).
fof(f4810,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ class_HOL_Oord(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,X0)),X2),X3),X4)),hAPP(X3,X4)))
| ~ class_Lattices_Olattice(tc_fun(X1,X0)) )
| ~ spl0_143
| ~ spl0_309 ),
inference(resolution,[],[f4582,f1705]) ).
fof(f100455,plain,
( spl0_1241
| ~ spl0_144
| ~ spl0_309 ),
inference(avatar_split_clause,[],[f4809,f4581,f1708,f100453]) ).
fof(f100453,plain,
( spl0_1241
<=> ! [X4,X0,X3,X2,X1] :
( ~ class_HOL_Oord(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,X0)),X2),X3),X4)),hAPP(X3,X4)))
| ~ class_Lattices_Olower__semilattice(tc_fun(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1241])]) ).
fof(f4809,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ class_HOL_Oord(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,X0)),X2),X3),X4)),hAPP(X3,X4)))
| ~ class_Lattices_Olower__semilattice(tc_fun(X1,X0)) )
| ~ spl0_144
| ~ spl0_309 ),
inference(resolution,[],[f4582,f1709]) ).
fof(f100451,plain,
( spl0_1240
| ~ spl0_142
| ~ spl0_309 ),
inference(avatar_split_clause,[],[f4804,f4581,f1700,f100449]) ).
fof(f100449,plain,
( spl0_1240
<=> ! [X4,X0,X3,X2,X1] :
( ~ class_HOL_Oord(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,X0)),X2),X3),X4)),hAPP(X2,X4)))
| ~ class_Lattices_Olattice(tc_fun(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1240])]) ).
fof(f4804,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ class_HOL_Oord(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,X0)),X2),X3),X4)),hAPP(X2,X4)))
| ~ class_Lattices_Olattice(tc_fun(X1,X0)) )
| ~ spl0_142
| ~ spl0_309 ),
inference(resolution,[],[f4582,f1701]) ).
fof(f100447,plain,
( spl0_1239
| ~ spl0_145
| ~ spl0_309 ),
inference(avatar_split_clause,[],[f4803,f4581,f1712,f100445]) ).
fof(f100445,plain,
( spl0_1239
<=> ! [X4,X0,X3,X2,X1] :
( ~ class_HOL_Oord(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,X0)),X2),X3),X4)),hAPP(X2,X4)))
| ~ class_Lattices_Olower__semilattice(tc_fun(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1239])]) ).
fof(f4803,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ class_HOL_Oord(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,X0)),X2),X3),X4)),hAPP(X2,X4)))
| ~ class_Lattices_Olower__semilattice(tc_fun(X1,X0)) )
| ~ spl0_145
| ~ spl0_309 ),
inference(resolution,[],[f4582,f1713]) ).
fof(f100443,plain,
( spl0_1238
| ~ spl0_225
| ~ spl0_297 ),
inference(avatar_split_clause,[],[f4510,f3943,f2299,f100441]) ).
fof(f100441,plain,
( spl0_1238
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),X1),hAPP(c_Complete__Lattice_OSup__class_OSup(X0),X2)))
| ~ class_Lattices_Oupper__semilattice(X0)
| ~ hBOOL(c_in(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X3),X2,X0))
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1238])]) ).
fof(f4510,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),X1),hAPP(c_Complete__Lattice_OSup__class_OSup(X0),X2)))
| ~ class_Lattices_Oupper__semilattice(X0)
| ~ hBOOL(c_in(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X3),X2,X0))
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) )
| ~ spl0_225
| ~ spl0_297 ),
inference(resolution,[],[f3944,f2300]) ).
fof(f100439,plain,
( spl0_1237
| ~ spl0_225
| ~ spl0_296 ),
inference(avatar_split_clause,[],[f4473,f3939,f2299,f100437]) ).
fof(f100437,plain,
( spl0_1237
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),X1),hAPP(c_Complete__Lattice_OSup__class_OSup(X0),X2)))
| ~ class_Lattices_Oupper__semilattice(X0)
| ~ hBOOL(c_in(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X3),X1),X2,X0))
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1237])]) ).
fof(f4473,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),X1),hAPP(c_Complete__Lattice_OSup__class_OSup(X0),X2)))
| ~ class_Lattices_Oupper__semilattice(X0)
| ~ hBOOL(c_in(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X3),X1),X2,X0))
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) )
| ~ spl0_225
| ~ spl0_296 ),
inference(resolution,[],[f3940,f2300]) ).
fof(f100435,plain,
( spl0_1236
| ~ spl0_212
| ~ spl0_295 ),
inference(avatar_split_clause,[],[f4434,f3935,f2247,f100433]) ).
fof(f100433,plain,
( spl0_1236
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2))
| ~ class_Lattices_Oupper__semilattice(X0)
| ~ class_Lattices_Olower__semilattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X2),X3)),X1) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1236])]) ).
fof(f4434,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2))
| ~ class_Lattices_Oupper__semilattice(X0)
| ~ class_Lattices_Olower__semilattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X2),X3)),X1) = X1 )
| ~ spl0_212
| ~ spl0_295 ),
inference(resolution,[],[f3936,f2248]) ).
fof(f100431,plain,
( spl0_1235
| ~ spl0_210
| ~ spl0_295 ),
inference(avatar_split_clause,[],[f4433,f3935,f2233,f100429]) ).
fof(f100429,plain,
( spl0_1235
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2))
| ~ class_Lattices_Oupper__semilattice(X0)
| ~ class_Lattices_Olower__semilattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X2),X3)) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1235])]) ).
fof(f4433,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2))
| ~ class_Lattices_Oupper__semilattice(X0)
| ~ class_Lattices_Olower__semilattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X2),X3)) = X1 )
| ~ spl0_210
| ~ spl0_295 ),
inference(resolution,[],[f3936,f2234]) ).
fof(f100357,plain,
( spl0_1234
| ~ spl0_212
| ~ spl0_294 ),
inference(avatar_split_clause,[],[f4397,f3931,f2247,f100355]) ).
fof(f100355,plain,
( spl0_1234
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2))
| ~ class_Lattices_Oupper__semilattice(X0)
| ~ class_Lattices_Olower__semilattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X3),X2)),X1) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1234])]) ).
fof(f4397,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2))
| ~ class_Lattices_Oupper__semilattice(X0)
| ~ class_Lattices_Olower__semilattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X3),X2)),X1) = X1 )
| ~ spl0_212
| ~ spl0_294 ),
inference(resolution,[],[f3932,f2248]) ).
fof(f100353,plain,
( spl0_1233
| ~ spl0_210
| ~ spl0_294 ),
inference(avatar_split_clause,[],[f4396,f3931,f2233,f100351]) ).
fof(f100351,plain,
( spl0_1233
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2))
| ~ class_Lattices_Oupper__semilattice(X0)
| ~ class_Lattices_Olower__semilattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X3),X2)) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1233])]) ).
fof(f4396,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2))
| ~ class_Lattices_Oupper__semilattice(X0)
| ~ class_Lattices_Olower__semilattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X3),X2)) = X1 )
| ~ spl0_210
| ~ spl0_294 ),
inference(resolution,[],[f3932,f2234]) ).
fof(f100349,plain,
( spl0_1232
| ~ spl0_233
| ~ spl0_293 ),
inference(avatar_split_clause,[],[f4384,f3927,f2645,f100347]) ).
fof(f100347,plain,
( spl0_1232
<=> ! [X3,X4,X0,X5,X2,X1] :
( hBOOL(hAPP(hAPP(hAPP(c_COMBS(X3,X4,X5),c_HOL_Oord__class_Oless(X0)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X2)),X1))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X1))
| ~ class_Lattices_Oupper__semilattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1232])]) ).
fof(f4384,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( hBOOL(hAPP(hAPP(hAPP(c_COMBS(X3,X4,X5),c_HOL_Oord__class_Oless(X0)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X2)),X1))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X1))
| ~ class_Lattices_Oupper__semilattice(X0) )
| ~ spl0_233
| ~ spl0_293 ),
inference(superposition,[],[f3928,f2646]) ).
fof(f100345,plain,
( spl0_1231
| ~ spl0_233
| ~ spl0_292 ),
inference(avatar_split_clause,[],[f4356,f3915,f2645,f100343]) ).
fof(f100343,plain,
( spl0_1231
<=> ! [X3,X4,X0,X5,X2,X1] :
( hBOOL(hAPP(hAPP(hAPP(c_COMBS(X3,X4,X5),c_HOL_Oord__class_Oless(X0)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X2)),X1))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ class_Lattices_Oupper__semilattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1231])]) ).
fof(f4356,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( hBOOL(hAPP(hAPP(hAPP(c_COMBS(X3,X4,X5),c_HOL_Oord__class_Oless(X0)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X2)),X1))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ class_Lattices_Oupper__semilattice(X0) )
| ~ spl0_233
| ~ spl0_292 ),
inference(superposition,[],[f3916,f2646]) ).
fof(f100341,plain,
( spl0_1230
| ~ spl0_150
| ~ spl0_288 ),
inference(avatar_split_clause,[],[f4241,f3899,f1732,f100339]) ).
fof(f100339,plain,
( spl0_1230
<=> ! [X4,X0,X3,X2,X1] :
( ~ hBOOL(hAPP(c_fequal(X0),X1))
| ~ hBOOL(c_in(X1,X2,X3))
| hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,c_Set_Oinsert(X0),X3,tc_fun(X4,tc_bool)),c_COMBK(c_False,tc_bool,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1230])]) ).
fof(f4241,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ hBOOL(hAPP(c_fequal(X0),X1))
| ~ hBOOL(c_in(X1,X2,X3))
| hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,c_Set_Oinsert(X0),X3,tc_fun(X4,tc_bool)),c_COMBK(c_False,tc_bool,X0))) )
| ~ spl0_150
| ~ spl0_288 ),
inference(superposition,[],[f3900,f1733]) ).
fof(f100337,plain,
( spl0_1229
| ~ spl0_80
| ~ spl0_288 ),
inference(avatar_split_clause,[],[f4208,f3899,f1365,f100335]) ).
fof(f100335,plain,
( spl0_1229
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_bool),v_P),X0))
| ~ hBOOL(c_in(hAPP(c_Not,v_P),X1,X2))
| hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,c_and,X2,tc_fun(X3,tc_bool)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1229])]) ).
fof(f4208,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_bool),v_P),X0))
| ~ hBOOL(c_in(hAPP(c_Not,v_P),X1,X2))
| hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,c_and,X2,tc_fun(X3,tc_bool)),X0)) )
| ~ spl0_80
| ~ spl0_288 ),
inference(superposition,[],[f3900,f1367]) ).
fof(f100333,plain,
( spl0_1228
| ~ spl0_79
| ~ spl0_288 ),
inference(avatar_split_clause,[],[f4170,f3899,f1361,f100331]) ).
fof(f100331,plain,
( spl0_1228
<=> ! [X5,X4,X0,X3,X2,X1] :
( ~ hBOOL(hAPP(X1,X2))
| ~ hBOOL(c_in(X1,X3,X4))
| hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X1),X4,tc_fun(X5,tc_bool)),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1228])]) ).
fof(f4170,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ hBOOL(hAPP(X1,X2))
| ~ hBOOL(c_in(X1,X3,X4))
| hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X1),X4,tc_fun(X5,tc_bool)),X2)) )
| ~ spl0_79
| ~ spl0_288 ),
inference(superposition,[],[f3900,f1362]) ).
fof(f100329,plain,
( spl0_1227
| ~ spl0_152
| ~ spl0_288 ),
inference(avatar_split_clause,[],[f4147,f3899,f1794,f100327]) ).
fof(f100327,plain,
( spl0_1227
<=> ! [X5,X3,X4,X0,X6,X2,X1] :
( ~ hBOOL(c_in(X0,X1,X2))
| hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X4),X2,tc_fun(X5,tc_bool)),X6))
| ~ hBOOL(hAPP(X0,X6)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1227])]) ).
fof(f4147,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] :
( ~ hBOOL(c_in(X0,X1,X2))
| hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X4),X2,tc_fun(X5,tc_bool)),X6))
| ~ hBOOL(hAPP(X0,X6)) )
| ~ spl0_152
| ~ spl0_288 ),
inference(resolution,[],[f3900,f1795]) ).
fof(f100325,plain,
( spl0_1226
| ~ spl0_153
| ~ spl0_288 ),
inference(avatar_split_clause,[],[f4146,f3899,f1798,f100323]) ).
fof(f100323,plain,
( spl0_1226
<=> ! [X5,X3,X4,X0,X6,X2,X1] :
( ~ hBOOL(c_in(X0,X1,X2))
| hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X4),X2,tc_fun(X5,tc_bool)),X6))
| ~ hBOOL(hAPP(X4,X6)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1226])]) ).
fof(f4146,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] :
( ~ hBOOL(c_in(X0,X1,X2))
| hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X4),X2,tc_fun(X5,tc_bool)),X6))
| ~ hBOOL(hAPP(X4,X6)) )
| ~ spl0_153
| ~ spl0_288 ),
inference(resolution,[],[f3900,f1799]) ).
fof(f100321,plain,
( spl0_1225
| ~ spl0_217
| ~ spl0_287 ),
inference(avatar_split_clause,[],[f4103,f3895,f2267,f100319]) ).
fof(f100319,plain,
( spl0_1225
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2))
| ~ class_Lattices_Olower__semilattice(X0)
| ~ class_Lattices_Oupper__semilattice(X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),X1)),X2) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1225])]) ).
fof(f4103,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2))
| ~ class_Lattices_Olower__semilattice(X0)
| ~ class_Lattices_Oupper__semilattice(X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),X1)),X2) = X2 )
| ~ spl0_217
| ~ spl0_287 ),
inference(resolution,[],[f3896,f2268]) ).
fof(f100317,plain,
( spl0_1224
| ~ spl0_38
| ~ spl0_910
| ~ spl0_1172 ),
inference(avatar_split_clause,[],[f100271,f94581,f69980,f1179,f100314]) ).
fof(f100314,plain,
( spl0_1224
<=> c_False = hAPP(c_Complete__Lattice_OInf__class_OInf(tc_bool),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1224])]) ).
fof(f94581,plain,
( spl0_1172
<=> ! [X0] :
( ~ hBOOL(X0)
| c_False = hAPP(c_Complete__Lattice_OInf__class_OInf(tc_bool),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1172])]) ).
fof(f100271,plain,
( c_False = hAPP(c_Complete__Lattice_OInf__class_OInf(tc_bool),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)))
| ~ spl0_38
| ~ spl0_910
| ~ spl0_1172 ),
inference(forward_demodulation,[],[f100068,f69981]) ).
fof(f100068,plain,
( ! [X0,X1] : c_False = hAPP(c_Complete__Lattice_OInf__class_OInf(tc_bool),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X1)))
| ~ spl0_38
| ~ spl0_1172 ),
inference(resolution,[],[f94582,f1180]) ).
fof(f94582,plain,
( ! [X0] :
( ~ hBOOL(X0)
| c_False = hAPP(c_Complete__Lattice_OInf__class_OInf(tc_bool),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),X0)) )
| ~ spl0_1172 ),
inference(avatar_component_clause,[],[f94581]) ).
fof(f100312,plain,
( spl0_1223
| ~ spl0_215
| ~ spl0_287 ),
inference(avatar_split_clause,[],[f4102,f3895,f2259,f100310]) ).
fof(f100310,plain,
( spl0_1223
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2))
| ~ class_Lattices_Olower__semilattice(X0)
| ~ class_Lattices_Oupper__semilattice(X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),X1)) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1223])]) ).
fof(f4102,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2))
| ~ class_Lattices_Olower__semilattice(X0)
| ~ class_Lattices_Oupper__semilattice(X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),X1)) = X2 )
| ~ spl0_215
| ~ spl0_287 ),
inference(resolution,[],[f3896,f2260]) ).
fof(f100308,plain,
( spl0_1222
| ~ spl0_217
| ~ spl0_286 ),
inference(avatar_split_clause,[],[f4065,f3891,f2267,f100306]) ).
fof(f100306,plain,
( spl0_1222
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2))
| ~ class_Lattices_Olower__semilattice(X0)
| ~ class_Lattices_Oupper__semilattice(X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X3)),X2) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1222])]) ).
fof(f4065,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2))
| ~ class_Lattices_Olower__semilattice(X0)
| ~ class_Lattices_Oupper__semilattice(X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X3)),X2) = X2 )
| ~ spl0_217
| ~ spl0_286 ),
inference(resolution,[],[f3892,f2268]) ).
fof(f100304,plain,
( spl0_1221
| ~ spl0_215
| ~ spl0_286 ),
inference(avatar_split_clause,[],[f4064,f3891,f2259,f100302]) ).
fof(f100302,plain,
( spl0_1221
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2))
| ~ class_Lattices_Olower__semilattice(X0)
| ~ class_Lattices_Oupper__semilattice(X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X3)) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1221])]) ).
fof(f4064,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2))
| ~ class_Lattices_Olower__semilattice(X0)
| ~ class_Lattices_Oupper__semilattice(X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X3)) = X2 )
| ~ spl0_215
| ~ spl0_286 ),
inference(resolution,[],[f3892,f2260]) ).
fof(f100300,plain,
( spl0_1220
| ~ spl0_233
| ~ spl0_285 ),
inference(avatar_split_clause,[],[f4049,f3887,f2645,f100298]) ).
fof(f100298,plain,
( spl0_1220
<=> ! [X3,X4,X0,X5,X2,X1] :
( ~ hBOOL(hAPP(hAPP(hAPP(c_COMBS(X3,X4,X5),c_lessequals(X0)),hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2)),X1))
| hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X1))
| ~ class_Lattices_Olower__semilattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1220])]) ).
fof(f4049,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ hBOOL(hAPP(hAPP(hAPP(c_COMBS(X3,X4,X5),c_lessequals(X0)),hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2)),X1))
| hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X1))
| ~ class_Lattices_Olower__semilattice(X0) )
| ~ spl0_233
| ~ spl0_285 ),
inference(superposition,[],[f3888,f2646]) ).
fof(f100296,plain,
( spl0_1219
| ~ spl0_218
| ~ spl0_285 ),
inference(avatar_split_clause,[],[f4033,f3887,f2271,f100294]) ).
fof(f100294,plain,
( spl0_1219
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(c_Complete__Lattice_OInf__class_OInf(X0),X1)),X2))
| ~ class_Lattices_Olower__semilattice(X0)
| ~ hBOOL(c_in(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),X2),X1,X0))
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1219])]) ).
fof(f4033,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(c_Complete__Lattice_OInf__class_OInf(X0),X1)),X2))
| ~ class_Lattices_Olower__semilattice(X0)
| ~ hBOOL(c_in(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),X2),X1,X0))
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) )
| ~ spl0_218
| ~ spl0_285 ),
inference(resolution,[],[f3888,f2272]) ).
fof(f100292,plain,
( spl0_1218
| ~ spl0_233
| ~ spl0_284 ),
inference(avatar_split_clause,[],[f4016,f3883,f2645,f100290]) ).
fof(f100290,plain,
( spl0_1218
<=> ! [X3,X4,X0,X5,X2,X1] :
( ~ hBOOL(hAPP(hAPP(hAPP(c_COMBS(X3,X4,X5),c_lessequals(X0)),hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2)),X1))
| hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2))
| ~ class_Lattices_Olower__semilattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1218])]) ).
fof(f4016,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ hBOOL(hAPP(hAPP(hAPP(c_COMBS(X3,X4,X5),c_lessequals(X0)),hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2)),X1))
| hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2))
| ~ class_Lattices_Olower__semilattice(X0) )
| ~ spl0_233
| ~ spl0_284 ),
inference(superposition,[],[f3884,f2646]) ).
fof(f100288,plain,
( spl0_1217
| ~ spl0_218
| ~ spl0_284 ),
inference(avatar_split_clause,[],[f4000,f3883,f2271,f100286]) ).
fof(f100286,plain,
( spl0_1217
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(c_Complete__Lattice_OInf__class_OInf(X0),X1)),X2))
| ~ class_Lattices_Olower__semilattice(X0)
| ~ hBOOL(c_in(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X3),X1,X0))
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1217])]) ).
fof(f4000,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(c_Complete__Lattice_OInf__class_OInf(X0),X1)),X2))
| ~ class_Lattices_Olower__semilattice(X0)
| ~ hBOOL(c_in(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X3),X1,X0))
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) )
| ~ spl0_218
| ~ spl0_284 ),
inference(resolution,[],[f3884,f2272]) ).
fof(f100284,plain,
( spl0_1216
| ~ spl0_51
| ~ spl0_233
| ~ spl0_275 ),
inference(avatar_split_clause,[],[f3836,f3652,f2645,f1237,f100282]) ).
fof(f100282,plain,
( spl0_1216
<=> ! [X5,X3,X4,X0,X6,X2,X1] : c_False = hAPP(hAPP(hAPP(c_COMBS(X3,X4,X5),hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X1)),X6),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X2),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1216])]) ).
fof(f3836,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] : c_False = hAPP(hAPP(hAPP(c_COMBS(X3,X4,X5),hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X1)),X6),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X2),X1))
| ~ spl0_51
| ~ spl0_233
| ~ spl0_275 ),
inference(forward_demodulation,[],[f3814,f1238]) ).
fof(f3814,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] : hAPP(hAPP(hAPP(c_COMBS(X3,X4,X5),hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X1)),X6),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X2),X1)) = hAPP(c_COMBK(c_False,tc_bool,X0),hAPP(X6,hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X2),X1)))
| ~ spl0_233
| ~ spl0_275 ),
inference(superposition,[],[f2646,f3653]) ).
fof(f100280,plain,
( spl0_1215
| ~ spl0_233
| ~ spl0_266 ),
inference(avatar_split_clause,[],[f3617,f3133,f2645,f100278]) ).
fof(f100278,plain,
( spl0_1215
<=> ! [X3,X4,X0,X5,X2,X1] :
( c_COMBK(c_False,tc_bool,X0) != hAPP(hAPP(hAPP(c_COMBS(X3,X4,X5),c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool))),X2),X1)
| c_COMBK(c_False,tc_bool,X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1215])]) ).
fof(f3617,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( c_COMBK(c_False,tc_bool,X0) != hAPP(hAPP(hAPP(c_COMBS(X3,X4,X5),c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool))),X2),X1)
| c_COMBK(c_False,tc_bool,X0) = X1 )
| ~ spl0_233
| ~ spl0_266 ),
inference(superposition,[],[f3134,f2646]) ).
fof(f100276,plain,
( spl0_1214
| ~ spl0_139
| ~ spl0_260 ),
inference(avatar_split_clause,[],[f3456,f3109,f1688,f100274]) ).
fof(f100274,plain,
( spl0_1214
<=> ! [X2,X0,X1] :
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2) = X2
| ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2)))
| ~ class_Lattices_Oupper__semilattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1214])]) ).
fof(f3456,plain,
( ! [X2,X0,X1] :
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2) = X2
| ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2)))
| ~ class_Lattices_Oupper__semilattice(X0) )
| ~ spl0_139
| ~ spl0_260 ),
inference(resolution,[],[f3110,f1689]) ).
fof(f100041,plain,
( spl0_1213
| ~ spl0_140
| ~ spl0_260 ),
inference(avatar_split_clause,[],[f3455,f3109,f1692,f100039]) ).
fof(f100039,plain,
( spl0_1213
<=> ! [X2,X0,X1] :
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2) = X2
| ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2)))
| ~ class_Lattices_Olattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1213])]) ).
fof(f3455,plain,
( ! [X2,X0,X1] :
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2) = X2
| ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2)))
| ~ class_Lattices_Olattice(X0) )
| ~ spl0_140
| ~ spl0_260 ),
inference(resolution,[],[f3110,f1693]) ).
fof(f100037,plain,
( spl0_1212
| ~ spl0_138
| ~ spl0_260 ),
inference(avatar_split_clause,[],[f3454,f3109,f1684,f100035]) ).
fof(f100035,plain,
( spl0_1212
<=> ! [X2,X0,X1] :
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2) = X1
| ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2)))
| ~ class_Lattices_Oupper__semilattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1212])]) ).
fof(f3454,plain,
( ! [X2,X0,X1] :
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2) = X1
| ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2)))
| ~ class_Lattices_Oupper__semilattice(X0) )
| ~ spl0_138
| ~ spl0_260 ),
inference(resolution,[],[f3110,f1685]) ).
fof(f100033,plain,
( spl0_1211
| ~ spl0_141
| ~ spl0_260 ),
inference(avatar_split_clause,[],[f3453,f3109,f1696,f100031]) ).
fof(f100031,plain,
( spl0_1211
<=> ! [X2,X0,X1] :
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2) = X1
| ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2)))
| ~ class_Lattices_Olattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1211])]) ).
fof(f3453,plain,
( ! [X2,X0,X1] :
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2) = X1
| ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2)))
| ~ class_Lattices_Olattice(X0) )
| ~ spl0_141
| ~ spl0_260 ),
inference(resolution,[],[f3110,f1697]) ).
fof(f100029,plain,
( spl0_1210
| ~ spl0_143
| ~ spl0_260 ),
inference(avatar_split_clause,[],[f3449,f3109,f1704,f100027]) ).
fof(f100027,plain,
( spl0_1210
<=> ! [X2,X0,X1] :
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X0) = X0
| ~ class_Orderings_Oorder(X1)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X0)),X0))
| ~ class_Lattices_Olattice(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1210])]) ).
fof(f3449,plain,
( ! [X2,X0,X1] :
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X0) = X0
| ~ class_Orderings_Oorder(X1)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X0)),X0))
| ~ class_Lattices_Olattice(X1) )
| ~ spl0_143
| ~ spl0_260 ),
inference(resolution,[],[f3110,f1705]) ).
fof(f100025,plain,
( spl0_1209
| ~ spl0_144
| ~ spl0_260 ),
inference(avatar_split_clause,[],[f3448,f3109,f1708,f100023]) ).
fof(f100023,plain,
( spl0_1209
<=> ! [X2,X0,X1] :
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X0) = X0
| ~ class_Orderings_Oorder(X1)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X0)),X0))
| ~ class_Lattices_Olower__semilattice(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1209])]) ).
fof(f3448,plain,
( ! [X2,X0,X1] :
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X0) = X0
| ~ class_Orderings_Oorder(X1)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X0)),X0))
| ~ class_Lattices_Olower__semilattice(X1) )
| ~ spl0_144
| ~ spl0_260 ),
inference(resolution,[],[f3110,f1709]) ).
fof(f100021,plain,
( spl0_1208
| ~ spl0_142
| ~ spl0_260 ),
inference(avatar_split_clause,[],[f3443,f3109,f1700,f100019]) ).
fof(f100019,plain,
( spl0_1208
<=> ! [X2,X0,X1] :
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X0),X2) = X0
| ~ class_Orderings_Oorder(X1)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X0),X2)),X0))
| ~ class_Lattices_Olattice(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1208])]) ).
fof(f3443,plain,
( ! [X2,X0,X1] :
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X0),X2) = X0
| ~ class_Orderings_Oorder(X1)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X0),X2)),X0))
| ~ class_Lattices_Olattice(X1) )
| ~ spl0_142
| ~ spl0_260 ),
inference(resolution,[],[f3110,f1701]) ).
fof(f100017,plain,
( spl0_1207
| ~ spl0_145
| ~ spl0_260 ),
inference(avatar_split_clause,[],[f3442,f3109,f1712,f100015]) ).
fof(f100015,plain,
( spl0_1207
<=> ! [X2,X0,X1] :
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X0),X2) = X0
| ~ class_Orderings_Oorder(X1)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X0),X2)),X0))
| ~ class_Lattices_Olower__semilattice(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1207])]) ).
fof(f3442,plain,
( ! [X2,X0,X1] :
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X0),X2) = X0
| ~ class_Orderings_Oorder(X1)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X0),X2)),X0))
| ~ class_Lattices_Olower__semilattice(X1) )
| ~ spl0_145
| ~ spl0_260 ),
inference(resolution,[],[f3110,f1713]) ).
fof(f100013,plain,
( spl0_1206
| ~ spl0_185
| ~ spl0_255 ),
inference(avatar_split_clause,[],[f3351,f3089,f2005,f100011]) ).
fof(f100011,plain,
( spl0_1206
<=> ! [X2,X0,X1] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X2) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X2)),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1206])]) ).
fof(f3351,plain,
( ! [X2,X0,X1] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X2) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X2)),X1)
| ~ spl0_185
| ~ spl0_255 ),
inference(resolution,[],[f3090,f2006]) ).
fof(f100009,plain,
( spl0_1205
| ~ spl0_184
| ~ spl0_255 ),
inference(avatar_split_clause,[],[f3350,f3089,f2001,f100007]) ).
fof(f100007,plain,
( spl0_1205
<=> ! [X2,X0,X1] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X2) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X2)),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1205])]) ).
fof(f3350,plain,
( ! [X2,X0,X1] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X2) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X2)),X2)
| ~ spl0_184
| ~ spl0_255 ),
inference(resolution,[],[f3090,f2002]) ).
fof(f100005,plain,
( spl0_1204
| ~ spl0_184
| ~ spl0_254 ),
inference(avatar_split_clause,[],[f3324,f3085,f2001,f100003]) ).
fof(f100003,plain,
( spl0_1204
<=> ! [X2,X0,X1] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X2),X1) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X2),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1204])]) ).
fof(f3324,plain,
( ! [X2,X0,X1] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X2),X1) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X2),X1))
| ~ spl0_184
| ~ spl0_254 ),
inference(resolution,[],[f3086,f2002]) ).
fof(f99916,plain,
( spl0_1203
| ~ spl0_139
| ~ spl0_253 ),
inference(avatar_split_clause,[],[f3300,f3081,f1688,f99914]) ).
fof(f99914,plain,
( spl0_1203
<=> ! [X2,X0,X1] :
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2) = X2
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2)),X2))
| ~ class_Orderings_Oorder(X0)
| ~ class_Lattices_Oupper__semilattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1203])]) ).
fof(f3300,plain,
( ! [X2,X0,X1] :
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2) = X2
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2)),X2))
| ~ class_Orderings_Oorder(X0)
| ~ class_Lattices_Oupper__semilattice(X0) )
| ~ spl0_139
| ~ spl0_253 ),
inference(resolution,[],[f3082,f1689]) ).
fof(f99912,plain,
( spl0_1202
| ~ spl0_140
| ~ spl0_253 ),
inference(avatar_split_clause,[],[f3299,f3081,f1692,f99910]) ).
fof(f99910,plain,
( spl0_1202
<=> ! [X2,X0,X1] :
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2) = X2
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2)),X2))
| ~ class_Orderings_Oorder(X0)
| ~ class_Lattices_Olattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1202])]) ).
fof(f3299,plain,
( ! [X2,X0,X1] :
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2) = X2
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2)),X2))
| ~ class_Orderings_Oorder(X0)
| ~ class_Lattices_Olattice(X0) )
| ~ spl0_140
| ~ spl0_253 ),
inference(resolution,[],[f3082,f1693]) ).
fof(f99908,plain,
( spl0_1201
| ~ spl0_138
| ~ spl0_253 ),
inference(avatar_split_clause,[],[f3298,f3081,f1684,f99906]) ).
fof(f99906,plain,
( spl0_1201
<=> ! [X2,X0,X1] :
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2) = X1
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2)),X1))
| ~ class_Orderings_Oorder(X0)
| ~ class_Lattices_Oupper__semilattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1201])]) ).
fof(f3298,plain,
( ! [X2,X0,X1] :
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2) = X1
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2)),X1))
| ~ class_Orderings_Oorder(X0)
| ~ class_Lattices_Oupper__semilattice(X0) )
| ~ spl0_138
| ~ spl0_253 ),
inference(resolution,[],[f3082,f1685]) ).
fof(f99904,plain,
( spl0_1200
| ~ spl0_141
| ~ spl0_253 ),
inference(avatar_split_clause,[],[f3297,f3081,f1696,f99902]) ).
fof(f99902,plain,
( spl0_1200
<=> ! [X2,X0,X1] :
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2) = X1
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2)),X1))
| ~ class_Orderings_Oorder(X0)
| ~ class_Lattices_Olattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1200])]) ).
fof(f3297,plain,
( ! [X2,X0,X1] :
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2) = X1
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2)),X1))
| ~ class_Orderings_Oorder(X0)
| ~ class_Lattices_Olattice(X0) )
| ~ spl0_141
| ~ spl0_253 ),
inference(resolution,[],[f3082,f1697]) ).
fof(f99900,plain,
( spl0_1199
| ~ spl0_143
| ~ spl0_253 ),
inference(avatar_split_clause,[],[f3293,f3081,f1704,f99898]) ).
fof(f99898,plain,
( spl0_1199
<=> ! [X2,X0,X1] :
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X0) = X0
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X0)))
| ~ class_Orderings_Oorder(X1)
| ~ class_Lattices_Olattice(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1199])]) ).
fof(f3293,plain,
( ! [X2,X0,X1] :
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X0) = X0
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X0)))
| ~ class_Orderings_Oorder(X1)
| ~ class_Lattices_Olattice(X1) )
| ~ spl0_143
| ~ spl0_253 ),
inference(resolution,[],[f3082,f1705]) ).
fof(f99896,plain,
( spl0_1198
| ~ spl0_144
| ~ spl0_253 ),
inference(avatar_split_clause,[],[f3292,f3081,f1708,f99894]) ).
fof(f99894,plain,
( spl0_1198
<=> ! [X2,X0,X1] :
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X0) = X0
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X0)))
| ~ class_Orderings_Oorder(X1)
| ~ class_Lattices_Olower__semilattice(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1198])]) ).
fof(f3292,plain,
( ! [X2,X0,X1] :
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X0) = X0
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X0)))
| ~ class_Orderings_Oorder(X1)
| ~ class_Lattices_Olower__semilattice(X1) )
| ~ spl0_144
| ~ spl0_253 ),
inference(resolution,[],[f3082,f1709]) ).
fof(f99892,plain,
( spl0_1197
| ~ spl0_142
| ~ spl0_253 ),
inference(avatar_split_clause,[],[f3287,f3081,f1700,f99890]) ).
fof(f99890,plain,
( spl0_1197
<=> ! [X2,X0,X1] :
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X0),X2) = X0
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X0),X2)))
| ~ class_Orderings_Oorder(X1)
| ~ class_Lattices_Olattice(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1197])]) ).
fof(f3287,plain,
( ! [X2,X0,X1] :
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X0),X2) = X0
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X0),X2)))
| ~ class_Orderings_Oorder(X1)
| ~ class_Lattices_Olattice(X1) )
| ~ spl0_142
| ~ spl0_253 ),
inference(resolution,[],[f3082,f1701]) ).
fof(f99888,plain,
( spl0_1196
| ~ spl0_145
| ~ spl0_253 ),
inference(avatar_split_clause,[],[f3286,f3081,f1712,f99886]) ).
fof(f99886,plain,
( spl0_1196
<=> ! [X2,X0,X1] :
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X0),X2) = X0
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X0),X2)))
| ~ class_Orderings_Oorder(X1)
| ~ class_Lattices_Olower__semilattice(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1196])]) ).
fof(f3286,plain,
( ! [X2,X0,X1] :
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X0),X2) = X0
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X0),X2)))
| ~ class_Orderings_Oorder(X1)
| ~ class_Lattices_Olower__semilattice(X1) )
| ~ spl0_145
| ~ spl0_253 ),
inference(resolution,[],[f3082,f1713]) ).
fof(f99884,plain,
( spl0_1195
| ~ spl0_233
| ~ spl0_252 ),
inference(avatar_split_clause,[],[f3277,f3077,f2645,f99882]) ).
fof(f99882,plain,
( spl0_1195
<=> ! [X5,X3,X4,X0,X6,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),hAPP(hAPP(hAPP(c_COMBS(X3,X4,X5),c_Set_Oinsert(X0)),X2),X1)),X6))
| hBOOL(c_in(X1,X6,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1195])]) ).
fof(f3277,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),hAPP(hAPP(hAPP(c_COMBS(X3,X4,X5),c_Set_Oinsert(X0)),X2),X1)),X6))
| hBOOL(c_in(X1,X6,X0)) )
| ~ spl0_233
| ~ spl0_252 ),
inference(superposition,[],[f3078,f2646]) ).
fof(f99880,plain,
( spl0_1194
| ~ spl0_190
| ~ spl0_251 ),
inference(avatar_split_clause,[],[f3230,f3073,f2025,f99878]) ).
fof(f99878,plain,
( spl0_1194
<=> ! [X2,X0,X1] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X2),X1) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X2),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1194])]) ).
fof(f3230,plain,
( ! [X2,X0,X1] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X2),X1) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X2),X1))
| ~ spl0_190
| ~ spl0_251 ),
inference(resolution,[],[f3074,f2026]) ).
fof(f99874,plain,
( spl0_1193
| ~ spl0_186
| ~ spl0_251 ),
inference(avatar_split_clause,[],[f3227,f3073,f2009,f99872]) ).
fof(f99872,plain,
( spl0_1193
<=> ! [X2,X0,X1] : hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X1),X2) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X1),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X1),X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1193])]) ).
fof(f99870,plain,
( spl0_1192
| ~ spl0_190
| ~ spl0_250 ),
inference(avatar_split_clause,[],[f3204,f3059,f2025,f99868]) ).
fof(f99868,plain,
( spl0_1192
<=> ! [X2,X0,X1] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X1),X2) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X1),X2)),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1192])]) ).
fof(f3204,plain,
( ! [X2,X0,X1] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X1),X2) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X1),X2)),X2)
| ~ spl0_190
| ~ spl0_250 ),
inference(resolution,[],[f3060,f2026]) ).
fof(f99866,plain,
( spl0_1191
| ~ spl0_186
| ~ spl0_250 ),
inference(avatar_split_clause,[],[f3201,f3059,f2009,f99864]) ).
fof(f99864,plain,
( spl0_1191
<=> ! [X2,X0,X1] : hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X1),X2) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X1),X2)),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1191])]) ).
fof(f3201,plain,
( ! [X2,X0,X1] : hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X1),X2) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X1),X2)),X1)
| ~ spl0_186
| ~ spl0_250 ),
inference(resolution,[],[f3060,f2010]) ).
fof(f99862,plain,
( spl0_1190
| ~ spl0_189
| ~ spl0_250 ),
inference(avatar_split_clause,[],[f3198,f3059,f2021,f99860]) ).
fof(f99860,plain,
( spl0_1190
<=> ! [X2,X0,X1] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X1),X2) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X1),X2)),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1190])]) ).
fof(f3198,plain,
( ! [X2,X0,X1] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X1),X2) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X1),X2)),X1)
| ~ spl0_189
| ~ spl0_250 ),
inference(resolution,[],[f3060,f2022]) ).
fof(f99858,plain,
( spl0_1189
| ~ spl0_210
| ~ spl0_233 ),
inference(avatar_split_clause,[],[f2963,f2645,f2233,f99856]) ).
fof(f99856,plain,
( spl0_1189
<=> ! [X3,X4,X0,X5,X2,X1] :
( ~ hBOOL(hAPP(hAPP(hAPP(c_COMBS(X3,X4,X5),c_lessequals(X0)),X2),X1))
| ~ class_Lattices_Olower__semilattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),hAPP(X2,X1)) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1189])]) ).
fof(f2963,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ hBOOL(hAPP(hAPP(hAPP(c_COMBS(X3,X4,X5),c_lessequals(X0)),X2),X1))
| ~ class_Lattices_Olower__semilattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),hAPP(X2,X1)) = X1 )
| ~ spl0_210
| ~ spl0_233 ),
inference(superposition,[],[f2234,f2646]) ).
fof(f99854,plain,
( spl0_1188
| ~ spl0_212
| ~ spl0_233 ),
inference(avatar_split_clause,[],[f2962,f2645,f2247,f99852]) ).
fof(f99852,plain,
( spl0_1188
<=> ! [X3,X4,X0,X5,X2,X1] :
( ~ hBOOL(hAPP(hAPP(hAPP(c_COMBS(X3,X4,X5),c_lessequals(X0)),X2),X1))
| ~ class_Lattices_Olower__semilattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),hAPP(X2,X1)),X1) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1188])]) ).
fof(f2962,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ hBOOL(hAPP(hAPP(hAPP(c_COMBS(X3,X4,X5),c_lessequals(X0)),X2),X1))
| ~ class_Lattices_Olower__semilattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),hAPP(X2,X1)),X1) = X1 )
| ~ spl0_212
| ~ spl0_233 ),
inference(superposition,[],[f2248,f2646]) ).
fof(f99850,plain,
( spl0_1187
| ~ spl0_224
| ~ spl0_233 ),
inference(avatar_split_clause,[],[f2958,f2645,f2295,f99848]) ).
fof(f99848,plain,
( spl0_1187
<=> ! [X3,X4,X0,X6,X5,X2,X1] :
( ~ hBOOL(hAPP(hAPP(hAPP(c_COMBS(X3,X4,X5),c_lessequals(tc_fun(X0,tc_bool))),X2),X1))
| hBOOL(hAPP(hAPP(X2,X1),X6))
| ~ hBOOL(hAPP(X1,X6)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1187])]) ).
fof(f2958,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] :
( ~ hBOOL(hAPP(hAPP(hAPP(c_COMBS(X3,X4,X5),c_lessequals(tc_fun(X0,tc_bool))),X2),X1))
| hBOOL(hAPP(hAPP(X2,X1),X6))
| ~ hBOOL(hAPP(X1,X6)) )
| ~ spl0_224
| ~ spl0_233 ),
inference(superposition,[],[f2296,f2646]) ).
fof(f99846,plain,
( spl0_1186
| ~ spl0_211
| ~ spl0_233 ),
inference(avatar_split_clause,[],[f2957,f2645,f2237,f99844]) ).
fof(f99844,plain,
( spl0_1186
<=> ! [X3,X4,X0,X5,X2,X1] :
( hAPP(hAPP(hAPP(c_COMBS(X3,X4,X5),c_Lattices_Olower__semilattice__class_Oinf(X0)),X2),X1) != X1
| hBOOL(hAPP(hAPP(c_lessequals(X0),X1),hAPP(X2,X1)))
| ~ class_Lattices_Olower__semilattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1186])]) ).
fof(f2957,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( hAPP(hAPP(hAPP(c_COMBS(X3,X4,X5),c_Lattices_Olower__semilattice__class_Oinf(X0)),X2),X1) != X1
| hBOOL(hAPP(hAPP(c_lessequals(X0),X1),hAPP(X2,X1)))
| ~ class_Lattices_Olower__semilattice(X0) )
| ~ spl0_211
| ~ spl0_233 ),
inference(superposition,[],[f2238,f2646]) ).
fof(f99842,plain,
( spl0_1185
| ~ spl0_208
| ~ spl0_233 ),
inference(avatar_split_clause,[],[f2949,f2645,f2225,f99840]) ).
fof(f99840,plain,
( spl0_1185
<=> ! [X3,X4,X0,X6,X5,X2,X1] :
( ~ hBOOL(c_in(X6,hAPP(hAPP(hAPP(c_COMBS(X3,X4,X5),c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool))),X2),X1),X0))
| hBOOL(c_in(X6,hAPP(X2,X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1185])]) ).
fof(f2949,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] :
( ~ hBOOL(c_in(X6,hAPP(hAPP(hAPP(c_COMBS(X3,X4,X5),c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool))),X2),X1),X0))
| hBOOL(c_in(X6,hAPP(X2,X1),X0)) )
| ~ spl0_208
| ~ spl0_233 ),
inference(superposition,[],[f2226,f2646]) ).
fof(f99838,plain,
( spl0_1184
| ~ spl0_207
| ~ spl0_233 ),
inference(avatar_split_clause,[],[f2936,f2645,f2221,f99836]) ).
fof(f99836,plain,
( spl0_1184
<=> ! [X3,X4,X0,X6,X5,X2,X1] :
( ~ hBOOL(c_in(X6,hAPP(hAPP(hAPP(c_COMBS(X3,X4,X5),c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool))),X2),X1),X0))
| ~ hBOOL(c_in(X6,hAPP(X2,X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1184])]) ).
fof(f2936,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] :
( ~ hBOOL(c_in(X6,hAPP(hAPP(hAPP(c_COMBS(X3,X4,X5),c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool))),X2),X1),X0))
| ~ hBOOL(c_in(X6,hAPP(X2,X1),X0)) )
| ~ spl0_207
| ~ spl0_233 ),
inference(superposition,[],[f2222,f2646]) ).
fof(f99832,plain,
( spl0_1183
| ~ spl0_221
| ~ spl0_233 ),
inference(avatar_split_clause,[],[f2911,f2645,f2283,f99830]) ).
fof(f99830,plain,
( spl0_1183
<=> ! [X3,X4,X0,X6,X5,X2,X1] :
( hBOOL(c_in(X6,hAPP(hAPP(hAPP(c_COMBS(X3,X4,X5),c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool))),X2),X1),X0))
| ~ hBOOL(c_in(X6,hAPP(X2,X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1183])]) ).
fof(f2911,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] :
( hBOOL(c_in(X6,hAPP(hAPP(hAPP(c_COMBS(X3,X4,X5),c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool))),X2),X1),X0))
| ~ hBOOL(c_in(X6,hAPP(X2,X1),X0)) )
| ~ spl0_221
| ~ spl0_233 ),
inference(superposition,[],[f2284,f2646]) ).
fof(f99828,plain,
( spl0_1182
| ~ spl0_219
| ~ spl0_233 ),
inference(avatar_split_clause,[],[f2909,f2645,f2275,f99826]) ).
fof(f99826,plain,
( spl0_1182
<=> ! [X3,X4,X0,X7,X6,X5,X2,X1] :
( ~ c_Fun_Oinj__on(X6,hAPP(hAPP(hAPP(c_COMBS(X3,X4,X5),c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool))),X2),X1),X0,X7)
| c_Fun_Oinj__on(X6,hAPP(X2,X1),X0,X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1182])]) ).
fof(f2909,plain,
( ! [X2,X3,X0,X1,X6,X7,X4,X5] :
( ~ c_Fun_Oinj__on(X6,hAPP(hAPP(hAPP(c_COMBS(X3,X4,X5),c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool))),X2),X1),X0,X7)
| c_Fun_Oinj__on(X6,hAPP(X2,X1),X0,X7) )
| ~ spl0_219
| ~ spl0_233 ),
inference(superposition,[],[f2276,f2646]) ).
fof(f99824,plain,
( spl0_1181
| ~ spl0_133
| ~ spl0_233 ),
inference(avatar_split_clause,[],[f2850,f2645,f1643,f99822]) ).
fof(f99822,plain,
( spl0_1181
<=> ! [X2,X3,X4,X0,X5,X1] : hAPP(hAPP(X5,X1),X1) = hAPP(hAPP(hAPP(c_COMBS(X2,X3,X4),X5),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0))),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1181])]) ).
fof(f2850,plain,
( ! [X2,X3,X0,X1,X4,X5] : hAPP(hAPP(X5,X1),X1) = hAPP(hAPP(hAPP(c_COMBS(X2,X3,X4),X5),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0))),X1)
| ~ spl0_133
| ~ spl0_233 ),
inference(superposition,[],[f2646,f1644]) ).
fof(f99820,plain,
( spl0_1180
| ~ spl0_123
| ~ spl0_233 ),
inference(avatar_split_clause,[],[f2848,f2645,f1603,f99818]) ).
fof(f99818,plain,
( spl0_1180
<=> ! [X2,X3,X4,X0,X5,X1] : hAPP(hAPP(X5,X1),X1) = hAPP(hAPP(hAPP(c_COMBS(X2,X3,X4),X5),hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)))),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1180])]) ).
fof(f2848,plain,
( ! [X2,X3,X0,X1,X4,X5] : hAPP(hAPP(X5,X1),X1) = hAPP(hAPP(hAPP(c_COMBS(X2,X3,X4),X5),hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)))),X1)
| ~ spl0_123
| ~ spl0_233 ),
inference(superposition,[],[f2646,f1604]) ).
fof(f99816,plain,
( spl0_1179
| ~ spl0_130
| ~ spl0_233 ),
inference(avatar_split_clause,[],[f2847,f2645,f1631,f99814]) ).
fof(f99814,plain,
( spl0_1179
<=> ! [X2,X3,X4,X0,X5,X1] : hAPP(hAPP(hAPP(c_COMBS(X2,X3,X4),X5),hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X1)),X1) = hAPP(hAPP(X5,X1),c_COMBK(c_False,tc_bool,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1179])]) ).
fof(f2847,plain,
( ! [X2,X3,X0,X1,X4,X5] : hAPP(hAPP(hAPP(c_COMBS(X2,X3,X4),X5),hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X1)),X1) = hAPP(hAPP(X5,X1),c_COMBK(c_False,tc_bool,X0))
| ~ spl0_130
| ~ spl0_233 ),
inference(superposition,[],[f2646,f1632]) ).
fof(f99812,plain,
( spl0_1178
| ~ spl0_133
| ~ spl0_233 ),
inference(avatar_split_clause,[],[f2820,f2645,f1643,f99810]) ).
fof(f99810,plain,
( spl0_1178
<=> ! [X2,X3,X4,X0,X5,X1] : hAPP(X1,hAPP(X5,X1)) = hAPP(hAPP(hAPP(c_COMBS(X2,X3,X4),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0))),X5),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1178])]) ).
fof(f2820,plain,
( ! [X2,X3,X0,X1,X4,X5] : hAPP(X1,hAPP(X5,X1)) = hAPP(hAPP(hAPP(c_COMBS(X2,X3,X4),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0))),X5),X1)
| ~ spl0_133
| ~ spl0_233 ),
inference(superposition,[],[f2646,f1644]) ).
fof(f99808,plain,
( spl0_1177
| ~ spl0_123
| ~ spl0_233 ),
inference(avatar_split_clause,[],[f2818,f2645,f1603,f99806]) ).
fof(f2818,plain,
( ! [X2,X3,X0,X1,X4,X5] : hAPP(X1,hAPP(X5,X1)) = hAPP(hAPP(hAPP(c_COMBS(X2,X3,X4),hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)))),X5),X1)
| ~ spl0_123
| ~ spl0_233 ),
inference(superposition,[],[f2646,f1604]) ).
fof(f99804,plain,
( spl0_1176
| ~ spl0_224
| ~ spl0_225 ),
inference(avatar_split_clause,[],[f2617,f2299,f2295,f99802]) ).
fof(f99802,plain,
( spl0_1176
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(c_in(X0,X1,tc_fun(X2,tc_bool)))
| ~ class_Complete__Lattice_Ocomplete__lattice(tc_fun(X2,tc_bool))
| hBOOL(hAPP(hAPP(c_Complete__Lattice_OSup__class_OSup(tc_fun(X2,tc_bool)),X1),X3))
| ~ hBOOL(hAPP(X0,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1176])]) ).
fof(f2617,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(c_in(X0,X1,tc_fun(X2,tc_bool)))
| ~ class_Complete__Lattice_Ocomplete__lattice(tc_fun(X2,tc_bool))
| hBOOL(hAPP(hAPP(c_Complete__Lattice_OSup__class_OSup(tc_fun(X2,tc_bool)),X1),X3))
| ~ hBOOL(hAPP(X0,X3)) )
| ~ spl0_224
| ~ spl0_225 ),
inference(resolution,[],[f2300,f2296]) ).
fof(f99800,plain,
( spl0_1175
| ~ spl0_218
| ~ spl0_224 ),
inference(avatar_split_clause,[],[f2604,f2295,f2271,f99798]) ).
fof(f99798,plain,
( spl0_1175
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP(X0,X1))
| ~ hBOOL(hAPP(hAPP(c_Complete__Lattice_OInf__class_OInf(tc_fun(X2,tc_bool)),X3),X1))
| ~ hBOOL(c_in(X0,X3,tc_fun(X2,tc_bool)))
| ~ class_Complete__Lattice_Ocomplete__lattice(tc_fun(X2,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1175])]) ).
fof(f2604,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(hAPP(X0,X1))
| ~ hBOOL(hAPP(hAPP(c_Complete__Lattice_OInf__class_OInf(tc_fun(X2,tc_bool)),X3),X1))
| ~ hBOOL(c_in(X0,X3,tc_fun(X2,tc_bool)))
| ~ class_Complete__Lattice_Ocomplete__lattice(tc_fun(X2,tc_bool)) )
| ~ spl0_218
| ~ spl0_224 ),
inference(resolution,[],[f2296,f2272]) ).
fof(f97325,plain,
( spl0_1174
| ~ spl0_51
| ~ spl0_1125 ),
inference(avatar_split_clause,[],[f82161,f81964,f1237,f97323]) ).
fof(f82161,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(X0)
| c_False = hAPP(c_Complete__Lattice_OInf__class_OInf(tc_bool),c_COMBK(X0,X1,X2)) )
| ~ spl0_51
| ~ spl0_1125 ),
inference(superposition,[],[f81965,f1238]) ).
fof(f95246,plain,
( spl0_1173
| ~ spl0_1014
| ~ spl0_1125 ),
inference(avatar_split_clause,[],[f82094,f81964,f80983,f95244]) ).
fof(f80983,plain,
( spl0_1014
<=> ! [X0] : hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_bool),X0),c_False) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1014])]) ).
fof(f82094,plain,
( ! [X0] :
( ~ hBOOL(X0)
| c_False = hAPP(c_Complete__Lattice_OInf__class_OInf(tc_bool),hAPP(c_HOL_Ominus__class_Ominus(tc_bool),X0)) )
| ~ spl0_1014
| ~ spl0_1125 ),
inference(superposition,[],[f81965,f80984]) ).
fof(f80984,plain,
( ! [X0] : hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_bool),X0),c_False) = X0
| ~ spl0_1014 ),
inference(avatar_component_clause,[],[f80983]) ).
fof(f94583,plain,
( spl0_1172
| ~ spl0_204
| ~ spl0_1125 ),
inference(avatar_split_clause,[],[f82093,f81964,f2187,f94581]) ).
fof(f2187,plain,
( spl0_204
<=> ! [X0] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),X0),c_False) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_204])]) ).
fof(f82093,plain,
( ! [X0] :
( ~ hBOOL(X0)
| c_False = hAPP(c_Complete__Lattice_OInf__class_OInf(tc_bool),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),X0)) )
| ~ spl0_204
| ~ spl0_1125 ),
inference(superposition,[],[f81965,f2188]) ).
fof(f2188,plain,
( ! [X0] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),X0),c_False) = X0
| ~ spl0_204 ),
inference(avatar_component_clause,[],[f2187]) ).
fof(f93690,plain,
( spl0_1171
| ~ spl0_64
| ~ spl0_1125 ),
inference(avatar_split_clause,[],[f82018,f81964,f1291,f93688]) ).
fof(f93688,plain,
( spl0_1171
<=> ! [X0,X1] : c_False = hAPP(c_Complete__Lattice_OInf__class_OInf(tc_bool),hAPP(hAPP(c_Set_Oinsert(X0),c_False),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1171])]) ).
fof(f1291,plain,
( spl0_64
<=> ! [X5,X1,X0] : hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X0),X1),X5),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_64])]) ).
fof(f82018,plain,
( ! [X0,X1] : c_False = hAPP(c_Complete__Lattice_OInf__class_OInf(tc_bool),hAPP(hAPP(c_Set_Oinsert(X0),c_False),X1))
| ~ spl0_64
| ~ spl0_1125 ),
inference(resolution,[],[f81965,f1292]) ).
fof(f1292,plain,
( ! [X0,X1,X5] : hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X0),X1),X5),X1))
| ~ spl0_64 ),
inference(avatar_component_clause,[],[f1291]) ).
fof(f92697,plain,
( spl0_1170
| ~ spl0_62
| ~ spl0_1125 ),
inference(avatar_split_clause,[],[f82017,f81964,f1283,f92695]) ).
fof(f1283,plain,
( spl0_62
<=> ! [X0,X1] :
( ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_62])]) ).
fof(f82017,plain,
( ! [X0] :
( c_False = hAPP(c_Complete__Lattice_OInf__class_OInf(tc_bool),hAPP(c_lessequals(X0),c_False))
| ~ class_Orderings_Oorder(X0) )
| ~ spl0_62
| ~ spl0_1125 ),
inference(resolution,[],[f81965,f1284]) ).
fof(f1284,plain,
( ! [X0,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X1))
| ~ class_Orderings_Oorder(X0) )
| ~ spl0_62 ),
inference(avatar_component_clause,[],[f1283]) ).
fof(f91691,plain,
( spl0_1169
| ~ spl0_63
| ~ spl0_1125 ),
inference(avatar_split_clause,[],[f82016,f81964,f1287,f91689]) ).
fof(f1287,plain,
( spl0_63
<=> ! [X0,X1] :
( ~ class_Orderings_Opreorder(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_63])]) ).
fof(f82016,plain,
( ! [X0] :
( c_False = hAPP(c_Complete__Lattice_OInf__class_OInf(tc_bool),hAPP(c_lessequals(X0),c_False))
| ~ class_Orderings_Opreorder(X0) )
| ~ spl0_63
| ~ spl0_1125 ),
inference(resolution,[],[f81965,f1288]) ).
fof(f1288,plain,
( ! [X0,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X1))
| ~ class_Orderings_Opreorder(X0) )
| ~ spl0_63 ),
inference(avatar_component_clause,[],[f1287]) ).
fof(f90979,plain,
( spl0_1168
| ~ spl0_61
| ~ spl0_1125 ),
inference(avatar_split_clause,[],[f82015,f81964,f1279,f90977]) ).
fof(f90977,plain,
( spl0_1168
<=> ! [X0] : c_False = hAPP(c_Complete__Lattice_OInf__class_OInf(tc_bool),hAPP(c_lessequals(tc_fun(X0,tc_bool)),c_False)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1168])]) ).
fof(f82015,plain,
( ! [X0] : c_False = hAPP(c_Complete__Lattice_OInf__class_OInf(tc_bool),hAPP(c_lessequals(tc_fun(X0,tc_bool)),c_False))
| ~ spl0_61
| ~ spl0_1125 ),
inference(resolution,[],[f81965,f1280]) ).
fof(f89987,plain,
( spl0_1167
| ~ spl0_813
| ~ spl0_1125 ),
inference(avatar_split_clause,[],[f82008,f81964,f65760,f89985]) ).
fof(f89985,plain,
( spl0_1167
<=> ! [X0] : c_False = hAPP(c_Complete__Lattice_OInf__class_OInf(tc_bool),c_SetInterval_Oord__class_OatLeastAtMost(c_False,c_False,tc_fun(X0,tc_bool))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1167])]) ).
fof(f65760,plain,
( spl0_813
<=> ! [X0,X1] : hBOOL(hAPP(c_SetInterval_Oord__class_OatLeastAtMost(X1,X1,tc_fun(X0,tc_bool)),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_813])]) ).
fof(f82008,plain,
( ! [X0] : c_False = hAPP(c_Complete__Lattice_OInf__class_OInf(tc_bool),c_SetInterval_Oord__class_OatLeastAtMost(c_False,c_False,tc_fun(X0,tc_bool)))
| ~ spl0_813
| ~ spl0_1125 ),
inference(resolution,[],[f81965,f65761]) ).
fof(f65761,plain,
( ! [X0,X1] : hBOOL(hAPP(c_SetInterval_Oord__class_OatLeastAtMost(X1,X1,tc_fun(X0,tc_bool)),X1))
| ~ spl0_813 ),
inference(avatar_component_clause,[],[f65760]) ).
fof(f89182,plain,
( spl0_1166
| ~ spl0_559
| ~ spl0_1152 ),
inference(avatar_split_clause,[],[f82254,f82247,f15833,f89180]) ).
fof(f89180,plain,
( spl0_1166
<=> ! [X0] : c_HOL_Oord__class_Oless(tc_bool) = hAPP(hAPP(c_Set_Oinsert(X0),v_P),c_HOL_Oord__class_Oless(tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1166])]) ).
fof(f82247,plain,
( spl0_1152
<=> hBOOL(hAPP(c_HOL_Oord__class_Oless(tc_bool),v_P)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1152])]) ).
fof(f82254,plain,
( ! [X0] : c_HOL_Oord__class_Oless(tc_bool) = hAPP(hAPP(c_Set_Oinsert(X0),v_P),c_HOL_Oord__class_Oless(tc_bool))
| ~ spl0_559
| ~ spl0_1152 ),
inference(resolution,[],[f82249,f15834]) ).
fof(f82249,plain,
( hBOOL(hAPP(c_HOL_Oord__class_Oless(tc_bool),v_P))
| ~ spl0_1152 ),
inference(avatar_component_clause,[],[f82247]) ).
fof(f82415,plain,
( spl0_1165
| ~ spl0_38
| ~ spl0_1125 ),
inference(avatar_split_clause,[],[f82030,f81964,f1179,f82413]) ).
fof(f82413,plain,
( spl0_1165
<=> ! [X0] : c_False = hAPP(c_Complete__Lattice_OInf__class_OInf(tc_bool),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1165])]) ).
fof(f82030,plain,
( ! [X0] : c_False = hAPP(c_Complete__Lattice_OInf__class_OInf(tc_bool),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)))
| ~ spl0_38
| ~ spl0_1125 ),
inference(resolution,[],[f81965,f1180]) ).
fof(f82300,plain,
( spl0_1164
| ~ spl0_489
| ~ spl0_496 ),
inference(avatar_split_clause,[],[f13409,f13396,f13221,f82298]) ).
fof(f82298,plain,
( spl0_1164
<=> ! [X0,X3,X2,X1] :
( ~ c_Finite__Set_Ofinite(hAPP(c_fequal(X1),X3),X1)
| c_Finite__Set_Ofinite(X0,X2)
| ~ c_Fun_Oinj__on(c_COMBK(X3,X1,X2),X0,X2,X1)
| c_COMBK(c_False,tc_bool,X2) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1164])]) ).
fof(f13221,plain,
( spl0_489
<=> ! [X0,X5,X8,X7] :
( ~ c_Finite__Set_Ofinite(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X0,tc_fun(tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),X8),c_Set_Oinsert(X0)),X7),X8,tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0)),X8,tc_fun(X0,tc_bool)),X0)
| c_Finite__Set_Ofinite(X5,X8)
| ~ c_Fun_Oinj__on(X7,X5,X8,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_489])]) ).
fof(f13409,plain,
( ! [X2,X3,X0,X1] :
( ~ c_Finite__Set_Ofinite(hAPP(c_fequal(X1),X3),X1)
| c_Finite__Set_Ofinite(X0,X2)
| ~ c_Fun_Oinj__on(c_COMBK(X3,X1,X2),X0,X2,X1)
| c_COMBK(c_False,tc_bool,X2) = X0 )
| ~ spl0_489
| ~ spl0_496 ),
inference(superposition,[],[f13222,f13397]) ).
fof(f13222,plain,
( ! [X0,X8,X7,X5] :
( ~ c_Finite__Set_Ofinite(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X0,tc_fun(tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),X8),c_Set_Oinsert(X0)),X7),X8,tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0)),X8,tc_fun(X0,tc_bool)),X0)
| c_Finite__Set_Ofinite(X5,X8)
| ~ c_Fun_Oinj__on(X7,X5,X8,X0) )
| ~ spl0_489 ),
inference(avatar_component_clause,[],[f13221]) ).
fof(f82296,plain,
( spl0_1163
| ~ spl0_202
| ~ spl0_466 ),
inference(avatar_split_clause,[],[f10850,f10800,f2080,f82294]) ).
fof(f82294,plain,
( spl0_1163
<=> ! [X4,X0,X3,X2,X1] :
( ~ hBOOL(c_in(X4,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X1),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X3),X2)),X0))
| hBOOL(hAPP(X3,X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1163])]) ).
fof(f10850,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ hBOOL(c_in(X4,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X1),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X3),X2)),X0))
| hBOOL(hAPP(X3,X4)) )
| ~ spl0_202
| ~ spl0_466 ),
inference(superposition,[],[f2081,f10801]) ).
fof(f82292,plain,
( spl0_1162
| ~ spl0_127
| ~ spl0_437 ),
inference(avatar_split_clause,[],[f9568,f9311,f1619,f82290]) ).
fof(f82290,plain,
( spl0_1162
<=> ! [X0,X3,X2,X1] :
( c_Finite__Set_Ofinite(hAPP(hAPP(c_Set_Oinsert(X0),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X2),X3)),X0)
| ~ c_Finite__Set_Ofinite(hAPP(hAPP(c_Set_Oinsert(X0),X1),X2),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1162])]) ).
fof(f9568,plain,
( ! [X2,X3,X0,X1] :
( c_Finite__Set_Ofinite(hAPP(hAPP(c_Set_Oinsert(X0),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X2),X3)),X0)
| ~ c_Finite__Set_Ofinite(hAPP(hAPP(c_Set_Oinsert(X0),X1),X2),X0) )
| ~ spl0_127
| ~ spl0_437 ),
inference(superposition,[],[f1620,f9312]) ).
fof(f82288,plain,
( spl0_1161
| ~ spl0_126
| ~ spl0_437 ),
inference(avatar_split_clause,[],[f9567,f9311,f1615,f82286]) ).
fof(f82286,plain,
( spl0_1161
<=> ! [X0,X3,X2,X1] :
( c_Finite__Set_Ofinite(hAPP(hAPP(c_Set_Oinsert(X0),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X2),X3)),X0)
| ~ c_Finite__Set_Ofinite(hAPP(hAPP(c_Set_Oinsert(X0),X1),X3),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1161])]) ).
fof(f9567,plain,
( ! [X2,X3,X0,X1] :
( c_Finite__Set_Ofinite(hAPP(hAPP(c_Set_Oinsert(X0),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X2),X3)),X0)
| ~ c_Finite__Set_Ofinite(hAPP(hAPP(c_Set_Oinsert(X0),X1),X3),X0) )
| ~ spl0_126
| ~ spl0_437 ),
inference(superposition,[],[f1616,f9312]) ).
fof(f82284,plain,
( spl0_1160
| ~ spl0_202
| ~ spl0_426 ),
inference(avatar_split_clause,[],[f8569,f8399,f2080,f82282]) ).
fof(f82282,plain,
( spl0_1160
<=> ! [X4,X0,X3,X2,X1] :
( ~ hBOOL(c_in(X4,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X2),X3)),X0))
| hBOOL(hAPP(X3,X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1160])]) ).
fof(f8569,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ hBOOL(c_in(X4,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X2),X3)),X0))
| hBOOL(hAPP(X3,X4)) )
| ~ spl0_202
| ~ spl0_426 ),
inference(superposition,[],[f2081,f8400]) ).
fof(f82280,plain,
( spl0_1159
| ~ spl0_209
| ~ spl0_412 ),
inference(avatar_split_clause,[],[f8294,f7695,f2229,f82278]) ).
fof(f82278,plain,
( spl0_1159
<=> ! [X2,X4,X0,X3,X5,X1] :
( ~ hBOOL(c_in(X5,c_Complete__Lattice_Ocomplete__lattice__class_OINFI(hAPP(hAPP(c_Set_Oinsert(X4),X2),X3),X1,X4,tc_fun(X0,tc_bool)),X0))
| hBOOL(c_in(X5,hAPP(X1,X2),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1159])]) ).
fof(f8294,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ hBOOL(c_in(X5,c_Complete__Lattice_Ocomplete__lattice__class_OINFI(hAPP(hAPP(c_Set_Oinsert(X4),X2),X3),X1,X4,tc_fun(X0,tc_bool)),X0))
| hBOOL(c_in(X5,hAPP(X1,X2),X0)) )
| ~ spl0_209
| ~ spl0_412 ),
inference(superposition,[],[f2230,f7696]) ).
fof(f82276,plain,
( spl0_1158
| ~ spl0_126
| ~ spl0_412 ),
inference(avatar_split_clause,[],[f8286,f7695,f1615,f82274]) ).
fof(f82274,plain,
( spl0_1158
<=> ! [X2,X4,X0,X3,X1] :
( c_Finite__Set_Ofinite(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(hAPP(hAPP(c_Set_Oinsert(X4),X2),X3),X1,X4,tc_fun(X0,tc_bool)),X0)
| ~ c_Finite__Set_Ofinite(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X3,X1,X4,tc_fun(X0,tc_bool)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1158])]) ).
fof(f8286,plain,
( ! [X2,X3,X0,X1,X4] :
( c_Finite__Set_Ofinite(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(hAPP(hAPP(c_Set_Oinsert(X4),X2),X3),X1,X4,tc_fun(X0,tc_bool)),X0)
| ~ c_Finite__Set_Ofinite(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X3,X1,X4,tc_fun(X0,tc_bool)),X0) )
| ~ spl0_126
| ~ spl0_412 ),
inference(superposition,[],[f1616,f7696]) ).
fof(f82272,plain,
( spl0_1157
| ~ spl0_42
| ~ spl0_1125 ),
inference(avatar_split_clause,[],[f82014,f81964,f1198,f82270]) ).
fof(f82270,plain,
( spl0_1157
<=> ! [X0] : c_False = hAPP(c_Complete__Lattice_OInf__class_OInf(tc_bool),hAPP(c_fequal(X0),c_False)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1157])]) ).
fof(f82014,plain,
( ! [X0] : c_False = hAPP(c_Complete__Lattice_OInf__class_OInf(tc_bool),hAPP(c_fequal(X0),c_False))
| ~ spl0_42
| ~ spl0_1125 ),
inference(resolution,[],[f81965,f1199]) ).
fof(f82268,plain,
( spl0_1156
| ~ spl0_223
| ~ spl0_410 ),
inference(avatar_split_clause,[],[f8131,f7687,f2291,f82266]) ).
fof(f82266,plain,
( spl0_1156
<=> ! [X2,X4,X0,X3,X5,X1] :
( hBOOL(c_in(X5,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_Set_Oinsert(X4),X2),X3),X1,X4,tc_fun(X0,tc_bool)),X0))
| ~ hBOOL(c_in(X5,hAPP(X1,X2),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1156])]) ).
fof(f8131,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( hBOOL(c_in(X5,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_Set_Oinsert(X4),X2),X3),X1,X4,tc_fun(X0,tc_bool)),X0))
| ~ hBOOL(c_in(X5,hAPP(X1,X2),X0)) )
| ~ spl0_223
| ~ spl0_410 ),
inference(superposition,[],[f2292,f7688]) ).
fof(f82264,plain,
( spl0_1155
| ~ spl0_220
| ~ spl0_410 ),
inference(avatar_split_clause,[],[f8129,f7687,f2279,f82262]) ).
fof(f82262,plain,
( spl0_1155
<=> ! [X2,X3,X4,X0,X6,X5,X1] :
( ~ c_Fun_Oinj__on(X5,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_Set_Oinsert(X4),X2),X3),X1,X4,tc_fun(X0,tc_bool)),X0,X6)
| c_Fun_Oinj__on(X5,hAPP(X1,X2),X0,X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1155])]) ).
fof(f8129,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] :
( ~ c_Fun_Oinj__on(X5,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_Set_Oinsert(X4),X2),X3),X1,X4,tc_fun(X0,tc_bool)),X0,X6)
| c_Fun_Oinj__on(X5,hAPP(X1,X2),X0,X6) )
| ~ spl0_220
| ~ spl0_410 ),
inference(superposition,[],[f2280,f7688]) ).
fof(f82260,plain,
( spl0_1154
| ~ spl0_122
| ~ spl0_410 ),
inference(avatar_split_clause,[],[f8120,f7687,f1599,f82258]) ).
fof(f82258,plain,
( spl0_1154
<=> ! [X2,X4,X0,X3,X1] :
( ~ c_Finite__Set_Ofinite(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_Set_Oinsert(X4),X2),X3),X1,X4,tc_fun(X0,tc_bool)),X0)
| c_Finite__Set_Ofinite(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,X1,X4,tc_fun(X0,tc_bool)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1154])]) ).
fof(f8120,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ c_Finite__Set_Ofinite(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_Set_Oinsert(X4),X2),X3),X1,X4,tc_fun(X0,tc_bool)),X0)
| c_Finite__Set_Ofinite(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,X1,X4,tc_fun(X0,tc_bool)),X0) )
| ~ spl0_122
| ~ spl0_410 ),
inference(superposition,[],[f1600,f7688]) ).
fof(f82253,plain,
( spl0_1152
| spl0_1153
| ~ spl0_80
| ~ spl0_213
| ~ spl0_416 ),
inference(avatar_split_clause,[],[f7981,f7848,f2251,f1365,f82251,f82247]) ).
fof(f82251,plain,
( spl0_1153
<=> ! [X0] : c_COMBK(c_False,tc_bool,X0) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),c_and),hAPP(c_fequal(X0),hAPP(c_Not,v_P))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1153])]) ).
fof(f7981,plain,
( ! [X0] :
( c_COMBK(c_False,tc_bool,X0) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),c_and),hAPP(c_fequal(X0),hAPP(c_Not,v_P)))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(tc_bool),v_P)) )
| ~ spl0_80
| ~ spl0_213
| ~ spl0_416 ),
inference(forward_demodulation,[],[f7966,f2252]) ).
fof(f7966,plain,
( ! [X0] :
( hBOOL(hAPP(c_HOL_Oord__class_Oless(tc_bool),v_P))
| c_COMBK(c_False,tc_bool,X0) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),hAPP(c_fequal(X0),hAPP(c_Not,v_P))),c_and) )
| ~ spl0_80
| ~ spl0_416 ),
inference(superposition,[],[f7849,f1367]) ).
fof(f82245,plain,
( spl0_1151
| ~ spl0_79
| ~ spl0_416 ),
inference(avatar_split_clause,[],[f7914,f7848,f1361,f82243]) ).
fof(f82243,plain,
( spl0_1151
<=> ! [X2,X0,X1] :
( hBOOL(X1)
| c_COMBK(c_False,tc_bool,X2) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),hAPP(c_fequal(X2),X1)),hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1151])]) ).
fof(f7914,plain,
( ! [X2,X0,X1] :
( hBOOL(X1)
| c_COMBK(c_False,tc_bool,X2) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),hAPP(c_fequal(X2),X1)),hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X1)) )
| ~ spl0_79
| ~ spl0_416 ),
inference(superposition,[],[f7849,f1362]) ).
fof(f82241,plain,
( spl0_1150
| ~ spl0_68
| ~ spl0_416 ),
inference(avatar_split_clause,[],[f7913,f7848,f1316,f82239]) ).
fof(f82239,plain,
( spl0_1150
<=> ! [X2,X0,X1] :
( hBOOL(X1)
| c_COMBK(c_False,tc_bool,X2) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),hAPP(c_fequal(X2),X1)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1150])]) ).
fof(f7913,plain,
( ! [X2,X0,X1] :
( hBOOL(X1)
| c_COMBK(c_False,tc_bool,X2) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),hAPP(c_fequal(X2),X1)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1)) )
| ~ spl0_68
| ~ spl0_416 ),
inference(superposition,[],[f7849,f1317]) ).
fof(f82237,plain,
( spl0_1149
| ~ spl0_79
| ~ spl0_414 ),
inference(avatar_split_clause,[],[f7771,f7704,f1361,f82235]) ).
fof(f82235,plain,
( spl0_1149
<=> ! [X2,X0,X1] :
( ~ hBOOL(X1)
| hAPP(c_fequal(X2),X1) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),hAPP(c_fequal(X2),X1)),hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1149])]) ).
fof(f7771,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(X1)
| hAPP(c_fequal(X2),X1) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),hAPP(c_fequal(X2),X1)),hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X1)) )
| ~ spl0_79
| ~ spl0_414 ),
inference(superposition,[],[f7705,f1362]) ).
fof(f82233,plain,
( spl0_1148
| ~ spl0_68
| ~ spl0_414 ),
inference(avatar_split_clause,[],[f7770,f7704,f1316,f82231]) ).
fof(f82231,plain,
( spl0_1148
<=> ! [X2,X0,X1] :
( ~ hBOOL(X1)
| hAPP(c_fequal(X2),X1) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),hAPP(c_fequal(X2),X1)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1148])]) ).
fof(f7770,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(X1)
| hAPP(c_fequal(X2),X1) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),hAPP(c_fequal(X2),X1)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1)) )
| ~ spl0_68
| ~ spl0_414 ),
inference(superposition,[],[f7705,f1317]) ).
fof(f82229,plain,
( spl0_1147
| ~ spl0_74
| ~ spl0_414 ),
inference(avatar_split_clause,[],[f7758,f7704,f1340,f82227]) ).
fof(f82227,plain,
( spl0_1147
<=> ! [X2,X0,X1] :
( hAPP(c_fequal(X0),c_Orderings_Otop__class_Otop(X1)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),hAPP(c_fequal(X0),c_Orderings_Otop__class_Otop(X1))),hAPP(c_lessequals(X1),X2))
| ~ class_Orderings_Otop(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1147])]) ).
fof(f1340,plain,
( spl0_74
<=> ! [X0,X1] :
( ~ class_Orderings_Otop(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),X1),c_Orderings_Otop__class_Otop(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_74])]) ).
fof(f7758,plain,
( ! [X2,X0,X1] :
( hAPP(c_fequal(X0),c_Orderings_Otop__class_Otop(X1)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),hAPP(c_fequal(X0),c_Orderings_Otop__class_Otop(X1))),hAPP(c_lessequals(X1),X2))
| ~ class_Orderings_Otop(X1) )
| ~ spl0_74
| ~ spl0_414 ),
inference(resolution,[],[f7705,f1341]) ).
fof(f1341,plain,
( ! [X0,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),X1),c_Orderings_Otop__class_Otop(X0)))
| ~ class_Orderings_Otop(X0) )
| ~ spl0_74 ),
inference(avatar_component_clause,[],[f1340]) ).
fof(f82225,plain,
( spl0_1146
| ~ spl0_368
| ~ spl0_1125 ),
inference(avatar_split_clause,[],[f82009,f81964,f6067,f82222]) ).
fof(f82222,plain,
( spl0_1146
<=> c_False = hAPP(c_Complete__Lattice_OInf__class_OInf(tc_bool),hAPP(c_lessequals(tc_bool),c_False)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1146])]) ).
fof(f6067,plain,
( spl0_368
<=> ! [X0] : hBOOL(hAPP(hAPP(c_lessequals(tc_bool),c_False),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_368])]) ).
fof(f82009,plain,
( c_False = hAPP(c_Complete__Lattice_OInf__class_OInf(tc_bool),hAPP(c_lessequals(tc_bool),c_False))
| ~ spl0_368
| ~ spl0_1125 ),
inference(resolution,[],[f81965,f6068]) ).
fof(f6068,plain,
( ! [X0] : hBOOL(hAPP(hAPP(c_lessequals(tc_bool),c_False),X0))
| ~ spl0_368 ),
inference(avatar_component_clause,[],[f6067]) ).
fof(f82220,plain,
( spl0_1145
| ~ spl0_80
| ~ spl0_137
| ~ spl0_402 ),
inference(avatar_split_clause,[],[f7647,f7144,f1680,f1365,f82218]) ).
fof(f7144,plain,
( spl0_402
<=> ! [X59,X0,X1,X54,X7,X14,X8,X60,X42,X61,X13] :
( hAPP(X7,hAPP(X13,X1)) != hAPP(X59,hAPP(X60,X42))
| hAPP(c_Fun_Ocomp(X7,X13,X8,X0,X14),X1) = hAPP(c_Fun_Ocomp(X59,X60,X54,X0,X61),X42) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_402])]) ).
fof(f7647,plain,
( ! [X2,X0,X1,X6,X7,X4] :
( hAPP(c_HOL_Oord__class_Oless(tc_bool),v_P) = hAPP(c_Fun_Ocomp(X0,X1,X6,X4,X7),X2)
| hAPP(c_HOL_Oord__class_Oless(tc_bool),v_P) != hAPP(X0,hAPP(X1,X2)) )
| ~ spl0_80
| ~ spl0_137
| ~ spl0_402 ),
inference(forward_demodulation,[],[f7646,f1367]) ).
fof(f7646,plain,
( ! [X2,X0,X1,X6,X7,X4] :
( hAPP(c_and,hAPP(c_Not,v_P)) = hAPP(c_Fun_Ocomp(X0,X1,X6,X4,X7),X2)
| hAPP(c_HOL_Oord__class_Oless(tc_bool),v_P) != hAPP(X0,hAPP(X1,X2)) )
| ~ spl0_80
| ~ spl0_137
| ~ spl0_402 ),
inference(forward_demodulation,[],[f7539,f1681]) ).
fof(f7539,plain,
( ! [X2,X3,X0,X1,X6,X7,X4,X5] :
( hAPP(c_HOL_Oord__class_Oless(tc_bool),v_P) != hAPP(X0,hAPP(X1,X2))
| hAPP(c_Fun_Ocomp(c_and,c_Not,X3,X4,X5),v_P) = hAPP(c_Fun_Ocomp(X0,X1,X6,X4,X7),X2) )
| ~ spl0_80
| ~ spl0_402 ),
inference(superposition,[],[f7145,f1367]) ).
fof(f7145,plain,
( ! [X59,X0,X1,X8,X54,X7,X14,X60,X42,X61,X13] :
( hAPP(X7,hAPP(X13,X1)) != hAPP(X59,hAPP(X60,X42))
| hAPP(c_Fun_Ocomp(X7,X13,X8,X0,X14),X1) = hAPP(c_Fun_Ocomp(X59,X60,X54,X0,X61),X42) )
| ~ spl0_402 ),
inference(avatar_component_clause,[],[f7144]) ).
fof(f82216,plain,
( spl0_1144
| ~ spl0_121
| ~ spl0_391 ),
inference(avatar_split_clause,[],[f7005,f6760,f1595,f82214]) ).
fof(f82214,plain,
( spl0_1144
<=> ! [X0,X3,X2,X1] :
( ~ c_Finite__Set_Ofinite(hAPP(hAPP(c_Set_Oinsert(X0),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X2),X3)),X0)
| c_Finite__Set_Ofinite(hAPP(hAPP(c_Set_Oinsert(X0),X1),X2),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1144])]) ).
fof(f7005,plain,
( ! [X2,X3,X0,X1] :
( ~ c_Finite__Set_Ofinite(hAPP(hAPP(c_Set_Oinsert(X0),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X2),X3)),X0)
| c_Finite__Set_Ofinite(hAPP(hAPP(c_Set_Oinsert(X0),X1),X2),X0) )
| ~ spl0_121
| ~ spl0_391 ),
inference(superposition,[],[f1596,f6761]) ).
fof(f82212,plain,
( spl0_1143
| ~ spl0_68
| ~ spl0_233
| ~ spl0_390 ),
inference(avatar_split_clause,[],[f6955,f6756,f2645,f1316,f82210]) ).
fof(f82210,plain,
( spl0_1143
<=> ! [X3,X4,X0,X5,X2,X1] : hAPP(hAPP(c_Set_Oinsert(X0),X2),X1) = hAPP(hAPP(hAPP(c_COMBS(X3,X4,X5),c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool))),hAPP(c_Set_Oinsert(X0),X2)),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1143])]) ).
fof(f6955,plain,
( ! [X2,X3,X0,X1,X4,X5] : hAPP(hAPP(c_Set_Oinsert(X0),X2),X1) = hAPP(hAPP(hAPP(c_COMBS(X3,X4,X5),c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool))),hAPP(c_Set_Oinsert(X0),X2)),X1)
| ~ spl0_68
| ~ spl0_233
| ~ spl0_390 ),
inference(forward_demodulation,[],[f6836,f1317]) ).
fof(f6836,plain,
( ! [X2,X3,X0,X1,X4,X5] : hAPP(hAPP(c_Set_Oinsert(X0),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X1)) = hAPP(hAPP(hAPP(c_COMBS(X3,X4,X5),c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool))),hAPP(c_Set_Oinsert(X0),X2)),X1)
| ~ spl0_233
| ~ spl0_390 ),
inference(superposition,[],[f6757,f2646]) ).
fof(f82208,plain,
( spl0_1142
| ~ spl0_122
| ~ spl0_390 ),
inference(avatar_split_clause,[],[f6880,f6756,f1599,f82206]) ).
fof(f82206,plain,
( spl0_1142
<=> ! [X0,X3,X2,X1] :
( ~ c_Finite__Set_Ofinite(hAPP(hAPP(c_Set_Oinsert(X0),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X3)),X0)
| c_Finite__Set_Ofinite(hAPP(hAPP(c_Set_Oinsert(X0),X2),X3),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1142])]) ).
fof(f6880,plain,
( ! [X2,X3,X0,X1] :
( ~ c_Finite__Set_Ofinite(hAPP(hAPP(c_Set_Oinsert(X0),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X3)),X0)
| c_Finite__Set_Ofinite(hAPP(hAPP(c_Set_Oinsert(X0),X2),X3),X0) )
| ~ spl0_122
| ~ spl0_390 ),
inference(superposition,[],[f1600,f6757]) ).
fof(f82204,plain,
( spl0_1141
| ~ spl0_184
| ~ spl0_373 ),
inference(avatar_split_clause,[],[f6437,f6087,f2001,f82202]) ).
fof(f82202,plain,
( spl0_1141
<=> ! [X0,X3,X2,X1] : hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X3),X1)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1141])]) ).
fof(f6437,plain,
( ! [X2,X3,X0,X1] : hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X3),X1))))
| ~ spl0_184
| ~ spl0_373 ),
inference(resolution,[],[f6088,f2002]) ).
fof(f82200,plain,
( spl0_1140
| ~ spl0_184
| ~ spl0_372 ),
inference(avatar_split_clause,[],[f6399,f6083,f2001,f82198]) ).
fof(f82198,plain,
( spl0_1140
<=> ! [X0,X3,X2,X1] : hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X3)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1140])]) ).
fof(f6399,plain,
( ! [X2,X3,X0,X1] : hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X3))))
| ~ spl0_184
| ~ spl0_372 ),
inference(resolution,[],[f6084,f2002]) ).
fof(f82196,plain,
( spl0_1139
| ~ spl0_186
| ~ spl0_366 ),
inference(avatar_split_clause,[],[f6324,f6059,f2009,f82194]) ).
fof(f82194,plain,
( spl0_1139
<=> ! [X0,X3,X2,X1] : hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X1),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X2),X3))),X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1139])]) ).
fof(f6324,plain,
( ! [X2,X3,X0,X1] : hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X1),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X2),X3))),X2))
| ~ spl0_186
| ~ spl0_366 ),
inference(forward_demodulation,[],[f6300,f460]) ).
fof(f460,axiom,
! [X0,X9,X5,X12] : hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X5),X9)),X12) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X5),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X9),X12)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__Diff_0) ).
fof(f6300,plain,
( ! [X2,X3,X0,X1] : hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X1),X2)),X3)),X2))
| ~ spl0_186
| ~ spl0_366 ),
inference(resolution,[],[f6060,f2010]) ).
fof(f82192,plain,
( spl0_1138
| ~ spl0_189
| ~ spl0_366 ),
inference(avatar_split_clause,[],[f6322,f6059,f2021,f82190]) ).
fof(f82190,plain,
( spl0_1138
<=> ! [X0,X3,X2,X1] : hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X2),X3))),X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1138])]) ).
fof(f6322,plain,
( ! [X2,X3,X0,X1] : hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X2),X3))),X2))
| ~ spl0_189
| ~ spl0_366 ),
inference(forward_demodulation,[],[f6297,f109]) ).
fof(f109,axiom,
! [X0,X9,X5,X12] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X5),X9)),X12) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X5),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X9),X12)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__assoc_0) ).
fof(f6297,plain,
( ! [X2,X3,X0,X1] : hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X1),X2)),X3)),X2))
| ~ spl0_189
| ~ spl0_366 ),
inference(resolution,[],[f6060,f2022]) ).
fof(f82188,plain,
( spl0_1137
| ~ spl0_190
| ~ spl0_366 ),
inference(avatar_split_clause,[],[f6303,f6059,f2025,f82186]) ).
fof(f82186,plain,
( spl0_1137
<=> ! [X0,X3,X2,X1] : hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X2),X3))),X3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1137])]) ).
fof(f6303,plain,
( ! [X2,X3,X0,X1] : hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X2),X3))),X3))
| ~ spl0_190
| ~ spl0_366 ),
inference(resolution,[],[f6060,f2026]) ).
fof(f82184,plain,
( spl0_1136
| ~ spl0_2
| ~ spl0_362 ),
inference(avatar_split_clause,[],[f6133,f6043,f1022,f82182]) ).
fof(f82182,plain,
( spl0_1136
<=> ! [X2,X0,X1] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),X1),X2)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),X0),X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1136])]) ).
fof(f6043,plain,
( spl0_362
<=> ! [X0,X6,X2,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X2),X6)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X6)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_362])]) ).
fof(f6133,plain,
( ! [X2,X0,X1] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),X1),X2)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),X0),X2))
| ~ spl0_2
| ~ spl0_362 ),
inference(resolution,[],[f6044,f1024]) ).
fof(f1024,plain,
( class_Lattices_Oupper__semilattice(tc_bool)
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f1022]) ).
fof(f6044,plain,
( ! [X2,X0,X1,X6] :
( ~ class_Lattices_Oupper__semilattice(X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X2),X6)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X6)) )
| ~ spl0_362 ),
inference(avatar_component_clause,[],[f6043]) ).
fof(f82006,plain,
( spl0_1135
| ~ spl0_2
| ~ spl0_361 ),
inference(avatar_split_clause,[],[f6131,f6039,f1022,f82004]) ).
fof(f82004,plain,
( spl0_1135
<=> ! [X2,X0,X1] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),X0),X1)),X2) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),X1),X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1135])]) ).
fof(f6039,plain,
( spl0_361
<=> ! [X0,X6,X2,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2)),X6) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X2),X6)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_361])]) ).
fof(f6131,plain,
( ! [X2,X0,X1] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),X0),X1)),X2) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),X1),X2))
| ~ spl0_2
| ~ spl0_361 ),
inference(resolution,[],[f6040,f1024]) ).
fof(f6040,plain,
( ! [X2,X0,X1,X6] :
( ~ class_Lattices_Oupper__semilattice(X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2)),X6) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X2),X6)) )
| ~ spl0_361 ),
inference(avatar_component_clause,[],[f6039]) ).
fof(f82002,plain,
( spl0_1134
| ~ spl0_8
| ~ spl0_358 ),
inference(avatar_split_clause,[],[f6125,f6027,f1052,f82000]) ).
fof(f82000,plain,
( spl0_1134
<=> ! [X2,X0,X1] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),X1),X2)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),X0),X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1134])]) ).
fof(f1052,plain,
( spl0_8
<=> class_Lattices_Olattice(tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).
fof(f6027,plain,
( spl0_358
<=> ! [X0,X6,X2,X1] :
( ~ class_Lattices_Olattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X6)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X6)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_358])]) ).
fof(f6125,plain,
( ! [X2,X0,X1] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),X1),X2)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),X0),X2))
| ~ spl0_8
| ~ spl0_358 ),
inference(resolution,[],[f6028,f1054]) ).
fof(f1054,plain,
( class_Lattices_Olattice(tc_bool)
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f1052]) ).
fof(f6028,plain,
( ! [X2,X0,X1,X6] :
( ~ class_Lattices_Olattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X6)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X6)) )
| ~ spl0_358 ),
inference(avatar_component_clause,[],[f6027]) ).
fof(f81998,plain,
( spl0_1133
| ~ spl0_8
| ~ spl0_357 ),
inference(avatar_split_clause,[],[f6106,f6022,f1052,f81996]) ).
fof(f81996,plain,
( spl0_1133
<=> ! [X2,X0,X1] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),X0),X1)),X2) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),X1),X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1133])]) ).
fof(f6022,plain,
( spl0_357
<=> ! [X0,X6,X2,X1] :
( ~ class_Lattices_Olattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2)),X6) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X6)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_357])]) ).
fof(f6106,plain,
( ! [X2,X0,X1] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),X0),X1)),X2) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),X1),X2))
| ~ spl0_8
| ~ spl0_357 ),
inference(resolution,[],[f6023,f1054]) ).
fof(f6023,plain,
( ! [X2,X0,X1,X6] :
( ~ class_Lattices_Olattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2)),X6) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X6)) )
| ~ spl0_357 ),
inference(avatar_component_clause,[],[f6022]) ).
fof(f81994,plain,
( spl0_1132
| ~ spl0_182
| ~ spl0_352 ),
inference(avatar_split_clause,[],[f5899,f5600,f1993,f81992]) ).
fof(f81992,plain,
( spl0_1132
<=> ! [X2,X0,X1] :
( c_Finite__Set_Ofinite(X1,X0)
| ~ c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X1),X2),X0)
| ~ c_Finite__Set_Ofinite(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X1),X2),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1132])]) ).
fof(f5899,plain,
( ! [X2,X0,X1] :
( c_Finite__Set_Ofinite(X1,X0)
| ~ c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X1),X2),X0)
| ~ c_Finite__Set_Ofinite(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X1),X2),X0) )
| ~ spl0_182
| ~ spl0_352 ),
inference(superposition,[],[f1994,f5601]) ).
fof(f81990,plain,
( spl0_1131
| ~ spl0_123
| ~ spl0_352 ),
inference(avatar_split_clause,[],[f5876,f5600,f1603,f81988]) ).
fof(f81988,plain,
( spl0_1131
<=> ! [X0,X1] : c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool))),X1)),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1131])]) ).
fof(f5876,plain,
( ! [X0,X1] : c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool))),X1)),X1)
| ~ spl0_123
| ~ spl0_352 ),
inference(superposition,[],[f5601,f1604]) ).
fof(f81986,plain,
( spl0_1130
| ~ spl0_184
| ~ spl0_350 ),
inference(avatar_split_clause,[],[f5765,f5592,f2001,f81984]) ).
fof(f81984,plain,
( spl0_1130
<=> ! [X2,X0,X1] : hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X2),X1)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1130])]) ).
fof(f5765,plain,
( ! [X2,X0,X1] : hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X2),X1)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X2)))
| ~ spl0_184
| ~ spl0_350 ),
inference(superposition,[],[f2002,f5593]) ).
fof(f81982,plain,
( spl0_1129
| ~ spl0_182
| ~ spl0_350 ),
inference(avatar_split_clause,[],[f5764,f5592,f1993,f81980]) ).
fof(f81980,plain,
( spl0_1129
<=> ! [X2,X0,X1] :
( c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X2),X0)
| ~ c_Finite__Set_Ofinite(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X2),X1),X0)
| ~ c_Finite__Set_Ofinite(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1129])]) ).
fof(f5764,plain,
( ! [X2,X0,X1] :
( c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X2),X0)
| ~ c_Finite__Set_Ofinite(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X2),X1),X0)
| ~ c_Finite__Set_Ofinite(X1,X0) )
| ~ spl0_182
| ~ spl0_350 ),
inference(superposition,[],[f1994,f5593]) ).
fof(f81978,plain,
( spl0_1128
| ~ spl0_185
| ~ spl0_349 ),
inference(avatar_split_clause,[],[f5701,f5588,f2005,f81976]) ).
fof(f81976,plain,
( spl0_1128
<=> ! [X2,X0,X1] : hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X1),X2)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1128])]) ).
fof(f5701,plain,
( ! [X2,X0,X1] : hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X1),X2)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X2)))
| ~ spl0_185
| ~ spl0_349 ),
inference(superposition,[],[f2006,f5589]) ).
fof(f81974,plain,
( spl0_1127
| ~ spl0_182
| ~ spl0_349 ),
inference(avatar_split_clause,[],[f5699,f5588,f1993,f81972]) ).
fof(f81972,plain,
( spl0_1127
<=> ! [X2,X0,X1] :
( c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X2),X0)
| ~ c_Finite__Set_Ofinite(X2,X0)
| ~ c_Finite__Set_Ofinite(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X1),X2),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1127])]) ).
fof(f5699,plain,
( ! [X2,X0,X1] :
( c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X2),X0)
| ~ c_Finite__Set_Ofinite(X2,X0)
| ~ c_Finite__Set_Ofinite(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X1),X2),X0) )
| ~ spl0_182
| ~ spl0_349 ),
inference(superposition,[],[f1994,f5589]) ).
fof(f81970,plain,
( spl0_1126
| ~ spl0_224
| ~ spl0_347 ),
inference(avatar_split_clause,[],[f5620,f5570,f2295,f81968]) ).
fof(f81968,plain,
( spl0_1126
<=> ! [X3,X4,X0,X5,X2,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2))
| ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(c_SetInterval_Oord__class_OatLeastAtMost(X3,X4,X0),X5))
| ~ hBOOL(hAPP(c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X0),X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1126])]) ).
fof(f5620,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2))
| ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(c_SetInterval_Oord__class_OatLeastAtMost(X3,X4,X0),X5))
| ~ hBOOL(hAPP(c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X0),X5)) )
| ~ spl0_224
| ~ spl0_347 ),
inference(resolution,[],[f5571,f2296]) ).
fof(f81966,plain,
( spl0_1125
| ~ spl0_56
| ~ spl0_1104 ),
inference(avatar_split_clause,[],[f81897,f81850,f1258,f81964]) ).
fof(f81850,plain,
( spl0_1104
<=> ! [X0] :
( c_False = hAPP(c_Complete__Lattice_OInf__class_OInf(tc_bool),X0)
| ~ hBOOL(c_in(c_False,X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1104])]) ).
fof(f81897,plain,
( ! [X0] :
( c_False = hAPP(c_Complete__Lattice_OInf__class_OInf(tc_bool),X0)
| ~ hBOOL(hAPP(X0,c_False)) )
| ~ spl0_56
| ~ spl0_1104 ),
inference(resolution,[],[f81851,f1259]) ).
fof(f81851,plain,
( ! [X0] :
( ~ hBOOL(c_in(c_False,X0,tc_bool))
| c_False = hAPP(c_Complete__Lattice_OInf__class_OInf(tc_bool),X0) )
| ~ spl0_1104 ),
inference(avatar_component_clause,[],[f81850]) ).
fof(f81962,plain,
( spl0_1124
| ~ spl0_213
| ~ spl0_345 ),
inference(avatar_split_clause,[],[f5547,f4970,f2251,f81960]) ).
fof(f81960,plain,
( spl0_1124
<=> ! [X2,X0,X1] :
( c_COMBK(c_False,tc_bool,X0) != hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X2),X1)
| hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X1),X2) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1124])]) ).
fof(f4970,plain,
( spl0_345
<=> ! [X5,X9,X0] :
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X5),X9) != c_COMBK(c_False,tc_bool,X0)
| hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X5),X9) = X5 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_345])]) ).
fof(f5547,plain,
( ! [X2,X0,X1] :
( c_COMBK(c_False,tc_bool,X0) != hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X2),X1)
| hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X1),X2) = X1 )
| ~ spl0_213
| ~ spl0_345 ),
inference(superposition,[],[f4971,f2252]) ).
fof(f4971,plain,
( ! [X0,X9,X5] :
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X5),X9) != c_COMBK(c_False,tc_bool,X0)
| hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X5),X9) = X5 )
| ~ spl0_345 ),
inference(avatar_component_clause,[],[f4970]) ).
fof(f81958,plain,
( spl0_1123
| ~ spl0_197
| ~ spl0_341 ),
inference(avatar_split_clause,[],[f5479,f4953,f2054,f81956]) ).
fof(f81956,plain,
( spl0_1123
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2))
| ~ c_Finite__Set_Ofinite(hAPP(c_fequal(X0),X1),X0)
| ~ hBOOL(c_in(X2,hAPP(c_fequal(X0),X1),X0))
| ~ class_Lattices_Olower__semilattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1123])]) ).
fof(f2054,plain,
( spl0_197
<=> ! [X0,X7,X3] : c_The(c_Finite__Set_Ofold1Set(X7,hAPP(c_fequal(X0),X3),X0),X0) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_197])]) ).
fof(f5479,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2))
| ~ c_Finite__Set_Ofinite(hAPP(c_fequal(X0),X1),X0)
| ~ hBOOL(c_in(X2,hAPP(c_fequal(X0),X1),X0))
| ~ class_Lattices_Olower__semilattice(X0) )
| ~ spl0_197
| ~ spl0_341 ),
inference(superposition,[],[f4954,f2055]) ).
fof(f2055,plain,
( ! [X3,X0,X7] : c_The(c_Finite__Set_Ofold1Set(X7,hAPP(c_fequal(X0),X3),X0),X0) = X3
| ~ spl0_197 ),
inference(avatar_component_clause,[],[f2054]) ).
fof(f81954,plain,
( spl0_1122
| ~ spl0_129
| ~ spl0_340 ),
inference(avatar_split_clause,[],[f5408,f4949,f1627,f81952]) ).
fof(f81952,plain,
( spl0_1122
<=> ! [X2,X4,X0,X3,X1] :
( hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X0),X2),hAPP(hAPP(c_Set_Oinsert(X0),X1),X3)),X4))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X0),X2),X3),X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1122])]) ).
fof(f5408,plain,
( ! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X0),X2),hAPP(hAPP(c_Set_Oinsert(X0),X1),X3)),X4))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X0),X2),X3),X4)) )
| ~ spl0_129
| ~ spl0_340 ),
inference(superposition,[],[f1628,f4950]) ).
fof(f81950,plain,
( spl0_1121
| ~ spl0_140
| ~ spl0_339 ),
inference(avatar_split_clause,[],[f5362,f4945,f1692,f81948]) ).
fof(f81948,plain,
( spl0_1121
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ class_Orderings_Opreorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X3),X2)))
| ~ class_Lattices_Olattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1121])]) ).
fof(f5362,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ class_Orderings_Opreorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X3),X2)))
| ~ class_Lattices_Olattice(X0) )
| ~ spl0_140
| ~ spl0_339 ),
inference(resolution,[],[f4946,f1693]) ).
fof(f81946,plain,
( spl0_1120
| ~ spl0_141
| ~ spl0_339 ),
inference(avatar_split_clause,[],[f5360,f4945,f1696,f81944]) ).
fof(f81944,plain,
( spl0_1120
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ class_Orderings_Opreorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X2),X3)))
| ~ class_Lattices_Olattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1120])]) ).
fof(f5360,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ class_Orderings_Opreorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X2),X3)))
| ~ class_Lattices_Olattice(X0) )
| ~ spl0_141
| ~ spl0_339 ),
inference(resolution,[],[f4946,f1697]) ).
fof(f81942,plain,
( spl0_1119
| ~ spl0_143
| ~ spl0_339 ),
inference(avatar_split_clause,[],[f5354,f4945,f1704,f81940]) ).
fof(f81940,plain,
( spl0_1119
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X3)))
| ~ class_Orderings_Opreorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X3))
| ~ class_Lattices_Olattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1119])]) ).
fof(f5354,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X3)))
| ~ class_Orderings_Opreorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X3))
| ~ class_Lattices_Olattice(X0) )
| ~ spl0_143
| ~ spl0_339 ),
inference(resolution,[],[f4946,f1705]) ).
fof(f81938,plain,
( spl0_1118
| ~ spl0_144
| ~ spl0_339 ),
inference(avatar_split_clause,[],[f5353,f4945,f1708,f81936]) ).
fof(f81936,plain,
( spl0_1118
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X3)))
| ~ class_Orderings_Opreorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X3))
| ~ class_Lattices_Olower__semilattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1118])]) ).
fof(f5353,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X3)))
| ~ class_Orderings_Opreorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X3))
| ~ class_Lattices_Olower__semilattice(X0) )
| ~ spl0_144
| ~ spl0_339 ),
inference(resolution,[],[f4946,f1709]) ).
fof(f81934,plain,
( spl0_1117
| ~ spl0_142
| ~ spl0_339 ),
inference(avatar_split_clause,[],[f5348,f4945,f1700,f81932]) ).
fof(f81932,plain,
( spl0_1117
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X3)))
| ~ class_Orderings_Opreorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ class_Lattices_Olattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1117])]) ).
fof(f5348,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X3)))
| ~ class_Orderings_Opreorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ class_Lattices_Olattice(X0) )
| ~ spl0_142
| ~ spl0_339 ),
inference(resolution,[],[f4946,f1701]) ).
fof(f81930,plain,
( spl0_1116
| ~ spl0_145
| ~ spl0_339 ),
inference(avatar_split_clause,[],[f5347,f4945,f1712,f81928]) ).
fof(f81928,plain,
( spl0_1116
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X3)))
| ~ class_Orderings_Opreorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ class_Lattices_Olower__semilattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1116])]) ).
fof(f5347,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X3)))
| ~ class_Orderings_Opreorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ class_Lattices_Olower__semilattice(X0) )
| ~ spl0_145
| ~ spl0_339 ),
inference(resolution,[],[f4946,f1713]) ).
fof(f81926,plain,
( spl0_1115
| ~ spl0_139
| ~ spl0_338 ),
inference(avatar_split_clause,[],[f5328,f4941,f1688,f81924]) ).
fof(f81924,plain,
( spl0_1115
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2)),X3))
| ~ class_Orderings_Opreorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X2),X3))
| ~ class_Lattices_Oupper__semilattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1115])]) ).
fof(f5328,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2)),X3))
| ~ class_Orderings_Opreorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X2),X3))
| ~ class_Lattices_Oupper__semilattice(X0) )
| ~ spl0_139
| ~ spl0_338 ),
inference(resolution,[],[f4942,f1689]) ).
fof(f81892,plain,
( spl0_1114
| ~ spl0_140
| ~ spl0_338 ),
inference(avatar_split_clause,[],[f5327,f4941,f1692,f81890]) ).
fof(f81890,plain,
( spl0_1114
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2)),X3))
| ~ class_Orderings_Opreorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X2),X3))
| ~ class_Lattices_Olattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1114])]) ).
fof(f5327,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2)),X3))
| ~ class_Orderings_Opreorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X2),X3))
| ~ class_Lattices_Olattice(X0) )
| ~ spl0_140
| ~ spl0_338 ),
inference(resolution,[],[f4942,f1693]) ).
fof(f81888,plain,
( spl0_1113
| ~ spl0_138
| ~ spl0_338 ),
inference(avatar_split_clause,[],[f5326,f4941,f1684,f81886]) ).
fof(f81886,plain,
( spl0_1113
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2)),X3))
| ~ class_Orderings_Opreorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X3))
| ~ class_Lattices_Oupper__semilattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1113])]) ).
fof(f5326,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2)),X3))
| ~ class_Orderings_Opreorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X3))
| ~ class_Lattices_Oupper__semilattice(X0) )
| ~ spl0_138
| ~ spl0_338 ),
inference(resolution,[],[f4942,f1685]) ).
fof(f81884,plain,
( spl0_1112
| ~ spl0_141
| ~ spl0_338 ),
inference(avatar_split_clause,[],[f5325,f4941,f1696,f81882]) ).
fof(f81882,plain,
( spl0_1112
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2)),X3))
| ~ class_Orderings_Opreorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X3))
| ~ class_Lattices_Olattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1112])]) ).
fof(f5325,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2)),X3))
| ~ class_Orderings_Opreorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X3))
| ~ class_Lattices_Olattice(X0) )
| ~ spl0_141
| ~ spl0_338 ),
inference(resolution,[],[f4942,f1697]) ).
fof(f81880,plain,
( spl0_1111
| ~ spl0_143
| ~ spl0_338 ),
inference(avatar_split_clause,[],[f5319,f4941,f1704,f81878]) ).
fof(f81878,plain,
( spl0_1111
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ class_Orderings_Opreorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),X1)),X2))
| ~ class_Lattices_Olattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1111])]) ).
fof(f5319,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ class_Orderings_Opreorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),X1)),X2))
| ~ class_Lattices_Olattice(X0) )
| ~ spl0_143
| ~ spl0_338 ),
inference(resolution,[],[f4942,f1705]) ).
fof(f81876,plain,
( spl0_1110
| ~ spl0_142
| ~ spl0_338 ),
inference(avatar_split_clause,[],[f5313,f4941,f1700,f81874]) ).
fof(f81874,plain,
( spl0_1110
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ class_Orderings_Opreorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X3)),X2))
| ~ class_Lattices_Olattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1110])]) ).
fof(f5313,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ class_Orderings_Opreorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X3)),X2))
| ~ class_Lattices_Olattice(X0) )
| ~ spl0_142
| ~ spl0_338 ),
inference(resolution,[],[f4942,f1701]) ).
fof(f81872,plain,
( spl0_1109
| ~ spl0_140
| ~ spl0_337 ),
inference(avatar_split_clause,[],[f5282,f4937,f1692,f81870]) ).
fof(f81870,plain,
( spl0_1109
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2))
| ~ class_Orderings_Opreorder(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X3),X2)))
| ~ class_Lattices_Olattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1109])]) ).
fof(f5282,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2))
| ~ class_Orderings_Opreorder(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X3),X2)))
| ~ class_Lattices_Olattice(X0) )
| ~ spl0_140
| ~ spl0_337 ),
inference(resolution,[],[f4938,f1693]) ).
fof(f81868,plain,
( spl0_1108
| ~ spl0_141
| ~ spl0_337 ),
inference(avatar_split_clause,[],[f5280,f4937,f1696,f81866]) ).
fof(f81866,plain,
( spl0_1108
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2))
| ~ class_Orderings_Opreorder(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X2),X3)))
| ~ class_Lattices_Olattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1108])]) ).
fof(f5280,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2))
| ~ class_Orderings_Opreorder(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X2),X3)))
| ~ class_Lattices_Olattice(X0) )
| ~ spl0_141
| ~ spl0_337 ),
inference(resolution,[],[f4938,f1697]) ).
fof(f81864,plain,
( spl0_1107
| ~ spl0_143
| ~ spl0_337 ),
inference(avatar_split_clause,[],[f5274,f4937,f1704,f81862]) ).
fof(f81862,plain,
( spl0_1107
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X3)))
| ~ class_Orderings_Opreorder(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X3))
| ~ class_Lattices_Olattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1107])]) ).
fof(f5274,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X3)))
| ~ class_Orderings_Opreorder(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X3))
| ~ class_Lattices_Olattice(X0) )
| ~ spl0_143
| ~ spl0_337 ),
inference(resolution,[],[f4938,f1705]) ).
fof(f81860,plain,
( spl0_1106
| ~ spl0_142
| ~ spl0_337 ),
inference(avatar_split_clause,[],[f5268,f4937,f1700,f81858]) ).
fof(f81858,plain,
( spl0_1106
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X3)))
| ~ class_Orderings_Opreorder(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2))
| ~ class_Lattices_Olattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1106])]) ).
fof(f5268,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X3)))
| ~ class_Orderings_Opreorder(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2))
| ~ class_Lattices_Olattice(X0) )
| ~ spl0_142
| ~ spl0_337 ),
inference(resolution,[],[f4938,f1701]) ).
fof(f81856,plain,
( spl0_1105
| ~ spl0_140
| ~ spl0_336 ),
inference(avatar_split_clause,[],[f5246,f4933,f1692,f81854]) ).
fof(f81854,plain,
( spl0_1105
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X3),X2)))
| ~ class_Lattices_Olattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1105])]) ).
fof(f5246,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X3),X2)))
| ~ class_Lattices_Olattice(X0) )
| ~ spl0_140
| ~ spl0_336 ),
inference(resolution,[],[f4934,f1693]) ).
fof(f81852,plain,
( ~ spl0_1
| spl0_1104
| ~ spl0_218
| ~ spl0_676 ),
inference(avatar_split_clause,[],[f18913,f18841,f2271,f81850,f1017]) ).
fof(f1017,plain,
( spl0_1
<=> class_Complete__Lattice_Ocomplete__lattice(tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).
fof(f18841,plain,
( spl0_676
<=> ! [X0] :
( c_False = X0
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_bool),X0),c_False)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_676])]) ).
fof(f18913,plain,
( ! [X0] :
( c_False = hAPP(c_Complete__Lattice_OInf__class_OInf(tc_bool),X0)
| ~ hBOOL(c_in(c_False,X0,tc_bool))
| ~ class_Complete__Lattice_Ocomplete__lattice(tc_bool) )
| ~ spl0_218
| ~ spl0_676 ),
inference(resolution,[],[f18842,f2272]) ).
fof(f18842,plain,
( ! [X0] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_bool),X0),c_False))
| c_False = X0 )
| ~ spl0_676 ),
inference(avatar_component_clause,[],[f18841]) ).
fof(f81848,plain,
( spl0_1103
| ~ spl0_141
| ~ spl0_336 ),
inference(avatar_split_clause,[],[f5244,f4933,f1696,f81846]) ).
fof(f81846,plain,
( spl0_1103
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X2),X3)))
| ~ class_Lattices_Olattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1103])]) ).
fof(f5244,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X2),X3)))
| ~ class_Lattices_Olattice(X0) )
| ~ spl0_141
| ~ spl0_336 ),
inference(resolution,[],[f4934,f1697]) ).
fof(f81844,plain,
( spl0_1102
| ~ spl0_143
| ~ spl0_336 ),
inference(avatar_split_clause,[],[f5238,f4933,f1704,f81842]) ).
fof(f81842,plain,
( spl0_1102
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X3)))
| ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X3))
| ~ class_Lattices_Olattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1102])]) ).
fof(f5238,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X3)))
| ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X3))
| ~ class_Lattices_Olattice(X0) )
| ~ spl0_143
| ~ spl0_336 ),
inference(resolution,[],[f4934,f1705]) ).
fof(f81840,plain,
( spl0_1101
| ~ spl0_144
| ~ spl0_336 ),
inference(avatar_split_clause,[],[f5237,f4933,f1708,f81838]) ).
fof(f81838,plain,
( spl0_1101
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X3)))
| ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X3))
| ~ class_Lattices_Olower__semilattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1101])]) ).
fof(f5237,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X3)))
| ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X3))
| ~ class_Lattices_Olower__semilattice(X0) )
| ~ spl0_144
| ~ spl0_336 ),
inference(resolution,[],[f4934,f1709]) ).
fof(f81836,plain,
( spl0_1100
| ~ spl0_142
| ~ spl0_336 ),
inference(avatar_split_clause,[],[f5232,f4933,f1700,f81834]) ).
fof(f81834,plain,
( spl0_1100
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X3)))
| ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ class_Lattices_Olattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1100])]) ).
fof(f5232,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X3)))
| ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ class_Lattices_Olattice(X0) )
| ~ spl0_142
| ~ spl0_336 ),
inference(resolution,[],[f4934,f1701]) ).
fof(f81832,plain,
( spl0_1099
| ~ spl0_145
| ~ spl0_336 ),
inference(avatar_split_clause,[],[f5231,f4933,f1712,f81830]) ).
fof(f81830,plain,
( spl0_1099
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X3)))
| ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ class_Lattices_Olower__semilattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1099])]) ).
fof(f5231,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X3)))
| ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ class_Lattices_Olower__semilattice(X0) )
| ~ spl0_145
| ~ spl0_336 ),
inference(resolution,[],[f4934,f1713]) ).
fof(f81828,plain,
( spl0_1098
| ~ spl0_139
| ~ spl0_335 ),
inference(avatar_split_clause,[],[f5211,f4929,f1688,f81826]) ).
fof(f81826,plain,
( spl0_1098
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2)),X3))
| ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X2),X3))
| ~ class_Lattices_Oupper__semilattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1098])]) ).
fof(f5211,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2)),X3))
| ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X2),X3))
| ~ class_Lattices_Oupper__semilattice(X0) )
| ~ spl0_139
| ~ spl0_335 ),
inference(resolution,[],[f4930,f1689]) ).
fof(f81824,plain,
( spl0_1097
| ~ spl0_140
| ~ spl0_335 ),
inference(avatar_split_clause,[],[f5210,f4929,f1692,f81822]) ).
fof(f81822,plain,
( spl0_1097
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2)),X3))
| ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X2),X3))
| ~ class_Lattices_Olattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1097])]) ).
fof(f5210,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2)),X3))
| ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X2),X3))
| ~ class_Lattices_Olattice(X0) )
| ~ spl0_140
| ~ spl0_335 ),
inference(resolution,[],[f4930,f1693]) ).
fof(f81820,plain,
( spl0_1096
| ~ spl0_138
| ~ spl0_335 ),
inference(avatar_split_clause,[],[f5209,f4929,f1684,f81818]) ).
fof(f81818,plain,
( spl0_1096
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2)),X3))
| ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X3))
| ~ class_Lattices_Oupper__semilattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1096])]) ).
fof(f5209,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2)),X3))
| ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X3))
| ~ class_Lattices_Oupper__semilattice(X0) )
| ~ spl0_138
| ~ spl0_335 ),
inference(resolution,[],[f4930,f1685]) ).
fof(f81816,plain,
( spl0_1095
| ~ spl0_141
| ~ spl0_335 ),
inference(avatar_split_clause,[],[f5208,f4929,f1696,f81814]) ).
fof(f81814,plain,
( spl0_1095
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2)),X3))
| ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X3))
| ~ class_Lattices_Olattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1095])]) ).
fof(f5208,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2)),X3))
| ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X3))
| ~ class_Lattices_Olattice(X0) )
| ~ spl0_141
| ~ spl0_335 ),
inference(resolution,[],[f4930,f1697]) ).
fof(f81812,plain,
( spl0_1094
| ~ spl0_143
| ~ spl0_335 ),
inference(avatar_split_clause,[],[f5202,f4929,f1704,f81810]) ).
fof(f81810,plain,
( spl0_1094
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),X1)),X2))
| ~ class_Lattices_Olattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1094])]) ).
fof(f5202,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),X1)),X2))
| ~ class_Lattices_Olattice(X0) )
| ~ spl0_143
| ~ spl0_335 ),
inference(resolution,[],[f4930,f1705]) ).
fof(f81772,plain,
( spl0_1093
| ~ spl0_142
| ~ spl0_335 ),
inference(avatar_split_clause,[],[f5196,f4929,f1700,f81770]) ).
fof(f81770,plain,
( spl0_1093
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X3)),X2))
| ~ class_Lattices_Olattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1093])]) ).
fof(f5196,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X3)),X2))
| ~ class_Lattices_Olattice(X0) )
| ~ spl0_142
| ~ spl0_335 ),
inference(resolution,[],[f4930,f1701]) ).
fof(f81768,plain,
( spl0_1092
| ~ spl0_140
| ~ spl0_334 ),
inference(avatar_split_clause,[],[f5174,f4925,f1692,f81766]) ).
fof(f81766,plain,
( spl0_1092
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2)),X3))
| ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),X2),X3))
| ~ class_Lattices_Olattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1092])]) ).
fof(f5174,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2)),X3))
| ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),X2),X3))
| ~ class_Lattices_Olattice(X0) )
| ~ spl0_140
| ~ spl0_334 ),
inference(resolution,[],[f4926,f1693]) ).
fof(f81764,plain,
( spl0_1091
| ~ spl0_141
| ~ spl0_334 ),
inference(avatar_split_clause,[],[f5172,f4925,f1696,f81762]) ).
fof(f81762,plain,
( spl0_1091
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2)),X3))
| ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X3))
| ~ class_Lattices_Olattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1091])]) ).
fof(f5172,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2)),X3))
| ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X3))
| ~ class_Lattices_Olattice(X0) )
| ~ spl0_141
| ~ spl0_334 ),
inference(resolution,[],[f4926,f1697]) ).
fof(f81760,plain,
( spl0_1090
| ~ spl0_143
| ~ spl0_334 ),
inference(avatar_split_clause,[],[f5166,f4925,f1704,f81758]) ).
fof(f81758,plain,
( spl0_1090
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2))
| ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),X1)),X2))
| ~ class_Lattices_Olattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1090])]) ).
fof(f5166,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2))
| ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),X1)),X2))
| ~ class_Lattices_Olattice(X0) )
| ~ spl0_143
| ~ spl0_334 ),
inference(resolution,[],[f4926,f1705]) ).
fof(f81756,plain,
( spl0_1089
| ~ spl0_142
| ~ spl0_334 ),
inference(avatar_split_clause,[],[f5160,f4925,f1700,f81754]) ).
fof(f81754,plain,
( spl0_1089
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2))
| ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X3)),X2))
| ~ class_Lattices_Olattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1089])]) ).
fof(f5160,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2))
| ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X3)),X2))
| ~ class_Lattices_Olattice(X0) )
| ~ spl0_142
| ~ spl0_334 ),
inference(resolution,[],[f4926,f1701]) ).
fof(f81752,plain,
( spl0_1088
| ~ spl0_303
| ~ spl0_332 ),
inference(avatar_split_clause,[],[f5144,f4916,f4556,f81750]) ).
fof(f81750,plain,
( spl0_1088
<=> ! [X4,X0,X3,X2,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X1),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,hAPP(c_Set_Oinsert(X0),X3),X4,tc_fun(X0,tc_bool))))
| ~ hBOOL(c_in(X1,X2,X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1088])]) ).
fof(f4916,plain,
( spl0_332
<=> ! [X5,X0,X9,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X5),X9))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Set_Oinsert(X0),X1),X5)),X9)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_332])]) ).
fof(f5144,plain,
( ! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X1),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,hAPP(c_Set_Oinsert(X0),X3),X4,tc_fun(X0,tc_bool))))
| ~ hBOOL(c_in(X1,X2,X4)) )
| ~ spl0_303
| ~ spl0_332 ),
inference(resolution,[],[f4917,f4557]) ).
fof(f4917,plain,
( ! [X0,X1,X9,X5] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Set_Oinsert(X0),X1),X5)),X9))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X5),X9)) )
| ~ spl0_332 ),
inference(avatar_component_clause,[],[f4916]) ).
fof(f81748,plain,
( spl0_1087
| ~ spl0_51
| ~ spl0_307 ),
inference(avatar_split_clause,[],[f4781,f4573,f1237,f81746]) ).
fof(f81746,plain,
( spl0_1087
<=> ! [X5,X3,X4,X0,X6,X2,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X4,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,c_COMBK(X0,X1,X2),X6,tc_fun(X4,tc_bool))),X0))
| ~ hBOOL(c_in(X3,X5,X6)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1087])]) ).
fof(f4781,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X4,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,c_COMBK(X0,X1,X2),X6,tc_fun(X4,tc_bool))),X0))
| ~ hBOOL(c_in(X3,X5,X6)) )
| ~ spl0_51
| ~ spl0_307 ),
inference(superposition,[],[f4574,f1238]) ).
fof(f81744,plain,
( spl0_1086
| ~ spl0_258
| ~ spl0_307 ),
inference(avatar_split_clause,[],[f4727,f4573,f3101,f81742]) ).
fof(f81742,plain,
( spl0_1086
<=> ! [X5,X3,X4,X0,X6,X2,X1] :
( ~ hBOOL(c_in(X0,X1,X2))
| c_Fun_Oinj__on(X3,c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,X4,X2,tc_fun(X5,tc_bool)),X5,X6)
| ~ c_Fun_Oinj__on(X3,hAPP(X4,X0),X5,X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1086])]) ).
fof(f4727,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] :
( ~ hBOOL(c_in(X0,X1,X2))
| c_Fun_Oinj__on(X3,c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,X4,X2,tc_fun(X5,tc_bool)),X5,X6)
| ~ c_Fun_Oinj__on(X3,hAPP(X4,X0),X5,X6) )
| ~ spl0_258
| ~ spl0_307 ),
inference(resolution,[],[f4574,f3102]) ).
fof(f81740,plain,
( spl0_1085
| ~ spl0_234
| ~ spl0_305 ),
inference(avatar_split_clause,[],[f4701,f4565,f2649,f81738]) ).
fof(f81738,plain,
( spl0_1085
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(c_in(X3,hAPP(hAPP(c_Set_Oinsert(X0),X1),X2),X0))
| hBOOL(c_in(X3,hAPP(c_fequal(X0),X1),X0))
| hBOOL(c_in(X3,X2,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1085])]) ).
fof(f4565,plain,
( spl0_305
<=> ! [X35,X9,X0,X5] :
( hBOOL(c_in(X35,X9,X0))
| hBOOL(c_in(X35,X5,X0))
| ~ hBOOL(c_in(X35,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X5),X9),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_305])]) ).
fof(f4701,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(c_in(X3,hAPP(hAPP(c_Set_Oinsert(X0),X1),X2),X0))
| hBOOL(c_in(X3,hAPP(c_fequal(X0),X1),X0))
| hBOOL(c_in(X3,X2,X0)) )
| ~ spl0_234
| ~ spl0_305 ),
inference(superposition,[],[f4566,f2650]) ).
fof(f4566,plain,
( ! [X0,X9,X35,X5] :
( ~ hBOOL(c_in(X35,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X5),X9),X0))
| hBOOL(c_in(X35,X5,X0))
| hBOOL(c_in(X35,X9,X0)) )
| ~ spl0_305 ),
inference(avatar_component_clause,[],[f4565]) ).
fof(f81736,plain,
( spl0_1084
| ~ spl0_51
| ~ spl0_303 ),
inference(avatar_split_clause,[],[f4683,f4556,f1237,f81734]) ).
fof(f81734,plain,
( spl0_1084
<=> ! [X5,X3,X4,X0,X6,X2,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X4,tc_bool)),X0),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,c_COMBK(X0,X1,X2),X6,tc_fun(X4,tc_bool))))
| ~ hBOOL(c_in(X3,X5,X6)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1084])]) ).
fof(f4683,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X4,tc_bool)),X0),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,c_COMBK(X0,X1,X2),X6,tc_fun(X4,tc_bool))))
| ~ hBOOL(c_in(X3,X5,X6)) )
| ~ spl0_51
| ~ spl0_303 ),
inference(superposition,[],[f4557,f1238]) ).
fof(f81731,plain,
( spl0_1083
| ~ spl0_258
| ~ spl0_303 ),
inference(avatar_split_clause,[],[f4631,f4556,f3101,f81729]) ).
fof(f81729,plain,
( spl0_1083
<=> ! [X5,X3,X4,X0,X6,X2,X1] :
( ~ hBOOL(c_in(X0,X1,X2))
| c_Fun_Oinj__on(X3,hAPP(X4,X0),X5,X6)
| ~ c_Fun_Oinj__on(X3,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,X4,X2,tc_fun(X5,tc_bool)),X5,X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1083])]) ).
fof(f4631,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] :
( ~ hBOOL(c_in(X0,X1,X2))
| c_Fun_Oinj__on(X3,hAPP(X4,X0),X5,X6)
| ~ c_Fun_Oinj__on(X3,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,X4,X2,tc_fun(X5,tc_bool)),X5,X6) )
| ~ spl0_258
| ~ spl0_303 ),
inference(resolution,[],[f4557,f3102]) ).
fof(f81727,plain,
( spl0_1082
| ~ spl0_268
| ~ spl0_297 ),
inference(avatar_split_clause,[],[f4511,f3943,f3623,f81725]) ).
fof(f81725,plain,
( spl0_1082
<=> ! [X4,X0,X3,X2,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),X1),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X3,X0)))
| ~ class_Lattices_Oupper__semilattice(X0)
| ~ hBOOL(c_in(X4,X2,X3))
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1082])]) ).
fof(f4511,plain,
( ! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),X1),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X3,X0)))
| ~ class_Lattices_Oupper__semilattice(X0)
| ~ hBOOL(c_in(X4,X2,X3))
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) )
| ~ spl0_268
| ~ spl0_297 ),
inference(resolution,[],[f3944,f3624]) ).
fof(f81723,plain,
( spl0_1081
| ~ spl0_268
| ~ spl0_296 ),
inference(avatar_split_clause,[],[f4474,f3939,f3623,f81721]) ).
fof(f81721,plain,
( spl0_1081
<=> ! [X4,X0,X3,X2,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),X1),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X3),X4,X0)))
| ~ class_Lattices_Oupper__semilattice(X0)
| ~ hBOOL(c_in(X1,X2,X4))
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1081])]) ).
fof(f4474,plain,
( ! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),X1),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X3),X4,X0)))
| ~ class_Lattices_Oupper__semilattice(X0)
| ~ hBOOL(c_in(X1,X2,X4))
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) )
| ~ spl0_268
| ~ spl0_296 ),
inference(resolution,[],[f3940,f3624]) ).
fof(f81719,plain,
( spl0_1080
| ~ spl0_183
| ~ spl0_295 ),
inference(avatar_split_clause,[],[f4432,f3935,f1997,f81717]) ).
fof(f81717,plain,
( spl0_1080
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2))
| ~ class_Lattices_Oupper__semilattice(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X2),X3)),X1))
| ~ class_Orderings_Opreorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1080])]) ).
fof(f4432,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2))
| ~ class_Lattices_Oupper__semilattice(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X2),X3)),X1))
| ~ class_Orderings_Opreorder(X0) )
| ~ spl0_183
| ~ spl0_295 ),
inference(resolution,[],[f3936,f1998]) ).
fof(f81715,plain,
( spl0_1079
| ~ spl0_183
| ~ spl0_294 ),
inference(avatar_split_clause,[],[f4395,f3931,f1997,f81713]) ).
fof(f81713,plain,
( spl0_1079
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2))
| ~ class_Lattices_Oupper__semilattice(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X3),X2)),X1))
| ~ class_Orderings_Opreorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1079])]) ).
fof(f4395,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2))
| ~ class_Lattices_Oupper__semilattice(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X3),X2)),X1))
| ~ class_Orderings_Opreorder(X0) )
| ~ spl0_183
| ~ spl0_294 ),
inference(resolution,[],[f3932,f1998]) ).
fof(f81711,plain,
( spl0_1078
| ~ spl0_187
| ~ spl0_293 ),
inference(avatar_split_clause,[],[f4368,f3927,f2013,f81709]) ).
fof(f81709,plain,
( spl0_1078
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ class_Lattices_Oupper__semilattice(X0)
| ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X3),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1078])]) ).
fof(f2013,plain,
( spl0_187
<=> ! [X2,X0,X1] :
( ~ class_Orderings_Oorder(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_187])]) ).
fof(f4368,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ class_Lattices_Oupper__semilattice(X0)
| ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X3),X2))) )
| ~ spl0_187
| ~ spl0_293 ),
inference(resolution,[],[f3928,f2014]) ).
fof(f2014,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2)) )
| ~ spl0_187 ),
inference(avatar_component_clause,[],[f2013]) ).
fof(f81707,plain,
( spl0_1077
| ~ spl0_188
| ~ spl0_293 ),
inference(avatar_split_clause,[],[f4367,f3927,f2017,f81705]) ).
fof(f81705,plain,
( spl0_1077
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ class_Lattices_Oupper__semilattice(X0)
| ~ class_Orderings_Opreorder(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X3),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1077])]) ).
fof(f2017,plain,
( spl0_188
<=> ! [X2,X0,X1] :
( ~ class_Orderings_Opreorder(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_188])]) ).
fof(f4367,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ class_Lattices_Oupper__semilattice(X0)
| ~ class_Orderings_Opreorder(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X3),X2))) )
| ~ spl0_188
| ~ spl0_293 ),
inference(resolution,[],[f3928,f2018]) ).
fof(f2018,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ class_Orderings_Opreorder(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2)) )
| ~ spl0_188 ),
inference(avatar_component_clause,[],[f2017]) ).
fof(f81703,plain,
( spl0_1076
| ~ spl0_192
| ~ spl0_293 ),
inference(avatar_split_clause,[],[f4366,f3927,f2033,f81701]) ).
fof(f81701,plain,
( spl0_1076
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ class_Lattices_Oupper__semilattice(X0)
| ~ class_Orderings_Oorder(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X3),X2)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1076])]) ).
fof(f2033,plain,
( spl0_192
<=> ! [X4,X0,X3] :
( ~ class_Orderings_Oorder(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X4),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X3),X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_192])]) ).
fof(f4366,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ class_Lattices_Oupper__semilattice(X0)
| ~ class_Orderings_Oorder(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X3),X2)),X1)) )
| ~ spl0_192
| ~ spl0_293 ),
inference(resolution,[],[f3928,f2034]) ).
fof(f2034,plain,
( ! [X3,X0,X4] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X4),X3))
| ~ class_Orderings_Oorder(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X3),X4)) )
| ~ spl0_192 ),
inference(avatar_component_clause,[],[f2033]) ).
fof(f81699,plain,
( spl0_1075
| ~ spl0_193
| ~ spl0_293 ),
inference(avatar_split_clause,[],[f4365,f3927,f2037,f81697]) ).
fof(f81697,plain,
( spl0_1075
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ class_Lattices_Oupper__semilattice(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X3),X2)),X1))
| ~ class_Orderings_Opreorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1075])]) ).
fof(f2037,plain,
( spl0_193
<=> ! [X2,X0,X1] :
( ~ class_Orderings_Opreorder(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X2),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_193])]) ).
fof(f4365,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ class_Lattices_Oupper__semilattice(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X3),X2)),X1))
| ~ class_Orderings_Opreorder(X0) )
| ~ spl0_193
| ~ spl0_293 ),
inference(resolution,[],[f3928,f2038]) ).
fof(f2038,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X2),X1))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ class_Orderings_Opreorder(X0) )
| ~ spl0_193 ),
inference(avatar_component_clause,[],[f2037]) ).
fof(f81695,plain,
( spl0_1074
| ~ spl0_187
| ~ spl0_292 ),
inference(avatar_split_clause,[],[f4340,f3915,f2013,f81693]) ).
fof(f81693,plain,
( spl0_1074
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ class_Lattices_Oupper__semilattice(X0)
| ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X2),X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1074])]) ).
fof(f4340,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ class_Lattices_Oupper__semilattice(X0)
| ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X2),X3))) )
| ~ spl0_187
| ~ spl0_292 ),
inference(resolution,[],[f3916,f2014]) ).
fof(f81641,plain,
( spl0_1073
| ~ spl0_188
| ~ spl0_292 ),
inference(avatar_split_clause,[],[f4339,f3915,f2017,f81639]) ).
fof(f81639,plain,
( spl0_1073
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ class_Lattices_Oupper__semilattice(X0)
| ~ class_Orderings_Opreorder(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X2),X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1073])]) ).
fof(f4339,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ class_Lattices_Oupper__semilattice(X0)
| ~ class_Orderings_Opreorder(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X2),X3))) )
| ~ spl0_188
| ~ spl0_292 ),
inference(resolution,[],[f3916,f2018]) ).
fof(f81637,plain,
( spl0_1072
| ~ spl0_192
| ~ spl0_292 ),
inference(avatar_split_clause,[],[f4338,f3915,f2033,f81635]) ).
fof(f81635,plain,
( spl0_1072
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ class_Lattices_Oupper__semilattice(X0)
| ~ class_Orderings_Oorder(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X2),X3)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1072])]) ).
fof(f4338,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ class_Lattices_Oupper__semilattice(X0)
| ~ class_Orderings_Oorder(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X2),X3)),X1)) )
| ~ spl0_192
| ~ spl0_292 ),
inference(resolution,[],[f3916,f2034]) ).
fof(f81633,plain,
( spl0_1071
| ~ spl0_193
| ~ spl0_292 ),
inference(avatar_split_clause,[],[f4337,f3915,f2037,f81631]) ).
fof(f81631,plain,
( spl0_1071
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ class_Lattices_Oupper__semilattice(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X2),X3)),X1))
| ~ class_Orderings_Opreorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1071])]) ).
fof(f4337,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ class_Lattices_Oupper__semilattice(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X2),X3)),X1))
| ~ class_Orderings_Opreorder(X0) )
| ~ spl0_193
| ~ spl0_292 ),
inference(resolution,[],[f3916,f2038]) ).
fof(f81629,plain,
( spl0_1070
| ~ spl0_187
| ~ spl0_291 ),
inference(avatar_split_clause,[],[f4317,f3911,f2013,f81627]) ).
fof(f81627,plain,
( spl0_1070
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ class_Lattices_Olower__semilattice(X0)
| ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X3)),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1070])]) ).
fof(f4317,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ class_Lattices_Olower__semilattice(X0)
| ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X3)),X2)) )
| ~ spl0_187
| ~ spl0_291 ),
inference(resolution,[],[f3912,f2014]) ).
fof(f81625,plain,
( spl0_1069
| ~ spl0_188
| ~ spl0_291 ),
inference(avatar_split_clause,[],[f4316,f3911,f2017,f81623]) ).
fof(f81623,plain,
( spl0_1069
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ class_Lattices_Olower__semilattice(X0)
| ~ class_Orderings_Opreorder(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X3)),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1069])]) ).
fof(f4316,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ class_Lattices_Olower__semilattice(X0)
| ~ class_Orderings_Opreorder(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X3)),X2)) )
| ~ spl0_188
| ~ spl0_291 ),
inference(resolution,[],[f3912,f2018]) ).
fof(f81621,plain,
( spl0_1068
| ~ spl0_192
| ~ spl0_291 ),
inference(avatar_split_clause,[],[f4315,f3911,f2033,f81619]) ).
fof(f81619,plain,
( spl0_1068
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ class_Lattices_Olower__semilattice(X0)
| ~ class_Orderings_Oorder(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1068])]) ).
fof(f4315,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ class_Lattices_Olower__semilattice(X0)
| ~ class_Orderings_Oorder(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X3))) )
| ~ spl0_192
| ~ spl0_291 ),
inference(resolution,[],[f3912,f2034]) ).
fof(f81617,plain,
( spl0_1067
| ~ spl0_193
| ~ spl0_291 ),
inference(avatar_split_clause,[],[f4314,f3911,f2037,f81615]) ).
fof(f81615,plain,
( spl0_1067
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ class_Lattices_Olower__semilattice(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X3)))
| ~ class_Orderings_Opreorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1067])]) ).
fof(f4314,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ class_Lattices_Olower__semilattice(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X3)))
| ~ class_Orderings_Opreorder(X0) )
| ~ spl0_193
| ~ spl0_291 ),
inference(resolution,[],[f3912,f2038]) ).
fof(f81613,plain,
( spl0_1066
| ~ spl0_187
| ~ spl0_290 ),
inference(avatar_split_clause,[],[f4294,f3907,f2013,f81611]) ).
fof(f81611,plain,
( spl0_1066
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ class_Lattices_Olower__semilattice(X0)
| ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),X1)),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1066])]) ).
fof(f4294,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ class_Lattices_Olower__semilattice(X0)
| ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),X1)),X2)) )
| ~ spl0_187
| ~ spl0_290 ),
inference(resolution,[],[f3908,f2014]) ).
fof(f81609,plain,
( spl0_1065
| ~ spl0_188
| ~ spl0_290 ),
inference(avatar_split_clause,[],[f4293,f3907,f2017,f81607]) ).
fof(f81607,plain,
( spl0_1065
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ class_Lattices_Olower__semilattice(X0)
| ~ class_Orderings_Opreorder(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),X1)),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1065])]) ).
fof(f4293,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ class_Lattices_Olower__semilattice(X0)
| ~ class_Orderings_Opreorder(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),X1)),X2)) )
| ~ spl0_188
| ~ spl0_290 ),
inference(resolution,[],[f3908,f2018]) ).
fof(f81605,plain,
( spl0_1064
| ~ spl0_192
| ~ spl0_290 ),
inference(avatar_split_clause,[],[f4292,f3907,f2033,f81603]) ).
fof(f81603,plain,
( spl0_1064
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ class_Lattices_Olower__semilattice(X0)
| ~ class_Orderings_Oorder(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1064])]) ).
fof(f4292,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ class_Lattices_Olower__semilattice(X0)
| ~ class_Orderings_Oorder(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),X1))) )
| ~ spl0_192
| ~ spl0_290 ),
inference(resolution,[],[f3908,f2034]) ).
fof(f81552,plain,
( spl0_1063
| ~ spl0_193
| ~ spl0_290 ),
inference(avatar_split_clause,[],[f4291,f3907,f2037,f81550]) ).
fof(f81550,plain,
( spl0_1063
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ class_Lattices_Olower__semilattice(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),X1)))
| ~ class_Orderings_Opreorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1063])]) ).
fof(f4291,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ class_Lattices_Olower__semilattice(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),X1)))
| ~ class_Orderings_Opreorder(X0) )
| ~ spl0_193
| ~ spl0_290 ),
inference(resolution,[],[f3908,f2038]) ).
fof(f81548,plain,
( spl0_1062
| ~ spl0_130
| ~ spl0_262
| ~ spl0_263
| ~ spl0_288 ),
inference(avatar_split_clause,[],[f4256,f3899,f3121,f3117,f1631,f81546]) ).
fof(f81546,plain,
( spl0_1062
<=> ! [X5,X4,X0,X6,X1] :
( hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X5,tc_fun(X6,tc_bool)),c_COMBK(c_False,tc_bool,X0)))
| ~ hBOOL(X1)
| ~ hBOOL(c_in(X1,X4,X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1062])]) ).
fof(f4256,plain,
( ! [X0,X1,X6,X4,X5] :
( hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X5,tc_fun(X6,tc_bool)),c_COMBK(c_False,tc_bool,X0)))
| ~ hBOOL(X1)
| ~ hBOOL(c_in(X1,X4,X5)) )
| ~ spl0_130
| ~ spl0_262
| ~ spl0_263
| ~ spl0_288 ),
inference(forward_demodulation,[],[f4235,f3466]) ).
fof(f4235,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] :
( ~ hBOOL(X1)
| ~ hBOOL(c_in(X1,X4,X5))
| hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X5,tc_fun(X6,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_COMBK(c_False,tc_bool,X2),X3,X2,tc_fun(X0,tc_bool)))) )
| ~ spl0_263
| ~ spl0_288 ),
inference(superposition,[],[f3900,f3122]) ).
fof(f81544,plain,
( spl0_1061
| ~ spl0_130
| ~ spl0_262
| ~ spl0_288 ),
inference(avatar_split_clause,[],[f4255,f3899,f3117,f1631,f81542]) ).
fof(f81542,plain,
( spl0_1061
<=> ! [X5,X4,X0,X6,X1] :
( hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X5,tc_fun(X6,tc_bool)),c_COMBK(c_False,tc_bool,X0)))
| ~ hBOOL(X1)
| ~ hBOOL(c_in(X1,X4,X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1061])]) ).
fof(f4255,plain,
( ! [X0,X1,X6,X4,X5] :
( hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X5,tc_fun(X6,tc_bool)),c_COMBK(c_False,tc_bool,X0)))
| ~ hBOOL(X1)
| ~ hBOOL(c_in(X1,X4,X5)) )
| ~ spl0_130
| ~ spl0_262
| ~ spl0_288 ),
inference(forward_demodulation,[],[f4234,f3466]) ).
fof(f4234,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] :
( ~ hBOOL(X1)
| ~ hBOOL(c_in(X1,X4,X5))
| hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X5,tc_fun(X6,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_COMBK(c_False,tc_bool,X2),X3,X2,tc_fun(X0,tc_bool)))) )
| ~ spl0_262
| ~ spl0_288 ),
inference(superposition,[],[f3900,f3118]) ).
fof(f81540,plain,
( spl0_1060
| ~ spl0_125
| ~ spl0_288 ),
inference(avatar_split_clause,[],[f4236,f3899,f1611,f81538]) ).
fof(f81538,plain,
( spl0_1060
<=> ! [X4,X0,X3,X2,X1] :
( ~ hBOOL(X1)
| ~ hBOOL(c_in(X1,X2,X3))
| hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X3,tc_fun(X4,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1060])]) ).
fof(f4236,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ hBOOL(X1)
| ~ hBOOL(c_in(X1,X2,X3))
| hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X3,tc_fun(X4,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)))) )
| ~ spl0_125
| ~ spl0_288 ),
inference(superposition,[],[f3900,f1612]) ).
fof(f81536,plain,
( spl0_1059
| ~ spl0_133
| ~ spl0_288 ),
inference(avatar_split_clause,[],[f4219,f3899,f1643,f81534]) ).
fof(f81534,plain,
( spl0_1059
<=> ! [X4,X0,X3,X2,X1] :
( ~ hBOOL(X1)
| ~ hBOOL(c_in(c_COMBK(c_False,tc_bool,X0),X2,X3))
| hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X3,tc_fun(X4,tc_bool)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1059])]) ).
fof(f4219,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ hBOOL(X1)
| ~ hBOOL(c_in(c_COMBK(c_False,tc_bool,X0),X2,X3))
| hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X3,tc_fun(X4,tc_bool)),X1)) )
| ~ spl0_133
| ~ spl0_288 ),
inference(superposition,[],[f3900,f1644]) ).
fof(f81532,plain,
( spl0_1058
| ~ spl0_123
| ~ spl0_288 ),
inference(avatar_split_clause,[],[f4217,f3899,f1603,f81530]) ).
fof(f81530,plain,
( spl0_1058
<=> ! [X4,X0,X3,X2,X1] :
( ~ hBOOL(X1)
| ~ hBOOL(c_in(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X2,X3))
| hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X3,tc_fun(X4,tc_bool)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1058])]) ).
fof(f4217,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ hBOOL(X1)
| ~ hBOOL(c_in(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X2,X3))
| hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X3,tc_fun(X4,tc_bool)),X1)) )
| ~ spl0_123
| ~ spl0_288 ),
inference(superposition,[],[f3900,f1604]) ).
fof(f81528,plain,
( spl0_1057
| ~ spl0_130
| ~ spl0_288 ),
inference(avatar_split_clause,[],[f4216,f3899,f1631,f81526]) ).
fof(f81526,plain,
( spl0_1057
<=> ! [X4,X0,X3,X2,X1] :
( ~ hBOOL(c_COMBK(c_False,tc_bool,X0))
| ~ hBOOL(c_in(X1,X2,X3))
| hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X3,tc_fun(X4,tc_bool)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1057])]) ).
fof(f4216,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ hBOOL(c_COMBK(c_False,tc_bool,X0))
| ~ hBOOL(c_in(X1,X2,X3))
| hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X3,tc_fun(X4,tc_bool)),X1)) )
| ~ spl0_130
| ~ spl0_288 ),
inference(superposition,[],[f3900,f1632]) ).
fof(f81524,plain,
( spl0_1056
| ~ spl0_146
| ~ spl0_288 ),
inference(avatar_split_clause,[],[f4157,f3899,f1716,f81522]) ).
fof(f81522,plain,
( spl0_1056
<=> ! [X3,X4,X0,X5,X2,X1] :
( ~ hBOOL(c_in(X0,X1,X2))
| hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,c_lessequals(tc_fun(X3,tc_bool)),X2,tc_fun(X4,tc_bool)),hAPP(hAPP(c_Set_Oinsert(X3),X5),X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1056])]) ).
fof(f4157,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ hBOOL(c_in(X0,X1,X2))
| hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,c_lessequals(tc_fun(X3,tc_bool)),X2,tc_fun(X4,tc_bool)),hAPP(hAPP(c_Set_Oinsert(X3),X5),X0))) )
| ~ spl0_146
| ~ spl0_288 ),
inference(resolution,[],[f3900,f1717]) ).
fof(f81520,plain,
( spl0_1055
| ~ spl0_139
| ~ spl0_288 ),
inference(avatar_split_clause,[],[f4154,f3899,f1688,f81518]) ).
fof(f81518,plain,
( spl0_1055
<=> ! [X3,X4,X0,X5,X2,X1] :
( ~ hBOOL(c_in(X0,X1,X2))
| hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,c_lessequals(X3),X2,tc_fun(X4,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),X5),X0)))
| ~ class_Lattices_Oupper__semilattice(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1055])]) ).
fof(f4154,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ hBOOL(c_in(X0,X1,X2))
| hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,c_lessequals(X3),X2,tc_fun(X4,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),X5),X0)))
| ~ class_Lattices_Oupper__semilattice(X3) )
| ~ spl0_139
| ~ spl0_288 ),
inference(resolution,[],[f3900,f1689]) ).
fof(f81516,plain,
( spl0_1054
| ~ spl0_140
| ~ spl0_288 ),
inference(avatar_split_clause,[],[f4153,f3899,f1692,f81514]) ).
fof(f81514,plain,
( spl0_1054
<=> ! [X3,X4,X0,X5,X2,X1] :
( ~ hBOOL(c_in(X0,X1,X2))
| hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,c_lessequals(X3),X2,tc_fun(X4,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),X5),X0)))
| ~ class_Lattices_Olattice(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1054])]) ).
fof(f4153,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ hBOOL(c_in(X0,X1,X2))
| hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,c_lessequals(X3),X2,tc_fun(X4,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),X5),X0)))
| ~ class_Lattices_Olattice(X3) )
| ~ spl0_140
| ~ spl0_288 ),
inference(resolution,[],[f3900,f1693]) ).
fof(f81381,plain,
( spl0_1053
| ~ spl0_138
| ~ spl0_288 ),
inference(avatar_split_clause,[],[f4152,f3899,f1684,f81379]) ).
fof(f81379,plain,
( spl0_1053
<=> ! [X3,X4,X0,X5,X2,X1] :
( ~ hBOOL(c_in(X0,X1,X2))
| hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,c_lessequals(X3),X2,tc_fun(X4,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),X0),X5)))
| ~ class_Lattices_Oupper__semilattice(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1053])]) ).
fof(f4152,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ hBOOL(c_in(X0,X1,X2))
| hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,c_lessequals(X3),X2,tc_fun(X4,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),X0),X5)))
| ~ class_Lattices_Oupper__semilattice(X3) )
| ~ spl0_138
| ~ spl0_288 ),
inference(resolution,[],[f3900,f1685]) ).
fof(f81377,plain,
( spl0_1052
| ~ spl0_141
| ~ spl0_288 ),
inference(avatar_split_clause,[],[f4151,f3899,f1696,f81375]) ).
fof(f81375,plain,
( spl0_1052
<=> ! [X3,X4,X0,X5,X2,X1] :
( ~ hBOOL(c_in(X0,X1,X2))
| hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,c_lessequals(X3),X2,tc_fun(X4,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),X0),X5)))
| ~ class_Lattices_Olattice(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1052])]) ).
fof(f4151,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ hBOOL(c_in(X0,X1,X2))
| hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,c_lessequals(X3),X2,tc_fun(X4,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),X0),X5)))
| ~ class_Lattices_Olattice(X3) )
| ~ spl0_141
| ~ spl0_288 ),
inference(resolution,[],[f3900,f1697]) ).
fof(f81373,plain,
( spl0_1051
| ~ spl0_143
| ~ spl0_288 ),
inference(avatar_split_clause,[],[f4141,f3899,f1704,f81371]) ).
fof(f81371,plain,
( spl0_1051
<=> ! [X5,X4,X0,X3,X2,X1] :
( ~ hBOOL(c_in(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2),X3,X4))
| hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,c_lessequals(X0),X4,tc_fun(X5,tc_bool)),X2))
| ~ class_Lattices_Olattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1051])]) ).
fof(f4141,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ hBOOL(c_in(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2),X3,X4))
| hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,c_lessequals(X0),X4,tc_fun(X5,tc_bool)),X2))
| ~ class_Lattices_Olattice(X0) )
| ~ spl0_143
| ~ spl0_288 ),
inference(resolution,[],[f3900,f1705]) ).
fof(f81369,plain,
( spl0_1050
| ~ spl0_144
| ~ spl0_288 ),
inference(avatar_split_clause,[],[f4140,f3899,f1708,f81367]) ).
fof(f81367,plain,
( spl0_1050
<=> ! [X5,X4,X0,X3,X2,X1] :
( ~ hBOOL(c_in(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2),X3,X4))
| hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,c_lessequals(X0),X4,tc_fun(X5,tc_bool)),X2))
| ~ class_Lattices_Olower__semilattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1050])]) ).
fof(f4140,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ hBOOL(c_in(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2),X3,X4))
| hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,c_lessequals(X0),X4,tc_fun(X5,tc_bool)),X2))
| ~ class_Lattices_Olower__semilattice(X0) )
| ~ spl0_144
| ~ spl0_288 ),
inference(resolution,[],[f3900,f1709]) ).
fof(f81365,plain,
( spl0_1049
| ~ spl0_142
| ~ spl0_288 ),
inference(avatar_split_clause,[],[f4135,f3899,f1700,f81363]) ).
fof(f81363,plain,
( spl0_1049
<=> ! [X5,X4,X0,X3,X2,X1] :
( ~ hBOOL(c_in(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2),X3,X4))
| hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,c_lessequals(X0),X4,tc_fun(X5,tc_bool)),X1))
| ~ class_Lattices_Olattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1049])]) ).
fof(f4135,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ hBOOL(c_in(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2),X3,X4))
| hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,c_lessequals(X0),X4,tc_fun(X5,tc_bool)),X1))
| ~ class_Lattices_Olattice(X0) )
| ~ spl0_142
| ~ spl0_288 ),
inference(resolution,[],[f3900,f1701]) ).
fof(f81361,plain,
( spl0_1048
| ~ spl0_145
| ~ spl0_288 ),
inference(avatar_split_clause,[],[f4134,f3899,f1712,f81359]) ).
fof(f81359,plain,
( spl0_1048
<=> ! [X5,X4,X0,X3,X2,X1] :
( ~ hBOOL(c_in(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2),X3,X4))
| hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,c_lessequals(X0),X4,tc_fun(X5,tc_bool)),X1))
| ~ class_Lattices_Olower__semilattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1048])]) ).
fof(f4134,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ hBOOL(c_in(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2),X3,X4))
| hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,c_lessequals(X0),X4,tc_fun(X5,tc_bool)),X1))
| ~ class_Lattices_Olower__semilattice(X0) )
| ~ spl0_145
| ~ spl0_288 ),
inference(resolution,[],[f3900,f1713]) ).
fof(f81357,plain,
( spl0_1047
| ~ spl0_183
| ~ spl0_287 ),
inference(avatar_split_clause,[],[f4099,f3895,f1997,f81355]) ).
fof(f81355,plain,
( spl0_1047
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2))
| ~ class_Lattices_Olower__semilattice(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),X1)))
| ~ class_Orderings_Opreorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1047])]) ).
fof(f4099,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2))
| ~ class_Lattices_Olower__semilattice(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),X1)))
| ~ class_Orderings_Opreorder(X0) )
| ~ spl0_183
| ~ spl0_287 ),
inference(resolution,[],[f3896,f1998]) ).
fof(f81353,plain,
( spl0_1046
| ~ spl0_183
| ~ spl0_286 ),
inference(avatar_split_clause,[],[f4061,f3891,f1997,f81351]) ).
fof(f81351,plain,
( spl0_1046
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2))
| ~ class_Lattices_Olower__semilattice(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X3)))
| ~ class_Orderings_Opreorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1046])]) ).
fof(f4061,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2))
| ~ class_Lattices_Olower__semilattice(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X3)))
| ~ class_Orderings_Opreorder(X0) )
| ~ spl0_183
| ~ spl0_286 ),
inference(resolution,[],[f3892,f1998]) ).
fof(f81349,plain,
( spl0_1045
| ~ spl0_271
| ~ spl0_285 ),
inference(avatar_split_clause,[],[f4020,f3887,f3635,f81347]) ).
fof(f81347,plain,
( spl0_1045
<=> ! [X4,X0,X3,X2,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X3,X0)),X4))
| ~ class_Lattices_Olower__semilattice(X0)
| ~ hBOOL(c_in(X4,X1,X3))
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1045])]) ).
fof(f4020,plain,
( ! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X3,X0)),X4))
| ~ class_Lattices_Olower__semilattice(X0)
| ~ hBOOL(c_in(X4,X1,X3))
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) )
| ~ spl0_271
| ~ spl0_285 ),
inference(resolution,[],[f3888,f3636]) ).
fof(f81345,plain,
( spl0_1044
| ~ spl0_271
| ~ spl0_284 ),
inference(avatar_split_clause,[],[f3987,f3883,f3635,f81343]) ).
fof(f81343,plain,
( spl0_1044
<=> ! [X4,X0,X3,X2,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X3,X0)),X2))
| ~ class_Lattices_Olower__semilattice(X0)
| ~ hBOOL(c_in(X4,X1,X3))
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1044])]) ).
fof(f3987,plain,
( ! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X3,X0)),X2))
| ~ class_Lattices_Olower__semilattice(X0)
| ~ hBOOL(c_in(X4,X1,X3))
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) )
| ~ spl0_271
| ~ spl0_284 ),
inference(resolution,[],[f3884,f3636]) ).
fof(f81341,plain,
( spl0_1043
| ~ spl0_227
| ~ spl0_765 ),
inference(avatar_split_clause,[],[f69797,f61698,f2580,f81339]) ).
fof(f81339,plain,
( spl0_1043
<=> ! [X0,X1] : hBOOL(c_in(X0,hAPP(hAPP(c_Set_Oinsert(tc_bool),X1),c_SetInterval_Oord__class_OatLeastAtMost(X0,X0,tc_bool)),tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1043])]) ).
fof(f61698,plain,
( spl0_765
<=> ! [X2,X0,X1] : hBOOL(c_in(X1,hAPP(hAPP(c_Set_Oinsert(X0),X2),hAPP(c_fequal(X0),X1)),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_765])]) ).
fof(f69797,plain,
( ! [X0,X1] : hBOOL(c_in(X0,hAPP(hAPP(c_Set_Oinsert(tc_bool),X1),c_SetInterval_Oord__class_OatLeastAtMost(X0,X0,tc_bool)),tc_bool))
| ~ spl0_227
| ~ spl0_765 ),
inference(superposition,[],[f61699,f2581]) ).
fof(f61699,plain,
( ! [X2,X0,X1] : hBOOL(c_in(X1,hAPP(hAPP(c_Set_Oinsert(X0),X2),hAPP(c_fequal(X0),X1)),X0))
| ~ spl0_765 ),
inference(avatar_component_clause,[],[f61698]) ).
fof(f81337,plain,
( spl0_1042
| ~ spl0_233
| ~ spl0_275 ),
inference(avatar_split_clause,[],[f3807,f3652,f2645,f81335]) ).
fof(f81335,plain,
( spl0_1042
<=> ! [X3,X4,X0,X5,X2,X1] : c_COMBK(c_False,tc_bool,X0) = hAPP(hAPP(hAPP(c_COMBS(X3,X4,X5),c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool))),hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X2)),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1042])]) ).
fof(f3807,plain,
( ! [X2,X3,X0,X1,X4,X5] : c_COMBK(c_False,tc_bool,X0) = hAPP(hAPP(hAPP(c_COMBS(X3,X4,X5),c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool))),hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X2)),X1)
| ~ spl0_233
| ~ spl0_275 ),
inference(superposition,[],[f3653,f2646]) ).
fof(f81333,plain,
( spl0_1041
| ~ spl0_80
| ~ spl0_271 ),
inference(avatar_split_clause,[],[f3792,f3635,f1365,f81331]) ).
fof(f81331,plain,
( spl0_1041
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,c_and,X2,X0)),hAPP(c_HOL_Oord__class_Oless(tc_bool),v_P)))
| ~ hBOOL(c_in(hAPP(c_Not,v_P),X1,X2))
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1041])]) ).
fof(f3792,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,c_and,X2,X0)),hAPP(c_HOL_Oord__class_Oless(tc_bool),v_P)))
| ~ hBOOL(c_in(hAPP(c_Not,v_P),X1,X2))
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) )
| ~ spl0_80
| ~ spl0_271 ),
inference(superposition,[],[f3636,f1367]) ).
fof(f81329,plain,
( spl0_1040
| ~ spl0_79
| ~ spl0_271 ),
inference(avatar_split_clause,[],[f3758,f3635,f1361,f81327]) ).
fof(f81327,plain,
( spl0_1040
<=> ! [X4,X0,X3,X2,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(X2),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X3,hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X1),X4,X2)),X1))
| ~ hBOOL(c_in(X1,X3,X4))
| ~ class_Complete__Lattice_Ocomplete__lattice(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1040])]) ).
fof(f3758,plain,
( ! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(hAPP(c_lessequals(X2),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X3,hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X1),X4,X2)),X1))
| ~ hBOOL(c_in(X1,X3,X4))
| ~ class_Complete__Lattice_Ocomplete__lattice(X2) )
| ~ spl0_79
| ~ spl0_271 ),
inference(superposition,[],[f3636,f1362]) ).
fof(f81325,plain,
( spl0_1039
| ~ spl0_68
| ~ spl0_271 ),
inference(avatar_split_clause,[],[f3757,f3635,f1316,f81323]) ).
fof(f81323,plain,
( spl0_1039
<=> ! [X4,X0,X3,X2,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(X2),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X3,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X4,X2)),X1))
| ~ hBOOL(c_in(X1,X3,X4))
| ~ class_Complete__Lattice_Ocomplete__lattice(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1039])]) ).
fof(f3757,plain,
( ! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(hAPP(c_lessequals(X2),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X3,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X4,X2)),X1))
| ~ hBOOL(c_in(X1,X3,X4))
| ~ class_Complete__Lattice_Ocomplete__lattice(X2) )
| ~ spl0_68
| ~ spl0_271 ),
inference(superposition,[],[f3636,f1317]) ).
fof(f81321,plain,
( spl0_1038
| ~ spl0_80
| ~ spl0_268 ),
inference(avatar_split_clause,[],[f3728,f3623,f1365,f81319]) ).
fof(f81319,plain,
( spl0_1038
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(c_HOL_Oord__class_Oless(tc_bool),v_P)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,c_and,X2,X0)))
| ~ hBOOL(c_in(hAPP(c_Not,v_P),X1,X2))
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1038])]) ).
fof(f3728,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(c_HOL_Oord__class_Oless(tc_bool),v_P)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,c_and,X2,X0)))
| ~ hBOOL(c_in(hAPP(c_Not,v_P),X1,X2))
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) )
| ~ spl0_80
| ~ spl0_268 ),
inference(superposition,[],[f3624,f1367]) ).
fof(f81317,plain,
( spl0_1037
| ~ spl0_79
| ~ spl0_268 ),
inference(avatar_split_clause,[],[f3694,f3623,f1361,f81315]) ).
fof(f81315,plain,
( spl0_1037
<=> ! [X4,X0,X3,X2,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(X2),X1),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X1),X4,X2)))
| ~ hBOOL(c_in(X1,X3,X4))
| ~ class_Complete__Lattice_Ocomplete__lattice(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1037])]) ).
fof(f3694,plain,
( ! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(hAPP(c_lessequals(X2),X1),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X1),X4,X2)))
| ~ hBOOL(c_in(X1,X3,X4))
| ~ class_Complete__Lattice_Ocomplete__lattice(X2) )
| ~ spl0_79
| ~ spl0_268 ),
inference(superposition,[],[f3624,f1362]) ).
fof(f81313,plain,
( spl0_1036
| ~ spl0_68
| ~ spl0_268 ),
inference(avatar_split_clause,[],[f3693,f3623,f1316,f81311]) ).
fof(f81311,plain,
( spl0_1036
<=> ! [X4,X0,X3,X2,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(X2),X1),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X4,X2)))
| ~ hBOOL(c_in(X1,X3,X4))
| ~ class_Complete__Lattice_Ocomplete__lattice(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1036])]) ).
fof(f3693,plain,
( ! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(hAPP(c_lessequals(X2),X1),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X4,X2)))
| ~ hBOOL(c_in(X1,X3,X4))
| ~ class_Complete__Lattice_Ocomplete__lattice(X2) )
| ~ spl0_68
| ~ spl0_268 ),
inference(superposition,[],[f3624,f1317]) ).
fof(f81309,plain,
( spl0_1035
| ~ spl0_169
| ~ spl0_245 ),
inference(avatar_split_clause,[],[f3042,f2694,f1865,f81307]) ).
fof(f81307,plain,
( spl0_1035
<=> ! [X2,X0,X1] :
( ~ class_Orderings_Oorder(tc_fun(X0,tc_bool))
| c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,tc_fun(X0,tc_bool)) = c_COMBK(c_False,tc_bool,tc_fun(X0,tc_bool))
| c_Finite__Set_Ofinite(X1,X0)
| ~ c_Finite__Set_Ofinite(X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1035])]) ).
fof(f3042,plain,
( ! [X2,X0,X1] :
( ~ class_Orderings_Oorder(tc_fun(X0,tc_bool))
| c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,tc_fun(X0,tc_bool)) = c_COMBK(c_False,tc_bool,tc_fun(X0,tc_bool))
| c_Finite__Set_Ofinite(X1,X0)
| ~ c_Finite__Set_Ofinite(X2,X0) )
| ~ spl0_169
| ~ spl0_245 ),
inference(resolution,[],[f2695,f1866]) ).
fof(f81305,plain,
( spl0_1034
| ~ spl0_195
| ~ spl0_233 ),
inference(avatar_split_clause,[],[f2973,f2645,f2045,f81303]) ).
fof(f81303,plain,
( spl0_1034
<=> ! [X2,X3,X0,X1,X8,X6,X7,X4,X5] : hAPP(X3,hAPP(hAPP(X4,X3),X8)) = hAPP(hAPP(hAPP(hAPP(c_COMBS(X5,X6,X7),c_COMBB(X0,X1,X2)),X4),X3),X8) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1034])]) ).
fof(f2973,plain,
( ! [X2,X3,X0,X1,X8,X6,X7,X4,X5] : hAPP(X3,hAPP(hAPP(X4,X3),X8)) = hAPP(hAPP(hAPP(hAPP(c_COMBS(X5,X6,X7),c_COMBB(X0,X1,X2)),X4),X3),X8)
| ~ spl0_195
| ~ spl0_233 ),
inference(superposition,[],[f2046,f2646]) ).
fof(f81301,plain,
( spl0_1033
| ~ spl0_183
| ~ spl0_233 ),
inference(avatar_split_clause,[],[f2964,f2645,f1997,f81299]) ).
fof(f81299,plain,
( spl0_1033
<=> ! [X3,X4,X0,X5,X2,X1] :
( ~ hBOOL(hAPP(hAPP(hAPP(c_COMBS(X3,X4,X5),c_lessequals(X0)),X2),X1))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(X2,X1)),X1))
| ~ class_Orderings_Opreorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1033])]) ).
fof(f2964,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ hBOOL(hAPP(hAPP(hAPP(c_COMBS(X3,X4,X5),c_lessequals(X0)),X2),X1))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(X2,X1)),X1))
| ~ class_Orderings_Opreorder(X0) )
| ~ spl0_183
| ~ spl0_233 ),
inference(superposition,[],[f1998,f2646]) ).
fof(f81297,plain,
( spl0_1032
| ~ spl0_261
| ~ spl0_763 ),
inference(avatar_split_clause,[],[f65095,f61292,f3113,f81295]) ).
fof(f81295,plain,
( spl0_1032
<=> ! [X0,X1] : c_COMBK(c_False,tc_bool,tc_fun(X0,tc_bool)) != c_SetInterval_Oord__class_OatLeastAtMost(X1,X1,tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1032])]) ).
fof(f3113,plain,
( spl0_261
<=> ! [X0,X1] : hAPP(c_fequal(X0),X1) != c_COMBK(c_False,tc_bool,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_261])]) ).
fof(f61292,plain,
( spl0_763
<=> ! [X0,X1] : hAPP(c_fequal(tc_fun(X0,tc_bool)),X1) = c_SetInterval_Oord__class_OatLeastAtMost(X1,X1,tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_763])]) ).
fof(f65095,plain,
( ! [X0,X1] : c_COMBK(c_False,tc_bool,tc_fun(X0,tc_bool)) != c_SetInterval_Oord__class_OatLeastAtMost(X1,X1,tc_fun(X0,tc_bool))
| ~ spl0_261
| ~ spl0_763 ),
inference(superposition,[],[f3114,f61293]) ).
fof(f61293,plain,
( ! [X0,X1] : hAPP(c_fequal(tc_fun(X0,tc_bool)),X1) = c_SetInterval_Oord__class_OatLeastAtMost(X1,X1,tc_fun(X0,tc_bool))
| ~ spl0_763 ),
inference(avatar_component_clause,[],[f61292]) ).
fof(f3114,plain,
( ! [X0,X1] : hAPP(c_fequal(X0),X1) != c_COMBK(c_False,tc_bool,X0)
| ~ spl0_261 ),
inference(avatar_component_clause,[],[f3113]) ).
fof(f81293,plain,
( spl0_1031
| ~ spl0_202
| ~ spl0_233 ),
inference(avatar_split_clause,[],[f2948,f2645,f2080,f81291]) ).
fof(f81291,plain,
( spl0_1031
<=> ! [X3,X4,X0,X6,X5,X2,X1] :
( ~ hBOOL(c_in(X6,hAPP(hAPP(hAPP(c_COMBS(X3,X4,X5),c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool))),X2),X1),X0))
| hBOOL(hAPP(hAPP(X2,X1),X6)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1031])]) ).
fof(f2948,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] :
( ~ hBOOL(c_in(X6,hAPP(hAPP(hAPP(c_COMBS(X3,X4,X5),c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool))),X2),X1),X0))
| hBOOL(hAPP(hAPP(X2,X1),X6)) )
| ~ spl0_202
| ~ spl0_233 ),
inference(superposition,[],[f2081,f2646]) ).
fof(f81289,plain,
( spl0_1030
| ~ spl0_190
| ~ spl0_233 ),
inference(avatar_split_clause,[],[f2947,f2645,f2025,f81287]) ).
fof(f81287,plain,
( spl0_1030
<=> ! [X3,X4,X0,X5,X2,X1] : hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),hAPP(hAPP(hAPP(c_COMBS(X3,X4,X5),c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool))),X2),X1)),hAPP(X2,X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1030])]) ).
fof(f2947,plain,
( ! [X2,X3,X0,X1,X4,X5] : hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),hAPP(hAPP(hAPP(c_COMBS(X3,X4,X5),c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool))),X2),X1)),hAPP(X2,X1)))
| ~ spl0_190
| ~ spl0_233 ),
inference(superposition,[],[f2026,f2646]) ).
fof(f81285,plain,
( spl0_1029
| ~ spl0_181
| ~ spl0_233 ),
inference(avatar_split_clause,[],[f2940,f2645,f1989,f81283]) ).
fof(f81283,plain,
( spl0_1029
<=> ! [X3,X4,X0,X5,X2,X1] :
( ~ c_Finite__Set_Ofinite(hAPP(hAPP(hAPP(c_COMBS(X3,X4,X5),c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool))),X2),X1),X0)
| c_Finite__Set_Ofinite(X1,X0)
| ~ c_Finite__Set_Ofinite(hAPP(X2,X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1029])]) ).
fof(f1989,plain,
( spl0_181
<=> ! [X5,X9,X0] :
( ~ c_Finite__Set_Ofinite(X9,X0)
| c_Finite__Set_Ofinite(X5,X0)
| ~ c_Finite__Set_Ofinite(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X5),X9),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_181])]) ).
fof(f2940,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ c_Finite__Set_Ofinite(hAPP(hAPP(hAPP(c_COMBS(X3,X4,X5),c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool))),X2),X1),X0)
| c_Finite__Set_Ofinite(X1,X0)
| ~ c_Finite__Set_Ofinite(hAPP(X2,X1),X0) )
| ~ spl0_181
| ~ spl0_233 ),
inference(superposition,[],[f1990,f2646]) ).
fof(f1990,plain,
( ! [X0,X9,X5] :
( ~ c_Finite__Set_Ofinite(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X5),X9),X0)
| c_Finite__Set_Ofinite(X5,X0)
| ~ c_Finite__Set_Ofinite(X9,X0) )
| ~ spl0_181 ),
inference(avatar_component_clause,[],[f1989]) ).
fof(f81281,plain,
( spl0_1028
| ~ spl0_194
| ~ spl0_233 ),
inference(avatar_split_clause,[],[f2933,f2645,f2041,f81279]) ).
fof(f81279,plain,
( spl0_1028
<=> ! [X5,X3,X4,X0,X6,X2,X1] :
( ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_COMBS(X3,X4,X5),c_Set_Oinsert(X0)),X2),X1),X6))
| hBOOL(hAPP(hAPP(X2,X1),X6))
| X1 = X6 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1028])]) ).
fof(f2933,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] :
( ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_COMBS(X3,X4,X5),c_Set_Oinsert(X0)),X2),X1),X6))
| hBOOL(hAPP(hAPP(X2,X1),X6))
| X1 = X6 )
| ~ spl0_194
| ~ spl0_233 ),
inference(superposition,[],[f2042,f2646]) ).
fof(f81277,plain,
( spl0_1027
| ~ spl0_187
| ~ spl0_233 ),
inference(avatar_split_clause,[],[f2923,f2645,f2013,f81275]) ).
fof(f81275,plain,
( spl0_1027
<=> ! [X3,X4,X0,X5,X2,X1] :
( ~ hBOOL(hAPP(hAPP(hAPP(c_COMBS(X3,X4,X5),c_HOL_Oord__class_Oless(X0)),X2),X1))
| ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),X1),hAPP(X2,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1027])]) ).
fof(f2923,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ hBOOL(hAPP(hAPP(hAPP(c_COMBS(X3,X4,X5),c_HOL_Oord__class_Oless(X0)),X2),X1))
| ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),X1),hAPP(X2,X1))) )
| ~ spl0_187
| ~ spl0_233 ),
inference(superposition,[],[f2014,f2646]) ).
fof(f81273,plain,
( spl0_1026
| ~ spl0_188
| ~ spl0_233 ),
inference(avatar_split_clause,[],[f2922,f2645,f2017,f81271]) ).
fof(f81271,plain,
( spl0_1026
<=> ! [X3,X4,X0,X5,X2,X1] :
( ~ hBOOL(hAPP(hAPP(hAPP(c_COMBS(X3,X4,X5),c_HOL_Oord__class_Oless(X0)),X2),X1))
| ~ class_Orderings_Opreorder(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),X1),hAPP(X2,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1026])]) ).
fof(f2922,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ hBOOL(hAPP(hAPP(hAPP(c_COMBS(X3,X4,X5),c_HOL_Oord__class_Oless(X0)),X2),X1))
| ~ class_Orderings_Opreorder(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),X1),hAPP(X2,X1))) )
| ~ spl0_188
| ~ spl0_233 ),
inference(superposition,[],[f2018,f2646]) ).
fof(f81269,plain,
( spl0_1025
| ~ spl0_192
| ~ spl0_233 ),
inference(avatar_split_clause,[],[f2921,f2645,f2033,f81267]) ).
fof(f81267,plain,
( spl0_1025
<=> ! [X3,X4,X0,X5,X2,X1] :
( ~ hBOOL(hAPP(hAPP(hAPP(c_COMBS(X3,X4,X5),c_HOL_Oord__class_Oless(X0)),X2),X1))
| ~ class_Orderings_Oorder(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(X2,X1)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1025])]) ).
fof(f2921,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ hBOOL(hAPP(hAPP(hAPP(c_COMBS(X3,X4,X5),c_HOL_Oord__class_Oless(X0)),X2),X1))
| ~ class_Orderings_Oorder(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(X2,X1)),X1)) )
| ~ spl0_192
| ~ spl0_233 ),
inference(superposition,[],[f2034,f2646]) ).
fof(f81265,plain,
( spl0_1024
| ~ spl0_193
| ~ spl0_233 ),
inference(avatar_split_clause,[],[f2920,f2645,f2037,f81263]) ).
fof(f81263,plain,
( spl0_1024
<=> ! [X3,X4,X0,X5,X2,X1] :
( ~ hBOOL(hAPP(hAPP(hAPP(c_COMBS(X3,X4,X5),c_HOL_Oord__class_Oless(X0)),X2),X1))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(X2,X1)),X1))
| ~ class_Orderings_Opreorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1024])]) ).
fof(f2920,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ hBOOL(hAPP(hAPP(hAPP(c_COMBS(X3,X4,X5),c_HOL_Oord__class_Oless(X0)),X2),X1))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(X2,X1)),X1))
| ~ class_Orderings_Opreorder(X0) )
| ~ spl0_193
| ~ spl0_233 ),
inference(superposition,[],[f2038,f2646]) ).
fof(f81261,plain,
( spl0_1023
| ~ spl0_184
| ~ spl0_233 ),
inference(avatar_split_clause,[],[f2907,f2645,f2001,f81259]) ).
fof(f81259,plain,
( spl0_1023
<=> ! [X3,X4,X0,X5,X2,X1] : hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),hAPP(X2,X1)),hAPP(hAPP(hAPP(c_COMBS(X3,X4,X5),c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool))),X2),X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1023])]) ).
fof(f2907,plain,
( ! [X2,X3,X0,X1,X4,X5] : hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),hAPP(X2,X1)),hAPP(hAPP(hAPP(c_COMBS(X3,X4,X5),c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool))),X2),X1)))
| ~ spl0_184
| ~ spl0_233 ),
inference(superposition,[],[f2002,f2646]) ).
fof(f81257,plain,
( spl0_1022
| ~ spl0_182
| ~ spl0_233 ),
inference(avatar_split_clause,[],[f2906,f2645,f1993,f81255]) ).
fof(f81255,plain,
( spl0_1022
<=> ! [X3,X4,X0,X5,X2,X1] :
( c_Finite__Set_Ofinite(hAPP(hAPP(hAPP(c_COMBS(X3,X4,X5),c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool))),X2),X1),X0)
| ~ c_Finite__Set_Ofinite(hAPP(X2,X1),X0)
| ~ c_Finite__Set_Ofinite(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1022])]) ).
fof(f2906,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( c_Finite__Set_Ofinite(hAPP(hAPP(hAPP(c_COMBS(X3,X4,X5),c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool))),X2),X1),X0)
| ~ c_Finite__Set_Ofinite(hAPP(X2,X1),X0)
| ~ c_Finite__Set_Ofinite(X1,X0) )
| ~ spl0_182
| ~ spl0_233 ),
inference(superposition,[],[f1994,f2646]) ).
fof(f81194,plain,
( spl0_1021
| ~ spl0_195
| ~ spl0_233 ),
inference(avatar_split_clause,[],[f2879,f2645,f2045,f81192]) ).
fof(f81192,plain,
( spl0_1021
<=> ! [X2,X3,X0,X1,X8,X6,X7,X4,X5] : hAPP(X3,hAPP(X4,hAPP(X5,X4))) = hAPP(hAPP(hAPP(c_COMBS(X6,X7,X8),hAPP(c_COMBB(X0,X1,X2),X3)),X5),X4) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1021])]) ).
fof(f2879,plain,
( ! [X2,X3,X0,X1,X8,X6,X7,X4,X5] : hAPP(X3,hAPP(X4,hAPP(X5,X4))) = hAPP(hAPP(hAPP(c_COMBS(X6,X7,X8),hAPP(c_COMBB(X0,X1,X2),X3)),X5),X4)
| ~ spl0_195
| ~ spl0_233 ),
inference(superposition,[],[f2646,f2046]) ).
fof(f81190,plain,
( spl0_1020
| ~ spl0_133
| ~ spl0_233 ),
inference(avatar_split_clause,[],[f2875,f2645,f1643,f81188]) ).
fof(f81188,plain,
( spl0_1020
<=> ! [X2,X4,X0,X3,X1] : hAPP(X1,c_COMBK(c_False,tc_bool,X0)) = hAPP(hAPP(hAPP(c_COMBS(X2,X3,X4),c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool))),X1),c_COMBK(c_False,tc_bool,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1020])]) ).
fof(f2875,plain,
( ! [X2,X3,X0,X1,X4] : hAPP(X1,c_COMBK(c_False,tc_bool,X0)) = hAPP(hAPP(hAPP(c_COMBS(X2,X3,X4),c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool))),X1),c_COMBK(c_False,tc_bool,X0))
| ~ spl0_133
| ~ spl0_233 ),
inference(superposition,[],[f2646,f1644]) ).
fof(f81186,plain,
( spl0_1019
| ~ spl0_123
| ~ spl0_233 ),
inference(avatar_split_clause,[],[f2873,f2645,f1603,f81184]) ).
fof(f81184,plain,
( spl0_1019
<=> ! [X2,X4,X0,X3,X1] : hAPP(X1,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool))) = hAPP(hAPP(hAPP(c_COMBS(X2,X3,X4),c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool))),X1),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1019])]) ).
fof(f2873,plain,
( ! [X2,X3,X0,X1,X4] : hAPP(X1,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool))) = hAPP(hAPP(hAPP(c_COMBS(X2,X3,X4),c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool))),X1),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)))
| ~ spl0_123
| ~ spl0_233 ),
inference(superposition,[],[f2646,f1604]) ).
fof(f81182,plain,
( spl0_1018
| ~ spl0_215
| ~ spl0_225 ),
inference(avatar_split_clause,[],[f2620,f2299,f2259,f81180]) ).
fof(f81180,plain,
( spl0_1018
<=> ! [X2,X0,X1] :
( ~ hBOOL(c_in(X0,X1,X2))
| ~ class_Complete__Lattice_Ocomplete__lattice(X2)
| ~ class_Lattices_Oupper__semilattice(X2)
| hAPP(c_Complete__Lattice_OSup__class_OSup(X2),X1) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2),hAPP(c_Complete__Lattice_OSup__class_OSup(X2),X1)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1018])]) ).
fof(f2620,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(c_in(X0,X1,X2))
| ~ class_Complete__Lattice_Ocomplete__lattice(X2)
| ~ class_Lattices_Oupper__semilattice(X2)
| hAPP(c_Complete__Lattice_OSup__class_OSup(X2),X1) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2),hAPP(c_Complete__Lattice_OSup__class_OSup(X2),X1)),X0) )
| ~ spl0_215
| ~ spl0_225 ),
inference(resolution,[],[f2300,f2260]) ).
fof(f81178,plain,
( spl0_1017
| ~ spl0_217
| ~ spl0_225 ),
inference(avatar_split_clause,[],[f2619,f2299,f2267,f81176]) ).
fof(f81176,plain,
( spl0_1017
<=> ! [X2,X0,X1] :
( ~ hBOOL(c_in(X0,X1,X2))
| ~ class_Complete__Lattice_Ocomplete__lattice(X2)
| ~ class_Lattices_Oupper__semilattice(X2)
| hAPP(c_Complete__Lattice_OSup__class_OSup(X2),X1) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2),X0),hAPP(c_Complete__Lattice_OSup__class_OSup(X2),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1017])]) ).
fof(f2619,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(c_in(X0,X1,X2))
| ~ class_Complete__Lattice_Ocomplete__lattice(X2)
| ~ class_Lattices_Oupper__semilattice(X2)
| hAPP(c_Complete__Lattice_OSup__class_OSup(X2),X1) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2),X0),hAPP(c_Complete__Lattice_OSup__class_OSup(X2),X1)) )
| ~ spl0_217
| ~ spl0_225 ),
inference(resolution,[],[f2300,f2268]) ).
fof(f81174,plain,
( spl0_1016
| ~ spl0_210
| ~ spl0_218 ),
inference(avatar_split_clause,[],[f2554,f2271,f2233,f81172]) ).
fof(f81172,plain,
( spl0_1016
<=> ! [X2,X0,X1] :
( ~ hBOOL(c_in(X0,X1,X2))
| ~ class_Complete__Lattice_Ocomplete__lattice(X2)
| ~ class_Lattices_Olower__semilattice(X2)
| hAPP(c_Complete__Lattice_OInf__class_OInf(X2),X1) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),hAPP(c_Complete__Lattice_OInf__class_OInf(X2),X1)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1016])]) ).
fof(f2554,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(c_in(X0,X1,X2))
| ~ class_Complete__Lattice_Ocomplete__lattice(X2)
| ~ class_Lattices_Olower__semilattice(X2)
| hAPP(c_Complete__Lattice_OInf__class_OInf(X2),X1) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),hAPP(c_Complete__Lattice_OInf__class_OInf(X2),X1)),X0) )
| ~ spl0_210
| ~ spl0_218 ),
inference(resolution,[],[f2272,f2234]) ).
fof(f81170,plain,
( spl0_1015
| ~ spl0_212
| ~ spl0_218 ),
inference(avatar_split_clause,[],[f2553,f2271,f2247,f81168]) ).
fof(f81168,plain,
( spl0_1015
<=> ! [X2,X0,X1] :
( ~ hBOOL(c_in(X0,X1,X2))
| ~ class_Complete__Lattice_Ocomplete__lattice(X2)
| ~ class_Lattices_Olower__semilattice(X2)
| hAPP(c_Complete__Lattice_OInf__class_OInf(X2),X1) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),X0),hAPP(c_Complete__Lattice_OInf__class_OInf(X2),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1015])]) ).
fof(f2553,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(c_in(X0,X1,X2))
| ~ class_Complete__Lattice_Ocomplete__lattice(X2)
| ~ class_Lattices_Olower__semilattice(X2)
| hAPP(c_Complete__Lattice_OInf__class_OInf(X2),X1) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),X0),hAPP(c_Complete__Lattice_OInf__class_OInf(X2),X1)) )
| ~ spl0_212
| ~ spl0_218 ),
inference(resolution,[],[f2272,f2248]) ).
fof(f80985,plain,
( spl0_1014
| ~ spl0_120
| ~ spl0_1012 ),
inference(avatar_split_clause,[],[f79976,f76725,f1591,f80983]) ).
fof(f76725,plain,
( spl0_1012
<=> ! [X0] : hAPP(X0,v_x) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_bool),hAPP(X0,v_x)),c_False) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1012])]) ).
fof(f79976,plain,
( ! [X0] : hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_bool),X0),c_False) = X0
| ~ spl0_120
| ~ spl0_1012 ),
inference(superposition,[],[f76726,f1592]) ).
fof(f76726,plain,
( ! [X0] : hAPP(X0,v_x) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_bool),hAPP(X0,v_x)),c_False)
| ~ spl0_1012 ),
inference(avatar_component_clause,[],[f76725]) ).
fof(f77631,plain,
( spl0_1013
| ~ spl0_120
| ~ spl0_1010 ),
inference(avatar_split_clause,[],[f77370,f75340,f1591,f77629]) ).
fof(f77629,plain,
( spl0_1013
<=> ! [X0] : c_False = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_bool),X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1013])]) ).
fof(f75340,plain,
( spl0_1010
<=> ! [X0] : c_False = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_bool),hAPP(X0,v_x)),hAPP(X0,v_x)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1010])]) ).
fof(f77370,plain,
( ! [X0] : c_False = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_bool),X0),X0)
| ~ spl0_120
| ~ spl0_1010 ),
inference(superposition,[],[f75341,f1592]) ).
fof(f75341,plain,
( ! [X0] : c_False = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_bool),hAPP(X0,v_x)),hAPP(X0,v_x))
| ~ spl0_1010 ),
inference(avatar_component_clause,[],[f75340]) ).
fof(f76727,plain,
( spl0_1012
| ~ spl0_51
| ~ spl0_262
| ~ spl0_602
| ~ spl0_912 ),
inference(avatar_split_clause,[],[f73161,f69988,f16916,f3117,f1237,f76725]) ).
fof(f16916,plain,
( spl0_602
<=> ! [X2,X0,X1] : c_COMBK(c_False,tc_bool,X0) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_COMBK(c_False,tc_bool,X1),X2,X1,tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_602])]) ).
fof(f69988,plain,
( spl0_912
<=> ! [X0,X1] : hAPP(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(t_a,tc_bool)),X0),X1),v_x) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_bool),hAPP(X0,v_x)),hAPP(X1,v_x)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_912])]) ).
fof(f73161,plain,
( ! [X0] : hAPP(X0,v_x) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_bool),hAPP(X0,v_x)),c_False)
| ~ spl0_51
| ~ spl0_262
| ~ spl0_602
| ~ spl0_912 ),
inference(forward_demodulation,[],[f73160,f1238]) ).
fof(f73160,plain,
( ! [X0] : hAPP(X0,v_x) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_bool),hAPP(X0,v_x)),hAPP(c_COMBK(c_False,tc_bool,t_a),v_x))
| ~ spl0_262
| ~ spl0_602
| ~ spl0_912 ),
inference(forward_demodulation,[],[f73087,f16917]) ).
fof(f16917,plain,
( ! [X2,X0,X1] : c_COMBK(c_False,tc_bool,X0) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_COMBK(c_False,tc_bool,X1),X2,X1,tc_fun(X0,tc_bool))
| ~ spl0_602 ),
inference(avatar_component_clause,[],[f16916]) ).
fof(f73087,plain,
( ! [X2,X0,X1] : hAPP(X0,v_x) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_bool),hAPP(X0,v_x)),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_COMBK(c_False,tc_bool,X1),X2,X1,tc_fun(t_a,tc_bool)),v_x))
| ~ spl0_262
| ~ spl0_912 ),
inference(superposition,[],[f69989,f3118]) ).
fof(f69989,plain,
( ! [X0,X1] : hAPP(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(t_a,tc_bool)),X0),X1),v_x) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_bool),hAPP(X0,v_x)),hAPP(X1,v_x))
| ~ spl0_912 ),
inference(avatar_component_clause,[],[f69988]) ).
fof(f75346,plain,
( spl0_1011
| ~ spl0_353
| ~ spl0_733 ),
inference(avatar_split_clause,[],[f29820,f27510,f5604,f75344]) ).
fof(f75344,plain,
( spl0_1011
<=> ! [X0,X3,X2,X1] : c_List_Ofilter(X2,c_List_Ofilter(X1,X3,X0),X0) = c_List_Ofilter(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X1),X2),c_List_Ofilter(X1,X3,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1011])]) ).
fof(f5604,plain,
( spl0_353
<=> ! [X9,X5,X0] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X5),X9) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X5),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X5),X9)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_353])]) ).
fof(f29820,plain,
( ! [X2,X3,X0,X1] : c_List_Ofilter(X2,c_List_Ofilter(X1,X3,X0),X0) = c_List_Ofilter(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X1),X2),c_List_Ofilter(X1,X3,X0),X0)
| ~ spl0_353
| ~ spl0_733 ),
inference(forward_demodulation,[],[f29802,f27511]) ).
fof(f29802,plain,
( ! [X2,X3,X0,X1] : c_List_Ofilter(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X1),X2),X3,X0) = c_List_Ofilter(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X1),X2),c_List_Ofilter(X1,X3,X0),X0)
| ~ spl0_353
| ~ spl0_733 ),
inference(superposition,[],[f27511,f5605]) ).
fof(f5605,plain,
( ! [X0,X9,X5] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X5),X9) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X5),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X5),X9))
| ~ spl0_353 ),
inference(avatar_component_clause,[],[f5604]) ).
fof(f75342,plain,
( spl0_1010
| ~ spl0_51
| ~ spl0_130
| ~ spl0_912 ),
inference(avatar_split_clause,[],[f73132,f69988,f1631,f1237,f75340]) ).
fof(f73132,plain,
( ! [X0] : c_False = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_bool),hAPP(X0,v_x)),hAPP(X0,v_x))
| ~ spl0_51
| ~ spl0_130
| ~ spl0_912 ),
inference(forward_demodulation,[],[f73072,f1238]) ).
fof(f73072,plain,
( ! [X0] : hAPP(c_COMBK(c_False,tc_bool,t_a),v_x) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_bool),hAPP(X0,v_x)),hAPP(X0,v_x))
| ~ spl0_130
| ~ spl0_912 ),
inference(superposition,[],[f69989,f1632]) ).
fof(f75338,plain,
( spl0_1009
| ~ spl0_275
| ~ spl0_733 ),
inference(avatar_split_clause,[],[f27669,f27510,f3652,f75336]) ).
fof(f75336,plain,
( spl0_1009
<=> ! [X0,X3,X2,X1] : c_List_Ofilter(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X2),X1),c_List_Ofilter(X1,X3,X0),X0) = c_List_Ofilter(c_COMBK(c_False,tc_bool,X0),X3,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1009])]) ).
fof(f27669,plain,
( ! [X2,X3,X0,X1] : c_List_Ofilter(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X2),X1),c_List_Ofilter(X1,X3,X0),X0) = c_List_Ofilter(c_COMBK(c_False,tc_bool,X0),X3,X0)
| ~ spl0_275
| ~ spl0_733 ),
inference(superposition,[],[f27511,f3653]) ).
fof(f75334,plain,
( spl0_1008
| ~ spl0_163
| ~ spl0_466 ),
inference(avatar_split_clause,[],[f10846,f10800,f1838,f75332]) ).
fof(f75332,plain,
( spl0_1008
<=> ! [X4,X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X1),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X3),X2)),X4))
| hBOOL(hAPP(X3,X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1008])]) ).
fof(f10846,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X1),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X3),X2)),X4))
| hBOOL(hAPP(X3,X4)) )
| ~ spl0_163
| ~ spl0_466 ),
inference(superposition,[],[f1839,f10801]) ).
fof(f75330,plain,
( spl0_1007
| ~ spl0_114
| ~ spl0_452 ),
inference(avatar_split_clause,[],[f10474,f9806,f1541,f75328]) ).
fof(f75328,plain,
( spl0_1007
<=> ! [X2,X0,X1] :
( c_Hoare__Mirabelle_Ohoare__derivs(X0,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X1,c_Com_Ocom_OSKIP,X2,t_a)),t_a)
| hBOOL(hAPP(hAPP(X1,v_sko__Hoare__Mirabelle__Xconseq1__1(X1,X2)),v_sko__Hoare__Mirabelle__Xconseq1__2(X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1007])]) ).
fof(f9806,plain,
( spl0_452
<=> ! [X35,X57,X11,X39,X65] :
( c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X11,X35,X57,t_a)),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X65,X35,X57,t_a)),t_a)
| hBOOL(hAPP(hAPP(X11,v_sko__Hoare__Mirabelle__Xconseq1__1(X11,X65)),v_sko__Hoare__Mirabelle__Xconseq1__2(X11,X65))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_452])]) ).
fof(f10474,plain,
( ! [X2,X0,X1] :
( c_Hoare__Mirabelle_Ohoare__derivs(X0,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X1,c_Com_Ocom_OSKIP,X2,t_a)),t_a)
| hBOOL(hAPP(hAPP(X1,v_sko__Hoare__Mirabelle__Xconseq1__1(X1,X2)),v_sko__Hoare__Mirabelle__Xconseq1__2(X1,X2))) )
| ~ spl0_114
| ~ spl0_452 ),
inference(resolution,[],[f9807,f1542]) ).
fof(f9807,plain,
( ! [X65,X39,X11,X57,X35] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X65,X35,X57,t_a)),t_a)
| c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X11,X35,X57,t_a)),t_a)
| hBOOL(hAPP(hAPP(X11,v_sko__Hoare__Mirabelle__Xconseq1__1(X11,X65)),v_sko__Hoare__Mirabelle__Xconseq1__2(X11,X65))) )
| ~ spl0_452 ),
inference(avatar_component_clause,[],[f9806]) ).
fof(f75326,plain,
( spl0_1006
| ~ spl0_114
| ~ spl0_451 ),
inference(avatar_split_clause,[],[f10473,f9802,f1541,f75324]) ).
fof(f75324,plain,
( spl0_1006
<=> ! [X2,X0,X1] :
( c_Hoare__Mirabelle_Ohoare__derivs(X0,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X1,c_Com_Ocom_OSKIP,X2,t_a)),t_a)
| hBOOL(hAPP(hAPP(X1,v_sko__Hoare__Mirabelle__Xconseq2__1(X2,X1)),v_sko__Hoare__Mirabelle__Xconseq2__2(X2,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1006])]) ).
fof(f9802,plain,
( spl0_451
<=> ! [X35,X57,X11,X64,X39] :
( c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X11,X35,X57,t_a)),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X11,X35,X64,t_a)),t_a)
| hBOOL(hAPP(hAPP(X64,v_sko__Hoare__Mirabelle__Xconseq2__1(X57,X64)),v_sko__Hoare__Mirabelle__Xconseq2__2(X57,X64))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_451])]) ).
fof(f10473,plain,
( ! [X2,X0,X1] :
( c_Hoare__Mirabelle_Ohoare__derivs(X0,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X1,c_Com_Ocom_OSKIP,X2,t_a)),t_a)
| hBOOL(hAPP(hAPP(X1,v_sko__Hoare__Mirabelle__Xconseq2__1(X2,X1)),v_sko__Hoare__Mirabelle__Xconseq2__2(X2,X1))) )
| ~ spl0_114
| ~ spl0_451 ),
inference(resolution,[],[f9803,f1542]) ).
fof(f9803,plain,
( ! [X39,X11,X57,X35,X64] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X11,X35,X64,t_a)),t_a)
| c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X11,X35,X57,t_a)),t_a)
| hBOOL(hAPP(hAPP(X64,v_sko__Hoare__Mirabelle__Xconseq2__1(X57,X64)),v_sko__Hoare__Mirabelle__Xconseq2__2(X57,X64))) )
| ~ spl0_451 ),
inference(avatar_component_clause,[],[f9802]) ).
fof(f75322,plain,
( spl0_1005
| ~ spl0_114
| ~ spl0_450 ),
inference(avatar_split_clause,[],[f10472,f9798,f1541,f75320]) ).
fof(f75320,plain,
( spl0_1005
<=> ! [X2,X0,X1] :
( c_Hoare__Mirabelle_Ohoare__derivs(X0,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X1,c_Com_Ocom_OSKIP,X2,t_a)),t_a)
| ~ hBOOL(hAPP(hAPP(X2,v_sko__Hoare__Mirabelle__Xconseq1__1(X1,X2)),v_sko__Hoare__Mirabelle__Xconseq1__2(X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1005])]) ).
fof(f9798,plain,
( spl0_450
<=> ! [X35,X57,X11,X39,X65] :
( c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X11,X35,X57,t_a)),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X65,X35,X57,t_a)),t_a)
| ~ hBOOL(hAPP(hAPP(X65,v_sko__Hoare__Mirabelle__Xconseq1__1(X11,X65)),v_sko__Hoare__Mirabelle__Xconseq1__2(X11,X65))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_450])]) ).
fof(f10472,plain,
( ! [X2,X0,X1] :
( c_Hoare__Mirabelle_Ohoare__derivs(X0,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X1,c_Com_Ocom_OSKIP,X2,t_a)),t_a)
| ~ hBOOL(hAPP(hAPP(X2,v_sko__Hoare__Mirabelle__Xconseq1__1(X1,X2)),v_sko__Hoare__Mirabelle__Xconseq1__2(X1,X2))) )
| ~ spl0_114
| ~ spl0_450 ),
inference(resolution,[],[f9799,f1542]) ).
fof(f9799,plain,
( ! [X65,X39,X11,X57,X35] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X65,X35,X57,t_a)),t_a)
| c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X11,X35,X57,t_a)),t_a)
| ~ hBOOL(hAPP(hAPP(X65,v_sko__Hoare__Mirabelle__Xconseq1__1(X11,X65)),v_sko__Hoare__Mirabelle__Xconseq1__2(X11,X65))) )
| ~ spl0_450 ),
inference(avatar_component_clause,[],[f9798]) ).
fof(f75318,plain,
( spl0_1004
| ~ spl0_114
| ~ spl0_449 ),
inference(avatar_split_clause,[],[f10471,f9794,f1541,f75316]) ).
fof(f75316,plain,
( spl0_1004
<=> ! [X2,X0,X1] :
( c_Hoare__Mirabelle_Ohoare__derivs(X0,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X1,c_Com_Ocom_OSKIP,X2,t_a)),t_a)
| ~ hBOOL(hAPP(hAPP(X2,v_sko__Hoare__Mirabelle__Xconseq2__1(X2,X1)),v_sko__Hoare__Mirabelle__Xconseq2__2(X2,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1004])]) ).
fof(f9794,plain,
( spl0_449
<=> ! [X35,X57,X11,X64,X39] :
( c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X11,X35,X57,t_a)),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X11,X35,X64,t_a)),t_a)
| ~ hBOOL(hAPP(hAPP(X57,v_sko__Hoare__Mirabelle__Xconseq2__1(X57,X64)),v_sko__Hoare__Mirabelle__Xconseq2__2(X57,X64))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_449])]) ).
fof(f10471,plain,
( ! [X2,X0,X1] :
( c_Hoare__Mirabelle_Ohoare__derivs(X0,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X1,c_Com_Ocom_OSKIP,X2,t_a)),t_a)
| ~ hBOOL(hAPP(hAPP(X2,v_sko__Hoare__Mirabelle__Xconseq2__1(X2,X1)),v_sko__Hoare__Mirabelle__Xconseq2__2(X2,X1))) )
| ~ spl0_114
| ~ spl0_449 ),
inference(resolution,[],[f9795,f1542]) ).
fof(f9795,plain,
( ! [X39,X11,X57,X35,X64] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X11,X35,X64,t_a)),t_a)
| c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X11,X35,X57,t_a)),t_a)
| ~ hBOOL(hAPP(hAPP(X57,v_sko__Hoare__Mirabelle__Xconseq2__1(X57,X64)),v_sko__Hoare__Mirabelle__Xconseq2__2(X57,X64))) )
| ~ spl0_449 ),
inference(avatar_component_clause,[],[f9794]) ).
fof(f75314,plain,
( spl0_1003
| ~ spl0_207
| ~ spl0_441 ),
inference(avatar_split_clause,[],[f9720,f9351,f2221,f75312]) ).
fof(f75312,plain,
( spl0_1003
<=> ! [X4,X0,X3,X2,X1] :
( ~ hBOOL(c_in(X4,hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X1),hAPP(hAPP(c_Set_Oinsert(X0),X2),X3)),X0))
| ~ hBOOL(c_in(X4,X3,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1003])]) ).
fof(f9720,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ hBOOL(c_in(X4,hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X1),hAPP(hAPP(c_Set_Oinsert(X0),X2),X3)),X0))
| ~ hBOOL(c_in(X4,X3,X0)) )
| ~ spl0_207
| ~ spl0_441 ),
inference(superposition,[],[f2222,f9352]) ).
fof(f75310,plain,
( spl0_1002
| ~ spl0_152
| ~ spl0_429 ),
inference(avatar_split_clause,[],[f9117,f8411,f1794,f75308]) ).
fof(f75308,plain,
( spl0_1002
<=> ! [X4,X0,X3,X2,X1] :
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X2),X3)),X4))
| ~ hBOOL(hAPP(X3,X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1002])]) ).
fof(f9117,plain,
( ! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X2),X3)),X4))
| ~ hBOOL(hAPP(X3,X4)) )
| ~ spl0_152
| ~ spl0_429 ),
inference(superposition,[],[f1795,f8412]) ).
fof(f75306,plain,
( spl0_1001
| ~ spl0_153
| ~ spl0_428 ),
inference(avatar_split_clause,[],[f8913,f8407,f1798,f75304]) ).
fof(f75304,plain,
( spl0_1001
<=> ! [X2,X4,X0,X3,X1] :
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X3)),X4))
| ~ hBOOL(hAPP(X1,X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1001])]) ).
fof(f8913,plain,
( ! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X3)),X4))
| ~ hBOOL(hAPP(X1,X4)) )
| ~ spl0_153
| ~ spl0_428 ),
inference(superposition,[],[f1799,f8408]) ).
fof(f75302,plain,
( spl0_1000
| ~ spl0_164
| ~ spl0_427 ),
inference(avatar_split_clause,[],[f8697,f8403,f1842,f75300]) ).
fof(f75300,plain,
( spl0_1000
<=> ! [X2,X4,X0,X3,X1] :
( ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X1),X3)),X4))
| hBOOL(hAPP(X1,X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1000])]) ).
fof(f8697,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X1),X3)),X4))
| hBOOL(hAPP(X1,X4)) )
| ~ spl0_164
| ~ spl0_427 ),
inference(superposition,[],[f1843,f8404]) ).
fof(f75248,plain,
( spl0_999
| ~ spl0_163
| ~ spl0_426 ),
inference(avatar_split_clause,[],[f8565,f8399,f1838,f75246]) ).
fof(f75246,plain,
( spl0_999
<=> ! [X4,X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X2),X3)),X4))
| hBOOL(hAPP(X3,X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_999])]) ).
fof(f8565,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X2),X3)),X4))
| hBOOL(hAPP(X3,X4)) )
| ~ spl0_163
| ~ spl0_426 ),
inference(superposition,[],[f1839,f8400]) ).
fof(f75244,plain,
( spl0_998
| ~ spl0_189
| ~ spl0_412 ),
inference(avatar_split_clause,[],[f8290,f7695,f2021,f75242]) ).
fof(f75242,plain,
( spl0_998
<=> ! [X4,X0,X3,X2,X1] : hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(hAPP(hAPP(c_Set_Oinsert(X4),X2),X3),X1,X4,tc_fun(X0,tc_bool))),hAPP(X1,X2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_998])]) ).
fof(f8290,plain,
( ! [X2,X3,X0,X1,X4] : hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(hAPP(hAPP(c_Set_Oinsert(X4),X2),X3),X1,X4,tc_fun(X0,tc_bool))),hAPP(X1,X2)))
| ~ spl0_189
| ~ spl0_412 ),
inference(superposition,[],[f2022,f7696]) ).
fof(f75240,plain,
( spl0_997
| ~ spl0_185
| ~ spl0_410 ),
inference(avatar_split_clause,[],[f8125,f7687,f2005,f75238]) ).
fof(f75238,plain,
( spl0_997
<=> ! [X2,X4,X0,X3,X1] : hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),hAPP(X1,X2)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_Set_Oinsert(X4),X2),X3),X1,X4,tc_fun(X0,tc_bool)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_997])]) ).
fof(f8125,plain,
( ! [X2,X3,X0,X1,X4] : hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),hAPP(X1,X2)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_Set_Oinsert(X4),X2),X3),X1,X4,tc_fun(X0,tc_bool))))
| ~ spl0_185
| ~ spl0_410 ),
inference(superposition,[],[f2006,f7688]) ).
fof(f75236,plain,
( spl0_996
| ~ spl0_83
| ~ spl0_416 ),
inference(avatar_split_clause,[],[f7905,f7848,f1385,f75234]) ).
fof(f75234,plain,
( spl0_996
<=> ! [X0,X3,X2,X1] : c_COMBK(c_False,tc_bool,X0) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),hAPP(c_fequal(X0),X1)),c_Finite__Set_Ofold1Set(X2,c_COMBK(c_False,tc_bool,X3),X3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_996])]) ).
fof(f1385,plain,
( spl0_83
<=> ! [X0,X1,X7] : ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(X7,c_COMBK(c_False,tc_bool,X0),X0),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_83])]) ).
fof(f7905,plain,
( ! [X2,X3,X0,X1] : c_COMBK(c_False,tc_bool,X0) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),hAPP(c_fequal(X0),X1)),c_Finite__Set_Ofold1Set(X2,c_COMBK(c_False,tc_bool,X3),X3))
| ~ spl0_83
| ~ spl0_416 ),
inference(resolution,[],[f7849,f1386]) ).
fof(f1386,plain,
( ! [X0,X1,X7] : ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(X7,c_COMBK(c_False,tc_bool,X0),X0),X1))
| ~ spl0_83 ),
inference(avatar_component_clause,[],[f1385]) ).
fof(f75232,plain,
( spl0_995
| ~ spl0_81
| ~ spl0_416 ),
inference(avatar_split_clause,[],[f7893,f7848,f1370,f75230]) ).
fof(f75230,plain,
( spl0_995
<=> ! [X0,X3,X2,X1] :
( c_COMBK(c_False,tc_bool,X0) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),hAPP(c_fequal(X0),X1)),hAPP(c_fequal(X2),X3))
| X1 = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_995])]) ).
fof(f7893,plain,
( ! [X2,X3,X0,X1] :
( c_COMBK(c_False,tc_bool,X0) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),hAPP(c_fequal(X0),X1)),hAPP(c_fequal(X2),X3))
| X1 = X3 )
| ~ spl0_81
| ~ spl0_416 ),
inference(resolution,[],[f7849,f1371]) ).
fof(f75228,plain,
( spl0_994
| ~ spl0_173
| ~ spl0_414 ),
inference(avatar_split_clause,[],[f7728,f7704,f1882,f75226]) ).
fof(f75226,plain,
( spl0_994
<=> ! [X0,X3,X2,X1] : hAPP(c_fequal(X0),X1) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),hAPP(c_fequal(X0),X1)),c_Finite__Set_Ofold1Set(X2,hAPP(c_fequal(X3),X1),X3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_994])]) ).
fof(f7728,plain,
( ! [X2,X3,X0,X1] : hAPP(c_fequal(X0),X1) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),hAPP(c_fequal(X0),X1)),c_Finite__Set_Ofold1Set(X2,hAPP(c_fequal(X3),X1),X3))
| ~ spl0_173
| ~ spl0_414 ),
inference(resolution,[],[f7705,f1883]) ).
fof(f75224,plain,
( spl0_993
| ~ spl0_75
| ~ spl0_414 ),
inference(avatar_split_clause,[],[f7720,f7704,f1344,f75222]) ).
fof(f75222,plain,
( spl0_993
<=> ! [X2,X0,X1] :
( hAPP(c_fequal(X0),X1) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),hAPP(c_fequal(X0),X1)),hAPP(c_lessequals(X2),c_Orderings_Obot__class_Obot(X2)))
| ~ class_Orderings_Obot(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_993])]) ).
fof(f7720,plain,
( ! [X2,X0,X1] :
( hAPP(c_fequal(X0),X1) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),hAPP(c_fequal(X0),X1)),hAPP(c_lessequals(X2),c_Orderings_Obot__class_Obot(X2)))
| ~ class_Orderings_Obot(X2) )
| ~ spl0_75
| ~ spl0_414 ),
inference(resolution,[],[f7705,f1345]) ).
fof(f75220,plain,
( spl0_992
| ~ spl0_221
| ~ spl0_391 ),
inference(avatar_split_clause,[],[f7016,f6760,f2283,f75218]) ).
fof(f75218,plain,
( spl0_992
<=> ! [X4,X0,X3,X2,X1] :
( hBOOL(c_in(X4,hAPP(hAPP(c_Set_Oinsert(X0),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X2),X3)),X0))
| ~ hBOOL(c_in(X4,X3,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_992])]) ).
fof(f7016,plain,
( ! [X2,X3,X0,X1,X4] :
( hBOOL(c_in(X4,hAPP(hAPP(c_Set_Oinsert(X0),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X2),X3)),X0))
| ~ hBOOL(c_in(X4,X3,X0)) )
| ~ spl0_221
| ~ spl0_391 ),
inference(superposition,[],[f2284,f6761]) ).
fof(f75216,plain,
( spl0_991
| ~ spl0_219
| ~ spl0_391 ),
inference(avatar_split_clause,[],[f7014,f6760,f2275,f75214]) ).
fof(f75214,plain,
( spl0_991
<=> ! [X3,X4,X0,X5,X2,X1] :
( ~ c_Fun_Oinj__on(X4,hAPP(hAPP(c_Set_Oinsert(X0),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X2),X3)),X0,X5)
| c_Fun_Oinj__on(X4,X3,X0,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_991])]) ).
fof(f7014,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ c_Fun_Oinj__on(X4,hAPP(hAPP(c_Set_Oinsert(X0),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X2),X3)),X0,X5)
| c_Fun_Oinj__on(X4,X3,X0,X5) )
| ~ spl0_219
| ~ spl0_391 ),
inference(superposition,[],[f2276,f6761]) ).
fof(f75212,plain,
( spl0_990
| ~ spl0_223
| ~ spl0_390 ),
inference(avatar_split_clause,[],[f6891,f6756,f2291,f75210]) ).
fof(f75210,plain,
( spl0_990
<=> ! [X4,X0,X3,X2,X1] :
( hBOOL(c_in(X4,hAPP(hAPP(c_Set_Oinsert(X0),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X3)),X0))
| ~ hBOOL(c_in(X4,X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_990])]) ).
fof(f6891,plain,
( ! [X2,X3,X0,X1,X4] :
( hBOOL(c_in(X4,hAPP(hAPP(c_Set_Oinsert(X0),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X3)),X0))
| ~ hBOOL(c_in(X4,X1,X0)) )
| ~ spl0_223
| ~ spl0_390 ),
inference(superposition,[],[f2292,f6757]) ).
fof(f75208,plain,
( spl0_989
| ~ spl0_120
| ~ spl0_969 ),
inference(avatar_split_clause,[],[f75089,f74983,f1591,f75206]) ).
fof(f75206,plain,
( spl0_989
<=> ! [X0] : c_False = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_bool),X0),c_Orderings_Otop__class_Otop(tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_989])]) ).
fof(f74983,plain,
( spl0_969
<=> ! [X0] : c_False = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_bool),hAPP(X0,v_x)),c_Orderings_Otop__class_Otop(tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_969])]) ).
fof(f75089,plain,
( ! [X0] : c_False = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_bool),X0),c_Orderings_Otop__class_Otop(tc_bool))
| ~ spl0_120
| ~ spl0_969 ),
inference(superposition,[],[f74984,f1592]) ).
fof(f74984,plain,
( ! [X0] : c_False = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_bool),hAPP(X0,v_x)),c_Orderings_Otop__class_Otop(tc_bool))
| ~ spl0_969 ),
inference(avatar_component_clause,[],[f74983]) ).
fof(f75204,plain,
( spl0_988
| ~ spl0_220
| ~ spl0_390 ),
inference(avatar_split_clause,[],[f6889,f6756,f2279,f75202]) ).
fof(f75202,plain,
( spl0_988
<=> ! [X2,X3,X4,X0,X5,X1] :
( ~ c_Fun_Oinj__on(X4,hAPP(hAPP(c_Set_Oinsert(X0),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X3)),X0,X5)
| c_Fun_Oinj__on(X4,X1,X0,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_988])]) ).
fof(f6889,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ c_Fun_Oinj__on(X4,hAPP(hAPP(c_Set_Oinsert(X0),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X3)),X0,X5)
| c_Fun_Oinj__on(X4,X1,X0,X5) )
| ~ spl0_220
| ~ spl0_390 ),
inference(superposition,[],[f2280,f6757]) ).
fof(f75181,plain,
( spl0_987
| spl0_41
| ~ spl0_51
| ~ spl0_200
| ~ spl0_382 ),
inference(avatar_split_clause,[],[f6608,f6524,f2066,f1237,f1193,f75179]) ).
fof(f75179,plain,
( spl0_987
<=> ! [X2,X0,X1,X3] : c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0)),X3,X2,t_a)),t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_987])]) ).
fof(f6608,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(c_False)
| c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0)),X3,X2,t_a)),t_a) )
| ~ spl0_51
| ~ spl0_200
| ~ spl0_382 ),
inference(forward_demodulation,[],[f6592,f1238]) ).
fof(f6592,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(hAPP(c_COMBK(c_False,tc_bool,X0),v_sko__Hoare__Mirabelle__Xescape__2(X1,hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0)),X2,X3)))
| c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0)),X3,X2,t_a)),t_a) )
| ~ spl0_200
| ~ spl0_382 ),
inference(superposition,[],[f6525,f2067]) ).
fof(f75177,plain,
( spl0_986
| ~ spl0_152
| ~ spl0_350 ),
inference(avatar_split_clause,[],[f5762,f5592,f1794,f75175]) ).
fof(f75175,plain,
( spl0_986
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X2),X1),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_986])]) ).
fof(f5762,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X2),X1),X3)) )
| ~ spl0_152
| ~ spl0_350 ),
inference(superposition,[],[f1795,f5593]) ).
fof(f75173,plain,
( spl0_985
| ~ spl0_153
| ~ spl0_349 ),
inference(avatar_split_clause,[],[f5698,f5588,f1798,f75171]) ).
fof(f75171,plain,
( spl0_985
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X1),X2),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_985])]) ).
fof(f5698,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X1),X2),X3)) )
| ~ spl0_153
| ~ spl0_349 ),
inference(superposition,[],[f1799,f5589]) ).
fof(f75169,plain,
( spl0_984
| ~ spl0_123
| ~ spl0_345 ),
inference(avatar_split_clause,[],[f5545,f4970,f1603,f75167]) ).
fof(f75167,plain,
( spl0_984
<=> ! [X0,X1] :
( c_COMBK(c_False,tc_bool,X0) != X1
| c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool))),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_984])]) ).
fof(f5545,plain,
( ! [X0,X1] :
( c_COMBK(c_False,tc_bool,X0) != X1
| c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool))),X1) )
| ~ spl0_123
| ~ spl0_345 ),
inference(superposition,[],[f4971,f1604]) ).
fof(f75165,plain,
( spl0_983
| ~ spl0_224
| ~ spl0_331 ),
inference(avatar_split_clause,[],[f5101,f4912,f2295,f75163]) ).
fof(f75163,plain,
( spl0_983
<=> ! [X4,X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X1),X2))
| hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X0),X3),X2),X4))
| ~ hBOOL(hAPP(X1,X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_983])]) ).
fof(f5101,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X1),X2))
| hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X0),X3),X2),X4))
| ~ hBOOL(hAPP(X1,X4)) )
| ~ spl0_224
| ~ spl0_331 ),
inference(resolution,[],[f4913,f2296]) ).
fof(f75161,plain,
( spl0_982
| ~ spl0_56
| ~ spl0_325 ),
inference(avatar_split_clause,[],[f5001,f4888,f1258,f75159]) ).
fof(f75159,plain,
( spl0_982
<=> ! [X3,X4,X0,X5,X2,X1] :
( ~ hBOOL(c_in(X0,X1,X2))
| hBOOL(c_in(X3,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,X4,X2,tc_fun(X5,tc_bool)),X5))
| ~ hBOOL(hAPP(hAPP(X4,X0),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_982])]) ).
fof(f5001,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ hBOOL(c_in(X0,X1,X2))
| hBOOL(c_in(X3,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,X4,X2,tc_fun(X5,tc_bool)),X5))
| ~ hBOOL(hAPP(hAPP(X4,X0),X3)) )
| ~ spl0_56
| ~ spl0_325 ),
inference(resolution,[],[f4889,f1259]) ).
fof(f75157,plain,
( spl0_981
| ~ spl0_56
| ~ spl0_324 ),
inference(avatar_split_clause,[],[f4989,f4884,f1258,f75155]) ).
fof(f75155,plain,
( spl0_981
<=> ! [X5,X4,X0,X3,X2,X1] :
( hBOOL(c_in(X0,hAPP(X1,X2),X3))
| ~ hBOOL(c_in(X2,X4,X5))
| ~ hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X4,X1,X5,tc_fun(X3,tc_bool)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_981])]) ).
fof(f4884,plain,
( spl0_324
<=> ! [X3,X4,X9,X0,X5,X8] :
( ~ hBOOL(c_in(X3,X5,X8))
| hBOOL(c_in(X4,hAPP(X9,X3),X0))
| ~ hBOOL(c_in(X4,c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,X9,X8,tc_fun(X0,tc_bool)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_324])]) ).
fof(f4989,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( hBOOL(c_in(X0,hAPP(X1,X2),X3))
| ~ hBOOL(c_in(X2,X4,X5))
| ~ hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X4,X1,X5,tc_fun(X3,tc_bool)),X0)) )
| ~ spl0_56
| ~ spl0_324 ),
inference(resolution,[],[f4885,f1259]) ).
fof(f4885,plain,
( ! [X3,X0,X8,X9,X4,X5] :
( ~ hBOOL(c_in(X4,c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,X9,X8,tc_fun(X0,tc_bool)),X0))
| hBOOL(c_in(X4,hAPP(X9,X3),X0))
| ~ hBOOL(c_in(X3,X5,X8)) )
| ~ spl0_324 ),
inference(avatar_component_clause,[],[f4884]) ).
fof(f75153,plain,
( spl0_980
| ~ spl0_146
| ~ spl0_289 ),
inference(avatar_split_clause,[],[f4279,f3903,f1716,f75151]) ).
fof(f75151,plain,
( spl0_980
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Set_Oinsert(X0),X1),X2)),X2))
| hAPP(hAPP(c_Set_Oinsert(X0),X1),X2) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_980])]) ).
fof(f4279,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Set_Oinsert(X0),X1),X2)),X2))
| hAPP(hAPP(c_Set_Oinsert(X0),X1),X2) = X2 )
| ~ spl0_146
| ~ spl0_289 ),
inference(resolution,[],[f3904,f1717]) ).
fof(f75025,plain,
( spl0_979
| ~ spl0_51
| ~ spl0_288 ),
inference(avatar_split_clause,[],[f4206,f3899,f1237,f75023]) ).
fof(f75023,plain,
( spl0_979
<=> ! [X5,X1,X4,X2,X0,X6,X3,X7] :
( ~ hBOOL(hAPP(X0,X4))
| ~ hBOOL(c_in(X3,X5,X6))
| hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,c_COMBK(X0,X1,X2),X6,tc_fun(X7,tc_bool)),X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_979])]) ).
fof(f4206,plain,
( ! [X2,X3,X0,X1,X6,X7,X4,X5] :
( ~ hBOOL(hAPP(X0,X4))
| ~ hBOOL(c_in(X3,X5,X6))
| hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,c_COMBK(X0,X1,X2),X6,tc_fun(X7,tc_bool)),X4)) )
| ~ spl0_51
| ~ spl0_288 ),
inference(superposition,[],[f3900,f1238]) ).
fof(f75021,plain,
( spl0_978
| ~ spl0_129
| ~ spl0_288 ),
inference(avatar_split_clause,[],[f4145,f3899,f1627,f75019]) ).
fof(f75019,plain,
( spl0_978
<=> ! [X5,X3,X4,X0,X6,X2,X1] :
( ~ hBOOL(c_in(X0,X1,X2))
| hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,hAPP(c_Set_Oinsert(X3),X4),X2,tc_fun(X5,tc_bool)),X6))
| ~ hBOOL(hAPP(X0,X6)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_978])]) ).
fof(f4145,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] :
( ~ hBOOL(c_in(X0,X1,X2))
| hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,hAPP(c_Set_Oinsert(X3),X4),X2,tc_fun(X5,tc_bool)),X6))
| ~ hBOOL(hAPP(X0,X6)) )
| ~ spl0_129
| ~ spl0_288 ),
inference(resolution,[],[f3900,f1628]) ).
fof(f75017,plain,
( spl0_977
| ~ spl0_183
| ~ spl0_271 ),
inference(avatar_split_clause,[],[f3744,f3635,f1997,f75015]) ).
fof(f75015,plain,
( spl0_977
<=> ! [X4,X0,X3,X2,X1] :
( ~ hBOOL(c_in(X0,X1,X2))
| ~ class_Complete__Lattice_Ocomplete__lattice(X3)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),hAPP(X4,X0)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,X4,X2,X3)))
| ~ class_Orderings_Opreorder(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_977])]) ).
fof(f3744,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ hBOOL(c_in(X0,X1,X2))
| ~ class_Complete__Lattice_Ocomplete__lattice(X3)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),hAPP(X4,X0)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,X4,X2,X3)))
| ~ class_Orderings_Opreorder(X3) )
| ~ spl0_183
| ~ spl0_271 ),
inference(resolution,[],[f3636,f1998]) ).
fof(f75013,plain,
( spl0_976
| ~ spl0_183
| ~ spl0_268 ),
inference(avatar_split_clause,[],[f3681,f3623,f1997,f75011]) ).
fof(f75011,plain,
( spl0_976
<=> ! [X4,X0,X3,X2,X1] :
( ~ hBOOL(c_in(X0,X1,X2))
| ~ class_Complete__Lattice_Ocomplete__lattice(X3)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,X4,X2,X3)),hAPP(X4,X0)))
| ~ class_Orderings_Opreorder(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_976])]) ).
fof(f3681,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ hBOOL(c_in(X0,X1,X2))
| ~ class_Complete__Lattice_Ocomplete__lattice(X3)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,X4,X2,X3)),hAPP(X4,X0)))
| ~ class_Orderings_Opreorder(X3) )
| ~ spl0_183
| ~ spl0_268 ),
inference(resolution,[],[f3624,f1998]) ).
fof(f75009,plain,
( spl0_975
| ~ spl0_108
| ~ spl0_260 ),
inference(avatar_split_clause,[],[f3462,f3109,f1516,f75007]) ).
fof(f75007,plain,
( spl0_975
<=> ! [X0,X1] :
( c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)) = X1
| ~ class_Orderings_Oorder(tc_fun(X0,tc_bool))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),X1),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_975])]) ).
fof(f3462,plain,
( ! [X0,X1] :
( c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)) = X1
| ~ class_Orderings_Oorder(tc_fun(X0,tc_bool))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),X1),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)))) )
| ~ spl0_108
| ~ spl0_260 ),
inference(resolution,[],[f3110,f1517]) ).
fof(f75005,plain,
( spl0_974
| ~ spl0_113
| ~ spl0_260 ),
inference(avatar_split_clause,[],[f3447,f3109,f1537,f75003]) ).
fof(f75003,plain,
( spl0_974
<=> ! [X0,X1] :
( c_COMBK(c_False,tc_bool,X1) = X0
| ~ class_Orderings_Oorder(tc_fun(X1,tc_bool))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),c_COMBK(c_False,tc_bool,X1)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_974])]) ).
fof(f3447,plain,
( ! [X0,X1] :
( c_COMBK(c_False,tc_bool,X1) = X0
| ~ class_Orderings_Oorder(tc_fun(X1,tc_bool))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),c_COMBK(c_False,tc_bool,X1)),X0)) )
| ~ spl0_113
| ~ spl0_260 ),
inference(resolution,[],[f3110,f1538]) ).
fof(f75001,plain,
( spl0_973
| ~ spl0_80
| ~ spl0_248 ),
inference(avatar_split_clause,[],[f3181,f3051,f1365,f74999]) ).
fof(f74999,plain,
( spl0_973
<=> ! [X2,X0,X1] :
( ~ c_Finite__Set_Ofinite(hAPP(c_HOL_Oord__class_Oless(tc_bool),v_P),X0)
| ~ hBOOL(c_in(hAPP(c_Not,v_P),X1,X2))
| c_Finite__Set_Ofinite(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,c_and,X2,tc_fun(X0,tc_bool)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_973])]) ).
fof(f3181,plain,
( ! [X2,X0,X1] :
( ~ c_Finite__Set_Ofinite(hAPP(c_HOL_Oord__class_Oless(tc_bool),v_P),X0)
| ~ hBOOL(c_in(hAPP(c_Not,v_P),X1,X2))
| c_Finite__Set_Ofinite(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,c_and,X2,tc_fun(X0,tc_bool)),X0) )
| ~ spl0_80
| ~ spl0_248 ),
inference(superposition,[],[f3052,f1367]) ).
fof(f74997,plain,
( spl0_972
| ~ spl0_79
| ~ spl0_248 ),
inference(avatar_split_clause,[],[f3151,f3051,f1361,f74995]) ).
fof(f74995,plain,
( spl0_972
<=> ! [X4,X0,X3,X2,X1] :
( ~ c_Finite__Set_Ofinite(X1,X2)
| ~ hBOOL(c_in(X1,X3,X4))
| c_Finite__Set_Ofinite(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X3,hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X1),X4,tc_fun(X2,tc_bool)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_972])]) ).
fof(f3151,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ c_Finite__Set_Ofinite(X1,X2)
| ~ hBOOL(c_in(X1,X3,X4))
| c_Finite__Set_Ofinite(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X3,hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X1),X4,tc_fun(X2,tc_bool)),X2) )
| ~ spl0_79
| ~ spl0_248 ),
inference(superposition,[],[f3052,f1362]) ).
fof(f74993,plain,
( spl0_971
| ~ spl0_68
| ~ spl0_248 ),
inference(avatar_split_clause,[],[f3150,f3051,f1316,f74991]) ).
fof(f74991,plain,
( spl0_971
<=> ! [X4,X0,X3,X2,X1] :
( ~ c_Finite__Set_Ofinite(X1,X2)
| ~ hBOOL(c_in(X1,X3,X4))
| c_Finite__Set_Ofinite(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X3,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X4,tc_fun(X2,tc_bool)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_971])]) ).
fof(f3150,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ c_Finite__Set_Ofinite(X1,X2)
| ~ hBOOL(c_in(X1,X3,X4))
| c_Finite__Set_Ofinite(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X3,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X4,tc_fun(X2,tc_bool)),X2) )
| ~ spl0_68
| ~ spl0_248 ),
inference(superposition,[],[f3052,f1317]) ).
fof(f74989,plain,
( spl0_970
| ~ spl0_126
| ~ spl0_248 ),
inference(avatar_split_clause,[],[f3144,f3051,f1615,f74987]) ).
fof(f74987,plain,
( spl0_970
<=> ! [X4,X0,X3,X2,X1] :
( ~ hBOOL(c_in(X0,X1,X2))
| c_Finite__Set_Ofinite(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X4),X2,tc_fun(X3,tc_bool)),X3)
| ~ c_Finite__Set_Ofinite(X0,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_970])]) ).
fof(f3144,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ hBOOL(c_in(X0,X1,X2))
| c_Finite__Set_Ofinite(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X4),X2,tc_fun(X3,tc_bool)),X3)
| ~ c_Finite__Set_Ofinite(X0,X3) )
| ~ spl0_126
| ~ spl0_248 ),
inference(resolution,[],[f3052,f1616]) ).
fof(f74985,plain,
( spl0_969
| ~ spl0_51
| ~ spl0_198
| ~ spl0_910
| ~ spl0_912 ),
inference(avatar_split_clause,[],[f73163,f69988,f69980,f2058,f1237,f74983]) ).
fof(f73163,plain,
( ! [X0] : c_False = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_bool),hAPP(X0,v_x)),c_Orderings_Otop__class_Otop(tc_bool))
| ~ spl0_51
| ~ spl0_198
| ~ spl0_910
| ~ spl0_912 ),
inference(forward_demodulation,[],[f73162,f1238]) ).
fof(f73162,plain,
( ! [X0] : hAPP(c_COMBK(c_False,tc_bool,t_a),v_x) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_bool),hAPP(X0,v_x)),c_Orderings_Otop__class_Otop(tc_bool))
| ~ spl0_198
| ~ spl0_910
| ~ spl0_912 ),
inference(forward_demodulation,[],[f73088,f69981]) ).
fof(f73088,plain,
( ! [X0] : hAPP(c_COMBK(c_False,tc_bool,t_a),v_x) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_bool),hAPP(X0,v_x)),hAPP(c_Orderings_Otop__class_Otop(tc_fun(t_a,tc_bool)),v_x))
| ~ spl0_198
| ~ spl0_912 ),
inference(superposition,[],[f69989,f2059]) ).
fof(f74981,plain,
( spl0_968
| ~ spl0_127
| ~ spl0_248 ),
inference(avatar_split_clause,[],[f3143,f3051,f1619,f74979]) ).
fof(f74979,plain,
( spl0_968
<=> ! [X4,X0,X3,X2,X1] :
( ~ hBOOL(c_in(X0,X1,X2))
| c_Finite__Set_Ofinite(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X4),X2,tc_fun(X3,tc_bool)),X3)
| ~ c_Finite__Set_Ofinite(X4,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_968])]) ).
fof(f3143,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ hBOOL(c_in(X0,X1,X2))
| c_Finite__Set_Ofinite(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X4),X2,tc_fun(X3,tc_bool)),X3)
| ~ c_Finite__Set_Ofinite(X4,X3) )
| ~ spl0_127
| ~ spl0_248 ),
inference(resolution,[],[f3052,f1620]) ).
fof(f74977,plain,
( spl0_967
| ~ spl0_119
| ~ spl0_248 ),
inference(avatar_split_clause,[],[f3142,f3051,f1587,f74975]) ).
fof(f74975,plain,
( spl0_967
<=> ! [X4,X0,X3,X2,X1] :
( ~ hBOOL(c_in(X0,X1,X2))
| c_Finite__Set_Ofinite(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X3,tc_bool)),X4),X2,tc_fun(X3,tc_bool)),X3)
| ~ c_Finite__Set_Ofinite(X4,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_967])]) ).
fof(f1587,plain,
( spl0_119
<=> ! [X5,X9,X0] :
( ~ c_Finite__Set_Ofinite(X5,X0)
| c_Finite__Set_Ofinite(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X5),X9),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_119])]) ).
fof(f3142,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ hBOOL(c_in(X0,X1,X2))
| c_Finite__Set_Ofinite(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X3,tc_bool)),X4),X2,tc_fun(X3,tc_bool)),X3)
| ~ c_Finite__Set_Ofinite(X4,X3) )
| ~ spl0_119
| ~ spl0_248 ),
inference(resolution,[],[f3052,f1588]) ).
fof(f1588,plain,
( ! [X0,X9,X5] :
( c_Finite__Set_Ofinite(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X5),X9),X0)
| ~ c_Finite__Set_Ofinite(X5,X0) )
| ~ spl0_119 ),
inference(avatar_component_clause,[],[f1587]) ).
fof(f74973,plain,
( spl0_966
| ~ spl0_24
| ~ spl0_242 ),
inference(avatar_split_clause,[],[f3039,f2682,f1123,f74971]) ).
fof(f74971,plain,
( spl0_966
<=> ! [X4,X0,X3,X2,X1] :
( c_COMBK(c_False,tc_bool,X0) = X1
| c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,c_COMBK(X2,tc_fun(X3,X4),X0),X0,tc_fun(X3,X4)) = X2
| ~ class_Complete__Lattice_Ocomplete__lattice(X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_966])]) ).
fof(f1123,plain,
( spl0_24
<=> ! [X75,X74] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X75)
| class_Complete__Lattice_Ocomplete__lattice(tc_fun(X74,X75)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_24])]) ).
fof(f2682,plain,
( spl0_242
<=> ! [X18,X0,X5,X8] :
( c_COMBK(c_False,tc_bool,X0) = X5
| ~ class_Complete__Lattice_Ocomplete__lattice(X8)
| c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,c_COMBK(X18,X8,X0),X0,X8) = X18 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_242])]) ).
fof(f3039,plain,
( ! [X2,X3,X0,X1,X4] :
( c_COMBK(c_False,tc_bool,X0) = X1
| c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,c_COMBK(X2,tc_fun(X3,X4),X0),X0,tc_fun(X3,X4)) = X2
| ~ class_Complete__Lattice_Ocomplete__lattice(X4) )
| ~ spl0_24
| ~ spl0_242 ),
inference(resolution,[],[f2683,f1124]) ).
fof(f1124,plain,
( ! [X74,X75] :
( class_Complete__Lattice_Ocomplete__lattice(tc_fun(X74,X75))
| ~ class_Complete__Lattice_Ocomplete__lattice(X75) )
| ~ spl0_24 ),
inference(avatar_component_clause,[],[f1123]) ).
fof(f2683,plain,
( ! [X0,X18,X8,X5] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X8)
| c_COMBK(c_False,tc_bool,X0) = X5
| c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,c_COMBK(X18,X8,X0),X0,X8) = X18 )
| ~ spl0_242 ),
inference(avatar_component_clause,[],[f2682]) ).
fof(f74969,plain,
( spl0_965
| ~ spl0_24
| ~ spl0_241 ),
inference(avatar_split_clause,[],[f3037,f2678,f1123,f74967]) ).
fof(f74967,plain,
( spl0_965
<=> ! [X4,X0,X3,X2,X1] :
( c_COMBK(c_False,tc_bool,X0) = X1
| c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,c_COMBK(X2,tc_fun(X3,X4),X0),X0,tc_fun(X3,X4)) = X2
| ~ class_Complete__Lattice_Ocomplete__lattice(X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_965])]) ).
fof(f2678,plain,
( spl0_241
<=> ! [X18,X0,X5,X8] :
( c_COMBK(c_False,tc_bool,X0) = X5
| ~ class_Complete__Lattice_Ocomplete__lattice(X8)
| c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,c_COMBK(X18,X8,X0),X0,X8) = X18 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_241])]) ).
fof(f3037,plain,
( ! [X2,X3,X0,X1,X4] :
( c_COMBK(c_False,tc_bool,X0) = X1
| c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,c_COMBK(X2,tc_fun(X3,X4),X0),X0,tc_fun(X3,X4)) = X2
| ~ class_Complete__Lattice_Ocomplete__lattice(X4) )
| ~ spl0_24
| ~ spl0_241 ),
inference(resolution,[],[f2679,f1124]) ).
fof(f2679,plain,
( ! [X0,X18,X8,X5] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X8)
| c_COMBK(c_False,tc_bool,X0) = X5
| c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,c_COMBK(X18,X8,X0),X0,X8) = X18 )
| ~ spl0_241 ),
inference(avatar_component_clause,[],[f2678]) ).
fof(f74965,plain,
( spl0_964
| ~ spl0_163
| ~ spl0_233 ),
inference(avatar_split_clause,[],[f2972,f2645,f1838,f74963]) ).
fof(f74963,plain,
( spl0_964
<=> ! [X5,X6,X4,X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(hAPP(c_COMBS(X4,X5,X6),hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X1)),X3),X2))
| hBOOL(hAPP(X2,hAPP(X3,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_964])]) ).
fof(f2972,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] :
( ~ hBOOL(hAPP(hAPP(hAPP(c_COMBS(X4,X5,X6),hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X1)),X3),X2))
| hBOOL(hAPP(X2,hAPP(X3,X2))) )
| ~ spl0_163
| ~ spl0_233 ),
inference(superposition,[],[f1839,f2646]) ).
fof(f74961,plain,
( spl0_963
| ~ spl0_164
| ~ spl0_233 ),
inference(avatar_split_clause,[],[f2971,f2645,f1842,f74959]) ).
fof(f74959,plain,
( spl0_963
<=> ! [X5,X6,X4,X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(hAPP(c_COMBS(X4,X5,X6),hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X1)),X3),X2))
| hBOOL(hAPP(X1,hAPP(X3,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_963])]) ).
fof(f2971,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] :
( ~ hBOOL(hAPP(hAPP(hAPP(c_COMBS(X4,X5,X6),hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X1)),X3),X2))
| hBOOL(hAPP(X1,hAPP(X3,X2))) )
| ~ spl0_164
| ~ spl0_233 ),
inference(superposition,[],[f1843,f2646]) ).
fof(f74957,plain,
( spl0_962
| ~ spl0_152
| ~ spl0_233 ),
inference(avatar_split_clause,[],[f2970,f2645,f1794,f74955]) ).
fof(f74955,plain,
( spl0_962
<=> ! [X5,X6,X4,X0,X3,X2,X1] :
( hBOOL(hAPP(hAPP(hAPP(c_COMBS(X4,X5,X6),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1)),X3),X2))
| ~ hBOOL(hAPP(X2,hAPP(X3,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_962])]) ).
fof(f2970,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] :
( hBOOL(hAPP(hAPP(hAPP(c_COMBS(X4,X5,X6),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1)),X3),X2))
| ~ hBOOL(hAPP(X2,hAPP(X3,X2))) )
| ~ spl0_152
| ~ spl0_233 ),
inference(superposition,[],[f1795,f2646]) ).
fof(f74953,plain,
( spl0_961
| ~ spl0_153
| ~ spl0_233 ),
inference(avatar_split_clause,[],[f2969,f2645,f1798,f74951]) ).
fof(f74951,plain,
( spl0_961
<=> ! [X5,X6,X4,X0,X3,X2,X1] :
( hBOOL(hAPP(hAPP(hAPP(c_COMBS(X4,X5,X6),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1)),X3),X2))
| ~ hBOOL(hAPP(X1,hAPP(X3,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_961])]) ).
fof(f2969,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] :
( hBOOL(hAPP(hAPP(hAPP(c_COMBS(X4,X5,X6),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1)),X3),X2))
| ~ hBOOL(hAPP(X1,hAPP(X3,X2))) )
| ~ spl0_153
| ~ spl0_233 ),
inference(superposition,[],[f1799,f2646]) ).
fof(f74949,plain,
( spl0_960
| ~ spl0_169
| ~ spl0_233 ),
inference(avatar_split_clause,[],[f2959,f2645,f1865,f74947]) ).
fof(f74947,plain,
( spl0_960
<=> ! [X3,X4,X0,X5,X2,X1] :
( ~ hBOOL(hAPP(hAPP(hAPP(c_COMBS(X3,X4,X5),c_lessequals(tc_fun(X0,tc_bool))),X2),X1))
| c_Finite__Set_Ofinite(X1,X0)
| ~ c_Finite__Set_Ofinite(hAPP(X2,X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_960])]) ).
fof(f2959,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ hBOOL(hAPP(hAPP(hAPP(c_COMBS(X3,X4,X5),c_lessequals(tc_fun(X0,tc_bool))),X2),X1))
| c_Finite__Set_Ofinite(X1,X0)
| ~ c_Finite__Set_Ofinite(hAPP(X2,X1),X0) )
| ~ spl0_169
| ~ spl0_233 ),
inference(superposition,[],[f1866,f2646]) ).
fof(f74945,plain,
( spl0_959
| ~ spl0_159
| ~ spl0_233 ),
inference(avatar_split_clause,[],[f2955,f2645,f1822,f74943]) ).
fof(f74943,plain,
( spl0_959
<=> ! [X3,X4,X0,X5,X2,X1] :
( c_Orderings_Otop__class_Otop(X0) != hAPP(hAPP(hAPP(c_COMBS(X3,X4,X5),c_Lattices_Olower__semilattice__class_Oinf(X0)),X2),X1)
| c_Orderings_Otop__class_Otop(X0) = hAPP(X2,X1)
| ~ class_Lattices_Obounded__lattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_959])]) ).
fof(f1822,plain,
( spl0_159
<=> ! [X5,X9,X0] :
( ~ class_Lattices_Obounded__lattice(X0)
| c_Orderings_Otop__class_Otop(X0) = X9
| c_Orderings_Otop__class_Otop(X0) != hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X5),X9) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_159])]) ).
fof(f2955,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( c_Orderings_Otop__class_Otop(X0) != hAPP(hAPP(hAPP(c_COMBS(X3,X4,X5),c_Lattices_Olower__semilattice__class_Oinf(X0)),X2),X1)
| c_Orderings_Otop__class_Otop(X0) = hAPP(X2,X1)
| ~ class_Lattices_Obounded__lattice(X0) )
| ~ spl0_159
| ~ spl0_233 ),
inference(superposition,[],[f1823,f2646]) ).
fof(f1823,plain,
( ! [X0,X9,X5] :
( c_Orderings_Otop__class_Otop(X0) != hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X5),X9)
| c_Orderings_Otop__class_Otop(X0) = X9
| ~ class_Lattices_Obounded__lattice(X0) )
| ~ spl0_159 ),
inference(avatar_component_clause,[],[f1822]) ).
fof(f74882,plain,
( spl0_958
| ~ spl0_209
| ~ spl0_233 ),
inference(avatar_split_clause,[],[f2950,f2645,f2229,f74880]) ).
fof(f74880,plain,
( spl0_958
<=> ! [X3,X4,X0,X6,X5,X2,X1] :
( ~ hBOOL(c_in(X6,hAPP(hAPP(hAPP(c_COMBS(X3,X4,X5),c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool))),X2),X1),X0))
| hBOOL(c_in(X6,X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_958])]) ).
fof(f2950,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] :
( ~ hBOOL(c_in(X6,hAPP(hAPP(hAPP(c_COMBS(X3,X4,X5),c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool))),X2),X1),X0))
| hBOOL(c_in(X6,X1,X0)) )
| ~ spl0_209
| ~ spl0_233 ),
inference(superposition,[],[f2230,f2646]) ).
fof(f74878,plain,
( spl0_957
| ~ spl0_163
| ~ spl0_233 ),
inference(avatar_split_clause,[],[f2944,f2645,f1838,f74876]) ).
fof(f74876,plain,
( spl0_957
<=> ! [X5,X3,X4,X0,X6,X2,X1] :
( ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_COMBS(X3,X4,X5),c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool))),X2),X1),X6))
| hBOOL(hAPP(hAPP(X2,X1),X6)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_957])]) ).
fof(f2944,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] :
( ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_COMBS(X3,X4,X5),c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool))),X2),X1),X6))
| hBOOL(hAPP(hAPP(X2,X1),X6)) )
| ~ spl0_163
| ~ spl0_233 ),
inference(superposition,[],[f1839,f2646]) ).
fof(f74874,plain,
( spl0_956
| ~ spl0_205
| ~ spl0_233 ),
inference(avatar_split_clause,[],[f2938,f2645,f2213,f74872]) ).
fof(f74872,plain,
( spl0_956
<=> ! [X3,X4,X0,X7,X6,X5,X2,X1] :
( c_Fun_Oinj__on(X6,hAPP(hAPP(hAPP(c_COMBS(X3,X4,X5),c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool))),X2),X1),X0,X7)
| ~ c_Fun_Oinj__on(X6,X1,X0,X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_956])]) ).
fof(f2213,plain,
( spl0_205
<=> ! [X9,X0,X5,X8,X7] :
( ~ c_Fun_Oinj__on(X7,X5,X0,X8)
| c_Fun_Oinj__on(X7,hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X5),X9),X0,X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_205])]) ).
fof(f2938,plain,
( ! [X2,X3,X0,X1,X6,X7,X4,X5] :
( c_Fun_Oinj__on(X6,hAPP(hAPP(hAPP(c_COMBS(X3,X4,X5),c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool))),X2),X1),X0,X7)
| ~ c_Fun_Oinj__on(X6,X1,X0,X7) )
| ~ spl0_205
| ~ spl0_233 ),
inference(superposition,[],[f2214,f2646]) ).
fof(f2214,plain,
( ! [X0,X8,X9,X7,X5] :
( c_Fun_Oinj__on(X7,hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X5),X9),X0,X8)
| ~ c_Fun_Oinj__on(X7,X5,X0,X8) )
| ~ spl0_205 ),
inference(avatar_component_clause,[],[f2213]) ).
fof(f74870,plain,
( spl0_955
| ~ spl0_206
| ~ spl0_233 ),
inference(avatar_split_clause,[],[f2937,f2645,f2217,f74868]) ).
fof(f74868,plain,
( spl0_955
<=> ! [X3,X4,X0,X6,X5,X2,X1] :
( ~ hBOOL(c_in(X6,hAPP(hAPP(hAPP(c_COMBS(X3,X4,X5),c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool))),X2),X1),X0))
| hBOOL(c_in(X6,X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_955])]) ).
fof(f2217,plain,
( spl0_206
<=> ! [X35,X9,X0,X5] :
( hBOOL(c_in(X35,X5,X0))
| ~ hBOOL(c_in(X35,hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X5),X9),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_206])]) ).
fof(f2937,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] :
( ~ hBOOL(c_in(X6,hAPP(hAPP(hAPP(c_COMBS(X3,X4,X5),c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool))),X2),X1),X0))
| hBOOL(c_in(X6,X1,X0)) )
| ~ spl0_206
| ~ spl0_233 ),
inference(superposition,[],[f2218,f2646]) ).
fof(f2218,plain,
( ! [X0,X9,X35,X5] :
( ~ hBOOL(c_in(X35,hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X5),X9),X0))
| hBOOL(c_in(X35,X5,X0)) )
| ~ spl0_206 ),
inference(avatar_component_clause,[],[f2217]) ).
fof(f74866,plain,
( spl0_954
| ~ spl0_168
| ~ spl0_233 ),
inference(avatar_split_clause,[],[f2932,f2645,f1858,f74864]) ).
fof(f74864,plain,
( spl0_954
<=> ! [X3,X4,X0,X7,X6,X5,X2,X1] :
( ~ c_Fun_Oinj__on(X6,hAPP(hAPP(hAPP(c_COMBS(X3,X4,X5),c_Set_Oinsert(X0)),X2),X1),X0,X7)
| c_Fun_Oinj__on(X6,hAPP(X2,X1),X0,X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_954])]) ).
fof(f2932,plain,
( ! [X2,X3,X0,X1,X6,X7,X4,X5] :
( ~ c_Fun_Oinj__on(X6,hAPP(hAPP(hAPP(c_COMBS(X3,X4,X5),c_Set_Oinsert(X0)),X2),X1),X0,X7)
| c_Fun_Oinj__on(X6,hAPP(X2,X1),X0,X7) )
| ~ spl0_168
| ~ spl0_233 ),
inference(superposition,[],[f1859,f2646]) ).
fof(f74862,plain,
( spl0_953
| ~ spl0_167
| ~ spl0_233 ),
inference(avatar_split_clause,[],[f2931,f2645,f1854,f74860]) ).
fof(f74860,plain,
( spl0_953
<=> ! [X3,X4,X0,X6,X5,X2,X1] :
( hBOOL(c_in(X6,hAPP(hAPP(hAPP(c_COMBS(X3,X4,X5),c_Set_Oinsert(X0)),X2),X1),X0))
| ~ hBOOL(c_in(X6,hAPP(X2,X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_953])]) ).
fof(f2931,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] :
( hBOOL(c_in(X6,hAPP(hAPP(hAPP(c_COMBS(X3,X4,X5),c_Set_Oinsert(X0)),X2),X1),X0))
| ~ hBOOL(c_in(X6,hAPP(X2,X1),X0)) )
| ~ spl0_167
| ~ spl0_233 ),
inference(superposition,[],[f1855,f2646]) ).
fof(f74858,plain,
( spl0_952
| ~ spl0_166
| ~ spl0_233 ),
inference(avatar_split_clause,[],[f2918,f2645,f1850,f74856]) ).
fof(f74856,plain,
( spl0_952
<=> ! [X3,X4,X0,X5,X2,X1] :
( c_Orderings_Obot__class_Obot(X0) != hAPP(hAPP(hAPP(c_COMBS(X3,X4,X5),c_Lattices_Oupper__semilattice__class_Osup(X0)),X2),X1)
| c_Orderings_Obot__class_Obot(X0) = hAPP(X2,X1)
| ~ class_Lattices_Obounded__lattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_952])]) ).
fof(f1850,plain,
( spl0_166
<=> ! [X5,X9,X0] :
( ~ class_Lattices_Obounded__lattice(X0)
| c_Orderings_Obot__class_Obot(X0) = X9
| c_Orderings_Obot__class_Obot(X0) != hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X5),X9) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_166])]) ).
fof(f2918,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( c_Orderings_Obot__class_Obot(X0) != hAPP(hAPP(hAPP(c_COMBS(X3,X4,X5),c_Lattices_Oupper__semilattice__class_Osup(X0)),X2),X1)
| c_Orderings_Obot__class_Obot(X0) = hAPP(X2,X1)
| ~ class_Lattices_Obounded__lattice(X0) )
| ~ spl0_166
| ~ spl0_233 ),
inference(superposition,[],[f1851,f2646]) ).
fof(f1851,plain,
( ! [X0,X9,X5] :
( c_Orderings_Obot__class_Obot(X0) != hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X5),X9)
| c_Orderings_Obot__class_Obot(X0) = X9
| ~ class_Lattices_Obounded__lattice(X0) )
| ~ spl0_166 ),
inference(avatar_component_clause,[],[f1850]) ).
fof(f74854,plain,
( spl0_951
| ~ spl0_223
| ~ spl0_233 ),
inference(avatar_split_clause,[],[f2912,f2645,f2291,f74852]) ).
fof(f74852,plain,
( spl0_951
<=> ! [X3,X4,X0,X6,X5,X2,X1] :
( hBOOL(c_in(X6,hAPP(hAPP(hAPP(c_COMBS(X3,X4,X5),c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool))),X2),X1),X0))
| ~ hBOOL(c_in(X6,X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_951])]) ).
fof(f2912,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] :
( hBOOL(c_in(X6,hAPP(hAPP(hAPP(c_COMBS(X3,X4,X5),c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool))),X2),X1),X0))
| ~ hBOOL(c_in(X6,X1,X0)) )
| ~ spl0_223
| ~ spl0_233 ),
inference(superposition,[],[f2292,f2646]) ).
fof(f74850,plain,
( spl0_950
| ~ spl0_220
| ~ spl0_233 ),
inference(avatar_split_clause,[],[f2910,f2645,f2279,f74848]) ).
fof(f74848,plain,
( spl0_950
<=> ! [X3,X4,X0,X7,X6,X5,X2,X1] :
( ~ c_Fun_Oinj__on(X6,hAPP(hAPP(hAPP(c_COMBS(X3,X4,X5),c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool))),X2),X1),X0,X7)
| c_Fun_Oinj__on(X6,X1,X0,X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_950])]) ).
fof(f2910,plain,
( ! [X2,X3,X0,X1,X6,X7,X4,X5] :
( ~ c_Fun_Oinj__on(X6,hAPP(hAPP(hAPP(c_COMBS(X3,X4,X5),c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool))),X2),X1),X0,X7)
| c_Fun_Oinj__on(X6,X1,X0,X7) )
| ~ spl0_220
| ~ spl0_233 ),
inference(superposition,[],[f2280,f2646]) ).
fof(f74846,plain,
( spl0_949
| ~ spl0_152
| ~ spl0_233 ),
inference(avatar_split_clause,[],[f2904,f2645,f1794,f74844]) ).
fof(f74844,plain,
( spl0_949
<=> ! [X5,X3,X4,X0,X6,X2,X1] :
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_COMBS(X3,X4,X5),c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool))),X2),X1),X6))
| ~ hBOOL(hAPP(hAPP(X2,X1),X6)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_949])]) ).
fof(f2904,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] :
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_COMBS(X3,X4,X5),c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool))),X2),X1),X6))
| ~ hBOOL(hAPP(hAPP(X2,X1),X6)) )
| ~ spl0_152
| ~ spl0_233 ),
inference(superposition,[],[f1795,f2646]) ).
fof(f74842,plain,
( spl0_948
| ~ spl0_120
| ~ spl0_944 ),
inference(avatar_split_clause,[],[f74174,f73673,f1591,f74840]) ).
fof(f74840,plain,
( spl0_948
<=> ! [X0] : c_False = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_bool),c_False),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_948])]) ).
fof(f73673,plain,
( spl0_944
<=> ! [X0] : c_False = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_bool),c_False),hAPP(X0,v_x)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_944])]) ).
fof(f74174,plain,
( ! [X0] : c_False = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_bool),c_False),X0)
| ~ spl0_120
| ~ spl0_944 ),
inference(superposition,[],[f73674,f1592]) ).
fof(f73674,plain,
( ! [X0] : c_False = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_bool),c_False),hAPP(X0,v_x))
| ~ spl0_944 ),
inference(avatar_component_clause,[],[f73673]) ).
fof(f74838,plain,
( spl0_947
| ~ spl0_170
| ~ spl0_233 ),
inference(avatar_split_clause,[],[f2878,f2645,f1869,f74836]) ).
fof(f74836,plain,
( spl0_947
<=> ! [X2,X3,X0,X1,X8,X6,X7,X4,X5] : hAPP(hAPP(X0,hAPP(X5,X4)),X4) = hAPP(hAPP(hAPP(c_COMBS(X6,X7,X8),c_COMBC(X0,X1,X2,X3)),X5),X4) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_947])]) ).
fof(f2878,plain,
( ! [X2,X3,X0,X1,X8,X6,X7,X4,X5] : hAPP(hAPP(X0,hAPP(X5,X4)),X4) = hAPP(hAPP(hAPP(c_COMBS(X6,X7,X8),c_COMBC(X0,X1,X2,X3)),X5),X4)
| ~ spl0_170
| ~ spl0_233 ),
inference(superposition,[],[f2646,f1870]) ).
fof(f74834,plain,
( spl0_946
| ~ spl0_169
| ~ spl0_225 ),
inference(avatar_split_clause,[],[f2618,f2299,f1865,f74832]) ).
fof(f74832,plain,
( spl0_946
<=> ! [X2,X0,X1] :
( ~ hBOOL(c_in(X0,X1,tc_fun(X2,tc_bool)))
| ~ class_Complete__Lattice_Ocomplete__lattice(tc_fun(X2,tc_bool))
| c_Finite__Set_Ofinite(X0,X2)
| ~ c_Finite__Set_Ofinite(hAPP(c_Complete__Lattice_OSup__class_OSup(tc_fun(X2,tc_bool)),X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_946])]) ).
fof(f2618,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(c_in(X0,X1,tc_fun(X2,tc_bool)))
| ~ class_Complete__Lattice_Ocomplete__lattice(tc_fun(X2,tc_bool))
| c_Finite__Set_Ofinite(X0,X2)
| ~ c_Finite__Set_Ofinite(hAPP(c_Complete__Lattice_OSup__class_OSup(tc_fun(X2,tc_bool)),X1),X2) )
| ~ spl0_169
| ~ spl0_225 ),
inference(resolution,[],[f2300,f1866]) ).
fof(f74830,plain,
( spl0_945
| ~ spl0_169
| ~ spl0_218 ),
inference(avatar_split_clause,[],[f2550,f2271,f1865,f74828]) ).
fof(f74828,plain,
( spl0_945
<=> ! [X2,X0,X1] :
( ~ hBOOL(c_in(X0,X1,tc_fun(X2,tc_bool)))
| ~ class_Complete__Lattice_Ocomplete__lattice(tc_fun(X2,tc_bool))
| c_Finite__Set_Ofinite(hAPP(c_Complete__Lattice_OInf__class_OInf(tc_fun(X2,tc_bool)),X1),X2)
| ~ c_Finite__Set_Ofinite(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_945])]) ).
fof(f2550,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(c_in(X0,X1,tc_fun(X2,tc_bool)))
| ~ class_Complete__Lattice_Ocomplete__lattice(tc_fun(X2,tc_bool))
| c_Finite__Set_Ofinite(hAPP(c_Complete__Lattice_OInf__class_OInf(tc_fun(X2,tc_bool)),X1),X2)
| ~ c_Finite__Set_Ofinite(X0,X2) )
| ~ spl0_169
| ~ spl0_218 ),
inference(resolution,[],[f2272,f1866]) ).
fof(f73675,plain,
( spl0_944
| ~ spl0_51
| ~ spl0_200
| ~ spl0_912 ),
inference(avatar_split_clause,[],[f73135,f69988,f2066,f1237,f73673]) ).
fof(f73135,plain,
( ! [X0] : c_False = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_bool),c_False),hAPP(X0,v_x))
| ~ spl0_51
| ~ spl0_200
| ~ spl0_912 ),
inference(forward_demodulation,[],[f73074,f1238]) ).
fof(f73074,plain,
( ! [X0] : hAPP(c_COMBK(c_False,tc_bool,t_a),v_x) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_bool),hAPP(c_COMBK(c_False,tc_bool,t_a),v_x)),hAPP(X0,v_x))
| ~ spl0_200
| ~ spl0_912 ),
inference(superposition,[],[f69989,f2067]) ).
fof(f72937,plain,
( spl0_943
| ~ spl0_761
| ~ spl0_763 ),
inference(avatar_split_clause,[],[f65084,f61292,f59316,f72935]) ).
fof(f72935,plain,
( spl0_943
<=> ! [X0,X1] : hAPP(c_Complete__Lattice_OSup__class_OSup(tc_fun(X0,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X1,tc_fun(X0,tc_bool))) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_943])]) ).
fof(f59316,plain,
( spl0_761
<=> ! [X0,X1] : hAPP(c_Complete__Lattice_OSup__class_OSup(tc_fun(X0,tc_bool)),hAPP(c_fequal(tc_fun(X0,tc_bool)),X1)) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_761])]) ).
fof(f65084,plain,
( ! [X0,X1] : hAPP(c_Complete__Lattice_OSup__class_OSup(tc_fun(X0,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X1,tc_fun(X0,tc_bool))) = X1
| ~ spl0_761
| ~ spl0_763 ),
inference(superposition,[],[f59317,f61293]) ).
fof(f59317,plain,
( ! [X0,X1] : hAPP(c_Complete__Lattice_OSup__class_OSup(tc_fun(X0,tc_bool)),hAPP(c_fequal(tc_fun(X0,tc_bool)),X1)) = X1
| ~ spl0_761 ),
inference(avatar_component_clause,[],[f59316]) ).
fof(f72518,plain,
( spl0_942
| ~ spl0_762
| ~ spl0_763 ),
inference(avatar_split_clause,[],[f65083,f61292,f60365,f72516]) ).
fof(f72516,plain,
( spl0_942
<=> ! [X0,X1] : hAPP(c_Complete__Lattice_OInf__class_OInf(tc_fun(X0,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X1,tc_fun(X0,tc_bool))) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_942])]) ).
fof(f60365,plain,
( spl0_762
<=> ! [X0,X1] : hAPP(c_Complete__Lattice_OInf__class_OInf(tc_fun(X0,tc_bool)),hAPP(c_fequal(tc_fun(X0,tc_bool)),X1)) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_762])]) ).
fof(f65083,plain,
( ! [X0,X1] : hAPP(c_Complete__Lattice_OInf__class_OInf(tc_fun(X0,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X1,tc_fun(X0,tc_bool))) = X1
| ~ spl0_762
| ~ spl0_763 ),
inference(superposition,[],[f60366,f61293]) ).
fof(f60366,plain,
( ! [X0,X1] : hAPP(c_Complete__Lattice_OInf__class_OInf(tc_fun(X0,tc_bool)),hAPP(c_fequal(tc_fun(X0,tc_bool)),X1)) = X1
| ~ spl0_762 ),
inference(avatar_component_clause,[],[f60365]) ).
fof(f71226,plain,
( spl0_941
| ~ spl0_227
| ~ spl0_742 ),
inference(avatar_split_clause,[],[f62631,f43271,f2580,f71224]) ).
fof(f62631,plain,
( ! [X0,X1] : hAPP(c_SetInterval_Oord__class_OatLeastAtMost(X0,X0,tc_bool),X1) = hAPP(hAPP(c_fequal(tc_bool),X1),X0)
| ~ spl0_227
| ~ spl0_742 ),
inference(superposition,[],[f43272,f2581]) ).
fof(f70153,plain,
( spl0_940
| ~ spl0_130
| ~ spl0_200
| ~ spl0_441 ),
inference(avatar_split_clause,[],[f9743,f9351,f2066,f1631,f70151]) ).
fof(f70151,plain,
( spl0_940
<=> ! [X2,X0,X1] : c_COMBK(c_False,tc_bool,X0) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),hAPP(c_fequal(X0),X1)),hAPP(hAPP(c_Set_Oinsert(X0),X1),X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_940])]) ).
fof(f9743,plain,
( ! [X2,X0,X1] : c_COMBK(c_False,tc_bool,X0) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),hAPP(c_fequal(X0),X1)),hAPP(hAPP(c_Set_Oinsert(X0),X1),X2))
| ~ spl0_130
| ~ spl0_200
| ~ spl0_441 ),
inference(forward_demodulation,[],[f9682,f2067]) ).
fof(f9682,plain,
( ! [X2,X0,X1] : hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0)),X2) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),hAPP(c_fequal(X0),X1)),hAPP(hAPP(c_Set_Oinsert(X0),X1),X2))
| ~ spl0_130
| ~ spl0_441 ),
inference(superposition,[],[f9352,f1632]) ).
fof(f70149,plain,
( spl0_939
| ~ spl0_150
| ~ spl0_199
| ~ spl0_437 ),
inference(avatar_split_clause,[],[f9614,f9311,f2062,f1732,f70147]) ).
fof(f70147,plain,
( spl0_939
<=> ! [X2,X0,X1] : hAPP(c_fequal(X0),X1) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Set_Oinsert(X0),X1),X2)),hAPP(c_fequal(X0),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_939])]) ).
fof(f9614,plain,
( ! [X2,X0,X1] : hAPP(c_fequal(X0),X1) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Set_Oinsert(X0),X1),X2)),hAPP(c_fequal(X0),X1))
| ~ spl0_150
| ~ spl0_199
| ~ spl0_437 ),
inference(forward_demodulation,[],[f9613,f1733]) ).
fof(f9613,plain,
( ! [X2,X0,X1] : hAPP(hAPP(c_Set_Oinsert(X0),X1),c_COMBK(c_False,tc_bool,X0)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Set_Oinsert(X0),X1),X2)),hAPP(c_fequal(X0),X1))
| ~ spl0_150
| ~ spl0_199
| ~ spl0_437 ),
inference(forward_demodulation,[],[f9539,f2063]) ).
fof(f9539,plain,
( ! [X2,X0,X1] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Set_Oinsert(X0),X1),X2)),hAPP(c_fequal(X0),X1)) = hAPP(hAPP(c_Set_Oinsert(X0),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X2),c_COMBK(c_False,tc_bool,X0)))
| ~ spl0_150
| ~ spl0_437 ),
inference(superposition,[],[f9312,f1733]) ).
fof(f70145,plain,
( spl0_938
| ~ spl0_164
| ~ spl0_412 ),
inference(avatar_split_clause,[],[f8289,f7695,f1842,f70143]) ).
fof(f70143,plain,
( spl0_938
<=> ! [X2,X3,X4,X0,X5,X1] :
( ~ hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(hAPP(hAPP(c_Set_Oinsert(X4),X2),X3),X1,X4,tc_fun(X0,tc_bool)),X5))
| hBOOL(hAPP(hAPP(X1,X2),X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_938])]) ).
fof(f8289,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(hAPP(hAPP(c_Set_Oinsert(X4),X2),X3),X1,X4,tc_fun(X0,tc_bool)),X5))
| hBOOL(hAPP(hAPP(X1,X2),X5)) )
| ~ spl0_164
| ~ spl0_412 ),
inference(superposition,[],[f1843,f7696]) ).
fof(f70141,plain,
( spl0_937
| ~ spl0_153
| ~ spl0_410 ),
inference(avatar_split_clause,[],[f8122,f7687,f1798,f70139]) ).
fof(f70139,plain,
( spl0_937
<=> ! [X2,X3,X4,X0,X5,X1] :
( hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_Set_Oinsert(X4),X2),X3),X1,X4,tc_fun(X0,tc_bool)),X5))
| ~ hBOOL(hAPP(hAPP(X1,X2),X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_937])]) ).
fof(f8122,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_Set_Oinsert(X4),X2),X3),X1,X4,tc_fun(X0,tc_bool)),X5))
| ~ hBOOL(hAPP(hAPP(X1,X2),X5)) )
| ~ spl0_153
| ~ spl0_410 ),
inference(superposition,[],[f1799,f7688]) ).
fof(f70137,plain,
( spl0_936
| ~ spl0_51
| ~ spl0_416 ),
inference(avatar_split_clause,[],[f7964,f7848,f1237,f70135]) ).
fof(f70135,plain,
( spl0_936
<=> ! [X4,X0,X3,X2,X1] :
( hBOOL(X0)
| c_COMBK(c_False,tc_bool,X4) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X4,tc_bool)),hAPP(c_fequal(X4),X3)),c_COMBK(X0,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_936])]) ).
fof(f7964,plain,
( ! [X2,X3,X0,X1,X4] :
( hBOOL(X0)
| c_COMBK(c_False,tc_bool,X4) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X4,tc_bool)),hAPP(c_fequal(X4),X3)),c_COMBK(X0,X1,X2)) )
| ~ spl0_51
| ~ spl0_416 ),
inference(superposition,[],[f7849,f1238]) ).
fof(f70133,plain,
( spl0_935
| ~ spl0_58
| ~ spl0_416 ),
inference(avatar_split_clause,[],[f7854,f7848,f1266,f70131]) ).
fof(f70131,plain,
( spl0_935
<=> ! [X2,X0,X1] :
( c_COMBK(c_False,tc_bool,X0) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),hAPP(c_fequal(X0),X1)),hAPP(c_HOL_Oord__class_Oless(X2),X1))
| ~ class_Orderings_Oorder(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_935])]) ).
fof(f1266,plain,
( spl0_58
<=> ! [X0,X1] :
( ~ class_Orderings_Oorder(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_58])]) ).
fof(f7854,plain,
( ! [X2,X0,X1] :
( c_COMBK(c_False,tc_bool,X0) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),hAPP(c_fequal(X0),X1)),hAPP(c_HOL_Oord__class_Oless(X2),X1))
| ~ class_Orderings_Oorder(X2) )
| ~ spl0_58
| ~ spl0_416 ),
inference(resolution,[],[f7849,f1267]) ).
fof(f1267,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X1))
| ~ class_Orderings_Oorder(X0) )
| ~ spl0_58 ),
inference(avatar_component_clause,[],[f1266]) ).
fof(f70129,plain,
( spl0_934
| ~ spl0_59
| ~ spl0_416 ),
inference(avatar_split_clause,[],[f7853,f7848,f1270,f70127]) ).
fof(f70127,plain,
( spl0_934
<=> ! [X2,X0,X1] :
( c_COMBK(c_False,tc_bool,X0) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),hAPP(c_fequal(X0),X1)),hAPP(c_HOL_Oord__class_Oless(X2),X1))
| ~ class_Orderings_Opreorder(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_934])]) ).
fof(f1270,plain,
( spl0_59
<=> ! [X0,X1] :
( ~ class_Orderings_Opreorder(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_59])]) ).
fof(f7853,plain,
( ! [X2,X0,X1] :
( c_COMBK(c_False,tc_bool,X0) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),hAPP(c_fequal(X0),X1)),hAPP(c_HOL_Oord__class_Oless(X2),X1))
| ~ class_Orderings_Opreorder(X2) )
| ~ spl0_59
| ~ spl0_416 ),
inference(resolution,[],[f7849,f1271]) ).
fof(f1271,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X1))
| ~ class_Orderings_Opreorder(X0) )
| ~ spl0_59 ),
inference(avatar_component_clause,[],[f1270]) ).
fof(f70125,plain,
( spl0_933
| ~ spl0_51
| ~ spl0_414 ),
inference(avatar_split_clause,[],[f7821,f7704,f1237,f70123]) ).
fof(f70123,plain,
( spl0_933
<=> ! [X4,X0,X3,X2,X1] :
( ~ hBOOL(X0)
| hAPP(c_fequal(X4),X3) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X4,tc_bool)),hAPP(c_fequal(X4),X3)),c_COMBK(X0,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_933])]) ).
fof(f7821,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ hBOOL(X0)
| hAPP(c_fequal(X4),X3) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X4,tc_bool)),hAPP(c_fequal(X4),X3)),c_COMBK(X0,X1,X2)) )
| ~ spl0_51
| ~ spl0_414 ),
inference(superposition,[],[f7705,f1238]) ).
fof(f70121,plain,
( spl0_932
| ~ spl0_64
| ~ spl0_414 ),
inference(avatar_split_clause,[],[f7715,f7704,f1291,f70119]) ).
fof(f70119,plain,
( spl0_932
<=> ! [X0,X3,X2,X1] : hAPP(c_fequal(X0),X1) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),hAPP(c_fequal(X0),X1)),hAPP(hAPP(c_Set_Oinsert(X2),X1),X3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_932])]) ).
fof(f7715,plain,
( ! [X2,X3,X0,X1] : hAPP(c_fequal(X0),X1) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),hAPP(c_fequal(X0),X1)),hAPP(hAPP(c_Set_Oinsert(X2),X1),X3))
| ~ spl0_64
| ~ spl0_414 ),
inference(resolution,[],[f7705,f1292]) ).
fof(f70117,plain,
( ~ spl0_5
| spl0_931
| ~ spl0_100
| ~ spl0_166
| ~ spl0_739 ),
inference(avatar_split_clause,[],[f62218,f41032,f1850,f1483,f70115,f1037]) ).
fof(f1037,plain,
( spl0_5
<=> class_Lattices_Obounded__lattice(tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).
fof(f70115,plain,
( spl0_931
<=> ! [X0,X1] :
( c_False = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),X1),X0)
| c_False != X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_931])]) ).
fof(f1483,plain,
( spl0_100
<=> c_False = c_Orderings_Obot__class_Obot(tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_100])]) ).
fof(f41032,plain,
( spl0_739
<=> ! [X0,X1] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),X1),X0)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_739])]) ).
fof(f62218,plain,
( ! [X0,X1] :
( c_False = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),X1),X0)
| c_False != X0
| ~ class_Lattices_Obounded__lattice(tc_bool) )
| ~ spl0_100
| ~ spl0_166
| ~ spl0_739 ),
inference(forward_demodulation,[],[f62217,f1485]) ).
fof(f1485,plain,
( c_False = c_Orderings_Obot__class_Obot(tc_bool)
| ~ spl0_100 ),
inference(avatar_component_clause,[],[f1483]) ).
fof(f62217,plain,
( ! [X0,X1] :
( c_False != X0
| c_Orderings_Obot__class_Obot(tc_bool) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),X1),X0)
| ~ class_Lattices_Obounded__lattice(tc_bool) )
| ~ spl0_100
| ~ spl0_166
| ~ spl0_739 ),
inference(forward_demodulation,[],[f62193,f1485]) ).
fof(f62193,plain,
( ! [X0,X1] :
( c_Orderings_Obot__class_Obot(tc_bool) != X0
| c_Orderings_Obot__class_Obot(tc_bool) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),X1),X0)
| ~ class_Lattices_Obounded__lattice(tc_bool) )
| ~ spl0_166
| ~ spl0_739 ),
inference(superposition,[],[f1851,f41033]) ).
fof(f41033,plain,
( ! [X0,X1] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),X1),X0)) = X0
| ~ spl0_739 ),
inference(avatar_component_clause,[],[f41032]) ).
fof(f70113,plain,
( spl0_930
| ~ spl0_62
| ~ spl0_414 ),
inference(avatar_split_clause,[],[f7714,f7704,f1283,f70111]) ).
fof(f70111,plain,
( spl0_930
<=> ! [X2,X0,X1] :
( hAPP(c_fequal(X0),X1) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),hAPP(c_fequal(X0),X1)),hAPP(c_lessequals(X2),X1))
| ~ class_Orderings_Oorder(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_930])]) ).
fof(f7714,plain,
( ! [X2,X0,X1] :
( hAPP(c_fequal(X0),X1) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),hAPP(c_fequal(X0),X1)),hAPP(c_lessequals(X2),X1))
| ~ class_Orderings_Oorder(X2) )
| ~ spl0_62
| ~ spl0_414 ),
inference(resolution,[],[f7705,f1284]) ).
fof(f70109,plain,
( spl0_929
| ~ spl0_63
| ~ spl0_414 ),
inference(avatar_split_clause,[],[f7713,f7704,f1287,f70107]) ).
fof(f70107,plain,
( spl0_929
<=> ! [X2,X0,X1] :
( hAPP(c_fequal(X0),X1) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),hAPP(c_fequal(X0),X1)),hAPP(c_lessequals(X2),X1))
| ~ class_Orderings_Opreorder(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_929])]) ).
fof(f7713,plain,
( ! [X2,X0,X1] :
( hAPP(c_fequal(X0),X1) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),hAPP(c_fequal(X0),X1)),hAPP(c_lessequals(X2),X1))
| ~ class_Orderings_Opreorder(X2) )
| ~ spl0_63
| ~ spl0_414 ),
inference(resolution,[],[f7705,f1288]) ).
fof(f70105,plain,
( spl0_928
| ~ spl0_61
| ~ spl0_414 ),
inference(avatar_split_clause,[],[f7712,f7704,f1279,f70103]) ).
fof(f70103,plain,
( spl0_928
<=> ! [X2,X0,X1] : hAPP(c_fequal(X0),X1) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),hAPP(c_fequal(X0),X1)),hAPP(c_lessequals(tc_fun(X2,tc_bool)),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_928])]) ).
fof(f7712,plain,
( ! [X2,X0,X1] : hAPP(c_fequal(X0),X1) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),hAPP(c_fequal(X0),X1)),hAPP(c_lessequals(tc_fun(X2,tc_bool)),X1))
| ~ spl0_61
| ~ spl0_414 ),
inference(resolution,[],[f7705,f1280]) ).
fof(f70101,plain,
( spl0_927
| ~ spl0_146
| ~ spl0_373 ),
inference(avatar_split_clause,[],[f6445,f6087,f1716,f70099]) ).
fof(f70099,plain,
( spl0_927
<=> ! [X0,X3,X2,X1] : hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X1),hAPP(hAPP(c_Set_Oinsert(X0),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X3),X1)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_927])]) ).
fof(f6445,plain,
( ! [X2,X3,X0,X1] : hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X1),hAPP(hAPP(c_Set_Oinsert(X0),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X3),X1))))
| ~ spl0_146
| ~ spl0_373 ),
inference(resolution,[],[f6088,f1717]) ).
fof(f70097,plain,
( spl0_926
| ~ spl0_179
| ~ spl0_372 ),
inference(avatar_split_clause,[],[f6427,f6083,f1980,f70095]) ).
fof(f70095,plain,
( spl0_926
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool))),X2))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_926])]) ).
fof(f6427,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool))),X2))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X1),X2)) )
| ~ spl0_179
| ~ spl0_372 ),
inference(superposition,[],[f6084,f1981]) ).
fof(f70093,plain,
( spl0_925
| ~ spl0_181
| ~ spl0_371 ),
inference(avatar_split_clause,[],[f6381,f6079,f1989,f70091]) ).
fof(f70091,plain,
( spl0_925
<=> ! [X0,X3,X2,X1] :
( ~ c_Finite__Set_Ofinite(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X1),X2),X0)
| c_Finite__Set_Ofinite(X1,X0)
| ~ c_Finite__Set_Ofinite(hAPP(hAPP(c_Set_Oinsert(X0),X3),X2),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_925])]) ).
fof(f6079,plain,
( spl0_371
<=> ! [X9,X0,X5,X3] :
( ~ c_Finite__Set_Ofinite(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X5),X9),X0)
| c_Finite__Set_Ofinite(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X5),hAPP(hAPP(c_Set_Oinsert(X0),X3),X9)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_371])]) ).
fof(f6381,plain,
( ! [X2,X3,X0,X1] :
( ~ c_Finite__Set_Ofinite(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X1),X2),X0)
| c_Finite__Set_Ofinite(X1,X0)
| ~ c_Finite__Set_Ofinite(hAPP(hAPP(c_Set_Oinsert(X0),X3),X2),X0) )
| ~ spl0_181
| ~ spl0_371 ),
inference(resolution,[],[f6080,f1990]) ).
fof(f6080,plain,
( ! [X3,X0,X9,X5] :
( c_Finite__Set_Ofinite(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X5),hAPP(hAPP(c_Set_Oinsert(X0),X3),X9)),X0)
| ~ c_Finite__Set_Ofinite(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X5),X9),X0) )
| ~ spl0_371 ),
inference(avatar_component_clause,[],[f6079]) ).
fof(f70089,plain,
( spl0_924
| ~ spl0_130
| ~ spl0_370 ),
inference(avatar_split_clause,[],[f6375,f6075,f1631,f70087]) ).
fof(f70087,plain,
( spl0_924
<=> ! [X2,X0,X1] :
( ~ c_Finite__Set_Ofinite(c_COMBK(c_False,tc_bool,X0),X0)
| c_Finite__Set_Ofinite(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Set_Oinsert(X0),X1),X2)),X2),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_924])]) ).
fof(f6075,plain,
( spl0_370
<=> ! [X9,X0,X5,X3] :
( c_Finite__Set_Ofinite(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X5),X9),X0)
| ~ c_Finite__Set_Ofinite(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X5),hAPP(hAPP(c_Set_Oinsert(X0),X3),X9)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_370])]) ).
fof(f6375,plain,
( ! [X2,X0,X1] :
( ~ c_Finite__Set_Ofinite(c_COMBK(c_False,tc_bool,X0),X0)
| c_Finite__Set_Ofinite(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Set_Oinsert(X0),X1),X2)),X2),X0) )
| ~ spl0_130
| ~ spl0_370 ),
inference(superposition,[],[f6076,f1632]) ).
fof(f6076,plain,
( ! [X3,X0,X9,X5] :
( ~ c_Finite__Set_Ofinite(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X5),hAPP(hAPP(c_Set_Oinsert(X0),X3),X9)),X0)
| c_Finite__Set_Ofinite(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X5),X9),X0) )
| ~ spl0_370 ),
inference(avatar_component_clause,[],[f6075]) ).
fof(f70085,plain,
( spl0_923
| ~ spl0_201
| ~ spl0_366 ),
inference(avatar_split_clause,[],[f6313,f6059,f2076,f70083]) ).
fof(f70083,plain,
( spl0_923
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X2),c_COMBK(c_False,tc_bool,X0)))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X2),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_923])]) ).
fof(f6313,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X2),c_COMBK(c_False,tc_bool,X0)))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X2),X1)) )
| ~ spl0_201
| ~ spl0_366 ),
inference(superposition,[],[f6060,f2077]) ).
fof(f70081,plain,
( spl0_922
| ~ spl0_51
| ~ spl0_365 ),
inference(avatar_split_clause,[],[f6278,f6055,f1237,f70079]) ).
fof(f70079,plain,
( spl0_922
<=> ! [X5,X4,X2,X7,X0,X6,X3,X1] :
( ~ hBOOL(c_in(X4,X5,X6))
| ~ hBOOL(c_in(X3,X5,X6))
| ~ c_Fun_Oinj__on(c_COMBK(X0,X1,X2),X5,X6,X7)
| X3 = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_922])]) ).
fof(f6278,plain,
( ! [X2,X3,X0,X1,X6,X7,X4,X5] :
( ~ hBOOL(c_in(X4,X5,X6))
| ~ hBOOL(c_in(X3,X5,X6))
| ~ c_Fun_Oinj__on(c_COMBK(X0,X1,X2),X5,X6,X7)
| X3 = X4 )
| ~ spl0_51
| ~ spl0_365 ),
inference(trivial_inequality_removal,[],[f6277]) ).
fof(f6277,plain,
( ! [X2,X3,X0,X1,X6,X7,X4,X5] :
( X0 != X0
| ~ hBOOL(c_in(X4,X5,X6))
| ~ hBOOL(c_in(X3,X5,X6))
| ~ c_Fun_Oinj__on(c_COMBK(X0,X1,X2),X5,X6,X7)
| X3 = X4 )
| ~ spl0_51
| ~ spl0_365 ),
inference(forward_demodulation,[],[f6192,f1238]) ).
fof(f6192,plain,
( ! [X2,X3,X0,X1,X6,X7,X4,X5] :
( hAPP(c_COMBK(X0,X1,X2),X4) != X0
| ~ hBOOL(c_in(X4,X5,X6))
| ~ hBOOL(c_in(X3,X5,X6))
| ~ c_Fun_Oinj__on(c_COMBK(X0,X1,X2),X5,X6,X7)
| X3 = X4 )
| ~ spl0_51
| ~ spl0_365 ),
inference(superposition,[],[f6056,f1238]) ).
fof(f70077,plain,
( spl0_921
| ~ spl0_169
| ~ spl0_347 ),
inference(avatar_split_clause,[],[f5619,f5570,f1865,f70075]) ).
fof(f70075,plain,
( spl0_921
<=> ! [X4,X0,X3,X2,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2))
| ~ class_Orderings_Oorder(X0)
| c_Finite__Set_Ofinite(c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X0),X0)
| ~ c_Finite__Set_Ofinite(c_SetInterval_Oord__class_OatLeastAtMost(X3,X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_921])]) ).
fof(f5619,plain,
( ! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2))
| ~ class_Orderings_Oorder(X0)
| c_Finite__Set_Ofinite(c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X0),X0)
| ~ c_Finite__Set_Ofinite(c_SetInterval_Oord__class_OatLeastAtMost(X3,X4,X0),X0) )
| ~ spl0_169
| ~ spl0_347 ),
inference(resolution,[],[f5571,f1866]) ).
fof(f70022,plain,
( spl0_920
| ~ spl0_90
| ~ spl0_343 ),
inference(avatar_split_clause,[],[f5510,f4961,f1419,f70020]) ).
fof(f5510,plain,
( ! [X2,X0,X1] :
( c_Finite__Set_Ofinite(hAPP(hAPP(c_Set_Oinsert(X0),X1),X2),X0)
| ~ c_Finite__Set_Ofinite(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X2),hAPP(c_fequal(X0),X1)),X0) )
| ~ spl0_90
| ~ spl0_343 ),
inference(superposition,[],[f1420,f4962]) ).
fof(f70018,plain,
( spl0_919
| ~ spl0_92
| ~ spl0_340 ),
inference(avatar_split_clause,[],[f5406,f4949,f1427,f70016]) ).
fof(f70016,plain,
( spl0_919
<=> ! [X0,X3,X2,X1] :
( ~ c_Finite__Set_Ofinite(hAPP(hAPP(c_Set_Oinsert(X0),X2),hAPP(hAPP(c_Set_Oinsert(X0),X1),X3)),X0)
| c_Finite__Set_Ofinite(hAPP(hAPP(c_Set_Oinsert(X0),X2),X3),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_919])]) ).
fof(f5406,plain,
( ! [X2,X3,X0,X1] :
( ~ c_Finite__Set_Ofinite(hAPP(hAPP(c_Set_Oinsert(X0),X2),hAPP(hAPP(c_Set_Oinsert(X0),X1),X3)),X0)
| c_Finite__Set_Ofinite(hAPP(hAPP(c_Set_Oinsert(X0),X2),X3),X0) )
| ~ spl0_92
| ~ spl0_340 ),
inference(superposition,[],[f1428,f4950]) ).
fof(f70014,plain,
( spl0_918
| ~ spl0_90
| ~ spl0_340 ),
inference(avatar_split_clause,[],[f5405,f4949,f1419,f70012]) ).
fof(f70012,plain,
( spl0_918
<=> ! [X0,X3,X2,X1] :
( c_Finite__Set_Ofinite(hAPP(hAPP(c_Set_Oinsert(X0),X2),hAPP(hAPP(c_Set_Oinsert(X0),X1),X3)),X0)
| ~ c_Finite__Set_Ofinite(hAPP(hAPP(c_Set_Oinsert(X0),X2),X3),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_918])]) ).
fof(f5405,plain,
( ! [X2,X3,X0,X1] :
( c_Finite__Set_Ofinite(hAPP(hAPP(c_Set_Oinsert(X0),X2),hAPP(hAPP(c_Set_Oinsert(X0),X1),X3)),X0)
| ~ c_Finite__Set_Ofinite(hAPP(hAPP(c_Set_Oinsert(X0),X2),X3),X0) )
| ~ spl0_90
| ~ spl0_340 ),
inference(superposition,[],[f1420,f4950]) ).
fof(f70010,plain,
( spl0_917
| ~ spl0_8
| ~ spl0_333 ),
inference(avatar_split_clause,[],[f5154,f4920,f1052,f70008]) ).
fof(f70008,plain,
( spl0_917
<=> ! [X0,X1] : hAPP(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(t_a,tc_bool)),X0),X1),v_x) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),hAPP(X0,v_x)),hAPP(X1,v_x)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_917])]) ).
fof(f4920,plain,
( spl0_333
<=> ! [X13,X8,X7] :
( ~ class_Lattices_Olattice(X8)
| hAPP(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(t_a,X8)),X7),X13),v_x) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X8),hAPP(X7,v_x)),hAPP(X13,v_x)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_333])]) ).
fof(f5154,plain,
( ! [X0,X1] : hAPP(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(t_a,tc_bool)),X0),X1),v_x) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),hAPP(X0,v_x)),hAPP(X1,v_x))
| ~ spl0_8
| ~ spl0_333 ),
inference(resolution,[],[f4921,f1054]) ).
fof(f4921,plain,
( ! [X8,X7,X13] :
( ~ class_Lattices_Olattice(X8)
| hAPP(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(t_a,X8)),X7),X13),v_x) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X8),hAPP(X7,v_x)),hAPP(X13,v_x)) )
| ~ spl0_333 ),
inference(avatar_component_clause,[],[f4920]) ).
fof(f70006,plain,
( spl0_916
| ~ spl0_185
| ~ spl0_332 ),
inference(avatar_split_clause,[],[f5151,f4916,f2005,f70004]) ).
fof(f70004,plain,
( spl0_916
<=> ! [X0,X3,X2,X1] : hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X1),hAPP(hAPP(c_Set_Oinsert(X0),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X3)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_916])]) ).
fof(f5151,plain,
( ! [X2,X3,X0,X1] : hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X1),hAPP(hAPP(c_Set_Oinsert(X0),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X3))))
| ~ spl0_185
| ~ spl0_332 ),
inference(forward_demodulation,[],[f5133,f396]) ).
fof(f396,axiom,
! [X3,X0,X9,X12] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Set_Oinsert(X0),X3),X9)),X12) = hAPP(hAPP(c_Set_Oinsert(X0),X3),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X9),X12)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__insert__left_0) ).
fof(f5133,plain,
( ! [X2,X3,X0,X1] : hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Set_Oinsert(X0),X2),X1)),X3)))
| ~ spl0_185
| ~ spl0_332 ),
inference(resolution,[],[f4917,f2006]) ).
fof(f70002,plain,
( spl0_915
| ~ spl0_184
| ~ spl0_332 ),
inference(avatar_split_clause,[],[f5132,f4916,f2001,f70000]) ).
fof(f70000,plain,
( spl0_915
<=> ! [X0,X3,X2,X1] : hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X2),hAPP(hAPP(c_Set_Oinsert(X0),X3),X1)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_915])]) ).
fof(f5132,plain,
( ! [X2,X3,X0,X1] : hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X2),hAPP(hAPP(c_Set_Oinsert(X0),X3),X1))))
| ~ spl0_184
| ~ spl0_332 ),
inference(resolution,[],[f4917,f2002]) ).
fof(f69998,plain,
( spl0_914
| ~ spl0_137
| ~ spl0_330 ),
inference(avatar_split_clause,[],[f5099,f4908,f1680,f69996]) ).
fof(f69996,plain,
( spl0_914
<=> ! [X2,X6,X4,X3,X7,X0,X5,X1] : hAPP(c_Fun_Ocomp(X0,c_Fun_Ocomp(X1,X5,X4,X2,X6),X2,X3,X6),X7) = hAPP(X0,hAPP(X1,hAPP(X5,X7))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_914])]) ).
fof(f4908,plain,
( spl0_330
<=> ! [X54,X0,X53,X14,X13,X8,X7] : c_Fun_Ocomp(X7,c_Fun_Ocomp(X13,X53,X54,X14,X0),X14,X8,X0) = c_Fun_Ocomp(c_Fun_Ocomp(X7,X13,X14,X8,X54),X53,X54,X8,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_330])]) ).
fof(f5099,plain,
( ! [X2,X3,X0,X1,X6,X7,X4,X5] : hAPP(c_Fun_Ocomp(X0,c_Fun_Ocomp(X1,X5,X4,X2,X6),X2,X3,X6),X7) = hAPP(X0,hAPP(X1,hAPP(X5,X7)))
| ~ spl0_137
| ~ spl0_330 ),
inference(forward_demodulation,[],[f5097,f1681]) ).
fof(f5097,plain,
( ! [X2,X3,X0,X1,X6,X7,X4,X5] : hAPP(c_Fun_Ocomp(X0,X1,X2,X3,X4),hAPP(X5,X7)) = hAPP(c_Fun_Ocomp(X0,c_Fun_Ocomp(X1,X5,X4,X2,X6),X2,X3,X6),X7)
| ~ spl0_137
| ~ spl0_330 ),
inference(superposition,[],[f1681,f4909]) ).
fof(f4909,plain,
( ! [X0,X54,X8,X7,X14,X53,X13] : c_Fun_Ocomp(X7,c_Fun_Ocomp(X13,X53,X54,X14,X0),X14,X8,X0) = c_Fun_Ocomp(c_Fun_Ocomp(X7,X13,X14,X8,X54),X53,X54,X8,X0)
| ~ spl0_330 ),
inference(avatar_component_clause,[],[f4908]) ).
fof(f69994,plain,
( spl0_913
| ~ spl0_137
| ~ spl0_330 ),
inference(avatar_split_clause,[],[f5098,f4908,f1680,f69992]) ).
fof(f69992,plain,
( spl0_913
<=> ! [X6,X4,X3,X0,X7,X5,X2,X1] : hAPP(c_Fun_Ocomp(c_Fun_Ocomp(X0,X1,X4,X6,X3),X2,X3,X6,X5),X7) = hAPP(X0,hAPP(X1,hAPP(X2,X7))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_913])]) ).
fof(f5098,plain,
( ! [X2,X3,X0,X1,X6,X7,X4,X5] : hAPP(c_Fun_Ocomp(c_Fun_Ocomp(X0,X1,X4,X6,X3),X2,X3,X6,X5),X7) = hAPP(X0,hAPP(X1,hAPP(X2,X7)))
| ~ spl0_137
| ~ spl0_330 ),
inference(forward_demodulation,[],[f5096,f1681]) ).
fof(f5096,plain,
( ! [X2,X3,X0,X1,X6,X7,X4,X5] : hAPP(X0,hAPP(c_Fun_Ocomp(X1,X2,X3,X4,X5),X7)) = hAPP(c_Fun_Ocomp(c_Fun_Ocomp(X0,X1,X4,X6,X3),X2,X3,X6,X5),X7)
| ~ spl0_137
| ~ spl0_330 ),
inference(superposition,[],[f1681,f4909]) ).
fof(f69990,plain,
( spl0_912
| ~ spl0_12
| ~ spl0_326 ),
inference(avatar_split_clause,[],[f5050,f4892,f1072,f69988]) ).
fof(f1072,plain,
( spl0_12
<=> class_HOL_Ominus(tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_12])]) ).
fof(f4892,plain,
( spl0_326
<=> ! [X9,X5,X8] :
( ~ class_HOL_Ominus(X8)
| hAPP(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(t_a,X8)),X5),X9),v_x) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(X8),hAPP(X5,v_x)),hAPP(X9,v_x)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_326])]) ).
fof(f5050,plain,
( ! [X0,X1] : hAPP(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(t_a,tc_bool)),X0),X1),v_x) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_bool),hAPP(X0,v_x)),hAPP(X1,v_x))
| ~ spl0_12
| ~ spl0_326 ),
inference(resolution,[],[f4893,f1074]) ).
fof(f1074,plain,
( class_HOL_Ominus(tc_bool)
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f1072]) ).
fof(f4893,plain,
( ! [X8,X9,X5] :
( ~ class_HOL_Ominus(X8)
| hAPP(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(t_a,X8)),X5),X9),v_x) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(X8),hAPP(X5,v_x)),hAPP(X9,v_x)) )
| ~ spl0_326 ),
inference(avatar_component_clause,[],[f4892]) ).
fof(f69986,plain,
( spl0_911
| ~ spl0_8
| ~ spl0_322 ),
inference(avatar_split_clause,[],[f4987,f4876,f1052,f69984]) ).
fof(f69984,plain,
( spl0_911
<=> ! [X0,X1] : hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),X0),X1),v_x) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(X0,v_x)),hAPP(X1,v_x)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_911])]) ).
fof(f4876,plain,
( spl0_322
<=> ! [X13,X8,X7] :
( ~ class_Lattices_Olattice(X8)
| hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,X8)),X7),X13),v_x) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X8),hAPP(X7,v_x)),hAPP(X13,v_x)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_322])]) ).
fof(f4987,plain,
( ! [X0,X1] : hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),X0),X1),v_x) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(X0,v_x)),hAPP(X1,v_x))
| ~ spl0_8
| ~ spl0_322 ),
inference(resolution,[],[f4877,f1054]) ).
fof(f4877,plain,
( ! [X8,X7,X13] :
( ~ class_Lattices_Olattice(X8)
| hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,X8)),X7),X13),v_x) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X8),hAPP(X7,v_x)),hAPP(X13,v_x)) )
| ~ spl0_322 ),
inference(avatar_component_clause,[],[f4876]) ).
fof(f69982,plain,
( ~ spl0_10
| ~ spl0_9
| spl0_910
| ~ spl0_628
| ~ spl0_645 ),
inference(avatar_split_clause,[],[f18795,f18689,f17471,f69980,f1057,f1062]) ).
fof(f1062,plain,
( spl0_10
<=> class_Orderings_Otop(tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).
fof(f1057,plain,
( spl0_9
<=> class_Orderings_Oorder(tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).
fof(f17471,plain,
( spl0_628
<=> ! [X0,X1] :
( c_Orderings_Otop__class_Otop(X0) = X1
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),c_Orderings_Otop__class_Otop(X0)),X1))
| ~ class_Orderings_Oorder(X0)
| ~ class_Orderings_Otop(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_628])]) ).
fof(f18689,plain,
( spl0_645
<=> ! [X4,X0,X3] : hBOOL(hAPP(hAPP(c_lessequals(tc_bool),X0),hAPP(c_Orderings_Otop__class_Otop(tc_fun(X4,tc_bool)),X3))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_645])]) ).
fof(f18795,plain,
( ! [X0,X1] :
( hAPP(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X1) = c_Orderings_Otop__class_Otop(tc_bool)
| ~ class_Orderings_Oorder(tc_bool)
| ~ class_Orderings_Otop(tc_bool) )
| ~ spl0_628
| ~ spl0_645 ),
inference(resolution,[],[f18690,f17472]) ).
fof(f17472,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(X0),c_Orderings_Otop__class_Otop(X0)),X1))
| c_Orderings_Otop__class_Otop(X0) = X1
| ~ class_Orderings_Oorder(X0)
| ~ class_Orderings_Otop(X0) )
| ~ spl0_628 ),
inference(avatar_component_clause,[],[f17471]) ).
fof(f18690,plain,
( ! [X3,X0,X4] : hBOOL(hAPP(hAPP(c_lessequals(tc_bool),X0),hAPP(c_Orderings_Otop__class_Otop(tc_fun(X4,tc_bool)),X3)))
| ~ spl0_645 ),
inference(avatar_component_clause,[],[f18689]) ).
fof(f69978,plain,
( spl0_909
| ~ spl0_57
| ~ spl0_310 ),
inference(avatar_split_clause,[],[f4841,f4585,f1262,f69976]) ).
fof(f69976,plain,
( spl0_909
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(c_in(X0,X1,X2))
| ~ hBOOL(c_in(X0,X3,X2))
| hBOOL(hAPP(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X3),X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_909])]) ).
fof(f4585,plain,
( spl0_310
<=> ! [X35,X9,X0,X5] :
( ~ hBOOL(c_in(X35,X5,X0))
| ~ hBOOL(c_in(X35,X9,X0))
| hBOOL(c_in(X35,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X5),X9),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_310])]) ).
fof(f4841,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(c_in(X0,X1,X2))
| ~ hBOOL(c_in(X0,X3,X2))
| hBOOL(hAPP(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X3),X1),X0)) )
| ~ spl0_57
| ~ spl0_310 ),
inference(resolution,[],[f4586,f1263]) ).
fof(f4586,plain,
( ! [X0,X9,X35,X5] :
( hBOOL(c_in(X35,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X5),X9),X0))
| ~ hBOOL(c_in(X35,X9,X0))
| ~ hBOOL(c_in(X35,X5,X0)) )
| ~ spl0_310 ),
inference(avatar_component_clause,[],[f4585]) ).
fof(f69974,plain,
( spl0_908
| ~ spl0_57
| ~ spl0_306 ),
inference(avatar_split_clause,[],[f4711,f4569,f1262,f69972]) ).
fof(f69972,plain,
( spl0_908
<=> ! [X0,X3,X2,X1] :
( hBOOL(c_in(X0,X1,X2))
| ~ hBOOL(c_in(X0,X3,X2))
| hBOOL(hAPP(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X2,tc_bool)),X3),X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_908])]) ).
fof(f4569,plain,
( spl0_306
<=> ! [X35,X9,X0,X5] :
( ~ hBOOL(c_in(X35,X5,X0))
| hBOOL(c_in(X35,X9,X0))
| hBOOL(c_in(X35,hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X5),X9),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_306])]) ).
fof(f4711,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(c_in(X0,X1,X2))
| ~ hBOOL(c_in(X0,X3,X2))
| hBOOL(hAPP(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X2,tc_bool)),X3),X1),X0)) )
| ~ spl0_57
| ~ spl0_306 ),
inference(resolution,[],[f4570,f1263]) ).
fof(f4570,plain,
( ! [X0,X9,X35,X5] :
( hBOOL(c_in(X35,hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X5),X9),X0))
| hBOOL(c_in(X35,X9,X0))
| ~ hBOOL(c_in(X35,X5,X0)) )
| ~ spl0_306 ),
inference(avatar_component_clause,[],[f4569]) ).
fof(f69970,plain,
( spl0_907
| ~ spl0_56
| ~ spl0_305 ),
inference(avatar_split_clause,[],[f4695,f4565,f1258,f69968]) ).
fof(f69968,plain,
( spl0_907
<=> ! [X0,X3,X2,X1] :
( hBOOL(c_in(X0,X1,X2))
| hBOOL(c_in(X0,X3,X2))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X1),X3),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_907])]) ).
fof(f4695,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(c_in(X0,X1,X2))
| hBOOL(c_in(X0,X3,X2))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X1),X3),X0)) )
| ~ spl0_56
| ~ spl0_305 ),
inference(resolution,[],[f4566,f1259]) ).
fof(f69966,plain,
( spl0_906
| ~ spl0_213
| ~ spl0_301 ),
inference(avatar_split_clause,[],[f4549,f3959,f2251,f69964]) ).
fof(f69964,plain,
( spl0_906
<=> ! [X0,X3,X2,X1] :
( hBOOL(c_in(X3,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X2),X1),X0))
| ~ hBOOL(hAPP(X2,X3))
| ~ hBOOL(c_in(X3,X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_906])]) ).
fof(f3959,plain,
( spl0_301
<=> ! [X11,X0,X5,X1] :
( hBOOL(c_in(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X5),X11),X0))
| ~ hBOOL(hAPP(X11,X1))
| ~ hBOOL(c_in(X1,X5,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_301])]) ).
fof(f4549,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(c_in(X3,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X2),X1),X0))
| ~ hBOOL(hAPP(X2,X3))
| ~ hBOOL(c_in(X3,X1,X0)) )
| ~ spl0_213
| ~ spl0_301 ),
inference(superposition,[],[f3960,f2252]) ).
fof(f3960,plain,
( ! [X0,X11,X1,X5] :
( hBOOL(c_in(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X5),X11),X0))
| ~ hBOOL(hAPP(X11,X1))
| ~ hBOOL(c_in(X1,X5,X0)) )
| ~ spl0_301 ),
inference(avatar_component_clause,[],[f3959]) ).
fof(f69962,plain,
( spl0_905
| ~ spl0_108
| ~ spl0_288 ),
inference(avatar_split_clause,[],[f4162,f3899,f1516,f69960]) ).
fof(f69960,plain,
( spl0_905
<=> ! [X4,X0,X3,X2,X1] :
( ~ hBOOL(c_in(X0,X1,X2))
| hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,c_lessequals(tc_fun(X3,tc_bool)),X2,tc_fun(X4,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_905])]) ).
fof(f4162,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ hBOOL(c_in(X0,X1,X2))
| hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,c_lessequals(tc_fun(X3,tc_bool)),X2,tc_fun(X4,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)))) )
| ~ spl0_108
| ~ spl0_288 ),
inference(resolution,[],[f3900,f1517]) ).
fof(f69958,plain,
( spl0_904
| ~ spl0_113
| ~ spl0_288 ),
inference(avatar_split_clause,[],[f4139,f3899,f1537,f69956]) ).
fof(f69956,plain,
( spl0_904
<=> ! [X4,X0,X3,X2,X1] :
( ~ hBOOL(c_in(c_COMBK(c_False,tc_bool,X0),X1,X2))
| hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,c_lessequals(tc_fun(X0,tc_bool)),X2,tc_fun(X3,tc_bool)),X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_904])]) ).
fof(f4139,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ hBOOL(c_in(c_COMBK(c_False,tc_bool,X0),X1,X2))
| hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,c_lessequals(tc_fun(X0,tc_bool)),X2,tc_fun(X3,tc_bool)),X4)) )
| ~ spl0_113
| ~ spl0_288 ),
inference(resolution,[],[f3900,f1538]) ).
fof(f69954,plain,
( spl0_903
| ~ spl0_51
| ~ spl0_271 ),
inference(avatar_split_clause,[],[f3791,f3635,f1237,f69952]) ).
fof(f69952,plain,
( spl0_903
<=> ! [X5,X3,X4,X0,X6,X2,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(X4),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,c_COMBK(X0,X1,X2),X6,X4)),X0))
| ~ hBOOL(c_in(X3,X5,X6))
| ~ class_Complete__Lattice_Ocomplete__lattice(X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_903])]) ).
fof(f3791,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] :
( hBOOL(hAPP(hAPP(c_lessequals(X4),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,c_COMBK(X0,X1,X2),X6,X4)),X0))
| ~ hBOOL(c_in(X3,X5,X6))
| ~ class_Complete__Lattice_Ocomplete__lattice(X4) )
| ~ spl0_51
| ~ spl0_271 ),
inference(superposition,[],[f3636,f1238]) ).
fof(f69950,plain,
( spl0_902
| ~ spl0_51
| ~ spl0_268 ),
inference(avatar_split_clause,[],[f3727,f3623,f1237,f69948]) ).
fof(f69948,plain,
( spl0_902
<=> ! [X5,X3,X4,X0,X6,X2,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(X4),X0),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,c_COMBK(X0,X1,X2),X6,X4)))
| ~ hBOOL(c_in(X3,X5,X6))
| ~ class_Complete__Lattice_Ocomplete__lattice(X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_902])]) ).
fof(f3727,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] :
( hBOOL(hAPP(hAPP(c_lessequals(X4),X0),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,c_COMBK(X0,X1,X2),X6,X4)))
| ~ hBOOL(c_in(X3,X5,X6))
| ~ class_Complete__Lattice_Ocomplete__lattice(X4) )
| ~ spl0_51
| ~ spl0_268 ),
inference(superposition,[],[f3624,f1238]) ).
fof(f69946,plain,
( spl0_901
| ~ spl0_245
| ~ spl0_260 ),
inference(avatar_split_clause,[],[f3464,f3109,f2694,f69944]) ).
fof(f69944,plain,
( spl0_901
<=> ! [X2,X0,X1] :
( X0 = X1
| ~ class_Orderings_Oorder(X2)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X2),X1),X0))
| c_COMBK(c_False,tc_bool,X2) = c_SetInterval_Oord__class_OatLeastAtMost(X1,X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_901])]) ).
fof(f3464,plain,
( ! [X2,X0,X1] :
( X0 = X1
| ~ class_Orderings_Oorder(X2)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X2),X1),X0))
| c_COMBK(c_False,tc_bool,X2) = c_SetInterval_Oord__class_OatLeastAtMost(X1,X0,X2) )
| ~ spl0_245
| ~ spl0_260 ),
inference(duplicate_literal_removal,[],[f3452]) ).
fof(f3452,plain,
( ! [X2,X0,X1] :
( X0 = X1
| ~ class_Orderings_Oorder(X2)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X2),X1),X0))
| ~ class_Orderings_Oorder(X2)
| c_COMBK(c_False,tc_bool,X2) = c_SetInterval_Oord__class_OatLeastAtMost(X1,X0,X2) )
| ~ spl0_245
| ~ spl0_260 ),
inference(resolution,[],[f3110,f2695]) ).
fof(f69942,plain,
( spl0_900
| ~ spl0_245
| ~ spl0_253 ),
inference(avatar_split_clause,[],[f3308,f3081,f2694,f69940]) ).
fof(f69940,plain,
( spl0_900
<=> ! [X2,X0,X1] :
( X0 = X1
| ~ hBOOL(hAPP(hAPP(c_lessequals(X2),X0),X1))
| ~ class_Orderings_Oorder(X2)
| c_COMBK(c_False,tc_bool,X2) = c_SetInterval_Oord__class_OatLeastAtMost(X1,X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_900])]) ).
fof(f3308,plain,
( ! [X2,X0,X1] :
( X0 = X1
| ~ hBOOL(hAPP(hAPP(c_lessequals(X2),X0),X1))
| ~ class_Orderings_Oorder(X2)
| c_COMBK(c_False,tc_bool,X2) = c_SetInterval_Oord__class_OatLeastAtMost(X1,X0,X2) )
| ~ spl0_245
| ~ spl0_253 ),
inference(duplicate_literal_removal,[],[f3296]) ).
fof(f3296,plain,
( ! [X2,X0,X1] :
( X0 = X1
| ~ hBOOL(hAPP(hAPP(c_lessequals(X2),X0),X1))
| ~ class_Orderings_Oorder(X2)
| ~ class_Orderings_Oorder(X2)
| c_COMBK(c_False,tc_bool,X2) = c_SetInterval_Oord__class_OatLeastAtMost(X1,X0,X2) )
| ~ spl0_245
| ~ spl0_253 ),
inference(resolution,[],[f3082,f2695]) ).
fof(f69887,plain,
( spl0_899
| ~ spl0_210
| ~ spl0_245 ),
inference(avatar_split_clause,[],[f3046,f2694,f2233,f69885]) ).
fof(f69885,plain,
( spl0_899
<=> ! [X2,X0,X1] :
( ~ class_Orderings_Oorder(X0)
| c_COMBK(c_False,tc_bool,X0) = c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X0)
| ~ class_Lattices_Olower__semilattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_899])]) ).
fof(f3046,plain,
( ! [X2,X0,X1] :
( ~ class_Orderings_Oorder(X0)
| c_COMBK(c_False,tc_bool,X0) = c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X0)
| ~ class_Lattices_Olower__semilattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2) = X1 )
| ~ spl0_210
| ~ spl0_245 ),
inference(resolution,[],[f2695,f2234]) ).
fof(f69883,plain,
( spl0_898
| ~ spl0_212
| ~ spl0_245 ),
inference(avatar_split_clause,[],[f3045,f2694,f2247,f69881]) ).
fof(f69881,plain,
( spl0_898
<=> ! [X2,X0,X1] :
( ~ class_Orderings_Oorder(X0)
| c_COMBK(c_False,tc_bool,X0) = c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X0)
| ~ class_Lattices_Olower__semilattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X1) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_898])]) ).
fof(f3045,plain,
( ! [X2,X0,X1] :
( ~ class_Orderings_Oorder(X0)
| c_COMBK(c_False,tc_bool,X0) = c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X0)
| ~ class_Lattices_Olower__semilattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X1) = X1 )
| ~ spl0_212
| ~ spl0_245 ),
inference(resolution,[],[f2695,f2248]) ).
fof(f69879,plain,
( spl0_897
| ~ spl0_215
| ~ spl0_245 ),
inference(avatar_split_clause,[],[f3044,f2694,f2259,f69877]) ).
fof(f69877,plain,
( spl0_897
<=> ! [X2,X0,X1] :
( ~ class_Orderings_Oorder(X0)
| c_COMBK(c_False,tc_bool,X0) = c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X0)
| ~ class_Lattices_Oupper__semilattice(X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X2),X1) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_897])]) ).
fof(f3044,plain,
( ! [X2,X0,X1] :
( ~ class_Orderings_Oorder(X0)
| c_COMBK(c_False,tc_bool,X0) = c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X0)
| ~ class_Lattices_Oupper__semilattice(X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X2),X1) = X2 )
| ~ spl0_215
| ~ spl0_245 ),
inference(resolution,[],[f2695,f2260]) ).
fof(f69875,plain,
( spl0_896
| ~ spl0_217
| ~ spl0_245 ),
inference(avatar_split_clause,[],[f3043,f2694,f2267,f69873]) ).
fof(f69873,plain,
( spl0_896
<=> ! [X2,X0,X1] :
( ~ class_Orderings_Oorder(X0)
| c_COMBK(c_False,tc_bool,X0) = c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X0)
| ~ class_Lattices_Oupper__semilattice(X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_896])]) ).
fof(f3043,plain,
( ! [X2,X0,X1] :
( ~ class_Orderings_Oorder(X0)
| c_COMBK(c_False,tc_bool,X0) = c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X0)
| ~ class_Lattices_Oupper__semilattice(X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2) = X2 )
| ~ spl0_217
| ~ spl0_245 ),
inference(resolution,[],[f2695,f2268]) ).
fof(f69871,plain,
( spl0_895
| ~ spl0_144
| ~ spl0_233 ),
inference(avatar_split_clause,[],[f2953,f2645,f1708,f69869]) ).
fof(f69869,plain,
( spl0_895
<=> ! [X3,X4,X0,X5,X2,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(hAPP(c_COMBS(X3,X4,X5),c_Lattices_Olower__semilattice__class_Oinf(X0)),X2),X1)),hAPP(X2,X1)))
| ~ class_Lattices_Olower__semilattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_895])]) ).
fof(f2953,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(hAPP(c_COMBS(X3,X4,X5),c_Lattices_Olower__semilattice__class_Oinf(X0)),X2),X1)),hAPP(X2,X1)))
| ~ class_Lattices_Olower__semilattice(X0) )
| ~ spl0_144
| ~ spl0_233 ),
inference(superposition,[],[f1709,f2646]) ).
fof(f69867,plain,
( spl0_894
| ~ spl0_143
| ~ spl0_233 ),
inference(avatar_split_clause,[],[f2952,f2645,f1704,f69865]) ).
fof(f69865,plain,
( spl0_894
<=> ! [X3,X4,X0,X5,X2,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(hAPP(c_COMBS(X3,X4,X5),c_Lattices_Olower__semilattice__class_Oinf(X0)),X2),X1)),hAPP(X2,X1)))
| ~ class_Lattices_Olattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_894])]) ).
fof(f2952,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(hAPP(c_COMBS(X3,X4,X5),c_Lattices_Olower__semilattice__class_Oinf(X0)),X2),X1)),hAPP(X2,X1)))
| ~ class_Lattices_Olattice(X0) )
| ~ spl0_143
| ~ spl0_233 ),
inference(superposition,[],[f1705,f2646]) ).
fof(f69863,plain,
( spl0_893
| ~ spl0_189
| ~ spl0_233 ),
inference(avatar_split_clause,[],[f2946,f2645,f2021,f69861]) ).
fof(f69861,plain,
( spl0_893
<=> ! [X3,X4,X0,X5,X2,X1] : hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),hAPP(hAPP(hAPP(c_COMBS(X3,X4,X5),c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool))),X2),X1)),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_893])]) ).
fof(f2946,plain,
( ! [X2,X3,X0,X1,X4,X5] : hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),hAPP(hAPP(hAPP(c_COMBS(X3,X4,X5),c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool))),X2),X1)),X1))
| ~ spl0_189
| ~ spl0_233 ),
inference(superposition,[],[f2022,f2646]) ).
fof(f69859,plain,
( spl0_892
| ~ spl0_186
| ~ spl0_233 ),
inference(avatar_split_clause,[],[f2939,f2645,f2009,f69857]) ).
fof(f69857,plain,
( spl0_892
<=> ! [X3,X4,X0,X5,X2,X1] : hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),hAPP(hAPP(hAPP(c_COMBS(X3,X4,X5),c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool))),X2),X1)),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_892])]) ).
fof(f2939,plain,
( ! [X2,X3,X0,X1,X4,X5] : hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),hAPP(hAPP(hAPP(c_COMBS(X3,X4,X5),c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool))),X2),X1)),X1))
| ~ spl0_186
| ~ spl0_233 ),
inference(superposition,[],[f2010,f2646]) ).
fof(f69855,plain,
( spl0_891
| ~ spl0_146
| ~ spl0_233 ),
inference(avatar_split_clause,[],[f2930,f2645,f1716,f69853]) ).
fof(f69853,plain,
( spl0_891
<=> ! [X3,X4,X0,X5,X2,X1] : hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),hAPP(X2,X1)),hAPP(hAPP(hAPP(c_COMBS(X3,X4,X5),c_Set_Oinsert(X0)),X2),X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_891])]) ).
fof(f2930,plain,
( ! [X2,X3,X0,X1,X4,X5] : hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),hAPP(X2,X1)),hAPP(hAPP(hAPP(c_COMBS(X3,X4,X5),c_Set_Oinsert(X0)),X2),X1)))
| ~ spl0_146
| ~ spl0_233 ),
inference(superposition,[],[f1717,f2646]) ).
fof(f69851,plain,
( spl0_890
| ~ spl0_140
| ~ spl0_233 ),
inference(avatar_split_clause,[],[f2915,f2645,f1692,f69849]) ).
fof(f69849,plain,
( spl0_890
<=> ! [X3,X4,X0,X5,X2,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(X2,X1)),hAPP(hAPP(hAPP(c_COMBS(X3,X4,X5),c_Lattices_Oupper__semilattice__class_Osup(X0)),X2),X1)))
| ~ class_Lattices_Olattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_890])]) ).
fof(f2915,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(X2,X1)),hAPP(hAPP(hAPP(c_COMBS(X3,X4,X5),c_Lattices_Oupper__semilattice__class_Osup(X0)),X2),X1)))
| ~ class_Lattices_Olattice(X0) )
| ~ spl0_140
| ~ spl0_233 ),
inference(superposition,[],[f1693,f2646]) ).
fof(f69847,plain,
( spl0_889
| ~ spl0_453
| ~ spl0_778 ),
inference(avatar_split_clause,[],[f63486,f62708,f9810,f69845]) ).
fof(f69845,plain,
( spl0_889
<=> ! [X0] : c_Orderings_Otop__class_Otop(tc_bool) = hAPP(c_Complete__Lattice_OSup__class_OSup(tc_bool),hAPP(hAPP(c_Set_Oinsert(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_889])]) ).
fof(f9810,plain,
( spl0_453
<=> ! [X0] : c_Orderings_Otop__class_Otop(tc_bool) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_453])]) ).
fof(f62708,plain,
( spl0_778
<=> ! [X0,X1] : hAPP(c_Complete__Lattice_OSup__class_OSup(tc_bool),hAPP(hAPP(c_Set_Oinsert(tc_bool),X0),X1)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),X0),hAPP(c_Complete__Lattice_OSup__class_OSup(tc_bool),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_778])]) ).
fof(f63486,plain,
( ! [X0] : c_Orderings_Otop__class_Otop(tc_bool) = hAPP(c_Complete__Lattice_OSup__class_OSup(tc_bool),hAPP(hAPP(c_Set_Oinsert(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),X0))
| ~ spl0_453
| ~ spl0_778 ),
inference(superposition,[],[f62709,f9811]) ).
fof(f9811,plain,
( ! [X0] : c_Orderings_Otop__class_Otop(tc_bool) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),X0)
| ~ spl0_453 ),
inference(avatar_component_clause,[],[f9810]) ).
fof(f62709,plain,
( ! [X0,X1] : hAPP(c_Complete__Lattice_OSup__class_OSup(tc_bool),hAPP(hAPP(c_Set_Oinsert(tc_bool),X0),X1)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),X0),hAPP(c_Complete__Lattice_OSup__class_OSup(tc_bool),X1))
| ~ spl0_778 ),
inference(avatar_component_clause,[],[f62708]) ).
fof(f69843,plain,
( spl0_888
| ~ spl0_139
| ~ spl0_233 ),
inference(avatar_split_clause,[],[f2914,f2645,f1688,f69841]) ).
fof(f69841,plain,
( spl0_888
<=> ! [X3,X4,X0,X5,X2,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(X2,X1)),hAPP(hAPP(hAPP(c_COMBS(X3,X4,X5),c_Lattices_Oupper__semilattice__class_Osup(X0)),X2),X1)))
| ~ class_Lattices_Oupper__semilattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_888])]) ).
fof(f2914,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(X2,X1)),hAPP(hAPP(hAPP(c_COMBS(X3,X4,X5),c_Lattices_Oupper__semilattice__class_Osup(X0)),X2),X1)))
| ~ class_Lattices_Oupper__semilattice(X0) )
| ~ spl0_139
| ~ spl0_233 ),
inference(superposition,[],[f1689,f2646]) ).
fof(f69839,plain,
( spl0_887
| ~ spl0_185
| ~ spl0_233 ),
inference(avatar_split_clause,[],[f2908,f2645,f2005,f69837]) ).
fof(f69837,plain,
( spl0_887
<=> ! [X3,X4,X0,X5,X2,X1] : hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X1),hAPP(hAPP(hAPP(c_COMBS(X3,X4,X5),c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool))),X2),X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_887])]) ).
fof(f2908,plain,
( ! [X2,X3,X0,X1,X4,X5] : hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X1),hAPP(hAPP(hAPP(c_COMBS(X3,X4,X5),c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool))),X2),X1)))
| ~ spl0_185
| ~ spl0_233 ),
inference(superposition,[],[f2006,f2646]) ).
fof(f69835,plain,
( spl0_886
| ~ spl0_201
| ~ spl0_233 ),
inference(avatar_split_clause,[],[f2877,f2645,f2076,f69833]) ).
fof(f69833,plain,
( spl0_886
<=> ! [X2,X4,X0,X3,X1] : c_COMBK(c_False,tc_bool,X0) = hAPP(hAPP(hAPP(c_COMBS(X2,X3,X4),c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool))),X1),c_COMBK(c_False,tc_bool,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_886])]) ).
fof(f2877,plain,
( ! [X2,X3,X0,X1,X4] : c_COMBK(c_False,tc_bool,X0) = hAPP(hAPP(hAPP(c_COMBS(X2,X3,X4),c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool))),X1),c_COMBK(c_False,tc_bool,X0))
| ~ spl0_201
| ~ spl0_233 ),
inference(superposition,[],[f2646,f2077]) ).
fof(f69831,plain,
( spl0_885
| ~ spl0_200
| ~ spl0_233 ),
inference(avatar_split_clause,[],[f2876,f2645,f2066,f69829]) ).
fof(f69829,plain,
( spl0_885
<=> ! [X2,X4,X0,X3,X1] : c_COMBK(c_False,tc_bool,X0) = hAPP(hAPP(hAPP(c_COMBS(X2,X3,X4),c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool))),X1),c_COMBK(c_False,tc_bool,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_885])]) ).
fof(f2876,plain,
( ! [X2,X3,X0,X1,X4] : c_COMBK(c_False,tc_bool,X0) = hAPP(hAPP(hAPP(c_COMBS(X2,X3,X4),c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool))),X1),c_COMBK(c_False,tc_bool,X0))
| ~ spl0_200
| ~ spl0_233 ),
inference(superposition,[],[f2646,f2067]) ).
fof(f69827,plain,
( spl0_884
| ~ spl0_178
| ~ spl0_233 ),
inference(avatar_split_clause,[],[f2874,f2645,f1976,f69825]) ).
fof(f69825,plain,
( spl0_884
<=> ! [X2,X4,X0,X3,X1] : c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)) = hAPP(hAPP(hAPP(c_COMBS(X2,X3,X4),c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool))),X1),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_884])]) ).
fof(f2874,plain,
( ! [X2,X3,X0,X1,X4] : c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)) = hAPP(hAPP(hAPP(c_COMBS(X2,X3,X4),c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool))),X1),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)))
| ~ spl0_178
| ~ spl0_233 ),
inference(superposition,[],[f2646,f1977]) ).
fof(f69823,plain,
( spl0_883
| ~ spl0_233 ),
inference(avatar_split_clause,[],[f2872,f2645,f69821]) ).
fof(f69821,plain,
( spl0_883
<=> ! [X7,X3,X4,X0,X8,X6,X5,X2,X1] : hAPP(hAPP(hAPP(c_COMBS(X3,X4,X5),X0),X2),X1) = hAPP(hAPP(hAPP(c_COMBS(X6,X7,X8),X0),X2),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_883])]) ).
fof(f2872,plain,
( ! [X2,X3,X0,X1,X8,X6,X7,X4,X5] : hAPP(hAPP(hAPP(c_COMBS(X3,X4,X5),X0),X2),X1) = hAPP(hAPP(hAPP(c_COMBS(X6,X7,X8),X0),X2),X1)
| ~ spl0_233 ),
inference(superposition,[],[f2646,f2646]) ).
fof(f69819,plain,
( spl0_882
| ~ spl0_232
| ~ spl0_233 ),
inference(avatar_split_clause,[],[f2871,f2645,f2641,f69817]) ).
fof(f69817,plain,
( spl0_882
<=> ! [X2,X4,X0,X3,X1] : hAPP(hAPP(c_Set_Oinsert(X0),X1),X1) = hAPP(hAPP(hAPP(c_COMBS(X2,X3,X4),c_Set_Oinsert(X0)),hAPP(c_Set_Oinsert(X0),X1)),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_882])]) ).
fof(f2641,plain,
( spl0_232
<=> ! [X5,X1,X0] : hAPP(hAPP(c_Set_Oinsert(X0),X1),X5) = hAPP(hAPP(c_Set_Oinsert(X0),X1),hAPP(hAPP(c_Set_Oinsert(X0),X1),X5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_232])]) ).
fof(f2871,plain,
( ! [X2,X3,X0,X1,X4] : hAPP(hAPP(c_Set_Oinsert(X0),X1),X1) = hAPP(hAPP(hAPP(c_COMBS(X2,X3,X4),c_Set_Oinsert(X0)),hAPP(c_Set_Oinsert(X0),X1)),X1)
| ~ spl0_232
| ~ spl0_233 ),
inference(superposition,[],[f2646,f2642]) ).
fof(f2642,plain,
( ! [X0,X1,X5] : hAPP(hAPP(c_Set_Oinsert(X0),X1),X5) = hAPP(hAPP(c_Set_Oinsert(X0),X1),hAPP(hAPP(c_Set_Oinsert(X0),X1),X5))
| ~ spl0_232 ),
inference(avatar_component_clause,[],[f2641]) ).
fof(f69815,plain,
( spl0_881
| ~ spl0_79
| ~ spl0_233 ),
inference(avatar_split_clause,[],[f2846,f2645,f1361,f69813]) ).
fof(f69813,plain,
( spl0_881
<=> ! [X2,X3,X4,X0,X5,X1] : hAPP(hAPP(X5,X1),X1) = hAPP(hAPP(hAPP(c_COMBS(X2,X3,X4),X5),hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X1)),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_881])]) ).
fof(f2846,plain,
( ! [X2,X3,X0,X1,X4,X5] : hAPP(hAPP(X5,X1),X1) = hAPP(hAPP(hAPP(c_COMBS(X2,X3,X4),X5),hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X1)),X1)
| ~ spl0_79
| ~ spl0_233 ),
inference(superposition,[],[f2646,f1362]) ).
fof(f69811,plain,
( spl0_880
| ~ spl0_68
| ~ spl0_233 ),
inference(avatar_split_clause,[],[f2845,f2645,f1316,f69809]) ).
fof(f69809,plain,
( spl0_880
<=> ! [X2,X3,X4,X0,X5,X1] : hAPP(hAPP(hAPP(c_COMBS(X2,X3,X4),X5),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1)),X1) = hAPP(hAPP(X5,X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_880])]) ).
fof(f2845,plain,
( ! [X2,X3,X0,X1,X4,X5] : hAPP(hAPP(hAPP(c_COMBS(X2,X3,X4),X5),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1)),X1) = hAPP(hAPP(X5,X1),X1)
| ~ spl0_68
| ~ spl0_233 ),
inference(superposition,[],[f2646,f1317]) ).
fof(f69807,plain,
( spl0_879
| ~ spl0_79
| ~ spl0_233 ),
inference(avatar_split_clause,[],[f2816,f2645,f1361,f69805]) ).
fof(f69805,plain,
( spl0_879
<=> ! [X2,X3,X4,X0,X5,X1] : hAPP(X1,hAPP(X5,X1)) = hAPP(hAPP(hAPP(c_COMBS(X2,X3,X4),hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X1)),X5),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_879])]) ).
fof(f2816,plain,
( ! [X2,X3,X0,X1,X4,X5] : hAPP(X1,hAPP(X5,X1)) = hAPP(hAPP(hAPP(c_COMBS(X2,X3,X4),hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X1)),X5),X1)
| ~ spl0_79
| ~ spl0_233 ),
inference(superposition,[],[f2646,f1362]) ).
fof(f69776,plain,
( spl0_878
| ~ spl0_68
| ~ spl0_233 ),
inference(avatar_split_clause,[],[f2815,f2645,f1316,f69774]) ).
fof(f69774,plain,
( spl0_878
<=> ! [X2,X3,X4,X0,X5,X1] : hAPP(hAPP(hAPP(c_COMBS(X2,X3,X4),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1)),X5),X1) = hAPP(X1,hAPP(X5,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_878])]) ).
fof(f2815,plain,
( ! [X2,X3,X0,X1,X4,X5] : hAPP(hAPP(hAPP(c_COMBS(X2,X3,X4),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1)),X5),X1) = hAPP(X1,hAPP(X5,X1))
| ~ spl0_68
| ~ spl0_233 ),
inference(superposition,[],[f2646,f1317]) ).
fof(f69772,plain,
( spl0_876
| spl0_877
| ~ spl0_80
| ~ spl0_230 ),
inference(avatar_split_clause,[],[f2732,f2633,f1365,f69770,f69767]) ).
fof(f69767,plain,
( spl0_876
<=> ! [X2,X1] : ~ c_Fun_Oinj__on(c_and,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X1,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_876])]) ).
fof(f69770,plain,
( spl0_877
<=> ! [X0] :
( hAPP(c_HOL_Oord__class_Oless(tc_bool),v_P) != hAPP(c_and,X0)
| hAPP(c_Not,v_P) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_877])]) ).
fof(f2732,plain,
( ! [X2,X0,X1] :
( hAPP(c_HOL_Oord__class_Oless(tc_bool),v_P) != hAPP(c_and,X0)
| hAPP(c_Not,v_P) = X0
| ~ c_Fun_Oinj__on(c_and,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X1,X2) )
| ~ spl0_80
| ~ spl0_230 ),
inference(superposition,[],[f2634,f1367]) ).
fof(f66683,plain,
( spl0_875
| ~ spl0_158
| ~ spl0_763 ),
inference(avatar_split_clause,[],[f65091,f61292,f1818,f66681]) ).
fof(f66681,plain,
( spl0_875
<=> ! [X0,X1] : hBOOL(c_in(X1,c_SetInterval_Oord__class_OatLeastAtMost(X1,X1,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_875])]) ).
fof(f1818,plain,
( spl0_158
<=> ! [X0,X1] : hBOOL(c_in(X1,hAPP(c_fequal(X0),X1),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_158])]) ).
fof(f65091,plain,
( ! [X0,X1] : hBOOL(c_in(X1,c_SetInterval_Oord__class_OatLeastAtMost(X1,X1,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)))
| ~ spl0_158
| ~ spl0_763 ),
inference(superposition,[],[f1819,f61293]) ).
fof(f1819,plain,
( ! [X0,X1] : hBOOL(c_in(X1,hAPP(c_fequal(X0),X1),X0))
| ~ spl0_158 ),
inference(avatar_component_clause,[],[f1818]) ).
fof(f66495,plain,
( spl0_874
| ~ spl0_123
| ~ spl0_198
| ~ spl0_199
| ~ spl0_471 ),
inference(avatar_split_clause,[],[f12438,f10965,f2062,f2058,f1603,f66493]) ).
fof(f66493,plain,
( spl0_874
<=> ! [X2,X0,X1] : c_COMBK(c_False,tc_bool,X0) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X2),X1)),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_874])]) ).
fof(f10965,plain,
( spl0_471
<=> ! [X9,X0,X12,X5] : hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X5),X12)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X9),X12)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X5),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X12),X9)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_471])]) ).
fof(f12438,plain,
( ! [X2,X0,X1] : c_COMBK(c_False,tc_bool,X0) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X2),X1)),X1)
| ~ spl0_123
| ~ spl0_198
| ~ spl0_199
| ~ spl0_471 ),
inference(forward_demodulation,[],[f12437,f2063]) ).
fof(f12437,plain,
( ! [X2,X0,X1] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X2),c_COMBK(c_False,tc_bool,X0)) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X2),X1)),X1)
| ~ spl0_123
| ~ spl0_198
| ~ spl0_471 ),
inference(forward_demodulation,[],[f12351,f2059]) ).
fof(f12351,plain,
( ! [X2,X0,X1] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X2),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X1),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)))) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X2),X1)),X1)
| ~ spl0_123
| ~ spl0_471 ),
inference(superposition,[],[f10966,f1604]) ).
fof(f10966,plain,
( ! [X0,X9,X5,X12] : hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X5),X12)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X9),X12)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X5),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X12),X9))
| ~ spl0_471 ),
inference(avatar_component_clause,[],[f10965]) ).
fof(f66491,plain,
( spl0_873
| ~ spl0_130
| ~ spl0_199
| ~ spl0_469 ),
inference(avatar_split_clause,[],[f12118,f10957,f2062,f1631,f66489]) ).
fof(f66489,plain,
( spl0_873
<=> ! [X2,X0,X1] : c_COMBK(c_False,tc_bool,X0) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X2),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_873])]) ).
fof(f10957,plain,
( spl0_469
<=> ! [X5,X0,X12,X9] : hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X5),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X9),X12)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X5),X9)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X5),X12)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_469])]) ).
fof(f12118,plain,
( ! [X2,X0,X1] : c_COMBK(c_False,tc_bool,X0) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X2),X1))
| ~ spl0_130
| ~ spl0_199
| ~ spl0_469 ),
inference(forward_demodulation,[],[f12010,f2063]) ).
fof(f12010,plain,
( ! [X2,X0,X1] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X1),X2)),c_COMBK(c_False,tc_bool,X0)) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X2),X1))
| ~ spl0_130
| ~ spl0_469 ),
inference(superposition,[],[f10958,f1632]) ).
fof(f10958,plain,
( ! [X0,X9,X5,X12] : hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X5),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X9),X12)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X5),X9)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X5),X12))
| ~ spl0_469 ),
inference(avatar_component_clause,[],[f10957]) ).
fof(f66487,plain,
( spl0_872
| ~ spl0_136
| ~ spl0_763 ),
inference(avatar_split_clause,[],[f65090,f61292,f1670,f66485]) ).
fof(f66485,plain,
( spl0_872
<=> ! [X0,X1] : c_Nitpick_Osko__Nitpick__XEx1__def__1__3(c_SetInterval_Oord__class_OatLeastAtMost(X1,X1,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_872])]) ).
fof(f1670,plain,
( spl0_136
<=> ! [X0,X1] : c_Nitpick_Osko__Nitpick__XEx1__def__1__3(hAPP(c_fequal(X1),X0),X1) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_136])]) ).
fof(f65090,plain,
( ! [X0,X1] : c_Nitpick_Osko__Nitpick__XEx1__def__1__3(c_SetInterval_Oord__class_OatLeastAtMost(X1,X1,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) = X1
| ~ spl0_136
| ~ spl0_763 ),
inference(superposition,[],[f1671,f61293]) ).
fof(f1671,plain,
( ! [X0,X1] : c_Nitpick_Osko__Nitpick__XEx1__def__1__3(hAPP(c_fequal(X1),X0),X1) = X0
| ~ spl0_136 ),
inference(avatar_component_clause,[],[f1670]) ).
fof(f66483,plain,
( spl0_871
| ~ spl0_130
| ~ spl0_201
| ~ spl0_469 ),
inference(avatar_split_clause,[],[f12102,f10957,f2076,f1631,f66481]) ).
fof(f66481,plain,
( spl0_871
<=> ! [X2,X0,X1] : c_COMBK(c_False,tc_bool,X0) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_871])]) ).
fof(f12102,plain,
( ! [X2,X0,X1] : c_COMBK(c_False,tc_bool,X0) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X2))
| ~ spl0_130
| ~ spl0_201
| ~ spl0_469 ),
inference(forward_demodulation,[],[f11999,f2077]) ).
fof(f11999,plain,
( ! [X2,X0,X1] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X1),X2)) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X2))
| ~ spl0_130
| ~ spl0_469 ),
inference(superposition,[],[f10958,f1632]) ).
fof(f66479,plain,
( spl0_870
| ~ spl0_125
| ~ spl0_198
| ~ spl0_199
| ~ spl0_464 ),
inference(avatar_split_clause,[],[f11545,f10791,f2062,f2058,f1611,f66477]) ).
fof(f66477,plain,
( spl0_870
<=> ! [X2,X0,X1] : c_COMBK(c_False,tc_bool,X0) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X1),X2)),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_870])]) ).
fof(f11545,plain,
( ! [X2,X0,X1] : c_COMBK(c_False,tc_bool,X0) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X1),X2)),X1)
| ~ spl0_125
| ~ spl0_198
| ~ spl0_199
| ~ spl0_464 ),
inference(forward_demodulation,[],[f11544,f2063]) ).
fof(f11544,plain,
( ! [X2,X0,X1] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X1),c_COMBK(c_False,tc_bool,X0)) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X1),X2)),X1)
| ~ spl0_125
| ~ spl0_198
| ~ spl0_464 ),
inference(forward_demodulation,[],[f11470,f2059]) ).
fof(f11470,plain,
( ! [X2,X0,X1] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X1),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X2),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)))) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X1),X2)),X1)
| ~ spl0_125
| ~ spl0_464 ),
inference(superposition,[],[f10792,f1612]) ).
fof(f66475,plain,
( spl0_869
| ~ spl0_126
| ~ spl0_466 ),
inference(avatar_split_clause,[],[f10844,f10800,f1615,f66473]) ).
fof(f66473,plain,
( spl0_869
<=> ! [X0,X3,X2,X1] :
( c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X1),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X3),X2)),X0)
| ~ c_Finite__Set_Ofinite(X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_869])]) ).
fof(f10844,plain,
( ! [X2,X3,X0,X1] :
( c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X1),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X3),X2)),X0)
| ~ c_Finite__Set_Ofinite(X3,X0) )
| ~ spl0_126
| ~ spl0_466 ),
inference(superposition,[],[f1616,f10801]) ).
fof(f66471,plain,
( spl0_868
| ~ spl0_122
| ~ spl0_429 ),
inference(avatar_split_clause,[],[f9116,f8411,f1599,f66469]) ).
fof(f66469,plain,
( spl0_868
<=> ! [X0,X3,X2,X1] :
( ~ c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X2),X3)),X0)
| c_Finite__Set_Ofinite(X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_868])]) ).
fof(f9116,plain,
( ! [X2,X3,X0,X1] :
( ~ c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X2),X3)),X0)
| c_Finite__Set_Ofinite(X3,X0) )
| ~ spl0_122
| ~ spl0_429 ),
inference(superposition,[],[f1600,f8412]) ).
fof(f66467,plain,
( spl0_867
| ~ spl0_121
| ~ spl0_428 ),
inference(avatar_split_clause,[],[f8910,f8407,f1595,f66465]) ).
fof(f66465,plain,
( spl0_867
<=> ! [X0,X3,X2,X1] :
( ~ c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X3)),X0)
| c_Finite__Set_Ofinite(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_867])]) ).
fof(f8910,plain,
( ! [X2,X3,X0,X1] :
( ~ c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X3)),X0)
| c_Finite__Set_Ofinite(X1,X0) )
| ~ spl0_121
| ~ spl0_428 ),
inference(superposition,[],[f1596,f8408]) ).
fof(f66463,plain,
( spl0_866
| ~ spl0_127
| ~ spl0_427 ),
inference(avatar_split_clause,[],[f8695,f8403,f1619,f66461]) ).
fof(f66461,plain,
( spl0_866
<=> ! [X0,X3,X2,X1] :
( c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X1),X3)),X0)
| ~ c_Finite__Set_Ofinite(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_866])]) ).
fof(f8695,plain,
( ! [X2,X3,X0,X1] :
( c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X1),X3)),X0)
| ~ c_Finite__Set_Ofinite(X1,X0) )
| ~ spl0_127
| ~ spl0_427 ),
inference(superposition,[],[f1620,f8404]) ).
fof(f66459,plain,
( spl0_865
| ~ spl0_126
| ~ spl0_426 ),
inference(avatar_split_clause,[],[f8563,f8399,f1615,f66457]) ).
fof(f66457,plain,
( spl0_865
<=> ! [X0,X3,X2,X1] :
( c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X2),X3)),X0)
| ~ c_Finite__Set_Ofinite(X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_865])]) ).
fof(f8563,plain,
( ! [X2,X3,X0,X1] :
( c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X2),X3)),X0)
| ~ c_Finite__Set_Ofinite(X3,X0) )
| ~ spl0_126
| ~ spl0_426 ),
inference(superposition,[],[f1616,f8400]) ).
fof(f66455,plain,
( spl0_864
| ~ spl0_152
| ~ spl0_391 ),
inference(avatar_split_clause,[],[f7007,f6760,f1794,f66453]) ).
fof(f66453,plain,
( spl0_864
<=> ! [X4,X0,X3,X2,X1] :
( hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X0),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X2),X3)),X4))
| ~ hBOOL(hAPP(X3,X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_864])]) ).
fof(f7007,plain,
( ! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X0),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X2),X3)),X4))
| ~ hBOOL(hAPP(X3,X4)) )
| ~ spl0_152
| ~ spl0_391 ),
inference(superposition,[],[f1795,f6761]) ).
fof(f66451,plain,
( spl0_863
| ~ spl0_153
| ~ spl0_390 ),
inference(avatar_split_clause,[],[f6882,f6756,f1798,f66449]) ).
fof(f66449,plain,
( spl0_863
<=> ! [X2,X4,X0,X3,X1] :
( hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X0),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X3)),X4))
| ~ hBOOL(hAPP(X1,X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_863])]) ).
fof(f6882,plain,
( ! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X0),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X3)),X4))
| ~ hBOOL(hAPP(X1,X4)) )
| ~ spl0_153
| ~ spl0_390 ),
inference(superposition,[],[f1799,f6757]) ).
fof(f66447,plain,
( spl0_862
| ~ spl0_122
| ~ spl0_350 ),
inference(avatar_split_clause,[],[f5761,f5592,f1599,f66445]) ).
fof(f66445,plain,
( spl0_862
<=> ! [X2,X0,X1] :
( ~ c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X2),X0)
| c_Finite__Set_Ofinite(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X2),X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_862])]) ).
fof(f5761,plain,
( ! [X2,X0,X1] :
( ~ c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X2),X0)
| c_Finite__Set_Ofinite(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X2),X1),X0) )
| ~ spl0_122
| ~ spl0_350 ),
inference(superposition,[],[f1600,f5593]) ).
fof(f66443,plain,
( spl0_861
| ~ spl0_81
| ~ spl0_763 ),
inference(avatar_split_clause,[],[f65087,f61292,f1370,f66441]) ).
fof(f66441,plain,
( spl0_861
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP(c_SetInterval_Oord__class_OatLeastAtMost(X1,X1,tc_fun(X0,tc_bool)),X2))
| X1 = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_861])]) ).
fof(f65087,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(c_SetInterval_Oord__class_OatLeastAtMost(X1,X1,tc_fun(X0,tc_bool)),X2))
| X1 = X2 )
| ~ spl0_81
| ~ spl0_763 ),
inference(superposition,[],[f1371,f61293]) ).
fof(f66439,plain,
( spl0_860
| ~ spl0_121
| ~ spl0_349 ),
inference(avatar_split_clause,[],[f5695,f5588,f1595,f66437]) ).
fof(f66437,plain,
( spl0_860
<=> ! [X2,X0,X1] :
( ~ c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X2),X0)
| c_Finite__Set_Ofinite(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X1),X2),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_860])]) ).
fof(f5695,plain,
( ! [X2,X0,X1] :
( ~ c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X2),X0)
| c_Finite__Set_Ofinite(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X1),X2),X0) )
| ~ spl0_121
| ~ spl0_349 ),
inference(superposition,[],[f1596,f5589]) ).
fof(f66435,plain,
( spl0_859
| ~ spl0_169
| ~ spl0_331 ),
inference(avatar_split_clause,[],[f5100,f4912,f1865,f66433]) ).
fof(f66433,plain,
( spl0_859
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X1),X2))
| c_Finite__Set_Ofinite(X1,X0)
| ~ c_Finite__Set_Ofinite(hAPP(hAPP(c_Set_Oinsert(X0),X3),X2),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_859])]) ).
fof(f5100,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X1),X2))
| c_Finite__Set_Ofinite(X1,X0)
| ~ c_Finite__Set_Ofinite(hAPP(hAPP(c_Set_Oinsert(X0),X3),X2),X0) )
| ~ spl0_169
| ~ spl0_331 ),
inference(resolution,[],[f4913,f1866]) ).
fof(f66431,plain,
( spl0_858
| ~ spl0_74
| ~ spl0_329 ),
inference(avatar_split_clause,[],[f5085,f4904,f1340,f66429]) ).
fof(f66429,plain,
( spl0_858
<=> ! [X0,X1] :
( ~ class_Orderings_Opreorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),c_Orderings_Otop__class_Otop(X0)))
| hBOOL(hAPP(hAPP(c_lessequals(X0),c_Orderings_Otop__class_Otop(X0)),X1))
| ~ class_Orderings_Otop(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_858])]) ).
fof(f4904,plain,
( spl0_329
<=> ! [X2,X0,X1] :
( ~ class_Orderings_Opreorder(X0)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| hBOOL(hAPP(hAPP(c_lessequals(X0),X2),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_329])]) ).
fof(f5085,plain,
( ! [X0,X1] :
( ~ class_Orderings_Opreorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),c_Orderings_Otop__class_Otop(X0)))
| hBOOL(hAPP(hAPP(c_lessequals(X0),c_Orderings_Otop__class_Otop(X0)),X1))
| ~ class_Orderings_Otop(X0) )
| ~ spl0_74
| ~ spl0_329 ),
inference(resolution,[],[f4905,f1341]) ).
fof(f4905,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2))
| ~ class_Orderings_Opreorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| hBOOL(hAPP(hAPP(c_lessequals(X0),X2),X1)) )
| ~ spl0_329 ),
inference(avatar_component_clause,[],[f4904]) ).
fof(f66427,plain,
( spl0_857
| ~ spl0_75
| ~ spl0_329 ),
inference(avatar_split_clause,[],[f5062,f4904,f1344,f66425]) ).
fof(f66425,plain,
( spl0_857
<=> ! [X0,X1] :
( ~ class_Orderings_Opreorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_Orderings_Obot__class_Obot(X0)),X1))
| hBOOL(hAPP(hAPP(c_lessequals(X0),X1),c_Orderings_Obot__class_Obot(X0)))
| ~ class_Orderings_Obot(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_857])]) ).
fof(f5062,plain,
( ! [X0,X1] :
( ~ class_Orderings_Opreorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_Orderings_Obot__class_Obot(X0)),X1))
| hBOOL(hAPP(hAPP(c_lessequals(X0),X1),c_Orderings_Obot__class_Obot(X0)))
| ~ class_Orderings_Obot(X0) )
| ~ spl0_75
| ~ spl0_329 ),
inference(resolution,[],[f4905,f1345]) ).
fof(f66423,plain,
( spl0_856
| ~ spl0_74
| ~ spl0_309 ),
inference(avatar_split_clause,[],[f4829,f4581,f1340,f66421]) ).
fof(f66421,plain,
( spl0_856
<=> ! [X0,X3,X2,X1] :
( ~ class_HOL_Oord(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(X1,X2)),hAPP(c_Orderings_Otop__class_Otop(tc_fun(X3,X0)),X2)))
| ~ class_Orderings_Otop(tc_fun(X3,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_856])]) ).
fof(f4829,plain,
( ! [X2,X3,X0,X1] :
( ~ class_HOL_Oord(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(X1,X2)),hAPP(c_Orderings_Otop__class_Otop(tc_fun(X3,X0)),X2)))
| ~ class_Orderings_Otop(tc_fun(X3,X0)) )
| ~ spl0_74
| ~ spl0_309 ),
inference(resolution,[],[f4582,f1341]) ).
fof(f66419,plain,
( spl0_855
| ~ spl0_75
| ~ spl0_309 ),
inference(avatar_split_clause,[],[f4806,f4581,f1344,f66417]) ).
fof(f66417,plain,
( spl0_855
<=> ! [X0,X3,X2,X1] :
( ~ class_HOL_Oord(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,X0)),X2)),hAPP(X3,X2)))
| ~ class_Orderings_Obot(tc_fun(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_855])]) ).
fof(f4806,plain,
( ! [X2,X3,X0,X1] :
( ~ class_HOL_Oord(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,X0)),X2)),hAPP(X3,X2)))
| ~ class_Orderings_Obot(tc_fun(X1,X0)) )
| ~ spl0_75
| ~ spl0_309 ),
inference(resolution,[],[f4582,f1345]) ).
fof(f66235,plain,
( spl0_854
| ~ spl0_13
| ~ spl0_186
| ~ spl0_309 ),
inference(avatar_split_clause,[],[f4805,f4581,f2009,f1077,f66233]) ).
fof(f66233,plain,
( spl0_854
<=> ! [X2,X0,X1,X3] : hBOOL(hAPP(hAPP(c_lessequals(tc_bool),hAPP(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X1),X2),X3)),hAPP(X1,X3))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_854])]) ).
fof(f4805,plain,
( ! [X2,X3,X0,X1] :
( ~ class_HOL_Oord(tc_bool)
| hBOOL(hAPP(hAPP(c_lessequals(tc_bool),hAPP(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X1),X2),X3)),hAPP(X1,X3))) )
| ~ spl0_186
| ~ spl0_309 ),
inference(resolution,[],[f4582,f2010]) ).
fof(f66037,plain,
( spl0_853
| ~ spl0_13
| ~ spl0_189
| ~ spl0_309 ),
inference(avatar_split_clause,[],[f4802,f4581,f2021,f1077,f66035]) ).
fof(f66035,plain,
( spl0_853
<=> ! [X2,X0,X1,X3] : hBOOL(hAPP(hAPP(c_lessequals(tc_bool),hAPP(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X1),X2),X3)),hAPP(X1,X3))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_853])]) ).
fof(f4802,plain,
( ! [X2,X3,X0,X1] :
( ~ class_HOL_Oord(tc_bool)
| hBOOL(hAPP(hAPP(c_lessequals(tc_bool),hAPP(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X1),X2),X3)),hAPP(X1,X3))) )
| ~ spl0_189
| ~ spl0_309 ),
inference(resolution,[],[f4582,f2022]) ).
fof(f66033,plain,
( spl0_852
| ~ spl0_49
| ~ spl0_763 ),
inference(avatar_split_clause,[],[f65086,f61292,f1228,f66031]) ).
fof(f66031,plain,
( spl0_852
<=> ! [X0,X1] : c_The(c_SetInterval_Oord__class_OatLeastAtMost(X1,X1,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_852])]) ).
fof(f1228,plain,
( spl0_49
<=> ! [X0,X1] : c_The(hAPP(c_fequal(X0),X1),X0) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_49])]) ).
fof(f65086,plain,
( ! [X0,X1] : c_The(c_SetInterval_Oord__class_OatLeastAtMost(X1,X1,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) = X1
| ~ spl0_49
| ~ spl0_763 ),
inference(superposition,[],[f1229,f61293]) ).
fof(f1229,plain,
( ! [X0,X1] : c_The(hAPP(c_fequal(X0),X1),X0) = X1
| ~ spl0_49 ),
inference(avatar_component_clause,[],[f1228]) ).
fof(f66029,plain,
( spl0_851
| ~ spl0_57
| ~ spl0_301 ),
inference(avatar_split_clause,[],[f4545,f3959,f1262,f66027]) ).
fof(f66027,plain,
( spl0_851
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(X0,X1))
| ~ hBOOL(c_in(X1,X2,X3))
| hBOOL(hAPP(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X2),X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_851])]) ).
fof(f4545,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(X0,X1))
| ~ hBOOL(c_in(X1,X2,X3))
| hBOOL(hAPP(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X2),X0),X1)) )
| ~ spl0_57
| ~ spl0_301 ),
inference(resolution,[],[f3960,f1263]) ).
fof(f66025,plain,
( spl0_850
| ~ spl0_79
| ~ spl0_288 ),
inference(avatar_split_clause,[],[f4215,f3899,f1361,f66023]) ).
fof(f66023,plain,
( spl0_850
<=> ! [X4,X0,X3,X2,X1] :
( ~ hBOOL(X1)
| ~ hBOOL(c_in(X1,X2,X3))
| hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X3,tc_fun(X4,tc_bool)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_850])]) ).
fof(f4215,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ hBOOL(X1)
| ~ hBOOL(c_in(X1,X2,X3))
| hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X3,tc_fun(X4,tc_bool)),X1)) )
| ~ spl0_79
| ~ spl0_288 ),
inference(superposition,[],[f3900,f1362]) ).
fof(f66021,plain,
( spl0_849
| ~ spl0_68
| ~ spl0_288 ),
inference(avatar_split_clause,[],[f4214,f3899,f1316,f66019]) ).
fof(f66019,plain,
( spl0_849
<=> ! [X4,X0,X3,X2,X1] :
( ~ hBOOL(X1)
| ~ hBOOL(c_in(X1,X2,X3))
| hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X3,tc_fun(X4,tc_bool)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_849])]) ).
fof(f4214,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ hBOOL(X1)
| ~ hBOOL(c_in(X1,X2,X3))
| hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X3,tc_fun(X4,tc_bool)),X1)) )
| ~ spl0_68
| ~ spl0_288 ),
inference(superposition,[],[f3900,f1317]) ).
fof(f66017,plain,
( spl0_848
| ~ spl0_234
| ~ spl0_256 ),
inference(avatar_split_clause,[],[f3368,f3093,f2649,f66015]) ).
fof(f66015,plain,
( spl0_848
<=> ! [X2,X0,X1] :
( hAPP(hAPP(c_Set_Oinsert(X0),X1),X2) != X2
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),hAPP(c_fequal(X0),X1)),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_848])]) ).
fof(f3368,plain,
( ! [X2,X0,X1] :
( hAPP(hAPP(c_Set_Oinsert(X0),X1),X2) != X2
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),hAPP(c_fequal(X0),X1)),X2)) )
| ~ spl0_234
| ~ spl0_256 ),
inference(superposition,[],[f3094,f2650]) ).
fof(f66013,plain,
( spl0_847
| ~ spl0_146
| ~ spl0_255 ),
inference(avatar_split_clause,[],[f3356,f3089,f1716,f66011]) ).
fof(f66011,plain,
( spl0_847
<=> ! [X2,X0,X1] : hAPP(hAPP(c_Set_Oinsert(X0),X1),X2) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Set_Oinsert(X0),X1),X2)),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_847])]) ).
fof(f3356,plain,
( ! [X2,X0,X1] : hAPP(hAPP(c_Set_Oinsert(X0),X1),X2) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Set_Oinsert(X0),X1),X2)),X2)
| ~ spl0_146
| ~ spl0_255 ),
inference(resolution,[],[f3090,f1717]) ).
fof(f66009,plain,
( spl0_846
| ~ spl0_146
| ~ spl0_254 ),
inference(avatar_split_clause,[],[f3330,f3085,f1716,f66007]) ).
fof(f66007,plain,
( spl0_846
<=> ! [X2,X0,X1] : hAPP(hAPP(c_Set_Oinsert(X0),X2),X1) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),hAPP(hAPP(c_Set_Oinsert(X0),X2),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_846])]) ).
fof(f3330,plain,
( ! [X2,X0,X1] : hAPP(hAPP(c_Set_Oinsert(X0),X2),X1) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),hAPP(hAPP(c_Set_Oinsert(X0),X2),X1))
| ~ spl0_146
| ~ spl0_254 ),
inference(resolution,[],[f3086,f1717]) ).
fof(f66005,plain,
( spl0_845
| ~ spl0_234
| ~ spl0_249 ),
inference(avatar_split_clause,[],[f3189,f3055,f2649,f66003]) ).
fof(f66003,plain,
( spl0_845
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X0),X1),X2),X3))
| hBOOL(hAPP(hAPP(c_fequal(X0),X1),X3))
| hBOOL(hAPP(X2,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_845])]) ).
fof(f3189,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X0),X1),X2),X3))
| hBOOL(hAPP(hAPP(c_fequal(X0),X1),X3))
| hBOOL(hAPP(X2,X3)) )
| ~ spl0_234
| ~ spl0_249 ),
inference(superposition,[],[f3056,f2650]) ).
fof(f66001,plain,
( spl0_844
| ~ spl0_51
| ~ spl0_248 ),
inference(avatar_split_clause,[],[f3180,f3051,f1237,f65999]) ).
fof(f65999,plain,
( spl0_844
<=> ! [X5,X4,X2,X0,X6,X3,X1] :
( ~ c_Finite__Set_Ofinite(X0,X4)
| ~ hBOOL(c_in(X3,X5,X6))
| c_Finite__Set_Ofinite(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,c_COMBK(X0,X1,X2),X6,tc_fun(X4,tc_bool)),X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_844])]) ).
fof(f3180,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] :
( ~ c_Finite__Set_Ofinite(X0,X4)
| ~ hBOOL(c_in(X3,X5,X6))
| c_Finite__Set_Ofinite(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,c_COMBK(X0,X1,X2),X6,tc_fun(X4,tc_bool)),X4) )
| ~ spl0_51
| ~ spl0_248 ),
inference(superposition,[],[f3052,f1238]) ).
fof(f65997,plain,
( spl0_843
| ~ spl0_90
| ~ spl0_248 ),
inference(avatar_split_clause,[],[f3141,f3051,f1419,f65995]) ).
fof(f65995,plain,
( spl0_843
<=> ! [X4,X0,X3,X2,X1] :
( ~ hBOOL(c_in(X0,X1,X2))
| c_Finite__Set_Ofinite(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,hAPP(c_Set_Oinsert(X3),X4),X2,tc_fun(X3,tc_bool)),X3)
| ~ c_Finite__Set_Ofinite(X0,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_843])]) ).
fof(f3141,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ hBOOL(c_in(X0,X1,X2))
| c_Finite__Set_Ofinite(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,hAPP(c_Set_Oinsert(X3),X4),X2,tc_fun(X3,tc_bool)),X3)
| ~ c_Finite__Set_Ofinite(X0,X3) )
| ~ spl0_90
| ~ spl0_248 ),
inference(resolution,[],[f3052,f1420]) ).
fof(f65993,plain,
( spl0_842
| ~ spl0_51
| ~ spl0_199
| ~ spl0_233 ),
inference(avatar_split_clause,[],[f2980,f2645,f2062,f1237,f65991]) ).
fof(f65991,plain,
( spl0_842
<=> ! [X2,X3,X4,X0,X5,X1] : c_False = hAPP(hAPP(hAPP(c_COMBS(X2,X3,X4),hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X1)),X5),c_COMBK(c_False,tc_bool,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_842])]) ).
fof(f2980,plain,
( ! [X2,X3,X0,X1,X4,X5] : c_False = hAPP(hAPP(hAPP(c_COMBS(X2,X3,X4),hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X1)),X5),c_COMBK(c_False,tc_bool,X0))
| ~ spl0_51
| ~ spl0_199
| ~ spl0_233 ),
inference(forward_demodulation,[],[f2838,f1238]) ).
fof(f2838,plain,
( ! [X2,X3,X0,X1,X4,X5] : hAPP(hAPP(hAPP(c_COMBS(X2,X3,X4),hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X1)),X5),c_COMBK(c_False,tc_bool,X0)) = hAPP(c_COMBK(c_False,tc_bool,X0),hAPP(X5,c_COMBK(c_False,tc_bool,X0)))
| ~ spl0_199
| ~ spl0_233 ),
inference(superposition,[],[f2646,f2063]) ).
fof(f65988,plain,
( spl0_841
| ~ spl0_51
| ~ spl0_198
| ~ spl0_233 ),
inference(avatar_split_clause,[],[f2979,f2645,f2058,f1237,f65986]) ).
fof(f65986,plain,
( spl0_841
<=> ! [X2,X3,X4,X0,X5,X1] : c_False = hAPP(hAPP(hAPP(c_COMBS(X2,X3,X4),hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X1)),X5),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_841])]) ).
fof(f2979,plain,
( ! [X2,X3,X0,X1,X4,X5] : c_False = hAPP(hAPP(hAPP(c_COMBS(X2,X3,X4),hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X1)),X5),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)))
| ~ spl0_51
| ~ spl0_198
| ~ spl0_233 ),
inference(forward_demodulation,[],[f2834,f1238]) ).
fof(f2834,plain,
( ! [X2,X3,X0,X1,X4,X5] : hAPP(hAPP(hAPP(c_COMBS(X2,X3,X4),hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X1)),X5),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool))) = hAPP(c_COMBK(c_False,tc_bool,X0),hAPP(X5,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool))))
| ~ spl0_198
| ~ spl0_233 ),
inference(superposition,[],[f2646,f2059]) ).
fof(f65984,plain,
( spl0_840
| ~ spl0_51
| ~ spl0_201
| ~ spl0_233 ),
inference(avatar_split_clause,[],[f2978,f2645,f2076,f1237,f65982]) ).
fof(f65982,plain,
( spl0_840
<=> ! [X2,X3,X4,X0,X5,X1] : c_False = hAPP(hAPP(hAPP(c_COMBS(X2,X3,X4),hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0))),X5),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_840])]) ).
fof(f2978,plain,
( ! [X2,X3,X0,X1,X4,X5] : c_False = hAPP(hAPP(hAPP(c_COMBS(X2,X3,X4),hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0))),X5),X1)
| ~ spl0_51
| ~ spl0_201
| ~ spl0_233 ),
inference(forward_demodulation,[],[f2822,f1238]) ).
fof(f2822,plain,
( ! [X2,X3,X0,X1,X4,X5] : hAPP(c_COMBK(c_False,tc_bool,X0),hAPP(X5,X1)) = hAPP(hAPP(hAPP(c_COMBS(X2,X3,X4),hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0))),X5),X1)
| ~ spl0_201
| ~ spl0_233 ),
inference(superposition,[],[f2646,f2077]) ).
fof(f65980,plain,
( spl0_839
| ~ spl0_51
| ~ spl0_200
| ~ spl0_233 ),
inference(avatar_split_clause,[],[f2977,f2645,f2066,f1237,f65978]) ).
fof(f65978,plain,
( spl0_839
<=> ! [X2,X3,X4,X0,X5,X1] : c_False = hAPP(hAPP(hAPP(c_COMBS(X2,X3,X4),hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0))),X5),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_839])]) ).
fof(f2977,plain,
( ! [X2,X3,X0,X1,X4,X5] : c_False = hAPP(hAPP(hAPP(c_COMBS(X2,X3,X4),hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0))),X5),X1)
| ~ spl0_51
| ~ spl0_200
| ~ spl0_233 ),
inference(forward_demodulation,[],[f2821,f1238]) ).
fof(f2821,plain,
( ! [X2,X3,X0,X1,X4,X5] : hAPP(c_COMBK(c_False,tc_bool,X0),hAPP(X5,X1)) = hAPP(hAPP(hAPP(c_COMBS(X2,X3,X4),hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0))),X5),X1)
| ~ spl0_200
| ~ spl0_233 ),
inference(superposition,[],[f2646,f2067]) ).
fof(f65976,plain,
( spl0_838
| ~ spl0_129
| ~ spl0_233 ),
inference(avatar_split_clause,[],[f2968,f2645,f1627,f65974]) ).
fof(f65974,plain,
( spl0_838
<=> ! [X5,X6,X4,X0,X3,X2,X1] :
( hBOOL(hAPP(hAPP(hAPP(c_COMBS(X4,X5,X6),hAPP(c_Set_Oinsert(X0),X1)),X3),X2))
| ~ hBOOL(hAPP(X2,hAPP(X3,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_838])]) ).
fof(f2968,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] :
( hBOOL(hAPP(hAPP(hAPP(c_COMBS(X4,X5,X6),hAPP(c_Set_Oinsert(X0),X1)),X3),X2))
| ~ hBOOL(hAPP(X2,hAPP(X3,X2))) )
| ~ spl0_129
| ~ spl0_233 ),
inference(superposition,[],[f1628,f2646]) ).
fof(f65972,plain,
( spl0_837
| ~ spl0_160
| ~ spl0_233 ),
inference(avatar_split_clause,[],[f2956,f2645,f1826,f65970]) ).
fof(f65970,plain,
( spl0_837
<=> ! [X3,X4,X0,X5,X2,X1] :
( c_Orderings_Otop__class_Otop(X0) != hAPP(hAPP(hAPP(c_COMBS(X3,X4,X5),c_Lattices_Olower__semilattice__class_Oinf(X0)),X2),X1)
| c_Orderings_Otop__class_Otop(X0) = X1
| ~ class_Lattices_Obounded__lattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_837])]) ).
fof(f1826,plain,
( spl0_160
<=> ! [X5,X9,X0] :
( ~ class_Lattices_Obounded__lattice(X0)
| c_Orderings_Otop__class_Otop(X0) = X5
| c_Orderings_Otop__class_Otop(X0) != hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X5),X9) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_160])]) ).
fof(f2956,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( c_Orderings_Otop__class_Otop(X0) != hAPP(hAPP(hAPP(c_COMBS(X3,X4,X5),c_Lattices_Olower__semilattice__class_Oinf(X0)),X2),X1)
| c_Orderings_Otop__class_Otop(X0) = X1
| ~ class_Lattices_Obounded__lattice(X0) )
| ~ spl0_160
| ~ spl0_233 ),
inference(superposition,[],[f1827,f2646]) ).
fof(f1827,plain,
( ! [X0,X9,X5] :
( c_Orderings_Otop__class_Otop(X0) != hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X5),X9)
| c_Orderings_Otop__class_Otop(X0) = X5
| ~ class_Lattices_Obounded__lattice(X0) )
| ~ spl0_160 ),
inference(avatar_component_clause,[],[f1826]) ).
fof(f65968,plain,
( spl0_836
| ~ spl0_164
| ~ spl0_233 ),
inference(avatar_split_clause,[],[f2945,f2645,f1842,f65966]) ).
fof(f65966,plain,
( spl0_836
<=> ! [X5,X3,X4,X0,X6,X2,X1] :
( ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_COMBS(X3,X4,X5),c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool))),X2),X1),X6))
| hBOOL(hAPP(X1,X6)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_836])]) ).
fof(f2945,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] :
( ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_COMBS(X3,X4,X5),c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool))),X2),X1),X6))
| hBOOL(hAPP(X1,X6)) )
| ~ spl0_164
| ~ spl0_233 ),
inference(superposition,[],[f1843,f2646]) ).
fof(f65964,plain,
( spl0_835
| ~ spl0_126
| ~ spl0_233 ),
inference(avatar_split_clause,[],[f2942,f2645,f1615,f65962]) ).
fof(f65962,plain,
( spl0_835
<=> ! [X3,X4,X0,X5,X2,X1] :
( c_Finite__Set_Ofinite(hAPP(hAPP(hAPP(c_COMBS(X3,X4,X5),c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool))),X2),X1),X0)
| ~ c_Finite__Set_Ofinite(hAPP(X2,X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_835])]) ).
fof(f2942,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( c_Finite__Set_Ofinite(hAPP(hAPP(hAPP(c_COMBS(X3,X4,X5),c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool))),X2),X1),X0)
| ~ c_Finite__Set_Ofinite(hAPP(X2,X1),X0) )
| ~ spl0_126
| ~ spl0_233 ),
inference(superposition,[],[f1616,f2646]) ).
fof(f65960,plain,
( spl0_834
| ~ spl0_129
| ~ spl0_233 ),
inference(avatar_split_clause,[],[f2929,f2645,f1627,f65958]) ).
fof(f65958,plain,
( spl0_834
<=> ! [X5,X3,X4,X0,X6,X2,X1] :
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_COMBS(X3,X4,X5),c_Set_Oinsert(X0)),X2),X1),X6))
| ~ hBOOL(hAPP(hAPP(X2,X1),X6)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_834])]) ).
fof(f2929,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] :
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_COMBS(X3,X4,X5),c_Set_Oinsert(X0)),X2),X1),X6))
| ~ hBOOL(hAPP(hAPP(X2,X1),X6)) )
| ~ spl0_129
| ~ spl0_233 ),
inference(superposition,[],[f1628,f2646]) ).
fof(f65956,plain,
( spl0_833
| ~ spl0_165
| ~ spl0_233 ),
inference(avatar_split_clause,[],[f2917,f2645,f1846,f65954]) ).
fof(f65954,plain,
( spl0_833
<=> ! [X3,X4,X0,X5,X2,X1] :
( c_Orderings_Obot__class_Obot(X0) != hAPP(hAPP(hAPP(c_COMBS(X3,X4,X5),c_Lattices_Oupper__semilattice__class_Osup(X0)),X2),X1)
| c_Orderings_Obot__class_Obot(X0) = X1
| ~ class_Lattices_Obounded__lattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_833])]) ).
fof(f1846,plain,
( spl0_165
<=> ! [X5,X9,X0] :
( ~ class_Lattices_Obounded__lattice(X0)
| c_Orderings_Obot__class_Obot(X0) = X5
| c_Orderings_Obot__class_Obot(X0) != hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X5),X9) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_165])]) ).
fof(f2917,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( c_Orderings_Obot__class_Obot(X0) != hAPP(hAPP(hAPP(c_COMBS(X3,X4,X5),c_Lattices_Oupper__semilattice__class_Osup(X0)),X2),X1)
| c_Orderings_Obot__class_Obot(X0) = X1
| ~ class_Lattices_Obounded__lattice(X0) )
| ~ spl0_165
| ~ spl0_233 ),
inference(superposition,[],[f1847,f2646]) ).
fof(f1847,plain,
( ! [X0,X9,X5] :
( c_Orderings_Obot__class_Obot(X0) != hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X5),X9)
| c_Orderings_Obot__class_Obot(X0) = X5
| ~ class_Lattices_Obounded__lattice(X0) )
| ~ spl0_165 ),
inference(avatar_component_clause,[],[f1846]) ).
fof(f65952,plain,
( spl0_832
| ~ spl0_153
| ~ spl0_233 ),
inference(avatar_split_clause,[],[f2905,f2645,f1798,f65950]) ).
fof(f65950,plain,
( spl0_832
<=> ! [X5,X3,X4,X0,X6,X2,X1] :
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_COMBS(X3,X4,X5),c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool))),X2),X1),X6))
| ~ hBOOL(hAPP(X1,X6)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_832])]) ).
fof(f2905,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] :
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_COMBS(X3,X4,X5),c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool))),X2),X1),X6))
| ~ hBOOL(hAPP(X1,X6)) )
| ~ spl0_153
| ~ spl0_233 ),
inference(superposition,[],[f1799,f2646]) ).
fof(f65948,plain,
( spl0_831
| ~ spl0_567
| ~ spl0_763 ),
inference(avatar_split_clause,[],[f65108,f61292,f16050,f65946]) ).
fof(f65946,plain,
( spl0_831
<=> ! [X0,X1] : c_Finite__Set_Ofinite(c_SetInterval_Oord__class_OatLeastAtMost(X1,X1,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_831])]) ).
fof(f65108,plain,
( ! [X0,X1] : c_Finite__Set_Ofinite(c_SetInterval_Oord__class_OatLeastAtMost(X1,X1,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool))
| ~ spl0_567
| ~ spl0_763 ),
inference(superposition,[],[f16051,f61293]) ).
fof(f65944,plain,
( spl0_830
| ~ spl0_122
| ~ spl0_233 ),
inference(avatar_split_clause,[],[f2903,f2645,f1599,f65942]) ).
fof(f65942,plain,
( spl0_830
<=> ! [X3,X4,X0,X5,X2,X1] :
( ~ c_Finite__Set_Ofinite(hAPP(hAPP(hAPP(c_COMBS(X3,X4,X5),c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool))),X2),X1),X0)
| c_Finite__Set_Ofinite(hAPP(X2,X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_830])]) ).
fof(f2903,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ c_Finite__Set_Ofinite(hAPP(hAPP(hAPP(c_COMBS(X3,X4,X5),c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool))),X2),X1),X0)
| c_Finite__Set_Ofinite(hAPP(X2,X1),X0) )
| ~ spl0_122
| ~ spl0_233 ),
inference(superposition,[],[f1600,f2646]) ).
fof(f65940,plain,
( spl0_829
| ~ spl0_225
| ~ spl0_233 ),
inference(avatar_split_clause,[],[f2890,f2645,f2299,f65938]) ).
fof(f65938,plain,
( spl0_829
<=> ! [X2,X4,X0,X3,X1] :
( hBOOL(hAPP(hAPP(hAPP(c_COMBS(X2,X3,X4),c_lessequals(X0)),c_Complete__Lattice_OSup__class_OSup(X0)),X1))
| ~ hBOOL(c_in(X1,X1,X0))
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_829])]) ).
fof(f2890,plain,
( ! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(hAPP(hAPP(c_COMBS(X2,X3,X4),c_lessequals(X0)),c_Complete__Lattice_OSup__class_OSup(X0)),X1))
| ~ hBOOL(c_in(X1,X1,X0))
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) )
| ~ spl0_225
| ~ spl0_233 ),
inference(superposition,[],[f2300,f2646]) ).
fof(f65936,plain,
( spl0_828
| ~ spl0_210
| ~ spl0_225 ),
inference(avatar_split_clause,[],[f2622,f2299,f2233,f65934]) ).
fof(f65934,plain,
( spl0_828
<=> ! [X2,X0,X1] :
( ~ hBOOL(c_in(X0,X1,X2))
| ~ class_Complete__Lattice_Ocomplete__lattice(X2)
| ~ class_Lattices_Olower__semilattice(X2)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),X0),hAPP(c_Complete__Lattice_OSup__class_OSup(X2),X1)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_828])]) ).
fof(f2622,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(c_in(X0,X1,X2))
| ~ class_Complete__Lattice_Ocomplete__lattice(X2)
| ~ class_Lattices_Olower__semilattice(X2)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),X0),hAPP(c_Complete__Lattice_OSup__class_OSup(X2),X1)) = X0 )
| ~ spl0_210
| ~ spl0_225 ),
inference(resolution,[],[f2300,f2234]) ).
fof(f65932,plain,
( spl0_827
| ~ spl0_212
| ~ spl0_225 ),
inference(avatar_split_clause,[],[f2621,f2299,f2247,f65930]) ).
fof(f65930,plain,
( spl0_827
<=> ! [X2,X0,X1] :
( ~ hBOOL(c_in(X0,X1,X2))
| ~ class_Complete__Lattice_Ocomplete__lattice(X2)
| ~ class_Lattices_Olower__semilattice(X2)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),hAPP(c_Complete__Lattice_OSup__class_OSup(X2),X1)),X0) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_827])]) ).
fof(f2621,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(c_in(X0,X1,X2))
| ~ class_Complete__Lattice_Ocomplete__lattice(X2)
| ~ class_Lattices_Olower__semilattice(X2)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),hAPP(c_Complete__Lattice_OSup__class_OSup(X2),X1)),X0) = X0 )
| ~ spl0_212
| ~ spl0_225 ),
inference(resolution,[],[f2300,f2248]) ).
fof(f65928,plain,
( spl0_826
| ~ spl0_215
| ~ spl0_218 ),
inference(avatar_split_clause,[],[f2552,f2271,f2259,f65926]) ).
fof(f65926,plain,
( spl0_826
<=> ! [X2,X0,X1] :
( ~ hBOOL(c_in(X0,X1,X2))
| ~ class_Complete__Lattice_Ocomplete__lattice(X2)
| ~ class_Lattices_Oupper__semilattice(X2)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2),X0),hAPP(c_Complete__Lattice_OInf__class_OInf(X2),X1)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_826])]) ).
fof(f2552,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(c_in(X0,X1,X2))
| ~ class_Complete__Lattice_Ocomplete__lattice(X2)
| ~ class_Lattices_Oupper__semilattice(X2)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2),X0),hAPP(c_Complete__Lattice_OInf__class_OInf(X2),X1)) = X0 )
| ~ spl0_215
| ~ spl0_218 ),
inference(resolution,[],[f2272,f2260]) ).
fof(f65924,plain,
( spl0_825
| ~ spl0_217
| ~ spl0_218 ),
inference(avatar_split_clause,[],[f2551,f2271,f2267,f65922]) ).
fof(f65922,plain,
( spl0_825
<=> ! [X2,X0,X1] :
( ~ hBOOL(c_in(X0,X1,X2))
| ~ class_Complete__Lattice_Ocomplete__lattice(X2)
| ~ class_Lattices_Oupper__semilattice(X2)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2),hAPP(c_Complete__Lattice_OInf__class_OInf(X2),X1)),X0) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_825])]) ).
fof(f2551,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(c_in(X0,X1,X2))
| ~ class_Complete__Lattice_Ocomplete__lattice(X2)
| ~ class_Lattices_Oupper__semilattice(X2)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2),hAPP(c_Complete__Lattice_OInf__class_OInf(X2),X1)),X0) = X0 )
| ~ spl0_217
| ~ spl0_218 ),
inference(resolution,[],[f2272,f2268]) ).
fof(f65920,plain,
( spl0_824
| ~ spl0_139
| ~ spl0_217 ),
inference(avatar_split_clause,[],[f2545,f2267,f1688,f65918]) ).
fof(f65918,plain,
( spl0_824
<=> ! [X2,X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X2),X1) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X2),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_824])]) ).
fof(f2545,plain,
( ! [X2,X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X2),X1) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X2),X1)) )
| ~ spl0_139
| ~ spl0_217 ),
inference(duplicate_literal_removal,[],[f2539]) ).
fof(f2539,plain,
( ! [X2,X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X2),X1) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X2),X1))
| ~ class_Lattices_Oupper__semilattice(X0) )
| ~ spl0_139
| ~ spl0_217 ),
inference(resolution,[],[f2268,f1689]) ).
fof(f65916,plain,
( spl0_823
| ~ spl0_138
| ~ spl0_215 ),
inference(avatar_split_clause,[],[f2507,f2259,f1684,f65914]) ).
fof(f65914,plain,
( spl0_823
<=> ! [X2,X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_823])]) ).
fof(f2507,plain,
( ! [X2,X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2)),X1) )
| ~ spl0_138
| ~ spl0_215 ),
inference(duplicate_literal_removal,[],[f2498]) ).
fof(f2498,plain,
( ! [X2,X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2)),X1)
| ~ class_Lattices_Oupper__semilattice(X0) )
| ~ spl0_138
| ~ spl0_215 ),
inference(resolution,[],[f2260,f1685]) ).
fof(f65912,plain,
( spl0_822
| ~ spl0_139
| ~ spl0_215 ),
inference(avatar_split_clause,[],[f2506,f2259,f1688,f65910]) ).
fof(f65910,plain,
( spl0_822
<=> ! [X2,X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_822])]) ).
fof(f2506,plain,
( ! [X2,X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2)),X2) )
| ~ spl0_139
| ~ spl0_215 ),
inference(duplicate_literal_removal,[],[f2500]) ).
fof(f2500,plain,
( ! [X2,X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2)),X2)
| ~ class_Lattices_Oupper__semilattice(X0) )
| ~ spl0_139
| ~ spl0_215 ),
inference(resolution,[],[f2260,f1689]) ).
fof(f65908,plain,
( spl0_821
| ~ spl0_144
| ~ spl0_212 ),
inference(avatar_split_clause,[],[f2390,f2247,f1708,f65906]) ).
fof(f65906,plain,
( spl0_821
<=> ! [X2,X0,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X1) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_821])]) ).
fof(f2390,plain,
( ! [X2,X0,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X1) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X1)) )
| ~ spl0_144
| ~ spl0_212 ),
inference(duplicate_literal_removal,[],[f2378]) ).
fof(f2378,plain,
( ! [X2,X0,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X1) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X1))
| ~ class_Lattices_Olower__semilattice(X0) )
| ~ spl0_144
| ~ spl0_212 ),
inference(resolution,[],[f2248,f1709]) ).
fof(f65901,plain,
( spl0_820
| ~ spl0_145
| ~ spl0_210 ),
inference(avatar_split_clause,[],[f2350,f2233,f1712,f65899]) ).
fof(f65899,plain,
( spl0_820
<=> ! [X2,X0,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_820])]) ).
fof(f2350,plain,
( ! [X2,X0,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2)),X1) )
| ~ spl0_145
| ~ spl0_210 ),
inference(duplicate_literal_removal,[],[f2331]) ).
fof(f2331,plain,
( ! [X2,X0,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2)),X1)
| ~ class_Lattices_Olower__semilattice(X0) )
| ~ spl0_145
| ~ spl0_210 ),
inference(resolution,[],[f2234,f1713]) ).
fof(f65897,plain,
( spl0_819
| ~ spl0_144
| ~ spl0_210 ),
inference(avatar_split_clause,[],[f2349,f2233,f1708,f65895]) ).
fof(f65895,plain,
( spl0_819
<=> ! [X2,X0,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_819])]) ).
fof(f2349,plain,
( ! [X2,X0,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2)),X2) )
| ~ spl0_144
| ~ spl0_210 ),
inference(duplicate_literal_removal,[],[f2337]) ).
fof(f2337,plain,
( ! [X2,X0,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2)),X2)
| ~ class_Lattices_Olower__semilattice(X0) )
| ~ spl0_144
| ~ spl0_210 ),
inference(resolution,[],[f2234,f1709]) ).
fof(f65893,plain,
( spl0_818
| ~ spl0_183
| ~ spl0_190 ),
inference(avatar_split_clause,[],[f2163,f2025,f1997,f65891]) ).
fof(f65891,plain,
( spl0_818
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X2),X1)))
| ~ class_Orderings_Opreorder(tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_818])]) ).
fof(f2163,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X2),X1)))
| ~ class_Orderings_Opreorder(tc_fun(X0,tc_bool)) )
| ~ spl0_183
| ~ spl0_190 ),
inference(resolution,[],[f2026,f1998]) ).
fof(f65889,plain,
( spl0_817
| ~ spl0_183
| ~ spl0_189 ),
inference(avatar_split_clause,[],[f2158,f2021,f1997,f65887]) ).
fof(f65887,plain,
( spl0_817
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X1),X2)))
| ~ class_Orderings_Opreorder(tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_817])]) ).
fof(f2158,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X1),X2)))
| ~ class_Orderings_Opreorder(tc_fun(X0,tc_bool)) )
| ~ spl0_183
| ~ spl0_189 ),
inference(resolution,[],[f2022,f1998]) ).
fof(f65885,plain,
( spl0_816
| ~ spl0_183
| ~ spl0_186 ),
inference(avatar_split_clause,[],[f2149,f2009,f1997,f65883]) ).
fof(f65883,plain,
( spl0_816
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),X1),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X1),X2)))
| ~ class_Orderings_Opreorder(tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_816])]) ).
fof(f2149,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),X1),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X1),X2)))
| ~ class_Orderings_Opreorder(tc_fun(X0,tc_bool)) )
| ~ spl0_183
| ~ spl0_186 ),
inference(resolution,[],[f2010,f1998]) ).
fof(f65881,plain,
( spl0_815
| ~ spl0_183
| ~ spl0_185 ),
inference(avatar_split_clause,[],[f2142,f2005,f1997,f65879]) ).
fof(f65879,plain,
( spl0_815
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X2)),X1))
| ~ class_Orderings_Opreorder(tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_815])]) ).
fof(f2142,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X2)),X1))
| ~ class_Orderings_Opreorder(tc_fun(X0,tc_bool)) )
| ~ spl0_183
| ~ spl0_185 ),
inference(resolution,[],[f2006,f1998]) ).
fof(f65877,plain,
( spl0_814
| ~ spl0_183
| ~ spl0_184 ),
inference(avatar_split_clause,[],[f2135,f2001,f1997,f65875]) ).
fof(f65875,plain,
( spl0_814
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X2)),X2))
| ~ class_Orderings_Opreorder(tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_814])]) ).
fof(f2135,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X2)),X2))
| ~ class_Orderings_Opreorder(tc_fun(X0,tc_bool)) )
| ~ spl0_183
| ~ spl0_184 ),
inference(resolution,[],[f2002,f1998]) ).
fof(f65762,plain,
( spl0_813
| ~ spl0_42
| ~ spl0_763 ),
inference(avatar_split_clause,[],[f65085,f61292,f1198,f65760]) ).
fof(f65085,plain,
( ! [X0,X1] : hBOOL(hAPP(c_SetInterval_Oord__class_OatLeastAtMost(X1,X1,tc_fun(X0,tc_bool)),X1))
| ~ spl0_42
| ~ spl0_763 ),
inference(superposition,[],[f1199,f61293]) ).
fof(f63566,plain,
( spl0_812
| ~ spl0_118
| ~ spl0_777 ),
inference(avatar_split_clause,[],[f63405,f62628,f1576,f63564]) ).
fof(f63564,plain,
( spl0_812
<=> ! [X0] : c_False = hAPP(c_Complete__Lattice_OInf__class_OInf(tc_bool),hAPP(hAPP(c_Set_Oinsert(tc_bool),c_False),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_812])]) ).
fof(f62628,plain,
( spl0_777
<=> ! [X0,X1] : hAPP(c_Complete__Lattice_OInf__class_OInf(tc_bool),hAPP(hAPP(c_Set_Oinsert(tc_bool),X0),X1)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),X0),hAPP(c_Complete__Lattice_OInf__class_OInf(tc_bool),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_777])]) ).
fof(f63405,plain,
( ! [X0] : c_False = hAPP(c_Complete__Lattice_OInf__class_OInf(tc_bool),hAPP(hAPP(c_Set_Oinsert(tc_bool),c_False),X0))
| ~ spl0_118
| ~ spl0_777 ),
inference(superposition,[],[f62629,f1577]) ).
fof(f62629,plain,
( ! [X0,X1] : hAPP(c_Complete__Lattice_OInf__class_OInf(tc_bool),hAPP(hAPP(c_Set_Oinsert(tc_bool),X0),X1)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),X0),hAPP(c_Complete__Lattice_OInf__class_OInf(tc_bool),X1))
| ~ spl0_777 ),
inference(avatar_component_clause,[],[f62628]) ).
fof(f62965,plain,
( spl0_811
| ~ spl0_213
| ~ spl0_733 ),
inference(avatar_split_clause,[],[f27516,f27510,f2251,f62963]) ).
fof(f62963,plain,
( spl0_811
<=> ! [X0,X3,X2,X1] : c_List_Ofilter(X2,c_List_Ofilter(X1,X3,X0),X0) = c_List_Ofilter(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X2),X1),X3,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_811])]) ).
fof(f27516,plain,
( ! [X2,X3,X0,X1] : c_List_Ofilter(X2,c_List_Ofilter(X1,X3,X0),X0) = c_List_Ofilter(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X2),X1),X3,X0)
| ~ spl0_213
| ~ spl0_733 ),
inference(superposition,[],[f27511,f2252]) ).
fof(f62931,plain,
( spl0_810
| ~ spl0_133
| ~ spl0_275
| ~ spl0_460
| ~ spl0_478 ),
inference(avatar_split_clause,[],[f12650,f12595,f10774,f3652,f1643,f62929]) ).
fof(f62929,plain,
( spl0_810
<=> ! [X0,X1,X3] :
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X1),X3) != X3
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X3),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_810])]) ).
fof(f10774,plain,
( spl0_460
<=> ! [X5,X0,X12,X9] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X5),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X9),X12)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X5),X9)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X5),X12)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_460])]) ).
fof(f12595,plain,
( spl0_478
<=> ! [X5,X0,X12,X9] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X12),X5))
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X5),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X9),X12)) != hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X5),X9)),X12) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_478])]) ).
fof(f12650,plain,
( ! [X3,X0,X1] :
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X1),X3) != X3
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X3),X1)) )
| ~ spl0_133
| ~ spl0_275
| ~ spl0_460
| ~ spl0_478 ),
inference(forward_demodulation,[],[f12649,f11143]) ).
fof(f11143,plain,
( ! [X2,X3,X0,X1] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X1),X3) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X2),X1)),X3))
| ~ spl0_133
| ~ spl0_275
| ~ spl0_460 ),
inference(forward_demodulation,[],[f11035,f1644]) ).
fof(f11035,plain,
( ! [X2,X3,X0,X1] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X2),X1)),X3)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X1),X3))
| ~ spl0_275
| ~ spl0_460 ),
inference(superposition,[],[f10775,f3653]) ).
fof(f10775,plain,
( ! [X0,X9,X5,X12] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X5),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X9),X12)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X5),X9)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X5),X12))
| ~ spl0_460 ),
inference(avatar_component_clause,[],[f10774]) ).
fof(f12649,plain,
( ! [X2,X3,X0,X1] :
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X2),X1)),X3)) != X3
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X3),X1)) )
| ~ spl0_133
| ~ spl0_275
| ~ spl0_478 ),
inference(forward_demodulation,[],[f12617,f1644]) ).
fof(f12617,plain,
( ! [X2,X3,X0,X1] :
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X2),X1)),X3)) != hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0)),X3)
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X3),X1)) )
| ~ spl0_275
| ~ spl0_478 ),
inference(superposition,[],[f12596,f3653]) ).
fof(f12596,plain,
( ! [X0,X9,X5,X12] :
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X5),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X9),X12)) != hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X5),X9)),X12)
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X12),X5)) )
| ~ spl0_478 ),
inference(avatar_component_clause,[],[f12595]) ).
fof(f62927,plain,
( spl0_809
| ~ spl0_127
| ~ spl0_412 ),
inference(avatar_split_clause,[],[f8287,f7695,f1619,f62925]) ).
fof(f62925,plain,
( spl0_809
<=> ! [X2,X4,X0,X3,X1] :
( c_Finite__Set_Ofinite(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(hAPP(hAPP(c_Set_Oinsert(X4),X2),X3),X1,X4,tc_fun(X0,tc_bool)),X0)
| ~ c_Finite__Set_Ofinite(hAPP(X1,X2),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_809])]) ).
fof(f8287,plain,
( ! [X2,X3,X0,X1,X4] :
( c_Finite__Set_Ofinite(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(hAPP(hAPP(c_Set_Oinsert(X4),X2),X3),X1,X4,tc_fun(X0,tc_bool)),X0)
| ~ c_Finite__Set_Ofinite(hAPP(X1,X2),X0) )
| ~ spl0_127
| ~ spl0_412 ),
inference(superposition,[],[f1620,f7696]) ).
fof(f62923,plain,
( spl0_808
| ~ spl0_121
| ~ spl0_410 ),
inference(avatar_split_clause,[],[f8119,f7687,f1595,f62921]) ).
fof(f62921,plain,
( spl0_808
<=> ! [X2,X4,X0,X3,X1] :
( ~ c_Finite__Set_Ofinite(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_Set_Oinsert(X4),X2),X3),X1,X4,tc_fun(X0,tc_bool)),X0)
| c_Finite__Set_Ofinite(hAPP(X1,X2),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_808])]) ).
fof(f8119,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ c_Finite__Set_Ofinite(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_Set_Oinsert(X4),X2),X3),X1,X4,tc_fun(X0,tc_bool)),X0)
| c_Finite__Set_Ofinite(hAPP(X1,X2),X0) )
| ~ spl0_121
| ~ spl0_410 ),
inference(superposition,[],[f1596,f7688]) ).
fof(f62885,plain,
( spl0_807
| ~ spl0_42
| ~ spl0_414 ),
inference(avatar_split_clause,[],[f7711,f7704,f1198,f62883]) ).
fof(f62883,plain,
( spl0_807
<=> ! [X2,X0,X1] : hAPP(c_fequal(X0),X1) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),hAPP(c_fequal(X0),X1)),hAPP(c_fequal(X2),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_807])]) ).
fof(f7711,plain,
( ! [X2,X0,X1] : hAPP(c_fequal(X0),X1) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),hAPP(c_fequal(X0),X1)),hAPP(c_fequal(X2),X1))
| ~ spl0_42
| ~ spl0_414 ),
inference(resolution,[],[f7705,f1199]) ).
fof(f62881,plain,
( spl0_806
| ~ spl0_38
| ~ spl0_414 ),
inference(avatar_split_clause,[],[f7710,f7704,f1179,f62879]) ).
fof(f62879,plain,
( spl0_806
<=> ! [X2,X0,X1] : hAPP(c_fequal(X0),X1) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),hAPP(c_fequal(X0),X1)),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_806])]) ).
fof(f7710,plain,
( ! [X2,X0,X1] : hAPP(c_fequal(X0),X1) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),hAPP(c_fequal(X0),X1)),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)))
| ~ spl0_38
| ~ spl0_414 ),
inference(resolution,[],[f7705,f1180]) ).
fof(f62877,plain,
( spl0_805
| ~ spl0_266
| ~ spl0_352 ),
inference(avatar_split_clause,[],[f5909,f5600,f3133,f62875]) ).
fof(f62875,plain,
( spl0_805
<=> ! [X2,X0,X1] :
( c_COMBK(c_False,tc_bool,X0) != X1
| c_COMBK(c_False,tc_bool,X0) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_805])]) ).
fof(f5909,plain,
( ! [X2,X0,X1] :
( c_COMBK(c_False,tc_bool,X0) != X1
| c_COMBK(c_False,tc_bool,X0) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X1),X2) )
| ~ spl0_266
| ~ spl0_352 ),
inference(superposition,[],[f3134,f5601]) ).
fof(f62873,plain,
( spl0_804
| ~ spl0_265
| ~ spl0_352 ),
inference(avatar_split_clause,[],[f5908,f5600,f3129,f62871]) ).
fof(f62871,plain,
( spl0_804
<=> ! [X2,X0,X1] :
( c_COMBK(c_False,tc_bool,X0) != X1
| c_COMBK(c_False,tc_bool,X0) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_804])]) ).
fof(f5908,plain,
( ! [X2,X0,X1] :
( c_COMBK(c_False,tc_bool,X0) != X1
| c_COMBK(c_False,tc_bool,X0) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X1),X2) )
| ~ spl0_265
| ~ spl0_352 ),
inference(superposition,[],[f3130,f5601]) ).
fof(f62869,plain,
( spl0_803
| ~ spl0_125
| ~ spl0_345 ),
inference(avatar_split_clause,[],[f5551,f4970,f1611,f62867]) ).
fof(f62867,plain,
( spl0_803
<=> ! [X0,X1] :
( c_COMBK(c_False,tc_bool,X0) != X1
| hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X1),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool))) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_803])]) ).
fof(f5551,plain,
( ! [X0,X1] :
( c_COMBK(c_False,tc_bool,X0) != X1
| hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X1),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool))) = X1 )
| ~ spl0_125
| ~ spl0_345 ),
inference(superposition,[],[f4971,f1612]) ).
fof(f62865,plain,
( spl0_802
| ~ spl0_150
| ~ spl0_340 ),
inference(avatar_split_clause,[],[f5449,f4949,f1732,f62863]) ).
fof(f62863,plain,
( spl0_802
<=> ! [X2,X0,X1] : hAPP(hAPP(c_Set_Oinsert(X0),X1),hAPP(c_fequal(X0),X2)) = hAPP(hAPP(c_Set_Oinsert(X0),X2),hAPP(c_fequal(X0),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_802])]) ).
fof(f5449,plain,
( ! [X2,X0,X1] : hAPP(hAPP(c_Set_Oinsert(X0),X1),hAPP(c_fequal(X0),X2)) = hAPP(hAPP(c_Set_Oinsert(X0),X2),hAPP(c_fequal(X0),X1))
| ~ spl0_150
| ~ spl0_340 ),
inference(forward_demodulation,[],[f5383,f1733]) ).
fof(f5383,plain,
( ! [X2,X0,X1] : hAPP(hAPP(c_Set_Oinsert(X0),X1),hAPP(hAPP(c_Set_Oinsert(X0),X2),c_COMBK(c_False,tc_bool,X0))) = hAPP(hAPP(c_Set_Oinsert(X0),X2),hAPP(c_fequal(X0),X1))
| ~ spl0_150
| ~ spl0_340 ),
inference(superposition,[],[f4950,f1733]) ).
fof(f62861,plain,
( spl0_801
| ~ spl0_74
| ~ spl0_339 ),
inference(avatar_split_clause,[],[f5375,f4945,f1340,f62859]) ).
fof(f62859,plain,
( spl0_801
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ class_Orderings_Opreorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),c_Orderings_Otop__class_Otop(X0)))
| ~ class_Orderings_Otop(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_801])]) ).
fof(f5375,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ class_Orderings_Opreorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),c_Orderings_Otop__class_Otop(X0)))
| ~ class_Orderings_Otop(X0) )
| ~ spl0_74
| ~ spl0_339 ),
inference(resolution,[],[f4946,f1341]) ).
fof(f62857,plain,
( spl0_800
| ~ spl0_75
| ~ spl0_338 ),
inference(avatar_split_clause,[],[f5316,f4941,f1344,f62855]) ).
fof(f62855,plain,
( spl0_800
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ class_Orderings_Opreorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_Orderings_Obot__class_Obot(X0)),X2))
| ~ class_Orderings_Obot(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_800])]) ).
fof(f5316,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ class_Orderings_Opreorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_Orderings_Obot__class_Obot(X0)),X2))
| ~ class_Orderings_Obot(X0) )
| ~ spl0_75
| ~ spl0_338 ),
inference(resolution,[],[f4942,f1345]) ).
fof(f62853,plain,
( spl0_799
| ~ spl0_75
| ~ spl0_337 ),
inference(avatar_split_clause,[],[f5271,f4937,f1344,f62851]) ).
fof(f62851,plain,
( spl0_799
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X1),c_Orderings_Obot__class_Obot(X0)))
| ~ class_Orderings_Opreorder(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2))
| ~ class_Orderings_Obot(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_799])]) ).
fof(f5271,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X1),c_Orderings_Obot__class_Obot(X0)))
| ~ class_Orderings_Opreorder(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2))
| ~ class_Orderings_Obot(X0) )
| ~ spl0_75
| ~ spl0_337 ),
inference(resolution,[],[f4938,f1345]) ).
fof(f62849,plain,
( spl0_798
| ~ spl0_74
| ~ spl0_336 ),
inference(avatar_split_clause,[],[f5259,f4933,f1340,f62847]) ).
fof(f62847,plain,
( spl0_798
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),c_Orderings_Otop__class_Otop(X0)))
| ~ class_Orderings_Otop(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_798])]) ).
fof(f5259,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),c_Orderings_Otop__class_Otop(X0)))
| ~ class_Orderings_Otop(X0) )
| ~ spl0_74
| ~ spl0_336 ),
inference(resolution,[],[f4934,f1341]) ).
fof(f62815,plain,
( spl0_797
| ~ spl0_75
| ~ spl0_336 ),
inference(avatar_split_clause,[],[f5235,f4933,f1344,f62813]) ).
fof(f62813,plain,
( spl0_797
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),c_Orderings_Obot__class_Obot(X0)))
| ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ class_Orderings_Obot(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_797])]) ).
fof(f5235,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),c_Orderings_Obot__class_Obot(X0)))
| ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ class_Orderings_Obot(X0) )
| ~ spl0_75
| ~ spl0_336 ),
inference(resolution,[],[f4934,f1345]) ).
fof(f62811,plain,
( spl0_796
| ~ spl0_74
| ~ spl0_335 ),
inference(avatar_split_clause,[],[f5223,f4929,f1340,f62809]) ).
fof(f62809,plain,
( spl0_796
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_Orderings_Otop__class_Otop(X0)),X1))
| ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X2),X1))
| ~ class_Orderings_Otop(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_796])]) ).
fof(f5223,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_Orderings_Otop__class_Otop(X0)),X1))
| ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X2),X1))
| ~ class_Orderings_Otop(X0) )
| ~ spl0_74
| ~ spl0_335 ),
inference(resolution,[],[f4930,f1341]) ).
fof(f62807,plain,
( spl0_795
| ~ spl0_75
| ~ spl0_335 ),
inference(avatar_split_clause,[],[f5199,f4929,f1344,f62805]) ).
fof(f62805,plain,
( spl0_795
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_Orderings_Obot__class_Obot(X0)),X2))
| ~ class_Orderings_Obot(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_795])]) ).
fof(f5199,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_Orderings_Obot__class_Obot(X0)),X2))
| ~ class_Orderings_Obot(X0) )
| ~ spl0_75
| ~ spl0_335 ),
inference(resolution,[],[f4930,f1345]) ).
fof(f62803,plain,
( spl0_794
| ~ spl0_74
| ~ spl0_334 ),
inference(avatar_split_clause,[],[f5187,f4925,f1340,f62801]) ).
fof(f62801,plain,
( spl0_794
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(X0),c_Orderings_Otop__class_Otop(X0)),X1))
| ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),X2),X1))
| ~ class_Orderings_Otop(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_794])]) ).
fof(f5187,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(X0),c_Orderings_Otop__class_Otop(X0)),X1))
| ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),X2),X1))
| ~ class_Orderings_Otop(X0) )
| ~ spl0_74
| ~ spl0_334 ),
inference(resolution,[],[f4926,f1341]) ).
fof(f62799,plain,
( spl0_793
| ~ spl0_146
| ~ spl0_332 ),
inference(avatar_split_clause,[],[f5140,f4916,f1716,f62797]) ).
fof(f62797,plain,
( spl0_793
<=> ! [X0,X3,X2,X1] : hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X1),hAPP(hAPP(c_Set_Oinsert(X0),X2),hAPP(hAPP(c_Set_Oinsert(X0),X3),X1)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_793])]) ).
fof(f5140,plain,
( ! [X2,X3,X0,X1] : hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X1),hAPP(hAPP(c_Set_Oinsert(X0),X2),hAPP(hAPP(c_Set_Oinsert(X0),X3),X1))))
| ~ spl0_146
| ~ spl0_332 ),
inference(resolution,[],[f4917,f1717]) ).
fof(f62795,plain,
( spl0_792
| ~ spl0_169
| ~ spl0_303 ),
inference(avatar_split_clause,[],[f4624,f4556,f1865,f62793]) ).
fof(f62793,plain,
( spl0_792
<=> ! [X4,X0,X3,X2,X1] :
( ~ hBOOL(c_in(X0,X1,X2))
| c_Finite__Set_Ofinite(hAPP(X3,X0),X4)
| ~ c_Finite__Set_Ofinite(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,X3,X2,tc_fun(X4,tc_bool)),X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_792])]) ).
fof(f4624,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ hBOOL(c_in(X0,X1,X2))
| c_Finite__Set_Ofinite(hAPP(X3,X0),X4)
| ~ c_Finite__Set_Ofinite(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,X3,X2,tc_fun(X4,tc_bool)),X4) )
| ~ spl0_169
| ~ spl0_303 ),
inference(resolution,[],[f4557,f1866]) ).
fof(f62791,plain,
( spl0_791
| ~ spl0_252
| ~ spl0_303 ),
inference(avatar_split_clause,[],[f4621,f4556,f3077,f62789]) ).
fof(f62789,plain,
( spl0_791
<=> ! [X4,X0,X3,X2,X1] :
( ~ hBOOL(c_in(X0,X1,X2))
| hBOOL(c_in(X3,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,hAPP(c_Set_Oinsert(X4),X3),X2,tc_fun(X4,tc_bool)),X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_791])]) ).
fof(f4621,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ hBOOL(c_in(X0,X1,X2))
| hBOOL(c_in(X3,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,hAPP(c_Set_Oinsert(X4),X3),X2,tc_fun(X4,tc_bool)),X4)) )
| ~ spl0_252
| ~ spl0_303 ),
inference(resolution,[],[f4557,f3078]) ).
fof(f62787,plain,
( spl0_790
| ~ spl0_1
| ~ spl0_300 ),
inference(avatar_split_clause,[],[f4539,f3955,f1017,f62785]) ).
fof(f62785,plain,
( spl0_790
<=> ! [X0,X1] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),X0),X1) = hAPP(c_Complete__Lattice_OInf__class_OInf(tc_bool),hAPP(hAPP(c_Set_Oinsert(tc_bool),X0),hAPP(c_fequal(tc_bool),X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_790])]) ).
fof(f3955,plain,
( spl0_300
<=> ! [X4,X0,X3] :
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),X4) = hAPP(c_Complete__Lattice_OInf__class_OInf(X0),hAPP(hAPP(c_Set_Oinsert(X0),X3),hAPP(c_fequal(X0),X4)))
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_300])]) ).
fof(f4539,plain,
( ! [X0,X1] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),X0),X1) = hAPP(c_Complete__Lattice_OInf__class_OInf(tc_bool),hAPP(hAPP(c_Set_Oinsert(tc_bool),X0),hAPP(c_fequal(tc_bool),X1)))
| ~ spl0_1
| ~ spl0_300 ),
inference(resolution,[],[f3956,f1019]) ).
fof(f1019,plain,
( class_Complete__Lattice_Ocomplete__lattice(tc_bool)
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f1017]) ).
fof(f3956,plain,
( ! [X3,X0,X4] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),X4) = hAPP(c_Complete__Lattice_OInf__class_OInf(X0),hAPP(hAPP(c_Set_Oinsert(X0),X3),hAPP(c_fequal(X0),X4))) )
| ~ spl0_300 ),
inference(avatar_component_clause,[],[f3955]) ).
fof(f62783,plain,
( spl0_789
| ~ spl0_1
| ~ spl0_299 ),
inference(avatar_split_clause,[],[f4537,f3951,f1017,f62781]) ).
fof(f62781,plain,
( spl0_789
<=> ! [X0,X1] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),X0),X1) = hAPP(c_Complete__Lattice_OSup__class_OSup(tc_bool),hAPP(hAPP(c_Set_Oinsert(tc_bool),X0),hAPP(c_fequal(tc_bool),X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_789])]) ).
fof(f3951,plain,
( spl0_299
<=> ! [X4,X0,X3] :
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X3),X4) = hAPP(c_Complete__Lattice_OSup__class_OSup(X0),hAPP(hAPP(c_Set_Oinsert(X0),X3),hAPP(c_fequal(X0),X4)))
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_299])]) ).
fof(f4537,plain,
( ! [X0,X1] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),X0),X1) = hAPP(c_Complete__Lattice_OSup__class_OSup(tc_bool),hAPP(hAPP(c_Set_Oinsert(tc_bool),X0),hAPP(c_fequal(tc_bool),X1)))
| ~ spl0_1
| ~ spl0_299 ),
inference(resolution,[],[f3952,f1019]) ).
fof(f3952,plain,
( ! [X3,X0,X4] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X3),X4) = hAPP(c_Complete__Lattice_OSup__class_OSup(X0),hAPP(hAPP(c_Set_Oinsert(X0),X3),hAPP(c_fequal(X0),X4))) )
| ~ spl0_299 ),
inference(avatar_component_clause,[],[f3951]) ).
fof(f62779,plain,
( spl0_788
| ~ spl0_138
| ~ spl0_297 ),
inference(avatar_split_clause,[],[f4532,f3943,f1684,f62777]) ).
fof(f62777,plain,
( spl0_788
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2)),X3)))
| ~ class_Lattices_Oupper__semilattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_788])]) ).
fof(f4532,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2)),X3)))
| ~ class_Lattices_Oupper__semilattice(X0) )
| ~ spl0_138
| ~ spl0_297 ),
inference(duplicate_literal_removal,[],[f4502]) ).
fof(f4502,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2)),X3)))
| ~ class_Lattices_Oupper__semilattice(X0)
| ~ class_Lattices_Oupper__semilattice(X0) )
| ~ spl0_138
| ~ spl0_297 ),
inference(resolution,[],[f3944,f1685]) ).
fof(f62746,plain,
( spl0_787
| ~ spl0_139
| ~ spl0_297 ),
inference(avatar_split_clause,[],[f4531,f3943,f1688,f62744]) ).
fof(f62744,plain,
( spl0_787
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X3))))
| ~ class_Lattices_Oupper__semilattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_787])]) ).
fof(f4531,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X3))))
| ~ class_Lattices_Oupper__semilattice(X0) )
| ~ spl0_139
| ~ spl0_297 ),
inference(duplicate_literal_removal,[],[f4504]) ).
fof(f4504,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X3))))
| ~ class_Lattices_Oupper__semilattice(X0)
| ~ class_Lattices_Oupper__semilattice(X0) )
| ~ spl0_139
| ~ spl0_297 ),
inference(resolution,[],[f3944,f1689]) ).
fof(f62742,plain,
( spl0_786
| ~ spl0_138
| ~ spl0_296 ),
inference(avatar_split_clause,[],[f4495,f3939,f1684,f62740]) ).
fof(f62740,plain,
( spl0_786
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X2),X1)),X3)))
| ~ class_Lattices_Oupper__semilattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_786])]) ).
fof(f4495,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X2),X1)),X3)))
| ~ class_Lattices_Oupper__semilattice(X0) )
| ~ spl0_138
| ~ spl0_296 ),
inference(duplicate_literal_removal,[],[f4465]) ).
fof(f4465,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X2),X1)),X3)))
| ~ class_Lattices_Oupper__semilattice(X0)
| ~ class_Lattices_Oupper__semilattice(X0) )
| ~ spl0_138
| ~ spl0_296 ),
inference(resolution,[],[f3940,f1685]) ).
fof(f62738,plain,
( spl0_785
| ~ spl0_139
| ~ spl0_296 ),
inference(avatar_split_clause,[],[f4494,f3939,f1688,f62736]) ).
fof(f62736,plain,
( spl0_785
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X3),X1))))
| ~ class_Lattices_Oupper__semilattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_785])]) ).
fof(f4494,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X3),X1))))
| ~ class_Lattices_Oupper__semilattice(X0) )
| ~ spl0_139
| ~ spl0_296 ),
inference(duplicate_literal_removal,[],[f4467]) ).
fof(f4467,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X3),X1))))
| ~ class_Lattices_Oupper__semilattice(X0)
| ~ class_Lattices_Oupper__semilattice(X0) )
| ~ spl0_139
| ~ spl0_296 ),
inference(resolution,[],[f3940,f1689]) ).
fof(f62734,plain,
( spl0_784
| ~ spl0_74
| ~ spl0_288 ),
inference(avatar_split_clause,[],[f4161,f3899,f1340,f62732]) ).
fof(f62732,plain,
( spl0_784
<=> ! [X4,X0,X3,X2,X1] :
( ~ hBOOL(c_in(X0,X1,X2))
| hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,c_lessequals(X3),X2,tc_fun(X4,tc_bool)),c_Orderings_Otop__class_Otop(X3)))
| ~ class_Orderings_Otop(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_784])]) ).
fof(f4161,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ hBOOL(c_in(X0,X1,X2))
| hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,c_lessequals(X3),X2,tc_fun(X4,tc_bool)),c_Orderings_Otop__class_Otop(X3)))
| ~ class_Orderings_Otop(X3) )
| ~ spl0_74
| ~ spl0_288 ),
inference(resolution,[],[f3900,f1341]) ).
fof(f62730,plain,
( spl0_783
| ~ spl0_75
| ~ spl0_288 ),
inference(avatar_split_clause,[],[f4138,f3899,f1344,f62728]) ).
fof(f62728,plain,
( spl0_783
<=> ! [X4,X0,X3,X2,X1] :
( ~ hBOOL(c_in(c_Orderings_Obot__class_Obot(X0),X1,X2))
| hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,c_lessequals(X0),X2,tc_fun(X3,tc_bool)),X4))
| ~ class_Orderings_Obot(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_783])]) ).
fof(f4138,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ hBOOL(c_in(c_Orderings_Obot__class_Obot(X0),X1,X2))
| hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,c_lessequals(X0),X2,tc_fun(X3,tc_bool)),X4))
| ~ class_Orderings_Obot(X0) )
| ~ spl0_75
| ~ spl0_288 ),
inference(resolution,[],[f3900,f1345]) ).
fof(f62726,plain,
( spl0_782
| ~ spl0_145
| ~ spl0_285 ),
inference(avatar_split_clause,[],[f4051,f3887,f1712,f62724]) ).
fof(f62724,plain,
( spl0_782
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2)),X3)),X2))
| ~ class_Lattices_Olower__semilattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_782])]) ).
fof(f4051,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2)),X3)),X2))
| ~ class_Lattices_Olower__semilattice(X0) )
| ~ spl0_145
| ~ spl0_285 ),
inference(duplicate_literal_removal,[],[f4024]) ).
fof(f4024,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2)),X3)),X2))
| ~ class_Lattices_Olower__semilattice(X0)
| ~ class_Lattices_Olower__semilattice(X0) )
| ~ spl0_145
| ~ spl0_285 ),
inference(resolution,[],[f3888,f1713]) ).
fof(f62722,plain,
( spl0_781
| ~ spl0_144
| ~ spl0_285 ),
inference(avatar_split_clause,[],[f4050,f3887,f1708,f62720]) ).
fof(f62720,plain,
( spl0_781
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X3))),X3))
| ~ class_Lattices_Olower__semilattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_781])]) ).
fof(f4050,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X3))),X3))
| ~ class_Lattices_Olower__semilattice(X0) )
| ~ spl0_144
| ~ spl0_285 ),
inference(duplicate_literal_removal,[],[f4030]) ).
fof(f4030,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X3))),X3))
| ~ class_Lattices_Olower__semilattice(X0)
| ~ class_Lattices_Olower__semilattice(X0) )
| ~ spl0_144
| ~ spl0_285 ),
inference(resolution,[],[f3888,f1709]) ).
fof(f62718,plain,
( spl0_780
| ~ spl0_145
| ~ spl0_284 ),
inference(avatar_split_clause,[],[f4018,f3883,f1712,f62716]) ).
fof(f62716,plain,
( spl0_780
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2)),X3)),X1))
| ~ class_Lattices_Olower__semilattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_780])]) ).
fof(f4018,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2)),X3)),X1))
| ~ class_Lattices_Olower__semilattice(X0) )
| ~ spl0_145
| ~ spl0_284 ),
inference(duplicate_literal_removal,[],[f3991]) ).
fof(f3991,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2)),X3)),X1))
| ~ class_Lattices_Olower__semilattice(X0)
| ~ class_Lattices_Olower__semilattice(X0) )
| ~ spl0_145
| ~ spl0_284 ),
inference(resolution,[],[f3884,f1713]) ).
fof(f62714,plain,
( spl0_779
| ~ spl0_144
| ~ spl0_284 ),
inference(avatar_split_clause,[],[f4017,f3883,f1708,f62712]) ).
fof(f62712,plain,
( spl0_779
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X3))),X2))
| ~ class_Lattices_Olower__semilattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_779])]) ).
fof(f4017,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X3))),X2))
| ~ class_Lattices_Olower__semilattice(X0) )
| ~ spl0_144
| ~ spl0_284 ),
inference(duplicate_literal_removal,[],[f3997]) ).
fof(f3997,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X3))),X2))
| ~ class_Lattices_Olower__semilattice(X0)
| ~ class_Lattices_Olower__semilattice(X0) )
| ~ spl0_144
| ~ spl0_284 ),
inference(resolution,[],[f3884,f1709]) ).
fof(f62710,plain,
( spl0_778
| ~ spl0_1
| ~ spl0_283 ),
inference(avatar_split_clause,[],[f3985,f3879,f1017,f62708]) ).
fof(f3879,plain,
( spl0_283
<=> ! [X5,X0,X3] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
| hAPP(c_Complete__Lattice_OSup__class_OSup(X0),hAPP(hAPP(c_Set_Oinsert(X0),X3),X5)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X3),hAPP(c_Complete__Lattice_OSup__class_OSup(X0),X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_283])]) ).
fof(f3985,plain,
( ! [X0,X1] : hAPP(c_Complete__Lattice_OSup__class_OSup(tc_bool),hAPP(hAPP(c_Set_Oinsert(tc_bool),X0),X1)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),X0),hAPP(c_Complete__Lattice_OSup__class_OSup(tc_bool),X1))
| ~ spl0_1
| ~ spl0_283 ),
inference(resolution,[],[f3880,f1019]) ).
fof(f3880,plain,
( ! [X3,X0,X5] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
| hAPP(c_Complete__Lattice_OSup__class_OSup(X0),hAPP(hAPP(c_Set_Oinsert(X0),X3),X5)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X3),hAPP(c_Complete__Lattice_OSup__class_OSup(X0),X5)) )
| ~ spl0_283 ),
inference(avatar_component_clause,[],[f3879]) ).
fof(f62630,plain,
( spl0_777
| ~ spl0_1
| ~ spl0_282 ),
inference(avatar_split_clause,[],[f3962,f3867,f1017,f62628]) ).
fof(f3867,plain,
( spl0_282
<=> ! [X5,X0,X3] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
| hAPP(c_Complete__Lattice_OInf__class_OInf(X0),hAPP(hAPP(c_Set_Oinsert(X0),X3),X5)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),hAPP(c_Complete__Lattice_OInf__class_OInf(X0),X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_282])]) ).
fof(f3962,plain,
( ! [X0,X1] : hAPP(c_Complete__Lattice_OInf__class_OInf(tc_bool),hAPP(hAPP(c_Set_Oinsert(tc_bool),X0),X1)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),X0),hAPP(c_Complete__Lattice_OInf__class_OInf(tc_bool),X1))
| ~ spl0_1
| ~ spl0_282 ),
inference(resolution,[],[f3868,f1019]) ).
fof(f3868,plain,
( ! [X3,X0,X5] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
| hAPP(c_Complete__Lattice_OInf__class_OInf(X0),hAPP(hAPP(c_Set_Oinsert(X0),X3),X5)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),hAPP(c_Complete__Lattice_OInf__class_OInf(X0),X5)) )
| ~ spl0_282 ),
inference(avatar_component_clause,[],[f3867]) ).
fof(f62626,plain,
( spl0_776
| ~ spl0_214
| ~ spl0_256 ),
inference(avatar_split_clause,[],[f3366,f3093,f2255,f62624]) ).
fof(f62624,plain,
( spl0_776
<=> ! [X2,X0,X1] :
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X2),X1) != X2
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_776])]) ).
fof(f3366,plain,
( ! [X2,X0,X1] :
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X2),X1) != X2
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X1),X2)) )
| ~ spl0_214
| ~ spl0_256 ),
inference(superposition,[],[f3094,f2256]) ).
fof(f62622,plain,
( spl0_775
| ~ spl0_145
| ~ spl0_233 ),
inference(avatar_split_clause,[],[f2954,f2645,f1712,f62620]) ).
fof(f62620,plain,
( spl0_775
<=> ! [X3,X4,X0,X5,X2,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(hAPP(c_COMBS(X3,X4,X5),c_Lattices_Olower__semilattice__class_Oinf(X0)),X2),X1)),X1))
| ~ class_Lattices_Olower__semilattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_775])]) ).
fof(f2954,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(hAPP(c_COMBS(X3,X4,X5),c_Lattices_Olower__semilattice__class_Oinf(X0)),X2),X1)),X1))
| ~ class_Lattices_Olower__semilattice(X0) )
| ~ spl0_145
| ~ spl0_233 ),
inference(superposition,[],[f1713,f2646]) ).
fof(f62618,plain,
( spl0_774
| ~ spl0_142
| ~ spl0_233 ),
inference(avatar_split_clause,[],[f2951,f2645,f1700,f62616]) ).
fof(f62616,plain,
( spl0_774
<=> ! [X3,X4,X0,X5,X2,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(hAPP(c_COMBS(X3,X4,X5),c_Lattices_Olower__semilattice__class_Oinf(X0)),X2),X1)),X1))
| ~ class_Lattices_Olattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_774])]) ).
fof(f2951,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(hAPP(c_COMBS(X3,X4,X5),c_Lattices_Olower__semilattice__class_Oinf(X0)),X2),X1)),X1))
| ~ class_Lattices_Olattice(X0) )
| ~ spl0_142
| ~ spl0_233 ),
inference(superposition,[],[f1701,f2646]) ).
fof(f62614,plain,
( spl0_773
| ~ spl0_141
| ~ spl0_233 ),
inference(avatar_split_clause,[],[f2916,f2645,f1696,f62612]) ).
fof(f62612,plain,
( spl0_773
<=> ! [X3,X4,X0,X5,X2,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),X1),hAPP(hAPP(hAPP(c_COMBS(X3,X4,X5),c_Lattices_Oupper__semilattice__class_Osup(X0)),X2),X1)))
| ~ class_Lattices_Olattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_773])]) ).
fof(f2916,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),X1),hAPP(hAPP(hAPP(c_COMBS(X3,X4,X5),c_Lattices_Oupper__semilattice__class_Osup(X0)),X2),X1)))
| ~ class_Lattices_Olattice(X0) )
| ~ spl0_141
| ~ spl0_233 ),
inference(superposition,[],[f1697,f2646]) ).
fof(f62610,plain,
( spl0_772
| ~ spl0_138
| ~ spl0_233 ),
inference(avatar_split_clause,[],[f2913,f2645,f1684,f62608]) ).
fof(f62608,plain,
( spl0_772
<=> ! [X3,X4,X0,X5,X2,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),X1),hAPP(hAPP(hAPP(c_COMBS(X3,X4,X5),c_Lattices_Oupper__semilattice__class_Osup(X0)),X2),X1)))
| ~ class_Lattices_Oupper__semilattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_772])]) ).
fof(f2913,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),X1),hAPP(hAPP(hAPP(c_COMBS(X3,X4,X5),c_Lattices_Oupper__semilattice__class_Osup(X0)),X2),X1)))
| ~ class_Lattices_Oupper__semilattice(X0) )
| ~ spl0_138
| ~ spl0_233 ),
inference(superposition,[],[f1685,f2646]) ).
fof(f62606,plain,
( spl0_771
| ~ spl0_184
| ~ spl0_233 ),
inference(avatar_split_clause,[],[f2888,f2645,f2001,f62604]) ).
fof(f62604,plain,
( spl0_771
<=> ! [X3,X4,X0,X5,X2,X1] : hBOOL(hAPP(hAPP(hAPP(c_COMBS(X3,X4,X5),c_lessequals(tc_fun(X0,tc_bool))),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X2)),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_771])]) ).
fof(f2888,plain,
( ! [X2,X3,X0,X1,X4,X5] : hBOOL(hAPP(hAPP(hAPP(c_COMBS(X3,X4,X5),c_lessequals(tc_fun(X0,tc_bool))),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X2)),X1))
| ~ spl0_184
| ~ spl0_233 ),
inference(superposition,[],[f2002,f2646]) ).
fof(f62602,plain,
( spl0_770
| ~ spl0_51
| ~ spl0_233 ),
inference(avatar_split_clause,[],[f2870,f2645,f1237,f62600]) ).
fof(f62600,plain,
( spl0_770
<=> ! [X1,X6,X4,X0,X3,X5,X2,X7] : hAPP(hAPP(hAPP(c_COMBS(X4,X5,X6),X7),c_COMBK(X0,X1,X2)),X3) = hAPP(hAPP(X7,X3),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_770])]) ).
fof(f2870,plain,
( ! [X2,X3,X0,X1,X6,X7,X4,X5] : hAPP(hAPP(hAPP(c_COMBS(X4,X5,X6),X7),c_COMBK(X0,X1,X2)),X3) = hAPP(hAPP(X7,X3),X0)
| ~ spl0_51
| ~ spl0_233 ),
inference(superposition,[],[f2646,f1238]) ).
fof(f62598,plain,
( spl0_769
| ~ spl0_51
| ~ spl0_233 ),
inference(avatar_split_clause,[],[f2840,f2645,f1237,f62596]) ).
fof(f62596,plain,
( spl0_769
<=> ! [X1,X6,X4,X0,X3,X5,X2,X7] : hAPP(hAPP(hAPP(c_COMBS(X4,X5,X6),c_COMBK(X0,X1,X2)),X7),X3) = hAPP(X0,hAPP(X7,X3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_769])]) ).
fof(f2840,plain,
( ! [X2,X3,X0,X1,X6,X7,X4,X5] : hAPP(hAPP(hAPP(c_COMBS(X4,X5,X6),c_COMBK(X0,X1,X2)),X7),X3) = hAPP(X0,hAPP(X7,X3))
| ~ spl0_51
| ~ spl0_233 ),
inference(superposition,[],[f2646,f1238]) ).
fof(f62506,plain,
( spl0_767
| spl0_768
| ~ spl0_51
| ~ spl0_120
| ~ spl0_137
| ~ spl0_230 ),
inference(avatar_split_clause,[],[f2780,f2633,f1680,f1591,f1237,f62504,f62501]) ).
fof(f62501,plain,
( spl0_767
<=> ! [X5,X3,X0,X6,X2,X1] : ~ c_Fun_Oinj__on(c_Fun_Ocomp(c_COMBK(X0,X1,X2),X3,X2,X1,t_a),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_bool)),X5,X6) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_767])]) ).
fof(f62504,plain,
( spl0_768
<=> ! [X4] : v_x = X4 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_768])]) ).
fof(f2780,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] :
( v_x = X4
| ~ c_Fun_Oinj__on(c_Fun_Ocomp(c_COMBK(X0,X1,X2),X3,X2,X1,t_a),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_bool)),X5,X6) )
| ~ spl0_51
| ~ spl0_120
| ~ spl0_137
| ~ spl0_230 ),
inference(trivial_inequality_removal,[],[f2779]) ).
fof(f2779,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] :
( X0 != X0
| v_x = X4
| ~ c_Fun_Oinj__on(c_Fun_Ocomp(c_COMBK(X0,X1,X2),X3,X2,X1,t_a),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_bool)),X5,X6) )
| ~ spl0_51
| ~ spl0_120
| ~ spl0_137
| ~ spl0_230 ),
inference(forward_demodulation,[],[f2778,f1238]) ).
fof(f2778,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] :
( hAPP(c_COMBK(X0,X1,X2),hAPP(X3,X4)) != X0
| v_x = X4
| ~ c_Fun_Oinj__on(c_Fun_Ocomp(c_COMBK(X0,X1,X2),X3,X2,X1,t_a),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_bool)),X5,X6) )
| ~ spl0_120
| ~ spl0_137
| ~ spl0_230 ),
inference(forward_demodulation,[],[f2729,f1681]) ).
fof(f2729,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] :
( hAPP(c_Fun_Ocomp(c_COMBK(X0,X1,X2),X3,X2,X1,t_a),X4) != X0
| v_x = X4
| ~ c_Fun_Oinj__on(c_Fun_Ocomp(c_COMBK(X0,X1,X2),X3,X2,X1,t_a),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_bool)),X5,X6) )
| ~ spl0_120
| ~ spl0_230 ),
inference(superposition,[],[f2634,f1592]) ).
fof(f62499,plain,
( spl0_766
| spl0_581
| ~ spl0_201
| ~ spl0_230 ),
inference(avatar_split_clause,[],[f2775,f2633,f2076,f16579,f62497]) ).
fof(f62497,plain,
( spl0_766
<=> ! [X4,X0,X3] : ~ c_Fun_Oinj__on(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0)),c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3,X4) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_766])]) ).
fof(f2775,plain,
( ! [X2,X3,X0,X1,X4] :
( X1 = X2
| ~ c_Fun_Oinj__on(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0)),c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3,X4) )
| ~ spl0_201
| ~ spl0_230 ),
inference(trivial_inequality_removal,[],[f2774]) ).
fof(f2774,plain,
( ! [X2,X3,X0,X1,X4] :
( c_COMBK(c_False,tc_bool,X0) != c_COMBK(c_False,tc_bool,X0)
| X1 = X2
| ~ c_Fun_Oinj__on(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0)),c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3,X4) )
| ~ spl0_201
| ~ spl0_230 ),
inference(forward_demodulation,[],[f2713,f2077]) ).
fof(f2713,plain,
( ! [X2,X3,X0,X1,X4] :
( c_COMBK(c_False,tc_bool,X0) != hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0)),X2)
| X1 = X2
| ~ c_Fun_Oinj__on(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0)),c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3,X4) )
| ~ spl0_201
| ~ spl0_230 ),
inference(superposition,[],[f2634,f2077]) ).
fof(f61700,plain,
( spl0_765
| ~ spl0_150
| ~ spl0_601 ),
inference(avatar_split_clause,[],[f17280,f16912,f1732,f61698]) ).
fof(f16912,plain,
( spl0_601
<=> ! [X0,X3,X2,X1] : hBOOL(c_in(X0,hAPP(hAPP(c_Set_Oinsert(X1),X2),hAPP(hAPP(c_Set_Oinsert(X1),X0),X3)),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_601])]) ).
fof(f17280,plain,
( ! [X2,X0,X1] : hBOOL(c_in(X1,hAPP(hAPP(c_Set_Oinsert(X0),X2),hAPP(c_fequal(X0),X1)),X0))
| ~ spl0_150
| ~ spl0_601 ),
inference(superposition,[],[f16913,f1733]) ).
fof(f16913,plain,
( ! [X2,X3,X0,X1] : hBOOL(c_in(X0,hAPP(hAPP(c_Set_Oinsert(X1),X2),hAPP(hAPP(c_Set_Oinsert(X1),X0),X3)),X1))
| ~ spl0_601 ),
inference(avatar_component_clause,[],[f16912]) ).
fof(f61456,plain,
( spl0_764
| ~ spl0_57
| ~ spl0_158
| ~ spl0_344
| ~ spl0_387 ),
inference(avatar_split_clause,[],[f44109,f6744,f4966,f1818,f1262,f61454]) ).
fof(f61454,plain,
( spl0_764
<=> ! [X2,X0,X1] :
( hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X2),hAPP(c_fequal(X0),X1)) = X2
| hBOOL(hAPP(X2,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_764])]) ).
fof(f44109,plain,
( ! [X2,X0,X1] :
( hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X2),hAPP(c_fequal(X0),X1)) = X2
| hBOOL(hAPP(X2,X1)) )
| ~ spl0_57
| ~ spl0_158
| ~ spl0_344
| ~ spl0_387 ),
inference(forward_demodulation,[],[f5529,f6784]) ).
fof(f6784,plain,
( ! [X2,X0,X1] : hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X1),hAPP(c_fequal(X0),X2)) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Set_Oinsert(X0),X2),X1)),hAPP(c_fequal(X0),X2))
| ~ spl0_158
| ~ spl0_387 ),
inference(resolution,[],[f6745,f1819]) ).
fof(f5529,plain,
( ! [X2,X0,X1] :
( hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Set_Oinsert(X0),X1),X2)),hAPP(c_fequal(X0),X1)) = X2
| hBOOL(hAPP(X2,X1)) )
| ~ spl0_57
| ~ spl0_344 ),
inference(resolution,[],[f4967,f1263]) ).
fof(f61294,plain,
( spl0_763
| ~ spl0_9
| ~ spl0_595 ),
inference(avatar_split_clause,[],[f16942,f16885,f1057,f61292]) ).
fof(f16885,plain,
( spl0_595
<=> ! [X2,X0,X1] :
( hAPP(c_fequal(tc_fun(X0,X1)),X2) = c_SetInterval_Oord__class_OatLeastAtMost(X2,X2,tc_fun(X0,X1))
| ~ class_Orderings_Oorder(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_595])]) ).
fof(f16942,plain,
( ! [X0,X1] : hAPP(c_fequal(tc_fun(X0,tc_bool)),X1) = c_SetInterval_Oord__class_OatLeastAtMost(X1,X1,tc_fun(X0,tc_bool))
| ~ spl0_9
| ~ spl0_595 ),
inference(resolution,[],[f16886,f1059]) ).
fof(f1059,plain,
( class_Orderings_Oorder(tc_bool)
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f1057]) ).
fof(f16886,plain,
( ! [X2,X0,X1] :
( ~ class_Orderings_Oorder(X1)
| hAPP(c_fequal(tc_fun(X0,X1)),X2) = c_SetInterval_Oord__class_OatLeastAtMost(X2,X2,tc_fun(X0,X1)) )
| ~ spl0_595 ),
inference(avatar_component_clause,[],[f16885]) ).
fof(f60367,plain,
( spl0_762
| ~ spl0_1
| ~ spl0_594 ),
inference(avatar_split_clause,[],[f16936,f16881,f1017,f60365]) ).
fof(f16881,plain,
( spl0_594
<=> ! [X2,X0,X1] :
( hAPP(c_Complete__Lattice_OInf__class_OInf(tc_fun(X0,X1)),hAPP(c_fequal(tc_fun(X0,X1)),X2)) = X2
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_594])]) ).
fof(f16936,plain,
( ! [X0,X1] : hAPP(c_Complete__Lattice_OInf__class_OInf(tc_fun(X0,tc_bool)),hAPP(c_fequal(tc_fun(X0,tc_bool)),X1)) = X1
| ~ spl0_1
| ~ spl0_594 ),
inference(resolution,[],[f16882,f1019]) ).
fof(f16882,plain,
( ! [X2,X0,X1] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X1)
| hAPP(c_Complete__Lattice_OInf__class_OInf(tc_fun(X0,X1)),hAPP(c_fequal(tc_fun(X0,X1)),X2)) = X2 )
| ~ spl0_594 ),
inference(avatar_component_clause,[],[f16881]) ).
fof(f59318,plain,
( spl0_761
| ~ spl0_1
| ~ spl0_593 ),
inference(avatar_split_clause,[],[f16934,f16877,f1017,f59316]) ).
fof(f16877,plain,
( spl0_593
<=> ! [X2,X0,X1] :
( hAPP(c_Complete__Lattice_OSup__class_OSup(tc_fun(X0,X1)),hAPP(c_fequal(tc_fun(X0,X1)),X2)) = X2
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_593])]) ).
fof(f16934,plain,
( ! [X0,X1] : hAPP(c_Complete__Lattice_OSup__class_OSup(tc_fun(X0,tc_bool)),hAPP(c_fequal(tc_fun(X0,tc_bool)),X1)) = X1
| ~ spl0_1
| ~ spl0_593 ),
inference(resolution,[],[f16878,f1019]) ).
fof(f16878,plain,
( ! [X2,X0,X1] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X1)
| hAPP(c_Complete__Lattice_OSup__class_OSup(tc_fun(X0,X1)),hAPP(c_fequal(tc_fun(X0,X1)),X2)) = X2 )
| ~ spl0_593 ),
inference(avatar_component_clause,[],[f16877]) ).
fof(f54981,plain,
( spl0_760
| ~ spl0_342
| ~ spl0_506
| ~ spl0_508 ),
inference(avatar_split_clause,[],[f44395,f13711,f13679,f4957,f54979]) ).
fof(f54979,plain,
( spl0_760
<=> ! [X5,X1,X0,X9,X8,X7] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,hAPP(hAPP(c_COMBB(X0,tc_fun(X0,tc_bool),X8),hAPP(c_COMBC(c_Set_Oinsert(X0),X0,tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0))),X7),X8,tc_fun(X0,tc_bool))),X9))
| ~ hBOOL(c_in(X1,X5,X8))
| hBOOL(c_in(hAPP(X7,X1),X9,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_760])]) ).
fof(f13679,plain,
( spl0_506
<=> ! [X5,X1,X0,X9,X8,X7] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X0,tc_fun(tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),X8),c_Set_Oinsert(X0)),X7),X8,tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0)),X8,tc_fun(X0,tc_bool))),X9))
| ~ hBOOL(c_in(X1,X5,X8))
| hBOOL(c_in(hAPP(X7,X1),X9,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_506])]) ).
fof(f13711,plain,
( spl0_508
<=> ! [X5,X0,X14,X9,X8,X7] : c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,hAPP(hAPP(c_COMBB(X8,tc_fun(X0,tc_bool),X14),X9),X7),X14,tc_fun(X0,tc_bool)) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X8,tc_fun(tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),X14),c_Set_Oinsert(X8)),X7),X14,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8)),X14,tc_fun(X8,tc_bool)),X9,X8,tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_508])]) ).
fof(f44395,plain,
( ! [X0,X1,X8,X9,X7,X5] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,hAPP(hAPP(c_COMBB(X0,tc_fun(X0,tc_bool),X8),hAPP(c_COMBC(c_Set_Oinsert(X0),X0,tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0))),X7),X8,tc_fun(X0,tc_bool))),X9))
| ~ hBOOL(c_in(X1,X5,X8))
| hBOOL(c_in(hAPP(X7,X1),X9,X0)) )
| ~ spl0_342
| ~ spl0_506
| ~ spl0_508 ),
inference(forward_demodulation,[],[f13680,f13758]) ).
fof(f13758,plain,
( ! [X2,X3,X0,X1] : c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X0,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X1,tc_fun(tc_fun(X1,tc_bool),tc_fun(X1,tc_bool)),X2),c_Set_Oinsert(X1)),X3),X2,tc_fun(X1,tc_bool),tc_fun(X1,tc_bool)),c_COMBK(c_False,tc_bool,X1)),X2,tc_fun(X1,tc_bool)) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X0,hAPP(hAPP(c_COMBB(X1,tc_fun(X1,tc_bool),X2),hAPP(c_COMBC(c_Set_Oinsert(X1),X1,tc_fun(X1,tc_bool),tc_fun(X1,tc_bool)),c_COMBK(c_False,tc_bool,X1))),X3),X2,tc_fun(X1,tc_bool))
| ~ spl0_342
| ~ spl0_508 ),
inference(superposition,[],[f13712,f4958]) ).
fof(f13712,plain,
( ! [X0,X8,X9,X7,X14,X5] : c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,hAPP(hAPP(c_COMBB(X8,tc_fun(X0,tc_bool),X14),X9),X7),X14,tc_fun(X0,tc_bool)) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X8,tc_fun(tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),X14),c_Set_Oinsert(X8)),X7),X14,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8)),X14,tc_fun(X8,tc_bool)),X9,X8,tc_fun(X0,tc_bool))
| ~ spl0_508 ),
inference(avatar_component_clause,[],[f13711]) ).
fof(f13680,plain,
( ! [X0,X1,X8,X9,X7,X5] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X0,tc_fun(tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),X8),c_Set_Oinsert(X0)),X7),X8,tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0)),X8,tc_fun(X0,tc_bool))),X9))
| ~ hBOOL(c_in(X1,X5,X8))
| hBOOL(c_in(hAPP(X7,X1),X9,X0)) )
| ~ spl0_506 ),
inference(avatar_component_clause,[],[f13679]) ).
fof(f54871,plain,
( spl0_759
| ~ spl0_342
| ~ spl0_505
| ~ spl0_508 ),
inference(avatar_split_clause,[],[f44394,f13711,f13566,f4957,f54869]) ).
fof(f54869,plain,
( spl0_759
<=> ! [X3,X0,X5,X8,X7] :
( ~ hBOOL(c_in(hAPP(X7,X3),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,hAPP(hAPP(c_COMBB(X8,tc_fun(X8,tc_bool),X0),hAPP(c_COMBC(c_Set_Oinsert(X8),X8,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8))),X7),X0,tc_fun(X8,tc_bool)),X8))
| hBOOL(c_in(X3,X5,X0))
| ~ c_Fun_Oinj__on(X7,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0,X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_759])]) ).
fof(f13566,plain,
( spl0_505
<=> ! [X3,X0,X5,X8,X7] :
( ~ hBOOL(c_in(hAPP(X7,X3),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X8,tc_fun(tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),X0),c_Set_Oinsert(X8)),X7),X0,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8)),X0,tc_fun(X8,tc_bool)),X8))
| hBOOL(c_in(X3,X5,X0))
| ~ c_Fun_Oinj__on(X7,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0,X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_505])]) ).
fof(f44394,plain,
( ! [X3,X0,X8,X7,X5] :
( ~ hBOOL(c_in(hAPP(X7,X3),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,hAPP(hAPP(c_COMBB(X8,tc_fun(X8,tc_bool),X0),hAPP(c_COMBC(c_Set_Oinsert(X8),X8,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8))),X7),X0,tc_fun(X8,tc_bool)),X8))
| hBOOL(c_in(X3,X5,X0))
| ~ c_Fun_Oinj__on(X7,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0,X8) )
| ~ spl0_342
| ~ spl0_505
| ~ spl0_508 ),
inference(forward_demodulation,[],[f13567,f13758]) ).
fof(f13567,plain,
( ! [X3,X0,X8,X7,X5] :
( ~ hBOOL(c_in(hAPP(X7,X3),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X8,tc_fun(tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),X0),c_Set_Oinsert(X8)),X7),X0,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8)),X0,tc_fun(X8,tc_bool)),X8))
| hBOOL(c_in(X3,X5,X0))
| ~ c_Fun_Oinj__on(X7,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0,X8) )
| ~ spl0_505 ),
inference(avatar_component_clause,[],[f13566]) ).
fof(f54867,plain,
( spl0_758
| ~ spl0_342
| ~ spl0_504
| ~ spl0_508 ),
inference(avatar_split_clause,[],[f44393,f13711,f13562,f4957,f54865]) ).
fof(f54865,plain,
( spl0_758
<=> ! [X0,X14,X13,X5,X8,X7] :
( ~ c_Fun_Oinj__on(X13,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,hAPP(hAPP(c_COMBB(X8,tc_fun(X8,tc_bool),X0),hAPP(c_COMBC(c_Set_Oinsert(X8),X8,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8))),X7),X0,tc_fun(X8,tc_bool)),X8,X14)
| ~ c_Fun_Oinj__on(X7,X5,X0,X8)
| c_Fun_Oinj__on(c_Fun_Ocomp(X13,X7,X8,X14,X0),X5,X0,X14) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_758])]) ).
fof(f13562,plain,
( spl0_504
<=> ! [X0,X14,X13,X5,X8,X7] :
( ~ c_Fun_Oinj__on(X13,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X8,tc_fun(tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),X0),c_Set_Oinsert(X8)),X7),X0,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8)),X0,tc_fun(X8,tc_bool)),X8,X14)
| ~ c_Fun_Oinj__on(X7,X5,X0,X8)
| c_Fun_Oinj__on(c_Fun_Ocomp(X13,X7,X8,X14,X0),X5,X0,X14) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_504])]) ).
fof(f44393,plain,
( ! [X0,X8,X7,X14,X5,X13] :
( ~ c_Fun_Oinj__on(X13,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,hAPP(hAPP(c_COMBB(X8,tc_fun(X8,tc_bool),X0),hAPP(c_COMBC(c_Set_Oinsert(X8),X8,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8))),X7),X0,tc_fun(X8,tc_bool)),X8,X14)
| ~ c_Fun_Oinj__on(X7,X5,X0,X8)
| c_Fun_Oinj__on(c_Fun_Ocomp(X13,X7,X8,X14,X0),X5,X0,X14) )
| ~ spl0_342
| ~ spl0_504
| ~ spl0_508 ),
inference(forward_demodulation,[],[f13563,f13758]) ).
fof(f13563,plain,
( ! [X0,X8,X7,X14,X5,X13] :
( ~ c_Fun_Oinj__on(X13,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X8,tc_fun(tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),X0),c_Set_Oinsert(X8)),X7),X0,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8)),X0,tc_fun(X8,tc_bool)),X8,X14)
| ~ c_Fun_Oinj__on(X7,X5,X0,X8)
| c_Fun_Oinj__on(c_Fun_Ocomp(X13,X7,X8,X14,X0),X5,X0,X14) )
| ~ spl0_504 ),
inference(avatar_component_clause,[],[f13562]) ).
fof(f54782,plain,
( spl0_757
| ~ spl0_342
| ~ spl0_500
| ~ spl0_508 ),
inference(avatar_split_clause,[],[f44392,f13711,f13484,f4957,f54780]) ).
fof(f54780,plain,
( spl0_757
<=> ! [X5,X0,X7] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X5),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,hAPP(hAPP(c_COMBB(X0,tc_fun(X0,tc_bool),X0),hAPP(c_COMBC(c_Set_Oinsert(X0),X0,tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0))),X7),X0,tc_fun(X0,tc_bool))))
| ~ c_Finite__Set_Ofinite(X5,X0)
| c_Fun_Oinj__on(X7,X5,X0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_757])]) ).
fof(f13484,plain,
( spl0_500
<=> ! [X5,X0,X7] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X5),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X0,tc_fun(tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),X0),c_Set_Oinsert(X0)),X7),X0,tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0)),X0,tc_fun(X0,tc_bool))))
| ~ c_Finite__Set_Ofinite(X5,X0)
| c_Fun_Oinj__on(X7,X5,X0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_500])]) ).
fof(f44392,plain,
( ! [X0,X7,X5] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X5),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,hAPP(hAPP(c_COMBB(X0,tc_fun(X0,tc_bool),X0),hAPP(c_COMBC(c_Set_Oinsert(X0),X0,tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0))),X7),X0,tc_fun(X0,tc_bool))))
| ~ c_Finite__Set_Ofinite(X5,X0)
| c_Fun_Oinj__on(X7,X5,X0,X0) )
| ~ spl0_342
| ~ spl0_500
| ~ spl0_508 ),
inference(forward_demodulation,[],[f13485,f13758]) ).
fof(f13485,plain,
( ! [X0,X7,X5] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X5),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X0,tc_fun(tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),X0),c_Set_Oinsert(X0)),X7),X0,tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0)),X0,tc_fun(X0,tc_bool))))
| ~ c_Finite__Set_Ofinite(X5,X0)
| c_Fun_Oinj__on(X7,X5,X0,X0) )
| ~ spl0_500 ),
inference(avatar_component_clause,[],[f13484]) ).
fof(f54736,plain,
( spl0_756
| ~ spl0_342
| ~ spl0_498
| ~ spl0_508 ),
inference(avatar_split_clause,[],[f44391,f13711,f13404,f4957,f54734]) ).
fof(f54734,plain,
( spl0_756
<=> ! [X9,X0,X5,X8,X7] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X8,tc_bool)),X9),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,hAPP(hAPP(c_COMBB(X8,tc_fun(X8,tc_bool),X0),hAPP(c_COMBC(c_Set_Oinsert(X8),X8,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8))),X7),X0,tc_fun(X8,tc_bool))))
| ~ c_Finite__Set_Ofinite(X5,X0)
| c_Finite__Set_Ofinite(X9,X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_756])]) ).
fof(f44391,plain,
( ! [X0,X8,X9,X7,X5] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X8,tc_bool)),X9),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,hAPP(hAPP(c_COMBB(X8,tc_fun(X8,tc_bool),X0),hAPP(c_COMBC(c_Set_Oinsert(X8),X8,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8))),X7),X0,tc_fun(X8,tc_bool))))
| ~ c_Finite__Set_Ofinite(X5,X0)
| c_Finite__Set_Ofinite(X9,X8) )
| ~ spl0_342
| ~ spl0_498
| ~ spl0_508 ),
inference(forward_demodulation,[],[f13405,f13758]) ).
fof(f54732,plain,
( spl0_755
| ~ spl0_342
| ~ spl0_497
| ~ spl0_508 ),
inference(avatar_split_clause,[],[f44029,f13711,f13400,f4957,f54730]) ).
fof(f54730,plain,
( spl0_755
<=> ! [X0,X14,X13,X5,X8,X7] :
( c_Fun_Oinj__on(X13,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,hAPP(hAPP(c_COMBB(X14,tc_fun(X14,tc_bool),X0),hAPP(c_COMBC(c_Set_Oinsert(X14),X14,tc_fun(X14,tc_bool),tc_fun(X14,tc_bool)),c_COMBK(c_False,tc_bool,X14))),X7),X0,tc_fun(X14,tc_bool)),X14,X8)
| ~ c_Fun_Oinj__on(c_Fun_Ocomp(X13,X7,X14,X8,X0),X5,X0,X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_755])]) ).
fof(f13400,plain,
( spl0_497
<=> ! [X0,X14,X13,X5,X8,X7] :
( c_Fun_Oinj__on(X13,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X14,tc_fun(tc_fun(X14,tc_bool),tc_fun(X14,tc_bool)),X0),c_Set_Oinsert(X14)),X7),X0,tc_fun(X14,tc_bool),tc_fun(X14,tc_bool)),c_COMBK(c_False,tc_bool,X14)),X0,tc_fun(X14,tc_bool)),X14,X8)
| ~ c_Fun_Oinj__on(c_Fun_Ocomp(X13,X7,X14,X8,X0),X5,X0,X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_497])]) ).
fof(f44029,plain,
( ! [X0,X8,X7,X14,X5,X13] :
( c_Fun_Oinj__on(X13,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,hAPP(hAPP(c_COMBB(X14,tc_fun(X14,tc_bool),X0),hAPP(c_COMBC(c_Set_Oinsert(X14),X14,tc_fun(X14,tc_bool),tc_fun(X14,tc_bool)),c_COMBK(c_False,tc_bool,X14))),X7),X0,tc_fun(X14,tc_bool)),X14,X8)
| ~ c_Fun_Oinj__on(c_Fun_Ocomp(X13,X7,X14,X8,X0),X5,X0,X8) )
| ~ spl0_342
| ~ spl0_497
| ~ spl0_508 ),
inference(forward_demodulation,[],[f13401,f13758]) ).
fof(f13401,plain,
( ! [X0,X8,X7,X14,X5,X13] :
( ~ c_Fun_Oinj__on(c_Fun_Ocomp(X13,X7,X14,X8,X0),X5,X0,X8)
| c_Fun_Oinj__on(X13,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X14,tc_fun(tc_fun(X14,tc_bool),tc_fun(X14,tc_bool)),X0),c_Set_Oinsert(X14)),X7),X0,tc_fun(X14,tc_bool),tc_fun(X14,tc_bool)),c_COMBK(c_False,tc_bool,X14)),X0,tc_fun(X14,tc_bool)),X14,X8) )
| ~ spl0_497 ),
inference(avatar_component_clause,[],[f13400]) ).
fof(f54708,plain,
( spl0_754
| ~ spl0_342
| ~ spl0_495
| ~ spl0_508 ),
inference(avatar_split_clause,[],[f44172,f13711,f13374,f4957,f54706]) ).
fof(f54706,plain,
( spl0_754
<=> ! [X35,X0,X5,X8,X1] :
( hAPP(c_fequal(X8),X35) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,hAPP(hAPP(c_COMBB(X8,tc_fun(X8,tc_bool),X0),hAPP(c_COMBC(c_Set_Oinsert(X8),X8,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8))),c_COMBK(X35,X8,X0)),X0,tc_fun(X8,tc_bool))
| ~ hBOOL(c_in(X1,X5,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_754])]) ).
fof(f13374,plain,
( spl0_495
<=> ! [X35,X0,X5,X8,X1] :
( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X8,tc_fun(tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),X0),c_Set_Oinsert(X8)),c_COMBK(X35,X8,X0)),X0,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8)),X0,tc_fun(X8,tc_bool)) = hAPP(c_fequal(X8),X35)
| ~ hBOOL(c_in(X1,X5,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_495])]) ).
fof(f44172,plain,
( ! [X0,X1,X8,X35,X5] :
( hAPP(c_fequal(X8),X35) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,hAPP(hAPP(c_COMBB(X8,tc_fun(X8,tc_bool),X0),hAPP(c_COMBC(c_Set_Oinsert(X8),X8,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8))),c_COMBK(X35,X8,X0)),X0,tc_fun(X8,tc_bool))
| ~ hBOOL(c_in(X1,X5,X0)) )
| ~ spl0_342
| ~ spl0_495
| ~ spl0_508 ),
inference(forward_demodulation,[],[f13375,f13758]) ).
fof(f13375,plain,
( ! [X0,X1,X8,X5,X35] :
( ~ hBOOL(c_in(X1,X5,X0))
| c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X8,tc_fun(tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),X0),c_Set_Oinsert(X8)),c_COMBK(X35,X8,X0)),X0,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8)),X0,tc_fun(X8,tc_bool)) = hAPP(c_fequal(X8),X35) )
| ~ spl0_495 ),
inference(avatar_component_clause,[],[f13374]) ).
fof(f54604,plain,
( spl0_753
| ~ spl0_342
| ~ spl0_491
| ~ spl0_508 ),
inference(avatar_split_clause,[],[f44390,f13711,f13234,f4957,f54602]) ).
fof(f13234,plain,
( spl0_491
<=> ! [X1,X0,X5,X8,X7] :
( hBOOL(c_in(hAPP(X7,X1),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X0,tc_fun(tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),X8),c_Set_Oinsert(X0)),X7),X8,tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0)),X8,tc_fun(X0,tc_bool)),X0))
| ~ hBOOL(c_in(X1,X5,X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_491])]) ).
fof(f44390,plain,
( ! [X0,X1,X8,X7,X5] :
( hBOOL(c_in(hAPP(X7,X1),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,hAPP(hAPP(c_COMBB(X0,tc_fun(X0,tc_bool),X8),hAPP(c_COMBC(c_Set_Oinsert(X0),X0,tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0))),X7),X8,tc_fun(X0,tc_bool)),X0))
| ~ hBOOL(c_in(X1,X5,X8)) )
| ~ spl0_342
| ~ spl0_491
| ~ spl0_508 ),
inference(forward_demodulation,[],[f13235,f13758]) ).
fof(f13235,plain,
( ! [X0,X1,X8,X7,X5] :
( hBOOL(c_in(hAPP(X7,X1),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X0,tc_fun(tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),X8),c_Set_Oinsert(X0)),X7),X8,tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0)),X8,tc_fun(X0,tc_bool)),X0))
| ~ hBOOL(c_in(X1,X5,X8)) )
| ~ spl0_491 ),
inference(avatar_component_clause,[],[f13234]) ).
fof(f54349,plain,
( spl0_752
| ~ spl0_342
| ~ spl0_489
| ~ spl0_508 ),
inference(avatar_split_clause,[],[f44389,f13711,f13221,f4957,f54347]) ).
fof(f54347,plain,
( spl0_752
<=> ! [X0,X5,X8,X7] :
( ~ c_Finite__Set_Ofinite(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,hAPP(hAPP(c_COMBB(X0,tc_fun(X0,tc_bool),X8),hAPP(c_COMBC(c_Set_Oinsert(X0),X0,tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0))),X7),X8,tc_fun(X0,tc_bool)),X0)
| c_Finite__Set_Ofinite(X5,X8)
| ~ c_Fun_Oinj__on(X7,X5,X8,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_752])]) ).
fof(f44389,plain,
( ! [X0,X8,X7,X5] :
( ~ c_Finite__Set_Ofinite(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,hAPP(hAPP(c_COMBB(X0,tc_fun(X0,tc_bool),X8),hAPP(c_COMBC(c_Set_Oinsert(X0),X0,tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0))),X7),X8,tc_fun(X0,tc_bool)),X0)
| c_Finite__Set_Ofinite(X5,X8)
| ~ c_Fun_Oinj__on(X7,X5,X8,X0) )
| ~ spl0_342
| ~ spl0_489
| ~ spl0_508 ),
inference(forward_demodulation,[],[f13222,f13758]) ).
fof(f54021,plain,
( spl0_751
| ~ spl0_342
| ~ spl0_487
| ~ spl0_508 ),
inference(avatar_split_clause,[],[f44387,f13711,f13114,f4957,f54019]) ).
fof(f54019,plain,
( spl0_751
<=> ! [X0,X8,X1,X7] : hBOOL(c_in(hAPP(X7,X1),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Otop__class_Otop(tc_fun(X8,tc_bool)),hAPP(hAPP(c_COMBB(X0,tc_fun(X0,tc_bool),X8),hAPP(c_COMBC(c_Set_Oinsert(X0),X0,tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0))),X7),X8,tc_fun(X0,tc_bool)),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_751])]) ).
fof(f13114,plain,
( spl0_487
<=> ! [X0,X8,X1,X7] : hBOOL(c_in(hAPP(X7,X1),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Otop__class_Otop(tc_fun(X8,tc_bool)),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X0,tc_fun(tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),X8),c_Set_Oinsert(X0)),X7),X8,tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0)),X8,tc_fun(X0,tc_bool)),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_487])]) ).
fof(f44387,plain,
( ! [X0,X1,X8,X7] : hBOOL(c_in(hAPP(X7,X1),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Otop__class_Otop(tc_fun(X8,tc_bool)),hAPP(hAPP(c_COMBB(X0,tc_fun(X0,tc_bool),X8),hAPP(c_COMBC(c_Set_Oinsert(X0),X0,tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0))),X7),X8,tc_fun(X0,tc_bool)),X0))
| ~ spl0_342
| ~ spl0_487
| ~ spl0_508 ),
inference(forward_demodulation,[],[f13115,f13758]) ).
fof(f13115,plain,
( ! [X0,X1,X8,X7] : hBOOL(c_in(hAPP(X7,X1),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Otop__class_Otop(tc_fun(X8,tc_bool)),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X0,tc_fun(tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),X8),c_Set_Oinsert(X0)),X7),X8,tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0)),X8,tc_fun(X0,tc_bool)),X0))
| ~ spl0_487 ),
inference(avatar_component_clause,[],[f13114]) ).
fof(f52438,plain,
( spl0_750
| ~ spl0_342
| ~ spl0_476
| ~ spl0_508 ),
inference(avatar_split_clause,[],[f44386,f13711,f12560,f4957,f52436]) ).
fof(f52436,plain,
( spl0_750
<=> ! [X38,X53,X0,X8] :
( c_Finite__Set_Ofinite(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X38,hAPP(hAPP(c_COMBB(X8,tc_fun(X8,tc_bool),X0),hAPP(c_COMBC(c_Set_Oinsert(X8),X8,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8))),X53),X0,tc_fun(X8,tc_bool)),X8)
| ~ c_Finite__Set_Ofinite(X38,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_750])]) ).
fof(f12560,plain,
( spl0_476
<=> ! [X38,X53,X0,X8] :
( c_Finite__Set_Ofinite(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X38,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X8,tc_fun(tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),X0),c_Set_Oinsert(X8)),X53),X0,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8)),X0,tc_fun(X8,tc_bool)),X8)
| ~ c_Finite__Set_Ofinite(X38,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_476])]) ).
fof(f44386,plain,
( ! [X38,X0,X8,X53] :
( c_Finite__Set_Ofinite(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X38,hAPP(hAPP(c_COMBB(X8,tc_fun(X8,tc_bool),X0),hAPP(c_COMBC(c_Set_Oinsert(X8),X8,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8))),X53),X0,tc_fun(X8,tc_bool)),X8)
| ~ c_Finite__Set_Ofinite(X38,X0) )
| ~ spl0_342
| ~ spl0_476
| ~ spl0_508 ),
inference(forward_demodulation,[],[f12561,f13758]) ).
fof(f12561,plain,
( ! [X38,X0,X8,X53] :
( c_Finite__Set_Ofinite(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X38,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X8,tc_fun(tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),X0),c_Set_Oinsert(X8)),X53),X0,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8)),X0,tc_fun(X8,tc_bool)),X8)
| ~ c_Finite__Set_Ofinite(X38,X0) )
| ~ spl0_476 ),
inference(avatar_component_clause,[],[f12560]) ).
fof(f45378,plain,
( spl0_749
| ~ spl0_158
| ~ spl0_344
| ~ spl0_387 ),
inference(avatar_split_clause,[],[f44032,f6744,f4966,f1818,f45376]) ).
fof(f45376,plain,
( spl0_749
<=> ! [X5,X1,X0] :
( hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X5),hAPP(c_fequal(X0),X1)) = X5
| hBOOL(c_in(X1,X5,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_749])]) ).
fof(f44032,plain,
( ! [X0,X1,X5] :
( hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X5),hAPP(c_fequal(X0),X1)) = X5
| hBOOL(c_in(X1,X5,X0)) )
| ~ spl0_158
| ~ spl0_344
| ~ spl0_387 ),
inference(forward_demodulation,[],[f4967,f6784]) ).
fof(f44398,plain,
( ~ spl0_55
| ~ spl0_732 ),
inference(avatar_contradiction_clause,[],[f44397]) ).
fof(f44397,plain,
( $false
| ~ spl0_55
| ~ spl0_732 ),
inference(resolution,[],[f1255,f26017]) ).
fof(f26017,plain,
( ! [X0] : ~ c_Hoare__Mirabelle_Ohoare__derivs(v_G,X0,t_a)
| ~ spl0_732 ),
inference(avatar_component_clause,[],[f26016]) ).
fof(f26016,plain,
( spl0_732
<=> ! [X0] : ~ c_Hoare__Mirabelle_Ohoare__derivs(v_G,X0,t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_732])]) ).
fof(f1255,plain,
( ! [X39,X0] : c_Hoare__Mirabelle_Ohoare__derivs(X39,c_COMBK(c_False,tc_bool,tc_Hoare__Mirabelle_Otriple(X0)),X0)
| ~ spl0_55 ),
inference(avatar_component_clause,[],[f1254]) ).
fof(f1254,plain,
( spl0_55
<=> ! [X0,X39] : c_Hoare__Mirabelle_Ohoare__derivs(X39,c_COMBK(c_False,tc_bool,tc_Hoare__Mirabelle_Otriple(X0)),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_55])]) ).
fof(f44015,plain,
( spl0_748
| ~ spl0_1
| ~ spl0_581 ),
inference(avatar_split_clause,[],[f23043,f16579,f1017,f44013]) ).
fof(f44013,plain,
( spl0_748
<=> ! [X0] : class_Complete__Lattice_Ocomplete__lattice(X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_748])]) ).
fof(f23043,plain,
( ! [X0] : class_Complete__Lattice_Ocomplete__lattice(X0)
| ~ spl0_1
| ~ spl0_581 ),
inference(superposition,[],[f1019,f16580]) ).
fof(f16580,plain,
( ! [X3,X4] : X3 = X4
| ~ spl0_581 ),
inference(avatar_component_clause,[],[f16579]) ).
fof(f44005,plain,
( spl0_747
| spl0_581
| ~ spl0_200
| ~ spl0_230 ),
inference(avatar_split_clause,[],[f2773,f2633,f2066,f16579,f44003]) ).
fof(f44003,plain,
( spl0_747
<=> ! [X4,X0,X3] : ~ c_Fun_Oinj__on(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0)),c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3,X4) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_747])]) ).
fof(f2773,plain,
( ! [X2,X3,X0,X1,X4] :
( X1 = X2
| ~ c_Fun_Oinj__on(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0)),c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3,X4) )
| ~ spl0_200
| ~ spl0_230 ),
inference(trivial_inequality_removal,[],[f2772]) ).
fof(f2772,plain,
( ! [X2,X3,X0,X1,X4] :
( c_COMBK(c_False,tc_bool,X0) != c_COMBK(c_False,tc_bool,X0)
| X1 = X2
| ~ c_Fun_Oinj__on(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0)),c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3,X4) )
| ~ spl0_200
| ~ spl0_230 ),
inference(forward_demodulation,[],[f2712,f2067]) ).
fof(f2712,plain,
( ! [X2,X3,X0,X1,X4] :
( c_COMBK(c_False,tc_bool,X0) != hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0)),X2)
| X1 = X2
| ~ c_Fun_Oinj__on(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0)),c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3,X4) )
| ~ spl0_200
| ~ spl0_230 ),
inference(superposition,[],[f2634,f2067]) ).
fof(f43985,plain,
( spl0_746
| ~ spl0_199
| ~ spl0_733 ),
inference(avatar_split_clause,[],[f27520,f27510,f2062,f43983]) ).
fof(f43983,plain,
( spl0_746
<=> ! [X2,X0,X1] : c_List_Ofilter(c_COMBK(c_False,tc_bool,X0),X2,X0) = c_List_Ofilter(c_COMBK(c_False,tc_bool,X0),c_List_Ofilter(X1,X2,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_746])]) ).
fof(f27520,plain,
( ! [X2,X0,X1] : c_List_Ofilter(c_COMBK(c_False,tc_bool,X0),X2,X0) = c_List_Ofilter(c_COMBK(c_False,tc_bool,X0),c_List_Ofilter(X1,X2,X0),X0)
| ~ spl0_199
| ~ spl0_733 ),
inference(superposition,[],[f27511,f2063]) ).
fof(f43981,plain,
( spl0_745
| ~ spl0_201
| ~ spl0_733 ),
inference(avatar_split_clause,[],[f27515,f27510,f2076,f43979]) ).
fof(f43979,plain,
( spl0_745
<=> ! [X2,X0,X1] : c_List_Ofilter(c_COMBK(c_False,tc_bool,X0),X2,X0) = c_List_Ofilter(X1,c_List_Ofilter(c_COMBK(c_False,tc_bool,X0),X2,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_745])]) ).
fof(f27515,plain,
( ! [X2,X0,X1] : c_List_Ofilter(c_COMBK(c_False,tc_bool,X0),X2,X0) = c_List_Ofilter(X1,c_List_Ofilter(c_COMBK(c_False,tc_bool,X0),X2,X0),X0)
| ~ spl0_201
| ~ spl0_733 ),
inference(superposition,[],[f27511,f2077]) ).
fof(f43720,plain,
( spl0_744
| ~ spl0_11
| ~ spl0_65
| ~ spl0_592 ),
inference(avatar_split_clause,[],[f16933,f16873,f1295,f1067,f43718]) ).
fof(f43718,plain,
( spl0_744
<=> ! [X0] : c_COMBK(c_False,tc_bool,X0) = hAPP(c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_fun(X0,tc_bool))),v_x) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_744])]) ).
fof(f1067,plain,
( spl0_11
<=> class_Orderings_Obot(tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).
fof(f1295,plain,
( spl0_65
<=> ! [X0] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_COMBK(c_False,tc_bool,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_65])]) ).
fof(f16873,plain,
( spl0_592
<=> ! [X0,X1] :
( c_Orderings_Obot__class_Obot(tc_fun(X0,X1)) = hAPP(c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_fun(X0,X1))),v_x)
| ~ class_Orderings_Obot(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_592])]) ).
fof(f16933,plain,
( ! [X0] : c_COMBK(c_False,tc_bool,X0) = hAPP(c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_fun(X0,tc_bool))),v_x)
| ~ spl0_11
| ~ spl0_65
| ~ spl0_592 ),
inference(forward_demodulation,[],[f16931,f1296]) ).
fof(f1296,plain,
( ! [X0] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_COMBK(c_False,tc_bool,X0)
| ~ spl0_65 ),
inference(avatar_component_clause,[],[f1295]) ).
fof(f16931,plain,
( ! [X0] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = hAPP(c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_fun(X0,tc_bool))),v_x)
| ~ spl0_11
| ~ spl0_592 ),
inference(resolution,[],[f16874,f1069]) ).
fof(f1069,plain,
( class_Orderings_Obot(tc_bool)
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f1067]) ).
fof(f16874,plain,
( ! [X0,X1] :
( ~ class_Orderings_Obot(X1)
| c_Orderings_Obot__class_Obot(tc_fun(X0,X1)) = hAPP(c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_fun(X0,X1))),v_x) )
| ~ spl0_592 ),
inference(avatar_component_clause,[],[f16873]) ).
fof(f43472,plain,
( spl0_743
| ~ spl0_10
| ~ spl0_588 ),
inference(avatar_split_clause,[],[f16923,f16857,f1062,f43470]) ).
fof(f43470,plain,
( spl0_743
<=> ! [X0] : c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)) = hAPP(c_Orderings_Otop__class_Otop(tc_fun(t_a,tc_fun(X0,tc_bool))),v_x) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_743])]) ).
fof(f16857,plain,
( spl0_588
<=> ! [X0,X1] :
( c_Orderings_Otop__class_Otop(tc_fun(X0,X1)) = hAPP(c_Orderings_Otop__class_Otop(tc_fun(t_a,tc_fun(X0,X1))),v_x)
| ~ class_Orderings_Otop(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_588])]) ).
fof(f16923,plain,
( ! [X0] : c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)) = hAPP(c_Orderings_Otop__class_Otop(tc_fun(t_a,tc_fun(X0,tc_bool))),v_x)
| ~ spl0_10
| ~ spl0_588 ),
inference(resolution,[],[f16858,f1064]) ).
fof(f1064,plain,
( class_Orderings_Otop(tc_bool)
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f1062]) ).
fof(f16858,plain,
( ! [X0,X1] :
( ~ class_Orderings_Otop(X1)
| c_Orderings_Otop__class_Otop(tc_fun(X0,X1)) = hAPP(c_Orderings_Otop__class_Otop(tc_fun(t_a,tc_fun(X0,X1))),v_x) )
| ~ spl0_588 ),
inference(avatar_component_clause,[],[f16857]) ).
fof(f43273,plain,
( spl0_742
| ~ spl0_170
| ~ spl0_568 ),
inference(avatar_split_clause,[],[f16519,f16054,f1869,f43271]) ).
fof(f16054,plain,
( spl0_568
<=> ! [X0,X1] : hAPP(c_fequal(X0),X1) = hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_568])]) ).
fof(f16519,plain,
( ! [X2,X0,X1] : hAPP(hAPP(c_fequal(X0),X1),X2) = hAPP(hAPP(c_fequal(X0),X2),X1)
| ~ spl0_170
| ~ spl0_568 ),
inference(superposition,[],[f1870,f16055]) ).
fof(f16055,plain,
( ! [X0,X1] : hAPP(c_fequal(X0),X1) = hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1)
| ~ spl0_568 ),
inference(avatar_component_clause,[],[f16054]) ).
fof(f43090,plain,
( spl0_741
| ~ spl0_564
| ~ spl0_566 ),
inference(avatar_split_clause,[],[f16418,f16046,f16038,f43088]) ).
fof(f16038,plain,
( spl0_564
<=> ! [X0,X1] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),X0),X1) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),X1),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_564])]) ).
fof(f16418,plain,
( ! [X0,X1] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),X1),X0)) = X0
| ~ spl0_564
| ~ spl0_566 ),
inference(superposition,[],[f16047,f16039]) ).
fof(f16039,plain,
( ! [X0,X1] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),X0),X1) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),X1),X0)
| ~ spl0_564 ),
inference(avatar_component_clause,[],[f16038]) ).
fof(f41088,plain,
( ~ spl0_5
| spl0_740
| ~ spl0_100
| ~ spl0_166
| ~ spl0_565 ),
inference(avatar_split_clause,[],[f16406,f16042,f1850,f1483,f41086,f1037]) ).
fof(f41086,plain,
( spl0_740
<=> ! [X0,X1] :
( c_False = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),X0),X1)
| c_False != X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_740])]) ).
fof(f16406,plain,
( ! [X0,X1] :
( c_False = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),X0),X1)
| c_False != X0
| ~ class_Lattices_Obounded__lattice(tc_bool) )
| ~ spl0_100
| ~ spl0_166
| ~ spl0_565 ),
inference(forward_demodulation,[],[f16405,f1485]) ).
fof(f16405,plain,
( ! [X0,X1] :
( c_False != X0
| c_Orderings_Obot__class_Obot(tc_bool) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),X0),X1)
| ~ class_Lattices_Obounded__lattice(tc_bool) )
| ~ spl0_100
| ~ spl0_166
| ~ spl0_565 ),
inference(forward_demodulation,[],[f16387,f1485]) ).
fof(f16387,plain,
( ! [X0,X1] :
( c_Orderings_Obot__class_Obot(tc_bool) != X0
| c_Orderings_Obot__class_Obot(tc_bool) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),X0),X1)
| ~ class_Lattices_Obounded__lattice(tc_bool) )
| ~ spl0_166
| ~ spl0_565 ),
inference(superposition,[],[f1851,f16043]) ).
fof(f41034,plain,
( spl0_739
| ~ spl0_563
| ~ spl0_565 ),
inference(avatar_split_clause,[],[f16344,f16042,f16034,f41032]) ).
fof(f16344,plain,
( ! [X0,X1] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),X1),X0)) = X0
| ~ spl0_563
| ~ spl0_565 ),
inference(superposition,[],[f16043,f16035]) ).
fof(f39822,plain,
( spl0_738
| ~ spl0_125
| ~ spl0_733 ),
inference(avatar_split_clause,[],[f27519,f27510,f1611,f39820]) ).
fof(f39820,plain,
( spl0_738
<=> ! [X2,X0,X1] : c_List_Ofilter(X1,X2,X0) = c_List_Ofilter(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),c_List_Ofilter(X1,X2,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_738])]) ).
fof(f27519,plain,
( ! [X2,X0,X1] : c_List_Ofilter(X1,X2,X0) = c_List_Ofilter(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),c_List_Ofilter(X1,X2,X0),X0)
| ~ spl0_125
| ~ spl0_733 ),
inference(superposition,[],[f27511,f1612]) ).
fof(f39818,plain,
( spl0_737
| ~ spl0_123
| ~ spl0_733 ),
inference(avatar_split_clause,[],[f27514,f27510,f1603,f39816]) ).
fof(f39816,plain,
( spl0_737
<=> ! [X2,X0,X1] : c_List_Ofilter(X1,X2,X0) = c_List_Ofilter(X1,c_List_Ofilter(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X2,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_737])]) ).
fof(f27514,plain,
( ! [X2,X0,X1] : c_List_Ofilter(X1,X2,X0) = c_List_Ofilter(X1,c_List_Ofilter(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X2,X0),X0)
| ~ spl0_123
| ~ spl0_733 ),
inference(superposition,[],[f27511,f1604]) ).
fof(f38621,plain,
( spl0_736
| ~ spl0_79
| ~ spl0_733 ),
inference(avatar_split_clause,[],[f27513,f27510,f1361,f38619]) ).
fof(f38619,plain,
( spl0_736
<=> ! [X2,X0,X1] : c_List_Ofilter(X1,X2,X0) = c_List_Ofilter(X1,c_List_Ofilter(X1,X2,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_736])]) ).
fof(f27513,plain,
( ! [X2,X0,X1] : c_List_Ofilter(X1,X2,X0) = c_List_Ofilter(X1,c_List_Ofilter(X1,X2,X0),X0)
| ~ spl0_79
| ~ spl0_733 ),
inference(superposition,[],[f27511,f1362]) ).
fof(f36610,plain,
( spl0_735
| ~ spl0_342
| ~ spl0_507
| ~ spl0_508 ),
inference(avatar_split_clause,[],[f26045,f13711,f13707,f4957,f36608]) ).
fof(f36608,plain,
( spl0_735
<=> ! [X5,X0,X14,X9,X8,X7] : c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,hAPP(hAPP(c_COMBB(X8,tc_fun(X0,tc_bool),X14),X9),X7),X14,tc_fun(X0,tc_bool)) = c_Complete__Lattice_Ocomplete__lattice__class_OINFI(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,hAPP(hAPP(c_COMBB(X8,tc_fun(X8,tc_bool),X14),hAPP(c_COMBC(c_Set_Oinsert(X8),X8,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8))),X7),X14,tc_fun(X8,tc_bool)),X9,X8,tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_735])]) ).
fof(f13707,plain,
( spl0_507
<=> ! [X5,X0,X14,X9,X8,X7] : c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,hAPP(hAPP(c_COMBB(X8,tc_fun(X0,tc_bool),X14),X9),X7),X14,tc_fun(X0,tc_bool)) = c_Complete__Lattice_Ocomplete__lattice__class_OINFI(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X8,tc_fun(tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),X14),c_Set_Oinsert(X8)),X7),X14,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8)),X14,tc_fun(X8,tc_bool)),X9,X8,tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_507])]) ).
fof(f26045,plain,
( ! [X0,X8,X9,X7,X14,X5] : c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,hAPP(hAPP(c_COMBB(X8,tc_fun(X0,tc_bool),X14),X9),X7),X14,tc_fun(X0,tc_bool)) = c_Complete__Lattice_Ocomplete__lattice__class_OINFI(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,hAPP(hAPP(c_COMBB(X8,tc_fun(X8,tc_bool),X14),hAPP(c_COMBC(c_Set_Oinsert(X8),X8,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8))),X7),X14,tc_fun(X8,tc_bool)),X9,X8,tc_fun(X0,tc_bool))
| ~ spl0_342
| ~ spl0_507
| ~ spl0_508 ),
inference(forward_demodulation,[],[f13708,f13758]) ).
fof(f13708,plain,
( ! [X0,X8,X9,X7,X14,X5] : c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,hAPP(hAPP(c_COMBB(X8,tc_fun(X0,tc_bool),X14),X9),X7),X14,tc_fun(X0,tc_bool)) = c_Complete__Lattice_Ocomplete__lattice__class_OINFI(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X8,tc_fun(tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),X14),c_Set_Oinsert(X8)),X7),X14,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8)),X14,tc_fun(X8,tc_bool)),X9,X8,tc_fun(X0,tc_bool))
| ~ spl0_507 ),
inference(avatar_component_clause,[],[f13707]) ).
fof(f36606,plain,
( spl0_734
| ~ spl0_342
| ~ spl0_508 ),
inference(avatar_split_clause,[],[f26037,f13711,f4957,f36604]) ).
fof(f36604,plain,
( spl0_734
<=> ! [X5,X0,X14,X9,X8,X7] : c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,hAPP(hAPP(c_COMBB(X8,tc_fun(X0,tc_bool),X14),X9),X7),X14,tc_fun(X0,tc_bool)) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,hAPP(hAPP(c_COMBB(X8,tc_fun(X8,tc_bool),X14),hAPP(c_COMBC(c_Set_Oinsert(X8),X8,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8))),X7),X14,tc_fun(X8,tc_bool)),X9,X8,tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_734])]) ).
fof(f26037,plain,
( ! [X0,X8,X9,X7,X14,X5] : c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,hAPP(hAPP(c_COMBB(X8,tc_fun(X0,tc_bool),X14),X9),X7),X14,tc_fun(X0,tc_bool)) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,hAPP(hAPP(c_COMBB(X8,tc_fun(X8,tc_bool),X14),hAPP(c_COMBC(c_Set_Oinsert(X8),X8,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8))),X7),X14,tc_fun(X8,tc_bool)),X9,X8,tc_fun(X0,tc_bool))
| ~ spl0_342
| ~ spl0_508 ),
inference(forward_demodulation,[],[f13712,f13758]) ).
fof(f27512,plain,
( spl0_733
| ~ spl0_16
| ~ spl0_404
| ~ spl0_406 ),
inference(avatar_split_clause,[],[f26052,f7160,f7152,f1090,f27510]) ).
fof(f7152,plain,
( spl0_404
<=> ! [X11,X57,X0,X66] : c_List_Ofilter(X11,c_List_Ofilter(X57,X66,X0),X0) = c_List_Ofilter(hAPP(hAPP(c_COMBS(X0,tc_bool,tc_bool),hAPP(hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),X0),c_and),X57)),X11),X66,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_404])]) ).
fof(f26052,plain,
( ! [X0,X11,X57,X66] : c_List_Ofilter(X11,c_List_Ofilter(X57,X66,X0),X0) = c_List_Ofilter(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X57),X11),X66,X0)
| ~ spl0_16
| ~ spl0_404
| ~ spl0_406 ),
inference(forward_demodulation,[],[f7153,f7676]) ).
fof(f7153,plain,
( ! [X0,X11,X57,X66] : c_List_Ofilter(X11,c_List_Ofilter(X57,X66,X0),X0) = c_List_Ofilter(hAPP(hAPP(c_COMBS(X0,tc_bool,tc_bool),hAPP(hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),X0),c_and),X57)),X11),X66,X0)
| ~ spl0_404 ),
inference(avatar_component_clause,[],[f7152]) ).
fof(f26018,plain,
( spl0_732
| spl0_281
| ~ spl0_581 ),
inference(avatar_split_clause,[],[f23015,f16579,f3862,f26016]) ).
fof(f23015,plain,
( ! [X0] : ~ c_Hoare__Mirabelle_Ohoare__derivs(v_G,X0,t_a)
| spl0_281
| ~ spl0_581 ),
inference(superposition,[],[f3864,f16580]) ).
fof(f22236,plain,
( spl0_731
| spl0_581
| ~ spl0_178
| ~ spl0_230 ),
inference(avatar_split_clause,[],[f2770,f2633,f1976,f16579,f22234]) ).
fof(f22234,plain,
( spl0_731
<=> ! [X4,X0,X3] : ~ c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool))),c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3,X4) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_731])]) ).
fof(f2770,plain,
( ! [X2,X3,X0,X1,X4] :
( X1 = X2
| ~ c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool))),c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3,X4) )
| ~ spl0_178
| ~ spl0_230 ),
inference(trivial_inequality_removal,[],[f2769]) ).
fof(f2769,plain,
( ! [X2,X3,X0,X1,X4] :
( c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)) != c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool))
| X1 = X2
| ~ c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool))),c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3,X4) )
| ~ spl0_178
| ~ spl0_230 ),
inference(forward_demodulation,[],[f2710,f1977]) ).
fof(f2710,plain,
( ! [X2,X3,X0,X1,X4] :
( c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)) != hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool))),X2)
| X1 = X2
| ~ c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool))),c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3,X4) )
| ~ spl0_178
| ~ spl0_230 ),
inference(superposition,[],[f2634,f1977]) ).
fof(f22232,plain,
( spl0_730
| ~ spl0_183
| ~ spl0_225 ),
inference(avatar_split_clause,[],[f2623,f2299,f1997,f22230]) ).
fof(f22230,plain,
( spl0_730
<=> ! [X2,X0,X1] :
( ~ hBOOL(c_in(X0,X1,X2))
| ~ class_Complete__Lattice_Ocomplete__lattice(X2)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X2),hAPP(c_Complete__Lattice_OSup__class_OSup(X2),X1)),X0))
| ~ class_Orderings_Opreorder(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_730])]) ).
fof(f2623,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(c_in(X0,X1,X2))
| ~ class_Complete__Lattice_Ocomplete__lattice(X2)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X2),hAPP(c_Complete__Lattice_OSup__class_OSup(X2),X1)),X0))
| ~ class_Orderings_Opreorder(X2) )
| ~ spl0_183
| ~ spl0_225 ),
inference(resolution,[],[f2300,f1998]) ).
fof(f22228,plain,
( spl0_729
| ~ spl0_183
| ~ spl0_218 ),
inference(avatar_split_clause,[],[f2555,f2271,f1997,f22226]) ).
fof(f22226,plain,
( spl0_729
<=> ! [X2,X0,X1] :
( ~ hBOOL(c_in(X0,X1,X2))
| ~ class_Complete__Lattice_Ocomplete__lattice(X2)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X2),X0),hAPP(c_Complete__Lattice_OInf__class_OInf(X2),X1)))
| ~ class_Orderings_Opreorder(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_729])]) ).
fof(f2555,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(c_in(X0,X1,X2))
| ~ class_Complete__Lattice_Ocomplete__lattice(X2)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X2),X0),hAPP(c_Complete__Lattice_OInf__class_OInf(X2),X1)))
| ~ class_Orderings_Opreorder(X2) )
| ~ spl0_183
| ~ spl0_218 ),
inference(resolution,[],[f2272,f1998]) ).
fof(f22224,plain,
( spl0_728
| ~ spl0_135
| ~ spl0_227 ),
inference(avatar_split_clause,[],[f3971,f2580,f1652,f22222]) ).
fof(f22222,plain,
( spl0_728
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(X1,c_SetInterval_Oord__class_OatLeastAtMost(X0,X0,tc_bool),tc_bool),X2))
| X0 = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_728])]) ).
fof(f3971,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(X1,c_SetInterval_Oord__class_OatLeastAtMost(X0,X0,tc_bool),tc_bool),X2))
| X0 = X2 )
| ~ spl0_135
| ~ spl0_227 ),
inference(superposition,[],[f1653,f2581]) ).
fof(f22220,plain,
( spl0_727
| ~ spl0_30
| ~ spl0_162 ),
inference(avatar_split_clause,[],[f1932,f1834,f1147,f22218]) ).
fof(f22218,plain,
( spl0_727
<=> ! [X0,X3,X2,X1] :
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,X1)),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,X1)),X2),X3)) = X2
| ~ class_Lattices_Olattice(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_727])]) ).
fof(f1834,plain,
( spl0_162
<=> ! [X2,X0,X1] :
( ~ class_Lattices_Olattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2)) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_162])]) ).
fof(f1932,plain,
( ! [X2,X3,X0,X1] :
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,X1)),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,X1)),X2),X3)) = X2
| ~ class_Lattices_Olattice(X1) )
| ~ spl0_30
| ~ spl0_162 ),
inference(resolution,[],[f1835,f1148]) ).
fof(f1835,plain,
( ! [X2,X0,X1] :
( ~ class_Lattices_Olattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2)) = X1 )
| ~ spl0_162 ),
inference(avatar_component_clause,[],[f1834]) ).
fof(f22216,plain,
( spl0_726
| ~ spl0_30
| ~ spl0_161 ),
inference(avatar_split_clause,[],[f1930,f1830,f1147,f22214]) ).
fof(f22214,plain,
( spl0_726
<=> ! [X0,X3,X2,X1] :
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,X1)),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,X1)),X2),X3)) = X2
| ~ class_Lattices_Olattice(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_726])]) ).
fof(f1830,plain,
( spl0_161
<=> ! [X2,X0,X1] :
( ~ class_Lattices_Olattice(X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2)) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_161])]) ).
fof(f1930,plain,
( ! [X2,X3,X0,X1] :
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,X1)),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,X1)),X2),X3)) = X2
| ~ class_Lattices_Olattice(X1) )
| ~ spl0_30
| ~ spl0_161 ),
inference(resolution,[],[f1831,f1148]) ).
fof(f1831,plain,
( ! [X2,X0,X1] :
( ~ class_Lattices_Olattice(X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2)) = X1 )
| ~ spl0_161 ),
inference(avatar_component_clause,[],[f1830]) ).
fof(f22212,plain,
( spl0_725
| ~ spl0_25
| ~ spl0_156 ),
inference(avatar_split_clause,[],[f1912,f1810,f1127,f22210]) ).
fof(f22210,plain,
( spl0_725
<=> ! [X0,X3,X2,X1] :
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,X1)),X2),X3) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,X1)),X3),X2)
| ~ class_Lattices_Olattice(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_725])]) ).
fof(f1810,plain,
( spl0_156
<=> ! [X2,X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_156])]) ).
fof(f1912,plain,
( ! [X2,X3,X0,X1] :
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,X1)),X2),X3) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,X1)),X3),X2)
| ~ class_Lattices_Olattice(X1) )
| ~ spl0_25
| ~ spl0_156 ),
inference(resolution,[],[f1811,f1128]) ).
fof(f1811,plain,
( ! [X2,X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X2),X1) )
| ~ spl0_156 ),
inference(avatar_component_clause,[],[f1810]) ).
fof(f22208,plain,
( spl0_724
| ~ spl0_26
| ~ spl0_154 ),
inference(avatar_split_clause,[],[f1908,f1802,f1131,f22206]) ).
fof(f22206,plain,
( spl0_724
<=> ! [X0,X3,X2,X1] :
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,X1)),X2),X3) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,X1)),X3),X2)
| ~ class_Lattices_Olattice(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_724])]) ).
fof(f1131,plain,
( spl0_26
<=> ! [X75,X74] :
( ~ class_Lattices_Olattice(X75)
| class_Lattices_Olower__semilattice(tc_fun(X74,X75)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_26])]) ).
fof(f1802,plain,
( spl0_154
<=> ! [X2,X0,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X1) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_154])]) ).
fof(f1908,plain,
( ! [X2,X3,X0,X1] :
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,X1)),X2),X3) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,X1)),X3),X2)
| ~ class_Lattices_Olattice(X1) )
| ~ spl0_26
| ~ spl0_154 ),
inference(resolution,[],[f1803,f1132]) ).
fof(f1132,plain,
( ! [X74,X75] :
( class_Lattices_Olower__semilattice(tc_fun(X74,X75))
| ~ class_Lattices_Olattice(X75) )
| ~ spl0_26 ),
inference(avatar_component_clause,[],[f1131]) ).
fof(f1803,plain,
( ! [X2,X0,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X1) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2) )
| ~ spl0_154 ),
inference(avatar_component_clause,[],[f1802]) ).
fof(f21681,plain,
( spl0_723
| ~ spl0_227
| ~ spl0_717 ),
inference(avatar_split_clause,[],[f21486,f21450,f2580,f21679]) ).
fof(f21679,plain,
( spl0_723
<=> ! [X0,X1] :
( c_SetInterval_Oord__class_OatLeastAtMost(X0,X0,tc_bool) != c_SetInterval_Oord__class_OatLeastAtMost(X1,X1,tc_bool)
| X0 = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_723])]) ).
fof(f21450,plain,
( spl0_717
<=> ! [X0,X1] :
( c_SetInterval_Oord__class_OatLeastAtMost(X0,X0,tc_bool) != hAPP(c_fequal(tc_bool),X1)
| X0 = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_717])]) ).
fof(f21486,plain,
( ! [X0,X1] :
( c_SetInterval_Oord__class_OatLeastAtMost(X0,X0,tc_bool) != c_SetInterval_Oord__class_OatLeastAtMost(X1,X1,tc_bool)
| X0 = X1 )
| ~ spl0_227
| ~ spl0_717 ),
inference(superposition,[],[f21451,f2581]) ).
fof(f21451,plain,
( ! [X0,X1] :
( c_SetInterval_Oord__class_OatLeastAtMost(X0,X0,tc_bool) != hAPP(c_fequal(tc_bool),X1)
| X0 = X1 )
| ~ spl0_717 ),
inference(avatar_component_clause,[],[f21450]) ).
fof(f21472,plain,
( spl0_722
| ~ spl0_130
| ~ spl0_200
| ~ spl0_440 ),
inference(avatar_split_clause,[],[f9668,f9347,f2066,f1631,f21470]) ).
fof(f21470,plain,
( spl0_722
<=> ! [X2,X0,X1] : c_COMBK(c_False,tc_bool,X0) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X1),hAPP(hAPP(c_Set_Oinsert(X0),X2),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_722])]) ).
fof(f9668,plain,
( ! [X2,X0,X1] : c_COMBK(c_False,tc_bool,X0) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X1),hAPP(hAPP(c_Set_Oinsert(X0),X2),X1))
| ~ spl0_130
| ~ spl0_200
| ~ spl0_440 ),
inference(forward_demodulation,[],[f9618,f2067]) ).
fof(f9618,plain,
( ! [X2,X0,X1] : hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X1),hAPP(hAPP(c_Set_Oinsert(X0),X2),X1)) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0)),hAPP(c_fequal(X0),X2))
| ~ spl0_130
| ~ spl0_440 ),
inference(superposition,[],[f9348,f1632]) ).
fof(f21468,plain,
( spl0_721
| ~ spl0_122
| ~ spl0_391 ),
inference(avatar_split_clause,[],[f7006,f6760,f1599,f21466]) ).
fof(f21466,plain,
( spl0_721
<=> ! [X0,X3,X2,X1] :
( ~ c_Finite__Set_Ofinite(hAPP(hAPP(c_Set_Oinsert(X0),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X2),X3)),X0)
| c_Finite__Set_Ofinite(X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_721])]) ).
fof(f7006,plain,
( ! [X2,X3,X0,X1] :
( ~ c_Finite__Set_Ofinite(hAPP(hAPP(c_Set_Oinsert(X0),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X2),X3)),X0)
| c_Finite__Set_Ofinite(X3,X0) )
| ~ spl0_122
| ~ spl0_391 ),
inference(superposition,[],[f1600,f6761]) ).
fof(f21464,plain,
( spl0_720
| ~ spl0_99
| ~ spl0_390 ),
inference(avatar_split_clause,[],[f6935,f6756,f1472,f21462]) ).
fof(f21462,plain,
( spl0_720
<=> ! [X0,X3,X2,X1] : c_COMBK(c_False,tc_bool,X0) != hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X2),hAPP(hAPP(c_Set_Oinsert(X0),X1),X3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_720])]) ).
fof(f1472,plain,
( spl0_99
<=> ! [X5,X0,X3] : hAPP(hAPP(c_Set_Oinsert(X0),X3),X5) != c_COMBK(c_False,tc_bool,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_99])]) ).
fof(f6935,plain,
( ! [X2,X3,X0,X1] : c_COMBK(c_False,tc_bool,X0) != hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X2),hAPP(hAPP(c_Set_Oinsert(X0),X1),X3))
| ~ spl0_99
| ~ spl0_390 ),
inference(superposition,[],[f1473,f6757]) ).
fof(f1473,plain,
( ! [X3,X0,X5] : hAPP(hAPP(c_Set_Oinsert(X0),X3),X5) != c_COMBK(c_False,tc_bool,X0)
| ~ spl0_99 ),
inference(avatar_component_clause,[],[f1472]) ).
fof(f21460,plain,
( spl0_719
| ~ spl0_121
| ~ spl0_390 ),
inference(avatar_split_clause,[],[f6879,f6756,f1595,f21458]) ).
fof(f21458,plain,
( spl0_719
<=> ! [X0,X3,X2,X1] :
( ~ c_Finite__Set_Ofinite(hAPP(hAPP(c_Set_Oinsert(X0),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X3)),X0)
| c_Finite__Set_Ofinite(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_719])]) ).
fof(f6879,plain,
( ! [X2,X3,X0,X1] :
( ~ c_Finite__Set_Ofinite(hAPP(hAPP(c_Set_Oinsert(X0),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X3)),X0)
| c_Finite__Set_Ofinite(X1,X0) )
| ~ spl0_121
| ~ spl0_390 ),
inference(superposition,[],[f1596,f6757]) ).
fof(f21456,plain,
( spl0_718
| ~ spl0_120
| ~ spl0_330 ),
inference(avatar_split_clause,[],[f5095,f4908,f1591,f21454]) ).
fof(f21454,plain,
( spl0_718
<=> ! [X2,X3,X4,X0,X5,X1] : hAPP(c_Fun_Ocomp(c_Fun_Ocomp(c_COMBK(X0,X1,X2),X3,X2,X1,X5),X4,X5,X1,t_a),v_x) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_718])]) ).
fof(f5095,plain,
( ! [X2,X3,X0,X1,X4,X5] : hAPP(c_Fun_Ocomp(c_Fun_Ocomp(c_COMBK(X0,X1,X2),X3,X2,X1,X5),X4,X5,X1,t_a),v_x) = X0
| ~ spl0_120
| ~ spl0_330 ),
inference(superposition,[],[f1592,f4909]) ).
fof(f21452,plain,
( spl0_717
| ~ spl0_227
| ~ spl0_689 ),
inference(avatar_split_clause,[],[f21216,f21018,f2580,f21450]) ).
fof(f21018,plain,
( spl0_689
<=> ! [X2,X0,X1] :
( hAPP(c_fequal(X0),X1) != hAPP(c_fequal(X0),X2)
| X1 = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_689])]) ).
fof(f21216,plain,
( ! [X0,X1] :
( c_SetInterval_Oord__class_OatLeastAtMost(X0,X0,tc_bool) != hAPP(c_fequal(tc_bool),X1)
| X0 = X1 )
| ~ spl0_227
| ~ spl0_689 ),
inference(superposition,[],[f21019,f2581]) ).
fof(f21019,plain,
( ! [X2,X0,X1] :
( hAPP(c_fequal(X0),X1) != hAPP(c_fequal(X0),X2)
| X1 = X2 )
| ~ spl0_689 ),
inference(avatar_component_clause,[],[f21018]) ).
fof(f21300,plain,
( spl0_716
| ~ spl0_13
| ~ spl0_146
| ~ spl0_309 ),
inference(avatar_split_clause,[],[f4823,f4581,f1716,f1077,f21298]) ).
fof(f21298,plain,
( spl0_716
<=> ! [X0,X3,X2,X1] : hBOOL(hAPP(hAPP(c_lessequals(tc_bool),hAPP(X0,X1)),hAPP(hAPP(hAPP(c_Set_Oinsert(X2),X3),X0),X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_716])]) ).
fof(f4823,plain,
( ! [X2,X3,X0,X1] :
( ~ class_HOL_Oord(tc_bool)
| hBOOL(hAPP(hAPP(c_lessequals(tc_bool),hAPP(X0,X1)),hAPP(hAPP(hAPP(c_Set_Oinsert(X2),X3),X0),X1))) )
| ~ spl0_146
| ~ spl0_309 ),
inference(resolution,[],[f4582,f1717]) ).
fof(f21296,plain,
( spl0_715
| ~ spl0_108
| ~ spl0_289 ),
inference(avatar_split_clause,[],[f4284,f3903,f1516,f21294]) ).
fof(f21294,plain,
( spl0_715
<=> ! [X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool))),X1))
| c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_715])]) ).
fof(f4284,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool))),X1))
| c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)) = X1 )
| ~ spl0_108
| ~ spl0_289 ),
inference(resolution,[],[f3904,f1517]) ).
fof(f21292,plain,
( spl0_714
| ~ spl0_64
| ~ spl0_288 ),
inference(avatar_split_clause,[],[f4133,f3899,f1291,f21290]) ).
fof(f21290,plain,
( spl0_714
<=> ! [X3,X4,X0,X5,X2,X1] :
( ~ hBOOL(c_in(X0,X1,X2))
| hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,hAPP(c_Set_Oinsert(X3),X4),X2,tc_fun(X5,tc_bool)),X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_714])]) ).
fof(f4133,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ hBOOL(c_in(X0,X1,X2))
| hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,hAPP(c_Set_Oinsert(X3),X4),X2,tc_fun(X5,tc_bool)),X4)) )
| ~ spl0_64
| ~ spl0_288 ),
inference(resolution,[],[f3900,f1292]) ).
fof(f21288,plain,
( spl0_713
| ~ spl0_62
| ~ spl0_288 ),
inference(avatar_split_clause,[],[f4132,f3899,f1283,f21286]) ).
fof(f21286,plain,
( spl0_713
<=> ! [X4,X0,X3,X2,X1] :
( ~ hBOOL(c_in(X0,X1,X2))
| hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,c_lessequals(X3),X2,tc_fun(X4,tc_bool)),X0))
| ~ class_Orderings_Oorder(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_713])]) ).
fof(f4132,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ hBOOL(c_in(X0,X1,X2))
| hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,c_lessequals(X3),X2,tc_fun(X4,tc_bool)),X0))
| ~ class_Orderings_Oorder(X3) )
| ~ spl0_62
| ~ spl0_288 ),
inference(resolution,[],[f3900,f1284]) ).
fof(f21284,plain,
( spl0_712
| ~ spl0_63
| ~ spl0_288 ),
inference(avatar_split_clause,[],[f4131,f3899,f1287,f21282]) ).
fof(f21282,plain,
( spl0_712
<=> ! [X4,X0,X3,X2,X1] :
( ~ hBOOL(c_in(X0,X1,X2))
| hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,c_lessequals(X3),X2,tc_fun(X4,tc_bool)),X0))
| ~ class_Orderings_Opreorder(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_712])]) ).
fof(f4131,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ hBOOL(c_in(X0,X1,X2))
| hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,c_lessequals(X3),X2,tc_fun(X4,tc_bool)),X0))
| ~ class_Orderings_Opreorder(X3) )
| ~ spl0_63
| ~ spl0_288 ),
inference(resolution,[],[f3900,f1288]) ).
fof(f21280,plain,
( spl0_711
| ~ spl0_61
| ~ spl0_288 ),
inference(avatar_split_clause,[],[f4130,f3899,f1279,f21278]) ).
fof(f21278,plain,
( spl0_711
<=> ! [X4,X0,X3,X2,X1] :
( ~ hBOOL(c_in(X0,X1,X2))
| hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,c_lessequals(tc_fun(X3,tc_bool)),X2,tc_fun(X4,tc_bool)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_711])]) ).
fof(f4130,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ hBOOL(c_in(X0,X1,X2))
| hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,c_lessequals(tc_fun(X3,tc_bool)),X2,tc_fun(X4,tc_bool)),X0)) )
| ~ spl0_61
| ~ spl0_288 ),
inference(resolution,[],[f3900,f1280]) ).
fof(f21276,plain,
( spl0_710
| ~ spl0_8
| ~ spl0_272 ),
inference(avatar_split_clause,[],[f3797,f3639,f1052,f21274]) ).
fof(f21274,plain,
( spl0_710
<=> ! [X0,X1] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),X0),X1) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),X0),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_710])]) ).
fof(f3797,plain,
( ! [X0,X1] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),X0),X1) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),X0),X1))
| ~ spl0_8
| ~ spl0_272 ),
inference(resolution,[],[f3640,f1054]) ).
fof(f21272,plain,
( spl0_709
| ~ spl0_2
| ~ spl0_269 ),
inference(avatar_split_clause,[],[f3732,f3627,f1022,f21270]) ).
fof(f21270,plain,
( spl0_709
<=> ! [X0,X1] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),X0),X1) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),X0),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_709])]) ).
fof(f3732,plain,
( ! [X0,X1] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),X0),X1) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),X0),X1))
| ~ spl0_2
| ~ spl0_269 ),
inference(resolution,[],[f3628,f1024]) ).
fof(f21268,plain,
( spl0_708
| ~ spl0_132
| ~ spl0_256 ),
inference(avatar_split_clause,[],[f3371,f3093,f1639,f21266]) ).
fof(f21266,plain,
( spl0_708
<=> ! [X0,X1] :
( c_COMBK(c_False,tc_bool,X0) != X1
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X1),c_COMBK(c_False,tc_bool,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_708])]) ).
fof(f3371,plain,
( ! [X0,X1] :
( c_COMBK(c_False,tc_bool,X0) != X1
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X1),c_COMBK(c_False,tc_bool,X0))) )
| ~ spl0_132
| ~ spl0_256 ),
inference(superposition,[],[f3094,f1640]) ).
fof(f21258,plain,
( spl0_707
| ~ spl0_178
| ~ spl0_256 ),
inference(avatar_split_clause,[],[f3364,f3093,f1976,f21256]) ).
fof(f21256,plain,
( spl0_707
<=> ! [X0,X1] :
( c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)) != X1
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool))),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_707])]) ).
fof(f3364,plain,
( ! [X0,X1] :
( c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)) != X1
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool))),X1)) )
| ~ spl0_178
| ~ spl0_256 ),
inference(superposition,[],[f3094,f1977]) ).
fof(f21254,plain,
( spl0_706
| ~ spl0_223
| ~ spl0_234 ),
inference(avatar_split_clause,[],[f3004,f2649,f2291,f21252]) ).
fof(f21252,plain,
( spl0_706
<=> ! [X0,X3,X2,X1] :
( hBOOL(c_in(X3,hAPP(hAPP(c_Set_Oinsert(X0),X1),X2),X0))
| ~ hBOOL(c_in(X3,hAPP(c_fequal(X0),X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_706])]) ).
fof(f3004,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(c_in(X3,hAPP(hAPP(c_Set_Oinsert(X0),X1),X2),X0))
| ~ hBOOL(c_in(X3,hAPP(c_fequal(X0),X1),X0)) )
| ~ spl0_223
| ~ spl0_234 ),
inference(superposition,[],[f2292,f2650]) ).
fof(f21250,plain,
( spl0_705
| ~ spl0_220
| ~ spl0_234 ),
inference(avatar_split_clause,[],[f3002,f2649,f2279,f21248]) ).
fof(f21248,plain,
( spl0_705
<=> ! [X4,X0,X3,X2,X1] :
( ~ c_Fun_Oinj__on(X3,hAPP(hAPP(c_Set_Oinsert(X0),X1),X2),X0,X4)
| c_Fun_Oinj__on(X3,hAPP(c_fequal(X0),X1),X0,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_705])]) ).
fof(f3002,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ c_Fun_Oinj__on(X3,hAPP(hAPP(c_Set_Oinsert(X0),X1),X2),X0,X4)
| c_Fun_Oinj__on(X3,hAPP(c_fequal(X0),X1),X0,X4) )
| ~ spl0_220
| ~ spl0_234 ),
inference(superposition,[],[f2280,f2650]) ).
fof(f21246,plain,
( spl0_704
| ~ spl0_214
| ~ spl0_234 ),
inference(avatar_split_clause,[],[f2982,f2649,f2255,f21244]) ).
fof(f21244,plain,
( spl0_704
<=> ! [X2,X0,X1] : hAPP(hAPP(c_Set_Oinsert(X0),X1),X2) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X2),hAPP(c_fequal(X0),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_704])]) ).
fof(f2982,plain,
( ! [X2,X0,X1] : hAPP(hAPP(c_Set_Oinsert(X0),X1),X2) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X2),hAPP(c_fequal(X0),X1))
| ~ spl0_214
| ~ spl0_234 ),
inference(superposition,[],[f2650,f2256]) ).
fof(f21242,plain,
( spl0_703
| ~ spl0_127
| ~ spl0_233 ),
inference(avatar_split_clause,[],[f2943,f2645,f1619,f21240]) ).
fof(f21240,plain,
( spl0_703
<=> ! [X3,X4,X0,X5,X2,X1] :
( c_Finite__Set_Ofinite(hAPP(hAPP(hAPP(c_COMBS(X3,X4,X5),c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool))),X2),X1),X0)
| ~ c_Finite__Set_Ofinite(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_703])]) ).
fof(f2943,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( c_Finite__Set_Ofinite(hAPP(hAPP(hAPP(c_COMBS(X3,X4,X5),c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool))),X2),X1),X0)
| ~ c_Finite__Set_Ofinite(X1,X0) )
| ~ spl0_127
| ~ spl0_233 ),
inference(superposition,[],[f1620,f2646]) ).
fof(f21238,plain,
( spl0_702
| ~ spl0_119
| ~ spl0_233 ),
inference(avatar_split_clause,[],[f2941,f2645,f1587,f21236]) ).
fof(f21236,plain,
( spl0_702
<=> ! [X3,X4,X0,X5,X2,X1] :
( c_Finite__Set_Ofinite(hAPP(hAPP(hAPP(c_COMBS(X3,X4,X5),c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool))),X2),X1),X0)
| ~ c_Finite__Set_Ofinite(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_702])]) ).
fof(f2941,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( c_Finite__Set_Ofinite(hAPP(hAPP(hAPP(c_COMBS(X3,X4,X5),c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool))),X2),X1),X0)
| ~ c_Finite__Set_Ofinite(X1,X0) )
| ~ spl0_119
| ~ spl0_233 ),
inference(superposition,[],[f1588,f2646]) ).
fof(f21234,plain,
( spl0_701
| ~ spl0_92
| ~ spl0_233 ),
inference(avatar_split_clause,[],[f2927,f2645,f1427,f21232]) ).
fof(f21232,plain,
( spl0_701
<=> ! [X3,X4,X0,X5,X2,X1] :
( ~ c_Finite__Set_Ofinite(hAPP(hAPP(hAPP(c_COMBS(X3,X4,X5),c_Set_Oinsert(X0)),X2),X1),X0)
| c_Finite__Set_Ofinite(hAPP(X2,X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_701])]) ).
fof(f2927,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ c_Finite__Set_Ofinite(hAPP(hAPP(hAPP(c_COMBS(X3,X4,X5),c_Set_Oinsert(X0)),X2),X1),X0)
| c_Finite__Set_Ofinite(hAPP(X2,X1),X0) )
| ~ spl0_92
| ~ spl0_233 ),
inference(superposition,[],[f1428,f2646]) ).
fof(f21230,plain,
( spl0_700
| ~ spl0_90
| ~ spl0_233 ),
inference(avatar_split_clause,[],[f2926,f2645,f1419,f21228]) ).
fof(f21228,plain,
( spl0_700
<=> ! [X3,X4,X0,X5,X2,X1] :
( c_Finite__Set_Ofinite(hAPP(hAPP(hAPP(c_COMBS(X3,X4,X5),c_Set_Oinsert(X0)),X2),X1),X0)
| ~ c_Finite__Set_Ofinite(hAPP(X2,X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_700])]) ).
fof(f2926,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( c_Finite__Set_Ofinite(hAPP(hAPP(hAPP(c_COMBS(X3,X4,X5),c_Set_Oinsert(X0)),X2),X1),X0)
| ~ c_Finite__Set_Ofinite(hAPP(X2,X1),X0) )
| ~ spl0_90
| ~ spl0_233 ),
inference(superposition,[],[f1420,f2646]) ).
fof(f21226,plain,
( spl0_699
| ~ spl0_121
| ~ spl0_233 ),
inference(avatar_split_clause,[],[f2902,f2645,f1595,f21224]) ).
fof(f21224,plain,
( spl0_699
<=> ! [X3,X4,X0,X5,X2,X1] :
( ~ c_Finite__Set_Ofinite(hAPP(hAPP(hAPP(c_COMBS(X3,X4,X5),c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool))),X2),X1),X0)
| c_Finite__Set_Ofinite(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_699])]) ).
fof(f2902,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ c_Finite__Set_Ofinite(hAPP(hAPP(hAPP(c_COMBS(X3,X4,X5),c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool))),X2),X1),X0)
| c_Finite__Set_Ofinite(X1,X0) )
| ~ spl0_121
| ~ spl0_233 ),
inference(superposition,[],[f1596,f2646]) ).
fof(f21222,plain,
( spl0_698
| ~ spl0_146
| ~ spl0_183 ),
inference(avatar_split_clause,[],[f2130,f1997,f1716,f21220]) ).
fof(f21220,plain,
( spl0_698
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Set_Oinsert(X0),X1),X2)),X2))
| ~ class_Orderings_Opreorder(tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_698])]) ).
fof(f2130,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Set_Oinsert(X0),X1),X2)),X2))
| ~ class_Orderings_Opreorder(tc_fun(X0,tc_bool)) )
| ~ spl0_146
| ~ spl0_183 ),
inference(resolution,[],[f1998,f1717]) ).
fof(f21215,plain,
( spl0_697
| ~ spl0_24
| ~ spl0_117 ),
inference(avatar_split_clause,[],[f1584,f1553,f1123,f21213]) ).
fof(f21213,plain,
( spl0_697
<=> ! [X0,X1] :
( c_Orderings_Obot__class_Obot(tc_fun(X0,X1)) = hAPP(c_Complete__Lattice_OSup__class_OSup(tc_fun(X0,X1)),c_COMBK(c_False,tc_bool,tc_fun(X0,X1)))
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_697])]) ).
fof(f1553,plain,
( spl0_117
<=> ! [X0] :
( c_Orderings_Obot__class_Obot(X0) = hAPP(c_Complete__Lattice_OSup__class_OSup(X0),c_COMBK(c_False,tc_bool,X0))
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_117])]) ).
fof(f1584,plain,
( ! [X0,X1] :
( c_Orderings_Obot__class_Obot(tc_fun(X0,X1)) = hAPP(c_Complete__Lattice_OSup__class_OSup(tc_fun(X0,X1)),c_COMBK(c_False,tc_bool,tc_fun(X0,X1)))
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) )
| ~ spl0_24
| ~ spl0_117 ),
inference(resolution,[],[f1554,f1124]) ).
fof(f1554,plain,
( ! [X0] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
| c_Orderings_Obot__class_Obot(X0) = hAPP(c_Complete__Lattice_OSup__class_OSup(X0),c_COMBK(c_False,tc_bool,X0)) )
| ~ spl0_117 ),
inference(avatar_component_clause,[],[f1553]) ).
fof(f21211,plain,
( spl0_696
| ~ spl0_24
| ~ spl0_116 ),
inference(avatar_split_clause,[],[f1582,f1549,f1123,f21209]) ).
fof(f21209,plain,
( spl0_696
<=> ! [X0,X1] :
( c_Orderings_Otop__class_Otop(tc_fun(X0,X1)) = hAPP(c_Complete__Lattice_OInf__class_OInf(tc_fun(X0,X1)),c_COMBK(c_False,tc_bool,tc_fun(X0,X1)))
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_696])]) ).
fof(f1549,plain,
( spl0_116
<=> ! [X0] :
( c_Orderings_Otop__class_Otop(X0) = hAPP(c_Complete__Lattice_OInf__class_OInf(X0),c_COMBK(c_False,tc_bool,X0))
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_116])]) ).
fof(f1582,plain,
( ! [X0,X1] :
( c_Orderings_Otop__class_Otop(tc_fun(X0,X1)) = hAPP(c_Complete__Lattice_OInf__class_OInf(tc_fun(X0,X1)),c_COMBK(c_False,tc_bool,tc_fun(X0,X1)))
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) )
| ~ spl0_24
| ~ spl0_116 ),
inference(resolution,[],[f1550,f1124]) ).
fof(f1550,plain,
( ! [X0] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
| c_Orderings_Otop__class_Otop(X0) = hAPP(c_Complete__Lattice_OInf__class_OInf(X0),c_COMBK(c_False,tc_bool,X0)) )
| ~ spl0_116 ),
inference(avatar_component_clause,[],[f1549]) ).
fof(f21207,plain,
( spl0_695
| ~ spl0_28
| ~ spl0_111 ),
inference(avatar_split_clause,[],[f1572,f1529,f1139,f21205]) ).
fof(f21205,plain,
( spl0_695
<=> ! [X2,X0,X1] :
( c_Orderings_Obot__class_Obot(tc_fun(X0,X1)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,X1)),X2),c_Orderings_Obot__class_Obot(tc_fun(X0,X1)))
| ~ class_Lattices_Obounded__lattice(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_695])]) ).
fof(f1139,plain,
( spl0_28
<=> ! [X75,X74] :
( ~ class_Lattices_Obounded__lattice(X75)
| class_Lattices_Obounded__lattice(tc_fun(X74,X75)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_28])]) ).
fof(f1529,plain,
( spl0_111
<=> ! [X0,X1] :
( ~ class_Lattices_Obounded__lattice(X0)
| c_Orderings_Obot__class_Obot(X0) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),c_Orderings_Obot__class_Obot(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_111])]) ).
fof(f1572,plain,
( ! [X2,X0,X1] :
( c_Orderings_Obot__class_Obot(tc_fun(X0,X1)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,X1)),X2),c_Orderings_Obot__class_Obot(tc_fun(X0,X1)))
| ~ class_Lattices_Obounded__lattice(X1) )
| ~ spl0_28
| ~ spl0_111 ),
inference(resolution,[],[f1530,f1140]) ).
fof(f1140,plain,
( ! [X74,X75] :
( class_Lattices_Obounded__lattice(tc_fun(X74,X75))
| ~ class_Lattices_Obounded__lattice(X75) )
| ~ spl0_28 ),
inference(avatar_component_clause,[],[f1139]) ).
fof(f1530,plain,
( ! [X0,X1] :
( ~ class_Lattices_Obounded__lattice(X0)
| c_Orderings_Obot__class_Obot(X0) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),c_Orderings_Obot__class_Obot(X0)) )
| ~ spl0_111 ),
inference(avatar_component_clause,[],[f1529]) ).
fof(f21203,plain,
( spl0_694
| ~ spl0_28
| ~ spl0_110 ),
inference(avatar_split_clause,[],[f1569,f1525,f1139,f21201]) ).
fof(f21201,plain,
( spl0_694
<=> ! [X2,X0,X1] :
( c_Orderings_Obot__class_Obot(tc_fun(X0,X1)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,X1)),c_Orderings_Obot__class_Obot(tc_fun(X0,X1))),X2)
| ~ class_Lattices_Obounded__lattice(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_694])]) ).
fof(f1525,plain,
( spl0_110
<=> ! [X0,X1] :
( ~ class_Lattices_Obounded__lattice(X0)
| c_Orderings_Obot__class_Obot(X0) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),c_Orderings_Obot__class_Obot(X0)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_110])]) ).
fof(f1569,plain,
( ! [X2,X0,X1] :
( c_Orderings_Obot__class_Obot(tc_fun(X0,X1)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,X1)),c_Orderings_Obot__class_Obot(tc_fun(X0,X1))),X2)
| ~ class_Lattices_Obounded__lattice(X1) )
| ~ spl0_28
| ~ spl0_110 ),
inference(resolution,[],[f1526,f1140]) ).
fof(f1526,plain,
( ! [X0,X1] :
( ~ class_Lattices_Obounded__lattice(X0)
| c_Orderings_Obot__class_Obot(X0) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),c_Orderings_Obot__class_Obot(X0)),X1) )
| ~ spl0_110 ),
inference(avatar_component_clause,[],[f1525]) ).
fof(f21199,plain,
( spl0_693
| ~ spl0_24
| ~ spl0_109 ),
inference(avatar_split_clause,[],[f1567,f1520,f1123,f21197]) ).
fof(f21197,plain,
( spl0_693
<=> ! [X0,X1] :
( c_Orderings_Otop__class_Otop(tc_fun(X0,X1)) = hAPP(c_Complete__Lattice_OSup__class_OSup(tc_fun(X0,X1)),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(X0,X1),tc_bool)))
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_693])]) ).
fof(f1520,plain,
( spl0_109
<=> ! [X0] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
| c_Orderings_Otop__class_Otop(X0) = hAPP(c_Complete__Lattice_OSup__class_OSup(X0),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_109])]) ).
fof(f1567,plain,
( ! [X0,X1] :
( c_Orderings_Otop__class_Otop(tc_fun(X0,X1)) = hAPP(c_Complete__Lattice_OSup__class_OSup(tc_fun(X0,X1)),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(X0,X1),tc_bool)))
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) )
| ~ spl0_24
| ~ spl0_109 ),
inference(resolution,[],[f1521,f1124]) ).
fof(f1521,plain,
( ! [X0] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
| c_Orderings_Otop__class_Otop(X0) = hAPP(c_Complete__Lattice_OSup__class_OSup(X0),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool))) )
| ~ spl0_109 ),
inference(avatar_component_clause,[],[f1520]) ).
fof(f21195,plain,
( spl0_692
| ~ spl0_24
| ~ spl0_107 ),
inference(avatar_split_clause,[],[f1564,f1512,f1123,f21193]) ).
fof(f21193,plain,
( spl0_692
<=> ! [X0,X1] :
( c_Orderings_Obot__class_Obot(tc_fun(X0,X1)) = hAPP(c_Complete__Lattice_OInf__class_OInf(tc_fun(X0,X1)),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(X0,X1),tc_bool)))
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_692])]) ).
fof(f1512,plain,
( spl0_107
<=> ! [X0] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
| hAPP(c_Complete__Lattice_OInf__class_OInf(X0),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool))) = c_Orderings_Obot__class_Obot(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_107])]) ).
fof(f1564,plain,
( ! [X0,X1] :
( c_Orderings_Obot__class_Obot(tc_fun(X0,X1)) = hAPP(c_Complete__Lattice_OInf__class_OInf(tc_fun(X0,X1)),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(X0,X1),tc_bool)))
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) )
| ~ spl0_24
| ~ spl0_107 ),
inference(resolution,[],[f1513,f1124]) ).
fof(f1513,plain,
( ! [X0] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
| hAPP(c_Complete__Lattice_OInf__class_OInf(X0),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool))) = c_Orderings_Obot__class_Obot(X0) )
| ~ spl0_107 ),
inference(avatar_component_clause,[],[f1512]) ).
fof(f21191,plain,
( spl0_691
| ~ spl0_28
| ~ spl0_102 ),
inference(avatar_split_clause,[],[f1559,f1492,f1139,f21189]) ).
fof(f21189,plain,
( spl0_691
<=> ! [X2,X0,X1] :
( c_Orderings_Otop__class_Otop(tc_fun(X0,X1)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,X1)),c_Orderings_Otop__class_Otop(tc_fun(X0,X1))),X2)
| ~ class_Lattices_Obounded__lattice(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_691])]) ).
fof(f1492,plain,
( spl0_102
<=> ! [X0,X1] :
( ~ class_Lattices_Obounded__lattice(X0)
| c_Orderings_Otop__class_Otop(X0) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),c_Orderings_Otop__class_Otop(X0)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_102])]) ).
fof(f1559,plain,
( ! [X2,X0,X1] :
( c_Orderings_Otop__class_Otop(tc_fun(X0,X1)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,X1)),c_Orderings_Otop__class_Otop(tc_fun(X0,X1))),X2)
| ~ class_Lattices_Obounded__lattice(X1) )
| ~ spl0_28
| ~ spl0_102 ),
inference(resolution,[],[f1493,f1140]) ).
fof(f1493,plain,
( ! [X0,X1] :
( ~ class_Lattices_Obounded__lattice(X0)
| c_Orderings_Otop__class_Otop(X0) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),c_Orderings_Otop__class_Otop(X0)),X1) )
| ~ spl0_102 ),
inference(avatar_component_clause,[],[f1492]) ).
fof(f21187,plain,
( spl0_690
| ~ spl0_28
| ~ spl0_101 ),
inference(avatar_split_clause,[],[f1557,f1488,f1139,f21185]) ).
fof(f21185,plain,
( spl0_690
<=> ! [X2,X0,X1] :
( c_Orderings_Otop__class_Otop(tc_fun(X0,X1)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,X1)),X2),c_Orderings_Otop__class_Otop(tc_fun(X0,X1)))
| ~ class_Lattices_Obounded__lattice(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_690])]) ).
fof(f1488,plain,
( spl0_101
<=> ! [X0,X1] :
( ~ class_Lattices_Obounded__lattice(X0)
| c_Orderings_Otop__class_Otop(X0) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),c_Orderings_Otop__class_Otop(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_101])]) ).
fof(f1557,plain,
( ! [X2,X0,X1] :
( c_Orderings_Otop__class_Otop(tc_fun(X0,X1)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,X1)),X2),c_Orderings_Otop__class_Otop(tc_fun(X0,X1)))
| ~ class_Lattices_Obounded__lattice(X1) )
| ~ spl0_28
| ~ spl0_101 ),
inference(resolution,[],[f1489,f1140]) ).
fof(f1489,plain,
( ! [X0,X1] :
( ~ class_Lattices_Obounded__lattice(X0)
| c_Orderings_Otop__class_Otop(X0) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),c_Orderings_Otop__class_Otop(X0)) )
| ~ spl0_101 ),
inference(avatar_component_clause,[],[f1488]) ).
fof(f21020,plain,
( spl0_689
| ~ spl0_150
| ~ spl0_684 ),
inference(avatar_split_clause,[],[f21016,f18896,f1732,f21018]) ).
fof(f18896,plain,
( spl0_684
<=> ! [X2,X0,X1] :
( hAPP(c_fequal(X0),X1) != hAPP(hAPP(c_Set_Oinsert(X0),X2),c_COMBK(c_False,tc_bool,X0))
| X1 = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_684])]) ).
fof(f21016,plain,
( ! [X2,X0,X1] :
( hAPP(c_fequal(X0),X1) != hAPP(c_fequal(X0),X2)
| X1 = X2 )
| ~ spl0_150
| ~ spl0_684 ),
inference(superposition,[],[f18897,f1733]) ).
fof(f18897,plain,
( ! [X2,X0,X1] :
( hAPP(c_fequal(X0),X1) != hAPP(hAPP(c_Set_Oinsert(X0),X2),c_COMBK(c_False,tc_bool,X0))
| X1 = X2 )
| ~ spl0_684 ),
inference(avatar_component_clause,[],[f18896]) ).
fof(f20076,plain,
( spl0_688
| ~ spl0_227
| ~ spl0_642 ),
inference(avatar_split_clause,[],[f18736,f18467,f2580,f20074]) ).
fof(f20074,plain,
( spl0_688
<=> ! [X0,X1] : hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(tc_bool),X1),c_SetInterval_Oord__class_OatLeastAtMost(X0,X0,tc_bool)),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_688])]) ).
fof(f18736,plain,
( ! [X0,X1] : hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(tc_bool),X1),c_SetInterval_Oord__class_OatLeastAtMost(X0,X0,tc_bool)),X0))
| ~ spl0_227
| ~ spl0_642 ),
inference(superposition,[],[f18468,f2581]) ).
fof(f18948,plain,
( ~ spl0_9
| spl0_687
| ~ spl0_260
| ~ spl0_368 ),
inference(avatar_split_clause,[],[f6114,f6067,f3109,f18946,f1057]) ).
fof(f18946,plain,
( spl0_687
<=> ! [X0] :
( c_False = X0
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_bool),c_False),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_687])]) ).
fof(f6114,plain,
( ! [X0] :
( c_False = X0
| ~ class_Orderings_Oorder(tc_bool)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_bool),c_False),X0)) )
| ~ spl0_260
| ~ spl0_368 ),
inference(resolution,[],[f6068,f3110]) ).
fof(f18922,plain,
( spl0_686
| ~ spl0_275
| ~ spl0_345 ),
inference(avatar_split_clause,[],[f5554,f4970,f3652,f18920]) ).
fof(f18920,plain,
( spl0_686
<=> ! [X2,X0,X1] : hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X1),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X2),X1)) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_686])]) ).
fof(f5554,plain,
( ! [X2,X0,X1] : hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X1),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X2),X1)) = X1
| ~ spl0_275
| ~ spl0_345 ),
inference(trivial_inequality_removal,[],[f5549]) ).
fof(f5549,plain,
( ! [X2,X0,X1] :
( c_COMBK(c_False,tc_bool,X0) != c_COMBK(c_False,tc_bool,X0)
| hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X1),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X2),X1)) = X1 )
| ~ spl0_275
| ~ spl0_345 ),
inference(superposition,[],[f4971,f3653]) ).
fof(f18902,plain,
( spl0_685
| ~ spl0_150
| ~ spl0_170
| ~ spl0_303
| ~ spl0_342 ),
inference(avatar_split_clause,[],[f5491,f4957,f4556,f1869,f1732,f18900]) ).
fof(f18900,plain,
( spl0_685
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),hAPP(c_fequal(X1),X2)),X0))
| ~ hBOOL(c_in(X2,X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_685])]) ).
fof(f5491,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),hAPP(c_fequal(X1),X2)),X0))
| ~ hBOOL(c_in(X2,X0,X1)) )
| ~ spl0_150
| ~ spl0_170
| ~ spl0_303
| ~ spl0_342 ),
inference(forward_demodulation,[],[f5490,f1733]) ).
fof(f5490,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_COMBK(c_False,tc_bool,X1))),X0))
| ~ hBOOL(c_in(X2,X0,X1)) )
| ~ spl0_170
| ~ spl0_303
| ~ spl0_342 ),
inference(forward_demodulation,[],[f5488,f1870]) ).
fof(f5488,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),hAPP(hAPP(c_COMBC(c_Set_Oinsert(X1),X1,tc_fun(X1,tc_bool),tc_fun(X1,tc_bool)),c_COMBK(c_False,tc_bool,X1)),X2)),X0))
| ~ hBOOL(c_in(X2,X0,X1)) )
| ~ spl0_303
| ~ spl0_342 ),
inference(superposition,[],[f4557,f4958]) ).
fof(f18898,plain,
( spl0_684
| ~ spl0_150
| ~ spl0_312 ),
inference(avatar_split_clause,[],[f4852,f4594,f1732,f18896]) ).
fof(f4594,plain,
( spl0_312
<=> ! [X4,X0,X3] :
( hAPP(hAPP(c_Set_Oinsert(X0),X3),c_COMBK(c_False,tc_bool,X0)) != hAPP(hAPP(c_Set_Oinsert(X0),X4),c_COMBK(c_False,tc_bool,X0))
| X3 = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_312])]) ).
fof(f4852,plain,
( ! [X2,X0,X1] :
( hAPP(c_fequal(X0),X1) != hAPP(hAPP(c_Set_Oinsert(X0),X2),c_COMBK(c_False,tc_bool,X0))
| X1 = X2 )
| ~ spl0_150
| ~ spl0_312 ),
inference(superposition,[],[f4595,f1733]) ).
fof(f4595,plain,
( ! [X3,X0,X4] :
( hAPP(hAPP(c_Set_Oinsert(X0),X3),c_COMBK(c_False,tc_bool,X0)) != hAPP(hAPP(c_Set_Oinsert(X0),X4),c_COMBK(c_False,tc_bool,X0))
| X3 = X4 )
| ~ spl0_312 ),
inference(avatar_component_clause,[],[f4594]) ).
fof(f18894,plain,
( spl0_683
| ~ spl0_62
| ~ spl0_309 ),
inference(avatar_split_clause,[],[f4801,f4581,f1283,f18892]) ).
fof(f18892,plain,
( spl0_683
<=> ! [X2,X0,X1,X3] :
( ~ class_HOL_Oord(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(X1,X2)),hAPP(X1,X2)))
| ~ class_Orderings_Oorder(tc_fun(X3,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_683])]) ).
fof(f4801,plain,
( ! [X2,X3,X0,X1] :
( ~ class_HOL_Oord(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(X1,X2)),hAPP(X1,X2)))
| ~ class_Orderings_Oorder(tc_fun(X3,X0)) )
| ~ spl0_62
| ~ spl0_309 ),
inference(resolution,[],[f4582,f1284]) ).
fof(f18890,plain,
( spl0_682
| ~ spl0_63
| ~ spl0_309 ),
inference(avatar_split_clause,[],[f4800,f4581,f1287,f18888]) ).
fof(f18888,plain,
( spl0_682
<=> ! [X2,X0,X1,X3] :
( ~ class_HOL_Oord(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(X1,X2)),hAPP(X1,X2)))
| ~ class_Orderings_Opreorder(tc_fun(X3,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_682])]) ).
fof(f4800,plain,
( ! [X2,X3,X0,X1] :
( ~ class_HOL_Oord(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(X1,X2)),hAPP(X1,X2)))
| ~ class_Orderings_Opreorder(tc_fun(X3,X0)) )
| ~ spl0_63
| ~ spl0_309 ),
inference(resolution,[],[f4582,f1288]) ).
fof(f18863,plain,
( spl0_681
| spl0_41
| ~ spl0_51
| ~ spl0_259
| ~ spl0_275 ),
inference(avatar_split_clause,[],[f3839,f3652,f3105,f1237,f1193,f18861]) ).
fof(f18861,plain,
( spl0_681
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X2),X1),X3))
| ~ hBOOL(hAPP(X1,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_681])]) ).
fof(f3839,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(c_False)
| ~ hBOOL(hAPP(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X2),X1),X3))
| ~ hBOOL(hAPP(X1,X3)) )
| ~ spl0_51
| ~ spl0_259
| ~ spl0_275 ),
inference(forward_demodulation,[],[f3827,f1238]) ).
fof(f3827,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(hAPP(c_COMBK(c_False,tc_bool,X0),X3))
| ~ hBOOL(hAPP(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X2),X1),X3))
| ~ hBOOL(hAPP(X1,X3)) )
| ~ spl0_259
| ~ spl0_275 ),
inference(superposition,[],[f3106,f3653]) ).
fof(f18859,plain,
( spl0_680
| ~ spl0_190
| ~ spl0_258 ),
inference(avatar_split_clause,[],[f3410,f3101,f2025,f18857]) ).
fof(f18857,plain,
( spl0_680
<=> ! [X4,X0,X3,X2,X1] :
( c_Fun_Oinj__on(X0,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3),X1,X4)
| ~ c_Fun_Oinj__on(X0,X3,X1,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_680])]) ).
fof(f3410,plain,
( ! [X2,X3,X0,X1,X4] :
( c_Fun_Oinj__on(X0,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3),X1,X4)
| ~ c_Fun_Oinj__on(X0,X3,X1,X4) )
| ~ spl0_190
| ~ spl0_258 ),
inference(resolution,[],[f3102,f2026]) ).
fof(f18855,plain,
( spl0_679
| ~ spl0_189
| ~ spl0_258 ),
inference(avatar_split_clause,[],[f3404,f3101,f2021,f18853]) ).
fof(f18853,plain,
( spl0_679
<=> ! [X4,X0,X3,X2,X1] :
( c_Fun_Oinj__on(X0,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3),X1,X4)
| ~ c_Fun_Oinj__on(X0,X2,X1,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_679])]) ).
fof(f3404,plain,
( ! [X2,X3,X0,X1,X4] :
( c_Fun_Oinj__on(X0,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3),X1,X4)
| ~ c_Fun_Oinj__on(X0,X2,X1,X4) )
| ~ spl0_189
| ~ spl0_258 ),
inference(resolution,[],[f3102,f2022]) ).
fof(f18851,plain,
( spl0_678
| ~ spl0_190
| ~ spl0_255 ),
inference(avatar_split_clause,[],[f3345,f3089,f2025,f18849]) ).
fof(f18849,plain,
( spl0_678
<=> ! [X2,X0,X1] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X2),X1)) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_678])]) ).
fof(f3345,plain,
( ! [X2,X0,X1] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X2),X1)) = X1
| ~ spl0_190
| ~ spl0_255 ),
inference(resolution,[],[f3090,f2026]) ).
fof(f18847,plain,
( spl0_677
| ~ spl0_186
| ~ spl0_255 ),
inference(avatar_split_clause,[],[f3342,f3089,f2009,f18845]) ).
fof(f18845,plain,
( spl0_677
<=> ! [X2,X0,X1] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X1),X2)) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_677])]) ).
fof(f3342,plain,
( ! [X2,X0,X1] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X1),X2)) = X1
| ~ spl0_186
| ~ spl0_255 ),
inference(resolution,[],[f3090,f2010]) ).
fof(f18843,plain,
( ~ spl0_9
| spl0_676
| ~ spl0_253
| ~ spl0_368 ),
inference(avatar_split_clause,[],[f6113,f6067,f3081,f18841,f1057]) ).
fof(f6113,plain,
( ! [X0] :
( c_False = X0
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_bool),X0),c_False))
| ~ class_Orderings_Oorder(tc_bool) )
| ~ spl0_253
| ~ spl0_368 ),
inference(resolution,[],[f6068,f3082]) ).
fof(f18839,plain,
( spl0_675
| ~ spl0_189
| ~ spl0_255 ),
inference(avatar_split_clause,[],[f3339,f3089,f2021,f18837]) ).
fof(f18837,plain,
( spl0_675
<=> ! [X2,X0,X1] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X1),X2)) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_675])]) ).
fof(f3339,plain,
( ! [X2,X0,X1] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X1),X2)) = X1
| ~ spl0_189
| ~ spl0_255 ),
inference(resolution,[],[f3090,f2022]) ).
fof(f18835,plain,
( spl0_674
| ~ spl0_190
| ~ spl0_254 ),
inference(avatar_split_clause,[],[f3319,f3085,f2025,f18833]) ).
fof(f18833,plain,
( spl0_674
<=> ! [X2,X0,X1] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X1),X2)),X2) = X2 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_674])]) ).
fof(f3319,plain,
( ! [X2,X0,X1] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X1),X2)),X2) = X2
| ~ spl0_190
| ~ spl0_254 ),
inference(resolution,[],[f3086,f2026]) ).
fof(f18831,plain,
( spl0_673
| ~ spl0_186
| ~ spl0_254 ),
inference(avatar_split_clause,[],[f3316,f3085,f2009,f18829]) ).
fof(f18829,plain,
( spl0_673
<=> ! [X2,X0,X1] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X1),X2)),X1) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_673])]) ).
fof(f3316,plain,
( ! [X2,X0,X1] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X1),X2)),X1) = X1
| ~ spl0_186
| ~ spl0_254 ),
inference(resolution,[],[f3086,f2010]) ).
fof(f18827,plain,
( spl0_672
| ~ spl0_189
| ~ spl0_254 ),
inference(avatar_split_clause,[],[f3313,f3085,f2021,f18825]) ).
fof(f18825,plain,
( spl0_672
<=> ! [X2,X0,X1] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X1),X2)),X1) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_672])]) ).
fof(f3313,plain,
( ! [X2,X0,X1] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X1),X2)),X1) = X1
| ~ spl0_189
| ~ spl0_254 ),
inference(resolution,[],[f3086,f2022]) ).
fof(f18823,plain,
( spl0_671
| ~ spl0_150
| ~ spl0_252 ),
inference(avatar_split_clause,[],[f3278,f3077,f1732,f18821]) ).
fof(f18821,plain,
( spl0_671
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),hAPP(c_fequal(X0),X1)),X2))
| hBOOL(c_in(X1,X2,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_671])]) ).
fof(f3278,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),hAPP(c_fequal(X0),X1)),X2))
| hBOOL(c_in(X1,X2,X0)) )
| ~ spl0_150
| ~ spl0_252 ),
inference(superposition,[],[f3078,f1733]) ).
fof(f18819,plain,
( spl0_670
| ~ spl0_184
| ~ spl0_252 ),
inference(avatar_split_clause,[],[f3266,f3077,f2001,f18817]) ).
fof(f18817,plain,
( spl0_670
<=> ! [X0,X3,X2,X1] : hBOOL(c_in(X0,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X0),X3)),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_670])]) ).
fof(f3266,plain,
( ! [X2,X3,X0,X1] : hBOOL(c_in(X0,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X0),X3)),X1))
| ~ spl0_184
| ~ spl0_252 ),
inference(resolution,[],[f3078,f2002]) ).
fof(f18815,plain,
( spl0_669
| ~ spl0_185
| ~ spl0_251 ),
inference(avatar_split_clause,[],[f3236,f3073,f2005,f18813]) ).
fof(f18813,plain,
( spl0_669
<=> ! [X2,X0,X1] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X2)),X1) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_669])]) ).
fof(f3236,plain,
( ! [X2,X0,X1] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X2)),X1) = X1
| ~ spl0_185
| ~ spl0_251 ),
inference(resolution,[],[f3074,f2006]) ).
fof(f18811,plain,
( spl0_668
| ~ spl0_184
| ~ spl0_251 ),
inference(avatar_split_clause,[],[f3235,f3073,f2001,f18809]) ).
fof(f18809,plain,
( spl0_668
<=> ! [X2,X0,X1] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X2)),X2) = X2 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_668])]) ).
fof(f3235,plain,
( ! [X2,X0,X1] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X2)),X2) = X2
| ~ spl0_184
| ~ spl0_251 ),
inference(resolution,[],[f3074,f2002]) ).
fof(f18807,plain,
( spl0_667
| ~ spl0_185
| ~ spl0_250 ),
inference(avatar_split_clause,[],[f3210,f3059,f2005,f18805]) ).
fof(f3210,plain,
( ! [X2,X0,X1] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X2)) = X1
| ~ spl0_185
| ~ spl0_250 ),
inference(resolution,[],[f3060,f2006]) ).
fof(f18803,plain,
( spl0_666
| ~ spl0_184
| ~ spl0_250 ),
inference(avatar_split_clause,[],[f3209,f3059,f2001,f18801]) ).
fof(f3209,plain,
( ! [X2,X0,X1] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X2),X1)) = X1
| ~ spl0_184
| ~ spl0_250 ),
inference(resolution,[],[f3060,f2002]) ).
fof(f18777,plain,
( spl0_665
| ~ spl0_185
| ~ spl0_234 ),
inference(avatar_split_clause,[],[f2998,f2649,f2005,f18775]) ).
fof(f18775,plain,
( spl0_665
<=> ! [X2,X0,X1] : hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),hAPP(c_fequal(X0),X1)),hAPP(hAPP(c_Set_Oinsert(X0),X1),X2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_665])]) ).
fof(f2998,plain,
( ! [X2,X0,X1] : hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),hAPP(c_fequal(X0),X1)),hAPP(hAPP(c_Set_Oinsert(X0),X1),X2)))
| ~ spl0_185
| ~ spl0_234 ),
inference(superposition,[],[f2006,f2650]) ).
fof(f18773,plain,
( spl0_664
| ~ spl0_51
| ~ spl0_130
| ~ spl0_233 ),
inference(avatar_split_clause,[],[f2976,f2645,f1631,f1237,f18771]) ).
fof(f18771,plain,
( spl0_664
<=> ! [X2,X3,X4,X0,X5,X1] : c_False = hAPP(hAPP(hAPP(c_COMBS(X2,X3,X4),hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X1)),X5),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_664])]) ).
fof(f2976,plain,
( ! [X2,X3,X0,X1,X4,X5] : c_False = hAPP(hAPP(hAPP(c_COMBS(X2,X3,X4),hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X1)),X5),X1)
| ~ spl0_51
| ~ spl0_130
| ~ spl0_233 ),
inference(forward_demodulation,[],[f2817,f1238]) ).
fof(f2817,plain,
( ! [X2,X3,X0,X1,X4,X5] : hAPP(hAPP(hAPP(c_COMBS(X2,X3,X4),hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X1)),X5),X1) = hAPP(c_COMBK(c_False,tc_bool,X0),hAPP(X5,X1))
| ~ spl0_130
| ~ spl0_233 ),
inference(superposition,[],[f2646,f1632]) ).
fof(f18769,plain,
( spl0_663
| ~ spl0_81
| ~ spl0_233 ),
inference(avatar_split_clause,[],[f2965,f2645,f1370,f18767]) ).
fof(f18767,plain,
( spl0_663
<=> ! [X3,X4,X0,X5,X2,X1] :
( ~ hBOOL(hAPP(hAPP(hAPP(c_COMBS(X3,X4,X5),c_fequal(X0)),X2),X1))
| hAPP(X2,X1) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_663])]) ).
fof(f2965,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ hBOOL(hAPP(hAPP(hAPP(c_COMBS(X3,X4,X5),c_fequal(X0)),X2),X1))
| hAPP(X2,X1) = X1 )
| ~ spl0_81
| ~ spl0_233 ),
inference(superposition,[],[f1371,f2646]) ).
fof(f18765,plain,
( spl0_662
| ~ spl0_113
| ~ spl0_233 ),
inference(avatar_split_clause,[],[f2899,f2645,f1537,f18763]) ).
fof(f18763,plain,
( spl0_662
<=> ! [X2,X4,X0,X3,X1] : hBOOL(hAPP(hAPP(hAPP(c_COMBS(X2,X3,X4),c_lessequals(tc_fun(X0,tc_bool))),X1),c_COMBK(c_False,tc_bool,X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_662])]) ).
fof(f2899,plain,
( ! [X2,X3,X0,X1,X4] : hBOOL(hAPP(hAPP(hAPP(c_COMBS(X2,X3,X4),c_lessequals(tc_fun(X0,tc_bool))),X1),c_COMBK(c_False,tc_bool,X0)))
| ~ spl0_113
| ~ spl0_233 ),
inference(superposition,[],[f1538,f2646]) ).
fof(f18761,plain,
( spl0_661
| ~ spl0_146
| ~ spl0_233 ),
inference(avatar_split_clause,[],[f2887,f2645,f1716,f18759]) ).
fof(f18759,plain,
( spl0_661
<=> ! [X3,X4,X0,X5,X2,X1] : hBOOL(hAPP(hAPP(hAPP(c_COMBS(X3,X4,X5),c_lessequals(tc_fun(X0,tc_bool))),hAPP(c_Set_Oinsert(X0),X2)),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_661])]) ).
fof(f2887,plain,
( ! [X2,X3,X0,X1,X4,X5] : hBOOL(hAPP(hAPP(hAPP(c_COMBS(X3,X4,X5),c_lessequals(tc_fun(X0,tc_bool))),hAPP(c_Set_Oinsert(X0),X2)),X1))
| ~ spl0_146
| ~ spl0_233 ),
inference(superposition,[],[f1717,f2646]) ).
fof(f18757,plain,
( spl0_660
| ~ spl0_139
| ~ spl0_233 ),
inference(avatar_split_clause,[],[f2886,f2645,f1688,f18755]) ).
fof(f18755,plain,
( spl0_660
<=> ! [X3,X4,X0,X5,X2,X1] :
( hBOOL(hAPP(hAPP(hAPP(c_COMBS(X3,X4,X5),c_lessequals(X0)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X2)),X1))
| ~ class_Lattices_Oupper__semilattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_660])]) ).
fof(f2886,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( hBOOL(hAPP(hAPP(hAPP(c_COMBS(X3,X4,X5),c_lessequals(X0)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X2)),X1))
| ~ class_Lattices_Oupper__semilattice(X0) )
| ~ spl0_139
| ~ spl0_233 ),
inference(superposition,[],[f1689,f2646]) ).
fof(f18753,plain,
( spl0_659
| ~ spl0_140
| ~ spl0_233 ),
inference(avatar_split_clause,[],[f2885,f2645,f1692,f18751]) ).
fof(f18751,plain,
( spl0_659
<=> ! [X3,X4,X0,X5,X2,X1] :
( hBOOL(hAPP(hAPP(hAPP(c_COMBS(X3,X4,X5),c_lessequals(X0)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X2)),X1))
| ~ class_Lattices_Olattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_659])]) ).
fof(f2885,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( hBOOL(hAPP(hAPP(hAPP(c_COMBS(X3,X4,X5),c_lessequals(X0)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X2)),X1))
| ~ class_Lattices_Olattice(X0) )
| ~ spl0_140
| ~ spl0_233 ),
inference(superposition,[],[f1693,f2646]) ).
fof(f18749,plain,
( spl0_658
| ~ spl0_56
| ~ spl0_231 ),
inference(avatar_split_clause,[],[f2792,f2637,f1258,f18747]) ).
fof(f18747,plain,
( spl0_658
<=> ! [X0,X3,X2,X1] :
( hBOOL(c_in(X0,X1,X2))
| X0 = X3
| ~ hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X2),X3),X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_658])]) ).
fof(f2792,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(c_in(X0,X1,X2))
| X0 = X3
| ~ hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X2),X3),X1),X0)) )
| ~ spl0_56
| ~ spl0_231 ),
inference(resolution,[],[f2638,f1259]) ).
fof(f18745,plain,
( spl0_657
| ~ spl0_143
| ~ spl0_217 ),
inference(avatar_split_clause,[],[f2534,f2267,f1704,f18743]) ).
fof(f18743,plain,
( spl0_657
<=> ! [X2,X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2)),X2) = X2
| ~ class_Lattices_Olattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_657])]) ).
fof(f2534,plain,
( ! [X2,X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2)),X2) = X2
| ~ class_Lattices_Olattice(X0) )
| ~ spl0_143
| ~ spl0_217 ),
inference(resolution,[],[f2268,f1705]) ).
fof(f18741,plain,
( spl0_656
| ~ spl0_144
| ~ spl0_217 ),
inference(avatar_split_clause,[],[f2533,f2267,f1708,f18739]) ).
fof(f18739,plain,
( spl0_656
<=> ! [X2,X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2)),X2) = X2
| ~ class_Lattices_Olower__semilattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_656])]) ).
fof(f2533,plain,
( ! [X2,X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2)),X2) = X2
| ~ class_Lattices_Olower__semilattice(X0) )
| ~ spl0_144
| ~ spl0_217 ),
inference(resolution,[],[f2268,f1709]) ).
fof(f18731,plain,
( spl0_655
| ~ spl0_142
| ~ spl0_217 ),
inference(avatar_split_clause,[],[f2528,f2267,f1700,f18729]) ).
fof(f18729,plain,
( spl0_655
<=> ! [X2,X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2)),X1) = X1
| ~ class_Lattices_Olattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_655])]) ).
fof(f2528,plain,
( ! [X2,X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2)),X1) = X1
| ~ class_Lattices_Olattice(X0) )
| ~ spl0_142
| ~ spl0_217 ),
inference(resolution,[],[f2268,f1701]) ).
fof(f18727,plain,
( spl0_654
| ~ spl0_145
| ~ spl0_217 ),
inference(avatar_split_clause,[],[f2527,f2267,f1712,f18725]) ).
fof(f18725,plain,
( spl0_654
<=> ! [X2,X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2)),X1) = X1
| ~ class_Lattices_Olower__semilattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_654])]) ).
fof(f2527,plain,
( ! [X2,X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2)),X1) = X1
| ~ class_Lattices_Olower__semilattice(X0) )
| ~ spl0_145
| ~ spl0_217 ),
inference(resolution,[],[f2268,f1713]) ).
fof(f18723,plain,
( spl0_653
| ~ spl0_143
| ~ spl0_215 ),
inference(avatar_split_clause,[],[f2495,f2259,f1704,f18721]) ).
fof(f18721,plain,
( spl0_653
<=> ! [X2,X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X1)) = X1
| ~ class_Lattices_Olattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_653])]) ).
fof(f2495,plain,
( ! [X2,X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X1)) = X1
| ~ class_Lattices_Olattice(X0) )
| ~ spl0_143
| ~ spl0_215 ),
inference(resolution,[],[f2260,f1705]) ).
fof(f18719,plain,
( spl0_652
| ~ spl0_144
| ~ spl0_215 ),
inference(avatar_split_clause,[],[f2494,f2259,f1708,f18717]) ).
fof(f18717,plain,
( spl0_652
<=> ! [X2,X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X1)) = X1
| ~ class_Lattices_Olower__semilattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_652])]) ).
fof(f2494,plain,
( ! [X2,X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X1)) = X1
| ~ class_Lattices_Olower__semilattice(X0) )
| ~ spl0_144
| ~ spl0_215 ),
inference(resolution,[],[f2260,f1709]) ).
fof(f18715,plain,
( spl0_651
| ~ spl0_145
| ~ spl0_215 ),
inference(avatar_split_clause,[],[f2488,f2259,f1712,f18713]) ).
fof(f18713,plain,
( spl0_651
<=> ! [X2,X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2)) = X1
| ~ class_Lattices_Olower__semilattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_651])]) ).
fof(f2488,plain,
( ! [X2,X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2)) = X1
| ~ class_Lattices_Olower__semilattice(X0) )
| ~ spl0_145
| ~ spl0_215 ),
inference(resolution,[],[f2260,f1713]) ).
fof(f18711,plain,
( spl0_650
| ~ spl0_139
| ~ spl0_212 ),
inference(avatar_split_clause,[],[f2384,f2247,f1688,f18709]) ).
fof(f18709,plain,
( spl0_650
<=> ! [X2,X0,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2)),X2) = X2
| ~ class_Lattices_Oupper__semilattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_650])]) ).
fof(f2384,plain,
( ! [X2,X0,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2)),X2) = X2
| ~ class_Lattices_Oupper__semilattice(X0) )
| ~ spl0_139
| ~ spl0_212 ),
inference(resolution,[],[f2248,f1689]) ).
fof(f18707,plain,
( spl0_649
| ~ spl0_140
| ~ spl0_212 ),
inference(avatar_split_clause,[],[f2383,f2247,f1692,f18705]) ).
fof(f18705,plain,
( spl0_649
<=> ! [X2,X0,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2)),X2) = X2
| ~ class_Lattices_Olattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_649])]) ).
fof(f2383,plain,
( ! [X2,X0,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2)),X2) = X2
| ~ class_Lattices_Olattice(X0) )
| ~ spl0_140
| ~ spl0_212 ),
inference(resolution,[],[f2248,f1693]) ).
fof(f18703,plain,
( spl0_648
| ~ spl0_138
| ~ spl0_212 ),
inference(avatar_split_clause,[],[f2382,f2247,f1684,f18701]) ).
fof(f18701,plain,
( spl0_648
<=> ! [X2,X0,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2)),X1) = X1
| ~ class_Lattices_Oupper__semilattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_648])]) ).
fof(f2382,plain,
( ! [X2,X0,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2)),X1) = X1
| ~ class_Lattices_Oupper__semilattice(X0) )
| ~ spl0_138
| ~ spl0_212 ),
inference(resolution,[],[f2248,f1685]) ).
fof(f18699,plain,
( spl0_647
| ~ spl0_141
| ~ spl0_212 ),
inference(avatar_split_clause,[],[f2381,f2247,f1696,f18697]) ).
fof(f18697,plain,
( spl0_647
<=> ! [X2,X0,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2)),X1) = X1
| ~ class_Lattices_Olattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_647])]) ).
fof(f2381,plain,
( ! [X2,X0,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2)),X1) = X1
| ~ class_Lattices_Olattice(X0) )
| ~ spl0_141
| ~ spl0_212 ),
inference(resolution,[],[f2248,f1697]) ).
fof(f18695,plain,
( spl0_646
| ~ spl0_139
| ~ spl0_210 ),
inference(avatar_split_clause,[],[f2343,f2233,f1688,f18693]) ).
fof(f18693,plain,
( spl0_646
<=> ! [X2,X0,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X2),X1)) = X1
| ~ class_Lattices_Oupper__semilattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_646])]) ).
fof(f2343,plain,
( ! [X2,X0,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X2),X1)) = X1
| ~ class_Lattices_Oupper__semilattice(X0) )
| ~ spl0_139
| ~ spl0_210 ),
inference(resolution,[],[f2234,f1689]) ).
fof(f18691,plain,
( spl0_645
| ~ spl0_51
| ~ spl0_636 ),
inference(avatar_split_clause,[],[f17625,f17503,f1237,f18689]) ).
fof(f17503,plain,
( spl0_636
<=> ! [X2,X0,X1] : hBOOL(hAPP(hAPP(c_lessequals(tc_bool),hAPP(X0,X1)),hAPP(c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_636])]) ).
fof(f17625,plain,
( ! [X3,X0,X4] : hBOOL(hAPP(hAPP(c_lessequals(tc_bool),X0),hAPP(c_Orderings_Otop__class_Otop(tc_fun(X4,tc_bool)),X3)))
| ~ spl0_51
| ~ spl0_636 ),
inference(superposition,[],[f17504,f1238]) ).
fof(f17504,plain,
( ! [X2,X0,X1] : hBOOL(hAPP(hAPP(c_lessequals(tc_bool),hAPP(X0,X1)),hAPP(c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X1)))
| ~ spl0_636 ),
inference(avatar_component_clause,[],[f17503]) ).
fof(f18687,plain,
( spl0_644
| ~ spl0_140
| ~ spl0_210 ),
inference(avatar_split_clause,[],[f2342,f2233,f1692,f18685]) ).
fof(f18685,plain,
( spl0_644
<=> ! [X2,X0,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X2),X1)) = X1
| ~ class_Lattices_Olattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_644])]) ).
fof(f2342,plain,
( ! [X2,X0,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X2),X1)) = X1
| ~ class_Lattices_Olattice(X0) )
| ~ spl0_140
| ~ spl0_210 ),
inference(resolution,[],[f2234,f1693]) ).
fof(f18683,plain,
( spl0_643
| ~ spl0_138
| ~ spl0_210 ),
inference(avatar_split_clause,[],[f2341,f2233,f1684,f18681]) ).
fof(f18681,plain,
( spl0_643
<=> ! [X2,X0,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2)) = X1
| ~ class_Lattices_Oupper__semilattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_643])]) ).
fof(f2341,plain,
( ! [X2,X0,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2)) = X1
| ~ class_Lattices_Oupper__semilattice(X0) )
| ~ spl0_138
| ~ spl0_210 ),
inference(resolution,[],[f2234,f1685]) ).
fof(f18469,plain,
( spl0_642
| ~ spl0_150
| ~ spl0_583 ),
inference(avatar_split_clause,[],[f16641,f16587,f1732,f18467]) ).
fof(f16587,plain,
( spl0_583
<=> ! [X0,X3,X2,X1] : hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X0),X2),hAPP(hAPP(c_Set_Oinsert(X0),X1),X3)),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_583])]) ).
fof(f16641,plain,
( ! [X2,X0,X1] : hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X0),X2),hAPP(c_fequal(X0),X1)),X1))
| ~ spl0_150
| ~ spl0_583 ),
inference(superposition,[],[f16588,f1733]) ).
fof(f16588,plain,
( ! [X2,X3,X0,X1] : hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X0),X2),hAPP(hAPP(c_Set_Oinsert(X0),X1),X3)),X1))
| ~ spl0_583 ),
inference(avatar_component_clause,[],[f16587]) ).
fof(f18131,plain,
( spl0_641
| ~ spl0_115
| ~ spl0_227 ),
inference(avatar_split_clause,[],[f3970,f2580,f1545,f18129]) ).
fof(f18129,plain,
( spl0_641
<=> ! [X0] : hBOOL(hAPP(c_SetInterval_Oord__class_OatLeastAtMost(X0,X0,tc_bool),c_Nitpick_Osko__Nitpick__XEx1__def__1__3(c_SetInterval_Oord__class_OatLeastAtMost(X0,X0,tc_bool),tc_bool))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_641])]) ).
fof(f1545,plain,
( spl0_115
<=> ! [X0,X1] : hBOOL(hAPP(hAPP(c_fequal(X0),X1),c_Nitpick_Osko__Nitpick__XEx1__def__1__3(hAPP(c_fequal(X0),X1),X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_115])]) ).
fof(f3970,plain,
( ! [X0] : hBOOL(hAPP(c_SetInterval_Oord__class_OatLeastAtMost(X0,X0,tc_bool),c_Nitpick_Osko__Nitpick__XEx1__def__1__3(c_SetInterval_Oord__class_OatLeastAtMost(X0,X0,tc_bool),tc_bool)))
| ~ spl0_115
| ~ spl0_227 ),
inference(superposition,[],[f1546,f2581]) ).
fof(f1546,plain,
( ! [X0,X1] : hBOOL(hAPP(hAPP(c_fequal(X0),X1),c_Nitpick_Osko__Nitpick__XEx1__def__1__3(hAPP(c_fequal(X0),X1),X0)))
| ~ spl0_115 ),
inference(avatar_component_clause,[],[f1545]) ).
fof(f17644,plain,
( spl0_640
| ~ spl0_64
| ~ spl0_390 ),
inference(avatar_split_clause,[],[f6931,f6756,f1291,f17642]) ).
fof(f17642,plain,
( spl0_640
<=> ! [X0,X3,X2,X1] : hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X2),hAPP(hAPP(c_Set_Oinsert(X0),X1),X3)),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_640])]) ).
fof(f6931,plain,
( ! [X2,X3,X0,X1] : hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X2),hAPP(hAPP(c_Set_Oinsert(X0),X1),X3)),X1))
| ~ spl0_64
| ~ spl0_390 ),
inference(superposition,[],[f1292,f6757]) ).
fof(f17640,plain,
( spl0_639
| ~ spl0_131
| ~ spl0_150
| ~ spl0_370 ),
inference(avatar_split_clause,[],[f6378,f6075,f1732,f1635,f17638]) ).
fof(f17638,plain,
( spl0_639
<=> ! [X2,X0,X1] :
( c_Finite__Set_Ofinite(X2,X0)
| ~ c_Finite__Set_Ofinite(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X2),hAPP(c_fequal(X0),X1)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_639])]) ).
fof(f6378,plain,
( ! [X2,X0,X1] :
( c_Finite__Set_Ofinite(X2,X0)
| ~ c_Finite__Set_Ofinite(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X2),hAPP(c_fequal(X0),X1)),X0) )
| ~ spl0_131
| ~ spl0_150
| ~ spl0_370 ),
inference(forward_demodulation,[],[f6373,f1636]) ).
fof(f6373,plain,
( ! [X2,X0,X1] :
( ~ c_Finite__Set_Ofinite(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X2),hAPP(c_fequal(X0),X1)),X0)
| c_Finite__Set_Ofinite(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X2),c_COMBK(c_False,tc_bool,X0)),X0) )
| ~ spl0_150
| ~ spl0_370 ),
inference(superposition,[],[f6076,f1733]) ).
fof(f17636,plain,
( spl0_638
| ~ spl0_79
| ~ spl0_345 ),
inference(avatar_split_clause,[],[f5544,f4970,f1361,f17634]) ).
fof(f17634,plain,
( spl0_638
<=> ! [X0,X1] :
( c_COMBK(c_False,tc_bool,X0) != X1
| hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X1),X1) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_638])]) ).
fof(f5544,plain,
( ! [X0,X1] :
( c_COMBK(c_False,tc_bool,X0) != X1
| hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X1),X1) = X1 )
| ~ spl0_79
| ~ spl0_345 ),
inference(superposition,[],[f4971,f1362]) ).
fof(f17509,plain,
( ~ spl0_3
| spl0_637
| ~ spl0_124
| ~ spl0_211 ),
inference(avatar_split_clause,[],[f2359,f2237,f1607,f17507,f1027]) ).
fof(f17507,plain,
( spl0_637
<=> ! [X0] :
( c_False != X0
| hBOOL(hAPP(hAPP(c_lessequals(tc_bool),X0),c_False)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_637])]) ).
fof(f1607,plain,
( spl0_124
<=> ! [X0] : c_False = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),X0),c_False) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_124])]) ).
fof(f2359,plain,
( ! [X0] :
( c_False != X0
| hBOOL(hAPP(hAPP(c_lessequals(tc_bool),X0),c_False))
| ~ class_Lattices_Olower__semilattice(tc_bool) )
| ~ spl0_124
| ~ spl0_211 ),
inference(superposition,[],[f2238,f1608]) ).
fof(f1608,plain,
( ! [X0] : c_False = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),X0),c_False)
| ~ spl0_124 ),
inference(avatar_component_clause,[],[f1607]) ).
fof(f17505,plain,
( spl0_636
| ~ spl0_13
| ~ spl0_108
| ~ spl0_309 ),
inference(avatar_split_clause,[],[f4830,f4581,f1516,f1077,f17503]) ).
fof(f4830,plain,
( ! [X2,X0,X1] :
( ~ class_HOL_Oord(tc_bool)
| hBOOL(hAPP(hAPP(c_lessequals(tc_bool),hAPP(X0,X1)),hAPP(c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X1))) )
| ~ spl0_108
| ~ spl0_309 ),
inference(resolution,[],[f4582,f1517]) ).
fof(f17501,plain,
( spl0_635
| ~ spl0_58
| ~ spl0_293 ),
inference(avatar_split_clause,[],[f4363,f3927,f1266,f17499]) ).
fof(f17499,plain,
( spl0_635
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2)),X2))
| ~ class_Lattices_Oupper__semilattice(X0)
| ~ class_Orderings_Oorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_635])]) ).
fof(f4363,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2)),X2))
| ~ class_Lattices_Oupper__semilattice(X0)
| ~ class_Orderings_Oorder(X0) )
| ~ spl0_58
| ~ spl0_293 ),
inference(resolution,[],[f3928,f1267]) ).
fof(f17497,plain,
( spl0_634
| ~ spl0_58
| ~ spl0_292 ),
inference(avatar_split_clause,[],[f4335,f3915,f1266,f17495]) ).
fof(f17495,plain,
( spl0_634
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2)),X1))
| ~ class_Lattices_Oupper__semilattice(X0)
| ~ class_Orderings_Oorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_634])]) ).
fof(f4335,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2)),X1))
| ~ class_Lattices_Oupper__semilattice(X0)
| ~ class_Orderings_Oorder(X0) )
| ~ spl0_58
| ~ spl0_292 ),
inference(resolution,[],[f3916,f1267]) ).
fof(f17493,plain,
( spl0_633
| ~ spl0_58
| ~ spl0_291 ),
inference(avatar_split_clause,[],[f4312,f3911,f1266,f17491]) ).
fof(f17491,plain,
( spl0_633
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2)))
| ~ class_Lattices_Olower__semilattice(X0)
| ~ class_Orderings_Oorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_633])]) ).
fof(f4312,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2)))
| ~ class_Lattices_Olower__semilattice(X0)
| ~ class_Orderings_Oorder(X0) )
| ~ spl0_58
| ~ spl0_291 ),
inference(resolution,[],[f3912,f1267]) ).
fof(f17489,plain,
( spl0_632
| ~ spl0_58
| ~ spl0_290 ),
inference(avatar_split_clause,[],[f4289,f3907,f1266,f17487]) ).
fof(f17487,plain,
( spl0_632
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X1)))
| ~ class_Lattices_Olower__semilattice(X0)
| ~ class_Orderings_Oorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_632])]) ).
fof(f4289,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X1)))
| ~ class_Lattices_Olower__semilattice(X0)
| ~ class_Orderings_Oorder(X0) )
| ~ spl0_58
| ~ spl0_290 ),
inference(resolution,[],[f3908,f1267]) ).
fof(f17485,plain,
( spl0_631
| ~ spl0_42
| ~ spl0_288 ),
inference(avatar_split_clause,[],[f4129,f3899,f1198,f17483]) ).
fof(f17483,plain,
( spl0_631
<=> ! [X4,X0,X3,X2,X1] :
( ~ hBOOL(c_in(X0,X1,X2))
| hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,c_fequal(X3),X2,tc_fun(X4,tc_bool)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_631])]) ).
fof(f4129,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ hBOOL(c_in(X0,X1,X2))
| hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,c_fequal(X3),X2,tc_fun(X4,tc_bool)),X0)) )
| ~ spl0_42
| ~ spl0_288 ),
inference(resolution,[],[f3900,f1199]) ).
fof(f17481,plain,
( spl0_630
| ~ spl0_74
| ~ spl0_260 ),
inference(avatar_split_clause,[],[f3461,f3109,f1340,f17479]) ).
fof(f17479,plain,
( spl0_630
<=> ! [X0,X1] :
( c_Orderings_Otop__class_Otop(X0) = X1
| ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),c_Orderings_Otop__class_Otop(X0)))
| ~ class_Orderings_Otop(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_630])]) ).
fof(f3461,plain,
( ! [X0,X1] :
( c_Orderings_Otop__class_Otop(X0) = X1
| ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),c_Orderings_Otop__class_Otop(X0)))
| ~ class_Orderings_Otop(X0) )
| ~ spl0_74
| ~ spl0_260 ),
inference(resolution,[],[f3110,f1341]) ).
fof(f17477,plain,
( spl0_629
| ~ spl0_75
| ~ spl0_260 ),
inference(avatar_split_clause,[],[f3446,f3109,f1344,f17475]) ).
fof(f17475,plain,
( spl0_629
<=> ! [X0,X1] :
( c_Orderings_Obot__class_Obot(X1) = X0
| ~ class_Orderings_Oorder(X1)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_Orderings_Obot__class_Obot(X1)),X0))
| ~ class_Orderings_Obot(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_629])]) ).
fof(f3446,plain,
( ! [X0,X1] :
( c_Orderings_Obot__class_Obot(X1) = X0
| ~ class_Orderings_Oorder(X1)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_Orderings_Obot__class_Obot(X1)),X0))
| ~ class_Orderings_Obot(X1) )
| ~ spl0_75
| ~ spl0_260 ),
inference(resolution,[],[f3110,f1345]) ).
fof(f17473,plain,
( spl0_628
| ~ spl0_74
| ~ spl0_253 ),
inference(avatar_split_clause,[],[f3305,f3081,f1340,f17471]) ).
fof(f3305,plain,
( ! [X0,X1] :
( c_Orderings_Otop__class_Otop(X0) = X1
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),c_Orderings_Otop__class_Otop(X0)),X1))
| ~ class_Orderings_Oorder(X0)
| ~ class_Orderings_Otop(X0) )
| ~ spl0_74
| ~ spl0_253 ),
inference(resolution,[],[f3082,f1341]) ).
fof(f17469,plain,
( spl0_627
| ~ spl0_75
| ~ spl0_253 ),
inference(avatar_split_clause,[],[f3290,f3081,f1344,f17467]) ).
fof(f17467,plain,
( spl0_627
<=> ! [X0,X1] :
( c_Orderings_Obot__class_Obot(X1) = X0
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X0),c_Orderings_Obot__class_Obot(X1)))
| ~ class_Orderings_Oorder(X1)
| ~ class_Orderings_Obot(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_627])]) ).
fof(f3290,plain,
( ! [X0,X1] :
( c_Orderings_Obot__class_Obot(X1) = X0
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X0),c_Orderings_Obot__class_Obot(X1)))
| ~ class_Orderings_Oorder(X1)
| ~ class_Orderings_Obot(X1) )
| ~ spl0_75
| ~ spl0_253 ),
inference(resolution,[],[f3082,f1345]) ).
fof(f17462,plain,
( spl0_626
| ~ spl0_1
| ~ spl0_242 ),
inference(avatar_split_clause,[],[f3038,f2682,f1017,f17460]) ).
fof(f17460,plain,
( spl0_626
<=> ! [X2,X0,X1] :
( c_COMBK(c_False,tc_bool,X0) = X1
| c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,c_COMBK(X2,tc_bool,X0),X0,tc_bool) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_626])]) ).
fof(f3038,plain,
( ! [X2,X0,X1] :
( c_COMBK(c_False,tc_bool,X0) = X1
| c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,c_COMBK(X2,tc_bool,X0),X0,tc_bool) = X2 )
| ~ spl0_1
| ~ spl0_242 ),
inference(resolution,[],[f2683,f1019]) ).
fof(f17458,plain,
( spl0_625
| ~ spl0_1
| ~ spl0_241 ),
inference(avatar_split_clause,[],[f3036,f2678,f1017,f17456]) ).
fof(f17456,plain,
( spl0_625
<=> ! [X2,X0,X1] :
( c_COMBK(c_False,tc_bool,X0) = X1
| c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,c_COMBK(X2,tc_bool,X0),X0,tc_bool) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_625])]) ).
fof(f3036,plain,
( ! [X2,X0,X1] :
( c_COMBK(c_False,tc_bool,X0) = X1
| c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,c_COMBK(X2,tc_bool,X0),X0,tc_bool) = X2 )
| ~ spl0_1
| ~ spl0_241 ),
inference(resolution,[],[f2679,f1019]) ).
fof(f17454,plain,
( spl0_624
| ~ spl0_153
| ~ spl0_234 ),
inference(avatar_split_clause,[],[f2995,f2649,f1798,f17452]) ).
fof(f17452,plain,
( spl0_624
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X0),X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_fequal(X0),X1),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_624])]) ).
fof(f2995,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X0),X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_fequal(X0),X1),X3)) )
| ~ spl0_153
| ~ spl0_234 ),
inference(superposition,[],[f1799,f2650]) ).
fof(f17450,plain,
( spl0_623
| ~ spl0_99
| ~ spl0_233 ),
inference(avatar_split_clause,[],[f2928,f2645,f1472,f17448]) ).
fof(f17448,plain,
( spl0_623
<=> ! [X3,X4,X0,X5,X2,X1] : c_COMBK(c_False,tc_bool,X0) != hAPP(hAPP(hAPP(c_COMBS(X3,X4,X5),c_Set_Oinsert(X0)),X2),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_623])]) ).
fof(f2928,plain,
( ! [X2,X3,X0,X1,X4,X5] : c_COMBK(c_False,tc_bool,X0) != hAPP(hAPP(hAPP(c_COMBS(X3,X4,X5),c_Set_Oinsert(X0)),X2),X1)
| ~ spl0_99
| ~ spl0_233 ),
inference(superposition,[],[f1473,f2646]) ).
fof(f17446,plain,
( spl0_622
| ~ spl0_64
| ~ spl0_233 ),
inference(avatar_split_clause,[],[f2892,f2645,f1291,f17444]) ).
fof(f17444,plain,
( spl0_622
<=> ! [X3,X4,X0,X5,X2,X1] : hBOOL(hAPP(hAPP(hAPP(c_COMBS(X3,X4,X5),hAPP(c_Set_Oinsert(X0),hAPP(X1,X2))),X1),X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_622])]) ).
fof(f2892,plain,
( ! [X2,X3,X0,X1,X4,X5] : hBOOL(hAPP(hAPP(hAPP(c_COMBS(X3,X4,X5),hAPP(c_Set_Oinsert(X0),hAPP(X1,X2))),X1),X2))
| ~ spl0_64
| ~ spl0_233 ),
inference(superposition,[],[f1292,f2646]) ).
fof(f17442,plain,
( spl0_621
| ~ spl0_57
| ~ spl0_223 ),
inference(avatar_split_clause,[],[f2584,f2291,f1262,f17440]) ).
fof(f17440,plain,
( spl0_621
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(c_in(X0,X1,X2))
| hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X1),X3),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_621])]) ).
fof(f2584,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(c_in(X0,X1,X2))
| hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X1),X3),X0)) )
| ~ spl0_57
| ~ spl0_223 ),
inference(resolution,[],[f2292,f1263]) ).
fof(f17438,plain,
( spl0_620
| ~ spl0_57
| ~ spl0_221 ),
inference(avatar_split_clause,[],[f2571,f2283,f1262,f17436]) ).
fof(f17436,plain,
( spl0_620
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(c_in(X0,X1,X2))
| hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X3),X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_620])]) ).
fof(f2571,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(c_in(X0,X1,X2))
| hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X3),X1),X0)) )
| ~ spl0_57
| ~ spl0_221 ),
inference(resolution,[],[f2284,f1263]) ).
fof(f17434,plain,
( spl0_619
| ~ spl0_202
| ~ spl0_213 ),
inference(avatar_split_clause,[],[f2411,f2251,f2080,f17432]) ).
fof(f17432,plain,
( spl0_619
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(c_in(X3,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X2),X1),X0))
| hBOOL(hAPP(X2,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_619])]) ).
fof(f2411,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(c_in(X3,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X2),X1),X0))
| hBOOL(hAPP(X2,X3)) )
| ~ spl0_202
| ~ spl0_213 ),
inference(superposition,[],[f2081,f2252]) ).
fof(f17430,plain,
( spl0_618
| ~ spl0_56
| ~ spl0_209 ),
inference(avatar_split_clause,[],[f2322,f2229,f1258,f17428]) ).
fof(f17428,plain,
( spl0_618
<=> ! [X0,X3,X2,X1] :
( hBOOL(c_in(X0,X1,X2))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X1),X3),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_618])]) ).
fof(f2322,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(c_in(X0,X1,X2))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X1),X3),X0)) )
| ~ spl0_56
| ~ spl0_209 ),
inference(resolution,[],[f2230,f1259]) ).
fof(f17426,plain,
( spl0_617
| ~ spl0_56
| ~ spl0_208 ),
inference(avatar_split_clause,[],[f2316,f2225,f1258,f17424]) ).
fof(f2316,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(c_in(X0,X1,X2))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X3),X1),X0)) )
| ~ spl0_56
| ~ spl0_208 ),
inference(resolution,[],[f2226,f1259]) ).
fof(f17415,plain,
( spl0_616
| ~ spl0_56
| ~ spl0_207 ),
inference(avatar_split_clause,[],[f2311,f2221,f1258,f17413]) ).
fof(f17413,plain,
( spl0_616
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(c_in(X0,X1,X2))
| ~ hBOOL(hAPP(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X2,tc_bool)),X3),X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_616])]) ).
fof(f2311,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(c_in(X0,X1,X2))
| ~ hBOOL(hAPP(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X2,tc_bool)),X3),X1),X0)) )
| ~ spl0_56
| ~ spl0_207 ),
inference(resolution,[],[f2222,f1259]) ).
fof(f17411,plain,
( spl0_615
| ~ spl0_56
| ~ spl0_206 ),
inference(avatar_split_clause,[],[f2306,f2217,f1258,f17409]) ).
fof(f17409,plain,
( spl0_615
<=> ! [X0,X3,X2,X1] :
( hBOOL(c_in(X0,X1,X2))
| ~ hBOOL(hAPP(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X2,tc_bool)),X1),X3),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_615])]) ).
fof(f2306,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(c_in(X0,X1,X2))
| ~ hBOOL(hAPP(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X2,tc_bool)),X1),X3),X0)) )
| ~ spl0_56
| ~ spl0_206 ),
inference(resolution,[],[f2218,f1259]) ).
fof(f17407,plain,
( spl0_614
| ~ spl0_108
| ~ spl0_183 ),
inference(avatar_split_clause,[],[f2132,f1997,f1516,f17405]) ).
fof(f17405,plain,
( spl0_614
<=> ! [X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool))),X1))
| ~ class_Orderings_Opreorder(tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_614])]) ).
fof(f2132,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool))),X1))
| ~ class_Orderings_Opreorder(tc_fun(X0,tc_bool)) )
| ~ spl0_108
| ~ spl0_183 ),
inference(resolution,[],[f1998,f1517]) ).
fof(f17403,plain,
( spl0_613
| ~ spl0_139
| ~ spl0_183 ),
inference(avatar_split_clause,[],[f2129,f1997,f1688,f17401]) ).
fof(f17401,plain,
( spl0_613
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2)),X2))
| ~ class_Orderings_Opreorder(X0)
| ~ class_Lattices_Oupper__semilattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_613])]) ).
fof(f2129,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2)),X2))
| ~ class_Orderings_Opreorder(X0)
| ~ class_Lattices_Oupper__semilattice(X0) )
| ~ spl0_139
| ~ spl0_183 ),
inference(resolution,[],[f1998,f1689]) ).
fof(f17399,plain,
( spl0_612
| ~ spl0_140
| ~ spl0_183 ),
inference(avatar_split_clause,[],[f2128,f1997,f1692,f17397]) ).
fof(f17397,plain,
( spl0_612
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2)),X2))
| ~ class_Orderings_Opreorder(X0)
| ~ class_Lattices_Olattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_612])]) ).
fof(f2128,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2)),X2))
| ~ class_Orderings_Opreorder(X0)
| ~ class_Lattices_Olattice(X0) )
| ~ spl0_140
| ~ spl0_183 ),
inference(resolution,[],[f1998,f1693]) ).
fof(f17395,plain,
( spl0_611
| ~ spl0_138
| ~ spl0_183 ),
inference(avatar_split_clause,[],[f2127,f1997,f1684,f17393]) ).
fof(f17393,plain,
( spl0_611
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2)),X1))
| ~ class_Orderings_Opreorder(X0)
| ~ class_Lattices_Oupper__semilattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_611])]) ).
fof(f2127,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2)),X1))
| ~ class_Orderings_Opreorder(X0)
| ~ class_Lattices_Oupper__semilattice(X0) )
| ~ spl0_138
| ~ spl0_183 ),
inference(resolution,[],[f1998,f1685]) ).
fof(f17391,plain,
( spl0_610
| ~ spl0_141
| ~ spl0_183 ),
inference(avatar_split_clause,[],[f2126,f1997,f1696,f17389]) ).
fof(f17389,plain,
( spl0_610
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2)),X1))
| ~ class_Orderings_Opreorder(X0)
| ~ class_Lattices_Olattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_610])]) ).
fof(f2126,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2)),X1))
| ~ class_Orderings_Opreorder(X0)
| ~ class_Lattices_Olattice(X0) )
| ~ spl0_141
| ~ spl0_183 ),
inference(resolution,[],[f1998,f1697]) ).
fof(f17387,plain,
( spl0_609
| ~ spl0_143
| ~ spl0_183 ),
inference(avatar_split_clause,[],[f2125,f1997,f1704,f17385]) ).
fof(f17385,plain,
( spl0_609
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X1)))
| ~ class_Orderings_Opreorder(X0)
| ~ class_Lattices_Olattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_609])]) ).
fof(f2125,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X1)))
| ~ class_Orderings_Opreorder(X0)
| ~ class_Lattices_Olattice(X0) )
| ~ spl0_143
| ~ spl0_183 ),
inference(resolution,[],[f1998,f1705]) ).
fof(f17383,plain,
( spl0_608
| ~ spl0_144
| ~ spl0_183 ),
inference(avatar_split_clause,[],[f2124,f1997,f1708,f17381]) ).
fof(f17381,plain,
( spl0_608
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X1)))
| ~ class_Orderings_Opreorder(X0)
| ~ class_Lattices_Olower__semilattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_608])]) ).
fof(f2124,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X1)))
| ~ class_Orderings_Opreorder(X0)
| ~ class_Lattices_Olower__semilattice(X0) )
| ~ spl0_144
| ~ spl0_183 ),
inference(resolution,[],[f1998,f1709]) ).
fof(f17379,plain,
( spl0_607
| ~ spl0_113
| ~ spl0_183 ),
inference(avatar_split_clause,[],[f2123,f1997,f1537,f17377]) ).
fof(f17377,plain,
( spl0_607
<=> ! [X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),X1),c_COMBK(c_False,tc_bool,X0)))
| ~ class_Orderings_Opreorder(tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_607])]) ).
fof(f2123,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),X1),c_COMBK(c_False,tc_bool,X0)))
| ~ class_Orderings_Opreorder(tc_fun(X0,tc_bool)) )
| ~ spl0_113
| ~ spl0_183 ),
inference(resolution,[],[f1998,f1538]) ).
fof(f17375,plain,
( spl0_606
| ~ spl0_197
| ~ spl0_227 ),
inference(avatar_split_clause,[],[f3975,f2580,f2054,f17373]) ).
fof(f17373,plain,
( spl0_606
<=> ! [X0,X1] : c_The(c_Finite__Set_Ofold1Set(X1,c_SetInterval_Oord__class_OatLeastAtMost(X0,X0,tc_bool),tc_bool),tc_bool) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_606])]) ).
fof(f3975,plain,
( ! [X0,X1] : c_The(c_Finite__Set_Ofold1Set(X1,c_SetInterval_Oord__class_OatLeastAtMost(X0,X0,tc_bool),tc_bool),tc_bool) = X0
| ~ spl0_197
| ~ spl0_227 ),
inference(superposition,[],[f2055,f2581]) ).
fof(f17371,plain,
( spl0_605
| ~ spl0_142
| ~ spl0_183 ),
inference(avatar_split_clause,[],[f2121,f1997,f1700,f17369]) ).
fof(f17369,plain,
( spl0_605
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2)))
| ~ class_Orderings_Opreorder(X0)
| ~ class_Lattices_Olattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_605])]) ).
fof(f2121,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2)))
| ~ class_Orderings_Opreorder(X0)
| ~ class_Lattices_Olattice(X0) )
| ~ spl0_142
| ~ spl0_183 ),
inference(resolution,[],[f1998,f1701]) ).
fof(f17367,plain,
( spl0_604
| ~ spl0_145
| ~ spl0_183 ),
inference(avatar_split_clause,[],[f2120,f1997,f1712,f17365]) ).
fof(f17365,plain,
( spl0_604
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2)))
| ~ class_Orderings_Opreorder(X0)
| ~ class_Lattices_Olower__semilattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_604])]) ).
fof(f2120,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2)))
| ~ class_Orderings_Opreorder(X0)
| ~ class_Lattices_Olower__semilattice(X0) )
| ~ spl0_145
| ~ spl0_183 ),
inference(resolution,[],[f1998,f1713]) ).
fof(f16941,plain,
( spl0_603
| ~ spl0_98
| ~ spl0_227 ),
inference(avatar_split_clause,[],[f3969,f2580,f1452,f16939]) ).
fof(f16939,plain,
( spl0_603
<=> ! [X0,X1] :
( ~ hBOOL(c_in(X1,c_SetInterval_Oord__class_OatLeastAtMost(X0,X0,tc_bool),tc_bool))
| X0 = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_603])]) ).
fof(f1452,plain,
( spl0_98
<=> ! [X4,X0,X3] :
( ~ hBOOL(c_in(X4,hAPP(c_fequal(X0),X3),X0))
| X3 = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_98])]) ).
fof(f3969,plain,
( ! [X0,X1] :
( ~ hBOOL(c_in(X1,c_SetInterval_Oord__class_OatLeastAtMost(X0,X0,tc_bool),tc_bool))
| X0 = X1 )
| ~ spl0_98
| ~ spl0_227 ),
inference(superposition,[],[f1453,f2581]) ).
fof(f1453,plain,
( ! [X3,X0,X4] :
( ~ hBOOL(c_in(X4,hAPP(c_fequal(X0),X3),X0))
| X3 = X4 )
| ~ spl0_98 ),
inference(avatar_component_clause,[],[f1452]) ).
fof(f16918,plain,
( spl0_602
| ~ spl0_130
| ~ spl0_262 ),
inference(avatar_split_clause,[],[f3466,f3117,f1631,f16916]) ).
fof(f16914,plain,
( spl0_601
| ~ spl0_146
| ~ spl0_252 ),
inference(avatar_split_clause,[],[f3272,f3077,f1716,f16912]) ).
fof(f3272,plain,
( ! [X2,X3,X0,X1] : hBOOL(c_in(X0,hAPP(hAPP(c_Set_Oinsert(X1),X2),hAPP(hAPP(c_Set_Oinsert(X1),X0),X3)),X1))
| ~ spl0_146
| ~ spl0_252 ),
inference(resolution,[],[f3078,f1717]) ).
fof(f16907,plain,
( spl0_600
| ~ spl0_146
| ~ spl0_251 ),
inference(avatar_split_clause,[],[f3241,f3073,f1716,f16905]) ).
fof(f16905,plain,
( spl0_600
<=> ! [X2,X0,X1] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Set_Oinsert(X0),X1),X2)),X2) = X2 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_600])]) ).
fof(f3241,plain,
( ! [X2,X0,X1] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Set_Oinsert(X0),X1),X2)),X2) = X2
| ~ spl0_146
| ~ spl0_251 ),
inference(resolution,[],[f3074,f1717]) ).
fof(f16903,plain,
( spl0_599
| ~ spl0_146
| ~ spl0_250 ),
inference(avatar_split_clause,[],[f3215,f3059,f1716,f16901]) ).
fof(f3215,plain,
( ! [X2,X0,X1] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X1),hAPP(hAPP(c_Set_Oinsert(X0),X2),X1)) = X1
| ~ spl0_146
| ~ spl0_250 ),
inference(resolution,[],[f3060,f1717]) ).
fof(f16899,plain,
( spl0_598
| ~ spl0_77
| ~ spl0_233 ),
inference(avatar_split_clause,[],[f2925,f2645,f1353,f16897]) ).
fof(f16897,plain,
( spl0_598
<=> ! [X3,X4,X0,X5,X2,X1] : hBOOL(c_in(X1,hAPP(hAPP(hAPP(c_COMBS(X3,X4,X5),c_Set_Oinsert(X0)),X2),X1),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_598])]) ).
fof(f1353,plain,
( spl0_77
<=> ! [X9,X0,X1] : hBOOL(c_in(X1,hAPP(hAPP(c_Set_Oinsert(X0),X1),X9),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_77])]) ).
fof(f2925,plain,
( ! [X2,X3,X0,X1,X4,X5] : hBOOL(c_in(X1,hAPP(hAPP(hAPP(c_COMBS(X3,X4,X5),c_Set_Oinsert(X0)),X2),X1),X0))
| ~ spl0_77
| ~ spl0_233 ),
inference(superposition,[],[f1354,f2646]) ).
fof(f1354,plain,
( ! [X0,X1,X9] : hBOOL(c_in(X1,hAPP(hAPP(c_Set_Oinsert(X0),X1),X9),X0))
| ~ spl0_77 ),
inference(avatar_component_clause,[],[f1353]) ).
fof(f16895,plain,
( spl0_597
| ~ spl0_75
| ~ spl0_233 ),
inference(avatar_split_clause,[],[f2893,f2645,f1344,f16893]) ).
fof(f16893,plain,
( spl0_597
<=> ! [X2,X4,X0,X3,X1] :
( hBOOL(hAPP(hAPP(hAPP(c_COMBS(X2,X3,X4),c_lessequals(X0)),X1),c_Orderings_Obot__class_Obot(X0)))
| ~ class_Orderings_Obot(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_597])]) ).
fof(f2893,plain,
( ! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(hAPP(hAPP(c_COMBS(X2,X3,X4),c_lessequals(X0)),X1),c_Orderings_Obot__class_Obot(X0)))
| ~ class_Orderings_Obot(X0) )
| ~ spl0_75
| ~ spl0_233 ),
inference(superposition,[],[f1345,f2646]) ).
fof(f16891,plain,
( spl0_596
| ~ spl0_186
| ~ spl0_224 ),
inference(avatar_split_clause,[],[f2598,f2295,f2009,f16889]) ).
fof(f16889,plain,
( spl0_596
<=> ! [X2,X0,X1,X3] :
( hBOOL(hAPP(X0,X1))
| ~ hBOOL(hAPP(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X2,tc_bool)),X0),X3),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_596])]) ).
fof(f2598,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(hAPP(X0,X1))
| ~ hBOOL(hAPP(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X2,tc_bool)),X0),X3),X1)) )
| ~ spl0_186
| ~ spl0_224 ),
inference(resolution,[],[f2296,f2010]) ).
fof(f16887,plain,
( spl0_595
| ~ spl0_31
| ~ spl0_97 ),
inference(avatar_split_clause,[],[f1480,f1448,f1151,f16885]) ).
fof(f1448,plain,
( spl0_97
<=> ! [X0,X3] :
( hAPP(c_fequal(X0),X3) = c_SetInterval_Oord__class_OatLeastAtMost(X3,X3,X0)
| ~ class_Orderings_Oorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_97])]) ).
fof(f1480,plain,
( ! [X2,X0,X1] :
( hAPP(c_fequal(tc_fun(X0,X1)),X2) = c_SetInterval_Oord__class_OatLeastAtMost(X2,X2,tc_fun(X0,X1))
| ~ class_Orderings_Oorder(X1) )
| ~ spl0_31
| ~ spl0_97 ),
inference(resolution,[],[f1449,f1152]) ).
fof(f1449,plain,
( ! [X3,X0] :
( ~ class_Orderings_Oorder(X0)
| hAPP(c_fequal(X0),X3) = c_SetInterval_Oord__class_OatLeastAtMost(X3,X3,X0) )
| ~ spl0_97 ),
inference(avatar_component_clause,[],[f1448]) ).
fof(f16883,plain,
( spl0_594
| ~ spl0_24
| ~ spl0_96 ),
inference(avatar_split_clause,[],[f1478,f1444,f1123,f16881]) ).
fof(f1444,plain,
( spl0_96
<=> ! [X0,X3] :
( hAPP(c_Complete__Lattice_OInf__class_OInf(X0),hAPP(c_fequal(X0),X3)) = X3
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_96])]) ).
fof(f1478,plain,
( ! [X2,X0,X1] :
( hAPP(c_Complete__Lattice_OInf__class_OInf(tc_fun(X0,X1)),hAPP(c_fequal(tc_fun(X0,X1)),X2)) = X2
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) )
| ~ spl0_24
| ~ spl0_96 ),
inference(resolution,[],[f1445,f1124]) ).
fof(f1445,plain,
( ! [X3,X0] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
| hAPP(c_Complete__Lattice_OInf__class_OInf(X0),hAPP(c_fequal(X0),X3)) = X3 )
| ~ spl0_96 ),
inference(avatar_component_clause,[],[f1444]) ).
fof(f16879,plain,
( spl0_593
| ~ spl0_24
| ~ spl0_95 ),
inference(avatar_split_clause,[],[f1476,f1440,f1123,f16877]) ).
fof(f1440,plain,
( spl0_95
<=> ! [X0,X3] :
( hAPP(c_Complete__Lattice_OSup__class_OSup(X0),hAPP(c_fequal(X0),X3)) = X3
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_95])]) ).
fof(f1476,plain,
( ! [X2,X0,X1] :
( hAPP(c_Complete__Lattice_OSup__class_OSup(tc_fun(X0,X1)),hAPP(c_fequal(tc_fun(X0,X1)),X2)) = X2
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) )
| ~ spl0_24
| ~ spl0_95 ),
inference(resolution,[],[f1441,f1124]) ).
fof(f1441,plain,
( ! [X3,X0] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
| hAPP(c_Complete__Lattice_OSup__class_OSup(X0),hAPP(c_fequal(X0),X3)) = X3 )
| ~ spl0_95 ),
inference(avatar_component_clause,[],[f1440]) ).
fof(f16875,plain,
( spl0_592
| ~ spl0_33
| ~ spl0_93 ),
inference(avatar_split_clause,[],[f1468,f1431,f1159,f16873]) ).
fof(f1159,plain,
( spl0_33
<=> ! [X75,X74] :
( ~ class_Orderings_Obot(X75)
| class_Orderings_Obot(tc_fun(X74,X75)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_33])]) ).
fof(f1431,plain,
( spl0_93
<=> ! [X8] :
( ~ class_Orderings_Obot(X8)
| hAPP(c_Orderings_Obot__class_Obot(tc_fun(t_a,X8)),v_x) = c_Orderings_Obot__class_Obot(X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_93])]) ).
fof(f1468,plain,
( ! [X0,X1] :
( c_Orderings_Obot__class_Obot(tc_fun(X0,X1)) = hAPP(c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_fun(X0,X1))),v_x)
| ~ class_Orderings_Obot(X1) )
| ~ spl0_33
| ~ spl0_93 ),
inference(resolution,[],[f1432,f1160]) ).
fof(f1160,plain,
( ! [X74,X75] :
( class_Orderings_Obot(tc_fun(X74,X75))
| ~ class_Orderings_Obot(X75) )
| ~ spl0_33 ),
inference(avatar_component_clause,[],[f1159]) ).
fof(f1432,plain,
( ! [X8] :
( ~ class_Orderings_Obot(X8)
| hAPP(c_Orderings_Obot__class_Obot(tc_fun(t_a,X8)),v_x) = c_Orderings_Obot__class_Obot(X8) )
| ~ spl0_93 ),
inference(avatar_component_clause,[],[f1431]) ).
fof(f16871,plain,
( spl0_591
| ~ spl0_28
| ~ spl0_89 ),
inference(avatar_split_clause,[],[f1464,f1415,f1139,f16869]) ).
fof(f16869,plain,
( spl0_591
<=> ! [X2,X0,X1] :
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,X1)),X2),c_Orderings_Obot__class_Obot(tc_fun(X0,X1))) = X2
| ~ class_Lattices_Obounded__lattice(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_591])]) ).
fof(f1415,plain,
( spl0_89
<=> ! [X0,X1] :
( ~ class_Lattices_Obounded__lattice(X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),c_Orderings_Obot__class_Obot(X0)) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_89])]) ).
fof(f1464,plain,
( ! [X2,X0,X1] :
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,X1)),X2),c_Orderings_Obot__class_Obot(tc_fun(X0,X1))) = X2
| ~ class_Lattices_Obounded__lattice(X1) )
| ~ spl0_28
| ~ spl0_89 ),
inference(resolution,[],[f1416,f1140]) ).
fof(f1416,plain,
( ! [X0,X1] :
( ~ class_Lattices_Obounded__lattice(X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),c_Orderings_Obot__class_Obot(X0)) = X1 )
| ~ spl0_89 ),
inference(avatar_component_clause,[],[f1415]) ).
fof(f16867,plain,
( ~ spl0_7
| spl0_590
| ~ spl0_183
| ~ spl0_488 ),
inference(avatar_split_clause,[],[f13351,f13217,f1997,f16865,f1047]) ).
fof(f1047,plain,
( spl0_7
<=> class_Orderings_Opreorder(tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).
fof(f16865,plain,
( spl0_590
<=> ! [X0] : ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_590])]) ).
fof(f13217,plain,
( spl0_488
<=> ! [X0] : hBOOL(hAPP(hAPP(c_lessequals(tc_bool),X0),c_Orderings_Otop__class_Otop(tc_bool))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_488])]) ).
fof(f13351,plain,
( ! [X0] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),X0))
| ~ class_Orderings_Opreorder(tc_bool) )
| ~ spl0_183
| ~ spl0_488 ),
inference(resolution,[],[f13218,f1998]) ).
fof(f13218,plain,
( ! [X0] : hBOOL(hAPP(hAPP(c_lessequals(tc_bool),X0),c_Orderings_Otop__class_Otop(tc_bool)))
| ~ spl0_488 ),
inference(avatar_component_clause,[],[f13217]) ).
fof(f16863,plain,
( spl0_589
| ~ spl0_28
| ~ spl0_88 ),
inference(avatar_split_clause,[],[f1462,f1411,f1139,f16861]) ).
fof(f16861,plain,
( spl0_589
<=> ! [X2,X0,X1] :
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,X1)),c_Orderings_Obot__class_Obot(tc_fun(X0,X1))),X2) = X2
| ~ class_Lattices_Obounded__lattice(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_589])]) ).
fof(f1411,plain,
( spl0_88
<=> ! [X0,X1] :
( ~ class_Lattices_Obounded__lattice(X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),c_Orderings_Obot__class_Obot(X0)),X1) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_88])]) ).
fof(f1462,plain,
( ! [X2,X0,X1] :
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,X1)),c_Orderings_Obot__class_Obot(tc_fun(X0,X1))),X2) = X2
| ~ class_Lattices_Obounded__lattice(X1) )
| ~ spl0_28
| ~ spl0_88 ),
inference(resolution,[],[f1412,f1140]) ).
fof(f1412,plain,
( ! [X0,X1] :
( ~ class_Lattices_Obounded__lattice(X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),c_Orderings_Obot__class_Obot(X0)),X1) = X1 )
| ~ spl0_88 ),
inference(avatar_component_clause,[],[f1411]) ).
fof(f16859,plain,
( spl0_588
| ~ spl0_32
| ~ spl0_87 ),
inference(avatar_split_clause,[],[f1460,f1407,f1155,f16857]) ).
fof(f1155,plain,
( spl0_32
<=> ! [X75,X74] :
( ~ class_Orderings_Otop(X75)
| class_Orderings_Otop(tc_fun(X74,X75)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_32])]) ).
fof(f1407,plain,
( spl0_87
<=> ! [X8] :
( ~ class_Orderings_Otop(X8)
| hAPP(c_Orderings_Otop__class_Otop(tc_fun(t_a,X8)),v_x) = c_Orderings_Otop__class_Otop(X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_87])]) ).
fof(f1460,plain,
( ! [X0,X1] :
( c_Orderings_Otop__class_Otop(tc_fun(X0,X1)) = hAPP(c_Orderings_Otop__class_Otop(tc_fun(t_a,tc_fun(X0,X1))),v_x)
| ~ class_Orderings_Otop(X1) )
| ~ spl0_32
| ~ spl0_87 ),
inference(resolution,[],[f1408,f1156]) ).
fof(f1156,plain,
( ! [X74,X75] :
( class_Orderings_Otop(tc_fun(X74,X75))
| ~ class_Orderings_Otop(X75) )
| ~ spl0_32 ),
inference(avatar_component_clause,[],[f1155]) ).
fof(f1408,plain,
( ! [X8] :
( ~ class_Orderings_Otop(X8)
| hAPP(c_Orderings_Otop__class_Otop(tc_fun(t_a,X8)),v_x) = c_Orderings_Otop__class_Otop(X8) )
| ~ spl0_87 ),
inference(avatar_component_clause,[],[f1407]) ).
fof(f16855,plain,
( spl0_587
| ~ spl0_28
| ~ spl0_86 ),
inference(avatar_split_clause,[],[f1458,f1403,f1139,f16853]) ).
fof(f16853,plain,
( spl0_587
<=> ! [X2,X0,X1] :
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,X1)),c_Orderings_Otop__class_Otop(tc_fun(X0,X1))),X2) = X2
| ~ class_Lattices_Obounded__lattice(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_587])]) ).
fof(f1403,plain,
( spl0_86
<=> ! [X0,X1] :
( ~ class_Lattices_Obounded__lattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),c_Orderings_Otop__class_Otop(X0)),X1) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_86])]) ).
fof(f1458,plain,
( ! [X2,X0,X1] :
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,X1)),c_Orderings_Otop__class_Otop(tc_fun(X0,X1))),X2) = X2
| ~ class_Lattices_Obounded__lattice(X1) )
| ~ spl0_28
| ~ spl0_86 ),
inference(resolution,[],[f1404,f1140]) ).
fof(f1404,plain,
( ! [X0,X1] :
( ~ class_Lattices_Obounded__lattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),c_Orderings_Otop__class_Otop(X0)),X1) = X1 )
| ~ spl0_86 ),
inference(avatar_component_clause,[],[f1403]) ).
fof(f16851,plain,
( spl0_586
| ~ spl0_28
| ~ spl0_85 ),
inference(avatar_split_clause,[],[f1456,f1399,f1139,f16849]) ).
fof(f16849,plain,
( spl0_586
<=> ! [X2,X0,X1] :
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,X1)),X2),c_Orderings_Otop__class_Otop(tc_fun(X0,X1))) = X2
| ~ class_Lattices_Obounded__lattice(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_586])]) ).
fof(f1399,plain,
( spl0_85
<=> ! [X0,X1] :
( ~ class_Lattices_Obounded__lattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),c_Orderings_Otop__class_Otop(X0)) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_85])]) ).
fof(f1456,plain,
( ! [X2,X0,X1] :
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,X1)),X2),c_Orderings_Otop__class_Otop(tc_fun(X0,X1))) = X2
| ~ class_Lattices_Obounded__lattice(X1) )
| ~ spl0_28
| ~ spl0_85 ),
inference(resolution,[],[f1400,f1140]) ).
fof(f1400,plain,
( ! [X0,X1] :
( ~ class_Lattices_Obounded__lattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),c_Orderings_Otop__class_Otop(X0)) = X1 )
| ~ spl0_85 ),
inference(avatar_component_clause,[],[f1399]) ).
fof(f16597,plain,
( spl0_585
| ~ spl0_125
| ~ spl0_150
| ~ spl0_171
| ~ spl0_412 ),
inference(avatar_split_clause,[],[f8323,f7695,f1873,f1732,f1611,f16595]) ).
fof(f1873,plain,
( spl0_171
<=> ! [X9,X0,X8] : c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)) = c_Complete__Lattice_Ocomplete__lattice__class_OINFI(c_COMBK(c_False,tc_bool,X8),X9,X8,tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_171])]) ).
fof(f8323,plain,
( ! [X2,X3,X0,X1] : hAPP(X2,X1) = c_Complete__Lattice_Ocomplete__lattice__class_OINFI(hAPP(c_fequal(X0),X1),X2,X0,tc_fun(X3,tc_bool))
| ~ spl0_125
| ~ spl0_150
| ~ spl0_171
| ~ spl0_412 ),
inference(forward_demodulation,[],[f8322,f1612]) ).
fof(f8322,plain,
( ! [X2,X3,X0,X1] : c_Complete__Lattice_Ocomplete__lattice__class_OINFI(hAPP(c_fequal(X0),X1),X2,X0,tc_fun(X3,tc_bool)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),hAPP(X2,X1)),c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)))
| ~ spl0_150
| ~ spl0_171
| ~ spl0_412 ),
inference(forward_demodulation,[],[f8195,f1874]) ).
fof(f1874,plain,
( ! [X0,X8,X9] : c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)) = c_Complete__Lattice_Ocomplete__lattice__class_OINFI(c_COMBK(c_False,tc_bool,X8),X9,X8,tc_fun(X0,tc_bool))
| ~ spl0_171 ),
inference(avatar_component_clause,[],[f1873]) ).
fof(f8195,plain,
( ! [X2,X3,X0,X1] : c_Complete__Lattice_Ocomplete__lattice__class_OINFI(hAPP(c_fequal(X0),X1),X2,X0,tc_fun(X3,tc_bool)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),hAPP(X2,X1)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(c_COMBK(c_False,tc_bool,X0),X2,X0,tc_fun(X3,tc_bool)))
| ~ spl0_150
| ~ spl0_412 ),
inference(superposition,[],[f7696,f1733]) ).
fof(f16593,plain,
( spl0_584
| ~ spl0_150
| ~ spl0_263
| ~ spl0_410 ),
inference(avatar_split_clause,[],[f8157,f7687,f3121,f1732,f16591]) ).
fof(f8157,plain,
( ! [X2,X3,X0,X1] : hAPP(X2,X1) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_fequal(X0),X1),X2,X0,tc_fun(X3,tc_bool))
| ~ spl0_150
| ~ spl0_263
| ~ spl0_410 ),
inference(forward_demodulation,[],[f8024,f3122]) ).
fof(f8024,plain,
( ! [X2,X3,X0,X1] : c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_fequal(X0),X1),X2,X0,tc_fun(X3,tc_bool)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),hAPP(X2,X1)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_COMBK(c_False,tc_bool,X0),X2,X0,tc_fun(X3,tc_bool)))
| ~ spl0_150
| ~ spl0_410 ),
inference(superposition,[],[f7688,f1733]) ).
fof(f16589,plain,
( spl0_583
| ~ spl0_64
| ~ spl0_340 ),
inference(avatar_split_clause,[],[f5403,f4949,f1291,f16587]) ).
fof(f5403,plain,
( ! [X2,X3,X0,X1] : hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X0),X2),hAPP(hAPP(c_Set_Oinsert(X0),X1),X3)),X1))
| ~ spl0_64
| ~ spl0_340 ),
inference(superposition,[],[f1292,f4950]) ).
fof(f16585,plain,
( spl0_582
| ~ spl0_64
| ~ spl0_233 ),
inference(avatar_split_clause,[],[f2924,f2645,f1291,f16583]) ).
fof(f16583,plain,
( spl0_582
<=> ! [X3,X4,X0,X5,X2,X1] : hBOOL(hAPP(hAPP(hAPP(hAPP(c_COMBS(X3,X4,X5),c_Set_Oinsert(X0)),X2),X1),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_582])]) ).
fof(f2924,plain,
( ! [X2,X3,X0,X1,X4,X5] : hBOOL(hAPP(hAPP(hAPP(hAPP(c_COMBS(X3,X4,X5),c_Set_Oinsert(X0)),X2),X1),X1))
| ~ spl0_64
| ~ spl0_233 ),
inference(superposition,[],[f1292,f2646]) ).
fof(f16581,plain,
( spl0_580
| spl0_581
| ~ spl0_51
| ~ spl0_230 ),
inference(avatar_split_clause,[],[f2783,f2633,f1237,f16579,f16576]) ).
fof(f16576,plain,
( spl0_580
<=> ! [X5,X0,X6,X2,X1] : ~ c_Fun_Oinj__on(c_COMBK(X0,X1,X2),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_bool)),X5,X6) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_580])]) ).
fof(f2783,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] :
( X3 = X4
| ~ c_Fun_Oinj__on(c_COMBK(X0,X1,X2),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_bool)),X5,X6) )
| ~ spl0_51
| ~ spl0_230 ),
inference(trivial_inequality_removal,[],[f2782]) ).
fof(f2782,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] :
( X0 != X0
| X3 = X4
| ~ c_Fun_Oinj__on(c_COMBK(X0,X1,X2),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_bool)),X5,X6) )
| ~ spl0_51
| ~ spl0_230 ),
inference(forward_demodulation,[],[f2731,f1238]) ).
fof(f2731,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] :
( hAPP(c_COMBK(X0,X1,X2),X4) != X0
| X3 = X4
| ~ c_Fun_Oinj__on(c_COMBK(X0,X1,X2),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_bool)),X5,X6) )
| ~ spl0_51
| ~ spl0_230 ),
inference(superposition,[],[f2634,f1238]) ).
fof(f16574,plain,
( spl0_579
| ~ spl0_74
| ~ spl0_217 ),
inference(avatar_split_clause,[],[f2543,f2267,f1340,f16572]) ).
fof(f16572,plain,
( spl0_579
<=> ! [X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| c_Orderings_Otop__class_Otop(X0) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),c_Orderings_Otop__class_Otop(X0))
| ~ class_Orderings_Otop(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_579])]) ).
fof(f2543,plain,
( ! [X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| c_Orderings_Otop__class_Otop(X0) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),c_Orderings_Otop__class_Otop(X0))
| ~ class_Orderings_Otop(X0) )
| ~ spl0_74
| ~ spl0_217 ),
inference(resolution,[],[f2268,f1341]) ).
fof(f16570,plain,
( spl0_578
| ~ spl0_227
| ~ spl0_567 ),
inference(avatar_split_clause,[],[f16490,f16050,f2580,f16568]) ).
fof(f16568,plain,
( spl0_578
<=> ! [X0] : c_Finite__Set_Ofinite(c_SetInterval_Oord__class_OatLeastAtMost(X0,X0,tc_bool),tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_578])]) ).
fof(f16490,plain,
( ! [X0] : c_Finite__Set_Ofinite(c_SetInterval_Oord__class_OatLeastAtMost(X0,X0,tc_bool),tc_bool)
| ~ spl0_227
| ~ spl0_567 ),
inference(superposition,[],[f16051,f2581]) ).
fof(f16566,plain,
( spl0_577
| ~ spl0_74
| ~ spl0_215 ),
inference(avatar_split_clause,[],[f2504,f2259,f1340,f16564]) ).
fof(f16564,plain,
( spl0_577
<=> ! [X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| c_Orderings_Otop__class_Otop(X0) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),c_Orderings_Otop__class_Otop(X0)),X1)
| ~ class_Orderings_Otop(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_577])]) ).
fof(f2504,plain,
( ! [X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| c_Orderings_Otop__class_Otop(X0) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),c_Orderings_Otop__class_Otop(X0)),X1)
| ~ class_Orderings_Otop(X0) )
| ~ spl0_74
| ~ spl0_215 ),
inference(resolution,[],[f2260,f1341]) ).
fof(f16562,plain,
( spl0_576
| ~ spl0_75
| ~ spl0_212 ),
inference(avatar_split_clause,[],[f2376,f2247,f1344,f16560]) ).
fof(f16560,plain,
( spl0_576
<=> ! [X0,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| c_Orderings_Obot__class_Obot(X0) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),c_Orderings_Obot__class_Obot(X0))
| ~ class_Orderings_Obot(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_576])]) ).
fof(f2376,plain,
( ! [X0,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| c_Orderings_Obot__class_Obot(X0) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),c_Orderings_Obot__class_Obot(X0))
| ~ class_Orderings_Obot(X0) )
| ~ spl0_75
| ~ spl0_212 ),
inference(resolution,[],[f2248,f1345]) ).
fof(f16558,plain,
( spl0_575
| ~ spl0_75
| ~ spl0_210 ),
inference(avatar_split_clause,[],[f2335,f2233,f1344,f16556]) ).
fof(f16556,plain,
( spl0_575
<=> ! [X0,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| c_Orderings_Obot__class_Obot(X0) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),c_Orderings_Obot__class_Obot(X0)),X1)
| ~ class_Orderings_Obot(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_575])]) ).
fof(f2335,plain,
( ! [X0,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| c_Orderings_Obot__class_Obot(X0) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),c_Orderings_Obot__class_Obot(X0)),X1)
| ~ class_Orderings_Obot(X0) )
| ~ spl0_75
| ~ spl0_210 ),
inference(resolution,[],[f2234,f1345]) ).
fof(f16554,plain,
( spl0_574
| ~ spl0_57
| ~ spl0_167 ),
inference(avatar_split_clause,[],[f1953,f1854,f1262,f16552]) ).
fof(f16552,plain,
( spl0_574
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(c_in(X0,X1,X2))
| hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X2),X3),X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_574])]) ).
fof(f1953,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(c_in(X0,X1,X2))
| hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X2),X3),X1),X0)) )
| ~ spl0_57
| ~ spl0_167 ),
inference(resolution,[],[f1855,f1263]) ).
fof(f16076,plain,
( spl0_573
| ~ spl0_178
| ~ spl0_219 ),
inference(avatar_split_clause,[],[f2557,f2275,f1976,f16074]) ).
fof(f16074,plain,
( spl0_573
<=> ! [X0,X3,X2,X1] :
( ~ c_Fun_Oinj__on(X2,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0,X3)
| c_Fun_Oinj__on(X2,X1,X0,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_573])]) ).
fof(f2557,plain,
( ! [X2,X3,X0,X1] :
( ~ c_Fun_Oinj__on(X2,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0,X3)
| c_Fun_Oinj__on(X2,X1,X0,X3) )
| ~ spl0_178
| ~ spl0_219 ),
inference(superposition,[],[f2276,f1977]) ).
fof(f16072,plain,
( spl0_572
| ~ spl0_75
| ~ spl0_217 ),
inference(avatar_split_clause,[],[f2531,f2267,f1344,f16070]) ).
fof(f16070,plain,
( spl0_572
<=> ! [X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),c_Orderings_Obot__class_Obot(X0)),X1) = X1
| ~ class_Orderings_Obot(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_572])]) ).
fof(f2531,plain,
( ! [X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),c_Orderings_Obot__class_Obot(X0)),X1) = X1
| ~ class_Orderings_Obot(X0) )
| ~ spl0_75
| ~ spl0_217 ),
inference(resolution,[],[f2268,f1345]) ).
fof(f16068,plain,
( spl0_571
| ~ spl0_75
| ~ spl0_215 ),
inference(avatar_split_clause,[],[f2492,f2259,f1344,f16066]) ).
fof(f16066,plain,
( spl0_571
<=> ! [X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),c_Orderings_Obot__class_Obot(X0)) = X1
| ~ class_Orderings_Obot(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_571])]) ).
fof(f2492,plain,
( ! [X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),c_Orderings_Obot__class_Obot(X0)) = X1
| ~ class_Orderings_Obot(X0) )
| ~ spl0_75
| ~ spl0_215 ),
inference(resolution,[],[f2260,f1345]) ).
fof(f16064,plain,
( spl0_570
| ~ spl0_74
| ~ spl0_212 ),
inference(avatar_split_clause,[],[f2388,f2247,f1340,f16062]) ).
fof(f16062,plain,
( spl0_570
<=> ! [X0,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),c_Orderings_Otop__class_Otop(X0)),X1) = X1
| ~ class_Orderings_Otop(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_570])]) ).
fof(f2388,plain,
( ! [X0,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),c_Orderings_Otop__class_Otop(X0)),X1) = X1
| ~ class_Orderings_Otop(X0) )
| ~ spl0_74
| ~ spl0_212 ),
inference(resolution,[],[f2248,f1341]) ).
fof(f16060,plain,
( spl0_569
| ~ spl0_74
| ~ spl0_210 ),
inference(avatar_split_clause,[],[f2347,f2233,f1340,f16058]) ).
fof(f16058,plain,
( spl0_569
<=> ! [X0,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),c_Orderings_Otop__class_Otop(X0)) = X1
| ~ class_Orderings_Otop(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_569])]) ).
fof(f2347,plain,
( ! [X0,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),c_Orderings_Otop__class_Otop(X0)) = X1
| ~ class_Orderings_Otop(X0) )
| ~ spl0_74
| ~ spl0_210 ),
inference(resolution,[],[f2234,f1341]) ).
fof(f16056,plain,
( spl0_568
| ~ spl0_16
| ~ spl0_174 ),
inference(avatar_split_clause,[],[f1973,f1887,f1090,f16054]) ).
fof(f1887,plain,
( spl0_174
<=> ! [X0,X3] : c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X3),X0) = hAPP(c_fequal(X0),X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_174])]) ).
fof(f1973,plain,
( ! [X0,X1] : hAPP(c_fequal(X0),X1) = hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1)
| ~ spl0_16
| ~ spl0_174 ),
inference(superposition,[],[f1888,f1091]) ).
fof(f1888,plain,
( ! [X3,X0] : c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X3),X0) = hAPP(c_fequal(X0),X3)
| ~ spl0_174 ),
inference(avatar_component_clause,[],[f1887]) ).
fof(f16052,plain,
( spl0_567
| ~ spl0_36
| ~ spl0_560 ),
inference(avatar_split_clause,[],[f16022,f15837,f1171,f16050]) ).
fof(f1171,plain,
( spl0_36
<=> ! [X0] : c_Finite__Set_Ofinite(c_COMBK(c_False,tc_bool,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_36])]) ).
fof(f15837,plain,
( spl0_560
<=> ! [X0,X1] :
( c_Finite__Set_Ofinite(hAPP(c_fequal(X0),X1),X0)
| ~ c_Finite__Set_Ofinite(c_COMBK(c_False,tc_bool,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_560])]) ).
fof(f16022,plain,
( ! [X0,X1] : c_Finite__Set_Ofinite(hAPP(c_fequal(X0),X1),X0)
| ~ spl0_36
| ~ spl0_560 ),
inference(resolution,[],[f15838,f1172]) ).
fof(f1172,plain,
( ! [X0] : c_Finite__Set_Ofinite(c_COMBK(c_False,tc_bool,X0),X0)
| ~ spl0_36 ),
inference(avatar_component_clause,[],[f1171]) ).
fof(f15838,plain,
( ! [X0,X1] :
( ~ c_Finite__Set_Ofinite(c_COMBK(c_False,tc_bool,X0),X0)
| c_Finite__Set_Ofinite(hAPP(c_fequal(X0),X1),X0) )
| ~ spl0_560 ),
inference(avatar_component_clause,[],[f15837]) ).
fof(f16048,plain,
( spl0_566
| ~ spl0_8
| ~ spl0_162 ),
inference(avatar_split_clause,[],[f1931,f1834,f1052,f16046]) ).
fof(f1931,plain,
( ! [X0,X1] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),X0),X1)) = X0
| ~ spl0_8
| ~ spl0_162 ),
inference(resolution,[],[f1835,f1054]) ).
fof(f16044,plain,
( spl0_565
| ~ spl0_8
| ~ spl0_161 ),
inference(avatar_split_clause,[],[f1929,f1830,f1052,f16042]) ).
fof(f1929,plain,
( ! [X0,X1] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),X0),X1)) = X0
| ~ spl0_8
| ~ spl0_161 ),
inference(resolution,[],[f1831,f1054]) ).
fof(f16040,plain,
( spl0_564
| ~ spl0_2
| ~ spl0_156 ),
inference(avatar_split_clause,[],[f1911,f1810,f1022,f16038]) ).
fof(f1911,plain,
( ! [X0,X1] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),X0),X1) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),X1),X0)
| ~ spl0_2
| ~ spl0_156 ),
inference(resolution,[],[f1811,f1024]) ).
fof(f16036,plain,
( spl0_563
| ~ spl0_3
| ~ spl0_154 ),
inference(avatar_split_clause,[],[f1907,f1802,f1027,f16034]) ).
fof(f1907,plain,
( ! [X0,X1] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),X0),X1) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),X1),X0)
| ~ spl0_3
| ~ spl0_154 ),
inference(resolution,[],[f1803,f1029]) ).
fof(f1029,plain,
( class_Lattices_Olower__semilattice(tc_bool)
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f1027]) ).
fof(f15847,plain,
( spl0_562
| ~ spl0_74
| ~ spl0_183 ),
inference(avatar_split_clause,[],[f2131,f1997,f1340,f15845]) ).
fof(f15845,plain,
( spl0_562
<=> ! [X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_Orderings_Otop__class_Otop(X0)),X1))
| ~ class_Orderings_Opreorder(X0)
| ~ class_Orderings_Otop(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_562])]) ).
fof(f2131,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_Orderings_Otop__class_Otop(X0)),X1))
| ~ class_Orderings_Opreorder(X0)
| ~ class_Orderings_Otop(X0) )
| ~ spl0_74
| ~ spl0_183 ),
inference(resolution,[],[f1998,f1341]) ).
fof(f15843,plain,
( spl0_561
| ~ spl0_75
| ~ spl0_183 ),
inference(avatar_split_clause,[],[f2122,f1997,f1344,f15841]) ).
fof(f15841,plain,
( spl0_561
<=> ! [X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),c_Orderings_Obot__class_Obot(X0)))
| ~ class_Orderings_Opreorder(X0)
| ~ class_Orderings_Obot(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_561])]) ).
fof(f2122,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),c_Orderings_Obot__class_Obot(X0)))
| ~ class_Orderings_Opreorder(X0)
| ~ class_Orderings_Obot(X0) )
| ~ spl0_75
| ~ spl0_183 ),
inference(resolution,[],[f1998,f1345]) ).
fof(f15839,plain,
( spl0_560
| ~ spl0_90
| ~ spl0_150 ),
inference(avatar_split_clause,[],[f1787,f1732,f1419,f15837]) ).
fof(f1787,plain,
( ! [X0,X1] :
( c_Finite__Set_Ofinite(hAPP(c_fequal(X0),X1),X0)
| ~ c_Finite__Set_Ofinite(c_COMBK(c_False,tc_bool,X0),X0) )
| ~ spl0_90
| ~ spl0_150 ),
inference(superposition,[],[f1420,f1733]) ).
fof(f15835,plain,
( spl0_559
| ~ spl0_56
| ~ spl0_128 ),
inference(avatar_split_clause,[],[f1666,f1623,f1258,f15833]) ).
fof(f1666,plain,
( ! [X2,X0,X1] :
( hAPP(hAPP(c_Set_Oinsert(X0),X1),X2) = X2
| ~ hBOOL(hAPP(X2,X1)) )
| ~ spl0_56
| ~ spl0_128 ),
inference(resolution,[],[f1624,f1259]) ).
fof(f15831,plain,
( spl0_558
| ~ spl0_26
| ~ spl0_78 ),
inference(avatar_split_clause,[],[f1390,f1357,f1131,f15829]) ).
fof(f1357,plain,
( spl0_78
<=> ! [X0,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X1) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_78])]) ).
fof(f1390,plain,
( ! [X2,X0,X1] :
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,X1)),X2),X2) = X2
| ~ class_Lattices_Olattice(X1) )
| ~ spl0_26
| ~ spl0_78 ),
inference(resolution,[],[f1358,f1132]) ).
fof(f1358,plain,
( ! [X0,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X1) = X1 )
| ~ spl0_78 ),
inference(avatar_component_clause,[],[f1357]) ).
fof(f15827,plain,
( spl0_557
| ~ spl0_25
| ~ spl0_69 ),
inference(avatar_split_clause,[],[f1378,f1320,f1127,f15825]) ).
fof(f1320,plain,
( spl0_69
<=> ! [X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X1) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_69])]) ).
fof(f1378,plain,
( ! [X2,X0,X1] :
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,X1)),X2),X2) = X2
| ~ class_Lattices_Olattice(X1) )
| ~ spl0_25
| ~ spl0_69 ),
inference(resolution,[],[f1321,f1128]) ).
fof(f1321,plain,
( ! [X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X1) = X1 )
| ~ spl0_69 ),
inference(avatar_component_clause,[],[f1320]) ).
fof(f15822,plain,
( spl0_556
| ~ spl0_79
| ~ spl0_346 ),
inference(avatar_split_clause,[],[f5568,f4974,f1361,f15820]) ).
fof(f15820,plain,
( spl0_556
<=> ! [X2,X0,X1] :
( c_COMBK(c_False,tc_bool,X0) != X1
| ~ hBOOL(c_in(X2,X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_556])]) ).
fof(f4974,plain,
( spl0_346
<=> ! [X9,X0,X5,X1] :
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X5),X9) != c_COMBK(c_False,tc_bool,X0)
| ~ hBOOL(c_in(X1,X9,X0))
| ~ hBOOL(c_in(X1,X5,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_346])]) ).
fof(f5568,plain,
( ! [X2,X0,X1] :
( c_COMBK(c_False,tc_bool,X0) != X1
| ~ hBOOL(c_in(X2,X1,X0)) )
| ~ spl0_79
| ~ spl0_346 ),
inference(duplicate_literal_removal,[],[f5556]) ).
fof(f5556,plain,
( ! [X2,X0,X1] :
( c_COMBK(c_False,tc_bool,X0) != X1
| ~ hBOOL(c_in(X2,X1,X0))
| ~ hBOOL(c_in(X2,X1,X0)) )
| ~ spl0_79
| ~ spl0_346 ),
inference(superposition,[],[f4975,f1362]) ).
fof(f4975,plain,
( ! [X0,X1,X9,X5] :
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X5),X9) != c_COMBK(c_False,tc_bool,X0)
| ~ hBOOL(c_in(X1,X9,X0))
| ~ hBOOL(c_in(X1,X5,X0)) )
| ~ spl0_346 ),
inference(avatar_component_clause,[],[f4974]) ).
fof(f15755,plain,
( spl0_555
| ~ spl0_342
| ~ spl0_508
| ~ spl0_553 ),
inference(avatar_split_clause,[],[f15747,f15742,f13711,f4957,f15753]) ).
fof(f15753,plain,
( spl0_555
<=> ! [X5,X0,X12,X9,X8,X7] :
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X8,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,hAPP(hAPP(c_COMBB(X8,tc_fun(X8,tc_bool),X0),hAPP(c_COMBC(c_Set_Oinsert(X8),X8,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8))),X7),X0,tc_fun(X8,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X9,hAPP(hAPP(c_COMBB(X8,tc_fun(X8,tc_bool),X0),hAPP(c_COMBC(c_Set_Oinsert(X8),X8,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8))),X7),X0,tc_fun(X8,tc_bool))) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X5),X9),hAPP(hAPP(c_COMBB(X8,tc_fun(X8,tc_bool),X0),hAPP(c_COMBC(c_Set_Oinsert(X8),X8,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8))),X7),X0,tc_fun(X8,tc_bool))
| ~ c_Fun_Oinj__on(X7,X12,X0,X8)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X5),X12))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X9),X12)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_555])]) ).
fof(f15742,plain,
( spl0_553
<=> ! [X5,X0,X12,X9,X8,X7] :
( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X5),X9),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X8,tc_fun(tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),X0),c_Set_Oinsert(X8)),X7),X0,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8)),X0,tc_fun(X8,tc_bool)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X8,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X8,tc_fun(tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),X0),c_Set_Oinsert(X8)),X7),X0,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8)),X0,tc_fun(X8,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X9,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X8,tc_fun(tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),X0),c_Set_Oinsert(X8)),X7),X0,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8)),X0,tc_fun(X8,tc_bool)))
| ~ c_Fun_Oinj__on(X7,X12,X0,X8)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X5),X12))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X9),X12)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_553])]) ).
fof(f15747,plain,
( ! [X0,X8,X9,X7,X5,X12] :
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X8,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,hAPP(hAPP(c_COMBB(X8,tc_fun(X8,tc_bool),X0),hAPP(c_COMBC(c_Set_Oinsert(X8),X8,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8))),X7),X0,tc_fun(X8,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X9,hAPP(hAPP(c_COMBB(X8,tc_fun(X8,tc_bool),X0),hAPP(c_COMBC(c_Set_Oinsert(X8),X8,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8))),X7),X0,tc_fun(X8,tc_bool))) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X5),X9),hAPP(hAPP(c_COMBB(X8,tc_fun(X8,tc_bool),X0),hAPP(c_COMBC(c_Set_Oinsert(X8),X8,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8))),X7),X0,tc_fun(X8,tc_bool))
| ~ c_Fun_Oinj__on(X7,X12,X0,X8)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X5),X12))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X9),X12)) )
| ~ spl0_342
| ~ spl0_508
| ~ spl0_553 ),
inference(forward_demodulation,[],[f15746,f13758]) ).
fof(f15746,plain,
( ! [X0,X8,X9,X7,X5,X12] :
( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X5),X9),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X8,tc_fun(tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),X0),c_Set_Oinsert(X8)),X7),X0,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8)),X0,tc_fun(X8,tc_bool)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X8,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,hAPP(hAPP(c_COMBB(X8,tc_fun(X8,tc_bool),X0),hAPP(c_COMBC(c_Set_Oinsert(X8),X8,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8))),X7),X0,tc_fun(X8,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X9,hAPP(hAPP(c_COMBB(X8,tc_fun(X8,tc_bool),X0),hAPP(c_COMBC(c_Set_Oinsert(X8),X8,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8))),X7),X0,tc_fun(X8,tc_bool)))
| ~ c_Fun_Oinj__on(X7,X12,X0,X8)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X5),X12))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X9),X12)) )
| ~ spl0_342
| ~ spl0_508
| ~ spl0_553 ),
inference(forward_demodulation,[],[f15745,f13758]) ).
fof(f15745,plain,
( ! [X0,X8,X9,X7,X5,X12] :
( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X5),X9),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X8,tc_fun(tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),X0),c_Set_Oinsert(X8)),X7),X0,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8)),X0,tc_fun(X8,tc_bool)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X8,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X8,tc_fun(tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),X0),c_Set_Oinsert(X8)),X7),X0,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8)),X0,tc_fun(X8,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X9,hAPP(hAPP(c_COMBB(X8,tc_fun(X8,tc_bool),X0),hAPP(c_COMBC(c_Set_Oinsert(X8),X8,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8))),X7),X0,tc_fun(X8,tc_bool)))
| ~ c_Fun_Oinj__on(X7,X12,X0,X8)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X5),X12))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X9),X12)) )
| ~ spl0_342
| ~ spl0_508
| ~ spl0_553 ),
inference(forward_demodulation,[],[f15743,f13758]) ).
fof(f15743,plain,
( ! [X0,X8,X9,X7,X5,X12] :
( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X5),X9),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X8,tc_fun(tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),X0),c_Set_Oinsert(X8)),X7),X0,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8)),X0,tc_fun(X8,tc_bool)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X8,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X8,tc_fun(tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),X0),c_Set_Oinsert(X8)),X7),X0,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8)),X0,tc_fun(X8,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X9,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X8,tc_fun(tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),X0),c_Set_Oinsert(X8)),X7),X0,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8)),X0,tc_fun(X8,tc_bool)))
| ~ c_Fun_Oinj__on(X7,X12,X0,X8)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X5),X12))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X9),X12)) )
| ~ spl0_553 ),
inference(avatar_component_clause,[],[f15742]) ).
fof(f15751,plain,
( spl0_554
| ~ spl0_247
| ~ spl0_527 ),
inference(avatar_split_clause,[],[f15644,f14866,f3033,f15749]) ).
fof(f15749,plain,
( spl0_554
<=> ! [X0,X1] :
( ~ class_Finite__Set_Ofinite_Ofinite(tc_fun(X0,tc_bool))
| c_Finite__Set_Ofinite(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_554])]) ).
fof(f3033,plain,
( spl0_247
<=> ! [X0,X1] :
( c_Finite__Set_Ofinite(X1,X0)
| ~ c_Finite__Set_Ofinite(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_247])]) ).
fof(f14866,plain,
( spl0_527
<=> ! [X0] :
( c_Finite__Set_Ofinite(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0)
| ~ class_Finite__Set_Ofinite_Ofinite(tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_527])]) ).
fof(f15644,plain,
( ! [X0,X1] :
( ~ class_Finite__Set_Ofinite_Ofinite(tc_fun(X0,tc_bool))
| c_Finite__Set_Ofinite(X1,X0) )
| ~ spl0_247
| ~ spl0_527 ),
inference(resolution,[],[f14867,f3034]) ).
fof(f3034,plain,
( ! [X0,X1] :
( ~ c_Finite__Set_Ofinite(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0)
| c_Finite__Set_Ofinite(X1,X0) )
| ~ spl0_247 ),
inference(avatar_component_clause,[],[f3033]) ).
fof(f14867,plain,
( ! [X0] :
( c_Finite__Set_Ofinite(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0)
| ~ class_Finite__Set_Ofinite_Ofinite(tc_fun(X0,tc_bool)) )
| ~ spl0_527 ),
inference(avatar_component_clause,[],[f14866]) ).
fof(f15744,plain,
spl0_553,
inference(avatar_split_clause,[],[f1002,f15742]) ).
fof(f1002,plain,
! [X0,X8,X9,X7,X5,X12] :
( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X5),X9),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X8,tc_fun(tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),X0),c_Set_Oinsert(X8)),X7),X0,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8)),X0,tc_fun(X8,tc_bool)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X8,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X8,tc_fun(tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),X0),c_Set_Oinsert(X8)),X7),X0,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8)),X0,tc_fun(X8,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X9,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X8,tc_fun(tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),X0),c_Set_Oinsert(X8)),X7),X0,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8)),X0,tc_fun(X8,tc_bool)))
| ~ c_Fun_Oinj__on(X7,X12,X0,X8)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X5),X12))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X9),X12)) ),
inference(forward_demodulation,[],[f696,f698]) ).
fof(f698,plain,
! [X0] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_COMBK(c_False,tc_bool,X0),
inference(forward_demodulation,[],[f581,f43]) ).
fof(f43,axiom,
! [X0,X11] : c_Collect(X11,X0) = X11,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Collect__def_0) ).
fof(f581,axiom,
! [X0] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_Collect(c_COMBK(c_False,tc_bool,X0),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__def_0) ).
fof(f696,plain,
! [X0,X8,X9,X7,X5,X12] :
( ~ c_Fun_Oinj__on(X7,X12,X0,X8)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X5),X12))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X9),X12))
| c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X5),X9),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X8,tc_fun(tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),X0),c_Set_Oinsert(X8)),X7),X0,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X8,tc_bool))),X0,tc_fun(X8,tc_bool)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X8,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X8,tc_fun(tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),X0),c_Set_Oinsert(X8)),X7),X0,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X8,tc_bool))),X0,tc_fun(X8,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X9,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X8,tc_fun(tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),X0),c_Set_Oinsert(X8)),X7),X0,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X8,tc_bool))),X0,tc_fun(X8,tc_bool))) ),
inference(definition_unfolding,[],[f24,f552,f552,f552]) ).
fof(f552,axiom,
! [X0,X8,X7,X5] : c_Set_Oimage(X7,X5,X8,X0) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X0,tc_fun(tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),X8),c_Set_Oinsert(X0)),X7),X8,tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))),X8,tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__eq__UN_0) ).
fof(f24,axiom,
! [X0,X8,X9,X7,X5,X12] :
( ~ c_Fun_Oinj__on(X7,X12,X0,X8)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X5),X12))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X9),X12))
| c_Set_Oimage(X7,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X5),X9),X0,X8) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X8,tc_bool)),c_Set_Oimage(X7,X5,X0,X8)),c_Set_Oimage(X7,X9,X0,X8)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__image__Int_0) ).
fof(f15679,plain,
( spl0_552
| ~ spl0_342
| ~ spl0_508
| ~ spl0_551 ),
inference(avatar_split_clause,[],[f15675,f15670,f13711,f4957,f15677]) ).
fof(f15677,plain,
( spl0_552
<=> ! [X5,X0,X12,X9,X8,X7] :
( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X5),X9),hAPP(hAPP(c_COMBB(X8,tc_fun(X8,tc_bool),X0),hAPP(c_COMBC(c_Set_Oinsert(X8),X8,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8))),X7),X0,tc_fun(X8,tc_bool)) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X8,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,hAPP(hAPP(c_COMBB(X8,tc_fun(X8,tc_bool),X0),hAPP(c_COMBC(c_Set_Oinsert(X8),X8,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8))),X7),X0,tc_fun(X8,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X9,hAPP(hAPP(c_COMBB(X8,tc_fun(X8,tc_bool),X0),hAPP(c_COMBC(c_Set_Oinsert(X8),X8,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8))),X7),X0,tc_fun(X8,tc_bool)))
| ~ c_Fun_Oinj__on(X7,X12,X0,X8)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X5),X12))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X9),X12)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_552])]) ).
fof(f15670,plain,
( spl0_551
<=> ! [X5,X0,X12,X9,X8,X7] :
( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X5),X9),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X8,tc_fun(tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),X0),c_Set_Oinsert(X8)),X7),X0,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8)),X0,tc_fun(X8,tc_bool)) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X8,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X8,tc_fun(tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),X0),c_Set_Oinsert(X8)),X7),X0,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8)),X0,tc_fun(X8,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X9,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X8,tc_fun(tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),X0),c_Set_Oinsert(X8)),X7),X0,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8)),X0,tc_fun(X8,tc_bool)))
| ~ c_Fun_Oinj__on(X7,X12,X0,X8)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X5),X12))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X9),X12)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_551])]) ).
fof(f15675,plain,
( ! [X0,X8,X9,X7,X5,X12] :
( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X5),X9),hAPP(hAPP(c_COMBB(X8,tc_fun(X8,tc_bool),X0),hAPP(c_COMBC(c_Set_Oinsert(X8),X8,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8))),X7),X0,tc_fun(X8,tc_bool)) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X8,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,hAPP(hAPP(c_COMBB(X8,tc_fun(X8,tc_bool),X0),hAPP(c_COMBC(c_Set_Oinsert(X8),X8,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8))),X7),X0,tc_fun(X8,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X9,hAPP(hAPP(c_COMBB(X8,tc_fun(X8,tc_bool),X0),hAPP(c_COMBC(c_Set_Oinsert(X8),X8,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8))),X7),X0,tc_fun(X8,tc_bool)))
| ~ c_Fun_Oinj__on(X7,X12,X0,X8)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X5),X12))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X9),X12)) )
| ~ spl0_342
| ~ spl0_508
| ~ spl0_551 ),
inference(forward_demodulation,[],[f15674,f13758]) ).
fof(f15674,plain,
( ! [X0,X8,X9,X7,X5,X12] :
( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X5),X9),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X8,tc_fun(tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),X0),c_Set_Oinsert(X8)),X7),X0,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8)),X0,tc_fun(X8,tc_bool)) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X8,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,hAPP(hAPP(c_COMBB(X8,tc_fun(X8,tc_bool),X0),hAPP(c_COMBC(c_Set_Oinsert(X8),X8,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8))),X7),X0,tc_fun(X8,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X9,hAPP(hAPP(c_COMBB(X8,tc_fun(X8,tc_bool),X0),hAPP(c_COMBC(c_Set_Oinsert(X8),X8,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8))),X7),X0,tc_fun(X8,tc_bool)))
| ~ c_Fun_Oinj__on(X7,X12,X0,X8)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X5),X12))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X9),X12)) )
| ~ spl0_342
| ~ spl0_508
| ~ spl0_551 ),
inference(forward_demodulation,[],[f15673,f13758]) ).
fof(f15673,plain,
( ! [X0,X8,X9,X7,X5,X12] :
( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X5),X9),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X8,tc_fun(tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),X0),c_Set_Oinsert(X8)),X7),X0,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8)),X0,tc_fun(X8,tc_bool)) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X8,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X8,tc_fun(tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),X0),c_Set_Oinsert(X8)),X7),X0,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8)),X0,tc_fun(X8,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X9,hAPP(hAPP(c_COMBB(X8,tc_fun(X8,tc_bool),X0),hAPP(c_COMBC(c_Set_Oinsert(X8),X8,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8))),X7),X0,tc_fun(X8,tc_bool)))
| ~ c_Fun_Oinj__on(X7,X12,X0,X8)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X5),X12))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X9),X12)) )
| ~ spl0_342
| ~ spl0_508
| ~ spl0_551 ),
inference(forward_demodulation,[],[f15671,f13758]) ).
fof(f15671,plain,
( ! [X0,X8,X9,X7,X5,X12] :
( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X5),X9),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X8,tc_fun(tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),X0),c_Set_Oinsert(X8)),X7),X0,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8)),X0,tc_fun(X8,tc_bool)) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X8,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X8,tc_fun(tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),X0),c_Set_Oinsert(X8)),X7),X0,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8)),X0,tc_fun(X8,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X9,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X8,tc_fun(tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),X0),c_Set_Oinsert(X8)),X7),X0,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8)),X0,tc_fun(X8,tc_bool)))
| ~ c_Fun_Oinj__on(X7,X12,X0,X8)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X5),X12))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X9),X12)) )
| ~ spl0_551 ),
inference(avatar_component_clause,[],[f15670]) ).
fof(f15672,plain,
spl0_551,
inference(avatar_split_clause,[],[f1001,f15670]) ).
fof(f1001,plain,
! [X0,X8,X9,X7,X5,X12] :
( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X5),X9),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X8,tc_fun(tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),X0),c_Set_Oinsert(X8)),X7),X0,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8)),X0,tc_fun(X8,tc_bool)) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X8,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X8,tc_fun(tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),X0),c_Set_Oinsert(X8)),X7),X0,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8)),X0,tc_fun(X8,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X9,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X8,tc_fun(tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),X0),c_Set_Oinsert(X8)),X7),X0,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8)),X0,tc_fun(X8,tc_bool)))
| ~ c_Fun_Oinj__on(X7,X12,X0,X8)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X5),X12))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X9),X12)) ),
inference(forward_demodulation,[],[f695,f698]) ).
fof(f695,plain,
! [X0,X8,X9,X7,X5,X12] :
( ~ c_Fun_Oinj__on(X7,X12,X0,X8)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X5),X12))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X9),X12))
| c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X5),X9),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X8,tc_fun(tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),X0),c_Set_Oinsert(X8)),X7),X0,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X8,tc_bool))),X0,tc_fun(X8,tc_bool)) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X8,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X8,tc_fun(tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),X0),c_Set_Oinsert(X8)),X7),X0,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X8,tc_bool))),X0,tc_fun(X8,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X9,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X8,tc_fun(tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),X0),c_Set_Oinsert(X8)),X7),X0,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X8,tc_bool))),X0,tc_fun(X8,tc_bool))) ),
inference(definition_unfolding,[],[f461,f552,f552,f552]) ).
fof(f461,axiom,
! [X0,X8,X9,X7,X5,X12] :
( ~ c_Fun_Oinj__on(X7,X12,X0,X8)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X5),X12))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X9),X12))
| c_Set_Oimage(X7,hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X5),X9),X0,X8) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X8,tc_bool)),c_Set_Oimage(X7,X5,X0,X8)),c_Set_Oimage(X7,X9,X0,X8)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__image__set__diff_0) ).
fof(f15667,plain,
( spl0_550
| ~ spl0_342
| ~ spl0_508
| ~ spl0_549 ),
inference(avatar_split_clause,[],[f15663,f15658,f13711,f4957,f15665]) ).
fof(f15665,plain,
( spl0_550
<=> ! [X5,X0,X9,X8,X7] :
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X8,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,hAPP(hAPP(c_COMBB(X8,tc_fun(X8,tc_bool),X0),hAPP(c_COMBC(c_Set_Oinsert(X8),X8,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8))),X7),X0,tc_fun(X8,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X9,hAPP(hAPP(c_COMBB(X8,tc_fun(X8,tc_bool),X0),hAPP(c_COMBC(c_Set_Oinsert(X8),X8,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8))),X7),X0,tc_fun(X8,tc_bool))) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X5),X9),hAPP(hAPP(c_COMBB(X8,tc_fun(X8,tc_bool),X0),hAPP(c_COMBC(c_Set_Oinsert(X8),X8,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8))),X7),X0,tc_fun(X8,tc_bool))
| ~ c_Fun_Oinj__on(X7,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0,X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_550])]) ).
fof(f15658,plain,
( spl0_549
<=> ! [X5,X0,X9,X8,X7] :
( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X5),X9),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X8,tc_fun(tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),X0),c_Set_Oinsert(X8)),X7),X0,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8)),X0,tc_fun(X8,tc_bool)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X8,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X8,tc_fun(tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),X0),c_Set_Oinsert(X8)),X7),X0,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8)),X0,tc_fun(X8,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X9,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X8,tc_fun(tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),X0),c_Set_Oinsert(X8)),X7),X0,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8)),X0,tc_fun(X8,tc_bool)))
| ~ c_Fun_Oinj__on(X7,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0,X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_549])]) ).
fof(f15663,plain,
( ! [X0,X8,X9,X7,X5] :
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X8,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,hAPP(hAPP(c_COMBB(X8,tc_fun(X8,tc_bool),X0),hAPP(c_COMBC(c_Set_Oinsert(X8),X8,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8))),X7),X0,tc_fun(X8,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X9,hAPP(hAPP(c_COMBB(X8,tc_fun(X8,tc_bool),X0),hAPP(c_COMBC(c_Set_Oinsert(X8),X8,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8))),X7),X0,tc_fun(X8,tc_bool))) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X5),X9),hAPP(hAPP(c_COMBB(X8,tc_fun(X8,tc_bool),X0),hAPP(c_COMBC(c_Set_Oinsert(X8),X8,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8))),X7),X0,tc_fun(X8,tc_bool))
| ~ c_Fun_Oinj__on(X7,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0,X8) )
| ~ spl0_342
| ~ spl0_508
| ~ spl0_549 ),
inference(forward_demodulation,[],[f15662,f13758]) ).
fof(f15662,plain,
( ! [X0,X8,X9,X7,X5] :
( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X5),X9),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X8,tc_fun(tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),X0),c_Set_Oinsert(X8)),X7),X0,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8)),X0,tc_fun(X8,tc_bool)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X8,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,hAPP(hAPP(c_COMBB(X8,tc_fun(X8,tc_bool),X0),hAPP(c_COMBC(c_Set_Oinsert(X8),X8,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8))),X7),X0,tc_fun(X8,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X9,hAPP(hAPP(c_COMBB(X8,tc_fun(X8,tc_bool),X0),hAPP(c_COMBC(c_Set_Oinsert(X8),X8,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8))),X7),X0,tc_fun(X8,tc_bool)))
| ~ c_Fun_Oinj__on(X7,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0,X8) )
| ~ spl0_342
| ~ spl0_508
| ~ spl0_549 ),
inference(forward_demodulation,[],[f15661,f13758]) ).
fof(f15661,plain,
( ! [X0,X8,X9,X7,X5] :
( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X5),X9),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X8,tc_fun(tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),X0),c_Set_Oinsert(X8)),X7),X0,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8)),X0,tc_fun(X8,tc_bool)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X8,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X8,tc_fun(tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),X0),c_Set_Oinsert(X8)),X7),X0,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8)),X0,tc_fun(X8,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X9,hAPP(hAPP(c_COMBB(X8,tc_fun(X8,tc_bool),X0),hAPP(c_COMBC(c_Set_Oinsert(X8),X8,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8))),X7),X0,tc_fun(X8,tc_bool)))
| ~ c_Fun_Oinj__on(X7,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0,X8) )
| ~ spl0_342
| ~ spl0_508
| ~ spl0_549 ),
inference(forward_demodulation,[],[f15659,f13758]) ).
fof(f15659,plain,
( ! [X0,X8,X9,X7,X5] :
( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X5),X9),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X8,tc_fun(tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),X0),c_Set_Oinsert(X8)),X7),X0,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8)),X0,tc_fun(X8,tc_bool)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X8,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X8,tc_fun(tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),X0),c_Set_Oinsert(X8)),X7),X0,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8)),X0,tc_fun(X8,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X9,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X8,tc_fun(tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),X0),c_Set_Oinsert(X8)),X7),X0,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8)),X0,tc_fun(X8,tc_bool)))
| ~ c_Fun_Oinj__on(X7,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0,X8) )
| ~ spl0_549 ),
inference(avatar_component_clause,[],[f15658]) ).
fof(f15660,plain,
spl0_549,
inference(avatar_split_clause,[],[f851,f15658]) ).
fof(f851,plain,
! [X0,X8,X9,X7,X5] :
( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X5),X9),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X8,tc_fun(tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),X0),c_Set_Oinsert(X8)),X7),X0,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8)),X0,tc_fun(X8,tc_bool)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X8,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X8,tc_fun(tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),X0),c_Set_Oinsert(X8)),X7),X0,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8)),X0,tc_fun(X8,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X9,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X8,tc_fun(tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),X0),c_Set_Oinsert(X8)),X7),X0,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8)),X0,tc_fun(X8,tc_bool)))
| ~ c_Fun_Oinj__on(X7,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0,X8) ),
inference(forward_demodulation,[],[f673,f698]) ).
fof(f673,plain,
! [X0,X8,X9,X7,X5] :
( ~ c_Fun_Oinj__on(X7,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0,X8)
| c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X5),X9),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X8,tc_fun(tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),X0),c_Set_Oinsert(X8)),X7),X0,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X8,tc_bool))),X0,tc_fun(X8,tc_bool)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X8,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X8,tc_fun(tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),X0),c_Set_Oinsert(X8)),X7),X0,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X8,tc_bool))),X0,tc_fun(X8,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X9,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X8,tc_fun(tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),X0),c_Set_Oinsert(X8)),X7),X0,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X8,tc_bool))),X0,tc_fun(X8,tc_bool))) ),
inference(definition_unfolding,[],[f74,f552,f552,f552]) ).
fof(f74,axiom,
! [X0,X8,X9,X7,X5] :
( ~ c_Fun_Oinj__on(X7,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0,X8)
| c_Set_Oimage(X7,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X5),X9),X0,X8) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X8,tc_bool)),c_Set_Oimage(X7,X5,X0,X8)),c_Set_Oimage(X7,X9,X0,X8)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__Int_0) ).
fof(f15655,plain,
( spl0_548
| ~ spl0_342
| ~ spl0_508
| ~ spl0_547 ),
inference(avatar_split_clause,[],[f15651,f15646,f13711,f4957,f15653]) ).
fof(f15653,plain,
( spl0_548
<=> ! [X5,X0,X9,X8,X7] :
( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X5),X9),hAPP(hAPP(c_COMBB(X8,tc_fun(X8,tc_bool),X0),hAPP(c_COMBC(c_Set_Oinsert(X8),X8,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8))),X7),X0,tc_fun(X8,tc_bool)) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X8,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,hAPP(hAPP(c_COMBB(X8,tc_fun(X8,tc_bool),X0),hAPP(c_COMBC(c_Set_Oinsert(X8),X8,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8))),X7),X0,tc_fun(X8,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X9,hAPP(hAPP(c_COMBB(X8,tc_fun(X8,tc_bool),X0),hAPP(c_COMBC(c_Set_Oinsert(X8),X8,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8))),X7),X0,tc_fun(X8,tc_bool)))
| ~ c_Fun_Oinj__on(X7,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0,X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_548])]) ).
fof(f15646,plain,
( spl0_547
<=> ! [X5,X0,X9,X8,X7] :
( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X5),X9),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X8,tc_fun(tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),X0),c_Set_Oinsert(X8)),X7),X0,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8)),X0,tc_fun(X8,tc_bool)) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X8,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X8,tc_fun(tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),X0),c_Set_Oinsert(X8)),X7),X0,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8)),X0,tc_fun(X8,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X9,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X8,tc_fun(tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),X0),c_Set_Oinsert(X8)),X7),X0,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8)),X0,tc_fun(X8,tc_bool)))
| ~ c_Fun_Oinj__on(X7,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0,X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_547])]) ).
fof(f15651,plain,
( ! [X0,X8,X9,X7,X5] :
( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X5),X9),hAPP(hAPP(c_COMBB(X8,tc_fun(X8,tc_bool),X0),hAPP(c_COMBC(c_Set_Oinsert(X8),X8,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8))),X7),X0,tc_fun(X8,tc_bool)) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X8,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,hAPP(hAPP(c_COMBB(X8,tc_fun(X8,tc_bool),X0),hAPP(c_COMBC(c_Set_Oinsert(X8),X8,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8))),X7),X0,tc_fun(X8,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X9,hAPP(hAPP(c_COMBB(X8,tc_fun(X8,tc_bool),X0),hAPP(c_COMBC(c_Set_Oinsert(X8),X8,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8))),X7),X0,tc_fun(X8,tc_bool)))
| ~ c_Fun_Oinj__on(X7,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0,X8) )
| ~ spl0_342
| ~ spl0_508
| ~ spl0_547 ),
inference(forward_demodulation,[],[f15650,f13758]) ).
fof(f15650,plain,
( ! [X0,X8,X9,X7,X5] :
( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X5),X9),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X8,tc_fun(tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),X0),c_Set_Oinsert(X8)),X7),X0,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8)),X0,tc_fun(X8,tc_bool)) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X8,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,hAPP(hAPP(c_COMBB(X8,tc_fun(X8,tc_bool),X0),hAPP(c_COMBC(c_Set_Oinsert(X8),X8,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8))),X7),X0,tc_fun(X8,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X9,hAPP(hAPP(c_COMBB(X8,tc_fun(X8,tc_bool),X0),hAPP(c_COMBC(c_Set_Oinsert(X8),X8,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8))),X7),X0,tc_fun(X8,tc_bool)))
| ~ c_Fun_Oinj__on(X7,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0,X8) )
| ~ spl0_342
| ~ spl0_508
| ~ spl0_547 ),
inference(forward_demodulation,[],[f15649,f13758]) ).
fof(f15649,plain,
( ! [X0,X8,X9,X7,X5] :
( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X5),X9),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X8,tc_fun(tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),X0),c_Set_Oinsert(X8)),X7),X0,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8)),X0,tc_fun(X8,tc_bool)) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X8,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X8,tc_fun(tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),X0),c_Set_Oinsert(X8)),X7),X0,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8)),X0,tc_fun(X8,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X9,hAPP(hAPP(c_COMBB(X8,tc_fun(X8,tc_bool),X0),hAPP(c_COMBC(c_Set_Oinsert(X8),X8,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8))),X7),X0,tc_fun(X8,tc_bool)))
| ~ c_Fun_Oinj__on(X7,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0,X8) )
| ~ spl0_342
| ~ spl0_508
| ~ spl0_547 ),
inference(forward_demodulation,[],[f15647,f13758]) ).
fof(f15647,plain,
( ! [X0,X8,X9,X7,X5] :
( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X5),X9),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X8,tc_fun(tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),X0),c_Set_Oinsert(X8)),X7),X0,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8)),X0,tc_fun(X8,tc_bool)) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X8,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X8,tc_fun(tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),X0),c_Set_Oinsert(X8)),X7),X0,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8)),X0,tc_fun(X8,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X9,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X8,tc_fun(tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),X0),c_Set_Oinsert(X8)),X7),X0,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8)),X0,tc_fun(X8,tc_bool)))
| ~ c_Fun_Oinj__on(X7,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0,X8) )
| ~ spl0_547 ),
inference(avatar_component_clause,[],[f15646]) ).
fof(f15648,plain,
spl0_547,
inference(avatar_split_clause,[],[f850,f15646]) ).
fof(f850,plain,
! [X0,X8,X9,X7,X5] :
( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X5),X9),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X8,tc_fun(tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),X0),c_Set_Oinsert(X8)),X7),X0,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8)),X0,tc_fun(X8,tc_bool)) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X8,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X8,tc_fun(tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),X0),c_Set_Oinsert(X8)),X7),X0,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8)),X0,tc_fun(X8,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X9,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X8,tc_fun(tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),X0),c_Set_Oinsert(X8)),X7),X0,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8)),X0,tc_fun(X8,tc_bool)))
| ~ c_Fun_Oinj__on(X7,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0,X8) ),
inference(forward_demodulation,[],[f672,f698]) ).
fof(f672,plain,
! [X0,X8,X9,X7,X5] :
( ~ c_Fun_Oinj__on(X7,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0,X8)
| c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X5),X9),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X8,tc_fun(tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),X0),c_Set_Oinsert(X8)),X7),X0,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X8,tc_bool))),X0,tc_fun(X8,tc_bool)) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X8,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X8,tc_fun(tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),X0),c_Set_Oinsert(X8)),X7),X0,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X8,tc_bool))),X0,tc_fun(X8,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X9,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X8,tc_fun(tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),X0),c_Set_Oinsert(X8)),X7),X0,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X8,tc_bool))),X0,tc_fun(X8,tc_bool))) ),
inference(definition_unfolding,[],[f170,f552,f552,f552]) ).
fof(f170,axiom,
! [X0,X8,X9,X7,X5] :
( ~ c_Fun_Oinj__on(X7,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0,X8)
| c_Set_Oimage(X7,hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X5),X9),X0,X8) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X8,tc_bool)),c_Set_Oimage(X7,X5,X0,X8)),c_Set_Oimage(X7,X9,X0,X8)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__set__diff_0) ).
fof(f15584,plain,
( spl0_546
| ~ spl0_342
| ~ spl0_508
| ~ spl0_545 ),
inference(avatar_split_clause,[],[f15580,f15575,f13711,f4957,f15582]) ).
fof(f15582,plain,
( spl0_546
<=> ! [X5,X0,X9,X8,X7] : hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,hAPP(hAPP(c_COMBB(X0,tc_fun(X0,tc_bool),X8),hAPP(c_COMBC(c_Set_Oinsert(X0),X0,tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0))),X7),X8,tc_fun(X0,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X9,hAPP(hAPP(c_COMBB(X0,tc_fun(X0,tc_bool),X8),hAPP(c_COMBC(c_Set_Oinsert(X0),X0,tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0))),X7),X8,tc_fun(X0,tc_bool)))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X8,tc_bool)),X5),X9),hAPP(hAPP(c_COMBB(X0,tc_fun(X0,tc_bool),X8),hAPP(c_COMBC(c_Set_Oinsert(X0),X0,tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0))),X7),X8,tc_fun(X0,tc_bool)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_546])]) ).
fof(f15575,plain,
( spl0_545
<=> ! [X5,X0,X9,X8,X7] : hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X0,tc_fun(tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),X8),c_Set_Oinsert(X0)),X7),X8,tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0)),X8,tc_fun(X0,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X9,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X0,tc_fun(tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),X8),c_Set_Oinsert(X0)),X7),X8,tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0)),X8,tc_fun(X0,tc_bool)))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X8,tc_bool)),X5),X9),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X0,tc_fun(tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),X8),c_Set_Oinsert(X0)),X7),X8,tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0)),X8,tc_fun(X0,tc_bool)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_545])]) ).
fof(f15580,plain,
( ! [X0,X8,X9,X7,X5] : hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,hAPP(hAPP(c_COMBB(X0,tc_fun(X0,tc_bool),X8),hAPP(c_COMBC(c_Set_Oinsert(X0),X0,tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0))),X7),X8,tc_fun(X0,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X9,hAPP(hAPP(c_COMBB(X0,tc_fun(X0,tc_bool),X8),hAPP(c_COMBC(c_Set_Oinsert(X0),X0,tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0))),X7),X8,tc_fun(X0,tc_bool)))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X8,tc_bool)),X5),X9),hAPP(hAPP(c_COMBB(X0,tc_fun(X0,tc_bool),X8),hAPP(c_COMBC(c_Set_Oinsert(X0),X0,tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0))),X7),X8,tc_fun(X0,tc_bool))))
| ~ spl0_342
| ~ spl0_508
| ~ spl0_545 ),
inference(forward_demodulation,[],[f15579,f13758]) ).
fof(f15579,plain,
( ! [X0,X8,X9,X7,X5] : hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X0,tc_fun(tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),X8),c_Set_Oinsert(X0)),X7),X8,tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0)),X8,tc_fun(X0,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X9,hAPP(hAPP(c_COMBB(X0,tc_fun(X0,tc_bool),X8),hAPP(c_COMBC(c_Set_Oinsert(X0),X0,tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0))),X7),X8,tc_fun(X0,tc_bool)))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X8,tc_bool)),X5),X9),hAPP(hAPP(c_COMBB(X0,tc_fun(X0,tc_bool),X8),hAPP(c_COMBC(c_Set_Oinsert(X0),X0,tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0))),X7),X8,tc_fun(X0,tc_bool))))
| ~ spl0_342
| ~ spl0_508
| ~ spl0_545 ),
inference(forward_demodulation,[],[f15578,f13758]) ).
fof(f15578,plain,
( ! [X0,X8,X9,X7,X5] : hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X0,tc_fun(tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),X8),c_Set_Oinsert(X0)),X7),X8,tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0)),X8,tc_fun(X0,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X9,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X0,tc_fun(tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),X8),c_Set_Oinsert(X0)),X7),X8,tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0)),X8,tc_fun(X0,tc_bool)))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X8,tc_bool)),X5),X9),hAPP(hAPP(c_COMBB(X0,tc_fun(X0,tc_bool),X8),hAPP(c_COMBC(c_Set_Oinsert(X0),X0,tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0))),X7),X8,tc_fun(X0,tc_bool))))
| ~ spl0_342
| ~ spl0_508
| ~ spl0_545 ),
inference(forward_demodulation,[],[f15576,f13758]) ).
fof(f15576,plain,
( ! [X0,X8,X9,X7,X5] : hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X0,tc_fun(tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),X8),c_Set_Oinsert(X0)),X7),X8,tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0)),X8,tc_fun(X0,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X9,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X0,tc_fun(tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),X8),c_Set_Oinsert(X0)),X7),X8,tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0)),X8,tc_fun(X0,tc_bool)))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X8,tc_bool)),X5),X9),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X0,tc_fun(tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),X8),c_Set_Oinsert(X0)),X7),X8,tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0)),X8,tc_fun(X0,tc_bool))))
| ~ spl0_545 ),
inference(avatar_component_clause,[],[f15575]) ).
fof(f15577,plain,
spl0_545,
inference(avatar_split_clause,[],[f770,f15575]) ).
fof(f770,plain,
! [X0,X8,X9,X7,X5] : hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X0,tc_fun(tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),X8),c_Set_Oinsert(X0)),X7),X8,tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0)),X8,tc_fun(X0,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X9,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X0,tc_fun(tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),X8),c_Set_Oinsert(X0)),X7),X8,tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0)),X8,tc_fun(X0,tc_bool)))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X8,tc_bool)),X5),X9),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X0,tc_fun(tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),X8),c_Set_Oinsert(X0)),X7),X8,tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0)),X8,tc_fun(X0,tc_bool)))),
inference(forward_demodulation,[],[f661,f698]) ).
fof(f661,plain,
! [X0,X8,X9,X7,X5] : hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X0,tc_fun(tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),X8),c_Set_Oinsert(X0)),X7),X8,tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))),X8,tc_fun(X0,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X9,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X0,tc_fun(tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),X8),c_Set_Oinsert(X0)),X7),X8,tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))),X8,tc_fun(X0,tc_bool)))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X8,tc_bool)),X5),X9),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X0,tc_fun(tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),X8),c_Set_Oinsert(X0)),X7),X8,tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))),X8,tc_fun(X0,tc_bool)))),
inference(definition_unfolding,[],[f127,f552,f552,f552]) ).
fof(f127,axiom,
! [X0,X8,X9,X7,X5] : hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),c_Set_Oimage(X7,X5,X8,X0)),c_Set_Oimage(X7,X9,X8,X0))),c_Set_Oimage(X7,hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X8,tc_bool)),X5),X9),X8,X0))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__diff__subset_0) ).
fof(f15499,plain,
( spl0_544
| ~ spl0_342
| ~ spl0_508
| ~ spl0_543 ),
inference(avatar_split_clause,[],[f15495,f15490,f13711,f4957,f15497]) ).
fof(f15497,plain,
( spl0_544
<=> ! [X5,X0,X9,X8,X7] : hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X8,tc_bool)),X5),X9),hAPP(hAPP(c_COMBB(X0,tc_fun(X0,tc_bool),X8),hAPP(c_COMBC(c_Set_Oinsert(X0),X0,tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0))),X7),X8,tc_fun(X0,tc_bool))),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,hAPP(hAPP(c_COMBB(X0,tc_fun(X0,tc_bool),X8),hAPP(c_COMBC(c_Set_Oinsert(X0),X0,tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0))),X7),X8,tc_fun(X0,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X9,hAPP(hAPP(c_COMBB(X0,tc_fun(X0,tc_bool),X8),hAPP(c_COMBC(c_Set_Oinsert(X0),X0,tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0))),X7),X8,tc_fun(X0,tc_bool))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_544])]) ).
fof(f15490,plain,
( spl0_543
<=> ! [X5,X0,X9,X8,X7] : hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X8,tc_bool)),X5),X9),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X0,tc_fun(tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),X8),c_Set_Oinsert(X0)),X7),X8,tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0)),X8,tc_fun(X0,tc_bool))),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X0,tc_fun(tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),X8),c_Set_Oinsert(X0)),X7),X8,tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0)),X8,tc_fun(X0,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X9,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X0,tc_fun(tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),X8),c_Set_Oinsert(X0)),X7),X8,tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0)),X8,tc_fun(X0,tc_bool))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_543])]) ).
fof(f15495,plain,
( ! [X0,X8,X9,X7,X5] : hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X8,tc_bool)),X5),X9),hAPP(hAPP(c_COMBB(X0,tc_fun(X0,tc_bool),X8),hAPP(c_COMBC(c_Set_Oinsert(X0),X0,tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0))),X7),X8,tc_fun(X0,tc_bool))),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,hAPP(hAPP(c_COMBB(X0,tc_fun(X0,tc_bool),X8),hAPP(c_COMBC(c_Set_Oinsert(X0),X0,tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0))),X7),X8,tc_fun(X0,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X9,hAPP(hAPP(c_COMBB(X0,tc_fun(X0,tc_bool),X8),hAPP(c_COMBC(c_Set_Oinsert(X0),X0,tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0))),X7),X8,tc_fun(X0,tc_bool)))))
| ~ spl0_342
| ~ spl0_508
| ~ spl0_543 ),
inference(forward_demodulation,[],[f15494,f13758]) ).
fof(f15494,plain,
( ! [X0,X8,X9,X7,X5] : hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X8,tc_bool)),X5),X9),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X0,tc_fun(tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),X8),c_Set_Oinsert(X0)),X7),X8,tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0)),X8,tc_fun(X0,tc_bool))),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,hAPP(hAPP(c_COMBB(X0,tc_fun(X0,tc_bool),X8),hAPP(c_COMBC(c_Set_Oinsert(X0),X0,tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0))),X7),X8,tc_fun(X0,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X9,hAPP(hAPP(c_COMBB(X0,tc_fun(X0,tc_bool),X8),hAPP(c_COMBC(c_Set_Oinsert(X0),X0,tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0))),X7),X8,tc_fun(X0,tc_bool)))))
| ~ spl0_342
| ~ spl0_508
| ~ spl0_543 ),
inference(forward_demodulation,[],[f15493,f13758]) ).
fof(f15493,plain,
( ! [X0,X8,X9,X7,X5] : hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X8,tc_bool)),X5),X9),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X0,tc_fun(tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),X8),c_Set_Oinsert(X0)),X7),X8,tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0)),X8,tc_fun(X0,tc_bool))),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X0,tc_fun(tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),X8),c_Set_Oinsert(X0)),X7),X8,tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0)),X8,tc_fun(X0,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X9,hAPP(hAPP(c_COMBB(X0,tc_fun(X0,tc_bool),X8),hAPP(c_COMBC(c_Set_Oinsert(X0),X0,tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0))),X7),X8,tc_fun(X0,tc_bool)))))
| ~ spl0_342
| ~ spl0_508
| ~ spl0_543 ),
inference(forward_demodulation,[],[f15491,f13758]) ).
fof(f15491,plain,
( ! [X0,X8,X9,X7,X5] : hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X8,tc_bool)),X5),X9),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X0,tc_fun(tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),X8),c_Set_Oinsert(X0)),X7),X8,tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0)),X8,tc_fun(X0,tc_bool))),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X0,tc_fun(tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),X8),c_Set_Oinsert(X0)),X7),X8,tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0)),X8,tc_fun(X0,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X9,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X0,tc_fun(tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),X8),c_Set_Oinsert(X0)),X7),X8,tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0)),X8,tc_fun(X0,tc_bool)))))
| ~ spl0_543 ),
inference(avatar_component_clause,[],[f15490]) ).
fof(f15492,plain,
spl0_543,
inference(avatar_split_clause,[],[f769,f15490]) ).
fof(f769,plain,
! [X0,X8,X9,X7,X5] : hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X8,tc_bool)),X5),X9),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X0,tc_fun(tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),X8),c_Set_Oinsert(X0)),X7),X8,tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0)),X8,tc_fun(X0,tc_bool))),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X0,tc_fun(tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),X8),c_Set_Oinsert(X0)),X7),X8,tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0)),X8,tc_fun(X0,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X9,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X0,tc_fun(tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),X8),c_Set_Oinsert(X0)),X7),X8,tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0)),X8,tc_fun(X0,tc_bool))))),
inference(forward_demodulation,[],[f660,f698]) ).
fof(f660,plain,
! [X0,X8,X9,X7,X5] : hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X8,tc_bool)),X5),X9),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X0,tc_fun(tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),X8),c_Set_Oinsert(X0)),X7),X8,tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))),X8,tc_fun(X0,tc_bool))),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X0,tc_fun(tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),X8),c_Set_Oinsert(X0)),X7),X8,tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))),X8,tc_fun(X0,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X9,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X0,tc_fun(tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),X8),c_Set_Oinsert(X0)),X7),X8,tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))),X8,tc_fun(X0,tc_bool))))),
inference(definition_unfolding,[],[f78,f552,f552,f552]) ).
fof(f78,axiom,
! [X0,X8,X9,X7,X5] : hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),c_Set_Oimage(X7,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X8,tc_bool)),X5),X9),X8,X0)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),c_Set_Oimage(X7,X5,X8,X0)),c_Set_Oimage(X7,X9,X8,X0)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__Int__subset_0) ).
fof(f15385,plain,
( spl0_542
| ~ spl0_213
| ~ spl0_342
| ~ spl0_508
| ~ spl0_541 ),
inference(avatar_split_clause,[],[f15381,f15376,f13711,f4957,f2251,f15383]) ).
fof(f15383,plain,
( spl0_542
<=> ! [X5,X0,X9,X8,X7] :
( c_COMBK(c_False,tc_bool,X8) != hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X8,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X9),X5),hAPP(hAPP(c_COMBB(X8,tc_fun(X8,tc_bool),X0),hAPP(c_COMBC(c_Set_Oinsert(X8),X8,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8))),X7),X0,tc_fun(X8,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X5),X9),hAPP(hAPP(c_COMBB(X8,tc_fun(X8,tc_bool),X0),hAPP(c_COMBC(c_Set_Oinsert(X8),X8,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8))),X7),X0,tc_fun(X8,tc_bool)))
| ~ c_Fun_Oinj__on(X7,X9,X0,X8)
| ~ c_Fun_Oinj__on(X7,X5,X0,X8)
| c_Fun_Oinj__on(X7,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X5),X9),X0,X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_542])]) ).
fof(f15376,plain,
( spl0_541
<=> ! [X9,X0,X5,X8,X7] :
( c_COMBK(c_False,tc_bool,X8) != hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X8,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X5),X9),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X8,tc_fun(tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),X0),c_Set_Oinsert(X8)),X7),X0,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8)),X0,tc_fun(X8,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X9),X5),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X8,tc_fun(tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),X0),c_Set_Oinsert(X8)),X7),X0,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8)),X0,tc_fun(X8,tc_bool)))
| ~ c_Fun_Oinj__on(X7,X9,X0,X8)
| ~ c_Fun_Oinj__on(X7,X5,X0,X8)
| c_Fun_Oinj__on(X7,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X5),X9),X0,X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_541])]) ).
fof(f15381,plain,
( ! [X0,X8,X9,X7,X5] :
( c_COMBK(c_False,tc_bool,X8) != hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X8,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X9),X5),hAPP(hAPP(c_COMBB(X8,tc_fun(X8,tc_bool),X0),hAPP(c_COMBC(c_Set_Oinsert(X8),X8,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8))),X7),X0,tc_fun(X8,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X5),X9),hAPP(hAPP(c_COMBB(X8,tc_fun(X8,tc_bool),X0),hAPP(c_COMBC(c_Set_Oinsert(X8),X8,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8))),X7),X0,tc_fun(X8,tc_bool)))
| ~ c_Fun_Oinj__on(X7,X9,X0,X8)
| ~ c_Fun_Oinj__on(X7,X5,X0,X8)
| c_Fun_Oinj__on(X7,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X5),X9),X0,X8) )
| ~ spl0_213
| ~ spl0_342
| ~ spl0_508
| ~ spl0_541 ),
inference(forward_demodulation,[],[f15380,f13758]) ).
fof(f15380,plain,
( ! [X0,X8,X9,X7,X5] :
( c_COMBK(c_False,tc_bool,X8) != hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X8,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X9),X5),hAPP(hAPP(c_COMBB(X8,tc_fun(X8,tc_bool),X0),hAPP(c_COMBC(c_Set_Oinsert(X8),X8,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8))),X7),X0,tc_fun(X8,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X5),X9),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X8,tc_fun(tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),X0),c_Set_Oinsert(X8)),X7),X0,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8)),X0,tc_fun(X8,tc_bool)))
| ~ c_Fun_Oinj__on(X7,X9,X0,X8)
| ~ c_Fun_Oinj__on(X7,X5,X0,X8)
| c_Fun_Oinj__on(X7,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X5),X9),X0,X8) )
| ~ spl0_213
| ~ spl0_342
| ~ spl0_508
| ~ spl0_541 ),
inference(forward_demodulation,[],[f15379,f2252]) ).
fof(f15379,plain,
( ! [X0,X8,X9,X7,X5] :
( c_COMBK(c_False,tc_bool,X8) != hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X8,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X5),X9),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X8,tc_fun(tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),X0),c_Set_Oinsert(X8)),X7),X0,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8)),X0,tc_fun(X8,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X9),X5),hAPP(hAPP(c_COMBB(X8,tc_fun(X8,tc_bool),X0),hAPP(c_COMBC(c_Set_Oinsert(X8),X8,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8))),X7),X0,tc_fun(X8,tc_bool)))
| ~ c_Fun_Oinj__on(X7,X9,X0,X8)
| ~ c_Fun_Oinj__on(X7,X5,X0,X8)
| c_Fun_Oinj__on(X7,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X5),X9),X0,X8) )
| ~ spl0_342
| ~ spl0_508
| ~ spl0_541 ),
inference(forward_demodulation,[],[f15377,f13758]) ).
fof(f15377,plain,
( ! [X0,X8,X9,X7,X5] :
( c_COMBK(c_False,tc_bool,X8) != hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X8,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X5),X9),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X8,tc_fun(tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),X0),c_Set_Oinsert(X8)),X7),X0,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8)),X0,tc_fun(X8,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X9),X5),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X8,tc_fun(tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),X0),c_Set_Oinsert(X8)),X7),X0,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8)),X0,tc_fun(X8,tc_bool)))
| ~ c_Fun_Oinj__on(X7,X9,X0,X8)
| ~ c_Fun_Oinj__on(X7,X5,X0,X8)
| c_Fun_Oinj__on(X7,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X5),X9),X0,X8) )
| ~ spl0_541 ),
inference(avatar_component_clause,[],[f15376]) ).
fof(f15378,plain,
spl0_541,
inference(avatar_split_clause,[],[f1000,f15376]) ).
fof(f1000,plain,
! [X0,X8,X9,X7,X5] :
( c_COMBK(c_False,tc_bool,X8) != hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X8,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X5),X9),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X8,tc_fun(tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),X0),c_Set_Oinsert(X8)),X7),X0,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8)),X0,tc_fun(X8,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X9),X5),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X8,tc_fun(tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),X0),c_Set_Oinsert(X8)),X7),X0,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8)),X0,tc_fun(X8,tc_bool)))
| ~ c_Fun_Oinj__on(X7,X9,X0,X8)
| ~ c_Fun_Oinj__on(X7,X5,X0,X8)
| c_Fun_Oinj__on(X7,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X5),X9),X0,X8) ),
inference(forward_demodulation,[],[f694,f698]) ).
fof(f694,plain,
! [X0,X8,X9,X7,X5] :
( ~ c_Fun_Oinj__on(X7,X9,X0,X8)
| ~ c_Fun_Oinj__on(X7,X5,X0,X8)
| c_Fun_Oinj__on(X7,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X5),X9),X0,X8)
| c_Orderings_Obot__class_Obot(tc_fun(X8,tc_bool)) != hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X8,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X5),X9),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X8,tc_fun(tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),X0),c_Set_Oinsert(X8)),X7),X0,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X8,tc_bool))),X0,tc_fun(X8,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X9),X5),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X8,tc_fun(tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),X0),c_Set_Oinsert(X8)),X7),X0,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X8,tc_bool))),X0,tc_fun(X8,tc_bool))) ),
inference(definition_unfolding,[],[f112,f552,f552]) ).
fof(f112,axiom,
! [X0,X8,X9,X7,X5] :
( ~ c_Fun_Oinj__on(X7,X9,X0,X8)
| ~ c_Fun_Oinj__on(X7,X5,X0,X8)
| c_Fun_Oinj__on(X7,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X5),X9),X0,X8)
| c_Orderings_Obot__class_Obot(tc_fun(X8,tc_bool)) != hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X8,tc_bool)),c_Set_Oimage(X7,hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X5),X9),X0,X8)),c_Set_Oimage(X7,hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X9),X5),X0,X8)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__Un_3) ).
fof(f15198,plain,
( spl0_540
| ~ spl0_342
| ~ spl0_508
| ~ spl0_539 ),
inference(avatar_split_clause,[],[f15194,f15191,f13711,f4957,f15196]) ).
fof(f15196,plain,
( spl0_540
<=> ! [X0,X14,X13,X5,X8,X7] : c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X0,tc_fun(tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),X14),c_Set_Oinsert(X0)),hAPP(hAPP(c_COMBB(X8,X0,X14),X7),X13)),X14,tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0)),X14,tc_fun(X0,tc_bool)) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,hAPP(hAPP(c_COMBB(X8,tc_fun(X8,tc_bool),X14),hAPP(c_COMBC(c_Set_Oinsert(X8),X8,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8))),X13),X14,tc_fun(X8,tc_bool)),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X0,tc_fun(tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),X8),c_Set_Oinsert(X0)),X7),X8,tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0)),X8,tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_540])]) ).
fof(f15191,plain,
( spl0_539
<=> ! [X0,X14,X13,X5,X8,X7] : c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X0,tc_fun(tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),X14),c_Set_Oinsert(X0)),hAPP(hAPP(c_COMBB(X8,X0,X14),X7),X13)),X14,tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0)),X14,tc_fun(X0,tc_bool)) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X8,tc_fun(tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),X14),c_Set_Oinsert(X8)),X13),X14,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8)),X14,tc_fun(X8,tc_bool)),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X0,tc_fun(tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),X8),c_Set_Oinsert(X0)),X7),X8,tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0)),X8,tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_539])]) ).
fof(f15194,plain,
( ! [X0,X8,X7,X14,X5,X13] : c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X0,tc_fun(tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),X14),c_Set_Oinsert(X0)),hAPP(hAPP(c_COMBB(X8,X0,X14),X7),X13)),X14,tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0)),X14,tc_fun(X0,tc_bool)) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,hAPP(hAPP(c_COMBB(X8,tc_fun(X8,tc_bool),X14),hAPP(c_COMBC(c_Set_Oinsert(X8),X8,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8))),X13),X14,tc_fun(X8,tc_bool)),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X0,tc_fun(tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),X8),c_Set_Oinsert(X0)),X7),X8,tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0)),X8,tc_fun(X0,tc_bool))
| ~ spl0_342
| ~ spl0_508
| ~ spl0_539 ),
inference(forward_demodulation,[],[f15192,f13758]) ).
fof(f15192,plain,
( ! [X0,X8,X7,X14,X5,X13] : c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X0,tc_fun(tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),X14),c_Set_Oinsert(X0)),hAPP(hAPP(c_COMBB(X8,X0,X14),X7),X13)),X14,tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0)),X14,tc_fun(X0,tc_bool)) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X8,tc_fun(tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),X14),c_Set_Oinsert(X8)),X13),X14,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8)),X14,tc_fun(X8,tc_bool)),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X0,tc_fun(tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),X8),c_Set_Oinsert(X0)),X7),X8,tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0)),X8,tc_fun(X0,tc_bool))
| ~ spl0_539 ),
inference(avatar_component_clause,[],[f15191]) ).
fof(f15193,plain,
spl0_539,
inference(avatar_split_clause,[],[f743,f15191]) ).
fof(f743,plain,
! [X0,X8,X7,X14,X5,X13] : c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X0,tc_fun(tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),X14),c_Set_Oinsert(X0)),hAPP(hAPP(c_COMBB(X8,X0,X14),X7),X13)),X14,tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0)),X14,tc_fun(X0,tc_bool)) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X8,tc_fun(tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),X14),c_Set_Oinsert(X8)),X13),X14,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8)),X14,tc_fun(X8,tc_bool)),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X0,tc_fun(tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),X8),c_Set_Oinsert(X0)),X7),X8,tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0)),X8,tc_fun(X0,tc_bool)),
inference(forward_demodulation,[],[f742,f698]) ).
fof(f742,plain,
! [X0,X8,X7,X14,X5,X13] : c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X8,tc_fun(tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),X14),c_Set_Oinsert(X8)),X13),X14,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X8,tc_bool))),X14,tc_fun(X8,tc_bool)),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X0,tc_fun(tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),X8),c_Set_Oinsert(X0)),X7),X8,tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0)),X8,tc_fun(X0,tc_bool)) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X0,tc_fun(tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),X14),c_Set_Oinsert(X0)),hAPP(hAPP(c_COMBB(X8,X0,X14),X7),X13)),X14,tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0)),X14,tc_fun(X0,tc_bool)),
inference(forward_demodulation,[],[f652,f698]) ).
fof(f652,plain,
! [X0,X8,X7,X14,X5,X13] : c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X8,tc_fun(tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),X14),c_Set_Oinsert(X8)),X13),X14,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X8,tc_bool))),X14,tc_fun(X8,tc_bool)),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X0,tc_fun(tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),X8),c_Set_Oinsert(X0)),X7),X8,tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))),X8,tc_fun(X0,tc_bool)) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X0,tc_fun(tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),X14),c_Set_Oinsert(X0)),hAPP(hAPP(c_COMBB(X8,X0,X14),X7),X13)),X14,tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))),X14,tc_fun(X0,tc_bool)),
inference(definition_unfolding,[],[f338,f552,f552,f552]) ).
fof(f338,axiom,
! [X0,X8,X7,X14,X5,X13] : c_Set_Oimage(X7,c_Set_Oimage(X13,X5,X14,X8),X8,X0) = c_Set_Oimage(hAPP(hAPP(c_COMBB(X8,X0,X14),X7),X13),X5,X14,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__image_0) ).
fof(f15045,plain,
( spl0_538
| ~ spl0_342
| ~ spl0_508
| ~ spl0_537 ),
inference(avatar_split_clause,[],[f15041,f15038,f13711,f4957,f15043]) ).
fof(f15043,plain,
( spl0_538
<=> ! [X45,X0,X14,X13,X8,X7] : c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X45,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X0,tc_fun(tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),X8),c_Set_Oinsert(X0)),c_Fun_Ocomp(X7,X13,X14,X0,X8)),X8,tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0)),X8,tc_fun(X0,tc_bool)) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X45,hAPP(hAPP(c_COMBB(X14,tc_fun(X14,tc_bool),X8),hAPP(c_COMBC(c_Set_Oinsert(X14),X14,tc_fun(X14,tc_bool),tc_fun(X14,tc_bool)),c_COMBK(c_False,tc_bool,X14))),X13),X8,tc_fun(X14,tc_bool)),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X0,tc_fun(tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),X14),c_Set_Oinsert(X0)),X7),X14,tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0)),X14,tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_538])]) ).
fof(f15038,plain,
( spl0_537
<=> ! [X45,X0,X14,X13,X8,X7] : c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X45,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X0,tc_fun(tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),X8),c_Set_Oinsert(X0)),c_Fun_Ocomp(X7,X13,X14,X0,X8)),X8,tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0)),X8,tc_fun(X0,tc_bool)) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X45,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X14,tc_fun(tc_fun(X14,tc_bool),tc_fun(X14,tc_bool)),X8),c_Set_Oinsert(X14)),X13),X8,tc_fun(X14,tc_bool),tc_fun(X14,tc_bool)),c_COMBK(c_False,tc_bool,X14)),X8,tc_fun(X14,tc_bool)),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X0,tc_fun(tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),X14),c_Set_Oinsert(X0)),X7),X14,tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0)),X14,tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_537])]) ).
fof(f15041,plain,
( ! [X0,X8,X45,X7,X14,X13] : c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X45,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X0,tc_fun(tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),X8),c_Set_Oinsert(X0)),c_Fun_Ocomp(X7,X13,X14,X0,X8)),X8,tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0)),X8,tc_fun(X0,tc_bool)) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X45,hAPP(hAPP(c_COMBB(X14,tc_fun(X14,tc_bool),X8),hAPP(c_COMBC(c_Set_Oinsert(X14),X14,tc_fun(X14,tc_bool),tc_fun(X14,tc_bool)),c_COMBK(c_False,tc_bool,X14))),X13),X8,tc_fun(X14,tc_bool)),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X0,tc_fun(tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),X14),c_Set_Oinsert(X0)),X7),X14,tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0)),X14,tc_fun(X0,tc_bool))
| ~ spl0_342
| ~ spl0_508
| ~ spl0_537 ),
inference(forward_demodulation,[],[f15039,f13758]) ).
fof(f15039,plain,
( ! [X0,X8,X45,X7,X14,X13] : c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X45,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X0,tc_fun(tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),X8),c_Set_Oinsert(X0)),c_Fun_Ocomp(X7,X13,X14,X0,X8)),X8,tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0)),X8,tc_fun(X0,tc_bool)) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X45,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X14,tc_fun(tc_fun(X14,tc_bool),tc_fun(X14,tc_bool)),X8),c_Set_Oinsert(X14)),X13),X8,tc_fun(X14,tc_bool),tc_fun(X14,tc_bool)),c_COMBK(c_False,tc_bool,X14)),X8,tc_fun(X14,tc_bool)),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X0,tc_fun(tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),X14),c_Set_Oinsert(X0)),X7),X14,tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0)),X14,tc_fun(X0,tc_bool))
| ~ spl0_537 ),
inference(avatar_component_clause,[],[f15038]) ).
fof(f15040,plain,
spl0_537,
inference(avatar_split_clause,[],[f741,f15038]) ).
fof(f741,plain,
! [X0,X8,X45,X7,X14,X13] : c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X45,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X0,tc_fun(tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),X8),c_Set_Oinsert(X0)),c_Fun_Ocomp(X7,X13,X14,X0,X8)),X8,tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0)),X8,tc_fun(X0,tc_bool)) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X45,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X14,tc_fun(tc_fun(X14,tc_bool),tc_fun(X14,tc_bool)),X8),c_Set_Oinsert(X14)),X13),X8,tc_fun(X14,tc_bool),tc_fun(X14,tc_bool)),c_COMBK(c_False,tc_bool,X14)),X8,tc_fun(X14,tc_bool)),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X0,tc_fun(tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),X14),c_Set_Oinsert(X0)),X7),X14,tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0)),X14,tc_fun(X0,tc_bool)),
inference(forward_demodulation,[],[f740,f698]) ).
fof(f740,plain,
! [X0,X8,X45,X7,X14,X13] : c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X45,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X0,tc_fun(tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),X8),c_Set_Oinsert(X0)),c_Fun_Ocomp(X7,X13,X14,X0,X8)),X8,tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0)),X8,tc_fun(X0,tc_bool)) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X45,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X14,tc_fun(tc_fun(X14,tc_bool),tc_fun(X14,tc_bool)),X8),c_Set_Oinsert(X14)),X13),X8,tc_fun(X14,tc_bool),tc_fun(X14,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X14,tc_bool))),X8,tc_fun(X14,tc_bool)),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X0,tc_fun(tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),X14),c_Set_Oinsert(X0)),X7),X14,tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0)),X14,tc_fun(X0,tc_bool)),
inference(forward_demodulation,[],[f651,f698]) ).
fof(f651,plain,
! [X0,X8,X45,X7,X14,X13] : c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X45,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X0,tc_fun(tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),X8),c_Set_Oinsert(X0)),c_Fun_Ocomp(X7,X13,X14,X0,X8)),X8,tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))),X8,tc_fun(X0,tc_bool)) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X45,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X14,tc_fun(tc_fun(X14,tc_bool),tc_fun(X14,tc_bool)),X8),c_Set_Oinsert(X14)),X13),X8,tc_fun(X14,tc_bool),tc_fun(X14,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X14,tc_bool))),X8,tc_fun(X14,tc_bool)),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X0,tc_fun(tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),X14),c_Set_Oinsert(X0)),X7),X14,tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))),X14,tc_fun(X0,tc_bool)),
inference(definition_unfolding,[],[f414,f552,f552,f552]) ).
fof(f414,axiom,
! [X0,X8,X7,X14,X45,X13] : c_Set_Oimage(c_Fun_Ocomp(X7,X13,X14,X0,X8),X45,X8,X0) = c_Set_Oimage(X7,c_Set_Oimage(X13,X45,X8,X14),X14,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__compose_0) ).
fof(f14957,plain,
( spl0_536
| ~ spl0_213
| ~ spl0_342
| ~ spl0_508
| ~ spl0_535 ),
inference(avatar_split_clause,[],[f14953,f14948,f13711,f4957,f2251,f14955]) ).
fof(f14955,plain,
( spl0_536
<=> ! [X5,X0,X9,X8,X7] :
( c_COMBK(c_False,tc_bool,X8) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X8,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X9),X5),hAPP(hAPP(c_COMBB(X8,tc_fun(X8,tc_bool),X0),hAPP(c_COMBC(c_Set_Oinsert(X8),X8,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8))),X7),X0,tc_fun(X8,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X5),X9),hAPP(hAPP(c_COMBB(X8,tc_fun(X8,tc_bool),X0),hAPP(c_COMBC(c_Set_Oinsert(X8),X8,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8))),X7),X0,tc_fun(X8,tc_bool)))
| ~ c_Fun_Oinj__on(X7,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X5),X9),X0,X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_536])]) ).
fof(f14948,plain,
( spl0_535
<=> ! [X9,X0,X5,X8,X7] :
( c_COMBK(c_False,tc_bool,X8) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X8,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X5),X9),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X8,tc_fun(tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),X0),c_Set_Oinsert(X8)),X7),X0,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8)),X0,tc_fun(X8,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X9),X5),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X8,tc_fun(tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),X0),c_Set_Oinsert(X8)),X7),X0,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8)),X0,tc_fun(X8,tc_bool)))
| ~ c_Fun_Oinj__on(X7,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X5),X9),X0,X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_535])]) ).
fof(f14953,plain,
( ! [X0,X8,X9,X7,X5] :
( c_COMBK(c_False,tc_bool,X8) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X8,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X9),X5),hAPP(hAPP(c_COMBB(X8,tc_fun(X8,tc_bool),X0),hAPP(c_COMBC(c_Set_Oinsert(X8),X8,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8))),X7),X0,tc_fun(X8,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X5),X9),hAPP(hAPP(c_COMBB(X8,tc_fun(X8,tc_bool),X0),hAPP(c_COMBC(c_Set_Oinsert(X8),X8,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8))),X7),X0,tc_fun(X8,tc_bool)))
| ~ c_Fun_Oinj__on(X7,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X5),X9),X0,X8) )
| ~ spl0_213
| ~ spl0_342
| ~ spl0_508
| ~ spl0_535 ),
inference(forward_demodulation,[],[f14952,f13758]) ).
fof(f14952,plain,
( ! [X0,X8,X9,X7,X5] :
( c_COMBK(c_False,tc_bool,X8) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X8,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X9),X5),hAPP(hAPP(c_COMBB(X8,tc_fun(X8,tc_bool),X0),hAPP(c_COMBC(c_Set_Oinsert(X8),X8,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8))),X7),X0,tc_fun(X8,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X5),X9),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X8,tc_fun(tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),X0),c_Set_Oinsert(X8)),X7),X0,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8)),X0,tc_fun(X8,tc_bool)))
| ~ c_Fun_Oinj__on(X7,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X5),X9),X0,X8) )
| ~ spl0_213
| ~ spl0_342
| ~ spl0_508
| ~ spl0_535 ),
inference(forward_demodulation,[],[f14951,f2252]) ).
fof(f14951,plain,
( ! [X0,X8,X9,X7,X5] :
( c_COMBK(c_False,tc_bool,X8) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X8,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X5),X9),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X8,tc_fun(tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),X0),c_Set_Oinsert(X8)),X7),X0,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8)),X0,tc_fun(X8,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X9),X5),hAPP(hAPP(c_COMBB(X8,tc_fun(X8,tc_bool),X0),hAPP(c_COMBC(c_Set_Oinsert(X8),X8,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8))),X7),X0,tc_fun(X8,tc_bool)))
| ~ c_Fun_Oinj__on(X7,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X5),X9),X0,X8) )
| ~ spl0_342
| ~ spl0_508
| ~ spl0_535 ),
inference(forward_demodulation,[],[f14949,f13758]) ).
fof(f14949,plain,
( ! [X0,X8,X9,X7,X5] :
( c_COMBK(c_False,tc_bool,X8) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X8,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X5),X9),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X8,tc_fun(tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),X0),c_Set_Oinsert(X8)),X7),X0,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8)),X0,tc_fun(X8,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X9),X5),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X8,tc_fun(tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),X0),c_Set_Oinsert(X8)),X7),X0,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8)),X0,tc_fun(X8,tc_bool)))
| ~ c_Fun_Oinj__on(X7,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X5),X9),X0,X8) )
| ~ spl0_535 ),
inference(avatar_component_clause,[],[f14948]) ).
fof(f14950,plain,
spl0_535,
inference(avatar_split_clause,[],[f876,f14948]) ).
fof(f876,plain,
! [X0,X8,X9,X7,X5] :
( c_COMBK(c_False,tc_bool,X8) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X8,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X5),X9),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X8,tc_fun(tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),X0),c_Set_Oinsert(X8)),X7),X0,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8)),X0,tc_fun(X8,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X9),X5),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X8,tc_fun(tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),X0),c_Set_Oinsert(X8)),X7),X0,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8)),X0,tc_fun(X8,tc_bool)))
| ~ c_Fun_Oinj__on(X7,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X5),X9),X0,X8) ),
inference(forward_demodulation,[],[f679,f698]) ).
fof(f679,plain,
! [X0,X8,X9,X7,X5] :
( ~ c_Fun_Oinj__on(X7,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X5),X9),X0,X8)
| c_Orderings_Obot__class_Obot(tc_fun(X8,tc_bool)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X8,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X5),X9),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X8,tc_fun(tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),X0),c_Set_Oinsert(X8)),X7),X0,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X8,tc_bool))),X0,tc_fun(X8,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X9),X5),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X8,tc_fun(tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),X0),c_Set_Oinsert(X8)),X7),X0,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X8,tc_bool))),X0,tc_fun(X8,tc_bool))) ),
inference(definition_unfolding,[],[f113,f552,f552]) ).
fof(f113,axiom,
! [X0,X8,X9,X7,X5] :
( ~ c_Fun_Oinj__on(X7,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X5),X9),X0,X8)
| c_Orderings_Obot__class_Obot(tc_fun(X8,tc_bool)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X8,tc_bool)),c_Set_Oimage(X7,hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X5),X9),X0,X8)),c_Set_Oimage(X7,hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X9),X5),X0,X8)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__Un_2) ).
fof(f14943,plain,
spl0_534,
inference(avatar_split_clause,[],[f828,f14941]) ).
fof(f14941,plain,
( spl0_534
<=> ! [X11,X0,X8,X7] :
( c_Finite__Set_Ofinite(hAPP(hAPP(c_COMBB(tc_fun(X0,tc_bool),tc_bool,X8),c_Ex(X0)),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(tc_fun(X0,tc_fun(tc_bool,tc_bool)),tc_fun(tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),X8),c_COMBS(X0,tc_bool,tc_bool)),hAPP(hAPP(c_COMBB(tc_fun(X0,tc_bool),tc_fun(X0,tc_fun(tc_bool,tc_bool)),X8),hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),X0),c_and)),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(tc_fun(X8,tc_bool),tc_fun(tc_fun(X0,X8),tc_fun(X0,tc_bool)),X8),c_COMBB(X8,tc_bool,X0)),c_fequal(X8)),X8,tc_fun(X0,X8),tc_fun(X0,tc_bool)),X7))),X8,tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),X11)),X8)
| ~ c_Finite__Set_Ofinite(X11,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_534])]) ).
fof(f828,plain,
! [X0,X11,X8,X7] :
( c_Finite__Set_Ofinite(hAPP(hAPP(c_COMBB(tc_fun(X0,tc_bool),tc_bool,X8),c_Ex(X0)),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(tc_fun(X0,tc_fun(tc_bool,tc_bool)),tc_fun(tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),X8),c_COMBS(X0,tc_bool,tc_bool)),hAPP(hAPP(c_COMBB(tc_fun(X0,tc_bool),tc_fun(X0,tc_fun(tc_bool,tc_bool)),X8),hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),X0),c_and)),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(tc_fun(X8,tc_bool),tc_fun(tc_fun(X0,X8),tc_fun(X0,tc_bool)),X8),c_COMBB(X8,tc_bool,X0)),c_fequal(X8)),X8,tc_fun(X0,X8),tc_fun(X0,tc_bool)),X7))),X8,tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),X11)),X8)
| ~ c_Finite__Set_Ofinite(X11,X0) ),
inference(forward_demodulation,[],[f827,f43]) ).
fof(f827,plain,
! [X0,X11,X8,X7] :
( ~ c_Finite__Set_Ofinite(X11,X0)
| c_Finite__Set_Ofinite(c_Collect(hAPP(hAPP(c_COMBB(tc_fun(X0,tc_bool),tc_bool,X8),c_Ex(X0)),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(tc_fun(X0,tc_fun(tc_bool,tc_bool)),tc_fun(tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),X8),c_COMBS(X0,tc_bool,tc_bool)),hAPP(hAPP(c_COMBB(tc_fun(X0,tc_bool),tc_fun(X0,tc_fun(tc_bool,tc_bool)),X8),hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),X0),c_and)),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(tc_fun(X8,tc_bool),tc_fun(tc_fun(X0,X8),tc_fun(X0,tc_bool)),X8),c_COMBB(X8,tc_bool,X0)),c_fequal(X8)),X8,tc_fun(X0,X8),tc_fun(X0,tc_bool)),X7))),X8,tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),X11)),X8),X8) ),
inference(forward_demodulation,[],[f520,f43]) ).
fof(f520,axiom,
! [X0,X11,X8,X7] :
( ~ c_Finite__Set_Ofinite(c_Collect(X11,X0),X0)
| c_Finite__Set_Ofinite(c_Collect(hAPP(hAPP(c_COMBB(tc_fun(X0,tc_bool),tc_bool,X8),c_Ex(X0)),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(tc_fun(X0,tc_fun(tc_bool,tc_bool)),tc_fun(tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),X8),c_COMBS(X0,tc_bool,tc_bool)),hAPP(hAPP(c_COMBB(tc_fun(X0,tc_bool),tc_fun(X0,tc_fun(tc_bool,tc_bool)),X8),hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),X0),c_and)),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(tc_fun(X8,tc_bool),tc_fun(tc_fun(X0,X8),tc_fun(X0,tc_bool)),X8),c_COMBB(X8,tc_bool,X0)),c_fequal(X8)),X8,tc_fun(X0,X8),tc_fun(X0,tc_bool)),X7))),X8,tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),X11)),X8),X8) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__image__set_0) ).
fof(f14925,plain,
( spl0_533
| ~ spl0_342
| ~ spl0_508
| ~ spl0_532 ),
inference(avatar_split_clause,[],[f14921,f14917,f13711,f4957,f14923]) ).
fof(f14923,plain,
( spl0_533
<=> ! [X5,X0,X9,X8,X7] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X8,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,hAPP(hAPP(c_COMBB(X8,tc_fun(X8,tc_bool),X0),hAPP(c_COMBC(c_Set_Oinsert(X8),X8,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8))),X7),X0,tc_fun(X8,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X9,hAPP(hAPP(c_COMBB(X8,tc_fun(X8,tc_bool),X0),hAPP(c_COMBC(c_Set_Oinsert(X8),X8,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8))),X7),X0,tc_fun(X8,tc_bool))))
| ~ c_Fun_Oinj__on(X7,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0,X8)
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X5),X9)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_533])]) ).
fof(f14917,plain,
( spl0_532
<=> ! [X5,X0,X9,X8,X7] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X8,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X8,tc_fun(tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),X0),c_Set_Oinsert(X8)),X7),X0,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8)),X0,tc_fun(X8,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X9,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X8,tc_fun(tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),X0),c_Set_Oinsert(X8)),X7),X0,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8)),X0,tc_fun(X8,tc_bool))))
| ~ c_Fun_Oinj__on(X7,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0,X8)
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X5),X9)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_532])]) ).
fof(f14921,plain,
( ! [X0,X8,X9,X7,X5] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X8,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,hAPP(hAPP(c_COMBB(X8,tc_fun(X8,tc_bool),X0),hAPP(c_COMBC(c_Set_Oinsert(X8),X8,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8))),X7),X0,tc_fun(X8,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X9,hAPP(hAPP(c_COMBB(X8,tc_fun(X8,tc_bool),X0),hAPP(c_COMBC(c_Set_Oinsert(X8),X8,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8))),X7),X0,tc_fun(X8,tc_bool))))
| ~ c_Fun_Oinj__on(X7,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0,X8)
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X5),X9)) )
| ~ spl0_342
| ~ spl0_508
| ~ spl0_532 ),
inference(forward_demodulation,[],[f14920,f13758]) ).
fof(f14920,plain,
( ! [X0,X8,X9,X7,X5] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X8,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X8,tc_fun(tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),X0),c_Set_Oinsert(X8)),X7),X0,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8)),X0,tc_fun(X8,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X9,hAPP(hAPP(c_COMBB(X8,tc_fun(X8,tc_bool),X0),hAPP(c_COMBC(c_Set_Oinsert(X8),X8,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8))),X7),X0,tc_fun(X8,tc_bool))))
| ~ c_Fun_Oinj__on(X7,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0,X8)
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X5),X9)) )
| ~ spl0_342
| ~ spl0_508
| ~ spl0_532 ),
inference(forward_demodulation,[],[f14918,f13758]) ).
fof(f14918,plain,
( ! [X0,X8,X9,X7,X5] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X8,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X8,tc_fun(tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),X0),c_Set_Oinsert(X8)),X7),X0,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8)),X0,tc_fun(X8,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X9,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X8,tc_fun(tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),X0),c_Set_Oinsert(X8)),X7),X0,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8)),X0,tc_fun(X8,tc_bool))))
| ~ c_Fun_Oinj__on(X7,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0,X8)
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X5),X9)) )
| ~ spl0_532 ),
inference(avatar_component_clause,[],[f14917]) ).
fof(f14919,plain,
spl0_532,
inference(avatar_split_clause,[],[f953,f14917]) ).
fof(f953,plain,
! [X0,X8,X9,X7,X5] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X8,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X8,tc_fun(tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),X0),c_Set_Oinsert(X8)),X7),X0,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8)),X0,tc_fun(X8,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X9,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X8,tc_fun(tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),X0),c_Set_Oinsert(X8)),X7),X0,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8)),X0,tc_fun(X8,tc_bool))))
| ~ c_Fun_Oinj__on(X7,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0,X8)
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X5),X9)) ),
inference(forward_demodulation,[],[f691,f698]) ).
fof(f691,plain,
! [X0,X8,X9,X7,X5] :
( ~ c_Fun_Oinj__on(X7,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0,X8)
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X5),X9))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X8,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X8,tc_fun(tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),X0),c_Set_Oinsert(X8)),X7),X0,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X8,tc_bool))),X0,tc_fun(X8,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X9,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X8,tc_fun(tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),X0),c_Set_Oinsert(X8)),X7),X0,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X8,tc_bool))),X0,tc_fun(X8,tc_bool)))) ),
inference(definition_unfolding,[],[f28,f552,f552]) ).
fof(f28,axiom,
! [X0,X8,X9,X7,X5] :
( ~ c_Fun_Oinj__on(X7,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0,X8)
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X5),X9))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X8,tc_bool)),c_Set_Oimage(X7,X5,X0,X8)),c_Set_Oimage(X7,X9,X0,X8))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__image__subset__iff_0) ).
fof(f14898,plain,
( spl0_531
| ~ spl0_342
| ~ spl0_508
| ~ spl0_530 ),
inference(avatar_split_clause,[],[f14894,f14890,f13711,f4957,f14896]) ).
fof(f14896,plain,
( spl0_531
<=> ! [X5,X0,X7] :
( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,hAPP(hAPP(c_COMBB(X0,tc_fun(X0,tc_bool),X0),hAPP(c_COMBC(c_Set_Oinsert(X0),X0,tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0))),X7),X0,tc_fun(X0,tc_bool)) = X5
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,hAPP(hAPP(c_COMBB(X0,tc_fun(X0,tc_bool),X0),hAPP(c_COMBC(c_Set_Oinsert(X0),X0,tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0))),X7),X0,tc_fun(X0,tc_bool))),X5))
| ~ c_Finite__Set_Ofinite(X5,X0)
| ~ c_Fun_Oinj__on(X7,X5,X0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_531])]) ).
fof(f14890,plain,
( spl0_530
<=> ! [X5,X0,X7] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X0,tc_fun(tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),X0),c_Set_Oinsert(X0)),X7),X0,tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0)),X0,tc_fun(X0,tc_bool))),X5))
| c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X0,tc_fun(tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),X0),c_Set_Oinsert(X0)),X7),X0,tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0)),X0,tc_fun(X0,tc_bool)) = X5
| ~ c_Finite__Set_Ofinite(X5,X0)
| ~ c_Fun_Oinj__on(X7,X5,X0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_530])]) ).
fof(f14894,plain,
( ! [X0,X7,X5] :
( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,hAPP(hAPP(c_COMBB(X0,tc_fun(X0,tc_bool),X0),hAPP(c_COMBC(c_Set_Oinsert(X0),X0,tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0))),X7),X0,tc_fun(X0,tc_bool)) = X5
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,hAPP(hAPP(c_COMBB(X0,tc_fun(X0,tc_bool),X0),hAPP(c_COMBC(c_Set_Oinsert(X0),X0,tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0))),X7),X0,tc_fun(X0,tc_bool))),X5))
| ~ c_Finite__Set_Ofinite(X5,X0)
| ~ c_Fun_Oinj__on(X7,X5,X0,X0) )
| ~ spl0_342
| ~ spl0_508
| ~ spl0_530 ),
inference(forward_demodulation,[],[f14893,f13758]) ).
fof(f14893,plain,
( ! [X0,X7,X5] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,hAPP(hAPP(c_COMBB(X0,tc_fun(X0,tc_bool),X0),hAPP(c_COMBC(c_Set_Oinsert(X0),X0,tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0))),X7),X0,tc_fun(X0,tc_bool))),X5))
| c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X0,tc_fun(tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),X0),c_Set_Oinsert(X0)),X7),X0,tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0)),X0,tc_fun(X0,tc_bool)) = X5
| ~ c_Finite__Set_Ofinite(X5,X0)
| ~ c_Fun_Oinj__on(X7,X5,X0,X0) )
| ~ spl0_342
| ~ spl0_508
| ~ spl0_530 ),
inference(forward_demodulation,[],[f14891,f13758]) ).
fof(f14891,plain,
( ! [X0,X7,X5] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X0,tc_fun(tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),X0),c_Set_Oinsert(X0)),X7),X0,tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0)),X0,tc_fun(X0,tc_bool))),X5))
| c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X0,tc_fun(tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),X0),c_Set_Oinsert(X0)),X7),X0,tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0)),X0,tc_fun(X0,tc_bool)) = X5
| ~ c_Finite__Set_Ofinite(X5,X0)
| ~ c_Fun_Oinj__on(X7,X5,X0,X0) )
| ~ spl0_530 ),
inference(avatar_component_clause,[],[f14890]) ).
fof(f14892,plain,
spl0_530,
inference(avatar_split_clause,[],[f999,f14890]) ).
fof(f999,plain,
! [X0,X7,X5] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X0,tc_fun(tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),X0),c_Set_Oinsert(X0)),X7),X0,tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0)),X0,tc_fun(X0,tc_bool))),X5))
| c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X0,tc_fun(tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),X0),c_Set_Oinsert(X0)),X7),X0,tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0)),X0,tc_fun(X0,tc_bool)) = X5
| ~ c_Finite__Set_Ofinite(X5,X0)
| ~ c_Fun_Oinj__on(X7,X5,X0,X0) ),
inference(forward_demodulation,[],[f998,f698]) ).
fof(f998,plain,
! [X0,X7,X5] :
( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X0,tc_fun(tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),X0),c_Set_Oinsert(X0)),X7),X0,tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0)),X0,tc_fun(X0,tc_bool)) = X5
| ~ c_Finite__Set_Ofinite(X5,X0)
| ~ c_Fun_Oinj__on(X7,X5,X0,X0)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X0,tc_fun(tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),X0),c_Set_Oinsert(X0)),X7),X0,tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))),X0,tc_fun(X0,tc_bool))),X5)) ),
inference(forward_demodulation,[],[f693,f698]) ).
fof(f693,plain,
! [X0,X7,X5] :
( ~ c_Finite__Set_Ofinite(X5,X0)
| ~ c_Fun_Oinj__on(X7,X5,X0,X0)
| c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X0,tc_fun(tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),X0),c_Set_Oinsert(X0)),X7),X0,tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))),X0,tc_fun(X0,tc_bool)) = X5
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X0,tc_fun(tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),X0),c_Set_Oinsert(X0)),X7),X0,tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))),X0,tc_fun(X0,tc_bool))),X5)) ),
inference(definition_unfolding,[],[f101,f552,f552]) ).
fof(f101,axiom,
! [X0,X7,X5] :
( ~ c_Finite__Set_Ofinite(X5,X0)
| ~ c_Fun_Oinj__on(X7,X5,X0,X0)
| c_Set_Oimage(X7,X5,X0,X0) = X5
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),c_Set_Oimage(X7,X5,X0,X0)),X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_endo__inj__surj_0) ).
fof(f14886,plain,
( spl0_529
| ~ spl0_342
| ~ spl0_508
| ~ spl0_528 ),
inference(avatar_split_clause,[],[f14882,f14878,f13711,f4957,f14884]) ).
fof(f14884,plain,
( spl0_529
<=> ! [X13,X0,X14,X8,X7] :
( ~ c_Finite__Set_Ofinite(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Otop__class_Otop(tc_fun(X8,tc_bool)),hAPP(hAPP(c_COMBB(X0,tc_fun(X0,tc_bool),X8),hAPP(c_COMBC(c_Set_Oinsert(X0),X0,tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0))),X13),X8,tc_fun(X0,tc_bool)),X0)
| c_Finite__Set_Ofinite(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Otop__class_Otop(tc_fun(X8,tc_bool)),hAPP(hAPP(c_COMBB(X14,tc_fun(X14,tc_bool),X8),hAPP(c_COMBC(c_Set_Oinsert(X14),X14,tc_fun(X14,tc_bool),tc_fun(X14,tc_bool)),c_COMBK(c_False,tc_bool,X14))),hAPP(hAPP(c_COMBB(X0,X14,X8),X7),X13)),X8,tc_fun(X14,tc_bool)),X14) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_529])]) ).
fof(f14878,plain,
( spl0_528
<=> ! [X13,X14,X0,X8,X7] :
( c_Finite__Set_Ofinite(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Otop__class_Otop(tc_fun(X8,tc_bool)),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X14,tc_fun(tc_fun(X14,tc_bool),tc_fun(X14,tc_bool)),X8),c_Set_Oinsert(X14)),hAPP(hAPP(c_COMBB(X0,X14,X8),X7),X13)),X8,tc_fun(X14,tc_bool),tc_fun(X14,tc_bool)),c_COMBK(c_False,tc_bool,X14)),X8,tc_fun(X14,tc_bool)),X14)
| ~ c_Finite__Set_Ofinite(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Otop__class_Otop(tc_fun(X8,tc_bool)),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X0,tc_fun(tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),X8),c_Set_Oinsert(X0)),X13),X8,tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0)),X8,tc_fun(X0,tc_bool)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_528])]) ).
fof(f14882,plain,
( ! [X0,X8,X7,X14,X13] :
( ~ c_Finite__Set_Ofinite(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Otop__class_Otop(tc_fun(X8,tc_bool)),hAPP(hAPP(c_COMBB(X0,tc_fun(X0,tc_bool),X8),hAPP(c_COMBC(c_Set_Oinsert(X0),X0,tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0))),X13),X8,tc_fun(X0,tc_bool)),X0)
| c_Finite__Set_Ofinite(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Otop__class_Otop(tc_fun(X8,tc_bool)),hAPP(hAPP(c_COMBB(X14,tc_fun(X14,tc_bool),X8),hAPP(c_COMBC(c_Set_Oinsert(X14),X14,tc_fun(X14,tc_bool),tc_fun(X14,tc_bool)),c_COMBK(c_False,tc_bool,X14))),hAPP(hAPP(c_COMBB(X0,X14,X8),X7),X13)),X8,tc_fun(X14,tc_bool)),X14) )
| ~ spl0_342
| ~ spl0_508
| ~ spl0_528 ),
inference(forward_demodulation,[],[f14881,f13758]) ).
fof(f14881,plain,
( ! [X0,X8,X7,X14,X13] :
( c_Finite__Set_Ofinite(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Otop__class_Otop(tc_fun(X8,tc_bool)),hAPP(hAPP(c_COMBB(X14,tc_fun(X14,tc_bool),X8),hAPP(c_COMBC(c_Set_Oinsert(X14),X14,tc_fun(X14,tc_bool),tc_fun(X14,tc_bool)),c_COMBK(c_False,tc_bool,X14))),hAPP(hAPP(c_COMBB(X0,X14,X8),X7),X13)),X8,tc_fun(X14,tc_bool)),X14)
| ~ c_Finite__Set_Ofinite(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Otop__class_Otop(tc_fun(X8,tc_bool)),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X0,tc_fun(tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),X8),c_Set_Oinsert(X0)),X13),X8,tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0)),X8,tc_fun(X0,tc_bool)),X0) )
| ~ spl0_342
| ~ spl0_508
| ~ spl0_528 ),
inference(forward_demodulation,[],[f14879,f13758]) ).
fof(f14879,plain,
( ! [X0,X8,X7,X14,X13] :
( c_Finite__Set_Ofinite(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Otop__class_Otop(tc_fun(X8,tc_bool)),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X14,tc_fun(tc_fun(X14,tc_bool),tc_fun(X14,tc_bool)),X8),c_Set_Oinsert(X14)),hAPP(hAPP(c_COMBB(X0,X14,X8),X7),X13)),X8,tc_fun(X14,tc_bool),tc_fun(X14,tc_bool)),c_COMBK(c_False,tc_bool,X14)),X8,tc_fun(X14,tc_bool)),X14)
| ~ c_Finite__Set_Ofinite(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Otop__class_Otop(tc_fun(X8,tc_bool)),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X0,tc_fun(tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),X8),c_Set_Oinsert(X0)),X13),X8,tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0)),X8,tc_fun(X0,tc_bool)),X0) )
| ~ spl0_528 ),
inference(avatar_component_clause,[],[f14878]) ).
fof(f14880,plain,
spl0_528,
inference(avatar_split_clause,[],[f859,f14878]) ).
fof(f859,plain,
! [X0,X8,X7,X14,X13] :
( c_Finite__Set_Ofinite(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Otop__class_Otop(tc_fun(X8,tc_bool)),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X14,tc_fun(tc_fun(X14,tc_bool),tc_fun(X14,tc_bool)),X8),c_Set_Oinsert(X14)),hAPP(hAPP(c_COMBB(X0,X14,X8),X7),X13)),X8,tc_fun(X14,tc_bool),tc_fun(X14,tc_bool)),c_COMBK(c_False,tc_bool,X14)),X8,tc_fun(X14,tc_bool)),X14)
| ~ c_Finite__Set_Ofinite(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Otop__class_Otop(tc_fun(X8,tc_bool)),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X0,tc_fun(tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),X8),c_Set_Oinsert(X0)),X13),X8,tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0)),X8,tc_fun(X0,tc_bool)),X0) ),
inference(forward_demodulation,[],[f858,f698]) ).
fof(f858,plain,
! [X0,X8,X7,X14,X13] :
( ~ c_Finite__Set_Ofinite(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Otop__class_Otop(tc_fun(X8,tc_bool)),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X0,tc_fun(tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),X8),c_Set_Oinsert(X0)),X13),X8,tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0)),X8,tc_fun(X0,tc_bool)),X0)
| c_Finite__Set_Ofinite(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Otop__class_Otop(tc_fun(X8,tc_bool)),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X14,tc_fun(tc_fun(X14,tc_bool),tc_fun(X14,tc_bool)),X8),c_Set_Oinsert(X14)),hAPP(hAPP(c_COMBB(X0,X14,X8),X7),X13)),X8,tc_fun(X14,tc_bool),tc_fun(X14,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X14,tc_bool))),X8,tc_fun(X14,tc_bool)),X14) ),
inference(forward_demodulation,[],[f677,f698]) ).
fof(f677,plain,
! [X0,X8,X7,X14,X13] :
( ~ c_Finite__Set_Ofinite(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Otop__class_Otop(tc_fun(X8,tc_bool)),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X0,tc_fun(tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),X8),c_Set_Oinsert(X0)),X13),X8,tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))),X8,tc_fun(X0,tc_bool)),X0)
| c_Finite__Set_Ofinite(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Otop__class_Otop(tc_fun(X8,tc_bool)),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X14,tc_fun(tc_fun(X14,tc_bool),tc_fun(X14,tc_bool)),X8),c_Set_Oinsert(X14)),hAPP(hAPP(c_COMBB(X0,X14,X8),X7),X13)),X8,tc_fun(X14,tc_bool),tc_fun(X14,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X14,tc_bool))),X8,tc_fun(X14,tc_bool)),X14) ),
inference(definition_unfolding,[],[f33,f552,f552]) ).
fof(f33,axiom,
! [X0,X8,X7,X14,X13] :
( ~ c_Finite__Set_Ofinite(c_Set_Oimage(X13,c_Orderings_Otop__class_Otop(tc_fun(X8,tc_bool)),X8,X0),X0)
| c_Finite__Set_Ofinite(c_Set_Oimage(hAPP(hAPP(c_COMBB(X0,X14,X8),X7),X13),c_Orderings_Otop__class_Otop(tc_fun(X8,tc_bool)),X8,X14),X14) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__range__imageI_0) ).
fof(f14868,plain,
( spl0_527
| ~ spl0_355
| ~ spl0_499 ),
inference(avatar_split_clause,[],[f13573,f13480,f5612,f14866]) ).
fof(f5612,plain,
( spl0_355
<=> ! [X0] : c_Fun_Oinj__on(hAPP(c_COMBC(c_Set_Oinsert(X0),X0,tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0)),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0,tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_355])]) ).
fof(f13480,plain,
( spl0_499
<=> ! [X0,X3,X2,X1] :
( c_Finite__Set_Ofinite(X0,X1)
| ~ c_Fun_Oinj__on(X2,X0,X1,X3)
| ~ class_Finite__Set_Ofinite_Ofinite(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_499])]) ).
fof(f13573,plain,
( ! [X0] :
( c_Finite__Set_Ofinite(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0)
| ~ class_Finite__Set_Ofinite_Ofinite(tc_fun(X0,tc_bool)) )
| ~ spl0_355
| ~ spl0_499 ),
inference(resolution,[],[f13481,f5613]) ).
fof(f5613,plain,
( ! [X0] : c_Fun_Oinj__on(hAPP(c_COMBC(c_Set_Oinsert(X0),X0,tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0)),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0,tc_fun(X0,tc_bool))
| ~ spl0_355 ),
inference(avatar_component_clause,[],[f5612]) ).
fof(f13481,plain,
( ! [X2,X3,X0,X1] :
( ~ c_Fun_Oinj__on(X2,X0,X1,X3)
| c_Finite__Set_Ofinite(X0,X1)
| ~ class_Finite__Set_Ofinite_Ofinite(X3) )
| ~ spl0_499 ),
inference(avatar_component_clause,[],[f13480]) ).
fof(f14864,plain,
( spl0_526
| ~ spl0_342
| ~ spl0_508
| ~ spl0_525 ),
inference(avatar_split_clause,[],[f14860,f14856,f13711,f4957,f14862]) ).
fof(f14862,plain,
( spl0_526
<=> ! [X9,X0,X5,X8,X7] :
( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X9,hAPP(hAPP(c_COMBB(X8,tc_fun(X8,tc_bool),X0),hAPP(c_COMBC(c_Set_Oinsert(X8),X8,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8))),X7),X0,tc_fun(X8,tc_bool)) != c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,hAPP(hAPP(c_COMBB(X8,tc_fun(X8,tc_bool),X0),hAPP(c_COMBC(c_Set_Oinsert(X8),X8,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8))),X7),X0,tc_fun(X8,tc_bool))
| X5 = X9
| ~ c_Fun_Oinj__on(X7,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X5),X9),X0,X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_526])]) ).
fof(f14856,plain,
( spl0_525
<=> ! [X5,X0,X9,X8,X7] :
( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X8,tc_fun(tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),X0),c_Set_Oinsert(X8)),X7),X0,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8)),X0,tc_fun(X8,tc_bool)) != c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X9,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X8,tc_fun(tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),X0),c_Set_Oinsert(X8)),X7),X0,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8)),X0,tc_fun(X8,tc_bool))
| X5 = X9
| ~ c_Fun_Oinj__on(X7,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X5),X9),X0,X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_525])]) ).
fof(f14860,plain,
( ! [X0,X8,X9,X7,X5] :
( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X9,hAPP(hAPP(c_COMBB(X8,tc_fun(X8,tc_bool),X0),hAPP(c_COMBC(c_Set_Oinsert(X8),X8,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8))),X7),X0,tc_fun(X8,tc_bool)) != c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,hAPP(hAPP(c_COMBB(X8,tc_fun(X8,tc_bool),X0),hAPP(c_COMBC(c_Set_Oinsert(X8),X8,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8))),X7),X0,tc_fun(X8,tc_bool))
| X5 = X9
| ~ c_Fun_Oinj__on(X7,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X5),X9),X0,X8) )
| ~ spl0_342
| ~ spl0_508
| ~ spl0_525 ),
inference(forward_demodulation,[],[f14859,f13758]) ).
fof(f14859,plain,
( ! [X0,X8,X9,X7,X5] :
( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X8,tc_fun(tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),X0),c_Set_Oinsert(X8)),X7),X0,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8)),X0,tc_fun(X8,tc_bool)) != c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X9,hAPP(hAPP(c_COMBB(X8,tc_fun(X8,tc_bool),X0),hAPP(c_COMBC(c_Set_Oinsert(X8),X8,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8))),X7),X0,tc_fun(X8,tc_bool))
| X5 = X9
| ~ c_Fun_Oinj__on(X7,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X5),X9),X0,X8) )
| ~ spl0_342
| ~ spl0_508
| ~ spl0_525 ),
inference(forward_demodulation,[],[f14857,f13758]) ).
fof(f14857,plain,
( ! [X0,X8,X9,X7,X5] :
( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X8,tc_fun(tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),X0),c_Set_Oinsert(X8)),X7),X0,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8)),X0,tc_fun(X8,tc_bool)) != c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X9,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X8,tc_fun(tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),X0),c_Set_Oinsert(X8)),X7),X0,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8)),X0,tc_fun(X8,tc_bool))
| X5 = X9
| ~ c_Fun_Oinj__on(X7,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X5),X9),X0,X8) )
| ~ spl0_525 ),
inference(avatar_component_clause,[],[f14856]) ).
fof(f14858,plain,
spl0_525,
inference(avatar_split_clause,[],[f917,f14856]) ).
fof(f917,plain,
! [X0,X8,X9,X7,X5] :
( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X8,tc_fun(tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),X0),c_Set_Oinsert(X8)),X7),X0,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8)),X0,tc_fun(X8,tc_bool)) != c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X9,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X8,tc_fun(tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),X0),c_Set_Oinsert(X8)),X7),X0,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8)),X0,tc_fun(X8,tc_bool))
| X5 = X9
| ~ c_Fun_Oinj__on(X7,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X5),X9),X0,X8) ),
inference(forward_demodulation,[],[f683,f698]) ).
fof(f683,plain,
! [X0,X8,X9,X7,X5] :
( X5 = X9
| c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X8,tc_fun(tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),X0),c_Set_Oinsert(X8)),X7),X0,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X8,tc_bool))),X0,tc_fun(X8,tc_bool)) != c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X9,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X8,tc_fun(tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),X0),c_Set_Oinsert(X8)),X7),X0,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X8,tc_bool))),X0,tc_fun(X8,tc_bool))
| ~ c_Fun_Oinj__on(X7,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X5),X9),X0,X8) ),
inference(definition_unfolding,[],[f61,f552,f552]) ).
fof(f61,axiom,
! [X0,X8,X9,X7,X5] :
( X5 = X9
| c_Set_Oimage(X7,X5,X0,X8) != c_Set_Oimage(X7,X9,X0,X8)
| ~ c_Fun_Oinj__on(X7,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X5),X9),X0,X8) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__Un__image__eq__iff_0) ).
fof(f14812,plain,
( spl0_524
| ~ spl0_342
| ~ spl0_508
| ~ spl0_523 ),
inference(avatar_split_clause,[],[f14808,f14804,f13711,f4957,f14810]) ).
fof(f14810,plain,
( spl0_524
<=> ! [X5,X0,X9,X8,X7] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X8,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,hAPP(hAPP(c_COMBB(X8,tc_fun(X8,tc_bool),X0),hAPP(c_COMBC(c_Set_Oinsert(X8),X8,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8))),X7),X0,tc_fun(X8,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X9,hAPP(hAPP(c_COMBB(X8,tc_fun(X8,tc_bool),X0),hAPP(c_COMBC(c_Set_Oinsert(X8),X8,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8))),X7),X0,tc_fun(X8,tc_bool))))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X5),X9)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_524])]) ).
fof(f14804,plain,
( spl0_523
<=> ! [X5,X0,X9,X8,X7] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X8,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X8,tc_fun(tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),X0),c_Set_Oinsert(X8)),X7),X0,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8)),X0,tc_fun(X8,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X9,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X8,tc_fun(tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),X0),c_Set_Oinsert(X8)),X7),X0,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8)),X0,tc_fun(X8,tc_bool))))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X5),X9)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_523])]) ).
fof(f14808,plain,
( ! [X0,X8,X9,X7,X5] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X8,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,hAPP(hAPP(c_COMBB(X8,tc_fun(X8,tc_bool),X0),hAPP(c_COMBC(c_Set_Oinsert(X8),X8,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8))),X7),X0,tc_fun(X8,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X9,hAPP(hAPP(c_COMBB(X8,tc_fun(X8,tc_bool),X0),hAPP(c_COMBC(c_Set_Oinsert(X8),X8,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8))),X7),X0,tc_fun(X8,tc_bool))))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X5),X9)) )
| ~ spl0_342
| ~ spl0_508
| ~ spl0_523 ),
inference(forward_demodulation,[],[f14807,f13758]) ).
fof(f14807,plain,
( ! [X0,X8,X9,X7,X5] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X8,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X8,tc_fun(tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),X0),c_Set_Oinsert(X8)),X7),X0,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8)),X0,tc_fun(X8,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X9,hAPP(hAPP(c_COMBB(X8,tc_fun(X8,tc_bool),X0),hAPP(c_COMBC(c_Set_Oinsert(X8),X8,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8))),X7),X0,tc_fun(X8,tc_bool))))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X5),X9)) )
| ~ spl0_342
| ~ spl0_508
| ~ spl0_523 ),
inference(forward_demodulation,[],[f14805,f13758]) ).
fof(f14805,plain,
( ! [X0,X8,X9,X7,X5] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X8,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X8,tc_fun(tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),X0),c_Set_Oinsert(X8)),X7),X0,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8)),X0,tc_fun(X8,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X9,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X8,tc_fun(tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),X0),c_Set_Oinsert(X8)),X7),X0,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8)),X0,tc_fun(X8,tc_bool))))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X5),X9)) )
| ~ spl0_523 ),
inference(avatar_component_clause,[],[f14804]) ).
fof(f14806,plain,
spl0_523,
inference(avatar_split_clause,[],[f855,f14804]) ).
fof(f855,plain,
! [X0,X8,X9,X7,X5] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X8,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X8,tc_fun(tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),X0),c_Set_Oinsert(X8)),X7),X0,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8)),X0,tc_fun(X8,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X9,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X8,tc_fun(tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),X0),c_Set_Oinsert(X8)),X7),X0,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8)),X0,tc_fun(X8,tc_bool))))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X5),X9)) ),
inference(forward_demodulation,[],[f674,f698]) ).
fof(f674,plain,
! [X0,X8,X9,X7,X5] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X5),X9))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X8,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X8,tc_fun(tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),X0),c_Set_Oinsert(X8)),X7),X0,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X8,tc_bool))),X0,tc_fun(X8,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X9,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X8,tc_fun(tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),X0),c_Set_Oinsert(X8)),X7),X0,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X8,tc_bool))),X0,tc_fun(X8,tc_bool)))) ),
inference(definition_unfolding,[],[f484,f552,f552]) ).
fof(f484,axiom,
! [X0,X8,X9,X7,X5] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X5),X9))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X8,tc_bool)),c_Set_Oimage(X7,X5,X0,X8)),c_Set_Oimage(X7,X9,X0,X8))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__mono_0) ).
fof(f14778,plain,
( spl0_522
| ~ spl0_342
| ~ spl0_508
| ~ spl0_521 ),
inference(avatar_split_clause,[],[f14774,f14771,f13711,f4957,f14776]) ).
fof(f14776,plain,
( spl0_522
<=> ! [X1,X0,X5,X8,X7] :
( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,hAPP(hAPP(c_COMBB(X8,tc_fun(X8,tc_bool),X0),hAPP(c_COMBC(c_Set_Oinsert(X8),X8,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8))),X7),X0,tc_fun(X8,tc_bool)) = hAPP(hAPP(c_Set_Oinsert(X8),hAPP(X7,X1)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,hAPP(hAPP(c_COMBB(X8,tc_fun(X8,tc_bool),X0),hAPP(c_COMBC(c_Set_Oinsert(X8),X8,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8))),X7),X0,tc_fun(X8,tc_bool)))
| ~ hBOOL(c_in(X1,X5,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_522])]) ).
fof(f14771,plain,
( spl0_521
<=> ! [X1,X0,X5,X8,X7] :
( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X8,tc_fun(tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),X0),c_Set_Oinsert(X8)),X7),X0,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8)),X0,tc_fun(X8,tc_bool)) = hAPP(hAPP(c_Set_Oinsert(X8),hAPP(X7,X1)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X8,tc_fun(tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),X0),c_Set_Oinsert(X8)),X7),X0,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8)),X0,tc_fun(X8,tc_bool)))
| ~ hBOOL(c_in(X1,X5,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_521])]) ).
fof(f14774,plain,
( ! [X0,X1,X8,X7,X5] :
( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,hAPP(hAPP(c_COMBB(X8,tc_fun(X8,tc_bool),X0),hAPP(c_COMBC(c_Set_Oinsert(X8),X8,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8))),X7),X0,tc_fun(X8,tc_bool)) = hAPP(hAPP(c_Set_Oinsert(X8),hAPP(X7,X1)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,hAPP(hAPP(c_COMBB(X8,tc_fun(X8,tc_bool),X0),hAPP(c_COMBC(c_Set_Oinsert(X8),X8,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8))),X7),X0,tc_fun(X8,tc_bool)))
| ~ hBOOL(c_in(X1,X5,X0)) )
| ~ spl0_342
| ~ spl0_508
| ~ spl0_521 ),
inference(forward_demodulation,[],[f14772,f13758]) ).
fof(f14772,plain,
( ! [X0,X1,X8,X7,X5] :
( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X8,tc_fun(tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),X0),c_Set_Oinsert(X8)),X7),X0,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8)),X0,tc_fun(X8,tc_bool)) = hAPP(hAPP(c_Set_Oinsert(X8),hAPP(X7,X1)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X8,tc_fun(tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),X0),c_Set_Oinsert(X8)),X7),X0,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8)),X0,tc_fun(X8,tc_bool)))
| ~ hBOOL(c_in(X1,X5,X0)) )
| ~ spl0_521 ),
inference(avatar_component_clause,[],[f14771]) ).
fof(f14773,plain,
spl0_521,
inference(avatar_split_clause,[],[f817,f14771]) ).
fof(f817,plain,
! [X0,X1,X8,X7,X5] :
( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X8,tc_fun(tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),X0),c_Set_Oinsert(X8)),X7),X0,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8)),X0,tc_fun(X8,tc_bool)) = hAPP(hAPP(c_Set_Oinsert(X8),hAPP(X7,X1)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X8,tc_fun(tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),X0),c_Set_Oinsert(X8)),X7),X0,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8)),X0,tc_fun(X8,tc_bool)))
| ~ hBOOL(c_in(X1,X5,X0)) ),
inference(forward_demodulation,[],[f667,f698]) ).
fof(f667,plain,
! [X0,X1,X8,X7,X5] :
( ~ hBOOL(c_in(X1,X5,X0))
| c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X8,tc_fun(tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),X0),c_Set_Oinsert(X8)),X7),X0,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X8,tc_bool))),X0,tc_fun(X8,tc_bool)) = hAPP(hAPP(c_Set_Oinsert(X8),hAPP(X7,X1)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X8,tc_fun(tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),X0),c_Set_Oinsert(X8)),X7),X0,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X8,tc_bool))),X0,tc_fun(X8,tc_bool))) ),
inference(definition_unfolding,[],[f172,f552,f552]) ).
fof(f172,axiom,
! [X0,X1,X8,X7,X5] :
( ~ hBOOL(c_in(X1,X5,X0))
| c_Set_Oimage(X7,X5,X0,X8) = hAPP(hAPP(c_Set_Oinsert(X8),hAPP(X7,X1)),c_Set_Oimage(X7,X5,X0,X8)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__image_0) ).
fof(f14497,plain,
( spl0_520
| ~ spl0_342
| ~ spl0_508
| ~ spl0_518 ),
inference(avatar_split_clause,[],[f14489,f14486,f13711,f4957,f14495]) ).
fof(f14495,plain,
( spl0_520
<=> ! [X3,X0,X9,X8,X7] : c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_Set_Oinsert(X8),X3),X9),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X0,tc_fun(tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),X8),c_Set_Oinsert(X0)),X7),X8,tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0)),X8,tc_fun(X0,tc_bool)) = hAPP(hAPP(c_Set_Oinsert(X0),hAPP(X7,X3)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X9,hAPP(hAPP(c_COMBB(X0,tc_fun(X0,tc_bool),X8),hAPP(c_COMBC(c_Set_Oinsert(X0),X0,tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0))),X7),X8,tc_fun(X0,tc_bool))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_520])]) ).
fof(f14486,plain,
( spl0_518
<=> ! [X3,X0,X9,X8,X7] : c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_Set_Oinsert(X8),X3),X9),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X0,tc_fun(tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),X8),c_Set_Oinsert(X0)),X7),X8,tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0)),X8,tc_fun(X0,tc_bool)) = hAPP(hAPP(c_Set_Oinsert(X0),hAPP(X7,X3)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X9,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X0,tc_fun(tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),X8),c_Set_Oinsert(X0)),X7),X8,tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0)),X8,tc_fun(X0,tc_bool))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_518])]) ).
fof(f14489,plain,
( ! [X3,X0,X8,X9,X7] : c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_Set_Oinsert(X8),X3),X9),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X0,tc_fun(tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),X8),c_Set_Oinsert(X0)),X7),X8,tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0)),X8,tc_fun(X0,tc_bool)) = hAPP(hAPP(c_Set_Oinsert(X0),hAPP(X7,X3)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X9,hAPP(hAPP(c_COMBB(X0,tc_fun(X0,tc_bool),X8),hAPP(c_COMBC(c_Set_Oinsert(X0),X0,tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0))),X7),X8,tc_fun(X0,tc_bool)))
| ~ spl0_342
| ~ spl0_508
| ~ spl0_518 ),
inference(forward_demodulation,[],[f14487,f13758]) ).
fof(f14487,plain,
( ! [X3,X0,X8,X9,X7] : c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_Set_Oinsert(X8),X3),X9),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X0,tc_fun(tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),X8),c_Set_Oinsert(X0)),X7),X8,tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0)),X8,tc_fun(X0,tc_bool)) = hAPP(hAPP(c_Set_Oinsert(X0),hAPP(X7,X3)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X9,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X0,tc_fun(tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),X8),c_Set_Oinsert(X0)),X7),X8,tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0)),X8,tc_fun(X0,tc_bool)))
| ~ spl0_518 ),
inference(avatar_component_clause,[],[f14486]) ).
fof(f14493,plain,
( spl0_519
| ~ spl0_173
| ~ spl0_227 ),
inference(avatar_split_clause,[],[f3974,f2580,f1882,f14491]) ).
fof(f3974,plain,
( ! [X0,X1] : hBOOL(hAPP(c_Finite__Set_Ofold1Set(X1,c_SetInterval_Oord__class_OatLeastAtMost(X0,X0,tc_bool),tc_bool),X0))
| ~ spl0_173
| ~ spl0_227 ),
inference(superposition,[],[f1883,f2581]) ).
fof(f14488,plain,
spl0_518,
inference(avatar_split_clause,[],[f748,f14486]) ).
fof(f748,plain,
! [X3,X0,X8,X9,X7] : c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_Set_Oinsert(X8),X3),X9),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X0,tc_fun(tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),X8),c_Set_Oinsert(X0)),X7),X8,tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0)),X8,tc_fun(X0,tc_bool)) = hAPP(hAPP(c_Set_Oinsert(X0),hAPP(X7,X3)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X9,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X0,tc_fun(tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),X8),c_Set_Oinsert(X0)),X7),X8,tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0)),X8,tc_fun(X0,tc_bool))),
inference(forward_demodulation,[],[f653,f698]) ).
fof(f653,plain,
! [X3,X0,X8,X9,X7] : c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_Set_Oinsert(X8),X3),X9),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X0,tc_fun(tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),X8),c_Set_Oinsert(X0)),X7),X8,tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))),X8,tc_fun(X0,tc_bool)) = hAPP(hAPP(c_Set_Oinsert(X0),hAPP(X7,X3)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X9,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X0,tc_fun(tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),X8),c_Set_Oinsert(X0)),X7),X8,tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))),X8,tc_fun(X0,tc_bool))),
inference(definition_unfolding,[],[f387,f552,f552]) ).
fof(f387,axiom,
! [X3,X0,X8,X9,X7] : c_Set_Oimage(X7,hAPP(hAPP(c_Set_Oinsert(X8),X3),X9),X8,X0) = hAPP(hAPP(c_Set_Oinsert(X0),hAPP(X7,X3)),c_Set_Oimage(X7,X9,X8,X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__insert_0) ).
fof(f14478,plain,
( spl0_517
| ~ spl0_342
| ~ spl0_508
| ~ spl0_516 ),
inference(avatar_split_clause,[],[f14474,f14470,f13711,f4957,f14476]) ).
fof(f14476,plain,
( spl0_517
<=> ! [X9,X0,X5,X8,X7] :
( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X9,hAPP(hAPP(c_COMBB(X8,tc_fun(X8,tc_bool),X0),hAPP(c_COMBC(c_Set_Oinsert(X8),X8,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8))),X7),X0,tc_fun(X8,tc_bool)) != c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,hAPP(hAPP(c_COMBB(X8,tc_fun(X8,tc_bool),X0),hAPP(c_COMBC(c_Set_Oinsert(X8),X8,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8))),X7),X0,tc_fun(X8,tc_bool))
| X5 = X9
| ~ c_Fun_Oinj__on(X7,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0,X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_517])]) ).
fof(f14470,plain,
( spl0_516
<=> ! [X5,X0,X9,X8,X7] :
( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X8,tc_fun(tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),X0),c_Set_Oinsert(X8)),X7),X0,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8)),X0,tc_fun(X8,tc_bool)) != c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X9,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X8,tc_fun(tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),X0),c_Set_Oinsert(X8)),X7),X0,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8)),X0,tc_fun(X8,tc_bool))
| X5 = X9
| ~ c_Fun_Oinj__on(X7,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0,X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_516])]) ).
fof(f14474,plain,
( ! [X0,X8,X9,X7,X5] :
( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X9,hAPP(hAPP(c_COMBB(X8,tc_fun(X8,tc_bool),X0),hAPP(c_COMBC(c_Set_Oinsert(X8),X8,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8))),X7),X0,tc_fun(X8,tc_bool)) != c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,hAPP(hAPP(c_COMBB(X8,tc_fun(X8,tc_bool),X0),hAPP(c_COMBC(c_Set_Oinsert(X8),X8,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8))),X7),X0,tc_fun(X8,tc_bool))
| X5 = X9
| ~ c_Fun_Oinj__on(X7,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0,X8) )
| ~ spl0_342
| ~ spl0_508
| ~ spl0_516 ),
inference(forward_demodulation,[],[f14473,f13758]) ).
fof(f14473,plain,
( ! [X0,X8,X9,X7,X5] :
( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X8,tc_fun(tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),X0),c_Set_Oinsert(X8)),X7),X0,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8)),X0,tc_fun(X8,tc_bool)) != c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X9,hAPP(hAPP(c_COMBB(X8,tc_fun(X8,tc_bool),X0),hAPP(c_COMBC(c_Set_Oinsert(X8),X8,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8))),X7),X0,tc_fun(X8,tc_bool))
| X5 = X9
| ~ c_Fun_Oinj__on(X7,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0,X8) )
| ~ spl0_342
| ~ spl0_508
| ~ spl0_516 ),
inference(forward_demodulation,[],[f14471,f13758]) ).
fof(f14471,plain,
( ! [X0,X8,X9,X7,X5] :
( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X8,tc_fun(tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),X0),c_Set_Oinsert(X8)),X7),X0,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8)),X0,tc_fun(X8,tc_bool)) != c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X9,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X8,tc_fun(tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),X0),c_Set_Oinsert(X8)),X7),X0,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8)),X0,tc_fun(X8,tc_bool))
| X5 = X9
| ~ c_Fun_Oinj__on(X7,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0,X8) )
| ~ spl0_516 ),
inference(avatar_component_clause,[],[f14470]) ).
fof(f14472,plain,
spl0_516,
inference(avatar_split_clause,[],[f916,f14470]) ).
fof(f916,plain,
! [X0,X8,X9,X7,X5] :
( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X8,tc_fun(tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),X0),c_Set_Oinsert(X8)),X7),X0,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8)),X0,tc_fun(X8,tc_bool)) != c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X9,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X8,tc_fun(tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),X0),c_Set_Oinsert(X8)),X7),X0,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8)),X0,tc_fun(X8,tc_bool))
| X5 = X9
| ~ c_Fun_Oinj__on(X7,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0,X8) ),
inference(forward_demodulation,[],[f682,f698]) ).
fof(f682,plain,
! [X0,X8,X9,X7,X5] :
( X5 = X9
| ~ c_Fun_Oinj__on(X7,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0,X8)
| c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X8,tc_fun(tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),X0),c_Set_Oinsert(X8)),X7),X0,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X8,tc_bool))),X0,tc_fun(X8,tc_bool)) != c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X9,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X8,tc_fun(tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),X0),c_Set_Oinsert(X8)),X7),X0,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X8,tc_bool))),X0,tc_fun(X8,tc_bool)) ),
inference(definition_unfolding,[],[f220,f552,f552]) ).
fof(f220,axiom,
! [X0,X8,X9,X7,X5] :
( X5 = X9
| ~ c_Fun_Oinj__on(X7,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0,X8)
| c_Set_Oimage(X7,X5,X0,X8) != c_Set_Oimage(X7,X9,X0,X8) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__image__eq__iff_0) ).
fof(f14097,plain,
( spl0_515
| ~ spl0_213
| ~ spl0_214
| ~ spl0_460
| ~ spl0_467
| ~ spl0_514 ),
inference(avatar_split_clause,[],[f14093,f14089,f10949,f10774,f2255,f2251,f14095]) ).
fof(f10949,plain,
( spl0_467
<=> ! [X5,X0,X12,X9] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X5),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X9),X12)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X5),X9)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X5),X12)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_467])]) ).
fof(f14089,plain,
( spl0_514
<=> ! [X9,X0,X12,X5] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X12),X5)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X5),X9)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X9),X12))) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X12),X5)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X5),X9)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X9),X12))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_514])]) ).
fof(f14093,plain,
( ! [X0,X9,X5,X12] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X12),X5)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X9),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X5),X12))) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X12),X5)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X9),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X5),X12)))
| ~ spl0_213
| ~ spl0_214
| ~ spl0_460
| ~ spl0_467
| ~ spl0_514 ),
inference(forward_demodulation,[],[f14092,f11566]) ).
fof(f11566,plain,
( ! [X2,X3,X0,X1] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X2),X3)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X2),X1)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X3))
| ~ spl0_214
| ~ spl0_467 ),
inference(superposition,[],[f10950,f2256]) ).
fof(f10950,plain,
( ! [X0,X9,X5,X12] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X5),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X9),X12)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X5),X9)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X5),X12))
| ~ spl0_467 ),
inference(avatar_component_clause,[],[f10949]) ).
fof(f14092,plain,
( ! [X0,X9,X5,X12] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X12),X5)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X5),X9)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X9),X12))) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X12),X5)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X9),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X5),X12)))
| ~ spl0_213
| ~ spl0_460
| ~ spl0_514 ),
inference(forward_demodulation,[],[f14090,f11031]) ).
fof(f11031,plain,
( ! [X2,X3,X0,X1] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X2),X3)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X2),X1)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X1),X3))
| ~ spl0_213
| ~ spl0_460 ),
inference(superposition,[],[f10775,f2252]) ).
fof(f14090,plain,
( ! [X0,X9,X5,X12] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X12),X5)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X5),X9)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X9),X12))) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X12),X5)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X5),X9)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X9),X12)))
| ~ spl0_514 ),
inference(avatar_component_clause,[],[f14089]) ).
fof(f14091,plain,
spl0_514,
inference(avatar_split_clause,[],[f777,f14089]) ).
fof(f777,plain,
! [X0,X9,X5,X12] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X12),X5)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X5),X9)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X9),X12))) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X12),X5)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X5),X9)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X9),X12))),
inference(forward_demodulation,[],[f776,f197]) ).
fof(f197,axiom,
! [X0,X9,X5] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X5),X9) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X9),X5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__commute_0) ).
fof(f776,plain,
! [X0,X9,X5,X12] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X5),X9)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X9),X12))),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X12),X5)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X12),X5)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X5),X9)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X9),X12))),
inference(forward_demodulation,[],[f165,f157]) ).
fof(f157,axiom,
! [X0,X9,X5] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X5),X9) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X9),X5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__commute_0) ).
fof(f165,axiom,
! [X0,X9,X5,X12] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X5),X9)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X9),X12))),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X12),X5)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X5),X9)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X9),X12))),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X12),X5)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Int__crazy_0) ).
fof(f13966,plain,
( spl0_513
| ~ spl0_342
| ~ spl0_508
| ~ spl0_512 ),
inference(avatar_split_clause,[],[f13962,f13959,f13711,f4957,f13964]) ).
fof(f13959,plain,
( spl0_512
<=> ! [X5,X0,X3,X8,X7] :
( hBOOL(c_in(hAPP(X7,X3),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X5),hAPP(c_fequal(X0),X3)),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X8,tc_fun(tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),X0),c_Set_Oinsert(X8)),X7),X0,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8)),X0,tc_fun(X8,tc_bool)),X8))
| ~ c_Fun_Oinj__on(X7,X5,X0,X8)
| c_Fun_Oinj__on(X7,hAPP(hAPP(c_Set_Oinsert(X0),X3),X5),X0,X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_512])]) ).
fof(f13962,plain,
( ! [X3,X0,X8,X7,X5] :
( hBOOL(c_in(hAPP(X7,X3),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X5),hAPP(c_fequal(X0),X3)),hAPP(hAPP(c_COMBB(X8,tc_fun(X8,tc_bool),X0),hAPP(c_COMBC(c_Set_Oinsert(X8),X8,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8))),X7),X0,tc_fun(X8,tc_bool)),X8))
| ~ c_Fun_Oinj__on(X7,X5,X0,X8)
| c_Fun_Oinj__on(X7,hAPP(hAPP(c_Set_Oinsert(X0),X3),X5),X0,X8) )
| ~ spl0_342
| ~ spl0_508
| ~ spl0_512 ),
inference(forward_demodulation,[],[f13960,f13758]) ).
fof(f13960,plain,
( ! [X3,X0,X8,X7,X5] :
( hBOOL(c_in(hAPP(X7,X3),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X5),hAPP(c_fequal(X0),X3)),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X8,tc_fun(tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),X0),c_Set_Oinsert(X8)),X7),X0,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8)),X0,tc_fun(X8,tc_bool)),X8))
| ~ c_Fun_Oinj__on(X7,X5,X0,X8)
| c_Fun_Oinj__on(X7,hAPP(hAPP(c_Set_Oinsert(X0),X3),X5),X0,X8) )
| ~ spl0_512 ),
inference(avatar_component_clause,[],[f13959]) ).
fof(f13961,plain,
spl0_512,
inference(avatar_split_clause,[],[f945,f13959]) ).
fof(f945,plain,
! [X3,X0,X8,X7,X5] :
( hBOOL(c_in(hAPP(X7,X3),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X5),hAPP(c_fequal(X0),X3)),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X8,tc_fun(tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),X0),c_Set_Oinsert(X8)),X7),X0,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8)),X0,tc_fun(X8,tc_bool)),X8))
| ~ c_Fun_Oinj__on(X7,X5,X0,X8)
| c_Fun_Oinj__on(X7,hAPP(hAPP(c_Set_Oinsert(X0),X3),X5),X0,X8) ),
inference(forward_demodulation,[],[f944,f723]) ).
fof(f723,plain,
! [X3,X0] : hAPP(c_fequal(X0),X3) = hAPP(hAPP(c_Set_Oinsert(X0),X3),c_COMBK(c_False,tc_bool,X0)),
inference(forward_demodulation,[],[f722,f698]) ).
fof(f722,plain,
! [X3,X0] : hAPP(hAPP(c_Set_Oinsert(X0),X3),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))) = hAPP(c_fequal(X0),X3),
inference(forward_demodulation,[],[f523,f43]) ).
fof(f523,axiom,
! [X3,X0] : hAPP(hAPP(c_Set_Oinsert(X0),X3),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))) = c_Collect(hAPP(c_fequal(X0),X3),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_singleton__conv2_0) ).
fof(f944,plain,
! [X3,X0,X8,X7,X5] :
( hBOOL(c_in(hAPP(X7,X3),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X5),hAPP(hAPP(c_Set_Oinsert(X0),X3),c_COMBK(c_False,tc_bool,X0))),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X8,tc_fun(tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),X0),c_Set_Oinsert(X8)),X7),X0,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8)),X0,tc_fun(X8,tc_bool)),X8))
| ~ c_Fun_Oinj__on(X7,X5,X0,X8)
| c_Fun_Oinj__on(X7,hAPP(hAPP(c_Set_Oinsert(X0),X3),X5),X0,X8) ),
inference(forward_demodulation,[],[f943,f698]) ).
fof(f943,plain,
! [X3,X0,X8,X7,X5] :
( hBOOL(c_in(hAPP(X7,X3),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X5),hAPP(hAPP(c_Set_Oinsert(X0),X3),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)))),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X8,tc_fun(tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),X0),c_Set_Oinsert(X8)),X7),X0,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8)),X0,tc_fun(X8,tc_bool)),X8))
| ~ c_Fun_Oinj__on(X7,X5,X0,X8)
| c_Fun_Oinj__on(X7,hAPP(hAPP(c_Set_Oinsert(X0),X3),X5),X0,X8) ),
inference(forward_demodulation,[],[f688,f698]) ).
fof(f688,plain,
! [X3,X0,X8,X7,X5] :
( ~ c_Fun_Oinj__on(X7,X5,X0,X8)
| c_Fun_Oinj__on(X7,hAPP(hAPP(c_Set_Oinsert(X0),X3),X5),X0,X8)
| hBOOL(c_in(hAPP(X7,X3),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X5),hAPP(hAPP(c_Set_Oinsert(X0),X3),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)))),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X8,tc_fun(tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),X0),c_Set_Oinsert(X8)),X7),X0,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X8,tc_bool))),X0,tc_fun(X8,tc_bool)),X8)) ),
inference(definition_unfolding,[],[f7,f552]) ).
fof(f7,axiom,
! [X3,X0,X8,X7,X5] :
( ~ c_Fun_Oinj__on(X7,X5,X0,X8)
| c_Fun_Oinj__on(X7,hAPP(hAPP(c_Set_Oinsert(X0),X3),X5),X0,X8)
| hBOOL(c_in(hAPP(X7,X3),c_Set_Oimage(X7,hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X5),hAPP(hAPP(c_Set_Oinsert(X0),X3),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)))),X0,X8),X8)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__insert_2) ).
fof(f13957,plain,
( spl0_511
| ~ spl0_81
| ~ spl0_227 ),
inference(avatar_split_clause,[],[f3968,f2580,f1370,f13955]) ).
fof(f13955,plain,
( spl0_511
<=> ! [X0,X1] :
( ~ hBOOL(hAPP(c_SetInterval_Oord__class_OatLeastAtMost(X0,X0,tc_bool),X1))
| X0 = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_511])]) ).
fof(f3968,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP(c_SetInterval_Oord__class_OatLeastAtMost(X0,X0,tc_bool),X1))
| X0 = X1 )
| ~ spl0_81
| ~ spl0_227 ),
inference(superposition,[],[f1371,f2581]) ).
fof(f13839,plain,
( spl0_510
| ~ spl0_342
| ~ spl0_508
| ~ spl0_509 ),
inference(avatar_split_clause,[],[f13835,f13832,f13711,f4957,f13837]) ).
fof(f13832,plain,
( spl0_509
<=> ! [X5,X0,X3,X8,X7] :
( ~ hBOOL(c_in(hAPP(X7,X3),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X5),hAPP(c_fequal(X0),X3)),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X8,tc_fun(tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),X0),c_Set_Oinsert(X8)),X7),X0,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8)),X0,tc_fun(X8,tc_bool)),X8))
| ~ c_Fun_Oinj__on(X7,hAPP(hAPP(c_Set_Oinsert(X0),X3),X5),X0,X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_509])]) ).
fof(f13835,plain,
( ! [X3,X0,X8,X7,X5] :
( ~ hBOOL(c_in(hAPP(X7,X3),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X5),hAPP(c_fequal(X0),X3)),hAPP(hAPP(c_COMBB(X8,tc_fun(X8,tc_bool),X0),hAPP(c_COMBC(c_Set_Oinsert(X8),X8,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8))),X7),X0,tc_fun(X8,tc_bool)),X8))
| ~ c_Fun_Oinj__on(X7,hAPP(hAPP(c_Set_Oinsert(X0),X3),X5),X0,X8) )
| ~ spl0_342
| ~ spl0_508
| ~ spl0_509 ),
inference(forward_demodulation,[],[f13833,f13758]) ).
fof(f13833,plain,
( ! [X3,X0,X8,X7,X5] :
( ~ hBOOL(c_in(hAPP(X7,X3),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X5),hAPP(c_fequal(X0),X3)),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X8,tc_fun(tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),X0),c_Set_Oinsert(X8)),X7),X0,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8)),X0,tc_fun(X8,tc_bool)),X8))
| ~ c_Fun_Oinj__on(X7,hAPP(hAPP(c_Set_Oinsert(X0),X3),X5),X0,X8) )
| ~ spl0_509 ),
inference(avatar_component_clause,[],[f13832]) ).
fof(f13834,plain,
spl0_509,
inference(avatar_split_clause,[],[f862,f13832]) ).
fof(f862,plain,
! [X3,X0,X8,X7,X5] :
( ~ hBOOL(c_in(hAPP(X7,X3),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X5),hAPP(c_fequal(X0),X3)),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X8,tc_fun(tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),X0),c_Set_Oinsert(X8)),X7),X0,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8)),X0,tc_fun(X8,tc_bool)),X8))
| ~ c_Fun_Oinj__on(X7,hAPP(hAPP(c_Set_Oinsert(X0),X3),X5),X0,X8) ),
inference(forward_demodulation,[],[f861,f723]) ).
fof(f861,plain,
! [X3,X0,X8,X7,X5] :
( ~ hBOOL(c_in(hAPP(X7,X3),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X5),hAPP(hAPP(c_Set_Oinsert(X0),X3),c_COMBK(c_False,tc_bool,X0))),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X8,tc_fun(tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),X0),c_Set_Oinsert(X8)),X7),X0,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8)),X0,tc_fun(X8,tc_bool)),X8))
| ~ c_Fun_Oinj__on(X7,hAPP(hAPP(c_Set_Oinsert(X0),X3),X5),X0,X8) ),
inference(forward_demodulation,[],[f860,f698]) ).
fof(f860,plain,
! [X3,X0,X8,X7,X5] :
( ~ hBOOL(c_in(hAPP(X7,X3),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X5),hAPP(hAPP(c_Set_Oinsert(X0),X3),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)))),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X8,tc_fun(tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),X0),c_Set_Oinsert(X8)),X7),X0,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8)),X0,tc_fun(X8,tc_bool)),X8))
| ~ c_Fun_Oinj__on(X7,hAPP(hAPP(c_Set_Oinsert(X0),X3),X5),X0,X8) ),
inference(forward_demodulation,[],[f678,f698]) ).
fof(f678,plain,
! [X3,X0,X8,X7,X5] :
( ~ c_Fun_Oinj__on(X7,hAPP(hAPP(c_Set_Oinsert(X0),X3),X5),X0,X8)
| ~ hBOOL(c_in(hAPP(X7,X3),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X5),hAPP(hAPP(c_Set_Oinsert(X0),X3),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)))),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X8,tc_fun(tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),X0),c_Set_Oinsert(X8)),X7),X0,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X8,tc_bool))),X0,tc_fun(X8,tc_bool)),X8)) ),
inference(definition_unfolding,[],[f317,f552]) ).
fof(f317,axiom,
! [X3,X0,X8,X7,X5] :
( ~ c_Fun_Oinj__on(X7,hAPP(hAPP(c_Set_Oinsert(X0),X3),X5),X0,X8)
| ~ hBOOL(c_in(hAPP(X7,X3),c_Set_Oimage(X7,hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X5),hAPP(hAPP(c_Set_Oinsert(X0),X3),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)))),X0,X8),X8)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__insert_1) ).
fof(f13713,plain,
spl0_508,
inference(avatar_split_clause,[],[f758,f13711]) ).
fof(f758,plain,
! [X0,X8,X9,X7,X14,X5] : c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,hAPP(hAPP(c_COMBB(X8,tc_fun(X0,tc_bool),X14),X9),X7),X14,tc_fun(X0,tc_bool)) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X8,tc_fun(tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),X14),c_Set_Oinsert(X8)),X7),X14,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8)),X14,tc_fun(X8,tc_bool)),X9,X8,tc_fun(X0,tc_bool)),
inference(forward_demodulation,[],[f655,f698]) ).
fof(f655,plain,
! [X0,X8,X9,X7,X14,X5] : c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,hAPP(hAPP(c_COMBB(X8,tc_fun(X0,tc_bool),X14),X9),X7),X14,tc_fun(X0,tc_bool)) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X8,tc_fun(tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),X14),c_Set_Oinsert(X8)),X7),X14,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X8,tc_bool))),X14,tc_fun(X8,tc_bool)),X9,X8,tc_fun(X0,tc_bool)),
inference(definition_unfolding,[],[f455,f552]) ).
fof(f455,axiom,
! [X0,X8,X9,X7,X14,X5] : c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Set_Oimage(X7,X5,X14,X8),X9,X8,tc_fun(X0,tc_bool)) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,hAPP(hAPP(c_COMBB(X8,tc_fun(X0,tc_bool),X14),X9),X7),X14,tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UN__simps_I10_J_0) ).
fof(f13709,plain,
spl0_507,
inference(avatar_split_clause,[],[f757,f13707]) ).
fof(f757,plain,
! [X0,X8,X9,X7,X14,X5] : c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,hAPP(hAPP(c_COMBB(X8,tc_fun(X0,tc_bool),X14),X9),X7),X14,tc_fun(X0,tc_bool)) = c_Complete__Lattice_Ocomplete__lattice__class_OINFI(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X8,tc_fun(tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),X14),c_Set_Oinsert(X8)),X7),X14,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8)),X14,tc_fun(X8,tc_bool)),X9,X8,tc_fun(X0,tc_bool)),
inference(forward_demodulation,[],[f654,f698]) ).
fof(f654,plain,
! [X0,X8,X9,X7,X14,X5] : c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,hAPP(hAPP(c_COMBB(X8,tc_fun(X0,tc_bool),X14),X9),X7),X14,tc_fun(X0,tc_bool)) = c_Complete__Lattice_Ocomplete__lattice__class_OINFI(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X8,tc_fun(tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),X14),c_Set_Oinsert(X8)),X7),X14,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X8,tc_bool))),X14,tc_fun(X8,tc_bool)),X9,X8,tc_fun(X0,tc_bool)),
inference(definition_unfolding,[],[f88,f552]) ).
fof(f88,axiom,
! [X0,X8,X9,X7,X14,X5] : c_Complete__Lattice_Ocomplete__lattice__class_OINFI(c_Set_Oimage(X7,X5,X14,X8),X9,X8,tc_fun(X0,tc_bool)) = c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,hAPP(hAPP(c_COMBB(X8,tc_fun(X0,tc_bool),X14),X9),X7),X14,tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_INT__simps_I10_J_0) ).
fof(f13681,plain,
spl0_506,
inference(avatar_split_clause,[],[f923,f13679]) ).
fof(f923,plain,
! [X0,X1,X8,X9,X7,X5] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X0,tc_fun(tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),X8),c_Set_Oinsert(X0)),X7),X8,tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0)),X8,tc_fun(X0,tc_bool))),X9))
| ~ hBOOL(c_in(X1,X5,X8))
| hBOOL(c_in(hAPP(X7,X1),X9,X0)) ),
inference(forward_demodulation,[],[f685,f698]) ).
fof(f685,plain,
! [X0,X1,X8,X9,X7,X5] :
( ~ hBOOL(c_in(X1,X5,X8))
| hBOOL(c_in(hAPP(X7,X1),X9,X0))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X0,tc_fun(tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),X8),c_Set_Oinsert(X0)),X7),X8,tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))),X8,tc_fun(X0,tc_bool))),X9)) ),
inference(definition_unfolding,[],[f22,f552]) ).
fof(f22,axiom,
! [X0,X1,X8,X9,X7,X5] :
( ~ hBOOL(c_in(X1,X5,X8))
| hBOOL(c_in(hAPP(X7,X1),X9,X0))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),c_Set_Oimage(X7,X5,X8,X0)),X9)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__subset__iff_0) ).
fof(f13568,plain,
spl0_505,
inference(avatar_split_clause,[],[f946,f13566]) ).
fof(f946,plain,
! [X3,X0,X8,X7,X5] :
( ~ hBOOL(c_in(hAPP(X7,X3),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X8,tc_fun(tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),X0),c_Set_Oinsert(X8)),X7),X0,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8)),X0,tc_fun(X8,tc_bool)),X8))
| hBOOL(c_in(X3,X5,X0))
| ~ c_Fun_Oinj__on(X7,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0,X8) ),
inference(forward_demodulation,[],[f689,f698]) ).
fof(f689,plain,
! [X3,X0,X8,X7,X5] :
( hBOOL(c_in(X3,X5,X0))
| ~ c_Fun_Oinj__on(X7,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0,X8)
| ~ hBOOL(c_in(hAPP(X7,X3),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X8,tc_fun(tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),X0),c_Set_Oinsert(X8)),X7),X0,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X8,tc_bool))),X0,tc_fun(X8,tc_bool)),X8)) ),
inference(definition_unfolding,[],[f91,f552]) ).
fof(f91,axiom,
! [X3,X0,X8,X7,X5] :
( hBOOL(c_in(X3,X5,X0))
| ~ c_Fun_Oinj__on(X7,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0,X8)
| ~ hBOOL(c_in(hAPP(X7,X3),c_Set_Oimage(X7,X5,X0,X8),X8)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__image__mem__iff_0) ).
fof(f13564,plain,
spl0_504,
inference(avatar_split_clause,[],[f942,f13562]) ).
fof(f942,plain,
! [X0,X8,X7,X14,X5,X13] :
( ~ c_Fun_Oinj__on(X13,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X8,tc_fun(tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),X0),c_Set_Oinsert(X8)),X7),X0,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8)),X0,tc_fun(X8,tc_bool)),X8,X14)
| ~ c_Fun_Oinj__on(X7,X5,X0,X8)
| c_Fun_Oinj__on(c_Fun_Ocomp(X13,X7,X8,X14,X0),X5,X0,X14) ),
inference(forward_demodulation,[],[f687,f698]) ).
fof(f687,plain,
! [X0,X8,X7,X14,X5,X13] :
( ~ c_Fun_Oinj__on(X7,X5,X0,X8)
| ~ c_Fun_Oinj__on(X13,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X8,tc_fun(tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),X0),c_Set_Oinsert(X8)),X7),X0,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X8,tc_bool))),X0,tc_fun(X8,tc_bool)),X8,X14)
| c_Fun_Oinj__on(c_Fun_Ocomp(X13,X7,X8,X14,X0),X5,X0,X14) ),
inference(definition_unfolding,[],[f207,f552]) ).
fof(f207,axiom,
! [X0,X8,X7,X14,X5,X13] :
( ~ c_Fun_Oinj__on(X7,X5,X0,X8)
| ~ c_Fun_Oinj__on(X13,c_Set_Oimage(X7,X5,X0,X8),X8,X14)
| c_Fun_Oinj__on(c_Fun_Ocomp(X13,X7,X8,X14,X0),X5,X0,X14) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comp__inj__on_0) ).
fof(f13537,plain,
( spl0_503
| ~ spl0_16
| ~ spl0_174
| ~ spl0_502 ),
inference(avatar_split_clause,[],[f13533,f13530,f1887,f1090,f13535]) ).
fof(f13535,plain,
( spl0_503
<=> ! [X35,X57,X11,X39] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(c_COMBK(hAPP(c_fequal(tc_Com_Ostate),v_sko__Hoare__Mirabelle__Xescape__2(X39,X11,X57,X35)),tc_fun(tc_Com_Ostate,tc_bool),t_a),X35,c_COMBK(hAPP(X57,v_sko__Hoare__Mirabelle__Xescape__1(X39,X11,X57,X35)),tc_fun(tc_Com_Ostate,tc_bool),t_a),t_a)),t_a)
| c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X11,X35,X57,t_a)),t_a) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_503])]) ).
fof(f13530,plain,
( spl0_502
<=> ! [X35,X57,X11,X39] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(c_COMBK(hAPP(c_COMBC(c_fequal(tc_Com_Ostate),tc_Com_Ostate,tc_Com_Ostate,tc_bool),v_sko__Hoare__Mirabelle__Xescape__2(X39,X11,X57,X35)),tc_fun(tc_Com_Ostate,tc_bool),t_a),X35,c_COMBK(hAPP(X57,v_sko__Hoare__Mirabelle__Xescape__1(X39,X11,X57,X35)),tc_fun(tc_Com_Ostate,tc_bool),t_a),t_a)),t_a)
| c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X11,X35,X57,t_a)),t_a) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_502])]) ).
fof(f13533,plain,
( ! [X39,X11,X57,X35] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(c_COMBK(hAPP(c_fequal(tc_Com_Ostate),v_sko__Hoare__Mirabelle__Xescape__2(X39,X11,X57,X35)),tc_fun(tc_Com_Ostate,tc_bool),t_a),X35,c_COMBK(hAPP(X57,v_sko__Hoare__Mirabelle__Xescape__1(X39,X11,X57,X35)),tc_fun(tc_Com_Ostate,tc_bool),t_a),t_a)),t_a)
| c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X11,X35,X57,t_a)),t_a) )
| ~ spl0_16
| ~ spl0_174
| ~ spl0_502 ),
inference(forward_demodulation,[],[f13531,f1973]) ).
fof(f13531,plain,
( ! [X39,X11,X57,X35] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(c_COMBK(hAPP(c_COMBC(c_fequal(tc_Com_Ostate),tc_Com_Ostate,tc_Com_Ostate,tc_bool),v_sko__Hoare__Mirabelle__Xescape__2(X39,X11,X57,X35)),tc_fun(tc_Com_Ostate,tc_bool),t_a),X35,c_COMBK(hAPP(X57,v_sko__Hoare__Mirabelle__Xescape__1(X39,X11,X57,X35)),tc_fun(tc_Com_Ostate,tc_bool),t_a),t_a)),t_a)
| c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X11,X35,X57,t_a)),t_a) )
| ~ spl0_502 ),
inference(avatar_component_clause,[],[f13530]) ).
fof(f13532,plain,
spl0_502,
inference(avatar_split_clause,[],[f886,f13530]) ).
fof(f886,plain,
! [X39,X11,X57,X35] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(c_COMBK(hAPP(c_COMBC(c_fequal(tc_Com_Ostate),tc_Com_Ostate,tc_Com_Ostate,tc_bool),v_sko__Hoare__Mirabelle__Xescape__2(X39,X11,X57,X35)),tc_fun(tc_Com_Ostate,tc_bool),t_a),X35,c_COMBK(hAPP(X57,v_sko__Hoare__Mirabelle__Xescape__1(X39,X11,X57,X35)),tc_fun(tc_Com_Ostate,tc_bool),t_a),t_a)),t_a)
| c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X11,X35,X57,t_a)),t_a) ),
inference(forward_demodulation,[],[f885,f723]) ).
fof(f885,plain,
! [X39,X11,X57,X35] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(c_COMBK(hAPP(c_COMBC(c_fequal(tc_Com_Ostate),tc_Com_Ostate,tc_Com_Ostate,tc_bool),v_sko__Hoare__Mirabelle__Xescape__2(X39,X11,X57,X35)),tc_fun(tc_Com_Ostate,tc_bool),t_a),X35,c_COMBK(hAPP(X57,v_sko__Hoare__Mirabelle__Xescape__1(X39,X11,X57,X35)),tc_fun(tc_Com_Ostate,tc_bool),t_a),t_a)),c_COMBK(c_False,tc_bool,tc_Hoare__Mirabelle_Otriple(t_a))),t_a)
| c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X11,X35,X57,t_a)),t_a) ),
inference(forward_demodulation,[],[f884,f698]) ).
fof(f884,plain,
! [X39,X11,X57,X35] :
( c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X11,X35,X57,t_a)),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(c_COMBK(hAPP(c_COMBC(c_fequal(tc_Com_Ostate),tc_Com_Ostate,tc_Com_Ostate,tc_bool),v_sko__Hoare__Mirabelle__Xescape__2(X39,X11,X57,X35)),tc_fun(tc_Com_Ostate,tc_bool),t_a),X35,c_COMBK(hAPP(X57,v_sko__Hoare__Mirabelle__Xescape__1(X39,X11,X57,X35)),tc_fun(tc_Com_Ostate,tc_bool),t_a),t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
inference(forward_demodulation,[],[f883,f723]) ).
fof(f883,plain,
! [X39,X11,X57,X35] :
( c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X11,X35,X57,t_a)),c_COMBK(c_False,tc_bool,tc_Hoare__Mirabelle_Otriple(t_a))),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(c_COMBK(hAPP(c_COMBC(c_fequal(tc_Com_Ostate),tc_Com_Ostate,tc_Com_Ostate,tc_bool),v_sko__Hoare__Mirabelle__Xescape__2(X39,X11,X57,X35)),tc_fun(tc_Com_Ostate,tc_bool),t_a),X35,c_COMBK(hAPP(X57,v_sko__Hoare__Mirabelle__Xescape__1(X39,X11,X57,X35)),tc_fun(tc_Com_Ostate,tc_bool),t_a),t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
inference(forward_demodulation,[],[f560,f698]) ).
fof(f560,axiom,
! [X39,X11,X57,X35] :
( c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X11,X35,X57,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(c_COMBK(hAPP(c_COMBC(c_fequal(tc_Com_Ostate),tc_Com_Ostate,tc_Com_Ostate,tc_bool),v_sko__Hoare__Mirabelle__Xescape__2(X39,X11,X57,X35)),tc_fun(tc_Com_Ostate,tc_bool),t_a),X35,c_COMBK(hAPP(X57,v_sko__Hoare__Mirabelle__Xescape__1(X39,X11,X57,X35)),tc_fun(tc_Com_Ostate,tc_bool),t_a),t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_escape_1) ).
fof(f13490,plain,
spl0_501,
inference(avatar_split_clause,[],[f997,f13488]) ).
fof(f13488,plain,
( spl0_501
<=> ! [X35,X4,X11,X57,X0,X40,X39] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),c_Hoare__Mirabelle_Otriple_Otriple(c_Hoare__Mirabelle_Opeek__and(X11,c_Fun_Ocomp(c_Not,X4,tc_bool,tc_bool,tc_Com_Ostate),X0),X40,X57,X0)),X0)
| c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),c_Hoare__Mirabelle_Otriple_Otriple(X11,c_Com_Ocom_OCond(X4,X35,X40),X57,X0)),X0)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),c_Hoare__Mirabelle_Otriple_Otriple(c_Hoare__Mirabelle_Opeek__and(X11,X4,X0),X35,X57,X0)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_501])]) ).
fof(f997,plain,
! [X40,X39,X0,X11,X57,X4,X35] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),c_Hoare__Mirabelle_Otriple_Otriple(c_Hoare__Mirabelle_Opeek__and(X11,c_Fun_Ocomp(c_Not,X4,tc_bool,tc_bool,tc_Com_Ostate),X0),X40,X57,X0)),X0)
| c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),c_Hoare__Mirabelle_Otriple_Otriple(X11,c_Com_Ocom_OCond(X4,X35,X40),X57,X0)),X0)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),c_Hoare__Mirabelle_Otriple_Otriple(c_Hoare__Mirabelle_Opeek__and(X11,X4,X0),X35,X57,X0)),X0) ),
inference(forward_demodulation,[],[f996,f723]) ).
fof(f996,plain,
! [X40,X39,X0,X11,X57,X4,X35] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X0)),c_Hoare__Mirabelle_Otriple_Otriple(c_Hoare__Mirabelle_Opeek__and(X11,c_Fun_Ocomp(c_Not,X4,tc_bool,tc_bool,tc_Com_Ostate),X0),X40,X57,X0)),c_COMBK(c_False,tc_bool,tc_Hoare__Mirabelle_Otriple(X0))),X0)
| c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),c_Hoare__Mirabelle_Otriple_Otriple(X11,c_Com_Ocom_OCond(X4,X35,X40),X57,X0)),X0)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),c_Hoare__Mirabelle_Otriple_Otriple(c_Hoare__Mirabelle_Opeek__and(X11,X4,X0),X35,X57,X0)),X0) ),
inference(forward_demodulation,[],[f995,f698]) ).
fof(f995,plain,
! [X40,X39,X0,X11,X57,X4,X35] :
( c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),c_Hoare__Mirabelle_Otriple_Otriple(X11,c_Com_Ocom_OCond(X4,X35,X40),X57,X0)),X0)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),c_Hoare__Mirabelle_Otriple_Otriple(c_Hoare__Mirabelle_Opeek__and(X11,X4,X0),X35,X57,X0)),X0)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X0)),c_Hoare__Mirabelle_Otriple_Otriple(c_Hoare__Mirabelle_Opeek__and(X11,c_Fun_Ocomp(c_Not,X4,tc_bool,tc_bool,tc_Com_Ostate),X0),X40,X57,X0)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool))),X0) ),
inference(forward_demodulation,[],[f994,f723]) ).
fof(f994,plain,
! [X40,X39,X0,X11,X57,X4,X35] :
( c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X0)),c_Hoare__Mirabelle_Otriple_Otriple(X11,c_Com_Ocom_OCond(X4,X35,X40),X57,X0)),c_COMBK(c_False,tc_bool,tc_Hoare__Mirabelle_Otriple(X0))),X0)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),c_Hoare__Mirabelle_Otriple_Otriple(c_Hoare__Mirabelle_Opeek__and(X11,X4,X0),X35,X57,X0)),X0)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X0)),c_Hoare__Mirabelle_Otriple_Otriple(c_Hoare__Mirabelle_Opeek__and(X11,c_Fun_Ocomp(c_Not,X4,tc_bool,tc_bool,tc_Com_Ostate),X0),X40,X57,X0)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool))),X0) ),
inference(forward_demodulation,[],[f993,f698]) ).
fof(f993,plain,
! [X40,X39,X0,X11,X57,X4,X35] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),c_Hoare__Mirabelle_Otriple_Otriple(c_Hoare__Mirabelle_Opeek__and(X11,X4,X0),X35,X57,X0)),X0)
| c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X0)),c_Hoare__Mirabelle_Otriple_Otriple(X11,c_Com_Ocom_OCond(X4,X35,X40),X57,X0)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool))),X0)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X0)),c_Hoare__Mirabelle_Otriple_Otriple(c_Hoare__Mirabelle_Opeek__and(X11,c_Fun_Ocomp(c_Not,X4,tc_bool,tc_bool,tc_Com_Ostate),X0),X40,X57,X0)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool))),X0) ),
inference(forward_demodulation,[],[f992,f723]) ).
fof(f992,plain,
! [X40,X39,X0,X11,X57,X4,X35] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X0)),c_Hoare__Mirabelle_Otriple_Otriple(c_Hoare__Mirabelle_Opeek__and(X11,X4,X0),X35,X57,X0)),c_COMBK(c_False,tc_bool,tc_Hoare__Mirabelle_Otriple(X0))),X0)
| c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X0)),c_Hoare__Mirabelle_Otriple_Otriple(X11,c_Com_Ocom_OCond(X4,X35,X40),X57,X0)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool))),X0)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X0)),c_Hoare__Mirabelle_Otriple_Otriple(c_Hoare__Mirabelle_Opeek__and(X11,c_Fun_Ocomp(c_Not,X4,tc_bool,tc_bool,tc_Com_Ostate),X0),X40,X57,X0)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool))),X0) ),
inference(forward_demodulation,[],[f513,f698]) ).
fof(f513,axiom,
! [X40,X39,X0,X11,X57,X4,X35] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X0)),c_Hoare__Mirabelle_Otriple_Otriple(c_Hoare__Mirabelle_Opeek__and(X11,X4,X0),X35,X57,X0)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool))),X0)
| c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X0)),c_Hoare__Mirabelle_Otriple_Otriple(X11,c_Com_Ocom_OCond(X4,X35,X40),X57,X0)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool))),X0)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X0)),c_Hoare__Mirabelle_Otriple_Otriple(c_Hoare__Mirabelle_Opeek__and(X11,c_Fun_Ocomp(c_Not,X4,tc_bool,tc_bool,tc_Com_Ostate),X0),X40,X57,X0)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool))),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_hoare__derivs_OIf_0) ).
fof(f13486,plain,
spl0_500,
inference(avatar_split_clause,[],[f903,f13484]) ).
fof(f903,plain,
! [X0,X7,X5] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X5),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X0,tc_fun(tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),X0),c_Set_Oinsert(X0)),X7),X0,tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0)),X0,tc_fun(X0,tc_bool))))
| ~ c_Finite__Set_Ofinite(X5,X0)
| c_Fun_Oinj__on(X7,X5,X0,X0) ),
inference(forward_demodulation,[],[f681,f698]) ).
fof(f681,plain,
! [X0,X7,X5] :
( ~ c_Finite__Set_Ofinite(X5,X0)
| c_Fun_Oinj__on(X7,X5,X0,X0)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X5),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X0,tc_fun(tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),X0),c_Set_Oinsert(X0)),X7),X0,tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))),X0,tc_fun(X0,tc_bool)))) ),
inference(definition_unfolding,[],[f323,f552]) ).
fof(f323,axiom,
! [X0,X7,X5] :
( ~ c_Finite__Set_Ofinite(X5,X0)
| c_Fun_Oinj__on(X7,X5,X0,X0)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X5),c_Set_Oimage(X7,X5,X0,X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__surj__inj_0) ).
fof(f13482,plain,
( spl0_499
| ~ spl0_17
| ~ spl0_489 ),
inference(avatar_split_clause,[],[f13229,f13221,f1094,f13480]) ).
fof(f1094,plain,
( spl0_17
<=> ! [X5,X0] :
( ~ class_Finite__Set_Ofinite_Ofinite(X0)
| c_Finite__Set_Ofinite(X5,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_17])]) ).
fof(f13229,plain,
( ! [X2,X3,X0,X1] :
( c_Finite__Set_Ofinite(X0,X1)
| ~ c_Fun_Oinj__on(X2,X0,X1,X3)
| ~ class_Finite__Set_Ofinite_Ofinite(X3) )
| ~ spl0_17
| ~ spl0_489 ),
inference(resolution,[],[f13222,f1095]) ).
fof(f1095,plain,
( ! [X0,X5] :
( c_Finite__Set_Ofinite(X5,X0)
| ~ class_Finite__Set_Ofinite_Ofinite(X0) )
| ~ spl0_17 ),
inference(avatar_component_clause,[],[f1094]) ).
fof(f13406,plain,
spl0_498,
inference(avatar_split_clause,[],[f902,f13404]) ).
fof(f902,plain,
! [X0,X8,X9,X7,X5] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X8,tc_bool)),X9),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X8,tc_fun(tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),X0),c_Set_Oinsert(X8)),X7),X0,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8)),X0,tc_fun(X8,tc_bool))))
| ~ c_Finite__Set_Ofinite(X5,X0)
| c_Finite__Set_Ofinite(X9,X8) ),
inference(forward_demodulation,[],[f680,f698]) ).
fof(f680,plain,
! [X0,X8,X9,X7,X5] :
( ~ c_Finite__Set_Ofinite(X5,X0)
| c_Finite__Set_Ofinite(X9,X8)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X8,tc_bool)),X9),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X8,tc_fun(tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),X0),c_Set_Oinsert(X8)),X7),X0,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X8,tc_bool))),X0,tc_fun(X8,tc_bool)))) ),
inference(definition_unfolding,[],[f23,f552]) ).
fof(f23,axiom,
! [X0,X8,X9,X7,X5] :
( ~ c_Finite__Set_Ofinite(X5,X0)
| c_Finite__Set_Ofinite(X9,X8)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X8,tc_bool)),X9),c_Set_Oimage(X7,X5,X0,X8))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__surj_0) ).
fof(f13402,plain,
spl0_497,
inference(avatar_split_clause,[],[f857,f13400]) ).
fof(f857,plain,
! [X0,X8,X7,X14,X5,X13] :
( c_Fun_Oinj__on(X13,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X14,tc_fun(tc_fun(X14,tc_bool),tc_fun(X14,tc_bool)),X0),c_Set_Oinsert(X14)),X7),X0,tc_fun(X14,tc_bool),tc_fun(X14,tc_bool)),c_COMBK(c_False,tc_bool,X14)),X0,tc_fun(X14,tc_bool)),X14,X8)
| ~ c_Fun_Oinj__on(c_Fun_Ocomp(X13,X7,X14,X8,X0),X5,X0,X8) ),
inference(forward_demodulation,[],[f676,f698]) ).
fof(f676,plain,
! [X0,X8,X7,X14,X5,X13] :
( c_Fun_Oinj__on(X13,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X14,tc_fun(tc_fun(X14,tc_bool),tc_fun(X14,tc_bool)),X0),c_Set_Oinsert(X14)),X7),X0,tc_fun(X14,tc_bool),tc_fun(X14,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X14,tc_bool))),X0,tc_fun(X14,tc_bool)),X14,X8)
| ~ c_Fun_Oinj__on(c_Fun_Ocomp(X13,X7,X14,X8,X0),X5,X0,X8) ),
inference(definition_unfolding,[],[f16,f552]) ).
fof(f16,axiom,
! [X0,X8,X7,X14,X5,X13] :
( c_Fun_Oinj__on(X13,c_Set_Oimage(X7,X5,X0,X14),X14,X8)
| ~ c_Fun_Oinj__on(c_Fun_Ocomp(X13,X7,X14,X8,X0),X5,X0,X8) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__imageI_0) ).
fof(f13398,plain,
spl0_496,
inference(avatar_split_clause,[],[f849,f13396]) ).
fof(f849,plain,
! [X0,X8,X5,X35] :
( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X0,tc_fun(tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),X8),c_Set_Oinsert(X0)),c_COMBK(X35,X0,X8)),X8,tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0)),X8,tc_fun(X0,tc_bool)) = hAPP(c_fequal(X0),X35)
| c_COMBK(c_False,tc_bool,X8) = X5 ),
inference(forward_demodulation,[],[f848,f723]) ).
fof(f848,plain,
! [X0,X8,X35,X5] :
( hAPP(hAPP(c_Set_Oinsert(X0),X35),c_COMBK(c_False,tc_bool,X0)) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X0,tc_fun(tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),X8),c_Set_Oinsert(X0)),c_COMBK(X35,X0,X8)),X8,tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0)),X8,tc_fun(X0,tc_bool))
| c_COMBK(c_False,tc_bool,X8) = X5 ),
inference(forward_demodulation,[],[f847,f698]) ).
fof(f847,plain,
! [X0,X8,X5,X35] :
( c_COMBK(c_False,tc_bool,X8) = X5
| hAPP(hAPP(c_Set_Oinsert(X0),X35),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X0,tc_fun(tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),X8),c_Set_Oinsert(X0)),c_COMBK(X35,X0,X8)),X8,tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))),X8,tc_fun(X0,tc_bool)) ),
inference(forward_demodulation,[],[f671,f698]) ).
fof(f671,plain,
! [X0,X8,X5,X35] :
( c_Orderings_Obot__class_Obot(tc_fun(X8,tc_bool)) = X5
| hAPP(hAPP(c_Set_Oinsert(X0),X35),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X0,tc_fun(tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),X8),c_Set_Oinsert(X0)),c_COMBK(X35,X0,X8)),X8,tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))),X8,tc_fun(X0,tc_bool)) ),
inference(definition_unfolding,[],[f578,f552]) ).
fof(f578,axiom,
! [X0,X8,X5,X35] :
( c_Orderings_Obot__class_Obot(tc_fun(X8,tc_bool)) = X5
| c_Set_Oimage(c_COMBK(X35,X0,X8),X5,X8,X0) = hAPP(hAPP(c_Set_Oinsert(X0),X35),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__constant__conv_1) ).
fof(f13376,plain,
spl0_495,
inference(avatar_split_clause,[],[f819,f13374]) ).
fof(f819,plain,
! [X0,X1,X8,X5,X35] :
( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X8,tc_fun(tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),X0),c_Set_Oinsert(X8)),c_COMBK(X35,X8,X0)),X0,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8)),X0,tc_fun(X8,tc_bool)) = hAPP(c_fequal(X8),X35)
| ~ hBOOL(c_in(X1,X5,X0)) ),
inference(forward_demodulation,[],[f818,f723]) ).
fof(f818,plain,
! [X0,X1,X8,X35,X5] :
( hAPP(hAPP(c_Set_Oinsert(X8),X35),c_COMBK(c_False,tc_bool,X8)) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X8,tc_fun(tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),X0),c_Set_Oinsert(X8)),c_COMBK(X35,X8,X0)),X0,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8)),X0,tc_fun(X8,tc_bool))
| ~ hBOOL(c_in(X1,X5,X0)) ),
inference(forward_demodulation,[],[f668,f698]) ).
fof(f668,plain,
! [X0,X1,X8,X5,X35] :
( ~ hBOOL(c_in(X1,X5,X0))
| hAPP(hAPP(c_Set_Oinsert(X8),X35),c_Orderings_Obot__class_Obot(tc_fun(X8,tc_bool))) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X8,tc_fun(tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),X0),c_Set_Oinsert(X8)),c_COMBK(X35,X8,X0)),X0,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X8,tc_bool))),X0,tc_fun(X8,tc_bool)) ),
inference(definition_unfolding,[],[f514,f552]) ).
fof(f514,axiom,
! [X0,X1,X8,X5,X35] :
( ~ hBOOL(c_in(X1,X5,X0))
| c_Set_Oimage(c_COMBK(X35,X8,X0),X5,X0,X8) = hAPP(hAPP(c_Set_Oinsert(X8),X35),c_Orderings_Obot__class_Obot(tc_fun(X8,tc_bool))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__constant_0) ).
fof(f13350,plain,
spl0_494,
inference(avatar_split_clause,[],[f1014,f13348]) ).
fof(f13348,plain,
( spl0_494
<=> ! [X35,X57,X11,X63,X30,X39,X1] :
( c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X11,X35,X57,t_a)),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X1,X35,X30,t_a)),t_a)
| ~ hBOOL(hAPP(hAPP(X1,X63),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2(X39,X11,X57,X35)))
| hBOOL(hAPP(hAPP(X30,X63),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3(X39,X11,X57,X35,X1,X30))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_494])]) ).
fof(f1014,plain,
! [X39,X11,X1,X57,X63,X35,X30] :
( c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X11,X35,X57,t_a)),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X1,X35,X30,t_a)),t_a)
| ~ hBOOL(hAPP(hAPP(X1,X63),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2(X39,X11,X57,X35)))
| hBOOL(hAPP(hAPP(X30,X63),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3(X39,X11,X57,X35,X1,X30))) ),
inference(forward_demodulation,[],[f1013,f723]) ).
fof(f1013,plain,
! [X39,X11,X1,X57,X63,X35,X30] :
( c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X11,X35,X57,t_a)),c_COMBK(c_False,tc_bool,tc_Hoare__Mirabelle_Otriple(t_a))),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X1,X35,X30,t_a)),t_a)
| ~ hBOOL(hAPP(hAPP(X1,X63),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2(X39,X11,X57,X35)))
| hBOOL(hAPP(hAPP(X30,X63),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3(X39,X11,X57,X35,X1,X30))) ),
inference(forward_demodulation,[],[f1012,f698]) ).
fof(f1012,plain,
! [X39,X11,X1,X57,X63,X35,X30] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X1,X35,X30,t_a)),t_a)
| ~ hBOOL(hAPP(hAPP(X1,X63),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2(X39,X11,X57,X35)))
| hBOOL(hAPP(hAPP(X30,X63),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3(X39,X11,X57,X35,X1,X30)))
| c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X11,X35,X57,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
inference(forward_demodulation,[],[f1011,f723]) ).
fof(f1011,plain,
! [X39,X11,X1,X57,X63,X35,X30] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X1,X35,X30,t_a)),c_COMBK(c_False,tc_bool,tc_Hoare__Mirabelle_Otriple(t_a))),t_a)
| ~ hBOOL(hAPP(hAPP(X1,X63),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2(X39,X11,X57,X35)))
| hBOOL(hAPP(hAPP(X30,X63),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3(X39,X11,X57,X35,X1,X30)))
| c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X11,X35,X57,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
inference(forward_demodulation,[],[f561,f698]) ).
fof(f561,axiom,
! [X39,X11,X1,X57,X63,X35,X30] :
( ~ hBOOL(hAPP(hAPP(X1,X63),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2(X39,X11,X57,X35)))
| hBOOL(hAPP(hAPP(X30,X63),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3(X39,X11,X57,X35,X1,X30)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X1,X35,X30,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X11,X35,X57,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conseq_1) ).
fof(f13346,plain,
spl0_493,
inference(avatar_split_clause,[],[f1010,f13344]) ).
fof(f13344,plain,
( spl0_493
<=> ! [X35,X57,X11,X63,X30,X39,X1] :
( c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X11,X35,X57,t_a)),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X1,X35,X30,t_a)),t_a)
| ~ hBOOL(hAPP(hAPP(X1,X63),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(X39,X11,X57,X35)))
| hBOOL(hAPP(hAPP(X30,X63),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3(X39,X11,X57,X35,X1,X30))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_493])]) ).
fof(f1010,plain,
! [X39,X11,X1,X57,X63,X35,X30] :
( c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X11,X35,X57,t_a)),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X1,X35,X30,t_a)),t_a)
| ~ hBOOL(hAPP(hAPP(X1,X63),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(X39,X11,X57,X35)))
| hBOOL(hAPP(hAPP(X30,X63),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3(X39,X11,X57,X35,X1,X30))) ),
inference(forward_demodulation,[],[f1009,f723]) ).
fof(f1009,plain,
! [X39,X11,X1,X57,X63,X35,X30] :
( c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X11,X35,X57,t_a)),c_COMBK(c_False,tc_bool,tc_Hoare__Mirabelle_Otriple(t_a))),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X1,X35,X30,t_a)),t_a)
| ~ hBOOL(hAPP(hAPP(X1,X63),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(X39,X11,X57,X35)))
| hBOOL(hAPP(hAPP(X30,X63),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3(X39,X11,X57,X35,X1,X30))) ),
inference(forward_demodulation,[],[f1008,f698]) ).
fof(f1008,plain,
! [X39,X11,X1,X57,X63,X35,X30] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X1,X35,X30,t_a)),t_a)
| ~ hBOOL(hAPP(hAPP(X1,X63),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(X39,X11,X57,X35)))
| hBOOL(hAPP(hAPP(X30,X63),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3(X39,X11,X57,X35,X1,X30)))
| c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X11,X35,X57,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
inference(forward_demodulation,[],[f1007,f723]) ).
fof(f1007,plain,
! [X39,X11,X1,X57,X63,X35,X30] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X1,X35,X30,t_a)),c_COMBK(c_False,tc_bool,tc_Hoare__Mirabelle_Otriple(t_a))),t_a)
| ~ hBOOL(hAPP(hAPP(X1,X63),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(X39,X11,X57,X35)))
| hBOOL(hAPP(hAPP(X30,X63),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3(X39,X11,X57,X35,X1,X30)))
| c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X11,X35,X57,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
inference(forward_demodulation,[],[f563,f698]) ).
fof(f563,axiom,
! [X39,X11,X1,X57,X63,X35,X30] :
( ~ hBOOL(hAPP(hAPP(X1,X63),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(X39,X11,X57,X35)))
| hBOOL(hAPP(hAPP(X30,X63),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3(X39,X11,X57,X35,X1,X30)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X1,X35,X30,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X11,X35,X57,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_hoare__derivs_Ointros_I6_J_1) ).
fof(f13240,plain,
spl0_492,
inference(avatar_split_clause,[],[f836,f13238]) ).
fof(f13238,plain,
( spl0_492
<=> ! [X0,X5,X8,X7] :
( c_COMBK(c_False,tc_bool,X0) != c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X0,tc_fun(tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),X8),c_Set_Oinsert(X0)),X7),X8,tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0)),X8,tc_fun(X0,tc_bool))
| c_COMBK(c_False,tc_bool,X8) = X5 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_492])]) ).
fof(f836,plain,
! [X0,X8,X7,X5] :
( c_COMBK(c_False,tc_bool,X0) != c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X0,tc_fun(tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),X8),c_Set_Oinsert(X0)),X7),X8,tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0)),X8,tc_fun(X0,tc_bool))
| c_COMBK(c_False,tc_bool,X8) = X5 ),
inference(forward_demodulation,[],[f835,f698]) ).
fof(f835,plain,
! [X0,X8,X7,X5] :
( c_COMBK(c_False,tc_bool,X8) = X5
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X0,tc_fun(tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),X8),c_Set_Oinsert(X0)),X7),X8,tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))),X8,tc_fun(X0,tc_bool)) ),
inference(forward_demodulation,[],[f669,f698]) ).
fof(f669,plain,
! [X0,X8,X7,X5] :
( c_Orderings_Obot__class_Obot(tc_fun(X8,tc_bool)) = X5
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X0,tc_fun(tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),X8),c_Set_Oinsert(X0)),X7),X8,tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))),X8,tc_fun(X0,tc_bool)) ),
inference(definition_unfolding,[],[f348,f552]) ).
fof(f348,axiom,
! [X0,X8,X7,X5] :
( c_Orderings_Obot__class_Obot(tc_fun(X8,tc_bool)) = X5
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != c_Set_Oimage(X7,X5,X8,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__is__empty_0) ).
fof(f13236,plain,
spl0_491,
inference(avatar_split_clause,[],[f813,f13234]) ).
fof(f813,plain,
! [X0,X1,X8,X7,X5] :
( hBOOL(c_in(hAPP(X7,X1),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X0,tc_fun(tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),X8),c_Set_Oinsert(X0)),X7),X8,tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0)),X8,tc_fun(X0,tc_bool)),X0))
| ~ hBOOL(c_in(X1,X5,X8)) ),
inference(forward_demodulation,[],[f663,f698]) ).
fof(f663,plain,
! [X0,X1,X8,X7,X5] :
( ~ hBOOL(c_in(X1,X5,X8))
| hBOOL(c_in(hAPP(X7,X1),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X0,tc_fun(tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),X8),c_Set_Oinsert(X0)),X7),X8,tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))),X8,tc_fun(X0,tc_bool)),X0)) ),
inference(definition_unfolding,[],[f329,f552]) ).
fof(f329,axiom,
! [X0,X1,X8,X7,X5] :
( ~ hBOOL(c_in(X1,X5,X8))
| hBOOL(c_in(hAPP(X7,X1),c_Set_Oimage(X7,X5,X8,X0),X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__eqI_0) ).
fof(f13227,plain,
spl0_490,
inference(avatar_split_clause,[],[f1006,f13225]) ).
fof(f13225,plain,
( spl0_490
<=> ! [X35,X57,X11,X64,X63,X39,X65] :
( c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X11,X35,X57,t_a)),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X65,X35,X64,t_a)),t_a)
| ~ hBOOL(hAPP(hAPP(X65,X63),v_sko__Hoare__Mirabelle__Xconseq12__2(X11,X65,X57,X64)))
| hBOOL(hAPP(hAPP(X64,X63),v_sko__Hoare__Mirabelle__Xconseq12__3(X11,X65,X57,X64))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_490])]) ).
fof(f1006,plain,
! [X65,X39,X11,X57,X63,X35,X64] :
( c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X11,X35,X57,t_a)),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X65,X35,X64,t_a)),t_a)
| ~ hBOOL(hAPP(hAPP(X65,X63),v_sko__Hoare__Mirabelle__Xconseq12__2(X11,X65,X57,X64)))
| hBOOL(hAPP(hAPP(X64,X63),v_sko__Hoare__Mirabelle__Xconseq12__3(X11,X65,X57,X64))) ),
inference(forward_demodulation,[],[f1005,f723]) ).
fof(f1005,plain,
! [X65,X39,X11,X57,X63,X35,X64] :
( c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X11,X35,X57,t_a)),c_COMBK(c_False,tc_bool,tc_Hoare__Mirabelle_Otriple(t_a))),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X65,X35,X64,t_a)),t_a)
| ~ hBOOL(hAPP(hAPP(X65,X63),v_sko__Hoare__Mirabelle__Xconseq12__2(X11,X65,X57,X64)))
| hBOOL(hAPP(hAPP(X64,X63),v_sko__Hoare__Mirabelle__Xconseq12__3(X11,X65,X57,X64))) ),
inference(forward_demodulation,[],[f1004,f698]) ).
fof(f1004,plain,
! [X65,X39,X11,X57,X63,X35,X64] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X65,X35,X64,t_a)),t_a)
| ~ hBOOL(hAPP(hAPP(X65,X63),v_sko__Hoare__Mirabelle__Xconseq12__2(X11,X65,X57,X64)))
| hBOOL(hAPP(hAPP(X64,X63),v_sko__Hoare__Mirabelle__Xconseq12__3(X11,X65,X57,X64)))
| c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X11,X35,X57,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
inference(forward_demodulation,[],[f1003,f723]) ).
fof(f1003,plain,
! [X65,X39,X11,X57,X63,X35,X64] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X65,X35,X64,t_a)),c_COMBK(c_False,tc_bool,tc_Hoare__Mirabelle_Otriple(t_a))),t_a)
| ~ hBOOL(hAPP(hAPP(X65,X63),v_sko__Hoare__Mirabelle__Xconseq12__2(X11,X65,X57,X64)))
| hBOOL(hAPP(hAPP(X64,X63),v_sko__Hoare__Mirabelle__Xconseq12__3(X11,X65,X57,X64)))
| c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X11,X35,X57,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
inference(forward_demodulation,[],[f562,f698]) ).
fof(f562,axiom,
! [X65,X39,X11,X57,X63,X35,X64] :
( ~ hBOOL(hAPP(hAPP(X65,X63),v_sko__Hoare__Mirabelle__Xconseq12__2(X11,X65,X57,X64)))
| hBOOL(hAPP(hAPP(X64,X63),v_sko__Hoare__Mirabelle__Xconseq12__3(X11,X65,X57,X64)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X65,X35,X64,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X11,X35,X57,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conseq12_1) ).
fof(f13223,plain,
spl0_489,
inference(avatar_split_clause,[],[f918,f13221]) ).
fof(f918,plain,
! [X0,X8,X7,X5] :
( ~ c_Finite__Set_Ofinite(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X0,tc_fun(tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),X8),c_Set_Oinsert(X0)),X7),X8,tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0)),X8,tc_fun(X0,tc_bool)),X0)
| c_Finite__Set_Ofinite(X5,X8)
| ~ c_Fun_Oinj__on(X7,X5,X8,X0) ),
inference(forward_demodulation,[],[f684,f698]) ).
fof(f684,plain,
! [X0,X8,X7,X5] :
( c_Finite__Set_Ofinite(X5,X8)
| ~ c_Fun_Oinj__on(X7,X5,X8,X0)
| ~ c_Finite__Set_Ofinite(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X0,tc_fun(tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),X8),c_Set_Oinsert(X0)),X7),X8,tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))),X8,tc_fun(X0,tc_bool)),X0) ),
inference(definition_unfolding,[],[f486,f552]) ).
fof(f486,axiom,
! [X0,X8,X7,X5] :
( c_Finite__Set_Ofinite(X5,X8)
| ~ c_Fun_Oinj__on(X7,X5,X8,X0)
| ~ c_Finite__Set_Ofinite(c_Set_Oimage(X7,X5,X8,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__imageD_0) ).
fof(f13219,plain,
( ~ spl0_8
| spl0_488
| ~ spl0_143
| ~ spl0_151 ),
inference(avatar_split_clause,[],[f3065,f1779,f1704,f13217,f1052]) ).
fof(f1779,plain,
( spl0_151
<=> ! [X0] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),X0),c_Orderings_Otop__class_Otop(tc_bool)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_151])]) ).
fof(f3065,plain,
( ! [X0] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_bool),X0),c_Orderings_Otop__class_Otop(tc_bool)))
| ~ class_Lattices_Olattice(tc_bool) )
| ~ spl0_143
| ~ spl0_151 ),
inference(superposition,[],[f1705,f1780]) ).
fof(f1780,plain,
( ! [X0] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),X0),c_Orderings_Otop__class_Otop(tc_bool)) = X0
| ~ spl0_151 ),
inference(avatar_component_clause,[],[f1779]) ).
fof(f13116,plain,
spl0_487,
inference(avatar_split_clause,[],[f713,f13114]) ).
fof(f713,plain,
! [X0,X1,X8,X7] : hBOOL(c_in(hAPP(X7,X1),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Otop__class_Otop(tc_fun(X8,tc_bool)),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X0,tc_fun(tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),X8),c_Set_Oinsert(X0)),X7),X8,tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0)),X8,tc_fun(X0,tc_bool)),X0)),
inference(forward_demodulation,[],[f649,f698]) ).
fof(f649,plain,
! [X0,X1,X8,X7] : hBOOL(c_in(hAPP(X7,X1),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Otop__class_Otop(tc_fun(X8,tc_bool)),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X0,tc_fun(tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),X8),c_Set_Oinsert(X0)),X7),X8,tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))),X8,tc_fun(X0,tc_bool)),X0)),
inference(definition_unfolding,[],[f123,f552]) ).
fof(f123,axiom,
! [X0,X1,X8,X7] : hBOOL(c_in(hAPP(X7,X1),c_Set_Oimage(X7,c_Orderings_Otop__class_Otop(tc_fun(X8,tc_bool)),X8,X0),X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rangeI_0) ).
fof(f12873,plain,
( spl0_486
| ~ spl0_150
| ~ spl0_485 ),
inference(avatar_split_clause,[],[f12869,f12866,f1732,f12871]) ).
fof(f12871,plain,
( spl0_486
<=> ! [X0,X1] : c_The(hAPP(hAPP(c_COMBB(tc_fun(X0,tc_bool),tc_bool,X0),hAPP(c_fequal(tc_fun(X0,tc_bool)),hAPP(c_fequal(X0),X1))),hAPP(c_COMBC(c_Set_Oinsert(X0),X0,tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0))),X0) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_486])]) ).
fof(f12866,plain,
( spl0_485
<=> ! [X0,X1] : c_The(hAPP(hAPP(c_COMBB(tc_fun(X0,tc_bool),tc_bool,X0),hAPP(c_fequal(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Set_Oinsert(X0),X1),c_COMBK(c_False,tc_bool,X0)))),hAPP(c_COMBC(c_Set_Oinsert(X0),X0,tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0))),X0) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_485])]) ).
fof(f12869,plain,
( ! [X0,X1] : c_The(hAPP(hAPP(c_COMBB(tc_fun(X0,tc_bool),tc_bool,X0),hAPP(c_fequal(tc_fun(X0,tc_bool)),hAPP(c_fequal(X0),X1))),hAPP(c_COMBC(c_Set_Oinsert(X0),X0,tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0))),X0) = X1
| ~ spl0_150
| ~ spl0_485 ),
inference(forward_demodulation,[],[f12867,f1733]) ).
fof(f12867,plain,
( ! [X0,X1] : c_The(hAPP(hAPP(c_COMBB(tc_fun(X0,tc_bool),tc_bool,X0),hAPP(c_fequal(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Set_Oinsert(X0),X1),c_COMBK(c_False,tc_bool,X0)))),hAPP(c_COMBC(c_Set_Oinsert(X0),X0,tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0))),X0) = X1
| ~ spl0_485 ),
inference(avatar_component_clause,[],[f12866]) ).
fof(f12868,plain,
spl0_485,
inference(avatar_split_clause,[],[f708,f12866]) ).
fof(f708,plain,
! [X0,X1] : c_The(hAPP(hAPP(c_COMBB(tc_fun(X0,tc_bool),tc_bool,X0),hAPP(c_fequal(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Set_Oinsert(X0),X1),c_COMBK(c_False,tc_bool,X0)))),hAPP(c_COMBC(c_Set_Oinsert(X0),X0,tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0))),X0) = X1,
inference(forward_demodulation,[],[f647,f698]) ).
fof(f647,plain,
! [X0,X1] : c_The(hAPP(hAPP(c_COMBB(tc_fun(X0,tc_bool),tc_bool,X0),hAPP(c_fequal(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Set_Oinsert(X0),X1),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))))),hAPP(c_COMBC(c_Set_Oinsert(X0),X0,tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)))),X0) = X1,
inference(definition_unfolding,[],[f539,f405]) ).
fof(f405,axiom,
! [X0,X56] : c_Set_Ocontents(X56,X0) = c_The(hAPP(hAPP(c_COMBB(tc_fun(X0,tc_bool),tc_bool,X0),hAPP(c_fequal(tc_fun(X0,tc_bool)),X56)),hAPP(c_COMBC(c_Set_Oinsert(X0),X0,tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)))),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_contents__def_0) ).
fof(f539,axiom,
! [X0,X1] : c_Set_Ocontents(hAPP(hAPP(c_Set_Oinsert(X0),X1),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))),X0) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_contents__eq_0) ).
fof(f12864,plain,
spl0_484,
inference(avatar_split_clause,[],[f456,f12862]) ).
fof(f12862,plain,
( spl0_484
<=> ! [X9,X51,X0,X12,X5] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X5),X12))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X9),X51))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X5),X9)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X12),X51))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_484])]) ).
fof(f456,axiom,
! [X51,X0,X9,X5,X12] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X5),X12))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X9),X51))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X5),X9)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X12),X51))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__mono_0) ).
fof(f12860,plain,
spl0_483,
inference(avatar_split_clause,[],[f284,f12858]) ).
fof(f12858,plain,
( spl0_483
<=> ! [X9,X51,X0,X12,X5] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X5),X12))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X9),X51))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X5),X9)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X12),X51))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_483])]) ).
fof(f284,axiom,
! [X51,X0,X9,X5,X12] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X5),X12))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X9),X51))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X5),X9)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X12),X51))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__mono_0) ).
fof(f12837,plain,
spl0_482,
inference(avatar_split_clause,[],[f230,f12835]) ).
fof(f12835,plain,
( spl0_482
<=> ! [X5,X51,X0,X12,X9] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X5),X12))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X51),X9))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X5),X9)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X12),X51))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_482])]) ).
fof(f230,axiom,
! [X51,X0,X9,X5,X12] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X5),X12))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X51),X9))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X5),X9)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X12),X51))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__mono_0) ).
fof(f12609,plain,
spl0_481,
inference(avatar_split_clause,[],[f985,f12607]) ).
fof(f12607,plain,
( spl0_481
<=> ! [X35,X57,X11,X30,X39,X1] :
( c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X11,X35,X57,t_a)),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X1,X35,X30,t_a)),t_a)
| ~ hBOOL(hAPP(hAPP(X57,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1(X39,X11,X57,X35)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3(X39,X11,X57,X35,X1,X30))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_481])]) ).
fof(f985,plain,
! [X39,X11,X1,X57,X35,X30] :
( c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X11,X35,X57,t_a)),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X1,X35,X30,t_a)),t_a)
| ~ hBOOL(hAPP(hAPP(X57,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1(X39,X11,X57,X35)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3(X39,X11,X57,X35,X1,X30))) ),
inference(forward_demodulation,[],[f984,f723]) ).
fof(f984,plain,
! [X39,X11,X1,X57,X35,X30] :
( c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X11,X35,X57,t_a)),c_COMBK(c_False,tc_bool,tc_Hoare__Mirabelle_Otriple(t_a))),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X1,X35,X30,t_a)),t_a)
| ~ hBOOL(hAPP(hAPP(X57,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1(X39,X11,X57,X35)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3(X39,X11,X57,X35,X1,X30))) ),
inference(forward_demodulation,[],[f983,f698]) ).
fof(f983,plain,
! [X39,X11,X1,X57,X35,X30] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X1,X35,X30,t_a)),t_a)
| ~ hBOOL(hAPP(hAPP(X57,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1(X39,X11,X57,X35)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3(X39,X11,X57,X35,X1,X30)))
| c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X11,X35,X57,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
inference(forward_demodulation,[],[f982,f723]) ).
fof(f982,plain,
! [X39,X11,X1,X57,X35,X30] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X1,X35,X30,t_a)),c_COMBK(c_False,tc_bool,tc_Hoare__Mirabelle_Otriple(t_a))),t_a)
| ~ hBOOL(hAPP(hAPP(X57,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1(X39,X11,X57,X35)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3(X39,X11,X57,X35,X1,X30)))
| c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X11,X35,X57,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
inference(forward_demodulation,[],[f565,f698]) ).
fof(f565,axiom,
! [X39,X11,X1,X57,X35,X30] :
( ~ hBOOL(hAPP(hAPP(X57,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1(X39,X11,X57,X35)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3(X39,X11,X57,X35,X1,X30)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X1,X35,X30,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X11,X35,X57,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_hoare__derivs_Ointros_I6_J_2) ).
fof(f12605,plain,
spl0_480,
inference(avatar_split_clause,[],[f981,f12603]) ).
fof(f12603,plain,
( spl0_480
<=> ! [X35,X57,X11,X30,X39,X1] :
( c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X11,X35,X57,t_a)),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X1,X35,X30,t_a)),t_a)
| ~ hBOOL(hAPP(hAPP(X57,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1(X39,X11,X57,X35)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3(X39,X11,X57,X35,X1,X30))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_480])]) ).
fof(f981,plain,
! [X39,X11,X1,X57,X35,X30] :
( c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X11,X35,X57,t_a)),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X1,X35,X30,t_a)),t_a)
| ~ hBOOL(hAPP(hAPP(X57,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1(X39,X11,X57,X35)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3(X39,X11,X57,X35,X1,X30))) ),
inference(forward_demodulation,[],[f980,f723]) ).
fof(f980,plain,
! [X39,X11,X1,X57,X35,X30] :
( c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X11,X35,X57,t_a)),c_COMBK(c_False,tc_bool,tc_Hoare__Mirabelle_Otriple(t_a))),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X1,X35,X30,t_a)),t_a)
| ~ hBOOL(hAPP(hAPP(X57,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1(X39,X11,X57,X35)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3(X39,X11,X57,X35,X1,X30))) ),
inference(forward_demodulation,[],[f979,f698]) ).
fof(f979,plain,
! [X39,X11,X1,X57,X35,X30] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X1,X35,X30,t_a)),t_a)
| ~ hBOOL(hAPP(hAPP(X57,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1(X39,X11,X57,X35)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3(X39,X11,X57,X35,X1,X30)))
| c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X11,X35,X57,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
inference(forward_demodulation,[],[f978,f723]) ).
fof(f978,plain,
! [X39,X11,X1,X57,X35,X30] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X1,X35,X30,t_a)),c_COMBK(c_False,tc_bool,tc_Hoare__Mirabelle_Otriple(t_a))),t_a)
| ~ hBOOL(hAPP(hAPP(X57,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1(X39,X11,X57,X35)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3(X39,X11,X57,X35,X1,X30)))
| c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X11,X35,X57,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
inference(forward_demodulation,[],[f570,f698]) ).
fof(f570,axiom,
! [X39,X11,X1,X57,X35,X30] :
( ~ hBOOL(hAPP(hAPP(X57,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1(X39,X11,X57,X35)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3(X39,X11,X57,X35,X1,X30)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X1,X35,X30,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X11,X35,X57,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conseq_2) ).
fof(f12601,plain,
spl0_479,
inference(avatar_split_clause,[],[f85,f12599]) ).
fof(f12599,plain,
( spl0_479
<=> ! [X5,X0,X12,X9] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X12),X5))
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X5),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X9),X12)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X5),X9)),X12) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_479])]) ).
fof(f85,axiom,
! [X0,X9,X5,X12] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X12),X5))
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X5),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X9),X12)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X5),X9)),X12) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Int__assoc__eq_1) ).
fof(f12597,plain,
spl0_478,
inference(avatar_split_clause,[],[f84,f12595]) ).
fof(f84,axiom,
! [X0,X9,X5,X12] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X12),X5))
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X5),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X9),X12)) != hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X5),X9)),X12) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Int__assoc__eq_0) ).
fof(f12566,plain,
spl0_477,
inference(avatar_split_clause,[],[f890,f12564]) ).
fof(f12564,plain,
( spl0_477
<=> ! [X62,X11,X57,X0,X39] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X0)),c_Hoare__Mirabelle_Otriple_Otriple(X11,c_Com_Ocom_OBODY(X62),X57,X0)),X39),hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),c_Hoare__Mirabelle_Otriple_Otriple(X11,c_Option_Othe(c_Com_Obody(X62),tc_Com_Ocom),X57,X0)),X0)
| c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),c_Hoare__Mirabelle_Otriple_Otriple(X11,c_Com_Ocom_OBODY(X62),X57,X0)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_477])]) ).
fof(f890,plain,
! [X39,X0,X11,X57,X62] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X0)),c_Hoare__Mirabelle_Otriple_Otriple(X11,c_Com_Ocom_OBODY(X62),X57,X0)),X39),hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),c_Hoare__Mirabelle_Otriple_Otriple(X11,c_Option_Othe(c_Com_Obody(X62),tc_Com_Ocom),X57,X0)),X0)
| c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),c_Hoare__Mirabelle_Otriple_Otriple(X11,c_Com_Ocom_OBODY(X62),X57,X0)),X0) ),
inference(forward_demodulation,[],[f889,f723]) ).
fof(f889,plain,
! [X39,X0,X11,X57,X62] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X0)),c_Hoare__Mirabelle_Otriple_Otriple(X11,c_Com_Ocom_OBODY(X62),X57,X0)),X39),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X0)),c_Hoare__Mirabelle_Otriple_Otriple(X11,c_Option_Othe(c_Com_Obody(X62),tc_Com_Ocom),X57,X0)),c_COMBK(c_False,tc_bool,tc_Hoare__Mirabelle_Otriple(X0))),X0)
| c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),c_Hoare__Mirabelle_Otriple_Otriple(X11,c_Com_Ocom_OBODY(X62),X57,X0)),X0) ),
inference(forward_demodulation,[],[f888,f698]) ).
fof(f888,plain,
! [X39,X0,X11,X57,X62] :
( c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),c_Hoare__Mirabelle_Otriple_Otriple(X11,c_Com_Ocom_OBODY(X62),X57,X0)),X0)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X0)),c_Hoare__Mirabelle_Otriple_Otriple(X11,c_Com_Ocom_OBODY(X62),X57,X0)),X39),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X0)),c_Hoare__Mirabelle_Otriple_Otriple(X11,c_Option_Othe(c_Com_Obody(X62),tc_Com_Ocom),X57,X0)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool))),X0) ),
inference(forward_demodulation,[],[f887,f723]) ).
fof(f887,plain,
! [X39,X0,X11,X57,X62] :
( c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X0)),c_Hoare__Mirabelle_Otriple_Otriple(X11,c_Com_Ocom_OBODY(X62),X57,X0)),c_COMBK(c_False,tc_bool,tc_Hoare__Mirabelle_Otriple(X0))),X0)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X0)),c_Hoare__Mirabelle_Otriple_Otriple(X11,c_Com_Ocom_OBODY(X62),X57,X0)),X39),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X0)),c_Hoare__Mirabelle_Otriple_Otriple(X11,c_Option_Othe(c_Com_Obody(X62),tc_Com_Ocom),X57,X0)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool))),X0) ),
inference(forward_demodulation,[],[f512,f698]) ).
fof(f512,axiom,
! [X39,X0,X11,X57,X62] :
( c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X0)),c_Hoare__Mirabelle_Otriple_Otriple(X11,c_Com_Ocom_OBODY(X62),X57,X0)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool))),X0)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X0)),c_Hoare__Mirabelle_Otriple_Otriple(X11,c_Com_Ocom_OBODY(X62),X57,X0)),X39),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X0)),c_Hoare__Mirabelle_Otriple_Otriple(X11,c_Option_Othe(c_Com_Obody(X62),tc_Com_Ocom),X57,X0)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool))),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_BodyN_0) ).
fof(f12562,plain,
spl0_476,
inference(avatar_split_clause,[],[f790,f12560]) ).
fof(f790,plain,
! [X38,X0,X8,X53] :
( c_Finite__Set_Ofinite(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X38,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X8,tc_fun(tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),X0),c_Set_Oinsert(X8)),X53),X0,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_COMBK(c_False,tc_bool,X8)),X0,tc_fun(X8,tc_bool)),X8)
| ~ c_Finite__Set_Ofinite(X38,X0) ),
inference(forward_demodulation,[],[f662,f698]) ).
fof(f662,plain,
! [X38,X0,X8,X53] :
( ~ c_Finite__Set_Ofinite(X38,X0)
| c_Finite__Set_Ofinite(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X38,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X8,tc_fun(tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),X0),c_Set_Oinsert(X8)),X53),X0,tc_fun(X8,tc_bool),tc_fun(X8,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X8,tc_bool))),X0,tc_fun(X8,tc_bool)),X8) ),
inference(definition_unfolding,[],[f272,f552]) ).
fof(f272,axiom,
! [X38,X0,X8,X53] :
( ~ c_Finite__Set_Ofinite(X38,X0)
| c_Finite__Set_Ofinite(c_Set_Oimage(X53,X38,X0,X8),X8) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__imageI_0) ).
fof(f11027,plain,
spl0_475,
inference(avatar_split_clause,[],[f991,f11025]) ).
fof(f991,plain,
! [X40,X39,X0,X11,X57,X35,X67] :
( c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),c_Hoare__Mirabelle_Otriple_Otriple(X11,c_Com_Ocom_OSemi(X35,X40),X67,X0)),X0)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),c_Hoare__Mirabelle_Otriple_Otriple(X57,X40,X67,X0)),X0)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),c_Hoare__Mirabelle_Otriple_Otriple(X11,X35,X57,X0)),X0) ),
inference(forward_demodulation,[],[f990,f723]) ).
fof(f990,plain,
! [X40,X39,X0,X11,X57,X35,X67] :
( c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X0)),c_Hoare__Mirabelle_Otriple_Otriple(X11,c_Com_Ocom_OSemi(X35,X40),X67,X0)),c_COMBK(c_False,tc_bool,tc_Hoare__Mirabelle_Otriple(X0))),X0)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),c_Hoare__Mirabelle_Otriple_Otriple(X57,X40,X67,X0)),X0)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),c_Hoare__Mirabelle_Otriple_Otriple(X11,X35,X57,X0)),X0) ),
inference(forward_demodulation,[],[f989,f698]) ).
fof(f989,plain,
! [X40,X39,X0,X11,X57,X35,X67] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),c_Hoare__Mirabelle_Otriple_Otriple(X57,X40,X67,X0)),X0)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),c_Hoare__Mirabelle_Otriple_Otriple(X11,X35,X57,X0)),X0)
| c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X0)),c_Hoare__Mirabelle_Otriple_Otriple(X11,c_Com_Ocom_OSemi(X35,X40),X67,X0)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool))),X0) ),
inference(forward_demodulation,[],[f988,f723]) ).
fof(f988,plain,
! [X40,X39,X0,X11,X57,X35,X67] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X0)),c_Hoare__Mirabelle_Otriple_Otriple(X57,X40,X67,X0)),c_COMBK(c_False,tc_bool,tc_Hoare__Mirabelle_Otriple(X0))),X0)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),c_Hoare__Mirabelle_Otriple_Otriple(X11,X35,X57,X0)),X0)
| c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X0)),c_Hoare__Mirabelle_Otriple_Otriple(X11,c_Com_Ocom_OSemi(X35,X40),X67,X0)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool))),X0) ),
inference(forward_demodulation,[],[f987,f698]) ).
fof(f987,plain,
! [X40,X39,X0,X11,X57,X35,X67] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),c_Hoare__Mirabelle_Otriple_Otriple(X11,X35,X57,X0)),X0)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X0)),c_Hoare__Mirabelle_Otriple_Otriple(X57,X40,X67,X0)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool))),X0)
| c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X0)),c_Hoare__Mirabelle_Otriple_Otriple(X11,c_Com_Ocom_OSemi(X35,X40),X67,X0)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool))),X0) ),
inference(forward_demodulation,[],[f986,f723]) ).
fof(f986,plain,
! [X40,X39,X0,X11,X57,X35,X67] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X0)),c_Hoare__Mirabelle_Otriple_Otriple(X11,X35,X57,X0)),c_COMBK(c_False,tc_bool,tc_Hoare__Mirabelle_Otriple(X0))),X0)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X0)),c_Hoare__Mirabelle_Otriple_Otriple(X57,X40,X67,X0)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool))),X0)
| c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X0)),c_Hoare__Mirabelle_Otriple_Otriple(X11,c_Com_Ocom_OSemi(X35,X40),X67,X0)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool))),X0) ),
inference(forward_demodulation,[],[f585,f698]) ).
fof(f585,axiom,
! [X40,X39,X0,X11,X57,X35,X67] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X0)),c_Hoare__Mirabelle_Otriple_Otriple(X11,X35,X57,X0)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool))),X0)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X0)),c_Hoare__Mirabelle_Otriple_Otriple(X57,X40,X67,X0)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool))),X0)
| c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X0)),c_Hoare__Mirabelle_Otriple_Otriple(X11,c_Com_Ocom_OSemi(X35,X40),X67,X0)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool))),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Comp_0) ).
fof(f11023,plain,
spl0_474,
inference(avatar_split_clause,[],[f977,f11021]) ).
fof(f977,plain,
! [X65,X39,X11,X57,X35,X64] :
( c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X11,X35,X57,t_a)),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X65,X35,X64,t_a)),t_a)
| hBOOL(hAPP(hAPP(X11,v_sko__Hoare__Mirabelle__Xconseq12__1(X11,X65,X57,X64)),v_sko__Hoare__Mirabelle__Xconseq12__2(X11,X65,X57,X64))) ),
inference(forward_demodulation,[],[f976,f723]) ).
fof(f976,plain,
! [X65,X39,X11,X57,X35,X64] :
( c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X11,X35,X57,t_a)),c_COMBK(c_False,tc_bool,tc_Hoare__Mirabelle_Otriple(t_a))),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X65,X35,X64,t_a)),t_a)
| hBOOL(hAPP(hAPP(X11,v_sko__Hoare__Mirabelle__Xconseq12__1(X11,X65,X57,X64)),v_sko__Hoare__Mirabelle__Xconseq12__2(X11,X65,X57,X64))) ),
inference(forward_demodulation,[],[f975,f698]) ).
fof(f975,plain,
! [X65,X39,X11,X57,X35,X64] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X65,X35,X64,t_a)),t_a)
| hBOOL(hAPP(hAPP(X11,v_sko__Hoare__Mirabelle__Xconseq12__1(X11,X65,X57,X64)),v_sko__Hoare__Mirabelle__Xconseq12__2(X11,X65,X57,X64)))
| c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X11,X35,X57,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
inference(forward_demodulation,[],[f974,f723]) ).
fof(f974,plain,
! [X65,X39,X11,X57,X35,X64] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X65,X35,X64,t_a)),c_COMBK(c_False,tc_bool,tc_Hoare__Mirabelle_Otriple(t_a))),t_a)
| hBOOL(hAPP(hAPP(X11,v_sko__Hoare__Mirabelle__Xconseq12__1(X11,X65,X57,X64)),v_sko__Hoare__Mirabelle__Xconseq12__2(X11,X65,X57,X64)))
| c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X11,X35,X57,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
inference(forward_demodulation,[],[f568,f698]) ).
fof(f568,axiom,
! [X65,X39,X11,X57,X35,X64] :
( hBOOL(hAPP(hAPP(X11,v_sko__Hoare__Mirabelle__Xconseq12__1(X11,X65,X57,X64)),v_sko__Hoare__Mirabelle__Xconseq12__2(X11,X65,X57,X64)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X65,X35,X64,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X11,X35,X57,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conseq12_0) ).
fof(f11019,plain,
spl0_473,
inference(avatar_split_clause,[],[f973,f11017]) ).
fof(f11017,plain,
( spl0_473
<=> ! [X35,X57,X11,X64,X39,X65] :
( c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X11,X35,X57,t_a)),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X65,X35,X64,t_a)),t_a)
| ~ hBOOL(hAPP(hAPP(X57,v_sko__Hoare__Mirabelle__Xconseq12__1(X11,X65,X57,X64)),v_sko__Hoare__Mirabelle__Xconseq12__3(X11,X65,X57,X64))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_473])]) ).
fof(f973,plain,
! [X65,X39,X11,X57,X35,X64] :
( c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X11,X35,X57,t_a)),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X65,X35,X64,t_a)),t_a)
| ~ hBOOL(hAPP(hAPP(X57,v_sko__Hoare__Mirabelle__Xconseq12__1(X11,X65,X57,X64)),v_sko__Hoare__Mirabelle__Xconseq12__3(X11,X65,X57,X64))) ),
inference(forward_demodulation,[],[f972,f723]) ).
fof(f972,plain,
! [X65,X39,X11,X57,X35,X64] :
( c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X11,X35,X57,t_a)),c_COMBK(c_False,tc_bool,tc_Hoare__Mirabelle_Otriple(t_a))),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X65,X35,X64,t_a)),t_a)
| ~ hBOOL(hAPP(hAPP(X57,v_sko__Hoare__Mirabelle__Xconseq12__1(X11,X65,X57,X64)),v_sko__Hoare__Mirabelle__Xconseq12__3(X11,X65,X57,X64))) ),
inference(forward_demodulation,[],[f971,f698]) ).
fof(f971,plain,
! [X65,X39,X11,X57,X35,X64] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X65,X35,X64,t_a)),t_a)
| ~ hBOOL(hAPP(hAPP(X57,v_sko__Hoare__Mirabelle__Xconseq12__1(X11,X65,X57,X64)),v_sko__Hoare__Mirabelle__Xconseq12__3(X11,X65,X57,X64)))
| c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X11,X35,X57,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
inference(forward_demodulation,[],[f970,f723]) ).
fof(f970,plain,
! [X65,X39,X11,X57,X35,X64] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X65,X35,X64,t_a)),c_COMBK(c_False,tc_bool,tc_Hoare__Mirabelle_Otriple(t_a))),t_a)
| ~ hBOOL(hAPP(hAPP(X57,v_sko__Hoare__Mirabelle__Xconseq12__1(X11,X65,X57,X64)),v_sko__Hoare__Mirabelle__Xconseq12__3(X11,X65,X57,X64)))
| c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X11,X35,X57,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
inference(forward_demodulation,[],[f572,f698]) ).
fof(f572,axiom,
! [X65,X39,X11,X57,X35,X64] :
( ~ hBOOL(hAPP(hAPP(X57,v_sko__Hoare__Mirabelle__Xconseq12__1(X11,X65,X57,X64)),v_sko__Hoare__Mirabelle__Xconseq12__3(X11,X65,X57,X64)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X65,X35,X64,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X11,X35,X57,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conseq12_2) ).
fof(f11015,plain,
spl0_472,
inference(avatar_split_clause,[],[f932,f11013]) ).
fof(f11013,plain,
( spl0_472
<=> ! [X9,X0,X5,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X5),hAPP(c_fequal(X0),X1))),X9))
| ~ hBOOL(c_in(X1,X5,X0))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X5),hAPP(hAPP(c_Set_Oinsert(X0),X1),X9))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_472])]) ).
fof(f932,plain,
! [X0,X1,X9,X5] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X5),hAPP(c_fequal(X0),X1))),X9))
| ~ hBOOL(c_in(X1,X5,X0))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X5),hAPP(hAPP(c_Set_Oinsert(X0),X1),X9))) ),
inference(forward_demodulation,[],[f931,f723]) ).
fof(f931,plain,
! [X0,X1,X9,X5] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X5),hAPP(hAPP(c_Set_Oinsert(X0),X1),c_COMBK(c_False,tc_bool,X0)))),X9))
| ~ hBOOL(c_in(X1,X5,X0))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X5),hAPP(hAPP(c_Set_Oinsert(X0),X1),X9))) ),
inference(forward_demodulation,[],[f26,f698]) ).
fof(f26,axiom,
! [X0,X1,X9,X5] :
( ~ hBOOL(c_in(X1,X5,X0))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X5),hAPP(hAPP(c_Set_Oinsert(X0),X1),X9)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X5),hAPP(hAPP(c_Set_Oinsert(X0),X1),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))))),X9)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insert__iff_3) ).
fof(f10967,plain,
spl0_471,
inference(avatar_split_clause,[],[f775,f10965]) ).
fof(f775,plain,
! [X0,X9,X5,X12] : hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X5),X12)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X9),X12)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X5),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X12),X9)),
inference(forward_demodulation,[],[f237,f460]) ).
fof(f237,axiom,
! [X0,X9,X5,X12] : hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X5),X12)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X9),X12)) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X5),X12)),X9),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__Int2_0) ).
fof(f10963,plain,
spl0_470,
inference(avatar_split_clause,[],[f471,f10961]) ).
fof(f471,axiom,
! [X0,X9,X5,X12] : hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X5),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X9),X12)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X5),X9)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X5),X12)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__Int_0) ).
fof(f10959,plain,
spl0_469,
inference(avatar_split_clause,[],[f457,f10957]) ).
fof(f457,axiom,
! [X0,X9,X5,X12] : hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X5),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X9),X12)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X5),X9)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X5),X12)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__Un_0) ).
fof(f10955,plain,
spl0_468,
inference(avatar_split_clause,[],[f305,f10953]) ).
fof(f10953,plain,
( spl0_468
<=> ! [X5,X0,X12,X9] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X9),X12)),X5) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X9),X5)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X12),X5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_468])]) ).
fof(f305,axiom,
! [X0,X9,X5,X12] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X9),X12)),X5) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X9),X5)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X12),X5)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Int__distrib2_0) ).
fof(f10951,plain,
spl0_467,
inference(avatar_split_clause,[],[f304,f10949]) ).
fof(f304,axiom,
! [X0,X9,X5,X12] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X5),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X9),X12)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X5),X9)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X5),X12)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Int__distrib_0) ).
fof(f10802,plain,
( spl0_466
| ~ spl0_465 ),
inference(avatar_split_clause,[],[f10798,f10795,f10800]) ).
fof(f10795,plain,
( spl0_465
<=> ! [X9,X0,X12,X5] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X5),X9)),X12) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X5),X12)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X9),X12)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_465])]) ).
fof(f10798,plain,
( ! [X0,X9,X5,X12] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X5),X9)),X12) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X5),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X12),X9))
| ~ spl0_465 ),
inference(forward_demodulation,[],[f10796,f775]) ).
fof(f10796,plain,
( ! [X0,X9,X5,X12] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X5),X9)),X12) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X5),X12)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X9),X12))
| ~ spl0_465 ),
inference(avatar_component_clause,[],[f10795]) ).
fof(f10797,plain,
spl0_465,
inference(avatar_split_clause,[],[f229,f10795]) ).
fof(f229,axiom,
! [X0,X9,X5,X12] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X5),X9)),X12) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X5),X12)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X9),X12)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__Int__distrib2_0) ).
fof(f10793,plain,
spl0_464,
inference(avatar_split_clause,[],[f228,f10791]) ).
fof(f228,axiom,
! [X0,X9,X5,X12] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X12),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X5),X9)) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X12),X5)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X12),X9)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__Int__distrib_0) ).
fof(f10789,plain,
spl0_463,
inference(avatar_split_clause,[],[f192,f10787]) ).
fof(f192,axiom,
! [X0,X9,X5,X12] : hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X5),X9)),X12) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X5),X12)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X9),X12)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Diff_0) ).
fof(f10785,plain,
( spl0_462
| ~ spl0_1
| ~ spl0_116 ),
inference(avatar_split_clause,[],[f1581,f1549,f1017,f10782]) ).
fof(f10782,plain,
( spl0_462
<=> c_Orderings_Otop__class_Otop(tc_bool) = hAPP(c_Complete__Lattice_OInf__class_OInf(tc_bool),c_COMBK(c_False,tc_bool,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_462])]) ).
fof(f1581,plain,
( c_Orderings_Otop__class_Otop(tc_bool) = hAPP(c_Complete__Lattice_OInf__class_OInf(tc_bool),c_COMBK(c_False,tc_bool,tc_bool))
| ~ spl0_1
| ~ spl0_116 ),
inference(resolution,[],[f1550,f1019]) ).
fof(f10780,plain,
spl0_461,
inference(avatar_split_clause,[],[f15,f10778]) ).
fof(f10778,plain,
( spl0_461
<=> ! [X5,X0,X12,X9] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X9),X12)),X5) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X9),X5)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X12),X5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_461])]) ).
fof(f15,axiom,
! [X0,X9,X5,X12] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X9),X12)),X5) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X9),X5)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X12),X5)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__Un__distrib2_0) ).
fof(f10776,plain,
spl0_460,
inference(avatar_split_clause,[],[f14,f10774]) ).
fof(f14,axiom,
! [X0,X9,X5,X12] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X5),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X9),X12)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X5),X9)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X5),X12)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__Un__distrib_0) ).
fof(f10767,plain,
spl0_459,
inference(avatar_split_clause,[],[f894,f10765]) ).
fof(f10765,plain,
( spl0_459
<=> ! [X35,X4,X11,X0,X39] :
( c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),c_Hoare__Mirabelle_Otriple_Otriple(X11,c_Com_Ocom_OWhile(X4,X35),c_Hoare__Mirabelle_Opeek__and(X11,c_Fun_Ocomp(c_Not,X4,tc_bool,tc_bool,tc_Com_Ostate),X0),X0)),X0)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),c_Hoare__Mirabelle_Otriple_Otriple(c_Hoare__Mirabelle_Opeek__and(X11,X4,X0),X35,X11,X0)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_459])]) ).
fof(f894,plain,
! [X39,X0,X11,X4,X35] :
( c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),c_Hoare__Mirabelle_Otriple_Otriple(X11,c_Com_Ocom_OWhile(X4,X35),c_Hoare__Mirabelle_Opeek__and(X11,c_Fun_Ocomp(c_Not,X4,tc_bool,tc_bool,tc_Com_Ostate),X0),X0)),X0)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),c_Hoare__Mirabelle_Otriple_Otriple(c_Hoare__Mirabelle_Opeek__and(X11,X4,X0),X35,X11,X0)),X0) ),
inference(forward_demodulation,[],[f893,f723]) ).
fof(f893,plain,
! [X39,X0,X11,X4,X35] :
( c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X0)),c_Hoare__Mirabelle_Otriple_Otriple(X11,c_Com_Ocom_OWhile(X4,X35),c_Hoare__Mirabelle_Opeek__and(X11,c_Fun_Ocomp(c_Not,X4,tc_bool,tc_bool,tc_Com_Ostate),X0),X0)),c_COMBK(c_False,tc_bool,tc_Hoare__Mirabelle_Otriple(X0))),X0)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),c_Hoare__Mirabelle_Otriple_Otriple(c_Hoare__Mirabelle_Opeek__and(X11,X4,X0),X35,X11,X0)),X0) ),
inference(forward_demodulation,[],[f892,f698]) ).
fof(f892,plain,
! [X39,X0,X11,X4,X35] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),c_Hoare__Mirabelle_Otriple_Otriple(c_Hoare__Mirabelle_Opeek__and(X11,X4,X0),X35,X11,X0)),X0)
| c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X0)),c_Hoare__Mirabelle_Otriple_Otriple(X11,c_Com_Ocom_OWhile(X4,X35),c_Hoare__Mirabelle_Opeek__and(X11,c_Fun_Ocomp(c_Not,X4,tc_bool,tc_bool,tc_Com_Ostate),X0),X0)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool))),X0) ),
inference(forward_demodulation,[],[f891,f723]) ).
fof(f891,plain,
! [X39,X0,X11,X4,X35] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X0)),c_Hoare__Mirabelle_Otriple_Otriple(c_Hoare__Mirabelle_Opeek__and(X11,X4,X0),X35,X11,X0)),c_COMBK(c_False,tc_bool,tc_Hoare__Mirabelle_Otriple(X0))),X0)
| c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X0)),c_Hoare__Mirabelle_Otriple_Otriple(X11,c_Com_Ocom_OWhile(X4,X35),c_Hoare__Mirabelle_Opeek__and(X11,c_Fun_Ocomp(c_Not,X4,tc_bool,tc_bool,tc_Com_Ostate),X0),X0)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool))),X0) ),
inference(forward_demodulation,[],[f511,f698]) ).
fof(f511,axiom,
! [X39,X0,X11,X4,X35] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X0)),c_Hoare__Mirabelle_Otriple_Otriple(c_Hoare__Mirabelle_Opeek__and(X11,X4,X0),X35,X11,X0)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool))),X0)
| c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X0)),c_Hoare__Mirabelle_Otriple_Otriple(X11,c_Com_Ocom_OWhile(X4,X35),c_Hoare__Mirabelle_Opeek__and(X11,c_Fun_Ocomp(c_Not,X4,tc_bool,tc_bool,tc_Com_Ostate),X0),X0)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool))),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Loop_0) ).
fof(f10734,plain,
spl0_458,
inference(avatar_split_clause,[],[f1015,f10732]) ).
fof(f10732,plain,
( spl0_458
<=> ! [X0,X5,X1,X30] :
( c_COMBK(c_False,tc_bool,X0) = X5
| ~ class_Lattices_Olower__semilattice(X0)
| ~ c_Finite__Set_Ofinite(X5,X0)
| ~ hBOOL(c_in(X30,X5,X0))
| hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X30))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X1),c_The(c_Finite__Set_Ofold1Set(c_Lattices_Olower__semilattice__class_Oinf(X0),X5,X0),X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_458])]) ).
fof(f1015,plain,
! [X0,X1,X5,X30] :
( c_COMBK(c_False,tc_bool,X0) = X5
| ~ class_Lattices_Olower__semilattice(X0)
| ~ c_Finite__Set_Ofinite(X5,X0)
| ~ hBOOL(c_in(X30,X5,X0))
| hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X30))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X1),c_The(c_Finite__Set_Ofold1Set(c_Lattices_Olower__semilattice__class_Oinf(X0),X5,X0),X0))) ),
inference(forward_demodulation,[],[f697,f698]) ).
fof(f697,plain,
! [X0,X1,X5,X30] :
( ~ class_Lattices_Olower__semilattice(X0)
| ~ c_Finite__Set_Ofinite(X5,X0)
| ~ hBOOL(c_in(X30,X5,X0))
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X5
| hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X30))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X1),c_The(c_Finite__Set_Ofold1Set(c_Lattices_Olower__semilattice__class_Oinf(X0),X5,X0),X0))) ),
inference(definition_unfolding,[],[f38,f30]) ).
fof(f30,axiom,
! [X0,X7,X5] : c_Finite__Set_Ofold1(X7,X5,X0) = c_The(c_Finite__Set_Ofold1Set(X7,X5,X0),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fold1__def_0) ).
fof(f38,axiom,
! [X0,X1,X5,X30] :
( ~ class_Lattices_Olower__semilattice(X0)
| ~ c_Finite__Set_Ofinite(X5,X0)
| ~ hBOOL(c_in(X30,X5,X0))
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X5
| hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X30))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X1),c_Finite__Set_Ofold1(c_Lattices_Olower__semilattice__class_Oinf(X0),X5,X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_below__fold1__iff_0) ).
fof(f10491,plain,
spl0_457,
inference(avatar_split_clause,[],[f479,f10489]) ).
fof(f479,axiom,
! [X0,X9,X5,X12] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X5),X9))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X9),X12))
| hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X9),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X12),X5)) = X5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__diff_0) ).
fof(f10487,plain,
( spl0_456
| ~ spl0_1
| ~ spl0_109 ),
inference(avatar_split_clause,[],[f1566,f1520,f1017,f10484]) ).
fof(f10484,plain,
( spl0_456
<=> c_Orderings_Otop__class_Otop(tc_bool) = hAPP(c_Complete__Lattice_OSup__class_OSup(tc_bool),c_Orderings_Otop__class_Otop(tc_fun(tc_bool,tc_bool))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_456])]) ).
fof(f1566,plain,
( c_Orderings_Otop__class_Otop(tc_bool) = hAPP(c_Complete__Lattice_OSup__class_OSup(tc_bool),c_Orderings_Otop__class_Otop(tc_fun(tc_bool,tc_bool)))
| ~ spl0_1
| ~ spl0_109 ),
inference(resolution,[],[f1521,f1019]) ).
fof(f10482,plain,
spl0_455,
inference(avatar_split_clause,[],[f473,f10480]) ).
fof(f473,axiom,
! [X0,X18,X8,X9,X5] : c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X8,tc_bool)),X5),X9),X18,X8,tc_fun(X0,tc_bool)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,X18,X8,tc_fun(X0,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X9,X18,X8,tc_fun(X0,tc_bool))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UN__Un_0) ).
fof(f10478,plain,
spl0_454,
inference(avatar_split_clause,[],[f462,f10476]) ).
fof(f462,axiom,
! [X0,X18,X8,X9,X5] : c_Complete__Lattice_Ocomplete__lattice__class_OINFI(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X8,tc_bool)),X5),X9),X18,X8,tc_fun(X0,tc_bool)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,X18,X8,tc_fun(X0,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X9,X18,X8,tc_fun(X0,tc_bool))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_INT__Un_0) ).
fof(f9812,plain,
( spl0_453
| ~ spl0_5
| ~ spl0_102 ),
inference(avatar_split_clause,[],[f1558,f1492,f1037,f9810]) ).
fof(f1558,plain,
( ! [X0] : c_Orderings_Otop__class_Otop(tc_bool) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),X0)
| ~ spl0_5
| ~ spl0_102 ),
inference(resolution,[],[f1493,f1039]) ).
fof(f1039,plain,
( class_Lattices_Obounded__lattice(tc_bool)
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f1037]) ).
fof(f9808,plain,
spl0_452,
inference(avatar_split_clause,[],[f969,f9806]) ).
fof(f969,plain,
! [X65,X39,X11,X57,X35] :
( c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X11,X35,X57,t_a)),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X65,X35,X57,t_a)),t_a)
| hBOOL(hAPP(hAPP(X11,v_sko__Hoare__Mirabelle__Xconseq1__1(X11,X65)),v_sko__Hoare__Mirabelle__Xconseq1__2(X11,X65))) ),
inference(forward_demodulation,[],[f968,f723]) ).
fof(f968,plain,
! [X65,X39,X11,X57,X35] :
( c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X11,X35,X57,t_a)),c_COMBK(c_False,tc_bool,tc_Hoare__Mirabelle_Otriple(t_a))),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X65,X35,X57,t_a)),t_a)
| hBOOL(hAPP(hAPP(X11,v_sko__Hoare__Mirabelle__Xconseq1__1(X11,X65)),v_sko__Hoare__Mirabelle__Xconseq1__2(X11,X65))) ),
inference(forward_demodulation,[],[f967,f698]) ).
fof(f967,plain,
! [X65,X39,X11,X57,X35] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X65,X35,X57,t_a)),t_a)
| hBOOL(hAPP(hAPP(X11,v_sko__Hoare__Mirabelle__Xconseq1__1(X11,X65)),v_sko__Hoare__Mirabelle__Xconseq1__2(X11,X65)))
| c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X11,X35,X57,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
inference(forward_demodulation,[],[f966,f723]) ).
fof(f966,plain,
! [X65,X39,X11,X57,X35] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X65,X35,X57,t_a)),c_COMBK(c_False,tc_bool,tc_Hoare__Mirabelle_Otriple(t_a))),t_a)
| hBOOL(hAPP(hAPP(X11,v_sko__Hoare__Mirabelle__Xconseq1__1(X11,X65)),v_sko__Hoare__Mirabelle__Xconseq1__2(X11,X65)))
| c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X11,X35,X57,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
inference(forward_demodulation,[],[f569,f698]) ).
fof(f569,axiom,
! [X65,X39,X11,X57,X35] :
( hBOOL(hAPP(hAPP(X11,v_sko__Hoare__Mirabelle__Xconseq1__1(X11,X65)),v_sko__Hoare__Mirabelle__Xconseq1__2(X11,X65)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X65,X35,X57,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X11,X35,X57,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conseq1_0) ).
fof(f9804,plain,
spl0_451,
inference(avatar_split_clause,[],[f965,f9802]) ).
fof(f965,plain,
! [X39,X11,X57,X35,X64] :
( c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X11,X35,X57,t_a)),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X11,X35,X64,t_a)),t_a)
| hBOOL(hAPP(hAPP(X64,v_sko__Hoare__Mirabelle__Xconseq2__1(X57,X64)),v_sko__Hoare__Mirabelle__Xconseq2__2(X57,X64))) ),
inference(forward_demodulation,[],[f964,f723]) ).
fof(f964,plain,
! [X39,X11,X57,X35,X64] :
( c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X11,X35,X57,t_a)),c_COMBK(c_False,tc_bool,tc_Hoare__Mirabelle_Otriple(t_a))),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X11,X35,X64,t_a)),t_a)
| hBOOL(hAPP(hAPP(X64,v_sko__Hoare__Mirabelle__Xconseq2__1(X57,X64)),v_sko__Hoare__Mirabelle__Xconseq2__2(X57,X64))) ),
inference(forward_demodulation,[],[f963,f698]) ).
fof(f963,plain,
! [X39,X11,X57,X35,X64] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X11,X35,X64,t_a)),t_a)
| hBOOL(hAPP(hAPP(X64,v_sko__Hoare__Mirabelle__Xconseq2__1(X57,X64)),v_sko__Hoare__Mirabelle__Xconseq2__2(X57,X64)))
| c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X11,X35,X57,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
inference(forward_demodulation,[],[f962,f723]) ).
fof(f962,plain,
! [X39,X11,X57,X35,X64] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X11,X35,X64,t_a)),c_COMBK(c_False,tc_bool,tc_Hoare__Mirabelle_Otriple(t_a))),t_a)
| hBOOL(hAPP(hAPP(X64,v_sko__Hoare__Mirabelle__Xconseq2__1(X57,X64)),v_sko__Hoare__Mirabelle__Xconseq2__2(X57,X64)))
| c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X11,X35,X57,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
inference(forward_demodulation,[],[f567,f698]) ).
fof(f567,axiom,
! [X39,X11,X57,X35,X64] :
( hBOOL(hAPP(hAPP(X64,v_sko__Hoare__Mirabelle__Xconseq2__1(X57,X64)),v_sko__Hoare__Mirabelle__Xconseq2__2(X57,X64)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X11,X35,X64,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X11,X35,X57,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conseq2_0) ).
fof(f9800,plain,
spl0_450,
inference(avatar_split_clause,[],[f961,f9798]) ).
fof(f961,plain,
! [X65,X39,X11,X57,X35] :
( c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X11,X35,X57,t_a)),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X65,X35,X57,t_a)),t_a)
| ~ hBOOL(hAPP(hAPP(X65,v_sko__Hoare__Mirabelle__Xconseq1__1(X11,X65)),v_sko__Hoare__Mirabelle__Xconseq1__2(X11,X65))) ),
inference(forward_demodulation,[],[f960,f723]) ).
fof(f960,plain,
! [X65,X39,X11,X57,X35] :
( c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X11,X35,X57,t_a)),c_COMBK(c_False,tc_bool,tc_Hoare__Mirabelle_Otriple(t_a))),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X65,X35,X57,t_a)),t_a)
| ~ hBOOL(hAPP(hAPP(X65,v_sko__Hoare__Mirabelle__Xconseq1__1(X11,X65)),v_sko__Hoare__Mirabelle__Xconseq1__2(X11,X65))) ),
inference(forward_demodulation,[],[f959,f698]) ).
fof(f959,plain,
! [X65,X39,X11,X57,X35] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X65,X35,X57,t_a)),t_a)
| ~ hBOOL(hAPP(hAPP(X65,v_sko__Hoare__Mirabelle__Xconseq1__1(X11,X65)),v_sko__Hoare__Mirabelle__Xconseq1__2(X11,X65)))
| c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X11,X35,X57,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
inference(forward_demodulation,[],[f958,f723]) ).
fof(f958,plain,
! [X65,X39,X11,X57,X35] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X65,X35,X57,t_a)),c_COMBK(c_False,tc_bool,tc_Hoare__Mirabelle_Otriple(t_a))),t_a)
| ~ hBOOL(hAPP(hAPP(X65,v_sko__Hoare__Mirabelle__Xconseq1__1(X11,X65)),v_sko__Hoare__Mirabelle__Xconseq1__2(X11,X65)))
| c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X11,X35,X57,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
inference(forward_demodulation,[],[f571,f698]) ).
fof(f571,axiom,
! [X65,X39,X11,X57,X35] :
( ~ hBOOL(hAPP(hAPP(X65,v_sko__Hoare__Mirabelle__Xconseq1__1(X11,X65)),v_sko__Hoare__Mirabelle__Xconseq1__2(X11,X65)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X65,X35,X57,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X11,X35,X57,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conseq1_1) ).
fof(f9796,plain,
spl0_449,
inference(avatar_split_clause,[],[f957,f9794]) ).
fof(f957,plain,
! [X39,X11,X57,X35,X64] :
( c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X11,X35,X57,t_a)),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X11,X35,X64,t_a)),t_a)
| ~ hBOOL(hAPP(hAPP(X57,v_sko__Hoare__Mirabelle__Xconseq2__1(X57,X64)),v_sko__Hoare__Mirabelle__Xconseq2__2(X57,X64))) ),
inference(forward_demodulation,[],[f956,f723]) ).
fof(f956,plain,
! [X39,X11,X57,X35,X64] :
( c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X11,X35,X57,t_a)),c_COMBK(c_False,tc_bool,tc_Hoare__Mirabelle_Otriple(t_a))),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X11,X35,X64,t_a)),t_a)
| ~ hBOOL(hAPP(hAPP(X57,v_sko__Hoare__Mirabelle__Xconseq2__1(X57,X64)),v_sko__Hoare__Mirabelle__Xconseq2__2(X57,X64))) ),
inference(forward_demodulation,[],[f955,f698]) ).
fof(f955,plain,
! [X39,X11,X57,X35,X64] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X11,X35,X64,t_a)),t_a)
| ~ hBOOL(hAPP(hAPP(X57,v_sko__Hoare__Mirabelle__Xconseq2__1(X57,X64)),v_sko__Hoare__Mirabelle__Xconseq2__2(X57,X64)))
| c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X11,X35,X57,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
inference(forward_demodulation,[],[f954,f723]) ).
fof(f954,plain,
! [X39,X11,X57,X35,X64] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X11,X35,X64,t_a)),c_COMBK(c_False,tc_bool,tc_Hoare__Mirabelle_Otriple(t_a))),t_a)
| ~ hBOOL(hAPP(hAPP(X57,v_sko__Hoare__Mirabelle__Xconseq2__1(X57,X64)),v_sko__Hoare__Mirabelle__Xconseq2__2(X57,X64)))
| c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X11,X35,X57,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
inference(forward_demodulation,[],[f573,f698]) ).
fof(f573,axiom,
! [X39,X11,X57,X35,X64] :
( ~ hBOOL(hAPP(hAPP(X57,v_sko__Hoare__Mirabelle__Xconseq2__1(X57,X64)),v_sko__Hoare__Mirabelle__Xconseq2__2(X57,X64)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X11,X35,X64,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X11,X35,X57,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conseq2_1) ).
fof(f9792,plain,
spl0_448,
inference(avatar_split_clause,[],[f295,f9790]) ).
fof(f9790,plain,
( spl0_448
<=> ! [X5,X0,X12,X9] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X12),X5))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X12),X9))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X12),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X5),X9))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_448])]) ).
fof(f295,axiom,
! [X0,X9,X5,X12] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X12),X5))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X12),X9))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X12),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X5),X9))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__subset__iff_2) ).
fof(f9788,plain,
spl0_447,
inference(avatar_split_clause,[],[f236,f9786]) ).
fof(f236,axiom,
! [X2,X0,X1,X6] :
( ~ class_Lattices_Olattice(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X6))),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X6)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distrib__sup__le_0) ).
fof(f9784,plain,
spl0_446,
inference(avatar_split_clause,[],[f163,f9782]) ).
fof(f163,axiom,
! [X2,X0,X1,X6] :
( ~ class_Lattices_Olattice(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X6))),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X2),X6)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distrib__inf__le_0) ).
fof(f9780,plain,
spl0_445,
inference(avatar_split_clause,[],[f146,f9778]) ).
fof(f9778,plain,
( spl0_445
<=> ! [X5,X0,X12,X9] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X5),X12))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X9),X12))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X5),X9)),X12)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_445])]) ).
fof(f146,axiom,
! [X0,X9,X5,X12] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X5),X12))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X9),X12))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X5),X9)),X12)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__subset__iff_2) ).
fof(f9774,plain,
spl0_444,
inference(avatar_split_clause,[],[f812,f9772]) ).
fof(f9772,plain,
( spl0_444
<=> ! [X0,X11,X3] :
( hAPP(hAPP(c_COMBS(X0,tc_bool,tc_bool),hAPP(hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),X0),c_and),hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X3))),X11) = c_COMBK(c_False,tc_bool,X0)
| hBOOL(hAPP(X11,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_444])]) ).
fof(f812,plain,
! [X3,X0,X11] :
( hAPP(hAPP(c_COMBS(X0,tc_bool,tc_bool),hAPP(hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),X0),c_and),hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X3))),X11) = c_COMBK(c_False,tc_bool,X0)
| hBOOL(hAPP(X11,X3)) ),
inference(forward_demodulation,[],[f811,f698]) ).
fof(f811,plain,
! [X3,X0,X11] :
( c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = hAPP(hAPP(c_COMBS(X0,tc_bool,tc_bool),hAPP(hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),X0),c_and),hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X3))),X11)
| hBOOL(hAPP(X11,X3)) ),
inference(forward_demodulation,[],[f553,f43]) ).
fof(f553,axiom,
! [X3,X0,X11] :
( hBOOL(hAPP(X11,X3))
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_Collect(hAPP(hAPP(c_COMBS(X0,tc_bool,tc_bool),hAPP(hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),X0),c_and),hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X3))),X11),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Collect__conv__if_1) ).
fof(f9768,plain,
spl0_443,
inference(avatar_split_clause,[],[f806,f9766]) ).
fof(f9766,plain,
( spl0_443
<=> ! [X0,X11,X3] :
( hAPP(c_fequal(X0),X3) = hAPP(hAPP(c_COMBS(X0,tc_bool,tc_bool),hAPP(hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),X0),c_and),hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X3))),X11)
| ~ hBOOL(hAPP(X11,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_443])]) ).
fof(f806,plain,
! [X3,X0,X11] :
( hAPP(c_fequal(X0),X3) = hAPP(hAPP(c_COMBS(X0,tc_bool,tc_bool),hAPP(hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),X0),c_and),hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X3))),X11)
| ~ hBOOL(hAPP(X11,X3)) ),
inference(forward_demodulation,[],[f805,f723]) ).
fof(f805,plain,
! [X3,X0,X11] :
( hAPP(hAPP(c_COMBS(X0,tc_bool,tc_bool),hAPP(hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),X0),c_and),hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X3))),X11) = hAPP(hAPP(c_Set_Oinsert(X0),X3),c_COMBK(c_False,tc_bool,X0))
| ~ hBOOL(hAPP(X11,X3)) ),
inference(forward_demodulation,[],[f804,f698]) ).
fof(f804,plain,
! [X3,X0,X11] :
( hAPP(hAPP(c_Set_Oinsert(X0),X3),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))) = hAPP(hAPP(c_COMBS(X0,tc_bool,tc_bool),hAPP(hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),X0),c_and),hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X3))),X11)
| ~ hBOOL(hAPP(X11,X3)) ),
inference(forward_demodulation,[],[f575,f43]) ).
fof(f575,axiom,
! [X3,X0,X11] :
( ~ hBOOL(hAPP(X11,X3))
| hAPP(hAPP(c_Set_Oinsert(X0),X3),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))) = c_Collect(hAPP(hAPP(c_COMBS(X0,tc_bool,tc_bool),hAPP(hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),X0),c_and),hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X3))),X11),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Collect__conv__if_0) ).
fof(f9764,plain,
( spl0_442
| ~ spl0_5
| ~ spl0_101 ),
inference(avatar_split_clause,[],[f1556,f1488,f1037,f9762]) ).
fof(f9762,plain,
( spl0_442
<=> ! [X0] : c_Orderings_Otop__class_Otop(tc_bool) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),X0),c_Orderings_Otop__class_Otop(tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_442])]) ).
fof(f1556,plain,
( ! [X0] : c_Orderings_Otop__class_Otop(tc_bool) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),X0),c_Orderings_Otop__class_Otop(tc_bool))
| ~ spl0_5
| ~ spl0_101 ),
inference(resolution,[],[f1489,f1039]) ).
fof(f9353,plain,
spl0_441,
inference(avatar_split_clause,[],[f774,f9351]) ).
fof(f774,plain,
! [X3,X0,X9,X5] : hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X5),hAPP(hAPP(c_Set_Oinsert(X0),X3),X9)) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X5),hAPP(c_fequal(X0),X3))),X9),
inference(forward_demodulation,[],[f773,f723]) ).
fof(f773,plain,
! [X3,X0,X9,X5] : hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X5),hAPP(hAPP(c_Set_Oinsert(X0),X3),X9)) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X5),hAPP(hAPP(c_Set_Oinsert(X0),X3),c_COMBK(c_False,tc_bool,X0)))),X9),
inference(forward_demodulation,[],[f536,f698]) ).
fof(f536,axiom,
! [X3,X0,X9,X5] : hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X5),hAPP(hAPP(c_Set_Oinsert(X0),X3),X9)) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X5),hAPP(hAPP(c_Set_Oinsert(X0),X3),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))))),X9),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__insert2_0) ).
fof(f9349,plain,
spl0_440,
inference(avatar_split_clause,[],[f772,f9347]) ).
fof(f772,plain,
! [X3,X0,X9,X5] : hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X5),hAPP(hAPP(c_Set_Oinsert(X0),X3),X9)) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X5),X9)),hAPP(c_fequal(X0),X3)),
inference(forward_demodulation,[],[f771,f723]) ).
fof(f771,plain,
! [X3,X0,X9,X5] : hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X5),hAPP(hAPP(c_Set_Oinsert(X0),X3),X9)) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X5),X9)),hAPP(hAPP(c_Set_Oinsert(X0),X3),c_COMBK(c_False,tc_bool,X0))),
inference(forward_demodulation,[],[f537,f698]) ).
fof(f537,axiom,
! [X3,X0,X9,X5] : hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X5),hAPP(hAPP(c_Set_Oinsert(X0),X3),X9)) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X5),X9)),hAPP(hAPP(c_Set_Oinsert(X0),X3),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__insert_0) ).
fof(f9322,plain,
( spl0_439
| ~ spl0_16
| ~ spl0_406
| ~ spl0_438 ),
inference(avatar_split_clause,[],[f9318,f9315,f7160,f1090,f9320]) ).
fof(f9320,plain,
( spl0_439
<=> ! [X9,X5] : hAPP(hAPP(c_and,c_List_Olistsp(X5,v_x,t_a)),c_List_Olistsp(X9,v_x,t_a)) = c_List_Olistsp(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(t_a,tc_bool)),X5),X9),v_x,t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_439])]) ).
fof(f9315,plain,
( spl0_438
<=> ! [X9,X5] : c_List_Olistsp(hAPP(hAPP(c_COMBS(t_a,tc_bool,tc_bool),hAPP(hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),t_a),c_and),X5)),X9),v_x,t_a) = hAPP(hAPP(c_and,c_List_Olistsp(X5,v_x,t_a)),c_List_Olistsp(X9,v_x,t_a)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_438])]) ).
fof(f9318,plain,
( ! [X9,X5] : hAPP(hAPP(c_and,c_List_Olistsp(X5,v_x,t_a)),c_List_Olistsp(X9,v_x,t_a)) = c_List_Olistsp(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(t_a,tc_bool)),X5),X9),v_x,t_a)
| ~ spl0_16
| ~ spl0_406
| ~ spl0_438 ),
inference(forward_demodulation,[],[f9316,f7676]) ).
fof(f9316,plain,
( ! [X9,X5] : c_List_Olistsp(hAPP(hAPP(c_COMBS(t_a,tc_bool,tc_bool),hAPP(hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),t_a),c_and),X5)),X9),v_x,t_a) = hAPP(hAPP(c_and,c_List_Olistsp(X5,v_x,t_a)),c_List_Olistsp(X9,v_x,t_a))
| ~ spl0_438 ),
inference(avatar_component_clause,[],[f9315]) ).
fof(f9317,plain,
spl0_438,
inference(avatar_split_clause,[],[f516,f9315]) ).
fof(f516,axiom,
! [X9,X5] : c_List_Olistsp(hAPP(hAPP(c_COMBS(t_a,tc_bool,tc_bool),hAPP(hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),t_a),c_and),X5)),X9),v_x,t_a) = hAPP(hAPP(c_and,c_List_Olistsp(X5,v_x,t_a)),c_List_Olistsp(X9,v_x,t_a)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_listsp__conj__eq_0) ).
fof(f9313,plain,
spl0_437,
inference(avatar_split_clause,[],[f394,f9311]) ).
fof(f394,axiom,
! [X3,X0,X9,X5] : hAPP(hAPP(c_Set_Oinsert(X0),X3),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X5),X9)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Set_Oinsert(X0),X3),X5)),hAPP(hAPP(c_Set_Oinsert(X0),X3),X9)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__inter__insert_0) ).
fof(f9309,plain,
spl0_436,
inference(avatar_split_clause,[],[f332,f9307]) ).
fof(f9307,plain,
( spl0_436
<=> ! [X5,X0,X12,X9] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X5),X9)),X12))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X5),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X9),X12))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_436])]) ).
fof(f332,axiom,
! [X0,X9,X5,X12] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X5),X9)),X12))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X5),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X9),X12))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__subset__conv_0) ).
fof(f9305,plain,
spl0_435,
inference(avatar_split_clause,[],[f331,f9303]) ).
fof(f9303,plain,
( spl0_435
<=> ! [X9,X0,X12,X5] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X5),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X9),X12)))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X5),X9)),X12)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_435])]) ).
fof(f331,axiom,
! [X0,X9,X5,X12] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X5),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X9),X12)))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X5),X9)),X12)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__subset__conv_1) ).
fof(f9301,plain,
spl0_434,
inference(avatar_split_clause,[],[f319,f9299]) ).
fof(f9299,plain,
( spl0_434
<=> ! [X9,X0,X5,X1] :
( hBOOL(c_in(X1,X9,X0))
| hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Set_Oinsert(X0),X1),X5)),X9) = hAPP(hAPP(c_Set_Oinsert(X0),X1),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X5),X9)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_434])]) ).
fof(f319,axiom,
! [X0,X1,X9,X5] :
( hBOOL(c_in(X1,X9,X0))
| hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Set_Oinsert(X0),X1),X5)),X9) = hAPP(hAPP(c_Set_Oinsert(X0),X1),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X5),X9)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__Diff__if_1) ).
fof(f9297,plain,
spl0_433,
inference(avatar_split_clause,[],[f282,f9295]) ).
fof(f9295,plain,
( spl0_433
<=> ! [X9,X0,X5,X3] :
( ~ hBOOL(c_in(X3,X5,X0))
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X5),hAPP(hAPP(c_Set_Oinsert(X0),X3),X9)) = hAPP(hAPP(c_Set_Oinsert(X0),X3),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X5),X9)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_433])]) ).
fof(f282,axiom,
! [X3,X0,X9,X5] :
( ~ hBOOL(c_in(X3,X5,X0))
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X5),hAPP(hAPP(c_Set_Oinsert(X0),X3),X9)) = hAPP(hAPP(c_Set_Oinsert(X0),X3),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X5),X9)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__insert__right_0) ).
fof(f9293,plain,
spl0_432,
inference(avatar_split_clause,[],[f281,f9291]) ).
fof(f9291,plain,
( spl0_432
<=> ! [X0,X12,X9,X3] :
( ~ hBOOL(c_in(X3,X12,X0))
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Set_Oinsert(X0),X3),X9)),X12) = hAPP(hAPP(c_Set_Oinsert(X0),X3),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X9),X12)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_432])]) ).
fof(f281,axiom,
! [X3,X0,X9,X12] :
( ~ hBOOL(c_in(X3,X12,X0))
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Set_Oinsert(X0),X3),X9)),X12) = hAPP(hAPP(c_Set_Oinsert(X0),X3),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X9),X12)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__insert__left_0) ).
fof(f9208,plain,
( ~ spl0_7
| spl0_431
| ~ spl0_183
| ~ spl0_368 ),
inference(avatar_split_clause,[],[f6108,f6067,f1997,f9206,f1047]) ).
fof(f9206,plain,
( spl0_431
<=> ! [X0] : ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_bool),X0),c_False)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_431])]) ).
fof(f6108,plain,
( ! [X0] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_bool),X0),c_False))
| ~ class_Orderings_Opreorder(tc_bool) )
| ~ spl0_183
| ~ spl0_368 ),
inference(resolution,[],[f6068,f1998]) ).
fof(f8418,plain,
spl0_430,
inference(avatar_split_clause,[],[f460,f8416]) ).
fof(f8413,plain,
spl0_429,
inference(avatar_split_clause,[],[f130,f8411]) ).
fof(f130,axiom,
! [X0,X9,X5,X12] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X5),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X9),X12)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X5),X9)),X12),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__assoc_0) ).
fof(f8409,plain,
spl0_428,
inference(avatar_split_clause,[],[f129,f8407]) ).
fof(f129,axiom,
! [X0,X9,X5,X12] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X5),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X9),X12)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X9),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X5),X12)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__left__commute_0) ).
fof(f8405,plain,
spl0_427,
inference(avatar_split_clause,[],[f110,f8403]) ).
fof(f110,axiom,
! [X0,X9,X5,X12] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X5),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X9),X12)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X9),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X5),X12)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__left__commute_0) ).
fof(f8401,plain,
spl0_426,
inference(avatar_split_clause,[],[f109,f8399]) ).
fof(f8397,plain,
spl0_425,
inference(avatar_split_clause,[],[f83,f8395]) ).
fof(f8395,plain,
( spl0_425
<=> ! [X35,X4,X40,X0,X3] :
( ~ class_Orderings_Oorder(X0)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X3),X4))
| hBOOL(hAPP(hAPP(c_lessequals(X0),X35),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X3,X4,X0)),c_SetInterval_Oord__class_OatLeastAtMost(X35,X40,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_425])]) ).
fof(f83,axiom,
! [X40,X3,X0,X4,X35] :
( ~ class_Orderings_Oorder(X0)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X3),X4))
| hBOOL(hAPP(hAPP(c_lessequals(X0),X35),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X3,X4,X0)),c_SetInterval_Oord__class_OatLeastAtMost(X35,X40,X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastatMost__subset__iff_0) ).
fof(f8393,plain,
spl0_424,
inference(avatar_split_clause,[],[f82,f8391]) ).
fof(f8391,plain,
( spl0_424
<=> ! [X35,X4,X40,X0,X3] :
( ~ class_Orderings_Oorder(X0)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X3),X4))
| hBOOL(hAPP(hAPP(c_lessequals(X0),X4),X40))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X3,X4,X0)),c_SetInterval_Oord__class_OatLeastAtMost(X35,X40,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_424])]) ).
fof(f82,axiom,
! [X40,X3,X0,X4,X35] :
( ~ class_Orderings_Oorder(X0)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X3),X4))
| hBOOL(hAPP(hAPP(c_lessequals(X0),X4),X40))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X3,X4,X0)),c_SetInterval_Oord__class_OatLeastAtMost(X35,X40,X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastatMost__subset__iff_1) ).
fof(f8389,plain,
spl0_423,
inference(avatar_split_clause,[],[f81,f8387]) ).
fof(f8387,plain,
( spl0_423
<=> ! [X35,X4,X40,X0,X3] :
( ~ class_Orderings_Oorder(X0)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X35),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X4),X40))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X3,X4,X0)),c_SetInterval_Oord__class_OatLeastAtMost(X35,X40,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_423])]) ).
fof(f81,axiom,
! [X40,X3,X0,X4,X35] :
( ~ class_Orderings_Oorder(X0)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X35),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X4),X40))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X3,X4,X0)),c_SetInterval_Oord__class_OatLeastAtMost(X35,X40,X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastatMost__subset__iff_3) ).
fof(f8385,plain,
spl0_422,
inference(avatar_split_clause,[],[f64,f8383]) ).
fof(f64,axiom,
! [X0,X36,X1,X8,X9,X5] :
( ~ hBOOL(c_in(X1,X36,X8))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),hAPP(X5,X1)),X9))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X36,X5,X8,tc_fun(X0,tc_bool))),X9)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UN__subset__iff_0) ).
fof(f8381,plain,
spl0_421,
inference(avatar_split_clause,[],[f62,f8379]) ).
fof(f8379,plain,
( spl0_421
<=> ! [X5,X19,X0,X36,X9,X8] :
( ~ hBOOL(c_in(X19,X36,X8))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X9),hAPP(X5,X19)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X9),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X36,X5,X8,tc_fun(X0,tc_bool)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_421])]) ).
fof(f62,axiom,
! [X0,X36,X8,X19,X9,X5] :
( ~ hBOOL(c_in(X19,X36,X8))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X9),hAPP(X5,X19)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X9),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X36,X5,X8,tc_fun(X0,tc_bool)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_INT__subset__iff_0) ).
fof(f8346,plain,
spl0_420,
inference(avatar_split_clause,[],[f303,f8344]) ).
fof(f8344,plain,
( spl0_420
<=> ! [X0,X6,X2,X1] :
( ~ class_Lattices_Odistrib__lattice(X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X6)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X6)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_420])]) ).
fof(f303,axiom,
! [X2,X0,X1,X6] :
( ~ class_Lattices_Odistrib__lattice(X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X6)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X6)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__inf__distrib1_0) ).
fof(f8342,plain,
spl0_419,
inference(avatar_split_clause,[],[f302,f8340]) ).
fof(f8340,plain,
( spl0_419
<=> ! [X0,X6,X2,X1] :
( ~ class_Lattices_Odistrib__lattice(X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X6)),X1) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X2),X1)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X6),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_419])]) ).
fof(f302,axiom,
! [X2,X0,X1,X6] :
( ~ class_Lattices_Odistrib__lattice(X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X6)),X1) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X2),X1)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X6),X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__inf__distrib2_0) ).
fof(f8338,plain,
spl0_418,
inference(avatar_split_clause,[],[f13,f8336]) ).
fof(f8336,plain,
( spl0_418
<=> ! [X0,X6,X2,X1] :
( ~ class_Lattices_Odistrib__lattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X2),X6)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X6)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_418])]) ).
fof(f13,axiom,
! [X2,X0,X1,X6] :
( ~ class_Lattices_Odistrib__lattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X2),X6)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X6)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__distrib1_0) ).
fof(f8334,plain,
spl0_417,
inference(avatar_split_clause,[],[f12,f8332]) ).
fof(f8332,plain,
( spl0_417
<=> ! [X0,X6,X2,X1] :
( ~ class_Lattices_Odistrib__lattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X2),X6)),X1) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X1)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X6),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_417])]) ).
fof(f12,axiom,
! [X2,X0,X1,X6] :
( ~ class_Lattices_Odistrib__lattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X2),X6)),X1) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X1)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X6),X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__distrib2_0) ).
fof(f7850,plain,
( spl0_416
| ~ spl0_16
| ~ spl0_406
| ~ spl0_415 ),
inference(avatar_split_clause,[],[f7846,f7843,f7160,f1090,f7848]) ).
fof(f7843,plain,
( spl0_415
<=> ! [X0,X11,X3] :
( c_COMBK(c_False,tc_bool,X0) = hAPP(hAPP(c_COMBS(X0,tc_bool,tc_bool),hAPP(hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),X0),c_and),hAPP(c_fequal(X0),X3))),X11)
| hBOOL(hAPP(X11,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_415])]) ).
fof(f7846,plain,
( ! [X3,X0,X11] :
( c_COMBK(c_False,tc_bool,X0) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),hAPP(c_fequal(X0),X3)),X11)
| hBOOL(hAPP(X11,X3)) )
| ~ spl0_16
| ~ spl0_406
| ~ spl0_415 ),
inference(forward_demodulation,[],[f7844,f7676]) ).
fof(f7844,plain,
( ! [X3,X0,X11] :
( c_COMBK(c_False,tc_bool,X0) = hAPP(hAPP(c_COMBS(X0,tc_bool,tc_bool),hAPP(hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),X0),c_and),hAPP(c_fequal(X0),X3))),X11)
| hBOOL(hAPP(X11,X3)) )
| ~ spl0_415 ),
inference(avatar_component_clause,[],[f7843]) ).
fof(f7845,plain,
spl0_415,
inference(avatar_split_clause,[],[f810,f7843]) ).
fof(f810,plain,
! [X3,X0,X11] :
( c_COMBK(c_False,tc_bool,X0) = hAPP(hAPP(c_COMBS(X0,tc_bool,tc_bool),hAPP(hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),X0),c_and),hAPP(c_fequal(X0),X3))),X11)
| hBOOL(hAPP(X11,X3)) ),
inference(forward_demodulation,[],[f809,f698]) ).
fof(f809,plain,
! [X3,X0,X11] :
( c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = hAPP(hAPP(c_COMBS(X0,tc_bool,tc_bool),hAPP(hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),X0),c_and),hAPP(c_fequal(X0),X3))),X11)
| hBOOL(hAPP(X11,X3)) ),
inference(forward_demodulation,[],[f583,f43]) ).
fof(f583,axiom,
! [X3,X0,X11] :
( hBOOL(hAPP(X11,X3))
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_Collect(hAPP(hAPP(c_COMBS(X0,tc_bool,tc_bool),hAPP(hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),X0),c_and),hAPP(c_fequal(X0),X3))),X11),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Collect__conv__if2_1) ).
fof(f7706,plain,
( spl0_414
| ~ spl0_16
| ~ spl0_406
| ~ spl0_413 ),
inference(avatar_split_clause,[],[f7702,f7699,f7160,f1090,f7704]) ).
fof(f7699,plain,
( spl0_413
<=> ! [X0,X11,X3] :
( hAPP(c_fequal(X0),X3) = hAPP(hAPP(c_COMBS(X0,tc_bool,tc_bool),hAPP(hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),X0),c_and),hAPP(c_fequal(X0),X3))),X11)
| ~ hBOOL(hAPP(X11,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_413])]) ).
fof(f7702,plain,
( ! [X3,X0,X11] :
( hAPP(c_fequal(X0),X3) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),hAPP(c_fequal(X0),X3)),X11)
| ~ hBOOL(hAPP(X11,X3)) )
| ~ spl0_16
| ~ spl0_406
| ~ spl0_413 ),
inference(forward_demodulation,[],[f7700,f7676]) ).
fof(f7700,plain,
( ! [X3,X0,X11] :
( hAPP(c_fequal(X0),X3) = hAPP(hAPP(c_COMBS(X0,tc_bool,tc_bool),hAPP(hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),X0),c_and),hAPP(c_fequal(X0),X3))),X11)
| ~ hBOOL(hAPP(X11,X3)) )
| ~ spl0_413 ),
inference(avatar_component_clause,[],[f7699]) ).
fof(f7701,plain,
spl0_413,
inference(avatar_split_clause,[],[f803,f7699]) ).
fof(f803,plain,
! [X3,X0,X11] :
( hAPP(c_fequal(X0),X3) = hAPP(hAPP(c_COMBS(X0,tc_bool,tc_bool),hAPP(hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),X0),c_and),hAPP(c_fequal(X0),X3))),X11)
| ~ hBOOL(hAPP(X11,X3)) ),
inference(forward_demodulation,[],[f802,f723]) ).
fof(f802,plain,
! [X3,X0,X11] :
( hAPP(hAPP(c_COMBS(X0,tc_bool,tc_bool),hAPP(hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),X0),c_and),hAPP(c_fequal(X0),X3))),X11) = hAPP(hAPP(c_Set_Oinsert(X0),X3),c_COMBK(c_False,tc_bool,X0))
| ~ hBOOL(hAPP(X11,X3)) ),
inference(forward_demodulation,[],[f801,f698]) ).
fof(f801,plain,
! [X3,X0,X11] :
( hAPP(hAPP(c_Set_Oinsert(X0),X3),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))) = hAPP(hAPP(c_COMBS(X0,tc_bool,tc_bool),hAPP(hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),X0),c_and),hAPP(c_fequal(X0),X3))),X11)
| ~ hBOOL(hAPP(X11,X3)) ),
inference(forward_demodulation,[],[f586,f43]) ).
fof(f586,axiom,
! [X3,X0,X11] :
( ~ hBOOL(hAPP(X11,X3))
| hAPP(hAPP(c_Set_Oinsert(X0),X3),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))) = c_Collect(hAPP(hAPP(c_COMBS(X0,tc_bool,tc_bool),hAPP(hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),X0),c_and),hAPP(c_fequal(X0),X3))),X11),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Collect__conv__if2_0) ).
fof(f7697,plain,
spl0_412,
inference(avatar_split_clause,[],[f497,f7695]) ).
fof(f497,axiom,
! [X3,X0,X8,X9,X5] : c_Complete__Lattice_Ocomplete__lattice__class_OINFI(hAPP(hAPP(c_Set_Oinsert(X8),X3),X5),X9,X8,tc_fun(X0,tc_bool)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),hAPP(X9,X3)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,X9,X8,tc_fun(X0,tc_bool))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_INT__insert_0) ).
fof(f7693,plain,
spl0_411,
inference(avatar_split_clause,[],[f467,f7691]) ).
fof(f7691,plain,
( spl0_411
<=> ! [X5,X37,X0,X36,X8] :
( ~ hBOOL(c_in(X37,X36,X0))
| c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X36,X5,X0,tc_fun(X8,tc_bool)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X8,tc_bool)),hAPP(X5,X37)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X36,X5,X0,tc_fun(X8,tc_bool))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_411])]) ).
fof(f467,axiom,
! [X0,X36,X37,X8,X5] :
( ~ hBOOL(c_in(X37,X36,X0))
| c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X36,X5,X0,tc_fun(X8,tc_bool)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X8,tc_bool)),hAPP(X5,X37)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X36,X5,X0,tc_fun(X8,tc_bool))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_INT__absorb_0) ).
fof(f7689,plain,
spl0_410,
inference(avatar_split_clause,[],[f275,f7687]) ).
fof(f275,axiom,
! [X3,X0,X8,X9,X5] : c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_Set_Oinsert(X8),X3),X5),X9,X8,tc_fun(X0,tc_bool)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),hAPP(X9,X3)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,X9,X8,tc_fun(X0,tc_bool))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UN__insert_0) ).
fof(f7685,plain,
( spl0_409
| ~ spl0_227
| ~ spl0_261 ),
inference(avatar_split_clause,[],[f6025,f3113,f2580,f7683]) ).
fof(f7683,plain,
( spl0_409
<=> ! [X0] : c_SetInterval_Oord__class_OatLeastAtMost(X0,X0,tc_bool) != c_COMBK(c_False,tc_bool,tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_409])]) ).
fof(f6025,plain,
( ! [X0] : c_SetInterval_Oord__class_OatLeastAtMost(X0,X0,tc_bool) != c_COMBK(c_False,tc_bool,tc_bool)
| ~ spl0_227
| ~ spl0_261 ),
inference(superposition,[],[f3114,f2581]) ).
fof(f7681,plain,
spl0_408,
inference(avatar_split_clause,[],[f71,f7679]) ).
fof(f7679,plain,
( spl0_408
<=> ! [X5,X37,X0,X36,X8] :
( ~ hBOOL(c_in(X37,X36,X0))
| c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X36,X5,X0,tc_fun(X8,tc_bool)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X8,tc_bool)),hAPP(X5,X37)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X36,X5,X0,tc_fun(X8,tc_bool))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_408])]) ).
fof(f71,axiom,
! [X0,X36,X37,X8,X5] :
( ~ hBOOL(c_in(X37,X36,X0))
| c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X36,X5,X0,tc_fun(X8,tc_bool)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X8,tc_bool)),hAPP(X5,X37)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X36,X5,X0,tc_fun(X8,tc_bool))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UN__absorb_0) ).
fof(f7244,plain,
( spl0_407
| ~ spl0_222
| ~ spl0_227 ),
inference(avatar_split_clause,[],[f3965,f2580,f2287,f7242]) ).
fof(f7242,plain,
( spl0_407
<=> ! [X0] : hAPP(c_Complete__Lattice_OSup__class_OSup(tc_bool),c_SetInterval_Oord__class_OatLeastAtMost(X0,X0,tc_bool)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_407])]) ).
fof(f2287,plain,
( spl0_222
<=> ! [X0] : hAPP(c_Complete__Lattice_OSup__class_OSup(tc_bool),hAPP(c_fequal(tc_bool),X0)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_222])]) ).
fof(f3965,plain,
( ! [X0] : hAPP(c_Complete__Lattice_OSup__class_OSup(tc_bool),c_SetInterval_Oord__class_OatLeastAtMost(X0,X0,tc_bool)) = X0
| ~ spl0_222
| ~ spl0_227 ),
inference(superposition,[],[f2288,f2581]) ).
fof(f2288,plain,
( ! [X0] : hAPP(c_Complete__Lattice_OSup__class_OSup(tc_bool),hAPP(c_fequal(tc_bool),X0)) = X0
| ~ spl0_222 ),
inference(avatar_component_clause,[],[f2287]) ).
fof(f7162,plain,
spl0_406,
inference(avatar_split_clause,[],[f768,f7160]) ).
fof(f768,plain,
! [X0,X11,X57] : c_Collect(hAPP(hAPP(c_COMBS(X0,tc_bool,tc_bool),hAPP(hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),X0),c_and),X11)),X57),X0) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X11),X57),
inference(forward_demodulation,[],[f767,f43]) ).
fof(f767,plain,
! [X0,X11,X57] : c_Collect(hAPP(hAPP(c_COMBS(X0,tc_bool,tc_bool),hAPP(hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),X0),c_and),X11)),X57),X0) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),c_Collect(X11,X0)),X57),
inference(forward_demodulation,[],[f519,f43]) ).
fof(f519,axiom,
! [X0,X11,X57] : c_Collect(hAPP(hAPP(c_COMBS(X0,tc_bool,tc_bool),hAPP(hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),X0),c_and),X11)),X57),X0) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),c_Collect(X11,X0)),c_Collect(X57,X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Collect__conj__eq_0) ).
fof(f7158,plain,
spl0_405,
inference(avatar_split_clause,[],[f766,f7156]) ).
fof(f766,plain,
! [X0,X11,X57] : c_Collect(hAPP(hAPP(c_COMBS(X0,tc_bool,tc_bool),hAPP(hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),X0),c_or),X11)),X57),X0) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X11),X57),
inference(forward_demodulation,[],[f765,f43]) ).
fof(f765,plain,
! [X0,X11,X57] : c_Collect(hAPP(hAPP(c_COMBS(X0,tc_bool,tc_bool),hAPP(hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),X0),c_or),X11)),X57),X0) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),c_Collect(X11,X0)),X57),
inference(forward_demodulation,[],[f409,f43]) ).
fof(f409,axiom,
! [X0,X11,X57] : c_Collect(hAPP(hAPP(c_COMBS(X0,tc_bool,tc_bool),hAPP(hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),X0),c_or),X11)),X57),X0) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),c_Collect(X11,X0)),c_Collect(X57,X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Collect__disj__eq_0) ).
fof(f7154,plain,
spl0_404,
inference(avatar_split_clause,[],[f580,f7152]) ).
fof(f580,axiom,
! [X0,X11,X57,X66] : c_List_Ofilter(X11,c_List_Ofilter(X57,X66,X0),X0) = c_List_Ofilter(hAPP(hAPP(c_COMBS(X0,tc_bool,tc_bool),hAPP(hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),X0),c_and),X57)),X11),X66,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_filter__filter_0) ).
fof(f7150,plain,
spl0_403,
inference(avatar_split_clause,[],[f472,f7148]) ).
fof(f7148,plain,
( spl0_403
<=> ! [X0] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
| c_Complete__Lattice_Ocomplete__lattice(c_Complete__Lattice_OSup__class_OSup(X0),c_Complete__Lattice_OInf__class_OInf(X0),c_COMBC(c_lessequals(X0),X0,X0,tc_bool),c_COMBC(c_HOL_Oord__class_Oless(X0),X0,X0,tc_bool),c_Lattices_Oupper__semilattice__class_Osup(X0),c_Lattices_Olower__semilattice__class_Oinf(X0),c_Orderings_Otop__class_Otop(X0),c_Orderings_Obot__class_Obot(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_403])]) ).
fof(f472,axiom,
! [X0] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
| c_Complete__Lattice_Ocomplete__lattice(c_Complete__Lattice_OSup__class_OSup(X0),c_Complete__Lattice_OInf__class_OInf(X0),c_COMBC(c_lessequals(X0),X0,X0,tc_bool),c_COMBC(c_HOL_Oord__class_Oless(X0),X0,X0,tc_bool),c_Lattices_Oupper__semilattice__class_Osup(X0),c_Lattices_Olower__semilattice__class_Oinf(X0),c_Orderings_Otop__class_Otop(X0),c_Orderings_Obot__class_Obot(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dual__complete__lattice_0) ).
fof(f7146,plain,
spl0_402,
inference(avatar_split_clause,[],[f470,f7144]) ).
fof(f470,axiom,
! [X59,X0,X1,X8,X54,X7,X14,X60,X42,X61,X13] :
( hAPP(X7,hAPP(X13,X1)) != hAPP(X59,hAPP(X60,X42))
| hAPP(c_Fun_Ocomp(X7,X13,X8,X0,X14),X1) = hAPP(c_Fun_Ocomp(X59,X60,X54,X0,X61),X42) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comp__cong_0) ).
fof(f7142,plain,
spl0_401,
inference(avatar_split_clause,[],[f384,f7140]) ).
fof(f384,axiom,
! [X51,X3,X0,X12] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X12),X51))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Set_Oinsert(X0),X3),X12)),hAPP(hAPP(c_Set_Oinsert(X0),X3),X51))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__mono_0) ).
fof(f7138,plain,
spl0_400,
inference(avatar_split_clause,[],[f307,f7136]) ).
fof(f307,axiom,
! [X0,X1,X9,X5] :
( ~ hBOOL(c_in(X1,X9,X0))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X5),X9))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Set_Oinsert(X0),X1),X5)),X9)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__subset_2) ).
fof(f7134,plain,
spl0_399,
inference(avatar_split_clause,[],[f287,f7132]) ).
fof(f7132,plain,
( spl0_399
<=> ! [X0,X6,X2,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X6))
| hBOOL(hAPP(hAPP(c_lessequals(X0),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X6))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_399])]) ).
fof(f287,axiom,
! [X2,X0,X1,X6] :
( ~ class_Lattices_Olower__semilattice(X0)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X6))
| hBOOL(hAPP(hAPP(c_lessequals(X0),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X6))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__greatest_0) ).
fof(f7130,plain,
( spl0_398
| ~ spl0_226
| ~ spl0_227 ),
inference(avatar_split_clause,[],[f3964,f2580,f2366,f7128]) ).
fof(f7128,plain,
( spl0_398
<=> ! [X0] : hAPP(c_Complete__Lattice_OInf__class_OInf(tc_bool),c_SetInterval_Oord__class_OatLeastAtMost(X0,X0,tc_bool)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_398])]) ).
fof(f2366,plain,
( spl0_226
<=> ! [X0] : hAPP(c_Complete__Lattice_OInf__class_OInf(tc_bool),hAPP(c_fequal(tc_bool),X0)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_226])]) ).
fof(f3964,plain,
( ! [X0] : hAPP(c_Complete__Lattice_OInf__class_OInf(tc_bool),c_SetInterval_Oord__class_OatLeastAtMost(X0,X0,tc_bool)) = X0
| ~ spl0_226
| ~ spl0_227 ),
inference(superposition,[],[f2367,f2581]) ).
fof(f2367,plain,
( ! [X0] : hAPP(c_Complete__Lattice_OInf__class_OInf(tc_bool),hAPP(c_fequal(tc_bool),X0)) = X0
| ~ spl0_226 ),
inference(avatar_component_clause,[],[f2366]) ).
fof(f7126,plain,
spl0_397,
inference(avatar_split_clause,[],[f176,f7124]) ).
fof(f7124,plain,
( spl0_397
<=> ! [X9,X0,X5,X1] :
( hBOOL(c_in(X1,X5,X0))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X5),X9))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X5),hAPP(hAPP(c_Set_Oinsert(X0),X1),X9))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_397])]) ).
fof(f176,axiom,
! [X0,X1,X9,X5] :
( hBOOL(c_in(X1,X5,X0))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X5),X9))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X5),hAPP(hAPP(c_Set_Oinsert(X0),X1),X9))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insert_0) ).
fof(f7122,plain,
spl0_396,
inference(avatar_split_clause,[],[f160,f7120]) ).
fof(f7120,plain,
( spl0_396
<=> ! [X21,X0,X26,X27,X24,X22,X25,X23,X20] :
( ~ c_Complete__Lattice_Ocomplete__lattice(X22,X20,X23,X24,X25,X26,X27,X21,X0)
| c_Complete__Lattice_Ocomplete__lattice(X20,X22,c_COMBC(X23,X0,X0,tc_bool),c_COMBC(X24,X0,X0,tc_bool),X26,X25,X21,X27,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_396])]) ).
fof(f160,axiom,
! [X21,X0,X26,X27,X24,X22,X25,X23,X20] :
( ~ c_Complete__Lattice_Ocomplete__lattice(X22,X20,X23,X24,X25,X26,X27,X21,X0)
| c_Complete__Lattice_Ocomplete__lattice(X20,X22,c_COMBC(X23,X0,X0,tc_bool),c_COMBC(X24,X0,X0,tc_bool),X26,X25,X21,X27,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complete__lattice_Odual__complete__lattice_0) ).
fof(f7118,plain,
spl0_395,
inference(avatar_split_clause,[],[f150,f7116]) ).
fof(f7116,plain,
( spl0_395
<=> ! [X4,X0,X3,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X3),X1))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X4),X1))
| hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X3),X4)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_395])]) ).
fof(f150,axiom,
! [X3,X0,X1,X4] :
( ~ class_Lattices_Oupper__semilattice(X0)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X3),X1))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X4),X1))
| hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X3),X4)),X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__supI_0) ).
fof(f6774,plain,
spl0_394,
inference(avatar_split_clause,[],[f870,f6772]) ).
fof(f6772,plain,
( spl0_394
<=> ! [X21,X3,X0,X26,X27,X4,X24,X22,X25,X23,X20] :
( hAPP(hAPP(X25,X3),X4) = hAPP(X22,hAPP(hAPP(c_Set_Oinsert(X0),X3),hAPP(c_fequal(X0),X4)))
| ~ c_Complete__Lattice_Ocomplete__lattice(X22,X20,X23,X24,X25,X26,X27,X21,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_394])]) ).
fof(f870,plain,
! [X21,X3,X0,X26,X27,X4,X24,X22,X25,X23,X20] :
( hAPP(hAPP(X25,X3),X4) = hAPP(X22,hAPP(hAPP(c_Set_Oinsert(X0),X3),hAPP(c_fequal(X0),X4)))
| ~ c_Complete__Lattice_Ocomplete__lattice(X22,X20,X23,X24,X25,X26,X27,X21,X0) ),
inference(forward_demodulation,[],[f869,f723]) ).
fof(f869,plain,
! [X21,X3,X0,X26,X27,X4,X24,X22,X25,X23,X20] :
( hAPP(hAPP(X25,X3),X4) = hAPP(X22,hAPP(hAPP(c_Set_Oinsert(X0),X3),hAPP(hAPP(c_Set_Oinsert(X0),X4),c_COMBK(c_False,tc_bool,X0))))
| ~ c_Complete__Lattice_Ocomplete__lattice(X22,X20,X23,X24,X25,X26,X27,X21,X0) ),
inference(forward_demodulation,[],[f534,f698]) ).
fof(f534,axiom,
! [X21,X3,X0,X26,X27,X4,X24,X22,X25,X23,X20] :
( ~ c_Complete__Lattice_Ocomplete__lattice(X22,X20,X23,X24,X25,X26,X27,X21,X0)
| hAPP(X22,hAPP(hAPP(c_Set_Oinsert(X0),X3),hAPP(hAPP(c_Set_Oinsert(X0),X4),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))))) = hAPP(hAPP(X25,X3),X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complete__lattice_OInf__binary_0) ).
fof(f6770,plain,
spl0_393,
inference(avatar_split_clause,[],[f868,f6768]) ).
fof(f6768,plain,
( spl0_393
<=> ! [X21,X3,X0,X26,X27,X4,X24,X22,X25,X23,X20] :
( hAPP(hAPP(X26,X3),X4) = hAPP(X20,hAPP(hAPP(c_Set_Oinsert(X0),X3),hAPP(c_fequal(X0),X4)))
| ~ c_Complete__Lattice_Ocomplete__lattice(X22,X20,X23,X24,X25,X26,X27,X21,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_393])]) ).
fof(f868,plain,
! [X21,X3,X0,X26,X27,X4,X24,X22,X25,X23,X20] :
( hAPP(hAPP(X26,X3),X4) = hAPP(X20,hAPP(hAPP(c_Set_Oinsert(X0),X3),hAPP(c_fequal(X0),X4)))
| ~ c_Complete__Lattice_Ocomplete__lattice(X22,X20,X23,X24,X25,X26,X27,X21,X0) ),
inference(forward_demodulation,[],[f867,f723]) ).
fof(f867,plain,
! [X21,X3,X0,X26,X27,X4,X24,X22,X25,X23,X20] :
( hAPP(hAPP(X26,X3),X4) = hAPP(X20,hAPP(hAPP(c_Set_Oinsert(X0),X3),hAPP(hAPP(c_Set_Oinsert(X0),X4),c_COMBK(c_False,tc_bool,X0))))
| ~ c_Complete__Lattice_Ocomplete__lattice(X22,X20,X23,X24,X25,X26,X27,X21,X0) ),
inference(forward_demodulation,[],[f535,f698]) ).
fof(f535,axiom,
! [X21,X3,X0,X26,X27,X4,X24,X22,X25,X23,X20] :
( ~ c_Complete__Lattice_Ocomplete__lattice(X22,X20,X23,X24,X25,X26,X27,X21,X0)
| hAPP(X20,hAPP(hAPP(c_Set_Oinsert(X0),X3),hAPP(hAPP(c_Set_Oinsert(X0),X4),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))))) = hAPP(hAPP(X26,X3),X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complete__lattice_OSup__binary_0) ).
fof(f6766,plain,
spl0_392,
inference(avatar_split_clause,[],[f442,f6764]) ).
fof(f442,axiom,
! [X0,X9,X5,X12] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X5),X9))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X9),X12))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X5),X12)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__trans_0) ).
fof(f6762,plain,
spl0_391,
inference(avatar_split_clause,[],[f396,f6760]) ).
fof(f6758,plain,
spl0_390,
inference(avatar_split_clause,[],[f395,f6756]) ).
fof(f395,axiom,
! [X3,X0,X9,X5] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X5),hAPP(hAPP(c_Set_Oinsert(X0),X3),X9)) = hAPP(hAPP(c_Set_Oinsert(X0),X3),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X5),X9)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__insert__right_0) ).
fof(f6754,plain,
spl0_389,
inference(avatar_split_clause,[],[f178,f6752]) ).
fof(f178,axiom,
! [X3,X0,X9,X12] :
( hBOOL(c_in(X3,X12,X0))
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X9),X12) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Set_Oinsert(X0),X3),X9)),X12) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__insert__left_1) ).
fof(f6750,plain,
spl0_388,
inference(avatar_split_clause,[],[f177,f6748]) ).
fof(f177,axiom,
! [X3,X0,X9,X5] :
( hBOOL(c_in(X3,X5,X0))
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X5),X9) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X5),hAPP(hAPP(c_Set_Oinsert(X0),X3),X9)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__insert__right_1) ).
fof(f6746,plain,
spl0_387,
inference(avatar_split_clause,[],[f34,f6744]) ).
fof(f34,axiom,
! [X0,X1,X9,X5] :
( ~ hBOOL(c_in(X1,X9,X0))
| hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X5),X9) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Set_Oinsert(X0),X1),X5)),X9) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__Diff1_0) ).
fof(f6680,plain,
( ~ spl0_5
| spl0_385
| ~ spl0_386
| ~ spl0_118
| ~ spl0_159 ),
inference(avatar_split_clause,[],[f1921,f1822,f1576,f6677,f6674,f1037]) ).
fof(f6674,plain,
( spl0_385
<=> ! [X0] : c_False = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_385])]) ).
fof(f6677,plain,
( spl0_386
<=> c_False = c_Orderings_Otop__class_Otop(tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_386])]) ).
fof(f1921,plain,
( ! [X0] :
( c_False != c_Orderings_Otop__class_Otop(tc_bool)
| c_False = X0
| ~ class_Lattices_Obounded__lattice(tc_bool) )
| ~ spl0_118
| ~ spl0_159 ),
inference(inner_rewriting,[],[f1916]) ).
fof(f1916,plain,
( ! [X0] :
( c_False != c_Orderings_Otop__class_Otop(tc_bool)
| c_Orderings_Otop__class_Otop(tc_bool) = X0
| ~ class_Lattices_Obounded__lattice(tc_bool) )
| ~ spl0_118
| ~ spl0_159 ),
inference(superposition,[],[f1823,f1577]) ).
fof(f6534,plain,
spl0_384,
inference(avatar_split_clause,[],[f882,f6532]) ).
fof(f882,plain,
! [X39,X11,X57,X35] :
( c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X11,X35,X57,t_a)),t_a)
| hBOOL(hAPP(hAPP(X11,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1(X39,X11,X57,X35)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(X39,X11,X57,X35))) ),
inference(forward_demodulation,[],[f881,f723]) ).
fof(f881,plain,
! [X39,X11,X57,X35] :
( c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X11,X35,X57,t_a)),c_COMBK(c_False,tc_bool,tc_Hoare__Mirabelle_Otriple(t_a))),t_a)
| hBOOL(hAPP(hAPP(X11,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1(X39,X11,X57,X35)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(X39,X11,X57,X35))) ),
inference(forward_demodulation,[],[f564,f698]) ).
fof(f564,axiom,
! [X39,X11,X57,X35] :
( hBOOL(hAPP(hAPP(X11,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1(X39,X11,X57,X35)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(X39,X11,X57,X35)))
| c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X11,X35,X57,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_hoare__derivs_Ointros_I6_J_0) ).
fof(f6530,plain,
spl0_383,
inference(avatar_split_clause,[],[f880,f6528]) ).
fof(f880,plain,
! [X39,X11,X57,X35] :
( c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X11,X35,X57,t_a)),t_a)
| hBOOL(hAPP(hAPP(X11,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1(X39,X11,X57,X35)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2(X39,X11,X57,X35))) ),
inference(forward_demodulation,[],[f879,f723]) ).
fof(f879,plain,
! [X39,X11,X57,X35] :
( c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X11,X35,X57,t_a)),c_COMBK(c_False,tc_bool,tc_Hoare__Mirabelle_Otriple(t_a))),t_a)
| hBOOL(hAPP(hAPP(X11,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1(X39,X11,X57,X35)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2(X39,X11,X57,X35))) ),
inference(forward_demodulation,[],[f566,f698]) ).
fof(f566,axiom,
! [X39,X11,X57,X35] :
( hBOOL(hAPP(hAPP(X11,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1(X39,X11,X57,X35)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2(X39,X11,X57,X35)))
| c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X11,X35,X57,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conseq_0) ).
fof(f6526,plain,
spl0_382,
inference(avatar_split_clause,[],[f878,f6524]) ).
fof(f878,plain,
! [X39,X11,X57,X35] :
( c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X11,X35,X57,t_a)),t_a)
| hBOOL(hAPP(hAPP(X11,v_sko__Hoare__Mirabelle__Xescape__1(X39,X11,X57,X35)),v_sko__Hoare__Mirabelle__Xescape__2(X39,X11,X57,X35))) ),
inference(forward_demodulation,[],[f877,f723]) ).
fof(f877,plain,
! [X39,X11,X57,X35] :
( c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X11,X35,X57,t_a)),c_COMBK(c_False,tc_bool,tc_Hoare__Mirabelle_Otriple(t_a))),t_a)
| hBOOL(hAPP(hAPP(X11,v_sko__Hoare__Mirabelle__Xescape__1(X39,X11,X57,X35)),v_sko__Hoare__Mirabelle__Xescape__2(X39,X11,X57,X35))) ),
inference(forward_demodulation,[],[f574,f698]) ).
fof(f574,axiom,
! [X39,X11,X57,X35] :
( hBOOL(hAPP(hAPP(X11,v_sko__Hoare__Mirabelle__Xescape__1(X39,X11,X57,X35)),v_sko__Hoare__Mirabelle__Xescape__2(X39,X11,X57,X35)))
| c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X11,X35,X57,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_escape_0) ).
fof(f6522,plain,
spl0_381,
inference(avatar_split_clause,[],[f403,f6520]) ).
fof(f6520,plain,
( spl0_381
<=> ! [X5,X0,X9,X1] :
( X5 = X9
| hBOOL(c_in(X1,X5,X0))
| hBOOL(c_in(X1,X9,X0))
| hAPP(hAPP(c_Set_Oinsert(X0),X1),X9) != hAPP(hAPP(c_Set_Oinsert(X0),X1),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_381])]) ).
fof(f403,axiom,
! [X0,X1,X9,X5] :
( X5 = X9
| hBOOL(c_in(X1,X5,X0))
| hBOOL(c_in(X1,X9,X0))
| hAPP(hAPP(c_Set_Oinsert(X0),X1),X9) != hAPP(hAPP(c_Set_Oinsert(X0),X1),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__ident_0) ).
fof(f6518,plain,
spl0_380,
inference(avatar_split_clause,[],[f389,f6516]) ).
fof(f6516,plain,
( spl0_380
<=> ! [X21,X3,X0,X26,X27,X24,X22,X25,X23,X20,X5] :
( ~ c_Complete__Lattice_Ocomplete__lattice(X22,X20,X23,X24,X25,X26,X27,X21,X0)
| hAPP(X20,hAPP(hAPP(c_Set_Oinsert(X0),X3),X5)) = hAPP(hAPP(X26,X3),hAPP(X20,X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_380])]) ).
fof(f389,axiom,
! [X21,X3,X0,X26,X27,X24,X22,X25,X23,X5,X20] :
( ~ c_Complete__Lattice_Ocomplete__lattice(X22,X20,X23,X24,X25,X26,X27,X21,X0)
| hAPP(X20,hAPP(hAPP(c_Set_Oinsert(X0),X3),X5)) = hAPP(hAPP(X26,X3),hAPP(X20,X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complete__lattice_OSup__insert_0) ).
fof(f6495,plain,
spl0_379,
inference(avatar_split_clause,[],[f388,f6493]) ).
fof(f6493,plain,
( spl0_379
<=> ! [X21,X3,X0,X26,X27,X24,X22,X25,X23,X20,X5] :
( ~ c_Complete__Lattice_Ocomplete__lattice(X22,X20,X23,X24,X25,X26,X27,X21,X0)
| hAPP(X22,hAPP(hAPP(c_Set_Oinsert(X0),X3),X5)) = hAPP(hAPP(X25,X3),hAPP(X22,X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_379])]) ).
fof(f388,axiom,
! [X21,X3,X0,X26,X27,X24,X22,X25,X23,X5,X20] :
( ~ c_Complete__Lattice_Ocomplete__lattice(X22,X20,X23,X24,X25,X26,X27,X21,X0)
| hAPP(X22,hAPP(hAPP(c_Set_Oinsert(X0),X3),X5)) = hAPP(hAPP(X25,X3),hAPP(X22,X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complete__lattice_OInf__insert_0) ).
fof(f6361,plain,
( ~ spl0_2
| spl0_378
| ~ spl0_84
| ~ spl0_138 ),
inference(avatar_split_clause,[],[f1738,f1684,f1392,f6359,f1022]) ).
fof(f6359,plain,
( spl0_378
<=> ! [X0] : hBOOL(hAPP(hAPP(c_lessequals(tc_bool),X0),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_378])]) ).
fof(f1392,plain,
( spl0_84
<=> ! [X0] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),X0),X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_84])]) ).
fof(f1738,plain,
( ! [X0] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_bool),X0),X0))
| ~ class_Lattices_Oupper__semilattice(tc_bool) )
| ~ spl0_84
| ~ spl0_138 ),
inference(superposition,[],[f1685,f1393]) ).
fof(f1393,plain,
( ! [X0] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),X0),X0) = X0
| ~ spl0_84 ),
inference(avatar_component_clause,[],[f1392]) ).
fof(f6105,plain,
spl0_377,
inference(avatar_split_clause,[],[f937,f6103]) ).
fof(f6103,plain,
( spl0_377
<=> ! [X57,X0,X11] :
( c_Finite__Set_Ofinite(hAPP(hAPP(c_COMBS(X0,tc_bool,tc_bool),hAPP(hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),X0),c_or),X11)),X57),X0)
| ~ c_Finite__Set_Ofinite(X57,X0)
| ~ c_Finite__Set_Ofinite(X11,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_377])]) ).
fof(f937,plain,
! [X0,X11,X57] :
( c_Finite__Set_Ofinite(hAPP(hAPP(c_COMBS(X0,tc_bool,tc_bool),hAPP(hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),X0),c_or),X11)),X57),X0)
| ~ c_Finite__Set_Ofinite(X57,X0)
| ~ c_Finite__Set_Ofinite(X11,X0) ),
inference(forward_demodulation,[],[f936,f43]) ).
fof(f936,plain,
! [X0,X11,X57] :
( ~ c_Finite__Set_Ofinite(X57,X0)
| ~ c_Finite__Set_Ofinite(X11,X0)
| c_Finite__Set_Ofinite(c_Collect(hAPP(hAPP(c_COMBS(X0,tc_bool,tc_bool),hAPP(hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),X0),c_or),X11)),X57),X0),X0) ),
inference(forward_demodulation,[],[f935,f43]) ).
fof(f935,plain,
! [X0,X11,X57] :
( ~ c_Finite__Set_Ofinite(X11,X0)
| ~ c_Finite__Set_Ofinite(c_Collect(X57,X0),X0)
| c_Finite__Set_Ofinite(c_Collect(hAPP(hAPP(c_COMBS(X0,tc_bool,tc_bool),hAPP(hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),X0),c_or),X11)),X57),X0),X0) ),
inference(forward_demodulation,[],[f406,f43]) ).
fof(f406,axiom,
! [X0,X11,X57] :
( ~ c_Finite__Set_Ofinite(c_Collect(X11,X0),X0)
| ~ c_Finite__Set_Ofinite(c_Collect(X57,X0),X0)
| c_Finite__Set_Ofinite(c_Collect(hAPP(hAPP(c_COMBS(X0,tc_bool,tc_bool),hAPP(hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),X0),c_or),X11)),X57),X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Collect__disjI_2) ).
fof(f6101,plain,
spl0_376,
inference(avatar_split_clause,[],[f926,f6099]) ).
fof(f6099,plain,
( spl0_376
<=> ! [X9,X0,X5,X8,X1] :
( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,X9,X8,tc_fun(X0,tc_bool)) != c_COMBK(c_False,tc_bool,X0)
| hAPP(X9,X1) = c_COMBK(c_False,tc_bool,X0)
| ~ hBOOL(c_in(X1,X5,X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_376])]) ).
fof(f926,plain,
! [X0,X1,X8,X9,X5] :
( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,X9,X8,tc_fun(X0,tc_bool)) != c_COMBK(c_False,tc_bool,X0)
| hAPP(X9,X1) = c_COMBK(c_False,tc_bool,X0)
| ~ hBOOL(c_in(X1,X5,X8)) ),
inference(forward_demodulation,[],[f925,f698]) ).
fof(f925,plain,
! [X0,X1,X8,X9,X5] :
( hAPP(X9,X1) = c_COMBK(c_False,tc_bool,X0)
| ~ hBOOL(c_in(X1,X5,X8))
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,X9,X8,tc_fun(X0,tc_bool)) ),
inference(forward_demodulation,[],[f213,f698]) ).
fof(f213,axiom,
! [X0,X1,X8,X9,X5] :
( ~ hBOOL(c_in(X1,X5,X8))
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = hAPP(X9,X1)
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,X9,X8,tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UNION__empty__conv_I1_J_0) ).
fof(f6097,plain,
spl0_375,
inference(avatar_split_clause,[],[f912,f6095]) ).
fof(f912,plain,
! [X40,X3,X0,X4,X35] :
( hAPP(hAPP(c_Set_Oinsert(X0),X3),hAPP(c_fequal(X0),X4)) != hAPP(hAPP(c_Set_Oinsert(X0),X35),hAPP(c_fequal(X0),X40))
| X4 = X40
| X3 = X40 ),
inference(forward_demodulation,[],[f911,f723]) ).
fof(f911,plain,
! [X40,X3,X0,X4,X35] :
( hAPP(hAPP(c_Set_Oinsert(X0),X3),hAPP(hAPP(c_Set_Oinsert(X0),X4),c_COMBK(c_False,tc_bool,X0))) != hAPP(hAPP(c_Set_Oinsert(X0),X35),hAPP(c_fequal(X0),X40))
| X4 = X40
| X3 = X40 ),
inference(forward_demodulation,[],[f910,f723]) ).
fof(f910,plain,
! [X40,X3,X0,X4,X35] :
( hAPP(hAPP(c_Set_Oinsert(X0),X3),hAPP(hAPP(c_Set_Oinsert(X0),X4),c_COMBK(c_False,tc_bool,X0))) != hAPP(hAPP(c_Set_Oinsert(X0),X35),hAPP(hAPP(c_Set_Oinsert(X0),X40),c_COMBK(c_False,tc_bool,X0)))
| X4 = X40
| X3 = X40 ),
inference(forward_demodulation,[],[f595,f698]) ).
fof(f595,axiom,
! [X40,X3,X0,X4,X35] :
( X4 = X40
| X3 = X40
| hAPP(hAPP(c_Set_Oinsert(X0),X3),hAPP(hAPP(c_Set_Oinsert(X0),X4),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)))) != hAPP(hAPP(c_Set_Oinsert(X0),X35),hAPP(hAPP(c_Set_Oinsert(X0),X40),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_doubleton__eq__iff_2) ).
fof(f6093,plain,
spl0_374,
inference(avatar_split_clause,[],[f906,f6091]) ).
fof(f906,plain,
! [X40,X3,X0,X4,X35] :
( hAPP(hAPP(c_Set_Oinsert(X0),X3),hAPP(c_fequal(X0),X4)) != hAPP(hAPP(c_Set_Oinsert(X0),X35),hAPP(c_fequal(X0),X40))
| X3 = X35
| X3 = X40 ),
inference(forward_demodulation,[],[f905,f723]) ).
fof(f905,plain,
! [X40,X3,X0,X4,X35] :
( hAPP(hAPP(c_Set_Oinsert(X0),X3),hAPP(hAPP(c_Set_Oinsert(X0),X4),c_COMBK(c_False,tc_bool,X0))) != hAPP(hAPP(c_Set_Oinsert(X0),X35),hAPP(c_fequal(X0),X40))
| X3 = X35
| X3 = X40 ),
inference(forward_demodulation,[],[f904,f723]) ).
fof(f904,plain,
! [X40,X3,X0,X4,X35] :
( hAPP(hAPP(c_Set_Oinsert(X0),X3),hAPP(hAPP(c_Set_Oinsert(X0),X4),c_COMBK(c_False,tc_bool,X0))) != hAPP(hAPP(c_Set_Oinsert(X0),X35),hAPP(hAPP(c_Set_Oinsert(X0),X40),c_COMBK(c_False,tc_bool,X0)))
| X3 = X35
| X3 = X40 ),
inference(forward_demodulation,[],[f597,f698]) ).
fof(f597,axiom,
! [X40,X3,X0,X4,X35] :
( X3 = X35
| X3 = X40
| hAPP(hAPP(c_Set_Oinsert(X0),X3),hAPP(hAPP(c_Set_Oinsert(X0),X4),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)))) != hAPP(hAPP(c_Set_Oinsert(X0),X35),hAPP(hAPP(c_Set_Oinsert(X0),X40),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_doubleton__eq__iff_0) ).
fof(f6089,plain,
spl0_373,
inference(avatar_split_clause,[],[f428,f6087]) ).
fof(f428,axiom,
! [X0,X9,X5,X12] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X9),X12))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X5),X9)),X12)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__subset__iff_1) ).
fof(f6085,plain,
spl0_372,
inference(avatar_split_clause,[],[f427,f6083]) ).
fof(f427,axiom,
! [X0,X9,X5,X12] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X5),X12))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X5),X9)),X12)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__subset__iff_0) ).
fof(f6081,plain,
spl0_371,
inference(avatar_split_clause,[],[f412,f6079]) ).
fof(f412,axiom,
! [X3,X0,X9,X5] :
( ~ c_Finite__Set_Ofinite(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X5),X9),X0)
| c_Finite__Set_Ofinite(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X5),hAPP(hAPP(c_Set_Oinsert(X0),X3),X9)),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Diff__insert_1) ).
fof(f6077,plain,
spl0_370,
inference(avatar_split_clause,[],[f411,f6075]) ).
fof(f411,axiom,
! [X3,X0,X9,X5] :
( c_Finite__Set_Ofinite(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X5),X9),X0)
| ~ c_Finite__Set_Ofinite(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X5),hAPP(hAPP(c_Set_Oinsert(X0),X3),X9)),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Diff__insert_0) ).
fof(f6073,plain,
spl0_369,
inference(avatar_split_clause,[],[f194,f6071]) ).
fof(f6071,plain,
( spl0_369
<=> ! [X5,X0,X8,X9,X1] :
( ~ hBOOL(c_in(X1,X5,X8))
| c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)) = hAPP(X9,X1)
| c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)) != c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,X9,X8,tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_369])]) ).
fof(f194,axiom,
! [X0,X1,X8,X9,X5] :
( ~ hBOOL(c_in(X1,X5,X8))
| c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)) = hAPP(X9,X1)
| c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)) != c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,X9,X8,tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_INTER__UNIV__conv_I2_J_0) ).
fof(f6069,plain,
( ~ spl0_11
| spl0_368
| ~ spl0_75
| ~ spl0_100 ),
inference(avatar_split_clause,[],[f1523,f1483,f1344,f6067,f1067]) ).
fof(f1523,plain,
( ! [X0] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_bool),c_False),X0))
| ~ class_Orderings_Obot(tc_bool) )
| ~ spl0_75
| ~ spl0_100 ),
inference(superposition,[],[f1345,f1485]) ).
fof(f6065,plain,
spl0_367,
inference(avatar_split_clause,[],[f185,f6063]) ).
fof(f185,axiom,
! [X0,X9,X5,X12] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X12),X5))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X12),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X5),X9))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__subset__iff_0) ).
fof(f6061,plain,
spl0_366,
inference(avatar_split_clause,[],[f184,f6059]) ).
fof(f184,axiom,
! [X0,X9,X5,X12] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X12),X9))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X12),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X5),X9))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__subset__iff_1) ).
fof(f6057,plain,
spl0_365,
inference(avatar_split_clause,[],[f139,f6055]) ).
fof(f139,axiom,
! [X0,X1,X8,X7,X5,X30] :
( X1 = X30
| ~ hBOOL(c_in(X30,X5,X0))
| ~ hBOOL(c_in(X1,X5,X0))
| ~ c_Fun_Oinj__on(X7,X5,X0,X8)
| hAPP(X7,X1) != hAPP(X7,X30) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__def_0) ).
fof(f6053,plain,
spl0_364,
inference(avatar_split_clause,[],[f134,f6051]) ).
fof(f6051,plain,
( spl0_364
<=> ! [X0,X6,X2,X1] :
( ~ class_Lattices_Olattice(X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2)),X6) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X2),X6)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_364])]) ).
fof(f134,axiom,
! [X2,X0,X1,X6] :
( ~ class_Lattices_Olattice(X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2)),X6) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X2),X6)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I6_J_0) ).
fof(f6049,plain,
spl0_363,
inference(avatar_split_clause,[],[f133,f6047]) ).
fof(f6047,plain,
( spl0_363
<=> ! [X0,X6,X2,X1] :
( ~ class_Lattices_Olattice(X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X2),X6)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X6)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_363])]) ).
fof(f133,axiom,
! [X2,X0,X1,X6] :
( ~ class_Lattices_Olattice(X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X2),X6)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X6)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I7_J_0) ).
fof(f6045,plain,
spl0_362,
inference(avatar_split_clause,[],[f132,f6043]) ).
fof(f132,axiom,
! [X2,X0,X1,X6] :
( ~ class_Lattices_Oupper__semilattice(X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X2),X6)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X6)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__left__commute_0) ).
fof(f6041,plain,
spl0_361,
inference(avatar_split_clause,[],[f131,f6039]) ).
fof(f131,axiom,
! [X2,X0,X1,X6] :
( ~ class_Lattices_Oupper__semilattice(X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2)),X6) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X2),X6)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__assoc_0) ).
fof(f6037,plain,
spl0_360,
inference(avatar_split_clause,[],[f108,f6035]) ).
fof(f6035,plain,
( spl0_360
<=> ! [X0,X6,X2,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2)),X6) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X6)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_360])]) ).
fof(f108,axiom,
! [X2,X0,X1,X6] :
( ~ class_Lattices_Olower__semilattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2)),X6) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X6)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__assoc_0) ).
fof(f6033,plain,
spl0_359,
inference(avatar_split_clause,[],[f107,f6031]) ).
fof(f6031,plain,
( spl0_359
<=> ! [X0,X6,X2,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X6)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X6)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_359])]) ).
fof(f107,axiom,
! [X2,X0,X1,X6] :
( ~ class_Lattices_Olower__semilattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X6)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X6)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__left__commute_0) ).
fof(f6029,plain,
spl0_358,
inference(avatar_split_clause,[],[f106,f6027]) ).
fof(f106,axiom,
! [X2,X0,X1,X6] :
( ~ class_Lattices_Olattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X6)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X6)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I3_J_0) ).
fof(f6024,plain,
spl0_357,
inference(avatar_split_clause,[],[f105,f6022]) ).
fof(f105,axiom,
! [X2,X0,X1,X6] :
( ~ class_Lattices_Olattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2)),X6) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X6)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I2_J_0) ).
fof(f5618,plain,
spl0_356,
inference(avatar_split_clause,[],[f951,f5616]) ).
fof(f5616,plain,
( spl0_356
<=> ! [X5,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X5),hAPP(c_fequal(X0),X1)))
| hAPP(c_fequal(X0),X1) = X5
| c_COMBK(c_False,tc_bool,X0) = X5 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_356])]) ).
fof(f951,plain,
! [X0,X1,X5] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X5),hAPP(c_fequal(X0),X1)))
| hAPP(c_fequal(X0),X1) = X5
| c_COMBK(c_False,tc_bool,X0) = X5 ),
inference(forward_demodulation,[],[f950,f723]) ).
fof(f950,plain,
! [X0,X1,X5] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X5),hAPP(hAPP(c_Set_Oinsert(X0),X1),c_COMBK(c_False,tc_bool,X0))))
| hAPP(c_fequal(X0),X1) = X5
| c_COMBK(c_False,tc_bool,X0) = X5 ),
inference(forward_demodulation,[],[f949,f698]) ).
fof(f949,plain,
! [X0,X1,X5] :
( hAPP(c_fequal(X0),X1) = X5
| c_COMBK(c_False,tc_bool,X0) = X5
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X5),hAPP(hAPP(c_Set_Oinsert(X0),X1),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))))) ),
inference(forward_demodulation,[],[f948,f723]) ).
fof(f948,plain,
! [X0,X1,X5] :
( hAPP(hAPP(c_Set_Oinsert(X0),X1),c_COMBK(c_False,tc_bool,X0)) = X5
| c_COMBK(c_False,tc_bool,X0) = X5
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X5),hAPP(hAPP(c_Set_Oinsert(X0),X1),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))))) ),
inference(forward_demodulation,[],[f947,f698]) ).
fof(f947,plain,
! [X0,X1,X5] :
( c_COMBK(c_False,tc_bool,X0) = X5
| hAPP(hAPP(c_Set_Oinsert(X0),X1),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))) = X5
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X5),hAPP(hAPP(c_Set_Oinsert(X0),X1),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))))) ),
inference(forward_demodulation,[],[f524,f698]) ).
fof(f524,axiom,
! [X0,X1,X5] :
( c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X5
| hAPP(hAPP(c_Set_Oinsert(X0),X1),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))) = X5
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X5),hAPP(hAPP(c_Set_Oinsert(X0),X1),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__singletonD_0) ).
fof(f5614,plain,
spl0_355,
inference(avatar_split_clause,[],[f751,f5612]) ).
fof(f751,plain,
! [X0] : c_Fun_Oinj__on(hAPP(c_COMBC(c_Set_Oinsert(X0),X0,tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0)),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0,tc_fun(X0,tc_bool)),
inference(forward_demodulation,[],[f515,f698]) ).
fof(f515,axiom,
! [X0] : c_Fun_Oinj__on(hAPP(c_COMBC(c_Set_Oinsert(X0),X0,tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0,tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__singleton_0) ).
fof(f5610,plain,
spl0_354,
inference(avatar_split_clause,[],[f469,f5608]) ).
fof(f5608,plain,
( spl0_354
<=> ! [X40,X41,X0,X3,X54,X14,X4,X8,X35] :
( hAPP(X3,hAPP(X4,X41)) = hAPP(X35,hAPP(X40,X41))
| c_Fun_Ocomp(X3,X4,X14,X8,X0) != c_Fun_Ocomp(X35,X40,X54,X8,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_354])]) ).
fof(f469,axiom,
! [X40,X3,X41,X0,X8,X54,X14,X4,X35] :
( hAPP(X3,hAPP(X4,X41)) = hAPP(X35,hAPP(X40,X41))
| c_Fun_Ocomp(X3,X4,X14,X8,X0) != c_Fun_Ocomp(X35,X40,X54,X8,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_o__eq__dest_0) ).
fof(f5606,plain,
spl0_353,
inference(avatar_split_clause,[],[f310,f5604]) ).
fof(f310,axiom,
! [X0,X9,X5] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X5),X9) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X5),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X5),X9)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__left__absorb_0) ).
fof(f5602,plain,
spl0_352,
inference(avatar_split_clause,[],[f263,f5600]) ).
fof(f263,axiom,
! [X0,X9,X5] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X5),X9)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X5),X9)) = X5,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Diff__Int_0) ).
fof(f5598,plain,
spl0_351,
inference(avatar_split_clause,[],[f204,f5596]) ).
fof(f5596,plain,
( spl0_351
<=> ! [X9,X5,X0] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X5),X9) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X5),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X5),X9)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_351])]) ).
fof(f204,axiom,
! [X0,X9,X5] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X5),X9) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X5),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X5),X9)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__left__absorb_0) ).
fof(f5594,plain,
spl0_350,
inference(avatar_split_clause,[],[f182,f5592]) ).
fof(f182,axiom,
! [X0,X9,X5] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X5),X9) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X5),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X9),X5)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Diff__cancel_0) ).
fof(f5590,plain,
spl0_349,
inference(avatar_split_clause,[],[f181,f5588]) ).
fof(f181,axiom,
! [X0,X9,X5] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X9),X5)),X5) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X9),X5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Diff__cancel2_0) ).
fof(f5586,plain,
spl0_348,
inference(avatar_split_clause,[],[f114,f5584]) ).
fof(f5584,plain,
( spl0_348
<=> ! [X9,X5,X0] : hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X5),X9) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X5),X9)),X9) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_348])]) ).
fof(f114,axiom,
! [X0,X9,X5] : hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X5),X9) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X5),X9)),X9),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__idemp_0) ).
fof(f5572,plain,
spl0_347,
inference(avatar_split_clause,[],[f93,f5570]) ).
fof(f93,axiom,
! [X40,X3,X0,X4,X35] :
( ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),X3),X4))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X3,X4,X0)),c_SetInterval_Oord__class_OatLeastAtMost(X35,X40,X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastatMost__subset__iff_2) ).
fof(f4976,plain,
spl0_346,
inference(avatar_split_clause,[],[f922,f4974]) ).
fof(f922,plain,
! [X0,X1,X9,X5] :
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X5),X9) != c_COMBK(c_False,tc_bool,X0)
| ~ hBOOL(c_in(X1,X9,X0))
| ~ hBOOL(c_in(X1,X5,X0)) ),
inference(forward_demodulation,[],[f231,f698]) ).
fof(f231,axiom,
! [X0,X1,X9,X5] :
( ~ hBOOL(c_in(X1,X9,X0))
| ~ hBOOL(c_in(X1,X5,X0))
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X5),X9) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_disjoint__iff__not__equal_0) ).
fof(f4972,plain,
spl0_345,
inference(avatar_split_clause,[],[f871,f4970]) ).
fof(f871,plain,
! [X0,X9,X5] :
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X5),X9) != c_COMBK(c_False,tc_bool,X0)
| hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X5),X9) = X5 ),
inference(forward_demodulation,[],[f18,f698]) ).
fof(f18,axiom,
! [X0,X9,X5] :
( hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X5),X9) = X5
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X5),X9) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__triv_0) ).
fof(f4968,plain,
spl0_344,
inference(avatar_split_clause,[],[f830,f4966]) ).
fof(f830,plain,
! [X0,X1,X5] :
( hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Set_Oinsert(X0),X1),X5)),hAPP(c_fequal(X0),X1)) = X5
| hBOOL(c_in(X1,X5,X0)) ),
inference(forward_demodulation,[],[f829,f723]) ).
fof(f829,plain,
! [X0,X1,X5] :
( hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Set_Oinsert(X0),X1),X5)),hAPP(hAPP(c_Set_Oinsert(X0),X1),c_COMBK(c_False,tc_bool,X0))) = X5
| hBOOL(c_in(X1,X5,X0)) ),
inference(forward_demodulation,[],[f382,f698]) ).
fof(f382,axiom,
! [X0,X1,X5] :
( hBOOL(c_in(X1,X5,X0))
| hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Set_Oinsert(X0),X1),X5)),hAPP(hAPP(c_Set_Oinsert(X0),X1),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)))) = X5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__insert__absorb_0) ).
fof(f4963,plain,
spl0_343,
inference(avatar_split_clause,[],[f756,f4961]) ).
fof(f756,plain,
! [X3,X0,X5] : hAPP(hAPP(c_Set_Oinsert(X0),X3),X5) = hAPP(hAPP(c_Set_Oinsert(X0),X3),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X5),hAPP(c_fequal(X0),X3))),
inference(forward_demodulation,[],[f755,f723]) ).
fof(f755,plain,
! [X3,X0,X5] : hAPP(hAPP(c_Set_Oinsert(X0),X3),X5) = hAPP(hAPP(c_Set_Oinsert(X0),X3),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X5),hAPP(hAPP(c_Set_Oinsert(X0),X3),c_COMBK(c_False,tc_bool,X0)))),
inference(forward_demodulation,[],[f544,f698]) ).
fof(f544,axiom,
! [X3,X0,X5] : hAPP(hAPP(c_Set_Oinsert(X0),X3),X5) = hAPP(hAPP(c_Set_Oinsert(X0),X3),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X5),hAPP(hAPP(c_Set_Oinsert(X0),X3),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__Diff__single_0) ).
fof(f4959,plain,
spl0_342,
inference(avatar_split_clause,[],[f749,f4957]) ).
fof(f749,plain,
! [X0,X5] : c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,hAPP(c_COMBC(c_Set_Oinsert(X0),X0,tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0)),X0,tc_fun(X0,tc_bool)) = X5,
inference(forward_demodulation,[],[f579,f698]) ).
fof(f579,axiom,
! [X0,X5] : c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,hAPP(c_COMBC(c_Set_Oinsert(X0),X0,tc_fun(X0,tc_bool),tc_fun(X0,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))),X0,tc_fun(X0,tc_bool)) = X5,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UN__singleton_0) ).
fof(f4955,plain,
spl0_341,
inference(avatar_split_clause,[],[f692,f4953]) ).
fof(f692,plain,
! [X3,X0,X5] :
( ~ class_Lattices_Olower__semilattice(X0)
| ~ c_Finite__Set_Ofinite(X5,X0)
| ~ hBOOL(c_in(X3,X5,X0))
| hBOOL(hAPP(hAPP(c_lessequals(X0),c_The(c_Finite__Set_Ofold1Set(c_Lattices_Olower__semilattice__class_Oinf(X0),X5,X0),X0)),X3)) ),
inference(definition_unfolding,[],[f276,f30]) ).
fof(f276,axiom,
! [X3,X0,X5] :
( ~ class_Lattices_Olower__semilattice(X0)
| ~ c_Finite__Set_Ofinite(X5,X0)
| ~ hBOOL(c_in(X3,X5,X0))
| hBOOL(hAPP(hAPP(c_lessequals(X0),c_Finite__Set_Ofold1(c_Lattices_Olower__semilattice__class_Oinf(X0),X5,X0)),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fold1__belowI_0) ).
fof(f4951,plain,
spl0_340,
inference(avatar_split_clause,[],[f603,f4949]) ).
fof(f603,axiom,
! [X2,X0,X1,X5] : hAPP(hAPP(c_Set_Oinsert(X0),X1),hAPP(hAPP(c_Set_Oinsert(X0),X2),X5)) = hAPP(hAPP(c_Set_Oinsert(X0),X2),hAPP(hAPP(c_Set_Oinsert(X0),X1),X5)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__commute_0) ).
fof(f4947,plain,
spl0_339,
inference(avatar_split_clause,[],[f451,f4945]) ).
fof(f451,axiom,
! [X2,X0,X1,X6] :
( ~ class_Orderings_Opreorder(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X2),X6))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X6)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__le__trans_0) ).
fof(f4943,plain,
spl0_338,
inference(avatar_split_clause,[],[f450,f4941]) ).
fof(f450,axiom,
! [X2,X0,X1,X6] :
( ~ class_Orderings_Opreorder(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X2),X6))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X6)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__le__less__trans_0) ).
fof(f4939,plain,
spl0_337,
inference(avatar_split_clause,[],[f435,f4937]) ).
fof(f435,axiom,
! [X2,X0,X1,X6] :
( ~ class_Orderings_Opreorder(X0)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X2),X6))
| hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X6)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__trans_0) ).
fof(f4935,plain,
spl0_336,
inference(avatar_split_clause,[],[f434,f4933]) ).
fof(f434,axiom,
! [X2,X0,X1,X6] :
( ~ class_Orderings_Oorder(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X6),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X2),X1))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X6),X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I8_J_0) ).
fof(f4931,plain,
spl0_335,
inference(avatar_split_clause,[],[f433,f4929]) ).
fof(f433,axiom,
! [X2,X0,X1,X6] :
( ~ class_Orderings_Oorder(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X2),X1))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X6),X2))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X6),X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I7_J_0) ).
fof(f4927,plain,
spl0_334,
inference(avatar_split_clause,[],[f432,f4925]) ).
fof(f432,axiom,
! [X2,X0,X1,X6] :
( ~ class_Orderings_Oorder(X0)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X2),X1))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X6),X2))
| hBOOL(hAPP(hAPP(c_lessequals(X0),X6),X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I6_J_0) ).
fof(f4922,plain,
spl0_333,
inference(avatar_split_clause,[],[f431,f4920]) ).
fof(f431,axiom,
! [X8,X7,X13] :
( ~ class_Lattices_Olattice(X8)
| hAPP(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(t_a,X8)),X7),X13),v_x) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X8),hAPP(X7,v_x)),hAPP(X13,v_x)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__fun__eq_0) ).
fof(f4918,plain,
spl0_332,
inference(avatar_split_clause,[],[f398,f4916]) ).
fof(f398,axiom,
! [X0,X1,X9,X5] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X5),X9))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Set_Oinsert(X0),X1),X5)),X9)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__subset_1) ).
fof(f4914,plain,
spl0_331,
inference(avatar_split_clause,[],[f397,f4912]) ).
fof(f397,axiom,
! [X0,X9,X4,X5] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X5),X9))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X5),hAPP(hAPP(c_Set_Oinsert(X0),X4),X9))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insertI2_0) ).
fof(f4910,plain,
spl0_330,
inference(avatar_split_clause,[],[f299,f4908]) ).
fof(f299,axiom,
! [X0,X54,X8,X7,X14,X53,X13] : c_Fun_Ocomp(X7,c_Fun_Ocomp(X13,X53,X54,X14,X0),X14,X8,X0) = c_Fun_Ocomp(c_Fun_Ocomp(X7,X13,X14,X8,X54),X53,X54,X8,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_o__assoc_0) ).
fof(f4906,plain,
spl0_329,
inference(avatar_split_clause,[],[f240,f4904]) ).
fof(f240,axiom,
! [X2,X0,X1] :
( ~ class_Orderings_Opreorder(X0)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| hBOOL(hAPP(hAPP(c_lessequals(X0),X2),X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__le__not__le_2) ).
fof(f4902,plain,
spl0_328,
inference(avatar_split_clause,[],[f196,f4900]) ).
fof(f4900,plain,
( spl0_328
<=> ! [X21,X0,X1,X26,X27,X22,X24,X5,X25,X23,X20] :
( ~ hBOOL(c_in(X1,X5,X0))
| hBOOL(hAPP(hAPP(X23,X1),hAPP(X20,X5)))
| ~ c_Complete__Lattice_Ocomplete__lattice(X22,X20,X23,X24,X25,X26,X27,X21,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_328])]) ).
fof(f196,axiom,
! [X21,X0,X1,X26,X27,X24,X5,X22,X23,X25,X20] :
( ~ hBOOL(c_in(X1,X5,X0))
| hBOOL(hAPP(hAPP(X23,X1),hAPP(X20,X5)))
| ~ c_Complete__Lattice_Ocomplete__lattice(X22,X20,X23,X24,X25,X26,X27,X21,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complete__lattice_OSup__upper_0) ).
fof(f4898,plain,
spl0_327,
inference(avatar_split_clause,[],[f195,f4896]) ).
fof(f4896,plain,
( spl0_327
<=> ! [X21,X20,X0,X1,X26,X27,X24,X5,X25,X23,X22] :
( ~ hBOOL(c_in(X1,X5,X0))
| hBOOL(hAPP(hAPP(X23,hAPP(X22,X5)),X1))
| ~ c_Complete__Lattice_Ocomplete__lattice(X22,X20,X23,X24,X25,X26,X27,X21,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_327])]) ).
fof(f195,axiom,
! [X21,X0,X1,X26,X27,X24,X5,X22,X23,X25,X20] :
( ~ hBOOL(c_in(X1,X5,X0))
| hBOOL(hAPP(hAPP(X23,hAPP(X22,X5)),X1))
| ~ c_Complete__Lattice_Ocomplete__lattice(X22,X20,X23,X24,X25,X26,X27,X21,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complete__lattice_OInf__lower_0) ).
fof(f4894,plain,
spl0_326,
inference(avatar_split_clause,[],[f183,f4892]) ).
fof(f183,axiom,
! [X8,X9,X5] :
( ~ class_HOL_Ominus(X8)
| hAPP(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(t_a,X8)),X5),X9),v_x) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(X8),hAPP(X5,v_x)),hAPP(X9,v_x)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__diff__def_0) ).
fof(f4890,plain,
spl0_325,
inference(avatar_split_clause,[],[f180,f4888]) ).
fof(f180,axiom,
! [X3,X0,X8,X9,X4,X5] :
( ~ hBOOL(c_in(X3,X5,X0))
| ~ hBOOL(c_in(X4,hAPP(X9,X3),X8))
| hBOOL(c_in(X4,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,X9,X0,tc_fun(X8,tc_bool)),X8)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UN__I_0) ).
fof(f4886,plain,
spl0_324,
inference(avatar_split_clause,[],[f66,f4884]) ).
fof(f66,axiom,
! [X3,X0,X8,X9,X4,X5] :
( ~ hBOOL(c_in(X3,X5,X8))
| hBOOL(c_in(X4,hAPP(X9,X3),X0))
| ~ hBOOL(c_in(X4,c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,X9,X8,tc_fun(X0,tc_bool)),X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_INT__D_0) ).
fof(f4882,plain,
( spl0_323
| ~ spl0_158
| ~ spl0_227 ),
inference(avatar_split_clause,[],[f3973,f2580,f1818,f4880]) ).
fof(f4880,plain,
( spl0_323
<=> ! [X0] : hBOOL(c_in(X0,c_SetInterval_Oord__class_OatLeastAtMost(X0,X0,tc_bool),tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_323])]) ).
fof(f3973,plain,
( ! [X0] : hBOOL(c_in(X0,c_SetInterval_Oord__class_OatLeastAtMost(X0,X0,tc_bool),tc_bool))
| ~ spl0_158
| ~ spl0_227 ),
inference(superposition,[],[f1819,f2581]) ).
fof(f4878,plain,
spl0_322,
inference(avatar_split_clause,[],[f17,f4876]) ).
fof(f17,axiom,
! [X8,X7,X13] :
( ~ class_Lattices_Olattice(X8)
| hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,X8)),X7),X13),v_x) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X8),hAPP(X7,v_x)),hAPP(X13,v_x)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__fun__eq_0) ).
fof(f4874,plain,
spl0_321,
inference(avatar_split_clause,[],[f6,f4872]) ).
fof(f4872,plain,
( spl0_321
<=> ! [X0,X6,X2,X1] :
( ~ class_Orderings_Oorder(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X2),X1))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X6),X2))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X6),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_321])]) ).
fof(f6,axiom,
! [X2,X0,X1,X6] :
( ~ class_Orderings_Oorder(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X2),X1))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X6),X2))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X6),X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I10_J_0) ).
fof(f4870,plain,
spl0_320,
inference(avatar_split_clause,[],[f5,f4868]) ).
fof(f4868,plain,
( spl0_320
<=> ! [X0,X6,X2,X1] :
( ~ class_Orderings_Opreorder(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X2),X6))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X6)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_320])]) ).
fof(f5,axiom,
! [X2,X0,X1,X6] :
( ~ class_Orderings_Opreorder(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X2),X6))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X6)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__trans_0) ).
fof(f4836,plain,
( spl0_319
| ~ spl0_136
| ~ spl0_227 ),
inference(avatar_split_clause,[],[f3972,f2580,f1670,f4834]) ).
fof(f4834,plain,
( spl0_319
<=> ! [X0] : c_Nitpick_Osko__Nitpick__XEx1__def__1__3(c_SetInterval_Oord__class_OatLeastAtMost(X0,X0,tc_bool),tc_bool) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_319])]) ).
fof(f3972,plain,
( ! [X0] : c_Nitpick_Osko__Nitpick__XEx1__def__1__3(c_SetInterval_Oord__class_OatLeastAtMost(X0,X0,tc_bool),tc_bool) = X0
| ~ spl0_136
| ~ spl0_227 ),
inference(superposition,[],[f1671,f2581]) ).
fof(f4620,plain,
spl0_318,
inference(avatar_split_clause,[],[f921,f4618]) ).
fof(f921,plain,
! [X58,X39,X0,X68] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),X58),X0)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X39,X68,X0)
| c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X0)),X58),X68),X0) ),
inference(forward_demodulation,[],[f920,f723]) ).
fof(f920,plain,
! [X58,X39,X0,X68] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X0)),X58),c_COMBK(c_False,tc_bool,tc_Hoare__Mirabelle_Otriple(X0))),X0)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X39,X68,X0)
| c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X0)),X58),X68),X0) ),
inference(forward_demodulation,[],[f587,f698]) ).
fof(f587,axiom,
! [X58,X39,X0,X68] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X39,X68,X0)
| c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X0)),X58),X68),X0)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X0)),X58),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool))),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_hoare__derivs_Oinsert_0) ).
fof(f4616,plain,
spl0_317,
inference(avatar_split_clause,[],[f834,f4614]) ).
fof(f4614,plain,
( spl0_317
<=> ! [X57,X0,X11] :
( ~ c_Finite__Set_Ofinite(hAPP(hAPP(c_COMBS(X0,tc_bool,tc_bool),hAPP(hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),X0),c_or),X11)),X57),X0)
| c_Finite__Set_Ofinite(X11,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_317])]) ).
fof(f834,plain,
! [X0,X11,X57] :
( ~ c_Finite__Set_Ofinite(hAPP(hAPP(c_COMBS(X0,tc_bool,tc_bool),hAPP(hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),X0),c_or),X11)),X57),X0)
| c_Finite__Set_Ofinite(X11,X0) ),
inference(forward_demodulation,[],[f833,f43]) ).
fof(f833,plain,
! [X0,X11,X57] :
( c_Finite__Set_Ofinite(X11,X0)
| ~ c_Finite__Set_Ofinite(c_Collect(hAPP(hAPP(c_COMBS(X0,tc_bool,tc_bool),hAPP(hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),X0),c_or),X11)),X57),X0),X0) ),
inference(forward_demodulation,[],[f408,f43]) ).
fof(f408,axiom,
! [X0,X11,X57] :
( c_Finite__Set_Ofinite(c_Collect(X11,X0),X0)
| ~ c_Finite__Set_Ofinite(c_Collect(hAPP(hAPP(c_COMBS(X0,tc_bool,tc_bool),hAPP(hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),X0),c_or),X11)),X57),X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Collect__disjI_0) ).
fof(f4612,plain,
spl0_316,
inference(avatar_split_clause,[],[f832,f4610]) ).
fof(f4610,plain,
( spl0_316
<=> ! [X57,X0,X11] :
( ~ c_Finite__Set_Ofinite(hAPP(hAPP(c_COMBS(X0,tc_bool,tc_bool),hAPP(hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),X0),c_or),X11)),X57),X0)
| c_Finite__Set_Ofinite(X57,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_316])]) ).
fof(f832,plain,
! [X0,X11,X57] :
( ~ c_Finite__Set_Ofinite(hAPP(hAPP(c_COMBS(X0,tc_bool,tc_bool),hAPP(hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),X0),c_or),X11)),X57),X0)
| c_Finite__Set_Ofinite(X57,X0) ),
inference(forward_demodulation,[],[f831,f43]) ).
fof(f831,plain,
! [X0,X11,X57] :
( c_Finite__Set_Ofinite(X57,X0)
| ~ c_Finite__Set_Ofinite(c_Collect(hAPP(hAPP(c_COMBS(X0,tc_bool,tc_bool),hAPP(hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),X0),c_or),X11)),X57),X0),X0) ),
inference(forward_demodulation,[],[f407,f43]) ).
fof(f407,axiom,
! [X0,X11,X57] :
( c_Finite__Set_Ofinite(c_Collect(X57,X0),X0)
| ~ c_Finite__Set_Ofinite(c_Collect(hAPP(hAPP(c_COMBS(X0,tc_bool,tc_bool),hAPP(hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),X0),c_or),X11)),X57),X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Collect__disjI_1) ).
fof(f4608,plain,
spl0_315,
inference(avatar_split_clause,[],[f826,f4606]) ).
fof(f4606,plain,
( spl0_315
<=> ! [X57,X0,X11] :
( c_Finite__Set_Ofinite(hAPP(hAPP(c_COMBS(X0,tc_bool,tc_bool),hAPP(hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),X0),c_and),X11)),X57),X0)
| ~ c_Finite__Set_Ofinite(X57,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_315])]) ).
fof(f826,plain,
! [X0,X11,X57] :
( c_Finite__Set_Ofinite(hAPP(hAPP(c_COMBS(X0,tc_bool,tc_bool),hAPP(hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),X0),c_and),X11)),X57),X0)
| ~ c_Finite__Set_Ofinite(X57,X0) ),
inference(forward_demodulation,[],[f825,f43]) ).
fof(f825,plain,
! [X0,X11,X57] :
( ~ c_Finite__Set_Ofinite(X57,X0)
| c_Finite__Set_Ofinite(c_Collect(hAPP(hAPP(c_COMBS(X0,tc_bool,tc_bool),hAPP(hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),X0),c_and),X11)),X57),X0),X0) ),
inference(forward_demodulation,[],[f517,f43]) ).
fof(f517,axiom,
! [X0,X11,X57] :
( ~ c_Finite__Set_Ofinite(c_Collect(X57,X0),X0)
| c_Finite__Set_Ofinite(c_Collect(hAPP(hAPP(c_COMBS(X0,tc_bool,tc_bool),hAPP(hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),X0),c_and),X11)),X57),X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Collect__conjI_1) ).
fof(f4604,plain,
( spl0_314
| ~ spl0_49
| ~ spl0_227 ),
inference(avatar_split_clause,[],[f3967,f2580,f1228,f4602]) ).
fof(f4602,plain,
( spl0_314
<=> ! [X0] : c_The(c_SetInterval_Oord__class_OatLeastAtMost(X0,X0,tc_bool),tc_bool) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_314])]) ).
fof(f3967,plain,
( ! [X0] : c_The(c_SetInterval_Oord__class_OatLeastAtMost(X0,X0,tc_bool),tc_bool) = X0
| ~ spl0_49
| ~ spl0_227 ),
inference(superposition,[],[f1229,f2581]) ).
fof(f4600,plain,
spl0_313,
inference(avatar_split_clause,[],[f824,f4598]) ).
fof(f4598,plain,
( spl0_313
<=> ! [X57,X0,X11] :
( c_Finite__Set_Ofinite(hAPP(hAPP(c_COMBS(X0,tc_bool,tc_bool),hAPP(hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),X0),c_and),X11)),X57),X0)
| ~ c_Finite__Set_Ofinite(X11,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_313])]) ).
fof(f824,plain,
! [X0,X11,X57] :
( c_Finite__Set_Ofinite(hAPP(hAPP(c_COMBS(X0,tc_bool,tc_bool),hAPP(hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),X0),c_and),X11)),X57),X0)
| ~ c_Finite__Set_Ofinite(X11,X0) ),
inference(forward_demodulation,[],[f823,f43]) ).
fof(f823,plain,
! [X0,X11,X57] :
( ~ c_Finite__Set_Ofinite(X11,X0)
| c_Finite__Set_Ofinite(c_Collect(hAPP(hAPP(c_COMBS(X0,tc_bool,tc_bool),hAPP(hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),X0),c_and),X11)),X57),X0),X0) ),
inference(forward_demodulation,[],[f518,f43]) ).
fof(f518,axiom,
! [X0,X11,X57] :
( ~ c_Finite__Set_Ofinite(c_Collect(X11,X0),X0)
| c_Finite__Set_Ofinite(c_Collect(hAPP(hAPP(c_COMBS(X0,tc_bool,tc_bool),hAPP(hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),X0),c_and),X11)),X57),X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Collect__conjI_0) ).
fof(f4596,plain,
spl0_312,
inference(avatar_split_clause,[],[f795,f4594]) ).
fof(f795,plain,
! [X3,X0,X4] :
( hAPP(hAPP(c_Set_Oinsert(X0),X3),c_COMBK(c_False,tc_bool,X0)) != hAPP(hAPP(c_Set_Oinsert(X0),X4),c_COMBK(c_False,tc_bool,X0))
| X3 = X4 ),
inference(forward_demodulation,[],[f609,f698]) ).
fof(f609,axiom,
! [X3,X0,X4] :
( X3 = X4
| hAPP(hAPP(c_Set_Oinsert(X0),X3),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))) != hAPP(hAPP(c_Set_Oinsert(X0),X4),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_singleton__inject_0) ).
fof(f4591,plain,
spl0_311,
inference(avatar_split_clause,[],[f750,f4589]) ).
fof(f4589,plain,
( spl0_311
<=> ! [X9,X0,X3] : hAPP(hAPP(c_Set_Oinsert(X0),X3),X9) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X3)),X9) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_311])]) ).
fof(f750,plain,
! [X3,X0,X9] : hAPP(hAPP(c_Set_Oinsert(X0),X3),X9) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X3)),X9),
inference(forward_demodulation,[],[f193,f43]) ).
fof(f193,axiom,
! [X3,X0,X9] : hAPP(hAPP(c_Set_Oinsert(X0),X3),X9) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X3),X0)),X9),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__def_0) ).
fof(f4587,plain,
spl0_310,
inference(avatar_split_clause,[],[f476,f4585]) ).
fof(f476,axiom,
! [X0,X9,X35,X5] :
( ~ hBOOL(c_in(X35,X5,X0))
| ~ hBOOL(c_in(X35,X9,X0))
| hBOOL(c_in(X35,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X5),X9),X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntI_0) ).
fof(f4583,plain,
spl0_309,
inference(avatar_split_clause,[],[f337,f4581]) ).
fof(f337,axiom,
! [X0,X1,X8,X7,X13] :
( ~ class_HOL_Oord(X8)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,X8)),X7),X13))
| hBOOL(hAPP(hAPP(c_lessequals(X8),hAPP(X7,X1)),hAPP(X13,X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__funD_0) ).
fof(f4579,plain,
spl0_308,
inference(avatar_split_clause,[],[f238,f4577]) ).
fof(f238,axiom,
! [X0,X9,X52,X5] :
( ~ hBOOL(c_List_Olistsp(X5,X52,X0))
| ~ hBOOL(c_List_Olistsp(X9,X52,X0))
| hBOOL(c_List_Olistsp(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X5),X9),X52,X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_listsp__infI_0) ).
fof(f4575,plain,
spl0_307,
inference(avatar_split_clause,[],[f217,f4573]) ).
fof(f217,axiom,
! [X3,X0,X8,X9,X5] :
( ~ hBOOL(c_in(X3,X5,X0))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X8,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,X9,X0,tc_fun(X8,tc_bool))),hAPP(X9,X3))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_INT__lower_0) ).
fof(f4571,plain,
spl0_306,
inference(avatar_split_clause,[],[f169,f4569]) ).
fof(f169,axiom,
! [X0,X9,X35,X5] :
( ~ hBOOL(c_in(X35,X5,X0))
| hBOOL(c_in(X35,X9,X0))
| hBOOL(c_in(X35,hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X5),X9),X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_DiffI_0) ).
fof(f4567,plain,
spl0_305,
inference(avatar_split_clause,[],[f102,f4565]) ).
fof(f102,axiom,
! [X0,X9,X35,X5] :
( hBOOL(c_in(X35,X9,X0))
| hBOOL(c_in(X35,X5,X0))
| ~ hBOOL(c_in(X35,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X5),X9),X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UnE_0) ).
fof(f4563,plain,
spl0_304,
inference(avatar_split_clause,[],[f55,f4561]) ).
fof(f4561,plain,
( spl0_304
<=> ! [X9,X0,X8,X5,X1] :
( ~ c_Finite__Set_Ofinite(X5,X0)
| ~ hBOOL(c_in(X1,X5,X0))
| c_Finite__Set_Ofinite(hAPP(X9,X1),X8)
| ~ c_Finite__Set_Ofinite(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,X9,X0,tc_fun(X8,tc_bool)),X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_304])]) ).
fof(f55,axiom,
! [X0,X1,X8,X9,X5] :
( ~ c_Finite__Set_Ofinite(X5,X0)
| ~ hBOOL(c_in(X1,X5,X0))
| c_Finite__Set_Ofinite(hAPP(X9,X1),X8)
| ~ c_Finite__Set_Ofinite(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,X9,X0,tc_fun(X8,tc_bool)),X8) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__UN_0) ).
fof(f4558,plain,
spl0_303,
inference(avatar_split_clause,[],[f32,f4556]) ).
fof(f32,axiom,
! [X3,X0,X8,X9,X5] :
( ~ hBOOL(c_in(X3,X5,X0))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X8,tc_bool)),hAPP(X9,X3)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,X9,X0,tc_fun(X8,tc_bool)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UN__upper_0) ).
fof(f4361,plain,
( spl0_302
| ~ spl0_42
| ~ spl0_227 ),
inference(avatar_split_clause,[],[f3966,f2580,f1198,f4359]) ).
fof(f4359,plain,
( spl0_302
<=> ! [X0] : hBOOL(hAPP(c_SetInterval_Oord__class_OatLeastAtMost(X0,X0,tc_bool),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_302])]) ).
fof(f3966,plain,
( ! [X0] : hBOOL(hAPP(c_SetInterval_Oord__class_OatLeastAtMost(X0,X0,tc_bool),X0))
| ~ spl0_42
| ~ spl0_227 ),
inference(superposition,[],[f1199,f2581]) ).
fof(f3961,plain,
spl0_301,
inference(avatar_split_clause,[],[f919,f3959]) ).
fof(f919,plain,
! [X0,X11,X1,X5] :
( hBOOL(c_in(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X5),X11),X0))
| ~ hBOOL(hAPP(X11,X1))
| ~ hBOOL(c_in(X1,X5,X0)) ),
inference(forward_demodulation,[],[f466,f43]) ).
fof(f466,axiom,
! [X0,X11,X1,X5] :
( ~ hBOOL(hAPP(X11,X1))
| ~ hBOOL(c_in(X1,X5,X0))
| hBOOL(c_in(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X5),c_Collect(X11,X0)),X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__Collect_2) ).
fof(f3957,plain,
spl0_300,
inference(avatar_split_clause,[],[f787,f3955]) ).
fof(f787,plain,
! [X3,X0,X4] :
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),X4) = hAPP(c_Complete__Lattice_OInf__class_OInf(X0),hAPP(hAPP(c_Set_Oinsert(X0),X3),hAPP(c_fequal(X0),X4)))
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) ),
inference(forward_demodulation,[],[f786,f723]) ).
fof(f786,plain,
! [X3,X0,X4] :
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),X4) = hAPP(c_Complete__Lattice_OInf__class_OInf(X0),hAPP(hAPP(c_Set_Oinsert(X0),X3),hAPP(hAPP(c_Set_Oinsert(X0),X4),c_COMBK(c_False,tc_bool,X0))))
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) ),
inference(forward_demodulation,[],[f383,f698]) ).
fof(f383,axiom,
! [X3,X0,X4] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),X4) = hAPP(c_Complete__Lattice_OInf__class_OInf(X0),hAPP(hAPP(c_Set_Oinsert(X0),X3),hAPP(hAPP(c_Set_Oinsert(X0),X4),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Inf__binary_0) ).
fof(f3953,plain,
spl0_299,
inference(avatar_split_clause,[],[f785,f3951]) ).
fof(f785,plain,
! [X3,X0,X4] :
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X3),X4) = hAPP(c_Complete__Lattice_OSup__class_OSup(X0),hAPP(hAPP(c_Set_Oinsert(X0),X3),hAPP(c_fequal(X0),X4)))
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) ),
inference(forward_demodulation,[],[f784,f723]) ).
fof(f784,plain,
! [X3,X0,X4] :
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X3),X4) = hAPP(c_Complete__Lattice_OSup__class_OSup(X0),hAPP(hAPP(c_Set_Oinsert(X0),X3),hAPP(hAPP(c_Set_Oinsert(X0),X4),c_COMBK(c_False,tc_bool,X0))))
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) ),
inference(forward_demodulation,[],[f380,f698]) ).
fof(f380,axiom,
! [X3,X0,X4] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X3),X4) = hAPP(c_Complete__Lattice_OSup__class_OSup(X0),hAPP(hAPP(c_Set_Oinsert(X0),X3),hAPP(hAPP(c_Set_Oinsert(X0),X4),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sup__binary_0) ).
fof(f3949,plain,
spl0_298,
inference(avatar_split_clause,[],[f453,f3947]) ).
fof(f3947,plain,
( spl0_298
<=> ! [X4,X9,X0,X8,X5,X3] :
( ~ hBOOL(c_in(X3,X5,X0))
| hBOOL(hAPP(hAPP(X9,X3),X4))
| ~ hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,X9,X0,tc_fun(X8,tc_bool)),X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_298])]) ).
fof(f453,axiom,
! [X3,X0,X8,X9,X4,X5] :
( ~ hBOOL(c_in(X3,X5,X0))
| hBOOL(hAPP(hAPP(X9,X3),X4))
| ~ hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,X9,X0,tc_fun(X8,tc_bool)),X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_INF1__E_0) ).
fof(f3945,plain,
spl0_297,
inference(avatar_split_clause,[],[f426,f3943]) ).
fof(f426,axiom,
! [X3,X0,X1,X4] :
( ~ class_Lattices_Oupper__semilattice(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),X3),X1))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X3),X4)),X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__supE_0) ).
fof(f3941,plain,
spl0_296,
inference(avatar_split_clause,[],[f425,f3939]) ).
fof(f425,axiom,
! [X3,X0,X1,X4] :
( ~ class_Lattices_Oupper__semilattice(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),X4),X1))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X3),X4)),X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__supE_1) ).
fof(f3937,plain,
spl0_295,
inference(avatar_split_clause,[],[f424,f3935]) ).
fof(f424,axiom,
! [X3,X0,X1,X4] :
( ~ class_Lattices_Oupper__semilattice(X0)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X0),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X3),X4))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__supI1_0) ).
fof(f3933,plain,
spl0_294,
inference(avatar_split_clause,[],[f423,f3931]) ).
fof(f423,axiom,
! [X3,X0,X1,X4] :
( ~ class_Lattices_Oupper__semilattice(X0)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X4))
| hBOOL(hAPP(hAPP(c_lessequals(X0),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X3),X4))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__supI2_0) ).
fof(f3929,plain,
spl0_293,
inference(avatar_split_clause,[],[f334,f3927]) ).
fof(f334,axiom,
! [X3,X0,X1,X4] :
( ~ class_Lattices_Oupper__semilattice(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X4))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X3),X4))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__supI2_0) ).
fof(f3917,plain,
spl0_292,
inference(avatar_split_clause,[],[f333,f3915]) ).
fof(f333,axiom,
! [X3,X0,X1,X4] :
( ~ class_Lattices_Oupper__semilattice(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X3),X4))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__supI1_0) ).
fof(f3913,plain,
spl0_291,
inference(avatar_split_clause,[],[f262,f3911]) ).
fof(f262,axiom,
! [X3,X0,X1,X4] :
( ~ class_Lattices_Olower__semilattice(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X3),X1))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),X4)),X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__infI1_0) ).
fof(f3909,plain,
spl0_290,
inference(avatar_split_clause,[],[f261,f3907]) ).
fof(f261,axiom,
! [X3,X0,X1,X4] :
( ~ class_Lattices_Olower__semilattice(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X4),X1))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),X4)),X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__infI2_0) ).
fof(f3905,plain,
spl0_289,
inference(avatar_split_clause,[],[f252,f3903]) ).
fof(f252,axiom,
! [X0,X9,X5] :
( X5 = X9
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X5),X9))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X9),X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equalityI_0) ).
fof(f3901,plain,
spl0_288,
inference(avatar_split_clause,[],[f210,f3899]) ).
fof(f210,axiom,
! [X3,X0,X8,X9,X4,X5] :
( ~ hBOOL(c_in(X3,X5,X0))
| ~ hBOOL(hAPP(hAPP(X9,X3),X4))
| hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,X9,X0,tc_fun(X8,tc_bool)),X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SUP1__I_0) ).
fof(f3897,plain,
spl0_287,
inference(avatar_split_clause,[],[f189,f3895]) ).
fof(f189,axiom,
! [X3,X0,X1,X4] :
( ~ class_Lattices_Olower__semilattice(X0)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X4),X1))
| hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),X4)),X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__infI2_0) ).
fof(f3893,plain,
spl0_286,
inference(avatar_split_clause,[],[f188,f3891]) ).
fof(f188,axiom,
! [X3,X0,X1,X4] :
( ~ class_Lattices_Olower__semilattice(X0)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X3),X1))
| hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),X4)),X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__infI1_0) ).
fof(f3889,plain,
spl0_285,
inference(avatar_split_clause,[],[f187,f3887]) ).
fof(f187,axiom,
! [X3,X0,X1,X4] :
( ~ class_Lattices_Olower__semilattice(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),X4))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__infE_1) ).
fof(f3885,plain,
spl0_284,
inference(avatar_split_clause,[],[f186,f3883]) ).
fof(f186,axiom,
! [X3,X0,X1,X4] :
( ~ class_Lattices_Olower__semilattice(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),X4))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__infE_0) ).
fof(f3881,plain,
spl0_283,
inference(avatar_split_clause,[],[f47,f3879]) ).
fof(f47,axiom,
! [X3,X0,X5] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
| hAPP(c_Complete__Lattice_OSup__class_OSup(X0),hAPP(hAPP(c_Set_Oinsert(X0),X3),X5)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X3),hAPP(c_Complete__Lattice_OSup__class_OSup(X0),X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sup__insert_0) ).
fof(f3869,plain,
spl0_282,
inference(avatar_split_clause,[],[f42,f3867]) ).
fof(f42,axiom,
! [X3,X0,X5] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
| hAPP(c_Complete__Lattice_OInf__class_OInf(X0),hAPP(hAPP(c_Set_Oinsert(X0),X3),X5)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),hAPP(c_Complete__Lattice_OInf__class_OInf(X0),X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Inf__insert_0) ).
fof(f3865,plain,
( ~ spl0_281
| ~ spl0_65
| ~ spl0_150
| spl0_280 ),
inference(avatar_split_clause,[],[f3860,f3855,f1732,f1295,f3862]) ).
fof(f3855,plain,
( spl0_280
<=> c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(c_COMBK(c_COMBK(c_False,tc_bool,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_bool),t_a),v_c,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_bool,tc_bool)),tc_fun(tc_fun(tc_Com_Ostate,tc_bool),tc_fun(tc_Com_Ostate,tc_bool)),t_a),c_COMBS(tc_Com_Ostate,tc_bool,tc_bool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_bool),tc_fun(tc_Com_Ostate,tc_fun(tc_bool,tc_bool)),t_a),hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),tc_Com_Ostate),c_and)),v_P)),t_a,tc_fun(tc_Com_Ostate,tc_bool),tc_fun(tc_Com_Ostate,tc_bool)),hAPP(hAPP(c_COMBB(tc_bool,tc_bool,tc_Com_Ostate),c_Not),v_b)),t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_280])]) ).
fof(f3860,plain,
( ~ c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(c_COMBK(c_COMBK(c_False,tc_bool,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_bool),t_a),v_c,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_bool,tc_bool)),tc_fun(tc_fun(tc_Com_Ostate,tc_bool),tc_fun(tc_Com_Ostate,tc_bool)),t_a),c_COMBS(tc_Com_Ostate,tc_bool,tc_bool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_bool),tc_fun(tc_Com_Ostate,tc_fun(tc_bool,tc_bool)),t_a),hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),tc_Com_Ostate),c_and)),v_P)),t_a,tc_fun(tc_Com_Ostate,tc_bool),tc_fun(tc_Com_Ostate,tc_bool)),hAPP(hAPP(c_COMBB(tc_bool,tc_bool,tc_Com_Ostate),c_Not),v_b)),t_a)),t_a)
| ~ spl0_65
| ~ spl0_150
| spl0_280 ),
inference(forward_demodulation,[],[f3859,f1733]) ).
fof(f3859,plain,
( ~ c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(c_COMBK(c_COMBK(c_False,tc_bool,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_bool),t_a),v_c,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_bool,tc_bool)),tc_fun(tc_fun(tc_Com_Ostate,tc_bool),tc_fun(tc_Com_Ostate,tc_bool)),t_a),c_COMBS(tc_Com_Ostate,tc_bool,tc_bool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_bool),tc_fun(tc_Com_Ostate,tc_fun(tc_bool,tc_bool)),t_a),hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),tc_Com_Ostate),c_and)),v_P)),t_a,tc_fun(tc_Com_Ostate,tc_bool),tc_fun(tc_Com_Ostate,tc_bool)),hAPP(hAPP(c_COMBB(tc_bool,tc_bool,tc_Com_Ostate),c_Not),v_b)),t_a)),c_COMBK(c_False,tc_bool,tc_Hoare__Mirabelle_Otriple(t_a))),t_a)
| ~ spl0_65
| spl0_280 ),
inference(forward_demodulation,[],[f3857,f1296]) ).
fof(f3857,plain,
( ~ c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(c_COMBK(c_COMBK(c_False,tc_bool,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_bool),t_a),v_c,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_bool,tc_bool)),tc_fun(tc_fun(tc_Com_Ostate,tc_bool),tc_fun(tc_Com_Ostate,tc_bool)),t_a),c_COMBS(tc_Com_Ostate,tc_bool,tc_bool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_bool),tc_fun(tc_Com_Ostate,tc_fun(tc_bool,tc_bool)),t_a),hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),tc_Com_Ostate),c_and)),v_P)),t_a,tc_fun(tc_Com_Ostate,tc_bool),tc_fun(tc_Com_Ostate,tc_bool)),hAPP(hAPP(c_COMBB(tc_bool,tc_bool,tc_Com_Ostate),c_Not),v_b)),t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| spl0_280 ),
inference(avatar_component_clause,[],[f3855]) ).
fof(f3858,plain,
~ spl0_280,
inference(avatar_split_clause,[],[f611,f3855]) ).
fof(f611,axiom,
~ c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(c_COMBK(c_COMBK(c_False,tc_bool,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_bool),t_a),v_c,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_bool,tc_bool)),tc_fun(tc_fun(tc_Com_Ostate,tc_bool),tc_fun(tc_Com_Ostate,tc_bool)),t_a),c_COMBS(tc_Com_Ostate,tc_bool,tc_bool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_bool),tc_fun(tc_Com_Ostate,tc_fun(tc_bool,tc_bool)),t_a),hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),tc_Com_Ostate),c_and)),v_P)),t_a,tc_fun(tc_Com_Ostate,tc_bool),tc_fun(tc_Com_Ostate,tc_bool)),hAPP(hAPP(c_COMBB(tc_bool,tc_bool,tc_Com_Ostate),c_Not),v_b)),t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f3671,plain,
spl0_279,
inference(avatar_split_clause,[],[f846,f3669]) ).
fof(f846,plain,
! [X0,X8,X5,X35] :
( c_COMBK(c_False,tc_bool,X8) = X5
| c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,c_COMBK(X35,tc_fun(X0,tc_bool),X8),X8,tc_fun(X0,tc_bool)) = X35 ),
inference(forward_demodulation,[],[f556,f698]) ).
fof(f556,axiom,
! [X0,X8,X5,X35] :
( c_Orderings_Obot__class_Obot(tc_fun(X8,tc_bool)) = X5
| c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,c_COMBK(X35,tc_fun(X0,tc_bool),X8),X8,tc_fun(X0,tc_bool)) = X35 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UN__constant_1) ).
fof(f3667,plain,
spl0_278,
inference(avatar_split_clause,[],[f845,f3665]) ).
fof(f845,plain,
! [X0,X8,X5,X35] :
( c_COMBK(c_False,tc_bool,X8) = X5
| c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,c_COMBK(X35,tc_fun(X0,tc_bool),X8),X8,tc_fun(X0,tc_bool)) = X35 ),
inference(forward_demodulation,[],[f555,f698]) ).
fof(f555,axiom,
! [X0,X8,X5,X35] :
( c_Orderings_Obot__class_Obot(tc_fun(X8,tc_bool)) = X5
| c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,c_COMBK(X35,tc_fun(X0,tc_bool),X8),X8,tc_fun(X0,tc_bool)) = X35 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_INT__constant_1) ).
fof(f3662,plain,
spl0_277,
inference(avatar_split_clause,[],[f754,f3660]) ).
fof(f3660,plain,
( spl0_277
<=> ! [X3,X0,X9,X8] : hAPP(c_fequal(X0),X3) = hAPP(hAPP(c_Set_Oinsert(X0),X3),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_COMBK(c_False,tc_bool,X8),X9,X8,tc_fun(X0,tc_bool))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_277])]) ).
fof(f754,plain,
! [X3,X0,X8,X9] : hAPP(c_fequal(X0),X3) = hAPP(hAPP(c_Set_Oinsert(X0),X3),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_COMBK(c_False,tc_bool,X8),X9,X8,tc_fun(X0,tc_bool))),
inference(forward_demodulation,[],[f753,f723]) ).
fof(f753,plain,
! [X3,X0,X8,X9] : hAPP(hAPP(c_Set_Oinsert(X0),X3),c_COMBK(c_False,tc_bool,X0)) = hAPP(hAPP(c_Set_Oinsert(X0),X3),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_COMBK(c_False,tc_bool,X8),X9,X8,tc_fun(X0,tc_bool))),
inference(forward_demodulation,[],[f752,f698]) ).
fof(f752,plain,
! [X3,X0,X8,X9] : hAPP(hAPP(c_Set_Oinsert(X0),X3),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))) = hAPP(hAPP(c_Set_Oinsert(X0),X3),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_COMBK(c_False,tc_bool,X8),X9,X8,tc_fun(X0,tc_bool))),
inference(forward_demodulation,[],[f530,f698]) ).
fof(f530,axiom,
! [X3,X0,X8,X9] : hAPP(hAPP(c_Set_Oinsert(X0),X3),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))) = hAPP(hAPP(c_Set_Oinsert(X0),X3),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Obot__class_Obot(tc_fun(X8,tc_bool)),X9,X8,tc_fun(X0,tc_bool))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UN__extend__simps_I1_J_0) ).
fof(f3658,plain,
spl0_276,
inference(avatar_split_clause,[],[f735,f3656]) ).
fof(f3656,plain,
( spl0_276
<=> ! [X5,X0,X8] : c_COMBK(c_False,tc_bool,X0) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,c_COMBK(c_COMBK(c_False,tc_bool,X0),tc_fun(X0,tc_bool),X8),X8,tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_276])]) ).
fof(f735,plain,
! [X0,X8,X5] : c_COMBK(c_False,tc_bool,X0) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,c_COMBK(c_COMBK(c_False,tc_bool,X0),tc_fun(X0,tc_bool),X8),X8,tc_fun(X0,tc_bool)),
inference(forward_demodulation,[],[f554,f698]) ).
fof(f554,axiom,
! [X0,X8,X5] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,c_COMBK(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool),X8),X8,tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UN__empty2_0) ).
fof(f3654,plain,
spl0_275,
inference(avatar_split_clause,[],[f734,f3652]) ).
fof(f734,plain,
! [X0,X9,X5] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X5),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X9),X5)) = c_COMBK(c_False,tc_bool,X0),
inference(forward_demodulation,[],[f311,f698]) ).
fof(f311,axiom,
! [X0,X9,X5] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X5),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X9),X5)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__disjoint_0) ).
fof(f3650,plain,
spl0_274,
inference(avatar_split_clause,[],[f309,f3648]) ).
fof(f3648,plain,
( spl0_274
<=> ! [X2,X0,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_274])]) ).
fof(f309,axiom,
! [X2,X0,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__left__idem_0) ).
fof(f3646,plain,
( spl0_273
| ~ spl0_38
| ~ spl0_177 ),
inference(avatar_split_clause,[],[f3485,f1940,f1179,f3643]) ).
fof(f3643,plain,
( spl0_273
<=> hBOOL(c_Orderings_Otop__class_Otop(tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_273])]) ).
fof(f1940,plain,
( spl0_177
<=> c_Orderings_Otop__class_Otop(tc_bool) = hAPP(c_Orderings_Otop__class_Otop(tc_fun(t_a,tc_bool)),v_x) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_177])]) ).
fof(f3485,plain,
( hBOOL(c_Orderings_Otop__class_Otop(tc_bool))
| ~ spl0_38
| ~ spl0_177 ),
inference(superposition,[],[f1180,f1942]) ).
fof(f1942,plain,
( c_Orderings_Otop__class_Otop(tc_bool) = hAPP(c_Orderings_Otop__class_Otop(tc_fun(t_a,tc_bool)),v_x)
| ~ spl0_177 ),
inference(avatar_component_clause,[],[f1940]) ).
fof(f3641,plain,
spl0_272,
inference(avatar_split_clause,[],[f308,f3639]) ).
fof(f308,axiom,
! [X2,X0,X1] :
( ~ class_Lattices_Olattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I4_J_0) ).
fof(f3637,plain,
spl0_271,
inference(avatar_split_clause,[],[f216,f3635]) ).
fof(f216,axiom,
! [X0,X18,X8,X19,X5] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X8)
| ~ hBOOL(c_in(X19,X5,X0))
| hBOOL(hAPP(hAPP(c_lessequals(X8),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,X18,X0,X8)),hAPP(X18,X19))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_INF__leI_0) ).
fof(f3633,plain,
spl0_270,
inference(avatar_split_clause,[],[f206,f3631]) ).
fof(f3631,plain,
( spl0_270
<=> ! [X2,X0,X1] :
( ~ class_Lattices_Olattice(X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_270])]) ).
fof(f206,axiom,
! [X2,X0,X1] :
( ~ class_Lattices_Olattice(X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I8_J_0) ).
fof(f3629,plain,
spl0_269,
inference(avatar_split_clause,[],[f205,f3627]) ).
fof(f205,axiom,
! [X2,X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__left__idem_0) ).
fof(f3625,plain,
spl0_268,
inference(avatar_split_clause,[],[f31,f3623]) ).
fof(f31,axiom,
! [X0,X18,X8,X19,X5] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X8)
| ~ hBOOL(c_in(X19,X5,X0))
| hBOOL(hAPP(hAPP(c_lessequals(X8),hAPP(X18,X19)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,X18,X0,X8))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__SUPI_0) ).
fof(f3139,plain,
spl0_267,
inference(avatar_split_clause,[],[f941,f3137]) ).
fof(f3137,plain,
( spl0_267
<=> ! [X0,X11] :
( ~ c_Finite__Set_Ofinite(hAPP(hAPP(c_COMBB(tc_bool,tc_bool,X0),c_Not),X11),X0)
| ~ c_Finite__Set_Ofinite(X11,X0)
| c_Finite__Set_Ofinite(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_267])]) ).
fof(f941,plain,
! [X0,X11] :
( ~ c_Finite__Set_Ofinite(hAPP(hAPP(c_COMBB(tc_bool,tc_bool,X0),c_Not),X11),X0)
| ~ c_Finite__Set_Ofinite(X11,X0)
| c_Finite__Set_Ofinite(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0) ),
inference(forward_demodulation,[],[f940,f43]) ).
fof(f940,plain,
! [X0,X11] :
( ~ c_Finite__Set_Ofinite(X11,X0)
| c_Finite__Set_Ofinite(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0)
| ~ c_Finite__Set_Ofinite(c_Collect(hAPP(hAPP(c_COMBB(tc_bool,tc_bool,X0),c_Not),X11),X0),X0) ),
inference(forward_demodulation,[],[f20,f43]) ).
fof(f20,axiom,
! [X0,X11] :
( ~ c_Finite__Set_Ofinite(c_Collect(X11,X0),X0)
| c_Finite__Set_Ofinite(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0)
| ~ c_Finite__Set_Ofinite(c_Collect(hAPP(hAPP(c_COMBB(tc_bool,tc_bool,X0),c_Not),X11),X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Collect__not_0) ).
fof(f3135,plain,
spl0_266,
inference(avatar_split_clause,[],[f844,f3133]) ).
fof(f844,plain,
! [X0,X9,X5] :
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X5),X9) != c_COMBK(c_False,tc_bool,X0)
| c_COMBK(c_False,tc_bool,X0) = X5 ),
inference(forward_demodulation,[],[f843,f698]) ).
fof(f843,plain,
! [X0,X9,X5] :
( c_COMBK(c_False,tc_bool,X0) = X5
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X5),X9) ),
inference(forward_demodulation,[],[f375,f698]) ).
fof(f375,axiom,
! [X0,X9,X5] :
( c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X5
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X5),X9) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__empty_0) ).
fof(f3131,plain,
spl0_265,
inference(avatar_split_clause,[],[f842,f3129]) ).
fof(f842,plain,
! [X0,X9,X5] :
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X5),X9) != c_COMBK(c_False,tc_bool,X0)
| c_COMBK(c_False,tc_bool,X0) = X9 ),
inference(forward_demodulation,[],[f841,f698]) ).
fof(f841,plain,
! [X0,X9,X5] :
( c_COMBK(c_False,tc_bool,X0) = X9
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X5),X9) ),
inference(forward_demodulation,[],[f374,f698]) ).
fof(f374,axiom,
! [X0,X9,X5] :
( c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X9
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X5),X9) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__empty_1) ).
fof(f3127,plain,
spl0_264,
inference(avatar_split_clause,[],[f730,f3125]) ).
fof(f3125,plain,
( spl0_264
<=> ! [X9,X0,X5,X8] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_COMBK(c_False,tc_bool,X8),X5,X8,tc_fun(X0,tc_bool))),X9) = X9 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_264])]) ).
fof(f730,plain,
! [X0,X8,X9,X5] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_COMBK(c_False,tc_bool,X8),X5,X8,tc_fun(X0,tc_bool))),X9) = X9,
inference(forward_demodulation,[],[f218,f698]) ).
fof(f218,axiom,
! [X0,X8,X9,X5] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Obot__class_Obot(tc_fun(X8,tc_bool)),X5,X8,tc_fun(X0,tc_bool))),X9) = X9,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UN__extend__simps_I2_J_0) ).
fof(f3123,plain,
spl0_263,
inference(avatar_split_clause,[],[f727,f3121]) ).
fof(f727,plain,
! [X0,X8,X9,X5] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X5),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_COMBK(c_False,tc_bool,X8),X9,X8,tc_fun(X0,tc_bool))) = X5,
inference(forward_demodulation,[],[f219,f698]) ).
fof(f219,axiom,
! [X0,X8,X9,X5] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X5),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Obot__class_Obot(tc_fun(X8,tc_bool)),X9,X8,tc_fun(X0,tc_bool))) = X5,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UN__extend__simps_I3_J_0) ).
fof(f3119,plain,
spl0_262,
inference(avatar_split_clause,[],[f726,f3117]) ).
fof(f726,plain,
! [X0,X8,X9,X5] : hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X5),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_COMBK(c_False,tc_bool,X8),X9,X8,tc_fun(X0,tc_bool))) = X5,
inference(forward_demodulation,[],[f8,f698]) ).
fof(f8,axiom,
! [X0,X8,X9,X5] : hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X5),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Obot__class_Obot(tc_fun(X8,tc_bool)),X9,X8,tc_fun(X0,tc_bool))) = X5,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_INT__extend__simps_I4_J_0) ).
fof(f3115,plain,
( spl0_261
| ~ spl0_99
| ~ spl0_150 ),
inference(avatar_split_clause,[],[f1789,f1732,f1472,f3113]) ).
fof(f1789,plain,
( ! [X0,X1] : hAPP(c_fequal(X0),X1) != c_COMBK(c_False,tc_bool,X0)
| ~ spl0_99
| ~ spl0_150 ),
inference(superposition,[],[f1473,f1733]) ).
fof(f3111,plain,
spl0_260,
inference(avatar_split_clause,[],[f487,f3109]) ).
fof(f487,axiom,
! [X3,X0,X4] :
( ~ class_Orderings_Oorder(X0)
| X3 = X4
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X4),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X4),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I11_J_0) ).
fof(f3107,plain,
spl0_259,
inference(avatar_split_clause,[],[f478,f3105]) ).
fof(f478,axiom,
! [X0,X1,X9,X5] :
( ~ hBOOL(hAPP(X5,X1))
| ~ hBOOL(hAPP(X9,X1))
| hBOOL(hAPP(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X5),X9),X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf1I_0) ).
fof(f3103,plain,
spl0_258,
inference(avatar_split_clause,[],[f443,f3101]) ).
fof(f443,axiom,
! [X0,X8,X9,X7,X5] :
( ~ c_Fun_Oinj__on(X7,X9,X0,X8)
| c_Fun_Oinj__on(X7,X5,X0,X8)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X5),X9)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__inj__on_0) ).
fof(f3099,plain,
spl0_257,
inference(avatar_split_clause,[],[f437,f3097]) ).
fof(f437,axiom,
! [X0,X9,X35,X5] :
( ~ hBOOL(c_in(X35,X5,X0))
| hBOOL(c_in(X35,X9,X0))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X5),X9)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subsetD_0) ).
fof(f3095,plain,
spl0_256,
inference(avatar_split_clause,[],[f271,f3093]) ).
fof(f271,axiom,
! [X0,X9,X5] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X5),X9))
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X5),X9) != X9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__Un__eq_1) ).
fof(f3091,plain,
spl0_255,
inference(avatar_split_clause,[],[f270,f3089]) ).
fof(f270,axiom,
! [X0,X9,X5] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X9),X5))
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X5),X9) = X5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__absorb2_0) ).
fof(f3087,plain,
spl0_254,
inference(avatar_split_clause,[],[f269,f3085]) ).
fof(f269,axiom,
! [X0,X9,X5] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X5),X9))
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X5),X9) = X9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__absorb1_0) ).
fof(f3083,plain,
spl0_253,
inference(avatar_split_clause,[],[f254,f3081]) ).
fof(f254,axiom,
! [X2,X0,X1] :
( ~ class_Orderings_Oorder(X0)
| X1 = X2
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X2),X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__eq__iff_2) ).
fof(f3079,plain,
spl0_252,
inference(avatar_split_clause,[],[f171,f3077]) ).
fof(f171,axiom,
! [X0,X1,X9,X5] :
( hBOOL(c_in(X1,X9,X0))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Set_Oinsert(X0),X1),X5)),X9)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__subset_0) ).
fof(f3075,plain,
spl0_251,
inference(avatar_split_clause,[],[f142,f3073]) ).
fof(f142,axiom,
! [X0,X9,X5] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X9),X5))
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X5),X9) = X9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__absorb1_0) ).
fof(f3061,plain,
spl0_250,
inference(avatar_split_clause,[],[f141,f3059]) ).
fof(f141,axiom,
! [X0,X9,X5] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X5),X9))
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X5),X9) = X5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__absorb2_0) ).
fof(f3057,plain,
spl0_249,
inference(avatar_split_clause,[],[f97,f3055]) ).
fof(f97,axiom,
! [X0,X1,X9,X5] :
( hBOOL(hAPP(X9,X1))
| hBOOL(hAPP(X5,X1))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X5),X9),X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup1E_0) ).
fof(f3053,plain,
spl0_248,
inference(avatar_split_clause,[],[f87,f3051]) ).
fof(f87,axiom,
! [X0,X36,X1,X8,X5] :
( ~ hBOOL(c_in(X1,X36,X0))
| ~ c_Finite__Set_Ofinite(hAPP(X5,X1),X8)
| c_Finite__Set_Ofinite(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X36,X5,X0,tc_fun(X8,tc_bool)),X8) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__INT_0) ).
fof(f3035,plain,
( spl0_247
| ~ spl0_125
| ~ spl0_126 ),
inference(avatar_split_clause,[],[f1661,f1615,f1611,f3033]) ).
fof(f1661,plain,
( ! [X0,X1] :
( c_Finite__Set_Ofinite(X1,X0)
| ~ c_Finite__Set_Ofinite(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0) )
| ~ spl0_125
| ~ spl0_126 ),
inference(superposition,[],[f1616,f1612]) ).
fof(f2701,plain,
( spl0_246
| ~ spl0_1
| ~ spl0_100
| ~ spl0_117 ),
inference(avatar_split_clause,[],[f1585,f1553,f1483,f1017,f2698]) ).
fof(f2698,plain,
( spl0_246
<=> c_False = hAPP(c_Complete__Lattice_OSup__class_OSup(tc_bool),c_COMBK(c_False,tc_bool,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_246])]) ).
fof(f1585,plain,
( c_False = hAPP(c_Complete__Lattice_OSup__class_OSup(tc_bool),c_COMBK(c_False,tc_bool,tc_bool))
| ~ spl0_1
| ~ spl0_100
| ~ spl0_117 ),
inference(forward_demodulation,[],[f1583,f1485]) ).
fof(f1583,plain,
( c_Orderings_Obot__class_Obot(tc_bool) = hAPP(c_Complete__Lattice_OSup__class_OSup(tc_bool),c_COMBK(c_False,tc_bool,tc_bool))
| ~ spl0_1
| ~ spl0_117 ),
inference(resolution,[],[f1554,f1019]) ).
fof(f2696,plain,
spl0_245,
inference(avatar_split_clause,[],[f900,f2694]) ).
fof(f900,plain,
! [X3,X0,X4] :
( c_SetInterval_Oord__class_OatLeastAtMost(X3,X4,X0) = c_COMBK(c_False,tc_bool,X0)
| ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),X3),X4)) ),
inference(forward_demodulation,[],[f279,f698]) ).
fof(f279,axiom,
! [X3,X0,X4] :
( ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),X3),X4))
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_SetInterval_Oord__class_OatLeastAtMost(X3,X4,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastatMost__empty__iff2_1) ).
fof(f2692,plain,
spl0_244,
inference(avatar_split_clause,[],[f898,f2690]) ).
fof(f2690,plain,
( spl0_244
<=> ! [X4,X0,X3] :
( c_SetInterval_Oord__class_OatLeastAtMost(X3,X4,X0) != c_COMBK(c_False,tc_bool,X0)
| ~ class_Orderings_Oorder(X0)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X3),X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_244])]) ).
fof(f898,plain,
! [X3,X0,X4] :
( c_SetInterval_Oord__class_OatLeastAtMost(X3,X4,X0) != c_COMBK(c_False,tc_bool,X0)
| ~ class_Orderings_Oorder(X0)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X3),X4)) ),
inference(forward_demodulation,[],[f459,f698]) ).
fof(f459,axiom,
! [X3,X0,X4] :
( ~ class_Orderings_Oorder(X0)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X3),X4))
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != c_SetInterval_Oord__class_OatLeastAtMost(X3,X4,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastatMost__empty__iff_0) ).
fof(f2688,plain,
spl0_243,
inference(avatar_split_clause,[],[f897,f2686]) ).
fof(f897,plain,
! [X3,X0,X4] :
( c_SetInterval_Oord__class_OatLeastAtMost(X3,X4,X0) = c_COMBK(c_False,tc_bool,X0)
| ~ class_Orderings_Oorder(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X4),X3)) ),
inference(forward_demodulation,[],[f248,f698]) ).
fof(f248,axiom,
! [X3,X0,X4] :
( ~ class_Orderings_Oorder(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X4),X3))
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_SetInterval_Oord__class_OatLeastAtMost(X3,X4,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastatMost__empty_0) ).
fof(f2684,plain,
spl0_242,
inference(avatar_split_clause,[],[f896,f2682]) ).
fof(f896,plain,
! [X0,X18,X8,X5] :
( c_COMBK(c_False,tc_bool,X0) = X5
| ~ class_Complete__Lattice_Ocomplete__lattice(X8)
| c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,c_COMBK(X18,X8,X0),X0,X8) = X18 ),
inference(forward_demodulation,[],[f551,f698]) ).
fof(f551,axiom,
! [X0,X18,X8,X5] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X8)
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X5
| c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,c_COMBK(X18,X8,X0),X0,X8) = X18 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SUP__const_0) ).
fof(f2680,plain,
spl0_241,
inference(avatar_split_clause,[],[f895,f2678]) ).
fof(f895,plain,
! [X0,X18,X8,X5] :
( c_COMBK(c_False,tc_bool,X0) = X5
| ~ class_Complete__Lattice_Ocomplete__lattice(X8)
| c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,c_COMBK(X18,X8,X0),X0,X8) = X18 ),
inference(forward_demodulation,[],[f549,f698]) ).
fof(f549,axiom,
! [X0,X18,X8,X5] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X8)
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X5
| c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,c_COMBK(X18,X8,X0),X0,X8) = X18 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_INF__const_0) ).
fof(f2676,plain,
spl0_240,
inference(avatar_split_clause,[],[f866,f2674]) ).
fof(f2674,plain,
( spl0_240
<=> ! [X21,X3,X0,X26,X27,X24,X22,X25,X23,X20] :
( hAPP(X22,hAPP(c_fequal(X0),X3)) = X3
| ~ c_Complete__Lattice_Ocomplete__lattice(X22,X20,X23,X24,X25,X26,X27,X21,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_240])]) ).
fof(f866,plain,
! [X21,X3,X0,X26,X27,X24,X22,X25,X23,X20] :
( hAPP(X22,hAPP(c_fequal(X0),X3)) = X3
| ~ c_Complete__Lattice_Ocomplete__lattice(X22,X20,X23,X24,X25,X26,X27,X21,X0) ),
inference(forward_demodulation,[],[f865,f723]) ).
fof(f865,plain,
! [X21,X3,X0,X26,X27,X24,X22,X25,X23,X20] :
( hAPP(X22,hAPP(hAPP(c_Set_Oinsert(X0),X3),c_COMBK(c_False,tc_bool,X0))) = X3
| ~ c_Complete__Lattice_Ocomplete__lattice(X22,X20,X23,X24,X25,X26,X27,X21,X0) ),
inference(forward_demodulation,[],[f526,f698]) ).
fof(f526,axiom,
! [X21,X3,X0,X26,X27,X24,X22,X25,X23,X20] :
( ~ c_Complete__Lattice_Ocomplete__lattice(X22,X20,X23,X24,X25,X26,X27,X21,X0)
| hAPP(X22,hAPP(hAPP(c_Set_Oinsert(X0),X3),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)))) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complete__lattice_OInf__singleton_0) ).
fof(f2672,plain,
spl0_239,
inference(avatar_split_clause,[],[f864,f2670]) ).
fof(f2670,plain,
( spl0_239
<=> ! [X21,X3,X0,X26,X27,X24,X22,X25,X23,X20] :
( hAPP(X20,hAPP(c_fequal(X0),X3)) = X3
| ~ c_Complete__Lattice_Ocomplete__lattice(X22,X20,X23,X24,X25,X26,X27,X21,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_239])]) ).
fof(f864,plain,
! [X21,X3,X0,X26,X27,X24,X22,X25,X23,X20] :
( hAPP(X20,hAPP(c_fequal(X0),X3)) = X3
| ~ c_Complete__Lattice_Ocomplete__lattice(X22,X20,X23,X24,X25,X26,X27,X21,X0) ),
inference(forward_demodulation,[],[f863,f723]) ).
fof(f863,plain,
! [X21,X3,X0,X26,X27,X24,X22,X25,X23,X20] :
( hAPP(X20,hAPP(hAPP(c_Set_Oinsert(X0),X3),c_COMBK(c_False,tc_bool,X0))) = X3
| ~ c_Complete__Lattice_Ocomplete__lattice(X22,X20,X23,X24,X25,X26,X27,X21,X0) ),
inference(forward_demodulation,[],[f527,f698]) ).
fof(f527,axiom,
! [X21,X3,X0,X26,X27,X24,X22,X25,X23,X20] :
( ~ c_Complete__Lattice_Ocomplete__lattice(X22,X20,X23,X24,X25,X26,X27,X21,X0)
| hAPP(X20,hAPP(hAPP(c_Set_Oinsert(X0),X3),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)))) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complete__lattice_OSup__singleton_0) ).
fof(f2668,plain,
spl0_238,
inference(avatar_split_clause,[],[f853,f2666]) ).
fof(f2666,plain,
( spl0_238
<=> ! [X21,X0,X26,X27,X24,X22,X25,X23,X20] :
( hAPP(X22,c_COMBK(c_False,tc_bool,X0)) = X21
| ~ c_Complete__Lattice_Ocomplete__lattice(X22,X20,X23,X24,X25,X26,X27,X21,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_238])]) ).
fof(f853,plain,
! [X21,X0,X26,X27,X24,X22,X25,X23,X20] :
( hAPP(X22,c_COMBK(c_False,tc_bool,X0)) = X21
| ~ c_Complete__Lattice_Ocomplete__lattice(X22,X20,X23,X24,X25,X26,X27,X21,X0) ),
inference(forward_demodulation,[],[f349,f698]) ).
fof(f349,axiom,
! [X21,X0,X26,X27,X24,X22,X25,X23,X20] :
( hAPP(X22,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))) = X21
| ~ c_Complete__Lattice_Ocomplete__lattice(X22,X20,X23,X24,X25,X26,X27,X21,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complete__lattice_OInf__empty_0) ).
fof(f2664,plain,
spl0_237,
inference(avatar_split_clause,[],[f852,f2662]) ).
fof(f2662,plain,
( spl0_237
<=> ! [X24,X23,X20,X0,X22,X27,X25,X21,X26] :
( hAPP(X20,c_COMBK(c_False,tc_bool,X0)) = X27
| ~ c_Complete__Lattice_Ocomplete__lattice(X22,X20,X23,X24,X25,X26,X27,X21,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_237])]) ).
fof(f852,plain,
! [X21,X0,X26,X27,X24,X22,X25,X23,X20] :
( hAPP(X20,c_COMBK(c_False,tc_bool,X0)) = X27
| ~ c_Complete__Lattice_Ocomplete__lattice(X22,X20,X23,X24,X25,X26,X27,X21,X0) ),
inference(forward_demodulation,[],[f350,f698]) ).
fof(f350,axiom,
! [X21,X0,X26,X27,X24,X22,X25,X23,X20] :
( hAPP(X20,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))) = X27
| ~ c_Complete__Lattice_Ocomplete__lattice(X22,X20,X23,X24,X25,X26,X27,X21,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complete__lattice_OSup__empty_0) ).
fof(f2660,plain,
spl0_236,
inference(avatar_split_clause,[],[f840,f2658]) ).
fof(f840,plain,
! [X0,X5] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X5),c_COMBK(c_False,tc_bool,X0)))
| c_COMBK(c_False,tc_bool,X0) = X5 ),
inference(forward_demodulation,[],[f839,f698]) ).
fof(f839,plain,
! [X0,X5] :
( c_COMBK(c_False,tc_bool,X0) = X5
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X5),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)))) ),
inference(forward_demodulation,[],[f357,f698]) ).
fof(f357,axiom,
! [X0,X5] :
( c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X5
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X5),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__empty_0) ).
fof(f2656,plain,
( spl0_235
| ~ spl0_1
| ~ spl0_100
| ~ spl0_107 ),
inference(avatar_split_clause,[],[f1565,f1512,f1483,f1017,f2653]) ).
fof(f2653,plain,
( spl0_235
<=> c_False = hAPP(c_Complete__Lattice_OInf__class_OInf(tc_bool),c_Orderings_Otop__class_Otop(tc_fun(tc_bool,tc_bool))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_235])]) ).
fof(f1565,plain,
( c_False = hAPP(c_Complete__Lattice_OInf__class_OInf(tc_bool),c_Orderings_Otop__class_Otop(tc_fun(tc_bool,tc_bool)))
| ~ spl0_1
| ~ spl0_100
| ~ spl0_107 ),
inference(forward_demodulation,[],[f1563,f1485]) ).
fof(f1563,plain,
( c_Orderings_Obot__class_Obot(tc_bool) = hAPP(c_Complete__Lattice_OInf__class_OInf(tc_bool),c_Orderings_Otop__class_Otop(tc_fun(tc_bool,tc_bool)))
| ~ spl0_1
| ~ spl0_107 ),
inference(resolution,[],[f1513,f1019]) ).
fof(f2651,plain,
spl0_234,
inference(avatar_split_clause,[],[f747,f2649]) ).
fof(f747,plain,
! [X3,X0,X5] : hAPP(hAPP(c_Set_Oinsert(X0),X3),X5) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),hAPP(c_fequal(X0),X3)),X5),
inference(forward_demodulation,[],[f746,f723]) ).
fof(f746,plain,
! [X3,X0,X5] : hAPP(hAPP(c_Set_Oinsert(X0),X3),X5) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Set_Oinsert(X0),X3),c_COMBK(c_False,tc_bool,X0))),X5),
inference(forward_demodulation,[],[f547,f698]) ).
fof(f547,axiom,
! [X3,X0,X5] : hAPP(hAPP(c_Set_Oinsert(X0),X3),X5) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Set_Oinsert(X0),X3),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)))),X5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__is__Un_0) ).
fof(f2647,plain,
spl0_233,
inference(avatar_split_clause,[],[f607,f2645]) ).
fof(f607,axiom,
! [X0,X11,X8,X57,X14,X67] : hAPP(hAPP(hAPP(c_COMBS(X8,X14,X0),X11),X57),X67) = hAPP(hAPP(X11,X67),hAPP(X57,X67)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_COMBS__def_0) ).
fof(f2643,plain,
spl0_232,
inference(avatar_split_clause,[],[f601,f2641]) ).
fof(f601,axiom,
! [X0,X1,X5] : hAPP(hAPP(c_Set_Oinsert(X0),X1),X5) = hAPP(hAPP(c_Set_Oinsert(X0),X1),hAPP(hAPP(c_Set_Oinsert(X0),X1),X5)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__absorb2_0) ).
fof(f2639,plain,
spl0_231,
inference(avatar_split_clause,[],[f390,f2637]) ).
fof(f390,axiom,
! [X3,X0,X4,X5] :
( X3 = X4
| hBOOL(c_in(X3,X5,X0))
| ~ hBOOL(c_in(X3,hAPP(hAPP(c_Set_Oinsert(X0),X4),X5),X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insertE_0) ).
fof(f2635,plain,
spl0_230,
inference(avatar_split_clause,[],[f94,f2633]) ).
fof(f94,axiom,
! [X2,X0,X1,X8,X7] :
( X1 = X2
| hAPP(X7,X1) != hAPP(X7,X2)
| ~ c_Fun_Oinj__on(X7,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0,X8) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_injD_0) ).
fof(f2631,plain,
spl0_229,
inference(avatar_split_clause,[],[f36,f2629]) ).
fof(f2629,plain,
( spl0_229
<=> ! [X21,X0,X26,X27,X24,X22,X25,X23,X20] :
( hAPP(X22,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool))) = X27
| ~ c_Complete__Lattice_Ocomplete__lattice(X22,X20,X23,X24,X25,X26,X27,X21,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_229])]) ).
fof(f36,axiom,
! [X21,X0,X26,X27,X24,X22,X25,X23,X20] :
( hAPP(X22,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool))) = X27
| ~ c_Complete__Lattice_Ocomplete__lattice(X22,X20,X23,X24,X25,X26,X27,X21,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complete__lattice_OInf__UNIV_0) ).
fof(f2627,plain,
spl0_228,
inference(avatar_split_clause,[],[f35,f2625]) ).
fof(f2625,plain,
( spl0_228
<=> ! [X24,X23,X20,X0,X22,X27,X25,X21,X26] :
( hAPP(X20,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool))) = X21
| ~ c_Complete__Lattice_Ocomplete__lattice(X22,X20,X23,X24,X25,X26,X27,X21,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_228])]) ).
fof(f35,axiom,
! [X21,X0,X26,X27,X24,X22,X25,X23,X20] :
( hAPP(X20,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool))) = X21
| ~ c_Complete__Lattice_Ocomplete__lattice(X22,X20,X23,X24,X25,X26,X27,X21,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complete__lattice_OSup__UNIV_0) ).
fof(f2582,plain,
( spl0_227
| ~ spl0_9
| ~ spl0_97 ),
inference(avatar_split_clause,[],[f1479,f1448,f1057,f2580]) ).
fof(f1479,plain,
( ! [X0] : hAPP(c_fequal(tc_bool),X0) = c_SetInterval_Oord__class_OatLeastAtMost(X0,X0,tc_bool)
| ~ spl0_9
| ~ spl0_97 ),
inference(resolution,[],[f1449,f1059]) ).
fof(f2368,plain,
( spl0_226
| ~ spl0_1
| ~ spl0_96 ),
inference(avatar_split_clause,[],[f1477,f1444,f1017,f2366]) ).
fof(f1477,plain,
( ! [X0] : hAPP(c_Complete__Lattice_OInf__class_OInf(tc_bool),hAPP(c_fequal(tc_bool),X0)) = X0
| ~ spl0_1
| ~ spl0_96 ),
inference(resolution,[],[f1445,f1019]) ).
fof(f2301,plain,
spl0_225,
inference(avatar_split_clause,[],[f498,f2299]) ).
fof(f498,axiom,
! [X0,X1,X5] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
| ~ hBOOL(c_in(X1,X5,X0))
| hBOOL(hAPP(hAPP(c_lessequals(X0),X1),hAPP(c_Complete__Lattice_OSup__class_OSup(X0),X5))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sup__upper_0) ).
fof(f2297,plain,
spl0_224,
inference(avatar_split_clause,[],[f448,f2295]) ).
fof(f448,axiom,
! [X0,X11,X1,X57] :
( ~ hBOOL(hAPP(X11,X1))
| hBOOL(hAPP(X57,X1))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X11),X57)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__predicate1D_0) ).
fof(f2293,plain,
spl0_223,
inference(avatar_split_clause,[],[f418,f2291]) ).
fof(f418,axiom,
! [X0,X9,X35,X5] :
( ~ hBOOL(c_in(X35,X5,X0))
| hBOOL(c_in(X35,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X5),X9),X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UnCI_1) ).
fof(f2289,plain,
( spl0_222
| ~ spl0_1
| ~ spl0_95 ),
inference(avatar_split_clause,[],[f1475,f1440,f1017,f2287]) ).
fof(f1475,plain,
( ! [X0] : hAPP(c_Complete__Lattice_OSup__class_OSup(tc_bool),hAPP(c_fequal(tc_bool),X0)) = X0
| ~ spl0_1
| ~ spl0_95 ),
inference(resolution,[],[f1441,f1019]) ).
fof(f2285,plain,
spl0_221,
inference(avatar_split_clause,[],[f417,f2283]) ).
fof(f417,axiom,
! [X0,X9,X35,X5] :
( ~ hBOOL(c_in(X35,X9,X0))
| hBOOL(c_in(X35,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X5),X9),X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UnCI_0) ).
fof(f2281,plain,
spl0_220,
inference(avatar_split_clause,[],[f325,f2279]) ).
fof(f325,axiom,
! [X0,X8,X9,X7,X5] :
( c_Fun_Oinj__on(X7,X5,X0,X8)
| ~ c_Fun_Oinj__on(X7,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X5),X9),X0,X8) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__Un_0) ).
fof(f2277,plain,
spl0_219,
inference(avatar_split_clause,[],[f324,f2275]) ).
fof(f324,axiom,
! [X0,X8,X9,X7,X5] :
( c_Fun_Oinj__on(X7,X9,X0,X8)
| ~ c_Fun_Oinj__on(X7,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X5),X9),X0,X8) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__Un_1) ).
fof(f2273,plain,
spl0_218,
inference(avatar_split_clause,[],[f277,f2271]) ).
fof(f277,axiom,
! [X0,X1,X5] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
| ~ hBOOL(c_in(X1,X5,X0))
| hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(c_Complete__Lattice_OInf__class_OInf(X0),X5)),X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Inf__lower_0) ).
fof(f2269,plain,
spl0_217,
inference(avatar_split_clause,[],[f268,f2267]) ).
fof(f268,axiom,
! [X2,X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2))
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2) = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__sup_0) ).
fof(f2265,plain,
spl0_216,
inference(avatar_split_clause,[],[f267,f2263]) ).
fof(f267,axiom,
! [X2,X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2))
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2) != X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__sup_1) ).
fof(f2261,plain,
spl0_215,
inference(avatar_split_clause,[],[f266,f2259]) ).
fof(f266,axiom,
! [X2,X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X2),X1))
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__absorb1_0) ).
fof(f2257,plain,
spl0_214,
inference(avatar_split_clause,[],[f197,f2255]) ).
fof(f2253,plain,
spl0_213,
inference(avatar_split_clause,[],[f157,f2251]) ).
fof(f2249,plain,
spl0_212,
inference(avatar_split_clause,[],[f145,f2247]) ).
fof(f145,axiom,
! [X2,X0,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X2),X1))
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2) = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__absorb2_0) ).
fof(f2239,plain,
spl0_211,
inference(avatar_split_clause,[],[f144,f2237]) ).
fof(f144,axiom,
! [X2,X0,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2))
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2) != X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__inf_1) ).
fof(f2235,plain,
spl0_210,
inference(avatar_split_clause,[],[f143,f2233]) ).
fof(f143,axiom,
! [X2,X0,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2))
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__inf_0) ).
fof(f2231,plain,
spl0_209,
inference(avatar_split_clause,[],[f136,f2229]) ).
fof(f136,axiom,
! [X0,X9,X35,X5] :
( hBOOL(c_in(X35,X5,X0))
| ~ hBOOL(c_in(X35,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X5),X9),X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntE_0) ).
fof(f2227,plain,
spl0_208,
inference(avatar_split_clause,[],[f135,f2225]) ).
fof(f135,axiom,
! [X0,X9,X35,X5] :
( hBOOL(c_in(X35,X9,X0))
| ~ hBOOL(c_in(X35,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X5),X9),X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntE_1) ).
fof(f2223,plain,
spl0_207,
inference(avatar_split_clause,[],[f63,f2221]) ).
fof(f63,axiom,
! [X0,X9,X35,X5] :
( ~ hBOOL(c_in(X35,X9,X0))
| ~ hBOOL(c_in(X35,hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X5),X9),X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_DiffE_1) ).
fof(f2219,plain,
spl0_206,
inference(avatar_split_clause,[],[f58,f2217]) ).
fof(f58,axiom,
! [X0,X9,X35,X5] :
( hBOOL(c_in(X35,X5,X0))
| ~ hBOOL(c_in(X35,hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X5),X9),X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_DiffE_0) ).
fof(f2215,plain,
spl0_205,
inference(avatar_split_clause,[],[f41,f2213]) ).
fof(f41,axiom,
! [X0,X8,X9,X7,X5] :
( ~ c_Fun_Oinj__on(X7,X5,X0,X8)
| c_Fun_Oinj__on(X7,hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X5),X9),X0,X8) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__diff_0) ).
fof(f2189,plain,
( spl0_204
| ~ spl0_100
| ~ spl0_203 ),
inference(avatar_split_clause,[],[f2156,f2153,f1483,f2187]) ).
fof(f2153,plain,
( spl0_203
<=> ! [X0] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),X0),c_Orderings_Obot__class_Obot(tc_bool)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_203])]) ).
fof(f2156,plain,
( ! [X0] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),X0),c_False) = X0
| ~ spl0_100
| ~ spl0_203 ),
inference(forward_demodulation,[],[f2154,f1485]) ).
fof(f2154,plain,
( ! [X0] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),X0),c_Orderings_Obot__class_Obot(tc_bool)) = X0
| ~ spl0_203 ),
inference(avatar_component_clause,[],[f2153]) ).
fof(f2155,plain,
( spl0_203
| ~ spl0_5
| ~ spl0_89 ),
inference(avatar_split_clause,[],[f1463,f1415,f1037,f2153]) ).
fof(f1463,plain,
( ! [X0] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),X0),c_Orderings_Obot__class_Obot(tc_bool)) = X0
| ~ spl0_5
| ~ spl0_89 ),
inference(resolution,[],[f1416,f1039]) ).
fof(f2082,plain,
spl0_202,
inference(avatar_split_clause,[],[f808,f2080]) ).
fof(f808,plain,
! [X0,X11,X1,X5] :
( ~ hBOOL(c_in(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X5),X11),X0))
| hBOOL(hAPP(X11,X1)) ),
inference(forward_demodulation,[],[f11,f43]) ).
fof(f11,axiom,
! [X0,X11,X1,X5] :
( hBOOL(hAPP(X11,X1))
| ~ hBOOL(c_in(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X5),c_Collect(X11,X0)),X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__Collect_1) ).
fof(f2078,plain,
spl0_201,
inference(avatar_split_clause,[],[f719,f2076]) ).
fof(f719,plain,
! [X0,X9] : c_COMBK(c_False,tc_bool,X0) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0)),X9),
inference(forward_demodulation,[],[f368,f698]) ).
fof(f368,axiom,
! [X0,X9] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))),X9),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__empty__left_0) ).
fof(f2068,plain,
spl0_200,
inference(avatar_split_clause,[],[f718,f2066]) ).
fof(f718,plain,
! [X0,X5] : c_COMBK(c_False,tc_bool,X0) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0)),X5),
inference(forward_demodulation,[],[f361,f698]) ).
fof(f361,axiom,
! [X0,X5] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))),X5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__Diff_0) ).
fof(f2064,plain,
spl0_199,
inference(avatar_split_clause,[],[f717,f2062]) ).
fof(f717,plain,
! [X0,X5] : c_COMBK(c_False,tc_bool,X0) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X5),c_COMBK(c_False,tc_bool,X0)),
inference(forward_demodulation,[],[f367,f698]) ).
fof(f367,axiom,
! [X0,X5] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X5),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__empty__right_0) ).
fof(f2060,plain,
spl0_198,
inference(avatar_split_clause,[],[f716,f2058]) ).
fof(f716,plain,
! [X0,X5] : hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X5),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool))) = c_COMBK(c_False,tc_bool,X0),
inference(forward_demodulation,[],[f283,f698]) ).
fof(f283,axiom,
! [X0,X5] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X5),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__UNIV_0) ).
fof(f2056,plain,
( spl0_197
| ~ spl0_150
| ~ spl0_196 ),
inference(avatar_split_clause,[],[f2052,f2049,f1732,f2054]) ).
fof(f2049,plain,
( spl0_196
<=> ! [X0,X7,X3] : c_The(c_Finite__Set_Ofold1Set(X7,hAPP(hAPP(c_Set_Oinsert(X0),X3),c_COMBK(c_False,tc_bool,X0)),X0),X0) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_196])]) ).
fof(f2052,plain,
( ! [X3,X0,X7] : c_The(c_Finite__Set_Ofold1Set(X7,hAPP(c_fequal(X0),X3),X0),X0) = X3
| ~ spl0_150
| ~ spl0_196 ),
inference(forward_demodulation,[],[f2050,f1733]) ).
fof(f2050,plain,
( ! [X3,X0,X7] : c_The(c_Finite__Set_Ofold1Set(X7,hAPP(hAPP(c_Set_Oinsert(X0),X3),c_COMBK(c_False,tc_bool,X0)),X0),X0) = X3
| ~ spl0_196 ),
inference(avatar_component_clause,[],[f2049]) ).
fof(f2051,plain,
spl0_196,
inference(avatar_split_clause,[],[f712,f2049]) ).
fof(f712,plain,
! [X3,X0,X7] : c_The(c_Finite__Set_Ofold1Set(X7,hAPP(hAPP(c_Set_Oinsert(X0),X3),c_COMBK(c_False,tc_bool,X0)),X0),X0) = X3,
inference(forward_demodulation,[],[f648,f698]) ).
fof(f648,plain,
! [X3,X0,X7] : c_The(c_Finite__Set_Ofold1Set(X7,hAPP(hAPP(c_Set_Oinsert(X0),X3),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))),X0),X0) = X3,
inference(definition_unfolding,[],[f542,f30]) ).
fof(f542,axiom,
! [X3,X0,X7] : c_Finite__Set_Ofold1(X7,hAPP(hAPP(c_Set_Oinsert(X0),X3),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))),X0) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fold1__singleton_0) ).
fof(f2047,plain,
spl0_195,
inference(avatar_split_clause,[],[f640,f2045]) ).
fof(f640,axiom,
! [X0,X11,X8,X57,X14,X67] : hAPP(hAPP(hAPP(c_COMBB(X8,X0,X14),X11),X57),X67) = hAPP(X11,hAPP(X57,X67)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ATP__Linkup_OCOMBB__def_0) ).
fof(f2043,plain,
spl0_194,
inference(avatar_split_clause,[],[f600,f2041]) ).
fof(f600,axiom,
! [X2,X0,X1,X5] :
( X1 = X2
| hBOOL(hAPP(X5,X1))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X0),X2),X5),X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__code_0) ).
fof(f2039,plain,
spl0_193,
inference(avatar_split_clause,[],[f509,f2037]) ).
fof(f509,axiom,
! [X2,X0,X1] :
( ~ class_Orderings_Opreorder(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X2),X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__asym_0) ).
fof(f2035,plain,
spl0_192,
inference(avatar_split_clause,[],[f506,f2033]) ).
fof(f506,axiom,
! [X3,X0,X4] :
( ~ class_Orderings_Oorder(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X4),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X3),X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I9_J_0) ).
fof(f2031,plain,
( spl0_191
| ~ spl0_100
| ~ spl0_180 ),
inference(avatar_split_clause,[],[f1987,f1984,f1483,f2029]) ).
fof(f2029,plain,
( spl0_191
<=> ! [X0] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_False),X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_191])]) ).
fof(f1984,plain,
( spl0_180
<=> ! [X0] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_180])]) ).
fof(f1987,plain,
( ! [X0] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_False),X0) = X0
| ~ spl0_100
| ~ spl0_180 ),
inference(forward_demodulation,[],[f1985,f1485]) ).
fof(f1985,plain,
( ! [X0] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),X0) = X0
| ~ spl0_180 ),
inference(avatar_component_clause,[],[f1984]) ).
fof(f2027,plain,
spl0_190,
inference(avatar_split_clause,[],[f293,f2025]) ).
fof(f293,axiom,
! [X0,X9,X5] : hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X5),X9)),X9)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__lower2_0) ).
fof(f2023,plain,
spl0_189,
inference(avatar_split_clause,[],[f292,f2021]) ).
fof(f292,axiom,
! [X0,X9,X5] : hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X5),X9)),X5)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__lower1_0) ).
fof(f2019,plain,
spl0_188,
inference(avatar_split_clause,[],[f265,f2017]) ).
fof(f265,axiom,
! [X2,X0,X1] :
( ~ class_Orderings_Opreorder(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__imp__le_0) ).
fof(f2015,plain,
spl0_187,
inference(avatar_split_clause,[],[f264,f2013]) ).
fof(f264,axiom,
! [X2,X0,X1] :
( ~ class_Orderings_Oorder(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__le__less_1) ).
fof(f2011,plain,
spl0_186,
inference(avatar_split_clause,[],[f164,f2009]) ).
fof(f164,axiom,
! [X0,X9,X5] : hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X5),X9)),X5)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__subset_0) ).
fof(f2007,plain,
spl0_185,
inference(avatar_split_clause,[],[f148,f2005]) ).
fof(f148,axiom,
! [X0,X9,X5] : hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X5),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X5),X9))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__upper1_0) ).
fof(f2003,plain,
spl0_184,
inference(avatar_split_clause,[],[f147,f2001]) ).
fof(f147,axiom,
! [X0,X9,X5] : hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X9),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X5),X9))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__upper2_0) ).
fof(f1999,plain,
spl0_183,
inference(avatar_split_clause,[],[f122,f1997]) ).
fof(f122,axiom,
! [X2,X0,X1] :
( ~ class_Orderings_Opreorder(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X0),X2),X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__le__not__le_1) ).
fof(f1995,plain,
spl0_182,
inference(avatar_split_clause,[],[f79,f1993]) ).
fof(f79,axiom,
! [X38,X39,X0] :
( ~ c_Finite__Set_Ofinite(X38,X0)
| ~ c_Finite__Set_Ofinite(X39,X0)
| c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X38),X39),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Un_2) ).
fof(f1991,plain,
spl0_181,
inference(avatar_split_clause,[],[f53,f1989]) ).
fof(f53,axiom,
! [X0,X9,X5] :
( ~ c_Finite__Set_Ofinite(X9,X0)
| c_Finite__Set_Ofinite(X5,X0)
| ~ c_Finite__Set_Ofinite(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X5),X9),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Diff2_0) ).
fof(f1986,plain,
( spl0_180
| ~ spl0_5
| ~ spl0_88 ),
inference(avatar_split_clause,[],[f1461,f1411,f1037,f1984]) ).
fof(f1461,plain,
( ! [X0] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),X0) = X0
| ~ spl0_5
| ~ spl0_88 ),
inference(resolution,[],[f1412,f1039]) ).
fof(f1982,plain,
spl0_179,
inference(avatar_split_clause,[],[f51,f1980]) ).
fof(f51,axiom,
! [X0,X5] : c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X5),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__UNIV__right_0) ).
fof(f1978,plain,
spl0_178,
inference(avatar_split_clause,[],[f50,f1976]) ).
fof(f50,axiom,
! [X0,X9] : c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool))),X9),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__UNIV__left_0) ).
fof(f1943,plain,
( spl0_177
| ~ spl0_10
| ~ spl0_87 ),
inference(avatar_split_clause,[],[f1459,f1407,f1062,f1940]) ).
fof(f1459,plain,
( c_Orderings_Otop__class_Otop(tc_bool) = hAPP(c_Orderings_Otop__class_Otop(tc_fun(t_a,tc_bool)),v_x)
| ~ spl0_10
| ~ spl0_87 ),
inference(resolution,[],[f1408,f1064]) ).
fof(f1906,plain,
( spl0_176
| ~ spl0_5
| ~ spl0_86 ),
inference(avatar_split_clause,[],[f1457,f1403,f1037,f1904]) ).
fof(f1457,plain,
( ! [X0] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),X0) = X0
| ~ spl0_5
| ~ spl0_86 ),
inference(resolution,[],[f1404,f1039]) ).
fof(f1893,plain,
spl0_175,
inference(avatar_split_clause,[],[f875,f1891]) ).
fof(f1891,plain,
( spl0_175
<=> ! [X2,X0,X1] :
( c_Nitpick_Osko__Nitpick__XEx1__def__1__3(hAPP(c_fequal(X0),X1),X0) = X2
| ~ hBOOL(hAPP(hAPP(c_fequal(X0),X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_175])]) ).
fof(f875,plain,
! [X2,X0,X1] :
( c_Nitpick_Osko__Nitpick__XEx1__def__1__3(hAPP(c_fequal(X0),X1),X0) = X2
| ~ hBOOL(hAPP(hAPP(c_fequal(X0),X1),X2)) ),
inference(forward_demodulation,[],[f874,f723]) ).
fof(f874,plain,
! [X2,X0,X1] :
( c_Nitpick_Osko__Nitpick__XEx1__def__1__3(hAPP(hAPP(c_Set_Oinsert(X0),X1),c_COMBK(c_False,tc_bool,X0)),X0) = X2
| ~ hBOOL(hAPP(hAPP(c_fequal(X0),X1),X2)) ),
inference(forward_demodulation,[],[f873,f698]) ).
fof(f873,plain,
! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_fequal(X0),X1),X2))
| c_Nitpick_Osko__Nitpick__XEx1__def__1__3(hAPP(hAPP(c_Set_Oinsert(X0),X1),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))),X0) = X2 ),
inference(forward_demodulation,[],[f872,f723]) ).
fof(f872,plain,
! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X0),X1),c_COMBK(c_False,tc_bool,X0)),X2))
| c_Nitpick_Osko__Nitpick__XEx1__def__1__3(hAPP(hAPP(c_Set_Oinsert(X0),X1),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))),X0) = X2 ),
inference(forward_demodulation,[],[f540,f698]) ).
fof(f540,axiom,
! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X0),X1),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))),X2))
| c_Nitpick_Osko__Nitpick__XEx1__def__1__3(hAPP(hAPP(c_Set_Oinsert(X0),X1),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))),X0) = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nitpick_OEx1__def_3) ).
fof(f1889,plain,
spl0_174,
inference(avatar_split_clause,[],[f739,f1887]) ).
fof(f739,plain,
! [X3,X0] : c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X3),X0) = hAPP(c_fequal(X0),X3),
inference(forward_demodulation,[],[f738,f723]) ).
fof(f738,plain,
! [X3,X0] : c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X3),X0) = hAPP(hAPP(c_Set_Oinsert(X0),X3),c_COMBK(c_False,tc_bool,X0)),
inference(forward_demodulation,[],[f378,f698]) ).
fof(f378,axiom,
! [X3,X0] : hAPP(hAPP(c_Set_Oinsert(X0),X3),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))) = c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X3),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_singleton__conv_0) ).
fof(f1884,plain,
( spl0_173
| ~ spl0_150
| ~ spl0_172 ),
inference(avatar_split_clause,[],[f1880,f1877,f1732,f1882]) ).
fof(f1877,plain,
( spl0_172
<=> ! [X0,X1,X7] : hBOOL(hAPP(c_Finite__Set_Ofold1Set(X7,hAPP(hAPP(c_Set_Oinsert(X0),X1),c_COMBK(c_False,tc_bool,X0)),X0),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_172])]) ).
fof(f1880,plain,
( ! [X0,X1,X7] : hBOOL(hAPP(c_Finite__Set_Ofold1Set(X7,hAPP(c_fequal(X0),X1),X0),X1))
| ~ spl0_150
| ~ spl0_172 ),
inference(forward_demodulation,[],[f1878,f1733]) ).
fof(f1878,plain,
( ! [X0,X1,X7] : hBOOL(hAPP(c_Finite__Set_Ofold1Set(X7,hAPP(hAPP(c_Set_Oinsert(X0),X1),c_COMBK(c_False,tc_bool,X0)),X0),X1))
| ~ spl0_172 ),
inference(avatar_component_clause,[],[f1877]) ).
fof(f1879,plain,
spl0_172,
inference(avatar_split_clause,[],[f715,f1877]) ).
fof(f715,plain,
! [X0,X1,X7] : hBOOL(hAPP(c_Finite__Set_Ofold1Set(X7,hAPP(hAPP(c_Set_Oinsert(X0),X1),c_COMBK(c_False,tc_bool,X0)),X0),X1)),
inference(forward_demodulation,[],[f531,f698]) ).
fof(f531,axiom,
! [X0,X1,X7] : hBOOL(hAPP(c_Finite__Set_Ofold1Set(X7,hAPP(hAPP(c_Set_Oinsert(X0),X1),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))),X0),X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fold1Set__sing_1) ).
fof(f1875,plain,
spl0_171,
inference(avatar_split_clause,[],[f714,f1873]) ).
fof(f714,plain,
! [X0,X8,X9] : c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)) = c_Complete__Lattice_Ocomplete__lattice__class_OINFI(c_COMBK(c_False,tc_bool,X8),X9,X8,tc_fun(X0,tc_bool)),
inference(forward_demodulation,[],[f301,f698]) ).
fof(f301,axiom,
! [X0,X8,X9] : c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)) = c_Complete__Lattice_Ocomplete__lattice__class_OINFI(c_Orderings_Obot__class_Obot(tc_fun(X8,tc_bool)),X9,X8,tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_INT__empty_0) ).
fof(f1871,plain,
spl0_170,
inference(avatar_split_clause,[],[f605,f1869]) ).
fof(f605,axiom,
! [X0,X11,X8,X57,X14,X67] : hAPP(hAPP(c_COMBC(X11,X8,X14,X0),X57),X67) = hAPP(hAPP(X11,X67),X57),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_COMBC__def_0) ).
fof(f1867,plain,
spl0_169,
inference(avatar_split_clause,[],[f449,f1865]) ).
fof(f449,axiom,
! [X0,X9,X5] :
( ~ c_Finite__Set_Ofinite(X9,X0)
| c_Finite__Set_Ofinite(X5,X0)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X5),X9)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__finite__subset_0) ).
fof(f1860,plain,
spl0_168,
inference(avatar_split_clause,[],[f399,f1858]) ).
fof(f399,axiom,
! [X3,X0,X8,X7,X5] :
( c_Fun_Oinj__on(X7,X5,X0,X8)
| ~ c_Fun_Oinj__on(X7,hAPP(hAPP(c_Set_Oinsert(X0),X3),X5),X0,X8) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__insert_0) ).
fof(f1856,plain,
spl0_167,
inference(avatar_split_clause,[],[f385,f1854]) ).
fof(f385,axiom,
! [X3,X0,X4,X5] :
( ~ hBOOL(c_in(X3,X5,X0))
| hBOOL(c_in(X3,hAPP(hAPP(c_Set_Oinsert(X0),X4),X5),X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__iff_2) ).
fof(f1852,plain,
spl0_166,
inference(avatar_split_clause,[],[f346,f1850]) ).
fof(f346,axiom,
! [X0,X9,X5] :
( ~ class_Lattices_Obounded__lattice(X0)
| c_Orderings_Obot__class_Obot(X0) = X9
| c_Orderings_Obot__class_Obot(X0) != hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X5),X9) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__eq__bot__eq2_0) ).
fof(f1848,plain,
spl0_165,
inference(avatar_split_clause,[],[f345,f1846]) ).
fof(f345,axiom,
! [X0,X9,X5] :
( ~ class_Lattices_Obounded__lattice(X0)
| c_Orderings_Obot__class_Obot(X0) = X5
| c_Orderings_Obot__class_Obot(X0) != hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X5),X9) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__eq__bot__eq1_0) ).
fof(f1844,plain,
spl0_164,
inference(avatar_split_clause,[],[f321,f1842]) ).
fof(f321,axiom,
! [X0,X1,X9,X5] :
( hBOOL(hAPP(X5,X1))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X5),X9),X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf1E_0) ).
fof(f1840,plain,
spl0_163,
inference(avatar_split_clause,[],[f320,f1838]) ).
fof(f320,axiom,
! [X0,X1,X9,X5] :
( hBOOL(hAPP(X9,X1))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X5),X9),X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf1E_1) ).
fof(f1836,plain,
spl0_162,
inference(avatar_split_clause,[],[f260,f1834]) ).
fof(f260,axiom,
! [X2,X0,X1] :
( ~ class_Lattices_Olattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2)) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__absorb_0) ).
fof(f1832,plain,
spl0_161,
inference(avatar_split_clause,[],[f244,f1830]) ).
fof(f244,axiom,
! [X2,X0,X1] :
( ~ class_Lattices_Olattice(X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2)) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__inf__absorb_0) ).
fof(f1828,plain,
spl0_160,
inference(avatar_split_clause,[],[f222,f1826]) ).
fof(f222,axiom,
! [X0,X9,X5] :
( ~ class_Lattices_Obounded__lattice(X0)
| c_Orderings_Otop__class_Otop(X0) = X5
| c_Orderings_Otop__class_Otop(X0) != hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X5),X9) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__eq__top__eq1_0) ).
fof(f1824,plain,
spl0_159,
inference(avatar_split_clause,[],[f221,f1822]) ).
fof(f221,axiom,
! [X0,X9,X5] :
( ~ class_Lattices_Obounded__lattice(X0)
| c_Orderings_Otop__class_Otop(X0) = X9
| c_Orderings_Otop__class_Otop(X0) != hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X5),X9) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__eq__top__eq2_0) ).
fof(f1820,plain,
( spl0_158
| ~ spl0_77
| ~ spl0_150 ),
inference(avatar_split_clause,[],[f1786,f1732,f1353,f1818]) ).
fof(f1786,plain,
( ! [X0,X1] : hBOOL(c_in(X1,hAPP(c_fequal(X0),X1),X0))
| ~ spl0_77
| ~ spl0_150 ),
inference(superposition,[],[f1354,f1733]) ).
fof(f1816,plain,
spl0_157,
inference(avatar_split_clause,[],[f199,f1814]) ).
fof(f1814,plain,
( spl0_157
<=> ! [X2,X0,X1] :
( ~ class_Lattices_Olattice(X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_157])]) ).
fof(f199,axiom,
! [X2,X0,X1] :
( ~ class_Lattices_Olattice(X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X2),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I5_J_0) ).
fof(f1812,plain,
spl0_156,
inference(avatar_split_clause,[],[f198,f1810]) ).
fof(f198,axiom,
! [X2,X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X2),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__commute_0) ).
fof(f1808,plain,
spl0_155,
inference(avatar_split_clause,[],[f159,f1806]) ).
fof(f1806,plain,
( spl0_155
<=> ! [X2,X0,X1] :
( ~ class_Lattices_Olattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X1) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_155])]) ).
fof(f159,axiom,
! [X2,X0,X1] :
( ~ class_Lattices_Olattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X1) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I1_J_0) ).
fof(f1804,plain,
spl0_154,
inference(avatar_split_clause,[],[f158,f1802]) ).
fof(f158,axiom,
! [X2,X0,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X1) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__commute_0) ).
fof(f1800,plain,
spl0_153,
inference(avatar_split_clause,[],[f99,f1798]) ).
fof(f99,axiom,
! [X0,X1,X9,X5] :
( ~ hBOOL(hAPP(X5,X1))
| hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X5),X9),X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup1CI_1) ).
fof(f1796,plain,
spl0_152,
inference(avatar_split_clause,[],[f98,f1794]) ).
fof(f98,axiom,
! [X0,X1,X9,X5] :
( ~ hBOOL(hAPP(X9,X1))
| hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X5),X9),X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup1CI_0) ).
fof(f1781,plain,
( spl0_151
| ~ spl0_5
| ~ spl0_85 ),
inference(avatar_split_clause,[],[f1455,f1399,f1037,f1779]) ).
fof(f1455,plain,
( ! [X0] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),X0),c_Orderings_Otop__class_Otop(tc_bool)) = X0
| ~ spl0_5
| ~ spl0_85 ),
inference(resolution,[],[f1400,f1039]) ).
fof(f1734,plain,
spl0_150,
inference(avatar_split_clause,[],[f723,f1732]) ).
fof(f1730,plain,
spl0_149,
inference(avatar_split_clause,[],[f593,f1728]) ).
fof(f1728,plain,
( spl0_149
<=> ! [X73,X0,X71,X29,X70,X32,X72] :
( X70 = X72
| c_Hoare__Mirabelle_Otriple_Otriple(X70,X32,X71,X0) != c_Hoare__Mirabelle_Otriple_Otriple(X72,X29,X73,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_149])]) ).
fof(f593,axiom,
! [X72,X70,X0,X71,X29,X73,X32] :
( X70 = X72
| c_Hoare__Mirabelle_Otriple_Otriple(X70,X32,X71,X0) != c_Hoare__Mirabelle_Otriple_Otriple(X72,X29,X73,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_triple_Oinject_0) ).
fof(f1726,plain,
spl0_148,
inference(avatar_split_clause,[],[f592,f1724]) ).
fof(f1724,plain,
( spl0_148
<=> ! [X70,X0,X71,X29,X73,X32,X72] :
( X29 = X32
| c_Hoare__Mirabelle_Otriple_Otriple(X70,X32,X71,X0) != c_Hoare__Mirabelle_Otriple_Otriple(X72,X29,X73,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_148])]) ).
fof(f592,axiom,
! [X72,X70,X29,X71,X0,X73,X32] :
( X29 = X32
| c_Hoare__Mirabelle_Otriple_Otriple(X70,X32,X71,X0) != c_Hoare__Mirabelle_Otriple_Otriple(X72,X29,X73,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_triple_Oinject_1) ).
fof(f1722,plain,
spl0_147,
inference(avatar_split_clause,[],[f591,f1720]) ).
fof(f1720,plain,
( spl0_147
<=> ! [X70,X0,X71,X29,X73,X32,X72] :
( X71 = X73
| c_Hoare__Mirabelle_Otriple_Otriple(X70,X32,X71,X0) != c_Hoare__Mirabelle_Otriple_Otriple(X72,X29,X73,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_147])]) ).
fof(f591,axiom,
! [X72,X70,X73,X71,X0,X29,X32] :
( X71 = X73
| c_Hoare__Mirabelle_Otriple_Otriple(X70,X32,X71,X0) != c_Hoare__Mirabelle_Otriple_Otriple(X72,X29,X73,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_triple_Oinject_2) ).
fof(f1718,plain,
spl0_146,
inference(avatar_split_clause,[],[f393,f1716]) ).
fof(f393,axiom,
! [X3,X0,X9] : hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X9),hAPP(hAPP(c_Set_Oinsert(X0),X3),X9))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insertI_0) ).
fof(f1714,plain,
spl0_145,
inference(avatar_split_clause,[],[f291,f1712]) ).
fof(f291,axiom,
! [X2,X0,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2)),X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__le1_0) ).
fof(f1710,plain,
spl0_144,
inference(avatar_split_clause,[],[f290,f1708]) ).
fof(f290,axiom,
! [X2,X0,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2)),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__le2_0) ).
fof(f1706,plain,
spl0_143,
inference(avatar_split_clause,[],[f286,f1704]) ).
fof(f286,axiom,
! [X2,X0,X1] :
( ~ class_Lattices_Olattice(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2)),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__ord_I2_J_0) ).
fof(f1702,plain,
spl0_142,
inference(avatar_split_clause,[],[f285,f1700]) ).
fof(f285,axiom,
! [X2,X0,X1] :
( ~ class_Lattices_Olattice(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2)),X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__ord_I1_J_0) ).
fof(f1698,plain,
spl0_141,
inference(avatar_split_clause,[],[f156,f1696]) ).
fof(f156,axiom,
! [X2,X0,X1] :
( ~ class_Lattices_Olattice(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__ord_I3_J_0) ).
fof(f1694,plain,
spl0_140,
inference(avatar_split_clause,[],[f155,f1692]) ).
fof(f155,axiom,
! [X2,X0,X1] :
( ~ class_Lattices_Olattice(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__ord_I4_J_0) ).
fof(f1690,plain,
spl0_139,
inference(avatar_split_clause,[],[f152,f1688]) ).
fof(f152,axiom,
! [X2,X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__ge2_0) ).
fof(f1686,plain,
spl0_138,
inference(avatar_split_clause,[],[f151,f1684]) ).
fof(f151,axiom,
! [X2,X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__ge1_0) ).
fof(f1682,plain,
spl0_137,
inference(avatar_split_clause,[],[f90,f1680]) ).
fof(f90,axiom,
! [X3,X41,X0,X8,X14,X4] : hAPP(X3,hAPP(X4,X41)) = hAPP(c_Fun_Ocomp(X3,X4,X14,X8,X0),X41),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_o__eq__dest__lhs_0) ).
fof(f1672,plain,
( spl0_136
| ~ spl0_81
| ~ spl0_115 ),
inference(avatar_split_clause,[],[f1580,f1545,f1370,f1670]) ).
fof(f1580,plain,
( ! [X0,X1] : c_Nitpick_Osko__Nitpick__XEx1__def__1__3(hAPP(c_fequal(X1),X0),X1) = X0
| ~ spl0_81
| ~ spl0_115 ),
inference(resolution,[],[f1546,f1371]) ).
fof(f1654,plain,
spl0_135,
inference(avatar_split_clause,[],[f794,f1652]) ).
fof(f794,plain,
! [X3,X0,X7,X4] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(X7,hAPP(c_fequal(X0),X3),X0),X4))
| X3 = X4 ),
inference(forward_demodulation,[],[f793,f723]) ).
fof(f793,plain,
! [X3,X0,X7,X4] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(X7,hAPP(hAPP(c_Set_Oinsert(X0),X3),c_COMBK(c_False,tc_bool,X0)),X0),X4))
| X3 = X4 ),
inference(forward_demodulation,[],[f538,f698]) ).
fof(f538,axiom,
! [X3,X0,X7,X4] :
( X3 = X4
| ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(X7,hAPP(hAPP(c_Set_Oinsert(X0),X3),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))),X0),X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fold1Set__sing_0) ).
fof(f1649,plain,
spl0_134,
inference(avatar_split_clause,[],[f709,f1647]) ).
fof(f1647,plain,
( spl0_134
<=> ! [X0,X1] : c_The(hAPP(hAPP(c_Set_Oinsert(X0),X1),c_COMBK(c_False,tc_bool,X0)),X0) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_134])]) ).
fof(f709,plain,
! [X0,X1] : c_The(hAPP(hAPP(c_Set_Oinsert(X0),X1),c_COMBK(c_False,tc_bool,X0)),X0) = X1,
inference(forward_demodulation,[],[f533,f698]) ).
fof(f533,axiom,
! [X0,X1] : c_The(hAPP(hAPP(c_Set_Oinsert(X0),X1),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))),X0) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nitpick_OThe__psimp_0) ).
fof(f1645,plain,
spl0_133,
inference(avatar_split_clause,[],[f707,f1643]) ).
fof(f707,plain,
! [X0,X9] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0)),X9) = X9,
inference(forward_demodulation,[],[f363,f698]) ).
fof(f363,axiom,
! [X0,X9] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))),X9) = X9,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__empty__left_0) ).
fof(f1641,plain,
spl0_132,
inference(avatar_split_clause,[],[f706,f1639]) ).
fof(f706,plain,
! [X0,X5] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X5),c_COMBK(c_False,tc_bool,X0)) = X5,
inference(forward_demodulation,[],[f362,f698]) ).
fof(f362,axiom,
! [X0,X5] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X5),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))) = X5,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__empty__right_0) ).
fof(f1637,plain,
spl0_131,
inference(avatar_split_clause,[],[f705,f1635]) ).
fof(f705,plain,
! [X0,X5] : hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X5),c_COMBK(c_False,tc_bool,X0)) = X5,
inference(forward_demodulation,[],[f365,f698]) ).
fof(f365,axiom,
! [X0,X5] : hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X5),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))) = X5,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__empty_0) ).
fof(f1633,plain,
spl0_130,
inference(avatar_split_clause,[],[f700,f1631]) ).
fof(f700,plain,
! [X0,X5] : hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X5),X5) = c_COMBK(c_False,tc_bool,X0),
inference(forward_demodulation,[],[f364,f698]) ).
fof(f364,axiom,
! [X0,X5] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X5),X5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__cancel_0) ).
fof(f1629,plain,
spl0_129,
inference(avatar_split_clause,[],[f610,f1627]) ).
fof(f610,axiom,
! [X2,X0,X1,X5] :
( ~ hBOOL(hAPP(X5,X1))
| hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X0),X2),X5),X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__code_2) ).
fof(f1625,plain,
spl0_128,
inference(avatar_split_clause,[],[f404,f1623]) ).
fof(f404,axiom,
! [X3,X0,X5] :
( ~ hBOOL(c_in(X3,X5,X0))
| hAPP(hAPP(c_Set_Oinsert(X0),X3),X5) = X5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__absorb_0) ).
fof(f1621,plain,
spl0_127,
inference(avatar_split_clause,[],[f336,f1619]) ).
fof(f336,axiom,
! [X38,X39,X0] :
( ~ c_Finite__Set_Ofinite(X38,X0)
| c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X38),X39),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Int_0) ).
fof(f1617,plain,
spl0_126,
inference(avatar_split_clause,[],[f335,f1615]) ).
fof(f335,axiom,
! [X38,X39,X0] :
( ~ c_Finite__Set_Ofinite(X39,X0)
| c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X38),X39),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Int_1) ).
fof(f1613,plain,
spl0_125,
inference(avatar_split_clause,[],[f235,f1611]) ).
fof(f235,axiom,
! [X0,X5] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X5),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool))) = X5,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__UNIV__right_0) ).
fof(f1609,plain,
( spl0_124
| ~ spl0_5
| ~ spl0_100
| ~ spl0_111 ),
inference(avatar_split_clause,[],[f1573,f1529,f1483,f1037,f1607]) ).
fof(f1573,plain,
( ! [X0] : c_False = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),X0),c_False)
| ~ spl0_5
| ~ spl0_100
| ~ spl0_111 ),
inference(forward_demodulation,[],[f1571,f1485]) ).
fof(f1571,plain,
( ! [X0] : c_Orderings_Obot__class_Obot(tc_bool) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),X0),c_Orderings_Obot__class_Obot(tc_bool))
| ~ spl0_5
| ~ spl0_111 ),
inference(resolution,[],[f1530,f1039]) ).
fof(f1605,plain,
spl0_123,
inference(avatar_split_clause,[],[f234,f1603]) ).
fof(f234,axiom,
! [X0,X9] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool))),X9) = X9,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__UNIV__left_0) ).
fof(f1601,plain,
spl0_122,
inference(avatar_split_clause,[],[f215,f1599]) ).
fof(f215,axiom,
! [X38,X39,X0] :
( c_Finite__Set_Ofinite(X39,X0)
| ~ c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X38),X39),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Un_1) ).
fof(f1597,plain,
spl0_121,
inference(avatar_split_clause,[],[f214,f1595]) ).
fof(f214,axiom,
! [X38,X39,X0] :
( c_Finite__Set_Ofinite(X38,X0)
| ~ c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X38),X39),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Un_0) ).
fof(f1593,plain,
spl0_120,
inference(avatar_split_clause,[],[f65,f1591]) ).
fof(f65,axiom,
! [X8,X7,X14,X35] : hAPP(c_Fun_Ocomp(c_COMBK(X35,X8,X14),X7,X14,X8,t_a),v_x) = X35,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_K__record__comp_0) ).
fof(f1589,plain,
spl0_119,
inference(avatar_split_clause,[],[f40,f1587]) ).
fof(f40,axiom,
! [X0,X9,X5] :
( ~ c_Finite__Set_Ofinite(X5,X0)
| c_Finite__Set_Ofinite(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X5),X9),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Diff_0) ).
fof(f1578,plain,
( spl0_118
| ~ spl0_5
| ~ spl0_100
| ~ spl0_110 ),
inference(avatar_split_clause,[],[f1570,f1525,f1483,f1037,f1576]) ).
fof(f1570,plain,
( ! [X0] : c_False = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),c_False),X0)
| ~ spl0_5
| ~ spl0_100
| ~ spl0_110 ),
inference(forward_demodulation,[],[f1568,f1485]) ).
fof(f1568,plain,
( ! [X0] : c_Orderings_Obot__class_Obot(tc_bool) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),X0)
| ~ spl0_5
| ~ spl0_110 ),
inference(resolution,[],[f1526,f1039]) ).
fof(f1555,plain,
spl0_117,
inference(avatar_split_clause,[],[f779,f1553]) ).
fof(f779,plain,
! [X0] :
( c_Orderings_Obot__class_Obot(X0) = hAPP(c_Complete__Lattice_OSup__class_OSup(X0),c_COMBK(c_False,tc_bool,X0))
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) ),
inference(forward_demodulation,[],[f522,f698]) ).
fof(f522,axiom,
! [X0] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
| c_Orderings_Obot__class_Obot(X0) = hAPP(c_Complete__Lattice_OSup__class_OSup(X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sup__empty_0) ).
fof(f1551,plain,
spl0_116,
inference(avatar_split_clause,[],[f778,f1549]) ).
fof(f778,plain,
! [X0] :
( c_Orderings_Otop__class_Otop(X0) = hAPP(c_Complete__Lattice_OInf__class_OInf(X0),c_COMBK(c_False,tc_bool,X0))
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) ),
inference(forward_demodulation,[],[f413,f698]) ).
fof(f413,axiom,
! [X0] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
| c_Orderings_Otop__class_Otop(X0) = hAPP(c_Complete__Lattice_OInf__class_OInf(X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Inf__empty_0) ).
fof(f1547,plain,
spl0_115,
inference(avatar_split_clause,[],[f745,f1545]) ).
fof(f745,plain,
! [X0,X1] : hBOOL(hAPP(hAPP(c_fequal(X0),X1),c_Nitpick_Osko__Nitpick__XEx1__def__1__3(hAPP(c_fequal(X0),X1),X0))),
inference(forward_demodulation,[],[f744,f723]) ).
fof(f744,plain,
! [X0,X1] : hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X0),X1),c_COMBK(c_False,tc_bool,X0)),c_Nitpick_Osko__Nitpick__XEx1__def__1__3(hAPP(hAPP(c_Set_Oinsert(X0),X1),c_COMBK(c_False,tc_bool,X0)),X0))),
inference(forward_demodulation,[],[f529,f698]) ).
fof(f529,axiom,
! [X0,X1] : hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X0),X1),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))),c_Nitpick_Osko__Nitpick__XEx1__def__1__3(hAPP(hAPP(c_Set_Oinsert(X0),X1),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))),X0))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nitpick_OEx1__def_2) ).
fof(f1543,plain,
spl0_114,
inference(avatar_split_clause,[],[f725,f1541]) ).
fof(f725,plain,
! [X39,X0,X11] : c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),c_Hoare__Mirabelle_Otriple_Otriple(X11,c_Com_Ocom_OSKIP,X11,X0)),X0),
inference(forward_demodulation,[],[f724,f723]) ).
fof(f724,plain,
! [X39,X0,X11] : c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X0)),c_Hoare__Mirabelle_Otriple_Otriple(X11,c_Com_Ocom_OSKIP,X11,X0)),c_COMBK(c_False,tc_bool,tc_Hoare__Mirabelle_Otriple(X0))),X0),
inference(forward_demodulation,[],[f584,f698]) ).
fof(f584,axiom,
! [X39,X0,X11] : c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X0)),c_Hoare__Mirabelle_Otriple_Otriple(X11,c_Com_Ocom_OSKIP,X11,X0)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool))),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_hoare__derivs_OSkip_0) ).
fof(f1539,plain,
spl0_113,
inference(avatar_split_clause,[],[f699,f1537]) ).
fof(f699,plain,
! [X0,X5] : hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),c_COMBK(c_False,tc_bool,X0)),X5)),
inference(forward_demodulation,[],[f369,f698]) ).
fof(f369,axiom,
! [X0,X5] : hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))),X5)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__subsetI_0) ).
fof(f1535,plain,
spl0_112,
inference(avatar_split_clause,[],[f589,f1533]) ).
fof(f589,axiom,
! [X39,X0,X68,X69] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X69,X68,X0)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X39,X69,X0)
| c_Hoare__Mirabelle_Ohoare__derivs(X39,X68,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_cut_0) ).
fof(f1531,plain,
spl0_111,
inference(avatar_split_clause,[],[f343,f1529]) ).
fof(f343,axiom,
! [X0,X1] :
( ~ class_Lattices_Obounded__lattice(X0)
| c_Orderings_Obot__class_Obot(X0) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),c_Orderings_Obot__class_Obot(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__bot__right_0) ).
fof(f1527,plain,
spl0_110,
inference(avatar_split_clause,[],[f342,f1525]) ).
fof(f342,axiom,
! [X0,X1] :
( ~ class_Lattices_Obounded__lattice(X0)
| c_Orderings_Obot__class_Obot(X0) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),c_Orderings_Obot__class_Obot(X0)),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__bot__left_0) ).
fof(f1522,plain,
spl0_109,
inference(avatar_split_clause,[],[f326,f1520]) ).
fof(f326,axiom,
! [X0] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
| c_Orderings_Otop__class_Otop(X0) = hAPP(c_Complete__Lattice_OSup__class_OSup(X0),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sup__UNIV_0) ).
fof(f1518,plain,
spl0_108,
inference(avatar_split_clause,[],[f296,f1516]) ).
fof(f296,axiom,
! [X0,X5] : hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X5),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__UNIV_0) ).
fof(f1514,plain,
spl0_107,
inference(avatar_split_clause,[],[f239,f1512]) ).
fof(f239,axiom,
! [X0] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
| hAPP(c_Complete__Lattice_OInf__class_OInf(X0),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool))) = c_Orderings_Obot__class_Obot(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Inf__UNIV_0) ).
fof(f1510,plain,
spl0_106,
inference(avatar_split_clause,[],[f77,f1508]) ).
fof(f1508,plain,
( spl0_106
<=> ! [X17,X33,X34,X31,X16,X28] :
( X28 = X31
| c_Com_Ocom_OCond(X28,X33,X34) != c_Com_Ocom_OCond(X31,X16,X17) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_106])]) ).
fof(f77,axiom,
! [X31,X28,X16,X34,X17,X33] :
( X28 = X31
| c_Com_Ocom_OCond(X28,X33,X34) != c_Com_Ocom_OCond(X31,X16,X17) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I4_J_0) ).
fof(f1506,plain,
spl0_105,
inference(avatar_split_clause,[],[f76,f1504]) ).
fof(f1504,plain,
( spl0_105
<=> ! [X17,X33,X34,X31,X16,X28] :
( X16 = X33
| c_Com_Ocom_OCond(X28,X33,X34) != c_Com_Ocom_OCond(X31,X16,X17) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_105])]) ).
fof(f76,axiom,
! [X31,X28,X16,X34,X17,X33] :
( X16 = X33
| c_Com_Ocom_OCond(X28,X33,X34) != c_Com_Ocom_OCond(X31,X16,X17) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I4_J_1) ).
fof(f1502,plain,
spl0_104,
inference(avatar_split_clause,[],[f75,f1500]) ).
fof(f1500,plain,
( spl0_104
<=> ! [X17,X33,X34,X31,X16,X28] :
( X17 = X34
| c_Com_Ocom_OCond(X28,X33,X34) != c_Com_Ocom_OCond(X31,X16,X17) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_104])]) ).
fof(f75,axiom,
! [X31,X28,X16,X17,X34,X33] :
( X17 = X34
| c_Com_Ocom_OCond(X28,X33,X34) != c_Com_Ocom_OCond(X31,X16,X17) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I4_J_2) ).
fof(f1498,plain,
spl0_103,
inference(avatar_split_clause,[],[f69,f1496]) ).
fof(f1496,plain,
( spl0_103
<=> ! [X0,X3] : c_The(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X3),X0) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_103])]) ).
fof(f69,axiom,
! [X3,X0] : c_The(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X3),X0) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_the__eq__trivial_0) ).
fof(f1494,plain,
spl0_102,
inference(avatar_split_clause,[],[f49,f1492]) ).
fof(f49,axiom,
! [X0,X1] :
( ~ class_Lattices_Obounded__lattice(X0)
| c_Orderings_Otop__class_Otop(X0) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),c_Orderings_Otop__class_Otop(X0)),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__top__left_0) ).
fof(f1490,plain,
spl0_101,
inference(avatar_split_clause,[],[f48,f1488]) ).
fof(f48,axiom,
! [X0,X1] :
( ~ class_Lattices_Obounded__lattice(X0)
| c_Orderings_Otop__class_Otop(X0) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),c_Orderings_Otop__class_Otop(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__top__right_0) ).
fof(f1486,plain,
( spl0_100
| ~ spl0_11
| ~ spl0_51
| ~ spl0_65
| ~ spl0_93 ),
inference(avatar_split_clause,[],[f1470,f1431,f1295,f1237,f1067,f1483]) ).
fof(f1470,plain,
( c_False = c_Orderings_Obot__class_Obot(tc_bool)
| ~ spl0_11
| ~ spl0_51
| ~ spl0_65
| ~ spl0_93 ),
inference(forward_demodulation,[],[f1469,f1238]) ).
fof(f1469,plain,
( hAPP(c_COMBK(c_False,tc_bool,t_a),v_x) = c_Orderings_Obot__class_Obot(tc_bool)
| ~ spl0_11
| ~ spl0_65
| ~ spl0_93 ),
inference(forward_demodulation,[],[f1467,f1296]) ).
fof(f1467,plain,
( hAPP(c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),v_x) = c_Orderings_Obot__class_Obot(tc_bool)
| ~ spl0_11
| ~ spl0_93 ),
inference(resolution,[],[f1432,f1069]) ).
fof(f1474,plain,
( spl0_99
| ~ spl0_65
| ~ spl0_94 ),
inference(avatar_split_clause,[],[f1438,f1435,f1295,f1472]) ).
fof(f1435,plain,
( spl0_94
<=> ! [X5,X0,X3] : hAPP(hAPP(c_Set_Oinsert(X0),X3),X5) != c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_94])]) ).
fof(f1438,plain,
( ! [X3,X0,X5] : hAPP(hAPP(c_Set_Oinsert(X0),X3),X5) != c_COMBK(c_False,tc_bool,X0)
| ~ spl0_65
| ~ spl0_94 ),
inference(forward_demodulation,[],[f1436,f1296]) ).
fof(f1436,plain,
( ! [X3,X0,X5] : hAPP(hAPP(c_Set_Oinsert(X0),X3),X5) != c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))
| ~ spl0_94 ),
inference(avatar_component_clause,[],[f1435]) ).
fof(f1454,plain,
spl0_98,
inference(avatar_split_clause,[],[f792,f1452]) ).
fof(f792,plain,
! [X3,X0,X4] :
( ~ hBOOL(c_in(X4,hAPP(c_fequal(X0),X3),X0))
| X3 = X4 ),
inference(forward_demodulation,[],[f791,f723]) ).
fof(f791,plain,
! [X3,X0,X4] :
( ~ hBOOL(c_in(X4,hAPP(hAPP(c_Set_Oinsert(X0),X3),c_COMBK(c_False,tc_bool,X0)),X0))
| X3 = X4 ),
inference(forward_demodulation,[],[f541,f698]) ).
fof(f541,axiom,
! [X3,X0,X4] :
( X3 = X4
| ~ hBOOL(c_in(X4,hAPP(hAPP(c_Set_Oinsert(X0),X3),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))),X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_singletonE_0) ).
fof(f1450,plain,
spl0_97,
inference(avatar_split_clause,[],[f789,f1448]) ).
fof(f789,plain,
! [X3,X0] :
( hAPP(c_fequal(X0),X3) = c_SetInterval_Oord__class_OatLeastAtMost(X3,X3,X0)
| ~ class_Orderings_Oorder(X0) ),
inference(forward_demodulation,[],[f788,f723]) ).
fof(f788,plain,
! [X3,X0] :
( c_SetInterval_Oord__class_OatLeastAtMost(X3,X3,X0) = hAPP(hAPP(c_Set_Oinsert(X0),X3),c_COMBK(c_False,tc_bool,X0))
| ~ class_Orderings_Oorder(X0) ),
inference(forward_demodulation,[],[f545,f698]) ).
fof(f545,axiom,
! [X3,X0] :
( ~ class_Orderings_Oorder(X0)
| hAPP(hAPP(c_Set_Oinsert(X0),X3),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))) = c_SetInterval_Oord__class_OatLeastAtMost(X3,X3,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastAtMost__singleton_0) ).
fof(f1446,plain,
spl0_96,
inference(avatar_split_clause,[],[f783,f1444]) ).
fof(f783,plain,
! [X3,X0] :
( hAPP(c_Complete__Lattice_OInf__class_OInf(X0),hAPP(c_fequal(X0),X3)) = X3
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) ),
inference(forward_demodulation,[],[f782,f723]) ).
fof(f782,plain,
! [X3,X0] :
( hAPP(c_Complete__Lattice_OInf__class_OInf(X0),hAPP(hAPP(c_Set_Oinsert(X0),X3),c_COMBK(c_False,tc_bool,X0))) = X3
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) ),
inference(forward_demodulation,[],[f548,f698]) ).
fof(f548,axiom,
! [X3,X0] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
| hAPP(c_Complete__Lattice_OInf__class_OInf(X0),hAPP(hAPP(c_Set_Oinsert(X0),X3),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)))) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Inf__singleton_0) ).
fof(f1442,plain,
spl0_95,
inference(avatar_split_clause,[],[f781,f1440]) ).
fof(f781,plain,
! [X3,X0] :
( hAPP(c_Complete__Lattice_OSup__class_OSup(X0),hAPP(c_fequal(X0),X3)) = X3
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) ),
inference(forward_demodulation,[],[f780,f723]) ).
fof(f780,plain,
! [X3,X0] :
( hAPP(c_Complete__Lattice_OSup__class_OSup(X0),hAPP(hAPP(c_Set_Oinsert(X0),X3),c_COMBK(c_False,tc_bool,X0))) = X3
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) ),
inference(forward_demodulation,[],[f528,f698]) ).
fof(f528,axiom,
! [X3,X0] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
| hAPP(c_Complete__Lattice_OSup__class_OSup(X0),hAPP(hAPP(c_Set_Oinsert(X0),X3),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)))) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sup__singleton_0) ).
fof(f1437,plain,
spl0_94,
inference(avatar_split_clause,[],[f602,f1435]) ).
fof(f602,axiom,
! [X3,X0,X5] : hAPP(hAPP(c_Set_Oinsert(X0),X3),X5) != c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__not__empty_0) ).
fof(f1433,plain,
spl0_93,
inference(avatar_split_clause,[],[f521,f1431]) ).
fof(f521,axiom,
! [X8] :
( ~ class_Orderings_Obot(X8)
| hAPP(c_Orderings_Obot__class_Obot(tc_fun(t_a,X8)),v_x) = c_Orderings_Obot__class_Obot(X8) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bot__fun__eq_0) ).
fof(f1429,plain,
spl0_92,
inference(avatar_split_clause,[],[f392,f1427]) ).
fof(f392,axiom,
! [X3,X0,X5] :
( c_Finite__Set_Ofinite(X5,X0)
| ~ c_Finite__Set_Ofinite(hAPP(hAPP(c_Set_Oinsert(X0),X3),X5),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__insert_0) ).
fof(f1425,plain,
( spl0_91
| ~ spl0_3
| ~ spl0_78 ),
inference(avatar_split_clause,[],[f1389,f1357,f1027,f1423]) ).
fof(f1423,plain,
( spl0_91
<=> ! [X0] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),X0),X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_91])]) ).
fof(f1389,plain,
( ! [X0] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),X0),X0) = X0
| ~ spl0_3
| ~ spl0_78 ),
inference(resolution,[],[f1358,f1029]) ).
fof(f1421,plain,
spl0_90,
inference(avatar_split_clause,[],[f391,f1419]) ).
fof(f391,axiom,
! [X3,X0,X5] :
( ~ c_Finite__Set_Ofinite(X5,X0)
| c_Finite__Set_Ofinite(hAPP(hAPP(c_Set_Oinsert(X0),X3),X5),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__insert_1) ).
fof(f1417,plain,
spl0_89,
inference(avatar_split_clause,[],[f341,f1415]) ).
fof(f341,axiom,
! [X0,X1] :
( ~ class_Lattices_Obounded__lattice(X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),c_Orderings_Obot__class_Obot(X0)) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__bot__right_0) ).
fof(f1413,plain,
spl0_88,
inference(avatar_split_clause,[],[f340,f1411]) ).
fof(f340,axiom,
! [X0,X1] :
( ~ class_Lattices_Obounded__lattice(X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),c_Orderings_Obot__class_Obot(X0)),X1) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__bot__left_0) ).
fof(f1409,plain,
spl0_87,
inference(avatar_split_clause,[],[f249,f1407]) ).
fof(f249,axiom,
! [X8] :
( ~ class_Orderings_Otop(X8)
| hAPP(c_Orderings_Otop__class_Otop(tc_fun(t_a,X8)),v_x) = c_Orderings_Otop__class_Otop(X8) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_top__fun__eq_0) ).
fof(f1405,plain,
spl0_86,
inference(avatar_split_clause,[],[f233,f1403]) ).
fof(f233,axiom,
! [X0,X1] :
( ~ class_Lattices_Obounded__lattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),c_Orderings_Otop__class_Otop(X0)),X1) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__top__left_0) ).
fof(f1401,plain,
spl0_85,
inference(avatar_split_clause,[],[f232,f1399]) ).
fof(f232,axiom,
! [X0,X1] :
( ~ class_Lattices_Obounded__lattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),c_Orderings_Otop__class_Otop(X0)) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__top__right_0) ).
fof(f1394,plain,
( spl0_84
| ~ spl0_2
| ~ spl0_69 ),
inference(avatar_split_clause,[],[f1377,f1320,f1022,f1392]) ).
fof(f1377,plain,
( ! [X0] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),X0),X0) = X0
| ~ spl0_2
| ~ spl0_69 ),
inference(resolution,[],[f1321,f1024]) ).
fof(f1387,plain,
( spl0_83
| ~ spl0_65
| ~ spl0_76 ),
inference(avatar_split_clause,[],[f1351,f1348,f1295,f1385]) ).
fof(f1348,plain,
( spl0_76
<=> ! [X0,X1,X7] : ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(X7,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_76])]) ).
fof(f1351,plain,
( ! [X0,X1,X7] : ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(X7,c_COMBK(c_False,tc_bool,X0),X0),X1))
| ~ spl0_65
| ~ spl0_76 ),
inference(forward_demodulation,[],[f1349,f1296]) ).
fof(f1349,plain,
( ! [X0,X1,X7] : ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(X7,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X1))
| ~ spl0_76 ),
inference(avatar_component_clause,[],[f1348]) ).
fof(f1376,plain,
spl0_82,
inference(avatar_split_clause,[],[f798,f1374]) ).
fof(f1374,plain,
( spl0_82
<=> ! [X0,X11,X1] :
( c_COMBK(c_False,tc_bool,X0) != X11
| ~ hBOOL(hAPP(X11,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_82])]) ).
fof(f798,plain,
! [X0,X11,X1] :
( c_COMBK(c_False,tc_bool,X0) != X11
| ~ hBOOL(hAPP(X11,X1)) ),
inference(forward_demodulation,[],[f797,f698]) ).
fof(f797,plain,
! [X0,X11,X1] :
( c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != X11
| ~ hBOOL(hAPP(X11,X1)) ),
inference(forward_demodulation,[],[f358,f43]) ).
fof(f358,axiom,
! [X0,X11,X1] :
( ~ hBOOL(hAPP(X11,X1))
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != c_Collect(X11,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Collect__empty__eq_0) ).
fof(f1372,plain,
spl0_81,
inference(avatar_split_clause,[],[f644,f1370]) ).
fof(f644,axiom,
! [X0,X56,X76] :
( X56 = X76
| ~ hBOOL(hAPP(hAPP(c_fequal(X0),X56),X76)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ATP__Linkup_Ofequal__imp__equal_0) ).
fof(f1368,plain,
spl0_80,
inference(avatar_split_clause,[],[f558,f1365]) ).
fof(f558,axiom,
hAPP(c_HOL_Oord__class_Oless(tc_bool),v_P) = hAPP(c_and,hAPP(c_Not,v_P)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__bool__def__raw_0) ).
fof(f1363,plain,
spl0_79,
inference(avatar_split_clause,[],[f420,f1361]) ).
fof(f420,axiom,
! [X0,X5] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X5),X5) = X5,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__absorb_0) ).
fof(f1359,plain,
spl0_78,
inference(avatar_split_clause,[],[f419,f1357]) ).
fof(f419,axiom,
! [X0,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X1) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__idem_0) ).
fof(f1355,plain,
spl0_77,
inference(avatar_split_clause,[],[f402,f1353]) ).
fof(f402,axiom,
! [X0,X1,X9] : hBOOL(c_in(X1,hAPP(hAPP(c_Set_Oinsert(X0),X1),X9),X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insertCI_1) ).
fof(f1350,plain,
spl0_76,
inference(avatar_split_clause,[],[f359,f1348]) ).
fof(f359,axiom,
! [X0,X1,X7] : ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(X7,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__fold1SetE_0) ).
fof(f1346,plain,
spl0_75,
inference(avatar_split_clause,[],[f344,f1344]) ).
fof(f344,axiom,
! [X0,X1] :
( ~ class_Orderings_Obot(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),c_Orderings_Obot__class_Obot(X0)),X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bot__least_0) ).
fof(f1342,plain,
spl0_74,
inference(avatar_split_clause,[],[f297,f1340]) ).
fof(f297,axiom,
! [X0,X1] :
( ~ class_Orderings_Otop(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),X1),c_Orderings_Otop__class_Otop(X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_top__greatest_0) ).
fof(f1338,plain,
spl0_73,
inference(avatar_split_clause,[],[f202,f1336]) ).
fof(f1336,plain,
( spl0_73
<=> ! [X29,X32,X28,X31] :
( X29 = X32
| c_Com_Ocom_OWhile(X28,X29) != c_Com_Ocom_OWhile(X31,X32) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_73])]) ).
fof(f202,axiom,
! [X31,X28,X29,X32] :
( X29 = X32
| c_Com_Ocom_OWhile(X28,X29) != c_Com_Ocom_OWhile(X31,X32) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I5_J_1) ).
fof(f1334,plain,
spl0_72,
inference(avatar_split_clause,[],[f201,f1332]) ).
fof(f1332,plain,
( spl0_72
<=> ! [X28,X31,X29,X32] :
( X28 = X31
| c_Com_Ocom_OWhile(X28,X29) != c_Com_Ocom_OWhile(X31,X32) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_72])]) ).
fof(f201,axiom,
! [X31,X28,X29,X32] :
( X28 = X31
| c_Com_Ocom_OWhile(X28,X29) != c_Com_Ocom_OWhile(X31,X32) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I5_J_0) ).
fof(f1330,plain,
spl0_71,
inference(avatar_split_clause,[],[f45,f1328]) ).
fof(f1328,plain,
( spl0_71
<=> ! [X17,X33,X34,X16] :
( X16 = X33
| c_Com_Ocom_OSemi(X16,X17) != c_Com_Ocom_OSemi(X33,X34) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_71])]) ).
fof(f45,axiom,
! [X16,X17,X34,X33] :
( X16 = X33
| c_Com_Ocom_OSemi(X16,X17) != c_Com_Ocom_OSemi(X33,X34) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I3_J_0) ).
fof(f1326,plain,
spl0_70,
inference(avatar_split_clause,[],[f44,f1324]) ).
fof(f1324,plain,
( spl0_70
<=> ! [X34,X16,X17,X33] :
( X17 = X34
| c_Com_Ocom_OSemi(X16,X17) != c_Com_Ocom_OSemi(X33,X34) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_70])]) ).
fof(f44,axiom,
! [X16,X17,X34,X33] :
( X17 = X34
| c_Com_Ocom_OSemi(X16,X17) != c_Com_Ocom_OSemi(X33,X34) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I3_J_1) ).
fof(f1322,plain,
spl0_69,
inference(avatar_split_clause,[],[f4,f1320]) ).
fof(f4,axiom,
! [X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X1) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__idem_0) ).
fof(f1318,plain,
spl0_68,
inference(avatar_split_clause,[],[f3,f1316]) ).
fof(f3,axiom,
! [X0,X5] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X5),X5) = X5,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__absorb_0) ).
fof(f1310,plain,
( spl0_67
| ~ spl0_60 ),
inference(avatar_split_clause,[],[f1277,f1274,f1308]) ).
fof(f1308,plain,
( spl0_67
<=> ! [X0] : c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)) != c_COMBK(c_False,tc_bool,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_67])]) ).
fof(f1274,plain,
( spl0_60
<=> ! [X0] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_60])]) ).
fof(f1277,plain,
( ! [X0] : c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)) != c_COMBK(c_False,tc_bool,X0)
| ~ spl0_60 ),
inference(forward_demodulation,[],[f1275,f698]) ).
fof(f1275,plain,
( ! [X0] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool))
| ~ spl0_60 ),
inference(avatar_component_clause,[],[f1274]) ).
fof(f1302,plain,
spl0_66,
inference(avatar_split_clause,[],[f711,f1299]) ).
fof(f1299,plain,
( spl0_66
<=> c_False = c_in(v_x,c_COMBK(c_False,tc_bool,t_a),t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_66])]) ).
fof(f711,plain,
c_False = c_in(v_x,c_COMBK(c_False,tc_bool,t_a),t_a),
inference(forward_demodulation,[],[f710,f606]) ).
fof(f606,axiom,
! [X0,X11,X8,X57] : hAPP(c_COMBK(X11,X0,X8),X57) = X11,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_COMBK__def_0) ).
fof(f710,plain,
hAPP(c_COMBK(c_False,tc_bool,t_a),v_x) = c_in(v_x,c_COMBK(c_False,tc_bool,t_a),t_a),
inference(forward_demodulation,[],[f273,f698]) ).
fof(f273,axiom,
hAPP(c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),v_x) = c_in(v_x,c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bot__empty__eq_0) ).
fof(f1297,plain,
spl0_65,
inference(avatar_split_clause,[],[f698,f1295]) ).
fof(f1293,plain,
spl0_64,
inference(avatar_split_clause,[],[f588,f1291]) ).
fof(f588,axiom,
! [X0,X1,X5] : hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X0),X1),X5),X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__code_1) ).
fof(f1289,plain,
spl0_63,
inference(avatar_split_clause,[],[f446,f1287]) ).
fof(f446,axiom,
! [X0,X1] :
( ~ class_Orderings_Opreorder(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__eq__refl_0) ).
fof(f1285,plain,
spl0_62,
inference(avatar_split_clause,[],[f445,f1283]) ).
fof(f445,axiom,
! [X0,X1] :
( ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),X1),X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__eq__iff_0) ).
fof(f1281,plain,
spl0_61,
inference(avatar_split_clause,[],[f438,f1279]) ).
fof(f438,axiom,
! [X0,X1] : hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X1),X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equalityE_0) ).
fof(f1276,plain,
spl0_60,
inference(avatar_split_clause,[],[f360,f1274]) ).
fof(f360,axiom,
! [X0] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UNIV__not__empty_0) ).
fof(f1272,plain,
spl0_59,
inference(avatar_split_clause,[],[f243,f1270]) ).
fof(f243,axiom,
! [X0,X1] :
( ~ class_Orderings_Opreorder(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__irrefl_0) ).
fof(f1268,plain,
spl0_58,
inference(avatar_split_clause,[],[f241,f1266]) ).
fof(f241,axiom,
! [X0,X1] :
( ~ class_Orderings_Oorder(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__le_1) ).
fof(f1264,plain,
spl0_57,
inference(avatar_split_clause,[],[f10,f1262]) ).
fof(f10,axiom,
! [X10,X0,X1] :
( hBOOL(hAPP(X10,X1))
| ~ hBOOL(c_in(X1,X10,X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mem__def_0) ).
fof(f1260,plain,
spl0_56,
inference(avatar_split_clause,[],[f9,f1258]) ).
fof(f9,axiom,
! [X10,X0,X1] :
( ~ hBOOL(hAPP(X10,X1))
| hBOOL(c_in(X1,X10,X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mem__def_1) ).
fof(f1256,plain,
( spl0_55
| ~ spl0_50 ),
inference(avatar_split_clause,[],[f1235,f1232,f1254]) ).
fof(f1232,plain,
( spl0_50
<=> ! [X0,X39] : c_Hoare__Mirabelle_Ohoare__derivs(X39,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool)),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_50])]) ).
fof(f1235,plain,
( ! [X39,X0] : c_Hoare__Mirabelle_Ohoare__derivs(X39,c_COMBK(c_False,tc_bool,tc_Hoare__Mirabelle_Otriple(X0)),X0)
| ~ spl0_50 ),
inference(forward_demodulation,[],[f1233,f698]) ).
fof(f1233,plain,
( ! [X39,X0] : c_Hoare__Mirabelle_Ohoare__derivs(X39,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool)),X0)
| ~ spl0_50 ),
inference(avatar_component_clause,[],[f1232]) ).
fof(f1252,plain,
( spl0_54
| ~ spl0_48 ),
inference(avatar_split_clause,[],[f1226,f1223,f1250]) ).
fof(f1250,plain,
( spl0_54
<=> ! [X0,X8,X7] : c_Fun_Oinj__on(X7,c_COMBK(c_False,tc_bool,X0),X0,X8) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_54])]) ).
fof(f1223,plain,
( spl0_48
<=> ! [X0,X8,X7] : c_Fun_Oinj__on(X7,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0,X8) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_48])]) ).
fof(f1226,plain,
( ! [X0,X8,X7] : c_Fun_Oinj__on(X7,c_COMBK(c_False,tc_bool,X0),X0,X8)
| ~ spl0_48 ),
inference(forward_demodulation,[],[f1224,f698]) ).
fof(f1224,plain,
( ! [X0,X8,X7] : c_Fun_Oinj__on(X7,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0,X8)
| ~ spl0_48 ),
inference(avatar_component_clause,[],[f1223]) ).
fof(f1248,plain,
( spl0_53
| ~ spl0_47 ),
inference(avatar_split_clause,[],[f1221,f1218,f1246]) ).
fof(f1246,plain,
( spl0_53
<=> ! [X0,X35] : ~ hBOOL(c_in(X35,c_COMBK(c_False,tc_bool,X0),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_53])]) ).
fof(f1218,plain,
( spl0_47
<=> ! [X0,X35] : ~ hBOOL(c_in(X35,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_47])]) ).
fof(f1221,plain,
( ! [X0,X35] : ~ hBOOL(c_in(X35,c_COMBK(c_False,tc_bool,X0),X0))
| ~ spl0_47 ),
inference(forward_demodulation,[],[f1219,f698]) ).
fof(f1219,plain,
( ! [X0,X35] : ~ hBOOL(c_in(X35,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0))
| ~ spl0_47 ),
inference(avatar_component_clause,[],[f1218]) ).
fof(f1243,plain,
spl0_52,
inference(avatar_split_clause,[],[f617,f1241]) ).
fof(f1241,plain,
( spl0_52
<=> ! [X75,X74] :
( ~ class_Finite__Set_Ofinite_Ofinite(X74)
| ~ class_Finite__Set_Ofinite_Ofinite(X75)
| class_Finite__Set_Ofinite_Ofinite(tc_fun(X74,X75)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_52])]) ).
fof(f617,axiom,
! [X74,X75] :
( ~ class_Finite__Set_Ofinite_Ofinite(X74)
| ~ class_Finite__Set_Ofinite_Ofinite(X75)
| class_Finite__Set_Ofinite_Ofinite(tc_fun(X74,X75)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Finite__Set_Ofinite_Ofinite) ).
fof(f1239,plain,
spl0_51,
inference(avatar_split_clause,[],[f606,f1237]) ).
fof(f1234,plain,
spl0_50,
inference(avatar_split_clause,[],[f599,f1232]) ).
fof(f599,axiom,
! [X39,X0] : c_Hoare__Mirabelle_Ohoare__derivs(X39,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool)),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty_0) ).
fof(f1230,plain,
spl0_49,
inference(avatar_split_clause,[],[f474,f1228]) ).
fof(f474,axiom,
! [X0,X1] : c_The(hAPP(c_fequal(X0),X1),X0) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_the__sym__eq__trivial_0) ).
fof(f1225,plain,
spl0_48,
inference(avatar_split_clause,[],[f372,f1223]) ).
fof(f372,axiom,
! [X0,X8,X7] : c_Fun_Oinj__on(X7,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0,X8),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__empty_0) ).
fof(f1220,plain,
spl0_47,
inference(avatar_split_clause,[],[f354,f1218]) ).
fof(f354,axiom,
! [X0,X35] : ~ hBOOL(c_in(X35,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__iff_0) ).
fof(f1216,plain,
spl0_46,
inference(avatar_split_clause,[],[f200,f1214]) ).
fof(f1214,plain,
( spl0_46
<=> ! [X46,X15] :
( X15 = X46
| c_Com_Ocom_OBODY(X15) != c_Com_Ocom_OBODY(X46) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_46])]) ).
fof(f200,axiom,
! [X46,X15] :
( X15 = X46
| c_Com_Ocom_OBODY(X15) != c_Com_Ocom_OBODY(X46) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I6_J_0) ).
fof(f1212,plain,
spl0_45,
inference(avatar_split_clause,[],[f86,f1210]) ).
fof(f1210,plain,
( spl0_45
<=> ! [X0,X1] : hBOOL(c_in(X1,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_45])]) ).
fof(f86,axiom,
! [X0,X1] : hBOOL(c_in(X1,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UNIV__I_0) ).
fof(f1208,plain,
spl0_44,
inference(avatar_split_clause,[],[f70,f1206]) ).
fof(f1206,plain,
( spl0_44
<=> ! [X17,X34,X16,X33,X28] : c_Com_Ocom_OSemi(X16,X17) != c_Com_Ocom_OCond(X28,X33,X34) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_44])]) ).
fof(f70,axiom,
! [X28,X16,X17,X34,X33] : c_Com_Ocom_OSemi(X16,X17) != c_Com_Ocom_OCond(X28,X33,X34),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I45_J_0) ).
fof(f1204,plain,
spl0_43,
inference(avatar_split_clause,[],[f57,f1202]) ).
fof(f1202,plain,
( spl0_43
<=> ! [X28,X17,X31,X29,X16] : c_Com_Ocom_OWhile(X28,X29) != c_Com_Ocom_OCond(X31,X16,X17) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_43])]) ).
fof(f57,axiom,
! [X31,X28,X29,X16,X17] : c_Com_Ocom_OWhile(X28,X29) != c_Com_Ocom_OCond(X31,X16,X17),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I52_J_0) ).
fof(f1200,plain,
spl0_42,
inference(avatar_split_clause,[],[f643,f1198]) ).
fof(f643,axiom,
! [X0,X1] : hBOOL(hAPP(hAPP(c_fequal(X0),X1),X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ATP__Linkup_Oequal__imp__fequal_0) ).
fof(f1196,plain,
( ~ spl0_41
| ~ spl0_40 ),
inference(avatar_split_clause,[],[f1191,f1187,f1193]) ).
fof(f1187,plain,
( spl0_40
<=> ! [X0,X1] : ~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_40])]) ).
fof(f1191,plain,
( ~ hBOOL(c_False)
| ~ spl0_40 ),
inference(forward_demodulation,[],[f1190,f606]) ).
fof(f1190,plain,
( ! [X0,X1] : ~ hBOOL(hAPP(c_COMBK(c_False,tc_bool,X0),X1))
| ~ spl0_40 ),
inference(forward_demodulation,[],[f1188,f698]) ).
fof(f1188,plain,
( ! [X0,X1] : ~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X1))
| ~ spl0_40 ),
inference(avatar_component_clause,[],[f1187]) ).
fof(f1189,plain,
spl0_40,
inference(avatar_split_clause,[],[f598,f1187]) ).
fof(f598,axiom,
! [X0,X1] : ~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bot1E_0) ).
fof(f1185,plain,
spl0_39,
inference(avatar_split_clause,[],[f415,f1183]) ).
fof(f1183,plain,
( spl0_39
<=> ! [X29,X16,X28,X17] : c_Com_Ocom_OSemi(X16,X17) != c_Com_Ocom_OWhile(X28,X29) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_39])]) ).
fof(f415,axiom,
! [X28,X29,X16,X17] : c_Com_Ocom_OSemi(X16,X17) != c_Com_Ocom_OWhile(X28,X29),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I47_J_0) ).
fof(f1181,plain,
spl0_38,
inference(avatar_split_clause,[],[f246,f1179]) ).
fof(f246,axiom,
! [X0,X1] : hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_top1I_0) ).
fof(f1177,plain,
spl0_37,
inference(avatar_split_clause,[],[f103,f1175]) ).
fof(f1175,plain,
( spl0_37
<=> ! [X15,X16,X17,X31] : c_Com_Ocom_OBODY(X15) != c_Com_Ocom_OCond(X31,X16,X17) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_37])]) ).
fof(f103,axiom,
! [X31,X16,X17,X15] : c_Com_Ocom_OBODY(X15) != c_Com_Ocom_OCond(X31,X16,X17),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I54_J_0) ).
fof(f1173,plain,
( spl0_36
| ~ spl0_23 ),
inference(avatar_split_clause,[],[f1121,f1118,f1171]) ).
fof(f1118,plain,
( spl0_23
<=> ! [X0] : c_Finite__Set_Ofinite(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_23])]) ).
fof(f1121,plain,
( ! [X0] : c_Finite__Set_Ofinite(c_COMBK(c_False,tc_bool,X0),X0)
| ~ spl0_23 ),
inference(forward_demodulation,[],[f1119,f698]) ).
fof(f1119,plain,
( ! [X0] : c_Finite__Set_Ofinite(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0)
| ~ spl0_23 ),
inference(avatar_component_clause,[],[f1118]) ).
fof(f1169,plain,
spl0_35,
inference(avatar_split_clause,[],[f624,f1167]) ).
fof(f1167,plain,
( spl0_35
<=> ! [X75,X74] :
( ~ class_HOL_Oord(X75)
| class_HOL_Oord(tc_fun(X74,X75)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_35])]) ).
fof(f624,axiom,
! [X74,X75] :
( ~ class_HOL_Oord(X75)
| class_HOL_Oord(tc_fun(X74,X75)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__HOL_Oord) ).
fof(f1165,plain,
spl0_34,
inference(avatar_split_clause,[],[f623,f1163]) ).
fof(f1163,plain,
( spl0_34
<=> ! [X75,X74] :
( ~ class_HOL_Ominus(X75)
| class_HOL_Ominus(tc_fun(X74,X75)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_34])]) ).
fof(f623,axiom,
! [X74,X75] :
( ~ class_HOL_Ominus(X75)
| class_HOL_Ominus(tc_fun(X74,X75)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__HOL_Ominus) ).
fof(f1161,plain,
spl0_33,
inference(avatar_split_clause,[],[f622,f1159]) ).
fof(f622,axiom,
! [X74,X75] :
( ~ class_Orderings_Obot(X75)
| class_Orderings_Obot(tc_fun(X74,X75)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Orderings_Obot) ).
fof(f1157,plain,
spl0_32,
inference(avatar_split_clause,[],[f621,f1155]) ).
fof(f621,axiom,
! [X74,X75] :
( ~ class_Orderings_Otop(X75)
| class_Orderings_Otop(tc_fun(X74,X75)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Orderings_Otop) ).
fof(f1153,plain,
spl0_31,
inference(avatar_split_clause,[],[f620,f1151]) ).
fof(f620,axiom,
! [X74,X75] :
( ~ class_Orderings_Oorder(X75)
| class_Orderings_Oorder(tc_fun(X74,X75)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Orderings_Oorder) ).
fof(f1149,plain,
spl0_30,
inference(avatar_split_clause,[],[f619,f1147]) ).
fof(f619,axiom,
! [X74,X75] :
( ~ class_Lattices_Olattice(X75)
| class_Lattices_Olattice(tc_fun(X74,X75)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Olattice) ).
fof(f1145,plain,
spl0_29,
inference(avatar_split_clause,[],[f618,f1143]) ).
fof(f618,axiom,
! [X74,X75] :
( ~ class_Orderings_Opreorder(X75)
| class_Orderings_Opreorder(tc_fun(X74,X75)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Orderings_Opreorder) ).
fof(f1141,plain,
spl0_28,
inference(avatar_split_clause,[],[f616,f1139]) ).
fof(f616,axiom,
! [X74,X75] :
( ~ class_Lattices_Obounded__lattice(X75)
| class_Lattices_Obounded__lattice(tc_fun(X74,X75)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Obounded__lattice) ).
fof(f1137,plain,
spl0_27,
inference(avatar_split_clause,[],[f615,f1135]) ).
fof(f1135,plain,
( spl0_27
<=> ! [X75,X74] :
( ~ class_Lattices_Odistrib__lattice(X75)
| class_Lattices_Odistrib__lattice(tc_fun(X74,X75)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_27])]) ).
fof(f615,axiom,
! [X74,X75] :
( ~ class_Lattices_Odistrib__lattice(X75)
| class_Lattices_Odistrib__lattice(tc_fun(X74,X75)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Odistrib__lattice) ).
fof(f1133,plain,
spl0_26,
inference(avatar_split_clause,[],[f614,f1131]) ).
fof(f614,axiom,
! [X74,X75] :
( ~ class_Lattices_Olattice(X75)
| class_Lattices_Olower__semilattice(tc_fun(X74,X75)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Olower__semilattice) ).
fof(f1129,plain,
spl0_25,
inference(avatar_split_clause,[],[f613,f1127]) ).
fof(f613,axiom,
! [X74,X75] :
( ~ class_Lattices_Olattice(X75)
| class_Lattices_Oupper__semilattice(tc_fun(X74,X75)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Oupper__semilattice) ).
fof(f1125,plain,
spl0_24,
inference(avatar_split_clause,[],[f612,f1123]) ).
fof(f612,axiom,
! [X74,X75] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X75)
| class_Complete__Lattice_Ocomplete__lattice(tc_fun(X74,X75)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Complete__Lattice_Ocomplete__lattice) ).
fof(f1120,plain,
spl0_23,
inference(avatar_split_clause,[],[f366,f1118]) ).
fof(f366,axiom,
! [X0] : c_Finite__Set_Ofinite(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite_OemptyI_0) ).
fof(f1116,plain,
spl0_22,
inference(avatar_split_clause,[],[f208,f1114]) ).
fof(f1114,plain,
( spl0_22
<=> ! [X34,X28,X33] : c_Com_Ocom_OSKIP != c_Com_Ocom_OCond(X28,X33,X34) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_22])]) ).
fof(f208,axiom,
! [X28,X34,X33] : c_Com_Ocom_OSKIP != c_Com_Ocom_OCond(X28,X33,X34),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I15_J_0) ).
fof(f1112,plain,
spl0_21,
inference(avatar_split_clause,[],[f111,f1110]) ).
fof(f1110,plain,
( spl0_21
<=> ! [X16,X17,X15] : c_Com_Ocom_OBODY(X15) != c_Com_Ocom_OSemi(X16,X17) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_21])]) ).
fof(f111,axiom,
! [X16,X17,X15] : c_Com_Ocom_OBODY(X15) != c_Com_Ocom_OSemi(X16,X17),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I48_J_0) ).
fof(f1108,plain,
spl0_20,
inference(avatar_split_clause,[],[f39,f1106]) ).
fof(f1106,plain,
( spl0_20
<=> ! [X15,X32,X31] : c_Com_Ocom_OBODY(X15) != c_Com_Ocom_OWhile(X31,X32) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_20])]) ).
fof(f39,axiom,
! [X31,X15,X32] : c_Com_Ocom_OBODY(X15) != c_Com_Ocom_OWhile(X31,X32),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I59_J_0) ).
fof(f1104,plain,
spl0_19,
inference(avatar_split_clause,[],[f642,f1102]) ).
fof(f1102,plain,
( spl0_19
<=> ! [X0,X11] : c_COMBI(X11,X0) = X11 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_19])]) ).
fof(f642,axiom,
! [X0,X11] : c_COMBI(X11,X0) = X11,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ATP__Linkup_OCOMBI__def_0) ).
fof(f1100,plain,
spl0_18,
inference(avatar_split_clause,[],[f505,f1098]) ).
fof(f1098,plain,
( spl0_18
<=> ! [X34,X33] : c_Com_Ocom_OSKIP != c_Com_Ocom_OSemi(X33,X34) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_18])]) ).
fof(f505,axiom,
! [X34,X33] : c_Com_Ocom_OSKIP != c_Com_Ocom_OSemi(X33,X34),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I12_J_0) ).
fof(f1096,plain,
spl0_17,
inference(avatar_split_clause,[],[f315,f1094]) ).
fof(f315,axiom,
! [X0,X5] :
( ~ class_Finite__Set_Ofinite_Ofinite(X0)
| c_Finite__Set_Ofinite(X5,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite_0) ).
fof(f1092,plain,
spl0_16,
inference(avatar_split_clause,[],[f43,f1090]) ).
fof(f1088,plain,
spl0_15,
inference(avatar_split_clause,[],[f37,f1086]) ).
fof(f1086,plain,
( spl0_15
<=> ! [X29,X28] : c_Com_Ocom_OWhile(X28,X29) != c_Com_Ocom_OSKIP ),
introduced(avatar_definition,[new_symbols(naming,[spl0_15])]) ).
fof(f37,axiom,
! [X28,X29] : c_Com_Ocom_OWhile(X28,X29) != c_Com_Ocom_OSKIP,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I17_J_0) ).
fof(f1084,plain,
spl0_14,
inference(avatar_split_clause,[],[f318,f1082]) ).
fof(f1082,plain,
( spl0_14
<=> ! [X15] : c_Com_Ocom_OBODY(X15) != c_Com_Ocom_OSKIP ),
introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).
fof(f318,axiom,
! [X15] : c_Com_Ocom_OBODY(X15) != c_Com_Ocom_OSKIP,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I18_J_0) ).
fof(f1080,plain,
spl0_13,
inference(avatar_split_clause,[],[f637,f1077]) ).
fof(f637,axiom,
class_HOL_Oord(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__HOL_Oord) ).
fof(f1075,plain,
spl0_12,
inference(avatar_split_clause,[],[f636,f1072]) ).
fof(f636,axiom,
class_HOL_Ominus(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__HOL_Ominus) ).
fof(f1070,plain,
spl0_11,
inference(avatar_split_clause,[],[f635,f1067]) ).
fof(f635,axiom,
class_Orderings_Obot(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Obot) ).
fof(f1065,plain,
spl0_10,
inference(avatar_split_clause,[],[f634,f1062]) ).
fof(f634,axiom,
class_Orderings_Otop(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Otop) ).
fof(f1060,plain,
spl0_9,
inference(avatar_split_clause,[],[f633,f1057]) ).
fof(f633,axiom,
class_Orderings_Oorder(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Oorder) ).
fof(f1055,plain,
spl0_8,
inference(avatar_split_clause,[],[f632,f1052]) ).
fof(f632,axiom,
class_Lattices_Olattice(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Olattice) ).
fof(f1050,plain,
spl0_7,
inference(avatar_split_clause,[],[f631,f1047]) ).
fof(f631,axiom,
class_Orderings_Opreorder(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Opreorder) ).
fof(f1045,plain,
spl0_6,
inference(avatar_split_clause,[],[f630,f1042]) ).
fof(f1042,plain,
( spl0_6
<=> class_Finite__Set_Ofinite_Ofinite(tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).
fof(f630,axiom,
class_Finite__Set_Ofinite_Ofinite(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Finite__Set_Ofinite_Ofinite) ).
fof(f1040,plain,
spl0_5,
inference(avatar_split_clause,[],[f629,f1037]) ).
fof(f629,axiom,
class_Lattices_Obounded__lattice(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Obounded__lattice) ).
fof(f1035,plain,
spl0_4,
inference(avatar_split_clause,[],[f628,f1032]) ).
fof(f1032,plain,
( spl0_4
<=> class_Lattices_Odistrib__lattice(tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).
fof(f628,axiom,
class_Lattices_Odistrib__lattice(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Odistrib__lattice) ).
fof(f1030,plain,
spl0_3,
inference(avatar_split_clause,[],[f627,f1027]) ).
fof(f627,axiom,
class_Lattices_Olower__semilattice(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Olower__semilattice) ).
fof(f1025,plain,
spl0_2,
inference(avatar_split_clause,[],[f626,f1022]) ).
fof(f626,axiom,
class_Lattices_Oupper__semilattice(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Oupper__semilattice) ).
fof(f1020,plain,
spl0_1,
inference(avatar_split_clause,[],[f625,f1017]) ).
fof(f625,axiom,
class_Complete__Lattice_Ocomplete__lattice(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Complete__Lattice_Ocomplete__lattice) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SWV834-1 : TPTP v8.1.2. Released v4.1.0.
% 0.09/0.10 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.11/0.30 % Computer : n026.cluster.edu
% 0.11/0.30 % Model : x86_64 x86_64
% 0.11/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.30 % Memory : 8042.1875MB
% 0.11/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.30 % CPULimit : 300
% 0.11/0.30 % WCLimit : 300
% 0.11/0.30 % DateTime : Tue Apr 30 05:05:34 EDT 2024
% 0.11/0.31 % CPUTime :
% 0.17/0.31 % (4782)Running in auto input_syntax mode. Trying TPTP
% 0.17/0.37 % (4784)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.17/0.37 % (4785)WARNING: value z3 for option sas not known
% 0.17/0.37 % (4783)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.17/0.37 % (4789)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)
% 0.17/0.37 % (4786)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.17/0.37 % (4788)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)
% 0.17/0.37 % (4787)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)
% 0.17/0.37 % (4785)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)
% 3.05/0.77 TRYING [1]
% 3.05/0.82 TRYING [2]
% 6.94/1.35 TRYING [1]
% 7.93/1.47 TRYING [2]
% 8.42/1.61 TRYING [3]
% 9.46/1.69 TRYING [1]
% 9.46/1.73 TRYING [2]
% 12.48/2.14 TRYING [3]
% 22.72/3.63 TRYING [3]
% 53.37/8.00 TRYING [4]
% 54.53/8.18 TRYING [4]
% 124.33/18.15 TRYING [4]
% 161.58/23.43 % (4787)First to succeed.
% 162.20/23.58 % (4787)Refutation found. Thanks to Tanya!
% 162.20/23.58 % SZS status Unsatisfiable for theBenchmark
% 162.20/23.58 % SZS output start Proof for theBenchmark
% See solution above
% 162.75/23.63 % (4787)------------------------------
% 162.75/23.63 % (4787)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 162.75/23.63 % (4787)Termination reason: Refutation
% 162.75/23.63
% 162.75/23.63 % (4787)Memory used [KB]: 101182
% 162.75/23.63 % (4787)Time elapsed: 23.183 s
% 162.75/23.63 % (4787)Instructions burned: 43407 (million)
% 162.75/23.63 % (4787)------------------------------
% 162.75/23.63 % (4787)------------------------------
% 162.75/23.63 % (4782)Success in time 23.119 s
%------------------------------------------------------------------------------